Velocities of a Particles from Radioactive Substances. 557 



consider the path of an a particle which passes through the 

 slit when the magnetic field is acting; let the initial inclination 



-p of this path to the x axis at o be p . As a first approxi- 

 mation w T e can assume the inclination of the path to the x 

 axis to be very small, so that its square is negligible com- 



d 2 y 



pared with unity, and write vg for the reciprocal of the 



radius of curvature of the path. The equation of the path is 

 tli en 



]_ = ^ / = HE 

 p dx 2 mv 

 Integrating 



«a mv ) 



and if we put oa = l^ ah — L 2 . 



the slope of the path at the slit a is 



The value of y at the slit is by a second integration 

 Jo ^ mi JoJo 



Thel(double integral reduces on integration by parts to the 

 simpler form 



~ h 



fa— os)n.dx. 



o 

 Hence , E 



1, 



E f' 1 



•^ 



But if the a particle is to pass through the slit, we must 

 have ^ = 0. 



i. e. 



md 



P, 



E C h 



=Pq H l rLdx= — r I wB.dx. 



' l ™*J mvl iJo 



Now taking a as origin of x 9 the equation of motion of the 



