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the nodes, one of which, viz. the descending node, appears at 0, by DN above B; the other node be ing hid from sight on this plane by the plate PP; and from both nodes, at proper distances, as in the other Qrrery, the limits of eclipses are marked, and all the solar and lunar eclipses are shewn in the same manner, for any given year within the limits of 6000, either before or after the Christian æra. On the plate that covers the wheel-work, under the Sun S, and round the knob K, are astronomical tables, by which the machine may be rectified to the beginning of any given year within these limits, in three or four minutes of time; and when once set right, may be turned backward for 300 years past, or forward for as many to come, without requiring any new rectification. There is a method for its adding up the 29th of February every fourth year, and allowing only 28 days to that month for every other three; but all this being performed by a particular manner of cutting the teeth of the wheels, and dividing the month-circle, too long and intricate to be described here, I shall only shew how these motions may be performed near enough for common use, by wheels with grooves and cat-gut strings round them; only here I must put the operator in mind, that the groove are to be made sharp-bottomed, (not round) to keep the strings from slipping.

The moon's axis moves up and down in the socket N, fixed into the bar 0, (which carries her round the earth) as she rises above or sinks below the ecliptic; and immediately below the inclined plane Tis a flat circular plate (between Y and T) on which the different eccentricities of the Moon's orbit are laid down; and likewise her mean anomaly and elliptic equation, by which her true place may be very nearly found at any time. Below this apogee.plate, which shews the anomaly, &c. is a circle Y divided into 29} equal parts, which are the

days of the Moon's age: and the forked end A of the index AB (Fig. II.) may be put into the apogee-part of this plate ; there being just such another index to put into the inclined plane T at the ascending node: and then the curved points B of these indexes shew the direct motion of the apogee, and retrograde motion of the nodes through the ecliptio R, with their places in it at any given time. As the moon M goes round the earth E, she shews her place every day in the ecliptic R, and the lower end of her axis shews her latitude and distance from her node on the inclined plane T, also her distance from her apogee and perigee, together with her mean anomaly, the then eccentricity of her orbit, and her elliptic equation, all on the apogee-plate, and the day of her age in the circle Y of 294 equal parts, for every day of the year, pointed out by ihe annual index Ü in the circle of months.

Having rectified the machine by the tables for the begiuning of any year, move the earth and moon forward by the knob K, until the annual index comes to any given day of the month, then stop, and not only all the above phenomena may be shewn for that clay, but also, by turning the earth round its axis, the declination, azimuth, amplitude, altitude of the Moon at any hour, and the times of her rising and setting, are shewn by the horizon, quadrant of altitude, and hour-index. And in moving the earth round the sun, the day's of all the new and full moons and eclipses in any given year are shewn. The phenomena of the harvest-moon, and those of the tides, by such a cap as that in plate IX. Fig. 10. put upon the earth and moon, together with the solution of many problems not here related, are made conspicuous.

The easiest, though not the best, way, that I can instruct any mechanical person to make the wheel

PLATE
VIII.

work of such a machine, is as follows: which is the way that I made it, before I thought of numbers exact enough to make it worth the trouble of cutting teeth in the wheels.

Fig. 3d of Plate VIII. is a section of this machine; in which ABCD is a frame of wood held to

Fig. III. gether by four pillars at the corners; two of which appear at AC and BD. In the lower plate CD of this frame are three small friction-wheels, at equal distances from each other; two of them appearing at e and e. As the frame is moved round, these wheels run upon the fixed bottom-plate EE, which supports the whole work.

In the centre of this last-mentioned plate is fixed the upright axis GFFf, and on the same axis is fixed the wheel HHH, in which are four grooves, 1, X, k, L, of different diameters. In these grooves are cat-gut strings going also round the separate wheels M, N, 0, and P.

