Time and frequency: theory and fundamentals - GovInfo

113316_3GOVPUB_C13_e1edb3c9f15cce79026b68215342ba26.pdf

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GAYLORD'HINTEDINU.S.A.

NationalBureauofStandard

TIMEANDFREQUENCY:

TheoryandFundamentals

ByronE.Blair,Editor

TimeandFrequencyDivision

InstituteforBasicStandards

\J ,$,NationalBureauofStandards

Boulder,Colorado-80302

JUL101974

U.S.DEPARTMENTOFCOMMERCE,FrederickB.Dent,Secretary NATIONALBUREAUOFSTANDARDS,RichardW.Roberts,Director

IssuedMay1974

LibraryofCongressCatalogNumber:73-600299

NationalBureauofStandardsMonograph140

Nat.Bur.Stand.(U.S.),Monogr.140,470pages(May1974)

CODEN:NBSMA6

^6-19^ ForsalebytheSuperintendentofDocuments.U.S.GovernmentPrintingOffice.Washington,D.C.20402 (OrderbySDCatalogNo.C13.44:140).Price$8.65

StockNumber0303-01202

ABSTRACT

ThisisatutorialMonographdescribingvariousaspectsoftimeandfrequency(T/F).Included arechaptersrelatingtoelementalconceptsofprecisetimeandfrequency;basicprinciplesofquartz oscillatorsandatomicfrequencystandards;historicalreview,recentprogress,andcurrentstatus ofatomicfrequencystandards;promisingareasfordevelopingfutureprimaryfrequencystandards; relevanceoffrequencystandardstootherareasofmetrologyincludingaunifiedstandardconcept; statisticsofT/FdataanalysiscoupledwiththetheoryandconstructionoftheNBSatomictime scale;anoverviewofT/Fdisseminationtechniques;andthestandardsofT/FintheUSA.The Monographaddressesboththespecialistinthefieldaswellasthosedesiringbasicinformation abouttimeandfrequency-TheauthorstracethedevelopmentandscopeofT/Ftechnology,its improvementoverperiodsofdecades,itsstatustoday,anditspossibleuse,applications,and developmentindaystocome. Keywords:Accuracy;Allanvariance;atomicfrequencystandards;atomictimescales;AT(NBS); BIH;buffergases;CCIR;clockensembles;clocks;crystalaging;Csfrequencystandard;dissemi- nationtechniques;figureofmerit;flickernoise;frequencydomain;frequencystability;frequency standards;frequency/timemetrology;hydrogenmaser;leapseconds;Loran-C;magneticreso- nance;masers;NBS-III;NBS-5;NBS/USNOtimecoordination;Omega;opticalpumping;pre- cision;quartzcrystaloscillators;radioT/Fdissemination;Rbfrequencystandards;satelliteT/F dissemination;short-termstability;SIUnits;TAI;televisionT/Fdissemination;thalliumbeam standards;time;timedispersion;timedomain;time/frequencystatistics;timescalealgorithm;time scales;"unifiedstandard";URSI;USAstandardtimezones;UTC(NBS);UTC(USNO).

PreparationofthisdocumentwassupportedinpartbytheDirectorateofCommunicationsEngineering,COMSEC/DataSystemsDivision,AirForceCommunications

Service.

in

FOREWORD

ItisindeedfittingthatatimeandfrequencyMonographshouldappearnow.Theyear1973 marksthe50thAnniversaryofthetransmissionofstandardradiofrequenciesonaregularly announcedschedulefromWWVatWashington,DC;the25thAnniversaryoftimeandfrequency broadcastsfromWWVHinHawaii;andthe25thAnniversaryofthefirstlaboratoryoperationofan atomicclock(attheNationalBureauofStandards,Washington,DC).Thatthefieldoftimeand frequencyisslowlyemergingasaspecialtytechnologyisnotsurprisingintoday'sworldoftime- referencedmeasurementsandsystemssuchasthoserequiredfornavigationandcommunication. Itisparadoxicalthattime,relatedcenturiesagosolelytothedailyapparentmovementofthesun, waterclocks,mechanicalinstruments,andthelike,shouldbeatthecenterofthiscomplexfield. Nevertheless,itisbecomingapreciseandimportantscientificdiscipline,incombinationwith elementsofphysics,chemistry,quantummechanics,electronics,radiopropagation,andstatistics toformatomicfrequencygenerators,timescales,andvariedtechniquesofdissemination. Theurgentdemandsofscientificendeavors,requiringprecisionmeasurementsinthe1950's, ledtheNationalBureauofStandards(NBS)topublishHandbook77 - athreevolumepublication ofPrecisionMeasurementandCalibration;oneofthesevolumes - ElectricityandElectronics containedasmalltimeandfrequencysection.Withtheadvanceinthe1960'sofscientificmeth- odology,standardsofmeasures,andcomplexexperimentaltechniques,NBSpublishedanew seriesofPrecisionMeasurementandCalibrationinsomeelevenvolumes - VolumeVofthis SpecialPublication300wasdevotedentirelytopapersonFrequencyandTimepublishedinthe

1960's.ThepresentMonographresultsfromrecommendationsofrecentTimeandFrequency

DivisionAdvisoryPanelstopublishcurrentinformationthatwouldbe"basic,understandable,and practical."ThePanelswereconcernedthatthegainsandutilityoftimeandfrequencytechniques bemadereadilyavailabletobothnewandexperiencedworkersinthefieldinatutorialandcompre- hensiblemanner.ThathasbeentheobjectiveoftheauthorsofthisMonograph. TheInstituteforBasicStandards(IBS),oneoffourInstitutesoftheNBS,isgiventhefollowing responsibility - it"shallprovidethecentralbasiswithintheUnitedStatesofacompleteandcon- sistentsystemofphysicalmeasurement;coordinatethatsystemwithmeasurementsystemsofother nations;andfurnishessentialservicesleadingtoaccurateanduniformphysicalmeasurements throughouttheNation'sscientificcommunity,industry,andcommerce."1Assuch,IBSisatthe centeroftheNationalMeasurementSystemwithaprimarygoalofcompatibilityamongstandards; i.e.,everyuserinameasurementsystemexpectstoobtainthesamevalueofameasurementbased onthesamereference,butindependentofthemeans.ApersondesiringtimemaylistentoWWVby radio,dialthetelephonetimenumber,orrecordasatellitetimesignal.Thedegreeofaccuracymay varybuttheinformationisrelatedtoacommonsourceandiscompatible. Ishouldemphasizethatthemajoreffortofthisworkistodescribebasicprinciplesandprac- tices;itisoflittleusetomaintainandupdatemeasurementstandardswithoutpublicizingtheir construction,theoryofoperation,capabilities,andmannerofuse.Wesincerelyhopethatthis Monographwillbecomeavaluablesourcebookofinformationtothepracticing"timeandfre- quency"specialistaswellastothosenewinthefieldseekinganunderstandingofcompatibility amongNationalandInternationaltimeandfrequencystandardsandtimescales,telecommunica- tion/navigationsystems,andvarieddisseminationtechniques.Itisequallyimportantthatthe materialmightstimulatenewideasandapplications,whichofthemselveswouldbroadenthedepth andscopeoftimeandfrequencytechnology.

E.Ambler,Director

InstituteforBasicStandards

NationalBureauofStandards

May8,1973

1U.S.DepartmentofCommerce,DepartmentalOrganizationalOrder30-2B,NBSMissionStatements,June12,1972(seeann.ll.A-chap.11).

IV

PREFACE

"NationalBureauofStandardsTime...ThisisradiostationWWV,FortCollins,Colorado broadcastingoninternationallyallocatedstandardcarrierfrequenciesof2.5,5,10,15,20and25 MegaHertz,providingtimeofday,standardtimeinterval,andotherrelatedinformation..." Behindsuchperiodicradioannouncementslieasubstantiveandstate-of-the-arttechnology whichhasadvancedtremendouslythelastseveraldecades.ItistheobjectiveofthisMonograph togivecomprehensivepicturesofvariousaspectsoftimeandfrequencystandardsintermsofthe past,presentandfuture.Assuch,wetrustitwillserveasatutorialreferencebookbyprovidinga historicalbackground,thepresentcapabilities,andthefuturepotentialofthepreciseandaccurate time-keepingtechnology. Thesubjectmatterispresentedin11majorchaptersofreprinted,updated,andnewmaterial authoredbystaffmembersoftheNBSTimeandFrequencyDivisionandseveralotheragencies, suchastheU.S.NavalObservatoryandtheU.S.ArmyElectronicsCommand.Chapter1describes basicconceptsoftime,frequency,andtimescalesincludingtheInternationalAtomicTime(TAI) scale.Followingbasictimeaspectsarechaptersdescribingcrystaloscillators,fundamentalprin- ciplesofatomicfrequencystandards,andboththehistoricaldevelopmentandrecentprogressin realizingvarioustypesofatomicfrequencystandards.Chapter5detailsimprovementsincesium beamstandardsattheNationalBureauofStandards(NBS)includingabriefdescriptionofthenew NBS-5;thisfrequencystandardshowsatentativepotentialaccuracyof2partsin1013whichis equivalenttoalossofasecondin~160,000years.(Needlesstosay,aclockwillnotrunsucha lengthoftime.However,thecurrentstateofthearttodayrequires6fxsinayearwhichisthesame relativeaccuracy.) Nextaretwochapterswhichprojectone'sthinkingtofuturepossibilities;oneofthesede- scribesareasofpromisefordevelopingtomorrow'sprimaryfrequencystandardswhilethesecond relatesfrequencystandardstoareasofmetrologywhichmightincludeaunifiedstandardfor frequency,time,andlength.Chapter8presentsbasicprinciplesofstatisticsusefulforanalyzing timeandfrequencydataandfordescribingthequalityofsuchmeasurements.Thisisfollowedby achapterwhichdepictsindetailboththetheoryandformationoftheNBSatomictimescaleAT (NBS).AT(NBS)isoneofseveninputstotheTAIscalemaintainedbytheBureauInternational d'Heure(BIH)inParis,France. Ifalaboratorymaintainsastate-of-the-artfrequencystandardandtimescale,suchstandards areofsmallvalueunlesstheycanbemadeavailablereadilytodistantusers.Chapter10describes variousdisseminationtechniquesforbridgingthegapbetweenafrequencystandardandvaried classesoftimeandfrequencyusers.TheMonographconcludeswithChapter11,ajointpaperof theNBSandUSNO,whichdepictsthestandardsoftimeandfrequencyintheUSA;thechapter detailsandcomparesthetimekeepingmissionsandresponsibilitiesofbothorganizations.By mutualagreement,timeatbothnationallaboratoriesismaintainedwithinabout±5/asofeach other.Chapter11includesabriefdescriptionofinternationalagenciesinvolvedwithtimekeeping responsibilitiesaswellastheUniformTimeActof1966oftheUSAgivenintheU.S.Code. Therehasbeenanearnestattempttothoroughlydocumenteachchapterwithacomplete referencelisting.Inmanyinstancesaselectedbibliographyalsohasbeenincludedtoaidareader seekingadditionalinformationinthegivensubjectareas.Wehaveattemptedtobeconsistentand completeinlistingthereferences;journaltitleabbreviationsarethosegiveninthe1961Chemical Abstracts - ListsofPublicationsorthe1966RevisedandEnlargedWordAbbreviationListfor USAZIZ39.5-1963 - AmericanStandardforPeriodicalTitleAbbreviations.Manyofthebiblio- graphiclistingscanbeseenatpublicoruniversitylibraries.NBSTechnicalNotesandpublications withaUSGPOnotationmaybepurchasedfrom: V

