# 1911 Encyclopædia Britannica/Calendar/Mahommedan Calendar

## Mahommedan Calendar

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${\displaystyle {\tfrac {11}{30}}}$ days, or 354 days 8 hours 48 min., which divided by 12 gives 29${\displaystyle {\tfrac {191}{360}}}$ 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 = ${\displaystyle \left({\tfrac {11Y+14}{30}}\right)_{r}}$,

the year is intercalary when R < 11.

Also the number of intercalary years from the year 1 up to the year Y inclusive = ${\displaystyle \left({\tfrac {11Y+14}{30}}\right)_{w}}$; and the same up to the year Y - 1 = ${\displaystyle \left({\tfrac {11Y+3}{30}}\right)_{w}}$.

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${\displaystyle \left({\tfrac {Y}{7}}\right)_{r}}$ + ${\displaystyle \left({\tfrac {11Y+3}{30}}\right)_{w}}$ (rejecting sevens).
But, 30 ${\displaystyle \left({\tfrac {11Y+3}{30}}\right)_{w}}$ + ${\displaystyle \left({\tfrac {11Y+3}{30}}\right)_{r}}$ = 11 Y + 3
gives 120${\displaystyle \left({\tfrac {11Y+3}{30}}\right)_{w}}$ = 12 + 44 Y - 4${\displaystyle \left({\tfrac {11Y+3}{30}}\right)_{r}}$,
or ${\displaystyle \left({\tfrac {11Y+3}{30}}\right)_{w}}$ = 5 + 2 Y + 3${\displaystyle \left({\tfrac {11Y+3}{30}}\right)_{r}}$ (rejecting sevens).

So that

w = 6 ${\displaystyle \left({\tfrac {Y}{7}}\right)_{r}}$ + 3 ${\displaystyle \left({\tfrac {11Y+3}{30}}\right)_{r}}$ (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 ${\displaystyle \left({\tfrac {C}{7}}\right)_{r}}$ + 6 ${\displaystyle \left({\tfrac {y}{7}}\right)_{r}}$ + 3 ${\displaystyle \left({\tfrac {11y+3}{30}}\right)_{r}}$ (rejecting sevens).

From this formula the following table has been constructed:—

TABLE VIII.

 Year of the Current Cycle (y) Number of the Period of Seven Cycles = ${\displaystyle \left({\tfrac {C}{7}}\right)_{r}}$ 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

${\displaystyle {\tfrac {\mbox{Year of Hegira}}{\mbox{Mean solar year}}}}$ = ${\displaystyle {\frac {354{\tfrac {11}{30}}}{365.2422}}}$ = 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
----
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.

TABLE IX.—Mahommedan Years.

