374 Miscellaneous. [Jury, 
interesting to the Government, to the scientific world, and to mankind in 
general. 
(Signed, ) W. H. Mun, D. D. V. P. 
W.N. Forses, Capt. Engineers. 
J. M. Sepprnes. 
J. LANGSTAFF. 
Asiatic Society's Apartments, J. N. Casanova, M. D. 
20th July, 1833. N. Watuicu, M. D. 
—— 
V1I.—Miscellaneous. 
Remarks on Hutton’s Mathematics. 
To the Editor of the Asiatic Journal. 
Sir, 
I observe occasional strictures on mathematical and physical works in the mis- 
cellaneous department of the Journal : J am therefore induced to send you the fol- 
lowing observations on some passages in Dr. Hurron’s Course, which if not incon- 
sistent with your plan you may perhaps find a place for. 
The first subject of remark is the Doctor’s method of treating the hyperbola in 
his conic sections*. Here he appears to have made it too much his object to point 
out the strong analogy which subsists between it and the ellipse, which is indeed 
both striking and interesting ; but in keeping to this one point he has sometimes 
gone too much on the general idea, and has not attended sufficiently to the specific 
properties of the curve in question, giving his demonstrations in the same words for 
both these sections of the cone, in one or two instances, where the correspondence 
was scarcely close enough to admit of this method of procedure. 
To come to particulars. In Prop. I. the squares of the ordinates are proved to be to 
each other as the rectangles of the abscisses, but only be it observed in regard to the 
primary curve. In Prop. II. Dr. H. comes to shew that the square of the transverse 
is to the square of the conjugate as the rectangle of the abscisses to the square of 
their ordinate ; but his first step consists in assuming the semi-conjugate to be an 
ordinate to the curve. Now this I contend is premature, for of the conjugate hyper- 
bola nothing has yet been said, but that it exists, and this in the definitions only. 
The difficulty might perhaps have been evaded by adding after Prop. I. something 
similar to the following : Scnottum.‘‘ The above proposition, as the reader will 
observe, is identical with Prop. I. of the ellipse, but the analogy between the 
curves is yet closer than these corresponding properties of the abscisses and ordi- 
nates would at first sight suggest ; for if, as in the ellipse, the square of the axis 
A Bis made to the square of another line passing through the bisecting point at 
right angles to A B, and bisected by A B, as the rectangle under the abscisses of 
an ordinate to the square of that ordinate, it will be a conjugate axis to A B corre- 
sponding to the conjugate axis of the ellipse, through which conjugate curves 
passing complete a conformity between these two sections of the cone, which is 
very close and remarkable.” 
From Prop. II. all goes on with apparent smoothness till Theor. X, where in 
proving that the parallelograms inscribed between four conjugate hyperbolas 
* See on this head @F,’s paper in GLEANINGS, iii. p. 161, 213.—Eb. 
