Hinton - The Fourth Dimension.pdf

RECAPITULATION AND EXTENSION 227
direction. Now, if rotation in one direction corresponds to
positive electricity, rotation in the opposite direction corresponds
to negative electricity, and the smallest electrified
particles would have their charges reversed by being
turned over—an absurd supposition.
If we fix on a mode of motion as a definition of
electricity, we must have two varieties of it, one for
positive and one for negative; and a body possessing the
one kind must not become possessed of the other by any
change in its position.
All three-dimensional motions are compounded of rotations
and translations, and note of them satisfy this first
condition for serving as a definition of electricity.
But consider the double rotation of the A and B kinds.
A body rotating with the A motion cannot have its
motion transformed into the B kind by being turned over
in any way. Suppose a body has the rotation x to y and
z to w. Turning it about the xy plane, we reverse the
direction of the motion x to y. But we also reverse the
z to w motion, for the point at the extremity of the
positive z axis is now at the extremity of the negative z
axis, and since we have not interfered with its motion it
goes in the direction of position w. Hence we have y to
x and w to z, which is the same as x to y and z to w.
Thus both components are reversed, and there is the A
motion over again. The B kind is the semi-negative,
with only one component reversed.
Hence a system of molecules with the A motion would
not destroy it in one another, and would impart it to a
body in contact with them. Thus A and B motions
possess the first requisite which must be demanded in
any mode of motion representative of electricity.
Let us trace out the consequences of defining positive
electricity as an A motion and negative electricity as a B
motion. The combination of positive and negative