THEORY OF POLYCONIC PROJECTIONS. 169 



along a system of small circles that would correspond to 

 the parallels of latitude in the ordinary projection. Some 

 great circle of the earth would correspond to the central 

 meridian. By this scheme a map of great extent in longi- 

 tude could be constructed without the usual trouble due 

 to the longitudinal scale error. The error in scale in this 

 case would appear along the great circles of the projection 

 that correspond to the meridians in the ordinary projection. 

 The most feasible plan for the construction of such a 

 projection would seem to be the following: Since such a 

 map would, no doubt, be planned for a large section of 

 the earth's surface, the ellipsoidal features would be neg- 

 ligible, and the ordinary tables could be employed, just as 

 if they had been computed for the sphere. With these 

 tables construct a projection in the usual way. After it 

 is constructed turn the projection so that the poles fall 



Fig. 48. — Transformation triangle for transverse poly conic projection. 



upon the Equator and then by means of the formulas for 

 the transformation of coordinates the intersections of the 

 parallels and meridians can be computed in terms of the 

 parameters that correspond to latitude and longitude on 

 the ordinary projection. After the projection has been 

 constructed and turned into the new position, the <p and X 

 values become what we shall denote by ^ and r;. The 

 values in degrees will be just the same as before, but they 

 will have the new designation. Figure 47 represents such 

 a scheme in outline. FF' is the central meridian, and 

 QQ' represents the Equator in the projection as constructed. 

 The projection is now turned and FF' becomes the chosen 

 great circle, and QQ' becomes a meridian on the map; ^ 



