oL-Particles with Hydrogen Nuclei. 493 



•with the improved relation. But before such recalculation 

 will be worth while, it will be necessary to have much more 

 accurate experiments to apply it to. 



In the actual experiments the a- particles went in all 

 directions and were observed in a fixed direction. This 

 makes rather a difficult geometrical problem, and it is simpler 

 to regard the matter as follows. Conceive that all the 

 a-particles are projected along a single line from the centre 

 of a sphere. If we take the total number that pass out of 

 the sphere and multiply by the ratio of the area of the 

 observing screen to the area of the whole sphere, we shall 

 get the same number as in the actual arrangement. More- 

 over, a foil covering the sphere will correspond to the plane 

 foil of experiment. Let I (fig. 2) be the radius of the sphere 

 and let Q a-particles be emitted from along OA. Consider 



■ Fig. 2. 



an element at distance Ixivom. 0. Then if N be the number 

 of atoms of hydrogen per c.c, QNTIoIt will be the number 

 of H-particles produced in the length Ida, for which the 

 angle of projection is 'less than 6. Here P is the quantity 

 defined in § 2, and it is to be regarded simply as an unknown 

 function of 6. We have neglected the diminution of Q, due 

 to the loss of those a-particles which make H-particles, as 

 this is very small indeed. By (2 # 1) the H-particles will all 

 have velocity greater than |V cos 6, where V is the 

 a-particle's velocity at A. We have to determine under 

 what conditions they will traverse the foil so as to scintillate. 

 If V is the initial velocity of t'ne a-particles and r their 



3 / fa 

 range measured in cms. in hydrogen, then V' = Y \ / 1 - 



o / /,, i m T 



by Geiger's rule, and so |Vcos#a/ 1 — — is the initial 

 velocity of the H-particle. It therefore has a residual 

 ( ^ 1 cos 3 6 (r — /.i'), or with sufficient accuracy 



3 



rano;e 



