Part 10

31,742,200 59,313,060 82,000,000 124,942,580 426,478,720 782,284,920

_But if the Sun’s Parallax be 11ʺ their distances are no more than_

29,032,500 54,238,570 75,000,000 114,276,750 390,034,500 715,504,500

Errors in distance a rising from the mistake of 1ʺ in the Sun’s Parallax

2,709,700 5,074,490 7,000,000 10,665,830 36,444,220 66,780,420

195. 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.

[Sidenote: Why the celestial Poles seem to keep still in the same points of the Heavens, notwithstanding the Earth’s motion round the Sun.]

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.

[Sidenote: The amazing velocity of light.

PLATE IV.]

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 great 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.

CHAP. X.

_The Circles of the Globe described. The different lengths of days and nights, and the vicissitudes of seasons, explained. The explanation of the Phenomena of Saturn’s Ring concluded._ (See § 81 and 82.)

[Sidenote: Circles of the Sphere.

Fig. II

Equator, Tropics, Polar Circles, and Poles.

Fig. II.

Earth’s Axis.

PLATE IV.

Meridians.]

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 23-1/2 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_, or 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.

[Sidenote: Zones.]

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.

[Sidenote: Fig. III.

A pleasant experiment shewing the different lengths of days and nights, and the variety of seasons.

Summer Solstice.]

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 you 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.

[Sidenote: PLATE IV.

Autumnal Equinox.]

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 days 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.

[Sidenote: Winter Solstice.]

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.

[Sidenote: Vernal Equinox.]

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.

[Sidenote: Remark.

Fig. III.

PLATE V.]

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 [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 23-1/2 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.

[Sidenote: Fig. I.

A concise view of the seasons.]

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.

[Sidenote: Fig. II.

PLATE V.

The Ecliptic.

The seasons shewn in another view of the Earth, and it’s Orbit.]

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 view 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.

[Sidenote: Vernal Equinox.]

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.

[Sidenote: Fig. II.]

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.

[Sidenote: Summer Solstice.]

When 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.

[Sidenote: Autumnal Equinox.

Winter Solstice.]

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 23-1/2 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.

[Sidenote: The Phenomena of Saturn’s Ring.

PLATE V.]

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 which 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.

[Sidenote: Fig. III.]