VISIBLE DEMONSTRATION OF THE EARTH'S ROTATION. [From the Watchman, May 14 ]

New Zealander, Volume 7, Issue 572, 8 October 1851, Page 3

VISIBLE DEMONSTRATION OF THE EARTH'S ROTATION. [From the Watchman, May 14 ]

Fon some weeks past all the scientific and would-be-scientific portion of the public have been wild about M. Faucault's pendulum-experiment in proof of the earth's rotation, whilst plain people in general, having in vain attempted to understand the explanations of the expeiiment and significance which have appeared in the periodical press, nnd finding themselves only the more mystified by their efforts, have resigned themselves to the contentment of ignorant and implicit faith. The first authentic, if not absolutely the fiist, account of this experiment which was given to the English public, appeared in the Liteuiry Gazelle for Match 2'2nd. This was followed by an account of thp matter in the Globe, which, in attempting to be succinct and popular, became unfortunately incorrect, for which reason we did not follow the example of the geneial press in copying it into our colnmns. The incorrectness of the account in the Globe was exposed in two letters published in the limes for April 11, one of them from the pen of that accomplished mathematician, Mr. Sylvester. Subsequently a letter appeared in the Times from a person more confident than competent, questioning altogether the value and significance of the experiment, to which Mr. Sylvester replied in a second very able letter, published in the Times for April 26. Besides these there have appeared several other letters in the public papers, some of them sufficiently obscure and incorrect, and others of great merit. We shall only refer to a very elegant illustrative letter published in the Spectator for April 26. A second article, also excellent and cautionary, appeared in the Literaiy Gazette for April 19. All these articles we have caiefully perused, in the hope of being able, by their united aid, to prepare such an account of the experiment in question as should at the same time be sufficiently exact, and popularly inti Ihgible. We must confess, however, that we have found ourselves unable fully to accomplish this ; and, after Mr. Sylvester's confession to the same effect, which we shall presently quote, we need feel uo scruple in avowing it. Still we shall be expected to do our best, and will take pains to be correct, so far as we go. We will first quote an introductory and generally descriptive paragraph from the Literary Gazette of March 22 :— " 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 v.ilhm the last tew weeks, when a youag and promising French physicist, M. Faucault, who was induced by certain reflections to repeat Galileo's experiments in the cellar of his mother's bouse 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. Faucault, however, h?s succeeded in showing that this is not the case, but that this plane is itself slowly moving round the fixed point as a centre in a direction contiary to the earth's rotation, i. c, with the apparent heavens, from east to west." M. Faucault obtained permission from the French Government to use the Pantheon for the purpose of his expeiimenta, the dome of that building affording a great elevation from which to suspend the pendulum, and thus enabling him to make the result visible on a larger scale, and to secure greater constancy and duration in the experiment. At the centre of the dome a Ine wire was attached, from which a spbeie of metal, four or five inches in diameter, was suspended so as to hang near the floor of the building. This was the pendulum. Under, and concentneal with it, was placed a circular table, some twenty feet in diameter, tbo circumference of which was divided into degiees, minutes, &c, and the divisions numbered. The pendulum was then set swinging in an accurately vertical or perpendicular plane. Now, we should have said beforehand that a pendulum thus swinging, with no lateral impulse or motion whatever, would constantly pass over the same points, situated in a right line, of the table underneath it. It is found, however, upon a careful scrutiny, that this is not the case, but that the points on the edge or circumference of the table over which the swinging sphere passes, are constantly moving round in a direction contrary to the earth's rotation, that is, with the sun, from east to west. The time required in the latitude of Paris for the pendulum, constantly swinging, to shift itself light round the table back to its original position, would be, as proved by calculation, about 32 hours 8 minutes. At London, being seveial degrees nearer the pole, the revolution would be accomphbhed in rather less time, viz., in 50 hours 40 minutes. At the pole itself the swinging pendulum would not be in the slightest degree diverted or any way affected by the rotation of the carth — the pole itself being, of course, unmoved and the pendulum being supposed to be suspended immediately over it. Here then the enrth would 101 l quite round the pendulum, ever swinging in the same iixed plane, exactly once in 24> hours. The pendulum therefore, seeming, in consequence of the earth's revolving motion, to be every instant changing its own position relatively to the earth, would here at the pole appear to revolve in the opposite direction to that of the earth's rotation, and would return to its original position, that is, would complete one apparent revolution