534 



NATURE 



[September 30, 1897 



gations of Amagat in a measure commensurate with their value. 

 These contain a counterpart for the liquid state of the results 

 already announced for gases. The change of volume throughout 

 enormous pressures and about 200° of temperature is considered 

 in detail for a number of important liquids. Only in one case, 

 and that the rather remarkable one of carbon tetrachloride, are 

 evidences of solidification encountered, and the conditions 

 determined. Amagat believes the absence of solidification to 

 be due to the occurrence of the lower critical temperature below 

 the isothermal of compression. In my own judgment, however, 

 the pressures necessary to reach this lower critical point will be 

 enormous even in units of 1000 atmospheres, for which reason 

 it is not in any case liable to be an easy conquest. 



Special mention, finally, is due to the thermal position of the 

 maximum density of water, which Tait had already studied. 

 Amagat shows definitely that the temperature of maximum 

 density moves towards the freezing point with increasing pres- 

 sure, so that at high pressures, as well as at high temperatures, 

 the behaviour of water loses its anomalous character. In 

 general, compressibility and expansion decrease with pressure 

 for all normal liquids, and expansion increases rapidly with 

 temperature. Other anomalous properties of water have been 

 investigated, among which the diminished viscosity of water 

 under pressure at ordinary temperature, studied by Rontgen, 

 Cohen and others, may be stated. 



After this cursory and wholly inadequate mention of the work 

 of Amagat and the physicists who, like Tait, Cailletet and 

 others, have been . engaged in closely allied researches, it will 

 repay us to look at some of the other as yet less splendidly de- 

 veloped contributions to piezometry. At the outset it is well to 

 make mention of the forms of pressure gauges which have come 

 into use. As far as 1000 atmospheres, the Bourdon gauge, if 

 well constructed, does good service, though in a somewhat 

 rough way. The corrected nitrogen closed manometer is more 

 accurate for a smaller range. A theoretically simpler pressure 

 gauge was proposed by Tait and Cailletet. In this case a 

 straight cylindrical elastic tube under internal or external pres- 

 sure is substituted for the Bourdon tube, and the expansion or 

 compression is directly measured. With due precautions against . 

 changes of temperature and the choice of a solid of constant j 

 bulk modulus and rigidity, this gauge can be used as far as about 

 2000 atmospheres with convenience. I 



Above 2000 atmospheres, Amagat's Bramah press manometer, 1 

 already mentioned,is the only trustworthy gauge, and though some- 

 what cumbersome has the advantage of giving absolute results. 

 However, a gauge based on the change of electric resistance of 

 mercury with pressure, a constant now fairly well known from i 

 Palmer's measurements, will in my judgment do good service j 

 for pressures which exceed even the range of the manometer. 

 With regard to methods for producing high pressures, the force i 

 pump, with a small steel plunger and the screw advancing bodily ■ 

 into a closed barrel filled with a liquid, have not yet been | 

 superseded. The efficiency of such apparatus depends essen- 

 tially on the means used for obviating leakage. These must, of 

 course, be very perfect. 



Amagat's work with liquids was extended chiefly in the 

 direction of high pressures. Experiments have since been made 

 by others throughout higher temperatures (310°), and of course 

 a smaller range of pressures (500 atm.). Leaving out the less 

 perspicuous results, I will here merely allude to the probable 

 existence of a remarkable law which these researches have de- 

 veloped. Dupre (1869) and afterwards Levy (1878), reasoning 

 from thermodynamic premises, were the first to suspect that the 

 isometrics or lines of equal volume of liquids are straight. In 

 other words, if there is to be no change of volume, then pres- 

 sure increments must vary proportionately to the tem- 

 perature increments {p ~ aQ - b), a result which implies 

 that the internal pressure of a body kept at constant volume 

 is proportional to its temperature. Levy's deduction 

 was, however, declared to be theoretically unwarrantable by 

 Clausius, Boltzmann and others. Some time after, the same 

 law reappeared in experimental form in a series of brilliant re- 

 searches on critical temperatures due to Ramsay and Young. 

 Fitzgerald, reasoning from Ramsay and Young's results, then 

 proved that for such liquids as possessed straight isometrics, 

 specific heat is a temperature function only, and energy and 

 entropy are each expressible as the sum of a mere temperature 

 function and a mere volume function. This is curiously like 

 the position from which Dupre and Levy started. Ramsay and 

 Young's work, however, applied specifically to vapours, and for 



NO. 



