_Of Solar and Sidereal Time._
[Sidenote: Sidereal days shorter than solar days, and why.]
221. The fixed Stars appear to go round the Earth in 23 hours 56 minutes
4 seconds, and the Sun in 24 hours: so that the Stars gain three minutes
56 seconds upon the Sun every day, which amounts to one diurnal
revolution in a year; and therefore, in 365 days as measured by the
returns of the Sun to the Meridian, there are 366 days as measured by
the Stars returning to it: the former are called _Solar Days_, and the
latter _Sidereal_.
[Sidenote: PLATE III.]
The diameter of the Earth’s Orbit is but a physical point in proportion
to the distance of the Stars; for which reason, and the Earth’s uniform
motion on it’s Axis, any given Meridian will revolve from any Star to
the same Star again in every absolute turn of the Earth on it’s Axis,
without the least perceptible difference of time shewn by a clock which
goes exactly true.
If the Earth had only a diurnal motion, without an annual, any given
Meridian would revolve from the Sun to the Sun again in the same
quantity of time as from any Star to the same Star again; because the
Sun would never change his place with respect to the Stars. But, as the
Earth advances almost a degree eastward in it’s Orbit in the time that
it turns eastward round its Axis, whatever Star passes over the Meridian
on any day with the Sun, will pass over the same Meridian on the next
day when the Sun is almost a degree short of it; that is, 3 minutes 56
seconds sooner. If the year contained only 360 days as the Ecliptic does
360 degrees, the Sun’s apparent place, so far as his motion is equable,
would change a degree every day; and then the sidereal days would be
just four minutes shorter than the solar.
[Sidenote: Fig. II.]
Let _ABCDEFGHIKLM_ be the Earth’s Orbit, in which it goes round the Sun
every year, according to the order of the letters, that is, from west to
east, and turns round it’s Axis the same way from the Sun to the Sun
again every 24 hours. Let _S_ be the Sun, and _R_ a fixed Star at such
an immense distance that the diameter of the Earth’s Orbit bears no
sensible proportion to that distance. Let _Nm_ be any particular
Meridian of the Earth, and _N_ a given point or place upon that
Meridian. When the Earth is at _A_, the Sun _S_ hides the Star _R_,
which would always be hid if the Earth never removed from _A_; and
consequently, as the Earth turns round it’s Axis, the point _N_ would
always come round to the Sun and Star at the same time. But when the
Earth has advanced, suppose a twelfth part of it’s Orbit from _A_ to
_B_, it’s motion round it’s Axis will bring the point _N_ a twelfth part
of a day or two hours sooner to the Star than to the Sun; for the Angle
_NBn_ is equal to the Angle _ASB_: and therefore, any Star which comes
to the Meridian at noon with the Sun when the Earth is at _A_, will come
to the Meridian at 10 in the forenoon when the Earth is at _B_. When the
Earth comes to _C_ the point _N_ will have the Star on it’s Meridian at
8 in the morning, or four hours sooner than it comes round to the Sun;
for it must revolve from _N_ to _n_, before it has the Sun in it’s
Meridian. When the Earth comes to _D_, the point _N_ will have the Star
on it’s Meridian at six in the morning, but that point must revolve six
hours more from _N_ to _n_, before it has mid-day by the Sun: for now
the Angle _ASD_ is a right Angle, and so is _NDn_; that is, the Earth
has advanced 90 degrees in it’s Orbit, and must turn 90 degrees on its
Axis to carry the point _N_ from the Star to the Sun: for the Star
always comes to the Meridian when _Nm_ is parallel to _RSA_; because
_DS_ is but a point in respect of _RS_. When the Earth is at _E_, the
Star comes to the Meridian at 4 in the morning; at _F_, at two in the
morning; and at _G_, the Earth having gone half round it’s Orbit, _N_
points to the Star _R_ at midnight, being then directly opposite to the
Sun; and therefore, by the Earth’s diurnal motion the Star comes to the
Meridian 12 hours before the Sun. When the Earth is at _H_, the Star
comes to the Meridian at 10 in the evening; at _I_ it comes to the
Meridian at 8, that is, 16 hours before the Sun; at _K_ 18 hours before
him; at _L_ 20 hours; at _M_ 22; and at _A_ equally with the Sun again.
A TABLE, shewing how much of the Celestial Equator passes over the
Meridian in any part of a mean SOLAR DAY; and how much the FIXED STARS
gain upon the mean SOLAR TIME every Day, for a Month.
