38  McoCruennanp and Hackerr—The Absorption of B Radium Rays by Matter. 
The previous work above referred to has shown that accurate values of 
the coefficient of absorption of 8 radium rays cannot be obtained unless the 
effects due to secondary radiation are taken into account. This was shown 
incidentally in a previous paper,* but the theoretical investigation required 
for the present work is given fully here. 
Let AB represent a plate through which 8 rays are passing. 
18 =| ee Y Ro 
| 
ye 
Let the energy of the incident radiation passing through unit area of the 
face A per unit time be &. 
Let the total downward flow of energy at depth x through unit area in 
unit time be #, and let the upward flow at same depth be +. 
FR is made up partly of unabsorbed primary radiation, and partly of secondary 
radiations, including under the term secondary not only true secondary radiation, 
but also tertiary and all successive radiations. ‘The upward flow 7 is composed 
entirely of secondary radiations. 
Now let » denote what the ¢rue coefficient of absorption would be if there 
were no secondary effects, and let « denote the ratio of the energy of the 
secondary radiation given out by the layer dv to the incident energy absorbed 
B 
by this layer. 
With this notation we have 
The first term on the right-hand side results from the absorption of primary 
radiation; the second term expresses that « times the energy absorbed is set 
free again as secondary radiation, of which, as an approximation, half is 
taken as travelling upwards and half downwards. The third term results from 
the fact that, in the layer considered, the quantity pr of the upward flow is 
* Trans. Roy. Dublin‘Soc., vol. ix., part ii., 1906. 
