Читать книгу: «Chambers's Edinburgh Journal, No. 418», страница 3

WHY DOES THE PENDULUM SWING?

The attention of the visitor to the recent Exhibition in Hyde Park was arrested, as he advanced westwards down the central promenade of the building, by a large clock busily at work marking off the seconds of passing time. That piece of mechanism had a remarkably independent and honest look of its own. The inmost recesses of its breast were freely bared to the inspection of every passer-by. As if aware of the importance of the work intrusted to its care, it went on telling, in the midst of the ever-changing and bustling crowd, with a bold and unhesitating click, the simple fact it knew; and that there might be no mistake, it registered what it told in palpable signs transmitted through the features of its own stolid face. Mr Dent's great clock was by no means the least distinguished object in the collection of the world's notabilities.

But there was one thing which nearly concerned that industrious and trusty monitor that he surely could not have known, or his quiet countenance would have shewn traces of perturbation. He was doing Exhibition work, but he was not keeping Exhibition time. The wonderful building in which he had taken up his temporary residence was, in fact, of too cosmopolitan a nature to have a time of its own. Its entire length measured off very nearly 1-42,000th part of the circle of terrestrial latitude along which it stretched. The meridian of the Liverpool Model was close upon thirty seconds of space farther west than the meridian of the Greek Slave. Imagine the surface of Hyde Park to have been marked off, before Messrs Fox and Henderson's workmen commenced their labours, by lines running north and south at the equal distance of a second of a degree from each other, just as one sees the surface of large maps traced by meridians, nearly thirty of those lines would then have been covered in by the east and west span of the crystal roof. Mr Dent's clock might have been set to the precise time of the Greek Slave, and it would yet have been nearly two seconds wrong by the time of the Liverpool Model. The pendulum swinging so steadily within its case had a longer and more stately stride than most of its congeners. It took a second and a half of time to complete its step from side to side. But notwithstanding this, if a string had been suddenly stretched across in space above the east end of the building, and left there in free suspension, independent of all connection with the terrestrial surface, it would have taken longer for the huge structure to be trailed beneath it by the earth's rotation—swift as that rotation is—than it did for the sober and leisurely mass of metal to finish its beat from side to side.

Our immediate business, however, at this present time is not with the geographical relations of Mr Paxton's building, but rather with that sober and leisurely-moving mass—the pendulum. Even in the seventeenth century, old Graunt was shocked when some irreverent babbler spoke of one of its honourable race by the rude epithet of 'a swing-swang;' and he penned an indignant protest on the subject to the Royal Society. Since that time the pendulum has done much more to merit the reverence of the world. Plain and simple as its outward bearing is, it really holds a high and dignified position in the annals of science.

Instead, however, of touching upon its pedigree and achievements, we proceed at once to speak of certain interesting peculiarities that enter as an element into all considerations in which it has concern. In the first place, what is that characteristic motion which it so constantly assumes—that restless swinging from side to side? Is it a property inherent in its own nature, or is it a power communicated to it from without? There is a train of wheelwork enclosed with it in the case. Is that the source of its vibratile mobility? Assuredly not. For if we arrest its motion with our hand at the instant that its form hangs perpendicularly suspended, that motion is not renewed although the wheels remain in unaltered relation. Those mechanical contrivances clearly do not comprise the secret of its swinging. We must look elsewhere if we would ascertain the fundamental cause.

Has the reader ever looked at the plain white building, with successive rows of little windows, which so often spans the breadth of our smaller streams? If he has, the thought has at once arisen that within those walls huge wheels and heavy-revolving stones remorselessly tear and crush to powder heaps upon heaps of yellow grain, with a power that is equal to the combined effort of a whole troop of horses concentred in the task. But we question very much whether he has as clearly seen whence those clattering wheels derive their many horse-power! If we were to ask him to tell us how they acquired their rolling strength, he would most probably answer—from the current of the stream. This reply would amount to nothing in the matter of explanation; the force of the current is as much a borrowed attribute as the force of the wheelwork. The running water is no more an independent and living agent than is the machinery which it turns. Beyond both is the one grand determining influence—the attractive energy inherent in the substance of the vast earth. This it is which makes the water run; this it is which enables the running water to move the wheelwork inserted into its channel. As the magnet draws to itself the fragment of steel, the earth draws to itself all ponderable matter; and whenever ponderable matter is free to move, it rushes as far as it can go towards the centre of the earth's substance, in obedience to the summons. Mobile water runs down from a higher to a lower level because the latter is nearer to the earth's centre than the former, and as it falls it pushes before it such minor obstructions as are unable to resist the influence of its weight. The float-boards of the mill-wheel are of this nature; they are striving to uphold the water by means of the rubbing and friction of the apparatus that is mechanically connected with the axle. But the resistance of the friction is less than the strength with which the earth tugs at the water, and therefore the wheel goes round and the water rushes down. The force which really grinds the hard corn into flour it terrestrial attraction! Gravitation of material substance towards material substance, acting with an energy proportioned to the relative masses and to the relative distances of the elements concerned.

Let us now suppose that the matter drawn towards the earth is not free to move. Let us fancy, for instance, a drop of the running water all at once stopped in its downward path by the attachment of a string from above. The earth would then tug at that string in its effort to get the drop of water, and would consequently stretch it to a certain extent. The power that was before expended in causing the drop to move, would be now employed in striving to tear asunder the substance of the string. A heavy body hanging by a cord from a fixed point is then in this predicament. It is drawn towards the earth, but is prevented from moving to it. It consequently finds a position of rest in which it is placed as near to the source of attraction as the suspending string allows; that is, it hangs perpendicularly and immovably beneath it, stretching the string by its tendency toward the ground.

