Collisions of a Particles with Hydrogen Nuclei. 933 



theory, the value of n for an angle of 30° and an a particle 

 of mean range 8'2 cm. is 4-4xl0~ 7 ; for an a, particle of 

 mean range 2*9 cm. it is 15*8 x 10" 7 . The corresponding- 

 observed values are 4*3 x 10" 5 and 6 x 10~ 5 respectively : 

 in the first case 100 times as great as the inverse square 

 number, in the second not quite 4 times as great. This 

 suggests that the inverse square forces would hold for the 

 collisions of a-rays of still lower velocity, and it may be 

 stated here that this anticipation is borne out by the results 

 to be described in the next section. 



It will frequently be necessary to compare our results 

 with the collision relations calculated by Darwin * for 

 various models of the a particle ; and for convenience of 

 comparison, the h, 6 curves of fig. 4 are translated into 

 the p, 6 curves of fig. 5, as this is the form in which Darwin 



Fig. 5. 

 JxlO~' 3 



t> 



expresses his results. If we define a quantity P as the 

 probability of the collision of a single ct particle with a 

 single H nucleus resulting in the projection of the H nucleus 

 within an angle 0, the quantity Jj is given by P = ttJ> : . 



« / n 



Hence p = w^r, where N = 5*41 x 10 19 , the number oi 



H atoms per c.c. of hydrogen gas at N.T.P. 



* Darwin, Phil. Mag. vol. xli. p. 4m5 (1021). 



