E222  Theorie plus complette des machines qui sont mises en mouvement par la reaction de l'eau
(A more complete theory of machines which are activated by their reaction to water)
Summary:
(based on Clifford A. Truesdell's introduction to Opera Omnia Series II, Volume 12)
In this, as well, as in E259, Euler goes into the entire theory of his main idea of E179 in greater generality. He then proceeds to calculate the optimum proportions for his proposed turbine.
According to C. G. J. Jacobi, a treatise with approximately the same title was presented to the
Berlin Academy on September 13, 1753.
Publication:

Originally published in Mémoires de l'académie des sciences de Berlin 10, 1756, pp. 227295

Opera Omnia: Series 2, Volume 15, pp. 157  218
 According to Jacobi, the manuscript of the printed treatise can be found in
the archive of the Berlin Academy.
 Extract reprinted in Correspondance sur l’école polytechnique 3, 1814/16, p. 234 (Hachette)
[E222a]
Documents Available:
 Original publication: E222
 E222 can be viewed or downloaded from Digitalisierte Akademieschriften und Schriften zur Geschichte der Königlich Preußischen Akademie der Wissenschaften, which includes serial publications of the Prussian Academy of Science in the 18th and 19th Centuries.
 Ostwald's Klassiker No. 182 contains a German translation, c.f. E. Brauer, "Euler's Turbinentheorie," Jahresber deutsch. Math. ver. 17, 3947 (1908)
 The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E222 include:
 Maltese G., “On the relativity of motion in Leonhard Euler's science.” Archive for History of Exact Sciences, 54 (4), pp. 319348 (2000).
 Reynolds TS., “Scientific influences on technology  case of the overshot waterwheel, 17521754.” Technology and Culture, 20 (2), pp. 270295 (1979).
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