Time and the Royal Society

Time and the Royal SocietyAuthor(s): Alan CookSource: Notes and Records of the Royal Society of London, Vol. 55, No. 1 (Jan., 2001), pp. 9-27Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/532142 .

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Notes Rec. R. Soc. Lond. 55 (1), 9-27 (2001)

TIME AND THE ROYAL SOCIETY

by

SIR ALAN COOK, F.R.S.

8 Wootton Way, Cambridge CB3 9LX, UK ([email protected])

SUMMARY

Fellows of The Royal Society have been concerned with the definition and measurement of time from the first days of the Society. John Flamsteed, F.R.S., 'Royal Astronomer', showed that the rotation of the Earth was isochronous and that the length of the solar day varied with the season because the path of the Earth about the Sun was an ellipse inclined to the Equator of the Earth. In the 20th century, D.W. Dye, F.R.S., made quartz oscillators that replaced mechanical clocks, and L. Essen, F.R.S., brought into use at the National Physical Laboratory the first caesium beam frequency standard and advocated that atomic time should replace astronomical time as the standard. The Society supported the development of chronometers for use at sea to determine longitude, and Fellows used the electric telegraph to find longitude in India. Edmond Halley, F.R.S., estimated the age of the Earth from the saltiness of lakes and seas; Lord Kelvin, F.R.S., estimated the rate at which energy was being radiated from the Sun; and Lord Rutherford, F.R.S., showed how the ages of rocks and of the Earth could be found from decay of radioactive minerals in them.

INTRODUCTION

A millennium, artificial as it may be, is a convenient marker of the steady flow of time that carries particular events in our ever-changing world. Time signifies many concepts, the psychological sense of progress from one state to another, landmarks of our individual and collective memories of the past, in physics the independent variable of dynamics. How can we quantify any of those senses of time? We measure time physically by counting the repetitions of a simply periodic system. What is a simply periodic system, how may we identify one and how may we choose one as the fundamental standard of time? The earliest astronomers had to face such questions, even if not explicitly, when they found various periodic motions of heavenly bodies to be incommensurable. In the earliest years of the Society, John Flamsteed, F.R.S. (figure 1), studied the equation of time. Was the solar day more fundamental, or the sidereal day, or a mechanical clock? Until almost the end of the last millennium, the day has been the fundamental measure of time. It is so no longer. In the last 2000 years the length of the day has increased by about 40 ms, and there are other, more rapid,

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© 2001 The Royal Society



Sir Alan Cook

Figure 1. John Flamsteed, ER.S., first Astronomer Royal. (Royal Society portrait.)

changes in the rotation of the Earth. Now, therefore, the fundamental unit of frequency, the reciprocal of time, is realized by frequencies of atomic transitions and time is the count of atomic oscillations.

As civilization has become more and more technical, people have had increasingly to coordinate their lives through common scales of time made widely accessible. Great cities like Bere and Strasbourg had civic clocks in the Middle Ages (figure 2), railways soon used accurate astronomical time distributed by telegraph. Now, in the present age, a vast range of activities from shopping and banking to the control of distant spacecraft depends on a common system of atomic time (UTC) accessible worldwide.

Dynamics is the theoretical study of how things change with time. Setting up scales of time for communal convenience and necessity involves also fundamental issues of the nature of dynamics as an abstract structure and its relation to the behaviour of the natural world.

Finding longitude is a matter of comparing times at different places. The Society

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Time and The Royal Society

Figure 2. The Zytgloggenturm (clock tower) in Berne. (Photograph: Alan Cook.)

supported the attempts of John and James Harrison to devise a clock that would keep time at sea. James Cook, F.R.S. (figure 3), on his second Pacific cruise, found that time transported by a Kendal watch was more reliable than time found from the place of the Moon, on which he had until then depended. When the electric telegraph was installed across India by Sir William Brooke O'Shaughnessy, F.R.S., longitudes in the Great Trigonometrical Survey of India were found with its help.

