314 To describe an Hyperbola. 



extremes of retardation, both by excess and by deficiency of tem- 

 perature, in the production of vapor. The reader will perceive 

 however that the actual order of occurrence of these six experiments 

 which began at a white heat and lasted, including intervals, 218.7 

 seconds, was 27.5, 28, 34, 39, 30, 33. It needs hardly be stated, 

 that the idea of instantaneous action between iron and water, derives 

 no confirmation from any of the foregoing series of experiments. 



Art. IX. — To describe an Hyperbola ; by Rowland G. Hazard. 

 Extract of a letter from Mr. Hazard, dated Hopkinton Springs, Feb. 22, 1831. 



TO PROFESSOR SILLIMAN. 



Hear Sir — Annexed is a mode of describing the hyperbola, which 

 I think more simple and easy than the one usually given, besides hav- 

 ing the advantage of showing very clearly the continual approximation 

 of the curve to its asymptote, without the possibility of meeting it. 

 I shall be gratified, if you think it worthy of a place in your Journal. 

 The manner in which it first occurred to me, may not be uninteresting 

 to you. About fourteen years since,* when at school, sitting near one 

 corner of a long room, in one side of which were three windows in- 

 serted in a thick brick wall, it occurred to me that I could see a less 

 distance into the recess of the second than of the first, and still less 

 into the third, and that a line drawn through the extreme points of 

 vision and continued in a similar manner, would form a curve which 

 would always approach, but could never meet, the inner superficies 

 of the wall. I at first used a figure drawn in exact accordance with 

 this first suggestion, to convince some of my incredulous companions 

 of the possibility of drawing a curve possessing that property, but 

 afterwards reduced the intermediate spaces to right lines, and finding 

 that I thus obtained a pretty and regular curve, commenced investi- 

 gating its properues, and found, under certain circumstances, the 

 coincidence with the h3'perbola Vi Inch is shown in the demonstration. 



Make AC equal to the transverse axis, and DE, at right angles to 

 it and bisected by the point C, equal to the conjugate. Bisect AC 

 by the point B; draw the asymptotes BE, ED produced indefinitely. 

 Through the point C draw CF, parallel to BE, and with the distance 

 BF find the equidistant points D, G, H, &ic. from which draw lines 

 parallel to BE. Draw AF and produce it to meet the next parallel 



* Other occupations frustrated the purpose, xvhi. h I then entertained, of pursuing 

 the subject. 



