Medium, according to the Principles of Fresnel. 13 



QOq. Taking, therefore, OT and V equal to OQ and OB, the 



locus of F^will evidently be the circle BOB ; and the locus of 

 T will be the ellipse A' Off, since the angle ffOT' is equal to 

 the angle BOQ. 



In the general case, OT and V, which are equal to OQ and 

 Oq, represent the velocities of the two different sorts of rays 

 having a common direction in the crystal ; and two right lines, 

 which lie in the plane of the greatest and least axes of the ellip- 

 soid, and are perpendicular to its two circular sections, are 

 called the optic axes. It appears, therefore, by the 6th Lemma, 

 that the difference of the squares of the reciprocals of the velo- 

 cities of the two rays, having a common direction in the crystal, 

 is proportional to the product of the sines of the angles which 

 that direction makes with the optic axes. This is the celebrated 

 law of M. Biot, to which he was led by analogy, and which he 

 afterwards found to agree with that previously laid down by 

 Dr. Brewster. 



Such, in their simplest form, are the principal features of the 

 Mechanical Theory of Double Refraction, invented by the late 

 M. Fresnel a theory which would do honour to the sagacity of 

 Newton, and which gives us ample reason to regret that the life 

 of its author was not longer spared, to enrich with further dis- 

 coveries his favourite science. Of him it may be said, as New- 

 ton said of Cotes and apparently with much greater reason 

 that if he had lived longer, we should have known something at 

 last of the laws of nature. 



