None
1 9 0.69 4>3 20 2 ^ 5 14 14 34 20 2048 0.20 1 l 3 0.70 4 16 21 2 S 11 8 14 26 1 4 20 40 20 26 55 0.21 1 17 0.71 4 20 22 2 14 17 8 20 32 1 4 26 46 2033 t 0.22 1 21 0.72 4 24 23 2 20 24 8 2638 M 3| S3 2039 7 0.23 1 24 0.73 4 27 24 2 2630 £ 3 ^ 44 M 38 59 2045 IJ 0.24 1 28 0.74 4 27 24 2 2630 £ 3 ^ 44 M 38 59 20 45 57 0.25 1 32 075 0.76 23842 8 44 57 1451 11 20 57 26 35 27 24449 5 3 14 57 8 21 3 32 O.27 39 0.77 0.78 4 43 28 2 505 8 57 9 5 324 21 938 O.28 14 3 1 40 4 46 2Q 2 7 9 3 16 M 9.10 21, $45 0.29 0.79 4 49 .TO 3 1 7 9 922 is is; 21 21 51 0.31 0.53 4 53 31 3 0H 91528 s 21 43 21 27 57 0.31 1 54 0.81 4 57 3* 31520 9 2134 52749 2'34 3 0.32 5 57 33 321 26 927 41 5 33 55 21 40 10 0.33 2 1 0.83 5 4 34 3 2732 9 33 47 5 40 21 46 16 0.34 0.84 5 8 1 3 33 35 9 39 53 1546 8 21 52 22 0.35 085 0.86 Si' 3 39 45 9 48 59 15 52 14 21 58 26 2 12 5 5 37 3 45 51 9 52 5 10 58 20 0.38 22 4 35 0.37 2 16 0.87 S '9 33 3 5' 57 95S 12 22 10 41  to 33 22 1 6 47 009 2 23 0>) 5 26 40 4 4 10 10 ro 24 16 1639 i<> 2245 22 22 %*% 0. 165 Table 36. LENGTH OP ONE DEGREE OP THE MERIDIAN AT DIFFERENT LATITUDE8. [Derivation of table explained on pp. xhri-xhruL] Latitude, Metres. Statute Miles, Geographic mm. t' of tbe Eq. Latitude. Metres, Statute Miles. Geographic I'ofthcEq. 0* i nose's 11056S.S 68.703 68,704 59-594 59-594 45° 46 111132,1 111151.9 111171,6 §$ 59-898 5*908 2 110569,8 6S.705 68,706 59-595 59-596 47 69-079 5*9»9 3 110571,5 48 111191,3 69.091 59-929 4 "°5739 6S.707 59-597 49 111210.9 69.103 59.940 5 110577.0 68.709 59-598 59600 50 111230,5 69,115 39W 6 110580.7 68.711 51 111249,9 69,127 5*>-w I 1 10585. 1 110590*2 6S.7U ; 68,717 £3 53 11 1269.2 11128S.3 69-^39 69.IU 59.972 59.981 9 1 10595.9 68,731 59-609 54 111307-3 69.163 5^99* 10 1 10602.3 68,725 50612 55 1 1 1326.0 fy t7 J 60.002 ii 110609.3 68,729 59.616 56 U 1344-5 KM 60.012 12 110617,0 68.734 59,620 57 111362,7 69,198 60,022 1J 1106*5,3 68-739 59-625 5* 111380.7 69.209 60032 u 110634.2 68.745 59.629 59 111398-4 691220 60041 15 1 10643-7 110653.8 1 10664.5 68.751 59-634 60 111415.7 69,230 60-051 60060 16 6S.7J7 68,763 59,640 61 1114327 69241 *7 50-646 62 111449-4 69.251 60.069 18 1 10675.7 68.770 59-653 63 1114657 69,26c 60077 19 110687.5 6S.778 59-658 64 1114B1.5 69,271 60086 20 110699.9 110712.0 68.786 59-665 65 IH497-0 69.281 60-094 21 68.794 59-673 66 111512.0 69,290 60.102 22 *3 1 10726.2 11074a! 68,802 68,810 g& 2 111526.5 111540.5 60.3S 60.MO 60118 24 110754.4 68-819 59-694 69 111554.1 69.316 60.115 25 110769.2 68-S20 6S.83S 59,702 70 111567,1 6*3** 60.132 26 110784.5 59-7*0 71 n 1579.7 69332 60.139 *7 1 10800,2 6S.848 5^719 72 1115916 1 11603.0 69*340 60.145 28 110816,3 68,858 68.868 59.727 73 69-347 60.151 *9 1 10832 J 59-736 74 n 1613.9 69.354 60.157 30 110S49.7 6&S79 59-745 75 1 11624.1 69,360 60.163 60.168 3 1 110866,9 68.SS9 59-7M 59764 76 111633,8 69.366 3 2 110884.4 6S.900 3 111642.8 69.372 60.173 33 H0902-3 68.911 59-774 111651.2 69.332 60.177 34 I IO92O.4 68.923 59-7^4 79 111659,0 60182 35 110938^ 68.934 59*794 59*§04 80 111666,2 69.386 601S6 36 110957*4 68,946 81 111672,6 69.390 60189 3 Z 38 11097&3 110995.3 sis 59.814 59-8*4 82 I 3 111688.1 69-394 69-397 60,192 60195 39 111014,5 6S.98I 59-834 84 69400 60,197 40 111033,9 68.993 59-84S 85 111691,9 69402 60199 4* 111053.4 69-005 1 59.866 86 1 1 1695.0 69404 60201 4^ 111073.0 69.017 1 1116974 69.405 60202 43 1 1 1092.6 69.029 59.876 111699.2 69407 60203 44 iiiji:„1 69,042 59-88? 89 1 1 1700.2 69-407 60204 45 111132,1 60054 59-898 90 1117000 69407 60204 Smithsonian Tablm. 166 Table 37. LENGTH OF ONE DECREE OP THE PARALLEL AT DIFFERENT LATITUDE8. [Derivation of table explained on p. xlix.] latitude. Metres. Statute Miles. Geographic I 7 of the Eq. Latitude. Metres. Statute Miles. Geographic Miles, i' of the Eq. 0° i 2 3 4 111321.9 1 1 1305.2 1 1 1254.6 111170.4 1 1 1052.6 69.162 69.130 69.005 60.000 59-991 59964 59.018 59-855 45° 46 4 £ 48 49 78850.0 77406.5 76050.2 74628.5 73'74-9 48.995 48.135 47261 46.372 45469 42498 41-753 40994 40223 39.440 5 6 I 9 110901.2 110716.2 1 104977 1 10245.8 109960.5 68.911 68.796 68.660 68.503 68.326 59-773 59-673 59-556 59.420 59.266 50 5i 52 53 54 71698.0 70200.8 68681.1 67140.3 65578.8 44-552 43.621 42.676 41.719 40.749 38644 37.837 37.018 36.187 35-346 10 ii 12 »3 109641.9 1 09290.1 108905.2 108487.3 108036.6 68.128 &3 09 67.670 67.411 67. 