PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 35 



JJ pr 



rr 2irp sin 9 e- a P dQ dp p 



M Vp 2 + R*-2pBcosd 



m s Ap j ^e-^p^^-2Bpcose + ^ df> 



For the portion included within a spherical surface, whose centre is 

 M and radius MA, we must have the limits 8 = 0, 8 = w and p less 

 than R\ for the remainder p is greater than R; 



hence ^ = ZAP.f R ?£ dpe""> {R + P -(R- P )\ 



+ %AP. r^dpe-"r{p + R-(p-R)} 



m ^ Ap rn ^pe-^dp I ^ Ap r- 4wr ., d 



- -9 a p \ ^ e ~ al (1 + <**) _ 4tt e— R \ 



-^ Ar \R~- a 2 a 2 ^RJ 



The coefficient -» being the same as obtained by the other method, 



a 



shews that equation (2) is correct; we also perceive that 



B = Ae~ al (l +al). 



14. The equation (1) will give a relation between a, c and the 

 other quantities which we proceed to investigate. 



From the value of D (10), 



^ = 2^ («-* + «**-•*) (X-*), 



also ~ = ^2^(B-Ae- aR -AaRe-' R )(X-x), 



E 2 



