Notes on Map Projections. 331 
projecting lines. Hence resulted a very distorted picture, but one 
in which each quadrilateral contains an area equal to and corres- 
ponding with its spherical correlative—a direct result of the rela- 
tion between the sphere and circumscribing cylinder. This was 
the sole recommendation of the method. 
De Lorgna’s projection is chiefly employed as a polar projec- 
tion of a hemisphere, for which use it is well adapted. A circle 
is determined equivalent in area to the hemisphere to be projected. 
Radii drawn to the graduations of its circumference represent 
meridians. A radius, graduated into ninety equal parts, is some- 
times used as the latitude scale; but the chords of the polar dis- 
tance of the parallels should be always employed. Hence results 
equality of areas between the projected and resultant quadrilate- 
rals in general. Outlines are traced by latitudes and longitudes, 
as usual. For projecting a polar hemisphere, this method is most 
excellent, as rectangular intersection is combined with conserva- 
tion both of figure and area. _ 
Ptolemy's modified conic projection is made by using the con- 
centric parallels of the pure conic development, and tracing curved 
or elliptical meridians across these in place of radial lines. By 
turning the convexities of these curves from the central line, and 
by skillful choice of curves, much of the distortion due to the 
extension of extreme parallels in development is obviated. This 
projection has been much used for maps of Asia, Africa, and 
putes his distance run, this variable scale is not by any means so 
Serious a defect as to offset the invaluable facility with which 
