300 On Douhh Refraction. 



rectangular axes. In imiaxal crystals, the three axes x\, B, C, must 

 be such that two of them are equal and of the same name ; while 

 the third, corresponding with the apparent axis, may be of the same 

 or of a dlfFerent name. In biaxal crystals, the three axes A, B, C, 

 are unequal, and in crystals with no double refraction the axes are 

 equal and destroy each other.* 



This approximation of these two classes of facts is too remarkable 

 to be accidental, and would go far to establish their dependence, 

 even if it were not indicated by other arguments which I shall pro- 

 ceed to illustrate. 



Among those crystals which have the obtuse rhomboid for their 

 primitive form, there are many with one axis of negative double re- 

 fraction, and only one or two with one axis of positive double refrac- 

 tion. In the former, the negative doubly refracting structure will be 

 produced round the axis of the rhombohedron by the compression 

 arising from attractions in the direction of two equal rectangular axes 

 A, B, which will dilate the molecules in the direction of the third 

 axis C, and make it a negative axis of double refraction, equal in 

 intensity to either of the other two. Here we require the combina- 

 tion only of two axes ; but if we suppose that there is in the direc- 

 tion of C a third axis of attraction either niore or less powerful than 

 the other two, then if it is less powerful, the compression of the 

 molecules produced by it will diminish the dilatation arising from the 

 united action of A and B, but will still leave an unbalanced dilata- 

 tion, or a single negative axis of double refraction in the axis of the 

 rhomb. 



If C, on the contrary, is an axis in which the attractive force of 

 the molecules is greater than along A and B, the compression which 

 it produces will exceed the dilatation arising from A and B, and we 

 shall have an axis of compression along C, or an axis of positive 

 double refraction as in quartz and dioptase.f The same observations 

 are applicable to minerals that crystallize in the pyramidal form. 



* In uniaxal crystals, the resultant of the two equal axes A, B, may have any 

 relation to C but that of equality ; excepting when C is of a ditfeient name from A 

 and B. In biaxal crystals, any two axes A, B, may be converted into three, A + C, 

 B±C, +C. See Phil. Trans. 1818. 



t Since this paper was written, I have seen the very valuable researches of M. 

 Savart on the structure of crystallized bodies as developed by sonorous vibrations. 

 The curious result of his experiments, that the axis of calcareous spar, a negative 

 axis of double refraction, is the axis of least elasticity, while the axis of quartz, an 

 axis of positive doable refraction, is the axis of greatest elasticity, harmonizes in a 

 remarkable manner with the above views. 



