DEPARTMENT OF THE INTERIOB

BULLETIN

OF THE

UNITED STATES

GEOLOGICAL SURVEY

No. 96

WASHINGTON

GOVERNMENT PRINTING OFFIOU 

1892

UNITED STATES GEOLOGICAL SUEVEY

J. W. POWELL, DIKECTOR

THE

VOLUME THERMODYNAMICS

OF

WASHINGTON

GOVERNMENT PRINTING OFFICE

1892

CONTENTS.

Page.

Letter of transmittal........................................................ 13

Preface..................................................................... 15

Chapter I. Method of obtainiug and of measuring very high pressures.. ...... 17

Introduction............................................................ 17

The screw compressor.................................................... 18

General method..................................................... 18

Special devices .................................................. ~. 18

Steel screw ......................................................... 18

Barrel. Head ...................................................... 19

Barrel. Head, improve;!............................................ 19

Barrel. Body ...................................................... 20

Barrel. End with piezometer tube.................................. 20

Piezometer tube. Vapor bath.......................................,( 20

Method of filling.................................................... 20

Case for protection................................................... 21

Vertical piezometer................................................. 2!

Pressure measurement .................................................. 22

Tait gauge. Adjustment.........'................................... 22

Tait gauge. Graduation............................................ 23

Tait gauge. Volume increase measured and computed .............. ' 29

Direct reading, Bourdon gauge...................................... 30

Concluding remarks ................................................ 31

Chapter II. The isometrics of liquids........................................ 33

Introduction............................................................ 33

Apparatus .............................................................. 33

Constant volume tube............................................... 33

Manipulation."..................................................... 34

Method of filling.................................................... 35

Vapor baths ......................................................... 36

Method of cooling piezometer........................................ 37

Method of temperature measurement ................................ 38

Method of pressure measurement.................................... 38

Preliminary results ..................................................... 38

Data for ether ...................................................... 38

Discussion.......................................................... 39

Definite results ......................................................... 40

Apparatus improved ..................".............................. 40

Notation............................................................ 41

Data for ether ...........................'........................... 41

Method of purifying ................................................ 42

Observations for ether .............................................. 42

Observations for alcohol ............................................ 44

Observations for thymol, para-toluidine, and diphcuylamine ......... 45
b CONTENTS.

Page 

Chapter II. The isometrics of liquids Continued.

Temperatures corrected ................................................. 46

Behavior of the torsion galvanometer ............................... 46

Air thermometer comparisons. Apparatus .......................... 47

Air thermometer comparisons. Observations........................ 48

Isometrics corrected as to temperature .............................. 51

Correction for the thermal and elastic volume changes of the glass

tubes............................................................. 54

Thermal expansion of glass......................................... 54

Compressibility of glass ........................ .................... 55

Compressibility of the above liquids ................................ 55

Deductions............................................................. 58

Curvature and slope of the isometrics............................... 58

Final interpretation ................................................ 60

Isometrics of solid glass .............................................. 61

Conclusion ......................................................... 62

Chapter III. A comparison of the Bourdon, the Tait, and the Amagat highpressure gauges .................................................. 63

Historical.............................................................. 63

The earlier work ............................J...................... 63

Amagat's manometer................................................ 63

Bourdon gauge ..................................................... 64

Discussion of results ................................................... 65

Multiplying mechanism.............................................. 65

Fraunhofer micrometer............................................. 66

Tait gauge ......................................................... 67

Summary............................................................... 69

Chapter IV. The continuity of solid and liquid ............................. 71

Introductory........................................................... 71

Scope of the Svork.................................................. 71

Other methods tested ............................................... 72

Advantages of the present method ................._................. 73

Apparatus.............................................................. 73

Temperature ........................ I............................... 73

Pressure............................................................ J4

The volume tube ................................................... 74

Method of measurement ............................... 7................ 77

Constants of the tube .............................................. 77

Volume of the charge. .............................. ^>............... 78

Correction for expansion and compressibility of envelopes........... 78

Eesistance measurement............................................ 79

Calibration......................................................... 79

Electrolytic resistance and temperature............................. 80

Volume in terms of resistance ...................................... 82

Pressure coefficient of the electrolyte ............................... 82

Results of the measurements ........................................... 83

Arrangement of the tables.......................................... 83

Solid isothermal, 63° ............................................... 84

Liquid-solid isothermals, 80°........................................ 85

Liquid-solid isothermals, 90°........................................ 85

Liquid-solid isothermals, 100°....................................... 86

Liquid solid isothermals, 117°....................................... 87

Liquid-solid isothermals, 130°....................................... 88

Deductions............................................................. 89

Graphic construction ............................................... 89

Hysteresis.......................................................... 89
CONTENTS. 7

Chapter IV. The continuity of solid and liquid Continued.

Deductions Continued. Pago.

James Thomson's double inflections .................................. 90

The characteristic specific volumes.................................. 91

Critical point....................................................... 92

. Solidifying points and melting points ............................... 93

Transitional point.................................................. 94

Solubility and pressure............................................. 95

Conclusion ............................................................. 96

ILLUSTRATIONS,

Pago. 

Plate I. Screw compressor, with parts in place ........................... 18

II. Diagram showing the isometrics of ethei', alcohol, thymol, paratolnidine, and dipkenylaminc ............................... 58

11F. Tubular piezometer, with appurtenances......................... 70

IV. Fusion isothermals of naphthalene. First set. .................. 86

V. Fusion isothermals of naphthalene. 'Second sot ................. 88

VI'. Fusion isothermals of naphthalene. Third sot................... 90

VII. Fusion isothermals of naphthalene. Fourth set ................. 92

VIII. Diagram showing the conditions of fusion and of solidification... 94 

Fig. 1. Chart showing the bow-shaped cycles obtained iu the gauge comparisons .........................................i.......... 25

2, 2a. Direct reading helical Bourdon gauge ........................... 29

3. Chart showing the action of the helical Boimlon gauge.......... 31

4. Constant volume tube; longitudinal section..................... 33

5. Constant volume tube; diagram................................ 34

6. Method of fastening the terminals .............................. 35

7. Vapor bath and piezometer tube; longitudinal section........... 37

8. Isometrics of ether; preliminary results......................... 40

9. Sectional vapor bath, for comparing air thermometer and thermocouple ................................................... 48

10. Longitudinal elevation of one of the halves, of vapor bath, showing the thermometers in place............................... 49

11. Comparison of the Amagat manometer and the Tait gauge....... 69

12. "Piston libre," for high pressure ................................ 70

13. Diagram of the volume tube .................................... 75

TABLES.

Page.

Table 1. Comparison of Tait gauge No. 0, and Bourdon gauge............... 24

2. The same gauge comparisons after long use........................ 24

3. High pressure tests....................................'............ 24

4. Comparison of large Bourdon gauge with Tait gauge JSIo. 1......... 26

5. Comparison of Tait gauges Nos. 1 and 4............................ 27

6. Calibrations of Tait gauges Nos. 1 and 4........................... 28

7. Comparison of Tait gauges Nos. 1 and 4............................ 28

8. Calibrations of Tait gauges Nos. 1 and 4 ..... 1..................... 28

9. Comparison of Bourdon gauge and the spiral gauge ................ 31

10. Isometrics of ether. Preliminary results.......................... 38

11. Digest of these data.............................................. 39

12. Isometrics of ether. Observations................................. 42

13. Isometrics of alcohol. Observations.............................. 44

14. Isometrics of thymol. Observations.............................. 45

15. Isometrics of para-toluidine. Observations ....................... 45

16. Isometrics of diphenylamine. Observations....................... 46

17. Constants of the torsion galvanometer and couple ................. 47

18. Comparison of thermocouple and air thermometer................. 50

19. Data interpolated from the above................................. . 50

20. Isometrics of ether. Temperatures corrected...................... 51

21. Isoruotrics of alcohol. Temperatures corrected.................... 53

22. Isometrics of thymol. Temperatures corrected.................... 53

23. Isometrics of para-toluidine. Temperatures corrected............. 54

24. Isometrics of diphenylamine. Temperatures corrected............ 54

25. Isometrics of solid glass........................................... 54

26. Correction factors, being compressibilities at 0° and p atm........ 56

27. Corrections for thermal and elastic volume changes of glass tubes.. 57

28. Isometrics'. Digest of probable results corrected ..........'........ 58

29. Observed initial slopes of the isometrics........................... 59

30. Order of values for internal pressure............................... 61

31. Cyclic comparison of the Bourdon gauge "with the Amagat manometer. Multiplying gear ....................................... . 64

32. Cyclic comparison of the Bourden gauge with the Amagat manometer. Fraunhofer micrometer.................................. 65

33. Cyclic comparison of the Tait gauge with the Amagat manometer.. 67

34. Volumes per unit of length....................................... 80

35. Temperature coefficients and pressure coefficients of concentrated

zinc sulphate solution........................................... 81

36. Relation of volume and resistance at different temperatures........ 82

37. Pressure coefficients............................................... 82

38. Isothermals of naphthalene at 63.5°............................... 84

39. Isothermals of naphthalene at 83° .................................. 85

40. Isothermals of naphthalene at 90°................................. 85

41. Isothermals of naphthalene at 100°................................ 86

42. Isothermals of naphthalene at 117°................................ 88

43. Isothermals of naphthalene at 130°................................ 88

44. Volumes of solid and liquid at solidifying points varying with pressure ............................................................ 91

45. Volumes of solid and liquid at melting points varying with pressure. 92

46. Showing the relation of solidifying point and melting point with

pressure. Naphthalene......................................... 94

11

LETTER OF TRANSMITTAL,

DEPARTMENT OF THE INTERIOR, 

U. S. GEOLOGICAL SURVEY, DIVISION OF CHEMISTRY AND PHYSIC^

Washington, D. 0., September 5, 1891.

SIR: I transmit herewith a manuscript by Dr. Carl Barns upon work 

done in the Physical Laboratory of this division, entitled " The Volume 

Thermodynamics of Liquids." I recommend that it be published as a 

bulletin of the Survey. 

Very respectfully,

F. W. CLARICE,

Chief Chemist. 

Hon. J. W. I'OWELL,

Director.

13

PREFACE.

In the following chapters, I have commenced a serious study of the 

volume thermodynamics of liquids and solids. The work is, as yet, confined t<5 volume, pressure, and temperature, Questions involving entropy and energy are also in active progress, but can .not be included 

in the present bulletin.

Accordingly the first and third chapters describe the method of generating and measuring high pressure (i. e., pressures up to 2,000 or 

3,000 atmospheres) in full. The second chapter treats of the isometrics 

of liquids, and it is found that they can be very nearly represented by 

straight lines (Levy, Eamsay, and Young). The fourth chapter finally 

traces the isothermals, as yet of but one substance; but the results are 

none the less noteworthy since they indicate the occurrence of a critical temperature solid-liquid, and show a probable method of coordinating the normal type of fusion with the ice type, in a continuous diagram. 

The far-reaching importance of hysteresis, as accompanying all changes 

of molecule, whether chemical or physical, Avhether induced by stress, 

magnetization, temperature, or the intervention of affinity, and whether 

observed electrically, mechanically, or chemically, etc., is emphasized.

The work as a whole is tributary to the geologic views of Mr. Clarence King, by whom the importance of a deeper insight into the volume changes of liquids and solids was pointed out. C. B.

15

ERRATUM.

In $ 74 there is, a wrong entry of volume. The effect is such a shifting of the coordinate axes that 0*5016 cm3 must be added to all the subsequent volumes to correct the results. More rigorously an additional 0-000,011 cm3 per degree centigrade 

is to be added, and 0'000,001,32 cm3 per atmosphere deducted. The relations are 

therefore practically unchanged, and hence the inferences are sustained throughout.
THE VOLUME THERMODYNAMICS OF LIQUIDS.

BY GAEL BARUS.

C H A P T E K I.

METHOD OF OBTAINING AND OF MEASURING VERY HIGH PRESSURES.

INTRODUCTION.

1. Andrews's screw compressor lias this advantage that the strains 

are all brought to bear within the compass of the barrel. In other 

arrangements, such for instance in which a cylindrical plunger is forced 

into the barrel, stress must be exerted on the bed plate or applied in 

a way tending to flexure of the plunger. It seemed to me, therefore, 

that the screw compressor might well be taken as a model for an apparatus of greater strength and efficiency than was necessary in Andrews's work. Indeed, Andrews himself seems to have been of this 

opinion, 1 and toward the close of his life devised an apparatus in which 

screw plungers are an essential part. Hannay and Hogarth,2 however, 

were the first to carry a practical improvement of the screw into execution. They reached pressures but slightly short of 900 atmospheres, 

stating that their reasons for stopping work at this datum are quite 

apart from the efficiency of their apparatus. With the screw compressor3 

described below I obtain 2,000 atmospheres with facility (§ 17, 23). It 

is so constructed that a considerable volume of liquid can be operated 

upon, admitting of compressions of bulk of 5 cubic inches. Finally, 

special provision is made for the insulation of parts, thus enabling the 

operator to apply the essential electric methods in studying his test 

samples.4

Particular notice should here be given of the remarkable modification of Desgoft'e's differential manometer, by which Amagat5 succeeded 

in reaching and measuring more than 3,000 atmospheres of hydrostatic

1 See Prof. Everett's account in Nature, vol. 39, 1889, p. 550.

»Hamuiy and Hogarth: Chem. News, vol. 41, 1880, p. 103.

3 It was constructed for mo by the American Tool Company, No. 84 Kingston street, Boston, Massa 

clitisetts, Benjamin J. Radford, superintendent.

4 1 here liavo special reference to Prof. Tait's ingenious device in Trans. Hoy. Soc.Ed., vol. 13,1385-85, 

p. 2, Of. Bieblatter, vol. 10, p. 149.

"Amagat: C. K., vol. 10:i, 1884, p. 429. Cf. chap. in.

17 

Bull. 90 2
18 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

pressure, but whereas on the one hand Amagat has as yet given only 

a meager account of his machine, Prof. Tait on the other has so recently 

described an apparatus on the principle of the "manometre a pistons 

libres," that it seems expedient to refer the reader to Prof. Tait's 

memoir.1

THE SCREW COMPRESSOR.

2. General method. The apparatus consists essentially of a strong 

wrought-iron barrel ABC. PI. I, the head of which A A is suitably 

threaded, so that a steel screw 8STT can be forced into it. The piezometer tubes are attached at the end C-C of the barrel. Barrel and 

tubes are quite filled with oil.

3. Special devices. It will facilitate comprehension if I state here at 

the outset the two chief devices used iu the construction of the machine. 

The first of these is the tinned screw. This is an ordinary, well-cut machine screw of iron or steel, covered with a uniform thin adhesive layer 

of solder by dipping it in a vessel of the fused metal, soldering salts being 

used in the ordinary way. Screws of this kind, when forced into their 

sockets, secure complete freedom from leakage. Gauges and other appurtenances may thus be attached to the barrel or removed from it 

with convenience. The -other device is the gasket of marine glue 2 or 

other very viscous liquid. A stuffing box is easily made, by which this 

substance is kept pressed against the threads of the screw, or against 

the smooth walls of a cylindrical plunger. The viscosity of marine glue 

is such that, whereas it easily admits of being shaped by pressure to 

fill up any cavity, the substance is yet far too viscous to flow through 

capillary interstices like those between the metallic parts of a wellfitting screw, except after the lapse of an enormous time (months). 

Thus I found the absolute viscosity of the glue to be 200x10°. It 

would therefore require 1,000 atmospheres to force the cement through 

a capillary aperture .Olcm in diameter and lcm long, at the small rate 

of only .05Gm per hour, supposing (an unfavorable supposition) that its 

viscosity does not increase under pressure. For larger pressures the 

rate is proportionately increased. JS"ow, it is the property of the above 

screw to close the apertures under pressure, since the metallic parts 

under these circumstances are bound more closely together. This probably further accounts for the insignificant leakage actually observed. 

I may note in passing that the viscosity of a pitchy substance like marine 

glue is therefore 20 billion times that of water.

4. Steel screw. To rotate the screw ST conveniently, it is provided 

with a lever and ratchet LDER. The ratchet wheel is shown at ItB 

in PI. i, 1 and 3, and is cut so as to correspond with the right and left 

click 1). A pin J7, sliding in a socket of the lever J/, and actuated

1 Tait: Challenger Reports, 1873-'76, Physics and Chemistry, vol. 2. See Nature, vol. 41, p. 361,1890. 

* Supplied by M. Ducretet, of Paris, or by the Societ6 Genevoise. It is a specially prepared mixture 

of rubber and shellac. It may be thickened by adding shellac. ^
O. 3. GEOLOGICAL SURVEY BULLETIN NO. 08 PL.

SCREW COMPRESSOR, WITH PARTS IN PLACE,
[BARUS. SCREW COMPRESSOR. 19

by a spring, enables the operator to adjust the ratchet either for forward or retrograde motion of the screw 81] or wholly to withdraw the 

click "from the ratchet, as shown in PL i, 3. The figure gives a full account of the manner in which the parts of the lever and ratchet are pufc 

together. The ratchet wheel is securely forged to the screw. Essential 

parts are made of steel.

The screw 8T is 1 inch in diameter. On the front half of it a thread 

of 12 turns to the inch is cut from the end to about 1 inch of the ratchet 

wheel. The rear half is a cylindrical shaft held in position by a journal 

HHH. The latter is bolted down to the bedplate -F(r, and additionally secured between slides, as shown in PI. i, 2.

5. Barrel. Head. The planed front end of the cast-iron bedplate FGr, 

the part FF of which is hollowed out so as to catch drippings, carries 

the barrel BBB already referred to. It is seen in cross-section in 

PI. I, 8, and its flat side is firmly secured to the plane of the bedplate by 

two bolts. The head A A of the barrel carries the stuffing box M", 

of special construction. The efficiency of the screw depends entirely 

on this arrangement, and it must therefore be described in detail. Ick 

is a hollow steel nut of the form shown, and provided with a large flange 

for screwing it in place. Both the inner and the outer cylindrical surfaces of the nut IcJc are threaded, with 12 turns to the inch. Moreover, 

the inner thread 1)11)1) of Ick is a continuation of the thread aaaa 

in the Avails of the barrel. And since the thread cccc also has 12 turns 

to the inch, it is clear that the nut IcJc can be forced in or out of the 

head AA, no matter what the position of the screw /ST may be. In 

practice cccc is cut first and the nut screwed in place. After this the 

whole thread bbaaaabb is cut at one time. To prevent leakage of the 

oil in the barrel through the threads of the screw, the gasket of marine 

engine mm is inserted and kept firmly pressed against the threads by 

the gland Ick. At high pressure the friction is sufficient to hold the 

nuts in place, thus obviating the need of lock. nut.

It is seen that after the screw enters the barrel the chief strain of 

compression is borne by the thread aaaa. The threads cccc and bbbb 

hold the material of the stuffing box forcibly in place.

6. Barrel. Head, improved. There is an objection to this form of 

stuffing box, inasmuch as at very high pressures the threads aaaa and 

bbbb tend to act as lock nuts on each other. ' To obviate this annoyance 

I devised the method shown in PI. i, 4 and 5. Here the thread aa is 

movable, being on the inside of a ring rr of steel, which fits snugly in 

a socket of the barrel. The ring rr, though capable of moving back 

and forth, can not rotate, being prevented by a projection corresponding to a slot in the barrel. In this way the material in the stuffing 

box is not forced into the barrel on actuating We. Note that the 

thread within Ttk is carried quite to the end, and that the inner face 

of Me is beveled very obliquely, thus allowing the gasket to encircle 

a greater number of threads of the screw 88. The strain is now borne 

by the thread 1)1). Experiment has shown this to be no disadvantage.
20 THE VOLUME'THERMODYNAMICS OF LIQUIDS. [BULL. 96.

7. Barrel. Body. This is perforated by four or more holes (PI. i, I) 

about three-eighths of an inch in diameter, and threaded to admit the 

tinned machine screws. Two of these MM are vertical, the other two 

N, 0 (PI. i, 8), .horizontal. They are of use in filling the barrel with oil, 

for attaching gauges and other appurtenances.

8. Barrel. End with piezometer tube.1 The steel tube uuu is inserted in such a way as to insulate it electrically from the barrel end 

(7(7. A screw is cut on the end of uuu, fitting into a cast-iron flange 

WW between two cylindrical jackets XX and YT of hard rubber or 

ivory. These parts Y, TV, Xare screwed to the end of the tube U, and 

the cylinders T and X are turned large enough to fit the hole of the 

barrel and the internal aperture of the steel gland ZZ snugly. All 

space within the head 0(7 is filled with marine glue dd. This is easily accomplished by melting the cement into*the crevices between Y and TV, 

TV and X, before putting the piezometer in place. A thick gasket dd is 

also inserted. After this the remaining annular space around TV, 

through which leakage might occur, is filled by forcing in the nut ZZ 

gradually, and at a temperature not too low.2 To obviate possible 

electric contact between TV and Z, the rubber jacket Y is flanged.

9. Piezometer tube. Vapor bath. The further end of the piezometer 

uu is closed with a tinned screw V. The substance to be examined is 

inserted in ways which must be specially described for each experiment. 

As a rule the same tubes are adjusted within the compass of a copper 

vapor bath ffff, PI. I, 6. This is a hollow cylinder, closed at both ends, 

through which a suitable thin copper tube hh passes somewhat above 

the middle and from end to end. The liquid yy to be boiled is introduced into ffff and heated with a large burner. The vapors escaping 

at g are condensed and run back, thus making the ebullition continuous. 

A number of baths of this kind are at hand, each containing a substance 

of suitable boiling point. In order to pass from one temperature to 

another it is merely necessary to slip oft' one vapor bath ff and slide 

on another. The copper vessels are to be surrounded with thick asbestos jackets in the usual way, and proper provision made to close up 

the ends of the tube hh so that convection currents may be obviated.

10. Method of filling. When the screw is in good adjustment leakages 

are small and fresh supplies of oil are not frequently necessary. A 

convenient method of filling the screw with oil is indicated in PI. T, 8. 

The steel rod oo, threaded at one end and provided with a strong cross

1 Weldless cold-drawn steel tubing of any dimension may be obtained from John S. Leng, New York, 

or of Philip S. Justice, Philadelphia, Pennsylvania.. Both gentlemen are agents of English houses 

whose address is not known to me.

2 The figure is somewhat diagrammatic here to exhibit the parts. In practice I use hard-rubber 

cylinders XT and YY, and two hard-rubber annular disks between YFand TFTFand WIFand XX, respectively. When ready for insertion, the cylinders are screwed against WW, so that there are mere 

films of marine glue left between contiguous plane*. Finally, th« nut ZZ is brought in contact with 

the flange YY (disk) by pressure. It is in view of the fact that Ylr is pressed radially inward toward 

the axis of J7U, as well w outward by pressure, that the arrangement holds so well. Repacking is only 

rarely necessary.
, PIEZOMETER. 21

handle at the other, is surrounded by a cyliudrical tube of brass P 

surmounted by a funnel-shaped inlet Q. Both Q and P are kept full 

of oil, and to prevent leakage there is an ordinary stuffing box at pp. 

A spring clamp (not shown in the figure) keeps the end of the tube P 

of the filler PQ appressed against the barrel BB, a leather washer 

being suitably interposed. To manipulate the filling arrangement, the 

pressure is taken off and oo screwed out without removing it from P. 

The oil in PQ will then follow the retreating screw 8T, PI. i, 1. To fill 

tlie barrel completely, one of the screws .M may be removed until oil 

exudes. It is clearly advisable to remove all the air out of the barrel 

and piezometer tubes, otherwise ST must be forced in to a considerable 

part of its length before the air spaces are sufficiently compressed to 

sustain high pressure. Ordinary sperm oil or machine oil of a thickish 

quality, yet sufficiently thin to flow, is available for filling the barrel. 

It has a great advantage over water in not rusting the barrel, and in

keeping the moving parts oiled. Mercury is objectionable, since it would 

dissolve the tin coating on the bolts, and thus soon produce leakage.

11. Case for protection. Working as fur as 2,000 atmospheres, explosions are not infrequent. They occur with slight detonation, scattering 

thin mists of oil. But there has been nothing of a serious nature. It 

is necessary, however, to surround the barrel with a case of 2-inch 

plank, and to put a barricade beyond the end of the piezometer tube. 

A tin pan, suitably fastened below the bed plate of the screw, is advantageous in catching oil. After filtering this may at once be used 

over again. 

12. Vertical piezometer. An adjustment similar to CCuu, but smaller 

in dimensions", and ending, below in a finely perforated screw, maybe 

attached at M. The piezometer is thus fixed in vertical position, and 

is easily adjusted or withdrawn, while the end of the barrel is available 

for other purposes. (§ 23.) A full view of the vertical piezometer is given 

in PI. i, 7, and PI. in, below, shows the same, with appurtenances.

In PL i, 7 aa is a hollow pear-shaped piece of steel, which can 

be attached to the barrel by means of the perforated tinned screw/. 

The piezometer tube of steel is shown at mi, and is provided with a 

steel flange piece cc. The hard rubber flanges for insulation are 

screwed on atd and e, and the system held in place* in a medium of marine glue, by the steel gland bb. The advantage of the vertical adjustment lies in the fact that a surface of separation or meniscus of mercury is very much less apt to be broken in the vertical position of the 

column than is any other. Et is also frequently desirable to produce 

gravitational separation of mixed liquids under pressure. Finally, since 

the apparatus PI. I, 7 is complete in itself, the electrical and other adjustments may be made, and all glass apparatus within uu fastened 

before the piezometer is screwed into the barrel. Note that the tube 

uu and the barrel are insulated from each other.
22 THE VOLUME THERMODYNAMICS OF LIQUIDS. IBUI.L 96. 

PRESSURE MEASUREMENT.

o

13. Tait gauge. Adjustment. The gauge connects at JV, PL I, 8, and 

is shown at qq, tt, ss. The essential part is the steel tube qq, closed at 

one end by the tinned bolt r, and connecting at the other with the reducing piece N~. I added JV because it is not advisable to cut a deep 

thread in the tube qq. Connection may be made with JVby a shallow 

line thread and solder, 'and the connecting thread cut in the thickwalled tube pf -2V". The tube qq is filled with oil. To measure the expansion of qq under pressure it is surrounded by a close-fitting glass 

tube tttt, one end of which is joined to the steel tube at ^aft by a layer 

of marine glue. The other end of tt communicates with the vertical 

capillary tube ss, by which the expansions, are measured.

It is clear that the shell-like space between the steel tube qq and the 

glass envelope tt must be filled with a liquid of small coefficient of expansion. I first tried mercury, but found it almost impossible to fill tt 

in such a way as to entirely exclude air. Moreover, in view of the friction of the mercury thread in ss, any trace of air in tt will produce irregular motion, and vitiate the experiment. Colored alcohol shows too 

much thermal expansion. I therefore used water colored with an 

alcoholic solution of fuchsine. Under these circumstances a sufficient 

constancy of temperature may be obtained by surrounding tt with a 

jacket uu of circulating cold water coming directly from the hydrant. 

Thus the temperature error may be reduced so as not to exceed 10 

atmospheres, reasonably slow motion of the screw presupposed. (See 

below.) To keep the liquid in ss at a given fiducial mark, a special adjustment for moving the meniscus suggests itself; but this is an exceedingly difficult device to apply, seeing that there must be the minimum of water in tt, and that obsolutely tight joints are essential. 

, Hence I raise or lower the meniscus and color it, when faded, by inserting filimentary glass tubes into the canal of ss. Such tubes are 

easily made by drawing out a wide glass tube and then covering the 

open wide end with a rubber cap. Using such tubes there is little 

difficulty either in adding more liquid to the thread in ss or in withdrawing liquid from it.

It is advisable to protect the steel tube qq from rusting, either by 

nickel-plating it or in other ways. I observed, however, that water 

free from air and containing a little alcohol-does not easily rust iron. 

After an exposure of several months, bright surfaces were still untarnished. A dilute solution of rubber may possibly be used for coating 

the tube. Thick coats are to. be avoided, because they interfere with 

the expansion.

In later experiments I made the joint at the closed end of the glass 

envelope hermetic and rigid, as follows: In PI. I, 8 a is a layer of marine glue between steel and glass, and u a plug of fusible metal, the 

whole being surrounded by an external close fitting copper envelope
TAIT GAUGE. 23

(wired to the glass) /?. The latter beiug a prolongation of the glass 

tube, the layers a and// are melted in, while the gauge is held in a vertical position. The effective part of the steel tube qq is about 100cm 

long, 1CI" thick externally, and -5cln in internal bore. A capillary tube 

of the rather wide bore -07cm is then sufficient for measurement, showing a displacement of meniscus of nearly 2cm per 100 atmospheres pressure. Data are given more accurately below. My reasons for using a 

long tube are these: That the effective length can be more accurately 

stated. In short tubes the error at the joint ^a is much more serious. 

Again, since the expansion corresponding to a given pressure increases 

in absolute magnitude with the length of qq, it is clear that a wider 

capillary tube at ss will suffice Avhen qq is long. A wide capillary .s-.v is 

obviously convenient, since it can be more easily adjusted for zero in 

the way just stated, and since the tube qq itself can be more easily 

filled by aid of the air pump. When the gauge is properly charged 

and adjusted, it must show no displacement of the fiducial zero during 

the interval of experiment,

In later experiments I bent the vertical tube $$, PL I, 8, horizontally, 

so that its measuring parts lay close to uu and immediately above a 

millimeter scale. A somewhat finer capillary corresponding to about 

2,000 atmospheres per meter was used with advan tage. So constructed 

the Tait gauge1 is very much more compact and less fragile.

