Let the above figure represent a portion of the Earth’s surface near the north pole N. Suppose the pendulum to be set in motion at m, so as to vibrate in the direction x y, which coincides with that of the meridian m N or m r. The Earth in the meantime is pursuing its easterly course, and the meridian line m N has come in six hours into the position n N. It has been hitherto supposed that the pendulum would now vibrate in the new direction n N, assumed by the meridian, but thanks to M. Foucault, we now know that this is a mistake. The pendulum will vibrate in a plane x n y, parallel to its original plane at m, as will be manifest if the plane of vibration points to some object in absolute space, such as a star. While the meridian line m N will in the course of 24 hours range round the whole circle of the heavens, and point successively in the direction n N, o N, p N, r N, s N, t N, and u N, the pendulum’s plane of vibration x y, whether at m, at n, at o, at p, at r, at s, at t, or at u, will always be parallel to itself, pointing invariably to the same star, and were a circular table placed under the pendulum, its plane of vibration, while really stationary, would appear to perform a complete revolution.
This stationary position of the plane of vibration at the pole seems to present little difficulty. We impress a peculiar motion on the pendulum in setting it a going. The Earth is at the same time carrying the pendulum eastward, but at the pole the one motion will not interfere with the other. The only action of the Earth on the pendulum there is that of attracting it towards its own (the Earth’s) centre. But this attraction is exactly in the plane of vibration and merely tends to continue the oscillatory motion without disturbing it. It is otherwise if the experiment is made at some other point, say 20 degrees distant from the pole. Supposing the vibrations to commence in the plane of the meridian, then as the tendency of the pendulum is to continue its vibrations in planes absolutely parallel to the original plane, it will be seen, if we trace both motions, that, while it is carried eastward with the Earth along a parallel of latitude, this tendency will operate to draw the plane of vibration away from a ‘great circle’ into a ‘small circle’ (that is, from a circle dividing the globe into two equal parts, into one dividing it into two unequal parts). But the pendulum must necessarily move in a ‘great circle,’ and hence to counteract its tendency to deviate into a ‘small circle,’ a correctory movement is constantly going on, to which the lengthening of the period necessary to complete a revolution must be ascribed. At Edinburgh the period is about 29 hours, at Paris 32, at Cairo 48, at Calcutta 63. At the Equator, the period stretches out to infinity. M. Foucault’s rule is, that the angular space passed over by the pendulum at any latitude in a given time, is equal to the angular motion of the Earth in the period, multiplied by the sine of the latitude. The angular motion of the Earth is 15 degrees per hour; and at the latitude of 30, for example, the sine being to radius as 500 to 1000, the angular motion of the pendulum will consequently be 7¹⁄₂ degrees per hour. It is, therefore, easily found. It follows that the motions of the pendulum may be employed in a rough way to indicate the latitude of a place.”[37]
[37] Supplement of the Manchester Examiner, of May 24, 1851.
Notwithstanding the apparent certainty of these pendulum experiments, and the supposed exactitude of the conclusions deducible therefrom, many of the same school of philosophy differed with each other, remained dissatisfied, and raised very serious objections both to the value of the experiments themselves, and to the supposed proof which they furnished of the Earth’s rotation. One writer in the Times newspaper of the period, who signs himself “B. A. C.,” says, “I have read the accounts of the Parisian experiment as they have appeared in many of our papers, and must confess that I still remain unconvinced of the reality of the phenomenon. It appears to me that, except at the pole where the point of suspension is immovable, no result can be obtained. In other cases the shifting of the direction of passage through the lowest point that takes place during an excursion of the pendulum, from that point in one direction and its return to it again, will be exactly compensated by the corresponding shifting in the contrary direction during the pendulum’s excursion on the opposite side. Take a particular case. Suppose the pendulum in any latitude to be set oscillating in the meridian plane, and to be started from the vertical towards the south. It is obvious that the wire by which it is suspended does not continue to describe a plane, but a species of conoidal surface; that when the pendulum has reached its extreme point its direction is to the south-west, and that as the tangent plane to the described surface through the point of suspension necessarily contains the normal to the Earth at the same point, the pendulum on its return passes through the same point in the direction north-east. Now, starting again from this point, we have exactly the circumstances of the last case, the primary plane being shifted slightly out of the meridian; when, therefore, the pendulum has reached its extreme point of excursion the direction of the wire is to the west of this plane, and when it returns to the vertical the direction of passage through the lowest point is as much to the west of this plane as it was in the former case to the west of the meridian plane; but since it is now moving from north to south instead of from south to north, as in the former case, its former deviation receives complete compensation, and the primary plane returns again to the meridian, when the whole process recurs.”
