The PARALLEL OF LATITUDE of any place, is a circle passing through that place, parallel to the Equator.

The DIFFERENCE OF LATITUDE between any two places, is an arch of a meridian intercepted between the corresponding parallels of latitude of those places. Hence, if the places lie between the Equator and the same Pole, their difference of latitude is found by subtracting the less latitude from the greater; but if they are on oppossite sides of the Equator, the difference of latitude is equal to the sum of the latitudes of both places.

The FIRST MERIDIAN is an imaginary semicircle, passing through any remarkable place, and is therefore arbitrary. Thus, the British esteem that to be the First Meridian, which passes through the Royal Observatory at Greenwich; and the French reckon for their First Meridian, that which passes through the Royal Observatory at Paris. Formerly, many French geographers reckoned the meridian of the island of Ferro to be their First Meridian; and others, that which was exactly 20 degrees to the west of the Paris Observatory. The Germans, again, considered the meridian of the Peak of Teneriffe to be the First Meridian. By this mode of reckoning, Europe, Asia, and Africa, are in east longitude; and North and South America, in west longitude. At present, the first meridian of any country is generally esteemed to be that which passes through the principal Observatory, or chief city of that country.

The LONGITUDE of any place is that portion of the Equator which is contained between the first meridian, and the meridian of that place; and is usually reckoned either east or west, according as the given place is on the east or west side of the first meridian; and, therefore, cannot exceed 180°*.

The DIFFERENCE OF LONGITUDE between any two places is the intercepted arch of the Equator between the meridians of those places, and cannot exceed 180°.

In order to illustrate the preceding definitions, let Pp (fig. 1st) represent the axis of the earth, EQ the equator, and PAP, PBp, the meridians of the two places A and B; then the portion AF, of the meridian of the place A, contained between it and the equator, will be the latitude of that place; in like manner, the intercepted arch BG, of the meridian PBp, will be the latitude of the place B—and the portion AH or BI, of the meridian passing through either of those places, contained between the parallels of latitude KAIL, MHBN, will be the difference of latitude: Hence, it is evident, by inspection of the figure, that the difference between the latitudes of any two places is equal to the difference, or sum, of their latitudes, according as the given places

* In order to prevent any ambiguity that might arise from the division of the longitude into east and west, some persons have reckoned it from the first meridian towards the east, until the first meridian again. Hence, 333" of longitude would, by the common methou of reckoning, be 27 W.

YOL. I.

are

are in the same, or in contrary hemispheres. Again, let PRP be the first meridian--then the arch of the equator RF, contained between the first meridian and the meridian of the place A, is the longitude of that place; RG is the longitude of the place G, and FG the difference of longitude of those places: Whence it is apparently obvious, that the difference of longitude between any two places, is equal either to the difference or sum of the longitudes of those places; according as they are on the same, or on contrary sides of the first meridian.

There are three different Horizons, the APPARENT, the SENSIBLE, and the TRUE.* The apparent or visible Horizon is the utmost apparent view of the sea or land. The sensible is a plane passing through the eye of an observer, perpendicular to a plumb line hanging freely : And the true or rational Horizon is a plane passing through the center of the Earth, parallel to the sensible Horizon.

Altitudes observed at sea, are measured from the visible Horizon. At land, when an astronomical quadrant is used, or when observations are taken with a Hadley's quadrant by the method of reflection, the altitude is measured from the sensible Horizon; and in either case, the altitude must be reduced to the true Horizon.

The ZENITH of any given place is the point immediately above that place, and is, therefore, the e.evated pole of the Horizon: The NADIR is the other pole, or point diametrically opposite.

A VERTICAL is a great circle passing through the Zenith and Nadir ; and, therefore intersecting the Horizon at right angles.

The ALTITUDE of any celestial body is that portion of a Vertical, which is contained between its center and the true Horizon. The Meridian Alitude is the distance of the object from the true Horizon, when on the Meridian of the place of observation. When the observed Altitude is corrected for the depression of the Horizon, and the errors arising from the instrument, it is called the apparent Altitude; and when reduced to the true Horizon, by applying the parallax in Altitude, it is called the true Altitude. Altitudes are expressed in degrecs, and parts of a degree.

