DEPARTMENT OF THE INTEBIOB

BULLETIN

UNITED STATES

GEOLOGICAL SURVEY

No. 93

WASHINGTON

GOVERNMENT PRINTING OFFICE 

1892
.l/}
UNITED STATES GEOLOGICAL SURVEY

j. w. POWELL, IUREUTOK

THE

COMPRESSIBILITY OF LIQUIDS

BY

CA.KL BA.IUJS

WASHINGTON

GOVERNMENT PRINTING OFFICE

1892

CONTENTS.

Pnro.

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

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

Chapter I. Fluid volume: Its dependence on pressure and temperature....... 17

Introduction:........................................................... 17

Literature of compressibility........................................ 17

Literature of heat expansion ........................................ J!)

Remarks 011 the literature. .......................................... 20

Apparatus.............................................................. 20

Force pump and appurtenances...................................... 20

Pressure tube and appurtenances.................................... 20

Method of charging the tube........................................ 21

Method of heating ....................................... ........... 22

Pressure measurement .............................................. 23

Volume changes of the glass tubes .................................. 25

Mercury tests....................................................... 25

Isothermals and adiabatics........................................... 20

Thermal expansion.................................................. 27

Experimental results.................................................... 28

Explanation........................................................ 28

Ether .............................................................. 28

Alcohol............................................................. 30

Palmitic acid....................................................... 32

Para-toluidine...................................................... 33

Diphcuylam ine ..................................................... 34

Capr in ic acid ....................................................... 35

Ben zoic acid........................................................ 35

Paraffiu ............................................................. 36

Thymol............................................................. 37

Naphthalene........................................................ 40

Method of discussion.................................................... 42

Plan pursued ....................................................... 42

Quadratic constants ................................................ 42

Compressibility increasing inversely as the pressure binomial ........... 43

Transition to exponential constants ................................. 43

Properties of the exponential eq nation .............................. 44

Exponential constants computed .................................... 4G

Mean exponential constants derived.................................. 48

Subsidiary results .................................................. 49

Isotherinals computed............................................... 50

Isometrics .......................................................... 5-1

Digression on thermal expansion ........................................ 55

Exponential equation proposed'...................................... 55

Observed contractions due to Cooling uin'.;;r press ir.v................. 5G
6 CONTENTS.

I»ag6.

Chapter I. Fluid volume: Its dependence on pressure and temperature Continued.

Compressibility increasing inversely as the second power of the pressure

binominal ........................................................ 61

Properties of the hyperbolic equation ............................... 61

Presumptive character of the isometrics............................. 62

Hyperbolic constants computed ..................................... 63

Mean hyperbolic constants derived.................................. 64

The isothermal band...............................................: 65

Conclusion ...............................-..........:.............. 6§

Chapter II. The effect of pressure on the electrical conductivity of mercury. 68

Introductory ............................................................ 68

Purposes of the work ............................................... 68

Literature.......................................................... 69

Simple methods and results ............................................. 69

Cailletet's tubes described .......................................... 69

Electrical apparatus ................................................ 70

Preliminary data ..................................................... 70

Correction for volume changes of tube .............................. 71

Preliminary result stated............................................ 71

Piezometer methods and results ......................................... 72

Tubular piezometer described....................................... 72

Results............................................................. 73

Deductions ............................................................. 74

Purely thermal variation of resistance............................... 74

Comparison with J. J. Thomson's equation .......................... 75

Zero of resistance................................................... 75

Lleelrical pressure mo.0.s:uv;!U'nt .................................... 7~>

Measurement of molting point and pressure,.......................... 7(5

(,'oue.lusion ......................................................... 76

Chapter 111. The compressibility of water above 100° and its solvent action on

glass ...................................;............................. 78

Introduction............................................................ 78

Behavior of water................................................... 78

Literature. Compressibility of water............................... 78

Literature. Solvent ae.tion of water ................................ 79

Method of measurement and results ."............................:....... 79

Apparatus.......................................................... 79

Low temperature, data .............................................. 80

High -temperature data.............................................. 80

Discussion of these results .......................................... 81

High temperature measurement repeated............................ 82

1 )iscussiou of these results .......................................... 82

Conclusion ........................... ............................... 83

Chapter TV. The solution of vulcanized iudia rubber ........................ 85

. The present application............................. ..'.. ............ 85

Solution in carbon disulphido....................................... 86

Solution in liquids of the paraffin series ............................. 87

Solution in turpentine .............................................. 87

Solution in chloroform and carbon tetraohloride..................... 87

Solution in aniline................................................... 88

Solution in animal oils.............................................. 88

Treatment with glycerin............................................ 88

Solution in benzol and higher aromatic hydrocarbons................ 88
CONTENTS. 7

Page. 

Chapter IV. Tlie solution of vulcanized india rubber Continued.

Solutions in ethylic and higher ethers................................... 88

Treatment with alcohols ................................................ 88

Treatment with ketones ................................................ 88

Treatment with water and mineral acids ................................ 88

Treatment for vulcanization. Liquid ebonite ........................... 89

Solution in mixtures of solvents, and solution of mixed gums ............ 89

. Direct devulcanization.................................................. 90

Fusion of impregnated rubber .......................................... 90

Behavior of reagents and solvents ....................................... 92

Summary of the results................................................. 93

Presumable conditions regarding the sol ution of carbon, eto ............. 93

Index .................................................................. 95

TABLES.

Pngo.

Table 1. Compressibility of air. Test of gauge............................. 24

2. Comparison of gauges............................................. 24

3. Compressibility of mercury. Test of tubes........................ 20

\ 4. Compressibility of ether .......................................... 29

5. Compressibility of ether, referred to 100 atmospheres .............. 30

6. Thermal expansion of ether, referred to 29° ....................... 30

7. Compressibility of alcohol ........................................ 31

8. Compressibility of alcohol, referred to 150 atmospheres ............ 31

9. Thermal expansion of alcohol, referred to 28C ...................... 32

10. Compressibility of palmitic acid .................................. 32

11. Thermal expansion of palmitic acid, referred to 65° ................ 33

12. Compressibility of para-toluidine................................. 33

13. Thermal expansion of para-toluidine, referred to 28°............... 34

11. Compressibility of diphenylainine................................. 34

15. Thermal expension of diphenylamine, referred to 66° .............. 34

16. Compressibility of caprinic acid................................... 35

17. Thermal expansion of caprinic acid, referred to 30°................ 35

18. Compressibility of benzoic acid ................................... 35

19. Compressibility of paraffin........................................ 36

20. Thermal expansion of paraffin, referred to 64° ..................... 36

21. Compressibility of paraffin.......................................t 37

22. Compressibility of thymol ........................................ 37

23. Thermal expansion of thymol, referred to 28°...................... 38

24. Compressibility of monobrom camphor ............................ 38 

25. Thermal expansion of monobrom camphor, referred to 100P ........ 39

26. Compressibility of a naphthol .................................... 39

27. Thermal expansion of a naphthol, referred to 100°................. 39

28. Compressibility of azobenzol...................................... 39

29. Thermal expansion of azobenzol, referred to 100°.................. 40

30. Compressibility of vanilliue ...................................... 40

31. Thermal expansion of vanilHue referred to 100° ................... 40

32. Compressibil ity of naphthalene ................................... 41

33. Compressibility of monochlor-acetic acid.......................... 4.1

34. Quadratic constants which reproduce the isothermal decrements... 43

35. Exponential constants which reproduce the isothermal decrements.

Direct computation............................................. 47

36. Mean exponential constants.......... ............................. 49

37. Compressibility at melting and at boiling points .................. 50

38. Isothcrmals of ether, referred to unit o'f volume at2 8° and 100

atmospheres.................................................... 51

39. Isothermals of alcohol, referred to unit of volume at 28° and 150

atmospheres. .................................................. 51

9
10 TABLES.

Table 40. Isoth'ermals of paraffin, referred to unit volume at 65° and 20 atmospheres ...................................................... 52

41. Isothermal of dipheuylamine, referred to unit volume at 65° and 0

atmosphere .......... .......................................... 52

42. Isothermals of para-toluidiue, referred to unit volume at 28° and 20

atmospheres.................................................... 53

43. Isothermals of thymol, referred to unit volume at 28° and 20 atmospheres ................. ........................................ 53

44. Expansion and compression constants of ether..................... 56

45. Contraction due to cooling under pressure. Paraffi n............... 5g

46. Contraction due to cooling under pressure. Paraffi n............... 58

47. Contraction due to cooling under pressure. Paraffin............... 59

48. Contraction due to cooling under pressure. Paraffin............... 60

49. Contraction due to cooling under pressure. Naphthalene.......... 60

50. Contraction due to cooling under pressure. Monochlor-acctic acid. 61

51. Hyperbolic constants which reproduce the isothermal decrements.

Direct computation. ......................................... j-.. 64

52. Mean hyperbolic constants........................................ 64

53. Isothermals of ether. Direct measurement........................ 66

54. Effect of compression on the resistance of mercury and of zinc sulphate solution.................................................. 70

55. Effect of isothermal compression on the electric resistance of mercury. Piezometer method ...................................... 73

56. Compressibility of water at 1 ow temperatures...................... 80

57. Compressibility of water at higher temperatures................... 81

58. Compressibility of water.......................................... 82

59. Contraction and compressibility of silicated water. Referred to

water at 24° and 20 atmospheres................................ £2
ILLUSTRATIONS.

Page.

Plate I. Capillary tube, with appurtenances, for measuring the compressibility of liquids. Scale, one-third .......................... 20

II. Approximate compressibility of mercury ...................... 26

{

Fig. 1. Relative isothermals of ether. jp0 =100 atmospheres, 

00=29°....,................................................ 28 

Fig. 2. Relative isopiestics of ether. jp0=100 atmospheres, 

00 =290 ...............-..................................... 28

{

Fig. 1. Relative isothermals of alcohol. j?o= 150 atmospheres, 

fl _OOO QO t/Q io - - . .... .... .... .... ...... .... .... .... .... .... .... .... O\J 

Fig. 2. Relative isopiestics of alcohol. pQ 15Q -atmospheres, 

0 =28 30 

{

Fig- 1. Relative isothermals of palmitic acid. p0=20 atmospheres, 00=65°............................................. 32 

Fig. 2. Relative isopiestics of palmitic acid. p0 =:20 atmospheres, 0n=65° ............................................. 32

f Fig. 1. Relative isothmals of toroidalo. j;0=20 atmospheres,

J 0,,= 28°. .................................................... ' 31

Fig. 2. Relative isopiestics of toluidine. j>() =20 atmospheres,

00=28°..................................................... 34

VTT ( Fig. 1. Relative isothermals of diphonylamiue. Po 0, 0;) =660 . 36 

' < Fig. 2. Relative isopiestics of diphenylamine. j>0 =0, 0n =66°.. 36

{

Fig. 1. Relative isothermals of caprhiic acid. pa=20 atmospheres, 0o=30° ............................................. 38 j. ; 

Fig. 2. Relative isopiestics of capriuic acid. j»0 =20 atmos 

pherca, 0n =30° ............................................. 38

{

Fig. 1. Relative isothermals of para.Win. j)0 =20 atmospheres, 

00=65°..................................................... 40 

Fig. 2. Relative isopiestics of paraffin. ^0 =20 atmospheres, 

00=65°..................................................... 40

X. Relative isothermals of paraffin. ^=0, 0_=65°............... 42

TFig. 1. Relative isothermals of thymol. pa 2Q atmospheres,

J. 00=280.........................:......................,.... 44

' "I Fig. 2. Relative isopiestics of tliymol. pa ~2Q atmospheres, 

[ 00=28°........................l............................ 44

XII. Relation of pressure coefficient ^and coniiiressibilily............ 46

Fig. 1. Isothermals of alcohol ................................. 48

XIIL Fig. 2. Isometrics of alcohol .................................. .48

^ Fig. 1. Isothermals of ether ................................... 50

J ' I Fig. 2. Isopiestics of ether .................................... 50

r C Fig. 1. Isothermals of paraffin.................................. 52

' ( Fig. 2. Isometrics of paraffin .................................. 52

XVI. Isothermals of diphonylaiuine

XVII. Isothermals of toluidine......

XVIII. Isothermals of thymol......................................... 58

11
12 ILLUSTRATIONS.

Plato XIX. Isometrics of ether, alcohol, paraffine, diphenylamine, toluidine,

and thymol compared....................................... 60

XX. Thermodynamic surface....................................... 62

XXI. Contraction on cooling. Para IT! n ............................. 61

-Fig. 1. Contraction on cooling under pressure. Paraffin. 20

and 400 atmospheres ........................................ 66

Fig. 2. Contraction on cooling under pressure. 20 and 500

XXII. < atmospheres................................................ 66

Fig. 3. Contraction on cooling under pressure. 20 and 600 

atmospheres................................................ 66

- Fig. 4. Relative rates of contraction. Paraffin................ 66

XXIII. Contraction on cooling under pressure. Paraffin.............. 68

XXIV. Contraction on cooling under pressure. Naphthalene ......... 70

f Fig. 1. Contraction on cooling under pressure. MonoehloraXXV. / cetic acid .................................................. 72

( Fig. 2. Relative rates of contraction. Monoehloracetic acid... 72

XXVI. Apparatus for compressing mercury........................... 74

XXVII. Chart showing the relations between corresponding values of 

the increments of specific resistance, hydrostatic pressure, 

and volume compression in case of mercury and a concentrated 

solution of zinc sulphate.................................... 7G

< Fig. 1. Time contraction of superheated silicated water....... 80

XXVIIi. < Fig. 2. Contraction and compressibility of silicated supcr-

( heated water ................................................ 80

[

Fig. 1. Successive isothermals of superheated silicated water. 

24° and 185° .. .................................'............. 82 

Fig. 2. Relation of compressibility and contraction of snperXXIX - 1 heated silicated water ...................................... 82

Fig. 3. Time contractions of superheated silicated water ...... 82

Fig. 4. Compressibility of paraffin and water compared........ 82
LETTER OF TRANSMITTAL.

DEPARTMENT OF THE INTERIOR,

U. S. GEOLOGICAL SURVEY, 

DIVISION OF CHEMISTRY AND PHYSICS,

Washington. D. (7., July 31, 1891.

SIR : I have the honor to transmit herewith the manuscript of a report by Dr. Carl Barns on "The Compressibility of Liquids," and to 

request that it be published as a bulletin of the U. S. Geological 

Survey.

Very respectfully,

F. W. CLARICE,

Chief Chemist 

HOD. J. W. POWELL,

Director U. 8. Gfeoloical Survey.

13

PREFACE.

The present volume is the outgoing installment of certain researches 

on the thermodynamics of liquids now in progress at this laboratory. 

The results are exhibited in four sections. In the first of these I endeavor to circumscribe the relation between the volume changes of a 

fluid, in their dependence on pressure and on temperature, fusion effects 

being excluded. In the second I describe the volume lag (hysteresis), 

identify it as a limit case of the phenomenon of viscosity, and discuss 

its fundamental bearing on the molecular structure of matter. In the 

third section (chapter n of this book) I submit an electric method by 

which the phenomenally small compressibility of metals can be studied 

with a facility unattainable in mere volume measurement. In the fourth 

part (chapter in), finally, the compressibility of water .above 100° is 

shown, particularly in relation to the solvent action 'of water on glass, 

and to the contraction of liquid bulk due to such action. In preparing 

the work for publication it was expedient to add the data on lag phenomena to my second bulletin on the viscosity of solids, soon fco a.ppear. 

The other matter is contained in the present volume.

Chapter iv has been added as an illustration of the easy application 

of the results deduced in chapter in to industrial problems.

I am aware that the subject of compressibility has to a considerable 

extent engaged the attention of Maj. J. W. Powell. The present work, 

however, was suggested, and in its general scope and character sharply 

outlined, by Mr. Clarence King, as will appear from a perusal of the 

geological inferences to which the present results are tributary. The 

experimental methods and discussions are mine; and purely physical 

inferences are, as a rule, given on my own responsibility.

The casual reader may ask, What has the behavior of complex organic matter and of liquid metal to do with geology? To such a one 

1 may reply: It is now generally conceded by the clearest thinkers that 

the crust of the earth is underlain by a liquid stratum, and that most 

surface phenomena of upheaval and subsidence are in some way (regarding which the clear thinkers by no means agree) referable to this 

liquid. ISTow, until quite recently the topography of the thermodynamic 

surface of fluids has been altogether unknown. Mathematicians like 

J. Willard Gibbs have done much toward mapping out its possible 

contours. But the experimental facts were vague and useless. To 

endeavor to obtain these from rock magmas, Avhich can be operated on

15
16 . PREFACE.

only under formidable difficulties, would at the present stage of research 

be manifestly absurd. Hence other substances of more definite character and more convenient fusing points are appropriately selected for 

examination; and the observer is throughout his work stimulated by 

the belief that an available analogy iu the thermodyuamic behavior of 

liquid matter in general, whether fusing at temperatures high or low, 

is not beyond the province of probability. The reader who is willing 

to peruse the following chapters with me may find evidence here and 

there that the suggestion of an analogy is not unreasonable.

Since the following work was done I have succeeded in constructing a 

screw compressor by aid of which 2,000 atmospheres may be applied 

with facility. I have also constructed a gauge by which these pressures 

may be accurately measured. The general adjustment is such that all 

necessary electric insulation of different j)arts of the apparatus is provided for, and most of the measurements may, therefore, be made electrically. With this apparatus I hope to subject the data which the 

following pages have laboriously shaped to a direct and more satisfactory test.

GAEL BARUS.

WASHINGTON, January, 1889.
THE COMPRESSIBILITY OF LIQUIDS.

BY CARL BARUS.

CHAPTER I.

FLUID VOLUME: ITS DEPENDENCE ON PRESSURE AND TEMPERATURE.

INTRODUCTION.

1. The present chapter purposes to investigate the probable contours of the isothermals and the isometrics of liquid matter, in so far as 

this can be done with the means now at iny disposal.

2. Literature of compressibility. The literature of the subject has 

recently been critically digested by Tate1 . Excellent excerpts are often 

to be found in the Fortschritte der Physik, so that I may content myself 

with brief mention. The work of Canton (17G2-1764), Perkiu (1S20-1826), 

Oersted (1822), Colladon and Sturm (1827), Eegnault (1847), Grassi 

(1851), Amanry and Uescainps (1869), is discussed in most text books. 

Since that date the contributions have been manifold and are fast 

increasing. I shall, therefore, principally confine myself to papers 

in which volume changes produced by the simultaneous action of both 

pressure and temperature are considered.

Setting aside the literature2 of critical points, which is too voluminous for discussion here, the work of Cailletet3 is first to be noticed as 

introducing a long range of pressures (700 atmospheres). Amagat's4 

early work contains a larger temperature interval (0° to 100°), but 

applies for pressures below 9 atmospheres. The results are discussed 

in reference to Dupre's5 equation. Passing Buchauan's6 and Van der 

Waals's7 results for the compressibility of water and of solutions, I came 

to an exceedingly important step in the subject made by L6vy,8 though 

he had been considerably anticipated by Dupre".9

L6vy seeks to prove that the internal pressure of a body kept at constant volume is proportional to its temperature, which follows thermodynamically if the internal work done by heating is a volume function 

only or if specific heat in case of constant volume is a temperature ftmc1 Tate: Properties of Matter.

3 Sec Lamlolt and Bornstein's Pliydikaliscu-chonmclio Tabollen, Berlin, J. Springer, 1883, p. 62.

3 Cailletet: C. E., vol. 75, 1872, p. 77.

« Amagiit: C. E,., vol. 85, 1877, p. 27. 139; Ann. cli. et pliys , vol. 11, 1877, p. 520.

« Dnpr6: C. K., vol. 59, 1864, p. 490; ibid, vol. 07, 1868, p. 392.

8 Buchanan: Nature, vol. 17, 1878, p. 4H9.

7 Van der Waals: Bcibliitter, vol. 1, 1877, p. 511.

 L6vy= C. K., vol. 87, 1878, pp. 449, 488, 67G, 554, 049, 820,

0 Dupr6: Theorie mecani<|no do la chaleur, 1869, p. 51.

Bull. 92 2 17
18 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

tion only. The position of Levy is sharply antagonized by II. F. Weber, 1 

Boltzmann,2 Claiisius,s and Massieu.4 See below.

Ainagat's5 important work on tlie compression of gases may be 

mentioned because of its important bearing on methods of pressure 

measurement. In two critical researches Mees6 perfects Kegnault's 

piezometer and redetennines the compressibility of water. TaitT and 

his pupils, Bnchanan,8 Marshall, Smith, Omond,9 and others, carry the 

inquiry of compressibility and maximum density of water much further, 

and the data are theoretically discussed by Tait. Pressures as high 

as 600 atmospheres are applied. Solutions of salt and alcohol are also 

tested. Pagliaui,J() Palazzo, and Vicentini, 11 using Regnault's piezometer, 

publish results for water and a number of other substances, mostly 

organic. They also examine mixtures. Temperature is varied between 

0° and 100°, and the results are considerably discussed and utilized to 

show that Dupre's formula is only approximate. Be Heen, 12 who has 

spent much time in studying volume changes of liquids, deduces a 

formula of his own, chiefly in reference to the thermal changes of compressibility. The theoretical results are tested by many experiments.

The research which Amagat13 published at about this time is remarkable for the enormous pressure applied hydrostatically (3,000 atmospheres). Ether and water are operated on. In later work14 these researches are extended to other liquid substances, with the ulterior 

object of finding a lower critical temperature. The behavior of water 

is fully considered. Grimaldi 15 critically discusses the earlier work on 

the maximum density of water. He16 also examines the volume changes 

produced in a number of organic substances by temperature (0° to 100°), 

and pressure (0 to 25 atmospheres), and finds both Dupre's and De 

Ileen's formula1- insufficient.

In further discussion he17 also shows the insufficiency of Konowalow's18 

formula. At this stage of progress the points of view gained in the

i IT. F. Webrr: C. R., vol. 87, 1878, p. 517. 

' 2 Boltzmann: C. R., vol. 87, 1878, pp. 593, 773. 

8 Clausius: C. R., vol. 87, 1878, p. 718. 

4 Massieu: C. R., vol. 87, 1878, p. 731.

6 Amagat: C. R., vol. 89, 1879, p. 437; ibid. ,vol. 90, 1880, pp. 863, 995; ibid., vol. 91, 1880, p. 428, and 

elsewhere.

6 Mees: Beiblatter, vol. 4. 1880, p. 512; vol. 8, 1884, p. 435.

7 Tait: Challenger Reports, vol/2, 1882, appendix, pp. 1 to 40; Nature, vol. 23, 1881, p. 595; Proc. 

Roy. Soc. Eil., vol. 12, 18S3-'84, p. 757; ibid., vol. 13, 1884-'85, p. 2; ibid., vol. 11,1882-'83, p. 813; ibid., 

vol. 12. 1883, pp. 45, 223, 220.

8 Biichanan: Proc. Roy. Soc. Ed., vol. 10, 1880, p. 697.

9 Marshall. Smith, and Omond: Proc. Roy. Soo.'Ed., vol. 11, 1882, pp. 626, 800.

10 Paj>liani and Palazzo: Beiblatter, vol. 8, 1884, p. 795; ibid., vol. 9, 1885, p. 149,

11 Pagliani and Vicentini: Beiblatter, vol. 8, 1884, p. 794; Journ. dophys. (2), vol. 30, 1883, p. 461.

12 l)e Heeii: Bull. Soe. Roy. Belg. (3), vol. 9, 1885, p. 550.

" Amagat: C. R., vol. 103, 1886, p.'429.

' ll Amagat: C. R., vol. 101, 1887, p. 1.159; ibid., vol. 105, 18S7, pp. 165, 1120; Journal d. phys. (2), voj, 8, 

1889, p. 197.

is Grimaldi: Beiblatter, vol. 10, 1880, p. 338.

> 6 Ibid., vol. 11, 1887, pp. 136, 137. 138.

" Urimahli: Zoitschr. f. phys. Clicm., vol. 2, 1888, p. 374,

'* Kouowalow; Zeitschr. f. phys. Cliem., 2, 1888, p. 1.
JUKUS.] ALLIED RESEARCHES. 19

extensive researches of Eamsay and Young 1 throw new light on the 

subject. They prove experimentally that, if pressure, _p, and temperature, 0, vary linearly (p = lv a), the substance operated on does not 

change in volume. The substances tested are ether, methyl and ethylalcohol, acetic acid, and carbon dioxide. Exceptional results for the 

case of acetic acid and nitrogen tetroxide are referred to dissociation. 

Utilizing James Thomson's 2 diagram they point out that the locus of 

the isothermal minima and maxima intersects the locus of maximum 

vapor tensions at the critical point. They show this to be the case for 

ether. Fitzgerald,3 reasoning from Eamsay and Young's results, 

proves that for such liquids as obey the linear law specific heat must be 

a temperature function only, and internal energy and entropy must be 

expressible as the sum of two terms, one of which is a temperature function only and the other a volume function only. Thus Fitzgerald and 

Kamsay and Young arrive at the same position from which Dupre" and 

Levy originally started. My own work was brought to a conclusion 

before 1 had read the above researches; it was therefore specially 

gratifying to me to find my results according with those of Eamsay and 

Young. The data which I give apply emphatically for liquids, that is, 

for substances very far below the critical temperature. My pressures 

are, therefore, over six times as great as those of the English chemists. 

In case of thymol and of para-toluidine I even observed 25° and 15° 

below the respective melting points (under-cooling). Furthermore, my 

method of discussion is different. Fitzgerald,4 has further a-pplied 

Clausius's 5 equation to a discussion of Eamsay and Young's results. 

Sarrau 6 similarly endeavored to adapt Aniagat's data. Dickson7 has 

digested Andrews's data. Tait,8 who is still actively at work on high 

pressures, has recently made publication on the effect of dissolved substances on internal pressure.

3. Literature of heat expansion. A few words relative to thermal expansion of liquids, which enters incidentally into the present paper, 

may be added. Many formula} have recently been devised or tested by 

Avenarius,9 l)e Heen,10 Meudeleeft',11 Thorpe and Eiicker, 12 Jouk,13 and 

others, 14 not to mention older observers. None of the forms seem, to be

*Ramsay and Young: "Phil. Mag. (5), vol. 23, 1887, p. 435; ibid., vol. 24, 1887, p. 196; Proc. Eoy. Soo. 

Lond., vol. 42, 1887, p. 3.

«.Tames Thomson: Phil. Mag., vol. 43. 1872, p. 227; Nature, vol. 9, 1873, p. 392. 

3 .Fitzgerald: 1'roc. Koy. Sou., vol. 42,1887, p. 50.

* Ibid., p. 210.

6 Clausins: Wied. Ann., vol. 9, 18«0, p. 337.

6 Sarr:in: C. It., vol. 94, 1882, pp. 039, 718, 845; ibid., vol. 101, 3885, p. 941.

7 Dickson: Phil. Mag., vol. 10, 1880, p. 40.

*Tait: Challenger Kcports, Phys. and Cliom., vol. 2, part 4, 1888; Proc. Eoy. Soc. Edinb., vol. 15, 

1888, p. 426.

» Avonariu.s: M61. phya. Ac. St.-Petorsb., vol. 10, 1877, p. 697; Boibliitter, vol. 2, 1878,"p. 211; ibid., 

vol. 8, 1884, p. 806.

'ODoHeeii: Bull. Ac. Koy. Bolg. (3), vol. 4, 3882, p. 526; Journ. Chem. Soc., vol. 45, 1884, p. 403,

"MeiiduleL'fl': Chem. Bo,r., vol. 17, 1881, p. 129; Heiblatter, vol. 8, 1884, p. 806,

12 Thorpo and Kiickcr: Journal Chom. >Soc., vol. 45, 1881, p. 135.

"Joiik: Beiblatter, vol. 8, 1884, p. 808.

i4 Kosouborg: Journ. d'Almuida, vol. 7, 1878, p. 350,
20 THE COMPRESSIBILITY OF LIQUIDS. [BUM, 92.

satisfactory when long ranges of temperature are introduced. This is 

shown in a critical research by Bartoli and Stracciati 1 relative to 

Mendeleeff's and Thorpe and Eiicker's formula} and by the discussion 

between Mendeleeff and Avenarius.

4. Remarks on the literature. Surveying the forcmentioned researches as a whole, it appears that at their present stage more work 

has been spent on the compressibility of water than the exceptional 

behavior of this substance justifies. In other words, the volume-pressure-teniperature changes of the great majority of liquids probably 

conform closely to a general thermodynamic law discovered by Dupr6 

and Le>y, and by Bamsay, Young, and Fitzgerald, severally. It is 

therefore first desirable to find experimentally the full importance of 

this law, and then to interpret exceptional cases with reference to it. 

Again, it appears that researches in which long-pressure ranges are 

applied simultaneously with long-temperature ranges are urgently 

called for, and that it is from such work that further elucidation of this 

important subject may be obtained.

Among pressure experiments the late researches of Amagat stand 

out by their originality and importance. One can not but admire the 

experimental prowess which has enabled him to penetrate legitimately 

into a region of pressures incomparably high without lowering his 

standard of accuracy.

