In all biaxial crystals the two _optic axes_ are inclined to each other, making what is called the _axial angle, 2V_, the apparent angle measured in air being _2E_. The optic axes lie in the plane, called the _axial plane_, which contains the principal vibration directions a and c. The axial angles are bisected by these principal vibration directions, the direction bisecting the acute angle being called the _acute bisectrix, Bx_{a}_, and that bisecting the obtuse angle the _obtuse bisectrix, Bx_{o}_. An approximate idea of the value of the axial angle can be obtained by the use of the petrographical microscope, as described later, p. 47. The axial angle is often a convenient distinction between such minerals as muscovite and biotite. The axial angle will vary with the temperature and with light of different wave-length or color, and this variation is called _dispersion_ of the optic axes. Dispersion of the principal vibration directions also takes place in monoclinic and triclinic crystals, but can be usually disregarded. In closing it is very important to remember that any section of an anisotropic crystal (not at right angles to an optic axis) will always transmit two rays of light with different velocities and with vibration directions in planes at right angles to each other. Isometric crystals, of course, produce no double refraction of light. CHAPTER II. THE PETROGRAPHICAL MICROSCOPE.[16] The _petrographical microscope_ is essentially an ordinary microscope[17] with the following important additional equipment. It must be provided with: 1° a _polarizer_ (a piece of apparatus for giving polarized light) placed below the stage; 2° an _analyzer_ (a piece of apparatus for analyzing the rays of light after they have passed through the polarizer and transparent section) placed between the objective and the eye; 3° a _stage rotating_ about an axis which is the line of sight of the microscope. A convenient type of microscope is that made by Seibert of Wetzlar (No. 11 _a_), Fig. 2. The reflector _a_ is usually fitted with a plane mirror on one side, and a parabolic mirror on the other. The plane mirror should be used with sunlight, and the parabolic mirror with artificial light, in order to make the rays of light as nearly parallel as possible. The _polarizer_ is in most cases a nicol prism, set in a suitable frame _b_, and made as follows: