Part 42
If a thread be tied loosely round two pins stuck in a table, and moderately stretched by the point of a black lead pencil carried round by an even motion and light pressure of the hand, an oval or ellipsis will be described; the two points where the pins are fixed being called the _foci_ or focuses thereof. The Orbits of all the Planets are elliptical, and the Sun is placed in or near to one of the _foci_ of each of them: and _that_ in which he is placed, is called the _lower focus_.
Footnote 3:
Astronomers are not far from the truth, when they reckon the Sun’s center the lower focus of all the Planetary Orbits. Though strictly speaking, if we consider the focus of Mercury’s Orbit to be in the Sun’s center, the focus of Venus’s Orbit will be in the common center of gravity of the Sun and Mercury; the focus of the Earth’s Orbit in the common center of gravity of the Sun, Mercury, and Venus; the focus of the Orbit of Mars in the common center of gravity of the Sun, Mercury, Venus, and the Earth; and so of the rest. Yet, the focuses of the Orbits of all the Planets, except Saturn, will not be sensibly removed from the center of the Sun; nor will the focus of Saturn’s Orbit recede sensibly from the common center of gravity of the Sun and Jupiter.
Footnote 4:
As represented in Plate III. Fig. I. and described in § 138.
Footnote 5:
When he is between the Earth and the Sun in the nearer part of his Orbit.
Footnote 6:
The time between the Sun’s rising and setting.
Footnote 7:
One entire revolution, or 24 hours.
Footnote 8:
These are lesser circles parallel to the Equator, and as many degrees from it, towards the Poles, as the Axis of the Planet is inclined to the Axis of it’s Orbit. When the Sun is advanced so far north or south of the Equator as to be directly over either Tropic, he goes no farther; but returns towards the other.
Footnote 9:
These are lesser circles round the Poles, and as far from them as the Tropics are from the Equator. The Poles are the very north and south points of the Planet.
Footnote 10:
A Degree is a 360th part of any Circle. See § 21.
Footnote 11:
The Limit of any inhabitant’s view, where the Sky seems to touch the Planet all round him.
Footnote 12:
This is not strictly true, as will appear when we come to treat of the Recession of the Equinoctial Points in the Heavens § 246; which recession is equal to the deviation of the Earth’s Axis from it’s parallelism: but this is rather too small to be sensible in an age, except to those who make very nice observations.
Footnote 13:
_Memoirs d’Acad. ann. 1720._
Footnote 14:
The Moon’s Orbit crosses the Ecliptic in two opposite points called the Moon’s Nodes; so that one half of her Orbit is above the Ecliptic, and the other half below it. The Angle of it’s Obliquity is 5-1/3 degrees.
Footnote 15:
CASSINI _Elements d’Astronomie_, _Liv._ ix. _Chap._ 3.
Footnote 16:
Optics, Art. 95.
Footnote 17:
Mr. WHISTON, in his Astronomical Principles of Religion.
Footnote 18:
As will be demonstrated in the ninth Chapter.
Footnote 19:
Optics, B. I. § 1178.
Footnote 20:
Astronomy, B. II. §. 838.
Footnote 21:
Philosophy, Vol. I. p. 401.
Footnote 22:
Account of Sir Isaac Newton’s _Philosophical Discoveries_, B. III. c. 2. § 3.
Footnote 23:
_Elements d’Astronomie_, § 381.
Footnote 24:
The face of the Sun, Moon, or any Planet, as it appears to the eye, is called it’s Disc.
Footnote 25:
The utmost limit of a person’s view, where the Sky seems to touch the Earth all around, is called his Horizon; which shifts as the person changes his place.
Footnote 26:
The Plane of a Circle, or a thin circular Plate, being turned edgewise to the eye appears to be a straight line.
Footnote 27:
A Degree is the 360th part of a Circle.
Footnote 28:
Here we do not mean such a conjunction, as that the nearer Planet should hide all the rest from the observer’s sight; (for that would be impossible unless the intersections of all their Orbits were coincident, which they are not, _See_ § 21.) but when they were all in a line crossing the standard Orbit at right Angles.
Footnote 29:
The ORRERY fronting the Title-page.
Footnote 30:
To make the projectile force balance the gravitating power so exactly as that the body may move in a Circle, the projectile velocity of the body must be such as it would have acquired by gravity alone in falling through half the radius.
