The fourth dimension

THE HIGHER WORLD 71

turn these rods in our space about the lines a and B, as the upper end of one, F, is going down, the lower end of the other, c, will be coming up. They will meet and conflict. But it is quite possible for these two rods each of them to turn about the two lines without altering their relative distances.

To see this suppose the y axis to go, and let the w axis take its place. We shall see the lines a and B no longer, for they run in the y direction from the points G and H.

Fig. 43 is a picture of the two rods seen in the space

of wzw. If they rotate in the

direction shown by the arrows—

in the z to w direction—they

D F move parallel to one another,

keeping their relative distances.

Each will rotate about its own

line, but their rotation will not

be inconsistent with their form-

ing part of a rigid body.

Fig, 43. Now we have but to suppose

a central plane with rods crossing

it at every point, like cp and EF cross the plane of ay,

to have an image of a mass of matter extending equal

distances on each side of a diametral plane. As two of

these rods can rotate round, so can all, and the whole mass of matter can rotate round its diametral plane.

This rotation round a plane corresponds, in four dimensions, to the rotation round an axis in three dimensions. Rotation of a body round a plane is the analogue of rotation of a rod round an axis.

In a plane we have rotation round a point, in threespace rotation round an axis line, in four-space rotation round an axis plane.

The four-dimensional being’s shaft by which he transmits power isa disk rotating round its central plane—

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