None
1 meter = 1 553 163.5 wave lengths of red light. = 1966249.7 " " green " = 2083 372.1 " blue " 1 Committee Meter (of U. S. Coast Survey) = 39. 370 0 inches = 1 meter (int.;. 1 ell [E, e] (cloth; Brit.) = 45. inches - 1,143 0 meters. 1 fathom (U. S.) = 6. feet = 1.828 8 (aprx. %) meters. 1 fathom (Brit.) = 6.080 feet = 1.853 2 (aprx. 1%) meters = Hooo nautical mile (Brit.). 1 rod [r], pole [p], or perch [p] (surveyor's) = 5 yards = 5.029 2 meters. 1 decameter or dekameter [dkm]=10. meters. 1 chain [ch] (Gunter's or surveyor's) = 100. links (surveyor's) = 66. feet = 20.117 meters = 4. rods, poles, or perches = 10 furlongs. 1 chain [ch] (engineer's) = 100. links (engineer's) = 100. feet = 30.480 meters. 1 chain [ch] (Philadelphia standard) = 100. yards = 30.556 meters. bolt (cloth) = 40. yards. 1 hectometer = 100. meters. 1 furlong [fur] = 660. feet = 20.1 7 meters = 40. rods, poles, or perches = 10. chains (Gunter's or surveyor's) = 8.8 miles. 1 cable or cable's length (Brit, navy) = 608. feet (sometimes stated as 608.6 feet) = 120. fathoms (U.S. Navy) = 720. feet = 219.457 meters = 120. fathoms (U.S.). 1 car-mile, see under units of Energy. 1 knot (telegraph; Brit.) = 2 029. yards = 1 855.32 meters. 1 geographical mile, sometimes used for nautical mile; see also under international geographical mile. 1 international nautical or sea mile = 6 076.10 feet = 1 852. meters = 1 0 of 1° of meridian. 1° of latitude at equator = 60. (aprx.) nautical miles. = 68.70 miles (statute), lat. 20° = 68.78 40° = 69.00 60° = 69.23 80° = 69.39 90° = 69.41 1° of longitude at equator = 60. (aprx.) nautical miles. = 69.16 m les (statute). " lat. 20° = 65.02 " " 40° = 53.05 " •• 60° = 34.67 •• •• 80° = 12.05 1 legua (California; legal) = 2.633 5 miles = 5 000. varas. 1 league (U. S.) = 4.828 05 kilometers = 3. miles (statute); also given ad 3. nautical miles. 1 international geographical mile = 24 350. 3 feet = 7 422. meters = 4.611 80 miles (statute) = 4. (aprx.) nautical miles = ii5 of 1° at equator. The term geographical mile is sometimes used also for nautical mile. 1 myriameter or miriameter=10. kilometers. 1 mean diameter of the earth J (astronomy ) = 12 742.0 kilometers = 7 917.5 miles. 1 mean diameter of earth's orhit§ (astronomy) = 149 340 870 ± 9G 101 kilometers = 92 796 950 ±59 715 miles. t Michelson; cadmium light waves for air at 15° C. and a pressure of ^0 mm. mercury. t Based on the accepted value of a nautical mile as defined above. § Harkness. LENGTHS. 33 LENGTHS (concluded). Foreign. These are mostly obsolete, as the metric system is now used in most foreign countries. The British measures are included among the U. S. measures, being very nearly, and sometimes quite the same. The trans- lated terms are merely synonymous, and not the exact equivalents. Germany. Prussia. Legal May 16, 1816. 1 Fuss (foot) = 12 Zoll (inches) of 12 Linien (lines). 1 Fuss (also called "rheinlaendischer Fuss," that is, Rhineland foot) = 0.313 853 5 meter. Road measure: 1 Meile (mile) -2 000 Ruthen (rods) of 12 Fuss (feet); 1 Meile = 7.5325 kilometers; 1 Ruthe = 3. 766 25 meters. From Jan. 1, 1872, to Jan. 1, 1874: 1 deutsche Meile (German mile) = 7. 500 kilometers. Trade measure: 1 Elle (yard) = 2H Fuss (feet) = 25 Zoll (inch) = 0.666 939 meter. 1 Lachter = 80 Zoll (inches) = 2.092 36 meters. Bavaria. 1 Fuss (foot) = 12 Zoll (inches) of 12 Linien (lines). More rarely 1 Fuss = 10 Zoll of 10 Linien. 1 Fuss = 0.291 859 meter. Saxony. 1 Fuss = 0.283 19 Meteorology. 1 Fuss = 0.286 49 meter; subdivisions like in Bavaria. Willettemberg. 1 Fuss = 0.286 49 meter; subdivisions like in Baden. Baden. 1 Fuss (foot) = 10 Zoll (inches) of 10 Linien (lines). 1 Fuss = 0.3 meter. Hanover. 1 Fuss = 0.292 1 meter. The following values of various German feet in inches are given in Nystern Mechanics: Bavaria, 11.42; Berlin, 12.19; Bremen, 11.38; Dresden, 11.14; Hamburg, 11.29; Hanover, 11.45; Leipzig, 11.11; Prussia, 12.36; Rhineland, 12.35; Strasbourg, 11.39. Also the following road measures: Germany, mile, long, 10126 yards; Hamburg mile, 8244 yards; Hanover mile, 11 559 yards; Prussia mile, 8 468 yards. France. "Old measures" (systeme ancien) used prior to 1812: 1 toise (fathom) = 6 pieds (du roi) (feet) of 12 pouces (inches) of 12 lignes (lines) of 12 points. In geodesy: 1 pied=10 pouces of 10 lignes of 10 points. 