14. Tait gauge. Graduation. To graduate the gauge I compared it 

with a large Bourdon gauge, reading from. 0 to 1000 atmosphere. The 

tube of the latter in this case communicates with the barrel through 

one of the screws M. This comparison with the Bourdon gauge is a 

check on both instruments, and the statistics are therefore given below. It affords no means of checking the correct value of the standard 

atmosphere employed. But since both gauges are based on Hooke's 

law, and provided with scales of equal parts, the relations are Avell indicated. In the table 2a 0, 2ft], and L, denote the internal, the external diameters, and the length of the steel tube qq, PI. I, 8, 2 />, is the 

bore of the capillary ss.

____________L_ 

1 The form of steel high pressure gauge based on Hooke's law recommended Irtifc not constructed by 

Prof. Tait (loc. cit.), is somewhat different.from the above. I think my form has the practical advantage of greater simplicity, being essentially a single-walled tube. The method of computation is due 

to Prof. Tait. It was my purpose to make the tube tt of brass, so that the heat of compression would 

bo more quickly dissipated. But I failed to obtain tubing of the proper bore and strength until quito 

recently.
THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 00.

TABLE 1. Comparison of Tail gauge No. 0, and Bourdon gunge.

[a0 == -27cm ; a, = 1.00cm ; L = 100Bm ; p = .034cm .]

Time =

Bourdon.

Atm. 

0 

100

200

300 

400

500

(iOO 

700

800

900

1000 

900

800

700

GOO 

500

400

s;;o

100

0

Krtte, in 

centimelit m o sjiliere...

15 m

Tait.

Cm. 

1-90 

3 -58

5 -20

7-05 

8 '70

10-50 *12 -50 

14-10

15 -65

17-22

18-80 

16-62

14 -65

12-80

10-95 9-30

7-55

5-95 4-50

3-04

1-74

I -.01 69

30"'

Tait.

Cm. 

2 -10 ' 3-70

5 -50

7-25 9-00

10-72

12 -50 

14-10

15 -70

17-20

19 -00 

10-70

14-70

12-80

11-00 9-28

7-55

6-00

3-12

1-90

 0171

45 

Tait,

Gin. 

2 '00

5-35

7-20

8 -nn

10 -70

12-45

15-70

17-30

19-00 

16 -80

14-63

12-75

11-00 9-23

 7-50

6-10 

4-60

3-15

1-DO

 0172

75 m

Tait.

Cm. 

2-18

7-45 9-10

10 -85

12-55 

- 14 -20

15-85

17 -45

19 -10 

16-80

12-92

11 -12

7-60

6-15 

4-60

3-20

2-00

 0172

90-

Tait.

Gih. 2-10

7-30

12-70

19-20

< 

11 -00

5 -85

1-60

* Break in the measurements. 

15. TABLE 2. The same (/auye comparisons (No.tf and Bourdon) after long use.

Large 

Bourdon.

100

200

300

400

500

Tait.

6-35

S

.ftO

13-26

Tait.

6-27

9-70

13-16

Factor.

 01715

1728

Mean .

 01722

Small 

Bom-don .

30 

120

Large 

Bourdon.

31 

121

Tait.

4-94 "6-42

8-04

9-60

Tait.

5-05

6 .CO

8-05

9-67

Factor.

 01722 

1767

16G7

1744

Moan.

. 01725

TABLE 3. Higli pressure tests.

P 0

2110

0

2160

0

\r _ A -on

5

.1 A

41-95 5-20

16. Table 1 contains five series of observations made at the times 

stated. In the first four series I went up to the maximum and down again 

gradually, but not slowly. The last I operated as fast as the experiment would permit. To determine the degree of accuracy it is well to 

consult the rates at the bottom of the table. These show that a mean 

displacement of '0171cm of the meniscus takes place in the pressure in-
HAHUS.] GUAGE COMPARISONS. 25

creasing series for each atmosphere pressure. Consulting data on the 

same horizontal row it appears that the differences of reading of the 

new gauge corresponding to a given reading of the Bourdon gauge a.re 

greatest in the region of low pressures. At zero the maximum difter40CrW

0 100 200 300 400 500 600 700 800 900 1000

FIG. 1. Chart showing the bow-shaped cycles obtained in the gauge comparisons.

ence observed is 40cm , equivalent to an error of 24 atmospheres. Again, 

comparing the two zero readings of the last column, the difterence of 

reading is 'SO0111 , corresponding to 33 atmospheres. This, therefore, is a 

maximum index of the inaccuracy of the Tait gauge due to thermal
26 THE VOLUME THERMODYNAMICS OP LIQUIDS. [BULL. 90.

effects of compression and unreasonably hasty work. To diminish this 

error further, it is necessary to decrease the bore of the glass tube tt 

in PL 1,8, thus making the thermometer property of the gauge of smaller 

importance. In the above apparatus this tube was l'15cm in internal 

diameter, corresponding therefore to a liquid interstratum -OT01" thick. 

Clearly this admits of further reduction. A> brass tube would in many 

respects be preferable to a glass tube, since in this case the heat of 

compression is more easily dissipated; but I did not find one of the 

necessary dimensions.

17. A second point of view is obtained by comparing the data of the 

pressure "on" and of the pressure "off" phases of the above experiments. For convenience I insert the Chart, Fig. 1, in which the data of 

Table 1 are inserted. It is seen at once that the degree of accordance 

in the " on" series is satisfactory. The errors are nowhere larger than 

10 atmospheres. The loci, apart for slight circumflexure, are straight 

lines. In the "off" series, however, this good uniformity is lost. The 

data lie on consecutive broken lines. The feature of particular importance is, however, this: The observation that the "off" data do not at 

all return on the lines of the "on" data. Indeed the two lines, "on" 

and "off," inclose a band the maximum width of which is even 1.5CI", 

corresponding to 90 atmospheres. Since tiiis band widens at once at 

900 atmospheres, and falls off at zero atmosphere, it is clearly due to a 

virtual shifting of the fiducial zero of the mechanism of the Bourdon 

gauge.

In the present comparisons, therefore, the "on" series of data need 

alone be considered. It appears for these, slow work presupposed, that 

the error of the gauge in the above form need not exceed 10 atmospheres, and that it can certainly be reduced decidedly below this limit 

by diminishing the bore of the glass envelope tt, PL T, 8.

18. TABLE 4. Comparison of large Bourdon gauge with Tail gauge No. 1. p = .02%0cm,

Large 

Bourdon.

Atm. 

0

100 

200 

300 

400 

500 

600 

700 

800 

900

tfo.l.

Cm. 

17-ia

21-30 

25-03 

28-85 

32-63 

36-50 

40-35 

44-05 

47-55 

51-25

Diff.

0»i.

3-49 

3-73 

3-82 

3-78 

3-87 

3-85 

3-70 

3-50 3-70

Large 

Bourdon.

Atm. 

900

800 

700. 

600 

500 

400 

300 

200 

100 

0

No. 1.

Cm. 

51-27

47-12 

43-10 

39-11 

35-12 

31-32 

27-75 

24-31 

2100 

17-96

Diff.

Cm.

4-15 

4-02 

4-00 

3-99 

3-80 

3-57 

3-44 

3-31 3-04

Second comparison. Another thread length.

0

100

200

300

400

500

600

700

800

900

1000

o *vQfi yo

9-42

13-17

17-00

20-74

24-60

28-45

32-35

35-78

39-57

43-36

3-46

3-75

3-83

3-74

3-86

3-85

3-70

3-63

3-79

3-79

1000

900

800

700

600

500

400

300

200

100

0

43-40

39-00

34-75

30-76

26-75

22-84

19-13

15-74

12-36 9-14

6-21

4-40

4-25

4-00

4-01

3-91

3-71

3-39

' 3-38 3-22

2-93
BAttUS.] GAUGE COMPAEISONS. 27

Third comparison. Large Bourbon gauge with Tait gauges jVos. 1 and 3. 

[No. 1, p = .0220"". No. 3, p = .0336 .]

Largo 

Bourdon.

A tin.

0

100

200

300

400

500

600

700

800

000

1000

No. 1.

Om. 4-72

8-29

12-03

15-85

19-48

23-40

27-32

31-04

34-08

38-53

43-J9

No. 31

Om.

26-59

28-17

29-81

31-50

33-11

34-82

86-59

38-23

39-81

41-53

43-28

Large 

Bourdon.

A tin.

1000

900

800

700

600

500

400

300 '200

100

0

No. 1.

Cm.

43-20

38-93

34-58

30-75

20-65

22-68

19-03

15-62

12-24

895 6-08

No. 3.

Om.

43-28

41-36

39-55

37-87

36-13

34-49

33-00

31-63

30-24

28-86

27-60

Cyclic comparisons.

0

300

200

300

400

300

200

100

0

0

 100

200

300

400

500

600

700

000

500

400

0

6-10

9-55

13-27

17-12

20-94

17-13

13-30 9-52

6-08

6-08

9-60

13-39

17-19

20-96

24-83

28-40

32-30

. 28-39

24-35

20-38

Acci 6-02

27-92

29-45

31-15

32-64

34-51

32-90

31-29

29-77

28-64

28-64

30-10

31-01

33-27

34-86

36-54

38-12

39-74

38-07

36-39

34-77

dent.

28-69

0

100

200

300

400

500

600

700

800

900

1000

3000

900

800

700

600

500

400

300

200

100

0

5'98

9-43

13-20

17-05

20-94

24-75

29-00

32-03

30-44

40-18

45-10

45-13

40-72

36-50

32-49

28-49

24-57

20-86

17-41

34-00

30-80 7-78

28-92

30-50

32-19

33-87

35-51

37-17

38-89

40-39

42-00

43-57

45-27

45-28

43-43

41-63

39-97

38-35

36-74

35-. 4

33-83

32-46

31-1.6

29-97

19. TAULE 5. Comparison of Tait gauges Nos. 1 and 4.

No. 1.

 -35 

6-42

13-10 

20-20 

30-08 

38-00 

31-49 

23-02 

16-90 

8-96 

1-35 

7-78 

15-67 

21-41 

28-54 

35-31 

40-00 

32-65 

25-86 

39-84 

13-38 

0-25 60

No. 4.

10-38 

13-43

16-43 

19-69 

24-09 

27-95 

24-71 

21-23 

18-02 

14-61 

11-22 

14-11 

17-66 

20-37 

23-56 

20-48 

28-67 

25-35 

22-39 

19-69 

16-69 

33-55 

11-02

No. 1. No. 4. No. 1. 

at m.

No. 4. 

a tin.

Now adjustment of No. 4.

1-39 

7-68 

14-45 

20-54 

28-40 

34-39 

40-07 

46-35 

52-75 

59-02 

63-75 

63-53 

63-11 

56-44 

47-36 

40-98 

33-61 

20-95 

19-24 

13-05 5-54

1-25

10-78 

13-54 

16-60 

19-33 

22-85 

25-53 

28-07 

31-05 

34-49 

38-18 

41-02 

41-25 

41-11 

38-26 

33-96 

31-32 

28-10 

25-11 

21-63 

18-80 

35-28

12-05

1761 

1755 

3745 

1564 

1317 

1145 

947 

766 

557 

389 

185

00

1783 

1760 

1750 

3579 

1320 

1161 

967 

787 

577 

407 

395

00
28 THE VOLUME THERMODYNAMICS OF LIQUIDS. 

TACLK 6. Calibrations of Tait gauges Nos. 1 and 4.

[BULL. 90.

No. 1.

 1-30 

2-28 

6-00 

9-06 

9-05 

5-90 

2-20 

 1-30

No. 4.

32-02 

33-63 

15-29 

10-97 

16-90 

15-20 

13-62 

12.04

Small 

Bourdon.

0 

100 

200 

300 

300 

200 

100 

0

No.l 

factor.

3-65 

3-69 

3-60 3-73

3-09

No. 4 

factor.

1-03 

1-67 

1-07 

.1-61

 i-co

TABLTC 7. Comparison of Tait gauges Nos. 1 and 4.

No. 1.

Cm.

 -40

8-38

18-23

28-43

38-36

50-04

59-93

 63-75

55-03

42.89

31-90

20-09 9-02

 -55

No. 4.

Cm.

.32-40

16-45

20-85

25-40

29-80

34-91

39-41

41-25

37-33

32-00

27-19

21-86

16-78

12-30

PIAtm.

0

244

517

801

1077

1401

1675

1781

1540

1202

897

569

202

 4

P«.

Atm.

0

252

525

807

3081

1399

1678

1791

1549

1221

93.9

588

272

G

TABLE 8. Calibrations of Tait gauges Nos. 1 and 4.

Small 

Bourdon.

Atm. 

0 

300 

200 

300 

300 

200 

100 

0

No. 1.

Cm. 

- -56 

2-90 

6-59 

10-35 

10-34. 

6-08 

3-38 

 -33

 No. 4.

Cm. 

12-30 

13-93 

15-56 

17-26 

17-26 

15'60 

14-05 

12-46

Factor 

No. 1.

3-57 

3-73 

3-5? 3-51

3-CO

Factor 

No. 4.

1-00 

1-60 

1-61 1-57

1-61
BABUS.] CONSTANTS FOE TAIT GAUGE. 29

20. Tait gauge. Volume increase measured and computed. With the 

aid of the above results it will now be easy to compute the volume increase of the steel tube ##, PI. i, 8, per atmosphere of internal pressure, 

aud then compare the datum thus obtained with the result computed

PIGS. 2, 2a. Direct reading helical Bourdon gauge.

by aid of Tait's formula. 1 From the dimensions a0, a^ I/, p given in 

table 1, it follows that the increase of the external volume of the 

cylindrical steel tube is 47/106 per unit of volume of qq, per centimeter, of 

displacement of the thread in the capillary ss. This corresponds to a 

volume increase of

vJV=. 00000080 ... (1)

per unit of volume of the steel tube, per atmosphere.

Tait shows that in case of internal pressure the changes per unit of 

length tangentially to a cross section of radius r and longitudinally for 

any part of the tube, are respectively

1 1 1 \ d £ °

- 73- 9« 1 *"><! di= ~~

/ *Jtv 11 X o '>

1 / Wj rf? _ Ug ft 

1

ok

1 Tait: Challenger Reports, Vol. 2, 1882, Appendix A, p. 20.
30 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

Hence the increase, -y per unit of volume of the external surface of 

the tube is

(2)

Here £ is the displacement of the point whose position is x centimeters from one end, and p the change of a point in a right section, 

originally distant r centimeters from the axis, // the internal pressure 

in atmospheres, and Ic and n the compressibility and the rigidity respectively, of the steel employed. I take k and n from E verett's tables, 1 

as follows :

fc = 1.84x!012 n = 8.2

Inserting these quantities into the equation, there results

'L 

~v = .00000073 .... (3)

It appears at once that this result is of the same order as (1). The 

difference is probably due to the constants Ic aucl M, which Prof. Everett 

doubtless found from a high-grade tool steel, whereas the above tubes, 

being made of low carbon steel, are nearer wrought iron in their properties. Beyond this the absolute gauge atmosphere is not vouched 

for; nor (being the mean value between 0 and 1000 atmospheres) are 

the coefficients at the end of table 1 quite free from thermal discrepancy.

When the observations are made for the purpose of measurement, 

there appears no doubt that equation (2) may actually be utilized to 

obtain serviceable values of (1/fc+l/w). For instance, a0 may be obtained accurately by filling in vacuo with mercury and weighing, and 

then from the known specific gravity of the steel tube and its weight 

when empty, at may be computed, p is similarly capable of accurate 

measurement. Therefore by combining (1) and (2), (1/fc+l/w) is measurable with the same accuracy with which // is known.

21. Direct reading, Bourdon gauge. It is well to insert my endeavors to adapt the Bourdon gauge for high pressures and direct reading. 

In order to achieve this result it is necessary to multiply the number 

of coils as well as to work with flat tubes. In Figs. 2 and 2a, the 

latter being the plan, the former the elevation, 1 have drawn a form 

of apparatus, with which I obtained some results. It consists essentially of a helix, A B C D E F, the spires of which do not touch each 

other. The end is provided with a needle F 8, moving over a millimeter 

scale 8 $,~supported by an arm T E 8. This gauge is screwed directly 

into the barrel. Being entirely of iron and metal it is very firm. The 

spires are hammered flat by heating them to redness, the tube being

1 Everett: Units aiid Physical Constants. Loiulon, Macmillan, 1879, p. 53.
BARUS.] HELICAL BOURDON GAUGE. 31

originally lcm ii\ external diameter and 5cm in bore. After winding 

hot, the internal diameter of the helix was found to be somewhat larger 

than 4cm. There were five spires in all, and the upper one E .F, with 

its needle, extended about a decimeter beyond the helix.

The following little table gives the results of a comparison Avith the 

Bourdon gauge:

TABLE 9. Comparison of Bourdon </ai<(/e find Ike spiral yauye.

Bourdon.

Atm.

0

100

200 300

400

500

Spiral.

Gin. o-oo

 17

 35

 54

 70

1-00

Bourdon.

Atm.

600

700

800

900

JOOO

0

Spiral.

Cm.1-28

1-55

1-87

2-30

Explodes. 1-16

Constructing these results graphically in Fig. 3, it will be seen that 

between 0 and 300 atmospheres, the permanent set is not appreciable.

0

^^

CWL r""~~"~l !

*^^ 1

^

s

x*

0 100 200 300 400 500 6*00 700 600 f>00

!FiO. 3. Chart showing the action of the lujlioal Bourdon gauge.

When pressure was taken off, the fiducial zero reappeared. Above 300 

atmospheres, however, permanent set becomes very marked. The helix 

was ruptured at 1,000 atmospheres, and the new zero after explosion indicates the large amount of permanent set during the course of the 

measurement. Connecting the final zero with the point for 900 atmospheres, a line is obtained nearly parallel to the line between 0 and 300 

atmospheres. The mean motion of the index was therefore -OOIT0"1 

per atmosphere. Since high pressure measurement was only contemplated, the gauge would have been serviceable except for the occurrence of permanent set. The chief cause of this insuperable difficulty 

is the fact that to flatten the gauge it must be heated to redness. By 

so doing the drawn hardness and resilience is destroyed, and the soft 

metal of the gauge then becomes useless for measurement. Owing to 

the rupture of the tube I did not experiment further, since the coiling 

and flattening is a tedious operation. Clearly the gauge might be 

used without flattening by suitably attaching a minor index. But this 

complicates the apparatus. 

22. Concluding remarks. i will conclude this description by a few
32 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

general remarks on the apparatus used. It is clear that instead of a 

single barrel, two barrels, the axis of one of which is the prolongation 

of the other, suggest themselves. The barrels would be used alternately, one being filled while the other is emptied. Again, instead of 

having the screw enter the barrel, good results must also be obtainable 

by forcing a cylindrical shaft into the barrel; for the device shown at 

the end of the barrel G C, PI. I, proves that the gasket of marine 

glue is quite as serviceable for cylindrical shafts as for screws. In 

case of a cylinderj however, the strain encountered in forcing in the 

shaft would be brought to bear on the bed plate, i. e.,.outside of the 

barrel. Specially strong devices would therefore have to be resorted 

to in bolting down the barrel, etc. These would make the apparatus, 

supposing the horizontal form retained, much more cumbersome. Indeed I conceived it to be an advantage of Andrews's screw, inasmuch 

as the chief stresses exist within the compass of the barrel. The necessary provision against twisting is much more easily applied. Finally 

I may state that it was my original object to obviate stuffing boxes 

altogether, by using a tinned screw S T. The maximum of pressure 

thus obtainable far exceeds the limits of the above screw-compressor 

with stuffing boxes. The tinned screw would have this disadvantage: 

it would have to be freshly coated whenever it became necessary to refill the barrel with oil, thus occasioning some loss of time. It is a device however, to be kept in mind, since it obviates the necessity of 

troublesome metallic gaskets, like those used in Mousson's well-known 

steel nut, for instance.

23. Caeteris paribus, the labor necessary in producing the above pressures decreases nearly as the fourth power of the diameter of the screw; 

for friction and leverage both increase as the radius, and the resisting 

pressure as the square of the radius. Similar advantage is gained by 

increasing the number of threads to the inch. Hence, by supposing 

the initial pressures to be produced by a thick screw (diameter 1 inch, 

say) at one end of the barrel, and the final pressures (above 2,000 atmospheres, when the inclosed liquids have become much more incompressible) produced by a thinner screw (diameter half an inch, say) 

at the other end of the barrel, the practical efficiency of the screw compressor would be increased. In such a case the piezometer 4tube must 

be vertical. (§ 12.) However, in limiting my present work to 2,000 

atmospheres, I have by no means exhausted the power of the above 

machine. My purpose in doing so was to avoid straining the gauges. 

I add, in concluding, that among the facilities of the above screw compressor is the almost micrometric accuracy with which pressure can be 

raised to and maintained at a given value for any reasonable length of 

time.

24 The facility with which the Tait gauge may be replaced by Amagat's manometer, the absolute calibration of the Tait gauge, its availability for the measurement of pressures indefinitely high, and allied 

subjects will be considered in chapter in.
CHAPTER II.

THE ISOMETRICS OF LIQUIDS.

25. Utilizing the advantages of the screw compressor described in. 

the foregoing chapter, I made the folio wing investigation on the isometrics of liquid matter: The nature of the problem, is clearly denned by 

the results of an earlier paper, 1 where it appears, conformably with the 

inferences of Dupre", Levy, Eamsay and Young, and Fitzgerald, that 

liquid isometrics are lines of small curvature.2 It is thus the purpose 

of the present work to investigate the amount of deviation from a 

straight line as accurately as possible.

The word " isometric" is used by J. Willard Gibbs 3 in his researches 

on graphic methods in the thermodynamics of fluids. It has the advantage of priority if not of expressiveness, and I do not feel the need of 

withdrawing "isometric" for "isochore," as do Eamsay and Young.4

APPARATUS.

26. Constant volume tube. The criterion for constant volume is to be 

given by a reliable electric contact. The liquid whose isometrics are 

to be determined is inclosed in a tube of constant volume, of the form

»____...... gem,..........^.j^rn^...........0crru.:...... ....

FIG. 4. Constant volume tube; longitudinal section.

shown in Figs. 4 and 5. This tube consists of three parts, a reservoir ef 

and two capillary stems ed and da separated by an enlarged portion d. 

A platinum wire c, passing through the walls of the tube, enters the 

cavity d, for the purpose of securing electric contact, as shoAvninFig. 5. 

The dimensions of the tube are given in Fig. 4, and the choice made is 

such as to admit of its easy introduction into the steel piezometer 

tube ww, chap. I, PI. I, Fig. 6.

Fig. 5 (diagram) shows the tube ready for use. The end of the tube 

fl is sealed, holding the platinum wire mm, which passes quite through 

the reservoir ef into the capillary stem. The substance having been

"Bull. IT. S. Geol: Survey, No. 92, 1892, chap, i, p. 54.

2 Am. Jour., 3d, ser., vol. 39, 1890, pp. 497 et seq.

3 Gibbs: Trans. Connecticut Acad., vol. n (2), p. 311, 1873; cf. ibid., p. 382.

'Kainsay and Young: Phil. Mag. (5), vol. 23, p. 435, 1887.

Bull, 90 3 ' 33
34 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

introduced into 

adjoining stem.

FiG. 5. Constant volume tube; diagramf, completely fills this space and about one-half of the 

The remainder of the tube is filled with mercury 7t/c, 

care being taken to guard against inclusions of air.

The tube thus adjusted is inserted into the piezometer, and the terminal c put in metallic connection 

with the walls of the steel tube, near 7, PI. i. The 

terminal ml is insulated by a glass tube,1 and after passing through the piezometer into the barrel, is there 

put in metallic connection with one of the vertical 

screws M. It will be remembered the barrel and piezometer are not in electric contact. A serviceable way 

of connecting the terminal with the barrel is shown in 

Fig. 6, where BB is part of the wall of the barrel. S 

is a perforated screw, slotted on its upper face, so 

that it can be inserted or removed easily. The end 

of the terminal lo is passed through the hole in $, and 

then coiled helically, as shown in the figure. The 

tinned screw .M is now inserted so as to bind the helix 

between its lower face and 8. This insures electric 

contact. A similar device is utilized at F, PI. I, Fig. 6, 

and the glass tube is thus held in horizontal position 

within the steel piezometer tube, by aid of its two 

tense terminals.

Before introducing the constant volume tube, both 

piezometer and barrel must be quite filled with oil, and 

the screws M and F, PI. I, are to be so fastened that 

air may be as far as possible excluded.

27. Manipulation. Supposing the constant volume 

tube in place, surrounded with oil, the screw 88 

(PI. i) is forced in. The pressure thus brought to 

bear uniformly on all parts of the tube, moves the 

thread of mercury inward by an amount corresponding to the compression of ef. Eventually, therefore, 

the meniscus near Ic and the sharp end of the platinum terminal near m come into electric contact. Now, 

as barrel and piezometer are in a simple circuit, including a suitable galvanoscope and a battery, a deflection 

in the galvanoscope occurs at the moment of contact.2 

This method of registration is very sharp and thoroughly reliable. Pressure is applied by means of a 

screw, and can be diminished or intensified with great 

nicety. Hence the position of the meniscus k can be 

controlled with almost inicrometric precision, even 

when the pressures are as high as 2,000 atmospheres.

'Kubber and other similar insulations are fused or dissolved at high pressure, and are therefore unsuitable.

2 Dojvices of this kind have been much used by Wejnljold, Crafts, Meudejjhall, a
BARUS.] PIEZOMETER AND APPURTENANCES. 35

When the machine is in satisfactory adjustment contact can be made 

and broken at 1cm without apparent variation of pressure, the difference being in fractious of an atmosphere. The delicacy, however, depends on the relative caliber of capillary tube and reservoir tube.

To avoid breakage of the thread Ic on being forced through m, the 

free end must be made as fine as practicable (-Olcm in diameter, say). 

Hence it is advisable to weld" a fine wire to the relatively thick terminal 

m (diameter 0-5cni).

28. In passing from one constant temperature to another, care must 

be taken to avoid the mercury thread from being forced either out of 

the tube or into the reservoir. This may be done by keeping the meniscus 7c always very nearly in contact with in. Hence, when a vapor 

bath is attached arid the burner started, pressure is increased in such 

a way as to keep the contact just made. On the other hand, Avhen temperature decreases, pressure is relieved in such a way as just to keep 

the contact broken.

29. When the series of isometrics are to be 

mapped out, the volume of liquid between 

the meniscus 1c and the sharp end of in is 

suitably changed. This volume may be conceived as either positive or negative. In the 

latter case the wire m penetrates the thread 

7i;. The advantage of such an arrangement 

is shown below.

30. Method of filling. When the substance 

to be compressed (ef, Fig. 5) is liquid at ordinary temperatures, like ether or water, the 

tube may easily be filled without an air pump,

J , , n . , Fio. 8. Method of fastening the by in akin g use of filamentary glass tubes with terminals, 

enlarged funnel-shaped heads. The filamentary end is introduced at a and pushed down to the bottom #, supposing the tube ag to be vertical and a uppermost. The liquid is allowed to 

run throughthe funnel, the top of which is kept filled until the reservoir 

e/and adjoining capillaries eda are quite filled. The operation is not 

stopped however until three or four times as much liquid lias run through 

ef as is necessary to fill it.

The tube is now tipped nearly horizontal and mercury passed into 

the bulb d by aid of similar funnel capillaries. The thread is then 

pushed forward from d into de by aid of an empty glass filament, by 

successively draining off small parts of the liquid in de, until the 

meniscus 7c has the desired proximity to m.

31. The greatest care must be taken to have all parts of the tube perfectly clean, to use pure, fresh mercury, and to avoid rubier connections 

or other material impregnated with sulphur. I find it desirable to 

draw off the mercury in abd by aid of a fine tube and a jet suction pump, 

and thus to thoroughly dry out this part of the stem. Fresh mercury
36 THE VOLUME THEEMODYNAMICS OF LIQUIDS. [BULL.96.

is then poured in through the glass filament until the tube is again 

fall.

When the mercury appears dead or fails to move as an unbroken 

column the tube is worthless. The cause of this by no means infrequent 

annoyance i,s usually found in th e presence of sulphurous dirt in the tubes 

or of sulphide in the sample liquid. It is advisable therefore to use 

fresh tubes only.

32. When the substance is solid like thymol or diphenylamirie, it 

must be introduced by aid of an air pump. For this purpose a wide 

glass tube about 20cm long is fused to the end a, Fig. 5. Into this the 

solid substance is put, after which the open end of the wide tube is 

drawn out to a filament and connected with the air pump. After the 

exhaustion of the system the solid is fused with a burner and allowed to 

run down into ef. The operation must be repeated many times and use 

made of vacuum ebullition to expel the last traces of air. The thread 

of mercury is introduced in the way already stated (§ 30), except in so 

far as it is essential to keep the tube in a warm bath to prevent solidification. When in adjustment it is inserted into a hot piezometer tube. 

These operations call for much skill on the part of the operator. If 

solidification occurs the mercury thread is drawn down into the bulb in 

consequence of the large volume contraction, and the charge is therefore 

lost.

33. Vapor baths. In order that the isometrics may be sharply traced, 

temperature must be regulated to a nicety. This is not oasy, seeing 

that the metallic piezometer tube is a good conductor. Hence the forms 

of vapor baths used in my earlier similar works1 are not applicable 

here. It is essential that vapor be directly in contact with the surface 

of the piezometer tube and that the reservoir of the constant volume 

tube be at a distance of 3 or more centimeters from the end walls of 

the bath.

