114 THe geOgRaPHiC anD
CaRTOgRaPHiC FRaMeWORK
stereographic Projection
If the light source is assumed to be at the opposite point on the globe from the tan-
gent plane, the stereographic projection is created. Here it is possible to show a little
more than one hemisphere, but less than the entire sphere. Normally, however, only a
hemisphere
is shown; to represent the entire earth a pair of hemispheres is used.
In Figure 6.26, it can be seen that the parallels and
meridians cross at right
angles and that the spacing of the parallels in pole-centered
cases become greater
as one approaches the equator. As one goes outward from the center of the projec-
tion, east–west stretching is introduced. On the stereographic projection, the spacing
of the parallels increases in the same proportion as the spreading of the meridians.
Thus, this is a conformal azimuthal projection.
On the stereographic projection, circles on the globe appear as either circles or
arcs of circles unless a great circle arc passes through the center of the projection—
these appear as straight lines.
gnomonic Projection
If a light source is imagined to
be in the center of the globe, the gnomonic (pro-
nounced
no mon
′
ic) projection is created. This appears to be the oldest projection
used, since it was known to Thales of Meletus about 600
bce
and he is usually given
credit for its development. On this projection, it is impossible to show an entire hemi-
sphere, and the distortion of shapes and areas is extreme (Figure 6.27). Despite these
disadvantages, it is a widely used projection because of one important quality: all
great circles appear as straight lines, and all straight lines on the map are great circle
arcs on the gnomonic projection. It is, therefore, of importance to navigators because
great circle routes can be easily plotted.
fIgURe 6.25.
The orthographic projection in oblique case.
The earth’s graticule and Projections 115
In
navigation, the gnomonic projection is used with the Mercator projection
to plot courses. Since the compass heading changes constantly along a great circle
course, too many corrections are required to fly or sail a true great circle course.
On a Mercator the compass heading does not change along a straight line, but this
line normally deviates significantly from a great circle route. It is possible, however,
