From this square, let it be supposed that that direction in which the figures are represented runs to the left hand. Thus we have a cube (1) running from the square above, in which the square itself is hidden, but the letters A, E, I, O, of the conclusion are seen. In this cube we have the minor premiss and the conclusion in all their moods, and all the figures represented. With regard to the major premiss, since the face (2) belongs to the first wall from the left in the original arrangement, and in this arrangement was characterised by the major premiss in the mood A, we may say that the whole of the cube we now have put up represents the mood A of the major premiss. [Illustration: Fig. 55.] Hence the small cube at the bottom to the right in 1, nearest to the spectator, is major premiss, mood A; minor premiss, mood A; conclusion, mood A; and figure the first. The cube next to it, running to the left, is major premiss, mood A; minor premiss, mood A; conclusion, mood A; figure 2. So in this cube we have the representations of all the combinations which can occur when the major premiss, remaining in the mood A, the minor premiss, the conclusion, and the figures pass through their varieties. In this case there is no room in space for a natural representation of the moods of the major premiss. To represent them we must suppose as before that there is a fourth dimension, and starting from this cube as base in the fourth direction in four equal stages, all the first volume corresponds to major premiss A, the second to major premiss, mood E, the next to the mood I, and the last to mood O. The cube we see is as it were merely a tray against which the four-dimensional figure rests. Its section at any stage is a cube. But a transition in this direction being transverse to the whole of our space is represented by no space motion. We can exhibit successive stages of the result of transference of the cube in that direction, but cannot exhibit the product of a transference, however small, in that direction. [Illustration: Fig. 56.] To return to the original method of representing our variables, consider fig. 56. These four cubes represent four sections of the figure derived from the first of them by moving it in the fourth dimension. The first portion of the motion, which begins with 1, traces out a more than solid body, which is all in the first figure. The beginning of this body is shown in 1. The next portion of the motion traces out a more than solid body, all of which is in the second figure; the beginning of this body is shown in 2; 3 and 4 follow on in like manner. Here, then, in one four-dimensional figure we have all the combinations of the four variables, major premiss, minor premiss, figure, conclusion, represented, each variable going through its four varieties. The disconnected cubes drawn are our representation in space by means of disconnected sections of this higher body.