414 Mr. R. E. Barnes on Saturation Specific Heats, $c, 

 I£ now we put z- = 1— t, we get 



. 26 8J .227 13544 _ 



18., 147. 3 7992., 



• _l + 9-+l«-. + MI -3+7992., 

 v -l-r-i- 5 - +25 + 875 ^ 



,_1 4-=4- 24 -' 816 -« + 



( fe - S ')/R=|c- 1( l + |, + g^^ + ...) 

 VPV=16<l-g^+...) 



Hv'-v)=4<l-g^+...). 



Thus in the neighbourhood of the critical point we may 

 write 7r = 4r— 3 or, with greater accuracy, 



tt = 1--8(6t-1)(1-t), 



and also \/RT = 6^/(1 — t) or, with very great accuracy, 

 X/RT = '12(27 + 23t) n /(1-t); further, the work of vapor- 

 ization is one-quarter of the latent heat. 



We likewise see that the mean of the saturation-densities 

 near the critical point is "1(11 — it) if '04(1— 7r) 2 is negligible, 

 so that within this limit only the law of the straight diameter 

 is exact with v. d. Waals' characteristic. 



Saturation with Clausius' characteristic. 

 With Clausius' characteristic 



R* c 



P 



V-OL t(v + {3) 



the critical state is given by V = 3a + 2£, P 2 =cR/2167 3 , 

 T 2 = 8c/27yR, where y = a + /3 ; and if we write 

 v= (v + /3)l (V + /3), the reduced characteristic becomes 



^ 8t _3 

 3v— -1 TV 2 