Substances useful for vapor baths are methyl alcohol, 60°; water, 

100°; amyl alcohol, 130°; turpentine, 160°; naphthalene, 215°; benzoic. 

acid, 250°; diphenylamine, 310°; phenanthren, 350°, and others 

These form a convenient series. They admit of being boiled in a brazed 

copper vessel and decompose very slowly. The fiducial or initial temperature is obtained by allowing a current of water from the hydrant to 

circulate around the piezometer tube.

At temperatures above 200°, the form ffff shown in PI. i, 6, is serviceable. The tubulures lih through which the piezometer passes may 

be closed with perforated cork stoppers.2 At higher temperatures hh are 

screw stuffing boxes, securing asbestos jackets. The vapors issuing 

from yy, the ebullition liquid (usually solid at ordinary temperature), are 

condensed in a lateral tube (not shown) and run back into the drum ffff. 

The thermocouple is inserted through g.

1 Bull. U. S. Geol. Surv. No. 92, p. 22; Am. Journal Sci. (3), vol. 39, p. 482,1890. 

* Rubber stoppers melt and are otherwise very objectionable above 200°.
IURUS.] VAPOE BATHS. 37

34. At temperature below 200°, this form of vapor batli is not convenient, since the substance yy is usually liquid and too easily spilt. 

Moreover the degree of constant' temperature obtainable in the drum 

ffffis probably insufficient. I therefore employed the circulating system shown in Fig. 7. Vapor is introduced into the timmfff from the 

boiler A and the influx pipe B. It is condensed in the tube C 0 carrying the cold water jacket D D. The condensed liquid falls into the 

funnel J57, which is cylindrical and thus subserves the purpose of a water 

gauge. The piezometer tube is shown at TJu u J7with the constant 

volume tube adeg in place. G- and G are cold-water jackets surrounding 

UUto prevent the spread of high temperatures along the tube. A

Fio. 7. Vapor bath and piezometer tnbe; longitudinal section.

single current of water (issuing from the gauge jacket, PL I, 8, above) 

passes through G, D, and G. This current is shunted, so that G D G 

can be cut out at pleasure and the vapor bath removed or replaced by 

a circulating water bath. It is to be noted that the parts of the vapor 

bath are rigidly connected, so that it can be rapidly withdrawn as a 

Avhole. H is a suitable electric clamp, corresponding to the other terminal K. All parts of the vapor bath are heavily jacketed with asbestos.

It is necessary that the vapor baths slide off and on easily. Any 

violent jarring of the piezometer tube will break the thread in the glass 

tube within.

35. Method of cooling piezometer. To cool the tube UU after the vapor 

bath has been removed, it is convenient to oil the piezometer with vase-
38 THE VOLUME THERMODYNAMICS OF LIQUIDS, [MILL. 96.

line. The jacket G- may then be slid to and fro very rapidly at first, 

care being taken to relieve the pressure in proportion as the tube cools.

36. Method of temperature measurement. For the measurement of 

temperature I used a platinum platinum-iridium thermocouple, the 

electromotive force of which was expressed in terms of the torsion of 

the platinum fiber which suspended the given astatic system. The torsion galvanometer serviceable for thermo-electric work I have already 

described elsewhere. 1 To calibrate this apparatus the boiling points of 

water and of mercury were first used. Finally I made elaborate comparisons with the reentrant glass air thermometer. §§ 48-50.

37. Method of pressure measurement. Pressure was measured in terms 

of the expansion of a given cold-drawn steel tube, as detailed in chapter i.

It is needless to say that the factor of the gauge was frequently 

checked during the course of the work. A small sensitive1 300-atmosphere Bourdon gauge with a tinned screw connection is very convenient 

for this purpose. About twenty or thirty minutes were allowed to secure isothermal conditions both for the gauge and the piezometer tube. 

Leaks of the apparatus must be so far as possible avoided, inasmuch 

as continued pumping changes the thermal state of the liquids operated 

on and is therefore a fertile source of error.

PRELIMINARY RESULTS.

37. Data for ether. The data of Tables 10 and 11 were obtained in 

the earlier experiments. Although neither the gauge nor the thermocouple was remarkably sensitive, these results bear directly on the 

matter below and must therefore be inserted. P and 9 are corresponding values of pressure and temperature, such that the volume of ether 

remains constant. Two or three observations were made for each datum, 

allowing five minutes' time per observation. This is essential where 

isothermal conditions are to be guaranteed. So far as these observations go, the corrections for volume changes of glass are negligible. 

During the first five series, extending over an interval between March 

14 and 19 the constancy of the fiducial pressure (at about 10°) is to be 

noted. In the remaining series it was not always possible to regain 

the fiducial pressure, owing to accidents.

TABLE 10. Isometrics of ether. Preliminary results.

P.

Atm.

293

305

888

888

1227

1231

300

301

885

0.

°0.

11-6

11-6

66

66

100

10011-6

11-6

60

r.

Atm.

887

1237

1242

1247

284

288

287

287

e.

°o.

66

100

100

10011-0

11-2

10-0 10-0

1 Larua: Phil. Mag. (5), vol. 29, p. 140, 1890.
liAUL'8. ISOMETRICS Otf ETHEIi. 

TABLE 10. Isometrics of ether. Preliminary results Continued.

P.

Atm.

276

289

277

1502

lf)10

1482

1480

279

278

875 

868 

874 

280

14

545

545

859

857

65

595

602

597

71

912

914

76

156

1087

1094

6.

°0.

9-4

9-9

9-8

127

128

123

1289-7

10-8

64 

66 

65 9-7

9-8

67

67

102

102

10-6

64

64

63

10-8

101

10010-8

10-8

114

115

P.

Atm.

101

647

645

972

966

1080

1063

51

1443

1436

91

80 

608 

611 

613

C14

614

925

924

921

920

919

84

1112

1112

1380

1421

1451

1446

94

627

630

926

924

e.

°o.

9-8

60

C7

103

103

119

12110-0

155

15810-8

10-3 

60 

06 

66

66

65

99

101

101

101

10010-3

119

120

153

156

101

162

11-2

66-5

66-4

98-8

98-5

TABLE 11. Digest of these data.

Ap

0

589

937

0

1216

0

590

0

531

844

0

530

840

0

934

e

11-5

60

100

9-8

127

10'2

65

9-8

67

102

10-7 

64

100

10-8

114

66

0

55

89

0

117

0

56

0

5690'

0 

55

89

0

103

 d)

1

 (2)

&p

0

570

893

996

1369

0

530

840

1030

1342

0

534

831

0

9-9

66

103

120

. 150

10-3

66

100

120

158

11-2

60

99

Ad

0

56

90

110

146

0

56

90

110

148

0

55

89

,

\ (3)

J

w

38. Discussion. In the digest, Table 11, the coordinates have been 

shifted, so-that the fiducial pressure and temperature are now zero. 

The graphic representation, Fig. 8, shows a distribution of points lying 

very closely along straight lines. So far as these data go, therefore, 

the linear character of the isometrics is maintained. The rates per atmosphere are respectively -01)5°, '-107°, -106°, -107°.
40 THE VOLUME THERMODYNAMICS OF LIQUIDS.

DEFINITE KESULTS.

[BULL. 96.

39. Apparatus improved. With the above data in hand I endeavored to carry the discrimination one step further by increasing the 

sensitiveness of both the pressure gauge and the thermocouple.

"FlO. 8. Isometrics of etlier; preliminary results.

Using the same steel tube for the registration of pressures by Hooke's 

law, as before, the gauge was made much more delicate by decreasing 

the caliber of the capillary measuring tube (ss, PI. I, 6), and by
BAUUS.] NOTATION. 41

making use of a more close-fitting glass jacket tt than before. The results have already been shown (§§ 15 to 19). Apart from errors due to 

viscosity and thermal effects, the gauge was sufficiently sensitive to 

register fractions of an atmosphere at 2,000 atmospheres.

Particular care was taken to redetermine the initial pressure corresponding to the initial or fiducial temperature (about 15°), before and 

after each high temperature observation. This is a certain check on 

the validity of the results obtained.

Again the temperature measurement was made more delicate by inserting a finer platinum fiber in the torsion galvanometer. Statistics 

will be given below.

At least ten minutes were allowed for each datum of pressure and 

temperature given. In proportion as the second of any two measurements made at a given temperature coincides with the first, the inference is warranted that the thermal effects of compression are fully dissipated. The observation at any temperature therefore lasted twenty 

or thirty minutes.

40. Notation. The notation is as follows:

N'g, deflection in degrees of arc observed at the torsion galvanometer;

£, temperature of the cold junction of thermocouple;

na , correction by which N~' is reduced to -flT., the deflection which Q> v (7 er

would be observed at the torsion galvanometer if t 20°;

9, temperature of the vapor bath surrounding the piezometer tube. 

9 is computed from N0 . 9 is therefore the temperature of the reservoir 

of the constant volume tube.

N~ , reading in centimeters observed at the capillary tube of the pressure gauge.

#, pressure corresponding to N in atmospheres. Hencep is the pressure bear lug on the substance in the constant volume tube;

dpi A®-> pressure and temperature obtained by shifting the coordinates, so that the initial pressure and temperature may be zero.

41. Data for ether. Table 12 contains fifteen series of observations 

made with ether. Series in which the constant volume tube and contents were changed are separated by heavy lines. It is necessary to 

consider these data somewhat in detail. Bach series contains at least 

one observation at the boiling point of water. Since the barometer 

was also noted, the data for the final reduction of the values 9 are at 

hand cf. §§ 48 et seq.

The first eight series need but little comment. In the first the gauge 

reading for p = 0 was 1.00cra ; in the second, third, fourth, fifth it was 

 2.00CU1 ; in the sixth, 3.50cm ; in the eighth, 1.70cm. Inasmuch as 

the relation between p and v is nearly linear, the gauge reading for 

p = 0 is of secondary importance. Owing to accidents the fiducial reading was lost at the end of the sixth and eighth series.

42. Comparing the first eight series with the remaining seven, it is 

seen that the fiducial pressure is very much more constant in the
THE VOLUME THERMODYNAMIC3 OF LIQUIDS. [BtJLL. 96.

former than in the latter; for the reading at the initial temperature 

in the one case does not vary more than 5 or 10 atmospheres; whereas 

iu the other the variation is as large as 100 atmospheres. The cause 

of this discrepancy is a strain permanently imparted to the gauge at 

the end of the eighth series, where it was necessary to work the machine 

with great violence and much above the pressure given., to counteract 

an accidental leak. Hence in constructing Ap for these series (9 to 

15) I deduct the fiducial pressure preceding and following any pair of 

high temperature data from the first and last of these data respectively. 

In this way the viscous error of the gauge is eliminated. Of the two 

values of Ap thus obtained at each temperature, the latter is the more 

nearly correct, since it has been coordinated with the fiducial pressure 

immediately following it. As the work proceeds, that is, in the thirteenth, fourteenth, and fifteenth series, the fiducial pressure is again 

more nearly constant, showing a gradual increase of the viscosity of 

the gauge.

43. In the ninth and tenth series, p = 0 is at .70cm ; in the eleventh, 

at .30C1D ; in the thirteenth, fourteenth, and fifteenth, at .50 cm. The 

last three series (13-15) were obtained with the same tube, and the 

work, done continuously, was throughout very satisfactory. Moreover 

the change of fiducial pressure still marked in series thirteen becomes 

of less prominence in the last two. series. These therefore were selected for the digest below.

44. Method of purifying. The ether employed was thoroughly dried 

with sodium, and then distilled in a small flask at a temperature only 

slightly above the boiling point. All parts of the condenser tube and 

flask were fused together, and rubber connections were scrupulously 

avoided. The distillation was frequently repeated, and the ether then 

at once used for filling the constant volume tube. I can not guarantee, 

however, that the ether after being introduced in the tube was quite 

free from water; for during the necessary manipulations some absorption of water out of the air was unavoidable.

45. Observations for ether. The data for ether are as follows:

TABLE 12. Isometrics of ether. Observations. -

N' d.

0

I.

4-115 

4-132

7-191 

7-209

II.

13-315 

13-176

6-946 

6-890 

3-849 

3-8-J9

t.

°0.

22-2 22-3

22-3 22-3

23-1 23-7

24-8 

25-0 

25-0 25-0

ne .

Cm.

 192 200

 200 200

 270 321

 418 

 438 

 438 438

Nv.

Cm. 54

4-16-(i7 

+16-86

+27-20 

4-27-29 

- -50

 23

+45-89 

+46-12 10

+28-01 

+28-00 

+ 17-59 

+17-61 69

0.

°0. 

15-1

67-5 

67-6 15-5

99-5 

99'6 15-5

15-4

157-9 

158-8

c 99-2 

98-8 

67-2 

67-3 15'0

PAtm. 

40

512 

517

800 

803 

41

48

1,312 

1,318

52

822 

822 

537 

537 

36

* 

°C.

4-307 

4-332

7-391 

7-409

13-385 

13-497

7-364 

7-328 

4-287 

4-287

Ap.

Atm. 

0

474 

479

702 

765 

0

0

1, 272 

1,278 

0

778 

778 

493 

 493 

0

A0.

 0

52-2 

52-3 0

84-0 

84-1 0

 0

142-4 

143-3 o

83-9 

83'5 

51-9 52-0

 o
BARUS.] ISOMETEICS OF ETHER. 

12. Isometrics of ether. Observations Continued.

43

N' e .

III.

7-.132 

7-100

IV.

15-337 

15-390

V.

16-403 

10-405 

16-536

7-297 

7-282

VI.

7-294 

7-294

VII.

7-083 

7-068 

4-1165 

4-074

VI11.

7-144 

7-118

20-050 

20-044

IX.

3-803 

3-926 

6-890 

6-911

N>9.

X.

7-303 

7-309

XL

4-206 

4-177 

7-191 

7-180

XII.

4-133 

4-136 

7-071 

7-080

12-961 

13-077

15-722 

15-725

XIII.

4-033 

4-033 

6-896 

6-896

12-834 

12-822

ID-540 

19-540

t.

22-9 23-0

23-8 23-8

20-8 

20-9 21-1

21-3 21-3

20-7 20-7

22-5 

22-6 

22-6 22-6

22-2 

22-4 

22-8 22-9

23-9 

23-9 

24-2 24-3

t.

21-0 21-2

22-6 

22-2 

22-2 22-2

22-4 

22-5 

22-7 22-8

' 23-i 

23-2

23-3 23-4

23-2 

23-3 

23-5 23-6

24-2 24-2

24-8 24-9

ne .

+ 254 262

 

 333 333

 068 

. -076 095

 112 112

 059 059

 218 

 226 

 226 226

 192 

 209 

 243 

 251

 342 

 342 

 367 375

V

 087 104

 175 

 192 

 192 192

 209 

 219 

 224 243

 270 279

 287 296

 279 

 287 

 306 313

 367 307

 418 426

ff,

7-386 

7-362

15-670 

15-723

16-471 

16-541 

16-631

7-409 

7-394

7-353 

. 7-353

7-301 

7-294 

4-291 

4-300

7-336 

7-327 

20-293 

20-295

4-235 

4-268 

7-257 

7-286

NB7-390 

7-413

4-381 

4-369 

7-383 

7-372

4-342 

4-355 

7-295 

7-323

13-231 

13-356

16-009 

16-021

4-312 

4-320 

7-202 

7-209

13-201 

13-189

19-958 

19-966

6.

15-9

99-5 

99-0 15-9

16-2

178-7 

179-2 16-2

15-9

185-7 

186-4 

187-3 15-8

99-8 

99-5 15-9

16-0

98-2 98-2

16-0

97-7 

97-5 

67-1 

67-4 16-2

16-4

98-1 

98-0 

219-5 

219-6

16-5

66-9 

67-0 

97:4 

97-5 16-7

e.

.16-6

99-5 

99-8 16-5

16-6

68-0 

68-0 

99-2 

99-0 16-6

16-6

67-9 

68-0 

98-5 

98-8 16-6

156-3 

157-6 10-7

182-0 

182-0 16-7

17-6

67-5 

67-6 

97-5 

97-5 17-7

156'2 

156-0 17-8

216-5 

216-6 17-9

NP1.55

28-95 

29-03 1-20

1-18

53-56 

53-65 90

' -40

53-51 

53-38 

53-06 04

27-97 

27-97 

 -08

 00

28-59 

28-62

1-20

26-88 

27-01 

16-81 

16-87 

 -97

+ -98

29-51 

29-55 

65-31 

65-20

+ 4-94

23-51 

23-73 

34-91 

35-01

*f

1-18

28-33 

28-41 1-48

1-60

18-91 

18-96 

29-14 

29-20 2-28

2-82

20-10 

20-15 

30-19 

30-34 3-58

50-61 

50-64 6-59

56-74 

56-71 6-87

1-61

17-88 

17-88 

27-59 

27-61 2-05

45-52 

45-52 2-78

62-60 

62-59 3-81

P44

793

795 

33

32

1,467 

1,470 

25

44

1,521 

1,517 

1,509 

54

821 

821 

53

96

879

880

63

832 

835 

556 

558 

69

73

854 

856 

1,836 

1,833

154

663 

669 

976 

978 

J194

A0.

0

83-0 

83-3 

0

51-4 

51-4 

82-6 

82-4 

0

0

51-3 

51-4 

81-9 

82-2 

0

139-7 

140-9 

0

165-3 

165-3 

0

0

49-9 

50-0 

79-8 

79-8 

0

138-5 

138-2

- o

198-7 

198-7 

0

A0.

 0

83-6 

83-1 0

162-5 

163-0 o

 0

1C9-8 

170-5 

171-4 0

83-9 

83-6 

.0

 0

82-2 82-2

 0

81-6 

81.4 

51-0 

51-3 0

 0

81-7 

81-6 

203-01 

203-2

 0

50-3 

50-4 

80-8 

80-9 

 -0

P32

770 

778 

40

44

518 

520 

798 

800 

62

7<7

551 

552 

827 

831 

98

1387 

1388 

180

1555 

1554 

189

489 

490 

756 

757 

56

1247 

1247

1715 

1715 

104

Ap.

0

755 

757 

0

1,439 

1,442 

0

0

1,472 

1,408 

1,160 

0

767 

768 

0

0

783 

784

767 

770 

491 

493 

0

0

781 

783 

1,763 

1,760

0

509 

515 

822 

824

AJJ.

0

740 

742 

0

465 

467 

' 745 

747 

0

0

463 

464 

739 

743

1289 

1208

1370 

1369 

0

0

439 

440 

706 

707 

0

1191 

1171

1639 

1611 

0
44 THE VOLUME THERMODYNAMICS OF LIQUIDS. 

TABLE 12. Isometrics of ether. Observations Continued.

[BULL. 96.

*v

XIV.

7-147 

7-132

20-080 

20-071

4-i44 

4-147

13-177 

13-194

XV.

20-371 

20-353

7-312 

7-265

4-397 

4-415

13-306 

13-330

t.

21-2 21-3

21-7 21-8

22-2 22-3

22-3 22-3

20-0 20-0

20-8 20-8

21-0 21-0

21-2 21-3

ne.

 104 112

 146 155

 192 200

 200 200

0 

0

 068 068

 087 087

 104 112

Ne .

7-251 

7-244

20-226 

20-226

4-336 

4-347

13-377 

13-394

20*371 

20-353

7-380 

7-333

4-484 

4-502

13-410 

13-442

0.

17-8

98-2 

98-0 18-0

218-8 

218-8 18-1

67-8 

68-0 

U81)

157-8 

157-9 17-9

17-4

220-2 

220-0 17-4

99-1 

98-8 17-4

69-1 

69-4 17-4

158-0 

158-3 17-4

**'

o.on

29-79 

29-86 4-29

64-30 

64-30

fMQ

21-14 

21-14 

(5-20)

49-04 

49-06

C.'JQ

4-18

64-17 

64-16

/1*9Q

30-83 

30-84 4'45

21-37 

21-35 4-43

48-93 

48-98 4-86

P104

816 

819 

118

1761 

1761 

142

579 

579 

(142)

1344 

1344 

148

114

1758 

1758 

116

845 

845

586 

585

191

1341 

1342 

133

A 9.

0

80-4 

80-0 

0

200-8 

200-7 

0

49-7 

49-9 

0

139-7 

140-0 

0

202-8 

202-6 

0

81-7 

81-4 

0

51-7 

52-0 

0

140-6 

140-9 

0

&p.

0

712 

701 

0

1643 

1619 

0

437 

437 

0

1202 

1196 

0

0

1644 

1642 

0

729 

723 

0

464 

464 

0

1220 

1209 

0

46: Observations for alcohol. Table 13 contains data for alcohol corresponding to those already given for ether. The two series, obtained 

with the same tube on successive days, are satisfactory throughout. 

The arrangement of data has been already explained.

The alcohol used was kindly furnished me by Dr. Stokes. I redistilledit over lime in small quantities immediately before filling the 

constant volume tube. Nevertheless some absorption of moisture from 

the air during the manipulations was not avoidable.

TABLE 13. Isometrics of alcohol. Observations.

N>e.

4-485 

4-491

7-285 

7-282

13-427 

13-424

7-377 

7-356

13-547 

13-541

4-100 

4-090

7-100 

7-077

t.

20-3 20-3

20-7 20-8

21-0 21-0

19-9 20-0

20-4 20-5

22-2 22-2

22-4 22-4

V

 025 025

 059 068

 087 087

- 008 

± 000

 034 042

 192 192

 209 209

Ne .

4-510 

4-516

7-344 

7-350

13-514 

13-511

7-370 

7-356

13-581 

13-583

4-292

4-282

7-:ns

7-286

0.

17-2

69-5 

69-7 17-2

98-9 

99-0 17-2

159-0 

159-0 17-2

17-0

99-2 

99-1 16-8

159-7 

159-7 16-9

16-9

67-4 

67-0 17-0

98-9 

98-5 17-0

»p4-92

25-46 

25-46 5-14

37-67 

37-68 5-27

63-04 

63-04 5-53

A'Q9

37-72 

37-70 5-12

63-20 

63-15 5-39

5-39

25-14 

25-16 5-69

38-36 

38-36 6-11

P135

697 

697

1032 

1032 

144

1727 

1727 

152

135

1034 

1033 

140

1732 

1730 

148

148

689 

689 

156

1051 

1051 

167

A0.

0

52-3 52-5

81-7 

81-8 

0

141-8 

141-8 

0

0

82-2 

82-3 

0

142-9 

142-8

0

50-5 

50-0 

0

81-9 81-5

A#.

502 

550 

0

891

888 

0

1583 

1575

0

899 

893 

0

1592 

1582 

0

541 

533 

0

895 

884 

0
BABUS.] THYMOL, TOLUIDINE, DIPHENYLAMINE. 45

47. Observations for thymol, para-toluidine, and diphenylamine. 

Tables 14,15,16 contain results for thymol, para-toluidine, and diphenylamine, arranged on the same plan as Tables 12 and 13. Thymol is 

particularly convenient since, after firing, it admits of undercooling 

much below its melting point. Observations can thus be made even 

at 17°. In case of the other two substances this is possible to a less 

extent, and it is necessary to insert the constant volume tube into a 

hot piezometer. A large bath of heated water must be at hand to 

prevent freezing during the manipulations. (§ 32.)

TABLE 14. Isometrics of thymol. Observations.

N<9 .

4-227 

4-253 

7-25!) 

7-235 

4-282 

4-324

7-230 

7-221

9-652 

9-610

4-306 

4-300

7-288 

7-315

9-875 

9-958

t.

» 

20-7 

20-8 

20.8 

20-9 

21-0 21-0

21-1 21-2

21-7 21-7

20-5 20-4

20-4 20-4

20-4 20-3

ne .

 059 

 068 

 068 

 076

 087 087

 095 104

 146 140

 042 034

 034 034

 034 025

Ne4-286 

4-321 

7-327 

7-311 

4-369 

4-411

7-325 

7-325

9-798 9-792'

4-348 

4-334

7-322 

7-349

9-909 

9-983

e.

67-1 

67-5 

98-8 

98-6 

68-1 

68-5 17-2

98-9 

98-9 17-2

123-5 

123-4 17-2

17-0

68-0 

67-8 16-9

98-9 

99-0 16-8

124-5 

125-3 16-8

NP32-65 

32-69 

49-11 

49-16 

33-02 

33-07 6-97

49-62 

49-69 7-35

62-40 

62-35 7-77

7-78

34.08 

34-11 7-51

50-07 

50-06 7-34

62-49 

62-58 7-C3

P895 

896 

1346 

1347 

905 

900 

191

1360 

1361 

201

1709 

1708 

213

213

934 

935 

206

1372 

1372 

201

1713 

1715 

209

A9.

49-9 

50-3 

81-6 

81-4 

50-9 

51-3 

0

81-7 

81-7 

0

106-3 

106-2 

0

0

51-0 

50-9 

0

82-0 

82-2 

0

107-7 

108-5 

0

&p.

704 

705 

1155 

11SG 

714 

715 

0

1169 

1160 

0

1508 

1495 

0

05

721 

729 

0

1166 

1171 

0

1512 

1506 

0

TABUS 15. Isometrics of para-toluidlne. Observations.

N'g .

4-206

4-182

7-147

7-132

4-162

4-153

9-578

9-572

4-071

4-100

13-000

13-006

4-035

4-027

t.

21-5

21-6

21-8

21-8

22-3

22-3

22-5

22-6

22-8

22' 8

23-1

23-2

23-5

23-6

V

 131

 138

 155

 158

 200

 200

 218

 226

 245

 245

 270

 279

 306

 313

Nv

4-337

4-320

7-302

7-290

4-382

4-353

9-796

9-798

4-316

4-345

13-270

13-285

4-341

4-340

e.

67-8

67-5

98-5

98-4

68-0

67-9

123-5

123-5 67-5

67-9

156-7

157-0 67-9

67-9

NP15-34

15-32

31-84

31-79

1569

15-66

45-20

45-24

16-06

16-04

57-51

57-50

16-45

16-46

P420

420

872

871

430

429

1238

1239

440

439

1576

1575

451

451

A0.

0

0

31-0

30-4

0

0

55-6

56-0

0

0

88-8

89-1

0

0

bp.

0

0

452

441

0

0

809

 799

0

0

1137

1124

0

0
THE VOLUME THERMODYNAMICS OF LIQUIDS. 

TAT.LF, 16. Isometrics of diphcnylamine. Observations.

[BULL. 9U,

N'e .

4-035

4.027

6-975

6-969

4-051

4-059

9-525

9-587

3-975

3-081

t.

23-1

23-1

23-4

23-4

23-8

23-8

24-0

24-0

24-2

24-2

V

 270

 270

 298

 298

 330

 330

 350

 350

 367

 367

Ne .

4-305

4-297

7-273

7-267

4-381

4-389

9-875

9-937

4-342

4.348

B.

67-5

67-5

98-2

98-2

68-1

68-3

124-1

124-9 07-8

68-0

V

18-01

18-02

36-26

36-30

18-53

]8-54

51-95

52-29 in-46

19-36

P493

494

993

995

508

508

1423

1433

533

530

A0.

0

0

30-7

30-1

0

0

55-8

57-1

0

0

AjB.

0

0

499

487

0

0

915

900

0

0

Another zero.

13-200

13-171

3-949

3-955

6-802

0-834

3-985

 4-012

9-470

.9-534

4-035

4-021

24-2

24-3

24-4

34-4

24-4

24-4

24-4

21-4

24-4

24-4

24-4

24-3

 367

 375

 384

 384

 384

 384

 384

 384

 384

 381: 384

 375

13-567

13-546

4-333

4-339

7-186

7-218

4-369

4-396

9-85 1

9-9L8

4-419

4-390

159-6

159-5

67-6

67-8

97-3

97-8

68-1

68-4

124-0

124-8 68-5

68 -5

65-15

65-12

16-02

15-93

33-49

' 33-48

15-98

15-98

49-34

49-39

16.39

16.41

1785

1784

439

437

918

917

438

438

1352

1353

449

450

0

92-0

91.9

0

0

29-5

29-7

0

0

55-6

50-2

0

0

1340

1345

0

0

481

479

0

0

914

904

0

0

TEMPERATURES CORRECTED.

48. Behavior of the torsion galvanometer. An inspection of the tables 

shows the temperatures to need correction, for the boiling points (water, 

for instance) are usually low. The cause of this discrepancy is to be 

sought in the temperature coefficient and perhaps also in the time coefficient of the magnets of the torsion galvanometer. This error is 

easily allowed for as follows: It is clear that the magnetic change 

which obtains affects all deflections (deflections for all temperatures) 

uniformly. Consequently if N'e be the twist corresponding to 100° on 

any day of observation, and if N6 be the corresponding twist on the day 

of calibration, both observed at the same torsion galvanometer, then 

N'e/'N'e is the factor for the reduction of all temperature observations 

for the former day to the scale of the calibration day.

To test this inference I made two independent calibrations of the 

same couple about a month apart. The constants a and 6 given in 

Table 17, where N~e= a (T t) + b (Tz t2 ), show considerable variation during this interval. 1 Computing the twists N~e and 2f'e for different temperatures T, when t= 20°, it is found that No/'N' 9 is constant within less than 3 per cent for the whole interval 50° to 400°. 

Clearly this is an error of observation, since the constants a and 6 never 

quite faithfully reproduce the calibration interval. Slight reciprocal 

changes of a and Z>, for instance, would wipe out the discrepancy 

I N'e), without appreciably slighting the observations.

> t are the temperatures at the junctions of the platiuum platinum-iridium thermo-couple.
BARUS.] AIR THERMOMETER COMPARISON. 47

TABUS 17. Constants of the torsion galvanometer and couple. Comparisons of T, April

' 20 and May 27. '

a=-, M. v 97 C a' -.0829. b==f0000717t May 27 J 6 ,=. 000| )(!9l.

