18 MR B. STEWART ON RADIANT HEAT. 
lst, That if Q represent the quantity of heat falling on the sur- c 
face of a medium in any direction CA, and aQ be the quantity of 
heat reflected, then (1—a) Q is the quantity of heat refracted into 
the medium in the direction AC’. This follows from the law of 
the conservation of vs viva. ° 
2d, That if the same heat Q originate in the medium, and strike 
A in the direction C’A, the quantity reflected back into the medium will be aQ 
and the quantity refracted out in the direction AC will be (1—a) Q. 
30. These preliminary propositions being established, and suppositions made, 
let us suppose that heat from the surface of lamp-black strikes the surface AB of the 
indefinitely thick medium (Fig. Art. 25) through a small angle 67 (i being the angle 
of incidence), by Proposition 2d, the quantity of this heat will be R.cos7di; while 
the part of it which enters the substance we shall call(1—a@)R cosidi. These rays 
will diverge in the substance through an angle 8 = ee oi (Prop. 3). 
But the quantity of heat that falls on AB from the interior through this angle 
will be 

/ 
ie = OTe. reo ue ie ote 
R’ cos 67 =R’ cos # — i=— cosidi 
ph > 
pcos? 


and the portion of this which leaves the medium will be (ira) - cos 10%, 
Equating this with (1—a) Rcosidi, which enters the medium, we have 
T= or R’=pR. With this supposition, therefore, the law of an equal and 
independent radiation of each particle will give us equilibrium of temperature in 
the particular case under consideration. Had R’ been a function of 7, it would 
have shown that the law of an equal and independent radiation was inconsistent 
with equilibrium of temperature. 
31. Only part, however, of the heat from the lamp-black falling on AB en- 
tered into the medium, a portion of it =a@Rcosidz being reflected back to the 
lamp-black, hence the total quantity of heat radiated and reflected which leaves 
the surface AB through the small angle 67 will be = Reos70%, the same as if 
the substance had been lamp-black, the only difference being, that, in the case 
of lamp-black, all this heat is radiated, whereas in other substances only part is 
radiated, the remainder being reflected heat. 
32. Although we have considered only one particular case, yet this is quite 
sufficient to make the general principle plain. Let us suppose we have an inclo- 
sure whose walls are of any shape, or any variety of substances (all at a uniform 
temperature), the normal or statical condition will be, that the heat, radiated and 
reflected together, which leaves any portion of the surface, shall be equal to the 
radiated heat which would have left that same portion of the surface, if it had 
been composed of lamp-black. And, indeed, we may see, from what has been 
