488 Mr. C. G. Darwin on the Collisions of 



physics, it is natural to suppose that the a-particle is the 

 complex one. From the first model we conclude with some 

 probability that the experiments cannot be accounted for, if 

 the a-particle is equally likely to be orientated in any 

 direction — in fact, Rutherford's suggestion of a plate is 

 supported. Two plate-like models are then tried, and are 

 seen to give closer resemblance to the experimental curves.. 

 For the present, however, until the latter are confirmed it 

 would appear undesirable to draw conclusions. 



2. The Collision Relation. 



Throughout the paper Ave shall be dealing with the action 

 of an a-particle in setting a hydrogen nucleus in motion.. 

 It will conduce to shortness to refer to the two simply as a 

 and H respectively. We shall first consider what conclusions 

 can be drawn purely inductively from any type of experi- 

 ment on the collisions of « with H. Neither particle may 

 now be assumed to be a point charge, and the law of inter- 

 action is supposed to be quite unknown. No experiments 

 on any line that could be devised (at present, at any rate) 

 could do more than give a statistical description of the 

 numbers of H projected in various directions and with 

 various velocities by a known beam of a. We shall see that 

 all such experiments can be made to lead to a certain relation 

 between three variables, which we shall call the collision 

 relation. 



In the first place, the velocity of H is determined by the 

 angle between the initial line oj: motion of a and the line of 

 final motion of H. This angle will be called the angle of 

 projection. For, let E, M be the charge and mass of a, and 

 let V be its initial velocity. Let e, m be the charge and 

 mass of H, initially at rest, and let u be its final velocity at 

 angle to the initial line of motion of a, so that 6 is the 

 angle of projection. 



Then by a simple application of momentum and energy it 

 is found that 



9T\T C 



u=^- s — Vcos0=|Vcos0, . . . (2-1) 



since M = 4?h. So it is a matter of indifference whether 

 the experiments observe a or 6. We shall use 6. 



In calculating the above it has been tacitly assumed that 

 the collision involves no emission of radiation or change in 

 the rotational motion of either body. Unless this is so, no- 

 progress can be made with the present method, as the 



