Smithsonian physical tables (9th revised edition)

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


5
Dalton (atomic inass unit R/I,).--Unit of mass, 1/16 inass of oxygen (801e)
g (Phys. scale). (See Table 26.)
atom, 1.66080 x
Density.-The mass per unit volume. The specific gravity of a body is the
ratio of a density to the density of a standard substance. Water and air are
commonly used as the standard substance.
in. ; 1/12 the apparent diameter of the sun or moon.

*Diopter.-Unit
of “power of a lens.” The diopter = the reciprocal of the
focal length in meters.
Digit.-3/4

Dyne.-The cgs, unit of force = that unbalanced force which acting for
1 second on body of 1 gram mass produces a velocity change of 1 cm/sec.
Energy.-The work done by a force produces either a change in the velocity
of a body or a change of its shape or position or both. In the first case it produces a change of kinetic energy, in the second, of potential energy.
Erg.-The cgs unit of work and energy = the work done by 1 dyne acting
through 1 centimeter.
Fluidity.-Reciprocal
Foot-pound.-The
standard g.

of viscosity.
work which will raise 1 pound. body 1 foot high for

Foot-pounda1.-The
1 foot.

work done when a force of 1 poundal acts through

Force ( f ) .-Force is the agent that changes the motion of bodies and is
measured by the rate of change of momentum it produces on a free body.
Gal = gravity standard = an acceleration of 1 cm set?.
Giga = lo9.
Gram.-The

standard of mass in the metric system. (See Table 31.)

Gram-centimeter.-The
Gram-molecule.-The
its molecular weight.
Gravitation constant.-(
cm2 g-2.

cgs gravitation unit of work.
mass in grams of a substance numerically equal to

G, in formula F = Gnz,wz2/rZ) = 6 . 6 7 0 ~lo-*dyne

Gravity (g).-The attraction of the earth for any mass. It is measured by
the acceleration produced on the mass under standard conditions. This acceleration g equals 980.665 cm sec-* or 32.17 ft sec-*.
Horsepower.-A
unit of mechanical power. The English and American
horsepower is defined by some authorities as 550 foot-pounds/sec and by
others as 746 watts. The continental horsepower is defined by some authorities as 75 kgm/sec and by others as 736 watts.
Joule.-Unit
of work (energy) = lo7 ergs. Joules = (volts2 x sec)/
ohms = watts x sec = amperes2 x ohms x sec = volts x amperes x sec.
Kilodyne.-1

,OOO dynes. About 0.980 gram weight.

SMITHSONIAN PHYSICAL TABLES


6

mv2
energy associated with the motion = - in ergs if
2
m i s in grams and v in cni/sec.
Kinetic energy.-The

(

Linear acceleration

a= $).-The

rate of change of velocity.

Table 32.

Liter.-See

Loschmidt number.-The
number of molecules per cm3 of an ideal gas at
0°C and normal pressure = 2.6S70 x 10l9molecules/cm3.
Megabaryes.-Unit
of pressure = 1,000,000 baryes = 1 bar = 0.957 atmosphere.
Meter.-See Table 31.
Micro.-A
Micron

prefix indicating the millionth part. (See Table 901.)
(p)

= one-millionth of a meter = one-thousandth of a millimeter.

Mil.-One-thousandth
Mile.-Statute
Mil1i.-A

of an inch.

= 5,280 feet; nautical or geographical = 6,050.20 feet.

prefix denoting the thousandth part.

Modulus of elasticity.-Ratio of stress to strain. The dimension of strain,
a change of length divided by a length, or change of volume divided by a
volume, is unity.
Mole or mo1.-Mass

equal numerically to molecular weight of substance.

Momentum ( M = mv) .-The quantity of motion in the Newtonian sense ;
the product of the mass and velocity of the body.
Moment of inertia ( I ) of a body about an axis is the 2mr2,where m is
the mass of a particle of the body and r its distance from the axis.
Newton.-The
3, part 2.)

unit of force in the MKS system = lo5 dynes. (See Table

Pound weight.-A
force equal to the earth's attraction for a mass of 1

pound. This force, acting on 1 lb mass, will produce an acceleration of 32.17
ft/sec2.
Pounda1.-The ft-lb sec unit of force. That unbalanced force which acting
on a body of 1 lb mass produces an acceleration of 1 ft/sec2.

Pi (~)=3.1416. (See Table 11.)
Power.-Activity

(p ="d) is the time rate of doing work.

Radian.-An
angle subtended by an arc equal to the radius. This angle
equals 180°/r= 57.29578" = 57" 17'45" =206265'!
Resilience.-The work done per unit volume of a body in distorting it to
the elastic limit or in producing rupture,
(32.17 lb) acquiring acceleration 1 ft s e P when continuously
Slug.-Mass
acted upon by force of 1 lb weight.
SMITHMNIAN PHYSICAL TABLES


7
Strain.-The
mension.

deformation produced by a stress divided by the original di-

Stress.-The
tion.

force per unit area of a body that tends to produce a deforma-

Tenth-meter.-lO-l,O

meter = 1 angstrom.

