Smithsonian Physical TablesNinth 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 EDITORS 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

TABLE 1.-TEMPERATURE

CONVERSION TABLE

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/

29 to 140A .

150 to a90

900

t o 1650

1660 to 2410L

2420 to 3000

C

-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

-459.4 -450 -440 -430 -420 -410 -400 -390 -380 -370 -360 -350 -340 -330

... ...

r

L

I

F29 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

'C

F150 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

-320-310 -300 -290 -280 -273 -270 -260 -250 -240 -230 -220 -210 -200 -190 -180 -170 -160 -150 -140 -130

... ... ... ... ... ... ... ... ... ... ... ... ... ... ...-459.4 -454 -436 -418 -400 -382 -364 -346 -328 -310-292

...

.,.

-274

-238 -220

-256

-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

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

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 21 2 !27 232 ?38 !43 !49

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

F 900 910 920 930 940 950 960 970 980 990 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

'

'c1327 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 15162420 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

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 10541060

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

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

.

- 78.9 - 84.4 - 67.8 73.3 - 62.2 - 56.7 - 51.1 - 45.6 - 40.0 - 28.9 - 34.4 - 17.8 - 23.3 - 17.2 - 16.1 - 16.7 - 15.6 - 14.4 15.0 - 13.9 - 13.3 - 12.8 - 12.2 - 11.7 - 11.1 - 10.0 - 10.6 - 9.44 - 8.89 - 7.78 - 8.33 - 6.67 722 - 6.11 - 5.56 - 5.00 - 4.44 - 3.89 - 2.78 - 3.33 - 2.22

-

-120 -110 -100 90 - 80 70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 8

-

-

-

9 I011 12 13 14 15 16 17 18 19 20 21

2323 24 25 26 27 28

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

203.0204.8 206.6 208.4 210.2 212.0 230 248 266 284

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 1 377 382 388 393 399 410 416 421 427 432 438 443 449 454

490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690

7007 10 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890Sanveur.

404

460 466471 477

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 3000Interpolation factor#

5018 5036 5054 5072 5090 5108 5126 5144 5162 5180 5198 5216 5234 5252 5270 5288 5306 5324 5342 5360 5378 5396 5414 5432

c

0.561.11 1.67 2.22 2.78 3.33 3.894.44 .. . .

1 2 3 4

56 7 8 9 10

5.00 5.56

F 1.8 3.6 5.4 7.2 9.0 10.8 12.6 14.4 16.2 18.0

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

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

lNTRODUCTIONU 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

2troduces 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 EF 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

3T 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], quantity precisely of the same form as a 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

4mensions 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 and mechanical units4

P a r t 1.-Geometrical

Activity (power).-Time Angle ( 4 j .-The the radian. -4ngstrom.-Unit

rate of doing work; unit, the watt.

ratio of the length of its circular arc to its radius ; unit, of wavelength= meter. (See Table 522.) rate of change of angular velocity.

Angular acceleration

(

a= -

z)

.-The

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 (0C) =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 Cubit = 18inches4*

of circle 1 inch in diameter.

For dimensional formula see Table 30, part 2. Some writers have used this term for 1 dyne/cm2.

SMITHSONIAN PHYSICAL TABLES

5Dalton (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. Foot-pounda1.-The 1 foot. of viscosity. work which will raise 1 pound. body 1 foot high for 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.) cgs gravitation unit of work. mass in grams of a substance numerically equal to Gram-centimeter.-The Gram-molecule.-The its molecular weight. Gravitation constant.-( cm2 g-2.

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

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 Liter.-See Table 32.

(

a= $).-The

rate of change of velocity.

Loschmidt number.-The number of molecules per cm3 of an ideal gas at 0C 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.of an inch.

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

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

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

7Strain.-The mension. Stress.-The tion. deformation produced by a stress divided by the original diforce per unit area of a body that tends to produce a deformameter = 1 angstrom.