A .5i 9ft 5 a=-0844, April 20 j b==f00007

[Computed from observations at 100° and 357°.]

T.

o

50

100

150

200

250

300

350

400

*r

2-683

7-440

12-557

18-031

23-805

30-057

36-G11

43-520

*v

2-032

7-298

12-311

17-C70

23-377

29-430

35-831

42-578

Ne,N'Q .

 9810

 9809

 9804

 9800

 9790

 9792

 9787

 9784

49. Air thermometers comparison. Apparatus. There is a more serious 

question relative to the degree of truth of the interpolation equation 

Ne a (T t) + b (T2 #). This can only be decided by direct air-thermometer comparisons, such as are given in Table 18. There are three 

complete time series and two comparisons in steam.

The air-thermometer bulb used was my reentrant form, combined 

with the Jolly-Pfaundler stand, by a platinum capillary. The method 

of work is described elsewhere.1 Here I need only remark that the 

metallic fiducial mark at the bulb end of the manometer, being nothing more than the sharpened end of the platinum capillary, the criterion 

of constant volume was given by an electric contact.

To heat the bulb I made-use of a large paraffin bath, being a cylinder 

about 7 inches long and 7 inches in diameter. This was heavily jacketed 

with a thickness of about 1 inch of asbestos. At the center of theb'ath 

the bulb of the air thermometer was placed; and being of the reentrant 

form the junction of the thermocouple in its turn was at. the center of 

the bulb.

The paraffin bath, Figs. 9, and 10, needs further description. It 

consists of two half cylindrical boxes of brazed copper, d ef and g b A;, 

which fit into each other on their flat sides. These are of thin sheet 

copper, provided with hemispherical cavities H and gutters 11 adapted 

to receive the air-thermometer bulb and thermocouple. The figure 

shows the thermocouple a o /9 and the air thermometer bulb H Ht in 

place, the stem of the latter and the insulator of the former issuing in 

opposite directions. Though filled with paraffin in the present experiments, the apparatus was constructed to be used as a vapor bath at 210° 

(naphthalene) or 310° (diphenylamine). In such a case the chimneys N 

are prolonged by iron gas pipe into which the vapors distill and condense, 

falling back into the charge below (indicated by the dotted horizontal 

line). In this way thoroughly constant temperature may be obtained, 

and the apparatus is therefore available for standardizing2 a porce1 Bull. IT. S. Geol. Snrv., No. 54, 1889, pp. 168 et seq., 188 et seq. 

»Cf, Barus; Bull. U, S, Geol. Surv., No. 54,1889, pp. 22, 208 et aeq,
48 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BUIX. SO.

lain (noninglazed) air thermometer, by aid of a glass air thermometer 

bulb of known constants, through the intervention of (or consecutive 

comparison with) the same platinum-iridiuua thermocouple.

In all cases the bath is to be heavily jacketed with asbestos, to a thickness of say 1 inch. T-wo burners are then sufficient.

CL:

FIG. 9. Sectional vapor Lath, for coinpariug air thermometer and thermocouple.

50. Observations. Observations were made during the period of cooling, after heating the bath to 300°; cooling must, therefore, take place 

so slowly that the temperature of the air thermometer bulb and of the 

thermocouple may be regarded as identical. Whether this is the case 

can be decided only by trial. Therefore, in making the following comparisons, the first and third series were observed during ordinary cooling 5 in the fifth series, however, a flat evaporating burner was placed 

under the paraffin bath to insure slower cooling. The liquid was stirred 

and paraffin gradually added to compensate fqr the contraction in cool-
BAETJS.] SECTIONAL VAPOR BATH. 49

ing. In the table Fis the volume of the air-thermometer bulb, v' that 

of the hot part of the stem, v" that of the cold stem and of the capillary 

connections and dead spaces; finally h0 is the observed pressure for the 

bulb in melting ice. It is advisable to work with slightly rarefied air, 

to avoid pressure on the bulb at the high temperatures.

N'20 is the twist observed at the torsion galvanometer at the time 

given, and when the temperature measured by the air thermometer was 

Ta, t. .From this I computed JST20, the twist which would have been oba, a,

Fio. 10. Longitudinal elevation of one of the halves of vapor bath, showing the thermometers in place.

served on the day of calibration (May 27), by the method shown in § 4S. 

Hence I made use of the series n and v (comparisons in steam) and of 

the low temperature comparisons between thermocouple and air thermometer, for here the cooling is so slow that no time lag need be apprehended.

From both N'e and Ne, the thermoelectric temperature equivalents. 

Ttc and Tl>e were then computed, by aid of the data of Table 17.. 

Bull 96 4
50 THE VOLUME THERMODYNAMICS OF LIQUIDS.

TABLE 18. Comparison of thermocouple and air thermometer. 

F=239'93CC ; -u'^-OaO ; t>"=.694« ; 7io=48-28cra .

[BULL. 96.

Time.

I. 21

36

44

52

61

7

18

34

45

58

17

34

50

12

35

9

40

58

19

39

II. ( 0

120

III. 34

45

 56

7

17

26

38

50

6

21

44

rv.rss

J 5

16

[25

(33

J42

]55

[9

f 3

Il3

I 24

[36

18

129

138

(52

<29

<39

V. (16

t{28

 <37

N'M.

28-464

25-531

24-001

22-648

20-456

19-438

18-052

16-060

14-893

13-571

12-155

10-840

9-912

8-639

7-598

6-359

5-448

4-975

4-479

4-075

7-245

7-264

28-174

26-136

24-400

22-050

20-731

19-338

18-036

16-799

15-184

13-899

12-237

1 29-702

29-223

28-744

28-410

22-025

21-492

20-866

20-293

14-334

13-590

12-720

11-897

9-487

8-943

8-567

7-9C6

6-618

6-335

7-205

7-221

7-199

Tat.

292-1

263-5

251-4

239-4

222.1

213-3

201-3

183-2

171-2

160-6

146-9

134-9

125-5

114-0

103-8

' 90-4 80-9

76-4

70-9

66-7

100-22

100-28

286.3

270-0

255-0

235-3

224-3

214-5

200-4

189-2

176-2

164-2

148-9

299-6

295-3

292-0

289-1

236-3

232-2

226-9

222-0

167-7

160-9

153-4

145-4

122-5

117-2

113-1

107-1 94-0

90-9

100-03

100-09

100-09

tf«-

28-749

25-786

24-241

22-874

20-660

19-632

18-233

16-227

15-042

13-707

12-277

10-948

10-011

8-725

7-674

6-423

5-502

5-025

4-524

4-116

7-317

7-337

28-456

26-397

24-644

22-270

20-938

19-531

18-2] 6

16-967

15-336

14-038

12359

30-147

29-661

29-175

28-836

22-355

21-814

21-179

20-597

14-549

13-794

12-911

12-076

9-629

9-077

8-696

8-086

6-717

6-430

7-313

7-329

7-307

Ttc.

291-6

267-8

255-1

243-6

224-6

215-5

203-1

185-2

174-2

161-8

148-5

135-4

126-4

113-6

103-1 90-3

80-5

75-4

70-0

65-7

99-4'

99-6

289-4

272-8

258-5

238-5

227-0

214.6

203.0

192-0

177-0

165-0

149-3

301-6

297-9

294-0

291-4

238-3

233-6

228-3

223-2

169-0

162-0

154-0

145-9

122-0

116-7

113-0

106-7 93-0

90-0

99-0

99-1

99-0

Diff.

+ '5

-4-3

-3-7

-4-2

-2-5

-2-2

-1-8

-2-0

-3-0

 1-2

-1-6

- -5

 -9

+ -4

+ -7

+ "I

+ -4

+1-0

+ '9

+1-0

+ '8

+ -7

-3-1

-2-8

 3-5

 3-2

-2-7

- .1

-2-6

-2-8

- -8

- -8

- -4

-2-0

 2-6

 2-0

 2-3

 2-0

 1-4

 1-4

-1-2

-1-3

-1-1

- -6

- -5

+ "5

' + -5

+ 'I

+ "4

+1-0

+ '9

+1-0

+ 1-0

+ 1-1

2V,.

294-0

270-0

257-3

245-6

226-5

217.4

204-7

186.5

175-6

163-2 149-7'

136-7

127-4

114-5

103-8 91-0

81-1

76-0

70'5

66-1

100-2

100-4

291-6

275-0

260-5

240-5

229-0

216-6

204-8

193-6

178-5

166-4

150-4

305-0

301-2

297-3

294-8

241-2

236-5

231-0

225-8

171-2

164-1

155-6

147-7

123-4

118-0

114-3

108-0 94-0

91-0

100-1

100-3

100-1

Diff.

=1-9

-6-5

-5-9

-6-2

-4-4

-4-1

-3-4

-3-3

-4-4

-2-6

-2-8

 1-8

-1-9

 '5

± -o

 -6

- -3

+ '4

+ "4

+ '6

± -o

 -1

-5-3

-5-0

-5-5

-0-2

-4-7

-2-1

-4-4

-4-4

-2-3

-2-2

-1-5

 5-4

 5-!)

-5-3

 5-7

 4-9

 4-3

 4-1

-3-8

-3-5

 3-2

-2-2

 2-3

-- -9

 -8

 1-2

 -9

± -o

+ -1

 -1

- -2

± -o

* Steam, temperature 100-11° 

t Steam temperature 99-93°.

TABLE 19. Interpolated from the above.

Tm (air thermometer).

N»... ... ........

50°

2-63

100°

7-30

150°

12-47

200°

18-05

250°

23-90

300°

30-20
BAUUS.] ISOMETRICS OF ETHEE. 51

Tables 17 and 18, or a graphic representation, show at once that 

throughout every stage of cooling, temperature as registered by the 

thermocouple is always higher than the corresponding temperature of 

the air thermometer. Inasmuch as the system cools from the outside 

of the air thermometer bulb, this is precisely what must occur in case 

of too rapid cooling. It is well, however, to note that in Table 18, 

series iv, notwithstanding much retarded cooling, the discrepancy between air thermometer and thermocouple retains its original magnitude. 

Without passing judgment, therefore, I have deduced Ta't and JV20 from 

all the observations, for use below. See Table 19.

51. Isometrics corrected as to temperature. Applying the- corrected 

temperatures investigated in the foregoing paragraph, I obtained the 

following data for the isometrics. Ne is the corrected twist and #a'< and 

9tc its thermal equivalent, as expressed by the air thermometer or the 

thermocouple (boiling points, H20 and Hg), respectively. The two data 

given under A 0 are to be similarly interpreted. Ap is the value already 

met in tables 12 to 16.

It follows from the slight irregularities still observable in the boiling 

points, that in order to use the torsion galvanometer satisfactorily, check 

measurements of the boiling point of water must be made before and 

after any series of temperature observations.

TABLE 20. Isometrics of ether.

N0 .

4-249

4-273

7-291 

7-309

13-301 

13-412

7-282 

4'2GO 

4-200

7-312 

7-288

15-513

6t,c.

15-1

67-5

fi7-Q

15-5

99-9

100-1 

15-5

15-4

159-4

100-5 

15-5

100-2

67-7 

67-7

T»'A

15-9

100-1 

99'9

16-2

180-1

6a,c.

15-1

68-2

08-4

15-5

99-9

100-1 

15-5

15-4

158-1

159-2 

15-5

100-2

99-8 

68-4 

68-5

1 f\'(\

15-9

100-1 

99-9

16-2

178-0

A9.

0

C 52-4 

I 53-1

f 52-3

I 52-9 

0

C 84-4 

i 84-4 

C 84-6 

I 84-6 

0

0

C 144-0 

\ 142-7 

< 145-0 

I 143-7

C 84-7

I 84-7 

C 84-5

\ 84-5 

C 52-4 

I 53-1 

f 52-7 

I 53-5 

0

0

C 84-2 

\ 84-2 

C 84-0 

\ 84-0

0

C 103-9

i 101-8

AJJ.

0

I 474

j 479

0

I 762

| 765 

0

0

| 1272

| 1278 

0

| 778

493

493 

0

0

^ 755 

I 757

0

I 1439

Ne .

15-506

10-245 

16-315

10-405

7-308 

7-293

7-300 

7-300

7-294 

7-287 

4-287

4-290

flf.c.

180-6

1 n.o

15'9

180:9 

187-5

188-4

15-8

100-1

99-9 

15-9

16-0

100-0 

100-0

16- 0

99-9 

100-0 

68-1

08-2

1fi-9

6a, t178-6 

16-2

15-9

184-5 

185-4

18(T-2

15-8

100-1 

99-9

10-0

100-0 

100-0

16- 0

99-9 

100-0 

68-5

68-0

if;. o

eA0.

( KU-il

1 1G2-4 

0

0

C 171-0 

) 108-6 

C 171-6 

> J09-5 C 172- C

0

C 84-3 

\ 84-3 

C 84-0 

> 84-0 

0

0

C 84-0 

5 84-0 

< 84-0 

I 84-0

0

I 83-9 

C 84-0 

I 84-0 

C 52-0 

\ 52-4

C 52-0 

I 52-4

&2>-

I 1442

0

} 1472 

| 1408

| MOO

0

| 707 

| 708

0

] 783

1 781

0

| 707 

} 770 

} 49]

| 493

0
52 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL; 96. 

TABLE 20. Isometrics of ether Continued.

*r

7-294 

7-285 

20-177 

20-179

4-251

4-284 

7-284 

7-313

7-308 

7-331

4-340

4-334 

7-325

7-314

4-342

4-355 

7-295

13-230

16-009 

16-021

9t,e.

16-4

99-9 

100-0 

222-0 

222-1

16-5

67-5

67-9 

99-8 

100-1

100-1 

100-3

16-6

68-6

68-5 

100-2

100-1 

16-6

16-6

68-5

68-7 

99-9 

100-2

16-6

158-8 

160-0

16-7

184-9 

185-0

16-7

17-6

6a,t.

16-4

99-9 

99-9 

219-0 

219-0

16-5

68-2

68-5 

99-8 

100-1

16-7

100-1 

100-3

16-6

69-1 

100-2

300-1 

16-6

16-6

69-2

69-4 

99-9

100-2 

16-6'

157-4

16-7

182-7

16-7

.17-0

A0.

0

C 83-5 

I 83-5 

C 83-6 

I 83-5 

< 205-6 

I 202-6 

C 205-7

< 909.fi

0

C 51-0

I 01 i C 51-4 

I 52-0 

5 83-1 

) 83-1 

C 83-4 

\ 83-4

0

0 

C 83-5 

\ 83-5 

( 83-8 

I 83-8

0

0

C 52-0

) 52-6 

C 51-9 

\ 52-5 

C 83-6 

) 83-6

C 83-5 

) 83-5 

0

0

C 51-9 

\ 52-6

C 52-1 

I 52-8 

C 83-3 

) 83-3 

C 83-6

I 83-6 

0

C 142-2 

I 140-8 

C 143-3

I 142-0 

0

C 168-2 

\ 166.0 

C 168-3

) 166-1 

0

0

Ap.

0

| 781 

j 783 

| 1763 

1 1760

0

I 509

J

1 515 

| 822

£ 824 

0

0 

| 740

| 742 

0

0

| 465 

j 467 

| 745

| 747 

0

0

| 463

\ 464 

| 739

| 743 

0

j 1289

0

* 1370 

| 1369

0

0

JT,

4'351 

4-359 

7-207 

7-272

13-320

20-138 

20-146

7-274 

7-267

20-290

20-291

4-350 

4-361

13-420

13-437

20-216 

20-198

7-324

7-277

4-450

4-468

13-308

6t,c.

68-6 

68-6 

99.7

99-7 

17-7

159-6

17'S

221-8

222<0 

17-9

17-8

99-7

99-7 

18-0

223-1

223-1

18-1

68-6

68-6 

(18-1)

160-4

160-5

17-9

17-4

222-4

222-3 

17.4

100-2

99-8 

17-4

69-8

69-9 

17-4

159-5

159-7

17-4

ea, t .

69'4 

69-5 

99-7

99-7 

17-7

158-2

17-8

218-5

218-7 

17-9

17-9

99.7

99-7 

18-0

219.9

219-9

18-1

69-2

69-5 

(18-1)

159-2

159.4

17-9

17-4

219-2

219-0 

17-4

100-2

99-8 

17-4

70-2

70-4 

17-4

158-1

17-4

A0.

f 51-0

I 51-8 

C 51-0 

I 51-9 

C 82-0 

I 82-0 

C 82-0 

I 82-0

C 141-9

I 140-5 

C 141-8

I 140-3 

0

C 204-0 

\ 200-7 

( 204-1 

I 200-8 

0

0

C 81.9 

I 81-9 

f 81-7 

I 81-7 

0

C 205-1

C 205-0

0

f 50-5 

I 51-1 

C 50'5 

i 51-4

C 142-3 

) 141-1 

C 142-7

I 141-5

0

0

5 205-0 

I 201-8 

C 204 '9 

I 201-6

C 82-8 

i so-a

5 82-4 

J 82-4 

0

C 52-4

S f%0«Q

C 52-5 

^ 53-0 

0

C 142-1

i 140-7 

( 142-1

) 141-0 

0

Ap.

| 439 

| 440 

| 706

| 707 

0

| 1191

| 1171 

0

| 1639

| 1611 

0

0

| 712

^ 701 

0

| 1643

| 1019

0

| 437

| 437 

0

| 1202

| 1196

0

0

^ 1644

| 1642 

0

| 729

| 723 

0

| 464

| 464 

0

| 1220

0
ISOMETRICS OF ALCOHOL AND THYMOL. 

TABLE 21. Isometrics of alcohol.

53

y&

4' 493

4-499

7-317

7-323

13-464

13-461

6t,c

17.O

70-1

70-2 

17-2

100-2

100-2

17-9

160-8

160-8 

17-2

17-0

100-4

Oa,t

17-2

70-6

70-9 

17-2

100-2

100-2 

17-2

159-0

159-6 

17-2

17-0

100-4

Ad

0

< 52-9 

I 53-4

( 53-0 

\ 53-7 

0

C 83-0 

I 83-0

f 83-0

I 83-0 

0

C 143-6 

I 142-4 

C 143-6

\ 142-4 

0

0

C 83-4

I 83-4

&p

0

| 562

1 556 

0

| 891

1 888

0

I 1583

] 1575 

0

0

| 899

Xe

7-323

13-520

13-522

4-310

4-300

7-345

7-316

6t,c

100-2 

16-8

161-4

161-4 

16-9

16"9

68-2

68-1 

17-0

100-4

100-2

17-0

0a,t

100-2

1«.Q

160-0

160-0 

16-9

i fi.n

68-9

68-8 

17-0

100-4

100-2

17-0

Ad

f 83-4

\ 83-4 

0

C 144-6 

I 143-2 

C 144-5

\ 143-1

0

C 51-3 

I 52-0

C 51-1 

) 51-8 

0

C 83-4 

I 83-4

C 83-2 

5 83-2

0

&p

j 8X( 

0

| 1592

| 1582 

0

0

| 541

I 533 

0

| 895

| 884

0

TABLE 22. Isometrics of thymol.

N9

4-273

4-308

7-305 

7-289 

4-356

4-398

7-303

7-303

9-769

6t,c

67-7

68-2

100-0 

99-9 

68-8

69-2 

17-2

100-0

100-0 

17-2

124-9

Oat

68-5

100-1 

99-9 

69-2

69-8 

17-2

100-0

100-0 

17-2

124-6

Ad

C 50-5 

) 51-3 

C 51-0

) 51-7 

C 82-8

I 82-9 

< 82-7 

I 82-7 

( 51-6 

I " 52-0

C 52-0 

I 52-6 

0

C 82-8 

} 82-8

f 82-8 

I 82-8 

0

C 107-7 

> 107-4

Ap

| 704

| 705

| 1155 

j 1156 

| 714

| 715 

0

| 1169

1 1160 

0

| 1508

NO

9-763

4-339 

4-325

7-307

7-334

9-889

9-963

6t,c

124-8 

17-2

17-0

68-5

68-4 

16-9

100-1

100-3 

16-8

126-1

126-9 

16-8

««,«

124-5 

17-2

17-0

69-1

69-0 

16-9

100-1

100-3 

16-8

J25-8

126-5 

16-8

Ad

C 107-6 

I 107-3 

0

0

C 51-5 

I 52-1 

C 51-5 

I 52-1 

0

< 83-2 

I 83-2 

C 83-5

i 83-5 

0

f 109-3 

I 109-0 

f 110-1

i 109-7

Ap

| 1495 

0

0

| 721

| 729 

0

| 1166

| 1171

| 1512

| 1506

About a month later, and after the gauge and appurtenances had been 

much used during intervening experiments, I repeated the work for 

thymol again, using the same tube as in Table 22. The results are 

given in the next table (22 supplement) and will be seen to be in excellent accord with the earlier data. This proves that there can have been 

no error in the method of measurement between times, and hence 

the exceptional behaviors noted in case of some of the following substances are actual peculiarities. The constancy of the gauge factors 

vouched for in this way is gratifying.

TABLE 22 (supplement). Isometrics of thymol. Check-work a month after the above.

N'e

6-513

8-896 

8-925

t

27-0

07.7

28-1 28-1-

nd

 665 673

 711 711

Nd

7-188

9-607 

9-636

e

25-9

100-0 

100-0 26-0

125-1 

125-5 26-0

NP

6-20

44-47 

44-50 6-60

57-25 

57-25 6-55

P

170

1218 

1219

181

1569 

1569 

179

Ad

0

74-1 74-0

0

99-1 

99-5 

0

Ap

0

10-48

1 A.OO

0

13-88 

13-90 

0
54 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 

TABLE 23. Isometrics of para-toluidine.

Nf)

4-328

4-311

7-286

7-274

4-352 

4-343

9-774

6t,c

68-4

68-2

99-9

99-7

68-6 68-5

124-8

6a,t

69-1

68-9

99-9

99-7

69-3 69-2

124-6

A0

0

C 31-7 

} 31-0

f 31-1 

i 30-4

0 

0

C 56-3 

} 55-4

Ap

0

| 452

I 441

0 

0

| 809

&B

9-776

4-307 

4-336

13-231

13-256

4-332 

4-331

C«,c

125-0

68-3 68-5

158-8

159-0

68-5 68-5

6a,t

124-8

68-9 09-2

157-4

157-8

69-0 

69.0

A0

C 56-7

I 55-9

0 

0

C 90-3 

> 88-2

< 90-5 

) 88-8

0 

0

&p

| 799

0 

0

J 1137

| 1124

0 

0

TABLE 24. Isometrics of diplienylamine.

N9

4-323

4-315

. 7-303

7-297

4-399 

4-407

9-916

9-978 

4-360

4-366

13-752

Ot,c

68-3

68-2

100-0

100.0

69.2 69-4

126-5

127-0 

68-7

68-8

163-7

Oa,t

69-0

69-0

100-0

100-0

69-8 69-9

126-0

126-6 

69-4

69-6

162-4

A0

0

C 31-8 

I 31-0

C 30-8 

I 30-2

0 

0

f 57-1

i 56-1

f 58-3 

I 57-2 

0

0

f 94-7 

I 92-8

&p

0

| 499

| 487

0 

0

| 915

I 900 

0

0

| 1346

NB

13-731

4-392 

4-398

7-284

7-316

4-428

4-455 

9-988

10-053

4-479

4-456

8t,c

163-4

69-0 69-2

99-9

100.2

(69-5) 69-5

69-7 

127-1

127-6

70-0

69*8

6a,t

162-2

69-6 69-8

99-8

100-2

(70-1) 70-1

70-5 

126-8

127-3

. 70-8

 70-6

A0

5 94-4

i 92-6

0 

0

C 30-7 

\ 30-0

C 30-7 

I 30-1

0

0 

C 57-4 

I 56-3

f 57-6 

\ 56-5

0

0

&p

| 1345

0 

0

| 481

| 479

0

0 

£ 914

| 904

0

0

CORRECTION FOR THE THERMAL AND ELASTIC VOLUME CHANGES OF THE GLASS

TUBES.

52. Thermal expansion of glass. The direct measurement of the elastic 

constants of glass throughout an interval of 300° and 2000 atmospheres 

is at present out of the question. Hence I selected liquid substances 

of large compressibility, in order that the discrepancies due to the compressibility of glass might be of smaller magnitude, and could, therefore, be at least in a measure applied by interpolation from known 

data. It is clear at the outset, moreover, that the correction in question is of smaller moment, because it is differential in character. Eise 

of temperature expands the glass tube, pressure again diminishes it. 

If the isometrics of solid glass and the'liquids were identical, the correction would be nil. Curiously enough this3 is nearly the case.

The expansion of glass throughout large intervals of temperature 

was measured by Dulong and Petit, 1 by Eecknagel,2 and by others. 

The results of the latter are the larger. For this reason I accept the 

former, seeing that in the case of compressibility of glass a datum

>Dulong and Petit: Ann. de chim. et pays. (2), VII, 1817, p. 113. 

*Kecknagel: Sitz. Ber. k. Bayr. Acad. (2), 1866, p. 327.
BARUS.] ISOMETRICS OF SOLID GLASS. 55

too sin all. must be accepted for want of data on the thermal variations. 

Dulong and Petit find that from 

0° to 100°, coefficient of expansion, /3 = 25S/10 7 

0° to 200°, coefficient of expansion, (3 =± 276/10 7 

0°"to 300°, coefficient of expansion, /? = 304/10 7. 

A chart may then be platted from which ft may be taken for any inter - 

val. It follows that the volnmes, 720 of the constant volume tube, in 

terms of the volume at 20°, will be (pressure = 1 atmosphere). 

T = 20° 5Qo looo 1500 200° 250° 300° 

720=1-00000 1-00075 1-00208 1-00350 1-00504 1-00670 1-00856 

Again, the corresponding volumes, 770 in terms of the volume at 70°, 

will be 

T = 700 1000 1500 2000 

770 = 1-00000 1-00080 1-00222 1-00376

53. Compressibility of glass. On the other hand the compressibility 

of glass, 1/fe, from corroborative results of Eegnault and Amagat', is 

1/4 x 1011 in terms of dynes and square centimeters. Bearing in mind, 

therefore, that no compensation of k in respect to temperature can be 

made, the volumes of the constant volume tube under any hydrostatic 

pressure, P will be 1 P x 106 //c, where

P = 500 1000 1500 2000 2500 3000 atmospheres, 

P/k = -00125 -00250 -00375 -00500 -00625 .00750 

Thus, when the initial temperature is 20°, the volumes will be as follows:

TABLE 25. Isometrics of solid glass, in terms of unit of volume at 20° and 1 atmosphere.

0 =

Pr^l itlT).

500 iti .

]o:'0 iti .

15' iO iti .

2000 iti .

2500 iti .

3000 atm.

20°

1-0000

 9087

 9975

 9902

 9950

-9937

 9925

50°

rooo7

 9995

.9982

 9970

 9957

 9945

 9932

100°

1-0021

1-0008

 9996

 9983

 9971

 9958

 9946

1500

1-0035

1-0022

1-0010

 9997

 9985

 9972

 9960

200°

1-0050

1-0030

1-0025

1-0013

1-OODO

 0988

 9975

250°

1-0067

1-0054

1-0042

1-0029

1-0017

1.0004

 9992

300°

1-0086

1-0073

1-0001

1.0048 i-oo:t«

1-0023 

1.0011

A similar table is easily constructed for unit of volume at 70° and 

1 atmosphere.

If these results are represented graphically, the volume changes dv, 

if the constant volume tubes can be at once obtained for each of the 

pairs of values of Ao and Ap given in tables 20 to 24. I have given a 

full list of the values, 8v} in table 27, where the arrangement adopted 

is such as to correspond to the earlier tables (12 to 16).

54. Compressibility of the above liquids. Having given these data, 

it is therefore finally necessary to find the pressure equivalent of the

1 Ainagat: C. K., CVin,1889, p. 1199; CVII, 1888, p. 018, or J.D. Everett's Tables (Macmillan, 1879, 

p. 53).
56 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96,

values dv; in other words, to find the value dp which will annul. 8v. 

To do this it is necessary to know the compressibility of each of the 

liquids under the given conditions of pressure and temperature. The 

results of my earlier papers 1 are available for this purpose, and from 

them I take the following mean values.

TABLE 26. Correction factors ( d( -y J/ dp \ being compressibilities at 0° and palm.

ETHER. A0=0 20°.

0

o 

70 

100 

160 

185 

220

10ed 

/v \ 

d(y)/dp

100 

95 

80 

70 

CO

P

600 

830 

1340 

1400 

1760

ALCOHOL. 40-0-20°.

o 

70 

100 

160

66 

63 

51

700 

1040 

1730

PARATOLUIDINE. A0 = 0 70°.

100 

136 

160

52 

50 

45

870 

1240 

1580

THYMOL. A0 = 0-20°.

e

o 

70 

100 

130

.10" v 

<£)/*

46 

44 

42

P

910 

1360 

1710

DIPHENYLAMINE. 

81 9 60°.

6

.100 

130 

160

10° X 

/ v\ 

d(v)/dp

43 

40 

38

P

960 

1390 

1780'

Knowing therefore the volume changes of the glass, and the compressibility of the inclosed liquid under the given conditions of pressure 

and temperature, the correcton dp follows by division. This is fully 

given in Table 27. Utilizing these values I constructed the final Table 

28, in which Ad and dp, such as would be observed if the glass tube 

were absolutely rigid, are inserted. This table 28 exhibits the importance of the correction dp, relative to dp. For AQ I give the thermoelectric values only, believing them to be the more nearly correct. The 

table also contains p0 and #0, which are the initial pressures and temperatures used in constructing dp and dd (cf. Tables 12 to 16). In case of 

paratoluidine and diphenylamine, p0 had to be estimated.

