In the block C we observe that red (light purple cube) touches light blue (light purple cube) by a point. Now these two cubes moving together remain in contact during the period in which they trace out the tesseracts red and light blue. This motion is along the yellow axis, consequently red and light blue touch by a yellow line. We have seen that the pink face moved in a yellow direction traces out a cube; moved in the blue direction it also traces out a cube. Let us ask what the pink face will trace out if it is moved in a direction within the tesseract lying equally between the yellow and blue directions. What section of the tesseract will it make? We will first consider the red line alone. Let us take a cube with the red line in it and the yellow and blue axes. The cube with the yellow, red, blue axes is shown in fig. 113. If the red line is moved equally in the yellow and in the blue direction by four equal motions of ¼ inch each, it takes the positions 11, 22, 33, and ends as a red line. [Illustration: Fig. 113.] Now, the whole of this red, yellow, blue, or brown cube appears as a series of faces on the successive sections of the tesseract starting from the ochre cube and letting the blue axis run in the fourth dimension. Hence the plane traced out by the red line appears as a series of lines in the successive sections, in our ordinary way of representing the tesseract; these lines are in different places in each successive section. [Illustration: Fig. 114.] Thus drawing our initial cube and the successive sections, calling them _b__{0}, _b__{1}, _b__{2}, _b__{3}, _b__{4}, fig. 115, we have the red line subject to this movement appearing in the positions indicated. We will now investigate what positions in the tesseract another line in the pink face assumes when it is moved in a similar manner. Take a section of the original cube containing a vertical line, 4, in the pink plane, fig. 115. We have, in the section, the yellow direction, but not the blue. From this section a cube goes off in the fourth dimension, which is formed by moving each point of the section in the blue direction. [Illustration: Fig. 115.] [Illustration: Fig. 116.] Drawing this cube we have fig. 116. Now this cube occurs as a series of sections in our original representation of the tesseract. Taking four steps as before this cube appears as the sections drawn in _b__{0}, _b__{1}, _b__{2}, _b__{3}, _b__{4}, fig. 117, and if the line 4 is subjected to a movement equal in the blue and yellow directions, it will occupy the positions designated by 4, 4_{1}, 4_{2}, 4_{3}, 4_{4}. [Illustration: Fig. 117.] Hence, reasoning in a similar manner about every line, it is evident that, moved equally in the blue and yellow directions, the pink plane will trace out a space which is shown by the series of section planes represented in the diagram.