DBPAETMBNT OF THE INTE1UOK

BULLETIN

OF THE

UNITED STATES

GEOLOGICAL SURVEY

No. 54

WASHINGTON

(GOVERNMENT PRINTING OFFICE

1839
i ft. 
X
. Disposition of apparatus for air thermoiuutry and boiling-point. Scale 5ld
UNITED STATES GEOLOGICAL SURVEY

J. W. POWELL, DIRECTOR

ON THE

THERMO-ELECTRIC MEASUREMENT

OF

HIGH TEMPERATURES

BY

WASHINGTON

GOVERNMENT PRINTING OFFICE

1889

CONTENTS.

Page.

Letter of transmittal........................................................ 15

Preface..................................................................... 17

Introduction................................................................ 23

General account of methods of pyrometry................................ 23

Earlier digests .....................- ......--....--.-...--- ----.-.. 23

Character of the measurements ..................'.................... 24

Classification of pyrometers ......................................... 25

Dilatation of solids ................................................. 25

Dilatation of liquids................................................. 27

Dilatation of gases (manometric methods) ........................... 27

Dilatation of gases (displacement methods) .......................... 36

Vapor tension....................................................... 38

Dissociation .................................................. ...... 38

Fusion ............................................................. 39

Specific heat........................................................ 40

Ebullition.......................................................... 42

Heat conduction .................................................... 42

Radiation........................................................... 43

Viscosity ........................................................... 46

Acoustics........................................................... 47

Thermo-electrics.................................................... 48

Electrical conductivity.............................................. 50

Magnetism..................... .................................... 52

Interpolation methods .............................................. 52

Advantages of thermo-electric pyrometry................................ 52

CHAPTER I. The degree of constant high temperature attained in metallic

vapor baths of large dimensions; by C. Barus and W. Hallock...... 56

Explanation ............................................................ 56

Apparatus ....__..................... r ................................ 57

Remarks............................................................. 57

Low boiling points.................................................. 58

Boiling points between 100° and 300° ................................ 59

Apparatus for mercury.............................................. 61

Boiling point of zinc .............................. ................... 62

Experimental results............................................ ........ 67

Methods of measurement................................... ........ 67

List of thermo-couples ........................ ...................... 68

Data for mercury vapor baths ....................................... 69

Data for zinc vapor baths ............. .............................. 70

Inferences relative to low percentage alloys ............................. 77

Reduction of data....................... ............................. 77

Series of alloys...................................................... 79

(659) 5
6 CONTENTS.

Page. 

CHAPTER II. The calibration of electrical pyrometers by the aid of fixed

thermal data ..................................................... 84

Explanation ............................................................ 84

Apparatus for low boiling points (100° to 500°)........................... 84

Original forms of boiling tubes ...................................... 84

Perfected forms of boiling tubes ..................................... 86

Boiling-point tubes for pressure work ......... ...................... 88

Dr. Gibbs's ring burner ...... ...................................... 90

Apparatus for high boiling points ....................................... ' 90

Original forms of boiling-point crucible.............................. 90

Perfected forms of boiling-point crucible......... ................... 91

Insulators .............................................................. 95

Method of measurement................................................. 97

Thermo-element ...... ............................................. 97

Standards of electromotive force..................................... 99

Method of computation.................................................. 103

Experimental results.................................................... 104

Exploration for constancy of temperature; water, aniline............ 104

Exploration for constancy of temperature, mercury................... 105

Exploration for constancy of temperature, sulphur........ ~ ........... 107

Exploration for constancy of temperature, zinc .... ...... ............ 108

Practical calibration .................................................... 110

Investigation of data................................................ 110

Discussion of data................................................... 114 *"

Time-variation of thermo-electric data............................... 116

Duration of continued ebullition, constant high temperature ......... 116

Duration of continued ebullition, constant low temperature.......... 116

Available substances for boiling points.......... '.................... 119

Points of volatilization..................................... *. ....... 121

Subsidiary data : antimony; bismuth; cadmium.................... 122

Thermo-electric datum for the melting point of platinum............. 124

CHAPTER III. Certain pyro-electric properties of the alloys of platinum...... 126

Explanation............................................................ 126

Fusion and mechanical treatment of the alloys........................... 128

Fusion and rolling .................................................. 128

Preliminary data, density ........................................... 128

Preliminary data, electrical resistance of rods........................ 131

Experimental data...... ................................................ 133

Further mechanical treatment; resistance of wires.................... 133

Thermo-electrics of wires............................................ 135

Temperature coefficient .............................................. 139

General digest .................................. .................... 143

Discussion and inferences................................................ 144

Earlier results ...................................................... 144

Resistance and density ............................................. 145

Resistance and thernio-electrics ..................................... 146

Electrical tests for purity ...................... .......... ........... 146

Electrical resistance and temperature coefficient ..................... 149

Other relevant results............. .......... ........................ 157 \

General remarks .................................................... 161

CHAPTER IV. The calibration of electrical pyrometers by direct comparison

with the air thermometer ......................................... 165

Displacement methods of thermometry................................... 165

Constant volume thermometers.......................................... 167

(060)
CONTENTS. 7

	Page. 

CHAPTER IV Continued.

Manometer ......................................................... 1GT

Metallic capillary tubes ......... ......................'............. 169

Porcelain air-thermometer bulbs..................................... 171

Machine for soldering porcelain...................................... 175

Revolving muffle.................................................... 180

Remarks regarding apparatus and manipulation.............. ...... . 185

Constant volume air thermometer method of computation............... 188

The general equation...... ............ .............................. 188

The equation simplified ............................................. 190

Errors of the approximations............................. .......... 190

Compensator........................................................ 192

Errors of measurement in general.................................... 195

Constant volume air thermometer experimental results .... ............. 198

Earlier results ...................................................... 198

Later results........................................................ 204

Digression.......................................................... 206

Constant pressure airthermometry apparatus.....'...................... 208

Constant pressure air thermometry method of computation.............. 210

The general equation................................................ 210

The equation simplified ............................................. 211

Volumetry of bulbs ................................................. 213

Errors of the approximations........................................ 214

Compensator ....................................................... 215

Constant pressure air thermometer experimental results ................ 216

Manipulation ................ .................. ............. ........ 216

Experimental data .................................................. 217

Graphic digests..................................................... 227

Constant pressure air thermometer discussion........................... 227

ErroBS of measurement, in general................................... 227

Accuracy of the measurements made, group I ........................ 231

Accuracy of the measurements made, group II ....................... 232

Boiling point of zinc ..............................i................. 233

Coefficient of heat expansion of porcelain ............................ 236

Remarks............................................................ 237

CHAPTER V. The pyrometric use of the principle of viscosity ................ 239

Introduction............................................................ 239

Remarks................................................ ............ 239

Literature .......................................................... 240

Transpiration subject to the Poiseuille-Meyer law........................ 242

Apparatus ............ ...... .......................... ............ ...... 242

General disposition of parts ......................................... 242

Apparatus for constant pressure ...................,..._.............. 244

The capillary apparatus............................................. 245

Differential apparatus............................................... 249

Method of heating................................................... 249

Methods of computation................................................. 251

The general equation................................................ 251

Case of t\vo cold ends, absolute apparatus........................... 252

Case of two cold ends, differential apparatus........................ 254

Experimental results..................................................... 255

Manipulation ....................................................... 255

Nomenclature....................................................... 256

Data ............................................................... 258

(661)
8 CONTENTS.

Page. 

CHAPTER V Continued.

Discussion .................................................. _......... 271

Viscosity at zero .......................................... ....... 271

Viscosity at high temperatures, kinetic inferences.................... 273

Sources of error................................................. 274

Diffusion ....................................................... 275

Sliding coefficient............................................... 276

Advantages of an exponential law ............................... 277

Effect of imperfect gaseity.....................................'.. 279

The new method of pyrometry .......................................... 281

Methods of computation ............................................. 281

Eesttlts ............................................................. 282

Transpiration not subject to the Poiseuille-Meyer law.................... 284

Objects of the investigation ......................................... 284

Hoffmann's researches............................................... 285

Experimental results.................................................... 287

Transpiration under variable pressure ............................... 287

Transpiration under constant pressure............................... 288

Transpirations compared differentially............................... 293

Discussion.............................................................. 295

Apparent viscosity and pressure..................................... 295

Apparent viscosity and temperature ................................. 297

Obliquity of the linear loci .........................»................ 297

Supplementary results .............................................. 298

General remarks .................................................... 300

The new method of pyrometry........................................... 302

Practical remarks................................................... 302

Appurtenances...................................................... 302

The transpiration pyrometer ..,...................................... 302

(662)
ILLUSTRATIONS.

FIG. 1. Apparatus for constant temperature between 0° and 100°............ 59

2. Apparatus for constant temperature between 100° and 300° .......... 60

3. Boiling-point apparatus for mercury............ .................... 61

4. Boiling-point'apparatus for zinc; earlier form ...................... 63

5. Boiling-point apparatus for zinc; later form; longitudinal section... 65

6. Boiling-point apparatus for zinc; later form; cross-section ......... 66

7. Boiling-point tube for mercury; original form...................... 84

8. Boiling-point tube for sulphur; original form ...................... 85

9. Boiling-point tube for water, etc.; original form.................... 86

10. Boiling-point tube; perfected form .....................'........... 87

10a. Boiling-point tube for annealing long wires ........................ 87

11. Boiling-point tube for pressure work............................... 88

lla. Boiling-point tube for pressure work with accessories ............... 88

12. Ring burner....................................................... 89

13. Original form of boiling-point crucible ............................. 91

14. Perfected form of boiling-point crucible ............................ 92

14a. Boiling-point crucible for pressure work............................ 94

15. Boiling-point crucible with open tube .............................. 94

16. Machine for pressing porcelain insulators........................... 96

17. Die for porcelain tubes............................................. 96

18. Disposition of thermo-electric apparatus ........................... 97

19. Double key....................'..................... ........... 97

20. Standard Daniell cell .............................................. 100

21. Chart showing the relation of temperature and electromotive force;

thermo-couples Nos. 17 and 18.................................... 114

22. Chart showing the relation of temperature and electromotive force ;

thermo-couples Nos. 22,35,36,37,38,39,40........................ 116

23. Apparatus for melting point of platinum ........................... 124

24. Resistometer ...................................................... 132

25. Detached rider .................................................... 132

26. Chart showing the relation between electrical resistance and temperature coefficient of platinum alloys.............. .................. 150

27. Chart showing the relation between electrical conductivity and temperature coefficient of platinum alloys........................... 162

28. Tubular displacement air thermometer ............................. 166

29. (Withdrawn.)

30. Diagram of Jolly air thermometer and bulb......................... 168

31. Non-inglazed, spherical air-thermometer bulb ...................... 172

32. Non-inglazed, re-entrant air-thermometer bulb..... ................. 173

33. Inglazed, spherical air-thermometer bulb........................... 174

34. Machine for soldering porcelain; elevation ........._............. 175

35. Machine for soldering porcelain; plan............................... 176

35a. Gasometers........................................................ 179

(663) 9
10 ILLUSTRATIONS.

Page. 

FIG. 36. Revolving muffle; diagram ........................................ 181

36a. Elliptic revolving muffle ; diagram................................. 181

37. Revolving muffle and furnace; longitudinal section ................ 182

38. Revolving muffle and furnace; plan................................ 184

39. Temperature and electromotive force of thermo-couples, in corresponding time series .................................................. 202

40. Constant pressure air thermometer ................................. 209

41. Chart showing the variation of thermo-electromotive force with tem-

 perature ........................................................ 226

42. Chart showing the variation of thermo-electromotive force with temperature ........................................................ 228

43. General disposition of apparatus for viscosity measurement......... 243

44. Diagram of receiver for distributing pressure....................... 246

45. Side elevation of the capillary apparatus ........................... 247

46. Plan of the capillary apparatus .................................... 248

47. Vertical section through helix...................................... 258

47a. Plan of helix and thermo-couples.....................i............. 264

48. Chart showing viscosity as a function of temperature .............. 264

49.

50

51. > Diagrams of practical transpiration pyrometers.................... 303

52.

53. J

54. Chart showing the relation between apparent viscosity and pressure.. 304

55. Disposition of apparatus for differential measurements.............. 305

(664)
TABLES.

Page.

TABLE 1. List of thermo-couples. .......................................... 69

2. Constancy of temperature in the mercury apparatus.............. 70

3. Constancy of temperature in the zinc apparatus.................. 72

4. Constancy of temperature; zinc apparatus; time series .......... 73

5. Constancy of temperature; zinc apparatus j time series .......... 74

6. Values of e^................................................... 78

7. General summary of results ..... ................................ 79

8. Equivalent thermo-electromotive forces.......................... 80

9. Comparison of standard elements................................ 101

10. Temperature coefficient of dark's cells........................... 102

11. Temperature coefficient of siphon Daniell standard................ 102

12. Constancy of temperature along the axis of boiling tube ; steam... 10">

13. Constancyof temperature along the axis of boiling tube ; mercury. 100

14. Constancy of temperature along the axis of boiling tube; sulphur.. 107

15. Constancy of temperature along the axis of boiling crucible; zinc.. 109

16. Calibration of thermo-couples Nos. 17,18,22,35,36 ................ 110

17. Values of 620 for thermo-couples Nos. 17,18,22,35,36............... 114

18. Crucible (fig. 13) charged with bismuth.......................'... 117

19. Crucible (fig. 13) charged with antimony...... ................... 117

20. Crucible (fig. 13) charged with cadmium......................... 118

21. Constancy of temperature in boiling tubes; sulphur.............. 119

22. Available substances for vapor baths .1.......................... 120

23. Calibration in zinc vapor..................................'...... 122

24. Calibration in zinc vapor........................................ 123

25. Calibration in hot tin............................................ 123

26. Calibration in bismuth .......................................... 123

27. Calibration in antimony......................................... 124

28. Thermo-electric datum for temperatures above the melting point

of platinum .................................................. 125

29. Density of platinum alloys.................................. .... 129

30. Electrical resistance of platinum alloys ; rods .................... 132

31. Electrical resistance of platinum alloys; wires ................... 134

32. Thermo-electrics of platinum alloys.............................. 136

33. Temperature coefficient of platinum alloys ....................... 139

34. Constants of platinum alloys; digest ............................ 143

35. Electrical tests for purity........................................ 147

36. Electrical tests for purity........................................ 147

37. Electrical tests for purity........................................ 147

38. Electrical tests for purity........................................ 148

39. Electrical tests for purity..'...................................... 148

40. Constants of the linear relation (initial tangent) between electrical

conductivity and temperature coefficient of platinum'alloys..... 155 

(665) . 11
12 ' TABLES.

Page. 

TABLE 40a. Showing Matthiessen's and Vogt'a results for the electrics of gold,

silver, and copper alloys ...................................... 158

40&. Showing Matthiessen's and Vogt's results for iron carburets....... 160

41. Dimensions of copper capillary tubes............................. 171

42. Dimensions of platinum capillary tubes.......................... 171

43. Capacity, etc., of porcelain air-thermometer bulbs................ 173

44. Values of k for divers T.......................................... 191

45. Values of Tc-\-W for divers T and t ................................ 192

46. Compensator volumetry ......................................... 194

47. Comparison of divers errors which affect the result one promille.. 196

48. Moisture error of unglazed bulbs................................. 198

49. Moisture error of unglazed bulbs ................................ 199

50. Comparison of air thermometer and thermo-couple ............... 200

51. Comparison of air thermometer and thermo-couple ..;............ 202

52. Comparison of air thermometer and thermo-couple; later results.. 204

53. Comparison of 620 and T from Table 52 ........................... 206

54. Comparison of air thermometer and thermo-couple; in-glazed bulb. 207

55. Comparison of e?0 and T from Table 54 ........................... 208

56. Volumetry ofbulbs.............................................. 213

57. Errors of the thermometer formulae............................... 215

58. Comparison of air thermometer and thermo-couple; method constant pressure; time series; Group I, Series I.................. 218

59. Comparison of air thermometer and thermo-couple; method constant pressure; time series; Group I, Series II.................. 218

60. Comparison of air thermometer and thermo-couple; method constant pressure ; time series; Group I, Series III................ 219

' 61. Comparison of air thermometer and thermo-couple; method constant pressure; time series ; Group I, Series IV................ 220

62. Comparison of air thermometer and thermo-couple; method constant pressure; time series; Group II, Series I................. 221

63. Comparison of air thermometer and thermo-couple; method constant pressure; time series; Group II, Series II................ 222

64. Comparison of air thermometer and thermo-couple; method constant pressure; time series; Group II, Series III............... 222

65. Comparison of air thermometer and thermo-couple; method constant pressure; time series; Group II, Series IV................ 223

66. Comparison of air thermometer and thermo-couple; method constant pressure; time series; Group II, Series V................ 223

67. e20 and T from Table 58 .......................................... 224

68. e20 and T from Table 59.......................................... 225

69. e2 o and T from Table 60.......................................... 225

70. e20 and T from Table 61.......................................... 225

71. e20 and T from Table 62.......................................... 225

72. eaoandTfrom Table 63.......................................... 226

73. e20 and T from Table 64.......................................... 226

74. 20 and T from Table 65.......................................... 226

75. e20 and T from Table 66.......................................... 227

76. Comparison of divers errors which affect the result one promille .. 229

77. Permanent volume variations of bulb ............................ 233

78. Interpolations near the boiling point of zinc...................... 235

79. Coefficient of heat expansion of porcelain........................ 236

80. Thermal constants of the petroleum argand lamp ....... ... 250

81. Viscosity of air.................................................. 259

82. Viscosity of hydrogen ........................................... 260

(666)
TABLES. 13

Page.

83. Viscosity of hydrogen ........................................... 262

84. Viscosity of air ................................................. 263

85. Viscosity of air, miscellaneous tests.............................. 265

86. Viscosity of air, miscellaneous tests.............................. 267

87. Viscosity of hydrogen ........................................... 268

88. Viscosity of hydrogen .. .................. ...... ....... 269

89. Viscosity of air ................................................. 269

90. Successive value of T/O ........................................... 271

91. Calculated zero values of ^........... ....................... 278

1)0

92. Temperatures measured thermo-electrically and by the transpiration pyrometer................................................ 283

93. Transpiration of air under variable pressure, burner not chimneyed. 287

94. Transpiration of air under variable pressure, chimneyed burner... 288

95. Transpiration of air under variable pressure ..................... 288

96. Apparent viscosity of air at high temperatures; absolute measurement ......................................................... 290

97. Apparent viscosity of air at high temperatures; absolute measurement ......................................................... 290

98. Apparent viscosity of air at high temperatures; absolute measurement ......................................................... 291

99. Apparent viscosity of air at high temperatures; absolute measurement ......................................................... 291

100. Apparent viscosity of air at high temperatures; absolute measurement ........................................... ........... 292

101. Apparent viscosity of air at high temperatures; differential

measurement.................................................. 294

102. Apparent viscosity of air at high temperatures; differential

measurement.................................................. 294

103. Apparent viscosity of air at high temperatures; differential

measurement......... .................................. 294

104. Transpkation and pressure in wide tubes ........................ 297

105. Transpiration and pressure in glass tubes ...... ... 298

106. Transpiration and pressure in silver tubes .. .. .......... 299

107. Transpiration and pressure in platinum tubes, air................ 299

108. Transpiration and pressure in platinum tubes, hydrogen......'.... 300

(667)

LETTER OF TRANSMITTAL.

DEPARTMENT OF THE INTERIOR,

UNITED STATES GEOLOGICAL SURVEY,

DIVISION OF CHEMISTRY, 

Washington, D. C., February 29,1888.

SIR: I have the honor to transmit herewith the manuscript of Dr. 

Carl Barus's report "On the Thermo-electric Measurement of High 

Temperatures," and to request that it be published as a bulletin of the 

U. S. Geological Survey.

Very respectfully,

F. W. CLARKE,

Chief Chemist. 

Hon. J. W. POWELL,

Director U. S. Geological Survey.

(669) 15

PREFACE.

The present publication is the first contribution to a research on 

the physical constants of rocks, the experiments of which are to follow 

a general plan devised by Mr. Clarence King, former Director of the 

U. S. Geological Survey. Retaining such questions as have an immediate bearing on dynamical geology for his own investigation, Mr. King 

honored me by placing the purely physical part of the inquiry into my

bauds. Our undertaking was begun some years ago. I was in communication with Mr. King as far back as the summer1 of 1881, and 

much work in the way of determining the possibilities of the problems, 

of organizing methods of research, and of selecting and devising suitable apparatus, was done prior to 1882.

Not, however, untilJanuary of 1882 were definite steps taken toward 

the organization of a physical laboratory. The work in view was of 

too elaborate a nature *to be undertaken by a single observer; and at 

my request Mr. King invited Dr. Vincent Strouhal, then of the University of Wiirzburg, to sbare my labors. Our early endeavors were of a 

pioneering kind. With the exception of a few instruments which had 

been used in the physical work in Nevada, and which came into our 

possession through the kindness of Mr. G. F. Becker, the early laboratory of the Survey was furnished entirely at the expense of Mr. King.

It is but just, in this place, to acknowledge a debt of gratitude which 

I in particular owe to Mr. Becker, by whom our efforts in the direction 

of physical research were befriended and advanced. It will be remembered that the first physical work on the Geological Survey was done 

under his direct supervision.2

The general scope of the problems to be undertaken, so far at least 

as their purely physical relations are concerned, has been briefly given 

in an article prepared under the direction of Mr. King, and printed by 

the Survey3 for the year ending June 30, 1882. In this article I classified the parts of the proposed research as follows:

(a) Phenomena of fusion. These would comprehend temperature of fusion, specific 

volume at this temperature of the solid and of the liquid materials respectively, heat expansion, compressibility, latent heat of fusion, specific 

heats all considered with especial reference to their variation with pressure.

l Cf. Second Ana. Kept. U. S. Geol. Survey, 1882, p. 40.

2 Of. First Ann. Kept. U. S. Geol. Survey, 1680, p. 4(i; Second Ann. Kept. U. S. Geol. 

Survey, 1882, pp. 311, 319-330.

3 Third Ann. Kept. U. S. Geol. Survey, 1883, pp. 3-9.

Bull, 54 2 671) 17
18 MEASUREMENT OF HIGH TEMPERATURES.

(b) Phenomena of elasticity and viscosity, considered, as before, with especial reference to their dependence on temperature and pressure.

(c) Phenomena of heat conductivity under analogous circumstances.

The article then proceeds to select the relation between melting point 

and pressure, as a problem the experimental difficulties of which are 

perhaps least formidable; as a problem, moreover, which for thermodynamic reasons may judiciously be decided upon as a point of departure. It develops certain general methods by aid of which increments 

of high melting point, however relatively small, are measurable even 

under conditions of very high pressure. It concludes by signaling the 

importance of special and preliminary researches on the measurement of 

high temperatures and of high pressures, with a view to the selection of 

such details of method as will best subserve the purposes in question.

Throughout the present research the points here mentioned have 

been carefully kept in mind. It is my judgment that few important 

steps in dynamical geology will be made until the methods for the 

accurate measurement of high temperatures and of high pressures have 

not only been perfected but rendered easily available. On the basis of 

this conviction the present memoir on high temperatures has been 

prepared; and though the experiments on temperatures may seem to 

have been pushed to some detail, I can not regard them either as profuse or as superfluously ambitious. Indeed, if the investigation be of 

any fullness, it is almost essential that the observer master the component parts of his research separately; and not until he has satisfactorily done this can he apply them conjointly. In work like the 

present, moreover, the value of the data can scarcely be determined 

except by the degree of uniformity of great numbers of results.

In June, 1882, Dr. Strouhal resigned his charge to take a professor 

ship at the University of Prague. At my request Dr. William Hallock 

was appointed to fill the vacancy, and, being at the time associated with

Dr. Strouhal in certain duties abroad, he was easily able to complete 

the work which the latter had been compelled to leave unfinished. Dr. 

Strouhal made the purchases of all the instruments we desired to buy 

in Germany, while Dr. Hallock, following my instructions, proceeded to 

purchase such apparatus as could best be obtained in France.

About this time the rooms which had been placed at my disposal by 

the American Museum at New York became temporarily unavailable. 

Moreover, as Dr. Hallock had joined me, more room than the museum 

afforded was desirable. After due deliberation we determined to rent 

a house in New Haven, Conn., and thither the laboratory was removed 

in November, 1882. Our reasons for selecting New Haven were, briefly, 

that a satisfactory house for practical laboratory purposes could be obtained more reasonably there than elsewhere; and that the city offered 

excellent library and other facilities for scientific work, such as can be 

met with only in the immediate vicinity of a large university. We have 

abundant cause to thank the gentlemen in charge of the scientific de-

(672)
BARUS.) PREFACE. 19

partment of Yale College for many favors which they kindly extended 

to us.

The researches made in Few Haven, in so far as they fall within the 

scope of the present volume, are recorded in Chapter I, The bulk of 

our New Haven work, however, was in organizing a working laboratory 

and determining the errors and the constants of the instruments, and 

solving other problems which do not command sufficient general interest to be chronicled. The high-temperature work prosecuted there was 

laid out on a large scale, and the practical management of it is largely 

due to Dr. Hallock. Following Deville and Troost, the plan was one in 

which large masses of substances are thermally operated upon. Undoubtedly these researches would have led to important results beyond 

those of Chapter I if there had been time to carry them consistently 

through to the end.

The work in New Haven was not satisfactorily completed. In July, 

1883, with the appointment of Prof, Fo W. Clarke as chief chemist of 

the Geological Survey, our laboratory became officially connected with 

the chemical laboratory. Conformably with the further decision of tb*e 

Director, by which the divers laboratories of the Geological Survey 

were united in one central laboratory in Washington, it was again necessary to change our basis of operations, this time (in November, 1884) from 

New Haven to Washington. In the quarters assigned to us in the U. S. 

National Museum, temperature Work on so large a scale as the New 

Haven work appeared impracticable, and it was therefore abandoned.

In the mean time Dr. Hallock had been placed in charge of a series 

of independent researches not connected with my work, and the experiments in hand were carried forward by myself to the point indicated 

in the present volume. Of course I owe much to the experience gained 

in our mutual efforts, detailed in Chapter I.

In the introductory pages I give a succinct account of the chief 

methods of pyrometry which have thus far been put to the test.

I was fortunate in being able to avail myself of the fine working 

library of the American Academy, and I owe much to the courtesy of 

Dr. Austin Holden, the librarian in charge.

The actual investigations, as contained in Chapters II, III, IV, and 

V, were adapted to the conditions prevailing at the National Museum. 

In place of the dangerous and cumbersome apparatus of the former 

laboratory, the endeavor is made to reduce all apparatus to the smallest dimensions compatible with reasonable accuracy of measurement.

Methods of calibration of this kind based upon known thermal data 

(boiling points) are developed in Chapter II.

I make in Chapter III a cursory survey of certain pyro-electric properties of the alloys of platinum. Curiously enough, the data of this chapter 

led to a striking result, inasmuch as it appears that the zero resistance 

/(O), if the resistance at t° be r=f(t) ), and the zero temperature coefficient /'((^//(O), are related to each other by a law which during the*

(673)
20 MEASUREMENT OF HIGH TEMPERATURES.

stages of low percentage alloying is independent of the ingredients of 

the alloy, except in so far as they modify its electrical conductivity.

In Chapter IV I develop a method for the direct and expeditious 

comparison of the thermo-couple with the air thermometer. A comparison of the data of Chapters II and IV gives me a criterion of the accuracy with which the data in the region of high temperature are known. 

This indirect method of arriving at such data is not apparently as rigorous as their direct evaluation by means of the air thermometer; but 

the indirect method requires much smaller quantities of substance and 

may be conveniently extended to much higher temperatures. Taking 

all liabilities to error into consideration, its inferior accuracy is only 

apparent.

The results recorded in these chapters will lead directly to the comparison of the data to be obtained with porcelain air thermometers 

containing different gases, or one and the same gas in all states of 

tenuity. When methods to be indicated in the text are pursued these 

comparisons can be made with great accuracy, since the stem errors 

and the expansion errors practically vanish. It is upon such results 

that the rigorous validity of known high-temperature data must ultimately depend. From my results, moreover, it does not seem absolutely 

essential to glaze the bulbs within. It thus appears probable that 

bulbs can be made of fire-clay body by which the upper limit of direct 

temperature measurement (1,500°) maybe materially increased.

Finally, I propose in Chapter V a new method of pyrometry based 

on the viscous behavior of gases. Using the results of the earlier 

chapters, I endeavor to investigate the law of variation of gaseous 

viscosity and temperature. Having found that the said variation 

takes place nearly as the two-thirds power of aosolute temperature, I 

proceed to indicate divers methods of utilizing this principle for practical high temperature measurement. The results show, I think, that 

when the law of thermal variation of gaseous viscosity is rigorously 

known, Poiseuille-Meyer's equation applied to transpiration data will 

enable us to measure temperature absolutely, over a wider thermal 

range, and with a degree of precision and convenience unapproached by 

any known method.

With regard to the contents of the present volume it is but just to 

remark that the work in all its essential parts was done either by Dr. 

Hallock and myself, or by myself alone without other assistance. The 

original practical construction of nearly all new apparatus, the designing and drawing of instruments, the extremely laborious computations 

which a task like the present involves, are our own work. If, therefore, in the writing of the present memoir I have apparently placed 

superfluous stress on mechanical details, I offer in explanation the fact 

that the result of personal experiences is my subject. It is much to be 

.regretted that the valuable researches of Messrs. Deville and Troost were 

not given to the world in more explicit form, for I have spent much

(674)
PREFACE. 21

time and pains in re-investigating and retesting methods and processes 

which, if more elaborate publications by these brilliant experimentalists 

were accessible, would not have been necessary.

In conclusion I wish to make some reference to the makers from whom 

such special apparatus and supplies as are described in this volume 

were obtained. Mr. William Grunow, 1 whose accomplishments as a 

mechanician are too well known to need characterizing here, made the 

fine parts of the apparatus for us; the cathetometer, the manometer 

stand, the micrometer and appurtenances, the revolving muffle, and 

other apparatus being from him. Those parts of the apparatus which 

are of fire-clay the furnaces, crucibles, tubes, etc. were obtained from 

Messrs. Hall & Sons.2 I desire especially to commend the technical 

skill of these gentlemen, as well as the pains and patience which they 

spent in making difficult parts of the work. Capillary tubes of platinum and silver I succeeded in inducing the Malvern Platinum Works 3

to draw for me. As I do not know whether platinum capillary tubes 

have previously been made, I wish to call attention to the fact that inasmuch as they can be heated to any temperature they are useful for 

many other purposes besides those given in this volume. Apparatus of 

porcelain, viz., air-thermometer bulbs and stems, fire crucibles, tubes, 

etc., were furnished in superior quality from MM. Morlent Freres,4 ancienne M. Gosse. This firm constructed the standard apparatus for 

Deville and Troost, and their artistic skill is unsurpassed. The porcelain of Bayeux used in their apparatus, besides being of the most refractory kind, has this additional advantage that its heat-expansion 

constants are known. Bulbs were also successfully made for me by the 

Royal Prussian Porcelain Works,5 at Berlin. These works are the 

makers of Professor Eieth's and Professor Angler's bulbs. The Saxon 

Porcelain Works,6 at Meissen, courteously placed duplicates of such 

bulbs as they had already made (Professor Braun's bulbs) at my disposal. The glass apparatus, boiling tubes in various open forms, were 

originally made for ine by Messrs. Whitall, Tatum & Co.,7 who have 

excellent facilities for annealing glass. Closed forms of boiling tube, as 

well as the reentrant air-thermometer bulb of glass, were constructed 

by Einil Greiner,8 with his usual accuracy and skill.

CARL BARUS.

PHYSICAL LABORATORY, U. S. GEOLOGICAL SURVEY, 

Washington, January, 1888.

1 William Gruuow, observatory, West Point, N. Y.

2 Hall & Sous, No. 69 Tonawanda street, Buffalo, N. Y.

3 Malvern Platinum Works, Jas. Queen & Co., agents, Chestnut street, Philadelphia.

4 Morlent Freres, No. 8 Rue Martel, Paris, France.

5 Koniglich Preussische Porzellan Manufactur, Berlin; M. Andersen, director.

6 Koniglich Sachsische Porzellan Manufactur, Meissen; F. K. Buttner, director.

7 Whitall, Tatutri & Co., Philadelphia, Pa.

8 Emil Greiuer, No. 63 Maiden Lane, New York.

(675)
22 MEASUREMENT OF HIGH TEMPERATURES.

SUPPLEMENTAL.

Lot me here add, before passing ou, that since this manuscript left 

my hands some additional work has been done in high-temper a ture 

thermometry. A form of standard air thermometer has been devised 

and is being made. A torsion galvanometer suitable for the measurement of thermo-electric powers, such as are here encountered, has also 

been constructed. To test the efficiency of this instrument I made a 

series of measurements on the variation of boiling points with pressure, 

using the re-entrant porcelain crucible and the closed boiling tube 

figured below (Chap. II, Figs. 14a and lla). The results for mercury, 

sulphur, cadmium, zinc, and bismuth, covering an interval of some 

1,500° C., are important, inasmuch as they indicate the probable truth 

of the principle of Groshans. (Pogg. Ann., vol. 78, 1849, p. 112.)

I will advert to the independent method of standardizing a non-inglazed re-entrant porcelain air thermometer bulb, by thermal comparison with a re-entrant glass thermometer bulb of known constants. 

Such comparison is to be made above 300° to obviate all moisture and 

condensation errors, and either directly in the elliptic revolving muffle, 

or indirectly through the-intervention of the same thermo-couple. The 

difficult estimation of the volume of the non-in-glazed bulb is thus 

superfluous.

Again, to insure union, the gradual sagging of a weighted porcelain 

stem, the lower end of which has been heated to the viscous condition 

before the oxyhydrogen blow-pipe, into the heated neck of a re-entrant 

in-glazed bulb on the revolving table, has suggested itself. Similarly, 

atmospheric pressure may be brought to bear externally on viscous 

parts of bulb or stem. (Of., p. 175.)

Regarding literature, I may briefly refer to a recent critical work by 

c. H. Boiz (Die Pyrometer, etc., 70 pp., Berlin, J. SpriDger, 1888), and 

M. H. Le Chatelier has recently extended his valuable pyrometric researches in various directions.

C. B.

Boston, Sept. 1, 1889.

NOTE. The thermo-djnamic reasons referred to on page 18 are briefly these: In the notation of 

Clausius (Wairue-theone, 2d'eel., I, Braunschweig, 1876, p. 172), the first and second laws together 

lead to the equivalent of James Thomson's equation: dT{dp T(cr -r)/Er'; and the second law gives 

the equation dr'fdT=c' k'-\-r'/T. Starting with these equations of fusion, I purposed to formulate 

the relation between melting point and pressure, f(p, T) = 0, from direct experimental measurements, 

using the relation only within the pressure limits of the experiment. From this point it is difficult to 

proceed, for it is next necessary either to measure er T as a function of pressure and temperature, or 

to measure the corresponding relation of r'. In addition to the above equations the more general re 

lations

T dpvdp , , T (dpv\*/d,,«>

c=°p- E -dT di and c .=c,+tf \-dft I -&

are available.

(676)
ON THE THERMO-ELECTRIC MEASUREMENT OF HIGH 

TEMPERATURES.

BY CARL BARUS.

INTRODUCTION. 

GENERAL ACCOUNT OP METHODS OF PYROMETRY.

Earlier digests. Some account of the literature of high temperatures, 

and particularly of the masterly .labors of Messrs. Deville and Troost, 

being essential here, it was deemed expedient to give a brief but fairly 

full digest of all th,e methods devised and applied for high temperature 

measurement. To do this I made the customary use of the Fortschritte 

der Physik and of the Beiblatter of the Annalen der Physik, though 

in nearly all cases I have gone back to the original authors. Much assistance was received from earlier summaries, those of Pelouze,1 Beequerel,2 Weinhold,3 Fischer,4 Sir William Thomson,5 Nicuols,6 Browne,7 

Lauth,8 and Shaw,9 all more or less complete and written with widely 

different ends in view. I must also refer to the reports (1881 and 1884) 

of the committee appointed by the British Association for the Advancement of Science to investigate the state of our knowledge of spectrum 

analysis..

I shall try to submit a tolerably full summary of what has been done, 

in most cases, however, giving no more than mere mention of the work 

of the individual observers. Nor shall I make many critical statements, 

for the cardinal difficulties surrounding divers processes described for

'Pelouze: Traite" complete cles Pyrometres; Paris, 1829.

2 Becquerel: Recherches sur la extermination des hautes temperatures, etc.; Ann. 

ch. et phys., vol. 68, 1863, p. 49.

3 Weiuhold : Pyrometrisclie Untersuchimgen; Pogg. Ann., vol. 149, 1873, p. 186.

4 Fischer: Ueber Thermometer und Pyrometer; Dingler'a Jour., vol. 225, 1877, pp. 

272, 463.

6 Thomson : Heat, § 10; Encyclopaedia Brit., 9th ed., vol. 11, 1880, p. 558.

c 'Nichols: Am. Jour. Sci., 3d series, vol. 22, 1881, p. 363.

7 Browne: Pyrometers; Nature, vol. 30, 1884, p. 366.

8 Lauth: Mesures pyrometriques a hautes temperatures; Bull. Soc. Ch., Paris,new 

series, vol. 46, 1886, p. 786. s

9 Shaw: Pyrometer; Encycl. Brit., 9fch ed., vol. 20, 1886, p. 129.

(677) 23
24 MEASUREMENT OF HIGH TEMPERATURES.

temperature measurement so readily suggest themselves to the student 

of modern physics that special attention to them is superfluous, whereas 

criticism of more searching value calls for special experiments. Such 

experiments, except in a few cases, I have not had occasion to repeat.

Character of the measurements, It is impossible to read the earlier 

memoirs on high temperature research without a feeling of uneasiness 

and disappointment. There is no lack of ingenious contrivances or 

of well-devised methods, but the results obtained are usually sadly at 

fault. In many cases no data for the absolute identification of the 

measurements made are discernible. In other cases not only do observers, using different methods, fail to reach accordant results, but it 

is not unusual to find even skilled observers using the same method 

with errors in results as high as 10 per cent, for the same fixed high temperature datum, the boiling point of zinc. To secure certain facilities 

of manipulation Deville and Troost, at the outset of their researches, 

used iodine vapor as a gas for thermal measurement. This step must 

be regarded as a misfortune to science, and one which retarded the 

progress of high-temperature research many years. After the tendency 

of the iodine molecule to dissociate had been suspected, and the relative 

imperviousness of porcelaiu as compared with platinum air-thermometer 

bulbs had been clearly pointed out, the values of the boiling point of 

zinc begin to increase from the exceptionally low values of Becquerel 

(884°), and to decrease from the exceptionally high values of Deville 

and Troost (13 040° 0.) over a total range of temperature of about 150°, 

until the final results of these observers (932° and 942°, respectively) 

agree to about 10°. Curiously enough, however, Weinhold, an observer 

of great assiduity and some experience, having made himself master 

of high-temperature measurement by the air thermometer methods, endeavors to redetermine the value of the boiling point of zinc, and finds 

a value (1,035°) as high as the highest datum of Deville and Troost, 

Fortunately the subject has been rescued from this condition of vagueness by the recent vigorous work of Violle, the results of wh'ich agree 

well with the mean data of Becquerel and of Deviile and Troost.

My chief object in giving this outline is to place before the reader the 

nature of the difficulties with which the problem of high temperature 

measurement is surrounded, and to indicate the diversity of the results 

reached even by the best of trained observers. Methods which in the 

hands of different investigators lead to data so widely different as the 

values just cited are not apt to inspire confidence. It is perhaps more 

for this reason than because of real difficulties of manipulation that the 

gas thermometer has been so little used as a standard of reference in 

high-temperature measurement. For the experimental operations are 

not necessarily more complex than those called for in some of the empiric 

methods of standardization methods which have further burdened 

the unfortunate subject of high-temperature research with their own 

allotment of vagueness of principle and inaccuracy.

(678)
BARUS.] METHODS OF PYROMETRY.

Classification of pyrometers, Thermometers which depend essentially 

on the properties of the substance used for thermal measurement are 

called by Thomson J intrinsic therinoscopes. They may be either continuous or not. it is with such intrinsic thermoscopes that practical 

pyrometry must be conducted, although the data of the gas thermometer, 

as appears from the recent pyro chemical researches of Langer and 

Meyer,2 may safely be regarded as non-intrinsic and absolute, particularly in the region of high temperatures. Almost every thermal phenomenon has been utilized for temperature measurement, and the devices employed may be conveniently classified by aid of these phenomena as follows:

I. Dilatation of solids.

1. A single solid.

2. Two solids acting differentially.

II. Dilatation of liquids.

III. Dilatation of gases.

1. Expansion measured in volume, manometrically.

2. Expansion measured in pressures, manometrically.

3. Expansion measured in volume, by displacement.

IV. Vapor tension. 

V. Dissociation. 

VI. Fusion.

Vlf. Ebullition. 

VIII. Specific beat.

IX. Heat conduction.

X. Heat radiation.

XI. Viscosity.

1. Of solids.

2. Of liquids.

3. Of gases.

XII. Spectropbototnetry and color, 

tary polarization.

XIII. Acoustics (wavelength).

XIV. Tbernio-electrics.

XV. Electrical resistance.

XVI. Magnetic moment. 

XVII. Miscellaneous.

RoDilatation of solids. Curiously enough the dilatation thermometers 

were not the first to.suggest themselves. Newton, in his scala graduum 

caloris, proposes a method of temperature measurement based on his 

law of cooling, almost as early as 1700. However Musschenbroek (1731), 

Ellicot (1736), Bouger (1745), and others availed themselves of singlebar expansion devices, and Mortimer made a thermometer on this principle in 1746.

The most celebrated apparatus of this kin'd (1782) is Wedgwood's3 

pyrometer, in which the attempt is made to express temperature in a 

scale based on the shrinkage experienced by a little compressed cylinder 

of clay after exposure to the said temperature. This apparatus came 

into much more general use than its inventor intended. Its indications 

were vigorously discussed by the physicists of the time, especially by 

Guyton-Morveau,4 who in attempting to convert Wedgwood's arbitrary 

thermal scale into degrees centigrade showed the apparatus to be un1 Encyclopedia Brit., 9tb ed., vol. 11, 1880, p. 580.

2 Langer and Meyer, Pyrochemiscbe Untersuchungen, Braunschweig, Vieweg u. 

Sohn, 1885; Berl. Ber., vol. 18, 1885, p. 1501.

3 Wedgwood: Pbil. Trans., Roy. Soc., vol. 72, 1784, p. 305; vol. 74, 1782, p. 358; 

Dingler's Jour., vol. 15, 1824, p. 230.

4 Guyton-Morveau: Anuales de cbimie, Paris, 1st series, vol. 46, 1803, p. 276; ibid., 

vol. 73, 1810, p. 254; ibid., vol. 74, 1810, pp. 18, 129; ibid., vol. 90, 1814, pp. 113, 225.

(679)
26 MEASUREMENT OP HIGH TEMPERATURES.

reliable because of the tendency of clay to shrink irregularly and to 

warp, and because of its dependence on the kind of clay used and on 

the time of exposure. After this the use of single-solid pyrometers 

seems to have been abandoned until quite recently, when Mr. Mchols,1 

in comparing the resistance-temperature formulae of Be"uoit, Siemens, and 

Matthiesseu with his own, found the linear dilatation of platinum very 

serviceable for the co-ordination of his data. He gives preference to 

the expansion thermometer over the resistance thermometer whenever 

the special constants of both instruments are unknown.

The absence of further devices for single-solid pyrometry is not remarkable when the vast numbers of pyrometers in which solids are combined differentially are taken into view. Some of the earliest attempts 

of this kind are due to JBorda,2 although Guyton-Morveau (loc. cit.) was 

probably the first observer who had pyrometric ends in view, the solids 

adopted being platinum, and porcelain. This physicist was at some 

pains in systematizing the dilatation of solids. More elaborate attempts 

to utilize the occurrence of different expansibility in solids for pyrometric purposes are due to Dauiell.3 Daniell's substances are platinum 

and black lead, with a suitable interposition of clay, and his work on 

the dilatation of solids is elaborate, but unfortunately without much 

permanent value.

Following Dauiell come a host of inventors whose apparatus, though 

often exceedingly ingenious, have only technical importance. These 

may therefore be passed over with a single brief mention here. Petersen4 has a platinum wire in an iron tube; Gibbon5 exposes rods of iron 

or steel, and copper provided with a contact lever; Oechsle6 utilizes an 

iron-brass spiral working on the principle of Br6guet's metallic thermometer, while Clement7 replaces the metals of such a spiral by platinum and silver. Prinsep,8 however, held that even this apparatus is 

not reliable on account of the tendency of the metals to alloy a conclusion which has Weiuhold's9 assent. Gauntlet, 10 Desbordes, 11 Oechsle,12

1 E. L. Nichols: Am. Jour. Sci., 3d series, vol. 22, 1881, p. 363.

2 Borda: Boit Trait6,1, 1816, p. 159. The use of iron and brass seems first to have 

been made by Felter in Braunschweig.

3 Daniell: Experiments with a new register pyrometer for measuring the expansion 

of solids; Jour. Royal Soc., London, vol. 11, p. 309; Philos. Mag., London, 2d series, 

vol. 10, 1831, pp. 191, 268, 297, 350; ibid., 3d series, vol. 1, 1832, pp. 197,261; Dingler's Jour., vol. 19, p. 416; vol.43, p. 189; vol. 46, pp. 174,241.

4 Petersen: Gehler. Phys. Worterb., 2d series, vol. 7, p. 994.

5 Gibbou: Dingler's Jour., vol. 68,1838, p. 436.

eOechsle: Ibid.,vol. 60, 1836, p. 191.

'Clement: Ibid.,vol. 80, 1843, p. 241.

8 Prinsep: Ibid., vol.28, 1828, p. 421.

9 Weinhold: Dingler's Jour., vol. 208, 1873, p. 125. 

wGauntlet: Ibid., vol. 157, I860, p. 279. 

» Desbordes: Ibid., vol. 157, 1860, p. 279. 

12 Oechsle: Ibid., vol. 160,1861, p. 112; ibid., vol. 196, 1870, p. 218.

(680) '
METHODS OF PYROMETRY. 27

Bock, 1 Lion and Guichard2 use iron and copper or iron and brass, either 

in the form of parallel rods or tubes bundled together or of a rod within 

a tube j in each case provided with a suitable index and dial arrangement. A like apparatus of metal and fire-clay (chamotte) is due to 

Bussius.3 Finally, the use of graphite for pyrometry, an idea which 

long ago occurred to Daniell, was resuscitated by v. Steinle and Hartiug. 4 In their apparatus an iron tube surrounds a rod of graphite, and 

an ingenious mechanism permits only those parts which are actually 

exposed to the high temperature to act differentially on the dial. Adjustment is made by means of mercury. Winkler, who first tested these 

apparatus, declared them serviceable, but his testimony is not corroborated by Beckert. He finds that the indications of graphite pyrometers 

are neither strictly comparable nor very decisive, and that they are 

quite unreliable above 600°. This criticism applies to the pyrometers 

of the present class generally.

Dilatation of liquids. Pyrometers based on liquid expansion are few 

in number and quite unavailable. An old apparatus is described anony 

mously in Dingler's Journal5 in which the expansion of a fused alloy in 

a porcelain bulb is registered by aid of a platinum rod moving along a 

scale. The division is in Wedgwood degrees. A similar apparatus 

was proposed by Achard.6 Here the expansion of the alloy is to be 

read off directly in the translucent stem of the porcelain bulb. The 

construction, therefore, is that of the ordinary mercury thermometer. I 

doubt whether either of .these instruments has ever been used. Person7 

applied a new principle. He found that mercury under 4 atmospheres 

pressure boils above 450°, under 30 atmospheres pressure above 500°; 

that the dilatation in these cases is quite notable. Here I may refer to 

experiments of Bystrom,8 to whom a hydro-pyrometer is due, and to 

Waterston,9 by whom the expansion of' water at high temperatures 

(300°) under pressure has been specially investigated. Waterston 

formulates his data and is led to the striking result that water at 300° 

expands at a greater rate than permanent gases. Water at high 

temperatures and pressures attacks glass, rendering it opaque and 

thus putting an end to the experiment.

Dilatation of gases (manometric methods}. According to Shaw10 a 

rudimentary air thermometer was built by Amonton in Paris about as

' Bock: Ibid,, vol. 195, 1870, p. 312.

2 Lion et Guichard : Ibid., vol. 220,1876, p. 37.

3 Bussius: Ibid., vol. 164,1862, p. 107. Berg- und Hiittenm. Zeitung, No. 10,1862.

4 v. Steinle and Harting: Clemens Winkler's report in Zeitschr. fiir Auulyt. Chern., 

vol. 19, 1880, p. 63; Beckert's report in ibid., vol. 21, 1882, p. 248. 

6 Dingler's Jour., vol. 32, 1829, p. 355. 

e See Becquerel: Ann. ch., 3d series, vol.78, 1863, p. 52. 

7 Person: Comptes Eendus, vol. 19, 1844, p. 757. 

8 Bys1rom : Berl. Ber., 1862, p. 344.

9 Waterstou : Philos. Mag., Lond., 4th series, vol. 26, 1863, p. 116. 

'°Enc. Brit., vol. 20, 1886, p. 129.

(681)
28 MEASUREMENT OF HIGH TEMPERATURES.

early as 1700. Guy ton-Morveau, 1 in whose thermal researches the dilatation of solids and the specific heat of platinum were discussed with 

reference to their availability in thermal measurements, also proposed 

gases for that purpose. Prinsep,2 however, appears to have been the 

first to construct an air thermometer and to apply it as an instrument 

of research. Prinsep's bulb was of gold. This was in pneumatic connection with a reservoir of olive-oil provided with a sensitive manometer. As the air in the bulb expanded it displaced the oil which exuded 

through a cock at the bottom of the reservoir. Pressure being maintained constant the amount of olive-oil discharged is equal in bulk to 

the amorint of air which enters the receiver at the given temperature. 

Hence by weighing the oil the temperature of the bulb may be calculated. Priusep's apparatus is unique, and his absolute thermal data 

are very much nearer the truth than those of his predecessors. Indeed 

they compare well with the known data of the present day. Prinsep's 

chief data refer to the melting points of alloys of gold, silver, and platinum which bear his name. To these I shall recur.

Leaving Davy, 3 who constructed an air thermometer in which the air 

expansion was weighed in .mercury, and Mill4 and Petersen,5 to whom 

also forms of air thermometers are due, the next observer seems to be 

Pouillet.6 Pouillet's researches are of prime importance. Having constructed a bulb of platinum, which enabled him to reach the highest temperatures, he then took the first definite steps in radiation-pyrometry 

by investigating the temperature at which solids glow, in calorimetric 

pyrornetry by determining the specific heat of platinum between 

0° and 1,200°, and in thermo-electric pyrometry by carefully calibrating a thermo-couple of iron and platinum. As these apparatus will be 

referred to again, I need only remark here that to Pouillet the form of 

constant pressure manometer is due very nearly as it is to be used in

pyrometric work to-day. This apparatus was perfected by Eepault,7

and afterwards accurately figured by Pouillet8 himself. Some time 

after this Silberinanu and Jacquelin9 described a platinum air-thermometer, of variable capacity, operating like a constant volume thermometer, but it does not seem to have led to practical results. Erman and 

Herster, 10 in their endeavor to measure the amount of permanent ex-

'Loc. cit.

2 Prinsep: Philos. Trans. Roy. Soc. Lond., 1827. Aiin. ch. et phys., 2d series, vol. 

41, 1829, p. 247.

3 Davy: Dingler's Jonr., vol. 46, 1832, p. 249. 

4 Mill: Gehler's Physikal. Worterbuch, 2d series, vol. 7, p. 997. 

5 Petersen: Ibid., pp. 998, 1004.

6 Ponillet: Recherches sur les hautes temperatures et sur plusieurs phe"nomenes qui 

en dependent; Comptes Rendus, vol. 3, 1836, pp. 782-790.

7 Regnault: Relation des Experiences, Paris, vol. 1, 1847, p. 168. 

8 Ponillet: Physique,vol. 1, 9th ed, 1853, p. 233.

9 Silbermanu et Jacquelin: Bull. Soc. d'Encouragement, 1853, p. 110; cf Becquerel, 

loc. cit.

10 Errnan and Herster: Pogg. Ann., vol. 97, 1856, p. 489.

(682)
BARVB.] METHODS OF PYROMETRY. 29

paiision of cast-iron at high, temperatures, availed themselves of bulbs 

of copper and of platinum for their thermal measurements. These were 

used much after the manner of vapor-density bulbs. The long capillary 

necks could be closed at the desired temperature by a faucet, and the 

temperature was then calculated from the amount of water which entered the cold bulb. These experiments form a natural transition 

to the earlier researches of Deville and Troost, 1 in which a splendid 

improvement in thermal measurements was made possible by the introduction of porcelain bulbs to replace those of metal and of glass. 

Deville and Troost here use Dumas's well-known method to evaluate 

both temperature and vapor density. In their search for a heavier 

thermal gas than air they select iodine vapor preferably to mercury, 

inasmuch as the inetal is apt to condense on the colder parts of the 

bulb and in falling down upon the hot parts to cause fracture. Using 

this iodiue thermometer, they find that cadmium and zinc boil at 860° 

and 1,040°, respectively. They also measure tlie coefficient of expansion of porcelain by noting the length of the necks of their bulbs at 

different (high) temperatures (0°, 860°, 1.000°). Having found these 

data they proceed to the measurement of vapor densities, with results 

which are not of interest here.

The high values for the boiling point of zinc thus obtained conflicted 

very seriously with certain measurements subsequently made by Becquerel.2 This observer used a platinum-palladium thermo-couple, the 

indications of which had to be carefully referred to Pouillet's platinum air thermometer. In this way Becquerel found the boiling point 

of zinc at 932°, more than 300° below that of Deville and Troost, as 

well as reaching a similarly low boiling point for cadmium, 740°. In 

the same paper the method of determining a series of melting points of 

metals is described and the data are fully given, and several final sections are devoted to radiation pyrometry. As regards accuracy of 

measurement and varied character of results, this paper is one of the 

most important in the history of pyrometry. It is to be noticed that 

Becquerel was aware of the probable permeability of platinum to gases 

at high temperatures. Further mention will be made of this later.

These discordant results necessarily provoked considerable discussion 

between Becquerel 3 and Deville and Troost,4 which temporarily resulted 

in favor of the former.

Deville and Troost naturally reject Becquerel's low values,'and be1 Deville et Troost: ttur la densit6 de vapour d'uu certain uotubre de tuatieres minerales; C. R., vol. 45, 1857, p. 821 (C. F. Berl. Ber., 1857. p. 73); C. R., vol. 49, 1859, p. 

239; Ann. ch. et phys., 3d series, vol. 58, 1860, p. 257.

2 Becquerel: Recherches sur la determination des hautes temperatures. Ann. ch. 

et pays., 3d series, vol. 58, 1863, p. 49.

3 Becquerel: C. R., vol. 57, 1863, p. 855; Inst., 1863, p. 369; C. R., vol. 57, pp. 902, 

925; Inst., 1863, p 385.

4 Deville et Troost: C. R., vol. 56, p. 977; Jnst., 1863, p. 161; C. R., vol. 57, 1863, 

pp. 894, 935; Inst., 1863, p. 377; ibid., p. 897.

(683)
30 MEASUREMENT OF HIGH TEMPERATURES.

lieve them to be erroneous because of the permeability of platinum at 

high temperatures. In doing this they refer to researches of their own1 

on the porosity of metals. Becquerel's reply is of an experimental 

character. He continues his work on air-thermometer pyrometry, replacing the platinum bulb with bulbs of porcelain, and availing himself 

both of constant pressure and of constant volume methods of measurement. Curiously enough the results of these new determinations are 

even below the former values, the boiling points of zinc and of cadmium 

being at 891° and 720°, respectively, while for the former as low a value 

as 884° was found. Becquerel dwells upon the excellence of the Pouillet method for high temperatures. Deville and Troost nevertheless 

refuse to regard these new results of Becquerel's as conclusive. They 

insist upon the impossibility of deriving accurate data with a porous 

reservoir. They point out that the large difference between Becquerel's 

present and former results is in itself to be looked upon with suspicion. 

They finally assert, inasmuch as Becquerel's pyrometers were not in 

immediate contact with zinc vapor, but were exposed in a closed lateral 

tube which issued from the zinc retort, that the datum measured is not 

the boiling point of zinc but a temperature below it. They finally repeat their own experiments with the same values as before. Becquerel 

again endeavors to show that the permeability of platinum did not seriously influence his results. He shows that his own researches are 

made in a way calling for much less skilled manipulation than those of 

Deville and Troost; and he finally adds that Deville and Troost have 

made but a single measurement with air, and that the use of iodine 

vapor as a gas for thermal measurement is not immediately warranted. 

Becquerel states the reasons for considering his boiling-point apparatus 

sufficient, but agrees that a possible error may be the impurity of his 

ziuc. With these remarks discussion ended, being left without a final 

issue; but it is well to state, in passing, that the results of subsequent 

observers, including Deville and Troost themselves, have proved beyond a doubt that the later inferences of Becquerel's were very nearly 

correct. Victor Meyer,2 1 believe, was the first to suggest the possible 

dissociation of the iodine, molecule at high temperatures, a behavior 

which he had established for chlorine. Meyer's views were corroborated and variously interpreted by Crafts and Meier,3 by V. Meyer himself,4 Crafts,5 Troost,6 Berthelot,7 and others.8

Seville and Troost: Porosite" dn platine. Re"p. chim. appl., 1863, p. 32fi; sur la 

permeability du fer a haute temperature; C. R., vol. 57, 1863, p. 935. 

2 V. and C. Meyer: Berl. Ber., vol. 12, 1879, p. 1426.

3 Crafts and Meier: C. R., vol. 90, 1880, p.-606; Berl. Ber., vol. 13, 1880, p. 851. 

<V. Meyer: Berl. Ber., vol. 13, 1880, p. 391; ibid., 1880, p. 1010. 

5 Crafts: Ibid., 1880, p. 1316. 

6 Troost: C. R., vol. 91, 1880, p. 54. 

7 Berthelot: ibid., p. 77. 

8 Cf. Deering: Chem. News, London, vol. 40, 1879, p. 87.

(684)
BAUUS.] METHODS OP PYROMETRY. 31

In 1863 Deville and Troost 1 began the publication of another series of 

investigations on high temperatures and boiling points. They describe 

their new porcelain air-thermometer bulb, which is a hollow sphere of 

porcelain, glazed both within and without, with a short neck, to which 

a capillary fissureless porcelain stem is soldered with feldspar, and the 

oxyfaydrogen blowpipe. They propose to discard iodine and to use air 

in its place, giving their apparatus a form nearly identical with 

Regnault's 2 normal air thermometer. They insist on the importance of 

spherical bulbs, and the air contained is dried at red heat by aid of a 

vacuum pump. All the zinc is carefully purified, and used in large 

quantities (charges of 17 kg.). It is but just to add here, to the great 

credit of Deville and Troost^ that the actual construction of the porcelain air thermometer occupied them for nearly seven years, working in 

concert with M. Gosse, in charge of the porcelain works at Bayeux. 

They were the first to use metallic vapor baths for constant high temperatures, a method which has been adopted by Becquerel and by

physicists generally since that time. In 1864 Deville and Troost 3 proceeded toward the accurate measurement of the heat expansion of the 

Bayeux porcelain. Using a porcelain bulb simultaneously and of the 

same material as the porcelain of the dilatation apparatus, they have 

the data sufficient to eliminate the error due to heat expansion from the 

thermal measurements made. Their method is necessarily one in which 

the linear expansion of a porcelain rod exposed in a zone of known 

constant temperature is measured by the cathetometer. Two platinum 

buttons, inserted in the ends of the stem, subserve the purpose of 

fiducial marks, and they are viewed through long lateral porcelain 

sight-tubes in the constant temperature apparatus. In this way they 

show that in some 200 measurements the cubical expansion of porcelain, 

between 0° and 1,500°, is 0.000016 to 0.000017. Above 1,500° it becomes rapidly larger. In addition to this normal heat expansion, 

porcelain experiences permanent dilatation, as is proved both by 

measuring the linear dimensions and by density tests applied to the 

porcelain after heating. Curiously enough, this density diminishes 

with frequent heating. The permanent expansion, which is a very 

serious error in the first heating (the volume of a bulb increasing from 

281.3CC to 285.6CC in six heatings, for instance), fortunately, soon, becomes negligible. Deville and Troost, at the end of their work, justly 

congratulate themselves on these results: " Nous couclurons que la porcelaine de Bayeux, matiere absolumeut impermeable et encore rigide 

aux 1,500° * * * capable de se dilater jusque la d'urie inaniereuuiforine, sans qu'on ait a tenir cornpte de sa dilatation permanente si ce 

n'est au butdes experiences." They again emphasize the excellence of 

soldering together, with feldspar in the oxyhydrogen flame, the accurately calibrated bulb and stem.

1 Deville and Troost, vol. 57, 1803, p. 897.

2 Regnault: loc. cit., PI. I, Figs. 7, et seq.

3 Deville and Troost: C. R., vol. 59. 1864, p. 162. 

(685)
32 . MEASUKEMENT OF HIGH TEMPERATUEES.

After these publications Deville and Troost made no further important contributions to high temperature thermometry for five years. 

The subject occupied Eegnault, 1 who proposed two methods. The 

first of these small flasks of iron or porcelain are partially charged 

with mercury, and closed above with a loosely-fitting valve or stopper. 

These are exposed at the temperature to be measured, and this is 

calculated from the weight of mercury left after cooling. The other 

method, being a displacement method, will be described bt'low. 

Shortly after this a series of very painstaking attempts in the measurements of high temperatures were made by Schiuz.3 Curiously enough, 

these papers, which contain a series of experiments admirably correct 

in principle, are but little known. Schiuz, after endeavoring in vain to 

utilize the principles of heat conduction in practical pyrometry, and 

after testing Beguault's displacement method with unfavorable results, 

applies the thermo-electric methods of Pouillet and of Becquerel. 

Schinz's air-thermometer bulb is a huge iron cylinder, from the center 

of one end of which an iron capillary tube passes to the manometric apparatus, while an iron tube for the insertion of the junction of the 

thermo-couple projects inward to the center of the figure through the 

other end of the cylinder bulb. In this respect Schinz's thermometer is 

unique, being the only form of re-entrant bulb hitherto devised. The 

great advantage of this form of bulb, which, quite independently of 

Schiuz, has been perfected in my experiments, will be emphasized below 

(Chap. IV). Nitrogen is the thermal gas in Schiuz's work, and the calibrations are carried as far as 1,000°. Giving him full credit for correctness of method and for the assiduity with which he endeavored to carry 

it out, Schinz's apparatus was doomed to fail because of its impractical 

clumsiness of construction, to say nothing of the permeability of iron at 

high temperatures. It is not possible to make much definite progress 

in the measurement of high temperatures with an apparatus which falls

short of the conditions of facility and certainty of manipulation. I shall 

revert to these measurements. For the special conveniences of the investigating chemist, Berthelot3 devised an apparatus intended to be 

compact and very sensitive, and provided with an easily adjustable empiric scale. His instrument is based on .the expansion of air and graduated by boiling points. Another instrument by Zabel4 is so adjusted 

as to ring an electric bell at any given temperature. It is perhaps expedient to advert in this connection to the thermometers of Weinhold5 

and of Crafts,6 both of which are constructed on Jolly's7 plan, but so adjusted that the conditions of constant volume are secured by the aid of

Eegnault: Ann. ch. et pays., 3d series, vol. 63, 18fil, p. 39. 

2 ScMnz: Dingler's Jour., vol. 177, 1865, p. 85; ibid., vol. 179, 1866, p. 436. 

3 Berthelot: Ann", ch. et phys., 4th series, vol. 13, 1868, p. 144. 

4 Zabel: Dingler'a Jour., vol. 195, 1870, p. 236. 

5 Weinhold: Pogg. Ann., vol. 149, 1873, p. 186. 

6 Crafts: Ann. de Chira. et de Phys., 5th series, vol. 14, 1878, p. 409, 

 Jolly: Pogg. Ann., Jubelband, 1874, p. 82.

(686)
BARUB.] METHODS OF PYROMETEY. 33

an electro-magnetic engine. The mechanism of Crafts' new thermometers appears to be particularly perfect in this respect. An air thermometer in which the pressure is directly measured manometrically is 

described by Codazza. 1 A rigorous investigation of the formula of the 

air thermometer, with a view toward the construction of an apparatus 

of exceptional delicacy, has lately been made by Grassi.2 Finally, the 

possible condensation of gases on metallic air thermometers of very 

large internal surface has been incidentally discussed by Fuess.3 Operating with bulb in form of a cylindrical ring, Fuess found that for a 

correct ice point the boiling point of water showed a value enormously 

high, which gradually decreased without reaching a normal value. His 

research is unfinished, however, and thus the full interpretation of these 

anomalous results is yet to be given.

After the earlier work of Deville and Troost and the papers of Scbinz, 

the most important memoir on high temperature measurement was

published by Weinhold.4 Having discussed the important methods of 

empirical pyroinetry, with reference to their availability for practical 

work or for research, Weinhold uses his air-thermometer for a redetermination of the boiling point of zinc. Unfortunately his high value, 

1,035° at 71.89cm, which is only a little below the erroneously large 

values of Deville and Troost, casts a slur over much of Weinhold's 

elaborate experimentation, and his criticism on the merits of Siemens' 

pyrometer, of caloriiuetric pyrometers, and of the dissociation pyrome 

ters fail to obtain the consideration which they probably deserve. 

Weinhold's bulb is of Meissen porcelain and his instrument of measurement is a modified Jolly thermometer.

In this place it is well to call attention to certain experiments commenced at about this time by Amagat and others to test the correctness 

of Boyle's law at different temperatures and high pressures. The constants hitherto adopted in high temperature air thermometry for all 

temperatures and pressures indiscriminately were those investigated 

by Kegnault5 and by Magnus.6 By Amagat,7 Cailletet,8 and others 

these researches were pushed to great nicety for pressures as high as

iCoda/za: Dingler's Jour., vol. 210, 1873, p. 255.

* Grassi: Rend, dell' Academia delli Scien/e fisiche e math., vol. 24, pp. 16,131,1885. 

Beiblatter, vol. 10, 1886, p. 387. 

3 Fuess: Zeitschr. fiir lustruraentenk., vol. 5, 1885, p. 274.

* Weinhold: Osterprogramrn der hoh. Gewerbesch. zu Chemnitz, 1873; Pogg. Ann., 

vol. 149, 1873, p. 186.

'Reguault: Eolation des experiences, Paris, 1847, pp. 15, 168.

6 Magnus: Pogg. Ann., vol. 55, 1842, p. 1.

i Amagat: Fortschr. d. Phys., 1869, p. 155 ; C. E., vol. 71, 1870, p. 67 ; C. E., vol. 73, 

1871, p. 183; Archives sci., phys. et flat. Geneve, 2d series, vol.40, 1871, p. 320; Ann. 

ch. ot Phys., 4th series, vol. 29, 1873, p. 246; ibid., 5th series, vol. 22,1881, p. 353, etc.; 

C. R., vol. 94, 1882, p. 847; C. E., vol. 95, 1882, p. 638; C. E., vol. 99, 1884, pp. 1017, 

1153; C.R., vol. 103, 1886, p. 429.

sCailletet: C. R., vol. 70, 1870, p. 1131. 

Bull 54 3

(687)
34 . MEASUREMENT OF HIGH TEMPERATURES.

500 atmospheres and for temperatures below 300°, and in the hands of 

Amagat they led to the discovery of minima of " pv." These researches, 

which must be passed over briefly here, are not as yet in a state of progress to enable the results to be at once applied. It is therefore reassuring to find in the labors of Langer and Meyer1 a number of data tending 

to show that at high temperatures and for moderate pressures the constancy of the co-efficient of expansion of gases may be warrantably 

assumed.

To return from this digression to the subject in hand I find an important research by Erhard and Schertel 2 in which the melting points 

of Prinsep's alloys are again carefully determined by the porcelain air 

thermometer. The bulbs are of Meissen porcelain, and the method of 

measurement is essentially that of Weinhold. Finally, in 1880, Deville and Troost 3 publish a succinct account of their results in high 

temperature measurement, and thus conclude the interval of comparative silence.4 They describe a new form of air thermometer, apparently 

superior to the liegnault normal form. In this instrument the air of the 

bulb is transferred into the measuring apparatus by a Sprengel's pump.

The bulb itself, being placed in a furnace fed by heavy petroleum oil, 

can be heated to any desired temperature by supplying a greater or 

smaller amount-of fuel, through a graduated stop-cock. To eliminate 

the stem error they again use the "compensator," which is a closed 

porcelain capillary tube identical with the stem of the air thermometer 

and exposed side by side with it. This compensator is provided with 

its own mauometric attachment. Nitrogen is used preferably to air.

The last memoir contains a full digest of their results on the boiling 

point of zinc. The methods of experiment and of measurement are also 

tersely given in chronological sequence. The authors put great stress 

on the purity of their zinc, on the fact that no iron was used in the retorts, on the great mass of zinc distilled (17 kg. to 20 kg.), on their 

methods of protecting their bulb from direct radiation by multiple 

screens, and on the great heat of the circumambient flame. The porcelain bulb, its peculiarities, and its construction are described with some 

detail. Their mean value for the boiling point of zinc, as Troost 5 subsequently remarks, is 942°, and the number of measurements made, 27. 

In some experiments made at a later date by Troost 6 the boiling point 

of selenium was found between 664° and 683°, the determination being 

feasible in a vessel of enameled iron. Troost 7 therefore concludes that

1 Langer u. Meyer: Pyrochemische Untersuchungen, 1885.

2 Erhard and Schertel: Jahrbuch filr das Berg-und-Hiitteuwesen, im Konigr. Sachsen, 1879, p. 154.

"Deville et Troost: C. R., vol. 90, 1880, pp. 727,773.

4 Deville: C. R., vol. 74, 1872, p. 145; is speculative, and refers to excessively high 

and to solar temperatures.

6 Troost: C. R., vol. 94,1882, p.788.

6 Troost: Ibid.,p. 1508.

7 Troost: Ibid., vol. 95,1882,p. 30.

(688)
HAKIM.] METHODS OF PYROMETRY. 35

vupor densities in seleuium vapor may safely be made in vessels of refractory glass, and recommends for that purpose the glass of Appert 

freres a Clichy, which is nearly rigid at this temperature. Other relevant results of Troost1 on the permeability of platinum to hydrogen 

and of silver to oxygen at high temperature have been adverted to. 

Berthelot2 points out the occurrence of unstable platinum hydrides. 

The value of the boiling point of zinc, to which the later researches of 

Deville and Troost had given a value compatible with that of Becquerel, was soon to be further fixed in position by the research of Violle.3 

Using a triple jacketed boiling point apparatus of enameled iron, he 

found by Deville and Troost's methods that zinc boils at 930°, thus 

giving further warrant to the data of Becquerel and Deville and 

Troost. In view of the accordance of these data, the problem of high 

temperature measurement may be regarded as solved with some accuracy as far as 1,500°. The greater share of the credit for this result is 

undoubtedly due to Deville .and Troost, notwithstanding their unfortunate beginning and the fact that they allowed the subject to slumber 

in their hands for so many years. Violle refers to the problem of mere 

high temperature measurement as being one of great simplicity, and 

finds his main difficulty in the construction of constant temperature 

apparatus. My experience is the reverse of this. It is not very 

difficult to get the zinc point; but it is difficult to obtain thoroughly 

accordant values for it when different bulbs are used. Violle, who used 

but a single bulb (so far as I have been able to make out), obtains values which are almost identical, but which really apply only to the particular bulb in hand. The error possible in measuring the constants of 

the bulb is one of a very serious kind, and in case of a single bulb it 

remains arbitrarily fixed. The data of Deville and Troost, which were 

obtained by using a large assortment of bulbs, bear evidence to this. 

The differences between their later results are by no means insignificant, and these observers were most scrupulous in perfecting their 

methods, even to the fine points of experimental detail. Becquerel, in 

using divers thermometer bulbs, encountered the same wide limits of 

error. Regarding BecquerePs later and very low values, moreover, it 

is probable that the criticism of Deville and Troost applies. BecquerePs boiling-points apparatus was imperfect. In the case of so large 

an object as the air-thermometer bulb, at so high a temperature as the 

boiling point of zinc, its data can not be regarded as identical with the 

temperature of the vapor unless it be in actual contact with it. Evidence bearing on all these points will be repeated in Chapter IV.

Eegarding Deville and Troost's experiments on the coefficient of expansion of porcelain, a short critical remark relative to the occurrence 

of permanent dilatation is in place here. When a porcelain rod is sus1 Troost: Ibid., vol. 98, 1884,p. 1427.

2 Berthelot: Ann. ch. et phys., 5th series, vol.30,1883, p.530. 

»Violle: C. R.. vol.94,1882, p.720. 

(689)
36 MEASUREMENT OF HIGH TEMPERATURES.

pended at one end and heated to extreme whiteness, it is probable that 

some permanent elongation will occur by virtue of the viscosity of the 

hot rod. The question therefore occurs whether thjs permanent expansion may not to some extent have produced the dilatation due to vitrification which they observed, or have been partially confounded with 

it. Messrs. Deville and Troost were careful to test the specific gravity 

of their heated porcelain, and they found a dirnunition of density, a result in harmony with the dilatation observed. Again, the fact that permanent expansion vanished after successive heating in their experiments is evidence in their favor.

And yet I regard this remark not superfluous, because, in my own 

experiments, in which careful volutnenoinetric tests of the volume of 

the bulb after successive heatings to 1,000° or 1,200° were made, I observed no permanent dilatation of volume. The increments I found 

would rather point to contraction. It does not seem probable, moreover, that porcelain which has been thoroughly fired in the manufacturer's furnace would continue to change in volume for some time after, 

at a temperature at which porcelain is appreciably viscous.

Dilatation of gases (displacement methods). The next important step 

in air thermonietry was made in Germany by V. Meyer and his pupils, 

although an ingenious suggestion, which was probably the main incentive to those researches, is due to the American, Crafts. So far as I 

have read, Eegnault 1 appears to have been the originator of methods 

of air thermometry in which the thermal gas, instead of being measured 

manometrically, is chased out or displaced by a second gas, which can 

subsequently be absorbed or otherwise eliminated. Eegnault's bulb 

is a large cylinder of iron provided with two capillary stems adjusted 

axially, and adapted for the admission and efflux of the gases. He 

bases his measurements on hydrogen, which is chased out, when the 

desired temperature is reached, by oxygen. Oxygen burns the hydrogen, and it is therefore necessary only to absorb and weigh the water 

thus produced. It is obvious that this operation may be repeated as 

often as is desirable.

Schinz (loc. cit.), who repeated these measurements, did not find them 

satisfactorily accurate. Nevertheless, a process which is of inferior 

accuracy below 1,500° may be very serviceable above the temperature 

at which the ordinary methods fail, and porcelain becomes viscous or 

even liquid. This appears to be the case with the displacement method 

as Crafts pointed out.

In 1878 Victor and C. Meyer 2 published an account of a new method 

of determining vapor density. In this the air contained was mechanically lifted or chased out at any given temperature by vapors issuing 

from the substance whose vapor density was to be determined. Inas1 Regnault: Ann. ch. et phys., 3d series, vol. 63, 1861, p. 39.

2 V. Meyer: Beii. Ber., vol. 11, 1878, p. 1867; V. u. C. Meyer- Ibid., 1878, p. 2253; 

Dingler's Jour., vol. 231, 1878, p. 330; vol. 232. 1879, p. 418.

(690)
BAiiLv.1 METHODS OF PYROMETRY. 37

much as all these operations can be carried on under atmospheric 

pressure the apparatus was specially adapted for high temperature 

work. Messrs. Meyer1 , utilizing these advantages, were able to obtain 

definite evidence on the probable dissociation of chlorine and iodine 

vapor. Crafts and Meier2 then pointed out that Meyer's method could 

very readily be adapted for temperature measurement. Optic, calorimetric, and electrical methods of temperature measurement, they contend, are all dependent on the air thermometer, the results of which are 

reliable only in the case of very perfect mechanism, and are not available 

above the temperature at which porcelain is rigid. By inserting a 

capillary platinum tube into the neck of Meyer's apparatus the air can 

be lifted out by a current of carbonic acid .gas or of hydrochloric acid 

gas, both of which are easily absorbed. It is possible to make vapor 

density measurement to alternate with thermal measurements} and 

since the operation may be completed in two minutes, absolute rigidity

of the porcelain vessel is not rigorously essential. Entering into the 

spirit of this suggestion, Meyer3 and his pupils opened a new field of 

pyrochernical research, in which, after establishing the constancy of 

the coefficient of expansion of permanent gases at high temperatures, 

they extend their inquiries further to vapors. Meyer's apparatus here 

X is a hollow sphere of porcelain provided with axial capillary tubes for 

influx and efflux of gas.

Following Meyer's summary, the linear character of the heat expansion of gases at high temperatures (barring dissociation) is to be 

regarded as established for selenium and tellurium (Deville and Troost), 

for nitrogen, oxygen, mercury vapor, and As2 O3 vapor (V. and C. 

Meyer), for hydrochloric acid, and carbonic acid gas (Crafts), and for 

hydrogen (Meyer and Ziiblin). These inferences antagonize the published opinion of Troost,4 who, with Berthelot's acquiescence, prefers to 

regard the expansion of gases at high temperature (iodine for instance) 

as a physical function of temperature rather than to accept the occurrence of dissociation.

Meyer5 and his pupils, however, push their investigations into much 

greater detail, adding to the number of gases of constant thermal c >- 

efficient and interpreting the variable behavior of others. Their new 

researches are carried on at temperatures even as high as 1,700°. Their 

apparatus is a long platinum tube provided with terminal capillary 

stems of platinum which have been ground into the somewhat narrower 

ends of the tube. This thermometric tube is surrounded by fire-cliiy 

which in its turn is enveloped by a second and wider platinum tube.

/ !V. 11. C. Meyer: Berl. Ber., vol. 12, 1879, p. 1426. 

\ 'Crafts and Meier: C. R., vol. 90, 1880, p. 606.

3 Meyer: Berl. Ber., vol. 13, 1880, p. 2019; il^id., vol. 15, 1882, p. 1161. 

4 Troost: C. R,, vol. 91, 1860, p. 54.

6 Lauger u. Meyer: Pyrocheinische Untersuchungen, Braunschweig, Vieweg a. 

Sohn, 1885; Berl. Ber., vol. 18, 1885, p. 1501.

(691)
38 MEASUREMENT OF HIGH TEMPERATURES.

To obtain the high temperatures in question retort carbon is burned in 

an air-blast. The displacement method shows that oxygen, nitrogen, 

sulphurous acid, and even carbonic dioxide are stable at 1,700°. Platinum absorbs much oxygen and must be saturated with it before the thermal measurements are commenced. On the other hand, chlorine, bromine, iodine, carbonic oxide, steam, and even hydrochloric acid are more 

or less dissociated. Following these researches into further consequences, Meyer and his pupils1 determine the vapor density of zinc, proving that all known metallic vapors are monatornic, and they even measure2 the vapor densities of antimony, phosphorus, and arsenic, at 1,437°.

These brilliant researches contain the most advanced work thus far 

done on the subject of high temperatures, and it is upon the validity of 

some of their results, the non-dissociative character of the expansion of 

the permanent gases at high temperatures, that all high temperature 

thermal measurement depends.

Vapor tension. Pyrometers of this kind have received little attention. 

Sajotschewsky3 pointed out that the vapor tensions of different quantities of liquid are identical as far as the absolute boiling point, after 

which the curves diverge. He further studied the temperature and 

pressure relation of twelve liquids in detail, at least as far as the critical 

point. T^he importance of vapor tension thermometers was signalized 

by Sir William Thomson,4 but the remarks refer principally to low 

temperatures. Shaw5 has recently inquired somewhat rigorously into 

such pressure-temperature relations. For moderately high temperatures 

Crafts's6 paper seems to be the only companion research to Sajotschewsky's. Crafts studied the boiling point and vapor tensions of 

mercury, and sulphur vapors, as well as of some carbon compounds 

with his hydrogen gas thermometer.

Dissociation. The difficulty in the way of a successful application of 

vapor tension thermometers, Lamy believed to have been overcome in

his dissociation thermometer. In the suppositive case of marble, lor 

instance, originally placed in a vacuum, the pressure due to the evolution of carbonic dioxide will increase with temperature, and would 

finally revert to the pressure zero when the original temperature is 

again reached. Debray's7 data for the dissociation of calcic carbonate 

and Isambert's8 further researches on the gaseous dissociation of solids, 

suggest a number of materials. Lamy9 incloses these in 'an exhausted

l Mensching u. Meyer: Berl. Ber., vol.19, 1886, p.3295. 

2 MeuscMng u. Meyer: Go.tt. Nachr., 1887, p.258. 

3 Sajotschewsky: Beiblatter, vol. 3, 1879, p. 741. 

 Thomson: Proc. Royal Soo., Edinburgh, vol. 10, 1880, p. 532. 

6 Shaw: Trans. Cambridge Phil. Soc., Eng., vol. 14, 1885, p. 30. 

6 Crafts: Nature, vol. 26, 1882, p. 466. 

7 Debray: C.R.,vol. 64, 1867, p. 603.

8 Isambert: These pre"sente a la Faculte" des sciences tie Paris, 1868. 

9 Lamy: C. R., vol. 69, 1869, p. 347 ; vol. 70,1870, p. 393. Dingler's Jour., vol. 194, 

1869, p. 209 ; vol. 195, 1870, p. 525.

(692)
BARUS.] METHODS OF PYROMETRY. 39

porcelain bulb. Weinhold (loc. cit.) who examined this apparatus condemns it, at least so far as the u pyrometre & marbre" is concerned. It 

appears that the carbon dioxide emitted is not again absorbed with 

sufficient regularity to subserve the purpose of thermal measurement. 

Perhaps Troost's1 diffusion method for studying high temperature dissociation is to be added to this paragraph.

Fusion. These pyrometers are discontinuous as well as intrinsic. 

Nevertheless, in virtue of their simplicity they are among the most serviceable of all the forms of pyrometers devised. As long ago as 1828, Prinsep,2 .using an air-therinometor bulb of gold, endeavored to measure the 

melting points of silver-gold, silver-platinum, and gold-platinum alloys. 

The brothers Appolt3 investigated similar data for copper-tin alloys, 

using a calorimetric thermometer for high temperature measurement. 

A special double crucible for fusion of silver-platinum alloys is given by 

Heeren.4 Temperatures estimated by alloy fusion were largely made use

of by Plattner. Becquerel,5 in his extended paper on the measurement 

of high temperatures, gave considerable attention to melting points. 

He used metallic wires and measured the fusing temperature with his 

calibrated thermo-couple. After him, Eiemsdyk6 made a series of measurements on metallic melting points. A very ingenious series of ringp» shaped cups, placed on a common axis in a tier, was suggested by 

Heeren.7 These cups contain rings of alloy, the consecutively varying 

melting points of which are stamped on the bottom of the cups. After 

each observation the rings are simply turned. Carnelley8 made use of 

fusion pyrometers, substances of known melting points being inclosed 

in capillary tubes to serve for the identification of similarly exposed 

substances of unknown melting point. Kesults on the melting points 

of platinum alloys are due to Roberts.9 A more elaborate series of researches is due to Yiolle,10 whose data for high melting points are presumably the best in hand. Violle makes a careful study of the relation 

between specific heat and temperature. Assuming this relation to hold 

as far as the melting point in each case, he fixes this point for silver 

(954°), gold (1,035°), copper (1,054°), palladium (1,500°), platinum 

(1,775°), and iridium (1,950°), calorimetrically. For metals which melt 

below the platinum point, either the metal itself or platinum may be

1 Troost: C. R., vol. 89, 1879, p. 306.

2 Priusep: Trans. Royal Soc., London, 1827; Ann. ch. et phys., 2d aeries, vol. 41, 

1829, p. 247; Pogg. Ann., vol. 13, 1828, p. 576; vol. 14, 1828, p. 529. 

3 Mitth. des Gewerbe Vereins fur Hanover, 1855, p. 345. 

4 Heeren: Dingler's Jour., vol. 161, 1861, p. 105. 

6 Becquerel: Ann. ch. et phys., 3d. series, vol. 68, 1863, p. 49. 

"Riemsdyk: Jahresber. d. Chem., 1869, p. 993; Chem. News, London, vol. 20, 1869, 

\ p. 32.

T Heeren: Zeitschr. des Vereins d. Ingenieure, 1876, p. 314. 

8 Carnelley: Jour. Chem. Soc., London, vol. 33. 1878, p. 281. 

9 Roberts: Ann. ch. et phys., 5th series, vol. 13, 1878, p. 111. 

10 Violle: C. R., vol. 85, 1877, p. 543; vol. 87, 1878, p. 981: vol. 89,1879, p. 702,

(693)
40 MEASUREMENT OP HIGH TEMPERATURES.

made the basis of measurement. Both methods give the same result. 

The thermal comparisons are based on the porcelain air-thermometer 

of Deville and Troost. Furthermore, Erbard and Schertel 1 at about 

this time made elaborate re-determinations of the melting poiuts of very 

pure Prinsep's and other precious alloys, by simultaneously exposing 

these alloys and a porcelain air-thermometer in a large muffle. Having 

obtained a series of silver-gold and gold-platinum alloys, melting between 984° and 1,408°, they apply these data practically, determining 

by means of them a table of melting points of known silicates (1,208° 

to 1,444°). Conechy,2 at the suggestion of Carnelley, used fusing points 

to find the temperature at which arsenic volatilizes. Silicious mixtures 

of gradually increasing fusing points have been investigated by Seger, 

in Germany, and his tables are printed in full by Lauth,3 who also gives 

some attention to alloy fusions. Seger's mixtures are made of feldspar, 

chalk, and kaolin, substances easily obtained, and they fuse between 

1,100° and 1,700°. Finally, the data of Le Ghatelier 4 must be mentioned, 

by whom fusing points, as well as temperatures of chemical decomposition, have been measured. Tables of melting points are published 

in great fullness by Carnelley.5 Excellent and serviceable tables of this 

kind are also to be found in Landolt and Boernstein's 6 Physikalischchemische Tabellen.

Specific lieat. The measurements of temperature calorimetrically 

dates as far back as Guyton-Morveau,7 in whose pyrometric researches 

it is definitely proposed. Schwarz 8 used both iron and water as well 

as platinum and mercury. Coulomb,9 in studying the relation between 

hardness and permanent magnetization, determined the temperatures 

before quenching or annealing, by submerging the rods in water under 

known conditions. Clement and Desormes 10 use iron and water for technological temperature measurement, as was proposed also by others.11 

In general, however, neither is any attention given to the variation 

of specific heat and temperature, nor is allowance made for errors 

by radiation.

I Erliard u. Schertel: Jahrbuch fur das Berg u. Hiitten-wesen im Konigr. Sachsen, 

1879, p. 154.

* Conechy: Chem. News, London, vol. 41, 1880, p. 189.

3 Luuth: Bull. Soc. chiru., Paris, vol. 46, 1886, p. 786.

4 Le Chatelier: Ibid., vol.47, 1887, p. 300.

s Thomas Carnelley: Melting and boiling point tables; London, Harrison & Sous, 

two vols., 1885.

6 Landolt u. Bornstein: Physikalisch-ohemische Tabellen, Berlin, Julius Springer, 

1883.

7 Guyton-Morveau: Ann. ch. et phys., vol. 46,1803, p. 276; vol. 73,1810, p. 254; vol. 

74,1810, pp. 18, 129; vol. 90, 1814, pp. 113,225. '

8 Schwarz: Bull. Soc. Mulhause, 1827, p. 22; Pogg. Ann., vol. 14, 1828, p.530.

9 Coulomb: Pogg. Ann., vol. 14, 1828, p. 530.

10 Clement and Desormes: Dingler's Jour., vol. 33,1829, p. 145.

II Anonymous: Pogg. Ann. 2d series vol. 39,1836,' p. 518.

(694)
BARUS.] METHODS OF PYROMETRY. .. 41

At this point Pouillet 1 took up these researches. He measured the 

^ specific heat of platinum between 0° and 1,200°, by direct comparisons 

with his platinum air-thermometer. The data found were so nearly 

constant as to give the calorimetric method of temperature measurement considerable importance. After a scientific basis had thus been 

'given, the method was soon practically developed and many special 

forms of application were devised. Miller 2 describes an apparatus in 

which iron or platinum is quenched in mercury. This apparatus is 

discussed by Schubarth.3 In an apparatus due to Wilson,4 platinum or 

even clay is cooled in water. Schinz5 recommends platinum and water. 

Siemens's6 data are based on calorimetric measurements with copper and 

water. Bystrom7 describes a platinum water pyrometer. Weinhold,8 

who reinvestigated the specific heat of platinum at high temperatures, 

found an anomalous behavior, while that ot iron was quite regular. 

From these results for iron Schueider9 calculated an extensive table. 

In view of the known anomalous behavior of iron at red heat, the 

regular variation of its specific heat, as compared with that of platinum, 

is certainly very remarkable, and quite at variance with more recent 

results of Piouchou (see below). Sallerou's10 pyrometer makes use of 

copper cooled in water. Special attention is to be given to Carnelley 

v and Williams's11 calorimetric work, in view of the many valuable data 

which these observers deduce by means .of it. In their experiment a 

platinum, vessel of special form is heated to the unknown temperature 

and then quenched in water, ^ischer's12 calorimeter again is adapted 

to furnace uses cooling in water. Hobson13 and, more thoroughly, 

Bradbury, 14 endeavored to apply a new method of calorimetric pyrometry. They cool the hot air of the blast with a known amount of cold air 

and measure the resulting temperature.

Thereupon Violle 15 began to publish the researches to which reference has already been made. By investigating formulated relations

1 Pouillet: C. R., vol. 3,1836, p. 782.

2 Miller: New Philos. Jour. Edinburgh, vol. 44,1848, p. 126; Dingler's Jour., vol. 108, 

1848; p.115.

3 Schubarth : Dingler's Jour., vol. 110,1848, p. 32.

4 Wilson: Philos.Mag.,London, 4th series, vol.4, 1852, p. 157; Dingler's Jour., vol. 

158, 1860, p. 108.

6 Schinz: Wiirme-messkunst, 1858, p. 53. 

6 Siemens: Dingler's Jour., vol.217, 1875, p.291.

'Bystrom: Mechanics'Jour., 2d series, vol. 8, 1862, p. 15; Fortschritte d. physik, 

1862, p. 344; ibid., 1863, p. 355. 

"Wei ahold: Pogg. Ann., vol.149, 1873, p. 186. 

9 Schneider: Zeitscbr. des Vereins Deutscher Ingen., 1875, p. 16. 

10 Sallerou: Sci.' Am., 1875, p. 50.

/ u Carnelley and Williams: Jour. Chem. Soc. London, vol. 1, 1876, p. 489. 

' 12 Fischer: Dingler's Jour., vol. 225, 1877, p. 467. 

"Hobson: Ibid., vol.222, 1876, p.46. 

"Bradbury: Ibid., vol. 223, 1877, p. 620.

15 Violle: C. R., vol. 85, 1877, p. 543$ Philos. Mag. Loud., 5th series, vol. 4, 1877, p. 

318; C. R., vol. 87, 1878, p. 981; Ibid., vol. 89, 1879, p. 702.

(695)
42 MEASUREMENT OF HIGH TEMPERATURES.

between specific heat and temperature almost as far as 2,000°, he made 

silver, gold, copper, palladium, platinum, and perhaps iridinm, available for thermal measurement. V. Meyer1 before adopting Craft's suggestion had measured his'temperatures calorimetrically. In America, 

practical calorimetric temperature measurement was studied with much 

success by Hoadley,2 who describes an apparatus and the precautions 

to be observed. Like Violle, he endeavors to arrive at the melting 

point of platinum, and finds a small value of about 1,600 C. Mr. 

Hoadley, however, questions the purity of his platinum. An elaborate 

research published by Bhrhardt3 proposes to find the specific heat of 

iodides, bromides, and chlorides throughout large ranges of temperature. Ehrhardt measures his temperatures with the porcelain air-thermometer and carries his investigations as far as 600°.

Finally, I desire to advert to an important research by Pionchon.4 

This observer makes a special study of the specific heat of iron between 

0° and 1,000°, and finds a regular cubical formula to obtain between 0° 

and 655°. Between 660° and 723° the increase is much more rapid, 

and between 723° and 1,000° the relation is nearly linear. This interesting result adds a new anomaly to the behavior of iron at red heat, for 

in the last mentioned interval (723°-l,000°) the specific heat of iron 

is nearly double that which holds for the first interval.

