﻿224 Mr. L. Vegard on the Properties of 



The values of u show that for all stations the evening 

 maximum for the whiter 1882-83 occurred about 1*3 hours 

 before magnetic midnight. 



We saw that auroras did not occur symmetrically with 

 regard to a plane through the sun and the axis of rotation. 

 Looking at the curves, we notice that there is also a marked 

 asymmetry with respect to the magnetic midnight, or with 

 respect to a plane through the sun and the magnetic axis. . 



Application of Mathematical Theory. 



6. Stormer's t calculations, founded on the radiation 

 hypothesis, should give us some means of determining from 

 theory tne diurnal distribution of aurorse. The part of his 

 researches which mostly interests us is the determination of 

 the orbits through the origin ±, and we shall mention a few 

 of the results which have reference to our problem. 



According to Stormer we get the various types of orbits 

 through the origin (the centre of the earth) by the variation 

 of a single integration constant 7. In order that rays 

 starting from the origin shall pass on towards infinity 7 

 cannot be outside the interval (I) 



— 1<7<0. 



But values of y inside this interval may or may not give 

 orbits through the origin with infinite branches. 



Numerical integration has shown that all values of 7 in 

 the interval (I { ) 



_7*<y<=0, 



give orbits through the origin which pass on towards infinity, 

 7* is found to be about 0'93. In the rest interval (I,) 

 — 1-<7<;7* there are an infinite number of orbits which 

 only reach a certain distance and then go back to the origin; 

 but also in this interval an infinitely large number of orbits 

 are found which have infinite branches. 



If the rays from the sun reach the earth they must 

 follow some path which is very near to one of those coming 



from the origin, and if the quantity c = \/ ^ § is less 



than the distance between the sun and the earth, the ravs 



t Loe. cit. 



\ See C, Stormer, Archives des Sci phus. et nat. Geneve, pp. 235-247 

 (1907). 



§ M is the magnetic moment of the earth, p is the radius of 

 curvature of the ray when moving. in a uniform field of strength JI U in a 

 plane perpendicular to the magnetic force, 