In the Liverpool Mercury of May 23, 1851, the following letter appeared:—“The supposed manifestation of the Rotation of the Earth.—The French, English, and European continental journals have given publicity to an experiment made in Paris with a pendulum; which experiment is said to have had the same results when made elsewhere. To the facts set forth no contradiction has been given, and it is therefore to be hoped that they are true. The correctness of the inferences drawn from the facts is another matter. The first position of these theorists is, that in a complete vacuum beyond the sphere of the Earth’s atmosphere, a pendulum will continue to oscillate in one and the same original plane. On that supposition their whole theory is founded. In making this supposition the fact is overlooked that there is no vibratory motion unless through atmospheric resistance, or by force opposing impulse. Perpetual progress in rectilinear motion may be imagined, as in the corpuscular theory of light; circular motion may also be found in the planetary systems; and parabolic and hyperbolic motions in those of comets; but vibration is artificial and of limited duration. No body in nature returns the same road it went, unless artificially constrained to do so. The supposition of a permanent vibratory motion such as is presumed in the theory advanced, is unfounded in fact, and absurd in idea; and the whole affair of this proclaimed discovery falls to the ground. It is what the French call a ‘mystification’—anglice a ‘humbug.’ Liverpool, 22nd May, 1851.” “T.”
Another writer declared that he and others had made many experiments and had discovered that the plane of vibration had nothing whatever to do with the meridian longitude nor with the Earth’s motion, but followed the plane of the magnetic meridian.
“A scientific gentleman in Dundee recently tried the pendulum experiment, and he says—‘that the pendulum is capable of showing the Earth’s motion I regard as a gross delusion; but that it tends to the magnetic meridian I have found to be a fact.’”[38]
[38] Liverpool Journal, May 17, 1851.
In many cases the experiments have not shown a change at all in the plane of oscillation of the pendulum; in others the alteration in the plane of vibration has been in the wrong direction; and very often the rate of variation has been altogether different to that which theory indicated. The following is a case in illustration:—“On Wednesday evening the Rev. H. H. Jones, F.R.A.S., exhibited the apparatus of Foucault to illustrate the diurnal rotation of the Earth, in the Library Hall of the Manchester Athenæum. The preparations were simple. A circle of chalk was drawn in the centre of the floor, immediately under the arched skylight. The circle was exactly 360 inches in its circumference, every inch being intended to represent one degree. According to a calculation Mr. Jones had made, and which he produced at the Philosophical Society six weeks ago, the plane of oscillation of the pendulum would, at Manchester, diverge about one degree in five minutes, or perhaps a very little less. He therefore drew this circle exactly 360 inches round, and marked the inches on its circumference. The pendulum was hung from the skylight immediately over the centre of the circle, the point of suspension being 25 feet high. At that length of wire, it should require 2¹⁄₂ seconds to make each oscillation across the circle. The brazen ball, which at the end of a fine wire constituted the pendulum, was furnished with a point, to enable the spectator to observe the more easily its course. A long line was drawn through the diameter of the circle, due north and south, and the pendulum started so as to swing exactly along this line; to the westward of which, at intervals of three inches at the circumference, two other lines were drawn, passing through the centre. According to the theory, the pendulum should diverge from its original line towards the west, at the rate of one inch or degree in five minutes. This, however, Mr. Jones explained, was a perfection of accuracy only attainable in a vacuum, and rarely could be approached where the pendulum had to pass through an atmosphere subject to disturbances; besides, it was difficult to avoid giving it some slight lateral bias at starting. In order to obviate this as much as possible, the steel wire was as fine as would bear the weight, ¹⁄₃₀th of an inch thick; and the point of suspension was adjusted with delicate nicety. An iron bolt was screwed into the frame-work of the skylight; into it a brass nut was inserted—the wire passed through the nut (the hollow sides of which were bell-shaped, in order to give it fair play), and at the top the wire ended in a globular piece, there being also a fine screw to keep it from slipping. * * * The pendulum was gently drawn up to one side, at the southern end of the diametrical line, and attached by a thread to something near. When it hung quite still the thread was burnt asunder, and the pendulum began to oscillate to and fro across the circle. * * * Before it had been going on quite seven minutes, it had reached nearly the third degree towards the west, whereas it ought to have occupied a quarter of an hour in getting thus far from its starting line, even making no allowance for the resistance of the atmosphere.”[39]
[39] “Manchester Examiner” (Supplement), May 24, 1851.