102 



BIRKELAND. THE NORWEGIAN AURORA POLARIS EXPEDITION, 19021903. 



Here / is assumed to be expressed in amperes, therefore K in dynes. This we will apply to a 

 current-system of the form mentioned above, assuming that the horizontal portion of the current lies at 

 a height h above the storm-centre, and has a length of 2 /. 



The distance from the storm-centre in degrees along the transverse axis, we will designate ip, the 

 horizontal magnetic force-component, produced by the portions of current /, //and ///along the transverse 



axis, respectively P/y, Piiy and Puiy, and the 

 other magnitudes as given in fig. 49. We will call 

 the force positive when it is directed towards the 

 storm-centre, if we are on the same side as the 

 point of convergence, and negative if we are on the 

 opposite side. 



We then obtain 



+J 



p u = i_ s 



lay \lyt _l_ s 



cos 



cos 



Fig. 49- 



n sm 



Here y = R -r 



sin 



where R is the radius of the earth, (i is determined by the equation 



4- // 



tan (f + ft) = 



The equation can thus be written in the form 



p i sin ft 



$R sin ty i 



In the storm-centre itself we have 



tan 



2 



cos 



//o 



We further obtain 



where 



and 



Pl</' 



If C is determined by the equation 



tan C = 



= 2 



IOJ' 



n = . - R cos 6, 

 sin a 



y = R sin 0, 



sin a 

 sm y = -151 



sin 



cos 6 = cos a cos (>. 



sm y 

 a 



R sin 



/? sin 9 sin a 



I n I R cos sin a 



-T - R cos 6 

 sin a 



we obtain 



sn 



r 1 ' 



" cos ^ J ==; 



,- 2sin Of sin 2 - 



sn 