The ZENITH DISTANCE of any object is its distance from the Zenith, or the complement of its Altitude.

The DECLINATION of any object is that portion of its meridian, which is contained between the equinoctial and the center of the object; and is either north or south, according as the object is between the equinoctial and the north or south pole.

The ECLIPTIC is that great circle in which the annual revolution of the Earth round the Sun is performed. It is so named, because Eclipses cannot happen but when the Moon is in, or near that circle. The inclination of the Ecliptic and Equinoctial is at present about 23° 28'; and by comparing ancient with modern observations, the obliquity of

It may also be necessary to mention another Horizon, which may be called the RrDUCED HORIZON. This is a plane passing through the earth's center, perpendicular to the radius answering to the reduced place of observation.

the

the Ecliptic is found to be diminishing-which dimunition, in the pre sent century, is about half a second yearly.+

The Ecliptic, like all other great circles of the sphere, is divided into 360°; and is further divided into twelve equal parts, called SIGNS each Sign, therefore, contains 30°. The names and characters of these Signs are as follow:

Aries,

Cancer, Libra, A Capricornus, s Taurus, 8 Leo, & Scorpio, m

Gemini,

Aquarius,

Since the Ecliptic and Equinoctial are great circles, they, therfore, bisect each other in two points, which are called the Equinoctial Points. The Sun is in one of these points in March, and in the other in September; hence, the first is called the Vernal, and the other the Autumnal Equinox-and that sign which begins at the Vernal Equinox is called Aries. Those points of the Ecliptic, which are equidistant from the equinoctial points, are called the Solstitial oints; the first the summer, and the second the winter solstice. That great circle which passes through the equinoctial points and the poles of the earth, is called the Equinoctial Colure; and the great circle which passes through the solstitial points and the poles of the earth, is called the Solstitial Colure.

When the Sun enters Aries, it is in the Equinoctial; and, therefore, has no declination. From thence it moves forward in the Ecliptic, according to the order of the signs, and advances towards the north pole, by a kind of retarded motion, till it enters Cancer, and is then most distant from the Equinoctial; and moving forward in the Ecliptic, the Sun apparently recedes from the north pole with an accelerated motion till it enters Libra, and being again in the Equinoctial, has no declination; the Sun moving through the signs Libra, Scorpio, and Sagittarius, enters Capricorn; and then its south declination is greatest, and is, therefore, most distant from the north pole; and moving forward through the signs Capricorn, Aquarius, and Pisces, again enters Aries: Hence, a period of the seasons is completed, and this period is called a Solar Year.

The signs Aries, Taurus, Gemini, Cancer, Leo, and Virgo, are called Northern Signs, because they are contained in that part of the Ecliptic which is between the Equinoctial and North Pole; and, there

+ It is also subject to two periodical inequalities; the first, arising from the attraction of the sun, is completed in six months, the maximum of which is only half a second; the other, called the Nutation of the Earth's Axis. is completed in a revolution of the Moon's Nodes, or 18 years 224 days, and is usually represented by supposing the pole of the earth to describe the periphery of an ellipse in a retrograde manner during a period of the Moon's Nodes, the greater axis being in the solstitial colure, and equal to 19′′. 1, and the least axis in the equinoctial colure, and equal to 14".2; the greater axis being to the less, as the cosine of the obliquity of the ecliptic, to the co-sine of double the obliquity.

The division of the Ecliptic into twelve equal parts was the invention of Cleostratus Tenedius. See Pliny, lib. 2. cap. 8. For the Moon was supposed to complete a lunation in 30 days, and in that period the Sun would have completed a twelfth part of the Ecliptic, or 30°, which was therefore called a Sign. C 2

fore

fore, while the Sun is in these signs, its declination is north: the other six signs are called Southern Signs. The signs in the first and fourth quarters of the Ecliptic are called Ascending Signs; because, while the Sun is in these signs, it approaches the north pole-and, therefore, in the northern, temperate and frigid zones, the Sun's meridian altitude daily increases; or, which is the same, the Sun ascends to a greater height above the horizon every day. The signs in the second and third quarters of the Ecliptic are called Descending Signs.

