A displacement of
in parametric latitude
along the meridional ellipse is illustrated in Figure 2.
The poleward displacement is
and the equatorial component is
From this we see that the geodetic and parametric latitudes are
related by

is the radius of curvature of the meridional arc at . The
radius of curvature in the perpendicular plane (i.e. in the plane of the
parallel), is given by

In Figure 3 we illustrate the result of a displacement of
in parametric
latitude
and of in
longitude, resulting in a Northerly displacement of
and an Easterly displacement of
, respectively.
By Pythagoras' theorem the displacement distance is
given by:

The true course is given by:

where we have again used Eqn. (2) to transform between reduced and geodetic latitude coordinates. Equations (5), (6) and (7) are the fundamental relations relating distances and directions on the spheroid at a point.

2002-03-21