Ebullition. Eeference to high temperature boiling points has already 

been made in the sections on air thermometry. Full data are given in 

the tables of Carnelley and of Landolt u. Bcernstein, just mentioned. In 

this place I desire to call attention to the data of Crafts,5 in which, by 

using napthaline and benzophenol, temperatures of ebullition between 

140° and 350° are obtainable by the mere variation of pressure from 

8.7cm to 230cm.

Heat conduction.-^-A simple device for a thermostat is made by 

Jourdes6 who inserts a bar of metal into the furnace and measures the 

temperatures at points cold enough for the mercury thermometer. Heat 

is conveyed along the bar by conduction, and there are cavities to receive the thermometers. A somewhat different attempt of this kind is 

due to Main,7 who surrounds a mercury thermometer bulb with asbestos and exposes it for stated lengths of time. Very elaborate attempts 

to determine the temperature on the inner surface of a furnace wall, by 

measuring the temperature of the outer surface under known conditions 

of conductivity, were published by Schinz.8 Following a method origiiMeyer: Berl. Ber., vol. 12, 1879, p. 1426.

2 Hoadley: Jour. Franklin lust., 3d series,vol. 84, 1882.

3 Ehrhardt: Wied. Ann., vol. 24, 1885, p. 215.

"Pionchon: C. R., vol. 102, 1886, p. 1454.

5 Crafts: Nature, vol. 26, 1882, p. 466.

6 Jourdes: C. R., vol. 51, 1860, p. 68; Dingler's Jour., vol. 157, 1860, p. 151.

7 Main : Ibid., vol 221, 1876, p. 117.

8 Schinz: Dingler's Jour., vol. 163.1862, p. 321; ibid, vol. 177,1865, p. 85.

(696)
BARUB.] METHODS OF PYROMETRY. 43

nally devised by Peclet,1 Schinz first made a number of measurements 

of the heat conductivity of the material composing the furnace walls, 

devising special apparatus for that purpose. Having duly tested the 

method, however, he abandoned it because of the irregularity of the 

conduction phenomenon within the walls and because of its want of 

sensitiveness as compared with electric methods.

All the above methods have failed in practice. On the other hand, 

the circulating water-pyrometer due to Bpulier2 and others, in which 

the heat passing by conduction into the explorer or measuring part 

of the instrument is carried off by a current of water flowing between 

known levels, seems to be gaining in favor. The thermal estimate is 

made by measuring the temperature of the water before entering and 

after leaving the furnace. The indications are, of course, wholly empiric. In Boulier's compact and ingenious apparatus the explorer is a 

cylindrical box, with internal cylindrical partitions so adjusted as to 

secure a flow of water in cylindrical sheets. Water enters the Outer 

compartment and leaves the inner, thus avoiding loss by radiation. 

According to Brown (loc. cit.) these apparatus, which are used with great 

success in connection with porcelain furnaces (Lauth), are due to Saintignon. Carnelley prefers a spiral explorer.

Radiation. I have mentioned that the first temperature scale proposed was that of Newton3 (1701) derived immediately from his law of 

cooling. A piece of red hot iron was experimented upon. Long after 

this M'Sweeney4 proposed to catch the heat radiated from a furnace by 

a concave mirror, at the focus of which he placed a thermometer. Following close upon Govi's5 photometric comparison of spectra, Becquerel6 

published his large memoir on high temperature pyrometry. Using the 

red copper glass, he investigates an exponential relation in which the 

photometric intensity of red light is expressed in terms of the temperature of the source of radiation. Green and blue glasses were also used. 

In addition to many results which must be omitted here, Becquerel 

proves that although all bodies have not the same power of radiation, 

truly opaque bodies like platinum, lime, magnesia, carbon, differ but 

little in this respect as far as the melting point of platinum. Oxdizable substances like iron and copper are not superficially opaque when 

covered by layers of oxide. Exterpolating by aid of his equation Becquerel finally concludes the 2,100° is probably the highest temperature 

electrically obtainable. The identity of emissive power accepted for

1 Peclet: Trait6 element, de Physique, 4th ed., vol. 1,1847, p. 418.

2 C. F. Amagat: C. R., vol. 97,1883, p. 1053 ; Lauth: Bull. Soc.ehimique Paris, n. s., 

vol. 40,1883, p. 108; Carnelley: Jour. Cheni. Soc.London, vol. 45, 1884, p. 237; Lauth: 

Bull. Soc. chimique, Paris, vol. 46,1866, p. 786, and others.

"Newton: Scala graduutn caloris; Philos. Trails., vol. 22, 1701, p. 824.

4 M'Sweeny: Pogg. Ann., vol. 14, 1828, p. 531.

«Govi: C. R., vol. 00, 1860, p*. 156.

6 Becquerel: C.XR., vol. 55, 1862, p. 826; Ann. ch. et phys., 3d series, vol. 68, 1863, 

p. 49. Also Draper: Fundamental researches, Philos. Mag., vol. 30, 1847, p. 845.

(697)
44 MEASUREMENT OF HIGH TEMPERATURES.

opaque bodies by Becquerel,1 involved him in a dispute with dela Provostaye 3 in which, however, the position of the former was not seriously 

impugned.

Decharme, repeating Pouillet's experiments, concludes that the intensity of the glow of metals, particularly of platinum, is largely dependent 

on the thickness of the wire. After this Crova 3 undertook a long series 

of experiments, in the course of which he made the subject of radiation 

pyrometry 4 practically his own. The law of emission being known, 

temperature may at once be measured spectro-photometrically. Crova 

in some of his experiments obtains his radiation directly from the bulb 

of a porcelain air thermometer. His results confirm Becquerel's datum 

that the emissive power of absolutely opaque bodies is the same. A 

series of experiments on radiation and temperature was published by 

Nichols,5 who also uses his own results for a critical discussion of the 

work of Crova (1. c.) and of the indications of the radiation pyrometer 

in general. In the same year Stefan 6 published'his law of radiation, 

according to which the amount of heat emitted by a hot body in vacuo 

increases as the fourth power of its absolute temperature. Yiolle,7 

using Gray's and Trannin's photometer, determined the photometric 

intensity of light emitted' by glowing platinum at different temperatures, results which he endeavors to formulate. Similar experiments 

he subsequently makes for silver nearly at its melting point. An experiment with reference to temperature and incandescence was published by Bezold.8 To put the law proposed by Stefan (1. c.) to a practical test, Schneebeli 9 commenced a series of experiments in which thermal measurements between 400° and 1,200° were made by a porcelain 

air thermometer of Schneebeli's 10 own construction. Eadiation measurements are made by a crude bolometer n of tiu foil, the instrument which 

Langley l2 has carried to a remarkable degree of perfection. Schnee1 Becquerel: C. R., vol. 57,1863, p. 681; Auualeschimie, 4th series, vol. 1,1864, p. 120.

s De la Provostaye: C. R. vol. 57, 1863, p. 637; Ibid., p. 1022. The older papers of 

de la Provostaye et Dessains; see Ann. de ch. et phys., 3d series, vol. 12,1844, p. 129; 

Ibid., vol. 16, 1846, p. 337; ibid., vol. 22, 1848, p. 358; also de la Provostaye: Ibid., 

vol. 67, 1863, p. 1. Dulong and Petit's older radiation Avork is given in Ann. ch., 2d 

series, vol. 7, 1817, pp. 113, 225.

3 Crova: C. R., vol. 87,1878, pp. 322,979 ; C. R., vol. 90, 1880, p. 252 ; Ann. chim. et 

phys., 5th series, vol. 19, 1880, p. 472 ; Jour, de phys., vol. 8, 1879, p. 196.

4 Regarding spectrophometric work upon which measurement like the present 

largely depends, see Govi: C.R., vol. 50, 1860, p.. 156; Trannin, Jour, de phys., 

Paris, vol. 5, 1876, p. 297; Vierordt: Pogg. Ann., vol. 1, 37, 1869, p. 200; Glan: Wied. 

Ann., vol. 1,1877, p. 351.

5 Nichols: Ani. Jour. Sci., 3d series, vol. 18, 1879, p. 446; ibid., vol.. 19, 1880, p. 42.

e Stefan : Wien. Ber., vol. 79, 2d series, 1879, p. 391.

7 Violle: C. R., vol. 92, 1881, p. 866,1204 ; C. R., vol. 96, 1883, p. 1033.

8 Bezold: Wied. Ann., vol. 21, 1884, p. 175.

oSchneebeli: Wied. Ann., vol. 22, 1884, p. 430.

10 Schneebeli: Arch, sci., pbys. etnat., Geneva, vol.8, 1882, p.244.

"Svanberg: Pogg. Ann., vol.84, 1851, p. 411. 

12 Langley: Am. Jour., 3d ser., vol. 21, 1631. p. 187.

(698)
BARUB.] METHODS OF PYROMETRY. 45

beli finds that the law of Stefan very closely interprets his experiments. In a series of beautiful experiments Schleiermacher J puts the 

same law to a rigorous test. He heats a platinum wire to incandescence in an inclosure, the walls of which can be heated to different 

constant temperatures (0° to 200°), and from which all air has been 

carefully exhausted. The actual temperature of the wire is calculated 

from its resistance, a series of subsidiary researches in which the wire 

is compared with the porcelain air thermometer having previously been 

made. The amount of heat generated in the wire following from Joule's 

law, Schleiermacher has the data necessary to test Stefan's law. In 

this way he proves that the heat emitted from platinum, covered or not 

with copper oxide, increases with temperature in greater rate than 

Stefan's law predicts. Schleiermacher then interprets the discrepancies observed. 

At the close of the present paragraph a few references to the use of

the radiation pyrometer for evaluating solar temperature and others 

of great intensity is in place. Passing over the earlier measurements 

we find a paper of Soret, 2 and at about the same time one by Violle.3 

The latter's memoir is particularly complete, containing the history 

of the subject and a discussion of methods and apparatus. Making 

his observations on Mount Blanc, Violle finds 2,500° for the surface temperature of the sun. After this, observations on the temperature of 

flames, of the electric arc, and of the sun, were published by Eossetti.4 

Using a thermo-couple, he investigates a law of radiation as far as 

the boiling point of mercury, which law he carefully formulates. With 

due allowance for atmospheric absorption, Eossetti finds 9,965°. as the 

sun's surface temperature. The process is, of course, one of extrapolation. The same method applied to the temperature of the electric arc; 

gives 2,500° and 3,900° as the temperatures of the negative and positive poles respectively. A further important contribution to solar surface temperatures is due to Crova.5

Other optic methods of pyronietry6 endeavor to establish the relations between temperature and the character of the spectrum. Dewar 

and Gladstone7 attempted and finally abandoned a project of this kind. 

On the other hand, however, Stas8 refers with some enthusiam to the

'Rclileiermacher: Wied. Ann., vol.26, 1885, p.287.

2 Soret: Ann. do 1'tScole norm. sup<5r., 3d.series, vol. 3, 1874, p. 435.

3 Violle: Ann. ch. et phys., Paris, vol. 10, 1877, p. 289.

4 Rossetti: Ann. ch. et phys., vol. 17, p. 177,1879 ; C. R., vol. 89, 1879, pp. 384, 781;' 

Philos. Mag., London, 5th series, vol. 8, 1879, p. 324.

sCrova: C. R., vol. 95, 1882, p. 1271.

6 Prof. Cleveland Abbe has called my attention to a paper in the Comptes Rendus, 

in which the continuous change of rotation of the plane of polarization of quartz, 

with temperature, is made the basis of thermal measurement. Unfortunately I can 

not now supply the reference.

7 Dewar and Gladstone : Chemical News, vol. 28, 1873, p. 174.

8 Stas: Boll. Acad. Roy. Belgique, 3d series, vol. 7, 1884, p. 290.

(G99)
46 MEASUREMENT OF HIGH TEMPERATURES.

research of Fievez, 1 in which the attempt to associate the wave-length - 

character of the spectrum with the temperature of the source has again 

been made. Recently a number of German physicists have undertaken 

a re-interpretation of Draper's law. I have only space to allude to 

the papers of H. F. Weber,2 Stenger,3 and Kovesligethy,4 by whom the 

questions relating to emission and absorption of light are being vigorously discussed. In America a series of well-known researches have 

been published by Laugley.5 Having perfected the bolometer, and 

thus developed a new method for the measurement of radiant heat and 

light, Laugley, in a series of researches which are still in progress, has 

determined the distribution of energy in prismatic solar spectra and in 

the spectrum of the grating. Proceeding thence to artificially incandescent bodies, Langley is actively engaged in mapping out the character of their spectra for all temperature 0° to 2,000° of the source.

Less adapted for accurate measurement are certain pyrognomic substances6 , which discolor with temperature, such as the iodides of copper 

and mercury, for instance. To this class belong the oxide coats 7 which 

form on iron and copper. The tints, however, depend not only on the 

temperature but very materially on the time of exposure.8

Viscosity. Very little use has been made of the viscous qualities 

of a substance for temperature measurement Sir William Thomson.9 ^ 

indeed, proposed a tihermoscope based on the change of viscosity of 

liquids, more especially of water with temperature; but it is intended 

for low temperatures, and does not seem ever to have been used.

In my own work I have found that kaolins d/nd fire clays could be 

classified by noting the amount of sag at a gi\en temperature and for 

a given time, which rods of the same form and dimensions experienced 

when spanning the distance between supports at a given length apart. 

The criterion here is flexural viscosity. Such a process would lend 

itself for temperature measurement conducted in a way similar to the

fusion experiments in the case of alloys. It seems curious, however, 

that no attempt has yet been made to base pyrometric measurements 

on the viscosity of gases. Following Maxwell's 10 well-known investigation, the viscosity of gases is independent of the pressure and dependent only on the absolute temperature. From a theoretic point of 

view, therefore, such pyrometers have almost as much in their favor as

1 Fievez: Bull. Acad. Roy. Belgique, 3d series, vol. 7, 1884, p. 348. 

2 H. F. Weber: Wied. Ann., vol. 32, Ib87, p. 256. 

3 Stenger: Ibid., 1887, p. 271. 

4 Kovesligethy: Wied. Ann., vol. 32, 1887, p. 699. 

s Langley: Arn. Jouru. Sci., 3d series, vol. 25, 1883, p. 169.

6 Hess: Dingl. Jour., vol. 218, 1875, p. 183. \ 

7 Fischer: Dingler's Jour., vol. 225, 1877, p. 278. 

»Barus & Strouhal: Bull. U. S. Geol. Survey, No. 18. 

"Thomson: Proc. Royal Soc., Edinburgh, vol. 10, 1880, p. 537. 

10 Maxwell: Philos. Mag., London, 4r,h seriet;, vol. 19, 1860, p, 11); ibid., vol.32,1866, 

p. 390; ibid., vol. 35, 1868, pp. 129, 185; Philos. Traus., vol. 1, 1866, p. 249.

(700)
BARUS.] METHODS OF PYROMETRY. 47

the air thermometer itself. The form of apparatus most easily used 

experimentally, viz, the platinum transpiration tube, is based on principles not quite as direct as Maxwell's law. Nevertheless Meyer 1 has 

succeeded in interpreting Graham's2 data, has discussed his experimental methods, and has more recently shown that both Graham's and 

Coulomb's vibration methods lead to the same results. Work of this 

kind *has also occupied Stefan.3 In Meyer's deduction the volume of 

gas transpiring per unit of time under given conditions, besides depending on the pressures, the internal friction, the length of tube, 

involves an expression containing the fourth power of the radius 

of the capillary tube and the ratio of internal to external, gaseous 

friction coefficiented by the third power of radius. Hence .in such a 

pyrometer the coefficient of heat expansion of platinum must be somewhat carefully predetermined. According to Nichols (1. c.) this is by

no means seriously difficult, Supposing a capillary platinum spiral to

terminate in two larger platinum tubes (of which owe may wholly envelop the other), we have given at once the effective part of the mechanism of a thermometer based on the viscosity of gases. Such a thermometer may be used as far as the melting point of platinum. For 

temperatures beyond this, porous fire-clay plugs in an impervious tube 

suggest themselves.

Acoustics. The next year after Pouillet's fundamental research on 

pyrometry, his brilliant and ingenious countryman, Cagniard-Latour,4 

acting in concert with Demonferrand, proposed an acoustic air thermometer. Inasmuch as the velocity of sound in dry air is proportional 

to the square root of the absolute temperature, Latour and Demonferrand easily wrought out a formula in which temperature is expressed 

in terms of the vibrations of the fundamental note of their apparatus at 

the high temperatures and at normal temperatures. They estimate that 

the error of a comma would not exceed 30° at 1,000°. This apparatus 

was afterwards reinvented by Mayer,5 who discusses its principle exhaustively. Mayer calculates tables for temperature, velocity of sound 

and wave length, between 300° and +2,000°, and suggests many 

devices of measurement. After Mayer the same principle was emphasized by Chautard,6 who simplified the apparatus necessary, but he 

expresses some doubt as to, its efficiency.

1 O. E. Meyer: Pogg. Ann., vol. 127, 1866, pp. 253, 353 ; ibid., vol. 125,1865, pp. 177, 

401; ibid., vol. 143, 1871, p. 14; Wied. Aim., vol. 32, 1887, p. 642; cf. Konig, ibid., p. 

193.

3 Graham's original researches. See Philos. Trans., London, 1846, p. 573; 1849, 

pt. 2, p. 349. The suggestion of using platinum capillary tubes at high, temperatures 

is my own.

3 Stefan: Wien. Ber., vol. 46, 1862, p. 495.

* Cagniard-Latour et Dernonferraud: C. R., vol. 4, 1837, p. 28.

6 Mayer: Pogg. Ann., vol. 148, 1873, p. 287.

e Chautard: C. R., vol. 78, 1874, p. 128; Pogg. Ann., vol. 153, 1874, p. 158.

(701)
48 MEASUREMENT OF HIGH TEMPERATURES.

Thermo-electrics. The use of the thermo-couple for high temperature 

pyrometry was suggested and carried to a high state of perfection iu 

the great research of Pouillet.1 He used iron and platinum for his 

couple. Subsequent observers suggested a wide range of substances for 

the purpose, and improved the methods of electrical measurement and 

thermal comparison, the best of them, however, following very closely 

in the footsteps of Pouilletfs research. Solly 2 proposed an iron-copper 

couple, without, however, attempting to calibrate it. Eegnault 3 tested 

an iron-platinum element but failed to obtain satisfactory results. Tins 

unfavorable dictum of the great experimentalist is much to be regretted, 

for it was probably the main reason which threw the subject of thermoelectric pyrometry into undeserved disrepute. Fortunately Becquerel4 

resuscitated the method, and in his hands it led to the new results cited 

above. Becquerel's elements were of platinum and palladium, of two 

different kinds of platinum, and of platinum and iron, among which he 

preferred the former. After Becquerel, Schinz 5 began thermo-electric pyrometry with great vigor and success, and it is indeed curious 

that Schinz's work is so little known. His iron air thermometer, 

adapted specially for calibration work, has been already described. 

Its chief merit is this, that an iron tube closed within, projects from the 

base of the cylindrical bulb into the interior. This tube, being co-axial 

with the stem of the bulb and the bulb itself, serves for the introduction of the thermo-couple, the junction of which may thus be exposed 

at the center of figure of the bulb. The re-entrant form of bulb, to which 

I myself was led in my experiments quite independently of the almost 

unknown paper of Schinz, I regard essential to accurate and expeditious 

calibration work. Deville and Troost 6 condemned bulbs of any other 

than spherical form, though, it seems to me, quite unjustly and without 

sufficient evidence against them. In thermo-electric comparisons the 

cbief end in view is to secure identical conditions of exposure for the

junction of the couple and the bulb of the thermometer; for the errors 

which result if this identity does not obtain, are apt to be much more 

serious than such as are due to small irregularities of contraction of the 

bulb. It does not seem proven, moreover, that a bulb will not contract 

regularly if its form is not spherical. Schinz's bulb is a large iron box, 

with which fine measurements can not possibly be made. The apparatus, moreover, is not at all adapted to the comparison of results obtained with different bulbs, a step which I regard as essential. My bulbs 

are of porcelain; they may be easily handled and exchanged one for another, and the whole method of exposure is such as to secure as much

iPouillet: C. R., vol. 3, 1836, p. 782; Dingler's Jour., vol. 63, 1837, p. 221. 

2 Solly: Philos. Mag., London, 3d series, vol. 19, 1841, p. 391. 

3 Reguault: Relation des Experiences, vol. 1, Paris, 1847, p. 246 (1845). 

4 Becquerel: Ann. ch. et phys., 3d series, vol. 68, 1863, p. 49. 

6 Schinz: Dingler's Jour., vol. 175, 1865, p. 87; Ibid., vol. 179, 1866, p. 436. 

6 Deville et Troost: C. R., vol. 57, 1863, p. 897.

(702)
BAKUS.] METHODS OF PYROMETRY. 49

facility of manipulation as is compatible with the character of the experiment. My object has been to place the calibration problem within 

the reach of the laboratory not specially equipped for high temperature 

work, and though I have worked independently, I am glad to defer the 

priority of principle to Schinz. In addition to his air thermometer 

Schiuz invented a torsion galvanometer on the principle of Coulomb's 

torsion balance, for the measurement of thermo currents. This instrument also does credit to his experimental sagacity. His couple is 

iron-platinum, having failed to obtain reliable data with Becquerel's 

platinum-palladium couple. Schinz does not give any absolute data, 

and it is easily seen that the absolute value of results with his bulb 

could not lay claim to accuracy. He fails, for instance, to discern the 

iron anomalies of which Tait1 subsequently made considerable study. 

Tait's memoir is well known. Following the suggestion of Thomson,2

Tait makes an elaborate survey of the diagram by which the thermoelectrics of metals generally are to be expressed. For the measurement of temperature Tait uses a, thermo-couple of platinum and platinum -iridium alloy, and, so far as I have been able to find, his researches 

are the first in which the pyrometric use of the platinum iridium alloy 

is recorded. I may add here that special attention to the platinumiridium alloys seems first to have been given by Deville and Debray,3 

to whom we owe so much of the metallurgy of the platinum group.

A special study of the thermo-electrics of platinum-indium and other 

alloys is due to Kuott and MacGregor.4 Diagrams are investigated for 

these alloys, applying between 45° and 400°, and for compositions as 

high as 20 per cent, of indium. They also study silver-palladium, irongold, and platinum-silver alloys with the same ends in view. In a 

late research Kuott, MacGregor, and Smith5 determine the thermoelectrics of cobalt. Having studied the platinum-iridium alloy calorirnetrically, Le Chatelier6 suggests the occurrence of an allotropic modification of the alloy above red heat, the behavior being the same as that 

shown by iron at about 700°, and between the melting points of silver 

and gold. Furthermore, with the object of checking the formulae of 

Avenarius7 and Tait,8 Le Chatelier9 avails himself of the fusing points 

of Violle. It appears that these formula apply up to a certain temperature, above which ( u brusquement") a second formula with new constants 

is applicable. Platinum, platinum alloys of iridium, copper and rho1 Tait: Trans. Royal Soc. Edinburgh, vol. 27, 1872-'73, p. 125. 

2 Thomson: Philos. Trans., London, vol. 146, 1856, p. 649.

3 Deville et Debray: C. R., vol. 81,1875, p. 839; Cf. Ann. ch. et phys., 3d series, vol. 

56, 1859, pp. 431 (iridium), 415 (rhodium).

"Kuott and MacGregor: Trans. Royal Soc. Edinburgh, vol. 28, 1876-'77, p. 321. 

5 K., M., and S.: Proc. Royal Soc. Edinburgh, vol. 9, 1876-77, p. 421. 

6 Le Chatelier: Bull. Soc. chimique, Paris, vol. 45, 1886, p. 482. 

7 Avenarius: Pogg. Ann., vol. 119, 1863, p. 406; Ibid., vol. 149, 1873, p. 372. 

8 Tait: Trans. Royal Soc. Edinburgh, vol. 27, 1872~'73, p. 125. 

9 Le Chatelier: C. R., vol. 102, 1886, p. 819.

Bull. 54 4 (703)
50 MEASUREMENT OF HIGH TEMPERATURES.

dium, ami palladium are tested, and he finds that high temperature 

measurements thermo electrically made can be relied upon to 20°. "II 

reunite de mes recherches," adds he, " que la loi d'Aveuarius et Tait 

continue a se verifier au-dessus de 400° avec une approximation 6gale 

a celle qu'elle comporte au-dessous, jusq'a une certaine temperature 

limite, variable avec la nature des couples considers." The superiority of the platinum-rhodium couple1 of Le Chatelier's (which is his special 

contribution to thermo-electric pyroraetry) over the iron platinum or 

platin-palladium couples is due to greater homogeneity of the former, 

and the fusing point calibration may be considered accurate within 5° 

C. In a very full paper recently published, Le Chatelier2 shows that 

the condemnation which was inflicted on Pouillet and Becquerel's 

methods was thoroughly unjust. Believing the fusing and boiling 

point method of calibration to be superior to direct comparison with the 

air thermometer, he selects the series, H2O (100°), Pb (323°), Hg (358°), 

Zn (415°), S (448°), ge (665°) Ag (945°), Au (1045°), Ou (1054°), Pd 

(1500°), Pt (1775°), most of which values are due to Violle (1. c.). 

Having, moreover, given attention to the errors due to homogeneity Le 

Chatelier concludes with Becquerel,3 an dm any others4 before him, that 

to make the Avenarius-Tait formula sufficiently applicable it is necessary either to add a cubical term or else to use two laws, one for low and 

the other for high temperatures. In a final memoir Le Chatelier5 invents 

an ingenious method for fusing point measurement, and compares his 

results with those of Carnelley (1. c.). The table given contains data for 

alkaline and metallic chlorides, cast-irons, nickle, etc., and the paper 

ends with an investigation of the temperature of chemical phenomena 

in which heat is absorbed or disengaged, or in which the substances 

undergo transformation. . 

Finally, I desire to add that the thermo-electric effect of changes of

physical state and of molecular changes in general, has not been left

unnoticed. Oberrnayer's6 experiments largely refer to alloys which 

melt at comparatively low temperatures. Tidblom7 investigates an 

amplified form of the thermo-electric equation, in which changes of the 

kind in question may be allowed for.

Electrical conductivity. The measurement of temperature in terms 

of electrical conductivity was not attempted at so early a date as the 

thermo-electric methods. Miiller8 attempted to co-ordinate temperature and resistance both for iron and for platinum, without, however, 

more than estimating the thermal datum. A resistance thermometer,

1 Le Chatelier: Bull. Soc. chimique, Paris, n. s., vol. 47, 1887, p. 2. 

s Le Chatelier: Jour, de physique, vol. 6, 1887, p. 23. 

3 Becquerel: Anu. cb. et phys., Paris, 3d series, vol. 68, 1863, p. 49. 

<Cf. Moussou: Physik, Ziirich, 2d ed., vol. 3, 1874, p. 384. 

5 Le Chatelier: Bull. Soc. chimique, Paris, n. s., vol. 47, 1887, p. 300. 

6 Obermayer: Wien. Ber., vol. 66, pt. 2, 1872, p. 63. 

"Tidblom : BeibL, vol. 1,1877, p. 151. 

8 Miiller: Pogg. Ann., vol. 103,1858, p. 176

(704)
BAKUS.J METHODS OF PYKOMETRY. 51

suggested by Quincke, was carried out practically by Reissig. 1 This is 

simpjy a wheatstorie-bridge adjustment, not different in any essential 

respect from C. W. Siemens's2 pyrometer, except in so far as the latter 

endeavored to calibrate his electrical apparatus by the calorirnetric 

method. Siemens's pyrometer is too well known to need special description. In the final form, currents are measured electrolytically, and to 

give the method greater sensitiveness two identical voltameters to correspond to the hot and the cold wires are used simultaneously. This 

makes the apparatus to some extent independent of the local and time 

errors of the galvanometer. Siemens's resistance-temperature measurements are made with platinum, copper, and iron, and the data obtained 

are formulated.

Siemens's pyrometers were tested by Weinhold (1. c.) and pronounced 

sufficiently in keeping with the air thermometer to be of reliable service to the metallurgist, After this Forster,3 Williamsei],4 and Fischer5

find that the effect of long-continued exposure of a Siemens pyrometer 

is an increment of the resistance of the exposed wire. Kecalibration 

from time to time is therefore essential. An important series of measurements of the relation between resistance and temperature was made 

for quite a number of metals by Be"noit.6 His temperatures run as high 

as 860° (boiling point), and all the relations are formulated. Iridioplatinum wire was tested with regard to its resistance at 15° and at 

white heat by BucknilJ.7 Formula applying for silver-platinum, irongold, and platiuum-iridium alloys were computed with great care and 

from many experiments by MacGregor and Knott;8 but their ranges 

of temperature did not much exceed 150°. A critical comparison of the 

data of the resistance temperature formulae of Siemens (1. c.), Beuoit 

(1. c.), which apply for platinum, was made by Nichols,9 and the discrepancies between these results fully pointed out. Mchols, moreover, 

expressed resistance in terms of his dilatation thermometer. Perhaps 

one of the most careful measurements of resistance as varying with 

temperature, and indeed the only ones which to my knowledge were 

made at high temperatures and by direct comparison with the porcelain 

air thermometer, are due to Schleiermacher.10 This observer wrapped 

his wires directly around the thermometer bulb or exposed them in similar unexceptionable ways. Eecoguizing the variable character of ordi1 Keissig: Diugler's Jour., vol. 171, 1864, p. 351.

2 Siemens: Proc. Royal Soc. London, vol. 19,1871, p. 443. Dingler's Jour., vol. 198, 

1870, p. 394; ibid., vol. 209, 1873, p. 419; ibid., vol. 217,1875, p. 291. 

3 Forster: Chemical News; vol. 30, 1874, p. 138. 

«Williamsen: Dingler's Jour., vol. 210,1873, p. 176. 

6 Fischer: Dingler's Jour., vol. 225, 1877, p. 463. 

6B6noit: C. R., vol. 76, 1873, p. 342. 

7 Bucknill: Jour. Soc. Tel., Eug., vol. 7,1878, p. 327.

8 MacGregor and Knott: Trails. Eoyal Soc. Edinburgh, vol. 29, I860, p. 599. 

9 Nichols: Am. Jour. Sci., 3d series, vol.22,1881, p. 363. 

10 Schleiermacher: Wied, Ann., vol. 26, 1885, p. 287.

(705)
52 MEASUREMENT OF HIGH TEMPERATURES.

nary platinum, he does not attempt to formulate his data. A final and 

more ambitious attempt to express the resistance of temperature relation is due to Callendar. 1 Wishing to establish a strictly comparable 

standard of high temperature, he avails himself of pure platinum. This 

he compares directly with an air thermometer as far as 600°. A feature 

of the experiments is the inclosure of the wires within the bulbs of the 

air thermometer. Great care is taken to guard against surface condensation of gas. Data are tabulated. The work enjoys the supervision 

of J. J. Thomson.

From a theoretical point of view the electrical conductivity of gases 

presents many phases available for temperature measurement. Experiments on the conductivity of hot gases are due to Buchanan.2

I am aware that Mr. C. A. Perkins, of Johns Hopkins University, has 

for some time been occupied with similar experiments.

Magnetism. A magnetic thermoscope was proposed by Thomson,3 

but it is specially intended for low temperature. High temperature 

thermoscopes of this kind must obviously fail from the irregularity of 

the magnetic behavior of metals at high temperatures.

Interpolation methods. Methods of this kind are of the utmost service 

and have been much in use. In the case of a furnace, whose temperature is increasing or decreasing regularly, a given unknown temperature may be fixed between two known temperatures by time-interpolation. The two or three known temperatures between which the 

unknown data lie may be convenient fusing points, sufficiently near 

together to make linear or quadratic interpolation practicable. Camelley4 and others have made much effective use of methods of this kind.

ADVANTAGES OF THERMO-ELECTRIC PYROMETRY.

Having thus indicated the chief methods of pyrometry so far employed, it next behooves me to state clearly in what respect the thermoelectric method deserves preference before all others. To do this I must 

reiterate the point of view already emphasized in the preface and from 

which the greater part of the present volume has been written. It is 

my belief that before important steps in most subjects directly bearing 

on dynamical geology can be made, our methods of high temperature 

measurement and of high pressure measurement must first be facilitated. 

Moreover, the solutions to be given to the thermal and to the mechanical problems must be such that the high temperatures may be measured 

under conditions of high pressure, and conversely.

When temperature measurements are to be made under these almost

1 Callendar: Proc. Royal Soc, London, vol. 41, 1886, p. 231.

2 Buchanan: PMlos. Mag., London, vol. 24, 1887, p.'287. The subject is now being 

vigorously discussed; but there is no space for further references here. (Schuster, 

Bloudlot, Elster n. Geitl, and others.)

3 Thomson: Proc. Royal Soc. Edinburgh, vol. 10, 1880, p. 538.

4 Carnelley: Jour. Chem. Soc. London, vol. 1, 1877, p. 365.

(706)
HARUB.] METHODS OF PYROMETRY. 53

insuperable difficulties, the kinds of pyrometers available dwindle down 

to a very small number. Indeed, the thermo-couple is almost the only 

instrument of research left. It is therefore most encouraging to find 

that, for purposes of high temperature measurement in general, the 

thermo-couple can be made to yield results which, apart from practical 

conveniences and easy manipulation, are warrantably as accurate as 

any known to us. I will summarize the advantages here in question 

as clearly as I can, so that they may be referred to in the bulk of the 

work:

1. Barring a few corrections, the thermo-couple of known properties 

is available for temperature measurement under all pressures. The corrections implied are those which become necessary in consequence of the 

changes of thermo-electric property with pressure; but these changes 

are slight and quite negligible in comparison with the thermal sensitiveness of the couples.

2. The temperature at the hot junction is dependent on the temperature at the cold junction and the constants of the couple only. It is 

independent of the distribution of temperature in the parts of the couple 

between the junctions. This is a great practical advantage, the importance of which is realized when temperature is to be measured under 

pressure.

3. The thermo couple is capable of measuring temperature when the 

dimensions of the hot space scarcely exceed a physical point. Small 

zones of constant temperature and relatively small apparatus for heating are therefore sufficient for thermal comparisons of relatively great 

accuracy. In this respect the thermo-couple deserves preference to 

the resistance thermometer, particularly when material fusible with 

great difficulty is operated upon.

4. The upper limit of temperature measurement is practically infinite, 

and lies much above the melting point of platinum; for by using refractory alloys of platinum, iridium, rhodium, and inclosing wires of 

these metals in tubes of calcined lime, distinct and powerful thermoelectric effects are obtained even when the contents of the tubes are 

fused.

5. The electromotive forces of suitable thermo-couples are easily measurable with an accuracy of 1 in 1,000. Almost with the same accuracy 

may the indications observed at the beginning of any year be compared 

with those at the beginning of the next or any other subsequent time. 

The secular errors of a thermo-electric pyrometer, when properly cared 

for, need not be larger, relatively, than the secular errors of a mercury 

thermometer.

6. Many couples are knowft which, in addition to the desideratum 

of thermal sensitiveness, possess great tenacity and ductility, and are 

unalterable under ordinary conditions of heating.

7. The thermal indications are as'nearly as possible instantaneous, 

and the discrepancy of the lag error is therefore a minimum or nil.

(707)
54 MEASUREMENT OF HIGH TEMPERATURES;

8. In view of the facts summarized in 2, insulation of the wires is not 

difficult even when the couple is to be used under pressure. This does 

not apply in case of the resistance thermometer.

9. When destroyed by silicificatiou or metallic corrosion the thermocouple may easily be purified by fusing it over again on a lime hearth 

and drawing to wire. With good metal the variation of constants thus 

produced is almost negligible.

10. Finally, the thermo-couple has this important property, that 

between temperatures lying not too far apart (100° to 200°) any intermediate temperature may be interpolated with great accuracy by the 

quadratic equation devised by Avenarius and Tait, and such interpolation, curiously enough, seems to be more trustworthy in proportion as 

temperature increases above the regions of incipient red heat. It is this 

property which specially recommends the thermo-couple for the measurement of relatively very small increments of temperature added to 

relatively large temperatures, possibly under conditions of high pressure, as is the case, for instance, in investigation relating to melting 

point and pressure of solids.

To use the thermo-element it is necessary to find the thermal equivalent of the electromotive force for all temperatures of the junctions. 

This is at present possible only by making detailed comparison with the 

air thermometer. An experimental problem of some difficulty is thus 

encountered at the outset. Inasmuch as the measuring part of a thermocouple is not much more than a sensitive point, and the corresponding 

part of the air thermometer is a sphere of relatively enormous dimensions, it is not easy to devise an environment which at temperatures 

high and low shall be thermally identical for both. When temperature 

varies, the indications of the air thermometer necessarily lag behind 

those of the thermo-element. It is therefore one of the chief purposes 

of the present volume to devise a method, such that the observed indications of air thermometer and thermo-element may be rigorously equivalent; in other words, to carry forward the methods of calibration to a 

degree of perfection subject only to the improvement of the air thermometer. I hope in some future publication to show the feasibility of a 

fire-clay air thermometer which will be available for temperature measurement much above those at which porcelain becomes too viscous for 

further use; but in much of the present volume the object is less to devise new methods, than to bring the old ones more within the scope of 

easy application than has hitherto been done. However, in Chapter 

V I submit a new method of pyrometry.

In calibrating thermo-couples I make use of two methods. The first 

of these is preliminary. The measurements made are based on known 

values of high boiling points. The second method, however, is a direct 

calibration with the air thermometer. In this way I arrive at an ultirior result; for a comparison of the two sets of data thus obtained is 

to some extent a criterion of the degree of accuracy with which thermal

(708)
BARUB.] METHODS OF PYEOMETRY. . 55

data in the regions of high temperature are known. Beyond this incidental result I do not attempt to fix the absolute value of any high temperature datum. To do this it is not only necessary to expend more 

time than I have now at my disposal, but it is expedient that the observer be specially equipped for the purpose. In the problems of this 

volume, on the other hand, where the end chiefly in view is the trial of 

available methods rather than the investigation of new and accurate 

results, such equipment is superfluous. In one case the variables of 

the thermal apparatus selected, including of course the limits of variation of its constants, are chiefly to be studied; in the other case additional time and pains must be spent in the absolute evaluation of the 

constants themselves.

(709)
CHAPTEE I.

THE DEGREE OF CONSTANT HIGH TEMPERATURE ATTAINED IN 

METALLIC VAPOR BATHS OF LARGE DIMENSIONS.

By C. BARUS AND W. HALLOCK. 

EXPLANATION.

The general character of this chapter is introductory. The experiments are therefore largely arranged with reference to a single point of 

view, viz, the degree of constancy attainable in metallic vapor baths 

at temperatures either high or low. To secure this end we profited by 

the experience of Messrs. Deville and Troost, who recommend the use of 

large masses of metal, and consequently large forms of boiling-point 

apparatus. The advantages gained in this way are twofold. It is obvious that if the quantity of substance used is indefinitely large, not 

only may the ebullition be prolonged for a considerable time a great 

desideratum when many pyrometers are to be calibrated but in the 

same measure, as the volume of vapor and consequently the space of 

constant temperature is larger, the probability of constant temperature 

at any one central point is proportionately increased.

There is, however, a second point of view from which the present experiments have been pursued. The questions to which this leads us 

do not conflict with the main purpose of the chapter, They are intimately connected with the thermal equivalents of the thermo-electric 

indications of small temperature variations upon which many of the 

following data must be based. The refractory alloys best adapted for 

measurements of high temperature are invariably of platinum body, in 

which relatively small amounts of the foreign metallic ingredient are 

added to platinum. This will be seen more fully below. Now it appears that alloys containing platinum and the other metal mixed in 

nearly equal amounts are either brittle or otherwise unsuited for wires. 

Often the second ingredient is of a relatively volatile or oxidizable 

kind. Escaping at high temperatures, this gives rise to changes of 

homogeneity or even of composition. Fortunately it is not difficult to 

find low percentage platinum alloys, which, when combined with pure 

platinum thermo-electrically, show electromotive forces so large that no 

difficulties of measurement can be apprehended. In fact the purely 

electrical measurement is a pnrt of the problem which may be solved 

with extreme nicety.

56 (710)
BARUS.] DEGREE OF CONSTANT TEMPERATURE. 57

Having these desirable properties of many platinum alloys in mind, 

it is a natural step in the argument to inquire into the nature of refractory alloys of platinum with gradually vanishing amounts of other 

metals or alloys, Given, for instance, a series of thermo-couples, one 

element in all of which is platinum and the other element an alloy of 

platinum in which the foreign ingredient diminishes from element to 

element in given small amounts. The limiting case of such a series is 

a thermo-element of pure platinum thermo-electrically combined with 

pure platinum. Now, a priori, it does not seem improbable that the 

series may possess certain properties in common, from the totality or 

grouping of all of which the properties of the thermo-couple platinumplatinum may be warrantably predicted, and that therefore thermoelectric measurement may actually be made by the limit couple platinumplatinum in question. The interest which attaches to any such endeavor 

is naturally enhanced by the fact that the said limit couple is possibly, 

though not necessarily, the point of convergence of any other series of 

alloys. In general, if any number of series of platinum alloys be made, 

in each of which series platinum is alloyed with small quantities of the 

same foreign metal, in amounts which diminish from alloy to alloy as 

far as zero; if, moreover, the individual members of the divers series 

in question be thermo-electrically. combined with pure platinum, then 

it is not impossible, inasmuch as the thermo-electric properties of all 

the series converge in the thermo-electric properties of the element platinum-platinum, that a reduction of all thermo-electric data to this limit 

couple may be feasible. We state distinctly that the identity of the 

limit couple for all series is a possible case. It is not a necessary case, 

for the interpretation to be given to the limit couple may be different 

for each of the divers series which converge in it. Again, since the 

thermo-electrics of an alloy bear no easily discernable relation to the 

thermo-electrics of its ingredients, it follows that the said interpretation is far from being simple, and that the question at issue is one 

which must be solved experimentally.

APPARATUS.

Remarks. The construction of apparatus for obtaining spaces of 

practically constant temperatures is a step introductory to all experiments in thermometry. It is important and even necessary, moreover, 

that the temperature be of the nature of a fixed datum; in other words, 

that it have always the same value under like easily reproducible circumstances, whether this value be known or unknown. To obtain 

such constant temperatures use has always been made of the boiling 

points of liquids; and boiling points conveniently disposed in the thermometric scale are at hand for selection, in the results of many 

observers.1 More especially for the high temperatures we are indebted

*Cf. Carnelley: Melting and Boiling-Point Tables; Landolt and Boernstein: Physikaliscli-chemische Tabellen, etc.

(711)
58 MEASUREMENT OP HIGH TEMPERATURES.

to the classical researches of Messrs. Deville and Troost. Availing 

ourselves of these, we adopt vapor baths, and in the present chapter 

uniformly adhere to them, all the temperatures chosen for calibration 

or definite comparison being boiling points.

With the exception of certain forms of bath for boiling points below 

100°, our apparatus consists essentially of a closed crucible provided 

with an axial tube for the efflux of vapor. This tube projects inward 

or upward as far as the center of figure of the crucible, and downward 

through the bottom, of which it is a part. Distillation therefore takes 

place per descensutn, through the tube, and the surface of the surrounding boiling liquid is kept as nearly as possible at constant level as 

regards its position in the crucible. In the case of low boiling points 

this apparatus is made of metal and appropriately jacketed. For high 

boiling points, crucibles of graphite or of clay are preferable. In the 

interior of the central tube and near the center of figure of the crucible the temperature is satisfactorily constant. Here, therefore, is 

placed the essential part or " explorer" of the pyrometer to be calibrated. 

It is thus exposed in the current of vapor circulating through the tube, 

the walls of which are permanently kept at the boiling point by the 

boiling liquid surrounding them. In this way a comparatively simple 

form of apparatus, available at all temperatures, both high and low, 

retains all the essential features of the ordinary boiling point apparatus; 

and it is only for very low temperatures (< 100°) that a special form is 

expedient.

Low boiling points. To describe in passing this form of apparatus 

for low temperatures ( < 100°), we insert Fig. 1, in which the position 

of the thermo-element is indicated by t a T. The cold junction t is 

kept at constant and comparatively low temperature by water coming directly from the water mains and continually circulating around 

it. This cold water is further used in condensing the vapor after circulating around the hot junction T. A glance at the cut will make 

the disposition clear. Water enters at w and vapor at i?, and after 

passing around the junctions t and T, respectively, they enter the condenser, diagrammat.ically shown at cc, the water entering an external 

compartment and the vapor an internal compartment. The condensed 

vapor is at once refed into the boiler or flask, thus enabling the 

observer to use this apparatus quite as long as desirable without interruption. At the cold end of the condenser the inner tube is in communication with the air. Ebullition thus takes place under atmospheric 

pressure. The apparatus is available for experiments with ether, methyl 

alcohol, alcohol and water. It fails, so far as practical convenience is 

concerned, for aniline, etc., because of the difficulty encountered both 

in conveying the vapor into it from the boiler without condensation, 

and because of the corrosive action of such vapors on the corks and rubber tubing of the apparatus. If made of a single piece of glass it is

(712)
HARUS.J DEGREE OF CONSTANT TEMPERATURE. 59

too liable to break at the fused joints. In the form used the tubes v T 

and wt were about 25cm long and about 2.5cm wide.

FIG. 1. Apparatus for constant temperature between 0° and 100°. Scale, $.

Boiling points between 100° and 300°. In Fig. 2 we give a form of apparatus constructed on the typical plan indicated above, and which is 

adapted to temperature between 100° and 300°. It consists essentially 

of a large sphere, A A A, of copper, 25cm in diameter, the joints of which 

are brazed.

Through the bottom of this a somewhat conical central tube, d d, projects into the interior as shown, the tube communicating below with an 

iron gas-pipe, efg 7t, leading to the condenser. The neck or head, fc, of 

the spherical copper bottle is in connection with a wide glass tube, 7c TO, 

kept in place by a gallows adjustment, the top of which, TO, is of iron 

and provided with two lateral steel rods or bolts. These being fastened

(713)
60 MEASUREMENT OF HIGH TEMPERATURES

below to a wide flange in the neck fc, secure the tube by screw pressure 

between the head m and the flange of &. It is often convenient to use 

gaskets of asbestos or any other kind of packing at the upper and lower 

end of the tube. The head m, moreover, is in communication with the 

condenser by means of the lateral tube of gas pipe, mnog. Hence the 

vapor arising from the surface of boiling liquid, a a, can escape either

FIG. 2. Apparatus for constant temperature between 100° and 300°. Scale, &.

above or below, and the respective circulations are regulated by a 

faucet, /, We found, however, that in case of corrosive or hot liquid, /

soon begins to leak, and that it is advantageous to partially stop up the 

lower passage by a ball suspended in the cone d d from a platinum 

wire passing through Jem I. In this way the use of the cock /may be 

avoided.

To heat the sphere A A A we used a large ring burner, S B, about 

22cm in diameter and provided on its inner surface with 130 jet holes, 

0.15cm each in diameter. This ring burner was so made that it could 

be used either with or without blast, according as temperatures relatively 

low or high were to be obtained. Its position is adjustable at pleasure 

by a clamp attached to the standard C C. Another clamp attached to 

the standard D D acts as a safeguard against lateral vibrations of the 

sphere A A A, the main weight of which is supported by the exit pipe 

d ef to the upper end of which it is screwed. A final clamp and standard, E r, facilitates the adjustment of the exit pipe o n m. The sphere 

is provided with a feed pipe, q </, and an appropriate gauge, p p, to

(714)
BAIIUS.] DEGREE OF CONSTANT TEMPERATURE. 61

register the height of the liquid. The capacity of the retort is about 

oiie gallon of liquid. If the liquid be fed in drops from a Mariotte flask, 

Fj no interruption of ebullition need take place.

In the apparatus given in the figure a space of constant temperature 

nearly 3cm wide and fully 60cm long is available. If the ring burner 

be so adjusted that the ebullition is fairly brisk the temperature within 

this spaceis almost perfectly constant. For relatively high temperatures 

it is generally advisable to discard the glass tube fc m, and to close the 

neck with a plate of metal suitably perforated to allow the introduction 

of thermo-couples. In general, however, the large tubular space is convenient both for the comparison of long-stemmed mercury thermometers 

and for the further comparison of electrical pyrometers with them.

"We omit special data relative to the degree of constant temperature 

here obtained, because it is questionable whether at these relatively 

low temperatures the use of large forms of vapor baths is to be recommended, and because none of the data of importance below depend 

upon the perfection of the large retort here described. In Chapter II 

data for smaller forms are fully given, and from these the efficiency of 

the larger forms may easily be inferred.

FIG. 3. Boiling-point apparatus for mercury. Scale, -fa.

Apparatus for mercury. The boiling-point apparatus just described 

is useful for substances boiling at a lower temperature than mercury 

when constancy of boiling point can not be accurately relied upon. 

Such substances are mostly of organic kind, and are apt to change 

their properties slightly after long ebullition. It is for this reason that 

the mercury thermometer remains indispensable. When, however, the 

boiling point is fixed and known, like that of mercury or sulphur, the

(715)
62 MEASUREMENT OF HIGH TEMPERATURES.

apparatus and the manipulations may be simplified. A form of vapor 

bath specially adapted to mercury calibrations is given in Fig. 3, onetenth actual size. The boiler or retort A A A is of cast-iron, and is a 

modified form of the well-known mercury still of the shops. By drilling a hole through the bottom and tapping into it a long nipple, the 

central tube d d ma>y be screwed down firmly in position. The nipple 

communicates below with a long tube of gas pipe, efg, leading to the 

condenser. The crucible A A A is closed above by a flat lid, the edge 

of which as well as the rim of the crucible has been carefully turned, 

and is held in place by a stout gallows connection not shown in the 

figure. Through the center of the lid passes a smaller iron tube, li t, 

the lower end of which is closed and projects into the central tube d d, 

somewhat below the level a a of the surrounding mercury. It is into 

the tube h t that the hofc junction of the thermo-elemeut is to be introduced as far as the base of the tube. A lateral tube, b It I «, largely of 

irou, subserves the purpose of replacing the mercury lost by evaporation, and communicates with a larger reservoir, B B, in which the mercury is practically at the same level, m m, as in A A. Hence the level 

in B B is to some extent a gauge of the level in A A. A supply reservoir, G C, enables the operator to keep in m at constant height. To 

keep up the ebullition we made use of a kind of ring burner, consisting 

of three distinct blast-burners symmetrically placed around the crucible, 

the flames impinging upon its sides. In this way full advantage was 

taken of the current of air furnished by Professor Eichards's pneumatic 

pump. The operation of boiling may therefore be prolonged indefinitely.

In the tables below we give a series of results by which the constancy of temperature attained during the successive stages of improvement of this apparatus is fully exhibited. These results will show that

variations in the disposition of parts is by no means without consequence.

Boiling point of zinc. The construction of apparatus first used was 

carried out by Mr. Hallock, and to him the following description is due:

In our earlier experiments an attempt was made to use the large clay 

retorts of the shops, but after some trials we abandoned them in favor 

of the special forms of retort now to be described.

Having in mind the form aud operation of the ordinary apparatus for 

checking the boiling points of thermometers a retort was constructed 

with a view to surrounding the thermo-element with a double jacket of 

the vapor in question. It soon became evident that the simpler forms 

were useless, owing to the condensation of the vapors and the clogging 

of the outlets. We were thus led after trials of several other simpler 

forms, to test the arrangement shown in Fig. 4 and constructed as

follows:

(716)
CO

O.

Q,

 ty///J7J.

lilJULLOlM 0 fl H 

Fig. 4. Boiling point apparatus for zinc; earlier for

X
64 MEASUREMENT OF HIGH TEMPERATURES.

The cylindrical reservoir, or retort proper, shown at A, Fig. 4, was 

made by screwing cast-iron caps N N, C 0, upon the ends of a piece 

of iron pipe 6 inches long and 6 inches in diameter. A piece of 1-iuch 

iron pipe, D, fitted in the upper cap C (7, and extended upward to an 

elbow, j&, and similar pipe, B, which latter passed out through the side 

wall of the anthracite furnace at 0 0. Thence the pipe B extends 

through the T at I I, 18 inches, into the iron pipe H J5T, which is 

screwed into the other end of the T. The third opening of the T is 

fitted with the short outlet pipe JT, 1 inch in diameter. A cap, G, 

closes the whole apparatus except the outlet at K. A small iron pipe, 

F Fj passing through the cap G, and extending 15 inches into the 

interior tube B B, and closed at its inner end was intended to receive 

the thermo-element. A perforated tube burner, LLL, Fletcher system, 

placed beneath the pipe E IT, was intended to prevent the solidification 

of the metal therein and consequent stoppage of the circulation of vapor. 

We hoped to be able with this apparatus to obtain a region of constant 

temperature in the inner end of the tube F, which would be surrounded 

by two distinct jackets of -the vapor of zinc. We expected the action 

to be as follows:

The vapor rising from the boiling zinc in the retort A, to pass through 

D and B B, out past the end of F, out of the end of B into H ff, 

thence backward through JET", and out at K, either still in the state of 

a vapor or condensed to a liquid in H.

Two difficulties made the apparatus impracticable. Whereas melted 

zinc or zinc vapor has little or no solvent effect upon iron, still zinc just 

at the boiling surface or at the point of condensation of the vapor does 

dissolve iron in considerable quantities. This action of the b'oiling zinc 

soon eats through the iron walls of the retort and makes the whole apparatus very short lived. Moreover, the spontaneous combustion of 

zinc vapor on coming to the air inevitably results in stopping up the 

outlet, causing the destruction of the apparatus. These objections, together with other minor ones, led to the abandoning of this form and 

ultimately of all forms constructed on a similar principle.

The principle next applied was that of downward distillation through 

the bottom of the crucible, a system that had already proved very good 

for mercury and some other substances, and which has been touched 

upon in an earlier part of this chapter.

The particular form ultimately constructed is shown in vertical crosssection in Fig. 6 and in vertical longitudinal section in Fig. 5. In this 

case the furnace formed an essential part, and was constructed simultaneously and as part of the whole. It covered 5 x 3 J feet on the floor and 

stood 5 feet high. It was built of brick, lined with fire-brick, on the 

double-reverberatory principle, entirely symmetrical. Each side was 

provided with a fire-box, A (Fig. 5), a grate, 0, ash-box, JS, ash-door, (7, 

blast inlet, $, and fire-box door at D. The zinc was contained in the

(718)
BAKU6.) DEGREE OF CONSTANT TEMPERATURE. 65

graphite crucible F F, which was 14 inches high, 11 inches in largest 

diameter, and -£ iuch thick. The graphite cover MM was luted on with' 

a paste of powdered graphite and water. Through the cover M M the 

iron tube L passed, extending downward into the crucible and closed 

at its lower end. An iron pipe, 0, 1£ inches in diameter, passed up 

through the bottom of the crucible about 6 inches, carrying the tireclay spherical shell K K, and protected by a coating of fire-clay, II.

FIG. 5. Boiling-point furnace for ziiic; later form; longitudinal section. Scale, ^.

Underneath the crucible a piece of stone-ware pipe, 6 inches in diameter, N Nj was built into the furnace concentric with the crucible and 

extending 15 inches below it. In practice this pipe J^Jf dips just below 

the surface of the water in a tank placed between the two fire-boxes 

A. A and not shown in the drawing.

Bull. 54 5 (719)
66 MEASUREMENT OF HIGH TEMPERATURES.

Fig. 6 shows a vertical section through the axis of the crucible at 

right angles to that shown in Fig. 5. The lettering in each case is the 

same. U and Fare the supporting arch between the two fires, and T T 

are flues to carry off the products of combustion. R B is the top of 

the furnace, S 8 are supporting columns, W is the entrance of the 

blast, and P the wind-box opening into the fires by Q Q, shown on Fig. 5.

FIG. 6. Boiling-point furnace for zinc; later form; cross section. Scale, Ty

The fuel used in this furnace was anthracite coal with a blast furnished 

by a 20-inch fan-blower, the ash-box door being of course closed during 

operation. The flames from the fire rising through the space E E impinged upon the crucible and passed thence off by the flues T T. In 

practice it was found that by applying fresh fuel in small quantities

(720)
BAUDS.] DEGREE OF CONSTANT TEMPERATURE. 67

alternately to the two furnaces at regular intervals (ten minutes) a comparatively constant condition could be maintained until the accumulation of ashes interfered with the draft. The furnace performed its 

part of the work satisfactorily, but from the largo dimensions at least 

one day was necessary to repair damages and prepare for a new "heat," 

and sometimes several days were necessary to get the crucible cleaned 

and ready again.

The crucible was filled with pieces of zinc and the powder and grains 

from previous distillings, mixed with powdered charcoal as a reducing 

agent. The cover was luted on as stated, and the tank placed under 

the stone pipe N N. In operation the vapor from the boiling metal 

rose around the sphere K and passed through holes into it, and down 

through G into N N, where it condensed and fell into the water, thus 

keeping the pipe L and the thermo-element contained therein at a 

comparatively constant temperature. The degree of constancy actually 

attained will be fully discussed later. Even in this apparatus the burning of the vapor proved a source of endless and unavoidable annoyance. 

There seems little doubt that the vapor of zinc is even able to decompose water vapor and liberate the hydrogen, itself producing a horn-like 

oxide, which is quite as apt to clog the outlets as the solid metal. Owiug to this, many and frequent were the cases where the " heat" proved 

incomplete, or a total failure, owing to stoppages and explosions or 

leaks. This will account for the incomplete series of determinations 

which may occur in subsequent tables. Before we were able thoroughly 

to profit by our experience the transfer of the laboratory to Washington interruDted the work and gave it a different direction.

EXPERIMENTAL RESULTS.

Methods of measurement. Whether two given temperatures are equal 

or not may be shown with great accuracy and certainty by thermo-electric comparison. Thermo-couples of platinum with palladium, low 

percentage alloys of platinum-iridium, platinum-nickel, platinum-rhodium, platinum-cobalt, and many others, are available for the purpose. 

Furthermore, since comparatively small increments of temperature are 

here to be observed, the degree of constant temperature obtained in 

any given space both as regards its variation at any given point with 

time, as well as the distribution of temperature existing in the said 

space at a given time, can be fairly estimated by thermo-elements of 

known power.

Many observations go to show that for practical purposes we may represent the partial electro-motive force at each junction of a thermo-element by an equation of the form.

eT=aT+bT2+cT3 + ............ (1)

where er is the (partial) electromotive force at the junction whose temperature is T, and a, &, c, . . . are thermo-electric constants rapidly 

decreasing in magnitude.

(721)
68 MEASUREMENT OF HIGH TEMPERATURES.

Hence in a couple in which the junctions are at temperatures Tand 

<, we find by difference

=eT -et =a (T t)+b (T2 -t*)+c (T3 -t3 }+ .' . . (2)

an equation which in most cases applies so fully that the terms of the 

right-hand member, whose powers of T and t are greater than the third, 

may be neglected. 

From equation (2) follows at once that

 dT±

Inasmuch as the constants a, &, c, . . decrease so rapidly in magnitude that a mean or approximate value of T may be introduced into 

equation (3), it appears that in proportion as the increment of temperature becomes smaller it may be measured with the same accuracy 

with which the constants a, 6, . . have been found. Methods of 

measuring e and of calibrating the thernio-eleinent will be indicated in 

the next chapter.

List of thermo-couples. It is expedient to insert for future reference 

a list of the thermo-couples used for measurement here, In the first 

part of this table the wires are given in the order in which their thermoelectric powers were originally determined. The other part contains 

the thermo-elemeuts used for temperature measurement. The table 

also contains values for the constants a and b in equation (1). In the 

case of Nos. 0 to 15 the calibration interval is not larger than 0° to 

200° j in the others as large as 0° to 400°, or 0° to 450°. The data are 

referred to a zinc sulphate Daniell standard, the electro- motive force of 

which is assumed to be one volt. Lord Eayleigh's recent value for 

this standard is 1.072 volt. Hence to reduce the data to absolute units, 

a and b must be increased 7.2 per cent. We have refrained from introducing this correction in the first two chapters because the relative 

values of the data there given are alone of interest, and because of the 

confusion and labor which a reconstruction of the whole series of data 

and of graphic representations would involve.

(722)
BAKUB.] DEGREE OF CONSTANT TEMPERATURE. 

TABLE l. Linl of thermo-couples.

69

No. 

0

1

2

3

4

5

C

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

Thermo-couple.

+

AK

Ag, 5% Pt

Ag,10%Pt

Ag,15%Pt

Ag,25%Pt

Pt

Pt soft

Pt hard

Pt Ir 59/0

Cu

Pd

in

Ni

Pd

Pt hard

Pd

Cu

Pt hard

Pt hard

Pt hard

Pt hard

Pd

Pt hard

Pt hard

Pt hard

Pt soft

Pt soft

Pt, Ir 5%

Pt, Ir 5%

Pt,Ir 5%

Pt com.

Pt com.

Ptcora.

Pt com.

Pt com.

Ptsoft

Pt soft

Pt soft

Ptsoft

Pt soft

Pt soft

-

Cu

Cu

Cu

Cu

Cu

Cu

Cu

Cu

Cu

Pt, Ir 20%

Cn

Cu

Pt soft

Pt hard

Pt,Ir20%

Pt,Ir20%

Cu

Pf,Ir20%

Pt,Ir20%

Pt,Ir 5%

Pt,Ir 5%

Pt hard

Pt, Ir 209/0

Pt, Ir 594

Pt, Ir 2%

Pt, Pd 3%

Pt, Pd 1096

Pt, Ir 109o

Pt, Ir 15%

Pt, Ir 209/0

Pt, Ni 5%

Pt, Ni 2%

Pt, Ni 396

Pt, Ir 596

Pt, Ir 7%

Pt, Ir 20%

Pt, Ir 20%

Pt, Ir 20%

Pt,Ir20%

Pt, Ir 209/0

Pt,Ir20%

a x 103

261

. 5730

7230

8964

9641

4024

3222

3760

906

3364

8590

. 20090

37630

5517

7197

32347

7660

7640

3075

3056

5253

7640

2972

1883

287

975

2362

3888

4507

8428

4560

1978

3639

4704

7180

7190

(7200)

(7200)

(7200)

(7200)

1 x 10C

174

7010

10100

11830

15220

11450

12740

9680

. 9150

3890

21100

22000

4900

8375

C325

16855

3900

3670

 96

-91

9700

3810

475

 1501

1194

2732

1525

2685

3982

505

48

519

1472

2073

6270

6290

(6300)

(0300)

(6300)

(6300)

"Where made, etc. Calibration interval.

Laboratory ; 0° to 190°.

Do.

Do.

Do.

Do.

Commercial ; 0° to 190°.

Paris ; 0° to 190°.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Commercial ; 0° to 190°.

Paris ; 0° to 450°.

Do.

Paris; 0° to 370°.

Do.

Do.

Paris; 0° to 450°.

Paris ; 0° to 370°.

Laboratory ; 0° to 370°.

Do.

Do.

Paris ; 0° to 370°.

Laboratory ; 0° to 370°.

Paris ; 0° to 370°.

Laboratory ; 0° to 370°.

Do.

Do.

Do.

Do.

Paris ; 0° to 450°.

Do.

Do.

Fused over from old elements.

Do.

Do.

Data for the mercury vapor baths. Returning from this digression to 

the subject proper, we insert Table 2 to exhibit the degree of constant 

temperature arrived at in the mercury apparatus. The observations 

are made in time series. T is the temperature of the hot junction, 

placed at i in Fig. 3, and t the temperature of the cold junction of the 

thermo-element No. 18, at the time specified in the same horizontal row. 

Tia computed from the thermo-electric data. In the first part of the

(723)
70 MEASUREMENT OF HIGH TEMPERATURES.

table, results are given for the case in which the thermo-element tube 

h i, Fig. 3, is simply submerged in liquid.

TABLE 2. Constancy of temperature in the mercury apparatus.

No.

18

18

t.

5.1

4.2

6.6

7.8

8.7

9.6

10.2

7.2

7.2

T.

357

337

356

358

356

357

359

359

360

Time.

/;. m.

2 30

35

3 20

30

50

4 5

20

6 20

35

Remarks.

1

J

.

Envelope of thermo-eloment (tube) submerged in the boiling liquid.

Envelope above liquid.

j

'

Apparatus Fig. 3, but with longer central tube dd.

Results irregular aud useless; DO satisfactory constancy.

18 15.0 

17.2

342 

357

3 40 

4 30

f Apparatus Fig 

S with plaster.

3, but with inner side of lid and walls heavily lined

Eesults again irregular; no satisfactory constancy.

18

18

9.0

10.0

10.8

11.6 

12,6 

13.8

14.8

15.2

6.8

7.4

8.1 

9.1

10.1

11.2

353.6

357.5

357.5

357.2 

356.9 

356. 4

356.5

336.4

354.3

356.8

356.6 

356.7

356.7

356.7

12 0

10

20

30 

45 

55

1 10

15

10 50

11 5

11 30 

11 50

12 20

12 55

]

S Apparatus Fig. 3, with central tube projecting inward only a8 far

as the center of figure. Apparatus without feed-pipe.

i

1

(

Apparatus Fig. 3, completed form.

'

Curiously enough, when the walls were lined with an inch coating of 

plaster above the plane of ebullition, although distillation took place 

with great rapidity, the thermo-element did not show the boiling point 

until about one hour had elapsed. Where no feed-pipe is used the temperature gradually falls as the charge of mercury diminishes in bulk. 

In the final form the negligible differences of temperature, amounting 

(after ebullition has set in) to less than 0.2°, are probably errors of 

measurement. The accuracy of the thermo-electric method is not warranted within 0.1 per cent.

Data for the zinc vapor laths. In digesting the data obtained for the 

variation of temperature in the zinc apparatus, it will be necessary to 

be more circumspect. For this reason we shall exhibit a very complete

(724)
BABUS.] DEGREE OF CONSTANT TEMPERATURE. 71

set of data. Early values, i. e., such as were derived with couples of 

palladium or of platinum-silver alloy are discarded, because during 

the course of the measurements such elements were usually corroded 

through, and little confidence could, therefore, be felt in the use of the 

constants of the uncorroded element. Assuming equation (1) above, the 

temperature, T, of the hot junction of the couple is

=^U /iZ 2&W +

where a and b are the constants of the element, and where, if t be the 

temperature of the cold junction and e the observed electro-motive force 

for temperatures t and T of the junctions

This value, £, is therefore the electro-motive force when the cold junction is at zero, other conditions remaining the same. The passage from 

e to £ usually involves only a small correction which may be interpolated 

from tables calculated for the purpose. Nevertheless the computation 

of T, where many results are in hand, is exceedingly tedious 5 and it is 

therefore preferable to avoid it by the use of graphic methods, as explained in Chapter II. In computing the values of T, the constants 

obtained in later and more refined apparatus are of course used, all older 

calibrations being allowed no more than corroborative importance.

In Table 3 we give some of our earlier results, the first of which were 

obtained by submerging a protected thermo-couple in boiling zinc contained in a large fire-clay retort. The charge was from 5 to 10 pounds, 

but special data are not at hand. After this the iron apparatus described in Fig. 4 was used. Owing to difficulties of manipulation, we 

thereupon returned to the retort pattern, providing it with a suitable 

condenser 5 exchanging this, eventually, for a graphite crucible on the 

general plan of Fig. 5, but of much smaller dimensions. It is in this 

order that the results in the tables are given. The third column of the 

table contains the number of kilogrammes distilled and the total number of kilogrammes of zinc charged ; e20 is the observed electro-motive 

force in microvolts, nearly when the hot junction is at T and the cold 

junction at 20° ; e20 is preferred to £, which applies for £=0° because t 

in the average case is usually in the neighborhood of 20°, and therefore 

the correction to be added is small. Ts and Tsn are thermo-electric 

data for the boiling point, when the calibration interval within which 

the constants apply is respectively 0° to 450° and 0° to 1000°. 1\ is 

therefore the result of exterpolation. Further remarks regarding these 

quantities must be reserved for Chapter II.

(725)
72 MEASUREMENT OP HIGH TEMPERATURES.

TABLE 3. Constancy of temperature in earlier forms of tlte zinc boiling-point apparatus.

Date,

Dec. 28,1883

Jan. 10,1884

Jan. 11,1884

Jan. 15,1884

Jan. 29,1884

Jan. 30,1884

Feb. 2, 1884

Feb. 4, 1884

Apparatus.

......do. ...................................

......do.....................................

......do ....................................

......do..'..................................

Kg. of Zn. 

distilled ; 

charge.

1

1

1

r

 )

O

No. of 

thermocouple.

14

14

14

14

38

18

18

18

ejo.

9150

9600

9030

9390

9216

9184

9191

(9281)

T..

847

880

883

867

860

856

857

 865

T*D .

914

950

953

934

924

921

922

930

It is to be borne in mind that the above data have a relative significance only. Their absolute values can not be discussed before Chapter 

IV. The same thermal and electric scales are uniformly used throughout Chapters I and II.

In Table 4 data showing the progressive stages of temperature of 

the zinc crucible are given in time series. The plan is identical with 

that of the preceding table, li denotes the number of hours elapsed 

from the beginnin-g to the end of the ebullition.

TABLE 4. Constancy of temperature in earlier forms of the zinc 'boiling-point apparatus;

time series.

Date.

Jan. 29,1884

Jan. 30,1884

Time.

h. m. 

4 25

32

37

48

55

2 35

45

3 00

20

35

40

45

50

55

4 10

15

30

40

50

5 00

10

15

25

h.

0.00

0.12

0.20

0.38

0.50

0.00

0.17

0.42

0.75

1.00

1.08

1.17

1.25

1.33

1.55

1.07

1.92

2.08

2.25

2.42

2. 58

2.67

2.83

No. of 

thermocouple.

18

18

18

18

18

18

18

18

18

18

.18

18

18

18

18

18

18

18

18

18

18

18

18

20.

9220

9180

9i70

9020

8580

6500

7510

8920

7800

8150

S910

9150

9180

9180

92GO

9260

9300

9370

9610

9770

flGSO

9540

9220

T..

860

857

850

8-16

815

658

736

840

756

784

839

834

856

836

8C4

864

867

870

886

898

890

882

860

Tin

925

921

920

910

872

693

682

900

807

836

899

919

920

920

928

928

933

938

956

970

961

951

924

Ilemarks.

Charge insufficient.

Furnace cools.

Approaching ebullition.

Blower stopped by accident.

Approaching ebullition.

Ebullition.

Charge distilled.

Superheating.

Furnace cools.

(72G)
BARU8.] DEGREE OF CONSTANT TEMPERATURE. 73

TABLE 4. Constancy of temperature in earlier forms of Hns sine loHing-point apparatus ;

time series Continued.

Date.

Feb. 2, 1884

Time.

h. m. 

'A 15

19

25

30

35

40

56

4 19

ft.

0.00

0.07

0.17

0.25

0.33

0.42

0.68

1.07

No. of 

thermocouple.

18

IS

18

18

18

18

18

18

C20.

7930

8100

8420

8740

9110

9170

9190

9220

T,.

768

780

802

825

851

856

857

860

Tin. 

818

833

SCO

884

915

920

921

924

Remarks.

1 Approaching ebullition.

Ebullition.

The second part of this table (Jan. 30) is complete. The third (Feb. 2) 

and the first (Jan. 29) part together make a series, showing in all cases 

the rise and fall of temperature at the inception and at the close of the 

distillation. The criterion of the occurrence of the boiling point is constancy of temperature; for the furnace is sufficiently hot to superheat 

the crucible when the charge of zinc is low or nearly distilled over as 

the second part of the table shows. An early stopping or a late beginning of the experiment is the result of accidents, which for the difficulty 

of the experiments are not infrequent.

As distinguished from the abo\7e data the following results are all obtained with very large apparatus, a "number 60" graphite crucible of 

Messrs. Dixon, with a capacity sufficient to hold 60 pounds of zinc, being 

used for the experiments. The apparatus and furnace have already 

been described and it will therefore suffice to summarize the data. This 

is done in the following very complete tables on a plan identical with 

the preceding.

TABLE 5. Constancy of temperature in the later form of zinc "boiling-point apparatus;

time series.

Date.

Apr. 15, 1884

Apr. 18, 1884

Time.

h. in.

2 15 

26

38

50

53

3 05

10

2 08 

15

20

30

40

50

ft.

0.00 

0.18

0.38

0.58

0.63

0.83

0.92

0.00 

0.12

1.20

0.37

0.53

0.70

No. of 

thermocouple.

18 

18

18

18

18

18

18

18 

18

18

18

18

18

£20.

7980 

8540

9110

9550

9710

9940

10020

9500 

9530

9640

9807

9960

9930

(727

T..

770 

812

852

882

893

910

915

880 

882

890

901

911

909

)

T&.

822 

868

915

952

905

983

990

947 

950

957

971

985

982

Remarks.

Charge 14 pounds.

Charge 20 pounds.

Furnace fired.
74 MEASUREMENT OF HIGH TEMPERATURES.

TABLE 5. Constancy of temperature in the later form of sine loiling-point apparatus;

time series Continued.

Date.

Apr. 18, 1884

Apr. 24, 1884

Apr. 30, 1884

May 12, 1881

Time.

h. m. 

3 00

10

20

30

42

4 00

10

20

30

42

3 33

50

4 00

10

20

30

43

50

5 00

10

22

33

50

55 

6 10

20

31

45 

55

7 05

1 53 

215

26

45

3 15

35

57

4 15

36

5 00

20

35

3 00

20

30-

38

40

45 

50

55

4 10 

30

5 00

15

33

A.

0.87

1.03

1.20

1.37

1.57

1.87

2.03

2.20

2.37

2.57

0.00

0.28

0.45

0.62

0.78

0.95

1.17

1.28

1.45

1.62

1.82

2.00

2.28

2.37 

2.62

2.78

2.97

3.20 

3.37

3.53

0.00 

0.37

0.55

0.87

1.37

1.70

2.07

2.37

2.72

3.12

3.45

3.70

0.00

0.33

0.50

0.63

0.67

0.75 

0.83

0.92

1.17 

1.50

2.00

2.25

2.56

No. of 

thermocouple.

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18 

18

18

18

18

18

18

18 

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18 

18

18

18 

18

18

18

18

eso10020

10110

10130

10080

10320

10480

10510

10500

10390

9910

7571

7990

8230

8570

8870

8930

9100

9120

9130

9130

9140

9130

9180

9190

9240

8530 

8970

9080

9140

9120

9160

9190

9220

9280

9340

9270

9280

7940

8520

8760

8880

8900

8950 

8960

8960

8960

8980

9000

9020

T..

915

920

922

920

935

945

^948

946

939

908

740

772

790

813

835

839

851

852

852

853

854

852

856

857

861

812 

842

850

854

853

856

858

859

864

868

863

864

768

811

828

837

838

842 

843

842

842 

842

844

845

846

m

990

995

998

995

1013

1025

1026

1026

1019

980

787

823

844

872

897

900

914

915

916

916

917

916

921

922

925

870 

905

912

918

915

920

922

924

930

934

930

930

799

868

887

896

900

902 

904

904

904 

904

906

907

908

Eemarks.

Do.

Eetort begins to leak.

Charge 50 pounds.

Furnace fired.

Do.

Do.

Approaching ebullition.

Furnace fired.

Do.

Ebullition.

Furnace fired.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Superheating ; F. fired.

25 pounds distilled.

Charge 50 pounds.

Ebullition.

28 pounds distilled.

Charge large.

Approaching ebullition.

(728)
BARU8.] DEGREE OP CONSTANT TEMPERATURE. 75

TABLE 5. Constancy of temperature in the later form of zinc boiling-point apparatus ;

time series Continued.

Date.

May 19, 1884

May 21, 1884

May 26, 1884

June 9, 1884

June 11, 1884

Time.

h.m.

3 00

15

30

 35

40

4 20

30

5 00

3 25

35

4 00

10

20

30

35

40

5 00

03 

2 25

35

45

3 05

15

35

50

4 20

40 

2 15 

30 

45 

3 05 

15 

19 

20 

25 

30 

40

55

4 10

25

40

55

5 08

25

40

50

3 45 

55 

4 00 

07 

12 

18 

25

h.

0.00

0.25

0.50

0.58

0.67

1.33

1.50

2.00

0.00

0.17

0.58

0.75

0.92

1.08

1.17

1.25

1.58

1.63 

0.00

0.17

0.33

0.67

0.83

1.1?

1.42

1.92

2.25 

0.00 

0.25 

0.50 

0.83 

1.00 

1.07 

1.08 

1.17 

1.25 

1.42

1.67

1.92

2.17

2.42

2.67

2.88

3.17

3.42

3.58

0.00 

0.17 

0.25 

0.37 

0.45 

0.55 

0.67

No. of 

thermocouple.

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18 

22

22

22

22

22

22

22

22

22 

19 

19 

Id 

19 

l'9 

19 

19 

19 

(20) 

(20)

(20)

19

19

19

19

19

19

19

19

19 

19 

19 

19 

19 

19 

19

C20.

8370

8750

8960

9050

9050

9270

9590

0330

7890

8250

8630

9030

9120

9240

9310

9360

9500

9540 

8840

9081

9110

9160

9200

9300

9330

9470

9450

2864

2830

2784

2709

2767

2738

2737

2732

2755

2803

2809

2808

2806

2848

2815

T..

. 800

827

841

847

848

863

885

934

764

790

819

847

853

862

867

870

879

881 

828

845

847

849

852

860

863

874

870 

716 

741 

782 

855 

934 

981 

987 

987

975

960

954

954

944

944

912

950

966

968

970

969

982

970

Tin.

855

885

903

911

911

929

055

1012

814

845

876

910

915

926

932

936

948

951 

890

908

910

915

918

927

930

940

940 

(672) 

(696) 

(735) 

(805) 

(880) 

(925) 

(930) 

930

920

907

901

901

891

891

890

899

913

915

915

915

925

915

Remarks.

Charge large.

Central tube cracks.

Superheating.

Charge large.

Central tube cracks.

Superheating. 

Charge large.

Ebullition.

Crucible explodes. 

Charge large.

(729)
76 MEASUREMENT OF HIGH TEMPERATURES.

TABLE 5. Constancy of temperature in the later form of zinc boiling-point apparatus;

time series Continued.

Date.

June 11, 1884

June 14, 1884

June 21, 1884

June 25, 1884

Time.

A.m. 

35

45

50

58 

5 10

15

OK 

/*>

30

3 23

3 47

d 1 o<f PT 

41

55

5 06

22

3 55

4 15

4 40

4 55

5 06

5 18

h.

0.83

1.00

1.08

1.22 

1.42

1.50 

1.67

1.75

0.00

0.40 

0.00

0.10

0.33

0.52

0.78

0.00

0.33

0.75

1.00

1.18

1.38

No. of 

thermocouple.

19

19

(23)

19 

19

19 

19

19

19

19 

23

23

23

23

23

23

23

23

23

23

23

C20.

2815

2806

2828

2824

2784

2811

2839

2907

2915

2919

2935

2809

2809

2829

2829

2829

2780

21.

970

970

974

972

960

970

970 

999

1002

1002

1004

1010

970

970

974

974

974

960

T n

915

915

920

916

907

914

921 

939

942

943

944

950

914

914

920

920

920

007

Remarks.

In the experiments made on the 15fch aud 18th of April the charges 

were obviously too small. Hence we fail to discern a boiling point in 

the first instance and obtain irregular results in the second, in both of 

which cases the zinc vapor is superheated. In the next series the 

charge of zinc is much increased and the results are regular. The value 

of Tzn is slightly low, a result which may be attributed to various extraneous causes, such as slight corrosion or zincification of the thermocouple, polarization errors in the measuring apparatus, etc. In this, as 

in the following series of experiments of the 30th of April, the temperature of the cold junction, in consequence of its unavoidable proximity 

to the furnace, rises as high as 70°. Otherwise both series are as complete as any we made. The effect of charging the furnace with fresh 

coal does not chill the retorts perceptibly, and the experiments were 

carried to an end without accident. In the series made on the 12th of 

May, as well as in all subsequent series, the cold junction was kept at 

a low temperature (ca. 15°) by submerging it in a current of running 

water. The values for Tzn found are lower than usual. The work done 

both on the 19th of May and on the 21st of May was interrupted by 

breakage of the central tube. There resulted a diminution of the charge 

of zinc, in consequence of leakage, and the thermo-element soon indicated the presence of superheated zinc vapor. No boiling point is discernible. The experiments on the 26th of May were again terminated 

at an early stage of progress by an explosion, due to stoppages in the 

efflux pipe for the zinc vapor. Both the elements No. 18 and No. 22

(730)
HAUL'S.] DEGREE OF CONSTANT TEMPERATURE. 77

were partially destroyed by these accidents, necessitating their replacement by No. 19. The constants and thermo-electrics of the new couple 

being different from the old, it is clear that the subsequent values ibr 

Tm are no longer immediately comparable with the preceding values for 

Tzn . To make them as nearly as possible comparable, however, the following method was pursued : The values for «2o, corresponding to Nos. 

19,20,23, and obtained ou the 2d of February, on the 24th of April, and 

on the 12th, 26th, and 30th of May, were averaged, and this mean value 

was assumed to correspond with the mean values of Tzn given by No. 

18 on the same days, respectively. A glance at the tables below shows 

that on these days one of the series of elements, Nos. 19,20, 23, and one 

of the series of elements, Nos. 17,18, 22, were simultaneously compared. 

From these data the constants of the former set (Nos. 19, 20, 23) and a 

graphic representation were investigated; from this finally we took the 

values of Tza given in Table 5. In this way the break in the results is 

reduced to the least value possible under the circumstances,

It is curious that in the subsequent work we were not able to obtain 

series of results as satisfactorily constant as in the earlier experiments. 

To speculate on the causes for discrepancy is of course futile, and the 

later data subserve no other purpose than that of comparing the thermoelectric behavior of the couples simultaneously calibrated.

INFEEENCES RELATIVE TO LOW PERCENTAGE ALLOYS.

^eduction of data. In view of the insufficient degree of constancy 

observable in the above results as a whole, it is necessary to resort to 

an artifice by which all thermo-electric forces may be referred to a fixed 

interval of temperature, 'T t. For the lower limit of this interval we 

selected 20°, a temperature as near the mean value of t as practicable; 

for the upper limit 930°, the assumed value of the boiling point of zinc. 

Then the reduction to the lower limit has the value

e20 -e=(t-2Q) ^ a+b (£+20) J>; 

and the reduction to the higher limit the value

e930 _e=(930-T) (a+b (93Q+T)).

 The method of correction was therefore a quadratic interpolation by 

which the thermo-electric interval is rectified at each end, and thus reduced to the uniform temperature interval. The constants a and & 

were carefully redetermined in a final calibration, so that the sole remaining difficulty in the equation is the choice of T. Fortunately it is 

only the variations of T with which the above equation is concerned, 

and this may be obtained either by linear reduction of the thermoelectric datum T8 to 930°, or we may calculate the constants for each 

element throughout the interval 0° to 930°, and then use the Tzn so 

obtained. The first method is less accurate than the second without 

being insufficiently accurate. At the same time the first method is so 

much more expeditious that we applied it.

(731)
78 MEASUREMENT OF HIGH TEMPERATURES.

TABLE 6. Values of eao030, approximately, in microvolts.

Date.

February^ 1884.............

Februarys, 1884.............

April 24, 1884....... ..........

April 24, 1884. ................

April 24, .1884....... ..........

April 24, 1884...... ...........

April24,1884.................

A riril 91 I QQX

April 24, 1884.... .............

April 24, 1884.. ...............

April24, 1884. ................

April 24, 1884.. ...............

April 24, 1884. ................

May 12, 1884. .................

May 12, 1884. .................

May 12, 1884...... ............

TWnvlO 1881

May 12, 1884.... .............

May 12, 1884. .................

May 12, 1884...... ............

May 12, 1884...... ............

May 12, 1884... ...............

May 12, 1884..................

May 12, 1884...... ............

May 12, 1884.... ..............

May 19, 1884 .................

TVTdT7 1Q Ififid

May 26, 1884......... ........

May 26, 1884. ................

May 26,1884 .................

TWoTr 9fi 1884.

May 26, 1884.... .............

May26, 1884. ................

May 26, 1884. ................

May 26, 1884. ................

May 26, 1884.. ...............

May 26, 1884.. ...............

May 26, 1884.. ...............

May 26, 1884. ................

May 26, 1884..... ............

May 26, 1884. ................

June 9, 1884. .................

No. of 

thermocouple.

18

18

18

18

18

18

18

17

18

19

18

18

'22

18

23

18

24

18

25

18

26

18

18

22

18

23

23

18

24

ia

25

1 Q

2G

18

18

24

00

19

22

20

00

99

OK

09

26

99

24

99

99

09

19

20

1Q

24

19

e^930.

9160

Q1 KO

9170

9180

9180

9180

9180

9320

91 CO

2816

9160

9100

9220

9100

2827

9120

770

9100

801

9090

2274

9070

O1 30

9280

9130

2830

2834

9130

786

919Q

898

9140

2333

9130

'780

onsn

OBI ft

QflQA

ORfln

9050

QEO

9000

990^

OfldO

817

OflQA

Q199

oAfin

ooon

2850

OQ°|1

791

2830

Date.

June 9, 1884.................

June 9, 1884.................

June 9, 1884.................

June 9,1884.................

June 11, 1884.................

June 11, 1884.................

June 11, 1884.................

June 11, 1884.................

June 11, 1884.................

June 11, 1884.................

Juno 11, 1884.................

June 11, 1884.................

June 11, 1884................

June 11, 1884.. ......... ......

June 11, 1884.................

June 14, 1884................

June 14, 1884.......°..........

June 14, 1884.................

June 14, 1884.................

June 14, 1884.................

June 21, 1884.. ...............

June 21, 1884.................

June 21, 1884.................

June 21, 1884.................

June 21, 1884.................

June 21, 1884.................

June25, 1884.................

June 25, 1884.................

June 25, 1884.................

June 25, 1884.................

Juno 25, 1884.................

June 25, 1884.................

June 25, 1884.................

June 25, 1884.................

June 25, 1884. ................

.Tune 25, 1884........... ......

Juno 25, 1884.................

No. of 

thermocouple

05

10

26

1Q

30

1Q

31

10

34

1Q

33

10,

32

19

32

10

19

22

19

27

19

28

19

29

19

23

19

17

19

18

19

34

33

10

23

34

91

33

23

32

23

23

31

23

30

23

29

23

28

23

27

23

eso930.

01 *

OQOC

2361

2823

7147

2824

3738

9891

5367

2827

4011

2829

1982

2830

1974

2830

2829

9363

2830

2908

2833

5030

2833

6482

2836

2830

2834

9250

2833

9330

2828

2832

5349

OQOO

6762

2835

S291

2834

3951

2835

901 fl

983Q

OOOA

3751

2830

7095

9RQ9

6416

2832

5029

2832

2974

2810

(732)
BAUUS.] DEGEEE OF CONSTANT TEMPERATURE. 79

From this table it is expedient to select the mean values for each 

element, and then to arrange the alloys in a series of the kind described 

on page 80. This has been done in Table 7, where, in addition to e2 o 9 3 °> 

the constants a and &, derived from the last definite calibration, are inserted (microvolts). The interval of calibration for a and 6 is only 0° 

to 400°, as has been stated. Knowing, therefore, e, a, and & we are able 

to compute T6, or the exterpolated value of the zinc boiling point, to 

which special reference will presently be made. The figures for e in 

parenthesis will be referred to in Chapter II.

TABLE 7. General summary of results.

Series 

No.

f

I.

I

H

(

"i

"1

f

v.

No.

17

18

19

20

22

23

24

25

26

27

28

29

30

31

32

33

34

Description of element.

Pt (h); Pt-Ir, 20%; annealed.

......do .......................

Pfc (h); Pt-Ir, 5%; annealed

......do.......................

Pt (h); Pt-Ir, 20%; annealed

Pt (h); Pt-Ir, 5%; .annealed

Pt (h); Pt-Ir, 2% ; annealed ..

Pt(s); PtPd, 3%; annealed..

Pt (s); Pt Pd, 10% ; annealed. .

Pt-Ir, 5%; Pt-Ir, 10%; annealed.

Pt-Ir, 5%; Pt-Ir, 15%; annealed.

Pt-Ir, 5%; Pt-Ir, 20%; annealed.

Pt (com.); Pt(com)-Ni, 5%; 

annealed.

Pt (com.); Pt(com)-Ni, 2%;

annealed.

Pt (com.); Pt(com.)-Ir, 3%;

annealed.

Pt (com.); Pt(com.)-Ir, 5%; 

annealed.

Pt com.); Pt(com.)-Ir, 7%;

annealed.

How, where, or by 

whom made.

Paris metallurgists..

....do................

....do................

....do................

....do................

....do................

Pt-Ir 5% fused into

Pt (s) in proper

ratio, at Lab., OHs

blast.

f Pd alloyed to Pt (s),

< at Lab., OHn blast.

] Pt Ir 596 and Pt

Ir 20% wires 

S fused together in

proper ratio, at 

j Lab., OHj blast.

1 Ni alloyed to Pt

, (com.), at Lab., 

I OHs blast.

Ir (com.) alloyed to 

J- Pt (com.), at Lab.,

OHs blow-pipe.

J '

Mean e.

c (9412) 

( 9235

r (9345)

( 9160

r (2861)

< 2823

c (2869)

I 2827

r (9453)

I 9230

r 2829

i (2885)

791

c 982

t 2297

2941

5030

6449

!

7121

3744

1998

3981

5336

a.

| 7. 00

I 7.00

C > Q O. (V7 Ul

i { O» 3 \I*J n^

( ? " It fin UU

J<2.97)

>

1.88

0.287

0.975

2.36

3.89

4.51

8.43

4.56

1.98

3.64

4.70

b.

-f 0. 00390

' 00385

-0. 00010

 0.00009

j A nnono T"u. UUOtfO

(+0. 00047)

 0. 00150

+0. 00119

-f 0. 00273

+0. 00152

+0. 00268

-f 0.00398

+0. 00050

+0. 00005

+0. 00052

+0. 00147

+0. 00207

Tt.

861

QC7 OOf

966

Q73 5MO

856

OTA otv

(*)

' 797

760

826

834

835

825

833

844

833

842

* Imaginary.

Series of alloys. Having reached this stage of the inquiry, we are 

prepared, so far as the set of data at present in hand go, to bring the 

considerations back to the probable properties of the zero elements,

(733)
80 MEASUREMENT OF HIGH TEMPERATURES.

platinum-platinum, when these elements are regarded as the limiting 

cases into which any series of thermo-couples of platinum alloys must 

ultimately converge. A series of couples such as is here understood 

has already been defined. In each member of such a series pure platinum is thermo-electrically combined with an alloy of platinum and a 

second metal, and the amount of the latter metallic ingredient decreases 

from alloy to alloy of the series as far as zero.

Having given a number of thermo-couples, A, B, C. D . . . , let the 

cold junction all be kept at the same constant temperature, t. In 

like manner let the hot junctions be exposed together to a second temperature, which, however, is made to vary continuously from a comparatively low value to as high a value as may be admissible. Then 

will a comparison of corresponding values of electro-motive force indicate in how far the variation .of the latter with temperature may be regarded as uniformly continuous. Thermo-electric anomalies, such, for 

instance, as are presented by iron, nickel, probably by some platinumiridium alloys, and by all metals at sufficiently high temperatures, are 

thus detected and located. In practice it is convenient to compare the 

thermo-couples in pairs j and like exposure of the hot junction is facilitated by melting them to a common spherule with the oxyhydrogen 

blow-pipe. A tube may be placed in Fletcher's organic combustionfurnace or in an anthracite blast-furnace and the insulated therino-elements heated within it, with their common junction near the center of 

the tube. All wires so compared are supposed, of course, to be homogeneous throughout their length.

TABLE 8. Equivalent thermo-electriupowers.

rt, Pt it- 20%.

No. 14.

810

1350

4290

4370

4770

5700

6140

7970

8370

T 

Pd, Pt It2096. 

No. 15.

1470

2510

8380

8600

9470

11610

12330

17210

18360

850°

Pt, Pt Ir

20%. 

No. 14.

810

1350

2250

4280

5690

7018

7680

T =

Pt, Pd. 

No. 13.

680

1150

1990

4200

5970

7860

8830

800°

Pt, Pt If

20%. 

No. 14.

810

1350

2706

3130

4640

6990

7750

T =

Pt, Ni. 

No. 12.

1830

2990

5120

5590

7000

9450

10210

800°

Pt, Ptlr 

20%. 

No. 14.

2900

8430

8470

8570

9030

9550

13190

1'==

i<

Pt.Ptlr

5%. 

No. 19.

]028

2605

2610

2500

2660

.2720

3090

1200°

At the end of this table the approximate value of the temperature 

reached in each of these comparisons is given. The values of electromotive forces in this table (No. 14 being the couple common to all) 

show that the variations are practically uniform, so far as the comparisons go. The table supplies an experimental test, which corresponds

(734)
DEGREE OF CONSTANT TEMPERATURE. 81

very closely to the mathematical examination of a function for continuity.

