337. By Fig. II it is plain, that the Sun is totally or centrally
eclipsed but to a small part of the Earth at any time; because the dark
conical shadow _e_ of the Moon _M_ falls but on a small part of the
Earth: and that the partial Eclipse is confined at that time to the
space included by the Circle _a 0 b_, of which only one half can be
projected in the Figure, the other half being supposed to be hid by the
convexity of the Earth _E_: and likewise, that no part of the Sun is
eclipsed to the large space _YY_ of the Earth, because the Moon is not
between the Sun and that part of the Earth: and therefore to all that
part the Eclipse is invisible. The Earth turns eastward on its Axis, as
from _g_ to _h_, which is the same way that the Moon’s shadow moves; but
the Moon’s motion is much swifter in her Orbit from _s_ to _t_: and
therefore, altho’ Eclipses of the Sun are of longer duration on account
of the Earth’s motion on its Axis, than they would be if that motion was
stopt, yet in 3 minutes and 13 seconds of time, the Moon’s swifter
motion carries her dark shadow quite over any place that its center
touches at the time of greatest obscuration. The motion of the shadow on
the Earth’s Disc is equal to the Moon’s motion from the Sun, which is
about 30-1/2 minutes of a degree every hour at a mean rate; but so much
of the Moon’s Orbit is equal to 30-1/2 degrees of a great Circle on the
Earth, § 320; and therefore the Moon’s shadow goes 30-1/2 degrees or
1830 geographical miles on the Earth in an hour, or 30-1/2 miles in a
minute, which is almost four times as swift as the motion of a
cannon-ball.
[Sidenote: PLATE XI.
Fig. IV.
Phenomena of the Earth as seen from the Sun or New Moon
at different times of the year.]
338. As seen from the Sun or Moon, the Earth’s Axis appears differently
inclined every day of the year, on account of keeping its parallelism
throughout its annual course. Let _E_, _D_, _O_, _N_, be the Earth at
the two Equinoxes and the two Solstices; _N S_ its Axis, _N_ the North
Pole, _S_ the South Pole, _Æ Q_ the Equator, _T_ the Tropic of Cancer,
_t_ the Tropick of Capricorn, and _ABC_ the Circumference of the Earth’s
enlightened Disc as seen from the Sun or New Moon at these times. The
Earth’s Axis has the position _NES_ at the vernal Equinox, lying towards
the right hand, as seen from the Sun or New Moon; its Poles _N_ and _S_
being then in the Circumference of the Disc; and the Equator and all its
parallels seem to be straight lines, because their planes pass through
the observer’s eye looking down upon the Earth from the Sun or Moon
directly over _E_, where the Ecliptic _FG_ intersects the Equator _Æ_.
At the Summer Solstice, the Earth’s Axis has the position _NDS_; and
that part of the Ecliptic _FG_ in which the Moon is then New, touches
the Tropic of Cancer _T_ at _D_. The North Pole _N_ at that time
inclining 23-1/2 degrees towards the Sun, falls so many degrees within
the Earth’s enlightened Disc, because the Sun is then vertical to _D_,
23-1/2 degrees north of the Equator _ÆQ_; and the Equator with all its
parallels seem elliptic curves bending downward, or towards the South
Pole as seen from the Sun: which Pole, together with 23-1/2 degrees all
round it, is hid behind the Disc in the dark Hemisphere of the Earth. At
the autumnal Equinox the Earth’s Axis has the position _NOS_, lying to
the left hand as seen from the Sun or New Moon, which are then vertical
to _O_, where the Ecliptic cuts the Equator _ÆQ_. Both Poles now lie in
the circumference of the Disc, the North Pole just going to disappear
behind it, and the South Pole just entering into it; and the Equator
with all its parallels seem to be straight lines, because their planes
pass through the observer’s eye, as seen from the Sun, and very nearly
so as seen from the Moon. At the Winter Solstice the Earth’s Axis has
the position _NNS_; when its South Pole _S_ inclining 23-1/2 degrees
toward the Sun falls 23-1/2 degrees within the enlightened Disc, as seen
from the Sun or New Moon which are then vertical to the Tropic of
Capricorn _t_, 23-1/2 degrees south of the Equator _ÆQ_; and the Equator
with all its parallels seem elliptic curves bending upward; the North
Pole being as far hid behind the Disc in the dark Hemisphere, as the
South Pole is come into the light. The nearer that any time of the year
is to the Equinoxes or Solstices, the more it partakes of the Phenomena
relating to them.
