by the electric forces on the corpuscle in its journey to the shortest distance from the charged body. If d is the shortest distance, e and e' the charge of the body and corpuscles, the work done is ee'/d; while if m is the mass and v the velocity with which the corpuscle starts the kinetic energy to begin with is
12
mv2; thus a considerable deflection of the corpuscle, i. e., a collision will occur only when ee'/d is comparable with
12
mv2 and d, the distance at which a collision occurs, will vary inversely as v2. As d is the radius of the sphere of action for collision and as the number of collisions is proportional to the area of a section of this sphere, the number of collisions is proportional to d2, and therefore varies inversely as v4. This illustration explains how rapidly the number of collisions and therefore the resistance offered to the motion of the corpuscles through matter diminishes as the velocity of the corpuscles increases, so that we can understand why the rapidly moving corpuscles from radium are able to penetrate substances which are nearly impermeable to the more slowly moving corpuscles from cathode and Lenard rays.
Cosmical Effects Produced by Corpuscles.
As a very hot metal emits these corpuscles it does not seem an improbable hypothesis that they are emitted by that very hot body, the sun. Some of the consequences of this hypothesis have been developed by Paulsen, Birkeland and Arrhenius who have developed a theory of the Aurora Borealis from this point of view. Let us sup,pose that the sun gives out corpuscles which travel out through interplanetary space; some of these will strike the upper regions of the Earth's atmosphere and will then or even before then, come under the influnce of the Earth's magnetic field. The corpuscles when in such a field, will describe spirals round the lines of magnetic force; as the radii of these spirals will be small compared with the height of the atmosphere; we may for our present purpose suppose that they travel along the lines of the Earth's magnetic force. Thus the corpuscles which strike the earth's atmosphere near the equatorial regions where the lines of magnetic force are horizontal will travel horizontally, and will thus remain at the top of the atmosphere where the density is so small that but little luminosity is caused by the passage of the corpuscles through the gas; as the corpuscles travel into higher latitudes where the lines of magnetic force dip, they follow these lines and descend into the lower and denser parts of the atmosphere, where they produce luminosity, which on this view is the Aurora.
As Arrhenius has pointed out the intensity of the Aurora ought to be a maximum at some latitude intermediate between the pole and the equator, for, though in the equatorial regions the rain of corpuscles from the sun is greatest, the earth's magnetic force keeps these in