SuperintendentofDocuments

U.S.GovernmentPrintingOffice

Washington,DC20402.

ReferencesshowinganADorNaccessionnumberandaNTISnotationareavailableatreproduc- tioncostsfromtheNationalTechnicalInformationServiceasfollows:

NationalTechnicalInformationService

U.S.DepartmentofCommerce

5285PortRoyalRoad

Springfield,VA22150.

Limitedreprintsofresearcharticlesandreportsareavailableusuallyfromindividualauthors. Wehavetriedtomaintainconsistencyintheuseofsymbolsortheirequivalentsinallchapters; definitionsaregivenintheGlossaryofSymbols - AnnexAofChapter8.Toaidreadersunfamiliar withlettersymbolsinthetimeandfrequencyfield,wehaveaddedanabbreviationfistingwhich followsthesubjectindex. Arapidlyincreasingnumberoftechnologiesanddisciplinesareemployingtimeandfrequency techniques.Includedareareassuchasnationaldefense,telecommunications,publicsafety, electricutilities,navigation,highspeeddata-computingnetworks,etc.Therearealsoindications thatalargenumberofsystemsindependentlygenerateanddisseminatetheirowntimeandfre- quencyinformation,largelythroughuseoftheradiospectrum.Wewouldpointoutthattheradio spectrummightbeconservedtoalargeextentifbothcommunicationandnavigationsystemswere designedtoincludesynchronizationpulseformatsconvenientforT/Fdisseminationwithoutcom- promisingprimarysystemconcerns.Bythesametoken,asystemdesignerbettercanaccommodate afrequencydisseminationfunctionthroughreferencingsystemfrequenciestorecognizednational frequencystandardsandchoosingconvenientsubsystemfrequencieswherefeasible. Theeditorwishestogratefullyacknowledgethecooperationandpatienceofthemanyauthors whohavecontributedtothisMonograph.ConsiderablehelpandsuggestionsweregivenbyDr. YardleyBeers,Mr.RogerEaston,Mr.DonaldHammond,Dr.RichardKlepsynski,Dr.Allan Mungall,Dr.DavidWait,Dr.BernardWieder,andmanystaffmembersoftheTimeandFrequency Division.CreditalsomustbegivenbothtotheNBSVisualInformationGroupforthemanydis- tinctiveillustrationsinthisbookandtotheNOAALibrarypersonnelforhelpinlocatingand verifyingmanyreferencecitations.LastbutnotleastspecialthanksaredueMrs.SharonErickson forherdiligenceandeffortinprocessingthefinalcopyofthispublication. TheauthorstrustthattheMonographwillprovehelpfulintheunderstandingoftheintriguing andeverchangingfieldoftimeandfrequency;theywouldwelcomesuggestions,commentsand/or questionsaboutthesubjectmaterial. Timemoveson;theWWVbroadcastproclaims"atthetonehours,minutes

GreenwichMeanTime."

ByronE.Blair,Editor

NationalBureauofStandards

Boulder,Colorado80302

April23.1973

VI

Contents

Page

Abstract'Ill

ForewordIV

ErnestAmbler,Director,InstituteforBasicStandards,NBS,Washington,DC20234

PrefaceV

ByronE.Blair,TimeandFrequencyDivision,NBS,Boulder,CO80302CHAPTER1.BASICCONCEPTSOFPRECISETIMEANDFREQUENCY1

JamesA.Barnes,TimeandFrequencyDivision,NBS,Boulder,CO80302

Introduction3

Clocksandtimekeeping3

Basicconceptsoftime4

Timescales4

InternationalAtomicTime(TAI)Scale10

Theconceptsoffrequencyandtimeinterval10

Usesoftimescales11

Conclusions13

References13

Bibliography14

AnnexA - DefinitionsofthesecondandTAI15

AnnexB - Standardfrequencyandtimebroadcastagreements29 AnnexC - Resultsof6thSessionofConsultativeCommitteeforDefinitionoftheSecond (CCDS)37CHAPTER2.PARTA-STATEOFTHEART-QUARTZCRYSTALUNITSANDOSCILLATORS41 EduardA.Gerber,ElectronicsComponentsLaboratory,U.S.ArmyElectronicsCommand,Ft. Monmouth,NJ07703,andRogerA.Sykes,BellTelephoneLaboratories,Inc.,Allentown,PA 18103

Introduction43

Quartzcrystalunits44

Frequencystabilityasafunctionof

Temperature48

Time(aging)48

Stress,vibrationandacceleration50

Drivelevel50

Nucleareffects51

Quartzcrystalcontrolledoscillators52

Conclusions55

PARTB-PROGRESSINTHEDEVELOPMENTOFQUARTZCRYSTALUNITSANDOSCIL-LATORSSINCE196657 EduardA.Gerber,ElectronicsTechnologyandDevicesLaboratory,U.S.ArmyElectronics Command,Ft.Monmouth,NJ07703,andRogerA.Sykes,formerlywithBellTelephoneLabora- tories,Inc.,Allentown,PA18103

Introduction59

Quartzcrystalunits59

Frequencystabilityasafunctionof

Temperature60

Time(aging)61

Stress,vibrationandacceleration61

Drivelevel61

Quartzcrystalcontrolledoscillators62

Conclusionsandpossiblefuturedevelopments62

References63CHAPTER3.THEPHYSICALBASISOFATOMICFREQUENCYSTANDARDS65 AllanS.Risley,TimeandFrequencyDivision.NBS.Boulder.CO80302

Introduction67

Atomicenergylevels67

Theinteractionbetweenatomsandelectromagneticradiation71

Choosingasuitableatom73

Thethreemajorexamplesofatomicfrequencystandards78

Summary83

References84

Bibliography84CHAPTER4.PARTA-AHISTORICALREVIEWOFATOMICFREQUENCYSTANDARDS85 RogerE.Beehler,FrequencyandTimeDivision,Hewlett-PackardCompany,PaloAlto,CA94304 (nowwithTimeandFrequencyDivision,NBS,Boulder,CO80302.)

Introduction87

Developmentofbasictechniques87

Applicationsofbasictechniquestothedevelopmentofspecifictypesofatomicfrequency standards93

Conclusions99

References99

VII PagePARTB-RECENTPROGRESSONATOMICFREQUENCYSTANDARDS101 RogerE.Beehler,TimeandFrequencyDivision,NBS.Boulder.CO80302

Introduction103

Laboratorycesiumstandards103

Hydrogenstandards105

Commercialcesiumstandards107

Commercialrubidiumstandards108

References108CHAPTER5.PARTA-IMPROVEMENTSINATOMICCESIUMBEAMFREQUENCYSTANDARDSATTHENATIONALBUREAUOFSTANDARDSIll

DavidJ.Glaze,TimeandFrequencyDivision,NBS.Boulder,CO80302

Introduction113

ModificationstotheNBS-IIISystem113

AccuracycapabilityofNBS-III(1969)115

Someimmediategoals116

Conclusions116

References117PARTB-THENEWPRIMARY'CESIUMBEAMFREOUENCYSTANDARD:NBS-5.... '. '. '.119 DavidJ.Glaze,HelmutHellwig,StephenJarvis,Jr.,ArthurE.Wainwright,andDavidW.Allan.

