466 Mr. N. R. Sen on Potentials of Uniform and 



within parenthesis. Since A," is a Fourier's Coefficient, 

 we have 



f v cos m(pd<p n 



J _,, (I+Tcos^ 1 "~ ^ Ml 



~ l ' (n-1) ! m!*^" 1 V ^ ' 2 ^ w + 1 ^j 



and 



T 77 cos n(f) d<f> 



J^(i+«costfr+» 



, (2n + l)! tt*» / 2n + 3 (1 2 \ 



- f-IV (2 " + 1) — '" — J— ■ 

 1 ; (n + 1)! n!" l'"" 1 '(1 + **)»+! ' 



also 



T 77 cos ?i^ f?<£ 



_ ff (1 + £? COS (/>)" + ! 



; (2n)J tt^ _1 



~ l ; n\ nl' 2"" 1 " (1 — «*)*+*' 



n being an integer and e<l. 



3. 



Taking the focus S as origin let the equation o£ the 

 ellipse be given bv 



/ 



^ 1 + e cos <p' 



Let P be any point (p, <$>) within the area o£ the ellipse 

 and A another point (r, 6) at a sufficient distance from it. 

 Taking the area to be of unit density the potential 



i 



v = 



= f" C i+ ' c ° 3 °]ogA-PpJpdcf>. 



J-ttJo 



Now 



AP 2 = /3 2 -2 / c>rcos(c£-6>)4-? 

 and 



lOo 



g AP = logr+J log [l-2 (Qcos (^-e) + (ey] 

 = !ogr-.^ ^"cosnft-*), 



