86 M. POUILLET ON SOLAR HEAT, 
It remains to examine whether, to undergo this loss, the globe 
must still have the temperature of the inclosure: now, if it must 
have, for example, a higher temperature, this excess being inde- 
pendent of its dimensions, it would be necessary that it should 
preserve it when it had sufficient volume to fill the inclosure ; 
whence it follows that there might be a permanent difference of 
temperature between two bodies which touch, or at least which 
are very near to one another, a thing that is contrary to all ex- 
periments. 
Thus, two equal surfaces, possessing a complete absorbing 
power, always emit equal quantities of heat when they are at the 
same temperature, whatever be the difference of matter or pro- 
perty between them. 
_ It is evident that, in this case, the principle of the equality of 
temperature, at equilibrium, cannot be demonstrated a@ priori, 
and that it results only from the general indications of ex- 
periment. 
But the second principle, that of the equality of the emis- 
sive powers of any two surfaces of the same temperature, which 
do not reflect, is immediately deduced from the first ; it is upon 
this point that some uncertainty remained *. 
Law of the Cosinus.—The law of the cosinus, which appears to 
leave a doubt on the mind of some natural philosophersf, is also 
deduced in a very simple manner from the same considerations. 
Since for the equilibrium we have always e=e/ and 6= sin? w 
where the globe and the inclosure have complete absorbing 
powers, and since each unity of surface of the inclosure trans- 
mits to the globe a quantity of heat expressed by e sin® w, w being 
the angle of emission, that is to say, the angle of the extreme 
rays with the normal on the surface, it is evident that, for an 
angle w a little larger than », the quantity of heat would be 
é sin? a! ; 
whence it follows that the quantity of heat emitted in the zone 
comprised between a! and » is 
e (sin? w! — sin? w) ; 
the surface of this zone being 27 (cos? w — cos w'), the quantity of 
heat emitted from the corresponding unity of surface is therefore 
e 
aie (cos w + cos a), 
or 
e 
— COs w, 
T 
supposing that the difference is very small between and !. 
That is to say, if we consider the element of a radiating sur- 
* M. Poisson, Z’héorie de la Chaleur, p. 42. + Ibid. p. 35. 
