674: .Mr. G-. A. Schott on Radiation from Moving Si/stem* 



the direction o£ transmission of the bundle is doubtless the 

 preponderating direction of motion of its individual particles. 

 Further, the velocity of a particle is not absolutely constant, 

 even in the interval between collisions, on account of the 

 retardation due to radiation pressure ; however, (24) shows 

 that this retardation is small on account of the smallness of 

 U/C, which is of order 1/1000 ; therefore we shall neglect 

 the retardation due to radiation pressure. Lastly, the velocity 

 is not the same, on the average, throughout the bundle. On 

 account of collisions it diminishes considerably as we pass 

 along the bundle in the direction of transmission. We shall 

 for simplicity treat the velocity as uniform on the average ; 

 for normal emission this leads to no error, for the radiation 

 practically all comes from the same section of the tube ; for 

 emission parallel to the rays, there is an error, but it cannot 

 be very large, for on account of absorption most of the 

 radiation comes from the end section of the tube. 



Let f(U)dJJ be the chance that in the section of the tube 

 considered the velocity of a system lies between U and 

 U + dU. Multiply each of the equations (24)... (33) by 

 f(U)d\J and integrate from U = to U=co, remembering 

 that A 20 ,... are functions of U. The functions R, R 2 v ^2 ••• 

 must also be treated as functions of U, for we cannot assume 

 that the disturbance o£ a system is the same when in motion 

 as it is when at rest. We may without appreciable error 

 neglect U/C ; therefore we may treat the structure of the 

 system as unaltered by the motion, but the amplitude of the 

 disturbance may be appreciably altered. We get 



A = - 3^ JKU/(U)rfU - J^ JR 2 A 20 TT/(U)rfU, j 

 r=-i rs fS 2 .A 21 .IJ/(U)rfU, > (84) 



(35). 



Z=-^ k U 3 .-B n .Vf(TT)dV, 



S = jR/XIiyU+ I | j2 jE 2 .A 20 Uy(U)rfU . . 



w= ijg jSuy(U)«nT + T ~ jl* . a 20 . uy(U)iu. (36) 



S 1 =^f{S/(U)dU+E 2 A 20 /(U)<iU+...|. . . (37) 



S 2 =^f{B/(U)^U + E 2 C 2 /(U)dU + ...} . . . (38) 



S/=l|y^5 2 .D 2 /(U)iU+...} (39)- 





