Chapter XVI: Part 16

389. This done, make a Scale of any convenient length as _W_, whereof each division is a minute of a degree; and take from it in your Compasses 54 Minutes 50 Seconds, the Sum of Semi-diameters of the Moon and Earth’s shadow; and with that extent as a Radius, describe that Circle _OVLG_ round _C_ as a Center.

From the same Scale take 39 Minutes 48 Seconds, the Semi-diameter of the Earth’s shadow, and therewith as a Radius, describe the Circle _UUUU_ for the Earth’s shadow, round _C_ as a Center. Subtract the Moon’s Semi-diameter from the Semi-diameter of the Shadow, and with the difference 24 Minutes 46 seconds as a Radius, taken from the Scale _W_, describe the Circle _YZ_ round the Center _C_.

Draw the right line _AB_ through the Center _C_ for the Ecliptic, and cross it at right Angles with the line _EG_ for the Axis of the Ecliptic.

Because the Moon’s Latitude in this Eclipse is North Descending, § 384, set off the Angle of her visible Path with the Ecliptic 5 Degrees 38 Minutes (Page 202.) from _E_ to _V_; and draw _VCv_ for the Axis of the Moon’s Orbit. Had the Moon’s Latitude been North Ascending, this Angle must have been set off from _E_ to _f_. _N. B._ When the Moon’s Latitude is South Ascending, the Axis of her Orbit lies the same way as when she has North Ascending Latitude; and when her Latitude is North Descending, the Axis of her Orbit lies the same way as when her Latitude is South Descending.

Take the Moon’s true Latitude 9ʹ 56ʺ in your Compasses from the Scale _W_, and set it off from _C_ to _F_ on the Axis of the Ecliptic because the Moon is north of the Ecliptic; (had she been to the South of it, her Latitude must have been set off the contrary way, as from _C_ towards _v_:) and through _F_, at right Angles to the Axis of the Moon’s Orbit _VCv_, draw the right line _LMHNO_ for the Moon’s Orbit, or her Path through the Earth’s shadow. _N. B._ When the Moon’s Latitude is North Ascending, or North Descending, she is above the Ecliptic: but when her Latitude is South Ascending, or South Descending, she is below it.

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.

[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.

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.

EXAMPLE II

_To find the Suns distance from the Node at the Time of New Moon in_
March, _the year before_ CHRIST _424, O. S._

The years 423 added to 1777 make 2200, or 22 Centuries.

Sun from Node
s ° ʹ
At the mean time of New Moon in _March 1777_, Tab. I. 8 23 33
From which subtract the Sun’s distance from the Node
for 2200 years, Table V 3 6 0
--------
Remains the Sun’s distance from the Ascending Node,
_March 21_, 424 years before CHRIST 5 17 33
Which, taken from 6 Signs, the distance of the Nodes
from each other 6 0 0
--------
Leaves the Sun’s distance at that time from the Descending
Node, Descending _viz._ 0 12 27

Which being less than 17 degrees, shews that the Sun was then eclipsed. And as from these short Calculations we find those two antient Eclipses taken at a venture, to be truly recorded; it is natural to imagine that so are all the rest in the catalogue.

Here follow ASTRONOMICAL TABLES, for calculating the Times of NEW and FULL MOONS and ECLIPSES.