The titles are not produced solely by the action of the moon. The sun has also a very considerable influence uponthe sea, but his distance is so great that he pro duces only a little more thanl of the effect. When the sun and moon are in conjunction or in opposition, and therefore exert their combined influence in raising the sea in the same direction, the tide is generally very high, and is called a spring tide. This effect is represented in Plate XLIV. Fig. 3, where the sun S, and the moon AL are drawing the waters of the earth ABCD. The effect produced by the single action of the moon is re presented by the spheroid c hgf,and the combined effect or the sun and moon by the spheroid EFGII. When the moon is in quadrature with the sun, the action of the one luminary diminishes the effect produced by the other. This is represented in Fig. 4, where cfghis the effect that would have been produced by the moon AI ; but as the attraction of the sun S tends to depress the waters at r and g, and to raise them at f and h, the com bined effect of the two luminaries will be EFGH. These tides are very small, and are called neap tides.
When the moon is in her perigee, the tides will evi dently be greater than when she is in any other part of her orbit ; and in like manner, the tides produced by the sun will be greatest in winter, when he is nearest the earth. If the moon, therefore, should be in perigee when she was either in conjunction or opposition, and when the sun was nearest the earth, the tides would then be extremely high. It appears, however, from observation, and from the theory of La Place, that the tides are highest at the time of the equinoxes, or rather a little after the autumnal equinox, and a little before the vernal equinox. When the moon is in perigee, therefore, at the time of her conjunction or opposition in February and March, or in September and October, the tides may be expected to be particularly great.
Since the tides depend chiefly upon the moon, and since it is high water at a certain time after the moon comes to the meridian, it must be high water 50 minutes later every day, as the moon is 50 minutes later every day in coining to the meridian, on account of her motion in her orbit from west to east.
As it has often been reckoned difficult for those un acquainted with physical astronomy, to understand why the water is raised on the side of the earth opposite to the moon, we shall endeavour to give a familiar expla nation of this difficulty. From a desire to give a popular illustration of this subject, the celebrated mathematician Mr Wallis, and after him Mr Ferguson, have been led into a considerable error in ascribing the rise of the sea on the side of the earth opposite to the moon, to the ex cess of the centrifugal force above the earth's attraction.
The moon, say these writers, moves round the common centre of gravity of the earth and moon, at•the distance of 6000 miles from that centre, and therefore the side of the earth opposite to the moon has a greater centrifu gal force than the side near it, while that side is less at tracted by the moon. The attraction of the earth, there fore, exceeding the centrifugal force of the nearest side of the moon, raises the waters, and the centrifugal force of the opposite side, being greater than the earth's at traction, raises the sea also on that side. It will be found, however, that the velocity of the farthest side of the moon is only 47 miles an hour, which is too small to create a centrifugal force capable of raising the waters of the ocean. The true cause of the rise of the sea may be understood from Plate XXXIX Fig. 7, where ABC is the earth, 0 the common centre of gravity of the earth and moon, round which the earth will revolve in the same manner as if it were acted upon by another body placed in that centre. Let AM, BN, CP, be the directions in which the points A, B, C, would move, if not acted upon by the central body, and let Bbn be the orbit into which the centre B of the earth is deflected from its tangential direction BN. Then since the waters at A are acted upon by a force as much less than that which influences the centre of the earth, as the square of OB is less than the square of OA, they cannot be deflected as much from their tangential direction AM, as the centre B of the earth ; that is, instead of describing the orbit Am, they will describe the orbit Aaf. In the same manner the waters at C being acted upon by a force as much greater than that which influences the center B of the earth, as the square of OB exceeds the square of OC, will he deflected farther from their tangential direction than the centre of the earth, and instead of describing the orbit CP, will describe the orbit Cci. The earth, therefore, will assume an oblate spheroidal form adce, so that the waters at c will rise towards the moon, and the waters at a will be left behind as it were, or will be less deflected than the other parts of the earth by the action of the moon, from that rectilineal direction in which all revolving bodies, if influenced only by a projec tile force, would naturally move. For farther informa tion on the tides, see Physical ASTRONOMY, Chap. xiii. p. 714 ; but particularly TIDES, where a full discussion of the subject may be expected. See also Robison's Elements of Mechanical Philosophy, vol. i. Ferguson's Lectures, vol. i. p. 50; vol. ii. p. 499. Ferguson's dstro =my, vol ii. containing the descrpition of a tide dial, and the references at the end of Physical ASTRONOMY.