145;, VOL 56] 



high temperatures (200°) their pressures did not exceed 60 

 atmospheres. The law has since beemtested for liquids as far as 

 1500 atmospheres and over 200° conjointly, and found in reason- 

 able accordance with experiment. Hence we infer that if the 

 thermodynamic change of a body is such that volume remains 

 constant, pressure and temperature will vary linearly with each 

 other, the increments being about o'i° C. per atmosphere. Now, 

 although any law relating to the liquid state would be welcome, 

 these volume isometrics are particularly so. In the geology 

 of the earth's crust, for instance, they would in a great measure 

 determine the conditions of possible convection ; and it is curious 

 to note that from the known values of bulk modulus and of the 

 expansion of solid glass, the isometrics would here again be 

 given by corresponding increments of about 01° per atmosphere. 

 For solid metals the isometrics are of a different order. 



Another line of research for liquids to which I attach supreme 

 importance has only just been begun : I refer to the systematic 

 study of the entropy of liquids. Among the first results on the • 

 I heat produced in suddenly compressing a liquid are those of 

 Tait. They are of too limited a range, however, and not in 

 I good accord with the more recent and extended data of Galopin. 

 \ Generally speaking, the change of temperature produced per 

 atmosphere of compression increases with temperature in a 

 marked degree, as one may infer from Kelvin's equation. For 

 organic bodies this increment at ordinary temperatures is of 

 the order of ^V° = "020° per atmosphere. In case of liquid 

 metals the order of values is decidedly different, being about 

 tV this value, recalling correspondingly divergent results 

 observed for the isometrics of volume. (^uite recently (1896) 

 the same subject has been taken up by Tammann (to whom 

 we also owe results for the correlative compressibilty), 

 particularly for solutions and with reference to the theory of 

 solutions. Tammann's data are of the order 0001'' per atmo- 

 sphere at 0°, and in better keeping with the thermodynamics 

 of the subject than the earlier experiments. Much more, how- 

 ever, must be done before anything like a degree of critical 

 accuracy is approached or a broad survey taken. Pressure 

 intervals are to be chosen wider, and the temperature measure- 

 ment given with greater certainty. 



Finally, I wish to touch upon the relations of melting-point 

 and pressure in their more recent development. Obviously 

 the classical work of Andrews on the continuous passage of a 

 liquid into the gaseous state will find some counterpart in the 

 manner in which the analogous passage from the solid into the 

 liquid state takes place. The character of these phenomena 

 may be shown from direct observations of melting-point and 

 pressure, as was done by the earlier observers. Full know- 

 ledge, however, can be obtained only by mapping out the 

 isothermals throughout the region of fusion very similarly 

 to the method pursued by Andrews himself for vaporisa- 

 tion. This has thus far been attempted for a single body 

 only, naphthalene, within 130° and 2000 atmospheres. Six iso- 

 therms (63', 83", 90", 100°, 117°, 130°) were traced within these 

 intervals, along each of which, excepting the first, the body 

 passed from the liquid to the solid state under the influence of 

 pressure only. An exhibit of these data shows strikingly that 

 in all cases the change of physical state takes place in accord- 

 ance with a cyclic law; i.e. a larger pressure is necessary to 

 change the body from the liquid to the solid state at a given 

 temperature, than the pressure at which the body at the same 

 temperature again spontaneously melts. Freezing almost always 

 seems to take place at once ; the corresponding fusion is apt to 

 be prolonged, and in its gradual occurrence traces the contours 

 of James Thomson's well-known doubly-inflectel isothermals 

 much more fully than does the allied case of vaporisation. 



The appearance of the cyclic parts of these isothermals is 

 suggestive, and may be described in terms of their dimensions 

 in the direction of volume and of pressure respectively. 

 The former dimensions indicate the probable fate of the 

 volume increment. They show that as pressure and tempera- 

 ture increase, the volume increment tends more and more 

 fully to vanish, and they thus imply a lower critical tem- 

 perature at which the solid would change into the liquid 

 continuously as far as volume is concerned. It does not fol- 

 low that other properties of the body would here also vary con- 

 tinuously. For naphthalene this point would lie in a region of 

 several thousand atmospheres, and several hundred degrees 

 Centigrade — therefore in a region too remote to admit of actual 

 approach. 



Again, the breadth of the cycles, measured along the pressure 



