334 POPULAR SCIENCE MONTHLY. 



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 Ynniv'; thus a considerable deflection 

 of the corpuscle, i. e., a collision will occur only when ee'/d is com- 

 parable with l^w^v-; and d, the distance at which a collision occurs, 

 will vary inversely as v-. 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 

 d-, and therefore varies inversely as i'*. 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 sub- 

 stances which are nearly impermeable to the more slowly moving cor- 

 puscles from cathode and Lenard rays. 



Cosmical Effects Produced hy 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 de- 

 veloped 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 inter- 

 planetary 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 Avill 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 lati- 

 tudes 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 



