' ^H

SB V

Sfia

m
\

rf&& NBS TECHNICAL NOTE 689

*<"?CAU O* *

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

A Simulation of the Fluctuations

of International Atomic Time
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

the Institute for Computer Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

States of a complete and consistent system of physical measurement; coordinates that system

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and commerce. The Institute consists of the Office of Measurement Services, the Office of Radiation Measurement and the following Center and divisions:

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for Radiation Research: Nuclear Sciences; Applied Radiation — Laboratory Astrophysics 2 — Cryogenics " — Electromagnetics " — Time and Frequency °. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized materials needed by industry, commerce, educational institutions, and Government; provides

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THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and

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1 Headquarters and Laboratories at Gaithersburg. Maryland, unless otherwise noted; mailing address Washington. DC. 20234.

- Located at Boulder, Colorado 80302.
i.QQ$! : .. .; as itamjarcrs

JAN 31 1877 A Simulation of the Fluctuations

of International Atomic Time

James A. Barnes

Time and Frequency Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

*o*T 0F cD \

>*&J

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward 0. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

-NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued November 1976
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 689

Nat. Bur. Stand. (U.S.), Tech Note 689, 23 pages (November 1976)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1976

For sale by the Superintendent of Documents, U.S. Government Printing Office , Washington, D.C. 20402

(Order by SD Catalog No. C13. 46:689). Price 55 cents (Add 25 percent additional for other than U.S. mailinj
A simulation of the fluctuations of International Atomic Time

James A. Barnes

In the Annual Report for 1975 the International Time Bureau (BIH)

published estimates of noise levels which model the fluctuations in

the International Atomic Time Scale (TAI). Based on these noise levels

for each type of noise, an Auto Regressive, Integrated, Moving Average

(ARIMA) model is constructed. A resulting ARIMA model, which can simulate time fluctuations in TAI, is given by the relation

(1 - if^B - <j) 2

B

2

) A

2 xt

= (1 - &,B - 6

2 B

2

- 9 3

B

3

- 8 4

B 4)a

t

where xt represents the time fluctuations in nanoseconds (ns) of TAI measured at successive intervals of ten days; B is the index-lowering

operator defined by B

n xt

= X+ > A is tne second difference operator

equivalent to (1 - B) ; a. are random, independent variables with a

2 normal distribution, zero mean, and variance of (147 ns) ; and the co- efficients <b. and 8. are given by

! = 1-79, e

1 = 2.93,

2

= -.795, e 2

= -3.12,

e 3

= 1.419,

4

- -0.233

Key words: Frequency stability, International Atomic Time; models

simulation; time scale.

TAI Simulation

In the Annual Report for 1975 [2], the International Time Bureau (BIH) has published the levels of noises thought to perturb the International Atomic Time Scale (TAI).

The levels of these noises which were adopted are as follows:

White phase noise a (t = 60d) = 0.3 x 10" 13 -13

Flicker frequency noise a w ( T ) = 0-5 x 10

-13

Random walk frequency noise a (x = 60d) = 0.15 x 10

where a (t) is the square root of the two-sample (or Allan) variance [3].

For this paper it is specifically assumed that each of these noises is statistically independent of the others, and each is Gaussian in nature. One knows [3] that

o" v (t) ~ xy for each of these noises, where u = -2 for white phase noise; u = for

flicker frequency noise; and u = +1 for random walk frequency noise. Thus, one can calculate the overall expected, two-sample variance, c? (x), for a large range of x-values

by adding the squares of the appropriate functions deduced from the BIH model. Figure 1 provides a graphical representation of this addition.

From the three noise types and the levels given in the BIH Annual Report, one can also determine the estimated power spectral density, S (f), of the time fluctuations,

x(t), of TAI by using the tables in Appendix II of Ref. [3]. That is
White phase noise S x

(f) = 16,124 (ns)

2 /(cycle/10d)

Flicker frequency noise S x (f) = ^f- ^ ns) /( cy cle / 10d )

Random walk frequency noise S v (f) = -t— (ns) /(cycle/10d)

,

where, for this paper, f is taken to be measured in cycles per 10 days (-1.16 x 10 Hz).

