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56 TABLES 29-36.4OMMON UNITS OF MEASUREMENT TABLE 29.-SPELLING AND ABBREVIATIONS OF T H E COMMON UNITS OF WEIGHT AND MEASURE The spelling of the metric units is that adopted by the International Committee on Weights and Measures and given in the law legalizing the metric system in the United States (1866). The use of the same abbreviation for singular and plural is recommended. It is also suggested that only small letters be used for abbreviations except in the case of A for acre, where the use of the capital letter is general. Unit acre are avoirdupois barrel board foot bushel carat, metric centare centigram centiliter centimeter chain cubic centimeter cubic decimeter cubic dekameter cubic foot cubic hectometer cubic inch cubic kilometer cubic meter cubic mile cubic millimeter cubic yard decigram deciliter decimeter decistere dekagram dekaliter dekameter dekastere dram dram, apothecaries' dram, avoirdupois dram, fluid fathom foot firkin furlong gaily grain gram hectare hectogram hectoliter hectometer hogshead hundredweight inch Abbreviation A a av bbl bd ft bu C ca W cl cm ch cm' dm' dkm' ft8 hm' in." km' ma mi' mm' yd' da dl dm ds dkl dkm dks dr dr ap or 3 dr av fl dr fath ft fir fur gal gr g ha hg hl hm hhd in. dka CWt Unit kilogram kiloliter kilometer link liquid liter meter metric ton micron mile milligram milliliter millimeter mi I lei mic roil minim ounce ounce, apothecaries' ounce, avoirdupois ounce, fluid ounce, troy peck pennyweight pint pound pound, apothecaries' pound, avoirdupois pound, troy quart rod scruple, apothecaries' square centimeter square chain square decimeter square dekameter square foot square hectometer square inch square kilometer square meter square mile square millimeter square rod square yard stere ton ton, metric troy yard Abbreviation kn kl km li. liq 1 m t P mi mg ml mm mCc min. or 0.2 oz ap or J oz av fl oz oz t pk dwf r; Ih ap Ih av Ibt qt rd savor 3 cm2 ch' dm2 dkm' ft' hm2 in? km2 m2 miz mm2 rd' yd2 tn t t yd S SYITHSONIAN PHYSICAL TABLES 57 TABLE 30.-DIMENSIONAL EQUATIONS OF FUNDAMENTAL AND DERIVED UNITS Conversion factors.-The dimensional formulas given in this table have many uses. One is to assist in changing a quantity from one system of units to another (see page 2). A simple scheme for transforming an expression from one set of units to another is given in Weniger's text, "Fundamentals of College Physics." Place the known number of the quantity with its units properly given, equal to an unknown number, x, of the same quantity properly expressed in the desired units. Proceed to cancel, treating the units just like algebraic quantities. Suppose it be desired to express 60 meters per second in miles per hour. Write : fiOm - xmi see hr Cancel scc and hr and write 3600 near the larger unit. Cancel m and mi and write 1609.3 near the larger unit. This gives : 1609.3 sec hr 3600 26.82 60 m - x mi - Solving, X = 134, and the desired expression is 134 mi/hr. More complicated expressions are handled in a similar manner. In a heat-flow problem, suppose it becomes necessary to express 15 Btu hr" ftP with a temperature gradient of 1F per ft in terms of cal sec-' cm-' with a gradient of l"C/cm. Write: 15Btu ft = xcal cm hr ft2 F seccm2 T Cancel ft in numerator and denominator, and cin similarly. Remember that 1 Btu is 252 cal, and cancel. A scc goes into 1 hr 3600 times. Cancel cm and ft and write 30.48. Remember that, 9F equal 5C. Solving, x = 0.062. (See Table 2.) If the numeric before the known quantity is unity, x comes out as the conversion factor for these units. The dimensional formulre lack one quality which is needed for completeness, an indica- tion of their vector characteristics ; such characteristics distinguish plane and solid angle, torque and energy, illumination and brightness. Part 1.-Fundamental units The fundamental units most commonly used are: length [I1 ; mass [nzl; time [tl; temperature [el ; and for the electrostatic system, dielectric constant [kl ; for the electro- magnetic system, permeability [b]. The formuk will also be given for the International System of electric and magnetic units based on the units length, resistance [rl, current lil, and time. When writing fractions, using the solidus, care is required to make the meaning definit; : i.e.,, Btu/hr/ft'("F/m), or Btu/(hr)(ft*)("F/m) is not clear, but Btu/[hr X ft2 X ("F/ml is definite. (con tin i d ) SMlTHSONlAN PHYSICAL TABLES 58 TABLE 30.