184 Trans. Acad. Sci. of St. Louis. 
Discussion of this equation shows that e may vary 
7 
from 0, when @+a =5 
to , when 6+a = 0 
cos @ 
A conic section of any desired eccentricity (between the 
limits) can therefore be cut from any cone of revolution by 
giving to the angle @+a a suitable value. 
The following geometrical construction gives the value of 
6+a for any assumed eccentricity. The construction is the 
same for elliptic, hyperbolic and parabolic sections; but to 
avoid confusion in the figure they are here considered 
separately. 
C 
Figure 1. 
For the elliptic section [e << 1], Figure 1, with C asa center 
