300 On Double Refraction. 
rectangular axes. In uniaxal crystals, the three axes A, 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 different 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 thi 
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 more 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, ane aa 
shall have an axis of compression along C, or an axis of positive 
double refraction as in quartz and dioptase.t| 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 different name yer 
and B. In biaxal crystals, any two axes A, B, may be converted into three, At? 
curious result of his experiments, that the axis of calcareous spar, @ esi 
axis of double refraction, is the axis of least elasticity, while the axis of se ‘ 
xis of positive double refraction, is the axis of greatest elasticity, hat — 
remarkable manner with the above views. 
