Influence of Temperature on Gas Reactions. 225 



If n is the number of molecules having velocities greater 

 than a critical value c, then 



We shall assume that chemical reaction can only take 

 place in consequence of the collisions of these n molecules. 



Before proceeding further we must obtain a suitable 

 expression for the above integral. We shall show that 



2 



Ntf -;r2 | «i'-f - — (- higher powers of ( — ) , 

 / m 



where 



The asymptotic expansion rapidly decreases for large values 

 of a?, and generally we find it justifiable to assume 



The proof is as follows : — 

 We have 



Hows : — 



4 f °° 

 n = _— Nl e- x2 ..v 2 .dz, 



V7T Jx l 



(i.) 



where / m 



Now 



( e~ x * . x 2 . dx = i [-^- 2 . «J " 4- i p <r* 2 . tf.r 



/*oo 



ij e~ x -.dx. . . . (ii.) 



2 c . t<-i 



t1? 



Putting w = - we have 





W-^Kdw 



\ ~.dt 



where t = ^(w* — 1) 



-^.^.-.(i+ty*.*. (iii.) 