TimeandFrequencyDivision.NBS,Boulder,CO80302

Introduction121TheNBS-5system121

Preliminaryexperimentalresults(statusApril1973)122 References124CHAPTER6.AREASOFPROMISEFORTHEDEVELOPMENTOFFUTUREPRIMARYFREQUENCYSTANDARDS125 HelmutHellwig,TimeandFrequencyDivision,NBS,Boulder,CO80302

Introduction127

Effectsonfrequency:particleinterrogation127

Effectsonfrequency:particleconfinement129

Effectsonfrequency:particlesandparticlepreparation130 Existingconceptsforquantumelectronicfrequencystandards131

Frequencystabilityforonesecondaveraging133

Accuracycapability133

Conclusions134

References135CHAPTER7.ACCURATEFREQUENCYMEASUREMENTS:RELEVANCETOSOMEOTHERAREASOFMETROLOGY137 HelmutHellwigandDonaldHalford,TimeandFrequencyDivision,NBS,Boulder,CO80302

Introduction139

Accuratefrequencymeasurements:principlesandmethods140

Surveyofaccuratefrequencymeasurements142

Significanceandimpactofaccuratefrequencymeasurements144

Summary145

References146

Selectedbibliography:futuretrendsinaccuratefrequency/timemetrology148 CHAPTER8.STATISTICSOFTIMEANDFREQUENCYDATAANALYSIS151 DavidW.Allan,JohnH.Shoaf,andDonaldHalford,TimeandFrequencyDivision,NBS,Boulder,CO80302

Introduction153

Definitionsandfundamentals153

Characterizationoffrequencystability154

Requirementsforameasureoffrequencystability155

Conceptsoffrequencystability156

Thedefinitionofmeasuresoffrequencystability(SecondMonerttype)156

Translationsamongfrequencystabilitymeasures159

Examplesofapplicationsofpreviouslydevelopedmeasures161 Measurementtechniquesforfrequencystability162Summaryoffrequencystabilitymeasures165 Practicalapplicationsoffrequencystabilityspecificationandmeasurements165 Terminologyforspecificationoffrequencystability165

Comparisonofmeasurementtechniques167

OperationalsystemsformeasurementoffrequencystabilityatNBS(highfrequencyregion)168 OperationalsystemsformeasurementoffrequencystabilityatNBS(microwaveregion)171

Conclusions/summary175

References175

AnnexA - Glossaryofsymbols176

AnnexB - Translationofdatafromfrequencydomaintotimedomainusingtheconversionchart (table8.1)178 AnnexC - Spectraldensities:frequencydomainmeasuresofstability178 VIII Pane

AnnexD - Asamplecalculationofscript=Sf180

AnnexE - AsamplecalculationofAllanVariance,o-^(t)181 AnnexF - Computingcounterprogramusinganefficientoverlappingestimatorfor(o-'^(/V=2,

T,r,fh))il2182

AnnexG - Selectedfrequencystabilityreferences:bibliography182 AnnexH - Detailedprocedureforcalibratingmicrowave(frequencystability)measurement system187 AnnexI - Measurementprocedurefordeterminingfrequencystabilityinthemicrowaveregion...188 AnnexJ - Tablesofbiasfunction,B\andB>.forvariancesbasedonfinitesamplesofprocesses withpowerlawspectraldensities190

Table8.1 - Stabilitymeasureconversionchart166

CHAPTER9.THENATIONALBUREAUOFSTANDARDSATOMICTIMESCALE:GENERATION,

STABILITY,ACCURACY,ANDACCESSIBILITY205

DavidW.Allan,JamesE.GrayandHowardE.Machlan,TimeandFrequencyDivision,NBS,

Boulder.CO80302

Introduction.-207

Basictimeandfrequencyconsiderations208

Clockmodeling208

TheAT(NBS)timescalesystem214

TheUTC(NBS)coordinatedscale220

UTC(NBS)accessibility221

TheInternationalAtomicTimeScale(TAI)223

Conclusions223

References224

AnnexA - Optimumfiltersforvariousnoiseprocesses(Eq(9.19))225 AnnexB - TimedispersionwithrecursivefilterappliedtoflickernoiseFM226 AnnexC - Mini-computerprogramforfirstordertimescalealgorithm227

AnnexD - Selectedbibliographyontimescalesandtheirformation230CHAPTER10.TIMEANDFREQUENCYDISSEMINATION:ANOVERVIEWOFPRINCIPLESANDTECHNIQUES233

ByronE.Blair,TimeandFrequencyDivision,NBS,Boulder,CO80302

Introduction235

Disseminationconcepts235

Radiodisseminationoftimeandfrequency239

Disseminationoftimeandfrequencyviaportableclock290TFDviaothermeans294

T/Fuserandsystemevaluation299

Conclusions302

References303.

AnnexA - Characteristicsofradiofrequencybands4through10310a AnnexB - Characteristicsofstandardfrequencyandtimesignalsinallocatedbands311 AnnexC - Characteristicsofstabilizedfrequencyandtime-signalemissionsoutsideallocated frequencyassignaments312 AnnexD - Characteristicsoffrequencystabilizednavigationsystemsusefulfortime/frequency comparisons313CHAPTER11.THESTANDARDSOFTIMEANDFREQUENCYINTHEUSA315 JamesA.Barnes,TimeandFrequencyDivision,NBS,Boulder,CO80302,andGemotM.R. Winkler,TimeServiceDivision,USNO,Washington,DC20390

Introduction317

Timescales - termsofreference317

Timeandfrequency(T&F)activitiesoftheNationalBureauofStandardsandtheU.S.Naval

Observatory318

Internationalorganizationsinvolvedinstandardtimeandfrequency323

Thelegaldefinitionof"standardtime"325

Summary325

References325

AnnexA - NBSenablinglegislation329

AnnexB - USNOauthorizingdocuments347

AnnexC - NBStimeandfrequencyresponsibilities359

AnnexD - USNOprecisetimeandtimeinterval(PTTI)responsibilities363

AnnexE - NBS/USNOtimecoordination/services377

AnnexF - Treatyofthemeter385

AnnexG - Legaldocumentsconcerning"standardtime"389

SubjectIndex415

TimeandFrequencyAbbreviationListing458

CHAPTER1

BASICCONCEPTSOFPRECISETIMEANDFREQUENCY*

JamesA.Barnest

Contents

Page

1.1.Introduction3

1.2.ClocksandTimekeeping3

1.3.BasicConceptsofTime4

1.4.TimeScales4

1.4.1.UniversalTime(UTO)5

1.4.2.UniversalTime1(UT1)6

1.4.3.UniversalTime2(UT2)6

1.4.4.EphemerisTime(ET)6

1.4.5.AtomicTime(AT)7

1.4.6.CoordinatedUniversalTime(UTC)Priorto19728

1.4.7.TheNewUTCSystem8

1.4.8.ComparisonsofTimeScales9

1.4.8.1.ReliabilityandRedundancy9

1.5.InternationalAtomicTime(TAI)Scale10

1.6.TheConceptsofFrequencyandTimeInterval10

1.6.1.TimeIntervalandTimeScales11

1.7.UsesofTimeScales11

1.7.1.TimeScalesforSystemsSynchronizationUses11

1.7.2.TimeScalesforCelestialNavigationandAstronomicalUses11

1.8.Conclusions13

1.9.References13

1.10.Bibliography14

Annexl.A.DefinitionoftheSecondandTAI15

Annexl.B.StandardFrequencyandTimeBroadcastAgreements29 Annexl.C.Resultsof6thSessionofConsultativeCommitteeforDefinitionoftheSecond (CCDS)37 •ManuscriptreceivedJanuary9,1973.

tTimeandFrequencyDivision,InstituteforBasicStandards,NationalBureauofStandards,Boulder,Colorado80302.

1 "Whatistime?Theshadowonthedial,thestrikingoftheclock,the runningofthesand,dayandnight,summerandwinter,months,years, centuries - thesearebutarbitraryandoutwardsigns,themeasureof time,nottimeitself..."

Longfellow,

Hyperion,Bk.ii,Ch.6.

Thischapterdescribessomeelementsoftimekeepingandgivesbasicconceptsoftimeand frequencysuchasdate,timeinterval,simultaneityandsynchronization.Thischapterdetailscharacter- isticsofnumeroustimescalesincludingastronomical,atomic,andcompromisesofboth.Theuni- versaltimescalesarebasedontheapparentmotionofthesuninthesky.whileatomictimescales arebasedontheperiodicfluctuationsofaradiosignalinresonancewithacertainspeciesofatoms. ThechapterincludesadescriptionoftheUTCtimescalebothbeforeandafterJanuary1,1972,and delineatesrequirementsofanInternationalAtomicTimescale. Keywords:Atomictime;clocks;ephemeristime;frequency;navigation/time;TAIscale;time;time interval;timescales;universaltime;UTCsystem. 2

1.1.INTRODUCTION

Themeasurementoftimeisabranchofscience

withaverylonghistory[1,2,3].

1Forthisreason,it

isdifficulttounderstandthecurrentoperationsof timeandfrequencymeasurementswithoutsome background.Thischapterpresentsabriefhistory ofthescientificandengineeringaspectsoftimeand frequency.Thediscussioncommenceswithabasic considerationofclocksandconceptsinvolvedin timemeasurements.Timescalesaredescribedand delineatedaseitherastronomical,atomic,orcom- promisesthereof.Universaltimescalesarebased ontheapparentmotionofthesuninthesky,while atomictimescalesarerelatedtoperiodicfluctua- tionsofaradiosignalinresonancewithacertain speciesofatoms.Thischapterincludesadescrip- tionoftheUTCsystemwhichcommencedJan- uary1,1972.Characteristicsandrequirementsof anInternationalAtomicTime(TAI)2scaleindicate thattheatomictimescaleoftheBureauInter- nationaldel'Heure(BIH)isalogicalchoice.How- ever,theTAIscalewillnotreplacesomeofthe needsforastronomicaltimescaleswhichareneces- saryforearthposition.Thereaderisreferredto

Chapter9fordetailsofconstructingandmaintain-

inganatomictimescale. 10 100

1.)PRIMARYDATAFROMWARD[41

,

MARRIS0N[5],&FRASER[12]

.