Footnote 31:
Astronomical Principles of Religion, p. 66.
Footnote 32:
Δὸς ποῦ στῶ, καὶ τὸν κόσμον κινήσω, _i. e._ Give me a place to stand on, and I shall move the Earth.
Footnote 33:
If the Sun was not agitated about the common center of gravity of the whole System, and the Planets did not act mutually upon one another, their Orbits would be elliptical, and the areas described by them would be exactly proportionate to the times of description § 153. But observations prove that these areas are not in such exact proportion, and are most varied when the greatest number of Planets are in any particular quarter of the Heavens. When any two Planets are in conjunction, their mutual attractions, which tend to bring them nearer to one another, draws the inferior one a little farther from the Sun, and the superior one a little nearer to him; by which means, the figure of their Orbits is somewhat altered; but this alteration is too small to be discovered in several ages.
Footnote 34:
Religious Philosopher, Vol. III. page 65.
Footnote 35:
This will be demonstrated in the eleventh Chapter.
Footnote 36:
A fine net-work membrane in the bottom of the eye.
Footnote 37:
Book I. Art. 57.
Footnote 38:
A medium, in this sense, is any transparent body, or that through which the rays of light can pass; as water, glass, diamond, air; and even a vacuum is sometimes called a Medium.
Footnote 39:
NEWTON’s _System of the World_, _p._ 120.
Footnote 40:
This is evident from pumps, since none can draw water higher than 33 foot.
Footnote 41:
Namely 10000 times the distance of Saturn from the Sun; p. 94.
Footnote 42:
See his Astronomy, p. 232.
Footnote 43:
As far as one can see round him on the Earth.
Footnote 44:
[Sidenote: Fig. V.]
An Angle is the inclination of two right lines, as _IH_ and _KH_, meeting in a point at _H_; and in describing an Angle by three letters, the middle letter always denotes the angular point: thus, the above lines _IH_ and _KH_ meeting each other at _H_, make the Angle _IHK_. And the point _H_ is supposed to be the center of a Circle, the circumference of which contains 360 equal parts called degrees. A fourth part of a Circle, called a Quadrant, as _GE_, contains 90 degrees; and every Angle is measured by the number of degrees in the arc it cuts off; as the angle _EHP_ is 45 degrees, the Angle _EHF_ 33, &c: and so the Angle _EHF_ is the same with the angle _CHN_, and also with the Angle _AHM_, because they all cut off the same arc or portion of the Quadrant _EG_; and so likewise the Angle _EHF_ is greater than the Angle _CHD_ or _AHL_, because it cuts off a greater arc.
The nearer an object is to the eye the bigger it appears, and under the greater Angle is it seen. To illustrate this a little, suppose an Arrow in the position _IK_, perpendicular to the right line _HA_ drawn from the eye at _H_ through the middle of the Arrow at _O_. It is plain that the Arrow is seen under the Angle _IHK_, and that _HO_, which is it’s distance from the eye, divides into halves both the Arrow and the Angle under which it is seen: _viz._ the Arrow into _IO_, _OK_, and the Angle into _IHO_ and _KHO_: and this will be the case whatever distance the Arrow is placed at. Let now three Arrows, all of the same length with _IK_, be placed at the distances _HA_, _HC_, _HE_, still perpendicular to, and bisected by the right line _HA_; then will _AB_, _CD_, _EF_, be each equal to, and represent _IO_; and _AB_ (the same as _IO_) will be seen from _H_ under the Angle _AHB_; but _CD_ (the same as _IO_) will be seen under the Angle _CHD_ or _AHL_; and _EF_ (the same as _IO_) will be seen under the Angle _EHF_, or _CHN_, or _AHM_. Also, _EF_ or _IO_ at the distance _HE_ will appear as long as _CN_ would at the distance _HC_, or as _AM_ would at the distance _HA_: and _CD_ or _IO_ at the distance _HC_ will appear as long as _AL_ would at the distance _HA_. So that as an object approaches the eye, both it’s magnitude and the Angle under which it is seen increase; and as the object recedes, the contrary.
Footnote 45:
The fields which are beyond the gate rise gradually till they are just seen over it; and the arms, being red, are often mistaken for a house at a considerable distance in those fields.