131 59.95 58.905 58.697 58.472 58.229 55 56 $ 59 63997-1 62395.7 60775.1 59.35-7 57478.1 39766 37.764 36.745 35715 34-493 33630 32757 31.873 30979 15 16 19 1075S3-I 107037.0 106488.5 105907.7 105294.7 66.830 66.510 66.169 65.808 65.427 57-395 57.082 57-395 57.082 56.751 60 61 P 64 55802.8 541 10.2 52400.9 50675.4 48934-3 34-674 33-622 31.488 30406 30.076 29.164 28.243 27-313 26.374 20 21 22 23 44 104649.8 103973-2 103265.0 102525.4 101754.6 65.026 64.606 64.166 63.227 56404 56.039 55-657 55-59 54-43 65 66 69 47178.0 45407.1 43622.2 41823.8 40012.4 20.315 28. 215 27.106 24.862 25.428 24473 235 11 25 26 % 29 100953.0 100120.6 98364.8 97441.9 62.729 62.212 61.676 61.12L 60.548 54.411 53963 53-498 53-516 52.519 70 7i 72 73 74 38188.6 363530 34506.2 32048.6 30780.9 23.729 22.589 21.441 20.287 19.126 20.583 17.597 16.590 30 31 32 33 34 96489.3 955073 94496.2 93456.3 92387.9 59-956 59-345 58.717 58.071 57407 52.006 51.476 50-93 50-37I 49-795 75 76 H 79 28903.6 27017.4 25122.8 23220.4 21310.8 17.960 16.788 15.61 14.428 13.242 15.578 14.562 13.541 1 1 1486 35 36 s 39 91  19394.6 X7472.4 15544.7 1 361 2.2 1 16755 12.051 10.857 8458 7.255 10.453 I378 7-337 6.293 40 41 43 44 853970 841384 82854.0 81544.2 80209.4 53-063 -52.281 50.669 49.840 46.027 44.656 43.950 43-231 85 86 89 9735-1 77917 &3 1949.4 6.049 4.841 3632 2422 1.211 5.247 4.200 3-15I 2.101 1.051 45 78850.0 48.995 42.498 90 0.0 0.000 167 Table 88. INTERCONVERSION OF NAUTICAL AND STATUTE MILES. Nautical Miles. Statute Miles. Statute Miles. Nautical Miles. 1 2 3 4 5 . 6 I 9 1-1516 23031 4.6062 57578 6.9093 8.0609 9.2124 10.3640 1 2 3 4 5 6 I 9 08684 17368 2.6052 3-4736 4-3420 5.2104 00788 6.9472 7.8155 Smithsonian Tables. At defined by the United States Coast and Geodetic Survey. Table 39. CONTINENTAL MEASURES OF LENGTH WITH THEIR METRIC AND ENGLISH EQUIVALENTS. The asterisk (*) indicates that the measure is obsolete or seldom used. Measure. El, Netherlands Fathom, Swedish = 6 feet Foot, Austrian, old French * Russian Rheinlandisch or Rheinlandisch (Prussia, Denmark, Norway) * Swedish* Spanish *=i vara Klafter, Wiener (Vienna) Line, old French = ^fa foot Mile, Austrian post = 24000 feet.... German sea Swedish = 36000 feet Norwegian = 36000 feet Netherlands (mijl) Prussian (law of 1868) Danish Palm, Netherlands Rode, Danish Ruthe, Prussian, Norwegian Sagene, Russian Toise, old French = 6 feet Vara, Spanish Mexican Werst, or versta, Russian = 500 sagene Metric Equivalent. English Equivalent 1 metre. 3.2808 feet 1.7814 « 5.8445 M 0.31608 M 1.0370 " 1.0657 " 0.32484 M 0.30480 M 1 0.31385 0.2969 a 1.0297 u 0.9741 " 0.2786 0.9140 u 1.89648 a 6.2221 ** 0.22558 cm. ao888inch. 7-8594 1.852 km. <« 4714 statute miles. 1. 1508 M ia6o „. « 6.642 " • 11.2986 M 7<02 u u 1 «< 0.6214 «• u 7.500 « 4.660 u 7.5324 M 4^804 " 0.1 metre. 0.3281 feet 3.7662 «« 12.356 " 21336 M I 1.0490 0.8380 1.0668 Smithsonian Tables. 168 Table 40* ACCELERATION (g) OF GRAVITY ON SURPACE OF EARTH AND DERIVED FUNCTIONS. 9-77989 + 0.05121 sin 4 = 9.80599 —  by Wm. Harkness, Professor of Mathematics at the University of Pennsylvania, U.S.N.; Washington: Government Printing Office, 1891. This is length of seconds pendulum. Table 41. LINEAR EXPANSIONS OF PRINCIPAL METALS IN MICRONS PER METRE (OR MILLIONTHS PER UNIT LENGTH). Name of metal. Aluminum. Brass. Copper. Glass. Iron. Iron, wrought. Lead. Platinum. Platinum. Platinum. Silver. Steel. Tin. Zinc. Expansion per  formula, AAT _ A log N fi = modulus of common logarithms = 0.43429448. For AlogiV = 1 unit in AiV N For A log JV = 4 units in AiV N (in round numbers) 4th place 5th " 6th " 7th " 4l49§ 4th place 5th " 6th " 7th " ToVt ldioo 100*007 1000000 U4904I Smithsonian Taslcs. 170 APPENDIX. CON8TANT8. Numerical Constants. Numbtr. Lofirithm. Base of natural (Napierian) logarithms, = * =2.7182818 0.4342945 Log s, modulus of common logarithms, = /* = 0.4342945 9.6377843- •10 Circumference of circle in degrees, = 360 2.5563025 ** " " in minutes, = 21600 4-3344538 u «« " in seconds, = 1296000 6.1126050 Circumference of circle, diameter unity, -=* = 3.14159265 0.4971499 Numbtr. Logarithm. 2* = 6.2831853 0.7981799 1/1^ = 0.1013212 9.0057003- •10 * = 1 .047 1 976 0.0200286 V» = 17724539 0.2485749 3 L= 0.3183099 9.5028501 — 10 -7-L = O.5641896 V » 9.7514251 - -10 «* = 9.8696044 0.9942997 V 7= 14142136 Vj= 1.7320508 0.1 5051 50 0.2385607 The arc of a circle equal to its radius is in degrees, p° = i8o/» - 57.29578 1.7581226 in minutes, p' = 60 p° - 3437-7468' 3.5362739 in seconds, p" —6op f - 206264.8" 5.3144251 For a circle of unit radius, the arc of i° = i/p° -0.0174533 8.2418774- -10 arc of 1' = i/p = 0.0002909 6.4637261 - - 10 arc (or sine) of 1"= i/p" = 0.00000485 4.6855749- -10 Qeodetical Constants. Dimensions of the earth (Clarke's spheroid, 1866) and derived quantities. Equatorial semi-axis in feet, = a = 20926062. 