-DIMENSIONAL EQUATIONS OF FUNDAMENTAL AND DERIVED UNITS (continued) Part 2.-Derived units (geometric and heat) Name of unit Area, surface .... ..... Volume . . . . . . . . . . . . . . Angle . . . . . . . . . . . . . . . . Solid angle . . . . . . . . . . Curvature . . . . . . . . . . . . Angular velocity . . . . . Linear velocity . . . . . . . Angular acceleration . . Linear acceleration . . . Density . . . . . . . . . . . . . . Moment of inertia.. . . . Intensity of attraction. Momentum . . . . . . . . . . Moment of momentum. Angular momentum .. Force . . . . . . . . . . . . . . . Moment of couple, torque . . . . . . . . . . . Work. energy ........ Power, activity . . . . . . . Intensity of stress.. . . . Modulus of elasticity. . Resilience . . . . . . . . . . . . Viscosity . . . . . . . . . . . . Compressibility . . . . - Conversion factor [rn"/~'t*] & X Y Z 0 2 0 0 3 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 1 -1 0 0 -2 0 1 -2 1 -3 0 1 2 0 0 1 -2 1 1 -1 1 2 -1 1 2 -1 1 1 -2 1 2 -2 1 2 -2 1 2 -3 1 -1 -2 1 -1 -2 -1 1 2 1 -1 -2 1 -1 -1 Name of units (Ireat and liaht) Quantity of heat: thermal units . . . . . thermometric units. dynamical units . . . Coefficient ,of thermal . . . . . . Tliernial conductivity : thermal units . . . . . thermometric units or diffusivity . . . . tlynamical units . . . Thcrnial capacity . . . cxpansion x y z u 1 0 0 1 0 3 0 1 1 2 - 2 0 0 0 0 - 1 1 -1 -1 0 0 2 - 1 0 1 1 -3 -1 1 0 0 0 Latent heat : thermal units . . . . . 0 0 0 1 dynsniical units . . . 0 2 -2 0 Joulc's equivalent. . . . 0 2 -2 -1 Entropy : hcatinthermalunits. 1 0 0 0 heat in tlynamical units . . . . . . . . . . . 1 2 -2 1 Imninous intensity . . 0 0 0 1* Illuniinaticin ........ 0 -2 0 1* Brightness . . . . .. . . . 0 -2 0 1* Visibility . . , . .. . _ . _ . -1 -2 3 1* Luniinous efficicucy. . -1 -2 3 1* . For these formula: the nunibers in the last column arc the exlionents of F where I; rrfers to the luminous flux. For definitions of thest. quantities see Tables 70 and 72. (cotlfi?tlred) SMITHSONIAN PHYSICAL TABLES 59 T A B L E 30.-DIMENSIONAL EQUATIONS O F F U N D A M E N T A L A N D D E R I V E D U N I T S (concluded) Part 3.-Derived units (electrical and magnetic) Conversion fwtor Electrostatic system ml/.vr*k r I-lectroniaanetic systrm m=/'f:/* I. emu esu .. ~ t Sym- Name of unit bol * Quantity of electricity.. ... Q Electric displacement ..... 1) Electric surface density.. . D Electric field intensity. .... F Electric potential ......... V Electromotive force ...... E Electrostatic capacity ..... c Dielectric constant ....... K Specific inductive capacity. - Current ................. I Electric conductivity ..... y Resistivity ............... p Conductance ............. g Resistance ............... R Magnetic pole strength. ... m Quantity of magnetism. ... m Magnetic flux ............ + Magnetic field intensity. ... H Magnetizing force ....... H Magnetic potential ....... 0 Magnetomotive force ..... :i i- r I. 7 r 0 0 0 \ 2 ? ; 0 --I. - 2 0 --; - 1 0 - 5 j -2 ; ! -2 3 ; -2 ; -1 2 -1 -2 2 -1 0 0 0 i -1 --f -2 1 -1 2 -1 1 -1 1 -1 1 -1 1 ; -1 f -1 4 -j -1 -f -3 -1 -3 3 -1 -3 $ -1 -4 I -1 f - ; -1 i -+ -1 t 0 0 1 0 0 1 -! -1 -4 1 0 1 1 0 1 -1 0 -1 1 -1 t ?' t i' 1 0 1 1 -2 1 1 -2 1 C C C 1 'c 1 1 0 1 0 0 1 0 0 0 0 0 0 -1 1 0 0 0 1 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 1 0 1 l c l c 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 CP C' -1 -1 0 0 -1 1 -1 1 1 $ ! - 2 f 0 0 - 1 1 0 0 1 - 1 0 1 - 1 1 0 -1 1 -1 t t 0 - 4 t ; 0 - $ 4 0 -L ; $ - 2 5 4 0 0 C C2 1 /c' 0 0 I 2 c' 1 /c2 1 /c 1 ,!c l / c 1 1 0 1 0 1 1 0 1 0 -1 0 C C C C 1 /c 1 /c 1 .'c 1 /c' l/c' 1 ic? 1 /c' c" C 0 -1 0 1 0 0 1 0 0 1 1 1 1 -2 1 1 -2 1 0 -1 1 0 -1 1 1 -2 0 0 0 1 0 0 1 0 0 -1 1 0 O$ 1 0 O$ Magnetic moment ........ - ; Intensity magnetization ... J Magnetic induction ....... B Magnetic susceptibility ... K 0 Magnetic permeability ... p 0 Current density - f Self-inductancc 2 0 Mutual inductance ....... $)]I 0 Magnetic reluctance ...... $R 0 .......... .......... 1 1 0 1 1 -1 1 1 Thermoelectric power$ , . . - $ t -1 -;$ 1 2 2 ' -2 +$ l/c Peltier coefficient$ ....... - 3 + -1 -$$ 1 2 2 ' -2 t$ l/c .As adopted by .