INTRODUCTION. II 
4 
upper Nicol or analyzer be turned about 90°, the field of the microscope will become 
light, because the light passing through the lower Nicol or polarizer passes through 
the analyzer, also, under the same conditions. If now, again, the amorphous section 
is introduced, the field will be still light. In general, place the Nicols as we will, the 
light will not be modified by placing an amorphous substance between them. More- 
over, an amorphous substance shows no definite cleavage lines, or no crystalline out- 
line. In New Hampshire we live in a region of old crystalline rocks; and hence, with 
some rare exceptions, we have but little to deal with amorphous substances. 
Isometric Crystals. Isometric crystals being developed symmetrically in each of 
their three directions, the elasticity of the ether is the same in all directions; and 
hence, in isometric crystals, light passes in all directions and planes with equal ease, 
and this gives to them the same optical character as amorphous substances. Isometric 
bodies in their sections can, however, commonly be recognized as crystals, since they 
generally possess either a definite polygonal outline or cleavage lines. These bodies, 
which possess simply the power of single refraction, are called isotropic. 
Tetragonal and Hexagonal Crystals. The case becomes quite different when any 
other body except those mentioned is placed between the Nicol prisms. Tetragonal 
and hexagonal crystals are not symmetrical in all directions; and hence the elasticity 
of the ether is different in different directions. It is either greater or less in the plane 
of the vertical axis than it is in the plane of the lateral axes; and, if a beam of light 
passes through a section of one of these crystals, which is cut parallel to the vertical 
axis, its vibrations will, in passing through the crystal, take place in these planes of 
elasticity ; and, as the elasticity is greater in one direction than the other, that part of the 
ray, the vibrations of which take place in the plane of greater elasticity, will be retarded 
less than those that take place in the plane of least elasticity, which is at right angles 
to the first; hence the ray of light will emerge from the crystal having all its vibrations 
reduced to two planes, and one of these sets of vibrations will be in advance of the 
other by a certain amount, depending upon the nature of the substance and the thick- 
ness of the section. In other words, the crystal in this direction is double refracting ; 
and the law may here be stated, that the light, by its entrance into any double refract- 
ing section, is divided into two rays, each of which is polarized. The planes of vi- 
bration of these rays are at right angles to one another; and these planes corre- 
spond to the directions of the greatest and least elasticity of the ether in the section. 
Let us now suppose such a section to be introduced into the field of the microscope 
while the Nicol prisms are crossed. If we place it so that the vertical axis of the crystal 
is parallel to the plane of vibration of the light as it issues from the lower Nicol, the 
light will pass through the crystal without further modification, since the plane of 
greatest or least elasticity in the crystal section corresponds with the plane of vibration 
of the light; and, as the light meets the crystal in one of the two planes in which it 
can pass, the crystal does not alter it, and it is therefore, as before, cut off by the upper 
Nicol, and the field remains dark. If, now, we revolve the table of the microscope a little, 
so that the principal axis of the crystal does not correspond with the plane of vibration 
