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 RowLanp G. Hazarp. 
Extract of a letter from Mr. Hazard, dated Hopkinton Springs, Feb. 22, 1851. 
TO PROFESSOR SILLIMAN. 
Dear 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 0 
vision and continued in a similar manner, would form a cutve which 
ey : 
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 properly, ati 
afterwards reduced the intermediate spaces to right lines, and findin 
that I thus obtained a pretty and regular curve, commenced investi 
gating its properties, and found, under certain circumstances, he 
coincidence with the hyperbola which is shown in the demonstratio’: 
Make AC equal to the transverse axis, and DE, at right oie 
it and bisected by the point C, equal to the conjugate. ioe 
by the point B; draw the asymptotes BE, BD produced indefinite’: 
Through the point C draw CF, parallel to BE, and with the distance 
BF find the equidistant points D, G, H, &c. from which draw a 
parallel to BE. “Draw AF and produce it to meet the next parave 
ntertained, of pursuing 
ig ican cs Cente 
* Other occupations frustrated the purpose, which I then € 
the subject. 
