﻿522 Mr. S. B. McLaren on Emission and Absorption 

 Or (36) may be written 



Z n / dt + B\F 1 ^dvdt = .... (38) 



4 



"Where it is understood that F x given as a function of the 

 time and the coordinates of any point of the field is not to be 

 varied^ but only the distribution and movement of charge. 



(39) 



Write (f, p -^dv = ®. ...... 



Then (36) gives the equations of motion 



d ( dLJ \ __ dL in _ d® _d /d®\ 

 dt\du r ) dq r ' dq r dt\du r )' ' ' ^ U) 



The coordinates defining the position of the charge being 



ffu <]* qr ... qn. (r=l, 2, ... n), 



and u > = -j7- 



dt 



If Ave transform to Hamilton's form 



• CiUr 



dp r _dH _d<5> _ d,d<Z>\ dqr o]H_ h ■ (41) 

 dt dq r dq r at\dv r J) dt dp r 



(r=l,2...n) J 



And (11) is true whatever may be the nature of the 

 coordinates. 



If we hold an atomic theory of matter n will be finite. 

 If, on the other hand, charge is continuously distributed 

 there will be an infinity of degrees of freedom. The only 

 method then available is to start from a configuration of 

 equilibrium or steady motion and to study the vibrations 

 about that as the mean position. 



The theory of emission and absorption which follows 

 applies in either case. But I am not able to cope with the 

 transition fiom one state of steady motion to another in- 

 volving a new system of vibrations. For in such a process 

 the degrees of freedom are no longer enumerable. It may 

 be that a radio-active transformation is an instance. Before 

 the change and after it we have an enumerable infinity of 

 degrees of freedom. There intervenes an action by which 

 one set of degrees of freedom disappears and the other is 



