Bumstead — Heating Effects produced by Rontgen Rays. 19 



of the secondary rays (of the more absorbable type) generated 

 in this element ; say 



The question is as to the valne of the fraction a necessary to 

 produce the observed secondary rays outside the metal. Let 

 us assume that half of the secondary rays so generated are 

 propagated straight back to the surface ; this will give us an over- 

 estimate of the rays which escape with a given value of a, or 

 an under-estimate of a necessary to account for the observed 

 secondary rays. The effect, at the surface, of the secondary 

 rays generated in the element dx will be then 



- \dxe 



and the total intensity of the secondary rays at the surface of 

 the metal will be 



00 GC 



/* —?i 2 ,x - r 



I 2 =i|/I 2 e dx= : ka\ 1 IJ e 



*y n */ n 



■?i 2 )x 

 ax 



The value of the coefficient of absorption in air, of the secondary 

 rays from brass, maybe obtained from Townsend's experiments* 

 and is 6*9 ; he did not measure the absorption in air of the 

 primary rays, but an estimate of its value may be got from the 

 statement that the number of ions produced by the primary 

 rays when they traverse a layer of air l cm thick is about half 

 as great as the number produced by complete absorption of 

 the secondary rays ; combining this with Allen's result that 

 complete absorption of the primary rays produced 1900 times 

 as many ions as complete absorption of the secondary rays, we 

 get, for the coefficient of absorption in air of the primary rays 

 used by Townsend, approximately 3-XlO" 4 . Assuming 

 that the ratio of the coefficients of absorption in the metal is 

 of the same order as that of the coefficients in air, we have 

 roughly 



and as 



I 1 2000 



we get 



a=10. 



*Camb. Phil. Soc. Proc, x, p. 217 (1899). 



