Year of the Number of the Period of Seven Cycles = (C/7)_r
Current Cycle (y) 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
Year of Hegira / Mean solar year = 354-11/30 / 365.2422 = 0.970224.
The year 1 began 16 July 622, Old Style, or 19 July 622, according to the
New or Gregorian Style. Now the day of the year answering to the 19th of
July is 200, which, in parts of the solar year, is 0.5476, and the number
of years elapsed = Y - 1. Therefore, as the intercalary days are
distributed with considerable regularity in both calendars, the date of
commencement of the year Y expressed in Gregorian years is
0.970224 (Y - 1) + 622.5476,
or 0.970224 Y + 621.5774.
This formula gives the following rule for calculating the date of the
commencement of any year of the Hegira, according to the Gregorian or New
Style.
_Rule._--Multiply 970224 by the year of the Hegira, cut off six decimals
from the product, and add 621.5774. The sum will be the year of the
Christian era, and the day of the year will be found by multiplying the
decimal figures by 365.
The result may sometimes differ a day from the truth, as the intercalary
days do not occur simultaneously; but as the day of the week can always be
accurately obtained from the foregoing table, the result can be readily
adjusted.
_Example._--Required the date on which the year 1362 of the Hegira begins.
970224
1362
--------
1940448
5821344
2910672
970224
-----------
1321.445088
621.5774
-----------
1943.0225
365
----
1125
1350
675
------
8.2125
Thus the date is the 8th day, or the 8th of January, of the year 1943.
To find, as a test, the accurate day of the week, the proposed year of the
Hegira, divided by 30, gives 45 cycles, and remainder 12, the year of the
current cycle.
Also 45, divided by 7, leaves a remainder 3 for the number of the period.
Therefore, referring to 3 at the top of the table, and 12 on the left, the
required day is Friday.
The tables, page 571, show that 8th January 1943 is a Friday, therefore the
date is exact.
For any other date of the Mahommedan year it is only requisite to know the
names of the consecutive months, and the number of days in each; these
are--
Muharram . . . . . . . 30
Saphar . . . . . . . . 29
Rabia I. . . . . . . . 30
Rabia II. . . . . . . . 29
Jomada I. . . . . . . . 30
Jomada II. . . . . . . 29
Rajab . . . . . . . . . 30
Shaaban . . . . . . . . 29
Ramadan . . . . . . . . 30
Shawall (Shawwal) . . . 29
Dulkaada (Dhu'l Qa'da) 30
Dulheggia (Dhu'l Hijja) 29 )
and in intercalary )
years . . . . . . . . 30 )
The ninth month, Ramad[=a]n, is the month of Abstinence observed by the
Moslems.
The Moslem calendar may evidently be carried on indefinitely by successive
addition, observing only to allow for the additional day that occurs in the
bissextile and intercalary years; but for any remote date the computation
according to the preceding rules will be most efficient, and such
computation may be usefully employed as a check on the accuracy of any
considerable extension of the calendar by induction alone.
The following table, taken from Woolhouse's _Measures, Weights and Moneys
of all Nations_, shows the dates of commencement of Mahommedan years from
1845 up to 2047, or from the 43rd to the 49th cycle inclusive, which form
the whole of the seventh period of seven cycles. Throughout the next period
of seven cycles, and all other like periods, the days of the week will
recur in exactly the same order. All the tables of this kind previously
published, which extend beyond the year 1900 of the Christian era, are
erroneous, not excepting the celebrated French work, _L'Art de vérifier les
dates_, so justly regarded as the greatest authority in chronological
matters. The errors have probably arisen from a continued excess of 10 in
the discrimination of the intercalary years.