242 FRESXEL ON DOUBLE REFRACTION. 



happily represented the movement of extraordinary rays in uni- 

 axal crystals, has led us to the discovery of the true laws of 

 double refraction in the general case of bi-axal crystals. Un- 

 doubtedly an important part of these laws was already known ; 

 Sir David Brewster and M. Biot, by numerous observations and a 

 skilful use of analogy, had already succeeded in discovering the 

 law of the direction of the planes of polarization of the two 

 beams and of their difference of velocity ; but they were mistaken 

 with regard to their absolute velocities, in supposing that of the 

 ordinary ray to remain constant, as in uni-axal crystals. The 

 experiments made by M. Biot on topaz to verify this hypothesis, 

 had not presented to him any sensible difference in the refraction 

 of the ray termed " ordinary ;" but we are no longer surprised 

 that these variations escaped the attention of so accurate an 

 observer, when it is known how small they are in almost all 

 directions except those in which they attain their maximum, and 

 which could not be indicated but by theory or a lucky chance. 



The mechanical considerations on the nature of luminous 

 vibrations and the constitution of doublj' refracting media, which 

 I have set forth in the Annales de Chimie et de Physique, tom. 

 xvii. p. 179 et seq., have enabled me at the same time to explain 

 the changes of the extraordinary refraction and the constant 

 velocity of the ordinary ray in uni-axal crystals. 



I soon perceived that the reason which I had assigned to my- 

 self for the uniformity of the velocity of the ordinary ray in uni- 

 axal crystals was not applicable to crystals with two axes ; and, 

 constantly following the same theoretical views, I perceived that 

 in these latter neither of the two rays ought to be subject to the 

 laws of ordinary refraction. This is exactly what I verified by 

 experiment, a month after having announced it to M. Arago. 

 I did not indeed present to him this result of my reflections as a 

 thing certain, but as a consequence of my theoretical views so 

 necessary, that I should be obliged to abandon them if experi- 

 ment did not confirm this singular character of double refraction 

 in bi-axal crystals. The theory did not announce to me in a 

 vague manner the variations of velocity of the ordinary ray ; it 

 gave me the means of deducing their extent from the elements 

 of double refraction of the crystal, that is to say, from its degree 

 of energy and the angle between the two axes. I had made 

 beforehand this calculation for limpid topaz, according to data 

 derived from the observations of M. Biot. The experiment 