\merican Institute of Electrical Engineers, 1915. t c is the velocity of an electromagnetic wave in the ether = 3 x 1O'O ap'proximately. t This conversion factor should include [#-'I. SMITHSONIAN PHYSICAL TABLES 1cm= 1 m = 1 in. = 1 ft= 1 yd= 1 cm'= 1 mz= 1 in.'= 1 ft' = I yd2= 1 cm3= 1 in?= 1 ft'= 1 ml= 1 liter = 1 gal = 1 g = 1 kg= 1 lb= 1 metric ton= 1 ton= Legal relation. TABLE 31.-FUNDAMENTAL UNITS OF LENGTH, AREA, VOLUME, AND MASS (As established by administrative action, National Bureau of Standards) cm 1 100 2.5400051 30.480061 91.440183 cm2 1 10' 6.4516258 929.03412 8361.3070 cm3 1 16.387162 2.8317017 x 10' 1.000028 1.000028 X lo3 3.7854345 X 10' g 1 1 0 3 .. 4.5359243 X 10' 9.0718486 x lo5 1 oe Part 1.-Some definitions and legal relations 1 in.* = (U0.3937) cm = 2.54000508 cm 1 Ib * = 453.5924277 g 1 I.T. cal t = 4.18674 ioules 1 gal * = 231 in? = 3.785329 liter = I.OOOSS~ calls = 252.161 calls 1 Btu t = 251.996 I.T. cal Part 2.4onversion factors, units of length m in. ft 0.01 0.3937 1 39 37 _ _ 0.025400051 1 0.30480061 12 0.91440183 36 ~ t As defined by International Steam Table Conference, London, 1929. 0.032808333 3.2808333 0.083333333 1 3 Part 3.-Conversion factors, units of area m2 in.2 ft2 1 1549.9969 10.763867 6.4516258 x lo-' 1 6.9444444 x lo-' O.WZ903412 144 1 0.83613070 1296 9 10-4 0.15499969 1.0763867 x Part 4.-Conversion factors, units of volume in.= ft3 ml 0.061023378 3.5314455 X 0.9999720 1 5.7870370 x lo-' 16.38670 1.728 x lo" 1 2.831622 x 10' 0.06102509 3.531544 X lod 1 61 .OX09 0.03531 544 10" 23 1 0.13368056 3.785329 x 10' Part 5.-Conversion factors, units of mass kg lb metric ton 10.' 2.2046223 x lo-' lo-' 1 2.2046223 10'' 0.45359243 1 4.5359243 X 103 2204.6223 1 907.18486 2000 0.90718486 rd 0.010936111 1.09361 11 0.027777778 0.33333333 1 yd' 1.1959853 x lo-* 1.1959853 7.7160494 x lo-' 0.11111 111 1 liter 0.9999720 x 10.' 1.638670 x lo-' 28.31622 0.001 1 3.785329 ton 1.1023112 X 10- 1.1023112 x 10" 0.0005 1.1 023 1 12 1 gal 2.6417047 X lo-' 4.3290043 x lo-* 7.4805195 2.641779 02641 79 X lo-' 1 61 TABLE 32.-TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES* Part 1.-Metric t o customary Capacity 7 litersor cut+ Centi- meters to Liters liters liters Linear centi. liters Deca- Hecto- inches feet yards to miles drams ounces quarts gallons h s h e k l$eters to Meters to hleters to Kilometers tofluid fluid to to tu 1 39.3700 3.28083 1.093611 0.62137 1 0.27 0.338 1.0567 2.6418 2.8378 2 78.7400 6.56167 2.187222 1.24274 2 0.54 0.676 2.1134 5.2836 5.6756 3 118.1100 9.84250 3.280833 1.86411 3 0.81 1.014 3.1701 7.9253 8.5135 4 157.4800 13.12333 4.374444 2.48548 4 1.08 1.353 4.2268 10.5671 11.3513 5 196.8500 16.40417 5.468056 3.10685 5 1.35 1.691 5.2836 13.2089 14.1891 6 236.2200 19.68500 6.561667 3.72822 6 1.62 2.029 6.3403 15.8507 17.0269 7 275.5900 22.96583 7.655278 4.34959 7 1.89 2.367 7.3970 18.4924 19.8647 8 314.9600 26.24667 8.748889 4.97096 8 2.16 2.705 8.4537 21.1342 22.7026 9 354.3300 29.52750 9.842500 5.59233 9 2.43 3.043 9.5104 23.7760 25.5404 1 2 3 Square > Squafe centi- Square Square meters meters meters to square to square to square Hectares inches feet yards tuacres 0.1550 10.764 1.196 2.471 1 0.3100 21.528 2.392 4.942 2 0.6200 43.055 4.784 9.884 4 0.7750 53.819 5.980 12.355 5 0.4650 32.292 3.588 7.413 3' 0.9300 64.583 7.176 14.826 6 1.0850 75.347 8.372 17.297 7 1.2400 86.111 9.568 19.768 8 1.3950 96.875 10.764 32.230 9 Cubic centi- meters to cubic inches 0.0610 0.1220 0.1831 0.2441 0.3051 Cubic deci- meters to cubic inches 61.023 122.047 183.070 244.094 305.117 Mass Milli- grams to grains 0.01543 0.03086 0.04630 0.06173 0.07716 0.09259 0.10803 0.12346 0.13889 Hecto- grams to Kilo. ounces grams to avoir- grains dupois 15432.36 3.5274 30864.71 7.0548 46297.07 10.5822 61 729.43 14.1096 77161.78 17.6370 92594.14 21.i644 108026.49 24.6918 123458.85 28.2192 138891.21 3 1.7466 Cubic Mazs Cubic meters to cubic feet 35.314 70.269 105.943 141.258 176.572 Cubic meters to cubic yards 1.308 2.616 3.924 5.232 6.540 Kilo- grams to wunds avoir- dupois 2.20462 4.40924 6.61387 8.81849 11.0231 1 13.22773 15.43236 17.63698 19.84160 1 2 3 4 5 Milliers or Quintals to tonnes to pounds av. pounds av. 220.46 2204.6 440.92 4409.2 661.39 6613.9 881.85 8818.5 1102.31 11023.1 Iiilo- grams to ounces troy 32.1507 64.3015 96.4522 128.6030 160.7537 6 0.3661 366.140 211.887 7.848 6 1322.77 13227.7 192.9045 7 0.4272 427.164 247.201 9.156 7 1543.24 15432.4 225.0552 8 0.4882 488.187 282.516 10.464 8 