The fourth dimension

18 THE FOURTH DIMENSION

turn the ring, over and when we reverse the direction of the current in the ring.

As hypotheses to explain the differences of these two fields and their effects we can suppose the following kinds of space motions :—First, a current along the conductor ; second, a current round the conductor—that is, of rings of currents strung on the conductor as an axis. Neither of these suppositions accounts for facts of observation.

Hence we have to make the supposition of a fourdimensional motion. We find that a four-dimensional rotation of the nature explained in a subsequent chapter, has the following characteristics :—First, it would give us two fields of influence, the one of which could be tured into the other by taking the circuit up into the fourth dimension, turning it over, and putting it down in our space again, precisely as the two kinds of fields in the plane could be turned one into the other by a reversal of the current in our space. Second, it involves a phenomenon precisely identical with that most remarkable and mysterious feature of an electric current, namely that it is a field of action, the rim of which necessarily abuts on a continuous boundary formed by a conductor. Hence, on the assumption of a four-dimensional movement in the region of the minute particles of matter, we should expect to find a motion analogous to electricity.

Now, a phenomenon of such universal occurrence as electricity cannot be due to matter and motion in any very complex relation, but ought to be seen as a simple and natural consequence of their properties. I infer that the difficulty in its theory isdue to the attempt to explain a four-dimensional phenomenon by a three-dimensional geometry.

In view of this piece of evidence we cannot disregard that afforded by the existence of symmetry. In this connection I will allude to the simple way of producing