the polyvalent element in the molecule. If more than one polyvalent atom is present, we do not know how many affinities are used in uniting the several polyvalent atoms together. We must also carefully satisfy ourselves of the absence of unsaturated affinities in the compound.

It is often difficult to decide whether this is the case, as the compound may not contain the full number of monovalent atoms if the element has feeble affinities.

The determination of the valency is a problem requiring great care in its solution, and it is not surprising that in the case of many elements the valency has not always been correctly determined, and that in many instances too low a value has been assigned.

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§ 42. Irregularities of the Chemical Valency. There are exceptions to the marked regularity in the relation of chemical valency to atomic weight. Certain compounds undoubtedly contain more chlorine, bromine, or oxygen than corresponds to their chemical valency. Many of these compounds may be regarded as molecular aggregations, formed by several complete molecules crystallising together. The beautiful crystalline compound PCl,Br1 may be regarded as PCl,Br2+Br1⁄2, or as PCl2+ Br2+Br; in the same way the unstable tri-iodide of potassium may be considered to be KI+I2=KI ̧. But all such compounds cannot be regarded in this light. Auric chloride, AuCl,, is undoubtedly a true chemical compound; and gold must be trivalent, not monovalent, as we should expect from its being a member of the first family. The molecular weight of cupric oxide, CuO, is not known, as the oxide is non-volatile. Its formula may be Cu-0-0-Cu; but cupric chloride, CuCl2, could not have an analogous formula. Copper is isomorphous with divalent zinc, and must therefore be divalent. It is shown to be a member of the first family by the fact that the chloride, CuCl2, is not volatile, but is decomposed by heat, losing half its chlorine, yielding cuprous chloride. The molecular weight deduced from the vapour density determination of Victor Meyer corresponds to Cu,Cl2, Cl-Cu-Cu-Cl, in which copper is again divalent. At present we can only point out these exceptions without attempting to offer any explanation.

§ 43. Theoretical Significance of Chemical Valency. Nature of Affinity. As science is not satisfied with a simple knowledge of facts, but endeavours to investigate their causal connection, theoretical chemistry has attempted to solve the problem of explaining the remarkable fact, that the chemical valency of different elements undergoes a systematic variation. It is very difficult to find an explanation, as very little is known as to the cause of the formation of chemical compounds. The cause is termed affinity, because the old chemists held that only those bodies are capable of uniting which possess a certain likeness or affinity for each other. Exactly the opposite view now prevails: namely, that the more unlike two bodies are, the more readily will they combine together; but the term affinity still survives.

Affinity is generally considered to be an attractive force existing in the atoms. This hypothesis is not the only one possible, nor is it, indeed, the most probable, but it is the most convenient, and consequently the most generally accepted. This hypothesis will be used for the present, and the consideration of other hypotheses (still imperfectly developed) which do not require the assumption of an attractive force, will be postponed. Affinity is probably closely allied to, if not identical with, electrical attraction; but no definite statement on this point can be made at present.

Affinity only acts at short distances; for bodies combine or decompose one another only when in direct contact. It is not in any way directly identical with the attraction which is produced by the ordinary electric charge or by magnetisation, which work at relatively large distances. We may imagine such a division of the magnetic or electric masses in the atom, as to produce an attractive force which could only be effective at a very small distance. But at present the state of our knowledge is not ripe for speculations of this nature.

Leaving aside the question of the true nature of affinity, we may still be able to draw some conclusions from the differences of chemical valency.

There is no doubt that the effect of affinity is to keep the atoms in a compound at a definite distance from one another,

for the space which a compound occupies in the solid or fluid state is fixed and definite. It varies regularly with the temperature and pressure, but depends on the nature of the constituents. The atoms cannot be immovable in the positions which the affinities have caused them to assume; for, according to the mechanical theory of heat, not only the molecules as such, but also the atoms in the molecules, are in a state of active motion, oscillating or rotating round points of equilibrium.

