plane, therefore, is passed through the normal of the curved surface. Hence we have for the radius of curvature the simple formula
Since an infinite number of planes may be passed through this normal, it follows that there may be infinitely many different values of the radius of curvature. In this case are regarded as constant, as variable. In order to make the latter depend upon a single variable, we take two fixed points apart on the great circle whose pole is Let their coordinates referred to the centre of the sphere be We have then
If we set
then we have
and the formula becomes
and likewise
Therefore, if we set
we shall have
If we put