Thus, in spite of the very wise decision of Barlow at the time of developing his theory of the homogeneous partitioning of space, to keep quite clear of attributing shape to the structural unit atoms or molecules, and to consider them as points, he, in common with the other contributors to that splendid geometrical work, appears driven to consider the question of shape when, in collaboration with his chemical colleague, he endeavours to apply his geometrical results to the practical problems of chemistry. It may be inevitable that we cannot get away from the idea of shape of the fundamental structural units. Yet the moment we do admit the idea, and begin to talk of polyhedra, or even of spheres, in close or any other packing, we enter the debatable land, concerning which the experimental evidence is as yet but shadowy and liable to many interpretations. Hence it is that we have the parallelohedra of Von Fedorow, having volumes proportional to the molecular volumes, the more general plane-faced cell of fourteen faces, the tetrakaidecahedron of Lord Kelvin and its deformed derivatives, and now the polyhedra of Pope and Barlow. The more indefinite “Fundamentalbereich” of Schönflies appears to be left behind, and we have embarked on a definite course of attributing shape to the component atoms or their regions of influence in the crystal structure. Von Fedorow has developed his particular theory in a very masterly manner, and with the aid of it professes, and with very considerable success in many cases, to determine the correct mode of setting up a crystal for truly comparative descriptive purposes, and has derived therefrom a remarkable method of crystallochemical analysis.

Moreover, there is yet another view, that of Sollas,[[30]] that the packing of the molecules is a more open one altogether, a view to which he has been guided by consideration of the molecular volume. Sollas has offered some remarkable explanations of crystal structure, notably in the case of the dimorphous forms of silver iodide. The abnormal contraction which occurs on heating this interesting substance, and its sudden transformation at 146° from the ordinary hexagonal into a cubic modification as discovered by Lehmann, appear capable of very clear explanation on the basis of his theory. According to this theory of Sollas the volumes of the spheres of influence of the atoms of the different elements of the same family group, such as those of the group of alkali metals or those of the halogens, chlorine, bromine, and iodine, vary progressively in a manner which is dependent on the atomic volumes of the elements, which have a real comparative significance when the elements belong to the same family group.

It is probable that there is a considerable substratum of truth behind these various apparently conflicting views, and what is now required is that the germ of real fact shall be winnowed from the husk of fallacious speculation, just as occurred in the happy recent settlement of the old issue between Haüy and Mitscherlich. As in that case, moreover, it will be experimental work of superlative accuracy which can alone offer the desirable evidence on which a satisfactory arbitration can be founded.

It is thus obvious that we have now arrived at a stage in the history of crystallography when more experimental data, and many more measurements of the most carefully conducted character, on pure materials and excellently developed crystals, are most urgently needed, in order to decide these important, indeed fundamental, questions, the present state of which the author has endeavoured to present with judicial impartiality. When one looks around, and sees the almost complete lack of opportunities for the training of investigators in this rapidly growing branch of science, the importance of which to chemistry and physics is increasing every day, while the field is ripe for the harvesters, one is inclined to feel depressed with the thought of the opportunities which are being lost. Our country has, in this science at any rate, a fine record, having with few breaks led the van of progress from the time of Wollaston, the inventor in the year 1809 of the reflecting goniometer, and of Miller, the originator of our method of describing crystals and the pioneer of accurate experimental work, down to the present day. It may be, also, that our country’s reputation is safe at this moment. But it is in the hands of a band of investigators so small, and often of the private and not professional nature, carrying on the work for sheer love of it and deep interest in it, that the wonder is that so much has been done, and it is the provision for carrying on our national tradition of leadership in crystallography in the future that is a matter for the deepest concern.

If the perusal of this book should have awakened sufficient interest in the minds of some of its readers to prompt them to offer themselves as recruits to this small band of investigators, and especially if it should have inspired the zeal and enthusiasm of a few young students looking around for a promising and fascinating field of work, and, finally, if it should prove to be of assistance in obtaining the means of training such recruits with the help of the best and most accurate experimental apparatus which can be obtained, the author’s main objects in writing it will have been attained.

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