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metrologia

The leap second: its history and possible future
R. A. Nelson, D. D. McCarthy , S. Malys, J. Levine, B. Guinot, H. F. Fliegel , R. L. Beard and T. R. Bartholome w

Abstract. This paper reviews the theoretica l motivatio n for the leap second in the context of the historica l evolutio n of time measurement . Th e periodic insertio n of a leap second step into th e scale of Coordinate d Universal Time (UTC) necessitates frequent changes in comple x timekeepin g systems an d is currentl y th e subject of discussion in working groups of variou s internationa l scienti c organizations. UTC is an atomi c tim e scale that agrees in rate with Internationa l Atomic Tim e (TAI), but differs by an integral number of seconds, and is the basis of civil time. In contrast, Universal Tim e (UT1) is an astronomical time scale de ned by the Earth's rotation an d is used in celestia l navigation . UTC is presently maintaine d to within 0.9 s of UT1. As the needs of celestia l navigatio n that depend on UT1 can now be met by satellit e systems, such as the Global Positioning System (GPS), option s for revising th e de nition of UTC an d the possible role of leap second s in the future ar e considered .

1. Introduction: why we have leap seconds Approximatel y once a year , a leap second is introduce d into UTC, the world's atomi c tim e scale for civil time , in order to keep it in phase with the rotatio n of the Earth. Leap seconds ensure that, on average , the Sun continue s to be overhead on the Greenwich meridia n at noon to within about 1 s. When the atomi c de nitio n of the Internationa l System of Units (SI) second was introduce d in 1967, it was effectivel y made equivalen t to an astronomica l secon d based on a mean solar day of 86 400 s in abou t 1820. However, over approximatel y the past 1000 years, th e Earth 's rotation has been slowing at an average rate of 1.4 ms per century, so that the day is now abou t 2.5 ms longer than it was in 1820. A differenc e of 2.5 ms per day amounts to about 1 s per
R. A. N elson : S atel li te E ngi neer i n g Researc h C orpor ati on , 770 1 Woodm on t Avenue , S ui te 208 , Bethesda , M D 20814 , U S A. D. D. M cCart hy : U S Nava l Observat ory , 345 0 M assachuset t s Avenue , NW , Washingt on , D. C., 20392 , U S A. S . M alys: Nati ona l Im ager y and M appi n g Agency , Resear c h and Technolog y O f ce AT T R ( MS D- 82) , 460 0 S angam or e R oad , B ethesda , M D 20816 , US A. J. L evine : N ati onal I nsti tut e of S t andar d s and Technology , D epar t men t of Com mer c e M S 847 , 32 5 Br oadway , Boul der , C O 80303 , U S A. B. Gui not : Observat oir e de P ar is, Depar temen t d' Astr onomi e б F ondam ent ale , 61 avenu e de l'Obser vat oir e , F- 7501 4 P ar is, F rance. H. F . F li egel : T he A erospac e C orpor ati on , 235 0 E . E l S egundo B lvd. , E l S egundo , C A 90245 , US A. R. L . Beard : Nava l R esearc h L aborat ory , 455 5 Over loo k Avenue , S W, Code 8150 , Washingt on , D. C., 20375 , U S A. T . R. Bart holom ew : L it ton TA S C, I nc., 13 1 Nat iona l Busines s P ar kway , Annapoli s Juncti on , M D 20701 , US A. M et rol ogi a , 2001, 38 , 509- 529

year and this is the reason for the mor e or less regular insertio n of leap seconds. Superimposed on this ver y slowly increasin g differenc e ar e shorter-term variation s in the length of the day. Periods between leap seconds are not, therefore, constant and, in fact, over the past thirty year s there hav e been several year s in which leap seconds have been omitted . The primar y reason for introducing th e concept of the leap secon d was to meet th e requiremen t of celestia l navigatio n to keep th e difference between solar time and atomi c time small. However, the motivatio n for the leap second has diminished because of th e wide availabilit y of satellit e navigatio n systems, such as GPS, while the operational complexitie s of maintainin g precise timekeepin g systems have made the insertio n of leap second adjustment s increasingl y dif cult and costly. The question currentl y bein g debate d in recentl y created working groups of various internationa l scienti c organization s is whether ther e continues to be a need for th e leap second, with its man y technical inconveniences , or whether it would be better simply to let atomic time run freely and accep t that the world's civil time scale will slowly diverge from the rotation of the Earth ? This articl e gives the histor y and detailed technica l background to the current practic e and outlines various solutions. 2. Measuremen t of tim e 2.1 Clocks Two element s ar e needed to measur e the passage of time : (a) a time "reckoner ", which is a repeatabl e 509


