The fourth dimension

THE SIGNIFICANCE OF A FOUR-DIMENSIONAL EXISTENCE 17

ring with a current in it in one direction be taken up and turned over, and put down again on the plane, it would be identical with the ring having a current in the opposite direction. An operation of this kind would be impossible to the plane being. Hence he would have in his space two irreconcilable objects, namely, the two fields of influence due to the two rings with currents in them in opposite directions. By irreconcilable objects in the plane I mean objects which cannot be thought of as transformed one into the other by any movement in the plane.

Instead of currents flowing in the rings we can imagine a different kind of current. Imagine a number of small rings strung on the original ring. A current round these secondary rings would give two varieties of effect, or two different fields of influence, according to its direction. These two varieties of current could be turned one into the other by taking one of the rings up, turning it over, and putting it down again in the plane. This operation is impossible to the plane being, hence in this case also there would be two irreconcilable fields in the plane. Now, if the plane being found two such irreconcilable fields and could prove that they could not be accounted for by currents in the rings, he would have to admit the existence of currents round the rings—that is, in rings strung on the primary ring. Thus he would come to admit the existence of a three-dimensional motion, for such a disposition of currents is in three dimensions.

Now in our space there are two fields of different properties, which can be produced by an electric current flowing in a closed circuit or ring. These two fields can be changed one into the other by reversing the currents, but they cannot be changed one into the other by any turning about of the rings in our space ; for the disposition of the field with regard to the ring itself is different when we

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