PART SECOND.
MATHEMATICAL.
ERRORS OF THE JULIAN CALENDAR.
It will be necessary in the first place to understand the difference between the Julian and Gregorian rule of intercalation. If the number of any year be exactly divisible by four it is leap year; if the remainder be 1, it is the first year after leap-year; if 2, the second; if 3, the third; thus:
And so on, every fourth year being leap-year of 366 days.
This is the Julian rule of intercalation, which is corrected by the Gregorian by making every centurial year, or the year that completes the century, a common year, if not exactly divisible by 400; so that only every fourth centurial year is leap-year; thus, 1,700, 1,800, and 1,900 are common years, but 2,000, the fourth centurial year, is leap year, and so on.
By the Julian rule three-fourths of a day is gained every century, which in 400 years amounts to three days. This is corrected by the Gregorian, by making three consecutive centurial years common years, thus suppressing three days in 400 years.
RULE.
Multiply the difference between the Julian and the solar year by 100, and we have the error in 100 years. Multiply this product by 4 and we have the error in 400 years. Now, 400 is the tenth of 4,000; therefore, multiply the last product by 10, and we have the error in 4,000 years. Now, as the discrepancy between the Julian and Gregorian year is three days in 400 years, making 3-400 of a day every year, so by dividing 365¼, the number of days in a year, by 3-400, we have the time it would take to make a revolution of the seasons.
SOLUTION.
(365 d, 6 h.) - (365 d, 5 h, 48 m, 49.62 s.) = (11 m, 10.38 s.) Now, (11 m, 10.38 s.) × 100 = 18 h, 37.3 m, the gain in 100 years. This is, reckoned in round numbers, 18 hours, or three-fourths of a day. Now, (¾ × 4) = (1 × 3) = 3: the Julian rule gaining three days, the Gregorian suppressing three days in 400 years. (3 × 10) = 30, the number of days gained by the Julian rule in 4,000 years. 365¼ ÷3 400= 48,700, so that in this long period of time, this falling back ¾ of a day every century would amount to 365¼ days; therefore, 48,699 Julian years are equal to 48,700 Gregorian years.
ERRORS OF THE GREGORIAN CALENDAR.
By reference to the preceding chapter it will be seen that there is an error of 37.3 minutes in every 100 years not corrected by the Gregorian calendar; this amounts to only .373 of a minute a year, or one day in 3,861 years, and one day and fifty-two minutes in 4,000 years.
RULE.
To find how long it would take to gain one day: Divide the number of minutes in a day by the decimal .373, that being the fraction of a minute gained every year. To find how much time would be gained in 4,000 years, multiply the decimal .373 by 4,000, and you will have the answer in minutes, which must be reduced to hours.
SOLUTION.
(24 × 60) ÷ .373 = 3,861, nearly; hence the error would amount to only one day in 3,861 years.
(.373 × 4,000) ÷ 60 = (24 h, 52 m,) = (1 d, 0 h, 52 m), the error in 4,000 years.
This trifling error in the Gregorian calendar may be corrected by suppressing the intercalations in the year 4,000, and its multiples, 8,000, 12,000, 16,000, etc., so that it will not amount to a day in 100,000 years.
RULE.
Divide 100,000 by 4,000 and you will have the number of intercalations suppressed in 100,000 years. Multiply 1 d, 52 m, (that being the error in 4,000 years) by this quotient, and you will have thediscrepancy between the Gregorian and solar year for 100,000 years. By this improved method we suppress 25 days, so that the error will only amount to 25 times 52 minutes.
SOLUTION.
100,000 ÷ 4,000 × (1 d, 52 m,) = (25d, 21 h, 40 m.) Now, (25d, 21 h, 40 m,) - 25 d = (21 h, 40 m,) the error in 100,000.
DOMINICAL LETTER.
Dominical (from the LatinDominus, Lord,) indicating the Lord’s day or Sunday. Dominical letter, one of the first seven letters of the alphabet used to denote the Sabbath or Lord’s day.
For the sake of greater generality, the days of the week are denoted by the first seven letters of the alphabet, A, B, C, D, E, F, G, which are placed in the calendar beside the days of the year, so that A stands opposite the first day of January, B opposite the second, C opposite the third, and so on to G, which stands opposite the seventh; after which A returns to the eighth, and so on through the 365 days of the year.
Now, if one of the days of the week, Sunday for example, is represented by F, Monday will be represented by G, Tuesday by A, Wednesday by B, Thursday by C, Friday by D, and Saturday by E; and every Sunday throughout the year will have the same character, F, every Monday G, every Tuesday A, and so with regard to the rest.
The letter which denotes Sunday is called the Dominical or Sunday letter for that year; and when the dominical letter of the year is known, the letters which respectively correspond to the other days of the week become known also. Did the year consist of 364 days, or 52 weeks invariably, the first day of the year and the first day of the month, and in fact any day of any year, or any month, would always commence on the same day of the week. But every common year consists of 365 days, or 52 weeks and 1 day, so that the following year will begin one day later in the week than the year preceding. Thus the year 1837 commenced on Sunday, the following year, 1838, on Monday, 1839 on Tuesday, and so on.
