Two important contributions by two of the foremost theorists of the day. Fourier’s treatise Théorie analytique de la chaleur appeared in 1822, but he published several further papers on the subject, including this present paper which appeared only a year before his death in 1830. Poisson produced a series of works in which he developped the basic equations of elastic theory, to which his ‘Mémoire’ is a contribution. This volume also contains articles by Cauchy, Fourier’s overview of the mathematical work of the Académie, and his ‘Éloge historique de M. Charles’ i.e. Jacques-Alexandre-César Charles, the balloonist and inventor.