Part 11

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

[Sidenote: Fig. I and III.]

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

[Sidenote: PLATE VI.

The Earth nearer the Sun in winter than in summer.

Why the weather is coldest when the Earth is nearest the Sun.]

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

[Sidenote: Fig. II.]

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

CHAP. XI.

_The Method of finding the Longitude by the Eclipses of Jupiter’s Satellites: The amazing Velocity of Light demonstrated by these Eclipses._

[Sidenote: First Meridian, and Longitude of places, what.]

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

[Sidenote: PLATE V.

Fig. II.

Hour Circles.

An hour of time equal to 15 degrees of motion.]

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

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

[Sidenote: And consequently to 15 degrees of Longitude.

Lunar Eclipses useful in finding the Longitude.]

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

[Sidenote: Eclipses of Jupiter’s Satellites much better for that purpose.]

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

[Sidenote: How to solve this important problem.

PLATE V.]

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

[Sidenote: Fig. II.

Illustrated by an example.]

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

[Sidenote: Fig. II.

We seldom see the beginning and end of the same Eclipse of any of Jupiter’s Moons.]

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

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

[Sidenote: PLATE VI.

Jupiter’s conjunctions with the Sun, or oppositions to him, are every year in different parts of the Heavens.]

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

[Sidenote: The surprising velocity of light.]

216. It is found by observation, that when the Earth is between the Sun and Jupiter, as at _g_, his Satellites are eclipsed about 8 minutes sooner than they should be according to the Tables: and when the Earth is at _B_ or _C_, these Eclipses happen about 8 minutes later than the Tables predict them. Hence it is undeniably certain, that the motion of light is not instantaneous, since it takes about 16-1/2 minutes of time to go through a space equal to the diameter of the Earth’s Orbit, which is 162 millions of miles in length: and consequently the particles of light fly about 164 thousand 494 miles every second of time, which is above a million of times swifter than the motion of a cannon bullet. And as light is 16-1/2 minutes in travelling across the Earth’s Orbit, it must be 8-1/4 minutes in coming from the Sun to us: therefore, if the Sun were annihilated we should see him for 8-1/4 minutes after; and if he were again created he would be 8-1/4 minutes old before we could see him.

[Sidenote: Fig. V.

Illustrated by a Figure.]

217. To illustrate this progressive motion of light, let _A_ and _B_ be the Earth in two different parts of it’s Orbit, whose distance is 81 millions of miles, equal to the Earth’s distance from the Sun _S_. It is plain, that if the motion of light were instantaneous, the Satellite 1 would appear to enter into Jupiter’s shadow _FF_ at the same moment of time to a spectator in _A_ as to another in _B_. But by many years observations it has been found, that the immersion of the Satellite into the shadow is seen 8-1/4 minutes sooner when the Earth is at _B_, than when it is at _A_. And so, as Mr. ROMER first discovered, the motion of light is thereby proved to be progressive, and not instantaneous, as was formerly believed. It is easy to compute in what time the Earth moves from _A_ to _B_; for the chord of 60 degrees of any Circle is equal to the Semidiameter of that Circle; and as the Earth goes through all the 360 degrees of it’s Orbit in a year, it goes through 60 of those degrees in about 61 days. Therefore, if on any given day, suppose the first of _June_, the Earth is at _A_, on the first of _August_ it will be at _B_: the chord, or straight line _AB_, being equal to _DS_ the Radius of the Earth’s Orbit, the same with _AS_ it’s distance from the Sun.

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

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

220. TABLES for converting mean solar TIME into Degrees and Parts of the terrestrial EQUATOR; and also for converting Degrees and Parts of the EQUATOR into mean solar Time.

+---------------------------------------------+ | TABLE I. For converting Time into | | Degrees and Parts of the Equator. | +-----+-------+-----+---------+-----+---------+ | | | *M. | D. M. | *M. | D. M. | |Hours|Degrees| S. | M. S. | S. | M. S. | | | | T. | S. T. | T. | S. T. | +-----+-------+-----+---------+-----+---------+ | 1 | 15 | 1 | 0 15 | 31 | 7 45 | | 2 | 30 | 2 | 0 30 | 32 | 8 0 | | 3 | 45 | 3 | 0 45 | 33 | 8 15 | | 4 | 60 | 4 | 1 0 | 34 | 8 30 | | 5 | 75 | 5 | 1 15 | 35 | 8 45 | +-----+-------+-----+---------+-----+---------+ | 6 | 90 | 6 | 1 30 | 36 | 9 0 | | 7 | 105 | 7 | 1 45 | 37 | 9 15 | | 8 | 120 | 8 | 2 0 | 38 | 9 30 | | 9 | 135 | 9 | 2 15 | 39 | 9 45 | | 10 | 150 | 10 | 2 30 | 40 | 10 0 | +-----+-------+-----+---------+-----+---------+ | 11 | 165 | 11 | 2 45 | 41 | 10 15 | | 12 | 180 | 12 | 3 0 | 42 | 10 30 | | 13 | 195 | 13 | 3 15 | 43 | 10 45 | | 14 | 210 | 14 | 3 30 | 44 | 11 0 | | 15 | 225 | 15 | 3 45 | 45 | 11 15 | +-----+-------+-----+---------+-----+---------+ | 16 | 240 | 16 | 4 0 | 46 | 11 30 | | 17 | 255 | 17 | 4 15 | 47 | 11 45 | | 18 | 270 | 18 | 4 30 | 48 | 12 0 | | 19 | 285 | 19 | 4 45 | 49 | 12 15 | | 20 | 300 | 20 | 5 0 | 50 | 12 30 | +-----+-------+-----+---------+-----+---------+ | 21 | 315 | 21 | 5 15 | 51 | 12 45 | | 22 | 330 | 22 | 5 30 | 52 | 13 0 | | 23 | 345 | 23 | 5 45 | 53 | 13 15 | | 24 | 360 | 24 | 6 0 | 54 | 13 30 | | 25 | 375 | 25 | 6 15 | 55 | 13 45 | +-----+-------+-----+---------+-----+---------+ | 26 | 390 | 26 | 6 30 | 56 | 14 0 | | 27 | 405 | 27 | 6 45 | 57 | 14 15 | | 28 | 420 | 28 | 7 0 | 58 | 14 30 | | 29 | 435 | 29 | 7 15 | 59 | 14 45 | | 30 | 450 | 30 | 7 30 | 60 | 15 0 | +-----+-------+-----+---------+-----+---------+

