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superseded by the comparatively clumsy and impracticable method of the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.