The first pendulum clock was based on the theoretical researches of Christiaan Huygens who, because of his astronomical observations, felt the need for a more exact timekeeper than had been previously available. In June 1657 the government of the United Netherlands granted to Salomon Coster of The Hague the exclusive rights for twenty-one years to make and sell clocks in that country based on Huygens's invention. Huygens discovered two years later that theoretically perfect isochronism (uniformity of oscillation) could be achieved by compelling the bob to describe a cycloidal arc. (A cycloid is the curve described by a point- like spot on a circular wheel that rolls without slipping along a straight line.) Great as was Huygens's achievement from the point of view of theory, particularly as set forth in his famous treatise Horologium oscillatorium, published in Paris in 1673, the practical solution of the problem of more accurate timekeeping came only with the invention of a new type of escapement.
Huygens's clock incorporated the verge type, but about 1670 a much improved type, the anchor type, was invented that interfered less with the pendulum's free motion. Although it is not clear who was responsible for this invention, John Smith in his Horological Disquisitions of 1694 attributed it to the London clockmaker William Clements. In this form of escapement, as a tooth of the scape-wheel escapes from the pallet at one end of the anchor, so a tooth on the other side engages with the pallet at the other end of the anchor. For satisfactory functioning, however, clocks incorporating the pendulum and the anchor type of escapement had to be placed on a level surface, and consequently in portable domestic clocks verge escapements were retained.
For those who were not astronomers the sundial remained the arbiter of local time against which clocks and watches were checked, although few common sundials in the seventeenth century were capable of showing time more accurately than to within half a minute at best. In the first comprehensive scientific treatise on the art of horology, William Derham's Artificial Clockmaker (first edition 1696), attention was drawn to the need to correct sundial readings for the effect of atmospheric refraction when the sun is low in the sky.
Although the earliest watches were driven by a spring, there was no
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Fig. 6 A drawing of Galileo's pendulum clock
. In 1637 Galileo devised a train of wheels actuated by a pendulum for counting oscillations, but the pendulum had to be controlled by hand. In 1641, the year before he died, Galileo considered how the pendulum itself could be used as a clock. In 1649 his son, Vincenzio, tried to construct a clock based on his father's design, but he died before completing it. (An inventory of his effects included an unfinished pendulum clock.) In 1659 a drawing by Galileo's friend and biographer Viviani of a clock based on Galileo's ideas was sent by one of his former disciples, Prince Leopold dei Medici, brother of the Grand Duke of Tuscany, to the French astronomer Ismael Boulliau. He passed it on to his friend Christiaan Huygens, who received it in January 1660. This drawing is reproduced above. Galileo's pendulum clock involved a new type of escapement which--was superior to the traditional verge type retained by Huygens. Each swing of the pendulum pushes the top wheel from one projecting pin to the next.
controlling spring on the balance-wheel. Neither the foliot for clocks nor the balance-wheel for watches had a truly regular motion of their own and consequently no precise timekeeping property. Both the rate of swing of a pendulum under gravity and the motion of a balance-wheel under the control of a spring are, however, periodic. Just as the invention
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FIG.I.
FIG.II.
FIG.III.
Fig. 7 Huygens's pendulum clock of 1673.
These diagrams relating to Huygens's pendulum clock are on page 4 of his Horologium Oscillatorium de Motu Pendulorum at Horologia Aptato, published in Paris in 1673 'Cum Privilegio Regis' and dedicated to Louis XIV. Fig. I illustrates the works of the clock complete with verge escapement; Fig. II the cycloidal cheeks controlling the oscillations of the pendulum; and Fig. III the external appearance of the clock. In this clock, unlike Huygens's earlier clock, the pendulum was hung between cycloidal cheeks, so that its time of oscillation was independent of the size of the arc of swing--an important property for accurate timekeeping.
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Fig. 8 The anchor escapement.
The anchor escapement consists of a wheel with pointed teeth and an anchor carrying, at places equidistant from its axis, two pallets which catch the teeth of the wheel in succession as each escapes from the action of the other.
