328 Notes on Map Projections. 
tion passes through the centre perpendicular to the central ray. 
This projection obviates the orthographic contraction or crowd- 
ing and the stereographic exaggeration in the outer rim of a pro- 
jected hemisphere. 
In the stereographic projection, the eye is taken on the surface 
of the earth at the pole of the great circle used as a plane of pro- 
jection. Circles are stereographically projected into circles. An 
increasing exaggeration of parts from the centre outwards is its 
great defect. 
In the gnomonic or central projection, the projection is on 4 
tangent plane—the eye is taken at the centre of the sphere. 
Great circles are gnomonically projected into straight lines, and 
‘all small circles into curves of the second order or conic sections. 
The entire hemisphere cannot thus be projected, and the portions 
become rapidly exaggerated in receding from the tangent points. 
CLASS I. 
Instead of projecting directly on planes, an intermediate cyl- 
inder or cone is employed in this class to receive the projection, 
which is then developed or rolled out on a tangent plane. € 
parallels and meridians on a cylinder tangent around the equator. 
On development, the parallels and meridians are found projected 
into perpendicular straight lines. 
A secant cylinder may be so determined that the entire area of 
the spherical zone projected shall be exactly equivalent to 118 pro- 
jection. These methods are limited in their advantageous 4p 
plication to a moderate equatorial belt. 
In projecting perspectively on a tangent cone for development, 
the eye is assumed at the earth’s centre, and the cone js taken 
tangent around the middle parallel of the zone to be projecte®. 
On developing this cone, the meridians appear as straight lines 
tric around this point, the middle parallel being in its true length. 
. ‘ ‘ rallels of 
tion of the extreme belts. This method of Ptolemy was rev!¥" 
by Mercator, and was used by De L’Isle in his map © d 
Murdoch proposed to make the area of the conic frustum me 
equal to that of the projected spherical zone—a good condition; 
though inconvenient in construction. De L’Isle proposed t a 
acone, through the limiting parallels. Euler proposed ant ee 
