1911 Encyclopædia Britannica/Calendar/Mahommedan Calendar
Mahommedan Calendar[edit]
The Mahommedan era, or era of the Hegira, used in Turkey, Persia, Arabia, &c., is dated from the first day of the month preceding the flight of Mahomet from Mecca to Medina, i.e. Thursday the 15th of July A.D. 622, and it commenced on the day following. The years of the Hegira are purely lunar, and always consist of twelve lunar months, commencing with the approximate new moon, without any intercalation to keep them to the same season with respect to the sun, so that they retrograde through all the seasons in about 32½ years. They are also partitioned into cycles of 30 years, 19 of which are common years of 354 days each, and the other 11 are intercalary years having an additional day appended to the last month. The mean length of the year is therefore 354 days, or 354 days 8 hours 48 min., which divided by 12 gives 29 days, or 29 days 12 hours 44 min., as the time of a mean lunation, and this differs from the astronomical mean lunation by only 2.8 seconds. This small error will only amount to a day in about 2400 years.
To find if a year is intercalary or common, divide it by 30; the quotient will be the number of completed cycles and the remainder will be the year of the current cycle; if this last be one of the numbers 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29, the year is intercalary and consists of 355 days; if it be any other number, the year is ordinary.
Or if Y denote the number of the Mahommedan year, and
 R = ,
the year is intercalary when R < 11.
Also the number of intercalary years from the year 1 up to the year Y inclusive = ; and the same up to the year Y  1 = .
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 + (rejecting sevens).
 But, 30 + = 11 Y + 3
 gives 120 = 12 + 44 Y  4,
 or = 5 + 2 Y + 3 (rejecting sevens).
So that
 w = 6 + 3 (rejecting sevens),
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 + 6 + 3 (rejecting sevens).
From this formula the following table has been constructed:—
Year of the Current Cycle (y) 
Number of the Period of Seven Cycles =  
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
 = = 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  1225 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 
Ramadān  30 
Shawall (Shawwāl)  29 
Dulkaada (Dhu'l Qa'da)  30 
Dulheggia (Dhu'l Hijja)  29 
 and in intercalary years  30 
The ninth month, Ramadān, 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.



Muharram 1,  New Year. 
" 10,  Ashura. 
Rabia I. 11,  Birth of Mahomet. 
Jornada I. 20,  Taking of Constantinople. 
Rajab 15,  Day of Victory. 
" 20,  Exaltation of Mahomet. 
Shaaban 15,  Borak's Night. 
Shawall 1,2,3,  Kutshuk Bairam. 
Dulheggia 10,  Qurban Bairam. 