The fourth dimension

200 THE FOURTH DIMENSION

Here (fig. 125) we have the null r, y, b points, and of the sectional space all we see is the plane throughthese three points in it.

In this figure we can draw the parallels to the red and yellow axes and see that, if they started at a point half way along the blue axis, they would each be cut at a point so as to be half of their previous length.

Swinging the tesseract into our space about the pink face of the ochre cube we likewise find that the parallel to the white axis is cut at half its length by the sectional space.

Hence in a section made when the tesseract had passed half across our space the parallels to the red, white, yellow

: axes, which are now in our Light green

space, are cut by the section Light purple

laa Null-b. Blue Fig, 125.

space, each of them half way along, and for this stage of the traversing motion we should have fig. 126. The section made of this cube by the plane in which the sectional space cuts it, is an equilateral triangle with purple, 1. blue, green points, and 1. purple, brown, 1. green lines.

Thus the original ochre triangle, with null points and pink, orange, light yellow lines, would be succeeded by a triangle coloured in manner just described.

This triangle would initially be only a very little smaller than the original triangle, it would gradually diminish, until it ended in a point, a null point. Each of its edges would be of the same length. Thus the successive

Blue L.blue bl. Section bz interior Light brown Fig, 126,