Mancheste)' Memoirs, Vol. Hi. (1908), No. 10. 49 



And the constancy of the amount of the substance 

 ABC requires 



{k^ + h + k.^ABG -l.BC.A-m.CA.B-fi.AB.C=o. 



There are seven equations in all, but only four can be 

 independent ; for the total amount of A that is present, 

 free and combined, cannot change, therefore 



A + AB^-AC^ABC 

 is constant, and there are two other such relations. 

 This reduction is verified ; for adding any one of the first 

 group of equations to the corresponding one of the 

 second group gives the same result, viz., 



a.BC + b. CA + c.AB=/.B . C + g. C.A + h.A.B, 

 and subtracting the sum of the first group from the last 

 equation also gives this result. 



We shall take the second group and the last equation 

 as the independent relations. To eliminate the inter- 

 mediate substances AB, BC, CA, we have from the former 



^^_ Ai.A BC +f.B.C 

 a + l.A 



and substituting in the last equation the value oi l.BC.A 

 thus derived, 



If.A.B.C-ak^.ABC mg.A.B.C-bK ABC 



a + / .A d + m . B 



nh.A.B. C-cK.ABC 



= 0, 



c + n . C 



a complicated relation which, in conjunction with the 

 expressions for binary combinations such as BC above, 

 and the total atomic amounts of interacting material, 

 determines the equilibrium. 



If //«, injb, n\c are very small, and 7^^, Ji correspond- 

 ingly large, so that the intermediate compounds AB, BC, 

 CA are all very transient, we have very approximately 



. (^+ '^+~)a.B.C= {k^ + k„^-^ k,)ABC, 



