PB 161561

'Moulder laboratories

9Zc. 60

AMPLITUDE AND PHASE OF THE LOWAND VERY- LOW- RADIOFREQUENCY

GROUND WAVE

BY J.R. JOHLER, L.C. WALTERS, AND CM. LILLEY

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS

technical *Vtote

No. 60

AMPLITUDE AND PHASE OF THE LOW- AND VERY

LOW-RADIOFREQUENCY GROUND WAVE

J, R, Johler

L, C, Walters

C. M. Lilley

Jiine 1, I960

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

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Price $ »75

CONTENTS

Page

Jr T6X0.C6 «««9»««0*«e«*«»»*«.»««***««g»«**i»«ft*e*«ft««»*o»ftft J.^^

List of Tables . , *...... 13-14

AMPLITUDE AND PHASE OF THE LOW- AND VERY

LOW-RADIOFREQUENCY GROUND WAVE

by

J. R. Johler

L. C. Walters

C. M. Lilley

ABSTRACT

Graphs and tables of the low- and very low-radiofrequency

ground wave are presented as a function of frequency, 100 c/s to

1000 kc.

PREFACE

Computation techniques for the classical Bremmer-van der Pol

I theory have been developed . As a result of various theoretical

ground wave pulse investigations during the past several years with

the aid of electronic computer programs p a considerable volume of

calculated data on the ground wave has been accumulated and is

J. R. Johler, W. J. Kellar, L. C. Walters, "Phase of the LowRadiofrequency Ground Wave, " NBS Circtolar 573, U. S, Gov. Print,

Off., Washington, D. C. , (1956). See also, J. R. Johler, L. C.

Walters, C, M, Lilley, "Low- and Very Low-Radiofrequency Tables

of Ground Wave Parameters for the Spherical Earth Theory: The

Roots of Riccati's Differential Equation, " NBS Technical Note No. 7,

PB 151366, February 1, 1959. An extensive bibliography is presented in the above papers. The following paper is of interest in the LFVLF spectrum: J. R. Wait and H, H. Howe, "Amplitude and Phase

Curves for Ground Wave Propagation in the Band 200 Cycles per

Second to 500 Kilocycles, " NBS Circtilar 574, U. S. Gov. Print.

Off., Washington, D. C. (1956).
herewith presented in tabular and graphical form , The computer

program employed the techniques described in NBS Circular 573,

hence, the forniulas will not be repeated here. The annplitude,

jE j volts/meter and the phase arg E = cj)^, radians have been

tabulated for various frequencies, f, distances, d, condxictivities

(T, dielectric constants e^, and vertical lapse of permittivity factors

CK, The tables employ standard tabular frequencies, f, and Gaussian

3

frequencies, f , described in published work on pulse propagation . IXl All fields, JE j, are normalized to a standard dipole current mount,

r 4

I i - 1, With the aid of the expression ,

P = 1. 6 (10"^^) J- (I l)^/z

r ^ o ' o

f

2

This tabulation was motivated by USAF Ground Electronics

Engineering and Installation Agency (GEEIA) requirements of NBS

project 8570-40-85472 ajid the application of the ground wave theory

to LF radio navigation systems such as L.oran-C (Cyctac) system

described in the following publication: W, P. Frantz, W, Dean,

R, L. Frank, "A Precision Multipurpose Radio Navigation System, " IRE 1957 Convention Record, Part 8, pp. 79-102,

3

See for example, J. R. Johler and L, C, Walters, "Propagation of a Ground Wave Pulse Around a Finitely Conducting Spherical Earth

from a Damped Sinusoidal Source Current, " IRE Trans, on antennas

and propagation, VoU AP-7j, NOo U January 1959s, pp. 1-10.

4

The notion of radiated power, P^,, is apparently due to S, Ballentine,

•'On the Radiation Resistance of a Simple Vertical Antenna at

Wavelengths Below the Fundamental, " Proc, IRE Vol« 12,, December

1924, pp. 823-839.
-3-

where z = 377 ohms, the conventioncd engineering notion of radiated

power, P , can be introduced. It is only necessary to employ a

linear translation of the scale, JE j volts/meter for dipole current

moments other than unity. These considerations, of course, do not

affect the phase.

The phase arg E = (j) is tabulated in radians. These values

can be readily converted to the conventional radio navigation system

microseconds, t , c

t = 10^ <j) /o) . c c'

The table entries include a number and an associated power of

ten (10), The integers to the right of each table entry, if present,

indicates the power of the factor ten (10) by which the entry is to be

mtiltiplied, thus, for example, 6.4307-1= 0.64307.

The number of terms (s + 1), s = 0, 1, 2, 3* • •

, of the series

of residues required for the calculation can be estimated with the

aid of Figs, 1, 2, assuming eight significant figure precision. Of

course, if less computation precision is required, fewer terms are

necessary^ Note the large increase in the number of terms required

at short distances and low frequencies as a result of the slow

convergence of the series of residue S9

Boulderp Colorado^ June 1, I960.
,List of Figures

Fig. 1 Highest order number, s = 0, 1, 2, 3* • • , of terms of the series of residues required

for eight significant figure computation

precision as a function of distance from the

source for various frequencies.

Fig, 2 Highest order number, s = 0, 1, 2, 3»»»,

of terms of the series of residues required

for eight significant figure computation

precision as a function of frequency for

various distances.

Figs, 3-8 Amplitude and phase of the ground wave.

Page

Fig. XT

15

a

0. 85

f, kc d, mi

3 0.0005 0.01-1000 15000-50 7

4 0.002 15 0. 85 0.01-1000 5000-50 8

5 0.005 15 0.85 0.01-1000 5000-50 9

6 0.0005 15 0.85 0.01-1000 12,49,329.

621, 1000 10

7 0.002 15 0. 85 0.01-1000 12.49,329,

621, 1000 11

8 5 80 0. 85 0.01-1000 12.49,329,

621, 1000 12
-5-

500

10 10 DISTANCE, d, STATUTE MILES

10

"

"

'" Fig. 1 - Highest order number, s - 0, 1, 2, 3 , of terras of the

series of residues required for eight significant figure

computation precision as a function of distance from the

source for various frequencies.
-6-

CO

CD ^ O

O

§

CO ^

S

"^O

+^ CD o "

CD ^H

-t-» O 4-> " ft

. o

CO u

rg f-t - bO • -< -rt CO '^ 0) • +-> o

,. tti Co " o -^

i^ W) CD ^ CD g

^ "^ u

'o O *+-< O _ -^^ 'do

"mo;

I

bO

•H

Q3aino3a S3m3S 3nais3d jo swa3i dO

'£'2'rO = S 'y39WnN y3aaO iS3H9IH
-7-

CO

10 -

10

1

1 1 1 ^

d=4000miA}^r^ - d = 3000mi-^>i;

^^^^^<^—

d = 2000 mi ^\^ V^l--'^^>^

1 d = IOOmi'^

1 1

10" lO"* 10' FREQUENCY, f, c/s

Fig. 3 - Amplitude and phase of the ground wave.
-8-

10'

10

I -

10

r^ /-d=5000mi

d=4000mi

d = 3000mi

d = 2000mi

d^lOOOmi

d= 500mi

d= 200 mile 10^ 10^ 10^ 10= 10^ FREQUENCY, f, c/s Fig. 4 - Amplitude and phase of the ground wave,
-9-

g 10

10

d-- 5000 m

.d = 4000m i d=3000mi

d =2000 mi- d=IOOOmi d=500mi

10 10^ 10^ 10^ FREQUENCY, f, c/s

10== 10"

Fig. 5 - Amplitude and phase of the ground wave.
-10-

FREQUENCY, f, C/S

Figo 6 - Amplitude and phase of the ground wave.
-11-

10'

§ 10

I -

10

1 1 1 1 g

\ ^^^\^'y^ \^^y 4/

'.if >^y \ ^-^""'"'''^ ^^^

>^ v"^

1 1 1 -^

1

10 iO*' FREQUENCY, f, C/S

Fig. 7 - Amplitude and phase of the ground wave,
-12-

10

CO

10 -

I -

10

1 1 1 1

1 1 1 1

10 10^ 10^ 10^ FREQUENCY, f, c/s

10== 10"

Fig. 8 - Amplitude and phase of the ground wave.
-13-

List of Tables

Page

Table f, kc d, mi (T *2 a

I 0.01-1000 5000-500 0.0005 15 0.1B5 15

2 200-50 16

3 0.02-1000 5000-500 0.002 17

4 200-50 18

5 0.1-1000 5000^500 0.005 19

6 200-50 20

7 0-50^ 12.49,329 0.0005 21

8 50-500* 22

9 500-1000^ 0.0005 23

10 0-50^ 621, 1000 24

II 50-500^ 25

U 500-1000' 26

13 0-50^ 12.49,329 0.002 27

14 50-500^ 28

15 500-1000' 29

16 0-50^ 621, 1000 30

17 50-500^ 31

18 500-1000^ 32

19 0-50^ 12.49,329 5 80 33

20 50-500^ 34

Tabulated at Gaussian frequencies^ f .
-14-

Paee

Table f, kc d, ml (T 2 a

21 500-1000' 35

22 0-50^ 621,1000 36

23 50-500' 37

24 500-1000' 38

25 153.5 50-600 0.001-0.006 0.75 39

26 153. 5 50-600 0.007-5 15,

80

0.75,

0.85 40

Tabulated at Gaussian frequencieSj £ . IljLX
-15-

Table 1

0- = Q, 0005 .,= 15 a = 0. 85*

d= 5000 miles d = 4000 miles

IM argE^ 1^1 argE^

1.0990 -12 1.8208 1.4845 -12 1.8787

6,6410 -12 1.4586 1 .040 5 -11 1.1502

9.2012 -12 1.7232 1.5876 -11 1.3446

1.1632 -11 2.2608 2.3738 -11 1.7663

1.1546 -11 2.8648 2.7736 -11 2.2504

9.4242 -12 3.7484 2.7674 -11 2.9626

4.9181 -12 5.7289 2.0276 -11 4,5636

1.9175 -12 2.1848 1.1144 -11 4.9710 - 1 2.8707 -13 7.8935 - 1 2.8306 -12 4.4540

1.0117 -16 5.8818 5.7607 -15 1.1197

1.05 -22 1.41 9.34 -20 1.46

3.74 -29 2.36 - 1 5.95 -25 5.59

1.966 -38 2.904

3.4618 -39 1.6389

d = 3000 miles dr: 2000 miles

2.4916 -12 2.1500 7.4449 -12 2,5822

1.7081 -11 8.6196 - 1 3.0635 -11 6.1766 - 1 2.8589 -11 9.7844 - 1 5.5865 -11 6.4262 - 1 5.0416 -11 1,2768 1.1495 -10 8.0551 - 1 6.9359 -11 1,6375 1.8531 -10 1.0347

8.4659 -11 2.1773 2.7646 -10 1.3958

8.7117 -11 3.3985 4.0007 -10 2.2340

6.7498 -11 5.0926 4.3720 -10 3.4052

2.9086 -11 1.8355 3.1967 -10 5.5003

3.4185 -13 2.6409 2.1697 -11 4,1622

8.68 -17 1.51 8.63 -14 1.57

9,87 -21 4.66 1.75 -16 3.72

2.369 -26 3.631 2.839 -20 8.536 - 1 1.9596 -31 3.1178 1.1865 -23 4.5968

f, kc

0.01

0.1

0.2

0.5

125 10

20

50

100

200

500

1000

0.01

0.1

0.2

0.5

12

5 10

20

50

100

200

500

1000

d = 1000 miles d = 500 miles

0.01

0.1 6.8851 -11 5.1809 - 1 1.3314 -10 8.3231 - 1 0.2 1.3706 -10 3.9547 - 1 2.8700 -10 4.2284 - 1 0.5 3.2211 -10 3.9541 - 1 7.2443 -10 2.6929 - 1

1 5.9590 -10 4.8016 - 1 1.4156 - 9 2.6434 - 1 2 1.0671 - 9 6.4934 - 1 2.7228 - 9 3.2905 - 1 5 2.1436 - 9 1.0870 6.2646 - 9 5.5584 - 1 10 3.2960 - 9 1.7262 1.1232 - 8 9.1797 - 1 20

