| 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 | ||||||||||
| ———— | ||||||||||
| 1 | 9 | 4 | 0 | 4 | 4 | 8 | ||||
| 5821344 | ||||||||||
| 2910672 | ||||||||||
| 970224 | ||||||||||
| ————— | ||||||||||
| 1 | 3 | 2 | 1 | . | 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.