Torque, moment of a couple, about an axis is the product of a force and the
distance of its line of action from the axis.
Volume.-Extent of space. Unit, a cube whose edge is the unit of length.
The volume of a body is expressed as V = CL8. The constant C depends on
the shape of the bounding surfaces.
Velocity (v=

%) is distance traversed per unit time.

Viscosity.-The property of a liquid by virtue of which it offers resistance
to flow. The coefficient of viscosity is the tangential force that must be applied
to the upper surface of a 1-cni cube of the liquid on an edge to produce a
velocity of 1 cm/sec in the face when the lower face is at rest.
W o r k (W).-The work done by an unbalanced force is the product of the
force by the component of the resulting displacement produced in the direction
of the force.
Young's modulus.-Ratio of longitudinal stress within the proportional
limit to the corresponding longitudinal strain.
Part P.-Hert

Unit85

Blackbody.-A body that absorbs all the radiation that falls upon it. From
this definition and certain assumptions it can be shown that its total radiation =

uT' (Stefan-Boltzmann Law) and that the spectral distribution of the radiation is given by the Planck Law : 5a

Brightness temperature (S).-The temperature of a non-blackbody determined from its brightness (with an optical pyrometer, see Table 77) as rf
it were a blackbody. Such temperatures are always less than the true temperatures.
British thermal unit (Btu).-The
amount of heat required to raise 1
pound of water at 60"F,1°F. This unit is defined for various temperatures,
but the general usage seems to be to take the Btu as equal to 252 calories. (See
calorie. See Table 7.)
Calorie.-The amount of heat necessary to raise 1 gram of water at 15"C,
1o r
I L.

5

For dimensional formulas see Table 30, part 2.

m An

easier way to write this exponential term is:

This form will be used hereafter.
SMITHSONIAN PHYSICAL TABLES


8
There are various calories depending upon the interval chosen. Sometimes
the unit is written as the gram-calorie or the kilogram-calorie, the meaning of
which is evident. There is some tendency to define the calorie in terms of its
mechanical equivalent. Thus the National Bureau of Standards defines the

calorie as 4.18400 joules. At the International Steam Table Conference held
in London in 1929 the international calorie was defined as 1/860 of the international watt hour (see Table 7), which made it equal to 4.1860 international
joules. With the adoption of the absolute system of electrical units, this becomes 1/859.858 watt hours or 4.18674 joules. The Btu was defined at the
same time as 251.996 international calories. Thus, until such a time as these
differences are taken care of, there will be some confusion.
Celsius temperature scale.-The
present-day designation of the scale
formerly known as the Centigrade scale.
C entigrade temperature scale.-The
temperature scale that divides the
interval between the ice point, taken as O'C, and the boiling point of water
with 100".
Coefficient of thermal expansion.-Ratio
of the change of length per
unit length (linear), or change of volume per unit volume (voluminal), to the
change of temperature.
Color temperature ( T s ).-The color temperature of a non-blackbody is
the temperature at which it is necessary to operate the blackbody so that the
color of its emitted light will match that of the source studied.
Emissivity.-Ratio of the energy radiated at any temperature by a nonblackbody to that radiated by a blackbody at the s a n e temperature. The
spectral emissivity is for a definite wavelength, and the total emissivity is
for all wavelengths.
Entha1py.-Total energy that a system possesses by virtue of its temperature. Thus, where U is the internal energy, then the enthalpy = U PV where
PV represents the external work.

+

Entropy.-A
unavailable.

measure of the extent to which the energy of the system is

Fahrenheit temperature scale.-A scale based on the freezing point .of
water taken as 32" and the boiling point of water taken as 212".
Graybody.-A

body that has a constant emissivity for all wavelengths.

Heat.-Energy transferred by a thermal process. Heat can be measured
in terms of the dynamical units of energy, as the erg, joule, etc., or in terms of
the amount of energy required to produce a definite thermal change in some
substance, as for example the energy required per degree to raise the temperature of a unit miLss of water at some temperature. The mechanical unit of
heat has the dimensional formula of energy ( M L 2 T 2 ) .The thermal unit
( H ) ,as used in many of these tables, is ( M e ) where 0 denotes a temperature
interval.
Joule's equivalent (J) o r the mechanical equivaient of heat.-Conversion factor for changing an expression of mechanical energy into an expression of thermal energy or vice versa (4.1855 J/cal).
6Gen. Electr. Rev., vol. 47, p. 26, 1944.
SMITHSONlAN PHYSICAL TABLES


9
Kelvin temperature scale.-Scale of temperature based on equal work for
equal temperatures for a working substance in a carnot cycle = Celsius (Centigrade) scale
273.16.