Thus, the overall spectrum of xU) for the BIH model is

S (f) = 16,124 + ^- + 9-4^- (ns)

2 /(cycle/10d) 0)

For the purpose of graphical display, Figure 2 is a plot of f S (f) rather than

just S (f). From Figure 2, one obtains the two "break frequencies" of 0.128 and

0.0032 cycles/lOd. These two frequencies will be needed for the development of

an ARIMA model [1] according to the methods given in Appendix B of Ref. [4]. (For

convenience of the reader, Appendix B of Ref. [4] is reproduced at the end of

this paper.)

Figure 3, then, is a Bode plot of the spectrum which is intended to be

modeled (dashed line) with a cascade of ARIMA filters. Superimposed is the

Bode plot of the filter cascade (solid line). Following Ref. [4], the filter

cascade is just

A

2 X

' t

= W

t w

t

= (1 - 0.98 B)u

t

(1 - 0.969 B)u

t

= v t

v t

= (1 - 0.92 B)r

t

(1 - 0.82 B) r

t

= s.t

(2;

s t

= (1 - 0.6 B)q

t

q

t

= (1 - 0.43 B)a

t

,

2 where B is the index lowering operator defined by Bxt = x+i » and A i s the

second-difference operator equivalent to (1 - B) . The coefficients of the

B-operators are calculated from the empirical formula [4]

1 - irf * or =

1 + uf

C

, (3)

c

where f is a "break frequency" in the Bode plot. An autoregressive (AR)

operator (<J>) is used when the Bode plot turns downward in Fig. 3, and a Moving-Average (MA) operator is used when the plot turns upward.

Eliminating the intermediate functions w., u. v. , r. , s. , and q, one obtains

(1 - KB -

<J) 2

B

2

) A

2 x[ = (1 - e-,B - 2 B2

- 9 3

B 3

- 6 4

B 4

)a

t (4)

2
where

1 = 1.79,

2

= -0.795,

2.93,

2 -3.12,

3

= 1.419,

4

" -0.233,

2 If the variance of a. , a , takes on the value

t a

a

2

= (147 ns)

2

, (5)

the spectrum of xj» S'(f), deduced from Equation 3.4.5 of Ref. [2], is a close

fit to the intended spectrum of Equation (1), (see. fig. 4).

One can simulate TAI fluctuations by selecting the initial conditions

xj. = a

t

= for t < 0,

and by letting a. for t M be random, normal deviates with zero mean and a variance

of (147 ns)

2 (see fig. 5). Of course, such simulations are merely representative of

the kinds of fluctuations present in TAI and are in no way estimates of actual TAI errors; that is, they have similar power spectral densities and nothing more. A com- puter algorithm was written to generate 1,000 x( values (1,000 x 10 days - 27.4 years)

simulating TAI. The square root of the two-sample variance, a (t) was computed for

various r-values and is plotted on figure 6 along with the BIH model (solid line). The

uncertainties were obtained from Refs. [5, 6, and 7].

Equation (4) can also be used as the optimum predictor for future fluctuations

in TAI if one has past values. One simply uses as input to the "filter" represented by (4) the optimum predictions of a. for future values. Since the a. are just random, uncorrelated numbers, the optimum prediction for future a. is just

the average value of a

f which has been assumed to be zero. The RMS errors of

such a prediction algorithm can be calculated [4], and are plotted on figure 7. For computational purposes, Equation (4) can be written in a more useful form.

In particular, x+ can be written explicitly as a function of the earlier x+ and the

a. . That is,

Xt

= 3.379xt

_-, - 5.375xt

_ 2 + 3.38Xt _ 3

- 0.795Xt _ 4 + a

t

- 2.93a

t _ 1 (6)

+ 3.12a

t

_ 2

- 1.419a

3 + 0.233 a t

_ 4

.
References

[1] Box, G.E.P., Jenkins, G. M., Time series analysis, Holden-Day, San Francisco,

California (1970).

