( 353 ) 



a — R^ — cr^ a + 7?., = CT, , . . . (H') 



It may liappcn, lluil several pairs of values r^ t, exist ; it may 

 also happen, that the point in (piestion is situated so as to be an 

 interior point for a certain time, an exterior point for another. 



It is easy to pass from the potential for a splierical shell to 

 that of a solid sphere, uniforndy charged, which is to be divided 

 into splierical shells. If b is the whole charge of the solid sphere, the 



charo-e 3 £7'''— is contained in a shell of radius r' and the thick- 



° a" 



ness di'\ Now it is only required to substitute r' for a and — r'^ dr' 



for 8 and to add an integration with respect to r' from to a ; 

 then we have : 



00 « 



Sec C^lr r , . , /I o. 



'■■"^ = J^JRJ'-""' ^''' 



u u 



To begin with Ave take an exterior point, for which Ey>a, and 

 a certain value t. Equations (11), in which r is to be substituted 

 for a, show, that A = 1, if ex lies between A' — r' and R -\- r\ or, 

 wdiat comes to the same thing, if r' > | A — c t | . Now two cases 

 are possible : \ R — cr \ uiay either be smaller than a or larger. 

 In the first case a triangle with the sides [a, R,er) is possible, not 

 in the second case. In the first case we have : 



a a 



Cx r' dr' ^ P' dr' = - (a^ - (7? - cr)% 



I li—cr 



in the second 



a 



ixr' dr' =iO . 



If we define a quantity y. by 



according as the triangle {a, R, cr) is possible or not, we can write 

 for an exterior point instead of (12) 



00 



8c rxdr 

 4.T./^- — - (14). 



u 



In the case of an Interior point, for which R < a, the equations 



