**ABC—XYZ**

680 CALENDAR [MAHOMETAN. So that /F = 6 J-) + 3 ll F+ 3 30

) r (ejecting sevens), the values of which obviously circulate in a period of 7 times 30 or 210 years. Let O denote the number of completed cycles, and y the year of the cycle ; then Y = 30 + y, and w ~ 5 (y) r + e(|) r + 3 (^-fjf- 8 ),. (rejecting sevens). From this formula the following table has been constructed: TABLE VIII. Year of the Number of the Period of Seven Cycles = ( y),- Current Cycle (*)

1 2 3 4 5 6

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 ?8 Thur. Tues. Sun. Frid. Wed. Mon. Sat.

- ,">
- 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 : Hale. 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 Year of Hegira 354 Mean solar year ~ 365 "2422 = 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 5476, and the number of years elapsed = Y - 1. Therefore, as the inter calary 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. Exarch. Required the date on which the year 1362 of the Hegira begins. 970224 1362 1321-44508 621-5774 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 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 670, show that 8th January 1 943 is a Friday ; therefore the date is exact. For any other date of the Mahometan year it is only requisite to know the names of the consecutive months, and the number of days in each; these are Muharram, 39 Saphar, 29 Habia I 30 liabia II., 29 Jornada I., 30 Jornada II. , 29 Enjab, 30 Shaaban, 29 Kamadan, ..... 30 Shawall, 29 Dulkaada, 30 Ja, 29 and in intercalary years 30 The ninth month, Ramadan, is the month of Abstinence observed by the Turks. The Turkish 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 Mahometan 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. Through out 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 pub lished, which extend beyond the year 1900 of the Chris tian era, are erroneous, not excepting the celebrated French work, L Art de verifier 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. Mahometan Years. 43d Cycle. 43d Cycle continued. Year of Commencement Year of Commencement Hegira. (1st of Muharram). Hegira. (1st of Muharram). 1261 Frid. 10 Jan. 1845 1286* Tues. 13 April 1869 1262* Tues. 30 Dec. 1845 1287 Sun. 3 April 1870 1263 Sun. 20 Dec. 1846 1288 Thur. 23 Mar. 1871 1264 Thur. 9 Dec. 1847 1289* Mon . 11 Mar. 1872 1265* Mon. 27 Nov. 1848 1290 Sat. 1 Mar. 1873 1266 Sat. 17 Nov. 1849 1267* Wed. 6 Nov. 1850 44th Cycle. 1268 Mon. 27 Oct. 1851 1269 Frid. 15 Oct. 1852 1291 Wed. 18 Feb. 1874 1270* Tues. 4 Oct. 1853 1292* Sun. 7 Feb. 1875 1271 Sun. 24 Sept. 1854 1293 Frid. 28 Jan. 1876 1272 Thur . 13 Sept. 1855 1294 Tues. 16 Jan. 1877 1273* Mon. 1 Sept. 1856 1295* Sat. 5 Jan. 1878 1274 Sat. 22 Aug. 1857 1296 Thur. 26 Dec. 1878 1275 Wed. 11 Aug. 1858 1297* Mon. 15 Dec. 1879 1276* Sun. 31 July 1859 1298 Sat. 4 Dec. 1880 1277 Frid. 20 July 1860 1299 Wed. 23 Nov. 1881 1278 s Tues. 9 July 1861 1300* Sun. 12 Nov. 1882 1279 Sun. 29 June 1862 1301 Frid. 2 Nov. 1883 1280 Thur. 18 June 1863 1302 Tues. 21 Oct. 1884 1281* Mon. 6 June 1864 1303* Sat. 10 Oct. 1885 1282 Sat. 27 May 1865 1304 Thur. 30 Sept. 1886 1283 Wed. 16 May 1866 1305 Mon. 19 Sept. 1887 1284* Sun. 5 May 1867 1306* Frid. 7 Sept. 1888 1285 Frid. 24 April 1868 1307 Wed.

28 Aug. 1889