208 SCIENCE PROGRESS 



set in motion by such a " head-on " collision. " Oblique 

 impacts " will be much more numerous, leading to smaller 

 resulting velocities, combined with angular deviation of direc- 

 tion from the path of the original a-particle stream. Darwin 

 found that the number of H atoms with a range not less than 

 i/m th part of the maximum range bore to the number of a 

 particles a ratio equal to 



a(Jm — i) (i) 



where a is a constant depending on the range of the a particles 

 used. Thus for a particles with a range of 7 cms. a — 1*46 x 

 10- 6 ; for shorter-range a particles it is larger, varying in fact 

 inversely as the 4/3 power of this range, so that, e.g., for a par- 

 ticles with a range of 5 cms., a=(7/$) i x 1-46 x 10- 6 . 



The main result of Rutherford's work on hydrogen is to 

 show that the number and distribution of the swift H atoms 

 is entirely different from that suggested by the formula. 

 According to it, the fraction of a particles giving rise to H 

 atoms with ranges equal to or greater than R/m \R = maximum 

 range] should decrease, as m decreases, to a zero value when 

 m — 1 corresponding to the maximum range — a result which 

 might be readily anticipated on general grounds. Instead, 

 Rutherford found that there was no decrease in the observed 

 fraction for ranges of H atoms between 9 and 19 cms. ; there- 

 after there was a slow decrease for longer ranges, followed by a 

 rapid fall to zero as the range approached the limit 28 cms. 

 He was using a particles from radium C with a range of 7 cms., 

 and the ranges above are estimated in air. Using a particles 

 with a smaller range, the same general result was obtained — 

 the observed fraction never decreased as rapidly with decreasing 

 m (i.e. increasing range) as the law indicated, using a particles 

 with ranges above 3 cms. 



Even when the law in (1) is fairly well obeyed, as is the 

 case when a particles with ranges under 3 cms. are used, the 

 observed number is greater than the calculated — i.e., the ob- 

 served constant, a, in (1) is greater than the calculated constant, 

 viz. (7/3)* x 1*46 x io~ 6 , etc. 



Rutherford concludes that the assumptions at the base of 

 Darwin's analysis cannot be justified. He advances calculations 

 to show that in these phenomena the nuclei of the a particles 

 and the H atoms must in some cases approach as near as about 