Special mention must be made of the celebrated papers of J. Willard 

Gibbs,2 by whom the scope of graphic method in exhibiting the thermodynamics of fluids has been surprisingly enlarged. The terms isometric, 

isopiestic, isothermal, isentropic, etc., are used in the present paper in 

the sense defined by Gibbs (loc. cit., p. 311).

APPARATUS.

5. Force pump and appurtenances. In making the experiments detailed in the following pages I used a large Cailletet compression pump, 

in the form constructed both by Ducretet, of Paris, and by the Societ6 

G6nevoise. Its efficiency is 1,000 atmospheres. It is made to be fed 

with water, but I found that by using thin mineral sperm oil it was 

possible to facilitate operations, because there is less danger of rusting 

the fine polished steel parts of the machine. The pump consists of two 

parts: the pump proper and the strong cylindrical wrought-iron trough 

in which the compression tubes are screwed. This trough is cannonshaped, its axis vertical, and the open end uppermost. Pump and 

trough are connected by strong phosphor-bronze tubing, and similar 

tubes lead to the large Bourdon manometer, by which the pressures 

are measured.

6. Pressure tube and appurtenances. The substance.to be tested is 

inclosed in capillary tubes of glass of very fine bore (0-03cm or less) and

!Bartoli and Stracciati: Beiblattcr, vol. 9, 3885, p. 5]0.

? J. W. Gibba: Truns. Coua. Acml, II (2), 1873, pp. 309, 382.
U. S. GEOLOG CAL SURVEY BULLETIN NO. 82 PL. I

m

-a

I

9 a

Capillary tube, with appurtenances, for measuring the compressibility of liquids. 

(Scale, one-third.)
BARUS.] APPARATUS MANIPULATION. ,y 21

about O6cm thick, snch as are often used for thermometers. In my 

earlier experiments I had cylindrical bulbs blown near the middle of 

these tubes, and to give them greater strength a cylinder of solder was 

cast in brass around the bulb. This arrangement is very much more 

delicate than a plain capillary; but the tnbes broke under pressures 

exceeding 200 atmospheres. For this reason, and because of the difficulty of adjusting a suitable vapor bath, the bulb tube was rejected in 

favor of a straight capillary tube. The length used was about 50cm or 

GO1 ' 111 . To insert them into the trough the solid glass of the capillary 

tube a&c, PI. i, was swelled or bulged at I, about 5oln from one end, and 

then pushed through an axially perforated steel flange ABJ1A, in which 

it fitted snugly. The bulged end and the flange faced the inside of 

the trough, so as to be acted against by the pressure. To seal the tube 

in the steel flange fusible metal ff was cast around it at the bulge, 

and the joint was then further tightened by a thick coating of marine 

glue, gg. A strong hollow nut of iron, surrounding both the lower end 

of the tube and the flange, fastened it to the trough, by forcing it 

against a leather washer. When completely adjusted the capillary 

tube projected about 40cm or 50°"' clear, above the trough. Pressure 

was communicated through the oil of the pump to the mercury in the 

trough, which was in immediate connection with the open lower end of 

the capillary tube.

7. Method of charging the tube. A thread of the solid substance to 

be acted on was introduced into the capillary between threads of mercury. This is a difficult operation, requiring much care. My first 

method was to pump out the air with a Sprengel pump; then to let the 

substance run down into it from a reservoir at the top of the tube by 

appropriate fusion. This method was far from perfect, and I found it 

almost impossible to insert the two mercury threads at the right place. 

After a variety of other trials of this kind I finally abandoned the 

vacuum method in favor of the following: Wide glass tubes (reservoirs) 

were fused both to the upper and the lower end of the capillary. The 

wide tube at the lower end was bent nearly at right angles to the axis 

of the capillary. I then poured mercury into the bent end, a continuous thread of which could be made to run quite through the capillary 

by properly inclining it. The substance was introduced into the upper 

reser\7 oir and fused, care being taken to boil out the air, so that eventually the thread of mercury came directly in contact with the fused 

substance. The capillary is now less inclined. Mercury thread slowly 

ran back toward the lower end, followed by a thread of the substance, 

kept fused by applying a burner on the outside of the tube. This operation was repeated a number of times, so as to cleanse the tube with the 

substance and expel the little bubbles of air which might adhere to the 

walls of the capillary canal. Finally, when the mercury thread, capped 

by the thread of substance, was of suitable length, a globule of mercury 

was also put into the upper reservoir, covered by the fused substance
22 ^ THE COMPRESSIBILITY OF LIQUIDS. " [BULL.92.

in such a way as to exclude air. By a quick motion the tube was then 

placed in nearly a vertical position, whereupon the lower thread of 

mercury ran down farther, followed by the thread of substance and an 

upper thread of mercury. The tube was now again brought back to the 

former position, with the thread of substance between the two threads 

of mercury, nearly in place. At this point the upper reservoir was 

cleansed with bibulous paper and, to seal it, filled with fused paraffine, 

in such a way that no air was left at the upper end of the upper mercury thread. Gently inclining the tube again, paraffine ran into the 

capillary, following'the other threads. When the paraffine thread was 

sufficiently long the tube was left to itself till the threads solidified. 

During the whole operation the capillary tube must be kept heated. 

Considerable skill is required to obtain a properly charged tube, and 

the method must be varied, of course, when volatile liquids are to be 

introduced. It is not advisable to seal the upper end of the glass 

by fusing it, because the strains introduced during cooling greatly 

diminish the strength of the tube. The paraffine thread must be kept 

solid by a cold-water jacket, GG. Under these conditions its viscosity 

is too great to admit of its being forced out of the capillary tube by any 

pressure (1,000 atmospheres) compatible with the strength of the tube. 

Faultless adhesion of the paraffine to the glass is essential. In case of 

hygroscopic substances, therefore, this method fails, and the tube must 

be sealed in other ways.

Passing from the top to the bottom of the charged capillary one 

therefore encounters the following succession of threads: Paraffin 

(5cra ), mercury (5cm ), substance (20cm , depending on its compressibilty 

however; in case of ether a thread lcm long is sometimes essential), 

mercury (25cm ), in communication with the mercury of the trough. 

Measurements are therefore made by observing the distance apart of 

the lower meniscus of the upper thread of mercury, and the upper 

meniscus of the lower thread, with Grunow's cathetometer. When the 

adjustment is perfect the motion at the upper thread is nearly zero. 

Any sliding here is fatal, and the tube must be readjusted when this 

occurs.

8. Method of heating. To heat the sample to any required temperature I surrounded the capillary tube, a&c, with one of niy closed boiling 

tubes, 1 eeee, PI. i, of clear glass.

By connecting the latter with a condenser at D, the ebullition may 

be prolonged for any length of time. The whole thread of the substance is thus virtually exposed in a vapor bath. Methyl alcohol (05°), 

water (100°), aniline (185°), and diphenylamine (310°) are available for 

boiling points. The position of these liquids is shown at M', and they 

are heated by Dr. Wolcott Gibbs's ring burner, jR, R. A thermometer 

is inserted at T. At high temperatures it is of course necessary to

1 Cf. Bulletin, U. S. Geol. Survey, No. 54, 1889, pp. 80 to 90.
BAROS.] MANIPULATION MEASUREMENT.- 23

jacket the boiling tube appropriately with asbestos wicking, leaving 

only two small windows exposed through which the substance may be 

seen 'with the telescope. When the tube is fully heated it is clear, and 

condensation takes place only in the condenser. By adjusting suitable 

white and black screens with reference to the line of sight the image 

of the meniscus may be sharpened. Intermediate temperatures are 

reached by boiling the substances under low pressures. For this purpose it is merely necessary to attach the open end of the condenser to 

Prof. E. H. Kichards's 1 pneumatic exhausting pump. The temperature 

is read on the thermometer at T.

It is scarcely necessary to state that the manipulations are difficult 

throughout, and that with the best of care breakage of tubes is a 

frequently recurring annoyance. Special attention must be given to 

obtain capillary tubes well annealed; otherwise internal strains add 

themselves to external strains and the strength of the tube is insufficient. Vapor baths must not be removed until the tube is thoroughly 

cold. With the best of care a tube will not outlast many series of experiments, for as pressure continues the glass undergoes a change very 

analogous to permanent set, so that eventually a tube may be broken at 

less tlian one-half the original test pressure.

9. Pressure measurement. As is easily seen the method of experiment 

must necessarily be such that temperature is kept constant while 

pressure is varied at pleasure. To measure pressures I used a Bourdon gauge 2 graduated in steps of 10 atmospheres each, up to 1,000. 

So graduated, the gauge registers smaller differences of pressure than 

can be measured in terms of the volume changes of the liquid in the 

capillary tubes. Hence the gauge is suitable.

To test the gauge 3 I compared it with a similar gauge graduated as 

far as 300 atmospheres and found the lack of accordance no larger than 

the error of reading. Again I compared the gauge indications with 

the changes of electrical resistance of mercury under identical conditions of pressure, with results equally satisfactory, as will be explained 

in the next chapter.

10. Curious results were obtained on comparing the gauge with a 

closed, manometer, the essential part of which was a capillary tube 

containing air. The results calculated with reference to Boyle's law, 

i. e., for isothermal expansion, were found to be wholly discrepant. 

The difficulty was interpreted by computing with reference to Poisson's 

law, i. e., for adiabatic expansion. Some results are given in Table 1:

i Richards: Trans. Am. Tust. Mining ling., vi, 1879, p. 1.

2 1 think Prof. Tait, who lias constructed other {ranges based OH Hookc's law, underestimates the ingenuity of Bourdon's gauge; and I believe that, either by increasing the number of coils or by suit, 

ably adjusting a mirror index, tho gauge can be made serviceable without a multiplying ccar. Koad 

off directly, the only limit to the scientific efficiency of tho gauge is the viscosity of tho Bourdon tube.

3 I have since compared the gauge directly with Amagat'b "Hanometre & pistons libres" and found 

my surmises substantiated.
24 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

p, V, k denotes pressure, volume, and tlie specific heat ratio, respectively. The error at p = 100 is due to the time lost in making the 

measurement, since it is here that volume changes are large and require special adjustments of telescope.

TABLE!. Compressibility of air. Test of gauge.

P

100 

200 

300 

400 

500

V

1,030 

550 

400 

329

log v*p

6-25 

6-10 

6-15 6-15

V

1,040 

552 

393 

324

285

log v*p

6-25 6-17- 

C-14 

6-16 6-16

It appears that in case of quick manipulation this method is available for the measurement of ft, particularly with reference to its variation with pressure. It appears also that when work is done on gases 

much time must be allowed in capillary tube experiments before the 

changes of volume obtained can be pronounced isothermal.

Since the gauge is based on Hooke's law, errors of the zero point are 

eliminated by working between indicated pressures and taking differences of reading. So far as relative pressure data are concerned it is 

then merely necessary that the attached dial and mechanism be virtually a scale of equal parts.

Finally, I compared the Bourdon gauge with a form of Tait gauge 

of my own, in which the volume expansion of a suitable steel tube is 

measured externally. Leaving further description to be given elsewhere, I will here insert a mere example of the results obtained. N. 

Gr. denotes the reading of the new gauge, an arbitrary0 scale being 

attached.

TABLE 2. Comparison of gauges.

Bourdon.

0

100

200

300

400

500

KG.

0

160

335

520

690

870

Bourdon.

600

700

800

900

1000

KG.

1045

1210

1370

1530

1700

Constructing the data graphically and remembering that all deviations are to be apportioned between the gauges, it appears that the 

error must everywhere be less than 10 atmospheres in most unfavorable 

cases.

No stress was placed on the absolute correctness of the standard 

atmosphere employed. The results sought follow equally well for an 

approximate staudardj correctly multiplied.
BAUUS.] METHOD OF MEASUREMENT. 25

11. Volume changes of Hie glass tubes. Prof. Tait1 lias given tlie following expression for the volume increment of a cylinder, subjected to 

internal hydrostatic pressure:

 ~^"a*n)

where TTis the pressure, ,- and n the compressibility and the rigidity

of the glass, and where a0 and % are the inner and the outer radius of 

the tube, respectively.

The internal and external radii of my tubes were 0-015cm and 0-3cm, 

respectively. It is easily seen that in case of so small a ratio the 

term of the above expression involving the compressibility of glass 

may be neglected with no greater error than a few tenths per cent. 

Hence, if proper value2 of n belntroduced and pressure be measured by 

atmospheres, the above expression reduces, approximately, to 47110-".

Unfortunately this correction is by no means negligible3 and may in 

unfavorable cases amount to as much as 5 per cent of the corresponding volume decrement of the liquid to be tested. The case is worse; 

most of the experiments are to be made at temperatures between 00° 

and 300°, for which interval the rigidity of glass can not be said to be 

known. To determine it myself was out of the question. Hence, instead of introducing arbitrary considerations, I resolved to neglect the 

correction altogether in favor of direct test experiments with mercury 

and with water.

12. Mercury tests. The compressibility of mercury is too small to be 

amenable to the present method of measurement. Hence, since its 

compressibility is known, it is well adapted for testing the errors of 

the apparatus. «

In Table 31 have given the temperature, 6, and the length of the mercur thread, L, observed; also the volume decrement v/V per unit of 

volume, for each pressure p, as well as the corresponding mean compressibility ft. Many methods were tried; best results were obtained for a 

thread of mercury inclosed between end threads of melted paraffin. 

At the low temperature, 30°, the lower thread was alcohol. The first 

column, v/V, was obtained by increasing p from 20 to 400 atmospheres, 

the second by decreasing p from 400 to 20 atmospheres, though the 

data given are means of a number of such measurements. Great care 

must be taken to keep the mercury thread free from adhering bubbles 

of air or volatile liquid {alcohol, for instance). At high temperatures 

these globules expand and may utterly vitiate the results, as I found 

in more than one instance.

1 Tait: Challenger Reports, 1882, Appendix, p. 29.

*Everott: Units and Physical Constants, Macmillan, 1879, p. 53.

3 Since the sectional expansion alone enters, the correction is smaller than the above estimate.
26 THE COMPRESSIBILITY OF LIQUIDS. 

TABLE 3. Compresftibilily of-mercury.

[BULL. 92.

e,L

30°

16 . 7cm

65° 

16-8 

100°

10 9

185°

17. lcm

p

f 911

1 100 

\ 200 

300

[ 400

(

9fl

100 

200 

, 300

[ 400

J

20

100 

200

300

400

f

20

100 

200 

300

400

o-o

o-o

0-3 

0'9

1'8

o-o

1'2 

2-1 

- 2-4 3-0

o-o

' 0-9 

1-2

2'4

2-7

o-o

1-0 

2-3 

2-0

4-5

o-o

0-3 

0-3

o-c

1-2

O'O

o-o

2'0 

1-7

2'9

o-o

0'(! 1-8

I'S

3'0

O'O

1-2 

2'2 

2'(i

3-9

/3X10"

2 

2 

3

4

8 

14

8

8

10 

9

8

8

14 

13 

9

11

ANOTHER THREAD, BETWEEN PARAFFIN.

185° 

19-3 

310° 

19-7 

f 10 

100

 j 200 

| 300

(_ 400

f 20

| 100 

4 200 

300

[ 400

o-o

0-8 

2-9 

3'7

4-9

O'O

1-0 

2-0 

3-9

5'3

0-8 

3-0 

3-0

4-5

O'O

1'4 

2-6 

4-1

« 2

10 

17 

14

13

15 

14 

15

14

Some of these results are shown in PI. n, pressure being the abscissae 

arid volume decrements, 103 x ?'/F the ordinates. This figure should 

be compared with the subsequent figures for organic substances.

Table 3 is reassuring. From the known low-temperature compressibility of mercury1 it appears that the error of /?, niacle by neglecting 

Tait's correction, is about 10~fi, and that it is not greater than the unavoidable errors of measurement. Again, since the compressibility of 

the organic substances to be examined is in almost all cases much 

greater than 60xlO- 6, the said error of ft is not much above 2 or 3 per 

cent.

By comparing table 3 with tables 4 to 18 ($}.. it will be seen that the 

results at high temperatures are even more favorable.

Similar results were obtained for water, which may therefore be 

omitted here.

13. Isothermals and adidbaties. To obtain the isothermals of the 

compressed liquids it would be necessary to wait a long time after each

1 Everett: Loc. cit., pp. 52, 53. Amagat: C. K., vol. 108, 1889, p. 228; Journ. lie pliys. (2), vol. 8, 

1889, p. 197. Tait: Loc. cit.
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. II

20O 300

Approximate compressibility of mercury.

400
 BARCS.] METHOD OF MEASUREMENT. . . 27

compression. But by so doing, at high temperatures, the tube would 

be seriously weakened in virtue of the diminished viscosity1 of the material, if not even distorted. It appears, moreover, that the distinction 

between isothermal and adiabatic compression is beyond the scope of 

the present method of volume measurement. Finally, since the substance is in the form of an extremely fine (capillary) filament, the conditions are exceptionally favorable to isothermal expansion, for the excess 

of heat of the thread is at once imparted to the thick AA^alls of the capillary tube. For this reason the discrepancy is not of such serious 

moment as would otherwise be the case. Hence I made my observations by varying pressure from 20 atmospheres to the maximum and 

then from the maximum back to 20 atmospheres, with only such allowance of time as was necessary for observation at the successive stages 

of pressure.

Near the critical temperature only is the distinction between isothermal and adiabatic decidedly larger than the errors of volume measurement.

The chief reliance was placed on the constancy of the fiducial zero. 

The volume increments must be identical, no matter whether they are 

observed during the pressure-increasing or during the pressure-decreasing inarch of the measurements.

14. Thermal expansion. My measurements of thermal expansion are 

incidental; but they are necessary for the coordination of results. 

Without a bulb-tube such measurements are not very accurate, ami the 

inaccuracy is much increased by the breaking' off of the ends of the 

mercury thread whenever the substance operated on solidifies. In 

passing from one constant temperature to another an exchange of boiling tubes is to be made, and it is almost impossible to keep the substance in the capillary tube fused during the whole of the time for 

readjustments. On solidification the substances contract as much as 10 

per cent. The mercury thread is therefore forced into the vacuities in 

the axis of the solid thread. After fusing again, it will be found that 

the lower column of mercury has broken into distinct little pieces, 

sometimes in great number, alternating with little threads of the substance. All of these must be measured, an operation which is not only 

excessively tedious, but makes the expansion measurement very inaccurate. For the same reason no correction need be added for the expansion of the glass. The error thus introduced is usually small, and not 

greater than 2 or 3 per cent in unfavorable cases of low temperature. 

See Tables 5 et seq. At high temperatures such a correction would be 

arbitrary, for the reason given in § 11. In these cases, however, it is 

probably altogether negligible, paxticularly so near the critical temperature.

1 It is interesting to note that continued prossiv&s weakens glass gradually, but without any apparent 

change of volume. The conditions of rupture may not bo reached till after the lapse of much time. 

The tubes used must be of well annealed glass. Any temper strain is sure to cause rupture at relatively low pressures.
28 THE COMPKESSIBILITY OF LIQUIDS. [BULL. 92.

EXPERIMENTAL RESULTS. *

15. Explanation. My first results were obtained with capillary tubes, 

the middle part of which had to be blown out into a bulb. Around 

this a jacket of solder was cast and the whole contained in a brass tube. 

I found, however, that breakage took place from pressures of only 200 

atmospheres, that corrections for glass expansion could not be estimated, and that the adjustment of the bath for constant temperature 

was unsatisfactory. I will therefore omit the data obtained, as they only 

corroborate the following results. Having thus found that compressibility would be measureable in cylindrical tubes, my next experiments 

were made in somewhat wider and thicker tubes than those discussed 

in §6. They have an advantage inasmuch as a filamentary thermo-. 

couple can be drawn through the tube without vitiating the volume 

measurement; but they broke under 300 atmospheres and were not 

conveniently thin for the thermal bath. These results are also rejected 

here, but will be cited in § 42, where the direct observations of contraction on cooling under pressure are exhibited. Finally 1 made use of the 

thermometer capillaries already described, § G. In the earlier work 

(naphthalene, monochlor aceticacid), Ididnotintroducetheupperthread 

of mercury, sealing the tube with a solid cold thread of the substance of 

the sample. This introduces arbitrary errors at the point where solid 

and fused substances meet; for on increasing pressures some of the 

liquid will be converted into solid, thus decreasing the length of the 

column. The reverse takes place on removing pressures. Nor is it 

possible to measure the length of thread of substance accurately, since 

the point of meeting of solid and liquid rises as the heating continues 

or when the stationary distribution of temperature is interfered with. 

Hence the facility of charging the tube is not compatible with accuracy 

of measurement, and I give these results only because many subsequent trials made to repeat them failed through accidents.

The bulk of the following experiments were made as detailed in § 6.

Throughout the following tables L is the length of the thread of substance, at the temperature 6; v/V, the corresponding volume-decrement due to the acting pressure p. Finally, ft is the mean compressibility between^,, the initial pressure, and the pressure given. Values 

marked observed and calculated and other information in the tables 

will be discussed below, §34 et seq.

16. Uther. My results for ether are given in Table 4. Manipulations were made exceedingly difficult because of some sulphur present 

in the liquid. This at once attacks the mercury and destroys the cohesion of the thread. Above 100°, the thermal expansion increases enor 

rnously, so that I found it necessary to operate with two threads, the 

long one for low temperature and the short one for 310°. The tubes 

were filled by the U-tube method, § 7.

For the reasons given the initial pressure could not be kept constant,
U. 8. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. Ill

FIG. 1. Relative isothermals of ether. ^>,,=100 atmospheres, 00=29° 

FIG. 2. Relative isopiestics of ether. £>0=100 atmospheres, 00=29°.
BARU8.1 COMPRESSIBILITY OF ETHER. 29

the tubes not being long enough. Hence Table 5 has been computed, 

in which all data are reduced to the uniform initial pressure, p$ 100 

atmospheres.

Table 6 finally shows the corresponding expansion data. It may be 

noticed that, supposing the given conditions to continue, ether would 

cease to expand at 1,100 atmospheres. These results are graphically 

repeated in PL in, Fig. 1, of which the curves are isothermal volume 

decrements referred to unit of volume, at the temperature given on the 

curve, and at the inital pressure p0 =- 100 atmospheres. In PI. in, Fig. 

2,1 have similarly given the isopiestic volume increments referred to 

unit of volume at 29° and at the pressure given on the curve.

The two rows of results for 103 x v/ F, given in tables 4, 7, et seq., 

were obtained during the pressure-increasing and the pressure-decreasing series of the experiments. This lias already been explained in § 13.

TABLE 4. Compressibility of ether. Direct measurements. B. P., 34°; critical temperature, 195°.

L, e

14-Gcm

29°

15 -5cm

64°

1C. 9rm

100°

177°

P

!

20

100

200

300

C 9ft

100

 200

q/W\

400

f 10 

100

I 200

300

( 400

(

50

100

150

300

350

4W

yX10»

o-o u-i

29 p l

42-8

o-o

20-1

39'7

<V7'1

71-6

o-o

65-8

106-5

0

30 too

148

109

i sr»

200

211

£xw

o-o

13-4

29'1

41-8

53'8

o-o

19-7

5C-8

71-9

0-0

fi4-9 87-5

105-5

0

80

148

186

212

/3X106

172

162

15.1

142

248

224

203

189

396

^no

272

1, 600

1 99M

990

815

605

Mean 0X10° 

0 to 400 

atmospheres.

SHORT FIBEE, £27 =5-34<

]4'6cm

310°

f 100

150

200

i 250

350 

400

' 0

287

382

431

485 

502

287

382

431

463

484 

002

5,740

2, 870

2, :«()

1, 9:(() 

l.OfcO

u
30 THE COMPiiESSIBILTTY OF LIQUIDS. [BULL. 92. 

TABLE 5. Compressibility of ether, referred to 100 atmospheres.

", JJ

29° 

14'37cm

65° 

15-18<°>

100° 

16-25 

185° 

20-08 

310°

*14. 59c,n

P

( 100

I 200 

| 300

( 400

( 100

1 200 

1 300

( 400

f 100

I 200 

1 300

( 400

f 100

I 200 

1 300

{ 400

f'lOO

J 200

1 300

( 400

Observed.

yX!0»

0-0

15-6

'40-8

o-o

20-7 37-7

KO.Q

o-o

30-5

72-2

o-o

74-1 

1155

143-5

0

382

462

502

p A J.U

156 

345

13C

207 

189

170

305 

' 268

741 

577

478

3,820

2.310

2,510

Computed.

V

yXlOS

o-o

15-4

28-9

40'9

o-o

20-5 37-8

52-8

o-o

29-9

72-8

o-o

71-5 

114-7

145-6

383

Diff.XlO3

+0-2 0

 j

+ '2

± -o

+ -6

-t -2

 6

-j-2-6

l -S

2-1

1

! 9

i?X10°

165

226

343

. 1, 005

194

282

497

..........

10, 060

* Second sample. 

TABLE 6. Thermal expansion of ellicr y XlO3, referred to 29°.

Atm. =

/) 0 IT! (

29°

65°

1000

185°

310°

100.

0

57

131

397

1,770

200.

0

300.

0

51 ; 48

114

315

733

103

274

528

400.

0

43

93

246

435

COMPUTED VALUES " = In (\ /3 (0 6) j *' ^- See § 41.

6=

f 29°

65°

\ 100°

I 1S5°

[ 310°

- 9

59

136

389

1, 750

 5

50

112

305

869

 6

45

100

2f>6

690

 4

40

89

232

562

17. Alcohol. The- alcohol used was not free from water, though 

commercially absolute. Table 7 contains the observations made for 

compressibility. The initial pressure had again to be changed at high 

temperatures. Hence I have computed Table 8, in which the initial 

pressure is uniformly 150 atmospheres. The corresponding values of 

thermal expansion are given in Table 9. Of the charts, PL iv, Figs. 1 

and 2, the former are isothermal decrements, each referred to unit of 

volume at the initial pressure, 150 atmospheres, and at the temperature 

marked on the curve. Similarly the isopicstics, Fig. 2, are referred to 

unit of volume at 28° and at the pressure on the curve, The results
VI. S. GEOLOGICAL SURVEY 

400

BULLETIN NO. 92 PL. IV

10) 200'

flg.1.

150 200 250 300 350 400

Fio. 1. Relative isothermals of alcohol. p0=150 atmospheres, 0o=28°, 

FIG. 2. Relative isopiestics of alcohol. pu=150 atmospheres, 00=28.
BARUS.] COMPRESSIBILITY OF ALCOHOL.

are more satisfactory than ether, because a single thread only was used. 

In constructing Tables 5 and 8 I had to sacrifice some observations. 

But it seemed better to do this than to reach the lower initial pressuie 

by more or less arbitrary hypotheses. The two sets of data (§ 16) are 

given side by side.

TABLK 7. Compressibility of alcohol. Boiling point, 7S°; critical temperature, 236°.

L,9

9 -f, Qr 111

27°

9- 93 ' 

63°

10-49 

.100°

12-25"" 

180°

21-75""

310°

P

( 20

| .100

 j 200 

300

[ 400

f 20

1 100 

 j 200 300

( 400

f 20

200 \ noo

300

[ 400

20

100 

 200 

300

400

( 150

1 200

J 250

| 300

350

[ 400

V

K X10*

0-0

0.7

18-6 27-1

34-1

o-o

9-4 

20-2 31-5

40-0

15-1 

28-4 42-0

52-9

o-o

35-9 

07-1 91-1

110-0

212

289

334

303

380

v

yXlO»

o-o

8'9

17-8 

20.0 33-G

o-o

9-C 

20'6 30-8

39-5

14-3 

29-1 41-6

53-1

o-o

35-3 

CO- 0 

90-3

110-0

0

208

291

333

304

385

/3X106

1.16

101 

95

90

118 

113 

111

104

184 

100 

150

140

445 

372 

324

290

4,200

2, 900

2, 220

1,820

1,530

TABLE 8. ComprMxilility of alcohol, referred to 150 atmospheres.

e,L

28° 

9--15- 

G.r>o

100° 

10- 27= 

185° 

11-02- 

310°

P

( 150

I 200

I 200

!

1'">0

200 

.300

400

f 150

J 200

f 150

1 200

"I 300

[ 400

Observed.

y-XlO"

o-o

4-3 

12-7

5-5

25*1

o-o

8-4 

21-6

o-o

16-0

0

211.

 335

3.84

86

8

K

81

110

i (in

168 

144

132

320 

274

245

4. 200

Computed.

V

yxio»

o-o

4-3 

12'6

l)n-9

o-o

5-6

25'5

o-o

7-6 

21-5

15-4

61-8

219

330

 o

 o

+ 1

 o

 o

_ -1

+ 4

 4

 0

+ '8 

+ -1

 9

 0

+ 6 

+ 2

 6

 8

+ 5

 1

t>

89

115

158

331.

13, 860

*o

101

136

201

598

.
32 THE COMPRESSIBILITY OF LIQUIDS. [BULL.92. 

TABLE 9. Thermal expansion of alcohol,- x 101 referred to 28°.

