INTRODUCTION. 13 
tion mica plate, the positive or negative character of uniaxial and biaxial crystals can be 
easily determined. This is an advantage for those who, on account of limited means, 
can possess but little apparatus; for, where, with a little trouble, an instrument can be 
so easily arranged, which will serve as a microscope, a stauroscope, and for the exami- 
nation with parallel and convergent polarized light, but little more is needed for optical 
study. Itis of course understood that crystals must have some size, in order to be 
thus studied. The optical properties of the minutest crystals can often be seen in the 
+ microscope; but when the ocular is removed, its magifying power is destroyed. 
The peculiarities of the hexagonal and tetragonal systems may then be summed up - 
to be, that all sections, except basal, when revolved in a horizontal plane on the stage 
of the microscope, the Nicols being crossed, are alternately dark and colored, being 
dark when the vertical axis corresponds with the plane of vibration of either Nicol, 
while basal sections are dark in all positions between the crossed Nicol prisms, save 
when examined by convergent light, when they exhibit a ring system traversed by a 
black cross. The tetragonal and hexagonal systems are distinguished from each other 
by the outline of the basal sections: tetragonal crystals having four or eight sides, 
while hexagonal crystals have some multiple of three as the number of their sides. 
-Orthorhombic Crystals. As the dimensions of orthorhombic crystals are different in 
all three directions, so the elasticity of the ether is different in each direction; yet 
orthorhombic crystals are so built that the axes of elasticity, and consequently the 
planes of vibration of the light as it passes through them, correspond with the crys- 
tallographic axes ; that crystallographic axis, in the direction of which the elasticity of 
the ether is greatest, is the direction of the axis of greatest elasticity; another corre- 
sponds to the direction of least elasticity ; and a third corresponds to the direction of 
mean elasticity. Hence the light, as it enters the section of an orthorhombic crystal 
cut in any direction, is broken and doubly refracted, and passes through the section in 
two sets of vibrations at right angles to one another, corresponding to the directions 
of greatest and least elasticity of the section; and these directions correspond with 
the directions which the crystallographic axes take through the section. 
If, now, any section of an orthorhombic crystal be brought into the field of the micro- 
scope between crossed Nicol prisms, whenever the direction of a crystallographic axis, 
as shown by the side of the prism or determined by the cleavage, is brought to corre- 
spond with the plane of vibration of the light, the section will remain dark, but will be 
colored when revolved away from this position, becoming dark again when it has been 
revolved go°. 
It is to be noted, however, that there are two directions through every crystal, with 
three different axes of elasticity, in which the two sets of vibrations, taking place at 
right angles to one another, have equal intensity. These directions lie in the plane of 
the greatest and least elasticity, and are called the optic axes; and, as there are two 
such directions, such crystals are called biaxial. If, now, a section be cut perpen- 
dicular to one of these axes, it is plain that, in parallel light, it will appear like an 
isotropic body. No interference of light will take place when it is placed between 
