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

152 Applications of Spherical Trigonometry.
Let Z denote the zenith distance ZS, A the azimuth from
the north, p the angle ZSP at the star; then, by Delambre's
Analogies,
cos Z. sin. (p +.) = cos 1t. cos i (8 - 4). (472)
cos Z. cos ~ (p +- ) = sin- t. sin L (8 + ). (473)
sin iZ. sin (p - A) = cos t. sin (8 - 4). (474)
sin Z. cos (p - ) = sin t. cos 3 (8 + <). (475)
Hence, when t, 8, 4 are given; that is, the hour angle and
declination of a heavenly body, and the latitude of the observer,
z, p, A can be found. In a similar manner may be solved the
converse problem:-Given the azimuth and altitude, to find the
hour angle and the declination.
4~. If a denote the altitude of the sun at 6 o'clock, and a' the
altitude when east or west; then
sin a = sin 8. sin <. (476)
sin a'= sin 8 - sin 4. (477)
EXERCISES. —XXXVI.
1. In latitude 45~ N., prove that the shadow at noon of a vertical object
is three times as long when the sun's declination is 15~ S. as when it
is 15~ N.
2. The altitude of a star when due east was 20~, and it rose EbN; required the latitude.
3. Given the sun's longitude, to find his right ascension and declination.
S
D
7
Fig. 61.
Let a denote the right ascension, 8 the declination, o the obliquity of
the ecliptic. Now let S denote the sun's place in the ecliptic rS. Draw