The fourth dimension

98 THE FOURTH DIMENSION

our space. It can only be represented by a device analogous to that by which the plane being represents a cube.

He represents the cube shown above, by taking four square sections and placing them arbitrarily at convenient distances the one from the other.

So we must represent this higher solid by four cubes: each cube represents only the beginning of the corresponding higher volume.

It is sufficient for us, then, if we draw four cubes, the first representing that region in which the figure is of the first kind, the second that region in which the figure is of the second kind, and so on. These cubes are the beginnings merely of the respective regions—they are the trays, as it were, against which the real solids must be conceived as resting, from which they start. The first one, as it is the beginning of the region of the first figure, is characterised by the order of the terms in the premisses being that of the first figure. The second similarly has the terms of the premisses in the order of the second figure, and so on.

These cubes are shown below.

For the sake of showing the properties of the method of representation, not for the logical problem, I will make a digression. I will represent in space the moods of the minor and of the conclusion and the different figures, keeping the major always in mood 4. Here we have three variables in different stages, the minor, the conclusion, and the figure. Let the square of the left-hand side of the original cube be imagined to be standing by itself, without the solid part of the cube, represented by (2) fig. 55. The a, £, 1, 0, which run away represent the moods of the minor, the A, E, 1, 0, which run up represent the moods of the conclusion. The whole square, since it is the beginning of the region in the major premiss, mood A, is to be considered as in major premiss, mood A.