73206875 in miles, - « - 3963-3 3.5980536 Polar semi-axis in feet, — £= 208551 21. 7-3192127 in miles, -. b = 3949.8 3.5965788 (Eccentricity) 2 = a ~ /* = 0.00676866 7*305030 — • 10 Flattening = g a — /- 1/294^784 7.5302098- -10 Perimeter of meridian ellipse, = 24859.76 miles. Circumference of equator, = 24901.96 • < Area of earth's surface, = 196940400 square miles. Mean density of the earth (Harkness) = 5.576 ±0.01 6. Surface density " u " = 2.56 ±0.16. Acceleration of gravity (Harkness) : g (cm. per second) = 980.60 (1 — 0.002662 cos 2$) for latitude <p and sea level. g, at equator = 977.99 ; g, at Washington > = 980.07 ; g % at Paris = « *8o.94; g, at poles = 983.21 ; g, at Greenwich = 98M7. Length of the seconds pendulum (Harkness) / = 39.012540 -f 0.208268 sin 2 <p inches = 0.990910 4* 0.005290 sin 2 <p metres. Uuthsomian Tables. nx APPENDIX. CONSTANTS. -Continued. Astronomical Constants (Habknkss) Sidereal year = 365.256 357 8 mean solar days. Sidereal day = 23.56 4.100 mean solar time. Mean solar day = 24.56 4.4646 sidereal time. Mean distance of the earth from the sun = 92.800.000 miles. Physical Constants. Velocity of light (Harkness) = 186.337 miles per second = 299878 km. per second. Velocity of sound through dry air = 1090.000 + 0.00367 (° C. feet per second. Weight of distilled water, free from air, barometer 30 inches : Weight in grains. Weight in grains. Volume. b°F. 4°C. 6°F. 4°C. 1 cubic inch (determination of 1890) 252.286 252.568 16.3479 1.63662 1 cubic foot (1890) at 62 F. 62.2786 lbs. A standard atmosphere is the pressure of a vertical column of pure mercury whose height is 760 mm. and temperature 0° C, under standard gravity at latitude 45 and at sea level. 1 standard atmosphere = 1033 grammes per sq. cm. = 14.7 pounds per sq. inch. Pressure of mercurial column 1 inch high = 34.5 grammes per sq. cm. = 0.491 pounds per sq. inch. Weight of dry air (containing 0.0004 of its weight of carbonic acid) : 1 cubic centimetre at temperature 32 F. and pressure 760 mm. and under the standard value of gravity weighs 100.293.05 grammes. Density of mercury at 0° C. (compared with water of maximum density under atmospheric pressure) = 13.5956. Freezing point of mercury = — 38.5 C. (Regnault, 1862.) Coefficient of expansion of air (at constant pressure of 760°) for 0° C. (do.) : 0.003°7°- Coefficient of expansion of mercury for Centigrade temperatures (Broch) : A = A = 0.0001.181.792 / — 0.00001.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0 0.2374 (from 0° to 100° C, Regnault). At constant volume, Kv = 0.1689. Ratio of the two specific heats of air (Rontgen) : Kp = 14053. Thermal conductivity of air (Graetz) : k = 0.0000484 (1 + 0.001 85 /°, C) E™""*- [The quantity of heat that passes in unit time through unit area of a plate of unit thickness, when its opposite faces differ in temperature by one degree.] Latent heat of liquefaction of ice (Bunskn) = 80.025 mass degrees, C. Latent heat of vaporization of water = 606.5 — 0.695 *° C. Absolute zero of temperature (Thomson, Heat, Encyc. Brit.) : — 273.*^ C. = — 459-°4 F. Mechanical equivalent of heat : 1 pound-degree, F. (the British thermal unit) = about 778 foot-pounds. 1 pound-degree, C. = 1400 foot-pounds. 1 calorie or kilogramme-degree, C. = 3087 foot-pounds = 426.8 kilogrammetres = 4187 joules (for g = 981 cm.). Smithsonian Tables. Based on Prof. Rowland's determinations. (Proc. A m. Acad, Arts md Scu, 1880.) APPENDIX. SYNOPTIC CONVERSION OF ENGLISH AND METRIC UNITS. English to Metric. 2.54000 0.304801 0.914402 1-60935 645163 >.836 929-034 0.8361 31 0404687 Units of length. 1 inch. 1 foot. 1 yard. 1 mile. Units of area, x square inch. 1 square foot. 1 square yard. 1 acre. 1 square mile. Units of volume. 1 cubic inch. 1 cubic foot. 1 cubic yard. Units of capacity, 1 gallon (U. S.) = 231 cubic inches. 1 quart (U. S.). 1 x Imperial gallon (British). 2 77463 cubic inches (1890). x bushel (U. S.) = 215042 cubic inches. 1 bushel (British). 