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nation of specific heat is not at present in so advanced a state as that of the relations between the volumes, pressures and temperatures of gases'.

32. The so-called 'law of isomorphism' affords a basis on which is founded another method for determining the atomic weights of elementary substances.

The Abbé Haüy, whose views were dominant in crystallography in the early days of this century, admitted a close connection between crystalline form and chemical composition, but he thought that each chemically distinct body must be characterised by a definite and peculiar form.

In 1816 Gay-Lussac noticed that the growth of crystals of potash alum was not affected by placing them in a solution of ammonia alum.

Various observations of this kind were made from time to time' until 1819, when E. Mitscherlich propounded the law of isomorphism, which, modified and developed, was stated by him in 1821 in the following terms : ‘Equal numbers of atoms

similarly combined exhibit the same crystalline form; identity ‘of crystalline form is independent of the chemical nature of 'the atoms, and is conditioned only by the number and con'figuration of the atoms.'

Since this date various observers have advanced the knowledge of the relations between crystalline form and chemical composition The more important generalisations are as follows.

Similar atomic structure is not necessarily accompanied by identical crystalline form ; e.g. PbCrO, monoclinic, and PbM00, quadratic;

AgCl and AgBr regular, and Agl hexagonal;
KNO, and (NH)NO, rhombic but not identical, CsNO, and

RENO, hexagonal.


2 For

1 See in connection with this subject Strecker, Wied. Ann. 13. 20; and Boltzmann, do. 13. 544: and 18. 309.

full historical account of the development of the conception of Isomorphism, with copious references, see the article •Isomorphie' in the Neues Handwörterbuch der Chemie, Bd. II. p. 844 et scq.

3 See especially Handwörterbuch, loc. cit. and Kopp's Lehrbuch der physikal. ischen und theoretischen Chemie (2nd Ed.), Bd. II. pp. 136--155. M. C.



Unlike atomic structure may be accompanied by similar or identical crystalline form: thus Marignac' shewed that the following salts crystallise in identical forms ;

KTiF6.H,O, K,NbOF6.H,O, K,WO,F4. H,O,

CuTiFe.41,0, CuNbOF, 41,0, CuWO,F4.4H,0. In these salts we must suppose isomorphism to occur between certain groups, e.g. TiF,, NbOF, and Wo. The isomorphism of potassium and ammonium salts shews that the atom K is crystallographically equivalent to the group of atoms NHL

The form of the constituents of isomorphous compounds cannot always be deduced from that of the compounds themselves; e.g. manganous and manganic sulphides crystallise in regular, but sulphur in rhombic or monoclinic forms, therefore manganese does not necessarily crystallise in regular forms. So also the sulphates of nickel, magnesium and zinc crystallise in rhombic forms, but the oxides of nickel and magnesium in regular, and oxide of zinc in hexagonal forms. Again, arsenic usually crystallises in rhombic forms, the crystals of phosphorus belong to the regular system, yet the analogous compounds of these elements are generally isomorphous. Kopp generalises such facts as these in the following statement:- Bodies possessing the same crystalline form combine ‘in fixed proportions to form crystals whose form is indepen'dent of, and often different from, that of their constituents.'

In other cases the constituents of isomorphous bodies are themselves isomorphous, e.g. the compound 3Ag, S.Sb,S, has the same crystalline form as the compound 3Ag, S. As, Se, Sb,S, and As, S, are isomorphous in rhombic forms, and arsenic and antimony form almost identical rhombic crystals. Hence we must distinguish strict isomorphism as applied to bodies which, with similar composition, exhibit the same or nearly the same crystalline form; and isomorphism as more loosely applied to bodies which, although not themselves crystallising in the same form, nevertheless combine with other bodies to produce strictly isomorphous compounds into which they enter as corresponding groups'. 1 Ann. Chim. Phys. 60. 257.

Kopp, Lehrbuch, &c. loc. cit.


A certain latitude is generally allowed in the application of the term “truly isomorphous crystals.' This latitude has gradually been more and more advanced until it has become difficult to give an exact meaning to the expression. The measurements of the angles of two salts are sometimes identical'; chemically analogous compounds sometimes crystallise in forms closely resembling one another, yet belonging to different systems”; salts with identical crystalline form sometimes exhibit optical differences Are all such salts to be called truly isomorphous? Kopp* proposes that only those salts, any one of which is capable of growing in unmodified form when immersed in a solution of any other, should be regarded as strictly isomorphous.

It would appear that all the constituents of a compound exert an influence on the form of that substance. Isomorphism may not be exhibited in comparatively simple compounds of two elements, but may appear in more complex compounds of the same elements; e.g. many of the simpler compounds of cadmium are not isomorphous with the analogous compounds of the metals of the magnesium group (Mg, Mn, Fe, Co, Ni, Zn, Cu, Ca), but comparatively complex cadmium salts—such as Caso, K, SO,.6H,0-are generally isomorphous with the corresponding compounds of those metals. So many simple salts of sodium and potassium are not isomorphous, although their composition is similar, but the alums are isomorphous.

