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

Author: James Ferguson

Release Date: November 3, 2019 [EBook #60619]

Language: English

Character set encoding: UTF-8

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The ORRERY, made by JAMES FERGUSON.

N. 1. The Sun, 2. Mercury, 3. Venus, 4. The Earth, 5. The Moon, 6. The Sydereal Dial plate, 7. The Hour Circle, 8. y^e Circle for y^e. Moon’s Age, 9. The Moon’s Orbit, 10. y^e Pointer, Shewing the Sun’s Place & Day of the Month, 11. The Ecliptic, 12. The Handle for turning y^e whole machine

J. Ferguson inv. et delin.

G. Child. Sculp.

In the Table facing Page 31, the Sun’s quantity of matter should be 227500. Page 40, l. last, for infinite read indefinite. Page 97, l. 20, for this read the next. Page 164, l. 2 from the bottom, for without any acceleration read as above, without any acceleration. Page 199, l. 16 for XIV read XV. Page 238, l. 16, for 40 read 406. Page 240, l. 15 from the bottom, for Tifri read Tisri, Page 249 l. 13; from the bottom for XVII read V.

1. Of all the sciences cultivated by mankind, Astronomy is acknowledged to be, and undoubtedly is, the most sublime, the most interesting, and the most useful. For, by knowledge derived from this science, not only the bulk of the Earth is discovered, the situation and extent of the countries and kingdoms upon it ascertained, trade and commerce carried on to the remotest parts of the world, and the various products of several countries distributed for the health, comfort, and conveniency of its inhabitants; but our very faculties are enlarged with the grandeur of the ideas it conveys, our minds exalted above the low contracted prejudices of the vulgar, and our understandings clearly convinced, and affected with the conviction, of the existence, wisdom, power, goodness, and superintendency of the SUPREME BEING! So that without an hyperbole,

2. From this branch of knowledge we also learn by what means or laws the Almighty carries on, and continues the admirable harmony, order, and connexion observable throughout the planetary system; and are led by very powerful arguments to form the pleasing deduction, that minds capable of such deep researches not only derive their origin from that adorable Being, but are also incited to aspire 2after a more perfect knowledge of his nature, and a stricter conformity to his will.

3. By Astronomy we discover that the Earth is at so great a distance from the Sun, that if seen from thence it would appear no bigger than a point; although it’s circumference is known to be 25,020 miles. Yet that distance is so small, compared with the distance of the Fixed Stars, that if the Orbit in which the Earth moves round the Sun were solid, and seen from the nearest Star, it would likewise appear no bigger than a point, although it is at least 162 millions of miles in diameter. For the Earth in going round the Sun is 162 millions of miles nearer to some of the Stars at one time of the year than at another; and yet their apparent magnitudes, situations, and distances from one another still remain the same; and a telescope which magnifies above 200 times does not sensibly magnify them: which proves them to be at least 400 thousand times farther from us than we are from the Sun.

4. It is not to be imagined that all the Stars are placed in one concave surface, so as to be equally distant from us; but that they are scattered at immense distances from one another through unlimited space. So that there may be as great a distance between any two neighbouring Stars, as between our Sun and those which are nearest to him. Therefore an Observer, who is nearest any fixed Star, will look upon it alone as a real Sun; and consider the rest as so many shining points, placed at equal distances from him in the Firmament.

5. By the help of telescopes we discover thousands of Stars which are invisible to the naked eye; and the better our glasses are, still the more become visible: so that we can set no limits either to their number or their distances. The celebrated Huygens carries his thoughts so far, as to believe it not impossible that there may be Stars at such inconceivable distances, that their light has not yet reached the Earth since it’s creation; although the velocity of light be a million of times greater than the velocity of a cannon bullet, as shall be demonstrated afterwards § 197, 216: and, as Mr. Addison very justly observes, this thought is far from being extravagant, when we consider that the Universe is the work of infinite power, prompted by infinite goodness; having an infinite space to exert itself in; so that our imaginations can set no bounds to it.

6. The Sun appears very bright and large in comparison of the Fixed Stars, because we keep constantly near the Sun, in comparison of our immense distance from the Stars. For, a spectator, placed as near to any Star as we are to the Sun, would see that Star a body as 3large and bright as the Sun appears to us: and a spectator, as far distant from the Sun as we are from the Stars, would see the Sun as small as we see a Star, divested of all its circumvolving Planets; and would reckon it one of the Stars in numbering them.

7. The Stars, being at such immense distances from the Sun, cannot possibly receive from him so strong a light as they seem to have; nor any brightness sufficient to make them visible to us. For the Sun’s rays must be so scattered and dissipated before they reach such remote objects, that they can never be transmitted back to our eyes, so as to render these objects visible by reflection. The Stars therefore shine with their own native and unborrowed lustre, as the Sun does; and since each particular Star, as well as the Sun, is confined to a particular portion of space, ’tis plain that the Stars are of the same nature with the Sun.

8. It is no ways probable that the Almighty, who always acts with infinite wisdom and does nothing in vain, should create so many glorious Suns, fit for so many important purposes, and place them at such distances from one another, without proper objects near enough to be benefited by their influences. Whoever imagines they were created only to give a faint glimmering light to the inhabitants of this Globe, must have a very superficial knowledge of Astronomy, and a mean opinion of the Divine Wisdom: since, by an infinitely less exertion of creating power, the Deity could have given our Earth much more light by one single additional Moon.

9. Instead then of one Sun and one World only in the Universe, as the unskilful in Astronomy imagine, that Science discovers to us such an inconceivable number of Suns, Systems, and Worlds, dispersed through boundless Space, that if our Sun, with all the Planets, Moons, and Comets belonging to it were annihilated, they would be no more missed out of the Creation than a grain of sand from the sea-shore. The space they possess being comparatively so small, that it would scarce be a sensible blank in the Universe; although Saturn, the outermost of our planets, revolves about the Sun in an Orbit of 4884 millions of miles in circumference, and some of our Comets make excursions upwards of ten thousand millions of miles beyond Saturn’s Orbit; and yet, at that amazing distance, they are incomparably nearer to the Sun than to any of the Stars; as is evident from their keeping clear of the attractive Power of all the Stars, and returning periodically by virtue of the Sun’s attraction.

10. From what we know of our own System it may be reasonably concluded that all the rest are with equal wisdom contrived, situated, 4and provided with accommodations for rational inhabitants. Let us therefore take a survey of the System to which we belong; the only one accessible to us; and from thence we shall be the better enabled to judge of the nature and end of the other Systems of the Universe. For although there is almost an infinite variety in all the parts of the Creation which we have opportunities of examining; yet there is a general analogy running through and connecting all the parts into one scheme, one design, one whole!

11. And then, to an attentive considerer, it will appear highly probable, that the Planets of our System, together with their attendants called Satellites or Moons, are much of the same nature with our Earth, and destined for the like purposes. For, they are solid opaque Globes, capable of supporting animals and vegetables. Some of them are bigger, some less, and some much about the size of our Earth. They all circulate round the Sun, as the Earth does, in a shorter or longer time according to their respective distances from him: and have, where it would not be inconvenient, regular returns of summer and winter, spring and autumn. They have warmer and colder climates, as the various productions of our Earth require: and, in such as afford a possibility of discovering it, we observe a regular motion round their Axes like that of our Earth, causing an alternate return of day and night; which is necessary for labour, rest, and vegetation, and that all parts of their surfaces may be exposed to the rays of the Sun.

12. Such of the Planets as are farthest from the Sun, and therefore enjoy least of his light, have that deficiency made up by several Moons, which constantly accompany, and revolve about them, as our Moon revolves about the Earth. The remotest Planet has, over and above, a broad Ring encompassing it; which like a lucid Zone in the Heavens reflects the Sun’s light very copiously on that Planet: so that if the remoter Planets have the Sun’s light fainter by day than we, they have an addition made to it morning and evening by one or more of their Moons, and a greater quantity of light in the night-time.

13. On the surface of the Moon, because it is nearer us than any other of the celestial Bodies are, we discover a nearer resemblance of our Earth. For, by the assistance of telescopes we observe the Moon to be full of high mountains, large valleys, and deep cavities. These similarities leave us no room to doubt but that all the Planets and Moons in the System are designed as commodious habitations for creatures endowed with capacities of knowing and adoring their beneficent Creator.

The Solar System

J. Ferguson delin.

J. Mynde Sculp.

514. Since the Fixed Stars are prodigious spheres of fire, like our Sun, and at inconceivable distances from one another, as well as from us, it is reasonable to conclude they are made for the same purposes that the Sun is; each to bestow light, heat, and vegetation on a certain number of inhabited Planets, kept by gravitation within the sphere of it’s activity.

15. What an august! what an amazing conception, if human imagination can conceive it, does this give of the works of the Creator! Thousands of thousands of Suns, multiplied without end, and ranged all around us, at immense distances from each other, attended by ten thousand times ten thousand Worlds, all in rapid motion, yet calm, regular, and harmonious, invariably keeping the paths prescribed them; and these Worlds peopled with myriads of intelligent beings, formed for endless progression in perfection and felicity.

16. If so much power, wisdom, goodness, and magnificence is displayed in the material Creation, which is the least considerable part of the Universe, how great, how wise, how good must HE be, who made and governs the Whole!

17. The Planets and Comets which move round the Sun as their center, constitute the Solar System. Those Planets which are nearer the Sun not only finish their circuits sooner, but likewise move faster in their respective Orbits than those which are more remote from him. Their motions are all performed from west to east, in Orbits nearly circular. Their names, distances, bulks, and periodical revolutions, are as follows.

18. The Sun , an immense globe of fire, is placed near the common center, or rather in the lower^[2] focus, of the Orbits of all 6the Planets and Comets^[3]; and turns round his axis in 25 days 6 hours, as is evident by the motion of spots seen on his surface. His diameter is computed to be 763,000 miles; and, by the various attractions of the circumvolving Planets, he is agitated by a small motion round the center of gravity of the System. All the Planets, as seen from him, move the same way, and according to the order of Signs in the graduated Circle ♈ ♉ ♎ ♋ &c. which represents the great Ecliptic in the Heavens: but, as seen from any one Planet, the rest appear sometimes to go backward, sometimes forward, and sometimes to stand still; not in circles nor ellipses, but in^[4] looped curves which never return into themselves. The Comets come from all parts of the Heavens, and move in all sorts of directions.

19. Having mentioned the Sun’s turning round his axis, and as there will be frequent occasion to speak of the like motion of the Earth and other Planets, it is proper here to inform the young Tyro in Astronomy, that neither the Sun nor Planets have material axes to turn upon, and support them, as in the little imperfect Machines contrived to represent them. For the axis of a Planet is a line conceived to be drawn through it’s center, about which it revolves as on a real axis. The extremities of this line, terminating in opposite points of the Planet’s surface, are called its Poles. That which points towards the northern part of the Heavens is called the North Pole; and the other, pointing towards the southern part, is called the South Pole. A bowl whirled from one’s hand into the open air turns round such a line within itself, whilst it moves forward; and such are the lines we mean, when we speak of the Axes of the Heavenly bodies.

20. Let us suppose the Earth’s Orbit to be a thin, even, solid plane; cutting the Sun through the center, and extended out as far as the Starry Heavens, where it will mark the great Circle called the Ecliptic. This Circle we suppose to be divided into 12 equal parts, called Signs; each Sign into 30 equal parts, called Degrees; each Degree into 60 equal parts, called Minutes; and every Minute into 60 equal parts, called Seconds: so that a Second is the 60th part of a Minute; a Minute 7the 60th part of a Degree; and a Degree the 360th part of a Circle, or 30th part of a Sign. The Planes of the Orbits of all the other Planets likewise cut the Sun in halves; but extended to the Heavens, form Circles different from one another, and from the Ecliptic; one half of each being on the north side, and the other on the south side of it. Consequently the Orbit of each Planet crosses the Ecliptic in two opposite points, which are called the Planet’s Nodes. These Nodes are all in different parts of the Ecliptic; and therefore, if the planetary Tracks remained visible in the Heavens, they would in some measure resemble the different rutts of waggon-wheels crossing one another in different parts, but never going far asunder. That Node, or Intersection of the Orbit of any Planet with the Earth’s Orbit, from which the Planet ascends northward above the Ecliptic, is called the Ascending Node of the Planet; and the other, which is directly opposite thereto, is called it’s Descending Node. Saturn’s Ascending Node is in 21 deg. 13 min. of Cancer ♋, Jupiter’s in 7 deg. 29 min. of the same Sign, Mars’s in 17 deg. 17 min. of Taurus ♉, Venus’s in 13 deg. 59 min. of Gemini ♊, and Mercury’s in 14 deg. 43 min. of Taurus. Here we consider the Earth’s Orbit as the standard, and the Orbits of all the other Planets as oblique to it.

21. When we speak of the Planets Orbits, all that is meant is their Paths through the open and unresisting Space in which they move; and are kept in, by the attractive power of the Sun, and the projectile force impressed upon them at first: between which power and force there is so exact an adjustment, that without any solid Orbits to confine the Planets, they keep their courses, and at the end of every revolution find the points from whence they first set out, much more truly than can be imitated in the best machines made by human art.

22. Mercury, the nearest Planet to the Sun, goes round him (as in the circle marked ☿) in 87 days 23 hours of our time nearly; which is the length of his year. But, being seldom seen, and no spots appearing on his surface or disc, the time of his rotation on his axis, or the length of his days and nights, is as yet unknown. His distance from the Sun is computed to be 32 millions of miles, and his diameter 2600. In his course, round the Sun, he moves at the rate of 95 thousand miles every hour. His light and heat from the Sun are almost seven times as great as ours; and the Sun appears to him almost seven times as large as to us. The great heat on this Planet is no argument against it’s being inhabited; since the Almighty could as easily suit the bodies and constitutions of it’s inhabitants to the heat of 8their dwelling, as he has done ours to the temperature of our Earth. And it is very probable that the people there have such an opinion of us, as we have of the inhabitants of Jupiter and Saturn; namely, that we must be intolerably cold, and have very little light at so great a distance from the Sun.

23. This Planet appears to us with all the various phases of the Moon, when viewed at different times by a good telescope; save only that he never appears quite Full, because his enlightened side is never turned directly towards us but when he is so near the Sun as to be lost to our sight in it’s beams. And, as his enlightened side is always toward the Sun, it is plain that he shines not by any light of his own; for if he did, he would constantly appear round. That he moves about the Sun in an Orbit within the Earth’s Orbit is also plain (as will be more largely shewn by and by, § 141, & seq.) because he is never seen opposite to the Sun, nor above 56 times the Sun’s breadth from his center.

24. His Orbit is inclined seven degrees to the Ecliptic; and that Node § 20, from which he ascends northward above the Ecliptic is in the 14th degree of Taurus; the opposite, in the 14th degree of Scorpio. The Earth is in these points on the 5th of November and 4th of May, new style; and when Mercury comes to either of his Nodes at his^[5] inferior Conjunction about these times, he will appear to pass over the disc or face of the Sun, like a dark round spot. But in all other parts of his Orbit his Conjunctions are invisible, because he either goes above or below the Sun.

25. Mr. Whiston has given us an account of several periods at which Mercury may be seen on the Sun’s disc, viz. In the year 1782, Nov. 12th, at 3 h. 44 m. in the afternoon: 1786, May 4th, at 6 h. 57 m. in the forenoon: 1789, Dec. 6th, at 3 h. 55 m. in the afternoon; and 1799, May 7th, at 2 h. 34 m. in the afternoon. There will be several intermediate Transits, but none of them visible at London.

26. Venus, the next Planet in order, is computed to be 59 millions of miles from the Sun; and by moving at the rate of 69 thousand miles every hour in her Orbit (as in the circle marked ♀), she goes round the Sun in 224 days 17 hours of our time nearly; in which, though it be the full length of her year, she has only 9¹⁄₄ days, according to Bianchini’s observations; so that in her, every day and night together is as long as 24¹⁄₃ days and nights with us. This odd 9quarter of a day in every year makes every fourth year a leap-year to Venus; as the like does to our Earth. Her diameter is 7906 miles; and by her diurnal motion the inhabitants about her Equator are carried 43 miles every hour: besides the 69,000 above-mentioned.

27. Her Orbit includes that of Mercury within it; for at her greatest Elongation, or apparent distance from the Sun, she is 96 times his breadth from his centre; which is almost double of Mercury’s. Her Orbit is included by the Earth’s; for if it were not, she might be seen as often in Opposition to the Sun as in Conjunction with him; but she was never seen 90 degrees, or a fourth part of a Circle, from the Sun.

28. When Venus appears west of the Sun she rises before him in the morning, and is called the Morning Star: when she appears east of the Sun she shines in the evening after he sets, and is then called the Evening Star: being each in it’s turn for 290 days. It may perhaps be surprising at first, that Venus should keep longer on the east or west of the Sun than the whole time of her Period round him. But the difficulty vanishes when we consider that the Earth is all the while going round the Sun the same way, though not so quick as Venus: and therefore her relative motion to the Earth must in every Period be as much slower than her absolute motion in her Orbit, as the Earth during that time advances forward in the Ecliptic; which is 220 degrees. To us she appears through a telescope in all the various shapes of the Moon.

29. The Axis of Venus is inclined 75 degrees to the Axis of her Orbit; which is 51¹⁄₂ degrees more than our Earth’s Axis is inclined to the Axis of the Ecliptic: and therefore the variation of her seasons is much greater than of ours. The North Pole of her Axis inclines toward the 20th degree of Aquarius, our Earth’s to the beginning of Cancer; and therefore the northern parts of Venus have summer in the Signs where those of our Earth have winter, and vice versâ.

30. The ^[6]artificial day at each Pole of Venus is as long as 112¹⁄₂ ^[7]natural days on our Earth.

31. The Sun’s greatest Declination on each side of her Equator amounts to 75 degrees; therefore her^[8] Tropics are only 15 degrees 10from her Poles; and her ^[9]Polar Circles as far from her Equator. Consequently, the Tropics of Venus are between her Polar Circles and her Poles; contrary to what those of our Earth are.

32. As her annual Revolution contains only 9¹⁄₄ of her days, the Sun will always appear to go through a Sign, or twelfth Part of her Orbit, in little more that three quarters of her natural day, or nearly in 18³⁄₄ of our days and nights.

33. Because her day is so great a part of her year, the Sun changes his Declination in one day so much, that if he passes vertically, or directly over head of any given place on the Tropic, the next day he will be 26 degrees from it: and whatever place he passes vertically over when in the Equator, one day’s revolution will remove him 36¹⁄₄ degrees from it. So that the Sun changes his Declination every day in Venus about 14 degrees more at a mean rate, than he does in a quarter of a year on our Earth. This appears to be providentially ordered, for preventing the too great effects of the Sun’s heat (which is twice as great on Venus as on the Earth) so that he cannot shine perpendicularly on the same places for two days together; and by that means, the heated places have time to cool.

34. If the inhabitants about the North Pole of Venus fix their South, or Meridian Line, through that part of the Heavens where the Sun comes to his greatest Height, or North Declination, and call those the East and West points of their Horizon, which are 90 degrees on each side from that point where the Horizon is cut by the Meridian Line, these inhabitants will have the following remarkables.

The Sun will rise 22¹⁄₂ degrees^[10] north of the East, and going on 112¹⁄₂ degrees, as measured on the plane of the ^[11]Horizon, he will cross the Meridian at an altitude of 12¹⁄₂ degrees; then making an entire revolution without setting, he will cross it again at an altitude of 48¹⁄₂ degrees; at the next revolution he will cross the Meridian as he comes to his greatest height and declination, at the altitude of 75 degrees; being then only 15 degrees from the Zenith, or that point of the Heavens which is directly over head: and thence he will descend in the like spiral manner; crossing the Meridian first at the altitude of 48¹⁄₂ degrees; next at the altitude of 12¹⁄₂ degrees; and going on thence 112¹⁄₂ degrees, he will set 22¹⁄₂ degrees north of the West; so that, after 11having been 4⁵⁄₈ revolutions above the Horizon, he descends below it to exhibit the like appearances at the South Pole.

35. At each Pole, the Sun continues half a year without setting in summer, and as long without rising in winter; consequently the polar inhabitants of Venus have only one day and one night in the year; as it is at the Poles of our Earth. But the difference between the heat of summer and cold of winter, or of mid-day and mid-night, on Venus, is much greater than on the Earth: because in Venus, as the Sun is for half a year together above the Horizon of each Pole in it’s turn, so he is for a considerable part of that time near the Zenith; and during the other half of the year, always below the Horizon, and for a great part of that time at least 70 degrees from it. Whereas, at the Poles of our Earth, although the Sun is for half a year together above the Horizon, yet he never ascends above, nor descends below it, more than 23¹⁄₂ degrees. When the Sun is in the Equinoctial, or in that Circle which divides the northern half of the Heavens from the southern, he is seen with one half of his Disc above the Horizon of the North Pole, and the other half above the Horizon of the South Pole; so that his center is in the Horizon of both Poles: and then descending below the Horizon of one, he ascends gradually above that of the other. Hence, in a year, each Pole has one spring, one harvest, a summer as long as them both, and a winter equal in length to the other three seasons.

36. At the Polar Circles of Venus, the seasons are much the same as at the Equator, because there are only 15 degrees betwixt them, § 31; only the winters are not quite so long, nor the summers so short: but the four seasons come twice round every year.

37. At Venus’s Tropics, the Sun continues for about fifteen of our weeks together without setting in summer; and as long without rising in winter. Whilst he is more than 15 degrees from the Equator, he neither rises to the inhabitants of the one Tropic, nor sets to those of the other: whereas, at our terrestrial Tropics he rises and sets every day of the year.

38. At Venus’s Tropics, the Seasons are much the same as at her Poles; only the summers are a little longer, and the winters a little shorter.

39. At her Equator, the days and nights are always of the same length; and yet the diurnal and nocturnal Arches are very different, especially when the Sun’s declination is about the greatest: for then, his meridian altitude may sometimes be twice as great as his midnight depression, and at other times the reverse. When the Sun is at his 12greatest Declination, either North or South, his rays are as oblique at Venus’s Equator, as they are at London on the shortest day of winter. Therefore, at her Equator there are two winters, two summers, two springs, and two autumns every year. But because the Sun stays for some time near the Tropics, and passes so quickly over the Equator, every winter there will be almost twice as long as summer: the four seasons returning twice in that time, which consists only of 9¹⁄₄ days.

40. Those parts of Venus which lie between the Poles and Tropics, and between the Tropics and Polar Circles, and also between the Polar Circles and Equator, partake more or less of the Phenomena of these Circles, as they are more or less distant from them.

41. From the quick change of the Sun’s declination it happens, that when he rises due east on any day, he will not set due west on that day, as with us; for if the place where he rises due east be on the Equator, he will set on that day almost west-north-west; or about 18¹⁄₂ degrees north of the west. But if the place be in 45 degrees north latitude, then on the day that the Sun rises due east he will set north-west by west, or 33 degrees north of the west. And in 62 degrees north latitude when he rises in the east, he sets not in that revolution, but just touches the Horizon 10 degrees to the west of the north point; and ascends again, continuing for 3¹⁄₄ revolutions above the Horizon without setting. Therefore, no place has the forenoon and afternoon of the same day equally long, unless it be on the Equator or at the Poles.

42. The Sun’s altitude at noon, or any other time of the day, and his amplitude at rising and setting, being so different at places on the same parallels of latitude, according to the different longitudes of those places, the longitude will be almost as easily found on Venus as the latitude is found on the Earth: which is an advantage we can never enjoy, because the daily change of the Sun’s declination is by much too small for that purpose.

43. On this Planet, wherever the Sun crosses the Equator in any year, he will have 9 degrees of declination from that place on the same day and hour next year; and will cross the Equator 90 degrees farther to the west; which makes the time of the Equinox a quarter of a day (almost equal to six of our days) later every year. Hence, although the spiral in which the Sun’s motion is performed, be of the same sort every year, yet it will not be the very same, because the Sun will not pass vertically over the same places till four annual revolutions are finished.

44. We may suppose that the inhabitants of Venus will be careful to add a day to some particular part of every fourth year; which will keep the same seasons to the same days. For, as the great annual 13change of the Equinoxes and Solstices shifts the seasons a quarter of a day every year, they would be shifted through all the days of the year in 36 years. But by means of this intercalary day, every fourth year will be a leap-year; which will bring her time to an even reckoning, and keep her Calendar always right.

45. Venus’s Orbit is inclined 3¹⁄₂ degrees to the Earth’s; and crosses it in the 14th degree of Gemini and of Sagittarius; and therefore, when the Earth is about these points of the Ecliptic at the time that Venus is in her inferiour conjunction, she will appear like a spot on the Sun, and afford a more certain method of finding the distances of all the Planets from the Sun than any other yet known. But these appearances happen very seldom; and will only be thrice visible at London for three hundred years to come. The first time will be in the year 1761, June the 6th, at 5 hours 55 minutes in the morning. The second 1996, June the 9th, at 2 hours 13 minutes in the afternoon. And the third in the year 2004, June the 6th, at 7 hours 18 minutes in the forenoon. Excepting such Transits as these, she shews the same appearances to us regularly every eight years; her Conjunctions, Elongations, and Times of rising and setting being very nearly the same, on the same days, as before.

46. Venus may have a Satellite or Moon, although it be undiscovered by us: which will not appear very surprising, if we consider how inconveniently we are placed for seeing it. For it’s enlightened side can never be fully turned towards us but when Venus is beyond the Sun; and then, as Venus appears little bigger than an ordinary Star, her Moon may be too small to be perceptible at such a distance. When she is between us and the Sun, her full Moon has it’s dark side towards us; and then, we cannot see it any more than we can our own Moon at the time of Change. When Venus is at her greatest Elongation, we have but one half of the enlightened side of her Full Moon towards us; and even then it may be too far distant to be seen by us. But if she has a Moon, it may certainly be seen with her upon the Sun, in the year 1761, unless it’s Orbit be considerably inclined to the Ecliptic: for if it should be in conjunction or opposition at that time, we can hardly imagine that it moves so slow as to be hid by Venus all the six hours that she will appear on the Sun’s Disc.

47. The Earth is the next Planet above Venus in the System. It is 81 millions of miles from the Sun, and goes round him (as in the circle ⊕) in 365 days 5 hours 49 minutes, from any Equinox or Solstice to the same again: but from any fixed Star to the same again, as 14seen from the Sun, in 365 days 6 hours and 9 minutes; the former being the length of the Tropical year, and the latter the length of the Sidereal. It travels at the rate of 58 thousand miles every hour, which motion, though 120 times swifter than that of a cannon ball, is little more than half as swift as Mercury’s motion in his Orbit. The Earth’s diameter is 7970 miles; and by turning round it’s Axis every 24 hours from West to East, it causes an apparent diurnal motion of all the heavenly Bodies from East to West. By this rapid motion of the Earth on it’s Axis, the inhabitants about the Equator are carried 1042 miles every hour, whilst those on the parallel of London are carried only about 580, besides the 58 thousand miles by the annual motion above-mentioned, which is common to all places whatever.

