Field Notebook: England, WY 1992

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SOKKIA™

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TRANSIT
FIELD BOOK

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No. 8152-00

Property of_ ,/s C' c— J_ — j ~)!/i Cy

Address -VpT- C'~f Cco/oyY V-

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This Book is manufactured of a High Grade
50% Rag Ledger Paper having a Water Resist¬
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Table
Table II
Table £
Table X
Table fl.

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

INDEX OF

CURVE AND REDUCTION TARLES

I—SLOPE STAKE

II—STADIA CORRECTION AND HORIZONTAL DISTANCES

III—TRIGONOMETRIC FORMULAE
TV-NATURAL TRIGONOMETRICAL FUNCTIONS
CURVE FORMULAE

V— T ANGENTS AND EXTERNALS TO A 1° CURVE
USEFUL RELATIONS

VI— INCHES TO DECIMALS OF A FOOT
Vn—MINUTES IN DECIMALS OF A DEGREE

VIII—MIDDLE ORDINATES OF RAILS

IX— SHORT RADIUS CURVES

X- RODS IN FEET, 10THS AND 100THS OF FEET

XI—LINKS IN FEET, 10THS AND 100THS OF FEET

Table

TABLE I. SLOPE STAKE

DISTANCES FROM SIDE STAKES FOR CROSS-SECTIONING

ROADWAY OF ANY WIDTH. SIDE SLOPES 1'/ 2 TO 1 5LO pe

STAKE

Cut o(
Fill

Distance out fropi Side or Shoulder Stake.

Cut oi

Fill

0

•»

3

.3

•«

.6

•«

• 7

■8

.9

0

000

0 15

0.80

0.45

0 60

0.75

0 90

1.05

1.20

1.35

0

1

1 50

1 65

i eo

1.95

2 10

2.25

2.40

2 55

2.70

2.85

1

2

3.00

3.15

8.30

3 45

3.60

3 75

3.90

4.05

4.20

4 35

2

3

4.50

4 65

4.80

4 95

5 10

5 25

5 40

5.55

5.70

5.85

3

4

6.00

6 15

6.30

6 45

6 60

6 75

6.90

7.05

7.20

7 35

4

5

7 50

7.65

7 80

7.95

8 10

8,25

8.40

8.55

8.70

8.85

5

6

900

9 15

9.30

9.45

9.60

9 75

9.90

10.05

10.20

10 35

6

7

10 50

10 65

io eo

10.95

11.10

11.25

11.40

11 55

11 70

11.85

7

8

12.00

12 15

12.80

12.45

12 60

12.75

12 90

13 05

13.20

13.35

8

9

13 50

13 65

18 80

13 95

14 10

14.25

14.40

14 55

14.70

14.85

9

10

15 00

15 15

15 80

15 45

15.60

15.75

15 90

18 05

16 20

10 35

10

it

16 50

16 65

18 80

16 95

17 10

17 25

17.40

17.55

17.70

17.85

11

12

18 00

18 15

18 30

18 45

18 60

18 75

18.90

19 05

19 20

19 85

12

13

19 50

19 65

10.80

19.95

20.10

20 25

20 40

20 55

20.70

20.85

13

14

21.00

21 15

21.30

21.45

21 60

21.75

21.90

22 05

22 20

22 85

14

15

22 50

22 63

22 80

22 95

23.10

23.25

23.40

23 55

23.70

23.85

15

16

24 00

24 15

24 30

24 45

24 60

24 75

24 90

25 05

25.20

25.35

16

17

25,50

25 65

25 80

25 95

26.10

26 25

26 40

20.55

20.70

20 85

17

18

27 00

27 15

27 30

27 45

27.60

27.75

27.90

28 05

28 20

28.35

18

19

28 60

28 85

28 80

28.95

29.10

29.25

29.40

29.55

29.70

29.85

19

20

30 00

30 15

30.30

30 45

30 80

30.75

30.90

31.05

31.20

31.85

20

21

31 50

31 65

31.80

31.95

32 10

32 25

32.40

32.55

32 70

82 85

21

22

33 00

33 15

33 30

33 45

33 60

33 75

33.90

34 05

34.20

34.35

22

23

34 50

34 65

34.80

34.95

35 10

85 25

35 40

35.55

35.70

35 85

23

24

86 00

86 15

36.30

36 45

36.60

36.75

36 90

37.05

37 20

37.35

24

25

37 50

37.65

37 80

37.95

38.10

38 25

38.40

38 55

38.70

38.85

25

28

39 00

39 15

39 80

39 45

39 60

39 75

30 90

40 05

40.20

40.35

26

27

40 50

40 65

40 80

40 95

41.10

41 25

41 40

41.55

41.70

41.85

27

28

42 OO

42 15

42 30

42 45

42,60

42 75

42.90

43.05

43 20

43.35

28

29

43 50

43 65

43.80

43 95

44 10

44 25

44 40

44,55

44.70

44 85

29

30

45 00

45 15

45 80

45 45

45.60

45.75

45 90

40.05

46 20

46.35

30

31

46.50

46.65

46.80

46 95

47 10

47,25

47.40

47.55

47.70

47.85

31

32

48 00

48 15

48.30

48 45

48.60

48 75

48.90

49.05

49 20

49.35

33

33

48 60

49 65

49 80

49.95

50.10

50 25

50.40

50.55

50 70

50.85

33

34

51 00

61.15

51.30

51.45

51.60

51.75

51.90

52.05

52 20

52.85

34

35

52 50

62 85

52 80

52.95

53.10

53 25

53.40

53.65

53 70

53.85

35

36

64 00

64 15

54 30

54 45

54.60

54.75

54.00

55.05

55 20

55.35

36

37

55 50

55 65

55.80

55 95

56 10

56.25

56.40

56 55

56.70

56.85

37

38

57 00

57.15

57.30

57 45

57.00

57 75

57.90

58.05

58 20

58 35

38

39

58 50

58.65

58 80

58 95

59.10

59 25

59.40

59 55

59.70

50.85

39

40

60 00

60 15

60 30

60 45

60 60

60.75

60 90

61.05

61 20

61.35

40

TABLE II. STADIA CORRECTION AND HORIZONTAL DISTANCES

STADIA REDUCTIONS FOR READING 100

Verticol Angle

Horizontal

Correction

Difference
in Elevation

Vertical Angle

Horizontal

Correction

Difference
in Elevation

2°—00'

0.1

3.5

18°—30'

10.1

30.1

3°—00'

0.3

5.3

19“-00'

10.6

30.8

4“—00'

0.5

7.0

19°—30'

11.2

31.5

5“—00'

0.8

8.7

20“—00'

11.7

32.1

6°-00'

1.1

10.4

20“-30'

12.3

32.8

7°—00'

1.5

12.1

21 “—00'

12.8

33.5

8°-00'

1.9

13.8

21 “—30'

13.4

34.1

9°-00'

2.5

15.5

22“-00'

14.0

34.7

10“-00'

3.0

17.10

22°—30'

14.7

35.4

10°—30'

3.3

17.9

23“-00'

15.3

36.0

ir-oo'

3.6

18.7

23°—30'

15.9

36.6

11°—30'

4.0

19.5

24“-00'

16.5

37.2

12“—00'

4.3

20.3

24“-30'

17.2

37.7

12°—30'

4.7

21.1

25“-00'

17.9

38.3

13“-00'

5.1

21.9

25°—30'

18.6

39.0

13°—30'

5.5

22.7

26“-00'

19.2

39.4

14°—00'

5.9

23.4

26“—30'

19.9

39.9

14°—30'

6.3

24.2

27“—00'

20.6

40.5

15“—00'

6.7

25.0

27“—30'

21.3

41.0

15“-30'

7.2

25.8

28“-00'

22.0

42.0

16°—00'

7.6

26.5

28“—30'

22.8

41.9

16°—30'

8.1

27.2

29“-00'

23.5

42.4

17“-00'

8.5

28.0

29“—30'

24.3

42.9

17--30'

9.0

28.7

30“-00'

25.0

43.3

18°—00'

9.5

29.4

Chains

to Feet

Feet

to Chains

1 .

... 66

100

... 1.515

2 .

.... 132

200

.... 3.030

O

•J .

.... 198

300

... 4.545

4 .

.... 264

400

... 6.060

5 .

.... 330

500

... 7.575

6 .

.... 396

600

9.090

7 .

... 462

700

... 10.606

8 .

... 528

800

... 12.121

9 .

... 594

900

... 13.636

10 .

.... 660

1,000

... 15.151

TABLE III. TRIGONOMETRIC FORMULAE

Given
a, b

a, c

A, a

A, b
A, c

Given

A, B, a

A, a, b

a, b.O

a, b, e

a, b, c
A, b, c

A, B, C, a

Required
A. B ,o

A, B, b

B. b, c

B, a, c
B, a, b

Required

b, c, O

B, c, C

A, B, c

A. B, O

Area
Area

Area

tan A = — = cot B, c = -v/a 2 + A 2 = a A /1 --

o \ a 2

cos B, b = y' (c + a) (c — a) = e 1 — ~

B = 90°— A, b = a cot A. c =

• a a
sin A — —
c

a

sin A.

B = 90°--A,a = b tan A,c= —

cos A.

