42 



SCIENTIFIC THOUGHT. 



definition of the kind of motion constituting a pencil of 

 homogeneous Hght in the free ether or in atmospheric 

 air had been given by Fresnel. Experimentally the 

 velocity of a wave motion of this kind was known ; it 

 was subsequently ascertained that this speed was not 

 the same in air as in the free ether, the so-called 

 vacuum. It was also known that this speed in an 

 elastic medium, such as the ether was supposed to be, 

 depends upon the density and the rigidity of the medium. 

 But when rays of light — i.e., the wave-motions of the 

 ether — arrive at the surface of liquid or solid bodies, 

 various changes are known to take place. These changes 

 had been to some extent described and brought into 

 measurable terms by experiment, and it had been shown 

 in a general way by Huygens, and more completely by 

 Fresnel, how these observed changes of reflexion, refrac- 

 tion, and dispersion could be translated into the language 

 of the vibratory theory. Complicated and yet very elegant 

 geometrical constructions, at which Fresnel arrived by an 

 intuitive or tentative process/ enabled the course of rays 

 inside transparent, doubly-refracting substances, such as 

 crystals, to be calculated ; a whole geometry of rays was 

 developed out of these representations ; new phenomena 



^ The equation of the wave-sur- 

 face was not expHcitly given by 

 Fresnel himself. M. Verdet says 

 (' CEuvres de Fresnel,' vol. i. p. 

 Ixxv) : " Fresnel n'a pu lui-meme 

 venir a bout de ces ditficulles et n'a 

 su obtenir I'equation de la surface 

 del'onde qu'eu la supposant a priori 

 du quatrieme degre, et calculant la 

 valeur de ses coefficients de maniere 

 qu'ils satisfissent ti certaines condi- 

 tions faciles h d^duire de la con- 



sideration des ondes planes normales 

 aux trois plans de sym(5tiie du 

 milieu. Ampere est le premier qui 

 ait eSectue le calcul d'une maniere 

 rigoureuse." However, "the con- 

 struction yields the wave-surface in 

 sucli a way that its singularities 

 are not obvious, and were only I'e- 

 marked by Sir W. R. Hamilton 

 several years after Fresnel's death " 

 (Fletcher, 'The Optical Indicat- 

 rix,' p. 31). 