50

100

200

500

1000 8.3616 -16 6.0759 8,3670 -12 5,3148 - 1

6,4543 -11 2.9167

6.8851 -11 5.1809

1.3706 -10 3.9547

3.2211 -10 3.9541

5.9590 -10 4.8016

1.0671 - 9 6.4934

2.1436 - 9 1.0870

3.2960 - 9 1.7262

4.0898 - 9 2.8858

1.6033 - 9 5.686

9.97 -11 1.62

3.62 -12 2.79

3.960 -14 4.359

8.3616 -16 6.0759

5.3842 -10 3,0340

1.3314 -10 8.3231

2.8700 -10 4.2284

7.2443 -10 2.6929

1.4156 - 9 2.6434

2.7228 - 9 3.2905

6.2646 - 9 5.5584

1.1232 - 8 9.1797

1.7982 - 8 1.5980

1.7020 - 8 3.3191

4.13 - 9 4.83

6.13 -10 5.48

5.56 -11 6.112

8,3670 -12 5.3148
.16-

Table 2

cr = 0.0005 6 = 15 a = 0, 85

d = 200 miles d = 100 miles

f.kc ]eJ argE^ ]e^] arg E^

0.01 8.5397 - 9 3.0982

0.1 7.3828 -10 2.2830

0.2 6.7000 -10 1.0639

0.5 1.8400 - 9 3.7040

1 3.7680 - 9 2.3100 - 1 7.4235 - 9 3.5798 - 1 2 7.5175 - 9 1.9968 - 1 1.5254 - 8 2.2213 - 1 5 1.8403 - 8 2.7898 - 1 3.8136 - 8 2.1141 - 1 10 3.5560 - 8 4.6014 - 1 7.5227 - 8 3.1147 - 1 20 6.5480 - 8 8.2889 - 1 1.4457 - 7 5.5008 - 1 50 1.0791 - 7 1.8435

100 6.86 - 8 3.00

200 2.03 - 8 3.51

500 5.706 - 9 3.509

1000 2.6896 - 9 3.5519

d = 50 miles

10 1.5356 - 7 2.4640 - 1 20 3.0137 - 7 3.9173 - 1 50 6.7009 - 7 8.8005 - 1 100 9.12 - 7 1.61

200 6.03 - 7 2.44

500 2.164 - 7 2.494

1000 1.480 - 7 2.252

7.4235

1.5254

3.8136

7.5227

1.4457

2.9011

2.96

1.24

4.278

2.6861

9 3.5798

8 2.2213

8 2.1141

8 3.1147

7 5.5008

7 1.2556

7 2.20

7 2.91

8 2.794

8 2.6223
-17-

f,kc

0- = 0.002

d = 5000 miles

Table 3

15 a :? 0. 85

arg E

d = 4000 miles

arg E

0.02

0.1

0.2

0.5

12

5 10

20

50

100

200

500

1000

0.02

0*1

0.2

0.5

12

5 10

20

50

100

200

500

1000

0.02

0.1

0.2

0.5

125 10

20

50

100

200

500

1000

2.1044 -12 1.3379

6.6346 -12 1.4488

9.1788 -12 1.7026

1.1542 -11 2.2050

1.1347 -11 2.7452

9.0964 -12 3.4898

4.6117 -12 5.0078

1.9103 -12 6.2694

4.9695 -13 3.8241

1.4156 -14 5.8833

7.91 -18 4.73

2.86 -25 3.84

1.06 -36 6.37

6.78 -47 4.71

d = 3000 miles

3.9322 -12 1.1543

1.7075 -11 8.5485

2.8560 -11 9.6386

5.0241 -11 1.2386

6.8794 -11 1.5573

8.3212 -11 2.0071

8.4539 -11 2.9334

6.8394 -11 4.0996

4.1642 -11 6.0631

7.3108 -12 4.9082

1.06 -13 5.67

3.88 -18 4.36

4.19 -25 6.22

9.33 -31 5.24

d= 1000 miles

2.9168 -11 2.4068

6.8848 -11 5.1420

1.3704 -10 3.8765

3.2199 -10 3.7563

5.9541 -10 4.4014

1.0657 - 9 5.6801

2.1474 - 9 8.7765

3.3900 - 9 1.2971

4.8356 - 9 2.0220

5.2378 - 9 3.9340

1.97 - 9 3.22

7.30 -11 3.32

2.30 -13 5.51

2.38 -15 9.15

- 1

2.8146 -12 1.19878

1.0398 -11 1.1417

1.5850 -11 1.3270

2.3607 -11 1.71933

2.7385 -11 2.1505

2.6955 -11 2.7482

1.9342 -11 3.9705

1.1197 -11 5.5048

4.4562 -12 1.8020

3.1513 -13 2.2542

8.97 -16 5.20

1.03 -21 2.14

6.54 -31 3.43

2.13 -38 4.26

d = 2000 miles

6.1780 -12 1.3967

1 3.0629 -11 6.1203

1 5.5838 -11 6,3119

1.1476 -10 7.7610

1.8458 -10 9.7402

2.7415 -10 1.2696

3.9494 -10 1.8968

4.4680 -10 2.6945

4.1622 -10 4.0412

1.8141 -10 1.2791

1.34 -11 6.14

1 1.56 -14 5.02

2.88 -19 2.72

4.37 -23 6.22

d = 500 miles 2.5786 -10 2.8466

1 1.3314 -10 8.2959

1 2.8699 -10 4.1737

1 7.2439 -10 2.5557

1 1.4156 - 9 2.3678

1 2.7236 - 9 2.7361

1 6.2927 - 9 4.1580

1.1496 - 8 6.3588

2.0013 - 8 1.0378

3.3925 - 8 2.1323

1 2.88 - 8 3.71

5.92 - 9 5.63

2.44 -10 6.24

1 2.09 -11 1.40

- 1
-18-

Table 4

(T = 0. 002

d = 200 miles

.2=15 a = 0. 85

100 miles

f,kc

0.5

0.2

12

5 10

20

50

100

200

500

1000

10

20

50

100

200

500

1000

arg E

1.8401 - 9 3.6179 - 1 6.6998 - 10 1.0605

3.7683 - 9 2.1376 - 1 7.4240 - 9 7.5206 - 9 1.6515 - 1 1.5258 - 8 1.9780 - 1 1.8458 - 8 1.9247 - 1 3.8205 - 8 1.5054 - 1 3.6019 - 8 2.8710 - 1 7.5789 - 8 1.8984 - 1 6.9075 - 8 4.8588 - 1 1.4901 - 7 3.0846 - 1 1.5000 - 7 1.0646 3.4859 - 7 6.8634 - 1 2.10 - 7 1.95 5.81 - 7 1.29

1.33 - 7 3.30 6.07 - 7 2.35

2.14 - 8 4.16 1.60 - 7 3.31

6.23 — 9 4.28 6.11 - 8 3.30

d = 50 m iles

1.5421 _ 7 1.6054 - 1 3.0655 - 7 2.2083 - 1 7.4244 - 7 4.6801 - 1 1.35 - 6 8.90 - 1 1.89 - 6 1.68

8.90 - 7 2.88

3.41 - 7 2.91
-19-

f.kc

0.1

0.2

0.5

12

5 10

20

50

100

200

500

1000

Table 5

0- = 0.005 *2 = 15 a == 0.85

d = 5000 m iles d = 4000 miles

]E ] arg E ]E J I arg E

J.

I " r

J J.J 6 J. 6.6322 -12 1.4452 1.0396 -11 1.1386

9.1704 -12 1.6951 1.5839 -11 1.3205

1.1507 -11 2.1846 2.3556 -11 1.7021

1.1269 -11 2.7013 2.7244 -11 2.1138

8.9575 -12 3.3947 2.6645 -11 2.6694

4.4371 -12 4.7418 1.8783 -11 3.7518

1.7980 -12 4.5550 - 2 1.0697 -11 5.0291

4.8447 -13 2.5605 4.3881 -12 7.7203 - 1 2.9901 -14 2.5585 5.7979 -13 5.8348

3.927 -16 5.616 2.097 -14 7.189 - 1 5.48 -21 1.27 3.09 -18 6.23

4.02 -34 4.28 9.28 -29 4.89 - 2 1.54 -44 l.H - 1 3.91 -37 5.08 - 1

d = 3000 miles d = 2000 miles

0.1

0.2

0.5

12

5 10

20

50

100

200

500

1000

1.7072 -11 8.5224 - 1 3.0627 -11 6.0995 - 1 2.8549 -11 9.5850 - 1 5.5828 -11 6.2698 - 1 5.0172 -11 1.2245 1.1469 -10 7.6529 - 1 6.8563 -11 1.5278 1.8427 -10 9.5173 - 1 8.2569 -11 1.9445 2.7304 -10 1.2232

8.2863 -11 2.7619 3.9072 -10 1.7725

6.6318 -11 3.7295 4.3974 -10 2.4301

4.1419 -11 5.2668 4.1816 -10 3.4784

1.1716 -11 2.8280 2.5323 -10 6.1045

1.167 -12 2.205 6.946 -11 3.691

1.82 -15 4.91 1.15 -12 3.59

2.23 -23 2.10 5.74 -18 4.14

1.03 -29 9.04 - 1 2.92 -22 1.30

d = 1000 miles d = 500 miles

0.1

0.2

0.5

12

5 10

20

50

100

200

500

1000

6.8847 -11 5.1277 1 1.3314 -10 8.2858 - 1 1.3704 -10 3.8477 1 2.8699 -10 4.1536 - 1 3.2194 -10 3.6837 1 7.2436 -10 2.5052 - 1 5.9516 -10 4.2544 1 1.4154 - 9 2.2665 - 1 1.0646 - 9 5.3811 1 2.7232 - 9 2.5323 - 1 2.1423 - 9 8.0055 1 6.2933 - 9 3.6426 - 1 3.3840 - 9 1.1379 1.1522 - 8 5.3156 - 1 4.9050 - 9 1.6924 2.0309 - 8 8.2657 - 1 6.3679 - 9 3.0981 3.8271 - 8 1.6079

4.812 - 9 5.178 4.795 - 8 2.786

8.41 -10 2.27 2.73 - 8 4.75

1.72 -12 6.19 1.11 - 9 9.33 - 1 9.63 -15 1.70 6.58 -11 1.89
-20-

Table 6

f,kc

0.

0.

0.

12

5 10

20

50

100

200

500

1000

20

50

100

200

500

cr = 0. 005 ^2 = 15 a = 0. 85

d = 200 miles d = 100 miles

Kl argE^ KI are E 5 r 7.3828 - 10 2.2806

6,6998 - 10 1.0592

1.8^01 - 9 3.5863 - 3.7683 - 9 2.0742 - 7.4241 - 9 3.4135 - 1 7.5209 - 9 1.5246 - 1.5259 - 8 1.8886 - 1 1.8466 - 8 1.6065 - 3.8216 - 8 1.2816 - 1 3.6091 - 8 2.2328 - 7.5882 - 8 1.4504 - 1 6.9687 - 8 3.5800 - 1.4978 - 7 2.1886 - 1 1.5921 - 7 7.4895 - 3.6034 - 7 4.6450 - 1 2.670 - 7 1.367 6.622 - 7 8.701 - 1 3.14 - 7 2.47 1.01 - 6 1.63

7.66 - 8 4.19 5.67 - 7 3.19

1.69 " 8 4.60 1.61 " 7 3.57

d = 50 mile s 3.0742 - 7 1.5765 - 1 7.5600 - 7 3.1110 - 1 1.451 - 6 5.846 - 1 2.53 - 6 1.12

2.67 - 6 2.44
-21.

