41 
SECTION VI. 
65. The stereographic construction of maps on the plane 
of the horizon of any place. Fig. 29. 
Fig. 29. 
Principle.—We are enabled by the oblique position of 
the sphere to represent the entire surface of the earth above 
the rational horizon, and to compare it with the surround 
ing regions below the horizon. For in all horizontal pro 
jections, the place one is in is considered as the centre of 
the map, the rational horizon being its extremity. The 
eye is supposed to be placed in the nadir, or point diamet 
rically opposite to the zenith of the place in the centre; 
and the plane of projection will be coincident with the 
plane of the horizon. Thus, suppose we were required to 
make a projection of this kind on the horizon of London, 
that city would be in the zenith, and our eye would be in 
the nadir; hence all rays of light falling from the globular 
surface upon the eye in the nadir, would pass through the 
horizon; and those portions of the earth’s surface about 
the place on which the projection is made will be con 
tracted, whilst those towards the plain of projection will be 
enlarged. 
In the diagram, Figure 28, the pole is projected within 
the primitive circle, or plane of projection; and its distance 
OP, from the centro 0, is equal to the tangent of half the 
complement of latitude. The method of drawing the meri 
dians and parallels of latitude will be found in the two fol 
lowing problems:—