Tenth-meter.-lO-l,O

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.-HertUnit85

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 = u ' (Stefan-Boltzmann Law) and that the spectral distribution of the radiaT tion 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, 1F. 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

m An

For dimensional formulas see Table 30, part 2.

easier way to write this exponential term is:

This form will be used hereafter.SMITHSONIAN PHYSICAL TABLES

8There 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

9Kelvin 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 ( lSC) per cm?. L a t e n t heat.-Quantity of matter. Pyron.-A Radiant energy.-Energy of heat required to change the state of a unit mass

unit of radiant intensity = 1 cal cniP inin-l. 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,A 0

as T approaches zero, of the ratio

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

10Part 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 [MLZ 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 ism 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 [ML: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 ~ O cni per sec. It is sometimes forgotten that the 10 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

11ELECTROSTATIC 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-'KiL ) 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 ] , which m =b.OOl, 1 = 0.1, t = 1, k-= 1 ; the factor is in 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

12ELECTROMAGNETIC 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) or [L-*Tp-']. TI 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] [M'L-'?"'p*]. or 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] [M'L -*T-'p']. or 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*], same as for electromotive force. the 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 [ L p ] . 1] 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;& l = 0.0645, 1 = 30.48, t = 60, and p = 1 ; ~n 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 in; ] tensity 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 STANDARDS

Part 1.-Selection

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 practiealSMITHSONIAN PHYSICAL TABLES

14purposes, 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 howeverSMITHSONIAN PHYSICAL TABLES

15generally 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.Part 2.-SomeWeber and Gauss Kelvinces

proposed systems o f unitsGiorgi

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

Moon 1891

(Prim. Stds.)

MKS

France 1914

B. A. Corn.,1863

Practical

( R . A. Corn.,1873)

Strout 1891

nim mg sec

cm R sec

dm KgS S

m Kg sec

mloeg

mg

lo-" gsec

lO'cm

lO'cm lo-' g sec

... . . ..

10

sec

sec

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 number8 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

16of 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 1OO 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 InternationalUnits. 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.1Q 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 by1OThere was, however, some slight error in these values that had to be taken into account for accurate work. (See Table 5.)SMITHSONIAN PHYSICAL TABLES

17measurement 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 anySMITHSONIAN PHYSICAL TABLES

18other 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. StandardsP a r t 4.-The ordinary and the ampere-turn magnetic unitsOrdinary magnetic units Ordinary units in 1 ampereturn unit

Bull., vol. 13, p. 599, 1916.

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

Quantity

Ampere-turn units

+

{

gilbert gilbert per cm maxwell maxwell per cm2 gauss oersted

ampere-turn ampere-turn per cm maxwell maxwell per cm2 {gauss

4s/104s/10

1 1

{

ampere-turn per maxwell maxwell per cm maxwell

1 4s/101/4s 1/4s

1 /4s

SMITHSONIAN PHYSICAL TABLES

19T A B L E 4.-THE NEW (1948) S Y S T E M O F E L E C T R I C A L U N I T S 1 2

In pursuance of a decision of the International Committee on Weights and Measures, the National Bureau of Standards introduced, as of January 1, 1948, revised values of the units of electricity. This consummated a movement, initiated in 1927 by the American Institute of Electrical Engineers, asking that the National Bureau of Standards undertake the additional research necessary in order that the absolute ohm and absolute ampere based on the cgs electromagnetic systein and the absolute volt, watt, and other units derived from them could be legalized in place of the international ohm and ampere and their derived units. This work was done, and the magnitude of the old international units in terms of the adopted absolute units is given in Table 5. This means that the electrical units now in use represent, as nearly as it is possible to make them, exact multiples of the cgs emu system, with the numerical relations shown in Table 6. Units of the new systeni will actually be maintained, as were the old international units, by groups of standard resistors and of standard cells, and consequently the change to be made is most simply represented by stating the relative magnitudes of the ohms and of the volts of the two systems. During the period of transition to the new units, in order to avoid any doubt as to the units used in giving precise data, the International Committee on Weights and Measures recomnlended that the abbreviations int. and abs. be used with the names of the electrical units. In a few years this will be unnecessary, except when referring to old data. The international units were intended to be exact multiples of the units of the centimeter-gram-second electromagnetic system, but to facilitate their reproduction, the ampere, the ohm, and the volt were defined by reference to three physical standards, namely (1) the silver voltameter, ( 2 ) a specified column of mercury, and (3) the Clark standard cell. This procedure was recommended by the International Electrical Congress of 1893 in Chicago and was incorporated in an Act of Congress of July 12, 1894. However, modifications of the international systeni were found to be necessary or expedient for several reasons. The original proposals were not sufficiently specific to give the precision of values that soon came to be required, and the independent definitions of three units brought the system into confiict with the customary simple form of Ohms Law, Z=E/R. Furthermore, with the establishment of national standardizing laboratories in several of the larger countries, other laboratories no longer needed to set up their own primary standards, and facility of reproduction of those standards became less important than the reliability of the units. I n preparation for the expected change in units, laboratories in several countries made absolute measurements of resistance and of current. The results of these measurements and the magnitudes of the international units as maintained in the national laboratories of France, Great Britain, Germany, Japan, the U.S.S.R., and the United States were correlated by periodic comparisons of standard resistors and of standard cells sent to the International Bureau of Weights and Measures. Nearly all the absolute measurements at the National Bureau of Standards were carried out under the direct supervision of Harvey L. Curtis, and the results of such measurements at the Bureau accepted by the International Committee on Weights and Measures at its meeting in Paris in October 1946 are as follows : 1 mean international ohm = 1.00049 absolute ohms 1 mean international volt = 1.00034 absolute volts12Nat. Bur. Standards Circ. C-459, 1947.SMITHSONIAN PHYSICAL TABLES

