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Table 900. The Earth's Rotation: Its Variation

Table 900. The Earth's Rotation: Its Variation

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Smithsonian

Physical Tables

Ninth Revised Edition



Prepared by

WILLIAM ELMER FORSYTHE



Norwich, New York

2003



PREFACE T O THE N I N T H REVISED EDITION

This edition of the Smithsonian Physical Tables consists of 901 tables giving data of general interest to scientists and engineers, and of particular interest to those concerned with physics in its broader sense. The increase in size

over the Eighth Edition is due largely to new data on the subject of atomic

physics. The tables have been prepared and arranged so as to be convenient

and easy to use. The index has been extended. Each set of data given herein

has been selected from the best sources available. Whenever possible an expert

in each field has been consulted. This has entailed a great deal of correspondence with many scientists, and it is a pleasure to add that, almost without

exception, all cooperated generously.

When work first started on this edition, Dr. E. U. Condon, then director of

the National Bureau of Standards, kindly consented to furnish any assistance

that the scientists of that institution were able to give. The extent of this help

can be noted from an inspection of the book. Dr. Wallace R. Brode, associate

director, National Bureau of Standards, gave valuable advice and constructive

criticism as to the arrangement of the tables.

D. H. Menzel and Edith Jenssen Tebo, Harvard University, Department of

Astronomy, collected and arranged practically all the tables on astronomy.

A number of experts prepared and arranged groups of related data, and

others either prepared one or two tables or furnished all or part of the data

for certain tables. Care has been taken in each case to give the names of those

responsible for both the data and the selection of it. A portion of the data was

taken from other published sources, always with the.consent and approval of

the author and publisher of the tables consulted. Due credit has been given in

all instances. Very old references have been omitted. Anyone in need of these

should refer to the Eighth Edition.

It was our intention to mention in this preface the names of all who took part

in the work, but the list proved too long for the space available. We wish,

however, to express our appreciation and thanks to all the men and women

from various laboratories and institutions who have been so helpful in contributing to this Ninth Edition.

Finally, we shall be grateful for criticism, the notification of errors, and

new data for use in reprints or a new edition.

W . E. FORSYTHE

Astrophysical Observatory

Smithsonian Institution

January 1951

EDITOR’S N O T E

The ninth edition of the Physical Tables was first published in June 19.54.

I n the first reprint (1956), the second reprint (1959), and the third (1964)

a few misprints and errata were corrected.



iii



CONVERSION TABLE



TABLE 1.-TEMPERATURE



The numbers in boldface type refer to the temperature either in degrees Centigrade or Fahrenheit which it is desired to convert into the other sale.



If converting from degrees Fahrenheit to Centigrade, the equivalent will be be found in the column on the left, while if converting from degrees Centigrade to Fahrenheit the answer will be found in the columr! on the right.



- 559.4 to 28

/



-273

-268

-262

-257

-251

-246

-240

-234

-229

-223

-218

-212

-207

-201

-196

-190

-184

-179

-173

-169

-168

-162

-157

-151

-146

-140

-134

-129

-123

-118

-112

-107

-101

- 95.6

- 90.0



29 to 140



-459.4

-450

-440

-430

-420

-410

-400

-390

-380

-370

-360

-350

-340

-330



-320

-310

-300

-290

-280

-273

-270

-260

-250

-240

-230

-220

-210

-200

-190

-180

-170

-160

-150

-140

-130



150 to a90



900



t o 1650



1660 to 2410



A

.



r



C



...

...



...



...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

.,.



