Theory of X Rays and Photoelectric Rays. 535 



There is an important difference between the two views. 

 The second is the one which leads to the most satisfactory 

 explanation of the phenomena observed, bnt as the first view 

 presents some interesting features, and as it is the simpler 

 of the two, I shall commence by discussing it. I shall, when 

 possible, relegate to an appendix mathematical matter which, 

 though necessary, may nevertheless be omitted in following; 

 the general trend of the arguments. 



(1) Action of a wave-train on the free electrons. — When a 

 beam of electromagnetic waves, travelling along the axis of 

 ei', encounters a free electron, the motion which the train 

 produces is generally treated as being wholly transverse to 

 the direction of the beam. This is, however, not quite true. 

 The magnetic field of the electromagnetic train acts on the 

 moving electron with a force parallel to the line of motion 

 of the beam, and, in the case of a free electron, this force is 

 such that the total velocity which it has produced since it 

 started to act is always in the direction of the advancing 

 wave, so that the electron will move in the direction of the 

 wave as well as in the transverse direction, as will be seen 

 from the following discussion. 



We shall suppose our electromagnetic train to be of some 

 finite length which it will not be necessary for us to specify. 

 The electron shall be situated initially at #=0. XYZ, 

 a ft <y shall refer to the electric and magnetic forces respec- 

 tively, all expressed in electromagnetic units, and we shall 

 mathematically specify our wave as follows: — 



For*<0anda?>0..., X = Y=Z = a=/3 = 7 = 0. . (1) 



For*>0and<tf>a?>0..., X=0, Y=Y<#(c*-*), Z=0, (2) 



<f>(ct — x) being an arbitrary function of ct — x. Such a 

 function satisfies the electromagnetic equations, which are 

 of the type 



etc., . (3) 



and corresponds to a wave travelling in the positive direction 

 along the x axis with the velocity c, which represents the 

 velocity of light. It may readily be verified from the electro- 

 magnetic equations that the values of a /9 7, corresponding 

 to the above values of X Y Z, are 



a £ 7 = 0.0.-^(c*-aO (4) 



1 BX By dp 



_'d*_'dZ BY 



c 2 ~dt ~ ^y ~dz ' 



bt '"by ~dz 