20The mean international units to which the above equations refer are the averages of units as maintained in the national laboratories of the six countries (France, Germany, Great Britain, Japan, U.S.S.R., and U.S.A.) which took part in this work before the war. The units maintained by the National Bureau of Standards differ from these average units by a few parts in a million, so that the conversion factors for adjusting values of standards in this country will be as follows :1 mean international ohm U.S. = 1.000495absolute ohms 1 mean international volt U.S. = 1.000333 absolute volts

Other electrical units will be changed by amounts shown in Table 5. The factors given should be used in converting values given in international units in National Bureau of Standards certificates to the new absolute system.T A B L E 5.-RELATIVE M A G N I T U D E OF T H E OLD I N T E R N A T I O N A L E L E C T R I C A L U N I f T S A N D THE N E W 1948 A B S O L U T E ELECTRICAL UNITS

1 1 1 1 1 1 1 1 1 1

mean international ohm = 1.00049 absoiute mean international volt = 1.00034 absolute international ohm (U.S.) = 1.000495 absolute international volt (U.S.) = 1.00033 absolute international ampere = 0.999835 absolute = 0.999835 absolute international coulomb = 1.000495 absolute international henry international farad = 0.999505 absolute international watt = 1.000165 absolute = 1.000165 absolute international joule

ohms volts ohms volts ampere coulomb henries farad watts joules

T A B L E 6.-RELATIVE

VALUES O F T H E T H R E E SYSTEMS O F ELECTRICAL UNITSElectromagnetic system emu Electrostatic system esu

Current strength ... Potentialdifference.. Resistance ......... Energy ............ Power ............ Capacitance ....... Inductance ........ Charge

Quantity

Symbol

Absolute unit

I E R W P C L

1 ampere = 1 volt = = 1 ohm 1 joule = 1 watt = 1 farad = 1 henry = 1 coulomb =

abampere abvolts abohms ergs ergs/sec abfarads loQ abhenrieslo-' 10' 10" lo' 10' 10'

= = =-

=

=

=

............

Q

10" abcoulornb =

3 x 10' statampere 1/300 statvolt (1/9) X lo-" statohm 10' ergs 10' ergs/sec 9 X 10" statafarad (1/9) X lo-" statahenry 3 X 10" statcoulomb

'Where 3 occurs it is to be taken as 2.99776 (from velocity of light). Where 9 occurs (not as an exponent), it is the sauare of this number.

SMITHSONIAN PHYSICAL TABLES

T A B L E 7 . 4 O N V E R S I O N F A C T O R S FOR UNITS O F ENERGY-

*Btu

Units

g mass (energy equiv.)

joule

cal

I.T. cal

kw-hr

1 II mass (energy equiv.) 1 jouleI

1 cal 1 I.T. cal t1 Btu

= = = ==

1 kw-hr

1 hp-hr 1 ft-lh (wt.) 1 ftq-lb (u.t.).!in.' = 1 liter-atm = 1 quantum ( A = 5 9 ) = 1 Mev = 1 amu5 =Units

= = =

1 1.112772 X lo-'' 4.65584 x lo-" 3.65888 X lo-" 1.174019 x lo-" 4.00598 x lo-* 2.98727 X 1.50872 X lo-" 2.17256 x I&" 1.127548 x lo-'* 3.6829 X lo-" 1.78270 10Y 1.66035 X lo-"

x

8.98656 X loz3 1 4.1840 t 4.18674 1.055040 x lo3 t 3.6 x loG 2.681525 x 10' 1.355821 1.952382 X 10' 1.013278 x 10' 3.3096 x i m o jX 1.49208 x lo-''ft-lb (wt.)