[2] Rapport Annuel Pour 1975, Bureau International de l'Heure.

[3] Barnes, J. A., et al . , Characterization of frequency stability, IEEE Trans, on Instrum. and Meas., IM-20 , 105-120 (May 1971).

[4] Barnes, J. A., Models for the interpretation of frequency stability measurements,

NBS Technical Note 683 (August 1976).

[5] Lesage, P., Audoin, C, Characterization of frequency stability: uncertainty due

to the finite number of measurements, IEEE Trans, on I&M, IM-22 , No. 2, 157-161

(June 1973).

[6] Lesage, P., Audoin, C. , Correction to: Characterization of frequency stability:

uncertainty due to the finite number of measurements, IEEE Trans, on Instrum.

& Meas., IM-23 , No. 1, 103 (March 1974).

[7] Lesage, P., Audoin, C. , Correction to: Characterization of frequency stability:

uncertainty due to the finite number of measurements, IEEE Trans, on Instrum.

& Meas., IM-25 , No. 3, 270 (September 1976).
T3O

L^ o

3:t—i ' caF - o

l/> S- >> 4-

fO "O (1)

n3

H

S- * fO

0) > E

•I— OJ

4-> 1—

CD E i

fC Q. on E 1 fO o

co S

1— o . o i

CD

x/»
1000

100

10

Flicker frequency

10

71 10

Frequency (cycles/10 days)

Figure 2 . Plot of f S (f ) for BIH model ° x

Dashed lines represent individual

noise components from BIH model.
10 13

>>

O)

to

S-

+-> o

CDQ.

I/O

SO)2

o

10

12

10

11

10

10

109

10

c

10'

10

l

10

v

10'

\ Slope -4 \ ^

Slope "3^^0w

j\

Slope -4

>v fc^—Slope -2

\v

^V

^ Slope

10" 3 10" 2 10

Frequency (cycles/10 days)

Figure 3. Bode plot of BIH model spectrum (dashed)

and ARIMA model spectrum (solid)

•1
1000

I/O

100

10

^^v\\NX\\ BIH model

ARIMA model '

10

-3 10" £ 10"

Frequency (cycles/10 days)

1

Figure 4. Plot of f S'(f) for ARIMA model

designed to simulate BIH model
—

O)o

o

UJ

t- 4-

I— o

I OCM

'srt) jouj3 >|do LD
-a

Ol +j O 03

i

<-

)

3

,

-—

v

—

l/) •i— >> c/1 i

03 CD T3 E "O O O

S- E

H

CU i—i » <_) CQ

O) c

cz 03 O

•i— - +->

4-> 03 T3

0) > 0)

1

S- Q. OJ 03

f= i— Q_

03 a- E

oo E O

03 CJ

1 03 O +-> 2 03

1) D

10
T1 year

Prediction Time (days^

T

10 years

10,000

Figure 7- RMS Prediction Errors for ARIMA Model of TAI

11
The following is an exact reproduction of Appendix B of

[4], "Models for the interpretation of frequency stability

measurements," NBS Technical Note 682 (August 1976)

12
Appendix B. Building an ARIMA Model to Fit a Given Spectrum

In general, ARIMA models can approximate a wide range of spectral shapes. This

appendix, however, will consider only a rather restricted set of these models. Also,

the objective of this appendix is to provide a means of building an ARIMA model to fit

a prescribed spectrum. Other techniques [12] emphasize the building of ARIMA models to fit a particular data set regardless of its spectrum.

One method of simulating a flicker noise with ARIMA models has already been published

[21]. The treatment here will be a graphical approach using Bode plots.

