90 



LEVELING 



TRIGONOMETRIC LEVELING 



Trigonometric leveling is the process of determining the rela- 

 tive elevations of two points, trigonometrically; that is, by 



solving a triangle of 

 which the unknown dif- 

 ference in elevation is 

 one side, the other 

 necessary data having 

 been measured. 



Problem I.-To deter- 



180' 



4r.2 & mine the height of a ver- 

 FlG. 1 tical flagstaff. 



Let DB, Fig. 1, represent the flagstaff, the height of which 

 is to be determined. Set a transit up at A, and then find the 

 intersection of the line of sight of the telescope, when perfectly 

 horizontal, with the flagstaff at C. Let this distance be found 

 by measurement to be 180 ft. Then measure the vertical angle 

 CAB; measure also CD, the height of the instrument over D, 

 and the diameter of the flagpole at C. Let these measurements 

 be respectively, CAB = 26 10' and CD = 4.2 ft. and let the diam- 

 eter of the flagstaff at C= 1.5 ft. Then, the vertical height of 

 B over the line AC is J?^ 



- X tan 26 



m 



10' = 88.81 ft., and the 

 total height BD = 88.81 

 +4.2 = 93.01 ft. 



Problem II. To 

 determine the elevation of 

 an inaccessible point. 



Let it be required to 

 determine the elevation 

 of the inaccessible point B over A, Fig. 2, and let the point D 

 also be inaccessible. Set the transit up at any point, as A, 

 and measure the vertical angle a. Select a point C' in the 

 vertical plane ABD; move to it the instrument, and measure 

 the angle c; then measure the horizontal distance m. Also, 

 determine y, the height of A over C'; then, 



FIG. 2 



