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Table 30. Dimensional Equations of Fundamental and Derived Units

# Table 30. Dimensional Equations of Fundamental and Derived Units

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58

T A B L E 30.-DIMENSIONAL

E Q U A T I O N S OF F U N D A M E N T A L A N D

D E R I V E D U N I T S (continued)

Part 2.-Derived

units (geometric and heat)

Conversion

factor

Name of units

[rn"/~'t*]

&

Name of unit

X

Y

Z

(Ireat and liaht)

x

y

z

u

0

0

0

2

3

0

0

0

0

1

0

Solid angle . . . . . . . . .

Curvature . . . . . . . . . .

Angular velocity . . . . .

0

0

0

0

0

0

Quantity of heat:

thermal units . . . . .

thermometric units.

dynamical units . . .

1

0 0

3

0

2-2

1

1

0

0

0

Linear velocity . . . . . . .

Angular acceleration . .

Linear acceleration . . .

0

0

0

Area, surface .... .....

Volume . . . . . . . . . . . . . .

Angle .. . . . . . . . . . . . .

..

..

.

.

Density . . . . . . . . . . . . .

Moment of inertia.. . . .

Intensity of attraction.

1

1

0

Momentum . . . . . . . . . .

Moment of momentum.

Angular momentum ..

1

Force . . . . . . . . . . . . . . .

M o m e n t of c o u p l e ,

torque . . . . . . . . . . .

Work. energy ........

-1

-3

-1

1

0

1

-1

-2

-2

2

1

0

0

-2

Coefficient ,of thermal

cxpansion . . . . . .

0

1

2-1

1 -3

Thcrnial capacity . . .

1

0

0

0

0

0

0

0

2 -2

1

0

0

2 -2

1

0

1

2 -2

1

1

-1

-1

-1

Latent heat :

thermal units . . . . .

dynsniical units . . .

1

1

-2

Joulc's equivalent. . . .

1

2

2

-2

-2

2

-3

-2

-2

Entropy :

hcatinthermalunits.

heat in tlynamical

units . . . . . . . . . . .

1

-1

-1

.

1

-1

-1

2

-2

-1

0-1

Tliernial conductivity :

thermal units . . . . .

thermometric units

or diffusivity . . . .

tlynamical units . . .

1

2

2

Power, activity . . . . . . . 1

Intensity of stress.. . . . 1

Modulus of elasticity. . 1

Compressibility

. . . --1

Resilience . . . . . . . . . . . . 1

Viscosity . . . . . . . . . . . . 1

.

0

Imninous intensity . . 0

Illuniinaticin . . . . . . . . 0

Brightness . . . . .. . . . 0

Visibility . . , . . . . _ _

. .-1

Luniinous efficicucy. . -1

0

-2

-2

-2

-2

0

-1

1 -1

-1

0

-1

0

0

1

0

0

0

3

3

1*

1*

1*

1*

1*

For these formula: the nunibers in the last column arc the exlionents of F where I; rrfers to the

luminous flux. For definitions of thest. quantities see Tables 70 and 72.

(cotlfi?tlred)

SMITHSONIAN PHYSICAL TABLES

T A B L E 30.-DIMENSIONAL

EQUATIONS O F FUNDAMENTAL AND

D E R I V E D U N I T S (concluded)

P a r t 3.-Derived

59

units (electrical and magnetic)

Conversion f w t o r

Electrostatic

system

I-lectroniaanetic

ml/.vr*k r

N a m e of u n i t

m=/'f:/*

Symbol *

I.

7

r

\

2

I.

;

0 --I.

0 --;

0 - 5

2

1

-

Electric field intensity. .... F

Electric potential . . . . . . . . . V

Electromotive force . . . . . . E

?

0

0

0

1

0

0

Current . . . . . . . . . . . . . . . . . I

Electric conductivity ..... y

Resistivity ............... p

\$

0

! - 2

0-1

Conductance ............. g

Resistance . . . . . . . . . . . . . . . R

Magnetic pole strength. ... m

0

1 - 1

1

0 -1

1 -1

Quantity of magnetism. ... m

Magnetic flux ............

Magnetic field intensity. ... H

;

0

t

t

0

0

0

0

1

1

0

f

1

1-1

t

0-4

0 - \$

;

4

\$ - 2

0

-L

0 -1

0 -2

0

0

4

i -1

0

2 -1

0 -2

0

0

CP

--f

1 -1

C

C2

-j

-1

-f

-1

-3

-3

3 -1

I -1

-!