[Sidenote: PLATE XI.
Various positions of the Earth’s Axis, as seen from the Sun
at different times of the year.]
339. Thus it appears, that from the vernal equinox to the autumnal, the
North Pole is enlightened; and the Equator and all its parallels appear
Semi-ellipses as seen from the Sun, more or less curved as the time is
nearer to or farther from the Summer Solstice; and bending downwards or
towards the South Pole; the reverse of which happens from the autumnal
Equinox to the vernal. A little consideration will be sufficient to
convince the reader, that the Earth’s Axis inclines towards the Sun at
the Summer Solstice; from the Sun at the Winter Solstice; and sidewise
to the Sun at the Equinoxes; but towards the right hand, as seen from
the Sun at the vernal Equinox; and towards the left hand at the
autumnal. From the Winter to the Summer Solstice, the Earth’s Axis
inclines more or less to the right hand, as seen from the Sun; and the
contrary from the Summer to the Winter Solstice.
[Sidenote: How these positions affect solar Eclipses.]
340. The different positions of the Earth’s Axis, as seen from the Sun
at different times of the year, affect solar Eclipses greatly with
regard to particular places; yea so far as would make central Eclipses
which fall at one time of the year invisible if they fell at another,
even though the Moon should always change in the Nodes and at the same
hour of the day: of which indefinitely various affections, we shall only
give Examples for the times of the Equinoxes and Solstices.
[Sidenote: Fig. IV.]
In the same Diagram, let _FG_ be part of the Ecliptic, and _IK_ _ik_
_ik_ _ik_ part of the Moon’s Orbit; both seen edgewise, and therefore
projected into right lines; and let the intersections _N_, _O_, _D_, _E_
be one and the same Node at the above times, when the Earth has the
forementioned different positions; and let the spaces included by the
Circles _P_, _p_, _p_, _p_ be the Penumbra at these times, as its center
is passing over the center of the Earth’s Disc. At the Winter Solstice,
when the Earth’s Axis has the position _NNS_, the center of the Penumbra
_P_ touches the Tropic of Capricorn _t_ in _N_ at the middle of the
general Eclipse; but no part of the Penumbra touches the Tropic of
Cancer _T_. At the Summer Solstice, when the Earth’s Axis has the
position _NDS_ (_iDk_ being then part of the Moon’s Orbit whose Node is
at _D_) the Penumbra _p_ has its center on the Tropic of Cancer _T_ at
the middle of the general Eclipse, and then no part of it touches the
Tropic of Capricorn _t_. At the autumnal Equinox the Earth’s Axis has
the position _NOS_ (_iOk_ being then part of the Moon’s Orbit) and the
Penumbra equally includes part of both Tropics _T_ and _t_ at the middle
of the general Eclipse: at the vernal Equinox it does the same, because
the Earth’s Axis has the position _NES_: But, in the former of these two
last cases, the Penumbra enters the Earth at _A_, north of the Tropic of
Cancer _T_, and leaves it at _m_, south of the Tropic of Capricorn _t_;
having gone over the Earth obliquely southward, as its center described
the line _AOm_: whereas in the latter case the Penumbra touches the
Earth at _n_, south of the Equator _ÆQ_, and describing the line _nEq_
(similar to the former line _AOm_ in open space) goes obliquely
northward over the Earth, and leaves it at _q_, north of the Equator.
In all these circumstances, the Moon has been supposed to change at noon
in her descending Node: had she changed in her ascending Node, the
Phenomena would have been as various the contrary way, with respect to
the Penumbra’s going northward or southward over the Earth. But because
the Moon changes at all hours, as often in one Node as the other, and at
all distances from them both at different times as it happens, the
variety of the Phases of Eclipses are almost innumerable, even at the
same places, considering also how variously the same places are situated
on the enlightened Disc of the Earth, with respect to the Penumbra’s
motion, at the different hours that Eclipses happen.
[Sidenote: How much of the Penumbra falls on the Earth at different
distances from the Nodes.]
