By RICHARD A. PROCTOR.
Science owes to M. Foucault the suggestion that the motions of a
pendulum so suspended as to be free to swing in any vertical plane
might be made to give ocular demonstration of the earth's rotation. The
principle of proof may be easily exhibited, though, like nearly all of
the evidences of the earth's rotation, the complete theory of the
matter can only be mastered by the aid of mathematical researches of
considerable complexity. Suppose A B (Fig. 1) to be a straight rod in a
horizontal position bearing the free pendulum C D suspended in some such
manner as is indicated at C; and suppose the pendulum to be set swinging
in the direction of the length of the rod A B, so that the bob D remains
throughout the oscillations vertically under the rod A B. Now, if A B be
shifted in the manner indicated by the arrows, its horizontality being
preserved, it will be found that the pendulum does not partake in this
motion. Thus, if the direction of A B was north and south at first, so
that the pendulum was set swinging in a north and south direction, it
will be found that, the pendulum will still swing in that direction,
even though the rod be made to take up an east and west position.
[Illustration: Fig. 1.]
Nor will it matter if we suppose B (say) fixed and the rod shifted by
moving the end A horizontally round B. Further, as this is true whatever
the length of the rod, it is clear that the same fixity of the plane
of swing will be observed if the rod be shifted horizontally as though
forming part of a radial line from a point E in its length. In these
cases the plane of the pendulum's swing will indeed be shifted _bodily_,
but the direction of swing will still continue to be from north to
south.
Now, let P O P' represent the polar axis of the earth; a b a horizontal
rod at the pole bearing a pendulum, as in Fig. 1. It is clear that if
the earth is rotating about P O P' in the direction shown by the arrow,
the rod a b is being shifted round, precisely as in the case first
considered. The swinging pendulum below it will not partake in its
motion; and thus, through whatever arc the earth rotates from west to
east, through the same arc will the plane of swing of the pendulum
appear to travel from east to west under a b.
But we cannot set up a pendulum to swing at the pole of the earth. Let
us inquire, then, whether the experiment ought to have similar results
if carried out elsewhere.
Suppose A B to be our pendulum-bearing rod, placed (for convenience of
description merely) in a north and south position. Then it is clear that
A B produced meets the polar axis produced (in E, suppose), and when,
owing to the earth's rotation, the rod has been carried to the position
A' B', it still passes through the point E. Hence it has shifted through
the angle A E A', a motion which corresponds to the case of the motion
of A B (in Fig. 1) about the point E,[1] and the plane of the pendulum's
swing will therefore show a displacement equal to the angle A E A'. It
will be at once seen that for a given arc of rotation the displacement
is smaller in this case than in the former, since the angle A E A' is
obviously less than the angle A K A'.[2] In our latitude a free pendulum
should seem to shift through one degree in about five minutes.
[Footnote 1: In reality A E moves to the position A' E over the surface
of a cone having E P' as axis, and E as vertex; but for any small part
of its motion, the effect is the same as though it traveled in a plane
through E, touching this cone; and the sum of the effects should clearly
be proportioned to the sum of the angular displacements.]
[Footnote 2: In fact, the former angle is less than the latter, in the
same proportion that A K is less than A E, or in the proportion of the
sine of the angle A E P, which is obviously the same as the sine of the
latitude.]
It is obvious that a great deal depends on the mode of suspension. What
is needed is that the pendulum should be as little affected as possible
by its connection with the rotating earth. It will surprise many,
perhaps, to learn that in Foucault's original mode of suspension the
upper end of the wire bearing the pendulum bob was fastened to a metal
plate by means of a screw. It might be supposed that the torsion of
the wire would appreciably affect the result. In reality, however, the
torsion was very small.
[Illustration: Fig. 2.]
Still, other modes of suspension are obviously suggested by the
requirements of the problem. Hansen made use of the mode of suspension
exhibited in Fig. 3. Mr. Worms, in a series of experiments carried out
at King's College, London, adopted a somewhat similar arrangement, but
in place of the hemispherical segment he employed a conoid, as shown in
Fig. 4, and a socket was provided in which the conoid could work freely.
From some experiments I made myself a score of years ago, I am inclined
to prefer a plane surface for the conoid to work upon. Care must be
taken that the first swing of the pendulum may take place truly in one
plane. The mode of liberation is also a matter of importance.
[Illustration: Fig.3.]
Many interesting experiments have been made upon the motions of a
free pendulum, regarded as a proof of the earth's rotation, and when
carefully conducted, the experiments have never failed to afford the
most satisfactory results. Space, however, will only permit me to dwell
on a single series of experiments. I select those made by Mr. Worms in
the Hall of King's College, London, in the year 1859:
"The bob was a truly turned ball of brass weighing 40 lb.; the
suspending medium was a thick steel wire; the length of the pendulum was
17 feet 9 inches. The amplitude of the first oscillation was 6° 42', and
during the time of the experiment--about half an hour--the arcs were
not much diminished. As I had to demonstrate to a large number of
spectators, I encountered considerable difficulty," says Mr. Worms, "in
rendering the small deviations of the plane of oscillation visible to
all. I accomplished it in three different ways." These he proceeds
to describe. He had first a set of small cones set up, which were
successively knocked down as the change in the plane of the pendulum
slowly brought the pointer under the bob to bear on cone after cone.
Secondly, a small cannon was so placed that the first touch of the
pendulum pointer against a platinum wire across the touch-hole completed
a galvanic circuit, and so fired the cannon. Lastly, a candle was placed
so as to throw the shadow of the pendulum bob upon a ground-glass
screen, and so to exhibit the gradual change of the plane of swing.
The results accorded most satisfactorily with the deductions from the
theory of the earth's rotation.
[Illustration: Fig.4.]
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