Chapter III: Part 3

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 it treated of at large by Drs. SMITH[19], LONG[20], DESAGULIERS[21], RUTHERFURTH, Mr. MACLAURIN[22], and M. DE LA CAILLE[23].

[Sidenote: Why the Sun appears to change his place.]

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.

[Sidenote: The Earth’s motion on it’s Axis demonstrated.]

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 waters thither. The Earth’s equatoreal diameter is 35 miles longer than its Axis.

[Sidenote: All bodies heavier at the Poles than they would be at the
Equator.]

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 2-169/1000 lines shorter at the Equator than at the Poles. A line is a twelfth part of an inch.

[Sidenote: How they might lose all their weight.]

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.

[Sidenote: The Earth’s motion cannot be felt.]

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.

[Sidenote: To the different Planets the Heavens appear to turn round on
different Axes.]

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 lying 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 23-1/2 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.

[Sidenote: Objections against the Earth’s diurnal motion answered.]

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 meets 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.

CHAP. IV.

_The Phenomena of the Heavens as seen from different parts of the
Earth._

[Sidenote: We are kept to the Earth by gravity.

PLATE II. Fig. I.

Antipodes.

Axis of the World. It’s Poles. Fig. II.]

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 figure 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.

[Sidenote: How our Earth might have an upper and an under side.]

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.

[Sidenote: PLATE II.]

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; he 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.

[Sidenote: Fig. I.

One half of the Heavens visible to an inhabitant on any part
of the Earth.

Phenomena at the Poles.

PLATE II.]

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 South 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 23-1/2 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.

[Sidenote: Phenomena at the Equator.

Fig. I.]

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_.

[Sidenote: Remark.]

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 straight 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].

[Sidenote: Phenomena between the Equator and Poles.

The Circles of perpetual Apparition and Occultation.]

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.

[Sidenote: PLATE II.]

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 toward 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.

[Sidenote: Why the Stars always describe the same parallel of motion,
and the Sun a different.]

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.

[Sidenote: Fig. I.

Parallel, Oblique, and Right sphere, what.]

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, by 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.

CHAP. V.

_The Phenomena of the Heavens as seen from different Parts of the Solar
System._

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 the 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.

[Sidenote: The Sun’s center the only point from which the true motions
and places of the Planets could be seen.]

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 days: 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.

[Sidenote: The judgment that a solar Astronomer would probably make
concerning the distances and bulks of the Planets.]

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.

[Sidenote: The Planetary motions very irregular as seen from the Earth.

PLATE III.]

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 loss 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.

[Sidenote: Those of Mercury and Venus represented.

Fig. I.]

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.

[Sidenote: PLATE III.]

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 Ecliptic 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.

[Sidenote: Fig. I.]

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 11-1/2 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 11-1/2 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.

CHAP. VI.

_The_ Ptolemean _System refuted. The Motions and Phases of Mercury and
Venus explained._

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.

[Sidenote: Appearances of Mercury and Venus.]

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.

[Sidenote: Experiment to prove they are round.]

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.

[Sidenote: PLATE II.

Experiment to represent the motions of Mercury and Venus.]

142. 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.

[Sidenote: Fig. III.

The elongations or digressions of Mercury from the Sun.

PLATE II.]

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 when 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.

[Sidenote: Fig. III.

The Elongations and Phases of Venus.

The greatest Elongations of Mercury and Venus.]

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.

[Sidenote: Morning and Evening Star, what.]

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.

[Sidenote: PLATE II.

The stationary places of the Planets variable.]

146. 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.

[Sidenote: The Elongations of all Saturn’s inferiour Planets as seen
from him.]