If two substances are found to be capable of crystallizing in the same geometric form, or in forms which may be referred to the same primitive, they are designated isomorphous-a term also applied to substances which, though themselves incapable of crystallizing, are found to replace each other in particular combinations without materially altering their crystalline form. This last sense of the term isomorphous, is that in which it is most frequently received, and may be illustrated by the three alkalies, potassa, soda, and oxide of ammonium, which replace each other in the class of salts known as the alums, without altering the crystalline form of the latter. The alums are double salts, composed of an alkaline sulphate and a sulphate of some basic sesquioxide, combined with a large amount of water of crystallization; the alums have all the same crystalline form. The observation of this isomorphism is often useful in enabling us to decide upon the atomic constitution of certain compounds.

FORMS OF CRYSTALS, &c.-We enter upon the subject of crystallography with some considerable hesitation, as it is not within the province of this work to discuss any subject belonging strictly to physics; and, moreover, as crystallography may at the present day be regarded as forming of itself an important branch of natural science. Since, however, it is usual, and frequently of very great importance, to pay some attention to the physical structure of the various solid compounds with which the chemist meets, both in nature and in his laboratorysince he is thereby frequently enabled to discriminate, with the greatest nicety and rapidity, between different substances, or, at any rate, to read therein something concerning their nature which may aid him considerably in his subsequent researches; and, as we shall also repeatedly make use of certain crystallographical terms in the description of elements and their compounds, we propose to give as brief and general an outline of this subject as we imagine will meet the wants of the student.

Most solid substances have a certain characteristic form in which they crystallize; this form is, however, not always peculiar to themselves, since many substances, widely different in their chemical character, crystallize in forms similar to each other. We have already made mention of a property possessed by some substances of crystallizing in two distinct forms. Examples of dimorphous bodies are carbon and sulphur.

If a smart blow be applied to a cube of rock-salt, or a prism of calcareous spar, and the smallest fragments resulting from the fracture of the two crystals examined, they will be found to be identical in form with the original masses. (The tendency possessed by crystalline forms to split in certain directions is termed their cleavage.) All crystals are therefore built up of small particles possessing a regular form, either identical with that of the crystal itself, or standing in some simple relation to it. We are not only enabled to reduce a crystal, by cleavage, to smaller forms, as already described, but it is also possible, by attending to certain precautions (§ 55), to add to the size of a crystal, without in any way altering its form. These facts, added to certain optical properties possessed by many crystals, prove that crystalline bodies possess a certain regular structure.

All crystalline forms exhibit faces or planes; edges, or lines of contact of two planes, and points or angles, which are formed by the meeting of three or more planes.

An imaginary line drawn from one angle to an opposite one, passing from side to side, or from end to end, through the centre of a crystal, is called its axis. The particles of a crystal may therefore be conceived to be symmetrically arranged round an axis of this description. A slight consideration will show that various crystals may possess a different numbers of axes, which have different lengths, and cross each other at different angles.

When a crystal is examined as to its form, it is held in such a manner that one of the axes is situated vertically in front of the observer's eye; if the axis

of a crystal vary in length, the longest is chosen for this vertical axis; if they are equal, any one may be chosen. The axis thus placed, is called the principal axis, while the others are called secondary.

All crystalline forms may, according to the nature of their axes, be arranged in six systems. These systems embrace what are called the primary forms of crystals, from which the secondary forms are produced. The meaning of the latter term may be explained in a few words.

If a crystal be allowed to grow in such a manner that each plane, angle, and edge is equally increased, it is self-evident that, however large the crystal becomes, its form will remain the same. If, however, from some cause, only one portion of the crystal be added to (if, for example, a crystal be not regularly turned about, as directed at § 55), the form of the crystal will undergo a change. Now, if this alteration of the form of a crystal be effected in a certain regular manner, new figures will result, which will stand in a direct geometrical relation to the form of crystal from which they were produced. Such forms are called secondary forms, belonging, of course, to the same system as their original or primary form. It is evident that a great variety of forms may be produced in this way, by the systematic removal, to a greater or less extent, of angles, edges, and planes.

We will now confine ourselves to a brief description of the principal forms belonging to the six different systems, generally accepted in crystallography. I. The regular system includes those crystals which have three equal axes, at right angles with each other.

The principal forms of this system are:

4. The cube, which is inclosed by six equal square planes.

5. The regular octohedron, inclosed by eight equilateral triangles.

6. The rhombic dodecahedron, inclosed by twelve equal rhombic planes. In the figures, the directions of the three axes are shown by the letters a―a.

7. The right square prism, of which the secondary axes terminate in the centres of the lateral planes.

8. The right square prism, of which the secondary axes terminate at the edges of the lateral planes.

9. The right square-based octohedron, of which the directions of the axes correspond to those of prism 7.

10. A similar octohedron, of which, however the directions of the axes correspond to those of prism 8.

III. The crystals belonging to the right prismatic system, have, like those of the former systems, three axes at right angles to each other; they are, however, all of unequal lengths. This will be observed in the following forms of this system :

11. The right rectangular prism, with the secondary axes terminating in the centres of the lateral planes.

12. The right rhombic prism, of which the secondary axes terminate at the edges of the lateral planes.

13. The rectangular-based octohedron, with axes corresponding to those of prism 11.

14. The right rhombic-based octohedron, with the axes corresponding to those of prism 12.

a-a principal axis. b-b, c-c, secondary axes.

