OPTICAL KNOWLEDGE OF THE ANCIENTS.
ON account of the rectilineal propagation of light, the phenomena of optics are easily ex pressed in the form of mathematical propositions, and seem, as it were, spontaneously to offer themselves to the study of geometers. Euclid perceiving this affinity, began to ap ply the science which he had already cultivated with so much success, to explain the laws of vision, before a similar attempt had been made with respect to any other branch of ter restrial physics, and at least fifty years before the researches of Archimedes had placed me chanics among the number of the mathematical sciences.
In the treatise ascribed to Euclid, there are, however, only two physical principles which have completely stood the test of subsequent improvement. The first of these is the proposition just referred to, that a point in any object is seen in the direction of a straight line drawn from the eye to that point ; and the second is, that when a point in an object is seen by reflection from a polished surface, the lines drawn from the eye and from the . object to the point whence the reflection is made, are equally inclined to the reflecting surface. These propositions are assumed as true ; they were, no 'doubt, known before the time of Euclid, and it is supposed that the discovery of them was the work of the Pla tonic school. The first of them. is the foundation of Optics proper, or. the theory of vi sion by direct light ; the second is the foundation of Catoptrics, or the theory of vision by reflected Dioptrics, or vision by refracted light, had not yet become an object. of attention.
Two other principles which adopted as postulates in his demonstrations, have not met with the same entire Confirmation from experiment, and are, indeed, true only in certain eases, and not universally, as he supposed. The first of these is, that we judge of the magnitude of an object altogether by the magnitude of the optical angle, or the angle which it subtends at the eye. It is ,true that this angle is an important ele.
meat in that judgment, and Euclid, by discovering this, came into the possession of a valuable truth ; but by a species of sophistry, very congenial to the human mind, he ex tended the principle too far, and supposed it to be the only circumstance which determines our judgment of visible magnitude. It is, indeed, the only measure which we are fur nished with directly by the eye itself ; but there are few cases in which we form our esti mate without first appealing to the commentary afforded by the sensations of touch, or the corrections derived from our own motion.
Another principle, laid down by the same geometer, is in circumstances nearly similar to the preceding. According to it, the place of any point of an object seen by reflection, is always the intersection of the reflected ray, with the perpendicular drawn from that point to the reflecting surface. The proof offered is obscure and defective ; the proposi
tion, however, is true, of plain speculums always, and of spherical as far as Euclid's inves tigations extended, that is, while the rays fall on the speculum with no great obliquity. His assumption, therefore, did not affect the truth of his conclusions, though it would have been a very unsafe guide in more general investigations. The book isin many other respects imperfect, the reasoning often unsound, and the whole hardly worthy of the great geometer whose name it bears. There is, however, no doubt that Euclid wrote on the subject of optics, and many have supposed that this treatise is a careless extract, or an un skilful abridgment of the original work.
Antiquity furnished another mathematical treatise on optics, that of the astronomer Ptolemy. This treatise, though known in the middle ages, and quoted by Roger Bacon, had disappeared, and was supposed to be entirely lost, till within these few years, when a manuscript on optics, professing to be the work of Ptolemy, and to be translated from the Arabic, was found in the King's Library at Paris. The most valuable part of this work is that which relates to refraction, from whence it appears that many experiments had been made on that subject, and the angles of incidence and refraction, for different trans parent substances, observed with so much accuracy, that the same ratio very nearly of the sines of these angles, from air into water, or into glass, is obtained from Ptolemy's num bers, which the repeated experiments of later times have shown to be true. The work, however, in the state in which it now appears, is very obscure, the reasoning often defi cient in accuracy, and the mathematical part much less perfect than might have been ex pected. Modern writers, presuming partly on the reputation of Ptolemy, and partly guided by the authority of Roger Bacon, had ascribed to this treatise more merit than it appears to possess ; and, of consequence, had allowed less to the Arabian author Alhazen, who come: next in the order of time, than of right belongs to him. Montuela, on the authority of Bacon, says, that Ptolemy ascribed the increase of the apparent magnitude of the heavenly bodies near• the horizon, to the greater distance at which they are supposed to be, on account of the number of intervening objects across which they are seen. Pto lemy's explanation, however, as stated by Delambre, from the manuscript just mention ed, is quite different from this, and amounts to no more than the vague and unsatisfactory remark, that an observer looks at the bodies near the zenith in a constrained posture, and in a situation to which the eye is not accustomed. The former explanation, therefore, given by Alhazen, but supposed to have been borrowed from Ptolemy, must now be re turned to its right owner. It is the best explanation yet known.