368 Intelligence and Miscellanies. 



and these chasms occurred frequently within intervals of half 

 a mile. They felled the tallest trees at right angles with the 

 chasms ; and stationed themselves upon the felled trees. By 

 this invention all were saved ; for the chasms occurred more 

 than once under these trees." 



1 0. New Instrument for drawing the curves of Conic Sec- 

 tions* 



(See the annexed plate.) 



A B C is a block of wood, but little larger than the draw- 

 ing, to which is screwed, the brass plate dd having the plate 

 D D attached to it by the hinge e e e. This plate may be 

 placed at any angle of elevation, and fixed in its position by 

 means of the brass slides passing over the quadrants Q, Q, 

 and tightened by the screws s s. The piece m m is screwed 

 to the plate D D, and is perforated at o. Through this hole 

 traverses the rod rp a foot in length, and about a quarter of 

 an inch in diameter, highly polished ; the other end of the 

 rod, to which the pencil p is attached passes through the cir- 

 cular opening gg in the plate D D. 



Now, if while one part of the rod is through o, the other is 

 moved round the circle g^ it is plain that the revolution will 

 form a cone, and (while the plate D D is in the position re- 

 presented in the figure) the pencil will describe an ellipse up- 

 on the plane xx. By varying the inclination of the plate 

 D D, the axis of the cone will form every possible angle with 

 the plane, and of course the four curves, in all their varieties, 

 may be drawn. 



It is not supposed that this instrument can be of much 

 practical use, because each one of the curves separately, can 

 be more easily and conveniently drawn by some method pe- 

 culiar to itself. This is offered only as a mode which may 



* To the Editor. 



Amherst College, Nov. 26, 1828. 



gilt Prof. Hitchcock requested me some time since, to send to you, for 



the Journal, a figure and description of a little instrument, which I had con- 

 trived for drawing the curves of conic sections. I have been postponing a 

 compliance with this request, on account of a practical difficulty in the con- 

 struction of the instrument, which I have not until lately remedied. The fol- 

 lowing drawing and description is now at your service. 



With much respect yours, 



J. Abbott. 