B — 90°— A, a = c sin A, b = c cos A t

Solution of Oblique Triangles

a ^~- t c = 180 °—(A + B),e = ^-2
in A ' sin A

b =

sin B= — ' - A ,C= 180 °—{A + B),e =

a sin A

A+B=m°-C,tBn\{A-B) A a ~ b)lan OA±B)

asinO a +6

a-fi+c . , . /i
» —-5-,sin \A = *J

sin A

< (*.- b)(.—c)

be

«in a’d ’°=IM°-(A+B)

CL -f- b C r -,

8 = o-, area = \/x(s—a) (s—b) ( 5 — 0 )

b c sin A

area =

- a 2 sin B sin C

area = -—— -

J sin A

REDUCTION TO HORIZONTAL

Horizontal distance

Horizontal distance - Slope distance multiplied by tbe
vL S i ne «° f *i he a P>' ,e Thus; slope distance -319. 4 ft

Vert, anule-5 10. hrom Table. IV. cos 5° ]O'= 9959

% Horizontal distance -319.4 * .9959 - 318 09 ft.

X Horizontal distance also —Slope distance minus slope
distance limes <I-cosine of vertical angle). With the
? ame figures as in the preceding example, the follow-
ing result is obtained Cosine 5° I O'^.9959. 1 - 9959 = 0041
319.4*.0041 =1.31. 319.4-1.31 =318.09 ft.

.we,. , .wti -I.dt. oia.4-1.31 =318.09 ft.

anno lofo^tK C r,se ls k . n fL wn - the . horizon!al distance is approximately:—the sloDe disi-
ce less the square of the rise divided by twice the slope distance. Thus: nse = 14 ft..

slope distance=302.6 ft. Horizontal distance=302.6- -H v 14 = 302 6-0 3^=309 9 K ft

2 x 302.6 *” ‘ ^

R |n

TABI.E IV. NATURAL TRIGONOMETRICAL FUNCTIONS

Angle

Sin

Ton.

Set.

Coset.

Cotg.

Cosin.

Angle

Sin.

Tan.

Set.

Coset.

Cotg.

Cosin.

0

0

0

1 .

00

00

1 .

90

8

1392

.1405

1.0098

7.185

7.115

.99027

82

10

0029

.0029

343.8

343.8

1 .

50

10

.1421

.1435

1.0102

7.040

6.968

.98986

50

20

.0058

.0058

171 .9

171 9

.99998

40

20

.1449

.1465

1.0107

6.900

6.827

.98944

40

30

.0087

.0087

1 14.6

1 14.6

.99996

30

30

.1478

.1495

1.01 1 1

6.766

6.691

.98902

30

40

.01 16

.01 16

1.0001

85.94

85.94

.99993

20

40

.1507

.1524

1.01 15

6.636

6.561

.98858

20

50

.0145

.0145

1.0001

68 76

68.75

99989

10

50

.1536

.1554

1.0120

6-512

6.435

.98814

10

1

.0175

.0175

1.0002

57.30

57.29

.99985

89

9

.1564

.1584

1.0125

6.394

6.314

.98769

81

10

.0204

.0204

1.0002

49.11

49.10

99979

50

10

.1593

.1614

1.0129

6.277

6 197

.98723

50

20

.0233

.0233

1.0003

42.98

42.96

.99973

40

20

.1622

.1644

1 -0134

6.166

6.084

.98676

40

30

.0262

.0262

1.0003

38.20

38.19

99966

30

30

1650

.1673

1.0139

6.059

5.976

.98629

30

40

.0291

.0291

1.0004

34.38

34 37

.99958

20

40

.1679

.1703

1.0144

5.955

5.871

.98580

20

50

.0320

.0320

1.0005

31.26

31.24

.99949

10

50

.1708

.1733

1.0149

5.855

5.769

.98531

10

2

.0349

.0349

1.0006

28.65

28.64

.99939

88

10

.1736

.1763

1.0154

5.759

5.671

98481

80

10

.0378

.0378

1.0007

26 45

26.43

.99929

50

10

.1765

.1793

1.0160

5.665

5.576

.98430

50

20

.0407

.0407

1 OOOB

24.56

24.54

.99917

40

20

.1794

.1823

1 0165

5.575

5 >485

98378

40

30

.0436

.0437

1.0010

22.93

22.90

.99905

3 G

30

.1822

.1853

1 .0170

5.488

5.396

.98325

30

40

.0465

.0466

1.001 1

21.49

21.47

.99892

20

40

.1851

.1883

1.0176

5.403

5.309

.98272

20

50

.0494

.0495

1 ,001 2

20.23

20.21

.99878

10

50

.1880

.1914

10181

5.320

5.226

98218

10

3

.0523

.0524

1.0014

19.11

19.08

99863

87

11

.1908

.1944

1.0187

j 5.241

5.145

.98163

79

10

.0552

.0553

1.0015

18.10

18.07

.99847

50

10

1937

1974

1.0193

15.164

5.066

.98107

50

20

.0581

.0582

1.0017

17.20

17.17

.99831

40

20

.1965

.2004

1.0199

5.089

4.989

.98050

40

30

.0610

.0612

1.0019

16-38

16.35

.99813

30

30

.1994

.2035

1.0205

5016

4.915

,97992

30

40

.0640

.0641

1 0020

15.64

15.60

.99795

, 20

40

,2022

.2065

1 021 1

4.945

4.843

.97934

20

50

.0669

.0670

1,0022

14.96

14.92

99776

10

50

.2051

.2095

1.0217

4.877

4.773

.97875

10

4

.0698

.0699

1.0024

14.34

14.30

.99756

86

12

,2079

.2126

1.0223

1 4.810

4.705

.97815

78

10

.0727

.0729

1 .0027

13.76

13.73

.99736

50

10

.2108

2156

1.0230

4.745

4.638

.97754

50

20

.0756

.0758

1.0029

13.23

1 3-20

99714

40

20

.2136

.2186

1.0236

4.682

4.574

.97692

40

30

.0785

.0787

1.0031

12.75

12.71

.99692

30

30

.2164

.22 7

1.0243

4.620

4.511

.97630

3 d

40

.0814

.0816

1.0033

12.29

12.25

.99668

20

40

.2193

.2247

1.0249

4.560

4.449

.97566

20

50

.0843

.0846

1 0036

1 1 87

1 1.83

.99644

10

50

.2221

. 22^8

1 0256

4.502

4.390

.97502

10

5

.0872

.0875

1.0038

1 1.47

11.43

.99619

85

13

.2250

.2309

1.0263

' 4.445

4.331

.97437

77

10

.0901

.0904

1 . 0041

1 1 .10

11.06

.99594

50

10

.2278

.2339

1.0270

4.390

4.275

.97371

50

20

.0929

.0934

1.0043

10.76

10.71

.99567

40

20

.2306

.2370

1.0277

4.336

4.219

.97304

40

30

.0958

.0963

1 .0046

10.43

10.39

.99540

30

30

.2334

.2401

1.0284

4.284

4.165

.97237

30

40

.0987

.0992

1,0049

10.13

10.08

.9951 1

20

40

.2363

.2432

1.0291

4.232

4.113

.97169

20

50

.1016

.1022

1.0052

9.839

9.788

.99482

10

50

.2391

.2462

1.0299

4.182

4.061

.97100

10

6

.1045

.1051

1.0055

9.567

9.514

.99452

84

14

.2419

.2493

1.0306

4.133

4.011

.97030

76

10

.1074

.1080

1.0058

9.309

9.255

.99421

50

10

.2447

.2524

1.0314

4.086

3.962

.96959

50

20

.1103

.11 10

1 .0061

9.065

9.010

.99390

40

20

.2476

.2555

1.0321

4.039

3.914

.96887

40

30

.1132

.1139

1.0065

8.834

8.777

.99357

30

30

.2504

.2586

1.0329

3.994

3.867

.96815

30

40

.1161

.1169

1.0068

8.614

8-556

.99324

20

40

.2532

.2617

1.0337

3.949

3.821

.96742

20

50

.1190

.1198

1 0072

8.405

8.345

.99290

10

50

.2560

.2648

1.0345

3.906

3.776

.96667

10

7

1219

.1228

1.0075

8.206

8.144

.99255

83

15

2588

2679

1.0353

3.864

3.732

96593

75

10

.1248

.1257

1.0079

8.016

7.953

.99219

50

10

.2616

2711

1 0361

3.822

3.689

.96517

50

20

.1276

.1287

1.0082

7.834

7.770

.99182

40

20

2644

2742

1.0369

3.782

3.647

96440

40

30

1305

.1317

1.0086

7.661

7.596

.99144

30

30

2672

2773

1.0377

3.742

3.606

.96363

30

40

1334

1346

1 0090

7.496

7.429

.99106

20

40

.2700

2805

1.0386

3.703

3.566

.96285

20

50

1363

1376

1.0094

7.337

7.269

.99067

10

82

50

2728

2836

1.0394

3.665

3.526

96206

10

74

Cosin

Cotg.

Coset.

Set.

Tan.

Sin.

Angle

Cosin.

Cotg.

Coset.

Set.

Tan.

Sin.

Angle

1

w

I

TARI F IV

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS

\

2756

2784

2812

,2840

2868

.2896

.2867

.2899

2931

2962

2994

3026

.2924

2952

2979

3007

3035

3062

3090

3118

.3145

.3173

.3201

.3228

.3256

.3283

.3311

3338

.3365

3393

3420

3448

3475

3502

.3529

3557

3584
3611
363B
.3665
.3692
.3719

3746

.3773

.3800

.3827

.3854

.3881

3907

3934

3961

3987

4014

4041

3057

3089

3121

3153

3185

3217

3249

3281

3314

3346

3378

3541

3574

Cotg.

