1 0/22/1 2^1 0/22/1

National Bureau of Standards ^ -t<ibrary, n.W. Bldg

APR 1 9 1963

^ecUnlcui ^^ote 173

TABLES TO FACILITATE THE DETERMINATION

OF THE FERRIMAGNETIC RESONANCE UNEWIDTH

OF NON-METALLIC MAGNETIC MATERIALS

CONSTANCE C. PRESTON AND WILLIAM E. CASE

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS

^ecknical *^liote. 173

ISSUED APRIL 15, 1963

TABLES TO FACILITATE THE DETERMINATION

OF THE FERRIMAGNETIC RESONANCE LINEWIDTH

OF NON-METALLIC MAGNETIC MATERIALS

Constance C. Preston and William E. Case

Radio Standards Laboratory

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 25 cents
Contents

Page

Introduction ---------------------- 1 Method ------------------------ 2

References --------------------- 6

Appendix ----------------------- 7

n
Tables to Facilitate the Determination of the Ferrimagnetic

Resonance Linewidth of Non- Metallic Magnetic Materials

Constance C. Preston and William. E. Case

A common test procedure for measuring ferrimagnetic resonance linewidth, AH, and gyromagnetic ratio, y» ^^ microwave ferrites is based upon a perturbation analysis of the complex frequency

shift obtained when a small sample is placed in a resonant cavity and

an applied dc magnetic field. However, this method necessitates the

plotting of a ferrimagnetic resonance loss curve. To find AH it is

possible to derive an equation using lumped circuit theory which reduces

the number of needed measurements to four attenuator readings.

This paper provides a table which gives values of attenuation

according to the following formula which facilitates the determination

of linewidth:

A - A

o r A = 20 log 2 - 20 log (10 ^° + 1) for A -A -0.41(0.01)32.40. o o » Or

INTRODUCTION

Microwave devices such as isolators, phase shifters, and

circulators utilize ferrite inaterials which exhibit ferrimagnetic resonance phenomena at microwave frequencies. Two important properties of ferrites at these frequencies are the effective gyromagnetic

ratio, Y, and the ferrimagnetic resonance linewidth, AH.

Both of these properties of a ferrite material can be determined by inserting a small sample in a cavity and measuring the transmission loss of the system. It is assumed that the sample is sufficiently small for the perturbation theory to be applicable. Measurements may be made by holding the input power to the cavity constant,

varying the applied dc field, measuring the complex resonant frequency

with and without the sample, and plotting the imaginary susceptibility

curve. Linewidth is defined as the separation of the two dc field values at which the power absorbed by the ferrite sample is one half the

maximum absorption.

^See reference 1 on page 6,
The above method requires a number of measurements to

complete the curve. By using the accepted expressions for the relationship between the Q and transmission loss of a loaded and unloaded

resonant cavity , it is possible to derive a formula (see Appendix I)

whereby the linewidth can be determined by making only four measurements. The Non-Metallic Magnetic Materials Subcommittee VII

of ASTM, Committee CZl, has proposed specifications for this method

in which spherical-shaped ferrite samples are measured in a rectangular TE resonant cavity.

METHOD

A block diagram of the experimental setup used for this

method is shown in Figure 1. A constant input power to the precision

calibrated attenuator as monitored by the power detector is assumed.

The frequency is adjusted to give cavity resonance for the empty cavity, and the precision attenuator is set to A to give a convenient output reference level as indicated on the output detector. The sample

is then inserted, the dc magnetic field adjusted for maximum absorption in the sample, the frequency adjusted for cavity resonance, and

the precision attenuator set to obtain the same output reference signal.

The new attenuator reading is defined as A , and the dc field reading

is defined as H .

The attenuator reading corresponding to the half-power points

on the ferrimagnetic resonance loss curve of the sample is calculated

fr'om the following formula as derived on page 12 of the Appendix:

A - A

o r 20 Ai = A + 20 log 2 - 20 log (10 + 1).

2 O

The attenuator is now set at the calculated Ai value. The dc magnetic

2 field necessary to return the output power to its previous level on one

side of resonance is then read and recorded. The dc field is then similarly adjusted and recorded for the other side of resonance. The difference between these two dc field measurements is the linewidth, AH.

For all measurements, the frequency must be adjusted to cavity resonance.

Calculating Al each time a measurement is made is timeconsuming and prone to error. Time delay between maximum loss

and half-power ineasurements can introduce error due to equipment

drift. Faster and more accurate data can be taken using the following

See reference 2 on page 6.
table which gives values of A for A^ - Aj, from . 41 to 32. 40 decibels

where A is defined as:

A - A

o r 20

A = 20 log 2 - 20 log (10 + 1) ,

and thus,

Ai = A + A

The above technique is essentially an rf substitution method.

However, an IF substitution method as shown in Figure 2 'may be used

for greater accuracy if a 30 Mc/s high precision piston attenuator is

available because, generally, a lower frequency IF piston attenuator

can be made more accurate than an rf attenuator. The IF system has

the advantage of greater accuracy, greater sensitivity, and that the

same IF attenuator can be used for different rf frequencies. Disadvantages of the system are that more equipment, more complicated

tuning, and separate local oscillators are required for each frequency.

The piston attenuator is inserted between the cavity and the output detector. The procedure is the same as for the rf substitution method

except that the input power to the cavity is held constant, and the power

level to the IF detector is maintained constant by adjusting the piston

attenuator.

The effective gyromagnetic ratio, y, is determined from the

sphere measurement data by the formula,

2TTf r H

r

where f^. is the microwave frequency required for cavity resonance at

maximum sample absorption, and H^. is the corresponding dc field.

The gyromagnetic ratio is sometimes expressed in terms of the apparent g factor in which case the above expression becomes

f f r _. r 1.3995H 1.4H

r r

if f is in Mc and H is in oersteds,

r r
ULU O car 1 1

Q=

O C33 z •<: O 1— ^ c=> = •«c QC CO LU s ^ > " 1= S CO

a.

t3£ oe

LU LU

o- ac *~) c

ae. \

LU 2 } , »— ' \—LU >-

»—

VARI

ATTE 1

1 1 1 1 tS "-^

T^- ^ LU >-U . 1-V»

FREQl EASU "^ ^

rf. oc

o- 1 o

CO

CD

CO

LU> LU 1— nr- «- ^ <^ —> 111 III 1 = ^ S' ^ _ CO O ^ ^

f- o

LjJ LU

LU

O

(T <

CO

LU

O <

LU
1 s

er: / 1— . 2S <=> 1 ''''' >—'

LU \

C3 5O \ ^

1— ^ ? " CJ 7

oc oc , 1 \ 1 1 11 1 i

LU LU O LU

a- 2E **^

oc LU <=» ^ ^ c^ S

?2 =3 <=> 1— «C 3^ •«c OS LU f"* 7^ 55 -a: ^^ 2 CO

t5 ^*J -^ ^c

LU LU

FREQl

MEASU "*^

<«- oc

D

OR

OLATO OCAL

LLATO ocLUX

TPUT

OWER ETER ^ ^ CO ^ o °- ^ o u

WAVE RCE

—1 oc LU O 1 K— OO Z -cC ^ C3 ^

-F LIFIER C3 —> — — ar <-> is ce CO LU > " tr "«C ^ ^ ^

OI- o

LU LU

LU CD

(T <

(^

O < tr S CD p ^ LI- < Q

LU

X

Q: I- oX

=> !=! UJ O ^ ^

LU 3 ^ I- ^ cr u.

Q- z iz O

LU

q: I- LU

CD LU

X < 2 I- ^Q CD< CD O ^ ^ H q: (^ < q: ^ ^ ^ r^ LU Ll. O X h-

(_) Li_ <

CO

O q:

C\J

LU

cr

CD

Ll.
REFERENCES

1. R. F. Soohoo, "Theory and Application of Ferrites, " p. Z60-263,

(Prentice-Hall, Inc. , Englewood Cliffs, New Jersey, I960).

Z. C. G. Montgomery (ed. ), "Techniques of Microwave

Measurements, " p. 289-291, (McGraw-Hill Book Company,

Inc. , New York, 1947).
APPENDIX

The equivalent circuit for a transmission microwave cavityis commonly shown as in Figure 3 (see reference 2).

