258 



Conic Sections. 



clouds in rapid, motion. There was a strong western gale. The 

 lightning appeared to issue from a 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. 

 In 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. 



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. Benedict, 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 supposed 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 Fjg;, i. 



ARH ; and let the common 

 section of these planes be 

 DRV, meeting AM, exten- 

 ded if necessary, at D and 

 ARH atR. Draw RL,RQ 

 perpendicular respectively 

 to AM,CK, meeting them 

 at L and Q. Through any 

 point V in RV which is 



assumed the axis of abscis- D C A L G 



sffi of the line RT, draw HK parallel to RQ, meeting ARH at H 

 and CK at K. Let HTZ be a section of the solid perpendicular to 

 CK. Let AM,HM, the rectangular coordinates of the point H 



