THEORY or POLYCONIC PROJECTIONS. 171 



The projection was constructed by Mr. Chas. H. Deetz, 

 cartographer of the United States Coast and Geodetic Sur- 

 vey, with the central great circle approximately the one 

 joining San Francisco and Manila. Another projection of 

 this kind was constructed by Mr. A. Lindenkohi, cartog- 

 rapher in the United States Coast and Geodetic Survey, 

 consisting of a map of the United States based on the 

 great circle intersecting the 95° meridian at 39° of latitude. 

 In this projection ^3 = 39° arid X is reckoned from the 95° 

 meridian. 



The meridian that corresponds to the Equator in the 

 projection as first constructed is an axis of symmetry for 

 the map, so that the coordinates of the intersections need 

 to be computed only for one-half of the map if the Equator 

 of the original projection corresponds to one of the meri- 

 dians that appear on the map, so that for each value of 

 + X we may have another intersection for —X, with the 

 latitude the same in both cases. In the one constructed 

 by Mr. Lindenkohl for the United States the meridians 

 were constructed for every 5° of longitude, so that the 

 meridian of 95° appeared upon the projection. If 94° had 

 been chosen in place of 95°, we should have had a meridian 

 to compute for a X of 4° E. and one for a X of 6° W., and 

 so on for the others. 



In the construction of the projection of which the fold- 

 ing plate is a copy the central great circle is the one that 

 is tangent to the parallel of 45° of latitude at the point of 

 its intersection with the 160° meridian west of Greenwich. 

 Mr. Deetz (in the construction of his projection) computed 

 the intersections of his original projection after it was 

 turned into the new position in terms of latitude and 

 longitude and then interpolated the even values of iater- 

 sections on this projection. From the original three equar- 

 tions we obtain 



tan X = sec (jS + r;) tan ^ 



sin ^ = sin (18+77) cos \p. 



In the case under consideration i8 = 45° and jS + r? is the 

 latitude of the intersection of any given great circle with 

 the 160° meridian. jS + t? is, therefore, constant for any 

 ^ven great circle. The amount of computation required 

 is about the same for either method of procedure. 