If any equation between electromotive force and temperature, such 

a one, for instance, as e=a(T t)+b(T2 t2 ), were rigidly true for all 

ranges of temperature, T, then our methods would enable us to calculate 

the constants a and b from measurements of e, T, t, made at temperatures not exceeding the boiling point of mercury, with a degree of 

accuracy which would introduce a perceptible error only at very much 

higher temperatures. If the thermo-electric equation hold, in other 

words, the calibration of a thermo-couple throughout an interval of temperature within which a glass-bulb air-thermometer is quite available, 

would enable us satisfactorily to measure temperatures lying in the 

regions of white heat. But such extrapolation is unwarranted because 

we possess no known criterion for the temperature above which the 

assumed equation appreciably fails.

In our original endeavor to surmount this difficulty we ventured to 

reason as follows: Suppose there be given a series of therino couples of 

the kind specified, in all of which platinum is the electro-positive metal 

and the platinum alloy the negative metal. In such a series the constants a and b both vanish with the amount of foreign metal alloyed to 

platinum. Hence the relation between electro-motive force and temperature is ultimately linear, and, a fortiori, within the limits prescribed by 

the foregoing paragraph, the assumed equation will apply more accurately as the couple approaches the final couple platinum-platinum, 

from which the foreign metal has been wholly eliminated. If the quadratic equation (1) is more than an empirical relation, it would be practically sufficient at an earlier stage of progress; i. e., it would be practically sufficient for couples lying between platinum-platinum and a 

couple the electro-negative part of which contains a certain determinate 

addition of the foreign metal of the series under consideration. To 

illustrate the manner of nsing such a principle, let a series of couples 

whose constants are known from a calibration between 0° and 350° be 

in hand; and then let a given fixed temperature (the boiling point of 

zinc for instance) be determined by each of them. There will be as 

many values for boiling point as elements. If we regard these as functions of the respective quantities of foreign metal in the negative parts 

of the couples, and if we represent the calculated boiling points as ordinates, and the percentage compositions of the alloys as abscissae, we 

obtain a locus the nature of which may be sufficiently obvious to enable 

us to prolong it as far as the axis Y. The point of intersection, therefore, approaches very closely to the datum of the hypothetical element 

platinum-platinum.

If the effect of alloying metals were merely that of joining them in 

multiple arc, the interest which belongs to the problem in hand would 

at once vanish.

For if ei and e2 be the electromotive forces of two wires theraio eleo 

Bull. 54 Q (735)
82 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

trically combined with platinum, and if w: and wz be the resistances of 

these wires, then

1+1*

where e is the equivalent electro-motive force. Hence if r=w\

which may be abbreviated

From this it follows that

If in this equation «?2 =ao> which supposes this metal to vanish from 

the alloy, and if additionally a^ and &i be made equal to zero, we arrive 

at an expression of T in terms of -£. This result shows that however *» 

near we may approach the limit couple platinum-platinum, any thermal 

datum derived by thermo-electric means will none the less be dependent on the properties of the metal combined in multiple arc with platinum.

In the case, however, of metals alloyed, the results are quite different; 

for here the thermo-electrics of the alloy bear no intelligible or general 

relation to the ingredient metals of the alloy, so far as our present knowledge goes. Indeed it is not infrequent to find the admixture of an 

electro-negative ingredient produce, a distinctly electro-positive result.

And hence it follows that constants referring to the final or infinitely 

dilute alloy have a special and unique significance. In the final alloy 

we have one metal combined by fusion with another in such a way 

as to produce absolutely no variation of molecular arrangement. If, 

therefore, data.for the limit couple be investigated, they are those from 

which a clue respecting the dependence of the thermo-electrics of the 

compound upon those of its constituents may most probably be obtained. 

Table 7 shows the sensitiveness of couples to be frequently such that 

the final element platinum-platinum may be approached very near, and it 

is for this purpose largely that the table was drawn up. With the object 

of basing the discussion on electric data exclusively, the constant a , 

may be taken as a symbol of the composition of the alloy-component of \ 

the thermo-couples of a given series; and hence the curves or loci here 

in question are obtained by representing any fixed datum (for instance 

the value of the boiling point of zinc which obtains for the special couple 

under consideration) as a function of a. We have attempted this with

(736)
BAKUS.] DEGEEE OF CONSTANT TEMPERATURE. 83

the data in hand, but they are not yet in sufficient number to give any 

definite hints as to the nature of the relations sought. It is necessary, 

moreover, to confine such work to data obtained from scrupulously pure 

platinum and from scrupulously pure alloys conditions which in case 

of the data of Table 7 are not vouched for. Indeed the table gives evidence of the varied character and purity of platinum derived from different sources and shows a widely different electrical behavior of nominally the same alloys.

There is one respect, however, in which the data of Table 7 are crucial. 

They show that extrapolations based on the equations of Avenarius and 

of Tait lead to very different high temperature results. They, therefore, 

prove that these equations are insufficient, and point out the probable 

tendency toward an anomalous.thermo-electric behavior, to allotropic 

modification and polymerization even in the most stable alloys.1 Herefroin it follows that the pyroraetric value of any alloy can only -be determined by a minute thermo-electric survey made by aid of the air-thermometer, throughout the whole range of variation of thermo-electromotive force and temperature.

Intimately connected with the present discussion are questions relating to the relative variations of a, &, or even higher constants of the 

thermo-electric formula. Tidblom (1. c.) has endeavored to throw light 

on this subject, not without success. If a and b vanish at the same rate, 

then the data of the limit couple are as truly intrinsic, i. e., as fully dependent on the metals of the series to which the couple belongs, as any 

other. But if 1) vanish at a rate which is relatively very yapid as regards a, then the thermo-electric, equation becomes ultimately linear. 

Extrapolations made by aid of the limit couple will therefore be more

justifiable in proportion as the fraction tends toward5 zero.

a

1 Cf. Le Cbatelier, loc. cifc. Our own.results (see Table 6) were completed in 1884, 

but in consequence of delays in moving the laboratory, publication was delayed (see 

Preface).

(737)
CHAPTER II.

THE CALIBRATION OF ELECTRICAL PYROMETERS BY THE AID 

OF FIXED THERMAL DATA.

EXPLANATION.

Iii the apparatus described in the foregoing chapter, great masses of 

metal were kept at the boiling point. The advantages gained from a 

brisk but perfectly free circulation of vapor, particularly in the case 

where the vapor is of small specific heat, have already been pointed 

out. It is to the use of large apparatus that Messrs. Deville and Troost 

had been led before us. In their experiments, however, the direct use 

of the air-thermometer made a boiler of considerable size essential from 

the outset.

Large and expensive apparatus, whatever be their special advantages, 

can never enjoy extensive use in the general laboratory. It is therefore the object of the present chapter to describe special forms of apparatus by which calibrations of thermo-elements may be quickly and safely 

made, and by which the problem of thermo-electric temperature measurement may be reduced to an ordinary laboratory experiment.1 The degree of error to which the observer is liable, the degree of constant temperature attained, the selection of substances having convenient boiling 

points, and finally the application of the apparatus to a variety of substances for boiling-point measurement will constitute the chief topics of

this chapter. The boiling-point apparatus must of course be such that 

ebullition may be kept up indefinitely.

APPARATUS FOR LOW BOILING POINTS (100° TO 500°).

Original forms of boiling-point tube. The original forms of boilingpoint apparatus for mercury, for sulphur, and for aniline, water, etc., 

are given in Figs.-7, 8, 9, drawn to a scale of £. They are all constructed 

on essentially the same principle, slight modifications being introduced 

to meet each case. The apparatus, Fig. 7, consists of an ordinary glass 

lamp chimney, aaac^ inverted as shown, and closed at its lower end by 

a plaster of Paris plug, &i, surrounded by a wrought-iron cap, cc. The 

cap cc is larger than the glass, and by pouring in the plaster in the 

moist condition and allowing it to set, the tube is firmly secured between

1 Siuce the completion of the work of the present chapter, M. Le Chatelier has made 

pyrometric experiments with ends in view similar to those here proposed. (Of. p. 50.) 

84 (738)
FIG. 7. FIG. 9.

r

a

I 1

P

'P

77^ 

'C

&

J

h

%

\

p^ ^

: V \

.: ;

; ;

r

'a,

CL>

771,

HsO

FIGS. 7, 8, and 9. Original forms of boiling-point tube, horizontal section. Scale, \.
BAUUB.I CALIBEATION OF ELECTRICAL PYROMETERS. 85

the body of plaster witbin and a layer of plaster braced against the 

iron cap without. The cap ec carries an iron tube, dd, closed above 

but open below, and occupying a central or axial position with respect 

to the glass tube, into which it projects about two inches clear. The 

top of the lamp-chirnney is closed by a suitable cork, ee, doubly perforated, through the central hole of which is inserted a wide glass tube, 

hi, partially closed above by a loosely fitting stopper. Through the 

other perforation passes a glass tube,/#, by aid of which some gas (N2 , 

CO2 ) may be introduced. The glass aaaa is partially filled with the 

substance whose boiling point is to be used (in the present instance 

mercury), only enough being poured in to submerge the central tube dd 

with the exception of about 0.5cm of its head. To keep the metal in 

ebullition, use is made of Dr. Wolcott Gibbs's ring-burner,1 rr, the flame 

of which is properly regulated. Very thin copper or brass gauze, or 

copper-foil, m w, surrounding the part of the glass tube encircled by the 

ring-burner, is sufficient to almost completely obviate the dangers of 

breakage; and a circular screen of thick asbestos, nn, bent in the shape 

of an inverted cone protects the top of the tube dd from direct radia- 

' tion. Above nn it is well to surround the tube aaaa with a thick jacket 

of asbestos, pppp, extending as far down as may be without shutting 

the surface of boiling mercury entirely out from view. The mercury 

which condenses on the sides of the tube falls back in small drops into 

the mass Iclc below. The process is therefore continuous.

The properly insulated thermo-couple is introduced into d d from below, and the hot junction is pushed forward quite as far as the top»of 

the tube d d and slightly above the surrounding surface of mercury. A 

screen may be fastened a little below the cap c c to shut off all radiation 

from the cold junction, which is submerged in oil.

The apparatus for sulphur in Fig. 8 differs from that in Fig. 7 only 

in that the wide central tube li h i i has within it a second glass tube, 

q t, partially closed above with a cork. This second tube whenever the 

passage below is stopped up by the distillation of sulphur may be at 

once removed and a similar clear tube inserted. A slow current of dry carbonic acid gas entering at g passes through the apparatus during ebullition. Subsequent experiments showed that with suitable changes in 

the apparatus the tube h li i i as well as gas current could be dispensed 

with. This will be referred to again below. The sulphur condenses on 

the sides of the tubes and by far the greater part runs back into the 

mass Tt k below. There is a line of dernarkation encircling the tube 

where the temperature is the melting point of sulphur.

For liquids with a boiling point below that of mercury and sufficiently 

low not to char a cork, the boiling tube may be considerably simplified 

in the way shown in Fig. 9. Here both ends of the lamp-chimney are 

closed with a cork centrally perforated to admit a long glass tube, d d,

1 The Gibbs ring-burners were introduced into this laboratory by Drs. Goocli and 

Chatavd, and have siuce become invaluable.

(739)
86 MEASUKEMENT OF HIGH TEMPEKATURES. [BULL. 54.

extending quite through the tube a a a a and open at both ends. The 

tube d d is wide enough to admit a mercury thermometer at its upper 

end, held in place by a cork, #, secured by an end of rubber tubing.' 

The lateral tube of the upper cork e e is here somewhat wide and long, 

its object being to allow of the escape of vapor, should this be necessary. By suitably regulating the flame of the ring-burner, however, 

the heat applied may easily be made such that the vapor condenses 

near the middle of the tube/# and returns to the liquid below. Thus 

the process is again continuous. A sharp line of demarkation around 

the tube fg shows the part of it where the temperature is just low 

enough for the condensation of the liquid used.

Many experiments were made with each of these three forms of apparatus, the results of which will be more appropriately given below in 

connection with other similar experiments.

Perfected form of boiling tube, The three forms of apparatus for low 

temperature just described, each of which contains certain special desiderata, can be combined into a single form adapted to the divers cases 

specified. This final form is given in Fig. 10, scale £. The glass parts were 

made for me by Messrs. Whitall, Tatum &' Co., in Philadelphia. Special 

care is of course to be taken to have the tubes well annealed. As the 

lettering of Fig. 10 is identical with that of Figs. 7 to 9, only a few additional words of explanation are necessary. The tube a a a a is completely 

closed above by the cork ee, and communication with the atmosphere is 

effected by the bent glass tube li i, ending in a little vessel, #, open below 

and filled with asbestos wool. The tube g is a filter, catching noxious 

mercurial fumes should any such escape. It also impedes entrance of 

air when the boiling tube is filled with some other gas. The central 

tube d d is closed, of course, either with a perforated cork carrying a 

mercury thermometer, or at higher temperatures with asbestos wicking

pushed downward into the tube almost as far as the point o of the thermocouple. The position of the thermo-couple o a and o /? is pretty well 

represented, the two wires being held apart by a doubly perforated insulator, o y, of porcelain or of fire-clay. The clamp attached to the lower 

end of the tube d, which holds the insulator o y in position, is easily imagined, and is therefore omitted in the figure. When the screen n n fits 

snugly it remains in place of its own accord, or it may be wired to 

the gauze covering TO m. The boiling-tube a a and the burner r r«being 

each supported by an ordinary retort holder with universal clamps, are 

easily adjustable at pleasure.

In the case of substances which are spontaneously inflammable at 

their boiling points, like sulphur, the oxygen of the tube is so soon exhausted that ebullition takes place without interruption. Hence the 

introduction of special gases like JST2 or CO2 is rarely necessary; a great 

advantage, inasmuch as the introduction of gas, no matter how slowly 

or how regularly, always interferes with the constancy of temperature. 

In case of mercury, however, the metal must be renewed from time to

(7-10)
1UUU8.1 CALIBRATION OF ELECTRICAL PYROMETERS. 87

time, otherwise the ebullition, which is regular in the case of pure 

metal, becomes irregular and bumping when it holds perceptible quantities of oxide in solution, or when such adhere to the glass. Solids 

may be either melted and poured into the tube from above, or they may

FIG. 10. Perfected form of boiling-tube. Scalr,

FIG. lOos. Boiling-point tube 

for annealing loiig wires. 

Scale, !\y.

be introduced as powders and then cautiously melted. In case of organic solids heat must be applied very gradually to prevent charring 

or gumming, until the whole mass is liquefied. Usually the substance 

may be left to cool and solidity in the tube without incurring liability 

to breakage, a special tube being set apart for each boiling-point substance.

(741)
88 MEASUREMENT OF HIGH TEMPERATURES. [HULL. 54.

If the thermo-element is removed and the lower end of the tube d d 

is prolonged downward by fastening on to it with a piece of rubber 

hose a similar glass tube, t, Fig. 10, closed below, these boiling tubes are 

obviously well adapted for annealing long wires of steel or metal, for 

magnetic or other purposes. Such wires are drawn regularly through 

the hot zone by clock-work; 1 a drum, (7, taking the place ot the hour 

hand, from which drum the wires to be annealed are suspended by a very 

fine copper wire, w. This method I have frequently used with success.

Boiling-point tubes for pressure icorlt. When it is desirable to boil 

substances under pressure greater or less than one atmosphere, a form

FIG. 11. Boiling-point tube for 

pressure work. Scale, J.

FIG. lla. Boiling-tube for pressure 

 work, -with accessories. Scale, &.

1 Cf. Am. Jonr. Sci., 3d series,'vol. 32, 1886, p. 279. 

(742)
1URUS.] CALIBRATION OF ELECTRICAL PYROMETERS. 89

of tube shown in Fig. 11 is convenient. This differs from the other 

forms only inasmuch as the outer tube a a is closed upon the central 

tube d d both above and below. A special lateral tubulure, *, commaincatmg with a mauometric arrangement subserves the purpose of varying the pressure by any amount compatible with the strength of the 

tubes. It is also through h that the substance to be boiled is intro. 

duced. It is by means of this arrangement, that I purpose to study the 

relation between boiling point and pressure over long ranges, and 

for mercury, sulphur, and divers other substances. The thermo-element for such purpose must be calibrated with the re-entrant glass airthermometer described in Chapter IV.

Tubes of this kind I obtained from M. Emil Greiner, of Nassau street, 

X ew-York. Glass of a specially hard quality is made by Appert freres, 

Uichy, France. Inasmuch as M. Troost was able to boil selenium in 

this material with impunity, the upper thermal limit of the glass boiling tube may be considered given by the boiling point of selenium, 

lubes ot the kind here described for investigating the boiling-point 

pressure functionality are the simplest and at the same time the most

o

FIG. 11. Riujr.iHH-mu.. Sc.ale, J. 

(743)
90 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

accurate forms yet devised. The completed adjustment is well shown 

in Fig. lla, where B is the boiling tube, R the ring burner, A the oil 

bath for the cold junction of the thermo-couple, E the thermometer of 

the cold junction. The central tube is closed by a piece of asbestos 

wicking, as shown. Communication with the air-pump takes place 

through C. Mr. Greiner has since succeeded in inserting a second 

tubulure in, the top of the boiling tube, Fig. 11, through which a mercury thermometer may be inserted, thus affording additional means of 

thermal comparison.

Dr. Gibbs's ring-burner. A final reference is to be made to the ringburner. This is shown diagratnmatically about one-half full size in Fig. 

12. The burner proper, a b c, is a circularly ben t tube of brass or iron, on 

the inner side of which about forty radially disposed holes, each about 

O.lcm in diameter, have been drilled. The straight tube cf connects the 

ring with the injector, the tube d e admitting of the influx of gas, the 

tube/o of the injection of air. Both the tubes d e and/o are provided 

with stop-cocks. Where only moderate intensity of flame is desirable 

gas may be passed in at/and the tube deleft open. Either of the 

tubes de or cf is available for clamping the burner in the ring stand. 

In the general case where a blast is necessary Professor Richards' 

pneumatic injector is most easily applicable. The pump which can be 

used equally well either for slight compressions or for exhaustions is 

now in such general laboratory use that special description is unnecessary.

It is probable that for special purposes boiling tubes of larger diameter will be preferable, but such tubes are more fragile and the manipulation is of necessity less expeditious.

APPARATUS FOR HIGH BOILING POINTS.

Original forms of boiling crucible, The tubes just described are no 

longer convenient when the boiling point of the substance exceeds low 

redness. In such a case bellows have to be used for injecting air and 

the glass tube itself, becoming more and more viscous, yields gradually 

to the charge of metal it contains. Hence for high temperatures it is 

necessary to replace the glass tube by crucibles of fire-clay or of porcelain. In Fig. 13 I have given the original form of an apparatus of this 

kind. It consists essentially of two French crucibles, a a a a and bbbb, 

put together on the flat open end, which it is well to grind smooth. 

Both crucibles are perforated. A porcelain tube, d d, has been cemented into the lower crucible with asbestos cement. This tube, 

closed above, open below, and glazed exteriorly, is to contain the thermoelement. Through the tube g h above, some reducing gas, notably 

hydrogen, may be introduced, the tube g li being either glass or porcelain. The lower crucible is partially filled by the metal or other; substance, fcfc, whose boiling point is to be used, care being taken to in-

(744)
CALIBRATION OF ELECTRICAL PYROMETERS. 91

troduce no more than is just necessary to cover the central tube &d. 

The lower crucible is surrounded by a furnace, FFFF, made of'the 

same non-conducting- mixture which is used in Fletcher's small injector 

furnace. Heat is communicated by means of the injector blow-pipe A 

B (7, gas entering at the tube G, air at E. Both C and E are provided 

with stop-cocks. The products of combustion escape at D. The cruFIG. 13. Original form of boiling crucible. Scale, \.

cible a a a a has been fitted into the bottom of FF, through which the 

central tube dd projects. All cracks and crevices are closed up with 

carded asbestos. Ju this way .the space below the furnace remains 

practically cold and the therino-element may be inserted or withdrawn 

with great convenience. A few screens protect the cold junction from, 

radiation altogether.

Perfected forms of boiling-point crucible. This double crucible apparatus, behaves excellently until the extreme white heats are reached, after 

which the porcelain and the cement become viscous, and leakage and 

failure of the experiment is the invariable result. Moreover, the influx

(745)
92 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

of cold hydrogen is not unobjectionable, and it is probable that by using 

closed forms H2 may be dispensed with. I was fortunate, therefore, in 

obtaining crucibles of fire-clay from Messrs. Hall & Son, made in such 

a way that both crucible and central tube are one single piece. A 

crucible of this kind is shown in place in Fig. 14, in which the parts 

have been numbered similarly to Fig. 13. A conical shape is here given

 S//////////////////////A. Y///////////7///77////////////7/A

FIG. 14. Perfected form of boiling-point crucible. Scale, J.

to the crucible, with the object of decreasing the essential charge of 

zinc and of thereby expediting the boiling. The furnace-body FJ?anCi 

lid jF I" are both properly bound with iron, as shown at mm, mm, mm, 

and the body rests on a bed-plate of iron, z z, provided with a hole 

through which the botttom of the crucible a a partly projects. Z Z 

is raised on rather tall legs, allowing the operator to manipulate the. 

therino-elements from below. The crucible projects above the furnace, 

and the lid b b is shouldered. A battery of three or four of these fur-

(746)
BARUS.] CALIBRATION OF ELECTRICAL PYROMETERS. 93

naces may be placed on the same bed-plate, in a row. Each furnace is 

provided with its own burner, all of which are fed from the same bellows 

and the same gas-supply (see frontispiece under D). It is best for this 

purpose to attach the bellows (Fletcher's pattern) to an engine, ou a 

very short crank. The pressure of air may then be regulated by increasing the length of the crank. Burners constructed on the plan 

described at length below (page 183), only on a smaller scale, are preferable. They do not explode back. For very high temperatures two 

and even three such burners may be made to impinge on the same 

crucible. For cadmium or zinc a single burner is more than sufficient. 

At high temperatures the efflux hole D may be partially closed with 

asbestos. The products of combustion escape uniformly ou all sides 

around the plane where the furnace-body and furnace-lid meet. A ring 

of asbestos, placed around the crucible to protect it from the flame of 

the burner, is soon fluxed down upon it, and is apt tc destroy the crucible. A ring of baked fire-clay, however, is good.

The crucible shown in Fig. 14a is intended for work in which the 

variations of boiling point and pressure are to be investigated. It is 

made of refractory porcelain and glazed within. The lid cab fits pre.tty 

snugly into the crucible efd, so that the two may be sealed hermetically 

at the joint c d by sodium tungstate (Gooch) or other material. The 

tube at a is in connection with the air-pump. Such cr.icibles are available for the ebullition of salts of selenium, cadmium, zinc, and probably 

antimony and bismuth in vacuum. Being made of porcelain they can 

be more elegantly shaped than fire-clay crucibles, but they become seriously viscous at a lower temperature.

A second form of boiling crucible is shown in Fig. 15. It differs from 

Fig. 14 only in this respect,'that the central tube d <?, which in Fig. 14 

is closed just below the surface of the boiling metal, in Fig. 15 extends 

quite through the crucible and out of the top. The latter form has the 

advantage that the degree of constancy of temperature along the length 

of the tube may be explored by inserting an insulated thermo-element. 

The part of this tube above the surface of ebullition is closed during the 

measurement with a fire clay plug, and at the top with asbestos wicking. The form shown in Fig. 15 may also be used for annealing wires 

at definite high temperatures, by drawing them through the zone of 

ebullition by clock-work (cf. Fig. 10a). This form has therefore many 

decided advantages over that in Fig. 14, with the one serious disadvantage of being much more fragile. Fortunately it appears from the data 

below, that the more practical form, Fig. 14, is quite reliable as regards 

accurate value of the boiling points attained.

In all cases the substance to be boiled, Ic Ic, must surround the tubes 

d d below the plane of the burners, even more than has been shown in 

Fig. 14. When this is the case no part of the tube d d will be at a temperature higher than the boiling point of k If, a desideratum.

In case of Zn, Cd, and other metals the crucible must be glazed in-

(747)
.'vT^-

MEASUEEMENT OF HIGH TEMPERATURES. [BULL. 54.

ternally either with borax, or with silicate of soda or with some fusible porcelain glazing, otherwise the vapors at once permeate the central 

tube d d and corrode the thermo-element within. The presence of 

vapor may be discovered by inserting a porcelain pipe-stem into d d

FIG. 14a. Boilihfj-poiiit crucible, 

for pressure work. Scale, |.

FIB. 15. Boiling-point crucible, open tube. Scale, J.

and rapidly withdrawing it. Metallic vapor, if present, usually coats 

the white stick with a black metallic covering, which rapidly oxidizes. 

Bi, Sb, Sn, Pb, etc., glaze the interior of the crucible in virtue of the 

fluxing power of their oxides. This corrosive action eventually becomes 

sufficiently active to eat its way through the central tube and discharge 

the contents through the bottom.

A single crucible seldom will stand more than one ebullition, but a 

single ebullition may be prolonged many hours. It a zinc crucible be 

broken open when cold the walls are found to be covered with a coat-

(748)
BABUS.) CALIBRATION OF ELECTRICAL PYROMETERS. .95

ing of metal consisting of solidified drops of zinc, which were distilled.

""* recondensed, and ran back again down the sides. In the same way the 

central tube is kept covered with a coating of zinc. Zinc dust escapes 

at the joint between lid and crucible, and eventually melts, forming an 

impervious joint. Zinc dust also escapes where the hydrogen tube 

enters the lid. In case of zinc and cadmium, this is an excellent criterion of ebullition. In all cases the burners are to be shut off until the 

escape of metallic dust at li is only just apparent. Metals like Sb, Bi, 

have no such boiling-point criteria, and whether or not the metal has 

boiled becomes a matter of conjecture. Tin charges slag so heavily that 

the metal is soon jacketed with a thick viscous coat and the state of

;. the metal under it can not be known. 1

INSULATORS.

A very essential part of the thermoelement is the insulator, The

device which after very many trials I finally adopted therefore deserves careful description here. These insulators are thin stems (0.45cin 

in diameter, or larger), containing two parallel canals, as far apart 

(0.20cm ). as possible, and about O.l cm in diameter each. In order that 

these stems may be of value,'they must be made in a way which affords 

' a perfect guaranty that throughout the length of the insulator the 

canals nowhere coalesce. The following machine, Figs. 1C, 17, by aid 

of which insulators of almost any diameter and with any number of 

 holes or canals may be made in lengths of 25cm to 30cm or more, gives 

( full warrant to this assumption. The tubes are simply pressed a,fter 

\ the well-known manner used in the manufacture of lead pipe.

In Fig. 16 (scale J) A B is a thick scantling of wood, fastened vertically, to which a short cross-scantling, G, is firmly braced by bolting two boards, shaped as in the figure laterally against both A B 

and B G. B G carries a barrel of strong gas-pipe, a a a a, out of 

which the porcelain is to be pressed. To secure a a a a the piece G has 

been cut apart in the middle parallel to the plane of the paper, and the 

hole for the barrel is somewhat scant. Eence when the two halves of G 

are drawn together by a couple of strong bolts the barrel is almost immovably fixed. The barrel is surmounted by a cap, c c, through which 

passes a piston or plunger, de, which can be moved up and down by 

the handle//; in the way which the figure readily shows. The lower 

end of the barrel is closed by the die-cap h h. A lateral hole, ft, allows 

j of the introduction of porcelain or fire-clay slip until the barrel is quite 

/ filled. Downward motion of the plunger forces the slip through the

1 Experiments since made with the crucibles, Fig. I4a, showed that the vacuum 

boiling point of Bi is easily reached. To get a tight joint at e d, the space between 

lid and crucible is first calked with fibrous asbestos. A ring of fusible metal is then 

, poured upon it. This melts at high temperatures; but when the joint is well made, 

it is not forced through into.the crucible.- In future experiments I purpose to have 

the whole crucible made in a single piece. Cf. Preface.

(749)
96 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

die, the construction of which is as follows: A narrow but strong arch1 

of brass, i i, carries two steel needles, n, which project symmetrically 

into and through the brass tube h It is obvious that the slip, on being 

forced around the arch and needles, issues from the tube A; as a biperlorated tube, the dimensions of which, either as to external diameter or 

diameter of canals, depends solely on the thickness of the needles and 

width of the tube It selected, and can therefore be varied at pleasure. 

It is also obvious that the number of canals is immaterial so far as the 

application of method is concerned. Fig. 17 (scale ^) gives the die for 

making the fine porcelain tubing used in the crucibles, Fig. 13, above.

FIG. 17. Die for porcelain tubes. Scale, {.

When the slip is of proper consistency the tubes issue from the die 

in a single length so long as the pressure of the plunger continues. 

Tubes longer than a foot, however, break by their own weight if suspended wet. Hence it is desirable to cut them off by a thin rectangular 

pine board of about 1 foot in length, held with its long edges nearly 

vertical and its plane also slightly oblique to the vertical. A great 

number of consecutive lengths of 1 foot may be laid side by side in 

this way, like the bars of a gridiron, and then allowed to dry on the 

board before firing. Insulators of porcelain are smooth and compact, 

but they become viscous and are even apt to fuse at higher temperatures. 

Under these circumstances they not only stick to the central tubes of

1 The brass arch, i i, to hold the pins n, was suggested to me by Doctor Hallock, 

In my original apparatus the ping were fastened to the plunger,

(750)
FIG. 1C. Machine for pressing porcelain insulators. Scale
BAKU8.] CALIBRATION OF ELECTRICAL PYROMETERS. 97

the crucibles (Figs. 13,14,15), but they become electrically conducting 

and are objectionable. Insulators of tire clay are therefore preferable, 

inasmuch as they are at least as refractorj7 as the crucibles, and Messrs. 

Hall & Sons, of Buffalo, to whom I sent the above machine, succeeded 

excellently in making them. Work with fire-clay calls for great experience and skilled manipulation, and it is therefore best to put this work 

into trained hands. The Buffalo insulators are 25cm to 30cm long. I 

received two sizes, the larger of which is 0.65cm thick and the smaller 

only 0.45cm thick. The capillary canals in both cases are slightly less 

than O.lcm in diameter. The rods are hard and firm and withstand considerable usage.

METHOD OF MEASUREMENT.

Thermo-element. A zero method of measurement has been used 

throughout. All results for thermo-electric force are referred to the

Latimer-Clarke, and other standards. This has the advantage of not 

requiring an iron-free observatory for magnetic work, a desideratum, 

with which I, for instance, had to dispense. The thermo electric use of 

the zero method was first introduced by Kohlrausch and Ammann.1 

Dr. Strouhal and I introduced certain improvements by which this 

method can be made to yield results of exceptionally great accuracy. 

These improvements have been described in Bulletin No. 14, U..S. Geol. 

Survey, p. 34, but in the interest of completeness it is desirable to recapitulate the chief features of this method here, also to make comparisons of the electromotive force of the hydroelectric standards.

FIG. 18. Disposition of thermo-electric apparatus. FIG. 19. Double key.

In Fig. 18 a diagram of the connections as actually made with some 

view to the practical disposition of apparatus is given. In this figure 

E Rl are rheostats with 1 to 50,000 ohms available, r a bridge rheostat with pairs of units 0.1, 1,10,100,1,000, and 10,000 ohms available. 

A and B are commutators, IT and G keys. The terminals of the thermocouple communicate respectively with the points PI and P2 . Tin's is

1 Kohlrausch u. Ammaim: Pogg. Ann., vol. 21, 1870, p. 450. 

Bull. 54 7 (751)
98 . MEASUREMENT OP HIGH TEMPERATURES. [BULL. M.

the cold junction of the couple, and to keep PI and P2 at the same ternperature they are submerged in petroleum. From P the copper wires 

pass through the commutator JS, and thence one of them passes through 

the double key K, through a second key, 0, to the terminal r3 of the 

bridge rheostat r. The other terminal passes through the galvanometer G and thence to TI. This is the first branch of the zero adjustment, 

the second branch being furnished by the rheostat r, the ends of which 

also terminate at TI and r3 . Finally the terminals of a pair of zinc sulphate Daniells E pass through the commutator A; from here one terminal passes through the'key K and through G to r3 , the other passes 

through the large rheostats E EI and then to r1} completing the third 

branch. 

When the current is zero in G

where e is the electro-motive force at e, E the electro-motive force at E in 

the figure; where R is the resistance at E E', and r the resistance at r in 

the figure. By means of the key TTtwo circuits conveying currents due 

to E and e are closed simultaneously. It is, however, essential that they 

be so closed as to act differentially on the galvanometer G at once. Otherwise there is danger of throwing the needle violently against the stops. 

Hence in filling the cups of mercury K^ _ZT2 , JT3 care is taken to keep 

the level of mercury in K2 and JT3 decidedly above that in Klt When 

the metallic prongs of the key descend to close the circuits, the one 

not passing through the galvanometer is closed first, and a moment after 

the differential current passes through G at once. A diagrammatic 

section through the mercury cups of Kis given in Fig. 19. The makecircuit strip K1 is of amalgamated copper on a spring which keeps it 

open against a stop. Circuits may, therefore, be made and broken 

almost instantaneously. The object of the key G is to enable the observer to use pairs of the resistances of the bridge rheostat r} either in 

series or in multiple arc. By connecting C4 and Ci only, these resistances are used in series; by connecting C) and c2 as well as c3 and c4 they 

are used in multiple arc. The available resistances are thus 0.05, 0.10, 

0.20, 0.5, 1.0, 2.0, etc., as far as about 20,000. The fine adjustment is 

made at E, which is variable in single units whose mean value is always large. Varying r in steps, in this way, greatly facilitates the 

computation.

The electro motive force obtained as above is never wholly due to the 

thermo-element at PI P2 alone. It contains a disturbing electro-motive 

force £, resulting from the accidental distribution of temperature, in 

connections which can not be thermo-electrically identical throughout. 

For a short period of time (that of an observation) £ may be considered 

nearly constant, or at least varying linearly. It may therefore be 

eliminated, very nearly at least, by two commutators. A, a.ncl J3? as I)r,

(752)
/JAKUS.) CALIBRATION OF ELECTRICAL PYROMETERS. 99

Strouhal and 1 have shown. 1 In a series of corresponding positions of 

these commutators, alternately opposite, the direct measurements would 

gi?e

+ e+e -e + «(! + «) +e+e(l + 2a) _____ * I _ ttl) SI ' __ * ____ ' _. (h/If , ' ______ ' \ ^ ' ' _ - 03, /¥ etc. f\4-f*

where an odd number of observations is made. Let MI be the mean of 

the; Odd right-hand members, and M2 the mean of the even right-hand 

members. Then

In the case of small electro-motive forces this elimination is essential.

Standards of electromotive force. luasinuch as all measurements are 

based upon the constancy of the double Daniell J7, it is obvious that 

the value of this electro-motive force will have to be frequently tested. 

This can be done very simply and with accuracy by replacing the 

thermo-couple by a Latimer-Clarke or other standard element and proceeding with the measurements as usual. It is to effect this compensation that the rheostat r must have a large resistance, 20,000 ohms, 

available. For thermo-electric work r = 0.1 to 500 ohms suffices. For 

V a similar reason two Daniells are used instead of one. Currents are 

made only momentarily, and approximate values of r and R are always 

known. The constancy of my Latimer-Clark's cells has certainly been 

exemplary, and it was thus easily possible to reduce the Washington 

results to the older results obtained in New Haven in a way that established the general accordance of data beyond a doubt. In addition to 

the Latimer-Clark standards, I possessed for comparison a number of 

siphon Daniells, certain Beetz's dry Daniells, and a special form of normal Daniell of my own which merits description. In this battery it is 

impossible, correct usage presupposed, for the copper sulphate to contaminate the zinc. Zinc and zinc sulphate, copper and copper sulphate, 

are kept in separate bottles, and are only in electric contact during the 

few minutes of measurement. In Fig. 20 the Zn-Zn SO4 bottle is on the 

left, the Cu-Cu SO4 bottle on the right. Each bottle is provided with 

an h-shaped siphon of glass, the longer shank of which, a b c, is closed 

above by a rubber cap, «, and below by a cap of parchment paper tied 

on. The shorter shank d dips into a little vessel, A, containing Zn S04 

in solution. When not in use the siphon tube is nearly empty. Before 

using both tubes are rinsed thoroughly with Zn SO4 solution by compressing and relieving the caps a. When clean they are filled in the 

same way with the Zn SO4 of the dish A. After using, both siphons are 

f emptied by working the cap a as usual, and the ends d are closed by 

special caps (not shown) to prevent evaporation. It is obvious that if 

the rinsing be properly done Cu SO4 can not possibly get into the zinc 

flask to contaminate the metal. Zu therefore remains bright for years.

U. 3. Geol. Survey, J(o. 14? p. 35,

(753)
100 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

Besults obtained by comparing divers standard elements from 1883 

to 1888 are given in the next tables. Unfortunately time-magnetic 

measurements are not feasible in our laboratory, with a degree of cer-

"Cu

FIG. 20. Standard Daniell. Scale, $.'

tainty to warrant their adoption. Nevertheless by comparing LatimerClark and Daniell standards, the respective tendencies to variation of 

which are probably of an opposite character, some corroborative information may be obtained. In the next table the time or date of comparison is given in the first column. The next five columns contain

data for Latiiner-Clark elements, of which Nos. D, E, F were made by 

myself. Nos. 114 and 115 are Elliott standards. Curiously enough, the 

latter are neither as rigorously constant, nor is their internal resistance 

as small relatively as is the case in my own standards. I have reason 

to believe that one or both of the Elliott standards suffered by transportation, for in the examination made in 1887 No. 115 was found 

entirely out of order and was necessarily discarded. In the siphon 

Daniells the two jars are like those in Fig. 20, except in so far as they 

are permanently joined by a siphon. This siphon is filled with zinc 

sulphate through a small vertical tubulure during use, and emptied 

after using. With all precautions, however, it is impossible to keep 

the copper sulphate from diffusing into the zinc jar and corroding the 

metal. Hence this siphon form is inferior in efficiency to the separate 

cell form Q already described. Beetz standards1 are also made by 

myself. Electromotive forces are given in volts.

»Wie<lemaun Ann., vol. 23, 1884, p. 402, 

(754)
BAftl/S.J CALIBRATION OF ELECTRICAL PYROMETERS. 101

TABLE 9. Comparison of standard elements.

[All values reduced to 20° C.]

Date.

Dec. 18, 1883 . . 

Jan. 2, 1884... 

Oct. 26, 1885.. 

Mar. 22, 1886 

Aug. 13, 1887 .

Latimer-Clark standards.

D.

1.420 

1.420 

1.420 

1.420 

1.420

E.

1.420 

1.420 

1.426 

1.427 

1.428

F.

1.420 

1.420 

1.426 

1.426 

1.430

Elliott, 

114.

1.384 

1.371 

1.350

Elliott, 

115.

1.403 

1.306

Standard Dauiell cells.

Siphon-joined cells.

a.

(1.056) 

1.050

1.076 

1. 07!)

JET.

1.050

I.

1.052

......

Separate 

cells.

Q1.074 

1.075

Beetz gypsum 

cells.

.£/ 

1.083 

1.022 

1.030

h.

1.083 

1.037 

1.024

t.

1.081 

1.013

Ternperature.

(*) 

H4° 

{19° 

§20° 

28°

* Immediately after mating the Latimer-Clark elements D, E, F. 

t Immediately after making the Danioll G, H, I. 

t Immediately after receiving the Elliott standards. 

§ Immediately after making the Daniell Q.

In the construction of this table the element D is assumed to be constant, and with this premise the data of the table are at once intelligityle. I need only remark that my Latimer-Clark standards, as compared 

with the separate-celled Daniell Q during the seventeen months of observation, are as good as absolutely constant. It is for this reason that 

I am warranted in placing much confidence in the data of both these 

couples, of which the Dauiell has the advantage of constancy and the 

disadvantage of less facile manipulation. The siphon Daniells are inferior to the form Q, as are also the Beetz patterns, concerning which, 

however, it is necessary to remark that the gypsum mixture of copper 

sulphate and zinc sulphate solutions were probably too moist. I found 

after a time that the line of demarkation had disappeared and that the 

solutions must have diffused into each other.

It will be seen that the elements D, E, jF7,'though identical among 

themselves, differ considerably from Elliott's Latimer-Clark's j not more 

so, however, than Elliott's elements differ among themselves. A much 

more curious result was obtained in measuring the temperature coefficients of the siphon Daniell's and the Latimer Clarke's. To do this 

the elements were first covered with melting snow and afterwards submerged in water heated to different temperatures. Measurements were 

made by the zero method described, and to give additional certainty an 

auxiliary Daniell was used for comparison. In other words, the elements g, /i, *, -E7, -F, heated to the temperature specified, were compared 

with D and B kept cold, by inserting them, alternately in the same connections ; D was compared by a galvanometer method. The main comparisons were made in 1883, certain corroborative data added in 1887. 

a is a mean constant, derived graphically and intended for practical 

reductions only. Electromotive forces are given in volts.

(755)
102 MEASUREMENT OF SiGfl TEMPERATURES. [BtLL. 64.

TABLE 10. Temperature variations of Ihe Latimer-Clarlc standards D,E, F.

1883.

t.

0

14

17

21 

27 

36 

41 

48 

54 

60

Standard No. E.

E.

1.424

1.421

1.420

1.419 

1.417 

1.414 

1.411 

1.407 

1.404 

1.400

Check 

Daniell 

at 20°.

1.072

1.072

1.072

1.072 

1.072 

1.072 

1.072 

1.072 

1.072 

1.072

Standard No. F.

E.

1.425

1.420

1.421

1. 419 

1.417 

1.414 

1.411 

1.407 

1.404 

1.400

Check 

Daniell 

at 20°.

1.072

1.072

1.072

1.072 

1.072 

1.072 

1.072 

1.072 

1.1)72 

1.072

Standard No. D.

t.

0

15

29

40

0 

10 

13

E.

1.422

1.420

1.415

1.409

1.425 

1.423 

1.421

a

Mean temperature coefficient of D, E, F.

Between 0° and 40°.

a= -0.00020.

(

Later and earlier 

data.

issr.

0

27

1.439

1.426

1.076 1.439

1.428

1.076

1.074

TABLE 11. Temperature variations of the siphon Daniell standards.

1883.

No. <?.

t.

0

14

15

15

24

33

44

50

E.

1.067

1.072

1.072

1. 072

1.072

1.074

1.075

1.075

. No. JET.

t.

0

14

15

15

24

33

43

51

E.

1.066

1.072

1.069

1.071

1.072

1.074

1.074

1.072

No.J.

t.

0

14

15

15

24

33

43

51

E.

1.069

1.073

1.073

1.073

1.074

1.076

1.075

1.075

a

Mean temperature coefficient of (?, H, I.

Between 0° and 30°.

a=+0.00021.

The electromotive force and temperature coefficient of the LatimerClark standard has been much discussed. Besides dark's 1 original investigation, v. Ettinghausen,2 who cites the relevant researches (Clark, 

Helmholtz, Kittler,Uppenborn, Alder Wright) and Eayleigh 3 have given 

it critical study. My own temperature coefficient is smaller than that 

ordinarily given, and indeed so small as usually to be negligible. The

1 Clark: Jonr. Soc. Tel. Engineers, vol. 7, 1878, p. 53.

2 v. Ettiughausen : Wiener Zeitscbr. f. Electrotecb., 1884, p. 1. 

3 Rayleigh: Kept. 54th Meeting Brit. Assoe., Adv. Sci., 1884, p. G51; Proc. Royal 

Soc., London, vol. 40, 1886, p. 79.

(756)
CALIBRATION OF ELECTRICAL PYROMETERS. 10$

cause of this variation may be sought for in the composition of the mixtures. I have, moreover, kept the paste wet with a layer of zinc sulphate, in this way decreasing the internal resistance. In the case of 

zero work, standards with enormous internal resistances are undesirable, 

because all necessary resistance is introduced by the rheostats. I made 

a number of experiments to study the dangers due to polarization in the 

batteries, and it is the outcome of this work that the large resistances 

in the connections have been retained. The data themselves are superfluous here.

METHOD OF COMPUTATION.

Many experiments go to show that the quadratic relation

e=a(T-t)+b(T2 -t2 ), 

where e is the electro-motive force for the temperatures T and t of the

junctions of the thermo-elemeut and a and & are constants, is a very complete iuterpolative equation, so long as the temperature Tis not too far 

above red heat. In general, however, it is desirable to express e graphically for each element. The method of measuring e has just been indicated. T is the temperature given either by some known high boiling 

point or by direct evaluation with the air- thermometer, while t is directly read off by a mercury thermometer. If the graphic chart thus 

obtainable is subsequently to be used for temperature measurement, it 

is desirable to refer all values of e to e 2o> i- e., to the electromotive force 

which obtains when the hot junction is at T?, the cold junction at 20°. 

This correction follows easily from equation (1), for if

e =a(T-t) +&(T2 -*2 ), and 

e20= a(T-20)+&(T2 -202 ),

e20 -e=a (t 20) +& (<2 -400).

The constant a and h may be determined from the steam and mercury 

vapor calibration. A table is then to be constructed for the correction 

2o e as varying with t. By adding this to any given value of e the 

temperature results are at once comparable with the values of the chart, 

in which e is represented as a Junction of T. t should of course be kept 

as near 20° as possible. °

In the measurement of e, a small table in which the log r is once for 

all inserted for each r, arid another in which the log E is inserted for 

each JK, greatly expedite the computations.

My original plan of calculating the constants of e as a function of T 

and t by the method of least squares was soon abandoned. These constants do not represent the function truly, and since many calibrations 

are to be made the computation becomes excessively laborious. Finally, 

T can be taken from the interpolation chart quite as accurately as it

(757)
104 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

can be measured and with much less liability to error. If equation (1) 

be solved with reference to T it follows that 

where

When many values of T are thus to be found the computation is by 

no means unlaborious.

By keeping r constant, and varying E, a table can be calculated once 

for all, for the function

r

in which a mean value is inserted for E. Such a table for frequently 

recurring values of the arbitrary constant r and for values of J?, increasing in arithmetical progression with a difference of 1,000, is of great 

service in facilitating the calculation of e. It insures greater exemption from error. A small correction for E is only necessary to correct 

the interpolated results.

Instead of applying a zero method like the .present, it is of course 

permissible to use simplified processes in which currents only are nieasured. A torsion galvanometer, such, for instance, as that actually used 

by Schinz (1. c., p. 49), suggests itself. By the aid of my boiling tubes 

and crucibles the scale of such an instrument may be at once graduated 

in terms of the centigrade thermometer. Not only can this be done 

with a great degree of accuracy, but the thermal calibration of the 

galvanometer may be checked with ease as often as desired. There 

can be no doubt that for practical purposes this apparatus is exceedingly convenient. Nevertheless the measurement of electromotive 

forces by the zero methods here discussed retains an advantage over 

current measurement, because measurements of electromotive force 

made at one time may be at once compared with corresponding measurement made at any subsequent time. The data are easily expressed 

in terms of a fixed absolute standard, in other words. All this is much 

more difficult in the case of current measurement, even if it were as 

accurate, for current measurement brings in the arbitrary constants of 

the galvanometer.

EXPERIMENTAL RESULTS.

Exploration for constancy of 'temperature ; water \ aniline. When the 

boiling tubes, Figs. 7 to 11, are to be used for temperature measurement, the chief point of interest is the degree of constancy attained \ 

throughout the- length of the central tube into which the thermo-eleinent is to be inserted. To obtain the requisite data it is sufficient to insert a thermo-eleinent, the constants of which are approximately known, 

into the tube mentioned, with the junction consecutively at different

(758)
BAiUJS.] CALIBRATION OF ELECTRICAL PYROMETERS. 105

heights above the surface of ebullition. In the following tables, therefore, the absolute values of the high temperature T is of less importance 

and of smaller accuracy, while the variations of T are represented with 

nicety. In the table the temperature t of the cold junction is constant; 

e (microvolts) is the measured electromotive force of a new element, 

Pt hard-Pt Ir 20 per cent., from which the temperature T is computed.

TABLE 12. Constancy of temperature along the axis of lotting tube. Steam. T=100°.

Height of junction above 

bottom.

Cm.

5

10

15

20

25

30

34

5

t.

°0.

20.0

20.0

20.0

20.0

20.0

20.0

20.0

20.0

e.

Microvolts.

660.7

673.0

672.2

672.0

672.0

672.0

666.0

683.7

T.

°0.

98.9

100.1

100.0

100.0

100.0

100.0

99.4

101.2

Kemarks.

Surrounded by liquid.

Surrounded by vapor.

Do.

Do.

Do.

Do.

Surrounded by cork.

Surrounded by liquid; burner lowered.

This table is cited as an example of many similar observations made 

with like results. The adjustment of heat was nearly perfect, so that 

no steam escaped. The ebullition was quiet and the water was left in 

the tube in almost undimiuished amount at the close of the experiment. 

The first observation 5em above bottom of tube is taken at about the 

middle of the boiling liquid and the temperature here depends upon 

whether the ring burner encircles the tube above or below this point. 

The next observation, 10cm from, the bottom, is about 2cin above the 

surface of ebullition, and from here to the upper cork the temperature 

is absolutely constant. To make these explorations it is necessary that 

the thermo-couple be new or perfectly homogeneous and annealed; otherwise the error of homogeneity will be falsely attributed to an error of 

the constancy of the boiling tube. Exploration with a mercury thermometer is less satisfactory than the thermo-couple test because the 

stem of the thermometer usually projects.

Similarly constant results may be obtained with aniline at 187°, 

which it is therefore not necessary to cite. They show that with the 

junction about lcm above the zone of ebullition, quiet boiling presupposed, its temperature may be regarded identical with that of a mercury thermometer placed contiguously with the mentioned junction 

and inserted from above.

Exploration/or constancy of temperature; mercury. In the case of mercury the zone of constant temperature is of course much less in height, 

and special investigations with respect to it are therefore essential. 

The data in the table are given on a plan identical with the foregoing. 

Kesults are also appended for mercury impure with oxide, in which

(759)
106 MEASUREMENT1 OF ttt&i TEMPERATURES. lathi. W.

case the liquid sometimes bumps violently during ebullition. The 

liquid surface is at 10cm from the bottom nearly.

TABLE 13. Constancy of temperature along axis of toiling tiibe. Mercury. T = 358°.

Height of 

junction above 

bottom.

Om.

In liquid J

12 

In vapor-}

1 15

f 5

In liquid \ 8 

( 9

flO 

In vapor { 

t lo

5

15

0

5

9

10 

12 

15

20

25

30

t.

o(7.

21.5 

21.5

21.5 

21.5 

21.5 

21.5

21.5

21.5 

21.5 

21.5 

21.5

24.0 

24.0

20.3

21.7

23.6

22.9 

23.4 

23.4

21.8

21.8

21.8

e.

Microvolts.

3320 

3414

3431 

3121 

3410 

3330

3393

3448 

3436 

3436 

3192

' 3425 

3393

3856

3300

3436

3431' 

3295 

3090

745

443

317

T.

 =(7.

347.4 

358.0

357.0 

356.2 

355.2 

348.2

353.9

358.4 

357.4 

357.4 

356.4

358.2 

325.3

391.3

345.8

358.8

357.8 

346.6 

329.1

94.5

58.2

42.6

Remarks.

i Fresh mercury; brisk and regular 

boiling. Liquid surface at 10cm .

Fresh mercury ; brisk and regular 

 boiling. Liquid surface at 10cm . 

Disks in the mercury tube.

) Violent boiling with bumping. 

) Liquid surface at 10cm.

)

Gentle ebullition with bumping. 

Liquid surface at 10em.

)

These tables show conclusively that for a distance along the central 

tube of about 1.5cm above and below the surface of ebullition, the temperature is that of the boiling point of mercury, with ail error of less than

a few tenths of a degree. Tbe temperature of the liquid below the surface and of the vapor above it depends on the position of the ring burner 

and of the intensity of ebullition. The suddenness with which temperature decreases between 5cm and 10cm above the surface of ebullition is 

well shown by the data of the last part of Table 13. Hence it is permissible to speak of a zone of ebullition comprising in vertical extent 

about 5cm of the boiling tube above the surface. The use of loose disks 

or screens of asbestos in the boiling space, to guide the vapor or prevent 

convection here, is of no obvious avail, probably from the great weight 

of mercury vapor as compared with that of air. These disks complicate 

the apparatus, and are therefore to be discarded. Table 13 is an example of many similar results. The two or three centimeters of avail, 

able space for constant temperature are amply sufficient lor the calibration and for many other purposes. At any given point of the space the 

constancy of temperature is almost perfect. If the outside of the tube 

is well jacketed with asbestos wicking, the height of the space of con-

(760)
OF ELECTRICAL PYROMETERS. 10?

staut temperature may be much increased. It has been stated that in 

the data of Table 13 the variations of boiling point, and not the absolute value of the boiling point, is the point of consideration.

Exploration for constancy of temperature; sulphur. From the nature 

of the case, the calibration with sulphur is more difficult, and calls for a 

more careful examination. Hence series of data are drawn up in Table 

14, both for gentle and for violent ebullition. The condition of constancy of the center of the zone of constant temperature is also tested 

by a special thermo-couple, inserted from time to time during the progress of the measurements. In the first part of Table 14 the surface of 

ebullition is at 12cm above the bottom; in the remaining parts about 

8.5CIri from the bottom. No carbonic-acid or other gas is introduced into 

the tube, and ebullition probaby takes place in,SO2 gas, formed from S 

vapor and the oxygen of the tube. To produce very violent ebullition 

the copper gauze surrounding the sulphur tube was heated even to redness. As before, the variation of T, and not the absolute value of the 

boiling point, is the chief consideration.

TABLE \4. ^Constancy of temperature along axis of boiling tube. Sulphur. T=449°.

Height above 

bottom of tube.

0

Cm. 

(15

IQ

r 11

In liquid . N

Q

12 

12

,18

T J 11

In vapor. >

i'9

f 8 

7

6

In liquid. <

1'

I 3

r 13 

i 11 In vapor. < 1C

I 9

8

5

I 4

t.

°0. 

15

15

I

K

16

16

16

16

16.6

17. 2

19.0 

ion

19 0

1Q ft

19.0

19 0

19.0

19.0

19.0

19 0

19.0

in. o

19 0

19.0

]9.0

19 0

19.0

19.0

19.0

'e.

Microvolts.

3056

4038

49(13

4226

4273

4157

3394

4206 

4198

3923 

4498

4517

4545

4629

4651

4577

4078

3448

977Q

3886 

4487

4545

4587

4643

4509

3221 J

T.

°G. 

339

433

448

451

455

445

373

449.5 

449.2

398.9 

445. 0

446 5

448.5

455.3

456.8

411 9

359.3

395.9

445.4

448.6

452. 1

445.8

403.8

339. 6

Time.

h. m. 

11 30 

12 10

2 15p.m.

3 15

Eemarks.

1

( n * lOcm

1

1

1

Mild ebullition. Liquid at

8.5 .

(761)
108 MEASUREMENT OP HIGH TEMPERATURES. [BULL. 54.

TABLE 14. Constancy of temperature along axis of boiling tube, etc. Continued.

Height above 

)ottom of mbe.

Cm.

f 13

11

In vapor, i ^

I 9

' I'7

In liquid. < \ 6

I 5

f !3

111

In vapor. <^ ^

( 9

f Q

f1 7

In liquid.-j 6

5

I 4

t.

°O.

19.0

19.0

19.0

19.0

19.0

19.0

19.0

19.0

19.0

19.0

19.0

19.0

19.0

19.0

19.0

19.0

19.0

1C. 6

17.2

19.3

19.2 

20.3

19.8

14.8

19.4

18.4

18.7

e.

Microvolts.

4487

4496

4511

 4529

4597

4657

4669

4423

4492

4502

4513

4550

4609

4669

4669

4478

3900

4206

4198

4190

4180 

4185

4183

4203

4171

4183

4187

T.

°0.

444.0

444.7

445.9

447.4

452.7

457.4

458.4

439.1

444.4

445.2

446.1

448.9

453. a

458.6

458.4

443.4

396.9

449.6

449.3

449.8

449.0 

449.8

449.8

448.2

448.5

448.8

449.3

Time.

3 45

5 15

5 30

S, 11 30 a. in.

12 10 p.m.

2 30 p. m.

3 00 p. in. 

5 30 p. m.

7 30 p. m.

|, 9 00 a. m.

12 00 p. m.

2 15 p. m.

5 30 p. m.

Remarks.

Violent ebullition. Liquid at

8.5^.

1

Violent ebullition. Liquid at

8.5cm.

J

Check observations made with

a special thermo-couple during the progress of the above

' measurements. Hotjutiction

just above surface of ebullition.

J

By plane of ebullition, an expression frequently to be used, I refer 

merely to the mean surface of the agitated liquid. Above this there is 

a similar well defined plane of condensation, and the zone of constant 

temperature lies between these planes, nearer the lower.

The data taken as a whole show that for lcm or 2cm above the plane of 

ebullition the variation of temperature is not more than two or three 

degrees from the boiliug point. These changes are produced by relatively great differences in the intensity of ebullition. The use of thick 

asbestos jackets increases the height of the space of constant temperature. As was the case with mercury, the zone of ebullition is sharply 

marked both above and below the surface of the liquid, and its height 

depends very materially on the violence of the boiling. The tube during ebullition is apt to be very dark brown, so that it is sometimes difficult to discern the boiling surface at all. It is well, therefore, to mark 

its position beforehand. Taking the above results as a whole, it appears that just above the surface of ebullition the temperature is constant for an indefinite period of time, and that it does nob differ from 

the boiling point of sulphur more than a degree at most.

Exploration for constancy of temperature; zinc. In Table 15 I give

(762)
BARUB.] CALIBKATION OF ELECTEICAL PYROMETERS. 109

similar observations relative to the constancy of temperature along the 

axis of a ziuc crucible. The form with open tube, Fig. 15, is used, so 

that the variation of temperature along as much as 14cm of the axis can 

be measured. During measurement the central tube is closed above 

with a loose plug of asbestos wicking. Experiments are made with two 

furnaces, placed side by side and heated simultaneously. It is difficult 

to define the surface of ebullition with reference to the crucible, for the 

ziuc is apt to be porous and of great bulk, and it is sure to be spattered 

against the top of the crucible and to solidify there. T in Table 15 is 

approximate, since the variation of T. is alone of interest here. It was 

necessary to finish the observations for the first crucible before commencing those of the second.

TABLE 15. Constancy of temperature alon'j the axis of the zinc crucible. Form, cf. Fig. 15

FUKNACE No. 1.

Height above 

bottom ' 

of crucible.

Cm.

4 

8 

10 

12 

8

4

t.

°o.

21.6 

21. C 

21.6 

21.6 

21.6 

21.6

em.-

Microvolts. 

11000 

11000 

10950 

10670 

11090 

11090

T.

°a.

.......

Time.

Hours. 

3.18 

3.25 

3.30 

3.33 

3.38 

3.43

> KemarkH.

1

Liquid surface about 8cm 

 1 above bottom.

J

FURNACE No. 2.

4 

8 

10 

12 

14 

10 

8 

4

21.6 

21.6 

21.6 

21.6 

21.6 

21.9 

21.9 

21.9

11040 

11060 

11040 

10970 

1083C 

11090 

11080 

11080

........

........

3.55 

.3.58 

3.67 

3.70 

3.77 

3. 85 

3.92 

4.00

1

Liquid surface about 8cm 

abov£ bottom.

J

To obtain a full understanding of the purport of these data it is necesSi\ry to turn to Fig. 15, p. 94, where the positions of the present points 

of observation have been marked with little circles. The data, therefore, show most remarkable and unexpected constancy, particularly so 

when compared with the results for mercury and sulphur. This is due 

to the fact that the distilled zinc condenses on the sides of the upper 

and colder parts of the crucible and then runs down on the walls a 

fact well demonstrated by breakage of the crucible after the experiment. Hence the interior is practically encased in an envelope of boiling zinc, although the exterior of the crucible by actual measurement 

shows 1,400° and more. A significant result of these explorations is 

tin's, that the passage from the region of boiling liquid into the region 

of vaporized zinc is not discernible in the data. Temperature is practically constant until the upper cold parts of the crucible are reached.,

(7G3)
no MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54

PRACTICAL CALIBRATION.

Investigation of data. Instead of extending these experiments into 

higher temperatures and determining further data for the fire-clay apparatus, it will be expedient to actually calibrate a series of elements. 

Such experiments will show both the constancy of the divers boiling 

points as regards time, as well as their "absolute correctness as compared with the data of Chapter I. Indeed, the degree of identity exhibited by distinct series of data obtained almost a year apart, by 

thoroughly different methods and under different circumstances in all 

other respects, will be the best available criterion of the validity of the 

said series of results. Hence the following table is given with considerable fullness. The boiling points taken are zinc (930°), sulphur (448°), 

mercury (357°), aniline (measured 187°), and water. All observations 

are made in time series; and for the temperatures t and T of the cold and 

hot junctions, the electromotive force e microvolts was observed at the 

time specified on the same horizontal row. The mean of these isolated 

observations being taken, the results are used for the calculation of the 

constants a and b in equation (1) above, by the method of least squares] 

a and b are inserted in the ninth column. The fifth contains the calculated value of e, and its difference from observed e is given in the 

sixth column. Finally, in the seventh and eighth columns are inserted 

the correction e2o e and the value <?2o of electro-motive force which 

hold for t=20. In addition to these data the table contains values 

parenthetically inserted. These are derived from the constants for the 

calibration if carried only as far as the boiling point of sulphur, to the 

exclusion of zinc. Hence these constants, being derived similarly to 

the extrapolation constants of Chapter I, are at once comparable with

them.

TABLE 16^ Calibration of thermo-couples Nos. 17, 18, 22, 35, 36.

No.

17...............

t.

°0.

20.4

20.7

20.8

21.4

21.4

O1 Q

99 0

99 ^

99 7

99 8

29 Q

OO Q

91 7

T.

0 o.

930

930

930

930

cnn

930

930

930

9 '0

non

930

930

QQn

e observed.

Microvolts. 

9101

9185

9169

9173

9169

91y9

nt 70

. 9169

9211

9211

9211

Q91 1

9

01 1

9180

e calculated.

Microvolts.

9334

Se.

Microvolts.

174

620 6.

Microvolts.

9

621..

Microvolts. 

9101

9185

9170

9175

9176

9183

9182

9227

9228

9999

9009

9229

9190

a and 6.

Microvolts. 

8.049

Time.

h. m. 

2 24

27*

3 00

7

00

00

4 2

15

40

4 5

50

55

56

(764)
BARUS.] CALIBRATION OF ELECTRICAL PYROMETERS. Ill

TABLE 16. Calibration of thermo-couples Nos. 17, 18, 22, 35, 3G Continued.

No.

17...............

.17...............

17 ...............

17...............

18...............

is

1 Q

18...............

18...............

Mean ......

22...............

Mean ......

22...............

Meap . ....

t.

°0. 

20.0

2L.4

22.1

21.2

20.5

21.0

 20.8

18.5

19.3

18.4

18.7

18.9

18.8

18.8

20.5

20.8

.21.6

22.1

21.2

20.0

21.5

22.2

20.9

20.6

21.0

20.8

18.4

19.3

18.8

18.9

18.7

18.8

20.6 

20.8

21.6

22.2

21.3

19.8

21.0

. 21.2

21.9

22.6

22.8

21.6

 "*

T.

°C.

448

448

448

448

357

357

357

186. 5

186.8

186.4

186.6

99.9

99.9

99.9

930

930

930

930

930

448

448

448

448

357

357

357

180.5

186.8

186.7

99.9

99.9

99.9

930 

930

930

930

930

448

448

448

448

448

448

448

e observed.

Microvolts.

4062

4050

4049

4054

3065

3068

3067

1438

1433

1435

1435

649.2

650.6

649.9

9122

9160

9122

9126

9133

3998

4004

4000

4001

3035

3037

3036

14-22

1415

1419

647.2

649.2

648.2

9198 

9202

9185

9181

9191

4030

4026

4026

4020

4019

4011

4022

e calculated.

Microvolts.

(4502)

3909

(3077)

3012

(1420)

1433

(659)

676

(ffift

(4005)

3883

(3041)

2986

(1409)

1420

(655)

669

9347

(4025)

3895

Se.

Microvolts.

(+2)

(+145)

(-10)

+55

(+14)

_1_9

(-9)

 20

 147

(-4)

+118

/ r\

+50

(+10)

 1

(-7)

 21

 157

/ Q\

+127

020 0.

Microvolts.

2

-10

O 3

0

 9

 9.3

6

8.6

 TTTO--

620.

Microvolts.

4058

4037

4065

4058

3065

Pfl79

3069

1426

1428

1425

1425

640.6

C41.3

9122

9162

9131

9138

3994

4012

4013

4004

3041

1410

1410

1410

638.6

639.1

638.9

8199 

9204

9194

9194

9197

4025

4030

4031

4031

4035

4029

4031

 en 

a and b.

Microvolts. 

(7. 66)

(0. 00390)

7. 973

0. 002352

n R&\

(0. 00367)

7 QQQ

 0--0- 

Time.

h. m.

71 l'<

12 4

33

3 1

4 37

10 14

51

1-45

12 10

34

2 Q^

3 15

43

4 18

11 30

12 10

Qfl

3

f.

4 42

]0 10

55

19 13

*JQ

2 40

3 17

48

d. 99

U 97

K t

CO

19 91

53

1 15

705)
112 MEASUREMENT OF HIGH TEMPERATURES [BULL. 54. 

TABLE 16. Calibration of thermo-couples Nos. 47, 18, 22, 55, 36. Continued.

No.

99

99

Mean .....

22...............

Mean.... .

35...............

35...............

35...............

35...............

Mean .....

35...............

Mean .....

t.

° 0. 

20.2

90 3

20.4

Ofl Q

21.0

 21.1

91 9

91 9

91 fl

21.0

20.8

18.4

19.1

1Q 9

Sg s

18.3

1Q Q

18.9

19.1

18 9

18.8

38.6

18.8

20.6

21.0

21.8

22.2

22.4

21.6

20.4

91 7

22.3

21.5

20.7

21 1

20.9

18.8

19.3

18.5

18.9

18.9

18.7

18.8

T.

° 0. 

357

OK7

3*V7

QK7

357

3>V7

357

117

357

3IV7

357

J86.5

186.5

186.8

186.8

186.4

186.4

186.6

99.9

99.9

99.9

99.9

99.9

930

930

930

930

930

930

448

448

448

448

357

357

357

186.5

186.8

186.4

186.6

99.9

99.9

99.9

e observed.

Microvolts.

3049

3057

3053

3051

3051

3054

3048

3048

3048

3050

3051

1426

1423

1423

1422

1422

1421

1423

646.7

647. 8

650.6

651.0

649.0

10226

10214

10219

10214

10257

10226

4297

4297

4295

4296

3220

3220

3220

1434

1427

1436

1432

632.1

634.5

633.3

e calculated.

Microvolts.

(3058)

3000

0412)

1423

(656)

671

10475

4108

(3216)

3119

(1420)

1438

(643)

668

Se.

Microvolts.

(-7)

+51

(+11)

-0

(-7)

 22

 249

/ 9M

+ 188

(+4)

+ 101

(+12)

 6

/ nt

-35

dm e.

Microvolts.

2

 9

-9.3

8.6

8

 9

 9.3

en.

Microvolts.

3047

3056

3052

3053

3057

3059

3053

3053

3052

3054

3053

1414

1416

1417

1418

1409

1410

1414

639.7

639.2

641.3

640.1

639.7

10226

10218

10229

10227

10272

10235

4296

4309"

3222

3225

3223

1425

1422

1424

1423

623.5

624.4

624.0

a and b.

Microvolts. 

(7. 64)

(0. 00381)

7.776

/7 1 Q\

(0.00627)

Time.

h. m.

2

A(\

53

3

9*1

4 30

KK

^ 9^

Q9

6 40

7

OO

1ft Q

3^

45

11 17

1 Q7

2 00

12 5

20

12 26

KA

2

AQ

3 26

4 00

9Q

q/»

11 43

4.1

q ic

4 47

10 21

11 6

1 53

12 18

12 42

(766)
J3ABUB.] CALIBRATION OF ELECTRICAL PYROMETERS. 113 

TABLE 16. Calibration of thermo-couples Nos. 17, 18, 22, 35, 36. Continued.

No.

36...............

36...............

36...............

36...............

36. ......2. ......

Mean......

t.

°O. 

20.7

21.2

21.7

22.3

21.5

9n a

21.8

22.4

21.7

20.8

21.1

21.4

19.0

19.4

18.6

18.8

19.0

19.1

18.6

 18.8

T.

°(7. 

930

930

930

930

930

448

448

448

448

357

357

357

186.5

186.8

186.4

186.6

99.9

99.9

99.9

eat)- 

served.

Microvolts.

10214

10205

10193

10245

10212

4309

4308

49QO

4303

3217

3221

3219

1443

1436

1437

1425

1435

631.2

636.1

633.6

e calculated.

Microvolts.

10467

(4329)

4108

(3214)

3121

(1422)

1440

ffij.3)

669

Se.

Microvolts.

 255

(-26)

+195

(+5)

+98

(+13)

 5

( 10)

-35

Om e.

.Microvolts.

8

9

7

 9

9 q

£20.

Micro, 

volts.

10216

10210

10909

10259

10220

4311

4318

4308

4312

3219

qoon

3S26

1435

1431

1426

1416

1426

624.3

625.2

624.3

a and &.

Microvolts.

7 781

0. 003913

n ill

(0. 00629)

Time.

h. tn. 

2K1

3 28

52

433

11 49

12 19

45

3 00

450

10 31

11 10

210

12 0

12 48

From the constants contained in these tables I have calculated the 

values of e20 when the difference of temperature varies between T 20= 

lOQo, ami T 20=1,500°, for the reason that I shall make use of these 

values below. In general there are three sets of values of e2o available; 

the first of these is calculated with the constants, including the zinc 

calibration j the second with the constants applying only as far as the 

sulphur calibration contained in this chapter; and the third with the 

constants applying as far as the mercury calibration contained in Chapter I. The last two sets having been made respectively in Washington 

and in New Haven will be so designated. To these couples are added 

results for Nos. 19 and 20, both of which are 5 per cent. Pt-Ir alloys. 

They will be referred to elsewhere.

Bull. 54 8

(767)
114 MEASUREMENT OF HIGH TEMPERATURES.

TABLE 17. Values of ejo wt microvolts. 

WASHINGTON AND NEW HAVEN.

T-t.

100.......

200.......

300.......

400.......

500.......

600 ......

700.......

800

900.......

1000......

1100......

1200......

13CO......

1400......

1500......

NO. 17,630 =

With 

zinc.

Washington.

838 

1723 

2655 

3635 

4661 

5734 

6855 

8023 

9238 

10500 

11809 

13165 

14569 

16020 

17517

Without zinc.

Washington.

821 

1719 

2696 

3751 

4883 

' 6094 

7383 

8749 

10194 

11718 

13319 

14998 

16755 

18589 

20602

Now 

Haven.

815 

1707 

2677 

3726 

4852 

6056 

7339 

8700 

10137 

11654 

13249 

14921 

16672 

18500 

20407

No. 18, ejo =

With 

zinc.

Washington.

830 

17C8 

2632 

3603 

4620 

5687 

6099 

7958 

9165 

10419 

11719 

13067 

14462 

15903 

17391

Without zinc.

Washington.

815 

1704 

2666 

3702 

4811 

5994 

7250 

8580 

9983 

11460 

13010 

14634 

16331 

18102 

19946

New 

Haven.

813

1704 

2671 

3751 

4836 

6034 

7309 

8661 

10091 

11590 

13179 

14839 

16576 

18390 

20281

No. 22, em =

With 

zinc.

Washington..

833 

1715 

2644 

3621 

4646 

5721 

6843 

8013 

9232 

10497 

11812 

13176 

14587 

16045 

17553

Without zinc.

Washington.

817 

1711 

2680 

3726 

4848 

6046 

7319 

8670 

10096 

11598 

13177 

14831 

16562 

19185 

20252

New 

Haven.

814 

1707 

2679 

3729 

4S57 

6065 

7350 

8714 

10157 

11678 

13278 

149f>6 

 1U714 

18548 

20463

WASHINGTON.

T-t.

100.........................

200.........................

300.........................

400.........................

etfA

600.........................

700.........................

800.........................

onn

1000........................

1100........................

1200........................

1300........................

1400........................

1500........................

No. 35, 620 =

With zinc.

832 

1743 

2733 

3801 

4950 

6177 

7482 

8868 

10331 

11875 

13497 

15335 

16978 

18837 

20775

Without 

zinc.

806 

1737 

2793 

3976

5283 

6715 

8273 

9957 

11766 

13700 

15759 

17944 

20255 

22690 

25252

No. 36, 620 =

With zinc.

833 

1745 

2734 

3801

4948 

6154 

7476 

8825 

10316 

11855 

13470 

15165 

16936 

18789 

20698

Without 

zinc.

807 

1739 

2798 

3982

5254 

6729 

8291 

9980 

11792 

13732 

15808 

17988 

20307 

22749 

25319

Nos. 19, 20, C2u =

With zinc.

297 

6dO 

906 

1218 

1533 

1852 

2177 

2506 

2840 

3178 

3520 

3868 

a=2. 9 

h=0.0 

(a-3.

<b=-

AVithont 

zinc.

305 

C09 

910 

1210 

1507

JSOS 

2097 

2389 

2U78 

2968 

3i54 

,3:>39 

44 

00255 

385). 

0. 000093)

Discussion of data. The most satisfactory method of discussing the 

results of Table 17 will consist in first mapping out its data graphically, 

and inserting upon the loci so drawn those results of Table 16 which 

are the immediate consequences of experiment. I will first consider a 

comparison of the results of Chapter I and of Chapter II for such cases 

in which the calibration was carried forward about as far as 400°, the

(768)
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FIG. 21. Chart showing the relation of einperature (T-t) and electromotive force (620); thermo-couples 17, 18, and 24.
JJAHUS.J CALIBRATION OP ELECTRICAL PYROMETERS. 115

constants then calculated from these data and used for trial extrapolations. It appears from this comparison that the results of these trials 

are almost perfectly coincident. In case of No. 17 the difference at 

1,500° is only 4°; in case of No. 18, 14°; in case of No. 22, 9°. Now, 

when it is remembered that the results of Chapter I are obtained by 

the large vapor apparatus there described and that the results of this 

chapter are obtained by the small practical forms, the coincidence of 

the results of this exceedingly severe test is most remarkable and 

gratifying. In Table 16, moreover, the relatively small differences betweeu the parenthetical results for observed and calculated e, is further 

evidence in favor of the statement just made.

If, however, we include the boiling point of zinc in the present comparisons and derive the constants by the method of least squares, the 

relatively large differences thus obtained at once show that the quadratic equation assumed is no louger applicable, so far as the results in 

hand are concerned. The loci corresponding to these new constants 

differ at 1,500° by amounts as follows: In case of No. 17, by 126°; in 

case of No. 18, by 115°; in case of No. 22, by 119°; in case of No. 35, 

by 120°; in case of No. 36, by 130°. Similarly the differences between 

observed and calculated e in Table 16 (without parentheses), differ by 

large values. To obtain a notion of the nature of this difference it is 

well to insert the observed result for zinc in the chart, Figs. 21 and 22. 

When this is done it appears that the position of the zinc point bears 

no observable relations to the positions of the sulphur, mercury, aniline, 

and water points. There are three causes for this large discrepancy to 

be considered: 1. Either the relation between temperature and electromotive force in case of platinum-iridium elements is circumflexed or 

anomalous between 500° and 1,000°; or the accepted value of the boiling point of zinc, 930°, is too large by about 75°; or the boiling point 

of zinc in the crucible calibration has not been reached. The last of 

these suppositions is easily disproved, both by the fact that during 

ebullition zinc dust escapes from the top of the crucible, and that after 

breaking the cold crucible the evidences of ebullition are apparent in 

drops of zinc scattered against the walls and solidified there after cooling. Again, the temperature on the outside of the crucible must have 

been at least 500° above the boiling point of zinc. Finally there is an 

almost complete coincidence between the zinc data for the large crucibles, in Chapter I, and the present data for small crucibles, as will 

presently be shown more at length. Hence the source of the zinc discrepancy in question is to be referred to one of two causes: either the 

platinum-iridium thermo-couple shows a circumflex like anomaly in the 

relation between electromotive force and temperature between 500° 

and 1,000°, or the values heretofore assumed for the boiling point of 

zinc (ca. 930°) are too high b 75°. To decide between these two difficulties, the importance or which is here regarded merely from the

(709)
116 MEASUREMENT OF HIGH TEMPEKATUKES. [BULL. 54.

standpoint of the present investigation, is not the purpose of the 

present chapter and will be touched upon later.

Time variations of thermo-electric data. In this place a consideration 

of the degree of coincidence between present and former zinc data is pertiuent. In the results given in Table 6, Chaper I (p. 78, June 11), the 

values for the boiling point of ziuc if expressed in (reduced) units of 

elctromotive force were :

Microvolts. 

No. 17...... ...... e20 = 9220

No. 18............ e2() = 9180 (188)

No. 22............ <?2

These values are available for comparison with the data of Table 1G, 

Chapter II, from which the corresponding mean values are found to be :

Microvolts. 

No. 17............ e20 = 9190

No. 18............ 3,o = 9UO (188)

No.22...... ...... e20

This slight difference of less than £ per cent, in the values of e20, and 

which amounts to only about 3° of temperature, is quite negligible and 

easily referable to the incidental errors of experiment. In the large 

furnaces of Chapter I such an error is possible, even at the cold junction.

Duration of continued ebullition, constant high temperatures. This 

brings me finally to a consideration of the constancy of the boiling point 

as observed with the crucibles described, when this constancy is considered with reference to the time during which ebullition has been 

going on. A series of such results are given in Table 16, and if necessary others may be supplied during the course of the discussion. Turning first to the results, e2o, for zinc, it appears that after the value of T 

has become constant at about 3 o'clock, the variation in e20 from this 

time until 5 o'clock (9180 microvolts to 9230 microvolts) are only a little 

more than £ per cent, of 620, corresponding to about 4° centigrade for 

the two hours of ebullition. This variation is an almost regular increase of T. This strikingly perfect degree of constancy of the ternperature of this crucible is additionally attested by the values of e20 

for the elements Nos. 18, 22, 35, 36, to which I might add many other 

results, were it at all necessary to supply further corroboration. By 

way of illustration, merely, I will give a few data obtained when the 

contents of the crucibles are antimony or bismuth instead of zinc. I 

will also add some results derived from commercial cadmium. In the 

case of bismuth the walls of the cold crucible, after boiling, were lined 

above the surface of the metal with a fine granular coating of bismuth, and 

very near the surface a narrow zone of little bismuth beads was apparent. Nevertheless, ebullition can only have commenced, as is proved 

by the thermo-electric data, and the incrustation is due to volatilization

(770)
 * 'ZZ 'S8 '9fi 'i£ '88 '66 'Of 

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BARUB.] CALIBRATION OF ELECTRICAL PYROMETERS 117

below tlie boiling point. The temperature in the cases of both bismuth 

and antimony was sufficiently high to partially fuse the porcelain insulator, and to cause it to stick fast in the central tube. This is a 

great annoyance, because platinum at high white heats has only small 

tensile strength, and is therefore easily pulled apart in the endeavor to 

withdraw the element from the tube. The difficulty is obviated by 

using fire-clay insulators.

TABLE 18. Ch'ucible, Fig. 13, charged with bismuth.

No.

17

t.

0 0.

19

19

19

19

19

19

19

e.

Microvolts.

8300

10710

11340

12010

12780

13670

14150

«so.

Microvolts.

8300

10700

11330

12000

12770

13660

14140

Time.

h. in.

2 00

5

6

7

10

15

20

The crucible after the last measurement, being fluxed through, began 

to leak, putting an end to the experiment. The value of T would of 

course only be approximate if obtained by using the zinc constants of 

Table 16 for extrapolation. Nevertheless, the continued rapid increase 

of temperature, T, shows that the boiling point has as yet by no means 

been reached. The behavior is therefore in striking contrast to the zinc, 

charged crucible.

TABLE 19. Crucible, Fig. 13, charged with antimony.

No.

17

17

17

17

Eler

t.

° G.

20

20

20

20

nent £

e.

Microvolte.

12410

12730

12790

12900

Jo. 17 p

e2o.

Microvolts.

12410

12730

12790

12900

ailed ap

Time.

h. m.

C 42

45

46

48

irt on

withdrawing it, No. 18 substituted for it.

18

18

18

18

18

18

22

23

23

23

23

24

12810

13210

13210

13390

13520

13600

12830

13230

13230

13410

13540

13640

7 25

30

32

36

40

42

Here the remarks already made under bismuth nearly apply. The 

crucible leaked after the last observation, and the experiment had there-

(771)
118 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 64.

fore to be discontinued. T would have the approximate signification 

stated. The porcelain tubes again soften.

In operating upon cadmium, I first tried glass tubes. But after many 

trials the experiment was abandoned, both because of the decidedly reduced viscosity of glass at low red heat, and because the simple ring 

burner, even while a powerful pair of bellows is used to intensify the 

blast, is not capable of easily boiling cadmium. Hence the clay crucibles were used and results were obtained as follows. The value of Tis 

here appended, as derived from Tabie 16, both for the case in which the 

exterpolation is made with zinc, and as made without zinc. The cadmium used is of commercial purity only. What I aim at here is a mere 

illustration of method.

TABLE 20. Crucible, Fig. 13, charged with cadmium.

No.

17

17

17

18

18

22

22

35

35

36

36

t.

0(7.

21.2

22.8

23.8

21.6

22.9

21.9

23.1

22.2

23.2

22.5

23.5

e.

Microvolts.

75G8

7626

7558

7541

7528

7568

7577

8346

8337

8333

8325

em.

MicroVultS.

7577

7648

7588

7553

7550

7583

7601

8363

8362

8352

8352

Time.

h. m.

12 38

1 0

18

12 43

1 3

12 47

1 6

12 52

1 10

12 55

1 12

Cum zinc 

T.

 °(7.

783

790

783

785

785

784

785

785

785

784

784

Sine zinc 

,. T.

°(7.

734

740

735

743

743

740

742

725

725

724

724

The results are given here chiefly by way of contrast with the above 

tables for bismuth and antimony, since they show an admirable degree of constant temperature maintained for nearly one hour at a 

relatively low temperature. Inasmuch as the interval between 500° 

and 1,000°, if the assumed boiling point of zinc be correct, is anomalous 

and not simply quadratic, the interpolation here made for the measurement of Tis unsafe, tlence I have given T both as exterpolated from 

calibrations (0° to 450°) excluding zinc, and as interpolated Irorn calibrations including zinc. If there were no anomaly the constancy of the 

values of T found by operating with divers elements would make these 

results very trustworthy.

I have made other similar experiments with selenium and with zinc 

chloride; but respecting all of these the remarks made for cadmium 

apply. Further data are therefore omitted here.

Duration of continuous ebullition, low temperatures. Returning from 

this digression,! will next exhibit the constancy of temperature for the

(772)
BARtJS.j CALIBRATION OF ELECTRICAL PYROMETERS. 119

time series of boiling-point experiments made in the glass boiling tubes. 

The data of Table 16 are again available with a few supplementary 

results to be inserted below. The variation of temperature during 

about an hour's uninterrupted boiling in sulphur in case of No. 17 is 

within £ per cent, of e2o; in case of No. 18 about £ per cent, of e20 ; in 

case of No. 22 within £ per cent, of e2o for almost two hours of boiling, 

etc. The constancy is satisfactory, and since the variations contain 

incidental errors it is probable that the boiling point itself is reached 

to within two or three degrees. To test this supposition I reversed the 

procedure, and by means of the given constants measured the boiling 

point of sulphur with the following results:

TABLE 21. Constancy of temperature in boiling lubes. Sulphur.

No.

17

18

22

t.

o O.

20.4

20.4

20.9

21.2

21.5

21.7

e.

Microvolts.

4005

4005

3974

3967

4000

4000

C20.

Microvolts.

4008

4008

3981

3976

4012

4013

T.

°0.

445

445

445

445

446

446

Time.

h. m.

11 15

23

11 25

32

11 37

40

These results corroborate the statements made. All these data are 

obtained with older forms of apparatus. I believe that if I were torepeat them with the newer forms (Figs. 14,15) the limits of error would 

be much decreased and the experiment materially gain in certainty.

Remarks of the same nature as the above apply to mercury, for which 

the conditions of constant temperature are much more favorable. A 

long time series was made with element No. 22, where ebullition was 

purposely prolonged nearly five hours. The total variation of boiling 

point is here about £ per cent, of e2o- This variation, too, is incidental, 

and is largely due to the fact that here, as in the case of sulphur, a 

gentle current of carbonic acid circulated through the tube. In later 

experiments I observed an almost absolute constancy; but it is not 

necessary to multiply these data here.

What has been said of sulphur and mercury is, of course, eminently 

true of lower boiling points, like aniline and water, as Table 16 aptly 

shows. In case of substances which boil at lower temperatures still, 

like alcohol and ether, special devices for condensing the v;ipor in the 

lateral tube, which projects above the boiling tube, Fig. 9, must be resorted to.

Available substances of fixed boiling points. With these results in 

hand I thought it advisable to test the availability of a few organic 

and other substances of fixed boiling points. Usually such substances? 

even liquids like aniline, char or become so heavily gummed during

(773)
120 MEASUREMENT OF HIGH TEMPERATURES. [BUI.T,. 64.

ebullition as to vary the boiling point very'perceptibly. Results-of 

of this kind are succinctly given in the following table. Succinic and 

pyrogallic acid, for instance, are failures, whereas naphthaline, beuzoic 

acid, and camphor, when heat is applied gently and gradually, supply 

almost as fixed a boiling point as inorganic substances. In the case of 

solids like the present there are two distinct planes of demarkation observable. The first of these is the plane of ebullition, and coincides 

with the mean surface of the agitated liquid. The other is the plane of 

condensation or of solidification, and is marked by an opaque ring of the 

substance encircling the inside of the tube. The distance between these 

planes can be enlarged at pleasure by cautiously increasing the intensity of the flame of the ring burner, or by surrounding the boiling tube 

with a thick jacket of asbestos wicking. Of course it is advisable to 

insert the hot junction in vapor just above the plane of ebullition. 

Most of the results of Table 22 are obtained by older and more primitive 

forms of apparatus, and could be much improved by conducting the experiments in the new forms. The table also contains corrosive sublimate, 

which has a very convenient boiling point for many purposes.

TABLE 22. Available substances for boiling-point experiments.

Elem. 

No.

36

36

36

36

Substance.

Corrosive sublimate, HgCl».

Succinic acid . . .

Naphthaline ....

i. yrog£hiiic acici -

£20.

Microvolts.

2632

2627

2606

2639

2649

2631

2631

2647

2094

2088

2104

2240

2300

1741

1696

1696

1691

1679

1692

1730

1730

1818

T.

° G.

300

300

299

301

303

300

300

303

255

255

256

270

276

210

205

205

205

204

205

209

2C9

218

Time.

 Not taken.

1

} Not taken.

h. m.

1 45

55

2 0

8

15

20

55

57

Remarks.

(

Apparatus closed by corks, both of which

are charred.

12 above surface of liquid (melted HgClj).

In vapor.

6cm above surface of liquid. In vapor.

Ocm above surface of liquid.

f The acid boils brown, i. e., chars and gums-

.-. boiling point rises rapidly.

'

Ebullition intensified.

Liquid very dark brown.

Boils well and clear; combustion tube element 2"m above surface of liquid. Very

distinct planes of demarkation.

More naphthaline added. This obviously

changes the composition of the mass and

the boiling point. 

No constancy of temperature. Decomposed,

forming a viscous mass.

(774)
BARU8-] CALIBRATION OF ELECTRICAL PYROMETERS. 121 

TABLE 22. Available substances for boiling point experiments Continued.

Elein. 

No.

36

36

Substance.

Benzole acid....

'

Camphor .......

ew

Microvolts. 

1731

2071

2071

2071

2071

2077

2077 

1632

1638

1638

1645

1G49

1642

1640

1634

1644

T.

o O. 

209

254

251

254

254

255

255 

209

210

210

211

211

211

211

210

211

Time.

2 25

30

37

45

3 0

25

35 

4 0

15

20

45

515

35

6 0

6 0

6 0

Remarks.

Boils quietly; perhaps more so than naphthaline.

Boils quietly. Preferable to benzoic acid.

Scarcely changes color. Inodorous.

Distance Between planes of dotnarkation =

12cm. Asbestos jacket even red hot at one

point.

 > just below upper plane of demarkation.

 > just above lower plane of deiuarkalion.

Data for the variation of boiling point with pressure with a special 

view to therrnornetric application have been investigated for naphthaline 

(218°) and benzoph-enol (306°) by Crafts.1 The possibility of using selenium in glass boiling tubes has been demonstrated by Troost.2 Y. Meyer3 

has made use of amylbenzoate, dipkenylamin, and phosphorous pentasulphide.

Volatilizing points. In addition to the experiments on boiling points, 

I made an attempt to utilize the above apparatus for measuring points 

of volatilization. Professor F. W. Clarke suggested the arsenic point as 

a desirable and insufficiently known datum and Mr. G. F. Becker made 

a special request for the point of volatilization of cinnabar. With both 

of these substances as well as with sal ammoniac I made large numbers of 

experiments, but failed in getting satisfactorily constant and reliable results. The effect of applying the ring burner around the sublimable solid 

in the tube is to form a very perfect hyperboloid of one nap, as it were; 

a figure, in other words, which resembles in form a united stalactite and 

stalagmite. The effect of heating is to volatilize the solid around the 

plane of the ring burner, and condensation takes place above and below 

the plane, forming the figure specified. A priori, it might be argued 

that so long as the hyperboloid remains intact and completely envelops 

the thermo-element, so long will the temperature of the junction not 

increase above the point of sublimation of the substance. Except in

»Crafts, Chem. Ber., vol. 20, 1887. p. 709.

2 Troost, C. R., vol. 95, 1882, p.30.

 Goldschmidt u. Meyer; Chem. Ber., 1882, vol. 10, p. 137.

irjrrc\ (775)
122 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 64.'

the case of H4NG1, in which sublimation is very rapid, I was not able 

by using the tubes to obtain very distinct points of sublimation, showing au unmistakable tendency of these substances to superheat, or 

at least to contain superheated vapor in the interstices of the mass. 

Arsenic, for instance, forms a distinct mirror on the tube before any 

constancy of temperature is reached, and, moreover, the temperature 

may be increased above this point almost to the limits of heating 

capacity of the burner. In the case of cinnabar the conditions are still 

further complicated by the tendency of this substance to decompose in 

air at high temperatures. It is necessary, therefore, to pass through 

the tube a current of carbonic acid. By doing so, however, the tend, 

ency to irregularities of thermal constancy are much increased. For 

the reasons stated I think it preferable to withhold my data from this 

chapter altogether, and to publish them in connection with certain experiments on the relation between boiling point and pressure which I 

have in view. For such experiments the above apparatus, Fig. 11, is 

eminently fie. Possibly if the given substances be under sufficient 

pressure to liquefy them at the subliming point, a true value for the temperature of ebullition may be found.

Subsidiary data. In conclusion I desire to insert here a number of 

subsequent results, the electro-motive force of which is given on a diferent scale from that heretofore adopted. These data are not to be put 

in relation with the results given above, but are subsidiary as regards 

the matter discussed in Chapter IY, on which they have au important 

bearing. In each case the apparatus used to obtain them has been the 

perfected form, and the results are therefore as trustworthy as my 

methods can make them. Allowing for the difference in the assumed 

value of the standards used, they agree with such results as have already been given, with all desirable nicety.

TABLE 23. Calibration in zinc vapor, December 10,1886. 

[Charge of crucible, 9 ounces.]

No.

22

35

36

37

22

38

39

40

22

22

t.

° 0.

20

21

22

23

24

25

26

27

28

28

e.

Microvolts.

9830

11070

10980

11010

9780

10980

10980

10980

9735

9780

620.

Microvolts.

9830

11078

10997

11036

9814

11023

11031

11040

9803

9848

Time.

h. m.

2 15

20

. 25

30

35

37

40

45

55

3 00

Mean ejo, 

37, 38, 39, 40.

Microvolts.

11033

The following results were obtained at a later date. The thermocouples are tested in three different furnaces, placed side by side and

(776)
BARUB.j CALIBRATION OF ELECTRICAL PYROMETERS. 123

heated at the same time to different degrees of redness. The mean temperature of the outside of crucible was measured and found to be 1,400°.

TABLE 24. Calibration in ziwi vapor, November 10, 1887.

Couple 

No.

37

37

37

38

38

38

39

39

39

40

22

t.

°G.

20.8

21.2

22. 8

23.0

24.0

24.8

25.3

26.0

26.6

27.0

27.3

e.

Microvolts.

11065

11065

11050

10995

11013

11030

11040

11075

11030

10995

9883

620.

Microvolts.

11070

11070

11070

11030

11050

11070

11080

11130

11090

11050

9950

Time.

A. m.

1 40

1 50

2 5

2 14

2 20

2 30

2 40

2 45

2 50

2 55

3 0

Furuace 

No.