48. The Earth’s Axis makes an angle of 23¹⁄₂ degrees with the Axis of it’s Orbit; and keeps always the same oblique direction; inclining towards the same fixed Stars^[12] throughout it’s annual course; which causes the returns of spring, summer, autumn, and winter; as will be explained at large in the tenth Chapter.

49. The Earth is round like a globe; as appears, 1. from it’s shadow in Eclipses of the Moon; which shadow is always bounded by a circular line § 314. 2. From our seeing the masts of a ship whilst the hull is hid by the convexity of the water. 3. From it’s having been sailed round by many navigators. The hills take off no more from the roundness of the Earth in comparison, than grains of dust do from the roundness of a common Globe.

50. The seas and unknown parts of the Earth (by a measurement of the best Maps) contain 160 million 522 thousand and 26 square miles; the inhabited parts 38 million 990 thousand 569: Europe 4 million 456 thousand and 65; Asia 10 million 768 thousand 823; Africa 9 million 654 thousand 807; America 14 million 110 thousand 874. In all, 199 million 512 thousand 595; which is the number of square miles on the whole surface of our Globe.

51. Dr. Long, in the first volume of his Astronomy, pag. 168, mentions an ingenious and easy method of finding nearly what proportion the land bears to the sea; which is, to take the papers of a large terrestrial globe, and after separating the land from the sea with a pair of scissars, to weigh them carefully in scales. This supposes the globe to be exactly delineated, and the papers all of equal thickness. 15The Doctor made the experiment on the papers of Mr. Senex’s seventeen inch globe; and found that the sea papers weighed 349 grains, and the land only 124: by which it appears that almost three fourth parts of the surface of our Earth between the Polar Circles are covered with water, and that little more than one fourth is dry land. The Doctor omitted weighing all within the Polar Circles; because there is no certain measurement of the land there, so as to know what proportion it bears to the sea.

52. The Moon is not a Planet, but only a Satellite or Attendant of the Earth, moving round the Earth from Change to Change in 29 days 12 hours and 44 minutes; and going round the Sun with it every year. The Moon’s diameter is 2180 miles; and her distance from the Earth 240 thousand. She goes round her Orbit in 27 days 7 hours 43 minutes, moving about 2290 miles every hour; and turns round her Axis exactly in the time that she goes round the Earth, which is the reason of her keeping always the same side towards us, and that her day and night taken together is as long as our lunar month.

53. The Moon is an opaque Globe like the Earth, and shines only by reflecting the light of the Sun: therefore whilst that half of her which is toward the Sun is enlightened, the other half must be dark and invisible. Hence, she disappears when she comes between us and the Sun; because her dark side is then toward us. When she is gone a little way forward, we see a little of her enlightened side; which still increases to our view, as she advances forward, until she comes to be opposite to the Sun; and then her whole enlightened side is towards the Earth, and she appears with a round, illumined Orb; which we call the Full Moon: her dark side being then turned away from the Earth. From the Full she seems to decrease gradually as she goes through the other half of her course; shewing us less and less of her enlightened side every day, till her next change or conjunction with the Sun, and then she disappears as before.

54. The continual changing of the Moon’s phases or shapes demonstrates that she shines not by any light of her own: for if she did, being globular, we should always see her with a round full Orb like the Sun. Her Orbit is represented in the Scheme by the little circle m, upon the Earth’s Orbit ⊕: but it is drawn fifty times too large in proportion to the Earth’s; and yet is almost too small to be seen in the Diagram.

55. The Moon has scarce any difference of seasons; her Axis being almost perpendicular to the Ecliptic. What is very singular, one half of her has no darkness at all; the Earth constantly affording it a strong light in the Sun’s absence; while the other half has a fortnight’s darkness and a fortnight’s light by turns.

1656. Our Earth is a Moon to the Moon, waxing and waneing regularly, but appearing thirteen times as big, and affording her thirteen times as much light, as she does to us. When she changes to us, the Earth appears full to her; and when she is in her first quarter to us, the Earth is in it’s third quarter to her; and vice versâ.

57. But from one half of the Moon, the Earth is never seen at all: from the middle of the other half, it is always seen over head; turning round almost thirty times as quick as the Moon does. From the line which limits our view of the Moon, or all round what we call her edges, only one half of the Earth’s side next her is seen; the other half being hid below the Horizon. To her, the Earth seems to be the biggest Body in the Universe; for it appears thirteen times as big as she does to us.

58. The Moon has no such Atmosphere, or body of air surrounding her as we have: for if she had, we could never see her edge so well defined as it appears; but there would be a sort of a mist or haziness round her, which would make the Stars look fainter, when they were seen through it. But observation proves, that the Stars which disappear behind the Moon retain their full lustre until they seem to touch her very edge, and then vanish in a moment. This has been often observed by Astronomers, but particularly by Cassini^[13] of the Star γ in the breast of Virgo, which appears single and round to the bare eye; but through a refracting Telescope of 16 feet appears to be two Stars so near together, that the distance between them seems to be but equal to one of their apparent diameters. The Moon was observed to pass over them on the 21st of April 1720, N. S. and as her dark edge drew near to them, it caused no change in their colour or Situation. At 25 min. 14 sec. past 12 at night, the most westerly of these Stars was hid by the dark edge of the Moon; and in 30 seconds afterward, the most easterly Star was hid: each of them disappearing behind the Moon in an instant, without any preceding diminution of magnitude or brightness; which by no means could have been the case if there were an Atmosphere round the Moon; for then, one of the Stars falling obliquely into it before the other, ought by refraction to have suffered some change in its colour, or in it’s distance from the other Star which was not yet entered into the Atmosphere. But no such alteration could be perceived though the observation was performed with the utmost attention to that particular; and was very proper to have made such a discovery. The faint light, which has been seen all around the Moon, in total Eclipses of the Sun, has been observed, during the time of darkness, to 17have it’s center coincident with the center of the Sun; and is therefore much more likely to arise from the Atmosphere of the Sun than from that of the Moon; for if it were the latter, it’s center would have gone along with the Moon’s.

59. If there were seas in the Moon, she could have no clouds, rains, nor storms as we have; because she has no such Atmosphere to support the vapours which occasion them. And every one knows, that when the Moon is above our Horizon in the night time, she is visible, unless the clouds of our Atmosphere hide her from our view; and all parts of her appear constantly with the same clear, serene, and calm aspect. But those dark parts of the Moon, which were formerly thought to be seas, are now found to be only vast deep cavities, and places which reflect not the Sun’s light so strongly as others, having many caverns and pits whose shadows fall within them, and are always dark on the sides next the Sun; which demonstrates their being hollow: and most of these pits have little knobs like hillocks standing within them, and casting shadows also; which cause these places to appear darker than others which have fewer, or less remarkable caverns. All these appearances shew that there are no seas in the Moon; for if there were any, their surfaces would appear smooth and even, like those on the Earth.

60. There being no Atmosphere about the Moon, the Heavens in the day time have the appearance of night to a Lunarian who turns his back toward the Sun; and when he does, the Stars appear as bright to him as they do in the night to us. For, it is entirely owing to our Atmosphere that the Heavens are bright about us in the day.

61. As the Earth turns round it’s Axis, the several continents, seas, and islands appear to the Moon’s inhabitants like so many spots of different forms and brightness, moving over it’s surface; but much fainter at some times than others, as our clouds cover them or leave them. By these spots the Lunarians can determine the time of the Earth’s diurnal motion, just as we do the motion of the Sun: and perhaps they measure their time by the motion of the Earth’s spots; for they cannot have a truer dial.

62. The Moon’s Axis is so nearly perpendicular to the Ecliptic, that the Sun never removes sensibly from her Equator: and the^[14] obliquity of her Orbit, which is next to nothing as seen from the Sun, cannot cause any sensible declination of the Sun from her Equator. Yet her 18inhabitants are not destitute of means for determining the length of their year, though their method and ours must differ. For we can know the length of our year by the return of our Equinoxes; but the Lunarians, having always equal day and night, must have recourse to another method; and we may suppose, they measure their year by observing the Poles of our Earth; as one always begins to be enlightened, and the other disappears, at our Equinoxes; they being conveniently situated for observing great tracks of land about our Earth’s Poles, which are entirely unknown to us. Hence we may conclude, that the year is of the same absolute length both to the Earth and Moon, though very different as to the number of days: we having 365¹⁄₄ natural days, and the Lunarians only 12⁷⁄₁₉; every day and night in the Moon being as long as 29¹⁄₂ on the Earth.

63. The Moon’s inhabitants on the side next the Earth may as easily find the longitude of their places as we can find the latitude of ours. For the Earth keeping constantly, or very nearly so, over one Meridian of the Moon, the east or west distances of places from that Meridian are as easily found, as we can find our distance from the Equator by the Altitude of our celestial Poles.

64. The Planet Mars is next in order, being the first above the Earth’s Orbit. His distance from the Sun is computed to be 123 millions of miles; and by travelling at the rate of 47 thousand miles every hour, as in the circle ♂, he goes round the Sun in 687 of our days and 17 hours; which is the length of his year, and contains 667¹⁄₄ of his days; every day and night together being 40 minutes longer than with us. His diameter is 4444 miles, and by his diurnal rotation the inhabitants about his Equator are carried 556 miles every hour. His quantity of light and heat is equal but to one half of ours; and the Sun appears but half as big to him as to us.

65. This Planet being but a fifth part so big as the Earth, if any Moon attends him, she must be very small, and has not yet been discovered by our best telescopes. He is of a fiery red colour, and by his Appulses to some of the fixed Stars, seems to be surrounded by a very gross Atmosphere. He appears sometimes gibbous, but never horned; which both shews that his Orbit includes the Earth’s within it, and that he shines not by his own light.

66. To Mars, our Earth and Moon appear like two Moons, a bigger and a less; changing places with one another, and appearing sometimes horned, sometimes half or three quarters illuminated, but never full; nor at most above a quarter of a degree from each other, although they are 240 thousand miles asunder.

1967. Our Earth appears almost as big to Mars as Venus does to us, and at Mars it is never seen above 48 degrees from the Sun; sometimes it appears to pass over the Disc of the Sun, and so do Mercury and Venus: but Mercury can never be seen from Mars by such eyes as ours, unassisted by proper instruments; and Venus will be as seldom seen as we see Mercury. Jupiter and Saturn are as visible to Mars as to us. His Axis is perpendicular to the Ecliptic, and his Orbit is 2 degrees inclined to it.

68. Jupiter, the biggest of all the Planets, is still higher in the System, being about 424 millions of miles from the Sun: and going at the rate of 25 thousand miles every hour in his Orbit, as in the circle ♃ finishes his annual period in eleven of our years 314 days and 18 hours. He is above 1000 times as big as the Earth, for his diameter is 81,000 miles; which is more than ten times the diameter of the Earth.

69. Jupiter turns round his Axis in 9 hours 56 minutes; so that his year contains 10 thousand 464 days; and the diurnal velocity of his equatoreal parts is greater than the swiftness with which he moves in his annual Orbit; a singular circumstance, as far as we know. By this prodigious quick Rotation, his equatoreal inhabitants are carried 25 thousand 920 miles every hour (which is 920 miles an hour more than an inhabitant of our Earth moves in twenty-four hours) besides the 25 thousand above-mentioned, which is common to all parts of his surface, by his annual motion.

70. Jupiter is surrounded by faint substances, called Belts, in which so many changes appear, that they are generally thought to be clouds: for some of them have been first interrupted and broken, and then have vanished entirely. They have sometimes been observed of different breadths, and afterwards have all become nearly of the same breadth. Large spots have been seen in these Belts; and when a Belt vanishes, the contiguous spots disappear with it. The broken ends of some Belts have been generally observed to revolve in the same time with the spots; only those nearer the Equator in somewhat less time than those near the Poles; perhaps on account of the Sun’s greater heat near the Equator, which is parallel to the Belts and course of the spots. Several large spots, which appear round at one time, grow oblong by degrees, and then divide into two or three round spots. The periodical time of the spots near the Equator is 9 hours 50 minutes, but of those near the Poles 9 hours 56 minutes. See Dr. Smith’s Optics, § 1004 & seq.

2071. The Axis of Jupiter is so nearly perpendicular to his Orbit, that he has no sensible change of seasons; which is a great advantage, and wisely ordered by the Author of Nature. For, if the Axis of this Planet were inclined any considerable number of degrees, just so many degrees round each Pole would in their turn be almost six of our years together in darkness. And, as each degree of a great Circle on Jupiter contains 706 of our miles at a mean rate, it is easy to judge what vast tracts of land would be rendered uninhabitable by any considerable inclination of his Axis.

72. The Sun appears but ¹⁄₂₈ part so big to Jupiter as to us; and his light and heat are in the same small proportion, but compensated by the quick returns thereof, and by four Moons (some bigger and some less than our Earth) which revolve about him: so that there is scarce any part of this huge Planet but what is during the whole night enlightened by one or more of these Moons, except his Poles, whence only the farthest Moons can be seen, and where their light is not wanted, because the Sun constantly circulates in or near the Horizon, and is very probably kept in view of both Poles by the Refraction of Jupiter’s Atmosphere, which, if it be like ours, has certainly refractive power enough for that purpose.

73. The Orbits of these Moons are represented in the Scheme of the Solar System by four small circles marked 1. 2. 3. 4. on Jupiter’s Orbit ♃; but are drawn fifty times too large in proportion to it. The first Moon, or that nearest to Jupiter, goes round him in 1 day 18 hours and 36 minutes of our time; and is 229 thousand miles distant from his center: The second performs it’s revolution in three days 13 hours and 15 minutes, at 364 thousand miles distance: The third in 7 days three hours and 59 minutes, at the distance of 580 thousand miles: And the fourth, or outermost, in 16 days 18 hours and 30 minutes, at the distance of one million of miles from his center. The Periods of these Moons are so incommensurate to one another, that if ever they were all in a right line between Jupiter and the Sun, it will require more than 3,000,000,000,000 years from that time to bring them all into the same right line again, as any one will find who reduces all their periods into seconds, then multiplies them into one another, and divides the product by 432; which is the highest number that will divide the product of all their periodical times, namely 42,085,303,376,931,994,955,904 seconds, without a remainder.

74. The Angles under which the Orbits of Jupiter’s Moons are seen from the Earth, at it’s mean distance from Jupiter, are as follow: The first, 3ʹ 55ʺ; the second, 6ʹ 14ʺ; the third, 9ʹ 58ʺ; and the 21fourth, 17ʹ 30ʺ. And their distances from Jupiter, measured by his semidiameters, are thus: The first, 5²⁄₃; the second, 9; the third. 14²³⁄₆₀; and the fourth, 25¹⁸⁄₆₀ ^[15]. This Planet, seen from it’s nearest Moon, appears 1000 times as large as our Moon does to us; waxing and waneing in all her monthly shapes, every 42¹⁄₂ hours.

75. Jupiter’s three nearest Moons fall into his shadow, and are eclipsed in every Revolution: but the Orbit of the fourth Moon is so much inclined, that it passeth by Jupiter, without falling into his shadow, two years in every six. By these Eclipses, Astronomers have not only discovered that the Sun’s light comes to us in eight minutes; but have also determined the longitudes of places on this Earth with greater certainty and facility than by any other method yet known; as shall be explained in the eleventh Chapter.

76. The difference between the Equatoreal and Polar diameters of Jupiter is 6230 miles; for his equatoreal diameter is to his polar as 13 to 12. So that his Poles are 3115 miles nearer his center than his Equator is. This results from his quick motion round his Axis; for the fluids, together with the light particles, which they can carry or wash away with them, recede from the Poles which are at rest, towards the Equator where the motion is quickest, until there be a sufficient number accumulated to make up the deficiency of gravity occasioned by the centrifugal force, which always arises from a quick motion round an axis: and when the weight is made up so, as that all parts of the surface press equally heavy toward the center, there is an equilibrium, and the equatoreal parts rise no higher. Our Earth being but a very small Planet, compared to Jupiter, and it’s motion on it’s Axis being much slower, it is less flattened of course; for the difference between it’s equatoreal and polar diameters is only as 230 to 229, or 35 miles.

77. Jupiter’s Orbit is 1 degree 20 minutes inclined to the Ecliptic. His North Node is in the 7th degree of Cancer, and his South Node in the 7th degree of Capricorn.

78. Saturn, the remotest of all the Planets, is about 777 millions of miles from the Sun; and, travelling at the rate of 18 thousand miles every hour, as in the circle marked ♄, performs his annual circuit in 29 years 167 days and 5 hours of our time; which makes only one year to that Planet. His diameter is 67,000 miles; and therefore he is near 600 times as big as the Earth.

79. He is surrounded by a thin broad Ring, as an artificial Globe is by its Horizon. This Ring appears double when seen through a good 22telescope, and is represented by the figure in such an oblique view as it is generally seen. It is inclined 30 degrees to the Ecliptic, and is about 21 thousand miles in breadth; which is equal to it’s distance from Saturn on all sides. There is reason to believe that the Ring turns round it’s Axis, because, when it is almost edge-wise to us, it appears somewhat thicker on one side of the Planet than on the other; and the thickest edge has been seen on different sides at different times. But Saturn having no visible spots on his body, whereby to determine the time of his turning round his Axis, the length of his days and nights, and the position of his Axis, are unknown to us.

80. To Saturn, the Sun appears only ¹⁄₉₀th part so big as to us; and the light and heat he receives from the Sun are in the same proportion to ours. But to compensate for the small quantity of sun-light, he has five Moons, all going round him on the outside of his Ring, and nearly in the same plane with it. The first, or nearest Moon to Saturn, goes round him in 1 day 21 hours 19 minutes; and is 140 thousand miles from his center: The second, in two days 17 hours 40 minutes; at the distance of 187 thousand miles: The third, in 4 days 12 hours 25 minutes; at 263 thousand miles distance: The fourth, in 15 days 22 hours 41 minutes; at the distance of 600 thousand miles: And the fifth, or outermost, at one million 800 thousand miles from Saturn’s center, goes round him in 79 days 7 hours 48 minutes. Their Orbits in the Scheme of the Solar System are represented by the five small circles, marked 1. 2. 3. 4. 5. on Saturn’s Orbit; but these, like the Orbits of the other Satellites, are drawn fifty times too large in proportion to the Orbits of their Primary Planets.

81. The Sun shines almost fifteen of our years together on one side of Saturn’s Ring without setting, and as long on the other in it’s turn. So that the Ring is visible to the inhabitants of that Planet for almost fifteen of our years, and as long invisible by turns, if it’s Axis has no Inclination to it’s Ring: but if the Axis of the Planet be inclined to the Ring, suppose about 30 degrees, the Ring will appear and disappear once every natural day to all the inhabitants within 30 degrees of the Equator, on both sides, frequently eclipsing the Sun in a Saturnian day. Moreover, if Saturn’s Axis be so inclined to his Ring, it is perpendicular to his Orbit; and thereby the inconvenience of different seasons to that Planet is avoided. For considering the length of Saturn’s year, which is almost equal to thirty of ours, what a dreadful condition must the inhabitants of his Polar regions be in, if they be half of that time deprived of the light and heat of the Sun? which must not be their case alone, if the Axis of the Planet be perpendicular 23to the Ring, but also the Ring must hide the Sun from vast tracks of land on each side of the Equator for 13 or 14 of our years together, on the south side and north side by turns, as the Axis inclines to or from the Sun: the reverse of which inconvenience is another good presumptive proof of the Inclination of Saturn’s Axis to it’s Ring, and also of his Axis being perpendicular to his Orbit.

82. This Ring, seen from Saturn, appears like a vast luminous Arch in the Heavens, as if it did not belong to the Planet. When we see the Ring most open, it’s shadow upon the Planet is broadest; and from that time the shadow grows narrower, as the Ring appears to do to us; until, by Saturn’s annual motion, the Sun comes to the plane of the Ring, or even with it’s edge; which being then directed towards us, becomes invisible on account of it’s thinness; as shall be explained more largely in the tenth Chapter, and illustrated by a figure. The Ring disappears twice in every annual Revolution of Saturn, namely, when he is in the 19th degree both of Pisces and of Virgo. And when Saturn is in the middle between these points, or in the 19th degree either of Gemini or of Sagittarius, his Ring appears most open to us; and then it’s longest diameter is to it’s shortest as 9 to 4.

83. To such eyes as ours, unassisted by instruments, Jupiter is the only Planet that can be seen from Saturn; and Saturn the only Planet that can be seen from Jupiter. So that the inhabitants of these two Planets must either see much farther than we do, or have equally good instruments to carry their sight to remote objects, if they know that there is such a body as our Earth in the Universe: for the Earth is no bigger seen from Jupiter than his Moons are seen from the Earth; and if his large body had not first attracted our sight, and prompted our curiosity to view him with the telescope, we should never have known any thing of his Moons; unless by chance we had directed the telescope toward that small part of the Heavens where they were at the time of observation. And the like is true of the Moons of Saturn.

84. The Orbit of Saturn is 2¹⁄₂ degrees inclined to the Ecliptic, or Orbit of our Earth, and intersects it in the 21st degree of Cancer and of Capricorn; so that Saturn’s Nodes are only 14 degrees from Jupiter’s, § 77.

85. The quantity of light, afforded by the Sun of Jupiter, being but ¹⁄₂₈th part, and to Saturn only ¹⁄₉₀th part, of what we enjoy; may at first thought induce us to believe that these two Planets are entirely unfit for rational beings to dwell upon. But, that their light is not so weak as we imagine, is evident from their brightness in the night-time; and also, that when the Sun is so much eclipsed to us as to have 24only the 40th part of his Disc left uncovered by the Moon, the decrease of light is not very sensible: and just at the end of darkness in Total Eclipses, when his western limb begins to be visible, and seems no bigger than a bit of fine silver wire, every one is surprised at the brightness wherewith that small part of him shines. The Moon when Full affords travellers light enough to keep them from mistaking their way; and yet, according to Dr. Smith^[16], it is equal to no more than a 90 thousandth part of the light of the Sun: that is, the Sun’s light is 90 thousand times as strong as the light of the Moon when Full. Consequently, the Sun gives a thousand times as much light to Saturn as the Full Moon does to us; and above three thousand times as much to Jupiter. So that these two Planets, even without any Moons, would be much more enlightened than we at first imagine; and by having so many, they may be very comfortable places of residence. Their heat, so far as it depends on the force of the Sun’s rays, is certainly much less than ours; to which no doubt the bodies of their inhabitants are as well adapted as ours are to the seasons we enjoy. And if we consider, that Jupiter never has any winter, even at his Poles; which probably is also the case with Saturn, the cold cannot be so intense on these two Planets as is generally imagined. Besides, there may be something in their nature or soil much warmer than in that of our Earth: and we find that all our heat depends not on the rays of the Sun; for if it did, we should always have the same months equally hot or cold at their annual returns. But it is far otherwise, for February is sometimes warmer than May, which must be owing to vapours and exhalations from the Earth.

86. Every person who looks upon, and compares the Systems of Moons together, which belong to Jupiter and Saturn, must be amazed at the vast magnitude of these two Planets, and the noble attendance they have in respect of our little Earth: and can never bring himself to think, that an infinitely wise Creator should dispose of all his animals and vegetables here, leaving the other Planets bare and destitute of rational creatures. To suppose that he had any view to our Benefit, in creating these Moons and giving them their motions round Jupiter and Saturn; to imagine that he intended these vast Bodies for any advantage to us, when he well knew that they could never be seen but by a few Astronomers peeping through telescopes; and that he gave to the Planets regular returns of days and nights, and different seasons to all where they would be convenient; but of no manner of service to us, 25except only what immediately regards our own Planet the Earth; to imagine, I say, that he did all this on our account, would be charging him impiously with having done much in vain: and as absurd, as to imagine that he has created a little Sun and a Planetary System within the shell of our Earth, and intended them for our use. These considerations amount to little less than a positive proof that all the Planets are inhabited: for if they are not, why all this care in furnishing them with so many Moons, to supply those with light which are at the greater distances from the Sun? Do we not see, that the farther a Planet is from the Sun, the greater Apparatus it has for that purpose? save only Mars, which being but a small Planet, may have Moons too small to be seen by us. We know that the Earth goes round the Sun, and turns round it’s own Axis, to produce the vicissitudes of summer and winter by the former, and of day and night by the latter motion, for the benefit of its inhabitants. May we not then fairly conclude, by parity of reason, that the end and design of all the other Planets is the same? and is not this agreeable to that beautiful harmony which reigns over the Universe? Surely it is: and raises in us the most magnificent ideas of the SUPREME BEING, who is every where, and at all times present; displaying his power, wisdom, and goodness among all his creatures! and distributing happiness to innumerable ranks of various beings!

87. In Fig. 2d, we have a view of the proportional breadth of the Sun’s face or disc, as seen from the different Planets. The Sun is represented N^o 1, as seen from Mercury; N^o 2, as seen from Venus; N^o 3, as seen from the Earth; N^o 4, as seen from Mars; N^o 5, as seen from Jupiter; and N^o 6, as seen from Saturn.

Let the circle B be the Sun as seen from any Planet, at a given distance; to another Planet, at double that distance, the Sun will appear just of half that breadth, as A; which contains only one fourth part of the area or surface of B. For, all circles, as well as square surfaces, are to one another as the squares of their diameters. Thus, the square A is just half as broad as the square B; and yet it is plain to sight, that B contains four times as much surface as A. Hence, in round numbers, the Sun appears 7 times larger to Mercury than to us, 90 times larger to us than to Saturn, and 630 times as large to Mercury as to Saturn.

88. In Fig. 5th, we have a view of the bulks of the Planets in proportion to each other, and to a supposed globe of two foot diameter for the Sun. The Earth is 27 times as big as Mercury, very little bigger than Venus, 5 times as big as Mars; but Jupiter is 1049 times as big as the Earth, Saturn 586 times as big, exclusive of his Ring; and the 26Sun is 877 thousand 650 times as big as the Earth. If the Planets in this Figure were set at their due distances from a Sun of two feet diameter, according to their proportional bulks, as in our System, Mercury would be 28 yards from the Sun’s center; Venus 51 yards 1 foot; the Earth 70 yards 2 feet; Mars 107 yards 2 feet; Jupiter 370 yards 2 feet; and Saturn 760 yards two feet. The Comet of the year 1680, at it’s greatest distance, 10 thousand 760 yards. In this proportion, the Moon’s distance from the center of the Earth would be only 7¹⁄₂ inches.

89. To assist the imagination in conceiving an idea of the vast distances of the Sun, Planets, and Stars, let us suppose, that a body projected from the Sun should continue to fly with the swiftness of a cannon ball; i. e. 480 miles every hour; this body would reach the Orbit of Mercury, in 7 years 221 days; of Venus, in 14 years 8 days; of the Earth, in 19 years 91 days; of Mars, in 29 years 85 days; of Jupiter, in 100 years 280 days; of Saturn, in 184 years 240 days; to the Comet of 1680, at it’s greatest distance from the Sun, in 2660 years; and to the nearest fixed Stars in about 7 million 600 thousand years.

