Part 12

The ordinary or civil day is the mean of all the solar days in a year.

81. Sun Time and Clock Time.--It is noon by the sun when the sun is on the meridian, and by the clock at the middle of the civil day. Now, as the civil days are all of the same length, while solar days are of variable length, it seldom happens that the middles of these two days coincide, or that sun time and clock time agree. The difference between sun time and clock time, or what is often called apparent solar time and mean solar time, is called the equation of time. The sun is said to be slow when it crosses the meridian after noon by the clock, and fast when it crosses the meridian before noon by the clock. Sun time and clock time coincide four times a year; during two intermediate seasons the clock time is ahead, and during two it is behind.

* * * * *

The following are the dates of coincidence and of maximum deviation, which vary but slightly from year to year:--

February 10 True sun fifteen minutes slow. April 15 True sun correct. May 14 True sun four minutes fast. June 14 True sun correct. July 25 True sun six minutes slow. August 31 True sun correct. November 2 True sun sixteen minutes fast. December 24 True sun correct.

One of the effects of the equation of time which is frequently misunderstood is, that the interval from sunrise until noon, as given in the almanacs, is not the same as that between noon and sunset. The forenoon could not be longer or shorter than the afternoon, if by "noon" we meant the passage of the sun across the meridian; but the noon of our clocks being sometimes fifteen minutes before or after noon by the sun, the former may be half an hour nearer to sunrise than to sunset, or vice versa.

The Year.

82. The Year.--The year is the time it takes the earth to revolve around the sun, or, what amounts to the same thing, the time it takes the sun to pass around the ecliptic.

(1) The time it takes the sun to pass from a star around to the same star again is called a sidereal year. This is, of course, the exact time it takes the earth to make a complete revolution around the sun.

(2) The time it takes the sun to pass around from the vernal equinox, or the first point of Aries, to the vernal equinox again, is called the tropical year. This is a little shorter than the sidereal year, owing to the precession of the equinoxes. This will be evident from Fig. 96. The circle represents the ecliptic, S the sun, and E the vernal equinox. The sun moves around the ecliptic eastward, as indicated by the long arrow, while the equinox moves slowly westward, as indicated by the short arrow. The sun will therefore meet the equinox before it has quite completed the circuit of the heavens. The exact lengths of these respective years are:--

Sidereal year 365.25636=365 days 6 hours 9 min 9 sec Tropical year 365.24220=365 days 5 hours 48 min 46 sec

Since the recurrence of the seasons depends on the tropical year, the latter is the one to be used in forming the calendar and for the purposes of civil life generally. Its true length is eleven minutes and fourteen seconds less than three hundred and sixty-five days and a fourth.

It will be seen that the tropical year is about twenty minutes shorter than the sidereal year.

(3) The time it takes the earth to pass from its perihelion point around to the perihelion point again is called the anomalistic year. This year is about four minutes longer than the sidereal year. This is owing to the fact that the major axis of the earth's orbit is slowly moving around to the east at the rate of about ten seconds a year. This causes the perihelion point P (Fig. 97) to move eastward at that rate, as indicated by the short arrow. The earth E is also moving eastward, as indicated by the long arrow. Hence the earth, on starting at the perihelion, has to make a little more than a complete circuit to reach the perihelion point again.

83. The Calendar.--The solar year, or the interval between two successive passages of the same equinox by the sun, is 365 days, 5 hours, 48 minutes, 46 seconds. If, then, we reckon only 365 days to a common or civil year, the sun will come to the equinox 5 hours, 48 minutes, 46 seconds, or nearly a quarter of a day, later each year; so that, if the sun entered Aries on the 20th of March one year, he would enter it on the 21st four years after, on the 22d eight years after, and so on. Thus in a comparatively short time the spring months would come in the winter, and the summer months in the spring.

Among different ancient nations different methods of computing the year were in use. Some reckoned it by the revolution of the moon, some by that of the sun; but none, so far as we know, made proper allowances for deficiencies and excesses. Twelve moons fell short of the true year, thirteen exceeded it; 365 days were not enough, 366 were too many. To prevent the confusion resulting from these errors, Julius Cæsar reformed the calendar by making the year consist of 365 days, 6 hours (which is hence called a Julian year), and made every fourth year consist of 366 days. This method of reckoning is called Old Style.

But as this made the year somewhat too long, and the error in 1582 amounted to ten days, Pope Gregory XIII., in order to bring the vernal equinox back to the 21st of March again, ordered ten days to be struck out of that year, calling the next day after the 4th of October the 15th; and, to prevent similar confusion in the future, he decreed that three leap-years should be omitted in the course of every four hundred years. This way of reckoning time is called New Style. It was immediately adopted by most of the European nations, but was not accepted by the English until the year 1752. The error then amounted to eleven days, which were taken from the month of September by calling the 3d of that month the 14th. The Old Style is still retained by Russia.

According to the Gregorian calendar, every year whose number is divisible by four is a leap-year, except, that, in the case of the years whose numbers are exact hundreds, those only are leap-years which are divisible by four after cutting off the last two figures. Thus the years 1600, 2000, 2400, etc., are leap-years; 1700, 1800, 1900, 2100, 2200, etc., are not. The error will not amount to a day in over three thousand years.

84. The Dominical Letter.--The dominical letter for any year is that which we often see placed against Sunday in the almanacs, and is always one of the first seven in the alphabet. Since a common year consists of 365 days, if this number is divided by seven (the number of days in a week), there will be a remainder of one: hence a year commonly begins one day later in the week than the preceding one did. If a year of 365 days begins on Sunday, the next will begin on Monday; if it begins on Thursday, the next will begin on Friday; and so on. If Sunday falls on the 1st of January, the first letter of the alphabet, or A, is the dominical letter. If Sunday falls on the 7th of January (as it will the next year, unless the first is leap-year), the seventh letter, G, is the dominical letter. If Sunday falls on the 6th of January (as it will the third year, unless the first or second is leap-year), the sixth letter, F, will be the dominical letter. Thus, if there were no leap-years, the dominical letters would regularly follow a retrograde order, G, F, E, D, C, B, A.

But leap-years have 366 days, which, divided by seven, leaves two remainder: hence the years following leap-years will begin two days later in the week than the leap-years did. To prevent the interruption which would hence occur in the order of the dominical letters, leap-years have two dominical letters, one indicating Sunday till the 29th of February, and the other for the rest of the year.

By Table I. below, the dominical letter for any year (New Style) for four thousand years from the beginning of the Christian Era may be found; and it will be readily seen how the Table could be extended indefinitely by continuing the centuries at the top in the same order.

To find the dominical letter by this table, look for the hundreds of years at the top, and for the years below a hundred, at the left hand.

Thus the letter for 1882 will be opposite the number 82, and in the column having 1800 at the top; that is, it will be A. In the same way, the letters for 1884, which is a leap-year, will be found to be FE.

Having the dominical letter of any year, Table II. shows what days of every month of the year will be Sundays.

To find the Sundays of any month in the year by this table, look in the column, under the dominical letter, opposite the name of the month given at the left.

From the Sundays the date of any other day of the week can be readily found.

Thus, if we wish to know on what day of the week Christmas falls in 1889, we look opposite December, under the letter F (which we have found to be the dominical letter for the year), and find that the 22d of the month is a Sunday; the 25th, or Christmas, will then be Wednesday.

In the same way we may find the day of the week corresponding to any date (New Style) in history. For instance, the 17th of June, 1775, the day of the fight at Bunker Hill, is found to have been a Saturday.