Question of the Homogeneity ofy-Rays. 735 



thus be written : — 



^ = 6 -* t +at[e;(-xt)]. ... (4) 



This is Schmidt's result, the factor XT in the second term 

 having been omitted through an oversight. The graph of 

 the function is shown by the lower curve in fig. 2 (PI- XII.), 



the lower curve representing log 10 — . The upper curve re- 



It ° . 



presents the value of log 10 f-, according to the simple expo- 



nential law. It will be seen that the curve somewhat resembles 

 the experimental curve, the slope at first decreasing until a 

 certain initial thickness has been penetrated, after which it 

 remains nearly constant. As Schmidt has pointed out for 

 values of XT greater than 5 the slope is about 1*1 6 times 

 greater than for the simple exponential curve. As drawn, 

 the slope over the range from XT = 2 to XT = 4, i. e., for a 

 thickness of lead from 4 to 8 cm., is very nearly 1*25 times 

 the slope of the exponential curve. 



The above solution, however, applies only to the case where 

 the cone of rays included subtends an angle of 180°. The 

 expression holding for a cone of any semi-angle 6 is, 

 however, readily obtained. If I ' and 1 T ' represent respec- 

 tively the quantities of radiation in a cone of semi-angle #, 

 before and after passage through the absorbing plate, 



?f = l-cos0, 



Xt/cos 6 



I f = fV XT/cos9 i(-cosfl) = XTf g.,/,, 



Xt 

 -It I „ — Xt / _ a\ r — Xt'cos© 



1/ 



i u 



-(cos 6) e- ATCOsy +xT[Ei(-XT)] 



-\T[Ei(- XT/cos 6)] } -Kl - cos °)- • ( 5 ) 



In the experimental disposition described with cylindrical 

 electroscope 1 2*8 cm. high and 10*5 cm. in diameter, and 

 the preparation 8'25 cm. below the upper surface of the base, 

 the base and top of the electroscope subtend respectively 

 cones of semi-angle about 22° and 14°. The mean semi- 

 angle may be taken as about 18°. A particular case was 



