SNELLIUS— LAW OF EEFRACTION. 109 



stancy, at a comparatively recent period, marks an era in the history of the 

 science ; and it Avas, as we shall see, the discovery of the laiv of refraction. 



TIk; ascertained index of refraction for water is 1.33582. If we m:dce a com- 

 pntation of its value from the measured angles of Ptolemy, we find a mean of 

 1.30147. But if we take his measurements at the incidence of SO-", where the 

 relative variations of the angles of incidence and refraction are most marked and 

 most easily measured, we obtain 1.33555, which is exceedingly near the truth. 



The true index of refraction for glass is between 1.48 and l.GO, according to 

 the materials and density. Crown glass varies from below 1.50 to about 1.525. 

 Ptolemy's mean determination would be 1.4S4. But at 50° he approaches 

 nearer the truth, his angles giving 1.5321. 



For rays passing from water to glass, the relative index computed from his 

 measurements would be 1.1390, the true being 1.14145. The near agreement 

 of these numbers with niodcrn determinations is remarkable, cspecnally consid- 

 ering that Ptolemy's measures arc given only to the nearest half degree. 



Ptolemy was unable, however, to derive any practical advantage from these 

 results, since the magnitudes of the angles seemed to be governed by no law 

 Avhich he could detect. And in this unsatisfactory condition the whole subject 

 of refraction remained for the fifteen succeeding centuries. 



As an astronomer, Ptolemy could hardly fail to notice the effect of atmos- 

 pheric refraction upon the ai)parent positions of the heavenly bodies; and he 

 has the merit of having recognized the fact, which others after him disputed, 

 that the displacement is always in a vertical plane, and also that it attains its 

 maximum in the horizon and is zero in the zenith. 



About half a century later than Ptolemy flourished Claudius Galen, the cele- 

 brated Greek ])hysician. In a treatise on the uses of the members of the human 

 bodv he speaks at some length of the phenomena of vision, and lays down the 

 fundamental law on which the stereoscope has been very recently constructed, 

 that the picture which we see of a solid body is made up of two pictures dis- 

 similar to each other, one seen by each eye separately. 



But it was impossible that optical science should make any important pro- 

 gress so long as the law which determines the path of a ray in passing from one 

 medium to another remained unknown. We are compelled, therefore, to descend 

 to the earlier portion of the 17th century before we find a practicable ground on 

 which to build a systematic science, or lay even a foundation for the splendid 

 superstructure which the futun; had in reserve in this department of physical 

 inquiry. In the year 1626 Wdlebrord Snellius, professor of mathematics at 

 Leyden, died at an early age, leaving behind hiin manuscripts, among which was 

 contained a statement of the important law in question under the following form: 

 If MN be a ])lane horizontal surface, dividing a denser 

 medium below it from a rarer one above, and if a point at D 

 -^~be observed by the eye at A, the apparent place of D will be 

 at B, vertically above D, in the line AC produced ; and what- 

 ever be th(! inclination of the ray to the surface, the line CD 

 Fig. 1. v.'ill be to the line CB in a constant ratio. Or, if CD be made 



the radius of the circular arc FDQ, and DE be drawn perpendicular to the 

 surface, the radius CI, being the visual ray AC produced, will be divided at B 

 in a constant ratio. If, at F, we draw to the circle the tangent FII, producing 

 CD and CB to meet it at II and G, then CH and CG, which have the same 

 ratio to each other as CD and CB, will be the secants of the angles HCF 

 and GCF, or the co-secants of the angles HCQ and GCQ, ( — ACP,) formed 

 by the refracted and incident rays with the perpendicular, PQ, to the refract- 

 ing surface MN, technically called the angles of refraction and of incidence. 

 Tlie geometrical law of Sn(dlius, therefore, translated into the language of 

 trigonometry, is this : That when a ray, passing from one medium to another, 

 underiroes refraction at the common surface, the ratio of the co-secaut of the 



