That is: take the given year, add to it its fourth part, and also the constant number 4 (which was the epact preceding the first year of the Christian era), divide the sum by 7, and what remains is the solar epact. (If there be no remainder, the epact may be called either 0 or 7.)
This is an excellent rule; the same, I believe, that is to this day prescribed for arriving at the Dominical letter of the Old Style. Let it be applied, for example, to find upon what day of the week the battle of Agincourt was fought (Oct. 25, 1415). Here we have 1415, and its fourth 353, and the constant 4, which together make 1772, divided by 7 leaves 1 as the solar epact; and this, added to 2, the _regular_ for the month of October, informs us that 3, or Tuesday, was the first day of that month; consequently it was the 22nd, and Friday, the 25th, was Saint Crispin's day.
But this rule of Bede's, in consequence of the addition, since his time, of a thousand years to the number to be operated upon, is no longer so convenient as a _mental_ resource.
It may be greatly simplified by separating the centuries from the odd years, by which the operation is reduced to two places of figures instead of four. Such a method, moreover, has the very great advantage of assimilating the operation of finding the solar epact, in both styles, the Old and the New; the only remaining difference between them being in the rules for finding the _constant number_ to be added in each century. These rules are as follow:--
_For the Old Style._--In any date, divide the number of centuries by 7, and deduct the remainder from 4 (or 11); the result is the constant for that century.
_For the New Style._--In any date, divide the number of centuries by 4, double the remainder, and deduct it from 6: the result is the constant for that century.
_For the Solar Epact, in either Style._--To the odd years of any date (rejecting the centuries) add their fourth part, and also the constant number found by the preceding rules; divide the sum by 7, and what remains is the solar epact.
As an example of these rules in _Old Style_, let the former example be repeated, viz. A.D. 1415:
First, since the centuries (14), divided by 7, leave no remainder, 4 is the constant number. Therefore 15, and 3 (the fourth), and 4 (the constant), amount to 22, from which eliminating the sevens, remains 1 as the solar epact.