The fourth dimension

NOMENCLATURE AND ANALOGIES 149

solid in contradistinction to his area solid, his twodimensional solid, must be conceived by him as something which has duration in it, under circumstances in which his matter disappears out of his world.

We may put the matter thus, using the conception of motion,

A null point moving in a direction away generates a yellow line, and the yellow line ends in a null point. We suppose, that is, a point to move and mark out the products of this motion in such a manner. Now suppose this whole line as thus produced to move in an upward direction; it traces out the two-dimensional solid, and the plane being gets an orange square. The null point moves in a red line and ends in a null point, the yellow line moves and generates an orange square and ends in a yellow line, the farther null point generates a red line and ends in a null point. Thus, by movement in two successive directions known to him, he can imagine his two-dimensional solid produced with all its boundaries. .

Now we tell him: “This whole two-dimensional solid can move in a third or unknown dimension to you. The null point moving in this dimension out of your world generates a white line and ends in a null point. The yellow line moving generates a light yellow twodimensional solid and ends in a yellow line, and thus two-dimensional solid, lying end on to your plane world, is bounded on the far side by the other yellow line. In the same way each of the lines surrounding your square traces out an area, just like the orange area you know. But there is something new produced, something which you had no idea of before ; it is that which is produced by the movement of the orange square. That, than which you can imagine nothing more solid, itself moves in a direction open to it and produces a three-dimensional