1

2

3

1

'2

3

1

2

3

3

3

Mean can, 

37, 88, 39, 40.

Microvolts.

11074

TABLE 25. Calibration in tin.

No.

22

35

22

22

22

36

37

t.

°G.

20

21

21

22

23

24

25

e.

Microwits.

15630

18460

15860

15300

16100

18950

18950

e?o.

Microvults.

15630

18468

15868

15317

16126

18984

18993

Time.

h. m.

6 30

35

40

40

40

no

55

An accident here stopped the experiment at intense white heat. It 

has been stated that a thick, viscous slag soon forms over the surface 

of the tin and the walls of the crucible, wholly enveloping the metal 

within it. A criterion for the boiling point of tin, therefore, will continue to be difficult of determination.

TABLE 26. Calibration in bismuth.

No.

22

22

22

22

22

22

22

22

22

22

t.

° C.

20

20

20

20

20

20

20

20

20

20

e.

Microvolts.

CJO.

Microvolts.

11790 ! 11790

12620

13940

14800

15780

16380

16510

16630

15550

1C900

12620

13940

14800

15780

16380

16510

1G630

15550

16900

Time.

h. m.

6 0

5

15

25

30

35

40

45

50

65

(777)
124 MEASUEEMENT OF HIGH TEMPERATUKES. [BULL. 54.

This is very nearly the electric datum for the boiling point of bismuth, 

at least globules of bismuth are scattered around the walls of the crucible. The bismuth slag is not so dark and opaque as the antimony slag, 

indeed, often quite colorless.

TABLE 27. Calibration in antimony.

No.

22

t.

°G.

20

20

20

20

e.

Microvolts.

15200

16000

17550

18000

020.

Microyolts.

15200

16000

17550

18000

Time.

h, m.

6 10

15

20

25

In these experiments intense white heats are produced by firing the 

furnace with two parallel blast burners, opposite in direction so as to 

blow a vortex of flame in the furnace. The crucible is finally corroded 

through, the antimony forming a corrosive opaque glaze with the clay 

of the crucible. A few small globules up as high as the flat lid of the 

crucible (Fig. 14) indicated very approximate ebullition. 

Many other experiments of the same class were made, m all of which 

the intensest degrees of white heat obtainable in the 

furnace (Fig. 14) were applied. Two and even three 

injectors were inserted, the blasts for which were furnished by a large bellows of Fletcher's pattern, run 

by a one horse power gas-engine. The data are subservient to the investigation in Chapter IV, where 

the attempt is made to calibrate the thermo-couple 

by direct comparison with the gas-thermometer, In 

this place, however, it is well to remark that definite 

data on the boiling point of antimony, bismuth, lead, 

tin, etc., will probably not be attainable by such a 

method as the present, except by heating these substances intensely in vacuo. Such experiments I 

hope to make at an early date, using for this purpose the form of crucible, Fig. 14a, which can be 

hermetically sealed. (See Preface, page 22.)

Thermo-electric datum for the melting point of platinum. Finally, it is interesting to contrast these hightemperature data with the values obtained when the 

junction of the platinum-platinum-iridium thermocouple is heated by the oxyhydrogen blow-pipe to 

extreme degrees of fusion. It is necessary for this 

purpose to make a thermo-couple of very thick wires 

. 23. Apparatus for and to insulate them by aid of tubes of calcined 

melting-point of Pia- Hme In Fig> ^ a c(mvenienfc method of experiment

(778)
13AUU8.] CALIBRATION OE ELECTEICAL PYROMETERS. 125

is shown. A A is a block of lime into which two capillary holes have 

been drilled, just large enough to receive the wires ft and y of the 

thermo-couple. These are united above by a little button of platinum 

lying at the base of a spherical cavity in the block A A. B is an oxyhydrogen blow-pipe by which the button is fused. A lid of calcined 

lime similar to the block A A in form but having a lateral outlet opposite B may be added. But the ignition is intense enough without this. 

In the following table are given the values for e20 obtained by heating 

the button in the open hearth, Fig. 23. The thermo-couple is old No. 

18, the. wires of which have been fused and drawn over again.

TABLK 28. Thermo-electric datum for temperatures above the melting point of platinu:n.

No.

18

t.

00.

20

20

20

20

20

620.

Microwits.

20400

20000

20400

20000

20400

Time.

h. m.

1 48

2 50

3 00.

5 33

50

Remarks.

First experiment.

Second experiment. Fresh

block of lime.

Third experiment. Fresh

block of lime.

The curiously constant electrical result for the temperature of the 

oxyhydrogen flame under the given circumstances is remarkable. It 

is interesting to note that when by any accident metallic connection is 

broken, there at once appear violent polarization disturbances. This 

shows that at the temperature of the OH2 blow-pfrpe, lime is quite a 

good conductor of electricity, for it is less probable that under the 

given conditions conduction should take place through the hot gases.

The thermal equivalent of the value of e in hand, however, is only 

1,600°, a datum certainly too small by 200° or more. This small value 

is significant. 1 It is in accordance with the small thermal datum for 

the boiling point of zinc, calculated from thermo-electric data, which 

apply only for the interval 0° to 400° (cf. p. 116). Hence it appears thut 

the equation e=aT+br a is an approximation, and that in high- temperature work the term

c (T3 -t3)

can not be neglected. This is equivalent to saying that, apart from 

considerations involving the Thomson effect, the electro-motive force 

at each junction of the thermo-couple has virtually the form

and that the real nature of the function c is not known. It is probable, 

however, that for practical thermometry an equation with three constants will suffice for all attainable ranges of temperature.

1 Cf. Introduction, pp. 49 and 50. 

(779)
CHAPTER III.

CERTAIN PYRO-ELECTRIC QUALITIES OF THE ALLOYS OF

PLATINUM.

EXPLANATION.

The immediate object of the investigations given in this chapter 

is to determine the approximate effect produced on the galvanic and 

the thermo-electric properties and 0:1 the density of platinum by alloying this metal with small amounts of some other metal. Not being 

sufficiently versed in the chemistry of the platinum group myself, and 

not wishing to burden my associates with the tedious task of rigorous 

chemical purification, I contented myself with a practical survey of the 

electrics of the platinum metals; nor was there enough time at my disposal to justify the attempt of an exhaustive examination.

The plan which under these circumstances suggested itself to me was 

to have a homogeneous ingot of platinum drawn down to a single length 

of tolerably thin wire, and then to compare the electrics of consecutive 

parts of this wire in their original and alloyed state with each other. 

A "coil of wire consisting of a single length about 131 meters and weighing nearly 420 grains was drawn down for me by the Malveru platinum 

works. The wire itself, weighing about 3.2 grains per meter, was 

nearly 0.043cm in diameter. I was the more easily able to acquiesce in 

this simple method of obtaining a platinum body for the alloys since, 

in earlier experiments of our own, samples of platinum and platinum 

alloys obtained in Paris could be fused over without producing any 

serious variation of constants, and since I inferred from the researches 

of Deville and Troost that the intense heating of platinum on a lime 

hearth before the oxyhydrogen blow-pipe, was itself a sufficient method 

of purification so far as the elimination of volatile and oxydizable constituents is concerned. Moreover, it has been stated in Chapter I that 

the general plan of work was to be such that special stress might be 

put on the effect of vanishing quantities of an alloying metal added to 

platinum. Hence I looked principally to obtaining a metallic body for 

the alloys showing fixed properties before and after melting.

In the course of the investigation, however, it became painfully obvious that the labor of making the alloys, the fusions, rolling and wire 

drawing, the experimental evaluation and the computation of the constants had been very much underrated. I found, in other words, after 

about one-half of my investigation had been completed, that the amount 

of work expended could have been justified only if the work had been 

126 (780)
*ABUB.] PYRO-ELECTRIC PEOPEETIES OF ALLOYS. 127

begun with absolutely pure materials. I found, too, that the purity 

tests which had originally been made were not rigorously sufficient; 

that portions of the single wire of platinum lying far apart differed 

more seriously in their electrics than I had apprehended, and that the 

platinum itself when exposed before the oxyhydrogen blow-pipe during 

long intervals of time (several hours) showed very measurable changes 

of the constants which had originally characterized it, and must therefore have changed somewhat in composition. . ^n exhibit of the numerical values of all discrepancies here involved will be given in the course 

of the chapter.

When so large a part of the investigation had been completed, however, it seemed expedient to push it to a close; for the classification 

diagram of the platinum alloys, which I was desirous of evolving, could 

not lead to serious misapprehension if only the scale of representation 

be chosen sufficiently small j if the profile, in other words, were reduced 

to a sufficiently small scale to make the errors negligible. Indeed, this 

appeared desirable because no general study of the electrics of the platinum alloys as complete as my own has as yet been made. Again, 

since in the scheme of fusing 2 per cent., 5 per cent., and 10 per cent, 

alloys, it was customary to use consecutive lengths of the platinum 

wire, the results at least show the effect of alloying a specified metal to 

a given body of platinum. Finally, the plan of operation by which the 

work was done is worthy of description, and with the amount of experience gained in prosecuting this tedious research I will, at an early 

opportunity, be able to repeat the work and bring the constants fully 

up to the standard of accuracy desired; in other words, to make the 

chemical measurement compatible with the electrical measurements.

Despite the discrepancies mentioned, this chapter is not barren in 

special results; and perhaps my main motive in publishing the data is 

due to the fact that they lead to a relation between the electrical conductivity of platinum alloys and the temperature coefficient of that 

conductivity, which is so nearly independent of the (alloyed) composition of the metals that I feel urged to ascribe to it the importance of a 

law. Very clearly does this appear when the present results for alloyed 

platinum are compared with a series of corresponding results long since 

found by Dr. Strouhal and myself when working with steel. I f'llly 

believe that in endeavoring to explain the mechanism of electrical resistance, the law in question will be more fruitful in suggestions than 

any allied phenomenon which has yet been investigated. Inasmuch as 

fused platinum appears to be the universal solvent for metals, the 

incontestable importance of series of data such as I here endeavor to 

investigate is more obvious in proportion as the number of metallic 

combinations obtainable is larger.

To recapitulate, therefore, the law in question (I use the term " law" 

simply to facilitate expression) is independent of the ingredients of the 

alloy except in so far as they modify its electrical conductivity. Alloy-

(781)
128 MEASUKEMENT OF HIGH TEMPERATURES. [BULL.54.

ing is here merely a method of modifying resistance, and the results 

are studied with regard to the resistance produced, not with regard to 

the way in which resistance is modified. In all of this work the chief 

object is to get nearer the true nature of electrical resistance, as a 

means possibly subsidiary to arriving at some results relative to tbe 

nature of electricity itself.

FUSION AND MECHANICAL TREATMENT OF THE ALLOYS.

Fusion, rolling. It has just been stated that it was my purpose 

to obtain groups of 2 per cent., 5 per cent., and 10 per cent, platinum 

alloys of as many metals as possible. The quantities were therefore 

weighed out in proper proportion and fused on a lime hearth, before 

the oxyhydrogen blow-pipe. The blow-pipe is identical with the one 

described in the next chapter. The hearths consisted of cubes or rectangular solids, cut with a hack saw from a large lump of lime as free 

from fissures as possible. Into each of the sides semicircular cavities 

were dug, with a semicircular-faced drill, on the lathe. Nickel, gold, 

copper, palladium, and tin were quietly absorbed by the melted platinum globule. Silver boiled perceptibly. Iron, and more particularly 

aluminium and manganese, were absorbed explosively. Chromium, 

cobalt, and even iridium were apt to splutter. Zinc, molybdenum, antimony, bismuth, lead, must be frequently added, but the quantity absorbed was usually sufficiently large to change the qualities of platinum 

perceptibly. With regard to rolling, it may be stated that the 10 per 

cent, gold and the 10 per cent, tin alloys are too brittle, and must therefore be diluted with further amounts of platinum. In the same way 5 

per cent, chromium, 5 per cent, aluminium, 10 per cent, copper, and 10 

per cent, nickel alloys, and others, usually break on rolling. Cobalt 

alloy, moreover, absorbs gas and inflates itself on cooling. Iron alloy, 

10 per cent., could be rolled by superficially fusing the rifts. This expedient, though not rigorously in favor of homogeneity of composition, 

had to be frequently resorted to; for instance, in case of antimony, bismuth, zinc, silver, and lead alloys which are more or less porous after 

fusion. Curious properties seem to be possessed by the tin alloys, inasmuch as the 10 per cent, alloy is brittle and hard enough to scratch 

iron. Experiments were made in rolling hot ingots, but with doubtful 

success, the quantities being too small to retain their heat for any length 

of time. I add, finally, that the work threw some light on the conditions of diffusion of any liquid metal in any other liquid metal, a 

phenomenon as yet imperfectly known.

Preliminary data, density. In all about fifty-two alloys were fused to 

buttons. These were then rolled to little bars of platinum about 10cm 

or more in length^ and about 0.013 n cm in section. Alloys of this length 

and section are suitable for preliminary measurements of resistance 

and density. The data for density are given in Table 29. They were 

obtained by suspending the platinum rods from a fiber of silk in a long

(782)
BABUB.] PYEO-ELECTRIC PROPERTIES OF ALLOYS. 129

stand-glass of distilled water and making the customary measurements. 

To make the process more convenient the left-hand scale-pan was replaced by a special lateral arm, being virtually a bent lever, the weight 

of which was concentrated as near its lower end as practicable, in order 

that the platinum rod might be hung as far from the center of figure or 

standard of the balance as possible. In this way abundant room for 

the stand-glass was easily secured. Measurements of density are subservient for the calculation of specific resistances, but they have an 

intrinsic value of their own.

Table 29 contains the results of the density experiments. In it Z, #, 

and m refer to the length ( cm ), the section (ncm), and the mass (g) of the 

bars of alloy. ^t and A0 denote their densities at t° and 0°, respectively. The alloys are usually arranged in series of increasing percentages of alloy, but where more than three alloys are examined these 

percentages must be inferred from the values of 4. Special analysis

of all the wires would be superfluous, for the reasons stated in the introduction. The results are intended to be purely physical.

TABLE 29. Density of platinum alloys.

No.

0

0

0

1

1

?,

?,

3

3

4

4

5

5

fi

0

7

7

8

a

0

n

10

10

is

11

12

12

13

13

14

14

Alloy.

....do.......................

....do.......................

Gold........................

....do.......................

. ...do. ................ ......

....do.......................

....do.......................

....do.......................

....do.......................

. ...do. ................ ......

....do.......................

....do.......................

....do. .....................

. ...do. .................. ....

....do.......................

....do.......................

....do.......................

....do .......................

....do.......................

....do.......................

....do.......................

....do.......................

. ...do ................. ......

....do.......................

....do.......................

....do.......................

....do....... ...............

"Rnll fi/1 O

I

99 sn

22.18

22.18

15.46

if; A.t\

15.50

15.48

35.80

35.82

15.22

15.23

23.92

24.05

24.05

24.04

16.66

16.65

16.10

16.11

17.60

17.60

16.34

16.27

16.00

16.01

17 Qi*

17.85

15.95

15.68

14.74

15.02

17.32

?

O ftlOQQ

1187

1187

0.01333

1QQ 1!

1343

1345

0746

0743

0. 01285

1282

1263

1265

0759

0758

0. 01252

1250

1316

1314

1280

1278

0. 01265

1265

1288

1289

1280

1282

0.01315

1317

1298

1293

1303

/7QO

m

5. 9889

5.6108

5. 6108

4. 3877

4 QQ77

4.4177

4.4177

S fidPd

5.6433

4. 1344

4. 1346

6. 3454

6.3798

P *IP77

3. 5381

4 37 fid

4. 3754

4. 3491

4. 3492

4. 4809

4. 4810

4. 3896

4. 3819

4. 3865

4. 3866

4. 8977

4. 8804

4. 3335

4. 2718

3.9415

3. 9990

\

')

t

o 

IQ <;

18.0

12.6

20.0

-ID O

oft O

13.4

13 d.

20.3

20.3

13.5

IP R

20.3

on 9

1 1 Q

0

13.5

IP fi

14.0

13 7

IP 0

14.2

14.3

14.3

14.5

14.6

14.8

14.8

15.4

14.8

15.0

15.5

15.8

At

91 3ft*\

01 9O7

91 3fl3

91 OQft

91 Ofift

01 Oftfi

91 911

01 10Q

01 1Q1

91 19Q

21. 163

on QOI

on ofii

1Q 9fift

19 394

9ft Q7^

21. 016

OA COO

20. 535

1Q 809

19 904

91 9P7

91 983

91 9Q9

01 O^O

O1 3/>Q

91 QHft

20. 662

20. 666

20. 584

OQ ^Q^

1 U f 1

Ao

01 QOI

01 311

91 919

OO QAft

01 07ft

01 OOO

01 991

01 1QQ

91 OA7

91 1^4.

01 173

01 flftO

on QQn

10 3Qfi

19. 405

on QQC

91 fl97

20. 534

20 546

19 903

19. 915

91 9/lfi

01 OQd

91 OQ3

21. 264

91 99ft

01 91fi

20. 674

Oft A7fi

20. 004

If 797

Ao 

Mean.

21. 315

91 9QQ

91 991

21. 172

21. 163

9ft QOI

19.400

21. 006

20.540

10 ono

21.271

91 07Q

91 31 Q

20. 676

20. COO
130 MEASUREMENT OP HIGH TEMPERATURES. [BULL. 54.

TABLE 29. Density of platinum alloys Continued.

Ho.

11

48

48

49

AQ

1R

1ft

17

17

18

IB

10

10

20

?,0

91

?,1

40

40

41

41

99

m

9Q

93

?4

?4

4?,

4?,

43

AI

JSfl

rri

51

51

91;

?,5

?,6

?,6

97

27

44

44

99

99

90

90

30

30

31

31

32

Alloy.

»

....do.......................

....do.......................

....do........... ............

....do .......................

Nickel......................

....do .......................

....do.......................

....do.......................

....do.......................

....do. ......................

....do .......................

....do.......................

....do.......................

....do.......................

. ...do. ................ ......

....do.......................

....do.......................

....do .......................

....do.......................

....do......................

....do .......................

. ...do. ......... ......... ....

....do.. ..................

....do.......................

....do .......................

....do.......................

....do.......................

....do.......................

Steel........................

....do.......................

....do .......................

....do.......................

....do .......................

....do .......................

....do.......................

....do .......................

....do.......................

....do.......................

....do.......................

Tin.........................

. ...do. ......... .............

....do.......................

....do.......................

....do.......................

....do.......................

....do.......................

..,,do. .....................

I

17.31

13.85

13.86

13.69

13.69

16.35

16.35

1H 73

15.73

15.98

15.99

14.49

14.50

15.41

15.41

18.96

18.95

14.20

14.18

13.38

13.40

14 54

14.54

14.92

14 91

13.27

13.26

13.22

13.23

12.71

12.73

13.24

13.24

13.00

13.00

12.14

12.14

14.84

14.84

17.38

17.39

14.64

14.64

14.34

14 34.

15.65

15.65

13.85

IS. 86

12.63

12.64

11.98

<?

1302

1216

1913

1933

1939

0.01261

1262

1303

1304

1346

1347

0. 01251

1261

1239

1239

19Qf»

1300

1235

1233

1218

1220

0. 01242

1245

1971

1971*

1274

1273

1211

1209

1227

1225

1228

1222

°1220

1220

0. 01314

1312

1208

1268

1314

1314

1209

1210

0. 01270

1270

1337

1331

1336

1335

0. 01233

1231

1265

(78

m

4. 2396

3. 5194

3. 5192

S QrtHrt

?.. 2999

4. 2606

4. 2670

4. 0777

4. 0776

4. 0350

A (13 iv*

3. 7625

3 7R9R

3. 7870

3. 7868

4. 7607

4. 7610

S. 3455

3. 3457

3. 4270

3. 4269

3. 7304

3. 7306

3. 8640

3. 8639

3. 3087

3. 3090

3. 1619

3. 1618

3. 2563

3. 2565

3. 1750

3.1748

3. 1627

3. 1629

3. 3329

3. 3331

3.8581

3. 8580

4. 6039

4. 6042

3. 6762

3. 6762

3.8445

3. 8447

4. 3782

4. 3774

3. 7835

3. 7836

3. 1842

3. 1844

3. 1387

*)

t

0

15.2

16.5

12 7

IDA

Ifi S

16.0

1 K C

15.6

16.2

16. 5

1^7

16.6

15.8

16.0

16.9

17 9

16.0

13.9

17.2

17.0

13.6

n

o

16.1

16.0

17 ^

17 >5

15.8

12.2

15.0

14.8

15.5

18.0

14.4

14.5

16.0

16.8

13.6

13.6

16.9

16.8

13.'7

18.4

14.2

16.8

13.6

16.8

13.6

16.8

13.5

16.8

10.5

16.8

At

IS 7QR

20. 890

20.922

1Q FlQfi

1Q ^fift

20. 686

'20. 660

19. 876

19. 876

18. 750

18. 727

20. 581

90 >V79

19. 825

19. 831

10 399

19. 310

19. 059

19. 116

21.013

20. 946

9fl fun

20. 589

20. 316

9A 31 Q

19. 564

19. 588

19. 730

19 747

20. 872

20. 875

19. 515

19.622

10 Q37

20. 888

20. 910

20. 493

20. 507

20. 154

20. 137

20. 761

20. 742

21. 098

21. 096

20. 921

21. 004

20. 438

20. 436

20. 444

20. 462

20. 712

Ao

18. 808

20. 903

20.932

19. 548

19. 574

20. 699

20. 673

10 880

19.889

18. 763

18. 740

20. 594

20. 585

19. 838

19.844

19. 335

19.323

19. 070

19. 130

21.027

20. 957

20. 653

20. 602

20. 329

20. 332

19. 577

19. 601

19. 740

19. 759

20. 884

20. 887

19. 529

19.633

19. 950

20.901

20. 921

20. 504

20. 520

20. 167

20. 148

20. 775

20. 753

21. Ill

21. 107

20. 934

21. 015

20.451

20. 447

20. 457

20. 470

20. 725

Ao 

Mean

18. 803

20. 917

19. 561

20. 686

19. 889

18. 751

20. 905

19. 841

19. 329

19. 100

20. 992

20.628

20. 330

19. 589

19. 750

20. 886

19.581

19.952

20. 911

20. 512

20.157

20. 764

21. 109

20. 974

20. 449

20.464.
BABUS.] PYRO-ELECTRIC PROPERTIES OP ALLOYS. 

TABLE 29. Density of platinum alloys Continued.

131

No.

3?

33

33

Ql

34

35

36

3fi

45

45

11

40

4fi

38

38

10

47

47

5?,

5?,

54

F.A

53

Alloy.

....do.......................

....do.......................

....do.......................

....do.......................

....do.......................

. ...do. .................... ..

....do.......................

....do.......................

....do.......................

....do .......................

....do.......................

...do .......................

....do.......................

....do.......................

... .do. ......................

I

12.00

11 44

11.44

14.35

14.34

12.87

14. 3C

14.36

13.76

13.76

16.86

14. 58

14.57

17.14

17.14

IP An

15.02

15.03

13.33

13.34

12.29

12.28

12.22

1

19R9

19QQ

19ft7

19Q7

0. 01320

1298

1296

19OQ

1991

O A197Q

1212

1911

0.01343

0.01311

1200

1 OA9

0. 01232

1998

1261

1262

1254

m

3

1QQQ

3

AQ71

3 A Q7O

3. 5870

3. 5867

3. 6090

3. 9585

3

QKQF:

3

KQfiQ

3. 5869

4. 5626

3

7 £07

3. 7539

4. 7703

4 77AQ

3. 7398

3. 8495

3 8495

3. 2990

O 9QQQ

3. 2496

3 9AQ.fi

3. 2667

t

o 

10.7

U o

13 ft

11.4

14.2

14.6

ICO

n

o

13 9

18.4

15.5

1 q A

17.6

15.8

19 A,

16.1

13.4

n

o

13.6

1C 9

19.8

20.0

At

9ft 71*;

20. 814

20. 779

19. 412

19 434

21. 250

91 9QC.

91 OfiA

91 9Q8

91 9Q1

91 IflT

21. 230

21. 228

20.722

21. 166

91 QQ7

21. 297

20. 065

20. 114

20. 959

20. 959

»

Ao

20. 724

on 7QA

19 421

19 445

91 9flQ

91 9f\9

91 97 A

91 3ftQ

91 9O.'!I

91 Iftft

21. 240

91 9^19

20.735

9A 779

91 1 7Q

91 Q47

21 311

20. 076

9ft 19R

20. 975

20. 975

(21. 315)

Ao 

Mean.

on 79d

9A SftT

19. 433

91 9R1

91 9rt1

91 3A9

91 Iftfi

21. 241

on 7eq

21. 179

91 *>90i

9ft 10.9

20.975

Preliminary data, electrical resistance of rods. Having given the 

values of 40 it is easy to measure the resistance of the bars of platinum 

alloy by carefully applying Matthiessen and Hockin's1 or other similar 

method. The resistometer shown in Fig. 24, is so conveniently applicable that a short description may be given of it even if its principles be 

well known. The appar atus may be made unusually compact by using 

Kohlrausch's admirable form of Wheatstone's bridge. In practice it is 

conveniently inserted in the same circuit with the thermopile adjustment, and the two Daniells used as a source of current. All circuits 

are to be made momentarily, of course.

In Fig. 24 the Kohlrausch bridge is shown at A. B is the attachment for small resistances, D the standard with which they are to be 

compared. Let s s be the small platinum rod to be tested. It is firmly 

clamped down by the insulated levers m m, which properly insert it in 

the bridge circuits, tin, m and the similar levers- nn, nn, may be moved 

along a stout horizontal rod at pleasure, and then clamped in any position. The part of ss to be electrically studied is stepped off by the 

rider e, the points of contact of which are knife edges at a known distance apart. The rider is also capable of being slid along a horizontal 

rod, parallel to the rod carrying nn, etc. When in use e is held down

£ Maxwell; Electricity and Magnetism,yd ed., 1881, p. 444. 

(785)
132 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

by a suitable spring. One of these riders (Fig. 25) is detached, and 

shown at r. In using Matthiessen and Hockin's method, it is merely 

necessary to connect a, 6,... .e, d, successively with the galvanometer.

FIGB. 24 and 25. Kesistometer with detached rider. Scale J.

Table 30 contains the numerical results investigated by aid of this 

apparatus. rt is the resistance (ohms) at the temperature t for the section q cm, and st the corresponding specific resistance (microhms). The 

length of rider indicates the efficient length of platinum rod for which 

any datum applies. The value of st in parenthesis refers to thin wire 

as containued in Table 31.

TABLE 30. Electrical resistance of platinum alloys (thick wires'). 

[rider length=10.04CID .]

No.

0

0

1

?,

4

 5

fi

7

8

fl

10

11

1?,

Alloy.

....do ...........................................

Gold.... ........................................

....do...........................................

....do...........................................

....do...........................................

... do...........................................

... .do........ ...................................

... do ...........................................

....do...........................................

....do........... ................................

n

19d"i

1285

1424

1678

3441

1516

1802

4586

i:,co

1628

1864

1571

1642

1909

t

20

18

20

21

2l

22

22

22

21

20

20

17

17

q

0. 01233

0. 01187

0. 01333

1343

0743

0.01285

1265

0759

0. 01252

1314

1280

0. 01265

1289

1280

St

15.35

15.26

18.98

22.44

25.58

19.48

22.79

34.80

19.53

21.40

23.86

19.87

21.17

24.43

(«)

15.55

15.55

19.23

22.73

25.91

19.73

23.09

35.25

19. 79

21, 68

24.17

20.13

21.44

24.75

(786)
BAKU8.] PYRO-ELECTRIC PROPERTIES OF ALLOYS. 133

TABLTC 30. Electrical resistance of platinum alloys (thick ivires) Continued.

[rider=length 10.04cm .)

No.

10

15

48

49

16

17

ia

19

?0

91

40

41

22

?,3

?4

42

48

nn

51

2

:

26

' 97

44

9,8

?,n

30

31

32

33

3d

35

36

45

37

46

38

39

47

5?,

54

53

Alloy.

....do ...........................................

....do...........................................

....do ...........................................

....do...........................................

Nickel..........................................

....do............................'............--.

....do...........................................

Cobalt..........................................

....do...........................................

.... do ...........................................

....do.. .........................................

....do...... .....................................

....do...........................................

....do...........................................

....do ...........................................

....do...........................................

....do...........................................

....do...........................................

....do...........................................

....do..........................................

. ...do. .................................... ......

Tin.............................................

....do...........................................

....do ...........................................

....do......:....................................

....do...........................................

....do ...........................................

....do...........................................

....do...........................................

....do ...........................................

..-.do ..........................................

Tl

2397

2628

4899

2118

1739

2110

2503

2379

3245

2680

3617

2004

9QR1

2946

5071

4585

2409

5025

3791

21G6

3294

3227

2652

1714

1942

2961

2001

1743

20.11

38.94

1273

1478

1438

1211

1457

2200

1223

lOQI

3894

1Q70

1191

t

16

17

17

17

17

18

18

18

18

19

20

16

15

20

20

?,0

18

18

17

17

21

21

21

15

21

20

20

20

19

17

17

16

16

15

16

16

18

19

15

14

22

18

9

0.01315

1OQO

i onq

1216

1232

0. 01261

1304

1346

0. 01261

1239

1299

1951

1218

1275

1274

 1209

1227

1222

1220

0. 01314

1268

1314

1210

0. 01270

1337

1336

0. 01233

1265

0. 01298

1287

0. 01320

1298

1223

0. 01278

121.2

0.01343

0.01311

1200

0.01232

0. 01261

0. 01254

8t

q-i CT

33 97

fi? 89

OK CQ

55.87

91 QQ

27.51

09 71

30.01

40.21

11 JM

44 69

9i AH

Q7 C7

fid fi9

55.65

29.51

61.70

46 24

28.47

41.75

42.41

0O Aft

91 78

OK O7

39.56

24.68

22.04

26.11

CA 1 1

16.79

10 1ft

17.61

15.48

n

,£Q

29.54

16.04

16.60

47 84

24.75

15.0

(«t)

qi no

34.41

61.65

2C.18

f\fi Q9

9-> 99

97 Q7

34.14

30.40

40.73

35.28

07 97

38.05

65.47

56.60

30. 00

62.86

47.11

28.84

4.9 3(1

4-9 Qfl

32.67

22.06

26.30

40.08

25.00

99 99

26.45

50.76

17.01

19.43

17 94

15.68

18.01

29.92

16.25

16.91

48.74

oc 01

EXPERIMENTAL DATA.

Further mechanical treatment resistance of wires. ^Leaving the discussion and comparison of these results for the text below, I may state 

that the experiments were continued by rolling and drawing down the 

wires in a wire-plate to a mean diameter of about .046cm. With these 

dimensions, the wires were manifestly well suited for a repetition of the 

resistance measurements just discussed under conditions thoroughly dif-

(787)
134 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

ferent from the above. In two respects, however, must the following 

results for specific.resistance vary essentially from the former results. 

During the process of drawing the wires down from the larger section 

(10G x q= 12,000 ncm) to the smaller section (106 x^-= 1,200 acm), breakages are not always avoidable nor even unfrequent; henc'e, it is necessary to refuse and to work the metal over thoroughly. Thus it happens 

that certain metallic constituents are partially volatilized. Again, the 

thin and thick wires can not be identical in homogeneity in the way 

called for by the present measurement unless the thick wires were 

themselves thoroughly homogeneous at the outset, a condition not to 

be premised. Hence the data of Table 31, the symbols of which have 

the same signification as in Table 30, will not be rigorously identical.

The present data of resistance of thin wires are to be compared in the 

sequel with, the thermo-electric and other data of the same wires. It is 

thus manifestly necessary to evaluate the respective constants of small 

lengths or parts of each of the wires. Inasmuch as all the data may be 

obtained accurately from less than 10cm of wire, and since for thermoelectric comparison only a mere point of this same partial length is necessary, it is obvious that the galvanic and thermo-electric constants may 

be obtained from a length of wire, the homogeneity of which may be 

assumed with impunity. For the total length being from 100cm to 200cm 

the efficient length is in every case less than one-tenth the length of the 

whole wire. It will be seen below that the stress I place on these results is by no means superfluous.

These remarks lead directly to Table 31.

TABLE 31. Electrical resistance of platinum alloys (thin wires).

No.

0

1

?,

3

4

5

f>

7

8

9

in

11

is

13

U

15

48

40

16

17

Alloy.

. ...do ............................................. ........

Gold......................................................

....do .....:...............................................

....do.....................................................

....do .....................................................

....do.....................................................

.. ..do ................................................... ..

....do. .............................................. ......

....do.....................................................

....do .....................................................

....do ...........................;.........................

....do.....................................................

... do .....................................................

....do .....................................................

Nickel.......;..........;.................................

....do...................,.............,....:.....:........

n

13300

15620

17380

13490

15450

22360

13170

 14170

16490

13110

13740

15960

20660

22000

40330

15160

31520

14170

17470

t

19

19

19

19

22

22

22

22

22

22

22

22

22

21

21

20

23

23

22

22

gxlO6

1257

1439

1452

1452

1466

1486

1548

1493

1520

1486

1534

1534

1520

1562

1548

1576

1713

1706

1583

1576

St

15.55

19.13

22.68

25.23

19.78

22.96

34.61

19.67

21.54

24.50

20.11

21.07

24.26

32.27

34.06

63.56

25.98

53.78

22.44

27.54

(788)
BABUS.] PYRO-ELECTRIC PROPERTIES OF ALLOYS. 135 

TABLE 31. Electrical resistance of platinum alloys (thin wires) Continued.

No.

18

19

20

21

40

41

fl?

23

?4

4?,

43

50

61

25

2fi

27

44

28

29

30

31

33

33

34

35

3fi

45

37

4fi

38

39

47

52

54

53

A 

C

Alloy.

Nickel...................................................

....do.....................................................

....do.........:...........................................

....do...................................... ...............

....do.....................................................

.. ..do.... .................................................

....do.....................................................

....do.....................................................

....do.....................................................

....do.......................... ...........................

....do.....................................................

Chromium.. ............................................ ..

. ..do. .............................................. ......

....do.....................................................

. ...do. ................................................ ....

Tin.......................................................

...do.....................................................

...do .....................................................

....do .....................................................

. ...do.... ....... ........ .......................... ........

... do ............................................... ......

.'...do .....................................................

Load..............*........................................

....do .....................................................

...do .....................................................

....do............*........................................

? Platinum purified by three fusions (half an hour of melt- 

' ing in all).

ft

21180

18510

25560

19950

26400

14720

23130

26620

37710

37510

17690

34870

28770

17600

26030

32670

13720

16090

24280

15700

13220

15900

29900

9700

11840

8940

10510

17830

9890

26340

14890

f 710 

) 504

<

22

22

22

22

23

23

22

23

23

23

23

23

23

23

23

23

23

22

22

22

22

22

22

22

22

22

23

23

23

23

23

23 

23

(/XIO0

1576

1576

1576

1590

1713

1676

1590

1590

1598

1670

1662

1735

1735

1590

1590

1619

1619

1633

1662

1655

1655

1655

1647

1720

1662

1720

1691

1691

1676

1691

1691

1810 

2781

ft'

33.38

29.17

40.29

31.72

45.24

24.68

36.78

42.33

60.28

62.88

29.39

60.51

49.91

27.99

41.39

52.90

22.21

26.27

40.35

25.98

21.88

26.31

49. 25

16. 68

19.67

15.37

17.76

30.14

16.57

44.55

25.17

12.86 

14.02

Thermo-electrics of wires. Having obtained this table in the way 

described, the marked ends of the wires were next subjected to thermoelectric measurement by exposing them to temperatures 100°, 358°, and 

448°, respectively, in the boiling tubes, already fully described in Chapter II. The results are given in Table 32. "No." refers to the individual wires of the couple examined, and gives the sign of the two metals 

thermo-electrically combined. Thus Auf+l 0) denotes that the goldalloy No. 1 is thermo-electrically positive to platinum No. 0. T and t 

are the temperatures of the thermo-electric junctions for which the 

electro-motive forces e (microvolts) apply, a and b the corresponding 

thermo-electric constants. Inasmuch as the thermo-electric data are 

necessarily most seriously affected by imparities in the alloys, it was

(789)
136 MEASUREMENT OF HIGH TEMPERATURES [BULL. 54.

deemed fully sufficient to compute a and & from extreme values for tf, T, 

e, and then to test this computation with the intermediate value. 

Laborious applications of the method of least squares were therefore 

discarded.

TABLE 32. Thermo-electrica of platinum alloys.

No

j

ATI .....<

Ag ......

Pd {

Ir ..<

'

+ 1-0

+ 1-0

+ 1-0

+ 2-0

+ 2-0

+ 2 0

+ 3-0

+ 3 0

+ 3-0

+ 4 0

+ 4-0

+ 4-0

+ 5-0

+ 5-0

+ 5 0

 + 6-0

+ 6-0

+ 6-0

- 7+0

 7+0

- 7+0

 - 8+0

 8+0

- 8+0

 9+0

- 9+0

-9+0

-10+0

-10+0

 10+0

 11+0

-11+0

-11+0

-12+0

-12+0

. -12+0

 -13+0

-13+0

 13+0

+14-0

-14+0

-14+0

+15-0

+15-0

-15 0

 48+0

t

16

19

17

16

19

18

17

19

18

18

19

18

18

22

18

18

22

18

18

20

18

19

20

18

19

20

19

19

18

19

19

18

19

19

18

19

18

18

19

18

18

20

19

18

20

18

T

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

e 

observed.

+ 46

+ 185

+ 242

+ 155

+ 637

+ 832

221

942

1225

7

6

18

32

88

105

107

428

558

- 86

- 526

 711

- 95

- 631

 869

- 120

- 821

-1127

- 222

-1066

 1384

- 336

 1584

 2035

- 517

 2480

-3228

- 15

 271

- 410

+ 44

 250

 392

+ 31

 257

 447

- 31

e 

calculated.

+ 46

+ 189

+ 242

+ 155

+ 648

+ 832

221

948

1225

7

18

18

32

94

105

107

436

558

- 86

 507

- 711

- 95

 600

- 869

 120

- 788

-1127

- 222

-1052

 1384

- 336

-1557

-2035

 517

 2453

-3228

- 15

 257

- 410

+ 44

 190

 392

+ 31

 227

 447

- 31

,.x«

+ 540

+ 1812

+ 2570

+ 100

+ 436

+ 1301

 844

»

- 869

 1073

 2548

 3904

- 5939

- 77

+ 1021

+ 867

 140

10«X&

' + 45

+ 263

+ 597

- 124

- 412

_ 7

-1738

-2472

-3327

 1453

 1799

 3394

-2212

-4139

-4083

 2026

(790)
BABUB.] PYRO-ELECTRIC PROPERTIES OF ALLOYS.

TABLE 28. Thermo-electrics of platinum alloys Continued.

137

No

Cu

Ni <

Co.......

Iron

Steel....,

-48+0

-48+0

+49-0

 49+0

 49+0

 16+0

-16+0

 16+0

 17+0

-17+0

 17+0

'-18+0

-18+0

-18+0

'+19-0

+19-0

+19-0

+20-0

+20 0

+20-0

+21-0

+21-0

+21-0

+40-0

+40-0

+40 0

+41-0

+41 0

 41+0

 22+0

-22+0

 22+0

-23+0

-23+0

 23+0

-24+0

 24+0

-24+0

-42+0

-42+0

-42+0

-43+0

-43+0

-43+0

f-50+0

 50+0

 50+0 

 51+0

 51+0

-51+0

t

23

19

18

23

19

19

18

20

19

1 Q J 8

20

19

18

'20

19

19

20

19

19

20

]9

19

20

19

20

15

19

20

16

19

15

20

19

15

20

19

15

21.

18

20

16

20

21

18

18

23

19 

19

24

19

T

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448

100

358

448 

100

358

448

e 

observed.

 326

 466

+ 41

+ 173

+ 305

 403

-1734

 2166

 745

- 3190

-3900

 946

-4134

-5095

+ 89

+ 61

 26

+ 164

+ 253

+ 170

+ 180

+ 149

+ 41

+ 347

+ 394

+ 327

+ 58

+ 18

+ 91

- 382

 2226

 3020

 402

 2401

 3313

 438

 2827

-3962

 465

 2983

 4274

 307

-1747

 2393

 474

 2945

-4159 

- 368

-2383

-3483

e 

calculated.

 305

 406

+ '41

+ 138

+ 305

- 403

-1710

 2166

 745

 3153

 3990

 946

-4019

-5095

+ 89

+ 81

- 26

+ 164

+ 277

+ 170

+ 186

+ 226

+ 41

+ 347

+ 551

+ 327

+ 58

+ 7

+ 91

- 382

 2200

 3020

 402

 2392

 3313

 438

 2818

 3962

 465

-2989

 4274

 307

 1730

 2393

- 474

 2927

-4159 

 368

 2419

 3483

10:'Xft

+ 915

 4905

 9065

-11469

+ 1481

+ 2560

+ 3033

+ 5519

+ 1038

 3887

 3969

 4085

 4222

 3246

 4500

 3305

10" X b

-3483

- 333

 552

 931

 3294

 4620

 6276

-10290

 2691

 6772

 8058

 11070

 1222

 4980

 11123

 10308

(791)
138 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54. 

TABLE 28. Thcrmo-elccirics of platinum alloys Continued.

No.

1

Cr.......

Sn.......

Al.......

Mn.....

Mo.....-;

Pb......

Sb......

 25+0 

 25+0

 25+0

-26+0

 26+0

-26+0 

-27+0

-27+0

-27+0

 44+0

-44+0

 4440

 -28+0

 28+0

-28+0

-29+0 

-29+0

-29+0

+30 0

 30+0

 30+0

 -31+0 

 31+0

-31+0 

 32-fO

 32+0 

. 32+0

 33+0

 33+0

 33+0 

 34+0

-34+0 

. 34+0

' 35+0

 35+0

 35+0

 36+0

 36+0

 36+0

 45+0

 45+0

 45+0

+37-0

+37 0

+37 0 

 46+0

 46+0

 46+0

r_38+0

' 38+0

1 38+0

*

19 

16

21

19

16

21 

18

16

21

16

21

19

19

17

20

18

17

20

18

17

19

18 

17

19 

19

18 

19

17

19

20 

I?

19 

19

17

19

19

18

19

25

17

22

19

19

20

20 

18

22

22

19

20

20

T

100

358

448

100

358

448 

100

358

448

100

358

448

100

358

448

100

OCQ OOo

448

100

358

448

100 

358

448 

100

358 

448

100

358

448 

100

358 

448

100

358

448

]00

358

448

100

358

448

100

358

448

iro

358

448

100

358

448

e 

observed.

 302 

 1687

-2239

 377

-2290

-3123 

 405

-2608

-3583

 347

-1918

-2605

- 30

 194

- 261

- 16 

 146

- 199

+ 16

 99

- 151

 102 

_ gg^

 779 

 130

 706 

 938

 90

 564

 758 

 253

-1C71 

 220G

 36

 202

 263

 275

 1320

 1673

 119

 557

 766

+ 43

+ 208

+ 268 

 ' 50

 258

 338

 131

 840

 1155

e 

calculated.

- 302 

-1653

-2239

- 377

-2253,

 3123 

 405

 2549

-3583

- 347

-1883

-2605

 30

 186

- 261

- 16 

_ ^34

 199

+ 1C

 71

 151

 102 

 568

 779 

 130

 691 

 938

 90

 541

 758 

- 253

-1561 

 2206

- 36

 193

 263

 275

 1287

 1673

 119

 570

 766

+ 43

+ 204

+ 268 

 50

. 248

 338

 131

 819

-1155

10'Xa

 3211

- 3733

 3766

 3494

 287

 10

+ 378

 1050

 1398

 869

 2360

- 378

 3170

 1312

 503

 549

 1261

106 Xb

 4334

 7636

 9860

 5522

 691

 771

 1562

 1641

 1688

 1925

-5957

 504

 1660

 1014

 264

 510

 3073

(702)
BARUS.] PYRO-ELECTRIC PROPERTIES OF ALLOYS. 139

TABLE 28. Thermo-clectrics of platinum alloys Continued.

No.

(-47+0

Bi ..... J 47+0

(_^7+0

C+52-0

-52+0

1 -52+0 

Zn ......<1+54-0

+54 0

I +54-0

t

18

22

19

19

24

19

19

24

19

T

100

358

448

100

358

448

100

358

448

e 

observed.

 39

 188

 245

+ 18

 248

 390

+ 19

+ 18

+ 24

e 

calculated.

 39

 184

 '245

+ 18

 215

 390

+ 19

+ 33

+ 24

103 X«

 443

+ 612

+ 296

10°X6

 274

 3288

 514

Temperature-coefficient. Table 33 contains the final series of data relative to the pyrometric constants of these wires. It contains mean 

values of the relation a between electrical resistance and temperature 

for each of the 52 wires of the above table. The marked ends of these, 

having been wrapped around the little insulating cylinders of porcelain 

so as to form a helix, the platinum spires of which do not touch each 

other (" open spiral spring"), were exposed to 25°, to 100°, and to 358°, 

respectively, in the space of constant temperature of my boiling tubes. 

To retain the helix, which is never more than 2cm long along its axis, in 

place, and likewise to connect the terminals of the bridge adjustment 

with it, the ends of the helix wire are fused to terminals of fairly-thick 

copper wire. One of these terminals passes through one canal of the 

porcelain insulator to connect with the upper end of the platinum helix, 

the oth'er terminal partially through the second canal in a suitable way 

to connect with the lower end of the helix. The measurements are 

then made in the customary way. Constancy of temperature along the 

2cm of length of helix may be assumed. The total length of platinum 

wire in the helix is that for which the above data, Table 31, apply.

In Table 33 therefore rt is the resistance corresponding to the temperature T, and a0100, <*o360 are the mean temperature-coefficients for the 

intervals of temperature 0° to 100° and 0° to 360°, respectively.

TABLE 33. Temperature-coefficients of platinum alloys.

» I

I

(

An.. 

I

No.

0

'0

0

1

1

1

2

2

2

3

3

3

T

25

100

357

20

100

357

21

100

357

22

100

357

n

0.759

0.883

1.296

0.408

0.464

0. 630

0.485

0.539

0.702

0.542

0. f-94

0.744

103 x a0 'o°

2.30

1.78

1.45

1.27

103xa1003«>

2.22

1.62

1.33

1.09

(793)
140 MEASUREMENT OF HIGH TEMPERATURES.

TABLE 33. Temperature-coefficients of platinum alloys Continued.

c

Ag..-

I

Pd..<

r

Ir...«

r

Cu..<

Ni..s

f

Co.J

t

No.

4

4

4

5

5

5

C

6

6

7

7

7

8

8

8

9

9

9

10

10

10

11

11

11

12

12

12

13

13

13

14

14

14

15

15

15

16

16

16

17

17

17.

18

18

18

19

19

19

T

23

100

357

25

100

357

25

100

357

19

100

357

19

100

357

19

100

357

19

100

357

18

100

357

18

100

357

18

100

357

18

100

357

18

100

357

17

ioo

357

17

100

357

18

100

357

18

100

357

rt

0.413

0. 468

0.635

0.472

0.522

0.675

0.631

0.678

0.794

0.408

0.464

0.630

0.441

0.494

0.658

0.501

0.552

0.701

0.408

0.463

0.628

0.425

0.480

0.641

0.495

0.546

0.697

0.640

0.686

0.821

0.678

0.722

0.847

1.205

1.225

1.286

0.443

0.503

0.668

0.506

0.561

0.714

0.673

0.730

0.880

0.572

0.622

0.772

103 Xao100

1.80

1.46

1.02

1.75

1.53

1.29

1.72

1.63

1.28

0.89

0.80

0.20

1.68

1.34

1.05

1.09

lOSXamo360

1.61

1.02

0.71

1.62

1.48.

1.18

1.61

1.50

1.21

0.83

0.72

0.20

1.46

1.19

0.87

1.04

(794)
BABUS.] PYRO-ELECTRIC PROPERTIES OF 4LLOYS.

TA.BLE 33. Temperature-coefficients of platinum alloys Continued.

141

f

Co..<

f

Fe.--

I

r

Cr...

r

Su.--

i

t

f " 1i

f

HO..-J

No.

20

20

20

21

21

21

22

22

22

23

23

23

24

24

24

25

25

25

20

26

26

27

27

27

28

28

28

29

29

29

30

30

30

31

31

31

32

32

32

33 

33

33

34

34

34

35

35

35

30

36

36

T

20

100

357

20

100

357

21

100

357

21

100

357

21

100

357

21

100

357

21

100

357

21

100

357

20

100

357

19

100

357

19

100

357

15

100

357

16

100

357

17 

100

357

18

100

357

19

100

357

19

100

357

n

0.783

, 0. 838

0.986

0.639

0.717

0.929

0.708

0.749

0.882

0.797

0.838

0.908

1.405

1.440

1.575

0.536

0.583

0.726

0.791

0.831

0.956

0.963

1.005

1.125

0.392

0.439

0.585

0.497

0.547

0.697

0.848

0.895

1. 038

0.489

0.524

0.681

0.408

0.460

0.614

0.488 

0.539

0.680

0.946

0.986

0.091

0.302

0.352

0.499

0.370

0. 421

0.577

a0 x 103

0.89

1.57

0.74

0.60

0.37

1.14

0.65

0.56

1. 55

1.27

0.69

0.85

1.56

1.28

0.52

2.13

1.76

a 100360 xl03

0.74

1.30

0.74

0.64

0.36

1.06

0.62

0.49

1.49

1.20

0.66

1.32

1.50

1.14

0.43

1.94

1.69

(705)
142 MEASUKEMENT OF HIGH TEMPEEATURES. [BULL. 54. 

TABLE 33. Temperature-coefficients of platinum alloys Continued.

,

Pb..-|

I

f

Sb.J

j Co.J

I

f

Co.<j

I

1

I

Crl

1

(

MoJ

H

» I 1

r

CU!.J

e.v

r

Zn.<j

.

No.

37

37

37

38

38

 JO

40

40

40

41

41

41

42

42

42

43

43

43

44

44

44

45

45

 45

46

46

46

47

47

47

48

48

48

49

49

49

50

50

50

51

51

51

52

52

52 

54

54

54

T

20

100

357

20

100

357

21

 100

357

22

100

357

22

MO

357

23

100

357

20

100

357

20

100 

357

20

100

357

20

100

357

19

100

357

19

100

357

19

100

357

39

ICO

357

15

100

357 

18

100

357

n

0.298

0.350

0. 514*

0.541

0.588

0.736

0.810

0.891

0.067

0.456

0.504

0.650

1.098

1.135

1.243

0.345

0.374

0.460

0.591

0. 635

0.766

0.227

0.263 

0.370

0.225

0.260

0.363

0.303

0.352

0.505

0.4C7

0.514

0.648

0.978

1.001

].038

0. 771

0.798

0.875

0.815

0.865

0.999

0.840

0.876

0.945 

0.391

0.433

0.547

00.0.0X103

2.28

1.11

1.30

1.39

0.44

1.12

0.95

2.06

2.02

2.10

1.27

0.29

0.44

0.77

0.51

1.34

Wxio.

2.23

1.09

0.83

1.27

0.39

0.98

0.87

1.88

1.82

2.03

1.14

0.15

0.39

0.64

0.32

1.14

(TOG)
BABUB.J PYRO-ELECTRIC PROPERTIES OF ALLOYS.

PURIFIED WIRES.

143

A. Thrice

fused.

C. Thrice

fused.

1 19

I 100

I 357

1 W <^ 100

I 357

0. 223 ]

0. 273 >

0.420J

0. 299 1

0. 357 I

' 0.545J

2.90

2.52

2.05

2.58

General digest. Following, in Table 34, is a general digest of the above 

results, in which density J0 at zero degrees, specific resistance st, as 

obtained from thick (I) and from thin (II) wires at mean room temperatures, mean temperature-coefficient a for the large and the small intervals 0° to 100° and 0° to 360°, respectively, specific resistance s0 for 0° 

computed with a, and, finally, the thermo-electric power a per degree 

centigrade at 0°, are carefully inserted. The data for purified wires 

are discussed below:

TABLE 34. Constants of platinum alloys. Digest.

No.

0

1

2

3

4

5

6

7

8

9

10

11

12

ID J.O

14

15

48 ' 49

16

17

18

10 A3

20

21

40

41

22

23

24

42

43

50

Metal alloyed 

to platinum.

Platinum .........

Gold..............

....do.............

....do.............

Silver .............

....do.............

. ...do. ............

Palladium ........

....do.............

....do.............

Iridiutn. ..........

....do.............

....do.............

Copper ...........

....do.............

. ...do. ......... ...

....do .............

....do.............

Nickel............

....do.............

... do .............

Cobalt............

....do.............

....do.............

....do .............

....do.............

Iron ..............

....do .............

....do .............

....do.............

....do.............

Steel..............

Ao

21. 315

21. 288

21. 221

21. 172

21. 163

20. 991

19. 400

21. 006

20.540

19. 909

21. 271

21. 279

21. 319

20. 670

20. 600

18. 803

20. 917

19. 561

20. 686

19.889

18. 751

20. 590

19.841

19. 329

19. 100

20. 992

20. 628

20. 330

19. 589

19. 750

20. 886

19. 581

I

(thick) 

#t

15.30

18.98

22.44

25.58

19.48

22.79

34.80

19.53

21.40

23.80

19.87

21.17

24.43

31.51

33.97

63.82

25.69

55.87

01 &L. Q1 yo

27.51

33.71

30.01

40.21

34.83

44.69

24.45

36.80

37.57

64.62

55. 55

29. 51

61.70

n

(thin)

St

15.55

10 LiJ. XOn

22.68

25.23

19. 78

22.96

34.61

19.67

21.54

24.50

20.11

21.07

24.26

qo 07 Ou. ui

34.00

63.56

25.98

53.78

22. 44

27.54

33.38

on 6fO» i J~ 7I

40. 29

31.72

45.24

24.68

36.78

42. 33

60. 28

62.88

29.39

60.51

103 Xa

2.30 2.22

1.78 1.62

1.45 1.33

1.27 1.09

1.80 1.61

1.46 1.02

1.02 0.71

1.75 1.62

1.53 1.48

1.29 1.18

1.72 1.61

1.63 1.50

1.28 1.21

0.89 0.83

0.80 0.72

0.20 0.20

1.27 1.14

0.29 0.15

1.68 1.46

1.34 1.19

1.05 0.87

1.09 1.04

0.89 0.74

1.57 1.30

...... 0.83

1.39 1.27

0.74 0.74

0. 66 0. 64

0.37 0.36

0.44 0.39

1.12 0.98

0.44 0.39

II

(thiu) 

So

14.91

18.53

22.13

24.67

19.06

22. 28

33.97

18.95

20.90

23.87

in xa J.«7. **&

20.40

23.64

91 OJ.. 7C 13

33.59

63.56

25.29

53.60

21.67

26.84

32.76

28.56

39.62

30. 70

44.57

23.97

36.33

41.80

59. 92

62.52

28.75

60.16

103 Xa

540

1812

2570

100

436

1301

- 844

- 869

- 1073

9>vlR

- 3904

- 5939

- 77

1021

867

- 140

915

yJOAC 

 3tUU*>

- 9065

-11470

1481

2560

3033

S519

1038

 Ooo PU87 J

- 3969

- 4085

- 4222

- 3246

- 4500

[/'(0):/(0)jX10«

2.33

1.84

1.49

1.33

1 B7 . 01

1.79

1.55

1.33

I

rjD 

. IO

1.67

1.30

0. 01OL

0.83

0.21

1.31

0.34

1 J.« 7*O

1.39

1.11

1.11

0.93

1.43

O f A <4

0.67

O O7 * 3f

0.40

1.21

0.46

(797)
144 MEASUREMENT OF HIGH TEMPERATURES. IBULL. 51. 

TABLE 34. Constants of platinum alloys. Digest Continued.

No.

51

25

26

27 

44

28

29 

30

31

32

33

84

35 

36

45

37

46

38

3d

47

59

54

KO

Metal alloyed 

to platinum.

....do.............

....do .............

....do............. 

....do............. 

Tin...............

....do............. 

....do.............

....do .............

....do.............

Molybdenum .... 

....do.............

....do.............

....do .............

....do .............

....do.............

Ao

19. 952

20. 911

20. 512

20. 157 

20. 764 

21. 109

20. 974 

20.449

20. 464

20.724

20. 807

19. 433

21. 263 

21. 261

21. 302 

21. 180

21. 241 

20. 753

21. 179

21. 329

20. 102

20. 975 

(2J.3)

I 

(thick)

«t

46.24

28. 47

41.75

42.41 

32.06 

21.78

25.97 

39.56

24.68

22.04

26.11

50.11

16.79 

19.18

17.61 

15.48

17.68 

29.54

16.04

16.60

47.84

24.75 

15.00

II 

(thin)

St

49.91

27.99

41.39

52.90 

31.71 

22.21

26.27 

40.35

95 oa

21.88

26.31

49.25

16.68 

19.67

17.17 

15.37

17.76 

30.14

16.57

44.55

25.17

10' X a

0.77 0.64

1.14 1.06

0.65 0.62

0.56 0.49 

0.95 0.87 

1.55 1.49

1.27 1.20 

0.69 O.C6

1 V>

1.56 1.50

1.28 1.14

0.52 0.43

2.13 1.94 

1.76 1.69

2.06 1.88 

2.28 2.23

2.02 1.82 

1.11 1.09

2. 10 2. 03

0.51 0.32

1.34 1.14

II

(thin) 

so

49.16

27.37

40.87

52.35 

31.09 

21.52

25.60 

39.86

95 Vt

21.18

25.64

48.87

15.96 

18.95

16.40 

14.64

17.00 

29.48

15.83

44 1Q

24.51

103 Xa

- 3305

- 3211

- 3733

-^3766 

- V 3494 

- 287

- 10 

+ 378

1050

- 1398

- 869

- 2360

- 379 

- 3170

 1312 

- 503

- 550 

 1261

 443

+ 612

+ 296

(/(0):/(0)JX105

0 31

1.17

0.66

0.58 

0.98 

1 57

1.29 

0.70

1.58

1

OO

0.55

2.20 

1.78

2.12 

2.30

2.09 

1.12

2.12

0 57

1.41

PURIFIED WIRES

fused.

C TMlTlPA

fused.

....do.............

12.86

14.02

2.90 2.65

2.52 2.58

12.04

13.27

2.96

2.50

DISCUSSION AND INFERENCES.

Earlier results. I shall pass rapidly over the above data for density 

resistance and thermo-electric behavior, since they are frequently provisional. They exhibit a definite method of work carried to an issue. 

The results are of increasing value in proportion, as they lead to the 

relation between electrical resistance and temperature-coefficient of 

electrical resistance, to which I have already adverted.

Here I may state that the original attempts to co-ordinate resistance and thermo-electric power were made by Dr. Strouhal and myself 1 

in discussing data for'steel. The striking success of this attempt, to 

which a large number of subsequent results gave additional and final 

warranty, led us naturally to seek for similar relations in alloys of one 

metal with consecutive small parts of a second metal. These results,

i Of. Wiecl. Ann., vol. 7,1879, p. 383 ; ibid, 1880, vol. 11, p. 930.

(70S)
UABUB.] PYKO-ELECTRIC PROPERTIES OF ALLOYS. 145

however, exhibit more complicated relations. Indeed, our data for 

alloys of silver with platinum, gold, copper, and zinc showed that the 

results for steel were due to causes intrinsically different from the 

causes varying the electrical properties of alloys. Owing partially to 

this negative result and partially to the necessity of changing our 

laboratory location from Wiirzburg to Prague and to Washington, 

these data1 for alloys remained unpublished in German until 1884, and 

in English2 until 1885.

In the mean time M. L. Weber,3 who, at the suggestion of Beetz, had 

sought for similar relations among the amalgams of mercury, was able 

to publish a fine and elaborate research on the galvanics and thermoelectrics of those substances. In addition to the results of Strouhal 

and myself for silver alloys, and Weber's results for amalgams, it was 

hoped that the present results for platinum alloys would supply such a 

sufficiency of new data that from all the results thus in hand certain 

general inferences bearing on the properties of alloys might safely be 

drawn. This discussion must, however, be deferred for the reasons 

already mentioned, page 125.

Resistance and density. Turning first to the columns for J0 > *« I, and 

se II, in Table 34, the number of strikingly large values of the specific 

resistance of platinum alloys at once meets the eye. If the specific resistance of good commercial platinum be put st=13, then it needs but 

trifling additions of chromium, or iron, or copper, or tin, or manganese, 

or zinc, etc., to increase this resistance nearly fivefold. In discussing 

results for silver alloys Dr. Strouhal and I observed that the galvanic 

effect produced by alloying increased with the differences of density of 

the ingredients of the alloy. In view of the exceptionally high density 

of platinum and the pronounced tendency of this metal to form alloys 

of high specific gravity, these inferences seem to be substantiated here, 

bearing in mind that the differences of density of the ingredients can 

only be one of many factors which go to determine the properties of the 

alloy produced. To go into further particulars is undesirable, but I may 

remark that though the effect produced by aluminium is exceptionally 

small, iridiuin and gold, both of large densities, produce small increments 

of resistance, whereas the enormous variations due to tin, chromium, 

iron, zinc, copper, manganese, cobalt, silver, nickel, palladium, decrease 

in general in the order of their increasing densities. The absorption of 

gases, the want of homogeneity, and the very probable tendency to 

form alloys of definite chemical composition are the main causes which 

tend to obscure the regularity of the physical phenomena. The differences between st I and st II, derived, respectively, from the bars and the 

wires, are no larger than may be easily referred to difficulties of manipulation. In the case of chromium, of iron, of cobalt, and of aluminium

1 Abb., kortigl. Bohm. Gesell. Wias., 6th series, vol. 12, 1884,

2 Bull. U. S. Geol. Survey, No. 14,1885, pp. 76 to 88,

3 Weber: Wied. Ann. vol. 23,1884, p. 447. 

(799)

Bull 54 10
146 MEASUREMENT OF HIGH TEMPERAUURES. [BULL. 54.

alloys, large discrepancies sometimes occur, showing that in these instances the base metal can not have been perfectly dissolved nor the 

alloy satisfactorily homogeneous. Inasmuch, however, as the method 

of comparing the specific resistance of the ingot as a whole, as it were, 

with a small part of the wire drawn from it is a very rigorous test for the 

homogeneity of the alloy, it appears from the coincidence of the results 

for st I and se II, that melted platinum may indeed be regarded as a 

solvent for metals generally. The importance of this quality has already 

been signalized above.

Resistance and tkermo-electrics. It has been stated that the thermoelectric results are the ones most influenced by impurities in the platinum, for the alloys of this metal, though exhibiting enormous diifereuces 

of resistance, are, with few exceptions, relatively without marked thermoelectric variability. This is an observation of importance, particularly 

if considered with reference to the position of the individual alloys in 

the series. It shows that there is probably no intrinsic relation whatever between specific resistance and thermo-electric power when the 

variations of both the quantities are produced by alloying. Curiously 

enough the extremes of the thermo-electric variations are the cobalt and 

the nickel alloys, the former being powerfully positive, the latter even 

more powerfully negative. The iridium alloy has the well-known extreme electro-negative position, as would also have the molybdenum 

alloys. On the other hand, the positions of iron, of chromium, of manganese are not nearly as extreme as would have been anticipated from 

their resistance values, whereas the powerfully resisting combinations 

of platinum-copper, platinum-zinc, platinum-tin show only insignificant 

values of thermo-electric power. In short, there appears to be no law 

for the co-ordination of the galvanic and thermo electric qualities discernible, and large values in the one case by no means imply large 

values in the other. 

Electrical tests for purity. Having thus briefly discussed the thermoelectric and resistance data in the above tables, it will be next in place 

to describe the experiments made to ascertain the condition of purity 

of the platinum used. These experiments have special importance, because they exhibit the electrical behavior of commercial platinum frequently treated before the oxyhydrogen blow-pipe, and therefore show 

what degree of purity of platinum is necessary in order that the metal 

may be safely used practically in thermo-electric temperature measure, 

ment.

The original experiments made, with a length marked A, and cut 

from the coil above described, behaved in such a way as to give rise to 

no serious apprehensions. This piece was first annealed, and then 

ther mo-electrically combined with No. 0, as were the wires in Table 32.

(800)
UAEUS.l PYRO-ELECTRIC PROPERTIES OF ALLOYS. 147

The following data were obtained, nomenclature as above:

TABLE 35. Electrical tests for purity.

Number.

J. A ft

+A 0... 

+A-0...

t

 20

18 

17

T

100

358 

448

e observed.

+ 68

+ 345 

+447

e calculated.

68

335 

446

«X103

777

&X10«

554

This wire A was then fused before the oxyhydrogen blow-pipe consecutively for five minutes each time and tested both for resistauce 

and for thermo-electric power after each fusion. The results investigated range as follows, being obtained, of course, from wires drawn and 

softened from the buttons, for each case:

TABLE 36. Electrical tests for purity.

Before fusion......

After one fusion. . .

After two fusions . .

After three fusions.

Galvanics.

rt

913

707

723

710

t

23

23

23

23

tfXlOS

1450

1890

1810

1810

St

13.5

13.3

13.1

12.9

Thermo-electrics.

Couple.

+A-0....

+A-0....

+J.-0....

+4-0....

T t

358 25

358 25

358 25

358 25

e

+336

+347

+337

+345

These results give clear evidence of the occurrence of volatilization 

during the whole of the fifteen minutes of fusion before the blow-pipe. 

But the amount of variation (6 per cent.), though large in itself, was not 

relatively so large with reference to the total variation due to alloying (500 

per cent.) as to be seriously apprehended. Moreover, the button could be 

purified by intensely fusing it on lime for some time before alloying it.

A second set of experiments, unfortunately made some time after these, 

gave rise to much more pronounced results. To determine the degree 

of homogeneity of the wire I compared parts of it of about 100cm each, 

the original positions of which were about equidistant along the whole 

130 meters of platinum wire. The galvanics and thermo-electrics of these 

samples ranged as follows, each having been softened before testing:

TABLE 37 . Electrical teats for purity.

No.

B

0

D

' E

F

Galvanics.

rt

11'15

1220

1198

1185

1058

t

23

23

23

23

23

gxlOo

1493

1493

1493

1493

1493

st

16.7

18.2

17.9

17.7

15.8

No.

 .B + 0

-0+0

-D+0

-E+0

+F 0

-0+A

Thpriuo-electrica.

t

25

25

25

25

25

25

T

358

358

358

358

358

358

e

 127

-358

-386

-284

+18

 691

(801)
148 MEASUREMENT OF HIGH TEMPEEATUKES. fliULL. 54.

Ihese wires, J3, (7, D, E, JP, were now fused thoroughly together and 

kept melted before the blow-pipe for fifteen minutes; thereupon drawn, 

annealed, and softened. The new wire on being tested gave the following results:

TABLE 38. Electrical tests for purity.

No.

(B+C+D+

E+F)

Galvanios.

n

786

t

23

gxlOB

1064

St

15.4

No.

-(J3+0+D

+J2+F) + 0

Thermo-electrics.

t

25

T

358

e

-241

The new wire was now again purified by fusing for fifteen minutes ; 

then drawing and annealing. The results obtained were :

TABLE 39. ^Electrical tests for purity.

No.

(E'+CP+D' 

+E'+F')

Galvanics.

re

504

t

23

gxlOG

2781

St

14.0.

No.

 (B'+C' + D1 

-t-jE'+.F'M-O

Thermo-electriss.

t

25

T

358

e

 170

The direct result for e in case of the couple C-\- A agrees well with 

the result which may be compounded from Tables 35 and 37. If now 

we compare the mean valuer of st from Table 37 (17.3) and the values 

in Tables 38 and 39 (15.4.14.0), it appears that the decrement or volatilization of the impurity is greatest during the first minutes of the fusion. 

Hence, since it was customary to heat the buttons beyond the fusing 

point for several minutes before alloying, and since, moreover, the range 

of specific resistances due to alloying is enormously large, it is probable

that impurities in th^ platinum have not distorted the data for resistance 

and density to a serious extent.

The same degree of reliance can not be placed on the thermo-electric 

data. Indeed, the behavior of the fused sample here is curious. In 

Table 36, for instance, the values of e oscillate, and are actually greater 

after the third fusion than originally, whereas the values of *t f'or the 

same wire, under the same circumstances, decrease with the utmost 

regularity. The mean values of Table 37, as compared with the values 

in Tables 38 and 30, show a similar irregularity of decrease. It follows 

therefore that the results for axlO3 must be regarded as distorted by 

an arbitrary constant, which remains nearly the same for a single set of 

alloys, but which varies from one set to another by an amplitude, the 

maximum total value of which can not be safely put less than 1,000. 

In other words, the error of ax 103 from series to series may be as large 

as i500. It is only the more powerful thermo-electric combinations in 

the above, t. e., alloys ot gold, cobalt, silver, manganese, chromium, iron,

(802)
HARUS.1 PYRO-ELECTRIC PROPERTIES OF ALLOYS. 149

nickel, iridiura, and molybdenum, which fall well outside of this zone of 

error, and for such. only, have thermo-electric inferences been drawn.

Electrical resistance and its temperature-coefficient. 1 have now to touch 

upon the main results of the present chapter, i. <?., the relation between 

the resistance (SQ ) and the temperature-coefficient of resistance (a). The 

results in the digest, Table 34, may be best exhibited in a chart, Fig. 26, 

in which a x ift3 is represented as a function of s0. It is well to remark 

in passing that a has been calculated by a linear formula, and from the 

three observations made at ordinary temperatures at 100° and at 357° two 

values of a may be reasonably deduced, since the measurement at room 

temperature is less liable to error. The equation a=(r r') / (rt' rf) 

furnishes a0m and tf0356, both of which are inserted in Table 36. s0 applies 

for 0° C. The assumption of the linear form has been wholly a matter of 

convenience, it being desirable to avoid the excessive computation which 

would have been necessitated by quadratic forms.

The figure contains both <V°° and a0*5G, the former of which is given in 

heavy or large dots; the latter is in comparatively light dots. Vertical 

lines pass through each datum, and at their ends the name of the platinum alloy is inscribed. For the sake of comparison, finally, there has 

been introduced into the chart a curve showing the results which Dr. 

Strouhal and i1 formerly obtained for iron-carburets, the data themselves ranging as follows: .

Specific electrical resistance and electrical temperature-coefficient of steel. Practical table.

s

cm 

- -sO0 CIW1

microhm.

10

11

12

13

14

15

16

17

18

19

20

a.

0. 0050

48

46

44

42

41

39

38

36

35

34

S

cm ---,0° cm-*

microhm.

21

22

23

24

25

20

27

28

29

30

31

a

0. 0033

32

31

29

28

27

27

26

25

24

23

8

?'%00 cm-*

microhm.

32

33

34

35

' 30

37

38

39

40

41

42

a

0. 0022

21

21

21

20

19

19

19

18

18

17

8

cm ---50° 

cm2

microhm.

43

44

45

46

47

48

49

50

60

70

80

a

0. 0017

17

16

 16

15

15

15

15

13

13

12

This curve is dotted in the figure, the alloy curve being given in a full 

line. . ° .

Returning to the curve for alloys, it appears that the difference between o-o100 and a<?56 is not larger than is quite in keeping with the occurrence of reasonable curvilinear relations between resistance and temperature, and that for the present purposes, where a general survey over 

the whole group of platinum alloys is to be attempted, <V°° may be 

accepted as coincident in value with the respective tangents of the

»Wied. Auu., vol. 20, 1883, p. 525; Bull. U. S. Geol. Survey, No. 14, 1885, p. 19.

(803)
 flj

CO

H

2! 

H

o

g

H

w

a 

H

g

K> 2O 30 4O 

FIG. 26. Chart showing the relation between electrical resistance (microhms) and 
BABUB.] PYRO-ELECTRIC PROPERTIES OF ALLOYS. 151

curvilinear relations in question. Large differences between aQ m and 

oV56 occur in case of one aluminium alloy, two cobalt alloys, and one 

silver alloy; but the exceptional data of the aluminium alloy, as well as 

the cobalt alloys, have already been adverted to above in discussing the 

density and resistance data. In the case of the aluminium alloy, I suspect that some error of measurement has eluded me, whereas the two 

cobalt alloys seem to be deficient in homogeneity, as is also the silver 

alloy. These inferences are permissible, because the remaining aluminium, cobalt, and silver alloys behave normally, and I am therefore 

warranted in excluding the three unmistakably exceptional data (Al, 

Co, Co) from the present considerations altogether.

Without any essential restrictions therefore I need only fix attention 

upon the large black dots of the chart, and from these 52 data it appears 

clearly that the alloys of platinum may be regarded as a class of materials possessing certain generic physical properties, inasmuch as the 

effect of alloying platinum with small amounts (less than 10 per cent.) 

of any other metal is a variation of the limiting ratio of resistance and 

temperature, when the latter approaches zero, in a way that is independent of the special ingredients of the alloy from which data may be 

obtained. Such variation depends only on the resistance-position of this 

alloy in the class.

In other words, if I put st =/(*), where/ is a series of powers of t then 

s0 =/(0) and a =f (0):/(0), and therefore s0 and o:9 considered theoretically, have to each other relations expressible by a first differential coefficient. According to the experimental result just stated, fur therm ore, 

/(O) :/(0) is such a function of/(O) that the dependence of/'(O): /(O) on 

/(O) is independent of the ingredients of the alloy by which the variations of/(O) may be produced, provided, of course, the point of view be 

that of obtaining a broad class distinction for the platinum alloys as a 

whole, and not to discern rigorously the characteristics of the individual alloy. To return again to the figure with a view of examining 

the discrepancies critically, I find that the divergence of data from the 

mean curve, drawn as carefully as possible through them, is largest toward the right-hand half of the figure. This, however, is easily accounted for, since in proportion as the resistance of the alloy is greater 

the results are more and more seriously distorted by an insufficiently 

homogeneous mixture or by imperfect alloying of the ingredients of the 

metal. The alloys of nickel, perhaps, are conspicuous as occupying a 

position above the mean curve, the alloys of copper as falling below it, 

but for the other alloys a uniformly exceptional position can not be said 

to be discernible. If the alloying be imperfect the corresponding a. will 

be erroneously large, and a tendency toward over-large values of a is 

the general character of the discrepancies which the figure presents.

Probably, too, the extreme end of the curve already partakes of the 

divergence, in virtue of which, in a retrograde movement, the diagram 

position of the metal alloyed to platinum must ultimately be reached.

(805)
152 MEASUREMENT OF HIGH TEMPERATURES. luuLL.64.

Having therefore obtained some general notions of the dependence 

of /'(O) :/(0) on/(0), it is next in place to endeavor to inquire into the 

form of dependence of these two classes of experimental data on each 

other. With a view of arriving at as simple a relation as possible I 

have tested the hyperbolic equation 

(I)

which contains three constants, and for the computation of which three 

pairs of values of/(0) and/'(0) :/(0) suffice. These may be taken from 

the figure, with some care as regards the judicious selection of points, as 

follows:

/(O) =11.7 f (0) : /(O) 0.00300

20.0 0.00164

60.0 0.00050

If we denote /(O) and /'(()) :/(0) for a moment by x and y, the values 

of I and m have the general forms

i(x x"}(xy x'y'} (x x'}(xy x"y"} , . 

~ 

which, together with equation (1) for the special values of a? and y, lead 

to the constants

1= -0.1360 w=0.0002548 w=0.03764. . 

Moreover, the curve

(/(0)-0.1360)(/(0):/(0) +0.0002548) =0.03764 ... (4)

does not differ appreciably from the curved line which, in Fig. 26, has 

been accepted as the locus of the larger black dots.

Equation (4), however, is exceedingly significant. Inasmuch as/(0) 

varies between 10 and 70, I is generally considerably less than 1 per 

cent. of/(0). Equation (4) therefore emphatically suggests that a simpler form of equation be assumed, in which 1=0. Equation (4), however, contains still another striking suggestion. The positive character 

of the constant m indicates that a larger value than <VOU, or the mean 

temperature-coefficient between zero and 100°, will tend to further 

simplify equation (4). Now, since, generally, <V00 >tfo356, it follows that

Hence, with these modifications implied,

)=» ....... (5)

will in all probability hold good for the observations as a whole even 

more nearly than (4).

(806)
BAMS.J PYRO-ELECTRIC PROPERTIES OF ALLOYS. 153

To avoid complete recalculation of a it is desirable to investigate 

some method for passing from a0m and a<?bl to a. If the values

s, s', s" correspond to t, t', t",

and if I accept

s s'

there follows :

a_

 ( Sf S't)(st"2 s"t2 ) (st" s"t)(st'2 s't2 

from which it is easy to deduce

-T, 100 ,,, 350

a-anm=st"2 s"t2 ist'2 s't2

st"-s"tl st'-s't

Now, st" s"t=D" and st' s't=D' are already known from the earlier 

computations; and for the present purpose, where a correction only is 

sought, s"t2 and s't? may be neglected as compared with st"2 and st'2, 

respectively, t being small in comparison with t' and t". Hence

/y_/y It 1 6ln 

which, since t"2/t12 is a constant, is a sufficiently convenient form, and 

much of the correcting may be done mentally. Finally, the three quantities <x0m, <*ioo35?> and ov357 have a similarly simple approximate relation 

to each other; for

° °__o./ylOO S ~S ,., 357 S ~S __ o.^357

 00 /7 _ o }QO _

whence

whence, furthermore, for instance,

t" t'

i fin W\T " " / i nh *tf,t\ sy 1UU i^^ >y OJ/ ^^ __________ / -y 1UU __ .-w «IO/ \

and since (t" t')/(t" t} is a constant these reductions are also mental. 

It has been observed that the corrections throughout affect only a 

few units of the last figure, and it is for this reason that the reductions 

are simple. As a matter of corroboratiou a for Nos. 0, 1, 2, 3 was calculated directly by the quadratic formula. The results were: 

No. 0......«=0.002328

1.... .«=0.001827

2-.....or=0.001492

3... ..«=0.001323

which agree substantially with the other values in Table 34.

(807)
154 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

The values of /(O) and/(0) :/(o) being thus carefully revised it will 

be expedient to follow the suggestion to which I adverted a moment 

ago, and put

)=» ....... (5)

By constructing the revised data in Table 34 and taking their graphic 

mean locus I derive the following pairs of correlative values:

x =12 y =0.00295

 x' =25 y1 =0.00130

#"=50 #"=0.00054

from which, deducing the constants m and w,

w=0.000226 w=0.0381

and the locus /(O) (/'(O) :/(0)+wi)=w does not differ appreciably from 

the mean locus graphically selected.

Having thus satisfactorily made this preliminary survey it is finally 

desirable to calculate the constants m arid n by the method of least 

squares. Before doing this equation (5) may be put under a better 

form for practice by writing

w ......... (6)

where f is simply the zero value of electrical conductivity of the

J \ /

alloy whose temperature-coefficient is f (0) :/(0). Equation (6), when 

operated on by the method of least squares, does not give inordinate preference to the values /(O) of high resistance, and since 

the high values can not be warranted with a greater degree of accuracy 

than the low values, equation (6) may most expediently be made the 

basis of computation. This I have done, and the results in Table 40 

contain the observed values of /(O) and / (0) : /(O), the calculated values 

/'(O) :/(0), and the errors, and finally the constants m and n, with the 

probable errors A* (m) and Aw (n) of each, supposing

^(w)=0.674

where & is the number of observations and the factor (1± '- ) has

V vfc/

been suppressed, and where a? and y stand, respectively, for/(0) and 

/(O) :/(0). The last three alloys, 10, 11, 12, were added subsequently

to the calculation.

(808)
BAEUB.] PYRO-ELECTRIC PROPERTIES OF ALLOYS. 

TABLE 40. Computation of in and n in equation (6).

155

No

0

1

2

3

4

7

8

9

13

14

15

48

4!)

16

17

18

19

20

41

22

23

24

42

43

50

51

25

26

27

44

28

29

30

32

33

34

35

36

45

37

46

38

47

52

54.

A

C

' 10

11

12

 f(0)

14.91

18.53

22.13

24.67

19.06

19.42

20.40

23. 64

31.75

33.59

63.56

25.29

53.60

21.07

26.84

32.76

28.56

39.62

23.97

36.33

41.80

59. 92

62.52

28.75

60.16

49.16

27. 37

40.87

52.35

31.09

21.52

25. CO

39. 86

21. 18

25.64

48.87

15.96

18.95

16.40

14. 64

17.00

29.48

15.83

44.19

24.51

12.04

13.27

19.42

20.40

23.64

Observed. 

/'(0):/(0)xlO

2.33

1.84

1.49

1.33

1.87

1.76

1.67

1.30

0.91

0.83

0.21

1.31

0.34

1.75

1.39

1.11

1.11

0.93

1.43

0.74

0.67

0.37

0.46

1.21

0.46

0.81

1.17

0.66

0.58

0.98

1.57

1.29

0.70

1.58

1.33

0. 55

2.20

1.78

2.12

2.30

2.09

1.12

2.12

0.57.

1.41

2.96

2.50

1.76

1.67

1.30

Calculated. ' 

f(0):/(0)x!0

2.34

1.84

1.51

1.34

1.79

1.75

1.66

1.40

1.00'

0.93

0.40

1.30

0.51

1.55

1.21

0.96

1.13

0.76

1.38

0.84

0.71

0.44

0.41

1.12

0.43

0.58

1.19

0.73

0.52

1.02

1.56

1.28

0.75

1.59

1.28

0.58

2.18

1.80

2.11

2.38

2.03

1.09

2.19

0.66

1.35

2.94

2.66

1.75

1.66

1.40

Error. 

xlO3

 0.01

 0.01

-0.02

 0.01

+0.08

+0.01

+ 0.01

-0.10

-0.09

 0.10

-0.19

+0.01

 0.17

+ 0.20

+0.18

+0.15

-0.12

+0.17

+0.05

-0.10

-0.04

-0. 07

+0.05

+0.09

+0.03

+0.23

 0.02

-0.07

+0.06

-0.04

+0. 01

+0.01

-0. 05

 0.01

+0.05

 0.03

+0.02

-0.02

+0.01

 0.08

+0.06

+0. 03

 0.07

-0.09

+0.06

+0.02

 0.16

+0.01

+0.01

 0.10

Alloy.

Pt

An

Au

An

Ag

 Pd

ra

Pd

Cu

Cu

Cu

Cu

Cu

Ni

Ni

Ni

Co

Co

Co

Fe

Fe

Fo

Fe

Fe

Steel

Steel

Cr

Cr

Cr

Cr

Sn

Sn

Sn

Al

Mn

Mn

Mo

Mo

Mo

Pb

Pb

Sb

Bi

Zn

Zn

Pt

Pt

Ir

Ir

Ir

(809)
156 MEASUREMENT OF HIGH TEMPEftATtJRES.

The constants to which the values of this table refer are

m=0.0001939± 0.0000233 %=0.0377S± 0.00054

The probable errors of m and n indicate that the inaccuracy is largely 

incurred in the measurement of /'(O) :/(0), whereas n is much more 

fully warranted. The equation is one, however, in which pairs of values of m and n, either both larger or both smaller than the critical 

values above, readily compensate each other. As usual, the constants 

which may be derived with a little forethought from careful graphic 

representations^ results are probably nearer the truth than the values 

which are mechanically computed by the method of least squares. 

The final results of this chapter may therefore be stated as follows : 

In endeavoring to describe the platinum alloys as a class possessing 

generic characteristics, it is permissible to abstract from the minute 

and individual behavior of the isolated alloy j and it appears that electrical temperature-coefficient /'(O) :/(0) varies as a linear function of 

conductivity (1 :/(0)) throughout the whole enormous variation of resistance (10 to 65 microhms, c. c.) which platinum alloys not too highly 

alloyed (<10 per cent.) present. In other words, if at t° the specific resistance of a platinum alloy be denoted by f(t)t where t symbolizes temperature, then

/(0)(/'(0):/(0)+0.000194)=0.0378 ..... (7)

It is perhaps not superfluous to remark in passing that if instead of the 

thoroughly arbitrary temperature 0° centigrade some other value more 

in keeping with the qualities of platinum alloys had been selected the 

constants m and in would present different values ; and it is easily conceivable that correlated values off(t) and/'(£) may exist, for which the 

constants is annulled and for which equation (7) takes its simplest 

form. The actual search for such a result involves more labor than I 

can at present apply. Clausius 1 was the first to call attention to the 

approximate proportionality of the resistance of most pure metals with 

their absolute temperature.

Accepting Matthiessen's general relation

8t=80(I+at-/3tz) a=0.00382 . /3=0.0000012G 

and putting

it appears that at, say, 60° the said proportionality is accurate. Again, 

since f(t) increases more rapidly than f'(t) decreases, with increasing 

temperature the passage of the equation

/(O) (/'(O) :/(0) + «)=ninto/(*)/'(« 

may be looked for in the region of positive t.

ius: Pogg. Ann., 4th series, vol. 14, 1858, p. 650; cf. Ball. TJ. S. Geol. Survey, 

No. 14. 1885, p. 24.

(810)
iiABUB.1 PYRO-ELECTRIC PROPERTIES OF ALLOYS. 157

Other relevant results. A. research into the relations of electrical conductivity and temperature makes up an important part of the labors of 

Matthiessen. In addition to his well-known results for pure metals, 

Matthiessen1 and his friends investigate the electrics of alloys Pb, Sn 

An, SnOu, SnAg, ZnCu, AuCu, AuAg, PtAg, PdAg, CuAg, FeAu, FeCu, PCu, AsCu, and some other metals. Unfortunately, not all of these 

alloys are available for the present discussion, for Matthiessen's purpose 

seems rather to have been the exploitation of a great number of series 

or groups of alloys. On the other hand, it is my purpose to examine 

the electrical behavior of as many alloys- as possible of a single given 

group. In Matthiesseu's work the three PbAg alloys and the two Sn Ag 

alloys lie too far apart.

Ou perusing Matthiessen's andVogt's results it appears that Pb alloys,2 

Sn alloys, and Fe alloys will have to be excluded from the present consideration, inasmuch as the data are either insufficient in number or lie 

too far apart from each other and from the extremes of the series, or because of mechanical difficulties encountered in making the alloys and 

shaping the wires. Perhaps there are other reasons. There remain a 

very full series of copper 'alloys, namely, CuSn, CuZn, CuFe, CuP, 

OuAs, a series of silver alloys, viz, AgAu, AgPt, AgPd, AgCu; and a 

few gold alloys, viz, AuCu, AuAg.

In view of the importance of these data I have computed the following tabular statement of Matthiessen's results, re-arranging the data in 

a way which, for my special purposes, is expedient; and I have also 

added Matthiessen's3 results for pure metals. In Table 40o. A'0 denotes 

the conductivity in Matthiessen's standards (Ag=100), a the temperature-coefficient of the alloy of which the composition is given on the 

same horizontal row. I have rounded off Matthiessen's large numbers, 

because the arbitrary errors introduced during the mechanical preparation of the alloys, together with the errors of structure and hardness 

and the more serious errors of imperfect homogeneity make the extreme 

accuracy of the electrical datum illusory. The table furthermore contains A 0 , the electrical conductivity in microhms referred to the cubic 

centimeter. This reduction is made by means of mercury.4 In the 

last two columns of Table 40& the value of <?, computed by the formula 

a-\-m=n\Q and the corresponding errors are inserted. Of these reresults further mention will be made below, and I need here state only 

that the constants m and »t, given at the end of the table, were derived 

from all the observations by the method of least squares. The com1 Matthiessen aud Vogt: Pogg. Ann., vol. 12, 1864, p. 19.

3 The metallic ingredient present in the alloy in larger amount is fitly used in designating the alloy.

3 Matthiessen u. v. Bose: Pogg. Ann., vol. 115, 1862, p. 353.

4 Jenlcin, who made similar reductions in the case of pure metals by means of 

lead, arrives afc somewhat different uuruhers. A satisfactory absolute table can not 

be constructed.

(811)
158 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

positions given are volume percents, except in the case of phosphides 

and arsenides of copper, where mass percents are meant.

TABLE 40a. Shoiving Mattliiessen's and Yogi's results for the electrics of gold, of silver,

and of copper alloys.

. (

Gold alloys ....<{

I

Silver alloys...'

(

Copper alloys.. .

I

Alloy.

AD 

AuCu

AnCn

AuAg

AuAg

Ag 

*AgCu 

AgCu

AgCu

AgPt

AgPt

AgPt

AgPd

AgAu

Cu 

CuAg

CuAg

CuAg

CuAu

CuAu

CuFe 

CuZn 

CuZn

CuZn

CnZn 

CuZn 

CuSn 

CuSn

CuSn

CuSn

CuSn

CuP

CuP

CuAs

CuAs 

CuAs

Composition.

1.6%Cu

18. 3 % Cu

20. 1 % Ag

47.9%AK

1. 5 % Cu 

8. 2 % Cu

46. 7 % Cu

2. 5 % Pt

6.0%Pt

9. 7 % Pt

23. 3 % Pd

19. 9 % Au

1.6% Ag

4.8% Ag

22.40/0 A g

0. 7 % Au

19. 2 % Au

0. 5 % Fe 

5. 0 % Zn 

10. 9 % Zn

23. 6 % Zn

29.4%Zn 

4'2. 1 % Zn 

1. 4 % Sn 

6. 0 % Sn

11.60/0 Sn

12. 3 % Su

14. 9 % Sn

1. 0 % P

2. 5 % P

Trace

2. 8 % As 

5. 4 % As

^f

79 

56.1

16.1

21.5

15.1

109 

. 79.7 

80.3

74.9

31.6

18.0

6.7

8.5

21.7

102 

89.5

82.3

69.8

84.0

20.5

38.9 

60.4 

46.9

21.3

21.7 

21.8 

62.5 

19.7

12.1

10.2

8.8

23.6

7.3

61.1

12.9 

6.3

Observed

axlO3

3.67 

2.65

0.75

1.11

0.70

3.82 

(2)4. 12 

2.75

2.80

1.24

0.77

. 0.33

0.32

0.90

3.87 

3.45

3.25

3.03

3.32

0.86

1.55 

2.47 

2.05

1.88

1.27 

1.37 

2.68 

l.OQ

4.69

0.67

0.55

1.32

0.48

2.64

0.74 

0.51

Microhms.

Ao x 103

506

, 359

103

137

9

691 

510 

514

480

202

115

43

55

139

653

573

527

447

538

131

249

300

136

139 

140

126

77

65

56

151

47

391

82 

40

Calculated.

axlO3

3.69 

2.63

0.79

1.03

0.74

3.83

2.88

2.69

1.20

0.73

0.34

0.41

0.86

3.98 

3.54

3.29

2.85

3.35

1.11

1.76 

2.52 

2.04

1.14

1.15 

1.16 

2.59 

1.08

0.89

0.74

0.69

1.22

0.64

2.54

0.84 

0.61

<5a x 10'

-2 

+ 2

 4

+8

 4

±0

-13

+ 11

+ 4

+ 4

_ j

- 9

+ 4 .

 11 

 9

 4

+ 18

_ 3

-25

 21 

 5

+ 1

+74

+12 

+21 

+ 9 

- 8

 12

 7

 14

+10

-16

+10

-10

__ Q

a -(- in = n Au

Gold alloys: m = 0.000045 ± 0.000030 

n = +0.00721 ±0.00010

Silver alloys: m = 0.000112 ± 0. 000031 

n = + 0.00538 ±0.00085

Copper alloys: m = 0. 000386 + 0. 000040 

n- + 0.000551 ±0.00012

' Rejected.

(812)
IIABUB.I PYKO-ELECTKIC PROPERTIES OF ALLOYS. 159

In interpreting these results graphically it is necessary to proceed 

with caution; for inasmuch as specific resistance enters into them reciprocally, large values of resistance will be only inadequately represented. 

The tables contain many such values, nevertheless, enough data remain to exhibit the striking linear character of the curves on which 

the gold, silver, and copper points, respectively, lie. It is certain that 

the initial tangent coincides with the initial curves throughout an enormous extent of their course. Matthiesseu, 1 who expressed this result 

under a somewhat involved form, was well justified in computing 

by means of it the conductivity of a pure metal from data found for 

metals slightly impure. This computation premises the truth of Matthiessen's other principle that, with certain distinct exceptions, the 

electrical temperature-coefficients of all pure metals are the same.

After Matthiessen and Vogt the curious relation in question seems to 

have failed to enlist further attention, It will be desirable therefore 

to endeavor to add to these results of Matthiessen and Vogt 2 and of 

myself, and to make a test of the corresponding properties of a group 

of metals whose electrical relations to temperature differ very largely 

from those relations which hold for platinum, silver, gold, copper, zinc, 

cadmium, tin, lead, arsenic, antimony, bismuth. I refer to the group of 

iron metals (iron, nickel, cobalt), more especially to the iron-carburets.2 

The latter also present an unusually large range of electrical variation; 

and the fairly complete set of results investigated by Dr. Strouhal 3 and 

myself is available for discussion. If to these be added Matthiessen's 

result for pure iron, and a mean curve be passed through all the observations graphically, the following principal co-ordinates of this curve,

07=15, 45, 70, 

2/=0.00420, 0.00166, 0.00130,

it interpreted by the equation (x+l)(y+m)=n, lead to the constants, 

Z=-3.73, m= -0.000706, w=0.0394.