I once met with a curious deception in a gentleman’s garden at _Hackney_, occasioned by a large pane of glass in the garden-wall at some distance from his house. The glass (through which the fields and sky were distinctly seen) reflected a very faint image of the house; but the image seemed to be in the Clouds near the Horizon, and at that distance looked as if it were a huge castle in the Air. Yet, the Angle under which the image appeared, was equal to that under which the house was seen: but the image being mentally referred a much greater distance than the house, appeared much bigger to the imagination.
Footnote 46:
The Sun and Moon subtend a greater Angle on the Meridian than in the Horizon, being nearer the Earth in the former case than the latter.
Footnote 47:
The Altitude of any celestial Phenomenon is an arc of the Sky intercepted between the Horizon and the Phenomenon. In Fig. VI. of Plate II. let _HOX_ be a horizontal line, supposed to be extended from the eye at _A_ to _X_, where the Sky and Earth seem to meet at the end of a long and level plain; and let _S_ be the Sun. The arc _XY_ will be the Sun’s height above the Horizon at _X_, and is found by the instrument _EDC_, which is a quadrantal board, or plate of metal, divided into 90 equal parts or degrees on its limb _DPC_; and has a couple of little brass plates, as _a_ and _b_, with a small hole in each of them, called _Sight-Holes_, for looking through, parallel to the edge of the Quadrant whereon they stand. To the center _E_ is fixed one end of a thread _F_, called _the Plumb-Line_, which has a small weight or plummet _P_ fixed to it’s other end. Now, if an observer holds the Quadrant upright, without inclining it to either side, and so that the Horizon at _X_ is seen through the sight-holes _a_ and _b_, the plumb-line will cut or hang over the beginning of the degrees at _o_, in the edge _EC_; but if he elevates the Quadrant so as to look through the sight-holes at any part of the Heavens, suppose to the Sun at _S_; just so many degrees as he elevates the sight-hole _b_ above the horizontal line _HOX_, so many degrees will the plumb-line cut in the limb _CP_ of the Quadrant. For, let the observer’s eye at _A_ be in the center of the celestial arc _XYV_ (and he may be said to be in the center of the Sun’s apparent diurnal Orbit, let him be on what part of the Earth he will) in which arc the Sun is at that time, suppose 25 degrees high, and let the observer hold the Quadrant so that he may see the Sun through the sight-holes; the plumb-line freely playing on the quadrant will cut the 25th degree in the limb _CP_ equal to the number of degrees of the Sun’s Altitude at the time of observation. _N. B._ Whoever looks at the Sun, must have a smoaked glass before his eyes to save them from hurt. The better way is not to look at the Sun through the sight-holes, but to hold the Quadrant facing the eye, at a little distance, and so that the Sun shining through one hole, the ray may be seen to fall on the other.
Footnote 48:
See the Note on § 185.
Footnote 49:
Here proper allowance must be made for the Refraction, which being about 34 minutes of a degree in the Horizon, will cause the Moon’s center to appear 34 minutes above the Horizon when her center is really in it.
Footnote 50:
By this is meant, that if a line be supposed to be drawn parallel to the Earth’s Axis in any part of it’s Orbit, the Axis keeps parallel to that line in every other part of it’s Orbit: as in Fig. I. of Plate V; where _abcdefgh_ represents the Earth’s Orbit in an oblique view, and _Ns_ the Earth’s Axis keeping always parallel to the line _MN_.
Footnote 51:
SMITH’s Optics, § 1197.
Footnote 52:
All Circles appear ellipses in an oblique view, as is evident by looking obliquely at the rim of a bason. For the true figure of a Circle can only be seen when the eye is directly over it’s center. The more obliquely it is viewed, the more elliptical it appears, until the eye be in the same plane with it, and then it appears like a straight line.
Footnote 53:
Here we must suppose the Sun to be no bigger than an ordinary point (as ·) because he only covers a Circle half a degree in diameter in the Heavens; whereas in the figure he hides a whole sign at once from the Earth.
Footnote 54:
Here we must suppose the Earth to be a much smaller point than that in the preceding note marked for the Sun.
Footnote 55:
If the Earth were cut along the Equator, quite through the center, the flat surface of this section would be the plane of the Equator; as the paper contained within any Circle may be justly termed the plane of that Circle.