+

Langley (ly).-A
new unit of radiation, surface density, has been suggested which equals 1 calorie ( lS°C) per cm?.
L a t e n t heat.-Quantity

of matter.
Pyron.-A

of heat required to change the state of a unit mass

unit of radiant intensity = 1 cal cniP inin-l.

Radiant energy.-Energy

traveling in the form of electromagnetic waves.

Radiant temperature.-The
temperature obtained by use of a total radiation pyrometer when sighted upon a non-blackbody. This is always less than
the true temperature.
R a n k i n temperature scale.-Absolute
scale
459.7.

+

Fahrenheit scale = Fahrenheit

R e a u m u r temperature scale.-A
scale based upon the freezing point of
water taken as 0"R and the boiling point of water taken as SOOR.
Specific heat.-Ratio of the heat capacity of a substance to the heat capacity
of an equal mass of water. When so expressed, the specific heat is a diniensionless number.
Standard temperature.-A
temperature that depends upon some characteristic of some substance, such as the melting, boiling, or freezing point, that
is used as a reference standard of temperature.

T h e r m a l capacitance.-The

heat capacity of a hody is the limiting value,

as T approaches zero, of the ratio

A 0

L*
where A T is the rise in temperature
AT
resulting from the addition to the body of a quantity of heat equal to A Q .

T h e r m a l conductivity.-Quantity of heat, Q , which flows normally across
a surface of unit area per unit of time and per unit of temperature gradient
normal to the surface. In thermal units it has the tliinensional forinula
( HO-lL-lT-l)or (ML-'T-'), in mechanical units ( I I ~ L T - ~ O P ) .
Thermodynamic temperature.-See
Thermodynamics.-Study

Kelvin teinperature scale.

of the flow of heat.

Thermodynamic laws : Zeroth ln.iu.-Two systems that are in thermal
equilibrium with a third are in thermal equilibrium with each other. First low:
When equal quantities of niechanical effect are produced by any means whatever from purely thermal effects, equal quantities of heat are put out of
existence or are created. S'ccoizd lnzw: It is impossible to transfer heat from
a cold body to a hot body without the perfornlance of mechanical work. Third
lnzv: I t is impossible by any means whatever to superpose only the images of

several light sources to obtain an image brighter than the brightest of the
source.
7

Aldrich et al., Science, vol. 106, p. 225, 1947.

SMITHSONIAN PHYSICAL TABLES


10
Part 3.-Electric

and Magnetic Units

A system of units of electric and magnetic quantities requires four fundamental quantities. A system in which length, mass, and time constitute three
of the fundamental quantities is known as an “absolute” system. There are
two abso1u:e systems of electric and magnetic units. One is called the electrostatic, in which the fourth fundamental quantity is the dielectric constant, and
one is called the electromagnetic, in which the fourth fundamental quantity is
magnetic permeability. Besides these two systems there will be described a
third, to be known as the absolute system, that was introduced January 1, 1948.
(See Table 4.)
I n the electrostatic system, unit quantity of electricity, Q, is the quantity
which exerts unit mechanical force upon an equal quantity a unit distance from
it in a vacuum. From this definition the dimensions and the units of all the
other electric and magnetic quantities follow through the equations of the
mathematical theory of electromagnetism. The mechanical force between two
quantities of electricity in any medium is

Q Q’
F= -

KrZ ’

where K is the dielectric constant, characteristic of the medium, and r the distance between the two points at which the quantities Q and Q‘ are located. K
is the fourth quantity entering into dimensional expressions in the electrostatic
system. Since the dimensional formula for force is [ M L T 2 ] ,that for Q is
[M’LZ T ’ K ’ ] .
The electroinagnetic system is based upon the unit of the magnetic pole
strength (see Table 466). The dimensions and the units of the other quantities
are built up from this in the same manner as for the electrostatic system. The
mechanical force between two magnetic poles in any medium is
m d
F= pr2 ’

in which p is the permeability of the medium and Y is the distance between two
poles having the strengths m and m‘. p is the fourth quantity entering into
dimensional expressions in the electromagnetic system. I t follows that the
dimensional expression for magnetic pole strength is [M’L:T 1 p * ] .
The symbols K and p are sometimes omitted in tlie dimensional formulae so
that only three fundamental quantities appear. There are a number of objections to this. Such formulae give no information as to the relative magnitudes
of the units i n the two systems. The omission is equivalent to assuming some
relation between mechanical and electrical quantities, or to a nlechanical explanation of electricity. Such a relation or explanation is not known.
The properties I< and p are connected by the equation I / V / K p = v , where v
is the velocity of an electromagnetic wave. For empty space or for air, K and
p being measnred in tlie same units, 1VKp=c, where c is the velocity of
light in vacuo, 2 . 9 9 7 7 6 ~10’O cni per sec. It is sometimes forgotten that the
omission of the dimensions of K or p is merely conventional. For instance,
magnetic field intensity and magnetic induction apparently have the same dimensions when p is omitted. This results in confusion and difficulty in understantling the theory of magnetism. The suppression of p has also led to the use
of the “centimeter” as a unit of capacity and of inductance ; neither is physically
the same as length.

