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VI1.

ter's

(the card upon

inches. Then taking a small cord of this length,

and fixing one end of it to the floor of a long room How to by a nail, with a black-lead pencil at the other end delineate I drew the curve ABCD, &c. and set off a degree of Jupi. and a half thereon, from A to T'; because Jupiter

moves only so much, while his outermost satellite Moons,

goes once round him, and somewhat more: so that
this small portion of so large a circle differs but ve-
ry little from a straight line. This done I divided
the space A T into 18 equal parts, as A B, B C,
&c. for the daily progress of Jupiter; and each
part into 24 for his hourly progress. The orbit of
each satellite was also divided into as many equal
parts as the satellite is hours in finishing its synodi-
cal period round Jupiter. Then drawing a right
line through the centre of the card, as a diameter
to all the four orbits upon it, I put
the line of Jupiter's motion, and transferred it to ev-
ery horary division thereon, keeping always the
same diameter-line on the line of Jupiter's path; and
running a pin through each horary division in the
orbit of each satellite as the card was gradually trans-
ferred along the line ABCD, &c. of Jupiter's mo-
tion, I marked points for every hour through the
card for the curves described by the satellites, as
the primary planet in the centre of the card was car-
ried forward on the line; and so finished the figure,
by drawing the lines of each satellite's motion through
those (almost innumerable) points: by which means,
this is, perhaps, as true a figure of the paths of these
satellites as can be desired. And in the same man-

ner might those of Saturn's satellites be delineated. The grand 270. It appears by the scheme, that the three first periods of satellites come almost into the same line of position Jupiter's

every seventh day; the first being only a little behind with the second, and the second behind with the 3d. But the period of the 4th satellite is so incommensurate to the periods of the other three, that it cannot

and Sa. turn's.

moons.

VII.

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be guessed at by the diagram when it would fall Platz
again into a line of conjunction with them between
Jupiter and the Sun. And no wonder; for suppos-
ing them all to have been once in conjunction, it will
require 3,087,043,493,260 years to bring them in
conjunction again. See , 73.

271. In Fig. 4th, we have the proportions of the Fig. IV.
orbits of Saturn's five satellites, and of Jupiter's four, The pro-
to one another, to our Moon's orbit, and to the disc the orbits
of the Sun. S is the Sun; M m the Moon's orbit of the pla-
(the Earth supposed to be at E); J Jupiter ; 1. 2. satellites.
3.4, the orbits of his four moons or satellites; Sat.
Saturn; and 1. 2. 3. 4. 5, the orbits of his five
moons. Hence it appears, that the Sun would much
more than fill the whole orbit of the Moon; for the
Sun's diameter is 763,000 miles, and the diameter
of the Moon's orbit only 480,000. In proportion to
all these orbits of the satellites, the radius of Saturn's
annual orbit would be 211 yards, of Jupiter's orbit
llg, and of the Earth's 24, taking them in round
numbers.
272. The annexed table shews at once what

proportion the orbits, revolutions, and velocities of all the satellites bear to those of their primary planets, and what sort of curves the several satellites describe. For those satellites, whose velocities round their primaries are greater than the velocities of their primaries in open

space, make loops at their conjunctions, $ 269; appearing retrograde as seen from the Sun while they describe the inferior parts of their orbits, and direct while they describe the superior. This is the case with Jupiter's first and second satellites, and with Saturn's first. But those satellites, whose velo. cities are less than the velocities of their primary planets, move direct in their whole circumvolutions ; which is the case of the third and fourth satellites of Jupiter, and of the second, third, fourth, and fifth satellites of Saturn, as well as of our satellite the Moon: but the Moon is the only satellite whose motion is always concave to the Sun.

Gg

Satellites

The

Proportion of Proportion of Proportion of
the Radius of the Time of the Velocity of

the Planet'sOr- the Planet's each Satellite
bit to the Ra- Revolution to to the Velocity
dius of the Or- the Revolution of its primary
bit of each Sa- of each Satel. Planet.
Itellite. lite.

of Saturn

1 As 5322 to 1 As 5738 to 1 As 5738 to 5322

4155 1 3912 1 3912 4155
2954 1 2347 1 2347 2954
1295 1 674 1

674 1295
432
134

134

432

of Jupiter

As 1851 to 1/As 2445 to 1 As 2445 to 1851

1165 1 1219 1 1219 1165
731 1 604 1 604 731
424 1 258

258 424

The As 337 to 1 As 124 to 1 As 124 to 337

There is a table of this sort in De la Caille's Astronomy, but it is very different from the above, which I have computed from our English accounts of the periods and distances of these planets and satellites.

CHAP. XVI.

The Phenomena of the Harvest-Moon explained by

a common Globe. The Years in which the Har.
vest Moons are least and most beneficial from 1751
to 1861. The long Duration of Moon-light at the
Poles in Winter.

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273. TT

T is generally believed that the Moon rises No Har.

about 50 minutes later every day than on vest-moon the preceding : but this is true only with regard to places on the equator. In places of considerable latitude there is a remarkable difference, especially in the harvest time, with which farmers were better acquainted than astronomers, till of late ; and gratefully ascribed the early rising of the full moon at that time of the year to the goodness of God, not doubting that he had ordered it so on purpose to give them an immediate supply of moon-light after sun-set, for their greater conveniency in reaping the fruits of the Earth.

In this instance of the harvest-moon, as in many others discoverable by astronomy, the wisdom and beneficence of the Deity is conspicuous, who really ordered the course of the Moon so, as to bestow more or less light on all parts of the Earth as their several circumstances and seasons render it more or less serviceable. About the equator, where there is no variety of seasons, and the weather changes sel. dom, and at stated times, moon-light is not necessary for gathering in the produce of the ground; and there the Moon rises about 50 minutes later every day or night ihan on the former. At considerable distances from the equator, where the weather and seasons are more uncertain, the autumnal full Moon rises very soon after sun-set for several evenings to

from it.

The rea

son of this.

But re. gether. At the polar circles, where the mild season markable is of very short duration, the autumnal full Moon to the dis. rises at sun-set from the first to the third quarter. tances of And at the poles, where the Sun is for half a year places

absent, the winter full Moons shine constantly without setting from the first to the third

quarter. It is soon said that all these phenomena are owing to the different angles made by the horizon and different parts of the Moon's orbit; and that the Moon can be full but once or twice in a year in those parts of her orbit which rise with the least angles. But to explain this subject intelligibly, we must dwell much longer upon it.

274. The* plane of the equinoctial is perpendicular to the Earth's axis; and therefore, as the Earth turns round its axis, all parts of the equinoctial make equal angles with the horizon both at rising and set. ting; so that equal portions of it always rise or set in equal times. Consequently, if the Moon's motion were equable, and in the equinoctial, at the rate of 12 degrees 11 min. from the Sun every day, as it is in her orbit, she would rise and set 50 minutes later every day than on the preceding; for 12 deg. 11 min. of the equinoctial, rise or set in 50 minutes of time in all latitudes.

275. But the Moon's motion is so nearly in the ecliptic, that we may consider her at present as moving in it. Now the different parts of the ecliptic, on account of its obliquity to the Earth's axis, make very different angles with the horizon as they rise or set. Those parts or signs which rise with the smallest angles set with the greatest; and vice versa. In equal times, whenever this angle is least, a greater portion of the ecliptic rises than when the angle is larger; as may be seen by elevating the pole of a globe to any considerable latitude, and then

* If a globe be cut quite through upon any circle, the fat surface where it is so divided is the plane of that circle.

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