Collisions of a Particles with Hydrogen Nuclei. 937 



nuclei. For example, the observed number of H particles 

 projected within 30° of the direction of incident a-rays of 

 range 82 cm. is more than 100 times as great as the 

 theoretical number ; the number projected within the same 

 angle by a-rays of range 4*3 cm. is 15 times the theoretical 

 number. Again, the observed variation of the numbers of 

 H particles with velocity of the a particle is in the opposite 

 direction from that given by the point-charge theory. For 

 example, a-rays of range 8 2 cm. project within an angle 

 of 30° nearly 3 times as many H particles as a-rays of range 

 4*3 cm. ; on the point-charge theory, the a-rays cf 4*3 cm. 

 range should give .nearly 3 times as many as the 8'2 cm. 

 a-rays. 



It seems clear, then, that in the collisions of high-velocity 

 a particles with H atoms the forces between the a particle 

 and the H nucleus do not vary according to the inverse 

 square law. On the other hand, the results obtained with 

 a particles of low velocity show that this law is approximately 

 true for larger distances of collision. It is our task to find 

 some field of force which will reproduce these effects. 



A similar task has been undertaken by C. G. Darwin * for 

 the experimental results of SirE. Hutherford. In his paper, 

 he has worked out the collision relations for all possible 

 models of the a particle which give integrable orbits. 



He showed that a square nucleus, in which the H nuclei 

 are arranged at the four corners of a square and the two 

 electrons together at the centre, w T ould give a field of force 

 very similar to that of a bipole; the collision relation of the 

 bipolewas roughly similar to that deduced from Rutherford's 

 experiments. 



Comparison of the p } 6 and p, (V /V) 2 curves for the 

 bipole with those of figs. 5 and 6 shows clearly that such 

 a system does not give our collision relation. Simple 

 calculations show that the forces around the bipole are 

 much too small to give the observed effects. It appears, 

 indeed, that any combination of four H nuclei and two 

 electrons with inverse square law forces cannot give our 

 collision relation, for this indicates that, at a certain distance, 

 the forces around the a particle increase with great rapidity. 



The simplest representation of such a field of force is 

 afforded by the hard elastic sphere. An H particle pro- 

 jected towards the sphere moves under inverse square Forc( S 

 until it strikes the sphere, when it rebounds elastically. 

 The J>, curves for the elastic sphere are given by Darwin 

 on p. 502 of his paper, and it will be seen that they are. at 

 * Darwin, loo. cit. 



Phil. Mag. S. 6. Vol. 42. No. 252. Dec. 1921. 3 Q 