-459.4

-454

-436

-418

-400

-382

-364

-346

-328

-310

-292



-274



-256



-238

-220



-202



-1.67

-1.11

-0.56

0

0.56

1.11

1.67

2.22

2.78

3.33

3.89

4.44

5.00

5.56

6.11

6.67

7.22

7.78

8.33

8.89

9.44

10.0

10.6

11.1

11.7

12.2

12.8

13.3

13.9

14.4

15.0

15.6

16.1

16.7

17.2



29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63



2420 to 3000



L



F



I



L



84.2

86.0

87.8

89.6

91.4

93.2

95.0

96.8

98.6

100.4

102.2

104.0

105.8

107.6

109.4

111.2

113.0

114.8

116.6

118.4

120.2

122.0

123.8

125.6

127.4

129.2

131.0

132.8

134.6

136.4

138.2

140.0

141.8

143.6

145.4



F



'C



66

71

77

82

88

93

99

100

104

110

116

121

127

I32

138

143

149

154

160

16G

171

I77

182

I88

193

199

!04

210

216

221

!27

232

?38

!43

!49



150

160

170

180

190

200

210

212

220

230

240

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

460

470

480



302

320

338

356

374

392

410

414

428

446

464

482

500

518

536

554

572

5%

608

626

644

662

680

698

716

734

752

770

788

806

824

842

860

878

896



c

482

488

493

499

504

510

516

521

527

532

538

543

549

554

560

566

571

577

582

588

593

599

604

610

616

621

627

632

638

643

649

654

660

666

671



F900

910

920

930

940

950

960

970

980

990

1000

1010

1020

1030

1040

1050

1060

1070

1080

1090

1100

1110

1120

1130

1140

1150

1160

1170

1180

1190

1200

1210

1220

1230

1240



1652

1670

1688

17Ot

1724

1742

176C

1778

1796

1814

1832

185C

1868

1886

1904

1922

1940

1958

1976

1994

2012

2030

2048

2066

2084

21 02

2120

2138

2156

2174

2192

2210

2228

2246

2264



904

910

916

921

927

932

938

943

949

954

960

966

971

977

982

988

993

999

1004

1010

1016

1021

1027

1032

1038

1043

1049

1054

1060



1066

1071

1077

I082

1088

1093



1660

1670

1680

1690

1700

1710

1720

1730

1740

1750

1760

1770

1780

1790

1800

1810

1820

1830

1840

1850

1860

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000



302(

3031

30%

307d

309;

311(

3121

314

316'

318;

320(

321t

3236

3254

327;

32%

3301

3326

3344

3362

338C

3398

3416

3434

3452

3476

3488

3506

3524

3542

3560

3578

3596

3614

3632



'



'c

1327

1332

1338

1343

1349

1354

1360

1366

1371

1377

1382

1388

1393

1399

1404

1410

1416

1421

1427

1432

1438

1443

1449

1454

1460

1466

1471

1477

1482

1488

1493

1499

I504

IS10

1516



2420

2430

2440

2450

2460

2470

2480

2490

2500

2510

2520

2530

2540

2550

2560

2570

2580

2590

2600

2610

2620

2630

2640

2650

2660

2670

2680

2690

2700

2710

2720

2730

2740

2750

2760



.



F

4388

4406

4424

4442

4464

4478

44%

4514

4532

4550

4568

4586

4604

4622

4640

4658

4676

4694

4712

4730

4748

4766

4784

4802

4820

4838

4856

4874

4892

4910

4928

4946

4964

4982

SO00



--- 84.4

78.9

73.3

-- 62.2

67.8

56.7

--- 51.1

45.6

-- 40.0

34.4

-- 28.9

23.3

17.8

- 17.2

- 16.7

16.1

- 15.6

- 14.4

15.0

13.9

13.3

12.8

12.2

11.7

- 11.1

- 10.6

10.0

9.44

8.89

8.33

7.78

722

- 6.67

6.11

- 5.56

- 5.00

- 4.44

-- 3.89

3.33

-- 2.78

2.22



-120

-110

-100

90

- 80

70

60

50

40

30

20

10

0

1

2

3

4

5

6

7

8



-



-



-



9

I0



17.8

18.3

18.9

19.4

20.0

20.6

-94

21.1

76

21.3

58

22.2

-40

22.8

22

23.3

- 4

23.9

14

24.4

32

33.8 25.0

35.6 25.6

37.4 26.1

39.2 26.7

41.0 27.2

42.8 27.8

44.6 28.3

46.4 28.9

48.2 29.4

50.0 30.0

51.8 30.6

53.6 31.1

55.4 31.7

572 32.2

59.0 32.8

60.8 33.3

62.6 33.9

64.4 34.4

66.2 35.0

68.0 35.6

69.8 36.1

716 36.7

739 37.2

75.2 37.8

77.0 43

78.8 49

80.6 54

82.4 60

-184

-166

-148

-130

-112



-



64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

110

120

130

140



147.2

149.0

150.8

152.6

154.4

156.2

158.0

159.8

161.6

163.4

165.2

167.0

168.8

170.6

172.4

174.2

176.0

177.8

179.6

181.4

183.2

185.0

186.8

188.6

190.4

192.2

194.0

195.8

197.6

199.4

2012



254

260

266

271

277

282

288

293

299

304

310

316

321

327

332

338

343

349

354

360



366



37 1

377

382

388

393

399



490

500

510

520

530

540

550

560

570

580

590

600

610

620

630

640

650

660

670

680

690



700



471

477



7 10

720

730

740

750

760

770

780

790

800

810

820

830

840

850

860

870

880

890



Ptcr-red by Alfred Sauveur; uud by the kind permiuion of bfr.