FIG. 3 EQUIVALENT CIRCUIT FOR TRANSMISSION LINE CAVITY

COUPLED TO MATCHED GENERATOR AND LOAD

where

R resistance representing loss of empty cavity

R = resistance representing loss due to sample

2

'1 -o Nt'^Z^ = resistance of matched generator

N Z = resistance of matched load

2 o Assume that the output power is kept constant by varying the input power

(input voltage NjE) by means of a matched precision adjustable attenuator. We now write the power [ Pioad ~ ^2^oUI 1 delivered to the

load for the following three conditions:

(1) Empty cavity E = E : R =

1 s

P = a ..222

N, N^ E, Z

1 2 1 o

[(N -1 + N_ )Z + R]

2 o

(2) Sample at maximum loss E = E2

Pb =

2 2 2

N^ N E^ Z

1 2 2 o

[(N, + N )Z + R + R ] 1 2 o s
(3) Sample at 2 maximum loss E = E

2 2 2

N, N^ E^ Z

p =

1 2 3 o 22

Since P = P and P = P , a b be

7 ? E, (N, + N^ )Z + R \/p7

1 120 = K ^ ^2 {n/+N,^)Z +R+ R ^ ^ 1 2 o s

E_ {n/+ N ^)Z +R+R n/pT

£ _ 1 2 o s_ _ K = - =3^22 ^

" 2-^/p-•

(N, + N, )Z + R + -^ 3

i 2 o 2

where Pj, P^ and P, are the powers delivered by the attenuator for the

three conditions.

Let

(N, ^ + N^^)Z + R = B

1 Z o

B

= K, B + R 1

B = K B + K,R

1 Is

B(l-K ) = K R

1 Is

B + R

^r=«2
K R

B = K B + -^^- R

Z 2 s

B(l-K^)= ^(K^-^)

R (K -2) K R

s 2 Is

2(1 -K^) 1 - Kj

K2-2-K^K2+2Kj=2K^-2KjK2

^2 ^ ^1^2 = 2

1^2 =

2

l + Kj

2

3

^P

1 + ^^2

^2

^3 V ^P^

1 + *2

Referring to Figure 4, we may develop the relationships

between the various power levels and the corresponding attenuator

readings.
PRECISION

ATTENUATOR

P1.P2.P3

CAVITY Pa-Pb=Pc ^Pq

FIG. 4 BLOCK DIAGRAM INDICATING POWER RELATIONSHIPS

where

P. = input power delivered to precision attenuator.

P = output power delivered to load,

o Assume P and P are held constant,

i o For empty cavity, let

A =: 10 log -— = 10 log P. - 10 log P, . o P^ 1 i

For cavity with sample at maximum loss, let

A = 10 log -^ = 10 log P - 10 log P . r ^ P .^ i ^ Z

For cavity with sample at ^ rnaximum loss, let

P.

Ai = 10 log -^ = 10 log P - 10 log P

2 P3 i 3

Aor- A = 10 log^2P - 10 log^1P = 10 log^ —P.

Ai - A = 10 log P - 10 log P = 10 log

Fromi above

10 log = A - A ^ P, or

10
\/p7

20 log -^= = A - A ^ ^^ o r

1

log

^ypT A - A

20

1 A - A

o r

Ai-A =Ai-A -(A -A)

