112 An Electromagnetic Theory of Radiation. 



Now by making a suitable choice of /(t) this may be 

 written in the form 



where L = m (c 2 — r 2 )* reminds us of a Hamiltonian function 

 used in the theory of relativity *, m being a constant of the 

 nature of mass. 



If a is zero in the case of an electron this may be in con- 

 sequence of the equations of motion of the electron and it 

 may be necessary to extend the expression for a by adding to 



T ( ~^~t' ) a ^ erm representing the effect of the external elec- 

 tric field, and possibly also a term — -^ to allow for a 



variation of m with position. The complete coefficient of 

 x — £ is then zero on account of the equations of motion, and 

 the complete coefficient of t — r should be zero on account of 

 the energy equation. 



This modification of a makes the introduction of a radiant 

 field depending on seem fairly reasonable, because the 

 coefficients in the numerator of may be regarded as com- 

 ponents of angular momentum when the denominator has 

 been suitably modified. It is possible, too, that there should 

 also be terms to represent the effect of impulsive couples 

 which act only at isolated intervals of time. These impulsive 

 couples may, perhaps, be produced by magnetic particles 

 emitted from other sources. 



7. It is, perhaps, a little hard to understand why the 

 electron should turn completely round a finite number of 

 times when emitting radiation. It may be that w particular 

 line of force is naturally associated with some particle at a 

 very great distance from S and that the line of force is 

 eventually recaptured by this particle after it has been once 

 torn away. This would account for the return of the line of 

 force to approximately the original direction. 



A further difficulty in the present theory is that when an 



* The corresponding- expression appropriate in Einstein's generalized 

 theory of relativity is easily written down, but the expression for r in 

 terms of x, y, z and t is not given by such a simple equation as (2). 



