﻿the Rays producing Aurora Borealis. 225 



from the sun which are to reach the earth must follow near 

 to orbits through the origin having infinite branches. The 

 condition mentioned only requires H /> F 0*38, and the 

 solar rays giving rise to the radiant forms here considered 

 most undoubtedly fulfil this condition, on account of the 

 fairly great penetrating power they possess ; for it only 

 means that the solar rays must be less deflectible than a 

 cathode particle which has acquired its velocity from a 

 potential fall of about 1/100 of a volt. 



In order to get an idea of the diurnal distribution we may 

 regard the distribution of precipitation of electric radiation, 

 which at a certain moment would be produced by a rich 

 supply of radiation from the sun 



Suppose the rays to come from a point S whose distance 

 from the point E corresponds to that between earth and sun. 

 Let SE, fig. 5, form an angle yjr with the plane perpendicular 



to the magnetic axis. Suppose the orbit to be projected on 

 this plane, and let the tangent (ET) of the projected orbit at 

 the origin form an angle <t> with the line S'E. As shown 

 by Stormer, 4> and y]r are single- valued functions of 7 ; but 

 we have to remember that <P and ijr only exist physically 

 for intervals of 7 which give orbits through the origin with 

 i nfinite branches. 



Numerical integration has shown that the two functions 

 *P = fi{y) Iin ^ ty^fsiy) are continuous and real in the 

 interval (Ij); in the interval (I 2 ), however, if we only con- 

 sider real values, thr» two functions /, (7) and f 2 (7) have a 



