Absorption of Energy by Electrons. 81 



The average value of the first two terms in (44) is zero, 

 but in any case in a steady state they will cancel, since t is 

 taken so far back that all the terms in the integral 



J'o dt 



dv 

 which are correlated with -j—e~ ipilb are included. 



dt h 



Thus the absorption between t b and t a reduces to 



-^^^W flS) ^i^^ dtdvdV - (45) 



Or if we integrate for all orbits in which the energy is 

 between iTand H+dH, the absorption can be expressed as 



-*&+?)£ %$■*(».) dB, .-. . (46) 



or, if we suppose f(H) to vary as e ^ , 



* 2( ^H^C* (x)rfjff ' • • • • (47) 



$(X) being a function of II, and the wave-length \. 



§ 6. The Emission of Radiation. 



Turn now to the question of emission. Take a point in 

 the direction 1 from the origin and at the distance R, which 

 is very great^ compared with the distance v of the electron. 

 The vector and scalar potential at this point at the time t 1 are 

 given by 



'-**('-':*)"' • ■ • • <«> 



♦-sfc-'af (*» 



See for (48) and (49) (Bucherer, Einfilhrung in der 

 Electronen Tlieone) 



tf-.-lI + S^+B 



c c c 



Phil. Mag. S. 6. Vol. 22. No. 127. «7wZy 1911. Q- 