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phenomenon whose motion or change of state is observable and obeys a de nite law, and (b) a time reference , with respect to which the position or state of the time reckoner can be determined . These element s correspond to th e two propertie s of time measurement : interva l an d epoch. Together , the time reckoner and the time reference constitut e a clock . From remote antiquity , the celestia l bodies ­ the Sun, Moon an d stars ­ have been the fundamenta l reckoner s of time. The rising and setting of th e Sun an d th e star s determin e the day and night; th e phases of the Moon determin e the month; and the position s of the Sun and star s along th e horizo n determin e the seasons. Sundials were among the rst instruments used to measur e the tim e of day. The Egyptians divided the day an d night into 12 h each, which varied with the seasons. While th e notio n of 24 equal hours was applied in theoretica l works of Hellenisti c astronomy, the unequal "seasonal hour" was used by the general public [1]. When the rst reliabl e water clock s were constructed , great care was taken to re ect the behaviour of a sundial instead of the apparent motion of the heaven s [2]. It was not until the fourteent h centur y that an hour of unifor m length becam e customar y due to the inventio n of mechanica l clocks. These clocks were signi cant, not only because they were masterpiece s of mechanica l ingenuity , but also because they altere d the public's perceptio n of time [3, 4]. In the er a of telescopi c observations, pendulum clock s served as the standard means of keeping time until th e introductio n of moder n electronics . Quartzcrystal clocks were develope d as an outgrowth of radio technolog y in the 1920s and 1930s [5]. Harold Lyon s [6] at the National Bureau of Standard s in Washington, D.C. (now the National Institute of Standards and Technology, Gaithersburg, Md.) constructe d the rst atomi c clock in 1948 using the microwave absorption line of ammoni a to stabiliz e a quartz oscillator . Louis Essen an d J. V. L. Parry [7] at the National Physical Laborator y in Teddington, UK, constructe d a practical caesium beam atomi c clock in 1955. Commercial caesium frequency standard s appeare d a year later . Norman Ramsey develope d the hydrogen maser at Harvard University in 1960 [8]. Once practica l atomi c clocks becam e operational , the Bureau Internationa l de l' Heure (BIH) an d several nationa l laboratorie s began to establish atomi c time scales [9]. The responsibility for th e maintenanc e of the internationa l standar d is now given to the Bureau Internationa l des Poids et Mesures (BIPM). Some form of atomi c time has been maintaine d continuously since 1955 [10]. 2.2 Time scales Three primar y method s of measurin g time have been in common use for modern application s in astronomy, physics and engineering . These methods hav e evolved 510

as th e design and constructio n of clocks have advance d in precisio n and sophistication . The rst is Universal Time (UT), the time scale based on the rotation of the Earth on its axis. Th e second is Ephemeri s Time (ET), the time scale based on the revolution of the Earth in its orbit aroun d th e Sun. The thir d is Atomic Time (AT), the time scale based on the quantum mechanic s of the atom . Each of these measures of tim e has had a variet y of re nement s and modi cation s for particula r applications. The true measur e of the Earth's rotatio n is UT1, which is the form of Universal Tim e correcte d for polar motion and used in celestia l navigation . However, owing to irregularitie s in the Earth's rotation , UT1 is not uniform . UT2 is UT1 corrected for the seasonal variation. Ephemeri s Time (ET) is a theoreticall y uniform time scale de ned by th e Newtonian dynamical laws of motion of the Earth, Moon, and planets. This measure of time has been succeede