E268 -- Lettre de M. Euler à M. de la Grange

(Letter of Mr. Euler to Mr. de Lagrange)

Originally published with the full title: Lettre de M. Euler à M. de la Grange… Recherches dur la propogation des ébranlemens dans une (!) milieu élastique.

Summary:

(based on Clifford A. Truesdell's introduction to Opera Omnia Series II, Volume 12)

This is a thorough abstract of the second of Euler's two great memoirs on the theory of sound. It served to establish his priority in the "discovery and publication of the material description for the motion of a continuum, in which the initial coordinates X, Y, and Z of the particles are taken, along with time, as independent variables." He shows that the complete history of the motion of the continuum is given by the functional equations

x = f(X, Y, Z, t), y = g(X, Y, Z, t), z = h(X, Y, Z, t).

Publication:

Originally published in Melanges de philosophie et de la mathematique de la societe royale de Turin 2, 1762, pp. 1-10
Opera Omnia: Series 2, Volume 10, pp. 255 - 263
Reprinted in Opera Postuma 1, 1862, p. 561 (only the beginning and end) [E268a]
Reprinted in Oeuvres de Lagrange 14, Paris 1892, pp. 178-188 (complete, but with the incorrect date “1er juin 1760”) [E268b]

Documents Available:

Original publication (the Euler Archive would like to thank the Academy of Sciences of Torino for these images): E268

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