341. When the Moon changes 17 degrees short of her descending Node, the
Penumbra _P_ 18 just touches the northern part of the Earth’s Disc, near
the North Pole _N_; and, as seen from that place the Moon appears to
touch the Sun, but hides no part of him from sight. Had the Change been
as far short of the ascending Node, the Penumbra would have touched the
southern part of the Disc near the South Pole _S_. When the Moon changes
12 degrees short of the descending Node, more than a third part of the
Penumbra _P 12_ falls on the northern parts of the Earth at the middle
of the general Eclipse: had she changed as far past the same Node, as
much of the other side of the Penumbra about _P_ would have fallen on
the southern part of the Earth; all the rest in the _expansum_, or open
space. When the Moon changes 6 degrees from the Node, almost the whole
Penumbra _P6_ falls on the Earth at the middle of the general Eclipse.
And lastly, when the Moon changes in the Node, the Penumbra _PN_ takes
the longest course possible on the Earth’s Disc; its center falling on
the middle thereof, at the middle of the general Eclipse. The farther
the Moon changes from either Node within 17 degrees of it, the shorter
is the Penumbra’s continuance on the Earth, because it goes over a less
portion of the Disc, as is evident by the Figure.
[Sidenote: The Earth’s diurnal motion lengthens the duration of solar
Eclipses, which fall without the polar Circles.]
342. The nearer that the Penumbra’s center is to the Equator at the
middle of the general Eclipse, the longer is the duration of the Eclipse
at all those places where it is central; because, the nearer that any
place is to the Equator, the greater is the Circle it describes by the
Earth’s motion on its Axis: and so, the place moving quicker keeps
longer in the Penumbra whose motion is the same way with that of the
place, tho’ faster as has been already mentioned § 337. Thus, (see the
Earth at _D_ and the Penumbra at _12_) whilst the point _b_ in the polar
Circle _abcd_ is carried from _b_ to _c_ by the Earth’s diurnal motion,
the point _d_ on the Tropick of Cancer _T_ is carried a much greater
length from _d_ to _D_: and therefore, if the Penumbra’s center goes one
time over _c_ and another time over _D_, the Penumbra will be longer in
passing over the moving place _d_ than it was in passing over the moving
place _b_. Consequently, central Eclipses about the Poles are of the
shortest duration; and about the Equator of the longest.
[Sidenote: And shortens the duration of some which fall within these
Circles.]
343. In the middle of Summer the whole frigid Zone included by the polar
Circle _abcd_ is enlightened; and if it then happens that the Penumbra’s
center goes over the north Pole, the Sun will be eclipsed much the same
number of Digits at _a_ as at _c_; but whilst the Penumbra moves
eastward over _c_ it moves westward over _a_, because with respect to
the Penumbra, the motions of _a_ and _c_ are contrary: for _c_ moves the
same way with the Penumbra towards _d_, but _a_ moves the contrary way
towards _b_; and therefore the Eclipse will be of longer duration at _c_
than at _a_. At _a_ the Eclipse begins on the Sun’s eastern limb, but at
_c_ on his western: at all places lying without the polar Circles, the
Sun’s Eclipses begin on his western limb, or near it, and end on or near
his eastern. At those places where the Penumbra touches the Earth, the
Eclipse begins with the rising Sun, on the top of his western or
uppermost edge; and at those places where the Penumbra leaves the Earth,
the Eclipse ends with the setting Sun, on the top of his eastern edge
which is then the uppermost, just at its disappearing in the Horizon.
[Sidenote: The Moon has no Atmosphere.]
344. If the Moon were surrounded by an Atmosphere of any considerable
Density, it would seem to touch the Sun a little before the Moon made
her appulse to his edge, and we should see a little faintness on that
edge before it were eclipsed by the Moon: But as no such faintness has
been observed, at least so far as I ever heard, it seems plain, that the
Moon has no such Atmosphere as that of the Earth. The faint ring of
light surrounding the Sun in total Eclipses, called by CASSINI _la
Chevelure du Soleil_, seems to be the Atmosphere of the Sun; because it
has been observed to move equally with the Sun, not with the Moon.
[Sidenote: PLATE XI.]
345. Having been so prolix concerning Eclipses of the Sun, we shall drop
that subject at present, and proceed to the doctrine of lunar Eclipses;
which, being more simple, may be explained in less time.
[Sidenote: Eclipses of the Moon.