Page 683 the smooth sheet 7373 



tucle between the central meridian and each station. (For north latitude, add if the station is above 

 the central parallel and subtract if below. For south latitude the reverse is true.) 



(3) With the distances thus obtained (corrected for distortion) as radii, swing arcs from stations 

 C and D in a direction toward the central parallel. Draw a line tangent to these arcs for the entire 

 width of the sheet. This line will be perpendicular to the central meridian and will be the central 

 conslrudion line of the projection. 



(4) The remainder of the projection is constructed according to the method given in Special 

 Publications No. 5 and 68 for large-scale projections. 



7373. Modified Methods 



The above two methods illustrate the general principles involved in the problem 

 of constructing a projection on a smooth sheet subsequent to its completion. It may 

 sometimes be necessary to modify the methods described because of special conditions 

 encountered. For example, where all the triangulation stations are on one side of the 

 central meridian, the rigid method is not applicable in its entirety and a combination 

 of the two methods must be used. In such cases the central meridian is determined 

 graphically and the intersection of the central parallel with a line between two of the 

 triangulation stations is computed. The F-coordinate of the intersection is plotted 

 and a perpendicular erected to the central meridian, the intersection of the two being 

 the center of the projection. 



Even in a small-scale survey, if the longitude extent is small enough, the curva- 

 ture of the parallels may be neglected and the graphic method will give the required 

 accuracy. 



There are also cases where the survey is a planetable traverse (392) or a running 

 ship purvey (3941) in which the azimuths and distances at one end are comparatively 

 accurate but which decrease progressively in accuracy toward the other end. Where 

 such a survey is plotted without a projection and selected stations are subsequently 

 located by triangulation and an attempt is made to place a projection on the sheet 

 adjusted to the triangulation stations, a single harmonious projection could not be 

 constructed. If the work is not to be replotted, then the only way to bring the entire 

 survey into harmony geographically is to place a discontinuous projection on it, each 

 portion being based on the triangulation in its vicinity. 



In adapting any of the methods to a particular problem in hand, the two considera- 

 tions to be kept in mind are the theory of the polyconic projection and the means 

 available for determining the distortion of the sheet. 



74. PLOTTING THE CONTROL 



After the projection has been made and checked, the next step in the preparation 

 of a smooth sheet is the plotting of the control (see section 21). There are two general 

 classifications of control insofar as a hydrographic survey is concerned. Fust, the 

 fixed control, also commonly loiown as shore control (see sections 22, 23, and 24) ; and 

 second, the floating control (see section 25). Before plottmg is begmi, a selection 

 should be made from the control falling within the limits of the smooth sheet and 

 only those stations plotted that were actually used to control the hydrography. The 

 boat sheet may be used as a guide (see 3245) , 



The control stations must be plotted with the utmost care and accuracy, since 

 inaccuracies in their positions may result in errors in the positions of the soundings, 

 the errors increasing with the distance from the control stations. Stations whose 

 geographic positions are known should be plotted with an accuracy that will ensure no 

 plottable error at the scale of the survey sheet. 