90. As the Earth is not the center of the Orbits in which the Planets move, they come nearer to it and go farther from it and at different times; on which account they appear bigger and less by turns. Hence, the apparent magnitudes of the Planets are not always a certain rule to know them by.

91. Under Fig. 3, are the names and characters of the twelve Signs of the Zodiac, which the Reader should be perfectly well acquainted with; so as to know the characters without seeing the names. Every Sign contains 30 degrees, as in the Circle bounding the Solar System; to which the characters of the Signs are set in their proper places.

92. The Comets are solid opaque bodies, with long transparent trains or tails, issuing from that side which is turned away from the Sun. They move about the Sun, in very excentric ellipses; and are of a much greater density than the Earth; for some of them are heated in every Period to such a degree, as would vitrify or dissipate any substance known to us. Sir Isaac Newton computed the heat of the Comet which appeared in the year 1680, when nearest the Sun, to be 2000 times hotter than red-hot iron, and that being thus heated, it must retain it’s heat until it comes round again, although it’s Period should be more than twenty thousand years; and it is computed to be only 575. The method of computing the heat of bodies, keeping at any known distance from the Sun, so far as their heat depends on the force of the Sun’s rays, is very easy; and shall be explained in the eighth Chapter.

2793. Part of the Paths of three Comets are delineated in the Scheme of the Solar System, and the years marked in which they made their appearance. It is believed, that there are at least 21 Comets belonging to our System, moving in all sorts of directions: and all those which have been observed, have moved through the ethereal Regions and the Orbits of the Planets without suffering the least sensible resistance in their motions; which plainly proves that the Planets do not move in solid Orbs. Of all the Comets, the Periods of the above-mentioned three only are known with any degree of certainty. The first of these Comets appeared in the years 1531, 1607, and 1682; and is expected to appear again in the year 1758, and every 75th year afterwards. The second of them appeared in 1532 and 1661, and may be expected to return in 1789 and every 129th year afterwards. The third, having last appeared in 1680, and it’s Period being no less than 575 years, cannot return until the year 2225. This Comet, at it’s greatest distance, is about 11 thousand two hundred millions of miles from the Sun; and at it’s least distance from the Sun’s center, which is 490,000 miles, is within less than a third part of the Sun’s semi-diameter from his surface. In that part of it’s Orbit which is nearest the Sun, it flies with the amazing swiftness of 880,000 miles in an hour; and the Sun, as seen from it, appears an hundred degrees in breadth; consequently, 40 thousand times as large as he appears to us. The astonishing length that this Comet runs out into empty Space, suggests to our minds an idea of the vast distance between the Sun and the nearest fixed Stars; of whose Attractions all the Comets must keep clear, to return periodically, and go round the Sun; and it shews us also, that the nearest Stars, which are probably those that seem the largest, are as big as our Sun, and of the same nature with him; otherwise, they could not appear so large and bright to us as they do at such an immense distance.

94. The extreme heat, the dense atmosphere, the gross vapours, the chaotic state of the Comets, seem at first sight to indicate them altogether unfit for the purposes of animal life, and a most miserable habitation for rational beings: and therefore ^[17]some are of opinion that they are so many hells for tormenting the damned with perpetual vicissitudes of heat and cold. But, when we consider, on the other hand, the infinite power and goodness of the Deity; the latter inclining, and the former enabling him to make creatures suited to all states and circumstances; that matter exists only for the sake of intelligence; and that wherever we find it, we always find it pregnant with life, or 28necessarily subservient thereto; the numberless species, the astonishing diversity of animals in earth, air, water, and even on other animals; every blade of grass, every tender leaf, every natural fluid, swarming with life; and every one of these enjoying such gratifications as the nature and state of each requires: when we reflect moreover that some centuries ago, till experience undeceived us, a great part of the Earth was judged uninhabitable; the Torrid Zone by reason of excessive heat, and the two Frigid Zones because of their intollerable cold; it seems highly probable, that such numerous and large masses of durable matter as the Comets are, however unlike they be to our Earth, are not destitute of beings capable of contemplating with wonder, and acknowledging with gratitude the wisdom, symmetry, and beauty of the Creation; which is more plainly to be observed in their extensive Tour through the Heavens, than in our more confined Circuit. If farther conjecture is permitted, may we not suppose them instrumental in recruiting the expended fuel of the Sun; and supplying the exhausted moisture of the Planets? However difficult it may be, circumstanced as we are, to find out their particular destination, this is an undoubted truth, that wherever the Deity exerts his power, there he also manifests his wisdom and goodness.

95. THE SOLAR SYSTEM here described is not a late invention; for it was known and taught by the wise Samian philosopher Pythagoras, and others among the ancients; but in latter times was lost, ’till the 15th century, when it was again restored by the famous Polish philosopher Nicholaus Copernicus, who was born at Thorn in the year 1473. In this, he was followed by the greatest mathematicians and philosophers that have since lived; as Kepler, Galileo, Descartes, Gassendus, and Sir Isaac Newton; the last of whom has established this System on such an everlasting foundation of mathematical and physical demonstration, as can never be shaken: and none who understand him can hesitate about it.

96. In the Ptolemean System the Earth was supposed to be fixed in the Center of the Universe; and that the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn moved round the Earth: above the Planets, this Hypothesis placed the Firmament of Stars, and then the two Crystalline Spheres; all which were included in and received motion from the Primum Mobile, which constantly revolved about the Earth in 24 hours, from East to West. But as this rude Scheme was found incapable to stand the test of art and observation, it was soon rejected by all true philosophers; notwithstanding the opposition and violence of blind and zealous bigots.

2997. The Tychonic System succeeded the Ptolemean, but was never so generally received. In this the Earth was supposed to stand still in the Center of the Universe or Firmament of Stars, and the Sun to revolve about it every 24 hours; the Planets, Mercury, Venus, Mars, Jupiter, and Saturn, going round the Sun in the times already mentioned. But some of Tycho’s disciples supposed the Earth to have a diurnal motion round it’s Axis, and the Sun with all the above Planets to go round the Earth in a year; the Planets moving round the Sun in the foresaid times. This hypothesis, being partly true and partly false, was embraced by few; and soon gave way to the only true and rational System, restored by Copernicus and demonstrated by Sir Isaac Newton.

98. To bring the foregoing particulars at once in view, with several others which follow, concerning the Periods, Distances, Bulks, &c. of the Planets, the following Table is inserted.

If the Moon’s projectile force was destroyed, she would fall to the Earth in 4 days 21 hours.

99. Matter is of itself inactive, and indifferent to motion or rest. A body at rest can never put itself in motion; a body in motion can never stop nor move slower of itself. Hence, when we see a body in motion we conclude some other substance must have given it that motion; when we see a body fall from motion to rest we conclude some other body or cause stopt it.

100. All motion is naturally rectilineal. A bullet thrown by the hand, or discharged from a cannon would continue to move in the same direction it received at first, if no other power diverted its course. Therefore, when we see a body moving in a curve of whatever kind, we conclude it must be acted upon by two powers at least: one to put it in motion, and another drawing it off from the rectilineal course which it would otherwise have continued to move in.

101. The power by which bodies fall towards the Earth is called Gravity or Attraction. By this power in the Earth it is, that all bodies, on whatever side, fall in lines perpendicular to it’s surface. On opposite parts of the Earth bodies fall in opposite directions, all towards the centre where the force of gravity is as it were accumulated. By this power constantly acting on bodies near the Earth they are kept from leaving it altogether; and those on its surface are kept thereto on all sides, so that they cannot fall from it. Bodies thrown with any obliquity are drawn by this power from a straight line into a curve, until they fall to the Ground: the greater the force by which they are thrown, the greater is the distance they are carried before they fall. If we suppose a body carried several miles above the Earth, and there projected in an horizontal direction, with so great a velocity that it would move more than a semidiameter of the Earth, in the time it would take to fall to the Earth by gravity; in that case, if there were no resisting medium in the way, the body would not fall to the Earth at all; but continue to circulate round the Earth, keeping always the same path, and returning to the point from whence it was projected, with the same velocity as at first.

102. We find the Moon moves round the Earth in an Orbit nearly circular. The Moon therefore must be acted on by two powers or forces; one which would cause her to move in a right line, another 32bending her motion from that line into a curve. This attractive power must be seated in the Earth; for there is no other body within the Moon’s Orbit to draw her. The attractive power of the Earth therefore extends to the Moon; and, in combination with her projectile force, causes her to move round the Earth in the same manner as the circulating body above supposed.

103. The Moons of Jupiter and Saturn are observed to move round their primary Planets: therefore there is such a power as gravity in these Planets. All the Planets move round the Sun, and respect it for their centre of motion: therefore the Sun must be endowed with attracting force, as well as the Earth and Planets. The like may be proved of the Comets. So that all the bodies or matter in the Solar System are possessed of this power; and perhaps so is all matter whatsoever.

104. As the Sun attracts the Planets with their Satellites, and the Earth the Moon, so the Planets and Satellites re-attract the Sun, and the Moon the Earth: action and re-action being always equal. This is also confirmed by observation; for the Moon raises tides in the ocean, the Satellites and Planets disturb one another’s motions.

105. Every particle of matter being possessed of an attracting power, the effect of the whole must be in proportion to the number of attracting particles: that is, to the quantity of matter in the body. This is demonstrated from experiments on pendulums: for, if they are of equal lengths, whatever their weights be, they always vibrate in equal times. Now, if one be double the weight of another, the force of gravity or attraction must be double to make it oscillate with the same celerity: if one is thrice the weight or quantity of matter of another, it requires thrice the force of gravity to make it move with the same celerity. Hence it is certain, that the power of gravity is always proportional to the quantity of matter in bodies, whatever their bulks or figures are.

106. Gravity also, like all other virtues or emanations issuing from a centre, decreases as the square of the distance increases: that is, a body at twice the distance attracts another with only a fourth part of the force; at four times the distance, with a sixteenth part of the force. This too is confirmed from observation, by comparing the distance which the Moon falls in a minute from a right line touching her Orbit, with the space which bodies near the Earth fall in the same time: and also by comparing the forces which retain Jupiter’s Moons in their Orbits. This will be more fully explained in the seventh Chapter.

107. The mutual attraction of bodies may be exemplified by a boat and a ship on the Water, tied by a rope. Let a man either in 33ship or boat pull the rope (it is the same in effect at which end he pulls, for the rope will be equally stretched throughout,) the ship and boat will be drawn towards one another; but with this difference, that the boat will move as much faster than the ship as the ship is heavier than the boat. Suppose the boat as heavy as the ship, and they will draw one another equally (setting aside the greater resistance of the Water on the bigger body) and meet in the middle of the first distance between them. If the ship is a thousand or ten thousand times heavier than the boat, the boat will be drawn a thousand or ten thousand times faster than the ship; and meet proportionably nearer the place from which the ship set out. Now, whilst one man pulls the rope, endeavouring to bring the ship and boat together, let another man, in the boat, endeavour to row her off sidewise, or at right Angles to the rope; and the former, instead of being able to draw the boat to the ship, will find it enough for him to keep the boat from going further off; whilst the latter, endeavouring to row off the boat in a straight line, will, by means of the other’s pulling it towards the ship, row the boat round the ship at the rope’s length from her. Here, the power employed to draw the ship and boat to one another represents the mutual attraction of the Sun and Planets, by which the Planets would fall freely towards the Sun with a quick motion; and would also in falling attract the Sun towards them. And the power employed to row off the boat represents the projectile force impressed on the Planets at right Angles, or nearly so, to the Sun’s attraction; by which means the Planets move round the Sun, and are kept from falling to it. On the other hand, if it be attempted to make a heavy ship go round a light boat, they will meet sooner than the ship can get round; or the ship will drag the boat after it.

108. Let the above principles be applied to the Sun and Earth; and they will evince, beyond a possibility of doubt, that the Sun, not the Earth, is the center of the System; and that the Earth moves round the Sun as the other Planets do.

For, if the Sun moves about the Earth, the Earth’s attractive power must draw the Sun towards it from the line of projection so, as to bend it’s motion into a curve; and the Earth being at least 169 thousand times lighter than the Sun, by being so much less as to it’s quantity of matter, must move 169 thousand times faster toward the Sun than the Sun does toward the Earth; and consequently would fall to the Sun in a short time if it had not a very strong projectile motion to carry it off. The Earth therefore, as well as every other Planet in 34the System, must have a rectilineal impulse to prevent its falling into the Sun. To say, that gravitation retains all the other Planets in their Orbits without affecting the Earth, which is placed between the Orbits of Mars and Venus, is as absurd as to suppose that six cannon bullets might be projected upwards to different heights in the Air, and that five of them should fall down to the ground; but the sixth, which is neither the highest nor the lowest, should remain suspended in the Air without falling; and the Earth move round about it.

109. There is no such thing in nature as a heavy body moving round a light one as its centre of motion. A pebble fastened to a mill-stone by a string, may by an easy impulse be made to circulate round the mill-stone: but no impulse can make a mill-stone circulate round a loose pebble, for the heaviest would undoubtedly carry the lightest along with it wherever it goes.

110. The Sun is so immensely bigger and heavier than the Earth^[18], that if he was moved out of his place, not only the Earth, but all the other Planets if they were united into one mass, would be carried along with the Sun as the pebble would be with the mill-stone.

111. By considering the law of gravitation, which takes place throughout the Solar System, in another light, it will be evident that the Earth moves round the Sun in a year; and not the Sun round the Earth. It has been shewn (§ 106) that the power of gravity decreases as the square of the distance increases: and from this it follows with mathematical certainty, that when two or more bodies move round another as their centre of motion, the squares of their periodic times will be to one another in the same proportion as the cubes of their distances from the central body. This holds precisely with regard to the Planets round the Sun, and the Satellites round the Planets; the relative distances of all which, are well known. But, if we suppose the Sun to move round the Earth, and compare its period with the Moon’s by the above rule, it will be found that the Sun would take no less than 173,510 days to move round the Earth, in which case our year would be 475 times as long as it now is. To this we may add, that the aspects of increase and decrease of the Planets, the times of their seeming to stand still, and to move direct and retrograde, answer precisely to the Earth’s motion; but not at all to the Sun’s without introducing the most absurd and monstrous suppositions, which would destroy all harmony, order, and simplicity in the System. Moreover, if the Earth is supposed to stand still, and the Stars to revolve in free spaces about the Earth in 24 hours, it is certain that the forces by 35which the Stars revolve in their Orbits are not directed to the Earth, but to the centres of the several Orbits: that is, of the several parallel Circles which the Stars on different sides of the Equator describe every day: and the like inferences may be drawn from the supposed diurnal motion of the Planets, since they are never in the Equinoctial but twice, in their courses with regard to the starry Heavens. But, that forces should be directed to no central body, on which they physically depend, but to innumerable imaginary points in the axe of the Earth produced to the Poles of the Heavens, is an hypothesis too absurd to be allowed of by any rational creature. And it is still more absurd to imagine that these forces should increase exactly in proportion to the distances from this axe; for this is an indication of an increase to infinity: whereas the force of attraction is found to decrease in receding from the fountain from whence it flows. But, the farther that any Star is from the quiescent Pole the greater must be the Orbit which it describes; and yet it appears to go round in the same time as the nearest Star to the Pole does. And if we take into consideration the two-fold motion observed in the Stars, one diurnal round the Axis of the Earth in 24 hours, and the other round the Axis of the Ecliptic in 25920 years § 251, it would require an explication of such a perplexed composition of forces, as could by no means be reconciled with any physical Theory.

112. There is but one objection of any weight that can be made to the Earth’s motion round the Sun; which is, that in opposite points of the Earth’s Orbit, it’s Axis which always keeps a parallel direction would point to different fixed Stars; which is not found to be fact. But this objection is easily removed by considering the immense distance of the Stars in respect of the diameter of the Earth’s Orbit; the latter being no more than a point when compared to the former. If we lay a ruler on the side of a table, and along the edge of the ruler view the top of a spire at ten miles distance; then lay the ruler on the opposite side of the table in a parallel situation to what it had before, and the spire will still appear along the edge of the ruler; because our eyes, even when assisted by the best instruments are incapable of distinguishing so small a change.

113. Dr. Bradley, our present Astronomer Royal, has found by a long series of the most accurate observations, that there is a small apparent motion of the fixed Stars, occasioned by the aberration of their light, and so exactly answering to an annual motion of the Earth, as evinces the same, even to a mathematical demonstration. Those who are qualified to read the Doctor’s modest Account of this great discovery may consult the Philosophical Transactions, N^o 406. Or they may find 36it treated of at large by Drs. Smith^[19], Long^[20], Desaguliers^[21], Rutherfurth, Mr. Maclaurin^[22], and M. de la Caille^[23].

114. It is true that the Sun seems to change his place daily, so as to make a tour round the starry Heavens in a year. But whether the Earth or Sun moves, this appearance will be the same; for, when the Earth is in any part of the Heavens, the Sun will appear in the opposite. And therefore, this appearance can be no objection against the motion of the Earth.

115. It is well known to every person who has sailed on smooth Water, or been carried by a stream in a calm, that however fast the vessel goes he does not feel its progressive motion. The motion of the Earth is incomparably more smooth and uniform than that of a ship, or any machine made and moved by human art: and therefore it is not to be imagined that we can feel it’s motion.

116. We find that the Sun, and those Planets on which there are visible spots, turn round their Axes: for the spots move regularly over their Disks^[24]. From hence we may reasonably conclude that the other Planets on which we see no spots, and the Earth which is likewise a Planet, have such rotations. But being incapable of leaving the Earth, and viewing it at a distance; and it’s rotation being smooth and uniform, we can neither see it move on it’s Axis as we do the Planets, nor feel ourselves affected by it’s motion. Yet there is one effect of such a motion which will enable us to judge with certainty whether the Earth revolves on it’s Axis or not. All Globes which do not turn round their Axes will be perfect spheres, on account of the equality of the weight of bodies on their surfaces; especially of the fluid parts. But all Globes which turn on their Axes will be oblate spheroids; that is, their surfaces will be higher, or farther from the centre, in the equatoreal than in the polar Regions: for, as the equatoreal parts move quickest, they will recede farther from the Axis of motion, and enlarge the equatoreal diameter. That our Earth is really of this figure is demonstrable from the unequal vibrations of a pendulum, and the unequal lengths of degrees in different latitudes. Since then, the Earth is higher at the Equator than at the Poles, the sea, which naturally runs downward, or towards the places which are nearest the centre, would run towards the polar Regions, and leave the equatoreal parts dry, if the centrifugal force of these parts did not raise and carry the 37waters thither. The Earth’s equatoreal diameter is 35 miles longer than its Axis.

117. Bodies near the Poles are heavier than those towards the Equator, because they are nearer the Earth’s centre, where the whole force of the Earth’s attraction is accumulated. They are also heavier because their centrifugal force is less on account of their diurnal motion being slower. For both these reasons, bodies carried from the Poles toward the Equator, gradually lose of their weight. Experiments prove that a pendulum, which vibrates seconds near the Poles vibrates slower near the Equator, which shews that it is lighter or less attracted there. To make it oscillate in the same time, ’tis found necessary to diminish it’s length. By comparing the different lengths of pendulums swinging seconds at the Equator and at London, it is found that a pendulum must be 2¹⁶⁹⁄₁₀₀₀ lines shorter at the Equator than at the Poles. A line is a twelfth part of an inch.

118. If the Earth turned round it’s Axis in 84 minutes 43 seconds, the centrifugal force would be equal to the power of gravity at the Equator; and all bodies there would entirely lose their weight. If the Earth revolved quicker they would all fly off, and leave it.

119. One on the Earth can no more be sensible of it’s undisturbed motion on it’s Axis, than one in the cabin of a ship on smooth Water can be sensible of her motion when she turns gently and uniformly round. It is therefore no argument against the Earth’s diurnal motion that we do not feel it: nor is the apparent revolutions of the celestial bodies every day a proof of the reality of these motions; for whether we or they revolve, the appearance is the very same. A person looking through the cabin windows of a ship as strongly fancies the objects on land to go round when the ship turns, as if they were actually in motion.

120. If we could translate ourselves from Planet to Planet, we should still find that the Stars would appear of the same magnitudes, and at the same distances from each other, as they do to us here; because the width of the remotest Planet’s Orbit bears no sensible proportion to the distance of the Stars. But then, the Heavens would seem to revolve about very different Axes; and consequently, those quiescent Points which are our Poles in the Heavens would seem to revolve about other points, which, though apparently in motion to us on Earth would be at rest as seen from any other Planet. Thus, the Axis of Venus, which lies almost at right Angles to the Axis of the Earth, would have it’s motionless Poles in two opposite points of the Heavens 38lying almost in our Equinoctial, where the motion appears quickest because it is performed in the greatest Circle. And the very Poles, which are at rest to us, have the quickest motion of all as seen from Venus. To Mars and Jupiter the Heavens appear to turn round with very different velocities on the same Axis, whose Poles are about 23¹⁄₂ degrees from ours. Were we on Jupiter we should be at first amazed at the rapid motion of the Heavens; the Sun and Stars going round in 9 hours 56 minutes. Could we go from thence to Venus we should be as much surprised at the slowness of the heavenly motions: the Sun going but once round in 584 hours, and the Stars in 540. And could we go from Venus to the Moon we should see the Heavens turn round with a yet slower motion; the Sun in 708 hours, the Stars in 655. As it is impossible these various circumvolutions in such different times and on such different Axes can be real, so it is unreasonable to suppose the Heavens to revolve about our Earth more than it does about any other Planet. When we reflect on the vast distance of the fixed Stars, to which 162,000,000 of miles is but a point, we are filled with amazement at the immensity of their distance. But if we try to frame an idea of the extreme rapidity with which the Stars must move, if they move round the Earth in 24 hours, the thought becomes so much too big for our imagination, that we can no more conceive it than we do infinity or eternity. If the Sun was to go round the Earth in a day, he must travel upwards of 300,000 miles in a minute: but the Stars being at least 10,000 times as far as the Sun from us, those about the Equator must move 10,000 times as quick. And all this to serve no other purpose than what can be as fully and much more simply obtained by the Earth’s turning round eastward as on an Axis, every 24 hours, causing thereby an apparent diurnal motion of the Sun westward, and bringing about the alternate returns of day and night.

Pl. II.

121. As to the common objections against the Earth’s motion on it’s Axis, they are all easily answered and set aside. That it may turn without being seen or felt to do so, has been already shewn, § 119. But some are apt to imagine that if the Earth turns eastward (as it certainly does if it turns at all) a ball fired perpendicularly upward in the air must fall considerably westward of the place it was projected from. This objection, which at first seems to have some weight, will be found to have none at all when we consider that the gun and ball partake of the Earth’s motion; and therefore the ball being carried forward with the air as quick as the Earth and air turn, must fall down again on the same place. A stone let fall from the top of a main-mast, if it 39meets with no obstacle, falls on the deck as near the foot of the mast when the ship sails as when it does not. And if an inverted bottle, full of liquor, be hung up to the cieling of the cabin, and a small hole be made in the cork to let the liquor drop through on the floor, the drops will fall just as far forward on the floor when the ship sails as when it is at rest. And gnats or flies can as easily dance among one another in a moving cabin as in a fixed chamber. As for those scripture expressions which seem to contradict the Earth’s motion, this general answer may be made to them all, viz. ’tis plain from many instances that the Scriptures were never intended to instruct us in Philosophy or Astronomy; and therefore, on those subjects, expressions are not always to be taken in the strictest sense; but for the most part as accommodated to the common apprehensions of mankind. Men of sense in all ages, when not treating of the sciences purposely, have followed this method: and it would be in vain to follow any other in addressing ourselves to the vulgar, or bulk of any community. Moses calls the Moon A GREAT LUMINARY (as it is in the Hebrew) as well as the Sun: but the Moon is known to be an opaque body, and the smallest that Astronomers have observed in the Heavens and shines upon us not by any inherent light of it’s own, but by reflecting the light of the Sun. If Moses had known this, and told the Israelites so, they would have stared at him; and considered him rather as a madman than as a person commissioned by the Almighty to be their leader.

122. We are kept to the Earth’s surface on all sides by the power of it’s central attraction; which, laying hold of all bodies according to their densities or quantities of matter without regard to their bulks, constitutes what we call their weight. And having the sky over our heads, go where we will, and our feet towards the centre of the Earth, we call it up over our heads, and down under our feet: although the same right line which is down to us, if continued through and beyond the opposite side of the Earth, would be up to the inhabitants on the opposite side. For, the inhabitants n, i, e, m, s, o, q, l stand with their feet toward the Earth’s centre C; and have the same 40figure of sky N, l, E, M, S, O, Q, L over their heads. Therefore, the point S is as directly upward to the inhabitant s on the south Pole as N is to the inhabitant n on the North Pole: so is E to the inhabitant e, supposed to be on the north end of Peru; and Q to the opposite inhabitant q on the middle of the island Sumatra. Each of these observers is surprised that his opposite or Antipode can stand with his head hanging downwards. But let either go to the other, and he will tell him that he stood as upright and firm on the place where he was as he now stands where he is. To all these observers the Sun, Moon, and Stars seem to turn round the points N and S as the Poles of the fixed Axis NCS; because the Earth does really turn round the mathematical line nCs as round an Axis of which n is the North Pole and s the South Pole. The Inhabitant U (Fig. II.) affirms that he is on the uppermost side of the Earth, and wonders how another at L can stand on the undermost side with his head hanging downwards. But U in the mean time forgets that in twelve hours time he will be carried half round with the Earth; and then be in the very situation that L now is, although as far from him as before. And yet, when U comes there, he will find no difference as to his manner of standing; only he will see the opposite half of the Heavens, and imagine the Heavens to have gone half round him.

123. When we see a globe hung up in a room we cannot help imagining it to have an upper and an under side, and immediately form a like idea of the Earth; from whence we conclude, that it is as impossible for persons to stand on the under side of the Earth as for pebbles to lie on the under side of a common Globe, which instantly fall down from it to the ground; and well they may, because the attraction of the Earth, being too strong for the attraction of the Globe, pulls them away. Just so would be the case with our Earth, if it were placed near a Globe much bigger than itself, such as Jupiter: for then it would really have an upper and an under side with respect to that large Globe; which, by it’s Attraction, would pull away every thing from the side of the Earth next to it; and only those on the top of the opposite or upper side could keep upon it. But there is no larger Globe near enough our Earth to overcome it’s central attraction; and therefore it has no such thing as an upper and an under side: for all bodies on or near it’s surface, even to the Moon, gravitate towards it’s center.

