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
Ptcrred 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 Ampereturn 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 915)
Treatment of Experimental Data (Tables 1625)
General Physical Constants (Tables 2628)
Common Units of Measurement (Tables 2936)
Constants for Temperature Measurement (Tables 3751)
The Blackbody and its Radiant Energy (Tables 5257)
Photometry (Tables 5877)
Emissivities of a Number of Materials (Tables 7884)
Characteristics of Some Lightsource Materials, and Some Light
Sources (Tables 85102)
Cooling by Radiation and Convection (Tables 103110)
Temperature Characteristics of Materials (Tables 111125)
Changes in Freezing and Boiling Points (Tables 126129)
Heat Flow and Thermal Conductivity (Tables 130141)
Thermal Expansion (Tables 142146)
Specific Heat (Tables 147158)
Latent Heat (Tables 159164)
Thermal Properties of Saturated Vapors (Tables 165170)
Heats of Combustion (Tables 171183)
Physical and Mechanical Properties of Materials (Tables 184209)
Characteristics of Some Building Materials (Tables 210217)
i
ii
iii
1
1
2
4
4
7
10
13
13
15
16
18
19
20
20
21
22
2336
3745
4655
5669
7078
7986
8797
98101
102111
112116
117130
131135
136144
145154
155164
165167
168178
179186
187228
229231
Physical Properties of Leather (Tables 218223)
Values of Physical Constants of Different Rubbers (Tables 224229)
Characteristics of Plastics (Tables 233236)
Properties of Fibers (Tables 233236)
Properties of Woods (Tables 237240)
Temperature, Pressure, Volume, and Weight Relations of Gases and
Vapors (Tables 241253)
Thermal Properties of Gases (Tables 254260)
The JouleThomson Effect in Fluids (Tables 261267)
Compressibility (Tables 268280)
Densities (Tables 281295)
Velocity of Sound (Tables 296300)
Acoustics (Tables 301310A)
Viscosity of Fluids and Solids (Tables 311338)
Aeronautics (Tables 339346A)
Diffusion, Solubility, Surface Tension, and Vapor Pressure
(Tables 347369)
Various Electrical Characteristics of Materials (Tables 370406)
Electrolytics Conduction (Tables 407415)
Electrical and Mechanical Characteristics of Wire (Tables 416428)
Some Characteristics of Dielectrics (Tables 429452)
Radio Propagation Data (Tables 453465)
Magnetic Properties of Materials (Tables 466494)
Geomagnetism (Tables 495512)
Magnetooptic Effects (Tables 513521)
Optical Glass and Optical Crystals (Tables 522555)
Transmission of Radiation (Tables 556573)
Reflection and Absorption of Radiation (Tables 574592)
Rotation of Plane of Polarized Light (Tables 593597)
Media for Determinations of Refractive Indices with the Microscope
(Tables 598601)
Photography (Tables 602609)
Standard Wavelengths and Series Relations in Atomic Spectra
(Tables 610624)
Molecular Constants of Diatomic Molecules (Tables 625625a)
The Atmosphere (Tables 626630)
Densities and Humidities of Moist Air (Tables 631640)
The Barometer (Tables 641648)
Atmospheric Electricity (Tables 649653)
Atomic and Molecular Data (Tables 654659)
Abundance of Elements (Tables 660668)
Colloids (Tables 669682)
Electron Emission (Tables 683689)
Kinetic Theory of Gases (Tables 690696)
232233
234238
239240
241245
246258
259267
268277
278281
282290
291305
306308
309317
318336
337353
354374
375396
397403
404420
421433
434450
451467
468502
503508
509534
535548
549556
557560
561
562567
568585
586591
592595
596605
606613
614617
618624
625629
630634
635637
638624
Atomic and Molecular Dimensions (Tables 697712)
Nuclear Physics (Tables 713730)
Radioactivity (Tables 731758)
Xrays (Tables 759784)
Fission (Tables 785793)
Cosmic Rays (Tables 794801)
Gravitation (Tables 802807)
Solar Radiation (Tables 808824)
Astronomy and Astrophysics (Tables 825884)
Oceanography (Tables 885899)
The Earth's Rotation: Its Variation (Table 900)
General Conversion Factors (Table 901)
Index
643650
651671
672691
692705
706709
710713
714718
719727
728771
772779
780
781785
787
lNTRODUCTION
U N I T S OF MEASUREMENT
The quantitative measure of anything is expressed by two factorsone,
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 considerationslength, surface, etc.lead to the need of a length ;
second, kinematical considerationsvelocity,
acceleration, etc.introduce
time ; third, mechanicstreating of masses instead of immaterial pointsinSMITHSONIAN 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 quantitiesthe
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 unitsnamely,
a measure of length, of time, of mass, of permeability o r of the dielectric
constant, and of temperatureit
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 intervaloftime
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 juststated 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 conversionfactor 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