AN ACCOUNT OF THE GREGORIAN OR NEW STYLE, TOGETHER WITH SOME CHRONOLOGICAL PROBLEMS, FOR FINDING THE EPACT, GOLDEN NUMBER, MOON'S AGE, &c.

POPE GREGORY the XIIIth made a reformation of the calendar. The Julian calendar, or old style, had, before that time, been in general use all over Europe. The year, according to the Julian calendar, consists of three hundred and sixty five days and six hours; which six hours being one fourth part of a day, the common years consisted of three hundred and sixty five days, and every fourth year, one day was added to the month of February, which made each of those years three hundred and sixty six days, which are usually called leap years.

This computation, though near the truth, is more than the solar year by eleven minutes, which, in one hundred and thirty one years, amounts to a whole day. By which the Vernal Equinox was anticipated ten days, from the time of the general council of Nice, held in the year 325 of the Christian Æra, to the time of Pope Gregory; who therefore caused ten days to be taken out of the month of October in 1582, to make the Equinox fall on the 21st of March, as it did at the time of that council. And, to pre

vent the like variation for the future, he ordered that three days should be abated in every four hundred years, by reducing the leap year at the close of each century, for three successive centuries, to common years, and retaining the leap year at the close of each fourth century only.

This was at that time esteemed as exactly conformable to the true solar year; but Dr. Halley makes the solar year to be three hundred and sixty five days, five hours, forty eight minutes, fifty four seconds, forty one thirds, twenty seven fourths, and thirty one fifths: According to which, in four hundred years, the Julian year of three hundred and sixty five days and six hours will exceed the solar by three days, one hour and fifty five minutes, which is near two hours, so that in fifty centuries it will amount to a day.

Though the Gregorian calendar, or new style, had long been used throughout the greatest part of Europe, it did not take place in Great Britain and America till the first of January, 1752; and in September following, the eleven days were adjusted by calling the third day of that month the fourteenth, and continuing the rest in their order.

CHRONOLOGICAL PROBLEMS.

PROBLEM I.

As there are three leap years to be abated in every four centuries: to shew how to find in which century the last year is to be a leap year, and in which it is not.

RULE.

Cut off two cyphers, and divide the remaining figures by 4; if nothing remain, the year is a leap year. EXAMP. 1. The year 18/00.

4)18(4

16

2

EXAMP. 3. The year 2000.

4)20(5

20

0

The first and second examples, having remainders, shew the years to be common years of three hundred and sixty five days; but the third and fourth, having no remainders, are leap years of three hundred and sixty six days.

PROBLEM II.

To find, with regard to any other years, whether any given year be leap year, and the contrary.

RULE.

Divide the proposed year by 4, and if there be no remainder, after the division, it is leap year; but if 1, 2 or 3 remain, it is the first, second or third after leap year.

EXAMP. 1. For the year 1784. EXAMP. 2. For the year 1786.

4)1784(446
16

18

16

24

24

0

PROBLEM III.

To find the Dominical Letter for any year, according to the Julian

method of calculation.
RULE.

Add to the year its fourth part and 4, and divide that sum by 7: if nothing remain, the Dominical Letter is G; but if there be any

remainder, it shews the letter in a retrograde order from G, beginning the reckoning with F; or, if it be subtracted from 7, you will have the index of the letter from A, accounting as follows: A B C D E F G

To find the Dominical Letter for any year according to the Gregorian computation. RULE.

Divide the year and its fourth part, less 1 (for the present century) by 7; subtract the remainder after the division, from 7, and this remainder will be the index of the Dominical Letter, as before if nothing remain it is G.

EXAMP. 1. For the year 1810.

Add

Given year=1810

Its fourth = 452

EXAMP. 2. For the year 1812.*

1812

453

Here it is to be observed, that every leap year has two Dominical Letters; that, found by this rule, is the Dominical Letter from the twenty fifth day of