1909] on Experiments at High Temperatures and Pressures. 543 



of solid and liquid acetic acid iu presence of each other under a 

 measured pressure and at a known temperature. The quantities 

 entering into the calculation are ascertained from other experiments — 

 notably the ratio of the change of volume to heat absorbed was 

 ingeniously ascertained by a modification of Bunsen's ice calorimeter. 

 The final result was that the rate of variation of temperature of 

 melting-point with increasing pressure was calculated to be ' 02421° 0. 

 per atmosphere as against • 02435° C. found by experiment — a differ- 

 ence of 0*57 per cent. I have dwelt on this work at some length 

 in the hope that it may make the nature of the problem clear. It 

 is to be noted that the experimental difficulties are considerable, and 

 are enhanced by the fact that we have no d priori reason to suppose 

 that the rate of change of melting-point with pressure is a constant 

 quantity independent of the pressure. In fact it was shown by Sir 

 Joseph Thomson about 1886 * that in calculating the change of 

 melting-point we ought to take into consideration "the difference 

 between the energy due to strains produced by the pressure in unit 

 mass before and after sohdification." Sir Joseph Thomson's reason- 

 ing, based as it is on a generalised Lagrangian method of treating 

 problems involving energy changes, is unsuited for discussion in a 

 non-mathematical address, but it is easy to see that if the compressi- 

 bilities of liquid and solid are different, then the change of volume 

 accompanying the change of state of unit mass must itself depend on 

 the pressure, and therefore the pressure change of melting-point 

 which is proportional to the change of volume must depend on the 

 square of the actual pressure so far as this part of the effect is 

 concerned. This anticipation was realised by Damien in 1891, who 

 showed that the melting-points of substances in terms of the pressure 

 could be expressed by a formula of the kind 



t = t, + a(p-l)-b(p-iy 



t^ being m.p. under 1 atmosphere pressure. 



I think we may add that there will also be a small effect depend- 

 ing on changes of energy in the capillary layer separating the phases. 



The first adequate investigation of the change of m.p. under 

 pressure over a wide range of pressures was made by Barus.f Time 

 does not permit me to do more than exhibit the results obtained, 

 though the apparatus employed was most cleverly designed. It 

 requires great experimental knowledge and ingenuity to infer with 

 accuracy changes of volume of a few per cent, of the original volume 

 at pressures of 1500 atmospheres, nearly 10 tons per square inch. If 

 we note the pressures and temperatures of melting, and plot the result 

 as a curve against the pressure and temperature, we obtain what is 



* Applications of Dynamics to Physics and Chemistry, 259. 

 t Bulletin No. 96 of the U.S.A. Geological Survey, 1892. 



