240 Apparent Radiation of Cold 



calorific emanations of the latter. Now the quantity reflected from 

 any surface, must always be in the compound ratio of the reflecting 

 power and the number of incident rays ; and, as in this case, the 

 reflecting powers of these bodies are augmented in the same ratio, 

 and the numberof incident rays incapable of being affected by the re- 

 moval of the pigment, it follows that the increments of reflection 

 from the two bodies have the same ratio to the quantities which 

 they respectively reflected before the removal of the pigment ; i. e. 

 the quantities reflected from both are increased in the same equal ratio. 

 And it has been proved, that the quantities radiated from both, are 

 diminished in the same equal ratio. Let i be the ratio in which the 

 reflection has been increased, and d that in which the radiation has 

 been diminished in both. Then according to the preceding prin- 



ment 1, by the painted surface of the body in A, r'-ff by that in 

 B ; and in experiment 2, the whole amount from the metallic sur- 

 face of the body in A is rXi+l, and from that in B r'X«+£ It 

 only remains now to demonstrate the value of this last expression 

 to be greater than that of r'+^. 



If unequal quantities be multiplied by equals, the greater will re- 

 ceive a greater increment than the less : Now r' is greater than r, 

 for the reflecting powers of the two bodies are equal, but the num- 

 ber of incident rays are greater in the warm atmosphere, in conse- 

 quence of the higher temperature of the thermometer from which 

 they emanate. Hence in the products r' Xi and r Xh r' in the first is 

 more increased than r in the last, by the common factor i. That 

 is r'i—r'>ri—r t for each side, is an expression for one of the in- 



Again, f =g for the radiation from a body, is not affected by 

 the temperature of surrounding bodies or that of the ambient air. 

 Hence £==i. Adding this to the above, we obtain 



'H-f.-r'yri+JL-r. 

 By subtracting from one side {',, and from the other its equal g, 

 we obtain 



ri' + +V) > H +X - (r + g). 



But r+£ the amount of reflection and radiation from the painted 

 metallic body in the chamber A, in experiment 1, has been shown 

 to be equal to ri -f- 1, the amount of reflection and radiation from 



