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Fig. 5.18 Reciprocal
normal section
normal sections. It can be seen that the reciprocal normal sections occur just
because the normals at points A and B are not in the same plane.
Note that for the two points A and B on the surface of the ellipsoid with different
longitudes and latitudes, the normal AK
a
at the point A will not lie in the same plane
as the normal BK
b
at the point B.
As we know, if the normals AK
a
and BK
b
lie in the same plane, the two straight
lines are either parallel to or intersecting each other. As shown in Fig.
5.18
, A and
B are not on the same meridian and thus have different longitudes. Generally, the
angles that the normals make with the minor axis vary, so the two normals are not
parallel to each other. Because the minor axis is the line of intersection of two
meridian planes, if the normals on the two meridian planes intersect each other, the
point of intersection will be at the minor axis.
Let the latitudes of the two points be B
1
and B
2
; then the normals AK
a
and BK
b
intersect the equatorial plane at point Q
1
and Q
2
, and from the Fig.
5.18
one obtains:
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