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Hence the solar day is about four minutes longer than the sidereal day. For the convenience of society, it is customary to call the solar day 24 hours long, and make the sidereal day only 23 hr. 56 min. 4 sec, in length, expressed in mean solar time. A sidereal day being shorter than a solar one, the sidereal hours, minutes, etc., are shorter than the solar; 24 hours of mean solar time being equal to 24hr. 3 min. 56 sec. of sidereal time. From what has been said, it follows that the earth makes 366 revolutions around its axis in 365 solar days. MEAN SOLAR TIME.—The solar days are of unequal length. To obviate this difficulty, astronomers suppose a mean sun moving through the equator of the heavens (which is a circle and not an ellipse) with a perfectly uniform motion. When this mean sun passes the meridian of any place, it is mean noon; and when the true sun is in the same position, it is apparent noon. This day is the average length of all the solar days in the year. The clocks in common use are regulated to keep mean time. When, therefore, it is twelve by the clock, the sun may be either a little past or a little behind the meridian. The difference between the sun-time (apparent solartime) and the clock-time (mean time), is called the “equation of time.” This is the greatest about the first of November, when the sun is sixteen and a quarter minutes in advance of the clock. The sun is the slowest about February 10th, when it is about fourteen and a half minutes behind mean time. Mean and apparent time coincide four times in the year—namely, April 15th, June 15th, September 1st, and December 24th. On those days the noon-mark on the sun-dial coincides with twelve o'clock. In

France, until 1816, apparent time was used; and the

confusion was so great, that Arago relates how the
town clocks would differ thirty minutes in striking the
same hour. As the time varied every day, no watch-
maker could regulate a watch or clock to keep it.
THE SUN-DIAL—The apparent time of the dial may
be readily changed to mean time, by adding or sub-
tracting the number of minutes given in the almanac
for each day in the year, under the heading “sun
slow” or “sun fast.” As a noon-mark is thus a
very convenient method of regulating a timepiece,
especially in the country, the following manner of ob-
taining one without a transit instrument may be
Select a level hard surface which is exposed to the
sun from about 9 A.M. to 3 P.M. Upon this carefully
describe, with compasses, a circle of eight or ten
inches in diameter. Take a piece of heavy wire, six
or eight inches in length, one end of which is
sharpened. Drive this perpendicularly into the cen-
tre of the circle, leaving it just high enough to allow

the extreme end of its shadow to fall upon the circle

about 9% or 10 A.M. Mark this point, and also the place

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a line from that to the centre of the circle, it will be the meridian line or noon-mark. WHY THE SOLAR DAYS ARE OF UNEQUAL LENGTH.— There are two reasons for this—the unequal orbital motion of the earth and the obliquity of the ecliptic. First: the orbit of the earth is an ellipse; and thus the apparent yearly motion of the sun along the ecliptic is variable. In perihelion, in January, the sun appears to move eastward daily 1° 1' 9.9"; while at aphelion, in July, only 57 11.5". As the earth in its diurnal motion revolves uniformly from west to east, and the sun passes eastward irregularly, this must produce a corresponding variation in the length of the solar day. The sun, therefore, comes to the meridian sometimes earlier and sometimes later than the mean noon, and they agree only at perihelion and aphelion. Second: as we have just seen, the mean sun is supposed to move in a circle and not an ellipse. This

would make Fig. 92. the motion P along the

ecliptic uni-
form, but the
obliquity of
the ecliptic |
would still I'é
cause an ir-

regularity in the length of the day. The mean sun is therefore supposed to pass along the equinoctial,

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which is perpendicular to the earth's axis; while the ecliptic is inclined to it 23° 28. Let A represent the vernal equinox, I the autumnal, AEI the ecliptic, AI the equinoctial, PK, PL, PM, etc., meridians. Let the distances AB, BC, CD, etc., be equal arcs of the ecliptic, which are passed over by the sun in equal times. Next, mark off on the equinoctial distances Aa, ab, bc, etc., equal to AB, BC, etc. These are equal arcs of right ascension, or hour-circles, through which the earth, revolving from west to east, passes in equal times. Now, meridians drawn through these divisions, would not agree with those drawn through equal divisions on the ecliptic. Hence, a sun moving along the ecliptic, which is inclined, would not make equal days, even though the ecliptic were a perfect circle. Let us see how thé mean and apparent solar days would compare. Let the real sun pass in its eastward course from A to B in a certain time, the mean sun moving the same distance would reach the point a, since the latter travels on the base and the former the hypothenuse of a triangle. The earth, revolving from west to east, would cause the real sun to cross any meridian earlier than the mean sun; hence, apparent time would be faster than clock-time. By holding the figure up above us toward the heavens, we can see how a westerly sun would cross the meridian earlier than an easterly one. Following the same reasoning, we can see that at the solstice, solar and mean time would agree; while beyond that point the mean time would be faster.

THE CIVIL DAY.—This is the mean solar day of which we have spoken. It extends from midnight to midnight. The present method of dividing the day into two portions of twelve hours each, was adopted by Hipparchus, 150 years B. C., and is now in general use over the civilized world. Until recently, however, very many nations terminated one day and commenced the next at sunset. Under this plan, 10 o'clock on one day would not mean the same as 10 o'clock on another day. The Puritans commenced the day at 6 P.M. The Babylonians, Persians, and modern Greeks begin the day at sunrise. The names of the days now in use are derived as

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THE YEAR.—The sidereal year is the interval of a complete revolution of the earth about the sun, measured by a fixed star. It comprises 365 d, 6 hrs., 9 min., 9.6 sec. of mean solar time. The mean solar year (tropical year) is the interval between two successive passages of the sun through the vernal equinox. It comprises 365 d., 5 hrs., 48 min., 49.7 sec. If the equinoxes were stationary, there would be no difference between the sidereal and tropical year. As the equinoxes retrograde along the ecliptic 50" of space annually, the former is 20 min., 20 sec. longer.

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