68 Prof. L. Yegard: Results of Nortldight Investigations 



produced by rays with the same velocity and penetrating 

 power. 



In other words, we may still assume that the rays coming 

 from the sun are made up of homogeneous groups which 

 may account for the definite maxima in the height-distri- 

 bution-curve and the existence of parallel bands. 



§ 6. Remarks regarding the Passage of Electric Rays through, 

 Matter under the Influence of a Magnetic Field. 



The result of Poincare and the calculations performed 

 by Stunner — already mentioned — are based on the assump- 

 tion that the velocity of the ray keeps constant, or that the 

 deviating force, due to the magnetic field, is the only one 

 acting on the corpuscle. On its way through the atmosphere 

 the corpuscle will be acted on b} r other forces. In the case 

 of the a-rays, which at the absence of the field move in 

 nearly straight lines, the force due to the medium may be 

 put equivalent to a resistance or a force always acting in 

 a direction opposite to the velocity. 



In the case of /3- or cathode-rays matters are much more 

 complicated, because the path without a magnetic field is 

 very irregular. If we follow the path of the ray, however,, 

 the velocity will on an average gradually diminish and the 

 diminution of kinetic energy is equal to the work done by 

 the resistance force. If we would try to solve the problem 

 of finding the path of the ray through matter, when exposed 

 to the magnetic field, we might first of all simplify the 

 problem by disregarding the effect of matter to deviate the 

 orbit of the ray, and only regard the resistance force and that 

 produced by the magnetic field. This simplification, which in 

 the case of positive rays ought to produce a very small error,, 

 will be much less accurate in the c;ise of (3- or cathode-rays. 

 The resistance force will be a somewdiat complicated function 

 of the velocity and will depend on the composition and 

 density of the matter at the point considered. Let K and m 

 be the resistance force and the mass of the corpuscle respect- 

 ively, then : 



K_dv_ ch 

 m~ dt~ V ch> 



where v is the velocity and ds an element of the orbit. 

 Let dp represent the mass of unit area of a strata of thick- 

 ness equal to ds. Then dp, = pds where p is the density of 

 the matter at the point, and 



K dv 



m ' dp, 



