ct-P articles ivitli Hydrogen Nuclei. 501 



Mm/(M + m), is projected along the same line and with the 

 same velocity as « in the actual problem. 



It is indifferent whether it is H or a that is reduced to 

 rest, and this shows that though it might be possible from 

 experiments to attribute definite structures with certainty 

 to H and a, yet the experiments could give no information 

 as to which had which. But there is strong evidence from 

 other sources that a is more complex than H, so in considering 

 our models we shall reduce a to rest and project H past it. 

 In all the cases we consider, H is a simple point charge. 



6. The Elastic Sphere. 



In our first model H is supposed to move according to the 

 ordinary law of the inverse square, unless or until it 

 approaches within a certain distance of the centre of a. If 

 it gets within this distance it bounces off, as if from a hard 

 elastic sphere. The calculation is quite straightforward, and 

 need only be given briefly. If an auxiliary angle A is taken, 

 given by the relation 



p = atanX, (6*1) 



where, as in (2*5), 



^ =i Km + ^)v*' 



then the orbit under the inverse square law is the hyperbola 

 ^-sinX= cos (X — (p)— cosX, . . . (6*2) 



and so the angle between the asymptotes is 2X. This is for 



the case where the apsidal distance ^cot- is greater than b, 



X 

 the radius of the sphere. If p cot- <b, that is if 



r < cot A, tan-, 



b 2 



an impact occurs and it occurs when (j) = <fi 1} where (/>! is 

 given by 



I sin X— cos {X — cpi) — cosX. 



In this case the angle between the asymptotes is simply 2^. 

 Phil. Mag. S. 6. Vol. 41. No. 243. March 1921. 2 L 