1763.70 17637.0 257.2059 9 0.5492 549.210 317.830 11.771 9 1984.16 19841.6 289.3567 In the United 5t:;tes since 1893 all units in the above table have been derived from the same standards c i h:gth a:!d mass. Therefore all equivalents (except those ii?volving the liter) depend oiily [ i n :iurrierical definitions. The liter is the volume of one kilogram of pure water at ttie tFmpcratcre of its maximum density and under a pressure equivalent to 760 millitneters of nir;cury. The liter was determined by the International :3ureau of Weights arid Measures in 1910 to equal 1.000027 dm3. (National Bureau of Standards.) .Quoted from sheets issued by the Kational Bureau of Standards (corttinzred) SMITHMNIAN PHYSICAL TABLES 62 TABLE 32.-TABLES FOR C0NVERTI:NG U. S. WEIGHTS AND MEASURES (continued) Part 2.-Cuetornary to metric 1 3 4 5 6 7 8 9 7 L 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 Linear Inches to Miles milli- Feet to Yards to to kilo- meters meters meters meters 25.4001 0.304801 0.914402 1.60935 50.8001 0.609601 1.828804 3.21869 76.2002 0.914402 2.743205 4.82804 101.6002 1.219202 3.657607 6.43739 127.0003 1.524003 4.572009 8.04674 152.4003 1.828804 5.48641 1 9.65608 177.8004 2.133604 6.400813 11.26543 203.2004 2.438405 7.315215 12.87478 228.6005 2.743205 8.229616 14.48412 Square Square inches to square centi- meters 6.452 12.903 19.355 25.807 32.258 Square feet to Square s uare yards to Acres ieci- square to meters meters hectares 9.290 0.836 0.4047 1 18.581 1.672 0.8094 2 27.871 2.508 1.2141 3 37.161 3.345 1.6187 4 46.452 4.181 2.0234 5 38.710 55.742 5.017 2.4281 6 45.161 65.032 5.853 2.8328 7 51.613 74.323 6.689 3.2375 8 58.065 83.613 7.525 3.6422 9 Cuhic Cuhic inches to Cuhic Cuhic Bushels cuhic feet to yards to to centi- cuhic cuhic hecto- meters meters meters liters 16.387 0.02832 0.765 0.35239 32.774 0.05663 1.529 0.70479 49.161 0.08495 2.294 1.05718 65.549 0.11327 3.058 1.40957 81.936 0.14159 3.823 1.761% 98.323 n.16990 4.587 2.11436 iii7To 0:iGSii 5.352 2Z675 131.097 0.22654 6.116 2.81914 147.484 0.25485 6.881 3.17154 Capacity Fluid drams to milli- Fluid liters or ounces Liquid cuhic to quarts Gallons centi- miili- to to meters liters liters liters 1 3.71) 29-57 0.94633 3.78533 i 7.39 59% 1.89267 7.57066 3 11.09 88.72 2.83900 11.35600 4 14.79 118.29 3.78533 15.14133 5 18.48 147.87 4.73167 18.92666 6 22.18 177.44 5.67800 22.71199 7 25.88 207.01 6.62433 26.49733 8 29.57 236.58 7.57066 30.28266 9 33.27 266.16 8.51700 34.06799 Mass Avoir- dupois Grains to ounces milli- to grams grams 64.7989 28.3495 129.5978 56.6991 194.3968 85.0486 259.1957 113.3981 323.9946 141.7476 Avoir- dupois pounds Troy to kilo- ounces grams to grams 0.45359 31.10348 0.90718 62.206% 1.36078 93.31044 1 A1437 124.41392 2.26796 155.5 1740 388.7935 170.0972 2.72155 186.62088 453.5924 198.4467 3.17515 217.72437 518.3913 226.7962 3.62874 248.82785 583.1903 255.1457 4.08233 279.93133 1 mile (statute) = 5280 feet 1 mile (nautical) = 6080.20 feet 1 Gunter's chain = 20.1168 meters 1 sq. statute mile = 259.000 hectares 1 fathom - 1.829 meters 1 nautical mile 1 foot - 0.304801 meter 1 avoir. pound = 453.5924 grams 15432.356 grains = 1.000 kilogram 1 liter = 1853.25 meters = 1000.028 k .004 cm' The length of the nautical mile given above, and adopted by the U. S. Coast and Geodetic Survey many years ago, is defined as that of a minute of arc of a great circle of a sphere whose surface equals that of the earth (Clarke's Spheroid of 1866). (continued) SMITHSONIAN PHYSICAL TABLES 63 TABLE 32.-TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES (concluded) Part 3.-Miscellaneous equivalents of U. S. and metric weights and measures" (For other equivalents than those below, see Tables 30, 31, and 33.) LINE.\R MEASURES 1 mil (.001 in.) =25.4001 p 1 in. = .000015783 mile 1 hand (4 in.) = 10.16002 cm 1 link (.66 ft) = 20.11684 cm 1 span (9 in.) = 22.86005 cm 1 fathom (6 ft) = 1.828804 m 1 rod (55 yd) (25 links) = 5.02910 m 1 chain (4 rods) = 20.11684 m 1 light year (9.5 X 10" km) = 5.9 X 10" miles 1 parsec (31 X 10" km) = 19 X 10'' miles ilk in. = .397 mm in. = .794 mm &in. = 1.588 mm 4 in. = 3.175 mm 4 in. = 6.350 mm 3 in. = 12.700 mrn 1 angstrom unit = .0000000001 m 1 micron ( p ) = B00001 m = .00003937 in. 1 millimicron (mp) = .000000001 rn 1 m = 4.970960 links = 1.09361 1 yd = .198838 rod= .04970% chain SQU.