1830.] 
On the Measure of Temperature , Spc. 
335 
II — On the Measure of Temperature, and the Communication of Heat. 
By Messrs. Dulong and Petit. 
PART II. 
On the Laws of Cooling. 
§ 3. On Cooling in a Vacuum. 
The observations on cooling in a vacuum, calculated as we have just explained, 
are all affected by an error ; small it is true, but which it is indispensible to correct! 
Ihis error is occasioned by the small quantity of air which remains in the balloon, 
the elasticity of which, in the greater number of experiments, was less than would 
have supported a column of 3 millimetres, (,12 inch.) 
It is not to the series of temperatures derived immediately from observation that 
this correction can he applied, but to the results deduced from calculation. It is, in 
fact, only necessary to diminish the latter by a quantity corresponding to the loss 
of heat occasioned by the residuum of air in the balloon. 
To determine the amount of this correction in each case, we observed the rate of 
cooling of our thermometer in the balloon, as tilled with air of different degrees of 
density, and we have calculated, for different excesses of temperature, the rate of 
cooling corresponding to each density. Subtracting again from these rates the 
values determined in a vacuum, we should have an exact measure of the quantities 
of heat carried off by the air in its different stages of rarefaction. We shall have, 
in fact, sufficiently exact determinations of these quantities, if for the rates in n va- 
cuum we substitute the approximate rates obtained in the balloon, though contain- 
ing a very minute portion of gas. 
Having thus obtained the quantity of beat carried off by the air for each excess 
of temperature, we perceived that these quantities followed a simple law, by the 
aid of which we have determined, with sufficient precision, the corrections to be ap- 
plied to the calculated rates. The numbers, therefore, which we shall present in 
the course of this section, may be considered as being exceedingly near what would 
be obtained from observations made in a perfect vacuum. 
Let us now, then, turn to the consideration of the several calculated and cor- 
rected series ; and to begin, let us take that in which the balloon was surrounded 
by ice at 0 °, the thermometer with its natural glassy surface : 
Excess of tempera- 
ture over that o 
the surrounding 
mass. 
Corresponding 
rates of cool- 
ing. 
240° 
10°, 69 
220 
8 ,81 
200 
7 ,40 
180 
6 ,10 
160 
4 ,89 
no 
3 ,88 
120 
3 ,02 
100 
2 ,30 
80 
1 ,74 
The first column contains the excess of temperature of the thermometer over the 
surrounding mass ; the second, the corresponding rates of cooling, calculated and 
corrected as above explained. These rates, as we have had occasion to mention 
before, are the number of degrees, by which the temperature would be lowered in 
a single minute, supposing the rate of cooling to be uniform during that minute. 
This first series is sufficient to show the inaccuracy of the law of Richmann ; for 
bv that law, the rate at 200 should be double what it is at 100°, and we >ee it is 
more than treble. In comparing again the loss of beat for an excess of 240 and 
ine of 80°, the first appears to be about six times greater, whereas by the law of 
Richmann it ought only to be treble. 
It would be easy enough to represent by a formula, consisting of two or three 
erms, the results contained in the preceding table, and thus empirically to determine 
he relation subsisting between the temperatures of bodies aud the corresponding 
ates of cooling. But formulae of this description, though useful for calculating in- 
