Our space as we ordinarily think of it is conceived as limited--not in extent, but in a certain way which can only be realized when we think of our ways of measuring space objects. It is found that there are only three independent directions in which a body can be measured--it must have height, length and breadth, but it has no more than these dimensions. If any other measurement be taken in it, this new measurement will be found to be compounded of the old measurements. It is impossible to find a point in the body which could not be arrived at by travelling in combinations of the three directions already taken. But why should space be limited to three independent directions? Geometers have found that there is no reason why bodies should be thus limited. As a matter of fact all the bodies which we can measure are thus limited. So we come to this conclusion, that the space which we use for conceiving ordinary objects in the world is limited to three dimensions. But it might be possible for there to be beings living in a world such that they would conceive a space of four dimensions. All that we can say about such a supposition is, that it is not demanded by our experience. It may be that in the very large or the very minute a fourth dimension of space will have to be postulated to account for parts--but with regard to objects of ordinary magnitudes we are certainly not in a four dimensional world. And this was the point at which about ten years ago I took up the inquiry. It is possible to say a great deal about space of higher dimensions than our own, and to work out analytically many problems which suggest themselves. But can we conceive four-dimensional space in the same way in which we can conceive our own space? Can we think of a body in four dimensions as a unit having properties in the same way as we think of a body having a definite shape in the space with which we are familiar? Now this question, as every other with which I am acquainted, can only be answered by experiment. And I commenced a series of experiments to arrive at a conclusion one way or the other. It is obvious that this is not a scientific inquiry--but one for the practical teacher. And just as in experimental researches the skilful manipulator will demonstrate a law of nature, the less skilled manipulator will fail; so here, everything depended on the manipulation. I was not sure that this power lay hidden in the mind, but to put the question fairly would surely demand every resource of the practical art of education. And so it proved to be; for after many years of work, during which the conception of four-dimensional bodies lay absolutely dark, at length, by a certain change of plan, the whole subject of four-dimensional existence became perfectly clear and easy to impart.