Page:Proceedings of the Royal Society of London Vol 4.djvu/414

Rh point of rational section as in the plane ellipse, shows that the tan- gent arc is at this point a minimum, and developes some other cu- rious analogies. It is a simple consequence of his formula that the spherical elliptic quadrant may be divided into two arcs whose dif- ference shall be represented by an arc of a great circle. This theorem, previously obtained by M. Catalan, is analogous to that of Fagnani, which shows that the difference of two plane elliptic arcs may be represented by a straight line.

The author concludes by reducing the quadrature of the surface of a cone of the second degree, bounded by a plane perpendicular to the axis, to the determination of a complete elliptic function of the second order.

The Society then adjourned over the Whitsun Recess, to meet again on the 26th instant.