strict law of gravitation, it would be flattened at the poles and elevated at the equator. By theory alone, Newton found that the polar diameter should be 1-230th shorter than the other; and actual measurement, and subsequent corrections, have fixed the proportion at 230 the polar, and 231 the equatorial. In consequence of this, the degrees of latitude, as measured by celestial observation, are longer near the poles than near the equator; because the surface is flatter, and the more flat any surface is, the more of it must be passed over, in order to produce the same angular change in the situation of a distant body. Similar effects are produced by the same cause, in the other planets.

SECTION VI.

MUTUAL EFFECT OF A PRIMARY AND SECONDARY-TIDES.

The influence which the primary planets exert upon each other, affects only their general motions, and these only to a very limited extent; but the influence of the secondaries, upon the fluid parts of their primaries, as far as we can judge of it from the influence of the moon upon the earth, is much more remarkable. As far as observation has extended, there is every reason to believe that all, at least, of the primary planets, are not only surrounded by fluid atmospheres, but have their surfaces partly occupied by liquids. Analogy would lead us to conclude, that there is a wonderful similarity in the economy of all the planetary surfaces, and that the variations which take place in their phenomena, are not differences in kind, but merely variations in degree. They move round the same centre,-they are retained in their orbits by the same force of gravitation,-they are lighted and warmed from the same source,-they have the same alternations of day and night, and the same changes of seasons; and therefore we may, without any violence to probability, conclude, that their seas, like ours, have their ebbings and their flowings,-that their lands, like ours, are refreshed by rains and watered by rivers,—that their winters, like ours, are chilled by frosts, and their summers, like ours, warmed by sunshine,-that their atmosphere, like ours, is tranquil with calms, and agitated by storms, and that, as is the case with the earth, the land, the sea, and the air, with theirs teem with life and enjoyment.

The air or atmosphere, with which the earth is surrounded, and the ocean, by which the greater part of its surface is covered, are both subject to the laws of gravitation; and as the parts, of which they are made up, do not adhere, or stick together, like those of solid substances, they always dispose themselves in exact conformity with the laws of gravitation, unless where they are restrained by some perceptible cause. The atmosphere diffuses itself everywhere, and if we attempt to exclude it, it presses upon every square inch of surface with a force of about sixteen pounds,the rivers run to the sea,-the sea, where not agitated by storms, rounds

itself to the mean curvature of the earth; and all this is the immediate effect of gravitation toward the earth, directly as the quantity of matter, and inversely as the square of the distance. As we ascend into the atmosphere, farther away from the centre of the earth, the pressure of the air becomes less, -as we dive into the ocean, nearer to the centre of the earth, the pressure of the water becomes greater; and the variation agrees so nearly with the law of gravitation, that from the alteration of the pressure we can tell the height or the depth.

But gravitation is universal; and, therefore,' all the particles of matter in the air and ocean must be drawn toward the celestial bodies-the sun or the moon for instance-with forces varying nearly as the squares of the distances; and though the forces with which they are thus drawn be not intense enough for detaching any part, either of the sea or the air, away from the earth's surface, yet, by altering the relative gravitation toward the earth, it must alter the form both of the atmosphere and the ocean. Those alterations are called TIDES.

As the atmosphere itself is invisible, the tides produced in it cannot be subjected to direct observation; but still it is matter of common remark, that changes in the weather take place most frequently at the times of new and full moon, the times at which the tides of the ocean are most conspicuous; and from this it is inferred, that the atmospheric tides, which we cannot see, are produced by the same force, and regulated by the same laws, as those tides of the ocean with which every one visiting its shores is perfectly familiar.

All the planets in the system, except the sun and moon, are too small and remote for producing any tide; but a tide is produced by the first of those luminaries in consequence of its great bulk, and by the second, in consequence of its small distance.

Though the whole gravitating force toward the sun be much greater than that toward the moon, yet its effect in producing tides is less; because the tide does not depend upon the whole gravitation, but upon its difference at different places. Half the diameter of the earth, or 4000 miles, is 1-60th of the mean distance of the moon; and, therefore, the tendency toward the moon, at those parts at which the moon is in the zenith, will be to that where the moon is 90° from the zenith as 60 × 60: 59 × 59, that is, as 3600 3481, or 36 to 35 nearly; that is, about 1-35th greater. 4000 miles is a very small fraction of 95,000,000, the sun's mean distance, and thus the difference of gravitation where the sun is vertical and where it is 90° distant from the zenith, is only about 1-11986th of the mean gravitation toward the sun. The entire calculation is too long for pursuing, in a work of so limited dimensions as this; but the result is, that the disturbing force of the moon, where greatest, is about three times that of the sun, and when least, about twice; so that the mean is 5 to 2; that is to say, if the

mean effect of the moon can raise a tide of five feet, that of the sun will raise a tide of two feet.

