Origin of the Radiation from Hot Bodies. 219 



Lord Rayleigh has shown (Phil. Mag. [5] xxvii. p. 460, 

 1889) that when /is expressed in the form (1), then 



Hence the energy radiated 



Thus the amount of the energy in waves whose frequency is 

 between q and q + dq is 



Let us now apply this result to the case of a corpuscle 

 moving through a body and coming into collision with its 

 molecules ; and let us follow a corpuscle from the beginning 

 to the end of its free path. At its start it is subject to a 

 great acceleration for a short time ; then it proceeds without 

 acceleration, and when it collides at the end of its p th 

 the acceleration is again very great. After the end or" the 

 collision it is again zero. 



We have, by Fourier's theorem, 



- if P/( 



f(f) =—) ) f(X) cos q(t - X) dX dq. . . (2 ) 



Now we may represent the acceleration during the free 

 path by supposing that /(A,) is zero, except when X is between 



— ~ and + ^, or between t 2 — ■£ and t 2 + <r, when it is very 



large ; thus X x and X 2 are the times occupied by the col- 

 lisions, and t 2 is the interval between them. If the accelera- 

 tions are symmetrical with respect to the beginning and end 

 of each collision, then equation (2) becomes 



i r°° 



fit) = — -l (<£iCOS qt + <j) 2 cos q(t — t 2 ))dq; 



71 Jo 

 where 



0i = I f(X) cos qX . dX, 



2 



(j) 2 = \ f(X) cos qX dX. 



Q2 