\RE MEASURES 1 sq. link (62.7264 in?) = 404.6873 cm2 1 sq. rod (625 sq. links) = 25.29295 m2 1 sq. chain (16 sq. rods) = 404.6873 m' 1 acre (10 sq. chains) = 4046.873 m2 1 sq. mile (640 acres) = 2.589998 km2 1 km2 = .3861006 sq. mile 1 m2 = 24.7104 sq. links = 10.76387 ft2 = .039537 sq. rod = .00247104 chain CUBIC ME.\SURES sq. 1 board foot (144 in.") = 2359.8 cma 1 cord (128 ft*) = 3.625 ma CAPACITY MEASURES 1 minim (Q) = .0616102 ml 1 fl. dram (60 n) = 3.69661 ml 1 fl. oz (8 fl. dr) = 1.80469 in." 1 gill (4 fl. oz.) = 7.21875 in." = 118.292 1 liq. pt (28.875 in?) = .473167 1 1 liq. qt (57.75 in.") = 946333 1 1 gallon (4 qt, 231 in?) = 3.785332 1 1 dry pt (33.6003125 in.") = S50599 1 1 dry qt (67.200625 in.") = 1.101198 1 1 pk (8 dry qt, 537.605 in?) = 8.80958 1 1 bu (4 pk, 2150.42 in.") = 35.2383 1 1 firkin (9 gallons) = 34.06799 1 1 liter = 264178 gal = 1.05671 liq. qt 1 ml. = 16.2311 minims. 1 dkl. = 18.1620 dry pt = 9.08102 dry qt =3.5729 ml ml = 33.8147 fl. oz = 270.518 fl. dr = 1.13513 pk = .28378 bu MASS ME.\SURES Avm'rdupois weights 1 grain = .064798918 g 1 dram av. (27.34375 gr) = 1.771845 g 1 oz av. (16 dr av.) = 28.349527 E 1 Ib av. (16 oz av..or 7000 gr) - = 14.583333 oz ap. (3) or oz t. = 1.2152778 or 7000/5760 lb ap. or t. =453S924277 u _ _ . 1 kg = 2.204622341 1s av. 1 g = 15.432356 gr = .5643833 dr av. - = .03527396 Oz av. 1 short hundred weight (100 Ib) 1 long hundred weight (112 lb) = 45.359243 kg = 50.802352 kn 1 short ton (2000 lb) = 907.18486 kg 1 long ton (2240 Ib) = 1016.04704 kg 1 metric ton = 0.98420640 long ton = 1.1023112 short tons Troy weights 1 pennyweight (dwt 24 gr) = 1.555174 g gr, oz, pd are same as apothecary '4 fiothr car ies' wrig hts 1 gr = 64.798918 mg 1 scruple ( 3,20 gr) = 1.2959784 g 1 dram (3.3 3 = 3.8879351 e 1 oz (QS) ' = 31.103481 1 Ib (125,5760 gr) 1 g = 15.432356 gr = 0.2572059 3 1 kg = 32.150742 3 1 metric carat = 200 mg = 3.0864712 gr U. S. 3 dollar should weigh 12.5 g and the = 373.24177 g = 0.771618 3 = .03215074 j = 2.6792285 lb smaller silver coins in proportion. -Taken from Circular 47 of the National Bureau of Standards, 1915, which see for more complete tables. . SMlTHSONIAN PHYSICAL TABLES 64 TABLE 33.-EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS AND MEASURES * (For U. S. Weights and Measures, see Table 32.) Part 1.-Metric to imperial LINEAR MEASURE MEASURE OF CAPACITY } = 0.0610 in? 1 milliliter (ml) (.001 liter) 1 centiliter (.OI liter) = { ~ . ~ ~ ~ ~ 4 g i ~ / 1 deciliter (.1 liter) = 0.176 pint (.001 m) 1 centimeter (.01 m) = 0.39370 in. 1 decimeter (.l m) = 3.93701 in. METER(^) . . .- 3.280843 ft 1 LITER (1,000 CU.} 1.09361425 yd centimeters or 1 = 1.75980pints 1 dekaliter (10 liters) = 2.200 gallons 1 kiloliter (1,ooO " ) = 3.437 quarters 1 cm' 0.03520 fluid ounce 1 mm' - 0.01693 minim cu. decimeter) } . . = 10.93614yd 1 dekameter 1 hectometer 1 hectoliter (100 '' ) = 2.75 bushels 1 kilometer ('Om) } . .= 109.361425yd 0.62137 mile APOTHECARIES' MEASURE 6.21372 miles 0.28157 fluid drachm 15.43236 grains weight w't) - 1 micron . . . . . 0.001 mm AVOIRDUPOIS WEIGHT SQUARE MEASURE - 1 cm' . . . . . . - 0.153 1 in.' CUBIC ME.\SURE 1 em8 (1,000mm8). . = 0.0610in.a 1 dm' (1,000 cm') . = 61.024 in? 1 ma or stere 35.3148 ft' (l,OOOdma)}' ' = { 1.307954 yda 1 milligram (mg) . .= 1 centigram (.Ol gr:m) = ) = 1 decigram (.l GRAM . . . . . .- 1 dekagram (10 gr!ys) = 1 hectogram (100 ) = - 1 KILOGRAM (1,000 " ) = 0.01543 grain 0.15432 grain 1.54324 grains 15.43236 grains 5.64383 drams 7 ' 5 2 3 i b 1 rrreins 1 myriagram (10 kg) = 22.046% Ib 1 quintal (100 " ) = 1.96841 cwt 1 millier or tonne . .= 0.9842 ton (1,000 kg) 1 TROY WEIGHT 0.03215 oz troy. 1CRAM. . .={ 0.64301 pennyweight 15.43236 grains APOTHECARIES' WEIGHT 0.25721 drachm NoTE.-The METER is the length, at the temperature of O"C, of the platinum-iridium bar deposited at the International Bureau of Weights and Measures at SGvres, near Paris, France. The present legal equivalent of the meter is 39.370113 inches, as above stated. The KILOGRAM is the mass of a platinum-iridium weight deposited at the same place. The LITER contains 1 kilogram weight of distilled water at its maximum density (4"C), the barometer being at 760 millimeters. In accordance with the schedule adopted under the Weights and Measures (metric system) Act. 1897. (continued) SMITHWNIAN PHYSICAL TABLES 65 TABLE 33.-EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS AND MEASURES (continued) (For U. S. Weights and Measures, see Table 32.) Part 2.-Metric to imperial, multiples Linear measure Measure of capacity ~ Millimeters Meters Meters Kilo- to to to meters inches feet yards tomiles 1 0.03937011 3.28084 1.09361 0.62137 2 0.07874023 6.56169 2.18723 1.24274 3 0.11811034 9.84253 3.28084 1.86412 4 0.15748045 13.12337 4.37446 2.48549 5 0.19685056 16.40421 5.46807 3.10686 6 0.23622068 19.68506 6.56169 3.72823 7 0.27559079 22.96590 7.65530 4.34960 8 0.31496090 26.24674 8.74891 4.97097 9 0.35433102 29.52758 9.84253 5.59235 Square measure < A Square centi- Square Square meters meters meters square square square to inches feet yards acres to to to Hectares Liters to pints 1 1.75980 2 3.51961 3 5.27941 4 7.03921 5 8.79902 Deka- liters to gallons 2.19975 4.39951 6.59926 8.79902 10.99877 Hecto- Kilo- liters to liters to bushels quarters 2.74%9 3.43712 5.49938 6.87423 8.24908 10.31135 10.99877 13.74846 13.74846 17.18558 6 10.55882 13.19852 16.49815 20.62269 7 12.31862 15.39828 19.24785 24.05981 8 14.07842 17.59803 21.99754 27.49692 9 15.83823 19.79778 24.74723 30.93404 Weight (Avoirdupois) ' 1 Milli- Kilo- Kilo- Quintals grams grams grams to f? '? to hundred- grains grains pounds weights 1 0.15500 10.76393 1.19599 2.4711 1 0.01543 15432.356 2.20462 1.96841 2 0.31000 21.52786 2.39198 4.9421 2 0.03086 30864.713 4.40924 3.93683 3 0.46500 32.29179 3.58798 7.4132 3 0.04630 46297.069 6.61387 5.90524 4 0.62000 43.05572 4.78397 9.8842 4 0.06173 61729.426 8.81849 7.87365 5 0.77500 53.81965 5.97996 12.3553 5 0.07716 77161.782 11.02311 9.84206 6 0.9300 64.58357 7.17595 14.8263 6 0.09259 92594.138 13.22773 11.81048 7 i.08500 75.34750 8.37194 i7.2974 7 0.10803 108026.495 15.43236 13.77889 8 1.24000 86.11143 9.56794 19.7685 8 0.12346 123458.851 17.63698 15.74730 9 1.39501 96.87536 10.76393 22.2395 9 0.13889 138891.208 19.84160 17.71572 CC ' Cubic deci- meters to cubic inches ibic measure Cubic' Cubic meters cubic cubic feet yards meters to to 1 61.02390 35.31476 1.30795 2 122.04781 70.62952 2.61591 3 183.07171 105.94428 3.92386 4 244.09561 141.25904 5.23182 5 305.11952 176.57379 6.53977 6 366.14342 7 427.16732 8 488.19123 9 549.21513 211.88855 7.84772 247.20331 9.15568 282.51807 10.46363 317.83283 11.77159 Apothe- caries' measure Cubic centi- meters to fluid drachms 0.28157 0.56314 0.84471 1.12627 1.40784 1.68941 1.97098 2.25255 2.53412 Apothe- Avoirdupois caries' (cont. ) Troy weight weight Milliers Grams Grams or to to Grams tonnes to ounces penny- to tons troy weights scruples 1 0.98421 0.03215 0.64301 0.77162 2 1.%841 0.06430 1.28603 1.54324 3 2.95262 0.09645 1.92904 2.31485 4 3.93683 0.12860 2.57206 3.08647 5 4.92103 0.16075 3.21507 3.85809 6 5.90524 0.19290 3.85809 4.62971 7 6.88944 0.22506 4.50110 5.40132 8 7.87365 0.25721 5.14412 6.17294 9 8.85786 0.28936 5.78713 6.94456 (continued) SMITHSONIAN PHYSICAL TABLES 66 TABLE 33.-EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS AND MEASURES (continued) (For U. S. Weights and Measures, see Table 32.) Part 3.-lmperial to metric LINEAR MEASURE 1 inch . . . . z 25.400 millimeters 1 foot (i2 in.) . . = 0.30480 meter 1 YARD (3 ft) . . = 0.914399meter 1 pole (54 yd) . = 5.0292 meters 1 furlong (220 yd) = 201.168 meters 1 mile (1,760 yd) . = 1.6093 kilometers lyard . . . . .={ (Tutton 1932) SQUaRE MEASURE (" yd Or = 20.1168 meters 100 links) 1420210. X CdrX in.2 . . . - 6.4516 rm2 .... . . ft2 (144 in.zj . . = - YD2 (9 ft2) . . . perch (304 yd2) = rood (40 perches) = ACRE (4840 yd2) = mi2 (640 acres) = -. . - . - -.-. 9.2903 dm2 0.836126 m2 25.293 m2 10.117 ares 0.40468 hectare 259.00 hectares CUBIC ME'SURE MEASURE OF CAP.\CITY 1 gill . . . = 1.42 deciliters 1 pint (4 g'illi) . . . = 0.568 liter 1 quart (2 pt) . . . = 1.136 liters 1 GALLON (4 qt) . . = 4.5459631 liters 1 peck (2 gal) . . . = 9.0921iters 1 bushel (8 gal) . . = 3.637 dekaliters 1 quarter (8 bu) . . = 2.909 hectoliters AVOIRDUPOIS WEIGHT 1 grain . . . . = 64.8 milligrams 1 dram . . . . .= 1.772 grams 1 ounce (16 dr) . = 28.350 grams p o ~ ~ & ( l ~ r ~ f ~ ~ = 0.45359243 kg 1 stone (14 lb) . . = 6.350 kg 1 quarter (28 Ib) = 12.70 kg 1 hundredweight 1 ton (20 cwt) . . = (112 lb) } = G:%%quintal 1.0160 tonnes or 1016 kilo- grams in? . . . .= 16.387cm' fts (1728 in?) = (,,,,,l7 ms or 28.317 YD' (27 ft*). .