Chapter C: O. H. Cl. Br. I. S (2)

_Capillarity and Surface Tension._--Reference should be made to the article CAPILLARY ACTION for the general discussion of this phenomenon of liquids. It is there shown that the surface tension of a liquid may be calculated from its rise in a capillary tube by the formula [gamma] = 1/2rhs, where [gamma] is the surface tension per square centimetre, r the radius of the tube, h the height of the liquid column, and s the difference between the densities of the liquid and its vapour. At the critical point liquid and vapour become identical, and, consequently, as was pointed out by Frankenheim in 1841, the surface tension is zero at the critical temperature.

Relation to molecular weight.

Mendeleeff endeavoured to obtain a connexion between surface energy
and constitution; more successful were the investigations of Schiff,
who found that the "molecular surface tension," which he defined as
the surface tension divided by the molecular weight, is constant for
isomers, and that two atoms of hydrogen were equal to one of carbon,
three to one of oxygen, and seven to one of chlorine; but these ratios
were by no means constant, and afforded practically no criteria as to
the molecular weight of any substance.

In 1886 R. Eotvos (_Wied. Ann._ 27, p. 452), assuming that two liquids
may be compared when the ratios of the volumes of the liquids to the
volumes of the saturated vapours are the same, deduced that
[gamma]V^{2/3} (where [gamma] is the surface tension, and V the
molecular volume of the liquid) causes all liquids to have the same
temperature coefficients. This theorem was investigated by Sir W.
Ramsay and J. Shields (_Journ. Chem. Soc._ 63, p. 1089; 65, p. 167),
whose results have thrown considerable light on the subject of the
molecular complexity of liquids. Ramsay and Shields suggested that
there exists an equation for the surface energy of liquids, analogous
to the volume-energy equation of gases, PV = RT. The relation they
suspected to be of the form [gamma]S = KT, where K is a constant
analogous to R, and S the surface containing one gramme-molecule,
[gamma] and T being the surface tension and temperature respectively.
Obviously equimolecular surfaces are given by (Mv)^{2/3}, where M is
the molecular weight of the substance, for equimolecular volumes are
Mv, and corresponding surfaces the two-thirds power of this. Hence S
may be replaced by (Mv)^{2/3}. Ramsay and Shields found from
investigations of the temperature coefficient of the surface energy
that T in the equation [gamma](Mv)^{2/3} = KT must be counted
downwards from the critical temperature T less about 6 deg. Their
surface energy equation therefore assumes the form [gamma](Mv)^{2/3} =
K([tau] - 6 deg.). Now the value of K, [gamma] being measured in dynes
and M being the molecular weight of the substance as a gas, is in
general 2.121; this value is never exceeded, but in many cases it is
less. This diminution implies an association of molecules, the surface
containing fewer molecules than it is supposed to. Suppose the
coefficient of association be n, i.e. n is the mean number of
molecules which associate to form one molecule, then by the normal
equation we have [gamma](Mnv)^{2/3} = 2.121([tau] - 6 deg.); if the
calculated constant be K1, then we have also [gamma](Mv)^{2/3} =
K1([tau]-6 deg.). By division we obtain n^{2/3} = 2.121/K1, or n =
(2.121/K1)^{3/2} the coefficient of association being thus determined.

The apparatus devised by Ramsay and Shields consisted of a capillary
tube, on one end of which was blown a bulb provided with a minute
hole. Attached to the bulb was a glass rod and then a tube containing
iron wire. This tube was placed in an outer tube containing the liquid
to be experimented with; the liquid is raised to its boiling-point,
and then hermetically sealed. The whole is enclosed in a jacket
connected with a boiler containing a liquid, the vapour of which
serves to keep the inner tube at any desired temperature. The
capillary tube can be raised or lowered at will by running a magnet
outside the tube, and the heights of the columns are measured by a
cathetometer or micrometer microscope.

Normal values of K were given by nitrogen peroxide, N2O4, sulphur
chloride, S2Cl2, silicon tetrachloride, SiCl4, phosphorus chloride,
PCl3, phosphoryl chloride, POCl3, nickel carbonyl, Ni(CO)4, carbon
disulphide, benzene, pyridine, ether, methyl propyl ketone;
association characterized many hydroxylic compounds: for ethyl alcohol
the factor of association was 2.74-2-43, for n-propyl alcohol
2.86-2.72, acetic acid 3.62-2.77, acetone 1.26, water 3.81-2.32;
phenol, nitric acid, sulphuric acid, nitroethane, and propionitril,
also exhibit association.

_Crystalline Form and Composition._

The development of the theory of crystal structure, and the fundamental principles on which is based the classification of crystal forms, are treated in the article CRYSTALLOGRAPHY; in the same place will be found an account of the doctrine of isomorphism, polymorphism and morphotropy. Here we shall treat the latter subjects in more detail, viewed from the standpoint of the chemist. Isomorphism may be defined as the existence of two or more different substances in the same crystal form and structure, polymorphism as the existence of the same substance in two or more crystal modifications, and morphotropy (after P. von Groth) as the change in crystal form due to alterations in the molecule of closely (chemically) related substances. In order to permit a comparison of crystal forms, from which we hope to gain an insight into the prevailing molecular conditions, it is necessary that some unit of crystal dimensions must be chosen. A crystal may be regarded as built up of primitive parallelepipeda, the edges of which are in the ratio of the crystallographic axes, and the angles the axial angles of the crystals. To reduce these figures to a common standard, so that the volumes shall contain equal numbers of molecules, the notion of molecular volumes is introduced, the arbitrary values of the crystallographic axes (a, b, c) being replaced by the topic parameters[18] ([chi],[psi],[omega]), which are such that, combined with the axial angles, they enclose volumes which contain equal numbers of molecules. The actual values of the topic parameters can then readily be expressed in terms of the elements of the crystals (the axial ratios and angles), the density, and the molecular weight (see Groth, _Physikalische Krystallographie_, or _Chemical Crystallography_).