2.14784 x 0.239006 1 1.000654 2.52161 X 8.60421 X 6.41617 X 0.324049 46.6630 24.2179 7.91021 X 3.82891 X 3.56616 X

10'

105105

lo-" lo-" lo-"1iter.atm

2.14664 x 10" 0.238849 0.999346 1 2.519% x 10' 8.59858 x 1Iy 6.41197 x lo5 0.323837 46.6325 24.2021 7.90504 x lo-3.82644 x lo-'' 3.56379 x lo-"quantum (A

8.51775 X 10" 0.947831 X lo-' 3.96573 x 10-3 3.96832 x lo-' 1 3.41220 X 10' 2.54448 x lo3 1.285089 X lo-' 0.185OS29 0.09604 16 3,13676 X lo-'? 1.51815 x lo-'' 1.41422 x lo-''

2.4%27 x 10' 2.77778 x lo-' 1.16222 X lo* 1.162983 x lo4 2.93065 x lo-' 1 0.745701 3.76614 X lo-' 5.42328 loJ 2.81466 X lo4 9.19342 x lo-" 3.44998 x 4.14453 x lo-"

x

hphr

f t9-11, (wt.) /in."

= .6p)

Mev

amu

1

g .

1 = 1 = = 1 1 = 1 kw-lir = 1 hp-hr = = 1 ft-lh ( W . ) 1 f N h (wt.)/in.' = 1 liter-atm = 1 quantum(h = . l i p ) = 1 Mev =~~~

mas (energy equiv.) joule cal I.T. c a l t Btu

= 3.34754 x 10'

3.72505 x lo-' 1.558562 x 1.559582X 3.9300s X i0-l 1.341020 1 5.05051 X 10.' 7.27273 x lo4 3.77452 X 1.23286 X lo-" 5.96751 X lo-"

6.62814 x loL3 0.737561 3.08595 3.08797 7.78156 x 10' 2.655218 10 1.98000 .X 10' 1 1.44 x 10' i4.735i 2.44116 x 1.18157 x lo-'' 1.10046 x lo-'"

x

4.60287 x 10" 5.12195 x 10P 2.14302 x lo-' 2.14343 x lo-' 5.40386 1.843902 X 10' 1.3750 X lo' 6.91444 x 1 0.518W6 1.69531 x lo-?' 8.20535 x lo-'' 7.64208 x lo-''

8.86880 x 10" 9.86896 x lo-* 4.12917 X lo-' -1.13187 x lo-' 10.41215 3.55281 x l(r 2.64935 x 10' 1.338054 X lo-' 1.9~797. . I 3.264520 X lo-'' 1.58100 x lo-'" 1.147247 x lo-''~~

2.71503 X lo" 3.02125 X 10'' 1.26109 X 10"' 1.26191 x 10'" 3.18754 x 10" 1.08765 X loz5 8.11062 X 10'' 4.09627 x 10'' 5.89862 2 10"

jIOiij6 j i l o w1 4.84001 X 1 0 4.50776 X 10'

5.60961 X 10" 6.24222 X 10" 2.61175 X 10" 2.61346 X 6.58580 X 10'' 2.24720 X 10"' 1.67574 X lo'$ S.46334 X 10'' 1.21872 6.32519 j i loll 2.06593 x 10' 1 9.31354 X 10'

6.02308 x 101" 6.70232 x 1 P 2.80425 x 10'" 2.80608 x 10" 7.07121 X lo'* 2.41283 x 10'" 1.79926 x 10" 9.0871 1 X 10' 1.30855 10" 6.79131 X 10" 2.21839 x 10-B 1.07371 X lo4 1

x

t Definition of calorie and Rto.

h r l n p t e d from National Burearl of

Standards Taliles

t: . \ s defined for Intermtionnl Steam Tables. P Vnit atnmic weight enerfr; erluivalent.