of the pendulum improved timekeeping by clocks, so the invention of the balance-spring about 1675 produced a similar improvement in the accuracy of watches. Robert Hooke ( 1635- 1702) and Huygens each laid claim to the invention of the balance-spring. To Hooke can definitely be attributed the law of springs ut tensio sic vis ('the extension is proportional to the tension'), which he published in 1678 and which is named after him. Meanwhile, Huygens had actually made a spiral balance-spring, the idea of which Hooke claimed had first occurred to him but had been communicated to Huygens by Henry Oldenburg, the Secretary of the Royal Society, whom Hooke denounced as a 'trafficker in intelligence'! We can only conclude that, whereas Huygens definitely produced a
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watch with a balance-spring, there is abundant evidence that Hooke was the kind of ingenious inventor who often fails to follow up his insights sufficiently far to justify his claims. The question of Hooke's contributions to horology has been carefully examined by the historian of science Rupert Hall.10
There is no doubt that the achievement of greater precision in mechanical timekeeping in the second half of the seventeenth century was a momentous advance, for it ultimately led to recognition of the importance of precise measurement generally in science and technology. Moreover, the invention of an accurate mechanical clock had a tremendous influence on the concept of time itself. For, unlike the clocks that preceded it, which tended to be irregular in their operation, the improved mechanical clock when properly regulated could tick away uniformly and continually for years on end, and so must have greatly strengthened belief in the homogeneity and continuity of time. The mechanical clock was therefore not only the prototype instrument for the mechanical conception of the universe but for the modern idea of time. An even more far-reaching influence has been claimed for it by Lewis Mumford, who has pointed out that 'It dissociated time from human events and helped create belief in an independent world of mathematically measurable sequences: the special world of science.'11
We have seen that in referring to the famous Strasbourg clock Boyle said that 'the engine being once set a-moving, all things proceed according to the artificer's first design'. In the case of a clock, 'design' refers to the action of its mechanism and has no teleological significance. The mechanical conception of the universe was in this respect clocklike and in marked contrast to Aristotle's conception of the universe, which had greatly influenced medieval natural philosophers. That was based on the importance Aristotle attached to the fully developed forms to which, in his view, all things inanimate as well as animate aspire. Consequently, for him the essences or special qualities of things, rather than temporal sequences, were the primary objects of scientific investigation. This way of thinking came under fire in the seventeenth century, because it was increasingly felt that it failed to explain anything. Instead of postulating ad hoc qualities, scientists who rejected the views of Aristotle and his medieval followers invoked hypothetical mechanical systems to elucidate natural phenomena. In so far as such a system operates from given initial conditions it has some similarity to a clock. If a clock is to indicate the correct time, its mechanism must not only function properly but the hands must be correctly set beforehand. The analogy can be considered
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either purely mechanistically or else mathematically. In the latter case the object is to calculate the course which a physical system will follow in time from given initial conditions.
This was the method ad
opted by Newton in the theory of gravitation which he developed in the Principia, published in 1687, the full title of which refers specifically to the mathematical principles of natural philosophy. As he said in one of his letters to Bentley, 'Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial I have left to the consideration of my readers.' Unlike his principal continental critics, Huygens and Leibniz, Newton was willing, at least in the Principia, to bypass the problem of explaining gravitation mechanistically. Instead, taking time as the independent variable, he formulated mathematical laws of motion and gravitation in terms of which gravitational phenomena can be described and predicted.
The particular concept of mathematical time used by Newton was based on the analogy between time and a geometrical straight line. Although this analogy had been used by Galileo and by others before him, notably Nicole Oresme in the fourteenth century, the first explicit account of it was given by Isaac Newton's predecessor in the chair of mathematics at Cambridge, Isaac Barrow, in his Geometrical Lectures, published in 1670. Barrow was greatly impressed by the kinematic method in geometry that had been developed by Galileo's pupil Torricelli. Barrow realized that to understand this method it was necessary to study time, and he was particularly concerned with the relation of time and motion. 'Time does not imply motion, so far as its absolute and intrinsic nature is concerned; not any more than it implies rest; whether things move or are still, whether we sleep or wake, Time pursues the even tenour of its way.' He regarded time as essentially a mathematical concept that has many analogies with a line, for 'Time has length alone, is similar in all its parts and can be looked upon as constituted from a simple addition of successive instants or a continuous flow of one instant.'12 Barrow's statement goes further than any of Galileo's, for Galileo used only straight line segments to denote particular intervals of time.
Barrow's views greatly influenced Newton. In particular, Barrow's idea that, irrespective of whether things move or are still, whether we sleep or wake, 'Time pursues the even tenour of its way' is echoed in the famous definition at the beginning of Newton Principia: 'Absolute, true and mathematical time, of itself, and from its own nature, flows
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equably without relation to anything external.' Newton regarded the moments of absolute time as forming a continuous sequence like the points on a geometrical line and he believed that the rate at which these moments succeed each other is independent of all particular events and processes.
Newton's adoption of the idea of absolute time, existing in its own right, was partly due to his belief that there must be a fundamental theoretical measure of time to compensate for the difficulty of determining a truly accurate practical time-scale. As has been discovered since (see pp. 167-8) and as Newton himself seems to have realized, in the long run we cannot obtain a truly fundamental time-scale from the observed motions of either the earth or the heavenly bodies. One of the difficulties of Newton's definition, however, is that there is no way of using it to obtain a practical means of measuring time. It has also been criticized by philosophers, since it ascribes to time the function of flowing; but, if time were something that flowed, then it would itself consist of a series of events in time, and this is meaningless. Time cannot itself be a process in time. Moreover, what is meant by saying that 'time flows equably' or uniformly? This would seem to imply that there is something which controls the rate of flow of time so that it always goes at the same speed. If, however, time exists 'without relation to anything external', what meaning can be attached to saying that its rate of flow is not uniform? If no meaning can be attached even to the possibility of non-uniform flow, what is the point of stipulating that its flow is 'equable'?
