1819.]| andonthe Laws of the Communication of Heat. 243 
We have thought it necessary, therefore, before endeavouring 
to find any law, to vary our observations as much as the nature 
of the subject would admit ; and we have been guided in this by 
a remark relative to the theory of radiation, which, we think, has 
not hitherto been made by any philosopher. 
In the theory of the exchanges of heat which has been 
adopted, the cooling of a body in vacuo is merely the excess of 
its radiation above that of the surrounding bodies. Therefore, 
if we call @ the temperature of the substance surrounding the 
vacuum in which the body cools, and ¢ + 64 the temperature of 
the body, we shall have in general forthe velocity, V, of cooling 
(observing that this velocity is null when ¢ is null), 
V=FRG¢+%)— F 
F denoting the unknown function of the absolute temperature, 
which represents the law of radiation. 
Ifthe functions F (¢ + 6) and F () were proportional to their 
variables ; that is to say, if they: were of this form, m (¢ + 6) 
and m (9) ; m being a constant quantity, we should find the velo- 
-eity of cooling equal to m ¢, and we should fall into"the law of 
Richmann ; since the velocity of cooling would be proportional 
to the excesses of temperature. These velocities would be at 
the same time independent of the absolute temperatures, as has 
been hitherto supposed. But if the function, F, be not, propor- 
tional to its variable, as our experiments proye, the expression 
Fé + 4) —F@, 
which represents the velocity of cooling, ought to depend at 
once upon the excess of temperature ¢ and the absolute temper- 
ature 6 of the surrounding medium. It was to vary this conse- 
quence that we observed the cooling of the thermometer in vacuo, 
raising successively the water surrounding the balloon to 20°, 
40°, 60°, 80°. The following table presents, in the same point 
of view, all the results of each of these series of observations, 
which were repeated several times. 
Excess of tem-|Velocity of 
perature of the cooling water 
thermometer. at 6°, 
Ditto water at| Ditto water at| Ditto water|Ditto water 
20°, 40°, at 60°. at 80°, 
| 
e400 =| «10-69 12-402 
220 | $61 
200 7-40 
180 6°10 
160 4°89 
140 3°88 
120 3-02 
100 2°30 
80 1-74 
60 as 
This table, which requires no explanation, confirms, as is 
evident, the principle which we have established; but the 
Q2 
