544 



Dr. "W. F. G. Swarm on the Pulse 



from (11) and (12) we derive 



1 fdy d?y e "ftY dyl _d 2 x e dV 

 c \ dt ' dt 2 m~dy ' dt J "~ dt 2 m ~&x 



(13) 



We do not wish, until we are compelled to do so, to confine 

 ourselves to a case where the restoring force is proportional 

 to the displacement, and so we shall at first take the more 

 general case where V is of the form Y x + "Vy, where V x is a 

 function only of x and V y is a function only of y. It will 

 be seen that for the cases we are going to consider this 

 assumption will be justified. (13) then integrates to 



the constant of 



integration 



being 



if 



we 



take 



a case 



zero 

 where when t is zero x=y=x=y = 0. 



Now suppose we imagine any atom with an electron in 

 the position A (fig. 2). It will be obvious 

 that a pulse moving in the direction of the 

 arrow would have a much better chance of 

 ejecting this electron than an electron at B, 

 since the natural period of B's tangential 

 motion would be much longer than that of 

 the pulse, so that resonance could not come 

 into play in the case of B. In the case of 

 electrons such as A, we see that for small 

 displacements Y x will be practically zero, 

 or at any rate this will be so for certain 

 arrangements of electrons in the atom, such an arrangement, 

 for example, in which there is a positive sphere with only two 

 electrons situated along a diameter *. In such cases we shall 

 have 



^\{\f+^Y ■ ■ ■ ■ ^ 



times the energy E which the electron has 

 wave, or practically so. If w is the 



\r + 



e 



1 



Yis - 

 m m 



absorbed from the 



* This is not intended to represent more than a rough picture of the 

 phenomenon. It would perhaps be "better to say that where an electron 

 is to be found capable of free motion parallel to the x axis, for small 

 displacements, that electron will have a better chance of being ejected 

 than any other. 



t In the Appendix (problem 4) the problem where Vx is not zero^is 

 considered. 



