Part 8

The following is from the _Scotsman_, which has always been distinguished for the accuracy of its scientific papers. The article bears the initials “C. M.,” which will at once be recognised as those of Mr. Charles Maclaren, for many years the accomplished editor of that journal:--“The beautiful experiment contrived by M. Foucault to demonstrate the rotation of the globe, has deservedly excited universal interest. * * * A desire has always been felt that some method could be devised of rendering this rotation palpable to the senses. Even the illustrious Laplace participated in this feeling and has left it on record. ‘Although,’ he says, ‘the rotation of the Earth is now established with all the certainty which the physical sciences require, still a direct proof of that phenomenon ought to interest both geometricians and astronomers.’ No man ever knew the laws of the planetary motions better than Laplace, and before penning such a sentence, it is probable that he had turned the subject in his mind, and without discovering any process by which the object could be attained; but it does not follow that if he had applied the whole force of his genius to the task, he would not have succeeded. Be this as it may, here we have the problem solved by a man not probably possessing a tithe of his science or talent; and, what is very remarkable, after the discovery was made, it was found to be legitimately deducible from mathematical principles. * * * In this, as in many other cases, the _fact_ comes first, and takes us by surprise; after which we find that we had long been in possession of the principles from which it flowed, and that, with the clue we had in our hands, theory should have revealed the fact to us long before. M. Foucault’s communication describing his experiments is in the _Comptes Rendus_ of the Academy of Sciences, for 3rd February, 1851. His first experiments were made with a pendulum only two metres (6ft. 6¹⁄₄in.) in length, consisting of a steel wire from ⁶⁄₁₀ths to ¹¹⁄₁₀ths of a millimetre in diameter (the millimetre is the 25th part of an inch); to the lower end of which was attached a polished brass ball, weighing 5 kilogrammes, or 11 English pounds. * * * A metallic point projecting below the ball, and so directed as if it formed a continuation of the suspension wire, served as an index to mark the change of position more precisely. The pendulum hung from a steel plate in such a manner as to move freely in any vertical plane. To start the oscillatory movement without giving the ball any bias, it was drawn to one side with a cord, which held the ball by a loop; the cord was then burned, after which the loop fell off, and the vibrations (generally limited to an arc of 15 or 20 degrees) commenced. In one minute the ball had sensibly deviated from the original plane of vibration towards the observer’s left. Afterwards he experimented at the Observatory with a pendulum 11 metres (30 feet) long, and latterly at the Pantheon with one still longer. The advantage of a large pendulum, as compared with a small one, is, that a longer time elapses before it comes to a state of rest; for machinery cannot be employed here, as in a clock, to continue the motion. The pendulum is suspended over the centre of a circular table, whose circumference is divided into degrees and minutes. The vibrations are begun in the manner above described, and in a short time it is observed that the pendulum, instead of returning to the same point of the circle from which it started, has shifted to the left. If narrowly observed, the change in the plane of vibration (says M. Foucault) is perceptible in one minute, and in half an hour, “Il saute aux yeux,” it is quite palpable. At Paris the change exceeds 11 degrees in an hour. Thus, supposing the oscillations to commence in a plane directed south and north, in two hours the oscillations will point SSW. and NNE.; in four hours they will point SW. and NE.; and in eight hours the oscillations will point due east and west, or at right angles to their original direction. To a spectator the change seems to be in the pendulum, which, without any visible cause, has shifted round a quarter of a circle; but the real change is in the table, which, resting on the Earth, and accompanying it in its rotation, has performed a fourth (and something more) of its diurnal revolution.

No one anticipated such a result; and the experiment has been received by some with incredulity, by all with wonderment; and one source of the incredulity arises from the difficulty of conceiving how, amidst the ten thousand experiments of which the pendulum has been the subject, so remarkable a fact could have escaped notice so long. Fully admitting that these experiments have generally been conducted with pendulums which had little freedom of motion horizontally, we still think odd that somebody did not stumble upon the curious fact.

Though all the parts of the Earth complete their revolution in the same space of time, it is found that the rate of horizontal motion in Foucault’s pendulum varies with the latitude of the place where the experiment is made. At the pole, the pendulum would pass over 15 degrees in an hour, like the Earth itself, and complete its circuit in 24 hours. At Edinburgh, the pendulum would pass over 12¹⁄₂ degrees in an hour, and would complete its revolution in 29 hours 7 minutes. At Paris, the rate of motion is 11 degrees and 20 minutes per hour, and the revolution should be completed in 32 hours.

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.

