381. Apply one side of a Square to the Line of the Moon’s Path, and move the Square backward or forward until the other side cuts the same hour and minute both in the Path of the Place (_London_, in this Construction) and Path of the Moon; and _that_ minute, cut at the same time in both Paths, will be the precise minute of visible Conjunction of the Sun and Moon at _London_, and therefore the time of greatest obscuration, or middle of the Eclipse at _London_; which time, in this Projection, falls at _t_, 34 minutes past 10 in the Moon’s Path; and at _u_, 34 minutes past 10 in the Path of _London_. Then, upon the Point _u_ as a center, describe the Circle _zYy_ whose Radius _uy_ is equal to the Sun’s semi-diameter 16ʹ 6ʺ § 367, taken from the Scale _CA_: And upon the Point _t_ as a center, describe the Circle _Hy_ whose Radius is equal to the Moon’s semi-diameter 14ʹ 58ʺ § 367, taken from the same Scale. The Circle _zYy_ represents the Disc of the Sun as seen from the Earth, and the Circle _Hy_ the Disc of the Moon. The portion of the Sun’s Disc cut off by the Moon’s shews the Quantity of the Eclipse at the time of greatest obscuration: and if a right Line as _yz_ be drawn across the Sun’s Disc through _t_ and _u_, the minute of greatest obscuration in both Paths, and divided into 12 equal parts, it will shew what number of Digits are then eclipsed. If these two Circles do not touch one another, the Eclipse will not be visible at the given Place. [Sidenote: It’s beginning and ending.] 382. Lastly, take the Semi-diameter of the Penumbra 31ʹ 4ʺ § 367, from the Scale _CA_ with your Compasses; and setting one foot in the Moon’s Path, to the left hand of the Axis of the Ecliptic, direct the other toward the Path of _London_; and carry this extent backwards or forwards until both Points of the Compasses fall into the same instants of time in both Paths: which will denote the time of the beginning of the Eclipse: then, do the same on the right hand of the Axis of the Ecliptic, and where both Points mark the same instants in both Paths, they will shew at what time the Eclipse ends. These trials give the Points _R_ in the Moon’s Path and _r_ in the Path of _London_, namely 9 minutes past 9 in the Morning for the beginning of the Eclipse at _London_, _April 1, 1764_: _t_ and _u_ for the middle or greatest obscuration, at 35 minutes past 10; when the Eclipse will be barely annular on the Sun’s lower-most edge, and only two thirds of a Digit left free on his upper-most edge: and for the end of the Eclipse, _S_ in the Moon’s Path and _x_ in the Path of _London_, at 4 minutes past 12 at Noon.