2.59000 259.000 16.3872 0.028317 0.764559 centimetres, metre. kilometres. square centimetres. square metre. hectares. square kilometres. hectares. square kilometres. hectares. cubic centimetres, cubic metres or steres. cubic metres or steres. 3.78544 litres. 0.94636 litres. 4.5468 Units of mass. 1 grain. 1 pound avoirdupois. 1 ounce troy. 1 ton (2240 lbs.). 1 ton (2000 lbs.). Units of velocity. 1 foot per sec. (0.6818 miles per hr. = 0.30480 metres per sec. = 1.0973 km. per hr. 1 mile per hr. (1.4667 feet per sec.) = 0.44704 metres per sec = 1.6093 km. per hr. 647990 0453593 28.3496 31.015 1.01 605 0.907106 3 litres. 35-2393 litres - 36.3477 litres. milligrammes. grammes. grammes. tonnes. 0404835 9.484 016 — 10 9-961 37 — 10 0.206 650 0.800669 2.968032 9.922 274 — 10 9.607 120 — 10 0413300 2-4*3 3°o 1. 214 504 8452 047 — 10 9.883 41 1 — 10 a 578 116 9.976056 — 10 0.657 709 1.547027 x. 560 477 1.811 568 9.656666—10 1.452 546 1.492 810 0.006914 9.957696—10 Units of force. 1 poundal. Weight of 1 grain (for g = 981 cm.). Weight of 1 pound av. (for ^ = 981 cm.). 13825.5 dynes. 6.57 dynes. 4.45 X 10 6 dynes. Units of stress — In gravitation mttsurt. 1 pound per square inch == 70. 307 1. grammes per sq. centimetre. 1 pound per square foot = 4.8824 kilogrammes per sq. metre. Units of work — In absolute 1 foot-poundal. 421 403 ergs. 4.140682 1.803 237 5048335 1.846997 0.688634 5.624698 — In gravitation menses. 1 foot-pound (for = 981 cm.) = 1356.3 × 10 4 ergs = 0.138255 kilogrammetres. Units of activity (rate of doing work). 1 foot-pound per minute (for = 981 cm.) = 0.022605 watts, x horse-power (33 000 foot-pounds per min.) = 746 watts = 1. 01 387 force de cheval. Units of heat. 1 pound-degree, F. 1 pound-degree, C. b 252 small calories or gramme-degrees, C. pound-degrees, F. tetMNiAN Tables. 173 APPENDIX. SYNOPTIC CONVERSION OF ENGLISH AND METRIC UNITS. Metric to English. Units of length. Logpratas. i metre (io 9 microns). 39-370O inches. 1.595165 328083 feet 0.515984 44 1. 09361 yards. CX038863 i kilometre. 0.62137 miles. 9-793350—IO Units of area. 1 square centimetre. a 1 5500 square inches. 9-I90 33I — W i square metre. 10.7639 square feet. 1.031 968 44 44 1-19599 square yards. CU077726 I hectare. 2.47104 acres. 0.392880 i square mile. 0.38610 square miles. 9.586701 — 10 Units of volume. i cubic centimetre. 0.0610234 cubic inches. 8.785496—10 i cubic metre or stere. 35-3*45 cubic feet 1-547 953 44 44 «4 x-30794 cubic yards. 0.116589 Units of capacity. i litre (61.023 cubic inches). 0.26417 gallons (U. S.). 9421884 — 10 44 X.0566S quarts (U. S.). 0.023944 44 0.21993 Imp. gallons (British). 9.342 291 — 10 1 hectolitre. 2-33774 bushels (U. S.). 0452973 (4 2.7 51 2 1 bus Imp. gallons (British). 9.342 291 — 10 1 hectolitre. 2-33774 bushels (U. S.). 0452973 (4 2.7 51 2 1 bus Imp. gallons (British). 9.342 291 — 10 1 hectolitre. 2-33774 bushels (U. S.). 0452973 (4 2.7 51 2 1 bus Imp. gallons (British). 9.342 291 — 10 1 hectolitre. 2-33774 bushels (U. S.). 0452973 (4 2.7 51 2 1 bus Imp. gallons (British). 9.342 291 — 10 1 hectolitre. 2-33774 bushels hels (British). Units of mass. 1 gramme. 15-43 2 4 grains. 1.188433 1 kilogramme, 2.20462 pounds avoirdupois. 0-343334 troy. 1.547454 44 32.1507 ounces troy. 1.507 190 1 tonne. a 9842 1 tons (2240 lbs.). 9.993086—10 u 1.10231 tons (2000 lbs.). 0.042304 Units of velocity. 1 metre per second. 32808 feet per second. 0.515984 44 (4 44 2.2369 miles per hour. 0.349653 1 km. per hr. (0.2778 m. per sec.). 0.62137 miles per hour. 9.793350—10 Units of force. 1 dyne (weight of (98 1) 1 grammes, for g=* 981 cm-) = 7-2330 X xcr* poundals. 0.204817 pounds per sq. inch. 1 kilogramme per square metre. 0.204817 pounds per sq. foot 1 standard atmosphere. 14.7 pounds per sq. inch. (See def. p. 172.) Units of work — In absolute merit. 1 erg. 2-3730 X xo" 8 foot poundals. x megalerg = 10* ergs; 1 joule = 10* ergs. —In grivKitlon 1 netturt. 