C H R O N 
nineteenth year; fo that at the twentieth year the epadt 
ji again; and hence the cycle of epadts expires with 
the golden number, or lunar cycle of nineteen years, and 
begins with the fame again. 
TABLE OF JULIAN 
epacts . 
Golden 
Numb. 
Epafts. 
Golden 
Numb. 
Epafts. 
CJolden 
Numb, 
Epafts. 
I 
I I 
VIII 
28 
XV 
IS 
II 
22 
IX 
9 
XVI 
26 
III 
3 
X 
20 
XVII 
8 
IV 
14 
XI 
I 
XVIII 
19 
V 
25 
xri 
12 
XIX 
3 ° 
VI 
6 
XIII 
23 
or 0 
VII 
17 
XIV 
4 
Again, as the new moons are the fame, or fall on the 
fame day, every nineteen years, fo the difference between 
the folarand lunar years is the fame every nineteen years. 
And becaufe the faid difference is always to be added to 
the lunar year, to adjuft or make it equal to the folar 
year; hence the faid difference refpedtively belonging to 
each year of the moon’s cycle, is called the epadt of the 
faid year, that is, the number to be added to the faid 
year, to make it equal to the folar year. Upon this mu¬ 
tual refpedt between the cycle of the moon and the cycle 
of the epadts, is founded the following Rule for fi?iding 
the Julian epadt, belonging to any year of the moon's cycle :— 
Multiply the golden number, or the given year of the 
moon’s cycle, by n, and the produdl will be the epadt if 
it be lefs than 30 ; but if it exceed 30, then throw out 
as many 30’s as the product contains, and the remainder 
will be the epadt. 
Rule to find the Gregorian epadt. —rft, The difference be¬ 
tween the Julian and Gregorian years being equal to the 
difference between -the folarand lunar year, or 11 days, 
therefore the Gregorian epadt for any year is the fame 
with the Julian epadt for the preceding year; and hence 
the Gregorian epadt will be found, by fubtradting 1 from 
the golden number, multiplying the remainder by u, 
and rejedling the 30’s. This rule will ferve till the" year 
1900; but after that year, the Gregorian epadt will be 
found by this rule: Divide the centuries of the given 
year by 4; multiply the remainder by 17; then to this 
produdl add 43 times the quotient, and alfo the number 
86, and divide the whole fum by 25, referving the quo¬ 
tient : next multiply the golden number by 11, and from 
the produdt fubtradt the referred quotient, fo fhall the 
remainder, after rejedling all the 30’s contained in it, be 
the epadt fought: The following table contains the 
golden numbers, with their correfponding epadts, till the 
year 1900. 
TABLE 
OF GREGORIAN EPACTS 
Golden 
Numb. 
Epafts. 
Golden 
Nurnb. 
Epafts. 
Golden 
Numb. 
Epafts. 
I 
O 
VIII 
17 
XV 
4 
II 
I I 
IX 
28 
XVI 
15 
III 
22 
X 
9 
XVII 
26 
IV 
3 
XI 
20 
XVIII 
7 
V 
14 
XII 
I 
XIX 
18 
VI 
*5 
XIII 
12 
I 
0 
VII 
6 
XIV 
23 
On the fubjedt of Epadts, fee Wolfius’s Elementa Chro- 
nologise, apud Opera, tom. iv. p. 133; alfo Philof. Tranf. 
vol. xlvi. p.417. 
Of the DIVISION of TIME by CYCLES, 
EPOCHS, &c. 
■Betides the common divifions of time, arifrng imme¬ 
diately from the above delcribed revolutions of the hea¬ 
venly Dodies, there are others, which are formed from 
iome of the lefs obvious confequences of thofe revolu- 
Vol, IV. No. 217, 
O L O G Y. 537 
tions, and are called cycles, or circles, becaufe they con- 
lilt of a certain feries of movements or meafures of time, 
. proceeding invariably from firft to laft, then returning 
again into the firlt, and thus circulating in a perpetual 
round. 
