Take again the orange face, that determined by the red and yellow axes; from it goes a brown cube in the blue direction, for red and yellow and blue are supposed to make brown. This brown cube is shown in three sections in the faces _b__{1}, _b__{2}, _b__{3}. In _b__{4} is the opposite orange face of the brown cube, the face called orange _b_, for it is distant in the blue direction from the orange face. As the tesseract passes transverse to our space, we have then in this region an instantly vanishing orange square, followed by a lasting brown square, and finally an orange face which vanishes instantly. Now, as any three axes will be in our space, let us send the white axis out into the unknown, the fourth dimension, and take the blue axis into our known space dimension. Since the white and blue axes are perpendicular to each other, if the white axis goes out into the fourth dimension in the positive sense, the blue axis will come into the direction the white axis occupied, in the negative sense. [Illustration: Fig. 108.] Hence, not to complicate matters by having to think of two senses in the unknown direction, let us send the white line into the positive sense of the fourth dimension, and take the blue one as running in the negative sense of that direction which the white line has left; let the blue line, that is, run to the left. We have now the row of figures in fig. 108. The dotted cube shows where we had a cube when the white line ran in our space—now it has turned out of our space, and another solid boundary, another cubic face of the tesseract comes into our space. This cube has red and yellow axes as before; but now, instead of a white axis running to the right, there is a blue axis running to the left. Here we can distinguish the regions by colours in a perfectly systematic way. The red line traces out a purple square in the transference along the blue axis by which this cube is generated from the orange face. This purple square made by the motion of the red line is the same purple face that we saw before as a series of lines in the sections _b__{1}, _b__{2}, _b__{3}. Here, since both red and blue axes are in our space, we have no need of duration to represent the area they determine. In the motion of the tesseract across space this purple face would instantly disappear. From the orange face, which is common to the initial cubes in fig. 107 and fig. 108, there goes in the blue direction a cube coloured brown. This brown cube is now all in our space, because each of its three axes run in space directions, up, away, to the left. It is the same brown cube which appeared as the successive faces on the sections _b__{1}, _b__{2}, _b__{3}. Having all its three axes in our space, it is given in extension; no part of it needs to be represented as a succession. The tesseract is now in a new position with regard to our space, and when it moves across our space the brown cube instantly disappears.