338 IHKKKI.ANU. THK NORWEGIAN AURORA POLARIS KXPKDITION, igO2 1903. 



83. We may here draw a comparison with the areas of precipitation that may be calculated 

 according to fig. 76, Part I, p. 160. 



If 6 is the angle that the sun's declination-circle makes with the meridian of the magnetic axis, 

 (J the sun's declination, and (90 rp) the angle made by the magnetic axis with the earth's axis, 

 i. e. (f> 78 20', we have 



A 



sin i/> = cos (y> 6) 2 sin 2 cos 6 cos rp , 



where (// has the same meaning as in Art. 53 in Part I. 



We will reckon the angle positive towards the west like 'P, thus standing for the time that 

 has passed since the sun crossed the meridian of the magnetic axis. 



The longitude of , as already stated, is 68 49' W, so that the period during the perturbations 

 under consideration here, namely io'' 23'' 2o m G. M. T. corresponds to values of 6 lying between about 



- 100 < 9 < + 100 

 which answers to about 



- 22.5" < y < - 9.5. 



Thus i// first increases from 22.5 to 9.5, and then decreases from 9.5 to 22.5. 



We will now see from these calculations what areas of precipitation we should expect to find. 



In making such comparison, we do not mean that the areas of precipitation we find by calculation 

 should exactly correspond with the various storm centres which occur during the perturbations. The 

 areas of precipitation found by calculation, are those in which the rays fall perpendiculary on the sur- 

 face of the Earth, what are actually calculated are rays which go to the origin, where the assumed 

 elementary magnet is situated. The regions that just correspond with these, must, in my opinion, best 

 be compared with the places where aurora occurs, but these do not always correspond with the storm- 

 centres of the magnetic disturbances. But we might, however, expect to find analogies and we will 

 therefore proceed here briefly to make such comparison. 



We will first consider the negative rays. For tp = 22.5 we find, as fig. 76 shows, no precipi- 

 tation, but as soon as ever ip has increased a couple of degrees, an area of precipitation appears on 

 the afternoon-side, at first spreading with considerable rapidity east and west, and subsequently dividing 

 more into two systems, one of which moves towards the morning-side and the other towards the evening- 

 side, as the sun approaches the meridian of the magnetic axis. 



Shortly after the formation of the first area of precipitation, a new one is formed upon the morning- 

 side, which also, as the sun rises higher, divides into two parts, one of which moves towards the night- 

 side of the earth, the other towards the morning-side. There will moreover be areas of precipitation 

 answering to rays that have passed round the earth before their descent, and correspond to values of 

 \<P\ that are greater than 360. These are not taken into consideration here. 



For positive rays we find more or less the same values of <? for the first two areas of precipitation. 



After the sun has crossed the meridian of the magnetic axis, it might be supposed that the pheno- 

 mena would be repeated in the reverse order, but with the whole area moved westwards. We will now 

 see whether analogies to these conditions are actually found. 



At first, then, we should expect to find two areas of precipitation, one on the afternoon-side, and 

 one on the morning-side. 



This agrees exceedingly well with what we found in the first section, where we pointed out the 

 two areas in which the storm was concentrated. One of these, the negative, appeared on the morning 

 and night side from Kingua Fjord to Fort Rae and Uglaamie, beginning slightly earlier at Fort Rac than 

 at the other two stations. The other, the positive, occurred on the afternoon and evening side, from 

 Little Karmakul to Ssagastyr. Here then there appear to be distinct analogies. 



