[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. 



MB CLERK MAXWELL ingeniously suggests the extension of the common 

 theory of the foci of the conic sections to curves of a higher degree of com- 

 plication 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 



Fig. 1. Two Foci. Ratios 1, 2. 



Fig. 2. Two Foci. Eatios 2, 3. 



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 

 VOL. I. * 



