The fourth dimension

APPENDIX I 237

have to be broken up, and the layers taken in order, the first layer of each for the representation of the aspect ot the block as it touches the plane.

Then the second layers will represent the appearance half way through, and the third layers will represent the final appearance.

It is evident that the slabs individually do not represent the same portion of the cube in these different presentations. In the first case each slab represents a section or a face perpendicular to the white axis, in the second case a face or a section which runs perpendicularly to the yellow axis, and in the third case a section or a face perpendicular to the red axis.

But by means of these nine slabs the plane being can represent the whole of the cubic block. He can touch and handle each portion of the cubic block, there is no part of it which he cannot observe. Taking it bit by bit, two axes at a time, he can examine the whole of it.

Our REPRESENTATION OF A BLOCK oF TESSERACTS.

Look at the views of the tesseract 1, 2, 3, or take the catalogue cubes 1, 2, 3, and place them in front of you, in any order, say running from left to right, placing 1 in the normal position, the red axis running up, the white to the right, and yellow away. -

Now notice that in catalogue cube 2 the colours of each region are derived from those of the corresponding region of cube 1 by the addition of blue. Thus null+blue= blue, and the corners of number 2 are blue. Again, red + blue=purple, and the vertical lines of 2 are purple. Blue+yellow=green, and the line which runs away is coloured green.

By means of these observations you may be sure that