There is one inherent difficulty, however, which renders all such speculations more or less chimerical, until we know very much more as to the structure of the chemical atom, and the organisation of the corpuscles composing it. Such speculations, however, are deeply interesting, and the difficulty alluded to accounts largely for the great variety of conception possible. It is this, that the matter of the molecules, and again that of the atoms composing them, is not necessarily, nor even probably, continuous and in contact throughout, but that on the contrary the space which may legitimately be assigned to the unit of the structure is partly void. How much of this unit space is matter and how much is unoccupied, and how the one is related to the other as regards its position or distribution in space, we have yet no means of knowing, although there are signs that the day is not far distant when we shall know at least something concerning it. The recent brilliant work of Sir J. J. Thomson and his school of physicists has rendered it clear that the chemical atom is composed of cycles of electronic corpuscles, the orbital motions of which determine its boundaries. In this condition of our knowledge obviously the only safe course is to consider each atom of the chemical molecule as occupying a “sphere of influence,” within the limits of which the material parts of the atom, the corpuscles in organised motion, are confined. The “Fundamentalbereich” of Schönflies and the “Sphere of Influence” of Barlow, are the conceptions which in all probability have the greatest value in the present state of our knowledge, and if we adopt the latter we shall not be committing ourselves to anything more than the experimental facts fully warrant. It may be quite definitely stated, however, that there is a considerable amount of experimental evidence that the unit of the space-lattice of the crystal structure is certainly not more complex than the chemical molecule, the idea of an aggregation of chemical molecules to form a “physical molecule” acting as a structural unit having proved to be a misleading myth. Fortunately, however, there is no necessity whatever to introduce the subject of the actual shape of the unit, and the greatest progress has been effected by disregarding it altogether, and agreeing to the representation of the unit by a point. This leads us at once to perceive the importance of the brilliant work of the geometricians, who have now completed their theory of the homogeneous partitioning of space into point-systems possible to crystals, the structural units of the latter being regarded as points. The investigations extend from those of Frankenheim in the year 1830 to the finishing touches given by Barlow in 1894, and prominently standing forth as those of the greatest contributors to the subject, besides the two investigators just mentioned, are the names of Bravais, Sohncke, Schönflies and von Fedorow.