= 0.76455m8 grains av) troy OUNCE (480 = 31.1035 grams i 1 pennyweight (24 = 1,5552 grams grains) APOTHECARIES' MEASURE 1 fluid ounce, f 5 drachms) 1 fluid drachm, f 3 lminim, 1 (0.91146 = 0.05919 = 3.5515 c m ~ (60 minims) 1 grain weight) 1 NoTE.-The apothecaries' gallon is of the same capacity as the Imperial gallon. TROY WEIGHT NoTE.-The troy grain is of the same weight as the avoirdupois grain. APOTHECARIES' WEIGHT 1 ounce (8 drachms) . . = 31.1035 grams 1 drachm, 3i (3 scruples) = 3.888 grams 1 scruple, 3 i (20 grains) = 1.296 grams NoTE.-The a othecaries' ounce is of the same weight as tie troy ounce. The apothecaries' grain is also of the same weight as the avoir- dupois grain. ~ NoTE.-The YARD is the length at 62"F, marked on a bronze bar deposited with the The POUND is the weight of a piece of platinum weighed in vacuo at the temperature of The GALLON contains 10 Ib weight of distilled water at the temperature of 62"F, the Board of Trade. O"C, and which is also deposited with the Board of Trade. barometer being at 30 inches. (continued) SMITHSONIAN PHYSICAL TABLES 67 TABLE 33.-EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS AND MEASURES (concluded) (For U. S. Weights and Measures, see Table 32.) Part 4.-lmperial t o metric, multiples 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 Linear measure Inches Miles to Feet Yards to centi- to to kilo. meters meters meters meters 2.539998 0.30480 0.91440 1.60934 5.079996 0.60960 1.82880 3.21869 7.619993 0.91440 2.74320 4.82803 10.159991 1.21920 3.65760 6.43737 12.699989 1.52400 4.57200 8.04671 15.239987 1.82880 5.48640 9.65606 17.779984 2.13360 6.40080 11.26540 20.319982 2.43840 7.31519 12.87474 22.859980 2.74320 8.22959 14.48408 Souare measure Square Square inches feet to Square to square square yards to centi- deci- square Acres to meters meters meters hectares 32.25794 46.45144 4.18063 2.02342 Measure of capacity -. Bushels Quarters Quarts Gallons to to to to deka- hecto. liters liters liters liters 1 1.13649 4.54596 3.63677 2.90942 2 2.27298 9.09193 7.27354 5.81883 3 3.40947 13.63789 10.91031 8.72825 4 4.545% 18.18385 14.54708 11.63767 5 5.68245 22.72982 18.18385 14.54708 6 6.81894 27.27578 21.82062 17.45650 7 7.95544 31.82174 25.45739 20.36591 8 9.09193 36.36770 29.09416 23.27533 9 10.22842 40,91367 32.73093 26.18475 Weight (avoirdupois) Hun- dred- Grajns Ounces Pounds weights to milli- to to kilo- to arams grams grams quintals 1 64.79892 28.34953 0.45359 0.50802 2 129.59784 56.69905 0.90718 1.01605 3 194.39675 85.04858 1.36078 1.52407 4 259.19567 113.39811 1.81437 2.03209 5 323.99459 141.74763 2.26796 2.54012 6 388.79351 170.09716 2.72155 3.04814 38.70953 55.74173 5.01676 2.42811 45.161 12 65.03201 5.85288 2.83279 7 453.59243 198.44669 3.17515 3.55616 51.61271 74.32230 6.68901 3.23748 8 518.39135 226.79621 3.62874 4.06419 58.06430 83.61259 7.52513 3.64216 9 583.19026 255.14574 4.08233 4.57221 Apothe- caries' Cubic measure Measure ~ kubic Fluid inches Cubic Cubic drachms to pubic feet yards tocubic centi- to cubic to cubic centi- meters meters meters meters 81.93511 0.14158 3.82276 17.75767 98.32213 0.16990 4.58732 21.30920 ii4.709is 0.i9822 5.35187 24.86074 131.0%17 0.22653 6.11642 28.41227 147.48319 0.25485 6.88098 31.96380 Apothe- Avoirdupois caries' ( c a t . ) Troy weight weight ~ Tons to Penny- milliers Ounces weights Scruples or to to to tonnes grams grams grams 1 1.01605 31.10348 1.55517 1.29598 2 2.03209 62.20696 3.11035 2.591% 3 3.04814 93.31044 4.66552 3.88794 4 4.06419 124.41392 6.22070 5.18391 5 5.08024 155.51740 7.77587 6.47989 6 6.09628 186.62088 9.33104 7.77587 7 7.11233 217.72437 10.88622 9.07185 8 8.12838 248.82785 12.44139 10.36783 9 9.14442 279.93133 13.9%57 11.66381 SMITHMNIAN PHYSICAL TABLES 68 TABLE 34.-VOLUME OF A GLASS VESSEL FROM THE WEIGHT OF ITS EQUIVALENT VOLUME OF MERCURY OR WATER If a glass vessel contains at t"C, P grams of mercury, weighed with brass weights in air at 760 mmHg pressure, then its volume in cm' P at the same temperature, t : V = P R = P-J d P at another temperature, fl : V = PR, = P - (1 + Y (ti - f)) d p =the weight, reduced to vacuum, of the mass of mercury or water which, weighed with brass weights, equals 1 gram; d = the density of mercury or water at t"C, and y the cubical expansion coefficient of glass. Tern p e r a - ture t 0" 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 R 1.001192 1133 1092 1068 1060 1068 1.001092 1131 1184 