Sec.

Cosec.

Cotg.

Cosin.

ngle

Sin.

Tan.

1.0403

3.628

3.487

96126

74

24

4067

4452

1.0412

3.592

3.450

96046

50

10

4094

4487

1.0423

3.556

3 412

95964

40

20

4120

4522

1.0429

3.521

3.376

95882

30

30

4147

4557

1.0438

3.487

3.340

95799

20

40

4173

4592

1 0448

3.453

3.305

95715

10

50

4200

4628

1.0457

3.420

3.271

95630

73

25

4226

4663

1 0466

3.388

3.237

95545

50

10

4253

4699

1.0476

3.357

3.204

95459

40

20

4279

4 734

1 0485

3.326

3.172

95372

30

30

4305

4770

1.0495

3 295

3.140

95284

20

40

4331

4806

1.0505

3.265

3.108

95195

10

50

4358

4841

1.0515

3.236

3.078

95106

72

26

4384

.4877

1.0525

3.207

3.048

95015

50

10

4410

.4913

1 0535

3.179

3.018

94924

40

20

4436

.4950

1.0545

3.152

2.989

94832

30

30

4462

4986

1.0555

3.1 24

2.960

94740

20

40

4488

.5022

1.0566

3.098

2.932

94646

10

50

4514

.50 5* 1

1.0576

3.072

2.904

.94552

71

27

4540

.5095

1.0587

3.046

2.877

94457

50

10

4566

.5132

1.0598

3.020

2.850

94361

40

20

4592

.5169

1 0608

2.996

2.824

.94264

30

30

4617

.5206

1.0619

2.971

2.798

.94167

20

40

4643

.5243

1 0631

2.947

2.773

.94068

10

50

4669

5280

1.0642

2.924

2.747

.93969

70

28

.4695

.5317

1 0653

2 900

2.723

93869

50

10

.4720

.5354

1.0665

2.878

2.699

93769

40

20

.4746

.5392

1 0676

2.856

2.675

93667

30

30

.4772

.5430

1,0688

2.833

2.651

93565

20

40

.4797

.5467

1.0700

2.81 1

2.628

.93462

10

50

.4823

.5505

1.0711

2.790

2.605

.93358

69

29

.4848

.5543

1 0723

2.769

2.583

93253

50

10

4874

5581

1.0736

2,749

2.560

.93148

40

20

4899

.5619

1.0748

2.729

2.539

.93042

30

30

4924

.5658

1.0760

2 709

2.517

.92935

20

40

4950

.5696

1.0773

2.689

2.496

92827

10

50

4975

.5735

1.0785

2.670

2.475

.92718

68

30

5000

.5774

1.0798

2.650

2.455

.92609

50

10

5025

.5812

1.081 1

2.632

2.434

.92499

40

20

5050

.5851

1.0824

2.613

2.414

.92388

30

30

5075

.5890

1 0837

2.595

2.394

.92276

20

40

5100

.5930

1.0850

2 577

2.375

92164

10

50

5125

5969

1.0864

2.559

2.356

.92050

67

31

5150

.6009

1.0877

2.542

2.337

91936

50

10

5175

.6048

1.0891

2.525

2.318

.91822

40

20

5200

.6088

1.0904

2.508

2.300

.91706

30

30

5225

6128

1.0918

2.491

2.282

.91590

20

40

5250

.6168

1.0932

2.475

2.264

.91472

10

66

50

5275

.6208

Cosec.

Sec.

Tan.

Sin.

Angle

Cosin.

Cotg.

0946

0961

.0975

0989

1004

1019

1034

1049

1064

1079

1095

1110

.1126

1142

.1158

1174

1190

1207

1223

,1240

1257

1274

.1291

1308

1.1326
1.1343
1.1361
1 1 379
1.1397
1 1415

1434
1 1452
1 1471
1 1490
1 1509
1 1528

1 1547
1.1566
1 1586
1.1606
1.1626
1.1646

2.459
2.443
2.427
2.41 1
2.396
2.381

2 366
2.351
2.337
2.323
2 309
2.295

2.281
2.268
2 254
2.241
2.228
2 215

2.203

2.190

2.178

2.166

2.154

2.142

Cotg.

2.246
2.229
2.211
2.194
2.177
2.161

2.145
2.128
2.112
2.097
2.081
2 066

2.050
2.035
2.020
2.006
1.991
1 .977

1.963

1.949

1.935

1.921

1.907

1.894

2.119
2.107
2.096
2.085
2.073

1.868
1.855
1.842
1.829
16

2.063

2.052

2.041

2.031

2.020

2.010

2 000
1.990
1.980
1.970
1.961
1.951

1 1666
1 1687
1.1707
1.1728
1749
1 1770

91355
91236
91 116
90996
90875
90753

90631

90507

90383

90259

90133

90007

89879

89752

89623

89493

89363

89232

89101

88968

88835

88701

.88566

88431

.88295

88158

88020

87882

87743

87603

1.804

1.792

1.780

1.767

1.756

1.744

1.732
1.720
1.709
1,698
1 686
1.675

1 .932
1.923
1.914
1.905
1.896

653
1.643
1.632
1.621
611

87462

87321

87178

87036

86892

86748

86603

86457

.86310

86163

86015

85866

85717

85567

85416

85264

85112

84959

Angle

tW

m

Jan

it pi

up*

. w
m

jpi

dim

s|js«

n'4sn

.BIOT

:|ot

rp

31

\M

isotaj

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS

Angle

Sin.

Ton.

Sec.

Cosec.

Cotg.

Cosin.

Anqle

Sin.

Ton

Sec.

Cosec.

Cotg.

Cosin.

32

.5299

.6249

1.1792

1.887

1.600

.84805

58

39

.6293

.8098

1 2868

1.589

1.235

.77715

51

10

.5324

.6289

1 1813

1.878

1.590

84650

50

10

.6316

.8146

1.2898

1.583

1.228

.77531

50

20

5348

6330

1.1835

1.870

1.580

84495

40

20

,6338

.8195

1.2929

1.578

1.220

.77347

40

30

.5373

.6371

1 1857

1 861

1.570

84339

30

30

.6361

8243

1.2959

1.572

1.213

.77162

30

40

.5398

.6412

1 1879

1.853

1 560

.84182

20

40

.6383

.8292

1.2991

1.567

1.206

.76977

20

50

.5422

.6453

1 1901

1.844

1.550

84025

10

50

.6406

.8342

1.3022

1.561

1.199

.76791

10

33

.5446

.6494

1 1924

1.836

1.540

83867

57

40

.6428

8391

1.3054

1 556

1,192

.76604

50

10

.5471

.6536

1 1946

1.828

1.530

83708

50

10

.6450

.8441

1.3086

1.550

1.185

.76417

50

20

.5495

.6577

1.1969

1.820

1.520

.83549

40

20

6472

.8491

1.3118

1.545

1.178

76229

40

30

.5519

.6619

1 1992

1.812

1.51 1

83389

30

30

.6494

.8541

13151

1.540

1,171

.76041

30

40

.5544

.6661

1.2015

1.804

1.501

.83228

20

40

.6517

8591

1.3184

1.535

1.164

.75851

20

50

.5568

.6703

1 2039

1.796

1.492

83066

10

50

.6539

.8642

1.3217

1.529

1.157

.75661

10

34

.5592

.6745

1.2062

1 788

1.483

.82904

56

41

6561

8693

1 3251

1.524

1.150

.75471

49

10

5616

.6787

1.2086

1.781

1 473

82741

50

10

6583

.8744

1 3284

1.519

1.144

.75280

50

20

.5640

6830

1.2110

1.773

1.464

.82577

40

20

.6604

.8796

1.3318

1,514

1.137

75088

40

30

.5664

.6873

1 2134

1.766

1.455

82413

30

30

.6626

,8847

1 3352

1.509

1.130

.74896

30

40

.5688

6916

1.2158

1.758

1 446

82248

20

40

6648

8899

1.3386

1 504

1.124

.74703

20

50

.5712

6959

1 2183

1.751

1.437

82082

10

50

.6670

.8952

1 3421

1.499

1.117

74509

10

35

.5736

.7002

1.2208

1.743

1 428

81915

55

42

6691

9004

1.3456

1.494

1.111

.74314

48

10

.5760

.7046

1 2233

1.736

1.419

81748

50

10

.6713

.9057

1.3492

1.490

1.104

.74120

50

20

.5783

7089

1.2258

1 729

1.411

81580

40

20

6734

.91 10

1 3527

1 485

1.098

.73924

40

30

.5807

.7133

1 2283

1.722

1.402

81412

30

30

.6756

.9163

1.3563

1.480

1.091

.73728

30

40

.5831

.7177

1.2309

1.715

1.393

.81242

20

40

6777

.9217

1.3600

1.476

1.085

.73531

20

50

.5854

.7221

1 2335

1.708

1.385

81072

10

50

6799

.927!

