on the Undulatory Hypothesis of Light. 483 



lie on the very surface, as it were, of the true theory of double 

 refraction, is not indicated a priori by most of the rigorous theo- 

 ries which have been advanced to account for the phenomenon." 

 I am not aware that it is strictly indicated a priori by any. 



The reproach which Fresnel cast on the mathematical theory 

 of the motion of fluids I claim to have removed by my hydrody- 

 namical researches. I have shown that transverse vibrations 

 necessarily take place in a fluid the pressure of which varies as 

 its density. The problems by the solution of which this result 

 is obtained are those which, among others, I referred to in my 

 article in the October Number as having the same kind of rela- 

 tion to general theoretical physics, as the dynamical problems 

 that Newton solved to physical astronomy. Not only the theory 

 of double refraction, but the whole of the undulatory theory of 

 light, is placed on an entirely new basis by the discovery of trans- 

 verse vibrations in an elastic fluid. The explanations of the 

 phenomena of dispersion and double refraction given in this 

 communication, will, I think, convince any mathematician who 

 can be induced to give them sufficient attention, that the basis 

 of the theory must be true. It has this character of truth, that 

 it not only explains phenomena, but accounts for the failure, or 

 partial success, of previous theories. It shows that Fresnel's 

 theory was true so far as it made the double refraction depend 

 on the different apparent elasticities of the aether in different 

 directions, but failed in not sufficiently distinguishing between 

 the crystalline medium and the sether, and especially in not 

 regarding the latter as a continuous fluid. It is wholly on the 

 last account that the supporters of FresneVs views have not been 

 able to show that the usual law of refraction holds good for an 

 ordinary ray in a principal plane, nor to determine in an unam- 

 biguous manner that the direction of the transverse vibrations 

 of an ordinary ray is perpendicular to the plane of polarization 

 — two results which, as is shown above, are very simply deduced 

 from the present theory. 



As this theory has been framed in strict accordance with the 

 fundamental hypotheses of Natural Philosophy enunciated (and 

 supported by a priori reasoning) in my last communication, and 

 as it satisfactorily exemplifies in several important particulars the 

 principles there maintained, I take occasion to say, not so much 

 with the expectation of receiving credit as for the purpose of 

 expressing my conviction of the truth and necessity of the mode 

 of philosophizing I have so long advocated, that the true theory of 

 double refraction no longer remains to be discovered. The same 

 assertion may be made with respect to the theory of dispersion, 

 the two theories being so intimately connected that they stand 

 or fall together. 



Cambridge, November 18, 1863. , 