 43rd Cycle. Year of Hegira. Commencement (1st of Muharram). 1261 Frid. 10 Jan. 1845 1262* Tues. 30 Dec. 1845 1263 Sun. 20 Dec. 1846 1264 Thur. 9 Dec. 1847 1265* Mon. 27 Nov. 1848 1266 Sat. 17 Nov. 1849 1267* Wed. 6 Nov. 1850 1268 Mon. 27 Oct. 1851 1269 Frid. 15 Oct. 1852 1270* Tues. 4 Oct. 1853 1271 Sun. 24 Sept. 1854 1272 Thur. 13 Sept. 1855 1273* Mon. 1 Sept. 1856 1274 Sat. 22 Aug. 1857 1275 Wed. 11 Aug. 1858 1276* Sun. 31 July 1859 1277* Frid. 20 July 1860 1278* Tues. 9 July 1861 1279 Sun. 29 June 1862 1280 Thur. 18 June 1863 1281* Mon. 6 June 1864 1282 Sat. 27 May 1865 1283 Wed. 16 May 1866 1284* Sun. 5 May 1867 1285 Frid. 24 April 1868 1286* Tues. 13 April 1869 1287 Sun. 3 April 1870 1288 Thur. 23 Mar. 1871 1289* Mon. 11 Mar. 1872 1290 Sat. 1 Mar. 1873 44th Cycle. 1291 Wed. 18 Feb. 1874 1292* Sun. 7 Feb. 1875 1293 Frid. 28 Jan. 1876 1294 Tues. 16 Jan. 1877 1295* Sat. 5 Jan. 1878 1296 Thur. 26 Dec. 1878 1297* Mon. 15 Dec. 1879 1298 Sat. 4 Dec. 1880 1299 Wed. 23 Nov. 1881 1300* Sun. 12 Nov. 1882 1301 Frid. 2 Nov. 1883 1302 Tues. 21 Oct. 1884 1303* Sat. 10 Oct. 1885 1304 Thur. 30 Sept. 1886 1305 Mon. 19 Sept. 1887 1306* Frid. 7 Sept. 1888 1307 Wed. 28 Aug. 1889 1308* Sun. 17 Aug. 1890 1309 Frid. 7 Aug. 1891 1310 Tues. 26 July 1892 1311* Sat. 15 July 1893 1312 Thur. 5 July 1894 1313 Mon. 24 June 1895 1314* Frid. 12 June 1896 1315 Wed. 2 June 1897 1316* Sun. 22 May 1898 1317 Frid. 12 May 1899 1318 Tues. 1 May 1900 1319* Sat. 20 April 1901 1320 Thur. 10 April 1902 45th Cycle. 1321 Mon. 30 Mar. 1903 1322* Frid. 18 Mar. 1904 1323 Wed. 8 Mar. 1905 1324 Sun. 25 Feb. 1906 1325 Thur. 14 Feb. 1907 1326 Tues. 4 Feb. 1908 1327* Sat. 23 Jan. 1909 1328 Thur. 13 Jan. 1910 1329 Mon. 2 Jan. 1911 1330* Frid. 22 Dec. 1911
 45th Cycle.—continued. Year of Hegira. Commencement (1st of Muharram). 1331 Wed. 11 Dec. 1912 1332 Sun. 30 Nov. 1913 1333* Thur. 19 Nov. 1914 1334 Tues. 9 Nov. 1915 1335 Sat. 28 Oct. 1916 1336* Wed. 17 Oct. 1917 1337 Mon. 7 Oct. 1918 1338* Frid. 26 Sept. 1919 1339 Wed. 15 Sept. 1920 1340 Sun. 4 Sept. 1921 1341* Thur. 24 Aug. 1922 1342 Tues. 14 Aug. 1923 1343 Sat. 2 Aug. 1924 1344* Wed. 22 July 1925 1345 Mon. 12 July 1926 1346* Frid. 1 July 1927 1347 Wed. 20 June 1928 1348 Sun. 9 June 1929 1349* Thur. 29 May 1930 1350 Tues. 19 May 1931 46th Cycle. 1351 Sat. 7 May 1932 1352* Wed. 26 April 1933 1353 Mon. 16 April 1934 1354 Frid. 5 April 1935 1355* Tues. 24 Mar. 1936 1356 Sun. 14 Mar. 1937 1357* Thur. 3 Mar. 1938 1358 Tues. 21 Feb. 1939 1359 Sat. 10 Feb. 1940 1360* Wed. 29 Jan. 1941 1361 Mon. 19 Jan. 1942 1362 Frid. 8 Jan. 1943 1363* Tues. 28 Dec. 1943 1364 Sun. 17 Dec. 1944 1365 Thur. 6 Dec. 1945 1366* Mon. 25 Nov. 1946 1367 Sat. 15 Nov. 1947 1368* Wed. 3 Nov. 1948 1369 Mon. 24 Oct. 1949 1370 Frid. 13 Oct. 1950 1371* Tues. 2 Oct. 1951 1372 Sun. 21 Sept. 1952 1373 Thur. 10 Sept. 1953 1374* Mon. 30 Aug. 1954 1375 Sat. 20 Aug. 1955 1376* Wed. 8 Aug. 1956 1377 Mon. 29 July 1957 1378 Frid. 18 July 1958 1379* Tues. 7 July 1959 1380 Sun. 26 June 1960 47th Cycle. 