1)24 



Physics. — "A new relation hetmeen the critical quantities, and on 

 the unity of all substances in their thermic behaviour ^ (Con- 

 tinuation.) By J. J. v.o Laar. (Conimuniccited bv Prof. H. A. 



LORENTZ.) 



(Communicated in the meeting of February 28, 1914). 



8. The shape of the function b = /{v). After weliave thus derived 

 some relations in the preceding paper'), by means of which all the 

 critical quantities are expressed in the one quantity y, the reduced 

 coefficient of direction of the so-called "straight diameter", we shall 

 examine what forms of b=f{v) satisfy the relations found. 



These relations, from which the table on p. 829 loc.cit. has been 

 calculated, are the following. [Cf. also the formulae (14) and (21) 

 loc.cit. p. 818j. 



J_±y 

 7 



(1+yr 



4y 



Vk 



'=^=.2(1-]- 7) 



X = 



7' 



(22) 



(1+7)^(87-1) 



pk 



1 , a 



27 ^'^è^ 



27 '' bk 



in which l^:^).^^). is put. The found values of ^j and P.^ appeared, 

 namely, not to differ, and / is always in the neighbourhood of 

 unity. Though y varies from 0,9 for "normal" substances to 0,5 for 

 "ideal" substances, I ranges only between the values 0,98 and 1. 

 We further found : 



(2y-l)^ , „ 8y-l 



1+^/ 



= 8y 



h'k = 



1 



h'l 



i^k = - 



4y(y+l) 

 vkb"k /'-4 2y-l 



4y(y + l) 



(23) 



l-b'k 



f 



'Jy 



In this (f 



-— ii',, m which |^(= — I — 

 — 1 vk \olyk 



We saw that S't 



is generally exceedingly small. 



We may still remark that the relations for b), and b"k may also 

 be written thus : 



bk vk 



b /, ~ — (1 - 6/,) , 



bk I'k 



(24) 



1) These Proc p. 808. 



