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this same direction, and brings about also a reduction of the terminal angle of the crystal.

In addition to these mixed crystals there are also amorphous heterogeneous aggregates, which are produced by the solidification of a mixture in a molten state.

§ 64. Density of Solid Bodies.-Great variations are exhibited by the densities of solid bodies; substances are known, e.g. certain metals, which are forty times as heavy as the lightest known solid, and more than twenty times as heavy as an equal bulk of water, the usual standard of comparison for solids. The apparent irregularities observed in the densities of various solids to a large extent disappear and certain regularities become apparent when the volumes occupied by the molecular weights or the stachiometric quantities represented by their formulæ are considered, as has already been done in the case of the elements in § 36. Investigations of this kind have been carried out by H. Kopp, H. Schroeder, Traube, and others.

The inexactitude of the determinations, and also the doubts as to the temperature at which the determination should be made, have combined to retard the realisation of the laws to which these quantities are doubtless subservient.

The simplest way of looking at this problem is to compare the space occupied by a compound with that filled by the constituent elements in the free state. When this is done it is found, as a rule, that the volume of the compound is approximately equal to the sum of the volumes of the constituent elements.

According to the table in § 36, the volumes of zinc and sulphur are

V (Zn) + V (S) 9.115.7 = 24.8.

The volume of the compound zinc sulphide formed by the union of these elements is obtained by dividing the stachiometric quantity ZnS by the density of zinc sulphide (blende), thus:

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Thus it is seen that the volume of the compound is approxi

mately equal to that of the sum of the constituents. Other monosulphides show the same relation, as is exhibited in the following table, in which under the sign Σ the sum of the volumes of the constituents are given for the sake of comparison :

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The agreement exhibited here is satisfactory, considering the difficulties surrounding the exact determination of the density. Consequently, no very great error would be made if the volumes of sulphur were calculated by subtracting from the volume of each sulphide the volume of the metal contained in it, thus:

V (ZnS) V (Zn)

=

24.09.1 14·9 = V (S).

In this manner the values under the heading V (S) in the above table have been obtained. The mean of these is 14.2

I

instead of 15.7. This difference appears to indicate that the combination is attended by a slight contraction.

The striking analogy exhibited by the elements sulphur and oxygen is sufficient to justify a calculation in a similar manner of the atomic volume of solid oxygen from the molecular volumes of the oxides. If this be done the following values are obtained, which agree fairly well with one another. In the following table in the first column are placed the stachiometric values; under d in the second the density; under V in the third the volume of the oxide is given, and in the fourth under V (R) the volume of the metal; finally under V (0) the volume of oxygen, which is the difference between the two preceding sets of numbers.

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Similar values may be obtained from the so-called sesqui

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These results show the space filled by the three atoms of oxygen to be nearly three times that occupied by one atom in the first series of oxides.

The values obtained for the atomic volume of oxygen are not always identical with those given in the above tables; thus, in the case of the oxides of the composition R2O, e.g. Ag2O, Cu2O, Hg2O, the space filled by the oxygen is much

greater, whilst it is much smaller in the oxides RO2; such as

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In cuprous oxide the atom of oxygen would appear to occupy twice the space occupied by it in cupric oxide. In stannic oxide, on the other hand, the volume is only half as great. In the case of the compounds of the lighter metals still more remarkable relationships obtain. The production of the majority of these compounds is apparently attended by a considerable contraction; so much so indeed is this the case that the volume of the compound is smaller than that of the constituent metal; thus, for example:

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It is needless to remark that in these and similar cases the method of interpretation employed in the case of the oxides cannot be used. Still some regularities amongst these compounds do become evident when a comparison is instituted between the volumes of analogous compounds of elements belonging to the same natural family or elements following one another in the periodic system. Still such relationships, despite the energy expended in their investigation, are at the present time but ill understood.

Of necessity the space filled by a solid body is not constant. Alterations in pressure, and more especially of temperature, affect this to a greater or less degree. When heat is applied to a solid body the volume increases. The expansion in the case of crystalline solids, save those crystallising in the regular system, is different in different directions; in fact, it appears probable that an expansion in one direction is accompanied by a contraction in another.

§ 65. Fusion and Solidification.-When heat is applied to a solid body, provided no chemical change is produced, then sooner or later the coherence of the particles is so far reduced that the solid melts; the individual particles are then able to

move freely around one another, but still their coherence has not been completely overcome.

In many instances other changes of solidity precede the liquefaction, whilst in others, as soon as a definite temperature, the melting point, is attained the solids suddenly and completely liquefy. Others again soften or become pasty before melting, passing, in fact, through a state intermediate between the solid and the liquid. In this plastic condition particles can be welded together by pressure, as is the case with metals like iron and platinum. Some metals and some of the semimetals, such as zinc, bismuth, and tellurium, before melting become brittle at a certain temperature, whilst at other temperatures they are malleable and ductile, and can then be either rolled into sheets or drawn into wire.

The change in the state of aggregation is associated with a greater or less absorption of heat. When the temperature of a solid is very much below its melting point, a definite amount of heat is required to produce a certain rise in temperature for each part by weight of the substance, and this is approximately the same for every degree of temperature. This amount of heat so required is styled 'the specific heat.' When the body begins to soften under the application of heat, the amount of heat required to produce a given rise in temperature increases more and more, until when the body melts the amount of heat absorbed is considerable, and is no longer perceptible as such, becoming, in fact, latent heat. The heat so absorbed serves in all probability to give an accelerated motion to the particles, and being thus converted into motion is no longer perceptible as heat. The fusion proceeds only in proportion as the heat is applied, and as this serves only for melting, the temperature remains stationary until the whole mass is fused. On the other hand, when a molten mass gives up the heat to surrounding objects its temperature is not necessarily lowered below the melting point, for the part solidifying will give out its latent heat of fusion. Nor is it until the whole has solidified that the temperature begins to sink. A molten body may, however, be frequently cooled below its melting point without solidifying. In this state of superfusion the particles are in a condition of unstable equilibrium, such that the slightest change suffices to bring

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