22

T A B L E 8.-FORMER

ELECTRICAL EQUIVALENTS

*

Abbreviations : int., international ; emu, electromagnetic units ; esu, electrostatic units ; cgs, centimeter-gram-second units. RESISTANCE: 1 international ohm = 1.00051 absolute ohms 1.0001 int. ohms (France, before 1911) 1.00016 Board of Trade units (England, 1903) 1.01358 B. A. units 1.00283 legal ohms of 1884 1.06300 Siemens units 1 absolute ohm = 0.99949 int. ohms 1 oractical emu io8c g S emu 1.11262 X lo- cgs esu CURRENT : 1 international ampere = 0.99995 absolute ampere 1.00084 int. amperes (U. S. before 1911) 1.00130 int. amperes (England, before 1906) 1.00106 int. amperes (England, 190608 ) 1,00010 int. amperes (England, 190910) 1.00032 int. amperes (Germany, before 1911) 1.W2 int. amperes (France, before 1911) 1 absolute ampere= 1.00005 int. amperes 1 practical emu 0.1 cgs emu 2.99776 x lo9 esu: CAPACITY 1 international farad = 0.99949 absolute farad 1 absolute farad= 1.00051 int. farads 1 practical emu 10. cgs emu 8.98776 X 10 cgs esu

1NDUCTANCE 1 international henry = 1.00051 absolute henries 1 absolute henry = 0.99949 int. henrv 1 practical emu log emu 1.11262 X lo- cgs esuA ENERGYN D POWER : (standard gravity = 980.665 cm/sec-) 1 international joule = 1.00041 absolute joules 1 absolute joule= 0.99959 int. joule lo ergs 0.737560 standard foot-pound 0.101972 standard kilocram-meter 0.277778 X kilowakhour

ELECTROMOTIVE: FORCE 1 international volt =

1.00046 absolute volts 1.00084 int. volts (U. S. before 1911) 1.00130 int. volts (England, before 1906) 1.00106 int. volts (England, 1906-08) 1.00010 int. volts (England, 1909-10) 1.00032 int. volts (Germany, before 1911) 1.00032 int. volts (France, before 1911) 1 absolute volt = 0.99954 int. volt 1 practical emu lo8 cgs emu 0.00333560 cgs esu

: RESISTIVITY 1 ohm-cm = 0.393700 ohm-inch = 10,000 ohm (meter, mmz) = 12,732.4 ohm (meter, mm) = 393,700 niicrohm-inch = 1,000,000 microhm-cm =6,015,290 ohm (mil, foot) 1 ohm (meter, gram) = 5710.0 ohm (mile, Dound)QC MAGNETIC A N T I T I E S : 1 int. gilbert = 0.99995absolu.tegilbert 1 absolute gilbert = 1.00005 int. gilberts 1 int. maxwell = 1.00046 absolute maxwells 1 absolute maxwell = 0.99954 int. maxwell 1 gilbert = 0.7958 ampere-turn 1 gilbert per cm = 0.7958 ampere-turn per cm = 2.021 ampere-turns per inch = 1 line 1 maxwell = 10. volt-second 1 maxwellpercmZ= 6.452 maxwells per in?

OF QUANTITY ELECTRICITY : (Same as current equivalents.) 1 international coulomb = 1/3600 ampere-hour 1/96494 faraday

and

*This table is now superseded by the adoption of the new system of electrical units in January 1948IS

given for reference only.

SMITHSONIAN PHYSICAL TABLES

T A B L E S 9-15.-SOME

MATHEMATICAL T A B L E SAND INTEGRALS

23

T A B L E 9.-DERIVATIVES

d ax

=a d r

J.r"dr

J$Jc'dx

- X"" --+ ,~ = logx

, unless

tc

=-I

J r"'dsJ.r"'Pdx

d c= d rn= d 1og.rti

= r= d.r = o ra'dx1 = 7d.r

Slog x d xJli

dv

J(a

+ Dx)"dx + .r2)-'dx1 n + r - _ log __ 2a a-x

.rr

= .r' ( 1

+ log, x ) d.rJ(n'

d sin xti

= cos .r dx = - sin x d x = secz x dx = - csc'x d x = tan x sec x d x- - cot x ' csc x d x = ( 1 - x p ) - *d x -- (1-x2)-*dx = (1 x*)-'dx = - (1 + x l ) - ' d x = c (2 1)-* dx ' - - A = * (x z - 1) -4 dx = cosh x dx = sinh x d x = sech' .r d r - - csch'x dx - - sech .r tanh x d.r - - csch x.coth x d s -