3

\$

-1

1

1

-1

t

+

-1

-1

-;\$

-\$\$

1

2

1

2

'

2

-2

' -2

2

4

t

1,!c

l/c

C

1

1

1

1

1

1

0

0

0

0

0

0

0

0 -1

0

0

0

1

0

1

0

0 -1

0

1

0

0

0

0

0

1

0

0

0

0

0

1

1

1

0

0

1

1

0

0 -1

1

0

0

0

1

0

0

1

1

1

1

1

-1

-1

-1

0

1

1

1

0

C

C

C

f

1/c

i 1 /c

-1

0

0

f

Thermoelectric power\$ , . . Peltier coefficient\$ . . . . . . . -

1

0

1 -2

1 -2

0

-4

-1

; -1

-+

0

0

0

C'

1 1/c'

-

Self-inductancc . . . . . . . . . . 2

Mutual inductance . . . . . . . \$)]I

Magnetic reluctance . . . . . . \$R

?'

l c

l c

2 -1

2 -1

0

0

1 -1

\$

Magnetic susceptibility . . . K

Magnetic permeability . . . p

Current density . . . . . . . . . . -

3

;

-1

5

-3

;

r

0

0

0

c'

1 -1

-1

0 -1

1

1 -1

1 1 /c2

0

2I

1

; -1

f 1/ c

Magnetizing force . . . . . . . H

Magnetic potential . . . . . . . 0

Magnetomotive force . . . . . :i

Magnetic moment . . . . . . . . Intensity magnetization . . . J

Magnetic induction . . . . . . . B

C

C

C

; 1 'c

j -2

! -2

; -2

Electrostatic capacity . . . . . c

Dielectric constant . . . . . . . K

Specific inductive capacity. -

0

0

-4

t

1.'c

1

1

1/c'

l/c'

C

t

0 -1

1 -2

1 -2

1

1

0

0 -1

i'

1

1

1

0

0 -1

1 -2

0

1 1 ic?

1

1

0

1 1/c'

c"

0 -1

-1

0

0

1

0

1

0 -1

1

1

1

1

0

0

+\$ l / c

t\$ l / c

. A s adopted by .\merican Institute of Electrical E n g i n e e r s , 1915.

t c is the velocity of a n electromagnetic wave i n the e t h e r = 3 x 1O'O ap'proximately.

t T h i s conversion factor should include [#-'I.

SMITHSONIAN PHYSICAL TABLES

~

i

-

Quantity of electricity.. ... Q

Electric displacement ..... 1)

Electric surface density.. . D

+

emu

esu

t

..

systrm

0

0

O\$

O\$

T A B L E 31.-FUNDAMENTAL

U N I T S OF L E N G T H , AREA, V O L U M E , A N D MASS

(As established by administrative action, National Bureau of Standards)

~

Part 1.-Some

definitions and legal relations

1 in.* = (U0.3937) cm = 2.54000508cm

1 Ib * = 453.5924277 g

1 gal * = 231 in? = 3.785329 liter

1 I.T.cal t = 4.18674 ioules

= I.OOOSS~calls

1 Btu t = 251.996 I.T. cal

= 252.161 calls

Part 2 . 4 o n v e r s i o n factors, units of length

cm

1cm=

1m=

1 in. =

1 ft=

1 yd=

1

100

2.5400051

30.480061

91.440183

in.

ft

rd

0.3937

0.032808333

3.2808333

0.083333333

1

3

0.010936111

1.0936111

0.027777778

0.33333333

1

m

0.01

1

0.025400051

0.30480061

0.91440183

39

_ _ 37

1

12

36

Part 3.-Conversion

cm2

1 cm'=

1 mz=

1 in.'=

1 ft' =

I yd2=

1

10'

6.4516258

929.03412

8361.3070

10-4

1

6.4516258 x lo-'

O.WZ903412

0.83613070

cm3

1 ft'=

1 ml=

1 liter =

1 gal =

1

16.387162

2.8317017 x 10'

1.000028

1.000028 X lo3

3.7854345 X 10'

in.=

kg

g

1

1 kg=

1 lb=

1 metric ton=

1 ton=

1.0.3

Legal relation.

4.5359243 X 10'

1oe

9.0718486 x lo5

10.'

1

0.45359243

103

907.18486

1.0763867 x

10.763867

6.9444444 x lo-'

1

9

yd'

1.1959853 x lo-*

1.1959853

7.7160494 x lo-'

0.11111111

1

factors, units o f volume

ft3

0.061023378

1

1.728 x lo"

0.06102509

61.OX09

231

3.5314455 X

5.7870370 x lo-'

1

3.531544 X lod

0.03531544

0.13368056

Part 5.-Conversion

1g =

ft2

0.15499969

1549.9969

1

144

1296

Part 4.-Conversion

1 cm3=

1 in?=

factors, units of area

in.2

m2

ml

0.9999720

16.38670

2.831622 x 10'

1

10"

3.785329 x 10'

liter

0.9999720 x 10.'

