258 Prof. J. J. Thomson on the Emission of 



from (4) we get 



doc . A. . 2?r w 



If dxjdt and f vanish simultaneously, substituting in (5), 

 we have 



or writing for — - ?, we have 



A 



dfi + ^ smd=0 - 



The equation of motion of a simple pendulum. Integrating 

 this equation, we find 



l/4ir\V<*fc\ a n AV 4tt v 



where C is the constant of integration. Substituting for f its 

 value z— Yt, we have 



1/4ttW x . dz\* Pj _AV 4tt,~ > 

 If cfe/d£ vanish when f=0, we have 



K?) , [{--t} , -]-s->-?<--)- 1 }. 



If w is the maximum value of dz/dt, we have 



"X. 2 A 2 ^ 2 

 47T 2 »r 

 hence if 



A5AV 

 4tt 2 w 2 ~~ ' 



the maximum value of the velocity of the corpuscle will be 

 equal to the velocity of light. If \ 2 A 2 2 2 /Wra 2 is a small 

 quantity, then the maximum value of iv is given by the 

 equation 



_ 1 \ 2 AV 1 



\ 2 A 2 ^ 2 

 Now e/m=10 7 , V=3 X 10 10 ; hence 4 ^ 8 y« =2-5A 2 \ 2 10" 9 , 



Here A is the maximum value of the magnetic force and \ 

 the wave-length. We see that for waves of sunlight 



