MEDICAL SCHOOL Hooper Foundation Accession SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLUME 71, NUMBER 1 SMITHSONIAN PHYSICAL TABLES REPRINT OF SE VENTH RE VISED EDITION PREPARED BY FREDERICK E. FOWLE AID, SMITHSONIAN ASTROPHYSICAL OBSERVATORY (PUBLICATION 2539) CITY OF WASHINGTON PUBLISHED BY THE SMITHSONIAN INSTITUTION 1921 3 78 ADVERTISEMENT. In connection with the system of meteorological observations established by the Smithsonian Institution about 1850, a series of meteorological tables was compiled by Dr. Arnold Guyot, at the request of Secretary Henry, and the first edition was published in 1852. Though primarily designed for meteoro- logical observers reporting to the Smithsonian Institution, the tables were so widely used by physicists that it seemed desirable to recast the work entirely. It was decided to publish three sets of tables, each representative of the latest knowledge in its field, and independent of one another, but forming a homo- geneous series. The first of the new series. Meteorological Tables, was published in 1893, the second, Geographical Tables, in 1894, and the third, Physical Tables, in 1896. In 1909 yet another volume was added, so that the series now comprises: Smithsonian Meteorological Tables, Smithsonian Geographical Tables, Smithsonian Physical Tables, and Smithsonian Mathe- matical Tables. The fourteen years which had elapsed in 1910 since the publication of the first edition of the Physical Tables, prepared by Professor Thomas Gray, had brought such changes in the material upon which the tables must be based that it became necessary to make a radical revision for the fifth and sixth revised editions published in 1910 and 1914. The latter edition was re- printed thrice. For the present seventh revision extended changes have been made with the inclusion of new data on old and new topics. CHARLES D. WALCOTT, Secretary of the Smithsonian Institution. June, PREFACE TO 7 REVISED EDITION. The present edition of the Smithsonian Physical Tables entails a considerable enlargement. Besides the insertion of new data in the older tables, about 170 new tables have been added. The scope of the tables has been broadened to include tables on astrophysics, meteorology, geochemistry, atomic and molecu- lar data, colloids, photography, etc. In the earlier revisions the insertion of new matter in a way to avoid renumbering the pages resulted in a somewhat illogical sequence of tables. This we have tried to remedy in the present edition by radically rearranging the tables; the sequence is now, mathematical, me- chanical, acoustical, thermal, optical, electrical, etc. Many suggestions and data have been received: from the Bureau of Stand- ards, including the revision of the magnetic, mechanical, and X-ray tables, from the Coast and Geodetic Survey (magnetic data), the Naval Observ- atory, the Geophysical Laboratory, Department of Terrestrial Magnetism, etc. ; from Messrs. Adams of the Mount Wilson Observatory, Adams of the Geo- physical Laboratory (compressibility tables), Anderson (mechanical tables), Bellinger, Hackh, Humphreys, Mees and Lovejoy of the Eastman Kodak Co. (photographic data), Miller (acoustical data), Van Orstrand, Russell of Prince- ton (astronomical tables), Saunders, Wherry and Lassen (crystal indices of refraction), White, Worthing and Forsythe and others of the Nela Research Laboratory, Zahm (aeronautical tables). To all these and others we are in- debted for valuable criticisms and data. We will ever be grateful for further criticisms, the notification of errors, and new data. FREDERICK E. FOWLE. ASTROPHYSICAL OBSERVATORY, SMITHSONIAN INSTITUTION, May, 1919. NOTE TO REPRINT OF ;TH REVISED EDITION. Opportunity comes with this reprint to insert in the plates a number of correc- tions as well as some newer data. Gratitude is especially due to Messrs. Wherry and Smith of the Bureau of Chemistry, Department of Agriculture, for sugges- tions. FREDERICK E. FOWLE. ASTROPHYSICAL OBSERVATORY, SMITHSONIAN INSTITUTION, March, 1921. TABLE OF CONTENTS. Introduction: units of measurement, dimensional and conversion formulae, standards: xxiii General discussion, xxiii; Fundamental units, xxiii; Derived units, xxiv; Con- version factors and dimensional formulae, xxv; Dimensional reason- ing, XXV. Dimensional formulae: xxvi Geometrical and mechanical units, xxvi; Heat units, xxviii; Electric and mag- netic units, xxix; Electrostatic system, xxx; Electromagnetic system, xxxi. Fundamental standards: xxxiii Standards of length, xxxiv; Standards of mass,.xxxiv; Standards of time, xxxiv; Standards of temperature, xxxiv. Numerically different systems of units: . . . xxxv Proposed systems of units (table I), xxxv; Gaussian systems, xxxv; Practical electromagnetic system, xxxvi; International electric units, xxxvi. The standards of the International Electric Units: xxxviii Resistance, xxxviii: Mercury standards, xxxviii; Secondary standards, xxxix; Resistance standards in practice, xxxLx; Absolute ohm, xxxix. Current, xl: Silver voltameter, xl; Resistance standards used in current measurements, xli; Absolute ampere, xli. Electromotive force, xli: International volt, xli; Weston normal cell, xli; Portable Weston cell, xliii; Absolute and semi-absolute volts, xliii. Quantity of electricity, xliv: Standards, xliv. Capacity, xliv. Inductance, xliv: Inductance standards, xliv. Power and energy, xlv: Watt, xlv; Standards and measurement, xlv. Magnetic units, xlv: Table II. The ordinary and ampere-turn units xlvi. TABLE PAGE 1. Spelling and abbreviations of common units of weight and measure . . 2 2. Fundamental and derived units, conversion factors 3 (a) Fundamental units 3 (b) Derived units 3 3. Tables for converting U. S. weights and measures: (1) Customary to metric 5 (2) Metric to customary 6 4. Miscellaneous equivalents U. S. and metric weights and measures . . 7 Vi CONTENTS. 5. Equivalents of metric and British imperial weights and measures: (1) Metric to imperial .................. 8 (2) Multiples, metric to imperial ............. 9 (3) Imperial to metric .................. 10 (4) Multiples, imperial to metric ............. 1 1 MATHEMATICAL TABLES 6. Derivatives and integrals .................... 12 7. Series ............................ 13 8. Mathematical constants .................... 14 9. Reciprocals, squares, cubes and square roots of natural numbers ... 15 10. Logarithms, 4-place, 1000-2000 ................. 24 11. Logarithms, 4-place . . ..................... 26 12. Antilogarithms, 4-place ....... 13. Antilogarithms, 4-place, 0.9000-1.0000 .............. 30 14. Circular (trigonometric) functions, arguments (, '). ......... 32 15. " " " " (radians) ....... 37 16. Logarithmic factorials, n!, n = i to 100 .............. 40 17. Hyperbolic functions . . . . .................. 41 18. Factorials, i to 20 ........ ............... 47 19. Exponential functions ................ ..... 48 20. Values of e* 2 and e~** and their logarithms ............ 54 21. " " V_" e -r " " ........ .- 55 22. " " /?* e ~ v ^ " ............ 55 23. " " t* " e-' " " " , x fractional ....... 56 24. Least squares: probability integral, argument hx ......... 56 25- " " _ "_ */r ......... 57 26. values of 0.6745 \/i/(n i) ............ 57 27. " " 0.6745 Vi/n^^ ........... 58 28. " " 0.8453 Vi/n(n - i) . . .......... 58 29- " " 0.8453 {i/V- 1 1 ........... 58 30. formulae .................... 59 31. Inverse probability integral, diffusion integral ........... 60 32. Logarithms of gamma function, n between i and 2 ......... 62 33. Values for the first seven. zonal harmonics, 9 = o to 6 = 90 . . . . 64 34. Cylindrical harmonics, oth and i st orders, x = o to 3. 5, 6-place. ... 66 35- " x = 4 to 15, 4-place .... 68 36. (a) ist ten roots cylindrical harmonic of zeroth order = o ...... 68 (b) " fifteen " " " ' first " =o ...... 68 Notes, general formulae of Bessel's functions ........... 68 37. Values f or I * (i - sin 2 6 sin 2 $) =*=*(/$; argument 6; also logs .... 69 *J o 38. Moments of inertia, radii of gyration, corresponding weights .... 70 39. International atomic weights, valencies .............. 71 CONTENTS. Vii 40. Volume of glass vessel from weight of its volume of H 2 O or Hg . ... 72 41. Reductions of weighings in air to vacuo 73 42. Reductions of densities in air to vacuo 73 MECHANICAL PROPERTIES 43. Introduction and definitions 74 44. Ferrous metals and alloys: Iron and iron alloys 75 45. " " " carbon steels 76 46. " " " " heat treatments 76 47 . " " " " alloy steels 77 48. " steel wire, specification values 78 49. " " " " . " experimental values 78 50. " " " " semi-steel 78 51. steel wire rope, specification values ... 79 52. " plow-steel rope, " .... 79 53. steel wire rope, experimental values ... 79 54. Aluminum, miscellaneous 80 55. Aluminum: (a) sheet, experimental values 80 (b) " specification values 81 56. Aluminum alloys 81 57. Copper: miscellaneous experimental values 82 58. rolled, experimental values 82 59. wire, specification values, hard-drawn 82 60. " " medium hard-drawn 83 61. " " soft or annealed 83 62. plates 83 63. Copper alloys: nomenclature 83 64. " copper-zinc alloys or brasses 84 " copper-tin " " bronzes 84 65. " " three or more metals 85 66. Miscellaneous alloys 88 67. metals: tungsten; zinc; white metal 89 68. Cement and concrete : (a) cement 90 " " " (b) cement and cement mortars 90 (c) concrete 91 69. Stone and clay products: (a) American building stones 92 " " " " (b} Bavarian building stones 92 " " " " (c) American building bricks 93 " " " (d) brick piers, terra-cot ta piers 93 " (e) various bricks 93 70. (a) Sheet rubber 94 (b) Leather belting 94 71. Manilla rope 95 72. Woods: hardwoods, metric units 96 73. " conifers, metric units 97 viii CONTENTS. 74. Woods: hardwoods, English units 98 75. " conifers, English units 99 76. Rigidity Modulus 100 77. Variation of moduli of rigidity with the temperature 100 78. Interior friction, variation with the temperature 101 79. Hardness 101 80. Relative hardness of the elements 101 81. Poisson's ratio 101 82. Elastic moduli of crystals, formulae 102 83. " ' " " " numerical results 103 COMPRESSIBILITY OF GASES 84. Compressibility of O, air, N, H, different pressures and temperatures . 104 85. " " ethylene at " " . 104 86. Relative gas volumes at various pressures, H, N, air, O, CC>2 .... 104 87. Compressibility of carbon dioxide, pressure- temperature variation . . 105 88. " gases, values of 105 89. " air and oxygen between 1 8 and 22 C 105 90. Relation between pressure, temperature and volume of sulphur dioxide 106 91. " " " " " " " ammonia . . . 106 92. Compressibility of liquids 107 93. " " solids 108 DENSITIES 94. Specific gravities corresponding to the Baume scale 109 95. Densities of the solid and liquid elements no 96. " various woods 112 97. " " " solids 113 98. " " alloys 114 99. natural and artificial minerals 115 100. " molten tin and tin-lead eutectic 115 101. Weight in grams per square meter of sheet metal 116 102. " various common units of sheet metal 116 103. Densities of various liquids 117 104. Density of air-free water between o and 41 C 118 105. Relative volume of water between o and 40 C 119 106. Density and volume of water, 10 to 250 C 120 107. " " " " mercury, -10 to 360 C 121 108. Density of aqueous solutions of salts, bases and acids 122 109. ethyl alcohol, temperature variation 124 no. methyl alcohol, cane-sugar, sulphuric acid . ... 126 in. " various gases 127 112. Volume of gases, values of i + 0.00367 /: (a) for values of t between o and 10 C by o. i steps .... 128 (b) " " "" " -90 and +1990 C by 10 steps . 129 CONTENTS. ix (c) logarithms for / between -49 and 399 C by i steps . . 130 (d) +400 and 1990*0 by 10 steps . 132 113. Density of moist air: h/ 7 60, h from i to 9 133 114. " " " " log A/y6o, h from 80 to 800 133 115. " " " 0.378^ in equation h = B 0.3786 135 116. Maintenance of air at definite humidities 135 117. Pressure of mercury and water columns 136 BAROMETRIC TABLES 1 1 8. Reduction of barometer to standard temperature 137 119. gravity, in. and mm, altitude term 138 120. " latitude 45, o to 45, mm 139 " 45 to 90, mm 140 122. o to 45, inches 141 123. " 45 to 90, inches 142 124. Correction to barometer for capillarity, mm and inches 143 125. Volume of mercury meniscus in mm 3 . 143 126. Barometric pressure corresponding to the boiling point of water: (a) metric scale 144 (b) inch scale 144 127. Determination of heights by the barometer 145 ACOUSTICS 128. Velocity of sound in solids 146 129. " " liquids and gases 147 130. Musical scales 148 131. " " 148 132. Fundamental tone, its harmonics and equal tempered scale 149 133. Relative strength of the partials of musical instruments 149 134. Characteristics of the vowels 149 135. Miscellaneous sound data 149 AERODYNAMICS 136. Kinetics of bodies in resisting medium, Stokes law 150 137. Flow of gas through tubes 150 138. Air pressure, large square normal planes, various speeds 151 139. Correction factor for small square normal planes 151 140. Effect of aspect ratio 152 141. Ratios of pressures on inclined and normal planes 152 142. Skin friction 152 143. Variation of air resistance with aspect and angle 153 144. " " shape and size 153 145. " " " " and speed 153 146. Friction . 154 X CONTENTS. 147. Lubricants 154 148. Lubricants for cutting tools 154 VISCOSITY 149. Viscosity of fluids and solids, general considerations 155 150. " water in centipoises, temperature variation 155 151. " ethyl-alcohol-water mixtures, temperature variation . . 155 152. and density of sucrose aqueous solutions, temp, variation . 156 153. " " " " glycerol " " at 20 C 156 154. " " castor oil, temperature variation 156 155. " of miscellaneous liquids ^ . 157 156. " organic liquids 158 157. Specific viscosity of solutions, density and temperature variation . . 159 158. " " " " atomic concentrations, 25 C 163 159. Viscosity of gases and vapors f 164 1 60. " : temperature and pressure variation . 165 161. Diffusion of an aqueous solution into pure water ......... 166 162. " vapors 167 163. " gases and vapors 168 164. " metals into metals 168 165. Solubility of inorganic salts in water, temperature variation .... 169 166. " " a few organic salts in water, temperature variation . . 170 167. " gases in water 170 168. " change of , produced by uniform pressure 171 169. Absorption of gases by liquids 172 170. Capillarity and surface tension, water and alcohol in air '. 173 171. " miscellaneous liquids in air .... 173 172. aqueous solutions of salts 173 173. " liquids-air, -water, -mercury .... 174 174. liquids at solidifying point 174 175. " thickness of soap films 174 VAPOR PRESSURES 176. Vapor pressures of elements 175 177. and rates of evaporation, Mo, W, Pt 175 178. organic liquids 176 179- " of ethyl alcohol 178 180. " " methyl alcohol 178 181. ( a ) carbon disulphide 179 (b) chlorobenzene J 79 (c) bromobenzene *79 (d) aniline 179 (e) methyl salicylate 180 (/) bromonaphthalene 180 (g) mercury 180 CONTENTS. xi 182. Vapor pressure of solutions of salts in water 181 183. Pressure of saturated water vapor over ice, low temperatures .... 183 184. " water, low temperatures . . 183 185. " o to 374 C 183 186. Weight in g per m 3 of saturated water vapor 185 187. Weight in grains per ft 3 of saturated water vapor 185 1 88. Pressure of aqueous vapor in atmosphere, various altitudes 185 189. " " " " " " sea-level 186 190. Relative humidity, arguments, vapor pressure and dry temperature . 187 191. wet and dry thermometers 189 THERMOMETRY 192. Stem correction for thermometers, centigrade 190 193. " Jena glass, o to 360 C 190 194. " " " " o " " " 191 195. " " " " " normal, o to 100 C . 191 196. Gas and mercury thermometers, formulae 192 197. Comparison of hydrogen and i6 UI thermometers, o to 100 C . . . . 192 198. " " " " 59 111 " o " 100 C. ... 192 199. " " " " 1 6 and 59 thermometers, -5 to -35 C 192 200. Comparison of air and i6 in thermometers, o to 300 C 193 201. " " " " 59 rn " 100 to 200 C 193 202. " hydrogen and various mercury thermometers .... 194 203. " air and high temperature (59 m ) mercury thermometer 194 204. " H, toluol, alcohol, petrol ether, pentane thermometers 194 205. Platinum resistance thermometry 195 206. Thermodynamic scale; temperature of ice point, Kelvin scale .... 195 207. Standard points for the calibration of thermometers 195 208. Calibration of thermo-element, PtPt-Rh 196 209. " " " Cu-constantan 196 210. Mechanical equivalent of heat, summary to 1900 (Ames) 197 211. " " " " best value 197 212. Conversion factors, work units 197 213. English and American horse power, altitude and latitude variation . 197 MELTING AND BOILING POINTS 214. Melting points of the chemical elements , . 198 215. Boiling points of the chemical elements .... .... 199 216. Melting points, effect of pressure .... 200 217. Freezing point of water, effect of pressure 200 218. Boiling point, effect of pressure 200 219. Inorganic c.ompounds, melting and boiling points, densities 201 X CONTENTS. 2 20. Organic compounds, melting and boiling points, densities: 203 (a) Paraffin series 203 (b) Olefine series 203 (c) Acetylene series 204 (d) Monatomic alcohols 204 (e) Alcoholic ethers 204 (/) Ethyl ethers 204 (g) Miscellaneous 205 221. Melting points of various mixtures of metals 206 222. " " " " " " " 206 223. Low-melting-point alloys 206 224. Transformation and melting points, minerals and eutectics 207 225. Lowering of freezing points by salts in solution 208 226. Raising of boiling points by salts in solution 210 227. Freezing mixtures 211 228. Critical temperatures, pressures, volumes, densities of gases .... 212 THERMAL CONDUCTIVITY 229. Thermal conductivity of metals and alloys 213 230. insulators, high temperatures 214 231. various substances 214 232. building materials 215 233. various insulators 216 234. water and salt solutions .......... 216 235. organic liquids 217 236. gases 217 237. Diffusivities 217 EXPANSION COEFFICIENTS 238. Linear expansion of the elements 218 239. " " miscellaneous substances 219 240. Cubical expansion of solids 220 241. " liquids 221 242. " gases 222 SPECIFIC HEATS 243. Specific heats of elements 223 244. Heat capacities, true and mean specific heats, and latent heats of fusion of the metallic elements, o to 1600 C 225 245. Atomic heats, atomic volumes, specific heats at 50 K, elements 226 246. Specific heats of various solids 227 247. " " water and mercury 227 248. " " various liquids 228 249. " heat of saturated liquid ammonia, -50 to +50 C ... 228 250. Heat contents of saturated liquid ammonia, 50 to +50 C .... 228 CONTENTS. Xiil 251. Specific heats of minerals and rocks 229 252. " (true and mean) of silicates, o to 1400 C 229 253. of gases and vapors, also cp/c v 230 LATENT HEATS 254. Latent heats of vaporization 231 255. formulae 232 256. ammonia 232 257. " Latent heat of pressure variation " of liquid ammonia 232 258. Latent and total heats of vaporization of elements, theoretical . . 233 259. Properties of saturated steam 234 260. Latent heats of fusion 240 HEATS OF COMBUSTION, FORMATION, ETC. 261. Heats of combustion of some carbon compounds 241 262. " " " miscellaneous compounds 241 263. Heat values and analyses of various fuels: (a) coals and coke .... 242 (b) peats and woods . . . 242 (c) liquid fuels 242 (d) gases 242 264. Chemical and physical properties of explosives 243 265. Additional data on explosives " 244 266. Ignition temperatures of gaseous mixtures 244 267. Explosive decomposition, ignition temperatures 244 268. Flame temperatures 244 269. Thermochemical data: heats of formation from elements 245 270. " " " " " of ions 246 271. " " " neutralization 246 272. " . " dilution of sulphuric acid ..... 246 RADIATION 273. Radiation formulae and constants for perfect (black-body) radiator . 247 274. in calories for perfect radiator, various temperatures . . . 247 275. distribution in spectrum for various temperatures .... 247 276. Black-body spectrum intensities, 50 to 20000 K 248 277. Relative emissive powers of various bodies for total radiation .... 249 278. Emissivities of metals and oxides 249 279. " " " " " 249 280. Temperature scale for tungsten, color, black-body and true tem- peratures 250 281. Color minus brightness temperature for carbon 250 COOLING BY RADIATION, CONDUCTION, AND CONVECTION 282. Cooling by radiation and convection: ordinary pressures 251 283. different pressures 251 XIV CONTENTS. 284. Cooling by radiation and convection: very small pressures 252 285. temperature and pressure effect 252 286. Conduction of heat across air spaces, ordinary temperatures .... 253 287. Convection of heat in air at ordinary temperatures 253 288. and conduction of heat by gases at high temperatures: . 254 (a) s as function of a/B 254 (b) ], p], [0], [>], and [>] will be adopted. These symbols will always represent simple numbers, but the magnitude of the number will depend on the relative magnitudes of the units the ratios of which they repre- sent. When the values of the numbers represented by these small bracketed letters as well as the powers of them involved in any particular unit are known, the factor for the transformation is at once obtained. Thus, in the above ex- ample, the value of / was 1/3, and the power involved in the expression for volume was 3; hence the factor for transforming from cubic feet to cubic yards was / 3 or i/3 3 or 1/27. These factors will be called conversion factors. To find the symbolic expression for the conversion factor for any physical quantity, it is sufficient to determine the degree to which the quantities length, mass, time, etc., are involved. Thus a velocity is expressed by the ratio of the number representing a length to that representing an interval of time, or \_L/T~\, and acceleration by a velocity number divided by an interval-of-time number, or [L/r 2 ], and so on, and the corresponding ratios of units must therefore enter in precisely the same degree. The factors would thus be for the just stated cases, \_l/t} and p/J 2 ]. Equations of the form above given for velocity and acceleration which show the dimensions of the quantity in terms of the fundamental units are called dimensional equations. Thus [_E~] = [ML 2 J"~ 2 ] will be found to be the dimensional equation for energy, and [MZ, 2 r~ 2 ] the dimensional formula for it. These expressions will be distinguished from the conversion factors by the use of bracketed capital letters. In general, if we have an equation for a physical quantity, Q = CL a M b T c , where C is a constant and L, M, T represent length, mass, and time in terms of one set of units, and it is desired to transform to another set of units in terms of which the length, mass, and time are L n M n T n we have to find the value of LJ L, Mj/M, Tj/Tj which, in accordance with the convention adopted above, will be /, m, t, or the ratios of the magnitudes of the old to those of the new units. Thus L t = LI, M, = Mm, T, = Tt, and if Q, be the new quantity number, & = CLfMfT*, = CL a l a M b m b T c t c = Ql a m b t c , or the conversion factor is pm fr / c ], a quantity precisely of the same form as the dimension formula [_L a M b T c ~\. Dimensional equations are useful for checking the validity of physical equa- tions. Since physical equations must be homogeneous, each term appearing in them must be dimensionally equivalent. For example, the distance moved by a uniformly accelerated body is 5 = vrf + %at 2 . The corresponding dimensional equation is [L] = \_(L/T)T] + [(L/T 2 )r 2 ], each term reducing to [L]. Dimensional considerations may often, give insight into the laws regulating physical phenomena. 1 For instance Lord Rayleigh, in discussing the intensity 1 See "On Physically Similar Systems; Illustrations of the Use of Dimensional Equations." E. Buckingham, Physical Review, (2) 4, p. 345, 1914. XXV111 INTRODUCTION. Absolute Force of a Center of Attraction, or " Strength of a Center," is the intensity of force at unit distance from the center, and is the force per unit mass at any point multiplied by the square of the distance from the center. The dimensional formula is FL 2 !/- 1 or Modulus of Elasticity is the ratio of stress intensity to percentage strain. The dimensional of percentage strain, a length divided by a length, is unity. Hence the dimensional formula of a modulus of elasticity is that of stress intensity Work is done by a force when the point of application of the force, acting on a body, moves in the direction of the force. It is measured by the product of the force and the displacement. The dimensional formula is [_FL] or \_M L 2 T~' r \. Energy. The work done by the force produces either a change in the veloc- ity of the body or a change of its shape or configuration, or both. In the first case it produces a change of kinetic energy, in the second, of potential energy. The dimensional formulae of energy and work, representing quantities of the same kind, are identical [ML 2 r~ 2 ]. Resilience is the work done per unit volume of a body in distorting it to the elastic limit or in producing rupture. The dimensional formula is [If L 2 r~ 2 L~ 3 ] or [ML- l T- 2 ~]. ' Power or Activity is the time rate of doing work, or if W represents work and P power, P = dw/dt. The dimensional formula is [_WT~ l ~\ or \_ML?T-*~], or for problems in gravitation units more conveniently \_FLT~ l ~], where F stands for the force factor. Exs. Find the number of gram-cms in one ft.-pd. Here the units of force are the attrac- tion of the earth on the pound and the gram of matter. (In problems like this the terms "grams" and "pd." refer to force and not to mass.) The conversion factor is [_JT\, where/ is 453.59 and I is 30.48. The.answer is 453-59 X 30-48 = 13825. Find the number of ft.-poundals in 1000000 cm-dynes. Here m = 1/453.59, I = I /3-48, / = i; mPr* = 1/453-59 X 30.48*, and loWr 2 = io 6 /453-59 X 30.48* = 2.373. If gravity produces an acceleration of 32.2 ft./sec./sec., how many watts are required to make one horse-power? One horse-power is 550 ft.-pds. per sec., or 550 x 32.2 = 17710 ft.