Atm. =

6=

f 28° 65°

I 100°

| 185°

(. 310°

150

 0

35

87 229'

1,290

200

0

35

82

217

826

300

0

31

78

,105

555

400

0

30

73

178

447

18. Palmitic acid, The data are. given in Tables 10 and 11, on a plan 

uniform with the above. O wing to accidents, two threads were observed; 

the first between 65° and 185°, and the second between 65° and 310°. 

At 65° solidification set in at 400 atmospheres. The necessary result is 

distortion of the curvature of the loci. Much difficulty was encountered 

because of breaks in the mercury thread. Hence the circumflexure in 

the isopiestics is probably an error of observation (Of.*PI. v).

TABLE 10. Compressibility of palmitic acid, Cn

point, 350°.

2 . Melting point, 6%c; lotting

L, e

65°

10- 72cm

100°

17-lOcm

185° 

18-50cm

P

f

20 

100 

200 

300 

1400

f 20 

1 100 

4 200 

1 300 

1. 400

(

20 

100 

200 

300 

400

Observed.

yXlO3

o-o

7-2 

15-0 

22-8 31-1

o-o

8-1 

1G-9 

25-5 33-3

o-o

12-1 

26-3 

37-2 

482

V

-y X UP

o-o

7-2 

15-3 

23-1 31-1

o-o

8-1 

16-3 

25-5 33-3

o-o

32-1 

-26-3 

37-8 47-7

J3X10"

90 

85 

82 

82

101 

93 

91

88

151 

140 

13-1

127

Computed.

y-XlO"

*o-o

7-1 

15' 3 

23-0 30-1

o-o

7-8 

16-9 

25-4 33-2

O'O 

12-1 

25-5 

37-5 48-5

Diff. X 101

o-o o-i

 0-1 

 0-1 

+0-2

o-o

+0-3 

 0-3 

-MK1 +0-1

o-o 

o-o

 0-2

o-o

-0-4

#X106

91

102

1GO

tfo X 10«

93

104

165

* Including the lower series for 65°.

SECOND SAMPLE.

t Solidifying.

65°

14-63cm

JL i ij-i

f 20

1 100

<! 200

300

[ 400

f 20

.100

4 200

1 300

( 400

o-o

6-5

15-1

22-9

29'5

o-o

23-4

47-4

60-3

82'6

o-o

6-9

15-1

22-3

29-5

o-o

24-6

48-3

67-9

84-3

84

84

81

78

300

265

240

220

o-o

23-7

47-5

67-2

83-8

+0-3

+0-4

-O'l

 0-3

oo n OKI
U. 8. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. V

200

100

20

10

0 100 200 30CT 400

FIG. 1. Relative isothermals of palmitic.acid. p0=20 atmospheres, 0o=65°

FIG. 2. Relative isopiestics of palmitic acid. p0=20 atmospheres, 00=G5°.
nARUS] COMPRESSIBILITY OF PARA-TOLUIDINE. 33

TABLE 11. Thermal expansion of palmitic acid, y X 103 referred to 65°.

A tin. =

( 65°

1 1.00°

1 185°

[ 310°

20

0

20

107

199

100

0

25

101

179

200

0

24

93

159

300

0

23

91

145

400

0

24

87

133

19. Para-toluidine. The following data, Tables 12 and 13, and the diagrams, PL vi, were obtained for toluidine. A feature of these results is 

the circumnexure of the isopiestic increments in the undercooled part 

of their course. This is probably not an error, since it recurs again 

under similar conditions, in case of thymol, § 25. It may be noted that 

if contraction due to cooling1 under pressure continued at the same rate 

as shown in Table 13, there would be no volume change at 1,4.00 atmospheres. I found that to solidify the undercooled liquid as much as 500 

atmospheres were necessary.

TABLE 12. Compressibility of para-toliddine, Cr

point, 43°.

!j. Boiling point, 198°; melting

6,L

*28°

14.14cm

65° 

14- 73'"'-

100° 

15 02""

185° 

16-301""

3100 

19-05 '

P

1

20 

300 

200 

300 

400

1

20 

100 

200 

300 

400

( 20 

100 

<^ 200 

300 

{ 400

f 20 

100 

< 200 

300 

[ 400

(

20 

100 

200 

300 

400

Observed.

yXlO'

o-o

4-3 10-0

15-8 20-G

o-o

0-5 

11-6 

17-4 23-5

o-o

6-3 

14-5

22-2 20-0

o-o

11-0 

22-8 

33-4 42-4

o-o

29-0 

50-1 

70-2 92-7

V

-yXlO-i

o-o

4-G 

10-0 

15 -G 20-9

o-o

5-5 

11-9 

17-4 23-5

o-o

G-3 

14-5 

223 

. 29-3

o-o

10-9 

22-8 

33.4 42-2

0-0 

29-4

?52-0 

75-7 92-5

/3 X 10°

56 

5G 

5fi 

55

G9 

65 

62

62

79 

81 

79

77

137 

127 

11:) 

112

365 

300 

271 

243

Computed.

V 

-yXlV

0.0 4-6 

10-2 35-5

20 '5

o-o

5-3 

11-7 

17-7 23-4

o-o

6-8 

14-7 

21-1 28-8

o-o

10-6 

22-5 

33-1 43-1

27-6 

54-5 

76-3 

94.5

Diff. X 10'

±0-0

 0-1 

 0-2 

+0-2 +0-2

4-0-0 

+0-2 ±0-0

 0-3

+OM

o-o

 0-5 

 0-2 +0-1

-t-0'4

o-o

+0.4 

-i-0'3 

+ 0-3 0-8

0-0 

4-2-0 

+2-0

 o-o

 0-2

#X10"

59

68

87

138

392

tf0 X 10"

60

69

88

142

422

,92-

' Liquid, tindercooled.

 3

Solidifies uijder 500 atmospheres,
34 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

TABLE 13. Thermal expansion of para-toluidine, -p-X 103, referred to 28°.

Atm.=

6 = 1

28

65

100

185

310

20

0

42

03

158

348

100

0

41

60

149

313

2UO

0

40

57

142

287

300

0

30

50

136

2G5

400

3

5

13

24

20. Diplienylamine. In the value for diphenylamine, given in Tables 

14 and 15, the initial pressure is unfortunately zero. This introduces a 

discrepancy between the present and the other results, in -which the 

initial pressure is significant. The observations are not as uniform as 

the above. Of. PI. YII. It may be noted that at 2,000 atmospheres, 

supposing the given conditions of PI. vn, Fig. 2, to last, no contraction 

would occur on cooling.

TABLE 14. Compressibility of diplienylamine. Melting point, 54°; boiling point, 810°.

L,6

16-2"' 

65°

16-4"» 

100°

17-7om

185°

19-7 

<20-3)< 

3100

P

0 

100 

200 

' 300 

400 

500

0 

100 

200 

300 

400 

500

f o

100 

1 200 

1 300 

400 

( 500

f o

100 

200 

' 300 

400 

[ 500

Observed.

-y-x 10"

o-o

6-5 

11-9 

17-9 

23-2 29-2

o-o

6-.1 

12-8 

19-3 

24-6 29-9

o-o

11-2 

20-6 

29-2 

37-1 44-1

O'O 

18-5 

36-1 

51-5 

62-4 74-1

-£xio'

o-o

0-0 

11-9 

17-3 

22-5 28-4

00 6-3 

13-1 

19-3 

25-1 30-5

o-o

10-7 

20-3 

28-9 

30-1 44-3

o-o

17-8 

36-1 

50 '7 

63-5 75-1

,3 X 108

63 

60 

59

57 

57

62 

(>4 

64 

6-i 

CO

110 

102 

97 

. 9i 

89

202 

190 

176 

161 

152

Computed.

-y X 10'

o-o

6-3 

12-2 

17-9 23-5

28-4

o-o

6-7 

13-1 

19-0 

24-7 30-1

0-0 

10-4 

20-0 

28-9 

37-0 44-7

0-0 

19-4 

30-0 

50-3 

63-1 74-6

Diff. X 103

 o-o 

 o-o

 0-2 

- 0-3 

 0-7 

+0-9

o-o

 0-5 

 fl-2 

+ 0-3 

+0-1 

+ 0-1

+0-0 

+0-6 

+0-5 

 0-1 

 0-4 

 0-5

o-o

 1-2 

-f-0-1 

+0'7 -O'l

o-o

dXlO"

65

69

110

213

<? X 10s

65

69

110

213

TABLE 15. Thermal expansion of diplienylamine, 10s X , referred to 66°.

Atm. =

( 650

1 100°

1 185°

[ 310°

0

o-o

12-4

93-0

235-0

100

o-o

12-4

88-0

221-0

200

o-o

11-3

83-1

2-05-0

300

o-o

10-1

80-0

193-0

400

o-o 10-1

78-0

186-0

500

o-o

11-0

76-0

178-0
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. VI

Fig.Z.

200" JOO

ZQ 100 ZOO 300

FIG. 1. Relative isothermals of toluidine. Po=20 atmospheres, Oo=38° 

FIG. 2. Relative isopiestics of toluidiue. ^0 =20 atmospheres, 00 =28°.
BABOB.] COMPRESSIBILITY OF CAPEINIC AND BENZOIC ACIDS. 35

21. Gaprinic acid. Tables 10 and 17, and Plate Yin, contain the results for capriuic acid. The thermal expansion is irregular, probably 

due to motion of the thread in the tube, so that virtually two different 

threads were observed. The substance has a low melting point, 30°. 

Undercooled to 25° I found that it solidified at 300 atmospheres pressure.

TABLE 16. Compressibility of caprinic acid, CioH..-0Oi2.

poin t, 269°.

Melting point, SO0; boiling

e,L

30° 

(Undercool cd.) 15-91"'"

65° 

14-39""

100° 

16-85""

185° 

18-30 

P

( 20 

1 100 

.{ 200 

300 

1 400

(

20 

300 

200 

300 

400

( 20 

100 

I 200 

1 300 

( 400

(

20 

100 

200 

300 

400

Observed.

V

y X 103

o-o

4-9 

13'4 

39-5 25-5

o-o

7-3 

10-1 

23-0 31-4

o-o

8-5 

19-1 

29-1 30-8

o-o

1:V3 

oJ-2 

45-4 57-4

V 

yXlO'

o-o 5-7

12-9 

19-8 25-8

o-o

7-0 

15-9 

23-9 31-1

o-o

9-1

20-1 

28-9 30-8

o-o

15-1 31-1

45-5 57-1

0 X 105

OG 

73 

71 

08

90

89 

84 

82

110 

109 

304 

97

190 

373 

363 

151

Computed.

V

yXlO*

o-o

5-9 

12-9 

19-5 25-7

o-o

7-3 

30-0 

23-8 31-3

o-o

9-0 

19-5 

29-1 37'8

o-o

34-9 31-2

45-2 57-7

Diff. X 101

o-o 

 o-o

+0-3 H-0-2

o-o

o-o

 O'l

o-o 

o-o 

o-o

o-o

 0-2 

-f O'l 

 0-1 +0-2

o-o

+ 0-3 o-o

-(-0.3 

 0-4

* X 10*

70

95

319

200

#o X 10"

76

97

121

207

V

TABLE 17. Thermal expansion of caprinic acid, -p X 10", referred to 30°.

Atm.=

( 30°

J 05°

1 100°

[ 385°

20

0

30

59

351

100

0

28

55

139

200

0

28

52

329

300

0

26

49

120

400

0

25

47

113

22. Bcnzoie acid. In vieAv of the high melting point only a single 

series of measurements was made. Table 18 contains the results.

TABLE 18. Compressibility of benzole acid, Cy

point, 249°.

a. Molting 2)olnt, 121° ; boiling

L,e

185° 

H-88cm

P

(

20 

.100 

200 

300 

400

Obso

V

yX30'

o-o

33/4 

22-3 

32-8 42-1

L-vcd.

V 

yXlO3

o-o

11-4 

22-1 

33-1 42-5

/3X106

142 

321 

318 

312

Computed.

O'O 

. 10-5 

22-3 

33-2 42-9

Diff. X 10"

o-o

+0-9 

 0-1. 

 0-2 

 0-ti

£ X 106

138

*o X 106

HI
3G THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

23. Paraffin. I made many measurements with paraffin, of which 

the following digest, Tables ID and 20, probably contains the best results. At 04° solidification set in at 400 atmospheres. This is well 

seen in PI. ix. Supposing the conditions to hold indefinitely, there 

would be no contraction on cooling under a pressure of 1,200 atmospheres.

TABLE 19. Compressibilily of paraffin. Mcltiny point, 50°.

£,0

64° 

15-86 

100° 

16-28cm

185° 

17-57""

310° 

- 19-70 

P

( 20 

100 

 200 

300 

t 400

20 

100 

 200 

300 

400

' 20 

100 

 200 

300 

400

' 20 

100 

200 

 300 

400

Observed.

-yX10»

o-o

G-8 

14-9 

23-0 

(*)

o-o

8-5 

18-5 

27-6 

35-0

O'O 

13-8 

27-9 

' 41-2 

52-3

O'O 

26-8 

51-9 

72-4 

89-9

V

yX!0»

o-o

6-5 

14-9 

23 '8 

(5(5-0)

o-o

8-5 

18-7 

27-7 

35-8

0-0 

13-8 

28-2 

41-4 

52-0

o-o

26-2 

52-1 

 71-8 

89-G

pXlO"

83 

83 

84 

(149)

_

106 

103 

99 

94

172 

156 

147 

137

X

331 

289 

257 

236

Computed.

V

yXHP

0 0 

0-8 

1-1-8

o-o

8-5 

18-5 

27-4 

35-8

o-o

13-3 

28-1 

41-1 

52-7

 o-o

20-0 

51'7 

72-7 

90-3

I »iff. x 103

 o-o

 0-1 

+0-1

 O'O

o-o

+0-1 

+0-2 

 0-1

o-o

+ 0-5

o-o

+ 0'2 

 05

o-o

+0-5 

+0'3 

 0-6 

 0-0

t>XlOB

88

111

178

300

dtt X 10"

89

114

184

392

* SolidifyiDg.

TABLE 20. Thermal expansion of paraffin, ~v X 10", referred to 64°.

'Aim. =

0= 64

100

18f)

310

20

O'O

26-4

108-0

241-0

100

o-o

24-1

100-0

210-0

200

o-o

23-1

92-9

190-5

300

o-o

22'0

87-8

181-0

400

0-0

22-1

83-8

167-0

24. Further results for paraffin are given in Table 21 and the chart, 

PL x. In this case the capillary tube was closed above by fusion, and 

the parffian introduced in vacuo. Solidification takes place at 65° under 

500 atmospheres. The divers columns v/V^&sQ obtained in separate 

experiments on different days.
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. VII

70

60

Fig.Z.

100 /

20O

3CO

65° I

4C

200°

s

30

20

10

fig A.

Jltmospteres

100 200 300 4-OO 50O 600

FIG. 1. Relative isothermals of diphenylamine. p0=0, 00=6G°.

FIG. 2. Relative isopiestics of diphenylamine. p0=0, 00=66°.
BARUS.] COMPRESSIBILITY OF PARAFFIN AND OF THYMOL. 

TABLE 21. Compressibility of paraffin. Melting point, 55°.

37

6,L

185°

1C- Grin

17'G"»

65°

17-0C "!

P

0

100 

200

300

400

 o

100 

200

OAA

400

CAA

{ 0 

1 100 

I 200

400 finn

V

yX303

O'O

17'G

45-0

Cft.1

o-o

11-4

99 .A

;u-o

OQ.O

O'O

10-li

Ofj.q

t34'G 80-0

V

y X 10»

O'O

17-8

QO.O

45-3

05'9

o-o

11-4

O'O

9-9 

38-1

34-3

V

-y-X 101

0-0

17-]

OO.'>

45-8

50-4

67-1

O'O

11-4

39'4

46-9

O'O

10-0

18-4

 y

yXlO1

00

18'1 32-4

45'7

56-9

(*)

O'O

11-4 21-5

30'0

38-9

46'9

O'O

9'8 

18-4

176 

161

1M

 141

114

QQ

94

100 

92

87

80

(100)

Computed.

V

-yXlO'

O'O

17-2

45-2

56-8

67-4

0-0

11-2

21-4

30-7

QQ-3

47-2

O'O

9'5 

18-4

20'G

i?o X 10°

186

118

100

* Tube breaks. t Solidifying, solid at 500 atmospheres.

25. Thymol. Tables 22 and 23 and the accompanying PL xi, give 

full account of the behavior of thymol. Like toluidine, §19, thymol admits of considerable undercooling, and the isopiestic increments show 

circumnexure in this region. (See Fig. 2, at a.) Supposing all conditions to hold, no volume change would ensue on cooling under 1,200 

atmospheres pressure.

TABLE 22. Compressibility of thymol, Melting point, 53°; lolling point, 233n .

9,L

*28" 

14- 07""'

64° 

15'29«"

100° 

15- 78""

P

' 20 

100 

 200 

800 

400

20 

100 

.200 

300 

400

( 20 

1100 

200 

300 

400

Observed.

V

yX10»

o-o

5'5 

10-9 

17-0 

21-8

o-o

5-6 

12-4 

19-6 

25-5

0-0 

7-0 

16-2 

24-4 

30-7

V

yX 103

o-o

5-3 

11-0 

17-0 

21-7

o-o

5-4 

12-3 

19-9 

24-5

O'O 

7-5 

16-2 

24-2 

30-9

ft X 10°

07

ci

61

57

69 

69 

70 

GO

94 

90 

86 

80

Computed.

V

yXlO'

o-o

5-1 

11-1 

10-7 

22-1

0-0 

5-7 

12-6 

19'0 

25 '1

0-0 

7-4

ic-o

23-9 

31-4

Diff. X 103

+0'3 

 O'l 

+0-3 

-0-4

 0'2 

 0-2 

+0-7 

 O'l

+0'1 

+0-2 

+ 0-4 

 0-6

i»X 10°

65

 74

96

i?o X 10°

66

75

97

: Liquid undercooled.
38 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92. 

TABIYE 22. Compressibility of thymol, CioHM0 Continued.

0,L

185° 

17-05""

310°

I9 .5cm

P

' 20 

100 

 200 

300 

400

20 

100 

200 

400 

300

Observed.

yXJO"

0-0 

12-3 

26-1 

38-0 

48-3

0-0 

33-0 

C.l-1 

83-6 

102-0

V

yX10»

O'O 

12-2 

25-9 

37-8 

48-5

o-o

32-0 

60-5 

83-6 

101-0 

/3 X 106 .

153 

144 

135 

127

407 

388 

299 

207

Computed.

V

yX10»

o-o

12-2 

25-8 

37-8 

48-8

o-o

31 

Cl 

84 

103

Diff. X 10"

o-o

+0-2

+0-1

 0-4

-I-0-2

-t-o-i 

 o-i

 0-2

£X 10"

161

448

#0 X10B

106

487

ANOTHER SAMPLE.

310°

16-47 

f 20

100

\ 200

300

[ 400

o-o

62-4

82-5

102-0

347

295

269

TABLE 23. Thermal expansion of thymol, - X 103 , referred

Atin. =

{

28°

65°

100°

185°

310°

20

42

76

162

329

100

43

73

154

293

200

41

71

145

263

300

39

68

138

239

400 '

39

65

130

220

26. In §§ 26 to 29 results are given for a variety of substances. In 

view of the high melting points, only two series for each were feasible. 

At 310° azobenzol decomposes. The results were rejected. -The use 

of this colored substance pointed out an irremediable error, due to the 

adhesion of a film of substance to the glass, between the mercury and 

the walls of the tube. In case of compression, the advancing thread of 

mercury therefore moves on a cushion, as it were.

TABLE 24. Compressibility of monobrom camphor, CioH)6BrO. Melting point, 76°;

boiling point, 274C .

0,L

100° 

14- 03 

185° 

U-SO'"

P

( 20 

J 100 

I 200 

[ 300

f 20 

J 100 

\ 200 

[ 300

Observed.

4X103

o-o

6-6 

14-1 21-5

o-o

<J-8 

20-0 29-7

-5x1*

o-o

6-6 

14-1 21-5

o-o

9-9 

19-9 29-9

(3X10°

82 

78 

77

123 

111 

106

Computed .

V

-pFXIOS

o-o

6-6 

14-3

21-4

o-o

9-5

20-2 30-1

Diff. X 103

0-0 

0-0 

-0-2

-t-o-i

o-o

4-0-4 

 0-2 

 0-3

tfXIO6

83

123

t?0 X 10°

85

126
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. VIII

300 400

FIG. 1. Relative isothermals of caprinic acid. p0=20 atmospheres, 00 =30°. 

FIG. 3. Relative isopiestics of caprinic acid. po=ZO atmospheres, 0U =80°.
1UUUS.] VARIOUS DATA FOE COMPRESSIBILITY. 39

TABLE 25. Thermal expansion of monobrom camphor, -y X 10s, referred to 100°.

Aim, =

°=* f 100°

} 185°

20

0-55

100-

0-51

200

0-49

300

0-40

TABLE 26. Compressibility of a-napl\-tlwl, Cio

279°.

. Melting point, 94°; "boiling point,

e,L

100° 

15-10C'»

185° 

15-97C1 "

¥

( 20 

| 100 

\ 200 

300 

I. 400

( 20

| 100 

{ 200 

300 

[ 400

Observed.

V

 yXHP

o-o

5-6 

10-3 

15-9 20-5

o-o

C-7 

.14-3 

2V3 28-6

V 

yXlO"

O'O

o-o

10-7 

10-1 20-5

o-o

G-8 

14-4 

21-0 28-4

(3X10°

72 

58 

57 

54

85 

80 

77 

75

Computed.

V

yXlO*

o-o

4-9 

10-6 

10-.1 21-3

o-o

(i-G 

14-4 

21-0 28-4

Diff. X103

o-o

+0-9 

 0-1 

 0-1 

 0-8

0-0

+0-2

o-o

 0-1

+0-1

^XlO6

G2

85

i»u X 19G

62

.

87

TABLE 27. Thermal expansion of a-naphthol, x 103 , referred to 100°.

Atm,=

6 =

( 100° 

I 185°

20

0 

58

100

0 

57

200

0

54

300

0 

51

400

0 

49

TABLE 28. Compressibility of azobenzol, a. Boiling point, 893°; melting point,

66°.

e,L

100° 

1G-20"1'

185°' 

17-49 

P

( 20 

100 

4 200 

300 

( 400

(

20 

100 

200 

300 

400

Observed.

V

y X 10*

o-o

6-5 

13-2 

20-3 20-4

o-o 10-1

21-2 

31-6 41-1

VT xio>

o-o

G-3 

13-3 

20-4 26-2

o-o

9-8 

21-3 

31-6 40-9

v 1 ~V*J

80 

74 

72 

69

125 

118 

113 

108

Computed.

V

-y-XlOS

o-o

6-2 

13-3 

20-1 26-6

o-o

10-0 

21-3 

31-4 40-9

DifF. X 10?

o-o

+0-2

o-o

+0-3 0-3

o-o 

o-o 

o-o

 0-2 o-i

iJXlO6

79

131

#o X 10°

80

134
40 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

TABLE 29. Expansion of azolenzol, -p? X 103, referred to 100°.

Atm.r=

6= C 100° 

i 185°

20

0

. 74

100

0 

71

200

0' 

66

300

0 

6f

400

0 

61

29. TABLE 30. Compressibility of vanilline, C

385°.

y. Melting point ,80°; lolling point,

e,L

100° 

15-04""

185° 

16-10cm

P

( 20 

J 100 

1 200 

[ 300

f 20 

j 100 

1 200 

[ 300

Observed.

Y-X103

o-o

4-1 

9-5 

16-1

o-o

7-1 

15-5

22-7

 y 

T X103

0.0 3-9 

9-6 

15-6

o-o

7-2 

]5-9 22-7

0X105

50 

53 

57

90 

87 

81

Computed.

O'O 

4-6 

9'9 

15-0

o-o

7-1 

15-4 23-1

Diff. X 10'

o-o 

 o-o

 0-3 

+0'9

o-o

+0-1 

+0-3 

. 0-4

i? X 10°

58

92

#o X 106

58

93

v TABLE 31. Expansion of vanilline, -y X103, ref&rred to 100°.

Atm.=

0= f 100° 

I 185°

20

0

71

100

0 

67

200

0 

65

300

0

0 

64

30. Naphthalene. The results of the following two tables were obtained without an upper mercury thread, and are therefore affected 

by the error discussed in § 15.° They contain many points of special 

interest, however, and, in view of the long threads (l/ = 20cm ), I think 

the discrepancy in question slight. It will be s£en that at 100° naphthalin solidifies at 600 atmospheres. Monochlor-acetic acid did not 

solidify outright. The compressibility observed for the solid column I 

believe to be due to the presence of an excess of water of crystallization in the hygroscopic acid. Compressibility here is a solution phenomenon, and the excessively large value of /3 is thus explicable. The 

same phenomenon will be observed below, Chapter in, in case of silicated water.

A few other substances (phenanthrene, sodic acetate) were tried, but 

without obtaining publishable results.
O. S. GEOLOGICAL SURVEY

.300

200

too

BULLETIN NO. 92 PL. IX

00

So

70

60

50

40

2i o° 3( o

Fig.

AUnosplu

O loo 20 3oo 4o

FIG. 1. Relative isothermals of paraffin. p0=20 atmospheres, 00=G5°

FIG. 2. Relative isopiestic of paraffin. ^o=20 atmospheres, 0o=65°
BAiitTs.] NAPHTHALENE AND OITLORAOETIC ACID. 41 

TABLE 32. Compressibility of naphthalene. Melting point, 80Q ; boiling point, 215°.

L,B

21-2"» 

185°

20-8'- 

153°

. 21-7 

100°

21.-7"" 

100°

P

{

50 

350 

250 

350 

450

f 50 

| 150 

4 250 

350

I 450

f 50 

1' 150 

250 

350 

450 

550

f 50 

| 300 

 j 400 

500 

[ *GOO

Observed.

 yXlO'

o-o

13-2 

24-3 

33-7 43-2

O'O 

11-1 

21-4 

30-1 37-8

0-0 

8-5 

.1.7-3 

25-1 32-3

o-o

20-7 

29-5 

3G-9 52-5

V - jrXlO*

o-o

12-5 

24-3 

33-7 42-4

o-o

8'3 

1(5-8 

24-G 

32-3 39-1

..........

::::::::::

/3X1Q6

129 

122 

112 

106

111 

107 

]01 

94

84

85

s;t

81

' 78

83 

84 

82 

90

Computed.

yXlO'

o-o

12-5 

23-8 

34-0 43-4

o-o

10-9 

208 

29-9 38-4

o-o

8-9 

17-2 

24'!) 

31-9 38-8

=

i»X10°

133

#o X 10°

i4i

1

115

93

i2i

97

i

* Solid.

31. TABLE 33. Compressibility of monochlor-acctic acid. Melting point, 62°; boiling

point, 188°.

e,L

185° 

22-2='"

65° 

20-3'-'"

*5C° 

17-8""

J)

( 50 

1 150 

 j 200 

350 

[ 450

f 50 

1 150 

J 250 

1 350 

450 

[ 550

f 50 

150 

\ 250 

350 

[ 450

Observed.

 y

-y-XlO3

0-0 

14-9 

25-2 

80-0 

44- G

o-o

7-4 

13-8 

20-3 

25-7 30-7

o-o

10-0 

17-0 

21.-4. 24-2

-y X 103

0-0

7-4

m 20-0

25-2

)3 X 106

149 

12(5 

320 

112

 74 

(19 

08 

04. 

Cl

Computed.

yXW

o-o

13-3 

25-2 

30' 0 45-7

o-o

6-9 

13-6 

19-8 

25-7 31-2

1

100 

85 

71 

Cl

t?o X 10°

142

..........

72

Column solid.
42 THE COMPRESSIBILITY OF LIQUIDS. |i5uu,02. 

METHOD OF DISCUSSION.

32. Plan pursued. I shall endeavor to discuss the above data in the 

following way: Having given certain relations between volume and 

pressure obtaining at any given temperature, let a close-fitting function be investigated, such that for the same pressures the calculated 

values of volume decrement must eventually be greater than the observed values will be. Let another function be investigated, such that 

for the same pressures the calculated values of volume decrement must 

eventually be less than the observed values can be. The actual data 

must therefore lie witliin the baud or pathway included between the 

two functions in question. In other words, the couple of functions maps 

out an isothermal zone, as it were.

ISTow, suppose it is possible (the proof will be given by trial) to so 

adjust the two functions that throughout the interval of observation 

they both fall within the limits of error, then it ifl probable that any 

property which is simultaneously predicted by both functions may confidently be assumed as the property of the unknown isothermal. So 

long, therefore, as the two functions do not diverge seriously, there is 

here given a judicious method of extrapolation, by which relations beyond the limits of experiment may be apprehended.

33. Quadratic constants. Now, in order to arrive at the probable 

nature of such functions, it is expedient to pass parabolas through the 

observations. The ordinary vertical parabola is clearly inapplicable. 

