between it and the sun, and then coming round so as to be beyond the earth with respect to this luminary although the moon's orbit would be sensibly affected by the sun's attraction, yet this having exerted itself during one revolution of the moon, all its effects would be repeated in the same order during the next revolution, and the relative positions of the sun and earth remaining the same, the moon would come finally to have a fixed orbit, and its principal lines or axes would never change. But this is not the case of nature. The earth swiftly turning in its orbit, and bearing with it its revolving satellite, by the time the moon has completed a revolution, the sun and earth have entirely changed their relative positions, and the moon cannot reach its perigee, or nearest distance from the earth, at the same point as in the preceding revolution.

By an attentive examination of this problem, it is found that the tendency is to cause the moon to reach its perigee earlier than it would do if not disturbed, and in this way the perigee of a fixed orbit appears to advance to meet the coming moon, and in the end to continue advancing until it actually revolves entirely round in a period which observation determines to be about nine years.

It is not my intention to enter into a detailed examination of all the effects resulting from the sun's disturbing power on the moon's motions; neither shall I attempt to exhibit all the effects produced by the moon on the earth.-This would require a train of investigation too elaborate and intricate to comport with my present purposes. My object is simply to show that changes must arise from the mutual and

reciprocal action of these three bodies, which the theory of gravitation must explain, and the telescope point out, before it be possible to obtain a perfect knowledge of these bodies.

The exact estimation of these changes can never be made until we shall have learned the relative masses of matter contained in the sun, earth, and moon. In other language, we must know how many moons it would require to weigh as much as the earth, and how many earths would form a weight equal to that of the sun.

But is it possible that man, situated upon our planet, 237,000 miles from the moon, and 95,000,000 of miles from the sun, can actually weigh these worlds against each other, and determine their relative masses of matter? Even this has been accomplished, and I shall now proceed to explain how the earth may be weighed against the sun. Dropping a heavy body at the earth's surface, the velocity impressed on it in the first second of time will measure the weight of the earth in one sense. If it were possible to take the same body to the sun, drop it, and measure the velocity acquired by the falling body in the first second of time, the relative distances passed through at the sun and at the earth by the same body in the same time, would show exactly the relative weight of the sun and earth, for their capacity to communicate velocity are exactly proportioned to their masses. Now, although this experiment cannot be performed in the exact terms announced, yet as we have already shown, the moon is constantly dropping towards the earth, and the earth is as constantly dropping towards the sun Now in case we measure the amount by which the

moon is deflected from a straight line in one second of time, this measures the intensity of the earth's power. But the amount by which the earth is deflected from a right line by the central power of the sun in one second, is easily measured from a knowledge of its period and the magnitude of its orbit. Executing these calculations, it is found that the sun's effect on the earth is rather more than twice as great as the earth's effect on the moon, and in case these effects were produced at equal distances, then would the sun be shown to contain rather more than twice as much matter as is found in the earth. But the sun produces its effect at a distance 400 times greater than that at which the earth acts on the moon: hence, as the force diminishes as the square of the distance increases, a sun acting at twice the distance at which the earth acts, must be four times heavier to produce an equal effect; at three times the distance, it must be nine times heavier, and at four times the distance, sixteen times heavier;-at 400 times the distance, 160,000 times heavier than the earth. Thus do we find that in case the sun's action on the earth were exactly equal to the earth's action on the moon, in consequence of the great distance at which it operates, its weight would be equal to that of 160,000 earths. But its actual effect is rather more than double that of the earth on the moon, and hence we find it contains rather more than double 160,000 earths, or exactly 351,936 times the quantity of matter contained in the earth.

This enormous mass of the sun is confirmed by an examination of its actual dimensions. An object with an apparent diameter equal to that of the sun

and at a distance of 95,000,000 of miles, must have a real diameter of 883,000 miles, a quantity so great that if the sun's centre were placed at the earth's centre, its vast circumference would give ample room for the moon to circulate within its surface, leaving as great a space between the moon's orbit and the sun's surface as now exists between the moon and earth.

It is this immense magnitude of the sun, when compared with the planets and their satellites, which renders the orbits of the planets comparatively unalterable. It is true that these bodies mutually affect each other, but these effects are comparatively slight, and astronomers regard them as perturbations, or mere disturbances of the original elliptic motion. Hence

we find the magnitude and position of the earth's elliptic orbit remain without any very sensible variation for two or three revolutions; but the slight disturbance experienced at each revolution, constantly accumulating in the same direction in a long series of years, occasions changes that cannot be lost sight of, and which, by a reflex influence, become in some instances exceedingly important in their practical applications.

As it will be impossible to treat fully the complex subject of perturbation, I will call your attention to a few points about which cluster peculiar interest, in consequence of their great difficulty, and the almost infinite reach of analysis displayed in their successful examination.

I have already explained how it is that the disturb ing influence of the sun occasions a constant fluctua tion in the periodic time of the moon, accelerating it

as the earth moves from perihelion to aphelion, and again retarding it from aphelion to perihelion. If, now, we take a large number of revolutions of the moon, say a thousand, add them all up, and divide by one thousand, we obtain a mean period of revolution, which, in case the earth's orbit remains invariable, will never change, but will be constantly the same for thousands of years. By such an examination during the last century, the mean motion of the moon was obtained with great precision. But on a comparison of eclipses recorded by the Babylonians with each other, it was discovered that the moon in those early ages required a longer time to perform her mean revolution than in modern times. A like comparison of the Babylonian eclipses with those recorded in the middle ages by the Arabian astronomers, confirmed this wonderful discovery, which was yet farther substantiated by comparing the Arabian eclipses with those observed in modern times. It thus became manifest that, to all appearance at least, the moon's mean motion was growing swifter and swifter from century to century; that it was approaching closer and still closer to the earth, and if no limit to this change was ever to be fixed, sooner or later the final catastrophe must come, and the moon be precipitated on the body of the earth, and the system be destroyed.

An effort was made to account for this acceleration of the moon, on the theory of gravitation; but for a long time there seemed to be no possibility of rendering a satisfactory explanation of the phenomena, far less of prescribing the limits which should circumscribe the changes. Some, to escape from the difficulty, rejected entirely the ancient eclipses, and