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 motions in the 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. I.) 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 shew the precession of the Equinoxes; which, in many annual revolutions will begin to be sensible as the Earth’s Axis slowly deviates from its parallelism § [246], towards 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 291⁄2 to 3651⁄4.
The Diameter of the Groove of the Wheel O, which turns the inclined Plane X with the Moon’s Nodes backward, must be to the Diameter of the Groove k as 20 to 18225⁄365. 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 Motion must cross between these Wheels; but all the rest of the strings go in their respective Grooves IM, kO, and LP without crossing.
The Cometarium.
437. The Cometarium. This curious Machine shews the Motion of a Comet or excentric Body moving round the Sun, describing equal Areas in equal times § [152], and may be so contrived as to shew such a Motion for any Degree of Excentricity. It was invented by the late Dr. Desaguliers.