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days, when either cause, taken singly, would make an agree ment between them. The sun and clock, therefore, are together, only when the two causes balance each other; that is, when one cause so counteracts the other, as to make a mutual agreement between them. This effect is produced four times in the year; namely, on the 15th of April, 15th of June, 31st of August, and 24th of December. On thesc days, the sun, and a clock keeping exact time, coincide, and on no others. The greatest difference between the sun and clock, or between the apparent and mean time, is 16 minutes, which takes place about the 1st of November.

PRECESSION OF THE EQUINOXES.

845. A tropical year is the time it takes the sun to pass from one equinox, or tropic, to the same tropic, or equinox, again.

846. A siderial year is the time it takes the sun to perform his apparent annual revolution, from a fixed star, to the same fixed star again.

Now it has been found that these two complete revolutions are not finished in exactly the same time, but that it takes the sun about 20 minutes longer to complete his apparent revolution in respect to the star, than it does in respect to the equinox, and hence the siderial year is about 20 minutes longer than the tropical year. The revolution of the earth from equinox to equinox, again, therefore, precedes its complete revolution in the ecliptic by about 20 minutes, for the absolute revolution of the earth is measured by its return to the fixed star, and not by the return of the sun to the same equinoctial point. This apparent falling back of the equinoctial point, so as to make the time when it meets the sun precede the time when the earth makes its complete revolution in respect to the star, is called the precession of the equinoxes.

The distance which the sun thus gains upon the fixed star, or the difference between the sun and star, when the

The inclination of the earth's axis would make the sun and clock agree four times in the year, and the form of the earth's orbit would make them agree twice in the year; now show the reason why they do not agree from these causes, on the above mentioned days, and why they do agree on other days. On what days do the sun and clock agree? What is a tropical year? What is a siderial year? What is the difference in the time which it takes the sun to complete nis revolution in respect to a star, and in respect to the equinox? Explain what is meant by the precession of the equinoxes.

sun has arrived at the equinoctial point, amounts to 50 seconds of a degree, thus making the equinoctial point recede 50 seconds of a degree, (when measured by the signs of the zodiac,) westward, every year, contrary to the sun's annual progressive motion in the ecliptic.

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To illustrate this by a figure, suppose S, fig. 215, to be the sun, E the earth, and o a fixed star, all in a straight line with respect to each other. Let it be supposed that this opposition takes place on the 21st of March, at the vernal equinox, and that at that time the earth is exactly between the sun and the star. Now when the earth has performed a complete revolution around its orbit b, a, as measured by the star, she will arrive at precisely the same point where she now is. But it is found that when the earth comes to the same equinoctial point, the next year, she has not gone her complete revolution in respect to the star; the equinoctial point having fallen back with respect to the star, during the year, from E to e, so that the earth, after having completed her revolution, in respect to the equinox, has yet to pass the space from e to E, to complete her revolution in respect to the star.

The space from E to e, being 50 seconds of a degree, and the equinoctial point falling this space every year short of the place where the sun and this point agreed the year before, it is obvious, that on the next revolution of the earth,

How many seconds of a degree does the equinox recede every year, when the sun's place is compared with a star? How does fig. 215 ilrustrate the precession of the equinoxes? Explain fig. 215, and show from what points the equinoxes fall back from year to year.

that a pendulum, which vibrates seconds at the equator, has its number of vibrations increased, when it is carried towards the poles; and as its number of vibrations depends upon its length, a clock which keeps accurate time at the equator, must have its pendulum lengthened at the poles. And so, on the contrary, a clock going correctly at, or near the poles, must have its pendulum shortened, to keep exact time at the equator. Hence the force of gravity is greatest at the poles, and least at the equator.

The manner in which the figure of the earth dif fers from that of a sphere, is represented by fig. 212, where n is the north pole, and s the south pole, the line from one of these points to the other, being the axis of the earth, and the line crossing this, the equator. It will be seen by this figure, that the surface of the earth, at the poles, is nearer its centre, than the surface at the equa

Fig. 212.
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tor. The actual difference between the polar and equatorial diameters is in the proportion of 300 to 301. The earth is herefore called an oblate spheroid, the word oblate signifying the reverse of oblong, or shorter in one direction than in another.