d by several new time scales that ar e consistent with the general theor y of relativity . The scale of Internationa l Atomic Time (TAI) is maintaine d by the BIPM with contribution s from nationa l timekeepin g institutions. TAI is a practica l realizatio n of a uniform time scale. The basis of civil tim e is Coordinate d Universal Time (UTC), an atomi c tim e scale that corresponds exactl y in rate with TAI but is kept within 0.9 s of UT1 by the occasiona l insertio n or deletio n of a 1 s step. The decision to insert this leap secon d is made by th e International Earth Rotatio n Service (IERS). Since 1972, when UTC was introduced , there hav e been twenty-tw o leap seconds, all of which have been positive. 3. Tim e measured by the rotation of the Eart h 3.1 Universal Time Universal Time (UT1) is the measur e of astronomica l time de ned by the rotation of the Earth on its axis with respect to th e Sun. It is nominall y equivalen t to mean solar tim e referred to the meridian of Greenwich and reckoned from midnight. Th e mean solar day is traditionall y described as th e time interva l between successive transits of the ctitiou s mean Sun over a given meridian . Historically , the unit of time , th e mean solar second, was de ned as 1/86 400 of a mean solar day [11, 12]. The eclipti c is the apparent annual path of the Sun against the background of stars. Th e intersectio n of the eclipti c with the celestial equato r provides a fundamenta l referenc e point called the vernal equinox. In practice , Universal Tim e is determined , not by the meridian transit of the mean Sun, but by the diurnal motion of the vernal equinox in accordanc e with a conventiona l formula specifyin g UT1 in terms of Greenwich Mean Sidereal Time (GMST). Th e
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The leap second: its history and possibl e future

current de ning relatio n for UT1 with respect to the astronomical referenc e system of the Fifth Fundamental Katalog (FK5) [13] is given in [14]. UT0, a designatio n no longer in common use, is UT1 corrupted by th e torque-free precessional motio n of the Earth's axis of rotatio n with respect to the Earth's surface [15]. This effect , called variatio n of latitude, was predicted by Leonhar d Euler [16] in 1765 as a property of rigid body motio n and was identi ed observationall y by Seth Chandler [17] in 1891. The difference [UT0 ­ UT1] has a maximum value of about 20 ms at mean latitud e [18]. Apparent solar time , as read directl y by a sundial or mor e precisel y determine d by the altitud e of the Sun, is th e local time de ned by the actual diurnal motion of the Sun. However, because of the tilt of the Earth's axis and the elliptica l shape of the Earth's orbit, the tim e interva l between successive passages of the Sun over a given meridian is not constant. The difference between mean and apparent solar time is calle d the equatio n of time . Th e maximu m amoun t by which apparent noon precede s mean noon is about 16.5 min aroun d 3 November , while the maximu m amount by which mean noon precede s apparent noon is abou t 14.5 min around 12 February. Until th e early nineteent h century, apparen t solar time was used as the argument for astronomical ephemerides . However, as clock s improved and their use by ships at sea and by railroad s grew, apparent solar tim e was gradually replaced by mean solar time . 3.2 Siderea l Time Local Sidereal Time (LST) is the measur e of astronomical time de ned by th e rotatio n of the Earth with respect to the stars. LST may be de ned as the right ascension of th e local meridian , which is the angle between the vernal equinox and the local meridia n measured along the celestial equator . In particular , Greenwich sidereal time is th e right ascensio n of the Greenwich meridian . The sidereal day is the time interval between successive transits of the vernal equinox. It represents the Earth's perio d of rotation relativ e to the star s and is approximatel y 86 164.0905 mean solar seconds. Owing to precession of the Earth's axis with respect to the celestia l referenc e system, the sidereal day is about 0.0084 s shorter than the actua l period of rotation in inertia l space. Thus the true rotationa l perio d of the Earth is approximatel y 86 164.0989 mean solar seconds. However, the mean solar day presently exceed s a day of exactl y 8 400 SI seconds by about 2.5 ms. Therefore, the Earth's period of rotation is currentl y about 86 164.1014 SI seconds. Even LST is not a uniform measure of astronomical time . In the early twentiet h century, the inherent accurac y of the Shortt free-pendulum clock s rst