_Polymorphism._--On the theory that crystal form and structure are the result of the equilibrium between the atoms and molecules composing the crystals, it is probable, _a priori_, that the same substance may possess different equilibrium configurations of sufficient stability, under favourable conditions, to form different crystal structures. Broadly this phenomenon is termed polymorphism; however, it is necessary to examine closely the diverse crystal modifications in order to determine whether they are really of different symmetry, or whether twinning has occasioned the apparent difference. In the article CRYSTALLOGRAPHY the nature and behaviour of twinned crystals receives full treatment; here it is sufficient to say that when the planes and axes of twinning are planes and axes of symmetry, a twin would exhibit higher symmetry (but remain in the same crystal system) than the primary crystal; and, also, if a crystal approximates in its axial constants to a higher system, mimetic twinning would increase the approximation, and the crystal would be pseudo-symmetric.

In general, polysymmetric and polymorphous modifications suffer transformation when submitted to variations in either temperature or pressure, or both. The criterion whether a pseudo-symmetric form is a true polymorph or not consists in the determination of the scalar properties (e.g. density, specific heat, &c.) of the original and the resulting modification, a change being in general recorded only when polymorphism exists. Change of temperature usually suffices to determine this, though in certain cases a variation in pressure is necessary; for instance, sodium magnesium uranyl acetate, NaMg(UO2)3(C2H3O2)9.9H2O shows no change in density unless the observations are conducted under a considerable pressure. Although many pseudo-symmetric twins are transformable into the simpler form, yet, in some cases, a true polymorph results, the change being indicated, as before, by alterations in scalar (as well as vector) properties.

For example, boracite forms pseudo-cubic crystals which become truly
cubic at 265 deg., with a distinct change in density; leucite behaves
similarly at about 560 deg.. Again, the pyroxenes, RSiO3 (R = Fe, Mg,
Mn, &c.), assume the forms (1) monoclinic, sometimes twinned so as to
become pseudo-rhombic; (2) rhombic, resulting from the pseudo-rhombic
structure of (1) becoming ultramicroscopic; and (3) triclinic,
distinctly different from (1) and (2); (1) and (2) are polysymmetric
modifications, while (3) and the pair (1) and (2) are polymorphs.

While polysymmetry is solely conditioned by the manner in which the mimetic twin is built up from the single crystals, there being no change in the scalar properties, and the vector properties being calculable from the nature of the twinning, in the case of polymorphism entirely different structures present themselves, both scalar and vector properties being altered; and, in the present state of our knowledge, it is impossible to foretell the characters of a polymorphous modification. We may conclude that in polymorphs the substance occurs in different phases (or molecular aggregations), and the equilibrium between these phases follows definite laws, being dependent upon temperature and pressure, and amenable to thermodynamic treatment (cf. CHEMICAL ACTION and ENERGETICS). The transformation of polymorphs presents certain analogies to the solidification of a liquid. Liquids may be cooled below their freezing-point without solidification, the _metastable_ (after W. Ostwald) form so obtained being immediately solidified on the introduction of a particle of the solid modification; and supersaturated solutions behave in a similar manner. At the same time there may be conditions of temperature and pressure at which polymorphs may exist side by side.

The above may be illustrated by considering the equilibrium between
rhombic and monoclinic sulphur. The former, which is deposited from
solutions, is transformed into monoclinic sulphur at about 96 deg.,
but with great care it is possible to overheat it and even to fuse it
(at 113.5 deg.) without effecting the transformation. Monoclinic
sulphur, obtained by crystallizing fused sulphur, melts at 119.5 deg.,
and admits of undercooling even to ordinary temperatures, but contact
with a fragment of the rhombic modification spontaneously brings about
the transformation. From Reicher's determinations, the exact
transition point is 95.6 deg.; it rises with increasing pressure about
0.05 deg. for one atmosphere; the density of the rhombic form is
greater than that of the monoclinic. The equilibria of these
modifications may be readily represented on a pressure-temperature
diagram. If OT, OP (fig. 6), be the axes of temperature and pressure,
and A corresponds to the transition point (95.6 deg.) of rhombic
sulphur, we may follow out the line AB which shows the elevation of
the transition point with increasing pressure. The overheating curve
of rhombic sulphur extends along the curve AC, where C is the
melting-point of monoclinic sulphur. The line BC, representing the
equilibrium between monoclinic and liquid sulphur, is
thermodynamically calculable; the point B is found to correspond to
131 deg. and 400 atmospheres. From B the curve of equilibrium (BD)
between rhombic and liquid sulphur proceeds; and from C (along CE) the
curve of equilibrium between liquid sulphur and sulphur vapour. Of
especial interest is the curve BD: along this line liquid and rhombic
sulphur are in equilibrium, which means that at above 131 deg. and 400
atmospheres the rhombic (and not the monoclinic) variety would
separate from liquid sulphur.

| P |D
| |
| B |
| / \
| / \ Liquid
| / \
| Rhombic / \
| / \ E
| / \ _ -
| / Monoclinic_ \ -
| / _ - C
| /_ -
| /A
| / Vapour
| /
|/
+----------------------------------
O T
FIG. 6.

Mercuric iodide also exhibits dimorphism. When precipitated from
solutions it forms red tetragonal crystals, which, on careful heating,
give a yellow rhombic form, also obtained by crystallization from the
fused substance, or by sublimation. The transition point is 126.3 deg.
(W. Schwarz, _Zeit. f. Kryst._ 25, p. 613), but both modifications may
exist in metastable forms at higher and lower temperatures
respectively; the rhombic form may be cooled down to ordinary
temperature without changing, the transformation, however, being
readily induced by a trace of the red modification, or by friction.
The density and specific heat of the tetragonal form are greater than
those of the yellow.

