Page 295 hydrography 3754 



plotted or the sheet and the various points of graduation. If the arc to be drawn is 

 within the angle made by the auxiliary line and the line between the stations, then the 

 angle to be set off on the protractor is (180° — a;). 



3754. Both Stations on the Sheet — Line of Centers on the Sheet 



This is the simplest case of all and is for the most part a graphic solution. The 

 radii of the arcs will usually be of such lengths that construction with a beam compass 

 will be feasible. 



Referring to figure 62, the distance a between the stations is determined by scaling 

 from the large-scale sheet and the midpoint D is plotted. Erect a perpendicular (Line 

 of Centers) at this point, and by means of equation (4) in 371 compute the d distances 

 along this perpendicidar for the entire range of arcs to be drawn on the sheet. ^Vliere 

 the centers for the arcs to be constructed are at a considerable distance from the mid- 

 point in relation to the distance between the stations, then the Line of Centers should 

 be determined as described in 3751. 



The centers can also be determined graphically by setting the angle a on a pro- 

 tractor and with its center on the Line of Centers and one arm in coincidence, shifting 

 it along the Line until the other arm passes thi'ough one of the control stations. Or 

 the locus of 2a can be plotted and its intersection with the Line of Centers obtained. 



The distance from each of the centers thus determined to either of the stations will 

 be the radius of the arc to be described. 



376. Various Methods of Use 



Wlien surveying an area with a circle sheet it will be of great help to run the sound- 

 ing lines parallel to one system of arcs. This is described in 3143. The ease and speed 

 with which positions can be plotted will be advantageous under many conditions. It 

 is even possible to cover a shoal thoroughly with evenly spaced lines without plotting^ 

 one position while sounding. Furthermore, it is usually possible to tell if a change 

 in course is necessary as soon as the angles are taken and before the position is plotted. 

 This method of surveying also permits the selection of stronger fixes, since stations, 

 beyond the limits of the sheet can be utilized. 



In making large-scale offshore surveys by this method, the small-scale sheet (pref- 

 erably an aluminum plate) on which all the control stations are plotted, should be 

 kept at hand, so that if one or more of the objects, for which systems of arcs have 

 been constructed, become momentarily obscured, other stations can be utilized for an 

 occasional position, which is plotted on the small-scale sheet and then transferred to 

 the circle sheet. 



The method can also be used advantageously wherever the stations are so distant 

 that they are near the ends of the protractor arms, and it is the only satisfactory way 

 to plot closely spaced lines using distant signals. Under such conditions the three- 

 arm protractor is unsatisfactory because of the errors due to the limitation of the 

 protractor and the distortion of the sheet. It is impossible to verify such a sheet, for 

 the same position will not plot in the same place after the sheet has been subjected to 

 any atmospheric changes. 



The method also has application in making enlargements of areas originally plotted 

 at a small scale where photographic enlargements are not sufficiently accurate In 

 such case a circle sheet is constructed by one of the methods described above and the 

 positions are plotted directly from the angles in the Sounding Record. 



