_Model 1._ _Model 2._ Gold corresponds to Silver Fawn „ „ Turquoise Terra-cotta „ „ Earthen Buff „ „ Blue tint Light-blue „ „ Quaker-green Dull-purple „ „ Peacock-blue Deep-blue „ „ Orange-vermilion Red „ „ Purple LINES. _Model 1._ _Model 2._ Orange corresponds to Leaf-green Crimson „ „ Dull-green Green-grey „ „ Dark-purple Blue „ „ Purple-brown Brown „ „ Dull-blue French-grey „ „ Dark-pink Dark-slate „ „ Pale-pink Green „ „ Indigo Reddish „ „ Brown-green Bright-blue „ „ Dark-green Leaden „ „ Pale-yellow Deep-yellow „ „ Dark The colour of the cube itself is invisible, as it is covered by its boundaries. We suppose it to be Sage-green. These two cubes are just as disconnected when looked at by us as the black and white squares would be to a plane-being if placed side by side on his plane. He cannot see the squares in their right position with regard to each other, nor can we see the cubes in theirs. Let us now consider the vermilion side of Model 1. If it move in the X direction, it traces the cube of Model 1. Its Gold point travels along the Orange line, and itself, after tracing the cube, ends in the Blue-green square. But if it moves in the new direction, it will also trace a cube, for the new direction is at right angles to the up and away directions, in which the Brown and Blue lines run. Let this square, then, move in the unknown direction, and trace a cube. This cube we cannot see, because the unknown direction runs out of our space at once, just as the up direction runs out of the plane of the table. But a plane-being could see the square, which the Blue line traces when moved upwards, by the cube being turned round the Blue line, the Orange line going upwards; then the Brown line comes into the plane of the table in the -X direction. So also with our cube. As treated above, it runs from the Vermilion square out of our space. But if the tessaract were turned so that the line which runs from the Gold point in the unknown direction lay in our space, and the Orange line lay in the unknown direction, we could then see the cube which is formed by the movement of the Vermilion square in the new direction.