1819.} and onthe Laws of the Communication of Heat. 249 
the real velocity of cooling of a tia in vacuo ought, for 
excesses of temperature in an arithmetical progression, to increase 
in a geometrical progression, diminished by a constant quantity. 
This number itself must vary itself, according to a geometrical 
progression, when the temperature of the surrounding medium 
(of which it represents the absolute radiation) varies according 
to an arithmetical progression. These different results are 
clearly expressed in the equation obtained above, making m a4 
= M. We have 
V =M(a —1) 
M is the number which we must take from the different terms 
of the geometrical progression expressed by M a? ; and we see, 
besides, that this number M is connected with 9 by the relation 
announced above. 
Since the yalue of a is independent of the nature of the sur- 
face, it follows that the law of cooling in vacuo is the same for 
all bodies ; so that the radiating power of different substances 
preserves the same ratio at all temperatures. We have found 
this ratio equal to 5°7 on comparing glass with silver. This 
result is a little less than that of Mr. Leslie ; owimg, no doubt, 
to the surface of our silvered thermometer being tarnished, 
while that of Mr. Leslie’s was polished. We see likewise, 
according to the hypothesis which has given us the law of abso- 
lute radiation, that we must make @ = 0 to render the velocity 
null ; which fixes the absolute zero at infinity. This opinion, re- 
jected by a great many philoscphers, because it leads to the notion 
that the quantity of heat in bodies is infinite, supposing their 
capacity constant, becomes probable, now that we know that the 
specific heats diminish as the temperatures sink. In fact, the 
law of this diminution may be such that the integral of the 
quantities of heat, taken to a temperature infinitely low, may, 
notwithstanding, haye a finite value. 
The law of cooling, such as we have represented it, and such 
as it may be represented in vacuo, applies solely to the velocities 
of cooling, estimated by the diminutions of temperature indicated 
by an air thermometer. We may see by the correspondence of 
all the thermometrical scales given in the first part of this 
memoir, that if we make use of any other thermometer, the rela- 
tions between the temperatures and velocities of cooling would 
lose that character of simplicity and generality which we have 
found them to possess, and which is the usual attribute of the 
laws of nature. If the capacities of bodies for heat were con- 
stant when we determine them by the same thermometer, the 
peenns law would still give the expression of the quantities of 
eat lost, in a function of the corresponding temperatures. But 
as we have proved that the specific heat of bodies is not con- 
stant in any thermometrical scale, we see that, in order to arrive 
at these real losses of heat, we must admit an additional element; 
_ namely, the variation of the capacity of the bodies subjected to 