1 toise = 1.949 037 meters. Road measure: 1 lieue (league) = 2 283 toises = 4449.65 meters; 1 lieue marine = 2854 toises = 5 562.55 meters; 1 lieue moyenne = 2 534 toises = 4 938.86 meters. Field measure: 1 perche (perch) = 18 or 22 pieds. For depths of the sea: 1 brasse = 5 pieds. Trade: 1 aune (yard) de Paris= 1.188 45 meters. According to Nystrom's Mechanics: 1 pied du roi= 12.79 inches; 1 league (lieue) marine = 6 075 yards; 1 league (lieue) marine = 4 861 yards; 1 league, common = 4 861 yards. "Usual" measures (systSme usuel) used from 1812 to 1840: 1 toise (fathom) = 2 meters; 1 pied (foot) = 1 meter; 1 aune (yard) = 1.2 meters. For subdivisions into other units see above under "old measures." 1 noeud = 1 knot or nautical mile. Austria. 1. Ruthe (rod) = 10 Fuss (feet) of 12 Zoll (inches) of 12 Linien (lines). 1 Fuss = 0.316 10 meter. 1 Meile (mile) = 7.586 kilometers = 4 000 Kilmer of 6 Fuss. 1 Elle (yard) = 2.46 Fuss. According to Nystrom's Mechanics: 1 Vienna foot = 12.45 inches. Sweden. 1 meile (mile) = 6 000 famn of 3 alnar of 2 foot (foot) of 10 turn (inches) (or 12 vorktum) of 10 linier (lines). 1 meile = 10.688 4 kilometers. 1 fot = 0.296 901 meter. 1 ruthe (rod) = 16 fot. 1 corde = 10 stangen of 10 fot. According to Nystrom's Mechanics: 1 Swedish foot = 11.69 inches; 1 Swedish mile = 11.70 yards. Russia. 1 werst = 500 saschehn of 3 arschin of 4 tschetwert of 4 wer-schock. 1 werst = 1.066 8 kilometers = 3 500 feet = 0.662 88 mile. 1 sa-schehn = 2.133 6 meters = 7.0 feet (U.S.). 1 arschin = 7 1.2 centimeters = 28.0 inches. 1 tschetwert = 17.780 centimeters = 7.0 inches. 1 werschock = 4.445 centimeters = 1.75 inches. The British foot is also used; 1 foot = 12 inches of 12 lines. According to Nystrom's Mechanics: 1 Russian foot = 13.75 inches; 1 Moscow foot = 13.17 inches; 1 Riga foot = 10.79 inches; 1 Warsaw foot = 14.03 inches; 1 verst = 1 167. yards. Switzerland. 1 Fuss (foot) = 10 Zoll (inches) of 10 Linien (lines). 1 Fuss = 0.3 meter. According to Nystrom's Mechanics: 1 Geneva foot = 19.20 inches; 1 Zurich foot = 11.81 inches; 1 Swiss mile = 9 153 yards. Holland. 1 Ruthe (rod) = 12 Fuss (feet). 1 Ruthe = 3.767 36 meters; 1 Fuss = 0.313 947 meter. According to Nystrom's Mechanics: 1 Amsterdam foot = 11.14 inches; 1 Utrecht foot = 10.74 inches; 1 Flanders mile = 10.74 inches; 1 Flanders mile = 10.74 inches. LENGTHS. 6869 yards; 1 Holland mile = 6 395 yards; 1 Netherlands mile = 10.93 yards. Spain. 1 vara (yard) = 32.874 8 inches = 0.835 022 meter. According to Nystrom's Mechanics: 1 Spanish foot = 11.03 inches; 1 toesas = 66.72 inches; 1 palmo = 8.64 inches; 1 Spanish common league = 7 416 yards. Italy. According to Nystrom's Mechanics: 1 Florence braccio = 21.69 inches; 1 Genoa palmo = 9.72 inches; 1 Malta foot = 11.17 inches; 1 Naples palmo = 10.38 inches; 1 Rome foot = 11.60 inches; 1 Sardinia palmo = 9.78 inches; 1 Sicily palmo = 9.53 inches; 1 Turin foot = 12.72 inches; 1 Venice foot = 13.40 inches; 1 Rome mile = 2 025 yards. Japan. Long measure: 1 ri = 36 chof 60 ken of 6 shaku of 10 sun of 10 bu. 1 jo = 10 shaku. 1 ri = 3.93 kilometers = 2.44 miles. 1 kilometer = 0.255 ri. 1 mile = 0.410 ri. For cloth measure: 1 jo = 10 shaku of 10 sun of 10 bu; the unit is the jo; in this measure the units are longer than those of the same name in the long measure. Miscellaneous (from Nystrom's Mechanics): Antwerp foot = 11.24 inches; Brussels foot = 11.45 Inches. Denmark mile = 8 244 yards; Copenhagen foot = 12.35 inches. Portugal league = 6 760 yards; Lisbon foot = 12.96 inches; Lisbon palmo = 8.64 inches. Ireland mile = 3038 yards; Scotland mile = 9 113 yards. Hungary mile = 9 113 yards. Bohemia mile = 10 137 yards. Hungary mile = 10 137 yards. Turkey berri = 1826 yards. Persia parasang = 6 086 yards; Persia arish = 38.27 inches. Arabia mile = 2 148 yards. China li = 629 yards; mathematician foot = 13.12 inches; builder's foot = 12.71 inches; tradesman's foot = 13.32 inches; surveyor's foot = 12.58 inches. Ancient. Biblical: 1 digit = 0.912 inch; 1 palm = 4 digits = 3. 648 inches; 1 span = 3 palms = 10.94 inches; 1 cubit = 2 spans = 21. 888 inches; 1 fathom = 3.46 cubits = 7.296 feet. Egyptian: 1 finger = 0.737 4 inch; 1 nahud cubit = 1.476 feet; 1 royal cubit = 1.722 feet. Grecian: 1 digit = 0.754 inch; 1 pous=16 digits = 1.007 3 feet; 1 cubit = 1.133 feet; 1 stadium = 604. 