1381 Thur. 15 June 1961 1382* Mon. 4 June 1962 1383 Sat. 25 May 1963 1384 Wed. 13 May 1964 1385* Sun. 2 May 1965 1386 Frid. 22 April 1966 1387* Tues. 11 April 1967 1388 Sun. 31 Mar. 1968 1389 Thur. 20 Mar. 1969 1390* Mon. 9 Mar. 1970 1391 Sat. 27 Feb. 1971 1392 Wed. 16 Feb. 1972 1393* Sun. 4 Feb. 1973 1394 Frid. 25 Jan. 1974 1395 Tues. 14 Jan. 1975 1396* Sat. 3 Jan. 1976 1397 Thur. 23 Dec. 1976 1398* Mon. 12 Dec. 1977 1399 Sat. 2 Dec. 1978 1400 Wed. 21 Nov. 1979
 47th Cycle.—continued. Year of Hegira. Commencement (1st of Muharram). 1401* Sun. 9 Nov. 1980 1402 Frid. 30 Oct. 1981 1403 Tues. 19 Oct. 1982 1404* Sat. 8 Oct. 1983 1405 Thur. 27 Sept. 1984 1406* Mon. 16 Sept. 1985 1407 Sat. 6 Sept. 1986 1408 Wed. 26 Aug. 1987 1409* Sun. 14 Aug. 1988 1410 Frid. 4 Aug. 1989 48th Cycle. 1411 Tues. 24 July 1990 1412* Sat. 13 July 1991 1413 Thur. 2 July 1992 1414 Mon. 21 June 1993 1415* Frid. 10 June 1994 1416 Wed. 31 May 1995 1417* Sun. 19 May 1996 1418 Frid. 9 May 1997 1419 Tues. 28 April 1998 1420* Sat. 17 April 1999 1421 Thur. 6 April 2000 1422 Mon. 26 Mar. 2001 1423 Frid. 15 Mar. 2002 1424 Wed. 5 Mar. 2003 1425 Sun. 22 Feb. 2004 1426* Thur. 10 Feb. 2005 1427 Tues. 31 Jan. 2006 1428* Sat. 20 Jan. 2007 1429 Thur. 10 Jan. 2008 1430 Mon. 29 Dec. 2008 1431* Frid. 18 Dec. 2009 1432 Wed. 8 Dec. 2010 1433 Sun. 27 Nov. 2011 1434* Thur. 15 Nov. 2012 1435 Tues. 5 Nov. 2013 1436* Sat. 25 Oct. 2014 1437 Thur. 15 Oct. 2015 1438 Mon. 3 Oct. 2016 1439* Frid. 22 Sept. 2017 1440 Wed. 12 Sept. 2018 49th Cycle. 1441 Sun. 1 Sept. 2019 1442* Thur. 20 Aug. 2020 1443 Tues. 10 Aug. 2021 1444 Sat. 30 July 2022 1445* Wed. 19 July 2023 1446 Mon. 8 July 2024 1447* Frid. 27 June 2025 1448 Wed. 17 June 2026 1449 Sun. 6 June 2027 1450* Thur. 25 May 2028 1451 Tues. 15 May 2029 1452 Sat. 4 May 2030 1453* Wed. 23 April 2031 1454 Mon. 12 April 2032 1455 Frid. 1 April 2033 1456* Tues. 21 Mar. 2034 1457 Sun. 11 Mar. 2035 1458* Thur. 28 Feb. 2036 1459 Tues. 17 Feb. 2037 1460 Sat. 6 Feb. 2038 1461* Wed. 26 Jan. 2039 1462 Mon. 16 Jan. 2040 1463 Frid. 4 Jan. 2041 1464* Tues. 24 Dec. 2041 1465 Sun. 14 Dec. 2042 1466* Thur. 3 Dec. 2043 1467 Tues. 22 Nov. 2044 1468 Sat. 11 Nov. 2045 1469* Wed. 31 Oct. 2046 1470 Mon. 21 Oct. 2047

TABLE XI.—Principal Days of the Mahommedan Calendar.

 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.