PHYSICS OF THE NINETEENTH CENTURY. LIGHT. 475 



presented with necessarily imperfect accounts of every discovery made 

 by Fresnel, Arago, Biot, Brewster, and others. The phenomena pre- 

 sented by polarized light are extremely interesting and varied, and it 

 is the glory of the undulatory theory to supply a consistent explana- 

 tion of facts so numerous and diverse. To fully exhibit the correspon- 

 dence between these facts and the theory would require the use of 

 mathematics of an order far beyond the due range of a popular work. 

 The power and fertility of the undulatory theory cannot be more 

 strikingly illustrated than by the verification of an a priori and highly 

 elaborate deduction from the theory, by direct observation of the cor- 

 responding previously unsuspected fact. Professor Tyndall, in his 

 " Notes on Light," has so felicitously compared the discovery alluded 

 to with the discovery of Neptune (page 423), that we take the liberty 

 of quoting the passage. 



" You regard, and justly so, the discovery of Neptune as a triumph 

 of theory. Guided by it, Adams and Leverrier calculated the position 

 of a planetary mass competent to produce the disturbances of Uranus. 

 Leverrier communicated the result of his calculation to Galle of Berlin, 

 and that same night Galle pointed the telescope of the Berlin Obser- 

 vatory to the portion of the heavens indicated by Leverrier, and found 

 there a planet 36,000 miles in diameter. It so happens that the un- 

 dulatory theory has also its Neptune. Fresnel had determined the 

 mathematical expression for the wave-surface in crystals possessing 

 two optic axes ; but he did not appear to have an idea of any refrac- 

 tion in such crystals other than double refraction. While the subject 

 was in this condition, the late Sir William Hamilton, a profound 

 mathematician, took it up, and proved the theory to lead to the con- 

 clusion that at four special points of the wave-surface the ray was 

 divided not into two parts but into an infinite number of parts, forming 

 at those points a continuous conical envelope instead of two images. 

 No human eye had ever seen this envelope when Sir William Hamilton 

 inferred its existence. If the theory of gravitation be true, said Le- 

 verrier in effect to Dr. Galle, a planet ought to be there ; if the theory 

 of undulation be true, said Sir William Hamilton to Dr. Lloyd, my 

 luminous envelope ought to be there. Lloyd took a crystal of arra 

 gonite, and following with the most scrupulous exactness the indica- 

 tions of theory, discovered the envelope which had previously been 

 an idea in the mind of the mathematician. Whatever may be the 

 strength which the theory of gravitation derives from the discovery of 

 Neptune, it is matched by the strength which the undulatory theory 

 derives from the discovery of conical refraction." 



