REDUCTION OF TEIANGULATION. 



65 



REDUCTION OF PRIMARY TRIANGULATION. 

 REDUCTION TO CENTER. 



In case any station was occupied off center, the directions as read must 

 first be reduced to center. In the diagram, let x be the 



E 



point occupied; y, the station, r the distance between them, A the point to 



which the direction is laid and the angle at that point, and R its distance, 



approximately known. Then, from the relations between the sides and the 



angles of the triangle, 



R : r : : sin x : sin A 



. . r sin x j A /. i N r sin x 



sinArz — ,=;— and A zz(in seconds) 



R — v y Rsinl" 



correction in seconds of arc. 

 The following example taken from the triangulation in Kansas will 

 serve to illustrate the form of effecting this reduction. The references are 

 to the diagram on page 67. 



Reduction to center of station ut Walton^. 

 [See explanation: Appendix No. 9, page Hi7. IT. S. Coast and Geodetic Survey report for 1882.] 



distance, inst. to center log meters — 9. 1652 Log r. 



Correction to angle a 



n too —0.31 +2.39= +2.08 

 I, a to /■ " 39 -1-7.71 = +5.32 

 r, = n to,, —0.31 7.71 = 4 7.40 

 e - V to </ —7. 71 —0. 46 8. 17 



d =. <i to r +0. 46 —3. 00 --- —2. 60 

 e = r to » +3. 06 —4. 36 = —1. 30 

 ft = a to .1 +0. 40 —4. 30 3 90 



f=> to n +4. 36 +0. 31 = +4. 07 



The angles are measured on a spherical surface and the sum of the 

 three measured angles of each triangle should equal ISO plus the spher- 



mon xxu- 