-poundals per second. One watt is io 7 ergs per sec., that is, io 7 dyne-cms per sec. The conversion factor is [mPt~ 3 ^\, where m is 453.59, I is 30.48, and Ms i, and the result has to be divided by io 7 , the number of dyne-cms per sec. in the watt. 17710 ml 2 r 3 /io 7 = 17710 x 453.59 X 3o.48 2 /io 7 = 746.3- HEAT UNITS. Quantity of Heat, measured in dynamical units, has the same dimensions as energy \_M L?T~ 2 ~\. Ordinary measurements, however, are made in thermal units, that is, in terms of the amount of heat required to raise the temperature of a unit mass of water one degree of temperature at some stated temperature. This involves the unit of mass and some unit of temperature. If we denote temperature numbers by 6, the dimensional formula for quantity of heat, //, will be QM0]. Unit volume is sometimes used instead of unit mass in the meas- urement of heat, the units being called thermometric units. The dimensional formula now changed by the substitution of volume for mass is INTRODUCTION. Specific Heat is the relative amount of heat, compared with water as standard substance, required to raise unit mass of different substances one degree in tem- perature and is a simple number. Coefficient of Thermal Expansion of a substance is the ratio of the change of length per unit length (linear), or change of volume per unit volume (voluminal), to the change of temperature. These ratios are simple numbers, and the change of temperature varies inversely as the magnitude of the unit of temperature. The dimensional formula is [0" 1 ]. Thermal Conductivity, or Specific Conductance, is the quantity of heat, H, transmitted per unit of time per unit of surface per unit of temperature gradient. The equation for conductivity is therefore K = H/L 2 TQ/L, and the dimen- sional formula \_H/QLT~] = \_ML~ l T~ l ~] in thermal units. In thermometric units the formula becomes |~Z, 2 r~ 1 ], which properly represents diffusivity, and in dynamical units [_M LT-*Qr ir \. Thermal Capacity is mass times the specific heat. The dimensional formula is Latent Heat is the quantity of heat required to change the state of a body divided by. the quantity of matter. The dimensional formula is [MQ/M~\ or ; in dynamical units it is [L 2 T~ 2 ]. NOTE. When is given the dimensional formula [X 2 J 1 " 2 ^, the formulae in thermal and dynamical units are identical. Joule's Equivalent, /, is connected with the quantity of heat by the equation ML 2 T~ 2 = JH or JMQ. The dimensional formula of / is [L 2 ^^- 1 ]. In dynamical units / is a simple number. Entropy of a body is directly proportional to the quantity of heat it contains and inversely proportional to its temperature. The dimensional formula is [MO/0] or [Ml In dynamical units the formula is [ML 2 !^ 2 - 1 ]. Exs. Find the relation between the British thermal unit, the large or kilogram-calorie and the small or gram-calorie, sometimes called the "therm." Referring all the units to the same temperature of the standard substance, the British thermal unit is the amount of heat required to warm one pound of water i C, the large calorie, i kilogram of water, i C, the small calorie or therm, i gram, i C. (i) To find the number of kg-cals. in one British thermal unit, m = .45359, 9 = 5/9; m& = .45359 X 5/9 = .25199. (2) To find the number therms in one kg-cal. m = 1000, and = i; md = 1000. (3) Hence the number of small calories or therms in one British thermal unit is 1000 x .25199 = 251.99. ELECTRIC AND MAGNETIC UNITS. A system of units of electric and magnetic quantities requires four funda- mental quantities. A system in which length, mass, and time constitute three of the fundamental quantities is known as an " absolute" system. There are two absolute systems of electric and magnetic units. One is called the electro- static, in which the fourth fundamental quantity is the dielectric constant, and one is called the electromagnetic, in which the fourth fundamental quantity is magnetic permeability. Besides these two systems there will be described a third in common use called the "international" system. XXX INTRODUCTION. In the electrostatic system, unit quantity of electricity, Q, is the quantity which exerts unit mechanical force upon an equal quantity a unit distance from it in a vacuum. From this definition the dimensions and the units of all the other electric and magnetic quantities follow through the equations of the mathe- matical theory of electromagnetism. The mechanical force between two quan- tities of electricity in any medium is where K is the dielectric constant, characteristic of the medium, and r the dis- tance between the two points at which the quantities Q and Q' are located. A' is the fourth quantity entering into dimensional expressions in the electrostatic system. Since the dimensional formula for force is [MLT~ 2 ], that for Q is The electromagnetic system is based upon the unit of the magnetic pole strength. The dimensions and the units of the other quantities are built up from this in the same manner as for the electrostatic system. The mechanical force between two magnetic poles in any medium is mm' * 7T > ^ in which /z is the permeability of the medium and r is the distance between two poles having the strengths m and m' . p is the fourth quantity entering into dimensional expressions in the electromagnetic system. It follows that the dimensional expression for magnetic pole strength is [J^Z^T 1 " 1 /**]. The symbols K and JJL are sometimes omitted in the dimensional formulae so that only three fundamental quantities appear. There are a number of objec- tions to this. Such formulae give no information as to the relative magnitudes of the units in the two systems. The omission is equivalent to assuming some relation between mechanical and electrical quantities, or to a mechanical expla- nation of electricity. Such a relation or explanation is not known. The properties K and ju, are connected by the equation i/\/ Kp = v, where v is the velocity of an electromagnetic wave. For empty space or for air, K and IJL being measured in the same units, i/^/Kfi = c, where c is the velocity of light in vacuo, 3 x io 10 cm per sec. It is sometimes forgotten that the omission of the dimensions of K or JJL is merely conventional. For instance, magnetic field intensity and magnetic induction apparently have the same dimensions when jj, is omitted. This results in confusion and difficulty in understanding the theory of magnetism. The suppression of /z has also led to the use of the "centi- meter" as a unit of capacity and of inductance; neither is physically the same as length. ELECTROSTATIC SYSTEM. Quantity of Electricity has the dimensional formula \_M* L*T~ l KY\, as shown above. Electric Surface Density of an electrical distribution at any point on a surface is measured by the quantity per unit area. The dimensional formula is the ratio of the formulae for quantity of electricity and for area or INTRODUCTION. XX\i Electric Field Intensity is measured by the ratio of the force on a quantity of electricity at a point to the quantity of electricity. The dimensional formula is therefore the ratio of the formulae for force and electric quantity or or Electric Potential and Electromotive Force. Change of potential is propor- tional to the work done per unit of electricity in producing the change. The dimensional formula is the ratio of the formulae for work and electrical quantity or MIST-iMiH^K* or Capacity of an Insulated Conductor is proportional to the ratio of the quan- tity of electricity in a charge to the potential of the charge. The dimensional formula is the ratio of the two formulae for electric quantity and potential or [M*L*T- 1 K*/M*L*T- 1 K-*1 or \_LK], Specific Inductive Capacity is the ratio of the inductive capacity of the sub- stance to that of a standard substance and therefore is a number. Electric Current is quantity of electricity flowing past a point per unit of time. The dimensional formula is the ratio of the formulae for electric quan- tity and for time or {_M*HT- l K*/r\ or \_M*L*T-*K?]. Electrical Conductivity, like the corresponding term for heat, is quantity per unit area per unit potential gradient per unit of time. The dimensional formula is fr&T-iKtVWT-iK-if or Resistivity is the reciprocal of conductivity. The dimensional formula is Conductance of any part of an electric circuit, not containing a source of electromotive force, is the ratio of the current flowing through it to the difference of potential between its ends. The dimensional formula is the ratio of the for- mulae for current and potential or [M*I*T+J&/ii*&T-*&Q or [_LT~ l fC\. Resistance is the reciprocal of conductance. The dimensional formula is \_L-IT K- I ~]. Exs. Find the factor for converting quantity of electricity expressed in ft.-grain-sec. units to the same expressed in c.g.s. units. The formula is [mW*t~ l k%~], in which m= 0.0648,. / = 30.48, / = i, k = i; the factor is 0.0648* X 30.482, or 42.8. Find the factor required to convert electric potential from mm-mg-sec. units to c.g.s. units. The formula is [m*l%t~ l k~%~\, in which m - o.ooi, / = o.i, / = i, k = i; the factor Js o.ooii X 0.12, or o.oi. Find the factor required to convert electrostatic capacity from ft.-grain-sec. and specific- inductive capacity 6 units to c.g.s. units. The formula is \_lk~\ in which I = 30.48, k = 6; the factor is 30.48 x 6, or 182.88. ELECTROMAGNETIC SYSTEM. Many of the magnetic quantities are analogues of certain electric quantities. The dimensions of such quantities in the electromagnetic system differ from those of the corresponding electrostatic quantities in the electrostatic system only in the substitution of permeability jit for K. XXxiv INTRODUCTION. ence standards are accurately compared copies, not necessarily duplicates, of the primaries for use in the work of standardizing laboratories and the produc- tion of working standards for everyday use. Standard of Length. The primary standard of length which now almost universally serves as the basis for physical measurements is the meter. It is defined as the distance between two lines at o C on a platinum-indium bar deposited at the International Bureau of Weights and Measures. This bar is known as the International Prototype Meter, and its length was derived from the "metre des Archives," which was made by Borda. Borda, Delambre, Laplace, and others, acting as a committee of the French Academy, recommended that the standard unit of length should be the ten-millionth part of the length, from the equator to the pole, of the meridian passing through Paris. In 1795 the French Republic passed a decree making this the legal standard of length, and an arc of the meridian extending from Dunkirk to Barcelona was measured by Delambre and Mechain for the purpose of realizing the standard. From the results of that measurement the meter bar was made by Borda. The meter is now denned as above and not in terms of the meridian length; hence subsequent measures of the length of the meridian have not affected the length of the meter. Standard of Mass. The primary standard of mass now almost universally used as the basis for physical measurements is the kilogram. It is defined as the mass of a certain piece of platinum-indium deposited at the International Bureau of Weights and Measures. This standard is known as the International Prototype Kilogram. Its mass is equal to that of the older standard, the " kilo- gram des Archives," made by Borda and intended to have the same mass as a cubic decimeter of distilled water at the temperature of 4 C. Copies of the International Prototype Meter and Kilogram are possessed by the various governments and are called National Prototypes. Standard of Time. The unit of time universally used is the second. It is the mean solar second, or the 864ooth part of the mean solar day. It is founded on the average time required for the earth to make one rotation on its axis rela- tively to the sun as a fixed point of reference. Standard of Temperature. The standard scale of temperature as adopted by the International Committee of Weights and Measures (1887) depends on the constant-volume hydrogen thermometer. The hydrogen is taken at an initial pressure at o c C of one meter of mercury, o C, sea-level at latitude 45. The scale is defined by designating the temperature of melting ice as o and of condensing steam as 100 under standard atmospheric pressure. This is known as the Centigrade scale (abbreviated C). A scale independent of the properties of any particular substance, and called the thermodynamic, or absolute scale, was proposed in 1848 by Lord Kelvin. In it the temperature is proportional to the average kinetic energy per molecule of a perfect gas. The temperature of melting ice is taken as 273.13, that of the boiling point, 373.13. The scale of the hydrogen thermometer varies from it only in the sense that the behavior of hydrogen departs from that of a perfect gas. It is customary to refer to this scale as the Kelvin scale (abbreviated K). INTRODUCTION. XXXV NUMERICALLY DIFFERENT SYSTEMS OF UNITS. The fundamental physical quantities which form the basis of a system for measurements have been chosen and the fundamental standards selected and made. Custom has not however generally used these standards for the meas- urement of the magnitudes of quantities but rather multiples or submultiples of them. For instance, for very small quantities the micron (JJL) or one-millionth of a meter is often used. The following table 1 gives some of the systems pro- posed, all built upon the fundamental standards already described. The centi- meter-gram-second (cm-g-sec. or c.g.s.) system proposed by Kelvin is the only one generally accepted. TABLE I. PROPOSED SYSTEMS OF UNITS- Weber and Gauss Kelvin c.g.s. Moon 1891 Giorgi MKS (Prim. Stds.) France 1914 B. A. Com., 1863 Practical (B. A. Com., 1873) Strout 1891 Length mm cm dm m m m io 9 cm io 9 cm Mass mg g Kg Kg I0 6 g g io- u g io-9g Time sec. sec. sec. sec. sec. sec. sec. sec. 10 Further the choice of a set of fundamental physical quantities to form the. basis of a system does not necessarily determine how that system shall be used in measurements. In fact, upon any sufficient set of fundamental quantities, a great many different systems of units may be built. The electrostatic and elec- tromagnetic systems are really systems of electric quantities rather than units. They were based upon the relationships F = QQ' / Kr 2 and mm'/pr*, respec- tively. Systems of units built upon a chosen set of fundamental physical quan- tities may differ in two ways: (i) the units chosen for the fundamental quanti- ties may be different; (2) the defining equations by which the system is built may be different. The electrostatic system generally used is based on the centimeter, gram, second, and dielectric constant of a vacuum. Other systems have appeared, differing from this in the first way, for instance using the foot, grain and second in place of the centimeter, gram and second. A system differing from it in the second way is that of Heaviside which introduces the factor 4?r at different places than is usual in the equations. There are similarly several systems of electromagnetic units in use. Gaussian Systems. "The complexity of the interrelations of the units is increased by the fact that not one of the systems is used as a whole, consistently for all electromagnetic quantities. The 'systems' at present used are therefore combinations of certain of the systems of units. 1 Circular 60 of the Bureau of Standards, Electric Units and Standards, 1916. The subse- quent matter in this introduction is based upon this circular. XXX VI INTRODUCTION. "Some writers l on the theory of electricity prefer to use what is called a Gaus- sian system, a combination of electrostatic units for purely electrical quantities and electromagnetic units for magnetic quantities. There are two such Gaus- sian systems in vogue, one a combination of c.g.s. electrostatic and c.g.s elec- tromagnetic systems, and the other a combination of the two corresponding Heaviside systems. "When a Gaussian system is used, caution is necessary when an equation contains both electric and magnetic quantities. A factor expressing the ratio between the electrostatic and electromagnetic units of one of the quantities has to be introduced. This factor is the first or second power of c, the number of electrostatic units of electric charge in one electromagnetic unit of the same. There is sometimes a question as to whether electric current is to be expressed in electrostatic or electromagnetic units, since it has both electric and magnetic attributes. It is usually expressed in electrostatic units in the Gaussian system." It may be observed from the dimensions of K given in Table i that [i/ KJJL] = [_L?/T' r \ which has the dimensions of a square of a velocity. This velocity was found experimentally to be equal to that of light, when K and JJL were ex- pressed in the same system of units. Maxwell proved theoretically that i/\/^M is the velocity of any electromagnetic wave. This was subsequently proved experimentally. When a Gaussian system is used, this equation becomes c/^KfjL = v. For the ether K = i in electrostatic units and /i = i in electromagnetic units. Hence c = v for the ether, or the velocity of an electromagnetic wave in the ether is equal to the ratio of the c.g.s. electromagnetic to the c.g.s. electro- static unit of electric charge. This constant c is of primary importance in elec- trical theory. Its most probable value is 2.9986 x io 10 centimeters per second. " Practical " Electromagnetic System. This electromagnetic system is based upon the units of io 9 cm, io~ u gram, the sec. and jj, of the ether. It is never used as a complete system of units but is of interest as the historical basis of the present International System. The principal quantities are the resistance unit, the ohm = io 9 c.g.s. units; the current unit, the ampere = io -1 c.g.s. units; and the electromotive force unit, the volt = io 8 c.g.s. units. The International Electric Units. The units used in practical measurements, however, are the "International Units." They were derived from the "practical " system just described, or as the latter is sometimes called, the "absolute" sys- tem. These international units are based upon certain concrete standards pres- ently to be defined and described. With such standards electrical comparisons can be more accurately and readily made than could absolute measurements in terms of the fundamental units. Two electric units, the international ohm and the international ampere, were chosen and made as nearly equal as possible to the ohm and ampere of the "practical" or "absolute" system. 1 For example, A. G. Webster, "Theory of Electricity and Magnetism," 1897; J. H. Jeans, "Electricity and magnetism," 1911; H. A. Lorentz, "The Theory of Electrons," 1909; and O. W. Richardson, "The Electron Theory of Matter," 1914. INTRODUCTION. XXXvii This system of units, sufficiently near to the "absolute" system for the pur- pose of electrical measurements and as a basis for legislation, was defined as follows : "i. The International Ohm is the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice, 14.4521 grams in mass, of a constant cross-sectional area and of a length of 106.300 centimeters. "2. The International Ampere is the unvarying electric current which, when passed through a solution of nitrate of silver in water, in accordance with speci- fication II attached to these Resolutions, deposits silver at the rate of o.ooi 11800 of a gram per second. "3. The International Volt is the electrical pressure which, when steadily applied to a conductor the resistance of which is one international ohm' will pro- .duce a current of one international ampere. "4. The International Watt is the energy expended per second by an unvary- ing electric current of one international ampere under the pressure of one inter- national volt." In accordance with these definitions, a value was established for the electro- motive force of the recognized standard of electromotive force, the Weston normal cell, as the result of international cooperative experiments in 1910. The value was 1.0183 international volts at 20 C. The definitions by the 1908 International Conference supersede certain defini- tions adopted by the International Electrical Congress at Chicago in 1893. Cer- tain of the units retain their Chicago definitions, however. They are as follows : "Coulomb. As a unit of quantity, the International Coulomb, which is the quantity of electricity transferred by a current of one international ampere in one second. "Farad. As a unit of capacity, the International Farad, which is the capacity of a condenser, charged to be a potential of one international volt by one international coulomb of electricity. "Joule. As a unit of work, the Joule, which is equal to io 7 units of work in the c.g.s. system, and which is represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm. " Henry. As the unit of induction, the Henry, which is the induction in a circuit when the electromotive force induced in this circuit is one interna- tional volt, while the inducing current varies at the rate of one ampere per second." "The choice of the ohm and ampere as fundamental was purely arbitrary. These are the two quantities directly measured in absolute electrical measure- ments. The ohm and volt have been urged as more suitable for definition in terms of arbitrary standards, because the primary standard of electromotive force (standard cell) has greater simplicity than the primary standard of current (silver voltameter). The standard cell is in fact used, together with resistance standards, for the actual maintenance of the units, rather than the silver vol- tameter and resistance standards. Again, the volt and ampere have some claim XXXV111 INTRODUCTION. for consideration for fundamental definition, both being units of quantities more fundamental in electrical theory than resistance." For all practical purposes the "international" and the "practical" or "abso- lute" units are the same. Experimental determination of the ratios of the corres- ponding units in the two systems have been made and the mean results are given in Table 382. These ratios represent the accuracy with which it was possible to fix the values of the international ohm and ampere at the time they were defined (London Conference of 1908). It is unlikely that the definitions of the international units will be changed in the near future to make the agreement any closer. An act approved July 12, 1894, makes the International units as above defined the legal units in the United States of America. THE STANDARDS OF THE INTERNATIONAL ELECTRICAL UNITS. RESISTANCE Resistance. The definition of the international ohm adopted by the London Conference in 1908 is accepted practically everywhere. Mercury Standards. Mercury standards conforming to the definition were constructed in England, France, Germany, Japan, Russia and the United States. Their mean resistances agree to about two parts in 100,000. To attain this accuracy, elaborate and painstaking experiments were necessary. Tubes are never quite uniform in cross-section; the accurate measurement of the mass of mercury filling the tube is difficult, partly because of a surface film on the walls of the tube; the greatest refinements are necessary in determining the length of the tube. In the electrical comparison of the resistance with wire standards, the largest source of error is in the filling of the tube. These and other sources of error necessitated a certain uniformity in the setting up of mercury standards and at the London Conference the following specifications were drawn up: SPECIFICATION RELATING TO MERCURY STANDARDS OF RESISTANCE. The glass tubes used for mercury standards of resistance must be made of a glass such that the dimensions may remain as constant as possible. The tubes must be well annealed and straight. The bore must be as nearly as possible uniform and circular, and the area of cross-section of the bore must be approximately one square millimeter. The mercury must have a resistance cf approximately one ohm. Each of the tubes must be accurately calibrated. The correction to be applied to allow for the area of the cross-section of the bore not being exactly the same at all parts of the tube must not exceed 5 parts in 10,000. The mercury filling the tube must be considered as bounded by plane surfaces placed in contact with the ends of the tube. The length of the axis of the tube, the mass of mercury the tube contains, and the electrical resistance of the mercury are to be determined at a temperature as near to o C as possible. The measurements are to be corrected to o C. For the purpose of the electrical measurements, end vessels carrying connections for the current and potential terminals are to be fitted on to the tube. These end vessels are to be spherical in shape (of a diameter of approximately four centimeters) and should have cylindrical pieces attached to make connections with the tubes. The outside edge of each end of the tube INTRODUCTION. XXX'ix is to be coincident with the inner surface of the corresponding end vessel. The leads which make contact with the mercury are to be of thin platinum wire fused into glass. The point of entry of the current lead and the end of the tube are to be at opposite ends of a diameter of the bulb; the potential lead is to be midway between these two points. All the leads must be so thin that no error in the resistance is introduced through conduction of heat to the mercury. The filling of the tube with mercury for the purpose of the resistance measurements must be carried out under the same conditions as the filling for the determination of the mass. The resistance which has to be added to the resistance of the tube to allow for the effect of the end vessels is to be calculated by the formula 0.80 /i i \ , A = - - + -i ) ohm, L r 2 / where r\ and r are the radii in millimeters of the end sections of the bore of the tube. The mean of the calculated resistances of at least five tubes shall be taken to determine the value of the unit of resistance. For the purpose of the comparison of resistances with a mercury tube the measurements shall be made with at least three separate fillings of the tube. Secondary Standards. Secondary standards, derived from the mercury standards and used to give values to working standards, are certain coils of manganin wire kept in the national laboratories. Their resistances are adjusted to correspond to the unit or its decimal multiples or submultiples. The values assigned to these coils are checked from time to time with the