388 



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. 



