And if, having put up the block, we coloured the sides of the cube we used as the fundamental cube, and told him how we had coloured it: if he coloured his and brought it to us, and we compared them, his would just as likely be the image of our cube, and not able to be turned into it. So that although, as arrangements, the structures we had put up were alike, still neither of us could use the other’s fundamental cube; and if we exchanged the fundamental cubes there would be an inconsistency in each of our arrangements. Now, are these blocks of cubes really the same? Are III. and IV. really the same in themselves, as all relationships in the one are to be found in the other? If so, the feeling on my part that they are different, and the inconceivability of their coinciding, must be due to some self-element which is mixed up with my apprehension of the cube. The Block IV. is like the Block III. in its known part—in its arrangement. It is unlike Block III. in its unknown part—the cube which must ultimately be supposed as the fundamental cube, by using which over and over again the whole is built up. Now, the properties of the unknown part—the little cube of matter which of some size or another, we must assume, are so mysterious that one does not feel any argument very safe which rests on it. Moreover, there is a very obvious consideration which reduces the importance of the part played by the material cube very considerably. It is possible to consider the Cube V., which is used to build up III., as the total of 27 cubes. But each of these cubes—the small cubes in Diag. V.—can be considered to be made up of 27 still smaller cubes. By going on in this way we can get our fundamental cube very small indeed. The difference between the Cubes III. and IV., in respect to this fundamental cube, will still remain. But omitting this difference they will be, considered as arrangements, identical. To state the matter over again. We start with a real cube, one inch each way, and build up the block in Diagram III. with it. If we try to build up the block in Diagram IV. with this same inch cube, we find that there is a disadjustment. But we are not obliged to have our fundamental cube one inch in size. We can take it as small as we like, and build up the block, using a greater number of such cubes. We can take it the twenty-seventh of the twenty-seventh of an inch cube; or, in fact, as small as ever we like. And if we take a very small cube as the fundamental one with which we build up the Block III., then, using this same fundamental cube to build up Block IV., we should find a disadjustment, although this disadjustment would only come in when we come down to the very minute cube, and studied its relationship to the whole Block IV. Thus, apparently, the Block IV. could never be built up consistently, using as its fundamental cube the fundamental cube out of Block III. But in saying this we have really made an assumption.