It is not to be wondered at that metageometricians and others should at first surmise that, in the four-space, they had found the key to the deep mysteries of nature in all branches of inquiry. For so vast was the domain and so marvelous were the possibilities which the new movement revealed that it was to be expected that those who were privileged to get the first glimpses thereof would not be able to realize fully their significance. But the stound of their minds and the attendant magnification of the elements which they discovered were but incidents in the larger and more comprehensive process of adjustment to the great outstanding facts of psychogenesis which is only faintly foreshadowed in the so-called hyperdimensional. The whole scope of inquiry connected with hyperspace is not an end in itself. It is merely a means to an end. And that is the preparation of the human mind for the inborning of a new faculty and consequently more largely extended powers of cognition. Metageometrical discoveries are therefore the excrescences of a deeper, more significant world process of mental unfoldment. They belong to the matutinal phenomena incident to this new stage of mental evolution. All such investigations are but the preliminary exercises which give birth to new tendencies which are destined to flower forth into additional faculties and capacities. So that it is well that the evolutionary aspect of the question be not overlooked; for there is danger of this on account of the magnitude and kosmic importance of its scope of motility. A geometric line is said to be a space of one dimension. A plane is a space of two dimensions and a cube, a space of three dimensions. In figure 7 below, the line _ab_ is said to be one dimensional; because only one coördinate is necessary to locate a point-position in it. The plane, _abcd_, figure 8, is said to be two dimensional because two coördinates, _ab_ and _db_ are required to locate a point, as the point _b_. The cube _abcdefgh_, figure 9, is said to be tridimensional, because, in order to locate the point _b_, for instance, it is necessary to have three coördinates, _ab_, _bc_ and _gb_. The tesseract is said to be four dimensional, because, in order to locate the point _b_, in the tesseract, it is necessary to have four coördinates, _ab_, _bc_, _bb'_ and _h'b_, figure 10. A -------------------------------- B FIG. 7. A +------------------------------+ B | | | | | | | | | | | | C +------------------------------+ D FIG. 8.