375 feet; 1 mile = 8 stadiums = 4 835 feet. Hebrew: 1 cubit = 1.822 feet; 1 Sabbath day's journey = 3 648 feet; 1 mile = 4 000 cubits = 7296 feet; 1 day's journey = 33. 164 miles; 1 sacred cubit = 2.02 feet. Roman: 1 digit = 0.725 7 inch; 1 uncia (inch) = 0.967 inch; 1 pes (foot) = 12 uncias = 11.60 inches; 1 cubit = 24 digits = 1.45 feet; 1 passus = 3.33 cubits = 4.835 feet; 1 millarium (mile) = 4.842 feet. Arabian: 1 foot = 1.095 feet. Babylonian: 1 foot = 1.14 feet. Lengths in which Overhead Telegraph Lines Are or Were Ex-pressed in Different Countries. (From Munro and Jamieson's Pocket Book.) The lengths here given are in English or statute miles of 5 280 feet. Arabia, mile 1.2204. Austria, mile 5.7534. Bohemia, mile 5.7596. Brabant, league 3.452 2. Burgundy, league 3.516 6. China, li 0.359 1. Denmark, mile 4.684 1. Flanders, league 3.90. Hamburg, mile 4.684 1. Hanover, mile 6.567 6. Hesse, mile 5.992 6. Holland, mile 4.602 8. Hun- gary, mile 5.1778. Italy, mile 1.1505. Lithuania, mile 5.5573. -Nor- way, mile 7.018 3. Oldenburg, mile 6.147 7. Poland, long mile 4.602 8: short mile 3.4517. Portugal, league 3.8409. Prussia, mile 4.8068; Rome, mile 0.925 0. Russia, verst 0.663 0. Saxony, mile 5.627 8. Silesia, mile 4.0244. Spain, common legua of 8000. varas, 4.2136; legal legua of 5 000 veras, 2.753 4. Swabia, mile 5.633 5. Sweden, mile 6.647 7. Switzerland, mile 5.200 5. Turkey, berri 1.037 5. Tuscany, mile 1.027 2. Westphalia, mile 6.903 9. LENGTHS. 35 Inches in Fractions, Decimals, Millimeters, and Feet. For every 64th of an inch up to 1 inch ; for every 32d of an inch up to 6 inches; for every 16th of an inch up to 12 inches; for every inch ap to 10 feet. The equivalents of other intermediate values, or of values beyond the table, may be found by adding together two or more values from the table; thus for 11%2 inches add that for 11 inches to that for %2- Milli- meters. Inches. Feet. Milli- meters. Inches. Feet. Milli- meters. Inches. Feet. Milli- meters. Inches. Feet. 51.593 9 2.031 250 0.169 3 96.043 9 325/32 3.781 250 0.315 1 52.387 6 21/16 2.062 500 0.171 9 96.837 7 313/16 3.812 500 0.317 7 53.181 4 23/32 2.093 750 0.1745 97.631 4 327/32 3.843 750 0.320 3 53.975 1 2.125 000 0.177 1 98.425 2 3.875 000 0.322 9 54.768 9 2%2 2.156 250 0.1797 99.218 9 329/32 3.906 250 0.325 5 55.562 6 2.16 2.187 500 0.182 3 100.013 315/10 3.937 500 0.328 1 56.356 4 27/32 2.218 750 0.1849 100.806 3% 3.968 750 0.330 7 57.150 1 2M 2.250 000 0.187 5 101.600 4 4 0.333 3 57.943 9 2.2 2.281 250 0.190 1 102.394 4H2 4.031 250 0.335 9 58.737 6 2%6 2.312 500 0.192 7 103.188 4^6 4.062 500 0.338 5 59.531 4 2%2 2.343 750 0.195 3 103.981 4%2 4.093 750 0.341 1 60.325 1 2H 2.375 000 0.197 9 104.775 4^ 4.125000 0.343 8 61.118 9 213/32 2.406 250 0.200 5 105.569 4%2 4.156 250 0.346 4 61.9126 27/16 2.437 500 0.203 1 106.363 43/16 4.187 500 0.349 0 62.706 4 215/32 2.468 750 0.205 7 107.156 47/32 4.218 750 0.351 6 63.500 1 2H 2.500 000 0.208 3 107.950 4M 4.250 000 0.354 2 64.293 9 2.531 250 0.2109 108.744 4.281 250 0.356 8 65.087 6 2.562 500 0.213 5 1.09. 37 Milli- meters. Inches. Feet. Milli- meters. Inches. Feet. Millimeters Feet and Inches. Millimeters. Feet and Inches. 304.801 1 foot 0 inches 1 676.40 5 feet 6 inches 330.201 1 1 1 701.80 5 7 355.601 1 2 1 727.20 5 8 381.001 1 3 1 752.60 5 9 406.401 1 4 1 778.00 5 10 431.801 1 5 1 803.40 5 11 457.201 1 6 1 828.80 6 0 482.601 1 7 1 854.20 6 1 508.001 1 8 1 879.60 6 2 533.401 1 9 1 905.00 6 3 558.801 1 10 1 930.40 6 4 584.201 1 11 1 955.80 6 5 609.601 2 feet 0 1 981.20 6 6 635.001 2 1 2 006.60 6 7 660.401 2 2 2 032.00 6 8 685.801 2 3 2 057.40 6 9 711.201 2 4 2 082.80 6 10 736.601 2 5 2 108.20 6 11 762.002 2 6 2 133.60 7 0 787.402 2 7 2 159.00 7 1 812.802 2 8 2 184.40 7 2 838.202 2 9 2 209.80 7 3 863.602 2 10 2 235.20 7 4 889.002 2 11 2 260.60 7 5 914.402 3 0 2 286.00 7 6 939.802 3 1 2 311.40 7 7 965.202 3 2 2 336.80 7 8 990.602 3 3 2 362.20 7 9 1 016.00 3 4 2 387.60 7 10 1 041.40 3 5 2413.00 7 11 1 066.80 3 6 2 438.10 8 0 1 092.20 3 7 2 463.80 8 1 117.60 3 8 2 •^SO./'O 8 2 143.00 3 9 2 51 Uil 8 3 168.40 3 10 2 /il-P.Ol 8 4 193.80 3 11 2505.11 8 5 219.20 4 0 2 500.81 8 6 244.60 4 1 2 6 