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.