Hexachlorethane is trimorphous, forming rhombic, triclinic and cubic
crystals; the successive changes occur at about 44 deg. and 71 deg.,
and are attended by a decrease in density.

Tetramorphism is exhibited by ammonium nitrate. According to O.
Lehmann it melts at 168 deg. (or at a slightly lower temperature in
its water of crystallization) and on cooling forms optically isotropic
crystals; at 125.6 deg. the mass becomes doubly refracting, and from a
solution rhombohedral (optically uniaxial) crystals are deposited; by
further cooling acicular rhombic crystals are produced at 82.8 deg.,
and at 32.4 deg. other rhombic forms are obtained, identical with the
product obtained by crystallizing at ordinary temperatures. The
reverse series of transformations occurs when this final modification
is heated. M. Bellati and R. Romanese (_Zeit. f. Kryst._ 14, p. 78)
determined the densities and specific heats of these modifications.
The first and third transformations (reckoned in order with increasing
temperature of the transition point) are attended by an increase in
volume, the second with a contraction; the solubility follows the same
direction, increasing up to 82.8 deg., then diminishing up to 125.6
deg., and then increasing from this temperature upwards.

The physical conditions under which polymorphous modifications are prepared control the form which the substance assumes. We have already seen that temperature and pressure exercise considerable influence in this direction. In the case of separation from solutions, either by crystallization or by precipitation by double decomposition, the temperature, the concentration of the solution, and the presence of other ions may modify the form obtained. In the case of sodium dihydrogen phosphate, NaH2PO4.H2O, a stable rhombic form is obtained from warm solutions, while a different, unstable, rhombic form is obtained from cold solutions. Calcium carbonate separates as hexagonal calcite from cold solutions (below 30 deg.), and as rhombic aragonite from solutions at higher temperatures; lead and strontium carbonates, however, induce the separation of aragonite at lower temperatures. From supersaturated solutions the form unstable at the temperature of the experiment is, as a rule, separated, especially on the introduction of a crystal of the unstable form; and, in some cases, similar inoculation of the fused substance is attended by the same result. Different modifications may separate and exist side by side at one and the same time from a solution; e.g. telluric acid forms cubic and monoclinic crystals from a hot nitric acid solution, and ammonium fluosilicate gives cubic and hexagonal forms from aqueous solutions between 6 deg. and 13 deg.

A comparison of the transformation of polymorphs leads to a twofold classification: (1) polymorphs directly convertible in a reversible manner--termed "enantiotropic" by O. Lehmann and (2) polymorphs in which the transformation proceeds in one direction only--termed "monotropic." In the first class are included sulphur and ammonium nitrate; monotropy is exhibited by aragonite and calcite.

It is doubtful indeed whether any general conclusions can yet be drawn as to the relations between crystal structure and scalar properties and the relative stability of polymorphs. As a general rule the modification stable at higher temperatures possesses a lower density; but this is by no means always the case, since the converse is true for antimonious and arsenious oxides, silver iodide and some other substances. Attempts to connect a change of symmetry with stability show equally a lack of generality. It is remarkable that a great many polymorphous substances assume more symmetrical forms at higher temperatures, and a possible explanation of the increase in density of such compounds as silver iodide, &c., may be sought for in the theory that the formation of a more symmetrical configuration would involve a drawing together of the molecules, and consequently an increase in density. The insufficiency of this argument, however, is shown by the data for arsenious and antimonious oxides, and also for the polymorphs of calcium carbonate, the more symmetrical polymorphs having a lower density.

_Morphotropy._--Many instances have been recorded where substitution has effected a deformation in one particular direction, the crystals of homologous compounds often exhibiting the same angles between faces situated in certain zones. The observations of Slavik (_Zeit. f. Kryst._, 1902, 36, p. 268) on ammonium and the quaternary ammonium iodides, of J.A. Le Bel and A. Ries (_Zeit. f. Kryst._, 1902, 1904, et seq.) on the substituted ammonium chlorplatinates, and of G. Mez (ibid., 1901, 35, p. 242) on substituted ureas, illustrate this point.

Ammonium iodide assumes cubic forms with perfect cubic cleavage;
tetramethyl ammonium iodide is tetragonal with perfect cleavages
parallel to {100} and {001}--a difference due to the lengthening of
the a axes; tetraethyl ammonium iodide also assumes tetragonal forms,
but does not exhibit the cleavage of the tetramethyl compound; while
tetrapropyl ammonium iodide crystallizes in rhombic form. The
equivalent volumes and topic parameters are tabulated:

+---------+----------+------------+-----------+----------+
| | NH4I. | NMe4I. | NEt4I. | NPr4I. |
+---------+----------+------------+-----------+----------+
| V | 57.51 | 108.70 | 162.91 | 235.95 |
| [chi] | 3.860 | 5.319 | 6.648 | 6.093 |
| [psi] | 3.860 | 5.319 | 6.648 | 7.851 |
| [omega] | 3.860 | 3.842 | 3.686 | 4.933 |
+---------+----------+------------+-----------+----------+

From these figures it is obvious that the first three compounds form a
morphotropic series; the equivalent volumes exhibit a regular
progression; the values of [chi] and [psi], corresponding to the a
axes, are regularly increased, while the value of [omega],
corresponding to the c axis, remains practically unchanged. This
points to the conclusion that substitution has been effected in one of
the cube faces. We may therefore regard the nitrogen atoms as
occupying the centres of a cubic space lattice composed of iodine
atoms, between which the hydrogen atoms are distributed on the
tetrahedron face normals. Coplanar substitution in four hydrogen atoms
would involve the pushing apart of the iodine atoms in four horizontal
directions. The magnitude of this separation would obviously depend on
the magnitude of the substituent group, which may be so large (in this
case propyl is sufficient) as to cause unequal horizontal deformation
and at the same time a change in the vertical direction.