2.)INTENTISTOSHOWBENCH-MARKSOFPROGRESS.VARIOUSCLOCKTYPESCANSHOWIMPR0VE0ACCURACIES.

3.)PRIORTO1000A.D.VARIEDTIMEKEEPERSWEREUSED

SUCHASMECHANICAL

WATERCLOCKS,N0CTURNIALS,SUNDIALS,TIMECANDLES

,

ETC.,OFLITTLEKNOWN

ACCURACY.

CESIUMCESIUMATOMIC|ATOMIC(IMPR0VED"(NBS-5EST)

NBSIII)I

BAROMETRIC

COMPENSATION

(ROBINSON)

PENDULUM(HUYGEN•IMPROVEDESCAPEMENT

(GRAHAM )

CROSS-BEAT

ESCAPEMENT

(BURGI )

VERGESF0LI0T

BALANCECLOCKS

14001600

CALEN0ARYEARS,A.D.

Fig.1.1.Progressintimekeepingaccuracy.

1.2.CLOCKSANDTIMEKEEPING

Inearlytimes,thelocationofthesuninthesky

wastheonlyreliableindicationofthetimeofday.

Ofcourse,whenthesunwasnotvisible,onewas

unabletoknowthetimewithmuchprecision.Peo- pledevelopeddevices(calledclocks)tointerpolate betweencheckswiththesun.Thesunwassortof a"masterclock"thatcouldbereadwiththeaidofa sundial.Anordinaryclock,then,wasadeviceused tointerpolatebetweencheckswiththesun.Thedif- ferentclockdevicesformaninterestingbranchof history;wewillnotreviewthemtoanyextenthere excepttopointouttheirgaininaccuracyovera periodofyearsasshowninfigure1.1andtorefer thereadertotheworksofWard,Marrison,andHood [4,5,6].(Timekeepinghasshownnearly10orders ofmagnitudeimprovementwithinthelast6cen- turieswithabout6ordersoccurringwithin70years ofthe20thcentury.)Thus,aclockcouldbea"pri- maryclock"likethepositionofthesuninthesky,or itcouldbeasecondaryclockandonlyinterpolate betweencheckswiththeprimaryclockortime standard.Historically,somepeoplehaveusedthe word"clock"withtheconnotationofasecondary timereferencebuttodaythisusagewouldbetoo restrictive.

1Figuresinbracketsindicatetheliteraturereferencesattheendofthischapter.

2The6thSessionoftheConsultativeCommitteefortheDefintionoftheSecond

recommendsthatInternationalAtomicTimebedesignedbyTAIinalllanguages(July

1972).

Whenonethinksofaclock,itiscustomaryto

thinkofsomekindofpendulumorbalancewheel andagroupofgearsandaclockface.Eachtimethe pendulumcompletesaswing,thehandsoftheclock aremovedapreciseamount.Ineffect,thegearsand handsoftheclock"count"thenumberofswingsof thependulum.Thefaceoftheclock,ofcourse,is notmarkedoffinthenumberofswingsofthepen- dulumbutratherinhours,minutes,andseconds.

Oneannoyingcharacteristicofpendulum-type

clocksisthatnotwoclockseverkeepexactlythe sametime.Thisisonereasonforlookingforamore stable"pendulum"forclocks.Inthepast,themost stable"pendulums"werefoundinastronomy.Here oneobtainsasignificantadvantagebecauseonly oneuniverseexists - atleastforobservationalpur- poses,andtimedefinedbythismeansisavailableto anyone - atleastinprinciple.Thus,onecanobtain averyreliabletimescalewhichhasthepropertyof universalaccessibility.Inthischapter,timescale isusedtorefertoaconceptuallydistinctmethodof assigningdatestoevents.

Inaveryrealsense,thependulumofordinary,

present-dayelectricclocksistheelectriccurrent suppliedbythepowercompany.IntheUnited

Statesthepowerutilitiesgenerallysynchronizetheir

generatorstotheNationalBureauofStandards (NBS)lowfrequencybroadcast,WWVB[7].Thus, therightnumberofpendulumswingsoccureach day.Sinceallelectricclockswhicharepoweredby thesamesourcehave,ineffect,thesamependulum, theseclocksdonotgainorlosetimerelativetoeach other;i.e.,theyrunatthesamerate.Indeed,they willremainfairlyclosetothetimeasbroadcastbyWWVB(±5seconds)andwillmaintainthesame timedifferencewithrespecttoeachother(±1milli- second)overlongperiodsoftime.

Ithasbeenknownforsometimethatatomshave

characteristicresonancesor,inaloosesense,"char- acteristicvibrations."Thepossibilitytherefore existsofusingthe"vibrationsofatoms"aspendu- lumsforclocks.Thestudyofthese"vibrations"has normallybeenconfinedtothefieldsofmicrowave andopticalspectroscopy.Presently,microwaveres- onances(vibrations)ofatomsarethemostpre- ciselydeterminedandreproduciblephysical phenomenathatmanhasencountered.Thereis ampleevidencetoshowthataclockwhichuses "vibratingatoms"asapendulumwillgeneratea timescalemoreuniformthanevenitsastronomical counterparts[8,9,10].

Butduetointrinsicerrorsinanyactualclocksys-

tem,onemayfindhimselfbackinthepositionof havingclockswhichdriftrelativetoothersimilar clocks.Ofcourse,therateofdriftismuchsmaller foratomicclocksthantheoldpendulumclocks,but nonethelessrealandimportant.Ifatallpossible,one wouldliketogaintheattributeofuniversalaccessi- bilityforatomictimealso.Thiscanbeaccomplished onlybycoordinationbetweenlaboratoriesgenerat- ingatomictime.Bothnationalandinternational coordinationareinorder.

1.3.BASICCONCEPTSOFTIME

Onecanusetheword"time"inthesenseofdate.

(By"date"wemeanadesignatedmarkorpointona timescale.)Onecanalsoconsidertheconceptof timeintervalor"length"oftimebetweentwo events.Thedifferencebetweentheseconceptsof dateandtimeintervalisimportantandhasoften beenconfusedinthesingleword"time".Thissec- tionexploressomebasicideasinherentinthevarious connotationsoftime.

Thedateofaneventonanearth-basedtimescale

isobtainedfromthenumberofcycles(andfractions ofcycles)oftheapparentsuncountedfromsome agreed-uponorigin.Similarly,atomictimescalesare obtainedbycountingthecyclesofasignalinreso- nancewithcertainkindsofatoms.(Severalatomic timescales[9]havechosenthe"zeropoint"atzero hoursJanuary1,1958(UT-2),butthisisnotuni- versalamongallatomictimescalesinexistence today.)Oneofthemajordifferencesbetweenthese twomethodsisthatthecyclesofatomicclocksare much,muchshorterthanthedailycyclesofthe apparentsun.Thus,theatomicclockrequiresmore sophisticateddevicestocountcyclesthanare requiredtocountsolardays.Theimportanceof thisdifferenceisamatteroftechnologicalcon- venienceandisnotveryprofound.Oftechnological significancearethefactsthatatomicclockscanbe readwithmuchgreatereaseandwithmanythou- sandsoftimestheprecisionoftheearthclock.In additionthereadingofanatomicclockcanbepre- dictedwithalmost100,000timesbetteraccuracy thantheearthclock.

IntheU.S.literatureonnavigation,satellitetrack-

ing,andgeodesy,theword"epoch"issometimes usedinasimilarmannertotheword"date."How- ever,dictionarydefinitionsofepochshowgra- dationsofmeaningssuchastimeduration,time instant,aparticulartimereferencepoint,aswellas ageologicalperiodoftime.Thus,epochoftensimul- taneouslyembodiesconceptsofbothdateanddura- tion.Becauseofsuchconsiderableambiguityinthe word"epoch,"3itsuseisdiscouragedinpreference totheword"date,"theprecisemeaningofwhichis neitherambiguousnorinconflictwithother,more popularusage.Thus,thedateofaneventmightbe:

30June1970,14h,35m,37.278954s,UTC,forexam-

ple,whereh,m,sdenotehours,minutes,andsec- onds.(ThedesignationUTC,meaningUniversal

TimeCoordinated,willbediscussedlater.)Onthe

otherhand,"date"shouldnotbeinterchangedindis- criminatelywith"epoch"or"time."

Anotheraspectoftimeisthatofsimultaneity;i.e.,

coincidenceintimeoftwoevents.Forexample,we mightsynchronizeclocksuponthearrivalofport- ableclocksatalaboratory.Hereweintroducean additionalterm,synchronization,whichimpliesthat thetwoclocksaremadetohavethesamereadingin someframeofreference.Notethattheclocksneed notbesynchronizedtoanabsolutetimescale.Asan example,twopeoplewhowishtocommunicatewith eachothermightnotbecriticallyinterestedinthe date,theyjustwanttobesynchronizedastowhen theyusetheircommunicationsequipment.Many sophisticatedelectronicnavigationsystems(and proposedcollisionavoidancesystems)donotdepend onaccuratedatesbuttheydodependuponvery accuratetimesynchronization.Evenordinarytele- visionreceiversrequireaccuratetimesynchroniza- tion.Wethusseesomeofthecomplexitiesinvolved inconceptsoftimeandhowvariedcombinationsof timeaspectsareembodiedinandinfluencevarious time-relatedactivities.

1.4.TIMESCALES

Asystemofassigningdatestoeventsiscalleda

timescale.Theapparentmotionofthesuninthe

3Thissuggestionawaitsdefinitiverecommendationsorstatementoftermsbyparties

suchastheCCIRStudyGroup7,InterimWorkingParty7/2on"FormsofExpression forUseoftheStandard-FrequencyandTimeSignalService";InternationalCouncilof ScientificUnions;andtheIEEEStandardsCommittees,amongothers. 4 skyconstitutesoneofthemostfamiliartimescales butiscertainlynottheonlytimescale.Notethatto completelyspecifyadateusingthemotionofthesun asatimescale,onemustcountdays(i.e.,makea calendar)fromsomeinitiallyagreed-uponbeginning.

