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 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. The wheels of machines, which revolve with the greatest rapidity, are made in the strongest manner, otherwise they will fly in pieces, the centrfugal force not only overcoming the gravity, but the cohesion of their parts.

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.

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 the 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 o'clock today, she is not precisely at the same place in respect to the

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 seconds? 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?

sun, that she was at 12 o'clock yesterday, or will be to-mor. row. 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 appears in the same direction from all parts of the earth's orbit, though 190 millions of miles in diameter.

If the earth had only a diurnal motion, her revolution, 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 advances 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.

B

A

Fig. 202.

S

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?

To make this plain, suppose the sun, s, fig. 202, to be exactly on a meridian line marked at e, on the earth A, on a given day. On the next day, the earth, instead of being at A, as on the day before, advances in its orbit to B, and in the mean time having completed her revolution, in respect to a star, the same meridian line is not brought under the sun, as on the day before, but falls short of it as at e, so that the earth has to perform more than a revolution, by the distance from e to o, in order to bring the same meridian again under the sun. So on the next day, when the earth is at C, she must again complete more than two revolutions, since leaving A, by the space frome to o, before it will again be noon at e.

Thus, it is obvious, that the earth must complete one revolution, and a portion of a second revolution, equal to the space she has advanced in her orbit, in order to bring the same meridian back again to the sun. This small portion of a second revolution amounts daily to the 365th part of her circumference, and therefore, at the end of the year, to one entire rotation, and hence in 365 days, the earth actually turns on her axis 366 times. Thus, as one complete rotation forms a siderial day, there must, in the year, be one siderial, more than there are solar days, one rotation of the earth, with respect to the sun being lost, by the earth's yearly revolution. The same loss of a day, happens to a traveller, who, in passing round the earth towards the west, reckons his time by the rising and setting of the sun. If he passes around towards the east, he will gain a day for the same reason.

Equation of Time.

As the motion of the earth about its axis is perfectly uniform, the siderial days, as we have already seen, are exactly of the same length, in all parts of the year. But as the orbit of the earth, or the apparent path of the sun, is inclined to the earth's axis, and as the earth moves with different velocities in different parts of its orbit, the solar, or natural days, are somtimes greater and sometimes less than 24 hours, as shown

Had the earth only a diurnal revolution, would the siderial and solar time agree? Show by fig. 202, how siderial, differs from solar time. Why does not the earth turn the same meridian to the sun at the same time every day? How many times does the earth turn on her axis in a year? Why does she turn more times than there are days in the year? Why are the solar days sometimes greater, and sometimes less than 24 hours?

by an accurate clock. The consequence is, that a true sun dial, or noon mark, and a true time piece, agree with each other, only a few times in a year. The difference between the sun dial and clock, thus shown, is called the equation of time.

The difference between the sun and a well regulated clock, thus arises from two causes, the inclination of the earth's axis to the ecliptic, and the elliptical form of the earth's orbit.

That the earth moves in an ellipse, and that its motion is more rapid sometimes than at others, as well as that the earth's axis is inclined to the ecliptic, have already been explained, and illustrated. It remains, therefore, to show how these two combined causes, the elliptical form of the orbit, and the inclination of the axis, produce the disagreement between the sun and clock. In this explanation, we must consider the sun as moving around the ecliptic, while the earth revolves on her axis.

Equal, or mean time, is that which is reckoned by a clock, supposed to indicate exactly 24 hours, from 12 o'clock, on one day, to 12 o'clock on the next day. Apparent time, is that, which is measured by the apparent motion of the sun in the heavens, as indicated by a meridian line, or sun dial.

Were the earth's orbit a perfect circle, fig. 196, and her axis perpendicular to the plane of this orbit, the days would be of uniform length, and there would be no difference between the clock and the sun; both would indicate 12 o'clock at the same time, on every day in the year. But on account of the inclination of the earth's axis to the ecliptic, unequal portions of the sun's apparent path through the heavens will pass any meridian in equal times. This may be readily explained to the pupil, by means of an artificial globe, but perhaps it will be understood by the following diagram.

What is the difference between the time of the sun dial, and a clock called? What are the causes of the difference between the sun and clock? In explaining equation of time, what motion is considered as belonging to the sun, and what motion to the earth? What is equal, or mean time? What is apparent time?

Fig. 203.

Let AN B S, fig. 203, be the concave of the heavens, in the centre of which is the earth. Let the line A B, be the equator, extending through the earth and the heavens, and let A, a, b C, c, and Rd, be the ecliptic, or the apparent path of the sun through the heavens. Also, let A, 1, 2, 3, 4, 5, be equal distances on the equator, and A, a, b, C, c and d, equal portions of the eclipNow we will sup

tic, corresponding with A 1, 2, 3, 4, and 5. pose, that there are two suns, namely, a false, and a real one; that the false one passes through the celestial equator, which is only an extension of the earth's equator to the heavens; while the real sun has an apparent revolution through the ecliptic; and that they both start from the point A, at the same instant. The false sun is supposed to pass through the celestial equator in the same time, that the real one passes through the ecliptic, but not through the same meridians at the same time, so that the false sun arrives at the points 1, 2, 3, 4, and 5, at the time when the real sun arrives at the points a, b, C, and c. When the two suns were at A, the starting point, they were both on the sume meridian, but when the fictitious sun comes to 1, and the real sun to a, they are not in the same meridian, but the real sun is westward of the fictitious one, the real sun being at a, while the false sun is on the meridian 1, consequently, as the earth turns on its axis from west to east, any particular place will

In fig. 203, which is the celestial equator, and which the ecliptic? Through which of these circles does the false, and through which does the true sun pass? When the real sun arrives to a, and the false one to 1, are they both on the same meridian? Which is then most westward? When the two suns are at 1 and a, why will any meridian come first under the real sun? Were the true sun in place of the false one, why would the sun and clock agree?