English Title

A physical inquiry into the cause of the ebb and flow of the sea


Leonhard Euler

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Content Summary

In this essay, Euler explains the tides based on the Newtonian principle of universal gravitation. He first reviews the various explanations of tides that have already been proposed, making criticisms along the way; in particular, he claims to have refuted Galileo's theory that the tides are the result of a combination of the diurnal and annual motions of the Earth since this theory is unable to produce the motion of the reciprocation of the seas. Euler goes on to calculate the magnitudes of the tide-generating forces and arrives at the following conclusions: (1) the lunar tide is greater than the solar tide; (2) a sphere is attracted as if its entire mass is concentrated at its center. He also determines the equilibrium figure of the ocean that the disturbing forces tend toward at all times. It is in this exploration that Euler comes across his principal contribution to the theory of tides: the inclination of the water's surface depends only on the horizontal component of the disturbing force. Here are some other accomplishments from this work: (3) Euler tabulates the height of the tide for several regions; (4) he shows that the force of the moon is four times that of the sun; (5) he calculates the rate of change of the disturbing forces as the luminaries move toward or away from the horizon; he gives the moon's hour angle at the time of high water in terms of the angular separation of the sun and moon. In the end, Euler brings together the explanations of the principal phenomena of the tides in open oceans and near islands, arranges them systematically, and compares them with observations. (Based on Eric Aiton's introduction to Opera Omnia Series II, Volume 31, and Clifford Truesdell's introduction to Opera Omnia Series II, Volume 12.)

Published as

Paris prize article

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Original Source Citation

Pièce qui ont remporté le prix de l'académie royale des sciences, Volume 1740, pp. 235-350.

Opera Omnia Citation

Series 2, Volume 31, pp.19-124.

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Mathematics Commons