FOUCAULT'S PENDULUM EXPERIMENTS.
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.
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.
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.
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.
Fig.4.