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1962 IRE TRANSACTIONS ON INSTRUMENTATION 259

Te Atomic Time ScaleWILLIAM MARKOWITZt

Summary-The atomic time scale A.1 is based on an assumed The atomic time scale, A.1, was defined as follows [3]:frequency of 9 192 631 770 cps of Ephemeris time, and is derivedfrom the operation of cesium resonators at 9 laboratories. Coordi- 1) A clock which keeps time A. 1 advances one secondnated transmissions of time and frequency make the atomic time in the interval required for 9 192 631 770 oscilla-scale available. The International Committee of Weights and tions of cesium at zero field.Measures may redefine the unit of time interval, the second, by anatomic transition in 1966. 2) At Oh Om Os UT2 on January 1, 1958, the value of

A.1 was Oh Om Os.INTRODUCTION

Tp HE CONSTRUCTION of a precise cesium-beam The difference in time between A. 1 and UT2 and be-atomic resonator at Teddington in 1955 made it tween A. 1 and time signals emitted from NBA andpossible to establish an atomic time scale which is WWV are given in the Time Service Bulletins issued by

independent of astronomical time scales, such as Ephem- the U. S. Naval Observatory. Values for WWV fromeris time and Universal time. The atomic time scale September 13, 1956, to January 1, 1959, are given inis generated by the quantum transition of an atom Time Service Notice No. 6, and are available back towhereas the astronomical time scales are generated by June 15, 1955.the motions of the celestial bodies. Although the atomic DERIVATION OF A. 1and astronomical time scales are independent, it isnecessary that the relation between all time scales be Thesytemof Atomi time,aAors is aed on tmaintained continuously with the highest possible operation of cesium resonators at the following 9precision, both as concerns the unit of time and epoch. laboratores: Naval Observatory, Washington; NavalThe frequency of cesium was determined by the Na- Research Laboratory, Washington; Naval Observatory

tional Physical Laboratory, Teddington, and the U. S. Time Service Substation, Richmond, Fla; NationalNaval Observatory, Washington, in 1958, to be 9 192 Bureau of Standards, Boulder; Cruft Laboratory,631 770 + 20 cps of Ephemeris time [1],[2]. On January 1 HaIrvard; National Research Council, Ottawa; National1959, the Naval Observatory established the system of Physical Laboratory, Teddington; Centre NationalAtomic time, A.l, based on the adopted frequency of dEtudes des Telecommunications, Paris; and, Labora-9 192 631 770 cps. The system A.1 is used for the inter- toire Suisse de Recherches Horlogeres, Neuchatel,national comparison of frequencies of atomic and molec- Switzerland. These laboratories monitor the frequencyuariof cymdevices, andforquenciesoftothin obser of NBA on 18 kc/s and report each month the value of theofarEpemeri tim Uni et .. frequency for each day with respect to its cesium reso-of Ephemeris time and Universal time.

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Since 1956, the fundamental unit of time has been nator.identical with the second of Ephemeris time. Recoin- A weight is accorded to each resonator which dependsmendations have been made that the second be rede- upon the deviation of the monthly average with respectfined in terms of an atomic transition, and such a change to the mean of all 9 stations. A systematic correctionmay be made in 1966. with respect to the weighted mean is obtained for each

resonator for each month. These corrections are appliedATOMIc TIME to obtain adopted deviations in frequency of NBA,

Atomic time is derived from the continuous operation GI3R, WWV, etc., for each day on the system A. 1.of an atomic clock. This is defined as any device which An analysis of the results obtained since 1960 showsindicates time and whose rate is governed by a quantum that the probable error of the deviation from the meantransition. The best way to construct an atomic clock of the frequency of a single cesium resonator is 1 part inthus far, is to operate a quartz-crystal oscillator and 1010, the stability from month to month is 5 partsin 1011,clock movement in conjunction with an atomic fre- and that the system A.1 is stable from month to monthquency source. The first two run continuously, but the to 2 parts in 1011. Improvements have been made inlatter is operated about an hour each day to check the atomic frequency devices recently and in the transferfrequency of the quartz oscillator. of time information, and the accuracy of the system A. 1An atomic clock does not furnish epoch, and the value is being increased.

of Atomic time at a particular epoch must be selected. TRANSFER OF ATOMIC TIME

* Received September 11, 1962. Presented at the 1962 Interna- The most accurate method of transferring time andtional Conference on Precision Electromagnetic Measurements as frequency is by radio transmlissions. Frequency may be

t U. S. Naval Observatory, Washington, D. C. calibrated to a few parts in 1011 by monitoring the phase

