computed that that of Saturn would retard it 100 days; making together nearly a year and three quarters. And the event proved that these computations were very accurate.

185. Though comets are sensibly disturbed by the planets, we have not the same evidence, that the planets are ever sensibly disturbed by them ; probably owing to their being generally very small and rare bodies, consisting of very little solid substance. In 1454, the moon is said to have been eclipsed by a comet, which therefore must have been very near both to the moon and earth. Yet it produced no sensible effect on either of these bodies ; there being no perceptible deviation from their accustomed path round the sun. The comet of 1770 came so near the earth, that La Place computed, that its periodical time would be increased by the disturbing aetion of the earth something more than two days; and if its solid contents had equalled those of the earth, it was calculated that it would have retarded the earth's motion in her orbit, and thereby have lengthened our year, 2 hours and 48 minutes. It is certain that no such increase took place; and therefore the disturbing force of the comet on the earth was insensible. The same comet passed through the midst of Jupiter's satellites.

We have stated that in ancient times comets were looked upon with terror as harbingers of evil. Their appearance and disappearance were phenomena totally unaccountable, But when Newton had developed the laws of their motion, and had assigned them their true place in the Solar System, the superstitious fear of the ancients gave way to the philosophical fear of the moderns; a fear, which (for all that we can see) most ever harass the mind, wbich is not disposed to acknowledge a Supporter and Governor of the universe as well as a Maker of it. When it was ascertained, that a great number (none can tell how many) of these bodies were continually moving in all directions through the different regions of our planetary system, it was apprehended that some of them might meet the earth in its course, and thereby produce a shock,

which might be nearly or quite destructive to the human race. Imagination was let loose ; and most of the great physical evils, which our race are said to have suffered, and the most direful which they can look forward te, have been traced with ingenuity to comets. So that long after the law of their motions was well known and understood, the appearance of a comet excited juster (because more definite) fear in the breast of the philosopher, than in the ancient peasant. Nor is this fear yet removed. Astronomers, it is true, have calculated the chances of collision between the earth and a comet, and have found the chance greatly against such an event. But according to their calculation, there is a chance of such an event; and while this is admitted, there must be fear that it will take place. This fear probably pervades most people more or less; and while we are confined to philosophy, and philosophy develops no new laws of motion, it is unavoidable, and can be resisted and overcome only by a full belief, that there is a Divine Providence overruling and directing all, even the most minute operations, which are exhibited to us in the natural world. There can be no occasion for fear of any effects resulting from operations, which we acknowledge to be directed and governed by divine wisdoin, which sees the end from the beginning; and the design of which, we feel assured, is the welfare and happiness of

man.

Sect. IV.

Of the Spheroidal Figure of the Earth and

.other Planets. 186. It has been stated, that as a body moves faster, its tendency to move in a straight line is greater. Now if two bodies describe unequal circles in the same time, as in one day, the body which describes the largest circle must manifestly move faster, than the body which describes the least ; consequently, its continual tendency to move in a straight line is greater than that of the other. For example, (Pl. IX, fig. 3,) if a body at A describe the circle A a, in the same time that a body at B does the circle B b, the body at A must obviously move faster than that at B; and consequently

it tends, in every part of the circle, to move in a straight line more than that at B does.

187. Now the parallels of latitude (Pl. III, fig. 1) on the globe, are circles of different lengths. The equator is the greatest circle, and parallels diminish towards the poles. Hence those bodies, which lie on or near the equator, are carried by the earth’s rotation on its axis. through larger circles in a day, than bodies lying vear the poles. Whence it follows, that bodies near the equator have a greater tendency to move in, straight lines, and consequently to recede farther from the earth's centre, than bodies near the poles ; while at the poles this tendency entirely ceases.

188. Were the earth composed of a liquid, as water, it is 'hence plain what would be its form. By rotation on its axis, the parts about the equator would swell outward, while the regions about the poles would be somewhat depressed and flattened. It would take something of the form of a flat turnip, or of two saucers put together. Now, though the earth be not a fluid, yet it is not a perfectly solid mass. Its parts are not very difficult of separation. By daily rotation it has actually taken something of the form, which it would take were it a fluid. Its diameter through the equator is greater than through the poles by about 26 miles. As most, if not all the heavenly bodies turn on an axis, most, if not all, partake of the same form as the earth.

189. There is one striking fact resulting from this figure of the earth. Pendulums vibrate by the force of gravity. When propelled sideways, gravity carries a pendulum back; and in carrying it back, gives it such velocity as to carry it as far on the other side ; whence it returns, and is again carried to the other side, and so

As these vibrations are continued by the force of gravity, they must be quicker as the force of gravity is increased. For any body, propelled by a greater force,

must move quicker than when propelled by a less. Now all bodies on the earth's surface are drawn to its centre; and more powerfully, as the square of their distance is less. Hence, if one portion of the earth's surface be farther from its centre than another, the force organity on a pendulum in one place must be less than in anothier; and consequently the pendulum will vibrate slower in one place than in another. This is found to be actually the case. Pendulums vibrate faster towards the poles, and slowest at the equator. This effect is considerably augmented by the centrifugal force of the body being increased as it approaches the equator. For the same reasons, budies are heavier at the polēs than at the equator.

Pendulums of the same length vibrate in the same time, however different in weight. Short pendulums vibrate qcicker than long ones. Pendulums vibrating seconds at London, are 39.2 inches in length; but at the equator 39.1 inch nearly.

TABLE
Showing the proportion of the Polar to the Equatorial

Diameters of the Planets ; as far as known.
Earth

326 to 327
Mars

15

16 Jupiter

13 Saturn

32 35

12;

SECT. V.

Of the Precession of the Equinoxes. 190. It has been stated that there is a difference between a solar and siderial year. A solar

is

place before it completes its revolution, which is a siderial year. For example, (Pl. IX, fig. 1,) if the sun S, earth E, and a star be in the same straight line at an equinox, the earth revolving through d, will not be at E at the same equinox, but somewhere at e. Hence it must revolve farther, from e to E, before it completes its revolution ; and the time of doing this is the differ-. ence between a solar and siderial year, and amounts to about 20 minutes. The distance e E is about 50% of a degree annually, and constitutes what is called the

precession of the equinoxes.

191. The precession of the equinoxes is to be accounted for in much the same way that the retrograde motion of the moon's nodes is. " It has been stated, that the diameter of the earth at the equator is greater than through the poles. Suppose this excess of matter about the equator to be a ring round the earth, but separate from it, leaving the earth a perfect globe or spherè. Let Ab B c (Pl. IX, fig. 2,) be a circle in the plane of the ecliptic. Let ACB be half the ring we have supposed, lying above the ecliptic, and making an angle with it of 23. Now the effect of the sun's attraction on this ring is the same, during a year, whether we suppose the earth to move round the sun, or the sun to move round the earth. Let us then suppose the sun to move round the earth in the circle a SV. While the sun is moving from a through S to V, that is, during half the year, the sun acts successively on all the parts.of the ring from A through C to B. This action tends to draw the ring into the plane of the ecliptic; and the effect is such as to make it cut the ecliptic somewhere at x, and not at B, where it did before. So while the sun is going the other half of its orbit, it acts in the same manner on the other half of the ring ; and makes it cut the ecliptic somewhere at d instead of A. Thus the equinoxes are constantly