834. The compression of the earth at the poles, and the consequent accumulation of matter at the equator, is probably the effect of its diurnal revolution, while it was in a soft or plastic state. If a ball of soft clay, or putty, be made to revolve rapidly, by means of a stick passed through its centre, as an axis, it will swell out in the middle, or equator, and be depressed at the poles, assuming the precise figure of the earth. This figure is the natural and obvious conse quence of the centrifugal force, which operates to throw the matter off, in proportion to its distance from the axis of motion, and the rapidity with which the ball is made to revolve.

In what proportion is the polar less than the equatorial diameter" What is the earth called, in reference to this figure? How is it supposed that it came to have this form? How is the form of the earth illustrated by experiment? Explain the reason why a plastic ball will swell at the equator, when made to revolve.

The parts about the equator would therefore tend to fly off, and leave the other parts, in consequence of the centrifugal force, while those about the poles, being near the centre of motion, would receive a much smaller impulse. Consequently, the ball would swell, or bulge out at the equator, which would produce a corresponding depression at the poles.

The

835. The weight of a body at the poles is found to be greater than at the equator, not only because the poles are nearer the centre of the earth than the equator, but because the centrifugal force there tends to lessen its gravity. wheels of machines, which revolve with the greatest rapidity, are made in the strongest manner, otherwise they will fly in pieces, the centrifugal force not only overcoming the gravity, but the cohesion of their parts.

836. It has been found, by calculation, that if the earth turned over once in 84 minutes and 43 seconds, the centrifugal force at the equator would be equal to the power of gravity there, and that bodies would entirely lose their weight. If the earth revolved more rapidly than this, all the buildings, rocks, mountains, and men, at the equator, would not only lose their weight, but would fly away, and leave the earth.

SOLAR AND SIDERIAL TIME.

836. The stars appear to go round the earth in 23 hours, 56 minutes, and 4 seconds, while the sun appears to perform the same revolution in 24 hours, so that the stars gain 3 minutes and 56 seconds upon the sun every day. In a year, this amounts to a day, or to the time taken by the earth to perform one diurnal revolution. It therefore happens, that when time is measured by the stars, there are 366 days in the year, or 366 diurnal revolutions of the earth; while, if measured by the sun from one meridian to another, there are only 365 whole days in the year. The former are called the siderial, and the latter solar days.

To account for this difference, we must remember that the earth, while she performs her daily revolutions, is constantly advancing in her orbit, and that, therefore, at 12

What two causes render the weights of bodies less at the equator than at the poles? What would be the consequence on the weights of bodies at the equator, did the earth turn over once in 84 minutes and 43 seconda? The stars appear to move round the earth in less time than the sun, what does the difference amount to in a year? What is the year measured by a star called? What is that measured by the sun called ?

o'clock to-day she is not precisely at the same place in respect to the sun, that she was at 12 o'clock yesterday, or will be to-morrow. But the fixed stars are at such an amazing distance from us, that the earth's orbit, in respect to them, is but a point; and, therefore, as the earth's diurnal motion is perfectly uniform, she revolves from any given star to the same star again, in exactly the same period of absolute time. The orbit of the earth, were it a solid mass, instead of an imaginary circle, would have no appreciable length or breadth, when seen from a fixed star, and therefore, whether the earth performed her diurnal revolutions at a particular station, or while passing round in her orbit, would make no appreciable difference with respect to the star. Hence the same star, at every complete daily revolution of the earth, appears precisely in the same direction at all seasons of the year. The moon, for instance, would appear at exactly the same point, to a person who walks round a circle of a hundred yards in diameter, and for the same reason a star ap pears in the same direction from all parts of the earth's or bit, though 190 millions of miles in diameter.

838. If the earth had only a diurnal motion, her revolu tion, in respect to the sun, would coincide exactly with the same revolution in respect to the stars; but while she is making one revolution on her axis towards the east, she ad vances in the same direction about one degree in her orbit, so that to bring the same meridian towards the sun, she must make a little more than one entire revolution.

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How is the difference in time between the solar and siderial year accounted for? The earth's orbit is but a point, in reference to a star; how is this illustrated?

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