Chambers's Edinburgh Journal, No. 457 / Volume 18, New Series, October 2, 1852

by Various

But both these weights, the one going upon the short journey, and the other upon the long, will start down exactly the same inclination or declivity. The reader will see that this must be the case if he will draw two circles on paper round a common centre, the one at the distance of one inch, and the other at the distance of nine inches. Having done this, let him cut a notch out of the paper, extending through both the circles to the centre, and including a twelfth part, or thirty degrees, of each between its converging sides. He will then observe, that the two arcs cut out by the notch are everywhere concentric with each other; therefore, their beginnings and endings are concentric or inclined in exactly the same degree to a perpendicular crossing their centres. These concentric beginnings and endings represent correctly the concentric directions in which the swinging weights commence their downward movements.

Now, since it has been shewn that bodies begin to run down equal descents with equal velocities, it follows that the weight on the short string and that on the long string must commence to move down the concentric curves of their respective arcs at an equal rate. But it has been also shewn that the one of these weights has a nine times longer journey to perform than the other; it is clear, therefore, that both cannot accomplish their respective distances in the same time. The weight on the shortest string in reality makes three vibrations, and the weight on the string that is next to this in length makes two vibrations, while the weight on the longest string is occupied about one; and the differences would be as 9, 4, and 1, instead of as 3, 2, 1, but that the weights moving in the longer arcs benefit most from acceleration of velocity. Although all the vibrating bodies begin to move at equal rates, they pass the central positions directly beneath their points of suspension at unequal ones. Those that have been the longest in getting down to these positions, have of necessity increased their paces the most while upon their route.

Suspended weights, then, only vibrate in equal times when hung upon equal strings; but they continue to make vibrations in equal times notwithstanding the diminution of the arcs in which they swing. This was the fact that caught the attention of Galileo; he observed that the vibrations of the lamp slowly died away as the effect of the disturbing force was destroyed bit by bit, but that, nevertheless, the last faint vibration that caught his eye, took the same apparent time for its performance as the fullest and longest one in the series.

The instrument that has been designated by the learned name of pendulum, is simply a weight of this description placed on the end of a metallic or wooden rod, and hung up in such a way that free sideways motion is permitted. This freedom of motion is generally attained by fixing the top of the rod to a piece of thin, highly elastic steel. A pendulum fitted up after this fashion, will continue in motion, if once started, for many hours. It only stops at last, because the air opposes a slight resistance to its passage, and because the suspending spring is imperfectly elastic. The effects of these two causes combined arrest the vibration at last, but not until they have long accumulated. The weight does not stand still at once, but its arc of vibration grows imperceptibly less and less, until at last there comes a time when the eye cannot tell whether the body is still moving or in absolute repose.

Now, suppose that a careful and patient observer, aware of the exact length of the suspending-rod of a vibrating pendulum, were to set himself down to count how many beats it would make in a given period, he would thenceforward be able to assign a fixed value to each beat, and would consequently have acquired an invariable standard whereby he might estimate short intervals. If he found that his instrument had made exactly 86,400 beats at the end of a mean solar day, and knew that the length of its rod was a trifle more than 39 inches, he would be aware that each beat of such a pendulum might always be taken as the measure of a second. The length of the rod of a pendulum which beats exact seconds in London is 39.13 inches.

But there are few persons who would be willing to go through the tedious operation of counting 86,400 successive vibrations. The invention of a mechanical contrivance that was able to break the monotony of such a task, would be hailed by any one who had to perform it as an invaluable boon. Even a piece of brass with sixty notches upon it, which he might slip through his fingers while noting the swinging body, would enable him to keep his reckoning by sixties instead of units, and so far would afford him considerable relief. But if the notched brass could be turned into a ring, and the pendulum be made to count the notches off for itself, round and round again continuously, registering each revolution as it was completed for future reference, the observer would attain the same result without expending any personal trouble about it. It is this magical conversion of brass and iron into almost intelligent counters of the pendulum's vibrations, that the clock-maker effects by his beautiful mechanism.

In the pendulum clock, the top of the swinging-rod is connected with a curved piece of steel, which dips its teeth-like ends on either hand into notches deeply cut in the edges of a brass wheel. The notched wheel is connected with a train of wheel-work kept moving by the descent of a heavy weight; but it can only move onwards in its revolution under the influence of the weight, as the two ends of the piece of steel are alternately lifted out of the notches by the swaying of the pendulum. The other wheels and pinions of the movement are so arranged that they indicate the number of turns the wheel at the top of the pendulum completes, by means of hands traversing round a dial-plate inscribed with figures and dots.

It is found convenient in practice to make the direct descent of a weight the moving power of the wheel-work, instead of the swinging of the pendulum, for the simple reason, that the excess of its power beyond what is required to overcome the friction of the wheel-work, is then employed in giving a slight push to the pendulum; this push just neutralises the retarding effects before named as inseparable from the presence of air and imperfect means of suspension. The train of wheel-work in a clock, therefore, serves two purposes—it records the number of beats which the pendulum makes, and it keeps that body moving when once started. As far as the activity of the pendulum is concerned, the wheel-work is a recording power, and a preserving power, but not an originating power. If there were no air, and no friction in the apparatus of suspension, the pendulum would continue to go as well without the wheel-work as with it. With the wheel-work it beats as permanently and steadily upon material supports and plunged in a dense atmosphere, as it would if it were hung upon nothing, and were swinging in nothing; and also performs its backward and forward business in solitude and darkness, to the same practical purpose that it would if the eyes of watchful and observant guardians were turned incessantly towards it.

Galileo published his discovery of the isochronous property of the pendulum in 1639. Richard Harris of London took the hint, and connected the pendulum with clock-work movement in 1641. Huyghens subsequently improved the connection, and succeeded in constructing very trustworthy time-keepers, certainly before 1658.

But notwithstanding all that the knowledge and skill of Huyghens could do, his most perfect instruments were still at the mercy of atmospheric changes. It has been said, that the time of a pendulum's vibration depends upon the length of its suspending-rod. This length is measured, not down to the bottom of the weight, but to the centre of its mass. For the weight itself is necessarily a body of considerable dimensions, and in this body some particles must be nearer to, and others further from the point of suspension. Those which are nearest will, of course, in accordance with the principles already explained, have a tendency to make their vibrations in shorter periods; and those which are furthest, in longer periods. But all these particles are bound together firmly by the power of cohesion, and must move connectedly. They, therefore, come to an agreement to move at a mean rate—that is, between the two extremes. The top particles hurry on the middle ones; the bottom particles retard them in a like degree. Consequently, the whole of the weight moves as if its entire mass were concentered in the position of those middle particles; and the exact place of this central position in relation to the point of suspension, becomes the important condition which determines the time in which the instrument swings.