Let us now suppose that the Radius of the circular curve described by the nail in the axle is to the Radius of the Circle which the pin in the nave describes round the axle as 337-1/2 to 1; which is the proportion of the Radius or Semidiameter of the Earth’s Orbit to that of the Moon’s; or of the circular curve _A_ 1 2 3 4 5 6 7 _B_ &c. to the little Circle _a_; and then, whilst the progressive nail describes the said curve from _A_ to _E_, the pin will go once round the nail with regard to the center of it’s path, and in doing so, will describe the curve _abcde_. The former will be a true representation of the Earth’s path for one Lunation, and the latter of the Moon’s for that time. Here we may set aside the inequalities of the Moon’s Moon, and also the Earth’s moving round it’s common center of gravity and the Moon’s: all which, if they were truly copied in this experiment, would not sensibly alter the figure of the paths described by the nail and pin, even though they should rub against a plain upright surface all the way, and leave their tracks visible. And if the chariot should be driven forward on such a convex piece of ground, so as to turn the wheel several times round, the track of the pin in the nave would still be concave toward the center of the circular curve described by the pin in the Axle; as the Moon’s path is always concave to the Sun in the center of the Earth’s annual Orbit. [Sidenote: Proportion of the Moon’s Orbit to the Earth’s.] In this Diagram, the thickest curve line _ABCD_, with the numeral figures set to it, represents as much of the Earth’s annual Orbit as it describes in 32 days from west to east; the little Circles at _a_, _b_, _c_, _d_, _e_ shew the Moon’s Orbit in due proportion to the Earth’s; and the smallest curve _abcdef_ represents the line of the Moon’s path in the Heavens for 32 days, accounted from any particular New Moon at _a_. The machine, Fig. 5th is for delineating the Moon’s path, and will be described, with the rest of my Astronomical machinery, in the last Chapter. The Sun is supposed to be in the center of the curve _A 1 2 3 4 5 6 7 B_ &c. and the small dotted Circles upon it represent the Moon’s Orbit, of which the Radius is in the same proportion to the Earth’s path in this scheme, that the Radius of the Moon’s Orbit in the Heavens bears to the Radius of the Earth’s annual path round the Sun; that is, as 240,000 to 81,000,000, or as 1 to 337-1/2. [Sidenote: Fig. II.]