One may suppose that the presence of a large number of isomorphous atoms exerts a dominating influence over smaller number of non-isomorphous atoms.

33. As we know the crystalline form of comparatively few elements, the statement that such or such elements form an isomorphous group, generally means only that the analogous compounds of these elements are for the most part isomorphous.

1 For examples see Roscoe and Schorlemmer's Treatise, 1. 742.
? See Marignac, Ann. Min. [5] 9. and 15. &c.
See Baker, C. S. Journal Trans. for 1879. 760.
* Bor. 12. 900 et seq.

5 See, for crystalline forms of elements in free state, Watts's Dictionary, vol. 111. p. 429.


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The more important groups of isomorphous elements, as thus understood, are as follows:

GROUP I. Fluorine, Chlorine, Bromine, Iodine, (Cyanogen]; in all compounds :

partially Manganese; in compounds of the type RMnO4

GROUP II. Sulphur, Selenion; in all compounds and as elements in monosymmetric forms: partially Tellurium; in compounds of the type R"Te :

Chromium, Manganese, Tellurium; in salts of their acids

belonging to type H SO,:

Arsenic, Antimony; in compounds of the type R"Sz. GROUP III. Arsenic, Antimony, Bismuth, Tellurium; as elements, and the three first-named in all corresponding compounds : partially Phosphorus and Vanadium; in salts of their acids :

Nitrogen with Phosphorus, Arsenic, Antimony; in organic

bases. GROUP IV. Lithium, Sodium, Potassium, Rubidium, Casium, [Ammonium]; in most compounds : partially Thallium; in some compounds :

Silver, in some compounds (especially with sodium). GROUP V. Calcium, Strontium, Barium, Lead; Magnesium, Zinc, Manganese, Iron; e.g. in carbonates : partially Nickel, Cobalt, Copper; with iron in some compounds, e.g.

sulphates : Lanthanum, Cerium, Didymium, Yttrium, Erbium; with

calcium, in compounds of type R"O: Copper, Mercury, with lead, in oxy-compounds: Beryllium, Cadmium, Indium ; with zinc, in some com


Thallium ; with lead, in some compounds. GROUP VI. Aluminium, Chromium, Manganese, Iron; in the sesquioxides (R,Og] and salts derived therefrom :

partially Cerium, Uranium; in their sesquioxides.
GROUP VII. Copper, Silver; in compounds of the type (R.)"O :

partially Gold; with silver.

GROUP VIII. Ruthenium, Rhodium, Palladium, Iridium, Platinum, Osmium; in most compounds: partially Iron, Nickel, Gold:

Tin [? Tellurium].
From article 'Isomorphie' in Neues Handwörterbuch, loc. cit.

GROUP IX. Carbon, Silicon, Titanium, Zirconium, Tin, Thorium ; partially in compounds of the type RO,, and salts derived from the

type H,RO: carbon with silicon in many correspond

ing so-called organic compounds.

Iron; with titanium.
GROUP X. Niobium, Tantalum ; in all their compounds.
GROUP XI. Molybdenum, Tungsten; in all their compounds:
partially Chromium; in salts of acids of the type H, RO

34. The terms dimorphous, trimorphous, polymorphous were used by Mitscherlich. Many examples of the phenomena to which these names are applied are now known: thus calcium carbonate crystallises in hexagonal forms as calcspar, and in rhombic forms as arragonite: titanium oxide assumes two distinct quadratic forms, one being known as rutile the other as anatase, and also crystallises in brookite as rhombic prisms: arsenious oxide crystallises in octahedral, antimonious oxide in rhombic forms, but if amorphous arsenious oxide is heated in a sealed tube so that one part of the tube is at 400° and the rest below this temperature, the oxide deposited in the middle part of the tube is found to be isomorphous with rhombic antimonious oxide; the latter oxide is also known in octahedral forms, so that the isodimorphism of these two oxides is complete.

35. If it is assumed that, as a general rule, those amounts of two substances which are crystallographically equivalent have analogous atomic constitutions; and if we suppose that of two compounds exhibiting identical crystalline form the atomic weights of the elements in one are known, it is evident in what way determinations of crystalline form may aid in fixing atomic weights.

To take an example:—from determinations of the specific gravities of gaseous compounds and analyses of these compounds, the value 524 is assigned to the atomic weight of chromium ; this number is verified by measurements of the specific heat of the same metal; the formula nCr,O, is hence assigned to the green oxide of chromium. But this oxide exhibits the same crystalline form as ferric oxide, hence the latter oxide should probably be represented by the formula

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