The fourth dimension

80 THE FOURTH DIMENSION

Let us consider a sphere of our three-dimensional 2 matter having a definite thickness. To represent iB this thickness let us supD pose that from every point of the sphere in fig. 44 rods project both ways, in and gy out, like Dandr. We can only see the external portion, because the internal parts are hidden by the ; sphere.

Dis In this sphere the axis Axis of x running towards ok supposed to come WATS RE towards the observer, the

axis of z to run up, the axis of y to go to the right. Now take the section determined by the zy plane. 2 This will be a circle as shown in fig. 45. If we let drop the 2 axis, this circle is all we have of the sphere. Letting the qw axis now run in the place of the old @ axis we have the space yzw, and in this space all that we have of the sphere is the circle. Fig. 45 then 4 represents all that there HAG. TS9- is of the sphere in the space of yzw. In this space it is evident that the rods cD and EF can turn round the circumference as an axis. If the matter of the spherical shell is sufficiently extensible to allow the particles c and E to become as widely separated as they would be in the positions D and F, then