Theory of tides

“Among all the great men who have philosophized about this remarkable effect, I am more astonished at Kepler than at any other. Despite his open and acute mind, and though he has at his fingertips the motions attributed to the earth, he nevertheless lent his ear and his assent to the moon's dominion over the waters, to occult properties, and to such puerilities.”

“Astronomy teaches the correct use of the sun and the planets. These may be put on a frame of little sticks and turned round. This causes the tides.”

“This world was once a fluid haze of light,The planets: then the monster, then the man.”

“The theory of the tides has been reduced [in this work] into an extremely simple form, which appears to agree better with all the phenomena, than the more intricate calculations which they have commonly been supposed to require.”

“We shall describe cursorily the ordinary phænomena of tides.”

“We shall explain the Equilibrium-Theory of Tides, including the first tidal theory given by Newton, and the more detailed theory of his successors, especially Daniel Bernoulli.”

“We shall give a sketch of Laplace's investigations, (founded essentially on the theory of the motion of water,) in the general form in which he first attempted the theory, as well as with the arbitrary limitations which he found it necessary to use for practical application.”

“We shall give an extended Theory of Waves on water, applying principally to the motion of water in canals of small breadth, but with some indications of the process to be followed for the investigation of the motion of Waves in extended surfaces of water.”

“The results of a few Experiments on Waves will be given, in comparison with the preceding theory.”

“We shall investigate the mathematical expressions for the Disturbing Forces of the Sun and Moon which produce the Tides, and shall use them in combination with the theory of Waves to predict some of the laws of Tides.”

“We shall advert to the methods which been used, or which may advantageously be used, for Observation of Tides, and for the Reduction of the Observations.”

“We shall give the results of extensive observations of the Tides, as well with regard to the change of the phænomena of tides at different times in the same place, as with respect to the relation which the time and height of tide at one place bear to the time and height at other places, and shall compare these with the results of the preceding theories, as far as possible.”

“And as Conclusion, we shall point out what we consider to be the present Desiderata in the Theory and Observations of Tides.”

“[W]e are precluded from further advance, partly by our almost necessary ignorance of the forms of the bottom in deep seas, and partly by the imperfection of our mathematics. ...the first principles of our explanation are correct.”

“Newton pointed out and assigned generally, not only the nature and the magnitude of the periodical forces which are concerned in producing the tides, but likewise indicated their true character as undulations, in one very remarkable proposition, as well as in a special explanation of... the tides of the Port of Batsha. The equilibrium theory of Daniel Bernoulli adopted the first part of Newton's views but altogether neglected the second.”