Chemical Combination of Gases. 259 



Let us suppose that things have got into a state of equi- 

 librium, then the differential coefficients of all the quantities 

 with respect to the time will vanish, so that these equations 

 may now be written 



m 2 _n m P 2 _.jZl 

 T, ti ' t 4 t% 



r 2 __ s mp _ u 

 t« U t 9 t A 



mr 

 t 3 



y . . . . : . (24) 



so 



that 



t± T\ T± „- 



T 2 2 ^i ~t 2 



u 2 = ^ J: ^ n g ; or say u 2 = ung 



8 '4 Il5 « 



or say v 2 = (3nr 



(25) 



T 3 ' *1 h ' " 'J 



Now the number of free atoms will in all practical cases 

 be very small compared with the number of molecules, so 

 that m } p, r are very small compared with n, q, s respec- 

 tively, so that we may put 



n-=\ (M — u — v) 

 q = i (N-ti) 



So that equations (25) become 



v 2 = i!3(M-u-v){'P-v), 



two equations to determine u and v. If we put M = N = P 

 we have two equations for u/M, v/M, the coefficients of 

 which do not involve M; so that unless a and ft are functions 

 of the density the same proportion of the gases will enter 

 into combination at all pressures. We see from equation (25) 

 that the number of molecules of the compound AB is pro- 

 portional to the geometric mean of the number of free mole- 

 cules of A and B, and similarly that the number of molecules 

 of the compound AC is proportional to the geometric mean 

 of the number of free molecules of A and C. If we look at 

 the value of a we see, by comparing it with the results given 

 in § 8, that it can be determined by experiments on the com- 

 bination of A and B by themselves. Thus from the experi- 

 ments of M. Lemoine we see that for hydrogen and iodine 



