A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

150 Applications of Spherical Trigonometry.
since QZis evidently equal to PR, PR is equal to the latitude;
but PR is the elevation of the pole above the horizon. Irence
the elevation of the pole above the horizon is equal to the latitude.
Again, if S be any heavenly body, such as the sun or a star,
its position is denoted by any one of four systems of spherical
co-ordinates as follows:
1~. The great circle ZST passing through the zenith and S,
and meeting the horizon in T, is called the vertical circle of S.
The arc HT, measured from the south point of the horizon, or
its equal the angle 1ZT, is called the azimuth, and ST the
altitude. lIT, ST are the spherical co-ordinates of the star S;
ZS is its zenith distance, and the arc RT its azimuth from the
north.
2~. Join SP, and produce to meet the equator in K. The
arcs QK, XS form the second system of spherical co-ordinates;
QK, or its equal the angle ZPS, is called the hour angle of S,
and KS the declination. The declination is positive when S is
north of the equator, and negative when south. The great
circle PSK is called the declination circle, and PS the polar
distance of S.
3~. The great circle which the centre of the sun, seen from
the centre of the earth, appears to describe annually among the
stars is called the ecliptic; and its inclination to the equator,
which is nearly 23"~, the obliquity of the ecliptic. The points of
intersection of equator and ecliptic are called the equinoxesone the vernal equinox (called also the first point of Aries),
and the other the autumnal equinox (the first point of Libra).
If wr denote the first point of Aries, then r'K is called the right
ascension, and KS the declination of the star; crK, KS are the
third system of spherical co-ordinates of S. The right ascension is counted eastward, from 0 to 360~.
4~. From S draw a great circle Sa- perpendicular to the
ecliptic; then rqp-, aS are the fourth system of spherical coordinates of S, and are called respectively its longitude and