In fig. 109 we take red, white, and blue axes in space, sending yellow into the fourth dimension. If it goes into the positive sense of the fourth dimension the blue line will come in the opposite direction to that in which the yellow line ran before. Hence, the cube determined by the white, red, blue axes, will start from the pink plane and run towards us. The dotted cube shows where the ochre cube was. When it is turned out of space, the cube coming towards from its front face is the one which comes into our space in this turning. Since the yellow line now runs in the unknown dimension we call the sections _y__{0}, _y__{1}, _y__{2}, _y__{3}, _y__{4}, as they are made at distances 0, 1, 2, 3, 4, quarter inches along the yellow line. We suppose these cubes arranged in a line coming towards us—not that that is any more natural than any other arbitrary series of positions, but it agrees with the plan previously adopted. [Illustration: Fig. 109.] The interior of the first cube, _y__{0}, is that derived from pink by adding blue, or, as we call it, light purple. The faces of the cube are light blue, purple, pink. As drawn, we can only see the face nearest to us, which is not the one from which the cube starts—but the face on the opposite side has the same colour name as the face towards us. The successive sections of the series, _y__{0}, _y__{1}, _y__{2}, etc., can be considered as derived from sections of the _b__{0} cube made at distances along the yellow axis. What is distant a quarter inch from the pink face in the yellow direction? This question is answered by taking a section from a point a quarter inch along the yellow axis in the cube _b__{0}, fig. 107. It is an ochre section with lines orange and light yellow. This section will therefore take the place of the pink face in _y__{1} when we go on in the yellow direction. Thus, the first section, _y__{1}, will begin from an ochre face with light yellow and orange lines. The colour of the axis which lies in space towards us is blue, hence the regions of this section-cube are determined in nomenclature, they will be found in full in fig. 105. There remains only one figure to be drawn, and that is the one in which the red axis is replaced by the blue. Here, as before, if the red axis goes out into the positive sense of the fourth dimension, the blue line must come into our space in the negative sense of the direction which the red line has left. Accordingly, the first cube will come in beneath the position of our ochre cube, the one we have been in the habit of starting with. [Illustration: Fig. 110.]