That moments of absolute time can exist in their own right is now generally regarded by scientists and philosophers as an unnecessary hypothesis. Events are simultaneous not because they occupy the same moment of time but because they occur together. Any two events that are not simultaneous are in a definite temporal order since one occurs before the other and not because they occupy different moments of time, one of which is earlier than the other. In other words, we derive time from events and not the other way round. This was the point of view taken by Newton's great contemporary Leibniz, who did not believe that moments of time can exist independently of events. He based his argument for this on what he called 'the principle of sufficient reason', according to which nothing happens without there being a reason why it should be so rather than otherwise. He applied this principle to time by considering the case of someone who asks why God did not create everything a year sooner and from this wishes to infer that God did something for which he could not possibly have had a reason to do it thus rather
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than otherwise. Leibniz's reply is that the inference would be true if time were something apart from temporal things, for it would be impossible that there should be reasons why things should have been applied to certain instants rather than to others when their succession remained the same. But this itself proves that instants apart from things are nothing and that they only consist in the successive order of things. If this remains the same, one of the states (for example, that in which the Creation was imagined to have occurred a year earlier) would be in no way different and could not be distinguished from the other. In Leibniz's view, time is the order of succession of phenomena, so that if there were no phenomena there would be no time.13
The nature of time and its relationship to different forms of existence, including the physical, had been considered long before the seventeenth century, notably by St Thomas Aquinas ( 1224-74) in his massive Summa theologica, in which he discussed three kinds of 'time'. Time, in the strict sense, he regarded as a state of succession that has a definite beginning and end. It applies only to terrestrial bodies and phenomena. Eternity, which exists all at once (tota simul), is essentially 'timeless' and the prerogative of God alone. The third concept, called aevum, originally due to the sixth-century philosopher Boethius, like time has a beginning but unlike time no end. Aquinas considered it to be the 'temporal' state of angels, heavenly bodies, and ideas (archetypum mundum).
Despite the difference between Newton's and Leibniz's views concerning the nature of physical time, in other respects their ideas about the concept were similar. Both believed that time was universal and unique, the universe comprising a succession of states, each of which exists for an instant, successive instants being like the order of points on an indefinitely extended straight line. This was the concept of time which was to dominate physical science until the advent of Einstein's special theory of relativity early this century.
Newton's views concerning time were not confined to the physical world but extended to human history and to prophecy. Like many of his contemporaries he believed that the world was coming to an end. He was convinced that the comet of 1680 had just missed hitting the earth, and in his biblical commentaries, on Revelations and the Book of Daniel he maintained that the end of the world could not long be delayed, but he was careful to avoid the prediction made by the millenarians who had settled upon a date. His contemporary and fellow scientist Robert Boyle also believed that 'the present course of nature shall not last always, but that one day this world . . . shall either be abolished by annihilation, or,
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which seems more probable, be innovated, and, as it were transfigured, and that, by the intervention of that fire, which shall dissolve and destroy the present frame of nature'.14
Newton Chronology of Ancient Kingdoms amended, posthumously published in 1728, and his Observations upon the Prophecies of Daniel and the Apocalypse of St John, published in 1733, can together be regarded as providing a universal history of mankind that was intended to be the counterpart of the physical history of the world set out in his Principia. By about 1700 chronology had become a subject of major concern to many thinkers because of its relevance for the authenticity of the Bible. The Old Te
stament as it has come down to us contains no dates. Bede had calculated the interval between Creation and Incarnation to be 3,952 years. Earlier, Eusebius obtained a figure of 5,198 years. By 1660 at least fifty different dates had been assigned to Creation, depending on which version of the Old Testament and which counting method were used.15 James Ussher, Archbishop of Armagh ( 1581-1656), proposed 23 October 4004 BC, and the Danzig astronomer Johannes Hevelius ( 1611-87) in his Prodromus astronomiae, posthumously published in 1690, computed the exact time to be 6 o'clock in the evening, 24 October 3963 BC.16 Newton, however, was careful not to assign a specific date for the Creation.
Newton devoted a good part of the last thirty years of his life to the careful study of chronology and sought to determine what he regarded as key dates, such as that of the Argonauts' expedition. Although he made use of literary references whenever necessary, he preferred to use astronomical techniques if possible. In particular, he thought that chronology could be put on a scientific basis by means of the accurate determination of the precession of the equinoxes. By its aid he believed that, if a relevant record could be found of the position of the sun relative to the fixed stars at the time of equinox, any event in the past could, in principle, be dated.
In a letter to Oldenburg of 7 December 1675, Newton explicitly stated his belief that 'nature is a perpetual circulatory worker'. Although later he argued that the 'amount of motion' in the world would of its own accord tend to decrease, unless God intervened to correct this, this proviso reveals his continuing belief in the essentially clocklike nature of the universe. In his view, God actually needed to intervene in the natural world from time to time to adjust its working in the same kind of way as a clockmaker needs occasionally to reset a clock so that it reads correctly.
Time in History: Views of Time From Prehistory to the Present Day Page 17