172 Mr. B. Stewart on the Radiative Powers of Bodies. 



fee. 



oYtf m =6V£ m . 



Now the quantity of heat A m absorbed by the first elementary 

 slice of M =A m a m OT, and for N this is =A m £ m oY. Hence from 

 (3) it follows that the quantity of the heat A m absorbed by an 

 elementary slice of M is equal to that absorbed by a similar 

 slice of N. Hence the quantity of heat A m which is absorbed in 

 passing through a thickness of M=t is equal to that which is 

 absorbed in passing through a thickness of N = t 7 ; and the same 

 equality subsists with respect to any other description of heat 

 which forms part of the heterogeneous radiation of the tempe- 

 rature t. • 



Hence it follows that, with the above relations between the 

 thicknesses of the plates, the portion of lampblack heat of the 

 temperature t which passes the one plate is equal in quality as 

 well as quantity to that which passes the other. 



10. It thus appears that if there are bodies of which the ulti- 

 mate particles or very thin plates radiate the same quality of heat 

 at the temperature t, and if such thicknesses of these bodies be 

 taken that they all pass the same proportion of the incident heat 

 for any one of the rays which compose the heterogeneous radia- 

 tion of that temperature, then they will also pass the same pro- 

 portion for any other of these rays. 



11. Our hypothesis has hitherto been, that the bodies M and 

 N have ultimate particles which radiate the same kind of heat at 

 the temperature t. Let us further suppose that the particles of 

 these bodies possess the same property at the temperature t\ and 

 in fine through a considerable range of temperatures. 



At the temperature f let us form equations similar to (1), (2), 

 (3). Now if we suppose, as we are undoubtedly entitled to do, 

 that the heat of t has some one ray in common with that of t, 

 we see at a glance that the plates M and N with their old thick- 

 nesses will perform the same office for the heat of temperature t 1 

 which they did for that of temperature t } the proportion of the 

 former heat which passes being the same for M as for N in 

 quantity and in quality. 



12. To conclude : if there be a group of bodies of nearly the 

 same refractive index the particles of which always radiate the 

 same quality of heat at the same temperature, and if we take slices 

 of these bodies of thicknesses such that they all permit to pass the 

 same proportion of any one kind of heat, then they will also pass 

 the same proportion of any other kind of heat. 



