22 



In this case we find that the whole ionisation (?) is given 

 by 



2.<?i 



Nln^U 



^(i? + ^-i>)-y(d)----— log. ^ 



ViE + d) ^ol^(R + d)+ ^/d\ 



and the ionisation due too the uncovered material by 



2s / 



Nln^D 



= ,/{R-^d)- Vd. 



If we had supposed the ionisation to be independent of 

 the velocity, we should have obtained the result 



D D D 



1/1= 1 1 loo-.— • 



In this case the effect of neglecting the variation of 

 ionisation with velocity is more serious. For instance, if in 

 the simpler formula we put Z)/i? = '25, we find that ?'//== '40; 

 whereas, if we use the fuller formula, and put D — 'lb, R = 3, 

 we find that i/I = 'AA8. 



These formulas are applicable to measurements of the 

 range due to induced activity, since it is to be supposed that 

 the active deposit is extremely thin. Curve B is plotted from 

 the fuller formula of the two, for the case in which R — 1. As 

 usual, d is put equal to 1*33. 



The following co-ordinates have been used in drawing the 

 curve : — 



DIR -061 -124 -250 -357 -500 -690 -833 

 ill -807 -612 -467 -335 -193 -077 -023 



CASE (c). 



Moderately thin layer of radio-active material. 



Let the air equivalent of the thickness of the material be D'. 



This must be considered in two parts. 



(i.) Where r is such that D-\-D'-\-r is less than /?, the 



-'D+D' -' I) 



limits of are cos — and cos ; and the limits of r 



R—r R-r 



ai 



e R-~ D — D' and zero. 