The measure of the loss of symmetry associated with the introduction of alkyl groups depends upon the relative magnitudes of the substituent group and the rest of the molecule; and the larger the molecule, the less would be the morphotropic effect of any particular substituent. The mere retention of the same crystal form by homologous substances is not a sufficient reason for denying a morphotropic effect to the substituent group; for, in the case of certain substances crystallizing in the cubic system, although the crystal form remains unaltered, yet the structures vary. When both the crystal form and structure are retained, the substances are said to be isomorphous.

Other substituent groups exercise morphotropic effects similar to those exhibited by the alkyl radicles; investigations have been made on halogen-, hydroxy-, and nitro-derivatives of benzene and substituted benzenes. To Jaeger is due the determination of the topic parameters of certain haloid-derivatives, and, while showing that the morphotropic effects closely resemble those occasioned by methyl, he established the important fact that, in general, the crystal form depended upon the orientation of the substituents in the benzene complex.

Benzoic acid is pseudo-tetragonal, the principal axis being remarkably
long; there is no cleavage at right angles to this axis. Direct
nitration gives (principally) m-nitrobenzoic acid, also
pseudo-tetragonal with a much shorter principal axis. From this two
chlornitrobenzoic acids [COOH.NO2.Cl = 1.3.6 and 1.3.4] may be
obtained. These are also pseudotetragonal; the (1.3.6) acid has nearly
the same values of [chi] and [psi] as benzoic acid, but [omega] is
increased; compared with m-nitrobenzoic acid, [chi] and [psi] have
been diminished, whereas [omega] is much increased; the (1.3.4) acid
is more closely related to m-nitrobenzoic acid, [chi] and [psi] being
increased, [omega] diminished. The results obtained for the (1.2) and
(1.4) chlorbenzoic acids also illustrate the dependence of crystal
form and structure on the orientation of the molecule.

The hydroxyl group also resembles the methyl group in its morphotropic
effects, producing, in many cases, no change in symmetry but a
dimensional increase in one direction. This holds for benzene and
phenol, and is supported by the observations of Gossner on [1.3.5]
trinitrobenzene and picric acid (1.3.5-trinitro, 2 oxybenzene); these
last two substances assume rhombic forms, and picric acid differs from
trinitrobenzene in having [omega] considerably greater, with [chi] and
[psi] slightly less. A similar change, in one direction only,
characterizes benzoic acid and salicylic acid.

The nitro group behaves very similarly to the hydroxyl group. The
effect of varying the position of the nitro group in the molecule is
well marked, and conclusions may be drawn as to the orientation of the
groups from a knowledge of the crystal form; a change in the symmetry
of the chemical molecule being often attended by a loss in the
symmetry of the crystal.

It may be generally concluded that the substitution of alkyl, nitro, hydroxyl, and haloid groups for hydrogen in a molecule occasions a deformation of crystal structure in one definite direction, hence permitting inferences as to the configuration of the atoms composing the crystal; while the nature and degree of the alteration depends (1) upon the crystal structure of the unsubstituted compound; (2) on the nature of the substituting radicle; (3) on the complexity of the substituted molecule; and (4) on the orientation of the substitution derivative.

_Isomorphism._--It has been shown that certain elements and groups exercise morphotropic effects when substituted in a compound; it may happen that the effects due to two or more groups are nearly equivalent, and consequently the resulting crystal forms are nearly identical. This phenomenon was first noticed in 1822 by E. Mitscherlich, in the case of the acid phosphate and acid arsenate of potassium, KH2P(As)O4, who adopted the term isomorphism, and regarded phosphorus and arsenic as isomorphously related elements. Other isomorphously related elements and groups were soon perceived, and it has been shown that elements so related are also related chemically.

Tutton's investigations of the morphotropic effects of the metals
potassium, rubidium and caesium, in combination with the acid radicals
of sulphuric and selenic acids, showed that the replacement of
potassium by rubidium, and this metal in turn by caesium, was
accompanied by progressive changes in both physical and
crystallographical properties, such that the rubidium salt was always
intermediate between the salts of potassium and caesium (see table;
the space unit is taken as a pseudo-hexagonal prism). This fact finds
a parallel in the atomic weights of these metals.

+---------+---------+---------+---------+---------+
| | V | [chi] | [psi] | [omega] |
+---------+---------+---------+---------+---------+
| K2SO4 | 69.42 | 4.464 | 4.491 | 4.997 |
| Rb2SO4 | 73.36 | 4.634 | 4.664 | 5.237 |
| Cs2SO4 | 83.64 | 4.846 | 4.885 | 5.519 |
+---------+---------+---------+---------+---------+
| K2SeO4 | 71.71 | 4.636 | 4.662 | 5.118 |
| Rb2SeO4 | 79.95 | 4.785 | 4.826 | 5.346 |
| Cs2SeO4 | 91.16 | 4.987 | 5.035 | 5.697 |
+---------+---------+---------+---------+---------+

By taking appropriate differences the following facts will be
observed: (1) the replacement of potassium by rubidium occasions an
increase in the equivalent volumes by about eight units, and of
rubidium by caesium by about eleven units; (2) replacement in the same
order is attended by a general increase in the three topic parameters,
a greater increase being met with in the replacement of rubidium by
caesium; (3) the parameters [chi] and [psi] are about equally
increased, while the increase in [omega] is always the greatest. Now
consider the effect of replacing sulphur by selenium. It will be seen
that (1) the increase in equivalent volume is about 6.6; (2) all the
topic parameters are increased; (3) the greatest increase is effected
in the parameters [chi] and [psi], which are equally lengthened.

