ON THE RADIATION OF CALORIC. 181 



From considering the subject, before I had seen Mr Daven- 

 port's papers, the following explanation occurred to me. It is 

 in principle the same with his, and only differs from his, in be- 

 ing, 1 think, more easily understood, and in showing from the 

 calculation, how Dr Murray's objection maybe completely obvi- 

 ated. Plate XL Fig. 4, let P be a polished body, and B a black 

 one. Let their combined powers of radiation and reflection, 

 when in (Equilibria with the thermometer, be represented by 1. 

 In P, let the reflection be f , the radiation \. In B, let the re- 

 flection be i, the radiation f . Now, it is only the radiation 

 which can be affected by changing their temperature. Let 

 their temperature be raised, till their radiating power is 



doubled. Then, Q J 



P T B 



P 



4 reflects, > radiates, fsum, > excess above the equilibrium, I 

 IB - l\ - |J - If J - - - - fj 



Now, as it is only the excess above the equilibrium that can 

 affect the thermometer ; B, which radiates 3 times as much as 

 P, will affect the thermometer 3 times as much. Now, let each 

 body be cooled, till it radiates only } as much as when in (equi- 

 libria. Then, 



rP ---i] - - ii -f] - -------- jl-] 



\ reflects, -radiates, >sum, ["defect from the equilibrium, I 



IB - - - £J - - fJ - f J - - * - - * - - - fj 



But it is the defect from the equilibrium only that can affect 

 the thermometer ; and therefore B, which, when heated, pro- 

 duces 3 times as much heat as P, when cooled, produces 3 

 times as much cold ; though in all cases it radiates 3 times as 



much 



