[From the Proceedings of the Royal Society of Edinburgh, Vol. II. April, 1846.]
I. On the Description of Oval Curves, and those having a plurality of Foci; with remarks by Professor Forbes. Communicated by PROFESSOR FORBES.
MR CLERK MAXWELL ingeniously suggests the extension of the common theory of the foci of the conic sections to curves of a higher degree of complication in the following manner: --
(1) As in the ellipse and hyperbola, any point in the curve has the sum or difference of two lines drawn from two points or foci = a constant quantity, so the author infers, that curves to a certain degree analogous, may be described and determined by the condition that the simple distance from one focus plus a multiple distance from the other, may be = a constant quantity; or more generally, m times the one distance + n times the other = constant.
(2) The author devised a simple mechanical means, by the wrapping of a thread round pins, for producing these curves. See Figs. 1 and 2. He then thought of extending the principle to other curves, whose property should be, that the sum of the simple or multiple distances of any point of
Fig. 1. Two Foci. Ratios 1, 2. Fig. 2. Two Foci. Ratios 2, 3.
