CHAP. VI., 6.] 



HEAT. FOURIER POISSON. 



153 



Dulong and Petit 1 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 

 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. 



(683.) Now, in the case of our globe and its atmosphere, 

 fined by we have a heated mass, suspended as it were, in space. 

 ier ' 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 j^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. 



(684.) 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 

 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 



knowledge. In the 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 ^tings 

 every kind into series of periodical quantities his g n pur" 6 * 

 treatment of problems, involving discontinuous laws mathema- 

 his solution of higher differential equations are tics - 

 all important additions to analysis, to the improvement 

 of which, as he has himself very justly observed, 

 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 less general interest. 



His experimental abilities, as we have said, were (686.) 

 not equal to his mathematical ; and it is to be re- Ex P eri - 

 gretted that his schemes for several practical appli- g^jf ~ 

 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 leave 

 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- (687.) 

 thematical Class of the French Academy of Sciences, His death, 

 and wrote several Eloges. He died no the 1 6th May 

 1830, generally respected. 



We will here, in a few words, comment on the (688.) 

 subsequent progress of the subject of the Conduction Fourie 

 of Heat. 



Whilst Fourier's papers were still in the archives (689.) 

 of the Institute, they were consulted by Poisson, who Poisson - 

 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 1835, 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. 



