* 
Engler — Foci of Sections, Cone of Revolution. 51 
Inspection of equations (1) and (2) shows that the values 
of #, and @, depend only on the values of a and 8, and that, 
for a given cone, if # is a constant, 0, and 0, are constants; 
or, the locus of the foci of similar sections consists of two 
cones of revolution whose axes coincide with the axis of the 
original cone and whose angles at the vertex are given by 
equations (1) and (2) respectively; and the locus of the foci 
x 
“1 
\ 
/ 
fo 
FIGURE 2. 
of parallel sections consists of two straight lines (SF, and SF, 
in Fig. 1) whose angles with the axis are given by equations 
(1) and (2) respectively. 7 
The following construction derived from equations (1) and 
(2) is identical for the cases of the ellipse (Fig. 2), the para- 
bola (Fig. 3), and the hyperbola (Fig. 4); and as corres- 
ponding points have the same letters in all these elfen i Renee 
Siento explens}icn applies to all three. nee 
