Take Model 5. There is on it a Vermilion square. Place this so that it touches the Vermilion square on Model 1. All the marks of the two squares are identical. This Cube 5, is the one traced by the Vermilion square moving in the unknown direction. In Model 5, the whole figure, the tessaract, produced by the movement of the cube in the unknown direction, is supposed to be so turned that the Orange line passes into the unknown direction, and that the line which went in the unknown direction, runs opposite to the old direction of the Orange line. Looking at this new cube, we see that there is a Stone line running to the left from the Gold point. This line is that which the Gold point traces when moving in the unknown direction. It is obvious that, if the Tessaract turns so as to show us the side, of which Cube 5 is a model, then Cube 1 will no longer be visible. The Orange line will run in the unknown or fourth direction, and be out of our sight, together with the whole cube which the Vermilion square generates, when the Gold point moves along the Orange line. Hence, if we consider these models as real portions of the tessaract, we must not have more than one before us at once. When we look at one, the others must necessarily be beyond our sight and touch. But we may consider them simply as models, and, as such, we may let them lie alongside of each other. In this case, we must remember that their real relationships are not those in which we see them. We now enumerate the sides of the new Cube 5, so that, when we refer to it, any colour may be recognised by name. The square Vermilion traces a Pale-green cube, and ends in an Indian-red square. (The colour Pale-green of this cube is not seen, as it is entirely surrounded by squares and lines of colour.) Each Line traces a Square and ends in a Line. The Blue line} {Light-brown square} and{Purple-brown line „ Brown „ }traces{Yellow „ }ends{Dull-blue „ „ Deep-yellow „ } a {Light-red „ } in {Dark „ „ Green „ } {Deep-crimson „ } a {Indigo „. Each Point traces a Line and ends in a Point. The Gold point} {Stone line} and{Silver point „ Buff „ }traces{Light-green „ }ends{Blue-tint „ „ Light-blue „ } a {Rich-red „ } in {Quaker-green „ „ Red „ } {Emerald „ } a {Purple „.