42 SCIENTIFIC THOUGHT. 



definition of the kind of motion constituting a pencil of 

 homogeneous light 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, 1 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 



1 The equation of the wave-sur- sideration des ondes planes normales 



face was not explicitly given by : aux trois plans de syme"trie du 



Fresnel himself. M. Verdet says ; milieu. Ampere est le premier qui 



('CEuvres de Fresnel,' vol. i. p. ait effectue le calcul d'uue maniere 



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

 venir a bout de ces difficulty's et n'a 

 su obtenir 1'equation de la surface 

 de 1'oude qu'eu la supposant a priori 

 du quatrieme degre, et calculaut la 



rigoureuse." However, "the con- 

 struction yields the wave-surface in 

 such a way that its singularities 

 are not obvious, and were only re- 

 marked by Sir W. R. Hamilton 



valeur de ses coefficients de maniere ! several years after Fresuel's death " 

 qu'ils satisfissent h certaines condi- , (Fletcher, ' The Optical Indicat- 

 tions faciles a de"duire de la con- I rix,' p. 31). 