These observations admit of ready explanation in the following
manner. The ordinary structural formula of potassium sulphate is

O
|
K--O--S--O--K.
|
O

If the crystal structure be regarded as composed of three
interpenetrating point systems, one consisting of sulphur atoms, the
second of four times as many oxygen atoms, and the third of twice as
many potassium atoms, the systems being so arranged that the sulphur
system is always centrally situated with respect to the other two, and
the potassium system so that it would affect the vertical axis, then
it is obvious that the replacement of potassium by an element of
greater atomic weight would specially increase the length of [omega]
(corresponding to the vertical axis), and cause a smaller increase in
the horizontal parameters [chi] and [psi]; moreover, the increments
would advance with the atomic weight of the replacing metal. If, on
the other hand, the sulphur system be replaced by a corresponding
selenium system, an element of higher atomic weight, it would be
expected that a slight increase would be observed in the vertical
parameter, and a greater increase recorded equally in the horizontal
parameters.

Muthmann (_Zeit. f. Kryst._, 1894), in his researches on the tetragonal
potassium and ammonium dihydrogen phosphates and arsenates, found that
the replacement of potassium by ammonium was attended by an increase
of about six units in the molecular volume, and of phosphorus by
arsenic by about 4.6 units. In the topic parameters the following
changes were recorded: replacement of potassium by ammonium was
attended by a considerable increase in [omega], [chi] and [psi] being
equally, but only slightly, increased; replacement of phosphorus by
arsenic was attended by a considerable increase, equally in [chi] and
[psi], while [omega] suffered a smaller, but not inconsiderable,
increase. It is thus seen that the ordinary plane representation of
the structure of compounds possesses a higher significance than could
have been suggested prior to crystallographical researches.

Identity, or approximate identity, of crystal form is not in itself sufficient to establish true isomorphism. If a substance deposits itself on the faces of a crystal of another substance of similar crystal form, the substances are probably isomorphous. Such parallel overgrowths, termed episomorphs, are very common among the potassium and sodium felspars; and K. von Hauer has investigated a number of cases in which salts exhibiting episomorphism have different colours, thereby clearly demonstrating this property of isomorphism. For example, episomorphs of white potash alum and violet chrome alum, of white magnesium sulphate and green nickel sulphate, and of many other pairs of salts, have been obtained. More useful is the property of isomorphous substances of forming mixed crystals, which are strictly isomorphous with their constituents, for all variations in composition. In such crystals each component plays its own part in determining the physical properties; in other words, any physical constant of a mixed crystal can be calculated as additively composed of the constants of the two components.

Fig. 7 represents the specific volumes of mixtures of ammonium and
potassium sulphates; the ordinates representing specific volumes, and
the abscissae the percentage composition of the mixture. Fig. 8 shows
the variation of refractive index of mixed crystals of potash alum and
thallium alum with variation in composition.

In these two instances the component crystals are miscible in all
proportions; but this is by no means always the case. It may happen
that the crystals do not form double salts, and are only miscible in
certain proportions. Two cases then arise: (1) the properties may be
expressed as linear functions of the composition, the terminal values
being identical with those obtained for the individual components, and
there being a break in the curve corresponding to the absence of mixed
crystals; or (2) similar to (1) except that different values must be
assigned to the terminal values in order to preserve collinearity.
Fig. 9 illustrates the first case: the ordinates represent specific
volumes, and the abscissae denote the composition of isomorphous
mixtures of ammonium and potassium dihydrogen phosphates, which
mutually take one another up to the extent of 20% to form homogeneous
crystals. The second case is illustrated in fig. 10. Magnesium
sulphate (orthorhombic) takes up ferrous sulphate (monoclinic) to the
extent of 19%, forming isomorphous orthorhombic crystals; ferrous
sulphate, on the other hand, takes up magnesium sulphate to the extent
of 54% to form monoclinic crystals. By plotting the specific volumes
of these mixed crystals as ordinates, it is found that they fall on
two lines, the upper corresponding to the orthorhombic crystals, the
lower to the monoclinic. From this we may conclude that these salts
are isodimorphous: the upper line represents isomorphous crystals of
stable orthorhombic magnesium sulphate and unstable orthorhombic
ferrous sulphate, the lower line isomorphous crystals of stable
monoclinic ferrous sulphate and unstable monoclinic magnesium
sulphate.

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. Mendeleeff, _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 minerale_.

_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 fur
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 Vortrage._

_Analytical._--For Blowpipe Analysis: C.F. Plattner, _Probirkunst mit
dem Lothrohr_. 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, _Ausgewahlte
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, _Handworterbuch 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. (C. E.*)

FOOTNOTES:

[1] The more notable chemists of this period were Turquet de Mayerne
(1573-1665), a physician of Paris, who rejected the Galenian
doctrines and accepted the exaggerations of Paracelsus; Andreas
Libavius (d. 1616), chiefly famous for his _Opera Omnia
Medicochymica_ (1595); Jean Baptiste van Helmont (1577-1644),
celebrated for his researches on gases; F. de la Boe Sylvius
(1614-1672), who regarded medicine as applied chemistry; and Otto
Tachenius, who elucidated the nature of salts.

[2] This dictum was questioned by the researches of H. Landolt, A.
Heydweiller and others. In a series of 75 reactions it was found
that in 61 there was apparently a diminution in weight, but in 1908,
after a most careful repetition and making allowance for all
experimental errors, Landolt concluded that no change occurred (see
ELEMENT).

[3] The theory of Berthollet was essentially mechanical, and he
attempted to prove that the course of a reaction depended not on
affinities alone but also on the masses of the reacting components.
In this respect his hypothesis has much in common with the "law of
mass-action" developed at a much later date by the Swedish chemists
Guldberg and Waage, and the American, Willard Gibbs (see CHEMICAL
ACTION). In his classical thesis Berthollet vigorously attacked the
results deduced by Bergman, who had followed in his table of
elective attractions the path traversed by Stahl and S. F. Geoffroy.

[4] Dalton's atomic theory is treated in more detail in the article
ATOM.

[5] Berzelius, however, appreciated the necessity of differentiating
the atom and the molecule, and even urged Dalton to amend his
doctrine, but without success.