SMITHSONIAN PHYSICAL TABLES


11
ELECTROSTATIC SYSTEM

Capacitance of an insulated conductor is proportional to the ratio of the
quantity of electricity in a charge to the potential of the charge. The dimensional formula is the ratio of the two formulae for electric quantity and
potential or [M'L:T-lK'/M'L'T-'K-'] or [ L K ] .
Conductance of any part of an electric circuit, not containing a source of
electromotive force, is the ratio of the current flowing through it to the difference of potential between its ends. The dimensional formula is the ratio of the
formulae for current and potential or [M'L;T-2K'/M'L'T'K-i] or [ L T - l K ] .
Electrical conductivity, like the corresponding term for heat, is quantity
per unit area per unit potential gradient per unit of time. The dimensional
formula is [ M ' L g T ' K 4 / L 2 ( M 4 L
*TT-'Ki
/ L ) T ] or [ T ' K ] .
Electric current (statampere-unit quantity) is quantity of electricity flowinn through a cross section per unit of time. The dimensional formula is the
raTio of tKe formulae for electric quantity and for time or [ M * L > P K ' / T or
]
[M3L;T2K'],
Electric field intensity strength at a point is the ratio of the force on a
quantity of electricity at a point to the quantity of electricity. The dimensional
formula is therefore the ratio of the formulae for force and electric quantity or
[ M L T-2/M L 2 T-lK' ] or [ h14L-3 T-lK-' I .
Electric potential difference and electromotive force (emf) (statvoltwork = 1 erg) .-Change of potential is proportional to the work done per unit
of electricity in producing the change. The dimensional formula is the ratio of
the formulae for work and electrical quantity or [ML2Z'2/M'L;T1K4]or
[MiLiT-'K-'].
Electric surface density of an electrical distribution at any point on a surface is the quantity of electricity per unit area. The dimensional formula is the

ratio of the formulae for quantity of electricity and for area or [ M'L-' T ' K ' ] .
Quantity of electricity has the dimensional formula [ M' LZT' K ' ] , as
shown above.
Resistance is the reciprocal of conductance. The dimensional formula is
EL-'TK-'].
Resistivity is the reciprocal of conductivity. The dimensional formula is
[ TK-'1 .
Specific inductive capacity is the ratio of the inductive capacity of the
substance to that of a standard substtnce and therefore is a number.
Exs.-Find the factor for converting quantity of electricity expressed in ft-grain-sec
units to the same expressed in cgs units. The formula is Im*lgt-'k'], in which m=0.0648,
1 = 30.48, t = 1, k = 1 ; the factor is 0.06483 X 30.481, or 42.8.
Find the factor reauired to convert electric ootential from mm-mp-sec units to CPS
units. The formula is [ m ' l * t - l / d ] ,in which m =b.OOl, 1 = 0.1, t = 1, k-= 1 ; the factor is
0.001, x 0.14, or 0.01.
Find the factor required to convert electrostatic capacity from ft-grain-sec and specificinductive capacity 6 units to cgs units. The formula is [Ikl in which I = 30.48, k = 6;
the factor is 30.48 X 6 , or 182.88.
Y

SMITHSONIAN PHYSICAL TABLES


12
ELECTROMAGNETIC SYSTEM

Many of the magnetic quantities are analogues of certain electric quantities.
The dimensions of such quantities in the electromagnetic system differ from
those of the corresponding electrostatic quantities in the electrostatic system
only in the substitution of permeability p for K.
Conductance is the reciprocal of resistance, and the dimensional formula is

[L-'Tp-11.
Conductivity is the quantity of electricity transmitted per unit area per unit
potential gradient per unit of time. The dimensional formula is [M'L'p-'/
L2(MfLgT-2p.1/L)
TI or [L-*Tp-'].
Current, I (abampere-unit magnetic field, Y = 1 cm), flowing in circle,
radius r, creates magnetic field at its center, 2 ~ l / r .Dimensional formula is
product of formulae for magnetic field intensity and length or [M'L'Fp-'I.
Electric field intensity is the ratio of electric potential or electroinotive
force and length. The dimensional formula is [M'L*T L p ' ] .
E le ctric potential, or electromotive force (emf) (abvolt-work- 1 erg),
as in the electrostatic system, is the ratio of work to quantity of electricity.
The dimensional formula is [ML2T-'/M'L'p-'] or [M'LI T ' p ' ] .
Electrostatic capacity is the ratio of quantity of electricity to difference of
potential. The dimensional formula is [ L-'T2p-'].
I n t e n s i t y of magnetization ( I ) of any portion of a magnetized body is
the ratio of the magnetic moinent of that portion and its volume. The dimensional formula is [MfLgT-1pL1/L3]
or [M'L-'?"'p*].
Magnetic field str e n g t h , magnetic i n t e n s i t y or magnetizing f o r c e ( I )
is the ratio of the force on a magnetic pole placed at the point and the magnetic
pole strength. The dimensional formula is therefore the ratio of the formulae
for a force and magnetic quantity, or [MLT2/M'LzT-'p']or [M*L-'T-'p-*].
Magnetic flux (a) characterizes the magnetized state of a magnetic circuit.
Through a surface enclosing a magnetic pole it is proportional to the magnetic
pole strength. The dimensional formula is that for magnetic pole strength.
Magnetic induction ( B ) is the magnetic flux per unit of area taken perpendicular to the direction of the magnetic flux. The dimensional formula is
[ M'Lz T-'p4/L2]or [M'L -*T-'p'].
Magnetic moment ( M ) is the product of the pole strength by the length of
the magnet. The dimensional formula is [M'LzT'lp.l].
Magnetic pole s t r e n g t h or q u a n t i t y of magnetism

