| L = 7m + 3 - x - | x 4 | w. |
This equation gives the dominical letter of any year from the commencement of the era to the Reformation. In order to adapt it to the Gregorian calendar, we must first add the 10 days that were left out of the year 1582; in the second place we must add one day for every century that has elapsed since 1600, in consequence of the secular suppression of the intercalary day; and lastly we must deduct the units contained in a fourth of the same number, because every fourth centesimal year is still a leap year. Denoting, therefore, the number of the century (or the date after the two right-hand digits have been struck out) by c, the value of L must be increased by 10 + (c - 16) - ((c - 16) / 4)w . We have then
| L = 7m + 3 - x - | x 4 | w + 10 + (c - 16) - | c - 16 4 | w; |
that is, since 3 + 10 = 13 or 6 (the 7 days being rejected, as they do not affect the value of L),
| L = 7m + 6 - x - | x 4 | w + (c - 16) - | c - 16 4 | w. |
This formula is perfectly general, and easily calculated.
As an example, let us take the year 1839. In this case,
| x = 1839, | x 4 | w = | 1839 4 | w = 459, c = 18, c - 16 = 2, and | c - 16 4 | w = 0. |
Hence
L = 7m + 6 - 1839 - 459 + 2 - 0