Examples for Practice on the preceding Table.

(1.) Find the Dominical letter for 301, N. s. B. C.

Under 3 centuries

N. S. B. C.; and against 1 on the right under N. s. will be found c the Dominical letter.

(2.) Also for 1727 o. s. Here 1727 700 leaves rem. 327, which gives A for Dominical letter after Christ, and E for the Sunday letter before Christ.

(3.) Required the day of the week 1st January, 1800, N. s. Á. C., and 12th February, 1852, N. s. A. C.

Here 1800 is a common year, and 1800÷400 leaves 200 rem. for the tabular date, viz. 2 centuries, and no remaining years. Under 2 centuries N. S. A. C. and against 0., the remaining years above centuries after Christ, on the left, is E, the Sunday letter; under E in the line of Jan. and against 1st, the date of the month, is Wednesday, the day of the week required. For the year 1852 take the remainder 252, which gives c, and is a leap year, whence 12th Feb. is Thursday.

(4.) Required the days of the week corresponding to the dates of the following registrations:- Samuel was born on December 16th, 1789; Hannah on 14th July, 1791; Rebecca on 11th October, 1800; Ann on 25th December, 1813; Alfred on 23rd February, 1821; Augustus on 20th May, 1823; Sarah on 30th January, 1826; Newton on 6th December, 1832; and Mary Ann on 26th December, 1834?

Ans. Samuel on a Wednesday; Hannah on a Thursday; Rebecca on a Saturday; Ann on a Saturday; Alfred on a Friday; Augustus on a Tuesday; Sarah on a Monday; Newton on a Thursday; and Mary Ann on a Friday.

(5.) What day of the month did the last Friday in January, February, August, and December, fall on in the year 1844, N. S. A. C. ?

Ans. 26th of January, 23rd of February, 30th August,

and 27th of December.

(6.) An elderly lady speaking of her age, says she was born in the year 1760, but does not know on what day of the month: she only recollects hearing her father say it was the second Wednesday in February; required the day of the month she was born? Ans. 13th.

(7.) In what years of the 19th century, after Christ, new style, does 29th February fall on a Friday ?

Look in the table for 29th the given date of the month, and on the same horizontal line find the given day of the week, Friday, directly over which, on the same horizontal line with Feb. (since 29th indicates leap year) will be found E. the dominical letter for the required year.

For the 19th century find E, in the column for two centuries N. S. A. C. On the same horizontal line will be found the remaining years above centuries after Christ, viz. 0, 6, 17, 23, 28, 34, 45, 51, 56, 62, 73, 79, 84, and 90, indicating 1800, 1806, &c.; the year 1800 is, however, excluded, since the 19th century does not begin before 1 Jan., 1801; moreover, for 29th February, leap years only are to be taken, whence the years required are 1828, 1856, and 1884.

(8.) On what years of the 19th century, New Style, does Midsummerday (24th June) fall on a Sunday?

Ans. 1804, 1810, 1821, 1827, 1832, 1838, 1849, 1855, 1860, 1866, 1877, 1883, 1888, and 1894.

(9.) Required the Dominical Letters for leap years and common years, when the 1st of January and February fall on a Sunday?

Ans. In leap years only G and c for January and February respectively; and in common years A and D.

(10.) According to Mr. Baily an eclipse of the sun happened 30th September, 610, B. C. o. S. Required the day of the week.

In the column of 6 centuries B. C. o. s. (being the centuries of the given date, 610), and on the same horizontal line with 10 (the remaining years of the given date, 610), among the remaining years above centuries before Christ will be found the Sunday letter B. With which, as before, we find Friday, the day of the week required. (11.) According to Archbishop Usher, the earth was created 23rd October, 4004, B. C. o. s. Required the day of the week.

Ans. Sunday. (12.) On what days of the week, in the year 1724, Old Style, did 17th of January, leap year, and 16th of December fall? and in what other years of the 18th and 19th centuries will the same dates of the month fall on the same days of the week?

Ans. In the year 1724, o. s., 17th January happened on a Friday, and 16th December on a Wednesday. And the only other leap year, O. S., in the 18th century, which answers the question, is 1752; and the only leap year, N. s., which in the 18th century answers the question is 1772, therefore 17th January falls on a Friday. Similarly, in the 19th century, the years are 1812, 1840, 1868, and 1896, in which 17th January falls on a Friday.

