RULE FOR FINDING THE DAY OF THE WEEK OF ANY GIVEN DATE, FOR BOTH OLD AND NEW STYLES.

By arranging the dominical letters in the order in which the different months commence, the day of the week on which any month of any year, or day of the month has fallen or will fall, from the commencement of the Christian era to the year of our Lord 4000, may be calculated. (Appendix G.) They have been arranged thus in the following couplet, in which At stands for January, Dover for February, Dwells for March, etc.

At Dover Dwells George Brown, Esquire,
Good Carlos Finch, and David Fryer.

Now if A be dominical or Sunday letter for a given year, then January and October being represented by the same letter, begin on Sunday; February, March and November, for the same reason, begin on Wednesday; April and July on Saturday; May on Monday, June on Thursday, August on Tuesday, September and December on Friday. It is evident that every month in the year must commence on some one day of the week represented by one of the first seven letters of the alphabet. Now let

Now each of these letters placed opposite the months respectively represents the day of the week on which the month commences, and they are the first letters of each word in the preceding couplet.

To find the day of the week on which a given day of any year will occur, we have the following

RULE.

Find the dominical letter for the year. Read from this to the letter which begins the given month, always reading from A toward G, calling the dominical letter Sunday, the next Monday, etc. This will show on what day of the week the month commenced; then reckoning the number of days from this will give the day required.

EXAMPLES.

History records the fall of Constantinople on May 29th, 1453. On what day of the week did it occur? We have then 1453 ÷ 43 = 63 +; 1453 + 363 = 1816; 1816 ÷ 7 = 259, remainder 3. Then 10 - 3 = 7; therefore, G being the seventh letter is dominical letter for 1453. Now reading from G to B, the letter for May, we have G Sunday, A Monday, and B Tuesday; hence May commenced on Tuesday and the 29th was Tuesday.

The change from Old to New Style was made by Pope Gregory XIII, October 5th, 1582. On what day of the week did it occur? We have then 1582 ÷ 4 = 395+; 1582 + 395 = 1977; 1977 ÷ 7 = 282, remainder 3. Then 10 - 3 = 7; therefore, G being the seventh letter, is dominical letter for 1582. Now reading from G to A, the letter for October, we have G Sunday, A Monday, etc. Hence October commenced on Monday, and the 5th was Friday.

On what day of the week did the 15th of the same month fall in 1582? We have then 1582 ÷ 4 = 395+; 1582 + 395 = 1977; 1977 ÷ 7 = 282, remainder 3. Then 6 - 3 = 3; therefore, C being the third letter, is the dominical letter for 1582. Now reading from C to A, the letter for October, we have C Sunday, D Monday, E Tuesday, etc. Hence October commenced on Friday, and the 15th was Friday.

How is this, says one? You have just shown by computation that October, 1582, commenced on Monday, you now say that it occurred on Friday. You also stated that the 5th was Friday; you now say that the 15th was Friday. This is absurd; ten is not a multiple of seven. There is nothing absurd about it. The former computation was Old Style, the latter New Style, the Old being ten days behind the new.

As regards an interval of ten days between the two Fridays, there was none; Friday, the 5th, and Friday, the 15th, was one and the same day; there was no interval, nothing ever occurred, there was no time for anything to occur; the edict of the Pope decided it; he said the 5th should be called the 15th, and it was so.

Hence to October the 5th, 1582, the computation should be Old Style; from the 15th to the end of the year New Style.On what day of the week did the years 1, 2 and 3, of the era commence? None of these numbers can be divided by 4; neither are they divisible by 7; but they may be treated as remainders after dividing by 7. Now each of these numbers of years consists of an even number of weeks with remainders of 1, 2 and 3 days respectively. Hence we have then for the year 1, 3 - 1 = 2; therefore, B being the second letter, is the dominical letter for the year 1. Now reading from B to A, the letter for January, we have B Sunday, C Monday, D Tuesday, etc. Hence January commenced on Saturday.

Then we have for the year 2, 3 - 2 = 1; therefore A being the first letter, is dominical letter for the year 2; hence it is evident that January commenced on Sunday. Again we have for the year 3, 10 - 3 = 7; therefore, G being the seventh letter, is dominical letter for the year 3. Now reading from G to A, the letter for January, we have G Sunday, A Monday; hence January commenced on Monday.

On what day of the week did the year 4 commence? Now we have a number that is divisible by 4, it being the first leap-year in the era, so we have 4 ÷ 4 = 1; 4 + 1 = 5; 5 ÷ 7 = 0, remainder 5. Then 10 - 5 = 5; therefore, E being the 5th letter, is dominical letter for that part of the year which follows the 29th of February, while F, the letter that follows it, is dominical letter for January and February. Now reading from F to A, the letter for January, we have F Sunday, G Monday, A Tuesday; hence January commenced on Tuesday.

Now we have disposed of the first four years of the era; the dominical letters being B, A, G, and F, E. Hence it is evident, while one year consists of an even number of weeks and one day, two years of an even number of weeks and two days, three years of an even number of weeks and three days, that every fourth year, by intercalation, is made to consist of 366 days; so that four years consist of an even number of weeks and five days; for we have (4 ÷ 4) + 4 = 5, the dominical letter going back from G in the year 3, to F, for January and February in the year 4, and from F to E for the rest of the year, causing the following year to commence two days later in the week than the year preceding.

The year 1 had 53 Saturdays; the year 2, 53 Sundays; the year 3, 53 Mondays, and the year 4, 53 Tuesdays and 53 Wednesdays, causing the year 5 to commence on Thursday, two days later in the week than the preceding year. Now what is true concerning the first four years of the era, is true concerning all the future years, and the reason for the divisions, additions and subtractions in finding the dominical letter is evident.

