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The dominical letter being known, it is easy to find the day of the week on which any month begins, by the following table.

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The following couplet is designed to assist the memory.

A Table showing at what Days

of the Months the Letters forAll days decline; great blessings end ; Good Christians find a during friend.

merly stood, and where the

Dominical Letters nou stand. The first letters of these twelve

D. Letters. A B C D E F G words are the same as those at the beginning of each month.

1 2 3 4 5 6 7 If the letter set at the first January 31 8 9 10 11 12 13 14 day of a month be before or af October 31 15 16 17 18 19 20 21 ter the dominical letter in any

22 23 24 25 26 27 28 year, the day on which the

29 30 31 month begins is before or after

1 2 3 4 the Lord's day, and is as far Feb. 28-29. 5 6 7 8 9 10 11 distant as the commencing let,

March 31. 12 13 14 15 16 17 18

19 20 21 22 23 24 25 ter is distant from the dominical Nov. 30. letter. Thus, if A be the do

26 27 28 29 30 31 minical letter, January begins

2 3 4 5 6 7 8 on the Sabbath ; February and April 30. 9 10 11 12 13 14 15 March on Wednesday. If B be July 31. 16 17 18 19 20 21 22 the dominical letter, January

23 24 25 26 27 28 29 begins on Saturday, February

30 31 and March on Tuesday.

1 2 3 4 5

6 7 8 9 10 11 12 Aug. 31.

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27282930 31

1 2 3 4 5 6 7 8 9 Sept. 30. 10 11 12 13 14 15 16 Dec. 31. 17 18 19 20 21 22 23

24 25 26 27 28 29 30 31

1 2 3 4 5 6

7 8 9 10 11 12 13 May 31. 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31

1 2 3

4 5 6 7 8 9 10 June 30. 11 12 13 14 15 16 17

18 19 20 21 22 23 24 25 26 27 28 29 30

What are periods? How long is the Chaldean period ? What takes place at the termination of this period ? How is the Julian period formed ? How long is it? What is its use? Of how many years does the cycle of the Sun consist ? What is effected by this cycle? How long is the cycle of the Moon, or golden number? What takes place at the expiration of this cycle? What is the Roman indiction? How are the cycle of the Sun, golden number and indiction found? What is the epact? How is the Julian epact found ? How is the Gregorian? Are the golden number, epact, and indiction of much use? What is the difference between old and new style in the present century. Which is the proper day for the celebration of Washington's birth? What constitutes a year? Of what does the civil solar year consist? How long is a lunar year? What was added to make this year coincide with the solar year? How did the Jews compute their time? What defect was there in their computation? Of what did the year of the Greeks consist ? Was their year easily connected with the solar year? When were the Olympic games celebrated ? At what season was the first month of the Grecian year? How did the ancient Romans compute time? They reckoned by lunar years, established by whom? Who established the Julian calendar? In this calendar how many years were common When was the day added in leap year? Why was it called bissextile ? On what day of March did the vernal equinox happen at the time of the Council of Nice, in the year 325 ? ' In 1582, what did Pope Gregory XIII. observe? To correct the style, what did he do? When was the Gregorian, or new style, adopted in England? Where does the Julian, or old style, still prevail ? What principle did Pope Gregory endeavor to establish? By his principle, how many bissextiles are to be omitted in four hundred years ? | How can it be ascertained what bissextiles are to be omitted?' Has any bissextile been of late omitted? Does the civil year, as now established, exactly coincide with the tropical ? What omission would bring the two con tations to great exactness ? What is a sidereal lunar month? What is the principal lunar month? Of how many kinds are civil months? Of what does the weekly month consists What is the true legal month? What are the other months ? Of what origin are they? How are the names ? What was the sixth month formerly called? Why was it called August? How was the compliment heightened ? °What seems to have been the foundation of weeks? What is an artificial day ? What is a natural day? When did the ancient Egyptians begin their day? What nations now begin their day at midnight? When did the Jews begin their day? How did they divide the night and the day? What modern nations begin their day at sunset? What ancient nations commenced their day at sunrising ? What moderns ? When does the nautical, or sea-day, commence ? How are the hours marked ? When does the astronomical day begin? How is it reckoned ? What is an hour? From whom did the Greeks learn their method of dividing the day? Who divided the day and the night each into four watches ? How long was a watch ? After hours, in what

order do all the remaining divisions of time proceed? How were the first seven letters of the alphabet formerly placed in almanacs ? Who introduced them? Why was one of these called dominical ? If a common year begins on Monday, on what day will the next year begin? What prevents the dominical letters from proceeding in a retrograde order, and returning again at the end of seven years ? In what order were the letters placed in almanacs? What causes two dominical letters in leap year? In how long time do the days of the week return to the same days of the month? What is a convenient couplet? Why is it convenient? If you know the letter at the beginning of a month, and the dominical letter, how will you find on what day of the week the month begins ?

