EPOCH OF YOUNG AXD FEESXEL. 105 



These investigations were published 14 in 1821. In succeeding years 

 Fresnel undertook to extend the application of his formulae to a case in 

 which they ceased to have a meaning, or, in the language of mathema- 

 ticians, became imaginary ; namely, to the case of internal reflection 

 at the surface of a transparent body. It may seem strange to those 

 who are not mathematicians, but it is undoubtedly true, that in many 

 cases in which the solution of a problem directs impossible arithmetical 

 or algebraical operations to be performed, these directions may be so 

 interpreted as to point out a true solution of the question. Such an 

 interpretation Fresnel attempted 15 in the case of which we now speak; 

 and the result at which he arrived was, that the reflection of light 

 through a rhomb of glass of a certain form (since called Fresncl's 

 rhomb], would produce a polarization of a kind altogether different 

 from those which his theory had previously considered, namely, that 

 kind which we have spoken of as circular polarization. The com- 

 plete confirmation of this curious and unexpected result by trial, is 

 another of the extraordinary triumphs which have distinguished the 

 history of the theory at every step since the commencement of Fres- 

 nel's labors. 



But anything further which has been done in this way, may be 

 treated of more properly in relating the verification of the theory. 

 And we have still to speak of the most numerous and varied class of 

 facts to which rival theories of light were applied, and of the establish- 

 ment of the undulatory doctrine in reference to that department ; I 

 mean the phenomena of depolarized, or rather, as I have already said, 

 rf/polarized light. 



Sect. 5. Explanation of Dipolar ization by the Undulatory Theory. 



WHEN- Arago, in 1811, had discovered the colors produced by pola- 

 rized light passing through certain crystals, 16 it was natural that 

 attempts should be made to reduce them to theory. M. Biot, ani- 

 mated by the success of Mains in dUecting the laws of double refrac- 

 tion, and Young, knowing the resources of his own theory, were the 

 first persons to enter upon this undertaking. M. Biot's theory, though 

 in the end displaced by its rival, is well worth notice in the history of 

 the subject. It was what he called the doctrine of moveable polariza- 

 tion. He conceived that when tho molecules of light pass through 



An. CJd,n. t. xvii. I5 Bullet, des Sc. Feb. 1S2S. 1G See chap. ix. 