similar coils of the other countries. The value now in use is based on the comparison made at the U. S. Bureau of Standards in 1910 and may be called the "1910 ohm." Later measurements on various mercury standards checked the value then used within 2 parts in 100,000. Thus the basis of resistance measurement is main- tained not by the mercury standards of a single laboratory, but by all the mer- cury standards of the various national laboratories; it is furthermore the same in all countries, except for very slight outstanding discrepancies due to the errors of measurement and variations of the standards with time. Resistance Standards in Practice. In ordinary measurements, working standards of resistance are usually coils of manganin wire (approximately 84 per cent Cu +12 per cent Mn + 4 per cent Ni). They are generally used in oil which carries away the heat developed by the current and facilitates regulation and measurement of the temperature. The best type is inclosed in a sealed case for protection against atmospheric humidity. Varying humidity changes the resistance of open coils often to several parts in 10,000 higher in summer than in winter. While sealed i ohm and o.i ohm coils may remain constant to about i part in 100,000. Absolute Ohm. The absolute measurement of resistance involves the pre- cise determination of a length and a time (usually an angular velocity) in a medium of unit permeability. Since the dimensional formula of resistance in the electromagnetic system is [Lju/T], such an absolute measurement gives R not in cm/sec, but in cm x ^i/sec. The definitions of the ohm, ampere and volt by the 1908 London conference tacitly assume a permeability equal to unity. The relation of the international ohm to the absolute ohm has been measured in different ways involving revolving coil, revolving disk, and alter- nate current methods. Probably the most accurate determination was made Xl INTRODUCTION. in 1913 by F. E. Smith of the National Physical Laboratory of England, using a modification of the Lorentz revolving disk method. His result was i international ohm = 1.00052 0.00004 absolute ohms, or, in other words, while one international ohm is represented by a mercury column 106.300 cm long as specified above, one absolute ohm requires a similar column 106.245 cm long. Table 305 of the 6th revised edition of these tables contains data relative to the various determinations of the ohm. CURRENT. The Silver Voltameter. The silver voltameter is a concrete means of meas- uring current in accordance with the definition of the international ampere. As used for the realization of the international ampere "it consists of a platinum cathode in the form of a cup holding the silver nitrate solution, a silver anode partly or wholly immersed in the solution, and some means to prevent anode slime and particles of silver mechanically detached from the anode from reach- ing the cathode. As a standard representing the international ampere, the silver voltameter includes also the chronometer used to measure time. The degree of purity and the mode of preparation of the various parts of the vol- tameter affect the mass of the deposit. There are numerous sources of error, and the suitability of the silver voltameter as a primary standard of current has been under investigation since 1893. Differences of as much as o.i per cent or more may be obtained by different procedures, the larger differences being mainly due to impurities produced in the electrolyte (by filter paper, for instance) . Hence, in order that the definition of current be precise, it must be accompanied by specifications for using the voltameter." The original specifications were recognized to be inadequate and an inter- national committee on electrical units and standards was appointed to com- plete the specifications. It was also recognized that in practice standard cells would replace secondary current standards so that a value must be fixed for the electromotive force of the Weston normal cell. This was attempted in 1910 at the Bureau of Standards by representatives of that institution together with one delegate each from the Physikalische-Technische Reichanstalt, The National Physical Laboratory and the Laboratoire Central d'Electricite. Voltameters from all four institutions were put in series under a variety of experimental con- ditions. Standard Weston cells and resistance standards of the four laboratories were also intercompared. From the joint comparison of standard cells and silver voltameters particular values were assigned to the standard cells from each laboratory. The different countries thus have a common basis of measure- ment maintained by the aid of standard cells and resistance standards derived from the international voltameter investigation of 1910. It was not found possible to draw up satisfactory and final specifications for the silver voltameter. Provisional specifications were submitted by the U. S. Bureau of Standards and more complete specifications have been proposed in correspondence between the national laboratories and members of the inter- INTRODUCTION'. xli national committee since 1910, but no agreement upon final specifications has yet been reached. Resistance Standards Used in Current Measurements. Precise measure- ments of currents require a potentiometer, a standard cell and a resistance standard. The resistance must be so designed as to carry the maximum current without undue heating and consequent change of resistance. Accordingly the resistance metal must have a small temperature resistance coefficient and a sufficient area in contact with the air, oil, or other cooling fluid. It must have a small thermal electromotive force against copper. Manganin satisfies these conditions and is usually used. The terminals of the standard must have suffi- cient contact area so that there shall be no undue heating at contacts. 1 It must be so designed that the current distribution does not depend upon the mode of connection to the circuit. Absolute Ampere. The absolute ampere (ro^c.g.s. electromagnetic units) differs by a negligible amount from the international ampere. Since the dimen- sional formula of the current in the electromagnetic system is \_IJM */ Tp,^ which is equivalent to \_F*/i^~\, the absolute measurement of current involves funda- mentally the measurement of a force in a medium of unit permeability. In most measurements of high precision an electrodynamometer has been used of the form known as a current balance. A summary of the various determinations will be found in Table 293 of the 6th Revised Edition of these tables. The best value is probably the mean of the determinations made at the U. S. Bureau of Standards, the National Physical Laboratory and at the University of Groningen, which gives i international ampere = 0.99991 absolute ampere. The separate values were 0.99992, 0.99988 and 0.99994, respectively. "The result may also be expressed in terms of the electrochemical equivalent of silver, which, based on the '1910 mean voltameter,' thus equals 0.00111810 g per absolute coulomb. By the definition of the international ampere, the value is 0.00111800 g per international coulomb." ELECTROMOTIVE FORCE. International Volt. " The international volt is derived from the interna- tional ohm and ampere by Ohm's law. Its value is maintained by the aid of the Weston normal cell. The national standardizing laboratories have groups of such cells, to which values in terms of the international ohm and ampere have been assigned by international experiments, and thus form a basis of reference for the standardization of the standard cells used in practical measurements." Weston Normal Cell. The Weston normal cell is the standard used to maintain the international volt and, in conjunction with resistance standards, to maintain the international ampere. The cell is a simple voltaic combination 1 See "Report to the International Committee on Electrical Units and Standards," 1912, p. 199. For the Bureau of Standards investigations see Bull. Bureau of Standards, 9, pp. 209, 493; 10, P- 475* 1912-14; 13, P- 147, 1915; 9, P- iSi, 1912: 13, pp. 447. 479, xliv INTRODUCTION. difference which exists between the terminals of a resistance of one international ohm when the latter carries a current of one absolute ampere. The emf of the Weston normal cell may be taken as 1.01821 semi-absolute volts at 20 C. QUANTITY OF ELECTRICITY. The international unit of quantity of electricity is the coulomb. The faraday is the quantity of electricity necessary to liberate i gram equivalent in electroly- sis. It is equivalent to 96,500 coulombs. Standards. There are no standards of electric quantity. The silver voltam- eter may be used for its measurement since under ideal conditions the mass of metal deposited is proportional to the amount of electricity which has flowed. CAPACITY. The unit generally used for capacity is the international microfarad or the one-millionth of the international farad. Capacities are commonly measured by comparison with standard capacities. The values of the standards are de- termined by measurement in terms of resistance and time. The standard is some form of condenser consisting of two sets of metal plates separated by a dielectric. The condenser should be surrounded by a metal shield connected to one set of plates rendering the capacity independent of the surroundings. An ideal condenser would have a constant capacity under all circumstances, with zero resistance in its leads and plates, and no absorption in the dielectric. Actual condensers vary with the temperature, atmospheric pressure, and the voltage, frequency, and time of charge and discharge. A well-constructed air condenser with heavy metal plates and suitable insulating supports is practically free from these effects and is used as a standard of capacity. Practically air condenser plates must be separated by i mm or more and so cannot be of great capacity. The more the capacity is increased by approach- ing the plates, the less the mechanical stability and the less constant the capac- ity. Condensers of great capacity use solid dielectrics, preferably mica sheets with conducting plates of tinfoil. At constant temperature the best mica con- densers are excellent standards. The dielectric absorption is small but not quite zero, so that the capacity of these standards with different methods of measure- ment must be carefully determined. INDUCTANCE. The henry, the unit of self-inductance, is also the unit of mutual inductance. The henry has been known as the " quadrant" and the "secohm." The length of a quadrant or quarter of the earth's circumference is approximately io 9 cms. and a henry is io 9 cms. of inductance. Secohm is a contraction of second and ohm; the dimensions of inductance are [TR] and this unit is based on the second and ohm. Inductance Standards. Inductance standards are measured in international units in terms of resistance and time or resistance and capacity by alternate- INTRODUCTION. xlv current bridge methods. Inductances calculated from dimensions are in abso- lute electromagnetic units. The ratio of the international to the absolute henry is the same as the ratio of the corresponding ohms. Since inductance is measured in terms of capacity and resistance by the bridge method about as simply and as conveniently as by comparison with standard inductances, it is not necessary to maintain standard inductances. They are however of value in magnetic, alternating-current, and absolute electrical meas- urements. A standard inductance is a circuit so wound that when used in a circuit it adds a definite amount of inductance. It must have either such a form or so great an inductance that the mutual inductance of the rest of the circuit upon it may be negligible. It usually is a wire coil wound all in the same direction to make self-induction a maximum. A standard, the inductance of which may be calculated from its dimensions, should be a single layer coil of very simple geometrical form. Standards of very small inductance, calculable from their dimensions, are of some simple device, such as a pair of parallel wires or a single turn of wire. With such standards great care must be used that the mutual inductance upon them of the leads and other parts of the circuit is negli- gible. Any inductance standard should be separated by long leads from the measuring bridge or other apparatus. It must be wound so that the distributed capacity between its turns is negligible; otherwise the apparent inductance will vary with the frequency. POWER AND ENERGY. Power and energy, although mechanical and not primarily electrical quanti- ties, are measurable with greater precision by electrical methods than in any other way. The watt and the electric units were so chosen in terms of the c.g.s. units that the product of the current in amperes by the electromotive force in volts gives the power in watts (for continuous or instantaneous values). The international watt, defined as "the energy expended per second by an unvarying electric current of one international ampere under an electric pressure of one international volt," differs but little from the absolute watt. Standards and Measurements. No standard is maintained for power or energy. Measurements are always made in electrical practice in terms of some of the purely electrical quantities represented by standards. MAGNETIC UNITS. C.G.S. units are generally used for magnetic quantities. American practice is fairly uniform in names for these units: the c.g.s. unit of magnetomotive force is called the "gilbert," of reluctance, the "oersted," following the provisional definitions of the American Institute of Electrical Engineers (1894). The c.g.s. unit of flux is called the "maxwell" as defined by the 1900 Paris conference. The name "gauss" is used unfortunately both for the unit of induction (A.I.E.E. 1894) and for the unit of magnetic field intensity or magnetizing force. "This double usage, recently sanctioned by engineering societies, is based upon the mathematical convenience of defining both induction and magnetizing force xlvi INTRODUCTION. as the force on a unit magnetic pole in a narrow cavity in the material, the cavity being in one case perpendicular, in the other parallel, to the direction of the magnetization: this definition however applies only in the ordinary electro- magnetic units. There are a number of reasons for considering induction and magnetizing force as two physically distinct quantities, just as electromotive force and current are physically different." In the United States " gauss" has been used much more for the c.g.s. unit of induction than for the unit of magnetizing force. The longer name of " max- well per cm 2 " is also sometimes used for this unit when it is desired to distin- guish clearly between the two quantities. The c.g.s. unit of magnetizing force is usually called the " gilbert per cm." A unit frequently used is the ampere-turn. It is a convenient unit since it eliminates 47T in certain calculations. It is derived from the "ampere turn per cm." The following table shows the relations between a system built on the ampere- turn and the ordinary magnetic units. 1 TABLE II. THE ORDINARY AND THE AMPERE-TURN MAGNETIC UNITS- Quantity Ordinary magnetic units Ampere-turn units. Ordinary units in i ampere- turn unit i Magnetomotive force 3F Gilbert Ampere-turn 47T/IO Magnetizing force H Gilbert per Ampere-turn per 47T/IO cm. cm. Magnetic flux $ Maxwell Maxwell I Magnetic induction ( B f Maxwell per f Maxwell per cm. 2 I \ cm. 2 Gauss \ Gauss Permeability M I Reluctance R Oersted f Ampere-turn per 47T/IO \ Maxwell Magnetization intensity J Maxwell per cm. 2 I/47T Magnetic susceptibility K I/47T Magnetic pole strength m Maxwell I/47T 1 Bellinger, International System of Electric and Magnetic Units, Bull. Bureau of Standards, 13, p. 599, PHYSICAL TABLES 2 TABLE 1. SPELLING AND ABBREVIATIONS OF THE 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 period is omitted after the metric abbreviations but not after those of the customary system. The exponents " 2 " and " 3 " are used to signify area and volume respectively in the metric units. 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. The following list is taken from circular 87 of the U. S. Bureau of Standards. Unit. Abbreviation. Unit. Abbreviation. acre A kilogram kg are a kiloliter kl avoirdupois av. kilometer km barrel bbl. link li. board foot bd. ft. liquid liq. bushel bu. liter 1 carat, metric c meter m centare ca metric ton t centigram eg micron M. centiliter cl mile mi. centimeter cm milligram mg chain ch. milliliter ml cubic centimeter cm 3 millimeter mm cubic decimeter dm 3 millimicron mju cubic dekameter dkm 3 minim min. or Tfl, cubic foot cu. ft. ounce oz. cubic hectometer hm 3 ounce, apothecaries' oz. ap. or 5 cubic inch cu. in. ounce, avoirdupois oz. av. cubic kilometer km 3 ounce, fluid fl. oz. cubic meter m 3 ounce, troy oz. t. cubic mile cu. mi. peck pk. cubic millimeter mm 3 pennyweight dwt. cubic yard decigram cu. yd. dg pint pound pt. Ib. deciliter dl pound, apothecaries' Ib. ap. decimeter dm pound, avoirdupois Ib. av. decistere ds pound, troy Ib. t. dekagram dkg quart qt. dekaliter dkl rod rd. dekameter dkm scruple, apothecaries' s. ap. or 9 dekastere dks square centimeter cm 2 dram dr. square chain sq. ch. dram, apothecaries' dram, avoirdupois dr. ap. or 5 dr. av. square decimeter square dekameter dm 2 dkm 2 dram, fluid fl. dr. square foot sq. ft. fathom fath. square hectometer hm 2 foot ft. square inch sq. in. firkin fir. square kilometer km 2 furlong fur. square meter m 2 gallon gal. square mile sq. mi. grain gr. square millimeter mm 2 gram g square rod sq. rd. hectare ha square yard sq. yd. hectogram hectoliter hg hi stere ton s tn. hectometer hm ton, metric t hogshead hhd. troy t. hundredweight cwt. yard yd. inch in. SMITHSONIAN TABLES. TABLE 2. ? FUNDAMENTAL AND DERIVED UNITS- Conversion Factors. To change a quantity from one system of units to another: substitute in the corresponding conversion factor from the following table the ratios of the magnitudes of the old units to the new and multiply the old quantity by the resulting number. For example: to reduce velocity in miles per hour to feet per second, the conversion factor is lr l ; I = 5280/1, t= 3600/1, and the factor is 5280/3600 or 1.467. Or \ve may proceed as follows: e. g., to find the equivalent of I c.g.s. unit of angular momentum in the pel. ft. m. unit, from the Table t g cm~/sec.=jc Ib. ft. 2 /rnin, where x is the factor sought. Solving, x=ig/\b. X cm' 2 /ft.' 2 X min./sec. = i X .002205 X .001076 X 6o=.oooi42c;. The dimensional formulae lack one quality which is needed for completeness, an indication of their vector characteristics; such characteristics distinguish plane and solid angle, torque and energy, illumination and brightness. (a) FUNDAMENTAL UNITS. The fundamental units and conversion factors in the systems of units most commonly used are: Length [/J; Mass \_m~\\ Time [f\\ Temperature {B~]\ and for the electrostatic system, Dielectric Constant [&]; for the electromagnetic system, Permeability [ju]. The formulae will also be given for the International System of electric and magnetic units based on the units length, resistance [Y], current [f], and time. (b) DERIVED UNITS. Name of unit. (Geometrical and dynamical. ) Conversion factor. faetof] Name of units. (Heat and light.) Conversion factor. lm*lvt*6] r X y 2 X . y z Area, surface Volume .... O O O O I I O I I I I I I I I I I 2 3 -I O I O I -3 2 I I 2 J I 2 2 o o o I I 2 2 -I -I 2 2 -2 -3 -2 Quantity of heat: thermal units O I o I I o o I I o o -I o 3 2 I 2 I 2 2 O 2 O -2 -2 O O 2 I I -3 o 2 -2 O o 3 3 I I O I O O I I I 1 I* I* I* I* I* Angle. . . . thermometric units. . dynamical units .... Coefficient of thermal expansion Thermal conductivity: thermal units Solid angle Curvature Angular velocity Linear velocity Angular acceleration. . . . Linear acceleration Density Moment of inertia Intensity of attraction . . Momentum thermometric units or diffusivity dynamical units .... Thermal capacity Latent heat: thermal units dynamical units. . . . Joule's equivalent Entropy: heat in thermal units heat in dynamical units Moment of momentum.. Angular momentum .... Force Moment of couple, torque Work energy Power activity Intensity of stress Modulus of elasticity Compressibility Luminous intensity.... Illumination Brightness Visibility Viscosity I I Luminous efficiency. . . . * For these formulae the numbers in the last column are the exponents of F where F refers to the luminous flux. For definitions of these quantities see Table 299, page 259. SMITHSONIAN TABLES. TABLE 2 (continued). FUNDAMENTAL AND DERIVED UNITS- Conversion Factors. (6) DERIVED UNITS. NAME OF UNIT. (Electric and magnetic.) Sym- bol* CONVERSION FACTOR. Electrostatic system. Electromagnetic system. emu International system. csu t m z lt*k v m^t 1 ^ r*W X y z X y 2 V .V y V Quantity of electricity Electric displacement Q D D V E C K I 7 P g R m m 3> H H 12 7 B K M 9R 91 f f I O o i o o I i I f 1 I o o * o f -1 -f i o f -2 -1 -I I I O i I \ O O o i -1 ~ 2 2 -I -2 i 2 -2 2 2 2 I _1 -I I -I O -i C C C i/c i/c I/C c 2 c 2 c o I I I I -I o I I o o o o I I I I I I I -I I I o o o I o o I I I o o o I o o o I I o -2 -2 I o -I I I o -I -I o I -2 2 -I -I -2 O O I I I o o o I o o o I I I o o o I I I I I o I I -I ot ot Electric surface density Electric field intensity Electric potential Electromotive force Electrostatic capacity Dielectric constant . . . Specific inductive capacity. Current . . . Electric conductivity Resistivity I -I o 2 I i I/C- c 2 I/c 2 i/c i/c i/c c c c c i/c I/C I/C I/C 2 I/C 2 c I/C 2 I/C 2 c 3 # Conductance Resistance -I i f I -1 -2 -2 -i -i -i i f I o o 2 2 -2 -2 o 2 2 -2 2 2 -2 -I -I I ~\ ~\ ~\ \ ~\ -1 -I I } I -I I -f} -it o 1 I f I o o i o 1 I 1 J -1 I 1 -I o :t -I I I -I 1 I -I -I I -I I I -I -I -I I I -I -2 -2 i i | f I i i _! I I I i| il Magnetic pole strength Quantity of magnetism Magnetic flux Magnetic field intensity . Magnetizing force Magnetic potential Magnetomotive force Magnetic moment Intensity magnetization. . . . Magnetic induction Magnetic susceptibility Magnetic permeability Current density. Self-inductance Mutual inductance Magnetic reluctance Thermoelectric power \ Peltier coefficient J. . . * As adopted by American Institute of Electrical Engineers, 1915. t c is the velocity of an electromagnetic wave in the ether = 3 X io 10 approximately. J This conversion factor should include [_6~ 1 ]. SMITHSONIAN TABLES. TABLES. TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES.* (1) CUSTOMARY TO METRIC. LINEAR. CAPACITY. Inches to Feet to Yards to Miles to Fluid drams to milliliters Fluid ounces Liquid quarts to Gallons to millimeters. kilometers or cubic liters. ners. centimeters. ! 25.4001 0.304861 0.914402 1.60935 i 3-70 29.57 0.94633 2 508001 0.609601 1.828804 3.21869 2 7-39 59.15 1.89267 7.57066 3 76.2002 0.914402 2.743205 4.82804 3 11.09 88.72 2.83900 11.35600 4 IOI.6OO2 I.2I92O2 3.657607 6-43739 4 14.79 118.29 3.78533 I 5- I 4i33 5 127.0003 1.524003 4.572009 8.04674 5 18.48 147.87 4-73*67 18.92666 6 152.4003 177.8004 1.828804 2.133604 5.486411 6.400813 9.65608 11.26543 6 7 22.18 25.88 177-44 207.01 5.67800 6-62433 22.71199 26.49733 8 203.2004 2.438405 7.315215 12.87478 8 29-57 236-58 7.57066 30.28266 9 228.6005 2.743205 8.229616 14.48412 9 33-27 266.16 8.51700 34.06799 SQUARE. WEIGHT. Square inches to square cen- timeters. Square feet to square decimeters. Square yards to square meters. Acres to hectares. Grains to milligrams. Avoirdu- pois ounces to grams. Avoirdu- pois pounds to kilo- grams. Troy ounces to grams. i 6.452 9.290 0.836 0.4047 i 64.7989 28.3495 0-45359 31.10348 2 12.903 18.581 1.672 0.8094 2 129.5978 56-6991 0.90718 62.20696 3 19-355 27.8 7 I 2.508 1.2141 3 194.3968 85.0486 1.36078 93-3 i 44 4 25-807 37.l6l 3-345 1.6187 4 2 59- I 957 113.3981 I.8I437 124.41392 5 32.258 46.452 4.181 2.0234 5 323.9946 141.7476 2.26796 1 55- 5 T 740 6 38.710 55-742 5.017 2.4281 6 388.7935 170.0972 2.72155 186.62088 7 8 9 45.161 5 r -6i3 58.065 65.032 74.323 83-613 6.689 7-525 2.8328 3-2375 3.6422 7 8 9 453-5924 518-3913 583-! 903 198.4467 226.7962 255-H57 3-I75I5 3.62874 4.08233 217.72437 248.82785 279-93I33 CUBIC. Cubic inches to cubic cen- timeters. Cubic feet to cubic meters. Cubic yards to cubic meters. Bushels to hectoliters. i Gunter's chain = 20.1168 meters. i sq. statute mile = 259.000 hectares. i fathom = 1.829 meters. r 16.387 0.02832 0.765 0.35239 i nautical mile = 1853.25 meters. 2 32-774 0.05663 1.529 0.70479 i foot = 0.304801 meter. 3 4 5 49.161 65.549 81.936 0.08495 0.11327 0.14159 2.294 3.0|8 1.05718 1.40957 1.76196 i avoir, pound = 453.5924277 grams. 1 5432.35639 grains = i.ooo kilogram. 6 98.323 o. 1 6990 4.587 2.11436 7 II47IO 0.19822 5-352 2.46675 i 131.097 0.22654 6.II6 2.81914 9 147.484 0.25485 6.881 3.'7i54 According to an executive order dated April 15, 1803, tne United States yard is denned as 3600/3937 meter, and the avoirdupois pound as 1/2.20462 kilogram. i meter (international prototype) 15^3164.13 times the wave-length of the red Cd. line. Benoit, Fabry and Perot. C. R. 144, 1907 differs only in the decimal portion from the measure of Michelson and Benoit 14 years earlier. 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 Sphe- roid of 1866). * Quoted from sheets issued by the United States Bureau of Standards. SMITHSONIAN TABLES. TABLE 3 (continual). TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES. (2) METRIC TO CUSTOMARV. LINEAR. CAPACITY. Millili- ters or ( Jenti- ' leca- Hecto- Meters to Meters to Meters to Kilometers cubic cen- li ters to iters liters inches. feet. vards. to miles. timeters fluid to to to fluid ounces. gallons. bushels. drams. i 39-3700 3.28083 1.093611 0.62137 , 0.27 0.338 1.0.567 2.6418 2.8378 2 78.7400 6.56167 2.187222 1.24274 2 0-54 0.676 2.1134 5.2836 3 IlS.IIOO 9.84250 3-280833 I.864II 3 0.8 1 I .014 3.1701 7-9253 8.5135 4 157.4800 J 3- I2 333 4-374444 2.48548 j 4 1. 