﻿926 



Mr. E. Buckingham on the 



the numerator of equation (4) ought to contain not R\ but 

 Rx(l + ?7), where rj is an infinitesimal of the order fig, q being 

 the ratio of the area 5 to the whole area of the shell walls. 

 The error in n caused by the omission of this factor (l-\-r)) 

 is infinitesimal and negligible. The changes caused in 

 equations (5) to (10) by using the exact value instead of the 

 mean value of R^ would all be of a lower order of magnitude 

 than the terms which have been retained. Hence the error 

 incurred by our treating the radiation as completely diffuse 

 is infinitesimal, and the result expressed in equations (9) and 

 (10) remains valid. 



One further point may be worth notice. If " the long 

 time t " appears to the reader to be possibly not long enough 

 to give all the finite amount of energy within the shell an 

 equal opportunity of being reflected from M in every one of 

 the infinite number of conceivable ways, there is no objection 

 to his making it longer, in other words, infinite. If this is 

 done we may still make Av or ctfts infinitesimal, as we want 

 it to be, making fis of the order t~ 2 ; and this may be accom- 

 plished either by making 



j3 — const. xt~ 2 



with s finite, or by making both ft and s of the order t" 1 . 

 There is nothing to prevent our adopting either course. The 

 use of the more concrete expression a " long " time instead 

 of an " infinite " time did not, therefore, involve an error in 

 the reasoning, while it obviated the necessity of interrupting 

 the argument at an inconvenient point. 



6. We have next to consider the change of the energy of 

 the radiation which accompanies its change of period, and we 

 assume that diffuse radiation exerts a pressure equal to one- 

 third of its density on the walls of a containing envelope. 

 This proposition may be deduced in several ways from 

 Maxwell's theory of the electromagnetic field, which has been 

 confirmed in so many respects that we need not regard 

 it as doubtful, but accept its consequences without further 

 discussion. 



During an expansion Av, the work given out is then 

 expressed by ^p\d\ . Av ; and since the expansion of radiation 

 within a perfect reflector is adiabatic, this work is equal to 

 the simultaneous decrease of the energy within the shell, and 

 we have 



ipxdXAv = -A(p x d\v), 



