EFACT
483
EPACT
proper Epacts for the years of the Lunar Cycle after
1582. These they found to be as follows: —
Golden Numbers 1 2 3 4
Epacts I XII XXIII IV
5 6 7 8 9 10
XV XXVI VII XVIU XXIX X
Golden Numbers 11 12 13 14
Epacts XXI II xiii XXIV
15 16 17 IS 19
V XVI XXVII VIII XIX
Now the essential difference between the Metonic Cycle and the Gregorian system of Epacts lies in this, that, whereas the sphere of apphcation of the former was held to be unlimited, that of the latter is bounded by the Lunar and Solar Equations. Since, then, a Solar Equation occurs in 1700, the Cycle of Epacts just given holds only for the period 15S2-1699, after which a new cycle must be formed. To understand the reason of the changes we must remember (1) that by treating 365 days as equivalent to one solar year and to 12 lunations plus 11 days, we under-estimate
the fifth day of the calendar moon. But, since no
extra day could be inserted in February, 1700, the
twenty-fourth and twenty-fifth of this month had to
be treated as the sixth daj' of the moon, and the age
of the moon on every subsequent day of the year 1700
was one day less than indicated bj' the Epact X. As
the moons of Januarj- and February are of very sec-
ondary importance in the Church calendar, we may
say that the age of the moon in 1700 and all subse-
quent years was one day less than indicated by the
above Cycle of Epacts, and thus the Epacts for the
years of the Lunar Cycle after 1700 are: —
Golden Numbers 1 2 3 4
Epacts * XI XXII III
5 6 7 8 9 10
XIV XXV VI XVII XXVIII IX
Golden Numbers 11 12 13 14
Epacts XX I XII XXIII
15 16 17 IS 19
IV XV XXVI VII XVIU
In the year 1800, both the Lunar and Solar Equations (i. e. the addition and subtraction of 1) occur and no
EPACTS
FROM 1 B. C
. TO A
. D. 3099
Golden
Numbers.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
1 B. c-
.4. D. 1582
XI
XXII
HI
XIV
XXV
VI
XVII
xxvm
IX
XX
I
xu
XXUI
IV
XV
XXVT
v-ii
XVIU
1582-1699
I
XII
XXIII
IV
XV
XXTl
VII
XVIII
XXIX
X
XXI
II
xm
XXIV
V
XVI
XXVU
VIII
XIX
1700-1899
XI
XXII
III
XIV
XXV
VI
XVII
xxvm
IX
XX
I
XII
XXIII
IV
XV
XXVI
VII
xvm
1900-2199
XXIX
X
XXI
II
XIII
XXIV
V
XVI
xxvu
VIII
XIX
XI
xxu
III
XIV
XXV
VT
XVU
2200-2299
XXVIII
IX
XX
I
xu
XXIII
IV
XV
XXVI
■ra
XVIU
XXIX
X
XXI
II
xm
XXIV
V
XVI
2300-2399
xx^^I
via
XIX
XI
XXII
in
XIV
XXV
VI
XVII
XXVIII
IX
XX
I
XII
XXUI
IV
XV
2400-2499
XX XIII
IX
XX
I
XII
XXIII
rv
XV
XXVI
VII
XVIU
XXIX
X
XXI
11
XIII
XXIV
V
XVI
2500-2399
xxvn
VIII
XIX
t
XI
xxu
ni
XIV
XXV
VI
xvu
XXVIU
IX
XX
I
XII
XXUI
IV
XV
2600-2899
XXVI
VII
xvm
XXIX
X
XXI
n
XUI
XXIV
V
XVI
XXVU
vm
XIX
XI
xxu
III
XIV
2900-3099
XXV
VI
xvn
XXVTH
IX
XX
I
xu
XXIII
IV
XV
XX\T
VI.
XS1U
XXIX
X
XXI
II
xin
This table may, with the help of the table of equations, be continued to 5199.
the solar year by about 5* hours and the lunations by
8 J hours; (2) that in consequence of this under-esti-
mation of the solar year, one day must be inserted in
every fourth solar year except in the case of the cen-
turial years not divisible by 400; and (3) that the
under-estimation of the lunations by 6 hours every
year (the additional 2i hours are compensated for in
the enibolismic months and by the Lunar Equation)
necessitates the insertion of one extra day in the lunar
calendar every fourth year without exception. To
take an example: the Epact of 1696 (its Golden
Number being 6) is XXVI, and since this Epact is
found opposite 4 February in the Church calendar we
know that in 1696 the new moon happened on that
date and that consequently 23 February was the
twentieth day of the calendar moon. But, since the
under-estimation of the lunations amounts to one day
in every four years, the following day (our 24 Feb.)
was only nominally the twenty-first day of the moon
and the proper twenty-first was our 25 February.
The Church therefore in.serted an extra day after 23
February antl treated this and the real 24 Feb. (our 24
and 25) as one continuous day in both the solar and
lunar calendars, and consequently 25 February (our
26) was again legitimately regarded as the twenty-
second day of the moon and the fifty-sixth day of the
astronomical solar year. Coming now to the year
1700, we find its p^pact to be X, consequently the new-
moon occurre<l on 19 February and 23 February was
change of Epacts takes place. In 1900 the Solar
Etiuation occurs and we must again subtract 1 from
the Epacts. No change takes place in 2000 or in
2100, the former being a leap yearand the latter having
both equations. In 2200 and in 2300, we must again
subtract 1, while in 2400, in which the Lunar Equa-
tion occurs and is not neutralized as usual by the Solar
Equation, we add 1 to all the Epacts. The accom-
panying table gives the Epact of every year from 1 B. c.
to A. D. 3099.
Examples. — (1) To find the Epact of the year 3097.
Golden Number is 1, since ' — '— = 163, with 1 as
remainder. Epact corresponding to Golden Number 1 after 2900 is XXV; therefore the Epact of 3097 is XXV.
(2) On what Sunday will Easter fall in the year 2459? Golden Number of 2459 is 9. and Epact of ninth year of Lunar Cycle after 2400 is XXVI. Since the Epact of 2459 is XXVI, the new moons of this year will occur on the days before which XX\T is placed in the Church calendar (e.g. in the Breviary). Now, since tlie paschal moon is that whose fourteenth day falls on or next after 21 March, the paschal new moon can never happen before 8 March. The first day after S March to which the Epact XXVI is prefixed in the Church calendar is 4 April; consequently the paschal new moon in the year 2459 will occur on 4 April.
