The writings of various Chinese, Arabic and Icelandic authors show that they paid some attention to the tides, but the theories advanced are fantastic. The writings of the classical authors of antiquity contain but a few references to the tides, for the Greeks and Romans lived on the shores of an almost tideless sea.

Johannes Kepler in the early 17th century recognized the tendency of the water of the ocean to move toward the sun and the moon, but Galileo's explanation referred the phenomenon to the rotation and orbital motions of the earth. It was Isaac Newton who, in his Principia of 1687, laid the foundation of the modern theon the tides when he brought his generalization of universal gravitation to bear on the subject. He gave a geometrical construction for the tide-generating force, and calculated the magnitude of the solar equilibrium tide. He considered a canal encircling the earth and applied to each particle of water the laws which he had deduced for a satellite. He accounted for many of the general properties of the tides, such as the phenomenon of springs and neaps, priming and lagging, diurnal and elliptic inequalities. The only important factor which he did not mention is the dynamical effect of the earth's rotation. Newton's work was continued bv D Bernoulli, L. Euler and C. Maclaurin who adopted not only the theory of gravitation but also Newton's method of the superposition of two ellipsoids. In 1746 jean le Rond d'Alembert wrote a paper on atmospheric tides, but this work, like Maclaurin's, is chiefly remarkable for the importance of collateral points.

The theory of the tidal movements of an ocean was almost untouched when in 1773 Pierre Laplace first undertook the subject. In his Mécanique céleste he formulated the equation of continuity and the dynamical equations, and applied them to the case of an ocean covering the whole earth. He also established the principle of forced oscillations, which forms the foundation of the harmonic methods.

The connection between the tides and the movements of the moon and sun is so obvious that tidal predictions founded on empirical methods were regularly made and published long before mathematicians had devoted their attention to them. The best example of this kind of tide table was afforded by Moses Holden's tables for Liverpool, based on 20 years of personal observation by a harbour master named William Hutchinson. The use of automatic tide gauges appears to have begun about 1830.

The work of J. Lubbock, Sr. and W. Whewell is chiefly remarkable for the co-ordination and analysis of data at various ports, and for the construction of tide tables. Sir George Airy in his Tides and Waves of 1842 studied profoundly the theory of tidal motions in canals, while in 1848 and 1851 F. W. Beechey published the results of a survey of tidal currents over the Irish sea, the English channel and the North sea.

About 1863 W. Thomson (afterward Lord Kelvin) became interested in the problems presented by earth tides. In 1866 he took up the analysis of ordinary tidal observations and established the harmonic methods, which quickly developed. He introduced the rotation of the earth into the tidal dynamics of small seas, and in 1872 he designed a tide-predicting machine. His theory that the revolution of the earth's poles in a 16-ft. circle every 14 months caused small ocean tides was confirmed by computers in the 1950s.

In 1874 W. Ferrel ' of the U.S. coast and geodetic survey, published his Tidal Researches which included a harmonic development of the generating potential, and from the same year A. W. Baird, of the survey of India, organized a service of observation and harmonic analysis for Indian tides. In 1882 G. H. Darwin took up harmonic analysis and produced memoirs which for a long time formed the standard manual on the subject, and about this time J. E. Pillsbury, of the U.S. coast survey, began the observations of currents by means of current meters. In 1885 C. Börgen introduced new ideas into the methods of harmonic analysis. Between 1870 and 1890 F. A. Forel made illuminating studies of the seiches of Lake Geneva, Switz., and about 1890 M. Margules investigated the dynamics of atmospheric tides.

From 1894 to 1907 R. A. Harris, of the U.S. coast survey, published his Manual of Tides. This work contained charts showing cotidal lines for the whole world, based on theories and hypotheses the leading feature of which was the principle of resonance. It was assumed that in each ocean there exist regions capable of free oscillation with a period near one of the principal tidal periods, and that the nature of these free oscillations may be calculated approximately, without allowing for the earth's rotation or the interaction with neighbouring regions.

After 1900,a number of Scandinavian oceanographers, notably V. W. Ekman, 0. Pettersson and J. P. Jacobsen, invented current meters and L. Favé observed tidal elevations in the open sea by means of his self -registering instrument.

In 1912 A. Blondel applied the narrow sea theory, through the principle of least action, to the tides of the Red sea. From 1913 to 1920 R. Sterneck and A. Defant developed the narrow sea theory with special reference to the Adriatic sea. Defant applied this theory to the Red sea, the Persian gulf, the English channel and the Irish sea.

After about 1895 the dynamical theory of tides and seiches was much advanced by the mathematicians: H. Lamb, H. H. Hough, J. H. Poincar6, Lord Rayleigh, G. Chrystal, E. Fichot, G. R. Goldsbrough, G. I. Taylor, Harold Jeffreys, G. Bertrand, S. Goldstein and J. Proudman; between 1920 and the 1960s much was done on the analysis of observations by A. T. Doodson, K. Hessen and H. Rauschelbach.