102 HISTORY OF OPTICS. 



Young's first published statement of tlie doctrine of transverse vibra- 

 tions was given in the explanation of the phenomena of dipolarization, 

 of which we shall have to speak in the next Section. But the primary 

 and immense value of this conception, as a step in the progress of the 

 undulatory theory, was the connexion which it established between 

 polarization and double refraction ; for it held forth a promise of 

 accounting for polarization, if any conditions could be found which 

 might determine what was the direction of the transverse vibrations. 

 The analysis of these conditions is, in a great measure, the work of 

 Fresnel ; a task performed with profound philosophical sagacity an ;1 

 great mathematical skill. 



Since the double refraction of uniaxal crystals could be explained by 

 undulations of the form of a spheroid, it Avas perhaps not difficult to 

 conjecture that the undulations of biaxal crystals would be accounted 

 for by undulations of the form of an ellipsoid, which differs from the 

 spheroid in having its three axes unequal, instead of two only ; and 

 consequently has that very relation to the other, in respect of symme- 

 try, which the crystalline and optical phenomena have. Or, again, 

 instead of supposing two different degrees of elasticity in different 

 directions, we may suppose three such different degrees in directions at 

 right angles to each other. This kind of generalization was tolerably 

 obvious to a practised mathematician. 



But what shall call into play all these elasticities at once, and pro- 

 duce waves governed by each of them ? And what shall explain the 

 different polarization of the rays which these separate waves carry with 

 them ? These were difficult questions, to the solution of which mathe- 

 matical calculation had hitherto been unable to offer any aid. 



It was here that the conception of transverse vibrations came in, 

 like a beam of sunlight, to disclose the possibility of a mechanical con- 

 nexion of all these facts. If transverse vibrations, travelling through a 



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uniform medium, come to a medium not uniform, but constituted so 

 that the elasticity shall be different in different directions, in the man- 

 ner we have described, what will be the course and condition of the 

 waves in the second medium ? Will the effects of such waves agree 



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with the phenomena of doubly-refracted light in biaxal crystals ? 

 Here was a problem, striking to the mathematician for its generality 

 and difficulty, and of deep interest to the physical philosopher, because 

 the fate of a great theory depended upon its solution. 



The solution, obtained by great mathematical skill, was laid before 

 'he French Institute by Fresnel in November, 1821, and was carried 



