EF. Adding these several parts of the meridian together, we obtain the length of the arc from A to O, in miles; and by observations on the north star, at each extremity of the arc, namely, at A and at O, we could determine the difference of latitude between these two points. Suppose, for example, that the distance between A and O is exactly five degrees, and that the length of the intervening line is three hundred and forty-seven miles; then, dividing the latter by the former number, we find the length of a degree to be sixtynine miles and four tenths. To take, however, a few of the results actually obtained, they are as follows:

This comparison shows, that the length of a degree gradually increases, as we proceed from the equator towards the pole. Combining the results of various estimates, the dimensions of the terrestrial spheroid are found to be as follows:

The difference between the greatest and the least is about twenty-six and one half miles, which is about one two hundred and ninety-ninth part of the greatest. This fraction is denominated the ellipticity of the earth, -being the excess of the equatorial over the polar di

ameter.

The operations, undertaken for the purpose of determining the figure of the earth, have been conducted with the most refined exactness. At any stage of the process, the length of the last side, as obtained by calculation, 1, may be actually measured in the same manner

as the base from which the series of triangles commenced. When thus measured, it is called the base of verification. In some surveys, the base of verification, when taken at a distance of four hundred miles from the starting point, has not differed more than one foot from the same line, as determined by calculation.

Another method of arriving at the exact figure of the earth is, by observations with the pendulum. If a pendulum, like that of a clock, be suspended, and the number of its vibrations per hour be counted, they will be found to be different in different latitudes. A pendulum that vibrates thirty-six hundred times per hour, at the equator, will vibrate thirty-six hundred and five and two thirds times, at London, and a still greater number of times nearer the north pole. Now, the vibrations of the pendulum are produced by the force of gravity. Hence their comparative number at different places is a measure of the relative forces of gravity at those places. But when we know the relative forces of gravity at different places, we know their relative distances from the centre of the earth; because the nearer a place is to the centre of the earth, the greater is the force of gravity. Suppose, for example, we should count the number of vibrations of a pendulum at the equator, and then carry it to the north pole, and count the number of vibrations made there in the same time,—we should be able, from these two observations, to estimate the relative forces of gravity at these two points; and, having the relative forces of gravity, we can thence deduce their relative distances from the centre of the earth, and thus obtain the polar and equatorial diameters. Observations of this kind have been taken with the greatest accuracy, in many places on the surface of the earth, at various distances from each other, and they lead to the same conclusions respecting the figure of the earth, as those derived from measuring arcs of the meridian. It is pleasing thus to see a great truth, and one apparently beyond the pale of human investigation, reached by two routes entirely independent of each other. Nor, in

deed, are these the only proofs which have been discovered of the spheroidal figure of the earth. In consequence of the accumulation of matter above the equatorial regions of the earth, a body weighs less there than towards the poles, being further removed from the centre of the earth. The same accumulation of matter, by the force of attraction which it exerts, causes slight inequalities in the motions of the moon; and since the amount of these becomes a measure of the force which produces them, astronomers are able, from these inequalities, to calculate the exact quantity of the matter thus accumulated, and hence to determine the figure of the earth. The result is not essentially different from that obtained by the other methods. Finally, the shape of the earth's shadow is altered, by its spheroidal figure, -a circumstance which affects the time and duration of a lunar eclipse. All these different and independent phenomena afford a pleasing example of the harmony of truth. The known effects of the centrifugal force" upon a body revolving on its axis, like the earth, lead us to infer that the earth is of a spheroidal figure; but if this be the fact, the pendulum ought to vibrate faster near the pole than at the equator, because it would there be nearer the centre of the earth. On trial, such is found to be the case. If, again, there be such an accumulation of matter about the equatorial regions, its effects ought to be visible in the motions of the moon, which it would influence by its gravity; and there, also, its effects are traced. At length, we apply our measures to the surface of the earth itself, and find the same fact, which had thus been searched out among the hidden things of Nature, here palpably exhibited before our eyes. Finally, on estimating from these different sources, what the exact amount of the compression at the poles must be, all bring out nearly one and the same result. This truth, so harmonious in itself, takes along with it, and establishes, a thousand other truths on which it rests.

LETTER VIII.

DIURNAL REVOLUTIONS.

"To some she taught the fabric of the sphere,
The changeful moon, the circuit of the stars,
The golden zones of heaven."-Akenside.

WITH the elementary knowledge already acquired, you will now be able to enter with pleasure and profit on the various interesting phenomena dependent on the revolution of the earth on its axis and around the sun. The apparent diurnal revolution of the heavenly bodies, from east to west, is owing to the actual revolution of the earth on its own axis, from west to east. If we conceive of a radius of the earth's equator extended until it meets the concave sphere of the heavens, then, as the earth revolves, the extremity of this line would trace out a curve on the face of the sky; namely, the celestial equator. In curves parallel to this, called the circles of diurnal revolution, the heavenly bodies actually appear to move, every star having its own peculiar circle. After you have first rendered familiar the real motion of the earth from west to east, you may then, without danger of misapprehension, adopt the common language, that all the heavenly bodies revolve around the earth once a day, from east to west, in circles parallel to the equator and to each other.

I must remind you, that the time occupied by a star, in passing from any point in the meridian until it comes round to the same point again, is called a sidereal day, and measures the period of the earth's revolution on its axis. If we watch the returns of the same star from day to day, we shall find the intervals exactly equal to each other; that is, the sidereal days are all equal. Whatever star we select for the observation, the same result will be obtained. The stars, therefore, always keep the same relative position, and have a common

movement round the earth,-a consequence that naturally flows from the hypothesis that their apparent motion is all produced by a single real motion; namely, that of the earth. The sun, moon, and planets, as well as the fixed stars, revolve in like manner; but their returns to the meridian are not, like those of the fixed stars, at exactly equal intervals.

The appearances of the diurnal motions of the heav enly bodies are different in different parts of the earth, -since every place has its own horizon, and different horizons are variously inclined to each other. Nothing in astronomy is more apt to mislead us, than the obstinate habit of considering the horizon as a fixed and immutable plane, and of referring every thing to it. We should contemplate the earth as a huge globe, occupying a small portion of space, and encircled on all sides, at an immense distance, by the starry sphere. We should free our minds from their habitual proneness to consider one part of space as naturally up and another down, and view ourselves as subject to a force (gravity) which binds us to the earth as truly as though we were fastened to it by some invisible cords or wires, as the needle attaches itself to all sides of a spherical loadstone. We should dwell on this point, until it appears to us as truly up, in the direction B B, C C, D D, when one is at B, C, D, respectively, as in the direction A A, when he is at A, Fig. 14.

Let us now suppose the spectator viewing the diurnal revolutions from several different positions on the earth. On the equator, his horizon would pass through both poles; for the horizon cuts the celestial vault at ninety degrees in every direction from the zenith of the spectator; but the pole is likewise ninety degrees from his zenith, when he stands on the equator; and consequently, the pole must be in the horizon. Here, also, the celestial equator would coincide with the prime vertical, being a great circle passing through the east and west points. Since all the diurnal circles are parallel to the equator, consequently, they would all, like the equator