91 



Ing, R, of the rod A B is the difference of the tangents of the angles of elevation, 

 w and n. Also, the distance a 6 is the difference of the tangents of these angles, 

 m and n, to distance unity, as given in the trigonometrical tables. 



Whence, to find the horizontal o C = D, we have simply to divide the reading of 

 the " Stadia Hod" by the difference of the tangents of the angles of elevation. Or, by 

 formula, 



R 



D = 



Tan. n Tan. m 



If one of the angles should be a depression or , we must then divide by the sum 

 of the tangents, and the formula would be 



R 



Tan. n -f- Tan. m 



Example. If n= 12 16', nat. Tan = .217426 



"m=1010', " " = .179328 



The difference of the tangents = .038098 



Then, if R = 12.26 feet, 



12.26 



= 322 feet. 



It may happen that our transit has no vertical circle, or that we have no trigono- 

 metrical tables at hand. In either case, introduce an auxiliary rod, cb between the 

 stadia rod and the plumb-time of transit, and at some known horizontal distance, 

 preferably 100 feet, from the latter, and note the intercept o 6. 



This intercept is the analogue of the difference of tangents used in the former 

 case, and must be used in the same manner, in dividing the reading of the stadia rod, 

 when we shall have the distance, D, in terms of the distance of the auxiliary rod from 

 the transit. 



Example. Suppose the intercept a 6 on the auxiliary rod, at distance 100 feet, is 

 .845 foot, and that the reading R, of the stadia rod is 12 feet, then 



oC = D = (12 -f- .845) X 100 = 1420 feet. 



XL: the height, H, of the foot of the stadia rod, above or below the height of 

 JLUbtrument, be wanted, it may be had from the following equation : 



H 



D. Tan. m, 



a which the -j- sign must be used for angles 01 el. vasion, and the sign for those 

 oi depression. 



Or it the auxiliary rod oe used instead of tne vertical arc, note the intercept a b 

 on this rod, between the level line o C and the ^ine 01 signt to the ioot oi tbe Stadia 

 rod, and 



Multiply iJ/iis intercept by Ite ratio 3? D M o c. 



Example in -Jie last case, if oci = 1.06 '^., oc being IOC icet, and D = 142C ft., 



CA H 



a ~ 



1.06 



15.05 icet. 



