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[1] in the form, "Nature always acts by the shortest course." From it the law of reflexion can readily lie derived, since the path described by light between a point on the incident ray and a point on the reflected ray is the shortest possible consistent with the condition of meeting the reflecting surfaces.[2] In order to obtain the law of refraction, Fermat assumed that “tho 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.[3] “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 ignore 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 consequently 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[4] of the Micrographia
- ↑ Epist. xlii, written at Toulouse in August, 1657, to Monsieur de la Chambre; reprinted in Œuvres de Fermat (ed. 1891), ii, p. 354.
- ↑ That reflected light follows the shortest path was no new result, for it had been affirmed (and attributed to Hero of Alexandria) in the Κεφάλαια τών οπτικών of Heliodorus of Larissa, a work of which several editions were published in the seventeenth century.
- ↑ Epist. xliii, written at Toulouse on Jan. 1, 1662; reprinted in Œuvres de Fermat, ii, p. 467; i, pp. 170, 173.
- ↑ The imprimatur of Viscount Brouneker, p.r.s., is dated Nov. 23, 1664.
