90 



which is that of the curre 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 de- 

 scription, r and / being the radients to any point of the curve from 

 the two foci ; 



»7i r + M / = 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 

 convei'gent at another point / within it ; and in this case the ratio 



— expresses the index of refraction of the medium. | 



If we denote by the power of either focus the number of strings 

 leading to it by Mr Maxwell's construction, and if one of the foci be 

 removed to an infinite distance, if the powers of the two foci be 

 equal the curve is a parabola ; if the power of the nearer focus be 

 greater than the other, the curve is an ellipse ; if the power of the 

 infinitely distant focus be the greater, the curve is a hyperbola. 

 The first case evidently corresponds to the case of the reflection of 

 parallel rays to a focus, the velocity being unchanged after reflec- 

 tion ; the second, to the refraction of parallel rays to a focus in a 

 dense medium (in which light moves slower) ; the third case to re- 

 fraction into a I'arer medium. 



The ovals of Descartes were described in his Geometry, where he 

 has also given a mechanical method of describing one of them, J but 

 only in a particular case, and the method is less simple than Mr 

 Maxwell's. The demonstration of the optical properties was given 

 by Newton in the Principia, Book I., prop. 97, by the laAv of the 

 sines ; and by Huyghens in 1690, on the Theory of Undulations in 

 his Traite de la Lumiere. It probably has not been suspected that 

 so easy and elegant a method exists of describing these curves by the 

 use of a thread and pins whenever the powers of the foci are com- 



* Ilerschel on Light, Art. 232; Lloyd on Light and Vision, Chap. vii. 

 t This was perfectly well shewn by Iluyghens in his Traite de la Lumiere, 

 p. 111. (1690.) 



I Edit. 1683. Geometria, Lib. II., p. 54. 