Footnote 56:
The two opposite points in which the Ecliptic crosses the Equinoctial, are called _the Equinoctial Points_: and the two points where the Ecliptic touches the Tropics (which are likewise opposite, and 90 degrees from the former) are called _the Solstitial Points_.
Footnote 57:
The Equinoctial Circle intersects the Ecliptic in two opposite points, called _Aries_ and _Libra_, from the Signs which always keep in these points: They are called the Equinoctial Points, because when the Sun is in either of them, he is directly over the terrestrial Equator; and then the days and nights are equal.
Footnote 58:
In this discourse, we may consider the Orbits of all the Satellites as circular, with respect to their primary Planets; because the excentricities of their Orbits are too small to affect the Phenomena here described.
Footnote 59:
If a Globe be cut quite through upon any Circle, the flat surface where it is so divided, is the plane of that circle.
Footnote 60:
The Figure shews the Globe as if only elevated about 40 degrees, which was occasioned by an oversight in the drawing: but it is still sufficient to explain the Phenomena.
Footnote 61:
The Ecliptic, together with the fixed Stars, make 366-1/4 apparent diurnal revolutions about the Earth in a year; the Sun only 365-1/4. Therefore the Stars gain 3 minutes 56 seconds upon the Sun every day: so that a Sidereal day contains only 23 hours 56 minutes of mean Solar time; and a natural or Solar day 24 hours. Hence 12 Sidereal hours are 1 minute 58 seconds shorter than 12 Solar.
Footnote 62:
The Sun advances almost a degree in the Ecliptic in 24 hours, the same way that the Moon moves: and therefore, the Moon by advancing 13-1/6 degrees in that time goes little more than 12 degrees farther from the Sun than she was on the day before.
Footnote 63:
This center is as much nearer the Earth’s center than the Moon’s as the Earth is heavier, or contains a greater quantity of matter than the Moon, namely about 40 times. If both bodies were suspended on it they would hang in _æquilibria_. So that dividing 240,000 miles, the Moon’s distance from the Earth’s center, by 40 the excess of the Earth’s weight above the Moon’s, the quotient will be 6000 miles, which is the distance of the common center of gravity of the Earth and Moon from the Earth’s center.
Footnote 64:
The Penumbra is a faint kind of shadow all around the perfect shadow of the Planet or Satellite; and will be more fully explained by and by.
Footnote 65:
Which is the time that the Eclipse would be at the greatest obscuration, if the motions of the Sun and Moon were equable, or the same in all parts of their Orbits.
Footnote 66:
The above period of 18 years 11 days 7 hours 43 minutes, which was found out by the _Chaldeans_, and by them called _Saros_.
Footnote 67:
A Digit is a twelfth part of the diameter of the Sun or Moon.
Footnote 68:
There are two antient Eclipses of the Moon, recorded by _Ptolemy_ from _Hipparchus_, which afford an undeniable proof of the Moon’s acceleration. The first of these was observed at _Babylon_, _December_ the 22d, in the year before CHRIST 383: when the Moon began to be eclipsed about half an hour before the Sun rose, and the Eclipse was not over before the Moon set: but by our best Astronomical Tables, the Moon was set at _Babylon_ half an hour before the Eclipse began; in which case, there could have been no possibility of observing it. The second Eclipse was observed at _Alexandria_, _September_ the 22d, the year before CHRIST 201; where the Moon rose so much eclipsed, that the Eclipse must have begun about half an hour before she rose: whereas by our Tables the beginning of this Eclipse was not till about 10 minutes after the Moon rose at _Alexandria_. Had these Eclipses begun and ended while the Sun was below the Horizon, we might have imagined, that as the antients had no certain way of measuring time, they might have been so far mistaken in the hours, that we could not have laid any stress on the accounts given by them. But, as in the first Eclipse the Moon was set, and consequently the Sun risen, before it was over; and in the second Eclipse the Sun was set, and the Moon not risen, till some time after it began; these are such circumstances as the observers could not possibly be mistaken in. Mr. _Struyk_ in the following Catalogue, notwithstanding the express words of _Ptolemy_, puts down these two Eclipses as observed at _Athens_; where they might have been seen as above, without any acceleration of the Moon’s motion: _Athens_ being 20 degrees West of _Babylon_, and 7 degrees West of _Alexandria_.
