Page:Catholic Encyclopedia, volume 5.djvu/549

 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.