JO. 21 8 7 270.00 4 2 2 641.61 8 8 295.40 4 3 2 C.67.01 8 9 320.80 4 4 2 692.41 8 10 346.20 4 5 2 717.81 8 11 371.60 4 6 2 743.21 9 0 397.00 4 7 2 768.61 9 1 422.40 4 8 2 794.01 9 2 447.80 4 9 2819.41 9 3 473.20 4 10 2 844.81 9 4 498.60 4 11 2 870.21 9 5 1 524.00 5 0 2 895.61 9 6 549.40 5 1 2921.01 9 7 574.80 5 2 2 946.41 9 8 600.20 5 3 2971.81 9 9 625.60 5 4 2997.21 9 10 651.00 5 5 3 022.61 9 11 3 048.01 10 feet  0.275 590 2.133 60 22.965 8 6.40081 7.655 28 11.2654 4.34959 8 203.200 0.314 960 2.43840 26.2467 7.31521 8.748 89 12.8748 4.97096 9 228.600 0.354 330 2.74321 29.527 5 8.229 62 9.84250 14.484 1 5.59233 10 254.001 0.393 700 3.04801 32.808 3 9.14402 10.936 1 16.093 5 6.21370 11 279.401 0.433070 3.35281 36.089 2 10.058 4 12.029 7 17.7028 6.835 07 12 304.801 0.472 440 3.65761 39.3700 10.9728 13.1233 19.3122 7.45644 13 330.201 0.511810 3.96241 42.650 8 11.8872 14.2169 20.921 5 3.077 81 14 355.601 0.551 180 4.26721 45.931 7 12.801 6. Conversion Tables for Lengths (CONCLUDED). Ins. = milimM Mms = inches. Feet = meters. Mtrs = feet.. yards. Yds.= meters. Miles= kilms. Klms= miles. 51 1 295.40 2.007 87 15.5448 167.323 46.634 5 55.774 2 82.0767 31.6899 52 1 320.80 2.047 24 15.849 6 170.603 47.5489 56.807 8 83.686 1 32.3112 53 1 346.20 2.08661 16.1544 173.884 48.463 3 57.9014 85.295 4 32.932 6 54 1371.60 2.12598 16.4592 177.165 49.3777 59.055 0 80.904 7 33.5540 55 1 397.00 2.16535 16.7640 180.446 50.292 1 00.148 6 88.514 1 34.1753 56 1 422.40 2.20472 17.0688 183.727 51.2065 61.2422 90.1234 34.796 7 57 1 447.80 2.24409 17.3736 187.008 52.1209 62.3358 91.7328 35.418 1 58 1 473.20 2.283 46 17.6784 190.288 53.035 3 63.429 4 93.342 1 36.039 5 59 1 498.60 2.32283 17.9832 193.569 53.949 7 64.523 1 94.951 5 36.660 8 60 1 524.00 2.362 20 18.2880 196.850 54.864 1 65.6167 90.5008 37.282 2 61 1 549.40 2.40157 18.5928 200.131 55.7785 66.7103 98.1702 37.903 6 62 1 574.80 2.44094 18.897 6 203.412 56.692 9 07.8039 99.779 5 38.524 9 63 1 600.20 2.48031 19.2024 206.693 57.607 3 68.897 5 101.389 39.1463 64 1 625.60 2.51968 19.5072 209.973 58.5217 09.991 1 102.998 39.767 7 65 1 651.00 2.559 05 19.8120 213.254 59.436 1 71.0847 104.608 40.389 0 66 1 676.40 2.598 42 20.1168 216.535 60.350 5 72.1783 106.217 41.0104 67 1701.80 2.63779 20.421 6 219.816 61.2649 73.2719 107.826 41.6318 68 1 727.20 2.677 16 20.7264 223.097 62.1793 74.3050 109.436 42.253 2 69 1 752.60 2.71653 21.0312 226.378 63.093 7 75.459 2 111.045 42.8745 70 1 778.00 2.75590 21.3360 229.658 64.008 1 76.552 8 112.654 43.495 9 71 1 803.40 2.795 27 21.6408 232.939 64.922 5 77.6464 114.264 44.1173 72 1 828.80 2.834 64 21.9456 236.220 65.8369 78.7400 115.873 44.738 6 73 1 854.20 2.87401 22.2504 239.501 66.751 3 79.833 6 117.482 45.3600 74 1 879.60 2.91338 22.555 2 242.782 67.665 7 80.927 2 119.092 45.981 4 75 1 905.00 2.952 75 22.8600 246.063 68.580 1 82.020 8 120.701 46.602 7 76 1 930.40 2.992 12 23.1648 249.343 69.4945 83.1144 122.310 47.224 1 77 1 955.80 3.031 49 23.469 6 252.624 70.408 9 84.208 1 123.920 47.8455 78 1981.20 3.07086 23.7744 255.905 71.3233 85.301 7 125.529 48.466 9 79 2 006.60 3.11023 24.079 2 259.186 72.2377 80.395 3 127.138 49.0882 80 2 032.00 3.14960 24.3840 262.467 73.1521 87.488 9 128.748 49.709 6 81 2 057.40 3.18897 24.688 8 265.748 74.0065 88.5825 130.357 50.331 0 82 2 082.80 3.228 34 24.9936 269.028 74.981 0 89.070 1 131.966 50.952 3 83 2 108.20 3.26771 25.298 4 272.309 75.8954 90.709 7 133.576 51.5737 84 2 133.60 3.30708 25.603 3 275.590 76.809 8 91.8033 135.185 52.1951 85 2 159.00 3.34645 25.908 1 278.871 77.7242 92.9509 136.795 52.8164 86 2 184.40 3.38582 26.2129 282.152 78.638 6 94.050 0 138.404 53.4378 87 2 209.80 3.425 19 26.5177 285 433 79.553 0 95.1442 140.013 54.0592 88 2 235.20 3.46456 26.8225 288.713 30.467 4 90.2378 141.623 54.680 6 89 2260.60 3.50393 27.1273 291.994 81.3818 97.331 4 143.232 55.301 9 90 2 286.00 3.54330 27.432 1 295.275 82.2962 98.425 0 144.841 55.923 3 91 2311.40 3.58267 27.7369 298.556 83.2106 99.5180 140.451 56.544 7 92 2 336.80 3.62204 28.041 7 301.837 84.1250 100.012 148.000 57.1660 93 2 362.20 3.66141 28.3465 305.118 85.039 4 101.700 149.009 57.787 4 94 387.60 3.700 78 28.651 3 308.398 85.953 8 102.799 151.279 58.408 8 95 2413.00 3.740 15 88.956 1 311.679 86.868 2 103.893 152.888 59.030 1 96 2438.40 3.77952 9.2609 314.960 