If the sixth and seventh Equations are augmented or diminished in a reciprocal _Ratio_ of the distance of the Moon from the Earth; _i. e._ in a direct _Ratio_ of the Moon's Horizontal Parallax, they will become more accurate: And this may be readily done, if Tables are first made to each minute of the said Parallax, and to every sixth or fifth degree of the Argument of the sixth Equation for the Sixth, as of the distance of the Moon from the Sun, for the Seventh Equation. From the Sun's Place, take the mean motion of the Moon's ascending Node, equated as above; the Remainder shall be the Annual Argument of the Node, whence its second Equation may be computed after the following manner in the preceding Figure. Let T, as before, represent the Earth; TS a Right Line, conjoining the Earth and Sun: Let also the Line TACB, be drawn to the Place of the ascending Node of the Moon, as above equated; and let STA be the Annual Argument of the Node. Take TA from a Scale, and let it be to AB :: as 56 to 3, or as 11⅔ to 1. Then bissect BA in C, and on C as a Centre, with the Distance CA, describe a Circle, as AFB, and make the Angle BCF, equal to double the Annual Argument of the Node before-found: So shall the Angle BTF, be the second Equation of the ascending Node; which must be added, when the Node is passing from the Quadrature to a Syzygy with the Sun; and subducted, when the Node moves from a Syzygy towards a Quadrature. By which means, the true Place of the Node of the Lunar Orbit will be gained: Whence from Tables made after the common way, the _Moon's Latitude, and the Reduction of her Orbit to the Ecliptick_, may be computed, supposing the Inclination of the Moon's Orbit to the Ecliptick, to be 4 degrees, 59 minutes, 35 seconds, when the Nodes are in Quadrature with the Sun; and 5 degrees, 17 minutes, 20 seconds, when they are in the Syzygys. And from the Longitude and Latitude thus found, and the given Obliquity of the Ecliptick, 23 degrees, 29 minutes, the Right Ascension and Declination of the Moon will be found. The Horizontal Parallax of the Moon, when she is in the Syzygys, at a mean distance from the Earth, I make to be 57 minutes, 30 seconds; and her Horary Motion, 33 minutes, 32 seconds, 32 thirds; and her apparent Diameter 31 minutes, 30 seconds. But in her Quadratures at a mean Distance from the Earth, I make the Horizontal Parallax of the Moon to be 59 minutes, 40 seconds, her Horary Motion 32 minutes, 12 seconds, 2 thirds, and her apparent Diameter, 31 minutes, 3 seconds. The Moon in an Octant to the Sun, and at a mean distance, hath her Centre distant from the Centre of the Earth about 60-2/9 of the Earth's Semi-diameters. The Sun's Horizontal Parallax I make to be 10 seconds, and its apparent Diameter at a mean distance from the Earth, I make 32 minutes, 15 seconds.