244 Prof. A. Schuster on the Influence of 



2. To treat the question in its simplest form 1 consider, in 

 the first place, a solid which is an absolute non-conductor 

 but capable of radiating and absorbing heat ; and 1 take the 

 flow of energy to be rectilinear, the isothermal surfaces 

 being parallel planes. 



If F be the total radiation sent out in unit time in all 

 directions by unit area of the surface of a perfectly black 

 body, the radiation emitted by unit surface of a sheet of 

 thickness dx of a partially transparent body is tcFdx, where 

 k is a constant depending on the nature of the substance, the 

 effects of wave-length on k being for the present neglected. 



Let A represent the energy of the stream of radiant heat 

 traversing unit surface of the sheet in unit time from the 

 positive to the negative side, while B represents the flow of 

 energy in the opposite direction. The total absorption of the 

 sheet will be «(A + ~B)dx ; and as its radiation towards the 

 two sides is 2/cFdx, it follows that if c be the heat capacity 

 per unit volume, u the temperature, and 6 the time, 



«(A + B-2F)= C g (1) 



If we were only considering the radiation normal to the 

 isothermal surfaces as Prof. Sampson has done in the paper 

 already quoted, the law of Balfour Stewart and Kirchhoff 

 would give 



:£=«( f - a ) « 



If A represents the total flow in all directions, the equation 

 still holds in the limiting case when the temperature is uniform. 

 For A is then independent of t r, and also equal to F. 



1 shall assume equation (2) to hold also in the case 

 which we are now considering, and shall discuss afterwards 

 how far this assumption invalidates the results. 



The corresponding equation for B is 



S=< B - F ) w 



By combining (2) and (3) we obtain 



^(A+B)=«(B-A), (4a) 



and 



~(A-B) = k(2F-A-B). ... (4/0 