Inaddition(dependingonaccuracyneeds)one

measuresthefractionsofaday(i.e.,"timeofday") inhours,minutes,seconds,andmaybeevenfrac- tionsofseconds.Thatis,onecountscycles(and evenfractionsofcycles)ofthesun'sdailyapparent motionaroundtheearth.

Therearebothastronomicaltimescales[11]and

atomictimescales[9]whichcanprovideabasisfor precisesynchronization.Asensibleuseofthe unqualifiedword"time"istheusewhichembodies allofthesevariousaspectsoftimescales,time measurement,andeventimeinterval(orduration).

Thisistotallyconsistentwiththedictionarydefini-

tionoftheword.Thus,thestudyofsynchronization wouldbeproperlysaidtobelongtothebroader studyoftimeingeneral.Thus,itisnotonlymislead- ingbutwrongtosaythat"time"isonlydetermined byastronomicalmeans.Indeed,therearemany classesoftime - astronomicaltime,biologicaltime, andatomictime,tonameafew[12].

Timederivedfromtheapparentpositionofthe

sunintheskyiscalledapparentsolartime.Asun- dialcanindicatethefractionsofcycles(i.e.,time ofday)directly[13J.Calendars,liketheGregorian

Calendar,aidincountingthedaysandnamingthem.

Copernicusgaveustheideathattheearthspins

onitsaxisandtravelsaroundthesuninanearlycir- cularorbit.Thisorbitisnotexactlycircular,how- ever,and,infact,theearthtravelsfasterwhen nearerthesun(perihelion)thanwhenfurtherfrom thesun(aphelion).Thedetailsoftheearth'sorbit andKepler'slawof"equalareas"allowsonetosee thatapparentsolartimecannotbeauniformtime [14].Thereisalsoaneffectduetotheinclinationof theearth'saxistotheplaneofitsorbit(ecliptic plane).Apictorialdiagramofthesun-earth-moon relationshipsisshowninfigure1.2.

1.4.1.UniversalTime(UTO)

Itispossibletocalculatetheseorbitalandincli-

nationeffectsandcorrectapparentsolartimeto obtainamoreuniformtime - commonlycalledmean solartime.Thiscorrectionfromapparentsolartime MAR21

VERNALEQUINOX

APHELION

JUL5,1966

PATH

PERIHELION

JAN3,1966

LUNARORBIT

NODALLINE

PERIOD=27.32DAYS

INCLINATIONOFEARTH'S

EQUATORTOITSORBIT

(23.45°)"20°TO26°

INCLINATIONOFLUNAR

ORBITTOEARTH'SEQUATOR

18.06°TO28.1°

5°INCLINATIONOFLUNAR

EQUATORTOITSORBIT

PERIGEE=3.64x1

0 8m -EARTH-MOON

APSIDELINE"

APOGEE=4.06x10m

Fig.1.2.Sun,earth,moonrelationships.(CourtesyofA.D.Watt) 5 tomeansolartimeiscalledtheEquationofTime andcanbefoundengravedonmanypresent-day sundials[13].

Ifoneconsidersadistantstarinsteadofourstar

- thesun - tomeasurethelengthoftheday,thenthe earth'sellipticorbitbecomesunimportantandcan beneglected.Thiskindoftimeistheastronomer's siderealtimeandisgenericallyequivalenttomean solartimesincebotharebased,ultimately,onthe spinoftheearthonitsaxis - thesecondofsidereal timebeingjustenoughdifferenttogiveasidereal yearonemore"day"thanthatofasolaryear.In actualpractice,astronomersusuallyobserveside- realtimeandcorrectittogetmeansolartime.Uni- versalTime(UTO)isequivalenttomeansolartime asdeterminedattheGreenwichMeridian,some- timescalledGreenwichMeanTime(GMT).

Time,ofcourse,isessentialtonavigationindeter-

mininglongitude[15].Ineffect,anavigatorusinga sextantmeasurestheanglebetweensomedistant starandthenavigator'szenithasshowninfigure1.3.

Itisapparentthatforagivenstarthereisalocusof

pointswiththesameangle.Bysightingonanother star,adifferentlocusispossibleandobviouslythe positionofthenavigatorisatoneoftheintersections ofthetwoloci.(Athirdsightingcanremovethe ambiguity.)Thepositionofthisintersectiononthe earthobviouslydependsontheearth'srotational position.Itisimportanttoemphasizethatcelestial navigationisbasicallyconnectedtoearthposition andonlytotimebecausetheearthalsodefinesa usefultimescale. LOCAL

Fig.1.3.Principleofcelestialnavigation.

1.4.2.UniversalTime1(UT1)

Inorderforthenavigatortousethestarsfornavi-

gation,hemusthaveameansofknowingtheearth's position(i.e.,thedateontheUTscale).Thus,clocks andsextantstogetherbecamethemeansbywhich navigatorscoulddeterminetheirlocations.With navigationprovidingabigmarketfortimeandfor goodclocks,betterclocksweredeveloped,and thesebegantorevealadiscrepancyinUniversal

Timemeasuredatdifferentlocations.Thecauseof

thiswastracedtothefactthattheearthwobbleson itsaxis;thelocationofthepoleasitintersectsthe earth'ssurfaceisplottedfor1964-69infigure1.4.

Ineffect,oneseesthelocationofthepolewandering

overarangeofabout15meters.Bycomparingastro- nomicalmeasurementsmadeatvariousobserva- toriesspreadovertheworld,onecancorrectfor thiseffectandobtainamoreuniformtime - denoted

UT1[16].

Fig.1.4.Pathofearth'spole1964-1969.

1.4.3.UniversalTime2(UT2)

Withtheimprovementofclocks - bothpendulum

andquartzcrystal - itwasdiscoveredseveralyears agothatUT1hadperiodicfluctuations(ofunknown origin)withperiodsofone-halfyearandoneyear.

Thenaturalresponsewastoremovethesefluctua-

tionsandobtainanevenmoreuniformtime - UT2.

Thus,thereexistsawholefamilyofUniversalTimes

basedonthespinoftheearthonitsaxisandvarious otherrefinementsasdiagrammedinfigure1.5.In thishistoricalprogression,onenotesthatUT1isthe truenavigator'sscalerelatedtotheearth'sangular position.UT2isasmoothedtimeanddoesnotreflect thereal,periodicvariationsintheearth'sangular position.

1.4.4.EphemerisTime(ET)

Atthispointitisdesirabletogobackintime -

neartheturnofthecentury - andtracesomeother astronomicalstudies.Inthelatter19thcentury, 6

UNIVERSALTIMEFAMILY

APPARENTSOLARTIME

CORRECTEDBY

EQUATIONOFTIME|MEANSOLARTIMET

[UTO]

CORRECTEDFOR

MIGRATIONOFPOIES

At-005secfUT1

CORRECTEDFOR

KNOWNPERIODICITY

AtO.05secmUT2

Fig.1.5.Universaltimefamilyinterrelationships.

SimonNewcombecompiledasetoftables,basedon

Newtonianmechanics,whichpredictedtheposi-

tionsofthesun,themoon,andsomeplanetsforthe future.Atableofthissortiscalledanephemeris.It wasdiscoveredthatthepredictedpositionsgrad- uallydepartedfromtheobservedpositionsina fashiontoosignificanttobeexplainedeitherby observationalerrorsorapproximationsinthetheory-

Itwasnoted,however,thatifthetimeweresome-

howinerror,allthetablesagreedwell.Atthispoint itwascorrectlydeterminedthattherotationalrate oftheearthwasnotconstant.Thiswaslatercon- firmedwithquartzclocksandatomicclocks[17,18,

19].Theastronomers'naturalresponsetothiswas,

ineffect,touseNewcombe'stablesforthesunin reversetodeterminetime - actuallywhatiscalled

EphemerisTime.EphemerisTimeisdeterminedby

theorbitalmotionoftheearthaboutthesun(notby rotationoftheearthaboutitsownaxis)andshould notbeaffectedbysuchthingsascoremantleslip- pageorothergeometricalchangesintheshapeof theearth. •100

170018001900

CALENDARYEARS,A.D.

2000
Fig.1.6.TrendofUT-ETforoverthreecenturies(datafrom

Brouwer[20]).

ThevariationsinUTscalesorearthrotationrates

havebeenstudiedextensivelybyBrouwerandmany others[20,21,22].Inthischapter,weneedonly pointoutthegeneralnatureandsizeofthevaria- tionswhichhavebeenobserved.Brouwer'sstudy coveredalongperiodoftime;thecurvesshownin figure1.6summarizemuchofhisdataandanalysis.

Theyreflecttherandombehavior[23JofUT,marked

onoccasionbysuddenerraticchangessuchasseen in1963[24J.Theabscissasinfigure1.6arepropor- tionaltotheastronomicaltimescale,ET.Atpresent

ETcanbeconsidereduniformwithrespecttoAT

[25Jandisagoodcomparisonscaletobeusedin detectinglong-term(gross)propertiesofatime scale.ItisofvaluetorecognizethatBrouwerdeter- minedthattherandomprocesseswhichaffectthe rotationoftheearthonitsaxiscausedthermsfluc- tuationsinUniversalTimetoincreaseast312 ,fort greaterthanoneyear.Forperiodsoftheorderofa yearorlessitappearsthatthevariationsintheUT2 timescalecausethermsfluctuationstoincreaseas thefirstpoweroft(flickernoisefrequencymodula- tion)[26J.Thecoefficientofthislineartermisabout

2X10~9oralmostafactorof105worsethansome

cesiumclocks.Thepresentmeansofdetermination ofETarenotadequatelyprecisetoallowdefinitive statementsaboutpossiblesystematicvariationsofET[11].