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reveale d th e periodic effect s of nutation . The principal term consists of an eighteen-yea r oscillatio n with an amplitud e of about 1 s. These effect s cannot be neglecte d and it becam e necessar y to introduce the concept of mean sidereal time , which is affecte d only by precession. Greenwich Mean Sidereal Time (GMST) is mean sidereal tim e with respect to the Greenwich meridian , from which Universal Time (UT1) is derived. In the past, UT1 was determine d using a worldwide network of visual transit telescopes , photographic zenit h tubes and impersonal (prismatic ) astrolabes. Three basic technique s are now used to estimat e UT1: (a) Very Lon g Baseline Interferometr y (VLBI) measurement s of selecte d radio point sources, mostly quasars; (b) satellit e laser ranging; and (c) trackin g of GPS satellites . Strictly speaking, because of th e motion of satellite orbital nodes in space, VLBI provides the only rigorous determinatio n of UT1. A revised conventiona l celestial referenc e fram e based on the observed positions of extragalacti c object s is bein g develope d that changes the basis for UT1, removes the need for th e equinox, an d changes the use of precession and nutation . 3.3 Variations in the Earth's rotation Three types of variatio n in the Earth's rotation have been identi ed: a stead y deceleration , random uctuations , and periodic changes [19]. As early as 1695, Sir Edmon d Halley [20] was led to suspect an acceleratio n in the mean motion of the Moon from a study of ancien t eclipse s of the Sun recorded by Claudius Ptolem y and the medieval Arabian astronomer, Muhammed al- Bat tanеУ . By the е mid-eighteent h century, th e lunar acceleratio n was fully established . In 1754, Immanuel Kant [21] suggested that this acceleratio n might be an apparent phenomenon caused by a steady deceleratio n in the Earth's rotation due to tidal friction . Part of the effect was later attributed to the variatio n in th e solar perturbatio n on the Moon's orbit. As shown by Pierre-Simo n Laplac e and John Couch Adams, the planetar y perturbation s cause the Earth 's orbital eccentricit y to diminish and, as a consequence , the Sun's mean actio n on the Moon also diminishes. In addition , the observed lunar acceleratio n is affecte d by th e recessio n of the Moon from the Earth in order to compensat e the decrease in the Earth's rate of spin by conservatio n of angular momentum . It was not until the twentiet h century that an apparen t acceleratio n of the Sun was also identi ed [22-24]. Recen t studies of eclipse s by F. R. Stephenson and L. V. Morrison [25, 26] suggest that the long- ter m average rate of increase in the length of the day is about 1.7 ms per centur y (­4.5 10­22 rad/s2 ). Although the increase in the length of day seem s miniscule , it has a cumulativ e effect on a time scale based on the Earth's 511


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rotation . In th e past 2000 year s th e Earth actin g as a clock has lost over 3 h. For example , th e calculate d path of the total eclipse of the Sun witnessed in Babylon in 136 B.C. would be in error by 48.8 , corresponding to a time differenc e of 11 700 s, assuming a unifor m rate of rotatio n [27]. Sir Harold Jeffrey s made th e rst quantitativ e estimat e of global tidal friction in 1920 [28, 29]. He found that the energ y dissipatio n in the shallow seas appeared to be of th e correct order of magnitude to account for the apparent lunar and solar accelerations . Th e rate of energy dissipation by tidal friction is now considered to correspond to a rate of increase in the length of day of 2.3 ms per century (­6.1 10­22 rad/s2 ). To account for th e observed deceleration , there must also be a componen t in th e opposite directio n of abou t 0.6 ms per centur y (+1.6 10­22 rad/s2 ), which is possibly associate d with changes in the Earth oblatenes s paramete r caused by post- glacia l rebound [30] or with deep ocean dissipation [31]. Evidenc e for a long- ter