134 Proceedings of the Royal Society of Edinburgh. [Sess. 
it then returns on its path, the magnetic structure gives back its rotational 
energy, which is now retransformed into kinetic energy of the electron, 
and after a complete reversal of all the previous motion the electron 
returns to x=—qc with its initial velocity u reversed, and the magnetic 
structure comes to rest : the two have had an elastic impact.” 
From equation (7) it is evident that when the initial velocity is small, 
the value of x at the point of reversal is large and negative, which means 
that the electron does not get far before it is stopped and reversed: for 
greater values of u, the reversal-point is nearer the magnetic structure, 
eM . . . 
and when u has the value ^he electron is able to get just as far as 
the magnetic structure but not to get beyond it : when u is greater than 
this value, the reversal-point is on the further side of the magnetic 
structure (we need not stop to describe any particular device for enabling 
the electron to pass through the matter of the bars), and when u has the 
value or any greater value, the electron is able to pass completely 
through and out of the magnetic structure so as to be free from its influence. 
Let us now consider what happens in this latter case, namely, when 
2eM . , , 
u is greater than so the initial kinetic energy of the electron is 
greater than U, where 
U = 
2e2M2 
(8) 
From equation (5) we see that if co denotes the final value of (namely, 
when x= oo), we have 
Aw = 2eM , (9) 
and from (6) we see that if v denotes the final velocity of the electron, 
then 
JAa)2 = ..... (10) 
From (9) we see that each side of (10) is equal to ^ . Thus an amount 
2g2M2 . 
of energy equal to precisely U or — is lost by the electron and gained 
J\. 
by the magnetic structure. Unless the initial energy of the electron is as 
great as U, the electron gives up no energy to the magnetic structure, hut 
experiences an ^'elastic impact”: if, however, the initial energy of the 
electron is greater than U, it gives up exactly the amount U of energy, and 
retains the rest 
It may be observed in passing that the critical energy U does not 
