108 EARLY WRITERS OX OPTICS. 



who endeavored to float liirusclf from sliorc to shore, across waters too deep to 

 be traversed by ordinary and simpler expedients, mnst have been strnck by the 

 sing:nlar distortion of his paddle at the line where it entered the water. The 

 natural alternations of light and darkness, their coincidence with the rising and 

 setting of the sun, the appearance and disappearance of the stars, the changes 

 of the moon, the rainbow in the clouds, the dilfcrences between different bodies 

 as luminous and non-luminous, transparent and opaque, and finally the very 

 fact of vision itself — all these phenomena constantly, from the earliest times, 

 presenting th(>mselves without being sought, must have excited the curiosity of 

 men and invited investigation, centuries before the systematic study of nature, 

 in any of her varied dejiartments, had had a beginning. 



But the difficulties which per])lcx the inquiry manifest themselves in the im- 

 perft'ction of the speculations Avhich have come down to us from the earliest 

 philosophers regarding the subject, and in the extremely slow progress of dis- 

 covery which marks much of the later history of this interesting branch of 

 ecience. A notion was for a very long time prevalent among the ancients that 

 vi.-ion is effected by means of rays proceeding irom the eye to the object. This 

 idea is not found in Aristotle; but it was introduced into the schooi of Plato, 

 and continued to be received for many centuries. The persistency of the doc- 

 trine is remarkable, inasmuch as the light which is self-evidently indispensable 

 to vision, proceeds from soitrces foreign to the observer. 



The elementary phenomena of reflection and refraction suggest a natural 

 division of the science of optics into two branches; and this distinction is made 

 by the earliest systematic writer on the subject whose works have descended 

 to us. This was Euclid — supposed to have been the geometrician of that 

 nam(^ — who lived about oOO years before our era. The general laws which 

 govern the reflection of light, being comparatively easy of detection, were stated 

 by him with tolerable correctness; but what he has written on refraction is of 

 little value. 



Ptolemy, the astronomer of Alexandria, who was born about the year 70 of 

 our era, attempted to discover the law of refraction by experiment. His appa- 

 ratus was ingenious, and was not different in principle from that which has been 

 employed by Silbermann, Soleil, and others, in our own time, for the same pur- 

 pose. He measured the angles of refraction corresponding to A'arioiis angles of 

 incidence, between 0"" and 90^, for both water and glass, and left his measure- 

 ments recorded in his System of Optics. In order that we may judge of the 

 degree of accuracy attained by him it is necessary to anticipate what is to follow, 

 so far as to define, in this place, a few technical expressions. By the angle of 

 incidrnre made by light falling upon a reflecting or refracting surface, is 

 meant the angle between the raif and {ho, perpendicular to the surface. By the 

 angle of refraction is meant the angle between the ray which has passed 

 through the surface and the same perpendicular on the other side. By the 

 angle" of reflection \& meant, in like manner, the angle between the reflected 

 rav and the perpendicular. By the plane of incidence, the plane of refraction, 

 or the plane of reflection is meant the plane which contains the incident ray 

 and the perpendicular, the refracted ray and the perpendicular, or the reflected 

 ray and the perpendicular. All these planes are coincident, except in cases 

 where double refraction takes place, when one of the planes of refraction is not 

 usually coincident Avith the corresponding plane of incidence. 



As a measure of the amount of deviation or change of direction produced in 

 a ray by refraction, the sine of any given angle of incidence is divided by the 

 sine of the corresponding angle of refraction, which latter is determined by ob- 

 servation. The quotient is constant for the same substance, no matter what be 

 the angle of incidence taken. It is called the index of refraction. The con- 

 stancy of this quotient was not known to I'tolcmy. The discovery of its con- 