2 o 2 r or

P P

A^- A = 10 log -- - 10 log --

o P3 P^

Ai - A =20 loi

2 o n/p^

20 log

1 + ^P-

\/p^

Ai - A = 20 log 2 - 20 log ( -= + 1 2 o \^

Ai = A + 20 log 2 - 20 loj

2 o

A - A

o r io"^°~+ 1

which is the working equation given in the text of this paper,

11
TABLES FOR DETERMINING THE HALF -POWER

POINTS ON THE FERRIMAGNETIC RESONANCE CURVE

ATTENUATOR READINGS

A - empty cavity

o A - sample in cavity- -maximura absorption of sample

r Aj^ - sample in cavity-- one half maLximum absorption of sample

2 WORKING EQUATIONS

A - A

o r 20

Ai = A + 20 log 2 - 20 log (10 +1) ,

or

Ai = A + A . 2 O

Tables give ^ values of A as a function of Aor- A ,

12
Ao -\ A Ao -Ar A An -A o r A ^o-^ A

0.41 -0.21 0.81 -0.41 1.21 -0.63 1.61 -0.84

0.42 -0.21 0.82 -0.42 1.22 -0.63 1.62 -0.85

0.43 -0.22 0.83 -0.43 1.23 -0.64 1.63 -0.85

0.44 -0.22 0.84 -0.43 1.24 -0.64 1.64 -0.86

0.45 -0.23 0.85 -0.44 1.25 -0.65 1.65 -0.86

0.46 -0.23 0.86 -0.44 1.26 -0.65 1.66 -0.87

0.47 -0.24 0.87 -0.45 1.27 -0.66 1.67 -0.88

0.48 -0.24 0.88 -0.45 1.28 -0.66 1.68 -0.88

0.49 -0.25 0.89 -0.46 1.29 -0.67 1.69 -0.89

0.50 -0.25 0.90 -0.46 1.30 -0.67 1.70 -0.89

0.51 -0.26 0.91 -0.47 1.31 -0.68 1.71 -0.90

0.52 -0.26 0.92 -0.47 1.32 -0.69 1.72 -0.90

0.53 -0.27 0.93 -0.48 1.33 -0.69 1.73 -0.91

0.54 -0.27 0.94 -0.48 1.34 -0.70 1.74 -0.91

0.55 -0.28 0.95 -0.49 1.35 -0.70 1.75 -0.92

0.56 -0.29 0.96 -0.49 1.36 -0.71 1.76 -0.93

0.57 -0.29 0.97 -0.50 1.37 -0.71 1.77 -0.93

0.58 -0.30 0.98 -0.50 1.38 -0.72 1.78 -0.94

0.59 -0.30 0.99 -0.51 1.39 -0.72 1.79 -0.94

0.60 -0.31 1.00 -0.51 1.40 -0.73 1.80 -0.95

0.61 -0.31 1.01 -0.52 1.41 -0.73 1.81 -0.95

0.62 -0.32 1.02 -0.53 1.42 -0.74 1.82 -0.96

0.63 -0.32 1.03 -0.53 1.43 -0.74 1.83 -0.96

0.64 -0.33 1.04 -0.54 1.44 -0.75 1.84 -0.97

0.65 -0.33 1.05 -0.54 1.45 -0.76 1.85 -0.97

0.66 -0.34 1.06 -0.55 1.46 -0.76 1.86 -0.98

0.67 -0.34 1.07 -0.55 1.47 -0.77 1.87 -0.99

0.68 -0.35 1.08 -0.56 1.48 -0.77 1.88 -0.99

0.69 -0.35 1.09 -0.56 1.49 -0.78 1.89 -1.00

0.70 -0.36 1.10 -0.57 1.50 -0.78 1.90 -1.00

0.71 -0.36 1.11 -0.57 1.51 -0.79 1.91 -1.01

0.72 -0.37 1.12 -0.58 1.52 -0.79 1.92 -1.01

0.73 -0.37 1.13 -0.58 1.53 -0.80 1.93 -1.02

0.74 -0.38 1.14 -0.59 1.54 -0.80 1.94 -1.02

0.75 -0.38 1.15 -0.59 1.55 -0.81 1.95 -1.03

0.76 -0.39 1.16 -0.60 1.56 -0.82 1.96 -1.04

0.77 -0.39 1.17 -0.61 1.57 -0.82 1.97 -1.04

0.78 -0.40 1.18 -0.61 1.58 -0.83 1.98 -1.05

0.79 -0.40 1.19 -0.62 1.59 -0.83 1.99 -1.05

0.80 -0.41 1.20 -0.62 1.60 -0.84 2.00 -1.06

13
Ao -A^ A Ao -\ A ^o '\ A K-\ A

2.01 -1.06 2.41 -1.29 ?.81 -1.52 3.21 -1.75

2.02 -1.07 2.42 -1.29 2.82 -1.52 3.22 -1.76

2.03 -1.07 2.43 -1.30 2.83 -1.53 3.23 -1.76

2.04 -1.08 2.44 -1.31 2.84 -1.54 3.24 -1.77

2.05 -1.09 2.45 -1.31 2.85 -1.54 3.25 -1.78

2.06 -1.09 2.46 -1.32 2.86 -1.55 3.26 -1.78

2.07 -1.10 2.47 -1.32 2.87 -1.55 3.27 -1.79

2.08 -I.IO 2.48 -1.33 2.88 -1.56 3.28 -1.79

2.09 -1.11 ^.49 -1.33 2.89 -1.57 3.29 -1.80

2.10 -1.11 2.50 -1.34 2.90 -1.57 3.30 -1.81

2.11 -1.12 2.51 -1.35 2.91 -1.58 3.31 -1.81

2.12 -1.13 2.52 -1.35 2.92 -1.58 3.32 -1.82

2.13 -1.13 2.53 -1.36 2.93 -1.59 3.33 -1.82

2.14 -1.14 2.54 -1.36 2.94 -1.59 3.34 -1.83

2.15 -1.14 2.55 -1.37 2.95 -1.60 3.35 -1.84

2.16 -1.15 2.56 -1.37 2.96 -1.61 3.36 -1.84

2.17 -1.15 2.57 -1.38 2.97 -1.61 3.37 -1.85

2.18 -1.16 2.58 -1.39 2.98 -1.62 3.38 -1.85

2.19 -1.16 2.59 -1.39 2.99 -1.62 3.39 -1.86

2.20 -1.17 2.60 -1.40 3.00 -1.63 3.40 -1.87

2.21 -1.18 2.61 -1.40 3.01 -1.64 3.41 -1.87

2.22 -1.18 2.62 -1.41 3.02 -1.64 3.42 -1.88

2.23 -1.19 2.63 -1.41 3.03 -1.65 3.43 -1.88

2.24 -1.19 2.64 -1.42 3.04 -1.65 3.44 -1.89

2.25 -1.20 2.65 -1.43 3.05 -1.66 3.45 -1.90

2.26 -1.20 2.66 -1.43 3.06 -1.66 3.46 -1.90

2.27 -1.21 2.67 -1.44 3.07 -1.67 3.47 -1.91

2.28 -1.22 2.68 -1.44 3.08 -1.68 3.48 -1.91

2.29 -1.22 2.69 -1.45 3.09 -1.68 3.49 -1.92

2.30 -1.23 2.70 -1.46 3.10 -1.69 3.50 -1.93

2.31 -1.23 2.71 -1.46 3.11 -1.69 3.51 -1.93

2.32 -1.24 2.72 -1.47 3.12 -1.70 3.52 -1.94

2.33 -1.24 2.73 -1.47 3.13 -1.71 3.53 -1.94

2.34 -1.25 2.74 -1.48 3.14 -1.71 3.54 -1.95

2.35 -1.25 2.75 -1.48 3.15 -1.72 3.55 -1.96

2.36 -1.26 2.76 -1.49 3.16 -1.72 3.56 -1.96

2.37 -1.27 2.77 -1.50 3.17 -1.73 3.57 -1.97

2.38 -1.27 2.78 -1.50 3.18 -1.74 3.58 -1.97

2.39 -1.28 2.79 -1.51 3.19 -1.74 3.59 -1.98

2.40 -1.28 2.80 -1.51 3.20 -1.75 3.60 -1.99

14
Aq ""r K -A

o r

3.61 -1.99 4.01 -2.23

3.62 -2.00 4.02 -2.24

3.63 -2.00 4.03 -2.25

3.64 -2.01 4.04 -2.25

3.65 -2.02 4.05 -2.26

3.66 -2.02 4.06 -2.27

3.67 -2.03 4.07 -2.27

3.68 -2.03 4.08 -2.28

3.69 -2.04 4.09 -2.28

3.70 -2.05 4.10 -2.29

3.71 -2.05 4.11 -2.30

3.72 -2.06 4.12 -2.30

3.73 -2.06 4.13 -2.31

3.74 -2.07 4.14 -2.31

3.75 -2.08 4.15 -2.32

3.76 -2.08 4.16 -2.33

3.77 -2.09 4.17 -2.33

3.78 -2.09 4.18 -2.34

3.79 -2.10 4.19 -2.35

3.80 -2.11 4.20 -2.35

3.81 -2.11 4.21 -2.36

3.82 -2.12 4.22 -2.36

3.83 -2.12 4.23 -2.37

3.84 -2.13 4.24 -2.38

