89 



Nieuwe Verhandelingen der Eerbte Klasse von het Koninklijk- 

 Nederlansche Instituut van Wetenschappen, Letterkunde en 

 Schoone Kunsten te Amsterdam. Deel XII., Stuk 1. — By 

 the Instltut. 



Monday, 6(h Ajxril 1846. 



Sir THOMAS M. BRISBANE, Bart., President, in the 

 Chair. 



The following Communications were read : — 



1. On the Description of Oval Curves, and those having a 

 plurality of Foci. By Mr Clerk Maxwell junior; with 

 remarks by Professor Forbes. Communicated by Pro- 

 fessor Forbes. 



Mr Clerk Maxwell ingeniously suggests the extension of the com- 

 mon 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 condi- 

 tion that the simple distance from one iocus 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 wrap- 

 ping of a thread round pins, for producing these curves. See Figs. 

 1 & 2 (Plate II.) 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 the curve from three or more points 

 or foci, should be = a constant quantity ; and this, too, he has effect- 

 ed mechanically, by a very simple arrangement of a string of given 

 length passing round three or more fixed pins, and constraining a 

 tracing point, P. See Fig. 3. Farther, the author regards curves of 

 the firet kind as constituting a particular class of curves of the second 

 kind, two or more foci coinciding in one, a focus in which two strings 

 meet being considered a double focus ; when three strings meet •<). 

 treble focus, &c. 



Professor Forbes observed that the equation to curves of the first 

 class are easily found, having the form 



'/x2+/^= a + bs/{x-cy-\-y'^. 



