RADIATION AND ABSORPTION, 61 
but this small globe was only 6 centimetres in diameter, and if 
we make the same calculations for a similar body having, for 
example, the dimensions of the earth, we find that in absolute 
cold this globe would take 
13,640 years to fall from 100° to 0, 
29,830 years to fall from 0 to — 100°. 
These examples may show that there has perhaps been some 
exaggeration in the ideas which have been hitherto entertained 
of absolute cold and the phenomena which would be manifested 
on the surface of the earth if the temperature of space were ex- 
cessively reduced below the zero of our thermometers; they show 
at the same time that the essential laws of heat are established 
upon such fixed principles that sudden changes of temperature 
are not less impossible in the system of the world than the sud- 
den changes resulting from mechanical actions. 
15. The theorem relative to the emission of heat enables us 
to determine the conditions of equilibrium of temperature of the 
atmosphere; for this purpose we shall proceed to consider in a 
general manner the conditions of equilibrium of temperature of 
a globe protected by any diathermanous covering and suspended 
with its envelope in the middle of a spherical inclosure. 
Let us designate by s, s", s' the surfaces of the globe, of the 
envelope, and of the inclosure; by e, e’, e the quantities of heat 
emitted in the unity of time by each of the unities of surface of 
8, s', s'; we designate by 4 the absorbing power which the dia- 
thermanous envelope exerts upon the heat emitted by the globe, 
and by 8! the absorbing power which it exerts upon the heat 
emitted by the inclosure. 
The globe emits in the unity of time a quantity of heat es; 
one portion bes is absorbed by the envelope, and one portion 
(1—4) es traverses the envelope to reach the inclosure. 
The inclosure emits a total quantity of heat és’; one part 
¢ s' sin? w falls upon the diathermanous envelope, designating by 
w the demi-angle at which the inclosure is placed with regard 
to the envelope; this latter absorbs a portion of it, e's! 5! sin? a, 
and it lets pass a portion, e's! (1—d') sin? w, 
The envelope emits a quantity of heat e" s" toward the globe, 
and an equal quantity of heat e” s’ toward the inclosure. 
The sum of the quantities of heat which the envelope loses is 
