16 MR B. STEWART ON RADIANT HEAT. 
heat entering the surface AB, to diverge into the interior through the same small 
angle CAD. For, by this arrangement, it is clear the particles in CAD get back 
as much heat as they give out. 
Part of the heat, no doubt, which fell on A in any direction DA, would be 
reflected back in the direction AD’, making the same angle with the surface as 
AD; but this loss would be made up for by part of the heat falling on A, in the 
direction D’A, being also reflected back in the direction AD. 
The internal reflection at A being thus compensated for, if the heat that really 
leaves the medium be also compensated for, then as much heat will be passing at 
A in the direction AD as will be passing in the direction DA. It will be the 
same, therefore, as if the body, instead of having a surface at A, were indefinitely 
extended upwards from A, as well as downwards; in which case, as has been 
already shown (Art. 20), there will be equilibrium of temperature, provided that 
the radiation of a particle is equal to its absorption, and that for every descrip- 
tion of heat. 
Before proceeding further with this investigation, it will be necessary to 
establish some preliminary propositions. 
26. 1st Preliminary Proposition. 
The heat which falls on the line AB in the directions contained in the very small 
angle CAD, is the same which falls on AE, perpendicular 
to EB, through the same very small angle. For every ray 
which fell on AB passed through AE, with the exception of 
a small quantity which passed through EF ; but the angle Ele 
EBF being very smal], EF is very small compared with 
AE, and consequently the heat falling on EF may be ne- 
elected in comparison with that falling on AE. 
It is clear also, that the heat falling on AB is proportional to AB, and to the 
size of the very small angle CAD. 
The above will still hold, if, instead of the substance of which AB is the sur- 
face being supposed below AB, and the rays falling on it through a vacuum, we 
suppose the substance to be indefinitely extended upwards, and the rays to 
originate in the substance itself, and fall on its surface AB. 
For, although any ray GE, which falls on E, will be partly absorbed between 
E and B, it will be as much recruited by the united radiation of the particles 
between E and B as it was absorbed; so far, indeed, as regards quality and inten- 
sity (from what has been already proved, Art. 20), we may consider such a ray 
to be traversing a vacuum, it being recruited just in proportion as it is ab- 
c D & 
sorbed. 
It is evident, also, that in this case the quantity of heat falling on AB will be 
proportional to the size of the very small angle CAD. 
