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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 watchmaker 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 subtracting 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 obtaining one without a transit instrument may be useful.

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 centre 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 where the shadow touches the circle in the afternoon. Take a point half-way between the two, and drawing

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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 Solas 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' 1L5". 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 the motion along the ecliptic uniform, but the obliquity of the ecliptic would still cause an irregularity in the length of the day. The mean sun is therefore supposed to pass along the equinoctial, 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 ka, ab, be, 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 the 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 tho 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.

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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 follows:

1. Dies Soils (Latin) Sun's day.

2. Dies Lunffi ( " )....Moon's day.

8. Tins daeg (Saxon) Tina's day.

4. Wodnes daeg...( " )....Woden's day.
6. Thames daeg..( " )....Thor's day.

6. Friges daeg ( " ) Friga's day.

1. Dies Saturn!...(Latin). ...Saturn's day.

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., 6hrs., 9 mill., 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., 5hrs., 48min., 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.

The anomalistic year is the interval between two successive passages of the earth through its perihelion. It is 4min., 40 sec. longer than the sidereal year.

The Ancient Year.—The ancients ascertained the length of the year by means of the gnomon. This was a perpendicular rod standing on a smooth plane on which was a meridian line. When the shadow cast on this line was the shortest, it indicated the summer solstice; and when it was the longest, the winter solstice. The number of days required for the sun to pass from one solstice back to it again determined the length of the year. This they found to be 365 days. As that is nearly six hours less than the true solar year, dates were soon thrown into confusion. If, at a certain date the summer solstice occurred on the 20th June, in four years it would fall on the 21st; and thus it would gain one day every four years, until in time the summer solstice would happen in the winter months.

Julian Calendar.—Julius Caesar first attempted to make the calendar year coincide with the motions of the sun. By the aid of Sosigenes, an Egyptian astronomer, he devised a plan of introducing every fourth year a leap-year, which should contain an ixtra day. This was termed a bissextile year, since 'he sixth (sextilis) day before the kalends (first day) if March was then counted twice.

Gregorian Calendar.—Though the Julian calendar was nearly perfect, it was yet somewhat defec

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