in precisely 24 hours. We have already implied that as we advance from the pole the period of the pendulum's apparent revolution would continually increase. At 60 degrees from the pole, that is in 30 ° lat., the term will be exactly 48 hours, that is double the period at tho pole. Towards the equator the rate of the pendulum's change of position becomes exceedingly slow — at length it scaicely shifts at all, and would take countless years to effect a complete levoluhon, — until finally, at the equator itself, the pendulum would be found never to change its relative position, but to swing backwards and foi wards steadfastly over the same track. Tt should be observed, however, that, in every case, and in whatever latitude, there are two points which remain, notwithstanding the apparent revolution of the plane of violation, fixed and invariable in their relations to each other and the revolving earth. These are the point of suspension and the lowest point to which the pendulum descends in its vibrations. This last is the fixed pomt — or rather the line joining these two points is the fixed line or axis, lound' which the eveislafting plane of the pendulum's vibration appears to revolve. And if this line, connecting the point of suspension with the lowest point of descent vveie piolonged downwards, through and below the earth's surface, it would pass tluough tbo earth's centre. In other words, and for obvious and elementary mechanical reasons, the lowest point to which the pendulum descends must always ho in tho right line connecting the point of suspension with the centio of attraction. Now, at the equator, the line of which we have been speaking, and which represents the height or length of the pendulum, is exactly perpendicular to the hue of

the earth's involving motion. Tbo earth volte with a level motion immediately beneath iho point of the pendulum's suspension, and therefore th.i winging pendulum no moro changes its position relatively to the earth or the equator, than a pendulum suspended from the roof of u railway carnage, which was proceeding smoothly and at a uniform late of mot in u would change its j'o,ition relatively to the moving tiain. But when, as ■ (lie case on either 6ide of the equator, the line of winch we have been speaking, and which connects the point of suspension, the lowest point of descent, and the contre of the eaith, meets the diiectiou of the earth's rotation obliquely, the case is nlteied ; and tbo weight of the pendulum not partaltin<r, because of its free suspension, directly and to the lull extent in that onwaid I motion which propels the point of suspension, while it is steadily constrained by the downward attractive force of the centre, falls,.in consequence, somewhat in the rear of the point of suspension, in its journey from west to ea.st, and therefore itself appears, by comparison, (o move, and does move relatively, backward from east to west, or with the visible heavens.. Near the equator, as we have said, and as H follows fiom the above remarks, tlus backward movement will be insensibly slow and small. But as we appioacb either pole it will become jnore direct anil iapid, till, as it has been shown, at the pole itself the pendulum becomes altogether independent of the earth's rotatory movement, and appears in consequence to levolve backnaids, or from east to west, punctually, once in 24 hours. To render this popular view of tho subject as compete as may be, we add here two quotations from letters of which wo have already spoken. Tho first is that which appeared in the Spectator. Ihe loltor is so compact and elegant that we give it almost untiie : — "Imagine that just over tho spot of tho Arctic regions where geogiaphers fix the linagtnaiy pivot of the world, theie is a mountain with a lofty cavern in it, from which you can h.ing a bulLt by a skein of unspun silk. Then, mentally, on the sui face of the rock under- J neat I) the bullet, piepare a levol circular space like the i table in the expenment of M. Fauoault; and round the margin of this table mark in two circular bands, one within the other, the twenty-four hours of tho day and their minutes and seconds, and the tlueo bundled and sixty degrees of a " great ciicle" with thoir minutes and seconds. You will thus have made an earth-dial, the i postering- '' shadow" on the face of which might be ihp flootmg wnko of the bullot as it should swing to and fio. Such n table would correspond with a small circle of latitude visibly marked on the earth; it would show the longitude of every place on it compared with some fixed point; and if you drew thiough it meridians from the Noith Pole to the South Pole, it would show the longitude of all places on the eaith. It would also show the time of day, if you could cause tho bullet to pass over the hour figures, on the hour figuies to pass under the bullet as it vibrated. Now, by the motion of the earth, the figures oa this table will actually be carried round the pole once in- l 2i hours; and if the bullet enn be kept vibrating in its original place, and pi even ted from following the figuies, the latter, in running round with the table and the world, will come successively under the bullet in the way we want, But the suspending skein of silk is so loose that it cannot do the least towards twisting- the bullet round with the world and the roof of the cavern to which it is fixed ; therefore the bullet u stationary in the way we want ; and