Sanveur.



11

12

13

14

15

16

17

18

19

20

21



23

23

24

25

26

27

28



203.0

204.8

206.6

208.4

210.2

212.0

230

248

266

284



404



410

416

421

427

432

438

443

449

454



460

466



914 677

932 682

950 688

968 693

986 699

1004 704

1022 710

1040 716

1058 721

1076 727

1094 732

1112 738

1130 743

1148 749

1166 754

1184 760

1202 766

1220 771

1238 777

1256 782

1274 788

1292 793

1310 799

1328 804

1346 810

1364 816

1382 821

1400 827

1418 832

1436 838

1454 843

1472 849

1490 854

1508 860

1526 866

1544 871

1562 877

1580 882

1598 888

1616 893

1634 899



1250

1260

1270

1280

1290

1300

1310

1320

1330

1340

1350

1360

1370

1380

1390

1400

1410

1420

1430

1440

1450

1460

1470

1480

1490

1500

1510

1520

1530

1540

1550

1560

1570

1580

1590

1600

1610

1620

1630

1640

1650



2282

2300

2218

2336

2354

2372

2390

2408

2426

2444

2462

2480

2498

2516

2534

2552

2570

2588

2606

2624

2642

2660

2678

2696

2714

2732

2750

2768

2786

2804

2822

2840

2858

2876

2894

2912

2930

2948

2966

2984

3002



1099

1104

1110

1116

1121

1127

1132

1138

1143

1149

1154

1160

1166

1171

1177

1182

1188

1193

1199

1204

1210

1216

1221

1227

1232

1238

1243

1249

1254

1260

1266

1271

1277

1282

1288

1293

1299

1304

1310

1316

1321



2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

2110

2120

2130

2 140

2150

2160

2170

2180

2190

2200

2210

2220

2230

2240

2250

2260

2270

2280

2290

2300

2310

2320

2330

2340

2350

2360

2370

2380

2390

2400

2410



3650

3668

3686

3704

3722

3740

3758

3776

3794

3812

3830

3848

3866

3884

3902

3920

3938

3956

3974

3992

4010

4028

4046

4064

4082

4100

4118

4136

4154

4172

4190

4208

4226

4244

4262

4280

4298

4316

4334

4352

4370



1521

1527

1532

1538

1543

1549

1554

1560

1566

1571

1577

1582

1588

1593

1599

1604

1610

1616

1621

1627

1632

1638

1643

1649



2770

2780

2790

2800

2810

2820

2830

2840

2850

2860

2870

2880

2890

2900

2910

2920

2930

2940

2950

2960

2970

2980

2990

3000



5018

5036

5054

5072

5090

5108

5126

5144

5162

5180

5198

5216

5234

5252

5270

5288

5306

5324

5342

5360

5378

5396

5414

5432



Interpolation

factor#



c



0.56

1.11

1.67

2.22

2.78

3.33

3.89

4.44

.. . .



5.00

5.56



1

2

3

4



5

6

7

8

9

10



F

1.8

3.6

5.4

7.2

9.0

10.8

12.6

14.4

16.2

18.0



Contents

(For detailed breakdown of tables, see index.)

Front Matter

Temperature Conversion Table (Table 1)

Preface to the Ninth Revised Edition

Introduction

Units of Measurement

Conversion Factors and Dimensional Formulae

Some Fundamental Definitions (Table 2)

Part 1. Geometrical and Mechanical Units

Part 2. Heat Units

Part 3. Electrical and Magnetic Units

Fundamental Standards (Table 3)

Part 1. Selection of Fundamental Quantities

Part 2. Some Proposed Systems of Units

Part 3. Electrical and Magnetic Units

Part 4. The Ordinary and the Ampere-turn Magnetic Units

The New (1948) System of Electric Units (Table 6)

Relative Magnitude of the Old International Electrical Units and the

New 1948 Absolute Electrical Units (Table 5)

Relative Values of the Three Systems of Electrical Units (Table 6)

Conversion Factors for Units of Energy (Table 7)

Former Electrical Equivalents (Table 8)

Some Mathematical Tables (Tables 9-15)

Treatment of Experimental Data (Tables 16-25)

General Physical Constants (Tables 26-28)

Common Units of Measurement (Tables 29-36)

Constants for Temperature Measurement (Tables 37-51)

The Blackbody and its Radiant Energy (Tables 52-57)

Photometry (Tables 58-77)

Emissivities of a Number of Materials (Tables 78-84)

Characteristics of Some Light-source Materials, and Some Light

Sources (Tables 85-102)

Cooling by Radiation and Convection (Tables 103-110)

Temperature Characteristics of Materials (Tables 111-125)

Changes in Freezing and Boiling Points (Tables 126-129)

Heat Flow and Thermal Conductivity (Tables 130-141)

Thermal Expansion (Tables 142-146)

Specific Heat (Tables 147-158)

Latent Heat (Tables 159-164)

Thermal Properties of Saturated Vapors (Tables 165-170)

Heats of Combustion (Tables 171-183)

Physical and Mechanical Properties of Materials (Tables 184-209)

Characteristics of Some Building Materials (Tables 210-217)



i

ii

iii

1

1

2

4

4

7

10

13

13

15

16

18

19

20

20

21

22

23-36

37-45

46-55

56-69

70-78

79-86

87-97

98-101

102-111

112-116

117-130

131-135

136-144

145-154

155-164

165-167

168-178

179-186

187-228

229-231



Physical Properties of Leather (Tables 218-223)

Values of Physical Constants of Different Rubbers (Tables 224-229)

Characteristics of Plastics (Tables 233-236)

Properties of Fibers (Tables 233-236)

Properties of Woods (Tables 237-240)

Temperature, Pressure, Volume, and Weight Relations of Gases and

Vapors (Tables 241-253)

Thermal Properties of Gases (Tables 254-260)

The Joule-Thomson Effect in Fluids (Tables 261-267)

Compressibility (Tables 268-280)

Densities (Tables 281-295)

Velocity of Sound (Tables 296-300)

Acoustics (Tables 301-310A)

Viscosity of Fluids and Solids (Tables 311-338)

Aeronautics (Tables 339-346A)

Diffusion, Solubility, Surface Tension, and Vapor Pressure

(Tables 347-369)

Various Electrical Characteristics of Materials (Tables 370-406)

Electrolytics Conduction (Tables 407-415)

Electrical and Mechanical Characteristics of Wire (Tables 416-428)

Some Characteristics of Dielectrics (Tables 429-452)

Radio Propagation Data (Tables 453-465)

Magnetic Properties of Materials (Tables 466-494)

Geomagnetism (Tables 495-512)

Magneto-optic Effects (Tables 513-521)

Optical Glass and Optical Crystals (Tables 522-555)

Transmission of Radiation (Tables 556-573)

Reflection and Absorption of Radiation (Tables 574-592)

Rotation of Plane of Polarized Light (Tables 593-597)

Media for Determinations of Refractive Indices with the Microscope

(Tables 598-601)

Photography (Tables 602-609)

Standard Wavelengths and Series Relations in Atomic Spectra

(Tables 610-624)

Molecular Constants of Diatomic Molecules (Tables 625-625a)

The Atmosphere (Tables 626-630)

Densities and Humidities of Moist Air (Tables 631-640)

The Barometer (Tables 641-648)

Atmospheric Electricity (Tables 649-653)

Atomic and Molecular Data (Tables 654-659)

Abundance of Elements (Tables 660-668)

Colloids (Tables 669-682)

Electron Emission (Tables 683-689)

Kinetic Theory of Gases (Tables 690-696)



232-233

234-238

239-240

241-245

246-258

259-267

268-277

278-281

282-290

291-305

306-308

309-317

318-336

337-353

354-374

375-396

397-403

404-420

421-433

434-450

451-467

468-502

503-508

509-534

535-548

549-556

557-560

561

562-567

568-585

586-591

592-595

596-605

606-613

614-617

618-624

625-629

630-634

635-637

638-624



Atomic and Molecular Dimensions (Tables 697-712)

