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 JulyA.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 354-11/30 days, or 354 days 8 hours 48 min., which divided by 12 gives 29-191/360 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 ifYdenote the number of the Mahommedan year, and
the year is intercalary whenR< 11.
Also the number of intercalary years from the year 1 up to the yearYinclusive = ((11Y+ 14) / 30)w; and the same up to the yearY- 1 = (11Y+ 3 / 30)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 ifw= 1indicate Sun.
2Mon.
3Tue.
4Wed.
5Thur.
6Frid.
7Sat.
the day of the week on which the yearYcommences will be
So that
the values of which obviously circulate in a period of 7 times 30 or 210 years.
LetCdenote the number of completed cycles, andythe year of the cycle; thenY= 30C+y, and
From this formula the following table has been constructed:—
TableVIII.
Year of theCurrent Cycle (y)
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
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 yearYexpressed in Gregorian years is
0.970224 (Y- 1) + 622.5476,or 0.970224Y+ 621.5774.
0.970224 (Y- 1) + 622.5476,or 0.970224Y+ 621.5774.
0.970224 (Y- 1) + 622.5476,
or 0.970224Y+ 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.
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'sMeasures, 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.
TableIX.—Mahommedan Years.
Year ofHegira.
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 ofHegira.
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 ofHegira.
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