340 
On the Measure of Temperature, 
[Nov. 
So extensive a series as the preceding ought to be sufficient proof, that the for- 
mula which represents the cooling of the glass bulb, is equally applicable to the 
silvered bulb, and that a has in each case the same value. However, not to neglect 
any means of verification in our power, we have varied the temperature of the sur- 
rounding mass, and eventually carried it to 80°. The coefficient of (a* — 1) must 
then be multiplied by a 60 which gives, 
V — 0,658 (at — 1) 
Excess of temp, 
or values of t. 
Observed 
values of V. 
Calculated 
values of V. 
240° 
3 ,40 
3°, 44 
220 
2 ,87 
2 ,86 
200 
2 ,35 
2 ,37 
ISO 
1 ,99 
1 ,94 
160 
1 ,56 
1 ,58 
140 
1 ,27 
1 ,26 
120 
0 ,99 
0 .98 
100 
0 ,75 
0 ,76 
60 
0 ,56 
0 ,55 
The simplicity and the generality of the law just established — the accuracy 
with which observation confirms it, in an extent of nearly 300° of the tlier- 
mometric scale, induces the belief, that it will strictly represent the progress 
of cooling in vacuo at every temperature, and for every substance. 
Let us now return to the investigation which has led to the discovery 
of this law. 
The radiation of the surrounding mass is represented by F (t), and we find 
its value to be 
7)i at -|- constant. 
Now the point from which the temperature t is reckoned, being arbitrary, 
may be so chosen that the constant shall — 0, which would reduce the pre- 
ceding expression to the form m at. We may then conclude that if it were 
possible to observe the absolute cooling of a body in vacuo , that is to say, the 
loss of heat of that body without its receiving any from surrounding bodies, 
this cooling would follow a law in which the rate would decrease in geometrical 
progression, while the temperature decreased in arithmetical progression : and 
further, that the ratio of this progression would be the same for all bodies, what- 
ever the state of their surfaces. 
From this very simple law, it is easy to deduce that of the actual cooling of 
bodies in vacuo. In fact, to pass from one to the other, it is only necessary to 
allow for the heat parted with at each moment by the surrounding matter; this 
quantity of heat will be constant if the temperature does not vary ; from which 
it follows, that the actual rate of cooling of a body in vacuo , for excesses of tem- 
perature in arithmetical progression, must increase as' the terms of a geoinetrica 
progression diminished by a constant number. This number must itself vary in 
geometrical progression when the temperature of the surrounding mass (of which, 
in fact, it represents the absolute radiation,) varies in arithmetical progression. 
These different results are all clearly expressed in the equation just obtamec . 
By putting in at — M , we have 
V = M (a 1 — 1) 
M is the number to be subtracted from the different terms of the geometric pro- 
gression expressed by M at, and we see, besides, that M depends upon t in t ie 
manner above explained. . , t 
Since the value of a is independent of the nature of the surface, it results tna 
the law of cooling in vacuo is the same for all bodies ; so that the radiating powers 
of different substances preserve the same relation at all temperatures. We have 
found this relation, or ratio, to he 5,7 in the case of glass and silver. This resu ^ 
is a little less than Mr. Leslie’s, but the difference has been occasioned most pro 
bably by our silver having a dull surface, while his was polished. 
We may also see, in supposing the law of absolute radiation to be expresser y 
the formula rna l , that we must put t = oo to have the rate = 0, which would ^ 
the absolute zero at infinity. This opinion, rejected by a number of enquirers, sim 
ply because it would lead to the conclusion, that the quantity of heat in bodies w 
