148 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



greater advantage, was mainly because he yielded to 

 the guidance of an imagination which often carried 

 him into fanciful speculation, yet which was strangely 

 \inited with dogmatism in maintaining what he had 

 once maintained, and a disposition to accuse others of 

 misinterpreting nature, whenever they arrived at con- 

 clusions inconsistent with his own. 



(658.) I Q suc ^ sc i ences as those which he chiefly culti- 

 vated, sciences eminently progressive, imperfect, 

 and dependent on experimental proof, a just appre- 

 ciation of the labours of others is one of the most 

 essential parts of the philosophic character, whilst 

 an absence of it infallibly condemns the dogmatic 

 theorist to be gradually left behind, even in the paths 

 which he had at first trod with the greatest distinc- 

 tion. With few exceptions, Sir J. Leslie carried his 

 scientific views of 1804 with him to the grave. The 

 possibility of the passing of heat, except solar and 

 highly luminous heat, through any solid body, such 

 as glass, though proved by Maycock, De la Roche, 

 and Powell, the existence of dark heating rays in the 

 sunbeam, less refrangible than the red, demonstrated 

 by Herschel, and afterwards confirmed by many 

 others, the doctrine of gases and vapours as laid 

 down by Dalton, the maximum density point of 

 water shown so ably by Hope and Rutnford, the 



existence of climates in the arctic regions of which 

 the mean annual temperature does not exceed of 

 Fahrenheit, proved by Parry and his successors, 

 all these, and many other demonstrated truths in his 

 own peculiar walk of science, were, we fear, practi- 

 cally ignored by him throughout life. (659.) 



But we willingly leave the ungrateful task of indi- Merit of h 

 eating defects. Let us recollect rather with pleasure t^re-" 1 

 how much we owe to his beautiful discoveries. It is searches. 

 perhaps not an insignificant test of their originality, 

 that though they were generally adopted (at least to 

 the extent which his own experiments justified), Les- 

 lie's observations were but rarely repeated, and that 

 only in the way of general confirmation and illustra- 

 tion. I mean that for a great many years the path 

 which he had opened, and the methods which he de- 

 scribed, were not seized upon by others, as leading to 

 a sure course of discovery. Until the time of Dulong, 

 his experiments on cooling were perhaps never care- 

 fully resumed, and a very great number of his sub- 

 jects of enquiry were only taken up thirty years after 

 their publication, as we shall see in a future section. 



The observations of Herschel on the Refrangibility (660.) 

 of Solar Heat, I shall include inthe notice of the 

 experiments of Berard and De la Roche, to which 

 we shall presently turn. 



6. FOURIER. Mathematical Theory of the Conduction of Heat. 

 Temperature of the Earth and of Space. 



Lambert; Poisson. 



(661.) It is stated by Arago, that when the Academy of 

 Theory of Sciences, above a century ago, proposed as a prize sub- 

 tton'of heat J ect " La . Nature et la Propagation du Feu ;" adding, 



Lam- " la question ne donne presque aucun prise a la geo- 



bert. metric," a majority of the candidates treated of the 

 methods of preventing the burning down of houses ! 

 It is true, however, that on that occasion, Euler sent 

 a memoir which, though crowned, was unworthy of 

 his genius. LAMBERT in his " Pyrometrie," in 1779, 1 

 had the rare merit of laying the foundations of the 

 science of conduction. He solved correctly this ques- 

 tion : " If a thin conducting bar of indefinite length 

 be kept with one extremity heated to a constant degree 

 above the surrounding space, required the tempera- 

 ture of any point in the axis of the bar ?" The solu- 

 tion is, that the temperatures, or rather excesses of 

 temperature, diminish in a geometric ratio, at dis- 

 tances reckoned in arithmetical progression, from the 

 origin of the heat. 2 In this solution it is assumed, 

 (1.) That the flow of heat along the bar, is at any point 

 proportional to the rapidity with which the tempera- 

 ture at that part of the bar is lessening as we recede 

 from the source ; in other words, that the flow of heat 

 from the hot part to the cold part, is more rapid in 



proportion as the difference of temperature of two 

 sections of the bar at a given short interval is greater. 

 (2.) That the bar parts with its heat to the surround- 

 ing space, exactly in proportion to its excess of tem- 

 perature at every part. 



This beginning, which perhaps like many of Lam- (662.) 

 bert's other writings was not very generally known, Biot. 

 had no sequel until 1804, when M. Biot attempted to 

 find the differential equation of the general movement 

 of heat on the same principles. But the form which 

 he obtained, including a mathematical solecism, be- 

 trayed some error in stating the conditions. Three 

 years later Fourier had more success. But, conform- 

 ably to the plan of this discourse, I shall premise 

 some facts regarding his early career, which was far 

 from commonplace. 



JOSEPH FOURIER was born in 1768, at Auxerre in (663.) 

 France. He was of humble parentage, and being Fourier- 

 early left an orphan, was educated by the Benedic- jjl 

 tine monks who, singularly enough, conducted with 

 success in that town a military school. It seemed 

 his fate to become either a priest or a soldier ; yet he 

 was neither, though ere long familiar with camps. 

 He became first a pupil of the old normal school of 



1 Pyrometrie, oder, von Maasse des Feuers und der Warme. Berlin, 4to, 1779. This work was posthumous, and contains many 

 riginal observations on Thermometry, Conduction, Solar Radiation, and Climate. 2 Pyrometrie, p. 184. 