08 I -3S3 4.2268 10.5671 i I.TSI? 5 196.8500 16.40417 5.468056 3.10685 5 J -35 I .691 5.2836 13.2089 14.1891 j 6 7 236.2200 275.5900 19.68500 22.96583 6.561667 7-655278 3.72822 4-34959 i 6 7 1.62 1.89 2.029 2.367 6-3403 7-3970 \\ .8507 .4924 17.0269 19.8647 8 314.9600 26.24667 8.748889 4.97096 8 2.16 f 705 8.4537 21 .1342 22.7026 9 354.3300 29.52750 9.842500 5.59233 9 2-43 3-043 9-5'4 23.7760 25-5404 SQUARE. | WEIGHT. Square Square Square Milli- Kilo- Hecto- Kilo- centimeters to square meters to square meters to square Hectares to acres. ' grams to grams to grams to ounces grams to pounds inches. feet. yards. grain . avoirdupois. avoirdupois. i 2 0.1550 0.3100 - 10.764 21.528 1.196 2.392 2.471 4.942 2 0.01543 0.03086 I 5432.36 30864.71 3-5274 7.0548 2.20462 4-40924 3 0.4650 32.292 3.588 7-4I3 3 0.04630 46297.07 10. ^822 6.61387 4 0.6200 43-055 4.784 9.884 4 0.06173 61729.43 M .1096 8.81849 5 0.7750 5.980 12355 5 0.07716 77161.78 6370 1I.O23II 6 7 0.9300 1.0850 64.583 75-347 7.176 8-372 14.826 17.297 6 7 0-09259 0.10803 92594.14 108026.49 21.1644 24.6918 I3-22773 15.43236 8 9 1.2400 1-395 86.1 1 1 96.875 9-568 10.764 19768 22.239 8 9 0.12346 0.13889 123458.85 138891.21 28.2192 31.7466 17.63698 19.84160 CUBIC. WEIGHT. Cubic centimeters to cubic Cubic decimeters to cubic Cubic meters to cubic Cubic meters to cubic Quintals to pounds av. Milliers or tonnes to pou ids Kilograms to ounces inches. inches. feet. yards. i 0.06 10 61.023 3S-3M 1.308 i 220.46 2204.6 32.1507 2 O.I22O 122.047 70.269 2.616 i 2 440.92 4409.2 64.3015 3 4 0.1831 0.2441 183.070 244.094 I0 5943 141.258 5^232 3 4 6ft. 881. s's 6613-9 8818.5 96.4522 128.6030 5 0.3051 305.117 176.572 6.540 | 5 1102.31 11023.1 160.7537 6 0.3661 366.140 211.887 7.848 6 1322.77 13227.7 192.9045 7 0.4272 427.164 247.201 9- T 5 6 7 1 543- 24 1543 225.0552 8 0.4882 488.187 282.516 10.464 8 1763.70 17637.0 257.2059 9 0.5492 549-210 3 '7-830 11.771 9 1984- 1 6 19841.6 289.3567 By the concurrent action of the principal governments of the world an International Bureau of Weights and Measures has been established near Paris. Under the direction of the International Committee, two ingots were cast of pure platinum-iridium in the proportion of 9 parts of the former to i of the latter metal. From one of these a certain number of kilograms were prepared, from the other a definite number of meter bars. These standards of weight and length were intercompared, without preference, and certain ones were selected as International proto- type standards. The others were distributed by lot, in September, 1889, to the different governments, and are called National prototype standards. Those apportioned to the United States were received in 1890, and are kept at the Bureau of Standards in Washington, I). C. The metric svstcm was legalized in the United States in 1866. The International Standard Meter is derived from the Metre des Archives, and its length is defined by the distance between two lines at o Centigrade, on a platinum-iridium bar deposited at the International Bureau of Weights and Measures. The International Standard Kilogram is a mass of platinum-iridium deposited at the same place, and its weight in vacuo is the same as that of the Kilogram des Archives. The liter is equal to the quantity of pure water at 4 C (760 mm. Hg. pressure) which weighs i kilogram and ~ 1.000027 cu. dm. (Trav. et Mem. Bureau Intern, des P. et M. 14, n;io, Benoit.) SMITHSONIAN TABLES. TABLE 4. MISCELLANEOUS EQUIVALENTS OF U. S- AND METRIC WEIGHTS AND MEASURES-* (For other equivalents than those below, see Table 3.) LINEAR MEASURES. mil (.001 in.) = 25.4061 ju in. = .000015783 mile hand (4 in.) = 10.16002 cm link (.66 ft.) = 20.11684 cm span. (9 in.) = 22.86005 cm fathom (6 ft.) = 1.828804 m rod (25 links) = 5.029210 m chain (4 rods) = 20.11684 m light year (9.5 X io 12 km) = 5.9 X io 12 miles i par sec (31 X io 12 km) = 19 X io 12 miles fa in. = .397 mm ^ in. = .794 mm & in. = 1.588 mm | in. = 3.175 mm j in. = 6.350 mm \ in. = 12.700 mm i Angstrom unit = .oooooooooi m i micron (ju) = .oooooi m = .00003937 in. i millimicron (m/x) = .00000000 1 m i m = 4.970960 links = 1.093611 yds. = .198838 rod = .0497096 chain SQUARE MEASURES. sq. link (62.7264 sq. in.) = 404.6873 cm 2 sq. rod (625 sq. links) = 25.29295 m 2 sq. chain (16 sq. rods) = 404.6873 m 2 acre (io sq. chains) = 4046.873 m 2 sq. mile (640 acres) = 2.589998 km 2 km 2 = .3861006 sq. mile m 2 = 24.7104 sq. links = 10.76387 sq. ft. = -039537 sq. rod. = .00247104 sq. chain CUBIC MEASURES. i board foot (144 cu. in) = 2359.8 cm 3 i cord (128 cu. ft.) = 3.625 m 3 CAPACITY MEASURES. i minim (TTJ.) = .0616102 ml i fl. dram (6oTTl) = 3.69661 ml i fl. oz. (8 fl. dr.) = 1.80469 cu. in. = 29.5729 ml i gill (4 fl. oz.) = 7. 21875 cu. in. = 118.292 ml i liq. pt. (28.875 cu. in.) = .473167 1 i liq. qt. (57.75 cu. in.) = .946333 1 i gallon (4 qt, 231 cu. in.) = 3.785332 1 i dry pt. (33.6003125 cu. in.) = .550599 1 i dry qt. (67.200625 cu. in.) = 1.101198 1 i pk. (Sdryqt., 537.605 cu. in.) = 8.80958 1 i bu. (4 pk., 2150.42 cu. in.) = 35.2383 1 i firkin (9 gallons) = 34.06799 1 i liter = .2641 78. gal. = 1.05671 liq. qt. = 33.8147 fl. oz. = 270.518 fl. dr. i ml = 16.2311 minims, i dkl = 18.620 dry pt. = 9.08102 dry qt. = 1.13513 pk. = .28378 bu. MASS MEASURES. Avoirdupois weights. i grain = .064798918 g i dram av. (27.34375 gr.) = 1.771845 g i oz. av. (16 dr. av.) = 28.349527 g i pd. av. (16 oz. av. or 7000 gr.) = I4-S83333 oz. ap. (5) or oz. t. = 1.2152778 or 7000/5760 pd. ap ort. = 453-5924277 g i kg = 2.204622341 pd. av. i g = 15.432356 gr. = .5643833 av. dr. = -03527396 av. oz. i short hundred weight (100 pds.) = 45-359 2 43 kg i long hundred weight (112 pds.) , = 50.802352 kg i short ton (2000 pds.) = 907.18486 kg i long ton (2240 pd.) = 1016.04704 kg i metric ton = 0.98420640 long ton = 1.1023112 short tons Troy weights. i pennyweight (d\vt, 24 gr.) = 1.555174 g: gr., oz., pd. are same as apothecary Apothecaries 1 weights. gr. = 64.798918 mg scruple O, 20 gr.) = 1.2959784 g dram (3, 3 9) = 3-8879351 g oz. (5,83) = 31.103481 g pd (125, 5760 gr.) = 373.24177 g g = 15.432356 gr. = 0.771618 3 = 0.2572059 3 = .03215074 5 i kg = 32.150742 5 = 2.6792285 pd. i metric carat = 200 mg = 3.0864712 gr. U. S. \ dollar should weigh 12.5 g and the smaller silver coins in proportion. * Taken from Circular 47 of the U. S. Bureau of Standards, 1915, which see for more complete tables. SMITHSONIAN TABLES. TABLE 5. EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS AND MEASURES.* (1) METRIC TO IMPERIAL. (For U.S. Weights and Measures, see Table 3.) LINEAR MEASURE. MEASURE OF CAPACITY. Im ") (mln |= '3937 -. 1 m iUer) er (ml) ( ' 01 | = - 6locub - in - I centimeter (.01 m.) = 0.39370 " I decimeter (.1 m) = 3-93701 i centiliter (.01 liter) = j ^Q^^II (39-370II3 " I METER (m.) . . . = < 3.280843 ft. i deciliter (.1 liter) . . = 0.176 pint, i LITER (1,000 cub. ) ( 1.09361425 yds. centimeters or I > = 1.75980 pints. i dekameter \ 01614. " cub. decimeter) ) (10 m.) }' i dekaliter (10 liters) . = 2.200 gallons. h > . . .= 0.62117 mile. ( 1,000 m.) ) m (iooom.) J- ' ' = 6 - 21 37 2 miles. APOTHECARIES' MEASURE. i micron . . . o ooi mm. i cubic centi- ) C 0.03520 fluid ounce. meter ( I ( == S 0.28157 fluid drachm. gram vv't) ) ( 15.43236 grains weight. i cub. millimeter = 0.01693 minim. SQUARE MEASURE. AVOIRDUPOIS WEIGHT. i sq. centimeter . . . = 0.1550 sq. in. i milligram (mgr.) . . = 0.01543 grain. (100 sq. centm ) ( = I 5-5 sc l- in< i centigram (.01 gram.) = 0.15432 i sq. meter or centi- f j 10.7639 sq. ft. i decigram (.1 " ) = 1.54324 grains. I GRAM I ^ 4^36 " eirc (TOO so. dcrn.J ) / 1.1900 scj. yds, I ARE (100 sq. m.) = 119.60 sq. yds. i hectare (100 ares 1 _ or 10,000 sq. m.) J = i dekagram (10 gram.) = 5.64383 drams. i hectogram (100 " ) = 3-52739 oz. C 2.2046223 lb I KILOGRAM ( I, OOO" ) =? I 5432.3564 ( grains. i myriagram (10 kilog.) =22.04622 Ibs. i quintal (TOO " ) = 1.96841 cwt. i millier or tonne 1 Rot- CUBIC MEASURE. (1,000 kilog.) p i cub. centimeter ) (c.c.) (1,000 cubic > = 0.0610 cub. in. TROY WEIGHT. millimeters) ) i cub. decimeter ) (c.d.) (1,000 cubic > = 61.024 " " centimeters) ) ( 0.03215 oz. Troy. I GRAM . . = ] 0.64301 pennyweight. / 1 5.43236 grains. i CUB. ME' rER ) f 35-3148 cub. ft. (1,000 c.d.) Y \ 1.307954 cub. yds. APOTHECARIES' WEIGHT. ( 0.25721 clr?chm. i GRAM ....=] 0.77162 scruple. ( 15.43236 grains. NOTE. Tlie 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 Sevres, near Paris, France. The present leeal 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 one kilogram weight of distilled water at its maximum density (4 C.), the barometer bein at 760 millimeters. *In accordance with the schedule adopted under the Weights and Measures (metric system) Act, 1897. SMITHSONIAN TABLES. TABLES. EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS AND MEASURES. (2) METRIC TO IMPERIAL. (For U.S. Weights and Measures, see Table 3.) LINEAR MEASURE. MEASURE OF CAPACITY. Millimeters to inches. Meters to feet. Meters to yards. Kilo- meters to miles. I 2 3 4 5 Liters to pints Dekaliters to gallons Hectoliters to busuels. Kiloliters to quarters. I 2 3 4 5 0.03937011 0.07874023 o.i 1811034 o.i 574804 s 0.19685056 3.28084 6.56169 9-84253 I 3- I 2 337 16.40421 1.09361 2.18723 3.28084 4-37446 5.46807 0.62137 1.24274 1.86412 2.48549 i 3.1o686i 1.75980 3-5I96' 5- 2 794I 7.03921 8.79902 2.19975 4-3995 1 6.59926 8.79902 10.99877 2-74969 549938 8.24908 10.99877 13.74846 3.43712 6.87423 io-3' 135 13.74846 17-18558 6 I 9 0.23622068 0.27559079 031496090 0-35433 ' 2 19.68506 22.96590 26.24674 29-52758 6.56169 7-65530 8.74891 9-84253 3.72823 4.34960 4.97097 5-59235 6 8 9 10.55882 12.31862 14.07842 15.83823 13.19852 15.39828 17-59803 19.79778 16.49815 19.24785 21.99754 24-74723 20.62269 24.05981 27.49692 30.93404 SQUARE MEASURE. WEIGHT (AVOIRDUPOIS). Square centimeters to square inches. Square meters to square feet. Square meters to square yards. Hectares to acres. Milli- grams to grains. Kilograms to grains. Kilo- grams to pounds. Quintals to hundred- weights. I 2 3 4 5 0.15500 0.31000 0.46500 O.62OOO 0.77500 10.76393 21.52786 32.29179 43-05572 53-8I965 1.19599 2.39198 3.58798 478397 5-97996 2.4711 49421 74132 9.8842 1 2-3553 I 3 4 5 0.01543 0.03086 0.04630 0.06173 0.07716 1 543 2 .356 30864.713 46297.069 61729.426 77161.782 2.20462 4.40924 6.61387 8.81849 11.0231 I 1.96841 3.93683 5-90524 7-87365 9.84206 6 8 9 0.93000 1.08500 I.240OO I-3950I 64.58357 75-34750 86 11143 96.87536 7-17595 8.37194 9-56794 10.76393 14.8263 17.2974 19.7685 22.2395 6 9 0.09259 0.10803 0.12346 0.13889 92594.138 108026.495 123458.851 138891.208 13.22773 I5-43 2 36 17.63698 19.84160 11.81048 I 3 .7 7 88 9 I5-74730 17.71572 CUBIC MEASURE. APOTHE- CARIES' MEASURE. AVOIRDUPOIS (font.) TROY WEIGHT. APOTHE- CARIES' WEIGHT. T 2 3 4 5 Cubic decimeters to cubic inches. Cubic Cubic meters to meters to cubic cubic feet. yards. Cub. cen- timeters to fluid drachms. Milliers or tonnes to tons. Grams to ounces Troy, Grams to penny- weights. Grams to scruples. 61.02390 122.04781 183.07171 244.09561 35- II 95 2 35-3 J 476 70.62952 105.94428 141.25904 176.57379 I-30795 2.61591 3.92386 5.23182 6-53977 0.28157 0.56314 0.8447 ' 1.12627 1.40784 I 3 4 5 0.98421 1.96841 2.95262 3-93683 4.92103 0.03215 0.06430 0.09645 0. 1 2860 0.16075 0.64301 1.28603 1.92904 2.57206 3.21507 0.77162 1.54324 2-31485 3.08647 3.85809 6 8 9 366.14342 427.16732 488.19123 549- 2 T 5 T 3 211.88855 247-20331 282.51807 317-83283 7.84772 9.15568 10.46363 11.77159 1.68941 1.97098 2-25255 2.53412 6 7 8 9 5-90524 6.88944 7-87365 8.85786 0.19290 0.22506 0.25721 0.28936 3.85809 4.5OIIO 5.I44I2 5-787I3 4.62971 5.40132 6.17294 6.94456 SMITHSONIAN TABLES. IO TABLE 5. EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS AND MEASURES. (3) IMPERIAL TO METRIC. (For U.S. Weights and Measures, see Table 3.) LINEAR MEASURE. MEASURE OF CAPACITY. ( 2 5.400 milli- i inch i o- or - gill = 1.42 deciliters. { meters, i foot (12 in.) . . = 0.30480 meter. pint (4 gills) . . . = 0.568 liter, quart (2 pints) . . = 1.136 liters. I YARD (3 ft.) . .= 0.9M399 ' GALLON (4 quarts) == 4.5459631 " i pole (5^ yd.) . .= 5.0292 meters. peck ( 2 galls.) . . = 9.092 " i chain (22yd. or ) _ 2O .n68 " 100 links) \ bushel (8 galls.) . = 3.637 dekaliters, quarter (8 bushels) = 2.909 hectoliters. i furlong (220 yd.) = 201.168 ( 1.6093 kilo- i mile (1,760 yd.) - { meters. AVOIRDUPOIS WEIGHT. SQUARE MEASURE. r grain . - \ 64 ' 8 minU 6.4516 sq. cen- i square inch . . = = timeters. | grams. Tram = 1.772 grams. ( 0.2903 sq. deci- ounce (16 dr.) . .= 28.350 i sq.ft. (144 sq. in.) = = { meters . { o 836 1 6 sq. .oL'M>(.6ozor> 0.45359243 kilogr. 7,000 grams) ) i SQ. YARD (9 sq. ft.) == i meters. stone ( 14 Ib.) . . = 6.350 ( 2;. 293 sq. me- i perch ( 3 oi sq. yd.) = j ^ quarter (28 Ib.) . = 12.70 hundredweight 1 _ \ 50.80 i rood (40 perches) == 10.117 ares. i i ACRE (4840 sq. yd.) = 0.40468 hectare. i sq. mile (640 acres) = | 259.00 hectares. (H2lb.) J = j 0.5080 quintal. ( 1.0160 tonnes < or 10 [6 k'lo- i ton (aocwt.) . == I grams> TROY WEIGHT. CUBIC MEASURE. I cub. inch = 16.387 cub. centimeters. i Troy OUNCE (480 J -31.1035 grams, grains avoir.) f i cub. foot (1728 1 (0.028317 cub me- cub. in.) f- ter, or 28.317 ( cub. decimeters. I i ptnnvweight (24 / grains) ] ~ i CUB. YARD (27 1.^0.76455 cub. meter, cub. ft.) J NOTE. The Troy grain is of the same weight as the Avoirdupois grain. APOTHECARIES' MEASURE. APOTHECARIES' WEIGHT. i gallon (8 pints or I _ 4.5459631 liters. 1 60 fluid ounces) J i fluid ounce, f 3 ) f 28.4123 cubic (8 drachms) f ( centimeters. i ounce (8 drachms) =31.1035 grams, i drachm, 3 i ( 3 scru- ( _ ggg pies) i i fluid drachm, f 3 ) 3-55 r 5 cubic (60 minims) ( centimeters, i minim, m (0.91 146 ( 0.05919 cubic i scruple 91 (20 I = g grains) ) tin weight) \ centimeters. NOTE. The Apothecaries' ounce is of the same weight as the Troy ounce. The Apothecaries' The Apothecaries' gallon is of the same grain is also of the same weight as the Avoirdupois capacity as the Imperial gallon. grain. NOTE. The YARD is the length at 6 2 Fahr., marked on a bronze bar deposited with the Board of Trade. The POUND is the weight of a piece of platinum weighed in vacuo at the temperature of o C., and which is also deposited with the Board of Trade. The GALLON contains 10 Ib. weight of distilled water at the temperature of 62 Fahr., the barometer being at 30 inches. SMITHSONIAN TABLES. (4) TABLE 5- EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS AND MEASURES. IMPERIAL TO METRIC. 1 I (For U.S. Weights and Measures, see Table 3.) 1- LINEAR MEASURE. MEASURE OF CAPACITY. Inches to centimeters. Feet to meters. Yards to meiers. Miles to kilo- meters. Quarts to liters. Gallons to liters. Bushels to dekaliters. Quarters to hectoliters. 4 5 2 -539998 5.079996 7.619993 10.159991 12.699989 0.30480 0.60960 0.91440 1.21920 1.52400 0.91440 1.82880 2.74320 3.65760 4.57200 1.60934 3.21869 4.82803 6-43737 8.04671 I 2 3 4 5 1.13649 2.27298 3-40947 ^ 4-54596 9.09193 I3-63789 18.18385 22.72982 3-63677 7-27354 10.91031 14.54708 18.18385 2.90942 5.81883 8.72825 11.63767 14.54708 6 8 9 15.239987 17.7/9984 20.319982 22.859980 1.82880 2.13360 2.43840 2.74320 5.48640 6.40080 7-31519 8.22959 9.65606 11.26540 12.87474 1 4.48408 6 8 9 6.81894 7-95544 9.09193 10.22842 27.27578 31.82174 36.36770 40.91367 21 82062 2545739 29.09416 3 2 -73093 17.45650 20.36591 23-27533 26.18475 SQUARE MEASURE. WEIGHT (AVOIRDUPOIS). Square inches to square centimeters. Square feet to square decimeters. Square yards to square meters. Acres to hectares. Grains to milli- grams. Ounces to grams. Pounds to kilo- grams. Hundred- weights to quintals. I 2 3 4 5 6-45 1 59 12.90318 J9-35477 25.80636 32.25794 9.29029 18.58058 27.87086 37.16115 46.45144 0.83613 1.67225 2.50838 3-3445 4.18063 0.40468 0.80937 1.21405 1.61874 2.02342 . 2 3 4 5 64.79892 129.59784 '94-39675 2 59- I 9567 323-99459 28.34953 56.69905 85.04858 113.39811 141.74763 0-45359 0.90718 1.36078 1.81437 2.26796 0.50802 1.01605 1.52407 2.03209 2.54012 6 7 8 9 3 8 -70953 45.16112 5i.6r27i 58.06430 55-74I73 65.03201 74.32230 83.61259 5.01676 5.85288 6.68901 7-525I3 2.42811 2.83279 3.23748 3.64216 6 8 9 388.79351 453-59243 5 ! 8.39135 583.19026 170.09716 198.44669 226.79621 255-M574 2.72155 3.I75I5 3.62874 4.08233 3.04814 3.556'6 4.06419 4.57221 CUBIC MEASURE. APOTHE- CARIES' MEASURE. AVOIRDUPOIS (cont.}. TROY WHKIHT . APOTHE- CARIES' WEIGHT Cubic inches to cubic centimeters. Cubic feet to cubic meters. Cubic yards to cubic meters. Fluid drachms to cubic centi- meters. Tons to milliets or tonnes. Ounces to grams. Penny- weights to grams. Scruples to grams. I 2 3 4 5 16.38702 3 2 -77404 49.16106 65.54808 81.93511 0.02832 0.05663 0.08495 0.11327 0.14158 0.76455 1.52911 2.29366 3.05821 3.82276 3-55I53 7.10307 10.65460 14.20613 I7-75767 I 2 3 4 5 1.01605 2.03209 3.048 1 4 4.06419 5.08024 31.10348 62.20696 93-3 J 044 12441392 I55-5I740 I-555I7 3*1035 4.66552 6.22070 777587 1.29598 2.59196 3.88794 5-!839i 6.47989 6 I 9 98.32213 114.70915 131.09617 147.48319 0.16990 0.19822 0.2265 ^ 0.25485 4-58732 5-35I87 6.1 1642 6.88098 21.30920 24.86074 28.41227 31.96380 6 8 9 6.09628 7-11233 8.12838 9.14442 186.62088 217.72437 248.82785 27 9-93 T 33 9.33I04 10.88622 12.44139 I3-99657 7.7758/ 9.07185 10.36783 u;66 SMITHSONIAN TABLES. 12 TABLE 6. DERIVATIVES AND INTEGRALS/ J 7 x n+i d arc d (IX /*<& n+i d t> = ( u % +v ^) dx f d * = logx ^ A*-*V f*<* \ 2 / e dx n = wre 71 " 1 dx fe ax dx =- e ax a d/(w) -^sr^s-* fx c** dx =~(^-i) de* -e* dx /n.* = u vfv du d log e x x /(a + bx)n d x _(a+bx) n+l (n+i)b dx* = x x (i+log e z) d sin re = cos x dx f( a 2 +x ^-l dx = - tan- 1 - = a a 1 sin- 1 * a v^^_j_ a 2 d cosx = -sin x dx f( a 1_yZ\-\dX = ^L log a+x J 2a a x dtanx = sec 2 x dx /(a 2 -re 2 )-* dx . x , x = sin" 1 -, or cos -1 - a a d cot x = csc 2 re dx /x(a 2 x 2 )~*dx = ( " rcfo-i) (M-2).y2 + _ _ + (d (-fcj! kl 3'~ (- ip 6^5 4- f(x+h) = f (x)+hf (x) + k ~ /"(*)+...+ ^ /<> (*) + rayl series. / / \ / / \ , x f i \ , x2 * , - ^ n r , n \ Maclaurin's / (x) =f(o)+ - )' (o) + - /" (o) + .../ () ( ) + . . . series> / i\ i i i i = hm( i+-) w =i+ - - -f- - - + -- 4 -- . +... V ;// i! 2! 3! 4 i T = i + x + -, H -- 1 H -- 1 -f- . . a x = l+x ] ga+ v - -^ + 3! .r i , i /x i \ " i /x i\ 3 i **=~ + - 2 () + -i(v; + = O - - M* - O 2 + H* - O 3 - lg ( T + *) = X $ X 2 4- i A; 3 j .T 4 + . . . . == l f.ix .-ix\ X * * 5 * 7 ~ ~^i (t ~ 3! + ? ~ T"! 4 cos .r = - (e'- r 4- g->) = i- H 1 +... = i_ versin .v 7T T^ T "7 >v5 T *? C A"7 . . i i i ' ^5 **' v5 *^ ~ 2 " 6 2*4"5" + 2*4*6'7 tan~ ! x = - cot. 1 # = a: # 3 H .r 5 - a- 7 4- ... 7T I I I i , x 3 * 5 Jc 7 smh s = ~(e*- e-*) = x + - + - + -,+... SMITHSONIAN TABLES. TABLE 7 (continued). SERIES. I , X* X* X cosh x = - (e x + -*) = i H , H : + zi + 2 v 2! 4! 6! ,,'<00) i 2 17 7 U 2 I) ii 131 i 3 5 i COSh-! x = log 2X _ - ^ ._ _ . __ ... - - - ^ .... (* 2 >I) tanh- 1 A; = x + - .v 3 + - .v 5 + - x 1 + . (A' 2 9*43 679*73*2 20.1742 20.1990 354 2.82486 125316 44361864 18.8149 | 409 2-44499 167281 68417929 20.2237 355 2.81690 126025 44738875 18.8414 410 2.43902 168100 68921000 20.2485 356 2.80899 126736 451 18016 18.8680 411 168921 69426531 20.2731 357 2.80112 127449 45499293 18.8944 412 2.42718 169744 69934528 20.2978 358 2.79330 128164 45882712 18.9209 4*3 2.42131 170569 70444997 20.3224 359 2.78552 128881 46268279 18.9473 4*4 2.41546 171396 70957944 20.3470 360 2.77778 129600 46656000 iS-9737 415 2.40964 172225 7*473375 20.37*5 361 2.77008 130321 4704588 r 1 9.0000 416 2.40385 173056 71991296 20.3961 362 2.76243 131044 47437928 19.0263 4*7 2.39808 173889 7251*713 20.4206 363 2.75482 131769 47832147 19.0526 418 2.39234 174724 73034632 20.4450 364 2.74725 132496 48228544 19.0788 419 2.38663 73560059 20.4695 365 2-73973 133225 48627125 19.1050 420 2.38095 176400 74088000 20-4939 366 367 2.73224 2.72480 1 33956 134689 49027896 49430863 19.1311 19.1572 421 422 2.37530 2.36967 177241 178084 74618461 7515*448 20.5183 20.5426 368 2.71739 1 35424 49836032 I 9'* 8 33 423 2.36407 178929 75686967 20.5670 369 2.71003 I36l6l 50243409 19.2094 424 2.35849 179776 76225024 20.5913 370 37 * 2.70270 2.69542 136900 1 3764 * 50653000 51064811 I9-2354 19.2614 425 426 2.35294 2.34742 180625 181476 76765625 77308776 20.6155 20.6398 372 2.68817 138384 51478848 19.2873 427 2.34192 182329 20.6640 373 2.68097 I39I29 19.3132 428 2-33645 183184 78402752 20.6882 374 2.67380 139876 523*3624 19-339* 429 2.33100 184041 789535% 20.7123 375 2.66667 140625 52734375 19.3649 430 2.32558 184900 79507000 20.7364 376 377 378 2.65957 2.65252 2.64550 MI376 I42I29 142884 53*57376 53582633 54010152 19.3907 19.4165 19.4422 43* 432 433 2.32019 2.31481 2.30947 185761 186624 187489 80062991 80621568 81182737 20.7605 20.7846 20.8087 379 2-63852 I4364I 54439939 19.4679 434 2.30415 188356 81746504 20.8327 380 38' 2-63158 2.62467 144400 I45l6l 54872000 55306341 19.4936 19.5192 435 436 2.29885 2-29358 189225 190096 82312875 82881856 _ -' 20.8567 20.8806 382 383 2.61780 2.61097 145924 146689 55742968 56181887 19.5448 19.5704 437 438 2-28833 2.28311 190969 191844 83453453 84027672 20.9045 20.9284 384 2.60417 147456 56623104 19-5959 439 2.27790 192721 84604519 20.9523 385 2.59740 148225 57066625 19.6214 440 2.27273 193600 85184000 20.9762 386 387 2^58398 148996 149769 575^456 57960603 19.6469 19.6723 44* 442 2.26757 2.26244 194481 195364 85766121 86350888 2I.OOOO 21.0238 388 2-57732 * 5544 58411072 19.6977 443 2-25734 196249 86938307 21.0476 389 2.57069 !5*32i 58863869 19.7231 444 2.25225 I97I36 87528384 21.0713 390 39* 2.56410 2-55754 152100 152881 59319000 59776471 19.7484 *9-7737 445 446 2.24719 2.24215 198025 198916 88121125 88716536 2I.O95O 2I.II87 39 2 2.55102 153664 60236288 19.7990 447 2.23714 199809 89314623 21.1424 393 394 2-54453 2.53807 154449 155236 60698457 61162984 19.8242 19.8494 448 449 2.23214 2.22717 200704 201601 899*5392 90518849 21. l66o 21.1896 SMITHSONIAN TABLE? TABLE 9 (continued). I VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS OF NATURAL NUMBERS. n looo.i 2 8 in n 1000.^ 2 1* 450 2.22222 202500 9II25OOO 21.2132 505 1.98020 255025 128787625 22.4722 45 1 2.21729 203401 9^3385! 21.2368 ! 506 1.97628 256036 I295542I6 22.4944 45 2 2.21239 204304 92345408 21.2603 ; 507 1.97239 257049 130323843 22.5167 453 2.20751 205209 92959677 21.2838 1 508 1.96850 258064 131096512 22.5389 454 2.2O264 2o6ll6 93576664 21.3073 59 1.96464 259081 131872229 22.5610 455 2.19780 207025 94196375 21.3307 510 1.96078 260100 I3265IOOO 22.5832 45 6 2.192 9 8 207936 94818816 21.3542 5 11 i -95695 26II2I I3343283I 22.6053 457 2.l88l8 208849 95443993 21.3776 512 I.953I2 262144 I342I7728 22.6274 458 2.18341 209764 96071912 2 1 .4009 5 J 3 1.94932 263169 135005097 22.6495 459 2.17865 2I068I 96702579 21.4243 5H 1-94553 264196 1 35796744 22.6716 460 2.I739I 2 1 1 6OO 97336000 21.4476 515 I.94I75 265225 136590875 22.6936 461 2.16920 2I252I 97972181 21.4709 516 1.93798 266256 137388096 22.7156 462 2.16450 213444 98611128 21.4942 5*7 1.93424 267289 138188413 22.7376 463 464 2- 1 5983 2.I55I7 214369 215296 99252847 99897344 21.5174 21.5407 518 5 r 9 1.93050 1.92678 268324 269361 138991832 139798359 22.7596 22.7816 465 2.15054 2l6225 100544625 21.5639 520 1.92308 27O4OO I4O6O8OOO 22.8035 466 2.14592 217156 101194696 21.5870 | 52i 1.91939 27I44I 141420761 22.8254 467 2.I4I33 218089 101847563 2I.6IO2 522 i-9!57i 272484 142236648 22.8473 468 2.13675 219024 102503232 21.6333 523 1.91205 273529 143055667 22.8692 469 2.13220 219961 103161709 21.6564 524 1.90840 274576 143877824 22.8910 470 2.12766 220900 103823000 21.6795 525 1.90476 275625 144703125 22.9129 4?i 2.I23I4 22I84I 104487111 21.7025 526 1.90114 276676 !4553!576 22.9347 472 2.II864 222784 105154048 21.7256 5 2 7 I-89753 277729 146363183 22.9565 473 2.II4I6 223729 105823817 21.7486 528 1.89394 278784 1 47 197952 22.9783 474 2.10970 224676 106496424 21.7715 529 1.89036 279841 148035889 23.0000 475 476 2.10526 2.10084 226576 107171875 107850176 21-7945 2I.8I74 i 530 53 1 1.88679 1.88324 280900 281961 148877000 149721291 23.0217 23-0434 477 478 2.09644 2.09205 227529 228484 I0 853!333 109215352 21.8403 21.8632 S3 2 533 1.87970 1.87617 283024 284089 150568768 151419437 23.0868 479 2.08768 229441 109902239 2I.886I 534 1.87266 285156 152273304 23.1084 480 481 2-08333 2.O79OO 230400 231361 110592000 111284641 21.9089 21.9317 535 536 1.86916 1.86567 286225 287296 I53U0375 153990656 23.1301 23-1517 482 2.07469 232324 111980168 21.9545 537 1.86220 288369 I54854I53 23- J 733 483 2.07039 233289 112678587 21.9773 538 1.85874 289444 155720872 23.1948 484 2.06612 234256 ii33799 4 22.0000 539 1.85529 290521 156590819 23.2164 485 486 487 2.06186 2.05761 2-05339 235225 236196 237169 114084125 114791256 ii5S OI 33 22.0227 22.0454 22.0681 540 54i 542 1.85185 1.84843 1.84502 291600 292681 293764 157464000 158340421 i 59220088 23.2379 23.2594 23.2809 488 2.04918 238144 116214272 22.0907 543 1.84162 294849 160103007 23.3024 489 2.04499 239121 116930169 22.1133 544 1.83824 295936 160989184 23-3238 490 2.04082 240100 117649000 22.1359 545 1.83486 297025 161878625 23-3452 491 2.03666 241081 118370771 22.1585 546 1.83150 298116 162771336 23.3666 492 2.03252 242064 119095488 22.l8ll 547 1.82815 299209 163667323 23.3880 493 2.02840 243049 119823157 22.2036 548 1.82482 300304 164566592 23-4094 494 2.02429 244036 120553784 22.2261 549 1.82149 3OI4OI 165469149 23-4307 495 496 2.O2O2O 2.Ol6l3 245025 246016 121287375 122023936 22.2486 22.2711 550 55 1 1.81818 1.81488 3O25OO 303601 166375000 167284151 23.4521 23-4734 497 2.01207 247009 122763473 22.2 9 35 552 1.81159 304704 168196608 23-4947 498 2.00803 248004 123505992 22.3159 553 1.80832 305809 169112377 23.5160 499 2.OO4OI 249001 124251499 22.3383 554 1.80505 306916 170031464 23-5372 50O 2.OOOOO 25OOOO 125000000 22.3607 555 i. 80 1 80 308025 170953875 23-5584 5 01 I.99DOI 25IOOI 12575^01 22.3830 ! 556 1.79856 309136 171879616 23.5797 502 1.99203 252004 i 26506008 22.4054 557 1-79533 310249 172808693 23.6008 53 1.98807 253009 127263527 22.4277 558 1.79211 3"364 173741112 23.6220 54 1.98413 254016 128024064 22.4499 559 1.78891 312481 174676879 23.6432 SMITHSONIAN TABLES. 2O TABLE 9 (continued}. VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS OF NATURAL NUMBERS. n lOOO.i # . 1* i /; IOOO.I * V 560 1-78571 313600 175616000 23.6643 615 1.62602 378225 232608375 24.7992 561 1-78253 176558481 23.6854 ! 