0- = 0. 0005

d = 12.49 miles

Table 7

15 a = 0, 85

d = 329 miles

f, kc

0.,030725

.16175

,39689

,73521

1 ,1753

1.,7153

2 ,3530

3,,0857

3,,9103

4 ,8233

5 ,8210

6.,8991

8.,0532

9.,2783

10 ,569

11 ,921

13 ,327

14 ,783

16,,281

17 ,816

19,,381

20,,969

22,,575

24,,190

25,,810

27,,425

29,,031

30,,619

32,,184

33,,719

35,,217

36 ,673

38,,079

39,,431

40,,722

41 ,947

43,,101

44,,179

45 ,177

46,,090

46 ,914

47 ,647

48 .285

48 ,825

49 ,265

49 ,603

49 ,838

49 .969

1.1456

2.1713

8.7482

4.5755

2.7036

1.7778

1.4836

1.6796

2.1409

2.7237

3.3756

4.0786

4.8254

5.6119

6.4348

7.2911

8.1773

9.0898

1.0025

1.0979

1.1947

1.2925

1.3910

1.4896

1.5880

1.6856

1.7822

1.8772

1.9703

2.0611

2.1492

2.2343

2.3161

2.3942

2.4684

2.5385

2.6041

2.6650

2.7211

2.7723

2.8182

2.8589

2.8942

2.9240

2.9482

2.9668

2.9797

2.9868

argE

5 3.1289^

6 3.0746

7 2.9746

7 2.8177

7 2.5709

7 2.1692

7 1.6078

7 1.1089

7 7.9887

7 6.1712

7 5.0469

7 4.3115

7 3.8124

7 3.4673

7 3.2286

7 3.0665

7 2.9617

7 2.9009

6 2.8744

6 2.8751

6 2.8978

6 2.9381

6 2.9926

6 3.0587

6 3.1339

6 3.2163

6 3.3041

6 3.3960

6 3.4905

6 3.5865

6 3.6829

6 3.7788

6 3.8732

6 3.9655

6 4.0548

6 4.1405

6 4.2220

6 4.2987

6 4.3703

6 4.4361

6 4.4958

6 4.5490

6 4.5955

6 4.6350

6 4.6673

6 4.6921

6 4.7094

6 4.7190

J1,,0573

3 ,3338

8 ,8931

1 ,6570

2 ,6295

3,,7981

5 ,1511

6 ,6750

1 8,,3551

1 1

,

.0175

,2117

1 1 ,4162

1 1

,

,6290

1 1 ,8478

1 2 .0704

1 2 ,2945

1 2 ,5176

1 2 ,7374

1 2,,9514

1 3 ,1576

1 3 ,3539

1 3 ,5384

1 3,.7096

1 3,,866

1 4 .007

1 4,,13

1 4,,24

1 4 ,33

1 4 ,41

1 4,,47

1 4,,52

1 4 ,56

1 4 ,58

1 4 ,59

1 4,.60

1 4 ,59

1 4,,59

1 4 ,57

1 4 ,56

1 4 ,54

1 4 ,52

1 4 ,50

1 4,,48

1 4 ,47

1 4,,45

1 4,,44

1 4 ,43

1 4,,43

argE

9 2.7485

10 7.4341

10 3.2068

9 2.3618

9 2.2055

9 2.3182

9 2.5746

9 2,9248

9 3.3452

8 3.8226

8 4.3489

8 4.9183

8 5.5261

8 6.1683

8 6.8413

8 7.5415

8 8.2652

8 9.0089

8 9.7690

8 1.0542

8 1.1324

8 1.2111

8 1.2899

8 1.369

8 1.447

8 1.52

8 1.60

8 1.67

8 1.75

8 1.82

8 1.88

8 1.95

8 2.01

8 2.07

8 2.12

8 2.18

8 2.22

8 2.27

8 2.31

8 2.35

8 2.38

8 2.41

8 2.43

8 2.45

8 2.47

8 2.48

8 2.49

8 2.50

t Gaussian frequencies, interval: 0-50 kc.
-22-

Table 8

0. 0005 = 15 a = 0. 85

t

f. kc

50 • 277

51 • 456

53 .572

56 .617

60 .578

65,.438

71 .177

77 .771

85 .193

93 .410

102 .39 112 .09

122 .48 133 .50

145,,12

157,.29 169 .95 183,.05 196,• 53

210,.34 224,,43

238,.72 253, 17

267,.71 282,,29

296,,83

311,,28

325,,57

339, 66

353,,47

366.,95

380. 05

392, 71 404,,88

416. 50

427, 52

437,,91

447,,61

456,,59

464,,81

472,,23

478,,82

484,,56

489, 42

493, 38

496, 43

498, 54

499,,72

d = 12.49 mi] es Kl argE^

3.0036 - 6 4.7416

3.0679 - 6 4.8286

3.1820 - 6 4.9855

3.3438 - 6 5.2128

3.5497 - 6 5.5103

3.7949 - 6 5.8772

4.0735 - 6 6.3113

4.3780 - 6 6.8092

4.7001 - 6 7.3665

5.0302 - 6 7.9771

5.3581 - 6 8.6344

5.6734 - 6 9.3303

5.9659 - 6 1.00 56

6.2264 - 6 1.0803

6.4472 - 6 1.1562

6.6224 - 6 1.2322

6.7485 - 6 1.3074

6.8246 - 6 1.3810

6.8519 - 6 1.4521

6.8338 - 6 1.5200

6.7754 - 6 1.5841

6.6828 - 6 1.6440

6.5628 - 6 1.6992

6.4222 - 6 1.7496

6.2674 - 6 1.7951

6.1043 - 6 1.8358

5.9378 - 6 1.8719

5.7721 - 6 1.9035

5.6105 - 6 1.9309

5.4552 - 6 1.9546

5.3081 - 6 1.9748

5.1702 - 6 1.9919

5.0422 - 6 2.0063

4.9243 - 6 2.0183

4.8165 - 6 2.0282

4.7186 - 6 2.0363

4.6303 - 6 2.0430

4.5512 - 6 2.0483

4.4809 - 6 2.0526

4.4188 - 6 2.0560

4.3646 - 6 2.0586

4.3181 - 6 2.0607

4.2786 - 6 2.0623

4.2459 - 6 2.0634

4.2198 - 6 2.0643

4.2001 - 6 2.0649

4.1865 - 6 2.0653

4.1791 - 6 2.0655

d = 329 miles

lE 1

.42

.37

.29

.14

.93

.03

.82

.51

.16

.82

.51

.25

.13

.33

.75

.52

.53

.75

.11

.59

.16

.81

.51

.25

.04

.86

.698

.563

.4453

.3433

.2545

.1769

.1089

.0494

.9725

.5148

.1138

.7632

.4577

.1929

.9650

.7709

.6081

.4745

.3684

.2885

.2337

.2035

- 8

- 8

- 8

- 8

- 8

- 8

- 8

- 8

- 8

- 8

- 8

- 8

- 8

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9 -10

-10

-10

-10

-10

-10

-10

-10

-10 -10

-10 -10 10

-10

arg E^

2.51

2.55

2.63

2.74

2.87

2.88

3.14

3.34

3.51

3.66

3.78

3.88

4.02

4.10

4.17

4.21

4.25

4.28

4.31

4.33

4.35

4.37

4.39

4.40

4.42

4.43

4.446

4.459

4.4704

4.4814

4.4919

4.5017

4.5110

4.5198

4.5281

4.5359

4.5431

4.5498

4.5560

4.5616

4.5666

4.5711

4.5750

4.5782

4.5809

4,5830

4.5844

4.5852

t Gaussian frequencies, interval: 50-500 kc.
-23-

Table 9

(T ± 0.0005 15 a = 0, 85

d = 12.49 miles

Tf.kc

500..31 501,.62 503,.97 507,.35 511,.75 517,.15 523,,53

530,.86 539,.10 548,.23 558,.21 568,.99 580,.53 592,.78 605,.69 619..21 633. 27

647,.83 662,.81 678. 16

693,.81 709,.69 725,.75 741,.90 758,.10 774,.25 790 .31 806,.19 821,.84 837,.19 852,.17 866,.73 880,.79 894,.31 907, 22

919,.47 931,.01 941,.79 951,,77

960 ,90

969,,14

976,.47 982 ,85

988 ,25

992 ,65

996 ,03

998,,38

999 ,69

arg E

4.1754 - 6 2.0656

4.1671 - 6 2.0658

4.1524 - 6 2.0662

4.1315 - 6 2.0667

4.1048 - 6 2.0673

4.0728 - 6 2.0678

4.0359 - 6 2.0683

3.9949 - 6 2.0687

3.9503 - 6 2.0688

3.9031 - 6 2.0688

3.8532 - 6 2.0684

3.8024 - 6 2.0676

3.7500 - 6 2.0664

3.6975 - 6 2.0648

3.6452 - 6 2.0627

3.5931 - 6 2.0604

3.5429 - 6 2.0575

3.4939 - 6 2.0542

3.4461 - 6 2.0506

3.3998 - 6 2.0469

3.3560 - 6 2.0427

3.3154 - 6 2.0388

3.2775 - 6 2.0335

3.2375 - 6 2.0288

3.2004 - 6 2.0250

3.1745 - 6 2.0221

3.1330 - 6 2.0130

3.0999 - 6 2.0087

3.0836 - 6 2.0076

3.0538 - 6 2.0000

3.0371 - 6 1.9978

3.0135 - 6 ?..9949

3.0557 - 6 1.9833

2.9261 - 6 1.9763

2.9456 - 6 2.0036

2.9758 - 6 1.9502

2.9678 - 6 1.9663

2.8875 - 6 1.9611

2.8976 - 6 1.9967

2.8472 - 6 1.9869

2.9055 - 6 1.9746

2.8803 - 6 1.9512

2.8839 - 6 1.9691

2.7757 - 6 1.9851

2.8165 - 6 1.9074

2.8653 - 6 1.9649

2.9340 - 6 1.9228

2.8464 - 6 1.9773

1 = 329 mile s E J

argE^

7,.1886 -10 4.5856

7,.1554 -10 4.5864

7,.0964 -10 4.5880

7 ,0128 -10 4.5903

6,.9064 -10 4,5932

6,.7794 -10 4.5968

6,.6342 -10 4.6011

6,.4734 -10 4.6060

6,,2998 -10 4.6115

6,.1162 -10 4.6176

5,.9251 -10 4.6242

5,.7291 -10 4,6314

5,.5305 -10 4.6391

5,.3315 -10 4,6473

5,.1338 -10 4,6559

4,.9390 -10 4,6649

4,.7485 -10 4,6743

4,.5634 -10 4,6840

4,.3844 -10 4.6941

4,.2123 -10 4,7044

4,.0474 -10 4,7149

3,.8902 -10 4,7256

3,,7408 -10 4,7365

3,.5993 -10 4,7474

3,.4657 -10 4,7584

3,.3399 -10 4,7694

3 ,2217 -10 4.7803

3,.1109 -10 4.7912

3,.0074 -10 4.8019

2,.9110 -10 4.8124

2,.8213 -10 4.8226

2,.7381 -10 4.8326

2,.6612 -10 4.8423

2,.5904 -10 4.8515

2,.5253 -10 4.8604

2,.4658 -10 4.8688

2,.4117 -10 4.8768

2..3627 -10 4.8842

2,.3187 -10 4,8911

2,.2794 -10 4,8974

2,.2449 -10 4,9030

2,.2148 -10 4,9081

2,.1891 -10 4,9125

2,.1677 -10 4,9162

2,.1504 -10 4.9192

2,.1373 -10 4.9215

2,.1283 -10 4.9232

2,.1233 -10 4.9241

t Gaussian frequencies, interval: 500-tOOX) kc.
-24-

Table 10

0- = 0. 0005

d = 621 miles

.2=15 a = 0. 85

d = 1000 miles

t f,kc I-J arg E^ |EJ arg E^

0.030725 7.9832 - 11 2.4046 2.2340 - 11 1.6720

0.16175 1.8504 - 10 4.4409 - ]L 1.1158 - 10 4.1786 - 1 0.39689 4.5575 - 10 2.9672 - ]L 2.6084 - 10 3.8290 - 1 0.73521 8.2308 - 10 2.9082 - ]L 4.5513 - 10 4.3354 - 1 1.1753 1.2781 - 9 3.2295 - ]L 6.8479 - 10 5.1098 - 1 1.7153 1.8107 - 9 3.7273 - ]L 9.4105 - 10 6.0287 - 1 2.3530 2.4106 - 9 4.3369 - ]L 1.2162 - 9 7.0530 - 1 3.0857 3.0676 - 9 5.0317 - ]L 1.5035 - 9 8.1662 - 1 3.9103 3.7715 - 9 5.7983 - ]L 1.7967 - 9 9.3602 - 1 4.8233 4.5117 - 9 6.6288 - ]L 2.0902 - 9 1.0630