Footnote 69:
Each _Olympiad_ began at the time of Full Moon next after the Summer Solstice, and lasted four years, which were of unequal lengths because the time of Full Moon differs 11 days every year: so that they might sometimes begin on the next day after the Solstice, and at other times not till four weeks after it. The first _Olympiad_ began in the year of the Julian Period 3938, which was 776 years before the first year of CHRIST, or 775 before the year of his birth; and the last _Olympiad_, which was the 293d, began _A. D._ 393. At the expiration of each _Olympiad_, the _Olympic Games_ were celebrated in the _Elean_ fields, near the river _Alpheus_ in the _Peloponnesus_ (now _Morea_) in honour of JUPITER OLYMPUS. See STRAUCHIUS’_s_ _Breviarium Chronologium_, p. 247-251.
Footnote 70:
The reader may probably find it difficult to understand why Mr. SMITH should reckon this Eclipse to have been in the 4th year of the 48th _Olympiad_; as it was only in the end of the third year: and also why the 28th of _May_, in the 585th year before CHRIST should answer to the present 10th of that month. But we hope the following explanation will remove these difficulties.
The month of _May_ (when the Sun was eclipsed) in the 585th year before the first year of CHRIST, which was a leap-year, fell in the latter end of the third year of the 48th _Olympiad_; and the fourth year of that _Olympiad_ began at the Summer Solstice following: but perhaps Mr. SMITH begins the years of the _Olympiad_ from _January_, in order to make them correspond more readily with _Julian_ years; and so reckons the month of _May_, when the Eclipse happened, to be in the fourth year of that _Olympiad_.
The Place or Longitude of the Sun at that time was ♉ 29° 43ʹ 17ʺ, to which same place the Sun returned (after 2300 years, _viz._) _A. D._ 1716, on _May_, 9^d. 5^h. 6^m. after noon: so that, with respect to the Sun’s place, the 9th of _May_, 1716 answers to the 28th of _May_ in the 585th year before the first year of CHRIST; that is, the Sun had the same Longitude on both those days.
Footnote 71:
Before CHRIST 413, _August 27_.
Footnote 72:
Before CHRIST 168, _June 20_.
Footnote 73:
STRUYK’s Eclipses are to the _Old Style_, all the rest to the _New_.
Footnote 74:
This Eclipse happened in the first year of the _Peloponnesian_ war.
Footnote 75:
Although the Sun and Moon are spherical bodies, as seen from the Earth they appear to be circular planes, and so would the Earth if it were seen from the Moon. The apparently flat surfaces of the Sun and Moon are called their _Disks_ by Astronomers.
Footnote 76:
A Digit is a twelfth part of the diameter of the Sun and Moon.
Footnote 77:
This is the same with _the annual Argument of the Moon_.
Footnote 78:
When the _Romans_ divided the Empire, which was about 38 years before CHRIST, _Spain_ fell to _Augustus_’s share: in memory of which, the _Spaniards_ dated all their memorable events _ab exordio Regni Augusti_; as Christians do from the birth of our SAVIOUR. But in process of time, only the initial letters _AERA_ of these words were used instead of the words themselves. And thus, according to some, came the word _ÆRA_, which is made use of to signify a point of time from whence historians begin to reckon.
Footnote 79:
When the Sun’s Anomaly is 0 signs 0 degrees, or 6 signs 0 degrees, neither the Sun nor the Moon’s Anomaly have any Equation; which is the case in this Example.
Footnote 80:
See the Remark, p. 195.
Footnote 81:
_Babylon_ is 42 deg. 46 min. east from the Meridian of _London_, which is equal to 2 hours 51 min. of time nearly. See § 220.
Footnote 82:
Our SAVIOUR was born in a leap-year, and therefore every fourth year both before and after is a leap-year in the _Old Stile_: but the Tables begin with the year _next after_ that of his birth.
Footnote 83:
When only one of the Nodes is mentioned, it is the Ascending Node that is meant, to which the Descending Node is exactly opposite.
Footnote 84:
When the Moon is North of the Ecliptic and going farther from it, her Latitude or Declination from the Ecliptic is called _North Ascending_: when she is North of the Ecliptic and going toward it, her Latitude is _North Descending_: when she is South of the Ecliptic and going farther from it, her Latitude is _South Descending_: and lastly, when she is South of the Ecliptic and going toward it, her Latitude is _South Ascending_.
Footnote 85:
See Page 193, Example II.
Footnote 86: