And when the few, who would give themselves the trouble of thoroughly understanding it, came to perceive its easiness of acquirement, its simplicity in practice, and its firm hold upon the memory, they might well marvel how so admirable a facility should have been so entirely forgotten, or by what perversion of judgment it could have been superseded by the comparatively clumsy and impracticable method of the Dominical letters.
Let us hear his description of it in his own words:
"QUÆ SIT FERIA IN CALENDIS.
"Simile autem huic tradunt argumentum ad inveniendam diem Calendarum promptissimum.
"Habet ergo regulares Januarius II, Februarius V, Martius V, Apriles I, Maius III, Junius VI, Julius I, Augustus IIII, September VII, October II, November V, December VII. Qui videlicet regulares hoc specialiter indicant, quota sit feria per Calendas, eo anno quo septem concurrentes adscripti sunt dies: cæteris vero annis addes concurrentes quotquot in præsenti fuerunt adnotati ad regulares mensium singulorum, et ita diem calendarum sine errore semper invenies. Hoc tantum memor esto, ut cum imminente anno bisextili unus concurrentium intermittendus est dies, eo tamen numero quem intermissurus es in Januario Februarioque utaris: ac in calendis primum Martiis per illum qui circulo centinetur solis computare incipias. Cum ergo diem calendarum, verbi gratia, Januarium, quærere vis; dicis Januarius II, adde concurrentes septimanæ dies qui fuerunt anno quo computas, utpote III, fiunt quinque; quinta feria intrant calendæ Januariæ. Item anno qui sex habet concurrentes, sume v regulares mensis Martii, adde concurrentes sex, fiunt undecim, tolle septem, remanent quatuor, quarta feria sunt Calendæ Martiæ."—Bedæ Venerabilis, De Temporum Ratione, caput xxi.
The meaning of this may be expressed as follows:—Attached to the twelve months of the year are certain fixed numbers called regulars, ranging from I to VII, denoting the days of the week in their usual order. These regulars, in any year whereof the concurrent, or solar epact, is 0 or 7, express, of themselves, the commencing day of each month: but in other years, whatever the solar epact of the year may be, that epact must be added to the regular of any month to indicate, in a similar manner, the commencing day of that month.
It follows, therefore, that the only burthen the memory need be charged with is the distribution of the regulars among the several months; because the other element, the solar epact (which also ranges from 1 to 7), may either be obtained from a short mental calculation, or, should the system come into general use, it would soon become a matter of public notoriety during the continuance of each current year.
Now, these solar epacts have several practical advantages over the Dominical letters. 1. They are numerical in themselves, and therefore they are found at once, and used directly, without the complication of converting figures into letters and letters into figures. 2. They increase progressively in every year; whereas the Dominical letters have a crab-like retrogressive progress, which impedes facility of practice. 3. The rationale of the solar epacts is more easily explained and more readily understood: they are the accumulated odd days short of a complete week; consequently the accumulation must increase by 1 in every year, except in leap years, when it increases by 2; because in leap years there are 2 odd days over 52 complete weeks. But this irregularity in the epact of leap year does not come into operation until the additional day has actually been added to the year; that is, not until after the 29th of February. Or, as Bede describes it, "in leap years one of the concurrent days is intermitted, but the number so intermitted must be used for January and February; after which, the epact obtained from cyclical tables (or from calculation) must be used for the remaining months." By which he means, that the epacts increase in arithmetical succession, except in leap years, when the series is interrupted by one number being passed over; the number so passed over being used for January and February only. Thus, 2 being the epact of 1851, 3 would be its natural successor for 1852; but, in consequence of this latter being leap year, 3 is intermitted (except for January and February), and 4 becomes the real epact, as obtained from calculation.
To calculate the solar epact for any year, Bede in another place gives the following rule:
"Si vis scire concurrentes septimanæ dies, sume annos Domini et eorum quartum partem adjice: his quoque quatuor adde, (quia) quinque concurrentes fuerunt anno Nativitatis Domini: hos partire per septem et remanent Epactæ Solis."