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LIX. The Decrease of Energy of a Particles on passing 

 through Matter. By G. H. Henderson, Ph.D* 



§ 1. Introduction. 



THE general laws governing the passage of u particles 

 through matter have been discussed theoretically by 

 both Darwin t and Bohr J. 



I£ E, M, and V be the charge, mass, and velocity of the a 

 particle and e and m be the charge and mass of an electron, 

 then, when the a. particle approaches an electron along a line 

 at a distance p from it, the energy given to the electron is, 

 by the ordinary laws of dynamics, 



Q- 2EV , n 



, E*(M + m) I3« 



Where . a ~ MmV* =^V? appr0X -' 



if the electron is free. 



In passing through a thickness A# of matter, the number 

 of encounters in which p lies between p and p -f dp is 



27rNwA^p dp, 



where N = the number of atoms in 1 cm. 3 

 and M = the number of electrons in one atom. 

 Then, if T is the energy of the a particle, 



AT ^ 47rEVNn C pdp 



Ax" mV 2 ]p 2 + a 2 ( ' 



If the limits of p in this integral be taken as and <^> , the 

 integral becomes infinite, i. e. an a particle could not pass 

 through an appreciable thickuess of matter at all. Evidently 

 some upper limit to the radius of action of the a particle 

 must be taken. 



In the first paper dealing with the motion of a particles, 

 Darwin made the assumption that the effect of the a particle 

 at any instant was confined to the electrons of the atom 

 through which it was passing. He was able to calculate the 

 motion of the a particles through matter for various arrange- 

 ments of electrons within the atom. Theoretical velocity 

 curves showing the variation of velocity with distance 



* Communicated by SirE. Rutherford, F.R.S. 



t Darwin, Phil. Mag. xxiii. p. 901 (1912). 



% Bohr, Phil. Mag. xxv. p. 10 (1913), and xxx. p. 581 (1915). 



