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.
We will suppose, then, that we are not in, but on the æther, only not on it in any known direction, but that the new direction is that which comes in. The æther is a smooth body, along which we slide, being distant from it at every point about the thickness of an atom; or, if we take our mean distance, being distant from it by half the thickness of an atom measured in this new direction.
Then, just as in space objects, a cube, for instance, can stand on the surface of a table, or on the surface over which the plane-being moves, so on the æther can stand a higher solid.
All that the plane-being sees or touches of a cube, is the square on which it rests.