1 kilogramme-metre  per unit area. Difference of Potential: quantity of work required to move a quantity of electricity; (work done) -4- (quantity) moved). Electric Force, or Electro-motive Intensity: (quantity) -f- (distance 2). Capacity of an accumulator: e -f- E, Specific Inductive Capacity. In Magnetics. Quantity of Magnetism, or Strength of Pole. Strength or Intensity of Field: (quantity) -7- (distance 2). Magnetic Force. Magnetic Moment: (quantity) X (length). Intensity of Magnetization: magnetic moment per unit volume. Magnetic Potential: work done in moving a quantity of magnetism; (work done) -r- (quantity moved). Magnetic Inductive Capacity. Dimensions in Symbol. electrostatic system. e [L» M* T" 1 ] <r [L-* M* IT*] E [L* M* T"»] Cor q k [L-* M» T-i] [L] [o] « ml I electro-magnetic system. [L» M* T-i] [L~* M* T"»] [L-* M» T"T [L 1 M* T-i] [L-* M* T-i] VoxD. [L*M*T"i] * [o] In Electro-magnetics. Symbol. Intensity of Current i Quantity of Electricity conveyed by current : * (intensity) X (time). Potential, or difference of potential: (work done) -7- (quantity of electricity upon which work is done). Electric Force: the mechanical force act- ing on electro-magnetic unit of quantity; (mechanical force) -f- (quantity). Resistance of a conductor : E-r-i. R Capacity: quantity of electricity stored up q per unit potential-difference produced by it. Specific Conductivity: the intensity of current passing across unit area under the action of unit electric force. Specific Resistance: the reciprocal of r specific conductivity. 1 In Nfins of electro-magnetic practical unit [L* M* T-i] Ampire. [L* M*] Coulomb. E [LI M* T-»] Volt E [L* M* n [LT-i] [L-i-P] [L-«T] [L« 1-*\ Ohm. Farad. llHTHSJONIAN TABLCS. 175 INDEX. PAGB Lcceleration, dimensions of 175 of gravity, formula for 171 table of values of 169 or, cubical expansion, specific heat, thermal conductivity, and weight of 172 dry, Sir George, treatise cited xcviii dbrecht, Dr. Th., treatise cited bra tlgebraic formulas xiii-xv alignment curve lvi aluminum, linear expansion of 170 impere, dimensions of 175 ingles, equivalents in arcs xviii sum of, in spheroidal triangle Ivii ingular velocity, dimensions of 175 Lunulus, circular, area of xxx Lntilogarithms, explanation of use of xcix 4-place table of 26, 27 Appendix t7 l -*7S Arcs, equivalents in angles xvii of meridians and parallels xlvi-1 table of lengths of meridional 78-80 table of lengths of parallel 81-83 table of time equivalents 162 ire xli Lrea, of circle xxx table of values of 23 of surface of earth 1-lii Areas, of continents lxv of oceans lxv of plane and curved surfaces xxix-xxxi of zones and quadrilaterals of the earth's surface 1-lii tables of values of 142-159 of regular polygons xxx Arithmetic means, progression, and series.. xiii Astronomical constants 172 co-ordinates lxvii latitude lxv time lxxii Astronomy lxvii-lxxxii References to works on lxxxii Atmosphere, mass of earth's lxvi standard pressure of 172 weight of unit of volume of 172 Average error, definition of lxxxiv Azimuth, astronomical and geodetic lxvi compoundation of differences of lxvi-lx determination of lxvi-lx Barometer, barometric formula of 160 Barometer, heights by 160 Binomial series xiv Brass, linear expansion of 170 Briinnow, F., treatise cited lxxxii Bushel, Winchester xxxv equivalent in litres 2 Cable length xxxviii Calorie, value of 172 Capacity, measures of, British xxxviii Metric xli Centare xli Chauvenet, Wm., treatise cited lxxxii Circumference, of circle xxviii Table of values of 23 of earth xlix, 171 of ellipse xxix C. G. S. system of units xlii Clarke, General A. R., spheroid of xliii treatise cited lxvi Coefficient, of cubical expansion of air and mercury 172 of linear expansion of metals 170 of refraction lxiii Compression, of earth xliii Computation, of differences of latitude, lon-gitude, and azimuth lviii of mean and probable errors xcv Conductivity, thermal, of air 172 Cone, surface of xxxi volume of xxxii Constants, astronomical 172 geodetic 171 numerical 171 of earth's spheroid xliv Continental measures (table of British and Metric equivalents) 168 Continents, areas of Ixv average heights of Ixv Conversion, of arcs into angles and angles into arcs xvii of British and Metric units. Co-ordinates [continued]. Table of, scale 1/126720 102-109 Table of, scale 1/63360 110-121 Table of, scale 1/20000 132-141 Table of, scale 1/80000 132-141 Table of, generating ellipse of earth's spheroid. xli v Copper, linear expansion of 170 Cord (of wood), volume of xxxix Correction, for astronomical refraction, table of mean values of 161 to observed angle for eccentric position of instrument briii to reduce measured base to sea level...lxiv Cosines, table of natural 28, 29 use of table explained c Cotangents, table of natural 30, 31 use of table explained c Coulomb, dimensions of 175 Cubic, of volumes xxxii Cubes, table of 4-22 Cube roots, table of 4-22 Cube roots, table of 4-22 Cylinder, surface of xxxii volume of xxxii Day, sidereal and solar