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