RADIATION AND ABSORPTION. 85 
Nore 1. 
The mode of demonstration which I have used in this article 
permits the solution of several difficulties which are still pre- 
sented by the most fundamental principles of radiant heat,— 
namely, the principle of the equality of temperature and of the 
equality of the emissive powers of two surfaces which do not 
reflect; the law of the cosinus; and the law of emission, con- 
sidered in relation to the constant which the calculation gives, 
and which is added to the function of temperature. 
Principle of the equality of temperature and of the equality 
of the emissive powers of two surfaces which have no reflective 
power.—It may be admitted as evident, that two equal surfaces 
of the same matter, both possessing a maximum emissive power, 
emit equal quantities of heat in the same time, when they have 
equal temperatures; for, all being identical, the quantities of 
heat emitted must be themselves identical. 
Thus, for this particular case, if the globe and the inclosure 
have the same temperature, we have e = ée, the equilibrum is 
established, and we have at the same time 0} = sin? a, 
This result is independent of the dimensions of the globe and 
the inclosure: now, the same globe, at the same temperature, 
losing always the same quantity of heat in the same time, it re- 
sults that all the inclosures, large or small, transmit to the globe 
the same quantity of heat; it results, consequently, that at any 
portion of a given inclosure, seen from the centre of the globe 
at a certain angle, we may always substitute a portion of another 
inclosure seen at the same angle; this tends to prove that the 
temperature of the globe is equal to that of the inclosure, not 
only when it is at the centre of that inclosure, but whatever be 
the position that it occupies. _ 
If now the globe is not of the same substance as the inclosure, 
if, in a word, it ceases to be identical with it, without ceasing to 
have, like it, a complete absorbing power, the loss of the globe 
will then be e,s; the portion of heat which it receives from the 
inclosure and which it absorbs will always be the same, namely, 
é's'sin?; and the sole condition required for the equilibrium 
will in like manner be, that the quantities of heat lost and ab- 
sorbed may be equal, which gives again 
e,s = e's! sin? a, 
whence 
ej =e; 
that is to say, even in this case it is necessary for the equili- 
brium that the unity of the surface of the globe loses in the 
same time as much heat as the unity of the surface of the in- 
closure. 