Modem clocks, mechanical as well as atomic, have run reliably over the last two or three centuries so that we have secure records of celestial motions that reveal variations in the rate of rotation of the Earth, in short as well as long periods. Times of very remote events, such as the deposition of rocks or the formation of the Earth, long before there were people to keep records, have to be derived from the outcome of processes that occur at known or estimated rates. So Edmond Halley, F.R.S.(figure 4), estimated the ages of oceans and lakes from their saltiness, Lord Kelvin, F.R.S., estimated a range of ages of the Earth from the radiant output of the Sun. More

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Sir Alan Cook

Figure 3. Captain James Cook, ER.S. (Royal Society portrait.)

securely, Lord Rutherford, F.R.S. (figure 5), showed how the ages of rocks and the Earth might be found from the accumulated products of radioactive decay of minerals.

CALENDARS

We celebrate the beginning of the Third Millennium according to the Christian calendar established in the 16th century, which is a revision of the pre-Christian calendar of Julius Caesar. There are two problems with practical calendars: how to reconcile the two incommensurable scales of time of the year and of the day, and when to start from. The Julian calendar accommodated the two timescales by adding a day to every fourth year so that on the average the year was 365.25 days long exactly. It started from the traditional year of foundation of the City of Rome, but when it was adopted as the Christian calendar the origin was changed to the supposed (but not

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Figure 4. Edmund Halley, ER.S., second Astronomer Royal and Savilian Professor of Geometry, Oxford. (Royal Society portrait.)

actual) year of the birth of the Saviour. The fact that the year is not exactly 365.25 days meant the solstices and equinoxes fell on changing dates, counted in days, as was already noticed by the Venerable Bede. That was inconvenient and, furthermore, a third scale of time-that of the revolution of the Moon about the Earth-is involved in religious festivals. Roman dates such as the ides and calends of the months were linked to the phases of the Moon, and so are the Christian festivals based on the Jewish Passover, itself related to the spring equinox. Over a millennium and a half it became very obvious that the spring equinox and the date of Easter according to daily timekeeping were out of step with that according to lunar timekeeping.

By the end of the 15th century, astronomers knew that the year was not exactly 365.25 days, but slightly less, and after some delays a new calendar, the Gregorian calendar was promulgated by Pope Gregory XIII in 1582. Years that were exact centuries were not to be leap years, corresponding to a year of 365.24 days, but that

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Sir Alan Cook

Figure 5. Lord Rutherford, P.P.R.S. (Royal Society portrait.)

was still not near enough. Accordingly, years divisible by 400, beginning with 1600 were to be leap years; the year 2000 just past was notable as the first centurial year to be a leap year since the introduction of the Gregorian calendar. 'Leap year', by the way, is an inappropriate term, for it might suggest that a day is missed out or leapt over; whereas, in fact, a day is added, as the alternative name, 'bisextile year' correctly indicates.

It is notorious that many countries hostile to the Roman Catholic Church did not adopt the Gregorian calendar until centuries had passed, and indeed it is still not fully accepted in some lands of the Orthodox faith. The change was long-delayed in Britain by ignorance, suspicion and prejudice (I forbear to hint at current parallels). That it eventually came about in 1752 was in part due to the powerful advocacy of the second Earl of Macclesfield, an able amateur astronomer and President of The Royal Society from 1752 to 1764 (figure 6).

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Figure 6. Lord Macclesfield, P.P.R.S. (Royal Society portrait.)

THE EQUATION OF TIME

The solar day is the interval between successive transits of the Sun across an observer's meridian. It is not constant. Apparent solar time is 14 seconds less than mean time in mid-February and 16seconds more in early November. The variation, the 'equation of time', had been known for many years before The Royal Society was founded. The most impressive demonstration was perhaps that provided by G.D. Cassini with the meridian line set out on the floor the basilica of San Petronio in Bologna in 1652, where Cassini (later elected to The Royal Society) was at that time Professor of Astronomy in the ancient university. The line was illuminated by light from the Sun shining through a hole in the roof of the aisle above the line, which is long enough for the variation in the length of the day to be evident. Cassini's studies of the orbit of the Earth about the Sun were well known to Flamsteed and others in England.

