In two space rotation takes place about a point, in three space about a line and we should therefore expect that in four space it would do so about a plane. This is easily shown to be the case although I do not propose to go into the proof here. The only important point is that whereas it is impossible to conceive a mass of three-dimensional spheres in a state of continuous rotation,--because they would be trying to drive each other in different directions and so would prevent the rotation,--in four dimensions this is not the case and a mass of "hyper-spheres" could be "self-driving," that is to say the rotation of each could be such as to assist and not to retard that of its neighbours. This fact is of interest because Lord Kelvin showed that the contradictory properties of the ether referred to above could only be reconciled by supposing it to be animated throughout by a motion of a vortical character. This "self-driving" effect of rotating hyper-spheres is worth glancing at a little more closely. It arises from the fact that there are two distinct sorts of rotation which such a sphere may possess. In three-dimensional rotation the motion may take place about any axis we please and the other two axes which can be drawn will change one into the other, so to speak, as the rotation takes place. But in four-dimensional space we have four axes and while the X and Y axes change place, say, there is nothing to prevent the W and Z axes doing so too. Thus we might have the X axis changing into the Y and the W into the Z. To reverse both of these motions so as to have the Y axis changing into the X and the Z into the W does not give us a new kind of motion any more than reversing the direction of an ordinary three-dimensional rotation does--it is only equivalent to looking at it from a different point of view. But if in the case of the four-dimensional rotation we reverse one only of the two rotational components we do get a new kind of motion, and this is of interest in view of the fact that electricity like other forces is regarded as a mode of etheric motion, and if this be so there would seem to be a certain need for two distinct kinds of it in order to correspond to positive and negative electricity respectively. It is just possible that there is some connection, as Mr. Hinton suggests, between this need and the two kinds of four-dimensional rotation referred to above. * * * * * Most writers on the subject of higher space make great play with the phenomena of symmetry and adduce its occurrence in nature as evidence of the existence of a fourth dimension. This view is not warranted by the facts and I shall therefore touch on it only very briefly. [Illustration: _Fig. 9_]