316 Mr. R. Har greaves on Radiation 



p* and jt/ 4 in the integrated form (6), and consider the in- 

 terpretation. With odd and even powers of r separated,, the 

 exact formula is 



(x-x')( 1 + 2 '- s -£)=$(x+x'); 



and if r is small, 



J(x-x')=«>(%+xO+f (*+%'), . ■ ■ m 



which gives a rough idea of the meaning. At a fixed plane 

 parallel to the moving reflector, the left-hand member gives 

 the excess of the rate of passage of the outgoing radiation 



above the returning radiation (radiation formula % J Yndn) ; 



the first term on the right is the rate at which energy-content 

 is supplied to the new space, and the second term is the rate 

 of working of pressure (formula f n . ten . %dn) . When r is 

 small, (7) gives the ratio x : x! correctly to the second order ; 

 but when r approaches 1 (or w approaches V) the difference 

 is important, and the exact formula makes %' vanish with 

 1— r. 



Electromagnetic theory gives the more detailed interpre- 

 tation through the form 



X §Yndn=x§ (Vn— w)(l— rw)d7i+w%f(l — rn)dn + wxftdn. (8) 



The radiation across a fixed plane provides (1) the ex- 

 change value, or flux at a moving surface, with (2) the 

 energy-content proper to a moving standpoint for the space 

 opened out, and (3) the work done by pressure. 



The formula for pressure in reflexion is 



X f nHn + x \ n'Hri or X- (1 - r>) + |-' (1 + r 3 ), 



and the exact division into parts with the meaning assigned 

 in (7) is 



2(X-X / )=^{x + X , -^( 1 -^)(X-X / )} 



+ ^[x+x / - y3 (x-x)}- 



§ 3. The collective formula presupposes a continuous range 