3.85 -2.14 4.25 -2.38

3.86 -2.14 4.26 -2.39

3.87 -2.15 4.27 -2.40

3.88 -2.16 4.28 -2.40

3.89 -2.16 4.29 -2.41

3.90 -2.17 4.30 -2.41

3.91 -2.17 4.31 -2.42

3.92 -2.18 4.32 -2.43

3.93 -2.19 4.33 -2.43

3.94 -2.19 4.34 -2.44

3.95 -2.20 4.35 -2.45

3.96 -2.20 4.36 -2.45

3.97 -2.21 4.37 -2.46

3.98 -2.22 4.38 -2.46

3.99 -2.22 4.39 -2.47

4.00 -2.23 4.40 -2.48

^o '\ A K'\ A

4.41 -2.48 4.81 -2.73

4.42 -2.49 4.82 -2.74

4.43 -2.49 4.83 -2.75

4.44 -2.50 4.84 -2.75

4.45 -2.51 4.85 -2.76

4.46 -2.51 4.86 -2.77

4.47 -2.52 4.87 -2.77

4.48 -2.53 4.88 -2.78

4.49 -2.53 4.89 -2.79

4.50 -2.54 4.90 -2.79

4.51 -2.54 4.91 -2.80

4.52 -2.55 4.92 -2.80

4.53 -2.56 4.93 -2.81

4.54 -2.56 4.94 -2.82

4.55 -2.57 4.95 -2.82

4.56 -2.58 4.96 -2.83

4.57 -2.58 4.97 -2.84

4.58 -2.59 4.98 -2.64

4.59 -2.60 4.99 -2.85

4.60 -2.60 5.00 -2.86

4.61 -2.61 5.01 -2.86

4.62 -2.61 5.02 -2.87

4.63 -2.62 5.03 -2.87

4.64 -2.63 5.04 -2.88

4.65 -2.63 5.05 -2.89

4.66 -2.64 5.06 -2.89

4.67 -2.65 5.07 -2.90

4.68 -2.65 5.08 -2.91

4.69 -2.66 5.09 -2.91

4.70 -2.66 5.10 -2.92

4.71 -2.67 5.11 -2.93

4.72 -2.68 5.12 -2.93

4.73 -2.68 5.13 -2.94

4.74 -2.69 5.14 -2.95

4.75 -2.70 5.15 -2.95

4.76 -2.70 5.16 -2.96

4.77 -2.71 5.17 -2.96

4.78 -2.72 5.18 -2.97

4.79 -2.72 5.19 -2.98

4.80 -2.73 5.20 -2.98

15
Ao -A^ A A^ -A

o r A A -A

o r A *o-\ A

5.21 -2.99 5.61 -3.25 6.01 -3.52 6.41 -3.78

5.22 -3.00 5.62 -3.26 6.02 -3.52 6.42 -3.79

5.23 -3.00 5.63 -3.26 6w03 -3.53 6.43 -3.80

5.24 -3.01 5.64 -3.27 6.04 -3.54 6.44 -3.80

5.25 -3.02 5.65 -3.28 6.05 -3.54 6.45 -3.81

5.26 -3.02 5.66 -3.28 6.06 -3.55 6.46 -3.82

5.27 -3.03 5.67 -3.29 6.07 -3.56 6.47 -3.82

5.28 -3.04 5.68 -3.30 6.08 -3.56 6.48 -3.83

5.29 -3.04 5.69 -3.30 6.09 -3.57 6.49 -3.84

5.30 -3.05 5.70 -3.31 6.10 -3.58 6.50 -3.84

5.31 -3.06 5.71 -3.32 6.11 -3.58 6.51 -3.85

5.32 -3.06 5.72 -3.32 6.12 -3.59 6.52 -3.86

5.33 -3.07 5.73 -3.33 6.13 -3.60 6.53 -3.87

5.34 -3.07 5.74 -3.34 6.14 -3.60 6.54 -3.87

5.35 -3.08 5.75 -3.34 6.15 -3.61 6.55 -3.88

5.36 -3.09 5.76 -3.35 6.16 -3.62 6.56 -3.89

5.37 -3.09 5.77 -3.36 6.17 -3.62 6.57 -3.89

5.38 -3.10 5.78 -3.36 6.18 -3.63 6.58 -3.90

5.39 -3.11 5.79 -3.37 6.19 -3.64 6.59 -3.91

5.40 -3.11 5.80 -3.38 6.20 -3.64 6.60 -3.91

5.41 -3.12 5.81 -3.38 6.21 -3.65 6.61 -3.92

5.42 -3.13 5.82 -3.39 6.22 -3.66 6.62 -3.93

5.43 -3.13 5.83 -3.40 6.23 -3.66 6.63 -3.93

5.44 -3.14 5.84 -3.40 6.24 -3.67 6.64 -3.94

5.45 -3.15 5.85 -3.41 6.25 -3.68 6.65 -3.95

5.46 -3.15 5.86 -3.42 6.26 -3.68 6.66 -3.95

5.47 -3.16 5.87 -3.42 6.27 -3.69 6.67 -3.96

5.48 -3.17 5.88 -3.43 6.28 -3.70 6.68 -3.97

5.49 -3.17 5.89 -3.44 6.29 -3.70 6.69 -3.97

5.50 -3.18 5.90 -3.44 6.30 -3.71 6.70 -3.98

5.51 -3.19 5.91 -3.45 6.31 -3.72 6.71 -3.99

5.52 -3.19 5.92 -3.46 6.32 -3.72 6.72 -3.99

5.53 -3.20 5.93 -3.46 6.33 -3.73 6.73 -4.00

5.54 -3.20 5.94 -3.47 6.34 -3.74 6.74 -4.01

5.55 -3.21 5.95 -3.48 6.35 -3.74 6.75 -4.02

5.56 -3.22 5.96 -3.48 6.36 -3.75 6.76 -4.02

5.57 -3.22 5.97 -3.49 6.37 -3.76 6.77 -4.03

5.58 -3.23 5.98 -3.50 6.38 -3.76 6.78 -4.04

5.59 -3.24 5.99 -3.50 6.39 -3.77 6.79 -4.04

5.60 -3.24 6.00 -3.51 6.40 -3.78 6.80 -4.05

16
Ao '\ A K'\ A A -A^

o r A A -A

o r A

6.81 -4.06 7.21 -4.33 7.61 -4.61 8.01 -4.90

6.82 -4.06 7.22 -4.34 7.62 -4.62 8.02 -4.91

6.83 -4.07 7.23 -4.35 7.63 -4.63 8.03 -4.91

6.84 -4.08 7.24 -4.35 7.64 -4.63 8.04 -4.92

6.85 -4.08 7.25 -4.36 7.65 -4.64 8.05 -4.93

6.86 -4.09 7.26 -4.37 7.66 -4.65 8.06 -4.93

6.87 -4.10 7.27 -4.37 7.67 -4.66 8.07 -4.94

6.88 -4.10 7.28 -4.38 7.68 -4.66 8.08 -4.95

6.89 -4. 11 7.29 -4.39 7.69 -4.67 8.09 -4.96

6.90 -4.12 7.30 -4.40 7.70 -4.68 8.10 -4.96

6.91 -4.13 7.31 -4.40 7.71 -4.68 3.11 -4.97

6.92 -4.13 7.32 -4.41 7.72 -4.69 8.12 -4.98

6.93 -4.14 7.33 -4.42 7.73 -4.70 8.13 -4.98

6.94 -4.15 7.34 -4.42 7.74 -4.71 8.14 -4.99

6.95 -4.15 7.35 -4.43 7.75 -4.71 8.15 -5.00

6.96 -4.16 7.36 -4.44 7.76 -4.72 8.16 -5.01

6.97 -4.17 7.37 -4.44 7.77 -4.73 8.17 -5.01

6.98 -4.17 7.38 -4.45 7.78 -4.73 8.18 -5.02

6.99 -4.18 7.39 -4.46 7.79 -4.74 8.19 -5.03

7.00 -4.19 7.40 -4.47 7.80 -4.75 8.20 -5.03

7.01 -4.19 7.41 -4.47 7.81 -4.76 8.21 -5.04

7.02 -4.20 7.42 -4.48 7.82 -4.76 8.22 -5.05

7.03 -4.21 7.43 -4.49 7.83 -4.77 8.23 -5.06

7.04 -4.22 7.44 -4.49 7.84 -4.78 8.24 -5.06

7.05 -4.22 7.45 -4.50 7.85 -4.78 8.25 -5.07

7.06 -4.23 7.46 -4.51 7.86 -4.79 8.26 -5.08

7.07 -4.24 7.47 -4.51 7.87 -4.80 8.27 -5.08

7.08 -4.24 7.48 -4.52 7.88 -4.81 8.28 -5.09

7.09 -4.25 7.49 -4.53 7.89 -4.81 8.29 -5.10

7.10 -4.26 7.50 -4.54 7.90 -4.82 8.30 -5.11

7.11 -4.26 7.51 -4.54 7.91 -4.83 8.31 -5.11

7.12 -4.27 7.52 -4.55 7.92 -4.83 8.32 -5.12

7.13 -4.28 7.53 -4.56 7.93 -4.84 8.33 -5.13

7.14 -4.28 7.54 -4.56 7.94 -4.85 8.34 -5.14

7.15 -4.29 7.55 -4.57 7.95 -4.85 8.35 -5.14

7.16 -4.30 7.56 -4.58 7.96 -4.86 8.36 -5.15

7.17 -4.31 7.57 -4.59 7.97 -4.87 8.37 -5.16

7.18 -4.31 7.58 -4.59 7.98 -4.88 8.38 -5.16

7.19 -4.32 7.59 -4.60 7.99 -4.88 8.39 -5.17

