The fourth dimension

NOMENCLATURE AND ANALOGIES 147

it closes around objects pushed through it, and, however the object alters its shape as it passes through it, let us suppose this film to run up to the contour of the object in eyery part, maintaining its plane surface unbroken.

Then we can push a cube or any object through the film and the plane being who slips about in the film will know the contour of the cube just and exactly where the film meets it.

Fig. 90 represents a cube passing through a plane film. The plane being now comes into contact with a very thin slice of the cube somewhere between the left and right hand faces. This very thin slice he thinks of as having no thickness, and consequently his idea of it is what we call a section. It is bounded by him by pink lines front and back, coming from

Fig-/ 90. the part of the pink face he is in contact with, and above and below, by light yellow lines. Its corners are not null-coloured points, but white points, and its interior is ochre, the colour of the interior of the cube.

If now we suppose the cube to be an inch in each dimension, and to pass across, from right to left, through the plane, then we should explain the appearances presented to the plane being by saying: First of all you have the face of a cube, this lasts only a moment; then you have a figure of the same shape but differently coloured. This, which appears not to move to you in any direction which you know of, is really moving transverse to your plane world. Its appearance is unaltered, but each moment it is something different—a section further on, in the white, the unknown dimension. Finally, at the