11 



passed thiougli the aluminium, and the images on the plate 

 should show a break, the lines being more widely separated 

 in one half of the picture than in the other. 



But M. Becquerel is under a misapprehension on this 

 point. Paradoxical as it may appear at first sight, no such 

 break ought to appear, and the photographic result is quite 

 in accordance with the theory that the a particles lose speed 

 as they pass through matter. 



In order that this may be clear, it is necessary first to 

 consider the order of the deflections of the a rays in the mag- 

 netic field, on the various theories that have been proposed. 



Suppose that an a particle is pro- 

 jected from O in the direction O N, with 

 velocity v^ , and that the action of a 

 field H causes it to describe the curved 

 path O A. 



In the first place, let the velocity be 

 constant throughout, and the path be 

 therefore circular, as M. Becquerel sup- 

 poses. Then, since the curvature is 

 small, A 'N=:a'i2p where A ]Sr = a and 

 p is the radius of curvature. 



A N 



He 



mv. 



In the second place let the velocity 

 diminish as the distance from O in- Fig. 1 



creases ; and let us take the extreme case, 



where the velocity vanishes at a distance a from O. Let 

 the path in this case be OA'. It does not make very much 

 difference what law of diminution of velocity we adopt : let 

 us suppose, as my experimental results seem to indicate, that 

 the particle spends its energy at a rate which is inversely 

 proportional to the square of its speed. In this case : 



dv 

 ds 



kv 



s being measured from 0, 



and therefore v* cc {a- s) 



,-, , v* a- s 

 so that — = 



