3742 



HYDROGRAPHIC MANUAL 



Page 292 



When this method is used, the preliminary construction on the layout sheet is accomplished as 

 before (see 3741a), except that enough arcs should be drawn to permit an accurate graphic interpola- 

 tion for intermediate arcs as explained below. The computation, however, is greatly simplified. 

 The computation required in 37416 (steps (2), (3), and (4)) can be omitted in this method since the 

 geographic position of a point C (fig. 65) on a locus of an angle a can be computed from the triangle 

 CMP, the angle MPC being scaled from the layout sheet. 



In figure 65, A and C are two points on the locus of angle a and near the margins of the survey 

 sheet. (These correspond to the selected points A and C in fig. 63.) The angle a is the observed angle 



BOAT SHEET 1:20.000 



Figure 65.— Drawing the arcs with the 

 use of a protractor. 



M Approximate Scale 1:400,000 



Figure 66.— Layout sheet for auxiliary 

 straight-line method. 



between the two triangulation stations M and P, and the angles x and x' are from the scaled azimuths 

 from the layout sheet. The geographic positions of A and C are computed by the method noted 

 above and the points are plotted on the survey sheet. 



The angle at B equals 180° — ix—x') and this holds true for any point along the arc AC. There- 

 fore, this angle is set on a metal protractor, using the movable arm that can be closed to a zero reading. 

 Two pins are firmly set at the plotted positions A and C. A pencil is centered in the protractor and 

 the arc is drawn by moving the protractor along, with the arms sliding against the pins. The portion 

 of the arc that falls beyond points A and C is plotted with the angle x- x' set on the protractca-. 



If the distance between A and C is too long to permit sliding the protractor very far from the 

 center of the sheet, then use is made of the geographic position of point B (see 37416(5)) for pivoting 

 the protractor arm. In such case, however, the angle set on the protractor is 180° minus the difference 

 in azimuths between the line to B and the line to A or C depending on which part of the arc is being 

 drawn. 



The same procedure is followed to lay off the other arcs on which points have been computed. 

 Intermediate arcs can be laid out in a similar manner by constructing graphs of the rate of change of 

 the angle a between each of the computed arcs and plotting scaled locations of intermediate positions 

 corresponding to A, B, and C. Graphs for the rate of change of the protractor angle are also needed 

 for use in determining the protractor setting for the intermediate arcs. 



3742. Auxiliary Straight-Line Method 



In this method use is made of two auxiliary straight Hnes graduated on the principle 

 of the graduated perpendicular and furnishing points through which the arcs may be 