been shown to have the dimensional formula [M'L;T-'p'].

(11%)

has already

Magnetic potential or magnetomotive force at a point is measured by
the work which is required to bring unit quantity of positive magnetism from
zero potential to the point. The dimensional formula is the ratio of the formulae
for work and magnetic quantity [ M L 2 T 2 / X i L ~ T - ' por
* ][M'L'T-'p-*].
Magnetic reluctance is the ratio of magnetic potential difference to magnetic flux. The dimensional formula is [ L ? p - l ] .
SMITHSONIAN PHYSICAL TABLES


Magnetic susceptibility ( K ) is the ratio of intensity of magnetization
produced and the intensity of the magnetic field producing it. The dimensional
formula is [M'L-'T-'p'/M'L-'T-' P 1 or [PI.

-'

Mutual inductance of two circuits is the electromotive force produced in
one per unit rate of variation of the current in the other. The dimensional
formula is the same as for self-inductance.
Peltier effect, coefficient of, is measured by the ratio of the quantit,ppf
heat and quantity of electricity. The diinensional formula is [ML2T2/M1L p '1
or [M*L~T-'p*],
the same as for electromotive force.
Q u a n t i t y of electricity is the product of the current and time. The diniensional formula is [M'L1p-+].
Resistance of a conductor is the ratio of the difference of potential between its ends and the constant current flowing. The dimensional formula is

[ll,f1L T-?p1/M4L1T-1p -& ] or [ L T - l p ] .
Resistivity is the reciprocal of conductivity as just defined. The dimensional formula is [ L 2 T 1 p ] .
Self-inductance is for any circuit the electromotive force produced in it by
unit rate of variation of the current through it. The dimensional formula is
the product of the formulae for electromotive force and time divided by that
for current or [ M 1 L 8 T 2 p 1 ~ T ~ M ' L ' T - 1 p - or
1] [ L p ] .
Thermoelectric power is measured by the ratio of electromotive force and
temperature. The dimensional formula is [ M'L2T-'pW1].
Exs.-Find the factor required to convert intensity of magnetic field from ft-grain-min
units to cgs units. The formula is [ m ~ / - ~ f - l p;&~n
l = 0.0645, 1 = 30.48, t = 60, and p = 1 ;
the factor is 0.0648: X 30.45-:, or 0.046108.
How many cgs units of magnetic moment make one ft-grain-sec unit of the same quantity? The formula is [ m i l t-'p!I ; 1% = 0.0648. 1 = 30.48, f = 1, and p = 1 ; the number
is 0.06481 x 30.48a, or 1305.6,
If the intensity of magnetization of a steel bar is 700 in cgs units, what will it be in
mm-mg-sec units? The formula is [ ? t z + l ~ f - * p; *m
] = 1000, 1 = 10, t = 1, p = 1 ; the intensity is 700 x 1000' X ,lo', or 70000.
Find the factor required to convert current from cgs units to earth-quadrant-lO-=
gram-sec units. The formula is [ ~ n * l + t - ' p - ;~ Inz = lo", 1 = lo-@,p = 1 ; the factor is
10V x lo-!, or 10.
Find the factor required to convert resistance expressed in cgs units into the same expressed in earth-quadrant-10"' gram-sec units. The formula is [ I t P p l ; I = lo-', t = 1,
p = 1 ; the factor is lo-'.
TABLE 3.-FUNDAMENTAL

Part 1.-Selection

STANDARDS

of fundamental quantities

The choice of the nature of the fundamental quantities already made does
not sufficiently define the system for measurements. Some definite unit or
arbitrarily chosen standard must next be taken for each of the fundamental
quantities. This fundamental standard should hzve the qualities of permanence, reproducibility, and availability and be suitable for accurate measures.
Once chosen and made it is called the primary standard and is generally kept
at some central bureau-for
instance, the International Bureau of Weights
and Measures at Scvres, France. A primary standard may also be chosen and
made for derived units (e.g., the new absolute (1945) ohm standard.), when
it is simply a standard closely representing the unit and accepted for practieal
SMITHSONIAN PHYSICAL TABLES


14
purposes, its value having been fixed by certain measuring processes. Secondary or reference standards are accurately compared copies, not necessarily
duplicates, of the primaries for use in the work-of standardizing laboratories
and the production of working standards for everyday use.