It predicts a maximum, and is therefore incompatible with the nature 

of the locus to be found. Nevertheless, the zero compressibility may 

thus be deduced with some certainty, and, moreover, from the relation 

of the two constants, additional inferences may be gleaned.

In Table 34 I have entered the two constants in question; respectively 

denoted by m and n, supposing that

ye= v/= mp np,

where ye is the volume decrement at the pressure j», under conditions 

of constant* temperature 6. The table further contains boiling and 

melting points (B. P. and M. P., respectively), as well as the total thermal expansion j&', from 6 = 0° to the value of 0 cited, \vhen# = 0.
U. 'S. GEOLOGICAL SURVEY

70

SO

BULLETIN NO. 92 PL. X

 A1

 fO

30

fo

ATMC (SPHERES

Relative isothermals of paraffin. j>0=0, 50=65.

6OO
BARUS.] . QUADRATIC CONSTANTS. 43 

TABLE 34. Quadratic constants which reproduce the isothermal decrements.

Substance.

Palmitic aoi<l : 

B. P., 350o 

M.P., 62o

Pai'a-toluicliiio: 

B. P., 198° 

M.P., 4.3°

Diphonylamine: 

B. P., 3.10° 

M.P., 54°

Uaprinio acid : 

B. P.. 270° 

M.P., 30°

Benzole iicid : 

15. P., 249° 

M.P.,121°

.Paraffiiie: 

At. P., 55°

Thymol : 

B.P., 233" 

M.P., 53°

e

f310°

J 185° 

1 100° 

[ 05°

(310° 

1185° 

\ 100° 

05° 

( 28°

f310° 

J .185° 

] 100° 

[ C5°

fl85° 

J 100° 

1 C5° 

[ 30°

1 185°

f310° 

Jl85° 

1, 100° 

[ 05°

!

310° 

185° 

100° 

05° 

28°

103 X m.

315 

101 

100

813

387 

141 

81 

69 

50

197 

113 

04 

02

196 

11C 

92 

71

143

319 

177 

130 

83

435 

159 

97 

09 

07

10° Xn. :10*X J?.

207 

93 

30 

25

404 

81 

0 

25 

3

92 

54 

3 

12

125 

40

27 

5

93

320 

110 

43 

9

484 

85 

40 

2 

20

199 

107 

20 

0

348 

158 

61! 

42 

0

235 

93 

12 

0

151 

59 

30 

0

210 

100 

24 

0

329 

162 

70 

42 

0

S nl» stance.

Afoiiobrom camphor: 

B.P., 274° 

M.P.-, 70°

aNaphthol: 

B. P., 280° 

M.P., 94°

Azoben/.ol : 

B. P., 293° 

M.P., 68°

Vanilliiie: 

B. P., 285° 

At. P., 80°

Alcohol : 

B. P., 78°

Ether : 

B. P., 34°

e

C18.'>° 

) 100°

C185° 

) 100°

< 185° 

\ 100°

C 185° 

1 100°

(

310° 

185° 

100° 

65° 

28°

!

310° 

185° 

100° 

65° 

29°

103 X TO.

129

85

85

70

127 

80

92 

47

3,280 

341 

178 

111

87

3,583 

770 

340 

224 

107

.10"Xw.

80 

28

29 

50

52 

29

39 

32

0,970

4] 8 

209 

28 

20

0, 367 

992 

346 

.170 

107

103 X E.

55 

0

58 

0

74

0

71 

0

1, 290 

229 

87 

35 

0

1,770 

397 

131.

57 

0

COMPRESSIBILITY INCREASING INVERSELY AS THE PRESSURE BINOMIAL.

34. Transition to exponential constants. There are two points of view 

from which the data of Table 34 are important:

(1) Compressibility TO increases at a rapidly accelerated rate with temperature, caet. par. (2) Compressibility m and the datum for curvature 

n are intimately related. This points out that a fundamental relation 

for yg and p will probably exist independently of the material operated 

upon. § 13. The quantity E serves for orientations only, since it is not 

a coefficient.

It is necessary to look at these points more in detail. In case of 

alcohol and ether at 310°, quadratic constants are impossible: for the 

maximum would either lie within the field of observation, or the observations would have to be grossly slighted. This is to some extent true 

for ether at 185°. The alcohol and ether data in Table 34 are therefore 

inserted merely for comparison.

Rejecting these exceptional cases, it appears, if the dependence of n 

on TO be considered separately for each substance L\S well as collectively
44 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

for all, that the quantities vary nearly linearly with eauh other. Suppose 2n = I (m a). 

To return to the above equation,

(1)

(2)

replace w by 3 and 2n/m by a, for the sake of distinction. Then inasmuch as (1) applies more accurately in proportion as# is small, equation 2 may be put

. ......... (3)

whence

.......... (4)

This equation has an advantage over the equation ( I) : it does not 

predict a maximum. It is, therefore, compatible with the character of 

the isothermals in the above tables. Furthermore, in view of its simplicity, and of the fact that generally y= o> when p= GO, it may be 

taken as the lower limit of the isothermal ribband described in § 32. 

For it is clear that when p o>, v/ V can not be greater than unity.

In passing I may insert a few remarks on the relation of constants. Since 3 = w and 2n/m = a, it follows that a = b(m a)/m and 

$/a-=mz /b(m a.) Hence approximate values for the constants in (4) 

may be derived from Table 34. From an inspection of this table I was 

moreover led to infer that at the melting point, compressibility is constant 

and independent of pressure. In other words, since 1/3 = I/a a/ab, 

3 = a would be the criterion of fusion. Subsequent results did not suljstantiate this surmise, § 38. Another similar notion that the resistance 

to compression is equal to the incipient resistance to extension even in 

liquids, and that therefore 1/3 must have a constant value at the boiling point independent of substance, is not warranted by the experiments made. Such a relation was suggested by the experiments of 

Kahlbauni1 corroborated by O. Schumann,2 according to which the boiling point corresponding to a given pressure is higher than the temperature of the same vapor tension. Ramsay and Young,3 who tested 

these experiments, do not corroborate them. They effectually substantiate Regnault's law according to which vapor tensions, whether obtained by the static or the dynamic method, are identical.

35. Properties of the exponential equation. It will facilitate discussion if certain salient properties of equation (4) are grouped together 

here. I may state that, a priori, the occurrence of y= IQs v/ V GO for 

p = GO, is not a fatal objection to its application; for the use of the

1 Kahlbaum : Chom. Ber., vol. 18, 1885, p. 3146. * Eamsay and Young: Chem. Ber., vol. 18, 1885,

2 0. Sclmmami: Chom. Ber., vol. 18, 1885, p. 2085. p. 2855; vol. 19, 1880, p. 69.
0. 8. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XI

FIG. 1. Relative isothermals of thymol. $>0=f!Q atmospheres, f0=28°, 

FIG. 2. Relative isopiestics of thymol. pu =~0 atmospheres, e0=28°
BARUS.J EXPONENTIAL CONSTANTS. 45

equation ceases at tlie point of solidification by pressure; therefore, at 

some finite value of p, as far as which the equation y = ln(l + ap)#la 

may faithfully represent the volume changes (decrements) observed. 

For this reason I originally accepted this equation with the assurance 

of its possessing a value beyond that of denning an arbitrary limit of 

the isothermal band. 

Suppose for a given substance

...... (5)

and, simultaneously,

y0 = ln(l+af^)9^ ....... (G)

where j»0 and p are any two consecutive intervals of pressure. Then

_ , , 0/a° 

y = y - ^ = in 1 - = In l + i p . (7)

Hence if

/v«

- and $ =

equation (7) may be put

op)*/a ........ (4)

Thus from the observations y, made along any arc of the whole curve, 

between p() and jp, it is at once possible to obtain, the constants of the 

whole curve referred to the origin at 0 atmosphere, by equations (8) or 

the equivalent equations :

a Sr «'o = fi.~^ and ^0 = 1^^ ..... (9)

so that the reductions are simple. Equations (9) suggest an important 

consequence: when <rp0>l> both <r0 and 50 become imaginary. Itfow it 

is a matter for curious remark that this takes place in case of ether 

and alcohol near or above the critical temperature. Hence I inferred

v

that the compressibility of liquids d~y/dp= 5/(l + ap) changes 

form and passes into the compressibility of gases

= _ 

dp p

through an imaginary expression.

In such a consideration the condition for critical temperature would 

be p = I/a,
46 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

When p is small, equation (4) becomes

which, is .shown to be capable of further simplification in the next section. 

The expression for compressibility 

has a counterpart which is applicable for thermal expansion, viz,

as will be shown in § 41.

Finally, the change of jp, when regarded as the function of the radius 

p of any unit sphere within the compressed liquid, is of interest. Let 

p be expressed by /(p), where p in the uncompressed liquid is unity. 

Then

1 / a(l-p')/* N

f(p}-= (e- -1 ) J \i ' a\ J

This equation shows the nature of the inadequacy of (4); for if p del/ «/* \ 

crease indefinitely,/(p) eventually becomes ( e 1 J. In the next

paragraph a/5 is found to be nearly 9. Hence the limit in question is 

8200/«'. In the cases where equation (4) applies this value is somewhere between 106 and 107 atmospheres. Hence the interval within 

which equation (4) may apply satisfactorily is reasonably large.

36. Exponential constants computed. After the suggestion contained 

in § 34 approximate values for the exponential constants in the equation. v/V=ln(l + ap)* a are easily derived.1 The constants thus obtained are very crude, and the calculated results show a wide margin 

of error. Hence, starting with these, I computed the accurate values 

by a method of gradual approximation, finally selecting such values of 

3 and a as reduced the errors to a reasonably small limit. This computation is exceedingly tedious and unsatisfactory at best, because 

pairs of values of 5 and cf, differing very widely from each other, are 

often found to satisfy the equation about equally well. Nevertheless, 

it was necessary to avoid any scheme of selection other than the criterion of errors specified, the object being to obtain a set of constants 

independent of any ulterior purposes or considerations.

The results are given in Table 35, in which the first column contains 

the boiling point (B. P.), melting point (M. P.), of the divers substances

1 Reference to y is conveniently dropped here. The constants refer to -y.
BULLETIN NO. 92 PL. XII

, ether. 

L, aicohot.

Ft, palmitic acid-,

2), (HphervyL curvLne. 

Ab, c^zobenzoL. 

J3C,morLobrom, Camphor 

C, caprinic ctctcL.

To, toluzdine para,. 

v, varu,llin& . 

JV, di-ruxphtoL. 

13,

To E 

60

'Compressibility)

100 ZOO 300 400 50O

Relation of pressure coefficient and compressibility.
BABUS.] EXPONENTIAL CONSTANTS. 47

as well as the initial pressure P0, for which. 3, the zero compressibility 

and a, the pressure coefficient, apply at the temperature 6. From these 

I pass to 30 Mid tf0 > which hold for the initial pressure 0 atmosphere, by 

equations 9, § 35. The table also contains the reciprocal of compressibility 1/3, or the resistance to compression which obtains under each 

of the given conditions. Finally, the value of Bo/tfo, with a coefficient 

2-3, by aid of which .the computation is reduced from naperian to common logarithms, is inserted in the last column. At the end of the table 

I have added the mean datum SO/MO, derived from all the values of the 

table, with its probable error. A chart (PL xn) accompanies the table.

TABLE 35. Exponential constants whicli reproduce the isothermal decrements Direct

computations.

Substance.

Palmitic ncid:

M.P.,02° ......

P0 -20 ........

Paratolnicline: 

B.P., 198°......

P0 -20. ........

Diplienylamino:

P0 -0. .........

Caprinic acid :

M P' 'iO°

7» _ on

Beii zoic ncid: 

B. P. ,2490...... 

M.P., 121°.....

Paraffin : M.P.,55o......

7> _ on

Tlmnol : 

'B.P.,233°......

J

> on

Monobrom campi i or: 

B. P., 2740...... 

M.P.,700...... 

P0 20.........

a Napbtliol :

M.Pl,94° ...... 

PO 20.........

e

( 310°

1 185°

1 100°

[ 65°

!

310° 

185°

100°

05°

28°

f 310° 

1 185° 

I 100°

[ 05°

( 185° 

1 -100°

1 65°

[ 30°'

i 185°

f 310° 

I 185° 

1 100°

[ 65°

(

310° 

185° 

100° 

65°

28°

I 185° 

f 100°

1 185° 

f 100°

8X1».

332

104

89

421 

145

82

68

57

216 

113

62

201 

114

92

77

140

302 

180 

113

89

466 

163 

34)0

74

05

121

82

80 

03

aXlO3

3-05

1-00

0-80

4-50 1-70

0-50

0-30

2-00 

1-20 0-50

0-30

1-90 1-00

0-70

0'70

1-40

3-20 

1-80 

1-3.20 0-80

4-00 

1-60 

1-20 0-70

o-oo

1-00 0-50

0-80 0-70

.;.

3, 010

9,610

31,240

2,370 

0,900

12, 200

173, 900

4,630 

8,850

10,, 130

4,970

10, 870

7,140

2,760 

5,500 

8,850

11, 240

2,350 

0, 335 

10, 000 

13,510

15, 380

8,260 

12, 200

32,500 

34, 290

i90 X 10°

353 

105

106

90

463 

150

89

76

61

216 

113

68

62

209

93

78

144

387 

187 

116

91

514 

168 

103

75

66

124 

83

87 

04

a0 X 103

3-25 1-55

1-02

0-81

4-95 1-76

0'56

0'32

2' 00 

1-20 0'50

0-30

1-98

1 -O9

0-71

0-71

1-44

3-42 

1-87 

1-3.5 0-81

5-14 

3-65 

1-22 0-71

0'61

1-02 0-51

0-81 0-71

i/*

2,830 

o, oeo

9, 030

11, 000

2,160 

6,670

13, 240

13, 250

16, 530

4,630 

8, 850 

14, 710

4,780

8 no ft

10, 750

12, 820 "

6,940

2,580 

5, 350 

8, 020

11, 050

3,950 

0,950 

9,710 

13, 300

8,000 

12, 050

11, 490 

15, 630

2-3 -(! X103 

ao

250 

245

238

257

215 

196

473

315

248

217

474

243

303

252

230

260 

231.

232

250

230 

234 . 

191 

243

279 

376

246

207
48 THE COMPRESSIBILITY OF LIQUIDS. 

TABLE 35. Exponential constants, etc. Continued.

[BULL- 92 

Substance.

Vanillino: 

B.P.,285°...... 

M.P.,80°......

__ O(\

Azobenzol: 

K P., 2930...... M.p.,c8°......

T> __ OA

Alcohol: 

B.P.,78°.......

P0 150........

Ether: 

B.P..35°....... 

P0 100........

9

1 185° 

f 100°

[ 185°

| -100°

( 310° 

185° 

I 100°

1 65°

[ 30°

f 310° 

1 185° 

4 100° 

65°

{ 30°

t> X 105

90 

59

130 

80

15, 000 

351 

164

110

88

33,800 

1, 130 

361 

225

167

a X 10s

0-90 0-50

1-20 0-80

140-00 

3 '90 2-00

1-20

o-oo

280-0 

12-0 3-8 

2-0

1-6

1/0

10, 420 

10, 950

7, 690 

12, 500

07 

2. 850 

6, 100

8,620

11, 300

314

885 

2,770 

4,440

5,990

t?0 X 10s

98 

60

133 

81

(*) 

836 

234

142

97

(*) 

(*)

583 

281

199

a0 X 101

0-92 0-51

1-23 0-81

(*) 

9-29 2-86

1-4G

0-66

(*) 

(*) 

6-13

2-50

1-91

l/*o

10, 200 

16, 700

7. 520 

12; 350

(*) 

1,200 

4,'270

7,040

10, 310

(*)

CO 

1, 720 

3,560

5,020

2-3 X103 

a o

235 

271

250 

229

247 

207 

189

223

336

261 

217 

218 

259

240

* Equation fails, indicating transition into gaseous state. 

Q " -oo 5} 1

Mean 2-3 ° =-2575 ± 83 = -1119 = 0 (say).

Of() CVQ «/

37. Mean exponential constants derived. The tabulated constants for 

ether and alcohol above 185° substantiates the remarks made in § 35 

relative to the limit of application if the equation v/ V In (1 + ap)^a . 

The critical temperatures of these substances' are 195° and 234°, respectively. "Hence ether shows an imaginary #0 as low as 185°, and 

both substances do so at 310°.

The point of special interest relative to this table follows from a consideration of the last column 2'3S0 /a0 . In Fig. 21, where these results 

are given graphically (3- as abscissa, a as ordinate), their signification 

fully appears. To obtain a figure of reasonable dimensions for ether 

and alcohol, I have divided large pairs of 3 and a, each by the same 

convenient number, as is indicated in the figure. This does not change 

their ratio. Looking at these results as a whole, and taking the enormous range of variation fully iuto consideration, it appears beyond 

question that 3- and a are not only closely related, but that this relation is probably linear. The computation of Table 35 was an entirely 

independent procedure, and I could easily have obtained data more 

nearly in keeping with the mean ratio §/a had I entered upon the 

work with any bias.

Hence I am justified in considering the equation given at the end of 

Table 35,

as applicable to the whole series of organic substances examined. With

1 Eanisey: Proc. Koy. vSoc., London, vol. 31, 1880, p. 194,; Haunay, ibid, vol. 30, 1880, p. 484; and 

pf,Uers. Cf. L,andolt and Boernstein's tables, 1. c.
U. S. GEOLOGICAL SURVEY

/of

-Joot /

600 / /

efuture.

BULLETIN NO. 92 PL. XIII

J3

Pressure.

9o Joo Zoo 3oo 3oo 600 70o 800 Qoo 

FIG. 1. Isothermals of alcohol. 

FIG. 2. Isometrics of alcohol.

looo lioo 1200 1300 .Moo J5oo
BARUS.] MEAN EXPONENTIAL CONSTANTS.

this as a point of departure, I made a recalculation of 5 and have inserted the results in Table 36. Naphthalin and mouochlor acetic acid 

are added.

TABLE 36. Mean exponential constants v/V= In (1 -|-93p) 4.

Substance.

Ether:

2>0 =100 a tin.. 

B.P. =34°...

Alcohol: 

j7ll =150atin.. 

B.P. =78°...

M.P. = G2°... 

B.P. =350°..

Paratoluidine: 

}> 203 ......

M. P.=43° .. 

B.P. 198°..

Diplieiiylaminc: 

pn =0. ....... M.r.=r.4°...

B.P. = 310°..

Caprinic acid : 

jV-20.......

M. P. = 30° . .

B. P. =270°..

Benzoic acid: 

j»n -20.......

M. P. r=121° .

p0 =20. ......

M.P. = 55°...

e

( 29°

05°

4 100° 

1 185°

1.310°

f 28° 

05° 

I 100° 

185°

1.310°

f fi5°

J 100°

I 185° 

[310°

f 28°

1 05°

-! 100° 

185°

1.310°

f 05° 

I 100°

} 185°

(.310°

f 30° 

J 05°

1 100°

[185°

(l85°

'

f 01°

) 100°

) 1,S5° 

(310°

i?X10c

105

220

343 

1, 005

89 

115 

158 

331

13, 830

91

102

1GO 

330

59

08

87 

138

392

05 

09

110

213

70 

95

119

138

88

111

178 

306

#o X 106

194

282

497 

.10, 000

 ( ' )

101 

130

201 

598

(*)

na

104.

105 

351

GO

09

88 

142

422

65 

09

110

213

76 

97

121

207

141

t89

114

184 

392

l/*o

6,061

4, 425

2,9.15 

995

11,240 

8, 700 

0, 330 

3,020

722

10,750

0, 000

285

10,670

14,490

11,360 

7,040

2, 370

15, 380

9,090

4,090

13, 160

8. 260

4, 830

7,090

.1.1. 240

8,770

5, 430 

2,550

Substance.

pv=0. .......

Thymol:

pn 20.......

M.P. = 5;i° .. 

15. P. = 233°..

Monobrom camphor:

ni Ort

M. P.-7G°..

li. P. 274°..

o-Ifaphthol :

M.P. = 94°...

B.P. =280°..

Azobfiizol :

j>,,-20.......

M.P. = 08°...

Vanillin:

po-20.......

M.P.=80°... 

B.P. 285°..

+ Naphth«liu :

M.P. = 80°... 

B.P. -21 5°..

t Mouochlor acetic acid: 

p«-0....,..,

M.P.=G2°...

B, P. = 18.8°..

e

( 05°

< 100°

( 185°

f 28°

1

(UO

100° 

185° 

310°

1 100°

^ .1 85°

)185 5

? 100° 

( 185°

hoo°

(185°

} 4B

( 100°

<153° 

(185°

? 65°

i>X 10'

( . .......

05

74

90 

101 

448

83

123

02 

85

79 

131

58 

92

93

115 

133

...,..,,

a0 X10f

tioo

.118

180

CO

71

97 

100

487

85

120

02

87

80 

134

58 

93

97

121 

141

72

142

]/*o

10, 000

8.470

5. 380

.15,150

13, 330

10,310 

0,020 

2,050

11, 760

7,940

10, 130 

11, 490

12,500 

7, 4GO

17,210 

10, 7oO

8, 200

13, 800

7, Q4Q

* Results of an older method. In ethor and alcohol the reciprocals of & arc takeu instead of l/#4, 

t Discrepancy in these results due to solidification. 

J Imaginary.

Availing myself of these constants, I computed the values of v/V 

given in Tables 4 to 33. By consulting- the differences between gbserved 

and calculated, it will be seen that the errors are as a rule within the 

range of accuracy specified in the critical paragraphs 9 to 15.

38. Sitbsidiary results. Certain subsidiary results of Table 36 are to. 

be mentioned. If 1/3-, the resistance to compression, be constructed as 

a function of temperature, /9, it will be seen that, except in the extreme 

cases of alcohol and ether, 1/5 decreases nearly proportional to 0. This 

rate of decrease is nearly the same for all substances examined.

In Table 37 I have given the approximate values of 3- at melting 

Bull, 92 -i
50 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

points, M. P., and at boiling points, B. P. No perspicuous relation is 

discernible, thus substantiating the inferences already drawn in § 34. 

It appears that compressibility is a quantity depending on other causes 

than the stability of molecular groups. °

» TABLE 37.- Compressibility at melting and at boiling points.

Substance.

Ether (d m) . ................

M.P.

62°

4't

30

55

53

70

94

80

08

SO

02

i»0 X 10°

90

02

00

76

83

70

60

05

00

72

B.P.

3500

 198

310

97n

233

274

280

215

188

78

34

i»0 X 106

^9Q(U

160

213

240

(170)

145

170

39. Isothcrmals computed. With these results in hand I am able to 

reach the chief issue of the present paper, viz., the construction of the 

actual isoth.erm.als for the substances in hand. The computation being 

somewhat laborious, it will scarcely be fruitful to consider those substances in which the heat expansion could not be accurately measured. 

§14. The data to be discussed are notably alcohol, ether, paraffin, 

thymol, para-toluidine, and diphenylamine.

To recapitulate: 'The volume decrement,

(10)

refers in all cases to unit of volume at the temperature B of the isothermal and under the initial pressure P0 . The compressed volume is therefore.

and if in consequence of the observed thermal expansion at P0, the volume at 6 be V$ the actual isothermal is obviously

...... (11)

referred to the initial temperature B0 . It is to be observed that v$ is 

directly measured, and that, therefore, the only hypothesis occurring 

in equation (11) is equation (10).

In Tables 38 to 43, I have given vep computed conformably, with 

equations (11) for pressure as high as 1,500 atmospheres and for the 

temperatures of observation. A chart accompanies each table, in 

which pressures, p, are given as abscissae volumes vep as ordiuates. 

From these charts, Plates XIIT to xvm, the conditions subject to which 

temperature and pressure must vary in order that vep may remain constant are at once given by drawing horizontals. Hence, to each of the 

Tables 38 to 43 I have a supplement, in which values of 6 and p for
U. S. GEOLOGICAL SURVEY 

I

BULLETIN NO. 92 PL. XIV

100 200 300 400 500 600 700 800 900 100

FIG. 1. Isothermals of ether. 

FIG. 2. Isopiestics of ether.

1100 1200 1300 1400 1500
BARDS.] ISOTHERMALS OF ETHER AND ALCOHOL. 51

v8p = const, are inscribed. These supplementary tables indicate the 

nature of the isometrics. V^ will be computed in the next section.

TABLE 38. Isothermals of ether, referred to -unit of volume at 38° and 100 atmospheres.

p

0

100 

200

300

400

500

600

700

1, 000

1, 100 '

1,400

1, 600

V

*3

(t)

Td0.

10°

2-77 1-70

1-50

i -^a

1-29

1-12

1-04

1-01

093 0-88

F*

18

(t)

Vd9.

5°

1-397 

1-298

1-236

1-193

1-009

1-039

1-001

0-983

V

10

1-131

1-070

1-050

1-033

0-983

0-976

0-902

0-955

v»e.

0°

1-131

1-071

1-049

1-030

0.904

0-955

0-929

0-9J4

V

6

1-057 

1-035

1-017

1-002

0-988

0-977

0-907

0-944

0-937

0-922

0-914

v$e.

5°

1-057 

1-035

1-0.17

0-987

0-974

0*953

0.935

0-904

0-893

\9.

2

1-000

0-971

G'0^9

0-949 0'9'i9

0-917

0-905

0-882

YdB.

3°

1-000

0-948 0-938

0-929

0-921

0'899

A.QQI

0-870

* Special measurement made later, t Equation fails. 

Critical conditions of constant volume.

0

28 

65

300

185

A-p.

0 

310

600

1,300

Volume.

J.-00

Eate= 0-12° per atmosphere. 

TABLE 39. Tsotliermals of alcohol, referred to unit of volume at 2S° and 150 atmospheres.

P

0

150

C50

1, 050

1.150

L450

V

31

(t)

^$9.

0°

2 : 29

1-47

1-37

1-24

1-19

1-16

1-12

1-09

1-06

1-00

0-90

V

18

1-229 

1-193

1-105

1-098

1-088

1-079

1-071

1-064

1-047

1-038

Yd0.

3-229 

1-193

1-165

1-142

1-122

1-089

1-063

1-041

1-013

0-997

V

10

1-087 

1-070

1-056

1-043

1-022

1-013

1-005

0-998

0-991

0'985

0-969

0-900

7M.

0°

1-087

1-057

1-033

1 -O99

1-013

1-004.

0-995

0-901

0-949

V

6£

i-035

1-013

1-004

0-995

0'980

0-974

0-968

0-962

0-956

0-942

0-934

VM.

°

1-035 

1-024

1-004

A.nQQ

0-973

0-966

0-954

0-938

0-928

V

28

i-666

A-OQI

. n.nQT

0-975

0-9G8

0-962

0-')56

0-951

0-945

0-910

YM.

o

1-00) 

0-991

0-909

0-940

0-9;i5 0*9° I

0*912

Critical conditions of constant volume.

6

28 

65

100

185

&p.

0 

360

740

1,470

Volume.

1-0

Bate = 0-12° per atmosphere.
52 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92. 

TABLE 40. Isothennals of paraffin, referred to unit volume at 65C and 20 atmospheres.

p

20

120

220

320

420

520

620

720

820

920

1,020

1,320

1, 520

'V Yd9.

310°

1-241

1.201

1-171

1-147

1-129

1-113

1-iOl

1-091

1-081

1-074

1-067

1-051

1-043

i

1-241

1-202

1-171

1-146

1-125

1-107

1-091

1-076

1-063

1-051

1-040

1-012

0-995

V VM.

185°

1 108

1-090

1-074

1-060

1-045

1-037

1-027

1-018

1-011

1-003

0-997

0-982

0-973

1-108

1-OHO

1-074

1-000

1-047

1-036

1-025

v ^.

100°

1-026

1-015

1-026

1-015

1-005 1-005

0-996

0-988

0-990

0-988

0-980 i 0-980

0-973

1-016 i 0-907

1-007

0-999

0-95)1

0-970

0-958

0-960

0-955

0-949

0-935

0-928

0-973

0-966

0-959

0-953

0-947

0-931

0-922

V yM.

65°

1-000

0-991

0-983

0-975

0-969

0-902

0-955

0-951

0-946

0-941

0-930

0-92-t

0-916

1-000 o-rgi

0-983

0-975

0-CU8

0-962

0-956

0-050

0-945

0-939

0-935

0-921.

0-912

Critical conditions of constant roltimc.

e

65

100

IBS

310

Ap.

0

250

880

1,430

Volume.

1-00

Rate = 0-13° per atmosphere.

TABLE 41. Isoiliermals of diplienylaminc, referred to unit volume at 65° and 0 atmospheres.

fi

0

100

200

300

400

500

600

700

800

900

1,000

1,300

1,500

Yv«. M.

310°

1-235

1-211

1-191

1-173

1-159

1-146

1-134

1-124

1-116

1-107

1-100

1-082

1-073

1-235

1-211

1-191

1-173

1-157

1-143

1-130

Vv M.

185°

1-093

1-081

1-071

1-061

1-052

1-044

1-034

1-119 i 1-030

1-108 i 1-023

1-0118 1-017

1-089 ! 1-012

1-061 i 0-997

1-050 0-989

1-093

1-082

1-071

1-061

vv. M.

