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dominical letters will have happened; and the 29th year the cycle begins again, when the same order of
ihe letters will return as were 28 years before. At the birth of Christ, nine years had passed in this cycle. The lunar cycle, or cycle of the moon, or golden number, is
a period of 19 years, containing all the variations of the days on which the new and full moons happen; after which tinie they fall on the same days they did
19 years before, and she begins again with the sun. But when a centesiinal or hundredth year falls in the cycle,
the new and full moon, according to the new style, will fall a day later than otlerwise. The birth of
Christ happened in the second year of this cycle. The Roman indiction is a cycle of 15 years, which first began
the third year before Christ.
RULE. Multiply the golden number for the given year by 1!; divide that product by 30, and from the remainder take 11, leaves the epact. If the remainder be less than 11, add 19.10 it, and the sum will be the epact.
EXAMPLES. (8) Find the epact for the year 1795. (9) Required the epact for the year 1796. 5. The epact of any year is the moon's age, at the
beginuing of that year, that is, the days past since the last new moon.
RULE. To the epact add the number and day of the month; their sum, if under 30, is the moon's age. But if that sum is above 30, the excess in months of 31 days, or the excess
above 29 in a month of 30 days, shows the age or days since the last conjunction. The moon's
age taken from 30 leaves the day of the next When the solar and lunar cycles begin together, the moon's age on the first of each month, or the monthly epacts, are called the numbers of the month, and are as follows; viz.
For Jan. Feb. Mar. April. May. June.
EXAMPLES (10) Required the moon's age on May 21, 1795. (11) What is the moon's age on the 24th of March, 1796? 6. The moon's age is = how many days are past since
the day of her change, which age never exceeds 30 days.
To find when Easter-day will happen.
RULE. Find on what day of March the new moon falls nearest to the 21st in common years, or nearest the 20th in leap years : then the Sunday next after the full, or 15th day of that new moon, will be Easter-day.
If the 15th day fall on a Sunday, the next Sunday is Easter-day.
EXAMPLES. (12) On what day does Easter-Sunday fall for the year 1795? (13) Required the time of Easter-day for the year 1796.
7. Easter is the time when Christians celebrate the resur
rection of Christ from the grave, and took its rise from Eastra, the name of the Saxon deity or goddess whose festival was celebrated about this time of the
and after its abolishment by Christianity, the naine was retained, and is to ihis day used to signify the festival of Christ's resurrection, as mentioned above.
To find the time of the moon's southing.
RULE. Multiply the moon's age by 4; divide the product by 5, quotes the hours; and the remainder, multiplied by 12, gives the additional minutes.
If this time be less than 12 hours, it is the time of southing after mid-day; but if greater, 12 hours taken from it leaves the southing atter midnight.
EXAMPLES. (14) Required the time of the moon's southing at London on
the 21st of May, 1795. (15) At what time does the moon come to the meridian at
Bristol quay, on March 24, 1796 ? 8. The moon's southing at any place is the time when
she comes to the meridian, or is full south of that place, which is every day later, by about 48 minutes; occasioned by the hours in a day being divided by the thirty times she passes the meridian from new moon to new
To find the time of high water at any place.
RULE. To the time of the moon's southing add the time the moon has passed the meridian, to make high water at that place, and the sum will show the time of high water.
The distance of the moon from the meridian, when high water at the following places, is : At London, ) bears N. E. or S. E. 3 h. Om. Bristol quay, D bears E. by S. and W. by N. 6 h. 45 m.
EXAMPLES. (16) On the 21st of May, 1795, at what time is it high
water at London ? (17). On the 24th of March, 1796, at what time is it high
water at Bristol quay ? 9. High water is the state of the tide when highest, or the
time it ceases to flow up.
QUESTIONS for Exercise at leisure Hours. (1) England was conquered by William I. October 4,
1066; his son, William II., came to the crown Sept. 8, 1087, and left it August 2, 1100; William III. received it Feb, 3, 1689, and died March 8, 1701. How many days did each of these princes govern, respect being had to the intercalary days, and to February every leap year, as they rose in the course
of time? (2) Richard I. succeeded his father Henry II. July 7,
1189; John, his brother, succeeded him April 6, 1199; Richard II. succeeded Edward III. on the 21st of June, 1977, and was deposed by Henry IV. on the 30th of September, 1399; Richard ill. caused his nephew, Edward V., and his brother, to be murdered on the 18th of June, 1483, and was slain himself on the 22d August, 1485. How many days was the realm governed by the three Richards, respect being
still had to the intercalary days as they happened ? (3) The first Queen Mary came to the crown July 8, 1553 ;
she reigned 5 years 4 months and 9 days; her sister Elizabeth succeeded, and James I. came to the throne the 14th of March, 1602, who left it to his son, Charles I., on the 27th of March, 1625, who was forced from it January 30, 1648. The question is, How many days did these princes reign? and at the death of Charles I. how long had England been under an uninterrupted succession of Protestant princes (Mary the first being the last professed papist that enjoyed the crown), not neglecting the intercalary
days in February as before? (4). A grant was made February 14, in the 10th of Henry I.,
who began his reign August 2, 1100; it was resumed
Norember 19, in the 4th of Henry III., who came to the crown October 19, 1215 ; it was revived the 16th dlay of July, in the 13th of Henry VII., who ascended the throne August 22, 1486; but it was a second time revoked, and finally suppressed, in the 16th of his successor, Henry VIII., on the 10th of May. Now, as this man's father died July 21, 1509, the question is, How many days was this grant in force, and how many did it lie dormant?
Examples on the TerrEsTRIAL Globe, or Maps. (1) WHAT is the latitude and longitude of Pekin, in China,
and Cape Horn ? (2) Required the name of that place whose latitude is 180
N. and longitude 7610 W.; also of another place,
whose latitude is 34. S. and longitude 164 E. (3) What is the difference of latitude between London and
Naples; also between the island of Barbadoes, and the
Cape of Good Hope? (4) Required the distance (in English miles) Jamaica is
from London ; also the names of all those places that
are at the same distance from London as Rome is. (5) Required the sun's declination, right ascension, and me
ridian altitude, on the 20th of May. (6) Required the time of the sun's rising and setting, on the
20th of May; also his amplitude at the same time;
likewise when the twilight begins and ends. (7) What is the sun's azimuth and altitude, on the 20th of
May, at 4 o'clock in the afternoon? (8) What is the angle of position, or bearing, of Port Royal
in Jamaica from London; and, on the contrary, Lon
don from Port Royal ? (9) When it is noon, or twelve o'clock, at London, what
o'clock is it at Pekin in China ? Also at what places are they breakfasting, dining, and supping, suppose they breakfast at 7 o'clock, dine at 1, and sup at a
quarter after 9 ? (10) What places are those to which the sun is vertical on the 2d of May ?