SECTION VIII.

THE TIDES.

81. ONE more effect arising from the connexion between the three bodies-the sun, moon, and earth-remains to be treated of before we dismiss them from our consideration.

The TIDES are certain movements produced in the waters, which in part surround the earth, by the attraction of the sun and moon on them.

In fig. 45, Plate VI., let z represent the moon, R the earth. Now the moon attracts every particle of the earth; and the water, being free to move, will tend towards her at o: it will be high tide, therefore, to those places situated at o and its neighbourhood, which have the moon on the meridian: but since the quantity of water remains the same, the places at n and s, 90° distant from o, will supply the rise at p; with them therefore, and down the line n Rs, it will be low water.

As the earth turns round with her diurnal motion, other places will advance towards the moon, or will have her in the meridian; it will therefore be high tide to them at that time. So far the matter is clear; but the peculiarity is, that when it is high tide at o, it will also be high at q, diametrically opposite, or with those places on whose inferior meridian the moon is situated.

82. To render our explanation of this fact more lucid, let us investigate the operation of attraction on three bodies, at different distances from the attractive body. (Fig. 12.)

The effect of a body, Y, operating on three others,

r, z, x, in the same line, would be to increase their mutual distances; for r would be drawn to w, through the

space rw; z being further off from Y, would be drawn through a less space, in the proportion of yr2: Y22 (§ 158)-viz. to v, zv being less than rw; x would be still less operated upon, and would pass through a less space towards the attracting body, viz. x t. The result will be, that the distances of the two bodies r and x from z will be increased; vw and vt, their new distances, being greater than zr and zx, their original distances.

83. Let the waters on either side of the earth R, in fig. 45, Pl. VI., be considered in the same circumstances as the two bodies x and r with respect to z in fig 12. The operation of the attraction of the moon z upon them and the earth will be to raise the waters at p, and to draw the earth, as it were, away from the waters at r, causing a simultaneous rising of the tides at o and q.

84. Not only is the moon an agent in producing tides, but the sun also in consequence, however, of his greater distance, his attraction is not so much felt; the whole force of attraction being in compound proportion of the mass directly, and the distance squared inversely (§ 158). The force of attraction thus deduced will give the sun's attraction: the moon's :: 2 : 5.

85. The operation, then, of the sun and the moon will produce two sets of tides every twenty-four hours,

as each body arrives at the superior and inferior meridian of any place; in other words, as the earth revolves, every part of the earth in succession, as it comes under these bodies, or has them in the meridian, or diametrically opposite, that is, both at o and q, will have high tide; while those down the line n Rs, and on the other side of the earth opposite, will have low water. It is found, however, that those two separate tides appear as one in general; when, however, these bodies are in conjunction or opposition to each other, certain phenomena occur, which are called spring and neap tides.

86. Let E in fig. 48, Plate VI., be the earth, м the moon in one of her quadratures, 90° distance from the sun, that is, when she is half full. In this case the moon will cause the waters to rise at z and y, while the sun will produce the same effect at r and q, but in a less degree; the quantity of water being always the same, the rise at z, under the moon's influence, will only be as much as her attraction exceeds that of the sun, that is, 5-2, or 3.

At new and at full moon, however, when the moon is at P, in opposition, or at Q, in conjunction with the sun, their attractions will both combine to cause the waters to rise at z and y; or the force exerted by the joint attractions will be 5+2, or 7. In the former case neap tides occur, when the water is neither very high nor very low at any place; in the latter, spring tides, when they rise much above the mean height at ≈ and y, and sink proportionally low down the line r G q.

87. The largest diameter of the spheroid formed by the elevation of the water, zy, will follow the moon in her motion round the earth. Now, as the moon ad