124. Let any man imagine that the Earth and every thing but himself is taken away, and he left alone in the midst of indefinite Space; 41he could then have no idea of up or down; and were his pockets full of gold, he might take the pieces one by one, and throw them away on all sides of him, without any danger of losing them; for the attraction of his body would bring them all back by the ways they went, and he would be down to every one of them. But then, if a Sun or any other large body were created, and placed in any part of Space several millions of miles from him, he would be attracted towards it, and could not save himself from falling down to it.

125. The Earth’s bulk is but a point, as that at C, compared to the Heavens; and therefore every inhabitant upon it, let him be where he will, as at n, e, m, s, &c. sees one half of the Heavens. The inhabitant n, on the North Pole of the Earth, constantly sees the Hemisphere ENQ; and having the North Pole N of the Heavens just over his head, his ^[25]Horizon coincides with the Celestial Equator ECQ. Therefore all the Stars in the Northern Hemisphere ENC, between the Equator and North Pole, appear to turn round the line NC, moving parallel to the Horizon. The Equatoreal Stars keep in the Horizon, and all those in the Southern Hemisphere ESQ are invisible. The like Phenomena are seen by the observer s on the South Pole, with respect to the Hemisphere ESQ; and to him the opposite Hemisphere is always invisible. Hence, under either Pole, only one half of the Heavens is seen; for those parts which are once visible never set, and those which are once invisible never rise. But the Ecliptic YCX or Orbit which the Sun appears to describe once a year by the Earth’s annual motion, has the half YC constantly above the Horizon ECQ of the North Pole n; and the other half CX always below it. Therefore whilst the Sun describes the northern half YC of the Ecliptic he neither sets to the North Pole nor rises to the South; and whilst he describes the southern half CX he neither sets to the South Pole nor rises to the North. The same things are true with respect to the Moon; only with this difference, that as the Sun describes the Ecliptic but once a year, he is for half that time visible to each Pole in it’s turn, and as long invisible; but as the Moon goes round the Ecliptic in 27 days 8 hours, she is only visible for 13 days 16 hours, and as long invisible to each Pole by turns. All the Planets likewise rise and set to the Poles, because their Orbits are cut obliquely in halves by the Horizon of the Poles. When the Sun (in his apparent way from X) arrives at C, which is on the 20th of March, he is just rising to an observer at n on the North Pole, and setting to another at s on the 42South Pole. From C he rises higher and higher in every apparent Diurnal revolution ’till he comes to the highest point of the Ecliptic y, on the 21st of June, and then he is at his greatest Altitude, which is 23¹⁄₂ degrees, or the Arc Ey, equal to his greatest North declination; and from thence he seems to descend gradually in every apparent Circumvolution, ’till he sets at C on the 23d of September; and then he goes to exhibit the like Appearances at the South Pole for the other half of the year. Hence the Sun’s apparent motion round the Earth is not in parallel Circles, but in Spirals; such as might be represented by a thread wound round a Globe from Tropic to Tropic; the Spirals being at some distance from one another about the Equator, but gradually nearer to each other as they approach nearer to the Tropics.

126. If the observer be any where on the Terrestrial Equator eCq, as suppose at e, he is in the Plane of the Celestial Equator; or under the Equinoctial ECQ; and the Axis of the Earth nCs is coincident with the Plane of his Horizon, extended out to N and S, the North and South Poles of the Heavens. As the Earth turns round the line NCS, the whole Heavens MOLl seem to turn round the same line, but the contrary way. It is plain that this observer has the Poles constantly in his Horizon, and that his Horizon cuts the Diurnal paths of all the Celestial bodies perpendicularly and in halves. Therefore the Sun, Planets, and Stars rise every day, and ascend perpendicularly above the Horizon for six hours, and passing over the Meridian, descend in the same manner for the six following hours; then set in the Horizon, and continue twelve hours below it. Consequently at the Equator the days and nights are equally long throughout the year. When the observer is in the situation e, he sees the Hemisphere SEN; but in twelve hours after, he is carried half round the Earth’s Axis to q, and then the Hemisphere SQN becomes visible to him; and SEN disappears, being hid by the Convexity of the Earth. Thus we find that to an observer at either of the Poles one half of the Sky is always visible, and the other half never seen; but to an observer on the Equator the whole Sky is seen every 24 hours.

The Figure here referred to, represents a Celestial globe of glass, having a Terrestrial globe within it; after the manner of the Glass Sphere invented by my generous friend Dr. Long, Lowndes’s Professor of Astronomy in Cambridge.

127. If a Globe be held sidewise to the eye, at some distance, and so that neither of it’s Poles can be seen, the Equator ECQ and all Circles parallel to it, as DL, yzx, abX, MO, &c. will appear to be 43straight lines, as projected in this Figure; which is requisite to be mentioned here, because we shall have occasion to call them Circles in the following Article^[26].

128. Let us now suppose that the observer has gone from the Equator e towards the North Pole n, and that he stops at i, from which place he then sees the Hemisphere MElNL; his Horizon MCL having shifted as many ^[27]Degrees from the Celestial poles N and S as he has travelled from under the Equinoctial E. And as the Heavens seem constantly to turn round the line NCS as an Axis, all those Stars which are as far from the North Pole N as the observer is from under, the Equinoctial, namely the Stars north of the dotted parallel DL, never set below the Horizon; and those which are south of the dotted parallel MO never rise above it. Hence, the former of these two parallel Circles is called the Circle of perpetual Apparition, and the latter the Circle of perpetual Occultation: but all the Stars between these two Circles rise and set every day. Let us imagine many Circles to be drawn between these two, and parallel to them; those which are on the north side of the Equinoctial will be unequally cut by the Horizon MCL, having larger portions above the Horizon than below it; and the more so, as they are nearer to the Circle of perpetual Apparition; but the reverse happens to those on the south side of the Equinoctial, whilst the Equinoctial is divided in two equal parts by the Horizon. Hence, by the apparent turning of the Heavens, the northern Stars describe greater Arcs or Portions of Circles above the Horizon than below it; and the greater as they are farther from the Equinoctial towards the Circle of perpetual Apparition; whilst the contrary happens to all Stars south of the Equinoctial: but those upon it describe equal Arcs both above and below the Horizon, and therefore they are just as long above as below it.

129. An observer on the Equator has no Circle of perpetual Apparition or Occultation, because all the Stars, together with the Sun and Moon, rise and set to him every day. But, as a bare view of the Figure is sufficient to shew that these two Circles DL and MO are just as far from the Poles N and S as the observer at i (or one opposite to him at o) is from the Equator ECQ; it is plain, that if an observer begins to travel from the Equator towards either Pole, his Circle of perpetual Apparition rises from that Pole as from a Point, and his Circle of perpetual Occultation from the other. As the observer advances 44toward the nearer Pole, these two Circles enlarge their diameters, and come nearer one another, until he comes to the Pole; and then they meet and coincide in the Equator. On different sides of the Equator, to observers at equal distances from it, the Circle of perpetual Apparition to one is the Circle of perpetual Occultation to the other.

130. Because the Stars never vary their distances from the Equinoctial, so as to be sensible in an age, the lengths of their diurnal and nocturnal Arcs are always the same to the same places on the Earth. But as the Earth goes round the Sun every year in the Ecliptic, one half of which is on the north side of the Equinoctial and the other half on it’s south side, the Sun appears to change his place every day, so as to go once round the Circle YCX every year § 114. Therefore whilst the Sun appears to advance northward, from having described the Parallel abX touching the Ecliptic in X the days continually lengthen and the nights shorten, until he comes to y and describes the Parallel yzx, when the days are at the longest and the nights at the shortest: for then, as the Sun goes no farther northward, the greatest portion that is possible of the diurnal Arc yz is above the Horizon of the inhabitant i; and the smallest portion zx below it. As the Sun declines southward from y he describes smaller diurnal and greater nocturnal Arcs, or Portions of Circles, every day; which causeth the days to shorten and nights to lengthen, until he arrives again at the Parallel abX; which having only the small part ab above the Horizon MCL, and the great part bX below it, the days are at the shortest and the nights at the longest; because the Sun recedes no farther south, but returns northward as before. It is easy to see that the Sun must be in the Equinoctial ECQ twice every year, and then the days and nights are equally long; that is, 12 hours each. These hints serve at present to give an idea of some of the Appearances resulting from the motions of the Earth; which will be more particularly described in the tenth Chapter.

131. To an observer at either Pole, the Horizon and Equinoctial are coincident; and the Sun and Stars seem to move parallel to the Horizon: therefore, such an observer is said to have a Parallel position of the Sphere. To an observer any where between the Poles and Equator, the Parallels described by the Sun and Stars are cut obliquely by the Horizon, and therefore he is said to have an Oblique position of the Sphere. To an observer any where on the Equator, the Parallels of Motion, described by the Sun and Stars are cut perpendicularly, or at Right angles, 45by the Horizon; and therefore he is said to have a Right position of the Sphere. And these three are all the different ways that the Sphere can be posited to all people, on the Earth.

132. So vastly great is the distance of the starry Heavens, that if viewed from any part of the Solar System, or even many millions of miles beyond it, its appearance would be the very same to us. The Sun and Stars would all seem to be fixed on one concave surface, of which the Spectator’s eye would be the centre. But the Planets, being much nearer than the Stars, their appearances will vary considerably with the place from which they are viewed.

133. If the spectator is at rest without their Orbits, the Planets will seem to be at the same distance as the Stars; but continually changing their places with respect to the Stars, and to one another: assuming various phases of increase and decrease like the Moon. And, notwithstanding their regular motions about the Sun, will sometimes appear to move quicker, sometimes slower, be as often to the west as to the east of the Sun; and at their greatest distances seem quite stationary. The duration, extent, and points in the Heavens where these digressions begin and end, would be more or less according to the respective distances of the several Planets from the Sun: but in the same Planet they would continue invariably the same at all times; like pendulums of unequal lengths oscillating together, the shorter move quick and go over a small space, the longer move slow and go over a large space. If the observer is at rest within the Orbits of the Planets, but not near the common center, their apparent motions will be irregular, but less so than in the former case. Each of the several Planets will appear bigger and less by turns, as they approach nearer or recede farther from the observer; the nearest varying most in their size. They will also move quicker or slower with regard to the fixed Stars, but will never be retrograde or stationary.

134. Next, let a spectator in motion view the Heavens: the same apparent irregularities will be observed, but with some variation resulting from his own motion. If he is on a Planet which has a rotation on it’s Axis, not being sensible of his own motion he will imagine 46the whole Heavens, Sun, Planets, and Stars to revolve about him in the same time that his Planet turns round, but the contrary way; and will not be easily convinced of the deception. If his Planet moves round the Sun, the same irregularities and aspects as above will appear in the motions of the Planets: only, the times of their being direct, stationary and retrograde will be accelerated or retarded as they concur with, or are contrary to his motion: and the Sun will seem to move among the fixed Stars or Signs, directly opposite to those in which his Planet moves; changing it’s place every day as he does. In a word, whether our observer be in motion or at rest, whether within or without the Orbits of the Planets, their motions will seem irregular, intricate and perplexed, unless he is in the center of the System; and from thence, the most beautiful order and harmony will be observed.

135. The Sun being the center of all the Planets motions, the only place from which their motions could be truly seen, is the Sun’s center; where the observer being supposed not to turn round with the Sun (which, in this case, we must imagine to be a transparent body) would see all the Stars at rest, and seemingly equidistant from him. To such an observer the Planets would appear to move among the fixed Stars, in a simple, regular, and uniform manner; only, that as in equal times they describe equal Areas, they would describe spaces somewhat unequal, because they move in elliptic Orbits § 155. Their motions would also appear to be what they are in fact, the same way round the Heavens; in paths which cross at small Angles in different parts of the Heavens, and then separate a little from one another § 20. So that, if the solar Astronomer should make the Path or Orbit of any one Planet a standard, and consider it as having no obliquity § 201, he would judge the paths of all the rest to be inclined to it; each Planet having one half of it’s path on one side, and the other half on the opposite side of the standard Path or Orbit. And if he should ever see all the Planets start from a conjunction with each other^[28]; Mercury would move so much faster than Venus as to overtake her again (though not in the same point of the Heavens) in a quantity of time almost equal to 145 of our days and nights; or, as we commonly call them, Natural Days, which include both the days and nights: Venus would move so much faster than the Earth as to overtake it again in 585 natural days: the Earth so much faster than Mars as to overtake him again in 778 such 47days: Mars is much faster than Jupiter as to overtake him again in 817 such days: and Jupiter so much faster than Saturn as to overtake him again in 7236 days, all of our time.

136. But as our solar Astronomer could have no idea of measuring the courses of the Planets by our days, he would very probably take the period of Mercury, which is the quickest moving Planet, for a measure to compare the periods of the others by. As all the Stars would appear quiescent to him, he would never think that they had any dependance upon the Sun; but could naturally imagine that the Planets have, because they move round the Sun. And it is by no means improbable, that he would conclude those Planets whose periods are quickest to move in Orbits proportionably less than those do which make slower circuits. But being destitute of a method for finding their Parallaxes, or, more properly speaking, as they could have no Parallax to him, he could never know any thing of their real distances or magnitudes. Their relative distances he might perhaps guess at by their periods, and from thence infer something of truth concerning their relative bulks, by comparing their apparent bulks with one another. For example, Jupiter appearing bigger to him than Mars, he would conclude it to be much bigger in fact; because it appears so, and must be farther from him, on account of it’s longer period. Mercury would seem bigger than the Earth; but by comparing it’s period with the Earth’s, he would conclude that the Earth is much farther from him than Mercury, and consequently that it must be really bigger though apparently less; and so of the rest. And, as each Planet would appear somewhat bigger in one part of it’s Orbit than in the opposite, and to move quickest when it seems biggest, the observer would be at no loss to determine that all the Planets move in Orbits of which the Sun is not precisely in the center.

137. The apparent magnitudes of the Planets continually change as seen from the Earth, which demonstrates that they approach nearer to it, and recede farther from it by turns. From these Phenomena, and their apparent motions among the Stars, they seem to describe looped curves which never return into themselves, Venus’s path excepted. And if we were to trace out all their apparent paths, and put the figures of them together in one diagram, they would appear so anomalous and confused, that no man in his senses could believe them to be representations of their real paths; but would immediately conclude, that such apparent irregularities must be owing to some Optic illusions. And after a good deal of enquiry, he might perhaps be at a 48loss to find out the true cause of these inequalities; especially if he were one of those who would rather, with the greatest justice, charge frail man with ignorance, than the Almighty with being the author of such confusion.

138. Dr. Long, in his first volume of Astronomy, has given us figures of the apparent paths of all the Planets separately from Cassini; and on seeing them I first thought of attempting to trace some of them by a machine^[29] that shews the motions of the Sun, Mercury, Venus, the Earth and Moon, according to the Copernican System. Having taken off the Sun, Mercury, and Venus, I put black-lead pencils in their places, with the points turned upward; and fixed a circular sheet of paste-board so, that the Earth kept constantly under it’s center in going round the Sun; and the paste-board kept its parallelism. Then, pressing gently with one hand upon the paste-board to make it touch the three pencils, with the other hand I turned the winch which moves the whole machinery: and as the Earth, together with the pencils in the places of Mercury and Venus, had their proper motions round the Sun’s pencil, which kept at rest in the center of the machine, all the three pencils described a diagram from which the first Figure of the third Plate is truly copied in a smaller size. As the Earth moved round the Sun, the Sun’s pencil described the dotted Circle of Months, whilst Mercury’s pencil drew the curve with the greatest number of loops, and Venus’s that with the fewest. In their inferiour conjunctions they come as much nearer the Earth, or within the Circle of the Sun’s apparent motion round the Heavens, as they go beyond it in their superiour conjunctions. On each side of the loops they appear Stationary; in that part of each loop next the Earth retrograde; and in all rest of their paths direct.

Plate III.

J. Ferguson delin.

J. Mynde Sc.

If Cassini’s Figures of the paths of the Sun, Mercury and Venus were put together, the Figure as above traced out, would be exactly like them. It represents the Sun’s apparent motion round the Ecliptic, which is the same every year; Mercury’s motion for seven years; and Venus’s for eight; in which time Mercury’s path makes 23 loops, crossing itself so many times, and Venus’s only five. In eight years Venus falls so nearly into the same apparent path again, as to deviate very little from it in some ages; but in what number of years Mercury and the rest of the Planets would describe the same visible paths over again, I cannot at present determine. Having finished the above Figure of the paths of Mercury and Venus, I put the Ecliptic round them as in the Doctor’s Book; and added the dotted lines from the Earth to the 49Ecliptic for shewing Mercury’s apparent or geocentric motion therein for one year; in which time his path makes three loops, and goes on a little farther; which shews that he has three inferiour, and as many superiour conjunctions with the Sun in that time, and also that he is six times Stationary, and thrice Retrograde. Let us now trace out his motion for one year in the Figure.

Suppose Mercury to be setting out from A towards B (between the Earth and left-hand corner of the Plate) and as seen from the Earth his motion will then be direct, or according to the order of the Signs. But when he comes to B, he appears to stand still in the 23d degree of ♏ at F, as shewn by the line BF. Whilst he goes from B to C, the line BF goes backward from F to E, or contrary to the order of Signs; and when he is at C he appears Stationary at E; having gone back 11¹⁄₂ degrees. Now, suppose him Stationary on the first of January at C, on the tenth thereof he will appear in the Heavens as at 20, near F; on the 20th he will be seen as at G; on the 31st at H; on the 10th of February at I; on the 20th at K; and on the 28th at L; as the dotted lines shew, which are drawn through every tenth day’s motion in his looped path, and continued to the Ecliptic. On the 10th of March he appears at M; on the 20th at N; and on the 31st at O. On the 10th of April he appears Stationary at P; on the 20th he seems to have gone back again to O; and on the 30th he appears Stationary at Q having gone back 11¹⁄₂ degrees. Thus Mercury seems to go forward 4 Signs 11 Degrees, or 131 Degrees; and to go back only 11 or 12 Degrees, at a mean rate. From the 30th of April to the 10th of May, he seems to move from Q to R; and on the 20th he is seen at S, going forward in the same manner again, according to the order of letters; and backward when they go back; which, ’tis needless to explain any farther, as the reader can trace him out so easily through the rest of the year. The same appearances happen in Venus’s motion; but as she moves slower than Mercury, there are longer intervals of time between them.

Having already § 120. given some account of the apparent diurnal motions of the Heavens as seen from the different Planets, we shall not trouble the reader any more with that subject.

139. The Tychonic System § 97, being sufficiently refuted by the 109th Article, we shall say nothing more about it.

140. The Ptolemean System § 96, which asserts the Earth to be at rest in the Center of the Universe, and all the Planets with the Sun and Stars to move round it, is evidently false and absurd. For if this hypothesis were true, Mercury and Venus could never be hid behind the Sun, as their Orbits are included within the Sun’s: and again, these two Planets would always move direct, and be as often in Opposition to the Sun as in Conjunction with him. But the contrary of all this is true: for they are just as often behind the Sun as before him, appear as often to move backwards as forwards, and are so far from being seen at any time in the side of the Heavens opposite to the Sun, that they were never seen a quarter of a circle in the Heavens distant from him.

141. These two Planets, when viewed with a good telescope, appear in all the various shapes of the Moon; which is a plain proof that they are enlightened by the Sun, and shine not by any light of their own: for if they did, they would constantly appear round as the Sun does; and could never be seen like dark spots upon the Sun when they pass directly between him and us. Their regular Phases demonstrate them to be Spherical bodies; as may be shewn by the following experiment.

Hang an ivory ball by a thread, and let any Person move it round the flame of a candle, at two or three yards distance from your Eye: when the ball is beyond the candle, so as to be almost hid by the flame, it’s enlightened side will be towards you, and appear round like the Full Moon: When the ball is between you and the candle, it’s enlightened side will disappear, as the Moon does at the Change: When it is half way between these two positions, it will appear half illuminated, like the Moon in her Quarters: But in every other place between these positions, it will appear more or less horned or gibbous. If this experiment be made with a circular plate which has a flat surface, you may make it appear fully enlightened, or not enlightened at all; but can never make it seem either horned or gibbous.

51142. If you remove about six or seven yards from the candle, and place yourself so that it’s flame may be just about the height of your eye, and then desire the other person to move the ball slowly round the candle as before, keeping it as near of an equal height with the flame as he possibly can, the ball will appear to you not to move in a circle, but rather to vibrate backward and forward like a pendulum; moving quickest when it is directly between you and the candle, and when directly beyond it; and gradually slower as it goes farther to the right or left side of the flame, until it appears at the greatest distance from the flame; and then, though it continues to move with the same velocity, it will seem to stand still for a moment. In every Revolution it will shew all the above Phases § 141; and if two balls, a smaller and a greater, be moved in this manner round the candle, the smaller ball being kept nearest the flame, and carried round almost three times as often as the greater, you will have a tolerably good representation of the apparent Motions of Mercury and Venus; especially, if the bigger ball describes a circle almost twice as large in diameter as the circle described by the lesser.

143. Let ABCDE be a part or segment of the visible Heavens, in which the Sun, Moon, Planets, and Stars appear to move at the same distance from the Earth E. For there are certain limits, beyond which the eye cannot judge of different distances; as is plain from the Moon’s appearing to be no nearer to us than the Sun and Stars are. Let the circle fghiklmno be the Orbit in which Mercury m moves round the Sun S, according to the order of the letters. When Mercury is at f, he disappears to the Earth at E, because his enlightened side is turned from it; unless he be then in one of his Nodes § 20, 25; in which case, he will appear like a dark spot upon the Sun. When he is at g in his Orbit, he appears at B in the Heavens, westward of the Sun S, which is seen at C: when at h, he appears at A, at his greatest western elongation or distance from the Sun; and then seems to stand still. But, as he moves from h to i, he appears to go from A to B; and seems to be in the same place when at i as when he was at g, only not near so big: at k he is hid from the Earth E by the Sun S; being then in his superiour Conjunction. In going from k to l, he appears to move from C to D; and when he is at n, he appears stationary at E; being seen as far east from the Sun then, as he was west from him at A. In going from n to o in his Orbit, he seems to go back again in the Heavens, from E to D; and is seen in the same place (with respect to the Sun) at o as when he was at l; but of a larger diameter at o, because he is then nearer the Earth E: and 52when he comes to f, he again passes by the Sun, and disappears as before. In going from n to h in his Orbit, he seems to go backward in the Heavens from E to A; and in going from h to n, he seems to go forward from A to E. As he goes on from f a little of his enlightened side at g is seen from E; at h he appears half full, because half of his enlightened side is seen; at i, gibbous, or more than half full; and at k he would appear quite full, were he not hid from the Earth E by the Sun S. At l he appears gibbous again; at n half decreased, at o horned, and at f new like the Moon at her Change. He goes sooner from his eastern station at n to his western station at h than from h to n again; because he goes through less than half his Orbit in the former case, and more in the latter.

144. In the same Figure, let FGHIKLMN be the Orbit in which Venus v moves round the Sun S, according to the order of the letters: and let E be the Earth as before. When Venus is at F she is in her inferiour Conjunction; and disappears like the New Moon because her dark side is toward the Earth. At G she appears half enlightened to the Earth, like the Moon in her first quarter: at h she appears gibbous; at I, almost full; her enlightened side being then nearly towards the Earth: at K, she would appear quite full to the Earth E; but is hid from it by the Sun S: at L, she appears upon the decrease, or gibbous; at M, more so; at N, only half enlightened; and at F she disappears again. In moving from N to G, she seems to go backward in the Heavens; and from G to N, forward: but, as she describes a much greater portion of her Orbit in going from G to N than from N to G, she appears much longer direct than retrograde in her motion. At N and G she appears stationary; as Mercury does at n and h. Mercury, when stationary seems to be only 28 degrees from the Sun; and Venus when so, 47; which is a demonstration that Mercury’s Orbit is included within Venus’s, and Venus’s within the Earth’s.

145. Venus, from her superiour Conjunction at K to her inferiour Conjunction at F is seen on the east side of the Sun S from the Earth. E; and therefore she shines in the Evening after the Sun sets, and is called the Evening Star: for, the Sun being then to the westward of Venus, he must set first. From her inferiour Conjunction to her superiour, she appears on the west side of the Sun; and therefore rises before him, for which reason she is called the Morning Star. When she is about N or G, she shines so bright, that bodies cast shadows in the night-time.

53146. If the Earth kept always at E, it is evident that the Stationary places of Mercury and Venus would always be in the same points of the Heavens where they were before. For example; whilst Mercury m goes from h to n, according to the order of the letters, he appears to describe the arc ABCDE in the Heavens, direct: and whilst he goes from n to h, he seems to describe the same arc back again, from E to A, retrograde: always at n and h he appears stationary at the same points E and A as before. But Mercury goes round his Orbit, from f to f again, in 88 days; and yet there are 116 days from any one of his Conjunctions, or apparent Stations, to the same again: and the places of these Conjunctions and Stations are found to be about 114 degrees eastward from the points of the Heavens where they were last before; which proves, that the Earth has not kept all that time at E, but has had a progressive motion in it’s Orbit from E to t. Venus also differs every time in the places of her Conjunctions and Stations; but much more than Mercury; because, as Venus describes a much larger Orbit than Mercury does, the Earth advances so much the farther in it’s annual path before Venus comes round again.

147. As Mercury and Venus, seen from the Earth, have their respective Elongations from the Sun, and Stationary places; so has the Earth, seen from Mars; and Mars, seen from Jupiter; and Jupiter, seen from Saturn. That is, to every superiour Planet, all the inferiour ones have their Stations and Elongations; as Venus and Mercury have to the Earth. As seen from Saturn, Mercury never goes above 2¹⁄₂ degrees from the Sun; Venus 4¹⁄₃; the Earth 6; Mars 9¹⁄₂; and Jupiter 33¹⁄₄: so that Mercury, as seen from the Earth, has almost as great a Digression or Elongation from the Sun, as Jupiter seen from Saturn.

148. Because the Earth’s Orbit is included within the Orbits of Mars, Jupiter, and Saturn, they are seen on all sides of the Heavens; and are as often in Opposition to the Sun as in Conjunction with him. If the Earth stood still, they would always appear direct in their motions, never retrograde nor stationary. But they seem to go just as often backward as forward; which, if gravity be allowed to exist, affords a sufficient proof of the Earth’s annual motion.