These constants do not reproduce the graphic curve satisfactorily,neither 

has the constant I here the negligibly small value found for it in working with platinum alloys. In view of these results, it is desirable to 

exclude the interpolated value for pure iron, and to use only our own 

values for steel and cast-iron. It is not possible to reduce Matthiessen's 

value to our own satisfactorily, and the small datum for pure iron (large 

reciprocal) has an undue influence in modifying the constants to be obtained by the method of least squares. If cast-iron be also withdrawn 

the results for steel form a unique series, the data being obtainable by

'Matthiessen and Vogt: Philos. Mag., London, 4th series, vol. 27, 1863, p. 467; 

Pogg. Ann., vol. 122, 1864, p. 19.

3 This is particularly desirable here, because Matthiessen's and Vogt's iron alloys do 

.not seem to conform to the principle here in question.

»JB.ull. U. g. Geol. Survey, NO, 14, 1885, p. 15.

(813)
160 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 34.

simply varying temper. It is obvious therefore that data derived from 

the steel series alone, will be more trustworthy than any others. From

x= 15.9, 

y= 0.00423,

28.9, 

0.00244,

45.7, 

0.00161,

as directly found for the steel series, there follows

Z=0.7S, w=-0.0001435, n= 0.0682.

Here the constant I is much smaller, being about 5 per cent, of the 

smallest steel value of x admitted. A similarly favorable result is 

obtained by adding cast-iron to the steel series, and I have therefore 

ventured to assume the equation x(y+m)=n, conformably with the 

method of discussion adopted in treating the platinum series.

Applying the method of least squares to data for steel and cast-iron, 

the results in Table 406 are obtained. /(O) (a+m}=n.

TABLE 40&. Computation of m and n for iron-carburets.

No.

Steel......

13 to 15....

Temper.

Soft .........................

Annealed light yellow ......

/(O)

15.9 

18.4

20.5

26.3

28.9 

45.7

78.5

a 

observed.

0. 00423 

0. 00360

0. 00330

0. 00280

0. 00244 

0. 00161

0. 00129

a

calculated.

0. 00417 

0. 00366

0. 00333

0. 00269

0. 00249 

0. 00173

0. 00119

Diff.

+ 6 

 6

- 3

+11

_ g 

-12

+ 10

m = -0. 000438 ± 0. 000097. 

n = + 0. 05930 ± 0. OC151.

Applied to steel alone the same method furnishes the constants

m= -0.000303 ± 0.000079 

n +0.0620 ±0.0017;

applied to Matthiessen's data for pure iron (a?=9.4, y=0.0052), in addition to the present data for steel and cast-iron

wi=0.001242± 0.000186 

w=0.0383 ±0.0034;

a

In the latter instance, as in the case above, the computed curve does 

not coincide well with the curve graphically obtained. It is curious to 

note, however, that the constant »i, where iron, steel, and cast-iron are 

selected, is near the same constant for' platinum alloys. The values are 

7i=0.0383 for iron-carburets and w=0.0378 for steel. Whether this is 

more than a coincidence I am not now prepared to say, and I have adhered to the values in Table 41, because these are most trustworthy SQ

(814)
BAJMJB.] - PYRO-ELECTRIC PROPERTIES OF ALLOYS. 161

far as the data go. Eeferred to Matthiessen's datum they yield an inordinately high value for the temperature-coefficient of iron. Eeferred 

to Be"noit's values for iron and for soft steel the agreement is better, 

but the computed results are nevertheless high.

/(0)=12.1;/'(0): /(O) computed=0.0053; found (B6noit) 0.0045 

f(0)=10.9$ /'(O): /(O) computed=0.0059j found (B6noit) 0.0050.

The results of this laborious analysis for iron-carburets has not been 

so satisfactory as the corresponding results for platinum alloy. The 

causes for irregularities are, however, not far to seek. Cast iron is at 

best an exceedingly heterogeneous product and the passage from pure 

iron to pure cast iron must be indefinite because of the divers modifications in which the carbon may occur in iron. The variations of occurrence are not fully under control. On the other hand, steel in passing 

from its lowest to its highest resistance does so largely in consequence 

of definite variations of structure. Finally, in working with ironcarburets the difficulties of measurement are of a serious kind. Hence, 

since data have here been co-ordinated, the changes of value of which 

are due to causes intrinsically different, it is surprising to find results 

as harmonious as these prove to be. To return therefore to the inference 

on page 157, with reference to the initial tangents of the loci of coppersilver, of silver-platinum, of gold-platinum, of gold-silver, and of the 

totality of platinum alloys, and of steel in all states of temper, it appears 

that all these lines show a common tendency to intersect in a small 

field lying very near the origin of co orclinates. The loci here in question express the relation between electrical conductivity and temperature.

To give perspicuity to the remarks of this paragraph it will be desirable finally to construct a chart of the linear, relations as they have been 

found. Unfortunately it is difficult to reduce the Matthiessen and Vogt 

data to the present standards. I have therefore withheld them from 

the larger chart now to be given. In Fig. 27 the individual data for 

platinum alloys and for steel and their computed mean linear loci are 

inserted. The disposition of points with reference to this line is very 

clearly shown. The steel line has an obviously different slope from the 

line of iron-carburets (marked Fe), while the latter (Fe) is not far from 

parallelism with the platinum line. It is worthy of note that the ironcarburet line contains pure iron, cast-iron, and glass hard steel, substances in which the carbon is largely chemically combined with iron, 

whereas annealed steels and soft steels, each of which contains carbon 

uncombined, has a linear locus of its own, differing from the iron-carburet locus. In the above, platinum alloys of nickel, cobalt, and iron, 

certain irregularities have been discerned, which may in like manner be 

referred to imperfect alloying.

General remarks. It is not improbable that the relations sketched 

would hold indefinitely, provided alloying were not necessarily acconiBull. 54 11 (815)
162 MEASUREMENT OF HIGH TEMPERATURES. [DULL. 54.

\

\

\

\

 \

\ A

FIG. 27. Chart showing the relation between electrical conductivity and temperature of platinum 

and other alloys.

(816)
J3ABU8.] PYKO-ELECTKIC PROPERTIES OF ALLOYS. 163

panied by a modification of molecular structure. The passage from the 

molecular type, which characterizes the first metal in the pure state, to 

the type which characterizes the second pure metal in the alloy is undoubtedly so complex that it is only on approaching very near the pure 

metals that the nature of the elementary principles of such a passage 

can be discerned. This is the interpretation which I venture to give 

to the linear loci investigated. Perhaps the following comment will 

make my meaning clearer:

The temperature-coefficients for pure metals are nearly constant and 

independent of the resistances of the metals themselves, whereas their 

specific resistances vary enormously. Hence the locus (Fig. 27), if extended for higher percents, must show very decided curvature. Moreover, there will be a special locus for each metal alloyed to platinum, 

which will terminate in the particular co-ordinates /(O), /'(O): /(O) of 

the metal in question. It is in the neighborhood of the two pairs of 

/(O), /'(O): /(O), which (one pair at each end) terminate the locus expressing the general relation between these two quantities, that the 

curious linear relation in question seems to hold.

In view of the fact that the relation between /(O) and /'(O): /(O) 

must ultimately be curvilinear, the inferences to be derived from equation 6 by making either /(0)=0 or /'(O): /(0)=0 are necessarily involved. To interpret it, similar relations would first have to be developed for low percentage alloys of many other metals. Nevertheless, 

these considerations are suggestive. They point to a limit, below which 

neither the electrical conductivity of metals nor the temperature-coefficient can be reduced. It appears therefore that a lower limit, both 

of conductivity and of temperature-coefficient, is among the conditions 

of metallic conduction, not to say of metallic state.

To make what I have here in mind clearer I will premise the following: In the case of conduction of electricity in metals (solid or liquid) 

the effect of temperature is a decided decrease of conductivity, continuing so long as temperature increases. In the case of conduction in 

non-metals or in electrolytes (solid or liquid), on the other hand, the 

effect of temperature is a decided increase of resistance, which, supposing the liquid state to be retained, continues as temperature increases. 

Hence conduction in metals is distinguished from conduction in electrolytes in this respect, that if the temperature-coefficient in one case 

(metals) be regarded positive its value in the other case (electrolytes) 

will necessarily be negative. Applying these general principles to the 

above inferences for alloys, it appears that the occurrence of a lower 

limit of electrical conductivity and of temperature-coefficient in the 

case of alloys may be regarded as significant or as being a unique expression of one of the conditions of metallic conduction.

I am thus led to inquire into the nature of that class of substances 

whose temperature-coefficient is zero; a class of substances, in other 

words, in which the metallic and the electrolytic modes of electric con-

(817)
164 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

ductivity may be supposed to converge, for a march from the extremes of high values of conductivity possessed by metals or by substances of positive temperature-coefficients to the extremes of low 

values of conductivity possessed by electrolytes or by substances of 

negative temperature-coefficients can hardly be supposed possible with 

the exclusion of the zero temperature-coefficient.

The point which I am endeavoring to make becomes even of greater 

importance if we associate with metallic conductivity the correlative 

property of optic opacity. Relations between light and electricity have 

long been investigated, and many curious experimental facts are known. 

Maxwell's electro-magnetic theory of light furnishes a theoretical basis 

for the fact that all true conductors must be exceedingly opaque. 

Looking for a special application of this general principle it appears 

that solid metals, no matter how high the temperature to which they 

are heated, retain positive values for the temperature-coefficient. 

Similarly, Govi's 1 careful experiments prove beyond a doubt that solid 

metals, even in extreme states of red heat, remain opaque. The case of 

liquid metals is by no means so definitely established; and however 

uncertain and indefinite the evidence, the questions relative to possible 

transparency of liquid metals at very high temperatures is an open one.2 

Considered from an electrical point of view, the increase of resistance 

of a metal from low temperature to the highest attainable, accompanied, 

as it is, by a diminution of the temperature-coefficient, points more emphatically to an ultimate occurrence of optical transparency after the 

metal has passed from the solid into the fused state. Finally, inasmuch as optical transparency may be considered as having been reached 

at the critical temperature, it is to this state that the occurrence of the 

zero temperature-coefficient is to be referred.

For the present I may state that the position to be taken with reference to the importance of this paragraph depends solely upon whether 

or not the result underlying Figs. 26 and 27 is to be taken as the expression of a law. I have ventured to accept it as such. The remainder 

of the text is an application of simple geometric methods. I am not 

conscious of having forced any point, and the equation between /(O) 

and/'(0) :/(0), at which I finally arrive (page 157), follows as an immediate inference. If in this equation either the first or second of these 

quantities be made zero, or if, in other words, the line be prolonged in 

a negative direction, the predictions of the line as a whole agree with 

the known electric behavior of metallic conductors, and with the known 

electrical behavior of electrolytic conductors, and furthermore suggest 

the possible occurrence of an intermediate class of conductors, such that 

the passage from metallic to electrolytic conduction may be made continuously.

1 Govi : C. R., vol. 85, 1877, p. 699; Secchi: Ibid., vol. 64, 1867, p. 778. 

2 W. Kam.say: Chem, News, vol. 55, 1887, pp. 104,175; Turnen Ibid,, p. 163.
OHAPTEE IV.

THEC ALIBRATION OF ELECTRICAL PYROMETERS BY DIRECT 

COMPARISON WITH THE AIR THERMOMETER.

DISPLACEMENT METHODS OF AIR THERMOMETRY.

Some time after the methods for measuring high temperatures and of 

measuring vapor densities at high temperatures had been fully developed in the admirable manner due to Deville and Troost, 1 a new method 

for high temperature vapor densities was published by Y, Meyer. A 

modification was at once introduced by Crafts and Meier, by which V. 

Meyer's method became available for the measurement of high temperatures. In these thermometers the gas used, instead of being kept at 

constant pressure or at constant volume, as in most air thermpmeters, or 

instead of being pumped out by a°mercury air-pump, as in Deville and 

Troost's apparatus, is simply chased out by a second gas. If therefore 

the two gases be collected over a liquid in which the displacing gas only 

is soluble, the volume of the gas which fills the thermometer at any temperature is easily measurable. Air, for instance, may be used for measurement, expelled by HC1 or C02 , and collected over water. A few 

minutes suffice for the displacement. Since all operations are conducted 

under atmospheric pressure, it is obvious that the Crafts and Meier 

devices can be used at temperature at which porcelain is seriously viscous and permeable to gas.

Special forms of the Crafts and Meier apparatus are made by MM. 

Morlent freres, among which the tubular form designed by Meyer 2 to 

fit the Fletcher organic combustion furnace would appear to be specially 

convenient for calibration work. In some earlier experiments Dr. Hallock and I endeavored to make use of it. The accompanying diagram, 

Fig. 28, drawn to the scale -j^, indicates the method of adjusting the 

thermometer for calibration.

The tubular thermometer of porcelain is shown at A B C. The ends 

A and C of both of the capillary tubes A 'F and E Care provided with 

three-way cocks of special construction, made of brass. Only one of 

these, D, is shown in the diagram, Fig. 28 being a longitudinal section 

with an end view cross-section through the canals. The thermo-element 

to be compared with the air thermometer is stretched along its axis with 

the hot junction at a, the center of figure. The two wires a b and a c pass 

through the capillary tubes A F and E C and through a corresponding

1 Cf. Introduction, p. 27 et seq., where the full references are given. 

2 V. Meyer: Chern. Ber., vol. 15, 1882, p. 1161.

(819) 165
166 MEASUEEMENT OF HIGH TEMPERATURES. [BULL. 54.

*

straight capillary canal in the stop-cocks. To prevent escape of air at 

these holes the wires are, during the measurements, sealed 

into them with resinous or other cement.

The capillary stem of the air thermometer communicates, however, with a second capillary canal in the stopcock Z>, at right angles with the other canal. It is through 

this second canal and. the three-way cock that either the 

soluble or the insoluble gas may be introduced into the 

thermometer, the two lateral tubes d g and / 1 being in 

connection with the corresponding gasometers. There is 

also a hole at n< through which either gasometer may communicate with the atmosphere.

We did not carry this method of calibration into great 

detail, chiefly because the temperature at any given point 

of the long tubular space of the Fletcher furnace, as well 

as the mean temperature of the whole length of tube, 

proved to be insufficiently constant. Nor can it be assumed that the temperature at the center a of Fig. 28 

(thermo-element) is identical with the mean temperature 

of the tubular column of gas. Moreover, since the capacity 

of the thermometers is not much over 100CC, measurements of gas volume must be made with very great care 

to be in keeping with the accuracy of calibration required. 

It is also inconvenient to insert a special thermo-element 

permanently for each series of measurements, the problem 

of calibration being usually of such a kind as to make it 

desirable to compare a series of thermo-elements either 

at once or else in rapid succession. Finally, the thermoelement to be compared must necessarily be filiform and 

very long, whereas the constants of short thick thermoelements are frequently in demand. Add to these even 

more serious sources of error, inasmuch as measurements 

are made in a tube not glazed internally and with a gas, 

the rigorous purity of which is not assured. Nevertheless 

this method of calibration may sometimes be convenient. 

(Of. p. 36.)

Taking the elaborate gasometric apparatus into account 

the method is not as simple as it appears. It occurred 

to me, however, that this simplicity might possibly be 

reached by displacing dry air with slightly superheated 

steam. But I made no experiments.

The application of Crafts's method, which can easily be made by inserting a platinum capillary tube into the stem of the air thermometer, 

deserves special notice, and by the aid of the metallic tubing, to be described below (Chap. Y), can be put to a rigorous test.

(820)
PORCELAIN AIR THERMOMETRY. 167 

CONSTANT-VOLUME THERMOMETERS.

In most of the present experiments the object has not been to test the 

rigorous accuracy of the air thermometer so much as to devise forms 

of apparatus in which such tests can be satisfactorily made. I have 

had in mind, moreover, that the thermometer is to be used as a means 

of calibrating the therino-element. Having found therefore that at 

temperatures not exceeding 1,300° the porcelain of Bayeux is quite 

rigid as regards excesses of pressure (internal or external) not exceeding one atmosphere, I made the early air-thermometer measurements by 

the constant-volume method. Jolly's 1 well-known and convenient manometer was largely used, with such modifications as the special work 

required. To connect bulb and manometer of the air-thermometer adjustment I used capillary metallic tubes. Such tubes had been used by 

Beguanlt 2 and others before. They enable the observer to place the 

manometric apparatus at some distance from the furnace and the bulb, 

a condition of accurate measurement which, at high temperatures, is 

almost essential. I will briefly describe the apparatus more in detail. 

The general disposition of apparatus is given in Fig. 29 (frontispiece), 

and there will be little difficulty in recognizing the parts to which the 

descriptions refer. Further comment is made below (p. 188).

Manometer. A very substantial form of manometer stand, made for 

the work by Mr. William Grunow, of West Point, is shown in the frontispiece, under B. The stand is essentially that of Jolly, as modified by 

Professor Pfaundler in Insbruck.3 It consists of two vertical parallel 

cylindrical slides made of brass, 160cm in length, 2.5cm in diameter, and 

about 13cra apart, measuring from center to center. These slides (tabular) are fastened below to a suitably large tripod support, and are 

braced above by a slender St. Anthony's cross, the lower end of which 

abuts against the tripod. Metallic clamps or sleeves, provided with 

suitable devices for carrying the manometer tubes, are thus free to slide 

along the whole vertical range of 160cm. A millimeter scale, about two 

meters long, is placed between the brass upright for approximate measurement. Finer measurements are made with a cathetometer. 4 Obvi* 

ously this stand is equally convenient as a support for both the constant 

volume and the constant pressure apparatus, either of which methods of 

air thermometry may be used with equal facility. The modification of 

the Jolly-Pfaundler stand, by which the brace is made to abut against 

the top of the slides instead of against the middle, as in the old form, is 

due to Dr. Hallock. I have modified the Jolly-Pfauudler stand by using 

four parallel slides of about the length and distance apart of those just 

described (Fig. 43). The two front slides are used for the manometer

1 Jolly: Poggendorff Annalen, Jubelband, 1874, p. 82. 

2 Regnault: Relation des expdriences, Paris, 1847, p. 264. 

3 Cf. Milller Pouillet, Physik, vol. 2, 1879, p. 119. 

4 Mr. Grunow's form.

(821)
168 MEASUEEMENT OF HIGH TEMPEKATURES. [BULL.54.

proper; the two rear slides for the "compensator" manometer for 

adjustable screens, etc. The four uprights, firmly screwed to a base 

below and to a cap plate above, possess all the stability desirable, without any braces at all. The cap piece carries threaded holes, into which 

vertical or horizontal rods can be screwed, to give further length or 

height to the apparatus whenever necessary. In figure 43 this form of 

stand is used to support the pneumatic apparatus in the viscosity 

measurements.

Fig. 30 gives a more succinct account of the method of adjusting the 

parts of the air thermometer, the parts being drawn about one-sixth of 

actual size.

The manometer proper, A B G D E F G, has the usual terminal glass 

tube A B about 2cm or more internal diameter, which is joined to a length 

of about 2 meters of rubber hose, doubly wrapped by a steel three-way 

stop-cock, B. This carries alateral tubulure, through which superfluous 

mercury in the tube A B may be tapped off, an operation often desirable 

when the constant-pressure method is used, in which case the tube A B 

may be expediently chosen wider. B may also be shut off to keep the 

mercury column at a fixed height. The metallic sleeve of the manometer stand, which clutches the tube just below the faucet jB, is provided 

with a micrometer screw (thread O.lcm apart) by which the height of the 

meniscus may be adjusted with nicety.

The other end, H, of the rubber tubing is joined to the lateral branch 

of this glass barometer tube H E F G, held by the second slide of the 

stand. This widens above between F and G to allow freer play of the 

upper meniscus. Inasmuch as it is frequently necessary to employ air 

thermometers, glazed on the outside only, it is desirable to work so far 

as possible with pressures less than an atmosphere. The result is a tendency to force the viscous glaze into the pores of the porcelain. Satisfactory work with low pressures is possible only when the upright branch 

E F is impervious to air. Hence it is made of glass, like an ordinary 

barometer tube, and all rubber connections and tubing here are discarded. It is convenient, however, to insert a glass stop-cock at F, (Fig. 

30), but not essential. A stop-cock is always an opportunity for leakage.

The top G of the tube E G may either be drawn to a fine aperture, 

just large enough to admit the end of the capillary platinum tube 

G IK MN 0, or it may be cut off straight and admit a rubber stopper 

sealed in with resinous cement, through which stopper the platinum tube 

passes. In either case this end of the platinum tube, sharpened to a 

needle-like point below the mouth of the capillary canal, subserves the 

purpose of a fiducial mark excellently. In the constant-volume method 

the volume of the space above the meniscus must be small and accurately known. Hence it should be nearly cylindrical in figure, and the 

part F G of the barometer tube not chosen too wide.

The extreme end of the capillary tube passes symmetrically through 

a metallic cap, 0, the top of which is soldered hermetically to the tube.

(822)
M\

\N

PIG. 30. Diagram of Jolly air thermometer and bull). Scale J.
BABUB.I PORCELAIN AIR THERMOMETRY. 169

The end iu question projects somewhat beyond the lower edge of the 

cap, the inner width of which is such as to lit snugly around the stem 

of the porcelain air thermometer 0 P. Capillary tube and stem are 

fastened with resinous cement 1 in this manner: The cap is clamped vertically with the open end uppermost iu a vise and filled with melted cement, kept slightly above the melting point by applying a burner. The 

stem of the air thermometer is then inserted from above and in such a 

way that the projecting capillary tube may pass into the capillary canal 

of the stem. The cement which exudes is not removed until the two 

parts have thoroughly cooled in the upright position in which they were 

clutched by the vise.

Metallic capillary tubes. The capillary tube being some two meters 

long, it is convenient, or perhaps even essential for quick manipulation, 

to insert an intermediate branch stop-cock of glass, L R, somewhere 

near the middle of the tube. By connecting this cock with the exhaust

pipe J? 8 of a mercury air-pump, the air of the thermometer bulb may 

be removed in any quantity, the bulb thoroughly dried at red heat, or 

even filled with other gases than air, in a way which is thoroughly satisfactory. To insert the ends of the capillary tubes into the cock the 

following method is reliable: The inner ends of the capillary tubes are 

bent at right angles to their axes, and then passed through the two 

parallel canals of a little piece of the porcelain cylinder used above for 

insulating the wires of the thermo-element. The parts near the right 

angles are additionally secured by being tied together with fine copper 

wire, whereupon the whole connection (excepting, of course, the ends 

of the capillary canals of the metal tubes, which, for this purpose, project beyond -the porcelain cylinder) is saturated with cement. The 

cylinder is then inserted into one tube of the glass faucet and sealed 

in it with cement in such a way as to leave a minimum of waste space 

between the cylinder and the plug of the faucet. It is well, moreover, 

to tie the tubes proper to a stick, so as to bridge over the severed part 

L, and thus avoid those leaks to which the joint is liable when suddenly 

jerked or otherwise interfered with seriously. It is convenient to make 

the exhaust-pipe E S of thin lead tubing, because this can be bent in all 

directions and is sufficiently rigid to maintain its figure and sufficiently 

impervious to gas. Two metallic capillary tubes may be coupled by 

pushing them in opposite directions into a short end of glass tubing, 

into which they fit snugly, till the ends meet near the center. Applying 

a drop of melted cement and the burner to the end of the glass tube, 

the cement is drawn into the space between the outer surface of the 

metallic tube and the inner surface of the glass tube by capillary attraction, so long as the cement remains liquid. This joint is excellent.

'Rosin and beeswax fused, together in equal parts. In soldering a wire or capillary tube axialJy into a large glass tube this cement must be added in thin horizontal layers, otherwise the cylinder of mastic, as it contracts on solidifying, draws itself 

away from the tube. Marine glue is doubtless a more reliable cement.

(823)
170 MEASUREMENT OF HIGH TEMPERATURES. lBurx.54.

Heat must be cautiously applied to prevent the cement from running 

in far enough to stop up the capillary canals. I may add here that in 

later experiments I found it best to solder the ends of the capillary 

tubes into a little cylinder of brass, retaining in other respects the adjustment of Fig. 30. The brass cylinder is, of course, provided with two 

holes to receive the tubes. I have also in definite work discarded 

stop-cocks altogether, cementing either an open glass tube or a little 

closed glass cup around the brass cylinder in question, according as I 

wished to exhaust or to dry the air in the bulb or to make thermal 

measurements.

Capillary tubes may be made either of copper, of silver, or of platinum. The latter are preferable, because they do not amalgamate, and 

if a mercury thread is accidentally forced into them, it can be forced 

out again cleanly, like the thread of a thermometer. Threads accidentally injected seldom pass beyond the stop-cock L R, and thus the fatal 

accident of the injection of mercury into the thermometer bulb P is 

avoided. The capillary tubes should be seamless. I succeeded in 

making them of copper pretty well as follows: Taking a cylindrical 

copper rod lcm in diameter and in convenient lengths of 5cm to 10cm, 

central holes were drilled into them about 0.4cm to 0.6cm in diameter, as 

nearly as possible co-axial with the rod. These holes were then filled 

with fusible metal, and when cold the rods were rolled and drawn 

down to fine wire of the diameter required. The tubes were submerged 

carefully in boiling aniline, commenciug at one end and passing to the 

other; this to prevent rupture in virtue of sudden expansion of the 

fusible core. By means of an air force-pump, or even of a high-pressure steam-boiler, acting at one end, sufficient pressure was brought to 

bear on the fused core to force it out completely. When this occurs 

bubbles issuing at the end of the tube rise in the aniline in great number. The tubes are then withdrawn from the bath, dried, and, with a 

current of steam passing through them, heated to redness, and tested. 

This process is very tedious, inasmuch as it is not always possible to 

so draw the tubes that the fusible metallic core remains central. When 

the canal is asymmetric there is liability to rupture, if it does not actually occur during the drawing.1 For each perfect tube two or three imperfect ones must be discarded. Tubes thus made have a larger caliber 

relative to their thickness than is obtainable in other ways. Thinwalled capillary tubes are often specially desirable, particularly when 

tubes are to be soldered (with glaze) into the stem of an air thermometer. In table 411 give the constants of copper tubes obtained by this 

process.

According to Rouina (cf. Spring: Cheni. Ber., vol. 15, 1882, p. 595) silver with a 

platinum core (Wollaston's method) is found to alloy after long drawing. I observed 

no effects of this kind, however, possibly because the metallic surfaces, in case of 

base metals, are not sufficiently clean. .

(824)
BARUS.] PORCELAIN AIR THERMOMETRY. 171

TABLE 41. Dimensions of copper capillarg tribes.

No.

1

2

3

 4

5

6

7

Weight.

9- 

5.81

5.39

10.81

4.74

7.34

7.07

2.99

Length.

cm. 

81.5

95.0

144.0

67.6

105.6

108.2

101.7

Thickness.

cm. 

0.119

0.103

0.123

0.119

0.118

0.119

0.077

Caliber.

cm. 

0.063

0.050

0.066

0.064

0.062

0.069

0.041

Volume 

per cin.

cc. 

0. 0031

0. 0020

0. 0034

0. 0032

0. 0031

0. 0037

0. 0013

Among these No. 7, a very perfect tube, is most remarkable. The 

tubes were made in February, 1884.

Since that time I was fortunate in inducing the Malveru Platinum 

Works to undertake the manufacture of such tubing in silver and platinum. With the latter metal they succeeded well, and the dimensions 

of samples of the (platinum) tubing made for me are given in Table 42.

TABLE 42. Dimensions of platinum capillary tubing.

No.

1

2

3

4

Weight.

0- 

9.02

7.25

7.07

7.62

Length.

cm. 

51.0

42.6

41.5

44.4

Thickness.

cin. 

0.115

0.115

0.115

0.115

Caliber.

cm. 

0. 0524

560

561

553

Volume 

per cm.

cc. 

0. 00215

246

247

240

These tubes may be obtained in any length not exceeding 5 meters. It 

is usually sufficient to use meter lengths only, cleaning each thoroughly 

with naphtha, alkalies, and acids; passing capillary iron wire quite 

through the tube, drying, and then heating to redness before inserting. 

The use of capillary tubes presupposes slow rise and fall of temperature 

during calibration. To this end rny furnaces have been constructed. 

The data of Tables 41 and 42 will appear more striking when placed in 

contrast with the capacities of the bulb and stem of the porcelain gas 

thermometer. These are 300CC and 0.012CC per centimeter, respectively.

Kundt has successfully used capillary glass tubes drawn out so thin 

as to be filamentary.

Platinum capillary tubes (the present being the first ever made, I 

believe) are an especially useful apparatus and subserve many ulterior 

purposes. They are used, in chap. V, for instance, as an essential part of 

the transpiration thermometer, and to investigate the laws of transpiration and gas viscosity at high temperatures.

Porcelain gas-thermometer bulbs. Yarious forms of gas-thermometer 

bulbs, as given in Figs. 31, 32, and 33, drawn to a scale of £, were used.

(825)
172 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

They were made by Morlent freres, Paris1 (formerly 'Mr. Gosse, the 

original constructor of the Deville and Troost apparatus), of the very 

refractory porcelain of Bayeux-. Fig. 3i is the earliest form. Bulb and

FIG. 31. Non-inglazed spberical air thermometer bulb. Scale £.

stein are one piece, put together by the maker. The fractured bulbs 

show that the ballon proper, to within a radius of I0111 of the neck (d d, 

Fig. 4), and the stem with attached neck (b d a <?), were made separately, 

and then put together by a skilled artist. After burning no discontinuity of porcelain at the circle of junction is visible. The glazed gasthermometer is perfectly smooth on the outside, and a longitudinal section differs in no essential respect from Fig. 31.

In consequence of the long capillary stem (O.lcm in diameter) it is 

exceedingly difficult to glaze these thermometers internally or to keep 

the stems from choking when the temperatures are high enough to 

soften the glaze. For this reason the bulbs are furnished without being 

glazed internally an error when data of high temperature are to be

sharply measured. I add here that on fracture the stems very frequently reveal clefts and lateral fissures communicating with the canal, 

I believe that a more compact stem could be made in the manner described above (p. 95) for the manufacture of porcelain insulators for the 

thermo-element. M. Gosse pressed his stems in a long mold over a 

core of zinc wire. The latter is melted and volatilized during the firing; 

but in spite of its ingenuity this method is imperfect, for the capillary 

canals made in this way, in addition to their liability to retain lateral 

fissures, are seldom perfectly central along the whole length of stem. 

In case of a stem made by my method this result necessarily follows 

whenever tbe apparatus has once been adjusted.

In Table 43 some values of the mean dimensions, etc., of the bulbs (Fig. 

31) are given. They are the results of mercury or water calibrations, 

of which for accurate measurements tbe water calibrations are preferable. Mercury does not so easily enter the fine fissures.

1 1 also had similar bulbs made in Berlin, and will communicate results obtained 

with them later.

(826)
BABUB.J PORCELAIN AIR THERMOMETRY. 173 

TABLE 43. Capacity, etc., of iwrcelain gas-thermometer lulls.

G1H.

9

9

Bulb.

iSness

cm.

0.27

0. 20

Capacity.

cc.

300.0

307. 4

Length.

cm.

40

40

Stc

Thickness.

cm.

0.8

0.8

m.

Mean 

caliber.

cm.

0.122

Volume 

per cm.

cc.

0. 0116

Probably owing to difficulties in burning the polar diameter is usually 

slightly less than the equatorial diameter.

To use this bulb for calibration it is necessary to have a space of very 

constant temperature, for the indications of the thermo-element are instantaneous, and refer only to the little space immediately surrounding 

the thermo-electric junction, whereas the gas thermometer passes relatively slowly from one temperature to another, and the temperature 

datum refers to the internal mean temperature of the whole exposed 

surface. These differences of character in the respective temperature indications may,of course, be seriously large. They are entirely arbitrary. 

With the object of eliminating these errors I had a bulb made in the 

shape of Fig. 32, the bottom of which is re-entrant, forming a cylindriFIG. 32. Non-inglazed re-entrant air thermometer bulb. Scale J.

cal tube, n m, the closed end m of which projects inward as far as the 

center of the bulb. It is into this tube that the properly insulated 

thermo-elemeut is introduced with, its junction at m. The insulators 

are sufficiently large to practically close the tube n m as with a plug, by 

which loss of heat by radiation is made imperceptible. The temperature of the thermo-element and of the gas thermometer may therefore 

be regarded identical. I add that the stem of the form (Fig. 32) is thicker 

than the stem in Fig. 31, in order that at high temperatures there may 

be less liability to bending, supposing the thermometer to be held in a 

horizontal position and the stem to be slightly viscous. The widening

(827)
174 MEASUREMENT OP HIGH TEMPERATURES. [BULL. 54.

of the stem does not seriously increase the value of the stem error 

by increasing the number of interstitial pores, as will be seen. In this 

re-entrant bulb symmetry of form has been sacrificed in order that 

greater identity in the exposure of the air thermometer and of the 

thermo-couple may be secured. Deville and Troost emphasize the 

desirability of spherical bulbs. But the expansion error is beyond 

question less serious than the calibration error, due to inequalities of 

temperature of bulb and thermo-electric junction.

The pressure which bulbs of this kind can withstand at high red heat 

(1,000°) without deforming appreciably is certainly greater than an 

atmosphere, probably much more. Bulbs in which water is confined 

explode at high temperature with detonation and great violence.

The results obtained with these forms of internally unglazed gas 

thermometers are called in question by Deville and Troost. Doubtless 

gas or moisture is forcibly retained in the pores of the porcelain. Hence 

the amount of gas in the bulb at low temperatures may be greater than 

the pressure datum indicates. Again, in the constant-pressure method 

of measurement the volume of the bulb, an essential part of the argument 

of the formula, can not be sharply defined. Hence the great desirability 

of performing the measurements with bulbs of porcelain^ glazed 

thoroughly both within and without. Such a form is given in Fig. 33.

FIG. 33. Inglazed spherical air thermometer bulb. Scale $.

Bulb c d fc and stem e b are here distinct parts. They are calibrated 

separately, and prior to using are soldered together with feldspar and 

the oxyhydrogen blow-pipe. The bulb c d Tc ends in a short neck, c d r «, 

the part res being just large enough to receive the stem ef snugly. 

The canal cd, through which the bulb is glazed, eventually becomes 

the prolongation of the capillary canal of the stem.

Soldering together the bulb and stem is a difficult operation, and calls 

for much skill and patience on the part of the operator. The bulbs are 

liable to breakage, and it is difficult so to solder the stem that the joint 

may be hermetically sealed. I therefore feel justified in describing a 

machine of my own, by which such soldering can be effected.

(828)
UA11US.J PORCELAIN AIR THERMOMETRY. 175

Machine for soldering porcelain. The elevation (Fig. 34) is largely in 

section, the cuts being taken through central planes of the apparatus, 

as will readily be understood by consulting the plan (Fig. 35). I give the 

drawing in a scale of 1V. The soldering machine consists essentially of

a whirling-table, of which A B is the large pulley and CD the spindle. 

The two wheels are connected by round leather belting, which can be 

tightened at pleasure by a screw adjustment, E F. The spindle axle

(829)
176 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

carries the gas thermometer bulb 3 G- to be soldered to the stem L K. 

The two parallel plates of brass, MM, NN, held at any desirable distance apart by three bolts, b a, subserve the purpose of securing the 

bulb G H firmly and symmetrically with respect to the axis of rotation.

It is easily seen that the two plates 

/If M and N N make with the bulb 

G E a joint that is practically of 

the ball-and-socket kind, hence the 

facility of adjustment. A lateral 

arm, 0 P, clamped to the fixed upright rod Q E, holds the stem K L 

hi position during the rotation, the 

latter passing through a little ring 

at P, Another lateral arm, U .7', 

similarly clamped to the rod Q fi, 

carries the adjustable lime furnace. 

j, This is a rectangular parallelopi- 

.2 pedon sawed out of a solid piece of 

& lime, provided with a large central 

= perforation passing quite through 

^ the block for the reception of the 

| neck and lower stem of the gasI thermometerj provided also with a 

^ smaller lateral perforation passing 

| only far enough to communicate 

| with the central hole. This block 

J> of lime is secured between two par- 

| allel plates of iron by aid of three 

1 bolts, two of which only appear 

* iii the figure. The plates are, of 

» course, ring-shaped, to correspond 

£ with the vertical perforation of the 

lime block, and the lower plate is 

riveted to the lateral arm If T. To 

obviate confusion of lines the lime 

furnace is omitted in the plan (Fig. 

35). I need only add that the arms 

0 P and U T can be removed at 

pleasure $ that the bulb, with its 

lantern-like support, can be withdrawn from the spindle by unclamping the screw TFj that, finally, the spindle itself is adjustable 

laterally at pleasure, passing, as it does, between two slides, XX and 

Y T. These slides are kept in position by two pairs of screws, by which, 

moreover, the slides and the base plate of the spindle may be forced 

firmly in contact and clamped,

(830)
BARUS.] POECELAIN AIR THERMOMETRY. 177

Having given the arrangement of the rotational apparatus, I have 

to add a description of the sliding oxyhydrogen blow-pipe. The blowpipe itself is shown at c d, and the plan contains dotted lines showing 

the construction of the interior. Hydrogen from the gasometers enters 

through a large tubulure, a, fully 0.5cm in diameter, compressed oxygen 

through a finer tubulure, d, the jet end of which is not quite 0.08cm in 

diameter. This blow-pipe burns quietly, and if well constructed the 

flame is visibly .one foot in length, tapering with perfect regularity from 

the large diameter 0.5cm to a point. The attachment of this blowpipe to the frame-work which carries it is such that in its horizontal 

position the flame plays through the lateral hole of the lime furnace, 

impinging upon the neck of the bulb to be soldered. The collar n, into 

which the blow-pipe is fastened by the screw e, has a lateral axis or 

swivel, in virtue of which the blow-pipe may be rotated around an axis 

perpendicular to itself (a kind of trunnion), and clamped at any given 

angle by the screw ~k. In this way the flame may be made to impinge 

against any part of the stem or neck of the bulb to be soldered, at 

pleasure. The sliding arrangement into which the swivel is clamped 

consists of two parts, the slide proper, #, moving freely along the rod 

ef, and the part w, which is practically a nut of the male screw g h. The 

parts q and m can be joined at pleasure by aid of the steel pin s s and 

corresponding clamp screw. If the latter be loosened the blow-pipe may 

be made to approach the air thermometer as near as desirable. The 

screw g h ends in a wheel, i », rotated by a belt, which passes over the 

lower spindle of the pulley-wheel A E. An axle, 1c Ic, carries two independent rollers, by which the direction of the belt is changed. In this 

way the screw is kept in motion to correspond with the rotation, of the 

air-thermometer bulb.

When, the flame is lit and the soldering commenced, the blow-pipe car-' 

riage is placed as near as practicable to the end li of the screw. As the 

rotation continues the flame gradually approaches the air thermometer, 

and the heat is therefore intensified with perfect regularity. Inasmuch as 

the flame impinges on the neck while in a state of rotation, it is quite 

obvious that the liability to fracture or breakage is by this device diminished to a minimum. I add that to prevent interferences the 

thread at the end of the screw g li has been cut away, so that when the 

nut m is near these end points there may be no further tendency to 

move. An intermediate rod, r r, and a sliding piece, e *, increases the 

steadiness of motion. The carriage as a whole is supported by two uprights, J J and Z Z.

The feldspar to be used for soldering is to be ground most carefully 

to an impalpable powder and mixed with mucilage or water to a plastic 

or pasty consistency. This is spread uniformly around the neck of the 

bulb, so as to form a ring where the edge of the neck shoulders against 

the stem. It is then allowed to dry. Stem and neck should fit snugly 

from the outset; at least all waste space should be calked with feldspar, 

l! 54 12 (831)
178 MEASUREMENT OF HIGH TEMPERATURES. [BULL.54.

It is perhaps best to commence the heating with the lime furnace removed, sliding it above the neck. When the parts are white hot and 

the frothing has largely ceased, it is expedient to conduct the further 

spidering by hand directly, the blow-pipe being for this purpose 

manipulated by the right hand and the spindle turned suitably with 

the left. Care must be taken not to melt the porcelain.' The heat is, 

however, sufficient to make porcelain quite viscous, and not only can 

the stem be bent, but the parts of the neck of the bulb surrounding the 

lower end of the stern may be pressed firmly against it, producing a 

weld joint, as it were. I have no doubt that porcelain can actually be 

welded in this way. Plat steel pliers, which if necessary may be notched 

by a cylindrical hole which fits closely around the neck, are closed 

quickly but firmly around the neck and then quickly withdrawn, rotation of the bulb being temporarily discontinued. The operation calls 

for Skilled manipulation. Indeed, it is not easy to make a vacuumproof joint, and samples neat in external appearance have frequently 

to be duplicated. It is essential to keep the whole neck at white heat 

a long time in order that its inner surface and the outer surface of the 

stem may be everywhere in contact. It is at this stage of the operation 

that the lime furnace may be appropriately lowered, and the final 

gradual coalescence of contiguous parts of the porcelain apparatus 

allowed to take place. Two oxyhydrogen flames impinging on the porcelain from opposite directions are preferable to a single flame with the 

lime furnace. The latter is essential, however, during cooling. Porcelain is specially liable to crack on cooling when it first becomes rigid. 

Hence it is expedient, after withdrawing the flame, to close up the furnace as far as possible with asbestus board and carded asbestus, and 

then to bury the whole furnace above the plate mm in a heap of slacked 

lime. But with the best precautions the feldspar is found to be fissured 

after cooling, and unless bulb and stem have thoroughly coalesced and

the joint be perfect at the internal faces, the apparatus will not be 

vacuum-proof. It is well to fuse feldspar upon the end of the stem 

around the hole. To keep this hole opposite the capillary hole in the 

neck a thick platinum tube or wire may be thrust through both. In 

this case the neck of the bulb may be quite filled with the slimy feldspar paste, and the stem then forced into it from above, keeping the 

capillary platinum tube in place. The feldspar which exudes is partially removed, and the bulb then allowed to dry. This process gives 

greater assurance that soldering will take place between the inner surface of the neck and the end of the stein than any other. I may add, in 

closing, that I have repeatedly tried to make air thermometers in which 

a capillary platinum tube is soldered into the stem with a glaze more 

fusible than feldspar. I have also attempted to glaze single-piece air 

thermometers, like Fig. 31, internally, as well as to solder platinum 

tubes into the stem. Although these attempts have thus far failed, it 

is but just to assert that the failures are due rather to the insufficient

(832)
BARU8.J PORCELAIN AIR THERMOMETRY. 179

technical skill of the operator than to crucial errors of method. I hope 

at an early day to produce a porcelain air thermometer made in one 

piece, glazed within and without, and provided with a tight-fitting capillary platinum stem. I also hope to make bulbs of fire-clay, suitably 

glazed without, apparatus which will be available for the measurement 

of temperature very much beyond the highest limit of the porcelain 

thermometer. The soldered air thermometer presupposes low-pressure 

measurements, such as this paper describes.

Bulbs which are not perfectly tight may sometimes be closed by heating in a large furnace with glaze. I have used the one described below 

for this purpose. This process, however, is difficult and expensive, even 

if low pressure is applied to suck the glaze into the capillary fissures and 

canals. It is best to endeavor to complete the soldering with the oxyhydrogen flame, testing the quality of the joint with the air-pump after

the bulb is again cold.

It is well to insert a word here about gasometers. I used the simple 

form of sheet zinc bell-jar G G 0 G (Fig. 35a), dipping in a reservoir of

fV^

K.

*-S "-M.

Q/ \

^ G_ rru

K

FIG. 35a. Gasometers. Scale ,» .

water, 11 in m. The bell-jar is provided with a guide, n n, and a counterpoise, K. The level of the water is shown at 11. Gasometers of this 

kind are well known, and are furnished by Ritchie & Co., in Boston. 

My purpose in this place is to indicate the great advantage gained by 

two stop-cocks, £, C, for each jar, GG,G G; for in this way any number 

pf single jars may be coupled together. In Fig. 35a, for instance, the

c (833)
180 MEASUREMENT OF HIGH TEMPERATURES. [BULL.54

stop-cock B is supposed to be in communication with the hydrogen 

generator5 the stop-cocks C and D are connected by rubber tubing; 

the stop-cock .27, finally, supplies the hydrogen to the blow-pipe, with 

which it is in communication. The advantage gained in this way is 

this, that the hydrogen may be generated and used at the same time 

a desideratum when large quantities of the gas are necessary.

Revolving muffle. In order that the temperature comparisons in question may be satisfactorily made, the apparatus to be compared must be 

placed in a space of practically constant temperature, which shall be 

variable at pleasure from ordinary temperatures to the most extreme 

degrees of white heat. Methods for securing constant temperatures for 

thermo-electric comparisons have already been given; but when one of 

the pieces of apparatus to be heated is as large as the bulb of an air 

thermometer, and when, moreover, this relatively large apparatus is to 

be compared with the sensitive point of the thernio-element, the difficulties of calibration are very much increased. In some of the earlier 

comparisons the efficient assay muffle-furnace made by the Buffalo 

Dental Manufacturing Company was used. This is practically a gigantic Bunsen burner, surmounted by a furnace of fire-clay, so constructed that the flame in a narrow sheet is compelled to pass around 

and completely to envelop the muffle. In the furnace used this muffle 

was fully 20cm long and 12cm high, offering ample space for the introduction of the bulb, and by wrapping asbestus paper and carded asbestus 

thickly around the bulb so as quite to fill the muffle, and binding muffle 

and therrno-element closely together, the two may be compared with 

some accuracy, Eesults of this kind are given below (p. 201.)

Unfortunately the introduction of metal envelopes is objectionable, in 

view of the danger of fluxing the contiguous parts of refractory clay. 

There are other and more serious difficulties encountered. The maximum 

temperature thus attainable is not greater than 1,000°, and hence the interval of calibration is limited. Moreover, the closed end of the muffle 

is at the center of heat of the furnace, whereas the open end is neither 

surrounded by flame nor are the provisions against loss of heat sufficient for constant temperature conditions which recommend the furnace for assay purposes, but which, inasmuch as they involve differences of temperature of several hundred degrees, are seriously objectionable for calibration purposes. Again, the rate of cooling of this 

furnace is too great. It is difficult to close up so completely as to 

exclude convective cooling due- to currents of air and diminish loss 

by radiation, the bottom of the furnace over the burner being large, 

open, and inaccessible, and the chimney large. ISTor is it conveniently 

possible to regulate the flame of the burner for intensities of heat less 

than the maximum. Finally, thermo elements must be compared singly, 

because they need to be tied to the bulb. In general consecutive comparisons of series of elements are desired.

Without question the form of the furnace could be modified to meet

(834)
BARUB.I PORCELAIN AIR THERMOMETRY. 181

the special requirements of the calibration problem, excepting, of course, 

the limited scope of temperature; but it is expedient to proceed more 

radically and introduce an entirely new and distinct furnace for the pur. 

poses in question. This I have done in a way indicated in plan in 

the diagrammatic Fig. 30. The body of the furnace is a thick cylindrical box, B B, surmounted by a hemispherical lid suitably perforated. 

In this cylindrical iuclosure a spherical muffle, provided with hollow 

lateral arms or axles, E and F, and placed symmetrically with respect 

to the center of figure of the furnace, is free to rotate around the horizontal axis of the arms. If the rate of rotation be sufficient this mechanism insures constancy of temperature within the'muffle around the 

horizontal E F. Two blast burners, Q and H, purposely placed tangentially or diagonally, so as to be equivalent to a couple, blow a cyclone 

of flame into this furnace, equalizing temperature around the central 

vertical, Virtually therefore the muffle, regarded as a geometrical

PIG. 3Ca. Elliptic revolving muffle; diagram. PIG. 36. Eevolving mufflo; diagram.

sphere, has two rotations, one about an axis, JE7JP, a second around the 

vertical, passing through 0. To make this apparatus theoretically perfect a third rotation around an axis passing through 0 and perpendicular toJEF would have to be supplied. This third rotation is a mechanical impossibility, bearing always in mind that cumbersome or complicated apparatus would rather detract from the end to be attained than 

add to it. The two rotations can be made to suffice. In the spherical 

space of constant temperature thus obtained is placed the bulb of the 

air thermometer, with its stem projecting into and through the arm F> 

The center of bulb and that of muffle a.; nearly as possible coincide. 

The bulb is held in position and free from the muffle by a clamp attached 

to stem on the outside of the fur.: ace. The thermo-element is introduced through the opposite arm E in such a way that the junction may 

be contiguous with the air thermometer. The insulating tubulure is 

also supported by a clamp on the outside of the furnace. It is an essential part of the construction of the present apparatus thai during rotation the muffle touches neither the air thermometer nor the thermoelement, both of which apparatus are stationary, and suspended quite 

free from all parts of the furnace.

Having thus indicated the general principles of the constant temperature apparatus, I shall next describe the practical form of this furnace, which, after many trials, has been found satisfactorily serviceable.
182 MEASUREMENT OF HIGH TEMPERATURES. [HULL. 54.

This is given in front elevation ami longitudinal section in Fig. 37 and 

in side elevation in Fig. 38, respectively, drawn one-fourth and one-half 

the actual size. The body of the furnace is shown at B B B 5, a thickwalled cylindrical pot, surmounted by a hemispherical dome, A" A A, 

the lid of the furnace. A central hole at A1 and a series of six symmetric lateral holes, a a, a a, . . .in the lid are sufficient for the escape 

of the products of combustion. ,

The burners HHHH&wl GGGG project into the furnace as far as 

the inner surface. Their diagonal position is well shown in the side 

elevation (Fig. 38) and their internal construction in the longitudinal 

section of Fig. 37. Compressed air from a centrifugal blower, run by a 

one horse-power gas-engine, enters the central tubes h h and gg, respectively. The inlets of gas are shown at c and c-'. Attached to the bottom of the burners are rectangular slides II and KK, respectively, 

which pass through guides L L and MM. In this way the burners can 

be easily inserted or withdrawn from the furnace. A little pin, d, 

prevents their being inserted too far into the interior, and a similar 

longer pin or roller, e, is so adjusted as to rest the greater part or the 

whole of their weight upon the bed plate 8 8, instead of on the friable 

mass of the furnace. The burners shown in the figure were constructed 

entirely of gas pipe, and the disposition of parts is such as suggested 

itself after many trials. Burners in which back explosion is obviated 

by surrounding the mouths with a sieve or net-work of iron wire (as is 

the case in some of Fletcher's apparatus) are thoroughly unsatisfactory. 

These sieves obstruct the blast and are not as much a safeguard against 

back explosions as is necessary in an apparatus where constancy, or at 

least very uniform variation of temperature, is the requisite. In the 

blower of Fig. 37 the blast tube li h extends to within an inch of the mouth 

of the burner. The column of gas surrounds this tube. With the fullcurrent of air sent through the furnace the gas may therefore be as 

nearly cut off as is at all desirable, or it may be quite cut off without 

incurring any risk of explosion, either in the blower or in the burner. 

I may add that the tubes c c and c' c' for gas supply should both point 

toward the more accessible side of the furnace, and there communicate 

with graduated stop-cocks, such as are furnished by the Buffalo Dental 

Company. For the furnace above half-inch supply-cocks are sufficient. 

The centrifugal blower which I used was of rather a smaller form than is 

usual in the market, being only about eleven inches in diameter and with 

paddles scarcely two and a half inches wide. It was taken from a portable forge. Doubtless even a smaller blower, i. e., a narrower blower, 

would have been desirable, so that the power of the engine may be 

spent in furnishing pressure of blast rather than quantity of air. The 

smallest form of Eoot blower (blacksmith's model) and larger forms of 

centrifugal blower had therefore to be discarded, for with the available 

power the blast obtained proved to be too large in quantity and too 

small in intensity. In the Eoot blower, moreover, the flame obtained

(836)
^\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\^^

FIG. 37. fievolviuj; muffle and furnace; longitudinal section. Scale J.
BABUS.J PORCELAIN AIR THEEMOMETBY. 186

is intermittent, and in this respect objectionable. It will be well to 

state that the flame issuing at the mouth of the burner when the blast 

is cut off (a great torch fully two feet in length) is reduced to a bliiQ 

cone scarcely eight inches in length for the maximum supply of gas. 

Placed in the position given the burners during the heating do not 

melt, but merely grow red hot at the mouth, and the oxidation is 

a minimum, because the general tendency is to reduce. It is well, 

however, to attach a reservoir of water behind the furnace and to tap 

it tli rough lead piping and small faucets, so as to fall drop by drop 

upon the burners and thus prevent all possibility of superheating. In 

none of my experiments did ferruginous fluxing of the furnace body 

occur. I found in the experiments that to secure the maximum temperature desirable (say 1,400°), it was not necessary to open the halfinch clear-way cocks more than one-third. From this downward the 

intensity may be diminished to the merest ribbon of flame, sending in 

reality ouly a vortex of hot air through the furnace. Indeed this adjustment is very satisfactory, so that with an accurately graduated 

arc attached to the cocks it is possible, after the necessary preliminary 

measurements have been made, to open it in such a way as to strike 

any given temperature with some nicety. The cupola A A, which can 

be lifted off from the body B B, along the plane A A, emphasized in Fig. 

38, has a suitable handle arrangement attached to it, which is omitted 

in the figure.

Having thus given a furnace which can be heated to any reasonable 

degree of temperature with extreme ease and convenience, I proceed 

next with the description of the revolving muffle. The muffle proper 

is shown at E C D F, in Fig. 37, and consists of two identical h.lives 

of refractory fire-clay, each of which is a hemisphere with two diametrically opposite guttered arras. The two halves are placed together, 

with their plane faces contiguous, but without cement. They are held 

together by surrounding their ends with appropriate collars of iron, 

NN N -Z\Taad N' N' N' N', the outer edges of which are widely flanged. 

These flanges, PP and P P', are turned circularly, with their circumferences carefully beveled, so as to fit nicety into the grooves of two 

pairs of friction-rollers, Q Q and Q' Q', of which R B and B1 B' are 

the respective axes. Here I may well say that it is difficult to bake 

the muffle in such a way that the plane faces are not warped. Moreover, the two tubes, when placed together, show rather an elliptic ringshaped section than a circular one, as is represented, with a little exaggeration perhaps, at //, Fig. 38. But this irregularity furnishes an 

exceedingly satisfactory way of fastening the muffle into the collar. 

For if the width of the bore be so chosen as to fit snugly on the major 

diameter of the axle of the muffle, a flat v/~\>-8haped spring of steel may 

be inserted in each narrow space between axle and collar, against the 

bulge of which (spring) set-screws tttt, sunk into an equatorial rib 

of the collar, press as firmly as is permissible; or this space may be

(837)
184 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

filled with fitting knife edged blades of steel, or with asbestus board, 

against which the screws t press. All of these methods are good. 

Even when the temperature is so high as to fuse the inner surface of 

the collar the screws t can be worked loose with a drop of oil or petroleum, and after removal show no serious injury. It is not easy to fit 

the axle of the muffle into the iron collar, because the silicious material 

does not yield easily to the file. It may, however, be ground on a grindstone, or, with greater advantage, by filing it with a piece of its own 

substance.

Having thus shown how to fasten the collars symmetrically, and at 

such a distance apart that the opposed flanges may fit in the grooves of 

the opposed rollers Q, Q and Q1 , $', it is next in order to describe the 

adjustment of the rollers themselves. Their axles, E, _K, J£', R', are 

mounted at suitable distances apart on a rectangular rod of cast-iron ? 

u u, provided with a -handle of wood, W. The rods u u, u' u' again 

are each adjustably fastened to Y shaped uprights Y, Y, T, Y, 1 and Y', 

Y', Y', Y' by aid of strong screws F, V. Loosening For F' the rod 

u u or u' u' may be raised or lowered or rotated around the center of 

F or V and clamped in any.desired position. It is in this way that the 

inner edge of the collars N N N N, N' N' N' N' may be nicely adjusted 

with reference to the lateral shouldered holes of the furnace through 

which the axle of the muffle projects. Eotation therefore takes place 

on the friction-rollers, in which the wheel or flange P P rolls smoothly. 

It will be seen that some such arrangement as this is essential, for the 

rolling parts must be placed so far away from the hot parts that they 

may be lubricated. At very high temperatures the muffle becomes 

more or less viscous, and hence it is necessary to obviate all such tendencies to twist or wrench off the axles as an imperfectly oiled mechanism constantly presents. There is one further adjustment to be made: 

After the firing neither do the axles of the muffles coincide in prolongation, nor are the axes of the cylinders straight lines. Hence the axles 

of the rollers R E, E1 R' are long cylindrical rods along which the 

rollers Q Q Q Q may slide laterally, their extreme positions being fixed 

by four adjustable set-screw collars #, x, x', x'.

To revolve the muffle a belt pulley of wood Z Z has been screwed to 

the flange-wheel P' at .a little distance from it. Over this passes roundleather belting, and the power is communicated by a corresponding 

pulley on a lateral shaft of the engine. The wooden belt-ring Z Z is far 

enough away from the hot parts to escape being charred. The belt, 

however, must be provided with a tightener.

irrhe uprights were given the Y-shaped form to prevent the possibility of lateral 

slipping of the muffle. In later experiments I found this safeguard unnecessary, so 

that a simple flat upright, with a vertical slot opening upward to admit the screws 

V, V, is far preferable. In other words, the uprights in the figure are to be sawed 

off square above the slot. By this means greater facility of adjustment is secured 

when the collar is to be fitted to the axle of the muffle or removed from it.

(838)
w//m//////////Mmmmmmmm^^^^^

Q

FIG. 38. Kevolving muffle furnace; side elevation. Scale J.
--JAUU8.J PORCELAIN AIR THERMOMETRY. 185

Finally, the figure shows the air thermometer// Jc i e in position, supported by the universal clamp m m attached to the vertical rod q q. A 

similar universal clamp, n n, on the opposite side of the furnace supports 

the insulator of the thermo-elemeut k Jc. The clamp n n attached to the 

rod r should be a spring, so that elements may easily be either inserted 

or withdrawn. The ends of the wires of the thermo-couple appear at 

a and /? and pass thence to a petroleum bath of known temperature, 

where they are suitably connected (page ) with the terminals of the 

measuring apparatus. The junction of the thermo-element is in contact 

either with the external surface or with the closed end of the re-entrant 

tube, according to the form of porcelain bulb selected. Of this further 

mention will be made. It is here in place to state the method of inserting the air thermometer, a method which must be convenient and expeditious. Supposing the collars N. . . , N'. . . to be removed the air-thermometer bulb is covered properly by the two halves of the muffle. The

collars themselves are completely cut through oil one side by a slit between two nearly contiguous axial planes, which slit passes through the 

flange P P,,as shown at s n in Fig. 38, as well as through the body of 

the collar, and is quite large enough to admit the capillary platinum tube 

of the air-thermometer. This slit does not seriously weaken the collar, 

strengthened as it is by the central rib into which the screws t are sunk, 

and by the flange P P. In this way the collar at the air-thermometer 

end of the muffle may be slipped on quite as readily as the other. Having therefore centered the muffle, as described above, it is then easy to 

fix and center the air thermometer, so that it may be quite free from 

contact with the muffle. In the case where a soldered air-thermometer of 

the form Fig. 33 is used, a muffle of an axis sufficiently wide to accommodate the neck must be used. A muffle of this kind is given in section in the diagram, Fig. 36. In place of adjusting the muffle it is often 

desirable to adjust the furnace. This may be done by four set-screws, 

tt tt, Fig. 38, which act in pairs at right angles to each other. An oildropper, by which the roller Q may be kept lubricated, is a- desirable 

addition. Some such non essential parts are omitted in the figure to 

prevent confusion of lines.

Remarks regarding the apparatus and manipulation. Bearing in mind 

that this furnace is as nearly as is practically convenient or possible 

the outcome of a theoretical principle for the construction of constanttemperature apparatus, that all manipulations to be applied may be 

made safely and with expedition, it is well to summarize the advantage 

gained, as well as to allude to such others as are easily within reach. The 

maximum temperature obtainable is indefinitely high, much higher than 

can be defined by porcelain air-thermometer'measurements. Any other 

temperatures below this extreme value can be obtained with requisite 

constancy. If these intermediate temperatures be in the region of red 

heat it is simply necessary to diminish the supply of gas by partially 

closing the gauge stop-cock. If the temperatures be below red heat

(839)
186 MEASUREMENT OF HIGH TEMPERATURES. [BULL.54.

the gas may be shut off altogether, and the furnace closed by shutting 

the flue holeb with a fire-clay plug or with asbestus. If all influx of air 

is cut off the furnace (below 500°) cools very slowly. During these 

stages of cooling it is not undesirable to continue a rotation of the muffle at a rate sufficiently slow to prevent currents of air from entering 

the polar parts and being hurled off centrifugally at the equatorial parts 

of the muffle. Here it is well to mention that the speed of rotation 

usually employed in the present experiments was about fifty revolutions 

per minute. Possibly this rate is too great, particularly at very high 

temperatures, at which the muffle becomes incipiently viscous, and 

much slower rates are therefore preferable. Protected from direct flame 

by the muffle, the fragile porcelain bulbs are heated with great regularity, and the liability of the thermometer to breakage is therefore nil. 

In order to determine the constant of the air thermometer (zero reading) it is sufficient to place a mercury normal thermometer in contact 

with the bulb (or better in the central tube of the re-entrant bulb) in 

the cold furnace before heating. The same operation must be repeated 

in the cold furnace after heating. The difference of zero readings thus 

obtained is a test of the validity of measurement, inasmuch as it shows 

whether during the course of the comparisons the bulb has remained of 

fixed normal volume and whether air or gas has leaked into or out of 

the air thermometer. The mercury thermometer is inserted and held in 

position by the same spring-clamp which, during calibration, holds the 

thermo-element. In the form of bulb, shown in Fig. 32, to which most 

of the present remarks apply, the mercury bulb is pushed quite into 

the re-entrant tube and an identity of environment of mercury and air 

thermometers is thus secured. Of course it is more nearly accurate, 

though less convenient, to submerge the bulb in water of known temperature in order to get the zero or fixed point. All this will be discussed 

below.

During the heating of the furnace to white heat, the hollow axles, 

which necessarily lie in the circumambient sheet of flame, are heated 

more easily and kept at a greater intensity of red heat than the body of 

the muffle. This is the objectionable feature, due to the absence of the 

third rotation referred to on page 182. But this error, thus introduced, 

is confined to a small part of the stem ; it does not extend as far as the 

muffle, in the interior of which, moreover, the hot air is churned around 

the bulb by the rotation; its harmful effect is fully obviated by the use 

of the re-entrant bulb, in which heat is communicated to the thermoelectric point junction through the surface of the air-thermometer bulb; 

it is entirely absent during the cooling of the furnace, conditions under 

which most of the experiments are made. Finally, the furnace has been 

so made that the zone of variable temperature, which surrounds the stem 

of the thermometer, is as narrow as possible when measured along the 

length of the stem. Indeed, the correction to be applied for the part of 

the porcelain stem, which has varying temperature, is almost nil. If,

(840)
BARUS.I PORCELAIN AIR THERMOMETRY. 187

following Deville and Troost, a compensator is used to correct the stem 

error, this apparatus may temporarily replace the insulating tubulure of 

the therino-element.

A final remark must be added with reference to silicification 1 of platinum. If the wires of the thermo-element be in contact with the surface 

of the air thermometer, and the temperature high enough to make the 

glaze appreciably viscous, the platinum is invariably attacked and destroyed as far as it is in contact with the glaze, and it is found embedded in it after cooling. The apparent effect is fusion, for the platinum thus silicified fuses at a temperature below that of the glaze. 

Quite aside therefore from the change of constants silicified platinum 

is unavailable for high-temperature measurement, because of its fusibility. Care must therefore be taken to avoid unnecessary contact of 

the thermo-electric wires with the glazed bulb, which is fortunately feasible, because the operator is able to see into the furnace as far as the 

air thermometer through the hollow axle at the side of the muffle on 

which the thermo-couple is inserted.

One great advantage enjoyed in using the present furnace is this, 

that even in case of. extremely high temperatures it is possible to approach very near it without discomfort. The temperature of the exterior 

surface does not exceed 300°, and may be even further reduced by appropriate jacketing of asbestus. Hence all manipulations near the furnace can be conducted with facility. In the case of the large furnaces, 

described in Chapter I, the radiation from the furnace is intense, and 

all close approach to it is difficult.

A sketch of a revolving muffle for the comparison of two air thermometers, containing either two distinct gases, or the same gas at different temperatures, is given in Fig. 36a, where B B is the body of the 

furnace, H, #, the two burners, CD the revolving muffle, and 0 and N 

the two air densities to be compared. The. revolving muffle is ellipsoidal in shape, and the appurtenances are the same as those described 

above. The stems of the air thermometers project at m and m, and 

capillary tubes connect each with the respective manometer. In the 

comparison of air thermometers both the expansion of the porcelain and 

the stem error compensate each other, and the data are thus as accurate 

as the environments are identical.

Finally, I desire to make a few remarks on the complete disposition 

of apparatus, as given in the frontispiece. The lower part of the figure

tendency of platinum to combine with silicon, forming very fusible products, 

has loug been known. Tait, endeavoring to use a bath of fused silicates for constant 

temperature, found the platinum wires, which he submerged therein, disintegrated. 

More recently, Colson (C. R., xciii, 1881, p. 1074; C. R., xciv, 1882, p. 26); Violle 

(C. R., xciv, p. 28) ; Pernolet (C. R., xciv, 1882, p. 99), have given especial prominence 

to this and similar phenomena. In these cases there seems to be a diffusion of the 

solids into each other, and the rneltiug point of silicified platinum may be reduced to 

that of glass. I have often found platinum wire fused on or even embedded in tho 

glaze of the air-thermometer bulb.

(841)
188 MEASUREMENT OF HIGH TEMPERATURES.

shows the position of the one horse-power gas-engine, to the left of 

which is the small centrifugal blower and to the right the bellows. The 

latter are worked by a short crank attached to the axle of the fly-wheel, 

and the blast obtained is small in quantity but high in pressure. The 

furnace-table completely surmounts the engine and carries on the left 

side (under D) a series of three or more small furnaces, resting on a 

special table of their own. These furnaces, fed by gas and the pressure 

blast of air from the bellows, contain crucibles of the form (Figs. 14 and 

15) above, and are used for boiling-point measurements. Thermo-elements are in serted from below and held in position by a suitable clamp. 

Observations and manipulations are made in the way carefully detailed 

in Chapter II. On the right side of the furnace-table (under C) is fixed 

the revolving muffle-furnace, the parts of which have just been described, and are therefore easily recognized.

Quite to the right of the engine (under J5), and screened from it by a 

wide board, is the manometric apparatus of the air thermometer (cf. 

page 209, below). The bulb and manometer are connected by a platinum 

capillary tube. A similar platinum tube connects the compensator with 

its manometer. Above the furnaces is an iron tube, through which the 

small furnaces may either be supplied with hydrogen or may be exhausted, as desired, the other end of this tube being simply attached to 

appropriate gasometric apparatus.

A set of air-thermometer bulbs are shown on a little shelf under A. 

The two vertical bulbs are of porcelain, being the forms Figs. 32 and 33 

above. The oblique bulb is a re-entrant air thermometer of glass.

CONSTANT- VOLUME THERMOMETER METHOD OF CALCULATION.

The general equation. It has already been suggested that it is expedient to choose such methods of thermometry in which the degree of 

constancy of the zero reading before and after the high-temperature calibration may afford a guaranty of the reliable character of the results 

obtained. This test can well be applied when the constant- volume 

method is used. If the work be done with low pressures (<1 atmosphere) it is also possible to adjust the quantity of air that at such temperatures at which porcelain tends to become viscous the tension of the 

inclosed heated gas may approach that of the atmosphere.

The most general expression for the variables involved in any case of 

air thermometry may be rigorously put

where F, V, V" . . . are zero volumes whose special temperatures are 

T, T', T" . . . for the pressure H, and £, t', t" . . . for the pressure h, 

where A is proportional to the excess of volume at T over that of the 

fixed mass of gas at t, and where a is the coefficient of expansion of the

(842)
BABU8.1 PORCELAIN AIR THERMOMETRY. 189

gas and /? the coefficient of cubical expansion of bulb, stem, etc. The 

equation assumes that the gas is perfect and that the bulb expands proportionally to its temperature. The equation is sufficient for the calculation of any one of the variables involved, supposing all the others to 

be known. In the method of constant volume, A=0.

In high-temperature measurement there are at least three parts of 

the air thermometer to be considered. The first of these is the hot region, and includes the bulb and the part of the stem at the same temperature; the second is the part of the stem in which temperature varies 

from the high value to that of the atmosphere; the third is the part in 

which the temperature is practically that of the atmosphere, and it includes the cold part of the porcelain stem, the capillary tubes, and the 

space of cold air above the meniscus of mercury. The whole of this 

may be appropriately called the coW part of the stem. It is obvious 

that the corrections to be applied are specially important when the temperatures of the bulb are high and the air is employed originally under 

small pressure. It is therefore expedient to derive the rigorous expression for temperature in terms of all the variables involved, and from 

this to derive a safe practical form by simplification.

The full expression in question introduces variables which may be 

symmetrically put as follows:

h H V a

t T V ft

t' T' v"

fll r£u

where h is the tension of the gas at the lower temperature, t of the 

bulb, and t' and t" of the variable and cold parts of the stem ; where H 

is the tension of the gas at the high temperature, 21, of the bulb, aod I' 

and T" of the variable and cold parts of the stem ; where v is the volume of the bulb and hot stem, v' the volume of the variable stem, and 

v' the volume of the cold stem, all at zeio degrees; where <*, finally, is 

the coefficient of expansion of the gas, and ft the coefficient of expansion of porcelain. The relation between these variables may then be 

rigorously expressed by the formula

'

l+at

-.vhere the symbol 2 denotes that similar expressions occur additively

vf v" v"! 

for each ^,>^~>^~ . . .

been doemed sufficient,

vf v" v"! 

for each ^,>^~>^~ . . . , to be considered, two of which, however, have
190 MEASUREMENT OF HIGH TEMPERATURES.

The equation simplified. To simplify this formula we replace li ^r ~~ l

by //o, or the tension which would be observed if the bulb were placed 

in melting snow. Equation (1)' then becomes, after solving for T,

where 2 stands for the whole bracket [ ] of equation (1). This equation 

is still rigorous, but it is very inconvenient for calculation. An equally 

rigorous but much more serviceable form is obtained by introducing T 

into the corrective member coefficiented by S. In this way equation (3) 

results

(3>

a form which is still rigorous, but may be conveniently used in practice 

with any desirable degree of approximation, as will presently appear. 

In equation (3) 2 has the form

* IV + PT h l + ^1 I «" IV + ftT" - h l + ^"1 (4} 

V L 1 + atf 1 + atf_\ ^ v L I + aT" 1 + at"J ' ' (*>

v' 

which may be further simplified. Fortunately is very small, for the

mean temperature Tf is only determinable with rough approximation. 

I will define r1 by the equation

and then use T in a simplified form of 2. In the second term of the 

form (4) T" t" very nearly. If, finally, H 7i0 and H h be regarded 

identical, equation (3) reduces finally to the approximate practical form

in which the terms fir' and fit" may also be neglected, as is obvious at 

once.

Error of the approximation. It next becomes necessary to determine 

the numerical importance of the approximation just made, viz, the 

approximation in equation (5), and furthermore T"=t", S h0=H h, 

\+p-t'-=\-\-fit"=\. in the correctives. It also is necessary to investigate the effect of the individual variables of measurement on the result. 

Regarding the quantity H h it is obvious that its value will be at once 

J[ hn when the bulb is surrounded by melting snow, as is usual. To

(844)
PORCELAIN AIR THERMOMETRY. 191

obtain the value of the other approximations 1 refer to Tables 41, 42, 

and 43 for the capacities of bulbs and steins. Moreover, an inspection 

of Fig. 37 shows that the 40cm of stem and 150cm of capillary tube may 

be subdivided into parts, of which the first 5cm of stem nearest the bulb 

have the temperature T of the bulb, and the 25cm of stem, which project 

out of the furnace, together with the capillary tubes and spaces, have 

the temperature t" of the air. The intermediate 10cm of stem have a 

varying temperature between T and *", the mean value of which has 

been symbolized by T". Hence the following volumes v, v' v" occur in 

the correctives :

v =

fl'=0.01] 6x10

v"= f stem, 0.0116x25

copper-cap tube, 100x0.0034

platinum-cap tube, 50x0.0025

meniscus, 0.4x1.22

glass cock, 0.2x0.13

300CC (Table 43)

=0.116 (Table 43)

(Table 43)

(Table 41)

=1,27 (Table 42)

whence it appears that

-=0.00039

v

.=0.00423.

With these data in hand it is expedient to return to formula (6), with

/V 1+ 6 T'\ '

the object of disposing of the corrective ;;'=(!+«T)( ^TTT i ) Assuming for a moment that T'=%T, there follows

TABLK 44.

T

o 

100

500

1, 000

1,500

K'

0. 00045

0. 00057

0. 00063

0. OOOG7

Hence the error n' is less than 1 : 1000, and it follows reasonably that 

i 1 may be replaced by %T without affecting the result more than T^

v per cent. The second corrective H"=(l+aT) ~ * s greater

consequence, and must be carefully evaluated in each experiment. 

The practical method consists in calculating an auxiliary table of 

double entry for K '+K", in which the arguments are T and t". T. in 

such a table is to vary by successive steps of 100° each, t" in steps of 

10°. From this table, computed once for all, the corrective for any 

value of Taud t" may easily be taken by graphic or linear jnterpola-

(845)
192 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

tion. By way of example, the following data for K'-\-K", taken from 

tables of the kind in question, may here be inserted :

TABLE 45. Values of K'+K" for divers Tand t".

t" = 10°

t" 20°

t" = 30°

T =

100°

0. 0000

0. 0058

0. OU57

500°

0.0121

0. 0117

0. 0114

1,000°

0. 0197

0.0191

0. 0185

1,500°

0. 0272

0. 0263

0. 0255

This table shows at once that if T" and t" 'differ by only a few degrees, 

the effect on the result will be less than -^^ of one per cent, per degree 

of difference of T", and t". Now, the walls of the furnace were purposely chosen thick. They are well jacketed, and it is therefore possible 

to screen off the radiation from the " cold" 25cra of stem entirely. The 

iii-e of capillary tubes of metal enables the operator to place the manometer at some distance from the furnace and in an environment of constant temperature. The high furnace table conduces to this purpose, 

since the mercury apparatus may be expediently placed below and on 

one side of the furnace plane, quite screened from it by the table. 

Hence the approximation T" t" involves no greater error than a few 

huudredths of one per cent.

From these considerations the practical convenience of equation (6), 

when many values of Tare to be reduced, appears at once. T computed 

simply as (H Ji0 ) (ali^ /3H} is in the extreme case within 3 per cent, 

of the correct result. By introducing this value into the corrective 

H'+K" the effect on the result (T) is in the extreme cases less than Tf^ 

of one per cent. Having therefore calculated a table of double entry for

K r+x?'=(l+aT)

T

l a

(7)

of which the variables are T and t" in the manner suggested, the approximate value Ti=(H ho) (ah0 /3H) may be corrected at once. It 

is in the interest of expeditious calculation moreover to compute a 

smaller table for j$R. Mention has been made that Ji0 is a mean value 

of measurements made before and after the calibration.

Compensator. This is an ingenious device of MM. Deville and Troost, 

by which the stem error may be corrected directly. A second stem 

closed at one end, but otherwise identicalin diameter, length, caliber, 

etc., with the stem of the air thermometer, is exposed simultaneously 

with it. The two stems are placed contiguously and so as to be in the 

same environment. MM. Deville and Troost, using volumetric methods,

(846)
PORCELAIN AIR THERMOMETRY. 193

exhaust the air from the closed auxiliary stem by means of a Sprengel 

pump. The correction follows from the measured amount of air exhausted. I have used the compensator advantageously in the constant, 

volume method by connecting it with a special small manometer of its 

own. The principle for the reduction of the measurements by means 

of this apparatus follows easily when it is remembered that the compensator is in the practical instance an air thermometer, the volume of 

the bulb of which is zero. Applying therefore the general equation 

(1) above, I have at once for the air thermometer

v(HK-hlc)+v'(HK'-M( )+v"(HK"-hk")=0 . . .*. (8) 

and for the compensator

-h1 Jc")=0 .... (9)

where E\ and hi are the tensions which correspond in the compensator 

to H and h of th e air thermometer, and where K, Jf', . . . and A;, A;', . . . 

are abbreviations for the functions

respectively. If the first equation be multiplied by HI and the second 

by Hand the resulting equations be then divided by vfft there follows

-lt'+ lc"}=0 . . . (10) 

-i y

and since Jc'=k" very nearly

. (11) x '

for which, with an error less than 0.2 per cent, at 2,000°, T may be 

deduced as follows :

- , v'+v" n^ h 1 

l-\

j

a ti r h - v'+v" S hi It'

Here the variable temperature T' is eliminated.

By the use of the compensator the discrepancies due to porosity 

of porcelain, to fissures aud other irregularities, may be partially obviated. It may be made to subserve another important purpose, viz, to 

measure v'+v", the true volume of the stem and capillary connections. To do this it is merely necessary to connect the compensator 

with the ^manometer, as has been explained with reference to the air 

thermometer, in such .a way, however, that the variable space above the 

Bull. 54 13 (847)
194 MEASUEEMENT OF HIGH TEMPERATURES. [BULL. 54.

upper meniscus of the manometer (see Fig. 30) may be read off in cubic 

centimeters. The volume v0 in question is then at once determinable 

volumetrically. For if p' and JP" be the tensions corresponding to the 

volumes v0 +v' and VQ+V" for the same mass of air, under constant 

temperature, then

p'v' p"v"

Vo== P"-P' 

The apparatus actually used was a burette of 50CC capacity, reading 

to within O.lcc, and which had been carefully calibrated. The lower 

end of.this was connected with the flexible hose of the manometer, the 

upper end with the platinum capillary tubes leading .to the stem. By 

aid of an interposed stop-cock (see page 170) the quantity of air in this 

system of tubes could be varied at pleasure. In the table following I 

give the results obtained, from which the general character of the 

measurement may be learned, v and p are the corresponding values; 

v' andjp' or v" and jptf, respectively, and v0 the zero volume of this set 

of canals above the fiducial mark. " Length " and u Diameter" refer to 

the porcelain stem :

TABLE 46. Compensator volumetry.

No.

a

a

a

a

a

1)

b

1

V

cc.

0.30

2.30

0.70

3.50

1.05

5.53

1.57

9.00

0.27

16.50

0.30

15.40

0.50

15.40

0.12

3. 65

0.40

3.69

6.00

1.02

8.62

1.03

3.85

0.48

0.58

4.28

P

cm. B.IJ.

77.49

38.98

66. 94

30.32

57.40

22.27

48.21

15. 42

76.46

8.31

76.50

15.48

75.16

15.60

75.40

30. 65 ,

68.69

30.78

31.13

76. 59

23.99

76.59

32.75

76.65

76.03

30. 57

vo

cc.

1.7

1.6

1.8

1.9

1.7

3.45

3.40

2.35

2.28

2.39

2.43

2.03

1.91

Length.

cm.

32

32

40

40

40

40

36

36

Diam.

cm.

0.8

0.8

0.8

0.8

0.8

0.8

0.8

.0.8

0.8

0.8

0.8

0.8

0.8

Bemarks.

The repetition of this series

leads to practically the

same result.

.New adjustment.

Do.

(848)
l'AKUS-1 PORCELAIN AIR THERMOMETRY. 195

TABLE 46. Compensator volnmetry Continued.

No.

2

3

4

V

cc.

0.32

4.40

4.50

0.30

0.85

4.45

5.44

0.65

5.20

1.20

1.20

8.23

0.30

3.44

3.50

0.22

3.54

0.80 

1.65

0.52

2.15

0.^2 

0.13

1.82

0.20

1.60 

3.35

1.10

Pcm. Hfj.

76.02

2R.80

28.87

78.13

75. 85

28.44

21.86

81.05

29.66

79.20

' 79. 12

20. 16

53.89

16.28

16. 39

56.85

31.37

75.13 

38. 23

78.55

30.68

78. 61 

76.17

21.19

69.54

23.03 

31.85-

75.82

VQ

cr..

2.20

2.16

1.31

1.47

1.20

1.21

LOG

1.11

1.16

0.55

0.52

0.52

0.49

0.53

Length.

cm.

40

40

40

40

40

40

40

40

40

Diam.

cm.

0.8

0.8

1.0

1.0

1.0

1.0

1.0

1.0

1.0

Ivomarks.

New adjustment.

Do.

Platinum capillary tubes

and glass stop-cock, without porcelain stem.

Platinum capillary tubes

and glas-i stop-cock, without porcelain stem ; new

adjustment.

Do.

The errors in these results are about O.I00, and they are easily referred to microscopic leaks, to variations of temperature, and to the 

possible occurrence of moisture in the stems.

From these data it appears, moreover, that the internal volume of 

stems 0.8em thick is not necessarily smaller than the internal volume of 

stems 1.0cm thick. Hence the observed differences of volume between 

the divers stems are largely due to internal fissures, such as can not be 

detected, except by breaking the stems. It is interesting to note that 

the volumes measured volumetrically are not more than twice as large 

as those measured by weight calibration. Hence the superior limit of 

the errors in Tables 44 and 45 is not more than double the values there 

given.

Errors of measurement in general. The degree of absolute accuracy

with which the divers quantities 7i0 , H, <*, /?, ?-., , must be measured in
196 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

order that the effect on Tmay not exceed 1: 1000 follows easily from the 

equation of errors

, _ dx T 

dT 1000 (12)

From this the following six special equations result, equations which 

are approximate and .put in such forms as may best facilitate the computation:

1 _?_ 1000 

(13)

da __

1000 . a

1000 a . (1+a'F) ' " "

L+a£T 1

1000 . (1+aT)

(14)

(15)

 (16)

___ 

1000 .

(18)

If into these equations we introduce 7/ 0 =16cm, the value which obtains 

in most of the examples below; if, moreover, <ar=0.00367 and /?=0.000017, 

i"=20°, then formulae (13) to (18) lead to the following tabular comparison. In the table both the absolute values of the errors £// 0 , dH, dp, 

'v'\ A?'"

,, 6 ( J, which give rise to an error of T/1000 in the result,

/V\ iv 1 /v"\ lv" 

as well as the relative errors 6fi/f3, d ( )j , and 6 ( ) / - - are fully

computed for a series of values of T.

TABLE 47. Comparison of divers errors which effect the result by 1 : 1000.

T

0

100

500

1,000

1,500

d'Ao

cm.

-0. 004

-0.010

-0. 012

-0. 013

SH

cm.

0.006

0.028

0.056

0.083

<5/3xld6

2.61

1.27

0.75

0.53

aft) x 10.

860

C80

610

580

'(? ).» 

780

380

230

170

 5/3 

ft

'

0.150

0.074

0.044

0.031

'(-I)

v'

V

2.2

1,7

1.6

1.5

 7

v"

V

0.184

0.089

0.054

0.039

Inasmuch as /»0 must be measured to 0.01C1" it is quite obvious that 

corroborative readings before and after heating are essential, and that

(850)
HAHU8.1 . PORCELAIN AIR THERMOMETRY. 197

the air thermometer during the intermediate measurements must be 

perfectly tight. Since the error decreases proportionally to 7i0 , the 

additional accuracy of greater zero tensions does not compensate the 

hurtful effect of .high internal pressures at high temperature. Hence 

low pressures are preferable. Regarding jET, it appears that rise or fall 

of temperature must not be so rapid that the retardation due to flow 

of gas through the capillary tubes main tain greater differences of pressure than 0.03cm to O.OScm of mercury. A good cathetometer presupposed, it is not difficult to measure both 7t0 and .ffwith the accuracy here 

called for.

Under most favorable circumstances the error of Tis as large as the 

error of a, a result which equation (15) approximately shows. The 

value chosen, 0.003665, is Regnault's1 constant-volume value, and has 

been found experimentally for the interval 0° to 100°. The use of the

same coefficient for temperature indefinitely high and for all tensions2

is to some extent arbitrary. The error thence resulting may be estimated at as much as one-half of one per cent. The convenience with 

which the constant pressure method is available for measurements 

with gas differing widely in normal density is one of its most valuable 

features. The desideratum of an elliptic revolving muffle for the comparison of the gas thermometer data of different gases, when the temperature of the same environment is measured, has been suggested.

The unusually small coefficient of cubical expansion /?=0.000016 to 

0.000017, which MM. Deville and Troost found for the porcelain of Bayeux, makes the necessary accuracy of the coefficient ft sufficiently attainable. The table shows that even in extreme cases, T= 1,500°, an 

error of 3 per cent, in ft is not serious, while the expansion coefficients 

of the metal and glass parts of the air thermometer need not be distinguished from ft, because these parts are almost negligible here. This 

exceptionally small value of ft is, however, only admissible in the case 

of thermometers which have frequently been heated. In the case of 

new thermometers these desirable qualities are vitiated by the occurrence of permanent expansion for each heating. In comparison with 

ft this permanent expansion (permanent diminution of density) is unfortunately enormously large, aggregating in the first six heatings, for 

instance, as much as 1.5 per cent. Whenever temperature increases 

too rapidly the temperature, and hence also the volume of the bulb, is 

larger than corresponds to the mean temperature of the gas. The reverse of this takes place on cooling.

Conformably with the numerical results on page 197, Table 47 shows

that may be affected by an error of almost twice its own magnitude

v

without seriously bearing on T, even in unfavorable cases. The impor-

'O 11

tanceof , however, increases rapidly as T increases, and must in un1 Reguault: Mernoires de 1'Insfc., vol. 21,1847, p. 91; ibid., p. 110. 

3 Cf. Literary Digest, pp. 36-38.

(851)
198 MEASUREMENT OF HIGH TEMPERATURES. I BULL. 54.

favorable cases be known within 4 percent. These 0 results are also

in v" keeping with Table 45, above. Fortunately ' it is feasible to measure

 'With the accuracy here required, as well as to sufficiently exclude

the effect of temperature.

A careful survey of the sources of error just discussed shows how exceedingly difficult the measurement of high temperatures, with an accuracy of 1: 1000, really is. Quite aside from these discrepancies and the 

arbitrariness of a and y#, the lag error, the environment error, the moisture error, the error due to the permeability of porcelain and to diffusion 

of some gases through it, and the error of unknown flaws, have yet to be 

discussed. In the face of these serious difficulties I was therefore pleased 

to find that greater harmony prevails in the established data for high 

temperatures than there was reason to anticipate at the outset. I may 

state here that a more rigorous discussion of errors is to be made in 

treating the constant-pressure method, since this method is very much 

better adapted for high-temperature measurement than the present 

one. I will (p. 228) give the methods of allowing for all arbitrary errors 

and such as are not considered here.

CONSTANT-VOLUME THERMOMETER EXPERIMENTAL RESULTS.

Earlier results. The measurements were commenced with the forms 

of bulb shown above in Fig. 32. These bulbs are not glazed internally, 

but consisting of but a single piece they can be manipulated with 

greater facility than the others, in which soldering must precede the 

temperature measurement. To obtain some idea of the availability of 

the unglazed bulbs, I made a number of measurements of thq boiling 

point of water. Examples of the results obtained are given in Table 

48, in which H and h0 are the tension of the air at 100° and at 0° in 

centimeters of mercury, It is to be remarked that /f 0 is here directly

obtained by surrounding the bulbs with melting snow for many hours. 

By way of comparison, the same temperature T is also measured by a 

glass air thermometer.

TABLE 48. Moisture error of unglazed bulbs.

~So.

Glass :

No. 1 ....

Porcelain :

No.l ....

No. 2 ....

No. 3 ....

No. 4 ....

ho

cm.

76.70

73.50

72.40

76.46

72.62

H

cm.

104. 47

141.90

115. 00

119. 58

102.98

T

cc.

100

256

1C2

155

115

Remarks.

Bulb not specially dried.

f Both bulbs dried by repeated exhaus-

 | tion after calibration -with water.

I Bulb at 100° during drying.

Bulb carefully dried by repeated exhaustion with mercury air-pump.

Bulb and stem at 100°.

(852) 
BABUS.l PORCELAIN AIR THERMOMETRY. 109

The results of this table are startling. They seem to show that bulbs 

not glazed internally are worthless for temperature measurement. The 

error is very largely due to the presence of moisture in the bulbs; probably also to the condensation of air in the pores of the uuglazed porcelain. An explanation of these results can be given by equation (13) 

and Table 48. This consideration exhibits an important principle, so 

far as drying by exhaustion is concerned, and may therefore be made 

here. Bulb No. 4, which is most carefully exhausted, need alone be 

discussed. It appears that the value of d H and tf It 0) which give rise

T

to an error of ^ are approximately 8 H = 2.7<:m , and $ h0 = 1.8cm.

Now, after a mercury air-pump has been much used for drying, moisture is apt to show itself in the receiver, after which the exhaustion can 

not be carried further than 2cm at ordinary temperatures. Hence it 

appears that unless the exhaustion be very frequently repeated a tension of aqueous vapor equivalent to about 2cm of mercury at 100° may 

fail to be removed, an amount nearly sufficient for the discrepancy in 

question. It is to be noted that like errors in H and h0 do not compensate each other. The amount of water thus remaining in the pores of 

the cold bulb is about 4m«.

These results point out the desirability of perfect exhaustion and 

the necessity of keeping the air-pump dry. In view of the enormous 

discrepancies cited in the last table, the uuglazed bulbs were discarded. 

Some years after, however, when the difficulty of soldering porcelain 

had been tried in many experiments, I resolved to test these unglazed 

bulbs again, with a view to perfecting them. In the first place it 

is obvious that if, instead of determining h0 directly with melting 

snow, this datum be calculated from measurements of li made at ordinary temperatures (25°), better results will probably be obtained, since 

the small impurity of vapor may in the latter case be more accurately 

treated, like a gas. Moreover, care was taken to dry the bulbs at red 

heat prior to using them for air thermometry. Table 49 contaius results for bulbs thus dried, all unglazed internally, except No. 1, which 

is the soldered form (Fig. 33), glazed internally.

TABLE 49. Moisture error of unglazed butts.

No.

Porcelain : 

No.l. ......

No. 2.......

No.3. ......

No.2. ......

No.3.......

No. 4. ......

H

cm. 

75.8

75.7

C2.6

35.7

48.5

70.3

17.20

h0

cm. 

94.2

94.3

78.9

45.7

61.1

97.0

T

°C. 

99

99

102 .

104

102

102

101.1

Eemarka.

(853)
200 MEASUREMENT OP HIGH TEMPERATURES. [BULL. 54.

These results are such an enormous improvement on the discrepancies 

of Table 48 that it seemed expedient to endeavor to further investigate 

the behavior of these instruments at high temperatures. If under these 

conditions the bulbs show no greater variations than is in accordance 

with the above data, the further improvement of the bulb presents itself emphatically. Values of high temperatures sufficiently approximate 

for the present purposes are obtainable by the method investigated in 

Chapter II, where apparatus for calibrating thermo-elements with 

known boiling points are described. It seemed especially desirable to 

make this high-temperature comparison in order that some definite preliminary notion of the degree of accuracy of high-temperature data 

in general might be independently obtained. Examples of these results are given in the following tables, 50 and 51. The first of these 

(Table 50) contains a comparison of the calibrated thermo-element 

and air thermometer made in the large gas-muffle furnace described on 

page 181. The junction of the thermo-couple having been tied with 

asbestus wicking to the equatorial parts of the air thermometer, the 

whole bulb was thereupon surrounded with a noil-conducting jacket of 

carded asbestus, from one to two inches thick, inclosed in a cylindrical 

asbestus box. Both the thermo-electric and the air thermometer measurements were made in time series, with one observer at each instrument.1 In this way the rate of heating or cooling of the furnace appears 

among the results. As usual k0 is the (calculated) zero reading of the 

air thermometer, H the corresponding reading at the high temperature 

T, and at the time given in the same horizontal row. Again, t is the 

temperature of the cold junction of the thermo-element, e the corresponding electro-motive force, in microvolts Thg and Tzn the calculated 

(thermoelectric) temperature when in the first case the calibration is 

carried only as far as the boiling point of mercury, in the second case 

when carried as far as the boiling point of zinc. Thg and Tm are the

results of graphic interpolation, as explained in Chapter II, page 114. 

TABLE 50. Comparison of air thermometer and thermo-element.

Bulb No. 3 ; h0 =26.'6°m

H "

cm.

330.1

464.3

637.9

705.7

759.4

817.1

T

°0.

66

207

389

462

519

581

Time.

hours.

12.46

.53

.57

.60

.63

.66

TLer mo-couple No. 36.

t

°0.

24.7

.8

.8

.9

25.0

.3

«20

microvolts.

650

1530

2220

4270

6400

7260

Thg

*0.

97

196

264

443

596

655

Tm

°0.

97

196

268

460

636

705

Time.

hours.

12.52

.55

.56

.61

.71

.79

1 Dr. Hallock kindly assisted rue in this series of measurements.

(854)
BAKUS.I PORCELAIN AIR THERMOMETRY. 201 

TABLE 50. Comparison of air thermometer and thermo-element. Cont'd.

Bulb No. 3; Ao=26.6"»

H

cm,.

847.9

898.7

928.7

965.5

1017. 3

1078. 5

1107.0

1150.6

1 179. 8

1187.8

.1198.8

1202. 8

1203. 3

1202. 8

1199.8

1126.5

1064.3

979.3

934.8

859.3

798.3

721.9

678.4

633.5

591.7

555.4

522.7

483.9

462.9

T

00.

613

670

700

741

797

863

896

942

973

984

996

1000

1000

1000

997

916

848

756

706

626

561

478

433

385

340 <

302

267

227

206

Time.

hours.

.69

.74

.79

.83

.90

1.01

.08

.25

1.35

.42

.50

.58

.67

75

Thermo-couple No. 36.

t

00.

.4

.5

. 5

.7

.9

26.3

.4

27.4

27.6

.7

.9

28.2

28.4

em

microvolts.

8400

8860

92CO

9710

10110

10530

10760

11570

11630

11700

11840

11970

12060

Thg

00.

732

755

777

802

826

850

864

908

911

915

924

928

934

ft.

00.

792

821

845

878

906

933

950

1000

1005

1010

1017

1026

1030

Time.

hours.

.86

.89

.94

1.00

.07

.17

.22

.45

1.50

.53

.61

.70

.75

Gas of furnace shut otF1.77h

1.81

.87

.92

.97

2.01

.07

.13

.19

.27

.35

.43

.53

2.63

.74

' .91

28.9

29.2

29.3

29.4

29.4

29.5

29.5

29.5

29.5

29.5

29.4

29.4

29.4

29.4

29.4

29.4

29.4

29.4

29.4

10780

9930

9130

8520

7570

7050

6590

6190

5170

4700

4310

3980

3400

3140

2850

2310

2000

1790

1660

864

815

769

733

675

640

610

584

515

476

445

421

372

348

324

274

245

226

214

951

893

838

794

727

686

651

621

538

496

46 1

436

384

338

332

277

246

220

214

1.87

.91

.95

.98

2.03

.06

' .09

.12

.21

.26

.30

.35

2.44

.48

.51

.68

.79

.87

.93

The following comparison (Table 51) of the data of thermo-element 

and air thermometer was made in the revolving muffle, described on page 

181. The simple round bulb (No. 4), not provided with a central tube, 

having been properly adjusted, the thermo-electric junction was placed 

nearly in contact with it. The table contains three independent series

(855)
MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

of measurements, and nomenclature used is identical with that of the 

foregoing table:

TA.KLE 51. Comparison of air thermometer and thermo-couple.

Bulb No. 4.

77 T Time.

Thermo-couple No. 37.

t e Thg T Time.

(a) ' [fco-16.74""]

cm.

82.2

88.9

89.2

89.3

°C.

1115

1238

1244

124G

hours.

1. 57

1.85

1.93

2.03

°0.

25.3

25.8

27.3

27.3

microvolts.

12920

14780

15430

15690

°G.

980

1.073

1102

1115

°c.

1082

1190

1233

1249

hours.

1.53

1.73

1.90

2.05

(b) [710=14.70""]

C2. G

C4.2

72. 5

76. C

77.3

78. G

'79.1

79.1

78.8

78.4

923

954

1118

1202

1218

1244

1251

1254

1248

1240

2.27

2.35

2.52

2.62

2.65

2.73

2.80

2.82

2.85

2.92

20.3

26.5

27.0

27.3

27.8

28. 2

28. 2

28.5

10480

11020

12250

14000

14760

15060

14970

14870

830

878

944

1034

1072

1085

1081

1075

930

972

1045

1150

1195

1213

1206

1201

2.22

2.33

2.47

2/60

2.72

2.82

2.87

2.92

Gas of furnace shut off.

72.8

66. 8

C2.8

57.3

51.4

46.3

42.0

3G.9

32. f.

24.8

77.0

77.4

68.5

52.7

1126

1000

927

819

704

603

519

4.22

337

188

1115

1122

957

659

3.03

3.12

3.22

3.30

3.47

3.68

3.92

4.27

4.G8

29.0

29.5

29.6

30.0

30. G

31.3

31.8

31.8

31.8

12930

10710

10090

9040

7690

6490

5340

4130

3140

980

801

827

765

683

604

524

430

350

1085

945

904

833

735

644

551

449

359

3.03

3. 17

3.20

0 00 

<). Ofl

3.48

3.68

3.92

4.27

4.70

[Ao=15.68c '"]

2.00

.03

.18

.53

29.0

29.0

29.0

29.0

14170

14270

10770

7090

1042

1046

865

644

1160.

116G

948

690

2.00

2.03

2.17

2.50

The results of these two tables, 50 and 51, may best be compared 

graphically by regarding the various, values of temperature as functions 

of time. This has been done in the chart, Fig. 39. The curves a, &, c 

correspond, respectively, to T, TZH , and Thg of Table 50; the curves h, fc, 

i to T, TmJ TW of Table 51, respectively; the curves /, 0, and m, n to T

(856)
1500

f400

1300

Q 20 3O 4O 5O 00 ID 2O 3O «*O 50 60

PIG. 39. Temperature and electromotive force of thermo-couples in corresponding time series.
BABUH.1 PORCELAIN AIR THERMOMETRY. 203

and Ttn of the same table. The curves d and e are supplied by way of 

example, and are values of Tm obtained by heating a Fletcher injector 

(muffle form heated by power blast) to maximum intensity and then 

allowing it to cool. A comparison of curves a, b, c shows that from 600° 

the heating takes place sufficiently slowly to make comparative measurements admissible. Throughout the stage of heating Tand T,n agree 

within 30°, usually much more closely, whereas Tand Thrj differ by as 

much as 90°. The maximum temperature is not above 1,000°. After 

the gas is. shut off the furnace cools too rapidly for calibration work, 

the thermo-couple cooling at somewhat greater rates than the air thermometer. The curves d and e for the muffle furnace, the form of which 

is a thick-walled cylindrical box, exhibit rates of cooling very much less 

than the curves a, 6, c a desideratum which is much more fully realized 

in work with the revolving muffle furnace, lor which the curves /t, 7c, i 

apply. Unfortunately, owing to accidents, the statistics of heating are 

only imperfectly shown; but beginning at about 900°, which is here 

nearly the maximum intensity for the amount of gas supplied, Tand Tm 

differ by only 10°, T and Thg by about 80°. The curves then rise rapidly, 

owing to the fact that the influx of gas has been increased, until at 1,250° 

T and Tm differ by nearly 40°, T and T^ by nearly 150°. For reasons 

of a practical kind, the temperature was not increased above 1,250°. 

Below 1,000° cooling takes place at rates sufficiently retarded to make 

calibration work practicable. Above 1,000° it is expedient to obtain 

the different degrees of constant temperature by regulating the supply 

of gas. A comparison made between the curves Ic and h throughout the 

course of cooling leads to the inference that the well-known thermoelectric formula e=ar-\-brff is insufficient for interpolation.

The extrapolated temperature Thg differs enormously at high temperatures from its air-thermometer value, the latter being the greater. 

Since below 900°, T< Tm1 the discrepancy can not be referred to friction 

of gas in the capillary tubes, the effect of which would be of the opposite sign. The only cause which would tend to cool the air thermometer 

at a greater rate than the thermo-couple is the effect of the entrance of 

the air above the meniscus of the manometer, while the mercury is 

gradually moving upward from a lowered position into contact with the 

fiducial mark. Or, finally, the error T Tzn may indicate superheating 

in the calibration work.

It is by no means the object to furnish in this place more than a statistical diagram, as it were, of the degree of accordance, which the hightemperature measurements made in widely different ways, present.

When comparisons are made in the Bunsen muffle the ascending values of Tm exceed the descending values of Tin for the same I. The 

ascending and descending values of Tzn in case of comparisons made in 

the revolving muffle are nearly the same. This is a pretty fair test for 

identity of environment. Nevertheless, if all values of Tzn obtained be 

laid off as functions of T, the band or pathway thus obtained is in some

(857)
204 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

instances nearly 100° wide and the boiling points of zinc fluctuate between 925° and 995°.

Later results. Following the suggestion of the results contained on 

pages 199 to 204,1 made the following series of additional comparisons. 

The bulb used is still the non-re-entrant form, not glazed internally. 

Great care was taken to dry it thoroughly by heating the bulb to 100°, 

and then exhausting the air to a few tenths millimeter. After being 

treated in this way the bulb was filled with air, dried over anhydrous 

phosphoric acid. In the last two series 7<0 is calculated from the tension 

observed at 100°. Special care was taken with the cathetoraetric measurements. The series of temperatures is ascending. The influx of gas 

is gradually increased by means of a graduated stop-cock, and the calibration measurements are made after each increment as soon as the 

temperature has again become stationary. In this way not only may 

any number of degrees of constant temperature be obtained, but the 

mean rate at which temperature increases may be reduced as near 

zero as is desirable. If therefore one observer1 notes the instant of 

contact between the upper meniscus of the manometer and the fiducial 

mark, the other observer may note the corresponding cathetometer 

reading of the lower meniscus for the same instant. From a comparison 

of the following results as a whole I infer that in proportion as the temperature of the muffle increases, equality of temperature for all points 

of its inner surface more nearly obtains. This is due to the fact that at 

high temperatures its heat conduction is better. For low temperature 

calibrations it is therefore advisable to use a muffle cooling from red heat 

in a closed furnace. In the tables e2o has been calculated for t=20°. 

The actual temperature (t) of the lower junction is given in Table 52 

for each case.

TABLE 52. Comparison of air thermometer and thermo-couple.

ho = l4.G6cm. Bulb No. 4.

H

cm.

27.35

30.25

31.68

33. 25

34.32

34.32

41.47

42.33

48.49

49. 99

50.86

57.80

T

°0.

241

297

324

354

375

375

512

529

648

678

694

831

Time.

hours.

2.78

2.88

2.99

3.14

3.35

3.42

3.73

3.78

4.00

4.07

4.11

4.31

Thermo-couple No. 37.

t

°0.

28.0

28.0

28.0-

28.0

27.8

27.8

27.8

28.3

28.3

28.3

28.3

28.3

em

microvolt*.

2545

2941

3060

3283

3792

3780

3780

5475

5820

7132

7706

8015

Time.

hours.

2.78

2.84

2.90

2.97

3.40

3.43

3.45

3.68

3.75

3.93

4.02

4.08

1 Mrs. Anna H. Barns assisted me in this work. 

(858)
BAHus.1 PORCELAIN AIR THERMOMETRY. 205 

TABLE 52. Comparison of air thermometer and thermo-couple. Cont'd.

fto = 14.66 . Bulb No. 4.

H

cm.

58.77

59.55

65.67

67.88

69.95

28.92

31.89

33.58

35.38

37.10

38.19

38.77

30.13

39. 45

41.00

45.46

40.73

47.87

48.80

50.18

51.32

51.29

52.59

54.81

56.69

53.56

58.95

65.40

68.40

68.86

69.87

72.03

73.72

75.68

76.85

77.69

78.62

79.11

79.47

T

°C.

850

866

985

1031

1072

271

327

360

394

426

448

459

466

472

502

588

613

635

653

680

703

702

727

771

808

845

852

982

1040

1049

1070

1112

1146

1186

1209

1227

1245

1255

1262

Time.

hours.

4.35

4.43

4.65

4.72

4.77

1.43

1.49

1.53

1.59

1.68

1.78

1.87

1.95

2.03

2.14

2.27

2.33

2.40

2.48

2.58

2.69

2.85

2.99

3.08

3.. 16

3.28

3.49

3.69

3.79

3.87

3.98

4.05

4.10

4.17

4.22

4.26

4.33

4.39

4.44

Thermo-couple Xo. 37.

t

°0.

28.3

28.8

29.0

29.3

29.3

29.3

29.3

27.8

27.8

27.8

27.8

27.8

27.8

28.8

28.8

28.8

28.8

28.8

29.3

29.3

30.3

30.8

30.8

31.3

31.3

31.8

32.6

33.0

33.3

33.8

33.8

33.8

34.3

34.3

34.3

34.4

34.6

£20

microvolts.

8254

10260

10357

10159

12622

13472

13902

3596

3925

4127

4457

4723

4847

5100

5100

6144

6507

7045

7281

7455

8270

8153

8872

9651

9910

10375

10289

13021

13423

13427

14297

14677

15191

15511

15732

15852

15963

Time.

hours.

4.12

4.33

4.37

4.43

4.68

4.75

4.78

1.45

1.50

1.53

1.60

1.70

1.78

2.00

2.03

2.17

2.20

2.30

2.37

2.42

2.75

2.88

3.00

3.12

3.17

3.33

3.50

3.73

3.83

3.92

4.00

4.05

4.12

4.17

4.22

4.30

4.42

In spite of the care taken with these observations the results do not 

show the uniformity and accuracy expected; this appears from a graphic 

representation of the following correlative values, Table 53, taken from 

Table 52.

(859)
206 MEASUREMENT OF HIGH TEMPERATURES 

TABLE 53. T and CIQ.

[BULL. 54.

I.

T

250

300

375

525

070

860

1016

3080

«20

2630

3050

3790

5800

7860

30400

12850

13800

'

II.

T

350'

400

450

470

550

600

630

702

730

820

847

1000

1050

1100

1150

3200

1250

0*0

4050

4490

48GO

5100

6560

7050

7350

8240

8860

10000

10360

11)000

13420

14540

15060

15640

15900

 III.

T

060

995

1080

1100

1130

1380

1240

3260

«?o

1138

1176

1340

1373

1445

1520

1610

1628

The values of temperature are small relative to the electro-motive 

forces. This would result if the stem error applied is too small by an 

amount quite within the range of possible error, but it is more likely that 

the thermo-couple is here at a temperature above that of the air thermometer; in other words, that the environments are not identical. A 

reverse of this takes place on cooling; hence the use of a simple non-reentrant bulb for comparison is not at once permissible. It is necessary 

if the results are to be uniform and comparable, that both bulb and ther. 

mo-electric junction be not only contiguous, but be enveloped in some 

thick non-conducting substance. Such additional appliance is objectionable, since it interferes with quick and facile manipulation, and at 

high temperatures is fused into the glaze of the bulb in a way that endangers it. Mere contiguity of the junction and the bulb, even in case 

of a revolving muffle, is not a sufficient guaranty for the accuracy of 

the calibration results obtained.

Digression. Before resolving to change the form of the bulb, I made 

another series of experiments, which have an ulterior interest, inasmuch 

as they are made with the soldered bulbs, glazed both within and without, which are described above, p. 1 75. It was also expedient, if not necessary, to change the method of measurement, and in the following 

results, Table 54, the coustaut-volume method is replaced by the constant-pressure method. The data are given in a way that will be fully 

explained in the next paragraph (p. 217), and it is here only necessary 

to refer to the time series of T, the temperature of the bulb, and of e20 , 

the corresponding electromotive force. Corresponding values of ew and

(860)
BARUS.] PORCELAIN ATE THERMOMETRY. 207

Tare collected in Table 55, and obtained as before by graphic interpolation. The results are inserted here because of the uori-re-entrant form 

of bulb employed.

TABLE 54. Comparison of air thermometer and thermo-coujtle.

Iu Rlazeil bulb No. 2 \f Z ^

V,

cc.

147.0

149.7

154.3

157.0

ICO. 4

163. 1 

163.4

192.5

ido.o

201. 9

202.5

211.7

216.0

210.0

217.4

219.0

2L>0. 7

222. 2

223.0

223.2

220.0

210.0

210.0

205.3

200. 2

189.8

180.8 

170.0 

160. 2

154.8

US. I)

140.4

129.8

124.9

1\

"C.

24.3

24.3

24.3

24. C

24.8

25.5 

25.4

26.1

26.2

23. 0

26.7

26.9

27.0

26.9

27.1

26.9

26.8

27.1

27.0

20.9

20.5

26.0

25.8

25.5

25.3

25.0

25.2 

25.2 

25.1

25.0

24.8

24.8

24.0

2.3. 7

Ho

0)1.

 76.40

76.46

76.46

76.46

76.46

76.46 

7G.4G

7G.46

7G. 46

70.40

70.46

76.46

76.46

76.46

76.46

76.46

76. -1G

76.46

7G. 46

76.46

76.40

76.46

76.46

76. -16

70.46

76.46

76. 53 

76.53 

76. 53

76. 53

76. 53

70. 53

76. 53

76.53

T

°C

333

345

366

379

396

409 

411

621

655

710

722

841

907

919

931

960

994

1019

10'3G

1041

985

903

828

767

707

602

528 

452 

396

369

323

307

267

251

Time. 

hours.

1.12

1.17

1.28

3.38

1.55

1.88 

1.98

2.28

2.37

2.78

2.84

3.12

3.33

3.47

3 67

3.82

3.38

4.13

4. 25

4.40

4. 58

4.68

4.78

4.87

4.97

5.20

5. 42 

5.C8 

5.93

6.05

6.30

G.42

0.68

6.80

i 

Thermo-couple No. 37,

<o

"C.

22.4

22.0

22.8

23.1

23.6

23.7

24.8

24.9

25.4

25.8

26.6

26.8

27.0

27.4

28.1

28.3

28.4

28.6

28.6

29.1

29.3

29.3

29.3

29.4

29.1

29.0 

28.8 

"28.7

28.6

28.6

28. G

28.4

28.2

27.6

«:o 

microvolt.

3039

3534

3743

3906

4110

. 4104

7160

7455

7926

8076

10270

10621

10748

10940

11602

11793

12052

12364

12170

10480

9503

8807

8155

7339

6404

5649 

5009 

4275

3835

3589

3344

2979

2759

2325

Time. 

hourn.

1.05

1. 22

1.34

1.48

1.78

1.92

2.33

2.42

2. G7

2.81

3.17

3.30

3.42

3.58

3.87

3.95

4.05

4.20

4. 37

4.65

4.73

4.81

4.88

5.00

5.18

5.33 

5. CO 

*5.73

5.88

5.98

6.08

6.27

 6.38

6.65

Gascock.

2

2

2

2

2

2

3

3

3

3

3.5

3.5

3.5

3.5

3.7

3.7

3.7

3.7

3.7

1

 1

n 

O

(861)
208 MEASUREMENT OF HIGH TEMPERATURES.

TABLE 55. T and CM from Table 54. 

[Non-re-entrant inglazed bulb No. 2; thermo-couple No. 37.]

[BULL. 54.

T

00.

333

345

366

379

396

409

411

655

716

722

ew

microvolt.

3240

3360

3640

3780

4000

4100

4110

7300

8040

8100

T

°C.

907

919

931

994

1019

1036

1041

903

828

620

microvolt.

10650

10800

11000

11860

12220

12400

12500

10150

9100

T

o0.

767

707

602

528

452

396

369

325

307 .

267

C20

microvolt.

8270

7550

6320

5320

, 4430

3710

'3410

2940

2720

2300

In the up-going series, in which observations were made only during 

periods of very constant temperature, the values of electro-motive force 

are normal in comparison with values of temperature^ The boiling 

point of zinc, for instance, is fixed at 930°. In the down-going series 

thermo-electroraotive force is too small, as usual. The effect, however, 

is possibly exaggerated by the great difficulty of making these bulbs 

absolutely tight. Nor is it possible to estimate the leak effect as a 

function of time, for the capillary canals change with temperature and 

even by accidental disturbances.

Difficulties such as are here described led rne to the construction 

of the re-entrant form of bulb, in which, by a simple device, they are 

wholly obviated. This will be shown at length in the final section, 

which follows. I have purposely given a full series of data in Tables 

50 to 55, in order to bring before the mind the extreme difficulty encountered in making comparisons between the thermo-couple and the 

air thermometer, when the conditions to be met are accuracy and expedition.

CONSTANT PRESSURE AIR THERMOMETRY APPARATUS.

The above data were investigated in the rational endeavor to adapt 

Jolly's very convenient form of air thermometer to high-temperature 

measurements.1 To do this I found it desirable to use low-pressure (< 1 

atmosphere) manometers, so that at high temperatures, when porcelain 

shows a tendency to become viscous, the pressures on the interior and on 

the exterior of the hot bulb may not differ by an amount sufficient to deform the bulb seriously. But while on the one hand this can never be 

perfectly accomplished, the difficulty of maintaining the air in the bulb 

and manometer at an invariable low pressure makes this instrument unusuallyliable to errors or accidents on the other. In the constant-pressure 

method of air thermometry, all hurtful excesses of pressure on the bulb

1 Weinhold, Erhardt, and Schertel tried it before (cf., p. 33,34). 

(862)
PORCELAIN AIR THERMOMETRY. 209

may be almost wholly excluded, the pressure 

chosen being, of course, that of the atmosphere. 

In this method, however, the volume of the bulb 

must be accurately known, a datum which is only 

of secondary importance in the constant-volume 

method.

Again, the above data are obtained with spherical bulbs of the non-re-entrant form. The difficulty experienced in obtaining a degree of satisfactory accordance in the various series of data 

is due to the fact that the environments are not 

identical. Hence in the following experiments the 

re-entrant form of bulb (Fig. 32) will be used, in 

which an identical exposure has been as nearly as 

possible realized. It will still be necessary to operate with bulbs not glazed internally. For final 

work bulbs of the re-entrant form, constructed in 

accordance with the Deville and Troost plan (Fig. 

33), so as to be easily glazed internally, are available.

A very convenient and simple apparatus for 

constant-pressure air thermometry is given in Fig. 

40, -fa actual size. The details of construction are 

very similar to those shown in Fig. 30, and it is 

therefore only necessary to indicate the essential 

points of difference. In the present instrument 

the platinum capillary tube A, the further end 

of which communicates with the air-thermometer 

bulb, is soldered with resinous cement into the 

top of a long cylindrical tube, B C. The length 

of this tube is at least 150cm ; it is accurately graduated in cubic centimeters, and the total capacity 

is about 300CC. In my apparatus the tube B C was 

closed below with a rubber cork, and this end 

then inserted with plaster of Paris into a suitable 

rest or foot. By removing the foot and the cork 

the tube admits of being cleaned, an operation 

which, for the case of imperfectly pure mercury, 

is sometimes necessary. Practically the tube is 

closed below, but it is provided at a short distance above its end with a horizontal tubulure, 

D E, to which a cloth-wrapped rubber hose, E F G, 

is attached. The upper end of E F G communicates by means of a three-way cock, H, with a large 

cylindrical vessel of mercury, K L L. The cock 

H has a lateral tubulure, 7t, through which merBull. 54 14 (863)

FIG. 40. Constant-pressure 

air-tbermomoter.
210 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

cury may be withdrawn either from the tube B C or from the reservoir 

K L L. The latter aud the cock H may be uoscrewecl from the steel 

piece inserted into the hose at Q in the manner shown in Fig. 30, above. 

This system is practically a U-tube, one of the arms of which may be 

varied in height or length at pleasure. For this purpose it is attached 

to the manometer stand, already described. (See frontispiece under B.) 

B C is fixed to one of the uprights with its weight mainly resting on the 

foot at C. The reservoir K L L and the cock H are fixed to the slide, 

\vhich may be moved at pleasure up or down and clamped in any position on the second parallel upright of the manometer stand. The slide 

is conveniently provided with ah ordinary micrometer screw, by which 

a finer adjustment is obtainable. Enough mercury is introduced to just 

fill the tube B C and leave a well-defined meniscus in the reservoir 

K L L. Moreover, the dimensions of K L L are- such that when it occupies its lowest position, and the mercury is almost complete! y out of 

the tube B 0, the reservoir may be about filled. Measurements are 

made with the cathetometer, which in this case, however, has no other 

purpose than to indicate identity in the level of the menisci in B G aud 

KLL. The pressure is then that of the barometer, which may be conveniently suspended from the same stand. (See frontispiece.) Volumes 

are read off directly on the glass tube B C. Two sensitive thermometers at the lower and upper parts of this tube, respectively, show its 

temperature.

This is the form in which the apparatus was used. It will be remembered that the chief purpose of the present memoir is to test the 

availability of methods. Whenever it becomes desirable to investigate 

data of extreme accuracy, it is, of course, necessary to surround B C 

with a jacket of water, so that the temperature throughout its length 

may be kept rigorously constant. Again, the increment of volume, 

corresponding to a given increment of temperature, decreases in proportion as temperature itself increases. Hence, if it be desirable to measure high temperatures, a volume tube may expediently be chosen, of 

which the lower part is of smaller diameter than the upper part. Data 

for the construction of such tubes for any special purposes will be fully 

given in the tables below. Long capillary metallic tubes cool down the 

gas to atmospheric pressure before it enters the volumenometer tube B C.

CONSTANT-PRESSURE THERMOMETRY METHOD OF COMPUTATION.

The general equation. Equation (I), on page-189,

applies here as it did in the case above. The former simplification consisted in so conducting the measurements that A=0. The present

(864)
BAKU8.1 PORCELAIN AIR THERMOMETRY. 211

experiments accomplish a similar purpose by making H=h ; for the 

value of A is easily found as

where V\ is the excess of the volume of the gas at the high-temperature 

measurement T over that at the low-temperature measurement t, and 

where T\ is the temperature of Vi . The older method therefore eliminates 

the volume factor ; the present method eliminates the pressure factor. 

If we expand equation (1) for the present case we find the following 

correlative variables :

v t T

v' t' T'

v 1 t" T"

where v is the volume of the bulb, v' the volume of the part of the 

stem along which temperature varies from T to t, v" . . . the volumes 

of the remaining capillary stem and capillary tubes of nearly constant 

temperature, Fl5 finally, the excess of volume of gas at the high-temperature measurement typified by J, over that of low-temperature measurement typified by t. Temperatures referring to the same volume are 

similarly accentuated. If for abbreviation

and

then equation (1) leads to the following value of T:

...... (2)

This equation is rigorously true j but it is unwieldy, and to be made 

practical must be simplified.

The equation simplified. Equation (2) may be easily put into the form

T= , .... (3)

which for H=h, the condition underlying the present method, and for

}- V\ 

(865)

M=f(t}- V\f(T,} ......... (4)
212 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

an abbreviating expression, reduces to ^

This is the form required. It is nearly rigorous, the approximations

Cr

having been inserted in the corrective member . It is perhaps interm

esting to annotate that the rigorous form (2), under the simplifying 

condition H=h reduces to the unique expression

A few remarks on the practical method of using equation (5) are now 

in place. Equation (4) shows that t, the lower temperature at which 

measurement is made, furnishes the fiducial or fixed point of the air 

thermometer, t is obviously the temperature at which 7i=0 under the 

given barometric pressure b, of the day on which the measurements are 

made. Now, if at the barometric height -B and at the temperature T 

one observes FI=V, then

where 2(v} is the total volume of the bulb and capillary stems as far 

as the zero mark of graduation on the tube B G. Equation (6) follows 

at ouce from equation (1) in the general form given on page 189, if we 

impose T=T'=T"= . . . 2\ and t=t'=t" . . . , the conditions given by 

the experiment. Equation (6) is thereforb generally true. Usually b 

and .B, t and r differ but slightly and v is nearly zero. Hence, having 

measured r, JB, v, it is easy to find the value of £, which corresponds to 

the barometric height 6 of the day ; and it is also easy to make allowance for any variation of barometric height occurring during the course 

of the experiment. These operations are simple and the corrections 

can mostly be made mentally. 

Mere inspection of equations (4) (5) (6) shows that it is expedient to

calculate a table for the function /(£)= "" , both for glass and for

-L-j oct

porcelain, once for all. Such a table in which t varies from 0° to 30°, 

in single degrees, will usually suffice. In this table, however, the data 

log/(£), which is more frequently in demand, must also be inserted for 

the same range of t.

If the re-entrant bulb be used, the mercury thermometer is conveniently inserted into the central tube while the bulb is in place in 

the revolving muffle. The stem of the mercury thermometer should be

(866)
IURHS.1 PORCELAIN AIR THERMOMETRY. 213

so long that the position of the thread may be seen. This furnishes t 

of equation (6). It is frequently convenient to make this measurement 

for unequal heights of the columns of mercury in the two arms of the 

manometer. In this case B, of course, is the effective tension of the gas. 

The difference in height of the menisci is read off by the cathetometer.1 

Volumetry of bulb. Equations (4) and (5) contain the quantity F, 

or the volume of the bulb of the air thermometer at zero centigrade. 

This may, of course, be measured directly, before the high temperature 

work, by calibrating with water. If, however, a bulb non-glazed internally be used it is exceedingly difficult to dry it again thoroughly. 

Hence I have applied the volumetric method already utilized above in 

the case of stems. In the case of a manometer like the one described 

in Fig. 40 this method is applicable with great elegance, inasmuch as 

pressure can be varied over a large range and volumes read off with 

facility, In the following table an example of data obtained in this

way is given. Vi and p are corresponding values of the volume of 

the gas in the manometer tube B G (Fig. 40), and of the pressure. 

Measurements are made with the bulb and manometer in the air, and 

no thermal correction is applied:

TABLE 56. Volumetry of bulb.

Date.

Oct. 14

Oct. 15

Oct. 16

 «i

cc.

4.9

122.2

4.8

122.2

3.0

120.2

30.0

120.2

9.7

120.8

6.5

120.8

4.0

120. 9

7.4

126.6

4.0

126.0

4.0

120.5

3.0

120.5

3.0

P

cm.

75.88

53.73

75.93

53. 77

75.65

53. 55

75. 60

53. 59

73. 37

53.56

74. 82

53.55

75.46

53.70

74.93

52.96

75.24

52. 64

75.22

53.41

75.54

53.38

75.53

vo

cc.

279.6

280.1

281.0

280.9

282.0

281.3

281.4

279.9

280.1

281.3

279.9

281.3

Mean DO = 280. 73

1 Many operations may be simplified by rising Landolt and Boe'rnstein's physical 

tables; Berlin, 1883 ; cf. pp. f> to 7.

(867)
214 MEASUREMENT OF HIGH TEMPERATURES. [HULL. 54.

The variations of v0 here observed I was first inclined to attribute to 

the difficulty of defining the volume of a bulb, the interior of which is 

not glazed ; but they are due to thermal disturbances. In order that 

the present method may be made to yield the best results. the temperature of the bulb and of the manometer tube B C (Fig. 40) must either 

be rigorously the same, or the respective temperatures must be known. 

For, if 2v be the volume of the bulb and capillary stems at the temperature t, and if Vi and V2 be the two volumes read off on the manometer tube B C at the temperature T1? and if HI and H2 be the pressures 

or gas tensions which correspond, respectively, to V\ and F2 ? then

an expression in which if T\ and t differ by as little as a few tenths of 

a degree the factor f(Ti)/f(t) can no longer be considered negligible. 

It will be seen below that 2 (v) must be measured with a degree of 

precision scarcely exceeding 0.02 per cent., i. e., to about O.lcc for the 

given capacity of bulb, if the absolute value of Tis to be correct to one 

pro mille. But after many measurements, the further citation of which 

is here superfluous, I convinced myself that when due -regard is paid t;o 

the temperature factor the accuracy in question is attainable. /( T, ) -4-/(£) 

is approximately 1+a (t T^, in which form it may be easily applied.

Errors of the approximations. It is necessary to discuss the corrective 

member of the equation (5).

m _

viz. _- -, or as it may be written with sufficient accuracy, J ^

For practice it is best to write for this the equivalent form v "T^ \ _

a

and then to calculate a table from which, for each value of T, the value 

of this corrective function may be taken at once. It is usually sufficient to proceed as follows : The full form of the corrective function is

For those parts of the capillary stem whose temperatures are constant, f(T") and f(t") are practically identical. Hence the part of the 

stem along which temperature varies from the high value to that of 

the atmosphere alone enters into the consideration. It follows that the 

last expression may be written

a v
BAJIUS.] PORCELAIN AIR THERMOMETRY. 215

Even this correction is small, and for 1,500° will not much exceed 5°. 

It is permissible therefore to put T=2T' and to insert for t' a mean 

value. Table 57 is of the kind here referred to, and exhibits the values

for each value of T and for £'=15°; v'/v is found by measurement to be 0.00043.

TABLTC 57. Errors of titermometer formula;.

T

°0

100

200

300

400

500

5

aM* I

°G

 0. 0 COO

 0. 1 700

 0. 2 i 800

 0.3

-0.4

900

1,000

S

 0.0

 0.8

 1.0

 1.2

-1.5

T

°0

1100

1200

1300

1400

1500

g

aM*

 1.8

- 2.2

 2.0

 2.9

- 3.4

It will be seen by comparing this table, 57, with the similar one above 

(Table 45) for the constant- volume method that the errors here are 

very much smaller in magnitude. A result of this kind was to be anticipated, and the occurrence of small stem corrections, added to the fact 

that measurements are made in such a way that the tension of the gas 

inside the bulb need not exceed atmospheric pressure, is the salient 

advantage of the present method of high-temperature measurement 

over the constant-volume method.

Compensator. In calculating the results of the last table no allowance is made for fissures or for the porosity of porcelain. Hence better results may be anticipated by using the compensator, though it 

always remains questionable whether the volumes of two nominally 

identical porcelain capillary stems are at all identical in fact. However, it is only the part of the compensator along which temperature 

varies from the high value T to that of the room that' need be identical 

with .the stem of the air thermometer. The remainder of the compensator may have any (capillary) volume, which need not be exactly the 

same as the volume of the capillary canals of the air thermometer. 

This appears fully from the formulae below.

The theoretical introduction of the data of this apparatus is here 

quite simple; for it is seen that the quantity marked S in the equation, page 212, is the one immediately given by the compensator. It 

will be remembered that this apparatus is essentially a porcelain stem 

identical with the stem of the air thermometer, provided, however, with 

a manometer tube of much smaller caliber than the tube B C of the 

manometer, page 210. Supposing therefore that the observations are 

made in the way already described for constant-pressure air thermometry, we have, at once

(869)
216 MEASUREMENT OF HIGH TEMPER ATURES. [BULL. 54.

where v\ and t\ have the same signification for the compensator that V\ 

and TI have for the air thermometer. Inserting the expression

into the equation (5) this becomes

- a

in which the correction is evaluated experimentally.

It will be shown below that the stem error is not of such serious importance in the constant-pressure method as it was in the constantvolume method; that the stem error rather falls below the other possible errors of measurement. Hence the use of the compensator is not 

to be as strenuously advised as it was above, and the correction derived 

merely from calibration and computation may be regarded satisfactory. 

This is, of course, a convenience, since it obviates the manipulation for 

the measurement of the two additional magnitudes -v\ and t\. Such 

statements, however, must be made with caution, for it will appear that 

in the constant-pressure method, inasmuch as the volume of the bulb 

enters fundamentally into the computation, the real object of the compensator is to define the volume of the bulb. The true volume of the 

bulb, when the compensator is used, is its own volume plus the volume 

of the part of the capillary tube, the length of which is the difference 

of length of stem and of compensator.

CONSTANT-PRESS ORE THERMOMETER EXPERIMENTAL RESULTS.

Manipulation, Before proceeding to the tabulation of final results it 

is expedient to refer to a few details of manipulation. On inserting the 

thermo-couple into the central tube ot the air-thermouieter bulb it is 

necessary to have the wires quite enveloped by the fire-clay insulators. 

This is done to avoid silicificatiou. It is well to have the insulator within 

the air thermometer of smaller diameter than the straight tube which 

passes from the bulb to the outside of the furnace, for the porcelain glaze 

becomes viscous at high temperatures, and is liable to be absorbed by the 

insulator. Hence it is desirable to avoid such close contact as would 

be given by a tube filling the hole snugly. With due precautionary 

preventives of this kind silicification is nil. Of course, the thermocouple must be kept in place while the furnace is cooling. If different 

thermo couples are to be inserted this must be done while the furnace 

is heated or during the stages of rising temperature. With a welldried bulb, symmetrically adjusted in the revolving muffle, the heating 

and cooling may be repeated almost indefinitely without breakage. 

Breakage is liable to occur when thermometers or muffles are exchanged. Wherever it is possible, it is well to avoid glass cocks.

(870)
BARUS.J PORCELAIN AIR THERMOMETRY. 217

Even when of best workmanship they are liable to leak after some 

usage. Moreover grease or vaseline is objectionable in consequence of 

the danger incurred of choking the capillary metal tubes.

Experimental data. The data obtained in the experiments with the 

constant-pressure method are fully given in Tables 58 to 66. It is to 

be borne in mind that the results are obtained by a single observer 

and that the chief object is to test the availability ot methods rather 

than to reduce the results to extreme fineness. The manometer is in 

air, screened, however, from the furnace by a thick board and at some 

distance from it. v0 denotes the volume of the bulb, and t is the fiducial temperature for the day. The bulbs are of the re-entrant form, 

not glazed internally. V: and TI are the volume and the temperature, 

respectively, of the air measured in the manometer tube B C (Fig. 40). 

jB0 is the current barometric height. T is the temperature of the bulb 

at the time specified, all observations being made in time series.

Thermo electric data are given on the same plan as above, t is the 

temperature of the cold junction, e2o the electro-motive force when the 

cold junction is 20° C. at the time specified. The figures of the last 

column refer to quantity of gas injected, as indicated by an arbitrary 

scale.

In Table 58 7\ was read off by but a single thermometer, and T is 

therefore less accurate. In Table 59 the thermo-couple had to be taken 

out of the bulb during the stage of cooling, owing to an accident; the 

error thus produced is quite perceptible. The results in the remaining 

tables were obtained without accident.

The data as a whole (Tables 58 to 66) may be divided into two groups. 

In the first of these (Tables 58 to 61) the results are obtained with the 

re-entrant bulb No. 1, and the thermo-couple No. 37. These data are 

probably less accurate than the more complete series of the second 

group (Tables 62 to 66) in which the results are obtained with the reentrant bulb No. 2 and the thermo-couples Nos. 37, 38, 39. The greater 

accuracy in the latter series of data is due to the fact that corrections 

are duly applied for the permanent contraction or dilatation of the porcelain bulb from measurements made after each heating. The method 

by which this may be done with extreme accuracy will be indicated 

below (p. 233).

Tables 58 to 61 contain the four series of observations classified under 

Group I.

(871]
218 MEASUREMENT OF HIGH TEMPERATURES. [HULL. 54,

TABLE 58. Comparison of air thermometer and thermo-couple. Series I- Method of constant pressure.

Ee-entrantbulbNo. 1. wo = 280°. < = 19°.6.

F,

cc.

152.0

157.0

100.0

161. 0

162.0

203.2

206.6

207.2

209.0

209.0

r,

°0.

23.5

23.9

23.8

23.9

23.9

24.9

25.0

25.0

25.0

25.0'

So

cm.

76.36

76.36

76.36

76.36

76.36

76.36

76.36

76.36

76.36

76.36

I

°C.

369

394

411

416

422

781

827

836

863

863

Time.

hours.

2.73

2.92

3.13

3.30

3.50

3.98

4.1.2

4. 25

4.45

4.50

Thermo-couple No. 37.

t

°C.

21.4

21.7

22.1

22.4

22.6

23.1

23.6

S3. 8

23.8

24.6

em

microvolt.

3454

3791

4076

4109

4189

8440

9226

9707

9981

10126

Time.

hours.

2.70

2.88

3.17

3.27

3.45

3.90

4.03

4.20

4. 33

4.48

.Gascock.

2

2

2

2

2

3

3

3

3

3

TABLK f>9. Comparison of air thermometer and thermo-couple. Series II. Method of con~

slant pressure.

Re-entrant bulb No. 1. *>o=2SO°. * = 18°.G.

Fi

cc.

191.5

197. 2

203.7

203.5

203.4

209.0

211.2

211.6

218.4

219.0

219.0

210.5

205.1

201. 0 

190. 0

180.8

167.5

138.0

132.9

Ti

00.

25.7

26.0

26.8

27.0

27.1

27.4

27.5

2707

28.1

28.2

28.4-

27.9

27.6

27.4 

27.1

26.8

26.4

25.5

25.3

Bo

cm.

76.01

76.01

76.01

76.01

76.01

75.96

76.90

75.96

75. 96

75. 96

75.96

75.95

75.95

75.95 

75.95

75. ,95

75.95

75. 95

75.95

T

00.

607

 661

728

724

722

788

818

823

923

932

928

803

737

090 

583

511 '

425

289

270

Time.

hours.

1.09

1. 28-

1.73

1.78

1.83

2.03

2.18

2.35

2.60

2.77

2.92

3.20

3.30

3.43 

3.63

3.87

4.17

4.92

5.05

Thermo-couple No. 37.

t

00.

23.6

23.6

24.6

24.9

25.4

25.6

26.1

26.0

26.6

27.6

27.6

28.1

28.6

29.4

29.1

29.3 

29.4

29.4

29.4

28.6

28.6

CIO

microvolt.

 6454

 7152

7807

8276

8280

8234

9404

9699

9743

11204

11318

1*1319

11354

8961

8040

7175 

6122

5179

4234

2574

2528

Time.

hours.

1.09

1.20

1.33

1.70

1.75

1.83

2.07

2.22

2.30

2. 58

2.68

2.80

3.00

3.25

3.35

3.48 

3.68

3.92

4.20

4.98

5.00

Gascock.

3

3

3

3

3

3

3.5

3.5

3.5

3.7

3.7

3.7

3.7

}

1

SBo

1 1

1 J

(872)
UAHtTS.l PORCELAIN AIR THERMOMETRY. 219

TABLTS 60. Comparison of air thermometer and thermo-couple. Series III. Method of

constant pressure.

Re-entrant bulb No. 1. i;o=:280. «=13. 8°.

r,

cc.

150.0

104. 6

172.5

173. 5

17G. 4

17G 1

198.7

202. 4

205. 5

20fi. 0 

207.0

215.4

218.8

 220. 5

221.1

223. 3

224.3

225.3

. 225. 5

225.5

222. 5

204.6

195.5.

183.8

175.7

1GO. 5 

150.9

147.8

144. G

Ti 

' oft

24.3

24.7

25.1

25. 2

25.5

25.5

25.7

25.1

25.8

26. 0 

20.0

20.2

2G.3

20.4

2G.5

26.7

27.0

27.0

27.0

27.1

26.9

25.8

25.9

26.0

25.8

25.5 

25.6

23.6

25.5

So

cm.

74.90

74. 9G

74.96

74.96

74. DG

74. 96

74. 98

. 74. 98

74.98

74.98 

74.98

75.06

75.06

75.06

75.06

75. 09

75. 09

75.09

75. 09

75.09

75. 12

75.12

75. 12

75.12

75.12

75.12 

75.12

75.12

75.12

I 

°C.

322

390

434

439

456

455

 633

671

704

709

720 

840.

891

918

928

938

972

991

994

994

943

700

600

509

455

370 

325

319

300

Time.

hours.

1.17

1.33

1.62

1.67

1.95

2.03

2.92

3.00

3.15

3.22 

3.37

3.58

3.73

3. 98

4.12

4.28

4.33

4.49

4.(B

4. 67

4.83

5.19

5.41

5.70

5.88

6.27 

6.52

6.61

G.63

Thermo-couple Jfo. 37.

t

°G.

22.4

22.6

23.1

23.'4

23.6

23.8

25. G

25. 8

26.1

20.3

25. G

26.8

27.2

27.6

27.8

27.8

28.2

28.4

28.6

28.6

28.9

29.0

29.1

29.1

29.1

28.8

28.6

28.6

28.6

ezo

microvolt.

2886

'3543

4302

4445

4690

4673

6654

7474

8117

8278

9382

10209

11038

11157

11632

11952

12290

' 12328

12363

12288

9515

7G91

6436

5660

5126 

3779

3573

3043

2795

Time.

hours.

1.15

1.25

1.55

1.65

1.87

2.00

2.87

2.97

. 3.18

3.33

3. 55

3.63

3.92

4.u3

4.24

4.32

4.46

4.57

4.63

4.77

c.oo

5.23

5.45

5.63

5.77 

6.22

6.32

6.67

6.70

Gascock.

2

2

2

2

2

2

3

3

3 '

3

3.5

3.5

3.5

3.5

3.7

3.7

3.7

3.7

3.7

1

SBo

OS b

(873)
MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

TABLE 61. Comparison of air thermometer and thermo-couple. Series IV. Method of

constant pressure.

Re-entrant bulb No. 1. i;o=280. t±=15.1°.

*

cc.

139.2

149.3

157.0

158.6

161. 6

162.1

173.5

179.4

184.5

186.0

194.3

197.0

202.0

203.0

208.5

210.8

212.4

215.2

216.4

218.8

219.7

220.9

221.2

221. 5

215. 7

210. 1

205. 1

200.1

194.9

190.0

184.4

180.0

163.8

155.2

 T,

°(7.

23.5

23.6

24.0

24.0

24.1

24.1

24.5

24.7

24.7

24.8

24.9

25.1

25.2

25.3

25.5

25.6

25.9

26.0

26.2

' 26.4

26.4

26.5

26.5

26.9

26.4

26.1

25.8

25.4

25.5

25.4

25.5

25.5

24.2

23.9

Bo

cm.

75.57

' 75. 57

75.57

75.57

75.57

75. 7

75. 53

75.55

75.55

75.55

75.58

75.58

75.58

75. 58

75.59

75.59

75.59

75.61

75.61

75.61

75.61

75.61

75.61

75.61

75.68

75.68

75.68

75.68

75.68

75.68

75.73

75. 73

75. 73

75.73

T

°(7.

288

330

364

372

387

390

455

494

532

543

616

641

693

704

770

801

819

861

879*

914

930

950

956

957

868

790

729

675

621

577

525

500

402

359

Time.

hours.

1.20

1.30

1.48

1.55

1.75

1.82

2.02

2.12

2.28

2.43

2.62

2.68

2.97

3.07

3.32

3.47

3.67

.3.87

3.98

4.13

4.22

4.38

4.48

4.70

4.84

4.97

5.07

5.17

5.28

5.40

5.55

5.65

6.03

6.25

Thermo-couple No. 37.

t

°(7.

21.6

21.6

21.8

22.0

22.4

22.6

 23.0

23.2

23.6

23.7

24.4

24.6

24.8

25.1

25.6

25.8

26.1

26.6

26.7

27.1

27.2

27.4

27.6

27.1

28.2

28.4

28.5

28.6

. 28.6

28.6

28.6

28.6

28.4

28.2

 20

microvolt.

2480

2952

3376

3579

3781

3836

4295

4961

5602

5729

6418

7386

7783

8001

8761

9277

9691

10193

10400

11023

11366

11675

11803

11869

11589

9998

8801

8146

7329

6108

5501

5003

3826

3460

Time.

hours.

1.18

1.27'

1.42

1.52

1.68

1.77

1.97

2.08

2.27

2.35

2.57

2.73

2.90

3.02

3.27

3.40

3.62

3.83

3.93

4.10

4.18

4.32

4.43

4.67

4.76

4.90

5.02

5.10

5.22

5.45

5.59

5.73

6.12

6.28

Gascock.

2

2

2

2

2

2

2.5

2.5

2.5

2.5

2.7

2.7

2.7.

2.7

3.0

3.0

3.0

3.3

3.3

3.5

3.5

3.5

3.5

3.5

sri

B> 

CS

Tables 62 to 66, exhibit the five series of observations classified as 

Group II. The last of these series (No. V) contains data for the measurement of the coefficient of expansion of the porcelain bulb. The 

method by which such data may be utilized is explained below on 

page 236.

(874)
BARUB.] PORCELAIN AIR THERMOMETRY. 221

TABLE 62.- Comparison of air thermometer and thermo'couple. Series I. Method of constant pressure.

Re-entrant. bulb No. 2. »o=286. «=16°.

r,

cc.

154.5

157.4

158.8

160.1

161.8

162.3

202.9

205.0

206.2

208.0

208.7

208.9

216.0

219.2

220.2

220.8

220.5

220.4

223.8

224.7

225.8

223.3

222.6

222.2

215.2

210.4

205.9

200.5

194.4

189.9

185.0

180.0

175.2

170.1

165.2

159.8

154.7

150.1

T,

°0.

21.6

21.7

22.0

22.2

22.5

22.6

23.8

24.4

25.0

26.0

26.5

26.6

26.5

27.1

27.1

27.1

27.2

27.4

28.8

28.5

28.1

28.7

28.7

28.1

27.7

27.3

27.2

27.0

26.8

26.7

26.5

26.4

26.4

26.1

26.0

25.7

25.7

25.7

J5o

cm.

77.17

77.17

77.17

77.17

77. 17

77.17

77.13

77.13

77.13

77.13

77.13

77.13

77.14

77.14

77.14

77. 14

77.14

77.14

77.10

77. 1C

77.16

77.16

77.16

77.18

77.18

77.18

77.18

77.18

77.18

77.19

77.19

77.19

77.19

77.19

77.19

77.19

77.19

77.23

T

°0.

359

373

379

385

393

396

703

733

744

758

762

763

866

910

928

938

931

927

972

991

1019

963

949

952

842

779

724

665

'606

567

529

493

460

430

402

375

351

330

Time

hours.

1.15

1.28

1.38

1.52

1.85

1.97

2.52

2.80

2.95

3.23

3.50

3.63

3.90

4.07

4.19

4.57

4.65

4.75

5.33

5.50

5.65

6.10

6.21

6.30

6.63

6.73

6.82

6.93

7.08

7.18

7.30

7.43

7.54

7.67

7.80

7.92

8.04

8.17

Therjno-couples NOB. 37, 39.

No.

37

37

37

37

39

39

39

39

39

37

37

37

37

37

37

39

39

39

39

39

37

37

37

37

37

37

37

37

37

37

 37

37

37

37

37

37

t

°(7.

20.0

20.1

20.6

20.8

21.1

21.2

22.6

22.8

23.4

24.6

25.1

25.6

26.4

26.6

27.0

27.7

27.9

28.8

29.1

29.5

30.2

30.4

30.6

30.6

30.6

30.6

30.8

30.8

30.7

30.6

30.5

30.4

30.1

30.0

29.8

29.8

em

microvolt

3521

3642

3747

3780

3837

3872

7742

8118

.8403

8791

8795

8799

10644

11000

11140

11088

11063

12125

12113

12476

11830

11552

11400

11057

9204

8500

7896

7131

6319

5821

5398

5032

4138

3853

3560

3291

Time.

hours.

1.22

1.32

1.43

1.57

1.80

1.90

2.42

2.58

2.88

 3.37

3.55

3.68

3.98

4.13

4.23

4.60

4.67

5.22

5.40

5.62

6.06

6.17

6.25

6.51

6.70

6.77

6.86

6.98

7.13

7.24

7.35

7.44

7.73

7.83

7.96

8.08

(875)
222 MEASUREMENT OF HIGH TEMPERATURES [DULL. 54.

TABLE 63. Comparison of air thermometer and thermo-coiqile. Series II. Method of

constant pressure.

Ee-entrant bulb No. 2. ifa - 286. t - 14°. 7.

7i

cc.

223.7

225.4

227.0

227.5

224.8

219.8

214.9

210.1

205.2

200. 3

195.0

190.2

185.1

180.4

175.0

170.0

T\

°0.

24.7

25.2

25.6

25.9

25.8

25.7

25.3

25.3

25.3

25.2

25.1

. 24.8

24.7

24.6

- 24.4

23.8

J5o

cm.

77.14

77.14

77.14

77.14

77.14

77.14

77.14

77.14

77.14

77.14

77.13

77.13

77.13

77.13

77.13

77.14

T

°G. '

1021

10J8

1075

1080

1027

934

858

789

726

671

618

575

534

499

462

433

Time.

hours.

2.18

2.30

2.47

2.60

2.77

2.85

Thermo-couple No. 37.

No.

37

37

37

37

37

37

2.95 | 37

3.04 '

3.15

3.25

3.38

3.49

3.62

3.73

3.85

37

37

37

37

37

37

37

37

3.97 i

t

°G.

22.1

22.6

23.6

23.8

24.6

24.8

25.1

25.5

25.8

25.8

26.2

26.4

26.6

26.5

26.6

«20

microvolt.

12654

13095

13341

13372

11592

10479

9560

8793

7997

7326

6662

6106

5444

5067

4643

Time.

hours.

2.22

2.38

2.53

2.63

2.82

2.92

3.00

3.08

3.18

3.28

3.40

3.52

3.67

3.77

3.90

TABLE (i4. Comparison of air thermometer and thermo-couple. Stries III. Method of

constant pressure.

Re-entrant bulb No. 2. « 0 =:279. t 13D .

r,

cc.

'J23. 5

224.9

225. 5

226.7

227.0

224.8

220.0

214.8

209.8

205. 2 

200.0 

195.2 

190.4

184.8

180.4

175.1

170.0

165.2

*

°G'.

23.9

23.8

24.0

24.1

24.3

23.8

23.6

23.4

23.2

23.0 

22.8 

22.7 

22.6

22.4

22.5

22.5

22.4

22 A

-»«

cm.

76.62

76. 62

76.62

76.62

76.62

76.60

76.60

76.60

76. CO

76.60 

76.60 

76.60 

76.60

76.60

76.60

76.60

76. GO

76. 62

T

98!)

1019

1028

1051

1055

1017

929

846

778

721 

664 

016 

573

527

494

458

426

403

Time.

hours.

2.58

2.73

2.83

3.02

3.12

3.27

3.37

3. .47

 3.56

3.65 

3.77 

3.87 

3.99

4.13

4.23

4.37

4.48

4.60

Thermo-couple No. 39.

«

o(7.

21.4

21.7

22.2

22.4

22.8

24.1

24.1

24.2

24.6

24.8 

24.9 

25.1 

25.2

25.3

25.2

25.1

25.1

«20

microvolt.

11544

12198

12509

J2710

12909

11567

10453

9536

8769

7454 

7067 

6443 

5920

5343

4977

4564

4214

Time.

hours.

2.4S

2.60

2.78

2.90

3.07

3.33

3.42

3.50

3.57

3.75 

3.82 

3.93 

4.05

4.18

4.28

4.41

4.52

Gascock.

4

4

4

4

4

,

off. Gas 

}

(876)
BAKUS.] POKCELAIN AIR THERMOMETRY. 223

TABLE 5. Comparison of air thermometer and thermo-couple.

constant pressure.

Series IV. Method of

Ee.ent.rant bulb No. 2. v0 = 279. t - 10°.4.

F,

cc.

227.8

228.5

228.6

229.0

225.0

220. 2

214.8

210.0

204.9

199.8

195. 2 

190.5

185.0

180.2

174.8

170.3

*

00.

27.2

27.3

27.4

27.6

27.5

27.4

27.3

27.2

27.1

27.0

26.9 

26.8

26.7

26.6

26.4

26.3

-Bo

cm.

76.01

76.01

76.01

76.01

76.01

76. 00

76.00

76.00

70.00

76.00

76.00 

76.01

76.01

76.01

76.01

75.98

I

°0.

976

990

990

995

923

847

773

714

659

609

569 

531

490

459

427

402

Time.

hours.

2.37

2.47

2.53

2.58

2.76

2.85

2.95

3.05

3.15

3.27

3.38 

3.50

3.63

3.75

3.87

3.98

Thermo-couple No. 37.

t

00.

25.6

25.8

25.9

26.0

26.3

26.6

27.0

27.2

27.4

27.6

27.8 

28.1

28.2

28.4

28.4

28.4

en

microvolt.

12027

12096

12133

12168

11586

10374

9560

8791

7845

7091

6467 

5945

5503

5040

4593

4163

Time.

hours.

2.43

2.50

2.57

2.60

2.73

2.82

2.89

2.97

3.08

3.20

3.32 

3.43

3.53

3.66

3.79

3.93

Gascock.

4

4

4

4

1

0

to 

a

o.

J

TABLE 66. Comparison of air thermometer and thermo-couple. Series V.

' . constant pressure.

Method of

Re-entrant bulb No. 2. t>0 = 279. t = 10°.

Ti

cc.

182.8

184.8

189.9

190.5 

105.6 

190.0 

105.8 

191.2

208.0

209.0

211.0 

212. 8 

225.4 

'226. 5 

121.4 

228.2 

125.2 

228.9

2'i

°C.

18.8

18.8

,19.3

19.4 

20.1 

19.7 

20.4 

20.3

21. 1

21,5

22.0 

22.5 

23.5 

23. (i 

24.6 

24.2 

25.1 

24.3

Et

cm.

76. 25

76. 25

76.20

70.20 

. 107. 04 

76.15 

107. 57 

76.12

76. OG

76.06

76.00

75. 92

118. 50 

118.50 

116. 72 

75.85

T

°C.

512

526

565

568

560

567

' 734

742

760 

774 

958 

978

1002

1006

Time.

hours.

11. 26

11.34

11.67

11.75 

11. 88 

12. 05 

12. 27 

12. 42

12.88

12.95

1.28 

1.82 

2.42 

2.57 

2.83 

2.97 

3.17 

3.27

Thernio-couplo No. 38.

t

°C.

16.6

17.0

17.4

18.6 

19.6 

?0.4 

20.8 

21.2

21.6

22.1

22.6 

23.6 

23.8 

23.8 

24.6 

24.8 

25.1 

25.4

«20

microvolt.

5093

5490

5851

6040 

6132 

8083 

8638

8781

8856

9004

9012 

11561 

11880 

11998 

12203 

12328 

12366 

12553

Time.

hours.

11.17

11.30

11. 51

12.07 

12. 48 

12.77 

1.01 

1.19

1.31

1.61

1.83 

2.37 

2.50 

2.62 

2.87 

3.00 

3.22 

3.38

Gascock.

2.5

2.5

2.5

2.5 

2.5 

3.0 

3.0 

3.0

3.0

3.0

3.0 

3.7 

3.7 

3.7 

3.7 

3.7 

3.7 

3.7

(877)
224 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

TABLE 66. Comparison of air thermometer and thermo-couple, 

constant pressure Continued.

Series V. Method of

Re-entrant bulb No. 2. va = 279. t = 10°.

F,

ce.

225. 0

219.6

215.1

209.6

205.0

200.0 

195.1 

190. 1

184.9

179.9

175.0

170. 0

T,

°c,

24.3

23.7

23.5

23.3

23.0

22.7 

22.3 

22.0

21.6

21.2

21.2

21.5

Bt

cm.

75.54

75.54

75.54

75.54

75. 56

75.56 

75.56 

75.56

75.57

75.57

75.57

75.54

T

°G

935

852

790

722

671

622 

579 

539

501

467

436

405

Time.

hours.

3.53

3.64

3.73

3.84

3.94

4.06 

4.18 

4.31

4.42

4.53

4..6G

4.78

Thermo-couple No. 38.

T

°C.

25.4

25.6

25.8

25.8

25.8

25.8 

25.8 

25.6

25.6

25.4

25.3

25.2

25.1

em

microvolt.

12439

10991

9893

8991

8126

7309 

6642 

6085

5480

5096

4763

4382

4134

Time.

hoiirs.

3.45

3.57

3.66

3.75

3.86

3:98 

4.10 

4.23

4.37

4.47

4.56

4.68

4.77

Gas 

cock.

Gas off.

J

The results of these tables were constructed graphically by representing on the same sheet T and e2o> respectively, as functions of time. 

For the pairs of curves thus obtained it is easy to select data for the 

construction of e20 as a function of T with a degree of accuracy consistent with the accuracy of measurement. Such, data are enumerated in 

Tables 67 to 70, which correspond, respectively, to the four tables just 

described.

It is perhaps well to remark that generally the interpolations are 

made linearly. This involves less assumption and less work than 

other graphic methods, and the points are sufficiently near together to 

make it available.

Tables 67 to 70 correspond to the data of Group I, Tables 58 to 61.

TABLE 67. Corresponding to Table 58.

Series I. He-entrant bulb No. 1.

No.

37

37

37

37

37

T

370

390

400

410

420

C20

3530

3810

3940

4050

4170

No.

37

37

37

37

37

37

T

780

800

820

840

850

860

eje

8950

9200

9470

9770

9940

10100

(878)
BARU8.] PORCELAIN AIR TIIERMOMETRY. 

TABLE 68. Corresponding to Table 59.

225

Series II. Re-entrant bulb No.l.

No.

37

37

37

37

37

37

37

T

610

640

667

720

727

800

820

em

6520

7160

7700

8290

8270

9410

9660

No.

37

37

37

37

37

37

37

T

824

920

930

933

750

700

650

«JO

9740

11200

11300

11330

8580

7820

7100

No.

37

37

37

37

37

37

37

T

600

550

500

450

400

350

300

e2o

6430

5820

5220

4640

'4030

3420

2800

TABLE 69. Corresponding to Tcible 60.

Series III Re-outraut bulb No. 1.

No.

37

37

37

37

37

37

37

37

37

37

37

T

330

360

425

440

453

630

660

690

710

718

840

«20

3120

3500

4300

4460

46CO

7100

7500

7860

8160

8270

9840

No.

37

37

37

37

37

37

37

37

37

37

37

T

860

880

900

920

960

980

990

994

950

900

850

en

10200

10500

10800

11150

11850

12170

12340

12370

11580

10760

10040

No.

37

37

37

37

37

37

37

37

37

37

37

T

800

750

700

650

600

550

500

450

400

350

300

em

9320

8640

7960

7250

6550

5880

5280

4700

 4080

3420

2840

TABLE 70. Corresponding to Table 61.

Series I V. He-entrant bulb No. 1.

No. '

37

37

37

37

37

37

37

37

37

37

37

T

330

350

370

390

480

500

520

540

640

660

680

«JO

3010

3330

3620

3850

4960

5220

5470

5740

7200

7430

7680

No.

37

37

37

37

37

37

37

37

37

37

37

T

 700

770

790

810

815

870

890

910

930

950

957

«JO

8050

9000

9280

9550

9650

10520

10860

11170

11470

11760

11860

No.

37

37

37

37

37

37

37

37

37

37

37

T

850

800

750

700

650

600

550

500

450

400

350

C20

10320

9470

8670

7970

7340

6660

5970

5280

4650

4020

3430

The series of Tables 71 to 75 correspond to the data of Group II, 

Tables 62 to 66.

(879) 

Bull. 54 15
226 MEASUREMENT OF HIGH TEMPERATURES. 

TABLE 71. Corresponding to Tabled.

[BULL. 54.

No.

37

37

37

37

39

39

39

39

39

37

37

37

620

microvolt.

pddfl G't'tU

3570

3700

.3770

3850

3900

7970

8310

8470

8670

8800

8800

T

°C.

359

373

379

385

393

396

703

733

744

758

762

763

No.

37

37

37

39

39

39

39

39

39

37

37

37

Series I

em

microvolt.

10640

10850

11080

11090

11070

11050

12120

12290

12440

11720

11470

11400

T

°a.

895

910

928

938

931

927

972

991

1019

963

949

952

No.

37

37

37

37

37

37

37

37

37

37.

37

37

37

37

eso

microvolt.

8900

8160

7450

6580

6080

5590

"5060

4730

 4330

3940

3660

3370

T

°0,

842

779

724

665

606

567

529

493 *

460

430

402

375

351

330

TABLE 72. Corresponding to Tables 63, 64, 65.

No.

37

37

37

37

37

37

37

37

37

37

37

37

37

37

37

Series II

620

microvolt.

12650

12870

13250

13360

11250

10150

9170

8240

7540

6780

6250

5660

5220

4820

T

°G.

1030

1048

1075

1080

934

858

789

726

671

618

575

534

499

462

433

No.

39

39

39

39

39

39

39

39

39

39

39

39

39

39

39

39

. 39

39

Series IL

em

microvolt.

11900

12370

12590

12850

12910

11570

11080

9880

8880

8180

7350

6780

6170

5550

5150

4700

4350

T

°G.

989

1019 '

1028^

1051

1054

965

929

816

778

721

064

616

573

527

494

458

426

403

No.

37

37

37

37

37

37

37 =

37

37

37

37

37

37

37

37

37

Series IV

620

microvolt.

12040

12060

12110

12140

11120

10040

8970

8110

7410

6740

6180

5640

5140

4740

4350

4140

T

00.

985

990.

990

995

923

847

773

7U

659

'609

569

531

490

459

427

413

(880)
/2OOO

J/OOO

toooo 

9OOO

BOOO

7OOO

6OOO

50OO

400O

3OOO

/

zooo

sooo

5

f

4

/

,/'

y

/ \

z

4

/

4

8 */

*Yy

/'

3.1

2

4

*.y »/

3

2

A

f

3

*

/3

/

*/*

$

1

TOUR SERIES BULB Nol

THERMOCOUPLE No. 37.

7

FIG. 41. Chart showing the variation of thermo-electromotive force (microvolts) with temperature;
HARKS.] PORCELAIN AIR THERMOMETRY. 

TABLE 75. Corresponding to Table 66.

227

Series V.

No.

38

38

38

38

 38

38

38

38

38

C20

microvolt.

5370

5560

 5900

5930

6030

. 6100

8340

8500

8850

T

°0.

512

526

565

568

560

567

734

742

760

No.

38

38

38

38

38

38

38

38

38

ew

microvolt.

9030

11700

11950

12300

12430

11470

10130

9190

8270

T

°G.

774

958

978

1002

1006

935

852

790

722

No.

38

38

38

38

38

38

38

38

 20

microvolt.

7580

6860

.0300

5740

5290

4880

4450

4100.

T

°(7.

671

622

579

539

501

467

436

405

Graphic digests.. The results of these four tables may be platted 

graphically by making e20 a function of T. This is done in Figs. 41 and 

42, which may be said to be the final result of the calibration problem 

in hand. Fig. 41 contains the data of Group I, Fig. 42 the data of Group 

II. In Fig. 41 numerals inserted show the series to which the point of 

observation refers. If temperature be increasing (heating) the numeral 

is placed above the point; if temperature be decreasing (cooling) the 

numeral is below the point. In Fig. 42 similar distinctions are carried 

out by caudal dashes. For increasing temperature these point upward 

or to the right; for decreasing temperature downward or to the left.

CONSTANT-PRESSURE THERMOMETER DISCUSSION.

Errors of measurement in general. The discussion of the data, Tables 

67 to 75, may expediently be introduced by an analysis of the effect of 

errors. The divers quantities, which enter saliently into the equation, 

derived for constant-pressure air thermometry, are here

t,T1: H

T'

to which may be added M and 8. As above, the degree of absolute accuracy with which they a,re to be measured in order that the effect on 

T may not exceed 1: 1000, follows from the equation

dx -dx T

dT 10UO

where x typifies any one of the quantities enumerated. From this follow the subjoined special equations, all of which are approximate, and 

put in such forms as will best facilitate the computation:

T

1000 (1+aT)2

(881)
228 MEASUREMENT OF HIGH TEMPERATURES. | BULL. 54.

T

1000

___

v "1000 /( Tt) (1+<*T)

*

X « 

0 ~

. av2 T v2 dM

/(Ti)

x a 

oa=1000

a 1 

: 10001 + a'/'

 ^ y\ f, m \V

_«)_ -iV

These forms have a more general importance, inasmuch as they show 

what correction is to be applied to T to compensate for unavoidable or 

current errors of any of the special quantities to which the formulae refer. Such errors, for instance, are the permanent changes of volume 

of the porcelain bulb in successive heatings, and due to the vitrification 

of porcelain. The correction to be applied is

ST= J-^y- V,(l+aT)23v.

OfV2 .' V 1 X

It is well to remark that in the above equations has approximately the value

since for the present purposes t and TI may be supposed identical.

(882)
/30OO

/20QO

//OOO

/OOOO

9OOO

6000

7000

eooo

5OOO

40OO

30OO

/ 

ZOOO

/OOO

/

/

j

/

/

/

/

/

__ JL /

/'A

N /

/-/

/ '

 / 

,

?&&?/£s /, BULB 2',CoupL£.37$3& 

' » //, " >' » 39,

T* " ///, " " " "

s* " /k" " " " 37,

*\ n If " " " 38,

3OO* 4OO^SQO* GOO* TOO* <BOO° QOO"

3. 42. Chart showing the variation of thermo-electromotive force (microvolts) with temperature.
BARUS.) PORCELAIN AIR THERMOMETRY. 229

must be derived from the general equation, which, after differentiation, is simplified by inserting H=li. 

If into these equations we introduce mean values, such as tf=20°,

17.

Tj=20o, #=0.00367, /3=0.000017; if, moreover, we insert for 1 the

values which may be taken from Tables 58 to 6G, above, then the said 

equations lead to the following tabular comparison; It is expedient in 

addition to the absolute values of the divers errors dt, dT^ 6V} , 6v', 

6v, da, 6/3, tfJBT, dM, 68, which individually influence the result by 

1:1000, to give also the relative values of some of these quantities, or 

again the error of the ratios, viz:

TJ" V

I/ \ Ckf JUL

~ )' ^ T "

TABLE 76. Comparison of divers errors which affect the result one pro milk.

T

°0.

100

500

1000

1500

Sv

cc.

 0. 276

 0. Ill

 0. 066

 0. 047

St

°C.

0.06

0.07

0.05

0.04

«/»//»

0.17

0.08

0.05

0.04

ST,

°0.

 0.29

 0.12

 0.07

 0.05

HF0 

V ti /

xlO6

211

245

180

140

5V,

cc.

0.059

O.OG9

0.051

0.039

*(-)

V v J

xlO3

 2. 26

 0.5G

 0.29

 0.20

Sy'

cc.

 0. 632

 0. 155

 0. 081

 0. 055

illfM xlU°

 268

 047

 736

 846

6/3x10°

2.7

1.3

0.8

0.6

SSJS

 5.27

 1.30

 0.68

 0.46

&H

cm.

0.016

0.019

0.014

0.011

'(I)

xlO6

211

245

183

141

iMxlQ6

 197

 228

 168

 130

v,

cc.

59. 9

173.9

215.3

233.6

SSxlO"

197

228

168

130

2'

0 (7.

100

500

1000

1500

From this table of errors a fully satisfactory inference of the value 

of the experiments made can be obtained, tf M and 68 and their relative values are primarily of interest. They indicate the degree of 

precision with which the logarithmic calculations must be made in 

order that the arithmetical operations may be consistent with the 

accuracy of the experimental data, d M, however, has further importance, inasmuch as this factor enters into most of the formulae for 

errors. By far the greater number of these may therefore be made 

more elegant and more practically serviceable by introducing 6 M in the 

manner shown on page 229.

Regarding the introductory measurements v the volume of the bulb 

and t the fiducial temperature it appears that the volumetric method 

for the estimation of v described on page 214 is acceptable5 for by cautious work with all parts at the same temperature a mean correct-

' (883)
230 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

ness of about O.lcc in a series of measurements is quite attainable. On 

the other band the determination of t, by inserting a good mercury 

thermometer into the re-entrant tube of the porcelain bulb while this 

apparatus is in place in the revolving muffle, is less satisfactory than it 

is convenient; but in a series of three or four such measurements a 

mean error greater than 0.5° 0. is improbable. It is understood that 

it has not been my object in this paper to push measurements of v and 

t to the extreme fineness desiraole; but it is quite clear that this may 

be done by water calibration and immersion in water.

Greater difficulty is encountered as we approach the main data of 

measurement, V^ 2\, H. Since Vt must be measured throughout with 

an accuracy of about O.occ, it is obvious at once that stages of practically 

constant temperature, or of very slow heating and cooling, are necessary 

for measurement. This is attainable in the revolving muffle very perfectly by proper manipulation of the graduated faucet for gas influx 

and by closing all apertures of the furnace daring- cooling. With due 

care, however, the measurement of variable Vi to 0.05CC will remain a 

problem of nice observation, particularly so since the total range of 

variation of T^is nearly 235CC. The difficulty is increased, inasmuch as 

TI must be known to 0.1° C.; hence it is not only desirable to jacket 

the tube B G (Fig. 40) with a current of circulating water, but small 

thermometers adjusted within the calibrated tube in such a way as to 

indicate the temperature of the air inclosed are a desideratum. Fortunately the hot air which emerges from the air thermometer may be completely cooled after passing through the metallic capillary tubes. It 

appears, moreover, that 150cm of platinum capillary tube of the dimensions given in Table 42 are not seriously detrimental in producing slight 

differences of pressure in the bulb and manometer; for if Vl be constructed as a function of T (thermo-electric) by aid of the data in Tables 

58 to 66 it will be seen that 7i obtained during the stage of increasing

temperatures (i. e., with the gas ou) is quite the same as the corresponding Vi obtained during the stage of decreasing temperatures (i. e., during 

cooling), cseteris paribus. This is a crucial test, which reflects favorably on the method as a whole. Fortunately the value of J2", or the barometer, is sufficiently given if measured to 0.01cm. This is not only 

easily done, but an interval of pressure of 0.01cm is larger than the friction of the gas passing through the capillary tubes can maintain for any 

interval of time as long as that of an observation.

The magnitudes of the corrective term 8 have already been referred 

to. It is seen that an error as large as 30 per cent, in v1 is without 

serious effect ou the result. In like manner S itself is sufficiently 

known to 50 per cent. It is this fortunate result which makes the use 

of a compensator a questionable desideratum; and if it be borne in 

mind that the distribution of internal fissures is usually such that two 

stems identical externally are by no means so internally, it is probable 

that here no advantage is derived from the compensator. This remark

(884),
BASUS.J PORCELAIN AIR THERMOMETRY. 231

refers, of course, to apparatus of porcelain. In the fire-clay air thermometer the porosity of stem will doubtless be greater and the compensator corrective essential.

Finally, it is seen that fi measured correctly within 5 per cent, is satisfactory. Concerning both a and ft much that has been said above is 

here applicable (Cf. page 198.)

Accuracy of the measurements made. After this tolerably full analysis of possible errors, the degree of certainty with which the present 

data attest the excellence of this method of air thermometry and of 

pyroinetric comparison employed may be satisfactorily discerned. It 

is expedient to use the graphic tabulation Figs. 41 and 42, in which all 

the data in question have been inserted.

Let us consider the result for Bulb No. 1 first. The points belonging to the divers Series I to IV for Bulb I are marked with numerals; 

moreover, when temperature increases (gas on) the numeral is placed 

above the point; when temperature decreases (gas off, furnace cooling) 

the numeral is placed below the point. In this way the amount of information contained in the diagram is much increased. With respect 

to Series I the remark has already been made that but a single thermometer was used in measuring Tv . Now, the temperature of a room 

in which furnace experiments are being made certainly differs in temperature by as much as 1° for a vertical height as great as B 0, Fig. 

40 (150cm ). Hence the exceptionally lateral position of the series of 

points marked "1" is easily accounted for. Nor was a correction applied in these cases for permanent variation of the volume v0 . Again, 

in Series II an accident by which the thermo-couple was withdrawn, 

from the air-thermometer bulb cooled the electrical apparatus abnormally. This occurred during the stage of decreasing temperature, and 

the lateral position of certain points marked "2" on the diagram is also 

accounted for. The remaining points are grouped in -close proximity 

to a uniform locus. The maximum elongation of any of the points, 2, 

3, 4, in question is not greater than 10°, whereas, as a rule, this difference is very much smaller. At the outset it is to be borne in mind 

that into this aggregate maximum discrepancy of 10° are crowded all 

the errors of the thermo-electric measurement, to say nothing of the 

errors incurred by the double graphic interpolation by which Fig. 41 was 

derived from the individual time series of observations of e and T. Of 

course, results of this kind are susceptible to great improvement if the 

observations are made by a number of observers instead of by one observer only, for in this way the time error may be eliminated, and 

observations may be made simultaneously. Quite apart from these 

considerations an error of 10° is easily incident to the method in its 

present stage of experimental development. However carefully the 

manometer may be screened from the furnace an error in T, of 0.2° C., 

or even more, is not improbable; nor was the attempt made to measure 

FI with greater precision than O.lcc. This already accounts for half of

(885)
232 MEASUREMENT OF HIGH TEMPERATURES. tum.t.64.

the observed maximum error, apportioning the remaining four or five 

degrees to the variety of discrepancies already enumerated, to which 

may be further added changes both of u, the capacity of the bulb, and 

of /?, due to vitrification or similar progressive change of the substance 

of the porcelain during successive heatings; to irregular differences of 

the stein error; to the possible occurrence of minute capillary leakage 

throughout the considerable length of connecting tube; to structural 

changes (crystallization, silicification, gaseous corrosion) of the metal 

of the thermo-couple. It is needless to make further mention.

Considering the figures 41 and 42 as a whole, it will be seen that the 

calibration curves are regular throughout In case of the 20 per cent. 

platinum-iridium alloy, therefore, no evidence of sudden allotropio 

changes or polymerization is anywhere discernable. Hence between 

300° and 1,300°, the availability of the given platinum-iridium alloy for 

thermo-electric pyrometry can not be disputed. I do not believe that 

the strictures which Le Chatelier (1. c.) has placed on the pyrometric use 

of the platiuum-iridium alloys are substantiated by experiment, though 

they may be true (Chap. I) for low percentage alloys. A full discussion 

of the divergence of the said curves (Figs. 41, 42) from the AvenariusTait equation, is beyond my present purpose.

A ccuracy of the measurements made, Group II. In a general way 

these critical remarks apply to the data obtained with Bulb II and inserted in the chart (Fig. 42). The method of designation is clear, the 

divers series being distinguished on the chart by dashes, which pass 

upward or to the right for ascending temperatures, and pass downward 

or to the left for descending temperatures. As a whole, the data for 

Bulb II are a marked improvement upon the data for Bulb I. This was 

brought about principally by correcting the calibrated volumeof the bulb 

by such permanent changes of volume as occur after each heating. Fortunately the value of this correction can be found with great accuracy 

and facility by the same method by which the fiducial temperature is 

determined (cf. page 213). If 6v be the permanent alteration of the volume of the bulb due to heating ; if bb and tb be the pressure and temperature before heating, and &0 and ta the pressure and temperature 

after heating, for which, in each case, the air is wholly in the bulb and 

capillary stems (i. e., Vi=0); and if 2(v) be the total original volume 

of bulb and capillary stems, then

»./(*.) 2v m

The quantity bf(t) occurring in this equation is the same already eval. 

uated in equation 6 (page 213). The following tabular exhibit of the 

values of dv in question was obtained from Bulb II.

(886)
PORCELAIN AIR THERMOMETRY.

TABLE 77. Permanent volume variations of lull.

233

After Series III.... 

After Series IV .....

V(0

72. 677

73. 240

73. 188

73. 210 

73. 180

73. 188

?xWi»

+6.98

 0.71

±0.00

-0.30 

+0.11

±0.00

vo

cc.

281. 26

m m

279. 30

279. 22 

279. 33

97Q *?A

Mean volumes

Vt>

cc.

! ... .280. 18

|..... .279. 20

! ... .279. 26

|..... 279.27 

|. .....279. 32

The values of v0 in the last column are therefore the closest approach 

to the respective zero volumes of the bulb during the successive series 

I to V in question. It is this corrective which makes the results 1 of

Fig. 42 very much more uniform than those of Fig. 41.

If Fig. 41. be compared with Fig. 42 it will be seen that the agreement of loci is very good. It is clear, beyond question, that the discrepancies involved are those incidental to the measurement; discrepancies, 

moreover, which are capable of considerable reduction by improving the 

experimental appurtenances in the way suggested above. It therefore 

follows that the degree of identity of the environment of the air thermometer and of the thermo couple is as nearly perfect as the calibration 

problem demands. Again, from the difficulty I have found in obtaining accordance between different series of results in the earlier experi. 

ments, I believe that with the use of the present form of re-entrant bulb 

the calibration problem has for the first time been rigorously solved; 

for it is obvious that if the=constants of either of the loci (Figs. 41 or 42) 

were calculated by the method of least squares their probable error 

would be decidedly within one pro mille.

Boiling point of zinc. This is the stage of progress at which my other 

duties will make it necessary to temporarily abandon the temperature 

problems and proceed toward a corresponding development of the pressure work. I need merely notice therefore in what respects the absolute data of this chapter substantiate the earlier inferences. For 

instance, if the values of e20 , which hold for the boiling point of zinc 

given at the end of Chapter II, be interpreted by aid of the final dia-

 A curious source of error may be noted here. When the centrifugal blower is insulated the friction of the belt electrifies it permanently. If, furthermore, the tubing 

be insulated the furnace will be charged with a current of electrified air. Through 

the wires of the thermo-couple this charge is distributed over the measuring apparatus. If now, any metallic part of this (for instance, the metal of a rheostat key) be 

touched with the finger there results a redistribution of the charge and invariably a 

large deflection of the galvanometer needle. This is seriously misleading, and the error 

is not always at once detected. Care should therefore always be taken that the tube 

conveying air to the furnace from the blower is not insulated.

(887)
234 MEASUREMENT OF HIGH TEMPERATURES. tntJLL.54.

grams (Figs. 41 and 42) the data so obtained are small, being not larger 

than 905° in the one case and 916° in the other. These values are to 

be finally corrected by the value for v0 , found after the completion of 

the measurements by direct water calibration. I may remark in passing, that the stem correction is negative, and that I applied a value 

which is certainly not too large. Hence the stem error has produced 

no erroneous negative increment of the value" of T.

In the case of Bulb I, the datum v0 is accepted as 280CC, an approximate value to be subsequently corrected, for permaneut changes of volume, etc. By the volumetric method (page 214) the volume of bulb, stem, 

and capillary tubes is found to be 280.73CC at the mean temperature 20°. 

From this is to be deducted the volume of the metallic capillary stems, 

0.40CC ; the volume of the porcelain capillary stem, 0.53CC ; and the 

amount of dead space at the joints of the tubes, 0.23CC. This leaves for

the volume of the bulb at 0°C. 

t

v0 =279.58cc.

The same volume was measured at the close of the work by direct calibration with water, and found to be

This difference of 0.52CC is due to the imperfection of the volumetric 

method in its present form. Preferring the latter value, the volume increment for Bulb I is

6v=-OM . ...... (I)

In the case of Bulb II, v0 is accepted in the computations provisorily 

as v0=279.3cc , and found by direct calibration with water to be

00=278.73C0.

Hence for Bulb II

^0 =-0.57 ....... (II)

If now the formula, page 229, viz :

be applied with the purpose of correcting the above approximate value 

for the boiling point of zinc, it appears since T=910°; Tj=25° 

/(T,)=0.916; v=279cc ; ^=220°°; (l+«T)2=19.2j that

3T=+ 12.5° for Bulb I, and dT=+ 7.6° for Bulb II.

In place of the single data obtained from Figs. 41 and 42 it is preferable to determine the values of T for each series. This is done in 

Table 78, in which, moreover, the data for increasing and decreasing

(888)
BARU8.] PORCELAIN AIR THERMOMETRY. 235

temperature are distinguished. The table applies for em =11,000 microvolts, the value found in Chapter II as the equivalent of T.

TABLE 78. Interpolations near tlie 'boiling point of zinc.

Bulb.

I 

I

II

II

II

n

ii

Series.

Ill, 

IV 3

11

II |

III).

IV

VJ

T 

temperature 

increasing.

o 

912 

900

925

914

T 

temperature 

decreasing.

o 

915

916

924

915

Moan T.

o 

| 909.0

1

*> 918.8

Hence, if to these mean values be added the corrections ST as just 

found, there follows T=921.5o for Bulb I and T=926.4° for Bulb II.

A final correction is still to be added. In tbe present reduction I 

assume e2o=H5 000 as the electrical equivalent of the boiling point .of 

zinc. The careful crucible experiments made soon after the air therinometry, a'ud detailed on page 123, show that e2o=ll,074. Hence, since

nearly, and since 6 e2o=+74, it follows that

ST = 4.7°.

The constants a and 6 are calculated from the data of diagram (Fig. 42), 

a sufficient approximation. Hence, finally,

T=926° for Bulb I, and T=931° for Bulb II.

This is the closest approximation to the boiling point of zinc which 

the method, in its present stage of development, permits.

This is a low result as compared with Deville and Troost's, and with 

Weinhold's data. It agrees admirably with the values of Becquerel and 

of Violle. But my datum is not as low as would have been anticipated 

from the constant-volume measurements (page 199) of this chapter, or 

from inferences deduced by purely thermo-electric measurement in 

Chapter II. As long, however, as rigorous measurement of the variable /?, the coefficient of expansion of the bulb, has not been made, and 

the effect of a non-glazed interior of the bulb has not been placed 

beyond all obscurity, it is wise to advert to the present value for the 

boiling point of zinc with only precautionary emphasis. Nevertheless, 

it is pleasant to note this accordance of data between the results of the 

French observers mentioned and my own data. I am specially ericonr-

(889)
236 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

aged in believing the non-inglazed thermometer bulb nearly as available and safe for high temperature measurement as the inglazed form.

Coefficient of heat expansion of porcelain. It is necessary, to state 

that in the present work no special measurements for ft have as yet 

been made. The value taken is that of Deville and Troost, which, for 

the porcelain in hand, is possibly too low. The probable effect of correcting ft will therefore be an increase of T, since increments of both 

§ and T have like signs. Not wishing at present to redetermine /3 I 

made corroborative tests in the following manner:

In Table 66 results are given from which approximate values of the 

coefficient of expansion of porcelain may be computed. Let the manometer volume be changed when the temperature of the bulb is nearly 

constant. Then if

z, F2 , T2

are two successive readings, it follows that

f(T2 )

HI 

where T is the temperature and v the zero volume of the t>ulb. It is 

expedient to make H2 the barometric height for the day, so the T can 

at once be computed by the ordinary formula. ft may then be computed for/(T). By making the measurements for T (i. e., J?i, Fl5 T{ ) 

alternate with the measurements for ft (i. e., H2 , F2 , T2 ) in time series, 

the value of T, which corresponds to the time at which the measurements 

for ft are made, may be accurately determined by graphic interpolation. 

The following results are computed from the data already given in Table 

66, Bulb II, Series V:

TABLE 79. Coefficient of heat expansion of porcelain.

Time.

h. in. 

11 45

11 53 

12 03

12 06 

12 25

2 34

2 50 

2 58

3 10 

3 16

T

o 

568

(564) 

560

(564) 

567

978

(993) 

1002

1004 

1006

ft

\ 0. 000022

I 0. 000026

} 0. 000037

I 0. 000027

In view of the fact that the quantities on which /3 ultimately depends 

are of the same order of magnitude as the stem error 2, this method' 

of determining ft can not be looked to for very close results. Indeed, if

(890)
BARUs.1 PORCELAIN AIR THERMOMETRY. 237

/? were known from special measurements this value could be used to 

compute 2. It is obvious therefore that for sharp values of /? it is 

necessary to work with a jacketed manometer, so that Tt may be constant. It is necessary also that T and H be constant, a condition which 

the above experiments do not quite fulfill. The above data, crude as 

they are, show, however, that ft is determinate by this method with the 

same degree of accuracy with which it is to be applied. In this respect 

the constant-pressure method is unique, since it admits of easy modifications 

by which the zero volume of the bulb, its coefficient of expansion, as well as 

all permanent changes of volume, may be evaluated without extra appliances. 

[Attention may again be directed to the independent method of standardization of a nou-inglazed re-entrant porcelain air-thermometer bulb by 

thermal comparison with a re-entrant glass thermometer bulb of known 

constants. Such comparison is to be made above 300° to obviate the 

moisture and condensation errors, and either directly in the elliptic revolving muffle (Fig. 36 a), or indirectly through the intervention of the 

same thermo-couple. In the last case each bulb is separately compared 

with the couple as explained above (Figs. 37, 38), and the results then 

co-ordinated. The hard-glass bulb, according to Troost (loc. cit.) may 

be safely regarded rigid as far as 600°. ]889.]-

Remarks. The manner of further development of the present thermal problems is now sufficiently obvious, and may be briefly summarized in a final remark. It is necessary in the first place to rigorously 

compare bulbs glazed interiorly with bulbs not glazed interiorly. The 

latter are so much more easily constructed that if their use be warranted 

practical air therrnometry will be in no small measure facilitated. For 

instance, if we suppose the bulb non-glazed interiorly to be admissible, 

then there are no serious obstacles in the way of a fire-clay thermometer 

bulb. Bulbs of such ware are naturally porous, but there is no doubt 

that enamel can be applied in sufficient quantity to the exterior to make 

them impervious to air. With these bulbs the upper limit of possible 

thermal measurement will closely approach the melting point of platinum. By aid of the volumetric method described on pages 195 and 

214, problems referring to the internal volume of the bulbs and stems, 

whether porous or not, admit of satisfactory solution. Again, it is necessary to compare the data of bulbs containing different gases, dry air, 

O2 , H2 , N2 , etc. All such comparisons can be made either directly, by 

exposing the bulbs contiguously in an elliptic revolving muffle of the 

kind sketched and described on pp. 182,188, or they may be made indirectly, by comparing the individual air-thermometer bulbs with the same 

thermo-couple. In the interest of greater accuracy the same re-entrant 

form of bulb, into which the divers gases are successively introduced, 

is expediently combined with one and the same thermo-couple, and the 

heating is conducted precisely in the mariner shown in this chapter. 

Until Charles's law has in this way been tested for large ranges of temperature it is hardly desirable to multiply the number of approximate

(891)
238 MEASUREMENT OF HIGH TEMPERATURES. tBUiA.54.

thermal data in the region of high temperatures by further data of an 

absolute kind, which at the present state of our knowledge must also 

be regarded as approximate. The first steps of a method by which 

rigorously accurate data may be reached the present chapter fully 

elucidates.

For purposes of ordinary high-temperature measurement the constant-pressure method of air thermornetry must undoubtedly be preferred. It is superfluous to reiterate the many reasons which the text 

contains. But for the ulterior and purely scientific purposes of studying laws relative to the expansion of gases at high temperatures, both 

methods are equally valuable, and it is highly probable that an investigation of the thermal-expansion phenomena of one and the same gas 

in all admissible states of tenuity will throw more light on the subject 

in hand than an inquiry into the analogous behavior of different gases. 

Fortunately, in ail such comparisons the stem errors so nearly counterbalance each other as to make it probable that the measurements can 

be made with great nicety.

(892)
. CHAPTER V.

THE PYROMETRIC USE OF THE PRINCIPLE OF VISCOSITY. 

INTRODUCTION.

Remarks. It has been said that a method for making metallic capillary tubes was described hypothetically by Kegnault in his celebrated 

memoir.1 So far as I know, however, the first platinum tubes made for 

actual high-temperature use are those described in the present volume. 

The dimensions of the capillaries used in the air-thermometer work 

have already been given $ similar tubes of silver and of copper were 

also in hand. It seemed expedieet therefore in view of the excellent 

quality which these tubes eventually came to possess, to put them to 

more general use .than originally contemplated. Indeed, the attempt 

to obtain absolute thermal measurements in the region of high temperatures, from the transpiration data obtainable by passing gases through 

red-hot capillary tubes of platinum, presented itself as an important 

final step in the present investigation. The kinetic theory of gases has 

not, as yet, given any satisfactory clue for the prediction of the thermal 

relations of gaseous viscosity. It is nevertheless probable, from the 

nature of a gas, that an experimental law, which might be found to hold 

between 0° and 1,200°, could be safely assumed to hold for a much 

larger interval of temperature. In other words, judicious extrapolation 

is much more nearly permissible in the case of thermal results applying 

to gases than it possibly can be-in the case of results which apply to 

liquids or to solids. Again, since the rate at which transpiration takes 

place varies inversely as the absolute temperature of the gas, as well as 

inversely as its viscosity, it is clear that the construction of a transpiration pyrometer will be practicable, even if the thermal variations 

of viscosity should prove unfavorable for such a purpose.

Apart from practical applications, however, physical science can not 

but profit by any attempt at high-temperature measurement, rationally 

based on some other phenomenon than the thermal expansion of a gas. 

This is proven, for instance, by the pains which V. Meyer, Troost, Berthelot, and others have taken to ascertain whether the coefficient of 

thermal expansion in all its high-temperature applications could be assumed to be rigorously constant. Even if the present method should 

fail of further purpose than the co-ordination of data in a field of high 

temperature, where absolute results are either isolated or wanting, its

1 Cf. pages 167,169.

(893) 239
240 MEASUREMENT OF HIGH TEMPERATURES. [Buix.54.

conditions of application deserve most careful scrutiny. I ain justified 

in believing that the favorable character of the results which this chapter contains will be sufficient to show that the transpiration pyrometer 

is more than equal to the demands made upon it. Interpreted by the 

Poiseuille-Meyer formula transpiration data must enable us to measure 

temperature absolutely, over a wider thermal range, and with greater 

convenience and accuracy than is now possible with any other instrument.

An important part of the present chapter is the new light it throws 

on the thermal relations of viscosity and on the thermal relations of the 

mean free path of the molecule of a perfect gas. The phenomena of 

diffusion, heat conductivity, and viscosity in gases, depending, as they 

do, in their thermal relations on the law of force between the molecules, 

have hitherto remained beyond the reach even of theory.

The present chapter is divided into two parts, the first of which contains experiments made with true capillaries. The second part contains 

experiments with tubes of larger bore with tubes, in other words, 

which do not strictly satisfy the capillary conditions of the PoiseuilleMeyer law.

