446 Journal of the Asiatic Society of Bengal. [Jnly, 1907^ 



But P« (cos v) 



Pn (/i) Fn (;«') + 22 )— -^ T U) T U') cos m<p-.^ 



(7j + 7n)! 

 whez^e the T's are Tessera! "harmonics. 



cos a 



2, [(cosa-i)-s» i.r:.[('-''')xr°^"H 



Similarly, when r is greater than c. 



Obs. It is clear that this method will enable us to find the- 

 potential due to a circular current in any S3^stenl of harmonics, 

 provided we choose the equivalent shell appropriate to these har- 

 monics. 



6. To find the solid angle subtended at any point P by a 

 circular wire in spheroidal harmonics (zonal). 



Let the axis of the zonal harmonics be the axis of revolution 

 of a spheroid having the plane of the circle as one of its plane- 

 sections, and, centre, the origin. 



w 



Then m ~ i ds . — 



J • an 



But from the theory of confocals, since r-= constant ^s a series- 

 of confocal spheroids we have 



pdp^crlc (c= the major axis), 



= h^rdr 



t 

 I 



where p is the perpendicular on the tangent plane at any pointr 

 from the centre 



and dp^=dn. 



' hh- 8r * \p/* 



0} = i ds 



B^t \^\ ^(2» + 1) Pn(fJi) Pn(/) Qn{r) . ^^C^'), 



+ terms depending on ' ^ 

 where /, ^' refer to tbe point P. 