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Although it was well known by the middle of the 17th century that the length of the day varied throughout the year, the explanation was obscure. By 1660 the Copemican description of the Solar System with the spinning Earth was generally accepted; and Kepler, who believed that the Sun and the planets were coupled by magnetic forces and that there was an essential relation between rotation and magnetism, thought that the spin angular velocity of the Earth upon its axis depended on the distance of the Earth from the Sun in its elliptical orbit. In 1672, Flamsteed argued that the Earth rotated with a constant angular velocity and that the length of the solar day varied because the angular velocity of the Sun around the Earth varied with the position of the Earth in its orbit about the Sun:' the elliptical orbit is inclined to the terrestrial Equator.

Flamsteed could solve the equation of time because the clocks he had at Greenwich, made by Thomas Tompion, were the most reliable of their day. He could compare clock time with solar time over a whole year, but it was not until almost 1688 that he had sufficient data to demonstrate that the clocks kept time with the rotation of the Earth on its axis. The course of his investigations can be followed in his correspondence.2 Newton advocated the use of sidereal (stellar) time in astronomy, which is indeed conceptually simpler than solar time, but Flamsteed kept to solar time corrected to mean time by the equation of time because, as he said, it is more familiar. Sundials, which show apparent solar time, sometimes carried tables of the equation of time, so that mean solar time could be read off.

Flamsteed's conclusion depended on the consistency of two different periodic systems-the rotation of the Earth and pendulum clocks-which remained in agreement over long periods. The motion of the Sun around the Earth was, relative to them, not isochronous, and that for well-understood reasons. Flamsteed's scheme was simpler and more comprehensive than the alternative, in which the rotation of the Earth varied with its orbital position. The arguments that justified the change from astronomical to atomic time are similar.

CLOCKS

By the time that Flamsteed set up the Royal Observatory at Greenwich in 1675, some astronomers saw that fundamental positions of celestial objects were best found from observations in the meridian. They also argued that open sights should be replaced by telescopes with micrometers in the eyepiece. Declinations, the complements of angles from the North Pole, would be found from zenith distances at meridian transits, while right ascension, measured round the Equator from the First Point of Aries, would be found from the times of those transits. At first Flamsteed, like other astronomers, lacked the necessary instruments, but in 1689 he acquired a satisfactory mural arc and clocks by Tompion. Two clocks had pendulums about 4m long that beat 2s (the half period) and kept going over long periods (figure 7). When Halley became Astronomer Royal he found that Mrs Flamsteed had removed all the instruments and he had to have new ones. George Graham, F.R.S., made the clocks, which were a great improvement on Tompion's; one was still running well until very recently.

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Figure 7. 'Prospectus intra Cameram Stellatum' of the Royal Observatory, Greenwich, with the dials of the two Tompion clocks in the background, to the left. (Reproduced

from the original engraving by Francis Place in the Archives of the Royal Observatory by permission of the Syndics of Cambridge University Library and of the Particle Physics

and Astronomy Research Council.)

John Shelton, who had worked for Graham, made a number of regulator clocks, one of them for The Royal Society (figure 8). The Society loaned its clock for a number of expeditions, for the transit of Venus in 1761 and 1769, for tests of gravity near the Equator, for checks on Harrison's chronometer in 1763, for geodetic observations in Pennsylvania and on Cook's circumpolar voyage. It seems to have been last used in 1815 on the Arctic expedition of Lieutenant Parry.3

DISCOVERING THE LONGITUDE

Even before Flamsteed began to study the equation of time, Robert Hooke, F.R.S., in England and Christian Huygens, F.R.S., in The Netherlands had made watches with hair springs in the hope that they might tell time at sea to find the longitude; the watches were inadequate. Differences of longitude had to be found from concurrent observations of a

