of the Phenomena of Dissociation in Gases, 27 



in which 



— (8) 



Jo 



i 



T y2 e -2V2/a* d y 



It will be seen that e is negative, and consequently, on the 

 hypothesis (a) V* < | a 2 , and E 2 < E a . We shall put E 2 = ^Ej 

 and proceed to calculate fi. 



§ 5. As a first approximation we may make use of the fol- 

 lowing method. Let a molecule which moves with velocity 

 V meet B x atoms and B 2 molecules during the unit of time, so 



that ^ =B 1 + B 2 . Let us also assume that Maxwell's law 



holds among the molecules, the velocity-modulus being /3, 

 which is small ; and that /3 = J^a 2 . We have then (taking the 

 volume v equal to unity) 



r «2 i oy2/ 1 v/« -i 



B 1 =N 1 B 12 V^[^- v2/ " a + 2J T~), e ~* da \> ■ < 1} 



B 2 =N 2 E 2 V^[/3«- v2 * 2 +^^-J o «-*»], . (2) 



where R 12 , B 2 are the characteristic radii for the collision of 

 molecules with an atom or a molecule respectively. In order 

 to calculate e, let us introduce into the two integrals mean 

 values B x and B 2 instead of the variable quantities B, and B 3 . 

 As mean values we take 



E> ^^CB 1 Y 2 e- v ^dY = 2^ 1 R li V^?+^), (3) 

 5=^7^f o B 2 VV v2 /eW=2N 2 W2^-/3, . . (4) 



.... (5) 



and obtain 



aWir(B l + B 2 ) 



where 



>v/« 



1-NxBuV^ [y'«~^+( 2 -7s)( V^]w^/*w, (6) 



J 8 =N 2 E 2 V^r [| e- v2 » 2 + (2- ^pV^] V'e-WdV. ■ (<) 