m deceleratio n in the Earth's rotation , extendin g over million s of years, also exists in coral fossils that exhibit both daily an d annual growth rings [32]. For example , several corals dating from the middle of the Devonian Period, some 370 millio n year s ago, indicat e that the number of days in the year was between 385 and 410. Th e evidenc e suggests that the rate of deceleratio n was substantiall y the same then as it is now [33]. Besides a stead y decrease, the Earth's rotation is subject to frequent small changes that ar e random and cumulativ e [34, 35]. This variatio n was inferred from studies of statistical irregularitie s in the displacement s of the Moon, Sun, Mercur y an d Venus in proportio n to their mean motions. Random uctuation s were rst observed directl y by atomi c clock s in the mid- 1950s [36]. There is also a periodic seasonal variatio n caused principall y by meteorologica l effects. Th e seasonal variatio n was rst reported in 1936 by A. Scheib e an d U. Adelsberger [37], who performed measurement s of th e Earth's rotation with excellen t quartz- crysta l clock s at the Physikalische- Technisch e Bundesanstalt (Germany). N. Stoyko [38] at the BIH in 1937 found that the length of the day in January exceede d that in July by 2 ms, based on the performance of Shortt pendulu m clocks and by comparison of th e rates of quartz- crysta l clock s at th e nationa l time services. The seasonal variatio n in the length of the day is now known to be of the order of 0.5 ms about the mean [39]. The rotatio n of th e Earth runs slow by about 30 ms in May an d runs fast by a simila r amount in November . By internationa l agreement , an empirical correctio n for the seasonal variatio n has been applie d since 1 Januar y 1956, resultin g in th e time scale UT2. The difference between UT2 an d UT1, as currentl y applied , is given in [40]. UT2 has a peak- to- peak amplitud e of about 60 ms. 512

4. Tim e measured by the orbital motions of the celestia l bodies The need for more uniform measures of astronomica l time resulted in the de nition of tim e scales determine d from the motions of th e celestia l bodies in the solar system. Originally based on Newtonian mechanics , they have been re ned to take into account the effect s of general relativity . In addition , the unit of time, previously within the exclusive domain of astronomy, was incorporate d into the creatio n of th e SI. In 1948, at the request of the International Union of Pure and Applied Physics (IUPAP), the 9th General Conference on Weights and Measures (CGPM) resolved to adop t for internationa l use a practical system of units covering all branches of metrology. A limite d set of base units, includin g the second, was selecte d by the 10th CGPM in 1954 and a representativ e list of derived units was compile d by the Internationa l Committe e for Weights and Measures (CIPM) in 1956. The SI was of ciall y establishe d by the 11th CGPM in 1960 [41]. 4.1 Ephemeris Tim e Because th e variation s in th e Earth's rotation are complex , the CIPM referred the study of a new de nition of the secon d to the Internationa l Astronomical Union (IAU) in 1948. At the suggestion of G. M. Clemenc e [42], the Conference on the Fundamental Constants of Astronomy held in Paris in 1950 recommended to the IAU that, instead of the period of rotatio n of the Earth on its axis, the new standard of time ought to be based on th e perio d of revolution of the Earth around the Sun, as represente d by Newcomb's Tables of the Sun published in 1895. The measur e of astronomica l tim e de ned in this way was given th e name Ephemeris Time (ET) . The working de nition of Ephemeris Tim e was through Newcomb's formula for the geometri c mean longitude of the Sun for an epoch of Januar y 0, 1900, 12h UT [43], L = 279 41 48 .04 + 129 602 768 .13 T + 1 .089 T2 , where is the tim e reckoned in Julian centurie s of 36 525 days. The linea r coef cient determine s the unit of time , while th e constan t determine s the epoch. Th e IAU adopted this proposal in 1952 at its 8th General Assembly in Rom e [44]. Initially , the period of revolution of the Earth was understood to be th e sidereal year . However, it was subsequently pointed out by AndreбDanjo n that the tropical year is more fundamental than th e sidereal year, as the length of th e tropical year (equinox to equinox ) is derived directl y from Newcomb's formula, whereas the length of th e sidereal year ( xed star to xed star) depends on the adopted value of th e precession [45]. From the value of th e linear coef cient in Newcomb's formula, th e tropica l year of 1900 contain s
