Vol. III. No. 7,1 Magnetic Induction in Splteroids^ 445 



For this, it will be necessary to prove the following lemma. 

 4. Lemma. To find tlie solid angle (o)) subtended by any 

 surface at any point. 



Let ds be the element of surface at any point ^, rj, C Let 

 a?, y, 0, be the co-ordinates of the point at which the solid angle 

 is to be found. 



Let ^ = angle between the outward drawn normal at the point 

 •and the line joining the two points. 



/) = distance between the points. 

 ^7i = element of outward drawn normal. 



Then o> 



m|(-«)+ + 





s 



■ -■(-')■ 



dn \pj 



5. Ex. To find the solid angle subtended by a circular 

 wire at any point P in zonal harmonics f spherical) - 



Describe a sphere of radius r with the origin (G) as the centre 

 and having the plane of the given circle as one of its plane sec- 

 tions. 



Let the axis of Z be the axis of the zonal harmonics, and a = 



angle subtended by the radius of the circle at the centre. 



Also let V = angle between any radius (5, f) and CP (= »*) 

 -ft.Tifl f}F!. the corresnondinff element of surface. 



Then oi 



7 ^ 1 



its 



^^ (c* + r^ — 2rc cos 1^)2 



: (-:v - 



(cos v) J if tZ.c 



08 a /•^TT ^ 



dfjulf 2 ( /I + 1 ) ~Ph (cos v) where /x m cas 9^ 



n 