With regard to 16th December, all years before 1752 are to be taken by Old Style; these years are 1702, 1713, 1719, 1724, 1730, 1741, and 1747, o. s.; the years after 1751 are to be taken by New Style, which, in the 18th century, are 1761, 1767, 1772, 1778, 1789, 1795. And, in the 19th century, 1801, 1807, 1812, 1818, 1829, 1835, 1840, 1846, 18 57, 1863, 1868, 1874, 1885, 1891, and 1896, in all which years 16th December happens on a Wednesday.

N. B. In England the year was commenced by the Church on the 25th of December, or Christmas-day, from the seventh to the twelfth century, and by civilians to the fourteenth century; from 1400 till 1752, the year began on the 25th of March; and from 1752 to the present time it began on the 1st of January: consequently, in some manuscripts, where the dates do not agree with the above calendar, between January 1st to the 25th of March, in any year from 1400 to 1752, one year should be added to the given year, before using either of the above Tables; also, from 700 to 1400, for dates between Christmas-day and the 1st of January, one year should be subtracted to give the correct date. But the whole of these particulars have been generally rectified in printed works on Chronology, &c. to agree with the historical year,

TO FIND EASTER SUNDAY FOR ANY YEAR IN PERPETUITY BY NEW OR OLD STYLE.

Easter Sunday is that Sunday which happens next after the Paschal fourteenth of the moon.

The paschal fourteenth of the moon is that fourteenth day of the moon's age which happens on or next after the 21st March.

The paschal fourteenth of the moon depends on the moon's age on some specific day, (the choice of which is arbitrary).

The epact of any year is the moon's age on the last day of the preceding year.

The paschal fourteenth has therefore a dependence on the epact.

The epact depends on a cycle of 19 years; the nineteen numbers of this cycle are called golden numbers; in the Julian or Old style a lunar correction is in strictness required; in the Gregorian or new style there is a second correction required, which may be called the solar correction. The lunar correction is a correction of 1 day every 312 years, or of 8 days in 2500 years; its cycle is a passage through 4 lunations, or 15 x 2500-37500 years, or 375 centuries, because it is only varied from century to century.

The solar correction depends only on the change of style from the Julian to the Gregorian; the three days taken away by Pope Gregory XIII. every 400 years amounts to an entire lunation or 30 days in 4000 years, which is therefore the cycle of the solar correction.

In the process of determining Easter there are several divisions, in some of which the integral quotient only is to be taken, and others in which the remainder only is required.

When the letter q is attached as an index to a formula of division, it denotes the integral quotient only is to be taken.

When the letter r is attached as an index to a formula of division, it

denotes that the remainder only is to be taken; thus in

quotient and 4 the remainder; then (176) q
(176) = 16,5

and

To find Easter Sunday for any Year after Christ, New

Style.

First. Let the given date of the year be called

Second. Let

α

a

(100). or the number of centuries contained in a, be

If e=24, change it always into 25. If e=25, change it into 26, pro

Fifth. Take 44-e, if e be less than 24; but if e exceed 24, take 74-e, and call the result

Sixth. Let 7.

{p+a+ (2)
),

(4) + (4) + [2 - (-9).

9

7

P

d

Seventh. Then p+d, if p+d does not exceed 31, is that day of March on which falls Easter Sunday.

And p+d-31, if p+ does exceed 31, is that day of April on which falls Easter Sunday.

In the above process

(1), which may be called g, is the golden number

of the year preceding the given date a; its cycle is 19 years.

(b + 1 - 0 ),

is the lunar correction (for which we may also take the

remainder after dividing by 30).

(4), + [30- (3%).]; is the solar correction (for which we may also

30

take the remainder after dividing by 30).

The sum of the above

two corrections, (b+1−c),

(b + 1 − c) + ( 4 ) 2+

or the remainder after dividing it by 30, is the luni-solar

correction; its cycle is 300000 years, being the least common multiple of the two partial cycles of 37500 and 4000 years.

e is the epact; its cycle is 19 x 300000=5700000 years, compounded of 19, the cycle of the Golden number, and 300000, the cycle of the luni-solar correction.

p is the paschal term, or the number of days from the last day of the preceding February to the day of the paschal fourteenth; its cycle is the same as that of the epact, viz. 5700000 years.

(),+ [2-(9),] is the week-day correction; its cycle is 400 years.

7-d is the dominical number; it determines the day of the week upon which falls the paschal fourteenth for, as 7-d is=0, 1, 2, 3, 4, 5, or 6, so does the paschal fourteenth fall upon Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, or Saturday.

d is the number of days by which Easter Sunday follows the paschal fourteenth.