PART II. POLAR MAGNETIC PHENOMENA AND TERRELLA EXPERIMENTS. CHAP. VI. 7OI 



iat is to say 



(tZ \ .(If (IZ \ " (IZ (l I (tZ \ (t^Z 



= and -7 I =- I = or =- -j I j- 1 ^ or . ., = < > 



(IZ \(lt / (it (IS \(1tJ (lf- 



In the same way we also find that -y-. r = for the boundary-circle. We have, then 



Disregarding the plane of the equator s = 0, we have 



3P 



id of course also 



P=0. 



If we introduce the actual expressions for P, - and - , it becomes 



a,. _ 



"" ~~ 



a ,ft_ = 

 r' r* ' r' ~ 



(c) t?M*R* a-,* = 0. 



From (c) we obtain 



V = 

 .id from (b) 



As of necessity r ^ 0, it must be that 



* = + ar 3 



;id thus 



r 2 

 From (a) we obtain 



icnce 



F~rom this we obtain by substitution of the value found for r- 



, r 

 (Cr 



Birkeland. The Norwegian Aurora Polaris Expedition, 19021903. 89 





