FOURIER, Joseph. Suite du Mémoire Intitulé : Théorie du Mouvement de la Chaleur dans les Corps Solides. [with:] Mémoire sur la Théorie Analytique de la Chaleur.
Paris: Imprimerie Royale, 1824. First edition.

Two rare offprints, one inscribed by François Arago and the other presented by Fourier to Arago, of memoires dealing with Fourier’s physical investigations on the diffusion of heat. Fourier’s famous book ‘Théorie Analytique de la Chaleur’ (1822) was an expansion of the mathematical section of his 1811 prize memoire; these two offprints were among those which he intended to expand into a book entitled ‘Théorie Physique de la Chaleur’ - but it was never achieved. The first of these two offprints is dated August 1824 (two years before it appeared in the Academy’s journal).

“Fourier’s achievements lie in the study of the diffusion of heat and in the mathematical techniques he introduced to further that study. … In 1807 he presented a long paper to the Academy on heat diffusion between disjoint masses and in special continuous bodies (rectangle, annulus, sphere, cylinder, prism), based on the diffusion equation ... (in three variables). Of the examiners, Laplace, Monge, and Lacroix were in favor of accepting his work, but Lagrange was strongly opposed to it—due, to some extent, to the Fourier series required to express the initial temperature distribution in certain of these bodies, which contradicted Lagrange’s own denigration of trigonometric series in his treatment of the vibrating string problem in the 1750’s. The paper was therefore never published.

A prize problem on heat diffusion was proposed [for the class of 1811], however, and Fourier sent in the revised version of his 1807 paper, together with a new analysis on heat diffusion in infinite bodies.

The last sections of the paper dealt with more physical aspects of heat, such as the intensity of radiation, and these became more important in Fourier’s thought during his later years. Fourier’s paper won the competition, but the jury—probably at the insistence of Lagrange—made criticisms on grounds of ‘rigor and generality,’ which Fourier considered an unjustified reproach. He expanded the mathematical parts of the paper into his book ‘Théorie analytique de la chaleur’. An extended treatment of the physical aspects was first planned for further chapters of this book and then for a separate book, ‘Théorie physique de la chaleur’, but it was never achieved.” (DSB, V:94-05).

Fourier’s book appeared in 1822 and when he was appointed permanent secretary of the Science Academy he also had his original 1811 prize memoire published in Academy’s journal. The 1811 memoire was published in two parts; 1st part (the mathematical section) as pp. 185-555 in volume 4 (for the years 1819-20) printed 1824 and 2nd part (physical section) as pp. 153-246 in volume 5 (for the years 1821-22) printed 1826.

The first paper offered here is a separately paginated offprint of the 2nd (physical) part of his 1811 prize memoire but with the imprint ‘De l’Imprimerie Royale. Août 1824.’ added to the final page (thus printed two years before the journal version). The first free end paper inscribed by Arago with the note ‘la première partie imprimée chez M. Didot serait le manuscrit couronné’.

The second paper offered here is a presentation offprint, inscribed by Fourier to Arago, of a memoire by Fourier in which he is concerned about “subjecting the two ends of a prism at temperatures entirely arbitrary expressed by two different functions of time, whether or not periodic.” The front wrapper inscribed by Fourier to Arago. The inscription of this offprint is large and bold, and when compared to the extreme shakiness of the inscription of the Haskell Norman copy of Fourier’s 1822 book, it seems to be from a relatively earlier date, e.g., before Fourier’s poor state of health (he died May 1830). This memoire is not dated but it seems likely from the inscription and the fact that it was found together with the first offered offprint (also from the library of Arago), which preceded the journal version with two years, that this offprint was also published prior to the journal version of it.

Offprints from the Academy’s memoires are rare; Fourier-presentations even more so.

Two offprints from ‘Mémoires de l'Académie des sciences de l'Institut de France’, vol. 5, pp.153-246 (for the years 1821-22, printed 1826); and vol. 8, pp.581-622 (for the year 1822, printed 1829). These offprints are separately paginated pp. 1-94; and pp. 1-42. The first offprint incudes one copper engraved plate. 4to: 275 x 215 mm. Uncut, sewn, in original plain blue wrappers.