Abstract
118. Let there be a body DAd (Fig. 6.1) consisting of two equal and similar parts placed on either side of the axis AC, and which we consider for more convenience as a plane figure. Let us imagine that this body is placed on the surface of a fluid at rest, so that the axis AC is vertical and the immersed part KAN in the fluid is a little less weighty than an equal volume of fluid. We ask, What is the law of oscillation of bodies?
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Notes
- 1.
Johann Bernoulli, father of Daniel and his Opera Omnia.
- 2.
In the Mss.107, “and ignoring the resistance that comes from the inertia of the fluid parts”: And I ignore the resistance derived from the inertia of the parts of the fluid.”
- 3.
This is not weight, but a volume or a two-dimensional surface. The same is applied to the next time the term weight appears.
- 4.
There are some misprints corrected. Besides, the symbols b, N and Q are used with two meanings.
- 5.
The g now represents the gravity.
- 6.
- 7.
See Recherches sur la précession des Equinoxes, article 26 et seq. (Original note).
- 8.
According with the context of the entire article, it seems to refer to an angle P rotating with a velocity dP/dt.
- 9.
In the original the symbol Δ is used both for the body and fluid density. We have maintained Δ for the fluid and introduced δ for the body.
- 10.
In the original, the letter M is used both the body volume and the moment of inertia. We have maintained M for the volume and introduced J for the second. Also, the moment of inertia should be respect an axis perpendicular to the plane mentioned.
- 11.
These equations are derived from formulas found in my Recherches sur la précession des Equinoxes, for determining the rotation of a body animated. (Original note).
- 12.
In the next and subsequent formulas, the moment of inertia K is missing but we have included it.
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Simón Calero, J. (2018). Oscillations of a Body Floating in a Fluid. In: Calero, J. (eds) Jean Le Rond D'Alembert: A New Theory of the Resistance of Fluids. Studies in History and Philosophy of Science, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-68000-2_6
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