Theory of Crookes's Force. 19 



If now we assume 



B 2 =b 1 (fjt?— J) + b 2 (l — (J?) cos 20 + 6 3 (1 —At- 2 ) sin cj> cos (j> 



+ b^x/l —(a 2 cos </> + b 5 fA\/ 1—fj? sin 0, 



as it must be of this form, we get, on putting our other quan- 

 tities into the forms of spherical harmonics, 



p = 



p 



P„=|mN^(b o -^ 1+ |j 2 ), 

 P y2 =iMN^ 3 =P,„ 



15 



P„=^MNeJ6 t =P„, 



Similarly, for the quantities of energy transferred we get 



MNu 3 



MNv 3 



Q*= -^° & JJ C V 1 -//, 2 cos ^c?(/> ; 



so that if we assume, as we evidently may, 



C x = Cifi + c 2 V 1 — (J? sin cj) + c 3 n/ 1 — yu, 2 cos 0, 

 we get 



Q y =|MN^ 2 , 



q s =|mn^ 3 . 



Even in this most general form we can see that there will 

 in general be a difference of pressure in different directions; 



C2 



