Take the Moon’s true horary motion from the Sun, viz. 28 Minutes 22 Seconds, from the Scale W in your Compasses; and with that extent make marks in the line of the Moon’s Path LMHNO: then divide each of these equal spaces into 60 equal parts or minutes of time: and set the hours to them as in the Figure, in such a manner that the precise time of Full Moon, as shewn by the Tables, may fall in the Axis of the Ecliptic at F, where the line of the Moon Path cuts it.
Lastly, Take the Moon’s Semi-diameter 15 Minutes 2 Seconds from the Scale W in your Compasses, and therewith as a Radius describe the Circles P, Q, R, S, and T on the Centers L, M, H, N, and O; the Circles P and T just touching the Earth’s Shadow UU, but no part of them within it; the Circles Q and S all within it, but touching at its edges; and the Circle R in the middle of the Moon’s Path through the shadow. So the Circle P shall be the Moon touching the shadow at the moment the Eclipse begins; the Circle Q the Moon just immersed into the shadow at the moment she is totally eclipsed; the Circle R the Moon at the greatest obscuration, in the middle of the Eclipse; the Circle S the Moon just beginning to be enlightened on her western limb at the end of total darkness; and the Circle T the Moon quite clear of the Earth’s shadow at the moment the Eclipse ends. The moments of time marked at the points L, M, H, N and O answer to these Phenomena: and according to this small projection are as follow. The beginning of the Eclipse at 8 Hours 36 Minutes P. M. The total immersion at 9 Hours 42 Minutes. The middle of the Eclipse at 10 Hours 26 Minutes. The end of total darkness at 11 Hours 12 Minutes. And the end of the Eclipse at 12 Hours 18 Minutes; but the Figure is too small to admit of precision.
The examination of antient Eclipses.
390. By computing the times of New and Full Moons, together with the distance of the Sun and Moon from the Nodes; and knowing that when the Sun is within 17 Degrees of either Node at New Moon he must be eclipsed; and when the Moon is within 12 Degrees of either Node at Full she cannot escape an Eclipse; and that there can be no Eclipses without these limits; ’tis easy to examine whether the accounts of antient Eclipses recorded in history be true. I shall take the liberty to examine two of those mentioned in the foregoing catalogue, namely, that of the Moon at Babylon on the 19th of March in the 721st year before Christ; and that of the Sun at Athens, on the 20th of March, in the 424th year before Christ.
The time of Full Moon for the former of these Eclipses is already calculated, Page [198], and the time of New Moon for the latter, Page [196], both to the Old Style; so that we have nothing now to do but find the Sun’s distance from the Nodes the same way as we did the Anomalies; and if the Full Moon in March 721 years before Christ was within 12 degrees of either Node, she was then eclipsed; and if the Sun, at the time of New Moon in March 424 years before Christ was within 17 degrees of either Node, he must have been eclipsed at that time.
EXAMPLE I.
To find the distance of the Sun and Moon from the Nodes, at the time of Full Moon in March, the year before Christ 721, O. S.
The years 720 added to 1780 make 2500, or 25 Centuries.
| Sun from Node | |||
|---|---|---|---|
| s | ° | ʹ | |
| To the mean time of Full Moon in March 1780, Table III. | 10 | 3 | 1 |
| Add the distance for 1 Lunation [See N. B. Page [195], and Example III, Page [198]] | 1 | 0 | 40 |
| Sum | 11 | 3 | 41 |
| From which subtract the Sun’s distance from the Node for 2500 years, Table V | 5 | 4 | 11 |
| Remains the Sun’s distance from the Node, March 19, 721 years before Christ | 5 | 29 | 30 |
| To which add 6 Signs for the Moon’s distance, because she was then in opposition to the Sun | 6 | 0 | 0 |
| The Sum is the Moon’s dist. from the Ascend. Node | 11 | 29 | 30 |
That is, she was within half a degree of coming round to it again; and therefore, being so near, she must have been totally, and almost centrally eclipsed.