+---------------------------------------------------+ | TABLE II. For converting Degrees and | | Parts of the Equator into Time. | +-----+--------+-----+--------+-------+-----+-------+ | *D. | H. M. | *D. | H. M. | | | | | M. | M. S. | M. | M. S. |Degrees|Hours|Minutes| | S. | S. T. | S. | S. T. | | | | +-----+--------+-----+--------+-------+-----+-------+ | 1 | 0 4 | 31 | 2 4 | 70 | 4 | 40 | | 2 | 0 8 | 32 | 2 8 | 80 | 5 | 20 | | 3 | 0 12 | 33 | 2 12 | 90 | 6 | 0 | | 4 | 0 16 | 34 | 2 16 | 100 | 6 | 40 | | 5 | 0 20 | 35 | 2 20 | 110 | 7 | 20 | +-----+--------+-----+--------+-------+-----+-------+ | 6 | 0 24 | 36 | 2 24 | 120 | 8 | 0 | | 7 | 0 28 | 37 | 2 28 | 130 | 8 | 40 | | 8 | 0 32 | 38 | 2 32 | 140 | 9 | 20 | | 9 | 0 36 | 39 | 2 36 | 150 | 10 | 0 | | 10 | 0 40 | 40 | 2 40 | 160 | 10 | 40 | +-----+--------+-----+--------+-------+-----+-------+ | 11 | 0 44 | 41 | 2 44 | 170 | 11 | 20 | | 12 | 0 48 | 42 | 2 48 | 180 | 12 | 0 | | 13 | 0 52 | 43 | 2 52 | 190 | 12 | 40 | | 14 | 0 56 | 44 | 2 56 | 200 | 13 | 20 | | 15 | 1 0 | 45 | 3 0 | 210 | 14 | 0 | +-----+--------+-----+--------+-------+-----+-------+ | 16 | 1 4 | 46 | 3 4 | 220 | 14 | 40 | | 17 | 1 8 | 47 | 3 8 | 230 | 15 | 20 | | 18 | 1 12 | 48 | 3 12 | 240 | 16 | 0 | | 19 | 1 16 | 49 | 3 16 | 250 | 16 | 40 | | 20 | 1 20 | 50 | 3 20 | 260 | 17 | 20 | +-----+--------+-----+--------+-------+-----+-------+ | 21 | 1 24 | 51 | 3 24 | 270 | 18 | 0 | | 22 | 1 28 | 52 | 3 28 | 280 | 18 | 40 | | 23 | 1 32 | 53 | 3 32 | 290 | 19 | 20 | | 24 | 1 36 | 54 | 3 36 | 300 | 20 | 0 | | 25 | 1 40 | 55 | 3 40 | 310 | 20 | 40 | +-----+--------+-----+--------+-------+-----+-------+ | 26 | 1 44 | 56 | 3 44 | 320 | 21 | 20 | | 27 | 1 48 | 57 | 3 48 | 330 | 22 | 0 | | 28 | 1 52 | 58 | 3 52 | 340 | 22 | 40 | | 29 | 1 56 | 59 | 3 56 | 350 | 23 | 20 | | 30 | 2 0 | 60 | 4 0 | 360 | 24 | 0 | +-----+--------+-----+--------+-------+-----+-------+

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

EXAMPLE I. | EXAMPLE II. | In 10 hours 15 minutes 24 | In what time will 153 degrees seconds 20 thirds, _Qu._ How | 51 minutes 5 seconds of the much of the Equator revolves | Equator revolve through the through the Meridian? | Meridian? | | Deg. M. S. | H. M. S. T. Hours 10 150 0 0 | Deg. { 150 10 0 0 0 Min. 15 3 45 0 | { 3 12 0 0 Sec. 24 6 0 | Min. 51 3 24 0 Thirds 20 5 | Sec. 5 20 ------------ | ------------ _Answer_ 153 51 5 | _Answer_ 10 15 24 20

CHAP. XII.

_Of Solar and Sidereal Time._

[Sidenote: Sidereal days shorter than solar days, and why.]