Note 7, [p. 4]. A hollow sphere. A hollow ball, like a bomb-shell. A sphere is a ball or solid body, such, that all lines drawn from its centre to its surface are equal. They are called radii, and every line passing through the centre and terminated both ways by the surface is a diameter, which is consequently equal to twice the radius. In fig. 3, Q q or N S is a diameter, and C Q, C N are radii. A great circle of the sphere has the same centre with the sphere as the circles Q E q d and Q N q S. The circle A B is a lesser circle of the sphere.
Note 8, [p. 4]. Concentric hollow spheres. Shells, or hollow spheres, having the same centre, like the coats of an onion.
Fig. 1.
Note 9, [p. 4]. Spheroid. A solid body, which sometimes has the shape of an orange, as in fig. 1; it is then called an oblate spheroid, because it is flattened at the poles N and S. Such is the form of the earth and planets. When, on the contrary, it is drawn out at the poles like an egg, as in fig. 2, it is called a prolate spheroid. It is evident that in both these solids the radii C q, C a, C N, &c., are generally unequal; whereas in the sphere they are all equal.
Fig. 2.
Note 10, [p. 4]. Centre of gravity. A point in every body, which if supported, the body will remain at rest in whatever position it may be placed. About that point all the parts exactly balance one another. The celestial bodies attract each other as if each were condensed into a single particle situate in the centre of gravity, or the particle situate in the centre of gravity of each may be regarded as possessing the resultant power of the innumerable oblique forces which constitute the whole attraction of the body.
Note 11, pp. [4], [6]. Poles and equator. Let fig. 1 or 3 represent the earth, C its centre, N C S the axis of rotation, or the imaginary line about which it performs its daily revolution. Then N and S are the north and south poles, and the great circle q E Q, which divides the earth into two equal parts, is the equator. The earth is flattened at the poles, fig. 1, the equatorial diameter, q Q, exceeding the polar diameter, N S, by about 261⁄2 miles. Lesser circles, A B G, which are parallel to the equator, are circles or parallels of latitude, which is estimated in degrees, minutes, and seconds, north and south of the equator, every place in the same parallel having the same latitude. Greenwich is in the parallel of 51° 28ʹ 40ʺ. Thus terrestrial latitude is the angular distance between the direction of a plumb-line at any place and the plane of the equator. Lines such as N Q S, N G E S, fig. 3, are called meridians; all the places in any one of these lines have noon at the same instant. The meridian of Greenwich has been chosen by the British as the origin of terrestrial longitude, which is estimated in degrees, minutes, and seconds, east and west of that line. If N G E S be the meridian of Greenwich, the position of any place, B, is determined, when its latitude, Q C B, and its longitude, E C Q, are known.