lxxii, 172 Degrees, number of, in unit radius xviii of terrestrial meridian xlvi, 166 of terrestrial parallel xlix, 167 Density, mean, of earth lxv mean, of superficial strata of earth lxv of mercury 172 Departures (and latitudes), table of 32-47 mode of use of table explained c Depths, average, of oceans lxv Determination, of azimuth lxxix of heights, by barometer 160 by trigonometric leveling lxi of latitude lxxvii of time l Difference, between astronomical and geodetic azimuth lvii of heights, by barometer 160 by trigonometric leveling lxi Differences, of latitude, longitude, and azimuth, on earth's spheroid lviii table for computation of 70-77 Differential formulas xxi Dimensions, of earth xliii, 171 of physical quantities 175 Dip, of sea horizon briii Distance, of sea horizon lxiii of sun from earth 172 Doolittle, Prof. C. L., treatise cited lxxxii Earth, compression of xliii, 171 Earth (continued). density of lxv dimensions of xliii, 171 ellipticity of xliii, 171 energy (of rotation) of lxvi equatorial perimeter of xliii, 171 flattening of xliii, 171 mass of lxvi meridian perimeter of xlix, 171 moments of inertia of lxvi shape of xlm surface area of In volume of lxv Eccentricity, of ellipse xlni of earth's spheroid xliv, 171 El, value of .168 Electric quantities, dimensions of 175 Electro-magnetic quantities, dimensions of .175 Ellipse, area of xzx equations to xliv length of perimeter of nix Ellipsoid, volume of (see Spheroid) xxxiii Ellipticity, of earth xliii, 171 Energy, dimensions of 175 of rotation of earth lxvi Equations, of ellipse xliv of Prototype Kilogrammes zl of Prototype metres zl Error, in ratio of English yard to Metre.. xxrvu Errors, probable, mean, average . .lxxxiv, lxxxvia table of, for interpolated quantities. .Ixxxvi theory of lxzxin Everett, J. D., treatise cited. xlii Excess, spherical or spheroidal lviii Expansion, cubical, for air and mercury ....173 linear, of principal metals 170 Farad, dimensions of 175 Fathom, length of xxzvm Swedish 168 Flattening, of earth xliii, 171 Foot, Austrian 168 British xxzvii French, Rhenish, Spanish, Swedish. . . .168 Force, dimensions of 17$ Formulas, algebraic xiii-zv for differentiation . • xxi for integration xxiii for solution of plane triangles xviii for solution of spherical triangles xt trigonometric zv Freezing point of mercury 172 Functions, trigonometric, of one angle zv of two angles xti special values of xv values in series irii INDEX. Gallon, British and wine xxxviii Gauss's formulas for spherical triangles xxi Geodetic latitude xliv Geodetic differences of latitude, longitude, and azimuth lviii Geodetic line lvii Geodetic constants 171 Geographical points, computation of.lviii-lxi Geodetic means, progression xiii Geometric means, progression xiii Glass, linear expansion of 170, 172 Gravity, acceleration of, formula for 171 Table of values of 169 Gunter's chain, length of xxxviii Harkness, Prof. Wm., memoir cited lxv, 169, 171, 172 Heat, dimensions of 175 latent, of liquefaction of ice 172 of vaporization of water 172 mechanical equivalent of 172 Hectare xli Heights, average, of continents lxv determination of, by barometer 16b trigonometrically lxi Helmert, Dr. F. R., treatise on geodesy cited lxvi treatise on theory of errors cited.xcviii Horizon, dip of sea lxiii Imperial pound and yard xxxiv Integrals, definite xxvi indefinite xxxiii Interconversion, of English and Metric units 2, 3, 173, 174 of sidereal and solar time lxx Imperial pound and yard xxxiv Integrals, definite xxvi indefinite xxxiii Interconversion, of English and Metric units 2, 3, 173, 174 of sidereal and solar time lxx Imperial pound and yard xxxiv Integrals, definite xxvi indefinite xxxiii Interconversion, of English and Metric units 2, 3, 173, 174 of sidereal and solar time lxx Imperial pound and yard xxxiv Integrals, definite xxvi indefinite xxxiii Interconversion, of English and Metric units 2, 3, 173, 174 of sidereal and solar time lxx Imperial pound and yard xxxiv Integrals, definite xxvi indefinite xxxiii Interconversion, of English and Metric units 2, 3, 173, 174 of sidereal and solar time lxx Imperial pound and yard xxxiv Integrals, definite xxvi indefinite xxxiii Interconversion In the tables for 164, 165 Iron, linear expansion of 170 Joule, value of 174 Kilogramme, Prototype xxxiv equations of xl relation to pound xxxvi, xli Kinetic energy, dimensions of 175 of rotation of earth lxvi