CHAP. VL, 6.] 



HEAT FOURIER. 



149 



'he Egyp- 

 ian Insti- 

 ute. 



(664.) 

 Fourier 

 first states 

 correctly 

 ;he analy- 

 ;ical form 

 )f the pro- 

 jlem of 

 conduction 



Pardy pub- 

 ication 

 ivalry in 

 ;he Insti- 

 :ute. 



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 which he was withdrawn by the requisition to join, 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 battles and treaties as with equations and 

 experiments. Yet he often referred afterwards with 

 partial recollection 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 procured for him a seat 

 in the Acad^mie Frangaisc. 



On his return to Europe, he was appointed Prefect 

 of the Isre 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, was finally printed, word for word, 

 as it stood in 1812. 1 Fourier's long absence from 

 Paris in a remote provincial town, rendered this in- 



(665.) 



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- l , s PyfJ~ 

 cise attention to physical considerations. In thishe s i on _ e x- 

 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 ittionsof 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 

 the merit of showing, for the first time, the necessity o 

 Leslie's experimental law of the intensity of emanated O f 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 



( 667 ) 



See Fourier's note at the commencement of his paper, in Memoirs of the Institute for 1819 (printed 1824). 