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[(360 60 60)/129 602 768.13] 36 525 86 400 = 31 556 925.9747 s. Therefore, at the recommendatio n of th e CIPM, th e 10th CGPM in 1954 proposed the followin g de nition of the second : "The second is the fractio n 1/31 556 925.975 of the length of the tropical year for 1900.0." But although the IAU approved this de nition at its General Assembly in 1955, Danjon commented that the fractio n ought to hav e a slightly mor e precise value to bring about exact numerica l agreemen t with Newcomb's formula [46]. Consequently, th e CIPM in 1956, under the authority given by the 10th CGPM in 1954, de ned the second of ephemeri s time to be "th e fractio n 1/31 556 925.974 7 of the tropica l year for 1900 January 0 at 12 hours ephemeri s time ". This de nition was rati ed by th e 11th CGPM in 1960 [47]. Referenc e to the year 1900 does not imply that this is the epoch of a mean solar day of 86 400 s. Rather, it is th e epoch of the tropical year of 31 556 925.974 7 s. Although ET was de ned in terms of the longitude of the Sun, in practic e it was realize d indirectl y by compariso n of observations of lunar positions with lunar ephemerides. Thus, a set of secondar y time scales (denoted by ET0, ET 1 an d ET2) were de ned that differed because of subsequent improvement s to the conventional ephemerides [48]. In 1958, the IAU General Assembly adopted a resolutio n that de ned the epoch of Ephemeri s Time to coincid e with Newcomb's formula as follows [49]: "Ephemeri s Time (ET) , or Temps des Ephemerides бб (TE), is reckoned from the instant, near th e beginning of the calenda r year A.D. 1900, when the geometri c mean longitude of the Sun was 279 41 48 .04, at which instant the measure of Ephemeris Time was 1900 January 0d 12h precisely." Th e resolutio n also include d the de nition of the second given by the CIPM in 1956. In a separate resolution, the epoch for Universal Time was chosen as 1900 Januar y 0d 12h UT based on the Fourth Fundamental Katalog (FK4) [50]. However, the equinox of Newcomb's Sun, the lunar theory, and the FK4 did not agree precisel y an d they were moving with respect to one another. Thus the actua l instant in time correspondin g to the epoch of ET was approximatel y 4 s late r than the epoch of UT [51]. Ephemeri s Time (ET) is a dynamical time determine d by the theor y of celestial mechanic s and is theoreticall y uniform [52]. ET may be characterize d as the independen t variabl e that brings the observed position s of the celestia l bodies into accord with their calculate d positions constructe d from the Newtonian law s of motion. Therefore, in effect, it is de ned by these law s [53].
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4.2 Relativisti c tim e scales In 1960, ET replace d UT1 as the independen t variabl e of astronomica l ephemerides . However, ET did not include relativisti c effects and did not distinguish between proper time and coordinat e time . Accordingly, at the 16th General Assembly in Grenoble in 1976, the IAU de ned time-lik e argument s that distinguish coordinat e system s with origins at the centr e of the Earth and the centr e of the solar system, respectively , and are consistent with the general theor y of relativit y [54]. In 1979, these time scales receive d the names Terrestrial Dynamica l Time (TDT) and Barycentri c Dynamical Time (TDB) [55]. TDT replaced ET in 1984 as the tabula r argument of the fundamenta l geocentri c ephemerides. TDT has an origin of 1 Januar y 1977 0 h TAI, with a unit interval equal to the SI second , an d maintain s continuit y with ET. At this epoch, a rate correctio n of ­10 10­13 was applied to TAI to bring the unit of TAI more closely into accor d with the SI second [56]. In 1991 the IAU rename d TDT simply Terrestria l Time (TT) . A practical realizatio n of TT is [57] [TT] = [TAI ] + 32.184 s. The constant offset represents the differenc e between ET and UT1 at th e de ning epoch of TAI on 1 Januar y 1958. The relationshi p between TT an d TAI is