240 IRE TRANSACTIONS ON INSTRUMENTATION Decemberof a stabilized VLF transmission over a 24-hour interval. 3) that the time signals should consist of impulses

Loran-C, which is a pulsed radio navigational system repeated at intervals of one second and maintainedoperating on 100 kc/s, offers the means of transferring within approximately 100 msec of Universal timetime with very high precision. The transmissions from (UT2). Changes in the phase of the pulses shouldthe master East Coast station at Cape Fear, N. C., are be exactly 50 msec and should be made simultane-controlled with respect to an atomic clock by the Naval ously by the stations concerned.Observatory with the cooperation of the NationalBureau of Standards. Synchronization of clocks within It is expected that jump changes in phase will beBurean of Stany ards.ation of aclmay betob- required possibly once in several years and possiblyrange of any station of a chain to 1 psec may be Ob_tained. For frequency control purposes, a local clock not at all.mav be compared to that at the master transmitting sta- The offset frequencies which have been used are astion to 0.1 ,usec. Hence, the average frequency of the follows, in parts in 1010: 1959, -170; 1960 and 1961,tioto

-15In 1962 Hence, the avensrage frrequenciesthlocal oscillator can be compared to that at the master -150; and 1962, -130. The transmitted frequenciesstation to 1 part in 1012 in 1 day or 1 part in 1013 in about are lower than that corresponding to 770.a week.

Experiments are planned for the use of the artificial QUARTZ-CRYSTAL OSCILLATORSsatellites, Telstar and Transit, to transfer time between Quartz-crystal oscillators play an important role incontinents. deriving and providing Atomic time. It is desired that

TRANSMISSION OF ATOM'IIc TIME oscillators used for these purposes shall have low fre-The introduction of Atomic time has made the total quency drift and shall be free from sudden changes in

number of time scales in use equal to seven, namely, rate.Atomic, Ephemeris, true sidereal, mean sidereal, UTO, The quartz oscillators that have been found to meetUTI, and UT2. There is required for immediate use the these requirements best use the 2.5-Mc crystal de-interval of Atomic time, for physics, and the epoch of veloped by A. W. Warner at the Bell Telephone Labora-Universal time, for navigation. The transmission of two tories. Model GS-60158, made by the Western Electrickinds of seconds pulses would result in confusion. Company, was developed in consultation with theThrough international cooperation a method has been Radio Techniques Division of the Naval Researchevolved which supplies both needs. Laboratory. Sulzer Laboratories have also developed a

In 1959, MSF, Rugby, began transmitting on a sys- 2.5-Mc oscillator, deinoted model 2.5. The 2.5-M1c crys-tem wherein the frequency was maintained conistant tals used in both oscillators were made by the Blileyduring each year but was offset from ... 770 so that the Electric Company.time pulses would remain close to UT2. In the same The drift rates with respect to A.1 of several of thesetzme~~~ ~ ~ ~ ~~ ~~c'ltrpulses arel locatedclosthoNaval lIlstneasameyear it was agreed to coordinate the transmissions of oscillators which are located at the Naval Observatorytime and frequency in the U. K. and U. S. from GBR or are under its control have been determined for inter-MSF, NBA, WWV, and WWVH, on this system. Other vals of 3 months to 1 yrear. Observed drift rates are 3stations which now participate in the coordination plan parts in 1011, 2 parts in 1012 (two oscillators), and 5include LOL, Argentina; VUP, Australia; CHU, parts in 10 per dayCanada; JJY, Japan; ZUO, South Africa; and, HBN,Switzerland. The coordinated stations emit time signals DEFINITION OF THE SECONDin synchronism to about 1 msec and transmit the same The fundamental unit of time interval, the second,frequency to about 1 part in 1010. was formerly defined as 1/86,400 of the mean solar day.The transmissions are now made in accordance with In 1956, the International Committee of Weights and

recommendations adopted at an interim meeting held Measures redefined the second as follows: "The secondin May, 1962, by the International Consultative Com- is the fraction 1/31,556,925.9747 of the tropical year formittee for Radio (CCIR). These are: 12h E. T. of January 0, 1900."

