54 M. C. Cellerier on the Distribution of 



CO 



first, that — depends only on the position of M" relatively 



to S'. It must be remarked that, if while preserving these 

 relative positions we change the general orientation of the 

 figure to make it correspond to another region &>, the functions 

 f, F will remain the same. 



Lastly, if we name H the total efficient space n'h found by 

 combining those of all the molecules of the second kind, we 

 shall get, by the preceding substitutions, 



5 = ^./(M").F(M",S). 



(It could be demonstrated that/(M") = RR', R and R' being 

 the principal radii of curvature of the surface S' at the 

 point M".) 



Case III. The data are the same as in the second, except 

 that, for each kind of molecules, S and S' can be oriented in 

 all ways, indifferently. It is clear that the equally frequent 

 orientations of S can be replaced by a numerous series of suit- 

 ably chosen orientations D x , D 2 , D 3 , &c, the character of 

 which could even be indicated by a differential notation ; but 

 it is needless to make a choice as regards the mode of deter- 

 mining them; only they possess the essential property that, if 

 they be all rotated one and the same angle in the same direc- 

 tion about parallel axes, they form an equivalent system of 

 equally frequent orientations. We shall designate by D\, D' 2 , 

 D' 3 , . . . the analogous orientations for 8'. 



The totality of the collisions will be divided into groups by 

 combining those in which the molecules of the first kind have 

 one and the same orientation D, and those of the second kind 

 one and the same D'. 



The efficient space for a single group is the number H which 

 we Lave just found, if n' be replaced by n", the number of mo- 

 lecules of the second kind in the group. Designating now by 

 H the total efficient volume for all the groups combined, we 

 shall have 



? = ^ t , Xn"fQ&."ye{w i s), 



the sum 2' applying to the orientations D'j, D' 2 , . . . , and % 

 to D 2 , D;,, &c. To form the latter, one has to leave the posi- 

 tion I)' of S' invariable, as well as M", so that/(M") is the 

 common factor ; then S is to be associated with them in the 

 successive positions D 1? D 2 , . . . , n" being always the corre- 

 sponding number of molecules of the second kind: this num- 

 ber is consequently sensibly constant. The positions once 



