Towards the right hand, let S be the Earth hung on the wire e, which is fixed into the Plate B; and let O be the Moon fixed on the Axis M, and turning round within the cap P, in which, and in the Plate C the crooked wire Q is fixed. On the Axis M is also fixed the Index K, which goes round a Circle h2, divided into 291⁄2 equal parts, which are the days of the Moon’s age: but to avoid confusion in the scheme, it is only marked with the numeral figures 1 2 3 4, for the Quarters. As the crank H carries this Moon round the Earth S in the Orbit t, she shews all her Phases by means of the cap P for the different days of her age, which are shewn by the Index K; this Index, turning just as the Moon O does, demonstrates her turning round her Axis as she still keeps the same side towards the Earth S § [262].
At the other end of the Plate C, a Moon N goes round an Earth R in the Orbit p; but this Moon’s Axis is stuck fast into the Plate C at S2; so that neither Moon nor Axis can turn round; and as this Moon goes round her Earth she shews herself all round to it; which proves, that if the Moon was seen all round from the Earth in a Lunation, she could not turn round her Axis.
N. B. If there were only the two wheels D and F, with a cat-gut string over them, but not crossing between them, the Axis of the Earth U would keep its parallelism round the Sun T, and shew all the seasons; as I sometimes make these Machines: and the Moon O would go round the Earth S, shewing her Phases as above; as likewise would the Moon N round the Earth R; but then, neither could the diurnal motion of the Earth U on its Axis be shewn, nor the motion of the Moon V round that Earth.
The Calculator.
436. In the year 1746 I contrived a very simple Machine, and described it’s performance in a small treatise upon the Phenomena of the Harvest Moon, published in the year 1747. I improved it soon after, by adding another wheel, and called it the Calculator. It may be easily made by any Gentleman who has a mechanical Genius.
Fig. I.
The great flat Ring supported by twelve pillars, and on which the twelve Signs with their respective Degrees are laid down, is the Ecliptic; nearly in the center of it is the Sun S supported by the strong crooked Wire I; and from the Sun proceeds a Wire W, called the Solar Ray, pointing towards the center of the Earth E, which is furnished with a moveable Horizon H, together with a brazen Meridian, and Quadrant of Altitude. R is a small Ecliptic, whose Plane co-incides with that of the great one, and has the like Signs and Degrees marked upon it; and is supported by two Wires D and D, which enter into the Plate PP, but may be taken off at pleasure. As the Earth goes round the Sun, the Signs of this small Circle keep parallel to themselves, and to those of the great Ecliptic. When it is taken off, and the solar Ray W drawn farther out, so as almost to touch the Horizon H, or the Quadrant of Altitude, the Horizon being rectified to any given Latitude, and the Earth turned round its Axis by hand, the point of the Wire W shews the Sun’s Declination in passing over the graduated brass Meridian, and his height at any given time upon the Quadrant of Altitude, together with his Azimuth, or point of Bearing upon the Horizon at that time; and likewise his Amplitude, and time of Rising and Setting by the hour Index, for any day of the year that the annual Index U points to in the Circle of Months below the Sun. M is a solar Index or Pointer supported by the Wire L which is fixed into the knob K: the use of this Index is to shew the Sun’s place in the Ecliptic every day in the year; for it goes over the Signs and Degrees as the Index U goes over the months and days; or rather as they pass under the Index U, in moving the cover plate with the Earth and its Furniture round the Sun; for the Index U is fixed tight on the immoveable Axis in the Center of the Machine. K is a knob or handle for moving the Earth round the Sun, and the Moon round the Earth.
As the Earth is carried round the Sun, its Axis constantly keeps the same oblique direction, or parallel to itself § [48], [202], shewing thereby the different lengths of days and nights at different times of the year, with all the various seasons. And, in one annual revolution of the Earth, the Moon M goes 121⁄3 times round it from Change to Change, having an occasional provision for shewing her different Phases. The lower end of the Moon’s Axis bears by a small friction wheel upon the inclined Plane T, which causes the Moon to rise above and sink below the Ecliptic R in every Lunation; crossing it in her Nodes, which shift backward through all the Signs and Degrees of the said Ecliptic, by the retrograde Motion of the inclined Plane T, in 18 years and 225 days. On this Plane the Degrees and Parts of the Moon’s North and South Latitude are laid down from both the Nodes, one of which, viz. the Descending Node appears at 0, by DN above B; the other Node being hid from Sight on this Plane by the plate PP; and from both Nodes, at proper distances, as in the other Orrery, 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 grooves are to be made sharp (not round) bottomed to keep the strings from slipping.
The Moon’s Axis moves up and down in the socket N fixed into the bar O (which carries her round the Earth) as she rises above or sinks below the Ecliptic; and immediately below the inclined Plane T is a flat circular plate (between Y and T) on which the different Excentricities 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 291⁄2 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 Ecliptic 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 Excentricity of her Orbit, and her elliptic Equation, all on the Apogee Plate, and the day of her age in the Circle Y of 291⁄2 equal parts; for every day of the year pointed out by the annual Index U in the Circle of months.