5.8210 5.2778 - 9 7.5174 - ][ 2.3788 - 9 1.1970

6.8991 6.0589 - 9 8.4594 - ]L 2.6576 - 9 1.3378

8.0532 6.8439 - 9 9.4505 - ]L 2.9219 - 9 1.4848

9.2783 7.6218 - 9 1.0486 3.1673 - 9 1.6375

10.569 8.3814 - 9 1.1563 3.3898 - 9 1.7955

11.921 9.1116 - 9 1.2674 3.5857 - 9 1.9582

13.327 9.8022 - 9 1.3817 3.7520 - 9 2.1248

14.783 1.0443 - 8 1.4986 3.8864 - 9 2.2948

16.281 1.1026 - 8 1.6175 3.9873 - 9 2.4673

17,816 1.1544 - 8 1.7379 4.0538 - 9 2.6417

19.381 1.1990 - 8 1.8592 4.0862 - 9 2.8171

20.969 1.2361 - 8 1.9809 4.0855 - 9 2.9926

22.575 1.2655 - 8 2.1024 4.0537 - 9 3.1676

24.190 1.287 - 8 2.223 3.993 - 9 3.341

25.810 1.301 - 8 2.342 3,908 - 9 3.512

27.425 1.308 - 8 2.460 3.801 - 9 3.680

29.031 1.308 - 8 2.575 3.677 - 9 3.845

30.619 1.302 - 8 2.687 3.539 - 9 4.004

32.184 1.291 - 8 2.796 3.392 - 9 4.159

33.719 1.275 - 8 2.901 3.240 - 9 4.308

35.217 1.26 - 8 3.00 3.09 - 9 4.45

36.673 1.23 - 8 3.10 2.93 - 9 4.59

38.079 1.21 - 8 3.19 2.78 - 9 4.71

39.431 1.18 - 8 3.28 2.64 - 9 4.84

40.722 1.15 - 8 3.36 2.50 - 9 4.95

41.947 1.13 - 8 3.43 2.37 - 9 5.05

43.101 1.10 - 8 3.50 2.25 - 9 5.15

44.179 1.07 - 8 3.57 2.14 - 9 5.24

45.177 1.05 - 8 3.62 2.04 - 9 5.32

46.090 1.03 - 8 3.68 1.96 - 9 5.39

46.914 1.01 - 8 3.72 1.88 - 9 5.46

47.647 9.88 - 9 3.76 1.81 - 9 5.51

48.285 9.71 - 9 3.80 1.75 - 9 5.56

48.825 9.57 - 9 3.83 1.70 - 9 5.60

49,265 9.46 - 9 3.85 1.67 - 9 5.63

49.603 9.37 - 9 3.87 1.64 - 9 5.66

49.838 9.31 - 9 3.88 1.62 - 9 5.67

49.969 9.28 - 9 3.89 1.61 - 9 5.68

t Gaussian frequencies, interval: 0-50kc.
-25-

Table 11

a- = 0.0005 15 a = 0. 85

d = 621 miles d = 1000 miles

1 f, kc

50.,277

51,,456

53 ,572

56..617

60,,578

65.,438

71.,177

77.,771

85.,193

102.,39

112.,09

122.,48

133 ,50

145.,12 157.,29

169 ,95 183.,05

196.,53

210.,34

224.,43

238.,72

253 ,17

2674 71

282.,29

296.,83

311.,28

325.,57

339.,66

353.,47

366 ,95

380 .05 392.,71

404.,88

416. 50

427. 52

437, 91

447.,61

456.,59

464,,81

472,,23

478 ,82

484,,56

489 ,42

493 ,38

496,,43

498,,54

499 ,72

E arg E J j.i ^ r 9.20 - 9 3.91

8.89 - 9 3.97

8.34 - 9 4.07

7.58 - 9 4.22

6.63 - 9 4.39

4.52 - 9 4.35

4.09 - 9 4.71

3.38 - 9 5.00

2.64 - 9 5.23

1.50 - 9 5.58

1.12 - 9 5.72

8.31 -10 5.85

6.27 -10 5.95

4.79 -10 6.04

3.70 -10 6.12

2.89 -10 6.20

2.29 -10 6.26

1.83 -10 4.48

1.48 -10 1.05

1.20 -10 1.62

9.92 -11 2.16

8.24 -11 2.68

6.92 -11 3.17

5.85 -11 3.65

4.99 -11 4.10

4.298 -11 4.529

3.729 -11 4.941

3.2601 -11 5.3352

2.8721 -11 5.7106

2.5493 -11 6.0679

2.2793 -11 6.4069

2.0525 -11 6.7278

1.8613 -11 7.0304

1.6996 -11 7.3145

1.5626 -11 7.5801

1.4462 -11 7.8268

1.3474 -11 8.0545

1.2636 -11 8.2630

1.1926 -11 8.4519

1.1329 -11 8.6210

1.0830 -11 8.7703

1.0418 -11 8.8993

1.0085 -11 9.0080

9.8238 -12 9.0962

9.6287 -12 9.1638

9.4960 -12 9.2107

9.4231 -12 9.2367

arg E

1.58 - 9 5.71

1.48 - 9 5.79

1.32 - 9 6.93

1.11 - 9 6.12

8.83 -10 5.78 - 2 4.64 -10 6.28

4.07 -10 5.00 - 1 3.05 -10 8.88 - 1 2.10 -10 1.20

1.38 -10 1.46

8.92 -11 1.67

5.77 -11 1.86

3.75 -11 2.02

2.48 -11 2.17

1.66 -11 2.30

1.13 -11 2.43

7.84 -12 2.55

5.51 -12 2.66

2 3.93 -12 2.77

2.84 -12 2.87

2.09 -12 2.97

1.55 -12 3.06

1.17 -12 3.15

8.96 -13 3.24

6.93 -13 3.33

5.43 -13 3.41

4.307 -13 3,486

3.456 -13 3.561

2.8048 -13 3.6336

2.3025 -13 3.7029

1.9113 -13 3.7690

1.6042 -13 3.8318

1.3611 -13 3.8914

1.1672 -13 3.9476

1.0116 -13 4.0005

8.8597 -14 4.0499

7.8402 -14 4.0958

7.0096 -14 4.1382

6.3312 -14 4.1769

5.7767 -14 4.2121

5.3239 -14 4,2435

4.9561 -14 4.2713

4.6598 -14 4.2953

4.4249 -14 4.3155

4.2436 -14 4.3319

4.1101 -14 4.3444

4.0202 -14 4.3531

3.9711 -14 4.3580

t Gaussian frequencies, interval: 50-500 kc.
-26-

Table 12

0- = 0.0005 = 15 a = 0, 85

t

f, kc

d = 621 miles

arg E

d = 1000 miles

arg E

500.31

501.62

503.97

507.35

511.75

517.15

523.53

530.86

539.10

548.23

558.21

568.99

580.53

592.78

605.69

619.21

633.27

647.83

662.81

678.16

693.81

709.69

725.75

741.90

758.10

774.25

790.31

806.19

821.84

837.19

852.17

866.73

880.79

894.31

907.22

919.47

931.01

941.79

951.77

960.90

969.14

976.47

982.85

988.25

992.65

996.03

998.38

999.69

9.3873 -12 9.2496 - 1 3 .9470 -14 4.3604

9.3075 -12 9.2786 - 1 3 .8937 -14 4.3657

9.1665 -12 9.3304 - 1 3 .8000 -14 4.3753

8.9683 -12 9.4047 - 1 3 .6697 -14 4.3891

8.7186 -12 9.6011 - 1 3 .5080 -14 4.4070

8.4243 -12 9.6188 - 1 3 .3206 -14 4.4289

8.0928 -12 9.7571 - 1 3 .1142 -14 4.4545

7.7322 -12 9.9151 - 1 2 .8951 -14 4.4838

7.3504 -12 1.0092 2 .6696 -14 4.5165

6.9553 -12 1.0286 2 .4433 -14 4.5524

6.5538 -12 1.0497 2 .2209 -14 4,5913

6.1525 -12 1.0722 2 .0064 -14 4.6330

5.7568 -12 1.0962 .8029 -14 4,6773

5.3714 -12 1.1215 .6125 -14 4,7238

4.9998 -12 1.1478 .4364 -14 4,7723

4.6450 -12 1.1752 .2753 -14 4.8225

4.3087 -12 1.2034 ,1294 -14 4.8743

3.9924 -12 1.2324 9..9821 -15 4.9273

3.6967 -12 1.2620 8 .8109 -15 4,9813

3.4217 -12 1.2920 7..7715 -15 5.0360

3.1671 -12 1.3223 6..8537 -15 5.0912

2.9325 -12 1.3529 6..0466 -15 5.1467

2.7170 -12 1.3835 5..3394 -15 5,2022

2.5197 -12 1.4140 4..7214 -15 5,2574

2.3396 -12 1.4444 4..1826 -15 5.3123

2.1755 -12 1.4745 3 .7136 -15 5.3665

2.0263 -12 1.5042 3..3060 -15 5.4198

1.8910 -12 1.5333 2..9519 -15 5.4721

1.7684 -12 1.5618 2..6446 -15 5.5232

1.6575 -12 1.5896 2. 3781 -15 5.5729

1.5575 -12 1.6165 2..1468 -15 5,6209

1.4673 -12 1.6425 .9463 -15 5.6673

1.3861 -12 1.6675 .7724 -15 5.7117

1.3133 -12 1.6914 6217 -15 5.7541

1.2480 -12 1.7140 4911 -15 5.7943

1.1897 -12 1.7354 .3781 -15 5.8322

1.1378 -12 1.7555 .2803 -15 5,8677

1.0918 -12 1.7742 1961 -15 5,9007

1.0512 -12 1.7914 1236 -15 5,9311

1.0157 -12 1.8070 0616 -15 5,9587

9.8483 -13 1.8212 0089 -15 5,9836

9.5837 -13 1.8337 9. 6450 -16 6,0056

9,3604 -13 1.8445 9. 2766 -16 6,0248

9.1762 -13 1.8537 8. 9769 -16 6.0409

9.0294 -13 1.8612 8. 7408 -16 6.0540

8.9184 -13 1.8669 8, 5639 -16 6,0641

8.8423 -13 1.8709 8. 4434 -16 6,0711

8.8002 -13 1.8731 8. 3771 -16 6,0749

t Gaussian frequencies, interval: 500-1000 kc.
-27-

Table 13

0- = 0, 002 ^2 = 15 a = 0. 85

tf.kc

d = 12.49 miles d = 329 rrliles

]E ] arg E ]E ] arg E ' r

° r

J 3-

J

" r

0.030725 1.1456 _ 5 3,1288 5,8965 _ 10 2.8187

0.16175 2.1713 - 6 3.0739 3 ,3338 - 10 7.3983 - 1 0.39689 8,7482 - 7 2.9729 8 .8931 - 10 3.1190 - 1 0.73521 4.5756 - 7 2.8146 1 .6570 - 9 2.1988 - 1 1.1753 2.7037 - 7 2.5658 2 ,6297 - 9 1.9444 - 1 1.7153 1.7778 - 7 2.1619 3 ,7992 - 9 1.9364 - 1 2.3530 1.4837 - 7 1.5977 5 ,1546 - 9 2.0501 - 1 3.0857 1.6799 - 7 1.0956 6 ,6838 - 9 2.2359 - 1 3.9103 2.1413 - 7 7.8208 - 1 8 ,3741 - 9 2.4710 - 1 4.8233 2.7246 - 7 5.9642 - 1 1 ,0212 - 8 2.7430 - 1 5.8210 3,3772 - 7 4.7971 - 1 1 ,2185 - 8 3,0446 - 1 6.8991 4.0813 - 7 4,0155 - 1 1 ,4278 - 8 3.3711 - 1 8.0532 4.8298 - 7 3.4669 - 1 1 ,6477 - 8 3.7191 - 1 9.2783 5.6187 - 7 3.0694 - 1 1 ,8767 - 8 4.0859 - 1 10.569 6 , 44 5

1

- 7 2.7753 - 1 2 ,1134 - 8 4.4692 - 1 11.921 7,3059 - 7 2.5554 - 1 2 ,3563 - 8 4.8670 - 1 13.327 8.1980 - 7 2,3905 - 1 2 .6038 - 8 5.2774 - 1 14.783 9.1181 - 7 2.2674 - 1 2 ,8545 - 8 5.6986 - 1 16.281 1.0063 - 6 2,1770 - 1 3 ,1070 - 8 6.1288 - 1 17.816 1.1028 - 6 2,1124 - 1 3 ,3597 - 8 6.5663 - 1 19.381 1.2011 - 6 2.0684 - 1 3 ,6113 - 8 7.0092 - 1 20.969 1.3006 - 6 2.0412 - 1 3 ,8603 - 8 7.4560 - 1 22.575 1.4011 - 6 2.0276 - 1 4 ,1056 - 8 7.9047 - 1 24.190 1.5020 - 6 2.0252 - 1 4 ,3459 - 8 8.3537 - 1 25.810 1.6030 - 6 2.0320 - 1 4 ,5801 - 8 8.8012 - 1 27.425 1.7037 - 6 2,0462 - 1 4 ,8072 - 8 9.2454 - 1 29.031 1.8036 - 6 2,0665 - 1 5 ,0262 - 8 9.6847 - 1 30.619 1.9023 - 6 2,0917 - 1 5 ,2364 - 8 1.0117

