53 



Let us now calculate I he dilfercnt dilfereiiiial quotients of f with 

 respect to in and n with the aid of {\a). We find : 



dT),r 



1 / aud 



r6 = YU^ + -^ 



(pp 

 dvdl 



d'p 

 dv\iT 



Hence for Ti, ( 0,, 



1 Vdp 

 ^=Tld^-^''' 



1 

 T 



:1. 



dp 

 dv 

 cPp 

 d7' 



dT' 



26 6' 



w 





+ 



= 



0" 



dp 

 dv 



= 0, 



d'p 



=•) 





e'\^ = 



i- XdvdTjk 



v^,t 



v-kTk f d^p 



ak 



Pkv'^k 

 ak 



(-2 + 6»'*) 

 {Q-Wk-^S\). 



pk \dv^dTJk PfcV^k 

 So we find for I : 



X = a' [l + {-2^6'k) + Ve(6-4^'yl- + ^"A-)]— i?[2 + (-2 + ^A)], 



i. e. 



X = a^\',6'k+'/,0"k)-^6'k. 

 As experimentally about (see also v. L. B, p. IJOl) : 



a' = 15; ^r=0,9; ■ A = 6,8 



has been found, we get : 



4,1 6'^ + 2,5 ^"'/c = 6,8. 

 Hence if O'k is very small — which is inevitable according to 

 {5a) (see above^i — 0"k will necessarily have to lie in the neigh- 

 bourhood of 2,7 (with 6'k = —0,l, 0"k would be found even 2,9). 

 We may therefore consider the value 2,7 as the lowest required to 

 make A = 6,8, as no doubt O'k will always have a negative value, 

 even though it be a very small one (see above). 



Granting this to be true — and it is hardlj- possible to deny the 

 above, when for the equation of state the form (la) js assumed with 

 h and a as functions of v — it is easy to see that the result found 

 leads to a perfectly impossible result for b"k, if the critical volume 

 etc. must also have the desired experimental value. 

 For from (2a), viz. 



r-l_ 2 \ — h'k 



~V ~~ J «> - 7, b"k ' 



