1603, the
title of which is given at the end of this article.

It has already been mentioned that the error of the Julian year was
corrected in the Gregorian calendar by the suppression of three
intercalations in 400 years. In order to restore the beginning of the year
to the same place in the seasons that it had occupied at the time of the
council of Nicaea, Gregory directed the day following the feast of St
Francis, that is to say the 5th of October, to be reckoned the 15th of that
month. By this regulation the vernal equinox which then happened on the
11th of March was restored to the 21st. From 1582 to 1700 the difference
between the old and new style continued to be ten days; but 1700 being a
leap year in the Julian calendar, and a common year in the Gregorian, the
difference of the styles during the 18th century was eleven days. The year
1800 was also common in the new calendar, and, consequently, the difference
in the 19th century was twelve days. From 1900 to 2100 inclusive it is
thirteen days.

The restoration of the equinox to its former place in the year and the
correction of the intercalary period, were attended with no difficulty; but
Lilius had also to adapt the lunar year to the new rule of intercalation.
The lunar cycle contained 6939 days 18 hours, whereas the exact time of 235
lunations, as we have already seen, is 235 x 29.530588 = 6939 days 16 hours
31 minutes. The difference, which is 1 hour 29 minutes, amounts to a day in
308 years, so that at the end of this time the new moons occur one day
earlier than they are indicated by the golden numbers. During the 1257
years that elapsed between the council of Nicaea and the Reformation, the
error had accumulated to four days, so that the new moons which were marked
in the calendar as happening, for example, on the 5th of the month,
actually fell on the 1st. It would have been easy to correct this error by
placing the golden numbers four lines higher in the new calendar; and the
suppression of the ten days had already rendered it necessary to place them
ten lines lower, and to carry those which belonged, for example, to the 5th
and 6th of the month, to the 15th and 16th. But, supposing this correction
to have been made, it would have again become necessary, at the end of 308
years, to advance them one line higher, in consequence of the accumulation
of the error of the cycle to a whole day. On the other hand, as the golden
numbers were only adapted to the J