32.184 1.9994 - 6 2,1206 - 1 5 ,4371 - 8 1.0542

33.719 2.0945 - 6 2.1524 - 1 5..6278 - 8 1.0956

35.217 2.1873 - 6 2.1864 - 1 5 ,8079 - 8 1.1359

36.673 2.2772 - 6 2.2217 - 1 5,.9773 - 8 1.1749

38.079 2.3641 - 6 2.2579 - 1 6..1356 - 8 1.2124

39.431 2.4474 - 6 2.2942 - 1 6 .2829 - 8 1.2483

40.722 2.5269 - 6 2.3302 - 1 6..4190 - 8 1.2825

41.947 2.6023 - 6 2.3655 - 1 6..5440 - 8 1.3149

43.101 2.6732 - 6 2.3997 - 1 6..6581 - 8 1.3453

44.179 2.7393 - 6 2.4323 - 1 6..7615 - 8 1.3736

45.177 2.8005 - 6 2.4630 - 1 6..8543 - 8 1.3997

46.090 2.8564 - 6 2.4916 - 1 6,.9370 - 8 1.4235

46.914 2.9069 - 6 2.5177 - 1 7 .0097 - 8 1.4450

47.647 2.9517 - 6 2.5413 - 1 7 ,0728 - 8 1.4641

48.285 2.9907 - 6 2,5619 - 1 7 ,1265 - 8 1.4806

48.825 3.0237 - 6 2,5795 - 1 7,.1712 - 8 1.4946

49.265 3.0505 - 6 2.5940 - 1 7..2070 - 8 1.5060

49.603 3.0712 - 6 2,6051 - 1 7..2341 - 8 1.5148

49.838 3.0855 - 6 2,6129 - 1 7 .2528 - 8 1.5209

49.969 3.0935 - 6 2,6172 - 1 7..2632 - 8 1.5243

t Gaussian frequencies, interval: 0-50 kc.
.28-

t

f, kc

50.277

51.456

53.572

56.617

60.578

65.438

71.177

77.771

85.193

93.410

102.39

112.09

122.48

133.50

145.12

157.29

169.95

183.05

196.53

210.34

224.43

238.72

253.17

267.71

282.29

296.83

311.28

325.57

339.66

353.47

366.95

380.05

392.71

404.88

416.50

427.52

437.91

447.61

456.59

464.81

472.23

478.82

484.56

489.42

493.38

496.43

498.54

499.72

- Table 14

0- = 0.002 ^2 = 15 a = 0.85

d= 12,49 miles d = 329 miles Kl arg E^ IM argE^

3.1122 _ 6 2.6275 L 7.2873 _ 8 1.5322

3.1841 - 6 2.6670 L 7.3775 - 8 1.5626

3.3127 - 6 2.7391 L 7.5300 - 8 1.6169

3.4973 - 6 2.8451 I 7.729 - 8 1.694

3.7364 - 6 2.9866 L 7.950 - 8 1.794

4.0281 - 6 3.1645 L 8.167 - 8 1.915

4.3699 - 6 3.3795 I 8.347 - 8 2.056

4.7590 - 6 3.6313 L 8.458 - 8 2.214

5.1919 - 6 3.9194 L 8.469 - 8 2.388

5.6643 - 6 4.2424 L 8.35 - 8 2.57

6.1717 - 6 4.5988 L 8.10 - 8 2.77

6.7088 - 6 4.9865 L 7.71 - 8 2.97

7.2697 - 6 5.4032 - L 7.19 - 8 3.17

7.8483 - 6 5.8463 I 6.56 - 8 3.37

8.4380 - 6 6.3132 L 1.09 - 7 3.42

9.0319 - 6 6.8011 L 5.00 - 8 3.65

9.6231 - 6 7,3068 L 4.41 - 8 3.91

1.0205 - 5 7.8274 I 3.79 - 8 4.11

1.0770 - 5 8.3598 L 3.21 - 8 4.28

1.1313 - 5 8.9007 - L 2.78 - 8 4.39

1.1828 - 5 9.4470 L 2.33 - 8 4.51

1.2310 - 5 9.9956 L 1.98 - 8 4.67

1.2755 - 5 1.0543 1.68 - 8 4.69

1.3160 - 5 1.1087 1.44 - 8 4,76

1.3522 - 5 1.1625 1.25 - 8 4.82

1.3841 - 5 1.2153 1.09 - 8 4.87

1.4116 - 5 1.2669 9.60 - 9 4,92

1.4349 - 5 1.3171 8.53 - 9 4,95

1.4539 - 5 1.3657 7.64 - 9 4,99

1.4691 - 5 1.4124 6.89 - 9 5,02

1.4806 - 5 1.4572 6.26 - 9 5,05

1.4888 - 5 1.4998 5.72 - 9 5,07

1.4941 - 5 1.5402 5.26 - 9 5.10

1.4968 - 5 1.5782 4.87 - 9 5,12

1.4973 - 5 1.6139 4.53 - 9 5,14

1.4960 - 5 1.6470 4.25 - 9 5,16

1.4934 - 5 1.6776 4.00 - 9 5.17

1.4896 - 5 1.7057 3.78 - 9 5.19

1.4851 - 5 1.7312 3.60 - 9 5.20

1.4802 - 5 1.7541 3.44 - 9 5.21

1.4751 - 5 1.7745 3.31 - 9 5.22

1.4701 - 5 1.7924 3.20 - 9 5.23

1.4654 - 5 1.8077 3.10 - 9 5.24

1.4612 - 5 1.8206 3.03 - 9 5.25

1.4576 - 5 1.8309 2.97 - 9 5.25

1.4547 - 5 1.8389 2.92 - 9 5.26

1.4527 - 5 1.8443 2.89 - 9 5,26

1.4515 - 5 1.8474 2.87 - 9 5.26

t Gaussian frequencies, interval: 50-500 kc.
-29-

tf,kc

500.31

501.62

503.97

507.35

511.75

517.15

523.53

530.86

539.10

5^8.23

558.21

568.99

580.53

592.78

605.69

619.21

633.27

647.83

662.81

678.16

693.81

709.69

725.75

741.90

758.10

774.25

790.31

806.19

821.84

837.19

852.17

866.73

880.79

894.31

907.22

919.47

931.01

941.79

951.77

960.90

969.14

976.47

982.85

988.25

992.65

996.03

998.38

999.69

(T = 0. 002

d = 12.49 miles

Table 15

15 a = 0. 85

E are E J J.

J to J. 1.4509 - 5 1.8489

1.4496 - 5 1.8522

1.4472 - 5 1,8582

1.4437 - 5 1.8668

1.4390 - 5 1.8779

1.4331 - 5 1.8913

1.4257 - 5 1.9069

1.4170 - 5 1.9246

1.4066 - 5 1.9441

1.3947 - 5 1.9652

1.3812 - 5 1.9878

1.3660 - 5 2.0115

1.3491 - 5 2.0361

1.3307 - 5 2.0614

1.3107 - 5 2.0871

1.2893 - 5 2.1129

1.2667 - 5 2.1387

1.2430 - 5 2.1642

1.2183 - 5 2.1892

1.1930 - 5 2.2135

1.1673 - 5 2.2370

1.1412 - 5 2.2595

1.1152 - 5 2.2808

1.0893 - 5 2.3010

1.0637 - 5 2.3199

1.0388 - 5 2.3374

1.0145 - 5 2.3537

9.9101 - 6 2.3686

9.6849 - 6 2.3823

9.4700 - 6 2.3946

9.2661 - 6 2,4058

9.0737 - 6 2,4158

8.8932 - 6 2,4247

8.7247 - 6 2,4326

8.5682 - 6 2,4396

8.4240 - 6 2,4457

8.2917 - 6 2,4510

8.1712 - 6 2,4556

8.0624 - 6 2,4596

7.9651 - 6 2,4630

7.8792 - 6 2,4658

7.8038 - 6 2,4682

7.7396 - 6 2,4702

7.6863 - 6 2,4718

7.6428 - 6 2,4730

7.6104 - 6 2,4740

7.5875 - 6 2,4746

7.5748 - 6 2,4750

d = 329 miles

Kl argE^

2 ,87 - 9 5,26

2 .85 - 9 5.26

2 .82 - 9 5,27

2 .77 - 9 5.27

2 .71 - 9 5.28

2 .64 - 9 5.28

2 .56 - 9 5.29

2 .47 - 9 5,30

2 .38 - 9 5.31

2 .28 - 9 5.32

2 .18 - 9 5.33

2 .08 - 9 5.34

.98 - 9 5.36

.88 - 9 5.37

.78 - 9 5.38

.69 - 9 5.40

.597 - 9 5.413

.510 - 9 6.428

i426 - 9 5,442

.347 - 9 5,457

.273 - 9 5,472

.203 - 9 5.486

,1379 - 9 5.5006

.0771 - 9 5.5148

.0205 - 9 5.5288

9 .6808 -10 5.5424

9 ,1959 -10 5.5558

8,,7485 -10 5.5687

8 ,3364 -10 5.5813

7,• 9578 -10 5,5934

7,,6106 -10 5.6051

7..2929 -10 5.6163

7<,0029 -10 5.6269

6..7389 -10 5.6370

6..4993 -10 5.6465

6. 2826 -10 5.6555

6. 0874 -10 5.6638

5, 9125 -10 5.6715

5..7567 -10 5.6786

5..6190 -10 5.6850

5..4984 -10 5.6908

5..3943 -10 5.6959

5. 3058 -10 5.7003

54 2324 -10 5.7040

5. 1736 -10 5.7070

5« 1290 -10 5.7093

5. 0984 -10 5.7109

5. 0814 -10 5.7118

t Gaussian frequencies, interval: 500-1000 kc.
.30-

Table 16

0- = 0. 002 ^2" 15 a = 0.85

tf,kc

d = 621 m: les d = 1000 milesi Ki argE^ IM arg E^

0.030725 7.9832 - 11 2.4037 2.2340 - 11 1.6708

0.16175 1.8503 - 10 4.3915 - 1 1.1157 - 10 4.1154 - 1 0.39689 4.5571 - 10 2.8455 - 1 2.6077 - 10 3.6725 - 1 0.73521 8.2296 - 10 2.6818 - 1 4.5486 - 10 4.0429 - 1 1.1753 1.2779 - 9 2.8658 - 1 6.8413 - 10 4.6379 - 1 1.7153 1.8106 - 9 3.1942 - 1 9.3983 - 10 5.3340 - 1 2.3530 2.4112 - 9 3.6026 - 1 1.2145 - 9 6.0917 - 1 3.0857 3.0705 - 9 4.0648 - 1 1.5017 - 9 6.8952 - 1 3.9103 3.7793 - 9 4.5683 - 1 1.7960 - 9 7.7370 - 1 4.8233 4.5294 - 9 5.1060 - 1 2.0930 - 9 8.6126 - 1 5.8210 5.3126 - 9 5.6736 - 1 2.3888 - 9 9.5192 - 1 6.8991 6.1212 - 9 6.2678 - 1 2.6803 - 9 1.0455

8.0532 6.9481 - 9 6.8859 - 1 2.9646 - 9 1.1417

9.2783 7.7863 - 9 7,5256 - 1 3.2395 - 9 1.2403

10.569 8.6291 - 9 8.1847 - 1 3.5031 - 9 1.3412

11.921 9.4704 - 9 8.8610 - 1 3.7538 - 9 1.4441

13.327 1.0304 - 8 9.5523 - 1 3.9902 - 9 1.5488

14.783 1.1125 - 8 1.0256 4.2111 - 9 1.6549

16.281 1.1928 - 8 1.0971 4.4158 - 9 1.7623

17.816 1.2708 - 8 1.1694 4.6035 - 9 1.8705

19.381 1.3461 - 8 1.2422 4.7738 - 9 1.9793

20.969 1.4182 - 8 1.3153 4.9264 - 9 2.0884

22.575 1.4870 - 8 1.3886 5.0613 _ 9 2.1974

24.190 1.5520 - 8 1.4616 5.1788 - 9 2.3059

25.810 1.6132 - 8 1.5342 5.2791 - 9 2.4136

27.425 1.6702 - 8 1.6060 5.3629 - 9 2.5202

29,031 1.7231 - 8 1.6770 5.4308 - 9 2.6252

30.619 1.7717 - 8 1.7467 5.4838 - 9 2.7283

32.184 1.8161 - 8 1.8149 5.5228 - 9 2.8291

33.719 1.8563 - 8 1.8814 5.5491 - 9 2.9274

35.217 1.8924 - 8 1.9460 5.5638 - 9 3.0227

36.673 1.9246 - 8 2.0084 5.5683 - 9 3,1147

38.079 1.9530 - 8 2.0683 5.5639 - 9 3.2032

39.431 1.9780 - 8 2.1257 5.5519 - 9 3.2877

40.722 1.9996 - 8 2.1802 5.5338 - 9 3.3680

41.947 2.0182 - 8 2.2318 5.5109 - 9 3.4439

43.101 2.0340 - 8 2.2801 5.4843 - 9 3.5150

44.179 2.0473 - 8 2.3251 5.4554 - 9 3.5812

45.177 2.0584 - 8 2.3666 5.4252 - 9 3.6422

46.090 2.0675 - 8 2.4045 5.3949 - 9 3,6979

46.914 2.0749 - 8 2.4386 5.3653 - 9 3,7479

47.647 2.0809 - 8 2.4688 5.3374 - 9 3,7923

48,285 2.0855 - 8 2,4950 5.3119 - 9 3.8308

48.825 2.0891 - 8 2.6171 5.2894 - 9 3,8634

49.265 2.0918 - 8 2.5352 5.2705 - 9 3,8899

49.603 2.0937 - 8 2.5490 5.2557 - 9 3,9102

49.838 2.0950 - 8 2.5586 5.2452 - 9 3.9243

49.969 2.0957 - 8 2.5640 5.2392 - 9 3,9321

t Gaussian frequencies, interval: 0-50 kc.
31-

1 i. kc

50 .277

51 ,456

53 .572

56 .617

60 .578

65,.438

71 .177

77 .771

85 .193

. 93 .410

102,.39 112..09 122,.48 133 .50 145,.12 157,.29 169,.95 183,.05 196,.53 210,.34 224. 43

