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.
[Illustration: Diagram VII.—Block III. built up with Cube V.]
[Illustration: Diagram VIII.—Block IV. built up with Cube V.—a disadjustment.]
Thus, if the same material cube is used, there is a disadjustment, and the figure IV. cannot be considered the same as the figure III. even as an arrangement, for the same parts of the cubes do not lie in an analogous manner. A certain corner of Cube V. is marked with the figure 7; this corner would be on the outside in Block III., but in building up Block IV. it would lie on the inside.
It is somewhat difficult to express this fact, but if the real cubes are looked at it becomes perfectly obvious.
Imagine the whole Block III. to be built up of a number of cubes, every one of which is alike. If the sides of these cubes be distinguished by any markings—if, for instance, the left-hand side is blue and the other sides are each of some special colour, then on building up the whole block the left-hand side of the whole block will be blue.
If, now, the same cubes be taken, and the attempt be made to build up the looking-glass image of the block with them, it will be found that there will be a disadjustment. If the blue sides are made to go to the right, as they must, to form an image block, then some other sides will be in different places to what they should be in order to produce an image of the original block. Although considered as an arrangement of cubes the new block will be an image of the original block, still, looking at the individual cubes of which it is composed, it will be seen that the new block is not an exact image of the old block.