149. As Venus and the Earth are superiour Planets to Mercury, they shew much the same Appearances to him that Mars and Jupiter do to us. Let Mercury m be at f, Venus v at F, and the Earth at E; in which situation Venus hides the Earth from Mercury; but, being in opposition to the Sun, she shines on Mercury with a full 54illumined Orb; though, with respect to the Earth, she is in conjunction with the Sun and invisible. When Mercury is at f, and Venus at G, her enlightened side not being directly towards him, she appears a little gibbous; as Mars does in a like situation to us: but, when Venus is at I, her enlightened side is so much towards Mercury at f, that she appears to him almost of a round figure. At K, Venus disappears to Mercury at f, being then hid by the Sun; as all our superiour Planets are to us, when in conjunction with the Sun. When Venus has, as it were, emerged out of the Sun beams, as at L, she appears almost full to Mercury at f; at M and N, a little gibbous; quite full at F, and largest of all; being then in opposition to the Sun, and consequently nearest to Mercury at f; shining strongly on him in the night, because her distance from him then is somewhat less than a fifth part of her distance from the Earth, when she appears roundest to it between I and K, or between K and L, as seen from the Earth E. Consequently, when Venus is opposite to the Sun as seen from Mercury, she appears more than 25 times as large to him as she does to us when at the fullest. Our case is almost similar with respect to Mars, when he is opposite to the Sun; because he is then so near the Earth, and has his whole enlightened side towards it. But, because the Orbits of Jupiter and Saturn are very large in proportion to the Earth’s, these two Planets appear much less magnified at their Oppositions or diminished at their Conjunctions than Mars does, in proportion to their mean apparent Diameters.

150. From the uniform projectile motion of bodies in straight lines, and the universal power of attraction, arises the curvilineal motions of all the Heavenly bodies. If the body A be projected along the right line ABX, in open Space, where it meets with no resistance, and is not drawn aside by any other power, it will for ever go on with the same velocity, and in the same direction. For, 55the force which moves it from A to B in any given time, will carry it from B to X in as much more time; and so on, there being nothing to obstruct or alter it’s motion. But if, when this projectile force has carried it, suppose to B, the body S begins to attract it, with a power duly adjusted, and perpendicular to it’s motion at B, it will then be drawn from the straight line ABX, and forced to revolve about S in the Circle BYTU. When the body A comes to U, or any other part of it’s Orbit, if the small body u, within the sphere of U’s attraction, be projected as in the right line Z, with a force perpendicular to the attraction of U, then u will go round U in the Orbit W, and accompany it in it’s whole course round the body S. Here, S may represent the Sun, U the Earth, and u the Moon.

151. If a Planet at B gravitates, or is attracted, toward the Sun, so as to fall from B to y in the time that the projectile force would have carried it from B to X, it will describe the curve BY by the combined action of these two forces, in the same time that the projectile force singly would have carried it from B to X, or the gravitating power singly have caused it to descend from B to y; and these two forces being duly proportioned, and perpendicular to one another, the Planet obeying them both, will move in the circle BYTU^[30].

152. But if, whilst the projectile force carries the Planet from B to b, the Sun’s attraction (which constitutes the Planet’s gravitation) should bring it down from B to I, the gravitating power would then be too strong for the projectile force; and would cause the Planet to describe the curve BC. When the Planet comes to C, the gravitating power (which always increases as the square of the distance from the Sun S diminishes) will be yet stronger for the projectile force; and by conspiring in some degree therewith, will accelerate the Planet’s motion all the way from C to K; causing it to describe the arcs BC, CD, DE, EF, &c. all in equal times. Having it’s motion thus accelerated, it gains so much centrifugal force, or tendency to fly off at K in the line Kk, as overcomes the Sun’s attraction: and the centrifugal force being too great to allow the Planet to be brought nearer the Sun, or even to move round him in the Circle Klmn, &c. it goes off, and ascends in the curve KLMN, &c. it’s motion decreasing as gradually from K to B as it increased from B to K, because the Sun’s attraction acts now against the Planet’s projectile motion just as much as it 56acted with it before. When the Planet has got round to B, it’s projectile force is as much diminished from it’s mean state about G or N, as it was augmented at K; and so, the Sun’s attraction being more than sufficient to keep the Planet from going off at B, it describes the same Orbit over again, by virtue of the same forces or laws.

153. A double projectile force will always balance a quadruple power of gravity. Let the Planet at B have twice as great an impulse from thence towards X, as it had before: that is, in the same length of time that it was projected from B to b, as in the last example, let it now be projected from B to c; and it will require four times as much gravity to retain it in it’s Orbit: that is, it must fall as far as from B to 4 in the time that the projectile force would carry it from B to c; otherwise it could not describe the curve BD, as is evident by the Figure. But, in as much time as the Planet moves from B to C in the higher part of it’s Orbit, it moves from I to K or from K to L in the lower part thereof; because, from the joint action of these two forces, it must always describe equal areas in equal times, throughout it’s annual course. These Areas are represented by the triangles BSC, CSD, DSE, ESF, &c. whose contents are equal to one another, quite round the Figure.

154. As the Planets approach nearer the Sun, and recede farther from him, in every Revolution; there may be some difficulty in conceiving the reason why the power of gravity, when it once gets the better of the projectile force, does not bring the Planets nearer and nearer the Sun in every Revolution, till they fall upon and unite with him. Or why the projectile force, when it once gets the better of gravity, does not carry the Planets farther and farther from the Sun, till it removes them quite out of the sphere of his attraction, and causes them to go on in straight lines for ever afterward. But by considering the effects of these powers as described in the two last Articles, this difficulty will be removed. Suppose a Planet at B to be carried by the projectile force as far as from B to b, in the time that gravity would have brought it down from B to 1: by these two forces it will describe the curve BC. When the Planet comes down to K, it will be but half as far from the Sun S as it was at B; and therefore, by gravitating four times as strongly towards him, it would fall from K to V in the same length of time that it would have fallen from B to 1 in the higher part of it’s Orbit, that is, through four times as much space; but it’s projectile force is then so much increased at K, as would carry it from K to k in the same time; being double of what it was at B, and is 57therefore too strong for the tendency of the gravitating power, either to draw the Planet to the Sun, or cause it to go round him in the circle Klmn, &c. which would require it’s falling from K to w, through a greater space than gravity can draw it whilst the projectile force is such as would carry it from K to k: and therefore the Planet ascends in it’s Orbit KLMN, decreasing in it’s velocity for the cause already assigned in § 152.

155. The Orbits of all the Planets are Ellipses, very little different from Circles: but the Orbits of the Comets are very long Ellipses; the lower focus of them all being in the Sun. If we suppose the mean distance (or middle between the greatest and least) of every Planet and Comet from the Sun to be divided into 1000 equal parts, the Excentricities of their Orbits, both in such parts and in English miles, will be as follows. Mercury’s, 210 parts, or 6,720,000 miles; Venus’s, 7 parts, or 413,000 miles; the Earth’s, 17 parts, or 1,377,000 miles; Mars’s, 93 parts, or 11,439,000 miles; Jupiter’s, 48 parts, or 20,352,000 miles; Saturn’s, 55 parts, or 42,735,000 miles. Of the nearest of the three forementioned Comets, 1,458,000 miles; of the middlemost, 2,025,000,000 miles; and of the outermost, 6,600,000,000.

156. By the above-mentioned laws § 150 & seq. bodies will move in all kinds of Ellipses, whether long or short, if the spaces they move in be void of resistance. Only, those which move in the longer Ellipses, have so much the less projectile force impressed upon them in the higher parts of their Orbits; and their velocities, in coming down towards the Sun, are so prodigiously increased by his attraction, that their centrifugal forces in the lower parts of their Orbits are so great as to overcome the Sun’s attraction there, and cause them to ascend again towards the higher parts of their Orbits; during which time, the Sun’s attraction acting so contrary to the motions of those bodies, causes them to move slower and slower, until their projectile forces are diminished almost to nothing; and then they are brought back again by the Sun’s attraction, as before.

157. If the projectile forces of all the Planets and Comets were destroyed at their mean distances from the Sun, their gravities would bring them down so, as that Mercury would fall to the Sun in 15 days 13 hours; Venus in 39 days 17 hours; the Earth or Moon in 64 days 10 hours; Mars in 121 days; Jupiter in 290; and Saturn in 767. The nearest Comet in 13 thousand days; the middlemost in 23 thousand days; and the outermost in 66 thousand days. The 58Moon would fall to the Earth in 4 days 20 hours; Jupiter’s first Moon would fall to him in 7 hours, his second in 15, his third in 30, and his fourth in 71 hours. Saturn’s first Moon would fall to him in 8 hours; his second in 12, his third in 19, his fourth in 68 hours, and the fifth in 336. A stone would fall to the Earth’s center, if there were an hollow passage, in 21 minutes 9 seconds. Mr. Whiston gives the following Rule for such Computations. “^[31]It is demonstrable, that half the Period of any Planet, when it is diminished in the sesquialteral proportion of the number 1 to the number 2, or nearly in the proportion of 1000 to 2828, is the time that it would fall to the Center of it’s Orbit.” This proportion is, when a quantity or number contains another once and a half as much more.

158. The quick motions of the Moons of Jupiter and Saturn round their Primaries, demonstrate that these two Planets have stronger attractive powers than the Earth has. For, the stronger that one body attracts another, the greater must be the projectile force, and consequently the quicker must be the motion of that other body, to keep it from falling to it’s primary or central Planet. Jupiter’s second Moon is 124 thousand miles farther from Jupiter than our Moon is from us; and yet this second Moon goes almost eight times round Jupiter whilst our Moon goes only once round the Earth. What a prodigious attractive power must the Sun then have, to draw all the Planets and Satellites of the System towards him; and what an amazing power must it have required to put all these Planets and Moons into such rapid motions at first! Amazing indeed to us, because impossible to be effected by the strength of all the living Creatures in an unlimited number of Worlds, but no ways hard for the Almighty, whose Planetarium takes in the whole Universe!

159. The celebrated Archimedes affirmed he could move the Earth if he had a place to stand on to manage his machinery^[32]. This assertion is true in Theory, but, upon examination, will be found absolutely impossible in fact, even though a proper place and materials of sufficient strength could be had.

The simplest and easiest method of moving a heavy body a little way is by a lever or crow, where a small weight or power applied to the long arm will raise a great weight on the short one. But then, the small weight must move as much quicker than the great weight 59as the latter is heavier than the former; and the length of the long arm of the lever to the length of the short arm must be in the same proportion. Now, suppose a man pulls or presses the end of the long arm with the force of 200 pound weight, and that the Earth contains in round Numbers 4,000,000,000,000,000,000,000 or 4000 Trillions of cubic feet, each at a mean rate weighing 100 pound; and that the prop or center of motion of the lever is 6000 miles from the Earth’s center: in this case, the length of the lever from the Fulcrum or center of motion to the moving power or weight ought to be 12,000,000,000,000,000,000,000,000 or 12 Quadrillions of miles; and so many miles must the power move, in order to raise the Earth but one mile, whence ’tis easy to compute, that if Archimedes or the power applied could move as swift as a cannon bullet, it would take 27,000,000,000,000 or 27 Billions of years to raise the Earth one inch.

If any other machine, such as a combination of wheels and screws, was proposed to move the Earth, the time it would require, and the space gone through by the hand that turned the machine, would be the same as before. Hence we may learn, that however boundless our Imagination and Theory may be, the actual operations of man are confined within narrow bounds; and more suited to our real wants than to our desires.

160. The Sun and Planets mutually attract each other: the power by which they do so we call Gravity. But whether this power be mechanical or no, is very much disputed. We are certain that the Planets disturb one another’s motions by it, and that it decreases according to the squares of the distances of the Sun and Planets; as light, which is known to be material, likewise does. Hence Gravity should seem to arise from the agency of some subtile matter pressing towards the Sun and Planets, and acting, like all mechanical causes, by contact. But on the other hand, when we consider that the degree or force of Gravity is exactly in proportion to the quantities of matter in those bodies, without any regard to their bulks or quantity of surface, acting as freely on their internal as external parts, it seems to surpass the power of mechanism; and to be either the immediate agency of the Deity, or effected by a law originally established and imprest on all matter by him. But some affirm that matter, being altogether inert, cannot be impressed with any Law, even by almighty Power: and that the Deity must therefore be constantly impelling the Planets toward the Sun, and moving them with the same irregularities and disturbances 60which Gravity would cause, if it could be supposed to exist. But, if a man may venture to publish his own thoughts, (and why should not one as well as another?) it seems to me no greater absurdity, to suppose the Deity capable of superadding a Law, or what Laws he pleases, to matter, than to suppose him capable of giving it existence at first. The manner of both is equally inconceivable to us; but neither of them imply a contradiction in our ideas: and what implies no contradiction is within the power of Omnipotence. Do we not see that a human creature can prepare a bar of steel so as to make it attract needles and filings of iron; and that he can put a stop to that power or virtue, and again call it forth again as often as he pleases? To say that the workman infuses any new power into the bar, is saying too much; since the needle and filings, to which he has done nothing, re-attract the bar. And from this it appears that the power was originally imprest on the matter of which the bar, needle, and filings are composed; but does not seem to act until the bar be properly prepared by the artificer: somewhat like a rope coiled up in a ship, which will never draw a boat or any other thing towards the ship, unless one end be tied to it, and the other end to that which is to be hauled up; and then it is no matter which end of the rope the sailors pull at, for the rope will be equally stretched throughout, and the ship and boat will move towards one another. To say that the Almighty has infused no such virtue or power into the materials which compose the bar, but that he waits till the operator be pleased to prepare it by due position and friction, and then, when the needle or filings are brought pretty near the bar, the Deity presses them towards it, and withdraws his hand whenever the workman either for use, curiosity or whim, does what appears to him to destroy the action of the bar, seems quite ridiculous and trifling; as it supposes God not only to be subservient to our inconstant wills, but also to do what would be below the dignity of any rational man to be employed about.

161. That the projectile force was at first given by the Deity is evident. For, since matter can never put itself into motion, and all bodies may be moved in any direction whatsoever; and yet all the Planets both primary and secondary move from west to east, in planes nearly coincident; whilst the Comets move in all directions, and in planes so different from one another; these motions can be owing to no mechanical cause of necessity, but to the free choice and power of an intelligent Being.

61162. Whatever Gravity be, ’tis plain that it acts every moment of time: for should it’s action cease, the projectile force would instantly carry off the Planets in straight lines from those parts of their Orbits where Gravity left them. But, the Planets being once put into motion, there is no occasion for any new projectile force, unless they meet with some resistance in their Orbits; nor for any mending hand, unless they disturb one another too much by their mutual attractions.

163. It is found that there are disturbances among the Planets in their motions, arising from their mutual attractions when they are in the same quarter of the Heavens; and that our years are not always precisely of the same length^[33]. Besides, there is reason to believe that the Moon is somewhat nearer the Earth now than she was formerly; her periodical month being shorter than it was in former ages. For, our Astronomical Tables, which in the present Age shew the times of Solar and Lunar Eclipses to great precision, do not answer so well for very ancient Eclipses. Hence it appears, that the Moon does not move in a medium void of all resistance, § 174; and therefore her projectile force being a little weakened, whilst there is nothing to diminish her gravity, she must be gradually approaching nearer the Earth, describing smaller and smaller Circles round it in every revolution, and finishing her Period sooner, although her absolute motion with regard to space be not so quick now as it was formerly: and therefore, she must come to the Earth at last; unless that Being, which gave her a sufficient projectile force at the beginning, adds a little more to it in due time. And, as all the Planets move in spaces full of æther and light, which are material substances, they too must meet with some resistance. And therefore, if their gravities are not diminished, nor their projectile forces increased, they must necessarily approach nearer and nearer the Sun, and at length fall upon and unite with him.

164. Here we have a strong philosophical argument against the eternity of the World. For, had it existed from eternity, and been left 62by the Deity to be governed by the combined actions of the above forces or powers, generally called Laws, it had been at an end long ago. And if it be left to them it must come to an end. But we may be certain that it will last as long as was intended by it’s Author, who ought no more to be found fault with for framing so perishable a work, than for making man mortal.

165. Light consists of exceeding small particles of matter issuing from a luminous body; as from a lighted candle such particles of matter continually flow in all directions. Dr. Niewentyt^[34] computes, that in one second of time there flows 418,660,000,000,000,000,000,000,000,000,000,000,000,000,000 particles of light out of a burning candle; which number contains at least 6,337,242,000,000 times the number of grains of sand in the whole Earth; supposing 100 grains of sand to be equal in length to an inch, and consequently, every cubic inch of the Earth to contain one million of such grains.

166. These amazingly small particles, by striking upon our eyes, excite in our minds the idea of light: and, if they were so large as the smallest particles of matter discernible by our best microscopes, instead of being serviceable to us, they would soon deprive us of sight by the force arising from their immense velocity, which is above 164 thousand miles every second^[35], or 1,230,000 times swifter than the motion of a cannon bullet. And therefore, if the particles of light were so large, that a million of them were equal in bulk to an ordinary grain of land, we durst no more open our eyes to the light than suffer sand to be shot point blank against them.

167. When these small particles, flowing from the Sun or from a candle, fall upon bodies, and are thereby reflected to our eyes, they excite in us the idea of that body by forming it’s picture on the retina^[36]. 63And since bodies are visible on all sides, light must be reflected from them in all directions.

168. A ray of light is a continued stream of these particles, flowing from any visible body in straight lines. That they move in straight, and not in crooked lines, unless they be refracted, is evident from bodies not being visible if we endeavour to look at them through the bore of a bended pipe; and from their ceasing to be seen by the interposition of other bodies, as the fixed Stars by the interposition of the Moon and Planets, and the Sun wholly or in part by the interposition of the Moon, Mercury, or Venus. And that these rays do not interfere, or jostle one another out of their ways, in flowing from different bodies all around, is plain from the following Experiment. Make a little hole in a thin plate of metal, and set the plate upright on a table, facing a row of lighted candles standing by one another; then place a sheet of paper or pasteboard at a little distance from the other side of the plate, and the rays of all the candles, flowing through the hole, will form as many specks of light on the paper as there are candles before the plate, each speck as distinct and large, as if there were only one candle to cast one speck; which shews that the rays are no hinderance to each other in their motions, although they all cross in the hole.

169. Light, and therefore heat so far as it depends on the Sun’s rays (§ 85, towards the end) decreases in proportion to the squares of the distances of the Planets from the Sun. This is easily demonstrated by a Figure which, together with it’s description, I have taken from Dr. Smith’s Optics^[37]. Let the light which flows from a point A, and passes through a square hole B, be received upon a plane C, parallel to the plane of the hole; or, if you please, let the figure C be the shadow of the plane B; and when the distance C is double of B, the length and breadth of the shadow C will be each double of the length and breadth of the plane B; and treble when AD is treble of AB; and so on: which may be easily examined by the light of a candle placed at A. Therefore the surface of the shadow C, at the distance AC double of AB, is divisible into four squares, and at a treble distance, into nine squares, severally equal to the square B, as represented in the Figure. The light then which falls upon the plane B, being suffered to pass to double that distance, will be uniformly spread over four times the space, and consequently will be four times thinner in every part of that space, and at a treble distance it will be 64nine times thinner, and at a quadruple distance sixteen times thinner, than it was at first; and so on, according to the increase of the square surfaces B, C, D, E, built upon the distances AB, AC, AD, AE. Consequently, the quantities of this rarefied light received upon a surface of any given size and shape whatever, removed successively to these several distances, will be but one quarter, one ninth, one sixteenth of the whole quantity received by it at the first distance AB. Or in general words, the densities and quantities of light, received upon any given plane, are diminished in the same proportion as the squares of the distances of that plane, from the luminous body, are increased: and on the contrary, are increased in the same proportion as these squares are diminished.

170. The more a telescope magnifies the disks of the Moon and Planets, they appear so much dimmer than to the bare eye; because the telescope cannot magnify the quantity of light, as it does the surface; and, by spreading the same quantity of light over a surface so much larger than the naked eye beheld, just so much dimmer must it appear when viewed by a telescope than by the bare eye.

171. When a ray of light passes out of one medium^[38] into another, it is refracted, or turned out of it’s first course, more or less, as it falls more or less obliquely on the refracting surface which divides the two mediums. This may be proved by several experiments; of which we shall only give three for example’s sake. 1. In a bason FGH put a piece of money as DB, and then retire from it as to A, till the edge of the bason at E just hides the money from your sight: then, keeping your head steady, let another person fill the bason gently with water. As he fills it, you will see more and more of the piece DB; which will be all in view when the bason is full, and appear as if lifted up to C. For, the ray AEB, which was straight whilst the bason was empty, is now bent at the surface of the water in E, and turned out of it’s rectilineal course into the direction ED. Or, in other words, the ray DEK, that proceeded in a straight line from the edge D whilst the bason was empty, and went above the eye at A, is now bent at E; and instead of going on in the rectilineal direction DEK, goes in the angled direction DEA, and by entering the eye at A renders the object DB visible. Or, 2dly, place the bason where the Sun shines obliquely, and observe where the shadow of the rim E falls on the bottom, as at 65B: then fill it with water, and the shadow will fall at D; which proves, that the rays of light, falling obliquely on the surface of the water, are refracted, or bent downwards into it.

172. The less obliquely the rays of light fall upon the surface of any medium, the less they are refracted; and if they fall perpendicularly thereon, they are not refracted at all. For, in the last experiment, the higher the Sun rises, the less will be the difference between the places where the edge of the shadow falls, in the empty and full bason. And, 3dly, if a stick be laid over the bason, and the Sun’s rays be reflected perpendicularly into it from a looking-glass, the shadow of the stick will fall upon the same place of the bottom, whether the bason be full or empty.

173. The denser that any medium is, the more is light refracted in passing through it.

174. The Earth is surrounded by a thin fluid mass of matter, called the Air, or Atmosphere, which gravitates to the Earth, revolves with it in it’s diurnal motion, and goes round the Sun with it every year. This fluid is of an elastic or springy nature, and it’s lowermost parts being pressed by the weight of all the Air above them, are squeezed the closer together; and are therefore densest of all at the Earth’s surface, and gradually rarer the higher up. “It is well known^[39] that the Air near the surface of our Earth possesses a space about 1200 times greater than water of the same weight. And therefore, a cylindric column of Air 1200 foot high is of equal weight with a cylinder of water of the same breadth and but one foot high. But a cylinder of Air reaching to the top of the Atmosphere is of equal weight with a cylinder of water about 33 foot high^[40]; and therefore if from the whole cylinder of Air, the lower part of 1200 foot high is taken away, the remaining upper part will be of equal weight with a cylinder of water 32 foot high; wherefore, at the height of 1200 feet or two furlongs, the weight of the incumbent Air is less, and consequently the rarity of the compressed Air is greater than near the Earth’s surface in the ratio of 33 to 32. And having this ratio we may compute the rarity of the Air at all heights whatsoever, supposing the expansion thereof to be reciprocally proportional to its compression; and this proportion has been proved by the experiments of Dr. Hooke and others. The result of the computation I have set down in the annexed Table, in the first column of which you have the height of the Air in miles, whereof 4000 make a semi-diameter of the 66Earth; in the second the compression of the Air or the incumbent weight; in the third it’s rarity or expansion, supposing gravity to decrease in the duplicate ratio of the distances from the Earth’s center. And the small numeral figures are here used to shew what number of cyphers must be joined to the numbers expressed by the larger figures, as 0.¹⁷1224 for 0.000000000000000001224, and 26956¹⁵ for 26956000000000000000.

From this Table it appears that the Air in proceeding upwards is rarefied in such manner, that a sphere of that Air which is nearest the Earth but of one inch diameter, if dilated to an equal rarefaction with that of the Air at the height of ten semi-diameters of the Earth, would fill up more space than is contained in the whole Heavens on this side the fixed Stars, according to the preceding computation of their distance^[41].” And it likewise appears that the Moon does not move in a perfectly free and un-resisting medium; although the air at a height equal to her distance, is at least 34000¹⁹⁰ times thinner than at the Earth’s surface; and therefore cannot resist her motion so as to be sensible in many ages.

175. The weight of the Air, at the Earth’s surface, is found by experiments made with the air-pump; and also by the quantity of mercury that the Atmosphere balances in the barometer; in which, at a mean state; the mercury stands 29¹⁄₂ inches high. And if the tube were a square inch wide, it would at that height contain 29¹⁄₂ cubic inches of mercury, which is just 15 pound weight; and so much weight of air every square inch of the Earth’s surface sustains; and every square foot 144 times as much, because it contains 144 square inches. Now as the Earth’s surface contains about 199,409,400 square miles, it must be of no less than 5,559,215,016,960,000 square feet; which, multiplied by 2016, the number of pounds on every foot, amounts to 11,207,377,474,191,360,000; or 11 trillion 207 thousand 377 billion 474 thousand 191 million and 360 thousand pounds, for the weight of the whole Atmosphere. At this rate, a middle sized man, whose surface may be about 14 square feet, is pressed by 28,224 pound weight of Air all round; for fluids press equally up and down and on all sides. But, because 67this enormous weight is equal on all sides, and counterbalanced by the spring of the internal Air in our blood vessels, it is not felt.

176. Oftentimes the state of the Air is such that we feel ourselves languid and dull; which is commonly thought to be occasioned by the Air’s being foggy and heavy about us. But that the Air is then too light, is evident from the mercury’s sinking in the barometer, at which time it is generally found that the Air has not sufficient strength to bear up the vapours which compose the Clouds: for, when it is otherwise, the Clouds mount high, the Air is more elastic and weighty about us, by which means it balances the internal spring of the Air within us, braces up our blood-vessels and nerves, and makes us brisk and lively.

177. According to ^[42]Dr. Keill, and other astronomical writers, it is entirely owing to the Atmosphere that the Heavens appear bright in the day-time. For, without an Atmosphere, only that part of the Heavens would shine in which the Sun was placed: and if an observer could live without Air, and should turn his back towards the Sun, the whole Heavens would appear as dark as in the night, and the Stars would be seen as clear as in the nocturnal sky. In this case, we should have no twilight; but a sudden transition from the brightest sunshine to the blackest darkness immediately after sun-set; and from the blackest darkness to the brightest sun-shine at sun-rising; which would be extremely inconvenient, if not blinding, to all mortals. But, by means of the Atmosphere, we enjoy the Sun’s light, reflected from the aerial particles, before he rises and after he sets. For, when the Earth by its rotation has withdrawn the Sun from our sight, the Atmosphere being still higher than we, has his light imparted to it; which gradually decreases until he has got 18 degrees below the Horizon; and then, all that part of the Atmosphere which is above us is dark. From the length of twilight, the Doctor has calculated the height of the Atmosphere (so far as it is dense enough to reflect any light) to be about 44 miles. But it is seldom dense enough at two miles height to bear up the Clouds.

178. The Atmosphere refracts the Sun’s rays so, as to bring him in sight every clear day, before he rises in the Horizon; and to keep him in view for some minutes after he is really set below it. For, at some times of the year, we see the Sun ten minutes longer above the Horizon than he would be if there were no refractions: and about six minutes every day at a mean rate.

179. To illustrate this, let IEK be a part of the Earth’s surface, covered with the Atmosphere HGFC; and let HEO be the^[43] sensible Horizon 68of an observer at E. When the Sun is at A, really below the Horizon, a ray of light AC proceeding from him comes straight to C, where it falls on the surface of the Atmosphere, and there entering a denser medium, it is turned out of its rectilineal course ACdG, and bent down to the observer’s eye at E; who then sees the Sun in the direction of the refracted ray edE, which lies above the Horizon, and being extended out to the Heavens, shews the Sun at B § 171.

