(18 Sep 1819 - 11 Feb 1868)
Physical Demonstration of the Earth’s Motion of Rotation, by Means of the Pendulum.
by Léon Foucault (1851)
[p.575] THE rotation of the earth around its axis is one of those physical truths which appear too incontestable for any one to venture to call in question. Notwithstanding this, we have indirect proofs only of its existence; some of these are derived from the apparent movement of the sun and of the vault of the heavens, others from the existence of centrifugal force, and others from the flattened form of the terrestrial globe at the poles, &c. To these proofs, M. Leon Foucault has just added a new direct one, of such kind as to convince the most incredulous, if any such still exist; for he has succeeded in rendering the rotation of the earth as evident to the sight as that of a spinning-top. In anticipation of our publication of the circumstantial details of his beautiful experiment, which M. Foucault has promised to communicate, we shall endeavour to give our readers a summary idea of it, from the extract which has appeared in the Comptes Rendus de l'Académie des Sciences for February the 3rd, 1851. M. Foucault remarks first, that the movement of translation of the earth may be discarded, as it exerts no influence upon the phenomenon in question; he then supposes an observer to be transported to the pole, and there to set up a pendulum of the utmost simplicity, i. e. a pendulum composed of a heavy, homogeneous spherical mass, suspended by a flexible wire to an absolutely fixed point; he supposes, moreover, that this point of suspension lies exactly in the prolongation of the axis of rotation of the globe, and that the solid pieces which support it do not participate in the diurnal motion. If, under these circumstances, the mass of the pendulum be moved from its position of equilibrium, and it be left simply to the action of gravity, an oscillatory movement is produced in the direction of an arc of a circle, the situation of which is distinctly defined, and to which the inertia of matter ensures an invariable position in space. If, then, these oscillations continue during a certain length of time, the motion of the earth, which incessantly turns from the west towards the east, will become sensible by contrast with the immobility of the plane of oscillation, the trace of which upon the ground will appear excited by a motion conformable to the apparent motion of the celestial sphere; and if the oscillations were capable of continuing for twenty-four hours, the trace of their plane would perform during the same period an entire revolution about the vertical projection of the point of suspension.
These are the ideal conditions under which the motion of rotation of the globe would become immediately evident to observation. But in reality we are obliged to take a point of support upon a moving surface; the rigid attachments of the upper extremity of the wire of the pendulum cannot be withdrawn from the influence of the diurnal motion, and it appears at first sight, that the motion communicated to the wire and to the mass of the pendulum would alter the direction of the plane of oscillation. But M. Foucault has succeeded [p.576] theoretically in ascertaining what has since been confirmed by experiment, that provided the wire of the pendulum be round and homogeneous, it may be made to turn round upon itself with tolerable rapidity in either direction, without sensibly influencing the position of the plane of oscillation, so that the experiment which we have just described would perfectly succeed at the pole. This remarkable independence of the plane of oscillation and of the point of suspension is a mechanical phenomenon dependent upon the inertia of matter, which may be rendered evident in another form, by means of a very simple experiment which led M. Foucault to the discovery. After having fixed upon the arbor of a lathe and in the direction of its axis, a round and flexible rod of steel, he set it in vibration by moving it from its position of equilibrium and leaving it to itself. He thus produced a plane of oscillation, which by the persistence of the visual impressions, was clearly delineated in space; and he remarked that on turning round with the hand the arbor which formed the support of this vibrating rod, the plane of oscillation was not disturbed, but always retained the same direction in space.
