II.

is in any part of its orbit (as suppose at K) a smaller LECT. body as L, within the sphere of attraction of the body K, be projected in the right line L M, with a force duly adjusted, and perpendicular to the line of attraction LK; then, the small body L will revolve about the large body K in the orbit N 0, and accompany it in its whole course round the yet larger body S. But then, the body K will no longer move in the circle AT W; for that circle will now be described by the common center of gravity between K and L. Nay, even the great body S will not keep in the center; for it will be the common center of gravity between all the three bodies S, K, and L, that will remain immoveable there. So, if we suppose S and K connected by a wire P that has no weight, and K and L connected by a wire q that has no weight, the common center of gravity of all these three bodies will be a point in the wire P near S; which point being supported, the bodies will be all in equilibrio as they move round it. Though indeed, strictly speaking, the common center of gravity of all the three bodies will not be in the wire P but when these bodies are all in a right line. Here, S may represent the sun, K the earth, and L the moon.

In order to form an idea of the curves described by two bodies revolving about their common center of gravity, whilst they themselves with a third body are in motion round the common center of gravity of all the three ; let us first suppose E (p. 30.) to be the sun, and e the earth going round him without any moon; and their

l moving forces regulated as above. In this case, whilst the earth goes round the sun in the dotted circle The curves RTU W X, &c. the sun will go round the circle by bodies A B D, whose center C is the common center of gravity Revolt ing:

about their between the sun and earth : the right line B8 represent-common ing the mutual attraction between them, by which they gravity. are as firmly connected as if they were fixed at the two

II.

LECT. ends of an iron bar strong enough to hold them. So, when the earth is at e, the sun will be at E; when the earth is at T, the sun will be at F; and when the earth is at g, the sun will be at G, &c.

Now, let us take in the moon q (at the top of the figure) and suppose the earth to have no progressive motion about the sun; in which case, whilst the moon revolves about in her orbit ABCD, the earth will revolve in the circle S 13, whose center R is the common center of gravity of the earth and moon; they being connected by the mutual attraction between them in the same manner as the earth and sun are.

But the truth is, that whilst the moon revolves about the earth, the earth is in motion about the sun: and now, the moon will cause the earth to describe an

ܪ

irregular curve, and not a true circle, round the sun ; it LECT.

II. being tie common center of gravity of the earth and moon that will then describe the same circle which the earth would have moved in, if it had not been attended by a moon. For, supposing the moon to describe a quarter of her progressive orbit about the earth in the time that the earth moves from e to f; it is plain, that when the earth comes to f, the moon will be found at r; in which time, their common center of gravity will have described the dotted arc R 1 T, the earth the curve R 5f. and the moon the curve q 14 r. In the time that the moon describes another quarter of her orbit, the center of gravity of the earth and moon will describe the dotted arc T 2 U, the earth the curve f 6 g, the moon the curve r 15 s, and so on. And thus, whilst the moon goes once round the earth in her progressive orbit, their common center of gravity describes the regular portion of a circle RIT 2 U3 V 4 W, the earth the irregular curve R 5 f 6 g 7 h 8 i, and the moon the yet more irregular

9

14 r 15 s 16 t 17 u ; and then the same kind of tracks over again.

The center of gravity of the earth and moon is 6000 miles from the earth's center towards the moon; therefore the circle S 13 which the earth describes round that center of gravity in every course of the moon round her orbit) is 12000 miles in diameter. Consequently the earth is 12000 miles nearer the sun at the time of full moon than at the time of new. (See the earth at f and at h.

To avoid confusion in so small a figure, we have supposed the moon to go only twice and a half round the earth, in the time that the earth goes once round the sun: it being impossible to take in all the revolutions which she makes in a year, and to give a true figure of her path, unless we should make the semidiameter of the earth's orbit at least 95 inches ; and then, the pro

curve

u.

LECT. portional semidiameter of the moon's orbit would be only a quarter of an inch.-For a true figure of the moon's path, I refer the reader to my Treatise of As tronomy.

A double

ty.

20

If the moon made any complete number of revolutions about the earth in the time that the earth makes one revolution about the sun, the paths of the sun and moon would return into themselves at the end of every year; and so be the same over again: but they return not into themselves in less than nineteen years nearly; in which time, the earth makes nearly nineteen revolutions about the sun, and the moon 235 about the earth. If the planet A" be attracted towards the sun, with projectile force balan- such a force as would make it fall from A to B, in the ces a quad- time that the projectile impulse would have carried it ruple power of gravi- from A to F, it will describe the arc AG by the combined action of these forces, in the same time that the former would have caused it to fall from A to B, or the latter have carried it from A to F. But, if the projectile force had been twice as great, that is, such as would have carried the planet from A to H, in the same time that now, by the supposition, it carries it only from A to F; the sun's attraction must then have been four times as strong as formerly, to have kept the planet in the circle A TW; that is, it must have been such as would have caused the planet to fall from A to E, which is four times the distance of A from B, in the time that the projectile force singly would have carried it from A to H, which is only twice the distance of A from F." Thus, a double projectile force will balance a quadruple power of gravity in the same circle; as appears plain by the figure, and shall soon be confirmed by an experiment.

The whirling-table is a machine contrived for shew- LECT

of wood, B a winch or handle fixed on the axis C of the wheel D, round which is the catgut string F, which also goes round the small wheels G and K, crossing between them and the great wheel D. On the upper end of the axis of the wheel G, above the frame, is fixed the round board d, to which the bearer MSX may be fastened occasionally, and removed when it is not wanted. On the axis of the wheel H is fixed the bearer NTZ; and it is easy to see that when the winch B is turned, the wheels and bearers are put into a whirling motion.

Each bearer has two wires, W, X, and Y, Z, fixed and screwed tight into them at the ends by nuts on the outside. And when these nuts are unscrewed, the wires may be drawn out in order to change the balls U and V, which slide upon the wires by means of brass loops, fixed into the balls, which keep the balls up from touching the wood below them. A strong silk line goes through each ball, and is fixed to it at any length from the center of the bearer to its end, as occasion requires, by a nut-screw at the top of the ball; the shank of the screw goes into the center of the ball, and presses the line against the under side of the hole that it goes through. The line goes from the ball, and under asmall pulley fixed in the middle of the bearer; then up through a socket in the round plate (see S and T) in

D

II.

The whirling-table described.