not strictl y rigorous for two fundamenta l reasons [58]. First, TAI is a statisticall y formed time scale based on contribution s from th e major timin g centres, whereas TT is theoreticall y uniform. Second, a scale of time based on the laws of gravitatio n may not be philosophicall y equivalen t to one based on the quantu m mechanics of th e atom. For ephemeride s referred to th e barycentr e of the solar system , the argumen t is TDB. Through an appropriatel y chosen scaling factor , TDB varies from TT or TDT by only periodic variations , with amplitudes less than 0.002 s. From the deliberation s of the IAU Working Group on Reference Systems formed in 1988, ther e arose nine recommendation s that were containe d in Resolution A4 adopted by the 21st IAU General Assembly in 1991 [59]. The general theory of relativit y was explicitl y introduce d as the theoretica l basis for th e celestia l referenc e frame and th e form of the space-tim e metric to post-Newtonian order was speci ed. Th e IAU also clari ed the de nition of Terrestria l Time (TT) and adopted two additiona l time scales, Geocentri c Coordinate Time (TCG) an d Barycentri c Coordinate Time (TCB) [60]. The "coordinate" time scales TCG and TCB are complementar y to the "dynamical " time scales TT (or TDT) and TDB. They differ in rate from TT and are relate d by four-dimensional space-tim e coordinat e transformation s [61]. These de nitions were 513


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further clari ed by resolutions adopted at the 24th IAU General Assembly held in Manchester in 2000 [62]. 5. International Atomic Tim e Although ET was a uniform time scale, it was not easily realize d or disseminated . Th e rapid developmen t of atomi c clock s permitted yet another de nition of time [63]. 5.1 Experimental atomic time scales Th e rst operationa l caesiu m beam frequency standar d appeared in 1955 at the National Physical Laboratory (NPL, UK) [64]. The Royal Greenwich Observator y (RGO) establishe d a tim e scale, known as Greenwich Atomic (GA), using free- running quartz- crysta l clock s periodicall y calibrate d in term s of this standard . A commercia l caesium frequency standard , the "Atomichron", was develope d in 1956 [65]. The US Naval Observator y (USNO) inaugurate d its A.1 atomi c time scale on 13 Septembe r 1956, initiall y based on a caesium clock at the Naval Research Laboratory (NRL) consisting of an Atomichron caesiu m standard and a quartz- crysta l clock. The frequency of th e crystal was matche d daily to the caesiu m standard, which was not operate d continuously [66]. The National Bureau of Standards (NBS) in Boulder , Colo., also maintaine d an atomi c time scale, NBS- A, startin g 9 October 1957. Th e epochs of A.1 and NBS-A were mad e coinciden t an d set equal to UT2 on 1 January 1958 [67]. The A.1 time scale was introduce d for world use on 1 January 1959. By 1961, A.1 was based on atomi c oscillator s at the USNO, NRL, NBS, USNO Tim e Service Sub- Statio n (Richmond , Florida) , Harvar d University, National Research Council (Ottawa), NPL, Centr e б National d'Etudes des Telecommunication s (Bagneux) , бб an d Observatoire de Neuchatel (Switzerland) [68, 69]. ц Once continuous atomic time becam e establishe d at variou s laboratories , th e BIH began a mean atomi c time scale based on frequency comparison s by mean s of VLF carrier s at 3 kHz to 30 kHz used for long- distance communication s and radio navigatio n [70]. Initiall y it was designate d AM, and then A3, representin g an average of th e three best scales. In 1960, th e BIH began publicatio n of th e difference s between UT2 and various individual atomi c times obtaine d by integratio n of accurat e frequency comparisons. By 1969 th e BIH had rede ned A3 to be an average d atomi c time scale (TA) based on several primar y laborator y standards. In 1971, this scale becam e the scale of International Atomic Tim e (TAI) [71]. 5.2 Atomic de nition of the second In June 1955, Louis Essen and J. V. L. Parry of the NPL measured th e operationa l resonance frequency of the laboratory 's caesium standar d with respect to th e second 514

of UT2 as (9 192 631 830 ± 10) Hz by compariso n with the adopted frequency of a quartz standard , which was calibrate d from astronomical measurement s performed at the RGO [72]. Over the follo