44 



J. P. KUENEN. 



From this law we shall now deduce the cliaracter of the function. 



If (1), (2) and (8) are satisfied, (4) must also be satisfied. ïïence if we 

 eliminate m t from (1) and (8) and m 3 from (2) and (4), we mnst in both 

 cases get the same relation between m 2 and m 4 and the températures. 



Clearly then it is necessary that in eliminating m i from (1) and (3) 

 we eliminate t x at the same time, as also everything that dépends on spé- 

 cial proporties of substance 1, and in the same way that t 2 disappears 

 when m§ is eliminated from (2) and (4). Confining ourselves to the 

 former élimination, and writing out (1) and (3) we have: 



a n ffl\ n -j~ a n-\ vi x n ~ x m 2 -}-... d\ m x m 2 n_1 -f- a 0 m% n = 0 . . . (1) 

 a>rl m \ n + a'n-i w x n ~ x m i + • • • a/ m t m, t n ~ l -\- a 0 m^ n — 0 ... (3) 



The coefficients a might in gênerai contairi t { , f 2 and and dépend 

 upon the properties of 1 and 2; the coefficients a contain t u / 4 and T 

 and dépend upon properties of 1 and 4. Even without going into the 

 complète theory, however it will be seen that the élimination of m lf and 

 the siinultaneous disappearance of from thèse équations is only pos- 

 sible in two spécial cases. 



A. The terms containiug both masses do not exist i. e. 



a n -i = a n - 2 = =«i = 0 



and 



a' n -i = a n -2 = = «i' = 0 



and at the same frime a a = aâ i. e. a n does not contain and is a 

 function of f { and T and the properties of substance 1 only ; not of sub- 

 stance 2; a 0 and a\ on tlie contrary cannot contain t x or any constant 

 depending on substance 1. In this case the équation would be: 



a n m^ 1 -f- a 0 m 2 n = 0 



or reducing to the first degree 



b { m 1 -4- b 2 m 2 = 0 (a) 



where ù i and ù 2 are again temperature-f unctions, depending on the pro- 

 perties of substances 1 and 2 and on the températures t x , T and t 2 , T 

 respectively. 



B. The équations are complète n th powers. In that case they may be 



