MANIPULATION OF THE TELESCOPIC ALIDADE 
119 
But 
GE = 100 CD = 100 AB cos m; 
therefore^ by substitution, 
GF = 100 AB cos2 m, 
by means of which the horizontal distance may be computed 
from the rod intercept and the angle of inclination. 
The correction to be applied to the observed distance on 
inclined sights may be determined without reference to tables or 
formulae by means of the Beaman stadia arc (see fig. 11) an 
attachment for the mechanical solution of the stadia problem, 
which will be described in greater detail in a subsequent para- 
graph. The arc carries two scales, a multiple scale and a reduc- 
tion scale, having coincident zero points marked 50 and 0, re- 
spectively. The reduction scale is, of the two, the more distant 
from the adjustable index and gives percentages of correction 
that may be used to reduce observed stadia distances to hori- 
zontal. The adjustable index should be set opposite the zero 
of the reduction scale when the telescope is level. To get the 
necessary correction, simply read the same scale with the line 
of sight cutting the distant station. Reading to the nearest per 
cent is usually sufficient. For example: the reduction scale 
reads 3 with an observed rod intercept of 16.2; then 3 per cent 
of 1620 = 48.6; 1620 — 48.6 = 1571.4 = corrected horizontal 
distance. 
Location of stations. The distance thus determined by stadia 
is scaled off on the line ruled in the direction of the rod station 
from the point representing the occupied station. The proper 
method is to place the fractional scale division on the plotted 
point and prick the new location with the needle, or mark it 
with a well sharpened pencil, at the even division at the end of 
the scale. This operation should be performed with the greatest 
care and preferably with the assistance of a pocket magnifier; 
more closure errors are to be attributed to careless plotting than 
to any other cause. If a needle is used, do not try to puncture a 
hole clear through the paper; push the needle point just far 
