10 The Theory of the Aether 



eventually introduced a new fundamental law, from which he 

 proposed to deduce the paths of rays of light. This was the 

 celebrated Principle of Least Time, enunciated* in the form, 

 " Nature always acts by the shortest course." From it the law 

 of reflexion can readily be derived, since the path described by 

 light between a point 011 the incident ray and a point on the 

 reflected ray is the shortest possible consistent with the con- 

 dition of meeting the reflecting surfaces. t In order to obtain the 

 law of refraction, Fermat assumed that " the resistance of the 

 media is different," and applied his "method of maxima and 

 minima " to find the path which would be described in the least 

 time from a point of one medium to a point of the other. In 

 1661 he arrived at the solution.* "The result of my work," he 

 writes, " has been the most extraordinary, the most unforeseen, 

 and the happiest, that ever was ; for, after having performed all 

 the equations, multiplications, antitheses, and other operations 

 of my method, and having finally finished the problem, I have 

 found that my principle gives exactly and precisely the same 

 proportion for the refractions which Monsieur Descartes has 

 established." His surprise was all the greater, as he had 

 supposed light to move more slowly in dense than in rare media, 

 whereas Descartes had (as will be evident from the demonstration 

 given above) been obliged to make the contrary supposition. 

 Although Fermat's result was correct, and, indeed, of high 

 permanent interest, the principles from which it was derived 

 were metaphysical rather than physical in character, and con- 

 sequently were of little use for the purpose of framing a 

 mechanical explanation of light. Descartes' theory therefore 

 held the field until the publication in 1667 of the Micrographics 



* Epist. XLII, written at Toulouse in August, 1657, to Monsieur de la 

 Chambre ; reprinted in (Euvres de Fermat (ed. 1891), ii, p. 354. 



t That reflected light follows the shortest path was no new result, for it had 

 been affirmed (and attributed to Hero of Alexandria) in the Ke<t>aA.cua rwv OTTTIKUHT 

 of Heliodorns of Larissa, a work of which several editions were published in the 

 seventeenth, century. 



J Epist. XLIII, written at Toulouse on Jan. 1, 1662 ; reprinted in (Euvres de 

 Fermat, ii, p. 457 ; i, pp. 170, 173. 



The imprimatur of Viscount Brouncker, P.R.S., is dated Nov. 23, 1664. 