1252 1333 1.001428 1536 1657 1790 1935 1.002092 2261 2441 2633 2835 1.003048 3271 3504 3748 4001 1 .oO4264 4537 4818 5110 5410 R1, tl = 10" 0.0735683 5798 5914 6029 6144 6259 0.0736374 6490 6605 6720 6835 0.0736951 7066 7181 7297 7412 0.0737527 7642 7757 7872 7988 0.0738103 8218 8333 8449 8564 0.0738679 8794 8910 9025 9140 R1, tl = 20" 0.0735867 5982 6098 6213 6328 6443 0.0736558 6674 6789 6904 7020 0.0737135 7250 7365 7481 7596 0.073771 1 7826 7941 8057 8172 0.0738288 8403 8518 8633 8748 0.0738864 8979 9094 9210 9325 Water Mercury L R1, tl = 10' R,. t? = 20' R 1.001443 1358 1292 1243 1210 1193 1.001192 1206 1234 1277 1333 1.001403 1486 1582 1690 1810 1.001942 2086 2241 2407 2584 1.002772 2970 3178 33% 3624 1.003862 41 10 4366 4632 4908 _I - 1.001693 1609 1542 1493 1460 1443 1.001442 1456 1485 1527 1584 1.001653 1736 1832 1940 2060 1.002193 2337 249 1 2658 2835 1.003023 3220 3429 3647 3875 1.0041 13 4361 4616 4884 5159 0.0735499 5633 5766 5900 6033 6167 0.0736301 6434 6568 6702 6835 0.0736969 7103 7236 7370 7504 0.0737637 7771 7905 8039 8172 0.0738306 8440 8573 8707 8841 0.0738974 9108 9242 9376 9510 SMITHSONIAW PHYSICAL TABLES TABLE 35.-EFFECT O F AIR ON WEIGHING 69 Reductions of weighings in air to vacuo When the weight M in grams of a body is determined in air, a correction is necessary for the buoyancy of the air equal to M6( l/d - I/&) where 6 = the density (wt. of 1 cms in grams = 0.0012) of the air during the weighing, d the density of the body, d~ that of the weights. 6 for various barometric values and humidities may be determined from Tables 631-632. The following table is computed for 6 = 0.0012. The corrected weight = M + kM/1000. Correction factor. k Densitv , .A of hod; 'Pt. Ir. Brass Quartz or weighed weights weights Al. weights d d,= 21.5 8.4 2.65 .5 + 2.34 .6 + 1.94 .7 + 1.66 .75 + 1.55 .80 + 1.44 .85 + 1.36 .90 + 1.28 .95 + 1.21 1.00 + 1.14 1.1 + 1.04 1.2 + 0.94 1.3 + .87 1.4 + .SO 1.5 + .75 + 2.26 + 1.86 + 1.57 + 1.46 + 1.36 + 1.27 + 1.19 + 1.12 + 1.06 + 0.95 + .86 + .78 + .71 + .66 + 1.95 + 1.55 + 1.26 + 1.15 + 1.05 + 0.96 + .88 + .81 + .75 + .64 + .55 + .47 + .40 + .35 Correction factor, k Density , of body Pt. Ir. Brass Ouartz or weighed weights weights Ai. weights d d,= 21.5 8.4 2.65 1.6 + 0.69 + 0.61 + 0.30 1.7 + .65 + .56 + .25 1.8 + .62 + .52 + .21 1.9 + .58 + .49 + .18 2.0 + .54 + .46 + .15 2.5 + .43 + .34 + .03 4.0 + .24 + .16 - .15 3.0 + .34 + .26 - .05 6.0 + .14 + .06 - .25 8.0 + .09 + .01 - .30 10.0 + .06 - .02 - .33 15.0 + .03 - .06 - .37 20.0 + .004 - .08 - .39 22.0 - .001 - .09 - .40 TABLE 36.-REDUCTlONS OF DENSITIES IN AIR TO VACUO (This correction may be accomplished through the use of the above table for each sepa- rate weighing.) If s is the density of the substance as ca!culated from the uncorrected weights, S its true density, and L the true density of the liquid used, then the vacuum correction to be applied to the uncorrected density, s, is 0.0012 (1 - s/L). Let W. = uncorrected weight of substance, W I = uncorrected weight of the liquid dis- placed by the substance, then by definition, s = LW./Wz. Assuming D to be the density of the balance of weights, W.{1 + 0.0012(1/S - l/D)} and Wt{l + 0.0012 (1/L - l/D)} are the true weights of the substance and liquid respectively (assuming that the weighings are made under normal atmospheric corrections, so that the weight of 1 cm' of air is 0.0012 gram). W,{1 + 0.0012(1/s- 1/D)} Wl{1 + O.O012(1/L - 1/D)} Then the true density S= But from above WJWI = s/L, and since L is always large compared with 0.0012, The values of 0.0012(1 - s/L) for densities up to 20 and for liquids of density 1 (water), s - s = 0.0012( 1 - s/L) 0.852 (xylene), and 13.55 (mercury) follow : Density of sub- ,- stance L=l z Water 0.8 + 0.00024 0.9 + .00012 1. 0.0000 2. - .0012 3. - .0024 4. - .0036 5. - .0048 6. - .0060 7. - .0072 8. - .0084 9. - .0096 10. - .0108 Corrections L = 0.852 Xylene - - - 0.0002 - .0016 - .0030 - .0044 - .0058 - .0073 - .0087 - .0101 - .0115 - .0129 L = 13.55 Mercury + 0.001 1 + .0010 + .om9 + .0008 + .oO08 + .0007 + .om + .om5 + .OM4 + .0003 Density Corrections of suh- Stance L=13.5r; Ll S Water Mercury 11. -0.0120 +0.0002 12. - .0132 + .OOO1 13. - .0144 O.oo00 14. - .0156 0.0000 15. - .0168 - .0001 16. - ,0180 - .0002 17. - .0192 - .OW3 18. - .0204 - .OW4 19. - .0216 - .OW5 20. - .0228 - .0006 SMITHSONIAN PHYSICAL TABLES