Cycles have chiefly arifen from the incommenfurabi- 
lity of the revolutions of the earth and ccleftial bodies 
to one another. The apparent revolution of the fun 
about the earth, having been divided into twenty-four 
hours, is the bafis or foundation of all our menfurations 
of time, whether by days, years, &c. But neither the 
annual motion of the fun, nor that of the other hea¬ 
venly bodies, can be meafured exadfly, and without any 
remainder, by hours, or their multiples. That of the 
fun, for example, is 363d. 5I1. 49 m. nearly, that of the 
moon, 29d. 12h. 44m. nearly . 
Hence, to fwallow up thefe fradtions in whole num¬ 
bers, and yet in numbers which only exprels days and 
years, cycles have been invented; which, comprehend¬ 
ing feveral revolutions of the fame body, replace it, after 
a certain number of years, exadtly in the lame point of 
the heavens from whence it firft departed ; or, which is 
the fame thing, in the fame place of the civil calendar. 
Thefe cycles are various ; as, the cycle of indidtion, the 
cycle of the moon, the cycle of the fun, &c. 
The cycle of mdidlion, commonly called the Roman in- 
didtion, is a feries of fifteen years, returning conftantly 
round like the other cycles; and commenced from the 
third year before Chrift; whence it happens that if 3 be 
added to any given year of Chrift, and the fum be di¬ 
vided by fifteen, what remains is the year of the indic¬ 
tion. The popes have dated their adts by the year of the 
Indidtion, which was fixed to the ift of January anno 
Domini 313, ever fince Charlemagne made them fove- 
reign; before that time, they dated them by the years 
of the Emperors. At the time of reforming tlie calendar, 
the year 1582 was reckoned the tenth year of the Indic¬ 
tion ; fo that beginning to reckon from hence, and di¬ 
viding the number of years elapfed between that time 
and this, by 15, the remainder, with the addition of io, 
rejedling 15 if the fum be more, will be the year of the 
Indidtion. But the Indidtion will be eafier found as 
above hinted, thus : Add 3 to the given year of Chrift ; 
divide the fum by 15, and the remainder after the divi- 
fion, will be the year of the indidtion : if there be no re¬ 
mainder, the indidtion is 15. In either of thefe ways, the 
indidtion for the year t8oi is 4. 
The cycle of the-moon, or the lunar cycle, is a period of 
nineteen years : in which time the new and full moons 
return to the fame day of the Julian year. This cycle is 
alfo called the Metonic period or cycle, from its inventor 
Meton, the Athenian j and alfo the Golden Number, from 
its excellent ufe in the calendar : though, properly fpeak- 
ing, the golden number is rather the particular number 
which fliews the year of the lunar cycle, which any given 
year is in. This cycle of the moon only holds true for 
3 IO /o years: for, though the new moons do return to 
the fame day after nineteen years; yet not to the fame 
^inte of the day, but near an hour and a half fooner; an 
error which in 310-^ years amounts to an entire day. 
Yet thofe employed in reforming the calendar went on 
a fuppofition that the lunations return precilely from 
nineteen years to nineteen years, for ever. The ufe of 
this cycle, in the ancient calendar, is to fhew the new 
moon of each year, and the time of Eafter. See Easter. 
In the new one, it only ferves to find the epadts ; which 
fhew, in either calendar, that the new moons falls eleven 
days too late. As the Orientals began the ufe of this 
cycle at the time of the council of Nice in 325, they af- 
fumed, that the firft year of the cycle the pafcal new moon 
fell on the 13th of March : on which account the lunar 
cycle 3 fell on the firft of January in the third year. The 
Occidentals, on the contrary, placed the number 1 to the 
ill of January, which occafioned a confiderable difference 
in the time of Eafter, Hence, Dionyfius Exiguus, ort 
6 X framing 
