Another peculiarity requires explanation. The epact 19′ (also distinguished by an accent or different character) is placed in the same line with 20 at the 31st of December. It is, however, only used in those years in which the epact 19 concurs with the golden number 19. When the golden number is 19, that is to say, in the last year of the lunar cycle, the supplementary month contains only 29 days. Hence, if in that year the epact should be 19, a new moon would fall on the 2nd of December, and the lunation would terminate on the 30th, so that the next new moon would arrive on the 31st. The epact of the year, therefore, or 19, must stand beside that day, whereas, according to the regular order, the epact corresponding to the 31st of December is 20; and this is the reason for the distinction.

Table III. Extended Table of Epacts.

Years.

Index.

Golden Numbers.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

1700 1800 8700

C

*

11

22

3

14

25

6

17

28

9

20

1

12

23

4

15

26

7

18

1900 2000 2100

B

29

10

21

2

13

24

5

16

27

8

19

*

11

22

3

14

25′

6

17

2200 2400

A

28

9

20

1

12

23

4

15

26

7

18

29

10

21

2

13

24

5

16

2300 2500

u

27

8

19

*

11

22

3

14

25

6

17

28

9

20

1

12

23

4

15

2600 2700 2800

t

26

7

18

29

10

21

2

13

24

5

16

27

8

19

*

11

22

3

14

2900 3000

s

25

6

17

28

9

20

1

12

23

4

15

26

7

18

29

10

21

2

13

3100 3200 3300

r

24

5

16

27

8

19

*

11

22

3

14

25′

6

17

28

9

20

1

12

3400 3600

q

23

4

15

26

7

18

29

10

21

2

13

24

5

16

27

8

19

*

11

3500 3700

p

22

3

14

25

6

17

28

9

20

1

12

23

4

15

26

7

18

29

10

3800 3900 4000

n

21

2

13

24

5

16

27

8

19

*

11

22

3

14

25′

6

17

28

9

4100

m

20

1

12

23

4

15

26

7

18

29

10

21

2

13

24

5

16

27

8

4200 4300 4400

l

19

*

11

22

3

14

25

6

17

28

9

20

1

12

23

4

15

26

7

4500 4600

k

18

29

10

21

2

13

24

5

16

27

8

19

*

11

22

3

14

25′

6

4700 4800 4900

i

17

28

9

20

1

12

23

4

15

26

7

18

29

10

21

2

13

24

5

5000 5200

h

16

27

8

19

*

11

22

3

14

25

6

17

28

9

20

1

12

23

4

5100 5300

g

15

26

7

18

29

10

21

2

13

24

5

16

27

8

19

*

11

22

3

5400 5500 5600

f

14

25

6

17

28

9

20

1

12

23

4

15

26

7

18

29

10

21

2

5700 5800

e

13

24

5

16

27

8

19

*

11

22

3

14

25′

6

17

28

9

20

1

5900 6000 6100

d

12

23

4

15

26

7

18

29

10

21

2

13

24

5

16

27

8

19

*

6200 6400

c

11

22

3

14

25

6

17

28

9

20

1

12

23

4

15

26

7

18

29

6300 6500

b

10

21

2

13

24

5

16

27

8

19

*

11

22

3

14

25′

6

17

28

6600 6800

a

9

20

1

12

23

4

15

26

7

18

29

10

21

2

13

24

5

16

27

6700 6900

P

8

19

*

11

22

3

14

25

6

17

28

9

20

1

12

23

4

15

26

7000 7100 7200

N

7

18

29

10

21

2

13

24

5

16

27

8

19

*

11

22

3

14

25′

7300 7400

M

6

17

28

9

20

1

12

23

4

15

26

7

18

29

10

21

2

13

24

7500 7600 7700

H

5

16

27

8

19

*

11

22

3

14

25

6

17

28

9

20

1

12

23

7800 8000

G

4

15

26

7

18

29

10

21

2

13

24

5

16

27

8

19

*

11

22

7900 8100

F

3

14

25

6

17

28

9

20

1

12

23

4

15

26

7

18

29

10

21

8200 8300 8400

E

2

13

24

5

16

27

8

19

*

11

22

3

14

25′

6

17

28

9

20

1500 1600 8500

D

1

12

23

4

15

26

7

18

29

10

21

2

13

24

5

16

27

8

19

As an example of the use of the preceding tables, suppose it were required to determine the moon's age on the 10th of April 1832. In 1832 the golden number is ((1832 + 1) / 19) = 9 and the line of epacts belonging to the century is C. In Table III, under 9, and in the line C, we find the epact 28. In the calendar, Table IV., look for April, and the epact 28 is found opposite the second day. The 2nd of April is therefore the first day of the moon, and the 10th is consequently the ninth day of the moon. Again, suppose it were required to find the moon's age on the 2nd of December in the year 1916. In this case the golden number is ((1916 + 1) / 19) = 17, and in Table III., opposite to 1900, the line of epacts is B. Under 17, in line B, the epact is 25′. In the calendar this epact first occurs before the 2nd of December at the 26th of November. The 26th of November is consequently the first day of the moon, and the 2nd of December is therefore the seventh day.