7.20 -4.33 7.60 -4.61 8.00 -4.89 8.40 -5.18

_1jL
Ao -A^ A Aq -A^ A A -Ao '^ A A -A^

o r A

8.41 -5.19 8.81 -5.48 9.21 -5.77 9.61 -6.07

8.42 -5.19 8.82 -5.48 9.22 -5.78 9.62 -6.08

8.43 -5.20 3»83 -5-49 9.23 -5.79 9.63 -6.09

8.44 -5.21 8.84 -5.50 9.24 -5.80 9.64 -6.09

8.45 -5.21 8.85 -5.51 9.25 -5.80 9.65 -6.10

8.46 -5.22 8.86 -5.51 9.26 -5.81 9.66 -6.11

8.47 -5.23 8.87 -5.52 9.27 -5.82 9.61 -6.12

8.48 -5.24 8.88 -5.53 9.28 -5.83 9.68 -6.12

8.49 -5.24 8.89 -5.54 9.29 -5.83 9.69 -6.13

8.50 -5.25 8.90 -5.54 9.30 -5.84 9.70 -6.14

8.51 -5.26 8.91 -5.55 9.31 -5.85 9.71 -6.15

8.52 -5.27 8.92 -5.56 9.32 -5.85 9.72 -6.15

8.53 -5.27 8.93 -5.57 9.33 -5.86 9.73 -6.16

8.54 -5.28 8.94 -5.57 9.34 -5.87 9.74 -6.17

8.55 -5.29 8.95 -5.58 9.35 -5.88 9.75 -6.18

8.56 -5.29 8.96 -5.59 9.36 -5.88 9.76 -6.18

8.57 -5.30 8.97 -5.60 9.37 -5.89 9.77 -6.19

8.58 -5.31 8.98 -5.60 9.38 -5.90 9.78 -6.20

8.59 -5.32 8.99 -5.61 9.39 -5.91 9.79 -6.21

8.60 -5.32 9.00 -5.62 9.40 -5.91 9.80 -6.21

8.61 -5.33 9.01 -5.62 9.41 -5.92 9.81 -6.22

8.62 -5.34 9.02 -5.63 9.42 -5.93 9.82 -6.23

8.63 -5.35 9.03 -5.64 9.43 -5.94 9.83 -6.24

8.64 -5.35 9.04 -5.65 9.44 -5.94 9.84 -6.25

8.65 -5.36 9.05 -5.65 9.45 -5.95 9.85 -6.25

8.66 -5.37 9.06 -5.66 9.46 -5.96 9.86 -6.26

8.67 -5.38 9.07 -5.67 9.47 -5.97 9.87 -6.27

8.68 -5.38 9.08 -5.68 9.48 -5.97 9.88 -6.28

8.69 -5.39 9.09 -5.68 9.49 -5.98 9.89 -6.28

8.70 -5.40 9.10 -5.69 9.50 -5.99 9.90 -6.29

8.71 -5.40 9.11 -5.70 9.51 -6.00 9.91 -6.30

8.72 -5.41 9.12 -5.71 9.52 -6.00 9.92 -6.31

8.73 -5.42 9.13 -5.71 9.53 -6.01 9.93 -6.31

8.74 -5.43 9.14 -5.72 9.54 -6.02 9.94 -6.32

8.75 -5.43 9.15 -5.73 9.55 -6.03 9.95 -6.33

8.76 -5.44 9.16 -5.74 9.56 -6.03 9.96 -6.34

8.77 -5.45 9.17 -5.74 9.57 -6.04 9.97 -6.34

8.78 -5.46 9.18 -5.75 9.58 -6.05 9.98 -6.35

8.79 -5.46 9.19 -5.76 9.59 -6.06 9.99 -6.36

8.80 -5.47 9.20 -5.77 9.60 -6.06 10.00 -6.37

18
^o-\ A A -A

o r A

o r A A. -Ao r A

10.01 -6.37 10.41 -6.68 10.81 -6.99 ]LI. 21 -7.30

10.02 -6.38 10.42 -6.69 10.82 -7.00 ]11.22 -7.31

10.03 -6.39 10.43 -6.70 10.83 -7.00 ]LI. 23 -7.32

10.04 -6.40 10.44 -6.70 10.84 -7.01 ]LI. 24 -7.32

10.05 -6.40 10.45 -6.71 10.85 -7.02 ]LI. 25 -7.33

10.06 -6.41 10.46 -6.72 10.86 -7.03 ]LI. 26 -7.34

10.07 -6.42 10.47 -6.73 10.87 -7.04 ]LI. 27 -7.35

10.08 -6.43 10.48 -6.73 10.88 -7.04 ]LI. 28 -7.36

10.09 -6.43 10.49 -6.74 10.89 -7.05 ]LI. 29 -7.36

10.10 -6.44 10.50 -6.75 10.90 -7.06 ]LI. 30 -7.37

10.11 -6.45 10.51 -6.76 10.91 -7.07 ]LI. 31 -7.38

10.12 -6.46 10.52 -6.76 10.92 -7.07 ]LI. 32 -7.39

10.13 -6.47 10.53 -6.77 10.93 -7.08 ]LI. 33 -7.40

10.14 -6.47 10.54 -6.78 10.94 -7.09 ]LI. 34 -7.40

10.15 -6.48 10.55 -6.79 10.95 -7.10 ]LI. 35 -7.41

10.16 -6.49 10.56 -6.80 10.96 -7.11 ]LI. 36 -7.42

10.17 -6.50 10.57 -6.80 10.97 -7.11 ]LI. 37 -7.43

10.18 -6.50 10.58 -6.81 10.98 -7.12 1LI. 38 -7.43

10.19 -6.51 10.59 -6.82 10.99 -7.13 ]LI. 39 -7.44

10.20 -6.52 10.60 -6.83 11.00 -7.14 ]LI. 40 -7.45

10.21 -6.53 10.61 -6.83 11.01 -7.14 ]LI. 41 -7.46

10.22 -6.53 10.62 -6.84 11.02 -7.15 ]LI. 42 -7.47

10.23 -6.54 10.63 -6.85 11.03 -7.16 ]LI. 43 -7.47

10.24 -6.55 10.64 -6.86 11.04 -7.17 ]L1.44 -7.48

10.25 -6.56 10.65 -6.86 11.05 -7.18 ]LI. 45 -7.49

10.26 -6.56 10.66 -6.87 11.06 -7.18 ]L1.46 -7.50

10.27 -6.57 10.67 -6.88 11.07 -7.19 ]LI. 47 -7.51

10.28 -6.58 10.68 -6.89 11.08 -7.20 ]LI. 48 -7.51

10.29 -6.59 10.69 -6.90 11.09 -7.21 ]LI. 49 -7.52

10.30 -6.60 10.70 -6.90 11.10 -7.21 ]L1.50 -7.53

10.31 -6.60 10.71 -6.91 11.11 -7.22 ]LI. 51 -7.54

10.32 -6.61 10.72 -6.92 11.12 -7.23 ]LI. 52 -7.54

10.33 -6.62 10.73 -6.93 11.13 -7.24 ]LI. 53 -7.55

10.34 -6.63 10.74 -6.93 11.14 -7.25 ]LI. 54 -7.56

10.35 -6.63 10.75 -6.94 11.15 -7.25 ]LI. 55 -7.57

10.36 -6.64 10.76 -6.95 11.16 -7.26 ]LI. 56 -7.58

10.37 -6.65 10,77 -6.96 11.17 -7.27 ]LI. 57 -7.58

10o38 -6.66 10.78 -6.97 11.18 -7.28 ]LI. 58 -7.59

10.39 -6.66 10.79 -6.97 11.19 -7.29 ]LI. 59 -7.60

10.40 -6.67 10.80 -6.98 11.20 -7.29 ]LI. 60 -7.61

19
Aq -Aj. ^o -\ o r A -A

o r

11.61 -7.62 12.01 -7.93 12.41 -8.26 12.81 -8.58

11.62 -7.62 12.02 -7.94 12.42 -8.26 12.82 -8.59

11.63 -7.63 12.03 -7.95 12.43 -8.27 12.83 -8-60

11. 6A -7.64 12.04 -7.96 12.44 -8.28 12.84 -8.60

11.65 -7.65 12.05 -7.97 12.45 -8.29 12.85 -8.61

11.66 -7.66 12.06 -7.97 12.46 -8.30 12.86 -8.62

11.67 -7.66 12.07 -7.98 12.47 -8.30 12.87 -8.63

11.68 -7.67 12.08 -7.99 12.48 -8.31 12.88 -8.64

11.69 -7.68 12.09 -8.00 12.49 -8.32 12.89 -8.64

11.70 -7.69 12.10 -8.01 12.50 -8.33 12.90 -8.65

11.71 -7.70 12.11 -8.01 12.51 -8.34 12.91 -3.66

11.72 -7.70 12.12 -8.02 12.52 -8.34 12.92 -8.67

11.73 -7.71 12.13 -8.03 12.53 -8.35 12.93 -8.68

11.74 -7.72 12.14 -8.04 12.54 -8.36 12.94 -8.69

11.75 -7.73 12.15 -8.05 12.55 -8.37 12.95 -8.69

11.76 -7.74 12.16 -8.05 12.56 -8.38 12.96 -8.70

11.77 -7.74 12.17 -8.06 12.57 -8.38 12.97 -8.71

11.78 -7.75 12.18 -8.07 12.58 -8.39 12.98 -8.72

