Hinton - The Fourth Dimension.pdf

THE EVIDENCES FOR A FOURTH DIMENSION 83
Let us now enquire what a vortex would be in a fourdimensional
fluid.
We must replace the line axis by a plane axis. We
should have therefore a portion of fluid rotating round
a plane.
We have seen that the contour of this plane corresponds
with the ends of the axis line. Hence such a fourdimensional
vortex must have its rim on a boundary of
the fluid. There would be a region of vorticity with a
contour. If such a rotation were started at one part of a
circular boundary, its edges would run round the boundary
in both directions, till the whole interior region was filled
with the vortex sheet.
A vortex in a three-dimensional liquid may consist of a
number of vortex filaments lying together producing a
tube, or rod of vorticity.
In the same way we can have in four dimensions a
number of vortex sheets alongside each other, each of which
can be thought of as a bowl-shaped portion of a spherical
shell turning inside out. The rotation takes place at any
point not in the space occupied by the shell, but from
that space to the fourth dimension and round back again.
Is there anything analogous to this within the range
of our observation?
An electric current answers this description in every
respect. Electricity does not flow through a wire. Its effect
travels both ways from the starting point along the wire.
The spark which shows its passing midway in its circuit
is later than that which occurs at points near its starting
point on either side of it.
Moreover, it is known that the action of the current
is not in the wire. It is in the region enclosed by the
wire, this is the field of force, the locus of the exhibition
of the effects of the current.
And the necessity of a conducting circuit for a current is