The result so obtained would in general be more accurate than the Jewish calculation, from which it may differ a day, as fractions of a day do not enter alike in these computations. Such difference may also in part be accounted for by the fact that the assumed duration of the solar year is 6 min. 3925/57 sec. in excess of the true astronomical value, which will cause the dates of commencement of future Jewish years, so calculated, to advance forward from the equinox a day in error in 216 years. The lunations are estimated with much greater precision.
The following table is extracted from Woolhouse’s Measures, Weights and Moneys of all Nations:—
Table VII.—Hebrew Years.
296 Cycle.
Jewish Year
Number of Days
Commencement (1st of Tisri).
5606
354
Thur.
2 Oct. 1845
07
355
Mon.
21 Sept. 1846
08
383
Sat.
11 Sept. 1847
09
354
Thur.
28 Sept. 1848
10
355
Mon.
17 Sept. 1849
11
385
Sat.
7 Sept. 1850
12
353
Sat.
27 Sept. 1851
13
384
Tues.
14 Sept. 1852
14
355
Mon.
3 Oct. 1853
15
355
Sat.
23 Sept. 1854
16
383
Thur.
13 Sept. 1855
17
354
Tues.
30 Sept. 1856
18
355
Sat.
19 Sept. 1857
19
385
Thur.
9 Sept. 1858
20
354
Thur.
29 Sept. 1859
21
353
Mon.
17 Sept. 1860
22
385
Thur.
5 Sept. 1861
23
354
Thur.
25 Sept. 1862
24
383
Mon.
14 Sept. 1863
297 Cycle.
5625
355
Sat.
1 Oct. 1864
26
354
Thur.
21 Sept. 1865
27
385
Mon.
10 Sept. 1866
28
353
Mon.
30 Sept. 1867
29
354
Thur.
17 Sept. 1868
30
385
Mon.
6 Sept. 1869
31
355
Mon.
26 Sept. 1870
32
383
Sat.
16 Sept. 1871
33
354
Thur.
3 Oct. 1872
34
355
Mon.
22 Sept. 1873
35
383
Sat.
12 Sept. 1874
36
355
Thur.
30 Sept. 1875
37
354
Tues.
19 Sept. 1876
38
385
Sat.
8 Sept. 1877
39
355
Sat.
28 Sept. 1878
40
354
Thur.
18 Sept. 1879
41
383
Mon.
6 Sept. 1880
42
355
Sat.
24 Sept. 1881
43
383
Thur.
14 Sept. 1882
298 Cycle.
5644
354
Tues.
2 Oct. 1883
45
355
Sat.
20 Sept. 1884
46
385
Thur.
10 Sept. 1885
47
354
Thur.
30 Sept. 1886
48
353
Mon.
19 Sept. 1887
49
385
Thur.
6 Sept. 1888
50
354
Thur.
26 Sept. 1889
51
383
Mon.
15 Sept. 1890
52
355
Sat.
3 Oct. 1891
53
354
Thur.
22 Sept. 1892
54
385
Mon.
11 Sept. 1893
55
353
Mon.
1 Oct. 1894
56
355
Thur.
19 Sept. 1895
57
384
Tues.
8 Sept. 1896
58
355
Mon.
27 Sept. 1897
59
353
Sat.
17 Sept. 1898
60
384
Tues.
5 Sept. 1899
61
355
Mon.
24 Sept. 1900
62
383
Sat
14 Sept. 1901
299 Cycle.
5663
355
Thur.
2 Oct. 1902
64
354
Tues.
22 Sept. 1903
65
385
Sat.
10 Sept. 1904
66
355
Sat.
30 Sept. 1905
67
354
Thur.
20 Sept. 1906
68
383
Mon.
9 Sept. 1907
69
355
Sat.
26 Sept. 1908
70
383
Thur.
16 Sept. 1909
71
354
Tues.
4 Oct. 1910
72
355
Sat.
23 Sept. 1911
73
385
Thur.
12 Sept. 1912
74
354
Thur.
2 Oct. 1913
75
353
Mon.