1 3636

I 471

1.079

.73333

10

36

.5878

.7265

1 2361

1.701

1.376

.80902

54

43

6820

.9325

1.3673

1.466

1.072

73135

47

10

.5901

.7310

1 2387

1.695

1.368

80730

50

10

.6841

.9380

1.371 1

1 462

1.066

.72937

50

20

.5925

7355

1.2413

1.688

1.360

.80558

40

20

6862

9435

1 3748

1.457

1.060

.72737

40

30

.5948

.7400

1 2440

1.681

1.351

80386

30

30

6884

.9490

1.3786

1 453

1 .054

.72537

30

40

.5972

.7445

1.2466

1.675

1.343

.80212

20

40

.6905

.9545

1.3824

1.448

1.048

72337

20

50

.5995

.7490

1 2494

1.668

1.335

.80038

10

50

6926

.9601

1.3863

1.444

1.042

.72136

10

37

.6018

.7536

1.2521

1 662

1.327

.79864

53

44

.6947

.9657

1.3902

1.440

1.036

.71934

46

10

.6041

.7581

1 2549

1.655

1.319

.79688

50

10

.6967

.9713

1 3941

1.435

1.030

71732

50

20

.6065

.7627

1.2577

1,649

1,31 1

.79512

40

20

.6988

9770

1.3980

1 431

1.024

71529

40

30

.6088

7673

1 2605

1.643

1.303

79335

30

30

.7009

.9827

1 4020

1.427

1.018

.71325

30

40

.6111

.7720

1.2633

1 636

1.295

.79158

20

40

7030

.9884

1.4061

1 422

1.012

.71121

20

50

.6134

.7766

1.2661

1.630

1.288

.78980

10

50

.7050

.9942

1.4101 1

1.418

1.006

.70916

10

38

.6157

.7813

1.2690

1.624

1.280

.78801

52

.7071

1 .

1.414

1.414

1 .

.70711

45

10

.6180

.7860

1.2719

1.618

1.272

78622

50

20

.6202

.7907

1.2748

1.612

1.265

.78442

40

30

.6225

.7954

1 2778

1.606

1.257

.78261

30

40

6248

,8002

1.2808

1.601

1.250

78079

20

50

6271

.8050

1 2838

1.595

1.242

.77897

10

Cosin.

Cotg.

Cosec.

Sec.

Tan.

Sin.

Angle

Cosin.

Cotg.

Cosec.

Sec.

Tan.

Sin.

Angle

CURVE FORMULAE

CURVE TABLE

Table of Tangent and External to a 1° Curve

To find Tangent and External for curve of any other
degree, divide by degree of curve and add correction
found in column of corrections.

Degree of curve with a given I may be found by divid¬
ing tangent, (or external), opposite I by given tangent,
(or external).

The distance from a point on the tangent to the curve
is very nearly the square of the tangent length divided
by twice the radius.

Radius:

CURVE FORMULAS

R 50
~ sin % D

A

Length of Curve: L = 100 -g-

also L = .0174533 x A X R

A

Degree of Curve: D = 100 -j—

Tangent: T = R tan % A

Long Cord: LC = 2R sin Vz A

Middle Ordinate: M= R (1 —Cos % A)
External: E = T tan Vi A

TABLE V. TANGENTS AND EXTERNALS TO A 1° CURVE

I

T

E

1:10°

0

50.OC

.218

10

58.34

.297

20

66.6'

.388

30

750

.491

T

40

83.34

.606

.03

50

91.6€

.733

EL

100.01

873

.001

10

108.35

1.024

20

116.6$

1.188

30

125.02

1.364

40

133 36

1 552

50

141.70

1.752

150.04

1.964

10 ° c.

10

158.3E

2.188

20

166.72

2.425

30

175.06

2.674

.06

40

183.40

2.934

E

50

191.74

3.207

.003

200.08

3.492

10'

208.4c

3.790

20

216 77

30'

225.12

4.421

40'

233.47

4.755

50'

241.81

5.100

15° C.

250.16

5.459

T

10'

258.51

5.829

.09

20'

266 86

6.211

30'

275.21

6.606

40'

283.57

7.013

004

50'

291.92

7.432

300 28

7 863

10'

308.64

8.307

20'

316.99

8.762

30'

325.35

9.230

.

40'

333.71

9.710

5,0'

342.08

10.202

T

.13

350.44

10.707

10'

358.81

11.224

20'

367.17

11.753

.006

30'

375.54

12.294

40'

383.91

12.847

50'

392.28

13.413

400.66

13.991

10'

409.03

14.582

20'

417.41

15.184

25" C.

30'

425.79

15.799

T

40'

434.17

16.426

50'

442.55

17.065

E

450.93

17.717

.007

10'

459.32

18.381

20'

467.71

19058

30'

476.10

19.746

40'

484.49

20.447

50'

492.88

21.161

0

501.28

21.887

30° C.

10'

509.68

22.624

T

20'

518.08

23.375

.19

30'

526.48

24.138

40'

534.89

24.913

E

50'

543.29

25.700

.008

I

T

E

1=20°

T

T

E

1=30°

1°

551.7C

26.500

4-

21 0

1061.9

97.577

10

560.11

27.313

5° C

10

1070.6

99.155

20

568 53

28.137

20

1079.2

100.75

30

576.95

28.974

30

1087 P

102.35

T

40

585.36

29 824

.06

40

1096.^

103.97

.10

50

593.79

30.686

E

50

1105.1

105.60

E

17°

602.21

31.561

.006

22°

1113.7

107.24

013

10

610 64

32.447

10'

1122.4

108.90

20

619.07

33.347

20'

1131.0

110.57

30

627.50

34.259

30'

1139.7

112.25

40

635.93

35.183

50'

644.37

36.120

50'

1157 0

115.66

3°

652.81

37.070

10° C.

23°

1165.7

117.38

10° C.

10'

661.25

38031

10'

1174.4

119.12

20'

669.70

39.006

20'

1183.1

120,87

30'

678.15

39.993

.13

30'

1191.8

122.63

.19

40'

686.60

40.992

E

40'

1200.5

124.41

E

50'

695.06

42.004

.011

50'

1209.2

126.20

.025

4°

703.51

43.029

24°

1217.9

128.00

10'

711.97

44.066

10'

1226.6

129.82

20'

720.44

45.116

20'

1235 3

30'

728.90

46.178

30'

1244.0

133.50

40'

737.37

47.253

40'

1252.8

135.35

50'

745.85

48.341

15° C.

50'

1261.5

137.23

15° C.

5°

754.32

49.441

T

25°

1270.2

139.11

T

10

762.80

50.554

.19

10'

1279.0

141.01

.29

20

771.29

51.679

20'

1287.7

142.93

30'

779.77

52.818

30'

1296.5

144.85

40'

788.26

53.969

.017

40'

1305.3

146.79

.038

50'

796.75

55.132

50'

1314.0

148.75

6°

805 25

56.309-

10'

813.75

57.498

10'

1331.6

152.69

20-

822 25

58.699

20'

1340.4

154.69

30'

830.76

59.914

30'

1349.2

156.70

40'

839.27

61.141

40'

1358.0

158.72

20° C.

50'

847,78

62.381

T

50'

1366.8

160.76

T

7°

856.30

63.634

26

27°

1375.6

162.81

.39

10'

864.82

64.900

10'

1384.4

164.86

E

20'

873.35

66.178

.022

20'

1393.2

166.95

051

30'

881.88

67.470

30'

1402.0

169.04

40'

890 41

68.774

40'

1410.9

171.15

50'

8°

907.49

71.421

28°

1428 6

175.41

10'

916.03

72.764

10'

1437.4

177.55

20'

924.58

74.119

20'

1446.3

179.72

25° C.

30'

933.13

75 488

T

30'

1455.1

181 89

T

40'

941.69

76.869

.32

40'

1464.0

184.08

50'

950.25

78.264

E

50'

1472.9

186.29

E

9°

958.81

79.671

.028

29°

1481.8

188.51

.065

10'

967.38

81 092

10'

1490.7

190.74

20'

975.96

82.525

20'

1499.6

192.99

30'

984.53

83 972

40'

993.12

85.431

40'

1517.4

197.53

50'

1001.7

86.904

50'

1526.3

199.82

0°

1010.3

88.389

30° C.

30°

1535.3

202.12

30° C.

