148 Mr Richardson, The Theory of the 



2 2 



viz., Oj = —r- a, X2 2 = —— /3 : we find that the total number of 



collisions made by a particle of each gas per second is given by 



+ TriV Jw + si* \i + - 8( 7ntr 2 on f^o 0>) Vr ; 



( m^a (111 + ^V) J <r j 



where i^ (p), s 1 : .F 2 (p), s 2 and F (p), cr are the respective attractions 

 and radii of spheres of action of the three possible kinds of pairs 

 of molecules. If the gas is all at the same temperature 



Il 2 Ail J 



W 9 



so that 



+ „J^ ^1 + = a )l + J&fj. W *) , etc. 



In applying these formulae to compute the rate of recombina- 

 tion of ions in gases we shall assume that practically every 

 collision results in recombination. This requires that the kinetic 

 energy which the two ions possess at the moment of collision 

 should be very rapidly dissipated. The necessary dissipation 

 probably takes place in two ways. 



(1) By direct radiation. The phenomena of a discharge tube 

 indicate that recombination is accompanied by the emission of 

 a considerable amount of radiant energy. 



(2) By the direct transference of the energy to the other 

 modes of vibration of the molecule. 



From the preceding formulae it follows that if there are JV a 

 negative ions, of mass m x and mean velocity D, lt and N 2 positive 

 ions, of mass m 2 , per cubic centimetre : then the number which 

 recombine per second is 



dN 1 dN 2 , r , r „ l\ ^ f 8 f 00 _, . _ ) 



-w = -^=^ N >°w l+ ^M 1+ ^^L F(p)dp \' 