cos .r

J(a' - x')-'dx

d tan .r d cot .r d sec x d csc x d sin-' .r d cos-' x d tan-' x

J(a' - x')-+dx

+

= & (a' & x z ) * - - $ cos x sin x Jsin' x d x 1.= sin x cos x fx Jcos' x d x = 1 sin'x .[sin x cos x d x J(sin x cos x)-'dx = log tan x Itan x d x - -logcosxJx(a' -C x')-fdx

+

+

d cot-' x d sec-' x d csc-' x d sinh x d cosh x d tanh x d coth x d sech .r d csch .r

Jtan' x d x Jcot x d x .fcot' x d x Jcsc x d x Jx sin x d x Jx cos x d x Jtanh x d x Jcoth x d.r Jsech x d x .fcsch x dx.[.r sinh x d x Jscosh x dx Jsinh' x dx .fcoshax dx

= tan .r - x = !og sin x = - cot x - x = log tan i x = sin -p - x cos x = log cosh I = log sinh x

= cos .r + .r sin x

= 2 tan-'cz = ,9d 11

d sinh-lx = ( 2

+ 1 ) - * d.r

= log tanh 3 2 = r cosh x - sinh x = x sinh x - cosh x = $ (sinh x cosh x - x )

d cash-' x = ( x z - 1) -4 d.r d t a n h - ' x = (1 - x Z ) - ' d x d coth-'x = (1 - x 2 ) - ' d x d sech-' x = - .r-' ( 1 - x ' ) -4 d.r d csch-' .r = (x' I ) - * d.r

+

Jsinh

. T

= (sinh x cosh r cosh x d x = icosh ( 2 x )

+x)

SM!THSON!AN

PHYSICAL. TABLES

24(x

T A B L E 10.-MATHEMATICAL

SERIES

+y)"=

x"

+ fx"-'y

$ .

~

n ( n 1) 2!

-

xn-syp

+.. .

n ( n - 1 ) . .. ( n - mm!

+ 12_ X"-

ym

+ .. .

(' Y

.346 .129 .1420

+.Go55 --.0001

-

-

.E}

-.0013 -.0010

-

-.00017-.0012

:%I

-.0001

-

...

:El +.ON32 :3-.00069 -.0001 +.Om23-

:%> : %- 6 : +,0001 I-

1

-

t

Copper: 100.197"C, kr = 1.043; 100-268",0.969; 100-370', 0.931; 100-541,0.902. Iron: 100-727"C, t = 0.202; 100-912",0.184; 100-124S0, k 0.191.

SMITHSONIAN PHYSICAL TABLES

T A B L E 135.-THERMAL

C O N D U C T I V I T Y OF I N S U L A T I N G

139 M A T E R I A L S .*ConductivityA

Air, 76 cmHg ... ................. Ashzstos w:d . . . . . . . .. .. .. . . ...

Material

Density g/cm3

t"C

joule/ (cm'sec "C/ cm)

cal/ (cmZsec "C/ cm)

.................... .................... with 85 percent M g O . . . . . . Br;jck, very porous, dry ..........."

.

vol. . . . . . . . . . . . . . . . ........... Calorox, fluffy minera matter. . . . Celluloid, white . . . . . . .... ... . ... Cement mortar . . . . . . .. ......... Chalk . . . . . . . . . . . . . . . ........... Charcoal . . . . . . . . . . . . . . . . . . . . . . . Coke dust ........... ........... Concrete . . . . . . . . . . . . ........... Cork . . . . . . . . . . . . . . . . ...........

machine-made, dry . . . . . . . . " moist, 1.2%

.00129 .40 .40 .40 .3 .71 .54 ,064 1.4 2.0 .18 1.0 1.6 .OS . . . .05 .35 .35 .08 .08 .08 .08.20

- 100

0

+ 10030 20 0 50 30 30 90 20 20 0 0 100 0 100 - 150 0 150 30

0

.00023 .00068 .00090 .00101 .00075 .00174 .00038 .OW96 .00032 .ow21 ,0055 .0092 .00055 .0015.008

.OW055 .000162 .000215 .00024 .000179 .00042 .000091 .00023 .000076 .000050 .0013 .0022 .00013 .00036 .002 .000076 .000098 .000146 .000189 .000091 .OW133 .00018 .00010.00022 .00021

Cotton, tightly p:cked.