238..72 253..17 267..71 282, 29

296..83 311. 28

325..57 339..66 353..47 366..95 380,.05 392. 71 404,.88 416. 50

427..52 437..91 447,.61 456,.59 464,.81 472..23 478,.82 484,.56 489..42 493,.38 496,.43 498..54 499,.72

0- = 0. 002

d = 621 miles

lE 1

2.0972

2.1021

2.1073

2.107

2.093

2.059

1.995

1.898

1.766

1.60

1.41

1.20

9.98

8.01

4.89

4.42

3.60

2.80

2.13

1.63

1.24

9.56

7.49

5.91

4.73

3.83

3.14

2.60

2.18

1.85

1.58

1.37

1.20

1.06

9.39

8.43

7.64

6.98

6.43

5.97

5.59

5.28

5.03

4.82

4.66

4.55

4.47

4.42

- 8 - 8 - 8 - 8 - 8

- 8

- 8

- 8

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9

- 9 10

•10

-10

•10

•10 -10

-10

-10

-10

-10

-10

-10

-10

-1

-1-1

-1

-1

-1

-1

-1-1

-1-1

-1

-1

-1

Table 17

15 a

arg E

2.5765

2.6245

2.7102

2.832

2.989

3.179

3.397

3.642

3.908

4.19

4.48

4.78

5.07

5.34

5.11

5.65

6.03

2.99

2.51

4.35

5.85

7.12

8.25

9.23

1.01

1.09

1.16

1.23

1.29

1.34

1.39

1.44

1.49

1.53

1.56

1.60

1.63

1.66

1.69

1.71

1.73

1.75

1.76

1.78

1.79

1.80

1.80

1.81

•0. 85

d = 1000 miles

arg E

5.2252 - 9 3.9505

5.1692 - 9 4,0210

5.0608 - 9 4,1466

4.889 - 9 4,326

4.643 - 9 4.555

4.314 - 9 4.831

3.905 - 9 5,150

3.425 - 9 5,505

2.900 - 9 5,890

2.36 - 9 1.30 - 2 1.84 - 9 4.30 - 1 1.37 - 9 8.47 - 1 9.78 -10 1.25

6.69 -10 1.62

2.79 -10 1.20

2.46 -10 2.00

1.81 -10 2.54

2 1.23 -10 2.94

1 8.11 -11 3.25

1 5.34 -11 3.50

1 3.55 -11 3.71

1 2.40 -11 3.89

1 1.65 -11 4.04

1 1.16 -11 4.18

8.26 -12 4.30

6.02 -12 4.41

4.46 -12 4.52

3.36 -12 4.61

2.58 -12 4.70

2.01 -12 4,79

1.59 -12 4.86

1.28 -12 4.94

1.04 -12 5.00

8.61 -13 5.07

7.22 -13 5.13

6.13 -13 5.18

5.28 -13 5,23

4.60 -13 5,28

4.06 -13 5.32

3.63 -13 5.36

3.29 -13 5.39

3.02 -13 5.42

2.80 -13 5.45

2.63 -13 5.47

2.50 -13 5.48

2.40 -13 5.50

2.34 -13 5.51

2.30 -13 5.51

t Gaussian frequencies, interval: 50-500 kc.
-32-

0- = 0. 002

d = 621 miles

r f, kc

500 .31 501 .62 503 .97

507 .35

511 .75 517 .15 523 .53

530 .86

539 .10

548 .23 558 .21 568 .99 580 .53 592 .78 605 .69 619..21 633,.27 647 .83 662 .81 678,.16 693 .81 709,.69 725 .75 741 .90 758,.10 774,.25 790 .31 806,.19 821 .84 837,.19 852,.17 866,.73 880 .79 894,.31 907,.22 919,.47 931,.01 941,.79 951,.77 960,.90 969, 14

976, 47

982,.85 988,.25 992,.65 996,.03 998, 38

999, 69

4.40

4,36

4,27

4,16

4,01

3,84

3.65

3.44

3,23

3,01

2,79

2,58

2.37

2.17

1.98

1.81

1.646

1.495

1.357

1.232

1.118

1.015

9.2218

8.3909

7.6471

6.9824

6.3895

5.8614

5.3915

4.9738

4.6029

4.2739

3.9823

3.7243

3.4962

3.2950

3.1181

2.9629

2.8274

2.7099

2.6087

2.5225

2.4503

2.3910

2.3440

2.3085

2.2843

2.2709

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-11

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

-12

Table 18

15 a = 0. 85

arg E^

1.81

1.81

1.82

1.83

1.84

1.85

1.87

1.89

1.91

1.93

1.95

1.98

2.01

2.04

2.07

2.10

2.128

2.160

2.192

2.224

2.256

2.289

2.3210

2.3529

2.3843

2.4152

2.4455

2.4750

2.5037

2.5315

2.5583

2.5840

2.6085

2.6319

2.6540

2.6747

2.6941

2.7121

2.7286

2.7436

2.7570

2.7689

2.7793

2.7879

2.7950

2.8004

2.8042

2.8063

d s 1000 miles

arg E

2.29 -13 5.51

2.25 -13 5,52

2.18 -13 5,53

2.09 -13 5.54

1.98 -13 5.56

1.86 -13 5.59

1.72 -13 5.61

1.57 -13 5.64

1.43 -13 5.68

1.28 -13 5,71

1.14 -13 5.75

1.01 -13 5,80

8.90 -14 5.84

7.78 -14 5.89

6.78 -14 5,94

5.88 -14 5.99

5.087 -14 6,041

4.390 -14 6.094

3.784 -14 6,148

3.260 -14 6.202

2.808 -14 6.257

2.420 -14 2.829 - 2 2.0887 -14 8.2694 - 2 1.8059 -14 1.3668 - 1 1.5650 -14 1.9005 - 1 1.3602 -14 2.4260 - 1 1.1860 -14 2.9414 - 1 1.0380 -14 3.4450 - 1 9.1215 -15 3,93 51 - 1 8.0516 -15 4,4103 - 1 7.1412 -15 4,8689 - 1 6.3661 -15 5,3097 - 1 5.7056 -15 5.7314 - 1 5.1425 -15 6.1327 - 1 4.6622 -15 6.5126 - 1 4,2524 -15 6.8700 - 1 3,9029 -15 7.2040 - 1 3,6052 -15 7.5138 - 1 3,3523 -15 7.7985 - 1 3,1380 -15 8.0575 - 1 2,9576 -15 8.2901 - 1 2,8070 -15 8.4958 - 1 2,6829 -15 8.6740 - 1 2,5826 -15 8.8244 - 1 2,5039 -15 8.9466 - 1 2,4452 -15 9.0403 - 1 2.4054 -15 9.1053 - 1 2.3835 -15 9.1415 - 1

t Gaussian frequencies, interval: 500-1000 kc.
I

-33-

Table 19

tr = 5 € = 80 a = 0.

d = 12, 49 miles

85

329 miles

tf,kc Ki argE^ K\ arg E^

0.030725 1.1456 - 5 3.1286 5.8965 -10 2.8181

0.16175 2.1713 - 6 3.0732 3.3337 -10 7.3633 - 1 0.39689 8.7482 - 7 2.9712 8.8928 -10 3.0328 - 1 0.73521 4.5756 - 7 2.8115 8.8928 -10 3.0328 - 1 1.1753 2.7037 - 7 2.5609 2.6294 - 9 1.6884 - 1 1.7153 1.7779 - 7 2.1547 3.7986 - 9 1.5623 - 1 2.3530 1.4837 - 7 1.5879 5.1536 - 9 1.5359 - 1 3.0857 1.6799 - 7 1.0826 6.6823 - 9 1.5605 - 1 3.9103 2.1414 - 7 7.6563 - 1 8.3726 - 9 1.6136 - 1 4.8233 2.7248 - 7 5.7613 - 1 1 .0254 - 8 1.7408 - 1 5.8210 3.3776 - 7 4.5522 - 1 1.2226 - 8 1.8190 - 1 6.8991 4.0820 - 7 3.7253 - 1 1.4319 - 8 1.9031 - 1 8.0532 4.8309 - 7 3.1282 - 1 1.6521 - 8 1.9910 - 1 9.2783 5.6204 - 7 2.6791 - 1 1.8820 - 8 2.0810 - 1 10.569 6.4476 - 7 2.3307 - 1 2.1202 - 8 2.1723 - 1 11.921 7.3095 - 7 2.0540 - 1 2.3656 - 8 2.2640 - 1 13.327 8.2030 - 7 1.8299 - 1 2.6169 - 8 2.3557 - 1 14.783 9.1250 - 7 1.6457 - 1 2.8732 - 8 2.4146 - 1 16.281 1.0072 - 6 1.4922 - 1 3.1334 - 8 2.5079 - 1 17.816 1.1041 - 6 1.3630 - 1 3.3959 - 8 2.5998 - 1 19.381 1.2027 - 6 1.2533 - 1 3.6597 - 8 2.6901 - 1 20.969 1.3026 - 6 1.1593 - 1 3.9236 - 8 2.7786 - 1 22.575 1.4036 - 6 1.0783 - 1 4.1866 - 8 2.8651 - 1 24.190 1.5051 - 6 1.0080 - 1 4.4477 - 8 2.9495 - 1 25.810 1.6068 - 6 9.4675 - 2 4.7059 - 8 3.0315 - 1 27.425 1.7082 - 6 8.9311 - 2 4.9603 - 8 3.1110 - 1 29.031 1.8089 - 6 8.4596 - 2 5.2099 - 8 3.1880 - 1 30.619 1.9085 - 6 8.0438 - 2 5.4539 - 8 3,2622 - 1 32.184 2.0066 - 6 7.6761 - 2 5.6916 - 8 3.3336 - 1 33.719 2.1028 - 6 7.3502 - 2 5.9222 - 8 3.40 21 - 1 35.217 2.1967 - 6 7.0608 - 2 6.1449 - 8 3.4676 - 1 36.673 2.2879 - 6 6.8035 - 2 6.3590 - 8 3.5299 - 1 38.079 2.3760 - 6 6.5747 - 2 6.5640 - 8 3.5891 - 1 39.431 2.4606 - 6 6.3711 - 2 6.7592 - 8 3.6450 - 1 40.722 2.5415 - 6 6.1900 - 2 6.9441 - 8 3.6976 - 1 41.947 2.6182 - 6 6.0292 - 2 7.1181 - 8 3.7468 - 1 43.101 2.6905 - 6 5.8867 - 2 7.2809 - 8 3.7925 - 1 44.179 2.7580 - 6 5.7608 - 2 7.4319 - 8 3.8347 - 1 45.177 2.8204 - 6 5.6501 - 2 7.5707 - 8 3.8733 - 1 46.090 2.8776 - 6 5.5533 - 2 7.6970 - 8 3.9083 - 1 46.914 2.9292 - 6 5.4694 - 2 7.8105 - 8 3.9396 - 1 47.647 2.9750 - 6 5.3975 - 2 7.9109 - 8 3,9672 - 1 48.285 3.0150 - 6 5.3369 - 2 7.9979 - 8 3.9911 - 1 48.825 3.0488 - 6 5.2869 - 2 8.0713 - 8 4.0112 - 1 49.265 3.0763 - 6 5.2471 - 2 8.1310 - 8 4.0275 - 1 49.603 3.0975 - 6 5.2170 - 2 8.1768 - 8 4,0400 - 1 49.838 3.1122 - 6 5.1963 - 2 8.2086 - 8 4.0486 - 1 49.969 3.1204 - 6 5.1849 - 2 8.2262 - 8 4.0535 - 1

t Gaussian frequencies, interval: 0-50 kc.
-34-

t

f.lkc

50 .277

51 .456

53 .572

56 .617

60 ,578

65 .438

71 ,177

77 ,771

85 ,193

93 ,410

102 .39 112 .09 122 ,48

133 ,50

1^5 .12 157 .29 169 .95 183 .05 196 .53 210 .34

22^ ,43

238 ,72

253,,17

267 .71 282,,29

296 .83 311,,28

325, 57

339, 66

353,,47

366,.95 380, 05

392,,71

404,,88

416, 50

427. 52

437,,91

447,,61

456,,59

464, 81

472, 23

478,,82

484,,56

489,,42

493.,38

496,,43

498,,54

499,,72

0- = 5 S " ^°

d = 12.49 miles

Table 20

a = 0.

