The fourth dimension

230 THE FOURTH DIMENSION

If we suppose the ether to be filled with vortices in the shape of four-dimensional spheres rotating with the A motion, the B motion would correspond to electricity in the one-fluid theory. There would thus be a possibility of electricity existing in two forms, statically, by itself, and, combined with the universal motion, in the form of a current.

To arrive at a definite conclusion it will be necessary to investigate the resultant pressures which accompany the collocation of solid vortices with surface ones.

To recapitulate :

The movements and mechanics of four-dimensional space are definite and intelligible. A vortex with a surface as its axis affords a geometric image of a closed cirenit, and there are rotations which by their polarity afford a possible definition of statical electricity.*

* These double rotations of the A and B kinds I should like to call Hamiltons and co-Hamiltons, for it is a singular fact that in his “Quaternions” Sir Wm. Rowan Hamilton has given the theory of either the A or the B kind. They follow the laws of his symbols, I, J, K.

Hamiltons and co-Hamiltons seem to be natural units of geometrical expression. In the paper in the “ Proceedings of the Royal Irish Academy,” Nov. 1903, already alluded to, I have shown something of the remarkable facility which is gained in dealing with the composition of three- and four-dimensional rotations by an alteration in Hamilton’s notation, which enables his system to be applied to both the A and B kinds of rotations.

The objection which has been often made to Hamilton’s system, namely, that it is only under special conditions of application that his processes give geometrically interpretable results, can be removed, if we assume that he was really dealing with a four-dimensional motion, and alter his notation to bring this circumstance into explicit recognition,