446. This polarization of the fluid passes in every direction; for every polar point is polar all around. Thus a spherical portion of the fluid is polarized round about the point. The fixable parts are spheroidally attracted and gather together from all sides around the point. For were the polarization not to traverse the whole mass, but only according to individual lines, the crystal must then indeed be jagged or indented.
447. In this manner the crystal would have been a globe, from the fixable particles lying together in distinct points, after the manner of pulp. But this is impossible, because the point of starting or departure is differently polarized to the fluidity, being negative according to observation. Every polar process does not operate in continuity, so that one end of the line should be purely positive, the other, however, purely negative; but every polar line is an infinity of poles, where, however, at one end the positive character only, at the other the negative preponderates. Such a line is e. g. as follows, + - + - + -, which begins with + and ends with-; it therefore has a preponderance of + at one end, of-at the other, and yet is both everywhere. By this infinity of polar change the fixable particles range themselves behind each other, while they separate from each other to an infinitely minute degree; these parts polarized behind each other are lines or fibres. Every crystal must accordingly consist of fibres; none possesses an homogeneous or pultaceous structure.
448. In the crystal one principal direction of polarization originates, which is effected by the antagonism of the point of crystallization with the fluid mass. It gives the direction of the crystal and its energy gives the length. This principal line consists of two poles that recede from each other, and these determine the two ends of the crystal, which are always similar, provided no mechanical obstacle be interposed.
449. From each of the mutually seceding poles lines of polarization issue at definite angles, which (like elliptical radii on the periphery) meet at the sides of the newly produced crystal. Then again between these radii tension arises, so that the fibres become lamellæ. The main line between the two mutually seceding poles is the central line or polar axis of the crystal; the angular lines which determine the position of the lamellæ, are the polar radii. The polar radii determine the nucleus of the crystal and are therefore nuclear lines; the polar axis determines the whole of the crystal, is the crystal, the central-line, and determines the form in general, or what has been called the secondary form.
450. Since all polar activities operate only in a straight line, there can thus be no globular crystal. Water is only susceptible of assuming the globular form upon a large as well as a small scale, because there are no fixed poles in it. The nucleus does not originate previous to the secondary form; since it is verily impossible for the polar rays to originate without a polar axis.
451. There are no actual degradations in the genesis of the crystal; they are only a mathematical expression for the finished form of the crystal.
452. The number of possible or actual nuclei is definite. They are based upon the combination of the laws of the globe with those of the polarity.
453. The simplest angular body must be circumscribed by at least four surfaces, and thus be a tetrahedron.
454. The fundamental nucleus of crystals is, however, the double tetrahedron or the hexahedron, namely the trilateral double-pyramid; for radii do not proceed simply from the point of commencement, but also from the extremities of the axis. When the superior and inferior radii meet, they must form a double-tetrahedron. The disposition to this form has been implanted in all crystals. If the nucleus becomes no such hexahedron, the aberration from, still admits of being referred to, the hexahedron.
455. There is no prismatic nucleus. The columns and parallelopiped nuclei are only mutilations.