Returning to the pendulum, the phenomenon which is in its greatest simplicity at the pole, becomes complicated, although continuing to exist, on descending towards our latitudes. In fact, in proportion as we approach the equator, the plane of the horizon, which at the pole was perpendicular to the axis of the earth, becomes more and more oblique to it; and the plumb-line, instead of turning upon itself, describes a more and more open cone, the summit of which in at the centre of the earth. The consequence is a retardation of the apparent motion of the plane of oscillation, which vanishes at the equator, previous to changing its direction in the other hemisphere; in fact, the angular displacement of the plane of oscillation is equal to the angular motion of the earth in the same time multiplied by the sine of the latitude. This motion of the plane of oscillation of a simple pendulum, whereby it appears to turn around the vertical line in the same direction as the stars, and which would cause it to complete an entire revolution in twenty-four hours at the pole, and a fraction of this revolution proportional to the sine of the latitude of the plane where the experiment is made, is a purely geometrical phenomenon, the explanation of which can be given by simple geometry, as has been done by M. Foucault. This was remarked by M. Poinsot, at the meeting of the Academy on the 25th of February, on suggesting in support of his opinion a new experiment to be made by M. Foucault.
We shall now show the manner in which M. Foucault has proceeded to determine the import and probable magnitude of the reality of the phenomenon which he had so well anticipated. We shall borrow the description of his experiment from the extract which he has given of it in the Comptes Rendus of the Academy.
“In the vaulted roof of a cellar, a strong piece of cast iron was firmly imbedded to afford a support to the point of suspension which emanates from the centre of a small mass of tempered steel, the free surface of which is perfectly horizontal. The suspending wire [p.577] consists of steel strongly hardened by the action of the draw-plate; its diameter varies from 6/10ths to 11/10ths of a millimetre; it extends to the length of two metres, and to its lower end is attached a sphere of brass turned and polished, and which moreover was hammered so that its centre of gravity should coincide with its centre of form. This sphere weighed five kilogrammes, and a sharp prolongation was fixed to it, apparently forming a continuation of the suspending wire.
“When it is wished to make the experiment, the first thing to be done is to put an end to the torsion of the wire and the rotatory oscillations of the sphere. Then, for the purpose of displacing it from its position of equilibrium, it is inclosed in a noose of silk thread, the free extremity of which is attached to some fixed point in the wall, at a small height above the ground. According to the length given to this thread, the displacement of the pendulum and the magnitude of the oscillations which it may be wished to communicate to it, are arranged arbitrarily. In general, in my experiments, these oscillations, at the beginning, comprised an arc of from 15 to 20 degrees. Before proceeding further, it is requisite to deaden by some obstacle, gradually withdrawn, the oscillatory motion still exercised by the pendulum while restrained by the thread and suspending wire. As soon as the pendulum has acquired a state of rest, the silk thread is burnt at some point of its extent, the noose which inclosed the sphere falls to the ground, and the pendulum, obeying the sole force of gravity, is set in motion and exhibits a long succession of oscillations, the plane of which soon experiences an appreciable displacement.
“At the end of half an hour this displacement is such as to be obvious; but it is more interesting to examine the phenomenon more closely, so as to be satisfied of the continuity of the effect. For this purpose a vertical point is made use of, a kind of style mounted on a support which is placed upon the ground, so that during its to and fro movement the sharp appendage at the base of the pendulum, when it reaches the extremity of its arc of oscillation, almost grazes the fixed point. In less than a minute the exact coincidence of the two points ceases to exist, the oscillating point becoming constantly displaced towards the left-hand of the observer, indicating that the deviation of the plane of oscillation takes place in the same direction as the horizontal component of the apparent motion of the celestial sphere. The mean magnitude of this motion, compared with the time occupied in its production, shows, conformably to the indications of theory, that in our latitudes the horizontal track of the plane of oscillation does not complete an entire revolution in twenty-four hours.
“To the politeness of M. Arago, and to the intelligent zeal of our able instrument-maker, M. Froment, who has so actively seconded me in the execution of this undertaking, I am indebted for being able to repeat this experiment upon a larger scale. Taking advantage of the lofty transit-room of the observatory, I have been enabled to give a length of eleven metres to the wire of the pendulum. The oscillations are thereby rendered longer and slower, so that between two consecutive returns of the pendulum to the starting-point, a sensible deviation towards the left becomes clearly perceptible.”— Bibliothéque Universelle de Genève, Mars 1851.