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



quite a simple matter, and in the discontinuities that may 

 result, the tangent on one side is vertical. There is no need 

 to treat o£ the matter further here, as examples occur in 

 § 8 and § 9. 



3. Methods of Reducing the Experiments. 



In Rutherford's experiments * a point source of radium C 

 was placed in an atmosphere of hydrogen. The a-particles, 

 going in all directions, encountered here and there the nuclei 

 of hydrogen atoms and gave them a high velocity. Some 

 of these H-particles struck a zinc sulphide screen and pro- 

 duced scintillations in it. The ranges of these scintillating 

 particles were found by interposing metal foils of varying 

 thickness in front of the screen, so as to stop the slower ones. 

 Our task is to deduce the collision relation from this rather 

 complicated experimental arrangement, w T hich was made 

 necessary by the extraordinary difficulty of the practical 

 problem. The process is more difficult than most reductions 

 of experiments, because it involves the solution of what is 

 really an integral equation, though one of a very degenerate 

 type. 



The actual observations were the ranges* of the H-particles, 

 but we can with fair confidence translate these ranges into 

 velocities. For there is a satisfactory theory explaining the 

 loss of velocity of a-particles in passing through matter, and 

 it is simple to modify this so as to apply to H-particles f. 

 According to this theory the rate of loss of velocity of an 

 H-particle should be the same as that of an a-particle of the 

 same speed. The theory fails to give a definite value for 

 the range, as it only deals with the higher velocities, but we 

 shall not be far wrong in saying that the ranges should be 

 equal. As we shall see, the experiments we are considering 

 give a partial confirmation of this. Since we are not going 

 to work to any high decree of accuracy we shall take Greiger's 

 empirical rule for the loss of velocity, different though it is 

 from the theoretical, and apply it to the H-particles. This 

 rule is that the remaining range of a particle at any distance 

 along its path is proportional to the cube of its velocity. It 

 is convenient as leading to an analytical expression, and the 

 errors introduced, if any, will be much less than those of 

 the actual experiments. It may, however, be remarked, 

 that should future experiments destroy the validity of Greiger's 

 rule, it would be quite possible to recast the following work 



* Rutherford, loc. cit. 

 t Darwin, loc. cit. 