To understand easily the way in which the tides are produced, we must suppose that the earth is covered with a uniform depth of water, and we must consider the effects of the two luminaries separately.

Now, at the point where the luminary is vertical, the whole of its influence will be directly opposed to terrestrial gravitation, while, at the circumference of that hemisphere, of which this point is the pole, terrestrial gravitation will act at right angles to the influence of the luminary, and, consequently, its tendency to diminish the terrestrial gravitation will be less than at the point where the luminary is vertical. But the directions of the two forces (which act in the same direction at the centre of the hemisphere, over which the luminary is vertical) become gradually more and more different from that centre to the circumference; and thus the force by which the gravitation toward the earth is diminished, gradually decreases, and the gravitation increases, till, at the circumference of the hemisphere, the influence of the luminary is the least, and consequently the gravitation toward the earth is the greatest possible. The water is, in consequence, elevated in the centre of the hemisphere, and depressed at the circumference. But as the two hemispheres must always balance each other, not only in their whole masses, but in those parts which have the same relative situation, it follows that whatever shape is assumed by the one over the centre of which the celestial body is, must be assumed by the other, and that the waters must put on the form of an elongated, or egg-shaped, spheroid, having its longest diameter pointed directly to the celestial body. As the earth turns round upon its axis, the two prominent parts, or places of high-water, with the circle of low-water midway between them, turn round the earth in the opposite direction ;-that is to say, as the earth turns round from west to east, the motion of the tides must be from east to west.

With reference to the earth, the sun is quite stationary, and, therefore, the motion of the tide produced by the sun must be the same as the apparent motion of the sun, or the real motion of the earth; but as the moon revolves round the earth in about 29 days, in the same direction with the earth's motion on its axis, the motion of the lunar tide must be slower than that of the solar tide by about 50 minutes each day,-that is, from high-water to high-water again, or from low-water to low-water again, will be 12 hours 25 minutes in the lunar tide, and 12 hours exactly in the solar.

These tides will, therefore, sometimes happen at the same hour, and sometimes they will happen at different hours. When they happen at the same time, their effects in raising the water at the two places of high water, and in depressing it at the circle of low-water, will be united, and the high-water will in consequence be raised, and the low depressed, These are called,

E

The way in which the spring tide is produced may be understood by barely inspecting this figure.

Let the unshaded circle, XII. VI. XII. VI. represent the solid or centrical part of the earth, and the shaded portion, H, L, H, L, the circle with which that nucleus is surrounded, and in which the tides are produced. Let S represent the sun, and M the moon; and let the oval of the least eccentricity, of which a portion is left unshaded at L and L, represent the form which the surface of the water would assume, if acted upon by the lunar tide only; and let the flattened oval, which is wholly shaded, represent the entire spring tide, as produced by both luminaries ;—the shaded spaces between the ovals, at H and H, representing the increase of high-water, and the white spaces at L and L, the depression at low-water, produced by the sun.

[In this figure no regard is paid either to the comparative magnitudes or the distances of the three bodies; because, had that been done, the figure representing the earth would have been so small, that nothing could have been explained by it.]

The line, XII. XII. represents a meridian. The right-hand XII. nearest the figure S, is the upper twelve o'clock, or mid-day; and the left-hand XII. is midnight. The motion of the earth is from the right-hand by the top, left-hand, and bottom, to the right-hand again, every twenty-four hours. The upper VI. being six o'clock in the evening, and the lower, six o'clock in the morning. The intermediate dots upon the circle represent the intermediate hours.

From this figure it is evident that when the moon has the situation either of the right-hand M, or of the left-hand M, both high waters, from both luminaries must happen at twelve o'clock. But the right-hand M is the situation at new moon-the moon being upon the same meridian with the

sun-and the left-hand M is the situation of full moon, the moon being on the meridian opposite to the sun. Therefore, spring tides happen at every new moon, and at every full moon to the same extent, generally speaking, and from the same causes; but they can happen at no other time of the month, because at no other time are the two luminaries either upon the same meridian, or upon opposite meridians.

Neap tides are produced when the action of the one luminary is opposed to that of the other; and a bare inspection of the above figure will show that this must be the case when the moon is at the end of the first and the third quarter of its revolution. For, at those times, while the high-water produced by the sun is at XII. and XII. as before; that produced by the moon will be at VI. and VI.; and though the total high-water will still follow the moon, in consequence of the disturbing force of that luminary being greatest, the sun's influence will cause a depression of the high-water at H and H, equal to the white space between the two ovals, and an elevation of the low-water at L and L, equal to the shaded space between the two ovals there.

It was already stated that the comparative disturbing influences are, 5 for the moon, and 2 for the sun, the height of the spring tide will, therefore, be to that of the neap tide as 7 to 8,