The fourth dimension

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{THE EVIDENCES FOR A FOURTH DIMENSION 79

no such thing as a bending over in four dimensions of any object of a size which we can observe. The region of the extremely minute is the one, then, which we shall have to investigate. We must look for some phenomenon which, occasioning movements of the kind we know, still is itself inexplicable as any form of motion which we know.

Now in the theories of the actions of the minute particles of bodies on one another, and in the motions of the ether, mathematicians have tacitly assumed that the mechanical principles are the same as those which prevail in the ease of bodies which can be observed, it has been assumed without proof that the conception of motion being three-dimensional, holds beyond the region from observations in which it was formed.

Hence it is not from any phenomenon explained by mathematies that we can derive a proof of four dimensions. Every phenomenon that has been explained is explained as three-dimensional. And, moreover, since in the region of the very minute we do not find rigid bodies acting on each other at a distance, but elastic substances and continuous fluids such as ether, we shall Have a double task.

We must form the conceptions of the possible movements of elastic and liquid four-dimensional matter, before we can begin to observe. Let us, therefore, take the fourdimensional rotation about a plane, and enquire what it becomes in the case of extensible fluid substances. If four-dimensional movements exist, this kind of rotation must exist, and the finer portions of matter must exhibit it.

Consider for a moment a rod of flexible and extensible material. It can turn about an axis, even if not straight ; a ring of india rubber can turn inside out.

What would this be in the case of four dimensions?