............................ ............................ ............................

Cotton wool, tightly packed.. . . . . . . Diatomite (binders may increase Diat;mite, dip0 . . . . . . . . . .. . . . . . . . Ehonite . . . . . . . . . . . . . . Fzlt,"

.............

.. . .. . . . ... .............

+

.00032 .00041 .00061 .00079 .00038 ,00056 .00076 .00042 .00052 .OW94 .OW86 ,00157 .00138 .00157 .00160 .00047 .00036 .00063.00052

100%)

........................

.20

,'

hair . . . . . . . . . . . . . . . . . . . . . . . wool . . . . . . . . . . . . . . . . . . . . . . "

......................... ......................... flax fibers.. . . . . . ...

1.19 1.19 1.19.18

.so .so

. . . . . . . . . . . . . . . . . . . . . . 2.59 2.59 ..................... w;ol . . . . . . . . . . . . . . . . . . . . . . .22 ...................... .22 ...................... .22 ' .22 ...................... GraEhite, 100 m:sh.. .... ......... .48 40 ............... .42 20 to 40 mesh. .. . . . . . . . .70 Horsehair, compressed . . . . . . . . . . . .17 Ice . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .92 Lea$er, chamois . . . . . . . . . . . . . . . . cowhide . . . . . . . . . . . . . .. . ' sole . . . . . . . .. . . . . . . .. . . . 1.o Linen ........................... Linoleum, cork . . . . . . . . . . . .. . . . . . .54 Mica, average ...................s$a'I

Flannel . ................... Fuller's earth . . . . . . . . . . . . . . . . . . . . G l y , lead . ....... ..............

.......................

.

.

.27 .15 .33 .53

0 400 0 400 - 190 - 78 0 30 30 40 30

.00012

.00037

.

30 15 20 100 50 100 200 300 40 40 40 20 0 85 85 30 20 20 50

.00101 .0060 .0072 ,0076 .00042 .00050 .00065 .00081 .0018 .0038 .0129 ,00051 .022 .00063 ,00176 .0016 .OW86 .00080 .0050

.00038 .00038 .00011 .000086 .000151 .000124 .000023 .00024 ,00143 .00172 ,00182 .000100 .000120 .000155 .000195 .00044 .00093,0031

.0w33

.000122 .0053 .OW151 .000421 .00038 .00021 .000191 .0012

Compiled from the International Critical Tables, which see for more complete data.

(continued)

SMITHSONIAN PHYSICAL TABLES

140T A B L E 135.-THERMAL C O N D U C T I V I T Y OF I N S U L A T I N G M A T E R I A L S (continued)Conductivity Material Densitydcm3t"C

. .. . . . . . .. . . .. . ... . . . . . . Mi;eral wzol . . . . . . . . . . . . . . . . . . . . .15 . . .. ... . . . . . . . . . . . . . . 0 3 Paper, rice . . .. . . . ... .. . .. .. . .. . . blotting . . . . . . . . . . . . . . . . . . . Paraffin wax . . . . . . . . . . . . . . . . . . . . .89 Py:t, dry . . . . . . . . . . . . . . . . . . .. . . . . . 9 1 blocks . . . . . . . . . . . . . . . .. . . . . .84 Poreclain . . . . . . . . . . . . . . . . . . . . , . . Rubber, rigid sponge, hard ........ . 9 0 sponge, vulcanized . . . . . . . .22 cornrnercial, 40% rukber . . .Micanite" "

(cmP sec "C/ cm)

joule/

(cm2 sec "C/ cm)

cal/

3 0 30 40 20 30 3 0 20 90 2 5 2 0 25 2 5 3 0

.0021.0042 .OW42 .00046 .00063 .0023 .00052 .0017 .0104 .00037 ,00054 .0028 .0016.00060

.00052

.05000 .00010 .00010 .00012 .OQO11 .00015.00055

92%

...

. .. . . ..... Snow . . . . . . . . . . . . . . . . . . . . . .. . . . , Steel wool . .. . . . . . . .. . .. . .. . . . .. . . .. . . . .. .. . . . .. .. .. . . . Wool, p