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.
In this Construction it is supposed that the Equator, Tropics, Parallel
of _London_, and Meridians through every 15th degree of Longitude are
projected in visible Lines on the Earth’s Disc, as seen from the Sun at
almost an infinite distance; that the Angle under which the Moon’s
diameter is seen, during the time of the Eclipse, continues invariably
the same; that the Moon’s motion is uniform, and her Path rectilineal,
for that time. But all these suppositions do not exactly agree with the
truth; and therefore, supposing the Elements § 367, given by the Tables
to be perfectly accurate, yet the time and phases of the Eclipse deduced
from it’s Construction will not answer exactly to what passeth in the
Heavens; but may be two or three minutes wrong though done with the
utmost care. Moreover, the Paths of all Places of considerable Latitude
go nearer the center of the Disc as seen from the Moon than these
Constructions make them; because the Earth’s Disc is projected as if the
Earth were a perfect sphere, although it is known to be a spheroid.
Consequently, the Moon’s shadow will go farther North in places of
northern Latitude, and farther South in places of southern Latitude than
these projections answer to. Hence we may venture to predict that this
Eclipse will be more annular at _London_ (that is, the annulus will be
somewhat broader on the southern Limb of the Sun) than the Diagram shews
it.
383. Having shewn how to compute the times and project the phases of a
Solar Eclipse, we now proceed to those of the Lunar. And it has been
already mentioned § 317, that when the Full Moon is within 12 degrees of
either of her Nodes, she must be eclipsed. We shall now enquire whether
or no the Moon will be eclipsed _May 18, 1761, N. S._ at 32 minutes past
10 at Night. See page 193.
[Sidenote: Table IV.