Literature. The work of the earlier observers has recently been 

discussed with great thoroughness by Mr. S. W. Holman 1 in the last 

of his fine treatises on the relation of viscosity of gases and temperature. Profiting by this, I will therefore dismiss the subject with a few 

cursory remarks, and refer those desiring more specific information to 

Mr. Holman's researches. Historical reference is also made in O. E. 

Meyer's2 extended article, where the salient features of Graham's3 classic 

experiments are analyzed. A clear account of the whole question is 

given by Meyer in his well-known book.4

Some years after Graham had published his experimental results, 

and after Clausius 5 had pointed out the kinetic importance of the mean

free path traversed by the gaseous molecule, the questions relating to 

the viscosity of gases were placed on a new theoretical footing by the 

remarkable results of Maxwell.6 Using Stokes's7 results to treat the 

viscosity of air, Maxwell is able to express the mean free path of the 

molecule absolutely. The data here in question were derived by Cou1 S. W. Holman: Proc. Am. Acad. Arts and Sci., vol. 21,1886, p. 1; Phil. Mag., London (5), vol. 21, 1886, p. 199.

2 O. E. Meyer: Pogg. Ann., vol. 127, 1866, pp. 253, 353.

3 Graham: Philos. Trans. Roy. Soc., London, 1846, p. 573; ibid, 1849, p. 349; Ann. 

der Chem. und Pharm., vol. 76, 1850, p. 138.

* Die kinetische Theorie der Gase, Breslau, 1877, p. 123.

6 Clausius: Pogg. Ann., 4th series, vol. 15, 1858, p. 239.

"Maxwell: Rept. 295th Meeting Brit. Assoct, 1859 (1860), notices, etc., p. 9; Phil. 

Mag. (4), vol. 19, 1850, p. 19. Less closely allied results in Phil. Mag. (4), vol. 20, 

I860, p. 21.

7 Stokes: Trans. Cambridge Philos. Soc., vol. 9, 1850, p. *166 ; ibid., vol. 10,1851, p. 

105. Portschr der Phyaik, 1850: 50; p. 101; Phil. mag. (4) I, 1851, p. 337.

- (894)
BABUB.] VISCOSITY OF GASES. 241

loinb's method of vibrating plates, a method which does not serve well 

for the determination of the thermal relations of mean free path, although 

it has been applied with this end more or less fully in view by Meyer,1 

by Maxwell 2 himself, by Puluj, 3 and others. Among these observers 

only Puluj, using an apparatus devised by Kundt and Warburg, succeeded in deriving good results. Very important service was therefore 

done to this branch of molecular kinetics by the elaborate researches 

of O. E. Meyer.4 Availing himself of the general differential equations 

for the motion of a viscous fluid published by Stokes,5 or those more 

recently published by Stefan,6 O. E. Meyer deduces the well-known 

equation, in which the rate of transpiration is fully expressed in terms 

of the terminal pressures, the viscosity of the gas, the coefficient of 

external friction, and of the dimensions of the capillary tube through 

which the gaseous flow takes place. Calculating from this result the 

volume of gas transpiring during a given time, under given conditions, 

Meyer reaches a result which, for gases, is the complete analogue of the 

law for liquids experimentally deduced by Poiseuille 7 and Hagen, 8 and 

to which Stokes 9 and others (Neumann, Wiedemann, Hagenbach, Stefan, Helmholtz) have given a theoretical foundation. It is by using 

this equation that Meyer 10 himself, discussing Graham's results, in later 

work,11 partly in conjunction with Springmiihl, 12 derived the first good 

results for the thermal coefficient of viscosity. Such results have since 

been obtained in greater number and with greater elegance in transpiration experiments, made by Puluj,13 v. Oberinayer, 14 E. Wiedemann,15 

Warburg,16 Schumann, 17 and particularly by Holmau,18 to whose elegant 

and elaborate researches I have already referred.

In all of these cases, however, the data in hand are essentially lowtemperature results. The largest range of temperatures occurs in 

Oberrnayer's later research,, in which the thermal relations of the visJ 0. E. Meyer: Pogg. Ann., vol. 125, 1865, p. 177 ; 5th series, vol. 23, 1871, p. 14.

2 Maxwell: Phil. Traus., 1866 (I), p. 249.

3 Puluj: Wien. Sitzungsber., vol. 73 (2), 1876, p. 589.

< O. E. Meyer: Pogg. Ann., vol. 127, 1866, pp. 253,35:3.

5 Stokes: Trans. Cambridge Philos. Soc., vol.8,1847, p. 287.

6Stefan: Wien. Ber., vol. 46 (2), 1862, p. 8.

7 Poiseuille: Mem. Sav. E"trang., vol. 9, 1846, p. 433; Ann.ch. et phys. (3), vol. 7, 

1843, p. 50.

»Hagen: Abh. cl. Berl. Akad., 1854, p. 17.

9 Stokes: Trans. Cambridge Philos. Soc., vol.8, 1847, p. 287. 

10 Meyer: Pogg. Ann., vol. 127, 1866, p. 367. 

"Meyer: Pogg. Ann., vol. 148, 1873, p. 1; ibid., p. 203.

12 Meyer u. Springmiihl: ibid., p. 503.

13 Puluj: Wiener Sitzungsber., vol. 69, p. 287 ; vol. 70, p. 243, 1874.

H V. Obermayer: Wiener Sitzungsber., vol. 71, 1875, p. 281; vol. 73, 1876, p. 433.

1S E. Wiedemann: Fortschr. d. Physik, vol. 32, 1876, p. 206.

1(3 Warburg: Pogg. Ann., vol. 159, 1876,p. 403.

17 0. Schumann: Wied. Ann.,vol.23, 1884, p.353.

l» Holmau: Proc. Ann. Acad. Arts and Sci., vol. 12,1876,-p. 41; ibid., vol. 21,1886, p. 1.

Bull. 54 16 (895)
242 MEASUREMENT OF HIGH TEMPERATURES. IBULL.S*.

cosity of a number of gases are studied between 21° and 280°. Mr. 

Holinan's later researches go as far as 224° for OO2 and 124° for air. E. 

Wiedemann observed in thermal baths of steam (100°) and aniline 

vapor (185°). Hence, if the transpiration data are eventually to subserve the purposes of temperature measurement, it is necessary in the 

first place to investigate the law of variation of viscosity and temperature for a range of variation extending above 300° as far as possible 

into the region of white heat.

Since this law is necessarily a fundamental consideration it will be inexpedient to report my work in the chronological order of development. 

It will be preferable, first, to give such results as have an immediate 

bearing on the law in question, and then to extend the work by an 

investigation of the flow of gases through tubes to which the term 

"capillary," taken in the sense of the conditions under which Meyer's 

formula holds, does not strictly apply. For very short tubes Navier1 

investigated the theory of efflux; for very long tubes these conditions 

are equally well known from the stated investigations of Poiseuille and 

Meyer. For tubes of intermediate dimensions, however, the information in hand is comparatively meager, although recent investigations of 

a relevant character have been published by Osborne Reynolds,2 by 

Guthrie,3 and by Hofl'mann.4

TRANSPIRATION SUBJECT TO THE POISEUILLE-MEYER LAW.

APPARATUS.

General disposition of parts. The great degree of perfection which 

Professor Eichards5 has attained in his jet aspirators suggests the use 

of this apparatus in the present experiments in a manner similar to 

that employed by Holman. Such adjustment was at first contemplated. 

Reasons, however, into which I need not enter here, together with the 

fact that in Some of the experiments larger pressures were demanded 

than those which the jet-pump could furnish in our laboratory, led to 

the employment of absolute methods and of the special apparatus now 

to be described. It consists essentially of two large vessels, one placed 

as far as may be necessary above the other and connected by wrapped 

rubber tubing. The upper of these vessels is filled with mercury and 

the lower contains the dry air to be forced through the train of capillary tubes in connection with it. IE this way a column of mercury of 

any desired height is brought to bear on the lower vessel, and the de. 

tails of adjustment are then to be such that this pressure may remain 

constant throughout the course of the experiment.

*Navier: M6m. Acad. Roy. des Sc.,voi. 9, 1830, p. 336.

2 O. Reynolds: Roy. Inst. Gr. Brit., 1884, p. 1; Beibliitter, vol. 10, 1886, p. 217. 

3 Guthrie: Phil. Mag.,.5th ser.. vol. 5, 1878, p. 433.

4 Hoffmann: Ann. der Physik, Wiedemann. new series, vol. 21, 1884, p. 470. 

6 Richards: Am. Jour. Sci., 3d series, vol. 8, p. 412; Trans. Am. Inst. Mining Engineers, vol. 6, 1879, p. 492.

(896)
UAKUB.l VISCOSITY OF GASES. 243

In Fig. 43 the apparatus for producing the pressure in question is 

fully given. The scaffolding consists 

of four vertical tubes of gas-pipe, «&, 

«&, «,&, db, about 15cm apart and 200cm 

high. They are screwed below to a 

suitable base and coupled together . 

above, forming together a long rectangular column of square section. 

The tops of each tube end in vertical 

and lateral screws «, a, a} a, to which 

similar pipe may be attached, either 

vertically or horizon tally, thus greatly 

increasing the efficiency of the standard either for the present purposes 

or for use in supporting the manometer tubes of an air thermometer (cf., 

pp. 168,209). The two vessels for mercury are sho.wu at A and J?, of which 

B is stationary, while A can be raised 

to any necessary height by the cord 

F Gr H passing over the pulley G and 

fastened by a flat-headed thumbscrew, H. The vessel A is practically 

a Mariotte flask, provided with a 

stop-cock at G. B has a similar stopcock atD, and the connecting rubber 

hose is shown at CE D. These connections, in addition to the stop-cocks 

C and D, should be of wide bore, so 

as to insure a nearly Motionless flow 

of mercury.

The head of the vessel B communicates with the capillary tube J, 

carries the open mercury manometer 

H for the measurement of pressures, 

and is in connection with a stop-cock 

(not shown in figure), by means of 

which atmospheric air or any other 

gas may be introduced into B through 

a desicating tube. As this will be 

more clearly shown in the diagram 

below, I need only say that the capillary tubes are shut oif by a faucet, 

K. Finally, a wide lateral tube, 

P Q, in communication with the

. (897)

FIG. 43. General disposition of apparatus 

for viscosity measurement. Scale TV
244 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

rubber hose at P, enables the observer to let the mercury flow into 

the receiver B from above by closing the stop-cock D. As this is 

the special feature of the present apparatus, and is essential for the 

maintenance of constant pressure, I will describe it further. Suppose 

the Mariotte flask A to be hoisted in and fixed in the high position; 

suppose the receiver B filled with air, and communication with the 

atmosphere and with the capillary tubes to be shut off, moreover, the 

stop cocks C and D closed. If now G be opened, mercury will flow 

from A to B through the hose and the lateral tube P Q. The head of 

mercury urging the influx will be the difference in height between Q 

(the point of influx) and the lower end of the tube d in the Mariotte 

flask A. The flow will continue until the manometer E registers the 

equivalent pressure. If, now, the stop-cock K of the capillaries be 

'opened, the air from B will be very slowly discharged into the atmosphere and the mercury from A will slowly flow into the receiver B, entering it from above in such a way that the pressure-is maintained constant throughout the course of the experiment; for the head of mercury between Q and the Mariotte level remains unchanged until B is 

quite filled, and the pressure value of the head is read off on the manometer R. Special care, however, must be taken with the construction of the Mariotte flask; for inasmuch as the flow from such a flask 

is necessarily intermittent, the period of iutermittence must be reduced 

to the smallest possible amount by compelling the air to enter A 

through d in very small bubbles. The lower end of the tube d is therefore drawn out into a capillary of, say, 0.05cm diameter, which is ground 

off obliquely in the usual way. It is still better to let the lower part 

of d end in a series of capillary platinum tubes, all cut off obliquely, 

with their open mouths nearly in the same horizontal plane. Air thus 

enters A in a spray of fine bubbles, and the intermi fctence seen at E,

even in the most unfavorable cases of extremely slow efflux of gas out 

of .B, is reduced to 0.01cm and less.

'.The air in B enters the capillary tube through the stop-cock K, as has 

been said. The capillary platinum tube itself is shown at J, and is 

wound in form of a truncated cone, so as to be uniformly heated by 

the adjustable burner n immediately below it, the gases of which are 

carried off by the adjustable chimney L. In other words, the helix of 

the platinum capillary tube is so wound as to lie quite withiu the zone 

of fusion of the Bunsen burner. The outer end of the tube I communicates directly with the air. The other end is soldered into a lateral 

arm of the tube K by means of resinous cement. In order to keep the 

joint cold and the inner end of the capillary at a known temperature 

a rapid current of cold water from the hydrant flows through the cylindrical sheet-iron box m, which surrounds the joint.

Apparatus for constant pressure. This form of apparatus was used in 

the earlier experiments, and the results obtained by means of it, some 

of which will be cited below, proved the feasibility of this method, at

(898)
BABua.1 Viscosity OF GASE&. 245

least for empirical temperature measurement, beyond a doubt. In later 

experiments the proximity of the burner n to the receiver B was found 

objectionable, and the cramped arrangement of this part of the apparatus interfered in other ways with accurate measurement. Ketainiug 

the essential features of Fig. 43 the apparatus was modified as follows:

In Fig. 44, B B is the receiver into which the mercury flows on passing out of the Mariotte flask. The lettering of this figure is in conformity with that of Fig. 43, but the disposition chosen is such as to 

show additional parts. The manometer R R1 R1 is here very clearly 

given, quite filled with mercury, as is the case at the outset of the experiment. It will be seen that as the pressure in B increases, the mercury in the reservoir R' R' passes into the tube R, leaving a vacant 

space in R' R1 above the lower meniscus. But as the experiment proceeds, and the receiver B fills with mercury, this metal eventually falls 

into the communication tube r, while the air displaced escapes into B 

through the capillary tube s. Hence each time B is filled with mercury 

a fixed volume of air must pass out of it, and the manometer R R' R' introduces no discrepancy. The cock D being closed, mercury falls into 

B from Q, as the column passes through the lateral tube P UQ. The top 

of R'R' is cut off obliquely, so as to guide the descending drops or little 

stream of mercury at once into B. The drying-tube of the apparatus 

communicates with «?, and may be shut off by the faucet 8. In this 

way dry air or any other gas may be easily introduced. The capillary 

tube is here placed at some distance from B and in connection with the 

lateral tube fc. A small sensitive thermometer sealed in the vertical 

tube T indicates the temperature of the gas as it escapes into the 

capillaries. For the sake of clearness in diagram the tubes $, JK, T 

are represented as placed in a single vertical plane. In practice the 

rubber cork is perforated symmetrically and larger tubes may be chosen. 

The tube P Q comes apart at Z7, and hence the tubes and the manometer 

may be easily withdrawn from B. When in use it is necessary to seal 

in the cork and the divers glass tubes with resinous cement.

It is easily seen that after B is full of mercury the Mariotte flask A 

may be lowered, and on opening the stop-cocks D and S mercury will 

flow back from B to A. The receiver B is thus filled with dry gas and 

again ready for experiment. But the order of manipulation is important, and will be indicated in connection with the data given below.

In using the method of compression preferably to a method of exhaustion, by both of which a flow of gas through the tubes can be 

secured, I was guided by the belief that the methods of measurement 

in the former case are more easily capable of variation. This the present 

chapter may show. Again, the tendency of the dissociated hydrocarbon gases of the burner to permeate the walls of the platinum capillary 

tubes at high temperatures, is of less disturbing effect when the current 

of gas is condensed than when it is rarified.

The capillary apparatus. In Fig. 44 there is ample room for air to

(899)
246 ' MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

FIG. 44. Diagram of receiver for distributing pressure. Scale J.

(900)
VISCOSITY OF GASES. 247

pass around the thermometer in the tube 

T, and thence by the lateral tube ft into 

the capillary apparatus. This is shown 

in side elevation in Fig. 45 and in plan in 

Fig. 46. The figures are sectional, and 

the lettering of Fig. 43 is retained. The 

scaffolding and non-essential parts are 

omitted. Regarding this figure in its general purposes, I will say here that there 

are three ways in which viscosity has 

been measured:

1. By measuring the time of efflux of 

the fixed volumes of air in B through the 

capillaries.

2. By measuring the rate at which air

passes out of the capillaries.

3. By differential methods.

The first of these methods is not generally as convenient as the second, because the volume of B is relatively large, 

and the time of efflux may become enormously large. Hence in my final experiments I used the second method, and it 

is to this that the present description 

largely applies. The gas enters from the 

tube /c (Fig. 45) through the stop-cock K, 

thence it passes through the tube g li into 

the coil of platinum capillary tube J, and 

out of this into the graduated tube llll, 

filled witti water. Here it is measured. 

The tube IIII is simply an inverted burette of about 60CC capacity. After filling it with gas and taking the observe, 

tion it is made ready at once for the next 

experiment by sucking the water out of 

the pneumatic trough M M up into the 

tube through the stop-cock o and closing 

it. To insure constancy of temperature 

this tube 11II is jacketed by a larger 

tube, i i i *, through which a rapid current 

of water, entering by the tube p <, continually circulates. The water escaping 

from the bottom ofiiii keeps the trough 

MM full of cold water, and finally escapes 

by-the lateral efflux pipe X. The upper 

vertical tube q is used in filling iiii with

(90X)

FIG. 45. Side elevation of capillary apparatus. Scale £.
248 MEASUREMENT OF HIGH TEMPERATURES. I BULL. 5i

water at the outset of the experiment, and is then closed by a pinchcock. It is easy to make the current swift enough to keep both the tube 

and the trough at a constant temperature even when the helix I is 

heated to extreme white heat.

The helix of the platinum capillary tube is wound in the form of a 

nearly compact spiral and with the internal radius just large enough 

to admit the insulator of the thermo-couple. Smaller and more compact 

coils are favorable to constant temperature throughout the length of the 

capillary tubes. It is convenient to use two or more such capillary tube, 

wound side by side, so as to make what may be called a fasciculated 

helix. The anterior ends of these capillaries are soldered to a small 

longitudinally perforated brass cylinder /«, which is then hermetically 

sealed into the adit tube g h. The posterior ends of the capillaries, which, 

like the other ends, return to the trough MM, are bent slightly upward, 

so as to discharge the gas into till. As leaks are fatal to the temperaFIG. 46. Plan of the capillary apparatus. Scale £.

ture measurement at I, the platinum tubes must be carefully soldered 

into the vertical wall of the trough M M, through which they pass. 

Soldering the tubes in place and sealing them is a difficult operation, 

and too much care can not betaken in guarding against clogging of the 

minute capillary canals. Moreover, solder must be kept away from the 

parts of J which are heated. Insufficiently cautious manipulation in 

this respect ruined more than one of my tubes. Unfortunately, the'only 

satisfactory check on the degree of perfection of the adjustments made

(902)
VISCOSITY otf GASES. 249

is given by an inspection of the results obtained. Any flaw in the connections can therefore be remedied only at the expense of much time.

Differential apparatus. Before passing to the method used for heating 

it may be well to insert a few remarks relative to the differential apparatus. This is closely analogous in character to a differential galvanometer, and the rates of transpirations through tubes, one of which is hot the 

other cold, are compared. The arrangement of this apparatus is readily 

seen in Fig. 46. A lateral arm, X /', of the tube g h communicates with 

the cold helix J', which is completely submerged in the water of the 

trough M M, and provided with its own graduated tube I' I and waterjacket i i'. Except in temperature, the capillaries and their pneumatic 

appurtenances are identical in form. Certain special desiderata will 

be indicated below.

Method of heating. All the soldered parts of the capillary apparatus 

being thus thermally protected by a current of water from the hydrant, 

the heating of the spiral is not a difficult problem. To make observations at the low temperature (as near 0° C. as couvenient) a current of 

water may be showered upon the helix out of the water pipes. But it 

is equally good to siphon the water out of the trough M M. For 100° 

the helix is appropriately surrounded by a non-conducting tube, through 

which steam circulates freely. Admirably constant mean temperatures 

are obtained as high as 1,000° by simply heating the helix in a chimneyed 

Buuseu burner. For 1,300° the Bunsen burner is replaced by a blastlamp fed by a regular current of air. In the case of these high temperatures the helix is surrounded by a cylindrical tube of asbestus, as 

shown at n n, Figs. 45 and 46. These cylinders are exceedingly convenient and may be made by soaking asbestus board in water and rolling it around a cylindrical stick of suitable diameter. After drying, 

the cylinders are ready for use, Parts liable to breakage are, of course, 

protected from radiation by asbestus screens. Such subsidiary screening is everywhere necessary1 , and need not be described here. Great 

difficulties were encountered in endeavoring to obtain satisfactorily constant temperatures between 300° and 1,000°. After much vain searching I finally tried an ordinary oil student lamp for the purpose, and obtained excellent results. The space in the chimney of such a lamp above 

the flame is available for a hot-air bath. In Fig. 45, n' n' shows the 

position of the chimney of this lamp. The temperatures thus obtainable, besides being constant or of very slow regular variations (increase)

(903)
250 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

may be made to differ over quite a wide range, as is shown by the following table:

TABLE 80. Thermal constants of the oil student lamp.

d

cm.

2

2 

2

2

3 

14

14

14

9

9

3 

3

14

14

Time.

in.

0

7 

14

21

10 

20

30

25

30

40 

60

63

69

e

4168

4201 

4255

4288

7437 

7593 

7647

7784

10690

10690

9563 

9563

11490

11490

6"

o

414

416 

421

423

669 

681 

685

695

904

904

825 

825

956

956

Incipient fusion of the glass 

chimney surrounding the 

flame. Devitrification.

Eemarks.

0

 Very low flame.

^Low flame.

j

1

 High flame.

J

} S Flame very high.

In Table 80, d denotes the depth of the junction of the thermo-couple 

below the top of the chimney, which top is about 20C1U above the mean 

height of the flame. 6", e, denote the temperature and the corresponding thermo-electric force of the thermo-couple used for measurement 

at the time given in the second column. The thermo-couple in this 

instance was No. 39 (calibrated above), and the junction, after being surrounded by a little cushion of carded asbestus, was enveloped 

by a jacket of thin platinum foil fastened to the stem insulator. The 

junction is, of course, placed in the axis of the chimney, since temperature decreases towards the walls. The highest temperatures are obtained by enveloping the chimney in the cylindrical tube of asbestus 

referred to above, in which case the glass is easily fused. Lower temperatures than those of the table may be obtained by lengthening the 

chimney .with the asbestus tube and observing near the top. The auxiliary tubes are suitably wired in position.

In addition to the large interval of temperature, the Argand lamp has 

the advantage of furnishing an air bath. Since platinum is pervious to 

hydrogen (see below), direct exposure to the Bunsen flame introduces 

an error because of the hydrogen which passes through the metal. But 

this error does not seem to be serious unless the temperatures are very 

high.

In all these cases the mean temperatures are satisfactorily constant, 

but it does not follow that temperature will be constant throughout the

(904)
VISCOSITY OF GASES. 251

volume of the platinum capillary. Indeed, variations of 100° within the 

spires of the helix at temperatures as high as 1,200° are not impossible. 

If, however, the interior of the helix be filled with some non-conducting 

substance like asbestus fiber, and the exterior surface be snugly surrounded by a little box of non-conducting substance, like mica, the degree of constant temperature is much improved. Better results are obtainable by surrounding the helix with alternate layers of good and bad 

conductor. But in its practical application this method is troublesome, 

and I have therefore preferred to measure temperatures at both the exterior and the interior surfaces of the helix. In the final experiments 

two thermo-electric junctions were in contact with the outside and one 

with the inside of the helix.

Pressures were read off in mercury columns by aid of the Grunow 

cathetometer already referred to. It is frequently necessary in this apparatus to open the stop-cocks at particular pressures. To obtain these, 

preliminary experiments are made ("EinscUessen"), and the desired 

positions of the meniscus are indicated by adjustable fiducial marks.

For the measurement of intervals of time an excellent chronometer 

of Brooking in Hamburg was available.

METHODS OF COMPUTATION.

The general equation. The computations of the present memoir are 

based on the Poiseuille-Meyer transpiration formula, the special application of which to gaseous flow is due to Meyer. 1 It is available in two 

forms. The first form is

where u denotes the velocity of a particle at a radius, r, from the axis 

of the capillary tube, the diameter (bore) and length of which are 2jK and 

£, respectively ; where Pand p are the pressures at the two ends of the 

capillary tube, and where ij denotes the coefficient of internal friction 

(viscosity), C the coefficient of slip (Gleitung's coefficient). The second 

form is obtained by integration from equation (1). It contains a new 

variable, viz, 7i the volume of gas transpiring through any section of 

the tube where the pressure is pi during the time t.

nt Pz

(2)

If this equation is to be used for the absolute evaluation of 77 it must

P2_p2

be borne in mind that the dimensions of 7-^- are those of a pressure.

Hence if P and p have been expressed in terms of the heights of columns of mercury, the factor 6g must be inserted in the right-hand inem1 Meyer: Pogg. Ann., vol. 127, 18G6, p. 269. 

(905)
252 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

ber. Here d is the density of the mercury column and g the acceleration of gravity at the place of observation. With this introduction 

the dimensions of 77, commuted from equation (2), are \iml~1 T~^ which 

are identical, of course, with the dimensions required by the fundamental formula of viscosity, or by the well-known equation of Maxwell, 

77=0.318p.QZy, deduced in the kinetic theory of gases. Equation (2) 

shows, moreover, that the dimensions of C are linear, agreeing with the 

thermo dynamic interpretation of C, which is proportional to the mean 

free path of the molecule of a gas. C has been called " Gleitung's coefficient" by Helmholtz, a name, the appropriateness of which appears,

inasmuch as C= - where e is the coefficient of eternal friction of the

e 

gas.

Neither formula (I) nor formula (2) contain direct reference to the 

temperature at which transpiration takes place. Such reference is, 

however, implied in the p occurring in the denominators of (1) and (2); 

for the value of p is given by Boyle-Charles's law as

3)

where p and 6 are the density and temperature corresponding to the 

pressure #, and where Jc is constant.

Regarding the general applications of (1) and (2) I will say that the 

derivation of these equations presupposes that p and p are independent 

of r, or that for the points of any given right section of the tube p and 

p are constant. Again it presupposes a nearly steady now, such that the

fJni

differential coefficients of u? and -,-. i. e., dx

du dhi d*u 

dx"1 dx*"1 dxdr'

where X is measured along the axis of the tube are practically zero. 

Finally equations (1) and (2) are true only for circular sections. In the 

case of elliptic sections, 1 with semi-axes a and 6, the equation (2) becomes (supposing C=0)

(3)

so that the equation, when a and & are not known, can only be used for 

the interpretation of relative measurements.

Case of two cold ends, absolute apparatus. Equation (2) is available 

for experimental measurement in a variety of ways. It presupposes, 

however, that the temperature of the capillary tube be the same throughout its length. This is, of course, a feasible precaution, for it is only 

necessary to weld the platinum capillary to platinum terminal tubes

1 Meyer: Ibid., p. 364 ; Matthieti: C. R., vol. 57, 1863, p. 320. 

(90G)
VISCOSITY OP GASES. 253

of larger bore. Methods of doing this will be described below. Such 

apparatus would, however, be expensive, and in an introductory investigation, in which easy variation of the capillary bore is one of the 

desiderata, the use of fixed forms of apparatus is unadvisable. Hence 

I have made use of platinum capillary tubes with cold ends in the way 

described in the preceding paragraph, inasmuch as these can be drawn 

down from the original to any. smaller radius, and then inserted into the 

pneumatic apparatus with comparative facility. The cold ends, however, introduce an error of a serious kind, for which allowance must be 

carefully made. Fortunately this can be done with ease and accuracy 

by successive applications of Meyer's equation.

As before, let R, L, 6, t be the symbols of radius, length, temperature, 

and time. Let the platinum capillary tube be supposed to be made up 

of three parts, I', Z", I1 ", so that l'+l"+l'"=L. Let the variables referring to these parts be similarly accentuated, Then the following scheme

of variables presents itself:

P V T! 1 1' R1 t1 -n 1 A+P ii1 V" 7?" 7" fi" i" -n" Afp n" V" 7?"' 7"' fl'" t111 «"' off « r yj.it yi t V )i jff ) ouC. ]) V }/!' j 6 , U , I ) t[ , ctlf* JJ r ^ J.\i ,6 ,u ,( ,// j (3uG. JJ

Of the three partial tubes thus given the first and third are ends, and 

-t-r hence I' and I'" are small as compared with I", and 6' and 0'" small as 

compared with the high temperature 8". Applied to the apparatus 

described, the following simplifications are admissible: R'=R'"=R') 

rf=r/"=rj] 6' =6'"= 6; moreover V'pl =V"p"=V'"p'"=Vp, and 

t'=.t"=t'"~t. The successive application of Meyer's equations thus 

leads to

16

(4)

Now, if ft be the mean coefficient of expansion of platinum, so that 

R"=R0" (!+/? 6") (R and R0 being supposed identical), I find finally that

' - 16 ~Y~ V-F~. ~ r

' L 1+4£ J (5)

If this equation is to express rf1 absolutely, and if P and p are measured in heights of columns of mercury, the factor dg must be inserted 

in the right-band member, as before (page 252). [Regarding the other 

quantities it is clear that they are measured in terms of c. g. s. units. 

The temperature of V is 0.

Equation (5) is capable of much simplification. In the above appal1 JL.IIH

ratus RO"=RO', hence care must be taken either in making ~ln as i

small as possible, or I1 and V" must be correctly measured. In the 

above apparatus very close contiguity of hot and cold parts of the spiral

(907)
254 MEASUREMENT OF HIGH TEMPEEATUEES. [BULL. 54.

is secured by the use of running water in the way described. Moreover

77 is small as compared with 77", because long ranges of temperature are

/ T> /t^t 

met with. In view of the factor ( -JL ) it is obvious that the corrective

\KoJ 

factor may be made to vanish speedily by selecting terminals of larger

bore. If 6=6", and therefore 77=77", equation (5) reduces at once to 

equation (2), supposing of course that R0"=R0 .

Case of two cold ends, differential apparatus. With this result in hand 

the question with regard to the equations applying to differential apparatus of the kind sketched above (page 250) is next in order. For the case 

of the hot helix there applies as before

) p V I"

and for the cold helix, the temperature of which is uniformly

V ,

whence, very nearly,

Now, if the two helices be identica.1 in radius and length, and if the 

times of transpiration be also identical, then, since t=tc ] Lc=Lj Z?0"=

14. +

R" l+ad V- L ^ 4 ....... (7)

Again, if as before, R" 0=R0=RC , and L=LC , but the same volumes 

are found to transpire in the times t and tc ; then, since V Vc

 n"

IT £ £

(908)
BAHUS.] VISCOSITY OF GASES.

Finally, if 6 6" equation (6) furnishes a very simple equation for the 

ratio of radii of capillary tubes. For if t=te

a relation which is frequently of use. 

c

EXPERIMENTAL RESULTS.

Manipulation. In describing the present series of experiments it will 

be advisable to proceed somewhat explicitly ; for the methods were frequently varied, and variations of an apparently trifling kind were frequently found of great practical importance. Neither is it expedient to 

retain wholly the chronologic order of experiment. The following tables, 

81 to 89, represent a connected series of experiments, in which the method 

used is gradually perfected, and in which the data therefore approach the 

true law of variation more fully as the experiments proceed.

In making these experiments the apparatus, Figs. 44 to 46, was used. 

The air which had transpired was therefore caught after efflux from the 

capillary tubes. Inasmuch as the receiver B is very large (550CC) and 

transpiration through the capillary tube takes place at a very slow rate, 

almost no effect is produced in the pressure of the gas in B when the 

cock K (Figs. 43, 46) is opened. This is a great convenience in manipulation and suggests the following scheme of operations : Suppose the 

Mariotte flask to be in its lowest position on the standard, aaaa bbbb, 

all cocks except JTopen, and the Mariotte uncorked. Mercury will then 

have run back into A, and the reservoir B will be filled with dry air. 

Now, close the cocks C and 8 and cork the Mariotte. Hoist the flask A 

to the level above B desired, and clamp it. Open C slightly at first 

until the mercury is seen just above D and then close D. Mercury will 

then flow into B through P U Q (the cock G being now fully open) until 

the maximum pressure is registered by the manometer R R'U'. Both 

the lower and upper meniscus of this are read. The gas in B is therefore 

practically under the pressure under which it is to be passed through 

the capillaries. Inasmuch as the volume of B is more than ten times 

as large as the volume to be measured after efflux, the pressure apparatus is ready for a number of consecutive experiments. After the 

receiver is quite filled with mercury and the cock Kis closed, C is closed 

also and the Mariotte flask is lowered and unstopped. Dis now opened 

and G is opened cautiously, so as to take the pressure out of the manometer. After this is done Sis opened, whereupon C may be fully 

opened and the mercury thus flows back to A, while B fills with dry 

air. The operations are then repeated and the gas in B is put under 

pressure for the next ten experiments. This is the mode of experimentation in the main, although accidents or divers special purposes suggest 

slight variations of it. It is desirable to draw no air through the ma-

(909)
256 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

nometer R E' B' ; for not only will such air be moist, but the mercury 

hurled out of E' R' by bubbling displaces the lower meniscus to a seriously low level some times. During the experiments the lower meniscus 

remains constant in level. Hence the upper meniscus need be read only 

for the detection of slight variations, and the fact that the lower meniscus is finally hid by the surrounding mercury is no disadvantage.

Nomenclature. The results were computed from equation (5), on page 

254. The data in the table are similarly designated, and their full signification is as follows:

P is the pressure of the gas at influx, i. e., when it enters the platinum capillary. P therefore is the zero height of the mercury column 

in the manometer plus the zero height of the barometer. Correction is 

to be made for capillary depression of the upper meniscus of the manometer. Correction is also to be made for optic displacement of the 

lower meniscus of the manometer when seen through the walls of the 

reservoir B (Fig. 44). As the mean effects produced by these two 

errors were in an opposite sense, and nearly the same in magnitude, I 

did not apply them. Moreover they have no effect on F (6"}.

p is the pressure of the gas at efflux. Hence it is equal to the zero 

height of the barometer increased by the mercury value of the depth 

of the efflux tubes below the level of water in the trough. Perhaps p 

ought also to have been increased by the capillary reaction effect of 

water at the point of efflux. But as I could not estimate this, I used 

large values of P in order to secure as steady and rapid a flow as permissible.

t is the time which corresponds to the volume of gas F0 measured 

after transpiration. It is usually advisable to make t nearly constant 

and measure the variation of F0 . The time errors made in opening and 

closing the stop-cock K are not larger than one-fifth of a second. Hence 

t can be measured sharply.

F0 is the volume of dry air escaping at the normal pressure 76cni 

and temperature 0° C. F(page 248) being the true variable, some pains 

must be taken in correcting it. In the first place, inasmuch as F is measured over water, it must be reduced to dryness, to zero centigrade, and 

to 76cm. This is conveniently done by the aid of Landolt and Boernstein's tables, it being remembered that Fis under atmospheric pressure 

minus the mercury value of the residuary column of water in the burette llll. Finally V must be corrected for the solubility of the gas, 

which in case of air may be neglected, but in case of hydrogen is as 

large as 2 per cent. Formula (5), however, calls for F at 6 and p. 

Hence, if Fis reduced at once to 0° and 76cm by tables, it is convenient 

to transform formula (5) into

rf' _ _

76 Fo I" l+4CV^o/ V

(910)
i« HUB.] VISCOSITY OP GASES. 257

Vp which easily results since .. , 0=76. F0 , and the effect of (l+a0) on the

corrective member of formula 5 may be neglected, when 6 is small.

Finally, Fmust be corrected for the amount of air left in the adit tube 

<7 7t, after the cock is closed. To reduce this dead space to the smallest 

value it is desirable to fill np the tube g Ji partially with glass rod. The 

residual space is easily measured, as follows: Let r be this residual 

volume. Then, if in the time £, which elapses between opening and 

closing the cock ft, the volume V escapes into the measuring tube, the 

volume ultimately found there is a= V+r. Again, if during the same 

time t the cock had been opened and closed n times (delays of opening 

and closing supposed to be allowed for) the volume found in the 

measuring tube is b= V-\-nv, Hence

whence v may be found.

0 is the temperature of the cold ends V and V" of the capillary as well 

as the temperature at which the wet air in the burette is measured. It 

is determined by submerging a thermometer in the trough MM.

6" is the temperature of the hot part I" of the platinum tube. Eeinarks concerning its measurement will be found with each table since 

this variable is the difficult one to evaluate correctly. The measurement of the actual value of 6" is directly dependent on the degree of 

constant temperature in the helix,

JR, finally, denotes the radius of the capillary tubes. It is this quantity 

which, in case of fine opaque capillary tubes, it is exceedingly difficult to 

determine. In some of tlie experiments below I subsequently filled the 

tubes with mercury in ways there to be indicated, and weighed the 

thread. But in the experiment. Tables 81 to 89, I did not wish to endanger the platinum tubes by employing this method. Nor did I think 

it safe to apply volumetric methods like those described on pp. 195, 214. 

The only procedure left therefore consists in weighing (mass m) 

known lengths, £, of the capillary, and measuring the external diameter R(X by screw calipers. From the known density 8 of platinum the 

internal radius M may be calculated at once in its square value as

Unfortunately this is a crude method at best, and the problem is even 

more seriously difficult, because formula 6 calls for thefourth power of B.

Hence the absolute values of rf 1 and 77 in the table are distorted 5 but 

since this distortion is uniform for all data, and since it does not therefore 

affect the relative values, the errors introduced by incorrect R do not 

Interfere with the chief purposes of the present investigation.

The attempt to obtain absolute values from metallic capillary tubes

Bull, 54 1? (9U)

V /
258 MEASUREMENT OF HIGH TEMPERATUKES. [BULL. 54.

is perhaps futile. It is impossible to guaranty that in such tubes the 

radius is either rigorously uniform throughout the length of the tube 

or that the capillary canal is truly circular in section. Coiling of tubes, 

so essential in very high temperature work, also flattens the section. 

In drawing tubes flaws or splinters of metal partially projecting iuto 

the capillary canal can not always be obviated. But all these effects 

are not hurtful where relative results are alone of interest. This is, of 

course, the case in pyrometry.

Hydrogen and air, as used in the following tables, are not intended 

to refer to absolutely pure gases. Both gases were dried, of course, in 

the usual way. But the hydrogen may contain traces of air or sulphide, and the air was not freed from carbonic acid. My object in the 

following experiments was to test the possibility of an identity of law 

in the case of two thoroughly different gases, the zero properties of each 

of which were continually redetermined, i. e., before each experiment. 

Inasmuch as these gases are to be true gases, all vaporous constituents 

were to be excluded. At high temperatures, however, even this precaution is not essential.

Data. Tables 8t and 82 contain the results of consecutive series of 

experiments made with air and with hydrogen, respectively. In these 

early experiments I did not venture to solder the terminals of the helix 

iuto the walls of the pneumatic trough from fear of injury to the tubes. 

Hence the trough leaked at high temperatures, and the water wetting 

the outside of the asbestus chimney or furnace which surrounds the 

helix and burner was the cause of an irregular distribution of temperature, which I did not foresee. Temperature being measured in the 

inside of the helix at a point nearest the trough is therefore

decidedly low, for it is here that the efl'ect of cooling the environment is seriously felt. The position of the thermocouple (No. 37, calibrated above) is nearly that given in 

Fig, 47. Moreover, the helix itself is naked, that is, not 

jacketed by an envelope of mica or other substance of low 

thermal conductivity. Temperatures near 1,000° are obtained by direct exposure to the flame of the chimneyed 

Bunsen burner; higher temperatures (usually above 1,200°) 

by exposure to the flume of the air-blast lamp. Temperatures below 800° (usually) are obtained in the air bath 

of the petroleum Argand burner, the chimney of which 

is suitably jacketed.

(912)

FIG. 47. Vertical 

section through 

helix. Scale £.
VISCOSITY OF GASESo 259

TADLE 81. Piscosily of air. Platinum capillary. Thermo-couple No. 37. 

[Capillary tube No. 10. i:=33.43 . I' H-Z"*-=4.4om. TJO = 0.0002508. 0 = 0°. ^=0.00794cra .]

p

124. 28

124. 28

124. 28

88.49

88.49

88.49

88.69

124. 66

124. 68

124. 76

124. 83

124. 51 

124. 64 

124.64 

124. 64 

124.63 

124. 61 

124.61

124. 77 

124. 84 

124.87 

124. 51 

124. 55

124. 55 

124. 73

124. 28 

124. 00 

124.01 

124. 01

124. 03 

124. 03

124. 77 

124. 77 

124.77 

124.77

194 *W

124. 53

194. ^n

124. 53

88.25

88.31

88.31

88.29

P

76.02

70.02

76.02

75.92

75.92

75.92

75.92

75.92

75.92

75. 92

75.92

75. 95 

75.95 

75. 95 

75. 95 

75.95 

75.95 

75.95

75.95 

75.95 

75.95 

75.95 

75.95

75.95 

75.95

76.19 

76.19 

76.19 

76.19

76.19 

76.19

76.39 

76.39 

76.39 

76.39

76.29

76.29

76.29

76 °9

76.29

76.29

7R 90

7fi 90

t"

165

162

ICO

770

810

795

810

155

160

160

ICO

725 

725 

760 

760 

780 

785 

810

935 

905 

900 

905 

 900

1485 

1470

1655 

1560 

1620 

1590

2080 

2110

20CO 

2070 

2085 

2040

160

.160

160

160

810

840

840

Yo

49 11

48.95

48.25

47.91

50.27

50.39

51.34

47.28

48.20

48.50

48.50

48.43 

47.73 

49.11 

48.11 

48.39 

47. 59 

48.44

49.85 

48.53 

48.49 

48.58 

48.44

49.74 

49.64

50.16 

47.66 

49.91 

48.56

47.67 

48.08

48.56 

49.16 

50.04 

49.30

48.75

48.71

48.65

48.71

50.49

50.60

50.60

6"

6

6

6

6

6

6

6

6

6

6

6

430 

442 

455 

464 

472 

483 

490

558 

554 

552 

546 

545

840

828

880 

871 

861 

865

1141 

1136

1127 

1125 

1114 

1104

6

6

6

6

6

6

6

6

1+4 £»/^"

2553

2558

0. 0002618

2625

2570

9fi1A

0. 0002557

2585

2580

2584

0. 0005255 

5265 

5276 

5324 

5370 

5425 

5463

0. 0005670 

5674 

5664 

5669 

5665

0. 0006824 

6869

0. 0007221 

7163 

7162 

7201

0. 0007829 

7903

0. 0007771 

7765 

7732 

7802

0. 0002546

2548

OKK1

2548

0. 0002619

2627

2627

2628

F(6")

2.096 

2.100 

2.105 

2. 123 

2.142 

2.164 

2.179

2.262 

2.263 

2.259 

2.261 

2.259

2.722 

2.740

2.879 

2.856 

2.855 

2.871

3.122 

3.151

3. 099 

3.096 

3.083 

3.111

(913)
260 MEASUREMENT OF HIGH TEMPERATURES. [BUM.. 54.

TABLE 82. Viscosity of hydrogen. 

[Capillary tube No. 10. £=33.i3cln. Z'+Z'"=4.4< . i)0=0.0001392.9=7°. J2=0.00794«m .]

p

124. 96 

124. 96 

124. 96

88.72 

88.71 

88.73 

88.75

124. 01 

124.62 

124. 62 

124.61

88.56 

88.60 

88.62

124. 53 

124. 54 

124. 58

125. 49 

125. 53 

125. 53 

125. 52 

125. 55 

125. 63 

125. 69

126. 71 

126. 55 

126. 67 

126.67 

126. 68 

126. 70 

126. 70 

126. 69 

126. 70 

126. 68

126. 53 

126. 57 

126. 64

Imm« 

126. 32 

126. 32

125. 35 

125.40

125. 02 

125. 02 

125. 03 

125. 06

P

76.72 

76. 72 

76.72

76.72 

76.72 

76.72 

76.72

76.72 

76.72 

76.72 

76.72

76.72 

76.72 

76.72

76.71 

76.71 

76.71

77.29 

77.29 

77.29 

77.29 

77.29 

77.29 

77.29

77.29 

77.29 

77.29 

77.29 

77.29 

77.29 

77.29 

77.29 

77.29 

77.29

77.26 

77. 26 

77.26

diately 

77.26 

77.26 

After 

77.43 

77.43

77.43 

77.43 

77.43 

77.43

t"

90 

90 

90

480 

485 

480 

450

90 

90 

90 

90

480 

460 

480

365 

360 

360 

Fresh 

380 

385 

395 

420 

420 

420 

440

530 

565 

570 

600 

600

780 

780 

780 

780 

815

1050 

1035 

1020

after th 

90 

89 

a day. 

90 

90 

Fresh 

90 

90 

90 

90

y

49.43 

49.47 

49.49

50.93 

51.58 

51.30 

48.06

49.34 

49.56 

49.60 

49.51

50.78 

49.15 

51.39

49.73 

48.62 

43.37 

lydroge 

49.99 

49.49 

49.65 

50.51 

49.49 

48.59 

49.52

50.26 

48.80 

48.22 

49.69 

48.12

48.40 

49.19 

48.89 

48.89 

50.92

48.'91 

48.98 

48.86

3 high-tc 

50.69 

50.19 

Fresh I. 

48.98 

49.02 

lydroge 

48.56 

48.45 

48.49 

43.52

9"

6 

6 

6

6 

6 

6 

6

6 

6 

6 

6

6 

6 

6

392 

380 

428 

i suppli 

398 

411 

424 

437 

452 

461 

474

565 

634 

644 

658 

668

848 

834 

835 

834 

'834

1006 

997 

994

mperatt 

7 

7 

ydrogen 

7 

7 

i suppli 

7 

 7 

7 

7

r,"

1+W/R"

0. 0001419 

1418 

1418

0. 0001497 

1478 

1488 

1491

0. 0001409 

1403 

1402 

1404

0. 0001481 

1472 

1470'

0. 0002749 

2747 

2874

Hi.

0. 0002792 

2810 

2822 

- 2899 

2905 

2932 

2968

0. 0003251 

3300 

3293 

3470 

3446

0. 0003807 

3766 

3786 

3791 

3799

0. 0004438 

4404 

4365

re measure 

0. 0001415 

1414 

supplied. 

0. 0001424 

1425 

3d. 

0. 0001425 

1428 

1427 

1427

F(6")

,

1.975 

1.974 

2.065

2.006 

2.019 

2.028 

2. 083 

2.087 

2.107 

2.133

2.336 

2.371 

2.366 

2.493 

2.476

2.735 

2.706 

2.720 

2.723 

2, 730

3.189 

3.165 

3.136

nent.
BAltUS.] VISCOSITY OF GASES. 

TABLE 82 Viscosity of hydrogen Continued.

Tro

48.52

48.56

48.02

48.98

261

p

125.07

89.43

89.41

89.42

P

77. 43

77.43

77.43

77.43

t"

90

480

480

480

0"

7

7

1+4-fe"

1428

0. 0001579

1574

1504

W

Bearing iu mind therefore that the curve

F(6")=-

as given by these results, is necessarily high, I constructed F(6") both 

for Table 81 and for Table 82. The result shows a most surprisingdegree of coincidence in the values for air and for hydrogen, proving 

beyond a doubt that the same law of variation F(&") must apply to 

both gases. Since the locus constructed falls below (l+afl")*-, where 

tf=0.003665, the coefficient of expansion of gases, the true value of F(0") 

must fall decidedly below (l+ad"}* and a fortiori below the formula

"-=1+0.002751* - 0.00000034*2

7/0

by which Holrnan reproduced the data of his fine observations for air 

between 0° C. and 100°. Now, although the data in the locus drawn fall 

below (l+a#")-2, it can not at once be assumed that (l+##")2 is to be

discarded as the value of *?-; for in view of the occurrence of the factor

1+4E

where C is essentially positive and increasing with 6", it does not follow

tliat'-Frfl") and V- are identical.

?7o

The curve shows the effect of .a cold environment in a very striking 

way; for the Bunsen-burner temperatures here lie at only 850°, and 

1,140° is the highest temperature reached by the blast-lamp. Clearly 

the mean temperature of the thermo-couple is only a nominal value for 

the mean temperature of the helix of platinum tube. This is proved 

by the high values of F(8") for hydrogen at 1,000°; for these large data 

are due to the fact that platinum is pervious to hydrogen, an effect 

which) in the following tables, does not produce a serious discrepancy 

until much higher temperatures are reached.

(915)
262 MEASUREMENT OP HIGH TEMPERATURES. 54.

In Tables 83 and 84 results are given for hydrogen and air, respectively, with an improved form of apparatus. The thermo-electric junction 

still occupies a position near the center of figure of the helix aud protected from direct action of the flame by a flat plug or pellicle of asbestus 

(Fig. 47c); but the terminal tubes of the helix are soldered into the 

walls of the pneumatic trough, through which they project. In this 

way a leakage of water is prevented, and the chimney of the burner 

remains dry and of unifrom temperature. The helix, however, is naked 

here, as in the foregoing experiment.

TABLE 83. Viscosity of hydrogen. 

[Capillary tube No. 10. i=33.43cm . I' + I"' = 4.4 . TJ = 0.0001410. 6 = 60 E = 0.00794"".]

p

123. 9?

123. 97

123. 97

123. 97

123. 98

ioq 09 X^o. o£

123.83

123. 81

123. 83

TOO or J.4O. O<->

TOD OQ AiO. OO

123. 88

123. 90

123. 92

123. 92

123. 92

123. 67

123. 68

123. 64

123. 64

123.85

123. 85

123. 85

123. 85

121. 75

121.73

124. 64

124. 63

124. 81

124. 83

124. 84

124. 65

124. 64

124. 65

124. 79

P

75.06

75.06

75.66

75.60

76.66

75.66

75.66

75.66

75.66

75.66

75.66

75. 00

75.00

75.00

75. 60

 75. 60

75.02

75.62

75.62

75.02

75. 62

75.62

75.62

75.62

75.72

75.72

76.25

76.25

76. 25

76. 25

76.25

76.32

76.32

70.32

70. 32

t"

95

90

90

90

90

90

90

90

90

on yu

90

440

440

440

410

440

630

660

660

680

660

660

660

660

1115

1115

1080

1080

1080

1080

1080

 1560

1560

1500

1560

To

51.38

48.73

48.70

48.80

48.78

48.33

48.37

48.42

48.37

4S <to. oyQQ 

48.37

50.64

49.83

49.04

49.61

47.89

50.63

50.96

50.23

50.93

51.75

51.55

50.95

50.14

50.82

50.77

50.82

50.73

51.10

51.19

51.21

51.24

51.26

51.45

52.23

e ll

6

6

6

6

6

6

6

0 6

6

6

6

482

490

490

504

511

671

695

705

715

688

691

700

707

985

985

1010

1010

1007

1005

1006

1222

1227

1224

1223

V

1+4S"/B"

0. 0001427

1420

1427

1424

1425

0. 0001432

1431

1429

1431

1431

1431

0. 0002813

2831

2842

2867

2874

0. 0*003244

3307

3320

0. 0003340

3295

3299

3306

3336

0.0004102

4165

0. 0004231

4237

4237

4238

4234

0.0005254

5LS9

5228

5176

F(8")

J.98G

1. 999

2.007

2. 021

2.030

2. 291

2.336

2.345

2.359

2.327

2.330

2. 335

2.356

2.939

2.941

2.987

2.992

2.992

2.993

2.990

3. 710

3.604

3.692

3.655

(910)
VISCOSITY OF GASES. 

TABLE 83. Viscosity of hydrogen Continued.

263

p

124. 31

124. 31

124. 31

124. 31

124.31

1OO QQ

123. 99

124. 03

124. 00

P

76.35

76.35

7fi 3^

76.35

76.35

76.37

76.37

76.37

76.37

t"

90

95

95

95

95

95

.95

95

95

Fo

47.52

50.56

50.85

50.96

50.96

50.51

50.50

50.47

50.51

5

5

5

5

5

5

5

5

ij"

l+^''/R"

0. 0001464

1453

1444

1441

1441

0. 0001441

14.42

1444

1442

F(B")

TABLE 84. Viscosity of air. 

[Capillary tube No. 10. I/= 33.43"'". l'+V" = 4.4cm. T; =0,0002472. 6 = 5°. R = 0.00794"111 .

p

325.24

125. 24

125. 23

125. 23

125. 25

125. 36

125. 08

125. 08

125. 08

125. 08

124.93

124. 93

124.95

124.77

124. 77

124. 74

124. 73

124. 73

124. 77

124. 76

124.04

124. 08

124. Of)

123.97

123. 88

123. 09

123.65

123. 04

123. 00

123. 37

123. 37

123. 37

123. 40

123.40

P

77.08

77.08

77.08

77.08

77.08

77.08

77.08

77.08

77.08

77.08

76.97

76.97

76.97

76.80

70.80

76.80

76.80

76.80

76.80

76.80

70.19

70.17

76.13

76.05

75.97

75.79

75.71

75.66

75.62

75.97

75.97

75.97

75. 97

75.97

t"

165

1C5

165

165

165

165

165

165

165

165

560

780

740

810

810

880

920

945

9CO

>980

1680

1665

1665

1665

1665

2780

2820

2860

2880

165

105

165

165

165

Fo

51.31

51.31

51.36

51. 46

51.36

51.52

51.16

51.16

51. 22

51. 22

50.77

51.90

52.20

51.83

51.11

51.57

51.43

51.67

51.57

51.94

50.02

51.42

50.98

51.15

51.61

51.21

50.87

50.81

50.85

50.10

49.99

50.15

50.03

50. 09

6"

5

5-

5-

5

5

5

5

5

5

5

335

473

448

491

499

536

563

575

585

595

930

917

919

914

912

1337

1337

1337

1340

5

5

5

5

5

1)"

1+W/R"

0. 0002517

2517

2514

2509

2515

2514

0. 0002514

2514

2511

2511

0. 0004385

4925

4805

0. 0005035

6050

5201

5285

5331

5377

5391

0. 0006910

6836

6882

6883

6822

0. 0008598

8784

8925

8966

0. 0002500

2505

2498

2505

2503

F(0")

1.774

1.993

1.944

2.037

2.043

2.104

2.138

2.157

2.175

2.181

2.790

2.706

2.784

2. 785

2.760

3.479

3.554

3.611

3.627

(GIT;
264 MEASUREMENT OF HIGH TEMPERATURES. (BULL. 54.

TIG. 47a. Plan of helix and thermo-couples.

8

J

These results (Tables 83 and 

84) justify the predictions made 

relative to the hurtful character 

of the leak. For if F(6") be constructed it falls decidedly below 

the earlier curve. Below 1,000°, 

moreover, the air and hydrogen 

loci show a striking degree of 

coincidence (see chart, Fig. 48), 

substantiating the earlier inference that F (6") has the same 

value for these two gases, and 

that the value of 6", thermo electrically measured, is not the true 

mean temperature at which transpiration actually occurs. Above 

1,000° the air and hy^drbgen 

curves diverge; but this is due 

to the fact that platinum is much 

more pervious to hydrogen than 

to air. Agaiu, in consequence of 

the tendency of the gases of the 

burner to enter the tubes, as well 

as the relatively large negative 

errors of 6" at high temperatures, 

the curvature of bo th loci changes 

from concavity downwards below 1,000° to concavity upwards 

abovel,000°. Hence above 1,000°

the true character of V'/Ao is 

marred by the occurrence of diffusion across the walls of the 

platinum capillary tube. It appears from the data, at extremes 

of high temperature (hydrogen 

0=1,225° nearly, air 0=1,335° 

nearly), that the large distortion 

produced by diffusion is nevertheless of a determinable kind. 

It may therefore be eliminated' 

by applying suitable corrections, 

as will be stated below. The occurrence of the consecutive hightemperature points, lying nearly 

vertically one above another, is 

due to the fact that the non-

(918)
BAllUS.] VISCOSITY OF GASES. 265

registered temperature at the outside of the helix continues to increase 

long after the internal and registered temperature is practically stationary. The mean temperature of the helix is thus still on the increase, after 

the temperature of the thermo-couple is constant, and the discrepancy 

in question points out an ordinary phenomenon of heat conduction. All 

these peculiarities appear clearly in Fig. 48, where points dashed upward refer to hydrogen, points dashed downward refer to air. Leaving 

the exceptional values out of consideration, the data of these tables are 

of special importance. They show that the locus F(6") does not only 

lie below (l+a 0")*, but that its value is most probably (l+a 6")$. 

Indeed, the close coincidence of the data between 400° and 800° with 

the function (l+a 6")^ is an exceedingly striking observation. When 

it is called to mind that theoretical reasons suggest the exponential

:; C 

form (l+a 6")*, that the effect of slip 1+4 g is in the opposite sense

to the necessarily negative error in 6", then the acceptation of 

(1+ctr #")3 as the simplest convenient expression for the co-ordination 

of all the data F(0") is easily justified.

Tables 81 to 84 have proved beyond a'doubt that the predominating 

error in the present experiment is introduced by the fact that the mean 

temperatures of the viscosity pyrometer and of the thermo-element are 

essentially different. The degree of constant temperature throughout 

the space occupied by these two instruments is therefore by no means 

sufficient; hence I made a few measurements on the effect produced by 

changing the position of the thermo-couple and of enveloping the^helix 

with layers of a non-conducting material. I also endeavored to test 'in 

how far a more reliable temperature datum could be obtained from the 

simultaneous indications of two or more thermo-couples touching different points on the inside and on the outside of the helix.

TABLE s5. Viscosity of air. Miscellaneous tests. 

[Capillary tube No. 10. £=33.43cm . l'+l'"=tAcm »;0=0.0002472. 0=6=. 12=0.00794"°.]

P P

«" To 0" i)"

1+4J/JB

F(9")

I. Tliermo-couplo nearly naked.

123. 11

123. 13

123. 15

123. 17

123. 17

124. 29

124. 31

124. 30

124. 17

124. 22

124. 27

75.93

75. 93

75.93

75.93

75.93

75.80

75.80

75.80

75.89

75.82

75.79

170

170

170

170

170

1800

1950

1845

2460

2460

2460

51.35

51.35

51.40

51.38

51.38

51.60

51.60

51.00

50.96

50.50

50.39

5

5

5

5

1055

1040

1062

1347

1338

1336

0. 0002497

2499

2497

2500

2500

0. 0006716

7359

6933

0. 0007684

7813

7852

2.717

2.977

2. 805

3.109

3.161

3.177
266 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

TABLE 85. Viscosity of air. Miscellaneous tests Continned.

p P

t" y0 9" i+mz F(B")

II. Two thermo-couples touching the inner face of the naked helix.

125. 30 

125. 29 

125. 29 

125.31 

125.40

124. 97

124. 95

124.89

124.85

124. 75

124. 78

124. 92

76.95 

 76. 95 

76.95 

76.95 

76.95

76.89

76.84

76.80

76.76

76.66

76.62

76.59

165 

165 

165 

165 

165

1780

1740

1770

1740

2520

2580

2700

51.38 

51.38 

51.35 

51.45 

51.68

52.74

51.69

52.47

52.05

51.30

51.31

51.51

6 

6 

6 

6 

6

964

962

959

956

1224

1227

1231

0. 0002514 

2513 

2514 

2511 

2506

0. 0006947

6942

6966

6917

0. 0008453

8594

9028

2.811

2. 809

2.819

2.789

3.420

3.477

3. 653

III. Temperature measured inside and (by contact) outside.

124. 71

124. 67 

124.70

76.61

76.58 

76.60

2940

1800 

1800

51.50

51.38 

51.07

C 1380 

) 1233

C 1332 

) 988 

C 1035 

i 974

1 0. 0009340

1 0.0006677 

1 0.0007021

3.778

2.702 

2.841

In the first part of Table 85 the couple is inserted into the helix, with 

its junction near the base, so as to be played upon directly by the flame 

of the burner. The temperatures so obtained fluctuate in value over 

so large an interval that it is difficult to get a fair mean value. This 

appears from the wide distribution of the points obtained on the curve, 

Their mean position, however, is unmistakably below (i+a0")s} a

result consistent with the results of the foregoing tables, inasmuch as 

the error of F(6") is here positive, because the error of 6" is positive. 

The helix in these experiments was naked.

In the second part of Table 85 two thermo-couples are inserted 

touching the inner face of the helix, with their junction at points respectively nearest to and farthest from the walls of the trough. The 

results indicate a series of points at 960°, which are nearer the curves 

than before, whereas the results at 1,230° are abnormally high. Comparing the temperatures at the two points of the internal face, I found 

6]" = 1,255° and 6Z"=1,235°, so that even at the temperatures of the 

blast-lamp the differences of temperature for points on the inner face 

of the helix are not of serious magnitude. The discrepancy must 

therefore be looked for in thermal differences between the inside and 

outside faces of the helix.

In the third part of Table 85 measurements of the kind just specified 

are given. The two figures under 6" are thermal data for the inside

(OL'O)
BARUS.J VISCOSITY OF GASES. 267

and outside faces of the helix, the latter being obtained by touching 

the surface with the junction of a thermo couple. The discrepancies 

thus obtained are alarmingly large (150°) j and although this datum 

can be only a superior limit for the discrepancy in question, it nevertheless points emphatically to the necessity of resorting to better means of 

insuring constancy of temperature throughout the space occupied by 

the two pyrometers. The final values of F(6") in this table are again 

abnormally large, so as to suggest that some vitiating error escaped 

detection. Comparing the thermo-couple which had been used in all 

these experiments with a fresh couple,.I found mean values for the 

temperature of the Argand air bath, 01 =S22° and <92"=804C , so that the 

result of repeated and prolonged firing can not have exceeded 20°.

The irregular results of Table 85 show the importance of jacketing 

the helix with non-conducting material, and of using at least three 

thermo-couples for the evaluation of 6". One thermo-couple on the 

inner face is sufficient, but at least two are necessary to measure 

temperature at the external face.

In Tables 86 to 89 the external face of the helix is enveloped by a 

layer of mica, pressed against the surface by platinum wires, drawn 

tensely around the mica. In Fig. 47a the helix of platinum capillary 

tube is shown at 6, the surrounding envelope of mica at a. The junctions of the thermo-couples placed at 1, on the inner face of the helix, 

pressed against it by a plug of asbestus, c, and at 2 and 3 between the 

outer face of the helix and the mica envelope. Junctions 2 and 3 are 

pressed against the helix by the external platinum wiring, which holds 

the mica jacket in place. Fine plates of mica insulate the ends of the 

thermo-couples from the helix above it. The stem insulators described 

on page 95 are of service in keeping the wires apart. In the tables, 

6{" denotes the temperature at the internal, Bz" the mean temperature 

of the external face. To secure identity in the thermo-electric indications the old junctions were cut off and new junctions were fused for 

each of the couples, Nos. 37, 38. 39, used in the measurement. The 

calibration of these was effected above, Chapter IV.

TABLE 86. Viscosity of air. 

[Capillary tube No. 10. L= 33.43 . Z'+«"_'=4.4<:m. i)0=0.0002491. 6=7°. J2=0.00794C "1 .]

p

124. 00

124. 00

124. 00

124. 00

124. 01

123. 51 

123. 45 

123. 38

P

76.08

76.08

76.08

76.08

76.. 08

75.92 

75.87 

75.81

t"

165

165

165

165

165

1750 

1760 

1740

To

49.95

49.83

49.84

49.94

49.94

51.35 

51.90 

51. 30

61"

7

7

7

7

7

984 

983 

984

/) //

7

7

7

7

7

1007 

1004 

1004

7}"

l+4$"/K"

0. 0002526

25;t2

2532

2527

2528

0. 0006693 

666G 

6054

F(0»)

2.C87 

2.676 

2.671

(921)
268 MEASUREMENT OF HIGH TEMPERATURES.

TABLE 86. Viscosity of aIr Continued.

[BULL. 54.

p

123. 32

123. 29

123. 25

123. 39

123. 65

123.61

123. 58

123. 61

123. 36

123. 37

123. 36

" 123. 36

123. 33

P

75.75

75.72

75.67

75.68

75.68

75.68

75.08

75.68

74.73

74.73

74.73

74.73

74.73

t"

2339

2340

2340

860

890

910

930

960

165

165

165

165

165

To

51. 05

50.48

50.76

52.69

50.91

51.00

50.79

51.37

49.59

49.59

49.50

49.59

49.63

0i

1200

1204

1204

515

557

557

580

592

8

8

8

8

8

1224

1230

1233

525

567

578

592

604

8

8

8

8

8

7}"

l+4£"/-K"

0. 0007757

7820

7765

0. 0004977

5114

5068

5210

£254

0. 0002547

2547

2552

2547

2543

F(6")

3.114

3.139

3.117

1.998

2.053

2.082

2.091

2.109

TABLE 87. Viscosity of hydrogen. 

[Capillary tube No 10. £=33.43 . Z'+Z"'=4.4cni . ij0 =0.0001294. 6=8°. J2=0.007544B1 .)

P

122.48

122.49

122. 50

322.50

122. 50

122. 20

122. 22

122. 24

122. 22

122.24

122. 30

122. 30

122. 32

122. 36

122.43

122.97

122. 94

122. 96

124. 56

124. 56

124. 56

124. 54

124. 56

124. 58

125. 09

125. 08

125. 09

125. 08

125.09

P

74.71

74.71

74.71

74.71

74.71

74. 62

74.62

74.62

74.62

74.62

74.69

74.73

74.75

74.81

74.86

74.93

74.96

74.99

76.86

76.86

76.86

76.86

76.86

76.86

77.08

77.08

77 i i . flW UO

77 1 1. UOOft 

77.08

t"

90

88

88

88

88

88

88

88

88

88

885

=- 870

870

875

900

1340

1350

1350

495

495

495

495

495

495

85

85

85

85

85

Vo

50.66

49.81

49.79

49. 69

49.68

49.51

49.51

49.55

49.62

49.58

50.11

4.9. 10

49.02

49.25

49.68

49.64

49.96

50.39

51.65

51.09

50.83

50.48

50.18

50.09

50.28

50.28

50.30

50.28

50.28

d // i

8

8

8

8

8

8

8

8

8

8

947

948

948

946

955

1196

1202

.1192

526

531

535

536

541

544

8

8

8

8

02"

8

8

8

8

8

8

8

8

8

8

970

972

976

978

984

1228

1228

1226

538

514

547

552

554

556

8

8

8

8

8

T)"

H-4$''/B"

0. 0001330

1323

1324

1326

1327

0. 0001323

1324

1324

1320

1323

0. 0003525

3528

3529

3533

3584

0. 0004588

4577

4550

0. 0002924

2939

2939

2952

2960

2957

0. 0001304

1304

1304

1304

1304

7-7 / rt//v J? (0")

2.725

2.726

2.727

2.731

2.770

3.546

3.538

3.521

2.260

2.271

2.271

2.281

2.287

2.285
BAHUB.] VISCOSITY OF GASES.

TABLE 88. Viscosity of hydrogen.

[Capillary tube No. 10. i = 33.43cm. l'+Z"'= 4.4°m. i}0 = 0.000 1294. 0=7°.

260

2 = 0.00794 .]

p

123. 30

123. 32

123.31

155. 27

155. 27

155.27

155. 30

155. 30

155. 27

155. 25

155.45

155.35

155. 45

156. 10

156. 07

156. 05

156. 07

P

76.95

76.95

76.95

76.55

76. 55

76.55

76.55

76. 55"

76,55

76.55

76.59

76.59

76.59

76.67

76.67

76.67

76.67

t" .

90

90

90

360

360

360

360

440

450

450

450

450

450

890

890

890

870

Fo

50.00

50.00

50.00

50.82

50.42

50.02

49.67

50.89

51.37

51.23

50.87

50.57

50. 63

50.89

51.00

51.43

50.01

d ll

1

7

7

7

410

412

416

420

504

509

512

514

516

517

954

954

952

94 G

02"

7

7

7

418

420

425

426

510

516

519

522

525

526

95C

953

951

946

r,"

1+4 ?'/ll"

0. 0001332

1333

1333

0. 0002518

2529

2536

2347

0. 0002741

2747

2747

0. 0002762

2770

2766

0. 0003635

3629

3600

3601

F(9")

1.946

1.954

1.960

1.968

2.118

2.123

2.124

2.135

2.141

2.138

C.809

2.805

2.787

2.783

TABLE 89. Viscosity of air.

[Capillary tube No. 10. £=33.24"". l'+l'"=4Acm. i»0=0.0002491. 0=8°. .R=0.0794CI".]

P

125. 50

125. 51

125. 53

124. 71

124.71

124. 69

124. 65

124. 73

124. 68

124. 68

124. 68

124. 95

124. 95

124. 95

124. 96

124. 96

124. 95

P

77.01

77.01

77.01

76.87

76.87

76.87

76.87

76.87

76.87

76.87

76.87

7C.89

76.89

76.89

76.98

76.98

76.98

*"

165

165

165

710

710

735

750

930

930

940

940

1710

.1715

1740

2370

2370

2370.

To

«JU. r,n 79i u

50.75

50.72

51.10

50.22

51.03

50.93

51.34

50.98

51.34

50.93

51.42

51.20

51. 25

51.27

51.17

51.25

A If "I

7

7

7

424

430

439

449

558

562

565

569

964

970

979

1206

1207

1207

08"

7

7

7

436

443

453

462

568

574

576

580

987

992

1000

1214

1214

1210

i\"

1-M'llt"

0. 0002579

2579

2581

0. 0004820

4865

4995

4937

0. 0005351

5351

5360

5364

0. 0006784

6645

6842

0. 0008013

8028

8017

F(0")

.........

1. 935

1.953

2. 005

1.982

2.148

2.148

2. 152

2.153

2. 723

2. 668

2.747

3.217

3.223

3.218

The results in Table 86 justify the predictions made. Compared 

amongst themselves the values are excellent. Below 1,000° the data 

lie below the function (1+«#")§, whereas the extreme points (1,215°)

(923)
270 MEASUREMENT OF HIGH TEMPERATUEES. [BULL. 54

coincide with (l-\-ad")$ almost perfectly. In general therefore the results of earlier investigations (Table 81-85) are emphatically corroborated. Having finished the measurements for air, I passed hydrogen 

through the same apparatus. The results, near 1,000° (Table 87), coincide almost perfectly with the curve (l+ad")%. The results above 1,200° 

are abnormally high, because platinum is pervious to hydrogen. I was 

not a little surprised therefore on finding the results ac 500°, although 

very good when compared amongst themselves, much too large to accord with the other data. The error is larger than can be referred to 

anything short of an undiscovered accident. I suspect the hydrogen 

of these experiments in some unforeseen way to have been contaminated 

with either air or moisture, since the error is constant for all the observations.

Not being able to discover the cause of the discrepancy, however, I 

resolved to repeat the work with the apparatus adjusted anew. These 

results are given in Table 88. The results agree much more closely 

with the exponential (1-f <*#")§, showing the corresponding data of the 

former series in error. The somewhat high values of F(#") are the result of the low value of T/O , to which these data are referred. The difficulties met with in operating with hydrogen induced me to investigate 

another series for air, which series is given in the last table, 89. The 

results fall slightly above (1+<*#")§ at 500°; slightly below the exponential at 1,000°; above it at 1,200°; but the accordance throughout is 

satisfactory. (See Fig. 48.)

The large number of data for B\ and #2) which the Tables 86-89 contain, show that the thermal discrepancy has been reduced to low limits, 

and that its effect is apt to be relatively large in case of low values of 

0. To properly jacket the helix is a practical problem of great difficulty, because accidental bending or twisting of the thin capillary tube 

is apt to produce fine longitudinal fissures, or variations of bore, or to 

introduce other sources of uncertainty or error. Mica insulations become friable and can not be thoroughly relied upon after prolonged 

heating. Hence all the manipulations must be effected with great 

care, and therefore consume much time. For these reasons I believe 

that to improve the results further it will be expedient to introduce a 

radical change of method, such as I will describe below.

As a whole, the above tables conclusively indicate that many residual 

errors are the result of variations in the composition of the gases. Hence, 

before proceeding to a general discussion of the above data, I shall insert a tabular view of the successive values of the viscosity of the gases 

at zero degrees centigrade. This is given in Table 90, in which, the 

temperatures 0, at which the quantities

(924)
UAKUB.J VISCOSITY OF GASES. 271

were found, are inserted, as well as the corresponding values of

Wo

computed for them by using Holman's equation,

^ =l+0.002751/9-0.0000003402.

I also insert the pressure P, at which the gas enters the platinum 

capillary.

TABLE 90. Successive values of q0-

Gas.

H2 ...

H3 ...

H2 ...

H2 ...

Air . . .

Air ..

Air

Air ...

Air...

Air...

Air . . .

Air ,

Hs ...

H,....

TI2 ....

IT,....

H2 ....

Ua ....

H2 ....

H3 ....

H2 ....

H2 ....

H,....

Air...

Air . . .

A ir . . .

Air . . .

Air...

Date.

March 26

March 23

March 21

Mnrch 20

March 26

March 20

...do ......

March 19

March 18

...do.....

March 15

...do......

March 14

..do......

March 13

...do......

March 10

...do ......

March 9

March 8

...do ......

...do ......

...do......

March 7

..do ......

March 3

..do ......

..do......

0

o

7

8

8

8

7

8

7

6

5

5

5

5

5

5

6

6

7

7

7

6

6

6

6

6

C

6

6

6

*> vine xiu

l+*R

133.3

130.4

132.3

132.6

. 254.8

254.7

252.9

251.2

250.0

250.2

251. 4

251.2

144.9

144.2

142.6

143.1

142.7

142. 5

141.5

141.8

141.8

140.4

147.8

254.8

 262. 5

255.5

260.7

257.7

. lo x!0s

^l

130.8

127.5

129.4

129.7

250.0

249.. 2

248.1

247.2

246.5

246.7

247. 9

247.7

142.9

142.2

140.4

140.9

140.0

139.8

138.8

139.6

146.4

138.2

145.6

250.8

258.5

251.5

256.5

253.5

P

123.3

125.1

122.2

122.5

125.5

123.4

124.0

125.3

123.1

123.4

125.2

125.1

124.3

124.0

124.0

123.8

125. 0

125.4

120.3

125.0

88.7

124.6

88.6

124.5

88.3

124.2

88.5

124.7

Mean rj0 x 10*

H2 . . . 129.4

Air ... 249.1

Air . ! . 247.2

H2 . . . 141.6

H2 . . . 139.5

Hj . . . 146.0)

Ha . . . 138.9

Air ... 250.8

(Air . . . 256.5)

Air ... 252.5

DISCUSSION.

Viscosity at zero. It is expedient to begin this paragrap h with an 

examination of the consecutive values of the zero-viscosity 770 of the several gases, since the constant JJQ must enter fundamentally into all the

(925)
272 MEASUREMENT OF HIGH TEMPERATURES. [HULL. 54.

inferences to be drawn. Turning to Table 90, on page 271, the singularly 

high values there incorporated at once strike the eye. The clue to these 

large discrepancies is, however, at hand ; for

^-p2 t R*

77 x ________ ' _____ J ___

'~ 16 p V L

«L (X TTJ

and it is therefore clear that since = 4 -^- even slight errors in R at

77 M

once produce serious effect on 77. I have stated that because of the difficulty encountered in constructing the capillary apparatus faultlessly, 

I did not wish to subject the tubes to any experiment which might tend 

to injure them ; I stated also that in the discussions of the present part 

of the chapter absolute data were of inferior interest. Hence, without 

forgetting the occurrence of the uniformly large values of 77 here found, 

the question may be waived, to be resumed in the next part in connection with other relevant data. The one property of 770 which has an 

important bearing on the present discussion is its degree of constancy 

as regards time. If the values of 770 in Table 90 be graphically constructed as they vary with the data belonging to each, the curves resulting show that 770 has a slight tendency to increase. Disregarding 

1 be data between March 3 and March 7, which refer to an earlier form 

of apparatus, it appears that in the hydrogen data between March 8 

and March 14 the mean increase of 7/0 is somewhat less than 0.5 per 

cent, per day of use; in the results for air between March 15 and 

March 26 less than 0.2 per cent, per day of use ; in the final results for 

hydrogen between March 20 and 26 the results vary irregularly, and 

their mean ascent is zero. These data constitute an exceedingly favorable verdict relative to the pyrornetric application of the principle of 

viscosity. They show that for large mercury pressures like 125cm and 

7Gcm , respectively, at the two ends of the platinum capillary tube, no 

serious change of the radius of the tube need be apprehended at temperatures even as high as 1,400° (white heat). In this respect the present results are valuable. The slight tendency of 770 to increase just 

mentioned, is in accordance with an increase of the capillary radius resulting from the excess of internal pressure. This follows from Meyer's 

equation, but whether the observed result may not be equally wel1 ex. 

plained as resulting from variations in the composition of the gases or 

from similar progressive causes can not be ascertained. It' suffices for 

the present purposes that the time variations of 770 have been found 

negligible, and that therefore the dimension of the platinum capillaries 

used in the above experiments have remained practically unchanged, 

when the mean excess of internal pressure at white heat was about £ 

of an atmosphere.

The use of different gases (air, hydrogen) in these experiments was 

pripcipally to vary the conditions of experiment and to detect the laws

(926)
BAUUS.] VISCOSITY OF GASES. 273

of variation with greater certainty. Hence ordinary care was taken in 

drying the gases, air being passed through a tube of Ca012 and hydrogen both through Ca012 and concentrated H2SO4 . But neither was 

the hydrogen purified of sulphide or air or other attendant gases, nor 

was air purified of carbon dioxide. I desisted from these special precautions because above red heat platinum is.pervious to the hydrogen 

gases of the Bunsen flame, so that in non-enameled platinum capillaries 

the purity of the transpiring gas could not be vouched for, even in the 

case of a gas originally pure. Again, at the temperatures (500° to 

1,300°) within which my data chiefly apply slightly moist air and dry air, 

pure and gaseously impure hydrogen, are probably equally perfect gases. 

Hence there occur in my results two values for the zero-viscosity of 

hydrogen, 140:106 and 129:106, respectively, which correspond to gases 

taken from different gasometers at different times. The variations of 

?;0 for air are smaller, ranging from 247:106 to 252:106. The variable 

character of r/0 made it necessary to make the low-temperature measurement before and after each series of high-temperature measurement 

made. Indeed, I did not anticipate such large fluctuations in r}0 , and 

despite the precautions taken the discrepancies here in question have 

produced no trifling distortions^ in the high temperature results which 

follow. This I shall soon have occasion to show. When the gases 

forced through the capillaries are urged forward by an advancing surface of mercury (as in the above experiments) traces of mercury vapor 

will also pass along with the gas, but the tension of mercury vapor at 

20° is only 0.002cm to 0.004cm . Hence this discrepancy is nil.

Finally, Table 90 con tains values for 770 derived both for P=125cra and 

for P=SScm. Curiously enough, the value of 7/0 for low pressures (P) is 

decidedly the greater, being about 5 per cent, greater for hydrogen and 

about 2 per cent, greater for air. This result belongs also to the discussion of the next section. Here it is sufficient to note that if measurements were made at smaller values of P than the ones customary //

(125cni), the relative values where 77" is a high-temperature viscosity,

would not be larger in value than those admitted into the above tables. 

In other words, so far as the present evidence goes, the zero-viscosity 

7/0 has not been increased by the relatively large values of P (125cm) em- if' 

ployed throughout the course of the work, and hence can not be ^o 

too small.

Viscosity at high temperatures, kinetic inferences. In order to proceed with the discussion of the high-temperature viscosities, Tables 83 

.to 89 may be consulted, the values of Tables 81 and 82 being in error 

in the sense already indicated. If all the values of F(6") be constructed 

as functions of 8", the graphic representation Fig. 48 will show that the 

individual data group themselves in a band or pathway, of which the 

function (\+aO") is so nearly the axis that it is at once justifiable to 

<i««ept it as such. Hence, even if there were no ulterior reasons for acBull. 54 IS (927)
274 MEASUREMENT OF HIGH TEMPERATURES. HULL. 54.

cepting the given function, it is, at the present stage of investigation, 

a justifiable inference that the viscosity of a perfect gas varies as the 

§ power of absolute temperature. Now, inasmuch as by the relation 

of Maxwell

77=0.318 

where p is the density, D. the velocity of the mean square, and L the

mean free path of the molecule of gas, and inasmuch a,s£l=

and L are the only variables in this equation whose values change with

6", it follows that

L=Lo

In other words, the mean free path of the molecule of a perfect gas 

varies as the sixth root of absolute temperature. Moreover, in view of 

the equation fl fl0 A/l+atf", it furthermore follows that the mean free 

path of the molecule of a perfect gas varies as the cube root of the 

velocity of the mean square. This result is suggestive, perhaps ; for 

if there be given a gas consisting of a fixed number of molecules in a 

fixed volume, or, in other words, if p be constant, then the only effect 

produced by varying the temperature 6" is a mean increase of £1 distributed uniformly throughout the volume of the gas. If the change 

of D. due to temperature be taken as a measure of the effect produced 

by temperature, as it were equally in all directions, then the part of 

this thermal effect apportioned to the linear magnitude L is plausibly 

represented by the cube root of fl. 

Again, if the equation of Clausius be considered, viz,

where A.3 is the mean volume per molecule and s the radius of Clausius's 

" Wirkungssphare," then it appears that the volume inclosed within 

the " Wirkungsphare" is diminished in magnitude by temperature; 

and that the diminution takes place proportionally to the square root 

of the velocity of the mean square (fl).

Sources of error. Having thus stated the general character of the 

results of the above tables, it is necessary to find the conditions upon 

which their validity depends, and to inquire as fully as the present researches permit into the facts which militate against the inferences 

drawn. This is by no means easy, nor even fully possible on the basis 

of the experimental material in hand.

The principal cause of discrepancy in the present work is this, that even 

in the most carefully adjusted forms of the present apparatus the mean,

(.928)
BARU8.J VISCOSITY OF GASES. 275

temperature registered by the thermo-couple and the mean temperature 

of the helix of capillary tube are not necessarily the same. Each of 

these pyrometers furnishes its own thermal datum correctly; but these 

data have reference to environments which are not thermally identical. 

In short, the degree of constant temperature throughout the space enveloping the helix is as yet far from satisfactory; and the residual 

differences of temperature between the inside and the outside of the 

helix or between its top and bottom surfaces have not been rigorously 

allowed for. To this must be added the fact that the thermo-couple 

was not compared with the air thermometer at temperatures above 

1,300°, and that the calibration in question loses in accuracy when 

these high temperatures are approached. (Of., Figs. 41 and 42.) Hence, 

in view of the great difficulties in the way of correct temperature measurement, it is hardly profitable to enter into more than a cursory consideration of the minor sources of error.

In addition to the extraneous causes for incorrect temperature measurement, there is also an internal cause, due to the expansion of the 

transpiring gas from the pressure P to the pressure p. Meyer has 

elaborately discussed this phenomenon. Again, the purely convective 

effect due to the introduction of cold gases into the capillary tube is not 

to be lost sight of. In experiments of the next section I found a cooling effect as high as 20°. In the present experiments, where thin tubes 

and slow currents alone occur, the convection error is nil.

To avoid incidental complications the radius of the capillary tubes 

here in question was chosen small (R <0.01cm), so that the Meyer formula fully applies. Again, preference is given to absolute methods of 

experiment; differential methods, inasmuch as they compare two magnitudes without fully characterizing either, would have encumbered the 

present research with an additional element of uncertainty.

Diffusion. The observed circumflexion of the curve which represents the mean distribution of the points in the diagram, Fig. 48, at a 

temperature near 1,000°, together with the fact that this change of the 

sign of curvature is much more pronounced for hydrogen than for air, 

points, I think significantly, to the occurrence of diffusion of gases 

through the walls of the platinum capillary tube. In the case of transpiration experiments with air, the hydrogen gases of the burner passing 

through the platinum septum combine with the oxygen of the capillary 

current within. There results an increase of the volume of the oxygen 

combined as 1:2; but as the water formed is absorbed in the pneumatic apparatus, it follows that the volume F0 actually measured by 

the burette is too small. Again, in the case of transpiration experiments with hydrogen the prevailing diffusion is from within outward, 

so that hydrogen simply leaks out of the tube. Thus the volume of F0 

actually measured is again too small. Hence in the case both of air 

and of hydrogen, since F0 is negatively in error, the error of >/', which 

varies inversely as F0 , will be positive. This accounts for the circuiQ-

(929)
2<f6 MEASUREMENT OF .HIGH TEMPERATURES [BULL. 54.

flexion discrepancy in question, or at least for the difference of behavior 

of hydrogen and air.

A final remark relative to the surface disintegration (Zerstaubung) 

of red hot platinuin 9 as observed by Nahrwold1 , Berliner2, Rayser3, and 

others, must be made.here. Unfortunately my work was too far advanced when this phenomenon4 was being discussed to permit me to 

make special investigations with .reference to it; nor do I now see how 

allowance for the phenomenon is to be made. I do not believe that 

the error thus left unaccounted for is of a serious kind. For instance, 

in Nahrwold's5 last paper it is shown that metallic particles fly off from 

red hot-platinum much less easily in hydrogen than in air.6 In case of 

both gases, however, the thermal relations of viscosity are subject to 

the same law. Hence the discrepancy due to surface disintegration is 

probably nil. 1880. :

Sliding coefficient. To return to the formula selected on page 273, it 

appears from the remarks there made that the full form in which it 

applies to transpiration work must be

£0 1+06"

where E0 is the zero radius and /? the mean coefficient of expansion of 

the platinum capillary through which transpiration takes place. This 

formula.follows at once for the law accepted above (?// =/70 (l + #0)3), 

and from the fact that C? which is Helmholtz's G-leituugs coefficient, has 

been proved by Meyer, Kundt, Warburg, and others to vary proportion 

ally to the mean free path. It is- usual to take

4-£

_a/o I?

as a quantity negligible in comparison with 1. If this b© permissible,

then will

, Co

E0 1+06"

within the limits of the present interval of temperatures also be negligible. For the coefficient

1+/J07'

'Nalirwold: Wicd. Ann., vol. 31, 1887, p. 473; vol. 35, p. 120, 1888. 

2 Berliner: Wied. Ann., vol. 33, 1888, p. 289. 

3 Kayser: Wied. Ann., vol. 34, 1888, p. 607. 

4 Prof. Cleveland Abbe kindly called my attention to it. 

»Nahrwold: Wied. Ann., vol. 35, 1888, p. 120. 

6 Cf. Elster n. Geitel: Wied. Ann., vol. 31, 1887, p. 109.

(930)
VISCOSITY oy GAS3fc». 277

at 500°, 1,0000, i} 500°, is not greater than 1.15, 1.22, 1.23, respectively 5 

whereas its probable maximum is reached at an earlier temperature. 

Hence, if the views maintained at the present stage of moleciikr 

kinetics be indeed correct, then no .effect of the thermal variation of 

the coefficient of external friction need in the present work be apprehended. This is an important inference, for it might easily be supposed that the relation which IJohnan found to hold between 0° and 100°

(

\

=1+0.002751* 0.

might be progressively retarded in proportion as high temperatures are 

reached, by the gradually increasing values of

and in this way lead to the results which I have found,

Advantages of an exponential law, It is next desirable to examine 

into the reasons in virtue of which, at the present stage of research, 

the equation 77=7/0 (l + ad")§ may be accepted preferably to any other 

form. I will state here, inasmuch as one of the chief purposes of the 

present investigation is the introduction of a new instrument of hightemperature measurement, that any exponential form (l+or0")n which 

is in good accordance with the observations in hand is particularly 

acceptable, because it facilitates the calculation of thermal data by the 

principle of viscosity. Hence, when the choice is open between a number of equations, apparently of equal availability, the exponential form 

will always be adopted, because of the practical advantages just stated. 

Strictly speaking, the formula accepted for rf1 (t/"=?jo(l+aO")Z) is 

applicable to the case of a diatomic gas. In the case of unouatomic 

gases, the supposition that the atoms are hard elastic solids leads to

the law rf Vl+tftf", as Maxwell and Meyer Hiave elaborately shown.1 

From this law Maxwell 2 was led to depart, after having made a series 

of experiments in which viscosity appeared to vary directly as the 

absolute temperature of the gas. Maxwell thereupon deduced a law 

of repulsion between the molecules of a gas varying inversely as tHie 

fifth power of the distance between them, an acceptation by which 

his equations were capable of much simplification. Inasmuch as all 

the subsequent experiments made by many observers have failed to 

confirm Maxwell's experiments, it appears from this and from other 

evidence which Meyer 3 adduces that Maxwell's law of fifth powers 

is untenable. 'No other law of repulsion between molecules having

'Maxwell: Phil. Mag. (4), vol. 19, 1860, p. 31; Moyer: Pogg. Aim., vol. 12."), 1H65, 

pp. 177, 401, 564.

2 Maxwell: Phil. Trans., I, p. 249, 1866.

3 Cf. Maxwell: Phil. Mag. (4), vol. 35, 1868, pp. 129, 185. Moyer; Kiiiotisolio Theorie der Gase, § 77.

(931)
278 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 64.

since been proposed, tlie question regarding the thermal variations of 

viscosity which depends on the said law remains theoretically unsolved. Hence, between forms of an equation for rf1 as a function of 

temperature, it is permissible to select the one among many applicable forms which confers the greatest practical advantage.

In the present instance (to give an example bearing on the remarks 

just made) there is another form of equation which, besides its inherent 

simplicity, might be applied to reproduce the observations in hand. This 

is 7/'=:77o (l+y6") ( Vl+a/9")? which means that L=L0 (1+7$"), and it 

seemed to me by no means idle to attempt to get some comparison with 

regard to the relevancy of these two forms. I think this can best be n" 

done by computing the zero value of JL- (which must be a unit of course) 77o

n" 

from the high-temperature values of -L, on the basis of each of the laws

T/O

cited. Table 91, the data of which are taken from Tables 86 to 89, contains the results.

77"

TABLE 91. Calculated zero values of -! . no

[a = 0.00367.]

1

(

Air (Table 89) . J

I

H2 (Table 87) . .'. j

c

H» (Table 88) . . . <j

I

6"

o

565

592 

995

1,216

442

569 

982

1,210

961 

1,212

418

512 

520

952

7,"

"o

2.068

2.100 

2.678

3.123

1.969

2.150 

2.713

3.219

2.727

3.535

1.957

2.122 

2.138

2.796

V . 1

r,o (l+afl'')t

0.98

0.97 

0.96

1.01

1.01

1.01 

0.98

1.04

1.00 

1.14

1.05

1.05 

1.05

1.03

Error.

+0.02

+ 3 

+ 4

 1

 0.01

+ 2

 4

±0.00 

. 0. 14

 0.05

 5 

 5

 3

7," 1

7)0 Vl+afl"

1.18

1.18 

1.24

1.34

1.22

1.22 

1.26

1.38

 1.28 

1.52

1.23

1.25 

1.25

1.32

yxlO6

318

304 

243

277

489

394 

270

315

295 

425

550

490 

489

336

Turning first to the air points of Table 91, it appears clearly that 

the errors

7/0

iu the results referring to Tables 86 and 89 are promiscuous in distribution, and not larger than is quite compatible with the extreme difficulties of experiment. In the hydrogen points the same errors, though 

larger, are of a nature which can easily be interpreted. The large discrepancy at 1,212° in the results from Table 87 has been referred to 

permeability of platinum to hydrogen at this temperature. The errors

(932)
VISCOSITY OF GASES. 279

in the results from Table 88 -are nearly constant in value, showing 

clearly that the value of 7/0, inserted iuto these computations, was too 

low. The nearly constant errors occurring here do not, therefore, in 

any degree invalidate the law 77" =770 (1+ «#")*» bnt furnish the best of 

evidence to corroborate it. Indeed, the plan here adopted of calculating

/n"\ the constant quantity ( J_ ) is singularly well adapted to exhibit the

true character of the experiments made.

On the other hand, the right-hand division of Table 91 would show 

that the errors

1-2 " 1 1

l+y6"

where 29<^xl05 <37 is to ''be introduced, are of a more serious kind 

than before. I have, therefore, contented myself in Table 91 with giving 

the individual values of y.

Effect of imperfect gaseity. The fact which most seriously antagonizes 

the relation

is the occurrence in the case of air and for temperatures below 200°, of 

a mean exponent of (1+ «$")", which is larger than f . (X B. Meyer's 

data for n Me between § and f ; Puluj's between 0.56 and 0.72; Warburg 

finds ?i=0.77, v. Obermayer w=0.76. Holman's elegant method leads 

to data which lie decidedly above 0.75, and which are of such a kind 

as to induce him to discard the exponential form of function altogether. 

