and Nature of the Cosmic Electric Rays. 69 



For a given absorbing substance we may for any kind of 



electric rays assume that -j- is nearly independent of the 



density. This only means that the effect of an atom to 

 diminish tbe velocity is independent of the distance to the 



neighbouring atoms. Consequently the quantity ~ is for 



any substance a definite function of the velocity, and can be 

 found if we determine the variation of velocity along the 

 orbit when the ray passes through a homogeneous stratum of 

 density p , for then we have at any point of the orbit : 



dv 1 dv 

 dfju p ds' 



If the curve v=f(s) is found experimentally we can 

 easily find by a graphical method the values of -7 corre- 

 sponding to various velocities, and thus determine the function 



and we get 



m r 



For a-rays we have according to Geiger 



Q- 



■■' s 



1 R' 



where R and v are initial range and velocity ; and thus the 

 resistance force is determined for a given velocity of the 

 ray and a given density of the substance. If the medium 

 traversed is composed of a number of substances with densities 

 /?!, p 2 , etc., we find 



— =v^pcb(v). 



m 1 t\ y 



As far as experience goes the functions <p(v) for a given 

 ray are similar for different substances, or for two substances 

 we might put 



where ki is the constant independent of velocity, and 



= V(j)(v)(p + l- 1 p i + . • • Kpn). 



