108 HISTORY OF OPTICS. 



so that no new property is needed. Polarization for a moment 



us : but not lono- ; for the direction of our vibrations is hitherto arbi- 



' O ' 



trary ; we allow polarization to decide it. Having done this for 

 the sake of polarization, we find that it also answers an entirely dif- 

 ferent purpose, that of giving the law of double refraction. Truth 

 may give rise to such a coincidence ; falsehood cannot. But the 

 phenomena become more numerous, more various, more strange; no 

 matter: the Theory is equal to them all. It makes not a single new 

 physical hypothesis ; but out of its original stock of principles it 

 educes the counterpart of all that observation shows. It accounts for, 

 explains, simplifies, the most entangled cases ; corrects known laws 

 and facts ; predicts and discloses unknown ones ; becomes the guide 

 of its former teacher, Observation; and, enlightened by mechanical 

 conceptions, acquires' an insight which pierces through shape and 

 color to force and cause. 



We thus reach the philosophical moral of this history, so important 

 in reference to our purpose ; and here we shall close the account of 

 the discovery and promulgation of the undulatory theory. Any 

 further steps in its development and extension, may with propriety be 

 noticed in the ensuing chapters, respecting its reception and verifica- 

 tion. 



[2nd Ed.] [In the Philosophy of the Inductive Sciences, B. xi. ch. 

 iii. Sect. 11, I have spoken of the Consilience of Inductions as one of 

 the characters of scientific truth. We have several striking instances 

 of such consilience in the history of the undulatory theory. The phe- 

 nomena of fringes of shadows and colored bands in crystals jump 

 tor/ether in the Theory of Vibrations. The phenomena of polarization 

 and double refraction jump together in the Theory of Crystalline 

 Vibrations. The phenomena of polarization and of the interference 

 of polarized rays jump together in the Theory of Transverse Vibrations. 



The proof of what is above said of the undulatory theory is con- 

 tained in the previous history. This theory has " accounted for, ex- 

 plained, and simplified the most entangled cases ;" as the cases of fringes 

 of shadows ; shadows of gratings ; colored bands in biaxal crystals, and 

 in quartz. There are no optical phenomena more entangled than these. 

 It has " corrected experimental laws," as in the case of M. Biot's law 

 of the direction of polarization in biaxal crystals. It has done this, 

 %< without making any new physical hypothesis ;" for the transverse 

 direction of vibrations, the different optical elasticities of crystals in 

 different directions, aid (if it be adopted) the hypothesis of finite 



