You have now a cube like that which is described in the text. For the sake of simplicity, in some cases, this cubic block can be reduced to one of eight cubes, by leaving out the terminations in each direction. Thus, instead of null, red, null, three cubes, you can take null, red, two cubes, and so on. It is useful, however, to practise the representation in a plane of a block of twenty-seven cubes. For this purpose take the slabs, and build them up against the piece of cardboard, or the book in such a way as to represent the different aspects of the cube. Proceed as follows:— First, cube in normal position. Place nine slabs against the cardboard to represent the nine cubes in the wall of the red and yellow axes, facing the cardboard; these represent the aspect of the cube as it touches the plane. Now push these along the cardboard and make a different set of nine slabs to represent the appearance which the cube would present to a plane being, if it were to pass half way through the plane. There would be a white slab, above it a pink one, above that another white one, and six others, representing what would be the nature of a section across the middle of the block of cubes. The section can be thought of as a thin slice cut out by two parallel cuts across the cube. Having arranged these nine slabs, push them along the plane, and make another set of nine to represent what 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 is a 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. It is, 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.