REPORT ON ELECTRICITY, MAGNETISM, AND HEAT. 19 
early period it had been noticed, as we have said, that the rate 
of cooling at high temperatures is faster than the theoretical 
rule. In 1817 the rule was reformed by MM. Dulong and Pe¬ 
tit, whose investigations on this subject are an admirable exam¬ 
ple both of laborious experiment and of sagacious induction. 
Without dwelling upon the steps of their process, we may ob¬ 
serve that they were led to this formula for the rate of cooling, 
m a (i a — 1), where 0 is the temperature of the surrounding 
space, and t the excess of temperature of the body. This formula 
shows that the quickness of cooling for a constant excess of tem¬ 
perature is not constant, hut increases in geometrical progres¬ 
sion when the temperature of the surrounding space increases in 
arithmetical progression. From this rule, and from the theory 
of exchanges which makes part of their reasoning, MM. Dulong 
and Petit find that the quickness of cooling, so far as it depends 
on the temperature of the hot body, increases as the terms of a 
geometrical progression diminished hy a constant number , when 
the temperature of the hot body increases in arithmetical pro¬ 
gression. This explains the deviations previously observed, and 
gives a complete rule, remarkable for its symmetrical character*. 
This correction of Newton’s law will materially affect the ma¬ 
thematical calculations belonging to the subject; but probably 
the general features of the results will be the same as on the old 
supposition. M. Libri, an Italian mathematician, is the only 
person, so far as I am aware, who has applied Dulong and Pe¬ 
tit’s law to calculations of this kind. With this law for his basis, 
he has undertaken the problem of the armil, in a memoir read to 
the Institute of France in 1825, and since published at Florence f. 
The application of mathematics to the problem of the com¬ 
munication of heat, requires not only the fundamental law of 
such communication to be given by experiment, but also certain 
numerical quantities which are different for different substances, 
and which express the specific power of conduction and of ra¬ 
diation for each substance. These quantities have been called 
by Fourier conductibilite or conducibilite exterieure et interieure. 
Such terms are obviously improper, except we could apply the 
adjectives conductible or conducible to the substances, which it 
would be a gross solecism to do; but we may say of substances, 
that they are more or less conduc^Tc, and we may therefore pro¬ 
perly speak of their exterior and interior conductivity. 
2. Fundamental MathematicalFornmlce. —Siqiposing New- 
* The temperatures in MM. Dulong and Petit’s formulae are those of the 
air thermometer. 
f Mem. dc Math, el de Phys., 1829. 
c 2 
