The fourth dimension

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REMARKS ON THE FIGURES 179

ochre cube, and the last bounding cube, the other ochre cube. Practically three intermediate sectional cubes will be found sufficient for most purposes. We will take then a series of five figures—two terminal cubes, and three intermediate sections—and show how the different regions appear in our space when we take each set of three out of the four axes of the tesseract as lying in our space.

In fig. 107 initial letters are used for the colours. A reference to fig. 103 will show the complete nomenclature, which is merely indicated here.

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aN > a & » - wh.®. bLT pl.bl. bIT, pl. bl. bl l.bhbl, o-whons interior interior interior interior {nterior Ochre L.Brown L.Brown L.Brown Ochre Fig. 107.

In this figure the tesseract is shown in five stages distant from our space: first, zero ; second, + in.; third, 7 in. ; fourth, 2 in.; fifth, 1 in.; which are called 60, 61, 52, b3, b4, because they are sections taken at distances O, 1, 2, 3, 4 quarter inches along the blue line. All the regions can be named from the first cube, the b0 cube, as before, simply by remembering that transference along the 6 axis gives the addition of blue to the colour of the region in the ochre, the 0 cube. In the final cube b4, the colouring of the original 50 cube is repeated. Thus the red line moved along the blue axis gives a red and blue or purple square. This purple square appears as the three purple lines in the sections bl, 52, 63, taken at 4, 7, # of an inch in the fourth dimension. If the tesseract moves transverse to our space we have then in this particular region, first of all a red line which lasts for @ moment, secondly a purple line which takes its