There is a method of approaching the matter, which settles all difficulties, and provides us with a nomenclature for every part of the tessaract. We have seen how by writing down the names of the cubes of a block, and then supposing that their number increases, certain sets of the names come to denote points, lines, planes, and solid. Similarly, if we write down a set of names of tessaracts in a block, it will be found that, when their number is increased, certain sets of the names come to denote the various parts of a tessaract. For this purpose, let us take the 81 Set, and use the cubes to represent tessaracts. The whole of the 81 cubes make one single tessaractic set extending three inches in each of the four directions. The names must be remembered to denote tessaracts. Thus, Corvus is a tessaract which has the tessaracts Cuspis and Nugæ to the right, Arctos and Ilex above it, Dos and Cista away from it, and Ops and Spira in the fourth or unknown direction from it. It will be evident at once, that to write these names in any representative order we must adopt an arbitrary system. We require them running in four directions; we have only two on paper. The X direction (from left to right) and the Y (from the bottom towards the top of the page) will be assumed to be truly represented. The Z direction will be symbolized by writing the names in floors, the upper floors always preceding the lower. Lastly, the fourth, or W, direction (which has to be symbolized in three-dimensional space by setting the solids in an arbitrary position) will be signified by writing the names in blocks, the name which stands in any one place in any block being next in the W direction to that which occupies the same position in the block before or after it. Thus, Ops is written in the same place in the Second Block, Spira in the Third Block, as Corvus occupies in the First Block. Since there are an equal number of tessaracts in each of the four directions, there will be three floors Z when there are three X and Y. Also, there will be three Blocks W. If there be four tessaracts in each direction, there will be four floors Z, and four blocks W. Thus, when the number in each direction is enlarged, the number of blocks W is equal to the number of tessaracts in each known direction. On pp. 136, 137 were given the names as used for a cubic block of 27 or 64. Using the same and more names for a tessaractic Set, and remembering that each name now represents, not a cube, but a tessaract, we obtain the following nomenclature, the order in which the names are written being that stated above: THIRD BLOCK.