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

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.

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,

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.

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.

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.

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.

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.

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.

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 161⁄2 minutes of time to go through a space equal to the diameter of the Earth’s Orbit, which is 162 millions of miles in length: and consequently the particles of light fly about 164 thousand 494 miles every second of time, which is above a million of times swifter than the motion of a cannon bullet. And as light is 161⁄2 minutes in travelling across the Earth’s Orbit, it must be 81⁄4 minutes in coming from the Sun to us: therefore, if the Sun were annihilated we should see him for 81⁄4 minutes after; and if he were again created he would be 81⁄4 minutes old before we could see him.

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 81⁄4 minutes sooner when the Earth is at B, than when it is at A. And so, as Mr. Romer first discovered, the motion of light is thereby proved to be progressive, and not instantaneous, as was formerly believed. It is easy to compute in what time the Earth moves from A to B; for the chord of 60 degrees of any Circle is equal to the Semidiameter of that Circle; and as the Earth goes through all the 360 degrees of it’s Orbit in a year, it goes through 60 of those degrees in about 61 days. Therefore, if on any given 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.

Hours Degrees *Min. Deg. Min. *Min. Deg. Min.
Sec. Min. Sec. Sec. Min. Sec.
Thirds Sec. Thirds Thirds Sec. Thirds
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.
*Deg. Hours Min. *Deg. Hours Min. Degrees Hours Minutes
Min. Min. Sec. Min. Min. Sec.
Sec. Sec. Thirds Sec. Sec. Thirds
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.

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

  Deg. M. S.
Hours 10 150 0 0
Min. 15 3 45 0
Sec. 24   6 0
Thirds 20     5
Answer 153 51 5
EXAMPLE II.

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

  H. M. S. T.
Deg. 150 10 0 0 0
3   12 0 0
Min. 51   3 24 0
Sec. 5   20
Answer 10 15 24 20