[6] The following symbols were also used by Bergman:--

which represented zinc, manganese, cobalt, bismuth, nickel, arsenic,
platinum, water, alcohol, phlogiston.

[7] The following are the symbols employed by Dalton:--

which represent in order, hydrogen, nitrogen, carbon, oxygen,
phosphorus, sulphur, magnesia, lime, soda, potash, strontia, baryta,
mercury; iron, zinc, copper, lead, silver, platinum, and gold were
represented by circles enclosing the initial letter of the element.

[8] Approximate values of the atomic weights are employed here.

[9] The definite distinction between potash and soda was first
established by Duhamel de Monceau (1700-1781).

[10] The reader is specially referred to the articles ALIZARIN;
INDIGO; PURIN and TERPENES for illustrations of the manner in which
chemists have artificially prepared important animal and vegetable
products.

[11] These observations were generalized by J.B. Dumas and Polydore
Boullay (1806-1835) in their "etherin theory" (_vide infra_).

[12] This must not be confused with the modern _acetyl_, CH3.CO, which
at that time was known as _acetoxyl_.

[13] It is now established that ortho compounds do exist in isomeric
forms, instances being provided by chlor-, brom-, and amino-toluene,
chlorphenol, and chloraniline; but arguments, e.g. E. Knoevenagel's
theory of "motoisomerism," have been brought forward to cause these
facts to support Kekule.

[14] Victor Meyer and G. Heyl (_Ber._, 1895, 28, p. 2776) attempted a
solution from the following data. It is well known that
di-ortho-substituted benzoic acids are esterified with difficulty.
Two acids corresponding to the formula of Kekule and Claus are
triphenyl acrylic acid, (C6H5)2C:C(COOH).C6H5, and triphenyl acetic
acid, (C6H5)3C.COOH. Experiments showed that the second acid was
much more difficult to esterify than the first, pointing to the
conclusion that Claus' formula for benzene was more probable than
Kekule's.

[15] H. Rose, _Ausfuhrliches Handbuch der analytischen Chemie_ (1851).

[16] F. Wohler, _Die Mineralanalyse in Beispielen_ (1861).

[17] For the connexion between valency and volume, see VALENCY.

[18] This was done simultaneously in 1894 by W. Muthmann and A. E.
H. Tutton, the latter receiving the idea from F. Becke (see _Journ.
Chem. Soc._, 1896, 69, p. 507; 1905, 87, p. 1183).

CHEMNITZ (or KEMNITZ), MARTIN (1522-1586), German Lutheran theologian, third son of Paul Kemnitz, a cloth-worker of noble extraction, was born at Treuenbrietzen, Brandenburg, on the 9th of November 1522. Left an orphan at the age of eleven, he worked for a time at his father's trade. A relative at Magdeburg put him to school there (1539-1542). Having made a little money by teaching, he went (1543) to the university of Frankfort-on-Oder; thence (1545) to that of Wittenberg. Here he heard Luther preach, but was more attracted by Melanchthon, who interested him in mathematics and astrology. Melanchthon gave him (1547) an introduction to his son-in-law, Georg Sabinus, at Konigsberg, where he was tutor to some Polish youths, and rector (1548) of the Kneiphof school. He practised astrology; this recommended him to Duke Albert of Prussia, who made him his librarian (1550). He then turned to Biblical, patristic and kindred studies. His powers were first brought out in controversy with Osiander on justification by faith. Osiander, maintaining the infusion of Christ's righteousness into the believer, impugned the Lutheran doctrine of imputation; Chemnitz defended it with striking ability. As Duke Albert sided with Osiander, Chemnitz resigned the librarianship. Returning (1553) to Wittenberg, he lectured on Melanchthon's _Loci Communes_, his lectures forming the basis of his own _Loci Theologici_ (published posthumously, 1591), which constitute probably the best exposition of Lutheran theology as formulated and modified by Melanchthon. His lectures were thronged, and a university career of great influence lay before him, when he accepted a call to become coadjutor at Brunswick to the superintendent, Joachim Morlin, who had known him at Konigsberg. He removed to Brunswick on the 15th of December 1554, and there spent the remainder of his life, refusing subsequent offers of important offices from various Protestant princes of Germany. Zealous in the duties of his pastoral charge, he took a leading part in theological controversy. His personal influence, at a critical period, did much to secure strictness of doctrine and compactness of organization in the Lutheran Church. Against Crypto-Calvinists he upheld the Lutheran view of the eucharist in his _Repetitio sanae doctrinae de Vera Praesentia_ (1560; in German, 1561). To check the reaction towards the old religion he wrote several works of great power, especially his _Theologiae Jesuitarum praecipua capita_ (1562), an incisive attack on the principles of the society, and the _Examen concilii Tridentini_ (four parts, 1565-66-72-73), his greatest work. His _Corpus doctrinae Prutenicum_ (1567), drawn up in conjunction with Morlin, at once acquired great authority. In the year of its publication he became superintendent of Brunswick, and in effect the director of his church throughout Lower Saxony. His tact was equal to his learning. In conjunction with Andrea and Selnecker he induced the Lutherans of Saxony and Swabia to adopt the _Formula Concordiae_ and so become one body. Against lax views of Socinian tendency he directed his able treatise _De duabus naluris in Christo_ (1570). Resigning office in infirm health (1584) he survived till the 8th of April 1586.

Lives of Chemnitz are numerous, e.g. by T. Gasmerus (1588), T. Pressel
(1862), C.G.H. Lentz (1866), H. Hachfeld (1867), H. Schmid in J.J.
Herzog's _Realencyklopadie_ (1878), T. Kunze in A. Hauck's
_Realencyklop. fur prot. Theol. und Kirche_ (1897); that by Hausle, in
I. Goschler's _Dict. encyclopedique de la theol. cath._ (1858), gives
a Roman Catholic view. (A. Go.*)

CHEMNITZ, a town of Germany, in the kingdom of Saxony, the capital of a governmental district, 50 m. W.S.W. of Dresden and 51 S.E. of Leipzig by rail. Pop. (1885) 110,817; (1895) 161,017; (1905) 244,405. It lies 950 ft. above the sea, in a fertile plain at the foot of the Erzgebirge, watered by the river Chemnitz, an affluent of the Mulde. It is the chief manufacturing town in the kingdom, ranks next to Dresden and Leipzig in point of population, and is one of the principal commercial and industrial centres of Germany. It is well provided with railway communication, being directly connected with Berlin and with the populous and thriving towns of the Erzgebirge and Voigtland. Chemnitz is in general well built, the enormous development of its industry and commerce having of late years led to the laying out of many fine streets and to the embellishing of the town with handsome buildings. The centre is occupied by the market square, with the handsome medieval Rathaus, now superseded for municipal business by a modern building in the Post-strasse. In this square are monuments to the emperor William I., Bismarck and Moltke. The old inner town is surrounded by pleasant promenades, occupying the site of the old fortifications, and it is beyond these that industrial Chemnitz lies, girdling the old town on all sides with a thick belt of streets and factories, and ramifying far into the country. Chemnitz has eleven Protestant churches, among them the ancient Gothic church of St James, with a fine porch, and the modern churches of St Peter, St Nicholas and St Mark. There are also a synagogue and chapels of various sects. The industry of Chemnitz has gained for the town the name of "Saxon Manchester." First in importance are its locomotive and engineering works, which give employment to some 20,000 hands in 90 factories. Next come its cotton-spinning, hosiery, textile and glove manufactures, in which a large trade is done with Great Britain and the United States. It is also the seat of considerable dyeworks, bleachworks, chemical and woollen factories, and produces leather and straps, cement, small vehicles, wire-woven goods, carpets, beer and bricks. The town is well provided with technical schools for training in the various industries, including commercial, public, economic and agricultural schools, and has a chamber of commerce. There are also industrial and historical museums, and collections of painting and natural history. The local communications are maintained by an excellent electric tramway system. To the northwest of the town is the Gothic church of a former Benedictine monastery, dating from 1514-1525, with a tower of 1897. Chemnitz is a favourite tourist centre for excursions into the Erzgebirge, the chain of mountains separating Saxony from Bohemia.

Chemnitz (_Kaminizi_) was originally a settlement of the Serbian Wends and became a market town in 1143. Its municipal constitution dates from the 14th century, and it soon became the most important industrial centre in the mark of Meissen. A monopoly of bleaching was granted to the town, and thus a considerable trade in woollen and linen yarns was attracted to Chemnitz; paper was made here, and in the 16th century the manufacture of cloth was very flourishing. In 1539 the Reformation was introduced, and in 1546 the Benedictine monastery, founded about 1136 by the emperor Lothair II. about 2 m. north of the town, was dissolved. During the Thirty Years' War Chemnitz was plundered by all parties and its trade was completely ruined, but at the beginning of the 18th century it had begun to recover. Further progress in this direction was made during the 19th century, especially after 1834 when Saxony joined the German Zollverein.

See Zollner, _Geschichte der Fabrik- und Handelsstadt Chemnitz_
(1891); and Straumer, _Die Fabrik- und Handelsstadt Chemnitz_ (1892).

CHEMOTAXIS (from the stem of "chemistry" and Gr. [Greek: taxis], arrangement), a biological term for the attraction exercised on living or growing organisms or their members by chemical substances; e.g. the attraction of the male cells of ferns or mosses by an organic acid or sugar-solution.

CHENAB (the Greek Acesines), one of the "Five rivers" of the Punjab, India. It rises in the snowy Himalayan ranges of Kashmir, enters British territory in the Sialkot district, and flows through the plains of the Punjab, forming the boundary between the Rechna and the Jech Doabs. Finally it joins the Jhelum at Trimmu.

The CHENAB COLONY, resulting from the great success of the Chenab Canal in irrigating the desert of the Bar, was formed out of the three adjacent districts of Gujranwala, Jhang, and Montgomery in 1892, and contained in 1901 a population of 791,861. It lies in the Rechna Doab between the Chenab and Ravi rivers in the north-east of the Jhang district, and is designed to include an irrigated area of 2-1/2 million acres. The Chenab Canal (opened 1887) is the largest and most profitable perennial canal in India. The principal town is Lyallpur, called after Sir J. Broad wood Lyall, lieutenant-governor of the Punjab 1887-1892, which gives its name to a district created in 1904.

CHENEDOLLE, CHARLES JULIEN LIOULT DE (1769-1833), French poet, was born at Vire (Calvados) on the 4th of November 1769. He early showed a vocation for poetry, but the outbreak of the Revolution temporarily diverted his energy. Emigrating in 1791, he fought two campaigns in the army of Conde, and eventually found his way to Hamburg, where he met Antoine de Rivarol, of whose brilliant conversation he has left an account. He also visited Mme de Stael in her retreat at Coppet. On his return to Paris in 1799 he met Chateaubriand and his sister Lucile (Mme de Caud), to whom he became deeply attached. After her death in 1804, Chenedolle returned to Normandy, where he married and became eventually inspector of the academy of Caen (1812-1832). With the exception of occasional visits to Paris, he spent the rest of his life in his native province. He died at the chateau de Coisel on the 2nd of December 1833. He published his _Genie de l'Homme_ in 1807, and in 1820 his _Etudes poetiques_, which had the misfortune to appear shortly after the _Meditations_ of Lamartine, so that the author did not receive the credit of their real originality. Chenedolle had many sympathies with the romanticists, and was a contributor to their organ, the _Muse francaise_. His other works include the _Esprit de Rivarol_ (1808) in conjunction with F.J.M. Fayolle.