Standard of length.-The primary standard of length which now almost
universally serves as the basis for physical measurements is the meter. I t is
defined as the distance between two lines at 0" C on a platinum-iridium bar
deposited at the International Eureau of Weights and Measures. This bar is
known as the International Prototype Meter, and its length was derived from
the ''metre des Archives," which was made by Eorda. Borda, Delambre,
Laplace, and others, acting as a committee of the French Academy, recommended that the standard unit of length should be the ten-millionth part of the
length, from the equator to the pole, of the meridian passing through Paris. In
1795 the French Republic passed a decree making this the legal standard of
length, and an arc of the meridian extending from Dunkirk to Barcelona was
measured by Delambre and Mechain for the purpose of realizing the standard.

From the results of that measurement the meter bar was made by Corda. The
meter is now defined as above and not in terms of the meridian length ; hence,
subsequent measures of the length of the meridian have not affected the length
of the meter.
S t a n d a r d of mass.-The primary standard of mass now almost universally
used as the basis for physical measurements is the kilogram. It is defined as
the mass of a certain piece of platinum-iridium deposited at the International
Bureau of Weights and Measures. This standard is known as the International
Prototype Kilogram. Its mass is equal to that of the older standard, the "kilogram des Archives," made by Borda and intended to have the same mass as a
cubic decimeter of distilled water at the temperature of 4" C.
Copies of the International Prototype Meter and Kilogram are possessed by
the various governments and are called National Prototypes.
unit of time universally used is the mean solar
S t a n d a r d of time.-The
second, or the 86400th part of the mean solar day. It is based on the average
time of one rotation of the earth on its axis relatively to the sun as a point of
reference= 1.002 737 91 sidereal second.
S t a n d a r d of temperature.-The standard scale of temperature, adopted by
the International Committee of Weights and Measures ( 1887), depends on
the constant-volume hydrogen thermometer. The hydrogen is taken at an
initial pressure at 0" C of 1 meter of mercury, 0" C, sea-level at latitude 45".
The scale is defined by designating the temperature of melting ice as 0" and of
condensing steam as 100" under standard atmospheric pressure.
Thermodynamic (Kelvin) Scale (Centigrade degrees).-Such
a scale
independent of the properties of any particular substance, and called the
thermodynamic, or absolute scale, was proposed in 1848 by Lord Kelvin. The
temperature is proportional to the average kinetic energy per molecule of a
perfect gas.

International temperature scale.-See

Table 37.

Numerically different systems of units.-The
fundamental physical
quantities which form the basis of a system for measurements have been chosen
and the fundamental standards selected and made. Custom has not however
SMITHSONIAN PHYSICAL TABLES


15
generally used these standards for the measurement of the magnitudes of
quantities but rather multiples or submultiples of them. For instance, for very
small quantities the niicron ( p ) or one-millionth of a meter is often used. The
following table gives some of the systems proposed, all built upon the fundamental standards aIready described. The centimeter-gram-second (cni-g-sec o r
cgs) system proposed by Kelvin is the only one generally accepted.
proposed systems o f units

Part 2.-Some

Length . . . . .
Mass . .. ....
Time

... . . ..

Giorgi

Weber

and
Gauss

Kelvin

MKS

France
1914

B. A.
Corn.,

Practical

( R . A.
Corn.,

ces

Moon
1891

(Prim.
Stds.)

nim
mg

cm

R

dm
Kg

m
Kg

m

m

lO'cm

loeg

g

lo-" g

lO'cm
lo-' g

sec

sec

sec

sec

sec

sec

sec

S

1863

1873)

Strout
1891

S

10

Further, the choice of a set of fundamental physical quantities to form the
basis of a system does not necessarily determine how that system shall be used
in measurements. In fact, upon any sufficient set of fundamental quantities, a
great many different systems of units may be built. The electrostatic and electromagnetic systems are really systems of electric quantities rather than units.
They were based upon the relationships F = QQ'/Kr' and 112712'/p~~,respectively. Systems of units built upon a chosen set of fundamental physical quantities may differ in two ways: ( 1 ) the units chosen for the fundamental
quantities may be different ; (2) the defining equations by which the system is
built may be different.
The electrostatic system generally used is based on the centimeter, gram,
second, and dielectric constant of a vacuum. Other systems have appeared,
differing from this in the first way-for instance using the foot, grain, and

