74 DOUBLE REFRACTION. 



is therefore probable that the density of the crystal is un- 

 equal in all the three directions. Such crystals are found to 

 have two optic axes. 



It has been stated that in uniaxal crystals the optic axis 

 is also the axis of form. In biaxal crystals, it did not at first 

 appear that the optic axes were in any manner related to the 

 lines which bound the elementary crystal. Sir David Brew- 

 ster, however, ascertained that if two lines be taken, one bi- 

 secting the acute, and the other the obtuse angle contained 

 by the optic axes, these (together with a third line at right 

 angles to both) are closely connected with the primitive 

 form. 



These relations between the optical properties of crystals 

 and their external forms are so close and intimate, that any 

 change (however produced) in one of them, is found to be 

 accompanied by a corresponding change in the other. Thus, 

 if the form of a crystal be altered by mechanical compression, 

 or change of temperature, its refracting properties undergo a 

 corresponding change. 



(94) It was long supposed that one of the refracted rays, 

 in every crystal, followed the ordinary law of the sines, while 

 the other was refracted according to the Huygenian law. 

 But Fresnel has proved, both from theory and by experiment, 

 that this is not the gase, and that in biaxal crystals, both rays 

 are refracted in an extraordinary manner, and according to a 

 new law. It is, in fact, a consequence of his beautiful theory 

 of double refraction, that the form of the wave, which is 

 propagated in the interior of such a crystal, is neither a 

 sphere nor spheroid, as in uniaxal crystals, but a curved 

 surface of the fourth order. This surface is composed of two 

 sheets ; and if tangent planes be drawn to these, after the 

 same manner as to the sphere and spheroid in the Huyge- 

 nian law, the points of contact determine the directions of 



