536 Dr. W. F. Gr. Swann on the Pulse 



(1), (2), and (4) satisfy the condition that XYZ, *Py are 

 continuous on the two sides o£ the advancing wave-front, 

 provided that <£(0)=0, a condition which would be satisfied 

 ty a sine function, for example. 



The equations of motion of our electron, neglecting 

 damping (see Appendix, problem 1), are 



P g=T^(c«-.r), (5) 



md 2 x dy Y dy , 



By eliminating cf>(ct — x) between (5) and (6) we obtain 



1 dy d 2 y _ d 2 x 

 c dt 'di? ~ It?' 



wdiich we can integrate to the form 



'£-*-hW-*}' ■ ■ ■ ■ (7) 



q } and </ 2 being the values of x and y just before the train 

 strikes the electron. If the electron is at rest at t = so 



that 'x=- ^-y 2 , we see that x must always be positive. 



This method of viewing the matter seems more direct 

 than one which involves considerations of the pressure of 

 radiation, which are always a little vague when applied to 

 an electron. 



We may suppose that before the electron was hit by the 

 train it was travelling with too small a speed to enable it to 

 leave the metal. If the velocity which it receives from the 

 pulse, however, is sufficiently great it will be able to get 

 away. Except for extremely large values of y, x is of 

 course only a small fraction of y; so that if the beam of 

 waves is travelling normally on to a metal plate, the electrons 

 will start off practically parallel to the surfaces. It will 

 only be by swinging round some of the atoms that an electron 

 will be able to get out; and when it does so, the main part 

 of its velocity will be controlled by the y part. The existence 

 of the velocity x destroys the symmetry on the two sides of 

 the plate in a way which may perhaps best be discussed as 

 follows : — 



First, we notice that g 1 and q 2 , which correspond to velo- 

 cities comparable with those of temperature agitation, are 

 so small compared with the velocities of the ft rays produced 



