﻿902 Mr. C. G. Darwin : A Theory oj the 



system necessarily involves that the helium atom, which is 

 formed from an a ray, has only two electrons, an assumption 

 which appears reasonable when it is remembered that the 

 a particle is expelled with enormous velocity from one atom 

 and is perpetually undergoing violent collisions with others, 

 so that it must be of a very simple nature. I proceed 

 parallel w T ith the alternative assumptions that the electrons 

 are distributed in the atom (1) throughout the volume of a 

 sphere round the centre and (2) over its surface. 



In passing through an atom an a ray will exert forces on 

 the centre and on all the electrons. It will set any charges 

 it approaches in motion and may succeed in pulling an 

 electron out of the atom. In doing so it will lose velocity, 

 while the ejection of the electron will be equivalent to 

 ionization. Now in the atom there is a complicated field of 

 forces acting between the electron and the rest of the system. 

 This field is quite unknown, but the ease of the occurrence of 

 ionization by collision suggests that it is not very great. 

 That is to say, while an a particle is passing an electron 

 their mutual forces are very much greater than the forces on 

 either of the rest of the atom. On account of its high 

 velocity the a particle will spend a very short time near an 

 electron, and in considering the motion of the a particle we 

 shall commit no great error in neglecting the effects of the 

 perturbation of the electron by the rest of the atom. With 

 regard to the motion of the electron this need not at all be 

 true. As soon as the a particle has passed, the predominat- 

 ing factor is the atomic field which may prevent the electron 

 from escaping or may greatly reduce its velocity. 



We therefore suppose that the a particle loses its velocity 

 by setting in motion a cluster of electrons whose interactions 

 are negligible. In actual atoms the electrons will probably 

 be already in motion, but it is possible to show that such 

 motion only affects the result by the ratio of the squares of 

 the velocities of electron and a particle, and this may pre- 

 sumably be regarded as a small quantity. 



In traversing matter some a particles encounter more 

 atoms than others and go deeper into them. Thus after 

 going a given distance the a particles will have straggled 

 out, and some will be moving faster than others. I have 

 not succeeded in finding the amount of this straggling in 

 the present problem ; but it is possible to prove with con- 

 siderable generality that the mean loss of velocity of the 

 particles after a given number of collisions is equal to the 

 sum of the mean losses in each collision, a proposition which 

 is not self-evident. It is this fact which makes the problem 