d = 329 miles

arg E

3.1396 - 6 5.1584 - 2 8 ,2676 - 8 4,0647 - 1 3.2134 - 6 5.0599 - 2 8 .4259 - 8 4,1077 - 1 3.3459 - 6 4.8952 - 2 8 .7072 - 8 4.1836 - 1 3.5364 - 6 4,6822 - 2 9 .1063 - 8 4.2903 - 1 3.7842 - 6 4.4412 - 2 9 .6157 - 8 4.4253 - 1 4.0883 - 6 4.1912 - 2 .0227 - 7 4.5853 - 1 4.4473 - 6 3.9474 - 2 .0929 - 7 4.7672 - 1 4.8597 - 6 3.7207 - 2 .1713 - 7 4.9679 - 1 5.3239 - 6 3.5182 - 2 ,2666 - 7 5.1845 - 1 5.8378 - 6 3.3434 - 2 ,3479 - 7 5.4143 - 1 6.3993 - 6 3.1974 - 2 ,4442 - 7 5.6549 - 1 7.0060 - 6 3.0799 - 2 ,5443 - 7 5.9042 - 1 7.6554 - 6 2.9894 - 2 ,6475 - 7 6.1603 - 1 8.3448 - 6 2.9239 - 2 ,7527 - 7 6.4216 - 1 9.0713 - 6 2.8813 - 2 ,8593 - 7 6.6867 - 1 9.8318 - 6 2.8592 - 2 ,9664 - 7 6.9541 - 1 1.0623 - 5 2.8554 - 2 2 ,0735 - 7 7.2228 - 1 1.1442 - 5 2.8679 - 2 2 ,1799 - 7 7.4918 - 1 1.2285 - 5 2.8947 - 2 2 .2851 - 7 7.7600 - 1 1.3149 - 5 2.9340 - 2 2 .3886 - 7 8,0267 - 1 1.4029 - 5 2.9841 - 2 2 .4902 - 7 8.2910 - 1 1.4922 - 5 3.0435 - 2 2 .5893 - 7 8,5522 - 1 1.5826 - 5 3.1108 - 2 2 .6857 - 7 8,8097 - 1 1.6735 - 5 3.1847 - 2 2 .7791 - 7 9,0627 - 1 1.7646 - 5 3.2640 - 2 2 .8694 - 7 9.3107 - 1 1.8554 - 5 3.3477 - 2 2 ,9564 - 7 9.5530 - 1 1.9457 - 5 3.4346 - 2 3 .0398 - 7 9.7891 - 1 2.0351 - 5 3.5239 - 2 3 ,1197 - 7 1.0019

2.1231 - 5 3.6146 - 2 3 .1958 - 7 1.0241

2.2094 - 5 3.7058 - 2 3,,2682 - 7 1.0455

2.2937 - 5 3.7969 - 2 3.,3367 - 7 1.0661

2.3756 - 5 3.8871 - 2 3,,4015 - 7 1,0859

2.4547 - 5 3.9756 - 2 3,,4623 - 7 1,1048

2.5307 - 5 4.0619 - 2 3,,5193 - 7 1,1227

2.6033 - 5 4.1453 - 2 2, 9404 5,0635

2.6722 - 5 4.2252 - 2 3, 6216 - 7 1.1555

2.7371 - 5 4.3012 - 2 3,,6670 - 7 1.1703

2.7977 - 5 4.3728 - 2 3, 7085 - 7 1.1841

2.8538 - 5 4.4394 - 2 3. 7463 - 7 1.1967

2.9051 - 5 4.5008 - 2 3. 7803 - 7 1.2082

2.9515 - 5 4.5565 - 2 3, 8105 - 7 1.2185

2.9927 - 5 4.6062 - 2 3, 8370 - 7 1.2276

3.0286 - 5 4.6496 - 2 3, 8597 - 7 1.2355

3.0589 - 5 4.6864 - 2 3,,8788 - 7 1.2421

3.0837 - 5 4.7165 - 2 3, 8943 - 7 1.2475

3.1027 - 5 4.7397 - 2 3,,9061 - 7 1.2517

3.1159 - 5 4.7558 - 2 3, 9142 - 7 1.2546

3.1233 - 5 4.7648 - 2 3,,9187 - 7 1.2562

t Gaussian frequencies, interval: 50-500 kc.
-35-

t f.kc

500.31

501.62

503.97

507.35

511.75

517.15

523.53

530.86

539.10

548.23

558.21

568.99

580.53

592.78

605.69

619.21

633.27

647.83

662.81

678.16

693.81

709.69

725.75

741.90

758.10

774.25

790.31

806.19

821.84

837.19

852.17

866.73

880.79

894.31

907.22

919.47

931.01

941,79

951.77

960.90

969.14

976.47

982.85

988.25

992.65

996.03

998.38

999.69

0- = 5 S ~ ^^

d = 12.49 miles

Table 21 a = 0.

arg E

d = 329 rniles

arg E

3.1269 - 5 4.7693 - 2 3..9210 - 7 1.2570

3.1351 - 5 4.7793 - 2 3..9260 - 7 1.2587

3.1498 - 5 4.7973 - 2 3..9350 - 7 1.2619

3.1709 - 5 4.8232 - 2 3..9478 - 7 1.2665

3.1984 - 5 4,8570 - 2 3<.9644 - 7 1.2724

3.2321 - 5 4,8985 - 2 3..9845 - 7 1.2797

3.2720 - 5 4,9476 - 2 4 .0080 - 7 1.2882

3.3177 - 5 5,0043 - 2 4..0347 - 7 1.2980

3.3692 - 5 5,0682 - 2 4..0644 - 7 1.3089

3.4263 - 5 5,1392 - 2 4 ,0966 - 7 1.3210

3.4886 - 5 5,2171 - 2 4 .1313 - 7 1.3340

3.5559 - 5 5,3016 - 2 4 .1681 - 7 1.3481

3.6280 - 5 5,3924 - 2 4 .2066 - 7 1.3630

3.7045 - 5 5.4891 - 2 4 .2467 - 7 1.3788

3.7851 - 5 5,5914 - 2 4..2881 - 7 1.3953

3.8695 - 5 5,6989 - 2 4..3303 - 7 1.4124

3.9573 - 5 5,8111 - 2 4 .3733 - 7 1.4301

4.0482 - 5 5,9276 - 2 4 .4166 - 7 1.4483

4.1418 - 5 6,0479 - 2 4..4602 - 7 1.4669

4.2376 - 5 6,1716 - 2 4..5036 - 7 1.4858

4.3353 - 5 6,2980 - 2 4..5468 - 7 1.5050

4.4344 - 5 6,4267 - 2 4i.5895 - 7 1.5243

4.5346 - 5 6,5571 - 2 4,.6315 - 7 1.5437

4.6355 - 5 6,6887 - 2 4. 6726 - 7 1.5630

4.7365 - 5 6,8208 - 2 4.,7128 - 7 1.5823

4.8373 - 5 6,9529 - 2 4,.7518 - 7 1.6014

4.9375 - 5 7.0845 - 2 4. 7896 - 7 1.6203

5.0366 - 5 7,2149 - 2 4..8260 - 7 1.6389

5.1342 - 5 7.3436 - 2 4i.8610 - 7 1.6571

5.2300 - 5 7.4701 - 2 4,.8 944 - 7 1.6749

5.3235 - 5 7.5937 - 2 4,.9263 - 7 1.6921

5.4142 - 5 7.7139 - 2 4..9566 - 7 1.7088

5.5019 - 5 7,8303 - 2 4..9852 - 7 1.7248

5.5862 - 5 7,9422 - 2 5 .0120 - 7 1.7402

5.6667 - 5 8,0492 - 2 5..0372 - 7 1.7548

5.7431 - 5 8,1509 - 2 5..0605 - 7 1.7686

5.8151 - 5 8,2467 - 2 5 .0821 - 7 1.7815

5.8823 - 5 8,3363 - 2 5..1020 - 7 1.7936

5.9445 - 5 8,4193 - 2 5..1200 - 7 1.8047

6.0014 - 5 8,4953 - 2 5,.1363 - 7 1.3149

6.0528 - 5 8.5640 - 2 5..1508 - 7 1.8241

6.0985 - 5 8.6250 - 2 5..1635 - 7 1.8322

6.1382 - 5 8,6782 - 2 5 .1745 - 7 1,8392

6.1719 - 5 8,7232 - 2 5..1837 - 7 1.8452

6.1993 - 5 8,7599 - 2 5..1911 - 7 1.8501

6.2204 - 5 8,7881 - 2 5..1968 - 7 1.8538

6.2351 - 5 8,8077 - 2 5<.2007 - 7 1,8564

6.2432 - 5 8,8187 - 2 ?,.2029 - 7 1.8578

t Gaussian frequencies, interval: 500-1000 kc.
-36-

Table 22

0- = 5 e = 80

Li a = 0. 85

t

f, kc

d = 621 miles d = IjOO miles

Kl argE^ IM argE^

0.030725 7.9832 -11 2.4028 2.2340 -11 1.6697

0.16175 1.8503 -10 4.3432 - 1 1.1156 -10 4.0535 - 1 0.39689 4,5565 -10 2.7263 - 1 2.6068 -10 3.5192 - 1 0.73521 8.2271 -10 2.4599 - 1 4.5449 -10 3.7562 - 1 1.1753 1.2772 - 9 2.5095 - 1 6.8306 -10 4,1755 - 1 1.7153 1.8089 - 9 2.6718 - 1 9.3739 -10 4.6530 - 1 2.3530 2.4080 - 9 2.8827 - 1 1,2097 - 9 5,1494 - 1 3.0857 3.0649 - 9 3.1166 - 1 1.4934 - 9 5.6489 - 1 3.9103 3.7705 - 9 3.3616 - 1 1.7829 - 9 6.1443 - 1 4.8233 4.5126 - 9 3.6220 - 1 2.0735 - 9 6.6311 - 1 5.8210 5.2907 - 9 3.8692 - 1 2.3617 - 9 7.1093 - 1 6.8991 6.0945 - 9 4.1166 - 1 2,6444 - 9 7.5766 - 1 8.0532 6.9170 - 9 4.3623 - 1 2,9191 - 9 8,0325 - 1 9.2783 7.7522 _ 9 4.6054 - 1 3,1840 - 9 8,4766 - 1 10.569 8.5944 - 9 4.8450 - 1 3.4377 - 9 8,9086 - 1 11.921 9.4385 - 9 5,0804 - 1 3.6794 - 9 9,3284 - 1 13.327 1.0280 - 8 5.3111 - 1 3.9083 - 9 9,7361 - 1 14.783 1.1117 - 8 5.5375 - 1 4.1241 - 9 1.0132