If, however, the suspended body be raised up from its position of forced repose by any interference that draws it to one side, the string being still kept on the stretch, it will be observed that it has been made to move in a curved line away from the earth's attracting mass, and that the pull of the attraction is then to a certain extent taken off from the string and transferred to the supporting hand; the force of the attraction consequently becomes then sensible as the weight of the body that is upheld. If in this state of affairs the supporting hand is taken away, the body at once rushes down sideways to the position it before occupied, with a pace accelerating considerably as it goes; for the earth continues to attract it during each instant of its descent. When it has reached the second stage of its journey, it is moving with a velocity that is caused by the addition of the attraction exercised in that stage to the attraction that had been exercised in the first stage; and so of the third, fourth, and other successive stages. It must go quicker and quicker until it comes to the place which was before its position of absolute repose.

But when it has at last arrived at this place, it cannot rest there, for during its increasingly-rapid journey downwards, it has been perseveringly acquiring a new force of its own—an onward impulse that proves to be sufficient to carry it forward and upward in spite of the earth's pressing solicitation to it to stay. Moving bodies can no more stop of their own accord than resting bodies can move of their own accord. Both require that some extraneous force shall be exerted upon them before the condition in which they are can be changed.

Now, in the case of the vibrating pendulum, it is the downward pull of the earth's attraction that first causes the stationary body to move, and as this commencing motion is downwards, in the direction of the pull, it is also an accelerating one. As soon, however, as this motion is changed by the resistance of the string into an upward one, it becomes a retarded one from the same cause. The body is now going upwards, away from the earth, and the earth's attraction therefore drags upon it and keeps it back instead of hastening it. As it travels up in its curved path, more and more of its weight is taken off the string, and thrown, so to speak, upon the moving impulse. In the descending portion of the vibration the weight of the body increases its movement; in the ascending portion it diminishes its movement. At last the upward movement becomes so slow, that the impulse of momentum is lost, and the earth's attraction is again unopposed. The body then begins to retrograde, acquires progressively increasing velocity as it descends, overshoots the place of its original repose, and once more commences the ascent on the opposite side.

Whenever, then, a heavy body suspended by a flexible string is drawn to one side, and dropped from the hand, a vibrating pendulum is made, because weight and acquired impulse influence it alternately with a sort of see-saw action, the power of the one diminishing as the power of the other augments. Weight pulls down—confers velocity and impulse during the pulling—and then velocity carries up. As velocity carries up, weight diminishes its impulse, and at last arrests it, and then begins to pull down again. In the middle of the vibration velocity is at its greatest, and weight at its least, as regards their influence on the motion. At the extremes of the vibration velocity is at its least, and weight at its greatest. Now here it is the earth's attraction clearly that confers the impulse of the downward movement, just as much as it is the earth's attraction that causes the downward movement of running water. Therefore the power which makes the pendulum swing is the same with the power which grinds the corn in the water-mill—the attraction of the earth's vast mass for the mass of a smaller body placed near to its surface under certain peculiar conditions of position.

But there is a very startling reflection connected with this consideration. How strange it is that the vast 'substantial fabric' of the earth should, after all, present itself as one grand source of motion in terrestrial things! Gravitation, weight, the majestic influence that holds the stable pyramid upon its base through centuries of time, condescending to turn the restless wheels of man's machinery! When the expansive burst of the vapour confined within the cylinder of the condensing steam-engine thrusts upwards the piston-rod with its mighty beams, it is simple weight—the weight of the superincumbent transparent atmosphere—that crushes the metal back with antagonistic force. When particles of water have been sublimated into the air by the heating power of the solar rays, it is simple weight—the weight of their own aqueous substance—that brings them down again, and that causes their falling currents to turn the countless mill-wheels implanted in the direction of their descent. When isolated tracts of the atmosphere have been rendered rare and light under the concentrated warmth of the sun, it is simple weight—the weight of colder and heavier portions of the air—that makes winds rush into the spots where the deficient downward pressure is, and that causes the sails of innumerable windmills to whirl before the impulse of the breeze.

In the steam-engine we see the earth's gravitation and artificial heat combining to effect sundry useful purposes, requiring enormous expenditure of effort. In windmills and watermills we see the earth's gravitation and natural or solar heat working together to perform like service. In the pendulum, the earth's gravitation acting alone as an enumerator of passing moments; for the momentum conferred by motion is after all but a secondary result, an offspring of the earth's attraction. In the steady oscillations of this little instrument no less a power is concerned than that grand elementary force of nature, that is able to uphold the orbitual movements of massive worlds. In the one case, the majestic presence is revealed in its Atlantean task of establishing the firm foundations of the universe; in the other, in its Saturnian occupation of marking the lapse of time. In the planetary movements, material attraction bends onward impulse round into a circling curve; in the pendulum oscillations, material attraction alternately causes and destroys onward impulse. In the former it acts by a steady sweep; in the latter by recurring broken starts. The reason of the difference is simply this: the planetary bodies are free to go as the two powers, attraction and impulse, urge them. The weight of the pendulum is prevented from doing so by the restraining power of the string or rod, that holds it bound by a certain invariable interval to a point of suspension placed farther than the weight from the source of attraction. A pendulum, in all its main features, is a terrestrial satellite in bonds—unable to fall to the surface of the earth, and unable to get away and circle round it, yet influenced by a resistless tendency to do both. Its vibrations are its useless struggles to free itself from the constraint of its double chains.