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. P