100°

1-012

1-005

0-999

0-993

1-053 ' 0-987

1-044 0-982

1-036 i 0-977

1-029

1-022

1 016

1-010

0-970

0-967

0-963

0-1)59

0 993 0-948

0-983 0-941

1-012

1-006

0-999

MO.

Vdd.

65°

1-000

0-994

0-987

0 993 0-881

0-1:88 0-976

0 5)82 0-971

0-976

0-972

0-907

0-962

0-958

0-945

0-938

0-966

0-962

0 957

0954

0-950

0-938

0-932

1-000

0^99 1

0-988

O'i.82

0-977

0-5)71

0-967

0-962

0-957

0-953

0-949

0-937

0-930

Critical conditions of constant volume.

*

65 

100

185

Ap.

0 

190

1.200

Volume.

' 1-00

Rate=0-09° per atmosphere.
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XV

11

loo Zoo 3oo 4oo Joo (ioo 7oo Soo 9oo laoo 1100 12ou 13oo J4oo ISoo.

FIG. 1. Isothermals of paraffin. 

FIG. 3. Isometrics of paraffin.
EAHtJS.]

TABLIC 42.-

ISOTIIERMALS OF TOLUIDIXE AND THYMOL. 53

-Isothermals of paratoluidine, referred to unit volume at 2S° and SO atmospheres.

p

20

12!)

220

32;)

420

520

020

720

820

920

1, 020

1, 320

1,520

V v$e.

310°

1-348 i-::oi

1-207

1-241

1-220

1-204

1-190

1-179

1-109

1-100

1-154

1-136

1-127

V Y&9.

185°

1-348 1-158

1-303 1-143

1-208 ' 1-120

. 1-2-iO i 1-117

1-158

1-143

1-130

1-117

V Y$8.

100°

1-063

1-051

1-003

V v»e.

65°

1-042

1-054 ! 1-035

1-046 1-046

1-039

1-210 i 1-100 ; 1-100 i 1-031

1-196 1-096 ! 1-090 1 1-025

1-178 i 1-087

1-162 1-079

1-147

1-134

1-071

1-005

1-122 1 1-058

1-090

1-072

1-042

1-032

1-087

1-078

1-009

1-062

1-019

1-013

1-029

l.-0:(8 1-022

1-030 ; 1-010

.1-023

1-017

1-011

1-007 : 1-005

1-002

1-055 0-997

1-035 ! 0-984

1-023 0-977

i-ooo

0-994

0-979

0-970

1-011

i-ooo

1-001

0-1106

0'992

0-B87

0-976

0-909

1-042

1-035

V Y&B.

23°

1-000

0-990

1-028 0-089

1-022

1-017

0-98::

0-078

1-011 : 0 973

1-000 0-908

1-001 0-91)4

0-!'9G : 0 900

0 992 ; 0-954

0 987 0 952

0-974 i 0-942

0-967 0-930

1-000

0-994

0-989

0983

0-J78

0-973

0-909

0-005

O-OHI)

0-05U

0-952

0-941

0-934

Critical conditions of constant volume.

e

28

65

IS.)

&p.

( 050)

25

270

1.200 

(1,850)

Volume.

1-0-i

..........

Kate = 0* 10° per atmosphere.

TABLE 43. Isothermals of thymol, referred to unit volume at 28° and 30 atmospheres.

p

20

120

220

320

V

» «.

*310°

1-329

1-277

1-240

1-212

420 1 1-192

520

620

720

820

920

1, 020

1,320

1,520

1-175

1-162

1-151

1-142

1-134

1-127

1-111

1-103

1-329

1-279

1-242

1-212

1-188

1-167

1-148

1-131

1-110

1-103

1-091

1-059

1-040

V "».

185°

1-102

1-145

1-129

1-116

1-104

1-093

1-084

1-075

.1-067

1-060

1-053

1-037

1-027

1-162

1-145

1-129

1-11.0

1-103

1-092

1-081

1-072

1-004

1-055

1-047

.1-020

1-014

!

V * .

100°

1-076

1-060

1-057

1-048

1-040

1-033

1-020

1-020

1-014

1-008

1-003

0-989

1-070

1-006

V V

65°

1-042

1-035

1-057 i 1-028

1-049

1-041

1-033

1-021 '

1-015

1-010

1-026 j 1-004

1-020

1-013

1-007

1-092

0-986

0-981 0-977

()-9:>9

0-994

0-989

0-985

0-973

0-960

1-042

1-035

1-028

1-021

1-015

n

28°

1-000

0 994

0-987

0-981

1-0

0-9

o-r

0-9

0 970 i 0-9

.1-009 ; 0-971

1-003 I 0-905

0-998 ' 0-0(11.

0-993 I 0 050

0-988 , 0 952

() !

0-!

0-9

0-9

0-9

0 983 0-948 1 0-9

0-970 : 0 937

0-961 0-931

0-!

0-9

' ' ' Speeiiil experiment, made iator. 

Critical conditions of constant volume.

e

28

65 

100

185

310

Ap.

( 020)

40 

410

1, OitO

1. 

' 500

 Volume.

1-01

Kate = 0* 10° per atmosphere.
54 THE COMPRESSIBILITY OF 'LIQUIDS. [BOLL. 91

40. Isometrics. From the importance of the subject it is necessary nt 

peruse the Tables 38 to 43 somewhat more in detail than was done io 

earlier work. In case of alcohol (Table 39) the curve/for 28° to 185°, 

PI. xni, are a family of like properties; the curve for 310°, however, 

intersects these iu the region of high pressures (1,500 atmospheres). 

Here, therefore, is additional corroboration of the remarks made in § 35, 

that above the critical temperature equation (10) is not applicable. 

The case may be more serious. It is also supposable that the 310° is 

only an accentuated expression of the shortcomings of equation (4) in 

general. I call to mind that this equation has only been used as the 

upper numerical limit of the isothermal band, for volume decrements; 

hence a lower limit for volumes. See next section.

The chief result of the present table is given by the supplementas 

tables: for V6p = T728,i5o = l, Q and2? as far as 185° are linear function! 

of each other. This is well shown in PL xni, Fig. 2, and PI. xix below. 

The rate of change is one-tenth degree 0. per atmosphere.

Eesults of the same kind hold for ether, Table 38, PI. xiv, although 

the high temperature discrepancy conformably with the lower critical 

temperature is somewhat more pronounced. The rate of variation of 

6 and p for V8p 7"28i ioo = 1 is here 0-12° 0. per atmosphere. This also 

is clearly shown iu PI. xni.

In case of paraffin, Table 40, which is the first substance solid at 

ordinary temperatures V0p = . . "Fes.m = 1 also shows a somewhat larger 

variation of 6 and p, the rate being 0-13° C. per atmosphere. A notable 

peculiarity of these curves is the occurrence of a discrepancy at 310° 

similar to that of ether antl alcohol, but much less pronounced.

For thymol Table 43, PI. xvm and xix, the results obtained resemble those for paraffin, but the agreement is not so good. The rate is 

0-11° C. per atmosphere, when V6p = T7G5] i 2o = lt04. Toluidine Table 42, 

PL xvn, shows the rate 0-10 per atmosphere, when F«p= VGr>im =l'M. 

For diphenylamine finally, Table 41, and Pis. xvi and xix, the rate is 

0-09° C. per atmosphere. In most of the solid substances the expansion difficulties, § 14, reuder the results inaccurate particularly in cases 

where two or more distinct threads were observed.

But taking the results as a whole (0° to 185°), it follows with considerable certainty, I think, that if temperature and pressure vary linearly 

with each other at the mean rate of about 0-11 C. per atmosphere, there ivill 

be no change of volume. Changes of state of aggregation are excluded 

from the considerations.

More rigorously this is expressed thus: If with the observed thermal 

expansion, compressibility be supposed to increase inversely as the 

first power of the pressure binominal (I/a + j?), then temperature and 

pressure must vary linearly to maintain constancy of volume.

In PL xix the chief isometrics have been grouped together for comparison. The linear march between 0° and 185° is well shown by ether, 

alcohol, and paraffin. For toluidine and thymol the irregularities are
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XVI

ZOO 300 40O 5OC GOO 70O 800 300 IOOO 1100 I2OO I30O 1400 I5OO

Isothermals of diphenylamine.
BARUS.] THERMODYNAMIC SURFACE THERMAL EXPANSION. 55

in an opposite sense, and for thymol the distribution of points is actually 

zigzag as far as 310°. Hence a march of errors can not be said to be 

discernible. The break in the undercooled region a, like the break 

between 185° and 310°, is marked. The latter will be specially discussed in the final paragraph of this chapter in connection with direct 

data.

The thermodynamic signification of the above results has already 

been suggested, § 2. -It follows, therefore, so far as the present work 

(§ 40) goes, that the therinodynainic surface Vdp will probably possess 

oblique symmetry as shown in PI. xx. This curve is generated by moving the initial section^, parallel to itself, but in the oblique direction, so 

that ten units of pressure may be passed for each unit of temperature. 

In this motion the left-hand branch of the curve which issues from the 

plane 6, v would rapidly run up to infinity, so that the surface is everywhere bounded on the left by an oblique infinite plane. This points 

out a recurrence of the insufficiency of equation (4) already adverted 

to in § 35. From an inspection of this surface it is, therefore, not possible to deduce the corresponding expression for thermal expansion.

The cause of this difficulty is probably to be referred to the fact that 

the ratio of 9 and# is not independent of Vep. Hence, in moving the 

initial section parallel to itself, the curve must be conceived to expand in 

its own plane in such a way that the oblique horizontal lines described 

by the consecutive points of the initial curve are not all parallel. In 

PI. xx, therefore, 1, 5=3, 7; 2, 6=4, 85 b, e=d, g; etc. But 1,3, 2, 4, 

b, d, etc., are not parallel.

DIGRESSION ON THERMAL EXPANSION.

41. Exponential equation proposed. Before proceeding to the coinpiv 

tations of the next paragraph, it is convenient to insert a digression here 

relative to thermal expansion. I made many computations, but the 

results are much more inaccurate and the. equations less satisfactory 

than was the case with compression. Expansion occurs at a rapidly 

accelerated rate with temperature, tf, in case of low pressures.

Hence the equation

a- ^V T

-dT=i=m -.... (ii)

Cvl' JL~~/v/v

whence

(12)

suggests itself. The first difficulty is the choice of an initial temperature, so that the two equations will be put
56 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 02.

An application of tliis equation to the data for ether is given in Table 

44, and the difference between observed and calculated inserted above 

in Table 5. Ap is the pressure increment, the initial pressure being 

UK) atmospheres. The table is one of double entry, so that 3- has also 

been inserted.

TABLE 44. Expansion and compression constants of ether.

t

29°

65°

100°

185°

310°

Ap = 0.

T X 10'.

1,824

1. 824

1,824

1,821

1,824

a x ios.

165

226

341!

1, 005

 84, 200

&p = WQ.

T X 10°.

1, 530

1. 530

1,530

1,530

1,530

& X W'.

165

226

343

1. 005

34, 250

bp 200. '

T X 106 .

3,380

1, 380

1, 380

1,380

1,380

i> X 10G .

165

.226

343

1,005

34, 250

Ap = 300.

T X 106 .

1,240

1.2JO

1. 240

1, 240

1,240

i> X 10".

165

226

343

1,005

34, 250

l/9

(nearly).

It is seen thai; the change of t: with pressure is less curvilinear and 

not nearly so rapid as the change of either 3 or l/'c> with temperature.

The curve ) itself, though fitting the extreme results very well, doea

so less nearly for the moderate expansions under 400 atmospheres, as 

the expansion under these conditions becomes more rapidly linear than 

the curve predicates.

Making the final step in these considerations, I supposed that the 

discrepancies in question might be remedied by a more general form,

v/V=ln T/ff

whence

and

But these relations are too coraplicated to be fruitfully discussed here. 

42. Observed contractions due to cooling under pressure. To corroborate the above results as a whole, I will also insert a series of direct
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XVII

100 EDO 300 400 300 60O 7OO 8OO 9QO

Isothermals of toluidine.

1000 MOO izoo woo woo isoo
BABUS.] CONTRACTION DUE TO COOLING UNDER. PRESSURE. 57

measurements on the contraction of substances, cooling under pressure. 

Experiments of this kind are difficult. The strain resulting from the 

continued application of high pressure produces much breakage, either 

of the parts of the apparatus or of the capillary tubes. It is clear that 

in method pursued the fiducial volume must be constantly redetcrmined. 

I therefore made the experiments at high pressures, alternate with lowpressure experiments, keeping the same interval of pressure and the 

same thermal environment throughout the series. In Table 45 the 

results were obtained with a relatively wide capillary, so that the filamentary platinum / platinum-iridium thermo-couple could be drawn 

through the tube, with its junction in the substance. This insures accuracy of thermal measurement; but tubes of this kind can not withstand high pressures. Hence, in subsequent experiments, Tables 40 

to 50, the filamentary couple was wrapped around the outside of the 

capillary in the thermal bath. Temperatures here merely subserve the 

purpose of coordinating the high and low pressure results. In all the 

experiments leaks were carefully guarded against and unsatisfactory 

attempts rejected.

In the tables P is the acting pressure, L the observed length of 

column, and -Wp/Fthe volume contraction per unit of volume due to P.

v Temperature 6 is given in arbitrary thermoelectric degrees, and y are

the successive volume decrements due to cooling. A chart accompanies each table. Cooling took place between 185° and 100°, care 

being taken that at the higher temperature the parts of the tube had 

been equally heated throughout before the ebullition of the vapor bath 

was stopped.
58 THE COMPRESSIBILITY OF LIQUIDS. [BULL.92. 

TABLE 45. Contraction due to cooling under pressure. Paraffin (first sample).

P = 150atm. 

J, = 22-Ocm .

y^ X103 =23-0

P=0 atm. 

£ = 22' 6"".

e

( o

2

5

10 

16 

23 

31

48

58 

04

72

78

88

94

102

f °

7

19

35 

54 

67

83

99

113

-y X 10'

o-o

0-9

2-7

4-1 

7-7 

10-5 

13-2 19-5

24-5 27-3

30-5

32-7

35-9

39-1

42'3

o-o

0-5

5-3

12-4 

20-0 26-5

33-0

40-0

46-0

P = 150 atm. 

L 22-0 .

y-X 103 = 23-0

9

( °

2

6

11 

18

24 

34 

50

58 

GO

74

82

-fxio«

0-0

1-4

3-2

5-5 

8-6 

10-5 14-1

205

24-1 20-8

30-0

33-2

TABLE 46. -Contraction due to cooling under pressure. Paraffin (second sample).

P=400 atm.

i^rW'O01".

y X103 = 57'0

1 =0atm.

7- __ Ori-Ortn dj £u ^lu .

P = 400 atm. Zi = 19'0cln .

i)y-X103 =57-0

0

f °

30

65

115

174

! 255

] 325 

405

510

585

660

715

0

15

65

140 

240

320 

 410

470

550

605

660

720

1,770

f o

30

85

175

260

 345

425

495

565

660

720

- x.o.

57 + 0-0 1-1

3-7

7-9

12-1

18-9

24-2 30'0

37'9

45-8

52-1

57-9

O'O

1-0

6-0

14-3 23-3

30-7 39-6

46-5

54-9

60-4

66-8

72-8

78-7

57 + 0-0 3-7

7-4

13-2

21-1

26-8

34-2

39-5

44' 7

54-2

59-5

P=0atm. !

L = 20-2"m . !

P= 400 atm.

-y^- X103 =57'0

,

P = 0 atm.

ij = 20 l 2cm .

0

( o

34

104

154

244

329

' 424 

484

564

614

674

.724

( o

24

64

149 

239

' 314 

414

484

564

664

.709

0

34

84

134

234

309

394

474

544

609

669

714

V 

-y X 103

o-o

2-4

 10-0 14-8

23-7

32'2

42-1 48-5

56-4

61-9

68-3

73-7

57 + 0-0 3-2

5-3

11-6 19-0

23-7 31-6

40-0

45-3

54-7

60' 0

o-o

2-0

6-9

12-4

22-3

30'2

38-6

46-5

53-9

60-9

67-3

72-3

P=400 atm.

i = ]9'0cnl .

y- X 103 =57'0

6 -yX303

'0 57 + 0-0

IS) 1-0

64 3-2

154 ! ]0'5

214 H-7

31.4 24-2

i 404 ! 30-6 

474 36-3

554 42-6

604 47-4

659 52-1

69 i 55-8
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL XVIII

100 ZOO -30O 4OO 50O 6OO 70O BOO 3OO

Isothermals of thymol.

IOOO MOO IZOO 1300 1400 I50O
BARUS.] CONTRACTION DUE TO COOLING UNDER PRESSURE. 59 

TABLE 47. Contraction due to cooling under pressure. Paraffin (third sample).

P = 400 atm.

y X 10S =52'9

i

P=20atm. |

I, = 22-5"".

Dp

y X 103 = 0

P= 400 atm. i:=21-3cm .

y X10»=52'9

e

0

13

43

98 

178

' 266 

348 

433

504

003

f o

14

48

1 103

1178

' 300

378 

456

526

623

0

18

r.QUO

128

202

 314

410 

513

567

622

662

1)

-Y X 10»

o-o

0-1

2-4

7-0 

-13-2

21-1 

27'7 33'8

40-0

48-3

O'O

0-5

5.3 10-7

18-2

31-1

37-8 46'2'

53'8

03-6

O'O

1-0

5'6 

10-3

10-4

24-4

32'4 41'3

45'1

50'0

54-4

P=500 atm.

y Xl03=62-7

P=20 atm.

L = 22'5cm .

y* X10'=0

P=500 atm. £ = 21'lcm .

y3 XlOJ =62-7

0

r o

20

52

109 '392

 277 

327 

392

458

507

.558

' o

15

51

1<>5

240

' 313 

375

440

500 

[555

' 0

32 

85

148

217

290 

351

415

480

545

V

'y X 101

O'O

1-9

3-8

9-0 

14-7

20-9 

25-1 30'0

34'6

38'4

42'6

O'O

1-0

6-0

17'8

25-3 \

33' 3 39'0

45'0

51-1 57-8

O'O

3-8 

8T'0

11-8

17'5

22' 7 27-5

32-7

37-9

42-6

P= 600 atm.

Vn

-y X103 =72-4

P=20at.m. Zi = 22'5cm .

Dn

 y X 103 = 0

P= 600 atm.

Vo

y X 103=72-4

0

' 0

18

58

1-10 

200

 270 

335

405

450

515

1570

!

o

15

55

. 145

235

[320

(

13

' '

V

y X 10S

o-o *o-o

4-3

9-1 

14-0

20-2 

25-5 30'3

34-2

38-0

42'8

o-o

2'2

5-8

15-6

25-3

33-3

o-o

O.A

ft V

'Tube slips (?). Tube breaks.

4 .Bates of contraction.

p

20

400

500

600

A9

500

500

500

500

V

A -y X 10"

51-1

41-1

38-7

37-7
60 THE COMPRESSIBILITY OF LIQUIDS. [HULL. 92.

TAISLK 48. Contraction due to cool'my under pressure.

capillary tube).

Paraffin (fourth sample, closed

P= 200 atm. 

L 18'3<'">.

y X103=28'7

P=20atm.

e

f o

15

100

105 

242 

' 297 

370 

412 

460

514

r o

16

70

112

.185 

 227 

294 

360

1442

J4S8

[525

V j ! y X 10'

o-o i-o

10-4

16-4 

23-5 

28-4 

33-9 

38-3 43-2

47-5

o-o

2-7

8-5

13-3

21-8 

26-1 

330 

3:t-9 48-4

53-2

50-9

P=200 atm. 

y X 1.0 ' = 28'7 |

P=400 atm. 

 ' XWl=53-2

e

f A

15

5(5 

130 

 188 

250 

370 

430

.491

f 0

20

80

129

190 

 250 

315 

372

430

482

530

y X 10'

o-o

9.7

Li 1

0 1 

13-7 

18-1 

23-5 

34-4 39-9

45'4

o-o

0-6

---

5-0 i 10-1

14'0 

19-6 24-1

28-5

33-0

38-0

40-8

P= 400 atm.

Vp

y 

e

( "

2?

8y

1-18 

210 

 280 

330 

382 

440

490

540

f 0

20

73

125 

192 

260 

' 315

380

435

<!80

520

500

$x».

0-0

2-7

9-0

16-0 

22-9 

30'3 

35'1 

41-0 40:3

51.0 50'9

O'O

1-2

6-2

8'9 

14'0 19'0

23-5

29'1

34'1

36.9 40-2

43'1

TABLH 49. Contraction dne to cooling underpressure. Naphthalene.

7' 400 ntm. L- 20-41'"1 .

Vp ^ V X1° ~ 37

P = 20 ntm. L 21'1C '°.

P=r400atm.

Jj iU 4 .

y X 101=37

e

f 0

35

85

170 

230 

- 3J5 

435

505

575

024

677

f 0

24

57

142

209 

 302 

3X2 

481.

530

591

048

f °

40

112

175

202

- 348

420

507

585

038

695

Vy X 10'!

003-4

6-9

13-3 ! 

IS 7 

20-0 : 33-0

39-9

40-8

50'2

55-1

o-o

0-5

4'2

1V3 17-1

24-2 

31-3 39'8

45-0

51-2

50-9

O'O

4-4

9-4

13-8 19-7

2C.-1 33-0

39-4

45-8

50-7

57-0

P = 20 atm.

P 400 atm.

£:=2U'3«">. . 

y1 X 103 = 37

P=20atm.

.Z/ = 21'lcm .

e

( 0

38

N8

178 

270 

. 351 

428

503

568

038

678

f 0

35

105

.185 

270 

 355 

-185 

5-15

015

075

730

35

93

107 

245

' 415

493

577

615

683

V

-y X 108

O'O

2-4 1

6-1 !

13-2 

20-9 

28'0 34'6

41-7

48-8

55'9

00-2

0-0

2-0

C'4

12-3 

17-2 

24-1 

36'4 42'4

46-8

54'2

Gl'5

o-o

1-9

6-2

13-3 19-5

35'1

41'2

48'8

53-5

CO'7

P=400 atm. 

y X 103 = 37

0

( o

29

09

181 

254 

< 334 

411

490

506

616

[689

V

y XW

O'O

2-0

4'4

13-3 

18'7 

24'6 31-0

38'9

45'3

48'3

55-6

Relative rates (initial}.

P.

20

iOO

A0.

500

50d

V

A -y X 103

41-0

36-6
U. S. GEOLOGICAL SURVEY

0°

1000 

50O

O 

500

O 

5OO

O

1000 

500

0 

500

0

500

0

o

tf

X

100 zoo9

300".

BULLETIN NO. 92 PL. XIX

rV

O" IOO° ZOO* 300"

Isometrics of ether, alcohol, paraffin, diphenylamine, toluidine, and thymol compared.
BAIIUS.] COOLING UNDER PRESSURE HYPERBOLIC CONSTANTS. 61 

TAULH 50. Contraction due to cooliny under pressure monoclllor acetic acid.

P - 200 atm.

P=20 ntm.

Jj zr'2*m .

P=200 atm.

L '^-Tm .

e

( 0

10

50

100

3.68 

 238 

336

366

427

480

528

f o

38

53

108

192 

 256

318

377

503

528

51)8

' 0

27

72

134

208

 977 til 1

342

400

462

548

574

V

.y X 10'

o-o1-9

7-2

13-5

23-3 

29-5 38-6

44-9

52-2

58-5

64-8

o-o

1-9

7-5

15-1

25-0 33-1

41-1

491

66' 5

on- 9

78-4

o-o

2-9

8-2

15-5

24-6 32-4

40-6

46-9

54-6

66-2

68-6

P=400 atm. i=20-30'".

P=20 atm.

x/ <Jl'2"n .

P=400 atm.

0

f o

29

166

206

336 

 402 

466

516

556

603

.641

f o

33

48

104

168 

 218

336

m

431

483

.538

0

35

75

145

237

' 295

370

403

400

520

V

y X10»

o-o

3-4

17-8

29-fl

37-4 

44-3 52-3

58-0

03-9

GO'0

74-9

o-o

1-4

7-1

14-2

23-2 32-5

41-1

48.2

56.1 63-2

70-8

o-o

3'5

7-4

15-3

23-2 32-1

40-4

44-3

51-3

58-1

P GOOiihri.

P.= 20atm.

 2i lcn> -

P=COO atm. 

X,

6

I "

30

40

300

305 

 233

:roo

357

428

485

.530

f o

29

85

155

225

 285

353

415

487

535

.600

' 0

20

70

195

265 

' 335

405

453

500

545

V

y x 101

o-o

1-5

7-1

12-6

20-1 "26-6 

34.2 40-7

4.S-7

53-8

60-4

o-o

4-8

32-7

22-2

30.7 39-6

49.1

571 04-6

70-3

79-8

o-o

2-0

8-1

21-1

29-0 37*2

45-2

50-3

55-3

60-9

P.

20

200

400

COO

AS

500

500

500

500

A-£-X10«

f-4'8

59-8

58-5

54-5

These data very fully corroborate each other and the statements of 

the above §§ 23, 30, 31, 33 and 41. Contraction under pressure when 

referred to unit of volume at tlie initial (high) temperature, decreases 

at a rapid rate with pressure. In case of paraffin, A\rere the observed 

conditions to hold indefinitely, contraction would altogether cease at 

a pressure less than 2,000 atmospheres. This follows in a less pronounced degree for naphthalene and chloracetic acid. The lines of 

cooling for the same low pressure are parallel.

COMPRESSIBILITY INCREASIN& INVERSELY AS THE SECOND POWER 

OF THE PRESSURE BINOMINAL.

43. Properties of the hyperbolic equation. The expression v/V=ln 

(1 + ap) &la, as utilized in § 39, furnishes a family of curves which must 

in their ultimate contours necessarily fall below the corresponding isotherm als of the substance under discussion. It is the object of the
62 THE COMPRESSIBILITY OF LIQUIDS. [BULL-92.

present section to investigate a similar family, the ultimate contours of 

which must be above the actual isothermals. This may be done by 

assuming

j v d Y

~dp~~(i+rpf I )

whence by integration

In this case when# = GO, ( v/F),)=x = jw/y, or, as will be seen in the 

following tables, (v/ V)p=a, = 2/9. In the actual case, v/ V, though it can 

not be greater than 1, will in all probability eventually exceed 2/9.

The method of discussion to be adopted is similar to that in the foregoing section.

Suppose in the first place that

and

Then 

or if

li = //o/(l + i"ol>o)a and v v0 (1 + r0p0 ) .... (3) 

there results

which is identical with the form (1). Hence if^0 and p are consecutive 

pressure intervals between 0 and p+p^ then the constants obtained 

from observation within the interval^ may be reduced to those applying for the whole interval by equations (3), or the equivalent expressions

44. Presumptive character of the isometrics. According to Mendeleef, 

Thorpe, and Eiicker (1. c.) the volume of liquids in case of thermal expansion may be represented by

(5),

the

temperature and A; the specific constant. Introducing equation (1)

where pressure is constant. Here Vg is the actual volume, 6 the
U. 8. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XX

Thermoclynanlic surface.
BARUS.] HYPERBOLIC CONSTANTS. 63

and denoting by F the volume for the pressure p and temperature 6, 1 

obtain

v- ¥ 

which for pressures and temperatures not too great may be put

If therefore F= Vc = constant,

so that in case of constant volume temperature varies linearly with 

pressure, small intervals of variation presupposed. The rigorous deduction of (1) and (5) is

which is linear in proportion as vp is small compared with 1. In § 40 

it has been shown that the relation of 6 to p is probably linear throughout a ranch greater interval. Hence it follows that equation (1) is 

insufficient for large pressures.

Kegarding equation (5) it follows that if 60 and 6 be two consecutive 

intervals of temperature, the former measured from zero, and if

and 

then

Equation (8) with the exception of the corrective member 7c2 #0 #/(l W) 

has the same form as (5). Hence the observations may be referred to 

any convenient temperature as a point of departure.

45. Hyperbolic constants computed. Applying equation (1) § 43 to the 

observations in §§ 16, 17, 19, 20, 23, 25, which are the most complete 

in hand, I obtained the constants given in Table 51. It is clear that 

v must be some function of /(; but the observations are too crude to indicate the precise nature of this function. If v be plotted as dependent on 

/^, the points are seen to group themselves about a straight line passing 

through the origin. Again if the ratios vf fj. be found, the consecutive 

results show no discernible march or grouping. Hence I have assumed 

the ratio as constant, and have added its mean value in the table,
64 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

The ether and the alcohol points for 310°are not amenable to this method 

of treatment, and the discrepancy is somewhat apparent in the ether 

point for 185°. In case of alcohol the relation of constants is irregular, 

showing unusually large errors of observation.

TAULK 51. Hyperbolic constants which reproduce the isothermal decrements. Direct

computation.

V/V=fip (l + vp).

Temp. AI X 10" v X 1.0°

Ether.

29° 109-0

05° 228 2

100° 352 9

18o° 1,027 -(5

*;t10° 10,842-0

28°

65°

100°

185°

*310°

830

1.023

1. 57:1

:;, K7o

18, 400

Alcohol.

