104 HISTOKY OF OPTICS. 



\vhat mode of vibration constituted polarization, that I caught sight of 

 the mechanical causes of double refraction." 



Having thus got possession of the principle of the mechanism of 

 polarization, Fresnel proceeded to apply it to the other cases of polar- 

 ized light, with a rapidity and sagacity which reminds us of the spirit 

 in which Newton traced out the consequences of the principle of uni- 

 versal gravitation. In the execution of his task, indeed, Fresnel was 

 forced upon several precarious assumptions, which make, even yet, a 

 wide difference between the theory of gravitation and that of light. 

 But the mode in which these were confirmed by experiment, compels 

 us to admire the happy apparent boldness of the calculator. 



The subject of polarization by reflection was one of those which 

 seemed most untractable ; but, by means of various artifices and con 

 jectures, it was broken up and subdued. Fresnel began with the sim- 

 plest case, the reflection of light polarized in the plane of reflection ; 

 which he solved by means of the laws of collision of elastic bodies. 

 He then took the reflection of light polarized perpendicularly to this 

 plane ; and here, adding to the general mechanical principles a hypo- 

 thetical assumption, that the communication of the resolved motion 

 parallel to the refracting surface, takes place according to the laws of 

 elastic bodies, he obtains his formula. These results were capable of 

 comparison with experiment ; and the comparison, when made by M. 

 Arago, confirmed the formulae. They accounted, too, for Sir D. Brews- 

 ter's law concerning the polarizing angle (see Chap, vi.) ; and this 

 could not but be looked upon as a striking evidence of their having 

 some real foundation. Another artifice which MM. Fresnel and Arago 

 employed, in order to trace the effect of reflection upon common light, 

 was to use a ray polarized in a plane making half a right angle with 

 the plane of reflection ; for the quantities of the oppositely 13 polarized 

 light in such an incident ray are equal, as they are in common light ; 

 but the relative quantities of the oppositely polarized light in the 

 reflected ray are indicated by the new plane of polarization ; and thus 

 these relative quantities become known for the case of common light. 

 The results thus obtained were also confirmed by facts ; and in this 

 manner, all that was doubtful in the process of Fresnel's reasoning, 

 seemed to be authorized by its application to real cases. 



13 It will be recollected all along, that oppositely polarized rays arc those 

 wliich are polarized in two planes perpendicular to each other. See above. 



;-hap. vi. 



