MANIPULATION OF THE TELESCOPIC ALIDADE 
115 
the difference of the two Stebinger readings; turn an equal 
number of divisions in the direction which brings the middle 
hair down onto the rod; observe the number, of feet between 
the top of the rod and the intersection of the middle hair. Add 
this to the length of the rod which was above the bottom hair at 
the first reading; the sum multiplied by 200 is the horizontal 
distance. For example:^ 12 feet of the rod are entirely visible 
and the middle hair is well above the rod when the bottom hair 
rests 12 feet below its top. In that position the Stebinger drum 
reads 24. Turn down until middle hair touches the top of the 
rod; Stebinger reading is now 60. The difference between the 
two readings is 36. Turn down 36 divisions more, to 96. The 
middle hair now intersects the rod 3.4 feet below its top. The 
horizontal distance is 200 X (12 + 3.4) or 3080 feet. 
4. If instrument is equipped as in 3 and there is at hand a 
table, previously prepared for this particular instrument, show- 
ing Stebinger factors,^® i.e., the differences in elevation at the 
unit distance of 100 feet corresponding to the vertical swing of 
the telescope denoted in divisions of the Stebinger drum, pro- 
ceed as follows: Place one hair on the top of the rod; read and 
record Stebinger. Turn down until that hair cuts the lowest 
visible primary division of the rod; read and record Stebinger. 
Take the difference of the two readings. Repeat for each of the 
other two hairs. The three results should check. Select from 
the table the Stebinger factor corresponding to that number of 
divisions. Note the number of feet passed over on the rod; 
multiply it by 100 and divide by the factor. The result is the 
horizontal distance. For example: 13 -feet of the rod are visible. 
With the middle hair resting on the top of the rod, the Stebinger 
reading is 62. When the middle hair is turned down to the 
primary division 13 feet lower, the reading is 106. Difference of 
the two readings is 44; corresponding factor is 0.4111; horizontal 
distance is 1300 0.4111 = 3160 feet. 
^ This, and the following examples apply only to those instruments in which a 
clock-wise rotation of the Stebinger drum depresses the objective end of the 
telescope. 
The preparation of such a table and the mathematical principles on which 
it is based are discussed in subsequent pages of this paper. 
