Mr. Hinton has a good deal to say in his books about various four-dimensional theories of electricity involving four-dimensional vortices. These are highly ingenious but there does not seem to be any considerable reason for supposing them to be anything more and I shall therefore not describe them here. Two of his ideas however are so striking, although for different reasons, that I think a brief outline will not be out of place. In his book "A new Era of Thought" he points out the remarkable analogy which exists between the properties of ether as postulated by physicists and those which a perfectly smooth solid sheet would present to the intelligence of two-dimensional beings living on it. The hypothesis of the ether was introduced to account for the transmission of light, heat, electricity, and so forth, and has proved of the utmost service to physicists. Most of my readers are probably acquainted with the general idea and I need not therefore discuss it in detail. It will be sufficient here to say that it is supposed to be a weightless, homogeneous medium extending throughout all space and permeating all bodies. Indeed Matter itself is supposed to be no more than the result of more or less complex disturbances in it. But although it accounts for the phenomena in connection with which it was called into being it is necessary to ascribe to it very contradictory properties. On the one hand it has been calculated that in order for it to transmit the forces which we know that it does transmit, for instance the force of gravitation, it must possess a rigidity some 3,000 times greater than that of the strongest known steel. On the other hand we must suppose it to be of a tenuity far in excess of the most perfect vacuum which we can obtain, for otherwise the earth and other planets which are moving at immense speed through this medium would be slowed down; which is not in practice the case. Now Hinton points out that to a two-dimensional being, a perfectly smooth solid sheet on the surface of which he lived would possess many of these properties. Being perfectly smooth it would be imperceptible to him and would offer no opposition to the passage of bodies over it. Yet it could, being solid, transmit vibration just as we know the ether does for us. Also it could be as rigid as you please without losing any of its imperceptibility. It could not be weighed and it could not be eliminated from any vessel no matter what care was taken to do so. The analogy is striking but it does not appeal to me and I do not think that even Mr. Hinton means it to be taken strictly, for in other passages he gives quite different suggestions as to the ether. One of the latter is derived from a consideration of the phenomena of rotation in four-dimensional space and is of some intrinsic interest.