158 BIRKELAND. THE NORWEGIAN AURORA POLARIS EXPEDITION, 1902 1903. 



come very near, or go right up to the elementary magnet. These paths will receive a special demon- 

 stration in other models, which will be described in the detailed treatment of the experiments with the 

 terrella (see also fig. 73). 



"From the form of the cyclo-median perturbations, and comparison with experiment and theory, we 

 find that the radius of the ring is here about 1.5 that of the earth. Now since the magnetic moment 

 of the earth, M, is 8.52 x io'- 3 , this gives, for the corpuscles that cause the cyclo-median perturbations, 



8.52 x io 25 

 ? = [^5 x 6.37 x lo^ = 93 milllons ' approximately. 



"In other words, the rays in these perturbations must be excessively stiff." 



It thus appears from Stermer's calculations that two cyclonic vortices, symmetrical with reference to 

 the equator, are produced, such that if we reckon with positive current-directions, the vortex north of 

 the equator is counter-clockwise, that south of the equator, clockwise. This is in accordance with our 

 observations in as far as the cyclo-median perturbation formed a counter-clockwise vortex. Judging from 

 the light effects produced by the experiments with the terrella, a cyclo-median perturbation should also 

 have a somewhat stronger effect in the polar regions. This assumption, unfortunately, cannot be verified, 

 as we have no observations from Dyrafjord for the 6th October. 



It should be remarked that the length of the arrows in fig. 72 has nothing to do with the inten- 

 sity of the current or of the magnetic effect. 



I have not yet proved the existence of electric current-vortices such as these experimentally, but 

 shall try to do so later on. This is a case in which mathematical analysis has shown a superiority to 

 experimental investigations. It is generally, as we know, only after the experimental discoveries have 

 been made that analysis steps in to explain and enlarge the comprehension of the results obtained; and 

 this has hitherto also been the case here. 



The discovery of the various districts of precipitation in the polar regions is experimental, and 

 from the results of the observations from the expeditions in 1882 83, we have found such simultaneous 

 districts of precipitation for the magnetic storms. This subject will be discussed in Part II of this -volume. 

 Later on, in Vol. II, a corresponding investigation of the distribution of simultaneous aurora will be 

 made, in which both our own collected material will be employed, and also that from the expeditions 

 of 188283. 



FURTHER COMPARISON WITH ST0RMER'S MATHEMATICAL THEORY. 



53. It seems as if Stermer's investigations would be of great importance in the problem of finding 

 theoretically also, the various districts of precipitation in the polar regions. This is apparent from the 

 following remarks, which Stermer allows me to quote: 



"All these remarkable light-phenomena, shown in figs. 47 and 68, can doubtless be explained 

 theoretically by my mathematical investigations of the paths of electrically charged corpuscles in the field 

 of an elementary magnet. We shall return to this subject in a subsequent section of this work. At 

 present I will only point out that the patches of light about the poles, obtained by sufficiently strong 

 magnetism, are probably due to cathode corpuscles flung out into paths in the immediate proximity of 

 those which, theoretically, would strike the elementary magnet in the centre of the terrella, and whose 

 field, at great distances, represents the magnetic field of the terrella. 



"As I have previously calculated a series of the simplest of such paths, all that is now necessary 

 for the re-finding of the districts of precipitation visible on the terrella is to employ these calculations. 

 Fig- 73 shows a wire model constructed for the case occurring in the experiments shown in fig. 47. 



