188 Trans. Acad. Sci. of St. Louis. 
The equation of a section of a cone of revolution, referred 
to its vertex and in terms of the angle at the vertex of the 
cone and the constants which define the position of the plane 
of the section, may be written 
— 
sin @ sin (€+2a) {+ 2¢ sina cosa 
er sin (0-+2a) wat b (4) 
cos’a. 
in which the same notation for angles is used as in (1) and 
¢ = the distance from the vertex of the cone to 
the nearest point of the section. 
In both these equations, (3) and (4), the upper signs are 
to be taken for the case of the elliptic section, and the lower 
signs for the case of the hyperbolic section. 
From the symmetry of equations (3) and (4) 
2csinacosa 
a gine + 4a) (>) 
and 
6, sin@ sin(@ + 2 a) 
eee = cos? a (6) 
Multiplying (5) by (6) 
26? ; 
— = 2csin # tana 
a 
or, by (2), 
252 
27 = 2" = 2c sin é tan u. (7) 
The perpendicular from the vertex of the cone to the plane 
of the section (= %) is evidently c sin 8; whence from (7) 
k (8) 
ro 
