72 Prof. L. Vegan! : Results of JS^orthlight Investigations 



distance from the pole although the number o£ turns they 

 make before reaching this distance may be very different. 

 It also follows that if a ray at a certain point suffer a change 

 of: velocity without change of direction relative to the 

 line of force through the point, this change will not alter 

 the minimum distance d. If then a ray is moving in 

 a homogeneous absorbing medium which only produces a 

 resistance force on the ray, the latter icill reach the same 

 minimum distance as if there had been no resistance force, 

 provided of course that the ray is not completely stopped 

 before this distance is reached. The effect of the force 

 will be to gradually diminish the cone-angle cf>, which is 

 equivalent to an increase of the number of turns round 

 the magnetic lines of force. The ray will no longer lie on 

 a cone of revolution, but be a geodetic line on a cone which 

 is described by a straight line through the pole that glides 

 along a spiral. When a cone of this sort is developed on a 

 plane and we draw the line of contact for each revolution 

 of the cone, we get figures like fig. 6 in. & iv. 



In fig. 6 in. the ray is supposed to be completely absorbed 

 before it reaches the minimum distance. In fig. 6 IV. the 

 ray is absorbed on its way back from the pole. 



H we would suppose the density of matter to diminish 

 according to an exponential law with the distance from the 

 pole, the resistance force would be a maximum at the point 

 of minimum distance and rapidly diminish on both sides of 

 it as we pass along the orbit. Let the penetrating power 

 of the ray be so great that it would be completely absorbed 

 at a distance d from a pole ; then if d^zd the ray will be 

 absorbed before reaching the minimum distance. But if 

 d becomes greater than d the absorption suffered by the ray 

 will diminish rapidly and wiil soon be too small to stop 

 the ray completely. A ray coining from infinite space 

 will return to infinite space, but with its velocity somewhat 

 reduced. 



The case d nearly equal to d is illustrated in fig. 6 VI- ; 

 the case of incomplete absorption in fig. 6 v. The ray 

 enters on a cone with a comparatively large opening 

 angle (f> and returns to infinity moving on a cone with 

 a small angle, and a corresponding increase of the number 

 of turns. The latter conditions are similar to those existing 

 in the higher strata of the atmosphere, where we have 

 converging lines of force, and a stratum which increases 

 rapidly towards the point of convergence. Now w r e know 

 from the measurements of the aurorse that the penetrating 

 power of the rays is sufficient to bring them down to 



