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observations, perfectly confirms these results of analysis. Future ages will develop these great inequalities, which at some most distant period will amount to many circumferences. They are indeed periodic; but who shall tell their period? Millions of years must elapse before that great cycle is accomplished; but such changes, though rare in time, are frequent in eternity.'
The moon is so near, that the excess of matter at the earth's equator occasions periodic variations in her longitude, and also that remarkable inequality in her latitude already mentioned as a nutation in the lunar orbit, which diminishes its inclination to the ecliptic when the moon's ascending node coincides with the equinox of spring, and augments it when that node coincides with the equinox of autumn. As the cause must be proportional to the effect, a comparison of these inequalities, computed from theory, with the same given by observation, shows that the compression of the terrestrial spheroid, or the ratio of the difference between the polar and equatorial diameters, to the diameter of the equator, is . It is proved analytically that, if a fluid mass of homogeneous matter, whose particles attract each other inversely as the square of the distance, were to revolve about an axis as the earth does, it would assume the form of a spheroid whose compression
is, whence it appears that the earth is not homogeneous, but decreases in density from its centre to its circumference. Thus the moon's eclipses show the earth to be round, and her inequalities not only determine the form, but the internal structure of our planet; results of analysis which could not have been anticipated. Similar inequalities in the motions of Jupiter's satellites prove that his mass is not homogeneous, and that his compression is . His equatorial diameter exceeds his polar diameter by about 6230 miles.
The phases of the moon, which vary from a slender silvery crescent soon after conjunction to a complete circle of light in opposition, decrease by the same degrees till the moon is again enves loped in the morning beams of the sun. These changes regulate the returns of the eclipses; those of the sun can only happen in conjunction, when the moon, coming between the earth and the sun, intercepts his light; and those of the moon are occasioned by the earth intervening between the sun and moon when in opposition. As the earth is opaque and nearly spherical, it throws a conical shadow on the side of the moon opposite to the sun, the axis of which passes through the centres of the sun and earth. The length of the shadow terminates at the point where the apparent diame
ters of the sun and earth would be the same When the moon is in opposition, and at her mean distance, the diameter of the sun would be seen from her centre under an angle of 19181; and that of the earth would appear under an angle of 69083; so that the length of the shadow is at least three times and a half greater than the distance of the moon from the earth, and the breadth of the shadow, where it is traversed by the moon, is about eight-thirds of the lunar diameter. Hence the moon would be eclipsed every opposition, were it not for the inclination of her orbit to the plane of the ecliptic, in consequence of which the moon in opposition is either above or below the cone of the earth's shadow, except when in or near her nodes; her position with regard to them occasions all the varieties in the lunar eclipses. Every point of the moon's surface successively loses the light of different parts of the sun's disc before being eclipsed. Her brightness therefore gradually diminishes before she plunges into the earth's shadow. The breadth of the space occupied by the penumbra is equal to the apparent diameter of the sun, as seen from the centre of the moon. The mean duration of a revolution of the sun, with regard to the node of the lunar orbit, is to the duration of a synodic revolution of the moon as 223 to 19; so that, after a
period of 223 lunar months, the sun and moon would return to the same relative position to the node of the moon's orbit, and therefore the eclipses would recur in the same order, were not the periods altered by irregularities in the motions of the sun and moon. In lunar eclipses, our atmosphere refracts the sun's rays which pass through it, and bends them all round into the cone of the earth's shadow; and as the horizontal refraction surpasses half the sum of the solar and lunar parallaxes, that is, half the sum of the semidiameters of the sun and moon, divided by their mutual distance, the centre of the lunar disc, supposed to be in the axis of the shadow, would receive the rays from the same point of the sun, round all sides of the earth, so that it would be more illuminated than in full moon, if the greater portion of the light were not absorbed by the atmosphere. Instances are recorded where this feeble light has been entirely absorbed, so that the moon has altogether disappeared in her eclipses.
The sun is eclipsed when the moon intercepts his rays. The moon, though incomparably smaller than the sun, is so much nearer the earth, that her apparent diameter differs but little from his, but both are liable to such variations, that they alternately surpass one another. Were the eye of a spectator in the same straight line with the
centres of the sun and moon, he would see the sun eclipsed. If the apparent diameter of the moon surpassed that of the sun, the eclipse would be total; if it were less, the observer would see a ring of light round the disc of the moon, and the eclipse would be annular. If the centre of the moon should not be in the straight line joining the centres of the sun and the eye of the observer, the moon might only eclipse a part of the sun. The variation, therefore, in the distances of the sun and moon from the centre of the earth, and of the moon from her node at the instant of conjunction, occasions great varieties in the solar eclipses. Besides, the height of the moon above the horizon changes her apparent diameter, and may augment or diminish the apparent distances of the centres of the sun and moon, so that an eclipse of the sun may occur to the inhabitants of one country, and not to those of another. In this respect the solar eclipses differ from the lunar, which are the same for every part of the earth where the sun and moon are above the horizon. In solar eclipses, the light reflected by the atmosphere diminishes the obscurity they produce; even in total eclipses the higher part of the atmosphere is enlightened by a part of the sun's disc, and reflects its rays the earth. The whole disc of the new moon is frequently visible from atmospheric reflection.