RADIATION AND ABSORPTION. 57 
» being the demi-angle at which the body is seen from a point 
of the inclosure. 
If we now consider what the body receives from the inclosure, 
we easily perceive that it is a certain fraction 4 of the quantity 
of total heat e’ which is emitted by each element, and conse- 
quently that it receives from the entire inclosure a quantity of 
heat expressed by bo 
Since the equilibrium is established, the quantity which the body 
receives is equal to the quantity which it loses, which gives 
be's =es 
3 
2 
whence Ss r 
Oe es C6 BIN ies 
Ss r 
that is to say, the entire body receives, from each element of the 
inclosure, a quantity of heat which is precisely equal to that 
which it imparts to it. 
But at equilibrium, the temperatures of the body and of the 
inclosure being equal, the quantities e and e! must also be equal, 
because their emissive power is the same; therefore 
6 = sin? w. 
Thus, whilst each element of the inclosure emits in all directions 
a certain quantity of heat e’, the body receives from that element 
only e' sin? w. 
It is clear, moreover, that if, the temperature of the inclosure 
remaining constant, that of the body changes, the body will not 
less receive from the inclosure this quantity e' sin? w which it 
received at equilibrium, e’ being always the total quantity of 
heat emitted in all directions by the unity of surface of the in- 
closure. 
Now if it be true that the absolute quantity of heat emitted in 
the unity of time by the unity of surface is expressed by a 
function of the form 
e=Bfa't? 
there results, for the total quantity es of heat lost by the body, 
es=s.B.fat’; 
at the same time, the inclosure having the same emissive power 
f and the temperature 4, we shall thus have 
?= 5 as 
