Although Kepler is celebrated principally in the his tory of optics for his invention of the astronomical tele scope, yet Ile had occasion to study with much carc the subjects of refraction and of vision. Ile found that be low 30° of incidence, the angle of refraction was nearly two-thirds of the angle of incidence; that when the angle of incidence was 90°, the angle of refraction in glass was 42° and some minutes; and that if the refract ed ray fell with greater obliquity than 42° upon the intc rior surface, it would be totally reflected back into the glass at an angle equal to the angle of incidence. Hav ing established these principles, he shows that piano convex glasses have their focus for parallel rays at a distance from the lens, equal to the diameter of the sphere, of which their convexity is a portion, and that those which are equally convex on both sides have their focal distance equal to the radius of the same sphere. AVhen the two surfaces arc unequally convex, he deter mines their focal distance by taking a mean between the radii of the two spheres, of which the convexities form a part. The same reasoning Ilc applies to concave lenses, with this difference only, that the focus is in this case between 'the lens and the radiant point. Kepler next endeavours to determine the focus of refracted rays, when the radiant point is at different distances from the lens. Having found that parallel rays unite in the focus of the lens as above determined, he shows that those which issue frotn this focus will emerge after re fraction in parallel directions. If they radiate from a point between this focus and the lens, they will diverge after refraction, but their divergency will be diminished. Those rays which issue from a point beyond the focus, will converge after refraction ; and when the distance of the radiant point is equal to twice the focal distance, the image will be formed at the same distance behind the glass.
The subject of vision is treated with great ingenuity by Kepler, in his ilstronomix Pars Optica. He disco vered that the images of external objects were painted on the retina by the union of the pencils of rays which issued from every point of them. He noticed also the inversion of these images; and he explained the man ner in which long-sighted and short-sighted persons were enabled, by mcans of convex and concave lenses, to converge the pencils of rays to a focus upon thc re tina. He justly ascribed erect vision from an inverted image to an operation of the mind, by which it teams. the rays back to the pupil, and thus refers the lower parts of the image to the upper side of the eye. Kep ler considered it as beyond our powers to determine die manner in which the mind perceives the images of ob jects upon the retina. The power of accommodating the eye to different distances was carefully studied by this active philosopher; and, in order to explain it, he supposed that the contraction of the ciliary process drew the sides of the eye-ball towards the crystalline lens, and thus lengthened the eye, and withdrew the re tina to a greater distance from the pupil, when the eye was adjusting itself to the vision of near objects.
It could not have been considered as an unusual step in thc progress of science, if the accurate experiments of Ptolemy on refraction had been immediateiy followed by the discovery of its true IlW. It is rather singular, indeed, that Alhazen and Viten° should have overlooked it, and still more so that it should have eluded the acute ness and sagacity of Kepler. 'fills important discovery was reserved for Willebrord Sncllius, professor of ma thematics at Leyden, who wrote a work on thc subject, which was never published, having died at the early age of 35. The MS. of this work fell into the hands of Professor Hortensius, who explained the discovery both publicly and privately. In comparing together the re fractions at different incidences, which he himself had determined by nu rnerous ex perimcnts, Snellius observed that if the refracted ray, and the incident ray continued from the point of incidence, were intercepted by a line parallel to the perpendicular at the point of incidence, the length of the refracted ray bore a constant propor tion to that of the incident ray continued. This pro portion was that of 4 to 3 in water, and 3 to 2 in glass, whatever was the angle of incidence. Hence it follows, that the co-secants of the angles of incidence and le fraction have a constant Iatio.
Although no right to a scientific discovery was ever more clearly established than that of Snellius to the true law of refraction, yct it is strange that so respectable an author as Montucla should still appear desirous of as clibing,some share of the discovery to his countryman Descat tcs. " lf," says he, " we do not precisely owc to
Descattcs the first discovery of the law of refraction, we cannot at least refuse him the merit of having esta blished upon this law the most curious geometrical re searches." It is no doubt true, that Descartes, in his Dioptrics, published in 1637, eleven years after the death of Sncllius, has announced it as a result of his own in quiries into the law of refraction, that the sines of the angles of incidence and refraction have a constant ratio, without taking the slightest notice of the discovery of Snellius, which had been made a considerable time be fore. Had Descartes distinctly said that he never heard of Snellius's law, we should not have disputed the de claration of such a distinguished character; but 1.ve arc informed by Vossius, in his work De Natura Lucis, that the heirs of Professor Hortensius had freely communi cated to Descartes the manuscripts of that professor, among which was that of Snellius's work ; and this tes timony is in a great degree confirmed by Huygens, who, in his remarks on refraction, prefixed to his Dioptries, distinctly informs us that he himself had sotnetimes seen Snellius's AIS. volume, and had heard that Des cartcs had also seen it.* Bossut has stated the casc too strongly against Descartes, when he says that Huygens assures us that Descartes-had seen thc Huygens, however, when he saw the MS. more than mice, must have seen it in the possession of Hortensius's neirs, who, no doubt, gave him sufficient evidence that it had been in the hands of Descartes. Although 'Mon tucla, however, has made this small reclamation in favour of his countryman Descattes, nevertheless says, 4c that it was reserved for Snellius to make this impor tant discovery, (viz. that of the true law of refraction,) to which he was probably conducted by the fruitless at tempts which Kepler had made to find it," and has thus given to the Dutch philosopher the decided merit of be ing the original discoverer.t Bossut, another French author, also concurs in asetibing the honour of it to Snel lius. In this decision he has been followed by Priestley, David Gregory, Muschenbroek, Smith, Robison, Play fait t, Hutton, Dr. Young ; and, so far as we know, by all other optical writers. In looking into M. Biot's Traite de Physique,(tom. p. 205,) 4.ve were in no slight de gree surprised to find the discovery of the law of re fraction ascribed solely to Descartes, and the name of SNELLIUS never once mentioned.§ Had M. Biot defend ed his countryman from the charge of plagiai ism, which is cleat ly implied in the opinions of Huygens, Bossut, and Playfair, and claimed for him the merit of a second discoverer, we might have applauded his zeal, and per haps concurred in his decision ; but when he sinks in oblivion not only the labours!! of Snellius, hut also his very name, every generous feeling is roused in defence of the injured philosopher. There is something about the history ancl fate of Snellius, which might have pro tected him against any harsh treatment, and which will probably excite many sympathies in his favour. His dis covery of the law of refraction was made in 1621, when he was scarcely thirty years old ; and before he had en joyed the high reputation to which he was thus entitled, he was cut off' by a premature death, in the thirty-fifth year of his age. The manuscript volume which contain ed his numerous experiments on refraction, and the ex planation of the law by which he generalized them, was never given to the world, but was unsuspectingly exhi bited to the very individual for whom all his honours have becn so unjustly claimed. Although Snellius was a good geometer, and published several works of consi derable merit, yet his name has been emblazoned in the temple of science solely by his optical discovery ; and philosophers of every country, and of every age, have gratefully paid their tribute of admiration at his youth ful shrine. In a case like this, national prepossessions might well have yielded to a nobler sympathy, and even if the tight of property had been ambiguous, the wreath which has crowned Descartes with immortality might have been allowed to spare one laurel for the brow of Snellius.