336 
On the Measure of Temperature , 
{Nov. 
termediate results in the series which has furnished the law of interpolation ; become 
almost always erroneous, when extended to cases without the limits of that series, 
on which they had been founded, and they ought, therefore, never to be considered 
as the expression of the true law of the phenomenon. 
We have therefore deemed it obligatory on us, previously to seeking for any law, 
to vary our experiments as much as the nature of them would permit. The following 
consideration, which does not appear to have suggested itself to the mind of any 
enquirer, has happily directed us in the choice of circumstances calculated to exhi- 
bit the true nature of the problem. 
In the theory generally adopted, of the distribution of heat, the cooling of any 
body in a vacuum is but the excess of its radiation over that of the surrounding 
bodies. Thus if we put t for the temperature of the surrounding matter within 
which any body is subjected to the cooling process, and / + t the temperature of 
this body, we shall have, generally, for an expression of tne rate or velocity of cool- 
ing V (it being observed that this rate is 0 when t = 0.) 
V— F(t + t)-F(t) 
F being used to designate the unknown function of the temperature which an- 
swers to the law of radiation. 
If the functions F ( t -f* t ) and F ( t ) were proportional to their variables, that 
is to say, if they were of the form m (t — f~ t ) and m (t), m being a constant, the 
rate of cooling would be found equal to mt ; and we should thus have the law of 
Richmann, inasmuch as the rates of cooling would he proportional to the excesses 
of temperature, at the same time that they were independent of the temperatures 
themselves, as indeed has been hitherto supposed. But it the function F be not 
proportional to its variables, the expression 
F(t -f- t) - Fit) 
which represents the rate of cooling, will depend at once upon the excess of tem- 
perature t y and on the absolute temperature of the surrounding matter. 
To verify this conclusion, we have observed the rate of cooling in a vacuum, by 
bringing successively the water in the tub, in which the balloon is immersed, to the 
temperatures 20°, 4U°, 60°, and 80°. The following table presents, at one view, 
all the results of each of these series of observations, which have, besides, been 
repeated several times. 
Excess of 
Temper- 
ature. 
Rate of cool- 
ing : the sur- 
rounding* mat- 
ter being at 
0. 
Rate of cool- 
ing: the sur- 
rounding mat- 
ter being- at 
*20°. 
Rate of cool- 
ing : the sur- 
rounding mat- 
ter beiug at 
40°. 
Rate of cool- 
ing : the sur- 
rounding mat- 
ter being at 
60°. 
Rate of cool- 
ing: the sur- 
rounding mat- 
ter being at 
80°. 
240° 
10°, 69 
12°, 40 
14°, 35 
220 
8 ,81 
10 ,41 
11 ,98 
200 
7 ,40 
8 ,58 
10 ,01 
11°, 64 
13°, 45 
180 
6 ,10 
7 ,04 
8 ,20 
9 ,55 
11 ,05 
ICO 
4 ,80 
5 ,67 
6 ,61 
7 ,68 
8 ,95 
140 
3 ,88 
4 ,57 
5 ,32 
6 ,14 
7 ,19 
120 
3 ,02 
3 ,56 
4 ,15 
4 ,84 
5 ,64 
100 
2 ,30 
2 ,74 
3 ,16 
3 ,68 
4 ,29 
80 
1 ,74 
1 ,90 
2 ,30 
2 ,73 
3 ,18 
60 
1 ,40 
1 ,62 
1 ,88 
2 ,17 
This table, which requires no explanation, confirms, as may he seen, the pnncip e 
we have just attempted to establish. The results contained in it suggest a veif 
simple relation, which has led us to the discovery of the law of cooling in a vacuum. 
If the corresponding numbers in the 2nd and 3rd columns are compared, that is o 
say, the rates of cooling for the same excesses of temperature, the surrounding mass 
being successively at Zero, and at 20°, the ratios of these rates will be found as 
follows : — 
1,16 1,18 1,16 1,15 1,16 1,17 1,17 1,18 1,15. 
These numbers, which differ but little amongst one another, and the differences 
which do not appear regular, would not require a greater change in some or 
rates, to become perfectly uniform, than about one-hundreth part. 
Let us compare, in the same way, the rates of cooling, when the surrounding ma 
is at 20° and 40°. The following will be found to be the ratios of these rates. 
1,16 1,15 1,16 1,16 1,17 1,16 1,17 1,15 1,16 1,16. 