Besides the irregularities so often observed in the time and direction of the pendulum vibrations, and which are quite sufficient to render them worthless as evidence of the Earth’s motion, the use which the Newtonian astronomers made of the general fact that the plane of oscillation is variable, was most unfair and illogical. It was proclaimed to the world as a visible proof of the Earth’s diurnal motion; but the motion was _assumed to exist_, and then employed to explain the cause of the fact which was first called a proof of the thing assumed! A greater violation of the laws of investigation was never perpetrated! The whole subject as developed and applied by the theoretical philosophers is to the fullest degree unreasonable and absurd--not a “jot or tittle” better than the reasoning contained in the following letter:--“Sir,--Allow me to call your serious and polite attention to the extraordinary phenomenon, demonstrating the rotation of the Earth, which I at this present moment experience, and you yourself or anybody else, I have not the slightest doubt, would be satisfied of, under similar circumstances. Some sceptical and obstinate individuals may doubt that the Earth’s motion is visible, but I say from personal observation its a positive fact. I don’t care about latitude or longitude, or a vibratory pendulum revolving round the sine of a tangent on a spherical surface, nor axes, nor apsides, nor anything of the sort. That is all rubbish. All I know is, I see the ceiling of this coffee-room going round. I perceive this distinctly with the naked eye--only my sight has been sharpened by a slight stimulant. I write after my sixth go of brandy-and-water, whereof witness my hand,”--“Swiggins”--_Goose and Gridiron, May 5, 1851._--“P.S. Why do two waiters come when I only call one?”[40]

[40] “Punch,” May 10, 1851.

The whole matter as handled by the astronomical theorists is fully deserving of the ridicule implied in the above quotation from _Punch_; but because great ingenuity has been shewn, and much thought and devotion manifested in connection with it, and the general public thereby greatly deceived, it is necessary that the subject should be fairly and seriously examined. What are the facts?

First.--When a pendulum, constructed according to the plan of M. Foucault, is allowed to vibrate, its plane of vibration is often variable--_not always_. The variation when it _does_ occur, is _not uniform_--is not always the same in the same place; nor always the same either in its rate or velocity, or in its direction. It cannot therefore be taken as evidence; for that which is inconstant cannot be used in favour of or against any given proposition. It therefore _is not evidence and proves nothing_!

Secondly.--If the plane of vibration _is_ observed to change, where is the connection between such change and the supposed motion of the Earth? What principle of reasoning guides the experimenter to the conclusion that it is the Earth which moves underneath the pendulum, and not the pendulum which moves over the Earth? What logical right or necessity forces one conclusion in preference to the other?

Thirdly.--Why was not the peculiar arrangement of the point of suspension of the pendulum specially considered, in regard to its possible influence upon the plane of oscillation? Was it not known, or was it overlooked, or was it, in the climax of theoretical revelry, ignored that a “ball-and-socket” joint is one which facilitates _circular_ motion more readily than any other? and that a pendulum so suspended (as was M. Foucault’s), could not, after passing over one arc of vibration, return through the same arc without there being many chances to one that its globular point of suspension would slightly turn or twist in its bed, and therefore give to the return or backward oscillation a slight change of direction? Let the _immediate cause_ of the pendulum’s liability to change its plane of vibration be traced; and it will be found not to have the slightest connection with the motion or non-motion of the surface over which it vibrates.

At a recent meeting of the French Academy of sciences, “M. Dehaut sent in a note, stating that M. Foucault (whose experiments on the pendulum effected a few years ago at the Pantheon, are of European notoriety) is not the first discoverer of the fact that the plane of oscillation of the free pendulum is invariable; but that the honour of the discovery is due to Poinsinet de Sivry, who, in 1782, stated, in a note to his translation of ‘Pliny,’ that a mariner’s compass might be constructed without a magnet, by making a pendulum and setting it in motion in a given direction; because, provided the motion were continually kept up, the pendulum would continue to oscillate in the same direction, no matter by how many points, or how often the ship might happen to change her course.”

SECTION 13.

PERSPECTIVE ON THE SEA.

It has been shown (at pages 25 to 34) that the law of perspective, as commonly taught in our Schools of Art, is fallacious and contrary to everything seen in nature. If an object be held up in the air, and gradually carried away from an observer who maintains his position, it is true that all its parts will converge to one and the same point; but if the same object be placed upon the ground and similarly moved away from a fixed observer, the same predicate is false. In the first case the _centre_ of the object is the _datum_ to which every point of the exterior converges; but in the second case the _ground_ becomes the _datum_, in and towards which every part of the object converges in succession, beginning with the lowest, or that nearest to it.

Instances:--A man with light trousers and black boots walking along a level path, will appear at a certain distance as though the boots had been removed, and the trousers brought in contact with the ground.

A young girl, with short garments terminating ten or twelve inches above the feet, will, in walking forward, appear to sink towards the Earth, the space between which and the bottom of the clothes will appear to gradually diminish, and in the distance of half-a-mile the limbs, which were first seen for ten or twelve inches, will be invisible--the bottom of the garment will seem to touch the ground.

A small dog running along will appear to gradually shorten by the legs, which, in less than half a mile, will be invisible, and the body appear to glide upon the earth.

Horses and cattle moving away from a given point will seem to have lost their hoofs, and to be walking upon the outer bones of the limbs.