11.79 -7.76 12.19 -8.08 12.59 -8.40 12.99 -8.73

11.80 -7.77 12.20 -8.09 12.60 -8.41 13.00 -8.73

11.81 -7.77 12.21 -8.09 12.61 -8.42 13.01 -8.74

11.82 -7.78 12.22 -8. 10 12.62 -8.43 13.02 -8.75

11.83 -7.79 12.23 -8.11 12.63 -8.43 13.03 -8.76

11.84 -7.80 12.24 -8.12 12.64 -8.44 13.04 -8.77

11.85 -7.81 12.25 -8.13 12.65 -8.45 13.05 -8.78

11.86 -7.81 12.26 -8.13 12.66 -8.46 13.06 -8.78

11.87 -7.82 12.27 -8.14 12.67 -8.47 13.07 -8.79

11.88 -7.83 12.28 -8.15 12.68 -8.47 13.08 -8.80

11.89 -7.84 12.29 -8. 16 12.69 -8.48 13.09 -8.81

11.90 -7.85 12.30 -8.17 12.70 -8.49 13.10 -8.82

11.91 -7.85 12.31 -8.17 12.71 -8.50 13.11 -8.82

11.92 -7.86 12-32 -8.18 12.72 -8.51 13.12 -8.83

11.93 -7.87 12.33 -8.19 12.73 -8.51 13.13 -8.84

11.94 -7.88 12.34 -8.20 12.74 -8.52 13.14 -8.85

11.95 -7.89 12.35 -8.21 12.75 -8.53 13.15 -8.86

11.96 -7.89 12.36 -8.22 12.76 -8.54 13.16 -8.87

11.97 -7.90 12.37 -8.22 12.77 -8.55 13.17 -8.87

11.98 -7.91 12.38 -8.23 12.78 -8.56 13.18 -8.88

11.99 -7.92 12.39 -8.24 12.79 -8.56 13.19 -8.89

12.00 -7.93 12.40 -8.25 12.80 -8.57 13.20 -8.90

20
A^ -A

o r A A -A^

o r A Ao -\ A

o r A

13.21 -8.91 13.61 -9.24 14.01 -9.57 14.41 -9.90

13.22 -8.91 13.62 -9.24 14.02 -9.58 14.42 -9.91

13.23 -8.92 13.63 -9.25 14.03 -9.59 14.43 -9.92

13.24 -8.93 13.64 -9.26 14.04 -9.59 14.44 -9.93

13.25 -8.94 13.65 -9.27 14.05 -9.60 14.45 -9.94

13.26 -8.95 13.66 -9.28 14.06 -9.61 14.46 -9.95

13.27 -8.96 13.67 -9.29 14.07 -9.62 14.47 -9.95

13.28 -8.96 13.68 -9.29 14.08 -9.63 14.48 -9.96

13.29 -8.97 13.69 -9.30 14.09 -9.64 14.49 -9.97

13.30 -8.96 13.70 -9.31 14.10 -9.64 14.50 -9.98

13.31 -8.99 13.71 -9.32 14.11 -9.65 14.51 -9.99

13.32 -9.00 13.72 -9.33 14.12 -9.66 14.52 -10.00

13.33 -9.01 13.73 -9.34 14.13 -9.67 14.53 -10.00

13.34 -9.01 13.74 -9.34 14.14 -9.68 14.54 -10.01

13.35 -9.02 13.75 -9.35 14.15 -9.69 14.55 -10.02

13.36 -9.03 13.76 -9.36 14.16 -9.69 14.56 -10.03

13.37 -9.04 13.77 -9.37 14.17 -9.70 14.57 -10.04

13.38 -9.05 13.78 -9.38 14.18 -9.71 14.58 -10.05

13.39 -9.05 13.79 -9.39 14.19 -9.72 14.59 -10.05

13.40 -9.06 13.80 -9.39 14.20 -9.73 14.60 -10.06

13.41 -9.07 13.81 -9.40 14.21 -9.74 14.61 -10.07

13.42 -9.08 13.82 -9.41 14.22 -9.74 14.62 -10.08

13.43 -9.09 13.83 -9.42 14.23 -9.75 14.63 -10.09

13.44 -9.10 13.84 -9.43 14.24 -9.76 14.64 -10.10

13.45 -9.10 13.85 -9.44 14.25 -9.77 14.65 -10.11

13.46 -9.11 13.86 -9.44 14.26 -9.78 14.66 -10.11

13.47 -9.12 13.87 -9.45 14.27 -9.79 14.67 -10.12

13.48 -9.13 13.88 -9.46 14.28 -9.79 14.68 -10.13

13.49 -9.14 13.89 -9.47 14.29 -9.80 14.69 -10.14

13.50 -9.15 13.90 -9.48 14.30 -9.81 14.70 -10.15

13.51 -9.15 13.91 -9.49 14.31 -9.82 14.71 -10.16

13.52 -9.16 13.92 -9.49 14.32 -9.83 14.72 -10.16

13.53 -9.17 13.93 -9.50 14.33 -9.84 14.73 -10.17

13.54 -9.18 13.94 -9.51 14.34 -9.84 14.74 -10.18

13.55 -9.19 13.95 -9.52 14.35 -9.85 14.75 -10.19

13.56 -9.19 13.96 -9.53 14.36 -9.86 14.76 -10.20

13.57 -9.20 13.97 -9.54 14.37 -9.87 14.77 -10.21

13.58 -9.21 13.98 -9.54 14.38 -9.88 14.78 -10.22

13.59 -9.22 13.99 -9.55 14.39 -9.89 14.79 -10.22

13.60 -9.23 14.00 -9.56 14.40 -9.89 14.80 -10.23

21
Ao -Ar A ^o -^r k ^o -A

r

Jk A

o -A

r A

14,.81 -10.24 15..21 -10..58 15..61 -10,.92 16..01 .27

14..82 -10.25 15..22 -10..59 15..62 -10..93 16.,02 -1 1

.

.27

14..83 -10..26 15..23 -10..60 15..63 -10.94 16.,03 -11..28

14..84 -10..27 15..24 -10..61 15..64 -10..95 16..04 -11..29

14..85 -10..27 15..25 -10..61 15..65 -10..96 16,.05 -11,.30

14..86 -10.> 28 15..26 -10..62 15..66 -10..96 16,,06 -11-.31

14..87 -10..29 15..27 -10..63 15..67 -10,.97 16..07 -11..32

14..88 -10.30 15..28 -10..64 15..68 -10..98 16..08 -11

.

.33

14..89 -10..31 15..29 -10.,65 15..69 -10..99 16..09 -11

,

.34

14..90 -10..32 15..30 -10..66 15..70 -11

.

.00 16.,10 -11..34

14..91 -10..33 15..31 -10.,67 15..71 -11..01 16.,11 -11..35

14.92 -10..33 15..32 -10.,67 15..72 -11

.

.02 16..12 -11..36

14..93 -10..34 15,.33 -10.,68 15..73 -11..03 16..13 -1 1

.

.37

14..94 -10..35 15..34 -10.,69 15..74 -11..03 16..14 -11..38

14.95 -10..36 15..35 -10.,70 15..75 -1 1..04 16..15 — 11

.

.39

14..96 -10..37 15..36 -10.,71 15..76 -11..05 16..16 -11..40

14..97 -10..38 15..37 -10,,72 15..77 -1 1

.

.06 16..17 -11

.

.40

14,,98 -10,.38 15..38 -10.,73 15..78 -11..07 16..18 -11..41

14..99 -10,.39 15..39 -10.,73 15..79 -11..08 16..19 -11..42

13..00 -10,.40 15..40 -10.,74 15..80 -11,.09 16,.20 -11

.

.43

15,.01 -10,.41 15..41 -10. 75 15..81 -11..09 16..21 -11..44

15,.02 -10..42 15,.42 -10.,76 15..82 -11..10 16..22 -11..45

15,.03 -10..43 15,.43 -10.,77 15..83 -11,,11 16,.23 -11..46

15,.04 -10,.44 15..44 -10,,78 15,.84 -11.12 16,.24 -11,.47

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26
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27
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28
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26.05 -20.45 26.45 -20.83 26.85 -21.22 27.25 -21.60

