_Of the Equation of Time._
[Sidenote: The Sun and Clocks equal only on four days of the year.]
224. The Earth’s motion on it’s Axis being perfectly uniform, and equal
at all times of the year, the sidereal days are always precisely of the
same length; and so would the solar or natural days be, if the Earth’s
orbit were a perfect Circle, and it’s Axis perpendicular to it’s orbit.
But the Earth’s diurnal motion on an inclined Axis, and it’s annual
motion in an elliptic orbit, cause the Sun’s apparent motion in the
Heavens to be unequal: for sometimes he revolves from the Meridian to
the Meridian again in somewhat less than 24 hours, shewn by a well
regulated clock; and at other times in somewhat more: so that the time
shewn by an equal going clock and a true Sun-dial is never the same but
on the 15th of _April_, the 16th of _June_, the 31st of _August_, and
the 24th of _December_. The clock, if it goes equally and true all the
year round, will be before the Sun from the 24th of _December_ till the
15th of _April_; from that time till the 16th of _June_ the Sun will be
before the clock; from the 16th of _June_ till the 31st of _August_ the
clock will be again before the Sun; and from thence to the 24th of
_December_ the Sun will be faster than the clock.
[Sidenote: Use of the Equation Table.]
225. The Tables of the Equation of natural days, at the end of the next
Chapter, shew the time that ought to be pointed out by a well regulated
clock or watch every day of the year at the precise moment of solar
noon; that is, when the Sun’s centre is on the Meridian, or when a true
Sun-dial shews it to be precisely Twelve. Thus, on the 5th of _January_
in Leap-year, when the Sun is on the Meridian, it ought to be 5 minutes
51 seconds past twelve by the clock; and on the 15th of _May_, when the
Sun is on the Meridian, the time by the clock should be but 55 minutes
57 seconds past eleven; in the former case, the clock is 5 minutes 51
seconds beforehand with the Sun; and in the latter case, the Sun is 4
minutes 3 seconds faster than the clock. The column at the right hand of
each month shews the daily difference of this equation, as it increases
or decreases. But without a Meridian Line, or a Transit-Instrument fixed
in the plane of the Meridian, we cannot set a Sun-dial true.
[Sidenote: How to draw a Meridian Line.]
226. The easiest and most expeditious way of drawing a Meridian Line is
this: Make four or five concentric Circles, about a quarter of an inch
from one another, on a flat board about a foot in breadth; and let the
outmost Circle be but little less than the board will contain. Fix a pin
perpendicularly in the center, and of such a length that it’s whole
shadow may fall within the innermost Circle for at least four hours in
the middle of the day. The pin ought to be about an eighth part of an
inch thick, with a round blunt point. The board being set exactly level
in a place where the Sun shines, suppose from eight in the morning till
four in the afternoon, about which hours the end of the shadow should
fall without all the Circles; watch the times in the forenoon, when the
extremity of the shortening shadow just touches the several Circles, and
_there_ make marks. Then, in the afternoon of the same day, watch the
lengthening shadow, and where it’s end touches the several Circles in
going over them, make marks also. Lastly, with a pair of compasses, find
exactly the middle point between the two marks on any Circle, and draw a
straight line from the center to that point; which Line will be covered
at noon by the shadow of a small upright wire, which should be put in
the place of the pin. The reason for drawing several Circles is, that in
case one part of the day should prove clear, and the other part somewhat
cloudy, if you miss the time when the point of the shadow should touch
one Circle, you may perhaps catch it in touching another. The best time
for drawing a Meridian Line in this manner is about the middle of
summer; because the Sun changes his Declination slowest and his Altitude
fastest in the longest days.
If the casement of a window on which the Sun shines at noon be quite
upright, you may draw a line along the edge of it’s shadow on the floor,
when the shadow of the pin is exactly on the Meridian Line of the board:
and as the motion of the shadow of the casement will be much more
sensible on the Floor, than that of the shadow of the pin on the board,
you may know to a few seconds when it touches the Meridian Line on the
floor, and so regulate your clock for the day of observation by that
line and the Equation Tables above-mentioned § 225.
[Sidenote: Equation of natural days explained.]
227. As the Equation of time, or difference between the time shewn by a
well regulated Clock and a true Sun-dial, depends upon two causes,
namely, the obliquity of the Ecliptic, and the unequal motion of the
Earth in it, we shall first explain the effects of these causes
separately considered, and then the united effects resulting from their
combination.
[Sidenote: PLATE VI.