40 Proceed'uKjs of the Bof/al In's/i Academy. 



Also 



A... = - 2X..B,K,in'R) ^^^^ = - 2X,Wn'E) 



where x' = 7i'R. 



The coefficient of B,,,Ki[n'B) in the Fourier term corresponding 

 to will then be 



- cos nz 



Ts^owj 



,/2 



+ 



- li') {xJ- - x'~) {a J + x'-) {u' - x') (w- - x'^-) {a J + ?^^-) I 



^^'ow, it is easily seen that 



X- X- 1 



X' - u- ' X- - 4ii- ' ' ' 2 ' 



whence our coefficient assumes the form 



- x'. cos «2 2„„ ,„ jz:^ — • 



{u- - X') {ir - x'-) {aj + ?r) 



iN'ow (see Transactions, E.I. A., ^ay, 1902), 



1 1 



causing our coefficient to assume the form 



,^ u 

 cos nz X 2> 



Ji" ' {u" - X') {ir - x'-f 

 or for 2 = 0, 