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Sir Alan Cook

common celestial event. Lunar eclipses were the easiest to observe, at sea as well as on land, but were infrequent. Occultations of the moons of Jupiter, suggested by Galileo and thoroughly studied by G.D. Cassini, could be observed regularly, but in the 17th and 18th centuries only with very long telescopes that were unmanageable at sea (see the frontispiece to this issue). The angular distance between the Sun and the Moon was a third measure of time, but the vagaries of the Moon's motion were large. Halley observed the moons of Jupiter on land in the course of his Atlantic cruises of 1699 to 1701, and he devoted his years as Astronomer Royal to systematic observations of the Moon. By the time James Cook went to Tahiti to observe the transit of Venus, the theory of the Moon had been improved by Leonhard Euler, F.R.S., and Tobias Mayer had constructed tables for Euler's theory. Cook used them to find longitudes from lunar distances on his first Pacific voyage of 1769. He took a Kendal watch on his second and third voyages and came to prefer it.4

The Board of Longitude was set up in 1714 to award a prize for such person 'as shall Discover the Longitude at Sea'. Halley as Savilian Professor and later as Astronomer Royal was a member ex officio. When John and James Harrison sought support for their attempts to gain the prize, John met Halley in E r London, who advised them to consult Graham. Figure 8. Regulator clock by John After the Harrisons' first model had been tried Shelton in The Royal Society. on voyages to Lisbon, The Royal Society gave a certificate signed by James Bradley, F.R.S., Graham, Halley and others, stating that Harrison deserved public encouragement. Cook's use of the Kendal watch in 1772 came some 40 years after Halley's death, but Harrison still recalled with gratitude the support given him by Halley and Graham.

Mariners used chronometers such as the Kendal watch to find longitude almost up to the present day, but the electric telegraph, when it was installed, was more convenient on land. Sir William Brooke O'Shaughnessy, F.R.S., laid out an extensive telegraph network across the Indian subcontinent between 1853 and 1855;5 it was used to transmit time signals for the determination of longitude in the Great Trigonometrical Survey of India.

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QUARTZ CLOCKS

Radio communications developed rapidly and extensively in the First World War for military uses. After the war, as broadcasting flourished, the young radio industry needed reliable measurements of frequency and accurate standards. D.W. Dye, F.R.S., who had applied the cathode-ray tube to electrical measurements, was in charge of alternating current measurements at the National Physical Laboratory (NPL) in the 1920s. The NPL was then overseen by a Board of Visitors, with strong representation from The Royal Society. Dye devised oscillatory circuits with very stable frequencies, and compared their frequencies with lower ones to determine their values in terms of the astronomical second, and with higher ones used for broadcasting. He first coupled a tuning fork electromechanically to an electrical oscillator, but the frequencies were inconveniently low and depended strongly on temperature, air pressure and other conditions. Vibrating quartz crystals coupled to electrical circuits by the piezo-electric effect were far better. Dye cut his crystals as rings, at first oscillating radially, but later cicumferentially with improved stability. He constructed oscillators with frequencies in the range of 10-100 kHz, developed multivibrator circuits to generate harmonics and subharmonics of the quartz crystal frequency, and began to make systematic comparisons of the frequencies of signals emitted by radio stations in Britain and Europe.6

L. Essen, F.R.S. (figure 9), joined Dye's group in 1929. After Dye's early death he developed the quartz ring into an exceptionally stable oscillator (figure 10).7 It ran very reliably and he could count oscillations over long periods and use it as a clock. He also used it to control the frequency of the emissions from a radio transmitter at the NPL, which provided a reference for commercial and other services.

ATOMIC CLOCKS AND ATOMIC TIME

Techniques for electrical measurements at up to 30 GHz were developed in the Second World War for radar. Afterwards they became available for molecular and atomic spectroscopy, and that led to suggestions that a suitable transition might form a standard of frequency that was not arbitrary, as the quartz oscillator was. In 1950, in Washington for a conference, Essen visited the (then) National Bureau of Standards and the Massachusetts Institute of Technology, where he saw studies of hyperfine transitions in the atom caesium-133 at about 9000MHz, using atomic beams. He set up a caesium atomic beam at the NPL and in 1956 found the transition at 9192.6MHz. He wrote afterwards:

We were incredibly lucky to find the right conditions after searching for a few days, and there was the resonance exactly as sharp as predicted. We invited the Director [Sir Edward Bullard, F.R.S.] to come and witness the death of the astronomical second and the birth of atomic time. And it was indeed the birth since much to our surprise it was another year before any clocks were working in the USA.7 (See figure 11.)