87-0

111-5 isj-7

:w s- 2

7.553-0

243

270

1,030

1, 755

Temp.

28°

05°

100°

185^

310°

05°

100°

l>-'5°

310°

15 : 770 !f

MX 105 vXW

Tohtidine.

50- 5

70-0

81-4

145-0

401-1

58

413

no

801

1,730

Diphcnylamine.

61-3

69-3

114-4

214-0

162

285

613 1

889

i

Temp.

050

100°

185°

310°

28°

05°

]IH)°

]8.)°

310°

,1X10" v X 10«

I'arailin.

85-1

111-5

181-5

31)8-1

191

475

840

1.510

Thymol.

 

07-8

69-5

99-3

162-5

465-2

 - - - -

405

157

553

715

2,000

* Exceptional valui's due to partial adiabatic expansion.

v Mean ratio = 4;-5.

46. Mean hyperbolic constants derived. The next table, 52, contains 

the values of yu obtained by accepting the equation ^=4-5 /y, derived 

at the end of the last table. The exceptional alcohol and ether points 

have been rejected. In general it will be seen that the diagram of ^ 

and v is not so smooth as was Plate xn, in §37, for a and 5. This 

shows, I thinlv, that the equation of the last section is more in keeping 

with the character of the observations made, than is the equation of 

this section.

TABLE 52. Mean hyperbolic constants.

4-5/4))'

Substance.

Ether..,.-,...

Alcohol.......

f 29°

050 

\ 100°

" [8fP

I 310°

f 28°

05°

\ 100°

185°

[310°

ju X 10"'

107

229

35 1

1. 221

89

115

163 340'

.........

Substance.

ToluUUnc-parii

Diphcnylamine

6)

f 2fi°

(i5° 

I 1(10°

1 JS^

(.3100

f 65°

j 100°

1 185°

[310°

juXlO15

59

(59 8">

141

412

64

69

112

210

Substance.

Paraffin.,.,.. .

I

&

{ 65°

j 100° 

1 185°

[310°

f 28°

65°

-j 10!,°

1 185°

[310°

/4X108

88

112

1SI

382 1

.

60

73

97

102

481

* Equation begins to fail.
Contraction on cooling. Paraffin.
BARUS.] ISOTHERMALS AND ISOMETRICS. 65

47. The isothermal band. Making use of the constants in Table 52, 

I calculated the actual isotherrnals in the way suggested in § 30. The 

expansions are directly observed, and the only hypothesis introduced 

is equation 1, § 43. The results so obtained are inserted in Tables 38 

to 43, where V^ are the actual volumes obtained by the hyperbolic 

equation § 43, and V&e refer to the exponential equation, §35. These 

two quantities, constituting the upper and lower limit of the isothermal 

band, are to be discussed together somewhat in detail.

In case of ether the divergence or width of the band at 1,000 atmospheres is about 0-4% at 28°, 1% at 65°, and 1% at 100°. At 185° the 

divergence would be 8%, but the hyperbola here begiu-s to fail. Better 

accordance could here be obtained as far as 185° by introducing 

y = 0-0003 + ||-/jt, as found from Table 51; but in consequence of the labor 

already spent I desisted from this additional trial. My purposes are 

sufficiently answered by the above computation. Constructing the 

relations (isometrics) for p and 0 when F(, = 1, it will be seen that 

whereas in the case o^ the exponential formula the straight line is 

predicted even as far as 185° and 1,300 atmospheres, this is not the case 

for the hyperbolic form. Divergence from the linear curve begins very 

appreciable at 100° and 600 atmospheres.

In case of alcohol the conformity of results is better throughout. 

At 1,000 atmospheres the curves for 28° do not diverge; at 65° the 

divergence is 0-2%; at 100°, 0-3%; at 185°, 2%. Putting F0 = l, it 

appears that whereas the exponential relation holds linearly as far 

as 185° and 1,500 atmospheres, the hyperbolic equation holds only 

a,s far as 100° and 700 atmospheres.

Divergence in case of paraffin at 1,000 atmospheres is 0-1% at 65°; 

0-2% at 100°; 0-7% at 185° ; 6% at 310°. As far as 185° and 900 atmospheres both isometrics are linear. At 310° both fail, but on opposite 

sides of the isometric. The agreement of the exponential is preferable 

throughout.

The observations for diphenylamine are less satisfactory, partly because of the choice of 0 atmospheres as initial pressure, partly because 

of some error in the expansion data. At 1,000 atmospheres the divergence of curves is 0-1% at 65°; 0-1% at 100°; 0-2% at 185°; 1% at 

310°. The interesting feature of these results is the fact that the 

isometrics seem to retain their linear character as far as 310°.

In case of thymol the divergence at 1,000 atmospheres is 0-1% at 

28°; 0-2% at 65°; 0-1% at 100°; 0-6% at 185°; 3% at 310°. Irregularities in expansion have also distorted these results.

Finally, in case of para-toluidine the divergence at 1,000 atmospheres 

at 28° is nil; at 65°, nil; at 100°, 0-3%; at 185°, 0-3%; at 310°, 3%.

48. Conclusion. Summarizing these results, it appears that the exponential v/V=ln(l-{-ap)d/a js more in keeping with the general 

character of the isot/herinals discussed than is the hyperbolic form 

v/V=fip/(L+vp). Both equations fail at 3JO°. It is difficult to assign 

Bull 92 5
66 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

a reason for this. It is not probably due to occluded air since the substances were boiled and introduced into a hot capillary tube. Moreover, in case of mercury (Table 3) an air-bubble discrepancy if present 

would necessarily have shown itself at 310°. The error, due to the 

fact that my curves must be in some small part adiabatic, would induce 

too slow a variation of volume and hence emphasize the high temperature break of the isometrics. There may be dissociation of many of 

the above organic substances at this high temperature. Azo-beuzol, 

for instance,-actually decomposes and turns black at 310°. But just 

what the effect of dissociation will be, in modifying the computed 

isothermal, is not easily conjectured, for the greater compressibility 

resulting is compensated by larger initial volumes. The high temperature break might result from inconstancy of temperature iu the boiling 

tube. I did not explore the distribution of temperature, for the behavior was such that I had no reason to suspect inconstancy.

To interpret these discrepancies I resolved to make direct measurements for ether, a case in which the high temperature break is most 

pronounced. Finding a tube which was strong enough to resist 1,000 

atmospheres at 310°, I obtained the following example, Table 53, of 

many similar results. The volumes are all referred to unit of volume 

at 100 atmospheres and 22°. To reduce them to 100 atmospheres and 

29° (which hold for the above designated isothermals, Table 38), the 

volumes at 300° must be decreased about 1*5%. By doing this I obtain the "observed" isothermal inserted in PI. xiv, Fig. 1. Since the 

length of thread L is now only l-85cm, the low temperature isothermal 

can not be accurately given. The tube broke, in my final endeavors to 

repeat the experiments, in such a way to exclude adiabatic conditions.

TABLE 53. Isothermals of ether. Direct measurement. 0 = 300°; i = 6 -00cm.

p

atm.

100. . . .

200. . . .

300.,..

Volume.

3-30

1-83

1-56

Volume.

3-12

1-76

1-52

P

atm.

400....

500. . . .

600....

Volume.

1-43

1-34

1-28

Volume.

1-41

1-32

1-26

P

atm.

700. . . .

800....

900....

Volume.

1-24

1-19

1-16

Volume.

1-23

1-19

1-16

0=22°; £=l-85<"».

100.... 

200....

1-00 

 -99 1-00 99 300.... 

400....

 97 

 96

 97 

 90

It follows from this table that the 300° point of the ether isometric 

may be looked for in the region of 2,000 atmospheres. Hence the observed results substantiate the computed isometric for ether given 

in Plate xiv, which predicts the corresponding poiut at about 2,200 

atmospheres. Nevertheless it can not be too carefully noted that if 

the isometrics for volumes 1-2, 1-3,1-4 be ^constructed (185° and 

310° being now available) the'break between 185° and 310° remains in 

full force? quite in. conformity with the other data (alcohol, paraffin.
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XXII -

50 

40

3C

20

to

0

x

^

^

'

>O 4C

Fig. 4.

/

^s/

0 6(

^^

/S

X «

 tj

o^to.

y/ s

/

2o^tm,.

TOJttms.

/^

/.

//

/

/

//

^

/Fi,q±

/

,

/^

/

Temp

^

 /

/

/

 *"

/

.

/

.20^1 

.,600^

cLecreasi

/

Fig.Z.

7i

nff. s

/

//

//

^/

/

/ ,

/

/

/

/

/F-Q

pi

/

» Zo^tnv

m.

 > IOO ZOO 3OO 4OO SOO 6OO* 7QO 6 IOO ZOO 3OO 4OO SOO 6OO . 7OO 

O IOO ZOO 3OO 4OO SOO 60O

FIG. 1. Contraction on cooling under pressure. Paraffin. 20 and 400 atmospheres.

FIG. 2. Contraction on cooling under pressure. 20 and 500 atmospheres.

FIG. 3. Contraction on cooling under pressure. 20 and 600 atmospheres.

FIG. 4. Relative rates of contraction. Paraffin.
BARDS.] ISOTHERMALS AND ISOMETRICS. 67

etc.). The full explanation of the occurrences here met with is of exceedingly great importance in its geological bearing and will therefore be made the subject of my subsequent work. Curved isometrics 

lead to certain interesting conditions of maximum volume.

The chief observational discrepancy encountered in these results 

is the expansion error in case of substances which solidify between observations at different temperatures. Hence the effect of different 

volumes on the slope of the isometrics can not be satisfactorily discussed. Since compression measurements retain their value independent of the thermal expansions and since the method pursued is such that 

all necessary measurement for thermal expansion can be made at atmospheric pressure, the difficulties may easily be rectified. By using 

a thermometer tube the purely thermal data can be supplied with any 

desired degree of accuracy. This I conceive to be the advantage of the 

mode of investigation set forth in the present paper.

Among the important results of the above tables is the fact that 

compressibility moves on the even tenor of its way quite independent 

of normal boiling points and melting points, provided of course the 

conditions are not such that boiling and melting can actually occur. 

For this reason compressibility is particularly adapted for exploring 

the nature of the environment of the molecule in its relations to temperature, i. e. for exhibiting the character of the thermal changes of 

the molecular fields of force.

49. The above work, though confined to relatively low ranges of 

pressure, was believed to have a more general value for reasons such 

as these: Instead of tracing the isothermals of a single substance 

throughout enormous ranges of pressure, similarly comparable results 

may possibly be obtained by examining different substances, conceived 

to exist in as widely different thermal states as possible. For in such a 

case, inasmuch, as the actual or total pressure is the sum of the pressures 

applied externally and the internal pressure, the total pressure in 

question virtually varies enormously. This calls to mind the remarks 

made in §§ 35 and 43 relative to observations confined to limited parts 

of an isothermal.

Finally, the work of the present paper may be looked at from quite a 

different point of view. Suppose, for instance, I regard the linear isometric proposed by Eamsey and Young (loc. cit.) as an established fact. 

Then the chief result of the present work, viz, that the exponential 

equation (2) if applied to the observed changes of volume predicts a 

linear isometric throughout an enormous range of pressure, affords 

favorable evidence of the probable truth of the exponential equation 

in question. In other words, it is probable that along any isothermal 

compressibility increases inversely as" pressure augmented by a constant. The interpretation of this constant ca.ii not now be giyei},
, OHAPTEE II.

THE EFFECT OF PRESSURE ON THE ELECTRICAL CONDUCTIVITY

OF MERCURY.

INTRODUCTORY.

50. Purposes of the work. In the endeavor to obtain data for the relation between melting point and pressure, a question which in its 

higher phases is of extreme geological importance, the difficulties of 

the general problem make it advisable to begin with material which 

can easily be operated on. Mercury suggests itself at once. Its melting point is very low, at temperatures where most resinous cements, 

marine glue for instance, are practically rigid. This greatly facilitates 

the construction of high-pressure apparatus, and the experiments 

therefore become of a less formidable character. The molecular 

structure of the metal is relatively simple, which is another advantage. 

Apart from practical considerations the behavior of any substance of 

definite character has its own intrinsic importance and must contribute essentially to a general diagram of the fusion phenomena in question.

Again, mercury in common with many other metals (K, Na, Sn, etc.) 

shows a marked increase of electrical resistance on passing from the 

solid to the liquid condition. Indeed, the resistance of the liquid may be 

from two to five times that of the solid metal, as the researches of 

Matteuci, Matthiessen, Siemens, L. de la Eive, Cailletet andBouty, 1 0. 

L. Weber, 2 Grunmach, 3 and others show. The change of resistance in 

question may therefore be expediently selected as a criterion of fusion, 

a principle which may be used, cautiously of course, in the cases 

of metals and even of some solid electrolytes. The conductivity of 

glass, for instance, increases at a phenomenally rapid rate while the 

solid passes through the viscous stages into fluidity (Buff, Beetz, Gray, 

Foussereau, Perry, and others 4 ). From all this it follows that the somewhat cumbersome problem of melting point and pressure may in many 

instances be translated into electrical resistance and pressure, a form in

'Cailletet and Bouty: C.R., vol. 100, 1885, p. 1188.

1C. L.Weber: Wied. Ami., vol. 25,3888, p. 245; ibid., vol. 37, 1889, p. 587; ibid., vol.38, 1889, p. 227. 

?Gruumach: Wied. Ann., vol.33, 1888, p.76'1; ibid., vol. 36,1889, p. 587; ibid., vol. 37,1889, p. 508. 

4 The literature is given in my paper op stressed glass (Am, Jour, Sci., vol. 37, 1889, pp. 339,340).

68
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XXIII

Contraction on cooling under pressure. Paraffin.
BABUS.] BIBLIOGEAPHY METHOD OF WORK. 69

which it is much better adapted for experimental attack. This indicates the general trend of my present work.

The present chapter shows this method to be feasible. 1 measure 

the effect of pressure on the conductivity of mercury at ordinary temperatures, the results of which work afford a sufficient preliminary test.

51. Literature. The effect of pressure on the conductivity of liquid 

metals is not well known. Chwolsou ' operated on solid metals, obtain 

ing results of '01% (copper and brass) to -1% (lead), per 100 atmospheres. These data are too small to be of practical use of the kind 

above in view, except in the case of lead perhaps. They are too easily 

distorted by the thermal effect of compression. Compared with my 

results for liquid mercury they suggest that distinctions between the 

solid and the liquid states may perhaps be feasible in a scale of compressibility. E. Lenz, 2 operating on mercury, found a diminution of resistance of 2% per 100 atmospheres, proportional to the pressure of 1 to 

60 atmospheres, a very favorably large result quite in keeping with 

my purposes. E. Pfeiffer, 3 using Cailletet's pump, communicates a 

method for the measurement of electrolytic resistance under pressure, 

and data for an aqueous solution of CO2 . J. W. Clarke 4 electi-olyzed 

dilute sulphuric acid in a closed space. L. Graetz 5 . taking a somewhat different line of departure, endeavors to arrive at the effect- of 

pressure on the resistance of solid salts.

Foussereau6 discovered some remarkable effects of long continued 

high pressure (175 atmospheres) on the conductivity of metallic chlorides (Fe, Al) in very dilute solution. The effect of pressure on the 

resistance of carbon, which lies beyond the present work, has been 

studied by Mendenhall7 and others.

This practically closes the list of more or less closely allied researches. 

The results of E. Lenz seem, therefore, to be the only special data in 

hand. Again, a study of the combined effect of temperature near the 

melting point of a metal and the superincumbent pressure has never 

been made.

SIMPLE METHODS AND RESULTS.

52. Caillctetfs tubes described. My first experiments were made with 

Cailletet's oxygen tubes, into the small end of which a platinum terminal was either fused or cemented with marine glue. The tubes 

themselves proved to be badly annealed and unexpectedly fragile 

when subjected to high pressure. I therefore took Prof. Eood's precaution of annealing them at 450°, until traces of polarization disappeared. 'For this purpose it was convenient to cover the glass with

'Chwolson: Carl's Reportoriura, vol. 14, 1878, p. 26, 27. Beibliitter, vol.5, 1881, p. 449. 

2 K. Lenz: Beibliitter, vol. 0, 1882, p. 802. Original (Stuttgart, 1882) not accessible. 

"Pfeiffer: Wied. Ann., vol. 23, 1884, p. 625. 

*Clarke: Phil. Mag. (5), vol. 20, 1885, p. 435.

5 Graetz: Wied. Ann., vol. 29, 1880, p. 314.

6 Fonsscroan: C. E., vol. 104, 1887, p. 11.01. . 7 Meudeuhall: Atn. Jour. Sci., 3d sor., vol. 24, 1882, p. 43.
70 THE COMPRESSIBILITY OF LIQtJIDS. [BULL, el

asbestus, surround this with a piece of iron gaspipe also covered with 

asbestus, and then expose it in a combustion furnace, Fletcher's being 

preferable. In spite of all precautionary preparation, I found the tubes 

in hand (external diameter 2o2 = l-8cm, internal diameter 2^ = O17cm ) 

to be incapable of withstanding more than 200 atmospheres internal 

pressure. In future experiments it will therefore be necessary to take 

advantage of smaller diameters.

Instead of platinum, amalgamated zinc terminals were used in case 

of the zinc sulphate solutions.

53 Electrical apparatus. The tubes were made part of a Wheatstone bridge of which the corresponding branch was a suitable rheostat X. If a/6 = x/R) and if I know the deflections of the galvanometer for any increment dx, I can at once compute the quantity dR produced by a given pressure. For in the case of like deflections, 

8x/x = dR/R. By this simple and convenient method I obtained the 

data of Table 54, by alternately increasing and decreasing fche pressure 

by increments of 25 atmospheres each. In Table 54, dp is the increment of pressure in atmospheres, practically in megadynes per square 

centimeter, since the Bourdon gauge (§ 9, 10) used is neither absolute 

nor very sensitive. dR/R is the corresponding increment of resistance 

for each dp. By adding to dR/R the correction dr/r due to the expansion of the glass tube (the method of computing dr/r will presently be 

shown, § 55) I obtain the final column dR0 /R0 , or the resistance effect 

of the hydrostatic pressure p. I may state that my galvanometer, in 

case of mercury, was sensitive enough to show deflections of 21cm readable to 0-01cm per 100 atmospheres.

54. Preliminary data. The initial pressure in the following table is 

25 atmospheres, insuring fixed positions of parts, and absence of small 

air bubbles. Commercial mercury was used.

TABLE 54. Effect of compression on the resistance of mercury, and of sine sulphate

solution.

[Cailletet tubes: Internal diameter, 0'08cm ; external diameter, 0-90cm .]

Commercial mercury.

fip.

Aim. 

25 .... 

50 .... 75 - - 

100 .... 

125 ....

WX 

Ut/R.

 ] "!

 2-2 

 3-2 

 4-3 

 5'5

103 X 

Br/r.

 0-1 

 0-2 

 0-3 

 0-4 

 0-5

WX 

WZo/J?o-

 1-0 

 3-0 

 2-9 

 3 9 5-0

Concentrated solution, sulphate zinc.

ip.

A. tm. 

(1) 40 

70

(2) 50

KPX 

6Ji,/B.

 2-7 4-0

 2-5

WX 

Sr/r.

-0-2 0-3

 "0-2

103 X 

tJtolEv.

 2' 5 3-7

 2-3

It can not be said that the effect of gaseous polarization in case of 

zinc sulphate is thus eliminated. I was riot surprised, therefore, to find 

these results less regular than in case of mercury. In the mean of two 

series of measurements with pressure increasing and pressure decreasing, respectively, the thermal effect of compression may be considered
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XXIV

60

SO

40

30

20

10

Temp LTlff.

100 ZOO 30O -40O 5OO 60O 7OO

O IOO 2OO 3OO 4OO 5OO

Contraction on cooling under pressure. Naphthalene.

6OO 7OO
BAUDS.] CORRECTIONS FOR VOLUME OF GLASS TUBE. 71

eliminated, provided the observer waits long enough between series 

and observations. During these intervals of waiting the assistant 

easily keeps the pressure constant by moving the screw injector of the 

Cailjetet pump.

55. Correction for volume changes of tube. Allowance may be made 

for the volume changes of the tube as follows : If r be the resistance, 

<r the specific resistance of a column of length I, section q and volume 

i) then

In case of internal pressure and a long cylindrical tube1

where p is the hydrostatic pressure applied, p { and p% the radii internal 

and external of the tube, 1/fc the compressibility, n the rigidity of the 

glass. Again, nearly enough,

where ,« is Young's modulus. Hence

in which equation, in case of capillary tubes, the last term is alone of 

interest. Everett's (loc. cit.) values for flint glass, this being the substance of my tubes, are

ft = 4-1 x 10" j n = 2-4 x 1011 ,1 = 6-0 x 10U atm. = 106,

Introducing these into equation (4), the values dr/r given in Table 

54 follow.

In addition to the gauge inaccuracies, the resistance of the mercury 

column of the Cailletet tube is too small for fine measurements. The 

galvanometer deflection is more or less fluctuating. Hence I have 

rounded off the data in Table 54. The resistance of the zinc sulphate 

column in such a tube is about 20,000 ohms. Having no sufficiently 

sensitive telephone or dynamometer, I made galvanometer measurements, though these are less well adapted for electrolytic work. Other 

technical difficulties are to be passed over here.

56. Preliminary result stated. The interesting result of table 54 is 

this : Both in the case of mercury (metal) and of zinc sulphate solution 

(electrolyte), the electrical effect of compression without change of 

temperature is a decrement of specific resistance, proportional to 

pressure. Eelatively speaking the order of this decrement in the two

1 Tait, loc. cit.
72 THE COMPRESSIBILITY OF LIQUIDS. [BOLL. 88.

cases is not very different, being less than one-half per cent per .100 

atmospheres. The greater coefficient found for zinc sulphate may be 

too large, because of the condensation of the polarization gases during 

compression.

PIEZOMETER METHODS AND RESULTS.

57. Tubular piezometer described. After these encouraging results I 

resolved to repeat the mercury experiment with greater accuracy. I 

availed myself for this purpose ot a change of method, by which much 

greater pressure could be applied to filamentary capillary tubes, similtaneously within and without. The apparatus used is practically a 

tubular piezometer of steel, the dimensions of which are necessarily 

slender. Filamentary tubes and metallic vessels insure greater constancy of temperature. In a thick glass tube the temperature of the 

mercury thread can not be certainly known.

The piezometer is shown in PI. xxvi. Here ddd is the steel tube 

screwed below into a flange FF, by which it is attached to the Cailletet 

pump. Of. § 5. The mercury to be compressed is contained in a glass 

tube acflc, the lower part cf of which is drawn out into a very fine 

capillary. The lower end communicates with another glass tube f] 

carrying a platinum capillary tube bent hook-shaped, If. Above, the 

platinum Avire ac (one electrode), has been inserted into the Avide part a 

of the tube and extends down as far as c, where it*is in contact with 

the mercury. The top is closed with a thread of marine glue, Avhich 

secures the platinum wire in place. To introduce the mercury into the 

capillary tube acli, it is withdrawn from the apparatus and filled in a 

suitable way by aid of a mercury air pump. A layer of marine glue 

gg holds the tube in place. Th.^ perforated screw ft, through which 

the platinum wire a passes without contact, closes the tube. Leakage 

is prevented by putting in &, Avhen hot, and dipping it in liquid marine 

glue before inserting. After these adjustments are made the steel tube 

ddd is inverted and mercury lilili poured in from below. A prolongation ee. ending below in a hook, is screwed iq ddd , so that 

when the tube is in position again it remains filled with mercury. The 

air pump may also be carefully used to make this filling. To facilitate 

the adjustment various other appliances are. necessary. I omit them 

here, as they easily suggest themselves to the physicist. Electric current enters on the outside of the iron trough, § 5, and passes via h into 

Jc and the mercury i; thence through the capillary mercury thread cf. 

and the platinum wire ca back to the battery.

Let ine add that the end a of the tube acJc is much stronger and of 

finer bore than has been shown in the figure. It Avill be noticed that 

fk is a reservoir, permitting contractions of the inclosed mercury during compression. When different low temperatures are necessary for 

observations, the whole length of steel tube ddd is to be jacketed 

with an appropriate thermal bath.
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XXV

100 aoo 

o

30O 100 4OO 5OO 60O 70O 

ZOO 3OO 400 500 600 

O IOO ZOO 3OO 40O

FIG. 1. Contraction on cooling under pressure. Monochloracetic acid. 

FIG. 2. Relative rates of contraction. Monochloracetic acid.

5OO 6OO
BAUDS.] RESISTANCE OF MERCURY UNDER PRESSURE. 73

58. Results. Most of the data of Table 55 were obtained at about 20°. 

In case of the work detailed in the last column, however, I surrounded 

the tube with a cold-water jacket, in this way guarding against thermal 

errors, p denotes the hydrostatic pressure, 3 R^/Ro the corresponding 

corrected decrement of resistance. Correction is easy in this case, being simply p/n, where n is the rigidity of the glass. The table also 

gives -B, the resistance in ohms of the divers mercury threads whose 

approximate length is I and mean radius /> lt The mean external diameter of the filamentary tubes is p2 . Experiments (1) and (4) were made 

with the same glass tube differently adjusted. Experiments (5), (6), 

(7), (8) with two other tubes. The last three experiments are the most 

complete of the series, pressure having been increased from zero to the 

maximum (300 to 500 atmospheres), and then again decreased from the 

maximum to zero. The mean of these pairs of data appears in the 

table, Again, (6) is obtained with a small Bourdon gauge (0 to 300 

atmospheres, cf. § 9), (7) and (8) with a large Bourdon gauge (0 to 

1,000 atmospheres). Hence the agreement of data (0), (7), (8), is.an 

excellent check on the gauges used, as Avell as a Avarrant for the validity 

of the results. This appeai-s clearly in PI. xxvii, thus substantiating 

certain remarks made in Chapter I, § 9.

TABLE 55. Effect of isothermal compression on the electric resistance of mercury.

zometer method.

PieSp

Atrn. 

15....

40....

65....

90

115....

140....

365....

215....

240.... 

205....

290. . . .

ill

K= 

1= 

Pi= 

Pi=

10»X 

6E0 lt

*(1) 

 0-03

1-50

..........

..........

18u 

15cm 

 005 

 03cm

10' X

SKq/R

(2) 

 0-49

-2-03

 3.47

..........

ISso 

15cm

 005""' 

0;!cm

10' X 

dRufR

(3) 

 0-37

1-22

 1-95

 3-41

 4-11

 4-84 

 5-15

 0-21

 7-09 

7-07-

8-20

18w 

15='" 

 005 

 03"°

10»X 

iR0 /R

W 0-58

 1-37

-2-13

2-89

 3-61

 4-38

Break.

..........

18u> 

15cm

 005""" 

 03«ra

*P

A tin. 

25. ..

75. ..

]00. ..

125. ..

175....

225. . . .

250. . . .

::co....

325....

375....

lt= 

l~

Pi = 

p.f=

10'X 

5H0 E

(5) 

 0.92

 1-09

-2-47

. 4-01

 4.71

Break.

10w 

J oc 'n 

 O07':1 " 

 035cni

10'X 

5^o 'R

(6) 

 0-79

-1-50

 2-31

3-10

 3-75

 5-31

 C-87

 7'50 

8-28

7-5<o 

15cm 

 008"* 

 035""

103 X 

SR0 /Jt

(7) 

 0-76

2-19

3-82

 5-35

 0-77 

""'8.22'

9-73

10-81

7-5o>

15cu,

 008«" 

 035cm

10J X 

Sli0/Ji

t(8)

1-44

3 p 02

4-42

5 91

7-43

8-66

10-41

''Average temperature, series (1) to series (7) is 18°.

t Average temperature, series (8), is 6°. At6p = 350 atmospheres no change of resistance was observable during 0 minutes of waiting.

In PI. xxvii, all these data are constructed graphically. The divers 

series of observations are numbered as in Table 55, and together they 

make up a diagonal line running quite across the chart. It is seen 

that the distribution of points differs quite as much for one and the 

same tube ((3), (2), (4), (1)), as it does for different tubes ((1) to (4), 

(5), (6) to (8)). Asa rule the deviations are errors largely avoidable. 

I will omit a discussion, and merely refer to the good agreement of the 

final series (6) to (8) already mentioned.
74 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 02.

DEDUCTIONS.

58. Purely thermal variation of resistance. Accepting Grassi's1 value 

for tlie compressibility of mercury, 3xlO~ G per atmosphere, wliich is a 

fair mean of the data of Colladou and Sturm, and of Oersted, the chart 

easily enables me to pass from dR/R as a function2 of p, to dR/R as 

a function of dv/v, where v is the symbol of volume. Again from the 

known electrical temperature coefficient 3 of mercury (0-0008 at ordinary 

temperatures), and the known coefficient of expansion (0-00018), it is 

easy to construct dR'/R' as a function of dv/v, when the cause of the 

simultaneous variation is change of temperature. Hence the chart 

contains two lines, showing the values of dR/R corresponding to the 

same volume decrement dv/v, when the causes of variation are temperature alone, and pressure alone, respectively. Curiously enough, 

dR/R> dR'/R', an important result, which I shall presently interpret. 

