§IO 



OF ARTS AND SCIENCES. 



397 



pie. We have merely to put the elasticity which we 

 have found In § 6, II., 



and Its derivative with respect to the volume, or /, which 

 amounts to the same thing, simultaneously equal to zero. 

 We shall first find an expression for the ratio oil' to /, in 

 the critical state itself, w^hich will enable us to calculate 

 successively the cohesive, the internal, the external pres- 

 sures, the density and the critical temperature, which lat- 

 ter, being found for one point of the curve, is the same of 

 course for all. These are all the constants which we 

 need to determine.'* 



The formula for the elasticity may also be written, since 

 P-\- P' + P" = o, 



P' /o/— 2/S , _, 



— ; ;/ ) -|- 2P , whence, substituting the 



B = 



values of P^ and P' in terms of P' and Pr 



o ? 



p; = 

 p: 



p' I 



3 



(7,-0 T (3/-2O 



T 7.1- 



l 



I' (/- 



h-r 



i—v 7: f—V 



2I' 



n 



+ 2 p: 



I' 



76 p 



P L -r p/j 



I. 



Differentiating with respect to /, and remembering that 

 all other factors are constant, we have 



dl 3 ^ 



2(/-( /-/-)+/(/-/-)-)/-(/-/-) (3/-2/O T [ 



lui—ryp ^ 



+ 36 A_ 



+ 



{i-iy 

 p: 



* The elasticity being zero, the coefficient of expansion will be indefinitely great at that point ; 

 the latent heat will disappear, and instead we shall find an enormous specific heat under a 

 sufficiently great constant pressure, falling off rapidly as the temperature is increased. The 

 surface tension is very closely related to the cohesive pressure, and the distinction between 

 vapor tension and external pressure disappears. 



