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Chemists have generally assumed that contiguous carbon atoms may be united in three ways, either by single affinities or by two affinities or by three affinities, leaving three, two or a single affinity free to unite with other radicles, thus iC-C; :C:C: -CiC-

Paraffinoid. Ethenoid. Acet(yl)enoid.

Accordingly in van't Hoff's spatial formulae, the two tetra- hedra are shown united either (i) by two apices, or (2) edge to edge, or (3) face to face. The three forms of union have ajl been regarded as possible in spite of the fact, that the assump- tion is made, that the four affinities of the carbon atom are exer- cised in the direction of four lines drawn from the centre of mass through the apices. It has been assumed that the affinities be- come more or less bent or stressed as in von Baeyer's well- known hypothesis: hence the instability and attractive power of the so-called unsaturated compounds. In effect the existence of a difficulty has been recognized but met by a compromise.

The only positive evidence brought forward in disproof of Frankland's contention that two atoms may be united by more than single affinities, and that when each has several affinities not engaged by other radicles they mutually satisfy each other, is that advanced by Julius Thomsen in the fourth volume of his celebrated Thermochemische Untersuchungen. Thomsen argued, from his thermo-chemical data, that in ethenoid and still more in acetenoid compounds, the bond of union was weaker, not stronger, than that in the equivalent paraffinoid compound. He also maintained that the oxygen atom was not held by two affinities in keto (CO) compounds; and he even threw doubt on the formulae assigned to ethylene oxide. Of late years, the chemist's peace of mind has been disturbed, and a suspicion created that all is not right with the symbolic system in use, by the discovery of unsaturated compounds in which the existence of single free affinities must seemingly be granted : Gomberg's triphenylmethyl , C(C6H 6 ) 3, being one of the most striking and compelling cases which no structural sophist has been able to explain away. On- paper it is all so easy, and chemists hitherto have been satisfied to work on paper to draw plans with the aid of certain conventions; now the time is at hand to attempt the representation of our ideas in the solid. There is reason to suppose that the study of solid structure, by geometric and X-ray methods in combi- nation, may carry us over our difficulty.

Conflict must arise of the difficulty of interpreting the evi- dence. This is true already in one very simple case that of common salt. The interpretation put on the results of X-ray analysis is that the chlorine and sodium units are so placed and so arranged relatively that there is no reason to believe in the existence of a molecular unit NaCl, within the mass. The chem- ist stands unconvinced before such a statement he is not pre- pared to sacrifice the cherished convictions of a lifetime, not being satisfied that the new method is one in which implicit faith may be placed the more as it has been shown, in the parallel case of potassium chloride, that a but slightly different arrange- ment of the units is required to give a geometrical structure, in entire harmony with all that is known of the geometrical and physical peculiarities of the crystal, involving no sacrifice of the chemist's view that the molecule KC1 has separate existence (see Barlow, Proc. Roy. Soc., 1914).

An attempt has been made, in recent years, to correlate out- ward form or crystalline structure with internal molecular struc- ture, based upon the conception introduced by Barlow and Pope, that, in the case at least of the elements carbon, hydrogen, oxy- gen and nitrogen, the volume occupied by the atom, in any given compound under given conditions, is proportional to its valency, and that, when changes are effected in a molecule, the ratio is maintained constant although the actual volume may be changed. Taking into account the 'extraordinary number and variety of the compounds of these four elements, their marked stability and the ease with which interchanges can be effected within the molecules, this conclusion is all but unavoidable; but the solid models built up of spheres of volume i, 2, 3 and 4, in accordance with such a valency-volume conception, have not answered expectation. A simple modification is possible, how-

ever, which is of promise. If a single unit sphere be taken to rep- resent an atom of unit valency, such as hydrogen, atoms which are either di- or tri- or tetra-valent (oxygen, nitrogen, carbon) may be represented by models composed respectively of two, three, and four such spheres in close contact (cf. Barlow, Proc. Roy. Soc., 1914, 9i'i6). Such complexes can be made into close-packed unlimited assemblages throughout which each sphere is in contact with 12 surrounding spheres; no such uni- formity can be attained if the spheres differ in volume.

The adoption of the method indicated has important conse- quences. In the case of carbon, the atom is represented by four unit spheres the centres of which lie at the four corners of a regu- lar tetrahedron. The four hollows on the four faces correspond- ing to the tetrahedron faces may be regarded each as the seat of an affinity; the union of two carbon atoms by single affinities, therefore, is to be represented by closely approximating two tet- rahedral groups face to face, so that the three spheres of a face of the one tetrahedron key into the three hollows between three spheres of the opposed face of the other; the two atoms are there- by oppositely oriented. The eight sphere centres of the complex thus formed mark the angles of a regular rhombohedron, the shorter face-diagonals of which equal the edges. If two spheres representing an oxygen atom be attached to one of the faces, in continuation of the two lines of spheres forming a face, the model may be taken as that of ethylene oxide and it has the peculiarity that, whilst the twin oxygen spheres face the hollow in one of the two carbon pyramids, only one of them touches the other carbon pyramid at one of its apices. The condition is much that sug- gested by Julius Thomsen certainly one of unsaturation. Such models can be made into close-packed assemblages of any dimen- sions, which is not the case when the models used are single spheres of varying volume. The adoption of such models has important consequences. In the case of carbon, the atom is represented by four unit-spheres piled in a pyramid. The four hollows on the four faces of the pyramid may be regarded each as the " seat " of an affinity: the union of two carbon atoms by single affinities, therefore, is to be represented by approximating two pyramids, face to face, rotating slightly, so that the three spheres of a face of the one tetrahedron fall into the hollows be- tween the three spheres of the opposed face of the other; this is equivalent to setting one of the pyramids on its base and inter- locking it with the second pyramid placed upside down.

The van't Hoff school has always assumed that the affinities act from the apices of the tetrahedra and have not taken the consequences of close-packing into account. One deduction from their assumption has been that single united carbon atoms are free to rotate but this is not in accordance with the facts. To take only the case of the aldhexose sugars, of the form COH. (CH.OH) 4. CH 2 .OH. The four OH units in the four (CHQH) groups can be arranged relatively to the two terminal groups in eight different positions and each of the forms has its optical opposite. Fourteen of the sixteen compounds there foreshad- owed are known and are stable substances. There must be at least one configuration of principal stability in such a system and if singly bound carbon atoms were free to rotate, a tendency to pass into this stable form should be in evidence. Nothing of the kind is observed: on the contrary, when change takes place it is confined to the part of the system that is directly attacked. The tetra-sphere model of the carbon atom does serve to bring out a certain face-grip between the two united carbon atoms.

By placing tetra-spheres together, in face contact, in the man- ner described, endless chains may be formed and it is conceivable that the carbon atoms in the paraffinoid hydrocarbons are ar- ranged in rectilinear columns presenting similar parallel sections. It is, however, possible that, under some conditions at least, as in the hexose sugars, there may be a tendency to form condensed systems or rings: peculiarities in the optical behaviour of com- pounds containing paraffinoid side chains have been noticed which seem to favour such a conclusion, change proceeding regularly and uniformly, from atom to atom, as the chain is in- creased in length but a different peculiar value is observed at the fifth carbon atom and at each subsequent fifth atom. It is