87.782 6 104.987 154.497 59.651 5 97 2 463.80 3.81889 9.565 7 318.241 88.6970 100.080 150.107 60.272 9 98 489.20 3.858 26 9.8705 321.522 89.6114 107.174 157.716 60.894 3 99 514.60 3.897 63 0.1753 324.803 90.525 8 108.208 159.325 61.5150 100 2 540.01 3.937 00 0.480 1 328.083 91.4402 109.301 160.935 62.1370 SURFACES. There are no fundamental standards of surfaces or areas, as these measures are all based on the linear measures, which see for their fundamental values. The legal U. S. yard, foot, inch, mile, etc., being about 3 parts in one million larger than the legal values in Great Britain, the U. S. square yard, square foot, etc., will be about 6 parts in one million larger than the British, a difference which is absolutely negligible in all but the most refined physical measurements. The values given in the following tables are based on the U. S. legal relation. To reduce the values in these tables to British square miles, square yards, square feet, and similar units, when very great accuracy is required, subtract 6 parts for every million from all those values of a square mile, square yard, etc.; for instance, add this correction in the value of one square mile in square meters, but not in square feet, as the latter is the same for both; or Add 6 parts for every million to all the values of other units which are given in terms of square miles, square yards, etc. This will never affect the 5th place of figures by more than one unit and generally less. A circular unit or measure (such as a circular mill) is the area of a circle whose diameter is one unit or measure (as one mill). It is used for cross-sections of round wires, pipes, rods, etc., and avoids the necessity of using the value of ir ( = 3.141 592 65). If the diameter of a circle is d, its area in circular units is simply d2. Some of the specific relations given in the table may also be expressed as follows: If d is the diameter of a circle expressed in one kind of a unit, then the area in the other unit will be: if d s in mils the area in sq.  d2X5.067.09. In inches, the area in sq. feet = d2X0.005.454.15. In feet, the area in sq. centimeters = d2X729.662. In feet, the area in sq. inches = d2X113.097. SURFACES; Circular or Cross-section Measures. Usual. Aprx. means within 2% ; "sq." means square and is often used as a suffix instead of the exponent (2), being simpler for printing and type-writing; thus sq. cm for era2; sq. ft for ft2. Checked by L. A. Fischer, Asst. Phys. National Bureau of Standards. 1 circular mil [CM]= 0.785 398. sq. mil. Aprx. %0. -. -0.000 645 163. Cmm. Aprx. ifa -*- 1 000. = 0.000 506 709* sq. mm. Aprx. V£-f- 1 000. = 0.000 001 circular inch 1 sq. mil [mil2] = 1.273 24* circular mils. Aprx. 1% = 0.000 821 447* circ. mm. Aprx. Vi2 •*• 100 = 0.000645 163* sq. millimeter. Aprx. %i-*-l 000 J_. = 0.000 001 sq. inch 6-000 0000 1 circular millimeter [Cmm]: = 1 550.00* circular mils. Aprx. i# X 1 000 3.190 3308 = 1 217.36* sq. mils. Aprx. % X 1 000 3.085 4207 = 0.785 398* sq. millimeter. Aprx. %0 1-895 0899 = 0.01 circular centimeter 2-000 0000 1 sq. millimeter [mm2] = 1 973.52* cir. mils. Aprx. 2 000. . 3.295 2409 = 1 550.00* sq. mils. Ap. 1% X 1 000 3-190 3308 = 1.273 24* circ. mm. Aprx. 1%. . . 0-104 9101 = 0.012 732 4* circ-. cm. Aprx. Ho 2-104 9101 = 0.01 sq. centimeter 2-000 0000 =0.001 550 00* sq. in. Aprx. %8 •*• 100 . 5.190 3308 42 SURFACES. 1 circular centimeter [Ccm]: = 155 000.* circular mils. Aprx. Ufa X 100 000 5-190 3308 121 736.* sq. mils. Aprx. 12 X 10 000 : 5-085 4207 = 100. circular millimeters 2-000 0000 78.539 8 * sq. millimeters. Aprx. 80 1-895 0899 = 0.785 398 * sq. centimeter. Aprx. 8/10 1-895 0899 = 0.155 000 * circular inch. Aprx. %3 1-190 3308 = 0.121 736 * sq. inch. Aprx. 12-^100 1-085 4207 = 0.001 076 39 * circular foot. Aprx. 108-^-100 000 3-031 9683 = 0.000 845 391 * sq. foot. Aprx. 1/12-^100 1-085 4207 1 sq. centimeter [cm2]: = 197 352.* circular mils. Aprx. 2 X 100 000 5-295 2409 155 000.* sq. mils. Aprx. 1/12-^100 1-085 3308 127.324 * circular millimeters. Aprx. 1/10 1000 2-1049 101 100. sq. millimeters 2. 