The fourth dimension

APPENDIX I 235

would be the appearance of the cube when it had almost completely gone through. This set of nine will be the same as the first set of nine.

Now we have in the plane three sets of nine slabs each, which represent three sections of the twenty-seven block.

They are put alongside one another. We see that it does not matter in what order the sets of nine are put. As the cube passes through the plane they represent appearances which follow the one after the other. If they were what they represented, they could not exist in the same plane together.

This isa rather important point, namely, to notice that they should not co-exist on the plane, and that the order in which they are placed is indifferent. When we represent a four-dimensional body our solid cubes are to us in the same position that the slabs are to the plane being. You should also notice that each of these slabs represents only the very thinnest slice of a cube. The set of nine slabs first set up represents the side surface of the block. Itis, as it were, a kind of tray—a beginning from which the solid cube goes off. The slabs as we use them have thickness, but this thickness is a necessity of construction. They are to be thought of as merely of the thickness of a line.

If now the block of cubes passed through the plane at the rate of an inch a minute the appearance to a plane being would be represented by :—

1. The first set of nine slabs lasting for one minute.

2. The second set of nine slabs lasting for one minute.

3. The third set of nine slabs lasting for one minute.

Now the appearances which the cube would present to the plane being in other positions can be shown by means of these slabs. The use of such slabs would be the means by which a plane being could acquire a