72 



A MANUAL OF TOPOGRAPHIC METHODS. 



For a full discussion of the Method of Least Squares and its application 

 to triangulation see "A Treatise on the Adjustment of Observations, by T. 

 W. Wright, B. A.," pp. 250-370. New York. D. Van Nostrand. 1884. 



COMPUTATION OF DISTANCES. 



In each triangle, starting with the base line, there is known at least 

 one side and the three angles. The remaining sides are computed by the 

 well-known proportion of sides to sines of opposite angles, or expressed 



mathematically, a z= — '-. — tj-. In this computation distances should be 



used in meters, and seven place logarithms should be employed. 



The following is an example of the correction of the angles and the 

 computation of the sides of triangles taken from the work in Kansas: 



Log <list. Newt- Walton 3.5771611 



Log sin Newt - - 9.9535952 



a. c. log sin Township corner 0.2257704 



Log dist. Township corner— Walton 3.7565267 



Logdist. Newt- Walton .(..".771011 



Log will Walton 9.9927124 



a. 0. log sin township corner 0.2257704 



Log dist. Township corner— Newt 3.7956439 



COMPUTATION OF GEODETIC COORDINATES. 



The next step is the computation of the latitude and longitude of the 

 stations and the azimuth or direction of the lines connecting them. Initially, 

 the latitude and longitude of some point is determined by astronomical 

 observations, and this point is connected with the triangulation. The 

 azimuth, or angle with a south line, of a line connecting this point with some 

 station in the triangulation is also determined by astronomical observations. 

 These, Avith the observed angles and the computed distances between the 

 stations, form the data from which the latitudes and longitudes of the sta- 

 tions and the azimuths of the lines connecting them are computed. The 



