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Rh to be expected that light will be thrown on problems of this order by studies, such as those Langmuir has initiated, of the space occupied by the molecules in liquid films.

The tetra-spheres may be arranged in sheets in any desired numbers, but from such sheets hexagonal blocks may be dissected out, consisting of six tetra-spheres arranged as in benzene, three base downwards and three base upwards, linked in a six-ring system. If to one such segment, six unit-spheres representing six hydrogen atoms be so added that they occupy the six hollows in the six exposed faces of the six tetra-spheres round the periphery of the model, a model of the benzene molecule is produced. The structure is only two layers high but the hydrogen atoms form a separate central chaplet, owing to their position in the hollows at the waist of the system. To pack benzene units together, it is necessary to displace the hydrogen spheres slightly from their central position, so as to bring half of them into the one and half .into the other outer layer of carbon unit-spheres. The operation is symbolic of the change involved in the passage of benzene from the liquid into the crystalline state.

The configuration of the benzene model thus contracted is that of two superposed triangles, each side having five spheres, the three corners being occupied each by a hydrogen sphere, the remaining space by unit carbon spheres. The two superposed triangles are in reversed positions, the apex of one falling upon the base of the other, whilst the carbon units of the upper layer fall into the hollows between those of the lower layer. The model is therefore hexagonal in outline with sloping sides.

A feature in the model is the presence both at the upper and lower surface of three unsatisfied "carbon faces." Benzene, in other words, is to be pictured as possessed of a bundle of three unsatisfied affinities at each free surface: these correspond to the six affinities directed inwards in the centric formula.

It is easy to construct models of benzene derivatives, proceeding on similar lines. A matter of interest to be mentioned, in this connexion, is the fact that, in close-packing the units, they cannot generally be arranged side by side but contiguous units must be made to differ in level by one layer in order to secure a fit; the mass therefore has a stepped surface; half its constituent molecular units range higher by the thickness of a layer than those of the other half, the two sets interpenetrating. In a num- ber of cases it has been found that the data deduced directly by geometrical methods from these models, taking into account the recorded characteristics of the compounds dealt with, are in practical agreement with the crystallographic data.

Spheres are used in the construction of the models as a con- venient means of showing the relative situations in space of the hypothetical constituent sub-centres of force referred to; these will present homogeneous symmetrical repetition such as is charac- teristic of crystalline structure. It is not intended, however, to suggest any difference in properties between the space contained within the spheres and that occupying the interstices between them. Indeed, but for the greater mechanical difficulties involved, a partitioning of space into identical cells of regular dodecahedral form would with profit take the place of a closest packed assem- blage of equal spheres of the cubic system of symmetry.

Barlow has succeeded in partitioning space into similar plane- faced cells, each having 13 faces, according to hemihedral cubic symmetry; he contends that, if pairs of the cells are symmetri- cally chosen to represent the molecules of potassium chloride, the arrangement of the pairs completely matches the crystal form; he points out that this highly symmetrical arrangement is de- rived, by a very simple modification, from the interpenetrated face-centered lattices assigned by the Braggs to the crystal in question. In a number of cases it has been found that the data deduced directly by geometrical methods from these models, taking into account the recorded characteristics of the com- pounds dealt with, are in agreement with the crystallographic data to an extent well within the ordinary errors of measurement. Necessarily, spheres are only suitable for the purpose of hand demonstrations. In developing the crystallographic forms, the compression the spheres undergo has to be taken into account. The simplest form of close-packing would involve their compres-

sion into dodecahedral cells; but both i3-facedand i4-faced solid units are also possible. The crystallographic peculiarities of po- tassium chloride may be completely matched on the assumption that the KC1 unit is formed of two such cells.

If, as argued, carbon- atoms cannot be united by more than single affinities, ethylene and still more acetylene are truly un- saturated and the conventional symbols C:C and C-C are to be read as implying merely certain degrees of unsaturation.

It is a logical consequence of the same conclusion, that only one form of carbon can exist the diamond. If so, graphite and charcoal are not composed of allotropes of carbon! The elementary nature of the prime constituents of these materials may be questioned on various grounds. Sir Charles Parsons, who has carried out an extended inquiry with the object of producing diamond, has thus far been unable to satisfy himself that it can be obtained by artificial means: he is inclined to think that the crystals obtained by Sir William Crookes may not have been diamond but perhaps silicon compounds of the carborundum type. Diamonds are found in volcanic vents and it is conceivable that they have been formed under transcendental conditions, which cannot now be realized. If allotropes, the two forms should be in equilibrium: as graphite has the higher heat of combustion, the production of graphite alone, without diamcnd, at high temperatures is remarkable to say the least, particularly in view of the behaviour of phosphorus. Graphite, apparently, however produced, always contains hydrogen. Most striking also is the whiteness and hardness of diamond and its resistance to all chemical agents, when contrasted with the blackness and softness of graphite and the amorphous carbons and the readiness with which these are oxidized. The conversion of the diamond into graphite (?), when it is bombarded by the cathode discharge, is very superficial and may well be due to the intervention of the trace of water which is necessarily present in any vacuum tube through which a discharge passes.

Lastly, the black colour of graphite and the charcoals is an indication of a complex ethenoid or it were better said benzenoid structure, such as the heaviest hydrocarbons are known to possess. The production of mellithic or benzenehexacarboxylic acid, Ce(COOH)6, when charcoal is oxidized, may be regarded as proof that, in charcoal, there is a nucleus in which a benzenoid system of carbon atoms is surrounded by several similar systems, and it is conceivable that, fringing these, there may be others. The stability of such a system, the maintenance of the benzenoid structure, might be secured by the addition of a few hydrogen atoms at the periphery, which would disturb the symmetry sufficiently to modify the electronic orbits and break up the diamond arrangement.

If the carbon atoms in diamond are in paraffinoid arrangement, the properties would be uniform throughout the mass, and the hardness of diamond may be supposed to be due to the manner in which every internally saturated atom is combined with four others: this explanation may be extended to carborundum, silicon being the analogue of carbon. In the benzenoid system of graphite, contiguous benzene units would perhaps be more firmly united than the superposed layers of the complexes: hence its softness and the readiness with which it is split into thin layers.

If valid deductions may be drawn from models such as have been described, it would seem probable that no structural alteration in the ordinary sense of the term is involved in the production of unsaturated compounds. In the case of the formation of quinone, for example, it is customary to suppose that not only are two atoms of hydrogen withdrawn from quinol but that the two oxygen atoms from which they are taken away become doubly united with the benzene system and that this is coincidently changed in structure:

The model suffers no such change : only the molecular units need to be rearranged to make good the withdrawals. The changes