second in place of the centimeter, gram, and second. A system differing from
it in the second way is that of Heaviside which introduces the factor 4x at
different places than is usual in the equations. There are similarly several
systems of electromagnetic units in use.
Gaussian systems.-"The
complexity of the interrelations of tlie units is
increased by the fact that not one of the systems is used as a whole, consistently
for all electromagnetic quantities. The 'systems' at present used are therefore
combinations of certain of the systems of units."
Some writers on the theory of electricity prefer to use what is called a
Gaussian system, a combination of electrostatic units for purely electrical quantities and electromagnetic units for magnetic quantities. There are two such
Gaussian systems in vogue-one a combination of cgs electrostatic and cgs electromagnetic systems, and the other a combination of the two corresponding
Heaviside systems.
1Vhen a Gaussian system is used, caution is necessary when an equation
contains both electric and magnetic quantities. A factor expressing tlie ratio
between the electrostatic and electromagnetic units of one of the quantities
has to be introduced. This factor is the first or second power of c, the number
8 Circular 60 of the National Bureau of Standards, Electric Units and Standards, 1916.
The subsequent matter in this introduction is based upon this circular.
For example, A. G. Webster, Theory of electricity and magnetism, 1897; J. H. Jeans,
Electricity and magnetism, 1911 ; H. A. Lorentz, The theory of electrons, 1909; and
0. W. Richardson, T h e electron theory of matter, 1914.

SMlTHSONIAN PHYSICAL TABLES


16
of electrostatic units of electric charge in one electromagnetic unit of the same.
There is sometimes a question as to whether electric current is to be expressed
in electrostatic or electromagnetic units, since it has both electric and magnetic

attributes. I t is usually expressed in electrostatic units in the Gaussian system.
It may be observed from the dimensions of K given in Table 2, part 3, that
[ I / K p ]= [ L 2 / T 2 ]which has the dimensions of a square of a velocity. This
velocity was found experimentally to be equal to that of light, when K and p
were expressed in the same system of units. Maxwell proved theoretically that
l/V/Kp is the velocity of any electromagnetic wave. This was subsequently
proved experimentally. When a Gaussian system is used, this equation becomes
c / V K i = z * . For the ether K = 1 in electrostatic units and p= 1 in electromagnetic units. Hence c=v for the ether, or the velocity of an electromagnetic
wave in the ether is equal to the ratio of the cgs electromagnetic to the cgs
electrostatic unit of electric charge. This constant c is of primary importance
in electrical theory. Its most probable value is 2.99776 x 1O’O centimeters per
second.
Part 3.-Electrical

and magnetic units

Absolute (“practical”) electromagnetic system (1948).-This
electromagnetic system is based upon the units of lo9 cm,
g, the sec and p of
the ether. The principal quantities are the resistance unit, the ohm= lo8 emu
units; the current unit, the ampere= lo-’ emu units; and the electromotive
force unit, the volt = lo8 emu units. (See Table 6.)

The International electric units.-The
units used before January 1,
1948, in practical electrical measurements, however, were the “International
Units.” They were derived from the “practical” system just described, or as
the latter is sometimes called, the “absolute” system. These international units
were based upon certain concrete standards that were defined and described.
With such standards electrical comparisons can be more accurately and readily

made than could absolute measurements in terms of the fundamental units.
Two electric units, the international ohm and the international ampere, were
chosen and made as nearly equal as possible to the ohm and ampere of the
“practical” or “absolute” systeni.1°
Q U A N T I T Y O F ELECTRICITY

The unit of quantity of electricity is the coulomb. The faraday is the
quantity of electricity necessary to liberate 1 gram equivalent in electrolysis.
It is equivalent to 96,488 absolute coulombs (Birge).
Standards.-There are no standards of electric quantity. The silver voltameter may be used for its measurement since under ideal conditions the mass
of metal deposited is proportional to the aiiiount of electricity which has flowed.
CAPACITY

The unit used for capacity is the microfarad or the one-millionth of the farad,
which is the capacity of a condenser that is charged to a potential of 1 volt by
1 coulomb of electricity. Capacities are commonly measured by comparison
with standard capacities. The values of the standards are determined by
1OThere was, however, some slight error in these values that had to be taken into
account for accurate work. (See Table 5.)
SMITHSONIAN PHYSICAL TABLES


17
measurement in terms of resistance and tiiiie. T h e standard is some form of
condenser consisting of two sets of metal plates separated by a dielectric.
T h e condenser should be surrounded by a metal shield connected to one set
of plates rendering the capacity independent of the surroundings. A n ideal
condenser would have a constant capacity under all circumstances, with zero
resistance in its leads and plates, and no absorption in the dielectric. Actual
condensers vary with tlie temperature, atmospheric pressure, and the voltage,

frequency, and time of charge and discharge. A well-constructed air condenser with heavy metal plates and suitable insulating supports is practically
free from these effects and is used as a standard of capacity.
Practically, air-condenser plates must be separated by 1 mrn or more and so
cannot be of great capacity. T h e more the capacity is increased by approaching
the plates, the less the mechanical stability and the less constant the capacity.
Condensers of great capacity use solid dielectrics, preferably mica sheets with
conducting plates of tinfoil. A t constant temperature the best mica condensers
are excellent standards. The dielecti ic absorption is sinall but not quite zero,
SO that tlie capacity of these stantlards found varies with different methods of
measurement, so for accurate results care must be taken.
INDUCTANCE

T h e henry, the unit of self-inductance and also the unit of mutual inductance,
is the inductance in a circuit when the electromotive force induced i n this
circuit is 1 volt, while the inducing current varies at the rate of 1 ampere per
second.

