Now, if we are situated analogously with regard to an ampler space, there must be some element in our experience corresponding to each element in the plane-being’s experience. And it is interesting to ask, in the case of the plane-being, what his opinion would be with respect to the surface on which he was. He would not recognize it as a surface with which he was in contact; he would have no idea of a motion away from it or towards it. But he would discover its existence by the fact that movements were transmitted along it. By its vibrating and quivering, it would impart movement to the particles of matter lying on it. Hence, he would consider this surface to be a medium lying between bodies, and penetrating them. It would appear to him to have no weight, but to be a powerful means of transmitting vibrations. Moreover, it would be unlike any other substance with which he was acquainted, inasmuch as he could never get rid of it. However perfect a vacuum be made, there would be in this vacuum just as much of this unknown medium as there was before. Moreover, this surface would not hinder the movement of the particles of matter over it. Being smooth, matter would slide freely over it. And this would seem to him as if matter went freely through the medium. Then he would also notice the fact that vibrations of this medium would tear asunder portions of matter. The plane surface, being very compact, compared to the masses of matter on it, would, by its vibrations, shake them into their component parts. Hence he would have a series of observations which tended to show that this medium was unlike any ordinary matter with which he was acquainted. Although matter passed freely through it, still by its shaking it could tear matter in pieces. These would be very difficult properties to reconcile in one and the same substance. Then it is weightless, and it is everywhere. It might well be that he would regard the supposition of there being a plane surface, on which he was, as a preferable one to the hypothesis of this curious medium; and thus he might obtain a proof of his limitations from his observations. Now, is there anything in our experience which corresponds to this medium which the plane-being gets to observe? Do we suppose the existence of any medium through which matter freely moves, which yet by its vibrations destroys the combinations of matter--some medium which is present in every vacuum, however perfect, which penetrates all bodies, and yet can never be laid hold of? These are precisely observations which have been made. The substance which possesses all these qualities is called the æther. And the properties of the æther are a perpetual object of investigation in science. Now, it is not the place here to go into details, as all we want is a basis for work; and however arbitrary it may be, it will serve if it enables us to investigate the properties of higher space.