1.4.5.AtomicTime(AT)

Aswaspointedoutpreviously,thedateofan

eventrelativetotheUniversalTimeScaleis obtainedfromthenumberofcycles(andfractionsof cycles)oftheapparentsuncountedfromsome agreed-uponorigin.(Dependingontheneed,one mayhavetoapplycorrectionstoobtainUTO,UT1,or

UT2.)Similarly,atomictimescalesareobtainedby

countingthecyclesofasignalinresonancewith certainkindsofatoms.

Inthelatterpartofthe1940's,HaroldLyonsat

theNationalBureauofStandardsannouncedthe firstAtomicClock[27].Duringthe1950'sseveral laboratoriesbeganatomictimescales[28.29.30].

TheBureauInternationaldel'Heure(BIH)hasbeen

maintainingatomictimeforsomeyearsnow,and thistimescalereceivedtheofficialrecognitionas

InternationalAtomicTime(TAI)oftheGeneralCon-

ferenceofWeightsandMeasures(CGPM)inOcto- ber1971[31](seeann.l.A).Beginning1January

1972,thisatomictimescalehasbeenbroadcast

(withsomemodifications)bymostcountries(see "ThenewUTCsystem"insec.1.4.7).

Inreview,wehavediscussedthreebroadclasses

oftimescalesasillustratedinfigure1.7.TheUni- versalTimefamilyisdependentontheearth'sspin onitsaxis;EphemerisTimedependsontheorbital motionoftheearthaboutthesun;andAtomicTime, whichdependsonafundamentalpropertyofatoms, isveryuniformandprecise.Becauseofthe"slow" 7

UNIVERSALTIME4

(UTO,UT1,UT2)T

MEASUREDTO3msIN1DAY

EPHEMERISTIME^

(ET)V

MEASUREDTO50msIN9YEARS

ATOMICTIME&MEASUREDTO<0.1MsIN1minT(DIFFUSIONRATESOF0.1Fs/day

FORENSEMBLESOFCLOCKS]

Fig.1.7.Classesoftimescaleswithtypicalaccuracies.

merit[33J.UTCwassupposedtoagreewithUT2to withinViosecond(V20secondbefore1963).On occasionitwasnecessarytoresettheUTCclockby

Viosecond(V20secondbefore1963)inordertostay

withinthespecifiedtolerancesasshowninfig- ure1.8.Also,byinternationalagreement[33J.the offsetsinclockratewereconstrainedtobeaninte- gralmultipleof5partsperbillion(1partperbillion before1963).Inaddition,afewstations(e.g.,WWVB)broadcastaSteppedAtomicTime(SAT) signalwhichwasderiveddirectlyfromanatomic clock(norateoffset)butwhichwasresetperiodic- ally(moreoftenthanUTC)tomaintainSATwithin aboutViosecondofUT2[34J. orbitalmotionoftheearth(1cycleperyear),meas- urementuncertaintieslimittherealizationofaccu- rateephemeristimetoabout0.05secondfora

9-yearaverage,whileUTcanbedeterminedtoa

fewthousandthsofasecondinaday,andATtoa fewbillionthsofasecondinaminuteorless.

1.4.6.CoordinatedUniversalTime(UTC)

Priorto1972

From1960through1971manybroadcasttimesig-

nals(e.g.,MSF,WWV,CHU)werebasedonatime scalecalledCoordinatedUniversalTime(UTC)[32].

TherateofaUTCclockwascontrolledbyatomic

clockstobeasuniformaspossiblefor1year,but thisratecouldbechangedatthefirstofacalendar year.TheyearlyratewaschosenbytheBIH. Table1.1liststhefractionaloffsetsinrateoftheUTCscalerelativetoapureatomictimescale.

Table1.1.FrequencyOffsetsofUTCfrom1960to1972

Offsetrateof

YearUTCinparts

per1010

1960-150

1961-150

1962-130

1963-130

1964-150

1965-150

1966-300

1967-300

1968-300

1969-300

1970-300

1971...-300

1972^future0

TheminussignimpliesthattheUTCclockranslow

(inrate)relativetoatomictime.Theoffsetinclock ratewaschosentokeeptheUTCclockinreason- ableagreementwithUT2.However,onecouldnot exactlypredicttheearth'srotationalrateanddis- crepancieswouldaccrue.Byinternationalagree-

COORDINATEDUNIVERSALTIME(UTC)

[PRIORfO1972) YEARS

UTC-AT

UI2-AI

ff =n»(50»lO"") it=1/10sec Fig.1.8.RelationshipbetweenUTCandUT2timescales - prior to1972.

1.4.7.TheNewUTCSystem

ThefactsthattheclockrateofUTChavebeen

offset(seetable1.1)fromthecorrect(atomic)rate andthatthisoffsetchangedfromtimetotimeneces- sitatedactualchangesinequipmentandofteninter- ruptedsophisticatedsystems.Astheneedsfor reliablesynchronizationhaveincreased,theoldUTCsystembecametoocumbersome.Anewcom- promisesystemwasneededtoaccountbetterforthe ever-growingneedsofprecisetimesynchronization.AnewUTCsystemwasadoptedbytheInter- nationalRadioConsultativeCommittee(CCIR)in

GenevainFebruary1971[35,36]andbecameeffec-

tive1January1972(seeann.LB).Inthisnewsys- temallclocksrunatthecorrectrate(zerooffset).

Thisleavesusinapositionofhavingtheclockrate

notexactlycommensuratewiththelengthoftheday.

Thissituationisnotunique.Thelengthoftheyear

isnotanintegralmultipleoftheday.Thisisthe originof"leapyear."Inthiscase,yearswhichare divisibleby4haveanextraday - February29 - unlesstheyarealsodivisibleby100,andthenonly iftheyarenotdivisibleby400.Thus,theyears1968,

1972,'1976,and2000areleapyears.Theyear2100

8 willnotbealeapyear.Bythismeansourcalendar doesnotgetoutofstepwiththeseasons.

Withthisasanexample,itispossibletokeepthe

clocksinapproximatestepwiththesunbytheinfre- quentaddition(ordeletion)ofasecond - calleda "leapsecond."Thus,theremaybespecialsituations wherea"minute"contains61(or59)seconds insteadoftheconventional60seconds.Thisshould notoccurmoreoftenthanaboutonceayear.By internationalagreement,UTCwillbemaintained withinabout0.7secondofthenavigators'timescale,

UT1.Theintroductionofleapsecondsallowsa

goodclocktokeepapproximatestepwiththesun.

Becauseofthevariationsintherateofrotationof

theearth,however,theoccurrencesoftheleap secondsarenotpredictableindetail.

1.4.8.ComparisonsofTimeScales

Itisofvalueincomparingtimescalestoconsider

foursignificantattributesofsometimescales: a.accuracyandprecision, b.reliability, c.universalaccessibility, d.extension.

Intheareasofaccuracyandprecision,atomic

timescaleshaveaclearadvantageovertheirastro- nomicalcounterpart.Atomicclocksmaybeableto makeareasonableapproachtothereliabilityand accessibilityofastronomicalclocks,however,astro- nomicaltimescalesarebasedona"single"clock whichisavailabletoeveryone(i.e.,onlyonesolar systemisavailableforstudy).Also,manyatomic clockscanshowdisagreements,animpossibility withonlyoneclock.Theextensionofdatestopast events(indeed,remote,pastevents)isafeature whichatomicclockswillneverpossess.Theirutility forfutureneeds,however,isquiteanothermatter.

Theneedsofthegeneralscientificcommunityand,

inparticular,thetelecommunicationsindustriesare makingevergreaterdemandsonaccurateandpre- cisetimingcoveringlongertimeintervals.Often theseneedscannotbemetbyastronomicaltime.

However,thecontinuedmotionofthesolarsystem

givesareliabilitytoastronomicaltimescaleswhich atomicclockshavenotyetattained.

Onecanimaginesynchronizingaclockwithahy-

potheticallyidealtimescale.Sometimeafterthis synchronizationourconfidenceintheclockreading hasdeteriorated.Figure1.9showstheresultsof somestatisticalstudieswhichindicatetheprobable errorsofsomeimportantclocksaftersynchroniza- tion.Therearereallytwothingsofsignificanceto noteinfigure1.9:First,AtomicTime(stateofthe art,1964)isabout10,000timesmoreuniformthan

UniversalTime,andsecond,measurementuncer-

taintytotallylimitsanyknowledgeofstatistical fluctuationsinEphemerisTime.

PROBABLECLOCKERRORS

(NON-UNIFORMITY) Fig.1.9.Probableerrorsof3clocktypesaftersynchronization.

1.4.8.1.ReliabilityandRedundancy

Inthepast,reliableoperationofatomicfrequency

standardshasbeenasignificantproblem.Presently, however,commercialunitswithaMeanTime

BetweenFailure(MTBF)exceeding1yeararenot

uncommon[37].Finiteatomsourcelifetimepre- ventsunlimitedoperationwithoutinterruption, however.

ItistruethataMTBFexceeding1yearreflects

significantengineeringaccomplishments,butthisis farfromcomparabletothehighreliabilityofastro- nomicaltime.Theobvioussolutionistointroduce redundancyintheclocksystem.Onecanusesev- eralatomicclocksinthesytemandthisshould certainlybethebestapproachinthesenseof accuracyandreliability - itisexpensive,however.