Fully cognizant of the purposes Mr. Holinan had in view in representing his results by a series of ascending powers of 6", I nevertheless 

think that at the present stage of research a conservative policy is 

wiser. Eesults lying within an interval of only 200° above 0° C. can 

not be depended upon as furnishing a definite or final critique. Moreover, a formula which fails when tested by exterpolation has no further

interest than 'the special one to which the author has applied it. The n"

expansion of-!- in terms of a limited number of powers of 6" alter-

% nately opposite in sign will lose all significance when applied beyond

the interval of observation, and if the interval be small the use of such 

a formula scarcely justifies the labor involved in the computation. I 

have, therefore, preferred to retain the older formula

and have endeavored to ascertain whether reasons might not be found in 

virtue of which n would tend to increase in proportion as low temperatures (0° C.) are approached. My experiments refer principally to 

temperatures above 400°, temperatures at which the conditions of perfect 

gaseity may be more justifiably accepted a priori and within which the 

true law of gases may be more clearly discerned. Dissociation is of

(933)
MEASUREMENT OF HIGH TEMPERATURES. [BULL. 64.

course excluded from the nature of the gases chosen. Passing from 

high to low temperature, it appeared to me that E. Wiedetnanu's results 

are available for the interpretation of the discrepancy in question. For 

Wiedemann found that the exponent w=0.73 for air between 0° and 100° 

actually changed to w=0.67 for temperatures between 100° and 185°. 

But the latter value n=0.67 is practically indentical with the exponent 

§ which rny experiments prove to hold as far as 1,330°. The conclusion, 

therefore, is natural that below 200° air does not rigorously fulfill the 

conditions of a perfect gas.

Looking for further data to substantiate this inference, it is well to remark that the frictional effect of decreasing temperature from the high 

to the low value is twofold in character; the purely kinetic friction is 

necessarily decreased. In proportion as "temperature decreases, however. the gas manifests cohesive friction in increasing degree. In other 

words, at low temperatures the phenomenon of residual affinity becomes 

of sufficient importance to lead to the formation of molecules, the parts 

of which cohere more or less loosely for a greater or shorter period of 

time. The occurrence of ephemeral molecular aggregates1 at low temperatures seriously complicates the interpretation of the observed phenomena, and equations for the kinetics of imperfect gases have been investigated only in a few instances. It is known, however, from the experiinents of many observers, among whom v. Obermayer has examined 

the greatest number of correlative results, that both the exponents n of 

the above formula^as well as the coefficients of thermal expansion show 

n very marked tendency to increase in proportion as the gas loses the 

properties of a perfect gas and tends to become vapor. These known 

facts are almost conclusive evidence in favor of the view I have expressed, and the iarge -exponent n which applies for air at low temperattires may be looked upon as a criterion of imperfect gaseity.

All these inferences are materially substantiated by the data obtained 

for hydrogen. Puluj's low temperature exponent for hydrogen is 

«=O.G9; Warburg's %=0.63; v. Obermayer's «=0.7(X Hydrogen, 

therefore, being (ccet.par.) more nearly a perfect gas than air, shows the 

same value of n at all temperatures above zero as far as I have observed ; or, in other words, shows at zero the same law which in the 

case of air begins to apply at temperatures above 200°. Probably the 

strongest evidence in favor of the law I adduce is the fact that at high 

temperatures air and hydrogen behave identicall}', or that the same 

law

appertains to each. This is proved conclusively by Tables 81 to 89, 

despite all thermal and incidental errors which the tables may contain. 

For these errors, affecting both gases alike, will not interfere with the 

identify of behavior, should it obtain. My data show that it does.

1 Cf. Natanson : Wied. Ann., vol 33, 1888, p. 683. 

(934)
VISCOSITY OF GASES. 281 

THE NEW METHOD OF PYROMETBY.

Methods of computation. In view of these liamiouious results, I am 

induced to place great reliance on the accuracy of the relation

as a law, which in the case of a diatomic perfect gas like air or hydrogen 

expresses the thermal variations succinctly. Subject to the validity of 

this law, the favorable character of my results therefore introduces a 

new method of high-temperature measurement j for by applying the 

Poiseuille-Meyer equation to transpiration data, such measurements 

can be made 'absolutely, throughout a wider thermal range, and with 

much greater convenience and accuracy than is the case with any other 

known method, not excepting the air thermometer. Moreover, the exclusive dependence of thermal data on the coefficient of thermal expansion can now be put to the test inasmuch as a series of analogous

data may be investigated on the basis of the above relation, and the 

two series of data can be compared throughout the whole interval of 

temperature observed.

Introducing rf'=r/o (l-\-a6")$mto Meyer's equation, and solving with 

respect to 0", the following form results :

m 

~r ^-"Wn

(11)

or more simply

?-^, 76 v0 i" RJ i"

Here T/O is the zero-viscosity of the gas selected for temperature 

measurement. 6 denotes the temperature of the cold ends of the capillary platinum tube, and y is Mr. Holman's coefficient for air, approximately ;j/ =0.00275. The remaining variables have the signification 

given on page 253. E0" and B0 being respectively the radii of the hot 

part (I"), and cold parts (Z', V") of the capillary tube at 0° C., are practically equal in my apparatus. Hence, to reproduce the temperature, in 

Tables 86 to 89 from the measurements of viscosity made, the equation 

takes the simple form

') (13)

\ "* I /** v / "" vv ' v ~-f\j- ' U X, S

or

(l-l.nff)"\§ it I /" 2 \

(035)
282 MEASUREMENT OF HIGH TEMPERATURES.

a form which also includes equation (12), since A and B are constants. 

In the case of any instrument the capillary bore of which is variable 

along the length of the tube, or which can not be determined, A and B 

may be found by exposing the viscosity pyrometer to two known temperatures. For greater accuracy such an instrument may be directly 

compared with the air thermometer in the way soon to be indicated. 

In this place it is pertinent to call to mind certain valuable properties 

of the explicit equations (12) and (13). In the first place it is clear, 

inasmuch as the right-hand member of the equations varies as the 

f power of absolute temperature, that the transpiration thermometer 

is unusually sensitive to variations of temperature. Again it appears 

that the one consideration in which the equations might seem to be of 

questionable applicancy, viz, the occurrence of the fourth power of 

(I-\-/36"), becomes of less serious moment because this expression only 

effects 1+a 6" in the 2.4 power of (l+(36"). Hence the coefficient of 

thermal expansion ot platinum, it known with an accuracy of only 

10 per cent.,would not affect the result more than 0.2 per cent, at 1,000°. 

Furthermore, in the case of known fixed thermal data, like those discussed in Chapter II, /? may be directly determined from transpiration 

measurements made with the instrument itself. For it is merely necessary to solve equation (14) with respect to fi in order to determine this 

constant with the same degree of accuracy with which it is to be used. 

Finally the quantity

.Bo4

which enters into equations (12) and (13) can also be directly determined, 

from measurements made at the low temperature. For, disregarding 

the unessential correction members, equation (5), on page 253 shows at 

oiice that

-i . J-l'O_

r) 16.70. LVQ ^ *>

in which if the measurements are made at #, t) may be reduced to 170 by 

Holman's coefficient. With this,operation the fiducial zero of the viscosity apparatus may be said to be determined. -EVAo is more accurately determiuable in this way than by gravimetric measurement 

of R.

Results. To give emphasis to the remarks on the probable excellence 

of the viscosity pyrometer, I will use the data in Tables 86 to 89 for 

the calculation of temperatures from data based on the viscosity of 

the gases operated with. In Table 92, 6" denotes the temperature, 

thermo-electrically measured, at the points of the helix shown in the 

diagram, Fig. 47&, [B"] is the corresponding datum of the transpiration 

pyrometer.

(936)
BAMJB.] VISCOSITY OF GASES. 283 

TABLE 92. Tender at urea measured thermo-electrically and lythe transpiration pyrometer.

Air......:

Air.......

Air.......

Air.......

Air .......

Air.......

Air.......

9"

520

562

567

58C

598

994

994

996

1212

1217

1219

430

436

446

455

563

568

570

575

97f; lO

981

990

. 1209

1210

1210

[«"]

511

549

558

572

583

964

963

966

1217

1227

1222

442

450

458

467

0(1 W1 

574

577' 

580

QfiR yuO

971

981

1245

1245

1247

Diff.

+ 9

+13

+ 9

+14

+15

"7~OU 1 DA

+31

+30

_ 5

-10

- 3

^ 19J.4

-14

-14

-12

Q o

- 6

- 7 

- 5

+10

.+10

+ 9

-36

-35

-37

Hydrogen .

Hydrogen .

Hydrogen .

Hydrogen .

Hydrogen.

0"

958

9CO

962

962

970

.1209

1212

1215

414

416

421

423

507

513

515

518

520.

521

940

952

954

955

10"]

956

958

959

960

975

1329

1338

1337

434

437

441

445

529

535

530

541

543

543

963

908

974

976

Diff.

+ 2

+ 2

+ 3

+ 2

- 5

-120*

-126

-122

- 20

- 21

- 20

- 22

- 22

+ 22

- 21

- 23

- 23

- 22

- 17

- 16

- 20

- 21

* Platinum pervious to hydrogen.

The errors of this table are apparently large in places; but they are 

by no means excessive when the great difficulties of experiment are 

justly taken into account. The observation of especial importance here 

is that the distribution of errors is promiscuous. A difference of 125° 

occurs in the case of hydrogen transpiring at 1,200°; but at this temperature platinum is seriously pervious to hydrogen. In some measure 

the errors are due to the fact that the gases referred to the same 770 

were not absolutely identical in composition. This is particularly the 

case in the final data for hydrogen in which the nearly constant error 

 20° is due to the erroneously low //0 here inserted as I have already 

pointed out, page 271. Beyond this I believe that the differences of 

temperature remaining indicate actual differences of thermal environment for the two thermometers here compared. They show that 

throughout the space enveloping the two pyrometers temperature was 

not rigorously constant, and it is quite in keeping with the present 

method of experiment to suppose that the mean temperature, (9", of three 

points as given by the thermo-element, and the mean temperature [f9"J, 

for the length of nearly 67?m of platinum capillary tube, will not even in

(937)
284 MEASUREMENT OF HIGH TEMPERATURES. [BULL. $4.

the final experiment have been identical within 20° at 1,000°. Taking 

the transpiration data alone they manifest a striking degree of accordance even above 1,300°, as may be readily proved by the earlier tables, 

81 to 85. Again the uniformity of variation of a given thermal datum, 

whether measured thermo-electrically or by the transpiration pyrometer, proves beyond a doubt that high thermal data are measurable at 

1,000° in terms of the viscosity in gases with an accuracy of a few tenths 

of a degree.

TRANSPIRATION NOT SUBJECT TO THE POISEUILLE-MEJER LAW.

Objects of the investigation. The chief difficulty in operating with capillary tubes of a bore so fine that Meyer's formula is rigorously applicable 

at low temperatures as well as at high temperatures lies in the fact that 

the flow in such tubes almost ceases when the degrees of white heat 

are approached. There are a number of ways of obviating this annoyance, in the first of which fascicles of tubes are used side by side; in 

the second of which the transpiring volumes are measured in graded 

apparatus, so that at high temperatures small volumes may be measured 

as accurately as large volumes at low temperatures. Again, transpiration may be allowed to take place through graded capillary tubes of 

platinum the length or bore of which increases by some given law; or ^

with the slow current in continuous flow, rates of transpiration ( ~T° )

may be measured by some applicable method of repetition.

It is nevertheless desirable, however well these means suffice for 

the attainment of the end in question, to try to arrive at practical 

results relative to tubes of a bore so large that Meyer's formula is no 

longer applicable. All these endeavors are decidedly in the interest of 

expeditious work, for I find that compared with each other such measurements are not lacking in accuracy, although, the total time consumed 

for observation may not exceed a minute.

To make these observations greater volumes of air are necessary. 

Hence I have found it desirable to measure the volumes before they 

enter the platinum capillary tube. I mention this here to point out an 

important peculiarity of the above apparatus. It is easily possible so 

to adjust it that the gas may be measured both before entering and 

after leading the platinum capillary. The observer then has it in his 

power not only to detect the presence of gross leaks in the apparatus 

with certainty, but to follow the gas in its motions either (normally) 

through the capillary canal or (by diffusion) through the white-hot walls 

of platinum tube. 1 Moreover, it will be noted that the experiment in 

gaseous flow through capillary tubes are accompanied by something re- ^ 

motely similar to self-induction on opening and on closing the circuit. For 

when the stop-cock Kin Fig. 45 is opened, the air rushes in the dead space

1 See remarks relative to impure hydrogen, p. 275. 

(938)
VISCOSITY OF GASES. 285

between stop cock andcapillary tube until the high pressurePis reached; 

and after closing the stop-cook the compressed air of the dead space is 

gradually discharged. The method of eliminating the positive error 

which is thus added to the transpiration volume (F0 ) has been indicated 

ou page 257. But when the transpiration volume has to be chosen small 

the dead space discrepancy is more serious in character even when reduced to the smallest value compatible with the practical efficiency of 

the apparatus. These difficulties are quite avoided by using tubes of 

large bore and larger volumes of gas, and hence a second reason why 

the experiments of the present paragraph are desirable.

Hoffmann^ft researches. From a theoretical point of view1 the considerations involved are, of course, of extreme difficulty and complicated in mathematical character. As such they must be here omitted. 

From an experimental point of view, the difficulties encountered are 

fortunately less formidable, and an excellent analysis of the subject,

based on a variety of observations, has been published by Hofftnano.2 

Hoffmaun, after recognizing thafc the chief discrepancy is introduced 

at the ends of the tubes, derives his first equation by successively applying Navier's equation vp=E2 TT n^ A/ ClnP~ for the ends of his

7T]

tubes, and the Poiseuille-Meyer equation for the intermediate parts. 

Unfortunately, even in the favorable case of slight variation from 

Poiseuille-Meyer's law, this process leads to very involved results i

R* Ttdg (TTt 2 - 7T22 ) j ;

where p\ and pz are the observed pressures just before entering and 

leaving the capillary tube, and n\ and 7t2 are the corresponding pressures in the first and final section; C= - an(j ^ remajn.

0.00129277

ing variables have a meaning which is easily understood from the 

discussion on page 253. #=3.1416 and e is the basis of the Naperian

irTlie literature is digested by Hofifnianu (1. c.) as follows: Navier: M6m. do I'Acad. 

de so.do Paris, vol. 6, 1823, p. 389; Poissou : Journale do l'6cole Polyteclinique, vol. 

13, 1831, p. 139; Stokes: Trans. Cambridge Philos. Soc., vol. 8, 1849, p. 287; Caucby: 

Exerc. de Matbe'in., vol. 3, 1828, p. 183; de Sb. Venant : C. E., vol. 17, 1843, p. 1240; 

Stefan: Wien. Ber., vol. 46 (2), 1862, p. 8.

2 Hoffinanu: Wiedemaun, Aunaleu Physik, new series, vol. 21, 1884, p. 470.

(939)
28G MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

logarithms. Unfortunately these values of it\ and rcz themselves contain vp, for which, however, the approximate value given by PoiseuilleMeyer's law may usually be substituted with sufficient accuracy.

In view of these difficulties Hoffinann investigates an empirical relation by observing that (cseteris paribus) the certain small length of 

maximum efflux is subject to Navier's law, whereas as length increases 

the efflux obeys Poiseuille-Meyer's law. If, therefore,.time of efflux 

(caiteris paribus) be studied as a function of length, Favier's law fixes 

a point, while Poiseuille-Meyer's law fixes an oblique line passing 

through the origin. Hoffmann then supposes on the basis of his experimental results that the actual passage from the point to the line takes 

place nearly along an hyperbola, of which the said point is the vertex 

and the said line the asymptote. A suitable modification of this hypothesis leads Hoffmaun to the equation

where

p _

1

I C , 2Pl 

V 0.43429 k ^+

and where &=(Z+4) (2 Z+4) and a has a tabulated value of nearly 1, but 

varying with the mean difference of pressure.

Hoffmann's equation contains difficulties of calculation of a very 

tedious and impracticable kind, particularly in view of the involved 

Occurrence Of the factor 0, which represents the thermal variations 

of the transpiring gas. With full deference, therefore, for the accuracy of application which Hoffmann has reached in his results, I shall 

nevertheless compute r; by the formula (5) on page 253, above; i. e., 

directly by the Poiseuille-Meyer law. Having done this, it was my 

further object to find from the known law of variation of 77 with temperature, what correction was to be applied to the Poiseuille-Meyer 

equation, to make the data for tubes not rigorously capillary conform 

with the data already in hand for truly capillary tubes. The plan 

which I have in mind is somewhat different from that of Hoffmann 

and more in harmony with the general tenor of my experiments. The 

form which I aim to give my correction is an exponential, in which 

the dimension of the capillary tube and the actual viscosity of the 

transpiring gas are the variables. I found, however, that to do this 

satisfactorily it would be necessary to repeat my experiments at greater 

length than I am now justified in doing; and observing that the data 

which I have in hand make up a diagram of the transpiration phe-

(940)
VJSCOSITY OP GASES. 287

nonienou iu wide tubes, of remarkable clearness and full of suggestion, 

I resolved to communicate these without elaborate reductions.

EXEKIMENTAL RESULTS.

Transpiration under variable pressure P p. I shall introduce these 

results by a number of experiments made at the outset of the present 

investigation, inasmuch <*s these have a direct bearing on the feasibility 

of the transpiration apparatus for pyrometric purposes. In these experiments neither Mariotte flask nor lateral tube was employed, so that 

the pressure fell from the initial to the final value at one end of the 

tube, the other being at atmospheric pressure. The helix itself was 

wound in a flat form of large radius so as to lie completely in the zone 

of fusion of the Bunsen burner. For each special part of the table the 

conditions of flow, however complex, are the same, t is the time of

efflux of the volume T7 ; L and I denote tbe length of tube and cold 

ends; R is the internal radius. In Table 95 the tempestuous influx of 

mercury into the receiver B was avoided by opening the stop-cock of 

the Mariotte flask until the flow of mercury had ceased, and then opening the stop-cock of the capillary.

TABLE 93. Transpiration of air under variable pressure. (Burner not chimneyed.)

[Capillary tubo No. 1. i=37cra. 1=8 . Ji'=0.025cm. F0 =5ROC<! . 0 = 20°.]

Time.

98

459

99

459

98

78

32.'i

78

314

78

189

57

187

55

187

Initial 

pressure.

1

;> 108

J

1

1

X 118

J

}

} 143

J

Final 

pressure.

97

107

'

132

Barometer.

(

78-

I

(

no

1

(

78-

j

Temperature.

20°.

Bright red heat (1,000°).

20°.

Bright red heat.

20°.

20°.

Bright red heat.

20°.

Bright rod heat.

20°.

Bright red heat.

20°.

Bright red heat.

2Qo.

Bright red heat.

(94 J)
288 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

TABLE 94. Transpiration of air under variable pressure. (Chimneyed burner.} 

fPlatinum capillary tube No. 1. Z-=37cm. Z=4cra . J2=0.0272C °'. F0 = 580CC .]

Time.

79

2-19

79

252

145

590

145

597

Initial 

pressure.

S 118

J

^

} 99

J

Final 

pressure.

112

91

Barometer.

f

|

1

(

7Q J

1

Temperature.

18°.

Bright red heat.

18°.

Bright red heat.

18°.

Bright red heat.

18°.

Bright red heat.

TABLE 95. Transpiration of air -under variable pressure.

 [£=37 . Z=4CI". ^=0.0272 . 6=5°. Y0 =:580CC .]

Time.

73

244

74

242

74

92

313

92

319

92

125

487 

125

478

125

195

900

900

196

Initial 

pressure.

1

] 120

J

1

|

> 111

J

1

1

101

]

I 92

J

Final 

pressure.

314

104

94

84

Barometer.

f

77 <

I

f

'77 <

(

77 <j

f

77 \

I

Temperature.

15°.

Bright red heat.

15°

Bright red heat.

15°.

150.

Bright red heat.

15o.

Bright red heat.

160.

16°.

Bright red heat. 

16°.

Bright red heat.

 16°.

16°.

Bright red heat.

Bright red heat.

16°.

Transpiration under constant pressure P p. The following tables, 96 

to 100, contain the results of precise experiments. As before, P and p 

are the pressures at the two ends of the platinum capillary, respectively; 6" the temperature of its hot parts L (l'+l'"), and 6 the temperature of its cold parts. Fis the zero-volume of air transpiring 

through the capillaries in the time t". R is the radius of the capillary 

and T the actual temperature of the air in the receiver B (Fig. 43), from

(942)
"Anus.] VISCOSITY OF GASES. 289

which temperature r the reduction to zero was made. F(6") has the 

above signification.

 El i Oll\ _ f) . 1?0

Unfortunately, the measurement of 6" in all these experiments was 

made as shown in the diagram, Fig. 47, and hence these values are not 

so good as those in Tables 86 to 89 above (helix very compact), r is 

directly read off on the thermometer T in the receiver J3, in Fig. 44, 

and the correction may be applied either to t" or to the final rf1 .

To measure F, I filled the receiver with mercury and weighed the 

volume of liquid contained. Similarly R was computed from the weight 

of the mercury thread which fills the capillary tube. But this operation in case of an opaque tube is very unsatisfactory. My plan was to 

seal the capillary helix (previously dried and weighed with care) into a 

glass tube with mastic, and then allow a current of mercury to pass 

through both. When all air was expelled 1 stopped up one end of the 

capillary with softwax, then removed the glass tube, cleansed the helix, 

and weighed again. The weights so obtained differ enough to make 

errors of 5 per cent, and 10 per cent, in E4 possible. Hence I put no 

stress on the absolute data, but consider them in their relative bearing 

only. For each such relative series B is constant. Perhaps volumetric 

methods might have led to better results (v. page 213), but I did not 

apply them.

To calculate rf" the formula on page 253 was employed in the usual 

way. This presupposes a knowledge of rj for the cold ends, corresponding to each pressure observed. It is necessary, therefore, first to construct T; as a function of pressure graphically, in order that the proper 

value may be inserted into the correction member of the formula for rf'.

The error due to cold ends here in question bears an intimate relation 

to the Navier effect; and this method of correcting for it presupposes 

that both the cold part and the hot part of the capillary has two ends. 

Hence it would seem that as there are in all but tivo ends, instead of 

four, to the capillary tube experimented upon, that the correction 

applied is not valid. I think, however, the following results show that 

the departure from Poiseuille-Meyer's law observed with metallic capillary tubes is largely due to unavoidable roughness of the internal surface (i. e., of the walls of the capillary canal), and hence the correction 

is warranted.

Bull. 54 19 (943)
290 MEASUKEMENT OF HIGH TEMPEEATURES. tA. Wt

TABLE 96. Apparent viscosity of air at high temperatures. Absolute measurement. 

[Capillary tube No. 10. J/=33.43cm. Z'+Z'" = 2.7 . 7=565.7C<!. R 0.00794cm. 0=7°.]

p

*ioq it

92.32

t!24.69

88.60

U25.64

125. 68 

§125.22 

124. 68

P-p

56.35

15.56

48.04

n

QR

49.18

49.22 

48.86 

48.32

1506

6545

1677

7930

1683

1660 

18000

1/!7O

P'-P\ t»

P

232000

224300

211COO

204400

218800

216000 

2321000 

213500

17

l+4f/.K

O HHA979

262

0. 000251

243

0. 000256 

0. 000255 

0. 000254

6"

o 

0

0

0

0

14

0 

977 

0

1"

1 + 4 £"/.«"

0.000266

257

246

998

0.0002588

{2508 

6858.

94 Q1

10 R

19.4

21.5

22.0

20.8

20.7 

22.8 

22.3

Jb(0")

2.743

* First ajnstraent, p = 76.76. 

t Second adjustment,^ = 76.65.

I Third adjustment, p=76.46. 

§p = 76.36.

TABLE 97. Apparent viscosity of air at high temperature. Atsolttte measurement.

[Capillary tube No. 9. L = -. -Rr=0.0184tm. 7=566"". 0 = 4°. Z'+Z'" = 1.5cm. Thermo-couple

No. 37.]

P

*121. 26

121. 25

121. 24

114. 31

114.16

107. 60

107.54

10).. 12

101. 10

94.24

94.23

87.41

87.44

87.44

t87. 91

87.85

94.81

95.00

101.45

101.75

115. 51

115.52

123.44

123. 50

|124.10

124. 24

§88. 33

88.19

11124.16

123. 99

r p

45.34

45.33

45.32

38.39

38.24

31.68

31.62

25.20

25.18

18.32

18.31

11.49

11.52

11.52

11.81

11.75

18.71

18.90

25.35

25.65

39.41

39.42

47.34

47.40

47.89

48.03

12.25

12.11

48.20

48.03

t"

183

183

183

211

211

250

250

306

306

407

405

621

616

614

856

846

556

551

419

418

283

281

241

241

1193

1188

5632

5624

1175

1187

P?-^x<"

P

21550

21550

21550

20290

20200

19150

19110

17980

17960

16710

16620

15350

15270

15220

21790

21420

23370

23420

24780

25060

28070

27890

29920

29960

150100

150100

149200

147000

149200

150100

6"

0

4

4

4

4

4

4

4

4

4

4

4

4

4

4

100

100

100

100

100

100

100

100

100

100

1026

1030

1024

1021

1026

1026

V

]+i"/-«"

0. 000367

365

364

343

341

324

323

302

302

282

280

259

258

257

0. 000280

275

300

301

319

322

361

359

385

385

0. 000591

589

591

586

590

592

T

20.5

19.2

18.8

18.5

18.5

18.5

18.5

18.3

18.3

18.0

18.0

17.8

17.8

17.8

19.6

19.9

20.2

20.1

20.0

20.1

20.3

20.3

20.3

20.3

21.0

21.2

22.0

23.0

22.7

21.5

) = 76.21.

(944)

> = 76.08. = 75.96.
BARUS.] VISCOSITY OF GASES. 291

TABLE 98. Apparent viscosity of air at high temperatures. Absolute measurement. 

[Capillary tube No. 3. i=42cm . Z=4 . J?=0.025cro . F=566cn . 6=5°. Thermo-couple No. 37.]

P

*87.6

91.9

97.0

102.2

107.6

112.0

117.1

t88.3

93.2

98.2

103.2

108.3

113.5

J89.6

94.7

100.5

§92.0

98.9

105.7

112.7

P VIf

11.3

15.6

20.7

25.9

31.3

35.7

40.8

11.3

16.2

21.2

26.2

31.3

36.5

12.8

17.9

23.7

15.0

21.9

28.7

35.7

t"

212

160

127

106

91

81

73

220

162

128

106

92

81

269

201

156

1209

796

585

453

 **-** x«»

P

5120

5480

5950

6410

6850

7120

7540

5300

5800

6158

6498

6930

7315

7460

8030

8530

39800

39740

39840

39840

0"

0

5

5

5

5

5

5

5

14

14

14

14

14

14

100

100

100

941

941

934

933

r,"

l+4£"/jR"

0. 000279

299

325

351

375

389

410

0. 000285

309

328

346

369

389

0. 000312

336

357

0. 000562

560

564

564

r

18.0

18.0

18.2

18.5

18.2

18.2

17.5

16.5

16.5

16.5

§#=77.0.

TABLE 99. Apparent viscosity of air at high temperatures. Absohite measurement. 

tCapillary tube No. 4. Z'+Z"'=4 . L=42.&m. 7=566 . JK=0.025c -». 0=4&. Thermo-couple No. 37.]

P

"86.4,

86.4

89.7

90.2

90.8

91.2

96.5

96.6

101.6

101.8

106.9

107.0

111.3

112.2

112.3

115.1

117.3

t88. 9

89.0

123.7

123.6

95.8

P-p

9.5

9.5

12.8

13.3

13.9

14.3

J9.6

19.7

24.7

24.9

30.0

30.1

34.4

35.3

35.4

38.2

40.4

12.0

12.1

46.8

46.7

18.9

t"

268

267

204

200

194

189

146

147

121

121

104

103

92

90

90

85

80

1000

1023

260

263

665

**-*%«»

P

5390

5400

5690

5780

5870

5920

6480

6530

6980

7010

7450

'7420

7750

7830

7840

8100

8170

25850

26850

31780

32060

28360

6"

o

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

 636

658

652

658

684

r,"

l+4£"/JZ"

0. 000266

267

281

285

289

292

319

321

345

345

0. 000368

366

385

386

382

403

400

0. 000428

435

514

516

446

22'

22

22

21

21

21

21

21

21

21

22

22

21

21

21

22

22

19

19

19

19

19

(945)
292 MEASUREMENT .OF HIGH TEMPERATUEES. [BULL. 54.

TABLE 99. Apparent viscosity of air at high temperatures. Absolute measurement Cout'd.

p

95.6

116.7

116.7

106.1

106.2

123.7

123.7

{95. 2

95.2

95.3

123.4

123.4

95.2

95.4

123.2

123.5

95.4

§123. 5

123.6

88.2

88.4

123.6

123.5

88.3

P-p

18.7

39.8

39.8

29.2

29.3

46.8

46.8

18.9

18.9

19.0

47.1

47.1

18.9

19.1

46.9

47.2

19.1

47.3

47.4

12.0

12.2

47.4

47.8

12.1

t"

681

317

317

431

434

268

268

697

724

767

305

311

835

847

327

3-26

864

363

366

1721

1688

366

369

1688

P*-P\t»

P

28670

31810

31810

29910

30330

32760

32760

29690

30840

32910

37640

38390

35550

36510

40140

40340

37270

44840

45540

44440

44320

45500

45770

44220

6"

o

695

687

690

687

689

688

687

721

744

786

808

848

855

860

862

864

875

988

994

998

1004

1005

1005

1004

ij"

1+4^'VJZ"

447

497

496

468

474

511

511

0. 000451

457

471

526

518

480

491

536

537

494

0. 000545

548

537

535

545

549

532

T

20

20

20

21

21

21

21

20

20

a

19

19

19

19

19

19

19

19

22

23

23

23

24

 24

24

*p=76.9. t#=76.9. {#=76.3. §#=76.2.

TABLE 100. Apparent viscosity of air at high temperatures. Absolute measurement. 

[Capillary tube No. 5. £=35.1. JJ=0.025cm. F=565.7CC . 0-7°. l'^-l"'=3.0cm-]

P

*123. 83

124.76

124. 53

89.20

89.17

t!24. 61

124. 67

{124. 24

124. 07

88.90

88.99

124. 31

124. 11

§108.44

109. 07

85.81

85.63

85.78

108. 96

108. 47

P-p

46.79

47.72

47.49

12.16

12.13

47.61

47.67

47.31

47.14

11.97

12.06

47.38

47. 18

31.59

32.22

8.96

8.78

8.93

32. 11

31.62

t"

436

426

428

1942

1935

423

422

337

338

1469

1458

334

334

92

90

261

263

262

90

92

P*-P* , 

P Xt

53200

53250

53100

50840

50640

52700

52660

41690

41630

_ 37910

37920

41390

41170

7008

7015

4949

4881

4Q>i1 :t<7i>.L

6985

7015

6"

1285

1286

1286

1286

1297

1300

1305

1048

1045

1044

1043

,1035

1035

70

ij"

l+i"/J?"

0. 000585

585

584

565

567

579

578

0. 000541

541

495

495

540

538

0. 000386

386

273

269

273

385

386

^

19.4

19.6

19.8

21.0

' 22.0

22.1

22.4

22.8

22.5

22.5

21.8

22.0

22.0

22.0

22.0

22.5

22.5

22.5

22.5

22.5

*J9=77.04. t#=77.00. {#=76.93. §#=76.85.

(946)
BABU8.] VISCOSITY OF GASES. 293

Among these tables the first is unique, and I shall therefore specially 

refer to it. The capillary tube used is the same with which the data 

in Tables 81 to 90 were investigated; but for the large volume V0 the 

time of efflux at red heat (977°) is five hours. During the whole of this 

time 6" and P were measured so as to obtain a fair mean result and 

eliminate unavoidable fluctuations of temperature. It is exceedingly 

gratifying to observe that the value of F (6") computed from these 

observations conforms very well with the data of Tables 81 to 89, and 

with the law rf'=770(1+ ao"}*, despite the great difference of method of 

measurement employed. Differences of T/O in different parts of the table 

are due to imperfections in the earlier adjustment; but the values of 

770 measured before and after the high temperature measurement agree 

satisfactorily. Variations of r/0 with P will be discussed below. The 

negative error of F(d") may also be anticipated, since in so long a 

period of efflux (five hours) even minute leaks in the compressing appa.

ratus would produce appreciable results.

Transpirations compared differentially. Before proceeding with the 

discussion of these results it is expedient to communicate the data 

obtained with a differential apparatus. The formula for this method 

of experimentation has already been given. Hence the results of the 

following Tables 101 to 103 need but little further elucidation. The adjustments here are identical in plan with those of the differential galvanometer. In Fig. 55, p. 305, air is supposed to enter at a and to pass 

through the stop-cock K, where the bifurcation of current is brought 

about. Supposing K open, a part of the air passes through the hot 

spiral H and thence to the measuring-tube Vs ; the remainder through 

the cold helix (7, and thence to the measuring-tube Fh. Fh and Vg corresponding respectively to the temperature 6 and 6" are given in the 

Tables. If 6=6", then the results contain data for the computation of 

the ratio of the radii of the two helices. If 0"> 0, the results lead to

the beauty of the method being this, that time and pressure measurements (in the case of capillary tubes of very small bore) are superfluous. 

I have purposely used tubes of large bore however. From

may be calculated by inserting the corresponding values of 77 from 

Tables 96 to 100.'

(947)
294 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

TABLE 101. Differential measurement. Apparent viscosity of air at high temperatures. 

| Capillary tubes Nos. 5 and 6. l'+l'"=Q. J"=35.1< . Z=35.1«ra. JZ=0.025«». Couple No. 37. p=75.3-

p-p

16.7

15.1

11.5

8.9

P-p

7.9

11.0

16.2

20.6

25.8

31.1

27.8

23.1

19.2

14.0

9.2

Fh

48.51

48.09

48.44

47.14

Fh

51.3

50.2

50.7

52.0

48.4

48.6

46.2

45.7

50.2

50.3

50.8

F6

52.17

x*(\ d.9

52.57

51.22

48.06

F6

16.5

16. 5

16.9

16.5

38.6

36.7

. 6.4

15.4

16.9

16.0

14.6

,"<i+ 4-£)

ij/a-Hs/.Rz)

1.30

' 1.22 .

1.15

1.18 .

0.92

0.99

0. 06

1.02

1.03

1. 10

1.22

6"

o 

4

4

4

4

4

6"

454

dSt

505

531

578

61 !

620

612

604

594

589

P

92.1

90.4

85.9

84.3

P

83.4

86.5

01.7

Qfi 1

101.3

306.6.

98.6

94.7

89.5

84.7

Rb/Ke

0.928

0.911

0.914

0.946

0.981

TABLK Iu2. Differential measurement. Apparent viscosity of air at high temperatures. 

[Capillary tubes Nos. 5 and 6. l'+l'"=5em . Z"=30.0cm. Z=35.0om. JZ=0.025cm. p=76.2. 0=946°].

P-p

48.3

12.0

48.2

11.9

11.8

49.3

11.8

51.7

12.4

51.7

51.6

12.3

53.0

Fb

50.54

51.95

52.59

51.59

51.09

51.62

49.79

52.77

52. 69

50.99

52.19

51.87

52.02

Ti

42.06

39.87

44.19

40.26

34.86

37.46

35.76

41.36

38.51

38.31

36.29

34.29

37.61

ij»(l+a0») a+/30)«

nff+afl) (i+/W7)*

1.37

1.48

1.36

1 46

1.66

1.57

1.58

1.45

1.56

1.51

1.63

1.71

1.57

0"

(1200)

(1300)

1160

1160

1160

1280

1280

1280

P

124.5

88.2

124.4

88.1

88.0

125.5

88.0

127.9

88.6

127.0

127.8

88.5

129,2

(948)
BARUS.] VISCOSITY OP GASES. 295

TABLE 103. Differential measurement. Apparent viscosity of air at high temperatures.

[Capillary tubes Nos. 5 and 6. l'+l"i = &". i"=30.4°m. J-=41.2«I». JB=0.0184CIB. Thermo-couple

No. 37. 0 = 4°.]

p-p

39.9

10.7

10.7

10.8

39 8

P-p

44.0

11.9

44.6

11.7

44.5

44.7

11.7

44.8

11.4

45.2

11.5

Fh

43.8

44 7

43.3

43.6

44.4

Fb

51.2

51.9

51.0

52.1.

61.3

51.6

52.5

52.1

52.8

61.5

52.4

V

R9 ^

KO O

51.9

52.1

51.3

v*

16.2

12.2

15.4

11.5

14.9

9.54

7.22

9.51

7.05

9.40

6.96

F(6")

1.38

1.78

1.37

1.86

1.40

1.61

2.17

1.63

2.23

1.63

2.24

6"

4

4

4

4

4

6"

587

605

614

624

630

973

974

977

977

978

979

P

117.4

QQ 0

88.2

88.3

m

o

P

121.5

89.4

122.1

89.2

122.0

122.3

89.3

122.4

89.0

122.8

89.1

P

77.5

77 *\

77 5

77 f\

P

77.5

77.5

77.5

77.5

77.5

77.6

77.6

77.6

77.6

77.6

77.6

JBh/^8

1

AA

1 M

1.00

1.00

i nl

1

1+y .

0.000362

259

364

258

363

0. 000364

258

364

257

365

258

1"

w£

0.000501

461

498

480

608

0. 000587

560

593

574

596

578

It was not my object in this place to carry this method to a high degree of perfection, but rather to show the feasibility of measurements 

made in this expeditious and simple way. This the tables effectually 

do. Table 101 shows that for tubes of the large radius .R=0.025cm the 

results are not accurate when so small a volume as 7=50CC transpiring 

at zero, is made the standard of comparison. They are irregular. On 

the other hand, when the standard volume transpires at high temperatures (0=900° and 0">0), this method proves to be quite feasible 

and the results regular (Table 102). For tubes of finer bore (jR=0.018cm ), 

Table 103 shows that the data are consistent at all temperatures.

Fortunately, in the differential. method the errors due to the dead 

space between stop-cock and the capillary, if this space be made small, 

is nearly eliminated.

DISCUSSION.

Apparent viscosity and pressure. To obtain a clear insight into the 

data of these tables, it will be necessary to construct them graphically. 

This has been done in Fig. 54, p. 304, in which the abscissae are P p, 

and the prdinates the value of rf1 given by the Poiseuille-Meyer formula, 

by inserting in it the given constants of the apparatus and the value of 

the pressure, time, and volume data observed. Commencing with Table

(949)
296 MEASUREMENT OP HIGH TEMPERATURES. [BULL. 54.

96, which contains data for the smallest radius occurring in the present 

work, jR=0.0079cm, it appears that the value of r/Q increases very perceptibly as P p increases. The different lines drawn correspond to 

differences in bore of the readjusted tubes. At 9.80°, owing to the 

length of time of a single observation, only one datum is at hand. 

Turning thence to Table 97, which .holds for tubes of a larger bore 

(.B=0.01S4cm), the values 7/4 77100 . . . are found to lie on very nearly 

straight lines, which, in comparison with those of the preceding table, 

have increased enormously in obliqueness; 77 therefore increases at a 

rapid rate with P p, which rate, however, diminishes as temperature 

increases, and is nearly zero at 1025°. Now, inasmuch as the rate 

of axial transpiration decreases with temperature, and inasmuch as 

Meyer's formula fails for values of the velocity of the particles above a 

certain datum, these curves suggest that the observed decrement of 

slope of the lines produced by temperature is due to the decrease of 

the axial velocity of the transpiring particles produced by the same 

cause. In this place the differential results of Table 103 are available, 

and furnish data for r/625. The values for 7/975, which Table 103 also contains, are, in general, in good accordance with the data of Table 97, 

and are therefore not essential to the diagram.

Tables 98,99, and 100 contain results for the largest value of radius, 

jR=0.027cm, occurring in these experiments. In Table 98 the results 7/5, 

*7i4, T/IOOJ show a tendency to curvilinear loci. But the true character of 

the phenomenon appears none the less clearly. The mean rate of 

increase of 77 with P p is distinctly larger than in the previous instance 

(Table 97). Again the slope decreases as temperature increases, and 

is practically zero at 930°. Here, therefore, the effect of the axial 

velocity of the transpiring particles is again apparent.

Table 99 is more full as regards the sequence of data contained, as 

well as more accurate j 7/4 shows a tendency to curvature, but the points 

may Serviceably be grouped on a straight line; 7/676 is the mean of the 

first set of results for tempsratures of the Argand air-bath. Inasmuch 

as pressures are high and low alternately in both this series and the 

next, the line connecting corresponding observations has fair claims to 

accuracy. The data substantiate the inferences drawn with reference 

to Table 88. The lines are all oblique and they approach horizontality 

in proportion as higher temperatures are reached.

I may notice here that in case of high temperatures the cooling* effect 

of air passing through the capillary under high pressure was very distinctly discernible, the thermo-couple showing differences of 20° to 40° 

between the maximum and minimum rates of flow.

Table 100 finally contains results of my largest radius, JS> 0.027cm, the 

exact value of which I do not now care to measure, because the capillary 

apparatus has been carefully put together and all mercury manipulations involve danger. In this emergency I made the permissible supposition that for P #=0, the value of 7^ is the same as that in Tables

(950)
BAKU8.] VISCOSITY OF GASES. '297

97 to 99. This enabled me to reduce my relative data to the same 

standard as holds for the Tables 97 to 90. The diagram obtained fully 

corroborates all the inferences deduced. The obliquity of the lines 

decreases from low to high temperatures, i. e., in proportion as the 

velocity of the axis flow decreases.

Appear ent^mscosity and temperature. Considering these results as a 

whole, and representing the values of 77 when P jp=0 as a function of 

temperature, 6", it appears that the curves lie farther away from the law 

r?"=r/0 (l+a#")5 in proportion as E is larger. Thus the results, 77, of 

Table 96, E=0.008cm, conform very fully with this law; the results of 

Table 97, JR=0.01Scm, fall considerably below it, and finally the results 

of Tables 98 to 100 where JR=0.025cm lie in a very pronounced way 

below the former. As the bore is chosen larger, therefore, the effect 

of temperature becomes gradually less pronounced, and for JK=0.025cm 

the law falls even as low as 7/"=7/0 Vl+a6". On the other hand, as the 

bore is chosen smaller the curves ultimately (12=0.008cm) coalesce with

Obliquity of the linear loci. In Table 104 1 give a perspicuous view of 

the observed obliquity of the lines in Fig. 54, p. 304, y> being the angle of 

these lines with the horizontal relatively expressed. The temperature

n" 

of transpiration being 6", the value in the table is computed from 7/0

 // \~w"~\

-L = (1+ <*#")* however is computed from Fig. 54 when P p=0.

W L.77J

TABLE 104. Transpiration of air in wide tubes.

6"

0

977

4

100

625

 1025

4

675

8C5

1000

7

1050

1280

*8

t8

 'i

R

0.008

(Table 90)

0,018

(Table 97)

0.025

(Table 99)

0.025

(Table 100)

0. 018

(Table 108)

0 012

(Table 107)

["]

L *)0 J

1.00

2.79

1.02

1.10

2.14

2.65

1.02

1.81

2.06

2.38

1.03

2.13

2.50

\~~-

tan <$>

20

(00)

314

298

64

7

461

228

166

30

488

128

44.

274

09

124

?" 

%

1.00

2.77

1.02

1.23

2.23

2.84

1.02

2.30

2.60

2.80

1.03

2.88

3.20

M* 10"

240

668

223

244

474

587

225

404

458

531

228

478

560

198

100

245

'Air. t Hydrogen.

(951)
298 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

For the given value of 0=4° the values of the tan cp decrease about 

as rapidly as the square of R. It is to be noticed, however, that the 

tan cp in the case of Table 96 is probably zero, since the observed positive tan <p in Table 104 is compensated by an observed negative tan cp 

in other similar cases. Hence if tan cp is to be represented in its dependence both on r)" or 6 and R, it will be necessary to assume an 

exponential form in which powers of both R and rf' are exponents.

Supplementary results. To further elucidate the relations under discussion I made a series of miscellaneous low-temperature experiments. 

Table 105 contains data for a glass tube of fine but not rigorously uniform 

capillary bore. Here the variations of ij with P p are quite insignificant, 

proving that the obliquity cp observed is not due to any imperfection of 

apparatus. The second part of the table contains results for a tube of 

larger bore than any of the metallic tubes. Nevertheless the variation 

of cp here is not proportionately large. The temperature of the receiver B, Fig. 44, is given under r.

TABLE 105. Transpiration in glass tubes.

[Capillary tube 2To. I. £=30.0<»». .72=0.0117 -. V 565.7". 0=6.6°. J

p

124. 06

123. 96

88.91

88.93

124. 08

124. 06

P

76.70

76.70

76.63

76. 63

76.50

76.50

394

398

1847

1838

394

394

p »«"

49040

' 49350

49220

49080

49430

49410

ff

6.6

6.6

6.6

6.6

C.6

6.6

21.0

20.8

21.2

21.4

21.6

21.8

7]"

4(T"

!**->

0. 0001505

1515

1511

1508

1517

1518

[CapillarytubeNo.il. L=U.2b . 12=0.0302"''. 7=565.7 . 0=6.6°.]

86.96

86.89

85.66

85.72

76.48

76.48

76.48

76.48

72

73

82

82

1613

1624

1597

1598

6.6

6.6

6.0

6.6

21.7

22.3

22.5

22.7

0. 0001946

1960

1933

1935

Table 106 shows that similar variations of rj with P p (i. e., the obliquity cp} occurs in case of silver tubes, the capillary being employed 

in two different lengths. Curiously enough, the value of cp here does 

not vary with L. There may, however, be a compensation in R. Silver 

capillary tubes could not be obtained in such excellent quality as the 

platinum tubes.

(952)
BARUB.) VISCOSITY OF GASES.

TABLE 106. Transpiration in silver tubes. 

[Silver capillary tube No. I. i=71.00cra . JZ-.0.0181 . F=566«. 0=6.7°.]

299

p

122. 61

122. 61

88.07

87.98

87.93

122.46

P

75.85

75.85

75.85

75.85

75.85

75.85

t"

281

282

986

992

992

280

P*-P* ,

p **»

34370

34400

26040

26010

25880

34120

0"

o 

6.7

6.7

6.7

6.7

6.7

6.7

T

22.7

22.7

22.7

22.9

23.0

23.1

n"

4£"

i+W,

0. 0002612

2620

1978

1976

19G9

2599

[Same spiral shortened. Zc=35.27cm.l

119. 59

119.56

87.30

87.44

119. 46

75.90

75.90

75.90

75.90

75.90

153

154

520

521

155

17220

17310

12820

12940

17380

6.7

6.7

6.7

6.7

6.7

22.2

22.0

21.8

21.6

21.2

0. 0002629

2631

1956

1971

2645

Table 107, with results for a fine platinum capi llary, has been incorporated here, and corroborates the present results.

TABLE 107. Transpiration in platinum tubes. Air. 

[Capillary tube No. 9. i=21.2cra. .J2=0.01.l8cin. 7=565.7°°. 0=7.0°.]

P

*123. 66

123. 80

88.17

88.05

83.30

1 123. 63

P

47.74

47.88

12.25

12.13

12.38

47. 74

t"

531

530

2137

M63

2112

525

P

66640

66740

56570

56660

56540

65900

e»

o 

7.0

7.0

7.0

7.0

7.0

7.0

T

19.0

19.5

20.1

20.6

21.2

22.4

~n

0. 0003049

3060

2601

2607

2609

3053

*p = 75.92. = 75.89.

Table 108, with which I will close the present series of supplementary 

data, has a direct and important bearing on the discussion. Hydrogen 

and air are here passed through the same platinum tube consecutively.

(953)
300 MEASUREMENT OF HIGH TEMPERATURES.

TABLE 108. Transpiration in platinum tubes. Hydrogen.

[Capillary tube No. 8. i=40.5<"n . JR=0.0182<"">. F=565.7CC. 0=7.8°. p=74.95°m .J

(nttu, 54.

p

112. 56

112. 52

112.06

85.75

85.72

85.64

112. 72

112. 67

P-^p

37.59

37.55

37.09

10.78

10.75

10.67

37.75

37.70

«"

107

107

108

352

354

355

107

107

P*~ p\t»

P

10060

10050

9990

8160

8160

8120

10110

10090

6"

o

7.8

7.8

7.8

7.8

7.8

7.8

7.8

7.8

T

22.6

22. 7

22.8

22.9

23.1

23.2

23.3

23.4

1"

1+W/M"

0. 0001354

1355

1347

1100

1101

1096

1365

1365

[Same apparatus with air.]

120. 47

120. 55

86.66

86.59

120. 52

45.55

45.63

11.74

11.67

45.60

202

201

676

675

202

24000

23930

17120

16980

24030

7.8

7.8

7.8

7.8

7.8

23.4

23.5

23.2

23.0

22.8

0. 000324Q

3235

2311

2292

3238

The results are very instructive. In the experiments (Fig. 54, p. 304) 

tan cp increases with the rate of flow, or, caeteris paribus, with the viscosity of the gas. Hence one would infer that in the ease of hydrogen 

and air passing through the same tube, cseteris paribus, the obliquity 

would be decidedly greater. The experiment shows precisely the reverse result; tan cp diminishes more than proportionally to the viscosity 

the ratio (Table 104) being as 3: 2.

General remarks. I regret that my research must be closed with 

these experiments, and that it is not expedient to continue the work

further. To do this I should need to repeat the work with special care 

in the measurement of temperature and iii the determination of the capillary radius. Nevertheless, the survey of the present field of inquiry 

is by no means unsatisfactory. My results show conclusively that the 

character of the internal surface of the transpiration tube is of marked 

influence on the result. The absence of obliquity ((p) in glass, and its 

frequent occurrence in metallic tubes, may be referred to the smoothness and roughness of the respective internal surfaces. Rough surfaces 

are associated with eddies along the line of flow, by which it is retarded 

and apparent viscosity is increased. The absolute value of viscosity 

measured by transpiration through metallic tubes is greater than the 

viscosity measured by transpiration through glass tubes. This I have 

in general found, and although the effect of the discrepancy, possibly 

due to roughness, is not vital in case of my smallest tube, No. 10 (Tables 

81 to 90, E = 0.008cm ), I have none the less thought it wise to state my 

result, r/'=rjQ (1+a 6"}* , with caution, and to pursue the present critical

(954)
VISCOSITY OF GASES. 301

inquiry as far as the present section indicates. Inasmuch as I have 

proved that as R decreases from my largest to my smallest radius, the 

value of -F(#"), which holds for P jp=0, increases and finally merges 

into (1.+ <* &")$ independently of pressure, I have accomplished the main 

purposes of this section. 

Intimately connected with the present discussion is the occurrence of 

surface condensation of gases on platinum. If the law of inverse 

squares holds, then there will be no tendency of gases to condense in 

the capillary canal, however finitely small. This follows from the constant potential of a homogeneous elliptical shell (of which the capillary 

tube may in a special sense be said to be compounded) on any points 

inclosed within it. But in the case of the law of inverse squares or 

any higher law, there may be condensation infinitely near the surfaces, 

together with the possibility that molecules condensed on the walls of 

the tube may again find their way into the canal. The occurrence of 

molecular aggregates in the canal or transpiring current of gas in virtue 

of surface action of the platinum can not therefore be assumed to be nil. 

[Kayser1 finds that the height of the coudensatioiioatmosphere of ammonia on glass may exceed .0002cm . Compared with the radius of my 

capillary tubes (JK=.008cm), this is by no means small. Hence there is 

reason to infer that the increased molecular aggregation of the transpiring gas is not negligible. In conformity with the results of Kayser 

and of Chappuis2, O. Schumann3 altogether rejects the transpiration 

method. I believe these strictures much too severe. Schumann's own 

observations are made at temperatures not exceeding 100°. Neither 

from these nor from any other earlier researches can the transpiration 

behavior of a gas between 400° and white heat be safely predicted. In 

tables 81 to 88 I have given the data in detail in order to show the excellent accordance of the data among themselves, even if an hour or 

more of heating to redness intervenes. The differences are clearly 

errors of observation. If, therefore, condensation discrepancies are 

present, their time of variation must be almost instantaneous.

Furthermore, the identity of law (1+a #) § for both air and hydrogen 

is most easily interpreted as an immediate fact. Otherwise it will be 

necessary to suppose that air and hydrogen as regards condensation on 

platinum behave identically; or that possible differences of the law for 

air and hydrogen are just compensated by the condensation discrepancy. Both of these alternative hypotheses are exceedingly improbable. Again, the law (l+« f))% applies for hydrogen at all temperatures 

between zero and white heat. It is therefore clear that in case of 

marked condensation the simple law in question would have to be replaced by a much more complicated function. If, finally, the transpi1 Kayser: Wied. Aim., vol. 14,1881, p. 450.

2 Chappnis: Wied. Anu., vol. 8, 1879, p. 1. Cf. J. W. Langley: Zeitschr, f. Phys. 

Chem.,vol.2,1888,p. 83.

3 0. Schumann: Wied. Ann., vol. 33,1881, pp. 381,385.

: (955)
302 MEASUKEMENT OP HIGH TEMPEEATURES. [BULL. 54.

ration method were to be rejected, it seems to me that very little experimental elucidation of the thermal variation of gaseous viscocity 

will be obtainable. 1889.]

Again, the quantity actually measured is not 77 but ^ , where C is

l+m

the coefficient of slip (Gleitungs coefficient); C being inversely -proportional to pressure1 , or according to Meyer2 and others, a direct expression for mean free path. Hence it must have a smaller value in the 

case of platinum tubes than in the case of tubes of glass, because of the 

tendency of gas to condense on metallic (platinum) surfaces. Whatever discrepancy is introduced by C will therefore be more serious in 

case of glass than in case of platinum. From this point of view results 

with metallic capillary tubes have greater claims to correctness. Further remarks on this quantity C I have given elsewhere.3

THE NEW METHOD OF PYEOMETRY.

PRACTICAL REMARKS.

Appurtenances. Having endeavored to investigate the theory of the 

transpiration thermometer it will be expedient to close this chapter ^ 

with a few practical remarks. Equation 12, on page 281, shows that 

thermal data can be measured in terms o^ time, <, or of volume, F0 , or

again in terms of the rate at which volume increases, --+-} or even in

p_,p 

terms of the pressure factor, - Any of these quantities varies as

the f power of absolute temperature, and hence the sensitiveness of 

the method. As regards expedition, however, the differential methods 

are possibly more serviceable; and either the volume method which I 

employ on page 293 or Mr. Holman's method used either with compression or exhaustion is available. Again, if a suitable jet-pump is not at 

hand and if the mercury apparatus, page 243, Fig. 43, presents too 

much practical inconvienence, a bell-jar arrangement, like the gasometer, Fig. 35a, page 179, in which the light bell may be weighted either 

positively or negatively, suggests itself. Such an apparatus may of 

course be made small and refilled for each measurement. Differential 

apparatus obviate the use of chronometers and of pressure measurements, and solution and other errors are similarly eliminated.

The transpiration pyrometer. To fully utilize the accuracy of measurement of which the transpiration pyrometer is capable, it is necessary to 

give the instrument a different form from that used in the present pioneering experiments. Inasmuch as it was my object to study effects iniKundtu. Warburg: Pogg.Ann., vol. 155, 1875, pp. 337, 525. 

8 Meyer: Kinetische Theorie d. Gase, p. 152. 

Barus: Wied. Ann., vol. 36, 1869, p. 383.

(956)
BARUB.] VISCOSITY OF GASES.. 303

volving changes of the capillary bore of the tubes, no fixed or elaborate 

form of transpiration pyrometer would have served as well as the improvised arrangement described in Figs. 45 and 46. Equation 12, however, contains the clue for the construction of a practical transpiration 

pyrometer. The equation shows that the correction for ends decreases 

with extreme rapidity with the ratio of bores of the cold and hot parts 

of the pyrometer, i. e., as the fourth power of B"0/B0. Hence the distorting effect of cold ends can be easily eliminated by making the cen. 

tral parts of the tube slightly more capillary than the terminal parts. 

The accompanying diagrams suggest some serviceable methods by which 

this may be done.

Fig. 49 represents an available form of apparatus in which the terminal tubes a and 6 are relatively large, each of semicircular section with 

their flat sides juxtaposed. The capillary tube is shown at c c, and may 

be wound in any desirable spiral form, open or closed. To protect it 

an envelope d of platinum surrounds the helix of capillary tube C C., 

With regard to this form, it is to be noticed that the interior volume in 

the terminal tubes a and b must be reduced as far as possible so that 

thermal changes of the air inclosed may not sensibly affect the result. 

In view of the difficulty of welding the capillary tube c c into the larger 

terminal a and 6, the form Fig. 50 has advantages. Here the terminal 

a is a circular tube, and is drawn down upon the capillary tube c by aid 

of the wire plate. By this method a tight joint may be produced in such 

a way as not to endanger the platinum capillary. Slight changes of the

FIG. 49.

FIG. 50.

FIG. 51.

FIG. 52.

FIGS. 49, 5P, 51, 52, 53. Diagrams of practical traspiration pyrometers.

(957)
304 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54.

capillary bore for tliQ small length 

d, where the two tubes are in contact, will only change the mean 

radius B^ and will be fully aljr>

lowed for in measuring in the

%

manner indicated. (See p. 282.) 

Another way of making capillary tubes with large terminal 

ends is shown in the exaggerated 

diagrams Figs. 51 and 52. In 

Fig. 51 a smaller capillary tube 

I is inserted at c in the larger tube

I a b. The latter is then drawn P.

g down in the wire plate until c has

k, the requisite small diameter.

I Again, a simple platinum wire c

? may be inserted into the tube a 6,

I as Fig. 52 suggests. These forms

P. have the advantage as consisting

q of uniform tnbes without solderI ing, so that the danger of leaks

i where the terminals join the tube

| is obviated.

g Finally, the simplest and surest

| method of decreasing the central

q1 capillary bore consists in rolling

I down the central part in a wire-

£ rolling mill, the two rollers of

§ such a mill being appropriately

* grooved.

g Without passing judgment on

* any of these forms, it is clear 

that the simple capillary tube 

used in the above experiments 

can be made to subserve the purposes of thermal measurement 

in the way shown in Fig. 53. 

Here the ends c' c' of the platinum capillary tube c1 c c c' are 

surrounded by the larger tubes 

a b, and a current of cold water 

circulates with great rapidity 

from a into b across the septum. 

Knowing the temperature of the cold ends of the capillary (this being 

the temperature of the water in a and &), the correction member oau be

(958)
BAUDS.] VISCOSITY OF GASES. 305

calculated. The tubes a and b are again made of semicircular section 

with their flat faces juxtaposed.

Returning from this digression to 

the typical form, Fig. 49, it appears 

that the practical dimensions given 

to the instrument need not exceed 

those of an ordinary mercurial thermometer. The capillary tube may 

easily be wound in a closed helicoidal 

form with an external diameter of FlG. 55. Di8p08iUon of apparatu9 for differ. 

not more than 0.6cm, and a length not ential measurement. 

greater than 2.5cm. Such a spiral can therefore be made to lie wholly 

within the central tube of my re-entrant porcelain air thermometer, Fig. 

33, and the comparison between transpiration pyrometer and air thermometer may then be effected with nicety in the same way as has been 

explained above, page 180. It is merely necessary to replace the thermo-couple by the transpiration pyrometer in the diagram of the revolving muffle, to carry out the present comparison in detail.

Again, it is curious to note that by selecting capillary tube of small 

external diameter and keeping the terminals a and 6 insulated by plates 

of mica and the turns of platinum capillary tube apart (Fig. 49) the 

platinum spiral may be heated to any degree of redness by the current 

of a dynamo electric machine. To obtain extreme degrees of temperature it is of coarse necessary to surround the tube c c with some nonconducting substance, for instance layers of carded asbestos. If the 

free space surrounding the axis of the helix of platinum wire be large 

enough to admit the insulator of a thermo-couple snugly, a comparison 

between the indication of the transpiration pyrometer and of the thermo-couple may be made at once, the degree of high temperature being 

regulated by the electric current Which circulates through the helix of 

the platinum capillary tube. This form of calibration apparatus appears to my mind-to be at once the simplest and the most elegant as 

well as the most efficient form yet devised. Perhaps I may add that if 

the resistance of a hot platinum capillary tube be measured the thermal 

variation of resistance is obtainable for long ranges of temperature.

Supposing, therefore, that for a given (diatomic) gas the law of sixth 

roots characterizes the thermal variations of mean free path, it appears 

finally that the present method is especially well adapted for the high 

temperature study of dissociation phenomena in gases; for dissociation 

here means the degree of discrepancy between the law holding under 

the given condition of. dissociation and the normal law of sixth roots. 

In the case where gases permeate platinum at high temperature (the 

. case of hydrogen and of many hydrocarbon gases) it is necessary to 

inclose the transpiration pyrometer in a glazed porcelain tube which 

fits snugly around it. This tube is closed at the hot end, and filled with 

the hydrogen or other gas in question at a pressure equal to the mean 

Buli. 54 20 (959)
306' MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54. f

<t

pressure \ (P+p), at which transpiration takes place. In this way the 

occurrence of diffusion across the walls of the tube is obviated and the 

undistorted phenomenon is observable. Indeed, the envelope of porcelain tube to surround the platinum capillary apparatus is advisable in 

all cases where the pyrometer is directly exposed to flame or under 

other circumstances in which the permeation discrepancy is to be 

apprehended.

(960) ;_
INDEX.

A.

Abbe, Prof. Cleveland, suggestions of, 276.

Acbard, pyrometer of, 27.

Acoustic pyrometry, 47.

Air thermometer, displacement form, 165. .

stand of, 167.

porcelain bulbs of, 171,188.

graded volume tube for, 210.

of constant volume, formulae for, 188,190.

experimental data for, 198.

constant volume form, 208. 

Air thermometer at constant pressure, formula 

for, 210.

compensator for, 215.

manipulation of, 216.

data for, 217-227.

graphic digest for, 227.

errors of formulas, 214.

errors discussed, 227.

advantages of, 237.

Air thermometry, displacement methods of, 36, 

165.

errors of, 195.

accuracy of, 231,232. 

Alloys dilute, thermo-electrics of, 82.

fusion of, 128. 

Alloys, platinum, resistance of, 131,145,149.

thermo-electrics of, 135,146.

temperature, coefficient of, 139,149.

density of, 128,145.

electrics of, 143.

electrical constants of, 151. 

Amagat, high-pressure work of, 33. 

Amonton, gas thermometer of, 27. 

Anomalies, thermo-electric tests for, 80.

thermo-electrics of platinum iridium alloy,

49,83,116.

Antimony, boiling point, data for, 117,124. 

Apparent viscosity and pressure, 304. 

Apparatus for Boiling points (see Boiling points),

«small forms, 84.

Apparatus, disposition of, for thermo-electric 

work, 97.

for constant pressure air thermometry, 209.

for transpiration described, 242.

for viscosity of gases, disposition of, 243. 

Appert Freres, hard glass of, 35,89. 

Appolt, fusion pyrometers of, 39. 

Argand lamp, temperatures of, 250.

air bath of, 250.

Assay furnace, made by Buffalo Dental Company, 180. 

Avenarius, thermo-electric, formula of, 49.

B.

Barus, Mrs. Anna H., air thermometer, measurement of, 203. 

Bayeux, porcelain of, 21, 31. 

Becker G. F., aids research, 17. 

Becker suggests volatilization work on cinna-

- bar, 121.

Beckert on the graphite pyrometer, 27. 

Becquerel, pyrometric work of, 23, 24.

air thermometry of, 29.

measures boiling point of zinc, 35,235.

radiation pyrometer of, 43.

thermo-electric pyrometry of, 48. 

Beets, dry cells of, 99, 100.

Bell jar, for pressures in transpiration work, 302 

Benoit, resistance, measurements of, 26,51,161. 

Berliner, on disintegration of platinum, 276. 

Berthelot, studies dissociation of iodine, 30.

air thermometer of, 32.

on expansion of gases, 248. 

Bezold, radiation work of, 44. 

Bismuth, boiling point, data for, 117,123. 

Blower, Root pattern, 182. 

Bock, expansion pyrometer of, 27. 

Boiling points of metals under low presure, 22.

at low temperatures, 95. 

Boiling points at low pressures, by Crafts, 121.

of zinc, measured, 233, 235.

tables, 40.

Boiling-point apparatus for low temperatures, 

58.

large forms of, described, 58.

for mean temperatures, 59.

for aniline, etc., 60.

for mercury, 61.

for cadmium and zinc, 62. 

Boiling crucible, original form of, 90.

perfected form of, 91.

with open tube, 93.

for pressure work, 93. 

Boiling tubes, original forms of, 84.

perfected forms of, 86. 

Boiling tube for annealing long wires, 88.

for pressure work, 88. 

Bolz, C. H., book of, on pyrometry, 22. 

Borda, expansion thermometer of, 26. 

Bouger, dilatation, thermometer of, 25. 

Bradbury, calorimetric pyrometer of, 41. 

Browne, pyrometers mentioned by, 23. 

Brown, circulating water pyrometer, 43. 

Brooking, chronometer of, 251. 

Buchanan, resistance of gases at high temperature, 52.

307
308 INDEX.

Bucknill measures resistance of iridioplatinum,

51. 

Bulb for air thermometer, consecutive volumes

of, 233. 

Bulbs, inglazed, data for, 206.

of fire-clay, 20,54,237.

porcelain, for air thermometer, 171.

re-entrant form used, 209.

unglazed, moisture in, 198.

volumetry of, for air thermometer, 213. 

Bulier, circulating water pyrometer, 43. 

Burners for muffle furnace, 182. 

Bussius, expansion pyrometer of, 27. 

Bystrom, hydro-pyrometer of, 27.

calorimetric pyrometer of, 41.

C.

Cadmium, boiling-point data for, 118. 

Cailletet, compresses gases, 33. 

Calibration, practical method of, data for, 110. 

Callendar, resistance, pyrometry of, 52. 

Calorimetric temperature measurement, 40. 

Capillary, platinum tubing, helix of, 244.

apparatus for transpiration work, 245. 

Capillary tubes, metallic, 169.

dimensions of, 171.

of platinum, 248.

radius of, 257.

form of helix of, 258,267.

radius of, obtained by transpiration, 282.

of platinum, construction of, 303. 

Carnelley, fusion pyrometer of, 39,40,42. 

Carnelley and Williams, calorimetric pyrometry of, 41. 

Carnelley, circulating water pyrometer, 43.

interpolation pyrometry of, 52.

boiling point tables of, 57. 

Cagniard-Latour, acoustic pyrometry of, 47. 

Cauchy, on transpiration in short tubes, 285. 

Cells, standard, compared, 99. 

Chappuis on condensation of gases by solids, 301. 

Chatard, suggested ring burner, 85. 

Chautard, acoustic pyrometer of, 47. 

Circulating water pyrometer, 43. 

Clarke, F. W., transmits research, 4.

suggests work on arsenic volatilizing point,

121. 

Clausius, K., thermodynamics of, 22.

introduces kinetic mean free path, 240.

on the Wirkungssphare, 274. 

Clement, expansion pyrometer of, 26. 

Clement and Desormes, calorimetric pyrometer of, 40.

Clock-work for annealing, 88. 

Codazza, air thermometer of, 33. 

Cold ends of capillary, correction for, 252.

differential correction for, 254. 

Colson, siliciflcation of platinum, 187. 

Comparison of large and small forms of vapor 

bath, 115.

of gas expansions, 238. 

Compensator, 34,192.

for constant pressure air thermometer, 215.

restricted use of, 216. 

Condensation, plane of, 108.

of gases on solids, 301.

Conductivity, electrical, pyrometers based on, 50

thermal, pyrometers based on, 42. 

Conechy determines volatilizing point of arsenic, 40.

Constancy of temperature in boiling tubes, 104. 

Constants, electrical, of platinum alloys, 151.

thermal, of argand lamp, 250. 

Constant pressure air thermometer described, 208

formulas for, 210.

accuracy of, 231.

advantages of, 237.

(See air thermometer, 216.) 

Constant volume air thermometer, 1G7.

formulae for, 188,195.

experimental data for, 198. 

Contents, table of, 5. 6, 78. 

Cooling, rates of, in muffle furnace, 203,204.

effect of transpiring gas, 296. 

Corrections, thermo-electric, 99,103. 

Corrosion of thermo-couples, 71. 

Coulomb, calorimetric pyrometer of, 40. 

Crafts studies dissociation of iodine, 30.

air thermometer of, 32.

vapor tension studied by, 38.

low-pressure boiling points of, 121.

and Meier displacement air thermometer, 36,

37,165. 

Crova, radiation researches of, 44.

on solar temperature, 45. 

Crucible, large form for zinc, 73.

small form of, for vapor bath, 90.

D.

Daniell, pyrometric work of, 26. 

Daniell cell, separate celled form of, 99.

standard forms of, 99. 

Data for Viscosity of gases, 258. 

Davy, air thermometer of, 28. 

Dead space, correction for, 257. 

Pebray studies dissociation of marble, 38.

(See Deville.)

Decharme, radiation measurements of, 44. 

Density of platinum alloys, 128,143,145.

Desbordes, expansion pyrometer of, 26. 

Deville and Debray study properties of platinum alloys, 49.

Deville and Troost, metallic vapor baths of, 19, 

23, 24.

vapor density bulbs of, 29.

final pyrometric work of, 31, 33,34,35, 36.

condemn non-spherical bulbs, 48.

vapor baths of, 56, 57.

large apparatus of, 84.

select spherical bulbs, 174.

compensator devised by, 192.

zinc, boiling point of, 235. 

Dewarand Gladstone, photometric pyrometry

of, 45.

Die for porcelain tubes and stems, 96. 

Differential transpirometer, 249.

apparatus for transpiration work, 249.

transpiration measurement, 293. 

Diffusion of gases through platinum, 275. 

Digest of electrics of platinum alloys, 143.

of constant pressuue air thermometer results, 

227.
INDEX. 309

Dilatation of solids, 25.

of gases, 27.

of liquids, 27.

Dimensions of capillary tubes, 171. 

Disintegration of platinum at high temperatures,

276. 

Displacement methods of air thermometry, 36.

air thermometer, 165.

Disposition of air thermometric apparatus, 187. 

Dissociation of iodine, 24.

pyrometry, 38.

effect of, on viscosity, 279.

transpiration method for, 305. 

Dixon graphite, crucible of, 73. 

Draper, law of radiation of, 43,46. 

Dumas, vapor density method of, 29. 

Duration of continuous ebullition, 116,118.

E.

Ebullition, use of, in pyrometry, 42.

plane of, 108.

continuous, duration of, 116,118. 

Elasticity, phenomena of, 17. 

Electrical conductivity, pyrometers based on, 50. 

Electric phenomena in furnace, 233,234. 

Ellicot, dilatation thermometer of, 25. 

Elliott, standard cell of, 100. 

Elster and Geitel on disintegration of platinum,

276. 

Erhardt and Schertel measure melting points of

alloys, 34.

fusion experiments of, 40. 

Erhardt, calorimetric work of, 42. 

Erhardt and Schertel test Jolly's air thermometer, 208.

Ermann and Herster, air thermometer of, 28. 

Errors of constant volume air thermometer

formulro, 190,195. 

simplified formulae, 214. 

of viscosity measurements, 274. 

v.Ettinghausen measures temperature coefficient

of Latimer Clark's cell, 102. 

Expansion of solids, 25.

of gases at high temperatures, 37. 

Exponential law, advantages of, in pyrometry,

277.

F.

Fiducial reading of air thermometer, 186. 

Fievez, photometric pyrometry of, 46.. 

Fire clay classified by viscosity measurements, 

1 46.

air thermometer, 20,54,237. 

Fischer, pyrometric work of, 23.

calorimetric pyrometer of, 41.

criticises Siemens' pyrometer, 51. 

Fletcher combustion furnace, 166. 

Forms of transpiration pyrometer, 303. 

Formula of Avenarius, insufficiency of, 125. 

Formulae, thermo-electric, how used, 103.

for constant vol ume air thermometer, 188,190.

for air thermometer, errors of, 190. 

Formulae for constant pressure air thermometer, 

210.

simplified, 211.

Formulae, errors of simplified forms of, 214.

for experimental errors in constant pressure 

air thermometry, 227.

for thermal changes of viscosity compared, 

 277.

for transpiration pyrometry, 281.

for wide transpiration tubes, 285. 

Forster criticizes Siemens's pyrometer, 51. 

Frontispiece described, 187. 

Fuess, metallic air thermometer of, 33. 

Furnace for boiling zinc, 64.

for small boiling crucible, 92.

for revolving muffle, 180,188. 

Fusing points measured by Violle, 39. 

Fusion, phenomena of, 17.

pyrometers, 39.

of wires of thermo-couples, effect of, 54.

of alloys, 128.

G.

Gaseity, effect of imperfect, 279,

Qas expansions, comparison of, 238. 

Gases, expansion of, 27.

high-temperature expansion of, 37.

electrical resistance of, 52.

condense on solids, 301. 

Gasometers, 179.

Gauntlet, expansion pyrometer of, 26. 

Gibbon, expansion pyrometer of, 26. 

Gibbs's ring-burner, 85,89,90. 

Glass re-entrant air thermometer, 237. 

Gleitungs coefficient, 276,302.

Helmholz on, 251,252. 

Gooch, suggests ring-burner, 85.

sodium tungstate luting of, 93. 

Gosse, apparatus of, 21,31. 

Govi, radiation pyrometer of, 43.

on transparency of metals, 164. 

Graham, transpiration work of, 47.

on gas transpiration, 241,241. 

Graphite crucible, large form, for zinc, 73. 

Grassi, studies dilitation of gases, 33. 

Gray and Trannin, photometer of, 44. 

Greiner, Emil, apparatus of, 21,

boiling tubes of, 89. 

Groshans, principle of, 22. 

Grunow, William, apparatus of, 21.

air-thermometer stand of, 167.

cathetometer of, 251.

Guthrie, on efflux through short tubes, 242. 

Guyton-Morveau, calorimetric pyrometer of, 40.

pyrometric work of, 25,26,28.

H.

Hagen, transpiration data of, 241.

Hall & Sons, apparatus of, 21.

Hallock, Dr. William, appointment of, 18.

work done by. 19,20.

constructs furnace for zinc, 62.

suggests arch for insulator machine, 96.

tests displacement thermometer, 165.

modifies the Jolly-Pfaundler stand, 167.

air-thermometer measurements of, 200.

(See Chapter I.) 

Heat conduction, phenomena of, 17.

pyrometry based on, 42.
310 INDEX.

Heat expansion of porcelain, 236. 

Heating, rates of, in muffle furnace, 203,204.

method of, for transpiration work, 249. 

Heeren, fusion pyrometer of, 39. 

Helmholtz on Gleitung's coefficient, 252,276,302. 

Helix of platinum capillary tubing, 244,305.

of capillary tube, how wound, 248.

of capillary tube, early form of, 258.

later form of, 267.

High temperature measurement, difficulties 

of, 24.

data, accuracy of, 54.

Historical account of methods of pyrometry, 24. 

Hoadley, calorimetric pyrometer of, 42. 

Hobson, calorimetric pyrometer of, 41. 

Hoffmann, on efflux through short tubes, 242. 

Hoffmann's formulae for wide, transpiration

tubes, 285.

Holden, Dr. Austin, aids research, 19. 

Holman, Silas W., on viscosity of gases, 240,241, 

242.

formula of, for viscosity and temperature,

279,280.

Holman, transpiration, method of, 302. 

Hydrogen permeates platinum, 204, 275,283.

I.

Illustrations, table of, 9,10. 

In-glazed porcelain bulbs, 174. 

Insulators, machine for making, 95. 

Interpolation methods of pyrometry, 52,54. 

Iodine vapor, pyrometric use of, 24,29. 

Isambert, studies dissociation of solids, 38.

J.

Jenkin, F., table of specific resistance of, 157. 

Jet pumps of Professor Richards, 242. 

Jolly, air thermometer of, 32.

form of air thermometer of, 167. 

Jourdes, heat conduction pyrometry of, 42.

K.

Kayser on condensation of gases by solids, 301.

on disintegration of platinum, 276. 

Kinetic inferences for viscosity of gases, 273. 

King, Clarence, suggests researches, 17.

instructions of, 17. 

Kittler measures temperature coefflcientof Latimer Clark's cell, 102.

Knott, MacGregor, and Smith, thermo-electrics 

of cobalt of, 49.

thermo-electrics of platinum alloys of, 49. 

K6 vesligethy, radiation work of, 46. 

Kohlrausch and Ammann, zero method of, 97. 

Kundt, capillary glass connectors of, 171. 

Kundt and Warburg, apparatus of, for viscosity, 241.

L.

Lamy, dissociation pyrometer of, 38. 

Landolt and Boernstein's tables, 40,42.

use of, 213.

Langer. (See Meyer.) 

Langley, bolometric work of, 44,46.

Latimer Clark's standard cell, 97,99,102. 

Lauth, pyrometric work of, 23.

studies fusion of silicious mixtures, 40.

circulating water pyrometer, 43. 

Law of fifth powers of Maxwell, 277. 

Le Chatelier, high temperature work of, 22.

fusion experiments of, 40,50.

thermo-electric work of, 49.

platinum-rhodium couple of, 50.

pyrometric work of, 84. 

Limit of thermo-electric thermoscopes, 53. 

Limit thermo-couples, 81,83. 

Lion and Guichard, expansion pyrometer of( 27. 

Liquids, dilitation of, 27. 

List of thermo-couples, 68.

M.

MacGregor. (See Knott.)

MacGregor and Knott, resistance of iridioplatinum, 51.

Machine for making insulators, 95. 

Machine for soldering porcelain, 175. 

Magnus, measures expansion of gases, 33. 

Magnetism, pyrometers based on, 52. 

Main, heat conduction pyrometry of, 42. 

Malvern Platinum Works, apparatus of, 21. 

Manipulation of revolving muffle, 185. 

Manometer for air thermometry, 167,188. 

Matthiessen, resistance measurements of, 26. 

Mntthiessen and Vogt, electrics of alloys of, 157. 

Mariotte flask, how improved, 244. 

Maxwell, viscosity of gases studied by, 46.

law of gaseous viscosity, 240,241,252. 

Maxwell on viscosity and temperature, 277.

on mean free path, 274. 

Mayor, A., acoustic pyrometer of,47. 

Mean free path introduced by Clausius, 240.

relations of, to temperature, 274. 

Mercury, vapor bath of, data for large, 69.

constant temperature of, 105.

small form of vapor bath for, 84. 

Metallic boiling points, 29,30.

Metals, specific heat of, by Violle, 41.

all dissolved by platinum, 127. 

Methods for viscosity measurement, 247. 

Meyer, O. E., transpiration formula of, 47.

on viscosity and transpiration of gases, 240, 

241.

derives transpiration formula of gases, 251.

on the sliding coefficient, 276.

on viscosity and temperature, 277.

temperature coefflcientof viscosity of, 279. 

Meyer, Victor, pyrochemic work of, 25,34.

dissociation of iodine, etc., 30.

vapor density method of, 36,37. 

Meyer, calorimetric work of, 42^ 

Meyer, Victor, suggests boiling-point substances, 121.

pyrochemical researches of, 37.

on expansion of gases, 248. 

Mill, air thermometer of, 28. 

Miller, calorimetric pyrometer of, 41. 

Moisture in unglazed bulbs, 198. 

Morlent Freres, porcelain work of, 21. 

McSweeney, radiation pyrometer of, 43.
INDEX. 311

Muffle furnace, rates of heating and cooling, 203, 

204.

Muffle, revolving, 180,183.

Miiller measures resistance at high temperatures, 50.

Multiple arc, thermo-electric effect of, 82.

Musschenbi'oeck, dilatation thermometer of, 25.

N.

Nahrwold on disintegration of platinum, 276. 

Natanson on molecular aggregation, 280. 

Navier on efflux from apertures, 242.

on transpiration in short tubes, 285,289. 

New Haven, Conn., laboratory work at, 18. 

Newton, Sir Isaac, radiation pyrometry of, 43. 

Nichols, pyrouietric work of, 23,26. 

Nichols, E. L., radiation pyrometry of, 44.

on expansion of platinum, 47.

criticises resistance pyrometers, 51. 

Nomenclature used in viscosity, 256.

Q.

Obermayer, thermo-electric work of, 50.

on transpiration of gases, 241.

temperature coefficient of viscosity of, 279,

280.

Oechsle, expansion pyrometer of, 26. 

Oxide coats on steel, 46. 

Oxyhydrogen blowpipe, 177.

P.

Peclet, heat conduction pyrometry of, 43. 

Pelouze, treatise of, on pyrometry, 23. 

Perkin, resistance of gases at high temperatures, 52.

Pernolet, silicification of platinum, 187. 

Person, mercury pyrometer of, 27. 

Petersen, expansion pyrometer of, 26.

air thermometer of, 28. 

Pfaundler, air thermometer stand of, 167. 

Photometric pyrometry, 43, 45. 

Pionchon, on specific heat of iron, 41. 

Plane of condensation, 108.

of ebullition, 108.

Platinum couples with vanishing amounts of 

impurity, 57.

Iridium couple, anomalies of, 115.

thermo-electric datum for melting-point, 124.

purified by heating, 126,146.

silicification of, 187.

pervious to hydrogen, 264,275,283.

disintegrates at high temperatures, 276. 

Plattner, fusion experiments of, 39. 

Poiseuille, law of transpiration of, 241. 

Poiseuille-Meyer, transpiration formula, 240,242, 

251.

law not applicable, 284. 

Poison on transpiration in short tubes, 285. 

Porcelain, stem sagged into bulb, 22.

air thermometer, standard form of, 22.

coefficient of expansion pf, 29.

air thermometer, 31.

expansion of, 31,35,36,236.

air thermometer bulbs, 171.

machine for soldering, 175.

Pouillet, pyrometric work of, 28.

air thermometer of, 28.

calorimetric pyrometry studied by, 41.

thermo-electric pyrometry of, 48. 

Practical calibration, data for, 110. 

Pressure, effect of, on thermo-couples, 53.

apparatus for transpiration work, 244.

effect of, on transpiration in wide tubes, 295. 

Prinsep, pyrometric work of, 26.

standard air thermometer of, 28.

fusion pyrometer of, 39. 

Prinsep's alloys for fusion work, 34,39. 

Problems to be undertaken, 17. 

De la Provostaye, radiation pyrometry discussed

by, 44.

Prussian porcelain works, apparatus of, 21. 

Puluj on viscosity and temperature, 241.

temperature coefficient of viscosity of, 279,

280.

Purity of platinum, 146. 

Pyrognomic substances, 46. 

Pyrometer based on circulating water, 43.

transpiration, forms of, 303. 

Pyrometers, classification of, 25.

of fusible alloys, 39.

limit of thermo-electric, 53.

based on specific heat, 40.

ebullition, 42.

viscosity, 46.

acoustics, 47.

thermo-electrics, 48.

electrical conductivity, 50. 

Pyrometry, advantages of thermo-electric, 52.

interpolation methods in, 52.

new viscous method of, computation for. 281.

results for transpiration, 282.

transpiration method of, practical remarks

on, 302. 

Pyrometry based on heat conduction, 42.

radiation, 43.

Q.

Quincke devises resistance pyrometer, 51. 

R.

Radiation pyrometry, 28,29.43. 

Radius of capillary tubes, 257.

how measured, 289.

obtained by transpiration, 282.

transpiration, measurement of, 255. 

Ramsay on transparency of metals, 164. 

Eayleigh, measures temperature coefficient of

Lutimer Clark's cell, 102. 

Reductions, thermo-electric, 67, 77. 

Re-entrant porcelain bulbs, 173. 

Regnault, standard air thermometer of, 28, 31, 

167,248.

measures expansion of gases, 33.

displacement pyrometer of, 36.

thermo-tlectrie pyrometer of, 48.

capillary tubes, 167,169. 

Reissig, resistance pyrometer of, 51. 

Resistance, electrical, pyrometers based on, 30.

of platinum alloys, 145,133. 

Resistometer, 131. 

Reynolds, Osborne, on efilux through short'

tubes, 242. 

Richai-ds, jet pumps of, 242.
312 INDEX.

Rierasdyk, fusion pyrometer of,39. 

Ring burner of Dr. Gibbs, 85,89,90. 

Roberts, fusion experiments of, 39. 

IJosetti on solar temperature, 45. 

Uouina tests "Wullaston's method', 170. 

Reverberatory furnace for zinc, 64. 

Revolving muffle furnace, 180. 

advantages of, 185.

S.

Saintignon, circulating water pyrometer, 43. 

Sajotschewsky, vapor tension studied by, 38. 

Salleron, calorimetric pyrometer of, 41. 

Salts, specific heat of, by Ehrhardt, 42. 

Saxon porcelain works, apparatus of, 21. 

Scala graduum caloris, 43. 

Schinz, calorimetric pyrometer of, 41.

pyrometric work of, 32,33.

displacement pyrometry of, 36.

heat conduction pyrometry of, 42,43.

thermo-electric pyrometry of, 48.

re-entrant air thermometer of, 48. 

Schinz's torsion galvanometer, 104. 

Schleiermacher tests Stefan's law of radiation, 44.

resistance pyrometry of, 51. 

Schneebeli tests Stefan's law of radiation, 44. 

Sclmeider, calorimetric table of, 41. 

Schubarth, calorimetric pyrometer of, 41. 

Schumann on transpiration of gases, 241.

on condensation of gases by solids, 301. 

Schwarz, calorimetric pyrometer of, 40. 

Secchion transparency of metals, 164. 

Seger studies fusion of siliceous mixtures, 40. 

Selenium,boiling point of, 34. 

Series of thermo-couples, 57.

of alloys, 79. 

Shaw, pyrometers classified by, 23,27.

vapor tension studied by, 38. 

Siemens, resistance measurements of, 26.

calorimetric researches of, 41. 

Siemens's pyrometer, 33,51. 

Silbermann and Jacquelin.alr thermometer of,

28.

Siliceous mixtures for fusion work, 40. 

Silicification of platinum, 187. 

Siphon Daniell,99. 

Sliding coefficient, 276,302. 

Solar temperatures, 45. 

Soldering of porcelain, 31, 175. 

Solids, dilatation of, 25. 

Solly, thermo-electric pyrometer of, 48. 

Soret, temperature of the sun measured by, 45. 

Specific heat, pyrometers based on, 40. 

Sprengel pump used by Deville and Troost, 34. 

Spring on wire drawing, 170. 

Springmiihl on transpiration of gases, 241. 

Standard cells, temperature coefficient of., 102. 

Standardization by comparison, 22,237.

of constant pressure air thermometer, 212. 

Stas photometric pyrometry discussed by, 46. 

Steam, superheated, used in displacement thermometer, 166. 

Stefan, law of radiation of, 44.

transpiration work of, 47.

flow of viscous liquids, 241.

pn transpiration in short tubes, 285.

v. Steinle and Hartung, graphite uvrometerof,

27.

Stenger, radiation work of, 46. 

Stokes on viscosity of air, 240.

flow of viscous liquids, 241.

on transpiration in short tubes, 285. ' 

Strouhal, Vincent, aids research, 17, IS.

electrics of steel, 144,149,159.

improved thermo-electric apparatus of, 97,98. 

de St. Venant on transpiration in short tubes,

285.

Substances for boiling points, 119. 

Summary of results for large vapor baths, 79. 

Sulphur, small form of vapor bath for, 85.

vapor bath, constant temperature of, 107. 

Sun, temperature of, 45.

T.

Table for (l+ftt)/ (l+a<), 212.

of errors in constant pressure air thermometry, 229.

Tables, list of, 11,12,13. 

Tait, thermo-electric researches of, 49.

Silicification of platinum, 187. 

Temperature, how computed thermo-electrically, 71.

coefficient, how measured, data, 139.

coefficient of standard cells, 102.

coefficient and resistance, 127.

coefficient, zero value of, 161.

effect of, on wide tube transpirations, 297. 

Temperatures, constancy of, in boiling tubes, 104.

equality of, tested thermo-electrically,67. 

Tenacity of thermo-couples, 53. 

Thermal conductivity, pyrometers based on, 42. 

Thermo-couples, list of, 68. 

Thermo-couple of platinum and platinum, 81. 

Thermo-electric pyrometry, advantages of, 52.

pyrometers, 48.

anomalies, tests for, 80.

computation, 103.

work, galvanometer measurement, 104.

calibration, practical data for, 110.

constants, time variations of, 116.

datum for fused platinum, 124.

equation, insufficiency of, 125. 

Thertno-electrics of platinum alloys, 135. 

Thermoscopes, classified by Thomson, 25.

magnetic, 52.

Thermostat and transpiration pyrometer, 305. 

Thomson, James, equation of, 22. 

Thomson, J. J., resistance pyrometry of, 52. 

Thomson, Sir William, article "Heat" of, 23, 25.

classifies pyrometers, 25.

vapor tension thermometer of, 38.

viscosity pyrometer of, 46. ,

thermo-electric diagram of, 49.

magnetic thermoscope of, 52. 

Tidblom, thermo-electric formulae of, 50. 

Time variationsof thermo-electric constants, 116., 

Tin, boiling point, experiments on, 123. 

Torsion galvanometer for high temperature 

measurement, 22.

for thermo-electric work, 104. 

Transparency of metals, 164,

V
INDEX. 313

Transpiration apparatus described, 242, 244.

manipulation of. 255.

Transpiration data vitiated by condensation of 

gas, 301.

devices for rapid, at high temperatures, 284.

differential measurement of, 293.

during long intervals, 2!)3. 

Transpiration formula?, conditions of, 252.

lor two cold ends, 252.

for differential apparatus and cold ends, 254. 

Transpiration in wide tubes, data for, 287, 288.

effect of pressure on, in-wide tubes, 295.

in wide tubes influenced by temperature, 

297.

in wide tubes, general remarks on, 300.

in glass tubes, 298.

in silver tubes, 299.

in platinum tubes, 300.

measurement of capillary radii, 255.

not subject to .Poiseuille-Meyer's law, 284. 

Transpiration pyrornetry, capillary apparatus

for, 245.

formula} for,281.

advantages of, 281.

results for, 282.

practical remarks on, 302.

forms of, 303.

protection of, 305.

Transpiration under variable pressure, 287. 

Troost, studies dissociation of iodine, 30.

measures boiling point of selenium, 34,35.

diffusion pyrometer, 39.

boils selenium in glass, 89.

boiling point of selenium, 121.

on expansion of gases, 248. 

Tubes, capillary, of metal, 1G9. 

Turner on transparency of metals, 1R4.

V.

Vacuum boiling points of metals, 95. 

Vapor bath, mercury, data for.large, 69.

of zinc, data for large, 70. 

Vapor bath, small form of, for low temp 

tures, 84.

for mercury, 84

for sulphur, 85.

>erajor suipnur, 00.

forms of, for high temperatures, 90. 

Vapor bath, of mercury, constant temperatur 

of, 105.

of sulphur, constant temperature of, 107.

of zinc, constant temperature of, 108. 

Vapor baths, liquids for, 119. 

Vapor tension pyrometry,38. 

Velocity of the mean square, 274. 

Violle, pyrometric work of, 24,49.

measures boiling point of zinc, 35.

fusion experiments of, 39.

important calorimetric work of, 41.

radiation pyrornetry of, 44.

temperature of the sun estimated by, 45.

silicification of platinum, 187.

zinc, boiling point of, 235. 

Viscosity, phenomena of, 17.

of fire clays, 40.

of platinum at high temperatures,293. 

Viscosity of gases, pyrometric use of, 46,248.

measurement, methods of, 247.

data for, 258.

values of, at zero degrees, 271.

kinetic inferences, 274.

advantages of an exponential law in, 277. 

Viscosity measurement, errors of, 274,275.

temperature coefficient of, 279-, 280. 

Vogt. (See Matthicssen.) 

Volatilization, experiments on, 121. 

Volume tube,graded for air thermometer, 210. 

Volumetry of compensator canal, 193.

of bulbs for air thermometer, 213.

W.

Warburg on transpiration of gases, 241.

temperature coefficient of viscosity of, 279,

280.

Water attacks glass at high pressures and temperatures^?.

Water jacket for volumeter, 210. 

Waterston, measures high temperature expansion of water, 27. f 

Weber, H. F., radiation work of, 40. 

Weber, L., electrics of alloys measured by, 145. 

Wedgwood, pyrometer of, 25. 

Weinhold, pyrometric work of, 23,24,26,32,33.

on dissociation pyrometry, 39.

calorimetric work of, 41.

studies resistance pyrometer, 51.

tries Jolly's air thermometer, 208.

zinc, boiling point of, 235. 

Whitall, Tatuin & Co., apparatus of,21. 

Wiedemann, E.,on transpiration of gases, 241,212.

temperature coefficient of viscosity of, 280. 

Williamson criticises Siemens' pyrometer,51. 

Wilson, calorimetric pyrometer of, 41. 

Wirikler on the graphite pyrometer, 27. 

Wires, platinum, mechanical treatment of, 128,

133. 

Wirkungssphiire, 274.

Zabel,air thermometer of, 32. 

Zero of temperature coefficient, 161. 

Zinc, boiling point of, 24,29,30,31,34,35.

boiling point, furnace for, 62.

large vapor b:ith of, data for,70.

large crucible for, 73. (

vapor bath, constant temperature of, 108.

coincidence of boiling point, data for, 115.

vapor,calibration in, 122,123.

boiling point of, measured, 233,235.