552 PROCEEDINGS OF THE, AMERICAN ACADEMY. 



behavior of ( — | found here is probably typical for any liquid. For 



mercury, [ — ) is initially negative, but it becomes greater alge- 

 braically with rising pressure, so that in the mercury paper it was 

 suggested that probably at high enough pressures the energy would 

 increase instead of decrease along an isothermal. Here we have an 

 actual case where the pressure has been pushed far enough to secure 

 this increase. This might have important applications to astrophysics 

 or geophysics, since it shows the possibility of storing up very large 

 amounts of energy in the interior of a star or the earth in virtue of the 

 pressure alone, quite apart from the high temperatures. 



Two other quantities of thermodynamic interest, the adiabatic com- 

 pressibility and the temperature effect of compression, may be roughly 

 approximated to. For these we have the formulae 





dv 

 and ['A=^'' 



( 



dp J 4, Cj 



p 



Both of these involve the specific heat, which cannot be found from the 

 data obtained, for the specific heat involves the temperature derivative 

 of the dilatation by the well-known relation 



\dpjr '"Wj^ 



Measurements of the compressibihty at a number of temperatures 



would be necessary to obtain this. At high pressures, however, I — 2 ) 



\dT Jp 



becomes less very rapidly. Amagat's data for water show that al- 

 ready at 3000 kgm. and for a temperature range at least from 0° to 30° 



( — I has vanished within the limits of accuracy. We may assume, 

 ydr-Jp 



then, that at high pressure Cp shows a very slow change. For the 

 rough approximation given here, Cp was taken as constant at 0.9. 

 Tumlirz found Cp at 2000 to be 0.86, but, as already remarked, 

 his value is probably too low. The merely suggestive values for 



( — I — ( — I and ( ^ ) calculated in this way are shown in Table 

 \dpj^ \dpj^ \dpj^ 