Supposethesynthesizer-countersubsystemofa

clocksystemshouldjumpasmallamountandcause adiscontinuityinitsindicatedtime.Itispossible thatsuchatransientmalfunctioncouldoccurwith nooutwardlyapparentsignsofmalfunctionofthe apparatus.Itisalsoapparentthatifonlytwoclocks areavailableforintercomparison,itisimpossibleto decidewhichclocksufferedthetransientmalfunc- tion.Thus,threeclocks(notnecessarilyallatomic) constituteanabsoluteminimumforreliableopera- tion.Ifoneormoreofthesehasanextendedprob- abledowntime(e.g.,whiletheatomsourceis replenished)then4or5clocksbecomeamorework- ableminimum. 9

Itshouldbenotedherethatonecouldassemblea

largegroupofclocksintoonesystemandthesystemMTBFcalculatedfromthe'individualMTBF's mightextendintogeologictimeintervals.Thissys- temMTBFisundoubtedlyover-optimisticdueto neglectofthepossibilitiesofcatastrophesoropera- torerrors.Nonetheless,withvariousatomicclocks spreadovertheearth,itshouldbepossibletomain- tainanatomictimescalewithareliabilitythatcould satisfyalmostanyfuturedemand.

1.5.INTERNATIONALATOMICTIME(TAI)SCALE

InrecentyearstheGeneralConferenceofWeights

andMeasures(CGPM)hasbeenencouragedto adoptanInternationalAtomicTime(TAI)scale[38] (seeann.l.A).Forsuchascaletobeofvaluethe followingattributesarerequired: a.Itmustprovidegreateraccuracyandconven- iencethantheastronomicalcounterparts. b.Itmustbehighlyreliablewithalmostno chanceofafailureoftheclocksystem.(This canbeaccomplishedbyusingmanyclocksdis- persedovertheworldbutwhichcanbeinter- comparedaccurately.) c.Theatomictimescalemustbereadilyavailable everywhere.

Indeed,allofthesepointsappeartobemorethan

adequatelycoveredbytheatomictimescaleofthe

BIH.InOctober1971theCGPMendorsedtheBIH

atomictimescaleastheInternationalAtomicTime scale[31](seeann.l.A)definedasfollows: "InternationalAtomicTimeisthetimereferencecoordi- nateestablishedbytheBureauInternationaldel'Heureon thebasisofthereadingsofatomicclocksfunctioningin variousestablishmentsinaccordancewiththedefinitionof thesecond,theS.I.Unit(InternationalSystemofUnits)of time."

TheAtomicTime(AT)scalesmaintainedinthe

U.S.(bybothNBSandUSNO)constitute~37Ya

percentofthestablereferenceinformationusedin maintainingastableTAIscalebytheBIH[39].The questionoftheaccuracyofrateoftheTAIscaleis notnowcompletelyspecified[40].Thereisaques- tionofformalaveragingproceduresforcorrecting

TAI.AspecialmeetingoftheConsultativeCommit-

teefortheDefinitionoftheSecond(CCDS)washeld inParis,France,July1972,toconsiderthestatusof atomicfrequencystandardsandimprovedrealiza- tionoftheTAI,amongotherpertinentquestions. Recommendationsofthiscommittee(6thSessionofCCDS)aregiveninAnnexl.C.

Dr.Guinot,DirectoroftheBIH,recommendeda

newmethodofcalculationofTAI.Byusingindivid- ualclockdatainplaceoflocaltimescalesfromvar- iouslaboratories,improvedweightingofclockdata isanticipated[40].Someadvantagesoftheindivid- ualclockprocedurehepointedoutareasfollows: "1.Mostofthelocaltimescalesarebasedonasmallnum- berofclocks.IrregularitiesofTAIareduetochangesof frequenciesofcertainTA(i)whichcannotbeseenatthelocal levelwhenthenumberofstandardsineffectiveusehastobe lessthan3.Thishappensfrequently.Inaglobaltreatment, suchirregularitieswouldbevisible.

2.Isolatedstandardscouldbeemployed.Forexample,at

least12cesiumstandardsconvenientlyavailableandcom- paredtotheLoranCpulsesorTVpulsesareavailablein

Europe,notincludingthoseattheLoranCstations.

3.Thetreatmentofallthestandardswouldbeunified,

describedindetail,andunderstoodbyall.Atpresent,itis practicallyimpossibletounderstandhowTAIiscalculated sinceitisnecessarytounderstandthemethodsofeach participatinglaboratory,methodswhicharenotalways published.

4.ThedirectcalculationofTAIwouldallowacomplete

freedomtothelaboratoriesinordertoestablishtheTA(i), accordingtotheircriteria,withoutwhichtheyhavetobe preoccupiedwiththecriteriaadoptedbyTAI."

AtentativescheduleforworkoftheBIHfor

improvingTAIisgiveninAnnexl.C.Acomplete descriptionoftheconstructionofalocalatomic timescaleistreatedbyD.Allanetal.inchapter9.

TheUTCscalesoftheUSAarecoordinatedwith

UTC(BIH)towithinatoleranceofabout±10fxs.

AlloftheUTCscalesaresupposedtoagreewith

UTC(BIH)to±1millisecondbyInternational

RadioConsultativeCommittee(CCIR)agree-

ment[36].ForthosedesiringaccurateUTinforma- tion,correctionsareencodedintostandardtime broadcasts[36].Yet,evenwiththeexistenceofan

InternationalAtomicTimescale,onemustrecog-

nizethattherewillbecontinuedneedforthe astronomicaltimescales.Apersondoingcelestial navigation,forexample,mustknowearthposition (UT1).

1.6.THECONCEPTSOFFRE-QUENCYANDTIMEINTERVAL

Thefourindependentbaseunitsofmeasure-

mentcurrentlyusedinsciencearelength,mass, time,andtemperature.Itistruethat,exceptfor fieldsofsciencesuchascosmology,geology,and astronomy,timeintervalisthemostimportant concept,and(astronomical)dateisofmuchless importancetotherestofscience.Thisistruebe- causethe"basiclaws"ofphysicsaredifferential innatureandonlyinvolvesmalltimeintervals.In essence,physical"laws"donotdependuponwhen (i.e.,thedate)theyareapplied.

Basedontheselawsandextensiveexperimenta-

tion,scientistshavebeenabletodemonstratethat frequencycanbecontrolledandmeasuredwiththe smallestpercentageerrorofanyphysicalquantity.

Thefrequencyofaperiodicphenomenonisthe

numberofcyclesofthisphenomenonperunitof time(i.e.,persecond).Thenameoftheunitoffre- quencyisthehertz(Hz)andisidenticaltoacycle persecond(cps).Sincemostclocksdependupon someperiodicphenomenon(e.g.,apendulum)in orderto"keeptime,"andsinceonecanmakereli- ableelectroniccounterstocountthe"swings"of 10 theperiodicphenomenon,wecanconstructclocks withtimekeepingaccuracy(rateaccuracy)equal totheaccuracyofthefrequencystandard.

Intermsoftheadvancementoftimescales,the

historyofthedefinitionofthesecondcanbe expressedverybriefly.Priorto1956,thesecond wasdefinedasthefraction1/(86,400)ofameansolar day;from1956to1967itwastheephemerissecond dennedasthefraction1/(31556925.9747)ofthe tropicalyearatOOh00m00s31December1899,and since1967,intermsofaresonanceofthecesium atom[41](seeann.LA).Thepresentdefinition ofthesecondstates: "Thesecondisthedurationof9192631770periodsofthe radiationcorrespondingtothetransitionbetweenthetwo hyperfinelevelsofthegroundstateofthecesium - 133 atom".(13thCGPM(1967),Resolution1),[42].

Today'smostpreciseandaccurateclocksincor-

porateacesiumatomicbeamasthe"pendulum"of theclock.

1.6.1.TimeIntervalandTimeScales

Oneshouldnotesourcesofconfusionwhichcan

existinthemeasurementoftimeandintheuseof theword"second."Supposethattwoevents occurredattwodifferentdates.Forexamplethe datesofthesetwoeventswere15December1970,

15h30m00.000000sUTCand15December1970,

16h30m00.000000sUTC.Atfirstthoughtonewould

saythatthetimeintervalbetweenthesetwoevents wasexactly1hour=3600.000000seconds,butthis isnottrue.(Theactualintervalwaslongerby about0.000108seconds[3600secondsX300X10"10 ].

Seetable1.1.)RecallthattheUTCtimescale(like

alltheUTscalesandtheETscale)wasnotdefined inaccordancewiththedefinitionoftheintervalof time,thesecond.Thus,onecannotsimplysubtract thedatesoftwoeventsasassignedbytheUTC scale(oranyUTscaleortheETscale)inorderto obtaintheprecisetimeintervalbetweenthese events.Historically,thereasonbehindthisstateof affairsisthatnavigatorsneedtoknowtheearth's position(i.e.,UT1) - notthedurationofthesecond.

Yet,manyscientistsneedtoknowanexactand

reproducibletimeinterval.Notethatthismight alsobetrueofthenewUTCsystemiftheparticular timeintervalincludedoneormoreleapseconds.

Itisalsoconfusingthatthedatesassignedbythe

UT,ET,andUTCscalesinvolvethesamewordas

theunitoftimeinterval,thesecond.Foraccurate andprecisemeasurements,thisdistinctioncanbe extremelyimportant.

1.7.USESOFTIMESCALES

Thestudyoftimescalescanbedividedintothe

studyoftimescalesusedforsystemssynchroniza- tionandtimescalesusedforcelestialnavigation andastronomy.

1.7.1.TimeScalesforSystemsSynchroniza-

tionUses

Longagopeopleweresimplycontenttoletthe

sungoverntheirfives.Sunriseindicatedtimeto ariseandbeginwork;sunsetsignalledtheday'send.

