﻿the a particles expelled from Radium and Actinium. 355 



But it is easily seen that the natural width of the photo- 

 graphic band without the electric field is given by 



•'■ ■ '■ • -k 



(K +1 > 



Therefore the increase D x of the breadth of the band by 

 the reversal of the electric field is given by 



Substituting the value of X, 



mu^V^hf Za 



— — md\*-T 2 ) 0) 



This gives the formula required for determining the value 



c rnu 2 



ot tor case 1. 



e 



Case 2. — In this case the electric field is supposed to be 

 sufficiently strong to deflect the a particle in passing between 

 the charged plates through a distance greater than d. 



Suppose the electric field urges the a particle towards the 

 plate AB (fig. 3 b). A little consideration shows that the 

 ol particle which forms the extreme edge of the photographic 

 impression at / must touch at grazing incidence the plate 

 CD. Let LKF be the direction of projection of such an 

 a, particle, intersecting the plate CD at K. The path of the 

 a particle under the action of the electric field is shown by 

 the dotted line in the figure. The path touches the plate 

 OD at H and emerges at B at grazing iucideuce. 



LetDH=y. 



Then with the same notation as before, d=\y 2 . 



The angle which the tangent to the parabola at B makes 

 with the direction of the plate AB is given by 



tan0=2Xy. 



The distance bf= l s tan 6 = 2\yl 3 . 



The total distance D between the extreme edges of the 

 photographic impression on the plate P by reversal of the field 

 is consequently given by 



D = 4Xyl s + d. 



Then (D-d) 2 = l(J\dl 3 2 . 



Substituting the value of X as before, 



5£ = 8V/ 3 2 ; m 



e (D-d)' 2 W 



2 A 2 



