Cuap. VI. § 6.] 
Dulong and Petit! upon the cooling of a body by 
radiation only within an envelope having a tem- 
perature lower than itself, include, as a particular 
case, that in which the body receives nothing from 
the envelope,—when the radiation is entirely that 
of loss without any gain; and yet the cooling pro- 
ceeds with a finite velocity. It could not with any 
HEAT.—FOURIER—POISSON. 
951 
knowledge. In tle opinion of many persons, it is to 
be desired that some at least of the problems of con- 
duction were treated in a somewhat different way, 
and approximations obtained by the application of a 
less abstruse calculus. But towards this desirable 
result, little has yet been done. 
As a pure mathematician, Fourier occupies a 
(685.) 
distinguished rank. His conversion of functions of Vitings 
kind into series of periodical quantitieshis oy roe” 
every kind into series of periodical quantities—his oy pure 
treatment of problems, involving discontinuous laws mathema- 
propriety be said in such a case, that the tempera- 
ture of the space in which the body cools is in- 
finitely low; it cannot be said to have any tempera- 
ture at all. 
—his solution of higher differential equations—are 
(683.) Now, in the case of our globe and its atmosphere, all important additions to analysis, to the improvement 
— by we have a heated mass, suspended as it were, in space. of which, as he has himself very justly observed, 
ourler, 
(684.) 
If there were no other bodies in the universe, the earth 
must by degrees lose its heat. We know indeed that 
it is cooling. The proportion of its native heat an- 
nually emitted, would melt a crust of ice A>th inch 
thick. This heat is dissipated in space. It may 
therefore be enquired, whether a sphere of known 
conducting power and of known temperature at the 
surface, is parting with its heat to space at a rate 
which supposes it to radiate without any requital, or 
whether it receives from space (or the bodies which 
space contains, independently of the sun) any portion 
of the heat which it thus dissipates. To solve this 
question, we must evidently know with great accu- 
racy the radiating power of the surface of the earth, 
than which, unfortunately, no datum is more com- 
pletely uncertain: and the influence of the atmo- 
sphere (which is truly a part of the earth) renders the 
solution still more indeterminate. It is not known 
what method Fourier took to arrive at a numerical 
result, but it is well known that he obtained it in a 
way which appeared satisfactory to himself, and that 
he often referred to it. He supposed the “ temper- 
ature of space” to be 50° or 60° below zero on the 
centigrade scale, and believed he did not err in fixing 
it by more than 8° or 10°. By this we understand, 
that after infinite ages, the earth, or any other body 
placed in the same situation and previously heated, 
would attain this temperature and no lower. 
This slight sketch gives an imperfect idea of the 
extent and originality of Fourier’s labours. But 
enough has been said to show, that he must rank 
physical problems are ever the most important ave- 
nues. Such considerations as Fourier treated of 
could hardly have entered into the mind of a mathe- 
matician not guided by a specific physical enquiry. 
His favourite subject of the solution of Numerical 
Equations, which brought forth his first essay—which 
occupied him even on the banks of the Nile—and an 
elaborate work on which was almost his last addition 
to science,—is of course one of Jess general interest. 
His experimental abilities, as.we have said, were 
tics. 
(686.) 
not equal to his mathematical; and it is to be re-Experi- 
gretted that his schemes for several practical appli- 
cations of theory seem to have been left imperfect. 
He invented a Thermometer of Contact, an instrument 
for determining the conductivity of bodies, which is 
but little known or used, and of which the theory 
was left incomplete. He also joined Oersted in ex- 
periments on Thermo-Electricity. He studied with 
great care the principles on which his theories were 
based, and seems throughout to have desired to Jeave 
no doubtful step in his reasonings, nor to make any 
tacit or unproved assumptions. His compositions 
are minutely clear, To them we might apply the re- 
mark attributed to Voltaire—* Whatever is obscure 
is not French.” If there be obscurity, it is only due 
to the abstruseness of the subject, not to the manner 
of conveying it. 
Fourier succeeded Delambre as Secretary of the Ma- 
ments— 
Style. 
(687.) 
thematical Class of the French Academy of Sciences, His death. 
and wrote several Eloges. 
1830, generally respected. 
He died no the 16th May 
We will here, in a few words, comment on the (688.) 
subsequent progress of the subject of the Conduction Fourier's 
of Heat. ery 
Whilst Fourier’s papers were still in the archives 689.) 
of the Institute, they were consulted by Poisson, who Poss. 
amongst the most considerable philosophers of his 
day. That he excited the jealousy of the great ma- 
thematical geniuses of the previous generation, and 
that his new train of research, though fully accepted 
by those who succeeded him, has as yet received but 
slight extension at their hands, are facts which con- 
cur to prove his originality and merit, That he 
did not solve more cases of the propagation of heat, 
and that some of his solutions are so complicated 
as hardly to be such in a practical sense, show only 
the extreme difficulties of a subject which touches 
every where the boundaries of existing mathematical 
published solutions of several problems based on 
Fourier’s principles, and coinciding in result with his. 
As the analysis used was somewhat different, the 
coincidence in so new a subject was not without im- 
portance. In 1836, the Theory of Heat of the same 
author appeared, based on the law of cooling, dis- 
covered by Dulong and Petit, which Poisson, with 
1 See the next Section. 
