Field of aii Electrical Current. 215 



first supposed constant and equal to -r- , the equation of a line 

 of force is 



if{(l + ^)K-2E}/w/S = constant. . . (49) 



With previous notation and approximation, we have 



„ , 8a Rcos 6 — 2m cos <b 



K = 1 °SH + Ya 



R^L-l- 2cos2g) + 8Rm cosgcos<^-8m 2 cos^ 

 + — * 16? ' [M) 



■-l + ^fe^, (") 



16a 2 



a /, R cos 0- 2m cos 6 , R 2 sin 2 <9\ 



p= 2a ( 1+ £ — + ^H' 



(52) 



E 2 



*"=i?> (53) 



where L = log — . Hence (49) becomes 



AaiCCr Rcos 6 — 2mcos(j> R 2 sin 2 0~|r T Rcos 6 — 2m coscf> 



XjJL 1+- ~^T~ - + -^r-]l L - 2 + - ~2a~ 



R 2 (L + l-2cos26>)+8Rmcos^cos(i-8??? 2 cos 2 (f)n^ 7n 7 

 +— ' 1^2 ?jRdRd x , • (54) 



it being understood that % ranges from to &>, and therefore 

 ty from to 7r, when (as in the calculation of ®) the inde- 

 pendent variable is changed from X to yfr. 



In addition to the integrals (38), (39), (41), (42), the 

 following are now required, and they are easily deduced like 

 the others : 



LR 3 ^R t / % =^{L(2777 2 + c 2 )-2c 2 }, . . (55) 



§R*dRd X = ^(2m 2 + c 2 ), (56) 



§LRdRd x = jL, (57) 



$$RdRd x =£, ........ (58) 



where L = loo- — . 



