RULES FOR FINDING THE DAY OF THE WEEK OF EVENTS THAT TRANSPIRED PRIOR TO THE CHRISTIAN ERA.

First, it should be understood that the year 4 is the first leap year in our era, reckoning from the year 1 B. C., which must necessarily be leap year; so that the odd numbers 1, 5, 9, 13, etc., are leap years. Hence every year that is divisible by four and one remainder, is leap year; if no remainder, it is the first year after leap-year; if 3, the second; if 2, the third, thus:

and so on, every year being divided by four and 1 remainder is leap-year of 366 days. It should be borne in mind that the same calendar was in use without any correction from the days of Julius CÆsar 46 B. C. to Pope Gregory XIII in 1582; consequently the method of finding the dominical letter is, in some respects, similar to the one already given on the 44th page. But in some respects the one is the reverse of the other, for we reckon backward and forward from a fixed point—the era; that is the numbers increase each way from the era. Also the dominical letters occur in the natural order of the letters in reckoning backward, but exactly the reverse in reckoning forward. See table on the 73d page, where the dominical letter is placed opposite each year from 45 B. C. to 45 A. D. Now we use the same number 3, because C, the third letter is dominical letter for the year 1 B. C., the point from which we reckon. But instead of taking the remainder, after dividing by 7, from 3 or 10, to find the number of the letter, as in Part Second, Chapter IV, (q. v.) we add the remainder to 3; hence we have the following:

RULE.

Divide the number of the given year by 4, neglecting the remainders, and add the quotient to the given number, divide this amount by 7, and add the remainder to 3, and that amount will give the number of the letter, calling A, 1; B, 2; C, 3, etc.; except the first year after leap-year, (which is the year exactly divisible by 4), the number of the letter is one less than is indicated by the rule.

This rule gives the dominical letter for January and February only, in leap-year, while the letter that precedes it, is the letter for the rest of the year. If the amount be greater than seven, we should reckon from A to A or B again.

It has already been stated in Part First, Chapter III, (q. v.), that a change was made by Augustus CÆsar about 8 B. C., in the number of days in the month; and, as this change effects the day of the week on which certain events fall, it becomes necessary that they should be presented as they were arranged by Julius CÆsar, and as corrected by Augustus. Julius CÆsar gave to February 29 days in common years, and in leap-year 30. This arrangement was the very best that could possibly be made, but, as has already been shown, it was interrupted to gratify the vanity of Augustus.

The left hand column in the table on the 72d page represents the number of days in each month from the days of Julius CÆsar to Augustus, a period of 37 years. The right hand column represents the number of days in the months as they now are, and have been since the change was made by Augustus, 8 B. C. Consequently the rule for finding the day of the week on which events have fallen for the 37 years prior to the last mentioned date, is not perfectly exact, and needs a little explanation here.

The rule itself is given, and fully explained in Part Second, Chapter V, (q. v.) but cannot be applied to the 37 years without some correction. In all the months marked with a star, events fall one day later in the week than that which is indicated by the rule. This should be borne in mind, and make the event one day later in the week than that which is found by the rule. For example, Julius CÆsar was assassinated on the 15th of March, 44 B. C. By giving to February 28 days the first day of March would fall on Wednesday, and, of course, the 15th would be Wednesday. But CÆsar gave to February 29 days, so that the first day of March fell on Thursday, and the 15th was Thursday.Hence, every event from March to September will fall one day later in the week than the rule indicates. But the rule is applicable to September, for it will make no difference whether there are 29 days in February or 31 in August, there are the same number of days from February to September. But the 31 days in September will cause all events to fall one day later in the week during the month of October, but they coincide again during the month of November. The order is interrupted again in December by giving 31 days to November. See following table:

PART THIRD.

CYCLES—JULIAN PERIOD—EASTER.

HEBREW CALENDAR.