322 Prof. Thomson, 



On Secondary Rontgen Radiation. By Prof. J. J. Thomson, 

 M.A., F.R.S. 



[Read 12 March 1906.] 



The greater part of the secondary radiation produced when 

 Rontgen rays pass through a medium is absorbed in the medium 

 itself, the part which emerges and which is all that can be 

 measured is but a small fraction of the whole secondary radiation. 

 We can find the relation between the energy of all the secondary 

 radiation and of that which emerges in the following way. Sup- 

 pose the absorbing medium is a plate of thickness h bounded by 

 planes at right angles to the axis of x, and let the primary rays 

 be travelling parallel to the axis of x. 



Let I be the amount of energy crossing unit area in unit 

 time for the primary waves when they enter the plate, A, the 

 coefficient of absorption of the primary radiation ; I the intensity 

 of the primary radiation when it has travelled a distance x in the 

 plate will be equal to I e~ Xx ; the amount of energy absorbed in a 

 distance dx is \I e~ kx dx, let the amount of this energy emitted 

 as secondary radiation be K\I e~ Xx dx. Half of this will travel 

 forward in the direction of the primary radiation and half will 

 travel backward. Let T, R be the amounts of energy in the 

 secondary rays travelling backwards and forwards respectively 

 which cross unit area in unit time at a distance x from the 

 front of the plate, /3 the coefficient of absorption of the secondary 

 rays ; we have 



dT = -I k\I e~ KX dx - fiTdx, 



— dR = ^fc\I e~ Xx dx - fiRdx ; 



the solutions of these equations satisfying the conditions that 

 T = when x = 0, and R = when x = h, are 



1 k\Iq _ 



2/3-X 1 h 



L p + A, 



To find the values when the secondary rays emerge from the 

 plate we put x = h in the expression for T and x = in the ex- 

 pression for R ; doing this we find 



T = - kXI ° ( 6 - Kh - e-? h ) 

 2/3-A, V ; ' 



1 K\I d_ -<ft+K)h\ 



