360 GREEK SCIENCE. 



of reflection, when the place of the eye and that of the image are 

 known : he satisfies himself with showing, generally, that the object is 

 before or behind the mirror, or the eye, or nearer to the mirror, or 

 more remote than the eye ; the relations being not measured, but indi- 

 cated vaguely. 



The fifth book of Ptolemy's ' Optics' contains his researches into the 

 nature of refraction. 



He explains the experiment of the piece of money so placed in a 

 vessel that its edges render it invisible, until water is poured in, when 

 the money is brought into sight, while it has remained quiescent. 

 After this, he proceeds to a curious set of experiments, which we 

 cannot here detail, in order to determine the relation between the 

 positions of the incident and refracted ray, the media being air and 

 water, for all degrees of incidence, varying by tens, up to 80. The 

 medium ratio of the sine of incidence to that of refraction, when the 

 ray passes from air into water, is 4 to 3*06936: according to the 

 experiments of Newton, the ratio of these sines is 4 to 2*99432. 

 When the ray passes from air into glass, the result of Ptolemy's 

 experiments is, that the sines of incidence and refraction are as 3 to 

 2*02158. Newton gives for the ratio of these sines 3 to 1*93048. 

 The correspondence between these respective ratios is greater than 

 might reasonably have been expected, considering that the instruments 

 employed by Ptolemy would not enable him to measure angles to 

 nearer than half a degree. Newton employed rain water : Ptolemy 

 has simply informed us that the water employed by him was always of 

 the same density. Newton, again, employed common glass : Ptolemy 

 calls his the purest glass : what that was we cannot say, because we 

 know nothing of the glass manufactory among the Egyptians in the 

 time of Ptolemy. 



In the explication of astronomical refraction, Ptolemy proceeded in 

 several respects as Cassini did in the last century. He, also, taught 

 expressly, that the more a star is elevated, the less will be the differ- 

 ence between the true and the apparent place, and that this difference 

 is nothing when the star is in the zenith, because the vertical ray does 

 not undergo any flexure. This Ptolemy demonstrates by means of a 

 figure ; from which it appears, that in all cases the refraction carries 

 the star towards the zenith. 



Ptolemy afterwards describes different experiments connected with 

 the subject of refraction ; but his deductions from them are, in general, 

 erroneous. Altogether, however, this fifth book of his ' Optics ' is 

 highly curious and interesting ; and, indeed, the whole work is me- 

 thodical and instructive; on which account, we have entered more 

 fully into description of it than has been usual among the historians of 

 optics. 



It is an interesting inquiry, but by no means of easy determination, 

 how far the ancients attempted to assist sight by dioptrical instru- 

 ments. Roger Bacon, in his piece * On the Secret Works of Nature 



