52 Trans. Acad. Sci. of St. Louis. 
With any point, C, on the axis of the cone, as a center, 
inscribe a sphere, radius CD; its intersection with the plane 
of the paper will be a circle asin the figure. From the center 
C draw a perpendicular to the plane of the section, which in 
the figure is the line Co, drawn perpendicular to Z,Z,. This 
line cuts the circle in two points, 0,ando,. The lines So, aud 
So,, joining these points, respectively, with the vertex, cut the 
plane of the section Z,Z, in the points F, and F,, respectively, 
which are the foci of the section. 
For, from the figure, 
Co, = CD = the radius = r= SC sin « 
and 
< Ook, =f 
0,4,=r cos 8 = SC sin a cos 8 
Ck, =r sin 2=8C sin a sin f = Ck, 
Sk, =SC+ Ck,=8C + 8C sin a sin 8 
=8C (1+ sin a sin B) 
Sk, = SC — Ck, = SO — SC sina sin 8 
= $C (1—sin a sin f) 
wherefore 
=e = = 50 (ein ea B) 
sin a cos 2 
~ 1+ sin a sin 2 
Oe, See 
— Shy <<. ee) 
= __sin a cos 2 
Tan asin 2 
