the third is that of the Olympiads, which began in Greece 776 years before Christ, in the 3938th year of the Julian period, the solar cycle being then 18, the lunar cycle 5, and the Roman indiction 8. The next remarkable epoch is that of the foundation of Rome towards the end of the third year of the 6th Olympiad, 753 years before Jesus Christ, in the 3961st year of the Julian Period, the cycle of the sun being then 13, the cycle of the moon 9, and the indiction 1.

The next in order of time is that of Nabonassar, king of Babylon, to famous in astronomy. It has been employed by Ptolemy, Albategnius, Alphonso, Copernicus, and many others, as the most proper era for calculating the motions of the stars. It began, according to Ptolemy, in the 4th of the calends of March, on a Friday, 747 years before Jesus Christ, in the year 3967 of the Julian Period, the first year of the 8th Olympiad, the solar cycle being 19, the lunar cycle 15, and the indiction 6.

After this epoch we have that of Alexander the Great, 424 Egyptian years after the commencement of the era of Nabonassar, for Alexander died at Babylon in the 33d year of his age, the first year. of the 114th Olympiad, on the 3d of the month Desii, according to some historians, but according to others, on the 23d or 27th of the Julian calendar, which is the 20th of May according to the one, and the 9th or 23d June according to the other, and according to some the 25th July.

But the astronomers who have employed those epochs, as Albategnius and others, fix it to the 12th of November, a Sunday at midday, the first day of the Egyptian month Thoth, 324 years before Jesus Christ, in the 4390th year of the Julian Period, 279 years before the commencement of the Julian Epoch, and 424 complete Egyptian years after the commencement of the era of Nabonassar.

The era of the Syrians and Chaldeans began in the reign of Seleucus Nicator, who succeeded Alexander the Great, and reigned in Syria and in part of Africa, after the death of Alexander the Great. The Julian epoch, adopted by Julius Cæsar, began on the 1st of January of the year of the Confusion, which is found to have been on a Tuesday. This prince, seeing that the year established by Numa Pompilius, the second king of Rome, consisted only of twelve lunar months, and that such a division of the year did not accord with the sun, ordered, in the fourth year of his consulship, 708 years after the foundation of Rome, in the 731st year of the Olympiads, 45 years before the birth of Jesus Christ, that, in future, the should consist of 365 days 6 hours, which was afterwards, and is still, called the Julian Year.

year

The Spanish Era began in the reign of Augustus, in the 7th year of the Julian Era, 38 years before Jesus Christ, 715 years after the foundation of Rome, and in the 738th year of the Olympiads. It is said it was occasioned by the division of the empire. Spain was given to Augustus, and when he first took possession, to render that day memorable, it was fixed upon for an epoch, and computed from afterwards, Ab Exordio Regni Augusti These four words were afterwards abridged, and reduced to the initial letters. This, accord

ing to some authors, was the origin of the word AERA, which now serves to mark the epoch from whence years are reckoned.

The next epoch following in the order of time, the most renowned, and the best known of any, is the Incarnation of our Lord Jesus Christ, which, on that account, is called the Christian Era.

It began the first minute after the 31st December immediately after his birth, which was on a Saturday, in the 4714th year of the Julian Period, 753 years after the foundation of Rome, in the 747th year of Nabonassar, and 324 years after the death of Alexander the Great, the solar cycle being 10, the lunar cycle 2, and the Roman indiction 4.

There are other periods less used, as that of the Emperor Dioclesian, beginning on the 21st April, in the 284th year of Jesus Christ, and 4997 of the Julian Period. There is also the Epoch of the Ethiopians, of the Abyssinians, and of the Martyrs, because of the great persecution that the Christians suffered in that reign.

There is also the Epoch of the Turks, which is called the Hegira, and which began with the Flight of Mahomet from Mecca to go to Gabriel, on Tuesday the 16th July, in the 622d year of the Christian Era, at which time Mahomet preached and spread his false doctrine.

That of the Persians is named the Jesdegird, from the name of one of their kings, who died on Wednesday the 16th July, in the year of the Christian Era.

632

The Jews, in their Calendar, reckon the creation of the world to have taken place 3760 years before the Christian Era.

To Draw a Meridian Line.

UPON a plain board, set parallel to the horizon, describe several ́ concentric circles; in the centre of these fix a gnomon, or stile, exactly perpendicular to the plane of the board, and of such a height as the shadow of it may fall upon the circumference of all the circles at different times of the day mark the point where the top of the stile falls in the forenoon, which will be on the circumference of one of the circles; then watch the time when the shadow falls on the same circle in the afternoon; and a line drawn from the centre or stile bisecting the distance between these points will be in the direction of the true meridian.

The reason of several circles being drawn, is to observe the shadow of the stile on any of them, in case the sun should not be shining out in the afternoon, when he would throw a shadow on the same circle; and also to perform the same operation with each circle, in order to ensure accuracy, by taking the mean of the observations.

The best time of the year for doing this, is about the time of the summer solstice, when the daily difference of declination is least. The reason of this opposition may easily be perceived-for at equal distances from the meridian, the sun will have equal altitudes, and, of course, the shadow of any object will have the same length,

Of finding the Latitude of a Place.

THE latitude of any place is equal to the altitude of the pole above the horizon of that place; therefore the poles will appear in the horizon of a place which has no latitude, or that is on the equator.

