MANIPULATION OF THE TELESCOPIC ALIDADE 
125 
3. Vertical arc determinations. Other and more accurate 
methods of measuring the difference in elevation between two 
stations depend upon the determination of the vertical angle 
between the line of sight from one station to the other and the 
line of sight through the level telescope. The methods differ 
only in respect to the reading or computation of that angle; all 
are based upon the same mathematical principle. In figure 7, 
FE represents the vertical distance from the intersection of the 
middle hair on the rod, AB, to the level of the instrument at G. 
CD is drawn perpendicular to the line of sight, GE, the angle of 
inclination of which is represented by m. 
By trigonometry ' 
CD = AB cos m 
and 
FE = GE sin m. 
But 
therefore 
GE = 100 CD = 100 AB cos m; 
FE = 100 AB sin m cos m = 100 AB X J sin 2m, 
the formula upon which stadia tables are based. 
The angle of inclination of the line of sight to the target may 
be read in degrees and minutes by means of the vertical arc. 
With loosened clamp the telescope is raised or lowered until the 
middle cross-hair rests near the selected target. The clamp is 
tightened and by means of the tangent screw the middle hair is 
accurately placed on the target. The point on the vertical arc 
opposite the zero of the vernier is read to the nearest minute and 
recorded. The telescope is then leveled, first loosening the 
clamp if* desired, and the bubble in the striding level centered 
by adjustment of the tangent screw. The point on the vertical 
arc now opposite the vernier zero is read and recorded; the dif- 
ference between the two readings is the desired vertical angle. 
The graduations of the vertical arc differ on alidades of dif- 
ferent manufacture, but one of the common graduations is indi- 
cated in figure 11 by the markings on the left half of the arc. 
The main scale of the arc is divided into degrees and half degrees. 
