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. [Sidenote: 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.