Also the number of intercalary years from the year 1 up to the Year Y inclusive= $9 w; and the same up to the year 1 1 Y+ 3

Y-. - (T),

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 t at 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. Hence1fw=1| 2 3 4 t 5 6 i 7

indicate Sun. Mon. Tues. Wed. Thur. F rid. Sat. the day of the week on which the year Y commences will be w =2+4 7+ w(rejecting sevens). But, 30 w+ (W r=11Y+3

gives 120 w=12+44Y-4 7,

or w =5-i-2 Y-I-3 7 (rejecting sevens So that

w=6(¥)f+f»<%')f

(rejecting sevens),

).

the values of which obviously circulate in a period of 7 times 30 or 2 10 Years.

Let C denote the number of completed cycles, and y the year of the cycle; then Y=30

C-1-y, and

112-}-3

w=5 V-}-6 V-I-3 (30) V (rejecting sevens). From this formula the following table has been constructed:- 970224

1362

1940448

5321344

2910672

970224

132 1 -445088

62I'5774

1943'0225

365

1125

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 pro osed year of the Hegira, divided by 30, gives 45 cycles, and remainder 12, the year of the current cycle.

Al? 45, divided by 7, leaves a remainder 3 for the number of the perio

Therefore, referring to 3 at the top of the table, and 12 on the left, the required day is Friday.

The tables, dpage 571, show that 8th January 1943 is a Friday, therefore the ate 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-Muharra

30 Sh b . 2

TABLE VIH' Saphar 29 Raigadgn 33 C Rabia I. 30 Shawall (Shawwil) 29 Year of the Number of the Period of Seven Cycles= 7 Rabiall. . 29 Dulkaada (Dhu'l Qa'da) 30 Current Cycle (yy, Jomada I. 30 Dulhe§ gia (Dhu'lH1jja) 29 0 I 2 3 4 5 6 Ior11adaII. 29 an in intercalary Rajab . 30 years . 30

0 8 Mon. Sat. Thur. Tues. Sun. F rid. Wed. The ninth month Ramadan is the month 1 17 25 Fr d. W d. Mon. Sat. Thur. Tues. Sun. -

• 2 *ig *18 *26 Tiles. Sueii. Frid. Wed. Mon. Sat. Thur. of Abstmence Observed bY the Moskims

3 II 19 27 Sun. F rid. Wed. Mon. Sat. Thur. Tues. The MOSICTII Calendar IHHY €VId€11f-lY 4 12 20 *28 Thur. Tues. Stan Flgrid. gled. gflocn. be carried on indefinitely by successive

• * * ' - —5

13 21 29 MOH- Sat- UF- €S- UP- fl - e - add1t10n observing only to allow for the

3° Inglis' ' additional day that occurs in the bis sex tile

5 *ie *24 sun Frid. Wed. M<m sat. t Thur. Tues. and Intercalary years; but for any remote 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 Hcégira by 30; the quotient is the number of cycles, and the remain er is the year of the current 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 W00lh0use's M easures, Weighls and M oneys of all Nalions, shows the dates of comcycle. 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 c cle on the left hand, the required day of the week is immediately shlown The intercalary years of the cycle are distinguished by an asterisk. For the computation of the Christian date, the ratio of a year of the Hegira to a solar year is Year of Hegira 3541 1

Mean solar year'365-2122 '0'970224 lTl€3l'l

The ear 1 be an 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 Ju y 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-I)+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 ear of the He ira, cut off six decimals from the product, and adld 621-5774. Tghe 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 da y 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 llegira begins

men cement of Mahommedan years from 1845 up to 2047, or from the 43rd to the 49th cycle inclusive, of the seventh period of seven cycles. period of seven cycles, and all other like periods, the days of the week will recur in exactly the same order. kind previously published, which extend of the Chrlstian era, are erroneous, not excepting the celebrated French work, L'Art de verzfier les dates, the greatest authority in chronological have probably arisen from a continued discrimination of the intercalary years. which form the whole

Throughout the next

All the tables of this

beyond the year 1900

so justly regarded as

matters. The errors

excess of 10 in the

TABLE IX -Mahommedan Years.

43rd Cycle.

Year of Commencement Year of Commencement Hegira (ISf of Muharram). Hegira (1st of Muharram). 1261 Frid. IO En. 1845 1273* Mon. 1 Sept. 1856 1262* Tues. 30 ec. 1845 1274 Sat. 22 Aug. 1857 1263 Sun. 20 Dec. 1846 1275 Wed. II Aug. 1858 1264 Thur. 9 Dec. 1847 1276* Sun. 31 July 1859 1265* Mon. 27 Nov. 1848 1277* Frid. 20 July 1860 1266 Sat 17 Nov. 1849 1278* Tues. 9 uly 1861 1267* Wed. 6 Nov 1850 1279 Sun. 29 une 1862 1268 Mon. 27 Oct. 1851 1280 Thur. 18, tune 1863 1269 Frid. 15 Oct. 1852 1281* Mon. 6 une 1864 1270* I'ues. 4Oct 1853 1282 Sat. 27 May 1865 1271 Sun. 24 Sept. 1854 1283 Wed. 16 May 1866

1 1272 "lhur. 13 Sept. 1855 1284* Sun 5 Ma; 1861!