258 Conic Sections. 
clouds in rapid motion. There was a strong western gale. The 
lightning appeared to issue froma cloud which was moving very 
swiftly towards Shelbyville. This cloud was permanently luminous, 
and between the flashes of lightning of the color of red hot iron. 
Tn shape it was double, and the two portions approached each other 
_ like the wings of an eagle, and on passing over the village, the wings 
suddenly coalesced and descended, and then became invisible to the 
observer. This occurred, as nearly as we could calculate, at the 
moment when the hurricane swept over the town. 
It has been suggested to me by a friend, that at the moment of 
the union of the two clouds, two contrary currents of air met, and 
produced the whirlwind, which was so destructive in its effects. 
ee 
Art. VII.—On the sections of a plane, with the solids formed by 
the revolution of the conic sections, about axes situated in their 
planes ; by Prof. Benepicz, of the University of Vermont. 
Let ARH be any conic section; AM the line of its principal 
axis; A its vertex; and CQK any right line in its plane about 
which it is apposed to revolve. Let DRVT be any plane, the 
common section of which, and the surface of the solid which is 
formed by the revolution of ARH is the line RT, whose form it is 
proposed to examine. Through CK let the plane DRHM pass 
perpendicular to the plane DRVT, intersecting the surface of the 
solid in the conic section 
ARH; and let the common 
section of these planes be 
DRY, meeting AM, exten- 
ded if necessary, at D and 
ARH atR. Draw RL,RQ 
perpendicular respectively 
to AM,CK, meeting them 
at LandQ. Through any 
point V in RV ds is 
assumed the axis of abscis- DC ~~ AL GOD 
se of the line RT, draw HK parallel to RQ, meeting ARH at H 
aah Kat K. Let HTZ bea section of the solid perpendicular to 
Let AM,HM, the rectangular coordinates of the point H 
Fig, 1. 