Nuclear Physics (Tables 713-730)

Radioactivity (Tables 731-758)

X-rays (Tables 759-784)

Fission (Tables 785-793)

Cosmic Rays (Tables 794-801)

Gravitation (Tables 802-807)

Solar Radiation (Tables 808-824)

Astronomy and Astrophysics (Tables 825-884)

Oceanography (Tables 885-899)

The Earth's Rotation: Its Variation (Table 900)

General Conversion Factors (Table 901)

Index



643-650

651-671

672-691

692-705

706-709

710-713

714-718

719-727

728-771

772-779

780

781-785

787



lNTRODUCTION

U N I T S OF MEASUREMENT

The quantitative measure of anything is expressed by two factors-one,

a certain definite amount of the kind of physical quantity measured, called the

unit; the other, the number of times this unit is taken. A distance is stated

as 5 meters. The purpose in such a statement is to convey an idea of this distance in terms of some familiar or standard unit distance. Similarly quantity

of matter is referred to as so many grams ; of time, as so many seconds, or

minutes, or hours.

The numerical factor definitive of the magnitude of any quantity must depend on the size of the unit in terms of which the quantity is measured. For

example, let the magnitude factor be 5 for a certain distance when the mile is

used as the unit of measurement. A mile equals 1,760 yards or 5,280 feet. The

numerical factor evidently becomes 8,800 and 26,400, respectively, when the

yard or the foot is used as the unit. Hence, to obtain the magnitude factor for

a quantity in terms of a new unit, multiply the old magnitude factor by the ratio

of the magnitudes of the old and new units ; that is, by' the number of the new

units required to make one of the old.

The different kinds of quantities measured by physicists fall fairly definitely

into two classes. In one class the magnitudes may be called extensive, in the

other, intensive. T o decide to which class a quantity belongs, it is often helpful

to note the effect of the addition of two equal quantities of the kind in question.

If twice the quantity results, then the quantity has extensive (additive) magnitude. For instance, two pieces of platinum, each weighing 5 grams, added

together weigh 10 grams; on the other hand, the addition of one piece of

platinum at 100" C to another at 100" C does not result in a system at 200" C.

Volume, entropy, energy may be taken as typical of extensive magnitudes;

density, temperature and magnetic permeability, of intensive magnitudes.

The measurement of quantities having extensive magnitude is a comparatively direct process. Those having intensive magnitude must be correlated

with phenomena which may be measured extensively. In the case of temperature, a typical quantity with intensive magnitude, various methods of measurement have been devised, such as the correlation of magnitudes of temperature

with the varying lengths of a thread of mercury.



Fundamental units.-It is desirable that the fewest possible fundamental

unit quantities should be chosen. Simplicity should regulate the choicesimplicity first, psychologically, in that they should be easy to grasp mentally,

and second, physically, in permitting as straightforward and simple definition

as possible of the complex relationships involving them. Further, it seems desirable that the units should be extensive in nature. I t has been found possible

to express all measurable physical quantities in terms of five such units : first,

geometrical considerations-length, surface, etc.-lead to the need of a length ;

second, kinematical considerations-velocity,

acceleration, etc.-introduce

time ; third, mechanics-treating of masses instead of immaterial points-inSMITHSONIAN PHYSICAL TABLES

1



2

troduces matter with the need of a fundamental unit of mass ; fourth, electrical,

and fifth, thermal considerations require two more such quantities. T h e discovery of new classes of phenomena may require further additions.

As to the first three fundamental quantities, simplicity and good use sanction

the choice of a length, L, a time interval, T , and a mass, M. F o r the measurement of electrical quantities, good use has sanctioned two fundamental quantities-the

dielectric constant, K , the basis of the “electrostatic” system, and

the magnetic permeability, p, the basis of the “electromagnetic” system. Besides these two systems involving electrical considerations, there is in common

use a third one called the “absolute” system, which will be referred to later.

