A SIMPLE METHOD FOR FINDING THE DAY OF THE WEEK OF EVENTS WHICH OCCUR QUADRENNIALLY.

The inaugural of the Presidents. The day of the week on which they have occurred, and on which they will occur for the next one hundred years:

Any one understanding what has been said in a preceding chapter concerning the dominical letter, can very easily make out such a table without going through the process of making calculations for every year. As every succeeding year, or any day of the year, commences one day later in the week than the year preceding, and two days later in leap-year, which makes five days every four years, and as the Presidential term is four years, so every inaugural occurs five days later in the week than it did in the preceding term.

Now, as counting forward five days is equivalent to counting back two, it will be much more convenient to count back two days every term. There is one exception, however, to this rule; the year which completes the century is reckoned as a common year (that is, three centuries out of four), consequently we count forward only four days or back three.

Commencing, then, with the second inaugural of Washington, which occurred on Monday, March 4, 1793, and counting back two days to Saturday in 1797, three days to Wednesday in 1801 and two days to 1805, and so on two days every term till 1901, when, for reasons already given, we count back three days again for one term only, after which it will be two days for the next two hundred years; hence anyone can make his calculations as he writes, and as fast as he can write. See table on 61st page.

SOME PECULIARITIES CONCERNING EVENTS WHICH FALL ON THE TWENTY-NINTH DAY OF FEBRUARY.

The civil year and the day must be regarded as commencing at the same instant. We cannot well reckon a fraction of a day, giving to February 28 days and 6 hours, making the following month to commence six hours later every year; if so, then March, for example, in

again, and so on.

Instead of doing so, we wait until the fraction accumulates to a whole day; then give to February 29 days, and the year 366. Therefore, events which fall on the 29th of February cannot be celebrated annually, but only quadrennially; and at the close of those centuries in which the intercalations are suppressed only octennially. For example: From the year 1696 to 1704, 1796 to 1804, and 1896 to 1904, there is no 29th day of February; consequently no day of the month in the civil year on which an event falling on the 29th of February could be celebrated. Therefore, a person born on the 29th of February, 1896, could celebrate no birthday till 1904, a period of eight years.

In every common year February has 28 days, each day of the week being contained in the number of days in the month four times; but in leap-year, when February has 29 days, the day which begins and ends the month is contained five times. Let us suppose that in a certain year, when February has 29 days, the month comes in on Friday; it also must necessarily end on Friday.

After four years it will commence on Wednesday, and end on Wednesday, and so on, going back two days in the week every four years, until after 28 years we come back to Friday again. This, as has already been explained, is the dominical or solar cycle. For example: February in

So that after 28 years we come back to Friday again; and so on every 28 years, until change of style in 1582, when the Gregorian rule of intercalation being adopted by suppressing the intercalations in three centurial years out of four interrupts this order at the close of these three centuries. For example—1700, 1800 and 1900, after which the cycle of 28 years will be continued until 2100, and so on. The cycle being interrupted by the Gregorian rule of intercalation, causes all events which occur between 28 and 12 years of the close of the centuries to fall on the same day of the week again in 40 years; and those events that fall within 12 years of the close of these centuries, to fall on the same day of the week again in 12 years; after which the cycle of 28 years will be continued during the century. See following table:

It will be seen from this table that in 1804 February had five Wednesdays; and then again in 1832, 1860 and 1888; then suppressing the intercalation in the year 1900 suppresses the 29th of February; so opposite 1900 in the table is blank, and the 29th of February does not occur again till 1904, and the five Wednesdays do not occur again till 1928—that is, 40 years from 1888, when it last occurred.

Again taking the five Mondays which occurred first in this century, in 1808, and then again in 1836, 1864 and in 1892, you will see, for reasons already given, that it will occur again in 12 years, that is, in 1904; and so on with all the days of the week, when it will be seen what is peculiar concerning the 29th of February.

But attention is particularly called to the five Thursdays, which occur first in this century 1816, and then again in 1844 and 1872, the last date being within 28 years of the close of the century. Suppressing the intercalation suppresses the 29th of February; consequently the five Thursdays do not occur again till 1912, that is 40 years from the preceding date, after which the cycle will be continued for two hundred years.

Hence it may be seen that the dominical or solar cycle of 28 years is so interrupted at the close of these centuries by the suppression of the leap-year, that certain events do not occur again on the same day of the week under 40 years, while others are repeated again on the same day of the week in 12 years; also the number of years in the cycle, that is 28 + 12 = 40.

And again the change of style in 1582, causes all events which occur between 28 and 8 years of that change, to fall again on the same day of the week in 36 years, and all that occur within 8 years of that change to be repeated again on the same day of the week in 8 years, after which the cycle of 28 years is continued for 100 years; also that the number of years in the cycle, that is, 28 + 8 = 36.