180. The higher the Sun rises, the less his rays are refracted, because they fall less obliquely on the surface of the Atmosphere § 172. Thus, when the Sun is in the direction of the line EfL continued, he is so nearly perpendicular to the surface of the Earth at E, that his rays are but very little bent from a rectilineal course.

181. The Sun is about 32¹⁄₄ min. of a deg. in breadth, when at his mean distance from the Earth; and the horizontal refraction of his rays is 33³⁄₄ min. which being more than his whole diameter, brings all his Disc in view, when his uppermost edge rises in the Horizon. At ten deg. height the refraction is not quite 5 min. at 20 deg. only 2 min. 26 sec.; at 30 deg. but 1 min. 32 sec.; between which and the Zenith, it is scarce sensible: the quantity throughout, is shewn by the annexed table, calculated by Sir Isaac Newton.

182. A Table shewing the Refractions of the Sun, Moon, and Stars; adapted to their apparent Altitudes.

69183. In all observations, to have the true altitude of the Sun, Moon, or Stars, the refraction must be subtracted from the observed altitude. But the quantity of refraction is not always the same at the same altitude; because heat diminishes the air’s refractive power and density, and cold increases both; and therefore no one table can serve precisely for the same place at all seasons, nor even at all times of the same day; much less for different climates: it having been observed that the horizontal refractions are near a third part less at the Equator than at Paris, as mentioned by Dr. Smith in the 370th remark on his Optics, where the following account is given of an extraordinary refraction of the sun-beams by cold. “There is a famous observation of this kind made by some Hollanders that wintered in Nova Zembla in the year 1596, who were surprised to find, that after a continual night of three months, the Sun began to rise seventeen days sooner than according to computation, deduced from the Altitude of the Pole observed to be 76°: which cannot otherwise be accounted for, than by an extraordinary quantity of refraction of the Sun’s rays, passing thro’ the cold dense air in that climate. Kepler computes that the Sun was almost five degrees below the Horizon when he first appeared; and consequently the refraction of his rays was about nine times greater than it is with us.”

184. The Sun and Moon appear of an oval figure as FCGD, just after their rising, and before their setting: the reason is, that the refraction being greater in the Horizon than at any distance above it, the lowermost limb G appears more elevated than the uppermost. But although the refraction shortens the vertical Diameter FG, it has no sensible effect on the horizontal Diameter CD, which is all equally elevated. When the refraction is so small as to be imperceptible, the Sun and Moon appear perfectly round, as AEBF.

185. We daily observe, that the objects which appear most distinct are generally those which are nearest to us; and consequently, when we have nothing but our imagination to assist us in estimating of distances, bright objects seem nearer to us than those which are less bright, or than the same objects do when they appear less bright and worse defined, even though their distance in both cases be the same. And as in both cases they are seen under the same angle^[44], our imagination 70naturally suggests an idea of a greater distance between us and those objects which appear fainter and worse defined than those which appear brighter under the same Angles; especially if they be such objects as we were never near to, and of whose real Magnitudes we can be no judges by sight.

186. But, it is not only in judging of the different apparent Magnitudes of the same objects, which are better or worse defined by their being more or less bright, that we may be deceived: for we may make a wrong conclusion even when we view them under equal degrees of brightness, and under equal Angles; although they be objects whose bulks we are generally acquainted with, such as houses or trees: for proof of which, the two following instances may suffice.

First, When a house is seen over a very broad river by a person standing on low ground, who sees nothing of the river, nor knows of it beforehand; the breadth of the river being hid from him, because the banks seem contiguous, he loses the idea of a distance equal to that breadth; and the house seems small, because he refers it to a less distance than it really is at. But, if he goes to a place from which the river and interjacent ground can be seen, though no farther from the house, he then perceives the house to be at a greater distance than he imagined; and therefore fancies it to be bigger than he did at first; although in both cases it appears under the same Angle, and consequently makes no 71bigger picture on the retina of his eye in the latter case than it did in the former. Many have been deceived, by taking a red coat of arms, fixed upon the iron gate in Clare-Hall walks at Cambridge, for a brick house at a much greater distance^[45].

Secondly, In foggy weather, at first sight, we generally imagine a small house, which is just at hand, to be a great castle at a distance; because it appears so dull and ill defined when seen through the Mist, that we refer it to a much greater distance than it really is at; and therefore, under the same Angle, we judge it to be much bigger. For, the near object FE, seen by the eye ABD, appears under the same Angle GCH, that the remote object GHI does: and the rays GFCN and HECM crossing one another at C in the pupil of the eye, limit the size of the picture MN on the retina; which is the picture of the object FE, and if FE were taken away, would be the picture of the object GHI, only worse defined; because GHI, being farther off, appears duller and fainter than FE did. But if a Fog, as KL, comes between the eye and the object FE, it appears dull and ill defined like GHI; which causes our imagination to refer FE to the greater distance CH, instead of the small distance CE which it really is at. And consequently, as mis-judging the distance does not in the least diminish the Angle under which the object appears, the small hay-rick FE seems to be as big as GHI.

187. The Sun and Moon appear bigger in the Horizon than at any considerable height above it. These Luminaries, although at great distances from the Earth, appear floating, as it were, on the surface of our Atmosphere HGFfeC, a little way beyond the Clouds; of which, those about F, directly over our heads at E, are nearer us than those about H or e in the Horizon HEe. Therefore, when the Sun or Moon appear in the Horizon at e, they are not only seen in a part of the Sky which is really farther from us than if they were at any considerable 72Altitude, as about f; but they are also seen through a greater quantity of Air and Vapours at e than at f. Here we have two concurring appearances which deceive our imagination, and cause us to refer the Sun and Moon to a greater distance at their rising or setting about e, than when they are considerably high as at f: first, their seeming to be on a part of the Atmosphere at e, which is really farther than f from a spectator at E; and secondly, their being seen through a grosser medium when at e than when at f; which, by rendering them dimmer, causes us to imagine them to be at a yet greater distance. And as, in both cases, they are seen^[46] much under the same Angle, we naturally judge them to be biggest when they seem farthest from us; like the above-mentioned house § 186, seen from a higher ground, which shewed it to be farther off than it appeared from low ground; or the hay-rick, which appeared at a greater distance by means of an interposing Fog.

188. Any one may satisfy himself that the Moon appears under no greater Angle in the Horizon than on the Meridian, by taking a large sheet of paper, and rolling it up in the form of a Tube, of such a width, that observing the Moon through it when she rises, she may, as it were, just fill the Tube; then tie a thread round it to keep it of that size; and when the Moon comes to the Meridian, and appears much less to the eye, look at her again through the same Tube, and she will fill it just as much, if not more, than she did at her rising.

189. When the full Moon is in perigeo, or at her least distance from the Earth, she is seen under a larger Angle, and must therefore appear bigger than when she is Full at other times: and if that part of the Atmosphere where she rises be more replete with vapours than usual, she appears so much the dimmer; and therefore we fancy her to be still the bigger, by referring her to an unusually great distance; knowing that no objects which are very far distant can appear big unless they be really so.

Plate IIII.

J. Ferguson delin.

J. Mynde Sculp.

190. Those who have not learnt how to take the ^[47]Altitude of any Celestial Phenomenon by a common Quadrant, nor know any thing of Plain Trigonometry, may pass over the first Article of this short Chapter, and take the Astronomer’s word for it, that the distances of the Sun and Planets are as stated in the first Chapter of this Book. But, to every one who knows how to take the Altitude of the Sun, the Moon, or a Star, and can solve a plain right-angled Triangle, the following method of finding the distances of the Sun and Moon will be easily understood.

Let BAG be one half of the Earth, AC it’s semi-diameter, S the Sun, m the Moon, and EKOL a quarter of the Circle described by the Moon in revolving from the Meridian to the Meridian again. Let CRS be the rational Horizon of an observer at A, extended to the 74Sun in the Heavens, and HAO his sensible Horizon; extended to the Moon’s Orbit. ALC is the Angle under which the Earth’s semi-diameter AC is seen from the Moon at L, which is equal to the Angle OAL, because the right lines AO and CL which include both these Angles are parallel. ASC is the Angle under which the Earth’s semi-diameter AC is seen from the Sun at S, and is equal to the Angle OAf because the lines AO and CRS are parallel. Now, it is found by observation, that the Angle OAL is much greater than the Angle OAf; but OAL is equal to ALC, and OAf is equal to ASC. Now, as ASC is much less than ALC, it proves that the Earth’s semi-diameter AC appears much greater as seen from the Moon at L than from the Sun at S: and therefore the Earth is much farther from the Sun than from the Moon^[48]. The Quantities of these Angles are determined by observation in the following manner.

Let a graduated instrument as DAE, (the larger the better) having a moveable Index and Sight-holes, be fixed in such a manner, that it’s plane surface may be parallel to the Plan of the Equator, and it’s edge AD in the Meridian: so that when the Moon is in the Equinoctial, and on the Meridian at E, she may be seen through the sight-holes when the edge of the moveable index cuts the beginning of the divisions at o, on the graduated limb DE; and when she is so seen, let the precise time be noted. Now, as the Moon revolves about the Earth from the Meridian to the Meridian again in 24 hours 48 minutes, she will go a fourth part round it in a fourth part of that time, viz. in 6 hours 12 minutes, as seen from C, that is, from the Earth’s center or Pole. But as seen from A, the observer’s place on the Earth’s surface, the Moon will seem to have gone a quarter round the Earth when she comes to the sensible Horizon at O; for the Index through the sights of which she is then viewed will be at d, 90 degrees from D, where it was when she was seen at E. Now, let the exact moment when the Moon is seen at O (which will be when she is in or near the sensible Horizon) be carefully noted^[49], that it may be known in what time she has gone from E to O; which time subtracted from 6 hours 12 minutes (the time of her going from E to L) leaves the time of her going from O to L, and affords an easy method for finding the Angle OAL (called the Moon’s horizontal Parallax, which is equal to the Angle ALC) by the following Analogy: As the time of the Moon’s 75describing the arc EO is to 90 degrees, so is 6 hours 12 minutes to the degrees of the Arc DdE, which measures the Angle EAL; from which subtract 90 degrees, and there remains the Angle OAL, equal to the Angle ALC, under which the Earth’s Semi-diameter AC is seen from the Moon. Now, since all the Angles of a right-lined Triangle are equal to 180 degrees, or to two right Angles, and the sides of a Triangle are always proportional to the Sines of the opposite Angles, say, by the Rule of Three, as the Sine of the Angle ALC at the Moon L is to it’s opposite side AC the Earth’s Semi-diameter, which is known to be 3985 miles, so is Radius, viz. the Sine of 90 degrees, or of the right Angle ACL to it’s opposite side AL, which is the Moon’s distance at L from the observer’s place at A on the Earth’s surface; or, so is the Sine of the Angle CAL to its opposite side CL, which is the Moon’s distance from the Earth’s centre, and comes out at a mean rate to be 240,000 miles. The Angle CAL is equal to what OAL wants of 90 degrees.

191. The Sun’s distance from the Earth is found the same way, but with much greater difficulty; because his horizontal Parallax, or the Angle OAS equal to the Angle ASC, is so small as, to be hardly perceptible, being only 10 seconds of a minute, or the 360th part of a degree. But the Moon’s horizontal Parallax, or Angle OAL equal to the Angle ALC, is very discernible; being 57ʹ 49ʺ, or 3469ʺ at it’s mean state; which is more than 340 times as great as the Sun’s: and therefore, the distances of the heavenly bodies being inversely as the Tangents of their horizontal Parallaxes, the Sun’s distance from the Earth is at least 340 times as great as the Moon’s; and is rather understated at 81 millions of miles, when the Moon’s distance is certainly known to be 240 thousand. But because, according to some Astronomers, the Sun’s horizontal Parallax is 11 seconds, and according to others only 10, the former Parallax making the Sun’s distance to be about 75,000,000 of miles, and the latter 82,000,000; we may take it for granted, that the Sun’s distance is not less than as deduced from the former, nor more than as shewn by the latter: and every one who is accustomed to make such observations, knows how hard it is, if not impossible, to avoid an error of a second; especially on account of the inconstancy of horizontal Refractions. And here, the error of one second, in so small an Angle, will make an error of 7 millions of miles in so great a distance as that of the Sun’s; and much more in the distances of the superiour Planets. But Dr. Halley has shewn us how the Sun’s distance from the Earth, and consequently the distances of all the Planets from the Sun, may be known to within a 500th part 76of the whole, by a Transit of Venus over the Sun’s Disc, which will happen on the 6th of June, in the year 1761; till which time we must content ourselves with allowing the Sun’s distance to be about 81 millions of miles, as commonly stated by Astronomers.

192. The Sun and Moon appear much about the same bulk: And every one who understands Geometry knows how their true bulks may be deduced from the apparent, when their real distances are known. Spheres are to one another as the Cubes of their Diameters; whence, if the Sun be 81 millions of miles from the Earth, to appear as big as the Moon, whose distance does not exceed 240 thousand miles, he must, in solid bulk, be 42 millions 875 thousand times as big as the Moon.

193. The horizontal Parallaxes are best observed at the Equator; 1. Because the heat is so nearly equal every day, that the Refractions are almost constantly the same. 2. Because the parallactic Angle is greater there as at A (the distance from thence to the Earth’s Axis being greater,) than upon any parallel of Latitude, as a or b.

194. The Earth’s distance from the Sun being determined, the distances of all the other Planets from him are easily found by the following analogy, their periods round him being ascertained by observation. As the square of the Earth’s period round the Sun is to the cube of it’s distance from him, so is the square of the period of any other Planet to the cube of it’s distance, in such parts or measures as the Earth’s distance was taken; see § 111. This proportion gives us the relative mean distances of the Planets from the Sun to the greatest degree of exactness; and they are as follows, having been deduced from their periodical times, according to the law just mentioned, which was discovered by Kepler and demonstrated by Sir Isaac Newton.

77195. These last numbers shew, that although we have the relative distances of the Planets from the Sun to the greatest nicety, yet the best observers have not hitherto been able to ascertain their true distances to within less than a twelfth part of what they really are. And therefore, we must wait with patience till the 6th of June, A. D. 1761; wishing that the Sky may then be clear to all places where there are good Astronomers and accurate instruments for observing the Transit of Venus over the Sun’s Disc at that time: as it will not happen again, so as to be visible in Europe, in less than 235 years after.

196. The Earth’s Axis produced to the Stars, being carried ^[50]parallel to itself during the Earth’s annual revolution, describes a circle in the Sphere of the fixed Stars equal to the Orbit of the Earth. But this Orbit, though very large in itself, if viewed from the Stars, would appear no bigger than a point; and consequently, the circle described in the Sphere of the Stars by the Axis of the Earth produced, if viewed from the Earth, must appear but as a point; that is, it’s diameter appears too little to be measured by observation: for Dr. Bradley has assured us, that if it had amounted to a single second, or two at most, he should have perceived it in the great number of observations he has made, especially upon γ Dragonis; and that it seemed to him very probable that the annual Parallax of this Star is not so great as a single second: and consequently, that it is above 400 thousand times farther from us than the Sun. Hence the celestial poles seem to continue in the same points of the Heavens throughout the year; which by no means disproves the Earth’s annual motion, but plainly proves the distance of the Stars to be exceeding great.

197. The small apparent motion of the Stars § 113, discovered by that great Astronomer, he found to be no ways owing to their annual Parallax (for it came out contrary thereto) but to the Aberration of their light, which can result from no known cause besides that of the Earth’s annual motion; and as it agrees so exactly therewith, it proves beyond dispute that the Earth has such a motion: for this Aberration compleats all it’s various Phenomena every year; and proves that the velocity of star-light is such as carries it through a space equal to the Sun’s distance from us in 8 minutes 13 seconds of time. Hence, the velocity of light is ^[51]10 thousand 210 times as 78great as the Earth’s velocity in it’s Orbit; which velocity (from what we know already of the Earth’s distance from the Sun) may be affected to be at least between 57 and 58 thousand miles every hour: and supposing it to be 58000, this number multiplied by the above 10210, gives 592 million 180 thousand miles for the hourly motion of light: which last number divided by 3600, the number of seconds in an hour, shews that light flies at the rate of more than 164 thousand miles every second of time, or swing of a common clock pendulum.

198. If the reader be hitherto unacquainted with the principal circles of the Globe, he should now learn to know them; which he may do sufficiently for his present purpose in a quarter of an hour, if he sets the ball of a terrestrial Globe before him, or looks at the Figure of it, wherein these circles are drawn and named. The Equator is that great circle which divides the northern half of the Earth from the southern. The Tropics are lesser circles parallel to the Equator, and each of them is 23¹⁄₂ degrees from it; a degree in this sense being the 360th part of any great circle which divides the Earth into two equal parts. The Tropic of Cancer lies on the north side of the Equator, and the Tropic of Capricorn on the south. The Arctic Circle has the North Pole for it’s center, and is just as far from the north Pole as the Tropics are from the Equator: and the Antarctic Circle (hid by the supposed convexity of the Figure) is just as far from the South Pole, every way round it. These Poles are the very north and south points of the Globe: and all other places are denominated northward or southward according to the side of the Equator they lie on, and the Pole to which they are nearest. The Earth’s Axis is a straight line passing through the center of the Earth, perpendicular to the Equator, and terminating in the Poles at it’s surface. This, in the real Earth and Planets is only an imaginary line; but in artificial Globes or Planets it is a wire by which they are supported, and turned round in Orreries, 79or such like machines, by wheel-work. The circles 12. 1. 2. 3. 4, &c. are Meridians to all places they pass through; and we must suppose thousands more to be drawn, because every place that is ever so little to the east or west of any other place, has a different Meridian from that other place. All the Meridians meet in the Poles; and whenever the Sun’s center is passing over any Meridian, in his apparent motion round the Earth, it is mid-day or noon to all places on that Meridian.

199. The broad Space lying between the Tropics, like a girdle surrounding the Globe, is called the torrid Zone, of which the Equator is in the middle, all around. The Space between the Tropic of Cancer and Arctic Circle is called the North temperate Zone. That between the Tropic of Capricorn and the Antarctic Circle, the South temperate Zone. And the two circular Spaces bounded by the Polar Circles are the two Frigid Zones; denominated north or south, from that Pole which is in the center of the one or the other of them.

200. Having acquired this easy branch of knowledge, the learner may proceed to make the following experiment with his terrestrial ball; which will give him a plain idea of the diurnal and annual motions of the Earth, together with the different lengths of days and nights, and all the beautiful variety of seasons, depending on those motions.

Take about seven feet of strong wire, and bend it into a circular form, as abcd, which being viewed obliquely, appears elliptical as in the Figure. Place a lighted candle on a table, and having fixed one end of a silk thread K, to the north pole of a small terrestrial Globe H, about three inches diameter, cause another person to hold the wire circle so that it may be parallel to the table, and as high as the flame of the candle I, which should be in or near the center. Then, having twisted the thread as towards the left hand, that by untwisting it may turn the Globe round eastward, or contrary to the way that the hands of a watch move; hang the Globe by the thread within this circle, almost contiguous to it; and as the thread untwists, the Globe (which is enlightened half round by the candle as the Earth is by the Sun) will turn round it’s Axis, and the different places upon it will be carried through the light and dark Hemispheres, and have the appearance of a regular succession of days and nights, as our Earth has in reality by such a motion. As the Globe turns, move your hand slowly so as to carry the Globe round the candle according to the order of the letters abcd, keeping it’s center even with the wire circle; and 80you will perceive, that the candle being still perpendicular to the Equator will enlighten the Globe from pole to pole in it’s motion round the circle; and that every place on the Globe goes equally through the light and the dark, as it turns round by the untwisting of the thread, and therefore has a perpetual Equinox. The Globe thus turning round represents the Earth turning round it’s Axis; and the motion of the Globe round the candle represents the Earth’s annual motion round the Sun, and shews, that if the Earth’s Orbit had no inclination to it’s Axis, all the days and nights of the year would be equally long, and there would be no different seasons. But now, desire the person who holds the wire to hold it obliquely in the position ABCD, raising the side ♋ just as much as he depresses the side ♑, that the flame may be still in the plane of the circle; and twisting the thread as before, that the Globe may turn round it’s Axis the same way as you carry it round the candle; that is, from west to east, let the Globe down into the lowermost part of the wire circle at ♑, and if the circles be properly inclined, the candle will shine perpendicularly on the Tropic of Cancer, and the frigid Zone, lying within the arctic or north polar Circle, will be all in the light, as in the Figure; and will keep in the light let the Globe turn round it’s Axis ever so often. From the Equator to the north polar Circle all the places have longer days and shorter nights; but from the Equator to the south polar Circle just the reverse. The Sun does not set to any part of the north frigid Zone, as shewn by the candle’s shining on it so that the motion of the Globe can carry no place of that Zone into the dark: and at the same time the south frigid Zone is involved in darkness, and the turning of the Globe brings none of it’s places into the light. If the Earth were to continue in the like part of it’s Orbit, the Sun would never set to the inhabitants of the north frigid Zone, nor rise to those of the south. At the Equator it would be always equal day and night; and as the places are gradually more and more distant from the Equator, towards the arctic Circle, they would have longer days and shorter nights, whilst those on the south side of the Equator would have their nights longer than their days. In this case there would be continual summer on the north side of the Equator, and continual winter on the south side of it.

Plate V.

J. Ferguson delin.

J. Mynde Sc.

But as the Globe turns round it’s Axis, move your hand slowly forward so as to carry the Globe from H towards E, and the boundary of light and darkness will approach towards the north Pole, and recede towards the south Pole; the northern places will go through less and less of the light, and the southern places through more and more of it; shewing how the northern days decrease in length, and the southern 81days increase, whilst the Globe proceeds from H to F. When the Globe is at E, it is at a mean state between the lowest and highest parts of it’s Orbit; the candle is directly over the Equator, the boundary of light and darkness just reaches to both the Poles, and all places on the Globe go equally through the light and dark Hemispheres, shewing that the days and nights are then equal at all places of the Earth, the Poles only excepted; for the Sun is then setting to the north Pole, and rising to the south Pole.

Continue moving the Globe forward, and as it goes through the quarter A, the north Pole recedes still farther into the dark Hemisphere, and the south Pole advances more into the light, as the Globe comes nearer to ♋; and when it comes there at F, the candle is directly over the Tropic of Capricorn, the days are at the shortest, and nights at the longest, in the northern Hemisphere, all the way from the Equator to the arctic Circle; and the reverse in the southern Hemisphere from the antarctic Circle; within which Circles it is dark to the north frigid Zone and light to the south.

Continue both motions, and as the Globe moves through the quarter B, the north Pole advances toward the light, and the south Pole recedes as fast from it; the days lengthen in the northern Hemisphere, and shorten in the southern; and when the Globe comes to G the candle will be again over the Equator (as when the Globe was at E) and the days and nights will again be equal as formerly: and the north Pole will be just coming into the light, the south Pole going out of it.

Thus we see the reason why the days lengthen and shorten from the Equator to the polar Circles every year; why there is no day or night for several turnings of the Earth, within the polar Circles; why there is but one day and one night in the whole year at the Poles; and why the days and nights are equally long all the year round at the Equator, which is always equally cut by the circle bounding light and darkness.

201. The inclination of an Axis or Orbit is merely relative, because we compare it with some other Axis or Orbit which we consider as not inclined at all. Thus, our Horizon being level to us whatever place of the Earth we are upon, we consider it as having no inclination; and yet, if we travel 90 degrees from that place, we shall then have an Horizon perpendicular to the former; but it will still be level to us. And, if this Book be held so that the 82^[52]Circle ABCD be parallel to the Horizon, both the Circle abcd, and the Thread or Axis K will be inclined to it. But if Book or Plate be held, so that the Thread be perpendicular to the Horizon, then the Orbit ABCD will be inclined to the Thread, and the Orbit abcd perpendicular to it, and parallel to the Horizon. We generally consider the Earth’s annual Orbit as having no inclination, and the Orbits of all the other Planets as inclined to it § 20.

202. Let us now take a view of the Earth in it’s annual course round the Sun, considering it’s Orbit as having no inclination; and it’s Axis as inclining 23¹⁄₂ degrees from a line perpendicular to it’s Orbit, and keeping the same oblique direction in all parts of it’s annual course; or, as commonly termed, keeping always parallel to itself § 196.

Let a, b, c, d, e, f, g, h be the Earth in eight different parts of it’s Orbit, equidistant from one another; Ns it’s Axis, N the north Pole, s the south Pole, and S the Sun nearly in the center of the Earth’s Orbit § 18. As the Earth goes round the Sun according to the order of the letters abcd, &c. it’s Axis Ns keeps the same obliquity, and is still parallel to the line MNs. When the Earth is at a, it’s north Pole inclines toward the Sun, and brings all the northern places more into the light than at any other time of the year. But when the Earth is at e in the opposite time of the year, the north Pole declines from the Sun, which occasions the northern places to be more in the dark than in the light; and the reverse at the southern places, as is evident by the Figure, which I have taken from Dr. Long’s Astronomy. When the Earth is either at c or g, it’s Axis inclines not either to or from the Sun, but lies sidewise to him; and then the Poles are in the boundary of light and darkness; and the Sun, being directly over the Equator, makes equal day and night at all places. When the Earth is at b it is half way between the Summer Solstice and Harvest Equinox; when it is at d it is half way from the Harvest Equinox to the Winter Solstice; at f half way from the Winter Solstice to the Spring Equinox: and at h half way from the Spring Equinox to the Summer Solstice.

203. From this oblique view of the Earth’s Orbit, let us suppose ourselves to be raised far above it, and placed just over it’s center S, looking down upon it from it’s north pole; and as the Earth’s Orbit differs but very little from a Circle, we shall have it’s figure in such a 83view represented by the Circle ABCDEFGH. Let us suppose this Circle to be divided into 12 equal parts called Signs, having their names affixed to them; and each Sign into 30 equal parts called Degrees, numbered 10, 20, 30, as in the outermost Circle of the Figure, which represents the great Ecliptic in the Heavens. The Earth is shewn in eight different positions in this Circle, and in each position Æ is the Equator, T the Tropic of Cancer, the dotted Circle the parallel of London, U the arctic or north polar Circle, and P the north Pole where all the Meridians or hour Circles meet § 198. As the Earth goes round the Sun the north Pole keeps constantly towards one part of the Heavens, as it keeps in the Figure towards the right hand side of the Plate.

When the Earth is at the beginning of Libra, namely on the 20th of March, in this Figure (as at g in Fig. I.) the Sun S as seen from the Earth appears at the beginning of Aries in the opposite part of the Heavens^[53], the north Pole is just coming into the light, the Sun is vertical to the Equator; which, together with the Tropic of Cancer, parallel of London, and arctic Circle, are all equally cut by the Circle bounding light and darkness, coinciding with the six o’clock hour Circle, and therefore the days and nights are equally long at all places: for every part of the Meridian ÆTLa comes into the light at six in the morning, and revolving with the Earth according to the order of the hour-letters, goes into the dark at six in the evening. There are 24 Meridians or hour-Circles drawn on the Earth in this Figure, to shew the time of Sun rising and setting at different Seasons of the Year.