F o r the fifth, or thermal fundamental unit, temperature is generally ch0sen.l



Derived units.-Having

selected the fundamental o r basic units-namely,

a measure of length, of time, of mass, of permeability o r of the dielectric

constant, and of temperature-it

remains to express all other units for physical

quantities in terms of these. Units depending on powers greater than unity of

the basic units are called “derived units.” Thus, the unit volume is the volume

of a cube having each edge a unit of length. Suppose that the capacity of some

volume is expressed in terms of the foot as fundamental unit and the volume

number is wanted when the yard is taken as the unit. T h e yard is three times

as long as the foot and therefore the volume of a cube whose edge is a yard is

3 x 3 x 3 times as great as that whose edge is a foot. T h u s the given volume

will contain only 1/27 as many units of volume when the yard is the unit of

length as it will contain when the foot is the unit. To transform from the foot

as old unit to the yard as new unit, the old volume number must be multiplied

by 1/27, o r by the ratio of the magnitude of the old to that of the new unit of

volume. This is the same rule as already given, but it is usually more convenient to express the transformations in terms of the fundamental units

directly. I n the present case, since, with the method of measurement here

adopted, a volume number is the cube of a length number, the ratio of two units

of volume is the cube of the ratio of the intrinsic values of the two units of

length. Hence, if I is the ratio of the magnitude of the old to that of the new

unit of length, the ratio of the corresponding units of volume is k . Similarly

the ratio of two units of area would be 12, and so on for other quantities.



CONVERSION FACTORS A N D D I M E N S I O N A L F O R M U L A E

F o r the ratio of length, mass, time, temperature, dielectric constant, and

permeability units the small bracketed letters, [ 1 J , [ m ] , [ t ], [ 01, [ K ] , and [ p ]

will be adopted. These symbols will always represent simple numbers, but the

magnitude of the number will depend on the relative magnitudes of the units

the ratios of which they represent. W h e n the values of the numbers represented

by these small bracketed letters as well as the powers of them involved in any

particular unit are known, the factor for the transformation is at once obtained.

Thus, in the above example, the value of 1 was 1/3, and the power involved

in the expression for volume was 3 ; hence the factor for transforming from

cubic feet to cubic yards was P o r 1/33 o r 1/27 These factors will be called

conversion factors.

1 Because of its greater psychological and physical simplicity, and the desirability that

the unit chosen should have extensive magnitude, it has been proposed to choose as the

fourth fundamental quantity a quantity of electrical charge, e . T h e standard units of electrical charge would then be the electronic charge. For thermal needs, entropy has been proposed. While not generally so psychologically easy to grasp as temperature, entropy is of

fundamental importance in thermodynamics and has extensive magnitude. (Tolman, R. C.,

The measurable quantities of physics, Phys. Rev., vol. 9, p. 237, 1917.)



SMlTHSONlAN PHYSICAL TABLES



3

T o find the symbolic expression for the conversion factor for any physical

quantity, it is sufficient to determine the degree to which the quantities, length,

mass, time, etc., are involved. Thus a velocity is expressed by the ratio of the

number representing a length to that representing an interval of time, or

[ L / T ] ,and acceleration by a velocity number divided by an interval-of-time

number, or [ L I T 2 ]and

,

so on, and the corresponding ratios of units must

therefore enter in precisely the same degree. The factors would thus be for

the just-stated cases, [Z/t] and [ 1 / t 2 ] . Equations of the form above given for

velocity and acceleration which show the dimensions of the quantity in terms of

the fundamental units are called dimensional equations. Thus [ E l = [ML2T-']

will be found to be the dimensional equation for energy, and [ M L 2 T 2 ]the

dimensional formula for it. These expressions will be distinguished from the

conversion factors by the use of bracketed capital letters.

In general, if we have an equation for a physical quantity,

Q = CLaMbTc,

where C is a constant and L , M , T represent length, mass, and time in terms

of one set of units, and it is desired to transform to another set of units in terms

of which the length, mass, and time are L1,M 1 , T 1 ,we have to find the value of

L,/L, M , / M , 1',/T, which, in accordance with the convention adopted above,

will be 1, m, t, or the ratios of the magnitudes of the old to those of the new

units.

Thus L,=Ll, M,=Mnz, T,=Tt, and if Ql be the new quantity number,

Q l = CL,ahllbTIC,

= CLalaMbmbTCtC=

Qlambtc,

or the conversion factor is [lambtc],

a quantity precisely of the same form as

the dimension formula [LaMbTC].

Dimensional equations are useful for checking the validity of physical equations. Since physical equations must be homogeneous, each term appearing in

theni must be dimensionally equivalent. For example, the distance moved by

a uniformly accelerated body is s=n,t +atz. The corresponding dimensional

equation is [ L ]= [ ( L / T )1'3 [ ( L / T 2 )T 2 ] each

,

term reducing to [ L ] .