1.638670 x lo-'

28.31622

0.001

1

3.785329

factors, units o f mass

lb

2.2046223 x lo-'

2.2046223

1

2204.6223

2000

t As defined by International Steam Table Conference, London, 1929.

metric ton

lo-'

10''

4.5359243 X

1

0.90718486

ton

1.1023112 X 101.1023112 x 10"

0.0005

1.1023112

1

gal

2.6417047 X lo-'

4.3290043 x lo-*

7.4805195

2.641779

0.2641779X lo-'

1

61

FOR CONVERTING U. S. WEIGHTS AND MEASURES*

TABLE 32.-TABLES

t o customary

P a r t 1.-Metric

Capacity

7

Linear

l\$eters to

inches

Meters to

feet

hleters to Kilometers

yards

to miles

litersor

cut+

centi.

meters

tofluid

drams

Centiliters

to

fluid

ounces

Decaliters

to

gallons

Liters

to

quarts

Hectoliters

tu

hshek

1 39.3700 3.28083 1.093611

2 78.7400 6.56167 2.187222

3 118.1100 9.84250 3.280833

4 157.4800 13.12333 4.374444

5 196.8500 16.40417 5.468056

0.62137

1.24274

1.86411

2.48548

3.10685

2

3

4

5

0.27

0.54

0.81

1.08

1.35

0.338

0.676

1.014

1.353

1.691

1.0567 2.6418 2.8378

2.1134 5.2836 5.6756

3.1701 7.9253 8.5135

4.2268 10.5671 11.3513

5.2836 13.2089 14.1891

6

7

8

9

3.72822

4.34959

4.97096

5.59233

6

7

8

9

1.62

1.89

2.16

2.43

2.029

2.367

2.705

3.043

6.3403

7.3970

8.4537

9.5104

236.2200

275.5900

314.9600

354.3300

19.68500

22.96583

26.24667

29.52750

6.561667

7.655278

8.748889

9.842500

1

>

1

Milligrams to

grains

Kilo.

grams to

grains

Hectograms to

ounces

avoirdupois

Kilograms to

wunds

avoirdupois

0.1550

0.3100

0.4650

0.6200

0.7750

10.764

21.528

32.292

43.055

53.819

1.196

2.392

3.588

4.784

5.980

2.471

4.942

7.413

9.884

12.355

1

2

3'

4

5

0.01543

0.03086

0.04630

0.06173

0.07716

15432.36

30864.71

46297.07

61729.43

77161.78

3.5274

7.0548

10.5822

14.1096

17.6370

2.20462

4.40924

6.61387

8.81849

11.02311

0.9300

1.0850

1.2400

1.3950

64.583 7.176

75.347 8.372

86.111 9.568

96.875 10.764

14.826

17.297

19.768

32.230

6

7

8

9

0.09259 92594.14

0.10803 108026.49

0.12346 123458.85

0.13889 138891.21

21.i644

24.6918

28.2192

3 1.7466

13.22773

15.43236

17.63698

19.84160

Quintals to

pounds av.

Milliers

or

tonnes to

pounds av.

Iiilograms to

ounces

troy

Cubic

6

7

8

9

17.0269

19.8647

22.7026

25.5404

Mass

Square

Squafe

centiSquare

Square

meters

meters

meters

to square to square to square Hectares

tuacres

feet

yards

inches

2

3

15.8507

18.4924

21.1342

23.7760

Mazs

Cubic

centimeters

to cubic

inches

Cubic

decimeters

to cubic

inches

meters to

cubic

feet

Cubic

meters to

cubic

yards

0.0610

0.1220

0.1831

0.2441

0.3051

61.023

122.047

183.070

244.094

305.117

35.314

70.269

105.943

141.258

176.572

1.308

2.616

3.924

5.232

6.540

1

2

3

4

5

220.46

440.92

661.39

881.85

1102.31

2204.6

4409.2

6613.9

8818.5

11023.1

32.1507

64.3015

96.4522

128.6030

160.7537

0.3661

0.4272

0.4882

0.5492

366.140

427.164

488.187

549.210

211.887

247.201

282.516

317.830

7.848

9.156

10.464

11.771

6

7

8

9

1322.77

1543.24

1763.70

1984.16

13227.7

15432.4

17637.0

19841.6

192.9045

225.0552

257.2059

289.3567

Cubic

I n the United 5t:;tes since 1893 all units in the above table have been derived from the

same standards c i h:gth a:!d mass. Therefore all equivalents (except those ii?volving the

liter) depend oiily [ i n :iurrierical definitions. T h e liter is the volume of one kilogram of

pure water at ttie tFmpcratcre of its maximum density and under a pressure equivalent t o

760 millitneters of nir;cury. T h e liter was determined by the International :3ureau of

Weights arid Measures in 1910 to equal 1.000027 dm3. (National Bureau of Standards.)

.Quoted

from sheets issued by the Kational Bureau of Standards

(corttinzred)

SMITHMNIAN PHYSICAL TABLES

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