PART III. KARTH CURRENTS AND EARTH MAGNETISM. CHAP. I. 



767 



n di ( cos 8 cos 



cos 



~ 3 L} 



- (R - L cos ft}J, + 2 da 



'2) k\ . R is very great. 

 If we here put 



V = i = i Q E s a, sin 2 np s t , 



can then write 



n 



f cosj? - 



-5 



- cos cos /? Q (L d) cos /? 



/? 



md we have 



(32) 



_. f ijrf. - f 

 ^ J " 



sin 2 /? 



-'/,, . 



(33) 



t this is inserted in equation (10) or (n), we have the current-function's expression for this extreme case, 



* 



_ f cos 8 cos g cos /? Z? 2 - 



A e . \ 



f 



] 



+ L) 



(34) 



i'here 



^1 



,"2 



' _ f c 

 4^ J 



cos cos cos /? /e 2 - Z 2 + d K (Rcosp + Z.) 

 sin 3 /? 7? . a?B 



T, = i . ^ s s 



"or the current-components we find 



. sn 2 



Qsind 



cos cos cos /? R* L* + d K (R cos / 



f = , 



(35) 



(36) 



(37) 





i 



?2j -Z 2 4-rf fl (^cos/? + L) 



R.<*R 



(38) 



.'here a\ and 2 have the same significance as before [see equations (19) and (20)]. 



In order to obtain the expressions for i\ m and i\Q, we need only put - in the place of T s in 



he last two lines. The expression for the value of the potential at the surface is given by equations 

 15) and (21), and we find, for Pmi(R) and Pf)i(R) , 



