538 Dr. W. F. Gr. Swann on tlie Pulse 



through in the backward direction as ( rdVL for the portion 

 of the egg-shaped surface in front of AB is to f rdQ, for the 

 portion behind AB. The same conclusion would obviously 

 apply if the waves were not polarized, so that the electrons 

 started off in several different directions. We must remark 

 that by as much as the number of j3 rays sent forward is 

 increased by the existence of x by so much is the number 

 sent backward decreased, so that although we cannot without 

 knowledge of the shape of the deflexion oval, and of the 

 coefficient of absorption for the rays, calculate the exact 

 want of symmetry produced, it is obvious that the value 

 x/y = l/10 is of an order of magnitude sufficient to account 

 for the want of symmetry observed both in number and 

 velocity, at any rate in certain cases of /3 rays ejected by 

 X rays*. A casual glance at the deflexion oval would make 

 it appear that we might expect a large number of /3 rays to 

 be emitted in directions such as DH inclined at a considerable 

 angle to the normal to the film; but we must remember that 

 those which move to any extent parallel to the surface of the 

 film have a much smaller chance of getting out than those 

 which are deflected normally to the film. We have thus 

 seen that, provided that the train of waves can give an 

 electron a velocity of the order 6 x 10 9 , this velocity will 

 automatically carry with it a want of symmetry in the 

 number and velocity of the right order for ft rays ; but we 

 must now inquire what order of magnitude the field in the 

 wave must have in order to account for such velocities. It 

 will be convenient to assume <f>(ct — x) to be of the form 



sin — (ct — x), and to determine the motion of the electron. 



^ 27T 



A solution of (5) and (6) with sin— (ct— x) written for 



(j>(ef—x) is (see Appendix, problem 2) to the degree of 

 accuracy to which we require it: 



dx 1 /Y £\\2 . 77-C /Q . 



T r = - r {- sm 4 T i, . . . . (b) 



at 2c \cmir / X 



-#= — — sm 2 T « (9) 



at emir A, 



W 7 e thus see that x and y are always positive. 



If we imagine the wave-train to end with X Y Z, a f3 y 



* On considering probable shapes of the deflexion oval it will be seen 

 that a value of .r/y equal to 0*1 will account for much more than a 

 10 per cent, want of symmetry in the numbers of electrons ejected. 



