1911 Encyclopædia Britannica/Calendar/Mahommedan Calendar

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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\tfrac{11}{30} days, or 354 days 8 hours 48 min., which divided by 12 gives 29\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 = \left(\tfrac{11 Y + 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 = \left(\tfrac{11 Y + 14}{30}\right)_w; and the same up to the year Y - 1 = \left(\tfrac{11 Y + 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\left(\tfrac{Y}{7}\right)_r + \left(\tfrac{11 Y + 3}{30}\right)_w (rejecting sevens).
But, 30 \left(\tfrac{11 Y + 3}{30}\right)_w + \left(\tfrac{11 Y + 3}{30}\right)_r = 11 Y + 3
gives 120\left(\tfrac{11 Y + 3}{30}\right)_w = 12 + 44 Y - 4\left(\tfrac{11 Y + 3}{30}\right)_r,
or \left(\tfrac{11 Y + 3}{30}\right)_w = 5 + 2 Y + 3\left(\tfrac{11 Y + 3}{30}\right)_r (rejecting sevens).

So that

w = 6 \left(\tfrac{Y}{7}\right)_r + 3 \left(\tfrac{11 Y + 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 \left(\tfrac{C}{7}\right)_r + 6 \left(\tfrac{y}{7}\right)_r + 3 \left(\tfrac{11 y +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 = \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

\tfrac{\mbox{Year of Hegira}}{\mbox{Mean solar year}} = \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.