The fourth dimension

THE ANALOGY OF A PLANE WORLD 13

sections, each lying a little further off in the unknown sete than the preceding. We can represent these sections as a number of solids.

Thus the cubes 4, B, C, D,

may be considered as

the sections at different intervalsin the unknown dimension of a higher cube. Arranged thus their coherence in the higher figure is destroyed, they are mere representations.

A motion in the fourth dimension from 4 through B, ¢, ete., would be continuous, but we can only represent it as the occupation of the positions 4, B, C, etc., in succession. We can exhibit the results of the motion at different stages, but no more.

In this representation we have left out the distance between one section and another; we have considered the higher body merely as a series of sections, and so left out its contents. The only way to exhibit its contents is to call in the aid of the conception of motion.

If a higher cube passes transverse to our space, it will appear as a cube isolated in space, the part that has not come into our space and the part that has passed through will not be visible.

The gradual passing through our space would appear as the change of the matter of the cube before us, One material particle in it is succeeded by another, neither coming nor going in any direction we can point to. In this manner, by the duration of the figure, we can exhibit the higher dimensionality of it; a cube of our matter, under the circumstances supposed, namely, that it has a motion transverse to our space, would instantly disappear. A higher cube would last till it had passed transverse to our space by its whole distance of extension in the fourth dimension.

= i

Fig. 11.