The caesium beam did not run continuously and Essen compared the frequency of a quartz oscillator running continuously with the atomic transition at regular intervals.

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Sir Alan Cook

Figure 9. Louis Essen, ER.S. (Royal Society portrait.)

Figure 10. The Essen quartz ring oscillator.

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Figure 11. The caesium beam atomic standard with Essen and Parry.

Later, continuous oscillators that were locked by servo control to caesium and other atomic transitions were built. Essen and his group at the NPL studied the hydrogen maser and did some experiments on a hyperfine transition in rubidium.

Essen clearly foresaw from the very beginning that an atomic standard of frequency would replace astronomical standards of time. In 1958, he and W. Markowitz of the US Naval Observatory in Washington determined the relation between the ephemeris second (derived from the period of the Earth about the Sun) and the caesium frequency. Their value now formally defines the second by international convention.

By 1950 the metre was no longer defined by the length of a metal bar but by a wavelength of light, and Essen and K.D. Froome had made some very careful determinations of the speed of light in terms of that wavelength. In 1957, Essen proposed that lengths should be calculated from times of travel of electromagnetic radiation, using a value of the speed adopted by international convention. The metre is now so defined. Other fundamental units are likewise related to frequency: electrical potential difference through Josephson tunnelling experiments and a conventional ratio of electronic charge to Planck's constant. Units and standards are defined in that way because frequency is by far the most precisely realized of all fundamental quantities, and standard values are readily accessible by radio. Together those properties provide a system of units and standards that is very precise and available to suitably equipped laboratories worldwide.

Atomic time, universally available, is the basis of a vast range of activities without which life today would be impossible. Ordinary clocks and watches are controlled from a radio station, the Interet with its multifarious possibilities is organized on atomic time,

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distances are measured by times of travel of light, and the control of spacecraft depends on universal timekeeping. All those applications have sprung from the quartz crystal standards of Dye and the first reliable atomic standard of Louis Essen.

THE ROTATION OF THE EARTH

In 1693 and 1695, Edmond Halley studied astronomical observations made about 800 and 1600 years earlier in Asia Minor, and suggested that the Moon was speeding up in her orbit about the Earth.8 Later analyses confirmed his suggestion. Pierre Simon Laplace, F.R.S., showed that effect was connected to a slow change in the orbit of the Earth about the Sun, which, so he calculated, could account for the whole observed change in the Moon's orbit. John Couch Adams, F.R.S., found an error in Laplace's algebra and showed that his theory could deliver only about half of the observed acceleration.9 Subsequently G.I. Taylor, F.R.S., and Harold Jeffreys, F.R.S., calculated the braking of the rotation of the Earth by tidal friction in the Irish Sea, and found the corresponding acceleration of the Moon to be close to the difference between the observed effect and Adams's calculation. Over some three centuries the astronomical estimates of the retardation of the Earth and the acceleration of the Moon have improved, especially at the Royal Observatory under Sir Harold Spencer Jones, F.R.S.'°

With better clocks and astrometric instruments changes in the Earth's rotation the length of the day-could be detected over periods much shorter than centuries. In the inter-war years, annual and possibly six-monthly changes in the length of the day were found with mechanical clocks. The quartz oscillator, and subsequently the atomic clock, being far more stable than the best mechanical regulators, led to more refined studies of the length of the day, now connected with seasonal changes in the angular momentum of the atmosphere and oceans (figure 12).

