﻿922 Mr. E. Buckingham on the 



Let a beam of approximately monochromatic radiation of 

 wave-lengths between X and X + dX be admitted to the en- 

 closure through a hole, which is then closed by a cover 

 similar in its properties to the rest of the walls. After a 

 short time the radiation within the shell becomes perfectly 

 diffuse, for the directed quality of the original beam is soon 

 obliterated by the successive irregular reflexions, so that 

 thereafter the value of R\ is the same at all points and in all 

 directions. These reflexions, however, do not change the 

 period of the radiation, since there is no absorption and 

 remission but only pure reflexion. The volume-density of 

 the energy is now 



«& = 4*5^: (i) 



where c is the velocity of light, and the whole amount of 

 energy within the shell is vp\d\> if v is the volume of the 

 shell. 



Let M be a small plane piece of the shell-wall of area s, 

 and let M be given a normal velocity /3c outward, /3 being 

 infinitesimal. This motion will disturb the perfect diffuseness 

 of R^ by an amount which we shall show to be negligible, 

 but at present we shall assume that R^ remains diffuse. 



The reflexion from M also causes a change of period, which 

 we must now proceed to evaluate. If a wave-train of period T 

 strikes M at an angle of incidence (£, it is easily seen that the 

 period T' of arrival of the waves at a given point of M is 



T 



T' 2= 



"~ 1 — y8 COS(/>* 



The period at a point of the moving surface is therefore 

 greater than at a fixed point in space in the ratio 



r a = l + £cos0, (2) 



terms of higher orders in j3 being negligible. A disturbance* 

 starting with the period T' at a point of the moving surface 

 and propagated at an angle \jr with the normal has, upon 

 arrival at a fixed point in space, the period 



/T"~T'(i + 0ooB+), 



so that the effect of departure is to increase the period in the 

 ratio 



r d =l+$coay> (3) 



Our problem is to find the total effect on the original period T 

 of all the arrivals and departures, at all possible angles <f> 



