In this manner Ptolemy. obtained the results in the following table, which contains the angles of refraction from .thr to TVater, from 10° up to 80° ol incidence.
In order to measure the angles of refraction from air into glass, Ptolemy adopted the ingenious idea of pro curing a semi-cylinder of pure glass, and adjusting the diameter of it so as to coincide with the horizontal dia meter of the graduated circle already described. By per forming the very same experiments which he made with water, he found that there was no refraction at a perpen dicular incidence ; but that lor every other position, the angle in the air was always greater than the angle in the glass, ancl the lefraction greater than in water. Whew the three bodies were placed in appearance in the same straight line, they always remained there, whether the eye was placed above the glass or below it. The follow ing are the refractions from .4ir to Glase, which he ob tained in this manner : When the semi-cylinder of glass was placed on the surface e‘of water, Ptolemy observed that the refractions from water into glass were less than any he had observed, because the difference of density between TVater and Glaas was less than between water and air. The follow ing were the results which he obtained : Ptolemy now proceeds to the important subject ot astronomical refraction, which he ascribes to the differ ence of density between ether and air. If the visual ray, he remarks, is stopped by an impenetrable body, it could not show us a body which is hid behind the first ; and if the second becomes visible, it can only be on account of the flexion of the visible ray. This flexion takes place at its passage into a medium of different density ; and the possibility of this flexion, he asserts, may be proved by the following phenomena. By observations on the stars, it was ft)und that the parallels drawn through the apparent place of those which rise or set, are then nearer the north pole than the parallels which pass through their apparent place when they are on the meridian ; and the nearer the stars are to the horizon, the greater is the approach of their parallels to the pole. By observing a circumpolar star, Ptolemy found that it was nearer the pole in its lower passage across the meridian ; but when it was near the zenith its pa rallel became greater in appearance, whet eas in the first case it became smaller. Hence it follows that refrac tion raises the stars towards the zenith. In order to ex plain the manner in which refraction operates, Ptolemy makes use of the saine figure upon which Cassini has since founded all his theory, and he employs almost the same reasoning in order to determine the quantity of thc refraction. He remarks, that the more a star is elevated,
the less will be the difference between its true and its apparent place, and that this difference will be nothing in the zenith, because a perpendicular ray experiences no flexion. He demonstrates by a figure, that in every case the refraction carries the star towards the zenith ; and hc states that the height of the atmosphere is un known, but that it must begin below the sphere of the moon. From this general account of the fifth book of the optics of Ptolemy, it will be seen that he gives a theory of astronomical refractions much more complete than that of any astronomer before the time of Cassini.
After a long interval of inactivity, the science of op tics was cultivated with assiduity in Arabia. AI Fara bius wrote a treatise on Perspective about A. D. 900; and Ebn Haithem is said to have produced a work which treated of direct, reflected, and refracted vision, and also of burning mirrors; but this production has been unfor tunately lost.
The only optical work, indeed, of the Arabian philo sophers, which has reached our times, is the Treatise on Optics,* by Alhazen, who flourished about the end of the eleventh century. Alontticla has stated, without sufficient evidence, that Alhazen seems to have borrowed from Ptolemy the greater part of his optics ; but NI. Delambre, in the paper already quoted, has succcssfully repelled this imputation against the honour of the Ara bian philosopher. Instead of finding any reason for be lieving that he has borrowed almost all his optics from Ptolemy, NI. Delambre supposes it quite probable that Ile may never even have read that work. In treating of refraction, Alltazen has not copied the tables of Ptolemy, which we have inserted above, and in what he says of as tronomical refraction, he has given a much less com plete view of the subject. The plan of Alhazen's work, too, as NI. Delambre remarks, is quite different ; hc speaks a language less metaphysical and more geome trical, and Ile discusses a number of questions, and re solves a quantity of problems, to which Potolemy does not even allude. The physics of Ptolemy are much more defective than those of Alhazen; and in the part which is purely geometrical, the work of Alhazen is also superior to that of Ptolemy.