As a consequence of Haüy’s law of rational intercepts, or, as it is more often called, the law of rational indices, it was proved by J. F. C. Hessel in 1830 that thirty-two types of symmetry are possible in crystals. Hessel’s work remained overlooked for sixty years, but the same important result was independently arrived at by the same method by A. Gadolin in 1867. At the present day, crystals are considered as belonging to one or other of thirty-two classes, corresponding with these thirty-two types of symmetry, and are grouped in six systems. More recently, theories of crystal structure have attracted attention, and have been studied as purely geometrical problems of the homogeneous partitioning of space.
The historical development of the subject is treated more fully in the article Crystallography in the 9th edition of this work. Reference may also be made to C. M. Marx, Geschichte der Crystallkunde (Karlsruhe and Baden, 1825); W. Whewell, History of the Inductive Sciences, vol. iii. (3rd ed., London, 1857); F. von Kobell, Geschichte der Mineralogie von 1650-1860 (München, 1864); L. Fletcher, An Introduction to the Study of Minerals (British Museum Guide-Book); L. Fletcher, Recent Progress in Mineralogy and Crystallography [1832-1894] (Brit. Assoc. Rep., 1894).
I. CRYSTALLINE FORM
The fundamental laws governing the form of crystals are:—
1. Law of the Constancy of Angle.
2. Law of Symmetry.
3. Law of Rational Intercepts or Indices.
According to the first law, the angles between corresponding faces of all crystals of the same chemical substance are always the same and are characteristic of the substance.
(a) Symmetry of Crystals.
Crystals may, or may not, be symmetrical with respect to a point, a line or axis, and a plane; these “elements of symmetry” are spoken of as a centre of symmetry, an axis of symmetry, and a plane of symmetry respectively.