616 1.62338 379456 233744896 24.8193 562 1.77936 3 1 5844 177504328 23.7065 | 617 1.62075 380689 234885113 24.8395 563 1.77620 316969 178453547 23.7276 618 1.61812 38*924 236029032 24.8596 564 1.77305 318096 179406144 23-7487 | 619 1-61551 383*61 237*76659 24-8797 565 1.76991 319225 180362125 23.7697 620 1.61290 384400 238328000 24.8998 566 1.76678 320356 181321496 23.7908 621 1.61031 385641 239483061 24.9199 1.76367 321489 182284263 23.8118 622 1.60772 386884 240641848 24.9399 568 1.76056 322624 183250432 23.8328 623 1.60514 388129 241804367 24.9600 569 1-75747 323761 184220009 23-8537 624 1.60256 389376 242970624 24.9800 570 1-75439 324900 185193000 23.8747 625 1.60000 390625 244140625 25.0000 571 I -75 I 3 I 326041 186169411 23.8956 626 1-59744 39*876 2453*4376 25.0200 572 1.74825 327184 187149248 23.9165 627 1.59490 393*29 246491883 25.0400 573 1.74520 328329 188132517 23-9374 628 1-59236 394384 247673152 25-0599 574 1.74216 329476 189119224 23-9583 629 1-58983 395641 248858189 25.0799 575 L739I3 330625 190109375 23-9792 630 1-58730 396900 250047000 25.0998 576 1.73611 33*776 191102976 24.OOOO : 63* 1.58479 398161 25*23959* 25.1197 577 i-733 10 332929 192100033 24.0208 632 1.58228 399424 25 2 435968 25.1396 578 1.73010 334084 193100552 24.O4I6 633 I-57978 400689 253636137 25-1595 579 1.72712 335241 194104539 24.0624 634 1.57729 401956 254840104 25.1794 580 1.72414 336400 195112000 24.O832 635 1.57480 403225 256047875 25.1992 581 1.72117 337561 196122941 24.1039 636 *-57233 404496 257259456 25.2190 582 1.71821 338724 *97*37368 24.1247 637 1.56986 405769 258474853 25.2389 583 584 1.71527 1-71233 339889 34*056 198*55287 199176704 24.1454 2 4 .l66l 638 639 1.56740 I-56495 407044 408321 2596940/2 260917119 25.2587 25.2784 585 1.70940 342225 200201625 24.1868 640 1.56250 409600 262144000 25.2982 586 1.70648 343396 201230056 24.2074 641 1.56006 410881 263374721 25.3180 587 1-70358 344569 202262003 24.2281 642 1.55763 412164 264609288 25-3377 588 1.70068 345744 203297472 24.2487 643 4*3449 265847707 25-3574 589 1.69779 346921 204336469 24.2693 644 1.55280 414736 267089984 25-3772 590 1.69492 348100 205379000 24.2899 645 I-55039 416025 268336125 25-3969 59 1 1.69205 349281 206425071 24.3IO5 646 1-54799 4*73*6 269586136 25-4*65 592 1.68919 350464 207474688 24-33*1 647 1.54560 418609 270840023 254362 593 1.68634 35*649 208527857 24-35*6 648 I-543 21 4*9904 272097792 25-4558 594 1.68350 352836 209584584 24.3721 649 1.54083 421201 273359449 254755 595 1.68067 354025 210644875 24.3926 650 1.53846 422500 274625000 25.4951 596 1.67785 211708736 244I3I 651 .53610 423801 275894451 25-5*47 597 1.67504 356409 212776173 244336 652 53374 425104 277167808 25-5343 598 1.67224 357604 213847192 24.4540 653 53*39 426409 278445077 25-5539 599 1.66945 358801 214921799 244745 6 5 4 .52905 427716 279726264 25-5734 600 1.66667 360000 216000000 244949 655 .52672 429025 281011375 25-5930 601 1.66389 361201 217081801 656 52439 430336 282300416 25.6125 602 1.66113 362404 218167208 24-5357 657 52207 43*649 283593393 25.6320 603 1.65837 363609 219256227 24.5561 658 .5*976 432964 284890312 25-65*5 604 1 -65563 364816 220348864 24-5764 659 5*745 434281 286191179 25.6710 605 1.65289 366025 221445125 24-5967 660 5*5*5 435600 287496000 25.6905 606 1.65017 367236 222545016 24.6I7I 66 1 .51286 436921 288804781 25.7099 607 1.64745 368449 223648543 24-6374 662 .51057 438244 290117528 25.7294 608 1.64474 369664 224755712 24-6577 663 .50830 439569 291434247 25-7488 609 1.64204 370881 225866529 24.6779 664 .50602 440896 292754944 25.7682 610 1-63934 372100 226981000 24.6982 665 .50376 442225 294079625 25.7876 611 612 1.63666 I-63399 37332* 374544 228099131 229220928 24.7184 247386 666 667 50*5 .49925 443S5 6 444889 295408296 296740963 25.8070 25.8263 613 1.63132 375769 230346397 247588 668 .49701 446224 298077632 25-8457 614 1.62866 376996 231475544 247790 669 49477 44756i 299418309 25.8650 SMITHSONIAN TABLES. TABLE 9 (continued). 21 VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS OF NATURAL NUMBERS. n lOOO.i 2 3 i* n 1 000.1 2 8 tf 670 1.49254 448900 300763000 25.8844 725 I -3793 I 525625 381078125 26.9258 671 1.49031 450241 3O2III7II 25.9037 726 I-3774I 527076 382657176 26.9444 672 1.48810 45I5 8 4 303464448 25.9230 727 1-37552 528529 384240583 26.9629 673 1.48588 452929 304821217 25.9422 728 I-37363 529984 385828352 26.9815 674 {.48368 454276 306182024 25.9615 729 I-37I74 53I44I 387420489 27.0000 675 1.48148 455625 307546875 25.9808 730 1.36986 532900 389017000 27.0185 676 1.47929 456976 308915776 26.OOOO 73 1 1.36799 53436i 390617891 27.0370 677 1.47710 458329 310288733 26.OI92 732 1.36612 535824 392223168 27-0555 678 679 1-47493 I-47275 459684 461041 311665752 313046839 26.0384 26.0576 733 734 1.36426 1.36240 537289 538756 393832837 395446904 27.0740 27.0924 680 1.47059 462400 314432000 26.0768 735 1.36054 540225 397065375 27.1109 68 1 1.46843 463761 315821241 26.0960 736 I-35870 541696 398688256 27.1293 682 1.46628 465124 317214568 26.1151 737 1-35685 543*69 400315553 27.1477 683 1.46413 466489 318611987 26.1343 738 l -3S5 l 544644 401947272 27.1662 684 1.46199 467856 320013504 26.1534 739 *-353 l8 546121 403583419 27.1846 685 1.45985 469225 321419125 26.1725 740 i-35'35 5476oo 405224000 27.2029 686 1-45773 470596 322828856 26.1916 74i 1 -34953 549081 40686902 i 27.2213 687 1.45560 471969 324242703 26.2IO7 742 i-3477i 550564 408518488 27-2397 688 1-45349 473344 325660672 26.2298 743 1.34590 552049 410172407 27.2580 689 i -45 J 38 474721 327082769 26.2488 744 1.34409 553536 411830784 27.2764 690 1.44928 476100 328509000 26.2679 745 1.34228 555025 413493625 27-2947 691 1.44718 477481 329939371 26.2869 746 1.34048 556516 415160936 27.3130 692 1.44509 478864 331373888 26.3059 747 1.33869 558009 416832723 27-33^3 693 1.44300 480249 332812557 26.3249 748 1.33690 559504 418508992 27.3496 694 1.44092 481636 334255384 26.3439 749 J-335 11 561001 420189749 27.3679 695 696 1.43885 1.43678 483025 484416 335702375 337153536 26.3629 26.3818 750 75' 1 -33333 I -33 I 5 6 562500 564001 421875000 42356475 1 27.3861 27.4044 697 1.43472 485809 338608873 26.4008 75 2 1.32979 565504 425259008 27.4226 698 1.43266 ; 487204 340368392 | 26.4197 753 1.32802 567009 426957777 27.4408 699 1.43062 488601 341532099 26.4386 754 1.32626 568516 428661064 27.4591 700 1.42857 490000 343OOOOOO 26.4575 755 1.32450 570025 430368875 27-4773 701 1.42653 491401 344472IOI 26.4764 756 1-32275 571536 432081216 27-4955 702 1.42450 492804 345948408 26.4953 757 1.32100 573049 433798093 27-5 * 36 703 1.42248 494209 347428927 26.5141 758 1.31926 574564 4355!95 12 27-53 18 704 1.42045 495616 348913664 26.5330 759 1-31752 576081 437245479 27.5500 705 1.41844 497025 350402625 26.5518 760 I -3 I 579 577600 438976000 27.5681 706 1.41643 498436 35I8958I6 26.5707 76i 1.31406 579121 440711081 27.5862 707 1.41443 499849 353393243 26.5895 762 1.31234 ! 580644 442450728 27.6043 708 1.41243 501264 354894912 26.6083 763 1.31062 i 582169 444194947 27.6225 709 1.41044 502681 356400829 26.6271 764 1.30890 583696 445943744 27.6405. 710 1.40845 504100 3579IIOOO 26.6458 765 1.30719 585225 447697125 27.6586 711 712 1.40647 1.40449 505521 506944 359425431 360944128 26.6646 26.6833 766 767 1.30548 1-30378 586756 588289 449455096 451217663 27.6767 27.6948 713 1.40252 508369 362467097 26.7O2I 768 1.30208 589824 452984832 27.7128 7H 1.40056 509796 3 6 3994344 26.7208 769 1.30039 591361 454756609 27.7308 715 1.39860 511225 365525875 26.7395 770 1.29870 592900 456533000 27.7489 716 1.39665 512656 367061696 26.7582 771 1.29702 594441 458314011 27.7669 717 1.39470 514089 368601813 26.7769 772 1-29534 595984 460099648 27.7849 718 1.39276 5*5524 370146232 26.7955 773 1.29366 597529 461889917 27.8029 719 1.39082 516961 371694959 26.8142 774 1.29199 599076 463684824 27.8209 720 1.38889 518400 373248000 26.8328 775 1.29032 600625 465484375 27.8388 721 1.38696 519841 374805361 26.8514 776 1.28866 602176 467288576 27.8568 722 1.38504 521284 376367048 26.8701 777 1.28700 603729 469097433 27.8747 723 724 1 -383 1 3 1.38122 522729 524176 377933067 379503424 26.8887 26.9072 778 779 1-28535 1.28370 605284 606841 470910952 472729139 27.8927 27.9106 SMITHSONIAN TABLES. 2 2 TABLE 9 (continued}. VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS OF NATURAL NUMBERS. n ooo.i # * <- n 1 000. J -. n* v <* 780 1.28205 608400 474552000 27.9285 835 1.19760 697225 582182875 28.8964 781 1.28041 609961 476379541 27.9464 ! 836 1.19617 698896 584277056 28.9137 782 1.27877 1 611524 4782II768 27.9643 1 837 1.19474 700569 5^6376253 28.9310 783 1.27714 613089 480048687 27.9821 838 I'I9332 702244 588480472 28.9482 784 1.27551 614656 48l89O3O4 28.OOOO 839 1.19190 703921 590589719 28.9655 785 786 1.27389 616225 483736625 28.0179 1.27226 617796 485587656 28.0357 840 841 1.19048 705600 1.18906 707281 592704000 594823321 28.9828 29.0000 1.27065 619369 487443403 28.0535 842 1.18765 708964 59694/6S8 29.0172 788 1.26904 620944 489303872 28.0713 843 1.18624 j 710649 599077107 29-0345 789 1.26743 622521 49H69069 28.0891 844 1.18483 712336 OOI2II584 29.0517 790 791 1.26582 624100 1.26422 625681 493039000 4949I367I 28.1069 28:1247 845 846 1-18343 1.18203 714025 715716 60335II25 605495/36 29.0689 29.0861 792 1.26263 627264 496793088 28.1425 847 1.18064 717409 607645423 29.1033 793 1.26103 628849 498677257 28.1603 848 1.17925 719104 609800192 29.1204 794 1.25945 630436 500566l84 28.1780 849 1.17786 720801 611960049 29.1376 795 1.25786 632025 502459875 28.1957 850 1.17647 722500 6I4I25OOO 29.1548 | 796 1.25628 633616 504358336 28.2135 851 1.17509 724201 6l6295O5I 29.1719 797 1.25471 6352O9 5O626I573 28.2312 852 725904 6l8470208 29.1890 798 I - 2 53 I 3 636804 5OSl69592 28.2489 853 1-17233 727609 620650477 29.2062 799 1-25156 638401 510082399 28.2666 854 1.17096 729316 622835864 29.2233 800 1.25000 64OOOO 512000000 28.2843 855 1.16959 731025 625026375 29.2404 80 1 1.24844 64I60I 5I392240I 28.3019 856 1.16822 732736 j 627222016 29.2 S7S 802 1.24688 643204 515849608 28.3196 857 1. 1 6686 I 734449 629422793 29.2746 803 !- 2 4533 644809 5I778l627 28.3373 858 1.16550 736164 63I6287I2 29.2916 804 1.24378 646416 5I97I8464 28.3549 859 1.16414 73788I 633839779 29.3087 805 1.24224 648025 52I660I25 28.3725 860 1.16279 739600 636050000 29.3258 806 1.24069 649636 523606616 28.3901 861 1.16144 741321 638277381 29.3428 807 1.23916 651249 525557943 28.4077 862 1.16009 743044 : 640503928 808 1.23762 652864 5275I4II2 28.4253 863 1.15875 ; 744769 642735647 29.3769 809 1.23609 654481 529475129 28.4429 864 '15741 746496 644972544 29-3939 810 1-23457 656100 53I44IOOO 28.4605 865 1.15607 748225 647214625 29.4109 811 1.23305 657721 5334II73I 28.4781 866 1-15473 749956 649461896 29.4279 812 I - 2 3 I 53 659344 535387328 28.4956 867 1-15340 751689 651714363 29.4449 813 1.23001 537367797 28.5132 868 1.15207 7534^4 653972032 29.4618 814 1.22850 662596 539353M4 28.5307 869 1.15075 755161 656234909 29.4788 815 1.22699 664225 541343375 28.5482 870 1.14943 756900 : 6^8503000 29.4958 816 1.22549 665856 543338496 28.5657 871 1.14811 758641 66O7763I I 29.5127 817 1.22399 667489 54533 8 5 J 3 28.5832 872 1.14679 760384 663054848 29.5296 818 1.22249 6691 24 547343432 28.6007 873 1.14548 762129 665338617 29.5466 .819 I.22IOO 670761 549353259 28.6182 874 1.14416 763876 667627624 29-5635 820 I.2I95I 6724OO 551368000 28.6356 875 1.14286 765625 669921875 29.5804 821 1.21803 674041 55338766r 28.6531 876 1-14155 767376 672221376 29-5973 822 823 1.21655 I.2I507 675684 677329 555412248 557441767 28.6705 28.6880 877 878 1.14025 1-13895 769129 770884 674526133 676836152 29.6142 29.63 1 1 824 I.2I359 678976 559476224 28.7054 879 1.13766 772641 1 679151439 29.6479 825 826 827 I.2I2I2 680625 I.2I065 682276 I.2O9I9 : 683929 561515625 28.7228 563559976 28.7402 565609283 28.7576 880 88 1 882 1.13636 1-13507 1-13379 774400 776161 777924 68I472OOO 683797841 686128968 29.6648 29.6816 29.6985 828 1.20773 685584 567663552 ; 28.7750 | 883 1.13250 779689 688465387 29-7153 829 I.2O627 687241 569722789 28.7924 1 884 1.13122 781456 69O8O7IO4 29.7321 830 831 1.20482 1.20337 688900 690561 571787000 573856191 28.8097 28.8271 885 886 1.12994 1.12867 783225 784996 693154125 695506456 29.7489 29.7658 832 I.2OI92 692224 575930368 28.8444 ! 887 1.12740 786769 697864103 29.7825 833 1.20048 693889 578009537 28.8617 888 1.12613 788544 700227072 29-7993 834 I.I9904 695556 580093704 28.8791 889 1.12486 790321 702595369 29.8161 SMITHSONIAN TABLES. TABLE 9 (continued'). 2 VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS OF NATURAL NUMBERS. n I OCX).,; n 2 3 1* n 1000.4 2 3 V* 890 891 892 .I236O .12233 .12108 792100 793881 795664 704969000 707347971 70 97 32288 29.8329 29.8496 29.8664 945 946 947 1.05820 1.05708 1 -5597 893025 894916 896809 843908625 846590536 849278123 30.7409 30-7571 30-7734 893 .11982 797449 7I2I2I957 29.8831 948 1.05485 898704 85i97<392 30.7896 894 .11857 799236 714516984 29.8998 949 1-05374 9OO6OI 854670349 30.8058 895 .11732 801025 7I69I7375 29.9166 950 1.05263 9O25OO 857375000 30.8221 896 .11607 802816 719323136 29-9333 95 1 1.05152 904401 860085351 30.8383 897 .11483 804609 721734273 29.9500 95 2 1.05042 906304 862801408 30-8545 898 II 359 806404 724150792 29.9666 953 1.04932 908209 865523177 30.8707 899 11235 808201 726572699 29-9833 954 1.04822 9IOIl6 868250664 1 30.8869 900 .inn 810000 729000000 30.0000 955 1.04712 912025 870983875 30.9031 901 .10988 811801 73I43270I 30.0167 956 i .04603 9 13936 873722816 30.9192 902 .10865 813604 733870808 30-0333 957 1.04493 915849 876467493 ! 30-9354 903 904 .10742 .10619 815409 817216 7363M327 738763264 3O.O5OO 30.0666 958 959 1.04384 1.04275 917764 919681 879217912 881974079 1 30.9516 30.9677 905 .10497 819025 74I2I7625 30.0832 960 1.04167 921600 884736000 30-9839 906 I0 375 820836 743677416 30.0998 961 i .04058 923521 887503681 31.0000 907 .10254 822649 746142643 30.1164 962 1.03950 9 2 5444 890277128 31.0161 908 .10132 824464 748613312 3- I 330 963 1.03842 927369 893056347 31.0322 909 .IOOII 826281 751089429 30.1496 964 1-03734 929296 895841344 31.0483 910 1.09890 828100 753571000 3O.I662 965 1.03627 931225 898632125 31.0644 911 1.09769 829921 756058031 30.1828 966 .03520 933^6 901428696 31.0805 912 9i3 1.09649 1.09529 S3I744 833569 758550528 761048497 30.1993 30.2159 967 968 03413 .03306 935089 937024 904231063 907039232 31.0966 31.1127 9*4 1.09409 835396 763SSI944 30.2324 969 .03199 938961 909-853209 31.1288 915 1.09290 837225 766060875 3O.249O 970 03093 940900 912673000 31.1448 916 1.09170 839056 768575296 30-2655 ! 971 .02987 942841 915498611 31.1609 917 1.09051 840889 77I0952I3 30.2820 | 972 .02881 944784 918330048 31.1769 918 1.08932 842724 773620632 30.2985 ; 973 .02775 946729 921167317 31.1929 919 1.08814 844561 776I5I559 30.3150 974 .02669 948676 924010424 31.2090 920 1.08696 846400 778688000 3-33 I 5 975 .02564 950625 926859375 31.2250 921 1.08578 848241 781229961 30.3480 976 .02459 95 2 576 929714176 31.2410 922 1.08460 850084 783777448 30-3645 977 02354 954529 932574833 3 I - 2 570 923 1.08342 851929 786330467 30.3809 978 1.02249 956484 935441352 31.2730 924 1.08225 853776 788889024 30-3974 i 979 1.02145 958441 9383^739 31.2890 925 1.08108 855625 79M53I25 30-4138 i 980 1.02041 960400 941192000 31-305 926 1.07991 857476 794022776 30.4302 981 01937 962361 944076141 31.3209 927 1.07875 859329 796597983 30.4467 982 01833 964324 946966168 3 * -3369 928 1.07759 861184 799178752 30.4631 983 .01729 966289 949862087 3I-3528 929 1.07643 863041 801765089 30-4795 984 .01626 968256 952763904 31.3688 930 1.07527 864900 804357000 30.4959 985 01523 970225 955671625 31-3847 93 r 1.07411 866761 806954491 3 -5 I2 3 986 .01420 972196 958585256 31.4006 932 1.07296 868624 809557568 30-5287 ; 987 .01317 974169 961 504803 31.4166 933 1.07181 870489 812166237 30-5450 988 .01215 976144 964430272 3M3 2 5 934 i .07066 872356 814780504 30.5614 989 I.OIII2 978121 967361669 31.4484 935 1.06952 874225 817400375 30-577S 990 I.OIOIO 980100 970299000 31-4643 936 937 1.06838 1.06724 876096 877969 820025856 822656953 30-594I 3O.6IO5 991 992 1.00908 1.00806 982081 984064 973242271 976191488 31.4802 31.4960 938 i. 06610 879844 825293672 30.6268 993 1.00705 986049 979146657 3 I 5 II 9 939 1.06496 881721 827936019 30-643 1 994 1 .00604 988036 982107784 3*-5278 940 1.06383 883600 830584000 30-6594 995 1.00503 990025 985074875 3 i -5436 941 1.06270 885481 833237621 30-6757 996 1.00402 992016 988047936 31-5595 942 943 1.06157 1.06045 887364 889249 835896888 838561807 3O.692O 30.7083 3 1.00301 1.00200 994009 996004 991026973 994011992 3*-5753 3-59i * 944 1.05932 891136 841232384 30.7246 999 I.OOIOO 998001 997002999 31.6070 SMITHSONIAN TABLES. TABLE 10. LOGARITHMS. N. 1 2 3 4 5 6 7 8 9 10 100 oooo 0004 0009 0013 0017 0022 0026 0030 003 5 0039 0043 101 0043 0048 0052 0056 0060 0065 0069 0073 0077 0082 0086 102 0086 0090 0095 0099 0103 0107 Oil I 0116 OI2O 0124 0128 I0 3 0128 0133 0141 0145 0149 0154 0158 Ol62 0166 0170 104 0170 0175 0179 0183 0187 0191 oi95 0199 0204 0208 0212 105 1 06 O2I2 02 53 0216 0257 0220 O26l 0224 0265 0228 0269 0233 0273 0237 0278 0241 0282 0245 0286 0249 0290 02 53 0294 107 0294 0298 0302 0306 0310 03 J 4 0318 0322 0326 033 334 108 0334 0338 0342 0346 35 0354 0358 0362 0366 0370 0374 109 0374 0378 0382 0386 0390 0394 0398 0402 0406 0410 0414 110 0414 0418 0422 0426 0430 0434 0438 0441 0445 0449 453 in 453 0457 0461 0465 0469 0473 0477 0481 0484 0488 0492 112 0492 0496 0500 0504 0508 0512 5 T 5 0519 5 2 3 0527 "3 0531 0535 0538 0542 0546 55 554 0558 056l 0565 0569 "4 0569 0573 0577 0580 0584 0588 0592 0596 0599 0603 0607 115 0607 0611 0615 0618 0622 0626 0630 0633 0637 0641 0645 116 0645 0648 0652 0656 0660 0663 0667 0671 0674 0678 0682 "7 0682 0686 0689 0693 0697 0700 0704 0708 O7II 0715 0719 118 "9 0719 755 0722 0759 0726 0763 766 0734 0770 0737 0774 0741 0777 0745 0781 0748 0785 0788 755 0792 120 0792 0795 0799 0803 0806 0810 0813 0817 0821 0824 0828 121 122 0828 0864 0831 0867 0835 0871 0839 0874 0842 0878 0846 0881 0849 0885 0853 0856 0888 0892 0860 0896 0864 0899 I2 3 0899 0903 0906 0910 0913 0917 0920 0924 0927 0931 0934 124 0934 0938 0941 0945 0948 0952 0955 0959 0962 0966 0969 125 0969 0973 0976 0980 0983 0986 0990 0993 0997 IOOO 1004 126 1004 1007 IOII 1014 1017 IO2I 1024 1028 IO3I I0 35 1038 127 1038 1041 1045 1048 1052 IO55 1059 1062 1065 1069 1072 128 1072 1075 1079 1082 1086 1089 1092 1096 1099 1103 1106 129 1106 1109 III3 1116 1119 "23 1126 1129 "33 1136 "39 130 "39 "43 1146 "49 "53 1156 "59 1163 1166 1169 "73 131 "73 1176 "79 1183 1186 1189 "93 1196 "99 1 202 1206 132 1206 1209 1212 1216 1219 1222 1225 1229 1232 1235 1239 133 1239 1242 1245 1248 1252 1255 1258 1261 1265 1268 1271 1271 1274 I2 7 8 1281 1284 1287 1290 1294 1297 1300 '303 135 1303 I3 7 1310 I3 ! 3 1316 1319 1323 1326 1329 1332 1335 136 1335 1339 1342 '345 1348 i 1351 1358 1361 1364 137 1367 1370 1374 1377 1380 1383 1386 1389 1392 '396 *399 138 1399 I4O2 1405 1408 1411 1414 1418 1421 1424 1427 143 J 39 1430 1433 1436 1440 1443 1446 1449 M52 1455 1461 140 1461 1464 1467 I 4 7I 1474 1477 1480 1483 1486 1489 1492 141 1492 M95 1498 I5OI 1508 1511 15*4 15^7 1520 1523 142 1523 1526 1529 1532 1535 1538 1541 1544 1547 1550 1553 X 43 J 553 I 5-56 1559 1562 j 565 1569 1572 'I 75 1578 1581 1584 144 15&4 I57 1590 1593 1599 1602 1605 1608 1611 1614 145 146 147 1614 1644 1673 1617 1647 1676 l620 1649 1679 1623 1(382 1626 !6% 5 i6c;8 1632 1661 1691 1$ 1694 1638 1667 1697 1641 1670 1700 1644 1673 1703 148 1703 1706 1708 1711 1714 1717 1720 1723 1726 1729 1732 149 1732 1735 1738 1741 1744 1746 1749 1752 '755 / 1761 SMITHSONIAN TABLES. TABLE1O (continued) LOGARITHMS. N. 1 2 3 4 5 6 7 8 9 10 150 1761 1764 1767 1770 1772 1775 1778 1781 1784 1787 1790 '5 1 1790 '793 1796 1798 1801 1804 1807 1810 1813 1816 1818 1 S 2 '53 1818 1847 1821 1850 1824 1853 1827 1855 1830 1858 1833 1861 1836 1864 1838 1867 1841 1870 1844 1872 1847 1875 154 1878 1881 1884 1886 1889 1892 1895 1898 1901 1903 155 1903 1906 1909 1912 1915 1917 1920 1923 1926 1928 '93* 156 I93 1 1934 J937 1940 1942 1945 1948 I95 1 1953 J 95 6 1959 1959 1962 1967 1970 1 973 1976 1978 1981 1984 1987 158 1987 1989 1992 1995 1998 2000 2003 2006 2009 2OII 2014 '59 2014 2017 2019 2O22 2025 2028 2030 2033 2036 2038 2041 160 161 2041 2068 2044 2071 2047 2074 2049 2076 2052 2079 2055 2082 2057 2084 2060 2087 2063 2090 2066 2O92 2068 2095 162 2095 2098 2IOI 2IO3 2106 2109 2III 2114 2117 2119 2122 163 2122 2125 2127 2130 2133 2135 2I 3 8 2140 2143 2146 2148 164 2148 2151 2154 2I 5 6 2159 2162 2164 2167 2170 2172 2175 165 2175 2177 2180 2183 2185 2188 2191 2193 2196 2198 2201 166 22OI 2204 22O6 220 9 2212 2214 2217 2219 2222 222 5 2227 167 2227 2230 2232 2235 2238 2240 2243 2245 2248 2251 2253 1 68 2253 2256 2258 226l 2263 2266 2269 2271 2274 2276 2279 169 2279 2281 2284 2287 2289 2292 2294 2297 2299 2302 2304 170 2304 2307 2310 2 3 I2 2315 2317 2320 2322 2323 2327 2330 171 2 33 2 333 2 335 2338 2340 2345 2348 2353 2355 172 2355 2358 2360 2363 2 3 6 5 2368 2370 2373 2375 2378 2380 173 238Q 2383 2385 2 3 88 2390 2393 2395 2398 2400 2403 2405 174 2405 2408 2410 2413 2415 2418 2420 2423 2425 2428 2430 175 176 2430 2455 2433 2458 2435 2460 2438 2463 2440 2465 2443 2467 2445 2470 2448 2472 2450 2475 2453 2477 2455 2480 177 2480 2482 2485 2487 2490 2492 2494 2497 2499 2502 2504 178 2504 2507 2509 2 5 I2 25M 2516 2519 2521 2524 2526 2529 179 2529 2 53 r 2533 2536 2538 2541 2543 2545 2548 2550 2553 180 2553 2555 2558 256O 2562 2565 2567 2570 2572 2574 2577 181 2577 2579 2582 2584 2586 2589 2591 2594 2596 2598 26OI 182 2601 2603 2605 2608 26lO 2613 2615 2617 262O 2622 2625 183 184 2625 2648 2627 2651 2629 2653 2632 2655 2634 2658 2636 2660 266? 2641 2665 2643 2646 2669 2648 2672 185 2672 2674 2676 2679 268l 2683 2686 2688 2690 2693 2695 186 2695 2697 2700 2702 2704 2707 2709 2711 2714 2716 2718 187 2718 2721 2723 2725 2728 2730 2732 2735 2737 2739 2742 1 88 189 2742 2765 2744 2767 2746 2769 2749 2772 2751 2774 2753 2776 2755 2778 2758 2781 2760 2783 2762 2785 fsl 190 2788 2790 2792 2794 2797 2799 2801 2804 2806 2808 28lO 191 28lO 2813 28l5 2817 2819 2822 2824 2826 2828 2831 2833 192 2833 2856 2835 2858 2838 2860 2840 2862 2842 2865 2844 2867 2847 2869 2849 2871 2851 2874 2853 2876 2856 2878 194 ^2878 2880 2882 2885 2887 2889 2891 2894 2896 2898 2900 195 29OO 2903 2905 2907 2009 2911 2914 2916 2918 2920 2923 196 2923 2925 2927 2929 2931 2934 2936 2938 2940 2942 2945 2945 2947 2949 29S 1 2953 2956 2 9 <;8 2960 2962 2964 2967 198 2967 2969 2971 2973 2975 2978 2980 2982 2984 2986 2989 199 2989 2991 2 993 2995 2997 2999 3OO2 3004 3006 3008 3010 SMITHSONIAN TABLES. 26 TABLE 11. LOGARITHMS. N 0123 456 789 P.I > L^w TV */ U / O *7 1 2 3 4 5 10 0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 4 8 12 17 21 ii 0414 0453 49 2 O 53 0569 0607 0645 0682 0719 0755 4 8 II 15 *9 12 0792 0828 0864 0899 0934 0969 1004 '038 1072 1 1 06 3 7 10 14 J 7 13 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 3 6 IO *3 16 14 1461 1492 1523 1553 1584 1614 1644 1673 '703 173* 3 6 9 12 15 15 1761 1790 1818 1847 *875 1903 1931 1959 1987 2014 3 6 8 II M 16 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 3 5 8 II 1 3 17 18 2 34 2330 2355 2380 2405 2430 2455 2480 2504 2529 2 553 2377 2601 2625 2648 2672 2695 2 7i8 2742 2765 2 2 5 5 7 7 10 9 12 12 1 9 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 2 4 7 9 II 20 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 2 4 6 8 II 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 2 4 6 8 IO 22 23 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 2 2 4 4 6 5 8 7 10 9 24 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 2 4 5 7 9 25 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 2 3 5 7 9 26 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 2 3 5 7 8 2 43 i 4 433 4346 43 62 4378 4393 4409 44 2 5 444 445 6 2 3 5 6 8 28 4472 4487 45 2 45 J 8 4533 4548 4564 4579 4594 4609 2 3 5 6 8 29 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 I 3 4 6 7 30 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 3 4 6 7 3 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 3 4 6 7 3 2 55 J 5 6 5 579 59 2 5 I0 5 5"9 S 1 3 2 5*45 5 J 59 5 J 72 3 4 5 7 33 34 5 l8 5 5!98 5211 5 22 4 5237 525 5263 5276 5289 532- 5315 5328 5340 5353 5366 5378 539i 5403 54i6 5428 3 3 4 4 5 5 6 6 35 544i 5453 5465 5478 549 5502 5514 5527 5539 5551 2 4 5 6 36 5563 5575 5587 5599 56" 5623 5^35 564? 5658 5670 2 4 5 6 37 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 2 3 5 6 38 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 2 3 5 6 -39 5911 5522. 5933 5944 5955 5966 5977 5988 5999 6010 2 3 4 6 40 6021 6031 6042 6053 6064 6075 6o8 5 6096 6107 6117 2 ' 3 4 5 4i 6128 6138 6149 6160 6170 6180 6r9i 6201 6212 6222 2 3 4 5 42 43 44 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 2 2 2 3 3 3 4 4 4 5 5 5 45 46 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 2 2 3 3 4 4 5 5 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 2 3 4 5 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 2 3 4 4 49 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 2 3 4 4 50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 2 3 3 4 5 1 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 2 3 3 4 5 2 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 2 2 3 4 53 7243 7251 7259 7267 7275 7284 7292 73 73 8 73 l6 2 2 3 4 54 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 2 2 3 4 SMITHSONIAN TABLES. TABLE 11 (continued}. LOGARITHMS. 