omputation of the Christian date, the ratio of a mean year of the
Hegira to a solar year is

Year of Hegira / Mean solar year = 354-11/30 / 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
----
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 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 . . . .