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 familiarity with our cube. Turn the catalogue cube (or imagine the coloured figure turned) so that the red line runs up, the yellow line out to the right, and the white line towards you. Then turn the block of cubes to occupy a similar position. The block has now a different wall in contact with the plane. Its appearance to a plane being will not be the same as before. He has, however, enough slabs to represent this new set of appearances. But he must remodel his former arrangement of them. He must take a null, a red, and a null slab from the first of his sets of slabs, then a white, a pink, and a white from the second, and then a null, a red, and a null from the third set of slabs. He takes the first column from the first set, the first column from the second set, and the first column from the third set. To represent the half-way-through appearance, which is as if a very thin slice were cut out half way through the block, he must take the second column of each of his sets of slabs, and to represent the final appearance, the third column of each set. Now turn the catalogue cube back to the normal position, and also the block of cubes. There is another turning—a turning about the yellow line, in which the white axis comes below the support. You cannot break through the surface of the table, so you must imagine the old support to be raised. Then the top of the block of cubes in its new position is at the level at which the base of it was before. Now representing the appearance on the plane, we must draw a horizontal line to represent the old base. The line should be drawn three inches high on the cardboard. Below this the representative slabs can be arranged. It is easy to see what they are. The old arrangements have to be broken up, and the layers taken in order, the first layer of each for the representation of the aspect of the block as it touches the plane. Then the second layers will represent the appearance half way through, and the third layers will represent the final appearance. It is evident that the slabs individually do not represent the same portion of the cube in these different presentations. In the first case each slab represents a section or a face perpendicular to the white axis, in the second case a face or a section which runs perpendicularly to the yellow axis, and in the third case a section or a face perpendicular to the red axis. But by means of these nine slabs the plane being can represent the whole of the cubic block. He can touch and handle each portion of the cubic block, there is no part of it which he cannot observe. Taking it bit by bit, two axes at a time, he can examine the whole of it. OUR REPRESENTATION OF A BLOCK OF TESSERACTS.