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:
| From | 400 | to | 500 | From | 4 | or | 11 | |
| " | 500 | " | 600 | " | 5 | " | 11 | |
| " | 600 | " | 700 | " | 6 | " | 13 | |
| " | 700 | " | 900 | " | 7 | |||
| " | 900 | " | 1000 | " | 1 | " | 8 | |
| " | 1000 | " | 1100 | " | 2 | " | 9 | |
| " | 1100 | " | 1300 | " | 3 | " | 10 | |
| " | 1300 | " | 1400 | " | 4 | " | 11 | |
| " | 1400 | " | 1500 | " | 5 | " | 12 | |
| " | 1500 | " | 1700 | " | 6 | " | 11 |
It will be found by calculation that from the year
| 400 | to | 500 | the | discrepancy | is | 1 | day |
| 500 | " | 600 | " | " | " | 2 | " |
| 600 | " | 700 | " | " | " | 3 | " |
| 700 | " | 900 | " | " | " | 4 | " |
| 900 | " | 1000 | " | " | " | 5 | " |
| 1000 | " | 1100 | " | " | " | 6 | " |
| 1100 | " | 1300 | " | " | " | 7 | " |
| 1300 | " | 1400 | " | " | " | 8 | " |
| 1400 | " | 1500 | " | " | " | 9 | " |
| 1500 | " | 1700 | " | " | " | 10 | " |
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.