The chart also contains the corresponding data for solution of zinc 

sulphate. dR/R is in the region of negative dR; dR'/R', however, in the 

region of positive dR. Numerically dR'/R' is very large in comparison 

with dR/R, besides having the opposite sign.

The line extending through the chart is very nearly straight. Compatibly with the accuracy of measurement it may, therefore, be inferred 

that the ratio of the quantity dR/R to dv/v, or to pressure, is constant 

throughout an interval of about 500 atmospheres. Hence the conclusions, § 56, drawn from Table 54, are materially substantiated by Table 

55. The chart expresses approximate relations which may be put succinctly as follows:

By subjecting commercial mercury to pressures between 10 and 400 

atmospheres isothermally, dR/R = 30 x 10~ 6 dp, where dR/R is the 

decrement of specific electrical resistance R, corresponding to the 

pressure increment dp. If v be the symbol of volume, then dv/v= 

3 x 10 - 6 8p. Hence SR /R = I0dv/v. "

If o be the symbol of temperature, the res tilts, wliich apply isopiesticallyat ordinary temperatures and pressures are dR'./R'=SQQxlO~6 do-, 

dv/v = 180 xlQ~6 do. Hence dR'/R'= 4:^ dv/v, where R' refers to 

electrical resistance considered in its thermal relations.

59. Again, by subjecting a concentrated solution of zinc sulphate to 

pressures between 10 and 150 atmospheres, isothermally, dR/R = 

50 x 10~6 dp. The other relations corresponding to the above must be 

estimated:

- dv/v 50 x 10~ G dp; -dR'/R'=0-4 30; and dv/v = 200 dff. 

The chief magnitudes are here of different order and even of sign from

1 The newer values of Tait and of -Amagat (loc. cit.) would not essentially modify the statements of 

the text.

2 The subscripts zero, which were used above to accentuate tho corrected values of R etc., are henceforth conveniently dropped. 

3 1 made a special measurement of this coefficient for the mercury used.
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XXVI

c

Apparatus for compressing mercury.
ELECTRICAL RESISTANCE AND PRESSURE. 75

those applying to mercury. Therefore, this estimate is sufficient for the 

following inferences:

The chart shows at once that to bring the compression loci into coincidence with the thermal loci, the former must be rotated around the 

origin in a direction contrary to the hands of a watch. The angle of 

rotation is much greater for zinc sulphate solution than it is for mercury. 

Hence, as before, both in the case of the metal and of the electrolyte, 

the effect of isothermal compression is a decrement of resistance proportional to pressure, and by deduction, the immediate electrical effect 

of rise of temperature, dR'/R' dR/R, is a decrement of specific resistance, loth in the case of the metal (Hg), and of the electrolyte(ZinSO4 -\-A<]).

This points out an inherent similarity between the metallic and 

the electrolytic conduction.

60. Comparison with J. J. Thomson's equation. In J. J. Thomson's1 

expression for specific resistance R = <r = (2-p/K)(q/mx), suppose, to fix 

the ideas, that /?, JL, and q are constant, whereas, m, the number of 

molecules splitting upper unit of volume, per unit of time, and x, the 

distance passed over by the partial molecule moving at a mean velocity 

c, during the interval of freedom t, are regarded as variable. Clearly a? 

can not be independent of m. Taking active molecules alone into consideration, supposing them to be symmetrically distributed and to move 

parallel to each other, x = 3 Jl/mt. Hence

R = (2rtpq/K)x3 /c.

This is in accord with the above data. Reduction of volume tiv/v, 

isothcrmally by pressure diminishes x only. Reduction of volume 

isopiestically, by cooling, diminishes both x and c. Hence the greater 

diminution of R in the former instance (pressure). Finally, by partial 

differentiation under the given conditions dR/dm= (4: -,3q/3KY^i/m5 . 

From this it may be conjectured (conjectured because t and m are not 

independent of each other) that the effect of R on an additional number of molecules splitting up, decreases rapidly with the total number 

m splitting up; i. e., that the numeric of the immediate electrical effect 

of temperature, dR'/R dR/R, is smaller for the metal than 'for the 

electrolyte. oThis also is in accord with the above data.

61. Zero of resistance. In connection with these results it is well to 

note in passing, that, supposing the laws to hold indefinitely, the zero 

of resistance would be reached only after compressing mercury with a 

force of 33,000 atmospheres; but that it would be reached considerably before the zero of volume.

62. Electrical pressure measurement. It follows, furthermore, from 

the above measurements, that the variation of the resistance of mercury 

is sufficiently marked, and bears a sufficiently simple relation to the 

superincumbent pressure, to suggest the use of this principle for 

pressure measurement.

1 J. J. Thomson: Application of dynamics, etc., London, Macmillan, 1888, p. 299.
76 THE COMPEESSIBILITY OF LIQUIDS. [BULL. 92.

63. Measurement of melting point and pressure. Curiously enough 

the results of Lenz (loc. cit.) for mercury are much larger than mine. 

Working between 0 and CO atmospheres, and upon pure mercury filled 

into a piezometer tube by Weinhold's vacuum apparatus, Lenz found 

a resistance decrement of '02% per atmosphere at zero degree centigrade. This is considerably larger than my result, '003% per atmosphere, at 18°. It is impossible to detect the cause of the difference. 

Lenz's work was done in a way which from the description accessible 

to me is faultlessly precise, and my own experiments were so frequently repeated that I can not believe them in error. Possibly slight 

changes of composition may effect a large difference of compressibility, 

and my mercury was not quite pure. It is useless to speculate on 

the causes of difference here. They are now of secondary interest. 

This part of the work can easily be perfected in any measure. The 

point of importance at present follows more emphatically from Lenz's 

large datum than from my smaller result. It is clear that in the usual 

course of my work I may anticipate electrical variations of resistance 

due to pressure to the extent of several per cent; but a resistance decrement, 8R/R, of this value, whenever methods of differential comparison are available, is virtually a very large quantity, capable of 

being followed with great accuracy. It is interesting to note, moreover, 

that the numerical value of SR/R in question is over ten times as large 

as the corresponding volume decrement, dv/v, and that the elastic or 

dimensional discrepancy is even in most unfavorable cases not above 

10% of the total decrement.

Hence I may confidently infer that the method sketched in the present chapter is sufficiently sensitive to throw much light on experimental questions relative to the continuity of the solid and liquid 

states. Prof. J. Willard Gibbs (ioc. cit.), by constructing entropy.energy 

and volume in the direction of three rectangular axes, has devised exceedingly beautiful geometric methods for the general study of continuous changes of physical state. Prof. Poyntiug 1 has discussed the 

subject with especial reference to the transition solid-liquid. Among 

others Amagat (loc. cit.) is searching for the lower critical temperature. 

Apart from these suggestive contributions, our knowledge of what actually takes place in liquid matter is meager in the extr&ine. Hence 

any general method capable of elucidating the unknown topography of 

the therinodynamic' surface of liquids deserves most painstaking scrutiny. The advantage of the above resistance method over the ordinary 

optic and other similar methods lies in the fact that in the above case 

the character of the fusion is described step by step. This is a much 

broader criterion than a merely arbitrary fusion test.2

64. Conclusion. In conclusion I may advert to the fact that a study 

of fusion phenomena in the manner indicated is destined to throw much

1 Poyntiug: Phil. Mag. (5). vol. 12,1881, p. 32.

3 Another available method for describing the degree of fusion is given by the volume changes at 

the melting point. Both of these I hope at uii early date to apply.
U. S. GEOLOGICAL SURVEY 

ff

.003 r"

BULLETIN NO. 92 PL. XXVII

.002

.001

.000

t

IE 

*

I*

-.005

-.006

300 X10

 SP.or

600

300 Atm.

XIO 900X16" 1200 XIO"

0 100 . 200 300 Atm 400

Chart showing the relations between corresponding values of the increments of specific resistance, 

hydrostatic pressure, and volume compression in case of mercury and a concentrated solution of 

zinc sulphate.
BARUS.] FUSION AND SOLUTION. 77

light on obscure points in. physical chemistry. The molecular mechanism through which energy is potentialized during fusion can not on the 

basis of any atomistic theory even be rationally conjectured. Retarded 

solidification, supersaturation, and allied phenomena point to occurrences at the melting point the signification of which is much underestimated. Recent minute researches into the nature of solution should 

not blind us to the fact that questions which apparently lie much 

nearer home, viz, the underlying molecular causes of change of physical state of aggregation, are as yet unsatisfactorily fathomed. 
CHAPTEE III.

THE COMPRESSIBILITY OF WATER ABOVE 100° AND ITS SOLVENT

ACTION ON GLASS. ' 

INTRODUCTION.

43

65. Behavior of water. When temperature rises the compressibility 

of water continually decreases until about 60° is reached. After this, 

temperature increasing further, the compressibility of water increases. 

It Was my original purpose to supplement these results by determining 

the compressibility of water between 100° and 310°, but I did not get 

higher than 185°. At this temperature, and obviously much below it, 

water attacks ordinary glass so rapidly as to make the measurements 

in glass tubes worthless.

66. Literature Compressibility of water. The peculiar behavior in 

question has attracted many physicists. Grassi 1 was the first to find 

that the compressibility (-/?) of water decreases with temperature, being 

50/10° at 0° and 44/106 at 53°. He also observed the compressibility of 

solution s to be less than th at of water. Amaury and Descamps 2 substantiate the latter result, but they only observe at a single temperature, 

15°, at which /? = 46/10". In Cailletet's 3 experiments, extended as far 

as 700 atmospheres, only a single temperature is given (|3 = 45/10°), and 

the same is true of Buchanan's 4 results. After this the siibject was 

vigorously attacked by Tait 5 and his pupils, at first particularly with 

reference to the depression of the temperature of maximum density of 

water 6 produced by pressure. In further experiments Tait 7 studies 

the thermal relations of the compressibility of water. Further results 

are due to Pagliani and Palazzo,8 working with mixtures of water and 

alcohol, but more directly to Pagliani and Vicentini.9 The last ob1 Grassi: Ann. de ch. et de pliys. (3), vol. 31,1851, p. 437. Cf.'Wertheim: Ann. ch. et phys. (3), vol. 23, 

1848, p. 434.

2 Amaury and Descamps: C. E., vol. 68,1869, p. 1564.

3 Cailletet: C. K., vol. 75,1872, p. 77.

* Buchanan: Nature, vol. 17,1878, p. 439.

8 Tait: Proc. Roy. Soc. Ed., vol. 11, 1881,p. 204. Marshall, Smith, and Omond: Ibid., vol. 11,1882,pp. 

626,809. Tait: Ibid.,p.813; ibid., vol. 12,1882-'83, p. 226; ibid., vol.13,1884-'85,p. 2.

6 The probability of such an occurrence had been inferred by Puschl and by Van der Waals. CfGrimaldi, loc. cit.

'Tait: Proc.Eoy. Soc.Ediub., vo].12,]8S2-'83,p.45; ibid.,p. 223; ibid., 1883-'S4, p. 757.

* Pagliani and Palazzo: Beibliitter, vol. 8,1884, \i. 795.

* Pagliani and Vjceutiui; Beibliitter, vol. 8,1884, pp. 270,794; Journal d. Phys. (2), vol, 30,1883, p, 4G1. 

78
BARDS.] METHOD OF EESEARCH. 79

servers corroborate Grassi's work, and find that water .shows a minimuni compressibility at 03°. Grimaldi 1 critically reviews the maximum-density experiments of Puschl, of Yan der Waals,2 of Marshall, 

Smith and Oinond, and of Tait. Amagat,3 applying a new method of 

pressure measurement, "a pistons libres," operates with pressures as 

high as 3,000 atmospheres and at temperatures between 0° and 50°. 

He shows that the peculiarities of the behavior of water vanish at high 

pressures and increasing temperatures (interval, 0° to 50°), corroborating Grassi. Tait,4 in a final paper, summarizes much of his work, 

and begins a series of experiments showing that the effect of solution 

is analogous to an increase of internal pressure.

67. Literature. Solvent action of water. From this brief summary it 

appears that results anticipating the contents of the present paper are 

not at hand. There is another class of experiments relating to the expansion of water compressed in glass tubes, to which I must advert. 

The experiments of Waterston5 are probably the most complete and 

carried as far as 300°, although for very high temperatures Daubre'e's0 

experiments relative to the action of water on hot glass are to be cited.

METHOD OF MEASUREMENT AND RESULTS.

68. Apparatus. The apparatus used in the present work is the 

arrangement already described, § 5 to 14. Pressures are applied by aid 

of Cailletet's large pump. The thread of water is inclosed in a capillary tube between two threads of mercury, and the distance a,part of 

the two inner menisci, measured by Grimow's cathetometer. The tube, 

suitably closed above, is exposed in a vapor bath (boiling tube). At 

185° (aniline), the thread of water soon loses its transparency, becoming white and cloudy. This makes the observation difficult. Fortunately the siliceous water is translucent. By placing a very bright 

screen behind it, the deinarkation between water and mercury remains 

sufficiently sharp for measurement. After the action has continued for 

some time, say an hour, the column is solid at high pressure (300 atmospheres), though it is probably only partially so at 20 atmospheres. The 

result is that threads of mercury break off during advance and retrogression of the column. Farther measurement is therefore not feasible. Toward the close of the experiment, moreover, the mercury 

thread advances inclosed by walls of semisolid siliceous water. The 

tliread is, therefore, of smaller diameter, and the measurement correspondingly inaccurate.

In obtaining these data I followed the customary plan of increasing 

pressure from zero to the maximum, then decreasing it from the maxi-

> Grimaldi: Beibliitter, vol. 10,1880, p. 338. 

J Cf. "Van dor Waals: Beiblatter, vol. 1,1877, p. 511.

3 Amagat: C. K., vol. 103,1886, p. 429; ibid., vol. 104,1887, p. 1159; ibid., vol. 105,1887, p. 1120. 

« Tait: Challenger Keports, vol. 2, part 4,1888.

* Waterston; Phil. Mng., (4) vol. 26, 1863, p. 110, Journ. do. Pliys. 2 (2) -vol. 8, 1R89, p. 197. 

; JStftiteg ijvutjiet. do geologic exper., PiU'JB, Duuod. edit 1879, p. 154 ot seq.
80 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

mum to zero, and taking the mean of the volume changes corresponding to a given pressure. When water does not attack glass, the fiducial 

mark (pressure zero) at the beginning of the series is regained at the 

end. When water attacks glass there is considerable shifting.

Boiled distilled water was used, and the glass is common lead glass.

69. Low temperature data. In Table 56 I have given some results for 

low temperature compression of water. The data are not very sharp, 

owing to the fact that I did not succeed in sealing the thread of water 

with its end threads of mercury faultlessly. I think I detected motion 

of the whole system, which, however, is to some extent eliminated by 

the method of experiment. The results serve a purpose in introducing 

the subsequent high temperature experiments. At 400 atmospheres the 

tube broke. L and o denote the length of the column of water and its 

temperature, v/ V is the observed amount of volume reduction per 

unit of volume, due to the burden of p. Finally, /3 = (v/ V)(l/p) denotes 

the mean compressibility between p = Q and the pressure corresponding. In view of the irregularities, it did not seem worth while to compute compressibility by more rigorous methods, and the last column 

simply gives the mean value of /?.

TABLE 56. Compressibility of water at low temperatures.

L,6

9-8 

31°

g.gcm

10-l'm

100°

P

atw. 

( 0

1 100 

{ 200

300

[ 400

f o

1 100 

I 200

300

[ 409

f °

100 

i 200

300

[ *400

£xio*

0-0

5.3 9-5

13-4

15-6

o-o

4-3 

10-4

16-2

 22-3

o-o

6-6 

11-1

15-9

20-0

£xio3

O'O

5-2 

9-7

12-3

10-1

o-o

4-2 

9-1

12-6

19-2

o-o

6-1 

11-9

16-4

19-2

0X105

52 

48

43

40

42

?48

Ky

63

57

54

49

Mean /3 X 106 

0 to 400 a tin.

46

49

56

* Tube breaks.

These results contain a mere corroboration of the work of earlier 

observers. The initial compressibility decreases between 28° and 64°, 

after which it increases to 100°. Of. § 12.

70, Hiyli temperature data. In the next table (57) the first experiments proper of this paper are described. The symbols used are the 

same as those in § 4, an additional datum, the time, t, of the observations having been added. The first series of data were obtained at 28°, 

and are similar to those of Table 56. The next 7 series for 185° are 

new. Unfortunately I did not observe when ebullition commenced, so 

that the first dates are not available. After closing the experiment, I
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XXVIII

cm.

1

CO

28° 

o

\

Ftg.l

Time

loo 6o m

FIG. 1. Time and contraction of superheated silicated water.

FIG. 2. Contraction and compressibility of silicated superheated water.
BAttUS.] COMPRESSIBILITY OF HOT WATER. 81

noticed that a filament of the upper thread of mercury had run down 

into the core of the silicated water below it. This means that the action had eroded its way between the mercury and glass. In this 

respect the observations are uncertain.

TABLE 57. Compressibility of water at higher lemperattires.

L,e, t

28° 

18-44 

185° 

20-45 

185° 

20-10'-'"

185° 

19-94 

P

atm.

( 20

| 100 

4 200 

300

( 400

c on

100 

4 200 

300

( 400

!

20

100

200 

300

400

(

on

100 

200 

300

400

V

yX10»

0-0

3-5 

9-4 

13-4

18-5

o-o

6-7 

14-4 21-1

29- 3

o-o

8-8

17-1

27-4

34-7

0-0

8-1 

18-3 27-9

38-3

/3X10"

44 

52 

48

49

84 

80 

75

77

109

95 

98

91

101 

102 

100

101

i, ft, t

185° 

19-57""

185° 

18-92 

II1' 05"

185°

18-42"" 

lO1- 10'"

17-78 

Hi, 20-"

P

atm.

( 20

1 .100 

 1 200 

300

[ 400

20

100 

 200 

300

400

f 20

100

4 200 

300

L 400

f 20

1 100 

4 200 

1 300

L *400

V

o-o

9-3 

2.1-0 32-7

42-8

o-o

11-7 

25-9 39-7

55'5

o-o

30-1 44-6

CO'2

o-o

15-0 

31-7 5G-2

71-8

/3X106

110 

114 

11.7

113

146 

144 

142

140

1C7 

159

158

188 

170 

201

189

* Solid since threads break off here. Compressibility still increasing.

71. Discussion of these results. To discuss these results I first plotted 

v/ Fas a function of p, thus obtaining a series of curves of somewhat 

irregular contour, the character of which is, however, obvious. This 

will be more accurately observed (PI. xxvin, Fig. 2) by plotting /? as a 

function of the length L of the column, since the time data are imperfect. The result is striking. It shows a mean increment of /? of about 

50/10° per centimeter of decrement of length of column. Toward the 

end of the experiment the values of ft increase much faster; but here 

they are uncertain because of solidification. The total observed decrement of L is therefore (20-l-17f8)/20-l, or more than 11%. Since the 

column at the moment when ebullition started must have been much 

longer, it follows that the combined volume of pure Avater and solid glass 

shrinks more than 11%, in virtue of the solution of glass in water up 

to the point of solidification at 185°. By plotting length L as a function of time (PI. xxvin, Fig. 1) the data, though incomplete, show that 

the volume contraction took place at the rate of 11 per cent per 40 minutes; that is (say), 0-3% per minute. The column therefore soon contracts to a smaller length than the original column at 28°. This is an 

enormously rapid rate; for were it possible for such action to be indefinitely prolonged the column would be quite swalloAved up in 5 hours. 

Hence it appears improbable that the action of water on glass will be

unaccompanied by heat phenomena. 

Bull 92 §

(See below. § 74.)
82 THE COMPEESSIBILITY OF LIQUIDS. [BULT,. 92.

72. High-temperature measurement repeated. From the importance 

of these results I resolved to repeat them with greater precautions. 

Table 58 contains the results given on the plan of Tables 55 and 56. 

The first series holds for 24°; the remaining 9 series for 185°. Time 

is given in minutes, dated from the period when ebullition had fairly 

commenced. The experiment therefore lasted about one hour. A subsidiary table, 59, contains the essential results (time, temperature 0, 

volume decrement (v/T7'), compressibility /5) of Table 58. The course 

of the experiment was very satisfactory.

TABLE 58. Compressibility of water.

e,L,t

240

13-96 

*185° 

15-42 

18°"

185° 

15-1? 

25'°

185° 

15-01 

30 

185°

14.gOcm

35m

P

Aim. 

( 20 

J 100 

1 200 

I 300

( 20 

j 100 

1 200 

[ 300

!

20 

100 

200 

300

!

20 

100 

200 

300

f 20 

j 100 

1 200 

[ 300

 £xio»

o-o

3'6 

7-9 

12-2

0-0 

6-2 

14-2 21-0

0-0 

7-6 

17-7

27-8

O'O 

8-7 

20-6 31-9

0-0 

9-8 

22-9 35-0

.flXiO"

45 

44 

44

77 

79 

75

95 

98 

99

iosj

114 

114

i23 

127 

125

6,L,t

1850 

14-58 

40m

185° 

14-34 

45m

185° 

14-03 

50-"

185° 

13-75 

55m

185° 

13-56 

CO 

P

A tin. 

( 20 

J 300 

) 200 

(. 300

f 20 

J 100 

1 200 

( 300

f 20 

J 100 

1 200 

[ 300

f 20 

j 100 

1 200 

[ 300

VT X10=>

o-o

11-7 

24-9 38-9

o-o

12-9 

29-3 46-1

o-o

14-7

32-8 52-0

o-o

18-3 

39-4 60-5

0X106

146 

138 

139

161 

163 

1U5

184 

182 

ISO

( Threads broken off; meas- 

< urement uncertain; silit ceous water, solid.

* Commenced boiling at Om, say.

TABLE 59. Contraction and compressibility of silicatcd ivater. Referred to water at

24° and 20 atmospheres.

9

24°

1850

1850

1850

1850

1850

1850

1850

1850

1850

T?xio*

± 0

+103

+ 86

+ 75

+ 60

+ 44

+ 27

+ 07

 15

 29

/3X106

44

77

97

112

125

14i

163

384

221

Time.

18m

25 

30"

35-"

40m

4501

50m

55m

73. Discussion of these results. The discussion of this table can be 

made on the lines followed in case of the other (§ 71). Note at the 

putset that after 55m have elapsed since exposure to 185° the turbid
U. S. GEOLOGICAL SURVEY BULLETIN NO. 92 PL. XXIX

FIG. 1. Successive isothermals of superheated silicated water. 24° and 185°. FIG. 3. Time and contraction of superheated silicated water. 

FIG. 2. Relation of compressibility and contraction of superheated silicated water. FIG. 4. Compressibility of paraffin and water compared.
BAEUS.] - COMPRESSIBILITY OF HOT WATER. 83

column is not so long as tlie original cold clear column at 24°. The 

hot compressibility after 55m has increased to five times the cold 

compressibility and more than three times the original hot compressibility. Some allowance must, however, be made for the finer advancing 

thread of mercury, as explained in § G8. If v/ Fbe plotted as a function 

of j», a series of curves is obtained as slunvn in PI. xxix, Fig. 1. Considering the difficulties of measurement, they are satisfactorily regular. 

Temperature and time have been inscribed on each curve. As usual, 

compressibility decreases Avith pressure. In Table. 59 (v/V) is really 

the ratio of increment of length to the original length at 24°, due to 

thermal expansion with concomitant chemical action. It is not the 

ratio of volumes of solution, because the radius of the tube widens in 

proportion as solution proceeds. Nevertheless, the datum suffices for 

the present purposes. Let /? be represented in its dependence on 

(v/V). The plotted curve is a line of remarkable regularity, as shown, 

in PI. xxix, Fig. 2. It follows from the chart that /5 increases 11/10° 

for each per cent of volume decrease of water undergoing silicincation. 

This is about 75/106 per centimeter of decrement of length, thus agreeing substantially with the former results. Again v/'V decreases 13% 

for the interval of observation of 42 minutes; that is, say, 18% during 

the whole hour of exposure, or 0-3% per minute, again agreeing with 

the above result § 71. See PI. xxix, Fig. 3.

The regularity of the present results enables me to draw a further 

inference. Suppose the line for /9, v/V to be prolonged as far as 

^/F=150/103 , which holds for time = 0. Since in this case the water 

is pure, the datum for /9 is the normal compressibility of water at 185°. 

Making the prolongation (see PI. xxix, Fig. 3), I find /? = 30/106 nearly. 

This is, of course, too small a result, and shows that the time at 

which chemical action began is not well indicated. But since ft85 can 

not be greater than 70/106, the compressibility of water above 100° continues to increase at an exceptionally slow rate, about one-fourth as 

.slow as paraffin, for instance (PI. xxix, Fig. 4). This indicates exceptional stability of the water molecule.

74. Conclusion. IsTow what is the underlying cause of this action? 

Clearly, I think, an instability of the glass molecules at 1-65°, much 

rather than any instability of the water molecule. This is in accordance with the evidence I obtained from the study of the electrolytic 

conduction of stressed glass,1 and corresponds also to the viscosity of 

glass at the stated temperature. At 185° the cohesive affinities of the 

water are sufficient to disintegrate the glass molecule.

The increase of /? with time must be due to solution of silicate. Indeed it would be difficult to devise an experiment in which the effect 

of continued solution can be so well discerned as is possible in the 

present incidental results. Curiously enough the effect of solution is 

here an increment of compressibility, whereas in most other cases (cf.

1 Pains: A-"*. Journ, Scj., vol. 37,1889, J>. 350.
84 THE COMPRESSIBILITY OF LIQUIDS. [BOLL. 92.

literature, § 66) it is a decrement of compressibility. I leave this without comment, believing-, however, that the silicate is in unstable equilibrium with its water when pressure is small, and that the compressibilities measured are solution effects. The possible occurrence of lag 

here (though I did not search for it) is obscured by the contraction of 

the silicated column of water. At all events, we have here a case of 

solidification by pressure from solution, analogous to solidification by 

pressure from fusion.

Finally, I may advert to the far-reaching geological importance of 

these results. In so far as the solvent action of hot water is accompanied by a contraction of the original! bulk of silicate and water, it is 

presumably accompanied by the evolution of heat. Hence, if water at a 

temperature above 200° and under a pressure sufficient to keep it liquid 

be so circumstanced that the heat produced can not easily escape, the 

arrangement in question is virtually a furnace; and since such conditions are necessarily met with in the upper layers of the earth's crust, 

it follows that the observed thermal gradient (i. e., the increase of temperature in depth below the earth's surface) will be steeper than a 

gradient which would result purely from the normal distribution of 

terrestrial heat. In other words, the observed rate of increase of temperature with depth is too large, since it contains the effecfs of a 

chemical phenomenon superimposed on the pure phenomenon of heat 

conduction.
CHAPTER IV.

THE SOLUTION OF VULCANIZED INDIA RUBBER.

75. In my work 1 on the solubility of glass in water, chapter m, I 

showed that in proportion, as the state of dissociation, or the molecular 

instability of glass is increased with rise of temperature, the solvent 

action of water also increases at an enormously rapid rate; that inasmuch as the solution takes place between a solid and a liquid, sufficient 

pressure must be applied to keep the fluid in the liquid state whenever 

the vapor tension at the temperature in question exceeds the atmospheric pressure. Thus, at 100° C. the action of liquid water on glass is 

nearly negligible, whereas at 180° solution occurs at so rapid a rate 

that the capillary tubes may become filled Avith solid hydrated silicate 

in place of water in an hour. Here, however, at least 10 atmospheres 

must be applied to keep the water in the liquid state essential to 

speedy reaction.

76. The present application. Having attempted to apply the same 

principle to the actual solution of vulcanized India rubber I obtained 

confirmatory results at once. To my knoAvledge this material has not 

heretofore been thoroughly dissolved in a volatile reagent, or in any 

reagent by which it is speedily and copiously taken into solution, and 

from which it may be speedily and easily obtained. It follows by 

analogy from § 75 that the rubber must be heated hot enough to be in 

a state of dissociation, i. e., that the coherence of the solid rubber-sulphur molecule must show an mstability in relation to whatever solvent 

may be used. It follows, moreover, that to facilitate reaction the system 

of rubber and solvent is to be kept under a pressure sufficient to insure the liquid state of the solvent. . It follows obviously that this 

temperature must not be so high, caet. par., as to change the useful 

character of the rubber deposited from solution. Hence I act on vulcanized India rubber at the lowest convenient temperature facilitating 

the solvent action, and a,t a pressure necessarily exceeding the vapor 

tension of the solvent at the given temperature. Whatever other favorable action pressure may exert, such, for instance, as forcing the fluid 

into the physical pores of the rubber by a principle akin to Henry's

1 Am. Jour. Sci., vol 38, 1889, p. 408. The paper was published in full in the February number of the 

Am. Jour Sci., 1891.