THE AGE OF THE EARTH

Counting oscillations of periodic systems can take us only a short way back into the past. Chance records of celestial phenomena such as comets, eclipses and planetary conjunctions may provide dates up to some two millennia ago. So people have attempted to identify the Star of Bethlehem and thus the date of our Lord's birth." Halley found the date and place of the landing of Julius Caesar in Kent from astronomical and tidal records. The orbit of Halley's comet has been constructed over almost 3000 years from Chinese and other records.'2

Between 1650 and 1654, Archbishop Ussher published his chronology of biblical events, based on a thorough study of the Old and New Testaments; the idea that the Earth was 4000 years old at the time of the birth of Christ is already to be found in medieval carols. In the years after the foundation of The Royal Society, days and years in biblical accounts came to be treated rather elastically and in particular the days of creation of the Hexaemeron might be considered to be symbols of the stages of

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4-

Durationoy I

r, ' Duration of the Day I f I 86400s + dt ms

o tl||l||lllllll li|li|»|iltlll ii' l {l|i|' l t l »lI 1960 1965 1970 1975 1980 1985 1990

Figure 12. Variations in the length of the day.

creation. Halley, without getting into theological trouble, estimated the ages of lakes from their sizes and saltiness combined with the rate at which rivers brought salt into them. He pointed out that ages so found were maxima, for if the lake had some original salt its actual age would be less than the estimate and he argued that the age of the Earth was finite. He also speculated, in a manner far from uncommon at the time, that the present world might have been preceded by earlier ones now destroyed.'2

Halley, Hooke, Ray and others thought that fossils were the remains of creatures that had lived in past seas and were evidence of earlier inundations, and of the existence of forms of life now extinct. They did not relate those changes directly to ages of rocks or the Earth, but clearly appreciated that fossils could be evidence for a great age of the Earth.'3 Biologists ever since have demanded long periods for evolution.

Newton constructed over many years a universal chronology based on a combination of biblical records and astronomical data. He never published it, but presented a copy to Queen Caroline. That copy came, after Newton's death, into the hands of Father Souciet, a French priest who criticized some of Newton's dates, including those of the Trojan War and the Voyage of the Argonauts, for being too recent. Halley, as Astronomer Royal and a friend of Newton, published a reply. The argument turned on the identification of certain stars in the constellation of Aries, as decribed by Hipparchos and others. In 1720, celestial coordinates were still too inaccurate to identify stars with certainty: stars had to be located by verbal descriptions that were sometimes ambiguous.

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So controversy often ensued, sometimes vitriolic, and it could cast doubt on times estimated from past appearances of the heavens. At the same time, the dispute with Souciet shows how far even Halley was from modem concepts of time and historicity. He accepted the Trojan War, the Argonauts and the Hexaemeron as historical events to which actual dates could be assigned, not as mythical or symbolic events.'2

Mankind always seems to want to put numbers, however specious, to events of the past. When geologists came to see the great changes that had brought about present geological structures, and the concomitant changes in the living creatures preserved in the rocks, they wanted the span of great ages to accommodate them. Yet physicists such as Lord Kelvin, who estimated the age of the Sun and hence of the Earth from the rate at which the Sun radiated its energy, set uncomfortably short limits to the age of the Earth. There seemed to be an impasse towards the end of the 19th century.

The apparent inconsistency between physical ages and geological requirements was resolved in two ways. Lord Rutherford saw that the amounts of daughter products of radioactive decay-helium and lead-preserved in rocks depended, like the saltiness of Halley's lakes, on the time from the formation of the minerals. At once the ages of the earliest rocks were extended to a thousand million years or more and geologists gained plenty of time for their processes. Rutherford and his colleagues, especially John Joly, F.R.S., in Dublin, quickly established the main principles and results of radiaoactive dating.

There remained the matter of the age of the Sun, which has sometimes seemed difficult to reconcile with the ages of the Earth and its oldest rocks. Even 70 years ago it was suggested that (unknown) nuclear processes might supply the energy radiated by the Sun. The nuclear reactions are now essentially understood, although some problems remain, and the ages of the Sun and of the Universe appear to be long enough to accommodate the age of the Earth.

