FRESNEL ON DOUBLE REFRACTION. 329 



axes. Hence the theory announced that the ordinary beam must 

 traverse the crystal, successively along the direction which 

 bisects the obtuse angle between the two axes, and perpen- 

 dicularly to their plane, in order to undergo the most perceptible 

 variations of velocity ; and in accordance with this indication it 

 was that I made the first experiment, by which 1 have proved 

 the existence of these variations. 



I have also in my experiments particularly endeavoured to 

 assure myself that the velocity of propagation of luminous waves 

 depends solely on the direction of their vibrations, or on the 

 plane of polarization in the crystal ; and that so long as this 

 plane does not change, the velocity of the rays remains constant, 

 whatever moreover may be their direction. Diffraction afforded 

 me very delicate methods for perceiving the slightest differences 

 of velocity. In truth, topaz is the only crystal on which I have 

 operated as yet; but I have sufficiently varied and multiplied 

 my observations to assure myself at least that this theorem is 

 rigorously exact in topaz ; and it must be supposed by analogy 

 that it is equally true for all other bi-axal crystals. Besides, 

 without giving a complete demonstration of it, the mechanical 

 considerations which I have set forth on this subject establish in 

 its favour very strong theoretical probabilities. 



Reflections on the probabilities presented by the Theory 

 explained in this Memoir. 

 The theorem which I have given, so admissible from its very 

 simplicity, the mechanical definition of luminous vibrations de- 

 duced from the laws of interference of polarized rays, and the 

 supposition that the homologous lines of crystallization are 

 parallel throughout the whole extent of the refracting media 

 which we have considered, are the three hypotheses, I might 

 say the three principles, on which rests the theory of double 

 refraction set forth in this memoir. If we had only to calculate 

 one phaenomenon, such as that of interferences, which depends 

 solely on the nature of luminous vibrations, their dafinition 

 would have sufficed for the explanation of the facts. But double 

 refraction being the consequence of a particular constitution of 

 the refracting medium, it was absolutely necessary to define this 

 constitution, embodying however in the definition only that 

 which was necessary for the explanation of the phaenomenon. 



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