Part 8
If such things as criticism, experience, and comparative observation did not exist, the tone of exultation in which the above article indulges might be properly shared in by the astronomical student; but let the following extracts be carefully read, and it will be seen that such a tone was premature and unwarranted. “Paris, Sept. 15, 1848. The only sittings of the Academy of late in which there was anything worth recording, and even this was not of a practical character, were those of the 29th ult. and the 11th inst. On the former day M. Babinet made a communication respecting the planet Neptune, which has been generally called M. Le Verrier’s planet, the discovery of it having, as it was said, been made by him from theoretical deductions, which astonished and delighted the scientific public. What M. Le Verrier had inferred from the action on other planets of some body which ought to exist was verified, at least so it was thought at the time, by actual vision. Neptune was actually seen by other astronomers, and the honour of the theorist obtained additional luster. But it appears from a communication of M. Babinet that _this is not the planet_ of M. Le Verrier. He had placed his planet at a distance from the Sun equal to thirty-six times the limit of the terrestrial orbit; Neptune revolves at a distance equal to thirty times of these limits, which makes a difference of nearly _two hundred millions of leagues_! M. Le Verrier had assigned to his planet a body equal to thirty-eight times that of the earth; Neptune has only _one third_ of this volume! M. Le Verrier had stated the revolutions of his planet round the Sun to take place in two hundred and seventeen years; Neptune performs its revolutions in one hundred and sixty-six years! Thus then Neptune is not M. Le Verrier’s planet; and all his theory as regards that planet falls to the ground! M. Le Verrier may find another planet, but it will not answer the calculations which he had made for Neptune. In the sitting of the 14th, M. Le Verrier noticed the communication of M. Babinet, and to a great extent admitted his own error! He complained indeed that much of what he said was taken in too absolute a sense; but he evinces much more candour than might have been expected from a disappointed explorer. M. Le Verrier may console himself with the reflection that if he has not been so successful as he thought he had been, others might have been equally unsuccessful, and as he has still before him an immense field for the exercise of observation and calculation, we may hope that he will soon make some discovery which will remove the vexation of his present disappointment.”[34]
[34] “Times” Newspaper, Monday, Sept. 18, 1848.
“As the data of Le Verrier and Adams stand at present there is a discrepancy between the predicted and the true distance; and in some other elements of the planet. It remains, therefore, for these or future astronomers to reconcile theory with fact; or, perhaps, as in the case of Uranus, to make the new planet the means of leading to yet greater discoveries. It would appear, from the most recent observations, that the mass of Neptune, instead of being as at first stated one nine thousand three hundredth is only one twenty three thousandth that of the Sun; whilst its periodic time is now given with a greater probability at 166 years; and its mean distance from the Sun nearly thirty. Le Verrier gave the mean distance from the Sun thirty-six times that of the Earth; and the period of revolution 217 years.[35]
[35] “Cosmos,” by Humboldt, p. 75.
“May 14, 1847. A Paper was read before the Royal Astronomical Society, by Professor Schumacher, ‘on the identity of the planet Neptune (M. Le Verrier’s) with a star observed by M. Lalande in May, 1795.’”[36]
[36] “Report of Royal Astronomical Society,” for Feb. 11, 1848, No. 4, vol. 8.
Such mistakes as the above ought at least to make the advocates of the Newtonian theory less positive, and more ready to acknowledge that at best their system is but hypothetical and must sooner or later give place to a philosophy the premises of which are demonstrable, and which is in all its details sequent and consistent.
PENDULUM EXPERIMENTS AS PROOFS OF EARTH’S MOTION.
In the early part of the year 1851, the scientific journals and nearly all the newspapers published in Great Britain and on the Continents of Europe and America were occupied in recording and discussing certain experiments with the pendulum, first made by M. Foucault, of Paris; and the public were startled by the announcement that the results furnished a practical proof of the Earth’s rotation.
The subject was referred to in the _Literary Gazette_, in the following words:--“Everybody knows what is meant by a pendulum in its simplest form, a weight hanging by a thread to a fixed point. Such was the pendulum experimented upon long ago by Galileo, who discovered the well-known law of isochronous vibrations, applicable to the same. The subject has since received a thorough examination, as well theoretical as practical, from mathematicians and mechanicians; and yet, strange to say, the most remarkable feature of the phenomenon has remained unobserved and wholly unsuspected until within the last few weeks, when a young and promising French physicist, M. Foucault, who was induced by certain reflections to repeat Galileo’s experiments in the cellar of his mother’s house at Paris, succeeded in establishing the existence of a fact connected with it which gives an immediate and visible demonstration of the Earth’s rotation. Suppose the pendulum already described to be set moving in a vertical plane from north to south, the plane in which it vibrates, to ordinary observation, would appear to be stationary. M. Foucault, however, has succeeded in showing that this is not the case, but that the plane is itself slowly moving round the fixed point as a centre in a direction contrary to the Earth’s rotation, _i.e._, with the apparent heavens, from east to west. His experiments have since been repeated in the hall of the observatory, under the superintendence of M. Arago, and fully confirmed. If a pointer be attached to the weight of a pendulum suspended by a long and fine wire, capable of turning round in all directions, and nearly in contact with the floor of a room, the line which this pointer appears to trace on the ground, and which may easily be followed by a chalk mark, will be found to be slowly, but visibly, and constantly moving round, like the hand of a watch dial; and the least consideration will show that this ought to be the case, and will excite astonishment that so simple a consequence as this is, of the most elementary laws of Geometry and Mechanics, should so long have remained unobserved. * * * The subject has created a great sensation in the mathematical and physical circles of Paris. It is proposed to obtain permission from the Government to carry on further observations by means of a pendulum suspended from the dome of the Pantheon, length of suspension being a desideratum in order to make the result visible on a larger scale, and secure greater constancy and duration in the experiment. The time required for the performance of a complete revolution of the plane of vibration would be about 32 hours 8 minutes for the parallel of Paris; 30 hours 40 minutes for that of London; and at 30 degrees from the equator exactly 48 hours. Certainly any one who should have proposed not many weeks back to prove the rotation of the Earth upon which we stand by means of direct experiment made upon its surface would have run the risk, with the mob of gentlemen who write upon mechanics, of being thought as mad as if he were to have proposed reviving Bishop Wilkins’s notable plan for going to the North American colonies in a few hours, by rising in a balloon from the Earth and gently floating in the air until the Earth, in its diurnal rotation, have turned the desired quarter towards the suspended æronaut, whereupon as gently to descend; so necessary and wholesome is it occasionally to reconsider the apparently simplest and best established conclusions of science.”
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.
[Illustration: FIG. 31.]
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.