172 Mr Mayall, On Current Sheets, especially [Feb. 26, 



and this can only be satisfied for all values of 6 when 



fx,^ = 2C\ - \, ^ 



> 



H'n 



= 2(7V. — A,„^, — X„ 



.(30). 



Any values of X and ix which satisfy this set of equations 

 give on substituting in (28) values for a, h which determine 

 proper forms for 11^, O^. 



The value of $ is given by 



47r<i> = 11^ - O^ (o- = o-J 



= 2 {anPn - bnQn) {06) siu ud 



= 2 ^ {PnQn - Pn Qn) (<^0) siu nO 



= — ^Xun (o"^) sin w^ 



^-^t\n{<^0y&irine by (29), 



.(31) 



or 



^^-^,%K(<reysir^ne (32). 



Using this value of 4>, equation (25) becomes 



2S%ip dd 



(adf da- '-^^" ^^^^ ^" ^^^ '^^ "*" ^"-'" 



Let p = kRj{crdy" so that the specific resistance varies as the 

 distance between the two consecutive surfaces 



cr = ctq and cr = 0-^ + dcr^ 



(this is analogous to the assumption made above as to the re- 

 sistance in an ellipsoidal shell), and the equation is now 



2SHp dd {aOf dd 



j^. ^ [thn {(70) Q,, sin 71^ + Ho] . . .(33). 



