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244     Wisconsin Academy of Sciences, Arts, and Letters.
   Faraday, in 1845, showed that this rotation of the azimuth of
-vibration could also be produced in substances not otherwise pos-
sessing it, by subjecting them to strong electro-magnetic influence,
something after the manner shown in Fig. 9, where N is the polar-
                                  Fig. 9.
izer which reduces the vibrations to a definite azimuth; G is the--
substance subjected to electro-magnetic strain; a and b are the
  " Where the rings have equal radii and equal and opposite angular
velocities,
they will approach each other and widen one another; so that finally when
they
are very near each other, their velocity of approach becomes continually
small-
er and smaller, and their rates of widening faster and faster. If they are
per-
fectly symmetrical, the velocity of fluid elements midway between them,
parallel to the axis, is zero, and here we might imagine a rigid plane to
be in-
serted, which would not disturb the motion, and so obtain the case of a vortex
ring which encounters a fixed obstacle. If the rings have the same direc-
tion of rotation, they travel in the same direction; the foremost widens
and
travels more slowly, the pursuer shrinks and travels faster, till finally,
if their
velocities are not too different, it overtakes the first and penetrates it.
So the
rings pass through each other alternately."
  In Fig. 7, No. 1 represents the rings rotating in the same direction at
start-
ing; No. 2 shows the forward ring, A, slackening its speed and dilating;
No.
8, the B ring contracting, accelerating its speed and passing through. Ring
B then slackens its speed, and dilates in turn, while A contracts.
  In Fig. 8, the gradual approach of the rings gyrating oppositely is not
well
shown. The long arrows are intended to show the direction in which the rings
would move, in virtue of their respective rotations, were they not influenced
by
each other.
  The motions of the fluids at various points surrounding a vortex filament
in the shape of a ring, are best traced by means of Elliptic Integrals of
the