Notes and Queries, Vol. IV, Number 99, September 20, 1851 / A Medium of Inter-communication for Literary Men, Artists, Antiquaries, Genealogists, etc.

by Various

VENERABLE BEDE'S MENTAL ALMANAC.

If our own ancient British sage, the Venerable Bede, could rise up from the dust of eleven centuries, he might find us, notwithstanding all our astounding improvements, in a worse position, in one respect at least, than when he left us; and as the subject would be one in which he was well versed, it would indubitably attract his attention.

He might then set about teaching us from his own writings a mental resource, far superior to any similar device practised by ourselves, by which the day of the week belonging to any day of the month, in any year of the Christian era, might easily and speedily be found.

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so admirable a facility should have been so entirely forgotten, or by what perversion of judgment it could have been superseded by the comparatively clumsy and impracticable method of the Dominical letters.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."

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.

For an example in New Style, let the present year be taken. In the first place, 18 divided by 4 leaves 2, which doubled is 4, deducted from 6 results 2, the constant number for the present century. Therefore 51, and 12 (the fourth), and 2 (the constant), together make 65, from which the sevens being eliminated, remains 2, the solar epact for this year.

But in appreciating the practical facility of this method, we must bear in mind that the constant, when once ascertained for any century, remains unchanged throughout the whole of that century; and that the solar epact, when once ascertained for any year, can scarcely require recalculation during the remainder of that year: furthermore, that although the rule for calculating the epact, as just recited, is so extremely simple, yet even that slight mental exertion may be spared to the mass of those who might benefit by its application to current purposes; because it might become an object of general notoriety in each current year. And I am not without hope that "NOTES AND QUERIES" will next year set the example to other publications, by making the current solar epact for 1852 a portion of its "heading," and by suffering it to remain, incorporated with the date of each impression, throughout the year.

Let us now recur to the allotment of the regulars at the beginning of Bede's description. Placed in succession their order is as follows:—

	April and July	I,	or Sunday
	January and October	II,	or Monday
	May	III,	or Tuesday
	August	IIII,	or Wednesday
	March, Feb., and November	V,	or Thursday
	June	VI,	or Friday
	September and December	VII,	or Saturday

There is no great difficulty in retaining this in the memory; but should uncertainty arise at any time, it may be immediately corrected by a mental reference to the following lines, the alliterative jingle of which is designed to house them as securely in the brain as the immortal and never-failing, "Thirty days hath September." The order of the allotment is preserved by appropriating as nearly as possible a line to each day of the week; while the absolute connexion here and there of certain days, by name, with certain months, forms a sort of interweaving that renders mistake or misplacement almost impossible.

"April loveth to link with July,

And the merry new year with October comes by,

August for Wednesday, Tuesday for May,

March and November and Valentine's Day,

Friday is June day, and lastly we seek

September and Christmas to finish the week."

Now, since we have ascertained, from the short calculation before recited, that the solar epact of this present year of 1851 is 2, and since the regular of October is also 2, we have but to add them together to obtain 4 (or Wednesday) as the commencing day of this next coming month of October. And, if we wish to know the day of the month belonging to any other day of the week in October, we have but to subtract the commencing day, which is 4, from 8, and to the result add the required day. Let the latter, for example, be Sunday; then 4 from 8 leaves 4, which added to 1 (or Sunday), shows that Sunday, in the month of October 1851, is either 5th, 12th, 19th, or 26th.

This additional application is here introduced merely to illustrate the great facilities afforded by the purely numerical form of Bede's "argumentum,"—such as must gradually present themselves to any person who will take the trouble to become thoroughly and practically familiar with it.

A. E. B.

Leeds, September, 1851.