26.06 -20.46 26.46 -20.84 26.86 -21.23 27.26 -21.61

26.07 -20.47 26.47 -20.85 26.87 -21.23 27.27 -21.62

26.08 -20.48 26.48 -20.86 26.88 -21.24 27.28 -21.63

26.09 -20.49 26.49 -20.87 26.89 -21.25 27.29 -21.64

26.10 -20.50 26.50 -20.88 26.90 -21.26 27.30 -21.65

26.11 -20.51 26.51 -20.89 26.91 -21.27 27.31 -21.66

26.12 -20.52 26.52 -20.90 26.92 -21.28 27.32 -21.67

26.13 -20.53 26.53 -20.91 26.93 -21.29 27.33 -21.68

26.14 -20.54 26.54 -20.92 26.94 -21.30 27.34 -21.69

26.15 -20.55 26.55 -20.93 26.95 -21.31 27.35 -21.69

26.16 -20.56 26.56 -20.94 26.96 -21.32 27.36 -21.70

26.17 -20.57 26.57 -20.95 26.97 -21.33 27.37 -21.71

26.18 -20.58 26.58 -20.96 26.98 -21.34 27.38 -21.72

26.19 -20.59 26.59 -20.97 26.99 -21.35 27.39 -21.73

26.20 -20.60 26.60 -20.98 27.00 -21.36 27.40 -21.74

26.21 -20.60 26.61 -20.99 27.01 -21.37 27.41 -21.75

26.22 -20.61 26.62 -21.00 27.02 -21.38 27.42 -21.76

26.23 -20.62 26.63 -21.01 27.03 -21.39 27.43 -21.77

26.24 -20.63 26.64 -21.01 27.04 -21.40 27.44 -21.78

26.25 -20.64 26.65 -21.02 27.05 -21.41 27.45 -21.79

26.26 -20.65 26.66 -21.03 27.06 -21.42 27.46 -21.80

26.27 -20.66 26.67 -21.04 27.07 -21.43 27.47 -21.81

26.28 -20.67 26.68 -21.05 27.08 -21.44 27.48 -21.82

26.29 -20.68 26.69 -21.06 27.09 -21.45 27.49 -21.83

26.30 -20.69 26.70 -21.07 27.10 -21.46 27.50 -21.84

26.31 -20.70 26.71 -21.08 27.11 -21.46 27.51 -21.85

26.32 -20.71 26.72 -21.09 27.12 -21.47 27.52 -21.86

26.33 -20.72 26.73 -21.10 27.13 -21.48 27.53 -21.87

26.34 -20.73 26.74 -21.11 27.14 -21.49 27.54 -21.88

26.35 -20.74 26.75 -21.12 27.15 -21.50 27.55 -21.89

26.36 -20.75 26.76 -21.13 27.16 -21.51 27.56 -21.90

26.37 -20.76 26.77 -21.14 27.17 -21.52 27.57 -21.91

26.38 -20.77 26.78 -21.15 27.18 -21.53 27.58 -21.92

26.39 -20.78 26.79 -21.16 27.19 -21.54 27.59 -21.92

26.40 -20.79 26.80 -21.17 27.20 -21.55 27.60 -21.93

29
Ao -Ar "o "^r Aq -Aj. Ao -Ai

27.61 -21.94 28.01 -22.33 28.41 -22.71 28.81 -23.10

27.62 -21.95 28.02 -22.34 28.42 -22.72 28.82 -23.11

27.63 -21.96 28.03 -22.35 28.43 -22.73 28.83 -23.12

27.64 -21.97 28.04 -22.36 28.44 -22.74 28.84 -23.13

27.65 -21.98 28.05 -22.37 28.45 -22.75 28.85 -23.14

21. bb -21.99 28.06 -22.38 28.46 -22.76 28.86 -23.15

27.67 -22.00 28.07 -22.39 28.47 -22.77 28.87 -23.16

27.68 -22.01 28.08 -22.40 28.48 -22.78 28.88 -23.17

27.69 -22.02 28.09 -22.41 28.49 -22.79 28.89 -23.18

27.70 -22.03 28.10 -22.41 28.50 -22.80 28.90 -23.19

27.71 -22.04 28.11 -22.42 28.51 -22.81 28.91 -23.20

27.72 -22.05 28.12 -22.43 28.52 -22.82 28.92 -23.21

27.73 -22.06 28.13 -22.44 28.53 -22.83 28.93 -23.21

27.74 -22.07 28.14 -22.45 28.54 -22.84 28.94 -23.22

27.75 -22.08 28.15 -22.46 28.55 -22.85 28.95 -23.23

27.76 -22.09 28.16 -22.47 28.56 -22.86 28.96 -23.24

27.77 -22.10 28.17 -22.48 28.57 -22.87 28.97 -23.25

27.78 -22.11 28.18 -22.49 28.58 -22.38 28.98 -23.26

27.79 -22.12 28.19 -22.50 23.59 -22.89 28.99 -23.27

27.80 -22.13 28.20 -22.51 23.60 -22.90 29.00 -23.28

27.81 -22.14 28.21 -22.52 28.61 -22.91 29.01 -23.29

27.82 -22.15 28.22 -22.53 28.62 -22.92 29.02 -23.30

27.83 -22.16 28.23 -22.54 28.63 -22.93 29.03 -23.31

27.84 -22.16 28.24 -22.55 28.64 -22.94 29.04 -23.32

27.85 -22.17 28.25 -22.56 28.65 -22.94 29.05 -23.33

27.86 -22.18 28.26 -22.57 28.66 -22.95 29.06 -23.34

27.87 -22.19 28.27 -22.58 28.67 -22.96 29.07 -23.35

27.88 -22.20 28.28 -22.59 28.68 -22.97 29.08 -23.36

27.89 -22.21 28.29 -22.60 28.69 -22.98 29.09 -23.37

27.90 -22.22 28.30 -22.61 28.70 -22.99 29.10 -23.38

27.91 -22.23 28.31 -22.62 28.71 -23.00 29.11 -23.39

27.92 -22.24 28.32 -22.63 28.72 -23.01 29.12 -23.40

27.93 -22.25 28.33 -22.64 28.73 -23.02 29.13 -23.41

27.94 -22.26 28.34 -22.65 28.74 -23.03 29.14 -23.42

27.95 -22.27 28.35 -22.66 28.75 -23.04 29.15 -23.43

27.96 -22.28 28.36 -22.67 28.76 -23.05 29.16 -23.44

27.97 -22.29 28.37 -22.67 28.77 -23.06 29.17 -23.45

27.98 -22.30 28.38 -22.68 28.78 -23.07 29.18 -23.46

27.99 -22.31 28.39 -22.69 28.79 -23.08 29.19 -23.47

28.00 -22.32 28.40 -22.70 28.80 -23.09 29.20 -23.48

30
Ao -Ar k ^ -Ar A Ao -Ar A Ao -Ar A

29..21 -23,.49 29,,61 -23. 87 30..01 -24..26 30..41 -24..65

29..22 -23,.50 29..62 -23.,88 30.02 -24,.27 30.,42 -24,.66

29..23 -23..50 29..63 -23..89 30..03 -24,.28 30,,43 -24..67

29..24 -23,.51 29,,64 -23..90 30.,04 -24,.29 30..44 -24..68

29..25 -23..52 29,.65 -23. 91 30.05 -24..30 30..45 -24,.69

29..26 -23,.53 29,.66 -23..92 30,06 -24,.31 30.,46 -24,.70

29..27 -23,,54 29,,67 -23..93 30..07 -24,,32 30..47 -24..71

29.,28 -23,.55 29,,68 -23. 94 30.08 -24,.33 30..48 -24..72

29..29 -23,,56 29,,69 -23. 95 30..09 -24,.34 30,.49 -24,.73

29..30 -23,,57 29,.70 -23..96 30.,10 -24,.35 30,.50 -24,.74

29..31 -23,,58 29,,71 -23..97 30,,11 -24,.36 30.,51 -24,.74

29..32 -23,,59 29,,72 -23..93 30..12 -24.,37 30.,52 -24,.75

29..33 -23,,60 29,,73 -23..99 30,.13 -24.,38 30..53 -24,.76

29..34 -23,,61 29.74 -24..00 30..14 -24,.39 30..54 -24,.77

29..35 -23,,62 29,,75 -24.,01 30,.15 -24,.40 30..55 -24,.78

29..36 -23,,63 29,,76 -24.,02 30..16 -24,,41 30..56 -24,.79

29..37 -23,,64 29,.77 -24.,03 30..17 -24,,41 30..57 -24..80

29..38 -23.,65 29..78 -24.,04 30.,18 -24,,42 30..58 -24,.81

29..39 -23.,66 29.,79 -24,,05 30.,19 -24,,43 30..59 -24..82

29..40 -23,,67 29,,80 -24.,06 30..20 -24.,44 30..60 -24.83

29..41 -23,,68 29.,81 -24.,07 30..21 -24,.45 30,.61 -24.,84

29..42 -23,,69 29.,82 -24.,08 30,,22 -24,.46 30,,62 -24..85

29..43 -23,.70 29,,83 -24.,09 30,,23 -24.,47 30,.63 -24..86

29..44 -23,,71 29,,84 -24.,10 30..24 -24..48 30,,64 -24..87

29..45 -23.,72 29,,85 -24.,10 30..25 -24,.49 30,.65 -24.88

29..46 -23,,73 29.,86 -24.,11 30,,26 -24,.50 30,.66 -24..89

29..47 -23,,74 29.,87 -24.,12 30.,27 -24,.51 30..67 -24..90

29..48 -23,,75 29,,88 -24. 13 30,,28 -24.,52 30,.68 -24..91

29..49 -23.,76 29,,89 -24. 14 30.,29 -24,.53 30,.69 -24.92

29..50 -23.,77 29..90 -24.,15 30..30 -24.,54 30,.70 -24..93