as much unconnected with the eaith as if it hung fiom the pole-star, which is not part ot the solar systam, but for the pui poses of this expei unent may bo taken as A fixed point in infinite space. This would be the expenment of M. Faucault in its simplest form, with positive results manifested in the greatest and purest degree. We can never actually perfoim it till we pass over the eleven degrees which have hitherto separated navigators from the Pole at the nearest approach they ever yet have made to it. " If now you imagine the experiment to be repeated at the Equator, you meet a wholly different and a negative result. At the Equator the suspending point for the bullet would go round with the earth, and no vibration of any bullet underneath that suspending point could mark tho rate at which any point of the earth revolved in space ; for the two points and the bullet would all be running in the same direction at the same rate. If the bullet swung East and West, it would, at each oscillation in Bpace, merely pass beyond, or fall eboit of, the teimini of its swing ia the preceding oscillation ; and if swung North and South, it would describe in space a zigzag composed of conoidal angles, the basis of which would 1)0 the distance the earth had passed between each half oscillation, and the points of which would be the returning point of each oscillation. Such a cour.se in space could not he marked on any table or other apparatus on the eat th ; but could be registered only by means of some belt like Saturn's ring, which bhould be stationary in space, and have the degrees and minutes maiked on it as they are marked on the ecliptic of our globes. This would be the experiment in its purely negative form, with indications at zero. " 13ut as you recede from the Equator you would be getting out of exact parallelism with the plane of the earth's levolution ; and would, by a geometrical law not comprehensible to the popular mind, be obtaining a more complex indication. The general leader will gain some feeling of the changed result from the image presented to tho eye by a diagram showing the very complicated track that would be given to the bullet ljy the combination of Hb independent swing" to and fro, with its circular advance to the world. At the Pole, to use the poeticul but strictly exact illustration of Mr. Sylvester, in the Times, " its track would be a series of loops or festoons regularly and symmetrically arranged around a common centre, much like a very composite corolla of a flower with a large number of extremely elongated and crowded petals grouped around its seed vessels." As the composite flower became laiger by the movement of the pendulum away from the Pole, I suppose the petals would become shoiter and more obtuse; tbe centre of the flower would open, and cecomeafree space; further towaids the Equator, the petals would be resolved into a succession of small eccentric circles ; and on tbe line of the equator itself, there would be only a thin line of a different sort of efflorescence, not very unlike the slanting edges of a wheel of acute teeth, set more in one direction than the other. Mr. Sylvester, who is known to the Cambrulgemen as one of the profoundest, though not yet one of the most distinguished mathematicians of the day, has corrected the loose explanation of the experiment which appeared in the Times ; and has stated the time which tbe bullet will take to make a revolution round the table at tho latitudes of Pans and London, lie asserts that the revolution will occupy 32 hours and 8 lninutep at Paris, and 30 hours and 40 minutes at moro northerly London. "So much for tbe principle of the experiment : a woid of doubt on its mechanical details. The descriptions 1 have read convey the idea that the metal ball continues to swing to and fro for 24 houis, and from day to day. This cannot be tho case without the help of machinery ; for the ball will be brought to a standstill by friction, (or the torsive power of tbe suspending wire,) ar.d the opposition of the air to its passage. You could not apply external machinery except in the way that you apply it to the pendulum of a clock. But in a clock the pendulum is imprisoned in a guide which twists it with the world; and you could not, in fact, strike tbe pendulum by unconnected machinery of any but tbe most elaborate character, in such a manner as not to change tbo piano in wbioh the pendulum vibrates. The impulse to the pendulum would, unless its aim were most delicately calculated and directed, have a tangental direction similar to that which the torison of a stiff pendulum rod would give." Tho paragraphs which follow are from Mr. Sylvester's £*cond letter to the Times : — " For the satisfaction of that numerous and respectable body of thinkers who form an intermediate class between those who are incapable of any proof except what appeais directly to the senses, and the elevated few who can comprehend tho foice of an analytical investigation, I offer a buef and rapid recapitulation of the argument lather hinted at than expressed in my previous letter. II At the pole it is obvious that the plane of vibration (abstraction made of tbe eaith 's annual movement) remains fixed in space, and therefore appears to revolve with and for the same reason as the sun, at the rate of 15° per hour, so as to tend to complete one revolution in four-and-twenty hours. At the Equator " tbe law of sufficient reason" shows