7372 



HYDROGRAPHIC MANUAL 



Page 682 



Determining east-west distortion. — If the east-west distortion of the sheet is not 

 available from the disposition of the triangulation stations on the sheet, it can be 

 determined in the following manner: 



(1) Compute the longitude crossings of the Hnes CB and CA (fig. 150) on the central parallel or 

 any other parallel that will give a distance long enough to determine a good distortion factor. 



This is accomplished on Form 27 in a manner similar to that described in (2) above for determining the latitude intersection. With 

 the azimuth of the line CB as previously determined and the known latitude increment or decrement (A0) , a value for (s) is found 

 by trial and error that will make the sum of the latitude terms in the computation formula equal to (A0). From this value of (s) 

 the required longitude (X') is computed. 



A close first approximation for the distance («) can be obtained by making A<t> equal to the 1st term in the latitude formula (neg- 

 lecting the 2nd term) and with the (s) value thus found, the 2nd term is computed. A new value for the 1st term is then found that 

 will make the sum of the two terms equal to A0. The resulting value of («) is then used in the longitude formula to obtain (X'). 



Because of the distances usually involved, it will seldom be necessary to carry the computation beyond the 2nd term in the lati- 

 tude formula. 



(2) Plot the computed distances Cf and Cg (corrected for distortion) along lines CB and CA 

 and at points / and g draw short lines parallel to the central meridian. Lay off to the south (in north 

 latitude) on these lines the F-coordinates from the polyconic projection tables for the appropriate 

 longitude distance and obtain points /' and g'. The scaled distance between these points compared 



with the tabular distance as determined from their A'-co- 

 ordinates will give the distortion factor in an east-west 

 direction (see 7361). 



If a linear interpolation of the A'-coordinate values given in the table is not 

 close enough for any latitude <i> and difference of longitude AX, then the interpo- 

 lation should be made by second differences or the values computed from the 

 formula: 



6,378,206 



AC 



BA 



AA 



X (in meters) = 



(1-0.00676866 sin2 0)'/2 



cot sin (AX sin <t>) 



AD 



The error due to neglecting second differences is no greater than one-eighth their 

 value. 



Wherever possible, advantage should be taken of the 

 location of some of the triangulation stations to reduce the 

 amount of computation for determining the east-west dis- 

 tortion. For example, in figure 150, the parallel through 

 station A can be used instead of the parallel through g, there- 

 by making it ununeessary to compute the longitude of A. 



7372. On Large-Scale Surveys 



For small areas such as those covered by the 

 large-scale topographic and hydrographic surveys of 

 Figure i5i.-construction of a polyconic projec- the Biircau, the polyconic projection is practically 

 tion on a completed survey sheet-for large- identical witli the rectangular projection or a modifi- 

 scae surveys. cation thereof (projection with converging merid- 



ians); therefore in reconstructing a projection on surveys of scale 1 : 10,000 or 

 larger, the following graphic method can be substituted for the more rigid method 

 described above. 



(1) After the distortion of the sheet has been determined, from comparisons between scaled and 

 computed distances, select two triangulation stations, A and B (fig. 151), near the north and south 

 extremities of the sheet and as close to the center of the sheet as possible. From the "Arcs of the 

 parallel" in the polyconic projection tables, o^btain the distance from each station to the central 

 meridian and with these distances (corrected for distortion, see 7361) as radii and the stations as 

 centers swing arcs. Draw a line tangent to these arcs for the entire length of the sheet. This line 

 is the central meridian of the projection. 



(2) Select two other triangulation stations C and D near the east and west extremities of the 

 sheet and as close to the central parallel as possible. From the "Meridional arcs" in the polyconic 

 projection tables obtain the distance in meters from each station to the central parallel. To these 

 distances add or subtract the F-coordinates from the tables corresponding to the difference in longi- 



