Himataya Mountains. 527 
the logarithm of the distance in feet; and for tangents itis to be added. By 
means of this table, the. caiculation of small spherical. triangles become 
as easy as plane ones, and this without any reference to the sperical excess, 
whicli is sometimes :troublesome. 
6. Tris now to be eonsidered what effect the figure of the earth will 
have on tlie determination of differences of latitude, lone and Azi-. 
muth. In the first place it ig very evident that the distance of ; aity point, 
from the meridian and perpendicular of. another, may be found without 
sensible ertor by considering the earth as a sphere (Art. 4). This then 
gives the latitude, of one end, of the perpendicular to the meridian; to 
find that of the other with the difference of longitude, and Asimuth i is 
| the second step. 
Let PC vepresent part: of Ahe-elliptic 
meridian, P being’ the pole and € thes centre 
of the earth... Let.4 B be the given. distance 
- from the. meridian being at right angles to P 
_ Bo. Tis required from. the latitude of: the 
| | . point..B, and the distance A B to determine 
first, the latitude of A: secondly, the difference of longitude or angle at P, 
and thirdly, the Azimuth of B from A. , 
Ar the point B draw the radius of curvature B E,* intersecting the 
z : wee 
ONS had 1 kus 
* If we-suppose the earth to-be-cut-at-any point by a plane perpendicular to the meridian, in 
that point the centre of curvature of this section, at the point. where it cuts the meridian, is. the 
point in which the direction of gravity or of the plumb line intersects the axis of the earths 
Prayrair’s Outlines of Natural Phil. p. 55. § 62. vol, 2d. 
VOL. XIV. 4O 