Dimensional considerations may often give insight into the laws regulating

physical phenomena.2 For instance, Lord Rayleigh, in discussing the intensity

of light scattered from small particles, in so far as it depends upon the wavelength, reasons as follows :



+



+



The object is to compare the intensities of the incident and scattered ray; for these will

clearly be proportional. T h e number (i) expressing the ratio of the two amplitudes is a

function of the following quantities:-V,

the volume of the disturbing particle; r, the

distance of the point under consideration from i t ; A, the wavelength; c , the velocity of

propagation of light ; D and D', the original and altered densities : of which the first three

depend only on space, the fourth on space and time, while the fifth and sixth introduce the

consideration of mass. Other elements of the problem there ar e none, except mere numbers

and angles, which do not depend upon the fundamental measurements of space, time, and

mass. Since the ratio i, whose expression we seek, is of no dimensions in mass, it follows

a t once that D and D' occur only under the form D : D', which is a simple number and may

therefore be omitted. It remains to find how i varies with V ,r, A, c.

Now, of these quantities, c is the only one depending on time ; and therefore, as i is of no

dimensions in time, c cannot occur in its expression. W e are left, then, with V ,r, and A ; and

from what we know of the dynamics of the question, we may be sure that i varies directly as

V and inversely as Y , and must therefore be proportional t o V t A?, V being of three diBuckingham, E., Phys. Rev., vol. 4,p. 345,1914 ; also Philos. Mag., vol. 42,p. 696, 1921.

Philos. Mag., ser. 4, voI. 41, p. 107, 1871. See also Robertson, Dimensional analysis,

Gen. Electr. Rev., vol. 33, p. 207, 1930.

SMITHSONIAN PHYSICAL TABLES



4

mensions in space. In passing from one part of the spectrum to another h is the only

quantity which varies, and we have the important law:

When light is Scattered by particles which are very small compared with any of the

wavelengths, the ratio of the amplitudes of the vibrations of the scattered and incident light

varies inversely as the square of the wavelength, and the intensity of the lights themselves

as the inverse fourth power.



The dimensional and conversion-factor formulae for the more commonly

occurring derived units are given in Table 30.

T A B L E 2.-SOM



E F U NDAM E N T A L DEFl N ITIONS



P a r t 1.-Geometrical



Activity (power).-Time

Angle ( 4 j .-The

the radian.

-4ngstrom.-Unit



and mechanical units



4



rate of doing work; unit, the watt.



ratio of the length of its circular arc to its radius ; unit,

of wavelength=



Angular acceleration



z)



(



a= -



.-The



meter. (See Table 522.)

rate of change of angular velocity.



Angular momentum ( ZW) .-The product of its moment of inertia about

an axis through its center of mass perpendicular to its plane of rotation and its

angular velocity.

Angular velocity.-The



time rate of change of angle.



Area.-Extent of surface. Unit, a square whose side is the unit of length.

The area of a surface is expressed as S = CL', where the constant C depends

on the contour of the surface and L is a linear dimension. If the surface is a

square and L the length of a side, C is unity ; if a circle and L its diameter, C

is x/4. (See Table 31.)

Atmosphere.-Unit



of pressure. (See Table 260.)



English normal= 14.7 lb/in.*=29.929 in.Hg= 760.1s mmHg ( 3 2 ° F )

U. S.=760 mmHg (0°C) =29.921 in.Hg= 14.70 Ib/in.'

Avogadro number.-Number

cules/mole.



of molecules per mole, 6.0228 x loz3mole-



Bar.4"-International unit of pressure lo6 dyne/cni'.

Barye.-cgs pressure unit, one dyne/cm2.

Carat.-The

diamond carat standard in U. S.=200 mg. Old standard=

205.3 mg=3.168 grains. The gold carat: pure gold is 24 carats; a carat is

1/24 part.

Circular area.-The square of the diameter = 1.2733 x true area. True

area = 0.785398 x circular area.

Circular inch.-Area



of circle 1 inch in diameter.



Cubit = 18inches

4*



For dimensional formula see Table 30, part 2.

Some writers have used this term for 1 dyne/cm2.



SMITHSONIAN PHYSICAL TABLES



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