re, terminated all difference as to the mode
of keeping Easter which is of historical note: the increasing defects of
the Easter Cycle produced in time the remonstrance of persons versed in
astronomy, among whom may be mentioned Roger Bacon,[751] Sacrobosco,[752]
Cardinal Cusa,[753] Regiomontanus,[754] etc. From the middle of the sixth
to that of the sixteenth century, one rule was observed.

5. The mode of applying astronomy to chronology has always involved these
two principles. First, the actual position of the heavenly body is not the
object of consideration, but what astronomers call its _mean place_, which
may be described thus. Let a fictitious sun or moon move in the heavens, in
such manner as to revolve among the fixed stars at an average rate,
avoiding the alternate accelerations and retardations which take place in
every planetary motion. Thus the fictitious (say _mean_) sun and moon are
always very near to the real sun and moon. The ordinary clocks show time by
the mean, not the real, sun: and it was always laid down that Easter
depends on the opposition (or full moon) of the mean sun and moon, not of
the real ones. Thus we see that, were the Calendar ever so correct {361} as
to the _mean_ moon, it would be occasionally false as to the _true_ one:
if, for instance, the opposition of the mean sun and moon took place at one
second before midnight, and that of the real bodies only two seconds
afterwards, the calendar day of full moon would be one day before that of
the common almanacs. Here is a way in which the discussions of 1818 and
1845 might have arisen: the British legislature has defined _the moon_ as
the regulator of the paschal calendar. But this was only a part of the
mistake.

6. Secondly, in the absence of perfectly accurate knowledge of the solar
and lunar motion (and for convenience, even if such knowledge existed),
cycles are, and always have been taken, which serve to represent those
motions nearly. The famous Metonic cycle, which is introduced into
ecclesiastical chronology under the name of the cycle of the golden
numbers, is a period of 19 Julian[755] years. This period, in the old
Calendar, was taken to contain exactly 235 _lunations_, or intervals
between new moons, of the mean moon. Now the state of the case is:

19 average Julian years make 6939 days 18 hours.

235 average lunations make 6939 days 16 hours 31 minutes.

So that successive cycles of golden numbers, supposing the first to