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.

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 20 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 A G by the comty. bined action of these forces, in the same time that the

A double

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 AT W; 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.

Note 20. See engraving at page 28.

Note 21. Here the arcs AG, A I must be supposed to be very small; otherwise A E, which is equal to HI, will more than quadruple A B, which is equal to F G.

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.

II.

LECT. the middle of each bearer; then through a slit in the middle of the square top (O and P) of each tower, and going over a small pulley on the top, comes down again the same way, and is at last fastened to the upper end of the socket fixed in the middle of the above mentioned round plate. These plates S and T have each four round holes near their edges, for letting them slide up and down upon the wires which make the corners of each tower. The balls and plates being thus connected, each by its particular line, it is plain that if the balls be drawn outward, or towards the ends M and N of their respective bearers, the round plates S and T will be drawn up to the top of their respective towers O and P.

matter to

There are several brass weights, some of two ounces, some of three, and some of four, to be occasionally put within the towers O and P, upon the round plates S and T: each weight having a round hole in the middle of it, for going upon the sockets or axes of the plates, and is slit from the edge to the hole, for allowing it to be slipped over the foresaid line which comes from each ball to its respective plate: thus

The experiments to be made by this machine are as follows:

1. Take away the bearer M X,22 and take the ivory ball a, to which the line or silk cord b is fastened at one end; and having made a loop on the other end of the cord, put the loop over a pin fixed in the center of the

board d. Then, turning the winch B to give the board The pro- a whirling motion, you will see that the ball does not pensity of immediately begin to move with the board, but, on ackeep the count of its inactivity, it endeavours to continue in the state of rest which it was in before.-Continue turning, until the board communicates an equal degree of motion. with its own to the ball, and then turning on, you will perceive that the ball will remain upon one part of the

state it is

in.

Note 22. See Engraving, page 33.

II.

board, keeping the same velocity with it, and having no LECT. relative motion upon it, as is the case with every thing that lies loose upon the plane surface of the earth, which having the motion of the earth communicated to it, never endeavours to remove from that place. But stop the board suddenly by hand, and the ball will go on, and continue to revolve upon the board, until the friction thereof stops its motion: which shews, that matter being once put into motion, would continue to move for ever, if it met with no resistance. In like manner, if a person stands upright in a boat before it begins to move, he can stand firm; but the moment the boat sets off, he is in danger of falling towards that place which the boat departs from: because, as matter, he has no natural propensity to move. But when he acquires the motion of the boat, let it be ever so swift, if it be smooth and uniform, he will stand as upright and firm as if he was on the plane shore; and if the boat strikes against any obstacle, he will fall towards that obstacle; on account of the propensity he has, as matter, to keep the motion which the boat has put him into.

2. Take away this ball, and put a longer cord to it, which may be put down through the hollow axis of the bearer MX, and wheel G, and fix a weight to the end of the cord below the machine; which weight, if left at liberty, will draw the ball from the edge of the whirlingboard to its center.

to fly out

Draw off the ball a little from the center, and turn the Bodies moving in winch; then the ball will go round and round with the orbits have board, and will gradually fly off farther and farther from a tendency the center, and raise up the weight below the machine which shews that all bodies revolving in circles have tendency to fly off from these circles, and must have some power acting upon them from the center of motion, to keep them from flying off.23 Stop the machine, and

of these a

Note 23. There is a very beautiful as well as simple mode of illus

orbits.

IL.

LECT. the ball will continue to revolve for some time upon the board; but as the friction gradually stops its motion, the weight acting upon it will bring it nearer and nearer to the center in every revolution, until it brings it quite thither. This shews, that if the planets met with any resistance in going round the sun, its attractive power would bring them nearer and nearer to it in every revolution, until they fell upon it.

Bodies

move

faster in small or

bits than in large

ones.

3. Take hold of the cord below the machine with one hand, and with the other throw the ball upon the round board as it were at right angles to the cord, by which means it will go round and round upon the board. Then observing with what velocity it moves, pull the cord below the machine, which will bring the ball nearer to the center of the board, and you will see the nearer the ball is drawn to the center, the faster it will revolve; as those planets which are nearest the sun revolve faster than those which are more remote; and not only go round sooner, because they describe smaller circles, but even move faster in every part of their respective circles. Their cen- 4. Take away this ball, and apply the bearer MX, trifugal whose center of motion is in its middle at w, directly over the center of the whirling-board d. Then put two balls (V and U) of equal weights upon their bearing wires, and having fixed them at equal distances from their respective centers of motion w and x upon their silk cords, by the screw nuts, put equal weights in the towers O and P. Lastly, put the catgut strings E and Fupon the grooves G and H of the small wheels, which being of equal diameters, will give equal velocities to the bearers above, when the winch B is turned and

forces

shewn.

trating the centrifugal (motion of a revolving body. It consists in filling a small pail with water, and it will be found, that the vessel may be made to revolve without any portion of the water being spilt. In all cases however, the velocity must be such, that the centrifugal force exceeds that of the gravitating force, otherwise the pail would discharge its contents when first inverted.