Part 6

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.