0-ioq 456 7 R 9 ] =>. P J. A O YWW / O *7 1 2 3 4 5 55 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 2 2 3 4 56 7482 7490 7497 755 75'3 75 2 75 2 8 7536 7543 755 1 2 2 3 4 57 7559 7566 7574 75 2 75 8 9 7597 7604 7612 7619 7627 2 2 3 4 58 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 I 2 3 4 59 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 I 2 3 4 60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 2 3 4 61 7853 7860 7868 7875 7882 7889 7896 7903 79io 7917 2 3 4 62 7924 793 i 793 s 7945 7952 7959 7966 7973 798o 79 8 7 2 3 3 63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 2 3 3 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 2 3 3 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 2 3 3 66 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 2 3 3 67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 2 3 3 68 69 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 2 2 3 3 3 3 70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 2 2 3 7i 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 2 2 3 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 2 2 3 73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 2 2 3 74 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 2 2 3 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 2 2 3 76 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 2 2 3 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 2 2 3 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 2 2 3 79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 2 2 3 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 2 2 3 81 9085 .9090 9096 9101 9106 9112 9117 9122 9128 9133 2 2 3 82 9138 '9143 9149 9154 9159 9165 9170 9175 9180 9186 2 2 3 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 2" 2 3 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 2 2 3 85 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 2 2 3 86 9345 935 9355 93 6 o 93 6 5 9370 9375 93 8 o 93 8 5 939 2 2 3 87 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 2 2 88 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 o 2 2 89 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 o 2 2 .90 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 2 2 '91 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 o 2 2 92 .9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 o 2 2 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 o 2 2 94 973 1 9736 974i 9745 975 9754 9759 9763 9768 9773 2 2 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 o 2 2 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 o 2 2 97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 2 2 98 9912 9917 9921 9926 9930 9934 9939 9943 9948 995 2 2 2 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 o 2 2 SMITHSONIAN TABLES. 28 TABLE 12. ANTILOGARITHMS. 01 2 3 456 789 ] 3 . p ^ A O Y/9 fO7 1 2 3 4 5 .00 IOOO IOO2 IOO5 IOO7 IOO9 IOI2 IOI4 IOl6 IOI9 IO2I o i .01 1023 1026 1028 1030 1033 1035 1038 1040 1042 1045 o o i .02 1047 I0 5 I0 5 2 I0 54 I0 57 I0 59 Io62 Io() 4 Io6 7 Io6 9 o i 3 1072 1074 1076 1079 1081 1084 1086 1089 1091 1094 i .04 1096 1099 1102 1104 1107 1109 iii2 1114 1117 1119 o I i .05 1122 1125 1127 1130 1132 1135 1138 1140 1143 I1[ 46 .06 1148 1151 1153 1156 1159 1161 1164 1167 tl&) 1172 o .07 1175 1178 1180 1183 1186 1189 1191 1194 1197 1199 o .08 1202 1205 1208 I2II 1213 I2l6 1219 1222 1225 I22 7 .09 1230 1233 1236 1239 1242 1245 1247 1250 1253 1256 o .10 1259 1262 1265 1268 1271 1274 1276 1279 1282 1285 o i .11 1288 1291 1294 1297 1300 1303 1306 1309 1312 1315 o 2 .12 1318 1321 1324 1327 1330 1334 1337 1340 1343 1346 o 2 13 1349 '35 2 *355 i35 8 !3 61 T 365 1368 1371 1374 '377 o 2 .14 1380 1384 1387 1390 1393 1396 1400 1403 1406 1409 o 2 .15 .16 1413 1416 1419 1422 1426 1429 1432 1435 1439 1442 1445 J 449 J 45 2 J 455 J 459 1462 1466 1469 1472 1476 o o 2 2 17 1479 J 483 T 486 1489 1493 X 496 1500 1503 1507 1510 o 2 .18 i5'4 I5 J 7 i5 21 J 5 2 4 i5 28 I53 1 J 535 J 538 i54 2 1545 2 .19 J 549 J55 2 !55 6 Z 5 6 J 5 6 3 Z 5 6 7 1570 1574 J 578 1581 o 2 .20 ^85 1589 I59 2 1596 1600 1603 1607 1611 1614 1618 j 2 .21 1622 1626 1629 1633 1637 1641 1644 1648 1652 1656 2 2 .22 1660 1663 1667 1671 1675 J ^79 J 683 1687 1690 1694 o 2 2 2 3 1698 1702 1706 1710 1714 1718 1722 1726 1730 1734 o 2 2 .24 1738 1742 1746 1750 1754 1758 1762 1766 1770 1774 o 2 2 .25 1778 1782 1786 1791 1795 T 799 l8 03 1807 1811 1816 o 2 2 .26 1820 1824 1828 1832 1837 1841 1845 l8 49 1854 1858 o . 2 2 .27 1862 1866 1871 1875 l8 79 1884 1888 1892 1897 1901 o 2 2 .28 1905 1910 1914 1919 1923 1928 1932 1936 1941 1945 2 2 .29 J 95 J 954 J959 T 9 6 3 1968.1972 1977 1982 1986 1991 o 2 2 .30 1995 2000 2004 2009 2014 2018 2023 2028 2032 2037 I 2 2 3 1 2042 2046 2051 2056 2061 2065 2070 2075 2080 2084 o I 2 2 3 2 2089 2094 2099 2104 2109 2113 2118 2123 2128 2133 o I 2 2 33 2138 2143 2148 2153 2158 2163 2168 2173 2178 2183 o I 2 2 34 2188 2193 2198 2203 2208 2213 2218 2223 2228 2234 I I 2 2 3 .35 2239 2244 2249 2254 2259 2265 2270 227? 2280 2286 I 2 2 3 36 2291 2296 2301 2307 2312 2317 2323 2328 2333 2339 I 2 2 3 37 2344 2350 2355 2360 2366 2371 2377 2382 2388 2393 2 2 3 38 2399 2404 2410 2415 2421 2427 2432 2438 2443 2449 2 2 3 39 2455 2460 2466 2472 2477 2483 2489 2495 2 5 2 5 6 2 2 3 .40 .41 2512 2518 2523 2529 2535 2541 2547 2553 2559 2564 2 57 2 576 2582 2588 2594 2600 2606 2612 2618 2624 2 2 2 2 3 3 .42 2630 2636 2642 2649 26 55 2661 266 7 26 73 26 79 268 5 2 2 1 43 2692 2698 2704 2710 2716 2723 2729 2735 2742 2748 2 3 3 44 2754 2761 2767 2773 2780 2786 2793 2799 2805 2812 2 3 3 .45 2818 . 2825 2831 2838 2844 2851 2858 2864 2871 2877 2 3 3 .46 2884 2891 2897 2904 2911 2917 2924 2931 2938 2944 2 3 3 47 2951 2958 2965 2972 2979 2985 2992 2999 3006 3013 2 3 3 .48 3020 3027 3034 3041 3048 3055 3062 3069 3076 3083 I 2 3 4 49 3090 3097 3105 3112 3119 3126 3133 3141 3M8 3*55 I 2 3 4 SMITHSONIAN TABLES. TABLE 12 (continued). ANTILOGARITHMS. 123 456 789 ] 3 . F 1 2 3 4 5 .50 3162 3170 3177 3184 3192 3199 3206 3214 3221 3228 i 2 3 4 5 1 3236 3243 3251 3258 3266 3273 3281 3289 3296 3304 2 2 3 4 S 2 33 11 33 T 9 33 2 7 3334 3342 3350 3357 3365 3373 3381 2 2 3 4 53 3388 3396 3404 3412 3420 3428 3436 3443 3451 3459 2 2 3 4 54 3467 3475 3483 349i 3499 358 35*6 3524 3532 3540 2 2 3 4 .55 3548 355 6 35 6 5 3573 358i 3589 3597 3606 3614 3622 2 2 3 4 .56 3 6 3! 3 6 39 3 6 48 3 6 56 3664 3673 3 6 8i 3 6 9o 3 6 98 3707 2 3 3 4 57 37i5 3724 3733 374i 3750 3758 3767 3776 3784 3793 2 3 3 4 58 3802 3811 3819 3828 3837 3846 3855 3864 3873 3882 2 3 4 4 59 3890 3899 3908 3917 3926 3936 3945 3954 3963 3972 2 3 4 5 .60 3981 3990 3999 4009 4018 4027 4036 4046 4055 4064 2 3 4 5 .61 4074 4083 4093 4102 4111 4121 4130 4140 4150 4159 2 3 4 5 .62 4169 4178 4188 4198 4207 4217 4227 4236 4246 4256 2 3 4 5 63 .64 4266 4276 4285 4295 4305 4315 4325 4335 4345 4355 43 6 5 4375 4385 4395 446 4416 4426 4436 4446 4457 2 2 3 3 4 4 5 5 .65 4467 4477 4487 4498 4508 4519 4529 4539 4550 4560 2 3 4 5 .66 4571 4581 4592 4603 4613 4624 4634 4645 4656 4667 2 3 4 5 .67 4677 4688 4699 4710 4721 4732 4742 4753 4764 4775 2 3 4 .68 4786 4797 4808 4819 4831 4842 4853 4864 4875 4887 2 3 4 6 .69 4898 4909 4920 4932 4943 4955 4966 4977 4989 5000 2 3 5 6 .70 5012 5023 5035 5047 5058 5070 5082 5093 5105 5117 2 4 5 6 7i 5129 5140 5152 5164 5176 5188 5200 5212 5224 5236 2 4 5 6 .72 5248 5260 5272 5284 5297 5309 5321 5333 5346 5358 2 4 5 6 73 5370 5383 5395 5408 5420 5433 5445 5458 5470 5483 3 4 5 6 74 5495 55o8 5521 5534 5546 5559 5572 5585 5598 5610 3 4 5 6 .75 .76 5623 5636 5649 5662 5675 5689 5702 5715 5728 5741 5754 5768 5781 5794 5808 5821 5834 5848 5861 5875 3 3 4 4 5 5 7 7 77 .78 5902 5916 5929 5943 5957 5970 5984 5998 6012 6026 6039 6053 6067 6081 6095 6TO9 6124 6138 6152 3 3 4 4 I 7 7 79 6166 6180 6194 6209 6223 6237 6252 6266 6281 6295 3 4 6 7 .80 6310 6324 6339 6353 6368 6383 6397 6412 6427 6442 i 3 4 6 7 .81 6457 6471 6486 6501 6516 6531 6546 6561 6577 6592 2 3 5 6 8 .82 83 6607 6622 6637 6653 6668 6683 6699 6714 6730 6745 6761 6776 6792 6808 6823 6839 6855 6871 6887 6902 2 2 3 3 5 5 6 6 8 8 .84 6918 6934 6950 6966 6982 6998 7015 7031 7047 7063 2 3 5 6 8 .85 7079 7096 7112 7129 7145 7161 7178 7194 7211 7228 2 3 5 7 8 .86 7244 7261 7278 7295 7311 7328 7345 7362 7379 7396 2 3 5 7 8 87 7413 743 7447 7464 7482 7499 75 l6 7534 755 1 75^8 2 3 5 7 9 .88 7586 7603 7621 7638 7656 7674 7691 7709 7727 7745 2 4 5 7 9 .89 7762 7780 7798 7816 7834 7852 7870 7889 7907 7925 2 4 5 7 9 .90 7943 7962 7980 7998 8017 8035 8054 8072 8091 8110 2 4 6 7 9 .91 8128 8147 8166 8185 8204 8222 8241 8260 8279 8299 2 4 6 8 9 .92 8318 8337 8356 8375 8395 8414 8433 8453 8472 8492 2 4 6 8 10 93 8511 8531 8551 8570 8590 8610 8630 8650 8670 8690 2 4 6 8 10 94 8710 8730 8750 8770 8790 8810 8831 8851 8872 8892 2 4 6 8 10 .95 8 9!3 8933 8954 8974 8995 9016 9036 9057 9078 9099 2 4 6 8 10 .96 9120 9141 9162 9183 9204 9226 9247 9268 9290 9311 2 4 6 8 ii ' 9 l 9333 9354 9376 9397 9419 9441 9462 9484 9506 9528 2 4 7 9 ii .98 955 9572 9594 9 6r6 9 6 3 8 9661 9683 9705 9727 9750 2 4 7 9 ii 99 9772 9795 98i7 9840 9863 9886 9908 9931 9954 9977 2 5 7 9 ii SMITHSONIAN TABLES. TABLE 13. ANTILOGARITHMS. 1 2 3 4 5 6 7 8 9 10 .900 7943 7945 7947 7949 7951 7952 7954 7956 7958 7960 7962 .901 7962 7963 7965 7967 7969 7971 7973 7974 7976 7978 798o .902 7980 7982 7984 7985 7987 7991 7993 7995 7997 7998 93 7998 8000 8002 8004 8006 8008 8009 Sou 8013 8015 8017 .904 8017 8019 8020 8022 8024 8026 8028 8030 8032 8033 8035 .905 8035 8037 8039 8041 8043 8045 8046 8048 8050 8052 8054 .906 8054 8056 8057 8059 8061 8063 8065 8067 8069 8070 8072 8072 8074 8076 8078 8080 8082 8084 8085 8087 8089 8091 .908 8091 8093 809 S 8097 8098 8100 8102 8104 8106 8108 8110 .909 8110 8ui 8113 8115 8117 8119 8121 8123 8125 8126 8128 .910 8128 8130 8132 8134 8136 8138 8140 8141 8143 8i45 8i47 .911 8147 8149 8151 8153 8155 8156 8158 8160 8162 8164 8166 .912 8166 8168 8170 8171 8173 8i75 8i77 8179 8181 8183 8185 9 1 3 8185 8187 8188 8190 8192 8194 8196 8198 8200 8202 8204 .914 8204 8205 8207 8209 8211 8213 8215 8217 8219 8221 8222 .915 8222 8224 8226 8228 8230 8232 8234 8236 8238 8239 8241 .916 8241 8243 8245 8247 8249 8251 8253 8255 8257 8258 8260 .917 8260 8262 $264 8266 8268 8270 8272 8274 8276 8278 8279 .918 8279 8281 8283 8285 8287 8289 8291 8293 8295 8297 8299 .919 8299 8300 8302 8304 8306 8308 8310 8312 83H 8316 8318 .920 .921 8318 8337 8320 8339 8321 8341 8323 8343 8325 8344 8327 8346 8329 8348 8331 8350 8333 8352 8335 8354 8337 8356 .922 8356 8358 8360 8362 8364 8366 8368 8370 8371 8373 8375 923 8375 8377 8379 8381 8383 8385 8387 8389 8391 8393 83951 924 8395 8397 8398 8400 8402 8404 8406 8408 8410 8412 8414 .925 8414 8416 8418 8420 8422 8424 8426 8428 8429 843 i 8433 .926 8433 8435 8437 ! 8439 8441 8443 8445 8447 8449 8451 8453 .927 8453 8455 8457 8459 8461 8463 8464 8466 8468 8470 8472 .928 8472 8474 8 47 6 8478 8480 8482 8484 8486 8488 8490 8492 929 8492 8494 8496 8498 8500 8502 8504 8506 8507 8509 8511 .930 8511 8513 8515 8517 8519 8521 8523 8525 8527 8529 8531 93 * 8531 8533 8535 8537 8539 8541 8543 8545 8547 8549 8551 932 8551 8553 8555 8557 8559 8561 8562 8564 8566 8568 8570 933 8570 8572 8574 8576 8578 8580 8582 8584 8586 8588 8590 934 8590 859? 8594 8596 8598 8600 8602 8604 8606 8608 8610 .935 8610 8612 8614 8616 8618 8620 8622 8624 8626 8628 8630 93 6 8630 8632 8634 8636 8638 8640 8642 8644 8646 8648 8650 937 8650 8652 8654 8656 8658 8660 ! 8662 8664 8666 8668 8670 938 8670 8672 8674 8676 8678 8680 8682 8684 8686 8688 8690 939 8690 8692 8694 8696 8698 8700 8702 8704 8706 8708 8710 .940 8710 8712 8714 8716 8718 8720 8722 8724 8726 8728 8730 .941 8730 8732 8734 8736 8738 8740 8742 8744 8746 8748 8750 942 8750 8752 8754 8756 8758 8760 8762 8764 8766 8768 8770 943 8770 8772 8774 8776 8778 8780 8782 8784 8786 8788 8790 944 8790 8792 8794 8796 8798 8800 8802 8804 8806 8808 8810 945 8810 8813 8815 8817 8819 8821 8823 8825 8827 8829 8831 .946 8831 8831 8835 8837 8839 8841 8843 8845 8847 8849 8851 947 8851 8853 8855 8857 8859 8861 8863 8865 8Sf> 7 8870 8872 .948 8872 8874 8876 8878 8880 8882 8884 8886 8888 8890 8892 949 8892 8894 8896 8898 8900 8902 8904 8906 8908 8910 8913 SMITHSONIAN TABLES. TABLE 13 (continued). ANTILOGARITHMS. 1 2 3 4 5 6 7 8 9 1C .950 95 i 8913 8933 8915 8935 8917 8937 8919 8939 8921 8941 8923 8943 8925 8945 8927 8947 8929 8950 8931 8952 8933 8954 952 8954 8956 8958 8960 8962 8964 8966 8968 8970 8972 8974 953 8974 8976 8978 8980 8983 8985 8987 8989 8991 8993 8995 954 8995 8997 8999 9001 9003 9005 9007 9009 9012 9014 9016 .955 9016 9018 9020 9022 9024 9026 9028 9030 9032 9034 9036 .956 9036 9039 9041 9043 9045 9047 9049 9Q5 1 9053 9055 9057 957 9 C 57 959 9061 9064 9066 9068 9070 9072 9074 9076 9078 958 9078 9080 9082 9084 9087 9089 9091 9093 9095 9097 9099 959 9099 9101 9103 9 I0 5 9108 9110 9112 9114 9116 9118 9120 .960 9120 9122 9124 9126 9129 913 1 9133 9135 9M7 9139 9141 .961 9141 9'43 9'45 9*47 9 r 5 9152 9154 9156 9158 9160 9162 .962 9162 9164 9166 9169 9171 9173 9 J 75 9177 9179 9181 9183 963 9183 9185 9188 91.90 9192 9194 9196 9198 9200 9202 9204 .964 9204 9207 9209 9211 9213 9215 9217 9219 9221 9224 9226 .965 9226 9228 9230 9232 9234 9236 9238 9241 9243 9245 9247 .966 9247 9249 9251 9253 9256 9258 9260 9262 9264 9266 9268 .967 9268 9270 9273 9275 9277 9279 9281 9283 9285 9288 9290 .968 9290 9292 9294 9296 9298 9300 933 935 937 939 93 11 .969 93" 9313 9315 9320 9322 9324 9326 9328 933 9333 ,970 9333 9335 9337 9339 934i 9343 9345 . 9348 9350 9352 9354 .971 9354 935 6 9358 9361 93 6 3 9365 93 6 7 9369 937i 9373 9376 972 9376 9378 938o 9382 9384 9386 9389 939 i 9393 9395 9397 973 9397 9399 9402 9404 9406 9408 9410 9412 9417 9419 974 9419 942i 9423 9425 9428 943 9432 9434 9436 9438 9441 .975 9441 9443 9445 9447 9449 945 i 9454 945 6 9458 9460 9462 .976 9462 9465 9467 9469 9473 9475 9478 9480 9482 9484 977 . 9484 9486 9489 949 1 9493 9495 9497 9499 9502 9504 9506 978 9506 9508 95 10 95 T 3 95 T 5 95!7 9S 1 9 9524 9526 9528 979 9528 953 9532 9535 9537 9539 954i 9543 9546 9548 955 980 955 9552 9554 9557 9559 95 6i 9563 9565 9568 9570 9572 .981 9572 9574 9576 9579 9581 9583 9585 9587 959 9592 9594 .982 959 6 9598 9601 9603 9605 9609 9612 9614 9616 983 9616 9618 9621 9623 9625 9627 9629 9632 9 6 34 9636 9638 .984 9638 9641 9643 9 6 45 9647 9649 9652 9654 9656 9658 9661 .985 9661 9663 9665 9667 9669 9672 9674 9676 9678 9681 9683 .986 9683 9685 9687 9689 9692 9694 9696 9698 9701 9703 9705 .987 9705 9707 9710 9712 97 H 9716 9719 9721 9723 9725 9727 .988 9727 973 9732 9734 97 3 6 9739 974i 9743 9748 9750 .989 975 9752 9754 9757 9759 9761 9763 9766 9768 9770 9772 .990 9772 9775 9777 9779 9781 9784 9786 9788 9790 9793 9795 99 * 9795 9797 9799 9802 9804 9806 9808 9811 9813 9815 9817 .992 9817 9820 9822 9824 9827 9829 9831 9833 9836 9838 9840 i -993 9840 9842 9845 9847 9849 9851 9854 9856 9861 9863 994 9863 9865 9867 9870 9872 9874 9876 9879 98^1 9883 9886 .995 9886 9888 9890 9892 9895 9897 9899 9901 9904 9906 9908 .996 9908 9911 9913 9917 9920 9922 9924 9927 9929 993 l 997 993 r 9933 993 6 993 9940 9945 9947 9949 9952 9954 .998 9954 9956 9959 9961 9963 9966 9968 9970 9972 9975 9977 i -999 9977 9979 9982 9984 9986 9988 9991 9993 9995 0000 SMITHSONIAN TABLES. TABLE 14. CIRCULAR (TRIGONOMETRIC) FUNCTIONS. (Taken from B. O. Peirce's " Short Table of Integrals," Ginn & Co.) 3^ U% SINES. COSINES. TANGENTS. COTANGENTS. 2* O Nat. Log. Nat. Log. Nat. Log. Nat. Log. o.oooo 000' .OOOO 00 I. OOOO O.OOOO .OOOO 00 oo oo ! 9OOO' 1.5708 0.0029 10 .0029 7.4637 i. oooo .oooo .0029 7.4637 343-77 2.5363! ' 50 0.0058 20 .0058 .7648 i. oooo .oooo .0058 .7648 171.89 .2352,; 40 1.5650 0.0087 3 .0087 .9408 i. oooo .oooo .0087 .9409 114-59 -0591 30 1.5621 0.0116 40 .0116 8.0658 .9999 .oooo i .0116 8.0658 85.940 1.9342 20 '.5592 0.0145 50 .0145 .1627 .9999 .oooo .0145 .1627 60.75 -8373 10 '5563 0.0175 I00' .0175 8.2419 .9998 9.9999 .0175 8.2419 57.290 1.7581 8 9 oo' '5533 0.0204 IO .0204 .3088 .9998 .9999 .0204 .3089 49.104 .6911 50 1-5504 0.0233 0.0262 20 30 .0233 .3668 .0262 .4179 9997 -9999 9997 -9999 0233 -3669 .0262 .4181 42.964 .6331 38.188 .5819 40 30 J -5475 1.5446 0.0291 40 .0291 .4637 .9996 .9998 .0291 .4638 34-368 .5362 2O I-54I7 0.0320 50 .0320 .5050 9995 -9998 0320 .5053 31.242 -4947J I0 1.5388 0.0349 200' 0349 8.5428 9994 9-9997 0349 8.5431. 28.636 1.4569 S8oo' '5359 0.0378 IO 0378 .5776 9993 -9997 0378 .5779 26.432 .4221 50 0.0407 20 .0407 .6097 9992 -9996 .0407 .6101 24.542 .3899 40 1.5301 0.0436 30 .0436 .6397 .9990 .9996 .0437 .6401 22-904 -3599 3 1.5272 0.0465 40 .0465 .6677 9989 -9995 .0466 .6682 21.470 .3318 20 1-5243 0.0495 50 .0494 .6940 .9988 .9995 .0495 -6945 20.206 .3055 10 0.0524 3 oo' .0523 8.7188 .9986 9.9994 0524 8.7194 19.081 1.2806 87oo r 1.5184 0-0553 IO 0552 .7423 .9985 .9993 0553 -7429 18.075 -2571 50 i-5i55 0.0582 20 .0581 .7645 .9983 .9993 .0582 .7652 17.169 .2348 40 1.5126 0.06 1 1 30 .0610 .7857 .9981 .9992 .0612 .7865 16.350 .2135 3 I -597| 0.0640 40 .0640 .80 ?9 .9980 .9991 .0641 .8067 , 15.605 .1933 20 1.5068 0.0669 50 .0669 .8251 9978 -9990 .0670 .8261 14.924 .1739 IO I -539 0.0698 4oo' .0698 8.8436 .9976 9.9989 .0699 8.8446 14.301 1.1554 86oo' 1.5010 0.0727 IO .0727 .8613 9974 -9989 .0729 .8624 I3-727 -1376 5 1.4981 0.0756 20 .0756 .8783 .9971 .9988 0758 .8795 13.197 .1205 40 I-495 2 0.0785 3 .0785 .8946 .9969 .9987 .0787 .8960 12.706 .1040 3 1.4923 0.0814 40 .0814 .9104 .9967 .9986 .0816 .9118 12.251 .0882 20 1.4893 0.0844 50 .0843 .9256 .9964 .9985 .0846 .9272 11.826 .0728 10 1.4864 0.0873 5oo / 0872 8.9403 .9962 9.9983 .0875 8.9420 11.430 1.0580 85oo' 1-4835 0.0902 IO 0901 .9545 9959 -9982 0904 -9563 11.059 .0437 50 i .4806 0.0931 20 0929 .9682 9957 -9981 .0934 .9701 10.712 .0299 40 1.4777 0.0960 30 1 0958 .9816 9954 .9980 .0963 .9836 10.385 .0164 30 1.4748 0.0989 40 0987 .9945 995 * -9979 .0992 .9966 10.078 .0034 20 1.4719 0.1018 50 .1016 9.0070 9948 -9977 .1022 9.0093 9.7882 0.9907 10 1.4690 0.1047 6oo .1045 9.0192 9945 9-9976 .1051 9.0216 9.5144 0.9784 84oo' 1.4661 0.1076 10 .1074 .0311 9942 -9975 ,I080 .0336 9.2553 .9664 50 1.4632 0.1105 20 .1103 .0426 9939 -9973 .1110 .0453 9.0098 -9547 40 1.4603 0.1134 0.1164 30 40 i 1132 -0539 .1161 .0648 9936 -9972 .9932 .9971 .1139 .0567 .1169 .0678 8.7769 .9433 8-5555 -9322 30 20 1-4574 1-45441 0.1193 50 .1190 .0755 .9929 .9969 .1198 .0786 8.3450 .9214 IO I45I5 0.1222 7oo' .1219 9.0859 .9925 9.9968 .1228 9.0891 8.1443 0.9109 8 3 oo' 1.4486 0.1251 0.1280 IO 20 .1248 .0961 .1276 .1060 .9922 .9966 .9918 .9964 I2 57 -0995 .1287 .1096 7-953 .9OO5 7.7704 .8904 5 40 1-4457 1.4428 0.1309 30 1305 -"57 .9914 .9963 .1317 .1194 7.5938 .8806 30 1.4399 0-I338 40 .1334 .1252 .9911 .9961 .1346 .1291 7.4287 .8709 20 1-4370 0-1367 50 T 3 6 3 -'345 9907 -9959 1376 -1385 7.2687 .8615 10 I-434I 0.1396 8oo' .1392 9.1436 9903 9-9958 .1405 9.1478 7.1154 0.8522 8200' 1.4312 0.1425 10 .1421 .1525 .9899 .9956 M35 ^569 6.9682 .8431 50 1.4283 0.1454 20 .1449 .1012 .9894 .9954 .1465 .1658 6.8269 .8342 4 1.4254 0.1484 30 .1478 .1697 .9890 .9952 1495 -'745 6.6912 .8255 30 1.4224 O.I5I3 40 .1507 .1781 .9886 .9950 .1524 .1831 6.5606 .8169 20 I-4I95 0.1542 50 .1536 .1863 .9881 .9948 1554 'i9 l $ 6.4348 .8085 IO 1.4166 O.I57I 9oo' .1564 9.1943 .9877 9.9946 .1584 9.1997 6.3138 0.8003 8ioo' I.4I37 Nat. Log. Nat. Log. Nat. Log. Nat. Log. 0) AM j^ COSINES. SINES. COTAN- GENTS. TANGENTS. w y Off! O SMITHSONIAN TABLES. TABLE 14 (.continued}. CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 33 1 P| SINES. COSINES. TANGENTS. COTANGENTS. Pi *** O Nat. Log. Nat. Log. Nat. Log. Nat. Log. 0.1571 9oo / .1564 9.1943 .9877 9.9946 .1584 9.1997 6.3138 0.8003 8l0& 1.4137 0.1600 10 .1593 .2O22 9872 -9944 .1614 .2078 6.1970 .7922 5 1.4108 0.1629 20 .1622 .2IOO .9868 .9942 .1644 .2158 6.0844 .7842 40 1.4079 0.1658 3 .1650 .2176 .9863 .9940 .1673 -2236 5.9758 .7764 30 1.4050 0.1687 40 .1679 .2251 .9858 .9938 .1703 .2313 5.8708 .7687 20 1.4021 0.1716 50 .1708 .2324 .9853 .9936 '733 -2389 5.7694 .7611 IO 1.3992 0.1745 I000' 1736 9-2397 .9848 9.9934 .1763 9.2463 5-67I3 0.7537 8ooo' 1-3963 0.1774 IO .1765 .2468 9843 -993 ' '793 -2536 5.5764 .7464 50 !-3934 0.1804 20 .1794 .2538 .9838 .9929 .1823 .2609 5.4845 .7391 40 1.3904 0-1833 30 .1822 .2606 9833 .9927 .1853 -2680 5-3955 .7320 30 I-3875 0.1862 40 .1851 .2674 .9827 .9924 .1883 .2750 5-3093 -7250 20 1.3846 0.1891 50 .1880 .2740 .9822 .9922 .1914 .2819 5.2257 .7181 10 1.3817 0.1920 iioo' .1908 9.2806 .9816 9.9919 .1944 9.2887 5.1446 0.7113 79 oo' 1.3788 0.1949 IO .1937 .2870 .9811 .9917 1974 -2953 5.0658 .7047 50 1-3759 0.1978 20 1965 -2934 .9805 .9914 .2004 .3020 4.9894 .6980 40 1-373 0.2007 3 .1994 .2997 9799 -99 i 2 2035 .3085 4-9 r 5 2 -6915 3 1.3701 0.2036 40 .2O22 .3058 9793 --9909 .2065 .3149 4.8430 .6851 20 1.3672 0.2065 50 2051 .3119 .9787 .9907 .2095 .3212 4.7729 -6788 10 1.3643 0.2094 I200' 2079 9-3 J 79 .9781 9.9904 .2126 9.3275 4.7046 0.6725 78oo' 1.3614 0.2123 IO .2108 .3238 9775 -9901 2156 -3336 4.6382 .6664 50 I-3584 0.2153 20 .2136 .3296 .9769 .9899 .2186 .3397 4.5736 .6603 40 1-3555 0.2182 30 .2164 .3353 .9763 .9896 .2217 .3458 4.5107 .6542 3 1-3526 O.22II 40 .2193 .3410 9757 -9893 2247 .35*7 4.4494 .6483 20 1-3497 0.2240 50 .2221 .3466 .9750 .9890 .2278 .3576 4.3897 .6424 10 1.3468 0.2269 13000' .2250 9.3521 9744 9-9887 .2309 9.3634 4-33 i 5 0-6366 77 00' J-3439 0.2298 IO .2278 -3575 9737 -9884 .2339 .3691 4.2747 .6309 50 1.3410 0.2327 20 .2306 .3629 .9730 .9881 .2370 .3748 4.2193 .6252 40 1.3381 0.2356 0-2385 30 40 .2334 .3682 2363 -3734 .9724 .9878 97i7 -9875 .2401 .3804 2432 -3859 4.1653 .6196 4.1126 .6141 30 20 1-3352 0.2414 5 .23 9 I .3786 .9710 .9872 .2462 .3914 4.061 1 .6086 IO 1-3294 0.2443 i4oo' 2419 9-3837 .9703 9.9869 .2493 9-3968 4.0108 0.6032 76oo' 1-3265 0.2473 10 .2447 .3887 .9696 .9866 .2524 .4021 3.9617 .5979 50 L3235 O.25O2 20 2476 -3937 -9689 -9863 .2555 .4074 3.9136 .5926 40 1.3206 0.2531 30 .2504 .3986 .9681 .9859 .2586 .4127 3.8667 .5873 30 I.3I77 0.2560 40 2532 4035 .9674 .9856 .2617 .4178 3.8208 .5822 20 1.3148 0.2589 50 .2560 .4083 .9667 .9853 .2648 .4230 3-776o .5770 10 1.3119 0.26l8 1 5oo / .2588 9.4130 .9659 9.9849 .2679 9.4281 37321 0.5719 75oo / 1.3090 0.2647 IO .2616 4177 .9652 .9846 .2711 .4331 3.6891 .5669 50 1.3061 0.2676 20 .2644 .4223 .9644 .9843 .2742 .4381 3.6470 .5619 40 1-3032 0.2705 30 .2672 .4269 .9636 .9839 .2773 .4430 3-6059 -5570 3 1-3003 0.2734 40 .2700 .4314 .9628 .9836 .2805 .4479 3.5656 .5521 20 1.2974 0.2763 5 2728 -4359 .9621 .9832 .2836 .4527 3.5261 .5473 10 1-2945 0.2793 i6oo' .2756 9.4403 .9613 9.9828 2867 9-4575 3.4874 0.5425 74 oo' 1.2915 O.2822 IO .2784 .4447 .9605 .9825 .2899 .4622 3-4495 .5378 50 1.2886 0.2851 0.2880 20 3 .2812 .4491 .2840 .4533 .9596 .9821 .9588 -.9817 .2931 .4669 .2962 .4716 3.4124 .5331 3-3759 -5284 40 30 1.2857 1.2828 0.2909 40 .2868 .4576 .9580 .9814 .2994 .4762 3.3402 .5238 20 1.2799 0.2938 50 .2896 .4618 .9572 .9810 .3026 .4808 3.3052 .5192 IO 1.2770 0.2967 0.2996 I 7 00' IO .2924 9.4659 .2952 .4700 9563 9-98o6 9555 -9802 357 9-4853 .3089 .4898 3.2709 0.5147 3.2371 .5102 73oo> 50 1.2741 1.2712 0.3025 20 .2979 .4741 .9546 .9798 .3121 .4943 3.2041 .5057 40 1.2683 0.3054 30 .3007 .4781 9537 -9794 3*53 -4987 3.1716 .5013 30 1.2654 0.3083 40 .3035 .4821 .9528 .9790 3185 .5031 3.1397 .4969 20 1.2625 0.3H3 5 .3062 .4861 .9520 .9786 3217 -5075 3.1084 .4925 10 1-2595 0.3142 i8oo' .3090 94900 .9511 9.9782 .3249 9.5118 3.0777 0.4882 7200 / 1.2566 Nat. Log. Nat. Log. Nat. Log. Nat. Log. w3 , Wy QJ5 COSINES SINES. COTAN- GENTS. TANGENTS o 3< SMITHSONIAN TABLES. 34 TABLE 14 (continued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS, ~g c/5 w w SINES. COSINES. TANGENTS. COTANGENTS x< O Nat. Log. Nat. Log. Nat. Log. Nat. Log. 0.3142 i8oo' .3090 9.4900 .9511 9.9782 .3249 9.5118 3.0777 0.4882 7200' 0.3171 10 .3118 .4939 .9502 .9778 .3281 .5161 3.0473 .4839 50 I - 2 537 0.3200 20 3'45 -4977 .9492 .9774 .3314 .5203 3.0178 .4797 40 1.2508 0.3229 30 3'73 -5015 9483 -97/0 3346 .5245 2.9887 .4755 3 1.2479 0.3258 40 .3201 .5052 9474 -9765 O378 .5287 2.9600 .4713 20 1.2450 0.3287 50 .3228 .5090 .9465 .9761 .3411 .5329 2.9319 .4671 10 1.2421 0.3316 i9oo' .3256 9.5126 9455 9-9757 -3443 9-537O 2.9042 0.4630 7ioo' 1.2392 0-3345 10 3283 -5163 9446 .9752 .3476 .5411 2.8770 .4589 5 1.2363 0-3374 20 33' i -5199 .9436 .9748 .3508 .5451 2.8502 .4549 40 0.3403 30 3338 -5235 -9426 .9743 .3541 .5491 2.8239 .4509 30 I - 2 35 0.3432 40 .3365 .5270 .9417 .9739 .3574 .5531 2.7980 .4469 20 1.2275 0.3462 50 3393 -5306 9407 -9734 -3607 .5571 2.7725 -4429 IO 1.2246 0.3491 2000' .3420 9.5341 9397 9-973 -3 6 4O 9-5 6 " 2-7475 0-4389 7ooo' 1.2217 0.3520 10 3448 -5375 9387 -9725 -3673 -5650 2.7228 .4350 5 1.2188 0-3549 20 3475 -5409 -9377 -972 1 .3706 .5689 2.6985 .4311 40 1.2159 0.3578 30 .3502 .5443 ! .9367 .9716 .3739 .5727 2.6746 .4273 3 1.2130 0.3607 40 3529 -5477 -9356 -9711 -3772 '.5766 2.6511 .4234 20 I.2IOI 0.3636 50 3557 -55' .9346 .9706 | .3805 .5804 2.6279 .4196 10 I.2O72 0.3665 2I00' 3584 9-5543 9336 9-9702 .3839 9.5842 2.6051 0.4158 69oo' 1.2043 0.3694 10 .3611 .5576 9325 -9697 -3872 .5879 2.5826 .4121 5 I.2OI4 0.3723 20 .3638 .5609 .9315 .9692 .3906 .5917 2.5605 .4083 40 1.1985 0.3752 3 .3665 .5641 ; .9304 .9687 .3939 .5954 2.5386 .4046 3 1.1956 0.3782 0.3811 40 50 .3692 .5673 .9293 .9682 i .3973 .5991 .3719 .5704 .9283 .9677 .4006 .6028 2.5172 .4009 2.4960 .3972 20 IO I.I926 I.I897 0.3840 2200' .3746 9-5736 -9272 9-9672 .4040 9.6064 2.4751 0.3936 68oo' I.I868 0.3869 10 3773 -5767 -9261 .9667 .4074 .6100 2.4545 .3900 5 1.1839 0.3898 2O .3800 .5798 .9250 .9661 .4108 .6136 2.4342 .3864 40 0.3927 3 .3827 .5828 ' .9239 .9656 .4142 .6172 2.4142 .3828 30 !:! 7 8? 0.3956 40 3854 -5859 : -9228 .9651. .4176 .6208 2-3945 -3792 20 1.1752 0-3985 50 .3881 .5889 .9216 .9646 .4210 .6243 2.3750 -3757 IO 1.1723 0.4014 2300' .3907 9.5919 .9205 9.9640 .4245 9.6279 2-3559 0.3721 6 7 oo' 1.1694 0.4043 0.4072 10 20 3934 -5948 .3961 .5978 .9194 .9635 .9182 .9629 .4279 .6314 .4314 .6348 2.3369 .3686 2.3183 .3652 50 4 1.1665 1.1636 0.4102 3 .3987 .6007 .9171 -9624 .4348 .6383 2.2998 .3617 30 1. 1606 0.4131 40 .4014 .6036 .9159 .9618 .4383 .6417 2.2817 .3581 20 1.1577 0.4160 50 .4041 .6065 .9147 .9613 .4417 .6452 2.2637 .3548 10 1.1548 0.4189 2400' .4067 9.6093 .9135 9.9607 .4452 9.6486 2.2460 0.3514 66oo' 1.1519 0.4218 IO .4094 .6121 .9124 .9602 .4487 .6520 2.2286 .3480 5 1.1490 0.4247 20 .4120 .6149 .9112 .9596 4522 .6553 2.2113 .3447 40 1.1461 0.4276 0.4305 30 40 .4147 .6177 .4173 .6205 .9100 .9590 .9088 .9584 4557 -6587 .4592 .6620 2.1943 .3413 2-1775 -3380 30 20 1.1432 .1403 0.4334 50 .4200 .6232 9075 -9579 .4628 .6654 2.1609 .3346 10 1-1374 0-4363 2500' .4226 9.6259 9063 9.9573 .4663 9.6687 2.1445 0.3313 65oo' 1-1345 0.4392 IO .4253 .6286 .9051 .9567 .4699 .6720 2.1283 -3280 50 1.1316 0.4422 20 .4279 .6313 .9038 .9561 .4734 .6752 2.1123 .3248 40 1.1286 0.4451 30 435 -6340 .9026 .9555 .4770 .6785 2.0965 -3215 30 1-1257 0.4480 40 .4331 .6366 .9013 .9549 .4806 .6817 2.0809 -3 '83 20 1.1228 0.4509 5 4358 .6392 .9001 .9543 .4841 .6850 2-0655 .3150 IO 1.1199 0.4538 2600' .4384 9.6418 -8988 9-9537 .4877 9.6882 2.0503 0.3118 64oo' 1.1170 0.4567 10 .4410 .6444 8975 -953 .4913 .6914 2-0353 -3086 5 1.1141 0.4596 20 .4436 .6470 .8962 .9524 .4950 .6946 2.0204 -3OS4 40 I.I I 12 0.4625 30 .4462 .6495 .8949 .9518 .4986 .6977 2.0057 .3023 30 I.I083 0-4654 40 .4488 .6521 .8936 .9512 .5022 .7009 1.9912 .2991 20 I.I054 0.4683 50 .4514 .6546 .8923 .9505 5.59 -7040 1.9768 .2960 IO I.IO25 0.4712 2700' .4540 9.6570 .8910 9.9499 .5095 9.7072 1.9626 0.2928 63oo' 1.0996 Nat. Log. Nat. Log. Nat. Log. Nat. Log. c/i ~ri COSINES. SINES. COTAN- GENTS. TANGENTS. O l< SMITHSONIAN TABLES. TABLE 14 (continued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 35 Q" 3 C/) SINES. COSINES. TANGENTS. COTANGENTS. S O Nat. Log. Nat. Log. Nat. Log. Nat. Log. 0.4712 2700' .4540 9.6570 .8910 9.9499 .5095 9.7072 1.9626 0.2928 6300' 1.0996 0.4741 IO .4566 .6595 .8897 .9492 .5132 .7103 1.9486 .2897 5 1.0966 0.4771 20 .4592 .6620 .8884 .9486 5'69 7134 1.9347 .2866 40 1 -937 0.4800 3 .4617 .6644 .8870 .9479 .5206 .7165 1.9210 .2835 30 1.0908 0.4829 40 .4643 .6668 -8857 -9473 5243 -7196 1.9074 .2804 20 1.0879 0.4858 50 .4669 .6692 .8843 -9466 .5280 .7226 1.8940 .2774 IO 1.0850 0.4887 2800 / .4695 9.6716 .8829 9-9459 53 ! 