2 DESCRIPTION OF OVAL CURVES. 



the curve from three or more points or foci, should be = a constant quantity ; 

 and this, too, he has effected mechanically, by a very simple arrangement of 

 a string of given length passing round three or more fixed pins, and con- 

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



Fig. 3. Three Foci. Ratios of Equality. 



of the first 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 a treble focus, &c. 



Professor Forbes observed that the equation to curves of the first class is 

 easily found, having the form 



which is that of the curve known under the name of the First Oval of 

 Descartes*. Mr Maxwell had already observed that when one of the foci was 

 at an infinite distance (or the thread moved parallel to itself, and was confined 

 in respect of length by the edge of a board), a curve resembling an ellipse 

 was traced ; from which property Professor Forbes was led first to infer the 

 identity of the oval with the Cartesian oval, which is well known to have this 

 property. But the simplest analogy of all is that derived from the method of 

 description, r and r being the radients to any point of the curve from the -two 



foci; 



mr + nr = constant, 



which in fact at once expresses on the undulatory theory of light the optical 

 character of the surface in question, namely, that light diverging from one 

 focus F without the medium, shall be correctly convergent at another point f 



* Herachel, On Light, Art 232 ; Lloyd, On LigfU and Vision, Chap. vn. 