'Barus: Am. Journ. (3), XXXIX, 1890, p. 501.
BATUTS.] CORRECTIONS FOR ENVELOPES. 57

TAIVLE 27. Corrections (dp) for thermal and elastic volume changes of glass tulcs.

ETHEE.

Ap

475 

765

1275 

780 

495

755 

1440

1470 

7C5

785

770 

490

780 

1760

5.1.0 

820

Ad

52 

84

144 

85 

51!

84 

104

170 

84

84

84 

52

84 

204

52 

83

&v X 10°

+ 100 

-(- 300

+ 700 

+ 300 

+ 100

+ 300 

+ 900

+ .1080 

+ 280

+ 300

+ 300 

+ 100

+ 300 

+ 1400

.+ 0 

+ 100

106 x 

d (-*-)/ dp.

110 

95

80 

95 

110

95 

70

70 

95

95

95 

110

95 

60

110 

95

6p

+ 1 

3

9

3 

1

3 

13

15 

3

3

3 

1

3 

23

0 

1

&p,p

740

465 

750 

465 

740 

1250 

1370

490 

760 

1250 

1710

816 

1760 

580 

1344

1760 

850 

590 

1340

Ad

84

52 

84 

53 

84 

142 

167

52 

82 

141 

202

82 

203 

51 

142

203 

83 

53 

141

ivXlQR

+ 350

+ 200 

+ 300 

+ 150 

+ 300 

+ 600 

+ 1150

 (- 250 

+ 400 

+ 900 

+ 1800

+ 400 

+ 1750 

+ 200 

+ 800

+ 1700 

+ 350 

+ 200 

+ 800

10« X

*(r)"*

95

110 

95 

110 

95 

80 

70

100 

95 

80 

CO

95 

60 

100 

80

60 

95

100 

80

tp

+ 4

2 

3 

1 

3 

7 

16

2 

4 

11 

30

4 

30 

2 

10

+ 28 

+ 4 

+ 2

+ 10

ALCOHOL.

700

1030

1730

1030

53

83

143

83

 100

 50

 100

 100

66

63

51

63

 2

 1

 2

 2

1730

690

1050

144

52

83

- 100

 00

 50

51

COi

63

 2

 0

 1

PAKATOLUIDINE.

870 

1240

31 

56

 300 

 410

52 

50

 6

 8

1580 89 - 300 45 7

THYMOL.

900

1350

910

1360

51

83

52

83

 500

- 750

- 5°0

- 750

46

44

46

44

 11

 17

 11

 17

1710

930

1370

1715

108

52

83

110

 950

. 500

 750

 850

42

40

44

42

 23

 11

 17

 20

DIPHENYLAMINE.

1000

1430

1780

31

58

93

 450

 650

 800

43

40

38

 10

 16

 21

920

1350

30

57

 400

 700

43

40

 9

 18
58 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULI, 96. 

TABLE 28. Isometrics Digest of probable results corrected.

Substance.

Ether.. .......

a i on

00-17".......

pa = 30 atin . . .

00 17°.......

Pn = 50 atm . . .

A0

f,n-f;

gi .0

142-5

205-0

5

O.K

82-6 

142,1

205-0

"w-n

no. A

143-C

*»1-9

83'4

144-5

Ap' 

83?'

JD7

2

701

4 

1196

10 

3619

30

404

2

723 

4

 t OAf\

10

1642

28

f;=\R

 2

OQQ

 1

1575

 2

IT-1

o

QQQ

^

1582 

 2

AI>

439

7f»r

1206

1649

466

727 

1219

1670

554

857

1573

CC1

888

1580

Substance.

00 GS°. ..."...

00-17°......-

|>0 = 80 atm . . .

/) _ T70

*Di phenyla0

.. ftQO

0 63°........

Ad

31-4

Kfi.C

90-4

51-3

82-7

107-7

51-5

83-3

109-7

31-3

30-7

57-5 

94-5

Ap> 

Sp'

 6

800

 8 

1124

_7

710

11

1158

 17 

1495 

 23

729

 11 

1171

17

]5'J6

-20

487

 10

16

479

 10 

904 

 18 

1345

 21

Ap

435

"7Q9

1117

700

1141

1472

718

1154

1486

477

fi£M

469

886 

1324

*2>0 = 400 atm., approximately. 

DEDUCTIONS.

55. Curvature and slope of the isometrics. The deductions to be made 

from the above laborious investigation can be briefly stated. It conduces to clearness to express graphically both the data of T-ables 20 

to 24, as yet unconnected for the volume changes of the glass tube containing the solutions, as well as the data of Table 28, in which this correction has been provisionally added. This is done in PI. n, 1 and 2, in 

both of which Ap are fully given, as is also A6 in 1. In 2 the change 

of Ad is represented, and the points are connected by straight lines to 

bring out the contour of the curves.

It is seen at a glance that below 1,000 atmospheres the curves are so 

nearly linear that they may be accepted as such with an error no larger 

than 1° or 2° at 1,000 atmospheres. This is quite within the unavoidable errors, as may be seen from an inspection of the individual points. 

The discrepancy is somewhat.greater for toluidine1 ; here, however, the 

initial temperature is high, being 70°.

Turning first (PL n, 1) to ether, the deviation from the right line 

at 1000 is less than 1° C.; at 1500 atmospheres, the deviation is 9-5° in 

one case and 10° in the other, showing an abrupt increase of curvature. The slopes of the isometric within the first 1000 atmospheres, are

1 Owing to breakage of the tube, I did not repeat toluidine.
U. 8. GEOLOGICAL SURVEY

BULLETIN NO, 86 PL. II

0° 10°20°30°40°50° / &=17°

DIAGRAM SHOWING THE ISOMETRICS OF ETHER, ALCOHOL, THYMOL, PARATOLUIDINE AND* DIPHENYLAMINE.
BARUS. ] INITIAL SLOPES OF THE ISOMETRICS. 59

104°/1000=-114 in one case and 115/1000 =-115° per atmosphere in 

the other.

Alcohol differs from all the other isometrics, inasmuch as the curvature is upward. The deviation at 1000 atmospheres is nearly 2°. The 

initial slope of the isometric 95°/1000='095° per atmosphere.

Thymol, curiously enough, is strikingly near a straight line. The 

deviation at 1000 is inappreciable. The slope of the isometric 71/1000=

 071° per atmosphere. 

Diphenylamine deviates from the straight line. The slope is 63/1000=

 063° per atmosphere.

In case of toluidine the slope is '070° per atmospere. In the two 

latter cases it must be remembered that the initial temperature is 78°, 

and the initial pressure 400 atmospheres. The deviation from the rectilinear path is an abrupt high-temperature occurrence.

Turning finally to pi. n, 2, the following slopes are found which may 

be compared with the slope of 1:

TABLE 29. Observed initial slopes of the isometrics.

Not corrected for volume 

changes of glass tulies ...... 

Corrected for volume changes

Initial pressure, atmosphere..

Ether.

°C./atm. 

f -114 > 

I '1155

c -no

I -114

17°

30 

34°

Alcohol.

°0. 1 atm. 

 095

 095 094

50 78°

Thymol.

°G. / atm. 

 071

 073 072

17°

80

oqqo

53°

Diphenylamine.

°G. / atm. 

'063 

 065?

 0055

68°

(400)

Para-toluidiiio.

°0. 1 atm. 

 070

 072

68°

(400) 198°

43°

It is seen from this table, as well as from Table 28, that the correction to be applied in consequence of nonrigidity of glass never exceeds 

2 per cent. In case of ether and alcohol it may be disregarded. In 

the other cases-the approximation made is probably warranted without 

elaborate measurements of the elastics of glass.

If the abrupt change of curvature above 1000 atmospheres were due 

to an unwarranted application of Hooke's law, the curvature of the 

isometrics would tend to change in similar ways for all curves at the 

same pressures. This is not the case for the above curves, in which the 

contour of each preserves anindividual character. Even after the gauge 

had been strained (§ 42) I detected no differences in the factor. Again, 

the repetition of the thymol work in Table 22 (supplement), made especially to throw light on the present question, shows that no time 

error in the constants of the pressure apparatus is to be apprehended.

The slopes given in the last table have no absolute value, since these 

data must vary with the initial volume under consideration. Volume 

measurements are beyond the scope of the present paper. I may state, 

however, that when volume measurements are included the complete 

thermodynamics of liquid matter are expressible in the family of curves 

obtained with a degree of accuracy which is experimentally the most 

precise.
60 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

58. Final interpretation. For the time being the above results admit 

of the following interpretation: Whenever a substance passes from the 

liquid to the gaseous state, no matter whether this takes place continuously above the critical temperature or discontinuously below it, the 

underlying cause is a change of molecule from a more complex to a less 

complex type. As long as the molecule remains unchanged the isometrics are straight. When the change of molecule takes place so as to 

begin with the liquid molecule and pass continuously into the gaseous molecule, the isometrics curve continuously for the linear isometric of the true liquid to that of the true gas. Such an explanation is 

of course tentative. It rests on evidence purely experimental and 

therefore of uncertain interpretation; and it is suggested by a controversy which I have summed up elsewhere 1 as follows: "The linear relation was predicted from theoretical considerations by Dupre" (1869) 

and by L6vy (1884) considerations soon proved to be inadequate by 

Massieu, H. F. Weber, Boltzmann, and Clausius. Eamsay and Young 

(1887) established2 the relation in question experimentally for vapors, 

but not, I think, very fully for liquids decidedly below their critical 

points. Eeasoning from these data, Fitzgerald (1887) investigated the 

consequences of the law, viz: (1) specific heat under constant volume 

is a temperature function only; (2) internal energy and entropy can be 

expressed as a sum of two terms, one of which is a volume function 

only and the other a temperature function only. Thus Eamsay, Young, 

and Fitzgerald arrive substantially at the same position from which 

Dupre" and L6vy originally started."

However, too much care can not be taken in keeping clearly in mind 

that pressures which, in relation to the usual laboratory facilities, are 

exceptionally large, may yet be mere vanishing increments when 

mapped out on the scale of the molecular pressures of liquids and 

solids.

Some notion of the internal pressures encountered maybe gained as 

follows:

Studying the compression of organic substances throughout an interval of 310° and 600 atmospheres, I found that the isothermal compression v/ Fcould be well represented by an equation v/ F=ln (l+«p) */a 

where & and a are constants and p denotes pressure. Taking this as a 

basis, I sought the mean values of the constants involved in some fiftythree isothermals, and found fl/V=ln(l-f 9#)] /9 to apply within the 

limits of error of my work. To this extent, therefore, compressibility 

increases as the reciprocal of the first power of the pressure binomial 

(l/9#+j)). The interpretation to be given to l/9# is that of an initial 

or internal pressure. Computing its value for the above or organic 

liquids, I found the data of Table 30.

'Am. Jour., Sci. 3d ser., vol. 38, 1889, p. 407.

Tor a pressure interval not exceeding about 80 atmospheres for a group of isometrics, nor about 30 

atmospheres for a single isometric. See Kamsay and Young, Phil. Mag.: 5th ser., vol. 23, 1887, p. 485.
BABUS.J INTERNAL PRESSURE.

V

Subst.

Etlier #o=100.

Aleoliol j»u =

i ^n

Thymol .......

1

©

°0.

29°

65°

100°

185°

310°

28°

650

100°

185°

310°

28°

64°

100°

185°

310°

Internal 

pressure.

Atm.

673

491

323

110

32

1,249

967

703

336

80

1,683

1,481

1,146

CC9

228

Subst. .

Par a-t o 1 n idiiie #o = 20.

Diphenylamino#o=0 ...

0

°<7.

28°

65°

100°

185°

310°

65°

100°

185°

310°

Internal 

pressure.

Atm.

. 1,852

1, 610

1, 262

671

263

1,709

1,610

1,010

521

If, however, compressibility be supposed to vary as the square of the 

pressure binomial, 1 viz:

the internal pressures corresponding, will have about twice the above 

values. Now it appears, from recent experiments of my own, that the 

last expression is probably the more nearly true. It follows therefore 

that at zero centigrade, internal pressures of the order of 1,000 to 4,000 

atmospheres are to be taken into account.

57. Isometrics of solid glass. A singularly curious inference is suggested in comparing the approximate isometrics of glass above deduced, (§§ 52, 53), with the liquid isometrics of the present and earlier 

papers. It appears that for solid glass the slope of the isometric is 

about 100°/1000 = .1° per atmosphere in its initial course. This coincides very nearly with the slope of the isometrics of the above organic 

liquids, varying as they do between .07° and .12° per atmosphere. In 

.view of the similarity of glass and the rock producing magma, this 

degree of isometric similarity is of great interest. In general the 

proximity of the solid and liquid isometric of compound matter is 

worthy of note.

The metallic isometrics are different from the above. So far as they 

can be obtained2 the slope of the isometric

- = 106 / Ic ft 

 p I

per atmosphere, where fc and /? are respectively the resilience of volume and the coefficient of expansion, is only -014° for steel, -010° for

1 Cf. Barns: Am. Jouni. Sci. (3), vol. 39, 1890, pp. 497-506.

2 Constants k and p arc taken from Evorott's tables.
62 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BOLL. 96.

iroii, and -011° for copper. They thus preserve an order of magnitude 

different from that of glass or the above organic liquids.

58. Conclusion. In conclusion I will advert to the easy possibility of 

obtaining families of isometrics, and from them a complete representation of the isometrics of liquids with a given pressure interval of say, 

.3000 atmospheres. For this purpose it is merely necessary to change 

the volume of liquid contained in the glass tubes, and to refer all volumes to the one obtaining at the initial temperature. Thus in the 

* above tube and in case of ether, temperatures pass from 20° to 220°, 

while pressure varies from 0 to 1,900 atmospheres, say. Suppose, now, 

that the electric contact is moved in such a way that at 200° the pressure producing contact is not much greater than the vapor tension of 

the liquid. Clearly, therefore, the isometrics may now be studied between 200° and a temperature between 300° and 400°, while pressure 

varies between 0 and 2,000 atmospheres as before, etc. Apart from 

the unavoidable tediousness of the work, the experimental devices 

suitable for accomplishing this easily suggest themselves.
CHAPTEEIII.

A COMPARISON OF THE BOURDON, THE TAIT, AND THE AMAGAT 

HIGH-PRESSURE GAUGES.

HISTORICAL.

59. The earlier work. In my earlier work (chapter n), while investigating the isometrics of liquids, I was obliged to content myself with 

an investigation of empiric pressure gauges. I found by comparing 

different Tait gauges with a large Bourdon gauge that so long as pressure continually increased from zero, the relation between the indication

of each under like conditions of pressure was linear; but that Avhen 

pressure again decreased from .the high value (1,00 ) atmospheres or 

more) to zero, this relation changed to a markedly curvilinear locus, of 

such a kind that eventually the original zero of both guages was regained. So long as increasing pressures alone were dealt with, either 

of these gauges could be used with safety. The present work, in which 

both gauges are directly compared with Ainagat's manome'tre a pistons 

libres, corroborates this inference, and shows that tliebow-shaped cycles 1 

represent the actual motion of the free end of the Bourdon tube. From 

this point of view the present datea are important, for they supply an 

example' of purely mechanical hysteresis, and possibly of metallic volume lag. The data also show that cyclic indications are absent in the 

steel Tait gauge, and that this instrument may be adopted, for the 

scientific measurement of pressures of any value whatever.

60. AmagaVs manometer. The instrument in my possession2 is constructed for the measurement of pressures as high as 3,000 atmospheres. At this extreme limit the height of the compensating column 

of mercury (the diameter.s of the two pistons being 549cm and 12-171'' 1 " 

respectively) will be about 464C1". To read so long a column with reasonable convenience, I fixed, a long, painter's ladder in a vertical position, 

and permanently attached to one side of it both the open manometer 

tube and the long millimetre scale, which I ruled with care on a wide 

strip of brass. A round leather belt, passing from top to bottom of tuo 

ladder and everywhere within easy reach, passed over a pulley adjust* 

meut, and was suitably connected with the mechanism for rotating the 

two "pistons libres." In this way I was able to make this essential adjustment immediately before taking my reading, no matter whab my 

position on the ladder might be.

'Phil. Mag., 5th ser., vol. 30, 1800, p. 338, Ibid., pi. x. In the paper cited I was of the opinion that 

the cycles wore thermal phenomena to he sought for in the Tait g'auge. 

* Marked E, H. Amagat, Lyon, 1890.

63
THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

I found by trial, that by using the thick mineral machine oil mentioned 

in my last paper 1, the manometer would be at once connected with my 

screw compressor, and that the charge of molasses was quite superfluous. I also floated the lower piston in this oil. Thus the same oily 

liquid for the transmission of pressure is used with advantage throughout the system of apparatus. Once put together, it is ready for use at 

all times and need not again be touched in years. Care of course must 

be taken to obtain oil free from grit or dust.

61. The Bourdon gauge. The gauge used was the one to which my 

earlier measurements apply, having a tube of steel. I made two series 

of comparisons of this gauge with the manometer. In the first of these 

the usual Bourdon multiplying gear was used; in the other the excursions of the free end of the Bourdon tube were read off directly with a 

Fraunhofer microscopic micrometer after the multiplying gear had been 

detached. Of many experiments of this kin d which I made I will give 

the following typical examples contained in Tables 31 and 32. In Table 

l^the Bourdon registry is given at once in atmospheres, the Amagat 

registry both in centimeters and in the atmospheres reduced therefrom. 

There are four series of observations, two of them within an interval ot 

500 atmospheres and the other two within 1,000 atmospheres. Two 

observations are made at each step of pressure. In Table 32 the micrometer position of the end of the Bourdon gauge is given in cm./^O, 

this being the scale part of the Fraunhofer gauge. In other respects 

the data are given as in Table 31. Observations were made in triplets, 

two at the manometer including each one at the Bourdon gauge.

TABLE 31. Cyclic comparison of the Bourdon gauge (steel tube) with the Amagat manometer. Multiplying gear.

Bourdon.

Atm.

188

174

322

312

457

446

310

313

162

165

27

29

172

168

317

305

462

444

433

224

995 ftud

83

84

20

Amagat.

Cm.

28-65

26-80

50.30

48.60

70-90

69-20

49-50

48-10

24-30

24-50 3-60

3-70

26-30

25-50

49-10

47-30

71-80

69-10

67-20

33-90 

34-10

12-10

12-10 2-50

Amagat.

Atm.

185

173

325

314

459

448

314

311

157

158

23

24

170

165

318

306

464

447

435

219

991 &&\.

78

78

16

Bourdon.

Atm.

21

242

231

472

457

660

640

859

844

991

977 

847

837

651

646

475

475

262

263

28

28

30

251

245

Amagat.

Om. 2-50

37-30

35-80

73-30

71-30

102-00

99-30

131-30

128-80

151-80

148-80 

126-00

124-20

93-60

92-90

65-10

64-90

34-50

34-70 2-50

2-70

2-90

38-60

37-50

A inagat.

Atm.

16

241

232

474

461

660.

642

849

833

982

962 Qi P; olu

804

606

601

421

420

223

225

16

17

- 19

250

243

Bourdon.

Atm.

465

458

650

645

855

838

985

977

964

950

840 

834

631

626

440

440

260

264

35

35

Amagat.

Om.

72-40

70.80

101-00

99-90

133-00

128-60

151-80

148-30

147-30

144-80

125.00

19O. Qft j.£io a\J

90-80

90-00

59-60

59-60

33-30

34-40 3-30

3-80

Amagat.

Atm.

468

458

653

647

860

832

982

960

954

937

809

ft OI/4 (19

587

582

386

386

215

222

21

25

'Phil. Mag., 5th. set., vol. 31,1891, p. 10. I have always found it preferable to use oily instead of 

aqueous liquids, by which fine parts of steel are liable to rust-
BOURDON'S AND AMAGAT'S GAUGES COMPARED. 65

TABLE 32. Cyclic comparison of the Bourdon gaugv (steel tube) with the Amagat manometer. Fraunhofer micrometer.

Bourdon.

Cm. /40

19-09

16-04

16-12

11-93

12-19 8-40

8-58

5-23

5-66

6-02

6-12

7-94

8-36

11-20

11-28

15-18

15-18

18-97

Amagat.

Cm. 00

35-30 35 -10*

80-80

80-10

119 -30

118 -30

149 -80

147 -80

141 -30

141 -30

116 -30

110 -30

82-70

82-60

38 -80

39-20

 00

Amagat.

Atm.

0

228

227

523

518

772

765

969

956

914

914

758

753

535

534

251

254

0

Bourdon.

Cm. /40

38-92

15 -83

15 -87

11 -91

32-20 8-86

9-18

5-25

5-70

0-16

6-33

8-20

8-39

11 -08

11-08

14 -80

14 -80

19 -06

Amagat.

Cm. 10

37-40

36 -90

80-80

79 -30

112 -bO

111-30

149 -80

147 -80

144 -50

139 -30

116 -80

114 -30

83 -30

. 83 -30

41-80

42-40 00

Amagat,

Atm.

1

242

239

523

513

730

720

969

956

935

901

756

739

539

539

270

274

0

DISCUSSION OF RESULTS.

62. Multiplying mechanism. Constructing Table 31 graphically, it 

appears that within the errors of reading the observations of the first 

two series lie on a straight line. In series 1 the "on" and "off" measurements possibly suggest a cycle whose maximum divergence is not 

above 5 atmospheres. The factor of the Bourdon gauge (7^7) taken 

from these data is '998 "on," and -987 "off." In series 2 this factor 

has changed to -984 "on," and -992 "off." There is no cyclic march. 

It follows from both series, barring observational errors, that a cyclic 

march within an interval of 500 atmospheres does not occur.

The third series "on " shows a change of rate above 700 atmospheres j 

thus the locus is composed of two straight lines. The return march is 

now distinctly cyclic, and at 500 shows a breadth of almost 50 atmos- 

. pheres. The zero is regained within 10 atmospheres. The mean factor 

is -991 below, and 1-008 above 700 atmospheres in the "on" march. 

The mean factor of the "off" march is of no interest. In the fourth series, 

finally, the remarks made relative to series 3 are substantiated throughout. The factor below 700 atmospheres is -982, and above 700 is 1-072. 

There is some error in this last result, probably due to unwarrantably 

vigorous tapping of the gauge. The width of the cycle at 500, about 

50 atmospheres.

Hence, the inferences drawn in the earlier paper from a direct comparison of the Bourdon and Tait gauges1 are valid throughout. It is 

gratifying to note that even the standard atmosphere formerly used is 

correct to -8 per cent. The present results, however, go further in showing that the cyclic march in question is in the Bourdon gauge, whereas 

the indications of the steel Tait gauge are probably very near the truth. 

Since I reversed the action of the Bourdon mechanism at different test

1 Phil. Mag., 5th ser., vol. 30, 1890, pp. 343 et seq.; ibid., § 18; the breadth of cyclea here was about 40 

atmospheres.

Bull. 96 5
66 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

readings it can not be supposed that these cycles are in the multiplying 

gear. Nevertheless this test is essential, and the results obtained are 

given in the next paragraph.

.63. Fraurihofer micrometer. Care was taken to fix the axis of the 

screw parallel to the line of motion of the free end of the Bourdon 

gauge, which makes an angle of nearly 45° with the tangent at the 

end of the tube. Table 32 shows the total motion to have been about 

4cm per 1,000 atmospheres, where it is to be noted, however, that the 

solid tapering conoidal plug at the end of the flat tube was about 10cm 

long. Of the two series given in Table 32, the "on" march of the first 

shows some convexity upward. The factor is 362cni per 1,000 atmospheres. The data of the "off" march show distinct convexity downward. Hence the two curves form a cycle whose breadth at 500 atmospheres is about 40 atmospheres, a result agreeing substantially with 

§ 62. The data of the second series, which show rather better agreement among themselves, corroborate the results of the first series 

throughout. The mean factor in the "on" mairch is -361om per 1,000 

atmospheres nearly identical with the above.

The bow-shaped cycles, therefore, obtained in the present and earlier 

paper 1 represent a case of actual hysteresis. A certain amount of 

strain is stored up in the Bourdon tube during the interval of compression, which, during removal of pressure, is always relieved more 

slowly than pressure decreases. The phenomenon is thus static in 

character, and I venture to regard it as depending on the occurrence 

of volume lag in those parts of the tube which are directly influenced 

by pressure. In other words, the molecules of metal near the inside of 

the Bourdon tube pass from the original to a second molecular state 

in proportion as a certain pressure P is approached and exceeded, 

whereas these molecules pass from the second molecular state back to 

the first again in proportion as pressure falls below a certain other

datum p, where P>jt?. Now, inasmuch as Table 31 shows that within 

500 atmospheres there is no appreciable hysteresis, while both Tables 

31 and 32 show marked cyclic changes between 0 and 1,000 atmospheres, it follows from the data in question that P must lie somewhere 

between 500 and 1,000 atmospheres, whereas p may lie below 300 atmospheres. Here, therefore, is a phenomenon very similar to the effect 

of pressure on an undercooled liquid.

Two other possible explanations of the cyclic changes may be noted. 

In the first place, it is conceivable that the Bourdon tube is hotter during the "off" inarch than during the "on" march. To test this 

directly it would be necessary to submerge the tube in a water bath, 

which is scarcely feasible without injuring the mechanism. But I 

hold such an explanation improbable. If it were true the comparison 

within 500 atmospheres (Table 1) should show a cyclic magnitude pro1 Phil. Mag., 5th ser., vol. 30, 1890, pp. 344 et seq. See PI. x. Cf. chap, i, § 16, above.
BARUS.] TAIT'S AND AMAGAT'S GAUGES COMPARED. 67

portional to the cycle corresponding to the interval 1,000 atmospheres, 

which it does not. Again, the cycles should quite vanish on long waiting (five minutes were allowed per observation in my earlier work), 

which they do not.

The other explanation, which seems to me equally improbable, is this: 

There may be two figures of equilibrium of the Bourdon tube, one corresponding to low pressure the other to high pressure, and the figure 

of labile equilibrium through which the tube passes from the first to 

the second may be maintained over a relatively large interval of pressure.

In general, therefore, it follows that if the Bourdon gauge is to be 

used for high pressures, it is necessary to take cognizance of discrepancies inherent in the chemical physics of the metal, in addition, to the 

mathematical difficulties discussed by Lord Eayleigh, Profs. Greenhill 

arid Worthington.

64. The Tait gange. In Table 33 I give two series of cyclic compari. 

sons of the Tait gauge with the Amagat manometer. The plan of 

work was similar to that described in section 61. Headings were made 

in triplets two at the Amagat manometer, including one at the Tait 

gauge. An interval of two minutes ivas allowed for cooling. The Tait 

gauge used is the same to which my earlier observations apply.1 The 

interval of comparison is 1,500 atmospheres. At the end of Table 33 

a short re"sum6 of the factors (cm. atrn.) corresponding to consecutive 

pressure intervals is given.

TABLE 33. Cyclic comparison of Tait gauge (steel tube) with the Amagat manometer.

Tait.

Om.

12-65

21-05

20-73

29-35

28-75

40-80

30-72

51-05

50-16

59-20

57-80

64-90

63-98

63-30

62-50

57-20

56-65

49-05

45-50

41-00

40-72

31-92

31-57

22-44

22-49

13-05

12-85

Amagat..

Gin. 20

38-30

37-00

75-30

72-30

124-30

118-70

168-00

163-70

201-70

195-60

225-60

221-30

218-60

215-40

192-70

190-10

157-70

155-20

123-00

121-40

83-30

82-00

41-90

42-10 10

 10

Amagat.

Atm.

1

248

239

487

468

804

768

1,087

1,059

1, 305

1,266

1,460

1,432

1, 414

1,394

1. 247

li 230

1,020

1,004

796

786

539

530

271

272

1

1

Tait.

Om.

12-90

21-30

20-95

30-17

29-25

38-82

38-09

50-14

49-10

60-19

58-58

05-42

64:05

62-50

62-00

58-50

58-15

49-49

49-28

40-45

40-23

29-86

29-50

20-01

20-06

12-85

12-93

Amagat.

Om. 00

38-QO

36-40

76-90

73-10

114-80

111-90

163-50

159-60

206-50

200-00

228-90

222-10

216-00

213-90

199-20

197-30

160-50

359-50

121-30

120-50

75-60

74-20

32-40

32-30 10

 10

Amagat.

Atm.

0

246

236

498

484

743

724

1057

1,033

1, 335

1,294

1,481

1,437

1,398

1,384

1, 289

1,277

1,038

1, 022

785

780

489

480

210

209

_ -^

 1

>Ptil. Mag., 5th ser., vol. 30,1890, p. 344, § 18, gauge No.l.
68 THE VOLUME THERMODYNAMICS OF LIQUIDS.

Factors of the Tait gauge.

[BULL. 96.

Scries.

I, oft1 .

I, off.

I, off.

H, on.

II, on.

IT, on.

H, off.

II, off.

II, off. .

Pressure interval.

Atm. 

200 to 1, 100

500 to 1, 200

200 to 1, 000

700 to 1, 500

800 to 1,400

200 to 1, 000

Factor-.

Gin. atin.

3640

3577

 03544

3625

 03604

3591

3579

Means on 

and off.

Gm./atni.

V -03028

-.

( -03576

,

( .nTiQfl

 j

( -6359i

Mean 

total.