CHAPTER X.

Obliquity.

The obliquity of the equator to the plane of the ecliptic, being the cause of the variety of seasons, the different length of days and nights, and the pleasing vicissitudes resulting from the varying year, is well deserving a place, even in a compendium of astronomy. The principal inquiry is, whether the obliquity remains the same, or is subject to a constant diminution.

“ The obliquity of the ecliptic to the equator," says Dr. Brewster, "was long considered a constant quantity. Even so late as the end of the 17th century, the difference between the obliquity, as determined by ancient and modern astronomers, was generally attributed to inaccuracy of observation, and a want of knowledge of the parallaxes and refraction of the heavenly bodies. It appears, however, from the most accurate modern observations, at great intervals, that the obliquity of the ecliptic is diminishing. By comparing about 160 observations of the ecliptic, made by ancient and modern ob

servers, with the obliquity of 23° 28' 16'', as observed by Tobias Mayer, in 1756, we have found that the diminution of the obliquity of the ecliptic, during a century, is 51; a result which accords wonderfully with the best observations." This would bring the obliquity at the present time, 1831, to 23° 27' 38“.

The above statement, though contrary to the opinion of some philosophers, is in accordance with the true principles of Newtonian philosophy, and is corroborated by the best modern astronomers. Professor Vince, having stated the observations of many authors, ancient and modern, concludes: “It is manifest, from these observations, that the obliquity of the ecliptic continually decreases; and the irregularity, which here appears in the diminution, we may ascribe to the inaccuracy of the observations; as we know that they are subject to greater errors than the irregularity of this variation.”

The following table will give, an idea of the diminution of the obliquity for many centuries. It was extracted from Rees's Cyclopædia.

Obliquity of the Ecliptic, from Observations

at different Times.

B. C. Pytheas,

324 23 49 23 Eratosthenes, 230 | 23 51 | 20 Hipparchus, 140 | 23 | 51 | 20

A. D.
Ptolemy,

140 | 23 48 | 45
Arzachel, 1104 | 23 33 | 30
Propatius,
Waltherus, 1476 23 30
Tycho Brahe, 1584 | 23 | 31 | 30
Kepler,

1627 | 23 | 30 | 30 Flamstead,

1690 23 29 Mayer,

1756 | 23 | 28 | 16 Maskelyne,

1800 | 23 27 56.6

Mean Obliquity for

40 Centuries. B. C.

1 900 23 50 26 400 23 46 30

0 | 23 | 43 | 15 A. D.

100 23 42 26 500 23 39 6 1000 23 34 51 1500 | 23 | 30 | 33 1700 | 23 28 49 1800 | 23 27 57 2000 | 23 | 26 | 13 2500 23 21 52 3000 23 17 31

A small difference will be seen between the statement of Dr. Rees and that of Professor Vince, respecting the obliquity, as observed by some of these authors. But as the general principle is not affected, it may be useless to attempt a reconciliation.

1

The part of the table on the left was taken from observation. It will be found very nearly to coincide with that on the right, formed by calculation from the observations of the most accurate modern astronomers.

The attraction of the Moon on the spheroidical figure of the Earth is, without doubt, the cause of the diminution above stated. [See a demonstration of this in the author's larger work on astronomy.] The action of the Sun upon the same figure must have an effect similar to that of the Moon ; but far less in quantity, on account of his immense distance. The principle is nearly similar to that of the tides, as may be seen in the demonstration.

If such be the cause of diminution, the obliquity must continually decrease, and in time become extinct. But, at the present ratio of diminution, such an event cannot occur under about 160,000 years, a period stretching beyond the most distant wish of the present inhabitants respecting the concerns of this world.

The variety of seasons, it is true, must cease at such an event. But long ere that time the earth may be dissolved;" or it may be renovated, so as to produce s seed time and harvest, and summer and winter.

Why does the obliquity of the equator to the plane of the ecliptic deserve a place in a compendium of astronomy? How was this obliquity long considered? To what was the difference between the obliquity, as determined by ancient and modern astronomers, long attributed ? Does it appear now, that the obliquity is increasing or diminishing? What is the diminution in a century ? What is the cause of the diminution? If the Moon's attraction on the spheroidical figure of the Earth be the cause of diminution in the obliquity, what must in time be the effect? According to the present diminution of the obliquity, how many years would be re. quired to bring the equator to the ecliptic? Ought the present inhabitants to be anxious respecting such an event?

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