Having rectified the Machine by the Tables for the beginning 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 day, 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 days 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 9] 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-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. III.
Fig. 3d of [Plate 8] is a section of this Machine; in which ABCD is a frame of wood held together by four pillars at the corners, whereof two 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 Center of this last mentioned Plate is fixed the upright Axis f FFG, and on the same Axis is fixed the wheel HHH in which are four grooves I, X, k, L of different Diameters. In these grooves are cat-gut strings going also round the separate wheels M, N, O 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 o o (which is PP, under the Earth, in Fig. I.) and to this Plate is fixed, at an Angle of 231⁄2 Degrees inclination, the Dial-plate below the 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 o o, 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 O in Fig. I.) 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 n; because, on the lower end of her Axis, which is turned inward, there is a small friction Wheel s running on the inclined Plane X (which is T in Fig. I.) and so causes the Moon alternately to rise above and sink below the little Ecliptic VV (R in Fig. I.) 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, and on the upper end of this Socket is put on tightly the Apogee-plate Y, (that immediately below T in Fig. I.) all these Axles turn in the upper Plate of the moveable frame at Q which Plate is covered with the thin Plate cc (screwed to it) whereon are the fore-mentioned Tables and month Circle in Fig. I.