Astronomy Explained Upon Sir Isaac Newton's Principles And made easy to those who have not studied mathematics

Part 26

Chapter 263,640 wordsPublic domain

The Eclipses from STRUYK were observed: those from RICCIOLUS calculated: the following from _L’Art de verifier les Dates_, are only those which are visible in _Europe_ for the present century: those which are total are marked with a _T_; and _M_ signifies Morning, _A_ Afternoon.

Visible ECLIPSES from 1700 to 1800.

+------+-----+----------+------------+ | Aft. | | Months | Time of | | Chr. | | and | the Day | | | | Days. | or Night. | +------+-----+----------+------------+ | 1701 | 🌑︎ | Feb. 22 | 11 A. | | 1703 | 🌑︎ | Jan. 3 | 7 M. | | 1703 | 🌑︎ | June 29 | 1 M. _T._ | | 1703 | 🌑︎ | Dec. 23 | 7 M. _T._ | | 1704 | 🌑︎ | Dec. 11 | 7 M. | | 1706 | 🌑︎ | Apr. 28 | 2 M. | | 1706 | ☉ | May 12 | 10 M. | | 1706 | 🌑︎ | Oct. 21 | 7 A. | | 1707 | 🌑︎ | Apr. 17 | 2 M. _T._ | | 1708 | 🌑︎ | April 5 | 6 M. | | 1708 | ☉ | Dec. 14 | 8 M. | | 1708 | 🌑︎ | Sept. 29 | 9 A. | | 1709 | ☉ | Mar. 11 | 2 A. | | 1710 | 🌑︎ | Feb. 13 | 11 A. | | 1710 | ☉ | Feb. 28 | 1 A. | | 1711 | ☉ | July 15 | 8 A. | | 1711 | 🌑︎ | July 29 | 6 A. _T._ | | 1712 | 🌑︎ | Jan. 23 | 8 A. | | 1713 | 🌑︎ | June 8 | 6 A. | | 1713 | 🌑︎ | Dec. 2 | 4 M. | | 1715 | ☉ | May 3 | 9 M. _T._ | | 1715 | 🌑︎ | Nov. 11 | 5 M. | | 1717 | 🌑︎ | Mar. 27 | 3 M. | | 1717 | 🌑︎ | May 20 | 6 A. | | 1718 | 🌑︎ | Sept. 9 | 8 A. _T._ | | 1719 | 🌑︎ | Aug. 29 | 9 A. | | 1721 | 🌑︎ | Jan. 13 | 3 A. | | 1722 | 🌑︎ | June 29 | 3 M. | | 1722 | ☉ | Dec. 8 | 3 A. | | 1722 | 🌑︎ | Dec. 22 | 4 A. | | 1724 | ☉ | May 22 | 7 A. _T._ | | 1724 | 🌑︎ | Nov. 1 | 4 M. | | 1725 | 🌑︎ | Oct. 21 | 7 A. | | 1726 | ☉ | Sept. 25 | 6 A. | | 1726 | 🌑︎ | Oct. 11 | 5 M. | | 1727 | ☉ | Sept. 15 | 7 M. | | 1729 | 🌑︎ | Feb. 13 | 9 A. _T._ | | 1729 | 🌑︎ | Aug. 9 | 1 M. | | 1730 | 🌑︎ | Feb. 4 | 4 M. | | 1731 | 🌑︎ | June 20 | 2 M. | | 1732 | 🌑︎ | Dec. 1 | 10 A. _T._ | | 1733 | ☉ | May 13 | 7 A. | | 1733 | 🌑︎ | May 28 | 7 A. | | 1735 | 🌑︎ | Oct. 2 | 1 M. | | 1736 | 🌑︎ | Mar. 26 | 12 A. _T._ | | 1736 | 🌑︎ | Sept. 20 | 3 M. _T._ | | 1736 | ☉ | Oct. 4 | 6 A. | | 1737 | ☉ | Mar. 1 | 4 A. | | 1737 | 🌑︎ | Sept. 9 | 4 M. | | 1738 | ☉ | Aug. 15 | 11 M. | | 1739 | 🌑︎ | Jan. 24 | 11 A. | | 1739 | ☉ | Aug. 4 | 5 A. | | 1739 | ☉ | Dec. 30 | 9 M. | | 1740 | 🌑︎ | Jan. 13 | 11 A. _T._ | | 1741 | 🌑︎ | Jan. 1 | 12 A. | | 1743 | 🌑︎ | Nov. 2 | 3 M. _T._ | | 1744 | 🌑︎ | Aug. 26 | 9 A. | | 1746 | 🌑︎ | Aug. 30 | 12 A. | | 1747 | 🌑︎ | Feb. 14 | 5 M. _T._ | | 1748 | ☉ | July 25 | 11 M. | | 1748 | 🌑︎ | Aug. 8 | 12 A. | | 1749 | 🌑︎ | Dec. 23 | 8 A. | | 1750 | ☉ | Jan. 8 | 9 M. | | 1750 | 🌑︎ | June 19 | 9 A. _T._ | | 1750 | 🌑︎ | Dec. 13 | 7 M. | | 1751 | 🌑︎ | June 9 | 2 M. | | 1751 | 🌑︎ | Dec. 2 | 10 A. | | 1752 | ☉ | May 13 | 8 A. | | 1753 | 🌑︎ | Apr. 17 | 7 A. | | 1753 | ☉ | Oct. 26 | 10 M. | | 1755 | 🌑︎ | Mar. 28 | 1 M. | | 1757 | 🌑︎ | Feb. 4 | 6 M. | | 1757 | 🌑︎ | July 30 | 12 A. | | 1758 | 🌑︎ | Jan. 24 | 7 M. _T._ | | 1758 | ☉ | Dec. 30 | 7 M. | | 1759 | ☉ | June 24 | 7 A. | | 1759 | ☉ | Dec. 19 | 2 A. | | 1760 | 🌑︎ | May 29 | 9 A. | | 1760 | ☉ | June 13 | 7 M. | | 1760 | 🌑︎ | Nov. 22 | 9 A. | | 1761 | 🌑︎ | May 18 | 11 A. _T._ | | 1762 | 🌑︎ | May 8 | 4 M. | | 1762 | ☉ | Oct. 17 | 8 M. | | 1762 | 🌑︎ | Nov. 1 | 8 A. | | 1763 | ☉ | Apr. 13 | 8 M. | | 1764 | ☉ | Apr. 1 | 10 M. | | 1764 | 🌑︎ | Apr. 16 | 1 M. | | 1765 | ☉ | Mar. 21 | 2 A. | | 1765 | ☉ | Aug. 16 | 5 A. | | 1766 | 🌑︎ | Feb. 24 | 7 A. | | 1766 | ☉ | Aug. 5 | 7 A. | | 1768 | 🌑︎ | Jan. 4 | 5 M. | | 1768 | 🌑︎ | June 30 | 4 M. _T._ | | 1768 | 🌑︎ | Dec. 23 | 4 A. _T._ | | 1769 | ☉ | June 4 | 8 M. | | 1769 | 🌑︎ | Dec. 13 | 7 M. | | 1770 | ☉ | Nov. 17 | 10 M. | | 1771 | 🌑︎ | Apr. 28 | 2 M. | | 1771 | 🌑︎ | Oct. 23 | 5 A. | | 1772 | 🌑︎ | Oct. 11 | 6 A. _T._ | | 1772 | ☉ | Oct. 26 | 10 M. | | 1773 | ☉ | Mar. 23 | 5 M. | | 1773 | 🌑︎ | Sept. 30 | 7 A. | | 1774 | ☉ | Mar. 12 | 10 M. | | 1776 | 🌑︎ | July 31 | 1 M. _T._ | | 1776 | ☉ | Aug. 14 | 5 M. | | 1777 | ☉ | Jan. 9 | 5 A. | | 1778 | ☉ | June 24 | 4 A. | | 1778 | 🌑︎ | Dec. 4 | 6 M. | | 1779 | 🌑︎ | May 30 | 5 M. _T._ | | 1779 | ☉ | June 14 | 8 M. | | 1779 | 🌑︎ | Nov. 23 | 8 A. | | 1780 | ☉ | Oct. 27 | 6 A. | | 1780 | 🌑︎ | Nov. 12 | 4 M. | | 1781 | ☉ | Apr. 23 | 6 A. | | 1781 | ☉ | Oct. 17 | 8 M. | | 1782 | 🌑︎ | Apr. 12 | 7 A. | | 1783 | 🌑︎ | Mar. 18 | 9 A. _T._ | | 1783 | 🌑︎ | Sept. 10 | 11 A. _T._ | | 1784 | 🌑︎ | Mar. 7 | 3 M. | | 1785 | ☉ | Feb. 9 | 1 A. | | 1787 | 🌑︎ | Jan. 3 | 12 A. _T._ | | 1787 | ☉ | Jan. 19 | 10 M. | | 1787 | ☉ | June 15 | 5 A. | | 1787 | 🌑︎ | Dec. 24 | 3 A. | | 1788 | ☉ | June 4 | 9 M. | | 1789 | 🌑︎ | Nov. 2 | 12 A. | | 1790 | 🌑︎ | Apr. 28 | 12 A. _T._ | | 1790 | 🌑︎ | Oct. 23 | 1 M. _T._ | | 1791 | ☉ | April 3 | 1 A. | | 1791 | 🌑︎ | Oct. 12 | 3 M. | | 1792 | ☉ | Sept. 16 | 11 M. | | 1793 | 🌑︎ | Feb. 25 | 10 A. | | 1793 | ☉ | Sept. 5 | 3 A. | | 1794 | ☉ | Jan. 31 | 4 A. | | 1794 | 🌑︎ | Feb. 14 | 11 A. _T._ | | 1794 | ☉ | Aug. 25 | 5 A. | | 1795 | 🌑︎ | Feb. 4 | 1 M. | | 1795 | ☉ | July 16 | 9 M. | | 1795 | 🌑︎ | July 31 | 8 A. | | 1797 | ☉ | June 25 | 8 A. | | 1797 | 🌑︎ | Dec. 4 | 6 M. | | 1798 | 🌑︎ | May 27 | 7 A. _T._ | | 1800 | 🌑︎ | Oct. 2 | 11 A. | +------+-----+----------+------------+

