n^2
-------
a + n
(n - ------- ) sin d.
2
k = a + ----------------------
R
The computation will be shorter, however, if we merely reduce the
inclination to the sine of the distance from the node for the first
correction of the arc AR, if we neglect the semi-monthly motion of the
axis; for this last correction diminishes the plus corrections, and the
first one increases it. If, therefore, one is neglected, it is better to
neglect the other also; especially as it might be deemed affectation to
notice trifling inequalities in the present state of the elements of the
question.
There is one inequality, however, which it will not do to neglect. This
arises from the displacement of the axis of the vortex.