KINETIC OR MECHANICAL VIEW OF NATURE. 13 



culation, to be accumulated. A real physical theory, 

 however, was impossible until the notions suggested 

 by common - sense were completely reversed, and an 

 ideal construction put in the place of a seemingly 

 obvious theory. This was done in astronomy at one 

 stroke by Copernicus ; in optics only gradually, tenta- 

 tively, and hesitatingly. The purely geometrical rela- 

 tions of straight lines, which light seemed to resemble ; 

 of pencils of rays, which were bent back or altered in 

 their direction at the surface of plane or curved mirrors 

 and of transparent bodies ; seemed to flow quite easily 

 and naturally when in the seventeenth century the 

 simple law of refraction had been added to that of 

 reflexion, known already to the ancients. The sciences 

 of catoptrics and dioptrics, with their application to the 

 telescope and microscope, were thus so complete and 

 useful that to many it must have seemed difficult and 

 unnecessary to plunge into a new theory ; 1 especially 



1 It has always been the aim of 

 " geometrical optics " to free itself 

 from every hypothesis on the physi- 

 cal nature of light, and to deduce 

 properties of light from a lew simple 

 geometrical constructions. Precisely 

 in the same way all geometrical and 

 many physical properties of the 

 stellar system can be deduced from 

 the kinematical formula of attrac- 

 tion, without discussing the nature 

 of gravitation. This desideratum 

 so far as optics is concerned 

 was before the mind of Sir W. R. 

 Hamilton, when, during the years 

 1824-33, he discovered and elabor- 

 ated the theory of the " character- 

 istic function, by the help of which 

 all optical problems, whether on the 

 corpuscular or on the undulatory 

 theory, are solved by one common 



process" (Tait, 'Light,' 2nd ed., p. 

 160). Owing to the difficulties 

 which have more and more pre- 

 sented themselves in the fundamen- 

 tal conceptions of the wave-theory 

 and the vibrating ether, of which 

 we shall learn more in the sequel of 

 this chapter, the desire to bring the 

 phenomena of refraction under a 

 purely geometrical formula, and to 

 emancipate the optics of crystals 

 from physical hypotheses, has be- 

 come very pronounced. Huygens' 

 geometrical construction of the 

 ordinary and extraordinary rays in 

 uniaxial crystals answered well. 

 For biaxial crystals Fresnel had in- 

 troduced the wave-surface, to which 

 corresponds Hamilton's character- 

 istic function. For didactic pur- 

 poses, and for the practical applica- 



