HISTORY OF THE STUDY OF TIDES (23). The writings of various Chinese, Arabic and Icelandic authors show that they paid some attention to the tides, but the theories ad vanced 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.
Kepler (q.v.) recognized the tendency of the water of the ocean to move towards the sun and moon, but Galileo's explanation referred the phenomenon to the rotation and orbital motions of the earth. It was Newton (q.v.) who, in his Principia of 1687, laid the foundation of the modern theory of 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 ellip tic inequalities. The only important factor which he did not mention is the dynamical effect of the earth's rotation. Newton's work was con tinued by D. Bernoulli, I.. Euler and C. Maclaurin (qq.v.) who adopted not only the theory of gravitation but also Newton's method of the super position of two ellipsoids. In 1746 J. le R. 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 1774 Laplace first undertook the subject. In his Mecanique Celeste 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 connexion 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 Holden's tables for Liverpool, based on twenty years of personal observation by a harbour-master named Hutchinson. The use of automatic tide-gauges appears to have begun about 1830.
The work of J. Lubbock (Senior) and W. Whewell is chiefly remarkable for the co-ordination and analysis of data at various ports, and for the construction of tide-tables. Airy in his Tides and Waves of 1842 studied profoundly the theory of tidal motions in canals, while in 1847 and F. W. Beechy published the results of a survey of tidal currents over the Irish Sea, the English Channel and the North Sea (Phil. Trans.).
About 1863 W. Thomson (afterwards Lord Kelvin) became interested in the problems presented by earth-tides. In i866 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 the tide-predicting machine.
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 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 i885 C. Borgen introduced new ideas into the methods of harmonic analysis (see K. Hessen, Ann. der Hydrog. [1920]). Between 187o and 1890 F. A. Forel made illuminating studies of the seiches of Lake Geneva, and about 1890 M. Margules investigated the dynamics of atmospheric tides (Sitz. Ber. Akad. Wiss. Wien).