74 Mr. S. B. McLaren on the Emission and 



There are altogether six sets of equations such as (11) 



and (12), where k, takes in succession six different values. 



dx 

 Multiply the first of the group (9) by ^- and the first of 



(11) by f ^and subtract : 



dj^cU_ d_ { dp\ ^d^( d, clp\ d, 



dt dfc *dt [dx/ ^ n tidx dp n \ n die ^ die J die K J 



Similarly from the first equations in (10) and (12) 



dt die dt\diej n =idpdp n \ n die t i K / 



There are altogether three equations, of which (13) is the 

 first, and three represented by (14). Add together the first 

 three and subtract them from the sum of the three others. 

 Then it can easily be shown that the terms involving II all 

 vanish, a well-known result in the theory of varied motion. 

 And 



a0>£ -*©=-*"& ■■■ • (15) 



f 15) represents six equations got by taking the six particular 

 values for k. On integration 



D t»- p s tB -'H- • • • (i6) 



*^0 



The question arises how t Q , the lower limit of integration 

 in (16), is to be determined. 



The deviation of an electron from the orbit it would 

 describe were there no disturbing force is continuous. In 

 order, however, to find the absorption produced, it is necessary 

 to take a section across this indivisible process. I shall 

 deal with the absorption between the times t b and t a . Take 

 the lower limit t Q in (16) such that t b — 1 is at least of 

 the order of the time in a free path. The deviation as given 

 by (16) is then reckoned zero at t Q , and between the time t b 

 and t a it is due wholly to the radiation which has acted from 

 the time t Q . Also the position and momentum in the undis- 

 turbed orbit between t b and t a bears no relation to the forces 

 of radiation which have produced the deviation. For this 

 orbit is the prolongation of that which the particle began 