 03596

Q5. Table 33 substantiates the inferences of section 62 relative to the 

absence of cycles in the registry of the Tait gauge. In the first series, 

u on,r the data above 300 atmospheres make up a straight lime. Between 0 and 300 atmospheres the registration of the Tait gauge is too 

high, being more in error as the pressure zero is approached, where the 

discrepancy is 30 atmospheres. In the " off" march all the points lie 011 

a straight line, excepting the zero, which is 10 atmospheres too high 

on the Tait gauge. Thus the locus consists of two straight lines converging at 1,500 atmospheres, and the cyclic character ol the data in 

section (il does not appear. In the second series, though preserving the 

general character of series 1, the "off" inarch practically returns in the 

line of the "on" march. Thus again true cyclic changes are absent.

As a whole, therefore, the observations lie on a very flat curve, which 

above 300 atmospheres passes into a straight line. (See Fig 11.) It is 

difficult to conjecture the cause of this curious low-pressure discrepancy 

in consequence of the great number of errors which may possibly be 

encountered, though it may be remarked that the rise "of temperature of 

ahquidperlOO atmospheres of compression may decrease with increasing 

pressure, since at0 low pressures compressibility is relatively large. 

Table 33 shows, finally, that the mean factor derived from all the series 

is .03596 cm./atm. This is to be increased about 4 per cent, to correct 

for the temperature of the mercury column of the manometer. Hence 

the factor is .0361 cm./atm. In my former paper the results1 were .0360 

to .0369 cm./atm., showing that my standard atmosphere must have been 

less than 2 per cent in error. It is altogether probable that this difference of factor (2 per cent) is the result of the excessive use and abuse 

to which the gauge was put during the intervening nine months. Eegarding the observations as a whole I believe the residual discrepancies to be due rather to unavoidable fluctuations of the temperature of 

the water jacket than to thermal effects of compression, or viscosity of 

metal. For this reason I doubt whether any permanent expansion of 

the metal within 1,500 atmospheres has been registered.

1 Phil. Mag. 5th ser., vol. 30, Table iv, p. 345. This table contains cm./atm. instead of cm. X 102/atm.
BATCUS.] "PISTON L1RKI5." G9

SUMMARY.

66. In the attempt to carry these comparisons above 2,000 atmospheres, I ruptured the stout tube 

which connected the compressor 

with the manometer. The above 

work, however, shows conclusively tli at the Tait gauge may 

be perfected so as to be available 

for preci se measurement. It in ay 

be permissible to indicate the 

way in which I am endeavoring 

to do this here; since many of 

the experimental contrivances 

involved have already been tested. The tables have shown that 

the most annoying difficulty is 

encountered in maintaining the 

temperature of the \vater jacket 

sufficiently constant. To this 

end the whole gauge is to be 

constructed of metal with closefitting jackets. Furthermore, 

choice is to be made of as thin 

walled a steel measuring tube 

as possible, in order .that the. 

volume increase due to pressure, 

may be large relatively to the 

simultaneous effects of fluctuations of temperature. There is - 

reason to believe that this can 

be accomplished by connecting 

the Tait gauge with the compressor by an interposed ''piston libre." In the annexed diagram, Fig. 12, let 7? be the cylindrical piston, consisting of a 

single piece, of which one end" 

is larger in diameter than the 

ot11er. Let this piston fit the hollow cylinder G G .0 accurately, 

so as to be capable of motion to ~ 

and fro a,nd of rotation, with the 

minimum of friction. Let the 

tube D be in connection with the ;_ 

compressor, the tube E in connection with the Tait gauge, and 

the whole apparatus be filled 

with oil. Then it is clear that

\
70 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL.96.

the exceptionally high pressure, acting only on the shoulder of the piston, 

can be counterbalanced by a relatively IOAV pressure at E. Leaving the 

essential details of construction out of consideration, a Tait gauge 

reading to only 1000 atmospheres may thus be made to indicate pressure 2, 3, or more times as large as this at D, by selecting suitable 

dimensions of piston and socket. Hence even very high pressures can 

be measured by aid of a thin-walled steel tube, the pressure expansions of which are so large that the accompanying thermal fluctuations 

of the environment dwindle to very small importance. I am far from 

underestimating the importance of Amagat's manometer as a standard

FIG. 12. "Piston libre," for higli pressure.

instrument leading at once to absolute results; but it is certainly inconvenient to be obliged to make readings on a column of mercury 

which may be 5 meters high, even when a stirring arrangement such as 

that described in § 60 is provided. I doubt, moreover, whether it would 

conduce to convenience, and certainty if the readings were made by 

some easily devised electrical method. On the other hand, in case of 

the Tait gauge, the pressures are read off on a horizontal tube about 

1 meter in length and as far as 2000 atmospheres without "pistons 

libres," and therefore quite without diminution of pressure in consequence of unavoidable leakage. Eegarding gauges quite free from 

leakage, I hope soon to be able to communicate results on the electrical 

behavior of pure mercury under pressure.
OHAPTEE IY.

THE CONTINUITY OF SOLID AND LIQUID.* 

INTRODUCTORY.

67. Scope of the icorTc. In my earlier papers 2 I entered somewhat 

minutely into the volume thermodynamics of fluid matter. The behavior of matter passing from liquid to solid and back again was only 

incidentally considered.3 This, however, is the very feature which gives 

character, or at least a more easily interpretable character, to the whole 

of the volume phenomena of the substance, and I have therefore reserved it for special research.

The problem may be looked upon from another point of view. Let 

it be required to find the relation of melting point and pressure. I 

have long since shown4 that in a comprehensive attack of tins question 

the crude optical or other methods hitherto used as criteria of fusion 

(criteria which have no inherent relation to the phenomenon to be 

observed) must be discarded. In their stead the volume changes which 

nearly always accompany change of physical state in a definite or 

simple substance are to be employed.

The present experiments were made with naphthalene only. They 

are by no means even near the degree of precision of which the applied 

plan of research admits. My chief object here has been to carry the 

method quite through to an issue preliminarily and to test it at every 

point. The data are sufficient, however, to show that the process 

adopted, though I approached it witli much misgiving, can be brought 

under control throughout, and that the attainable accuracy is only 

limited by the patience, discernment, and skill of the observer. I was 

in some degree surprised therefore to find that my method led to new 

results at the outset.

The literature of the subject I shall omit here, since the more important experiments have entered the text-books and since I shall Lave 

occasion to refer to it elsewhere. I need merely mention Sir William

1 The geological interpretation of this work is in the hands of Mr. Clarence King, by whom the 

inquiry was suggested.

a Am. Jour. Sci., 3d ser.. vol. 38, 1889, p. 407; ibid., vol. 39, 1890, p. 478; ibid., vol. 40, 1890, p. 219; 

ibid., vol. 41, 1891, p. 110; Phil. Mag., 5th ser., vol. 30, 1890, p. 338.

a Am. Jour. Sci., 3d ser., vol. 38, 1889, p. 408; ibid., vol. 3i), 1890, pp. 490, 491, 494. Most of my 

earlier work on this subject has thus far remained unpublished.

4 Am. Jour. Sci., loc. cit. More pointedly with an indication of methods in Phil. Mag., 5th ser., vol. 31i 

1891, p. 14.

71
72 THE VOLUME THERMODYNAMICS OP LIQUIDS. lnuu,9C.

Thomson (1850), Bunsen (1850), Hopkius (1854), Moussou (1858), 

Poynting (1881), Peddle (1884), Amagat (1887), Battelli (1887), and some 

others (cf. § 95, 96).

68. Other methods tested. In applying this principle I first made 

direct volume observations on substances inclosed in capillary tubes 

of glass. In the case of naphthalene and many others I thus obtained 

satisfactory results 1 . Such work is, however, limited to relatively low 

pressures (600 or 800 atmospheres); it does not admit of sufficient cor. 

rection for the volume changes of the glass, and for the small quantity 

of substance examined and the relatively frequent occurrence of nuclear 

condensation, volume lags are often obscured. Hence the definition 

which, after making these experiments, I was inclined to adopt, viz, 

that a pressure which when acting isotherinally for an infinite time will 

just solidify the liquid and just liquify the solid, stands to the given 

temperature in the relation of melting point and pressure, is not in 

accordance with the facts.

In a second method2 1 endeavored to measure the characteristic difference of specific volume by passing current through the thin, hot 

walls of the tube which contained both the substance and the mercury 

thread or index. The whole apparatus is in this case surrounded by 

the oil of the piezometer in which the tube is inserted, and the changes 

of resistance of the arrangement indicate the motion of the index and 

hence the degree of compression produced. Here, however, a new and 

unexpected annoyance was encountered, inasmuch as both the medium 

of oil and the glass possess seriously large pressure coefficients. 3 

Moreover it is only with great difficulty that perfect insulation can be 

maintained in an apparatus of which water jackets make up an essential part. I therefore abandoned this project.

In a third method similar to the preceding I expressed the motion 

of the mercury thread or index in terms of the resistance of a very fine 

platinum wire passing through the axis of the tube. The successive 

intercepts thus indicated the changes of volume to be observed. This 

method gave good indications of the pressure positions of the melting 

points of the sample. It failed, however, to give serviceable values for 

the fluid volume changes. This is due to the fact that contacts in such 

a case are essentially loose. Again thermo-currents can only with 

great difficulty, if at all, be allowed for, seeing that the successive 

isothermal temperatures are to vary over a large range.

Finally all of the methods above described must necessarily fail after 

the substance has become solid, for in this case the thread or index is 

broken and forced into the interstices of the solidified material. Thus 

it is manifestly impossible to retain a uniform meniscus after solidification has once set in, and it is therefore impracticable both to arrive

1 Cf. American Journal of Science, vol. 38, 1889, p. 408. 

2Phil. Mag., 5th ser.. vol. 31, 1891, p. 14. 

»Ibid., pp. 18 to 24, et aeq.
METHOD APPARATUS. 73

at the behavior of the solid, as well as to rigorously coordinate successive series of experiments.

69. Advantages of the present method. Hence I endeavored to modify 

Kopp's1 specific volume flask iu a way to make it available under any 

temperature or pressure. Here the readings are independent of the 

unbroken character of the meniscus immediately in contact with the 

solidifying substance, whereas on the other hand, as I shall presently 

show, the expansion measurements can be made electrically2 with almost any desirable degree of accuracy. Furthermore, by charging the 

flask with properly apportioned quantities of substance and of mercury, 

the error due to the compressibility of the glass may be eliminated in 

any degree whatever, and an apparatus obtained which is practically 

rigid in relation to pressure. The data show that from each sing]e series 

of experiments I thus obtain the isothermals and isopiestics, and therefore also the isometrics, both for the liquid and for the solid; furthermore the relation of melting point and of solidifying point to pressure, 

and finally the changes of the isothermal specific volumes of solid and 

liquid at the melting points, with pressure. From these results the 

character of the fusion and the probable position of critical (§92) and 

transitional (§94) points can already be pretty well predicted. It is 

then only necessary to examine a great number of substances, of substances existing under widely different conditions of thermal state, in 

order to broaden the evidence and possibly to reach results of a uniform bearing on matter in general. This I indicated elsewhere.3

APPARATUS.

70. Temperature. Inasmuch as pressure varies at a mean rate of, say, 

30 atmospheres per degree, so that temperature is as it were the coarse 

adjustment and pressure the fine adjustment for the conditions of melting point, it is clear that the method of experiment should be such that 

temperature may be kept rigorously constant while pressure is made 

to vary over the necessary interval. To obtain constant temperatures 

I constructed a set of vapor baths of well-brazed, thin sheet iron heavily 

jacketed with asbestos. Of. PI. in, pppp. These were cylindrical in 

form, 10om in diameter and 20cm high. Axial tubulures, the upper of 

which, ss, projected outward, the lower, oooo, both inward and outward, 

allowed the vertical tubular piezometer to pass axially through the vapor baths, and suitable stuffing boxes obviated all possibility of leakage. Again the upward projection of the lower tubulure (both of them 

fit the piezometer snugly) formed an annular trough with the walls and 

bottom of the vapor bath, in which a sufficient quantity of the ebullition liquid could be placed and boiled by aid of a flat spiral burner

1 Kopp, Ann. Cheiu. u. Pharm., vol. 93, 1885, p. 129.

2 Tho absolute expansion and compressibility of mercury being now known § 73.

3 " Instead of tracing the isothermals of a single substance throughout enormous ranges of pressure, 

similarly comparable results may possibly bo obtained by examining different subatances conceived 

to exist in widely different thermal states." (Am. Journ., loc. cit., p. 510.)
74 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BUM.. 00.

placed below. The top of the vapor hath was provided with two other 

lateral tubulures, one of which served for the permanent attachment of 

a vertical condenser and the other for the introduction of a suitable 

thermometer or thermocouple. Here also the quantity of ebullition 

liquid present could at any time be tested and its amount increased or 

diminished, or its quality directly purified by fractional distillation (an 

operation always necessary when amyl alcohol is used). With a good 

condenser the boiling may be kept up indefinitely, since the condensed vapors fall back into the trough below. For temperatures 

below 100° it is expedient to avali oneself of the high latent heat of 

water and to boil this liquid under diminished pressure. Temporarily 

attaching Kichards's jet pump to the end of the condenser, pressure 

may be so regulated that any boiling point between 50° and 100° is 

maintained indefinitely. For higher temperatures amyl alcohol, turpentine, naphthalene, benzole acid, diphenylamine, phenanthren, sulphur, etc., subserve the same purposes, though less thoroughly. Low 

latent heats 1 in most of these substances make it difficult to guarantee 

perfect thermal constancy throughout a length of say 10cra . (Of. §72, 

where a view of the apparatus is given.)

Temperature was measured by aid of a Baudin thermometer of known 

errors and also computed from the vapor tension of steam under known 

conditions. Thermolectric measurements are similarly applicable.

71. Pressure. To obtain pressures as high as 2,000 atmospheres I used 

my screw compressor described elsewhere.2 I made use, however, of a 

vertical piezometer, identical with the horizontal piezometer there described, except in so far as it could be removed from the barrel as a 

whole. As before, moreover, piezometer and barrel are insulated. 

When in adjustment the piezometer was surrounded by the following 

parts enumerated from bottom to top (see PI. in): An insulated conical 

protector or guard preventing spilled water, etc., from reaching the insulation, the lower cold-water jacket, the flat burner, the vapor bath, and 

finally the upper cold-water jacket. For temperatures below 200° the 

latter may be dispensed with.

Internally the piezometer was filled with thick petroleum, oil, as stated 

elsewhere.3

For pressure measurement I am now able to avail myself of a superb 

Amagat manometre a pistons libres, which can be immediately attached 

to my compressor with advantage.

72. The volume tube. A careful description of this apparatus, together with the operations necessary in standardizing it, is essential 

here. In one case these preliminary operations have led to a result of 

an interest apart from the present special purposes.

The tube is shown in the annexed diagram, Fig. 13, while PI. in

*It is my object in further experiments to boil water under pressure.

*Proc. Am. Acad., vol. 25, 1890, p. 93, Chapter I, above. 

8 Phil. Mag., 5th ser., vol. 31,1891, p. 10, chapter in, above.
BA11US.] VOLUME TUBE. 75

shows the tube in place in the tubular piezometer^ It consists of an 

external cylindrical envelope, A B, of glass, closed below, open 

above, about 2Gcm long and .4cm or ,5cm in diameter. Throughout 

the greater part of its length, the tube A B is divided into two coaxial 

cylindric compartments, by a central glass partition tube, Ck 0, open at 

both ends and fused to the tube A B along the ring C G about 7cm below 

the open top A. This central tube Glc G is about 17cm long and 

.13°'" internal diameter, and drawn as thinwalled and as 

even in caliber as possible, so that the greater part of 

its lower length may be available for measurement. It 

extends nearly to the bottom of A B.

The substance to be examined is introduced into the 

annular space E E, care being taken that when fused 

under the highest temperature to be applied its lower 

boundary may be 4cm or more above the end Ic of Glc G. 

My fused samples were about 13cm long. Immediately in 

contact with the substance EE and extending upward 

into the central tube Ck 0 is the plug of mercury FF with 

its free meniscus at g. When E 'E is solid g must be, say, 

2cm above the end A; of Gk 0, and when E E is liquid at 

the highest temperature to be applied g must still bo at 

about an equal distance below G G. The remainder of 

the tube above g is quite filled with .a concentrated solution of zinc sulphate Ghg, into which an amalgamated 

zinc terminal, J), has been submerged andfixed in position 

by aid of platinum wire a, fused to the sides of the tube 

A JB, as shown. The other terminal, &, is fused into the 

bottom of the tube A and in metallic connection with the 

mercury, F JP, therein contained.

The tube thus adjusted is completely submerged in the 

oil contained within the tubular piezometer, PI. in, and 

pressure is uniformly transmitted to it through the oil. 

The terminal a is piit into metallic connection with the 

insulated piezometer; the terminal fe, completely insulated therefrom by a coating of glass tube, is in metallic 

connection with the barrel; the tube A B itself is thus ^ 

held in position by tensely stretching the fixed wires a 

and b and so adjusting their lengths that the parts E E 

and hg, with reference to which the measurements are ^tii^voTmne^fbe.0' 

made, may lie wholly within the vapor reservoir of the cylindrical vapor 

bath surrounding the piezometer. The method of fastening the ends a 

and 6 is a somewhat delicate operation, which, however, I will not further 

describe. So adjusted the tube is in position (vertical as shown in 

PI. in) for any number of experiments and it is only necessary to attach the vertical piezometer to the barrel by aid of a tinned axially perforated screw.
76 THE VOLUME THERMODYNAMICS OF LIQUIDS. [Buu,96.

An inspection of the diagram shows at once that if a current enter 

the outside of the barrel it will pass through 6, /<;, </, /&, .7), and a into 

the outside of the piezometer and thence back to the battery. The 

only relatively significant resistance encountered in this course need 

be that between g and li of the thread of zinc-sulpli ate solution; but this 

resistance, cseteris paribus, varies directly with the length of gh, and 

therefore proportionally to the volume contraction of the substance E E. 

Hence the volume variations of the substance to be studied are directly 

and rigorously measurable in terms of the resistance of the circuit. 

If Kohlrausch's method 1 of intermittent currents, bridge, and telephone 

be used for the resistance measurement of the electrolyte, solidification 

or fusion breaks upon the ear with a loud roar, whereas the ordinary 

volume changes (solid or liquid) are indicated by mere intensification of 

sound, sufficiently pronounced to subserve the purposes of measurement.

It is seen that any breakage of the surface of separation between E E 

and F F is entirely without influence on this result, and that, even in 

the case of the solidification of E E, when mercury is forced into the 

interstices left after contraction, the compressibility of E E will still 

be measurable.

The charging of the tube, free from air, is an operation which I have 

not thus far accomplished satisfactorily. If a volatile substance like 

naphthalene be filled into E E and fused in vacuo, the vapor subsequently condensing in gh will soil the tube and interfere with measurement. From the solid E E I doubt whether air can be quite eliminated 

in vacuo. Hence in the present work the substance was not air-free, 

a condition of things to which I gave less attention because I do not 

believe the melting points can be appreciably influenced by dissolved 

air, nor that other of the measurements made are seriously distorted 

by this error. In the future, however, I will endeavor to meet this 

difficulty by fusing the end A A of the tube A B inverted to the top 

of a barometer tube, in addition to a lateral tnbulure leading to a 

Sprengel pump. If now, after exhaustion, the lower meniscus of the 

barometric column is adjustable, so that the column as a whole maybe 

raised quite into the tube A B or withdrawn from, it at pleasure, it is 

probable that a thorough vacuum filling may be effected. Rubber connections, which corrode and blacken warm mercury, must be scrupulously avoided.

If the whole apparatus be charged with pure mercury in the place 

of the substance E E, the expansion and compression constants of the 

tube may be found as stated in the next paragraph.

Again, even if the measuring thread in yh should break into parts 

alternating with threads of.zinc sulphate (a possibility when the 

thread is worked up and down many hundred times, particularly in 

view of the suddenness of solidification), the constants of reduction are 

not thereby necessarily vitiated, always supposing that the number of

jch: Wied. Ann., vol. ii, 1880, p. 653; Long: ibid., 1880, p. 37.
0. S. GEOLOGICAL SURVEY BULLETIN NO. 96 PL. Ill

m

.r.

.h

f

TUBULAR PIEZOMETER, WITH APPURTENANCES.
BABUS.] PIEZOMETEE AND CONTENTS. 77

such breaks is not greater than one or two. Special care, however, must 

be taken to avoid contact of the mercury thread and the upper zinc terminal. Such an occurrence would either add to or deduct from the length 

of the thread and produce shifting in the coordination of the volume 

measurements. The formation of zinc amalgam after the long continued passage of intermittent currents or the possible electric solution 

of mercury is again to be kept in. view, as is also the probable change 

of compressibility of amalgamated mercury. 'On all these points I shall 

make special tests. Solution of mercury, however, can not become of 

serious consequence, since the column gh is continually washed by the 

zinc terminal I).

To give a succinct view of the method of work I will insert PJ. in, 

Avhich shows the volume tube rr in place in the tubular piezometer 

uuuu. The upper terminal rw is in contact with the screw plug v, 

where w is fastened. The lower terminal rxx is completely insulated 

from un by a glass tube (not shown) and metallically fastened to the 

perforated connecting screw #, by which the piezometer is attached to 

the barrel (not shown) of the compressor. The insulation of uu from 

W) and « has been described in section 12 above, cc being of steel, dd 

and lilt of hard rubber, the whole being made tight by a medium of 

marine glue and secured by the steel gland ee. The hard-rubber disc 

22, prevents the external terminal ggg of the piezometer from coming 

in contact with the metallic parts below and the barrel, Avhile a conical 

screen or umbrella of sheet iron, ////, additionally protects the lower 

insulation from water or liquid drippings from above. Note that ffis 

insulated from nn by a rubber cork, hh. The vapor bath, pppp, placed as 

shown, is heated by the plate burner rr, adjustable at pleasure, and an 

asbestos jacket, uu, keeps superfluous heat away from, the tube uu. The 

axial tube oooo of the vapor bath is sealed below by a piece of rubber 

hose, mm, or by a metallic stuffing box, care having been taken to make 

oooo fit the piezometer tube closely and thus take as little liquid out of 

the annular ebullition trough already described as possible. The condenser qq is connected above with an air pump (not shown). Finally 

water jackets tt and II, through which a current continually circulates, 

confine the heat to the central parts of the piezometer tube uuuu,

METHOD OF MEASUREMENT.

73. Constants of the tube. In order that the present measurements 

may be carried out absolutely it is necessary to know 

(1) The volume of the charge at a fiducial temperature and pressure.

(2) The volume of the plug of mercury under the same conditions.

(3) The volume of the central or measuring tube 7c/&per centimeter of 

length.

(4) The resistance of the thread of zinc sulphate solution per centimeter of length under all the stated conditions of temperature and 

pressure. From 3 and 4 there follows at once 
78 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

(5) The resistance of the thread of zinc sulphate per unit of volume 

under stated conditions of temperature and pressure. Thus it is necessary to investigate preliminarily 

(6) The isopiestic relation of resistance and temperature of the given 

concentrated solution of zinc sulphate and

(7) The isothermal relation of resistance and pressure of the same 

solution. In other words, it is necessary to know what may be called 

the isoelectrics relative to temperature and pressure of the measuring 

electrolyte. Furthermore, it is necessary to find or to know 

(8) The compressibility of glass in its relations to pressure and temperature, and

(9) The compressibility of mercury under the same conditions, and, 

finally,

(10) The thermal expansion of glass and

(11) The thermal expansion of mercury under the given conditions of 

pressure.

The measurements 8 to 111 did not make directly; they are of smaller 

importance, seeing that the substances on which I operate are all characterized by relatively large volume change. Such measurements are, 

however, easily feasible, since both the expansion constants and the 

compression constants of pure mercury (thanks to the recent labors of 

Amagat, Tait, and Guillamne) are now thoroughly known, and it is also 

known that the thermal changes of the elastics of glass are of no relative consequence (Amagat), even as far as 200°. I assumed the compressibility of my glass1 to be -0000022, that of mercury2 being -0000039; 

moreover, the coefficient of expansion of glass3 to be -000025, that of 

mercury4 being -000182 between 60° and 130°.

74. Volume of the charge. Clearly the fiducial conditions to which 

volume is to be referred are given by the (normal) melting point under atmospheric pressure. By weighing the tube before and after charging I found the mass of naphthalene inclosed to have been -763 gramme.

In a special and duplicate set of pycnometer experiments I furthermore 

found the density of naphthalene, fused at 82°, to have been -724. 

Hence the volume of the charge at 82° is -552cm3, which I accepted as 

identical with the volume at the melting point (80°).

75. Corrections for expansion and compressibility of envelopes. The 

plug of mercury weighed 7-74 grammes. Its volume is therefore -571om:) 

at 20°, aud its mean volume between 60° and 130°, being between -575 

and -582, is sufficiently near -SS01 "3.

Thus the volume of the glass tube containing both the charge of 

naphthalene and mercury was l-13ciu3. Its expansion per degree centigrade 00002SCI1' 3, while the expansion of the actually inclosed mercury 

per degree centigrade was '000105cm3, where the apparent expansion

i E. H. Amngat: Ann. cK. et phys., 1891, p. 125. 

* Ibid., p. 137.

'Landolt u. Boernstein's Tables, 1883, p. C9. 

'Ibid., p. 37,
BABUS.] METHOD OF CALIBRATION. 79

 000077cm3 per degree. Therefore if, in place of the fiducial volume 

.552011.3 folmci ju §74.^ the following volumes be substituted, viz,

60° -5565C '>' 3 100° -oSSB^3

80° -5550 120° -5519

90° -5512 130° -5311

the tube may be treated as free from thermal expansion. Here at 80° 

.5550 appears, instead of .5524, to correct for the fiducial volume of the 

stem k h (Fig. 13), as will presently be explained. (§ 83.)

Again, the compression of the l-13em3 of glass and -58cm3 of mercury 

will be

100 atrn.: glass, -00025 cm3 ; mercury,-00023 cm3 ; difference, -00002cm3

500 124 113 11

1000 249 226 23

1500 373 339 34

2000 497 452 45

Thus these corrections, which would individually be appreciable (affecting the increments say 3 per cent), are differentially negligible (0.3 per 

cent), where they fall below the electrical pressure coefficient of the zinc 

sulphate solution. (§ 80.) This has already been intimated above (§ 69), 

and is one of the interesting advantages of the volume tube Fig. 13.

76. Resistance measurement. In making the measurements of resistance of thread it is convenient to use Kohlrausch's interrupter, bridge, 

and telephone. To facilitate audition I joined the cup of the telephone 

to a graphophoue tube and listened with both ears. The resistances, 

however, are rather higher than contemplated in Kohlrausch's method, 

Avhen an ordinary Bell telephone is used. Hence the measurements, 

particularly near and in the solid state, are far below the limit of 

attainable accuracy. I shall in future measurements wind telephones 

specially adapted for my purposes, and endeavor to use both ends of 

the magnet to actuate diaphragms connected respectively with each 

ear by an independent tube.

When zinc sulphate is inclosed between terminals of amalgamated 

zinc a galvanometer is available. In this way I made most of the 

calibration measurements. Supposing the mercury index to be slightly 

deadened in its electro-negative qualities by zinc, it may also be used in 

case of the tube.

77. Calibration. In. view of the fact that the central tube li Tc (Fig. 13) 

is insufficiently uniform in caliber, it is necessary to express volume as 

a function of length. This I did by weighing threads of mercury whose 

length in successive parts of the tube had to be measured, obtaining 

the results of the first two columns of Table 34. The fiducial zero is 

here arbitrarily placed 2cm below the ring G C (Fig. 13), the caliber 

above this being too variable. 

It is next necessary to express the resistance of a filament of the 

concentrated solution of zinc sulphate as a function of length referred 

to the same fiducial zero at some convenient (atmospheric) temperature. 

To do this I drew a zinc wire to a diameter slightly less than the caliber
80 THE VOLUME THEKMODYNAMICS OF LIQUIDS. [BULL. 96.

of the tube to be calibrated. Opening the bottom of the tube A B (Tig. 

13) and closing the top, so as to hold the terminal D firmly in position, 

I inverted the tube and quite rilled it with the solution. The tube was 

then placed in a water bath with the terminal a insulated, and the terminal 1) replaced by the zinc wire referred to, and so adjusted that I 

could slide it up and down the central tube and fix it in any position. 

Measuring the distance between the ring G G (in this case, the neck was 

quite filled by the fitting terminal) and the free end of the wire with 

Grunow's cathetometer, and measuring at the same time the resistance 

corresponding to this length by means of Kohlrausch's Wheatstone 

bridge (§ 76), I obtained the data necessary for constructing resistance 

as a function of length for the temperature of the bath. In this way 

the second and third columns of Table 34 were investigated.

Combining the results of these four columns by graphic interpolation, I obtained the data of the fifth and sixth columns, in which volume is expressed in terms of resistance at 17-8° with regard to the 

fiducial mark in question.

TABLE 34. Volumes per unit of length. Calibration resistance per unit of length, 

0=17-8°. Volume per unit of resistance, Q=17-8°.

Length.

Cm. 3-00

1115

4-45 

9-79 

15-42

3-30 

7-20 

11-40

15-60

2-75 o-io

9-65

13-40

Volume.

Cm3 .

 0491

 1609

 0735 

 1430 

 2145

 0538 

 1076 

 1614

 2152

 0470 

 0940

 1410

 1880

Length.

Cm.

 06

. 2-13 4-75

12-06

1-38

6-18 

9-00 

11-49

 11 

2-78 

Air bul

Resistance.

