So that successive cycles of golden numbers, supposing the first to start
right, amount to making the new moons fall too late, gradually, so that the
mean moon _of this cycle_ gains 1 hour 29 minutes in 19 years upon the mean
moon of the heavens, or about a day in 300 years. When the Calendar was
reformed, the calendar new moons were four days in advance of the mean moon
of the heavens: so that, for instance, calendar full moon on the 18th
usually meant real full moon on the 14th.
7. If the difference above had not existed, the moon of the heavens (the
mean moon at least), would have returned {362} permanently to the same days
of the month in 19 years; with an occasional slip arising from the unequal
distribution of the leap years, of which a period contains sometimes five
and sometimes four. As a general rule, the days of new and full moon in any
one year would have been also the days of new and full moon of a year
having 19 more units in its date. Again, if there had been no leap years,
the days of the month would have returned to the same days of the week
every seven years. The introduction of occasional 29ths of February
disturbs this, and makes the permanent return of month days to week days
occur only after 28 years. If all had been true, the lapse of 28 times 19,
or 532 years, would have restored the year in every point: that is, A.D. 1,
for instance, and A.D. 533, would have had the same almanac in every matter
relating to week days, month days, sun, and moon (mean sun and moon at
least). And on the supposition of its truth, the old system of Dionysius
was framed. Its errors, are, first, that the moments of mean new moon
advance too much by 1 h. 29 m. in 19 average Julian years; secondly, that
the average Julian year of 3651/4 days is too long by 11 m. 10 s.
8. The Council of Trent, moved by the representations made on the state of
the Calendar, referred the consideration of it to the Pope. In 1577,
Gregory XIII[756] submitted to the Roman Catholic Princes and Universities
a plan presented to him by the representatives of Aloysius Lilius,[757]
then deceased. This plan being approved of, the Pope nominated a commission
to consider its details, the working member of which was the Jesuit
Clavius. A short work was prepared by Clavius, descriptive of the new
Calendar: this {363} was published[758] in 1582, with the Pope's bull
(dated February 24, 1581) prefixed. A larger work was prepared by Clavius,
containing fuller explanation, and entitled _Romani Calendarii a Gregorio
XIII. Pontifice Maximo restituti Explicatio_. This was published at Rome in
1603, and again in the collection of the works of Clavius in 1612.
9. The following extracts from Clavius settle the question of the meaning
of the term _moon_, as used in the Calendar:
"Who, except a few who think they are very sharp-sighted in this matter, is
so blind as not to see that the 14th of the moon and the full moon are not
the same things in the Church of God?... Although the Church, in finding
the new moon, and from it the 14th day, _uses neither the true nor the mean
motion of the moon_, but measures only according to the order of a cycle,
it is nevertheless undeniable that the mean full moons found from
astronomical tables are of the greatest use in determining the cycle which
is to be preferred ... the new moons of which cycle, in order to the due
celebration of Easter, should be so arranged that the 14th days of those
moons, reckoning from the day of new moon _inclusive_, should not fall two
or more days before the mean full moon, but only one day, or else on the
very day itself, or not long after. And even thus far the Church need not
take very great pains ... for it is sufficient that all should reckon by
the 14th day of the moon in the cycle, even though sometimes it _should be
more than one day before or after_ the mean full moon.... We have taken
pains that in our cycle the new moons should _follow_ the real new moons,
so that the 14th of the moon should fall either the day before the mean
full moon, or on that day, or not long after; and this was done on purpose,
for if the new moon of the cycle fell on the same day as the mean new moon
of the {364} astronomers, it might chance that we should celebrate Easter
on the same day as the Jews or the Quartadeciman heretics, which would be
absurd, or else before them, which would be still more absurd."
From this it appears that Clavius continued the Calendar of his
predecessors in the choice of the _fourteenth_ day of the moon. Our
legislature lays down the day of the _full moon_: and this mistake appears
to be rather English than Protestant; for it occurs in missals published in
the reign of Queen Mary. The calendar lunation being 291/2 days, the middle
day is the _fifteenth_ day, and this is and was reckoned as the day of the
full moon. There is every right to presume that the original passover was a
feast of the _real full moon_: but it is most probable that the moons were
then reckoned, not from the astronomical conjunction with the sun, which
nobody sees except at an eclipse, but from the day of _first visibility_ of
the new moon. In fine climates this would be the day or two days after
conjunction; and the fourteenth day from that of first visibility
inclusive, would very often be the day of full moon. The following is then
the proper correction of the precept in the Act of Parliament:
Easter Day, on which the rest depend, is always the First Sunday after the
_fourteenth day_ of the _calendar_ moon which happens upon or next after
the Twenty-first day of March, _according to the rules laid down for the
construction of the Calendar_; and if the _fourteenth day_ happens upon a
Sunday, Easter Day is the Sunday after.
10. Further, it appears that Clavius valued the celebration of the festival
after the Jews, etc., more than astronomical correctness. He gives
comparison tables which would startle a believer in the astronomical
intention of his Calendar: they are to show that a calendar in which the
moon is always made a day older than by him, _represents the heavens better
than he has done, or meant to do_. But it must be observed that this
diminution of the real moon's age has {365} a tendency to make the English
explanation often practically accordant with the Calendar. For the
fourteenth day of Clavius _is_ generally the fifteenth day of the mean moon
of the heavens, and therefore most often that of the real moon. But for
this, 1818 and 1845 would not have been the only instances of our day in
which the English precept would have contradicted the Calendar.
11. In the construction of the Calendar, Clavius adopted the ancient cycle
of 532 years, but, we may say, without ever allowing it to run out. At
certain periods, a shift is made from one part of the cycle into another.
This is done whenever what should be Julian leap year is made a common
year, as in 1700, 1800, 1900, 2100, etc. It is also done at certain times
to correct the error of 1 h. 19 m., before referred to, in each cycle of
golden numbers: Clavius, to meet his view of the amount of that error, put
forward the moon's age a day 8 times in 2,500 years. As we cannot enter at
full length into the explanation, we must content ourselves with giving a
set of rules, independent of tables, by which the reader may find Easter
for himself in any year, either by the old Calendar or the new. Any one who
has much occasion to find Easters and movable feasts should procure
Francoeur's[759] tables.
12. _Rule for determining Easter Day of the Gregorian Calendar in any year
of the new style._ To the several parts {366} of the rule are annexed, by
way of example, the results for the year 1849.