Bumstead — Heating Effects produced by liontgen Hays. 21 



which produce them. Thus if \ x and \ are the coefficients of 

 absorption in zinc of the primary and secondary rays respec- 

 tively, we have 



Now in the experiment described at length above, the absorp- 

 tion by the zinc strip was about - 8 ; the two-tenths observed 

 behind the zinc included not only the primary rays which got 

 through but also some of the more penetrating secondary rays 

 from the rear surface. Hence e— ^<.0'2, and as I = 

 O08 cm 



A 2 >A ] >20. 



If we assume, as before, that one-half of the secondary rays 

 generated in any element are propagated straight back toward 

 the front surface (which will exaggerate the intensity of the 

 secondary rays), we get for the intensity of the secondary rays 

 escaping from the front surface 



i. <1 L a i i _A_/ 1 _ e -(A 1+ ^\ 



Writing this 



the fraction is seen to be of the form 



l — e~ x 



which (for positive values of x) increases as x diminishes. 

 Hence 



l 2 <ial 3 (l-e- 40 



The primary rays absorbed in the zinc strip 



A^I/l— e.^O^iCl-e -20 *); hence 



T 1 z,-40£ f 



1 » cr^a -±a(l+e- m ) ■ or ■=* 



A I <4a 1 _ e -20^-* a(1+e >> 01 A, 



in which of course, if there is to be no generation of fresh 

 energy, a must be less than unity. 



We may make a similar calculation for the rear surface, but 

 it is sufficient to observe that even if all the effect observed 

 behind the metal is due to secondary rays, the ratio of these 

 to the primary rays absorbed cannot be greater than 0"2. So 

 that by considerably exaggerating all possibilities in favor of 

 the production and escape of secondary rays we are unable to 

 give to the secondary rays which escape an intensity one-half 

 as great as that of the primary rays absorbed. Now in order 



