( 354 ) 



(11') require, that cr must he smaller lliaii r -\- 7? and larger than 

 r — A', so as not to let X vanish. Accordingly r' mnst be ^ cr — -E 

 and <^CT -\- R. Now three cases are possible : 



a), cr — E<^a, cr-\-R^a, triangle {a, R, cr) possible. 



h). cr -\- R <[ a, conseqiienth^ cr — R <^ a, triangle [a, R, cr) im- 

 possible, a the largest of the three sides a, R, cr. 



c). cr — R^ a, conseqnentlj cr -\- R^ a, triangle (rf, R, cr) im- 

 possible, a not the largest of the three sides a, R, cr. 



In these three cases we evident Iv have: 



a a 

 J).r'dr'=Jr'.Jr' = -{a'-{cr-RY) (a) 



rz-R 



a rr^R 



j 1 r' Jr' — I r' dr' = 2 cr R (b) 



U 'CT~-R 



n 



I 







;. r' <lr' = (o) 



Now if we define the quantity y. by (13) in the cases a) and r), 

 but by 



crR 

 5^ = 6 — (18') 



in the case h), the potential is given by (14) for interior points as 

 well, according to equation (20) of my former paper. 



Notwithstanding the simplicity of our (piantities P. and x, it is 

 easier for further purposes, to replace them l)y an analytical expres- 

 sion, holding good for all values of r. 



As for an expression of )., we know, that 



Q 



ƒ 



ds rr jr 



misx—^=i-\-— or (15] 



s 2 2 







according as :v is positive or negative. Now : 



1 i . 



sin sa sin sR sin scr ■= — ( sin s (a -\- R^ — cr) 4- sm s (a — ^ -|- cr) — 

 4 I 



— sin s {a -{- R -\- cr) — sin s (a — R — cr) [ (1^) 



As for the four quantities 



a -{- R — cr , a — R -\- cr , — a — R — cr , — a -\- R -{- cr 

 three are positive and one negative if the triangle (ry, /?, ct) is possible, 