7 9-7257 1.8807 0.2743 6200' 1.0821 0.4916 10 .4720 .6740 8816 .9453 5354 -7287 1.8676 .2713 5 1.0792 0.4945 20 .4746 .6763 .8802 .9446 5392 -73'7 1.8546 .2683 40 1.0763 0.4974 3 .4772 .6787 .8788 .9439 .5430 .7348 1.8418 .2652 3 1-0734 0.5003 40 .4797 .6810 .8774 .9432 .5467 .7378 1.8291 .2622 20 1.0705 0.5032 50 .4823 .6833 .8760 .9425 .5505 .7408 1.8165 .2592 10 1.0676 0.5061 2900' .4848 9.6856 .8746. 9.9418 5543 9-7438 1.8040 0.2562 6ioo' 1.0647 0.5091 10 .4874 .6878 .8732' .9411 .5581 .7467 I-79I7 -2533 5 1.0617 0.5120 20 .4899 .6901 .8718 -9404 .5619 .7497 1.7796 .2503 40 1.0588 0.5149 3 .4924 .6923 8704 -9397 5658 -7526 1.7675 .2474 30 1-0559 0.5178 40 .4950 .6946 .8689 .9390 .5696 .7556 1.7556 .2444 20 '0530 0-5207 50 .4975 .6968 -8675 -9383 5735 7585 1.7437 .2415 IO 1.0501 0.5236 30oo' .5000 9.6990 .8660 9.9375 5774 97614 1.7321 0.2386 6ooo' .0472 0.5265 IO .5025 .7012 .8646 .9368 .5812 .7644 1.7205 .2356 5 0443 0.5294 20 5050 ' -7033 .8631 .9361 5851 -7673 1.7090 .2327 40 .0414 0-5323 3 575 -7055 8616 .9353 .5890 .7701 1.6977 -2299 30 0385 0-535 2 40 .5100 .7076 .8601 .9346 5930 -773 1.6864 .2270 20 0356 0.5381 50 5 I2 5 -7097 8587 .9338 5969 -7759 1.6753 -2241 10 .0327 0.5411 3ioo' .5150 9.7118 8572 9-933 1 .6009 9.7788 1.6643 O.22I2 59oo' .0297 0.5440 IO 5'75 -7 T 39 8557 -9323 .6048 .7816 1.6534 .2184 5 .0268 0.5469 20 .5200 .7160 .8542 .9315 .6088 .7845 1.6426 .2155 40 .0239 0.5498 3 5225 -7181 .8526 .9308 .6128 .7873 1.6319 .2127 30 .0210 40 .5250 .7201 .8511 .9300 .6168 .7902 I.62I2 .2098 20 1.0181 0.5556 5 .5275 .7222 .8496 .9292 .6208 .7930 I.6lO7 .2070 IO 1.0152 0-5585 3200' .5299 9.7242 .8480 9.9284 .6249 9.7958 1.6003 0.2042 58oo' 1.0123 0.5614 IO .5324 .7262 .-8465 .9276 .6289 .7986 I.59OO .2OI4 50 1.0094 0.5643 20 .5348 .7282 .8450 .9268 .6330 .8014 1.5798 .1986 40 1.0065 0.5672 0.5701 3 40 5373 -7302 5398 -7322 .8434 .9260 .8418 .9252 .637 1 .8042 .6412 .8070 I-5697 -1958 '5597 -'93 3 20 i .0*036 i .0007 0.5730 50 .5422 .7342 .8403 .9244 .6453 .8097 1.5497 .1903 10 0.9977 0.5760 33000' .5446 9.7361 8387 9-9236 .6494 9.8125 1.5399 0.1875 57oo' 0.9948 0.5789 10 .5471 .7380 .8371 .9228 6536 -8133 1.5301 .1847 50 0.9919 0.5818 20 .5495 .7400 8355 -9219 .6577 .8180 1.5204 .1820 40 0.9890 0.5847 3 55*9 -7419 8339 -92H .6619 .8208 1.5108 .1792 30 0.9861 0.5876 40 5544 .7438 8323 -9203 .6661 .8235 1.5013 .1765 20 0.9832 0.5905 50 .5568 .7457 .8307 .9194 .6703 .8263 1.4919 .1737 IO 0.9803 0-5934 0-5963 34oo' IO 5592 9-7476 .5616 .7494 .8290 9.9186 .8274 .9177 .6745 9.8290 .6787 -8317 1.4826 0.1710 1.4733 .1683 56oo' 50 0.9774 0-9745 0.5992 20 .5640 .7513 .8258 .9169 .6830 .8344 1.4641 .1656 40 0.9716 0.602 1 3 .5664 .7531 .8241 .9160 .6873 .837' 1.4550 .1629 30 0.9687 0.6050 0.6080 40 5 .5688 .7550 .5712 .7568 .8225 .9151 .8208 .9142 .6916 .8398 6959 -8425 1.4460 .1602 1.4370 .1575 20 10 0-9657 0.9628 0.6109 35oo' 5736 97586 .8192 9.9134 .7002 9.8452 1.4281 0.1548 55 oo' 0.9599 0.6138 10 .5760 .7604 .8175 .9125 .7046 .8479 1.4193 .1521 50 0.95/0 0.6167 20 .5783 .7622 .8158 .9116 .7089 .8506 1.4106 .1494 40 0.9541 0.6196 3 .5807 .7640 .8141 .9107 7133 -8533 1.4019 .1467 30 0.9512 0.6225 40 583 1 -7657 .8124 .9098 7177 -8559 1.3934 .1441 20 0.9483 0.6254 5 5854 -7675 8107 .9089 7221 .8586 1.3848 .1414 IO 0.9454 0.6283 3 6oo' .5878 9.7692 8090 9.9080 .7265 9.8613 1.3764 0.1387 54oo' 0.9425. Nat. Log. Nat. Log. Nat. Log. Nat. Log. : W A rf COSINES. SINES. COTAN- GENTS. TANGENTS. O P SMITHSONIAN TABLES. TABLE 14 (continued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. I c/3 SINES. COSINES. TANGENTS. COTANGENTS. O Nat. Log. Nat. Log. Nat. Log. Nat. Log. 0.6283 3 6oo' .5878 9.7692 .8090 9.9080 .7265 9.8613 .3764 0.1387 54oo' 0.9425 0.6312 10 .5901 .7710 .8073 .9070 .7310 .8639 .3680 .1361 50 0.9396 0.6341 0.6370 20 3 .5925 .7727 .5948 .7744 .8056 .9061 .8039 .9052 7355 -8666 .7400 .8692 3597 -1334 .3514 .1308 40 3 0.9367 0-9338 0.6400 40 .5972 .7761 .8021 .9042 7445 -8718 .3432 .1282 20 0.9308 0.6429 50 5995 7778 .8004 .9033 .7490 .8745 335 1 - I2 55 IO 0.9279 0.6458 37 oo' 6018 9-7795 .7986 9.9023 7536 9-877I .3270 0.1229 53oo' 0.9250 0.6487 IO .6041 .7811 .7969 .9014 .7581 .8797 .3190 .1203 5 0.9221 0.6516 20 .6065 .7828 .7951 .9004 .7627 .8824 .3111 .1176 40 0.9192 0.6545 3 .6088 .7844 7934 -8995 .7673 .8850 .3032 .1150 3 0.9163 0.6574 40 .6111 .7861 .7916 .8985 .7720 .8876 .2954 .1124 20 0.9134 0.6603 50 .6134 .7877 .7898 .8975 .7766 .8902 .2876 .1098 10 0.9105 0.6632 0.6661 38oo' IO 6157 97893 .6180 .7910 .7880 9.8965 .7862 .8955 .7813 9.8928 .7860 .8954 .2799 0.1072 .2723 .1046 5200' 5 0.9076 0.9047 0.6690 20 .6202 .7926 .7844 .8945 .7907 .8980 .2647 .1020 40 0.9018 0.6720 3 .6225 .7941 .7826 .8935 .7954 .9006 .2572 .0994 30 0.8988 0.6749 40 .6248 .7957 .7808 .8925 .8002 .9032 .2497 .0968 20 0.8959 0.6778 50 .6271 .7973 .7790 .8915 .8050 .9058 .2423 .0942 10 0.8930 0.6807 39oo' .6293 9.7989 .7771 9.8905 .8098 9.9084 .2349 0.0916 5ioo' 0.8901 0.6836 IO .6316 .8004 7753 -8895 .8146 .9110 .2276 .0890 5 0.8872 0.6865 20 .6338 .8020 .7735 .8884 .8195 .9135 .2203 .0865 40 0.8843 0.6894 3 .6361 .8035 .7716 .8874 .8243 .9161 .2131 .0839 3 0.8814 0.6923 40 .6383 .8050 .7698 .8864 .8292 .9187 .2059 .0813 20 0.8785 0.6952 50 .6406 .8066 .7679 .8853 .8342 .9212 .1988 .0788 10 0.8756 0.6981 40oo' .6428 9.8081 .7660 9.8843 .8391 9.9238 .1918 0.0762 5ooo' 0.8727 0.7010 IO .6450 .8096 .7642 .8832 .8441 .9264 .1847 .0736 5 0.8698 0.7039 20 .6472 .8111 .7623 .8821 .8491 .9289 .1778 .0711 40 0.8668 3 .6494 .8125 .7604 .8810 8541 -93 J 5 .1708 .0685 3 0.8639 0.7098 40 .6517 .8140 .7585 .8800 8591 -9341 .1640 .0659 20 0.8610 0.7127 5 6539 - 8l 55 .7566 .8789 .8642 .9366 .1571 .0634 10 0.8581 0.7156 4ioo' .6561 9.8169 7547 9-8778 8693 9-9392 . 1 504 0.0608 49oo' 0.8552 0.7185 IO .6583 .8184 .7528 .8767 .8744 .9417 .1436 .0583 50 0.8523 0.72,14 20 .6604 .8198 .7509 .8756 .8796 .9443 J369 -557 40 0.8494 0.7243 30 .6626 .8213 .7490 .8745 .8847 -9468 .1303 .0532 3 0.8465 0.7272 40 .6648 .8227 7470 .8733 .8899 .9494 .1237 .0506 20 0.8436 0.7301 50 .6670 .8241 .7451 .8722 8952 -95 T 9 .1171 .0481 10 0.8407 0.7330 4200' .6691 9.8255 .7431 .9.8711 .9004 9.9544 .1106 0.0456 48oo' 0.8378 0.7359 IO .6713 .8269 .7412 .8699 9057 -9570 .1041 .0430 50 0.8348 0.7389 20 .6734 .8283 .7392 -8688 .9110 .9595 .0977 .0405 40 0.8319 0.7418 30 .6756 .8297 7373 -8676 .9163 .9621 0913 -379 3 0.8290 0-7447 40 .6777 .8311 7353 -8665 .9217 .9646 .0850 .0354 20 0.8261 0.7476 5 .6799 .8324 7333 -8653 .9271 .9671 .0786 .0329 IO 0.8232 0.7505 43oo' .6820 9.8338 .7314 9.8641 .9325 9.9697 .0724 0.0303 47oo' 0.8203 0-7534 10 .6841 .8351 .7294 .8629 .9380 .9722 .0661 .0278 50 0.8174 o-75 6 3 20 .6862 .8365 .7274 .8618 9435 -9747 0599 -0257 40 0.8145 0.7592 30 .6884 .8378 .7254 .8606 .9490 .9772 .0538 .0228 3 0.8116 0.7621 40 .6905 .8391 .7234 .8594 9545 -9798 .0477 .0202 20 0.8087 0.7650 50 .6926 .8405 .7214 .8582 .9601 .9823 .0416 .0177 10 0.8058 0.7679 44oo' .6947 9.8418 .7193 9.8569 .9657 9.9848 0355 - OI 52 46oo / 0.8029 0.7709 IO .6967 .8431 7173 -8557 .9713 .9874 0295 .0126 50 0.7999 0.7738 20 .6988 .8444 7153 -8545 9770 .9899 0235 .0101 40 0.7970 0.7767 0.7796 3 40 .7009 .8457 .7030 .8469 7133 -8532 .7112 .8520 .9827 .9924 .9884 .9949 0176 .0076 0117 .0051 30 20 0.7941 0.7912 0.7825 50 .7050 .8482 .7092 .8507 .9942 .9975 0058 .0025 IO 0.7883 0.7854 45oo' .7071 9.8495 .7071 9.8495 I.OOOO O.OOOO I .OOOO O.OOOO 45oo / 0.7854 Nat. Log. Nat Log. Nat. Log. Nat. Log. c/i -c/5 COSINES. SINES. COTAN- GENTS TANGENTS. O 2* SMITHSONIAN TABLES. TABLE 15. CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 37 C/3 * < s < Pti o.oo .01 .02 3 .04 SINES. COSINES. TANGENTS COTANGENTS. DEGREES. Nat. Log. Nat. Log. Nat. Log. Nat. Log. o.ooooo oo .01000 7-99999 .02000 8.30100 .03000 -47706 03999 - 6oi 94 I .OOOOO O.OOOOO 0-99995 9-99998 .99980 .99991 99955 -99980 .99920 .99965 oo co o.oiooo 8.00001 .02000 .30109 .03001 .47725 .04002 .60229 oo oo 99-997 1-99999 49-993 -69891 33-323 -52275 24.987 .39771 oooo' oo 34 01 09 oi 43 02 18 % .07 .08 .09 0.04998 8.69879 05996 77789 .06994 .84474 .07991 .90263 .08988 .95366 0.99875 9.99946 .99820 .99922 99755 -99894 .99680 .99861 99595 -99824 0.05004 8.69933 .06007 -77867 .07011 .84581 .08017 .90402 .09024 .95542 19.983 1.30067 16.647 -22133 14.262 -15419 12.473 -09598 11.081 -04458 0252' 03 26 04 oi 0435 5 9 O.IO .11 .12 T 3 .14 0.09983 8.99928 .10978 9.04052 .11971 .07814 .12963 .11272 .13954 .14471 0.99500 9.99782 .99396 .99737 .99281 .99687 .99156 .99632 .99022 .99573 0.10033 9.00145 .11045 -043 I 5 .12058 .08127 .13074 .11640 .14092 .14898 9.9666 0.99855 9.0542 .95685 8.2933 -9J873 7.6489 .88360 7.0961 .85102 ^8 4 ' 06 53 07 27 08 oi ;!l 17 .18 .19 0.14944 9.17446 .15932 .20227 .16918 .22836 .17903 .25292 .18886 .27614 0.98877 9.99510 .98723 .99442 98558 -99369 .98384 .99293 .98200 .99211 0.15114 9.17937 .16138 .20785 .17166 .23466 .18197 .26000 .19232 .28402 6.6 1 66 0.82063 6.1966 .7921; 5.8256 .76534 5.4954 .74000 5- '997 -71598 o8 3 6' 09 10 09 44 10 19 !o 53 O.2O .21 .23 .24 0.19867 9.29813 .20846 -31902 .21823 .33891 .22798 .35789 23770 -37603 0.98007 9.99126 .97803 .99035 .97590 .98940 97367 -98841 .97134 .98737 0.20271 9.30688 .21314 .32867 .22362 .34951 .23414 .36948 .24472 .38866 4.9332 0.69312 4.6917 .67133 4.4719 .65049 4.2709 .63052 4.0864 .61134 II28' 12 02 12 36 I 3 II 1345 3 .27 .28 .29 0.24740 9.39341 .25708 .41007 .26673 -42607 .27636 .44147 .28595 .45629 0.96891 9.98628 .96639 .98515 96377 -98397 .96106 -98275 .95824 .98148 0.25534 9.40712 .26602 .42491 .27676 .44210 .28755. -45872 .29841 .47482 3.9163 0.59288 3-7592 .57509 3-6i33 -55790 3.4776 .54128 3.3511 .52518 I 4 i 9 ' 1454 1528 16 03 1637 0.30 3 1 3 2 33 34 0.29552 9.47059 .30506 .48438 3 J 457 -4977 T .32404 .51060 33349 -52308 -95534 9-98016 95233 -97879 .94924 .97737 .94604 -9759 1 94275 -97440 0-30934 9-49043 32033 -50559 33 '39 -52034 .34252 .53469 35374 -54868 3.2327 0.50957 3.1218 .49441 3.0176 .47966 2.9195 .46531 2.8270 .45132 17! i' 17 46 18 20 18 54 1929 o-35 36 :| 39 0.34290 9.53516 .35227 .54688 .36162 .55825 .37092 .56928 .38019 .58000 0-93937 9-97284 93590 .97123 93233 -96957 .92866 .96786 .92491 .96610 0-36503 9-56233 .37640 -57565 .38786 .58868 .39941 .60142 .41105 -61390 2-7395 0.43767 2.6567 .42435 2.5782 .41132 2-5037 -39858 2.4328 .38610 2003' 2038 21 12 21 46 22 21 0.40 .41 .42 ; -43 44 0.38942 9.59042 .39861 -60055 .40776 .61041 41687 .62000 .42594 .62935 0.92106 9.96429 .91712 .96243 .91309 .96051 .90897 .95855 .90475 .95653 0.42279 9.62613 .43463 .63812 .44657 .64989 .45862 .66145 .47078 .67282 2-3652 0.37387 2.3008 .36188 2-2393 -35 011 2.1804 -33855 2.1241 .32718 2255 / 23 29 24 04 2438 25 13 0-45 .46 47 .48 49 0.43497 9-63845 .44395 .64733 .45289 .65599 .46178 .66443 .47063 .67268 0.90045 9.95446 .89605 .95233 89157 -95015 .88699 .94792 88233 .94563 0.48306 9.68400 49545 -69500 5797 .70583 .52061 .71651 -53339 -72704 2.0702 0.31600 2.0184 .30500 1.9686 .29417 1.9208 .28349 1.8748 .27296 2547' 26 21 2656 27 30 28 04 o 50 0.47943 9.68072 0.87758 9.94329 0.54630 9-73743 1.8305 0.26257 28 39 ' SMITHSONIAN TABLES. TABLE 1 5 (continued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. RADIANS. II SINES. COSINES. TANGENTS I COTANGENTS. DEGREES. 1 Nat. Log. Nat. Log. Nat. Log. Nat. Log. 0.50 0-47943 9-68072 0.87758 9.94329 0.54630 9-73743 1.8305 0.26257 2S39' 5 1 .48818 .68858 .87274 .94089 55936 .74769 .7878 -25231 29 '3 52 .49688 .69625 .86782 .93843 .57256 .75782 .7465 .24218 2948 53 50553 -70375 .86281 .93591 .58592 .76784 .7067 .23216 30 22 54 .51414 .71108 85771 -93334 59943 -77774 .6683 .22226 3 56 o-55 0.52269 9.71824 0.85252 9.93071 0.61311 9.78754 1.6310 0.21246 3 I 3 I/ 56 .53119 .72525 .84726 .92801 62695 .79723 .5950 .20277 32 05 57 53963 -73 210 .84190 .92526 .64097 .80684 .5601 .19316 32 40 .58 .54802 .73880 .83646 .92245 65517 -81635 .5263 .18365 33 H 59 -55636 .74536 .83094 .91957 .66956 .82579 4935 -17421 3348 0.60 0.56464 9.75177 0.82534 9.91663 0.68414 9.83514 1.4617 0.16486 3423' .61 .62 .57287 .75805 .58104 .76420 .81965 .91363 .81388 .91056 .69892 .84443 .71391 .85364 4308 .15557 .4007 .14636 34 57 35 3 1 63 .58914 .77022 .80803 -9743 .72911 .86280 .3715 .13720 3606 .64 .59720 .77612 .80210 .90423 .74454 .87189 .3431 .12811 3 6 40 0.65 0.60519 9.78189 0.79608 9.90096 0.76020 9.88093 1.3154 0.11907 37i5' .66 .61312 .78754 .78999 .89762 .77610 .88992 .2885 .11008 37 49 .67 .62099 .79308 .78382 .89422 .79225 .89886 .2622 .10114 3823 .68 .62879 .7985 r 77757 -89074 .80866 .90777 .2366 .09223 38 58 -69 .63654 .80382 .77125 .88719 .82534 .91663 .2116 .08337 3932 0.70 0.64422 9.80903 0.76484 9.88357 0.84229 9.92546 1.1872 0.07454 40o6' -7i .65183 .81414 .75836 .87988 .85953 .93426 .1634 .06574 4041 .72 .65938 .81914 .75181 .87611 87707 .94303 .1402 .05697 41 15 73 .66687 .82404 .74517 .87226 .89492 .95178 .1174 .04822 41 5 74 .67429 .82885 .73847 .86833 .91309 .96051 .0952 .03949 42 24 o-75 0.68164 9.83355 0.73169 9.86433 0.93160 9-96923 1.0734 0.03077 4258' .76 .68892 .83817 .72484 .86024 .95045 -97793 .0521 .02207 4333 77 .69614 .84269 .71791 .85607 96967 .98662 .0313 .01338 44 07 -78 .70328 .84713 .71091 .85182 .98926 9.9953 1 1.0109 .00469 44 41 79 .71035 .85147 .70385 .84748 i .0092 0.00400 0.99084 9.99600 45 l6 0.80 0.71736 9.85573 0.69671 9.84305 1.0296 0.01268 0.97121 9.98732 455o' .81 .72429 .85991 .68950 .83853 .0505 .02138 .95197 .97862 46 25 .82 .73115 .86400 .68222 -83393 .07 1 7 .03008 93309 -96992 46 59 83 73793 -86802 .67488 .82922 0934 -03879 .91455 .96121 47 33 .84 .74464 .87195 .66746 .82443 .1156 .04752 89635 -95248 48 08 0.85 0.75128 9.87580 0.65998 9.81953 1.1383 0.05627 0.87848 9-94373 4 8 4 2' .86 .75784 .87958 .65244 .81454 .1616 .06504 .86091 -93496 49 16 .87 .88 .76433 .88328 .77074 .88691 .64483 .80944 .63715 .80424 .1853 .07384 .2097 .08266 .84365 .92616 .82668 .91734 49 5 1 5025 .89 .77707 .89046 .62941 .79894 .2346 .09153 .80998 .90847 51 oo 0.90 0-78333 9-89394 0.62161 9-79352 1.2602 0.10043 0-79355 9-89957 5'34' .91 .78950 .89735 6i375 -78799 .2864 .10937 .77738 .89063 52 08 .92 .79560 .90070 .60582 .78234 3'33 ' Il8 35 .76146 .88165 5243 93 .80162 -90397 59783 -77658 .3409 .12739 .74578 .87261 53 17 -94 .80756 .90717 58979 -77070 .3692 .13648 .73034 .86352 53 5 1 o-95 0.81342 9.91031 0.58168 9.76469 1.3984 0.14563 0.71511 9.85437 54 26' .96 .81919 .91339 5735 2 .75855 .4284 .15484 .70010 .84516 5500 97 .82489 .91639 56530 -75228 .4592 .16412 .68531 .83588 5535 .98 .83050 .91934 .55702 .74587 .4910 .17347 .67071 .82653 5609 .99 .83603 .92222 .54869 .73933 .5237 .18289 .65631 .81711 5643 1. 00 0.84147 9.92504 0.54030 9.73264 1.5574 0.19240 0.64209 9.80760 57i8' SMITHSONIAN TABLES. TABLE 15 (.continued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 39 RADIANS.! SINES. COSINES. TANGENTS. COTANGENTS. DEGREES. 1 Nat. Log. Nat. Log. Nat. Log. Nat. Log. 1. 00 0.84147 9.92504 0.54030 9.73264 1.5574 0.19240 0.64209 9.80760 57i8' .OI .02 .84683 .92780 .85211 -9349 .53186 .72580 .52337 .71881 .5922 .20200 .6281 .21169 .62806 .79800 .61420 .78831 57 52 58 27 3 8573 -933 i 3 .51482 .71165 .6652 .22148 .60051 .77852 590i .04 .86240 .93571 .50622 .70434 .7036 .23137 .58699 .76863 5935 1.05 0.86742 9-93823 0-49757 9-69686 1.7433 0.24138 0.57362 9-75 8 62 60 i o' .06 .87236 .94069 .48887 .68920 .7844 .25150 .56040 .74850 60 44 .07 .87720 .94310 .48012 .68135 .8270 -26175 54734 -73825 61 18 .03 .88196 -94545 47133 -67332 .8712 .27212 .53441 .72788 61 53 .09 .88663 -94774 .46249 .66510 .9171 .28264 .52162 .71736 6227 I.IO 0.89121- 9.94998 0.45360 9.65667 1.9648 0.29331 0.50897 9.70669 6 3 02' .11 8 9570 -95 2I 6 .44466 .64803 2.0143 -30413 .49644 .69587 6336 .12 .90010 .95429 43568 -63917 .0660 .31512 .48404 .68488 64 10 13 .90441 .95 6 37 .42666 .63008 .1198 .32628 47175 -67372 6445 J 4 90863 .95839 .41759 .62075 1759 .33763 .45959 .66237 65 19 '15 0.91276 9.96036 0.40849 9.61118 2.2345 0.34918 0-44753 9-65082 6553' .16 .91680 .96228 39934 -60134 .2958 .36093 43558 -63907 6628 17 .92075 .96414 .39015 .59123 .3600 -37291 .42373 .62709 67 02 .18 .92461 -96596 .38092 .58084 4273 -38512 .41199 .61488 67 37 .19 .92837 .96772 .37166 -57015 4979 -39757 .40034 .60243 68 ii i. 20 0.93204 9.96943 0.36236 9.55914 2.5722 0.41030 0.38878 9.58970 68 45 ' .21 .93562 .97110 .35302 .54780 .6503 .42330 3773 1 -57670 69 20 .22 .93910 .97271 34365 -53611 .7328 .43660 36593 -56340 69 54 2 3 .94249 .97428 .33424 .52406 .8198 .45022 35463 -54978 7028 .24 94578 -97579 .32480 .51161 .9119 .46418 34341 -53582 7i 03 1.25 0.94898 9.97726 0.31532 9.49875 3.0096 0.47850 0-33227 9-52 J 5 7i37' .26 .95209 .97868 .30582 .48546 .1133 .49322 .32121 .50678 72 12 .27 .95510 .98005 .29628 -47 [ 70 .2236 .50835 .31021 .49165 7246 .28 .95802 -98137 .28672 -45745 .3413 -52392 .29928 .47608 73 20 .29 .96084 .98265 .27712 .44267 4672 .53998 .28842 .46002 73 55 I. 3 0.96356 9.98388 0.26750 9.42732 3.6021 0.55656 0.27762 9-44344 742 9 ' 3 1 .96618 .98506 .25785 .41137 .7471 -57369 i -26687 -42631 75 3 3 2 .96872 .98620 .24818 .39476 933 -59*44 | -25619 .40856 7538 33 .97115 .98729 . .23848 .37744 4.0723 .60984 .24556 .39016 7612 34 .97348 .98833 22875 -35937 -2556 -62896 23498 -37104 76 47 i-35 0-97572 9-98933 0.21901 9.34046 4.4552 0.64887 0.22446 9-35 IJ 3 77W 36 .97786 .99028 .20924 .32064 .6734 .66964 21398 -33036 77 55 37 .97991 .99119 .19945 .29983 9 l 3 l -69135 .20354 .30865 78 3 38 .98185 .99205 .18964 .27793 5.1774 .71411 .19315 .28589 79 4 39 .98370 .99286 .17981 .25482 .4707 .73804 .18279 .26196 7938 1.40 0-98545 9-993 6 3 0.16997 9.23036 5-7979 0.76327 0.17248 9.23673 80 1 3' .41 .98710 .99436 .16010 .20440 6.1654 .78996 .16220 .21004 8047 .42 98865 .99504 .15023 .17674 6.5811 .81830 .15195 .18170 8l 22 43 .99010 .99568 .14033 .14716 7.0555 .84853 .14173 .15147 8 1 56 44 .99146 .99627 .13042 .11536 7.6018 .88092 -13155 .11908 82 30 1.45 0.99271 9.99682 0.12050 9.08100 8.2381 0.91583 0.12139 9.08417 8305' .46 99387 -99733 .11057 .04364 8.9886 .95369 .11125 -04631 8 3 39 47 99492 -99779 .10063 .00271 98874 .99508 .10114 .00492 84 13 .48 .99588 .99821 .09067 8.95747 10.983 1.04074 .09105 8.95926 8448 49 .99674 .99858 .0807 1 .90692 12.350 .09166 .08097 .90834 85 22 1.50 0.99749 9.99891 0.07074 8.84965 14.101 1.14926 0.07091 8.85074 Q P O f ^f 5 57 SMITHSONIAN TABLES. 40 TABLES 15 (continued) AND 16. CIRCULAR FUNCTIONS AND FACTORIALS. TABLE 15 (continued). Circular (Trigonometric) Functions. RADIANS. SINES. COSINES. TANGENTS. COTANGENTS. DEGREES. 1 Nat. Log Nat. Log Nat. Log. Nat. Log. 1.50 5 1 5 2 53 54 0-99749 9-9989I .99815 .99920 .99871 .99944 .99917 .99964 99953 -99979 0.07074 8.84965 .06076 -78361 .05077 .70565 .04079 .61050 .03079 .48843 14.101 1.14926 16.428 -21559 19.670 .29379 24.498 .38914 32.461 .51136 0.07091 8.85074 .06087 -78441 .05084 .70621 .04082 .6ro86 .03081 .40864 85^57' 86 31 87 05 87 40 88 14 56 59 0.99978 9.99991 0.99994 9-99997 1. 00000 0.00000 0.99996 9.99998 0.99982 9.99992 0.02079 8.31796 .01080 8.03327 .00080 6.90109 -.00920 7.9639611 -.01920 8.2833611 48.078 1.68195 92.621 1.96671 1255.8 3.09891 108.65 2 -36o3 52.067 1.71656 0.02080 8.31805 .01080 8.03329 .00080 6.90109 -.00920 7-96397" -.01921 8.2834411 88 49 ' 8923 89 57 90 32 91 06 1.60 0-99957 9-9998i -0.02920 8.4653811 34-233 1-53444 -0.02921 8.4655611 9i4o' 90== 1.570 7963 radians. TABLE 16. Logarithmic Factorials. Logarithms of the products 1.2.3 n, n from I to 100. See Table iS'for Factorials I to 20. See Table 32 for log. r (w+i), values of n between I and 2. . log (n!) n. log (/) n. log (/) n. log (.') 1 2 o.oooooo 0.301030 26 27 26.605619 28.036983 51 5 2 66.190645 67.906648 76 77 111.275425 113.161916 3 0.778151 28 29.484141 53 69.630924 78 115.054011 4 1.380211 29 30.946539 54 71-363318 79 116.951638 5 2.079181 30 32.423660 55 73.103681 80 118.854728 6 2-857332 31 33.915022 56 74.851869 81 120.763213 8 3-702431 4.605521 32 33 35.420172 36.938686 3 76.607744 78.371172 82 83 122.67/027 124.596105 9 5-559763 34 38.470165 59 80.142024 84 126.520384 10 6.559763 35 40.014233 60 81.920175 85 128.449803 11 7.601156 36 41.570535 61 83-705505 86 130.384701 12 8.680337 37 43- i 387 37 62 85.497896 8/ 132.323821 J 3 9.794280 38 44.718520 63 87.297237 88 134.268303 14 10.940408 39 46-309585 64 89.103417 89 136.217693 15 12.116500 40 47.911645 65 90.916330 90 138.171936 16 13.320620 41 49.524429 66 92.735874 91 140.130977 17 18 14.551069 15.806341 42 43 51.147678 52.781147 67 68 94.561949 96.394458 92 93 142.094765 144.063248 19 17.085095 44 54.424599 i 69 98.233307 94 146.036376 20 18.386125 45 56.077812 70 100.078405 95 148.014099 21 19.708344 46 57.740570 ! 71 101.929663 96 149.996371 22 21.050767 47 59.412668 72 103.786996 97 151.983142 2 3 22.412494 48 61.093909 73 105.650319 98 I53-974368 24 23.792706 49 62.784105 74 107.51955 ! 99 155.970004 25 25.190646 50 64.483075 75 109.394612 | IOO 157.970004 SMITHSONIAN TABLES. TABLE 17. HYPERBOLIC FUNCTIONS. u sinh. u cosh, u tanh. u coth. u gd u Nat. Log. Nat. Log. Nat. Log. Nat. LOR. O.OO .or .02 3 .04 O.OOOOO 00 .01000 8.00001 .02000 .30106 .03000 .47719 .04001 .60218 I .OOOOO O.OOOOO .OOOO5 .OOOO2 .00020 .00009 .OOO45 -OOO2O .00080 -00035 0.00000 00 .01000 7.99999 .02000 8.30097 .02999 .47699 .03998 .60183 00 00 IOO.OO3 2.OOOOI 50.007 1.69903 33-343 1-52301 25.013 1.39817 oooo' o 34 i 09 1 43 2 17 :ol .07 .08 .09 0.05002 8.69915 .06004 .77841 .07006 .84545 .08009 .90355 .09012 .95483 I.OOI25 0.00054 .OOlSo .OOO/8 .00245 .00106 .00320 -00139 .00405 .00176 0.04996 8.69861 .05993 -77763 .06989 .84439 .07983 .90216 08976 -95307 20.017 1-30139 16.687 -22237 14.309 .15561 12.527 .09784 11.141 -04693 2 5J 3 26 4 oo 4 35 5 09 O.IO .11 .12 13 .14 0.10017 9.00072 .IIO22 .04227 .12029 .08022 .13037 .11517 .14046 .14755 I.OO5OO O.OO2I7 .00606 .OO262 .00721 .00312 .00846 .00366 .00982 .00424 0.09967 8.99856 .10956 9-03965 .11943 .07710 .12927 .11151 13909 -14330 10.0333 1.00144 9.1275 0.96035 8-3733 -92290 7.7356 -88849 7.1895 .85670 5 43 6 17 652 7 26 8 oo 1 .19 0.15056 9.17772 .16068 .20597 .17082 .23254 .18097 .25762 .19115 .28136 I.OII27 0.00487 .01283 .00554 .01448 .00625 .01624 .OO7OO .OlSlO .00779 0.14889 9.17285 .15865 .20044 .16838 .22629 .17808 .25062 18775 -27357 6.7166 0.82715 6.3032 .79956 5-9389 -77371 5.6154 .74938 5.3263 .72643 834 9 08 9 42 10 15 10 49 O.2O .21 .22 2 3 .24 0.20134 9.30392 21155 -32541 .22178 .34592 23203 .36555 .24231 .38437 I .O2OO7 0.00863 .O22I3 .00951 .02430 .01043 .02657 -01139 .02894 -01239 0.19738 9-29529 20697 .31590 .21652 .33549 22603 .35416 23550 -37198 5.0665 0.70471 4.8317 .68410 4.6186 .66451 4.4242 .64584 4.2464 .62802 ii 23 ii 57 12 30 13 04 13 37 :ll % .29 0.25261 9.40245 .26294 .41986 .27329 .43663 .28367 .45282 .29408 .46847 1.03141 0.01343 03399 -QMS 2 .03667 .01 564 .03946 .01681 .04235 .01801 0.24492 9.38902 .25430 .40534 .26362 .42099 .27291 .43601 .28213 .45046 4.0830 0.61098 3-93 2 4 .59466 3-7933 -57901 3.6643 .56399 3-5444 -54954 14 ii 14 44 15 J 7 15 50 16 23 0.30 3 1 32 33 34 0.30452 9.48362 .31499 .4983 .32549 -51254 .33602 .52637 34659 -53981 1.04534 0.01926 .04844 .02054 .05164 .02187 .05495 -02323 .05836 .02463 0.29131 9.46436 .30044 .47775 .30951 .49067 .31852 .50314 .32748 .51518 34327 0.53564 .3285 .52225 2309 -50933 .1395 .49686 .0536 .48482 16 56 17 29 18 02 18 34 19 7 0-35 3 6 % 39 0.35719 9-55290 .36783 .56564 37850 .57807 .38921 .59019 .39996 .60202 1. 06188 0.02607 .06550 .02755 .06923 .02907 .07307 .03063 .07702 .03222 0-33638 9.52682 34521 .53809 35399 -54899 .36271 .55956 .37136 .56980 2.9729 0.47318 .8968 .46191 .8249 .45101 .7570 .44044 .6928 .43020 i9 39 2O 12 20 44 21 16 21 48 0.40 .41 .42 43 44 0.41075 9.61358 .42158 .62488 .43246 .63594 .44337 .64677 .45434 .65738 1.08107 0.03385 08523 -03552 .08950 .03723 .09388 .03897 .09837 .04075 0-37995 9-57973 .38847 .58936 39693 -59871 .40532 .60780 .41364 .61663 2.6319 0.42027 .5742 .41064 .5193 .40129 .4672 .39220 4i75 -38337 22 20 22 52 23 2 3 23 55 24 26 0-45 .46 47 .48 49 0.46534 9.66777 .47640 .67797 .48750 .68797 .49865 .69779 .50984 .70744 1.102970 .04256 .10768 .04441 .11250 .04630 .11743 .04822 .12247 .05018 0.42190 9.62521 .43008 .63355 .43820 .64167 .44624 .64957 .45422 .65726 2.3702 0.37479 .3251 .36645 .2821 .35833 .2409 .35043 .2016 .34274 24 57 25 28 2 5 59 26 30 27 01 0.50 0.52110 9.71692 1.12763 0.05217 0.46212 9.66475 2.1640 0.33525 27 31 SMITHSONIAN TABLES TABLE 17 (continued). HYBERBOLIC FUNCTIONS. sinh. u cosh, u tanh. u ooth. u Nat, Log. Nat. Log. Nat. Log. Nat. Log. 0.50 5 1 52 53 54 0.52110 9.71692 .53240 .72624 54375 -73540 .55516 .74442 56663 .75330 1.12763 0.05217 .13289 .05419 .13827 .05625 .14377 .05834 .14938 .06046 0.46212 9.66475 .46995 .67205 .47770 .67916 .48538 .68608 .49299 .69284 2.1640 0.33525 .1279 -32795 .0934 .32084 .0602 -31392 .0284 .307 1 6 2 7 3 r 28 02 28 32 29 02 29 32 ^ : 59 0-57815 9-76204 .58973 .77065 .60137 .77914 .61307 .7875! .62483 .79576 1.15510 0.06262 .16094 .06481 .16690 .06/03 .17297 .06929 .17916 .07157 0.50052 9.69942 .50798 .70584 .51536 .71211 .52267 .71822 .52990 .72419 1.9979 0.30058 .9686 .29416 .9404 .28789 .9133 .28178 .8872 .27581 30 02 30 32 31 01 31 31 32 oo 0.60 .61 .62 63 .64 0.63665 9.80390 .64854 .81194 .66049 - 8l 9 8 7 .67251 .82770 68459 -83543 1.18547 0.07389 .19189 .07624 .19844 .O/86l .20510 .08102 .21189 .08346 0-53705 9-73 001 54413 -73570 .55113 .74125 .55805 .74667 56490 -75 1 97 1.8620 0.26999 .8378 .26430 .8141; .25875 7919 -25333 .7702 .24803 32 29 32 58 33 27 33 55 34 24 0.65 .66 .67 .68 .69 0.69675 9.84308 .70897 .85063 .72126 .85809 .73363 -86548 .74607 .87278 1.21879 o.o8s93 .22582 .08843 .23297 .09095 .24025 .09351 .24765 .09609 0.57167 9.75/15 .57836 .76220 .58498 .76714 .59152 .77197 .59798 .77669 1.7493 0.24285 .7290 .23780 7095 -23286 .6906 .22803 .6723 .22331 34 52 35 20 3548 36 16 3 6 44 0.70 7i .72 73 74 0.75858 9.88000 .77117 .88715 .78384 .89423 79659 -90123 .80941 .90817 1.25517 0.09870 .26282 .10134 .27059 .10401 .27849 .10670 .28652 .10942 0.60437 9.78130 .61068 .78581 .61691 .79022 .62307 .79453 .62915 .79875 1.6546 0.21870 .6375 .21419 .6210 .20978 .6050 .20547 .5895 .20125 37 " 37 38 3805 38 32 38 59 I 0.75 .76 77 78 79 0.82232 9.91504 .83530 .92185 .84838 .92859 86153 .935 2 7 .87478 .94190 1.29468 0.11216 .30297 .11493 3"39 -"773 .31994 .12055 .32862 .12340 0.63515 9.80288 .64108 .80691 .64693 .81086 .65271 .81472 .65841 .81850 1.5744 0.19712 5599 -19309 .5458 .18914 .5321 .18528 .5188 .18150 39 26 39 52 40 19 40 45 41 ii \ 0.80 .81 .82 83 .84 0.88811 9.94846 .90152 .95498 .91503 .96144 .92863 .96784 .94233 .97420 1-33743 0.12627 .34638 .12917 35547 -13209 .36468 .13503 .37404 .13800 0.66404 9.82219 .66959 .82581 67507 -82935 .68048 .83281 .68581 .83620 1.5059 0.17781 4935 1 74i9 .4813 -17065 .4696 .16719 .4581 .16380 4i 37 42 02 42 28 42 53 43 18 ! is .87 .88 .89 0.95612 9.98051 .97000 .98677 98398 .99299 .99806 .99916 1.01224 0.00528 1 -38353 0.14099 .39316 .14400 .40293 .14704 .41284 .15009 .42289 .15317 0.69107 9.83952 .69626 .84277 .70137 .84595 .70642 .84906 .71139 .85211 1.4470 0.16048 .4362 .15723 .4258 .15405 .4156 .15094 .4057 .14789 43 43 44 08 44 32 44 57 45 21 0.90 .91 .92 93 94 1.02652 0.01137 .04090 .01741 05539 -02341 .06998 .02937 .08468 .03530 1.43309 0.15627 44342 .15939 .45390 .16254 .46453 .16570 .47530 .16888 0.71630 9.85509 .72113 .85801 .72590 .86088 .73059 .86368 .73522 .86642 1.3961 0.14491 .3867 .14199 .3776 .13912 .3687 .13632 .3601 .13358 45 45 46 09 46 33 46 56 47 20 $ 99 1.09948 0.04119 .11440 .04704 .12943 .05286 .14457 .05864 .15983 .06439 1.48623 0.17208 49729 - r 753 i .50851 .17855 .51988 .18181 .53141 .18509 0.73978 9.86910 .74428 .87173 .74870 .87431 .75307 .87683 .75736 .87930 1.3517 0.13090 .3436 .12827 .3356 -12569 .3279 .12317 .3204 .12070 47 43 48 06 48 29 48 51 49 M I.OO 1.17520 0.07011 1.54308 0.18839 0.76159 9.88172 1.3130 0.11828 49 3 6 SMITHSONIAN TABLES. TABLE 17 (continued). HYPERBOLIC FUNCTIONS. 