10'

1018.9

39.888

T

10'

1544.2

204.44

T

20'

1027.5

91.399

20'

1553.1

206.77

30

1036.1

92.924

30'

1562.1

209.12

40'

1044.7

94.462

E

40'

1571.0

211.48

50'

1053.3

96.013

.034

50'

1580.0

213.86

,078

T = R tan Vzl

E = R exsec */ 2 1

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 1° CURVE

T

1589.0

1598.0

1606.9

1615.9

1624.9

1633.9

1643.0
1652.0
1661.0
1670.0
1679.1
1688 1

1697.2

1706.3

1715.3

1724.4

1733.5

1742.6

17517

1760.8

1770.0

1779.1

1788.2
1797.4

1806.6

1815.7

1824.9

1834.1

1843.3

1852.5

1861.7

1870.9
1880.1
1889.4
1898 6

1907.9

1917.1

1926.4

1935.7

1945.0

1954.3

1963.6

1972.9

1982.2
1991 5

2000.9

2010.2
2019.6

2029.0

2038.4

2047.8

2057.2

2066.6

2076.0

2085.4

2094.9

2104.3
2113.8

2123.3
2132.7

E

216.3
218.7
221.1
223.5
226.0

228.4

230.9

233.4

235.9

238.4
241.0

243.5

L=40°

5 C.
T
13
E

.023

246.1
248.7
251.3
253.9
256.5

259.1

261.8

264.5

267.2
269.9

272.6

275.3

278.1
280.8
283 6
286.4
289 2
292 0

294.9

297.7

300.6

303.5

306.4

309.3

312.2

315.2

318.1

321.1

324.1

327.1

330.2
333 2

336.3

339.3
342 4
345.5

348.6

351.8

354.9
358.1
361.3
364.5

367.7
371.0
374.2
377.5

380.8
384.1

10- C.
T
26
E

.046

15 C.

T

.40

E

.070

|20 C.
T

.53

E

093

25 C.
T
67
E

117

30 C.

T

.80

E

141

2142.2

2151.7
2161 2

2170.8

2180.3

2189.9

2199 4
2209.0
2218.6
2228.1
2237.7
2247.3

2257.0
2266 6
2276 2
2285,9
2295 6
2305 2

10 '

20

30’

40'

50'

2314.9
2324 6
2334.3
2344.1
2353.8
2363.5

2373 3
2383 1
2392.8
2402 6
2412 4
2422 3

2432 1
2441 9
2451.8
2461.7
2471,5
2481 4

2491 3
2501 2
2511.2
2521 1
2531.1
2541.0

2551.0
2561 0
2571.0
2581 0
2591.0
2601.1

2611 2
2621.2
2631 3
2641 4

2651.5

2661.6

2671.8

2681.9
2692.1
2702,3
2712.5
2722.7

E

387.4

390.7

394.1

397.4

400.8

404.2

407 6
411.1
414.5
418,0
421.4
425.0

428.5
432.0

435.6
439.2
442.8
446.4

450.0

453.6
457.3
461.0

464.6
468 4

472.1
475.8
479.6
483.4

487.2
491.0

494.8

498.7

502.5

506.4

510.3

514.3

518.2

522.2

526.1

530.1
534.

538.2

542 2

546.3

550.4

554.5

558.6
562.8

566.9
571.1
575 2-
579 5
583.8
5880

592.3
596 6
600.9

605.3
609 6
614.0

1=50°

+

5 c C.

T

.17

E

.037

10 s C.
T

.34

E

.075

15" C.

T

.51

E

.116

20 c C.
T

.68

E

.151

25 C.

T

.85

E

189

30" C
T

1.02

E

.227

10 '

20

30

40

50'

2732 9

2743.1
2753.4
2763.7
2773.9

2784.2

2794.5

2804.9

2815.2
2825 6
2835 9

2846.3

2856.7
2867.1
2877.5
2888.0
2898 4
2908.9

2919.4
2929.9
2940 4
2951.0

2961.5
2972.1

2982.7
2993.3
3003 9
3014.5
3025.2

3035.8

3046.5

3057.2
3067 9
3078.7
3089 4

3100.2

3110.9
3121.7
3132.6
3143 4
3154.2
3165.1

3176 0
3186.9

3197.8

3208.8
3219 7
3230.7

3241.7

3252.7
3263 7

3274.8
3285 8

3296.9

3308.0
3319.1
3330.3
3341 4
3352.6
3363.8

E

618.4

622.8

627.2

631.7

636.2

640.7

645.2

649.7

654.3

658.8

663.4
6680

672.7

677.3
682.0

686.7

691.4
696.1

700.9

705.7

710.5

715.3

720.1

725.0

729.9

734.8

739.7

744.6

749.6

754.6

759.6
764 6

769.7

774.7

779.8

784.9

790.1

795.2
800.4
805 6
810.9
816.1

821 4

826.7
832.0
837.3

842.7
848.1

853.5
858.9
864 3

869.8
875.3

880.8

886.4
892.0

897.5
903.2
908.8

914.5

1=60°

5° C.

T

.21

E

.056

10° C.
T

.42

E

112

15 C.

T

.63

E

168

20 C.
T

.84

E

.225

25 C.
T

1 05
E

.283

30 C.
T

1.27

E

.340

T = R tan Vz I

E = R exsec VzZ

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 1° CURVE

r

T

E

1= 70°

I

T

E

61°

3375.0

920.2

71 0

4086.9

1308.2

10'

3386.3

925.9

10'

4099.5

1315.6

20'

3397,5

931.6

20'

4112.1

1322.9

30'

3408 8

937.3

T

30'

4124 8

1330.3

40'

3420.1

943.1

25

40'

4137.4

1337.7

50'

3431.4

948 9

E

50'

4150.1

1345.1

62°

3442.7

954.8

080

72 0

4162.8

1352,6

10'

3454.1

960.6

10'

4175.6

1360.1

20'

3465.4

966.5

20'

4188.5

1367.6

30'

3476 8

972.4

30'

4201.2

1375.2

40'

3488 3

978.3

40'

4214.0

1382.8

50'

3499 7

984.3

50'

4226.8

1390.4

63°

3511.1

990.2

10 C.

73°

4239.7

1398.0

10'

3522 6

996.2

10'

4252,6

1405.7

20'

3534.1

1002.3

51

20'

4265.6

1413.5

30'

3545.6

1008.3

30'

4278.5

1421.2

40'

3557.2

1014 4

E

40'

4291.5

1429.0

50'

3568.7

1020.5

159

50'

4304.6

1436.8

64°

3580.3

1026.6

74°

4317.6

1444.6

10'

3591.9

1032.8

10'

4330.7

1452.5

20'

3603.5

1039.0

20'

4343.8

1460.4

30'

3615.1

1045.2

30'

4356.9

1468.4

40'

3626.8

1051.4

40'

4370.1

1476.4

50'

3638.5

1057.7

15 C.

50'

4383.3

1484.4

65°

3650.2

1063.9

T

75°

4396.5

1492.4

10'

3661 9

1070.2

76

10'

4409.8

1500.5

20'

3673.7

1076.6

E

20'

4423.1

1508.6

30'

3685.4

1082.9

.240

30'

4436.4

1516.7

40'

3697.2

1089.3

40’

4449.7

1524.9

50'

3709.0

1095.7

50'

4463.1

1533.1

66°

3720.9

1102.2

76°

4476.5

1541.4

10'

3732.7

1108.6

10'

4489.9

1549.7

20'

3744.6

1115.1

20'

4503.4

1558.0

30'

3756.5

1121.7

20° C.

30'

4516.9

1566.3

40'

3768.5

1128.2

40'

4530.4

1574.7

50'

3780.4

1134.8

T

1.02

50'

4544.0

1583.1

67°

3792.4

1141.4

77°

4557.6

1591.6

10'

3804.4

1148.0

10'

4571.2

1600.1

20'

3816.4

1154.7

.321

20'

4584.8

1608.6

30'

3828.4

1161.3

30'

4598.5

1617.1

40'

3840.5

1168.1

40'

4612.2

1625.7

50'

3852.6

1174.8

50'

4626.0

1634.4

68°

3864 7

1181.6

78°

4639.8

1643.0

10'

3876.8

1188.4

25 C.

10'

4653.6

1651.7

20'

3889.0

1195.2

20'

4667 4

1660.5

30'

3901.2

1202 0

T

30'

4681.3

1669.2

40'

3913.4

1208.9

1.28

40'

4695.2

1678.1

50'

3925.6

1215 8

E

50'

4709.2

1686.9

69°

3937.9

1222.7

403

79 c

4723.2

1695.8

10'

3950.2

1229.7

10'

4737.2

1704.7

20'

3962.5

1236.7

20'

4751.2

1713.7

30'

3974.8

1243.7

30'

4765 3

1722.7

40'

3987.2

1250.8

40'

4779.4

1731.7

50'

3999.5

1257.9

50'

4793.6

1740.8

70°

4011.9

1265.0

30" C.

80°

4807.7

1749.9

10'

4024.4

L 272.1

T

10'

4822.0

L 759.0

20'

4036.8

L279.3

1.54

20'

4836.2

L 768.2

30'

4049.3

L286.5

30'

4850.5

1777.4

40'

4061.8

[293.6

40'

4864.8

1786.7

50'

4074.4

1300.9

.485

50'

4879.2

1796.0

1=80°

I

T

E

1=90°

81°

4893.6

1805.3

5° C.

1C

4908.C

1814.7

20

4922.5

1824.1

5 C.

T

30

4937.C

1833.6

T

.30

40'

4951.5

1843.1

.36

E

50

4966.1

1852.6

E

.110

82°

4980.7

1862.2

149

10'

49954

1871.8

20'

5010.C

1881.5

30'

5024.8

1891.2

40'

5039.5

1900.9

50'

5054.3

1910.7

0

0

83°

5069.2

1920.5

10 C.

T

10'

5084.C

1930.4

.61

20'

5099.G

1940.3

30'

5113.9

1950 3

.72

E

40'

5128.9

1960.2

E

.220

50'

5143.9

1970.3

.299

84°

5159.0

1980.4

10'

5174.1

1990.5

20'

5189.3

2000.6

30'

5204.4

2010.8

40'

5219.7

2021.1

15° C.

50'

5234.9

2031.4

15-C.

T

85°

5250.3

2041.7

T

.91

10'

5265.6

2052.1

1.09

E

20'

5281.0

2062,5

E

.332

30'

40'

5296.4

5311.9

2073,0

2083.5

450

50'

5327.4

2094.1

86°

5343.0

2104.7

10'

5358.6

2115.3

20'

5374.2

2126.0

20° C.

30'

40'

5389.9

5405.6

2136.7

2147.5

20° C.

