E331  De motu fluidorum a diverso caloris gradu oriundo
(On the motion of fluids arising from different degrees of heat)
Summary:
(based on Clifford A. Truesdell's introduction to Opera Omnia Series II, Volume 12)
In this paper, Euler corrects and works out the ideas that he first suggested in
E225. It contains the first
correct physical explanation of convection currents as the result of the slight
compressibility of a heavy fluid; it also has the first attempt at a mathematical treatment. Further,
it strongly suggests the theory of line integrals and Kelvin diaphragms. Euler also provides
a counterexample, a furncae, for the "now common cry that the theorist should keep abreast of the
latest experimental discoveries." Among the ideas that Euler considers in this paper are the following:
 the motion of a whole fluid mass induced by different degrees of heat rather than the "intestine
motion considered by many to constitute heat"
 the question: "Given a reentrant tube of any shape and amplitude, at whose several points
a certain degree of heat, quickly communicated to the water flowing by, is established; and if this tube is filled with water, which is first brought to rest by the insertion of a diaphragm at some
point; then when the diaphragm is removed, it is required to find the motion which is induced in the
water because of the different temperature of the heat."
He also considers the situation of a vessel with enough water in it with one part hotter and
argues that in this case, the water in the lower portion of the vessel will "continually rise
from the cold part to the hot, and contrariwise, in the higher portion will be carried down from the
hot part toward the cold." Euler spends the remainder of the paper analyzing this type of flow in
tubes.
a.s.
According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy
on January 19, 1764.
According to the records, it was presented to the Petersburg Academy on
August 23, 1764.
Publication:

Originally published in Novi Commentarii academiae scientiarum Petropolitanae 11, 1767, pp. 232267

Opera Omnia: Series 2, Volume 12, pp. 244  271
Documents Available:
 Original publication: E331
 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 E331 include:
 Askey R., “Chapter12 of Ramanujan 2nd notebook  continued fractions  appendix.” Rocky Mountain Journal of Mathematics, 15 (2), pp. 311318 (1985).
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