As the Earth moves in the Ecliptic according to the order of the letters ABCD, &c. through the Signs Libra, Scorpio, and Sagittarius, the north Pole comes more and more into the light; the days increase as the nights decrease in length, at all places north of the Equator Æ; which is plain by viewing the Earth at b on the 5th of May, when it is in the 15th degree of Scorpio^[54], and the Sun as seen from the Earth appears in the 15th degree of Taurus. For then, the Tropic of Cancer T is in the light from a little after five in the morning till almost seven in the evening; the parallel of London from half an hour past four till half an hour past seven; the polar Circle U from three till nine; and a large track round the north Pole P has day all the 24 hours, for many rotations of the Earth on it’s Axis.

84When the Earth comes to c, at the beginning of Capricorn, and the Sun as seen from the Earth appears at the beginning of Cancer, on the 21st of June, as in this Figure, it is in the position a in Fig. I; and it’s north Pole inclines toward the Sun, so as to bring all the north frigid Zone into the light, and the northern parallels of Latitude more into the light than the dark from the Equator to the polar Circles; and the more so as they are farther from the Equator. The Tropic of Cancer is in the light from five in the morning till seven at night, the parallel of London from a quarter before four till a quarter after eight; and the polar Circle just touches the dark, so that the Sun has only the lower half of his Disc hid from the inhabitants on that Circle for a few minutes about midnight, supposing no inequalities in the Horizon and no Refractions.

A bare view of the Figure is enough to shew, that as the Earth advances from Capricorn toward Aries, and the Sun appears to move from Cancer toward Libra, the north Pole recedes toward the dark, which causes the days to decrease, and the nights to increase in length, till the Earth comes to Aries, and then they are equal as before; for the boundary of light and darkness cut the Equator and all it’s parallels equally, or in halves. The north pole then goes into the dark, and continues therein until the Earth goes half way round it’s Orbit; or, from the 23d of September till the 20th of March. In the middle between these times, viz. on the 22d of December, the north Pole is as far as it can be in the dark, which is 23¹⁄₂ degrees, equal to the inclination of the Earth’s Axis from a perpendicular to it’s Orbit: and then, the northern parallels are as much in the dark as they were in the light on the 21 of June; the winter nights being as long as the summer days, and the winter days as short as the summer nights. It is needless to multiply words on this subject, as we shall have occasion to mention the seasons again in describing the Orrery, § 439. Only this must be noted, that all that has been said of the northern Hemisphere, the contrary must be understood of the southern; for on different sides of the Equator the seasons are contrary, because, when the northern Hemisphere inclines toward the Sun the southern declines from him.

204. As Saturn goes round the Sun, his obliquely posited ring, like our Earth’s Axis, keeps parallel to itself, and is therefore turned edgewise to the Sun twice in a Saturnian year, which is almost as long as 30 of our years § 81. But the ring, though considerably broad, is too thin to be seen when it is turned round edgewise to the Sun, at 85which time it is also edgewise to the Earth; and therefore it disappears once in every fifteen years to us. As the Sun shines half a year on the north pole of our earth, then disappears to it, and shines as long on the south pole; so, during one half of Saturn’s year the Sun shines on the north side of his ring, then disappears to it, and shines as long on it’s south side. When the Earth’s Axis inclines neither to nor from the Sun, but sidewise to him, he instantly ceases to shine on one pole, and begins to enlighten the other; and when Saturn’s Ring inclines neither to nor from the Sun, but sidewise to him, he ceases to shine on the one side of it, and begins to shine upon the other.

Let S be the Sun, ABCDEFGH Saturn’s Orbit, and IKLMNO the Earth’s Orbit. Both Saturn and the Earth move according to the order of the letters, and when Saturn is at A his ring is turned edgewise to the Sun S, and he is then seen from the Earth as if he had lost his ring, let the Earth be in any part of it’s Orbit whatever, except between N and O; for whilst it describes that space, Saturn is apparently so near the Sun as to be hid in his beams. As Saturn goes from A to C his ring appears more and more open to the Earth: at C the ring appears most open of all; and seems to grow narrower and narrower as Saturn goes from C to E; and when he comes to E, the ring is again turned edgewise both to the Sun and Earth: and as neither of it’s sides are illuminated, it is invisible to us, because it’s edge is too thin to be perceptible: and Saturn appears again as if he had lost his ring. But as he goes from E to G, his ring opens more and more to our view on the under side; and seems just as open at G as it was at C; and may be seen in the night-time from the Earth in any part of it’s Orbit, except about M, when the Sun hides the Planet from our view. As Saturn goes from G to A his ring turns more and more edgewise to us, and therefore it seems to grow narrower and narrower; and at A it disappears as before. Hence, while Saturn goes from A to E the Sun shines on the upper side of his ring, and the under side is dark; but whilst he goes from E to A the Sun shines on the under side of his ring, and the upper side is dark.

It may perhaps be imagined that this Article might have been placed more properly after § 81 than here: but when the candid reader considers that all the various Phenomena of Saturn’s Ring depend upon a cause similar to that of our Earth’s seasons, he will readily allow that they are best explained together; and that the two Figures serve to illustrate each other.

86205. The Earth’s Orbit being elliptical, and the Sun constantly keeping in it’s lower Focus, which is 1,377,000 miles from the middle point of the longer Axis, the Earth comes twice so much, or 2,754,000 miles nearer the Sun at one time of the year than at another: for the Sun appearing under a larger Angle in our winter than summer, proves that the Earth is nearer the Sun in winter, (see the Note on Art. 185.) But here, this natural question will arise, Why have we not the hottest weather when the Earth is nearest the Sun? In answer it must be observed, that the excentricity of the Earth’s Orbit, or 1 million 377 miles bears no greater proportion to the Earth’s mean distance from the Sun than 17 does to 1000; and therefore, this small difference of distance cannot occasion any great difference of heat or cold. But the principal cause of this difference is, that in winter the Sun’s rays fall so obliquely upon us, that any given number of them is spread over a much greater portion of the Earth’s surface where we live; and therefore each point must then have fewer rays than in summer. Moreover, there comes a greater degree of cold in the long winter nights, than there can return of heat in so short days; and on both these accounts the cold must increase. But in summer the Sun’s rays fall more perpendicularly upon us, and therefore come with greater force, and in greater numbers on the same place; and by their long continuance, a much greater degree of heat is imparted by day than can fly off by night.

206. That a greater number of rays fall on the same place, when they come perpendicularly, than when they come obliquely on it, will appear by the Figure. For, let AB be a certain number of the Sun’s rays falling on CD (which, let us suppose to be London) on the 22d of June: but, on the 22d of December, the line CD, or London; has the oblique position Cd to the same rays; and therefore scarce a third part of them falls upon it, or only those between A and e; all the rest eB being expended on the space dP, which is more than double the length of CD or Cd. Besides, those parts which are once heated, retain the heat for some time; which, with the additional heat daily imparted, makes it continue to increase, though the Sun declines toward the south: and this is the reason why July is hotter than June, although the Sun has withdrawn from the summer Tropic; as we find it is generally hotter at three in the afternoon, when the Sun has gone toward the west, than at noon when he is on the Meridian. Likewise, those places which are well cooled require time to be heated again; for the Sun’s rays do not heat even 87the surface of any body till they have been some time upon it. And therefore we find January for the most part colder than December, although the Sun has withdrawn from the winter Tropic, and begins to dart his beams more perpendicularly upon us, when we have the position CF. An iron bar is not heated immediately upon being put into the fire, nor grows cold till some time after it has been taken out.

207. Geographers arbitrarily choose to call the Meridian of some remarkable place the first Meridian. There they begin their reckoning; and just so many degrees and minutes as any other place is to the eastward or westward of that Meridian, so much east or west Longitude they say it has. A degree is the 360th part of a Circle, be it great or small; and a minute the 60th part of a degree. The English Geographers reckon the Longitude from the Meridian of the Royal Observatory at Greenwich, and the French from the Meridian of Paris.

208. If we imagine twelve great Circles, one of which is the Meridian of any given place, to intersect each other in the two Poles of the Earth, and to cut the Equator Æ at every 15th degree, they will be divided by the Poles into 24 Semicircles which divide the Equator into 24 equal parts; and as the Earth turns on it’s Axis, the planes of these Semicircles come successively after one another every hour to the Sun. As in an hour of time there is a revolution of 15 degrees of the Equator, in a minute of time there will be a revolution of 15 minutes of the Equator, and in a second of time a revolution of 15 seconds. There are two tables annexed to this Chapter, for reducing mean solar time into degrees and minutes of the terrestrial Equator; and also for converting degrees and parts of the Equator into mean solar time.

209. Because the Sun enlightens only one half of the Earth at once, as it turns round it’s Axis he rises to some places at the same moments of absolute Time that he sets to others; and when it is mid-day to some places, it is mid-night to others. The XII on the middle of the Earth’s enlightened side, next the Sun, stands for mid-day; and the 88opposite XII on the middle of the dark side, for mid-night. If we suppose this Circle of hours to be fixed in the plane of the Equinoctial, and the Earth to turn round within it, any particular Meridian will come to the different hours so, as to shew the true time of the day or night at all places on that Meridian. Therefore,

210. To every place 15 degrees eastward from any given Meridian, it is noon an hour sooner than on that Meridian; because their Meridian comes to the Sun an hour sooner: and to all places 15 degrees westward it is noon an hour later § 208, because their Meridian comes an hour later to the Sun; and so on: every 15 degrees of motion causing an hour’s difference in time. Therefore they who have noon an hour later than we, have their Meridian, that is, their Longitude 15 degrees westward from us; and they who have noon an hour sooner than we, have their Meridian 15 degrees eastward from ours: and so for every hour’s difference of time 15 degrees difference of Longitude. Consequently, if the beginning or ending of a Lunar Eclipse be observed, suppose at London, to be exactly at mid-night, and in some other place at 11 at night, that place is 15 degrees westward from the Meridian of London: if the same Eclipse be observed at one in the morning at another place, that place is 15 degrees eastward from the said Meridian.

211. But as it is not easy to determine the exact moment either of the beginning or ending of a Lunar Eclipse, because the Earth’s shadow through which the Moon passes is faint and ill defined about the edges; we have recourse to the Eclipses of Jupiter’s Satellites, which disappear so instantaneously as they enter into Jupiter’s shadow, and emerge so suddenly out of it, that we may fix the phenomenon to half a second of time. The first or nearest Satellite to Jupiter is the most advantageous for this purpose, because it’s motion is quicker than the motion of any of the rest, and therefore it’s immersions and emersions are more frequent.

212. The English Astronomers have made Tables for shewing the times of the Eclipses of Jupiter’s Satellites to great precision, for the Meridian of Greenwich. Now, let an observer, who has these Tables with a good Telescope and a well-regulated Clock at any other place of the Earth, observe the beginning or ending of an Eclipse of one of Jupiter’s Satellites, and note the precise moment of time that he saw the Satellite either immerge into, or emerge out of the shadow, and compare that time with the time shewn by the Tables for Greenwich; then, 15 degrees difference of Longitude being allowed for every 89hour’s difference of time, will give the Longitude of that place from Greenwich, as above § 210; and if there be any odd minutes of time, for every minute a quarter of a degree, east or west must be allowed, as the time of observation is before or after the time shewn by the Tables. Such Eclipses are very convenient for this purpose at land, because they happen almost every day; but are of no use at sea, because the rolling of the ship hinders all nice telescopical observations.

213. To explain this by a Figure, let J be Jupiter, K, L, M, N his four Satellites in their respective Orbits 1, 2, 3, 4; and let the Earth be at f (suppose in November, although that month is no otherways material than to find the Earth readily in this scheme, where it is shewn in eight different parts of it’s Orbit.) Let Q be a place on the Meridian of Greenwich, and R a place on some other Meridian. Let a person at R observe the instantaneous vanishing of the first Satellite K into Jupiter’s shadow, suppose at three o’clock in the morning; but by the Tables he finds the immersion of that Satellite to be at midnight at Greenwich: he can then immediately determine, that as there are three hours difference of time between Q and R, and that R is three hours forwarder in reckoning than Q, it must be 45 degrees of east Longitude from the Meridian of Q. Were this method as practicable at sea as at land, any sailor might almost as easily, and with equal certainty, find the Longitude as the Latitude.

214. Whilst the Earth is going from C to F in it’s Orbit, only the immersions of Jupiter’s Satellites into his shadow are generally seen; and their emersions out of it while the Earth goes from G to B. Indeed, both these appearances may be seen of the second, third, and fourth Satellite when eclipsed, whilst the Earth is between D and E, or between G and A; but never of the first Satellite, on account of the smallness of it’s Orbit and the bulk of Jupiter; except only when Jupiter is directly opposite to the Sun; that is, when the Earth is at g: and even then, strictly speaking, we cannot see either the immersions or emersions of any of his Satellites, because his body being directly between us and his conical shadow, his Satellites are hid by his body a few moments before they touch his shadow; and are quite emerged from thence before we can see them, as it were, just dropping from him. And when the Earth is at c, the Sun being between it and Jupiter hides both him and his Moons from us.

In this Diagram, the Orbits of Jupiter’s Moons are drawn in true proportion to his diameter; but, in proportion to the Earth’s Orbit they are drawn 81 times too large.

90215. In whatever month of the year Jupiter is in conjunction with the Sun, or in opposition to him, in the next year it will be a month later at least. For whilst the Earth goes once round the Sun, Jupiter describes a twelfth part of his Orbit. And therefore, when the Earth has finished it’s annual period from being in a line with the Sun and Jupiter, it must go as much forwarder as Jupiter has moved in that time, to overtake him again: just like the minute hand of a watch, which must, from any conjunction with the hour hand, go once round the dial-plate and somewhat above a twelfth part more, to overtake the hour hand again.

216. It is found by observation, that when the Earth is between the Sun and Jupiter, as at g, his Satellites are eclipsed about 8 minutes sooner than they should be according to the Tables: and when the Earth is at B or C, these Eclipses happen about 8 minutes later than the Tables predict them. Hence it is undeniably certain, that the motion of light is not instantaneous, since it takes about 16¹⁄₂ minutes of time to go through a space equal to the diameter of the Earth’s Orbit, which is 162 millions of miles in length: and consequently the particles of light fly about 164 thousand 494 miles every second of time, which is above a million of times swifter than the motion of a cannon bullet. And as light is 16¹⁄₂ minutes in travelling across the Earth’s Orbit, it must be 8¹⁄₄ minutes in coming from the Sun to us: therefore, if the Sun were annihilated we should see him for 8¹⁄₄ minutes after; and if he were again created he would be 8¹⁄₄ minutes old before we could see him.

217. To illustrate this progressive motion of light, let A and B be the Earth in two different parts of it’s Orbit, whose distance is 81 millions of miles, equal to the Earth’s distance from the Sun S. It is plain, that if the motion of light were instantaneous, the Satellite 1 would appear to enter into Jupiter’s shadow FF at the same moment of time to a spectator in A as to another in B. But by many years observations it has been found, that the immersion of the Satellite into the shadow is seen 8¹⁄₄ minutes sooner when the Earth is at B, than when it is at A. And so, as Mr. Romer first discovered, the motion of light is thereby proved to be progressive, and not instantaneous, as was formerly believed. It is easy to compute in what time the Earth moves from A to B; for the chord of 60 degrees of any Circle is equal to the Semidiameter of that Circle; and as the Earth goes through all the 360 degrees of it’s Orbit in a year, it goes through 60 of those degrees in about 61 days. Therefore, if on any given 91day, suppose the first of June, the Earth is at A, on the first of August it will be at B: the chord, or straight line AB, being equal to DS the Radius of the Earth’s Orbit, the same with AS it’s distance from the Sun.

218. As the Earth moves from D to C, through the side AB of it’s Orbit, it is constantly meeting the light of Jupiter’s Satellites sooner, which occasions an apparent acceleration of their Eclipses: and as it moves through the other half H of it’s Orbit, from C to D, it is receding from their light, which occasions an apparent retardation of their Eclipses, because their light is then longer ere it overtakes the Earth.

219. That these accelerations of the immersions of Jupiter’s Satellites into his shadow, as the Earth approaches towards Jupiter, and the retardations of their emersions out of his shadow, as the Earth is going from him, are not occasioned by any inequality arising from the motions of the Satellites in excentric Orbits, is plain, because it affects them all alike, in whatever parts of their Orbits they are eclipsed. Besides, they go often round their Orbits every year, and their motions are no way commensurate to the Earth’s. Therefore, a Phenomenon not to be accounted for from the real motions of the Satellites, but so easily deducible from the Earth’s motion, and so answerable thereto, must be allowed to result from it. This affords one very good proof of the Earth’s annual motion.

92220. TABLES for converting mean solar Time into Degrees and Parts of the terrestrial Equator; and also for converting Degrees and Parts of the Equator into mean solar Time.

93These are the Tables mentioned in the 208th Article, and are so easy that they scarce require any farther explanation than to inform the reader, that if, in Table I. he reckons the columns marked with Asterisks to be minutes of time, the other columns give the equatoreal parts or motion in degrees and minutes; if he reckons the Asterisk columns to be seconds, the others give the motion in minutes and seconds of the Equator; if thirds, in seconds and thirds: And if in Table II. he reckons the Asterisk columns to be degrees of motion, the others give the time answering thereto in hours and minutes; if minutes of motion, the time is minutes and seconds; if seconds of motion, the corresponding time is given in seconds and thirds. An example in each case will make the whole very plain.

In 10 hours 15 minutes 24 seconds 20 thirds, Qu. How much of the Equator revolves through the Meridian?

In what time will 153 degrees 51 minutes 5 seconds of the Equator revolve through the Meridian?

221. The fixed Stars appear to go round the Earth in 23 hours 56 minutes 4 seconds, and the Sun in 24 hours: so that the Stars gain three minutes 56 seconds upon the Sun every day, which amounts to one diurnal revolution in a year; and therefore, in 365 days as measured by the returns of the Sun to the Meridian, there are 366 days as measured by the Stars returning to it: the former are called Solar Days, and the latter Sidereal.

The diameter of the Earth’s Orbit is but a physical point in proportion to the distance of the Stars; for which reason, and the Earth’s uniform motion on it’s Axis, any given Meridian will revolve from any 94Star to the same Star again in every absolute turn of the Earth on it’s Axis, without the least perceptible difference of time shewn by a clock which goes exactly true.

If the Earth had only a diurnal motion, without an annual, any given Meridian would revolve from the Sun to the Sun again in the same quantity of time as from any Star to the same Star again; because the Sun would never change his place with respect to the Stars. But, as the Earth advances almost a degree eastward in it’s Orbit in the time that it turns eastward round its Axis, whatever Star passes over the Meridian on any day with the Sun, will pass over the same Meridian on the next day when the Sun is almost a degree short of it; that is, 3 minutes 56 seconds sooner. If the year contained only 360 days as the Ecliptic does 360 degrees, the Sun’s apparent place, so far as his motion is equable, would change a degree every day; and then the sidereal days would be just four minutes shorter than the solar.

Let ABCDEFGHIKLM be the Earth’s Orbit, in which it goes round the Sun every year, according to the order of the letters, that is, from west to east, and turns round it’s Axis the same way from the Sun to the Sun again every 24 hours. Let S be the Sun, and R a fixed Star at such an immense distance that the diameter of the Earth’s Orbit bears no sensible proportion to that distance. Let Nm be any particular Meridian of the Earth, and N a given point or place upon that Meridian. When the Earth is at A, the Sun S hides the Star R, which would always be hid if the Earth never removed from A; and consequently, as the Earth turns round it’s Axis, the point N would always come round to the Sun and Star at the same time. But when the Earth has advanced, suppose a twelfth part of it’s Orbit from A to B, it’s motion round it’s Axis will bring the point N a twelfth part of a day or two hours sooner to the Star than to the Sun; for the Angle NBn is equal to the Angle ASB: and therefore, any Star which comes to the Meridian at noon with the Sun when the Earth is at A, will come to the Meridian at 10 in the forenoon when the Earth is at B. When the Earth comes to C the point N will have the Star on it’s Meridian at 8 in the morning, or four hours sooner than it comes round to the Sun; for it must revolve from N to n, before it has the Sun in it’s Meridian. When the Earth comes to D, the point N will have the Star on it’s Meridian at six in the morning, but that point must revolve six hours more from N to n, before it has mid-day by the Sun: for now the Angle ASD is a right Angle, and so is NDn; that is, the Earth has advanced 90 degrees in it’s Orbit, and must turn 90 degrees on its Axis to carry the point N from the Star to the Sun: for the 95Star always comes to the Meridian when Nm is parallel to RSA; because DS is but a point in respect of RS. When the Earth is at E, the Star comes to the Meridian at 4 in the morning; at F, at two in the morning; and at G, the Earth having gone half round it’s Orbit, N points to the Star R at midnight, being then directly opposite to the Sun; and therefore, by the Earth’s diurnal motion the Star comes to the Meridian 12 hours before the Sun. When the Earth is at H, the Star comes to the Meridian at 10 in the evening; at I it comes to the Meridian at 8, that is, 16 hours before the Sun; at K 18 hours before him; at L 20 hours; at M 22; and at A equally with the Sun again.

A Table, shewing how much of the Celestial Equator passes over the Meridian in any part of a mean Solar Day; and how much the Fixed Stars gain upon the mean Solar Time every Day, for a Month.

96222. Thus it is plain, that an absolute turn of the Earth on it’s Axis (which is always completed when the same Meridian comes to be parallel to it’s situation at any time of the day before) never brings the same Meridian round from the Sun to the Sun again; but that the Earth requires as much more than one turn on it’s Axis to finish a natural day, as it has gone forward in that time; which, at a mean state is a 365th part of a Circle. Hence, in 365 days the Earth turns 366 times round it’s Axis; and therefore, as a turn of the Earth on it’s Axis compleats a sidereal day, there must be one sidereal day more in a year than the number of solar days, be the number what it will, on the Earth, or any other Planet. One turn being lost with respect to the number of solar days in a year, by the Planet’s going round the Sun; just as it would be lost to a traveller, who, in going round the Earth, would lose one day by following the apparent diurnal motion of the Sun: and consequently, would reckon one day less at his return (let him take what time he would to go round the Earth) than those who remained all the while at the place from which he set out. So, if there were two Earths revolving equably on their Axes, and if one remained at A until the other travelled round the Sun from A to A again, that Earth which kept it’s place at A would have it’s solar and sidereal days always of the same length; and so, would have one solar day more than the other at it’s return. Hence, if the Earth turned but once round it’s Axis in a year, and if that turn was made the same way as the Earth goes round the Sun, there would be continual day on one side of the Earth, and continual night on the other.

223. The first part of the preceding Table shews how much of the celestial Equator passes over the Meridian in any given part of a mean solar day, and is to be understood the same way as the Table in the 220th article. The latter part, intitled, Accelerations of the fixed Stars, affords us an easy method of knowing whether or no our clocks and watches go true: For if, through a small hole in a window-shutter, or in a thin plate of metal fixed to a window, we observe at what time any Star disappears behind a chimney, or corner of a house, at a little distance; and if the same Star disappears the next night 3 minutes 56 seconds sooner by the clock or watch; and on the second night, 7 minutes 52 seconds sooner; the third night 11 minutes 48 seconds sooner; and so on, every night, as in the Table, which shews this difference for 30 natural days, it is an infallible Sign that the machine goes true; otherwise it does not go true; and must be regulated accordingly: and as the disappearing of a Star is instantaneous, we may depend on this information to half a second.

Pl. VI.

J. Ferguson inv. et delin.

J. Mynde Sc.

224. The Earth’s motion on it’s Axis being perfectly uniform, and equal at all times of the year, the sidereal days are always precisely of the same length; and so would the solar or natural days be, if the Earth’s orbit were a perfect Circle, and it’s Axis perpendicular to it’s orbit. But the Earth’s diurnal motion on an inclined Axis, and it’s annual motion in an elliptic orbit, cause the Sun’s apparent motion in the Heavens to be unequal: for sometimes he revolves from the Meridian to the Meridian again in somewhat less than 24 hours, shewn by a well regulated clock; and at other times in somewhat more: so that the time shewn by an equal going clock and a true Sun-dial is never the same but on the 15th of April, the 16th of June, the 31st of August, and the 24th of December. The clock, if it goes equally and true all the year round, will be before the Sun from the 24th of December till the 15th of April; from that time till the 16th of June the Sun will be before the clock; from the 16th of June till the 31st of August the clock will be again before the Sun; and from thence to the 24th of December the Sun will be faster than the clock.

225. The Tables of the Equation of natural days, at the end of the next Chapter, shew the time that ought to be pointed out by a well regulated clock or watch every day of the year at the precise moment of solar noon; that is, when the Sun’s centre is on the Meridian, or when a true Sun-dial shews it to be precisely Twelve. Thus, on the 5th of January in Leap-year, when the Sun is on the Meridian, it ought to be 5 minutes 51 seconds past twelve by the clock; and on the 15th of May, when the Sun is on the Meridian, the time by the clock should be but 55 minutes 57 seconds past eleven; in the former case, the clock is 5 minutes 51 seconds beforehand with the Sun; and in the latter case, the Sun is 4 minutes 3 seconds faster than the clock. The column at the right hand of each month shews the daily difference of this equation, as it increases or decreases. But without a Meridian Line, or a Transit-Instrument fixed in the plane of the Meridian, we cannot set a Sun-dial true.

226. The easiest and most expeditious way of drawing a Meridian Line is this: Make four or five concentric Circles, about a quarter of 98an inch from one another, on a flat board about a foot in breadth; and let the outmost Circle be but little less than the board will contain. Fix a pin perpendicularly in the center, and of such a length that it’s whole shadow may fall within the innermost Circle for at least four hours in the middle of the day. The pin ought to be about an eighth part of an inch thick, with a round blunt point. The board being set exactly level in a place where the Sun shines, suppose from eight in the morning till four in the afternoon, about which hours the end of the shadow should fall without all the Circles; watch the times in the forenoon, when the extremity of the shortening shadow just touches the several Circles, and there make marks. Then, in the afternoon of the same day, watch the lengthening shadow, and where it’s end touches the several Circles in going over them, make marks also. Lastly, with a pair of compasses, find exactly the middle point between the two marks on any Circle, and draw a straight line from the center to that point; which Line will be covered at noon by the shadow of a small upright wire, which should be put in the place of the pin. The reason for drawing several Circles is, that in case one part of the day should prove clear, and the other part somewhat cloudy, if you miss the time when the point of the shadow should touch one Circle, you may perhaps catch it in touching another. The best time for drawing a Meridian Line in this manner is about the middle of summer; because the Sun changes his Declination slowest and his Altitude fastest in the longest days.