50'

5421.4

2158 4

T

1.22

1 45

87°

5437.2

2169 2

10'

5453.1

2180.2

.445

20'

5469.0

2191.1

.603

30'

5484.9

2202.2

5500.9

5517,0

2213.2

2224.3

50'

88°

5533.1

2235.5

25' C.

10'

5549.2

2246.7

25- C.

20'

5565.4

2258.0

T

30'

5581.6

2269.3

T

1.53

40'

5597.8

2280.6

1.83

E

50'

5614.2

2292.0

E

.558

89°

5630.5

2303.5

.756

10'

5646.9

2315.0

20'

5663.4

2326.6

30'

5679.9

2338.2

40'

5696.4

2349.8

50'

5713.0

2361.5

30° C.

90°

5729.7

2373.3

30' C.

T

10'

5746.3

2385.1

T

1.84

20'

5763.1

2397.0

2.20

30'

5779.9

2408.9

40'

5796.7

2420.9

E

.671

50'

5813.6

2432.9

.910

T = R tan V 2 T

E = R exsec V 2 1

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 1° CURVE

I

T

E

1 = 100°

1

T

L=no°

I

T

E

1 =120°

91 0

5830.5

2444,9

101 °

6950.6

3278.1

111 0

8336.7

4386.1

+

10'

5847.5

2457,1

10'

6971.3

3294.1

10'

8362.7

4407.6

20'

5864.6

2469.3

5° C

20'

6992.0

3310.1

5° C

20'

8388.9

4429.2

30'

5881.7

2481.5

T

30'

7012.7

3326.1

T

30'

8415.1

4450.9

40'

5898.8

2493.8

40'

7033.6

3342 3

51

40'

8441.5

4472.7

62

50'

5916.0

2506.1

E

50'

7054.5

3358.5

E

50'

8468 0

4494.6

E

92°

5933.2

2518.5

.200

102 °

7075.5

3374.9

268

112 °

8494.6

4516.6

.360

10'

5950.5

2531.0

10'

7096.6

3391.2

10'

8521.3

4538.8

20'

5967.9

2543.5

20'

7117.8

3407.7

20'

8548.1

4561.1

30'

5985.3

2556.0

30'

71390

3424.3

30'

8575.0

4583.4

40'

6002.7

2568.6

40'

7160.3

3440.9

40'

8602.1

4606.0

50'

6020.2

2581.3

50'

7181.7

3457.6

50'

8629.3

4628.6

93°

6037.8

2594.0

10 U C.

103°

7203.2

3474,4

10° C

113°

8656 6

4651.3

10^ C.

10'

6055.4

2606.8

10’

7224.7

3491.3

10'

8684.0

4674.2

T

20'

6073.1

2619.7

20'

7246.3

3508 2

20'

8711.5

4697.2

30'

6090.8

2632.6

86

30'

7268.0

3525.2

. 103

30'

8739.2

4720.3

40'

6108.6

2645.5

E

40

7289.8

3542.4

E

40'

8767.0

4743.6

E

50'

6126.4

2658.5

401

50'

7311.7

3559 6

.536

50'

8794.9

4766.9

.721

940

6144.3

2671.6

104°

7333.6

3576.8

114°

8822.9

4790.4

10'

6162.2

2684.7

10'

7355.6

3594.2

10'

8851.0

4814.1

20'

6180.2

2697.9

20'

7377.8

36117

20'

8879.3

4837.8

30'

6198.3

2711.2

30'

7399.9

3629.2

30'

8907.7

4861.7

40'

6216.4

2724.5

40'

7422.2

3646 8

40'

8936.3

4885.7

50'

6234.6

2737.9

15 C.

50'

7444.6

3664.5

15 C.

50'

8965.0

4909.9

15-C

95°

6252.8

2751.3

T

105°

7467.0

3682.3

T

115°

8993.8

4934.1

T

10'

6271.1

2764.8

1.30

10'

7489.6

3700.2

1.56

10'

9022.7

4958.6

1.93

20'

6289.4

2778.3

20'

7512.2

3718.2

20'

9051.7

4983.1

E

30'

6307.9

2792.0

30'

7534.9

3736.2

30'

9080.9

5007,8

40'

6326.3

2805.6

.604

40

7557.7

3754.4

.806

40'

9110.3

5032.6

50'

6344.8

2819.4

50'

7580.5

3772.6

50'

9139.8

5057.6

6363.4

2833.2

106°

7603.5

3791.0

116°

9169.4

5082.7

10'

6382.1

2847.0

10'

7626.6

3809.4

10'

9199.1

5107.9

20'

6400.8

2861.0

20'

7649.7

3827.9

20'

9229.0

5133.3

30'

6419.5

2875.0

30'

7672.9

3846.5

30'

9259.0

5158 8

40'

6438.4

2889.0

40'

7696.3

38652

40'

9289.2

5184.5

50'

6457.3

2903.1

T

50'

7719.7

3884.0

T

50'

9319.5

5210.3

T

1.74

2.08

2.52

970

6476 2

2917.3

_

107°

7743.2

3902.9

117°

9349.9

5236.2

10'

6495.2

2931.6

10'

7766.8

,3921.9

10'

9380.5

5262.3

20'

6514.3

2945.9

.809

20’

7790.5

3940.9

1.08

20'

9411.3

5288.6

1.46

30'

6533.4

2960.3

30'

7814.3

3960.1

30'

9442.2

5315.0

2974 7h

40'

7838,1

3979 4.

9473 2

5341.5

50'

6571.9

2989.2

50'

7862.1

3998.7

50'

9504.4

5368.2

98°

6591.2

3003.8

108°

7886.2

4018.2

118°

9535.7

5395.1

10'

6610.6

3018.4

nr r-

io-

7910.4

4037 8

10'

9567.2

5422.1

i~

20'

6630 1

3033.1

20'

7934.6

4057.4

20'

9598.9

5449.2

30'

6649.6

3047.9

T

30'

7959.C

4077 2

T

30'

9630.7

5476.5

T

40'

6669.2

3062.8

2 18

40'

7983.5

4097,1

2.61

40'

9662.6

5504.0

3 16

50'

6688.8

3077.7

E

50'

8008.0

4117.0

E

50'

9694 7

5531.7

E

990

6708.6

3092.7

1 02

109°

8032.7

4137,1

1.36

119°

9727.0

5559.4

1.83

10'

6728.4

3107.7

10’

8057.4

4157,3

10'

9759.4

5587.4

20'

6748.2

3122.9

20'

8082.3

4177.5

20'

9792.0

5615.5

30'

6768.1

3138.1

30'

8107.3

4197.9

30'

9824.8

5643.8

40'

6788.1

3153 3

40'

8132.3

4218.4

40'

9857.7

5672.3

50'

6808.2

3168.7

50'

8157.5

4239.0

50'

9890.8

57009

100 °

6828.3

3184.1

30° C

110 °

8182.8

4259.7

30 C.

120 °

9924.0

5729.7

30 C.

10'

6848.5

3199.6

T

10'

8208.2

4280.5

T

10'

9957.5

5758.6

T

20'

6868.8

3215.1

2.62

20'

8233.7

4301.4

20'

9991.0

5787.7

30

6889.2

3230.8

30'

8259.3

4322.4

30'

10025.0

5817.0

40

6909.6

3246.5

£

40'

8285.0

4343.6

E

40'

10059.0

5846.5

E

50

6930.1

3262.3

1.22

50'

8310.8

4364.8

1.63

50'

10093.0

5876.1

2.20

T = R tan V2I E = R exsec Vz I

nHw

USEFUL RELATIONS

Lineal feet

X.00019

=

miles

Lineal yards

X .0006

=

miles

Square inches

X -007

=

square feet

Square feet

X.lll

=

square yards

Square yards

X.0002067

=

acres

Acres

X4840

=

square yards

Cubic inches

X.00058

=

cubic feet

Cubic feet

X.03704

=

cubic yards

Links

X .22

=

yards

Links

X .66

=

feet

Feet

X1-5

=

links

360° = 21600’ = 1296000"

Radius = arc of 57.2957790°

Arc of 1° (radius = 1) = .017453292

Arc of 1' (radius = 1) = .000290888

Arc of 1" (radius = 1) = .000004848

Curvature of Earth’s surface = about 0.7 feet in 1 mile
Curvature in feet = 0.667 (Dist. in miles) 1
Difference between arc and chord length, 0.05 feet in 11%
miles

Probable error of a single observation = 0.6754
Error in chaining of 0.01 feet in 100 feet:

Due to—-

1. Length of tape error of 0.01 feet

2. Alignment. One end 1.4 feet out of line

3. Sag of tape at center of 0.61 feet.

4. Temperature difference of 15°

5. Difference of pull of 15 lbs.

SQUARE MEASURE
144 sq. inches = 1 sq. ft.

9 sq. ft. 1 sq. yard
3014 sq. yds. = 1 sq. rd.

40 sq. rds. = 1 rood.

4 roods = 1 acre
640 acres = 1 sq. mile.

SURVEYORS’ MEASURE
7.92 inches = 1 link.

25 links = 1 red.

4 rds. = 1 chain.

10 sq. chains or 160 sq. rods = 1 acre.

640 acres = 1 sq. mile.

36 sq. miles (6 miles sq.) = 1 township.

TABLE VI. INCHES TO DECIMALS OF A FOOT

In.

