The fourth dimension

12 THE FOURTH DIMENSION

his plane, each lying in the third dimension a little further off from his plane than the preceding one. These sections he can represent as a series of plane figures lying in = his plane, but in so representing wae them he destroys the coherence of them in the higher figure. The set of squares, A, B, C, D, represents the section parallel to the plane of the cube shown in figure, but they are not in their proper relative positions.

The plane being can trace out a movement in the third dimension by assuming discontinuous leaps from one section to another. Thus, a motion along the edge of the cube from left to right would be represented in the set of sections in the plane as the succession of the corners of the sections A, B, C, D. A point moving from a through BCD in our space must be represented in the plane as appearing in A, then in B, and so on, without passing through the intervening plane space.

In these sections the plane being leaves out, of course, the extension in the third dimension ; the distance between any two sections is not represented. In order to realise this distance the conception of motion can be employed.

Let fig. 9 represent a cube passing transverse to the

plane. It will appear to the plane being as a

square object, but the matter of which this

object is composed will be continually altering.

One material particle takes the place of another,

but it does not come from anywhere or go

anywhere in the space which the plane being Fig. 9. knows.

The analogous manner of representing a higher solid in our case, is to conceive it as composed of a number of

Fig. 8