Klafter, Wiener, in terms of foot and metre 168 Latitude, astronomical, geocentric, and reduced xliv determination of lxxvii Latitudes and departures, table of 32-47 mode of use of table explained c Lead, linear expansion of 170 Least squares, method of lxxxvi references to works on xcviii Legendre's theorem for solution of spheroidal triangles lvii Length, of arc of meridian xlvi of arc of parallel xlix of equator of earth 171 of meridian circumference of earth 171 of perimeter of ellipse xxix of Prototype Metres Nos. 21 and 27 xl of seconds pendulum, formula for 171 table of values of 169 Leveling, trigonometric lxi Line (French), value of 168 lines, lengths of xxviii on a spheroid lvi Linear measures, British xxxvii Metric xli tables for interconversion of. Measures (continued). of surface, British xxxviii Metric xli tables for interconversion of..2, 3, 173, 174 Mechanical equivalent of heat 172 Mechanical units, dimensions of 175 Mensuration xxviii-xxxiii Mercury, density and cubical expansion of 172 Meridian, arcs of terrestrial xlvi table of lengths of 78-80 circumference of earth xlix, 171 Method of least squares Ixxxvi Metre, Prototype xxxiv equations of Nos. 21 and 27 xl relation to British yard xxxvi, xli Metric system xl Mile, Austrian 168 British (statute) xxxvii Danish, German sea, Netherlands, Norwegian, Prussian, Swedish 168 Nautical 168 Modulus of common logarithms xv Moivre's formula xvi Moment of inertia of mass, dimensions of. 175 Moments of inertia of earth lxvi Momentum, dimensions of 175 Napierian base (of logarithms) xiv, 171 Napierian logarithms xiv Napier's analogies xx Natural logarithms xiv Nautical mile, table of equivalents in statute miles 168 Numerical constants 171 Ohm, dimensions of 175 Palm, length of, English xxxviii Netherlands 168 Parallel, arcs of terrestrial xlix table of lengths of 81-83 Pendulum, length of seconds 171 table of lengths of 169 Perch (of masonry) volume of xxxix Perimeter, of circle xxviii of ellipse xxix of regular polygon xxviii, xxx Physical constants 172 Physical quantities, dimensions of 175 Physical quantities, dimensions of 175 Platinum, linear expansion of 170 Platinum iridium, linear expansion of 170 Polygonic projection of maps liii graphical process of, explained cii Polygons, regular, areas of xn lengths of lines of xxtn Potential (electric), dimensions of 175 Potential (electric), dimensions of 175 Potential (electric), dimensions of 175 Probable error, definition of lxxzhr compoundation of xc? Projection of maps liii, cii Prototype Kilogrammes and Metres xxot equations of xl Quadrilaterals, of earth's surface, areas of 1 tables of areas of 142-159 Quantity, of electricity, dimensions of 175 Radii, of curvature xl? Radius of curvature, of meridian, table of logarithms of 48-56 of section normal to meridian, table of logarithms of 57-65 Radius vector of earth's surface 1 Rate of working (power), dimensions of 175 Ratio, of pound to kilogramme xxxvi of specific heats of air 172 of yard to metre xxxvi Recip Crocals, of natural numbers, table of. Sidereal time lxii Table for conversion to mean time.. 165 Signs, of trigonometric functions xv Silver, linear expansion of 170 Sines, table of natural 28*29 [ explanation of use of c Solar time lxxii Table for conversion of mean solar to sidereal 164 Solution, of plane triangles xviii of spherical triangles xx of spheroidal triangles lvii Span, length of xxxviii Specific heat of air 172 Sphere, equal in surface with earth lii equal in volume with earth lii surface of xxxi volume of xxxii Spherical excess (see Spheroidal excess)....lviii Spheroid, representing the earth xliii surface of xxxi volume of earth's lxv Spheroidal excess lviii example of computation of ci Spheroidal triangle lvii Square roots, table of 4-22 Squares, table of 4-22 Standards, of length and mass xxxiv Steel, linear expansion of 170 Stere xli Stress, dimensions of 175 units of 173, 174 Sums, of arithmetic and geometric progression, and special series xiii Surfaces (see Areas) xxix Surface measures, British xxxviii Metric xli tables for interconversion of...2, 3, 173, 174 Surface, of continents lxv of earth's spheroid lii of oceans Ixv of sphere and spheroid xxxi Surveyor's chain, length of xxxviii Table for conversion of arc into time 162 conversion of mean into sidereal time.. 164 conversion of sidereal into mean time.. 165 conversion of time into arc 163 determination of heights by barometer.. 