21 Sept. 1914
76
385
Thur.
9 Sept. 1915
77
354
Thur.
28 Sept. 1916
78
355
Mon.
17 Sept. 1917
79
383
Sat.
7 Sept. 1918
80
354
Thur.
25 Sept. 1919
81
385
Mon.
13 Sept. 1920
300 Cycle.
Jewish Year
Number of Days
Commencement (1st of Tisri).
5682
355
Mon.
3 Oct. 1921
83
353
Sat.
23 Sept. 1922
84
384
Tues.
11 Sept. 1923
85
355
Mon.
29 Sept. 1924
86
355
Sat.
19 Sept. 1925
87
383
Thur.
9 Sept. 1926
88
354
Tues.
27 Sept. 1927
89
385
Sat.
15 Sept. 1928
90
353
Sat.
5 Oct. 1929
91
354
Tues.
23 Sept. 1930
92
385
Sat.
12 Sept. 1931
93
355
Sat.
1 Oct. 1932
94
354
Thur.
21 Sept. 1933
95
383
Mon.
10 Sept. 1934
96
355
Sat.
28 Sept. 1935
97
354
Thur.
17 Sept. 1936
98
385
Mon.
6 Sept. 1937
99
353
Mon.
26 Sept. 1938
5700
385
Thur.
14 Sept. 1939
301 Cycle.
5701
354
Thur.
3 Oct. 1940
02
355
Mon.
22 Sept. 1941
03
383
Sat.
12 Sept. 1942
04
354
Thur.
30 Sept. 1943
05
355
Mon.
18 Sept. 1944
06
383
Sat.
8 Sept. 1945
07
354
Thur.
26 Sept. 1946
08
385
Mon.
15 Sept. 1947
09
355
Mon.
4 Oct. 1948
10
353
Sat.
24 Sept. 1949
11
384
Tues.
12 Sept. 1950
12
355
Mon.
1 Oct. 1951
13
355
Sat.
20 Sept. 1952
14
383
Thur.
10 Sept. 1953
15
354
Tues.
28 Sept. 1954
16
355
Sat.
17 Sept. 1955
17
385
Thur.
6 Sept. 1956
18
354
Thur.
26 Sept. 1957
19
383
Mon.
15 Sept. 1958
302 Cycle.
5720
355
Sat.
3 Oct. 1959
21
354
Thur.
22 Sept. 1960
22
383
Mon.
11 Sept. 1961
23
355
Sat.
29 Sept. 1962
24
354
Thur.
19 Sept. 1963
25
385
Mon.
7 Sept. 1964
26
353
Mon.
27 Sept. 1965
27
385
Thur.
15 Sept. 1966
28
354
Thur.
5 Oct. 1967
29
355
Mon.
23 Sept. 1968
30
383
Sat.
13 Sept. 1969
31
354
Thur.
1 Oct. 1970
32
355
Mon.
20 Sept. 1971
33
383
Sat.
9 Sept. 1972
34
355
Thur.
27 Sept. 1973
35
354
Tues.
17 Sept. 1974
36
385
Sat.
6 Sept. 1975
37
353
Sat.
25 Sept. 1976
38
384
Tues.
13 Sept. 1977
303 Cycle.
5739
355
Mon.
2 Oct. 1978
40
355
Sat.
22 Sept. 1979
41
383
Thur.
11 Sept. 1980
42
354
Tues.
29 Sept. 1981
43
355
Sat.
18 Sept. 1982
44
385
Thur.
8 Sept. 1983
45
354
Thur.
27 Sept. 1984
46
383
Mon.
16 Sept. 1985
47
355
Sat.
4 Oct. 1986
48
354
Thur.
24 Sept. 1987
49
383
Mon.
12 Sept. 1988
50
355
Sat.
30 Sept. 1989
51
354
Thur.
20 Sept. 1990
52
385
Mon.
9 Sept. 1991
53
353
Mon.
28 Sept. 1992
54
355
Thur.
16 Sept. 1993
55
384
Tues.
