710
CHRONOLOGY.
9 - 1+2
and-is a whole number. Suppose it = p, then is 9n + 2
19
19p—2
= l9p, and n =- , therefore 9 must divide 19 p — 2 ; but
it divides 18/), therefore it must also divide p — 2 , and
p —2
is a whole number or nothing. Let it be equal to nothing, then19/)—2
is/; =s 2 , and -= n= 4, and 19:7 = 28n + 21 = 133. From
9
the preceding operations it appears that one of the number is 112 ,and the other 133, consequently their sum 245 is the number re-quired. lienee w hen the cycle of the sun is 21 , and that of themoon 17, the year of the Dionysian period is 245.
HI. The iudiction is a revolution of 13 years, used only bv theRomans for indicating the times of certain payments made by thesubjects to the republic: it was established bv Constantine,A. D. 312.
The year of our Saviour’s birth, according to the vulgar era,was the 9th year of the solar cycle, the first year of the lunarcycle ; and the 312th year after his birth was the first year of theRoman indiction. Therefore, to find the year of the solar cycle,add 9 to any given year of Christ, and divide the sum by 23, thequotient is the number of cycles elapsed since his birth, and theremainder is the cycle for the given year: if nothing remains, thecycle is 23. To find the lunar cycle, add one to the given yearof Christ, and divide the sum by 19 ; the'quotient is the numberof cycles elapsed in the interval, and the remainder is the cyclefor the given year: if nothing remains, the cycle is 19. Lastly,subtract 312 from the given year of Christ, and divide the remain-der by 15 ; and what remains after this division is the iudiction forthe given year: if nothing remains, the indiction is 15. 1
Of these three cycles of the sun, moon, and indiction, hv theircontinued multiplication the Julian period of 7980 years is com-posed. This period had its beginning 710 years before (he creation,and is not yet comoleted, and therefore it comprehends all otherperiods, cycles, and epochs, and the times of all memorable actionsand histories. There is but one year in the whole period, whichhas the same numbers for the three cycles of which it is made up ;and therefore if historians had remarked in their annals the cyclesof each year, there would have been no dispute about the time ofan v event. The year before the birth of Christ was the 4713thyear of the Julian period. And therefore if to the current yearof Christ we add 4713, the sum will he the year of the Julian pe-riod. On the contrary, from the year of the Julian period sub-tract 4713, and the remainder will he the year of the Chris-tian xra.
Example 1 . In what year of the Julian period is this present year«f Christ 1810.
Answer. 4713+ 1810 = 6523, the year of the Julian periodrequired. '
Example 2. When the year of the Julian period is 7000, wlia'tis the year of Christ ? ,
Answer. 7000 — 4713= 2287, the year of Christ required.
Having the years of the cycle of the sun, moon, and iudiction,to find the year of the Julian period. This problem may besolved in the same manner as before shewed in the finding theyear of the Dionysian period, viz. by finding three numbers, such4 s that the first will be a multiple of 19 and 15, or of their pro-duct, but being divided by 28, leaves the number of the cycle ofthe Sun for a remainder. The second number must be a multi-ple of 28 and 15, or of their product 420, but being divided by39, leaves the year of the cycle of the moon. Lastly, the thirdmust be a multiple of 28 and 19, but being divided by 15 leavesthe year of the iudiction. The sum of these numbers, if less-than 7980, is the year of the Julian period; but if the sumbe greater, divide by 7930, and the remainder will be the•year of the period required.
Although the deficiency in the lunar cycle of 1-J hour every 19years be but small, yet in time it becomes so sensible as to make awhole natural day in 310 years. So that, although this cycle be ofuse, when the golden numbers are rightly placed against the days ofthe inopthAu the calendar, as in the Common Prayer Books, for
finding the days of the mean conjunctions or oppositions of thesun and moon, and consequently the lime of Easter; it will onlyservo for 310 yearn, old style. For as the now and full moons an-ticipate a day m that time, the golden numbers ought to be placedone clay earlier in the calendar for the next 310 years to come.These numbers were rightly placed against the days of the newmoon in the calendar, by the council of Nice, A. D. 325; butthe anticipation, which has been neglected ever since, is nowgrow n almost into five clays : and therefore all the golden number*ought now to be placed five days higher in the c alendar for theold style than they were at the time of the said council ; or sixclays lower for the new style, because at present it differs elevenclays Irom the old. Jn the following table, the golden numbersunder the months stand against the clay before the new moou in theleft hand column for the new style ; adapted chietly to the se-cond year alter lcap-vear, which is the nearest mean for all the-four; and may serve till"the year 1900. Therefore, to find theday of the new moon in any month of a given year till that time,look for the golden number of that year (which will be found byTable II.) under the desired month, and against it you have inthe left hand column a number to which, if 1 be added, it willgive the day of the new moon required. Thus, suppose it wererequired to find the day of the new moon in May, 1810 ; thegolden number for that year is 6 , which I look for under May,and right against it in the left hand column you will find 2 , and 1being added to it, will give May 3, for the day of the new moonin that month.
N. B. If all the golden‘numbers, except 17 and 6 , were set oneclay lower in the table, it would serve from the beginning of theyear 1900 till the end of the year 2199.
TABLE L
| Days.
«—1
CJ
3
Feb.
March.
April.
May.
June.
U.
E-
vf
>
c
OQ
Sept.
Oct.
55
o
< .
a *
p
i
9
9
17
17
(i
11
19
2
17
t>
14
;4
3
11
19
3*
17
6
17
6
3
11
19
8
8
4
6
6
14
14
3
19
8
16 .
5i
14
3
11
li
19
8
16
6\
14
3
14
3
19
1 C
5
5
7|
3
3
11
11
19
8
16
13
8 I
11
19
8
8
16
5
5
13
9!
11
19
11
19
13
2
10
19
8
8
4
16
16
5
13
2
10 ,
11
19
8
5
13
2
2
10
12
8
16
8
16
16
5
10
18 ,
13
5
13
13
2
10
18
7
14
16
5
16
5
O
10
18
IS
7
15
5
5
13
13
2
7
15
16
13
2
10
10
18
7
15
17
13
2
13
o
18
7
15
4
4 ,
18
2
2
10
10
18
15
12
19
10
18
7
7
15
4
4
12
20
10
18
10
18
15
15
12
1
1
21
18
18
7
7
15
4
12
9
22
7
15
4
4
12
1
1
9
23
7
15
7
15
12
9*
17
17
24
j
15
4
4
12
1
9
6
25
15
4
12
1
9
17
17
6
26
1 4
4
12
1
6
15
27
i
12
1
1
9
9
17
6
14
28
12
1
12
9
17
(i
14
14
3
3
29
1
1
9
17
3
11
30
17
6
6
14
3
11
31
9
1
9
14
3.
ii
1 “
Thr