CORPORATE SUPPORT FOR SCIENCE

The Royal Society has never been organized and funded to do research as the Accademia del Cimentol4 was in Medici Florence, or as the Academie Royale des Sciences was in Paris. Very few advances in natural knowledge have been made by the Society as a society. Flamsteed, Astronomer Royal, was paid out of public funds by the Ordnance Office, while Dye and Essen were on the staff of the NPL, then a government establishment. Towards the end of Flamsteed's time at Greenwich, the President and other Fellows of the Society were appointed as a Board of Visitors to oversee the operations of the Observatory. Flamsteed took that as an insult, but Halley and most of his successors found that the Board supported them. The Society strongly supported the formation of the NPL, which was originally under the control of the Society, and between the First and Second World Wars there were many Fellows in a Board of Visitors that had functions similar to that for the Royal Observatory. Thus the Society was responsible for assessing research plans and for checking that they were carried on effectively and responsibly. Neither Board now exists.

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The Society, through the Boards of Visitors, helped to ensure that appropriate time services were maintained. It did much more to promote and organize special programmes. It organized the various expeditions to observe the transit of Venus in 1769, after those of 1761, organized by de L'sle, had been bedevilled by bad weather.

The very reliable pendulum clock by Shelton, owned by the Society, was used in observations of the transits of Venus in both 1761 ad 1769, as well as in a number of other special programmes of observation, in Britain and overseas, for which an accurate reliable timekeeper was essential.

ABSOLUTE TIME AND STANDARDS OF TIME

In the Scholium to Definitio VIII of Book I of Philosophiae Naturalis Principia Mathematica, Newton defined 'absolute', or true, or mathematical time, as flowing uniformly, of itself and free of external influences; it was the independent variable in mathematics. Times measured by particular physical means ('sensible motions'), such as the rotation of the Earth or the beat of a pendulum, he called 'relative' times, measured in hours, or days, or years. Absolute and relative time, according to Newton, may be related by the equation of common time. Newton here seems to be implying that sidereal time is a realization of absolute time, but he also says that it is possible that there is no uniform celestial motion by which absolute time can be measured. His absolute time seems to be an ideal Platonic time, an abstract concept, which is realized most closely by sidereal time. He is certainly not using the terms absolute and relative in the sense that they have acquired in relativity theory. He wrote the Principia before Ole Romer (1644-1710) found the speed of light, and seems to have had no perception that there might be problems in defining times of events at a distance.

A closed dynamical system with constant parameters may be described by an angle variable proportional to time and an action variable that is constant. The independent dynamical variable t is the absolute time in Newton's terms.

If 0 is the angle variable for an ideal pendulum and Y is the angle by which the pendulum is displaced from its equilibrium position, then Y is equal to oPexp(iO) or W0exp (iot), where co is dO/dt and is constant for a simply periodic system. Let a relative time, T, be measured by counting the intervals between passages of the pendulum through its rest point. Those points occur when cot is equal to ni, and if we put z,1 equal to (n2-n)lf, wherefis some conventional factor, then 2,1 = co(t2-t)lf, that is to say, the time indicated by the pendulum is proportional to the absolute dynamical time.

We may not go on to infer that we can determine Newton's absolute time, for that depends on there being some particular simply periodic physical system, isolated from external influences, of constant energy and fully described by a single pair of variables. Any deviation from those three conditions would cause the apparent measured time to deviate from Newton's absolute time. (If two or more pairs of variables are needed for a full description of the system, the motion will be the superposition of incommensurable harmonic components and not simply periodic.) It is in fact

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impossible to confirm that the three conditions are indeed satisfied. All that is possible is to compare different systems. So we find, for example, that the rotation of the Earth is erratic compared with the best quartz and atomic clocks, and that quartz clocks and atomic clocks do not keep time exactly together. We choose a system on grounds such as a fundamental physical (atomic) basis, convenience, consistency, and then declare that to be the international standard. We cannot say that it keeps absolute dynamical time, nor can we say anything about the constancy of its rate, for we cannot compare it with itself at different epochs. It is not that the chosen system is isochronous but that when we declare it to be the standard system the question of its changing with epoch loses meaning. Any attempt to identify a unique absolute time in Newton's sense is vain; absolute time is the time told by whatever clock we choose to be the arbitrary standard, and that time is the independent variable in a system of dynamics in which the behaviour of the chosen clock is simply periodic.

