304 BIRKELAND. THE NORWEGIAN AURORA POLARIS EXPEDITION, IQO2 1903. 



magnetic effect of the corpuscular current with the effect of a galvanic current, and endeavour to deter- 

 mine the strength of the current, or rather, obtain some idea of its magnitude by assuming, as a first, 

 most simple approximation, that the magnetic effect outwards might be satisfied by a linear galvanic 

 current of a certain strength, situated at a certain height. 



In describing the separate elementary storms, we were able to show that the main features of the 

 distribution of force in those perturbations were explained by the assumption of two vertical electric 

 currents with opposite directions, connected by a horizontal portion of current. In Art. 36 we investi- 

 gated the effect of a current-system such as this, and found a very close agreement with the actual 

 circumstances during the polar elementary storms. The results there arrived at might now be employed 

 for the purpose of estimating the operating strength of the currents. If, however, we look at the sta- 

 tions that are situated at all near the auroral zone, we can there simplify the problem considerably. It 

 is immediately manifest that observations from points on the transverse axis of the system and near the 

 storm-centre, must be favorable for a determination of the strength of the current. The field in the 

 immediate vicinity of a linear conductor is somewhat similar to the field about an infinitely long, 

 rectilinear current along the tangent at the nearest point on the conductor. When both stations have 

 the same point on the conductor as their nearest, the field for both of them, at the place under con- 

 sideration, will be determined by one infinitely long, rectilinear current; and as this is horizontal, it 

 will simplify the reckoning considerably, and at the same time furnish a calculation of the degree of 

 proximity of the current to the earth. 



Fortunately for the solution of our problem, Axeleen and Kaafjord, in a number of perturbations, 

 occupy this very position; and we shall only take those cases in which the current passes between the 

 two stations, as we shall thus obtain a more certain determination of the altitude. 



The question now is whether it is possible to decide when the current-system is thus situated in 

 relation to the two stations. This must be decided separately in each case. We will only mention, as 

 a necessary condition, that the current-arrows for Axeleen and Kaafjord must point in the same direc- 

 tion, and their vertical components be in opposite directions. 



A calculation, similar to that given below, of the currents that cause polar storms, was made by me 

 some years ago, for the stations Bossekop and Jan Mayen, with the aid of material from the expeditions 

 of 1882 and iSSst 1 ). 



We shall now proceed to calculate the current-strength and altitude of an infinitely long, rectilinear, 

 horizontal current above the surface of the earth, when we know its effect in magnitude and direction 

 at two points on the earth's surface. 



Since we cannot on the whole lay claim to accuracy, we will here assume that the surface of the 

 earth in the district in question is a plane surface. 



A B is the horizontal projection of the current; (/) and (2) represent re- 

 spectively Kaafjord and Axeleen. 



. According to the above, the connecting line between the points (/) and (2} 



should be perpendicular to A B. This would be an ideal case, which will only 

 approximately be attained. We will therefore assume that the lines form an 

 angle, ip, with one another. In cases in which the calculation will be employed, 

 this angle will be nearly 90. 



We will further imagine the system projected upon a plane perpendicular 



Fi j to the line of the current. This line and the two points (/) and (2) on the earth's 



surface are then projected as three points, C, S\ and S a . 



(') Expedition Norvcgienne de 18991900, p. 27. 



