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it is obvious that if 365 be divided by 7, the quotient will be 52 weeks and 1 day over: this day will consequently be the last of December, which should be letter A, but we have previously remarked that this is used for January.
Supposing the year to consist only of three hundred and sixty-four days, there would be an even number of fifty two weeks: in which case all the years would begin on the same day of the week, but being three hundred and sixty-five days, the year ends with the same day it begins with. Thus in any common year, supposing the first day of January to fall upon a Sunday, the next year will commence on a Monday, and Sunday will be the seventh day of January or letter G; and as the subsequent year will begin on Tuesday, and the Sunday happen on the sixth day, the Dominical letter then will be F, &c.
Every fourth year, however, is called a Bissextile or Leap-year, and consists of three hundred and sixty-six days, and therefore the order of the Dominical letter will be interrupted, and will not return again till the completion of the sun's cycle, which shows that there are seven leap-years in each cycle. If, therefore, the first of January should fall on Sunday in a leap-year, and the Dominical letter should be A, the twenty-fourth of February will fall on a Friday, and the twentyfifth on Saturday, and the letter used for both days will be F. Then the next day, being
Sunday, will have the letter G, so that every leap-year has two Dominical letters, one, which serves from the first of January to the twenty-fourth of February, and the other from the twenty-fifth of February to the end of the year.
The general rule for finding the Dominical letter is as follows:-Add to the given year its fourth part omitting fractions; then divide that sum by 7, and the remainder subtracted from 7 will represent the number of the letter according to the order of the alphabet; thus 1 will signify A, 2 B, &c. But if nothing remain after dividing by 7, then G is the Dominical letter.
The letter found according to this rule will be the Dominical letter from the twentyfourth of February to the thirty-first of December; and the other letter from the first of January to the twenty-fourth of February, will be always the next in the order of the alphabet.
To find the Dominical letter after the commencement of the nineteenth century, the reader must attend to the following rule: Supposing the Dominical letter for 1845 to be required-Cut off two figures thus 18 | 45, divide the first two, viz. 18, by 4, regarding no remainder: the quotient will be 4, from which subtract 1, and the remainder will be 3, which taken from the original number will leave 15; this number subtracted from 21, (the number of seven nearest eighteen) leaves
6, the new number to be added to the given year, besides its fourth; then divide by 7 as in the preceding rule, and the remainder will show the number answering to the Dominical letter.
Of the General Principles of a Celestial Globe, with Problems, &c.
THE artificial celestial globe is intended to represent the face of the heavens, on which all the fixed stars hitherto perceived by astronomers are placed in their natural positions and respective magnitudes; and when the globe is turned round on its axis from east to west, it exhibits the apparent diurnal motion of the sun, moon, and stars, in the ethereal regions.
There are two circles on this globe which intersect each other; one called the ecliptic, represents the sun's apparent path, and the other the equator, or the circle of our earth, which in celestial problems, however, is transferred in idea to the heavens. The former is distinguished by eight circles drawn parallel to it on each side, including the twelve signs of the zodiac, divided into thirty degrees each, and forming together a com
plete circle of three hundred and sixty degrees. The latter, when transferred to the heavens, is called the equatorial circle, because it only seems to divide the celestial sphere into two equal parts, being precisely equidistant from each extremity of its apparent diurnal motions.
At 23 degrees from the equatorial circle and parallel with it, two circles are drawn, one on the north and the other on the south side, which touch the ecliptic in two points. These circles are called the tropics or solstices; and the great circle which passes through the points where the tropics touch the ecliptic, is called the solsticial colure. Another great circle which passes in like manner, where the ecliptic and equatorial intersect each other, is termed the equinoctial colure; and the circles drawn at 23 degrees from the poles are called the polar circles.
On the plane of the horizon of the celestial globe, are delineated the figures and signs of the zodiac; the degrees of which answer to the days of the months, as the months correspond to the signs which the sun is in at each period. On this place also are described the principal and collateral points of the compass, -The brazen circle which crosses the globe north and south is styled the general meridian, from its representing that circle which passes over every place on the earth.
The altitude of any heavenly body is its height above the horizon.
Meridian Altitude is its greatest height, and when it arrives at that height, it is said to culminate.
Declination, is the distance of the sun, or any star, from the equator or equinoctial, counted on the brazen meridian in degrees, and is called north or south, according to the side of the equinoctial on which the declination is.
Right Ascension, is an arch of the equinoctial contained between the sign Aries, and the degree of the equinoctial that is cut by the brazen meridian, when the sun or star is brought to the meridian.
Oblique Ascension, is that arch of the equinoctial contained between the sign Aries and the degree of the equinoctial, which is cut by the horizon at the rising of the sun or star.
Ascensional Difference, is the difference of degrees between the right and oblique_ascension, which converted into time by allowing 15 degrees for every hour, shows how much the sun, or star, rises or sets before or after six o'clock.
Latitude of a Star, is its distance from the ecliptic, being an arch of a circle of longitude, reckoned from the ecliptic towards its pole, either north or south.
Longitude of a Star, is an arch of the ecliptic intercepted between the first point of Aries, and the circle of latitude which passes through the star. This is reckoned eastward only.