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Robert Morris Hearing God is not something you do Hearing God Frequency: Tune in Hear God someone you are The Christian Broadcasting Network
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-Everybody Always by Bob Goff -Love Does by Bob Goff Growing Spiritually: -Frequency: Tune In Hear God By Robert Morris
the smart resonance tube - Mechatronics
mechatronics engineering nyu edu/ pdf /tsrt-report pdf
Robert Morris (Clarkstown High School North) DC Motor, position and sound sensors, a frequency generator, and a seven segment display The hope is to
Time and frequency: theory and fundamentals
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It is indeed fitting that a time and frequency Monograph should appear now Robert J Harrach, "Some accuracy limiting effects in an atomic
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Morris on Rhythmic symbols and so forth page 1 Robert Morris 1) Rhythmic symbols say B is the frequency of the clicks and d is the wavelength
ROBERT E PIPHER GLENN K MORRIS Frequency modulation (FM
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Frequency modulation (FM) is defined by Dumortier (1963) as a change in carrier frequency during the course of a signal Such changes occur within the
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RAINFALL FREQUENCY ATLAS OF THE MIDWEST
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RAINFALL FREQUENCY ATLAS OF THE MIDWEST by Floyd A Huff and James R Angel Midwestern Climate Center Climate Analysis Center National Weather Service
113430_3nbsmonograph140.pdf
DATEDUE
WOTI.921teILL
- , - ____
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