As the year consists of 52 weeks and 1 day, it is evident that the day which begins and ends the year must occur 53 times; thus the year 1837 begins on Sunday and ends on Sunday; so the following year, 1838, must begin on Monday. As A represented all the Sundays in 1837 and as A always stands for the first day of January, so in 1838 it will represent all the Mondays, and the dominical letter goes back from A to G; so that G represents all the Sundays in 1838, A all the Mondays, B all the Tuesdays, and so on, the dominical letter going back one place in every year of 365 days.
While the following year commences one day later in the week than the year preceding, the dominical letter goes back one place from the preceding year; thus while the year 1865 commenced on Sunday, 1866 on Monday, 1867 on Tuesday, the dominical letters are A, G and F, respectively. Therefore, if every yearconsisted of 365 days, the dominical cycle would be completed in seven years, so that after seven years the first day of the year would again occur on the same day of the week.
But this order is interrupted every four years by giving February 29 days, thereby making the year to consist of 366 days, which is 52 weeks and two days, so that the following year would commence two days later in the week than the year preceding, thus the year 1888 being leap-year, had two dominical letters, A and G; A for January and February, and G for the rest of the year. The year commenced on Sunday and ended on Monday, making 53 Sundays and 53 Mondays, and the following year, 1889, to commence on Tuesday. It now becomes evident that if the years all consisted of 364 days, or 52 weeks, they would all commence on the same day of the week; if they all consisted of 365 days, or 52 weeks and one day, they would all commence one day later in the week than the year preceding; if they all consisted of 366 days, or 52 weeks and two days, they would commence two days later in the week; if 367 days or 52 weeks and three days, then three days later, and so on, one day later for every additional day. It is also evident that every additional day causes the dominical letter to go back one place. Now in leap-year the 29th day of February is the additional or intercalary day. So one letter for January and February, and another for the rest of the year. If the number of years in the intercalary period were two, and seven being the number of days in the week, their product would be 2 × 7 = 14; fourteen, then, would be the number of years in thecycle. Again, if the number of years in the intercalary period were three, and the number of days in the week being seven, their product would be 3 × 7 = 21; twenty-one would then be the number of years in the cycle. But the number of years in the intercalary period is four, and the number of days in the week is seven, therefore their product is 4 × 7 = 28; twenty-eight is then the number of years in the cycle.
This period is called the dominical or solar cycle, and restores the first day of the year to the same day of the week. At the end of the cycle the dominical letters return again in the same order, on the same days of the month. Thus, for the year 1801, the dominical letter is D; 1802, C; 1803, B; 1804, A and G; and so on, going back five places every four years for twenty-eight years, when the cycle, being ended, D is again dominical letter for 1829, C for 1830, and so on every 28 years forever, according to the Julian rule of intercalation.
But this order is interrupted in the Gregorian calendar at the end of the century by the secular suppression of the leap-year. It is not interrupted, however, at the end of every century, for the leap-year is not suppressed in every fourth centurial year; consequently the cycle will then be continued for two hundred years. It should be here stated that this order continued without interruption from the commencement of the era until the reformation of the calendar in 1582, during which time the Julian calendar, or Old Style was used.
It has already been shown that if the number of years in the intercalary period be multiplied by seven, the number of days in the week, their product will bethe number of years in the cycle. Now, in the Gregorian calendar, the intercalary period is 400 years; this number being multiplied by seven, their product would be 2,800 years, as the interval in which the coincidence is restored between the days of the year and the days of the week.
This long period, however, may be reduced to 400 years; for since the dominical letter goes back five places every four years, in 400 years it will go back 500 places in the Julian and 497 in the Gregorian calendar, three intercalations being suppressed in the Gregorian every 400 years. Now 497 is exactly divisible by seven, the number of days in the week, therefore, after 400 years the cycle will be completed, and the dominical letters will return again in the same order, on the same days of the month.
In answer to the question, “Why two dominical letters for leap-year?†we reply, because of the additional or intercalary day after the 28th of February. It has already been shown that every additional day causes the dominical letter to go back one place. As there are 366 days in leap-year, the letter must go back two places, one being used for January and February, and the other for the rest of the year. Did we continue one letter through the year and then go back two places, it would cause confusion in computation, unless the intercalation be made at the end of the year. Whenever the intercalation is made there must necessarily be a change in the dominical letter. Had it been so arranged that the additional day was placed after the 30th of June or September, then the first letter would be used until the intercalation is made in June orSeptember, and the second to the end of the year. Or suppose that the end of the year had been fixed as the time and place for the intercalation, (which would have been much more convenient for computation,) then there would have been no use whatever for the second dominical letter, but at the end of the year we would go back two places; thus, in the year 1888, instead of A being dominical letter for two months merely, it would be continued through the year, and then passing back to F, no use whatever being made of G, and so on at the end of every leap-year. Hence it is evident that this arrangement would have been much more convenient, but we have this order of the months, and the number of days in the months as Augustus Cæsar left them eight years before Christ. The dominical letter probably was not known until the Council of Nice, in the year of our Lord 325, where, in all probability, it had its origin.
