Page 137 control and signal building 2555 



are observed. The three angles in each successive triangle are next measured simultaneously (see 22S2) by sextant observers stationed 

 at the respective buoys in turn until a buoy is reached which may be located by a three-point fix on shore stations to tie the scheme 

 again to shore control (see J in fig. 32). The observed angles should be read to half minutes, and careful simultaneous observations 

 should result in triangle closure errors no greater than 4 minutes per triangle. 



Current observations are required at the tie-in buoys at ends of the scheme, but not at the intermediate buoys unless the current 

 is dissimilar at the three buoys of a triangle. 



The position computations for this type of scheme are made on the regular forms for the computation of geodetic positions. Buoys 

 -4 and B are computed by the three-point problem on Form 655, the resulting data being used to solve the triangles on Form 25 and 

 compute the positions on Form 27. The resulting positions are reduced to the anchor positions from the current data, and the length 

 and azimuth of the line AB are computed on Form 662, Inverse Position Computation. (See 2511.) Positions are then computed 

 for all buoys, including buoy J. Buoy J is also computed from the three-point fix and the resulting position is reduced to the anchor 

 [losition as for buoys .1 and B. 



The two positions of buoy J will rarely agree within plottable limits and it will be necessary to adjust the positions in the scheme 

 for the discrepancy. The accuracy of the method does not warrant a least-square adjustment, and a proportional adjustment through 

 the scheme is sufficient. In the scheme illustrated seven triangles were used between the starting base AB and buoy J. Accepting 

 the positions of buoys A and B as correct, one-seventh of the discrepancy at buoy Jshould be applied to buoy C, two-sevenths to buoy 

 />, three-sevenths to buoy E, etc., and the three-point fix position of buoy J should be accepted. These adjustments are made as cor- 

 rections to the latitudes and longitudes of the original computed positions, based on the differences of latitude and longitude for the 

 two positions of buoy J. 



2555. Buoy Triangiilation — Quadrilaterals 



Two lines of buoys anchored to form well-shaped quadrilaterals may be used instead 

 of the scheme of single triangles described in 2554. A scheme such as that shown in 

 figure 33 will be found useful for the survey of a wide shoal area extending offshore, 

 where a single line of buoys would not furnish adequate control. 



Approximate Scale 



,.-- ..-.yy \ \ ... 



\ yj \ r-y--" ° - 



X y- 



~^" 



Figure 33.— Buoys located by sextant triangulation (quadrilaterals). 



The necessary ol servations and position computations are similar to those described in 2554, where three-point sextant fixes are 

 measured at the initial buoys .4 and B and current observations are obtained by which the observed positions can be reduced to the 

 anchor positions. Simultaneous sextant angles are measured at the four buoys in each quadrilateral in succession, but two sets of obser- 

 vations are made in each so that the angles of each pair of triangles are measured independently. In the first set, angles are measured 

 as follows: the observers at .4 measure the angles BAD and I'.4Cand the observers at D measure the angles CD A and ADB, while 

 observers at B and Cmeasure only the sum angles DBA and ACD respectively. Following this the angle measurements are repeated, 

 but this time the observers at .4 and D measure only the sum angles and the observers at B and C measure the two separate angles at 

 each buoy station. In like manner, simultaneous angles are measured in each quadrilateral of the scheme. 



The two sets of independent observations, when obtained as described above, will furnish data permitting two independent sets of 

 position computations through the scheme, each starting from the base AB. One set of computations is made through the diagonals 

 AD, CF, EH, and GKand the other through the diagonals BC, DE, FG, and HJ. The resulting positions will differ slightly and their 

 means should be used to plot the positions on the smooth sheet. 



