Page 671 the smooth sheej? 7325 



to ab through the points m2, nu, nii, and 7^3, respectively, and the distances mx, tnxi, 111x2, mxz, mxi, 

 and mx;, are laid off along these construction lines from the central meridian. It is especially impor- 

 tant that these distances be laid off from the central parallel and the central meridian. The succes- 

 sive points TOi, mz, etc., and x, Xi, X2, etc., must never be laid off from one another. 



The projection tables are novs^ entered and "Y" values under the table headed "Coordinates of 

 curvature" are found corresponding to the respective x-points. These values are laid off parallel 

 to the central meridian, north of the construction lines if the projection is north of the Equator. These 

 are usually short distances and difficult to plot. Best results can be attained by plotting an arbitrary 

 distance, such as 100 or 200 meters on a 1:20,000 scale, south of the 3;-points and then plotting the 

 arbitrary distance plus the "Y" values north from the arbitrary points. 



"Y" values for latitudes intermediate between those given in the tables can be obtained by linear 

 interpolation, but for longitudes intermediate between the tabular values, the following relationship 

 should be used: 



The ratio of any two successive ordinates of curvature expressed in meters, equals tlie ratio of the squares of the corresponding 

 abscissas expressed in minutes or degrees. 



This approximation is close enough under most conditions. 



f]ach of the points plotted north of its respective a:-point represents the intersection of a meridian 

 and a parallel. Curved lines drawn through these points represent the meridians and parallels. 

 Because it is difficult, in practice, to draw a curve of very large radius, the intersection points must 

 be frequent enough so that the curved meridians and parallels can be drawn as a series of chords which 

 will approximate the true curves. The projection must be left in pencil until verified and the control 

 has been plotted. Finally the projection should be checked by measuring the intercepted distances 

 between the adjacent meridians and parallels. 



On projections of scales 1:10,000 or larger, it is generally sufficient to apply the F-coordinates at 

 the extreme meridians only, joihing these points and the corresponding points on the central meridian 

 with straight lines. The parallels so drawn are then subdivided equally for determining the inter- 

 mediate meridians. 



The construction of a polyconic projection is fully explained in Special Publication 

 No. 5, "The Polyconic Projection Tables/' and on pages 60-62 of Special Publication 

 No. 68, Elements of Map Projection. The latter publication also gives the formula 

 from which the errors of scale and area of any polyconic projection may be determined. 



7325. Continuous Construction 



The construction of a projection must be continuous, that is, it must not be begun 

 and then laid aside to be resumed at a later date. It should be completed and checked 

 on the same day, if possible. Construction on days of excessive humidity or excessive 

 drjmess should be avoided. When possible the projection should be made at a time of 

 day and during a period of weather when the atmospheric conditions are stable and 

 nearly average for the conditions under which the smooth sheet is to be used. It is 

 important during construction that the projection be not exposed to the direct rays of 

 the sun. 



7326. Verification of the Projection 



All details of the construction of the projection must be checked. This must be 

 done while the projection is still in pencil, and must consist of a verification of the values 

 taken from the polyconic projection tables and a complete check by measurement of the 

 construction of the projection. Finally, corresponding diagonal distances should be 

 compared with one another. It is to be noted that the polyconic projection is symmet- 

 rical with respect to the central meridian. Therefore, the diagonal distance between 

 any two intersections on one side of the central meridian is equal to the diagonal dis- 

 tance between two corresponding intersections on the opposite side of the central me- 

 ridian. A good construction check is a comparison of the long diagonal distance from 