000 0000 1.273 21 circular centimeters. Aprx. 1% 0-104 9101 = 0.197 352 circular inch. Aprx. 1% 0-295 2409 = 0.155 000 sq. inch. Aprx. %8 1-190 3308 = 0.01 sq. decimeter 2-000 0000 = 0.001 370 50 circular foot. Aprx. 1% 0-s- 1 000 3-136 8784 = 0.001 076 387 sq. foot. Aprx. 108 -=-100 000 3-031 9683 circular inch [Gin]: = 1 000 000. circular mills 6-000 0000 = 785 398. sq. mills. Aprx. % X 1 000 000 5-895 0899  = 0.785 398 sq. inch. Aprx. %0 1-895 0899 = 0.006 944 44 circular foot. Aprx. 7-1 000 3-841 6375 = 0.005 454 15 sq. foot. Aprx. «/n-v- 100 3-736 7274 1 sq. inch [in2]= 1 273 240.* cir. mils. Aprx. HX 10000 000 6-104 9101 = 1 000 000. sq. mils 6-000 0000 = 821.447 * cir. mm. Aprx. %X 1 000 2-914 5793 = 645.163 * sq. mm. Aprx. %X 1 100 2-809 6692 = 6.451 63 * sq. cm. Aprx. 1% 0-809 6692 = 1.273 24 * circular inches. Aprx. 1% 0-104 9101 = 0.064 516 3 * sq. Decimeter. Aprx. %i- 10.... 2-809669? = 0.008841 94 circular foot. Aprx. 9-=- 1 000.. 3-9465476 = 0.006 944 44 * sq. foot. Aprx. ftooo 3-841 6375 I sq. decimeter [dm2] = 100. sq. centimeters 2-000 0000 = 15.5000* sq. inches. Aprx. 1VrX 10. 1.1903308 = 0.107 638 7* sq. foot. Aprx. 11 -=- 100.. 1-031 968? = 0.01 sq. meter 2-000 000( = 0.011 9599* sq. yard. Aprx. 12-4-1000 2-0777253 1 circular foot [Cft] = 929.034* cir. cm. Aprx. 1^2 X 1 000.. 2-968 0317 = 729.662* sq. cm. Aprx. 5/u X 1 000 2-863 1216 144. circular ins. Aprx. M- X 1000. 2-1583625 = 113.097* sq. inches. Aprx. %0 1 000. 2-0534524 = 0.785 398* sq. foot. Aprx. %0 1-895 0893 1 sq. foot [ft2] (Brit.) = 0.999 994 2 sq. foot (U. S.). Aprx. 1 L999 9975 = 0.092902 9 sq. meter. Aprx. Hia- 10. 2-9680292 1 sq.foot [ft2] (U.S.) = 1 182.88' cir. cm. Aprx. %X 1 000. 3-0729410 = 929.034* sq. cm. Aprx. n/12 X 1 000. 2-968 0317 = 183.346* cir. in. Aprx. %X 100 2-2632723 = 144. sq. ins. Aprx. V7 X 1 000... 2-158 3625 = 9.290 34* sq. dm. Aprx. H12X 10... 0-968 0317 = 1.273 24* circular feet. Aprx. 1%... 0-104 9101 = 1.000005 7 sq. feet (Brit.). Aprx. 1... 0-000 0025 = 0.111 111* sq. yard, or V9 1-0457575 = 0.092 903 4* sq. meter. Aprx. 1... 1-999 9975 = 0.836 126 sq. meter. Aprx. %M 1.9 Isq. yard [yd2] (Brit. )= 0.999 994 3 sq. yard (U.S.). Aprx. 1... 1-999 9975 = 0.836 126 sq. meter. Aprx. %M 1.9 Isq. yard [yd2] (Brit. )= 0.999 994 3 sq. yard (U.S.). Aprx. %M 1.9 Isq. yard [yd2] (Brit. )= 0.999 994 3 sq. yard (U.S.). Aprx. %M 1.9 Isq. yard [yd2] (Brit. )= 0.999 994 3 sq. yard (U.S.). Aprx. %M 1.9 Isq. yard [yd2] (Brit. )= 0.999 994 3 sq. yard (U.S.). Aprx. %M 1.9 Isq. yard [yd2] (Brit. )= 0.999 994 3 sq. yard (U.S.). Aprx. %M 1.9 Isq. yard [yd2] (Brit. )= 0.999 994 3 sq. yard (U.S.). Aprx. %M 1.9 Isq. yard [yd2] (Brit. )= 0.999 994 3 sq. yard (U.S.). Aprx. %M 1.9 Isq. yard [yd2] (Brit. )= 0.999 994 3  1.031 9708 = 10.763 87 sq. ft. (U. S.). Aprx. 1%i X 10 1.031 9683 = 1.19599 sq. yds. (Brit.). Aprx. = 3097600. = 2589999. = 25 900.0 = 640. = 259.000 = 2.590 00 sq. feet. Aprx. X 10 000 000 7-445 2678 sq. yards. Aprx. 31 X 100 000... 6-491 0253 sq. meters. Aprx. 26 X 100 000... 6-413 2996 acres 2-806 1800 hectares. Aprx. 260 2-413 2996 sq. kilometers. Aprx. 26 -^ 10 0-413 2996 sq. kilometers. Aprx. 26 -^ 10 0-413 2996 SURFACES (continued). Unusual, Special Trade, or Obsolete. 1 milliare = 0.1 sq. meter. 1 cei tare, centar, or centaire = 10.763 87 sq. feet = 1. sq. meter. 1 square (building) = 100. sq. feet. 1 declare = 10. sq. meters = 0.1 arc. 1 sq. rod, or sq. pole, or sq. perch = 625. sq. links (surveyor's) = 272M sq. feet. = 30M sq. yards = 25. 293 sq. meters = 25. 293 sq. meters = 1.60 acre. 1 sq. chain (Gunter's or surveyor's) = 4. 356 sq. sq. feet = 484. sq. yards = 404.687 sq. meters = 16. sq. rods, poles, or perches = 4.046 87 acres = 0.0404687 hectare = 0.000 404 687 sq. kilometer = 0.000 156 250 sq. mile. SURFACES. 1 sq. meter = 0.002 471 04 sq. chain. 1 area = 0.247 104 sq. chain. 1 area = 10. sq. chains. 1 area = 24. 7 10 4 sq. chains. 1 acre (not used) = 1.000 sq. meters = 10. areas. 1 rod ("R") = 10.890 sq. feet = 1.210 sq. yards = 1.011.72 sq. meters = 40. sq. rods, poles, or perches = 3. acre. Fardingdeal (Brit.) - 1. rod. 1 circular acre = 235.504 feet diameter. 1 section (of land) = 1. 1 mile square. 1 township = 36. sq. miles. 1 sq. myriameter or miriameter = 100. sq. kilometers = 38.610 1 sq. miles. SURFACES (concluded). Foreign. These are mostly obsolete as the metric system is now used in most foreign countries. The British measures are included among the U. S. measures, being very nearly, and sometimes quite, the same. The translated terms are merely synonymous, and not the exact equivalents. Germany. Prussia 1 Morgen = 180 sq. Ruthen (rods). 