85
86 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

law, is clear gain. In my machine 1 it is rather more convenient to act 

under 100 or 200 atmospheres than at lower pressures. Hence I did 

not scruple to use pressures as large as this.

77. Solution m carbon disulphide, I will state here that the samples 

of vulcanized rubber acted on were five in number and of the character 

detailed as follows. By elastic I mean stretchable or extensible, with 

resumption of the original form'when the pull ceases:

(a) Very elastic sheet rubber, usually non-pigniented and translucent 

in thin films, brownish in color. Used for rubber bands, for bellows, 

for chemical rubber tubing, etc.

(&) Less elastic and harder rubber, pigmented gray, opaque. Largely 

used for rubber tubing, sheeting, etc.

(c) Non-elastic pigmented rubber, used for low-class rubber tubing 

and low-class merchandise in general.

(d) Ebonite.

(e) Same as a, rotted by age and exposure.

From experiments made at 100° and 160° C., it appears that elastic 

sheet rubber (a) is not fully soluble in liquid carbon disulphide in a 

reasonable time, if at all. It is quite soluble at 185° and soluble to a 

remarkable degree and at a remarkably rapid rate at 210°. Hence the 

pressure under which solution takes place is here necessarily greater 

than 15 atmospheres, and need never exceed 30 or 40 atmospheres. 

Inasmuch as carbon disulphide thus unites with rubber in any proportions clear brown solutions of any degree of viscosity may be obtained. 

On diluting such solutions with cold CS2 the solvent is at first greedily 

absorbed, but the final complete dilute solution (without agitation) 

takes place very slowly. Hence it is well to complete the process for 

any desirable degree of solution at the high temperature. Finally, by 

exposing any of the solutions to air the carbon disulphide evaporates 

and the dissolved vulcanized India rubber is regained without sacrifice of its original non-viscid quality so far as I can judge from laboratory experiments. Similarly fissured sheet rubber (e) which has become useless for practical purposes by age, is quite as soluble in CS2 

at 200°, so far at least as the undecomposed parts are concerned. 

Again, elastic gray rubber (6) dissolves completely to a gray liquid 

in which the pigment is suspended. The concentrated solution hardens at once on exposure to air, to a rubber of nearly the original 

qualities (&). In treating rubbers of this class a difficulty is sometimes

'SeeProc. Am. Academy, vol. 25, 1890, p. 93, or Phil. Mag., October, 1890, p. 338. My method of 

work was simple: Glass tubes 10cm or 15 long and - 3cm or'-4cnl in diameter, closed at one end and 

drawn out to a capillary canal with two or three enlargements at the other, were filled with a charge 

of vulcanized rubber and solvent, and then introduced into the steel piezometer tube. I made use of 

the tempera tares of boiling turpentine (160°), uapthaline (210°), anliue (185°,), and diphenylaniine(310°). 

To separate the charge from the oil of the piezometer which transmits pressure, I first employed a 

thread of mercury inserted into the capillary canal. Finding, however, § 91, that the metal acted on 

the charge I replaced it with much advantage by a thread of water. Charges were usually introduced 

in the ratio of one part, by volume, rubber to three or more of solvent, unless more concentrated solutions were desired. About lcc to 2CC were obtained per heating. I made jconsidorably over 150 experiments, most of them at 200° and 100 atmospheres to 200 atmospheres.
BAKUS.] SOLUTION IN VOLATILE OILS. 87

encountered in consequence of their action on the hot CS2 . Gas is 

often evolved, and I was therefore at first inclined to attribute this 

effect to the pigments. For example, at 200° such a reaction as 

CS2 + 2ZnO = 2ZnS + CO2 might be surmised, but I shall disprove 

tliis in §§ 89, 93 by direct tests. Samples of gray non-elastic rubber (c) 

can be partially devulcanized and softened in CS2 at 200°. They do 

not easily dissolve, however. Gas is often evolved. Little advantage 

is gained by treating with GS2 at 300°, in which case much of the rubber is converted into a granular state, probably due to decomposition. 

Commercial ebonite (d) at 200° is at first partially devulcanized, and 

eventually dissolves in excess of the solvent. The partially devulcanized ebonite is elastic on drying, but finally hardens further to a tough 

solid having a leathery quality. The solution leaves a glossy black 

stain with much sulphur apparent after evaporating. Gases are usually evolved, As a whole, my experiments show that excess of sulphur 

is first removed by the solvent, after which the vulcanized rubber 

itself passes into solution. Cf. § 89, where similar experiments are given.

78. Solution in liquids of the paraffin series. Both the fresh (a) and 

the rotten (e) elastic sheet rubber dissolve easily in liquid mineral oils 

at 200°. The pressure necessary will of course vary with the boiling 

point of the oil used. It may be as high as 50 atmospheres in some of 

the very volatile gasolines. Commercial gasoline is a good solvent of 

the elastic rubbers (a and e). The most concentrated solutions, however, appear to be less thick than in § 77. On exposure to air gasoline 

evaporates,' leaving a residue which gradually hardens. The gray 

rubbers (b and c) dissolve with less facility.

Petroleum1 dissolves the rubbers a and e very easily. The solutions, 

however, only harden after much time, and probably only in thin films.

79. Solution in turpentine. In case of a, complete solution is at 

once effected at 200°, forming a viscid sirup-like liquid. It seems to 

dry in thin films, after long exposure, thus possibly indicating a difference in the product obtained by dissolving rubber suddenly, out of 

contact with air, and by dissolving it more or less in contact with air 

by long-continued digestion. The latter mixtures are permanently 

sticky. Special experiments made at 160° 0. showed that no reasonably speedy solution takes place in liquid turpentine, thus corroborating the inferences and experiments of §§ 75-77. Gray rubber is acted 

on with greater difficulty. The solution leaves a white glossy stain, 

which hardens. Pressure need not exceed 5 atmospheres.

80. Solution in chloroform and carbon tetracliloride. Elastic sheet 

rubber (a] dissolves at once in the liquid chloroform at 200°. Pressure

1 Looking up the literature of the subject, I found that John J. Montgomery, of Fruitland, California 

(of. Letters Patent No. 308,180, November, 1884, United States Patent Office), describes a process for 

the solution of vulcanized rubber. His statements of the temperature and pressure necessary are substantially correct, and he mates iise of a petroleum oil boiling at about 200° C. The oil is subsequently driven oil' by injections of steam. This is the nearest approach to a case of an available 

solution (a solution which does not remain permanently sticky) which I have found. It will be seen 

that the essential peculiarity of the above methods is the solution in volatile solvents.
88 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

must exceed 15 atmospheres and need never be larger than 25 or 30 

atmospheres. Solutions of any degree of viscosity seem to be obtainable. They dry at once on exposure to air, leaving a hard residue. 

Eubber dissolved in this way turns darker in color, and the elasticity 

is in part sacrificed, so far as I can judge. 1 Gray rubber is attacked 

with decomposition of the solvent and evolution of gas. Although 

at 200° a simple reaction like 3ZnO + 2CHCl3 = 3ZiiCl2 + H2O + 2CO 

might be suspected, I believe the gas to be obtained in the way set 

forth in § 89.

81. Solution in aniline. Solution in the liquid at 200° takes place at 

once in case of rubbers like a. Pressure need not exceed a few atmospheres. Thin films, apparently dry after long exposure.

82. Solution in animal oils. Neither in the case of sperm oil or of 

lard oil at 200° was the sample (a) dissolved on removing from the 

press. Both, however, disintegrated on standing to a quasi-solution, 

often with slow evolution of gas.

83. Treatment with glycerine. At 200° no solution occurs. Glycolic 

alcohols were not examined. Cf. § 86.

84. /Solution in benzol and Maker aromatic hydrocarbons. The elastic 

sheet rubber (a) dissolves at once in the liquid at 200°. Pressure must 

exceed 7 atmospheres, but need never be higher than 30 atmospheres. 

The solution exposed to air hardens at once. Solution of gray rubber 

is more difficult.

Solution of elastic rubber (a) in toluol at 200° takes place with great 

ease. The liquid dries slowly. Pressures of less than 10 atmospheres 

suffice.

85. Solution in ethylic and higher ethers. Elastic sheet rubber (a) 

dissolves at once in ethylic ether at 200°. Pressure must exceed 25 

atmospheres, but need not be greater than 40 or 50 atmospheres. The 

solution hardens immediately on exposure to air. Gray rubber is attacked with difficulty.

86. Treatment iviili alcohols.- At 200° india rubber (a) is not dissolved in methyl or ethyl alcohol, and only slightly so in amyl alcohol. 

In the latter case the sample shows some change, toward a pasty consistency.

87. Treatment with Icetones. India rubber (a) treated with acetone at 

200° is converted into a sticky paste, from which it hardens at once 

on exposure to air. Pressure must exceed 15 atmospheres, but need 

not be greater than 30 or 40 atmospheres.

88. Treatment with water and mineral acids. In no case was there a 

trace of true solution at 200°. Pressure must exceed 7 atmospheres, 

but need not be greater than 15 atmospheres. Water probably enters 

the physical pores of the rubber (a) ; at least this substance becomes 

superficially rough 'and warty on drying at 200° in steam after being 

treated with water at 200°. It does not melt (§ 92). Strong hy1 Such an effect would be produced, for instance, by the presence of sulphur in the chloroform.
BAIICS.] VULCANIZATION MIXED GUMS. 89

drochloric acid lias no obvious effect, while strong sulphuric acid 

(diluted with twice its bulk of water) seems only to char the rubber. 

Treating the gray rubber (6) with HC1, I found its solubility in CS2, 

CPH6 , and gasolene to have decreased. The quality of the rubber has 

therefore been injured, so far as its solubility is concerned.

89. Treatment for vulcanization. Liquid ebonite. Ammonium polysulphide acting on elastic gray rubber much above 200° converts it 

externally into a chocolate-like friable skin, covering a musky gray 

core. This disintegrates in CS2 to a brown solution and a gray granular precipitate. The solution hardened on exposure to air, to decomposed rubber.

Ammonium polysulphide at 185° or 200° does not change the appearance of the same rubber markedly; but the sample has lost its elasticity 

and shows a semiplastic leathery consistency. This I believe to be due 

to further vulcanization induced by the polysulphide. If now this sample be treated with liquid CS2 at 200°, the solvent is decomposed with 

evolution of much gas and the rubber restored to its original elastic quality. It is interesting to note that gas is liberated throughout the mass 

of rubber, so that the sample when taken out of the tube has the form, 

of an enormously inflated cellular sack, which issues from the glass tube 

explosively, but soon collapses on exposure to air. As a whole the 

present results agree with the behavior found for ebonite in § 77. In 

both cases it is possible to pass from the more vulcanized india rubbers to a less vulcanized product.

It will be shown below that the gas evolved is due to double decomposition of water and CS2 (§ 93).

More interesting is the direct vulcanization of rubber solution to 

liquid ebonite by aid of a sulphur solution. In case of elastic rubber (a) 

this begins at 160°, but is more complete'at 185° and 200°. In case of 

pure nonvulcanized rubber dissolved in CS2 scarcely any change in fleshcolor is observed at 160° and the sulphur crystallizes out in needles on 

exposure. At 185° and 2.00°, however, the charge turns black, shoAving complete vulcanization. If equal parts of vulcanized rubber (a) 

and sulphur be acted on, the product after heating to 200° is not dissolved nor soluble until the excess of sulphur is removed by washing 

(§§ 77, 89). Gas is often evolved (§§ 91, 93). In proportion as less sulphur relatively to the rubber is used, the product becomes more soluble 

and less gas is evolved. By adding about 20 or 25 % of dissolved sulphur to the vulcanized rubber (a) I obtained serviceable solutions of 

ebonite on treating at 200° either in CS2 alone or in mixtures (§ 90) of 

this with gasoline or benzol, etc. In most cases these harden very 

quickly to a jet-black enamel. With less sulphur the color is brown in 

thin films.

90. Solution in mixtures of solvents, and solution of mixed gums. By 

acting on vulcanized rubber with mixed solvents of the above kind, I 

obtained equally satisfactory results. All the rubbers mentioned
90 THE COMPEESSIBILITY OP LIQUIDS. [BUU..M.

(a to e), ebonite excepted, pass into true solutions by aid of such treatment. Thus the gray elastic rubber (&) dissolves at once fn a mixture 

of CS2 and gasoline; and the gray nonelastic rubber (e) dissolves with 

like ease in mixtures of CS2 with gasoline, or with benzol, or with ether, 

etc.; or of benzol and toluol; or, less easily, in mixtures of gasoline 

and benzol. Ebonite is partially devulcanized, and would probably be 

dissolved in large excess of solvent. No gas was evolved in any case, 

and this constituted an advantage of this method,.§ 93. In all cases 

the solution hardens at once on exposure to air, yielding the rubber 

if the solution be shaken, or a purer residue if the sediment be removed 

by subsidence and decantation.

Equally feasible is the solution of mixed gums, at 200°. Thus I 

made liquid mixtures of vulcanized rubber and gutta-percha in CS2 , 

which hardended at once on exposure to air; liquid mixtures of rubber 

and shellac dissolved in OS2 , hardening more slowly; liquid mixtures of 

vulcanized rubber and rosin in OS2, and in gasoline, which dried only 

in thin films after much time, etc.

91. Direct devulcanization. When by aid of any of the above methods 

a true solution of vulcanized rubber is obtainable, direct devulcauization may be attempted by mixing the charge with some sulphur absorbent. Preferably such material should be chosen, which at 200° 

reacts neither on the rubber nor the solvent. Metallic filings do not 

appear to be available at high temperature. Treating ebonite with 

CS2, gasoline, or benzol to which copper filings had been added, I 

found the charge after exposing' to 200° to be disintegrated, while an 

enormous amount of gas was evolved. Scarcely any solvent remained 

in the liquid tube. From direct experiments made on copper and on 

sulphur in carbon disulphide at 200°, I inferred that these reactions 

are insufficient to account for the gas evolved, although copper is superficially coated with sulphide. The gas must, therefore, be produced 

either at the expense of the rubber or of the reagent in presence of 

ebonite, and since all the solvents used behave alike, probably out of the 

rubber. Steel is scarcely attacked1 . I mention this, since the identification of the gas may throw some clew on the chemical character of the 

rubber. Decomposition frequently sets in on exposure of a highly 

vulcanized solution at ordinary room temperatures, whereas at 0° and 

under slight pressures (1 or 2 atmospheres) the gas remains in combination.

92. Fusion of impregnated rubber. If vulcanized India rubber be 

impregnated or saturated by digesting it with the cold reagent or solvent for a suitable time (a few minutes to many hours), the swollen 

mass not- only shows a relatively low melting point, but it remains 

liquid after cooling, provided, of course, the solvent is not allowed to

1 Fortunately, therefore, steel apparatus is available. An interesting question occurs here, as to 

what becomes of the carbon in the case where mercury, sodium, copper, etc. are attacked by hot CSa 

under pressure, and not by cold CSa.
BARUS.] FUSION OF IMPREGNATED RUBBER. 91

escape. This is an observation, of practical importance, since the retorts 

can thus be charged with solid or dry rubber, a minimum of solvent be 

sacrificed in treating, or by evaporation, and concentrated solutions be 

obtained often fit to be worked at once. The rubber so melted hardens 

on exposure to its original quality. Finally, the pressure necessary in 

this place is the smallest possible, and may be even below the data 

above given for the divers solvents.

Experiments niay.be cited as follows: Nonimpregnated vulcanized 

rubbers (samples a to e) do not melt if exposed in a closed tube to 210°. 

Only in a case of very slightly vulcanized pure rubber gum is there a 

trace of fusion perceptible at the edges, and here it may even be due to a 

stain of dirt (oil) accidentally deposited there. Gray rubber with a 

superficial film of exuded sulphur turns black, due to the formation of a 

film, of ebonite.

All the samples of rubber (a to e) fuse at 210° when previously saturated, or nearly so, with cold carbon disulphide and exposed ill a 

close-fitting closed glass tube. If the pressure be lowered by a capillary 

hole at one end of the closed glass tube, or if the tube be only partially 

filled and the empty end kept cool, the solvent is merely distilled off, 

and no fusion takes place. Whereas at 160° fusion scarcely occurs, 

melting seems to be complete at 175°. There is, therefore, an approximate coincidence of temperature in the present and in the above paragraphs. Similar results are obtained with benzol, with gasoline, and 

higher petroleum oils, etc. Fusion is absent or only incipient at 160°, 

and more than complete at 210°, provided only the solvent used be not 

too volatile. The gray rubbers (&, a) fuse to a more viscous or pasty mass 

than the gum rubbers (o>), the consistency of the clear cold solution in 

the latter case being about that of treacle. In general the occurrences 

of this paragraph resembles the fusion of a salt in its water of crystallization, with this exception, that impregnated vulcanized rubber after 

fusion retains a consistence which is liquid relatively to the original 

impregnated charge.

The analogy with starch or gluten solutions is much more perfect. 

All of these substances swell up when submerged in the solvent. To 

effect solution or quasi solution, temperature must be raised to below 

100° in the former cases, and considerable above 150° in case of 

rubber. Thus the only real difference in the process is an apparent 

one; for starch, the solvent water is still a liquid at the solution temperature, whereas for rubber the usual solvents, under atmospheric 

pressure, are vaporized at the solution temperature. It is interesting 

to note that a similarly detailed analogy in the thermodynamic behavior of rubber and of soft gelatins has recently been pursued at length 

by Bjernken1 . Under sufficient longitudinal stress, both these substances contract on heating, and they are, therefore, heated on farther 

extension, as was proved by Thomson. Bjernken concludes that water

1 Bjernken.
92 THE COMPRESSIBILITY OF LIQUIDS. [BULL. 92.

in the gelatins occurs as water and is not in a state of solution or 

combination.

To account for the behavior of rubber toward solvents, I have supposed coherence to be due to cohesive affinities, forces capable of being 

saturated like the ordinary chemical affinities, but of smaller intensity 

and probably greater number. If, therefore, rubber is impregnated with 

the solvent, a part of the cohesive affinities of the rubber combines with 

similar affinities of the solvent, and the result is so decided a decrease of 

the tenacity of the sample that it may now be triturated. If the 

impregnated material is to be liquid, the residual cohesive affinities of 

the rubber must be withdrawn from action. This may be done by heat 

(dissociation). The liquid thus obtained I do not conceive to be a true 

solution, i. e., one in which the division of solid has reached a definite 

molecule, but rather consisting of a suspension of excessively small 

rubber particles in the solvent. Conditions under which this takes 

place I have already discussed elsewhere 1 , and the probable size of the 

ultimate particles is there indicated. Hence on cooling the solution 

need not at once become solid again. Diffusion, if occurring at all, is 

now an excessively slow process. Hence the aggregation of particles 

takes place gradually, until at length the whole body forms one coherent 

mass. In other words, all rubber solutions coagulate, and the solid 

structure in this case is probably that of a network or sponge holding 

solvent in its interstices.

If the coagulated solution be again heated (under pressure) a thin 

viscid liquid is again obtained which in its turn coagulates, etc. Hence 

even if the original rubber be chemically different from the dissolved 

product (polymerization) my reasoning would hold for the coagulated 

material.

Finally, I may add that the rubber deposited from any of the above 

solutions presents a curious case of slowly reacting elasticity, If a 

thread (say lmm in diameter) be twisted and tben let go on a frictionless 

surface, it will squirm like a live worm for some minutes after. If it be 

stretched, the original length is regained with visible slowness. The 

internal changes probably take place along lines of very nearly neutral 

equilibrium.

93. Behavior of reagents and solvents. Owingtothefrequentoccurrence 

of gaseous products in the above experiments I made special investigations on the decomposition of the reagents. Benzole and gasoline were 

found stable at 210°, and often above this temperature, whether mixed 

with water or with sulphur. Of. § 95. Carbon disulphide, however, in 

addition to relatively slight decompositions noted in § 91, is decomposed 

by sodium and by mercury at 210°, although it remains stable in presence of bright steel or of sulphur. It is also stable in presence of zinc 

white (rubber pigment) at 210°. Violent double decomposition, however, occurs at this temperature in mixtures of water and CS2 , with the

1 Barus; Am. Jour., Sci., vol. 37, 1889, pp. 126-128.
SUMMARY SOLUTION OF CARBON AND OF WOOD. 93

evolution of much gas, presumably 2H2 S and CO2 . Thus it appears 

tliat a thread of mercury to shut oft' the experimental tubes § 70 is 

generally objectionable, as is also a thread of water in case of CS2 . 

For this reason, moreover, the absence of gaseous reaction in case of 

mixed solvents, § 90, is to be attributed to the fact that CS2 and water 

are not immediately in contact but separated by layers of benzole or 

gasoline.

An interesting question is suggested here, as to whether it be possible to express affinity on a scale of temperatures. For instance, let it 

be required to determine the affinity of a metal for sulphur. At ordinary temperatures not even sodium decomposes carbon disulphide, 

whereas such decomposition occurs in case of many metals if the temperature be sufficiently high. Hence the temperature at which such 

decomposition definitely sets in (for copper sooner than for iron, etc.) 

is to some extent a reciprocal expression of the affinity of the given 

metal for sulphur, bearing always in mind that the stability of the 

solid* metallic molecule als"o enters into the consideration. Thus the 

arbitrary reagent CS2 , in its relations to all the metals to be examined, 

fulfills a similar purpose to an arbitrary spring balance in measuring 

gravitational forces. Of. § 95.

94. Summary of the results. In the above paragraphs I have therefore indicated a method by aid of which vulcanized india rubber of any 

quality or character whatever, as well as the undecomposed or reclaimable part of rubber waste, may be dissolved or liquefied in a 

reasonably short time 1 , and into solutions of any desirable degree of 

viscosity or° diluteness into solutions, moreover, from which india 

rubber may be regained on evaporation of the solvent. I have also indicated methods for passing from dissolved vulcanized rubber toward pure 

rubber, though I see little use for such a step.

I have elsewhere described divers forms of apparatus by which any 

of the above operations may be carried out on a large scale. They are 

of no interest here, but I mention them, since it is only from such experiments that a full insight into the quality of the rubber deposited 

from any given solution may be obtaiued. Throughout my work the 

constancy of the dissociation temperature has been a marked feature. 

Thus, in the case of GS2 , of turpentine, of the vulcanization of dissolved 

pure rubber, etc., no action took place below 160°. It may be noted 

I hat even this temperature is higher than where vulcanization is 

effected in the dry way, where 110° to 140° are deemed sufficient. 

Moreover, solution of vulcanized rubber takes j lace at 185°, quite as 

easily under 700 atmospheres as under the miniiL-iun admissible say 20 

atmospheres.

95. Presumable conditions regarding the solution of carbon, etc. From 

the above paragraphs I inferred that the difficulty encountered in dissolving carbon is probably attributable to the relatively high dissociation

J Practically at ouce, if the material is not too bulky.
94 THE COMPRESSIBILITY OP LIQUIDS. luutL.92.

temperature of the solid carbon molecule. I made many experiments 

to test this view, in all of which 1 failed to obtain solution even at low 

red heat and 600 atmospheres. My work thus corroborates the negative results of Hannay 1 on the direct solution of carbon. My experiments were made with gasoline, water, chloroform, benzole, and carbon 

disulphide, usually at 500° and 500 atmospheres. In case of gasoline 

I went as far as low red heat and 000 atmospheres. In most cases the 

reagents were decomposed (particularly carbon disulphide, benzole, 

chloroform) to gaseous products, while the carbon remained unaltered. 

Decomposition by metals if they yielded carbon (copper corroded by 

CS2 and gasoline acted on by palladium) showed sooty deposits only. 

It appears therefore that the dissociation temperature of the amorphous 

carbon molecule must be looked for in the region of red heat.

In conclusion, I may state that experiments were also made with 

wood. This material swells up in water, and the inference is, compatibly with the above text, § 92, that if the temperature be sufficiently 

raised woody tissue must pass into solution. Many tests made upon 

cellulose in this way showed that the material is decomposed before 

solution sets in. The phenomena seems to be an ordinary dry distillation in spite of the presence of water under pressure. This is 

unfortunate, for if it were possible to dissolve wood, our forests would 

be digestible. At least, any such successful process must contribute 

essentially to the food products of the race.

'Hannay: Proc. Eoy. Soc., vol. 80, 1880, p. 188; Chem. News, vol. 41, 1880, p. 100. Cf. Hannay and 

Hogarth: Chem. News,'vol. 41, 1880, p. 103; Mallet and Hannay: Nature, vol. 22, 1880, p. 192.
INDEX.

	Page. 

A cids, efTocfc of. on rubber................ 88

Ad i abatics............................... 26

Affinity, measurement of ................ 93

Alcohol, compressibility of............... 30

Alcohols, effect of, on rubber............. 88

Aniline dissolves rubber................. 88

Azobenzol, compressibility of............ 39

Benzole acid, compressibility of ......... 35

Benzol dissolves India rubber............ 88

Bibliography of compressibility.......... 17

Bibliography of heat expansion.......... 19

Bibliography of conduction underpressure 08,09

Bibliography of compressibility of water. 78

Bjernken, thermal behavior of gelatin ... 91

Broin camphor, compressibility of ....... 38

Cailletet force pump..................... 20

Caprinic acid, compressibility of......... 35

Carbon, solution of ...................... 93

Carbon disulphido dissolves rubber...... 80

Carbon letracliloricle dissolves rubber.,. 87

Chloracetic acid, compressibility of...... 41

Chloroform dissolves rubber ............. 87

Compressibility, bibliography of......... 17

Compressibility, data for ................ 28-41

Compressibility at molting and boiling

points.................................. 50

Compressibility of water ................78, 80, 82

Compression, quadratic constants for.... 42

Compression, exponential constants for.. 43

Compression, hyperbolic constants for ... 01

Compression equations com pared........ 05

Contraction, thermal, under pressure.... 50

Contraction due to aqueous solution..... 81,82

Cooling under pressure.................. 50

Devulcanizatiou ......................... 90

Piphenylamine, compressibility of....... 34

Ebonite, liquid........................... 89

Ebonite, devulcanizat ion of.............. 90

Ether, compressibility of................ 28, CO

Ethers dissolve rubber.................. 88

Expansion due to heat, bibliography of... 19

Exponential constants for compression.. 43,44

Exponential constants, mean values for.. 49

Fitzgerald, work of...................... 20

Force pump of Cailletet.................. 20

iFusion of impregnated rubber........... 90

Gauges for pressure measurement....... 23

	Pago. 

Gibb.s, J. W., work of.................... 20

Glycerine, effects of, on rubber........... 88

Gums, mixed, solution of................. 89

Heat evolved in aqueous solution........ 81, 84

Hyperbolic constants for compression... 01

Hyperbolic constants for compression,

mean values of......................... 04

India rubber, solution of................. 85

India rubber dissolved in carbon disulphide .................................. 80

India rubber dissolved in turpentine,

chloroform, etc......................... 87

India rubber dissolved in petroleum...... 87

India rubber dissolved in aniline, benzol,

toluol, ether, acetone................... 88

India rubber treated with oils, glycerine,

alcohols, ac.ids......................... 88

Isometrics computed..................... 02, 00, 54

Isothermals.............................. 20

Isothermals computed................... 50,54

Isothermal band......................... 05

Ketones dissolve rubber.................. 88

King, Clarence, aids research............ ] 5

Levy, work of............................ 20

Melting point and pressure .............. 70

Mendeleef, expansion formula............ 02

Mercury, resistance tinder pressure...... 70, 73

Montgomery, J. J., discovery of......... 87

Naphthalene, compressibility of.......... 40

Naphthol, compressibility of............. 39

Oils, effect of, on rubber................... 88

Piezometer ............ .................. 20,72

Pressure, measurement of................ 23,75

Pressure binomial........................ 43, 01

Pressure, effect of, on thermal contraction 50

Pressure, effect of, on electric conduction. 08

Palmitic acid, compressibility of......... 32

Paraffin, compressibility of.............. 30

Paraffin oils dissolve rubber ............. 87

Poynting, views of....................... 70

Quadratic constants for compression..... 42

Ramsay, work of......................... 20

Resistance, purely thermal variation of.. 74

.Kiicker expansion formula............... 02

Solution of carbon........................ g;{

Solution of india rubber.................. 85

Solution of rub ber, theory«of............. 91
96 INDEX.

Page.

Solution of glass by water................ 79,83

Solution of wood......................... 93

Solvents for rubber, behavior of ......... 92

Solvents, mixed, for rubber.............. 80

Tait'scorrectionforpiexoinetricexpansioii 25,71

Thermal expansion ...................... 27

Thermal expansion, data for............. 28-41

Thermal expansion, equation for......... 55

Thomson, J. J., equation of.............. 75

Tliorpe, expansion formula............... 62

Thymol, compressibility of............... 37

Page. 

Tolnidine. compressibililty of............ 33

Tubes for measuring compression........ 21

Turpentine dissolves rubber ............. 87

Vanillin, compressibility of.............. 40

Vapor bath............................... 22

Volume changes of glass tubes........... 25,71

Vulcanization............................ 89, 90

Water, compressibility of................82, 80, 78

Wood, solution of........................ 93

Young, work of.......................... 20

Zinc sulphate, resistance under pressure. 70