| When E < 24, |  | P = 24 - E | ||||
| l = 27 - E, or |  | 27 - E 7 |  | r, | ||
| When E > 23, | | P = 54 - E | ||||
| l = 57 - E, or | | 57 - E 7 | | r. | ||
By substituting one or other of these values of P and l, according as the case may be, in the formula p = P + (L - l), we shall have p, or the number of days from the 21st of March to Easter Sunday. It will be remarked, that as L - l cannot either be 0 or negative, we must add 7 to L as often as may be necessary, in order that L - l may be a positive whole number.
By means of the formulae which we have now given for the dominical letter, the golden number and the epact, Easter Sunday may be computed for any year after the Reformation, without the assistance of any tables whatever. As an example, suppose it were required to compute Easter for the year 1840. By substituting this number in the formula for the dominical letter, we have x = 1840, c - 16 = 2, ((c - 16) / 4)w = 0, therefore
L = 7m + 6 - 1840 - 460 + 2
= 7m - 2292
= 7 × 328 - 2292 = 2296 - 2292 = 4
L = 4 = letter D . . . (1).
For the golden number we have N = ((1840 + 1) / 19)r; therefore N = 17 . . . (2).
For the epact we have
| N + 10(N - 1) 30 | r = | 17 + 160 30 | r = | 177 30 | r = 27; |