The Dioptrics of Descartes, though stained by the omission of the name of Snellius, added in a very high degree to the optical knowledge of the times. As lenses of a spherical form had been found not to converge pa rallel rays to one point, Descartes set himself to inquire if any surface existed, by which an accurate convergence to a single point might be effected. Kepler had already conjectured from analogy that the conic sections might have this property ; but it was left to Descartes to com plete the investigation. He solved the problem in a very general and elegant manner, and showed how this object could be accomplished by curves, which he called ovals, and which, in certain cases, particularly wanted in optical instruments, become ellipses and hyperbolas. Descartes could not fail to see thc apparent advantages of this result ; but, ignorant of the principal causes of the imperfections of telescopes, he expected much more from this discovery than it was capable of yielding. He immediately contrived machines for grinding elliptical and hyperbolical lenses, and when he was at Paris in the year 1628, he engaged a mathematical instrument maker of the name of Ferrier to enter into his views. This artist, after much labour, succeeded in completing a tolerably good hyperbolical convex lens, but he failed in the concave ones, and being disgusted with the dif ficulty of the work, he abandoned the undertaking. The hopes of Descartes, however, were not so easily sub dued. Holding out the promise of discovering, by means of such lenses, the smallest objects in the stars, and assisted by the friendly instigation of AI. Huygens, the father of the celebrated philosopher, he persuaded some Dutch artists to renew the unsuccessful attempts of Ferrier. The same difficulties, however, were expe ricnced, and, though succeeding philosophers have wasted their ingenuity in detising machines for the same purpose, elliptical and hyperbolical lenses have had no existence but in the theoretical writings of op ticians; and there is sotne reason for doubting, ir the reflecting telescope has derived much improvement from the attempts which are generally made to give a parabolic form to the great speculum. In perfecting the theory of the rainbow, ihe fine genius of Descartes shines with new lustre ; ancl we wish it could have been added, that this lustre was not impaired by another act of selfish appropriation. Although Antonio de Dominis had observed and published the true principle. of this theory, Descartes never even mentions his name ; ancl, as in the case of the unfortunate Snellius, Biot has, in opposition to the decision of all ages. assisted Des cartes in depriving- the Italian prelate of the only dis covery which has signalized his name. The exterior rainbow, which had baffled the ingenuity of preceding philosophers, received the most satisfactory explanation from Descartes. He shows that the rays of the sun entering the inferior part of the drop, and experiencing one refraction, suffered two reflections within, and then emerged by a second refraction. Hence he accounted for the inversion of the colours in the excel ior bow, and the comparative faintness of its light Descartes also explains, in a very satisfactory planner, why the interior bow has a diameter of 42°, and the exterior one of 52°, and he has done all that could be expected on this sub ject, previous to the great discovery of the different re frangibility of light. We owe also to Descartes a num ber of interesting observations on vision. His remarks on the method by which the eyc judges of distances and magnitudes are ingenious, and sometimes sound; and lie ast.ribed the adaptation of the eye to different distances to a. change of curvature in the crystalline lens, which he supposed to be a muscle, having the ciliary processes for its tendons.
Schciner, whose improvement on the telescope we have already had occasion to mention, added some im portant facts to the subject of vision. By cutting away the coats from the posterior part of the eyes of sheep and oxen, and holding several objects before them at the usual distance at which vision is performed, he saw the most distinct images of them beautifully painted on the naked retina. The same experiment lie performed with the human cye, and exhibited it at Rome in the year 1625. This ingenious author notices the analogy between the eye and the camera obscura, and explains the erectness of the object from the inversion of the image, as Kepler had done, by stating that the mind traces thc rays back to the pupil, and refers them to that part of the object from which they seem to have proceeded. The contraction of the pupil, when the eye
examines near objects, was also well known to Scheiner; and man) other curious, though less important, facts re specting vision through small apertures. He examined with considerable care the refracting powers of the hu mours of the eye ; and lie concludes that the aqueous humour has a refracting power differing little from wa ter; that the refracting power of the crystalline humour differs little from glass, (in which he was greatly mis taken,) and that the vitreous humour has a refractive power, of an intermediate magnitude. He traces the progress of the rays through ail the humours of the eye, arid, after much judicious reasoning, he refutes the opinion, that the crystalline lens is the seat of vision ; and establishes the doctrine, which, he says, %YDS that of Alhazen, Vitcllo, and Kepler, that the retina is the true scat of vision.
Among the .discoveries of this period, there is none more curious in itself, or more important in its conse quences, than that of double refraction, which was made by Erasmus Bartholinus. Having obtained from some Danish merchants, who frequented Iceland, a " crystal stone, like a rhombic prism, which, when broken into small pieces, kept the same figure," and afterwards from its locality called Iceland crystal ; lie made many optical and chemical experiments with it, and disco vered that it possessed the retnarkable property of a double refraction. Ile found that one of those refrac tions, whose index was 1.667, was performed according to the law of Snellius, which is common to all transpa rent solids and fluids, while the other is performed ac cording to an extraordinary law, which had not previ ously been observed by philosophers. An account of these experiments our author published at Copenhagen, in the year 1669, under the title of Experimenta Crys talli Islandici Dis-diaclastici quibus nzira et insolita re fractio detegitur ; and lie afterwards communicated an account of them to the Royal Society, in a letter to Dr: Oldenburg, which appeared in No. 67, of the Philoso phical Transactzons.* In this new and interesting field of inquiry, Barth°. linus was followed by Christian Huygens, a Dutch phi losopher, one of the finest geniuses of the age in which he lived, and equally distinguished by his astronomical, his optical, his mathematical, and his horological disco veries. A few years after the publication of Bartholi nus's work, the attention of this celebrated individual was directed to the subject of double refraction. He was induced to begin this investigation, principally, with the view of obviating ahy objection that might be drawn from the facts discovered by Bartholinus against his own thcory of ordinary refraction ; and he was led to the par ticular vicv,s which he has published. from a desire to assimilate the two classes of phenomena. His researches on this subject form the fifth chapter of his Traite de la Lumiere, which is entitled De l'estrange refraction clu Crzstal d'Islande. This work was composed about the year 1678, and read to several of the members of the Academy of Sciences, but it was not published till the year 1690, when Huygens was resident in Holland. After descrihing the general appearances exhibited by Iceland spar, he shows that all the phenomena are re lated to the short diagonal, or axis of the rhomb, along which the double refraction is nothing ; that it gradu ally increases, according to.a. law which,he explains, as the inclination of the refracted ray to the axis increases, and becomes a maximum when that inclination is 90°. He then proceeds to ekplain his theory of double re fraction. founded on the hypothesis of light being the undulation of an ethereal medium, by which he had al ready given an elegant explanation of all the phenomena of refraction and reflexion. He supposes the.ordinary refraction to be produced by spherical undulations pro pagated through the crystal, while the.extraordinary refraction arises from spheroidal undulations, thc form of this generating ellipse tieing determined by the ratio of the two refractions. 'lie then proceeds to show that the deNiation of the extraordinary ray, calculated upon this hypothesis, agrees precisely with observation.