708 



SPHERE, DOCTRINE OF THE. 



SPHERE, DOCTRINE OF THE. 



710 



heavens (p 1 being that of the earth) is the angle N E p. Now suppose 

 the earth and the spectator to diminish until they cannot be distin- 



guished from the point o, the sphere of the heavens remaining the 

 same. All angles at o remain unaltered : the altitude of the pole of 

 the heavens becomes Q o p, equal to the angle A o E, the latitude of the 

 spectator, and the horizon of the latter coincides with the great circle 

 drawn through R q perpendicular to o z. The great circle, Q P z R, 

 passing through the pole and the zenith, is the meridian ; the second- 

 ary to the horizon perpendicular to the meridian is the prime vertical. 

 We here exhibit a skeleton of the sphere, showing nM z P N, half the 



meridian ; N En, the horizon (N, E, , its north, east, and south points) ; 

 7. E, the prime vertical ; a portion of po, the axis; EM, the equator, 

 perpendicular to the axis. 



We now give three positions of the sphere, differing only in the 

 manner of projecting the figure. Each one represents the state of the 

 heavens some two or three hours before noon in an October morning, 

 in a latitude somewhat greater than our own. The first figure is pro- 

 jected on the plane of the meridian ; that is, the meridian is the 

 circle which bounds the view of the sphere. The second is projected 

 on the prime vertical; the third, on the horizon. 



The diagrams have many letters and numerals which are useless, 

 except in tracing the affinities of the figures. The meridian. v '/. x ; 

 the prime vertical, ZEZ; the horizon, nit s, and its poles, the zenith 

 and nadir, z and 2 ; the equator, M E m, and its poles p and p (which 

 are called the poles, from their importance), are supposed to be well 

 known. The reader who is new to the subject should learn to see the 

 following propositions in each of the ft/tires, namely : the poles of the 

 meridian are the east and west points of the horizon ; the poles of the 

 prime vertical are the north and south points of the horizon ; the 

 equator and prime vertical make an angle equal to the latitude of 

 the place ut observation (which ifl P >', or the angle oil's); the equator 



and horizon make an angle equal to the colatitude (90 lat.) of the 

 place of observation ; a star which is distant from the north pole by 

 less than the latitude of the place of observation can never set nor go 

 below the horizon (it is called a circmnpolar star). 



The diurnal motion carries the sphere round the axis in the direction 

 of the arrows marked upon the equator. The meridian, horizon, and 

 prime vertical, must be considered as detached from the sphere, and 

 not moving with it. Every point of the sphere describes a small 

 circle parallel to the equator : and all stars which are at the same dis- 

 tance from the pole describe the same small circle. The whole revolu- 

 tion takes place in what is called a sidereal day [TIME], about f out- 

 minutes less than the mean solar day shown by a good clock. A 

 secondary to the equator describes angles uniformly about the pole at 

 the rate of 360 to 24 sidereal hours, or 15 to 1 sidereal hour.' [ANOLE.] 

 Hence if we would know how long it will be before the diurnal motion 

 will bring a star at K into the position s, we must turn the angle s p K, 

 which is measured by the arc y5, iuto sidereal time at the rate of 15' 

 to l h , and then turn the sidereal time so obtained into common clock 

 time, at the rate of about 23 h 56 m of clock time to 24 h of siderei-l 

 tune. For purposes of general explanation, the two species of timo 

 may be confounded. The sidereal day is always made to begin when 

 a certain point of the eqxiator, presently to be noticed (the vernal 

 equinox), comes on the south side of the meridian, and the hours arc 

 measured on to 24 h . 



We shall now explain the systems of co-ordinates which are made 

 use of in describing the positions of stars. 



1. Horizontal System. Altitude and Azimuth. In this case the 

 horizon is the primitive circle employed ; its north point, N, is ths 

 origin, and the position of a point w is determined by its azimuth, N I , 

 and its altitude, L w ; z w L being a secondary to the horizon. Since 

 the altitude and azimuth are reckoned by means of a fixed circle, both 



