MR B. STEWART ON RADIANT HEAT. 19 
already proved, that, should such a state of things only once take place, it would 
always remain, there being no disposition to alter it. 
Let us suppose, for instance, that the walls of this inclosure were of polished 
metal, then only a very small quantity of heat would be radiated; but this heat 
would be bandied backwards and forwards between the surfaces, until the total 
amount of radiated and reflected heat together became equal to the radiation 
of lamp-black.* 
33. The equation R’=yR must necessarily hold for every individual description 
of heat. We have, therefore, two laws necessary to the equilibrium of tempera- 
ture,—ls¢, That the absorption of a particle is equal to its radiation, and that for 
every description of heat; 2d, That the flow of heat from the interior upon the 
surface of a substance of indefinite thickness, is proportional ceteris paribus to its 
index of refraction, and that for every description of heat. It will, however, be 
borne in mind, that the former of these Jaws has been verified by experiment, 
while the latter is only deduced from a theoretical investigation. It will also be 
seen, that by increasing the thickness of the radiating plate indefinitely, the 
radiation becomes ultimately independent of the diathermancy of the plate and 
is regulated only by its refractive index. 
34. The connection which we have attempted to trace between the refractive 
and radiative power of a substance, presumes that those rays which we have been 
considering, have the power of forming wave lengths within the medium under 
consideration; that is, of being capable of proper reflection and refraction. 
It may be, however, that glass and other similar substances are so opaque, with 
respect to most of the rays of heat of low temperature, as to stop them almost 
entirely at the surface. 
As such rays may, therefore, be conceived to be absorbed within the limit of 
the physical surface of the medium, the corresponding radiation may be conceived 
to proceed from this physical surface. To such a case we may perhaps sup- 
pose reasoning similar to that of FourreR (as given by Professor Forbes in the 
* This will be clearly seen if we consider only those rays that are radiated perpendicular to the 
surface in the case of two parallel plates of polished metal of the same description radiating to one 
another. For let r be the common radiation of the point C in direction CD, and c 
of the point D in the direction DC, then since these radiations are bandied 
backwards and forwards in the directions CD, DC, until they are extinguished, | 
we have the total quantity of heat falling on D in the direction CD (if ar de- D 
note the proportion of r reflected after one single reflection) expressed as follows :— 
=r(l+a+a?+a3) 
rT 
= 5 =; (since a<1) 

Total heat radiated and reflected, _ r+ar+a'r+, &e. 
falling on D, : - +ar+ar+ar+, &. 
But 1 —a denotes the absorptive power of the metallic surface (all the heat not reflected being absorbed), 
Hence, since the radiative powers of bodies are proportional to their absorptive. powers (LEsiixz’s 
Inquiry), 1 being the absorptive power of lamp-black, the perpendicular radiation of a lamp-black 
point will be= — which is the very same expression we have obtained for the total heat radiated 
and reflected together, falling on D, in the same perpendicular direction from the metallic point C. 