29..51 -23,,78 29.,91 -24.,16 30,,31 -24.,55 30,.71 -24..94

29..52 -23,,79 29.,92 -24.,17 30,,32 -24.,56 30,.72 -24,.95

29..53 -23.,79 29.,93 -24.,18 30,,33 -24,.57 30,.73 -24.96

29..54 -23,,80 29..94 -24..19 30,,34 -24,,58 30..74 -24..97

29..55 -23,,81 29.,95 -24..20 30..35 -24,,59 30,.75 -24..98

29..56 -23,.32 29.,96 -24..21 30.,36 -24.,60 30..76 -24..99

29..57 -23,,83 29,,97 -24. 22 30,,37 -24,,61 30,.77 -25..00

29..58 -23,,84 29..98 -24..23 30,.38 -24.,62 30,.78 -25,.01

29..59 -23,.85 29.,99 -24.,24 30.,39 -24.,63 30,.79 -25..02

29,.60 -23.,86 30.,00 -24.,25 30.,40 -24.,64 30,.80 -25..03

31
Kor-A^ A Aor-A A Ao^-A^ A A^Or-A

30.81 -25.04 31.21 -25.43 31.61 -25.81 32.01 -26.20

30.82 -25.05 31.22 -25.44 31.62 -25.82 32.02 -26.21

30.83 -25.06 31.23 -25.44 31.63 -25.83 32.03 -26.22

30.84 -25.07 31.24 -25.45 31.64 -25.84 32.04 -26.23

30.85 -25.08 31.25 -25.46 31.65 -25.85 32.05 -26.24

30.86 -25.08 31.26 -25.47 31.66 -25.86 32.06 -26.25

30.87 -25.09 31.27 -25.48 31.67 -25.87 32.07 -26.26

30.88 -25.10 31.28 -25.49 31.68 -25.88 32.08 -26.27

30.89 -25.11 31.29 -25.50 31.69 -25.89 32.09 -26.28

30.90 -25.12 31.30 -25.51 31.70 -25.90 32.10 -26.29

30.91 -25.13 31.31 -25.52 31.71 -25.91 32.11 -26.30

30.92 -25.14 31.32 -25.53 31.72 -25.92 32.12 -26.31

30.93 -25.15 31.33 -25.54 31.73 -25.93 32.13 -26.32

30.94 -25.16 31.34 -25.55 31.74 -25.94 32.14 -26.33

30.95 -25.17 31.35 -25.56 31.75 -25.95 32.15 -26.34

30.96 -25.18 31.36 -25.57 31.76 -25.96 32.16 -26.35

30.97 -25.19 31.37 -25.58 31.77 -25.97 32.17 -26.36

30.98 -25.20 31.38 -25.59 31.78 -25.98 32.18 -26.37

30.99 -25.21 31.39 -25.60 31.79 -25.99 32.19 -26.38

31.00 -25.22 31.40 -25.61 31.80 -26.00 32.20 -26.39

31.01 -25.23 31.41 -25.62 31.81 -26.01 32.21 -26.40

31.02 -25.24 31.42 -25.63 31.82 -26.02 32.22 -26.41

31.03 -25.25 31.43 -25.64 31.83 -26.03 32.23 -26.42

31.04 -25.26 31.44 -25.65 31.84 -26.04 32.24 -26.43

31.05 -25.27 31.45 -25.66 31.85 -26.05 32.25 -26.44

31.06 -25.28 31.46 -25.67 31.86 -26.06 32.26 -26.45

31.07 -25.29 31.47 -25.68 31.87 -26.07 32.27 -26.46

31.08 -25.30 31.48 -25.69 31.88 -26.08 32.28 -26.47

31.09 -25.31 31.49 -25.70 31.89 -26.09 32.29 -26.48

31.10 -25.32 31.50 -25.71 31.90 -26.10 32.30 -26.49

31.11 -25.33 31.51 -25.72 31.91 -26.11 32.31 -26.50

31.12 -25.34 31.52 -25.73 31.92 -26.12 32.32 -26.51

31.13 -25.35 31.53 -25.74 31.93 -26.13 32.33 -26.52

31.14 -25.36 31.54 -25.75 31.94 -26.14 32.34 -26.53

31.15 -25.37 31.55 -25.76 31.95 -26.15 32.35 -26.54

31.16 -25.38 31.56 -25.77 31.96 -26.16 32.36 -26.55

31.17 -25.39 31.57 -25.78 31.97 -26.17 32.37 -26.56

31.18 -25.40 31.58 -25.79 31.98 -26.18 32.38 -26.57

31.19 -25.41 31.59 -25.30 31.99 -26.19 32.39 -26.58

31.20 -25.42 31.60 -25.81 32.00 -26.20 32.40 -26.59

32

* U. S. GOVERNMENT PRINTING OFFICE : 1963 O - 679852


!*

U. S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the iol lowing listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized researcn, development, and engineering! in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the

front cover. WASHINGTON, D. C.

Electricity. Resistance and Reactance. ElectroGhemistry. Electrical Instruments. Magnetic Measurements

Dielectrics. High Voltage.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering Metrology.

Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Piure Substances. Spectrochemistry. Solution Chemistry. Standard Refer- ence Materials. Applied Analytical Research, Crystal Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Polymers. Macromolecules: Synthesis and Structure. Polymer Chemistry. Polymer Physics. Polymer Characterization. Polymer Evaluation and Testing. A^jplied Polymer Standards and Research. Dental Research.

Metallurgy. Engineering Metallurgy. Microscopy and Diffraction. Metal Reactions. Metal Physics. Electrolysis

and Metal Deposition.

Inorganic Solids. Engineering Ceramics. Class. Solid State Chemistry. Crystal Growth. Physical Properties.

Crystallography.

Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Metallic Bunding Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics. Operations Research. Data lYocessing Systems. Components and Techniques. Computer Technology. Measurements Automation.

Engineering Applications. Systems Analysis.

Atomic Physics. Spectroscopy. Infrared Spectroscopy. Far Ultraviolet Physics. Solid State Physics. Electron Physics. Atomic Physics. Plasma Spectroscopy.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy. Ele- mentary Processes. Mass Spectrometry. Photochemistry and Radiation Chemistry.

Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering Laboratory. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Cryogenic Technical Services. CENTRAI. RADIO PROPAGATION LABORATORY

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research. Prediction Services, Sun-Earth Relationships. Field Engineering. Radio Warning Services. Vertical Soundings Research.

Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements. Tropo^heric Analysis. Propagation-Terrain Effects. Radio-MeteOTology. Lower Atmosphere Physics.

Radio Systems. Applied Electromagnetic Theory. High Frequency and Very High Frequency Research. Fre- quency Utilization. Modulation Research. Antenna Research. Radiodetermination.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. High Latitude Ionosphere

Physics. Ionosphere and Exosphere Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.

RADIO STANDARDS LABORATORY

Radio Physics. Radio Broadcast Service. Radio and Microwave Materials. Atomic Frequency and Time-Interval

Standards. Radio Plasma. Millimeter^Wave Research.

Circuit Standards. High Frequency Electrical Standards. High Frequency Calibration Services. High Frequency

Impedance Standards. Microwave Calibration Services. Microwave Circuit Standards. Low Frequency Calibration

Services.
NBS"