Tsothermah of Isopentane. 81 



but differences just as great have occurred in the past in 

 inquiries of this kind between the results of independent 

 observers experimenting on the same substance. For the 

 present, then, and pending the confirmation of Prof. Young's ' 

 results by some other observer, we may take the simple formula 

 given above as representing all that we certainly know con- 

 cerning the behaviour of isopentane under the conditions of 

 volume specified. 



The formula proposed may be employed to calculate the 

 critical constants ; this may be done by a method depending 

 solely on Ramsay and Young's linear law. Let us take the 

 equation 



p = bT — a, 



and differentiate it with respect to v, keeping T constant, 



dp _ m dh da 



dv dv dv' 

 Differentiate again 



<Pp mcFb d 2 a 



dv'- dv 2 dv 2 ' 



dx) d 10 

 At the critical point -4- and -r-^ vanish together, so we have 



rp M da _ n 



dv dv ~ ' 

 ,„ d 2 b d 2 a __ 

 d?~dv~ 2 

 Eliminating T this gives 



dh d 2 a d 2 b da 

 dv dv 2 dv 2 dv ~ 



When v has been calculated from this equation we may 

 obtain T by putting 



rp da db 



dv ' dv 1 



and when v and T are known the original isothermal equation 



will give p. 



[n this way we may obtain the following results : — 

 C critical volume =4*5, 

 -< critical temperature = 191°' 7 C, 

 (^critical pressure = 26250, 



which agree fairly well with the numbers found experimentally 

 by Prof. Young. 



Phil. Mac/. S. 5. Vol. 44. No. 266. July 1897. G 