1 Morgen = 25.53225 ares = 2 553.225 sq. meters = 0.630 912 acres. According to Nystrom's Mechanics, 1 Berlin Morgen, great, = 6 786 sq. yards; ditto, small, = 3 054 sq. yards. 1 Hamburg Morgen = 11 545 sq. yards. 1 Hanover Morgen = 3 100 sq. yards. 1 Prussian Morgen = 3 053 sq. yards. France. 1 arpent (acre) = 100 sq. perches (French, nearly same as U. S.) = 34.19 are, or 51.07 are = 0.8 44 849 acres, or 1.261 96 acres. Austria. 1 Joch=1600 sq. Klafter = 5755 sq. meters = 1.422 08 acres. 1 Vienna Joch = 6 889 sq. yards. Sweden. 1 Tunnland = 56 000 sq. fot = 49.364 1 acres. According to Nystrom, it is equal to 5 900 sq. yards. Russia. 1 Dessaetine = 2 400 sq. saschehn = 10 925 sq. meters = 2.699 61 acres. 13 066.2 sq. yards (Nystrom). Switzerland. 1 Geneva arpent = 6 179 sq. yards; 1 faux = 7 855 sq. yards; 1 Zurich acre = 3 875.0 sq. yards. Spain. 1 fanegada (since 1801) = 1. 5871 acres = 69 134.08 sq. feet; according to Nystrom, it is equal to 5 500 sq. yards. Japan. 1 ch (apparently not 1 ch) = 10 tan of 10 se of 30 tsubo. 1 tsubo = 1 ken square = 3. 31 square meters = 35. 6 square feet. 1 square meter = 0.302 tsubo. 1 square foot = 0.028 1 tsubo. 1 square foot = 0.028 1 tsubo. 1 ch = 2. 45 acres. Miscellaneous. (From Nystrom's Mechanics.) 1 fanegada, Canary Isles, = 2422 sq. yards. 1 acre, Ireland, = 7 840 sq. yards. 1 acre, Scotland, = 6 150 sq. yards. 1 moggia, Naples, = 3998 sq. yards. 1 Pezza, Rome, = 3 158 sq. yards. 1 Geira, Portugal, = 6 970 sq. yards. Conversion Tables for Surfaces. Sq. in.= Sq. cm. = Sq. m.  1 38.709 8 45.1614 51.6130 58.064 6 64.5163 0.155000 0.309 999 0.464999 0.619999 0.774 998 0.929 998 1.08500 1.23999 1.39500 1.55000 0.092 903 0.185807 0.278 710 0.371 614 0.464517 0.557 420 0.650 324 0.743227 0.836 131 0.929 034 10.763 9 21.5277 32.291 6 43.0555 53.8193 64.583 2 75.347 1 86.1110 96.874 8 107.639 0.836 13 1.67226 2.508 39 3.344 52 4.18065 5.01678 5.85291 6.689 05 7.525 18 8.36131 1.19599 2.391 97 3.58796 4.783 94 5.979 93 7.17591 8.371 90 9.567 88 10.7639 11.9599 0.404 687 0.809 375 1.21406 1.61875 2.023 44 2.428 12 2.83281 3.237 50 3.642 19 4.04687 2.471 04 4.942 09 7.41313 9.884 18 12.3552 14.8263 17.297 3 19.768 4 22.239 4 24.7104 VOLUMES. 45 VOLUMES. Cubic and Capacity Measures. The fundamental standard measures of volumes in the United States are; (a) the cubes of linear dimensions in terms of units based on the international meter; (b) the liter which is the volume of the mass of one international kilogram of pure water at its maximum density, and at 760 mm. barometric pressure; (c) the gallon, which is equal to exactly 231 cubic inches; (d) the bushel (the old Winchester bushel of England) which is equal to exactly 2 150.42 cubic inches. The inch here referred to is the one derived from this meter. The liter, being based on this kilogram, is the same in all the countries participating in the international convention. These four measures of volumes and capacities are those now used by the National Bureau of Standards in Washington and are in general use in this country. They are definite and accurate, except that the precise volume of the liter expressed in cubic centimeter is still slightly uncertain as explained below. The liter is, according to the decision some years ago of the International Committee of Weights and Measures, defined as "the volume of the mass of one kilogram of pure water at its maximum density, and under normal atmospheric pressure." The accepted temperature, at present, at which the density of water is a maximum, is 4° C., but this may be altered slightly by subsequent determinations. The normal atmospheric pressure referred to is that exerted by a vertical column of mercury 760 mm. high, at latitude 45° and at sea level, the mercury having a density of 13.595 93. This definition of the liter has been adopted by the National Bureau of Standards. It was originally intended that the kilogram should be the weight of a cubic decimeter of water, thus making the liter exactly a cubic decimeter. The kilogram, however, being now fixed definitely as the weight of a certain piece of metal, and as this establishes the