Consider a random, uncorrected, Gaussianly distributed, discrete time series, a f , 2 with mean zero and variance a . Also consider a time series au deduced from the a

t by

the equation

to. - 0-, to. n -4>oW, „ - . .

. -* to, „ - a, - 6-, a. -, t 1 t-1 r

2 t-2 Y p t-p t 1 t-1

} 2 a t-2 " ••• " q

a t-q'

(B-l)

where the cJj^'s and -

' s are constants. We can define the index-lowering operator, B,

by the relation

BXt^Xt-T (B-2)

This allows (B-l) to be rewritten in the form

(1 - ^B - <j> 2 B - ... - * B

p

) a)t

= (1 - 0.B - (D 2

B

2

- . .

. - <j> B q

)a. (B-3)

The expression in parentheses on the left side of (B-3) is called the Auto Regressive (AR)

operator of order p. That on the right is called the Moving Average (MA) operator of

order q. We can further define another time series, Z t by the relation

A

d

Z t

= oj t

, (B-4)

where AZ

t = (l-B)Zt = Z. - Z

t

_-| . That is, Z

t is the d-fold (finite) integral of to t

. Thus,

Z. is an Auto Regressive, Integrated, Moving Average process defined by the cj> - 's,6 n

- 's , o\,

and the d differences of (B-4). In particular it is an ARIMA (p,d,q) process.

In order for to t to be stationary and invertible, there are restrictions on the cD's and e's [12]. However, for the present discussions it will suffice to consider only the

following two processes

to t

= (1 - 6B)a

t (B-5)

(1 - *B)x

t

= yt (B-6)

For this case it is sufficient that -1 < 6 < 1 and -1 < <d < 1

.

13
In these equations one sees that if one sets <J> = 8 and y^ = co^., then one obtains

Xf = a t

. That is, if one considers (B-5) and (B-6) to define two digital filters,

then (B-5) and (B-6) are inverse filters for each other when cj> = 9. Thus, it is a simple

matter to extend any understanding one gains about one filter to the other.

It is of value to consider the effect of a single MA filter of the form (B-5) when

9 is further restricted to the interval <_ 9 < 1. Figure (B-l) shows the general behavior

of the transfer function (magnitude squared) of such a filter and the straight-line approximations to this transfer function. The "knee" in the approximation occurs at a frequency

f

c which is related to 9 by the empirical relationship

1—rrf 9 * tt^t • < B

" 7 > c

which will not be derived here.

Similarly, Fig. (B-2) is the transfer function of the AR filter with cj> = 9 = 0.728 as

in Fig. (B-l). Hence, also,

1-TTf

1+fff

c

We can now construct an approximation to a process which is a mixture of flicker noise

and white noise. Figure (B-3) shows the Bode plot of the desired filter transfer function.

The frequency axis of Fig. (B-3) is in terms of cycles per data spacing. Thus, the Nyquist

frequency is just 1/2. For the sake of the example, we will assume that it is sufficient

to approximate the spectrum to a lower frequency of .002 (cycles per data spacing).

Figure (B-4) superimposes the Bode plot of the filter which will be used onto the

spectrum of Fig. (B-3). From each of the "knees" in the approximation one can determine

the appropriate <(> or 9 for a filter to be cascaded in series.

Thus, from "knees" at the frequencies of .0233 and .0033, one obtains <j>'s for the

AR filters (eq. B-6) of .8636 and .9795, respectively. These numbers have been calculated

from eq. (B-8). Similarly, from the "knees" at the frequencies of .062 and .0087, one obtains 9 values of .6740 and .9468, respectively, for the MA filters. One decides to use an AR filter if the function turns downward in response with increasing frequency as

in Fig. (B-2). Correspondingly, one chooses a MA filter when the function turns upward as

in Fig. (B-l).

