204: PROCEEDINGS OF SECTION A. 
Having given the co-ordinates « and y of a point A, the 
distance AB being equal to s, and the angle which AB makes 
with the meridian of reference being represented by a, the co- 
ordinates x, and y, of the point B, and also the back bearing a! 
from B to A, are found by the formulee— 
m y mn 
q =YyYtn— 7 r 
nn J 2 r* 6 r 
Presid Se a Ue i! 
9 6 r 
m 2 mn 
= + 180° — : 
— r* sin | 3r* sin 1 
in which r is the mean radius of the earth at latitude of point 
midway between A and B (that is, square root of product of radii 
of curvature of meridian and perpendicular to the meridian), 
m= ssinaandn = s cosa. 
ALTITUDES OF STATIONS. 
The heights of the various stations of the survey are determined 
from observations of the zenith distances of the surrounding 
points, made at each station visited by the observing surveyor. 
The simultaneous observation at each end of the line involved, 
which is necessary to an ideal determination of relative heights 
(for by that means only is it made certain that the co-efficients of 
refraction at the two ends of the line are the same) has, of course, 
been impracticable. The work, however, is performed always at 
the same time of the day, so as to secure, as far as possible, the 
same atmospheric conditions in the reciprocalfobservations. The 
actual field work consists in the measurement, with a theodolite 
having a 10-inch circle, of the elevations of all the stations in the 
surround, noting, at the time of sighting to each, the reading of a 
level the axis of which is in the direction of the line being sighted, 
any variations of the level being subsequently applied to the 
circle reading. The instrument is then reversed and a similar 
round taken, each such pair of rounds constituting a set from 
which the differences of height may be derived. The question 
may arise whether the number of sets taken has not of recent 
years been too much limited to give a reasonable assurance that 
the mean result will represent anything corresponding to a mean 
condition of the air, and though the resulting heights prove fairly 
accurate yet improvement may be expected to follow an increase 