liter, it still remains to determine by measurement the precise volume of the liter in cubic decimeters. The International Bureau began this determination some five years ago, and the results thus far obtained indicate that the liter is about 25 parts in 1 000000 greater than the cubic decimeter. As this relation will always be subject to slight corrections, and as the difference is of no consequence in practice, the National Bureau of Standards has for the present assumed that the liter and the cubic decimeter are equivalent; this identity is assumed also in all the tables in this book. The difference above mentioned would at most affect only the fifth place of figures slightly, and generally only the sixth. The capacities of vessels are determined by weighing the water necessary to fill them, and not by measuring their dimensions (see the table of the weights and volumes of water). The Customs Service and the Internal Revenue Bureau uses the gallon of 231 cubic inches above referred to; it is the old British wine gallon. In these tables, this gallon and the measures based on it are indicated as "liquid; U.S." to distinguish them from the "dry"; U.S. measures and the Imperial or "Brit." measures. The gallon and liter are the units for measuring liquids, while the bushel and liter are the units for dry measures, as for grain, fruits, vegetables, etc. The "dry" measures are about one sixth greater than the corresponding "liquid" measures; accurately: dry measures XI. 163 65 (aprox. add) = liquid measure (log 0-065 8213) liquid measures X 0.859 367 (aprox. subtr. Vr) = dry measure (log 1.934 1787) The fluid ounce is in use chiefly by apothecaries. The barrel is no fixed unit, and no value of a barrel has ever been adopted by Congress; in the Customs Service and Internal Revenue Bureau, every barrel is gauged. Concerning the bushel, the Revised Statutes of the United States, under the ascertainment of duties on grain, chapter 6, sec. 2919, says: "For the purpose of estimating the duties on importations of grain, the number of cubic centimeters of water at 4° C. to be 0.999 955 kg. This makes a liter about 45 parts in 1000000 greater than a cubic decimeter. But it seems that no formal adoption of any value has yet been made. Number of bushels shall be ascertained by weight, instead of by measuring; and sixty pounds of wheat, fifty-six pounds of corn, fifty-six pounds of rye, forty-eight pounds of barley, thirty-two pounds of oats, sixty pounds of pease and forty-two pounds of buckwheat, avoirdupois weight, shall respectively be estimated as a bushel. In Great Britain, the liter is exactly the same as in the United States. The gallon, which in this country is often called the Imperial or British gallon, was originally defined as the volume of "ten imperial pounds of distilled water, weighed in air against brass weights, with the water and the air at the temperature of 62° Fahrenheit, the barometer being at 30 inches." According to the latest computations of the Standards Office in London, the British or Imperial gallon is equal to 4.545963 1 liters; this value was made legal in 1896 to Great Britain, and is the one used as a basis throughout these tables, even for computing such values as the gallon in cubic inches; the figures are therefore quite consistent throughout, except that the U. S. yard, foot, inch are used, which are about 3 parts in one million larger than the British, a difference too small to be considered in any but the most refined physical measurements. Owing to this difference, the U. S. cubic yard, cubic foot, etc., are about 9 parts in one million greater than the British. Hence to reduce these values in those Table to British yards, feet, and inches, when very great accuracy is required, subtract 9 parts for every million from all the values of a cubic yard, cubic foot, and cubic inch given in terms of other units than yards, feet, and inches; for instance, add this correction in the value of a cubic foot in cubic meters, but not in cubic inches, as the latter is the same for both; or add 9 parts for every million to all the values of other units given in terms of cubic yards, cubic feet, and cubic inches. This will never affect the fifth place of figures by more than one unit, and generally not that much. 