.4 great circle of the sphere, is that whose plane passes through the centre, and consequently divides the sphere into two equal parts or hemispheres.
A small circle of the sphere is that whose plane does not pass through the centre, but divides the sphere into two unequal parts.
Every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds. 1 hese different subdivisions are denoted by the signs ° thus 12° 15' 10" mean 12 degrees, 15 minutes, and 10 seconds.
The length of an arch is expressed by the number of de grees, minutes, and seconds which it contains ; thus the fourth part of a circle, or a quadrant, is said to be equal to 90°.
The distance between two points, on the surface of a sphere, is measured by an arch of a great circle intercepted between them.
All great circles of a sphere are equal, and intersect one another in two points diamett ically oppo'site.
The angle formed by the intersection of two great circles, is measured by the arch of another great circle, cutting the other two at the distance of 90° from the point of intersec tion in each.
When two great circles make with one another an angle of 90°, that is, when their planes are at right angles to one another, they pass through each other's poles, the poles of a great circle being 90° distant from its circumference.
THE heavenly bodies, as seen from the earth, appear to he placed in the concave surface of a hollow sphere, having the earth in its centre, and seem to describe circles every 24 hours of a greater or less circumference, according as they are farther from, or nearer to a certain point, that ap pears fixed. Diametrically opposite to this point is an other, about which also the heavenly bodies seem to de scribe circles, thus exhibiting the same appearance, as if the whole celestial sphere revolved about a diameter from east to west. In this motion, which is called the diurnal re volution of the sphere, all the heavenly bodies seem to par ticipate, but the sun, with others of them called planets, have also a proper motion of their own in a contrary direc tion, by which, in a certain time, they perform a complete revolution of the sphere, though this is generally a very long pet iod, compared with that of their diurnal revolution.
Thus the sun, by his pro per motion from west to east, de scribes a circle of the It lestial sphere in 365 days, the moon in 27, and the other planets in different periods be tween 87 and 30689 clays. In order to illustrate these mo tions, as well as to determine the relative positions of the bodies themselves, certain imaginary points and lines are supposed to be marked or traced out on the surface of the celestial sphere. The most important of these we now pro ceed to explain.
The north and south poles of the world, are those points in the celestial sphere that appear to be fixed. The poles are also termed arctic and antarctic ; the arctic or north pole being that which is visible in this as well as in every other country of Europe.
The axis of the world is that diameter of the sphere which connects the poles, and about which the whole sphere seems to revolve.
The zenith of any place on the earth, is that point in the celestial sphere which is directly over the place, or it is the point in which the plumb-line at that place, if produced upwards, would meet the celestial sphere. When the sun or any other heavenly body is in the zenith of a place, it is said to be vertical to that place.
The nadir is a point in the sphere diametrically opposite to the zenith.
The equinoctial is a great circle of the sphere whose poles coincide with the poles of the world.
The horizon is a great circle whose poles are the zenith and nadir.
The cardinal points of the horizon are its north, south, east, and west points, which divide it into four quadrants, the two first being opposite to each other, as also the two last. The point of the horizon nearest the north pole is called the north point.
Meridians, called also hour circles and circles of right as cension, are great circles perpendicular to the equinoctial, and consequently passing c.hrough the poles of the world.