+-----+-----------+-----+------------+-----+------------+
| Time| Motion. | Time| Motion. |Time | Motion. |
| | | | | | |
+-----+-----------+-----+------------+-----+------------+
|Hours| D. M. S. | *M. | D. M. S. | *M. | D. M. S. |
| | | S. | M. S. T. | S. | M. S. T. +
| | | T. | S. T. ʺʺ | T. | S. T. ʺʺ |
+-----+-----------+-----+------------+-----+------------+
| 1 | 15 2 28 | 1 | 0 15 2 | 31 | 7 46 16 |
| 2 | 30 4 56 | 2 | 0 30 5 | 32 | 8 1 19 |
| 3 | 45 7 24 | 3 | 0 45 7 | 33 | 8 16 21 |
| 4 | 60 9 51 | 4 | 1 0 10 | 34 | 8 31 24 |
| 5 | 75 12 19 | 5 | 1 15 12 | 35 | 8 46 26 |
+-----+-----------+-----+------------+-----+------------+
| 6 | 90 14 47 | 6 | 1 30 15 | 36 | 9 1 29 |
| 7 | 105 17 15 | 7 | 1 45 17 | 37 | 9 16 31 |
| 8 | 120 19 43 | 8 | 2 0 20 | 38 | 9 31 34 |
| 9 | 135 22 11 | 9 | 2 15 22 | 39 | 9 46 36 |
| 10 | 150 24 38 | 10 | 2 30 25 | 40 | 10 1 39 |
+-----+-----------+-----+------------+-----+------------+
| 11 | 165 27 6 | 11 | 2 45 27 | 41 | 10 16 41 |
| 12 | 180 29 34 | 12 | 3 0 30 | 42 | 10 31 43 |
| 13 | 195 32 2 | 13 | 3 15 32 | 43 | 10 46 46 |
| 14 | 210 34 30 | 14 | 3 30 34 | 44 | 11 1 48 |
| 15 | 225 36 58 | 15 | 3 45 37 | 45 | 11 16 51 |
+-----+-----------+-----+------------+-----+------------+
| 16 | 240 39 26 | 16 | 4 0 39 | 46 | 11 31 53 |
| 17 | 255 41 53 | 17 | 4 15 41 | 47 | 11 46 56 |
| 18 | 270 44 21 | 18 | 4 30 44 | 48 | 12 1 58 |
| 19 | 285 46 49 | 19 | 4 45 47 | 49 | 12 17 1 |
| 20 | 300 49 17 | 20 | 5 0 49 | 50 | 12 32 3 |
+-----+-----------+-----+------------+-----+------------+
| 21 | 315 51 45 | 21 | 5 15 52 | 51 | 12 47 6 |
| 22 | 330 54 13 | 22 | 5 30 54 | 52 | 13 2 8 |
| 23 | 345 56 40 | 23 | 5 45 57 | 53 | 13 17 11 |
| 24 | 360 59 8 | 24 | 6 0 59 | 54 | 13 32 13 |
| 25 | 376 1 36 | 25 | 6 16 2 | 55 | 13 47 16 |
+-----+-----------+-----+------------+-----+------------+
| 26 | 391 4 4 | 26 | 6 31 4 | 56 | 14 2 18 |
| 27 | 406 6 32 | 27 | 6 46 7 | 57 | 14 17 21 |
| 28 | 421 9 0 | 28 | 7 1 9 | 58 | 14 32 23 |
| 29 | 436 11 28 | 29 | 7 16 11 | 59 | 14 47 26 |
| 30 | 451 13 56 | 30 | 7 31 14 | 60 | 15 2 28 |
+-----+-----------+-----+------------+-----+------------+
Accelerations
of the
Fixed Stars.
+----+----------+
| D. | H. M. S. |
+----+----------+
| 1 | 0 3 56 |
| 2 | 0 7 52 |
| 3 | 0 11 48 |
| 4 | 0 15 44 |
| 5 | 0 19 39 |
+----+----------+
| 6 | 0 23 35 |
| 7 | 0 27 31 |
| 8 | 0 31 27 |
| 9 | 0 35 23 |
| 10 | 0 39 19 |
+----+----------+
| 11 | 0 43 15 |
| 12 | 0 47 11 |
| 13 | 0 51 7 |
| 14 | 0 55 3 |
| 15 | 0 58 58 |
+----+----------+
| 16 | 1 2 54 |
| 17 | 1 6 50 |
| 18 | 1 10 46 |
| 19 | 1 14 42 |
| 20 | 1 18 38 |
+----+----------+
| 21 | 1 22 34 |
| 22 | 1 26 30 |
| 23 | 1 30 26 |
| 24 | 1 34 22 |
| 25 | 1 38 17 |
+----+----------+
| 26 | 1 42 13 |
| 27 | 1 46 9 |
| 28 | 1 50 5 |
| 29 | 1 54 1 |
| 30 | 1 57 57 |
+----+----------+
[Sidenote: PLATE III.
An absolute Turn of the Earth on it’s Axis never finishes a
solar day.