This problem is nothing else, than finding the elevation of the pole above the horizon; but as there is no star exactly in the pole of the heavens, take any star which is not more than 80 or 10° from the pole, and observe with a quadrant its greatest and least meridianal altitudes; then if both observations are on the same side of the zenith, half the sum of the altitude is the latitude. If the observations are on different sides of the zenith, half the difference of the altitudes is the co-latitude.

Note.

There will be about twelve hours between the observations.

Of the Magnitude of the Earth,

To find the magnitude of the earth is a problem of such importance in astronomy, that it has been attempted by some of the ablest mathematicians, in almost every age, since the days of Eratosthenes to the present. The French mathematicians, by connecting a series of triangles, have lately measured the distance from Dunkirk to Formentera, which corresponds to an arc of the meridian, of 12° 22′ 13"-395; and from this extensive base the circumference of the earth is computed to be 24,855-42 English miles.

f

A degree of the meridian has been measured in different latitudes, by several astronomers, in order to ascertain the true figure of the earth, as well as to determine its magnitude. Mapertius, along with some other mathematicians, measured a degree in Lapland, at lat. 66° 20′, and found it 57,438 toises.

Another, by La Hire, at latitude 49° 22′, which was found to be 57,074 toises.

A Toise is = 1.06577 fathoms.

By comparing these numbers with each other, and taking the arithmetical mean of the whole, the equatorial axis is to the polar, as 230 to 228:92974, which is nearly what Sir I. Newton made it by calculation long before.

From this it is plain the earth is not exactly spherical, but is a kind of oblate spheroid, flattened at the poles.

This proportion makes the equatorial axis exceed the polar by about 34 miles, but some think this statement rather exceeds the truth, and give the compression at 30.63 25.66 miles.

The method of performing the operation of measuring a degree of the meridianal arc, and its corresponding arc of the earth's surface, is abundantly simple in theory, although there is scarcely any operation more difficult in execution. It is performed by measuring a base line as nearly as possible in the direction of the meridian, then finding exactly the difference of latitude between the extremities of the base line. Then, as the difference of latitude or celestial arc is to the measured base line, so is one degree of the celestial arc to the length of a degree of the earth's surface, in the same measure as the base line was taken.

In a similar manner may the circumference of the earth's orbit be obtained from knowing the sun's parallax: thus,

smd.

semids.

82": 360° : 1 :: 149538,

the circumference of the earth's orbit.

To find the distance of the sun and earth; then

3.1416×2: 149538 :: 1 : 23799-8,

the earth's distance from the sun.

From the above dimensions of the earth, it appears that one degree on the globe is nearly 69 English miles.

The length of a degree may be found, very nearly, by the following theorem:

Let L

the latitude, then 60761-(295-75) co-sine 2 L* will be the length of a degree.

Example.-Required the length of a degree of the meridian, at latitude 51°? Here the co-sine of the latitude is 6293, which multiplied by 2, and by the number 295-75, gives 370, which subtracted from 60761, leaves 60392 fathoms for the length of a degree of the meridian, at latitude 51°.

To find the Obliquity of the Ecliptic.

Rule.--LET the meridian altitude of the sun's centre be observed, on the days of the summer and winter solstices; the difference of those altitudes will be the distance of the tropics; and half that distance will be the obliquity of the ecliptic.

Rule 2.-Or if the latitude of the place be known, the meridian altitude of the sun, at the summer solstice, lessened by the co-latitude, will give the obliquity of the ecliptic.

The obliquity of the ecliptic for the year 1825, is 23° 27′ 44′′. By comparing ancient observations with what have lately been made, it appears that the obliquity is decreasing at the rate of "annually. Remark. By this last rule the declination of a fixed star may also be determined.

* The number 60761 is the radius of the globe, at latitude 45°, in fathoms.

To find the Time of an Equinox.

Ar a place, the latitude of which is known, let the sun's meridian altitude be taken the day before the equinox is expected to happen, and also the day after, then the difference between those altitudes, and the co-latitude, will be the sun's declination on those two days when the altitudes were taken.

If either of the altitudes be equal to the co-latitude, that observation was made at the time of the equinox. If not proceed thus:

D

B

L

E

C

Let A B C be a portion of the equator, and DBE an arc of the ecliptic, D the place of the sun at the first observation, E his place at the second, and B the equinoctial point; also, A D the declination at first observation, and EC at second; then in the right-angled spherical triangles, A B D and E BC, there are given the obliquity of the ecliptic, and the declination A D and EC, to find the sides DB and EB, which being found, are to be added together: then say, DB E B is to DB, so is 24 hours to the time between the first observation and the moment the sun entered the equinoctial point.

To find the Periodic Time of a Planet.

THIS is best done when the planet has no latitude, or in the ecliptic, it will then be in one of its nodes; this time is to be carefully noted, and compared with the time when the planet has a like position, both in latitude, longitude, right ascension, and the line of its apsides. If the planet has only performed one revolution, the interval betwixt the two observations will be the periodic time of the planet; but if it has performed more revolutions, the interval is to be divided by the number of revolutions, and the quotient will be the periodic time. From this it is evident, the greater the interval, or the greater the number of revolutions, the more accurately will the periodic time of the planet be found.

In this manner the length of the tropical year is found to be 365d 5 48′ 48′′; the sidereal year 365d 6h 9′11′′; and the anomalistic year 365a 6h 14′ 2′′.

The tropical year being shorter by 20′ 23′′ than the sidereal, shows that the sun has returned to the same point of the ecliptic, before he