immediately that tbeie can be no pei maneut rotation either way. For, suppose tbe pendulum to be set moving in any direction across the equinoctial line, at the beginning and end of the first semi-oscillation it will be on different sides of the equator, and considerations of symmetry show that, whatever ciu^o should be supposed to exist for making the north ond of the plane of vibration turn round as the sun turns lound when it is north of the Equator, an equal cmse would operate to make tho south end ot the same plane turn lound when it is south of the Equator. Pint clearly these two equal motions asenbod to the piano aro inconsistent with or would neutialue one another, just; 1 ;, a tuinstilo capable of going round both wayp, which two people on opposite sides of tbe pivot should be pressing ogamst with equal strength, would admit

passage to noitlier of them. Jk it well obseivcd that this reasoning applies to experiments supposed to be made at the equator, and at no other point of the earth's suri'dce. ******

" Irrespective of all geometry and arithmetic, it is clear to common sense that if the motion bu 15 degrees per hour :it each pole, and zero at the equator, it will lie some quantity gradually tapei ing off from 15 degrees to nothiug— that is to say, the time required for a c<un« plcte 1 evolution will go on increasing from 24 hours to an eternity, as we pass up and dowu lrom the poles to the equator. " But I have found many persons exceedingly perplexed to follow in tlieir mind this relative motion at intermediate points, and who think it a hard tax. upon their faith to believe that when the eaith has gone once fairly round the status quo as between the horison and the plane of vibration should not be lestored. Some, accordingly, are driven to suppose that the motion is 15 degieeajjer hour everywhere except at the cquntor; others, like your coricspondent, that it is 15 degrees nowhote except at the pole. 'Hie truth is, that such pet sons are striving to put a greater load upon common sense, or what should be termed immediate intuition, than it will well bear. The motion is the result ot a latiomil and mathematical investigation, and extra to the pole cannot well be followed by the mere conceptive faculty ; in fact, except at the pole, wheie the plane of vibration is iixed and the earth passes under it, two things have to be considered— not merely the motion of the earth, but that of the plane of vibration itself (if this mode of explanation be attempted to be kept up), and it will be the difference of thche two motions which becomes apparent to obseivation. Nothing, however, is gained by this mode of looking at the question, and the public should not be so unieasonable as to expect that eveiy conclusion of calculation admits of being made clear to popular apprehension. " The experiments connected with the practical demonstration of the phenomenon require to be conducted with great cat c; and some discredit has been brought ' upon the attempts to illustrate it in this country by persons who have not taken the necessary precautions to protect the motion from the eccentric deviation to which it is liable, and which may, and indeed mast, have the effect of causing, in some cases, an apparent failure, and in others a still more distressing, because fallacious, success. I believe, from the character of the persons connected with the experiments, that the true phenomenon has been accurately pioduccd and observed in Paiis. I doubt whether as much can be said, with entire confidence, of any of the experiments hitherto performed heie at home. " Any want of symmetry in the arrangements for the suspension of the wire, or in the centring of the weight, exposure to currents of air, or the tremulous motion occasioned by the passage of vehicles, may operate to cause a phenomenon to be brought about curious enough in itself, as a result of mathematical laws, Lut quite difleient from that supposed. 'I he phenomenon of the progression of the apsides of an oval oibit here alluded to is familiar to all students in mechanics. " It is perfectly absurd for persons unacquainted with mechanical and geometrical science to presume to make the expeiiment. Indeed, such efforts deserve rather the name ot conjuring than of experiment ; but m this, as in many other matters of life, it is tiue that ' fools rush in wheie angels fear to tread.' Perhaps the 00-hasty rush at the experimental verification of Faucault's law may account for some persons in England, whose opinions when given with due deliberation are entitled to respect, having allowed themselves to express doubts (which 1 understand, however, have been since retracted) as to the tiuth of the law itself. In Paiis, there was no difTeterca of opinion among such men as Lame, Poinsol, Binet, Leonville, Sturm, Chasles, Bruvues, I believe, Arago, Hermite, and many otheis with whom I conversed on the subject, except as to the best mode of making the theory popularly intelligible." Tbe reader bo 9 now before him — at as great length as our space will permit, in as popular a form as tbe essential nature of the subject can be made to assume, and with all the authenticity that science has hitherto given to it, — an explanation of the process and the value of the experiment that, from its relatian to one of the primordial facts of the planet which the human race has been destined to colonige, may rank among the most interesting of modern discoveries.}