The final filter can be obtained by cascading the output of one filter to the input

of the next in the form

Ut = (1 - .6740B)a

t

(1 - .8636B) x

t

= "

t (B _ g)

yt

= (1 - -9468B)x

t

(1 - .9795B) z t

= y t

14
10

co

Q-

</) HI

.1

.001 Frequency

Fig. (B-l) Transfer Function of Simple MA- Filter

15
f = 0.05

c

*^

\

(1 - *B)Z

t

= a

t \\

<() = 0.728 \V

V

\\

Slope \ \^^

-6 db/oct. \

\

001 .0' 1 1 Frequency

Fig. (B-2) Transfer Function of Simple AR-Filter

16
S. Slope ^^ -3 db/oct.

.001 .01 1 Frequency

Fig- (B-3) Bode Plot of Desired Spectrum

17
100

10

>>

CD o

CL OO

\

\

\N f = .0033

c \

\N \ CI \ Slope ^ \ -6 db/oct

\ \

\\

\ f = .0233

f = .0087

c . \ Slope N \ -6 db/oct.

\\

f = .062

c

,001 .01 1 Frequency

Fig. (B-4) Bode Plot of Filter Cascade

18
where a t is the input to the cascade and z

t is the output. One can eliminate ut

, Xt

and yt and write an equivalent expression in the form

(1 - ^B - 4> 2

B

2 )z

t

= (1 - e.,B - 6

2 B

2 )a

t

, (B-10)

where

c|>, = 1.8431, 9, = 1.6208

1 ' (B-ll)

<J> 2

= -.8459,

2

= -.6381 .

Making use of equation (4.2) one can obtain the spectrum corresponding to (B-10).

Figure (B-5) is a plot of the spectrum superimposed on the Bode plot of Figure (B-3).

The parameter a

2

= 0.319 was selected to make the spectrum fit the Bode plot in amplitude.

In this example, one could let Zj- model the frequency of an oscillator, and it is clearly stationary [12]. To model the phase, one could define a parameter v^ by the

relation

(1 - 4>'B)v

t = z t (B-12)

where -. -

, is large compared to any data sample to be tested.

In the current example f^ was taken as .002. Thus, one could select <|> ' ~ .99999

to be quite adequate. Note that v

t is also stationary.

By selecting <j>' = .99999 one obtains a stationary model for v

t if one so desires.

Of course, for actually generating a data set one could use <J>' = 1, since no observational difference in the simulated data would result--that is why <j>' was chosen as close to unity as it was. Thus, the entire difference between a stationary and a nonstationary model (v t

) for the phase is centered in whether one chooses .99999 or unityfor tj>'. Further, this choice is totally unobservable for short data sets

(N ~ l/f

a

= 500).

Clearly, these techniques could be used to develop an ARIMA model to simulate

data over a much broader range of frequencies than done here. In any event, equations

(B-10) and (B-12) allow one to simulate a stationary noise with the desired spectrum.

19
.001 f = .002

Frequency

Fig. (B-5) Actual Spectrum of ARIMA (2,0,2) Model

20
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS-TN-689

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Simulation of the Fluctuations of International Atomic Time

5. Publication Date November 1976

6. Performing Organization Code

277.00

7. AUTHOR(S)

James A. Barnes

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2770900

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as Item 9

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

In the Annual Report for 1975 the International Time Bureau (BIH) published

estimates of noise levels which model the fluctuations in the International Atomic

Time Scale (TAD. Based on these noise levels for each type of noise, an Auto Regressive, Integrated, Moving Average (ARIMA) model is constructed. A resulting ARIMA

model, which can simulate time fluctuations in TAI, is given by the relation

(1 - (f>.|B - cf> 2 B

2

) A

2xt

= (1 - 6-jB - 9

2 B

2

- 9

3

B

3

- 6

4

B4)a

t where x+ represents the time fluctuations in nanoseconds (ns) of TAI measured at

successive intervals of ten days; B is the index-lowering operator defined by B x+ = Xt-n> a2 1S tne second difference operator equivalent to (1 - B)2; a^ are random,

independent variables with a normal distribution, zero mean, and variance of (147 ns)2

and the coefficients <f>. and 0. are given by

*! = 1-79, 9

1 = 2.93,

<f> 2

= -.795, e

2

= -3.12,

e 3

= 1.419,

e 4

= -0.233.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Frequency stability; International Atomic Time; models; simulation; time scale

simulation.

