and Nature of the Cosmic Electric Rays. 81 



fairly broad or the luminosity is confined to the extreme 

 bottom edge. 



/3 and cathodic rays combine a sufficiently great magnetic 

 deflectibility and penetrating power to explain the luminosity 

 distribution, and also to explain the height of the lower limit 

 o£ the aurorae in the way previously proposed. As regards 

 the ordinary positive rays, the question is whether rays with 

 a sufficiently great magnetic deflectibility will have a suffi- 

 ciently great penetrating power. Professor Bohr * has worked 

 out a general theory of the absorption of electrified particles 

 in passing through matter, and this theory has been found 

 by Darwin f and Rutherford to be in good agreement with 

 observations in the case of ordinary a-rays, and if we take 

 the law to hold also for ordinary positive rays we should be 

 able to calculate the air equivalent of any positive ray. We 

 suppose various rays to be absorbed in hydrogen at atmo- 



M 



spheric pressure. Let the ray have the mass ^ and the 



charge ne, where N is Avogadro's number and n the number 

 of elementary charges carried by the ray. Then the range x 

 in hydrogen is given by the expression 



x = k d>( v) — s, 



where <f>(v) is a function of the velocity which should be the 

 same for all rays. If a relation of the same form also holds 

 for other absorbing gases, we should be able to calculate the 

 range in nitrogen by means of a similar formula. 



Now the function <f> (v) can be determined from the relation 

 between velocity and range (R) that is found for ordinary 

 a-rays. 



We put M = 4, w = 2, and 



R x = h'4>(v) = kv* 

 M 



or 



,3 



>r 



The constant k for nitrogen can be found from the range 

 found for a-rays of given velocity ; e. g., rays from RaC 



o-ive 



7 ' 08 =i-oo.io- 



(1-92. 10 y ) 



M 



or x = 10 21 — , . v 3 cm. 



n z 



* Bohr, Phil. Mag. xxv. p. 10 (1913). 



t Darwin, Phil. Mag. xxvii. p. -499 (1914). 



Phil. Maq. S. 6. Vol. 42. No. 247. July L921. G 



