MANIPULATION OF THE TELESCOPIC ALIDADE 
129 
tiples for obtaining differences in elevation. The zero point of 
this scale is marked 50 and its divisions are so spaced as to be 
proportional to one-half the sine of twice the angle through 
which the telescope moves. 
To determine differences in elevation read the distance subtended 
on rod and express in feet (for example, 8.7 = 870 feet). Clamp 
telescope and level. Set index exactly at 50, by means of the tangent 
screw back of arc, and do not touch this tangent screw again. 
Then, by means of the customary clamp and tangent movement, 
raise or lower telescope until there is brought exactly opposite the 
index such a graduation on the multiple scale as will throw the middle 
stadia wire somewhere on the rod, it does not matter where. The arc 
reading, minus 50, multiplied by the observed stadia distance gives 
the difference in elevation between the instrument and a known point 
on the rod — that is, the height on rod indicated by middle wire. Set- 
tings of both index and arc should be made carefully under reading 
glass. 
Example: Suppose observed stadia distance is 6.3 (630 feet) and that 
telescope is so inclined that multiple scale reads 58, at which exact 
setting the middle wire on rod reads 7.2 (7.2 feet above base of rod) 
then multiple is 58 — 50 = -h 8, and computation for a fore sight 
would be ‘ 
6.3 
X8 
+50.4 
-7.2 
+43.2 feet = base of rod aboye H. I. 
If middle wire were set on H. I. or top or other fixed point on rod 
and the arc were read by estimation (for example, 54.2) to obtain a 
multiple, the result would be approximate only; therefore this method 
is not to be used with this attachment. 
If the half-wire interval is read and this reading is then doubled to 
get the stadia distance, it occasionally happens that no even multiple 
arc setting which will throw middle wire on rod can be found. In this 
case make arc setting that will throw the lower wire anywhere on rod ; 
the middle wire will then be somewhere above the top of the rod. 
Then take multiple as read on arc, but compute position of middle 
