94 PROPERTIES OF CIRCULAR CURRENTS. 



The components of the action of the first surface A are then 



*--*- 



Y a = ~ T~ = ~ 4 7r iX/i + 2/ 2 / + 3/3/ 1 + . . . ). 

 ftp 



If u 2 = r 2 + x 2 , the value of the coefficients found above (736) 

 give 



* a 



/ ^ 3 ^y 3-5 r**3'*-4* 2 y 4 , \ 



"*\- 2* 3 2 (2.4)2 3 2 ^ --y' 



3-5 



2.4 U 2 U 2 (2.4)2 fc* * 



If we take the centre of the coil as the origin of the co- 

 ordinates, we may replace x by x - b in the preceding expressions, 

 which become 



On the second base of the coil, the density is - n 1 ; we shall 

 obtain the components X & and Y & of the action which this second 

 surface produces at the point P, if we change the sign of n lt and 

 replace b by -b. 



The components X and Y of the action of the two bases, are 

 given by the terms Xa + X and Y0 + Y. 



Putting 



we thus get 



Vx + b x-b s(x + b x-b\ 



x=2Tm l ---- +^( i --- r } r y +-- > 



[_ V U 2 2 \ V 5 U b / J 



