=v 



, vdV'/dn 



= dV/dn, 



B„= 



1 + v + l/rc 



a* n + l A n . 



in Rectangular Order upon a Medium. 498 



Y n denoting the spherical surface harmonic of order n. And 

 from the surface conditions 



we find 



1 _„ 



(52) 



We must now consider the limitations to be imposed upon 

 Y». In general, 



Y n = 2" ©J (H, cos s<j> + K sin s<£), . . (53) 

 where 



e; = sin^(cos"-^- {n ~ 2 %n-l)~ 1) cos "~ 6 ~ 26>+ • • •) ( 5i ) 



being supposed to be measured from the axis of x (parallel 

 to a), and <£ from the plane of xz. In the present application 

 symmetry requires that s should be even, and that Y„ (except 

 when n=0) should be reversed when (ir—0) is written for 0. 

 Hence even values of n are to be excluded altogether. 

 Further, no sines of s<p are admissible. Thus we may take 



Yi = cos6>, (55) 



Y 3 =cos 3 0- | cos + H 2 sin 2 6 cos cos 2<j>, . (56) 



Y 5 = cos 5 - \? cos 3 + &■ cos 



+ L 2 sin 2 (cos 3 — J cos 0) cos 2$ 



+ L 4 sin 4 cos cos 4$ (57) 



In the case where /3=y symmetry further requires that 



H 2 = 0, L 2 = (58) 



In applying Green's theorem (4) the only difference is that 

 we must now understand by 5 the area of the surface bounding 

 the region of integration. If C denote the total current 

 flowing across the faces fiy, "V^ the periodic difference of 

 potential, the analogue of (6) is 



«C-/3 r Y 1 + 47rB 1 = (59) 



We suppose, as before, that the system of obstacles, ex- 

 tended without limit in every direction, is yet infinitely more 

 extended in the direction of a than in the directions of /3 and 7. 



Phil Mag. S. 5. Vol. 34. No. 211. Dec. 1892. 2 M 