CONCLUSION

The measurement of time was an important issue in the first years of the Society and some distinguished Fellows, Flamsteed in particular, but Halley and Graham as well, helped to develop instruments to do so. Three hundred years later other Fellows led the replacement of astronomical by atomic time. The classical structure of dynamics has been developed in the physical sciences along with elucidation of the concept of dynamical time and improvement of the means of measuring it. But biological systems change also, and no doubt dynamical theories for biology should use the same independent variable as physical theories since, ultimately, atomic time is now the basis of all practical timekeeping. It is a question that might be looked at further, for just as atomic oscillations seem the most natural basis for times of physical systems, so it may be that there is some natural timescale for biology, even if at present there seems no indication of one. Similar remarks may apply to the dynamics of economic systems, for which an obvious basis is the solar day, or maybe the hour, derived from atomic time adjusted to the apparent solar day. Here, however, almost instantaneous worldwide trading means that some economic processes can occur far faster than in the past.

Time has many meanings outside the regular evolution of celestial systems, and Fellows of the Society have helped to define the meaning of times of events long past and to devise ways of estimating them. As the scope of dynamical studies extends from physics to biology and to economics, may we not expect other questions about the meaning, measurement and standards of time, to which, no doubt, Fellows of the Society will give attention.

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NOTES

1 J. Wallis, Jeremiae Horrocii opera posthuma (G. Godbit for J. Martyn, London, 1673). 2 E.G. Forbes, L. Murdin and F. Willmoth, The correspondence of John Flamsteed, the first

Astronomer Royal, vols I and II (The Institute of Physics Publishing, Bristol and Philadelphia, 1995 and 1997).

3 The clock by John Shelton, made about 1767, belonging to The Royal Society (figure 8), was used in observations of the transit of Venus in 1769 and later in astronomical observations in North America.

4 J.C. Beaglehole, The life of Captain James Cook (Adam and Charles Black, London, 1974). 5 J.A. Bridge, 'Sir William Brooke O'Shaughnessy, M.D., F.R.S., F.R.C.S., F.S.A.: a

biographical appreciation by an electrical engineer', Notes Rec. R. Soc. Lond. 52, 103-120 (1998).

6 E.V. Appleton,' David William Dye', Biogr Mem. Fell. R. Soc. Lond. 7, 75-78 (1933). 7 A. Cook, 'Louis Essen, O.B.E.', Biogr. Mem. Fell. R. Soc. Lond. 44, 141-158 (1998). 8 E. Halley, 'Emendationes ac notae in vetustas Albatenii observationes astronomicas cum

restitutione tabularum lunisolarium ejusdem authoris', Phil. Trans. R. Soc. Lond. 17, 913-921 (1693). E. Halley, 'Some account of the ancient state of the City of Palmyra with short remarks upon the inscriptions found there', Phil. Trans. R. Soc. Lond. 19, 160-175 (1695).

9 J.C. Adams,' On the secular variation of the Moon's mean motion', Phil. Trans. R. Soc. Lond. 143,397-406(1853).

10 K. Lambeck, The Earth s variable rotation (Cambridge University Press, 1980). 11 C. Humphreys, 'The Star of Bethlehem', Science and Christian Belief 5, 83-101 (1993). 12 A. Cook, Edmond Halley, Charting the Heavens and the Seas (Clarendon Press, Oxford,

1998). 13 J. Ray, Observations topographical, moral and physiological made in ajourney through part

of the Low Countries, Germany, Italy and France, with a catalogue ofplants (London, John Martyn, London, 1673). Ray lists places where he found fossils and explains why he thinks them to be remains of creatures once living.

14 M. Beretta, 'At the source of Western science: the organization of experimentalism in the Accademia del Cimento (1657-1667). Notes Rec. R. Soc. Lond. 54, 131-151 (2000).

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Documents

Time and the Royal Society