L = 7m - 2290 = 7 × 328 - 2290.
L = 6 = letter F.
The year therefore begins with Tuesday. It will be remembered that in a leap year there are always two dominical letters, one of which is employed till the 29th of February, and the other till the end of the year. In this case, as the formula supposes the intercalation already made, the resulting letter is that which applies after the 29th of February. Before the intercalation the dominical letter had retrograded one place less. Thus for 1840 the formula gives D; during the first two months, therefore, the dominical letter is E.
In order to investigate a formula for the epact, let us make
E = the true epact of the given year;
J = the Julian epact, that is to say, the number the epact would have been if the Julian year had been still in use and the lunar cycle had been exact;
S = the correction depending on the solar year;
M = the correction depending on the lunar cycle;
then the equation of the epact will be
E = J + S + M;
so that E will be known when the numbers J, S, and M are determined.
The epact J depends on the golden number N, and must be determined from the fact that in 1582, the first year of the reformed calendar, N was 6, and J 26. For the following years, then, the golden numbers and epacts are as follows:
1583, N = 7, J = 26 + 11 - 30 = 7;