Professor Thomson, On the Scattering etc. 465 



On the Scattering of rapidly moving Electrified Particles. By 

 Sir J. J. Thomson, Cavendish Professor of Experimental Physics. 



[Read 21 February, 1910.] 



When rapidly moving electrified particles pass through matter, 

 each particle as it passes through an atom of the substance, or 

 perhaps even when it passes close to such an atom, is deflected. 

 The amount of the deflection will vary with the way the par- 

 ticle strikes the atom ; there will, however, be a mean value 

 for the deflection produced by an atom on the direction of 

 motion of a particle passing through it, and when we are con- 

 sidering only the effects produced by large collections of particles 

 we may suppose that the path of each particle suffers the mean 

 deflection. The direction of this deflection is quite arbitrary. 

 Let us consider now the case when a large number of particles 

 pass through a large number of atoms and consider what would 

 be the average deflection of the particles after they have passed 

 through n atoms. Since the direction of the deflections are quite 

 arbitrary, it is evident that the problem is the same as that of 

 finding the average value of the resultant of n displacements of 

 arbitrary phase and of constant amplitude 6; if ^ is the average 

 deflection of a particle passing through an atom. This average 

 value is known (see Lord Rayleigh, Theory of Sound, 2nd Edition, 

 Vol. I, p. 35) to be \/n . 9. Thus if the electrified particles are 

 corpuscles moving normally through a plate of thickness t, then 

 if there are N atoms per unit volume of the plate, and if h is the 

 radius of an atom, the number of atoms traversed by a particle 

 on its journey through the plate is JSfirb^t, and hence the mean 

 value of the deflection experienced by a particle when passing 

 through the plate is '^Nirh-t . 6. 



This supposes that the particle is not bent so much in passing 

 through the plate that the length of its path is materially 

 different from t. 



We shall now proceed to calculate the value of 9. 



Regarding the atom as consisting of Nq negative corpuscles, 

 accompanied by an equal quantity of positive electricity, the 

 deflection a negatively electrified particle experiences when 

 passing through the atom arises from two causes. (1) The 

 repulsion of the corpuscles distributed through the atom, and 

 (2) the attraction of the positive electricity in the atom. 



The amount of deflection due to (2) will depend upon whether 

 the positive electricity is uniformly distributed through the atom, 



