236 BIRKELAND. THE NORWEGIAN AURORA POLARIS EXPEDITION, igO2 1903. 



distribution of the effect, the current cannot lie near the earth, but should be at a distance of at least 

 the same magnitude as the earth's radius. If this were the case, we should expect to find similar distur- 

 bances in the vertical intensity near the poles, and, still more, an increase in this force in the north. 

 It is at once apparent that the form of the vertical curve for Axeleen has some resemblance to that of 

 the //-curves at Dehra Dun and Batavia; and the quiet character of the curve may perhaps indicate that 

 here we have not principally direct effects of the polar storms. The deflection really answers to an 

 increase in V, and remains powerful and so constant that the probability of its being caused only by 

 the powerful storms about the auroral zone is not very great. 



A calculation of the magnetic effect produced at various places by a circular current round the 

 earth at a considerable distance from it, may here be of some interest. 



Let us first assume that such a corpuscular circular current has the same magnetic effect as a 

 galvanic linear current. This circular current we will suppose to be situated almost in the plane of the 

 magnetic equator, its centre coinciding with that of the earth, and its radius equal to 2 R, R being the 

 radius of the earth. 



The effect of such a current upon a magnetic mass i cm. 3 /2 gr.V3 sec.-i, situated in the plane of 

 the current, we find to be 



f 

 _ I (a / cos <p) d(p 



I 10 (a 2 -(- P 2a/cos(p) I* 

 J 



o 



where a is the radius of the current-circle, / the distance of the magnetic pole from the centre of this 

 circle, / the current in amperes, and F the force expressed in C. G. S. units. 



This integral may easily be transformed into elliptical integrals of the normal types. 



We have here calculated it numerically for the values a = 2 R, I = R, and we find that 



in 



F 1 = 1.23 



ioR 

 In the centre of the current-circle we have 



_ in 

 ' 2= ioR 



It will be seen that the force is somewhat less at the centre of the earth than in the equatorial 

 districts; but the difference is not very great. 



We will now consider the earth as a homogeneous magnetisable sphere, situated in a uniformly 

 magnetic field of a strength 



P in 



~7oR 



The magnetisation produced in the sphere will give rise to the forces 



respectively at the pole and at the equator, where 



fi being the permeability of the sphere. (See Mascart: L'Electricite et le Magnetisme. Paris, 1896; p. 417.) 

 The value of /.i, that may be used for the earth, is very difficult to determine. F. Pock els 

 (Wiedemanns Analen 63, p. 199, 1897) gives values of about i.i for basalt for the smallest field-intensities. 

 For other minerals, however, we find values of even a hundred times greater, e. g. magnetite, pyrrhotite, 

 haematite, limonite, etc. 