328. _A List of Eclipses, and historical Events, which happened about the same Times, from_ RICCIOLUS.

[Sidenote: Historical Eclipses.]

After CHRIST. | | 59 | _April_ 30 | An Eclipse of the Sun. This is reckoned among | | the prodigies, on account of the murther of | | _Agrippinus_ by _Nero_. | | 237 | _April_ 12 | A total Eclipse of the Sun. A sign that the reign | | of the _Gordiani_ would not continue long. A sixth | | persecution of the Christians. | | 306 | _July_ 27 | An Eclipse of the Sun. The Stars were seen, | | and the Emperor _Constantius_ died. | | 840 | _May_ 4 | A dreadful Eclipse of the Sun. And _Lewis_ the | | Pious died within six months after it. | | 1009 | ---- | An Eclipse of the Sun. And _Jerusalem_ taken by | | the _Saracens_. | | 1133 | _Aug._ 2 | A terrible Eclipse of the Sun. The Stars were | | seen. A schism in the church, occasioned by there | | being three Popes at once.

[Sidenote: The superstitious notions of the antients with regard to Eclipses.

PLATE XI.]

329. I have not cited one half of RICCIOLUS’s list of potentous Eclipses; and for the same reason that he declines giving any more of them than what that list contains: namely, that ’tis most disagreeable to dwell any longer on such nonsense, and as much as possible to avoid tiring the reader: the superstition of the antients may be seen by the few here copied. My author farther says, that there were treatises written to shew against what regions the malevolent effects of any particular Eclipse was aimed: and the writers affirmed, that the effects of an Eclipse of the Sun continued as many years as the Eclipse lasted hours; and that of the Moon as many months.

[Sidenote: Very fortunate once for CHRISTOPHER COLUMBUS.]

330. Yet such idle notions were once of no small advantage to CHRISTOPHER COLUMBUS; who, in the year 1493, was driven on the island of _Jamaica_, where he was in the greatest distress for want of provisions, and was moreover refused any assistance from the inhabitants; on which he threatened them with a plague, and that in token of it there should be an Eclipse: which accordingly fell on the day he had foretold, and so terrified the Barbarians, that they strove who should be first in bringing him all sorts of provisions; throwing them at his feet, and imploring his forgiveness. RICCIOLUS’s _Almagest_, Vol. I. 1. v. c. ii.

[Sidenote: Why there are more visible Eclipses of the Moon than of the Sun.]

331. Eclipses of the Sun are more frequent than of the Moon, because the Sun’s ecliptic limits are greater than the Moon’s § 317: yet we have more visible Eclipses of the Moon than of the Sun, because Eclipses of the Moon are seen from all parts of that Hemisphere of the Earth which is next her, and equally great to each of these parts; but the Sun’s Eclipses are visible only to that small portion of the Hemisphere next him whereon the Moon’s shadow falls; as shall be explained by and by at large.

