Also the number of intercalary years from the year 1 up to the year Y inclusive = ((11 Y + 14) / 30)w; and the same up to the year Y - 1 = (11 Y + 3 / 30)w.
To find the day of the week on which any year of the Hegira begins, we observe that the year 1 began on a Friday, and that after every common year of 354 days, or 50 weeks and 4 days, the day of the week must necessarily become postponed 4 days, besides the additional day of each intercalary year.
|
Hence if w = 1 indicate Sun. |
2 Mon. |
3 Tue. |
4 Wed. |
5 Thur. |
6 Frid. |
7 Sat. |
the day of the week on which the year Y commences will be
| w = 2 + 4 | Y 7 | r + | 11 Y + 3 30 | w (rejecting sevens). |
| But, 30 | 11 Y + 3 30 | w + | 11 Y + 3 30 | r = 11 Y + 3 |
| gives 120 | 11 Y + 3 30 | w = 12 + 44 Y - 4 | 11 Y + 3 30 | r, |
| or | 11 Y + 3 30 | w = 5 + 2 Y + 3 | 11 Y + 3 30 | r (rejecting sevens). |
So that
| w = 6 | Y 7 | r + 3 | 11 Y + 3 30 | r (rejecting sevens), |