PART III. EARTH CURRENTS AND EARTH MAGNETISM. CHAP. 



cos^ 



cos 2 m 



ifter some reduction, that 



-/'te, pi) 



~ 



cos- 



"T .; , 



1/Z cos 2 

 4 



s 2 -^- (F(, 9%) F(k, r/),)) 4 cos 4 -^ ((, I/),) (, r/>i) 

 2 4 



- 2 cos- J cos 

 4 2 



765 



(25) 



(26 a) 



R-v^RLcos 



(26 b) 



ihcre /'(/t, 1/1) and E(k , cp) are defined as before [see equations (17) and (18), p. 427]. 

 Further, 



it & 



- - 



2 4 



()/L - i) cot - 



4 



.nd finally 



Vom this we can deduce by derivation the corresponding expressions for the force-components 

 hemselves. 



By equation (24) we find directly 



di 



cos 6 cos cos /J 



f = 



sin 2 ? sin 9 



CQS 



., . -i 



/J+ L)^ (Lcosfi + K)J.,\ . (27) 



f = /'i 



"or the determination of Pg,- we may start from equations (14) and (21), whence we easily deduce 



R o o 



-ii 



>y employing the abbreviations we introduced into equations (19) and (20), we obtain 



3 /cos 8 cos cos ft Q cos p -\- d L\ o cos ft -|- d L Q(Q L cos ft) 



j0 I :_ a I V ~ rt l I T^" I" rt - 



Vr \\ill then determine the integral 



R 

 Lcosft) , [ lj Q(Q L cos / 



A 



[ , f y? IP ' 



p 



- R 



Birkeland. The Norwegian Aurora Polaris Expedition, 19021903. 



