the values of which obviously circulate in a period of 7 times 30 or 210 years.
Let C denote the number of completed cycles, and y the year of the cycle; then Y = 30 C + y, and
| w = 5 | C 7 | r + 6 | y 7 | r + 3 | 11 y +3 30 | r (rejecting sevens). |
From this formula the following table has been constructed:—
Table VIII.
Year of the | Number of the Period of Seven Cycles = (C/7)r | |||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | ||||
0 | 8 | Mon. | Sat. | Thur. | Tues. | Sun. | Frid. | Wed. | ||
1 | 9 | 17 | 25 | Frid. | Wed. | Mon. | Sat. | Thur. | Tues. | Sun. |
*2 | *10 | *18 | *26 | Tues. | Sun. | Frid. | Wed. | Mon. | Sat. | Thur. |
3 | 11 | 19 | 27 | Sun. | Frid. | Wed. | Mon. | Sat. | Thur. | Tues. |
4 | 12 | 20 | 28 | Thur. | Tues. | Sun. | Frid. | Wed. | Mon. | Sat. |
*5 | *13 | *21 | *29 | Mon. | Sat. | Thur. | Tues. | Sun. | Frid. | Wed. |
6 | 14 | 22 | 30 | Sat. | Thur. | Tues. | Sun. | Frid. | Wed. | Mon. |
*7 | 15 | 23 | Wed. | Mon. | Sat. | Thur. | Tues. | Sun. | Frid. | |
*16 | *24 | Sun. | Frid. | Wed. | Mon. | Sat. | Thur. | Tues. | ||
To find from this table the day of the week on which any year of the Hegira commences, the rule to be observed will be as follows:—
Rule.—Divide the year of the Hegira by 30; the quotient is the number of cycles, and the remainder is the year of the current cycle. Next divide the number of cycles by 7, and the second remainder will be the Number of the Period, which being found at the top of the table, and the year of the cycle on the left hand, the required day of the week is immediately shown.
The intercalary years of the cycle are distinguished by an asterisk.
For the computation of the Christian date, the ratio of a mean year of the Hegira to a solar year is