18. AVAILABILITY \\2 Unlimited

I For Official Distribution. Do Not Release to NTIS

J Order From Sup. of Doc, U.S. Government Printing. Of fie Washington, D.C. 20402, SD Cat. No. C13 -4b : o9

1 ! Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

23

22. Price

$0.55

it u. S. GOVERNMENT PRINTING OFFICE: 1977—777-045/1211 REGION NO. 8 USCOMM-DC 29042-P74

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special publications appropriate to this grouping such

as wall charts, pocket cards, and bibliographies.

Applied Mathematics Series—Mathematical tables, manuals, and studies of special interest to physicists, engineers, chemists, biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides

quantitative data on the physical and chemical properties of materials, compiled from the world's literature and critically evaluated. Developed under a world-wide

program coordinated by NBS. Program under authority

of National Standard Data Act (Public Law 90-396).

NOTE: At present the principal publication outlet for these data is the Journal of Physical and Chemical

Reference Data (JPCRD) published quarterly for NBS

by the American Chemical Society (ACS) and the American Institute of Physics (AIP). Subscriptions, reprints,

and supplements available from ACS, 1155 Sixteenth

St. N.W., Wash. D. C. 20056. Building Science Series—Disseminates technical infor- mation developed at the Bureau on building materials,

components, systems, and whole structures. The series presents research results, test methods, and performance criteria related to the structural and environmental

functions and the durability and safety characteristics

of building elements and systems.

Technical Notes—Studies or reports which are complete

in themselves but restrictive in their treatment of a

subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under proce- dures published by the Department of Commerce in Part

10, Title 15, of the Code of Federal Regulations. The

purpose of the standards is to establish nationally rec- ognized requirements for products, and to provide all concerned interests with a basis for common understanding of the characteristics of the products. NBS

administers this program as a supplement to the activities of the private sector standardizing organizations.

Consumer Information Series—Practical information,

based on NBS research and experience, covering areas

of interest to the consumer. Easily understandable language and illustrations provide useful background knowledge for shopping in today's technological marketplace.

Order above NBS publications from: Superintendent

of Documents, Government Printing Office, Washington,

B.C. 20^02. Order following NBS publications—NBSIR's and FIPS

from the National Technical Information Services,

Spyingfield, Va. 22161. Federal Information Processing Standards Publications (FIPS PUBS)—Publications in this series collectively constitute the Federal Information Processing Standards Register. Register serves as the official source of information in the Federal Government regarding stand- ards issued by NBS pursuant to the Federal Property

and Administrative Services Act of 1949 as amended,

Public Law 89-306 (79 Stat. 1127), and as implemented

by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal

Regulations).

NBS Interagency Reports (NBSIR)—A special series of interim or final reports on work performed by NBS for outside sponsors (both government and non-government). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Services (Springfield, Va. 22161) in paper copy or microfiche form.

BIBLIOGRAPHIC SUBSCRIPTION SERVICES

The following current-awareness and literature-survey

bibliographies are issued periodically by the Bureau:

Cryogenic Data Center Current Awareness Service. A

literature survey issued biweekly. Annual subscription: Domestic, $20.00; Foreign, $25.00.

Liquified Natural Gas. A literature survey issued quarterly. Annual subscription: $20.00.

Superconducting Devices and Materials. A literature survey issued quarterly. Annual subscription: $20.00.

Send subscription orders and remittances for the pre- ceding bibliographic services to National Bureau of Standards, Cryogenic Data Center (275.02) Boulder,

Colorado 80302.
U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Washington. D.C. 20234

OFFICIAL BUSINESS

Penalty for Private Use. $300

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