crease or diminish the height or depression of the water occasioned by the lunar attraction. But, were every part of the Earth equally attracted by the heavenly bodies, no tide could be produced. The unequal attraction, or the attraction of one part of the terraqueous globe more forcibly than the other, may be considered as the true cause of the tides. The force of attraction in any body decreases, as the squares of the distances from that body increase. Hence the farther distant any body is from the centre of attraction, the less the operation on that body. The water, therefore, on the side of the Earth next to the Moon, is more forcibly attracted than the body of the Earth, and the body of the Earth than the water on the opposite side. Suppose three particles of matter, one on the surface of the Earth next to the Moon, one at the centre of the Earth, and one on the surface opposite to the Moon. By the laws of gravitation, the particle nearest to the Moon would be more attracted by her, than that at the centre, and that at the centre more attracted than the particle on the opposite side. By the unequal attractions, the distances between these particles would be increased. One would be elevated from the centre, and the centre particle would be drawn from that on the side opposite to the Moon, amounting to the same thing as if the opposite particle were elevated. For, when the distance between the centre of the Earth and a particle at the surface is increased, the particle will appear raised from the surface. We take notice of a tide, because the water rises on the adjacent land. This will be the case when the distance between the surface of the water and the centre of the Earth is increased, whether the water be elevated from the Earth, or the Earth be withdrawn from the water. No more

difficulty, therefore, arises in accounting for the tide on the side of the Earth opposite the Moon, than for that on the surface nearest to her, both being the effect of unequal attraction.

The points directly under and opposite to the Moon,

may be considered as the centres of highest elevation ; and 90° from these, or half the distance between them, as the circle of low water. This extends wholly round the Earth, and moves as the Moon moves.

Let NE OE be the Earth, (Plate vi. Fig. 3,) C the centre; M the Moon; N the point on the Earth's surface next to the Moon; O a point on the opposite surface; E E the circle of low water. The attraction

of the Moon, M, being unequal at the different parts, from the circle E E, the water on the side next to the Moon is more attracted than the centre, C, where the solid body of the Earth may be considered as concentrated; and the centre, C, more attracted than the water on the opposite side. The water, therefore, will rise at N, increasing the distance from the centre, C. On the same principle, C, the centre, and with it the mass of the Earth, will be attracted from the surface at O, enlarging the distance, and leaving the water, which, being farther from the centre, is higher to the observer; high and low, in respect to the Earth, always relating to the distance from the centre.

Some have accounted for the tide on the side of the Earth opposite to the Moon, by the motion of the Earth and Moon round a common centre.) In the revolution of these bodies, the side of the Earth farthest distant from the Moon must have a swifter motion than the side nearest to her. The water, endeavoring to escape, must rise towards the highest part, the point opposite to the Moon. Some effect may be attributed to this; but, without doubt, the unequal attraction is the principal cause.

The tides, travelling as the Moon travels, have her declination) and the declination opposite. As the Moon revolves round the Earth, they revolve, following her in her perpetual motion. Below the polar circles, therefore, every place, in its diurnal rotation, must have two tides in about 24 h. 50 m. 28 s.

When the Moon is in the equator, the circle of low

water, 90°) distant, must extend from pole to pole. Every place, from the equator to the poles, must have its regular return of tides; and these, uninfluenced by extraneous causes, must return at equal intervals.

As the Moon moves from the equator towards either tropic the circle of low water recedes from the poles towards the polar circles, arriving at these when she arrives at the tropics. (Plate vi. Fig. 4 and 5.)

This departure of the Moon from the equator must make flood tide at the poles, increasing as her declination increases, and highest when she is farthest distant from the equator. On her return, the tides ebb at the poles; where it becomes low water, when she arrives at the equinoctial. In a revolution of the Moon, therefore, two tides only occur at the poles, full sea returning at intervals of about 133 days. During the interval in which the circle of low water is distant from the poles, places in any parallel, touching (the highest point of that circle, have but one tide, in a revolution from the Moon round to the Moon again. Places between that circle and the poles, in the same time, have but one, and that a partial tide; while all below its highest point have two tides in succession.