[Sidenote: Fig. I.

Total and annular Eclipses of the Sun.

PLATE XI.]

332. The Moon’s Orbit being elliptical, and the Earth in one of its focuses, she is once at her least distance from the Earth, and once at her greatest in every Lunation. When the Moon changes at her least distance from the Earth, and so near the Node that her dark shadow falls on the Earth, she appears big enough to cover the whole [75]Disc of the Sun from that part on which her shadow falls; and the Sun appears totally eclipsed there, as at _A_, for some minutes: But when the Moon changes at her greatest distance from the Earth, and so near the Node that her dark shadow is directed towards the Earth, her diameter subtends a less angle than the Sun’s; and therefore she cannot hide his whole Disc from any part of the Earth, nor does her shadow reach it at that time; and to the place over which the point of her shadow hangs, the Eclipse is annular as at _B_; the Sun’s edge appearing like a luminous ring all around the body of the Moon. When the Change happens within 17 degrees of the Node, and the Moon at her mean distance from the Earth, the point of her shadow just touches the Earth, and she eclipseth the Sun totally to that small spot whereon her shadow falls; but the darkness is not of a moment’s continuance.

[Sidenote: The longest duration of total Eclipses of the Sun.]

333. The Moon’s apparent diameter when largest exceeds the Sun’s when least only 1 minute 38 seconds of a degree: And in the greatest Eclipse of the Sun that can happen at any time and place, the total darkness continues no longer than whilst the Moon is going 1 minute 38 seconds from the Sun in her Orbit; which is about 3 minutes and 13 seconds of an hour.

[Sidenote: To how much of the Earth the Sun may be totally or partially eclipsed at once.]

334. The Moon’s dark shadow covers only a spot on the Earth’s surface, about 180 _English_ miles broad, when the Moon’s diameter appears largest and the Sun’s least; and the total darkness can extend no farther than the dark shadow covers. Yet the Moon’s partial Shadow or Penumbra may then cover a circular space 4900 miles in diameter, within all which the Sun is more or less eclipsed as the places are less or more distant from the Center of the Penumbra. When the Moon changes exactly in the Node, the Penumbra is circular on the Earth at the middle of the general Eclipse; because at that time it falls perpendicularly on the Earth’s surface: But at every other moment it falls obliquely, and will therefore be elliptical; and the more so, as the time is longer before or after the middle of the general Eclipse; and then, much greater portions of the Earth’s surface are involved in the Penumbra.

[Sidenote: Duration of general and particular Eclipses.

The Moon’s dark shadow.

And Penumbra.]

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.

PLATE XI.

Fig. III.]

To an observer on the Earth at _b_, the eastern limb of the Moon at _d_ seems to touch the western limb of the Sun at _W_, when the Moon is at _M_; and the Sun’s Eclipse begins at _b_; appearing as at _A_ in Fig. III at the left hand; but at the same moment of absolute time to an observer at _a_ in Fig. II the western edge of the Moon at _c_ leaves the eastern edge of the Sun at _V_, and the Eclipse ends, as at the right hand _C_ of Fig. III. At the very same instant, to all those who live on the Circle marked _1_ on the Earth _E_ in Fig. II, the Moon _M_ cuts off or darkens a twelfth part of the Sun _S_, and eclipses him one Digit, as at _1_ in Fig. III: to those who live on the Circle marked _2_ in Fig. II the Moon cuts off two twelfth parts of the Sun, as at _2_ in Fig. III: to those on the Circle _3_, three parts; and so on to the center at _12_ in Fig. II, where the Sun is centrally eclipsed as at _B_ in the middle of Fig. III: under which Figure there is a scale of hours and minutes, to shew at a mean state how long it is from the beginning to the end of a central Eclipse of the Sun on the parallel of _London_; and how many Digits are eclipsed at any particular time from the beginning at _A_ to the middle at _B_, or the end at _C_. Thus in 16 minutes from the beginning, the Sun is two Digits eclipsed; in an hour and five minutes, 8 Digits; and in an hour and thirty-seven minutes, 12 Digits.

[Sidenote: Fig. II.

The Velocity of the Moon’s shadow on the Earth.

Fig. IV.]

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.]