1) that the standard frequency and time pulses at The General Conference of Weights and M1easureseach transmitting station be generated from the recommended in 1960 that consideration be given at thesame oscillator; next general conference, to be held in 1966, to redefin-

2) that the frequency be maintained constant each ing the second in terms of a quantum transition. Ayear with reference to atomic standards of fre- similar recommendation was adopted by the Consulta-quency, but be offset to keep the time pulses in tive Committee for the Definition of the Second in 1961.close agreement with UT2; the offset to be used We may inquire with what probable error the fre-each year will be that adopted by the Bureau quency of a selected transition could be determinedde l'Heure after consultation with the observa- about 1965, with respect to the second as now definedtories concerned. This offset is expressed in the and as obtained through observations of the moon.time scale in which the frequency of cesium has The fundamental measure of Ephemeris time is basedthe value f(C8) =0 192 631 770 cps; on the orbital motion of the earth about the sun. The

1962 Markowitz: The Atomic Time Scale 241position of the earth is obtained by observing the sun. In 1965, there will be available 10 years of lunar ob-In his Tables of the Sun [5], Simon Newcomb gives the servations made by photography and from observationsfollowing formula for the mean longitude of the sun, of occultations and meridian transits. This materialthat is, the longitude with periodic terms removed; should furnish the frequency of cesium with a probable

error of about + 5 cps, assuming there is no error in theL 2790 41' 48.04 + 129 602 768.:13T + 1-f089T2* (1) lunar ephemeris. What contribution to the total errorThe unit of time, T, is 1 Julian ephemeris Century. will be due to the ephemeris cannot be forecast with

This is 365.25X 100OXK86,400=3,155,760,000 ephemeris much certainty.Thiseconds365.2F (1) h been adopted as tphemfra One type of uncertainty in the lunar theory is in theseconds. Formula (1) has been adopted as the funda-petrainpodcdb th plitsfrwihmental definition of Ephemeris time. By definition, the perturbations produced by the planets, for whichepoch when T=O is denoted 12h Ephemeris time of Brown's developments have not yet been verified.January 0, 1900, which is the same as 12h Ephemeris A second uncertainty is the value of the coefficient oftime of December 31,1899. the quadratic term in (2), which was introduced to allowThe length of the tropical year is the time required for for the effect of tidal friction the motion of the moon.

L to increase 366'. It may be found that this equals We are not certain what portion of the observed secular31,556,925.9747 seconds of Ephemeris time when T=O. acceleration of the moon is due to tidal friction, whichThe sun moves slowly with respect to the stars, about affects both the speed of rotation of the earth and the

0"04 per second. The moon moves more rapidly, about motion of the moon, and what portion is due to the ir-0"55 per second, and is more suitable for determining regular variation in speed of rotation of the earth, whichEphemeris time. In 1955, the International Astronomi- does not affect the moon. The two effects can be sepa-cal Union (I.A.U.) recommended that observations of rated by utilizing observations of the motions of thethe moon should be used in conjunction with the Im- planets, but not with the accuracy that is desired.proved Lunar Ephemeris to obtain Ephemeris time in D. Brouwer [6] found that the coefficient of thepractice. quadratic term required a correction of +2"'2 with aThe Improved Lunar Ephemeris is based on the probable error of + 2 "6. An error of 1 " in the coefficient

theory of the motion of the moon1 developed by E. W. of T2 would cause an error in the time scale of Ephem-Brown, with the following corrections recommended by eris time of 1.2 X 10-9 T, where T is in centuries fromthe I.A.U. added: 1900. For observations made up to 1965, the mean epoch

will be near 1960, and the probable error in the time1) The empirical term with coefficient 10"71 and scale would be + 18 X 10-1.

period 257 years should be removed. A third source of uncertainty in the lunar ephemeris2) There is to be added to the mean longitude of the is due to possible errors in the values of the constants

moon: which enter in the periodic terms. C. A. Murray haspointed out that Brown adopted 1/294 for the oblate-

Al = - 8"72 - 26".'74T - 11"22T2. (2) ness of the earth for his lunar theory whereas the ac-3) Two periodic terms, whose sum amounts at most cepted value is about 1/298. A change from 1/294 to

to O'025, are to be added. 1/298 would require that Ephemeris time determinedwith the Improved Lunar Ephemeris should be corrected

The Improved Lunar Ephemeris was published in a by +0S36 sin Q, where Q is the mean longitude of theseparate volume for the years 1952 through 1959. Since moon's node. The period of this term is 18.6 years.1960, it is given in the national ephemerides. Brown knew that the best value of the oblateness was

It should be noted that the fundamental definition of 1/298. His problem was to adopt numerical values forEphemeris time is contained in (1). If a new theory of about 50 constants, not all independent, so that histhe sun should be constructed in the future it would be lunar theory would best produce agreement with ob-necessary that the first two coefficients be retained. servations made in the past, that is, up to about 1900.However, if a new lunar ephemeris were constructed all I have studied this problem recently and havethree terms in (2) might be modified. analyzed t...