335. When the Penumbra first touches the Earth the general Eclipse
begins: when it leaves the Earth the general Eclipse ends: from the
beginning to the end the Sun appears eclipsed in some part of the Earth
or other. When the Penumbra touches any place the Eclipse begins at that
place, and ends when the Penumbra leaves it. When the Moon changes in
the Node, the Penumbra goes over the center of the Earth’s Disc as seen
from the Moon; and consequently, by describing the longest line possible
on the Earth, continues the longest upon it; namely, at a mean rate, 5
hours 50 minutes: more, if the Moon be at her greatest distance from the
Earth, because she then moves slowest; less, if she be at her least
distance, because of her quicker motion.
[Sidenote: Fig. II.]
336. To make the last five articles and several other Phenomena plainer,
let _S_ be the Sun, _E_ the Earth, _M_ the Moon, and _AMP_ the Moon’s
Orbit. Draw the right line _Wc 12_ from the western edge of the Sun at
_W_, touching the western edge of the Moon at _c_ and the Earth at _12_:
draw also the right line _Vd 12_ from the eastern edge of the Sun at
_V_, touching the eastern edge of the Moon at _d_ and the Earth at _12_:
the dark space _ce 12 d_ included between those lines is the Moon’s
shadow, ending in a point at _12_ where it touches the Earth; because in
this case the Moon is supposed to change at _M_ in the middle between
_A_ the Apogee, or farthest point of her Orbit from the Earth, and _P_
the Perigee, or nearest point to it. For, had the point _P_ been at _M_,
the Moon had been nearer the Earth; and her dark shadow at _e_ would
have covered a space upon it about 180 miles broad, and the Sun would
have been totally darkened as at _A_ (Fig I) with some continuance: but
had the point _A_ (Fig. II) been at _M_, the Moon would have been
farther from the Earth, and her shadow would have ended in a point about
_e_, and therefore the Sun would have appeared as at _B_ (Fig. I) like a
luminous ring all around the Moon. Draw the right lines _WXdh_ and
_VXcg_, touching the contrary sides of the Sun and Moon, and ending on
the Earth at _a_ and _b_: draw also the right line _SXM 12_, from the
center of the Sun’s Disc, through the Moon’s center, to the Earth at
_12_; and suppose the two former lines _WXdh_ and _VXcg_ to revolve on
the line _SXM 12_ as an Axis, and their points _a_ and _b_ will describe
the limits of the Penumbra _TT_ on the Earth’s surface, including the
large space _a0b12a_; within which the Sun appears more or less eclipsed
as the places are more or less distant from the verge of the Penumbra
_a0b_.
[Sidenote: Digits, what.]
Draw the right line _y 12_ across the Sun’s Disc, and parallel to the
plane of the Moon’s Orbit; divide this line into twelve equal parts, as
in the Figure, for the twelve [76]Digits of the Sun’s diameter: and at
equal distances from the center of the Penumbra _TT_ to its edge on the
Earth, or from _12_ to _0_, draw twelve concentric Circles, as marked
with the numeral Figures _1_ _2_ _3_ _4_ &c. and remember that the
Moon’s motion in her Orbit _AMP_ is from west to east, as from _s_ to
_t_. Then,
[Sidenote: The different phases of a solar Eclipse.