The works of Chenedolle were edited in 1864 by Sainte-Beuve, who drew
portraits of him in his _Chateaubriand et son groupe_ and in an
article contributed to the _Revue des deux mondes_ (June 1849). See
also E. Helland, _Etude biographique et litteraire sur Chenedolle_
(1857); Cazin, _Notice sur Chenedolle_ (1869).

CHENERY, THOMAS (1826-1884), English scholar and editor of _The Times_, was born in 1826 at Barbados. He was educated at Eton and Caius College, Cambridge. Having been called to the bar, he went out to Constantinople as _The Times_ correspondent just before the Crimean War, and it was under the influence there of Algernon Smythe (afterwards Lord Strangford) that he first turned to those philological studies in which he became eminent. After the war he returned to London and wrote regularly for _The Times_ for many years, eventually succeeding Delane as editor in 1877. He was then an experienced publicist, particularly well versed in Oriental affairs, an indefatigable worker, with a rapid and comprehensive judgment, though he lacked Delane's intuition for public opinion. It was as an Orientalist, however, that he had meantime earned the highest reputation, his knowledge of Arabic and Hebrew being almost unrivalled and his gift for languages exceptional. In 1868 he was appointed Lord Almoner's professor of Arabic at Oxford, and retained his position until he became editor of _The Times_. He was one of the company of revisers of the Old Testament. He was secretary for some time to the Royal Asiatic Society, and published learned editions of the Arabic classic _The Assemblies of Al-Hariri_ and of the _Machberoth Ithiel_. He died in London on the 11th of February 1884.

CHENG, TSCHENG or TSCHIANG (Ger. _Scheng_), an ancient Chinese wind instrument, a primitive organ, containing the principle of the free reed which found application in the accordion, concertina and harmonium. The cheng resembles a tea-pot filled with bamboo pipes of graduated lengths. It consists of a gourd or turned wooden receptacle acting as wind reservoir, in the side of which is inserted an insufflation tube curved like a swan's neck or the spout of a tea-pot. The cup-shaped reservoir is closed by means of a plate of horn pierced with seventeen round holes arranged round the edge in an unfinished circle, into which fit the bamboo pipes. The pipes are cylindrical as far as they are visible above the plate, but the lower end inserted in the wind reservoir is cut to the shape of a beak, somewhat like the mouthpiece of the clarinet, to receive the reed. The construction of the free reed is very simple: it consists of a thin plate of metal--gold according to the Jesuit missionary Joseph Amiot,[1] but brass in the specimens brought to Europe--of the thickness of ordinary paper. In this plate is cut a rectangular flap or tongue which remains fixed at one end, while at the other the tongue is filed so that, instead of closing the aperture, it passes freely through, vibrating as the air is forced through the pipe (see FREE-REED VIBRATOR). The metal plate is fastened with wax longitudinally across the diameter of the beak end of the pipe, a little layer of wax being applied also to the free end of the vibrating tongue for the purpose of tuning by adding weight and impetus. About half an inch above the horn plate a small round hole or stop is bored through the pipe, which speaks only when this hole is covered by the finger. A longitudinal aperture about an inch long cut in the upper end of the bamboo pipe serves to determine the length of the vibrating column of air proper to respond to the vibrations of the free reed. The length of the bamboo above this opening is purely ornamental, as are also four or five of the seventeen pipes which have no reeds and do not speak, being merely inserted for the purposes of symmetry in design. The notes of the cheng, like those of the concertina, speak either by inspiration or expiration of air, the former being the more usual method. Mahillon states that performers on the cheng in China are rare, as the method of playing by inspiration induces inflammation of the throat.[2] Amiot, who gives a description of the instrument with illustrations showing the construction, states that in the great Chinese encyclopaedia _Eulh-ya_, articles _Yu_ and _Ho_, the _Yu_ of ancient China was the large cheng with nineteen free reeds (twenty-four pipes), and the _Ho_ the small cheng with thirteen reeds or seventeen pipes described in this article. The compass of the latter is given by him as the middle octave with chromatic intervals, the thirteenth note giving the octave of the first. Mahillon gives the compass of a modern cheng as follows:

E.F.F. Chladni,[3] who examined a cheng sent from China to Herr Muller, organist of the church of St Nicholas, Leipzig, at the beginning of the 19th century, gives an excellent description of the instrument, reproducing in illustration a plate from Giulio Ferrario's work on costume.[4] Muller's cheng had the same compass as Mahillon's. Chladni's article was motived by the publication of an account of the exhibition of G.J. Grenie's _Orgue expressif_, invented about 1810, in the Conservatoire of Paris.[5] Grenie's invention, perfected by Alexandre and Debain about 1840, produced the harmonium. Kratzenstein (see under HARMONIUM) of St Petersburg was the first to apply the free reed to the organ in the second half of the 18th century. Inventions of similar instruments, which after a short life were relegated to oblivion, followed at the beginning of the 19th century. An interesting reproduction of a Persian cheng dating from the 10th or 11th century is to be seen on a Persian vase described and illustrated together with a shawm in the _Gazette archeologique_ (tome xi., 1886). (K. S.)

FOOTNOTES:

[1] _Memoire sur la musique des Chinois_ (Paris, 1779), pp. 78 and
82, pl. vi., or _Memoire sur les Chinois_, tome vi. pl. vi.

[2] _Catalogue descriptif_, vol. ii. (Ghent, 1896), p. 91; also vol.
i. (1880), pp. 29, 44, 154.

[3] "Weitere Nachrichten von dem ... chinesischen Blasinstrumente
Tscheng oder Tschiang," in _Allgemeine musikalische Zeitung_
(Leipzig, 1821), Bd. xxiii. No. 22, pp. 369, 374 et seq., and
illustration appendix ii.

[4] _Il Costume anticho e moderno_ (Milan, 1816), pl. 66, vol. i.

[5] See _Allg. mus. Zt._ (Leipzig, 1821), Bd. xxiii. Nos. 9 and 10,
pp. 133 and 149 et seq.