CHAP. IV.] ADOLESCENCE 1844 TO 1847. 79 



dense medium (in which light moves slower) ; the third 

 case, to refraction into a rarer medium. 



The Ovals of Descartes were described in his Geometry, 

 where he has also given a mechanical method of descrihing 

 one of them, 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. 9 7, by the law of the sines, and by Huyghens 

 in 1690, on the Theory of Undulations, in his TraiU de la 

 Lumi&re. 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 commensurable. For instance, the curve, Fig. 2, 

 drawn with powers 3 and 2 respectively, give the proper 

 form for a refracting surface of glass, whose index of refrac- 

 tion is 1*50, in order that rays diverging from / may be 

 refracted to F. 



As to the higher classes of curves, with three or more 

 focal points, we cannot at present invest them with equally 

 clear and curious physical properties, but the method of 

 drawing a curve by so simple a contrivance, which shall 

 satisfy the condition, 



mr + nr' +pr" + etc., = constant, 



is in itself not a little interesting ; and if we regard, with 

 Mr. Maxwell, the ovals above described, as the limiting case 

 of the others by the coalescence of two or more foci, we 

 have a further generalisation of the same kind as that so 

 highly commended by Montucla, by which Descartes eluci- 

 dated the conic sections as particular cases of his oval 

 curves. 



This was the beginning of the lifelong friendship 

 between Clerk Maxwell and James D. Forbes. "I 

 loved James Forbes " was his own emphatic statement 

 to me in 1869. Maxwell's gratitude to all from whom 

 he had received any help or stimulus was imperishable. 



The curve -drawing, and the problems connected ^ 14 ' 15 - 