160 interconversion of British and Metric units 2,3, 173, 174 interconversion of nautical and statute miles 168 Table of acceleration of gravity and derived quantities 169 Table of {continued). antilogarithms, 4-place 26, 27 areas of quadrilaterals of earth's surface of 10° extent in latitude and longitude 142 i° extent in latitude and longitude 144.14S 30' extent in latitude and longitude 146.148 15' extent in latitude and longitude 146.148 15' extent in latitude and longitude 156.159 areas of regular polygons xxx circumference and area of circle 23 constants, astronomical 172 geodetical 171 numerical 171 for interconversion of English and Metric units 2, 3, 173, 174 Continental measures of length 168 co-ordinates for projection of maps — scale 1/250000 84-91 scale 1/125000 92-101 scale 1/125000 102-109 scale 1/63360 1 10-12 1 scale 1/2200000 1 22-131 scale 1/80000 132-141 departures and latitudes 32-47 dimensions of physical quantities 175 errors of interpolated values from numerical tables lxxxvi expansions (linear) of principal metals 170 formulas for solution of plane triangles 170 formulas for variation of change in number due to change in its logarithm 170 latitudes and departures 32-47 lengths of arcs of meridian 78-80 of arcs of parallel 81-83 of i° of meridian 166 of i° of parallel 167 linear expansions of metals 170 logarithms, 4 Place 24, 25 anti-, 4-place 26, 27 of factors for computing spheroidal excess 68, 69 of factors for computing differences of latitude, longitude, and azi-muth 70-77 of meridian radius of curvature. 48-55 of radius of curvature of normal section 56-65 of radius of curvature of oblique sections 66, 67 mean astronomical refraction 161 measures and weights — British, of capacity xxxix 182 INDEX. Table of {continued). British, of length xxxviii British, of surface xxxviii British, of weight xxxix Metric zli tables for interconversion of 2, 3» *73» "74 natural cosines 28, 29 natural tangents 30, 31 radii of curvature, logarithms of, for meridian section 4&-55 for normal section 56-65 for oblique section 66, 67 reciprocals, squares, cubes, square roots, cube roots, and logarithms of natural numbers 4-22 refraction, mean astronomical 161 signs of trigonometrical functions xv values for computing areas and dimensions of regular polygons xxx for computing perimeter of ellipse xxix of log (1 — 2m) and log (1 — m) used in trigonometric leveling...lxii weights and measures (see Table of measures and weights) 2, 3, 173, 174 Table, traverse (see Traverse table) 32-47 Tangents, natural, table of 30, 31 use of table explained c Taschenbuch, Des Ingenieurs xcix Taylor's series xxii Temperature, absolute zero of 172 of freezing mercury 1 72 Theory of errors lxxxiii-xcviii references to works on xcviii Thermal conductivity, dimensions of 175 of air 172 Three-point problem lxiv Time, determination of brxiv equivalents in arc, table of 163 example of use of table civ interconversion of sidereal and solar, Tables for 164, 165 Tin, linear expansion of 170 Toise, value in feet and metres 168 Tonne 173, 174 Tonne 173, 174 Tonne 173, 174 Trapezoid, area of xxix Traverse table 3 2 ~47 explanation of use of c Triangles, plane, solution of xviii Triangles (continued). spherical, solution of xz spheroidal, solution of ltii Triangulation, primary and secondary, differ- ences of latitude, longitude, and azimuth in lviii-lx Trigonometric functions, of one angle xv of two angles xvi series for xvii Trigonometric leveling hi Units, British System xxxvii m C. G. S. System xlii Metric System xl standards of length and mass xxriv tables for interconversion of British and Metric 2, 3, 173, 174 Useful formulas xiii-xxvii Vara, Mexican and Spanish 168 Velocity, dimensions of 175 of light and sound 172 Versta, Russian 168 Vertical section curve on spheroid lvi Volt, dimensions of 175 Volume, of earth lxv of solids xxxii Weight, of distilled water 172 Weights and measures (see Measures and weights), tables for interconversion of British and Metric 2, 3, 173, 174 Werst, Russian 168 Work, dimensions of 175 Wright, Prof. T. W., treatise cited xcviii Yard, imperial xxxhr ratio of, to metre xxxvi, xxxvii Zachariae, G., treatise cited xlvi Zenith distances, use of, in trigonometric leveling hi Zenith telescope, use of lxxiz Zero, of absolute temperature .172 Zinc, linear expansion of 170 Zones, of earth's surface, area of 1 fit V. 