There are two starting-points, either of which we can adopt. We can start with the real material cube, or we can start with the act of arranging. When I speak of the real material cube I do not want to call attention to the kind of matter of which it is composed, or to the nature of matter, but to the fact that it is to be a real cube such as can be made, and which, if one edge or corner be marked, will retain that mark just where it is—a cube which is not a product of the imagination, but an object, with the properties of objects in general.
Diagram IV. is its image block.
Diagram VI.
Let us start with the real material cube. Let us take the cube shown in Diagram V., which is the model on a small scale of the Block III. The numbers in it show the small cubes of which we suppose it to be built up after the pattern of Block III. The numbers also serve to show the distinction of positions—that is, we can refer to the right-hand corner or edge, &c., by saying the numbers of the small cube which lies there.
Now, using the cube of Diagram V. to build up the block in Diagram III. we get a perfectly orderly result, as shown in Diagram VII., and we can go to bigger and bigger blocks, or down to smaller and smaller ones without any hitch. But if we use the cube of Diagram V. to build up the block of Diagram IV., there is a disadjustment which can be discerned in Diagram VIII. Thus, when V. is used to build up III., the small cubes in V., 1, 4, 7, lie in same edge as the cubes 1, 4, 7, in the big Cube III. But when V. is used to build up IV., the small cubes 3, 6, 9, lie on the edge which is occupied by the cubes 1, 4, 7, in big Cube IV.
Diagram VII.—Block III. built up with Cube V.