At the equator, the intervals between high and low water, or between a tide and a succeeding tide, remain equal, whatever may be the declination of the Moon. When she is in the equator, the tides return at equal intervals in all latitudes. But when she is in any degree of declination, places on each side of the equator, cutting the circle of low water in their diurnal rotation, or which are below the highest point of ebb tide, have unequal duration of ebb and flood, or of time between high and low water in different parts of the lunar day; the farther distant from the equator, the more unequal the returns.

The Moon being in her north declination, places in the northern hemisphere have their highest tides when she is above the horizon, (Plate vi. Fig. 5 ;) but when

she is in south declination, the opposite tides the highest. (Plate vi. Fig. 4.) In the southern hemisphere, the whole is reversed.

The tide, as raised by the Moon, is greater on the side of the Earth next to her, than that on the opposite side. The cause of this is apparent. For, as she is nearer to that side, the semi-diameter of the Earth bears the greater proportion to the shorter distance.

For convenience of explication, the highest tides have been considered directly under and opposite the Moon. It is, however, learned from observation, that the tide is not at its greatest height above or below the horizon, till after the Moon has passed the meridian ; because the water, having obtained a direction, continues that direction after the Moon has passed, till prevented by external force. Similar occurrences are common. The heat of the day is most intense after the Sun has passed the meridian; and the extreme of summer heat is generally not till some time after the summer solstice.

The tides are in some measure altered by the inclination of the Moon's orbit to the plane of the ecliptic. Hence the highest elevation of water may at times be more than 50 above the tropics; and the region of single tide reduced as much below the polar circles.

The tides, as we have seen, are affected by the influence of the Sun. The attraction of the Sun is more powerful at the Earth than that of the Moon, but has less effect in raising tides. The immense distance of the Sun from the Earth, causes his attraction on the different parts to be nearly equal; the semi-diameter of the Earth bearing but a very small proportion to this immense distance. The influence of the Sun causes the tides to be earlier in the first and third quarters of the Moon; later in her second and fourth. In the former case, the tide of the Moon is preceded by that of the Sun; in the latter, it is succeeded and retarded by the elevation of water raised by the Sun. The

highest tides are denominated spring tides. These happen at the conjunctions and oppositions of the Sun and Moon or at the changes and fulls. (Plate vi. Fig. 6.) Neap tides, so called, are the lowest. These are at the quadratures, or when the Moon is in her quarters. (Plate vi. Fig. 7.) The tides happening at the change and full, about the equinoxes, are higher than those of other seasons. Both luminaries, being then in the equator, have a greater influence upon the Earth, in respect to tides, than at other seasons. The equatorial diameter of the Earth being longer than any other, the attraction of the Moon and Sun on the different parts of the Earth is most disproportioned, when they are in the plane of the equator, or in the direction of that diameter. But the principal cause of unusual height in these tides, is, the centre of elevation in the water is at the equator, where the diurnal motion of the Earth is the greatest; and the tides, extending from pole to pole, are met directly by every part of the Earth's surface, in its diur

nal rotation.

The Moon produces a higher tide when she is in perigee than when she is in apogee. The Sun also, being nearest to the Earth in winter, has his greatest influence on the tides at that season. The highest tides known are those happening/a little before the vernal equinox, and a little after the autumnal equinox, when the Moon is in perigee; there being then a concurrence of all the causes which operate in the production of tides.

Small seas, unconnected with the ocean and lakes, have not sufficient extent of water for perceptible tides. The Baltic and the Mediterranean communicate with the ocean; but are too small in themselves, and have straits too narrow to admit an influx of water sufficient for tides of any considerable height.

The regular return of the tides, according to the motions of the Moon, is greatly interrupted. Incidents external vary the height of the tides, and the time of