Withtheadvancementofcivilization,growthof

commerceandcitylifeandtechnologicalgains, communitieswereestablishedwhichinstituted clockssettoagreeroughlywiththeapparent movementofthesun.Thusdevelopedtheideaof localtimeandeachcommunitycouldhaveitsown localtime.Clearly,whenalmostallcommunications andbusinesstransactionsoccurwithinagivencom- munityorlocale,thisisaworkablesolution.With theadventofrailroadsandhencemorerapidcom- munications,this"crazy-quilt"mazeofindividual localtimeshadtoend.Therailroadsaregenerally creditedwithunifyingthevariouslocaltimesinto timezonesinthecontinentalU.S.,resultingina muchmoreworkablenationaltimesystem.In1884 aninternationalconferencerecommendedthatthe meridianofGreenwich,Englandbethestandard referencemeridianforlongitudeandtime[43].

Longitudemeridians,each15°,represent1hour

time-zonedifferences±12hourseastandwestof

Greenwich.Figure1.10showsthestandardtime

zonesoftheworldineffecttoday.

Thisbriefhistoricalsequenceillustratesthat,as

communicationsbecomemorerapidandmorefar- reaching,thegreaterarethedemandsonanall- pervasiveandunifyingconventionofsynchronizing clockswitheachother.Thatis,thisconventionis amatterofconvenienceandthereisnothingsacred orabsoluteaboutwhatourclocksread;it'sjust importantthattheyreadthesametime(orhavea well-definedtimedifferenceasbetweenthetime zones).Inthedayswhentherailroadswerethe primarymeansoftransportationacrosstheNorth

Americancontinent,anaccuracyofafewseconds

oftimewasimportantandsufficient.Nowadays, withtheexistenceofsophisticatedtelecommunica- tionsequipmentcapableofsendingandreceiving severalmillionalphanumericcharacterseach second,therearerealneedsforclocksynchroniza- tionsataccuracylevelsofamillionthofasecond andbetter.

1.7.2.TimeScalesforCelestialNavigation

andAstronomicalUses

Aspointedoutpreviously,timeisessentialfor

celestialnavigation.Ifoneknowswhattimeitis (i.e.,solartime)atsomereferencepoint - saythe

GreenwichMeridian - andalsohislocaltimeas

indicatedbyasundial - onecanfigurehislongitude. 11 oooooooo 12 sincetheearthmakesonecompleterevolution (360°)onitsaxisinabout24hours.Forexample, noonGreenwichMeanTimeis0200HawaiianStand- ardTimeor10hoursdifferent.Thus,onecaneasily calculatethatHawaiiisabout10/24oftheway aroundtheworldfromGreenwich,England - i.e., about150°westofthePrimeMeridian.Ifthis personweretomeasuretheactualpositionofthe sunintheskyusing,say,anavigator'ssextant, thenhecouldgetaratheraccuratedetermination oflocalsolartime.Thekeyproblemisknowledge ofcorrecttimeontheGreenwichMeridian.

Nearly200yearsago,amaninEnglandnamed

Harrisonwasawarded£20,000fordesigningand

buildingachronometerwhichwouldallowthe accuratedeterminationoflongitudewhileatsea (lessthan1minuteerrorafter5monthsatsea[44]).

Untilradiosignalswereavailableintheearly1900's,

navigationatseawastotallydependentupongood clocks.Today,therearemanystandardtimebroad- caststationsintheworldwhichcanprovidetime signalsaccuratetobetterthan1secondofearth time,UT1[45].

Ifastronomicaltimecouldbemeasuredwith

sufficientaccuracyandconvenience,thenastro- nomicaltimecouldbeusedforsystemsynchroniza- tionusesalso.Inactuality,astronomicaltimeis difficulttomeasure,andaccuraciesofafew thousanthsofasecondmayberealizedonlyafter theaveragingofawholeevening'ssightingsbya sophisticatedandwell-equippedobservatory.The accuratedeterminationofUT1involvesmeasure- mentsat,atleast,twoobservatorieswidelysepa- ratedinlongitude.

1.8.CONCLUSIONS

Twoverydifferentusesfortimehavebeendis-

cussed.Thefirstisaconventionwhich,when universallyaccepted,allowsbothrapidandefficient communicationssystemstofunction.Theneeds hereareforextremelypreciseanduniformmeas- urementsoftime.Theseconduseisforcelestial navigationandastronomicalobservations.Here thereisnottheneedforhighlyprecisetime,atleast nottothesamedegreeasthefirstmentioneduse.

Becauseoftheconflictingrequirementsimposed

ontimescalesbythesetwocategoriesoftimescale users,therehasbeenagreatdealofefforttoobtain acompromisetimescalewhichadequatelyreflects therelativeimportanceofthesetwousergroups.

Asonemightwellimagine,withthegrowing

importanceandsophisticationofcommunications systemsandtheimplementationofelectronic navigationsystems(toreplacecelestialnavigation), thetrendinthecompromisetimescaleshasbeen awayfromtimescalesbasedontheearth'srotation (i.e.,astronomicaltimescales)andtowardapure atomictimescale.

Inthiscompromisescale,UTC,onefindshimself

inaratherfamiliarsituation.Thereisnotawhole numberofdaysintheyearandonedoesn'twantthe calendartogetbadlyoutofstepwiththeseasons.

Similarly,thereisnotawholenumberofseconds

inasolardayandonedoesn'twantourclocksto getbadlyoutofstepwiththesun.Thesolution (asnotedabove)isanalogoustotheleapyearwith itsextraday;wehaveanextrasecond - aleap secondwhichmustbeaddedordeletedonoccasion.

1.9.REFERENCES

[1]Needham,J.,Ling,W.,anddeSollaPrice,D.J.,Heavenly

Clockwork,254pages(TheUniversityPress,Cambridge,

London,England,1960).

[2]Jones,H.Spencer,"Themeasurementoftime,"Reportson

ProgressinPhysics,4,pp.1-26(1937)(TheUniversity

Press,Cambridge,London,England,1938).

[3]Mueller,I.I.,SphericalandPracticalAstronomyasApplied toGeodesy,pp.319-400(FrederickUngarPublishingCo.,NewYork,N.Y.10003,1969). [4]Ward,F.A.B.,TimeMeasurement,Pt.1-HistoricalReview,

60pages(H.M.S.O.,WilliamClowesandSonsLtd.,

London,England,1961).

[5|Marrison,W.A.,"Theevolutionofthequartzcrystal clock,"BellSys.Tech.J.,27,No.3,pp.510-588(July

1948).

[6]Hood,P.,HowTimeisMeasured,64pages(OxfordUni- versityPress,London,England,1955). [7]Cohn,N.,"Powersystems-timeandfrequency,"Leadsand

NorthrupTech.J.,No.7,pp.3-11(Fall1969).

[8]Lyons,H.,"Atomicclocks,"ScientificAmerican,196,

No.2,pp.71-82(February1957).

[9]Essen,L.,"Timescales,"Metrologia,4,No.4,pp.161-165 (July1969). [10]Becker,G.,"VonderAstronomischenzurAtomphysikali- schenDefinitionderSekunde,"(Fromtheastronomicalto theatomicdefinitionofthesecond.)PTB-Mitteilungen,

76,No.4,pp.315-323andNo.5,pp.415-419(August/

October1966)(inGerman).

[11]Kovalevsky,J.,"Astronomicaltime,"Metrologia,1,No.4, pp.169-180(October1965). [12]Fraser,J.T.,VoicesofTime,pp.281,296,312,401(George

Braziller,Inc.,OneParkAvenue,NewYork,N.Y.

10016,1966).

[13]Cousins,F.W.,Sundials - ASimplifiedApproachbyMeans oftheEquatorialDial,249pages(UniverseBook,Inc.,NewYork,N.Y.10016,1970). [14]Mueller,I.I.,seeRef.[3],pp.141-145. [15]Mueller,I.I.,seeRef.[3],pp.476-518. [16]Guinot,B.,Feissel,M.,andGranveaud,M.,BureauInter- nationaldeI'HeureAnnualReportfor1970,pp.37-62 (BIH,Paris,France,1971). [17]Scheibe,A.,andAdelsberger,U.,"DieTechnischen

EinrichtungenderQuarzuhrenderPhysikalisch-Tech-

nischenReichsansalt,"(Technicaldevelopmentofquartz clocksofthePTR)Hochfrequenz-technikundElektro- akustic,43,pp.37-47(February1934)(inGerman). [18]Essen,L.,Parry,J.V.L.,Markowitz,W.,andHall,R.G., "Variationinthespeedofrotationoftheearthsince1955,"

Nature{Lett.),181,No.4615,p.1054(April12,1958).

[19]Essen,L.,Parry,J.V.L.,andSteele,J.McA.,"Frequency variationsofquartzoscillatorsandtheearth'srotationin termsoftheN.P.L.cesiumstandard,"Proc.Inst.Elec.

Eng.(England),107,PartB,No.33,pp.229-234(May

1960).

[20]Brouwer,D.,"Astudyofthechangesintherateofrotationof theearth,"Astron.J.,57,No.5,pp.125-146(Septem- ber1952). 13 [21]Munk,W.H.,andMacDonald,G.D.F..TheRotationofthe

Earth,Chap.8(CambridgeUniversityPress,London,

England,1960).

[22]Sidorenkov,N.S.,"Neravnomervost'vrashscheniyazemli podannymastronomicheskikhnoblyudeniyzaperiod

1955.5-1965.0gg,"(Non-uniformityintherotationofthe

earthaccordingtothedataofastronomicobservations fortheperiod1955.5-1965.0),AstronomicheskiyJ.(USSR),

44,No.3,pp.650-662(1967-Englishtranslation,NTIS,AD667076,January1968).

[23]Blackman,R.B.,andTukey,J.W.,Th