1887.] Dynamical Principles to Physical Phenomena. 



299 



ticularly the results of what is called by the chemists "mass-action," 

 of which a particular case is the division of a base between two 

 acids. 



The general problem investigated is that in which we have four 

 substances A, B, C, D present, such that A by its action on B 

 produces C and D, while C by its action on D produces A and B. The 

 relation between the quantities of A, B, C, D present when there is 

 equilibrium is obtained and found to involve the temperature ; when 

 the temperature is constant it agrees in some cases with that given by 

 Guldberg and Waage, though in others it differs in some important 

 respects. Thus if f, y, £, e be the number of molecules of A, B, C, 

 D respectively, when there is equilibrium, the absolute temperature, 

 H the amount of heat given out when the chemical process which 

 results in the increase of f by unity takes place, and k a quantity 

 which is the same for all substances, then it is proved that — ■ 



— '- — Ceke. 



where C is a constant; p, q, r, s are quantities such that if (A) 

 represents the molecule of A, with a similar notation for the other 

 molecules, then the chemical reaction can be represented by the 

 equation — 



p{A}+ q {B} =r{G}+s{D}. 



Thus if A, B, C, D be respectively sulphuric acid, sodium nitrate, 

 nitric acid, and sodium sulphate, in which case the reaction is 

 represented by — 



H 3 S0 4 + 2NaNO s = 2Hff0 8 + Na 3 S0 4 . 



Then if the molecules of sodium nitrate and nitric acid be repre- 

 sented by NalSTOg and HN0 3 , 



p = 1, q = 2, r — 3, and s = 1. 



If, however, the molecules of sodium nitrate and nitric acid are 

 represented respectively by Na 2 N 3 6 and H 3 N 3 6 , then since the 

 chemical reaction may be written — 



E^SOj+NaaNgOg = H 3 N 3 O a + Na 3 S0 4 , 



p — 1, q — \^ r = 1, and s = 1. 



According to Guldberg and Waage the relation between y, e 

 is — 



h = 



VOL. XLII. Z 