The Declaration of Independence was signed July 4, 1776. On what day of the week did it occur? We have then 1776 ÷ 4 = 444; 1776 + 444 = 2220; 2220 ÷ 7 = 317, remainder 1. Then 7 - 1 = 6, therefore F and G are the dominical letters for 1776, G for January and February, and F for the rest of the year. Now reading from F to G, the letter for July, we have F Sunday, G Monday; hence July commenced on Monday, and the fourth was Thursday. On what day of the week did Lee surrender to Grant, which occurred on April 9th, 1865? We have then 1865 ÷ 4 = 466+; 1865 + 466 = 2331; 2331 ÷ 7 = 333, remainder 0. Then 1 - 0 = 1; therefore, A being the first letter, is dominical letter for 1865. Now reading from A to G, the letter for April, we have A Sunday, B Monday, C Tuesday, etc. Hence April commenced on Saturday, and the 9th was Sunday.

Benjamin Harrison was inaugurated President of the United States on Monday, March 4, 1889. On what day of the week will the 4th of March fall in 1989? We have then 1989 ÷ 4 = 497+; 1989 + 497 = 2486; 2486 ÷ 7 = 355, remainder 1. Then 2 - 1 = 1; therefore, A being the first letter, is dominical letter for 1989. Now, reading from A to D, the letter for March, we have A Sunday, B Monday, C Tuesday, and D Wednesday; hence March will commence on Wednesday, and the 4th will fall on Saturday. Columbus landed on the island of San Salvador on Friday, October 12, 1492. On what day of the month and on what day of the week will the four hundredth anniversary fall in 1892?

The day of the month on which Columbus landed is, of course, the day to be observed in commemoration of that event. The Julian calendar, which was then in use throughout Europe, and the very best that had ever been given to the world, made the year too long by more than eleven minutes. Those eleven minutes a year had accumulated, from the council of Nice, in 325, to the discovery of America, in 1492, to nine days, so that the civil year was nine days behind the true or solar time; that is, when the Earth, in her annual revolution, had arrived at that point of the ecliptic coinciding with the 21st of October, the civil year, according to the Julian calendar, was the 12th.

Now, to restore the coincidence, the nine days must be dropped, or suppressed, calling what was erroneously called the 12th of October, the 21st. Since the Julian calendar was corrected by Gregory, in 1582, we have so intercalated as to retain, very nearly, the coincidence of the solar and the civil year. It has already been shown in Chapter III, (q. v.) that in the Gregorian calendar, the cycle which restores the coincidence of the day of the month and the day of the week, is completed in 400 years; so that after 400 years, events will again transpire in the same order, on the same day of the week. Now, as Columbus landed on Friday, October 21st, 1492, so Friday, October 21st, 1892, is the day of the month and also the day of the week to be observed in commemoration of that event. We have then 1892 ÷ 4 = 473; 1892 + 473 = 2365; 2365 ÷ 7 = 337, remainder 6. Then 8 - 6 = 2; therefore, B and C are dominical letters for 1892, C for January and February, and B for the rest of the year. Now, reading from B to A, the letter for October, we have B Sunday, C Monday, etc. Hence October will commence on Saturday and the 21st will be Friday.

Although there was an error of thirteen days in the Julian calendar when it was reformed by Gregory, in 1582, there was a correction made of only ten days. There was still an error of three days from the time of Julius CÆsar to the Council of Nice, which remained uncorrected. Gregory restored the vernal equinox to the 21st of March, its date at the meeting of that council, not to the place it occupied in the time of CÆsar, namely, the 24th of March. Had he done so it would now fall on the 24th, by adopting the Gregorian rule of intercalation. Appendix H.

If desirable calculations may be made in both Old and New Styles from the year of our Lord 300. There is no perceptible discrepancy in the calendars, however, until the close of the 4th century, when it amounts to nearly one day, reckoned in round numbers one day. Now in order to make the calculation, proceed according to rule already given for finding the dominical letter, and for New Style take the remainders after dividing by seven from the numbers in the following table:

It will be found by calculation that from the year

Hence the necessity, in reforming the calendar in 1582, of suppressing ten days. (See table on 59th page.) On what day of the week did January commence in 450? We have then 450 ÷ 4 = 112+; 450 + 112 = 562; 562 ÷ 7 = 80, remainder 2. Then 3 - 2 = 1; therefore, A being the first letter, is dominical letter for 450, Old Style, and January commenced on Sunday. For New Style we have 4 - 2 = 2; therefore, B being the second letter, is dominical letter for the year 450. Now reading from B to A, the letter for January, we have B Sunday, C Monday, D Tuesday, etc.

Hence, January commenced on Saturday. Old Style makes Sunday the first day; New Style makes Saturday the first and Sunday the second. On what day of the week did January commence in the year 1250? We have then 1250 ÷ 4 = 312+; 1250 + 312 = 1562; 1562 ÷ 7 = 223, remainder 1. Then 3 - 1 = 2; therefore, B being the second letter, is dominical letter for the year 1250, Old Style. Now, reading from B to A, the letter for January, we have B Sunday, C Monday, etc. Hence January commenced on Saturday. B is also dominical letter, New Style; for we take the remainder after dividing by 7, from the same number.

As both Old and New Styles have the same dominical letter, so both make January to commence on the same day of the week; but Old Style, during this century, is seven days behind the true time, so that when it is the first day of January by the Old, it is the eighth by the New.

[Pg 59 & 60]

It is here seen by the errors of the Julian Calendar the Vernal Equinox is made to occur three days earlier every 400 years, so that in 1582 it fell on the 11th instead of the 21st of March.

By the Gregorian rule of intercalation the coincidence of the solar and civil year is restored very nearly every 400 years. Appendix I.