RULE FOR FINDING THE DOMINICAL LETTER.
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 if the remainder be less than three, take it from 3; but if it be 3 or more than 3, take it from 10 and the remainder will be the number of the letter calling A, 1; B, 2; C, 3, etc.
By this rule the dominical letter is found from the commencement of the era to October 5th, 1582. O. S.From October 15th, 1582, till the year 1700, take the remainder as found by the rule from 6, if it be less than 6, but if the remainder be 6, take it from 13, and so on according to instructions given in the table on 49th page. It should be understood here, that inleap-yearsthe letter found by the preceding rule will bethedominical letter for that part of the year that follows the 29th of February, while the letter which follows it will be the one for January and February.
EXAMPLES.
To find the dominical letter for 1365, we have 1365 ÷ 4 = 341 +; 1365 + 341 = 1706; 1706 ÷ 7 = 243, remainder 5. Then 10 - 5 = 5; therefore E being the fifth letter is the dominical letter for 1365.
To find the dominical letter for 1620, we have 1620 ÷ 4 = 405; 1620 + 405 = 2025; 2025 ÷ 7 = 289, remainder 2. Then 6 - 2 = 4; therefore, D and E are the dominical letters for 1620; E for January and February, and D for the rest of the year. The process of finding the dominical letter is very simple and easily understood, if we observe the following order:
1st. Divide by 4.
2d. Add to the given number.
3d. Divide by 7.
4th. Take the remainder from 3 or 10, from the commencement of the era to October 5th, 1582. From October 15th, 1582 to 1700, from 6 or 13. From 1700 to 1800, from 7, and so on. See table on 49th page.
We divide by 4 because the intercalary period is four years; and as every fourth year contains the divisor 4 once more than any of the three preceding years, so there is one more added to the fourth year than thereis to any of the three preceding years; and as every year consists of 52 weeks and one day, this additional year gives an additional day to the remainder after dividing by 7. For example, the year
Hence the numbers thus formed will be 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, and so on.
We divide by 7, because there are seven days in the week, and the remainders show how many days more than an even number of weeks there are in the given year. Take, for example, the first twelve years of the era after being increased by one-fourth, and we have
From this table it may be seen that it is these remainders representing the number of days more than an even number of weeks in the given year, that we have to deal with in finding the dominical letter.
Did the year consist of 364 days, or 52 weeks,invariably, there would be no change in the dominical letter from year to year, but the letter that represents Sunday in any given year would represent Sunday in every year. Did the year consist of only 363 days, thus wanting one day of an even number of weeks, then these remainders, instead of being taken from a given remainder, would be added to that number, thus removing the dominical letter forward one place, and the beginning of the year, instead of being one day later, would be one day earlier in the week than in the preceding year.
Thus, if the year 1 of the era be taken from 3, we would have 3 - 1 = 2; therefore, B being the second letter, is dominical letter for the year 1. But if the year consist of only 363 days, then the 1 instead of being taken from 3 would be added to 3; then we would have 3 + 1 = 4; therefore, D being the fourth letter would be dominical letter for the year 1. The former going back from C to B, the latter forward from C to D; or which amounts to the same thing, make the year to consist of 51 weeks and 6 days; then 10 - 6 = 4, making D the dominical letter as before.
As seven is the number of days in the week, and the object of these subtractions is to remove the dominical letter back one place every common year, and two in leap-year, why not take these remainders from 7? We answer, all depends upon the day of the week on which the era commenced. Had G, the seventh letter been dominical letter for the year preceding the era, then these remainders would be taken from 7; and 7 would be used until change of style in 1582. But we know from computation that C, the third letter, is dominicalletter for the year preceding the era; so we commence with three, and take the smaller remainders, 1 and 2 from 3; that brings us to A. We take the larger remainders, from 3 to 6, from 3 + 7 = 10. We add the 7 because there are seven days in the week. We use the number 10 until we get back to C, the third letter, the place from whence we started. For example, we have
The cycle of seven days being completed, we commence with the number three again, and so on until 1582, when on account of the errors of the Julian calendar, ten days were suppressed to restore the coincidence of the solar and civil year. Now every day suppressed removes the dominical letter forward one place; so counting from C to C again is seven, D is eight, E is nine, and F is ten. As F is the sixth letter, we take the remainders from 1 to 5, from 6; if the remainder be 6, take it from 6 + 7 = 13. Then 6 or 13 is used till 1700, when, another day being suppressed, the number is increased to 7. And again in 1800, for the same reason, a change is made to 1 or 8; in 1900 to 2 or 9, and so on. It will be seen by the table on the 49th page that the smaller numbers run from 1 to 7; the larger ones from 8 to 13.
From the commencement of the Christian era to October 5th, 1582, take the remainders, after dividing by 7, from 3 or 10; from October 15th,
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 then1453 ÷ 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 dayof 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 theera; 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 occurredon 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 eclipticcoinciding 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 ofCæsar, 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.
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.