If the casement of a window on which the Sun shines at noon be quite upright, you may draw a line along the edge of it’s shadow on the floor, when the shadow of the pin is exactly on the Meridian Line of the board: and as the motion of the shadow of the casement will be much more sensible on the Floor, than that of the shadow of the pin on the board, you may know to a few seconds when it touches the Meridian Line on the floor, and so regulate your clock for the day of observation by that line and the Equation Tables above-mentioned § 225.

227. As the Equation of time, or difference between the time shewn by a well regulated Clock and a true Sun-dial, depends upon two causes, namely, the obliquity of the Ecliptic, and the unequal motion of the Earth in it, we shall first explain the effects of these causes separately considered, and then the united effects resulting from their combination.

99228. The Earth’s motion on it’s Axis being perfectly equable, or always at the same rate, and the ^[55]plane of the Equator being perpendicular to it’s Axis, ’tis evident that in equal times equal portions of the Equator pass over the Meridian; and so would equal portions of the Ecliptic if it were parallel to or coincident with the Equator. But, as the Ecliptic is oblique to the Equator, the equable motion of the Earth carries unequal portions of the Ecliptic over the Meridian in equal times, the difference being proportionate to the obliquity; and as some parts of the Ecliptic are much more oblique than others, those differences are unequal among themselves. Therefore, if two Suns should start either from the beginning of Aries or Libra, and continue to move through equal arcs in equal times, one in the Equator, and the other in the Ecliptic, the equatoreal Sun would always return to the Meridian in 24 hours time, as measured by a well regulated clock; but the Sun in the Ecliptic would return to the Meridian sometimes sooner, and sometimes later than the equatoreal Sun; and only at the same moments with him on four days of the year; namely, the 20th of March, when the Sun enters Aries; the 21st of June, when he enters Cancer; the 23d of September, when he enters Libra; and the 21st of December, when he enters Capricorn. But, as there is only one Sun, and his apparent motion is always in the Ecliptic, let us henceforth call him the real Sun, and the other which is supposed to move in the Equator the fictitious; to which last, the motion of a well regulated clock always answers.

Let Z♈z♎ be the Earth, ZFRz it’s Axis, abcde &c. the Equator, ABCDE &c. the northern half of the Ecliptic from ♈ to ♎ on the side of the Globe next the eye, and MNOP &c. the southern half on the opposite side from ♎ to ♈. Let the points at A, B, C, D, E, F, &c. quite round from ♈ to ♈ again bound equal portions of the Ecliptic, gone through in equal times by the real Sun; and those at a, b, c, d, e, f, &c. equal portions of the Equator described in equal times by the fictitious Sun; and let Z♈z be the Meridian.

As the real Sun moves obliquely in the Ecliptic, and the fictitious Sun directly in the Equator, with respect to the Meridian, a degree, or any number of degrees, between ♈ and F on the Ecliptic, must 100be nearer the Meridian Z♈z, than a degree, or any corresponding number of degrees on the Equator from ♈ to f; and the more so, as they are the more oblique: and therefore the true Sun comes sooner to the Meridian whilst he is in the quadrant ♈ F, than the fictitious Sun does in the quadrant ♈ f; for which reason, the solar noon precedes noon by the Clock, until the real Sun comes to F, and the fictitious to f; which two points, being equidistant from the Meridian, both Suns will come to it precisely at noon by the Clock.

Whilst the real Sun describes the second quadrant of the Ecliptic FGHIKL from ♋ to ♎; he comes later to the Meridian every day, than the fictitious Sun moving through the second quadrant of the Equator from f to ♎; for the points at G, H, I, K, and L being farther from the Meridian than their corresponding points at g, h, i, k, and l, they must be later of coming to it: and as both Suns come at the same moment to the point ♎, they come to the Meridian at the moment of noon by the Clock.

In departing from Libra, through the third quadrant, the real Sun going through MNOPQ towards ♑ at R, and the fictitious Sun through mnopq towards r, the former comes to the Meridian every day sooner than the latter, until the real Sun comes to ♑, and the fictitious to r, and then they both come to the Meridian at the same time.

Lastly, as the real Sun moves equably through STUVW, from ♑ towards ♈; and the fictitious Sun through stuvw, from r towards ♈, the former comes later every day to the Meridian than the latter, until they both arrive at the point ♈, and then they make noon at the same time with the clock.

229. The annexed Table shews how much the Sun is faster or slower than the clock ought to be, so far as the difference depends upon the obliquity of the Ecliptic; of which the Signs of the first and third quadrants are at the head of the Table, and their Degrees at the left hand; and in these the Sun is faster than the Clock: the Signs of the second and fourth quadrants are at the foot of the Table, and their degrees at the right hand; in all which the Sun is slower than the Clock: so that entering the Table with the given Sign of the Sun’s place at the head of the Table, and the Degree of his place in that Sign at the left hand; or with the given Sign at the foot of the Table, and Degree at the right hand; in the Angle of meeting is the number of minutes and seconds that the Sun is faster or slower than the clock: or in other words, the quantity of time in which the real Sun, when in that 101part of the Ecliptic, comes sooner or later to the Meridian than the fictitious Sun in the Equator. Thus, when the Sun’s place is ♉ Taurus 12 degrees, he is 9 minutes 49 seconds faster than the clock; and when his place is ♋ Cancer 18 degrees, he is 6 minutes 2 seconds slower.

230. This part of the Equation of time may perhaps be somewhat difficult to understand by a Figure, because both halves of the Ecliptic seem to be on the same side of the Globe; but it may be made very easy to any person who has a real Globe before him, by putting small patches on every tenth or fifteenth degree both of the Equator and Ecliptic; and then, turning the ball slowly round westward, he will see all the patches from Aries to Cancer come to the brazen Meridian sooner than the corresponding patches on the Equator; all those from Cancer to Libra will come later to the Meridian than their corresponding patches on the Equator; those from Libra to Capricorn sooner, and those from Capricorn to Aries later: and the patches at the beginnings of Aries, Cancer, Libra, and Capricorn, being also on the Equator, shew that the two Suns meet there, and come to the Meridian together.

231. Let us suppose that there are two little balls moving equably round a celestial Globe by clock-work, one always keeping in the Ecliptic, and gilt with gold, to represent the real Sun; and the other keeping in the Equator, and silvered, to represent the fictitious Sun: and that whilst these balls move once, round the Globe according to the order of Signs, the Clock turns the Globe 366 times round it’s Axis westward. The Stars will make 366 diurnal revolutions from the brasen Meridian to it again; and the two balls representing the real and fictitious Sun always going farther eastward from any given Star, 102will come later than it to the Meridian every following day; and each ball will make 365 revolutions to the Meridian; coming equally to it at the beginnings of Aries, Cancer, Libra, and Capricorn: but in every other point of the Ecliptic, the gilt ball will come either sooner or later to the Meridian than the silvered ball, like the patches above-mentioned. This would be a pretty-enough way of shewing the reason why any given Star, which, on a certain day of the year, comes to the Meridian with the Sun, passes over it so much sooner every following day, as on that day twelvemonth to come to the Meridian with the Sun again; and also to shew the reason why the real Sun comes to the Meridian sometimes sooner, sometimes later, than it is noon by the clock; and, on four days of the year, at the same time; whilst the fictitious Sun always comes to the Meridian when it is twelve at noon by the clock. This would be no difficult task for an artist to perform; for the gold ball might be carried round the Ecliptic by a wire from it’s north Pole, and the silver ball round the Equator by a wire from it’s south Pole, with a few wheels to each; which might be easily added to my improvement of the celestial Globe, described in N^o 483 of the Philosophical Transactions; and of which I shall give a description in the latter part of this Book, from the 3d Figure of the 3d plate.

232. ’Tis plain that if the Ecliptic were more obliquely posited to the Equator, as the dotted Circle ♈x♎, the equal divisions from ♈ to x would come still sooner to the Meridian Z0♈ than those marked A, B, C, D, and E do: for two divisions containing 30 degrees, from ♈ to the second dott, a little short of the figure 1, come sooner to the Meridian than one division containing only 15 degrees from ♈ to A does, as the Ecliptic now stands; and those of the second quadrant from x to ♎ would be so much later. The third quadrant would be as the first, and the fourth as the second. And it is likewise plain, that where the Ecliptic is most oblique, namely about Aries and Libra, the difference would be greatest: and least about Cancer and Capricorn, where the obliquity is least.

234. Having explained one cause of the difference of time shewn by a well-regulated Clock and a true Sun-dial; and considered the Sun, not the Earth, as moving in the Ecliptic; we now proceed to explain the other cause of this difference, namely, the inequality of the Sun’s apparent motion § 205, which is slowest in summer, when the Sun is farthest from the Earth, and swiftest in winter when he is nearest to it. But the Earth’s motion on it’s Axis is equable all the year round, 103and is performed from west to east; which is the way that the Sun appears to change his place in the Ecliptic.

235. If the Sun’s motion were equable in the Ecliptic, the whole difference between the equal time as shewn by a Clock, and the unequal time as shewn by the Sun, would arise from the obliquity of the Ecliptic. But the Sun’s motion sometimes exceeds a degree in 24 hours, though generally it is less: and when his motion is slowest any particular Meridian will revolve sooner to him than when his motion is quickest; for it will overtake him in less time when he advances a less space than when he moves through a larger.

236. Now, if there were two Suns moving in the plane of the Ecliptic, so as to go round it in a year; the one describing an equal arc every 24 hours, and the other describing sometimes a less arc in 24 hours, and at other times a larger; gaining at one time of the year what it lost at the opposite; ’tis evident that either of these Suns would come sooner or later to the Meridian than the other as it happened to be behind or before the other: and when they were both in conjunction they would come to the Meridian at the same moment.

237. As the real Sun moves unequably in the Ecliptic, let us suppose a fictitious Sun to move equably in it. Let ABCD be the Ecliptic or Orbit in which the real Sun moves, and the dotted Circle abcd the imaginary Orbit of the fictitious Sun; each going round in a year according to the order of letters, or from west to east. Let HIKL be the Earth turning round it’s Axis the same way every 24 hours; and suppose both Suns to start from A and a, in a right line with the plane of the Meridian EH, at the same moment: the real Sun at A, being then at his greatest distance from the Earth, at which time his motion is slowest; and the fictitious Sun at a, whose motion is always equable because his distance from the Earth is supposed to be always the same. In the time that the Meridian revolves from H to H again, according to the order of the letters HIKL, the real Sun has moved from A to F; and the fictitious with a quicker motion from a to f, through a larger arc: therefore, the Meridian EH will revolve sooner from H to h under the real Sun at F, than from H to k under the fictitious Sun at f; and consequently it will be noon by the Sun-dial sooner than by the Clock.

As the real Sun moves from A towards C, the swiftness of his motion increases all the way to C, where it is at the quickest. But notwithstanding this, the fictitious Sun gains so much upon the real, soon after his departing from A, that the increasing velocity of the real Sun does not bring him up with the equally moving fictitious Sun till 104the former comes to C, and the latter to c, when each has gone half round it’s respective orbit; and then being in conjunction, the Meridian EH revolving to EK comes to both Suns at the same time, and therefore it is noon by them both at the same moment.

But the increased velocity of the real Sun, now being at the quickest, carries him before the fictitious; and therefore, the same Meridian will come to the fictitious Sun sooner than to the real: for whilst the fictitious Sun moves from c to g, the real Sun moves through a greater arc from C to G: consequently the point K has it’s fictitious noon when it comes to k, but not it’s real noon till it comes to l. And although the velocity of the real Sun diminishes all the way from C to A, and the fictitious Sun by an equable motion is still coming nearer to the real Sun, yet they are not in conjunction till the one comes to A and the other to a; and then it is noon by them both at the same moment.

And thus it appears, that the real noon by the Sun is always later than the fictitious noon by the clock whilst the Sun goes from C to A, sooner whilst he goes from A to C, and at these two points the Sun and Clock being equal, it is noon by them both at the same moment.

238. The point A is called the Sun’s Apogee, because when he is there he is at his greatest distance from the Earth; the point C his Perigee, because when in it he is at his least distance from the Earth: and a right line, as AEC, drawn through the Earth’s center, from one of these points to the other, is called the line of the Apsides.

239. The distance that the Sun has gone in any time from his Apogee (not the distance he has to go to it though ever so little) is called his mean Anomaly, and is reckoned in Signs and Degrees, allowing 30 Degrees to a Sign. Thus, when the Sun has gone suppose 174 degrees from his Apogee at A, he is said to be 5 Signs 24 Degrees from it, which is his mean Anomaly: and when he is gone suppose 355 degrees from his Apogee, he is said to be 11 Signs 25 Degrees from it, although he be but 5 Degrees short of A in coming round to it again.

240. From what was said above it appears, that when the Sun’s Anomaly is less than 6 Signs, that is, when he is any where between A and C, in the half ABC of his orbit, the true noon precedes the fictitious; but when his Anomaly is more than 6 Signs, that is, when he is any where between C and A, in the half CDA of his Orbit, the fictitious noon precedes the true. When his Anomaly is 0 Signs 0 Degrees, that is, when he is in his Apogee at A; or 6 Signs 0 Degrees, which is when he is in his Perigee at C; he comes to the 105Meridian at the moment that the fictitious Sun does, and then it is noon by them both at the same instant.

241. The annexed Table shews the Variation, or Equation of time depending on the Sun’s Anomaly, and arising from his unequal motion in the Ecliptic; as the former Table § 229 shews the Variation depending on the Sun’s place, and resulting from the obliquity of the Ecliptic: this is to be understood the same way as the other, namely, that when the Signs are at the head of the Table, the Degrees are at the left hand; but when the Signs are at the foot of the Table the respective Degrees are at the right hand; and in both cases the Equation is in the Angle of meeting. When both the above-mentioned Equations are either faster or slower, their sum is the absolute Equation of Time; but when the one is faster, and the other slower, it is their difference. Thus, suppose the Equation depending on the Sun’s place, be 6 minutes 41 seconds too slow, and the Equation depending on the Sun’s Anomaly, be 4 minutes 20 seconds too slow, their Sun is 11 minutes 1 second too slow. But if the one had been 6 minutes 41 seconds too fast, and the other 4 minutes 20 seconds too slow, their difference had been 2 minutes 21 seconds too fast, because the greater quantity is too fast.

106242. The obliquity of the Ecliptic to the Equator, which is the first mentioned cause of the Equation of Time, would make the Sun and Clocks agree on four days of the year; which are, when the Sun enters Aries, Cancer, Libra, and Capricorn: but the other cause, now explained, would make the Sun and Clocks equal only twice in a year; that is, when the Sun is in his Apogee and Perigee. Consequently, when these two points fall in the beginnings of Cancer and Capricorn, or of Aries and Libra, they concur in making the Sun and Clocks equal in these points. But the Apogee at present is in the 9th degree of Cancer, and the Perigee in the 9th degree of Capricorn; and therefore the Sun and Clocks cannot be equal about the beginning of these Signs, nor at any time of the year, except when the swiftness or slowness of Equation resulting from one cause just balances the slowness or swiftness arising from the other.

243. The last Table but one, at the end of this Chapter, shews the Sun’s place in the Ecliptic at the noon of every day by the clock, for the second year after leap-year; and also the Sun’s Anomaly to the nearest degree, neglecting the odd minutes of a degree. Their use is only to assist in shewing the method of making a general Equation Table from the two fore-mentioned Tables of Equation depending on the Sun’s Place and Anomaly § 229, 241; concerning which method we shall give a few examples presently. The following Tables are such as might be made from these two; and shew the absolute Equation of Time resulting from the combination of both it’s causes; in which the minutes, as well as degrees, both of the Sun’s Place and Anomaly are considered. The use of these Tables is already explained, § 225; and they serve for every day in leap-year, and the first, second, and third years after: For on most of the same days of all these years the Equation differs, because of the odd six hours more than the 365 days of which the year consists.

Example I. On the 15th of April the Sun is in the 25th degree of ♈ Aries, and his Anomaly is 9 Signs 15 Degrees; the Equation resulting from the former is 7 minutes 23 seconds of time too fast § 229; and from the latter, 7 minutes 27 seconds too slow, § 241; the difference is 4 seconds that the Sun is too slow at the noon of that day; taking it in gross for the degrees of the Sun’s Place and Anomaly, without making proportionable allowance for the odd minutes. Hence, at noon the swiftness of the one Equation balancing so nearly the slowness of the other, makes the Sun and Clocks equal on some part of that day.

107Example II. On the 16th of June, the Sun is in the 25th degree of ♊ Gemini, and his Anomaly is 11 Signs 16 Degrees; the Equation arising from the former is 1 minute 48 seconds too fast; and from the latter 1 minute 50 seconds too slow; which balancing one another at noon to 2 seconds, the Sun and Clocks are again equal on that day.

Example III. On the 31st of August the Sun’s place is 7 degrees 52 minutes of ♍ Virgo (which we shall call the 8th degree, as it is so near) and his Anomaly is 2 Signs 0 Degrees; the Equation arising from the former is 6 minutes 41 seconds too slow; and from the latter 6 minutes 39 seconds too fast; the difference being only 2 seconds too slow at noon, and decreasing towards an equality will make the Sun and Clocks equal in the afternoon of that day.

Example. IV. On the 23d of December the Sun’s place is 1 degree 41 minutes (call it 2 degrees) of ♑ Capricorn, and his Anomaly is 5 Signs 23 Degrees; the Equation for the former is 43 seconds too slow, and for the latter 58 seconds too fast; the difference is 15 seconds too fast at noon; which decreasing will come to an equality, and so make the Sun and Clocks equal in the evening of that day.

And thus we find, that on some part of each of the above-mentioned four days, the Sun and Clocks are equal; but if we work examples for all other days of the year we shall find them different. And,

244. On those days which are equidistant from any Equinox or Solstice, we do not find that the Equation is as much too fast or too slow, on the one side, as it is too slow or too fast on the other. The reason is, that the line of the Apsides § 238, does not, at present, fall either into the Equinoctial or Solsticial points § 242.

245. If the line of the Apsides, together with the Equinoctial and Solsticial points, were immoveable, a general Equation Table might be made from the preceding Equation Tables, which would always keep true, because these Tables themselves are permanent. But, with respect to the fixed Stars, the line of the Apsides moves forwards 12 seconds of a degree every year, and the above points 50 seconds backward. So that if in any given year, the Equinoctial points, and line of the Apsides were coincident, in 100 years afterward they would be separated 1 degree 43 minutes 20 seconds; and consequently 108in 5225.8 years they would be separated 90 degrees, and could not meet again, so that the same Equinoctial point should fall again into the Apogee in less than 20,903 years: and this is the shortest Period in which the Equation of Time can be restored to the same state again, with respect to the same seasons of the year.

246. It has been already observed, § 116, that by the Earth’s motion on it’s Axis, there is more matter accumulated all round the equatoreal parts than any where else on the Earth.

The Sun and Moon, by attracting this redundancy of matter, bring the Equator sooner under them in every return towards it than if there was no such accumulation. Therefore, if the Sun sets out, as from any Star, or other fixed point in the Heavens, the moment he is departing from the Equinoctial or either Tropic, he will come to the same again before he compleats his annual course, so as to arrive at the same fixed Star or Point from whence he set out.

When the Sun arrives at the same ^[56]Equinoctial or Solstitial Point, he finishes what we call the Tropical Year, which, by long observation, is found to contain 365 days 5 hours 48 minutes 57 seconds: and when he arrives at the same fixed Star again, as seen from the Earth, he compleats the Sidereal Year; which is found to contain 365 days 6 hours 9 minutes 14¹⁄₂ seconds. The Sidereal Year is therefore 20 minutes 17¹⁄₂ seconds longer than the Solar or Tropical year, and 9 minutes 14¹⁄₂ seconds longer than the Julian or Civil year, which we state at 365 days 6 hours: so that the Civil year is almost a mean betwixt the Sidereal and Tropical.

247. As the Sun describes the whole Ecliptic, or 360 degrees, in a Tropical year, he moves 59ʹ 8ʺ of a degree every day; and consequently 50ʺ of a degree in 20 minutes 17¹⁄₂ seconds of time: therefore, he will arrive at the same Equinox or Solstice when he is 50ʺ of a degree short of the same Star or fixed point in the Heavens from which he set out in the year before. So that, with respect to the fixed Stars, 109the Sun and Equinoctial points fall back (as it were) 30 degrees in 2160 years; which will make the Stars appear to have gone 30 deg. forward, with respect to the Signs of the Ecliptic in that time: for the same Signs always keep in the same points of the Ecliptic, without regard to the constellations.

To explain this by a Figure, let the Sun be in conjunction with a fixed Star at S, suppose in the 30th degree of ♉, on the 20th day of May 1756. Then, making 2160 revolutions through the Ecliptic VWX, at the end of so many Sidereal years, he will be found again at S: but at the end of so many Julian years, he will be found at M, short of S: and at the end of so many Tropical years, he will be found short of M, in the 30th deg. of Taurus 110at T, which has receded back from S to T in that time, by the Precession of the Equinoctial points ♈ Aries and ♎ Libra. The Arc ST will be equal to the amount of the Precession of the Equinox in 2160 years, at the rate of 50ʺ of a degree, or 20 min. 17¹⁄₂ sec. of time, annually: this, in so many years, makes 30 days, 10¹⁄₂ hours; which is the difference between 2160 Sidereal and Tropical years: And the Arc MT will be equal to the space moved through by the Sun in 2160 times 11 min. 3 sec. or 16 days, 13 hours 48 minutes, which is the difference between 2160 Julian and Tropical years.

248. From the shifting of the Equinoctial points, and with them all the Signs of the Ecliptic, it follows that those Stars which in the infancy of astronomy were in Aries are now got into Taurus; those of Taurus into Gemini, &c. Hence likewise it is, that the Stars which rose or set at any particular season of the year, in the time of Hesiod, Eudoxus, Virgil, Pliny, &c. by no means answer at this time to their descriptions. The preceding table shews the quantity of this shifting both in the heavens and on the earth, for any number of years to 25,920; which compleats the grand celestial period: within which any number and its quantity is easily found; as in the following example, for 5763 years; which at the Autumnal Equinox, A. D. 1756, is thought to be the age of the world. So that with regard to the fixed Stars, the Equinoctial points in the heavens, have receded 2^s 20° 2ʹ 30ʺ since the creation; which is as much as the Sun moves in 81^d 5^h 0^m 52^s. And since that time, or in 5763 years, the Equinoxes with us have fallen back 44^d 5^h 21^m 9^s; hence, reckoning from the time of the Julian Equinox, A. D. 1756, viz. Sept. 12th, it appears that the Autumnal Equinox at the creation was on the 26th of October.

249. The anticipation of the Equinoxes, and consequently of the seasons, is by no means owing to the Precession of the Equinoctial and Solsticial points in the Heavens, (which can only affect the apparent motions, places and declinations of the fixed Stars) but to the difference between the Civil and Solar year, which is 11 minutes 3 seconds; 111the Civil year containing 365 days 6 hours, and the Solar year 365 days 5 hours 48 minutes 57 seconds. The following table shews the length, and consequently the difference of any number of Sidereal, Civil, and Solar years from 1 to 10,000.

250. The above 11 minutes 3 seconds, by which the Civil or Julian year exceeds the Solar, amounts to 11 days in 1433 years: and so much our seasons have fallen back with respect to the days of the months, since the time of the Nicene Council in A.D. 325, and therefore in order to bring back all the Fasts and Festivals to the days then settled, it was requisite to suppress 11 nominal days. And that the same seasons might be kept to the same times of the year for the future, to leave out the Bissextile day in February at the end of every century of years not divisible by 4; reckoning them only common years, as the 17th, 18th and 19th centuries, viz. the years 1700, 1800, 1900, &c. because a day intercalated every fourth year was too much, and retaining the Bissextile-day at the end of those Centuries of years which are divisible by 4, as the 16th, 20th and 24th Centuries; viz. the years 1600, 2000, 2400, &c. Otherwise, in length of time the seasons would have been quite reversed with regard to the months of the years; though it would have required near 23,783 years to have brought about such a total change. If the Earth had made exactly 365¹⁄₄ diurnal rotations on its axis, whilst it revolved from any Equinoctial or Solstitial point to the same again, the Civil and Solar years would always have kept pace together; and the style would never have needed any alteration.

251. Having already mentioned the cause of the Precession of the Equinoctial points in the heavens, § 246, which occasions a flow deviation of the earth’s axis from its parallelism, and thereby a change of the declination of the Stars from the Equator, together with a slow apparent motion of the Stars forward with respect to the Signs of the Ecliptic; we shall now describe the Phenomena by a Diagram.

Let NZSVL be the Earth, SONA its Axis produced to the starry Heavens, and terminating in A, the present north Pole of the Heavens, which is vertical to N the north Pole of the Earth. Let EOQ be the Equator, T♋Z the Tropic of Cancer, and VT♑ the Tropic of Capricorn: VOZ the Ecliptic, and BO its Axis, both which are immoveable among the Stars. But, as ^[57]the Equinoctial points recede 112in the Ecliptic, the Earth’s Axis SON is in motion upon the Earth’s center O, in such a manner as to describe the double Cone NOn and SOs, round the Axis of the Ecliptic BO, in the time that the Equinoctial points move quite round the Ecliptic, which is 25,920 years; and in that length of time, the north Pole of the Earth’s Axis produced, describes the Circle ABCDA in the starry Heavens, round the Pole of the Ecliptic, which keeps immoveable in the center of that Circle. The Earth’s Axis being 23¹⁄₂ degrees inclined to the Axis of the Ecliptic, the Circle ABCDA, described by the north Pole of the Earth’s Axis produced to A, is 47 degrees in diameter, or double the inclination of the Earth’s Axis. In consequence of this, the point A, which at present is the North Pole of the Heavens, and near to a Star of the second magnitude in the tail of the constellation called the Little Bear, must be deserted by the Earth’s Axis; which moving backwards a degree every 72 years, will be directed towards the Star or Point B in 6480 years hence: and in double of that time, or 12,960 years, it will be directed towards the Star or Point C; which will then be the North Pole of the Heavens, although it is at present 8¹⁄₂ degrees south of the Zenith of London L. The present position of the Equator EOQ will then be changed into eOq, the Tropic of Cancer T♋Z into Vt♋, and the Tropic of Capricorn VT♑ into t♑Z; as is evident by the Figure. And the Sun, in the same part of the Heavens where he is now over the earthly Tropic of Capricorn, and makes the shortest days and longest nights in the Northern Hemisphere, will then be over the earthly Tropic of Cancer, and make the days longest, and nights shortest. So that it will require 12,960 years yet more, or 25,920 from the present time, to bring the North Pole N quite round, so as to be directed toward that point of the Heavens which is vertical to it at present. And then, and not till then, the same Stars which at present describe the Equator, Tropics, polar Circles, and Poles, by the Earth’s diurnal motion, will describe them over again.