IV. The crystals of the oblique prismatic system have, like the foregoing, three axes, but they are no longer all at right angles. The two secondary axes of these are at right angles, but the principal axis is perpendicular to one of these, and oblique to the other. This system is represented by the following forms, of which the axes stand in the same relation to each other as those of the forms given of the former system :

15, the oblique rectangular prism; 16, the oblique rhombic prism; 17, the oblique rectangular-based octohedron; 18, the oblique rhombic-based octohedron.

a-a principal axis. b-b, c-c, secondary axes.

V. In the crystals of this, which may be called the doubly-oblique prismatic system, all the three axes are oblique to each other. This system is represented in the figure, by two prisms, 19 and 20, and two octohedra, 21 and 22.

1004

a-a principal axis. b-b, c-c, secondary axes.

VI. The rhombohedral system. The forms of this system differ considerably from those of the foregoing, by containing four axes, instead of three. Of these four, the vertical or principal axis is perpendicular to the other three, which lie all in the same plane, are equal, and inclined to each other at an angle of 60°. The examples here given of the forms belonging to this system are: 23, the regular six-sided prism; 25, the rhombohedron; 24 and 26, two species of dodecahedra. Fig. 24.

Fig. 23.

Fig. 25.

Fig. 26.

a—a principal axis. b-b secondary axes.

It has been already explained how the so-called secondary forms may be derived from primary forms; the following figure, showing the passage of the cube to the octohedron may serve to render this point more intelligible.

There is one other important class of crystals that demands some slight explanation, this is the hemihedral class. If the alternate planes or faces of a crystal be allowed to grow excessively, it will be found that the other planes gradually become diminished, and at length they are perfectly obliterated, a new form of crystal being the result. This kind of action is shown in the conversion of the octohedron into the tetrahedron.

The foregoing statements will at once convince the student of the great importance of possessing some means of submitting crystals to an accurate measurement, in order to ascertain to what system they belong. Several instruments have been constructed for measuring the angles of crystals; they have received the name of goniometers.

WATER OF CONSTITUTION AND CRYSTALLIZATION.-Crystalline salts frequently contain water in two different states of combination, which are distinguished by the terms water of constitution (or sometimes basic water, or water of hydration), and water of crystallization.

The water of crystallization is much less intimately combined with the salt than the water of constitution, and is therefore more easily expelled.

In order to exhibit this difference, the water of hydration is usually expressed by its chemical formula (HO), and is incorporated in the formula of the salt; whilst the water of crystallization is represented by the mechanical symbol (Aq), and is connected with the formula by the sign+, as will be seen in the examples given below.

The reason for applying the term water of crystallization to that portion of the combined water which is most easily expelled, is found in the influence which it exerts upon the crystallization of the salt. Most salts containing water of crystallization lose their crystalline form upon its expulsion, and crumble to an amorphous powder.

This water of crystallization is retained by different salts with very different degrees of force, but rare are the cases where it cannot be entirely expelled at a temperature of 212° F. (100° C.)

Many salts lose this water by simple exposure to air of ordinary dryness; and as the escape of the water is usually attended by a peculiar opaque appearance assumed by the surface of the crystals, such salts are said to be efflorescent. The ordinary phosphate of soda (2NaO.HO.PO,+24Aq) and the sulphate of soda (NaO.SO+10Aq) are familiar examples of such salts.

Other salts effloresce only in perfectly dry air, or in vacuo, as will be more fully explained in the section upon desiccation.

Those salts which do not effloresce at ordinary temperatures, generally do so when exposed to a moderate degree of heat, and in most cases lose the whole of their water of crystallization at 212° F. (100° C.); this loss of water is frequently attended with an alteration in the color as well as in the form of the salt; the well-known blue crystals of sulphate of copper (blue vitriol, CuO. SO, HO+4Aq) for example, crumble down to a nearly white powder when heated in the water-bath, the four equivalents of water of crystallization being thus eliminated.

A salt is sometimes met with in crystals of different form, containing different quantities of water of crystallization.

Thus, ordinary borax (biborate of soda, NaO.2BO,+10Aq) crystallizes in six-sided prisms, containing, as indicated by the formula, ten equivalents of water of crystallization, whilst octohedral borax contains but five equivalents.

Again, the common phosphate of soda (2NaO.HO.PO,) crystallizes in two different forms, containing respectively 14 and 24Aq, whilst two forms of the sulphate of soda are known with 8 and 10 equivalents of water.

When heat is applied to salts containing water of crystallization, they sometimes dissolve in this water, undergoing, as it is termed, the aqueous fusion; when the water of crystallization has been expelled, they generally become solid again, and undergo the true or igneous fusion when the temperature is still further increased. The behavior of phosphate of soda (2NaO.HO.PO,+24Aq), when heated, affords a good example of this.

Crystals destitute of water of crystallization, do not, of course, undergo the