138. Dr. LONG, in his first volume of _Astronomy_, has given us figures of the apparent paths of all the Planets separately from CASSINI; and on seeing them I first thought of attempting to trace some of them by a machine[29] that shews the motions of the Sun, Mercury, Venus, the Earth and Moon, according to the _Copernican System_. Having taken off the Sun, Mercury, and Venus, I put black-lead pencils in their places, with the points turned upward; and fixed a circular sheet of paste-board so, that the Earth kept constantly under it’s center in going round the Sun; and the paste-board kept its parallelism. Then, pressing gently with one hand upon the paste-board to make it touch the three pencils, with the other hand I turned the winch which moves the whole machinery: and as the Earth, together with the pencils in the places of Mercury and Venus, had their proper motions round the Sun’s pencil, which kept at rest in the center of the machine, all the three pencils described a diagram from which the first Figure of the third Plate is truly copied in a smaller size. As the Earth moved round the Sun, the Sun’s pencil described the dotted Circle of Months, whilst Mercury’s pencil drew the curve with the greatest number of loops, and Venus’s that with the fewest. In their inferiour conjunctions they come as much nearer the Earth, or within the Circle of the Sun’s apparent motion round the Heavens, as they go beyond it in their superiour conjunctions. On each side of the loops they appear Stationary; in that part of each loop next the Earth retrograde; and in all rest of their paths direct. [Illustration: Plate III. _J. Ferguson delin._ _J. Mynde Sc._] [Sidenote: PLATE III.] If _Cassini_’s Figures of the paths of the Sun, Mercury and Venus were put together, the Figure as above traced out, would be exactly like them. It represents the Sun’s apparent motion round the Ecliptic, which is the same every year; Mercury’s motion for seven years; and Venus’s for eight; in which time Mercury’s path makes 23 loops, crossing itself so many times, and Venus’s only five. In eight years Venus falls so nearly into the same apparent path again, as to deviate very little from it in some ages; but in what number of years Mercury and the rest of the Planets would describe the same visible paths over again, I cannot at present determine. Having finished the above Figure of the paths of Mercury and Venus, I put the Ecliptic round them as in the Doctor’s Book; and added the dotted lines from the Earth to the Ecliptic for shewing Mercury’s apparent or geocentric motion therein for one year; in which time his path makes three loops, and goes on a little farther; which shews that he has three inferiour, and as many superiour conjunctions with the Sun in that time, and also that he is six times Stationary, and thrice Retrograde. Let us now trace out his motion for one year in the Figure. [Sidenote: Fig. I.]