The wheel M is fixed on a solid spindle or axis, the lower pivot of which turns at R in the under plate of the moveable frame ABCD; and on the upper end of this axis is fixed the plate oo (which is PP, under the earth, in Fig. 1.), and to this plate is fixed at an angle of 23 degrees inclination, the dial-plate below ihe earth T; on the axis of which, the index q is turned round by the earth. This axis, together with the wheel M, and plate oo, keep their parallelism in going round the sun S.

On the axis of the wheel M is a moveable socket, on which the small wheel N is fixed, and on the upper end of this socket is put on tight (but so as it may be occasionally turned by hand) the bar ZZ (viz. the bar 0 in Fig. 1.) which carries the moon m round the earth T, by the socket n, fixed into the bar. As the moon goes round the earth, her axis rises and falls in the socket 11; because, on the lower end of her axis, which is turned inward, there is a small friction-wheel s running

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on the inclined plane X (which is T'in Fig. 1.), and so causes the moon alternately to rise above and sink below the little ecliptic VV (R in Fig. 1.) in every lunation.

On the socket or hollow axis of the wheel N, there is another socket, on which the wheel O is fixed; and the moon's inclined plane X is put tightly on the upper end of this socket, not on a square, but on a round, that it may be occasionally set by hand without wrenching the wheel or axle.

Lastly, on the hollow axis of the wheel O is another socket, on which is fixed the wheel P, ayd on the upper end of this socket is put on tightly the apogee.plate Y (that immediately below 7'in Fig. 1.) All these axles turn in the upper plate of the moveable frame at Q'; which plate is covered with the thin plate ec (screwed to it), whereon are the forementioned tables and month-circle in Fig. 1.

The middle part of the thick fixed wheel HHH is much broader than the rest of it, and comes out between the wheels M and O almost to the wheel N. To adjust the diameters of the grooves of this fixed wheel to the grooves of the separate wheels M, N, O, and P, so as they may perform their motion in their proper times, the following method must be observed.

The groove of the wheel M, which keeps the parallelism of the earth's axis, must be precisely of the same diameter as the lower groove I of the fixed wheel HHH; but, when this groove is so well adjusted as to shew, that in ever so many annual revolutions of the Earth, its axis keeps its parallelism, as may be observed by the solar ray W (Fig. 1.) always coming precisely to the same degree of the small ecliptic R at the end of every annual revolution, when the index M points to the like degree in the great ecliptic; then, with the edge of a thin file, give the groove of the wheel M a small rub all round, and, by that means lessening the diameter of the groove perhaps about the 20th part of a hair's breadth, it will cause the earth to

a shew the precession of the equinoxes; which, in many annual revolutions, will begin to be sensible, as the earth's axis deviates slowly from its parallelism, | 246, toward the antecedent signs of the ecliptic.

The diameter of the groove of the wheel N, which carries the moon round the earth, must be to the diameter of the groove X, as a lunation is to a year, that is, as 291 to 3651.

The diameter of the groove of the wheel 0, which turns the inclined plane X with the moon's nodes backward, must be to the diameter of the groove k, as 20 to 18935. And,

Lastly, the diameter of the groove of the wheel P, which carries the moon's apogee forward, must be to the diameter of the groove L, as 70 to 62.

But after all this nice adjustment of the grooves to the proportional times of their respective wheels turning round, and which seems to promise very well in theory, there will still be found a necessity of a farther adjustment by hand; because proper allowance must be made for the diameters of the cat-gut strings: and the grooves must be so adjusted by hand, as, that in the time the earth is moved once round the sun, the moon must perform 12 synodical revolutions round the earth, and be almost 11 days old in her 13th revolution. The inclined plane with its nodes must go once round backward through all the signs and degrees of the small ecliptic in 18 annual revolutions of the earth, and 225 days over. And the apogee-plate must go once round forward, so as its index may go over all the signs and degrees of the small ecliptic in eight years (or so many annual revolutions of the earth) and 312 days over. N. B. The string which goes

round the grooves X and N, for the moon's notion, must cross between these wheels; but all the rest of the strings

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