Absorption of Energy by Electrons. 73 



r + D for x and p + P for p in (7) and (8) and expand, retain- 

 ing only first powers of the displacement. 

 Then 



d\ »=, 6 d 2 R 7 -w 



dt n=l dx dp n n 



dfk-.f d?H F1 



dt n=1 dydp n 



dv n ^> d 2 H 

 dt n =i dz dp n n 



<?g_"£ 6 d 2 H g _ 

 dt n=1 dpdp n n ~ 



*?_f *» o 



dt n =idqdp n n 

 dt n =idrdp n ' 



eE, 



(9) 



(10) 



In (9) and (10) p n takes in succession the six values 

 x y z p q r and <r n the values f rj J X p, v. 



(7) and (8) determine implicitly the values of r and p as 

 functions of the time and of six arbitrary constants, say the 

 initial values of the coordinates and momenta. Denote these 

 constants, however specified, by K\ k 2 k 5 k± k 5 k 6 . Differen- 

 tiate (7) and (8) with respect to any one of the k's : 



d /dp 



d*n d Pn 



=o 



dt \dKj , != i dx dp n die 



dt\dic) n =idydp n dx 



d /dr\ h '£« cPH dp H =Q 

 dt\d«J n=1 dzdp n dK 



= } 



J 



(11) 



d, {dx 

 dt 



d 2 H dp n 



( x \ _ 2 Pn = 



\d/c/ n =\dpdp n dK 







d (M_ n fJiK^Pn 



dt \dK 



d(dz\ 



dt \dic) 



dqdp n d/c 



= Y 



"g 6 d*H dp n ^ 



?i-i dr dp n dK 



(12) 