6 Sept. 1994
56
355
Mon.
25 Sept. 1995
57
383
Sat.
14 Sept. 1996
304 Cycle.
Jewish Year
Number of Days
Commencement (1st of Tisri).
5758
354
Thur.
2 Oct. 1997
59
355
Mon.
21 Sept. 1998
60
385
Sat.
11 Sept. 1999
61
353
Sat.
30 Sept. 2000
62
354
Tues.
18 Sept. 2001
63
385
Sat.
7 Sept. 2002
64
355
Sat.
27 Sept. 2003
65
383
Thur.
16 Sept. 2004
66
354
Tues.
4 Oct. 2005
67
355
Sat.
23 Sept. 2006
68
383
Thur.
13 Sept. 2007
69
354
Tues.
30 Sept. 2008
70
355
Sat.
19 Sept. 2009
71
385
Thur.
8 Sept. 2010
72
354
Thur.
29 Sept. 2011
73
353
Mon.
17 Sept. 2012
74
385
Thur.
5 Sept. 2013
75
354
Thur.
25 Sept. 2014
76
385
Mon.
14 Sept. 2015
305 Cycle.
5777
353
Mon.
3 Oct. 2016
78
354
Thur.
21 Sept. 2017
79
385
Mon.
10 Sept. 2018
80
355
Mon.
30 Sept. 2019
81
353
Sat.
19 Sept. 2020
82
384
Tues.
7 Sept. 2021
83
355
Mon.
26 Sept. 2022
84
383
Sat.
16 Sept. 2023
85
355
Thur.
3 Oct. 2024
86
354
Tues.
23 Sept. 2025
87
385
Sat.
12 Sept. 2026
88
355
Sat.
2 Oct. 2027
89
354
Thur.
21 Sept. 2028
90
383
Mon.
10 Sept. 2029
91
355
Sat.
28 Sept. 2030
92
354
Thur.
18 Sept. 2031
93
383
Mon.
6 Sept. 2032
94
355
Sat.
24 Sept. 2033
95
385
Thur.
14 Sept. 2034
306 Cycle.
5796
354
Thur.
4 Oct. 2035
97
353
Mon.
22 Sept. 2036
98
385
Thur.
10 Sept. 2037
99
354
Thur.
30 Sept. 2038
5800
355
Mon.
19 Sept. 2039
01
383
Sat.
8 Sept. 2040
02
354
Thur.
26 Sept. 2041
03
385
Mon.
15 Sept. 2042
04
353
Mon.
5 Oct. 2043
05
355
Thur.
22 Sept. 2044
06
384
Tues.
12 Sept. 2045
07
355
Mon.
1 Oct. 2046
08
353
Sat.
21 Sept. 2047
09
384
Tues.
8 Sept. 2048
10
355
Mon.
27 Sept. 2049
11
355
Sat.
17 Sept. 2050
12
383
Thur.
7 Sept. 2051
13
354
Tues.
24 Sept. 2052
14
385
Sat.
13 Sept. 2053
307 Cycle.
5815
355
Sat.
3 Oct. 2054
16
354
Thur.
23 Sept. 2055
17
383
Mon.
11 Sept. 2056
18
355
Sat.
29 Sept. 2057
19
354
Thur.
19 Sept. 2058
20
383
Mon.
8 Sept. 2059
21
355
Sat.
25 Sept. 2060
22
385
Thur.
15 Sept. 2061
23
354
Thur.
5 Oct. 2062
24
353
Mon.
24 Sept. 2063
25
385
Thur.
11 Sept. 2064
26
354
Thur.
1 Oct. 2065
27
355
Mon.
20 Sept. 2066
28
383
Sat.
10 Sept. 2067
29
354
Thur.
27 Sept. 2068
30
355
Mon.
16 Sept. 2069
31
383
Sat.
6 Sept. 2070
32
355
Thur.
24 Sept. 2071
33
384
Tues.
13 Sept. 2072
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 321/2 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 35411/30 days, or 354 days 8 hours 48 min., which divided by 12 gives 29191/360 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
