140 COEFFICIENTS OF INDUCTION. 



If we expand ^ = Vtf 2 + oc 1 as a function of increasing powers of - , 

 we have 



2 X 2.4 X 3 2. 4... 272 X 2n ~ 1 ' 



which gives, by carrying out the calculations, and making x = l l y = a', 



i g' 2 p 3.4^ 3.5.6 fl*_-l 



2.2 2 /i 2 L2 2.4^ 2 2.4.6 */^ 4 J 



i a'* [-2.3.4 3>4-5.6 2 -i 

 + 3(2.4)2 / ; 4 L 2 2.4 '5I* 



_^ __ a /6 

 4(2.4.6)2 A* L 2 2.4 



/6 . 3.4. 5. 6 3.4.5.6.7.8^2 



a' 2 



If the ratios - and are of the same order, and we only take 



the first term into account, we get 



[a f i a' 2 a\~\ 

 '-7A I+ 8^-^)J- 



773. POTENTIAL OF A HOMOGENEOUS SPHERICAL BOWL. Let 

 us consider a homogeneous spherical layer, of unit density, bounded 

 by a small circle HK (Fig. 144). Let C be the centre of the sphere, 

 O the centre of the circle, A the pole of the circle. 



Let 



OCH = a, 

 CP = *, 



and let us investigate the potential of the layer at P . 



