Instead of imagining a direction he did not know, the plane-being could think of the Dark-blue square as lying in his plane. But in this case the Black square would be out off his plane, and only the Orange line would remain in it. Diagram (3) shows the Dark-blue square lying in his plane, and Diagram (4) shows it turning round the Gold point. Here, instead of thinking about his plane and also that at right angles to it, he has only to think how the square turning round the Gold point will cut the line, which runs left to right from G, viz., the dotted line. The French-grey line is cut by the dotted line in a point. To find out what would come in at other parts, he need only treat a number of the plane sections of the cube perpendicular to the Black square in the same manner as he had treated the Dark-blue square. Every such section would turn round a point, as the whole cube turned round the Blue line. Thus he would treat the cube as a number of squares by taking parallel sections from the Dark-blue to the Light-yellow square, and he would turn each of these round a corner of the same colour as the Blue line. Combining these series of appearances, he would discover what came into his plane as the cube turned round the Blue line. Thus, the problem of the turning of the cube could be settled by the consideration of the turnings of a number of squares. As the cube turned, a number of different appearances would be presented to the plane-being. The Black square would change into a Light-buff oblong, with Dark-blue, Blue-green, Light-yellow, and Blue sides, and would gradually elongate itself until it became as long as the diagonal of the square side of the cube; and then the bounding line opposite to the Blue line would change from Blue-green to Bright-blue, the other lines remaining the same colour. If the cube then turned still further, the Bright-blue line would become White, and the oblong would diminish in length. It would in time become a Vermilion square, with a Deep-yellow line opposite to the Blue line. It would then pass wholly below the plane, and only the Blue line would remain.