375. Make a line of Sines equal in length to _Ng_ or _Nh_, and take off
with your Compasses from it the Sine of the Sun’s distance from the
nearest Solstice, which in the present case is 77° 51ʹ § 367, and set
that distance to the right hand, from _N_ to _P_, on the line _gNh_,
because the Sun being in Aries § 359, the Earth’s Axis lies to the right
hand of the Axis of the Ecliptic § 374: then draw the straight line
_C_XII_P_, for the Earth’s Axis and the Universal Meridian; of both
which _P_ is the North Pole.
[Sidenote: Path of a given Place on the Disc as seen from the Sun.]
376. To draw the parallel of Latitude of any given Place (suppose
_London_) which parallel is the visible Path of the Place On the Disc,
as seen from the Sun, from the time that the Sun rises till it sets;
subtract the Latitude of the Place (_London_) 51-1/2 degrees from 90
degrees, and there remains 38-1/2; which take from the Line of Chords in
your Compasses, and set it from _h_ (where the Universal Meridian _CP_
cuts the periphery of the Semi-disc) to VI and VI; and draw the occult
Line VI_L_VI. Then, on the left hand of the Earth’s Axis, set off the
Chord of the Sun’s Declination 4° 48ʹ 5ʺ § 367, from VI to _D_ and to
_F_; set off the same on the right hand from VI to _E_ and to _G_; and
draw the occult Lines _DsE_ and _F_XII_G_ parallel to VI _L_ VI.
[Sidenote: Situation of the Place on the Disk from Sun-rise to Sun-set.]
377. Bisect _s_ XII in _K_, and through the point _K_ draw the black
Line VI_K_V1 parallel to the occult or dotted Line VI_L_VI. Then, making
_AC_ the Radius or length of a Line of Lines, set off the Sine of 38-1/2
degrees, the Co-Latitude of _London_, from _K_ to VI and VI; and with
that extent as a Radius, describe the Semi-Circle VI 7 8 9 &c. and
divide it into 12 equal parts, beginning at VI. From these divisions,
draw the occult Lines 7_m_, 8_l_, 9_k_, &c. all to the Line VI_K_VI, and
parallel to _C_XII_P_. Then, with _K_XII as a Radius, describe the
Circle _abcdef_, round the Center _K_, and divide the Quadrant _a_XII
into six equal parts, as _ab_, _bc_, _cd_, _de_, &c. Then, through these
points of division _b_, _c_, _d_, _e_, and _f_, draw the occult Lines
VII_b_V, VIII_c_IIII, IX_d_III, &c. intersecting the former Lines 7_m_,
8_l_, 9_k_, 10_i_, &c. in the points VII, VIII, IX, X, XI, &c. which
points mark the situation of _London_ on the Earth’s Disc as seen from
the Sun at these hours respectively, from six in the morning till six at
night: and if the elliptic Curve VI, VII, VIII, &c. be drawn through
these points, it will represent the parallel of _London_, or the path it
seems to describe as viewed from the Sun, from Sun-rise to Sun-set.
_N.B._ When the Sun’s Declination is North, the said Curve is the
diurnal Path of _London_; and the opposite part VI_s_VI is it’s
nocturnal Path behind the Disc, or in the obscure part thereof, § 338,
339. But if the Sun’s Declination had been South, the Curve VI_s_VI
would have been the diurnal path of _London_; in which case the Lines
7_m_, 8_l_, &c. must have been continued thro’ the right Line VI_K_VI,
and their lengths beyond that line determined by dividing the Quadrant
_s a_ of the little Circle _abcd_ into six equal parts, and drawing the
parallels VII_b_, VIII_c_ &c. through that division, in the same manner
as done on the side _K_ XII; and the Curve VII, VIII, IX, &c. would have
been the nocturnal Path. It is requisite to divide the hours of the
diurnal Path into quarters, as in the Diagram; and if possible into
minutes also.
[Sidenote: Axis of the Moon’s Orbit.]
378. From the Line of Chords § 372 take the Angle of the Moon’s visible
Path with the Ecliptic, _viz._ 5° 38ʹ § 367: and note, that when the
Moon’s Latitude is _North Ascending_, as in the present case, the Chord
of this Angle must be set off to the left hand of the Axis of the
Ecliptic _CH_, as from _H_ to _M_, and the right line _CM_ drawn for the
Axis of the Moon’s Orbit: but when the Moon’s Latitude is _North
Descending_, this Angle and Axis must be set to the right hand, or from
_H_ toward _h_. When the Moon’s Latitude _South Ascending_, the Axis of
her Orbit lies the same way as when her Latitude is _North Ascending_;
and when _South Descending_, the same way as when _North Descending_.
[Sidenote: Path of the Penumbra’s center over the Earth.]
379. Take the Moon’s Latitude, 40ʹ 9ʺ § 367, from the Scale _CA_, and
set it from _C_ to _T_ on the Axis of the Ecliptic; and through _T_, at
right Angles to the Axis of the Moon’s Orbit _CM_, draw the straight
Line _RTS_; which is the Moon’s Path, or Line that the center of her
shadow and Penumbra describes in going over the Earth’s Disc. The Point
_T_ in the Axis of the Ecliptic is the Place where the true Conjunction
of the Sun and Moon falls, according to the Tables; and the Point _W_,
in the Axis of the Moon’s Orbit, is that where the center of the
Penumbra approaches nearest to the center of the Earth’s Disc, and
consequently the middle of the general Eclipse.
[Sidenote: It’s Place on the Earth’s Disc shewn for every minute of it’s
Transit.]
380. Take the Moon’s true Horary Motion from the Sun 27ʹ 50ʺ § 367, from
the Scale _CA_ with your Compasses (every division of the Scale being a
minute of a Degree) and with that extent make marks in the Line of the
Moon’s Path _RTS_: then divide each of these equal spaces by dots into
60 equal parts or horary minutes, and set the hours to every 60th
minute, in such a manner that the dot; signifying the precise minute of
New Moon by the Tables, may fall in the Point _T_ where the Axis of the
Ecliptic cuts the Line of the Moon’s Path; which, in this Eclipse, is
the 25th minute past ten in the Forenoon: and then the other marks will
shew the places on the Earth’s Disc where the center of the Penumbra is,
at the hours and minutes denoted by them, during its transit over the
Earth.
[Sidenote: Middle of the Eclipse.