730 Mr. & Mrs. Soddy and Mr. A. S. Russell on the 



represent the primary hard 7-rays capable o£ penetrating 

 1 cm. o£ lead, together with the equilibrium amount of 

 secondary radiation they produce in the absorbing material. 

 I£ only hard 7-rays were present, on the simple theory (ibid. 

 p. 641), assuming the ionization produced by secondary and 

 primary to be directly proportional to their absorption 

 coefficients, one would expect the following relation to hold: — 



-J? =(! + £) e^'-^*, where /3 = -^?- .... (1) 



Here I T and I refer to the ionizations, \j and \ 2 to the 

 coefficients of absorption of the primary and secondary 

 radiations respectively and k is the coefficient of transfor- 

 mation, or fraction of the energy of absorbed primary 

 transformed into secondary. For great thicknesses the 

 second negative exponential term becomes negligible if \ 2 is 

 greater than X x . The two radiations are in equilibrium and 

 the relation becomes : — 



H i+ ^>- v (2) 



This is the equation of the dotted-line curves. Since for 

 thicknesses greater than 1 cm. nf lead the curves are 

 exponential it may be assumed that X 2 is always much 

 greater than \ x . The relation indicates that when the radi- 

 ations are in equilibrium the ionization is due to the two parts, 



one, e- x i T , due to the primary and the other, >-^V €_XlT 5 



due to the secondary. Now for different substances k may 



possess any value between and 1, and since ^ _■. is not 



very much greater than unity, it follows that for equivalent 

 thicknesses of various materials the ionization cannot vary 

 very much more than in the ratio of 1 to 2. So far as can be 

 seen the results certainly bear this out. At equivalent 

 thicknesses 56 — the greatest examined for card — the ratio of 

 the ionizations of lead and card are 2'15, and, at 2'6, of pine- 

 wood and lead are 2'5. A similar 2:1 ratio in the emergence 

 radiation from different elements for the 7-rays of radium is 

 to be seen in Bragg and Madsen's curves (figs. 2 and 3, 

 Phil. Mag. 1908, xvi. p. 925). It was not possible with 

 the lighter substances to extend the curve sufficiently far to 

 give all the information required, for the source of radiation 

 was too weak to be removed to a greater distance to allow of 

 greater thicknesses of absorbing material being used. A 



