10 MINERALOGY AND LITHOLOGY. 
scope, any angle of a crystal section can be measured by bringing first one and then 
the other side of the angle in coincidence with the one of the lines. The angle of 
revolution is read off upon the graduated circle that is made upon the outer edge of 
the disc-formed stage. Angles can be rudely measured by a Leeson’s goniometer, or 
by projecting the image on a sheet of paper, with a camera, and drawing it, and meas- 
uring the angle with an ordinary arc of a circle. 
Cleavage. One of the most valuable aids in determining a species is the cleavage 
that minerals show in sections. Minerals that possess characteristic cleavage always 
show it; for, if it does not exist in microscopic lines originally, it is certain to be de- 
veloped by the process of grinding. For example: hornblende and augite are easily 
distinguished by their cleavage; for, as the cleavages of hornblende parallel to the 
faces of the prism cross one another at 124°, the corresponding cleavages in augite 
cross one another at a right angle. It is plain that augite might be so cut as to givea 
section with an obtuse cleavage angle; but, as there are commonly some sections that 
show the relationship of the section to the form of the crystal, and as there is much 
difference in the ease and perfection of the cleavage of the two minerals, this feature is 
very valuable. In other cases, such as in the micas, the observation of the perfect 
cleavage is equivalent to a determination. Its almost entire absence, as in the case 
of olivine, is well-nigh as valuable for the identification of a species. 
Optical Properties. When a beam of light passes from a lighter into a denser me- 
dium, it is broken or refracted, but, when it enters a non-crystalline body in which the 
particles are arranged about no definite lines, it proceeds on its course with no further 
modification than an alteration of direction. Such bodies are called single refracting 
bodies ; but crystalline bodies, being formed and held together by certain forces that 
have acted in certain definite directions, allow the light to pass through them, accord- 
ing to certain laws which are dependent on the structure of the crystal. These laws 
are very simply applied in the examination of microscopic sections; and by their aid 
the determination of the crystalline system to which a substance belongs is made easy. 
The optical principles, as applied to the examination of sections of minerals of the 
different systems, as seen under the microscope, are as follows: 
Amorphous Bodies. It has been stated, that for examination of sections, it is neces- 
sary to have a Nicol prism above and one below the stage, so arranged that the planes 
of vibration of the polarized rays that pass through them can be fixed in any given direc- 
tion. Suppose the planes of these two prisms to stand at right angles to one another, 
and to correspond with the spider lines in the ocular of the microscope: the light which 
passes through the lower Nicol will be reduced to a plane, and this plane will correspond 
with that plane in the upper Nicol in which light is totally reflected in passing through 
it. Hence, on looking into the microscope when thus arranged, the field of the micro- 
scope will be dark, since the light which passes through the first Nicol is cut off by the 
second. If, now, the section of any amorphous substance be introduced into the field 
of the microscope, it having no structural arrangement, cannot modify the plane of the 
light, and consequently the field of the microscope will remain dark. If, now, the 