16.281 1.1941 - 8 5.7578 - 1 4.3268 - 9 1.0515

17.816 1.2751 - 8 5.9725 - 1 4.5163 - 9 1.0886

19.381 1.3545 - 8 6.1812 - 1 4.6930 - 9 1.1244

20.969 1.4320 - 8 6.3839 - 1 4.8570 - 9 1.1591

22.575 1.5074 - 8 6.5804 - 1 5.0089 - 9 1.1925

24.190 1.5806 - 8 6.7704 - 1 5.1491 - 9 1.2247

25.810 1.6512 - 8 6.9540 - 1 5.2782 - 9 1.2557

27.425 1.7194 - 8 7.1309 - 1 5.3967 - 9 1,2854

29.031 1.7848 - 8 7.3011 - 1 5.5052 - 9 1.3140

30.619 1.8474 - 8 7.4643 - 1 5.6042 - 9 1.3413

32.184 1.9072 - 8 7.6207 - 1 5.6945 - 9 1.3673

33.719 1.9641 - 8 7,7699 - 1 5.7764 - 9 1.3921

35.217 2.0181 - 8 7.9120 - 1 5.8507 - 9 1.4157

36.673 2.0691 - 8 8.0468 - 1 5.9178 - 9 1.4380

38.079 2.1171 - 8 8.1742 - 1 5.9783 - 9 1.4591

39.431 2.1621 - 8 8,2942 - 1 6.0326 - 9 1.4789

40.722 2.2041 - 8 8.4068 - 1 6.0812 - 9 1.4974

41.947 2.2430 - 8 8.5117 - 1 6.1246 - 9 1.5147

43.101 2.2790 - 8 8.6090 - 1 6.1632 - 9 1.5306

44,179 2.3119 - 8 8,6986 - 1 6.1972 - 9 1,5453

45.177 2.3419 - 8 8,7804 - 1 6.2272 - 9 1,5588

46.090 2.3688 - 8 8,8544 - 1 6.2533 - 9 1,5709

46.914 2.3929 - 8 8,9205 - 1 6.2758 - 9 1,5817

47.647 2.4139 - 8 8.9787 - 1 6,2951 - 9 1,5912

48.285 2.4321 - 8 9.0290 - 1 6,3113 - 9 1,5994

48.825 2.4473 - 8 9.0713 - 1 6,3246 - 9 1,6063

49.265 2.4596 - 8 9.1055 - 1 6.3352 - 9 1,6119

49.603 2.4690 - 8 9.1318 - 1 6.3432 - 9 1,6162

49.838 2.4755 - 8 9,1499 - 1 6,3486 - 9 1,6192

49.969 2.4791 - 8 9.1600 - 1 6.3516 - 9 1.6208

t Gaussian frequencies, interval: 0-50 kc.
-37-

Table 23

0- = 5

d = 621 miles

.2= 80 a = 0. 85

t

f, kc Ki

50 .277 2, 4875

51 .456 2. 5195

53 ,572 2, 5755

56 .617 2. 6529

60 .578 2. 7483

65 ,438 2, 8580

71 .177 2, 9782

77 .771 3. 1050

85 .193 3. 2350

93 .410 3. 3652

102 .39 3, 4930

112 .09 3, 6163

122 .48 3. 7336

133 .50 3. 8437

145,,12 3. 9459

157 ,29 4, 0396

169,,95 4, 1247

183,,05 4. 2012

196,,53 4. 2692

210 ,34 4. 3291

224,,43 4, 3813

238 .72 4. 4263

253 ,17 4. 4645

267 ,71 4. 4964

282 ,29 4. 5227

296 .83 4, 5439

311 .28 4. 5605

325 .57 4,,5730

339 .66 4, 5819

353 .47 4. 5878

366,,95 4, 5909

380 .05 4, 5918

392 .71 4. 5908

404 .88 4, 5882

416 .50 4. 5845

427 .52 4, 5798

437 .91 4, 5745

447 .61 4. 5689

456 .59 4, 5630

464 .81 4, 5572

472 .23 4, 5516

478 .82 4. 5463

484 .56 4, 5415

489 .42 4< 5373

493 .38 4, 5338

496 .43 4, 5311

498 .54 4, 5291

499 .72 4. 5280

arg E

d = 1000 miles

arg E

9.1836 1 6 ,3586 - 9 1.6247

9.2736 1 6,,3844 - 9 1.6393

9.4321 1 6,,4267 - 9 1.6652

9,6543 1 6,,4796 - 9 1.7013

9.9335 1 6,,5357 - 9 1.7466

1.0263 6,,5877 - 9 1.7998

1.0634 6, 6291 - 9 1.8598

1.1041 6,,6547 - 9 1.9254

1.1477 6 ,6610 - 9 1.9954

1.1936 6,,6462 - 9 2.0690

1.2413 6,,6098 - 9 2.1454

1.2904 6,,5525 - 9 2.2239

1.3405 6,,4758 - 9 2,3038

1.3913 6, 3820 - 9 2.3848

1.4425 6,,2734 - 9 2.4663

1.4939 6,,1526 - 9 2.5480

1.5453 6,,0220 - 9 2,6296

1.5964 5. 8843 - 9 2,7108

1.6472 5. 7414 - 9 2,7915

1.6975 5, 5956 - 9 2,8712

1.7472 5. 4486 - 9 2,9500

1.7961 5, 3018 - 9 3,0275

1.8442 5.,1567 - 9 3,1037

1.8913 5,,0142 - 9 3,1783

1.9373 4,,8754 - 9 3,2512

1.9822 4..7410 - 9 3,3223

2.0258 4,,6115 - 9 3,3914

2.0682 4 ,4874 - 9 3,4583

2.1091 4,.3690 - 9 3,5231

2.1485 4,.2566 - 9 3,5855

2.1864 4,.1503 - 9 3,6454

2.2227 4 ,0502 - 9 3,7027

2.2572 3,,9564 - 9 3,7573

2.2900 3 .8689 - 9 3,8091

2.3209 3,.7876 - 9 3,8580

2.3500 3,.7126 - 9 3,9039

2.3770 3, 6436 - 9 3,9467

2.4021 3..5807 - 9 3,9863

2.4251 3,.5238 - 9 4,0227

2.4461 3,.4728 - 9 4,0557

2.4648 3. 4275 - 9 4,0854

2.4814 3. 3879 - 9 4,1116

2.4958 3. 3 540 - 9 4,1342

2.5079 3, 3256 - 9 4,1534

2.5177 3. 3027 - 9 4,1689

2.5253 3. 2853 - 9 4,1808

2.5305 3. 2732 - 9 4,1891

2.5334 3. 2665 - 9 4.1937

t Gaussian frequencies, interval: 50-500 kc.
-38-

Table 24 t

f, kc

500.31

501.62

503.97

507,35

511.75

517.15

523.53

530.86

539.10

548.23

558.21

568.99

530.53

592.78

605.69

619.21

633.27

647.83

662.81

678.16

693.81

709.69

725.75

741.90

758.10

774.25

790.31

806.19

821.84

837.19

852.17

866.73

880.79

894.31

907.22

919.47

931.01

941.79

951.77

960.90

969.14

976.47

982.85

988,25

992.65

996.03

998.38

999.69

0- = 5 d = 621 miles

4.5275

4.5262

4.5240

4,5208

4.5165

4.5111

4,5045

4.4968

4.4879

4.4776

4.4661

4.4533

4,4392

4,4238

4,4072

4,3893

4,3703

4,3502

4,3291

4.3072

4,2844

4,2610

4,2371

4,2128

4,1882

4,1635

4,1387

4,1141

4,0898

4,0658

4,0424

4,0196

3,9975

3,9762

3,9560

3.9367

3.9186

3.9016

3.8860

3.8717

3,8587

3,8473

3.8373

3.8288

3.8220

3.8167

3.8130

3,8110

.2 =80

a = 0. 85

1000 miles

arg E^

2,5349

2,5381

2,5439

2,5522

2,5630

2,5762

2,5917

2,6094

2,6293

2,6511

2,6748

2,7003

2,7274

2,7560

2,7858

2,8168

2,8489

2,8818

2,9154

2,9496

2,9842

3,0191

3,0541

3,0890

3,1238

3,1583

3,1924

3,2259

3,2587

3,2907

3,3218

3,3518

3,3807

3,4084

3,4347

3,4595

3,4828

3,5046

3,5246

3,5429

3,5594

3,5740

3,5867

3,5974

3,6061

3,6128

3,6175

3,6201

arg E 3 .2632 - 9 4,1960 3 .2558 - 9 4.2011 3 .2425 - 9 4.2102 3 .2236 - 9 4,2233 3 .1992 - 9 4.2404 3 ,1696 - 9 4.2612 3 .1352 - 9 4,2857 3 .0962 - 9 4,3137 3 .0530 - 9 4,3450

3..0062 - 9 4,3795 2 ,9562 - 9 4,4170 2 ,9033 - 9 4.4572 2 ,8482 - 9 4,5000 2 ,7911 - 9 4.5450 2 ,7327 - 9 4,5922 2 ,6732 - 9 4,6411 2 ,6132 - 9 4.6917 2 ,5529 - 9 4.7436 2 ,4929 - 9 4,7967 2 ,4333 - 9 4,8506 2 ,3744 - 9 4,9052 2 ,3166 - 9 4,9602 2 ,2601 - 9 5,0154 2 ,2051 - 9 5,0705 2 ,1517 - 9 5,1254 2 ,1001 - 9 5,1798 2 ,0505 - 9 5,2335

2,,0029 - 9 5,2863

,9575 - 9 5,3381

,9142 - 9 5,3885

,8732 - 9 5.4375

8344 - 9 5.4849

,7979 - 9 5.5304

,7638 - 9 5.5740

,7319 - 9 5.6154

7024 - 9 5.6546

,6752 - 9 5.6913

6503 - 9 5.7256

6277 - 9 5.7572

6073 - 9 5.7860

5892 - 9 5.8119

5734 - 9 5.8350

5597 - 9 5,8549

5483 - 9 5.8719

5391 - 9 5.8856

5320 - 9 5.8962

5271 - 9 5.9035

5244 - 9 5.9076
-39-

d, miles

50

60

70

80

100

200

300

400

500

600

50

60

70

80

100

200

300

400

500

600

50

60

70

80

100

200

300

400

500

600

0- = 0.001

€ =: 15 cr= 0,75

Table 2 5

f = 153. 5 kc

arg E

1.33 - 6 1.75

1.00 - 6 1.90

7.77 - 7 2.04

6.17 - 7 2.17

4.08 - 7 2.39

8.68 - 8 3.22

2.77 - 8 3.87

1.06 - 8 4.49

4.44 - 9 5.12

1.94 - 9 5.77

(T = 0., 003

K

15).75

1.96 - 6 1.10

1.56 - 6 1.21

1.29 - 6 1.31

1.08 - 6 1.40

7.93 - 6 1.58

2.57 - 7 2.34

1.10 - 7 3.02

5.23 - 8 3.67

2.63 - 8 4.32

1.37 - 8 4.97

0- = 0. 005

€^ = 15) c/ = 0..7 5 2.10 - 6 8.68

1.70 - 6 9.57

1.41 - 6 1.04

1.20 - 6 1.12

9.04 - 7 1.27

3.27 - 7 1.94

1.55 - 7 2.55

8.06 - 8 3.15

4.42 - 8 3.75

2.49 - 8 4.35

0- = 0.002

6^15

cr= 0. 75

arg E

1.80 - 6 1.32

1.41 - 6 1.45

1.15 - 6 1.56

9.48 - 7 1.67

6.77 - 7 1.86

1.91 - 7 2.66

7.23 - 8 3.34

3.09 - 8 3.98

1.42 - 8 4.61

6.74 - 9 5.24

(T = 0. 004

€t = 15 C^ =: 0, 75 2.04 - 6 9.62

1.65 - 6 1.06

1.36 - 6 1.15

1.15 - 6 1.24

8.60 - 7 1.40

2.99 - 7 2.11

1.36 - 7 2.75

6.84 - 8 3.38

3.63 - 8 4.01

1.98 - 8 4.63

0- = 0. 006

i-,= 15 C^ = 0. 75

- 1 2.133 - 6 7.983

- 1 1.732 - 6 8.810

1.447 - 6 9.591

1.233 - 6 1.034

9.338 - 7 1.175

3.479 - 7 1.806

1.684 - 7 2.393

8.987 - 8 2.971

5.033 - 8 3.548

2.896 - 8 4.127

- 1
-40-

Table 26

f = 153. 5 kc

d, miles

0- = 0.007

.2=15 a = 0.75

arg E

o- = 0. 01

£ = 15 (/= 0.7 5

arg E

50

60

70

80

100

200

300

400

500

600

50

60

70

80

100

200

300

400

500

600

50

60

70

80

100

200

300

400

500

600

2.159 - 6 7.436

1.758 - 6 8.213

1.471 - 6 8.948

1.257 - 6 9.652

9.559 - 7 1.099

3.634 - 7 1.701

1.790 - 7 2.265

9.711 - 8 2.823

5.522 - 8 3.381

3.224 - 8 3.941

cr = 0. 02 r.

15

0. 75

2.2647 - 6 4.5998

1.8599 - 6 5.1114

1.5699 - 6 5.6030

1.3518 - 6 6.0798

1.0453 - 6 7.0025

4.2808 - 7 1.1372

2.2518 - 7 1.5678

1.2960 - 7 2.0028

7.7860 - 8 2.4423

4.7913 - 8 2.8847

<j = 0. 005

'i\

15

0, 85

2.09 - 6 8.74

1.69 - 6 9.65

1.40 - 6 1.05

1.19 - 6 1.13

8.94 - 7 1.29

3.18 - 7 1.98

1.47 - 7 2.63

7.47 - 8 3.27

3.98 - 8 3.92

2.18 - 8 4.56

1 2.208 - 6 6.310

1 1.805 - 6 6.983

1 1.517 - 6 7.623

1 1.300 - 6 8.238

9.968 - 7 9.415

3.925 - 7 1.480

1.995 - 7 1.995

1.114 - 7 2.507

6.507 - 8 3.021

3.899 - 8 3.538

0- = 5 €,= 80

(/= 0. 75 2.3175995 - 6 6.8680500 - 2 1.9110039 - 6 8.2034550 - 2 1.6192783 - 6 9.6247370 - 2 1.3994859 - 6 1.1121350 - 1.0897548 - 6 1.4312537 - 4.5842073 - 7 3.3207809 - 2.4498846 - 7 5.5295098 - 1.4212180 - 7 7.9135687 - 8.5620686 - 8 1.0387779

5.2676120 - 8 1.2903433
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