0

1

2

3

4

5

6

7

8

9

10

n

In.

o

.0833

.1667

.2500

.3333

.4167

.5000

.5833

.6667

.7500

.8333

.9167

0

1-32

.0026

.0859

.1693

.2526

. 3359 , .4193

.5026

.5859

.6693

.7526

.8359

9193

1-32

1-16

.0052

.0885

.1719

.2552

.3385

.4219

.5052

.5885

.6719

.7552

.8385

.9219

1-16

3-32

.0078

.0911

.2578

.3411

.4245

.5078

.5911

.6745

.7578

.8411

.9245

3-32

1 8

.0104

.0938

.1771

.2604

.3438

.4271

.5104

. 5938

.6771

.7604

.8438

.9271

1-8

5-32

.0130

.0964

.1797

.2630

. MW 1 .4297

. 51:10

.5964

.6797

.7630

.8464

.9297

5-32

3-16

.0156

.0990

.1823

.2656

.3490

,4323

.5156

. 59901.6823

.7656

.8490

.9323

3-16

7-33

.0183

.1016

.1849

.2682

.3516

.4349

.5182

.6016 .6849

.7682

.8516

.9349

7-32

1_4

.0208

.1042

.1875

.2708

,3542

.4375

.5208

.6042

.3875

.7708

.8542

.9375

1^1

9-32

.0234

.1068

.1901

2734

.3568

.4401

.5234

.6068

.6901

.7734

.8568

.9401

9-32

5-16

.0260

.1094

.1927

.2760

.3594

.4427

.5260

.6094

.6927

.7760

.8594

.9427

6-16

11-32

.0286

.1120

.1953

.2786

.3620

.4453 . 5236

.6120

.6953

.7786

.8620

.9453

11-32

3-8

.0313

.1146

.1979

.2813

.3646

.4479

.5313

.6146 .6979

.7813

.8646

.9479

3-8

13-32

.0339

1178

.2005

.2839

.3672

,4505

.5339

.6172

.7005

.7839

.8672

.9505

13-32

7 16

,0365

.1108

.2031

.2865

.3698

.4531

.5365

.6198

.7031

.7865

.8698

.9531

7-16

15-32

.0391

.1224

.2057

.2891

.3724

.4557

.5391

.6224

.7057

.7891

.8724

.9557

15-32

1-2

.0417

.1250

.ms

.2917

.3750

.4583

.5417

.6250

.7083

.7917

.8750

.9583

1-2

17-32

.0443

.1276 .2109

.2943

.3776

.4609

5443

.6276

.7109

.7943

.8776

.9609

17-32

9-16

.0469

.1302 . 2135

.2969

.3802

Lt 4635 -

75469

.6302

.7135

.7969

.8802

.9635

9-16

19-32

.0495

.1328

l _2461

.2995

.3828

.4001

5495

.6328

.7161

.7995

.8828

.9661

19-32

5-8

.0521

.1354

.2188

.3021

.3854

.4688

.5521

.6354

. 711 *

.8021

.8854

.9688

5-8

21-32

. 054 ? .1380 ,2214

.3047

.3880

.4714

.5547

.6380

.7214

.8047

.8880

.9714

21-32

11-16

.0573

.1406 . 2*240

.3073

.3906 4740

.5573

.6406

.7240

.8073

.8906

.9740

11-16

23-32

.0599

.1432

.2266

.3099

.3932

. 4766,.5599

.6432

.7266

.8099

.8932

.9766

23-32

3-4

.0625

1458

.2292

.3125

.3958

.4792

. 56251.6458

.7292

.8125

.8958

.9792

3-4

25-32

.0651

.1484

.2318

.3151

3984

.4818

.5651

.6484

. 7318 i .8151

.8984

.9818

25-32

13-16

.0677

.1510

2344

3177

.4010

.4844

.5677

.6510

.7344

.8177

.9010

.9844

13-16

27-32

.0703

1536

.2370

.3203

.4036

.4870

.5703

.6536

.7370

.8203

.9036

.9870

27-32

7-8

.0729

.1563

.2396

.3229

.4063

.4896

.5729

.6563

.7396

.8229

.9063

.9896

7-8

29-32

.0755

.1589

.2422

.3255

.4089

.4922

.5755

.6589

.7422

.8255

.9089

.9922

29-32

15-16

.0781

.1615

.2448

.3281

.4115

.4948

.5781

.6615

.7448 .8281

.9115

.9948

15-16

31-32

.0807

.1641

.2474

.3307

.4141

.4974

.5807

.6641

.7474

.8307

.9141

.9974

31-32

0

i

2

3

4

5

6

7

8

9

10

11

TABLE VII. MINUTES IN DECIMALS OF A DEGREE

0 ' 30 "

.00833

10 ' 30 "

.17500

20 ' 30 "

.34167

30 ' 30 "

.50833

40 ' 30 "

67500

50 ' 30 "

.84167

1 00

.01667

11 00

.18333

21 00

.35000

31 00

.51667

41 00

68333

51 00

.85000

30

.02500

30

.19167

30

.35833

30

.52500

30

.69167

30

.85833

2 00

.03333

12 00

.20000

22 00

.36667

32 00

.53333

42 00

.70000

52 00

.86667

30

.04167

30

.20833

30

.37500

30

.54167

30

.70833

30

.87500

3 00

.05000

13 00

.21667

23 00

.38333

33 00

.55000

43 00

.71667

53 00

.88333

30

.05833

30

.22500

30

.39167

30

.55833

30

.72500

30

.89167

4 00

.06667

14 00

23333

24 00

.40000

34 00

.56667

44 00

.73333

54 00

.90000

30

.07500

30

.24167

30

.40833

30

.57500

30

.74167

30

.90833

5 00

.08333

15 00

.25000

25 0(1

.41667

35 00

.58333

45 00

.75000

55 00

91667

30

.09167

30

25833

30

.42500

30

.59167

30

.75833

30

.92500

6 00

.10000

16 00

.26667

26 00

.43333

36 00

.60000

46 00

.76667

56 00

.93333

30

.10833

30

.27500

30

.44167

30

.60833

30

.77500

30

94167

7 00

.11667

17 00

28333

27 00

.45000

37 00

.61667

47 00

.78333

57 00

.95000

30

.12500

30

.29167

30

.45833

30

.62500

30

.79167

30

.95833

8 00

.13333

18 00

.30000

28 00

.46667

38 00

.63333

48 00

.80000

58 00

.96667

30

.14167

30

.30833

30

.47500

30

.64167

30

.80833

30

.97500

9 00

.15000

19 00

.31667

29 00

.48333

39 00

.65000

49 00

.81667

59 00

.98333

30

.15833

30

.32500

30

.49167

30

.65833

30

.82500

30

.99167

10 00

.16667

20 00

.33333

30 00

.500000

40 00

.66667

50 00

.83333

60 00

1.00000

TABI.E VIII. MIDDLE ORDINATES OF RAILS

Length of Rail (feet)

c

o t

R

Feet

30

Inch

28

Inch

26

Inch

24

Inch

22

Inch

20

Inch

c

o

R

Feet

30

Inch

28

Inch

26

Inch

24

Inch

22

Inch

20

Inch

0-20

17189

.08

.07

.06

.05

.04

.03

8

716.8

1.88

1.64

1.42

1.20

1.01

.84

0-40

8594

.16

.14

.12

.10

.08

.07

9

637.3

2.12

1.84

1.60

1.35

1.14

.94

1-0

5730

.24

.20

.18

.15

.13

.10

10

573.7

2.36

2.05

1.78

1.50

1.27

1.04

1-20

4297

.31

.27

.23

.20

.17

.13

11

521.7

2.59

2.26

1.95

1.65

1.39

1.15

1-40

3438

.39

.34

.29

.25

. 21

.17

12

4783

3.83

2.47

2.15

1.81

1 54

1.26

2-0

2865

.47

.41

.35

.30

.25

.20

13

441.7

3.05

2.66

2.30

1.96

1 66

1 36

2-20

'2456

.65

.48

.41

.35

.29

.23

14

410.3

3.30

2.87

2.48

2.10

1.78

1.46

2-40

2149

.63

.55

.47

.40

.33

.27

15

383.1

3 54

3.08

2.68

2 26

1.91

1.67

3-0

1910

.71

.62

.53

.45

.38

.31

16

359.3

3.76

3.28

2.83

2.40

2.04

1.67

3-20

1719

.78

.68

.59

.50

.42

.35

17

338.3

4.00

3.48

3.02

2.57

2 16

1.78

3-40

1563

.86

.75

.65

.55

.46

.38

18

319.6

4.21

3.67

3.18

2.70

228

1.87

4-0

1433

.94

.82

.71

.60

.50

.42

19

302.9

4.45

3.89

3.36

286

2.41

1.98

4-20

1323

1.02

.89

.77

.65

.55

.45

20

287.9

4.70

4.09

3 65

3.00

2.64

2.09

4-40

1228

1.10

96

.83

.70

.59

.48

22

262.0

5.16

4 44

3.84

3.30

2.80

229

5

1146

1.18

1 03

.89

.75

.63

.52

24

240.5

5 64

4.92

4 20

3 69

3.04

2.60

6

955.3

1 41

1.23

1.06

.90

.76

.62

26

222.3

6.07

5.29

4 58

3.88

3.29

2.70

7

819.0

1.65

1 44

1.24

1.05

.89

.73

TABLE IX. SHORT RADIUS CURVES

Radian

Feet

Chord

Feet

Central

Angle

Deflection

Angle

Deflection
for 1 Foot

35

10

16-26

8-13

49.3

45

10

12-46

6-23

38.3

50

15

17-16

8-38

34.5

60

15

14-22

7-11

28.8

75

15

11-30

5-45

23.0

100

20

11-30

5-45

17.3

120

20

9-34

4-47

14.3

150

20

7-39

3-49

11.5

190

25

7-32

3-46

9.15

200

25

7-10

3-35

8.6

225

25

6-25

3-12

7.7

240

25

5-58

2-59

7.2

250

25

5-44

2-52

6.9

275

25

5-12

2-36

6.2

288

50

9-58

4-59

6.0

300

50

9-32

4-46

5.7

350

50

8-12

4-06

4.9

376

50

7-40

3-50

4.6

400

50

7-10

3-35

4.3

410

50

7-00

3-30

4.2

To find length ot curve divide angle from P. C. to P. T. by central angle of chord,
and multiply by length of chord.

