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The materials of the present investigation are five months’ tide observations made at Plymouth; three months observations made at Liverpool, under the direction of Captain Denham, R. N.; and twelve months’ observations made at Bristol, by Mr. Bunt, by means of his tide-gauge. According to the theory of the tides, the height of the surface of the water at a given place will increase as the sine, while the time increases as the arc. Hence if the time he made the abscissa, and the height the ordinate, the curve representing one tide would be thefigure of signs . The author on making the com­parison of the empirical curve of the rise and fall of the water, de­duced from observation, with this theoretical curve, finds a general agreement between them; subject to certain deviations, consisting principally in the empirical curve indicating that both the rise and the fall are not symmetrical, like the theoretical curve, in consequence of the fall being generally more rapid than the rise, and thus occasioning a displacement of the summit of the curve towards that branch of it which corresponds to the fall.

Researches on the tides. Twelfth series. On the laws of the rise and fall of the sea’s surface during each tide