In the solid state the molecules of most bodies arrange themselves systematically, forming crystals. The form of the crystal is determined by the composition of the molecules and the nature of the atoms contained in the molecule, and is characteristic of both. As the different parts of a crystal exhibit certain points of difference, and the nature of this difference depends on the composition of the molecules and the nature of the atoms, it seems probable that these points of difference must already exist in the atoms and molecules themselves. The attractive force of affinity is active at these points. It endeavours to attract the other atoms and keep them in positions, which lie in these lines of force at a definite distance from the centre of gravity of the first atom. The distances between the centres of gravity may vary considerably for different atoms. There will be only one such position in the vicinity of a monovalent atom, in which a second atom can be fixed; but there will be two such points for a divalent and three for a trivalent atom, &c.

We may also venture to determine the position of these points in space. In the case of a compound consisting of two monovalent atoms only the distance between the atoms is fixed; the system will be in a state of equilibrium in any position. This may be the reason why compounds formed of two monovalent atoms generally crystallise in the regular system. A polyvalent atom requires a number of points corresponding to its chemical valency; these positions must be symmetrically arranged, at equal distances from the centre of gravity of the polyvalent atom. If this is not the case an exchange in the position of the atoms will produce isomeric compounds-that is, compounds possessing the same composition, but exhibiting

dissimilar properties. For example, there would be two potassium hydroxides, K-0---H, and H-0---K, and two

Instances of what appeared to be examples of this kind of isomerism have from time to time been discovered, but on closer investigation they have invariably been proved to be spurious. It is, therefore, exceedingly probable that the points are symmetrically arranged at equal distances round the surface of a sphere. In a divalent atom the points will be diametrically opposite each other; in a trivalent atom the points will be arranged in a circle, at angles of 120°; in a tetravalent atom the points will be arranged in space like the angles of a regular tetrahedron; in a hexavalent atom the points will occupy the solid angles of an octahedron, or the centres of the faces of a cube; in an octovalent atom the points are arranged like the corners of a regular cube, or the centres of the faces of an octahedron. A perfectly symmetrical arrangement of five or seven points on the surface of a sphere is not possible, but it is probable that in this case the arrangement will be as symmetrical as possible.

Starting from these assumptions, it is easy to represent the configuration of the molecules, which are composed of monovalent atoms and only one polyvalent atom. A compound consisting of two monovalent atoms, or two monovalent and one polyvalent atom, is represented by a formula lying in a straight line:-

One trivalent and three monovalent atoms lie in a plane :

One tetravalent and four monovalent atoms are arranged round the centre of a tetrahedron, at the solid angles. In fact, physical investigations of such compounds have made it

exceedingly probable that their molecules really possess this form.1

It is difficult to follow this hypothesis when the monovalent atoms are wholly or partly replaced by polyvalent atoms, for one atom cannot occupy several positions at the same time. Attempts to overcome this difficulty are made by assuming that the atom alternately occupies the different positions, moving between them like a pendulum, or rotating about them. This view receives support from the observation that compounds containing polyvalent atoms attached to each other by multiple linkings occupy a larger space than those compounds do in which the polyvalent atoms are united together by a single linking. Again, it is observed that those carbon compounds which contain doubly or trebly linked carbon atoms easily split up at the points where the double or treble linking exists. Great importance must not be attached to such speculations at present, as they are much too hypothetical; but they may serve a useful purpose by enabling us to survey a variety of observations from a common standpoint.

§ 44. Investigation of the Constitution of Chemical Compounds. The chemical valency of the elements and the composition of their compounds are intimately related. Not only the number of the atoms, but their arrangement in the molecule, depends on the valency of the elements. The possibility of investigating and ascertaining the manner in which the atoms are arranged was for a long time a disputed question. Although some chemists attempted to investigate the arrangement of the atoms, others looked upon such investigations as absolutely valueless. But even the followers of the latter school could not avoid holding certain views regarding the manner in which the atoms combine together to form compounds, for they rejected as unwarranted the doubts which existed as to the correctness and permissibility of their views. This dispute lasted more than twenty years, and, strange to say, it ended in the overthrow of these old dogmas by new hypotheses, by means of which we have acquired an unexpected insight into the nature of chemical

'Conclusions drawn from the friction of gases, with reference to the size of the section of molecules, appear to confirm these views.