SPHERICAL ASTRONOMY. 87 
equator at right angles, it will be the circle of latitude of the place, and that 
part of the circle intercepted between the place and the equator, will be its 
geographical latitude, which may consequently range from 0° to 90°. Any 
place at the equator has a latitude of 0°; at the poles the latitude will be 
90°. Now, as the altitude of the poles is equal to the latitude of the place 
of observation, we know the one when we know the other. For the deter- 
mination of the altitude of the pole, a knowledge of the mutual situation of 
the zenith and pole, with reference to the horizon and equator, is necessary, 
and this can only be obtained by measurement of the altitudes of certain 
stars. In practice, therefore, the determination of the altitudes of the pole 
will depend upon the accuracy with which this measurement can be 
effected. Various methods have been devised to meet the wants of obser- 
vation, as also the uncertainties which result from the declination of the 
star employed, its parallax, and refraction, so that the following eight 
methods of determining polar altitudes have been suggested and followed. 
1, By the meridian altitude of the star; 2, by circummeridian altitudes ; 
3, by two culmination altitudes at the superior and inferior transits across 
the meridian; 4, by two meridian altitudes in the southern and northern 
parts of the meridian; 5, by the altitude of the polar star; 6, by equal 
altitudes of the circumpolar stars; 7, by altitudes of two stars and the 
observed interval of time; 8, by the observation of a star in its passage 
through the eastern and western part of the prime vertical. 
The geographical longitude of a place is the arc of the equator inter- 
cepted between the circle of latitude of the place, and the circle of latitude 
of another place, assumed as a fixed point of reference. The latter circle 
of latitude is then called the first meridian, and the former the meridian of 
the place whose longitude is to be determined. Since nature indicates no 
definite line or circle of departure for the determination of longitude, as she 
has done in the equator for the determination of latitude, it is evident that 
the position of the prime vertical, and consequently the amount of the lon- 
gitude, must be entirely arbitrary. This uncertainty has had for its conse- 
quence, the assumption of various standards, inconvenient in practice, and 
very often producing mischievous effects upon the interests of navigation, 
which, although now palliated, have not been entirely removed. The 
difference in the estimate of longitude has, however, been hitherto still 
greater among astronomers than among navigators, although a difference 
in estimating the longitude among the former, where calculation is appealed 
to for assistance, is much less troublesome than among the latter. Almost 
every astronomer counted the geographical longitude from his own observa 
tory. The meridian of Paris has, however, more recently been selected by 
the astronomers of the continent of Europe, to which almost all observations 
and geographical longitudes are referred. It is generally customary in astro. 
nomy, at the present time, to regard only the meridian difference of two places 
of observation, or the angle which the meridian or noon circles of the two 
places bear to each other, at the pole lying nearest tothém. This angle is, of 
course, measured by the arc of the equator lying between the two meridian 
circles. This difference of geographical longitude is often called the 
87 
