This fourth dimension is supposed to run at right angles to any of the three space dimensions, as the third space dimension runs at right angles to the two dimensions of a plane, and thus it gives us the opportunity of generating a new kind of volume. If the whole cube moves in this dimension, the solid itself traces out a path, each section of which, made at right angles to the direction in which it moves, is a solid, an exact repetition of the cube itself. The cube as we see it is the beginning of a solid of such a kind. It represents a kind of tray, as the square face of the cube is a kind of tray against which the cube rests. Suppose the cube to move in this fourth dimension in four stages, and let the hyper-solid region traced out in the first stage of its progress be characterised by this, that the terms of the syllogism are in the first figure, then we can represent in each of the three subsequent stages the remaining three figures. Thus the whole cube forms the basis from which we measure the variation in figure. The first figure holds good for the cube as we see it, and for that hyper-solid which lies within the first stage; the second figure holds good in the second stage, and so on. Thus we measure from the whole cube as far as figures are concerned. But we saw that when we measured in the cube itself having three variables, namely, the two premisses and the conclusion, we measured from three planes. The base from which we measured was in every case the same. Hence, in measuring in this higher space we should have bases of the same kind to measure from, we should have solid bases. The first solid base is easily seen, it is the cube itself. The other can be found from this consideration. That solid from which we measure figure is that in which the remaining variables run through their full range of varieties. Now, if we want to measure in respect of the moods of the major premiss, we must let the minor premiss, the conclusion, run through their range, and also the order of the terms. That is we must take as basis of measurement in respect to the moods of the major that which represents the variation of the moods of the minor, the conclusion and the variation of the figures. Now the variation of the moods of the minor and of the conclusion are represented in the square face on the left of the cube. Here are all varieties of the minor premiss and the conclusion. The varieties of the figures are represented by stages in a motion proceeding at right angles to all space directions, at right angles consequently to the face in question, the left-hand face of the cube. Consequently letting the left-hand face move in this direction we get a cube, and in this cube all the varieties of the minor premiss, the conclusion, and the figure are represented. Thus another cubic base of measurement is given to the cube, generated by movement of the left-hand square in the fourth dimension.