An important distinction separates true mixed crystals and crystallized double salts, for in the latter the properties are not linear functions of the properties of the components; generally there is a contraction in volume, while the refractive indices and other physical properties do not, in general, obey the additive law.

Isomorphism is most clearly discerned between elements of analogous chemical properties; and from the wide generality of such observations attempts have been made to form a classification of elements based on isomorphous replacements. The following table shows where isomorphism may be generally expected. The elements are arranged in eleven series, and the series are subdivided (as indicated by semicolons) into groups; these groups exhibit partial isomorphism with the other groups of the same series (see W. Nernst, Theoretical Chemistry).

Series 1. Cl, Br, I, F; Mn (in permanganates). 2. S, Se; Te (in tellurides); Cr, Mn, Te (in the acids H2RO4); As, Sb (in the glances MR2). 3. As, Sb, Bi; Te (as an element); P, Vd (in salts); N, P (in organic bases). 4. K, Na, Cs, Rb, Li; Tl, Ag. 5. Ca, Ba, Sr, Pb; Fe, Zn, Mn, Mg; Ni, Co, Cu; Ce, La, Di, Er, Y, Ca; Cu, Hg, Pb; Cd, Be, In, Zn; Tl, Pb. 6. Al, Fe, Cr, Mn; Ce, U (in sesquioxides). 7. Cu, Ag (when monovalent); Au. 8. Pt, Ir, Pd, Rh, Ru, Os; Au, Fe, Ni; Sn, Te. 9. C, Si, Ti, Zr, Th, Sn; Fe, Ti. 10. Ta, Cb (Nb). 11. Mo, W, Cr.

For a detailed comparison of the isomorphous relations of the elements the reader is referred to P. von Groth, Chemical Crystallography. Reference may also be made to Ida Freund, The Study of Chemical Composition; and to the Annual Reports of the Chemical Society for 1908, p. 258.

Bibliography.—History: F. Hoefer, Histoire de la chimie (2nd ed., 1866-1869); Hermann Kopp, Geschichte der Chemie (1869), Entwickelung der Chemie in d. neueren Zeit (1871-1874); E. von Meyer, Geschichte der Chemie (3rd ed., 1905, Eng. trans.); A. Ladenburg, Entwickelungsgeschichte der Chemie (4th ed., 1907); A. Stange, Die Zeitalter der Chemie (1908). Reference may also be made to M.M. Pattison Muir, History of Chemical Theories and Laws (1907); Ida Freund, Study of Chemical Composition (1904); T.E. Thorpe, Essays in Historical Chemistry (2nd ed., 1902). See also the article [Alchemy].

Principles and Physical.—W. Ostwald, Principles of Inorganic Chemistry (3rd Eng. ed., 1908), Outlines of General Chemistry, Lehrbuch der allgemeinen Chemie; W. Nernst, Theoretische Chemie (4th ed., 1907, Eng. trans.); J.H. van’t Hoff, Lectures on Theoretical and Physical Chemistry; J. Walker, Introduction to Physical Chemistry (4th ed., 1907); H.C. Jones, Outlines of Physical Chemistry (1903); D. Mendeléeff, Principles of Chemistry (3rd ed., 1905).

Inorganic.—Roscoe and Schorlemmer, Inorganic Chemistry (3rd ed., Non-metals, 1905; Metals, 1907); R. Abegg, Handbuch der anorganischen Chemie; Gmelin-Kraut, Handbuch der anorganischen Chemie; O. Dammer, Handbuch der anorganischen Chemie; H. Moissan, Chimie minérale.

Organic.—F. Beilstein, Handbuch der organischen Chemie; M.M. Richter, Lexikon der Kohlenstoffverbindungen (these are primarily works of reference); V. Meyer and P.H. Jacobson, Lehrbuch der organischen Chemie; Richter-Anschutz, Organische Chemie (11th ed., vol. i., 1909, Eng. trans.); G.K. Schmidt, Kurzes Lehrbuch der organischen Chemie; A. Bernthsen, Organische Chemie (Eng. trans.). Practical methods are treated in Lassar-Cohn, Arbeitsmethoden für organisch-chemische Laboratorien (4th ed., 1906-1907). Select chapters are treated in A. Lachmann, Spirit of Organic Chemistry; J.B. Cohen, Organic Chemistry (1908); A.W. Stewart, Recent Advances in Organic Chemistry (1908); and in a series of pamphlets issued since 1896 with the title Sammlung chemischer und chemisch-technischer Vorträge.

Analytical.—For Blowpipe Analysis: C.F. Plattner, Probirkunst mit dem Löthrohr. For General Analysis: C.R. Fresenius, Qualitative and Quantitative Analysis, Eng. trans, by C.E. Groves (Qualitative, 1887) and A.I. Cohn (Quantitative, 1903); F.P. Treadwell, Kurzes Lehrbuch der analytischen Chemie (1905); F. Julian, Textbook of Quantitative Chemical Analysis (1904); A. Classen, Ausgewählte Methoden der analytischen Chemie (1901-1903); W. Crookes, Select Methods in Chemical Analysis (1894). Volumetric Analysis: F. Sutton, Systematic Handbook of Volumetric Analysis (1904); F. Mohr, Lehrbuch der chemisch-analytischen Titrirmethode (1896). Organic Analysis: Hans Meyer, Analyse und Konstitutionsermittlung organischer Verbindungen (1909); Wilhelm Vaubel, Die physikalischen und chemischen Methoden der quantitativen Bestimmung organischer Verbindungen. For the historical development of the proximate analysis of organic compounds see M.E.H. Dennstedt, Die Entwickelung der organischen Elementaranalyse (1899).

Encyclopaedias.—The early dictionaries of Muspratt and Watts are out of date; there is a later edition of the latter by H.F. Morley and M.M.P. Muir. A. Ladenburg, Handwörterbuch der Chemie, A. Wurtz, Dictionnaire de chimie, and F. Selmi, Enciclopedia di chimica, are more valuable; the latter two are kept up to date by annual supplements.