(695.) 
Their ap- 
paratus. 
_ and any other gas could be introduced into it. 
(696.) 
Velocity of 
cooling not 
simply as 
the excess 
of heat. 
(697.) 
Effect of 
contact of 
air on the 
rate of 
cooling. 
Cuar. VIL, § 7.] 
of air was absent, the influence of the latter became 
less and less perceptible. 
The principal apparatus of Dulong consisted of a 
balloon of thin copper about a foot in diameter, coated 
internally with lamp black, and placed in connection 
with an air-pump, so that any portion of atmospheric 
air could be extracted up to about 332 of the whole, 
The 
temperature of the balloon could be nicely regulated by 
introducing it entirely into a water trough. Into the 
centre of the balloon, thermometers of different sizes, 
or having different kinds of surface, could be intro- 
duced. The temperature of the balloon having been 
first regulated, the thermometer under experiment 
(being itself the radiating and cooling body) was 
heated nearly to the boiling point of mercury, and 
inserted in the balloon so as to occupy the centre of 
it. The exhaustion and other arrangements being 
made, the observations on the rate of cooling of the 
thermometer commenced when its temperature was 
as high as 250° or 300° centigrade, equivalent to 482° 
and 572° Fahrenheit. 
With respect to simple radiation, or when the 
effect of air in the balloon is estimated as nothing, 
the inaccuracy of the Newtonian law was soon ap- 
parent. Whilst the excess of temperature of the 
cooling body above the envelope or balloon remained 
constant, and the absolute temperature of both was 
made to vary, the velocity of cooling, instead of 
being constant, increased rapidly with the tempera- 
ture. Thus the excess of temperature being in every 
case 200° centigrade, and the temperature of the 
balloon being me 4s 20: 40°, 60°, 80°; 
the rate of cooling was 74, 8-6, 10-0, 11-6, 13-4. 
The whole of an elaborate series of observations was 
beautifully and satisfactorily represented by a for- 
mula admitting of this simple physical interpre- 
tation, viz., that the cooling of the thermometer is 
the difference between the heat which it parts with to 
the envelope and the heat which it receives from the 
envelope; and that the heat thus parted with, either 
by the thermometer or the envelope, varies in a geo- 
metric ratio with its temperature. 
The effect of contact of a gas in cooling the ther- 
mometer is more complex. It is independent of the 
texture of the surface, as Leslie had already supposed. 
The cooling power of a gas is proportional to a cer- 
tain power of its elasticity, which varies for each ; it 
takes place more rapidly in hydrogen than in any 
other known gas, which was likewise discovered by 
Leslie. It also comes out rigorously, that the ratio 
of the radiating power of different surfaces is the same 
at all temperatures, This ratio for glass and silver 
HEAT.—DULONG AND PETIT. 
953 
is 5°707: 1. Assuming this last principle, and also 
that the cooling due to the contact of air is indepen- 
dent of the surface, the law of cooling in vacuo may 
be deduced from the observed cooling of two thermo- 
meters suspended in air, and having glass and sil- 
vered surfaces respectively. Dulong and Petit found 
that, when they analyzed their experiments in this 
way, they obtained values for the radiation in vacuo 
almost absolutely coinciding with what direct experi- 
ment had already given. No more perfect criterion 
could be desired of the soundness of every link of the 
chain of experiment and induction. 
We shall not analyze Dulong’s other memoirs. 
They regarded matters in the science of Heat requir- 
ing the same skill in devising apparatus and in mani- 
pulation, the same caution in eluding errors, and the 
same just principles of calculation as in the investi- 
gations already specified. They did not, however, 
lead to the discovery of laws so striking and so ge- 
neral. They included the very delicate and difficult 
subject of the laws of the thermal expansion of 
bodies, particularly that of air and of mercury, which 
were applied to the theory of the thermometer, the 
very basis of all exact knowledge in the doctrine of 
heat. Another referred to the specific heat of the 
gases, an enquiry of the very greatest difficulty, in 
which we still find physicists disagreed. Dulong 
bethought himself of using Laplace’s celebrated cor- 
rection for the velocity of sound due to the heat de- 
veloped during the compression of an elastic medium 
(art. 433), and proposed to deduce the heat thus 
developed, by a comparison of the observed and theo- 
retical (Newtonian) velocity of sound, and thence to 
obtain the specific heat. The theoretical velocity is 
easily obtained from the density of a gas under a 
given pressure: the observed velocity was ingeni- 
ously found by sounding one and the same organ 
pipe with the different gases in succession, and ascer- 
taining the pitch by the aid of Cagniard de Latour’s 
Siréne. (441.) 
One of Dulong’s latest, most elaborate, and most 
useful labours, was ascertaining the elasticity of high- 
pressure steam in terms of its temperature. These 
experiments were carried as far as 24 atmospheres 
of pressure. In the course of them the law of Ma- 
riotte and Boyle was verified up to the same limit. 
The condensation of air was found to be exactly pro- 
portional to the pressure. We shall return to the 
subject of these later experiments of Dulong in men- 
tioning the still more recent ones of M. Regnault. 
Dulong was unfortunately lost to the world at the 
comparatively early age of 54. His was the peculiar 
merit of a well-balanced scientific mind, He felt 
1 Thus symbolically expressed :— 
V=m (at+4- £)3 
where V is the “ velocity of cooling,” or depression of the thermometer in centigrade degrees in one minute, supposing it to con- 
tinue constant for so long; ¢ is the temperature of the envelope; t + 4, that of the thermometer ; a is a constant independent of 
the size and surface of the cooling body, and which is =-1:0077 ; m is a constant depending on the dimensions and surface of 
the body. 
VOL. I. 
68 
(698.) 
Other me- 
moirs of 
Dulong on 
the laws 
of heat. 
Specific 
heat of 
(699.) 
On the elas- 
ticity of 
steam. 
(700.) 
Character 
of Dulong. 