Ohms.

2720

5780

10190

16200 

24340

4630

iy£\) 

12790 

18220 

23140

4«7Ol/

7050 

)ble error.

Resistance. 

0 17 -8°.

Ohms.

2800

5530

8850

12530 

16270 

20250 

24250 

28500

Volume. 

0=17-8°.

Cm3 .

 oooo

 0350

 0640

 0920 

 1190 

 1450 

 1705 

 1960

78. Electrolytic resistance and temperature. It is next necessary to 

express the variation of the resistance of the concentrated zinc sulphate solution with temperature. This is a general problem apart 

from the apparatus used. Nevertheless I made two sets of measurements, in the first of which I measured the resistance of the thread 

khj Fig. 13, between fixed terminals of zinc, when the whole was kept at 

successive constant temperatures and under pressure sufficient to keep 

the thread liquid and to thoroughly condense all polarization gases. 

The first four columns of Table 35 contains these results, all easily intelligible except the last column perhaps, where under RjRm the relative resistance referred to the resistance at 100° 0. is inserted. At 

100° the pressures were varied to. measure the pressure coefficients dis-
BARDS.] ZINC SULPHATE SOLUTION. 81

cussed in the next paragraph. In the second and third parts of the 

table the above tube was replaced by a plain straight tube. Eesistances are much smaller here, but the column JR/Rm makes both series 

comparable.

TABLE 35. Temperature coefficients and pressure coefficients of concentrated zinc sulphate

solution.

[First series. Length of thread 10.70cm or 8.7cm from fiducial mark. Diameter of tube .13 .]

Temperature.

°(7 

6-3 

6-5

66-8 

67-3 

68-0 

67-8 

67-8 67'7

100-0 

100-0 

100-0 100-0

100-0 

100-0 100-0

100.0 

100-0 

100-0

127-6 

127-8 

127-8

6-5 

6-3

Pressure.

Aim. 

100 

100

140 

140 

140 

140 

140 

140

137 

137 

479 

469 

1019 

996 

1507 

1443 

129 

139

158 

158 

158

1.16 

116

.Resistance.

Ohms. 

26960 

20960

6178 

6120 

6050 

'6061 

6075 

6075

4550 

4540 

4470 

4480 

4370 

«80 

4310 

4320 

4360 

4360

3740 

3730 

3730

27140 

27000

R/Rm

6-059 

6-059

1-388 

1. 376 

1-360 

1-362 

1-365 

1-365

1-023 

1-020 

1-005 

1-007 

 982 

 985 

 909 

 970 

 980 980

 840 

 838 838

0-100 

6-067

[Second series. Plain straight tube, 

diameter .30cm .

6-7

6-7

99-6

72 

465 

458 

906 

830 

498 

492 

139 

147

191

7280 

7090 

7120 

7020 

7020 

7130 

7050 

7190 

7160

1237

5-824 

5-672 

5-700 

5-616 

5-616 

5-704 

5-640 

5-752 

5-728

.990

Temperature.

°0

126-0 

120-0 

127-8 

127-8 

160.5 

160-5 

160-5

Pressure.

Atrn. 

186 

471 

448 

1011 

981 

503 

507 

126

357 

157 

149 

149 

154 

154 

154

Resistance.

Ohms. 

1242 

1222 

.1210 

H98 

3203 

1232 

1232 

1202

1002 

1062 

1.058 

1058 

980 

984 

984

R/ltm

 994 

 978 

 968 

 958 

 962 

 986 

 986 

1. 010

 850 

 850 

 846 

 840 

 787 

 787 787

[Third series. Same tube. ]

16-4 

16-4 16-4

6-4 

6-4 

6-4

61-3 

61-3 61-3

85-8 

85-8 85-8

99-6 

99-6 99-6

147 

147 

147

138 

138 

138

170 

170 

170

180 

180 

180

189 

189 

189

4980 

5000 

5020

7440 

7500 

7500

1900 

1900 

1913

1359 

1359 

1364

1247 

1253 

1253

3-984 

4-000 

4-016

5-952 

6-000 

6-000

1-520 

1-520 

1£30

1-088 

1-088 

1-091

1-000 

1-002 

1-002

If the values "jR/jRioo be constructed graphically, as a function of 

temperature for nearly the same pressures, the results of all the series 

in Table 35 are found to be in good accord. Moreover the results for 

the large interval 6° to 160° lie on a locus which in form closely resembles an hyperbola.1 From this point of view these data are remarkably interesting, for if this be true then a suitable inversion of the 

locus indicates that the electric conductivity of the electrolyte varies 

linearly with temperature. Such a result would not only possess 

theoretic interest, but would make measurements of the kind necessary

i Experiments recently made by Prof. Iddings and myself with diabase (See Am. Journal Sci., xuv, 

pp. 242 and 255) showed a geometrical progression of resistances to correspond to an arithmetical 

progression of temperature, caet. par. Thus the nature of the above locus is exponential.

Bull. 96 6
82 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

in the present paper feasible with, a high degree of certainty. I must 

withhold my opinion for the present, however, until I can trace the 

above locus as far as 300°, and the interpolations of this paper were 

made empirically.

79. Volume in terms of resistance. With the data of §§ 77 and 78 in 

hand it is now possible to express the volume of the capillary tube lik, 

Fig. 31, in terms of the resistance of the thread of electrolyte observed 

at any temperature. This is done in the next table, 36, where the temperatures, #, are those occurring in the tables of isothermals below.

TABLE 36. Relation of volume and resistance at different temperatures.

Volume.

Cm*.

 0000

 0350

 0640

 0920

 1190

 1450

 1705

 1960

Resistance.

6=63-5°.

Ohms.

1064

2101

3363

4761

6183

7695

9215

10830

fl=:83°.

Ohms.

818

1615

2584

3659

4751

5913

7081

8322

fl=90".

Ohms.

776

1532

2451

3471

4507

5609

6717

7895

0 = 100".

Ohms.

722

1427

2283

3233

4198

5224

625G

7353

0=>117°.

Ohms.

636

1255

2009

2844

3693

4597

5505

6470

0=130°.

Ohms.

608

1200

1920

2719

3531

4394

5262

6185

80. Pressure coefficient of the electrolyte. The divers results of Table 

35 for variable pressure and constant temperature are summarized in 

the small Table 37. Here 9 denotes the temperature and fc the pressure 

coefficient, which is negative in sign, showing that pressure decreases 

the resistance of zinc sulphate. The braces show the manner in which 

the means were taken, where Ic = 3 R/R0 dp. R is the symbol of resistance, p of pressure, and E0 holds at 0° (7.

o TABLE 37. Pressure coefficients.

6.

7"

100"

Pressure.

119) 

479^ 

868

157) 

482$ 

996

k X 103 .

i -43 

\ -35

) -64 

S -49

6.

100-

Pressure.

137) 

474> 

1007^ 

1475

fcXlQS.

) -43 

> -35

Mean k= - -000045

This table shows that the pressure coefficient is independent of temperature, and that it decreases somewhat with pressure. The results, 

however, are not quite consistent, and a graphic construction of the 

detailed results of Table 35 shows a differenceof march in the pressure 

"on" and the pressure "off" movements. I have yet to learn whether 

this be due to insufficient fixed terminals or to polarization, as well as 

to find conditions under which the pressure coefficient may be a minimum. As the results stand the mean value lc= 45/10G is probably

within 20 per cent of the truth, and hence in the extreme case of 2,000
BAUDS.] RESULTS. . 83

atmospheres the uncertainty of the pressure coefficient will not affect 

the volume increments more than 2 per cent.

I may add in passing that the value, investigated in an earlier paper,1 

between 0 and 150 atmospheres was found to be If = 50/106, agreeing 

pretty well with Table 37, and I there called attention to the strikingly 

close proximity of this datum to the corresponding coefficient for mercury, -30/10.2

The pressure coefficient is of considerable interest, inasmuch as it 

indicates a certain relation between elasticity and the chemical equilibrium of the solid or liquid operated on.2 Specially for zinc sulphate 

compression, which might be regarded as having a concentrative effect 

on the solution between the terminals, increases the conductivity, whereas 

the conductivity of a nearly concentrated solution (density >1.29) not 

under pressure decreases on further concentration.

The admixture of polarization with the pressure coefficient points out 

the nature of its instability.

RESULTS OF THE MEASUREMENTS.

81. Arrangement of the tables. The following Tables 38 to 43, in which 

the isothermals of naphthalene are fully given, are constructed on the 

same plan throughout. The first column contains the time in minutes 

at which the observation was made, the first date being arbitrary. The 

(unconnected) resistance as actually found at the pressure given is 

shown under R in ohms.* The factor lop is the correction for pressure 

coefficient to be added per unit of .72, after which this datum can be 

graphically expressed as a volume increment, referred as yet to an 

arbitrary fiducial zero in the way indicated in §§ 79, 80. To deduce 

from this the corresponding actual volume (last column of the tables.) 

the initial volume values of § 75 are available, relative to which further 

explanation will be given in § 83. Two data are given for each step of 

pressure, the second of which, obtained after long waiting, is more 

nearly isothermal than the first. The difference is not of seriously 

large magnitude. In most cases, after the volume has become solid, 

a small amount of additional volume decrement takes place viscously, 

or in consequence of gradual decrease of temperature immediately after 

solidification.

The experiments were made on different days and altogether extended over more than a week. This is somewhat too long a time to 

employ the tube without special readjustment, and some shifting of 

coordinates may thus have occurred (§§ 91, 92).

Parentheses occur in the following tables, to show that for the data 

inclosed the measurement was made along a part of the measuring 

tube lilt (Fig. 13), whose caliber is not adequately uniform. Without

'American Jour., vol. 40, 1890, p. 219. This paper was published some two years after the work was 

done. 

2Barus: Phil. Mag. (5th ser.), vol. 31,1891, p. 24 et seq.
84 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

knowing the full expansions at the higher temperatures and low pressures, it is, a priori, impossible so to fill the tube that all measurements 

fall within the calibrated parts and all other calibration conditions are 

complied with. (§§ 75 et seq.) These approximations, however, refer 

only to the liquid state, and are therefore of smaller consequence in 

this paper. (§67).)

1 may add finally that the melting point of naphthalene in air is 80°, 

its solidifying point below this; the density of the solid 1-14, and the 

.density of the liquid at 82°, -724. (§ 74.) Hence naphthalene, if melted 

in water, sinks or swims, according as its temperature is sufficiently 

below or above 80°.

82. Solid isothermal^ 63°. Since the naphthalene melts at 80°, the 

isothermal at 63° refers to the solid state. There must clearly be 

much greater uncertainty in operating on a substance when solid than 

when liquid. Indeed it is rather remarkable that the solid isothernmls 

are approachable at all. The liquid solidifies to a fissured or honeycombed structure, and it is therefore essential that the mercury should 

completely fill these interstices before the true compressilbility of the 

substance can be indicated. Similarly the error due to the compressibility, of the envelopes now becomes of much greater importance. 

It is thus solely by comparing these data with similar solid isothermals 

obtained at much higher temperatures and pressures that their validity 

may be inferred (§ 72).

TABLE 38. Isothermals of (solid) naphthalene at 6 = 63-5°, referred to 55cra:i at the

normal melting point.

Time.

in.

36

19

20

23

25

29

34

37

Pressure.

Atm.

70

68

289

281

491

481

675

662

B.

Ohms.

7600

7430

7760

7630

8160

8010

8050

7880

itpXlO3 .

3

3

13

13

22

22

30

30

Volume.

cm.3

 4127

 4156

 4085

 -4109

 4003

 4027

 4010

 4039

Time.

m.

38

40

42

44

46

49

51

67

Pressure.

Atm.

859

850

972

966

565

565

100

65

R.

Ohms.

8240

8120

8310

8310

7600

7600

7270

7340

fcpXlO'.

3!)

38

44

44

25

25

4

3

Volume.

cm.3

 3065

 3988

 :i945

 3945

 4U97

 4097

 4183

 4173

With regard to this series it is curious to note that the recoil of volume (pressure decreasing) is more rapid than the compression. The 

reverse of this would have been anticipated, supposing that mercury 

lodged in the interstices after compression. Finally I may state that 

telephonic resistance measurement, when the values are so high, is not 

unaccompanied by inappreciable errors. (§ 76.)

83. Liquid-solid isothermal, 83°. Table 39 contains three independent 

series of measurements, the last of which is fragmentary and the second obtained after the experience of the first, probably the best. The 

solidifying point is here very gradually approached and the locus shows 

an initial step of James Thomson's double inflections.

It is from these isothermals that I obtained the fiducial zero of the
1URUS.1 TROTTTERMALS AT 83° AND 90°. 85

measuring tube hlc, Fig. 13. For if R be constructed as a function of 

pressure it will be found that pressure zero lies at 00241' 1 " 3 of volume 

decrement. Hence the value of § 74 ( 5524( '"' :t) increased by this correction is the fiducial volume (-Sof) 01 " 1 ') here to be used and from thiw the 

others are derived as already explained. (§ 75.)

TABLE 39. Isothermals of naphthalene at 0:=83°, referred to J5cm3 at the normal melting point.

Time.

in.

-14

-10

_ 7

- 2

0

+ 7

10

10

18

20

Pressure.

Atm.

47

45

164

157

259

243

239

238

358

355

fcpXlO3 .

2

2

7

7

12

11

11

11

Hi

16

It.

*0hms.

938

938

1114

1100

1247

4406

5007

5007

5800

5800

Volume.

cm*.

 5490

 5490

 54 04

 5410

 53-10

 4432

 4141

 4142 410')

 4105

Time.

m.

22

28

HO

30

38

41!

40

51

fit

00

Pressure.

A tin.

175

179

110

120

81

86

86

33

30

37

fyXlO3.

8

8

5

5

4

4

4

1

2

2

It.

Olims.

5493

5493

5061

5173

4263

 4000

3762

2-1 4 8

923

910

Volume.

on,3 .

 4183

 4183

 4285

 4200

 4474

 4540

 4599

 4949

 1)498

' '5505

 SECOND SERIES.

36

39

44

46

51

53

59

60

63

64

73

75

39

226

221

250

244

267

265

303

322

317

299 '127

2

10

10

11

11

12

12

13

14

14

13

6

923

1183

1158

1223

1198

1232

1227

1288

1320

5007

5712

5250

 5493

 537'

 5382

 5355

 5305

 5318

 5351

 5322

 5300

 4138

 4128

 4241

79

81

87

91

9(i

97

104

115

12.)

.122

127

129

89

93

93

70

70

74

70

75

49

52

6

4

4

4

3

3

3

3

3

2

2

5250

4747

4348

4348

3651

3250

2031

1615

1480

920

905

 4241

 41)58

 -4453

 4453

 4G30

 4732

 5002

 5172

 5250

 5500

 5508

THIRD SERIES.

9

11

38

135

2

6

910

1032

 5504

 5444

I

21

23

131

345

0

15

1024

5450

 5447

 4184

84. Liquid-solid isothermal at 90°. Two independent series of results 

are given in Table 40. In consequence of slight variation of the artificial atmosphere, the temperature of the first °is somewhat below that of 

the second. Thus in series I there is some lack, of coincidence in the 

liquid "on" and a off" inarch, whereas the two are identical in scries n.

S 40. Isothermals of naphthalene at 6=90°, referred to 55CI" :1 at Hie normal inciting point.

Time.

m.

-10

-8

 0

 2

0

+5

7

20

22

27

28

Pressure

A ton.

83

83

257

238

434

425

549

527

445

44G

375

fcpx.101 .

4

4

12

11

19

19

25

24

20

20

17

E.

Ohms.

845

812

1049

1010

1247

1217

5250

5329

5211

5173

5100

Volume.

cm1

 5502

 5504

 5392

 5410

 5296

 5309

 4147

 4130

 41G3

 4172

 4193

Time.

in.

33

34

30

41

47

51

59

02

07

70

Pressure.

A t.m.

340

287

273

277

274

275

272

190

192

08

fcpXlO".

1C

13

12

13

12

12

12

8

8

3

R.

Ohms.

5055

441!.")

4051

3514

2969

 2077

 1950

923

923

790

Volume.

cm3

 -1205

 4357

 4455

' !597

 4730

 4831

 5042

 0457

 5157

 5532
THE VOLUME THERMODYNAMICS OF LIQUIDS. [*ui.t.. 06.

TABLK 40. Isothermal* of naphthalene at 0 = 00°, referred to SS''" 1 " at the normal meltiny point Continued.

SECOND SERIES, SAME ADJUSTMENT.

Time.

m.

.16

18

24

26

31

' 33

40

42

44

46

57

Pressure.

Atm.

57

231

222

422

406

490

474

507

532

555

544

ikpXlO3 .

3

10

10

19

18

22

21

23

24

25

24

R.

Ohms.

773

972

957

1188

1155

1247

1232

1258

1288

5250

5290

Volume.

cm3

 5542

 5432

 5439

 5322

 5338

 5293

 5302

 5292

 5276

 4147

 4139

Time.

in.

60

65

67

73

76

81

83

89

91

95

Pressure.

Atm.

316

322

280

283

283

278

175

179

81

83

A^XIO*.

14

14

13

13

13

13

8

8

4

4

It.

Ohms.

4618

4555

3855

2333

1985

1618

897

902

793

802

Volume.

C»l*

 4311

 4326

 4504

 4929

 5028

 5152

 5472

 5168

 5530

 5524

85. .Liquid-solid isothermals at 100°. Table 41 contains four independent series of results, together with some preliminary measurements. 

These are my earliest result with the above tube and are therefore in 

greater number. The liquid isothermals should be identical in the 

"on" and "off" marches. This is, as a rule, very nearly the case, the 

preliminary series and "on" march of the first alone lying below the 

others. In the latter the telephone used was more sensitive than in the 

orrner.

TABLE 41. Isothermals of naphthalene at 8 = 100°, referred to -55cmn at the normal meltIn <j point.

PRELIMINARY MEASUREMENTS.

Time.

771.

5

10

Ki

15

17

19

21

23

24

27

30

32

Pressure.

Atm.

170

1.70

384

355

593

558

630

610

051

688

196

176

fcpXlO3 .

7

7

7

16

27

25

28

27

29

31

9

8

R.

Ohms.

780

780

1006

984

1225

1209

1277'

1261.

1301

1330

812

783

Volume.

cm?.

 5499

 5499

 5307

 5380

 5255

 5264

 5232

 5239

 5221

 5204

 5480

. -5497

TUBE AGAIN ADJUSTED. FIRST

SERIES.

21

25

26

28

30

32

3335'

37

40

41 

43 

44

48

49

50

59

61

130

280

284

557

540

655

642

636

622

662

f\QO Woo

769 

759

875

862

856

843

720

6

13

13

25

24

29

29

29

28

30

01OL

35 

35

39

39

39

38

32

707

884

876

1169

1156

1296

1279

1274

1247

1307

iqoo

J O44

1405 

1392

4840

4720

4720

4720

4720

( 5545)

 5436

 5441

 5283

 5289

 5222

 5230

 5232

 5245

 5218

 5210 

 5172 

 5178

 4137

 4169

 4169

 4170

 4177

Time.

m.

C6

08

70

74

78

81

83

88

97

100

102

104

107

109

. 112

117

120 

122

125

128

129

131

132

125

137

139

140

142

144

145

Pressure.

Atm.

720

631

633

623

611

600

595

593

592

587

561

556

553

549

545

544

542 

503

499

497

461

458

417

413

358

358

296

296

87

87

fcpXW.

32

28

28

28

27

27

27

27

27

26

25

25

25.

25

24

24

e\t A'l

22

22

22

21

21

19

18

16

16

13

13

4

4

R.

Ohms.

4720

4420

4500

4420

4420

4370

4370

4280

4350

4350

3600

2840

2150

1530

1240

1120

1140 

1080

1068

1050

10 L9

1019

978

978

921

924

862

866

660

656

Volume.

cm*.

 4177

 4249

 4225

 4259

 42UO

 4274

 4274

 4296

 4278

 4279

 4483

 4708

 4915

 5127

 5250

 5307

 £OOQ DJVJo

 5327

 5335

 5343

 5360

 5300

 5381

 5381

 5414

 5432

 5449

 5447

( 5575)

( 5578)

SECOND SERIES. SAME ADJUSTMENT.

20

27

29

116

116

281

5

5

13

667

667

852

(-5575)

( 5575)

 5455
U. 6. GEOLOGICAL SURVEY

BULLETIN NO. 98 PL. IV

atm 

2000

FUSION ISOTHERMALS OF NAPHTHALENE. FIRST SET.
BARTTS.J ISOTHERMALS AT 100° AND 117°. 87

M. Tsotliermala of naphthalene at $=100°, referred to -55em*at the normal mdtiny point Continued.

Time.

in.

36

45

47

53

56

63

64

69

75

76

85

91

93

102

107

108

116

121

122

133

148

150

157

159 

165 

167 

168

109 

171 

173 

176 

178 

180 

184 

187 

208 

213 

216 

225 

227 

235 

237 

244

Pressure.

Aim.

274

460

670

653

795

766

808

797

780

818

813

785

850

850

820

908

888

890

921

914

906

769

772

644 

652 

560

562 

558 

558 

558 

558 

557 

552 

553 

553 

546 

429 

430 

287 

292 

81 

86

*xio..

12

21

30

29

35

34

36

36

35

37

36

35

39

38

37

41

40

40

41

41

41

35

35

29 

29 

25

25 

25 

25 

25 

25 

25 

25 

25 

25 

25 

19 

19 

13 

13 

4 

4

K.

Ohms.

835

1020

1223

' 1198

1331

1300

1353

1353

1336

1370

1370

1336

1415

1410

1370

1439

1439

1439

4814

4882

4882

4714

4714

4556 

4556 

3808 

3202

2846 

2279 

1889 

1600 

1416 

1300 

1174 

1160 

1158 

1160 

988 

992 

845 

852 

645 

650

Volume.

cm3.

 5404

 5360

 5255

 5266

 5204

 5219

 5195

 5195

 5202

 5185

 5187

 5202

 5107

 5169

 5185

 5155

 5155

 5155

 4141

 4125

 4124

 4175

 4175

 4224 

 4224 

 4425 

 459!)

 4707 

 4877 

 5000 

 5102 

 5175 

 5224 

 5280 

 5287 

 5288 

 5287 

 5375 

 5375 

 5459 

 5454 

(-5585) 

( 5583)

THIRD SERIES. SAME ADJUSTMENT.

7

12

15

20

22

28

31

38

41

47

87

88

274

267

489

476

666

649

837

820

4

4

12

12

22

21

30

29

38

37

653

653

838

828

1045

1008

1208

1220

1375

1359

(-5583)

(-5583)

 5462

 5468

 5345

 5365

 5262

 5256

 5185

 5191

Time.

in.

49

56

70

. 81

83

88

90

93

96

100

102

107

115

123

131

133

135

136

.138

189

141

143

Pressure.

Aim.

874

864

770

760

675

677

578

581

581

580

571

574

569

571

566

557

547

490

484

276

77

80

JtpXlO 3 .

39

39

35

34

30

31

26

26

26

26

26

26

26

26

25

25

25

22

22

13

4

4

E.

Ohms.

4814

4883

4814

4780

4714

4682

4000

3975

3608

3525

3255

2732

2390

2087

1829

1611

1380

1070

1033

835

631

638

Volume.

cm*.

 4143

 4126

 4149

 4159

 4181

 4187

 4371

 4377

 4480

 4503

 4581

 4739

 4845

 4934

 5018

 5097

 5189

 5333

 5351

 5404

(-5600)

( 5590)

FOURTH SERIES. SAME ADJUSTMENT.

6 

9 

13 

19 

21 

23 

33 

36 

42 

44 

50 

57 

59 

65 

67 

73

74

79

81

85

87

93

99

105

110

112

120

122

127

129

135

72 

72 

266 

257 

252 

451 

418 

689 

642 

818 

811 

853 

903 

900 

1018 

1005

879

865

690

694

575

581

549

549

539

488

484

294

295

89

97

3 

3 

12 

12 

11 

20 

19 

31 

29 

37 

36 

38 

40 

40 

45 

45

40

39

31

31

26

26

25

25

24

22

22

13

13

4

4

620 

622 

828 

805 

802 

1008 

957 

1247 

1169 

1353 

1331 

1364 

4882 

4917 

4988 

5024

4882

4814

4587

4587

4000

3785

1631

1165

1123

1041

1012

832

835

634

647

( 5605) 

( 5605) 

 5468 

 5481 

 5483 

 5365 

 5393 

.5243 

.5280 

.15194 

.5204 

.5188 

.4125 

.4115 

. 4089 

.4080

.4125

.4143

.4213

.4213

.4371

.4430

.5090

.5280

.5306

. 5347

.5363

. 5465

.5463

(. 5505)

(. 5585)

86. Liquid solid isothermals at 117°, Table 42 contains a series of 

results. The vapor bath in this case was filled with amyl alcohol, from 

which the water was not extracted. Hence the peculiarly broken 

isothermal obtained is in correspondence with the known inconstancy 

of temperature along the vertical. This feature is, however, of considerable interest, and throws light on certain characters of the other 

isothermals, inasmuch as it shows the behavior in case of partial solidification.
THE VOLUME THERMODYNAMICS OF LIQUIDS. [BTTLI, 96.

TABLK-12. Tuothermals of naphthalene, atQ = 117", referred to 5<5cin;! at the normal melting point.

Time.

m.

4

5

7

12

14

20

22

27

29

35

37

39

50

52

58

59

Pressure.

atm.

86

86

277

272

490

468

089

051

910

895

1092

 1080

1068

1254

1226

1326

kpXlW

4

4

13

13

22

21

31

29

41

40

49

49

48

50

55

60

JR.

ohms.

408

408

600

585

784

740

946

894

ll'JS

1097

2257

277)

2704

4208

4208

4203

Volume.

cm3 .

( -5709)

( -5709)

( -5547)

( 55i9) 5U1

 54H9

 5309

 5339

 5210

 5224

 4756

 4579

 4601

 4114

 4115

 4091

Time.

m.

64

66

72

75

81

84

90

91

95

97

102

103

! 107

109

115

Pressure.

atm.

1317

1055

1053

1051

1054

877

877

701

707

517

523

285

290

96

100

kp X 103

59

47

47

47

47

40

40

31

31

232'5

13

13

5

5

X.

ohms.

4263

3546

2448

2279

2175

1253

1198

953

938

760

765

565

572

412

414

Volume.

cm'.

 4094

 4325

 4692

 4749

 4786

 5149

 5174

 5307

 5*11

 5426

 5421

( -5571)

( -5561)

( -5699)

( -5699)

87. Liquid solid isothermals at 130°. Table 43, finally, contains four 

series of results obtained at 130°. The vapor bath in this case contained ainyl alcohol, thoroughly dried by copious distillations. Slight 

differences in the liquid "on" and "off" march are only apparent in 

the last series. The temperature of the third series, was about 129.6°.

TABLE 43. Isometrics of naphthalene at B=130°, referred to 55cm3 at the normal melting point.

FIRST SERIES. SAME ADJUSTMENT.

Time..,

TO.

32

34

36

42

46

52

50

61

65

70

72

79

85

90

94

102

105

111

114

119

fcpXlO3

7

7

22

21

45

45

63

63

76

70

63

03

63

63

45

41

25

24

7

7

Pressure.

atm.

151

146

496

461

998

978

1403

1379

1713

1686

1432

1438

1433

1423

1013

897

558

540

145

154

It.

ohms.

272

270

522

493

862

845

1119

1105

3808

3785

2600

1392

1326

1294

. 847

786

548

538

266

275

Volume.

cm3.

( 5821)

(-5821)

( 5566)

(-5591)

 5316

 5328

 5166

 5171

 4148

 4156

 4578

 5039

 5069

 5081

 5326

 5365

( 5546)

(-5551)

( 5821)

( 5810)

SECOND SERIES. SAME ADJUSTMENT.

5

7

11

14

18

35

37

57

59

61

63

G4

7

21

20

41

40

58

59

65

65

74

74

74

151

464

451

921

881

1338

1336

1464

1459

1581

3656

1651

276

495

484

808

770

1057

1057

1132

1132

1223

1278

1262

( 5811)

( 5586)

( 5601)

 5351

 5378

 5200

 5200

 5158

 5158

 5109

 5083

 5091

Time.

m.

65

68

71

76

78

84

86

96

98

106

113

123

125

131

135

139

141

145

148

153

JfcpXlO'

78

78

81

79

85

85

72

72

65

65

65

65

56

56

44

44

25

26

7

7

Pressure.

atm.

1737

1723

1794

1777

1907

1880

1574

1575

1463

1463

1458

1456

1245

1244

990

994

565

580

155

168

JR.

ohms.

1329

1320

3878

3926

3926

3950

3695

3695

2876

1690

1481

1490

1021

1021

845

850

505

570

275

289

Volume.

cm 5 .

 5057

 5061

 4119

 4106

 4099

 4091

 4190

 4190

 4480

 4914

 5000

 4996

 5220

 5221

 5327

 5325

( 551)6)

(-5531)

( 5811)

( 5796)

THIRD SERIES. SAME ADJUSTMENT.

9

12

.15

22

28

31

34

43

45

50

53

59

61

63

66

6

6

21

21

44

43

65

63

72

70

74

74

81

81

70

135

134

468

456

971

960

1467

1420

1579

1561

1605

1632

1794

1784

1564

263

263

517

504

845

825

1164

1114

1242

1212

3739

3762

3831

3831

3651

( 5831)

( 5831)

( 5571)

(-5581)

 5327

 5341

 5143

 51C8

 5101

 5116

 4173

 4166

 4135

 4135

 4206
U. S. GEOLOGICAL SURVEY BULLETIN NO. 98 PL. V

1000 1500 ,2000abm

FUSION ISOTHERMALS OF NAPHTHALENE. SECOND SET.
IUHU8.] DEDUCTIONS. 89

»

TA.IU/K 43. hornet rics of va-p'hihalene at Q = 130°, referred to '55 C111S at the normal inelliny point Con tinned.