Inductance standards.-Inductance
standards are measured in international units in terms of resistance and time or resistance and capacity by alternate-current bridge methods. Inductances calculated froni dimensions are in
absolute electroniagnetic units. T h e ratio of the international to the absolute
henry is the same as the ratio of tlie corresponding ohms.
Since inductance is measured i n terms of capacity and resistance by the
Iiridge method ahout as siinply and as conveniently as by comparison with
standard inductances, it is not necessary to maintain standard inductances.
They are however of value i n magnetic, ~lternating-current, antl absolute
electrical measurenients. A standard inductance is a circuit so wound that
when used i n a circuit it adds a definite ainount of inductance. I t must have
either such a form o r so great an inductance that the mutual inductance of tlie
rest of the circuit upon it may he negligible. I t usually is a wire coil wound all
in tlie saiiie direction to make sel f-induction a iiiaxiniuiii. X standard. tlie inductance of which may be calculated from its dimensions, should be a single

layer coil of very simple geometrical form. Stantlards of very siiiall inductance,
calculable from their tliiiiensions, are of soiiie simple device, such as a pair of
parallel wires or a single turn of wire. With such standards great care must
be used that tlie mutual inductance upon them of tlie leads and other parts of
tlie circuit is negligil)le. Any intluctance standard should be separated by long
leads from the measuring bridge or other apparatus. It must be wound so that
the distributed capacity between its turns is neg1igil)le ; otherwise the apparent
inductance will vary with tlie frequency.
POWER A N D ENERGY

Power and energy, although mechanical antl not primarily electrical quantities, are nieasural)le with greater precision I)y electrical methods than in any
SMITHSONIAN PHYSICAL TABLES


18
other way. The watt and the electric units were so chosen in terms of the cgs
units that the product of the current in amperes by the electromotive force in
volts gives the power in watts (for continuous or instantaneous values). The
watt is defined as the energy expended per second by an unvarying electric
current of 1 ampere under an electric pressure of 1 volt.
Standards and measurements.-No standard is maintained for power or
energy. Measurements are always made in electrical practice in terms of some
of the purely electrical quantities represented by standards.
MAGNETIC U N I T S

Cgs units are generally used for magnetic quantities. American practice is
fairly uniform in names for these units : the cgs unit of magnetomotive force
is called the gilbert; magnetic intensity, the oersted; magnetic induction, the
gauss; magnetic flux, the waxwell, following the definitions of the American
Institute of Electrical Engineers ( 1894).

Oersted, the cgs emu of magnetic intensity exists at a point where a force
of 1 dyne acts upon a unit magnetic pole at that point, i.e., the intensity 1 cm
from a unit magnetic pole.
Maxwell, the cgs emu magnetic flux is the flux through a cm2 normal to a
field a t 1 cm from a unit magnetic pole.
Gauss, the cgs emu of magnetic induction has such a value that if a conductor 1 cm long moves through the field at a velocity of 1 cm/sec, length and
induction mutually perpendicular, the induced emf is 1 abvolt.
Gilbert, the cgs emu of magnetomotive force is a field such that it requires
1 erg of work to bring a unit magnetic pole to the point.
A unit frequently used is the ampere-turn. It is a convenient unit since it
eliminates 4~ in certain calculations. It is derived from the “ampere turn per
cm.” The following table shows the relations between a system built on the
ampere-turn and the ordinary magnetic units.”
11

Dellinger, International system of electric and magnetic units, Nat. Bur. Standards

Bull., vol. 13, p. 599, 1916.
P a r t 4.-The

ordinary and the ampere-turn magnetic units
Ordinary
magnetic
units

Quantity

Magnetomotive force ....... 3
Magnetizing force .......... H

+

Magnetic flux ..............
Magnetic induction ......... B
Permeability ............... p
Reluctance ................. R
Magnetization intensity ..... J
Magnetic susceptibility ...... K
Magnetic pole strength. . . . . . m

SMITHSONIAN PHYSICAL TABLES

{

gilbert
gilbert per
cm
maxwell
maxwell per
cm2 gauss
oersted

Ampere-turn
units

ampere-turn
ampere-turn per
cm
maxwell
maxwell per cm2

{gauss

{

ampere-turn per
maxwell
maxwell per cm‘
maxwell

Ordinary
units in 1
ampereturn unit

4s/10
4s/10

1
1

1
4s/10
1/4s
1/4s

1 /4s