The Egyp- 
tian Insti- 
tute. 
(664.) 
Fourier 
first states 
correctl 
the analy- 
tical form 
of the pro- 
blem of 
conduction. 
- Tardy pub- 
lication— 
rivalry in 
~ the Insti- 
_ tute. 
Cuar. VIL, § 6.] 
Paris, when Lagrange, Laplace, and. Berthollet were 
amongst the professors. He had already presented 
to the Academy, at the age of 21, a paper on the nu- 
merical solution of equations, a subject of predilec- 
tion with him, and to which we shall presently return. 
After leaving the Normal School, he was named one 
of the original professors of the Polytechnic School, 
a station of which he was justly proud, but from 
which he was withdrawn by the requisition to join, 
along with Monge and other savans, the Expedition 
to Egypt under Napoleon. It was the singular fancy 
of that extraordinary man, to create an Egyptian 
Institute, of a constitution similar to that of France. 
Fourier was perpetual secretary. But it proved little 
better than a waste of talent. The arts of Egypt were 
not regenerated, and France was despoiled of some 
of her ablest philosophers. Fourier had quite as much 
to do with batiles and treaties as with equations and 
experiments, Yet he often referred afterwards with 
partial reccllection to those stirring times, and re- 
counted, with the ardour of a somewhat garrulous 
temper, the valiant feats of arms which he had wit- 
nessed. Fourier edited the account of the Expedition 
to Egypt, and wrote the historical preface, the com- 
position of which ultimately procu.ed for him a seat 
in the Académie Frangaise. 
On his return to Europe, he was appointed Prefect 
of the Isére in 1802, and Grenoble became his 
home for some years. Whilst he devoted a just 
share of his attention to his public duties, he found 
time to produce his greatest work, The Analytical 
Theory of Heat, His first paper on this subject 
dates from 1807. It was communicated to the Aca- 
demy of Sciences, but not printed. The subject was 
however proposed for a prize, to be decided in 1812, 
when Fourier’s essay was crowned, but, strange to 
say, not published. The cause, it is to be feared, lay 
in the jealousy of the greatest mathematicians of the 
age. Laplace, Lagrange, and Legendre, the committee 
of the Academy, whilst applauding the work, and ad- 
mitting the accuracy of the equations of the move- 
ment of heat thus for the first time discovered, insi- 
nuated doubts as to the methods of obtaining them, 
and likewise as to the correctness of the integrations, 
which were of a bold and highly original kind. 
These disparaging hints were not supported by any 
precise allegations ; and we can scarcely blame Fou- 
rier for feeling indignant at the tyranny of the mathe- 
matical section, and little disposed to regard with 
favour the few and comparatively insignificant efforts 
of several of its members subsequently to ratify and 
extend the discoveries ‘which he had unquestionably 
made. The manuscript, after lying for twelve years in 
the archives of the Institute, where it was consulted 
by different persons, wasfinally printed, word for word, 
as it stood in 1812.1 Fourier’s long absence from 
Paris in a remote provincial town, rendered this in- 
HEAT—FOURIER. 
947 
dignity possible at first; and afterwards, it was his 
misfortune to be unable to hold a political station 
without offence, amidst the violent intestine conflicts 
with which France was afflicted. He alternately dis- 
pleased his old master Napoleon and the Bourbons, 
and the consequence was, that after the Restoration 
he found himself dispossessed of every employment, 
master of not one thousand pounds, and refused by 
the government even a seat at the Institute. This 
indigence, so honourable to himself, and this neglect, 
so disgraceful to others, tended, no doubt, to increase 
an irritability, such as intense mental exertion often 
produces, and which the injustice of his scientific 
countrymen had already aggravated. Finally, how- 
ever, he received a modest post connected with the 
civil administration of the department of the Seine; 
he was also elected a member of the physical section 
of the Academy of Sciences, and he finally became 
perpetual secretary of that body. , 
Fourier’s papers on Heat show a remarkable com- 
bination of mathematical skill with a strict and pre- 
cise attention to physical considerations, In this he 
(665.) 
His physi- 
cal preci- 
sion—ex- 
excels almost every writer of his time, and especially periments. 
his colleague and younger rival, Poisson. His expe- 
rimental skill is not to be so highly praised, although 
he illustrated several of his solutions by actual trials, 
which he submitted to calculation, and showed to 
agree with theory. Their degree of precision, how- 
ever, hardly allows them to be considered as tests 
of theory. 
Fourier assumes the correctness of Newton’s law, 
(666.) 
as well for communication of heat from point to point Assump- 
of a solid, as for the external radiation by which ittions of the 
parts with its heat into the surrounding space. In 
‘the former case, the flow of heat is proportional to 
the rapidity of the depression of temperature, in the 
direction in which the motion of the heat is considered; 
in the latter, it varies as the excess of temperature 
of the surface of the hot body above the surrounding 
space, affected, of course, by a constant depending on 
the radiating power of the surface. These, as I have 
said, were also the Postulates of Lambert’s solution. 
Fourier’s researches, fortunately perhaps, preceded 
for the most part Dulong and Petit’s enquiry into the 
true law of cooling. I say fortunately, since other- 
wise Fourier might have been discouraged from at- 
tempting the solution of problems which are highly 
important even in an approximate form. 
With regard to the law of radiation, Fourier had 
A 
Theory, 
nalytical 
(667.) 
the merit of showing, for the first time, the necessity Myre 
Leslie’s experimental law of the intensity of emanated of emana- 
heat being proportional to the sine of the angle which tion. 
the direction of emanation makes with the surface. 
This he considered both mathematically and physi- 
cally. Mathematically, he showed that were this law 
not true, a body might be maintained for an indefinite 
time within an envelope of constant temperature, and 
1 See Fourier’s note at the commencement of his paper, in Memoirs of the Institute for 1819 (printéd 1824). 
