"The Academy of Sciences at Paris proposed The Tides as the subject for a prize essay in 1740. Four essays were published in consequence at Paris. One essay was by a Jesuit named Cavallieri; this adopted the Cartesian system of vortices. The other essays were by Daniel Bernoulli, Maclaurin, and Euler; these are reprinted in the Jesuits' edition of the Principia, and it is stated that many errors in the original impression have been corrected. ...The second chapter of Daniel Bernoulli's essay contains some lemmas relating to the Attraction of Bodies. ...he determines the attraction at any superficial or internal point of an ellipsoid of revolution which is nearly spherical, neglecting powers of the ellipticity beyond the first. The method used consists in finding accurately the attraction of a sphere, and then approximately the attraction of the difference between the sphere and the ellipsoid on a particle at the pole or at the equator... this method had been previously used by Clairaut. But Daniel Bernoulli seems to claim the method as his own... Although Daniel Bernoulli employed attraction for the purpose of his essay, yet he seems to have had but a weak faith in the principle... Daniel Bernoulli added nothing to our subject; all his results respecting Attraction are included in the formulæ given by Clairaut in 1737. But his theory of the Tides is very important in the history of that subject..."