TABLE X. RODS IN FEET, 10THS AND 100TIIS OF FEET

1

2

3

4

5

6

7

8
9

10

11

12

13

14

15

16

17

18

19

20

Feet

16.

33.

49

66

82.

99

115

132

148

165

181.

198.

214.

231

247

264

280

297

313

330

50

00

50

00

50

00

50

00

50

.00

50

00

50

.00

.50

.00

50

.00

50

.00

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

Feet

346.50
363.00

379.50
396.00

412.50
429.00

445.50
462.00

478.50
495.00

511.50
528.00

544.50
561.00

577.50
594.00

610.50
627.00

643.50
660.00

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Feet

676.50
693.00

700.50
726.00

742.50
759.00

775.50
792.00

808.50
825.00

841.50
858.00

874.50
891.00

907.50
924.00

940.50
957.00

973.50
990.00

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

Feet

1006

1023

1039

1056

1072

1089

1105

1122 .

1138

1155

1171

1188.

1204

1221

1237

1254

1270

1287

1303

1320

50

00

50

00

50

.00

.50

00

50

00

50

00

,50

.00

.50

00

.50

.00

50

.00

«

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99
100

Feet

1336.50
1353.00

1369.50
1386.00

1402.50
1419.00

1435.50
1452.00

1468.50
1485.00

1501.50
1518.00

1534.50
1551.00

1567.50
1584.00

1600.50
1617.00

1633.50
1650.00

TABLE XI. LINKS IN FEET, 10THS AND lOOTHS OF FEET

C/7

03

07

ID

07

JS

c

Feet

C

Feet

C

Feet

C

Feet

c

Feet

c

Feet

J

i-4

i

0.66

18

11.88

35

23.10

52

34.32

69

45.54

86

56.76

2

1.32

19

12.54

36

23.76

53

34.98

70

46.20

87

57.42

3

1.98

20

13.20

37

24.42

54

35.64

71

46.86

88

58.08

4

2.64

21

13.86

38

25.08

55

36.30

72

47.52

89

58.74

5

3.30

22

14.52

39

25.74

56

36.96

73

48.18

90

59.40

6

3.96

23

15.18

40

26.40

57

37.62

74

48.84

91

60.06

7

4.62

24

15.84

41

27.06

58

38.28

75

49.50

92

60.72

8

5.28

25

16.50

42

27.72

59

38.94

76

50.16

93

61.38

9

5.94

26

17.16

43

28.38

60

39.60

77

50.82

94

62.04

10

6.60

27

17.82

44

29.04

61

40.26

78

51.48

95

62.70

11

7.26

28

18.48

45

29.70

62

40.92

79

52.14

96

63.36

12

7.92

29

19.14

46

30.36

63

41.58

80

52.80

97

64.02

13

8.58

30

19.80

47

31.02

64

42.24

81

53.46

98

64.68

14

9.24

31

20.46

48

31.68

65

42.90

82

54.12

99

65.34

15

9.90

32

21.12

49

32.34

66

43.56

83

54.78

100

66.00

16

10.56

33

21.78

50

33.00

67

44.22

84

55.44

101

66.66

17

11.22

34

22.44

51

33.66

68

44.88

85

56.10

102

67.32

HSOFFCET

ll 90 lm
91 1501.51
921 1518.01
19.3 1531 50

98 1617.00

99 1633.51
1001 1650.00

as OF FEET

— r

Feel

L

I

£

45.54 1

8t' :

46.20 1

81 i

46.86

8! :

47.52

89 '

48.18

90 ;

48.84

91

49.50

92 <

50.16

93'

50.82

94

51.48

9S

'■ 52.14

99

52.80

91

i 53.46

98

54.12

9)

101

55.44

101

jl5610_

®

Sokkia Surveying Systems,
Instruments, Equipment and Supplies

•Total Stations

•Electronic Field Book

•Mapping Software

•EDM Systems

•Theodolites

•Levels

•Transits

•Tripods

•Rods

•Hand Levels
•Tapes
•Planimeters
•Accessories

The paper in this book is a fine quality thick 50% rag ledger
specially treated during the making to give "High Wet
Strength." It retains is strength and writing surfaces when dried
after having been subjected to extreme weather conditions.

FIELD BOOKS

SOKKIA"

Rain-resistant fine quality ledger paper, bound in high-
visibility durable yellow imitation leather. Printed in
waterproof ink.

Stock No. 8152-00 Transit Field Book. Size 47= x 7’/<
inches.

Stock No. 8152-05 Economy Field Book. Spiral bound,
Paperback. Size 4 'k x 7V< inches.

Stock No. 8152-10 Economy Field Book. Same as above
except saddle stitched (stapled).

Left page blue horizontal lines; red vertical lines.

Right page 4 horizontal and 8 vertical blue lines; red
vertical center line.

Stock No. 8152-20 Mining Transit Book. Size 4’/s x 7'/<
inches.

Left page blue horizontal lines; red vertical center line.
Right page 8x8 blue lines; red vertical lines.

Stock No. 8152-30 Engineers Field Book. Size 47= x 7'A
inches.

Left page blue horizontal'lines; red vertical lines.

Right page 10 x 10 blue lines; red vertical center line. Inch
lines heavy.

Stock No. 8152-50 Level Book Size 4 x 6'h inches.

Stock No. 8152-55 Level Book Size 4'/2 x 7'A inches.

Both pages blue horizontal lines; red vertical lines. 6
vertical columns.

Stock No. 8152-60 Field Book. Size 4'h x 7'/* inches.

Left page blue horizontal lines; red vertical lines.

Right page 4x4 blue lines; red vertical center line.

Stock No. 8152-75 Cross Section Book. Size 6'fc x 8'/z
inches.

Both pages 10 x 10 blue lines; inch lines slightly heavier.

Stock No. 8152-80 Duplicating Transit Book. Size 4'h x
7’A inches.

Left page blue horizontal lines; red vertical lines.

Right page 4 horizontal and 8 vertical blue lines; red
vertical center line. Pages numbered and
perforated. Carbon paper.

CURVE FORMULAE

D = Degree of Curve
1° = 1-Degree of Curve
2° = 2-Degree of Curve

P.C. = Point of Curve
P.T. = Point of Tangent
P.I. = Point of Intersection
I = Intersection of Angle

L

between Two Tangents
= Length of Curve,
from P.C. to P.T. f
T =Tangent Distance
E = External Distance
R = Radius
L.C. = Length of Chord
M = Length of Middle Ordin
c = Length of Sub-Chord
d = Angle of Sub-Chord

L.C.

R =

L.C.

2

2 sin £ I

T = R tan £ I =
I

L.C.

2 cos £ I

= R sin D 1° = R = 5730, D 2° =

5730
2 ’

D =

5730

R

M = R (1 — cos
E + R I

R

I), = R — R cos i

R - M I

R

c = 2 R sin £ d, d =

L.C. = 2 R sin £ I, E = R (sec £ I - 1), = R sec _ — R

Minutes in Decimals of a Degree

1'

-0167

11'

■1833

21'

•3500

31'

•5167

41'

•6833

51'

■8500

2

■0333

12

■2000

22

■3667

32

•5333

42

•7000

52

■8667

3

•0500

13

•2167

23

•3833

33

•5500

43

•7167

53

•8833

4

•0667

14

•2333

24

■4000

34

' -5667

44

•7333

54

•9000

5

■0833

15

■2500

25

■4167

35

■5833

45

•7500

55

•9167

6

• 1000

16

•2667

26

•4333

36

■6000

46

•7667

56

•9333

7

1167

17

-2833

27

•4500

37

■6167

47

■7833

57

•9500

8

•1333

18

■3000

28

•4667

38

•6333

48

■8000

58

•9667

9

•1500

19

■3167

29

■4833

39

•6500

49

•8167

59

•9833

10

•1667

20

•3333

30

•5000

40

•6667

50

•8333

60

1-0000

Inches in Decimals of a Foot

A

•0052

A

•0078

4

•0104

A

•0156

i

•0208

A

•0260

i

•0313

■ i

•0417

t

•0521

i

•0625

i

•0729

1

•0833

2

■1667

3

•2500

4

■3333

5

•4167

6

•5000

7

•5833

8

•6667

9

■7500

10

•8333

11

•9167

H

SOKKIA"

^ - •

4

MADE IN U.S.A.