1889.] A. Mukhopadhyay — Elliptia Functions and Mean Values. 217 

 and for 



(0=0 , X = a. 



Therefore 



Hence, since A is independent of r, we have 



JKdr=ab C .^—^ J J C {\^-r^)idr. 

 0 \{a^^)>?yi\^-h^yi\^-c^)^ Jo 

 Substituting 



r = A. sin f 

 dr=\ cos <p df, 



we get 



sin '■ - 



r\dr=al r , f cos^f^^ 



A 



^008^ <t> d<p = ^ sin if cos i/> — jsia^ cos i/> + §<?>. 

 ce, finally, 



A.Zr = a& j T--^^ T , (14) 



0 Jb (a2-A2j^(A2-i2)^(A2-c2)^ 



where 



■^^ > ~8AV A2 8AV A2 

 l\W A2'''4A8\/ Aa 



+ -sin 1^ -8-^ 'a- 



To calculate 



substitute in (11) 



6 



/<,2 = a2 cos^w+L^ sin»w, 