The Longitude of the Sun, is that portion of the Ecliptic, which is contained between the Vernal Equinox and the Sun's center.

The Right ascension of any celestial object, is that arch of the Equinoctial, which is intercepted between its meridian, and the Vernal Equinox.

The TROPICS are circles parallel to the Equinoctial, whose distance therefrom, is equal to the obliquity of the Ecliptic. The Northern Tropic touches the Ecliptic at the begining of Cancer, and is, therefore, called the Tropic of Cancer; and the Southern Tropic touches the Ecliptic at the beginning of Capricorn, and is hence called the Tropic of Capricorn.

Circles about the poles of the Equinoctial, and passing through the poles of the Ecliptic, are called POLAR CIRCLES; the distance, therefore, of each Polar Circle from its respective Pole, is equal to the inclination of the Ecliptic and Equinoctial. That Circle which circumscribes the North Pole, is called the Arctic or North Polar Circle ; and that towards the South Pole, the Antartic, or South Polar Circle..

That semicircle which passes through a Star, or any given point of the heavens, and the Poles of the Ecliptic, is called a CIRCLE of LATITUDE.

The REDUCED PLACE of a Star is that point of the Ecliptic, which is intersected by the circle of Latitude passing through that Star.

The LATITUDE of a Star is that portion of the circle of latitude contained between the Star and its reduced place—and is either north or south, according as the Star is between the Ecliptic and the north or south pole thereof.

The LONGITUDE of a Star is that portion of the Ecliptic, contained between the Vernal Equinox and the reduced place of the Star thus: PAP, is a Circle of declination; and PSR = ASB, the angle of position.

That semicircle which passes through a Star, and the Poles of the Equinoctial, is called A CIRCLE OF DECLINATION.

The ANGLE OF POSITION of a Star is the angle contained between the Circles of latitude and declination, which pass through that Star. The Nonagesimal Degree, is that point of the Ecliptic, which is equidistant, or 90° from each of its intersections with the horizon. The Altitude of the Nonagesimal, is an Arch of a Vertical Circle, contained between it and the horizon.

The Longitude of the Nonagesimal is that Arch of the Ecliptic which is contained between it and the Vernal Equinox.

Let

Let the Circle PEQ (fig. 2.) represent the Solstitial Colure, EQ the Equinoctial, P, p its Poles; the Ecliptic, whose Poles are Ř, r; and S the position of a Star with respect to these Circles: then is AS the declination, and A the right ascension of that Star; B is its reduced place: Hence, BS is the latitude, and Bthe longitude of the Star.

CHA P. III.

Of the LENGTH of the YEAR.

TH

HE orbit of the earth is an ellipse, in one of whose foci is the sun. That point of the earth's orbit which is most distant from the sun is called the Aphelion; and that which is nearest is called the Perihelion; and the line joining these is called the Line of the Apsides. Since, in common language, it is usual to attribute the motion of the earth to the sun, the first of these points is called the Apogee of the sun, and the second, the Perigee.

A YEAR is that period or portion of time, in which a revolution of the earth, with respect to some point in the heavens, is completed. As the equinoctial points and the line of the apsides have a slow motion, with respect to the fixed stars; there are, therefore, three different kinds of Years-a Solar or Tropical, a Sidereal or Periodical, and an Anomalistic Year.

A SOLAR OF TROPICAL Year, is the interval of time between two successive returns of the sun, to the same equinoctial or solstitial point. The seasons are regulated by this Year.

A SIDEREAL OF PERIODICAL Year, is the interval of time between two successive returns of the earth to the same fixed star.

An ANOMALISTIC Year, is the interval of time between two successive returns of the earth to the same apsis.

Of the TROPICAL YEAR.

The length of the Solar Year is ascertained by comparing the times of oervation of two corresponding equinoxes; and the more distant

these