to size and density, and insert the ends of a short stick or wire into them, so as to place one at each end of the stick, we shall find that the two balls, not being of the same size and density, do not balance each other when the stick is held in the middle; but that, if we would balance them across the finger, the larger ball must be placed much nearer to it than the smaller one. When so balanced, we shall have found the common centre of gravity of the two.

Now it is a remarkable fact, that the observations of astronomers perfectly agree with the theory of the mathematician, in deciding that the Earth, instead of moving accurately along the line of the ellipsis which, generally speaking, forms its orbit, is drawn out of the line of the ellipsis, by the attraction of the Moon, towards it, both at the new and at the full and as it has been deter. mined that the common centre of gravity of the Earth and Moon is on an average about 3530 miles from the Earth's centre, so the aberration of the Earth from the line of its orbit towards the Moon at the new, is about 3530 miles, being somewhat less than its semi-diameter; and the same at the full.

M

B

O

In the upper diagram, let S be the Sun, M the Moon, E the Earth, and A B, a portion of the Earth's orbit.

The Moon, being in conjunction, draws the Earth out of its regular orbit, so that the Earth's centre is removed towards the Sun and Moon 3530 miles. In the lower diagram, the Moon, being in opposition, draws the Earth as much out of its orbit, away from the Sun, on the other side; so that, it is evident that the orbit of the Earth, instead of being accurately an oval, partakes in a slight degree of the form of the Moon's orbit.

*The Earth contains about 68 times more matter than the Moon. Their common centre of gravity is therefore 68 times nearer the Earth than the Moon; so that, if we divide 240,000 miles, the distance of the Moon from the centre of the Earth, by 68, the excess of the Earth's weight above the Moon's, the result will be 3530; which therefore is the distance of their common centre of gravity from the Earth's centre. If therefore, we reckon the diameter of the Earth to be in round numbers 8000 miles, the half of that, (being the distance from the centre to the circumference) is 4000. Then, if the common centre of gravity be distant 3530 miles from the centre of the Earth, it will be removed that distance by the attraction of the Moon at the new and full from the regular line of its orbit, or somewhat less than its semi-diameter.

LECTURE VI.

Of Eclipses of the Sun and Moon—Of Tides.

I. Of Eclipses.

WE may now be supposed to be in possession of a sufficient number of the principal facts relating to the movements of the Earth and Moon, to judge that the astronomer by his observations, and the mathematician by his calculations, and by the assistance they render to each other, are fully competent to explain the movements of these bodies, and hence also to calculate eclipses; and we are now less astonished, than we were before the scene had been opened to us, that eclipses should be foretold with such perfect accuracy, and for so great a length of time before they happen.

Yet, although we should be prepared to acknowledge that the movements of these luminaries are completely understood, it is still matter of astonishment to us who feel so vastly inferior, who have observed little and calculated less, that the end of all these observations and calculations should be so completely successful :that the day, the hour, the minute, and the place in the sphere, at which eclipses are to happen years to come, should be foretold to the greatest nicety, and that the proportion of the body to be eclipsed should also be known. How many circumstances must be accurately ascertained before the calculation commences! The

distance of the Earth from the Sun-its precise place in the ecliptic, and all the variations of motion to which it is subject; the Moon's distance-its precise situation in its orbit, and all the aberrations to which it is liable; -the influence of the attraction of the Earth and Sun for it--both conjoint and separate, and the variations of nodes; and to these must be added, a knowledge of the precise effects of parallax and refraction. Ferguson, in his admirable treatise on Astronomy, gives the following as the elements (in technical language) for the calculation of an eclipse of the Moon: they are 8 in number.

1st. The true time of full moon-and at that time, 2nd, the Moon's horizontal parallax. 3rd, the Sun's semi-diameter. 4th, the Moon's semi-diameter. 5th, the semi-diameter of the Earth's shadow at the Moon. 6th, the Moon's latitude. 7th, the angle of the Moon's visible path with the ecliptic. 8th, the Moon's true horary motion from the Sun.

The phenomena called Eclipses were once the terror of mankind; for when the sciences were not sufficiently advanced to enable the observer to calculate their periods, they were supposed to be the super-natural forerunners of pestilence, famine, or the sword: so that in ancient, and even in comparatively modern history, we find the records of them accompanied by the detail of some remarkable event soon after, or during their occurrence. Thus in the year 431 before the Christian era, a total eclipse of the Sun is recorded, together with the appearance of a comet, and of a plague at Athens; and in the year 1133 of our era, a terrible eclipse of the Sun, so that the stars were seen; and with this was associated in the same record, a schism in the church, occasioned by there being three popes at once. But the

advancement of science has completely assured us that eclipses result from the peculiar and uniform motions of the heavenly bodies; and therefore the idle notions of their being the forerunners of disasters, moral, civil, or political, have altogether vanished.

As every planet in the system, primary and secondary, derives its light from the Sun, it must cast a shadow toward that part of the sphere of the fixed stars, which is opposite to the Sun. A shadow therefore is only a privation of the light of the Sun, in the space hid from it, by the opake body that intercepts its rays. A shadow will consequently be proportionate to the relative sizes of the Sun and the Planet. If they were both of the same size, the form of the shadow cast by the planet, would in that case be cylindrical; of the same size as each of those bodies, and continue of the size without coming to a point. If the sun were less than the planet, then the shadow it would cast, would go on increasing in size through space: but, as on the contrary, the Sun is many times larger than the largest of the planets, or than the bulk of the whole number if they were all in one mass, so the shadow cast by any one of the planets must be proportionate to its dimension and its distance. from the Sun, and must converge to a point.

Such is the bulk of the Sun, that the shadow cast by each of the primary planets converges to a point, much short of the distance of the next planet; so that not one of the primary planets can eclipse another: the shadow cast by no one of them is long enough to eclipse any other body than one of its own moons, and this can only