Time.

m.

75

77

83

85

91

100

105

111

118

120

122

128

kp X 103

70

67

C7

63

63

63

47

47

26

26

7

7

Pressure.

aton.

1558

1484

1509

1412

1416

1412

1044

1044

576

584

146

160

E.

ohms.

3651

3405

3310

2334

1217

1198

855

865

560

560

266

279

Volume.

cm3

 4206

 4291

 4324

 4670

 5117

 5126

 5319

 5312

( 5536)

( 5531)

(-5821)

(-5801)

FOURTH SEEIES.

45

48

50

55

g

g

19

19

196

196

427

416

320

320

490

480

( 5769)

( 5769)

( 559.1)

( 5601)

Time.

TO.

57

63

67

72

74

' 8487

90

92

96

98

104

108

112

118

119

124

126

127

134

140

kp X 10'

28

27

36

36

45

43

54

54

65

63

74

72

72

54

54

39

39

22

22

7

7

Pressure.

aim.

626

611

801

789

1022

956

1215

1200

1432

1412

1634

1606

1603

1196

1199

859

862

498

503

151

160

R.

ohms.

653

634

770

755

930

845

1050

1033

1203

1174

1331

1320

1320

1029

985

755

765

515

525

282

290

Volume.

em3

 5465

 5479

 5379

 5389

 5276

 5329

 5206

 5214

 5123

 5139

 5059

 5065

 5067

 5217

 5240

 5387

 5381

(-557J)

( 5561)

(-5781,

( 5781)

DEDUCTIONS.

88. Graphic construction. To obtain a comprehensive survey over 

this series of individual data, it will be necessary to resort to the pictorial method and represent volume as a function of pressure, under 

successive conditions of constant temperature. Moreover it will be 

expedient to represent the whole group of first series on a single chart, 

the second series on another chart, etc., and thus obtain about four 

distinct sets of results, covering the whole interval 60° to 130°, and 

about 1,900 atmospheres. This has been done in Pis. iv, V, VI, and vn, in 

which the ordinates are volumes (the fiducial volume being the 5524CI1 '3 

at 80°, arbitrarily chosen), the abscissas are pressures, and in which 

the temperatures of the isotherinals are inscribed at the beginning 

and end of each curve. Finally the dates or times in minutes at which 

the individual observations were made are all given by small numerals 

attached to the points. Thus it is easy to know at once whether an 

observation was taken during the "on" march or the "off" march of 

pressure; but to farther facilitate inspection arrows are subjoined to the 

contours of the curves, showing their drift. It is seen from the figures 

that the solid seems to be comparable as regards compressibility with 

the liquid, but on this point I shall not now lay much stress, for reasons repeatedly stated in the above paragraphs, §§ 70, 82.

89. Hysteresis. The inherent 'character of all these curves is pronouncedly cyclic. The isothermal pressure necessary to solidify naphthalene being at all temperatures decidedly in excess of the pressure at 

which it again liquefies. Then the results which I obtained in other experiments and with other substances some time ago l are thus eniphat1 Am. Jour. Sci., vol. 38, 1890, p. 408. The full paper and the deductions there made are as yet unpublished.
90 THE VOLUME THERMODYNAMICS OF LIQUIDS. [p. ,. DO.

ically corroborated. Evidences of the thoroughly static character of 

these phenomena are abundant and obtained by observing the times 

of successive points. I need only mention solid isothermal, 100° PI. iv, 

where I waited from 50m to 100m at a pressure below the solidifying 

point of the liquid without obtaining fusion; whereas after this with 

only a slight further reduction of pressure fusion sets in and is complete between 101m and 112ra ; liquid isothermal, 100°, PI. v, where I 

waited from 47m to 121m at a pressure greater than that at which fusion 

of the solid takes place without obtaining solidification, which, however, sets in at once (121m 122m ) when the pressure interval is only 

slightly increased; same plate solid isothermal 130°, I waited from 86m 

to 96m at a pressure below the solidifying point without any change of 

volume or fusion whatever; solid isothermal, 130° PI. vi, where I waited 

from 66m to 83m without obtaining fusion, and from 66m to 75 m without 

appreciable change of volume; liquid isothermal, 100°, PI. vii, where 

I waited from 36m to 90m without obtaining solidification, and from 741U 

to 87m on the solid isothermal without obtaining fusion, etc. If high 

temperature conditions are unfavorable to lag, the results at 130° are 

specially good evidence in favor of the point of view taken. I have 

already pointed out 1 that it is a phenomenon inherent in the passage 

from one molecular condition to another which lies at the root of all 

manifestations of hysteresis, whether observed electrically (Cohn, Ewing, Schumann) or magnetically (Warburg, Ewing), or as a purely mechanical result in my work,2 during fusion, as above, during solution, 

§ 95, etc.

90. James Thomson's double inflections. Solidification almost always 

sets in at once. This is what one should expect, for, if there be condensation or crystallization at any point, it will form a nucleus for which 

the whole column will be solidified. Only in one case (PI. v, liquid 

isothermal 83°, 60 to 63ra ) did I obtain evidences of curvature, whereas 

in PI. iv, at the same temperature, the whole path, though observable 

(Om, 7m, 10m), is precipitous.

The reverse of this holds true in case of fusion. Here the initial 

or stable contours of James Thomson's circumflexures are always 

marked. It is true that fusion rarely takes place instantaneously, because of the difficulty in supplying heat fast enough. Hence it might 

be plausibly argued that the fusion contours are necessarily more gradual than the solidification contours. It is also supposible that, if temperature be not quite identical throughout the height of the column of 

substance, fusion will first take place at the hotter planes below and 

proceed thence to the top. This state of things I have actually observed in glass capillary tubes when the vapor baths were imperfect. 

In the present experiments, however, the phenomenon occurs with the 

same uniformity at all temperatures and is quite as pronounced in a

1 Am. Journal, 1. c.; Phil. Mag. (5), vol. 31, 1891, p. 27.

2 Chapter in, above.
I). 8. IDEOLOGICAL SURVEY BULLETIN NO. 98 PL. VI

35cc atm atm 

1000

atm 

1500

atm 

2000

FUSION ISOTHERMALS OF NAPHTHALENE. THIRD SET.
1UTUJS.] CHARACTERISTIC VOLUMES. 91

steam bath. Moreover the column is not above 10om long. Hence, 

taking this into account in connection with the evidence cited in the 

foregoing paragraph (89), I conclude that the initial solid contours are 

static, and hence regard them as evidencing James Thomson's 1 wellIs nown inference relative to the doubly inflected contours of the isothermals accompanyin g change of physical state. When fusion actually 

sets in the phenomenon is no longer observable, for the physical parts 

of the substance now exist in widely different thermal states.

Here I may expediently point out the advantages gained by operating in a thin shell of substance (see Fig. 13 and PL in), the heat 

Avithin which is rapidly dissipated. The conditions, therefore are specially favorable for isothermal work.

91. The characteristic specific volumes. Mere inspection of the charts,, 

Pis. IV to VII, shows that the volume at which solidification takes place 

decreases with temperature, and the volume after solidification either 

increases or remains stationary in value. In Table 44 I have inscribed 

the corresponding values of pressure and volume, observed at the solidification points, in each of the four series; and in PI. vin these data 

have been plotted, volumes being the abscissae and pressures the ordinates. To distinguish the points they are surrounded by little circles 

to which the number of the series is attached, and the pressures are 

given on the right side of the diagram.

TABLE 44. Volumes solid and liquid at the solidifying points, varying with the pressure.*

Series.

'M

IT. £

IT r. | 

,T.{

Temperature 83°.

Solid 

pressure. 

Solid 

volume.

260 

 415 

320 

 415 

345

Liq iiid 

pressure. 

Liquid 

volume.

260 

 534 

320 

 530 

345

Temperature 90°.

Solid 

pressure. 

Solid 

volume.

550 

 413 

555 

 415 

550 418

Liquid 

pressure. 

Liquid 

volume.

550 

 523 

550 ' -527

Temperature 117°.

Solid 

pressure. 

Solid 

volume.

 415

Temperature 100°.

Solid 

pressure. 

Solid 

volume.

875 

 416 

920 

 413 

870 

 413 

900 412

Liquid 

pressure. 

Liquid 

volume.

875 

 510 

920 

 515 

870 

 510 

900 517

Temperature 130°.

Solid 

pressure. 

Solid 

volume.

1720 

 415 

1790 

 412 

1665 

 417 

1720

Liquid' 

pressure. 

Liquid 

volume.

1720 

 505 

1700 

 505 

1665 

 507 

1720 505

* See remarks on Table 46.

A similar and equally important table may be deduced by finding 

the values of the characteristic volumes at the successive 

points. These are inscribed in Table 45, on the plan of Table 44.

melting

> J. Thomson: Phil. Mag. (4), vol. 42, 1872, p. 227.
92 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 90. 

TABLE 45. Volumes solid and liquid at the melting points, varying with pressure.*

Series.

«f 

 {

'{

Temperature 83°.

Solid 

pressure. 

Solid 

volume.

80 

 435 

80 450

Liquid 

pressure. 

Liquid 

volume.

80 

 547 

80 548

Temperature 90°.

Solid 

pressure. 

Solid 

volume.

275 

 425 

280 440

Liquid 

pi'essure. 

Liquid 

volume.

275 

 540 

280 541

Temperature 117°.

Solid 

pressure. 

Solid 

volume .. 

Liquid 

volume.

1050 ) 

 430 £ 

 515 >

Temperature 100°.

Solid 

pressure. 

Solid 

volume.

560 

 440 

560 

 435 

580 440

570 440

Liquid 

pressure. 

Liquid 

volume.

560 

 528 

560 

 531 

580 528

570 531

Temperature 130°.

Solid 

pressure. 

Solid 

volume.

1430 

 435 

1465 

 4UO 

1410 440

Liquid 

pressure. 

Liquid 

volume.

1430 

 515 

1465 

 515 

1410 517

* See remarks on Table 46.

If these data be inscribed in a chart like PI. vm, both the solid and 

the liquid volumes will closely resemble the curves already mapped 

out for solidifying point; but since the solid volumes can obviously 

only be approximately given, and since the liquid volumes contain no 

new feature, I omit them to avoid confusing the figure.

A noticeable part of this diagram is the close accordance of the three 

groups of points between 0 and 1,000 atmospheres, during which, measurements vapor of water was the medium of constant temperature, as 

compared with the one group of points between 1,000 and 2,000 atmospheres, where vapor amyl alcohol was used. I account for this by 

supposing the solidification in the latter case (130°) to have been premature, a result to be associated with insufficient constancy of the 

vapor bath (§ 70, 86, 89), hence the liquid volumes found are too large. 

There may, however, have been some gradual change in the contents 

of the tube, which in the lapse of time became appreciable (§70, 81). 

Thus the zinc gradually deposited by the intermittent currents in the 

mercury, the possible detachment of the end of the mercury thread in 

Me (Fig. 13) after repeated motion back and forth, changes in the 

quality of the solution of zinc sulphate, etc., woiild produce a shifting 

of the volume constants and a result like that observed in PI. vni. 

Further experiments must decide this point. Regarding the solid volumes, it is clear at once that no device can define them as accurately as 

the liquid volumes, and the degree of coincidence attained is one of 

the valuable accomplishments of the present method.

To summarize, therefore, I have in PI. vin placed chief reliance on 

the water points (0 to 1,000 atmospheres) and drawn the locus accordingly.

92. Critical point. The area inclosed by the figure a b . . . c d, supposing 1) and- c eventually to coalesce, has the same signification as 

Andrews' area of vapor tensions. The same would be true of the similar figure for the characteristic volumes at the melting points, or
U. S. GEOLOGICAL SURVEY BULLETIN NO. 86 PL. VII

a-tm 

1000

FUSION ISOTHERMALS OF NAPHTHALENE. FOURTH SET.
BAUDS.] SOLIDIFICATION AND FUSION. 93

finally to the figure in which the solidification volumes are taken at 

the solidification points, and the fusion volumes at the melting points. 

All of these diagrams point out the probable occurrence of a critical 

point in the region of positive pressure and reached in the direction of 

increasing temperature, at which point liquid would pass to solid or 

solid to liquid without paroxysmal change of volume, and consequently 

without volume log. This position of this point may be conjectured to 

lie at several hundred degrees centigrade and several thousand atmospheres, naphthalene being the material operated on.

93. Solidifying points and melting points. The cycles as depicted in 

Pis. iv to vii have two prominent characteristics: They gradually decrease in vertical extent from left to right, and they gradually decrease 

in lateral extent toward both sides of the chart. Each of these qualities 

throws important light on the phenomena as a whole.

Table 46 gives the numerical values of the pressures corresponding 

to solidification and to fusion at the different temperatures, together

with other information of importance, as sharply as the statement can 

be made. Let the solidifying points and the melting points be constructed as a function of pressure. This is done in PL vin, and the 

points form a long spindle-shaped figure running diagonally across the 

chart. Points obtained from all the four sets of results (Pis. iv to vn) 

are inscribed and these points are numbered to show the series to which 

they belong. The parts of the curves actually observed are given in 

full lines and the inferential prolongations in dotted lines.

From the nature of the case the solidification points can not be 

sharply measured. (§ 89.) Thus, if the temperature of the column be 

not .uniform, (and incase of an ebullition liquid of small specific heat 

and possibly not homogeneous in composition, the tube is sure to be 

hotter at the bottom than at the top), the colder parts will solidify first, 

and at once induce solidification throughout the whole length of the column. This is markedly shown in the isothermal for 117°, and given in PI. 

vii, where the solidifying and fusing points are practically in coincidence. (§ 86.) Similarly all jarring and percussion, too rapid increase 

of pressure, a vibratile wire running through the column as in some of 

my earlier work, etc., will cause the whole labile framework to topple 

into solidification. Hence the solidifying point must be fairly crept 

upon and surprised, as it were, and hence my present results, in which 

these precautions were taken, show high solidifying points as compared 

with my other work. These conditions do not seem to hold in like importance in case of fusion, for the melting points, as a rule, show much 

greater coincidence.
94 THE VOLUME THERMODYNAMICS OF LIQUIDS. [BULL. 96.

TABLE 46. Shoiving the relation of solidifying point andof'melting point with pressure. 

Naphthalene.

Series 

No.

I ......

II .....

Ill ....

IV.....

Temperature 63°.

Solid 

at 

Atm.

Fusing 

at 

Atm. 

(a)

Temperature 83°.

Solid 

airAtm. 

&260 

0320 

e345

Fusing 

at 

Atm. 

c80 

80

Temperature

90°.

Solid 

afrAtm. 

ef)50 

d555

Fusing 

at 

Atm.

d 275

Temperature

100°.

Solid 

at 

Atm.

0875 

ri920 

7(870

( Factor: Melting point and pressure 80° to 130°, 

k < Factor: Solidifying point and pressure 80° to 10 

(Factor: Solidifying point and pressure, 100° to

Fusing 

at 

A tin. 

d560

d 58'.) 

(Z57U 

28-5 atm 

30, 36-0 a 

130°, 29'5

Temperature

117°.

Solid 

at 

Atm.

;1090 

. °C., o 

tm./°C 

atm./°

Fusing 

at 

Atm.

J1050 

r -0351 °( 

, or '027£ 

C. ,or-033

Temp

Solid 

at 

Atm. 

e!720

 i 16(i5 

cl.720 

3. / atm 

°0./1 

91°C.

erature

Fusing 

at 

Atm. 

/1430 

/14G5 

/1410

itm . 

/I atm.

a Negative.

6Not crept upon. First result at <83°, second and third at >83°. Solidification gradual; other 

solidificatiouH take place at once.

c Fusing very viscously throughout a pressure interval of 50 atmospheres.

d Crept upon.

e Not crept upon.

/Fusion relatively rapid; more-nearly resembling the solidification inarch than is the case at lower 

temperatures.

g Crept upon. First result at < 83°, second and third at >83°. Solidification gradual; other solidiflcations take place at once.

h Intermediate between a and b.

i Intermediate between a and b. Temperature, 129- 6°.

j Temperature lower at top than at bottom of the column. Partial fusions. Vapor bath containing 

aqueous amyl alcohol.

k Chief!y with reference to Series n.

In drawing PI. vni I have therefore placed chief reliance on the data 

of Series n, obtained as they were with the experience of Series i, to 

guide nie. The horizontal breadth of the spindle-shaped area indicates 

the pressure amount of volume lag corresponding to any temperature.

94. Transitional point. If the two curves be prolonged in the direction of increasing temperature, it is clear that they must eventually 

coalesce. For, at the critical temperature, liquid will pass to solid and 

vice versa without paroxysmal change of specific volume, and hence 

there can be no volume lag.

If the curves be prolonged in the direction of decreasing ternperature, 

then the data emphatically indicate the probable occurrence of an intersection in the region of negative pressure. Beyond the point of intersection the substance would solidify at a lo\ver pressure than that at 

which it fuses, and fuse at a higher pressure than that at which it solidifies. I believe this observation may be interpreted as follows: The 

normal type of fusion changes continuously into the ice type of fusion, 

through a transitional type characterized by the zero of volume lag. 

The position of this transitional type for naphthalene, so far as I can 

now discern it, may be placed at, say, 50° and 1,000 atmospheres. It 

may be noted that with the understanding here laid down, the normal 

type of fusion is reached from the ice type in the direction of increasing temperature.

Throughout the present chapter I have avoided the discussion of the 

isopiestics, since I shall consider them in detail in connection with 

special experiments. It is well to state, however, that the transitional 

temperature is related to the prospective intersection of the prolonged
U. S. GEOLOGICAL SURVEY

5000

BULLETIN NO. 98 PL. VIM

44CC 46 CC 52°° 54*°

DIAGRAM SHOWING THE CONDITIONS OF FUSION AND SOLIDIFICATION.
BABUS.] TEANSITIONAL POINT SOLUTION. 95

liquid and solid isopiestics, of a given substance, at the same pressure 

in both cases. Thus a reason why hysteresis may vanish is again suggested. A given substance on one side of the transitional temperature 

need not necessarily differ niolecularly from the same substance on the 

other side.

Practically only one of the states is attainable, for the other implies 

an application of negative pressure.

If the chart, PI. iv, is to represent in diagram a field of isothermals 

for the ice type, the solid and liquid phases of the chart are to be exchanged. The solid march for the ice type takes place along loci of 

greater specific volumes and the liquid march along loci of smaller specific volumes. Thus the chart of isothermals must show intersecting 

loci, identical points corresponding, however, to different molecular 

states. In other respects the character of the figure need not be modified, supposing always that increase of temperature and pressure be 

taken in the algebraic sense, so that negative quantities are included. 

Beyond the transitional point I am therefore tempted to look for the 

proper critical temperature of the ice type in a region of positive external pressures and in the direction of decreasing temperatures.

Thus, curiously enough, the observer is confronted by periodic relations, which in all probability will admit of a chemical interpretation. 

(§§ 05, 96.)

95. Solubility and pressure. In view of the detailed analogy which 

holds between many characters of fusion and of solution, much that 

can be investigated for the simpler of these phenomena (fusion apparently) will be applicable to the other. A substance may be transferred 

from the solid to the liquid state either by heating it or by dissolving 

it. In general, excess of temperature or of solvent favor the diminution of viscosity here in question. A liquid on the verge of solidification or a concentrated solution is solidified or deposits crystals on 

cooling; and in both cases the nice adjustment of labile molecular 

equilibrium is accompanied by volume hysteresis, undercooling, etc., in 

the one case, supersaturation, etc., in the other. Hence I conclude 

logically, I think, that if under proper thermal conditions pressure 

alone can solidify a liquid, it can also under proper solutional conditions induce crystallization, or the deposit of solid from solution.

I am the more justified in drawing these references, as in my article 1 on the solvent action of hot water on glass I already adduced 

the necessary evidence. Since from one point of view the isothermal 

compressibility increased proportionally to the time during which the 

solvent action has been going on, and from another, with the amount 

of silicate dissolved, to more than three times its original value, the inference is pretty closely at hand that what pressure did in this instance 

was a mere precipitation of a proportionate amount of dissolved silicate. The volume change thence resulting were put into computation

'American Journal, vol. 41, p. 110,1891.
96 THE VOLUME THEEMODYNAMICS OF LIQUIDS. [BULL. 96.

as increments of compressibility, for the precipitated silicate is again 

dissolved when pressure is withdrawn.

Thus the present work bears upon the nature of solution, for I can 

not believe that what I have ventured to call cohesive affinities' can 

not differ, except in degree, from the affinities which determine 

valency. At least, proceeding on such an assumption, I am lead naturally to a theory regarding changes of physical state which I will indicate elsewhere.

Finally, in justice to myself let me say that the manuscript left my 

hands before the kindred deductions of Orme Masson 2 or of Bainsay 3 

had reached me. In fact, what these gentlemen have deduced from 

the solution behavior liquid-liquid I had legitimately derived from the 

solution behavior solid-liquid, as set forth in my own work. My preceding paper was at fault only in postulating an unnecessary change 

of hydration of the silicated water (loc cit., p. 116).

It is gratifying to note that evidence of the similar solution behavior 

solid-solid is forthcoming, and to be found in the work of Osmond, of 

C. A. Carus-Wilson,4 and of myself, as I have already pointed out.5

CONCLUSION.

96. In the above pages I have merely endeavored to describe the results directly obtained by experiment, and to draw such conclusion, 

which, in tlie light of known facts, seemed to be admissible or even obvious. In view of the detailed analogy which holds between many 

characters of fusion and of solution, I believe that much that can be 

investigated for the simpler of these phenomena (fusion) will be applicable also to the other. How far the above conclusions as a whole are 

to stand or fall will depend on similar investigations, which I shall continue to make with a variety of other substances specially selected with 

reference to their position in a scale of thermal state. How such selection is to be made I am now unable to surmise. Substances, for instance, which fuse continuously, like glass or sealing wax, might at first 

sight beQconjectured to lie near their critical points, but I believe these 

cases are mere solution phenomena of relatively small interest. At all 

events the experiments must deal with substances of definite and preferably crystalline character and not with mixtures. I feel confident 

that in an examination of many types some will be found lying relatively nearer the critical point, while others lie nearer or even beyond 

the transitional point; and that if the above method be applied with 

greater rigor than was done in the present paper light will be thrown 

on the long-neglected department of fusion thermodynamics. From

'American Journal, vol. 41, p. 115.

2 Masson: Nature, vol. 43,1891, p. 345.

3 Kanisay: Nature, vol. 43,1891, p. 589.

« C. A. Carus-Wilson: Phil. Mag., vol. 29, p. 200.

«Barua: Phil. Mag., vol. 31,1891, pp. 26-28.
BARUS.) ___ RECURRING HYSTERESIS. 97

this stage of progress it will then be possible to approach nearer the 

next of the kindred phenomena, which I conceive to be nothing less 

than the kind of hysteresis or higher order of volume lag commonly 

known as chemical affinity.

To obviate the occurrence of a bald statement like the last, I will indicate my views on the distribution, or successive orders of volume lags. 

These are to be sought I, during the passage of a given atom into 

the next consecutive in a scale of decreasing atomic weights; II, during the occurrence of dissociation of the molecule, including solutions 

gas-fluid. They are demonstrable, HI, the region of Andrews's 

vapor tensions, including the Alexe*ef-Masson solutions liquid-liquid; 

IV, in the region of the solid-liquid phenomena of the present paper, 

including solutions solid-liquid; Y, in the region of solid-solid phenomena categorically distinguishable as "permanent set" (Osmond, CarusWilson, Barus). They are to be sought for finally, VI, during the passage of a given atom into the next consecutive in a scale of increasing

atomic weights.

The enumeration is systematic, and inasmuch as VI is virtually identical with I, the inherent nature of these changes is periodic. Hence, 

under suitable thermal conditions and continually increasing pressure, 

the evolution of atoms, of molecules, of changes of physical state, are 

successive stages of periodically recurring hysteresis. 

Bull. 96 7

INDEX.

Affinity, chemical, relation to hysteresis. 97 

Air thermometer comparisons ...... 47,50

Alcohol, isometrics of....... 44,53

Amagat, manometreof...............-.17,32,63

on compressibility of glass and of 

mercury...___... .. .... 78

Andrews's screw compressor............. 17,82

Bibliography of isometrics........... 60

for melting point and pressure....... 71

Bourdon gauge....................23,25,26,63,64

helical.................................. 29,30

mechanism of.......... .. 65

theory of................. ...... 67

Calibration of fusion tube ......... 79

Carus-Wilson, experiments of............ 96

Compressibility of glass.._........ 55

of organic liquids ..._....... .... 55,56

of glass and of mercury........ . 78

Constants of fusion tube.................. 77

Continuity of solid and liquid.. _ ___ 71 

Corrections for volume changes of glass 

tubes............... ................... 57,78

Criteria for fusion _........ .. 71

Critical points..,.......................... 92,96

Curvature of isometrics ...... ..... 58,59

Cycles in gauge comparisons.... 25,27,64,66,67

Data for fusion under pressure .......... 92,94

Desgoffe, differential manometer of ..... 17

Diphenylamine,isometrics of...._..... 45,54

Dupre" on isometrics... ...... 60 

Electrolytes, temperature and pressure 

coefficients of............................ 82

Ether, purified .................. ....... 42

isometrics of .....................38,41,42,51

Expansion (thermal) of glass............ 54

Frauuhofer micrometer............_.. 66

Fusion under pressure, methods of..._ 72,77 

tube for... .. ..... . 74

data for................................ 92,94

Fusion tube, constants f or ........ i...... 77

Fusion, types of......................__ 94

Galvanometer, torsion........ ...._.. 46

Gasket of marine glue.................... 18

Gauge comparisons, cyclic .. __25,27,64,66,67 

summary ......_. 69

Gibbs, notation of......................... 33

Glass, thermal expansion of.....___ 54

compressibility of ........__.... 55

isometrics of.._..._...__.. 55,61

dissolved by hot water .._.._. 95

Grunow, cathetonieter of...__...... 80

Page. 

Hannay and Hogarth, screw compressor

of......................................... n

Hysteresis, in gauge comparisons ___ 66

on fusion and solidifying ... 89

bibliography of............... 90

recurring orders of.._..... 97

Ice type of fusion.......................... 94,95

Iddings on fusion of diabase. _ _ ___ 81

Isometrics, liquids .. _.__.. _.. _ 33

ether......'...... ..................38,41,42,51

alcohol................................. 44,53

toluidine............................... 45,54*

diphenylamine........................ 45,54

thymol....._....._......._.__.. 45,53

corrected..........._............__ 51

curvature of......................_ _ 58

initial slopes of.._..........._._ 59

bibliography of..___...;.._ 60 

glass..................................... 55,61

Isopiestics, relation of, to transitional 

point..................................... 94

Isothermals of solid naphthalene ...._ 84

of solid-liquid naphthalene ...85,86,87,88,89

of naphthalene, charts for. _. _. _ 89

Kopp'svolume flask_.._..._.._ 73

L6vy on isometrics ..___.....__ 60

M-inometre of Amagat_..............18,32,63

Marine glue, gasket of __..._..._. 18 

Masson, views of......_.._........... 96

Melting and.solidifying points ........... 93

Methods for studying fusion under pressure .._...............________ 72,77

Mousson, compressor of....._...__ 32

Naphthalene, isothermals of ..84,85,86,87,88,89 

Notation of Gibbs, Ramsay and Young, 

etc... ....... .. .......... 33

Periodic relations..__._.___.... 95

Piezometer......................._.20,21,37,74

fully adjusted...................._... 77

"Piston libre" ............................ 70

Pressure, high,measured....___. 17

internal............................_. 61

reducer of ............ ...__ 70

coefficient of electrolytes. _ _ __ 82 

effect of, on solution..........__. 95,97

Ramsay and Young on isometrics.. __ 60 

views of............................_ 98

Resistance, how measured.__..__ 79 

electrolytic relation to temperature 

and pressure..____.__...... 80
100 INDEX.

Page. 

Screw compressor of Andrews...... . 17

of Hannay and Hogarth _...4....... 17

for high pressures .... . ...... 18,31

Slopes, initial of isometrics ......._ 59

Solidifying and melting points. .. 92 

Solution under pressure._._.._ 95,97 

Steel tube cold drawn, weldless.___. 20 

Taitdescribes Amagat's manometre..... 18

gauge Of.................22,23,25,26,32,63,67

on elastics of tubes ........._.... 29

Tinned screw............ . . 18

Temperature coefficient of electrolytes.. 82 

Thomson, James, double inflections of.. 90 

Thymol, isometrics of............__... 45,53

Toluidine, isometrics of .................. 45,54

Page-. 

Torsion galvanometer........_._.... 4$

Transitional point related to Isopiestics. 94 

Tube of constant volume _____...... 3&

Tubes, glass, corrections for ...____. 57,78 

Tube for fusion under pressure _... . 73,74 

Types of fusion.__...__......_ . 94

Vapor baths .'......................20,36,47,48,73:

Volume flask of Kopp........ . . 73

Volume of tube in terms of electric resistance _...___ ___._.... 821

Volumes, characteristic specific_. __ 91 

Volume lag, successive orders of . .. 97 

Young. See Ramsay. 

Zinc sulphate solution, thermal and pressure coefficients of....................... 81