43 u sinh. u cosh, u tanh. u coth u gd u Nat. Log. Nat. Log. Nat. Log. Nat. Log. 1. 00 .OI .02 03 .04 1.17520 0.07011 .19069 -07580 .20630 .08146 .22203 -08708 .23788 .09268 1.54308 0.18839 .55491 .19171 .56689 .19504 .57904 .19839 .59134 .20176 0.76159 9.88172 .76576 .88409 .76987 .88642 .77391 .88869 .77789 .89092 1.3130 0.11828 .3059 .11591 .2989 .11358 .2921 .11131 .2855 .10908 49036' 49 58 5O 21 50 42 5 1 04 I>0 | .06 .07 .08 .09 1.25386 0.09825 .26996 .10379 .28619 .10930 .30254 .11479 .31903 .12025 1.60379 0.20515 .61641 .20855 .62919 .21197 .64214 .21541 .65525 .21886 0.78181 9.89310 .78566 .89524 .78946 .89733 .79320 .89938 .79688 -90139 1.2791 0.10690 .2728 .10476 .2667 .10267 .2607 .10062 .2549 .09861 51 26 5 1 47 5208 5 2 29 5 2 5 1. 10 .11 .12 13 .14 1.33565 0.12569 .35240 .13111 .36929 .13649 .38631 .14186 .40347 .14720 1.66852 0.22233 .68196 .22582 69557 -22931 .70934 .23283 .72329 .23636 0.80050 9-90336 .80406 -90529 .80757 .90718 .8lIO2 -90903 .81441 .91085 1.2492 0.09664 .2437 . .09471 .2383 .09282 .2330 .09097 .2279 .08915 53 ii 53 3 1 53 52 54 12 54 32 .l6 .19 1.42078 0.15253 .43822 .15783 .45581 .16311 47355 -16836 .49143 .17360 I.7374I 0.23990 .75171 .24346 .76618 -24703 .78083 .25062 79565 ^5422 0.81775 9.91262 .82104 .91436 .82427 .91607 .82745 .91774 .83058 .9193 s 1.2229 0.08738 .2180 .08564 .2132 .08393 .2085 .08226 .2040 .08062 54 52 55 ii 55 3i 55 50 5 6 09 1.20 .21 2^ 23 .24 1.50946 0.17882 .52764 .18402 .54598 .18920 .56447 .19437 .58311 .19951 1. 81066 0.25784 .82584 .26146 .84121 .26510 .85676 .26876 .87250 .27242 0.83365 9.92099 .83668 .92256 .83965 .92410 .84258 .92561 .84546 .92709 1.1995 0.07901 .1952 -07744 .1910 .07590 .1868 -07439 .1828 .07291 56 29 5 6 47 57 06 57 25 57 43 l :ll .27 .28 .29 1.60192 0.20464 .62088 .20975 .64001 .21485 .65930 .21993 .67876 .22499 1.88842 0.27610 .90454 .27979 .92084 .28349 .93734 .28721 .95403 .29093 0.84828 9.92854 .85106 .92996 85380 .93135 .85648 .93272 859*3 -93406 1.1789 0.07146 .1750 .07004 .1712 .06865 .1676 .06728 .1640 .06594 58 02 58 20 58 38 58 55 59 13 T. 3 31 32 33 34 1.69838 0.23004 .71818 .23507 .73814 .24009 .75828 .24509 .77860 .25008 1.97091 0.29467 .98800 .29842 2.00528 -30217 .02276 .30594 .04044 .30972 0.86172 9.93537 .86428 -93665 .86678 .93791 86925 .93914 .87167 .94035 1.1605 0.06463 1570 -06335 .1537 .06209 .1504 .06086 .1472 .05965 59 3i 59 48 60 05 60 22 60 39 i-35 36 i 39 1.79909 0.25505 .81977 .26002 .84062 .26496 .86166 .26990 .88289 -27482 2.05833 0.31352 .07643 .31732 .09473 .32113 .11324 .32495 .13196 .32878 0.87405 9.94154 .87639 .94270 .87869 .94384 .88095 -94495 .88317 .94604 1.1441 0.05846 .1410 .0573 .1381 .05616 i35 T -05505 1323 -05396 60 56 61 13 61 29 61 45 62 02 1.40 .41 .42 43 44 1.90430 0.27974 .92591 .28464 .94770 .28952 .96970 .29440 .99188 .29926 2.15090 0.33262 17005 .33647 .18942 .34033 .20900 .34420 .22881 .34807 0-88535 9.94712 .88749 -94817 .88960 .94919 .89167 .95020 .89370 .95119 1.1295 0.05288 .1268 .05183 .1241 .05081 .1215 .04980 .1189 .04881 62 18 6234 62 49 63 05 63 20 1.45 .46 47 .48 49 2.01427 0.30412 .03686 .30896 05965 -3 ! 379 .08265 .31862 .10586 .32343 2.24884 0.35196 26910 .35585 28958 .35976 .31029 .36367 33123 .36759 0.89569 9.95216 89765 -953 11 89958 .95404 .90147 .95495 90332 .95584 1.1165 0.04784 .1140 .04689 .1116 .04596 1093 -04505 .1070 .04416 63 36 63 5i 64 06 6 4 21 64 36 | 1-50 2.12928 0.32823 2.35241 0.37151 0.90515 9.95672 1.1048 0.04328 64 51 SMITHSONIAN TABLES. 44 TABLE 17 (continued). HYPERBOLIC FUNCTIONS, u siiih. u cosh. u tanh. u coth. u gd. u Nat. Log. Nat. Log. Nat. Log. Nat. Log. 1.50 5 1 5 2 53 54 2.12928 0.32823 I5 A 9 I >333 S 3 '7676 .33781 .20082 .34258 .22510 .34735 2.35241 0.37151 37382 -37545 39547 -37939 41736 .38334 43949 -3873 0.90515 9.95672 .90694 .95758 .90870 .95842 .91042 .95924 .91212 .96005 1.1048 0.04328 .1026 .04242 .1005 .04158 .0984 .040/6 0963 .03995 64 51' 65 5 65 2O 65 34 65 4 '3 i 59 2.24961 0.35211 27434 -35686 .29930 .36160 .32449 -36633 3499 1 -37105 2.46186 0.39126 .48448 .39524 50735 -39921 .53047 .40320 .55384 .40719 -9I379 9-96084 .91542 .96162 .91703 .96238 .91860 .96313 .92015 .96386 1.0943 0.03916 .0924 .03838 0905 -03762 .0886 .03687 .0868 .03614 66 02 66 16 66 30 66 43 66 57 1.60 .61 .62 3 2-37557 0.37577 40146 .38048 .42760 -38518 45397 -38987 .48059 .39456 2.57746 0.41119 .60135 .41520 .62549 .41921 .64990 .42323 .67457 .42725 0.92167 9.96457 .92316 .96528 .92462 .96597 .92606 .96664 .92747 .96730 1.0850 0.03543 0832 -03472 .0815 .03403 .0798 .03336 .0782 .03270 67 10 67 24 67 37 67 50 68 03 'I '.69 2.50746 0.39923 53459 -4039 1 .56196 .40857 .58959 .41323 .61748 .41788 2.69951 0.43129 72472 .43532 .75021 .43937 .77596 -44341 .80200 -44747 0.92886 9.96795 .93022 .96858 93 J 55 -96921 .93286 .96982 934i5 -9/042 1.0766 0.03205 .0750 .03142 735 -03079 .0720 .03018 .0705 -02958 68 15 68 28 68 41 68 53 69 05 1.70 7i .72 73 74 2.64563 0.42253 .67405 .42717 .70273 .43180 .73168 .43643 .76091 .44105 2.82832 0.45153 8549 1 -45559 .88180 .45966 .90897 .46374 .93643 .46782 o.9354i 9-97ioo 93665 -97158 .93786 .97214 .93906 .97269 94023 .97323 1.0691 0.02900 .0676 .02842 .0663 .02786 .0649 .02731 .0636 .02677 69 18 69 30 69 42 69 54 70 05 !-75 .76 77 .78 79 2.79041 0.44567 .82020 .45028 .85026 .45488 .88061 .45948 .91125 .46408 2.96419 0.47191 .99224 .47600 3.02059 .48009 .04925 .48419 .07821 .48830 0.94138 9.97376 .94250 .97428 .94361 -97479 94470 .975 2 9 94576 .97578 1.0623 0.02624 .0610 .02572 .0598 .02521 .0585 .02471 .0574 .02422 70 17 70 29 70 40 70 51 7i 03 i. 80 .81 .82 83 .84 2.94217 0.46867 -97340 47325 3.00492 .47783 .03674 .48241 .06886 .48698 3.10747 0.49241 .13705 .49652 .16694 .50064 .19715 .50476 .22768 .50889 0.94681 9.97626 .94783 .97673 .94884 .97719 .94983 .97764 .95080 .97809 1.0562 0.02374 .0550 .02327 .0539 .02281 .0528 .02236 .0518 .02191 71 14 71 25 7 1 3 6 71 46 7i 57 , 1.85 .86 87 .88 .89 3.10129 0.49154 .13403 .49610 .16709 .50066 .20046 .50521 .23415 .50976 3-25853 0.51302 .28970 .51716 .32121 .52130 35305 -52544 38522 .52959 0.95175 9-97852 .95268 .97895 95359 -97936 .95449 -97977 95537 -98017 1.0507 0.02148 .0497 .02105 .0487 .02064 .0477 .02023 .0467 .01983 72 08 72 18 i 72 29 ! 72 39 i 72 49 1.90 .91 .92 93 .94 3.26816 0.51430 .30250 .51884 .33718 .52338 .37218 .52791 .40752 .53244 3-4I773 0.53374 45 58 .53789 .48378 .54205 5*733 -54621 55123 -55038 0.95624 9.98057 .95709 .98095 95792 -98133 .95873 .98170 95953 -98206 1.0458 0.01943 .0448 -oi905 .0439 .01867 .0430 .01830 .0422 .01794 72 59 73 09 73 r 9 73 29 73 39 '28 $ 99 3.44321 0.53696 .47923 .54148 .51561 .54600 55234 -55051 .58942 .55502 3.58548 0.55455 .62009 -55872 65507 -56290 .69041 .56707 .72611 .57126 0.96032 9.98242 .96109 .98276 .96185 .98311 96259 -98344 9633 1 -98377 1.0413 0.01758 .0405 .01724 .0397 .01689 .0389 .01656 .0381 .01623 73 48 73 58 74 07 74 17 74 26 2.00 3.62686 0.55953 3.76220 0.57544 0.96403 9-98409 1.0373 0.01591 74 35 SMITHSONIAN TABLES. TABLE 17 (continued). HYPERBOLIC FUNCTIONS. 45 u sinh. u cosh, u tanh. u coth. u. gd. u Nat. Log. Nat. Log. Nat. Log. Nat. Log. 2.OO .OI .02 3 .04 3.62686 0.55953 .66466 .56403 .70283 .56853 .74138 .57303 .78029 .57753 3.76220 0.57544 .79865 .57963 .83549 .58382 .87271 .58802 .91032 .59221 0.96403 9.98409 .96473 .98440 .96541 .98471 .96609 .98502 .96675 .98531 I -373 0.01591 .0366 .01560 .0358 .01529 .0351 .01498 .0344 .01469 7435' 74 44 74 53 75 02 75 ii 2 : l .07 .08 .09 3.81058 0.58202 .85926 .58650 89932 ^9099 93977 -59547 .98061 .59995 3.94832 0.59641 .98671 .60061 4.02550 .60482 .06470 .60903 .10430 .61324 0.96740 9.98560 .96803 .98589 .96865 .98617 .96926 .98644 .96986 .98671 I -337 0.01440 .0330 .01411 .0324 .01383 .0317 .01356 .0311 .01329 75 20 75 28 75 37 75 45 75 54 2.10 .11 .12 13 .14 4.02186 0.60443 .06350 .60890 10555 -61337 .14801 .61784 .19089 .62231 4.14431 0.61745 .18474 .62167 .22558 .62589 .26685 -63011 .30855 .63433 0.97045 9.98697 .97103 .98723 97*59 .98748 .97215 .98773 .97269 .98798 1.0304 0.01303 .0298 .01277 .0292 .01252 .0286 .01227 .0281 .01202 76 02 76 10 76 19 i 76 27 76 35 2.15 .l6 .18 .19 4.23419 0.62677 .27791 .63123 32205 -63569 .36663 -64015 .41165 .64460 4.35067 0.63856 .39323 .64278 .43623 .64701 .47967 .65125 52356 -65548 0-97323 9-98821 97375 -98845 .97426 .98868 .97477 .98890 .97526 .98912 1.0275 O.OII79 .O27O -OII55 .0264 .01132 .0259 .01110 .0254 .OIO88 76 43 76 5 1 76 58 77 06 77 H 2. 2O .21 .22 23 .24 4.45711 0.64905 .50301 .65350 .54936 .65795 .59617 .66240 .64344 .66684 4.56791 0.65972 .61271 .66396 65797 .66820 .70370 .67244 .74989 .67668 0-97574 9-98934 .97622 .98955 .97668 .98975 .97714 .98996 97759 -99016 I.O249 O.OIO66 .0244 .01045 .0239 .OIO25 .0234 .OIOO4 .0229 .00984 77 21 77 29 77 3 6 77 44 77 5 1 *:% 3 .29 4.69117 0.67128 73937 -67572 .78804 .68016 .83720 .68459 .88684 .68903 4.79657 0.68093 .84372 .68518 .89136 .68943 .93948 .69368 .98810 .69794 0.97803 9.99035 .97846 .99054 .97888 .99073 .97929 .99091 .97970 .99109 1.0225 0.00965 .O22O .00946 O2l6 .00927 .0211 .00909 .0207 .00891 77 58 78 05 78 12 78 19 78 26 2.30 31 32 33 34 4.93696 0.69346 .98758 .69789 5.03870 .70232 .09032 .70675 .14245 .71117 5.03722 0.70219 .08684 .70645 .13697 .71071 .18762 .71497 .23878 .71923 0.98010 9.99127 .98049 .99144 .98087 .99161 .98124 .99178 .98161 .99194 1.0203 0.00873 .0199 .00856 .0195 .00839 .0191 .OO822 .0187 .00806 78 33 78 40 i 78 46 j 78 53 79 oo 2-35 3 6 :$ 39 5.19510 0.71559 .24827 .72002 .30196 .72444 .35618 .72885 41093 .73327 5.29047 0.72349 .34269 .72776 .39544 .73203 .44873 .73630 .50256 74056 0.98197 9.99210 .98233 .99226 .98267 .99241 .98301 .99256 98335 -99271 1.0184 O.OO79O .Ol8o .OO774 0176 -OO759 .0173 .00744 .0169 .00729 79 06 1 79 13 79 T 9 79 2 5 79 32 2.40 .41 .42 43 44 5.46623 0.73769 .52207 .74210 .57847 .74652 63542 .75093 69294 -75534 5-55695 0.74484 .61189 .749H 66739 75338 .72346 .75766 .78010 .76194 0.98367 9.99285 .98400 .99299 9843 1 -993 i 3 .98462 .99327 98492 -99340 I. Ol66 0.00715 0163 .OO70I .0159 .00687 .0156 -00673 .0153 .00660 7938 79 44 79 5 79 56 80 02 2.45 .46 47 .48 .49 5.75103 0.75975 .86893 -76856 .92876 .77296 .98918 .77737 5.83732 0.76621 .89512 .77049 9535 2 -77477 6.01250 .77906 .07209 .78334 0.98522 9.99353 9855 1 -99366 98579 -99379 .98607 .99391 .98635 .99403 I.OI50 0.00647 .OI47 .00634 .OI44 .OO62I .0141 .00609 .0138 .00597 80 08 80 14 80 20 80 26 80 31 2.50 6.05020 0.78177 6.13229 0.78762 0.98661 9.99415 I.OI36 0.00585 80 37 SMITHSONIAN TABLES. 4 6 TABLE 17 (continued), HYPERBOLIC FUNCTIONS. a sinh. u cosh, u tanh. u coth. u gd. u Nat. Log. Nat. Log. Nat. Log. Nat. Log. 2.50 51 52 53 54 6.05020 0.78177 .11183 -78617 .17407 .79057 .23692 .79497 .30040 .79937 6.13229 0.78762 .19310 79 I 9 I 25453 -79619 .31658 .80048 .37927 .80477 0.98661 9.9941 5 .98688 .99^26 .98714 .99438 98739 -99449 .98764 .99460 1.0136 0.00585 OI 33 .00574 .0130 .00562 .0128 .00551 .0125 .00540 80 37' So 42 80 48 80 53 80 59 *$ :P 59 6.36451 0.80377 .42926 .80816 .49464 .81256 .56068 .81695 .62738 .82134 6.44259 0.80906 .50656 .81335 .57118 .81764 .63646 .82194 .70240 .82623 0.98788 9.99470 .98812 .99481 98835 .9949 i .98858 .99501 .98881 .99511 1.0123 0.00530 .OI2O .00519 .OIl8 .00509 .0115 .00499 .0113 .00489 81 04 81 10 81 15 ! 81 20 81 25 2.60 .61 .62 ! g 6.69473 0.82573 .76276 .83012 .83146 .83451 .90085 .83890 .97092 .84329 6.76901 0.83052 .83629 .83482 .90426 -83912 .97292 .84341 7.04228 .84771 0.98903 9.99521 .98924 .99530 .98946 .99540 .98966 .99549 98987 -99558 i.oui 0.00479 .0109 .00470 .0107 .00460 .0104 .00451 .0102 .00442 81 30 81 35 81 40 81 45 81 50 \*% .67 .68 .69 7.04169 0.84768 .11317 .85206 .18536 .85645 .25827 .86083 .33190 .86522 7.11234 0.85201 .18312 .85631 .25461 .86061 .32683 .86492 .39978 .86922 0.99007 9.99566 .99026 .99575 99045 -99583 .99064 .99592 99083 -99600 i.oioo 0.00434 .0098 .00425 .0096 .00417 .0094 .00408 .0093 .00400 81 55 82 oo 82 05 82 09 82 14 2.70 7i 72 73 74 7.40626 0.86960 48137 .87398 .55722 .87836 .63383 .88274 .71121 .88712 7.47347 0.87352 5479 1 -87/83 .62310 .88213 .69905 .88644 .77578 .89074 0.99101 9.99608 .99118 .99615 .99136 .99623 99153 -99631 .99170 .99638 1.0091 0.00392 .0089 .00385 .0087 .00377 .0085 .00369 .0084 .00362 82 19 82 23 82 28 82 32 82 37 ! 2 9 79 2.80 .81 .82 83 .84 7.78935 0.89150 .86828 .89588 .94799 .90026 8.02849 .90463 .10980 .90901 8.19192 0.91339 .27486 .91776 .35862 .92213 .44322 .92651 .52867 .93088 7.85328 0.89505 93 '57 -89936 8.01065 -90367 09053 -90798 .17122 .91229 8.25273 0.91660 .33506 .92091 .41823 .92522 .50224 .92953 58710 .93385 0.99186 9.99645 .99202 .99652 .99218 .99659 99233 .99666 .99248 .99672 0.99263 9.99679 .99278 .99685. ,99292 .99691 .99306 .99698 .99320 .99704 1.0082 0.00355 .0080 .00348 .0079 .00341 .0077 -00334 .0076 .00328 1.0074 0.00321 0073 -00315 .007 1 .00309 .0070 .00302 .0069 .00296 82 41 82 45 82 50 82 54 82 58 83 02 8 3 7 83 II 83 15 83 19 2.85 .86 .87 .88 .89 8.61497 0.93525 .70213 .93963 .79016 .94400 .87907 .94837 .96887 .95274 8.67281 0.93816 .75940 .94247 .84686 .94679 .93520 .95110 9.02444 .95542 0-99333 9-99709 99346 .99715 99359 -99721 .99372 .99726 .99384 .99732 1.0067 0.00291 .0066 .00285 .0065 .00279 .0063 .00274 .0062 .00268 83 2 3 i 83 2 7 j & 83 34 83 3 8 2.90 .91 .92 93 94 9.05956 0.95711 .15116 .96148 .24368 .96584 .33712 .97021 43 '49 -97458 9.11458 0.95974 .20564 .96405 .29761 .96837 .39051 .97269 .48436 .97701 0.99396 9-99737 .99408 .99742 .99420 .99747 99531 -99752 99443 -99757 i. 006 r 0.00263 .0060 .00258 .0058 -00253 .0057 .00248 .0056 .00243 83 42 83 46 83 50 83 53 83 57 2 -95 .96 97 .98 99 9.52681 0.97895 .62308 -98331 .72031 .98768 .81851 .99205 .91770 .99641 9-579I5 0.98133 .67490 .98565 .77161 .98997 .86930 .99429 .96798 .99861 0.99454 9.99762 .99464 .99767 99475 -99771 99485 .99776 .99496 -99780 1.0055 0.00238 .0054 .00233 .0053 .00229 .0052 .00224 .0051 .00220 84 oo 84 04 84 08 84 ii 84 15 3.00 10.01787 1.00078 10.06766 1.00293 0.99505 9-99785 1.0050 0.00215 84 18 SMITHSONIAN TABLES. TABLE 17 (continued). HYPERBOLIC FUNCTIONS. 47 u sinh. u cosh, u tanh. u coth. u gd. u Xat. Log. Nat. Log. Nat. Log. Nat. Log. 3.0 .2 3 4 IO.OI79 1.00078 11.0765 .04440 12.2459 .08799 '3-5379 -i3*SS 14.9654 .17509 10.0677 1.00293 II.I2I5 .04616 12.2866 .08943 13.5748 .13273 14.9987 .17605 0.99505 9.99785 99595 -99824 .99668 .99856 .99728 .99882 .99777 .99903 1.0050 0.00215 .0041 .00176 .0033 .00144 .0027 .OOIlS .OO22 ' .00097 84 1 8' 84 50 85 20 85 47 86 ii 3-5 9 16.5426 1.21860 18.2855 .26211 20.2113 .30559 22 -3394 -3497 .24.6911 .39254 16.5728 1.21940 18.3128 .26275 20.2360 .30612 22.3618 .34951 24.7113 .39290 0.99818 9.99921 .99851 .99935 .99878 .99947 .99900 .99957 .99918 .99964 I.OOlS 0.00079 .0015 .00065 .0012 .00053 .OOIO .OOO43 .OOO8 .00036 86 32 86 52 87 10 87 26 87 41 4.0 .2 3 4 27.2899 1.43600 30.1619 47946 33-3357 .5 22 9i 36.8431 .56636 40.7193 .60980 27.3082 1.43629 30.1784 4797 33-3507 .52310 36.8567 .56652 40.7316 .60993 0-99933 9-99971 -99945 -99976 99955 -99980 .99963 .99984 .99970 .99987 I.OOO7 O.OOO29 .OOO5 .OOO24 .0004 .00020 .OOO4 .OOOl6 .OOO3 .OOOI3 11% 88 17 88 27 88 36 4-5 '& 9 45.0030 1.65324 49-7371 .69668 54.9690 .74012 60.7511 .78355 67.1412 .82699 45.0141 1-65335 49.7472 .69677 54.9781 .74019 60.7593 -78361 67.1486 .82704 0-99975 9-99989 .99980 .99991 99983 -99993 .99986 .99994 .99989 -99995 1.0002 o.ooen .0002 .00009 .0002 .00007 .0001 .00006 .0001 .00005 88 44 88 51 88 57 8903 8909 5.0 74.2032 1.87042 74.2099 1.87046 0.99991 9-99996 i.oooi 0.00004 89 M TABLE 18, Factorials. See Table 16 for logarithms of the products 1.2.3. * from i to 100. See Table 32 for log. T (n + i) for values of n between i.ooo and 2.000. n i n : n: = i. 2. 3. 4 . . . n n l i. i I 2 -5 2 2 3 .16666 66666 66666 66666 66667 6 3 4 .04166 66666 66666 66666 66667 24 4 5 00833 33333 33333 33333 33333 1 20 5 6 0.00138 88888 88888 88888 88889 720 6 7 .00019 84126 98412 69841 26984 5040 7 8 9 .00002 48015 87301 58730 15873 .00000 27557 31922 39858 90653 40320 3 62880 8 9 10 .00000 02755 73192 23985 89065 36 28800 10 ii o.ooooo 00250 52108 38544 17188 399 16800 ii 12 .OOOOO OOO2O 87675 69878 68099 4790 01600 12 T 3 .00000 oooo i 60590 43836 82161 62270 20800 J 3 14 15 .00000 ooooo 11470 74559 77297 .00000 ooooo 00764 71637 31820 8 71782 91200 130 76743 68000 H 15 16 o.ooooo ooooo 00047 79477 33239 2092 27898 88000 16 T 7 .ooooo ooooo 00002 81145 72543 35568 74280 96000 T 7 18 .ooooo ooooo ooooo 15619 20697 6 40237 37057 28000 18 ^9 .ooooo ooooo ooooo 00822 06352 121 64510 04088 32OOO !9 20 .ooooo ooooo ooooo 00041 10318 2432 90200 81766 40000 20 SMITHSONIAN TABLES. 4 8 TABLE 19. EXPONENTIAL FUNCTION. X log, ('*) ex e-x X logio(< 1 _ 1) - This factor occurs in the equation r =o.6745A/ ' - for the probable error of the arithmetic mean. w = 1 2 3 4 5 6 7 8 9 00 0.4769 0-2754 0.1947 o. 1 508 0.1231 o. 1 04 1 0.090 1 0.0795 10 0.0711 0.0643 .0587 .0540 .0500 .0465 0435 .0409 .0386 0365 20 .0346 .0329 .0314 .0300 .0287 .0275 .0265 0255 .0245 .0237 30 .0229 .0221 .OJI4 .0208 .0201 .0196 .0190 .0185 .0180 0175 40 .0171 .0167 .0163 .0159 O'SS .0152 .0148 .0145 .0142 .0139 50 0.0136 0.0134 0.0131 0.0128 0.0126 0.0124 O.OI22 0.0119 0.0117 0.0115 60 .0113 .Oil I .01 10 .0108 .0106 .0105 .0103 .0101 .0100 .0098 ?o .0097 .0096 .0094 .0093 .0092 .0091 .0089 .0088 .0087 .0086 80 .0085 .0084 .0083 .0082 .0081 .0080 .0079 .0078 .0077 .0076 90 .0075 .0075 .0074 .0073 .0072 .0071 .OO7I .0070 .0069 .0068 TABLE 28. -LEAST SQUARES. Values of the factor 0.8453\/ y- 1 - \ ?i\?i xj This factor occurs in the approximate equation r =0.8453 ( for the probable error of a single observation. ( / ) n = 1 2 3 4 5 6 7 8 9 00 0.5978 0-345 1 0.2440 0.1890 0.1543 0.1304 0.1130 0.0996 10 0.0891 0.0806 .0736 .0677 .0627 05^3 .0546 0513 .0483 0457 20 0434 .O4I2 0393 .0376 .0360 345 033 2 .0319 .0307 .0297 30 .0287 .0277 .0268 .0260 .0252 .0245 .0238 .0232 .0225 .0220 40 .0214 .0209 .0204 .0199 .0194 .0190 .0186 .0182 .0178 .0174 50 0.0171 O.OI67 0.0164 0.0161 0.0158 0.0155 0.0152 o.oi 50 0.0147 0.0145 60 .0142 .0140 0137 0135 0133 .0131 .0129 .0127 .0125 .0123 70 .0122 .0120 .0118 .0117 .0115 .0113 .0112 .0111 .0109 .0108 80 .OIO6 .OIO5 .0104 .0102 .OIOI .0100 .OO99 .0098 .0097 .0096 90 .0094 .0093 .0092 .0091 .0090 .0089 .0089 .0088 .0087 .0086 TABLE 29. -LEAST SQUARES. Values of 0.8453 r This factor occurs in the approximate equation r n =: 0.8453 n 1 for the probable error of the arithmetical mean. n 1 2 3 4 5 6 7 8 9 00 * 0.4227 0.1993 0.1220 0.0845 0.0630 0.0493 0.0399 0.0332 10 0.0282 0.0243 .0212 .oiScS .0167 .0151 .0136 .0124 .01 14 .0105 20 .0097 .0090 .0084 .0078 .0073 .0069 .0065 .0061 .0058 0055 30 .0052 .0050 .0047 .0045 .0043 .0041 .0040 .0038 .0037 0035 40 .0034 .0033 .0031 .0030 .0029 .0028 .0027 .0027 .0026 .0025 50 0.0024 0.002T 0.0023 O.OO22 O.OO22 O.OO2I 0.0020 O.OO2O 0.0019 0.0019 60 .0018 .OOlS .0017 .OOI7 .OOI7 .OOl6 .OOl6 .OOl6 .0015 .0015 70 .0015 .OOI4 .0014 .0014 .0013 .0013 .OOI3 .OOI3 .0012 .0012 80 .0012 .OOI2 .0011 .0011 .OOI I .OOI I .OOI I .0010 .0010 .OOIO 90 .0010 .0010 .0010 .OOO9 .OOO9 .0009 .0009 .0009 .0009 .0009 SMITHSONIAN TABLES. TABLE 3O. LEAST SQUARES. Observation equations : aizi + b!Z 2 + . . . liz q = M b weight p t a 2 zi + b 2 z 2 + . . . I 2 z q = M 2 . weight p 2 a n z! + b n z 2 + . . . l n zq = M n , weight p n . Auxiliary equations : [paa] = piaf + P2af + p n a^. [pab] = Piaib! + p 2 a 2 b 2 + . . . p n a n b n . [paM] = piaiMi -f p 2 a 2 M 2 -f . . . p n a n M n . Normal equations : fpaa]zi-f [pab]z 2 + . . . [pal]z q = [paM] pabJ Zl + [pbb]z2 + . . . [pbl]z q = [pbM] [pla] Zl + [plb]z 2 + . . .' [plljzq = Solution of normal equations in the form, Zl = AJpaM] + BifpbM] -f . . . I z 2 = A 2 [paM] + B 2 [pbM] + . . . I zq = A n [paM] + B n [pbMJ + .'. . L n [plM], gives : weight of zi = pzi = (Aj) 1 ; probable error of zi = - weight of z 2 = pz 2 = (B 2 ) -1 ; probable error of z 2 = \/Pz 2 weight of z q = p Zq = (Ln)" 1 ; probable error of z q = wherein r = probable error of observation of weight unity = 0.6745 -i/ (q unknowns.) Arithmetical mean, n observations: _ r = 0.6745 A/ (approx.) =probable error of ob- * n I \/n(n i)' servation of weight unity. / S V2 _ 0.8453 2 V -- V _ 0.453 V r = 0.67 45\/ : -- 7==. (approx.) = probable error \n(n-i) n Vn-i of mean. Weighted mean, n observations: /Spv2 r r = 0.6745 \ ~ ; r = -==o. Probable error (R) of a function (Z) of several observed quantities zi, z 2 , . . . whose probable errors are respectively, i - i, r.> Z'= f (" Zl , z 2 , . . .) Examples : Z --= zi z 2 + . . . R2 = r\ + r\ Z = Az! Bza . . . R 2 =A 2 r\ + Z = zi z 2 . R- = z i 2 r!5-fj SMITHSONIAN TABLES. 6o TABLE 31 . DIFFUSION. Inverse * values of < /c = i -77 log x = log (2y) + logx/Xtf. t expressed in seconds. = log 6 + logx/^A / expressed in days. = log 7 + log \/kf. " years. k = coefficient of diffusion.! c = initial concentration. v = concentration at distance x, time t. v/c log 2? 2? logfi 6 log y Y 0.00 + 00 + 00 + 00 + 00 oo oo .01 0.56143 3.6428 ! 3-02970 1070.78 4.31098 20463. .02 S'719 3.2900 ; 2.98545 967.04 .26674 18481. 3 .48699 3.0690 .95525 902.90 23654 17240. .04 .46366 2.9044 .93132 85373 .21261 16316. 005 0.44276 2.7718 2.91102 814.74 4.19231 r 557i- .06 .42486 2.6598 .89311 781.83 .17440 14942. .07 .40865 i 2.5624 .87691 753-20 .15820 14395- .08 39372 2.475 .86198 727.75 M327 13908. .09 37979 2-3977 .84804 704.76 12933 13469. 0.10 .1 1 0.36664 2.3262 .35414 2.2602 2.83490 .82240. 66+36 4.11619 .10369 13067. 12697. .12 .34218 2.1988 .81044 646.31 .09173 12352- T 3 .33067 2.1413 79893 629.40 .08022 12029. .14 .31954 2.0871 .78780 613.47 .06909 11724. 0.15 0.30874 2.0358 2.77699 598.40 4.05828 11436. .16 .29821 1.9871 .76647 584.08 .04776 11162. 17 .28793 1.9406 75619 57041 .03748 10901. .18 .27786 1.8961 .74612 557-34 .02741 10652. .19 .26798 1.8534 .73624 544.80 OI 753 10412. 0.20 0.25825 1.8124 2.72651 532.73 4.00780 10181. .21 .24866 1.7728 .71692 521.10 3.99821 9958.9 .22 .23919 1.7346 .70745 509.86 .98874 9744.1 2 3 .22983 1.6976 .69808 498.98 97937 9536.2 .24 .22055 i. 6617 .68880 488.43 .97010 9334-6 025 .26 0.21134 .20220 1.6268 I -593 2.67960 .67046 478.19 468.23 3.96089 95^75 9138.9 8948.5 ' -27 .19312 1.5600 .66137 458.53 .94266 8763-2 .28 .18407 1.5278 .65232 449.08 .93361 8582.5 .29 .17505 1.4964 .6433! 439-85 .92460 8406.2 0.30 0.16606 | 1.4657 2.63431 430.84 3.91560 8233-9 3 1 .15708 1.4357 62533 422.02 .90662 8065.4 3 2 .14810 1.4064 .61636 4I3-39 89765 7900.4 33 .13912 1.3776 .60738 404.93 .88867 7738.8 34 13014 1-3494 .59840 396.64 .87969 7580-3 035 0.12114 1.3217 2.58939 388.50 3.87068 7424.8 36 37 .11211 .10305 1.2945 1.2678 .58037 57I3 1 38051 372.66 .86166 .85260 7272.0 7122.0 38 .09396 1.2415 .56222 364-93 .8435' 6974.4 39 .08482 I.2I57 55308 357-34 .83437 6829.2 0.40 .41 .42 43 0.07563 I.I9O2 .06639 1.1652 .05708 1.1405 .04770 1.1161 2-54389 .53464 52533 5*595 349.86 342.49 335-22 328.06 3.82518 .81593 .80662 79724 6686.2 6545-4 6406.6 6269.7 44 .03824 1.0920 .50650 320.99 .78779 6134.6 045 002870 1.0683 2.49696 314.02 3-77825 6001.3 .46 .01907 1.0449 48733 307-13 .76862 5869.7 47 .00934 1.0217 .47760 300.33 75889 5739-7 .48 9.99951 0.99886 46776 293.60 74905 5611.2 49 .98956 0.97624 45782 286.96 739 11 5484.1 050 9-97949 \ 0.95387 2-44775 280.38 3.72904 5358.4 t Kelvin, Mathematical and Physical Papers, vol. III. p. 428 ; Becker, Am. Jour, of Sci. vol. III. 1897, p. 280*. *For direct values see table 24. SMITHSONIAN TABLES. TABLE 31 (continued). DIFFUSION. 61 vie log 2? 2q log 6 6 logy Y 0.50 9-97949 0.95387 2-44775 280.38 3.72904 5358.4 5 1 .96929 93 '74 43755 273-87 .71884 5234.I 5 2 .95896 .90983 .42722 26743 .70851 5 1 1 1 .0 53 .94848 .88813 .41674 261.06 .69803 4989.1 54 93784 .86665 .40610 254-74 .68739 4868.4 0.55 9.92704 0.84536 2-3953 248.48 3-67659 4748.9 56 .91607 .82426 38432 242.28 .66561 4630-3 57 .90490 80335 373 l6 236.13 65445 4512.8 .58 89354 .78260 .36180 230.04 .64309 4396.3 59 .88197 .76203 35023 223.99 .63152 4280.7 0.60 9.87018 0.74161 2.33843 217.99 3-6I973 4166.1 .61 85815 72135 ! -32640 212.03 .60770 4052.2 .62 .84587 .70124 .31412 2O6. 1 2 59541 3939-2 63 83332 .68126 3 OI 57 200.25 .58286 3827.0 .64 .82048 66143 . .28874 194.42 57003 37I5-6 0.65 9.80734 0.64172 2.27560 I88.6 3 3.55689 3604.9 .66 .79388 .62213 .26214 182.87 54343 3494-9 .67 .78008 .60266 24833 I77.I5 .52962 3385.4 .68 .76590 58331 .23416 171.46 5 I 545 3276.8 .69 7 5 '33 56407 .21959 165.80 .50088 3168.7 0.70 9-73 6 34 0.54493 2.20459 160.17 3.48588 3061.1 7* .72089 .52588 .18915 154.58 47044 2954.2 .72 70495 .50694 .17321 I49.OI 4545 2847.7 73 .68849 .48808 15675 143-47 43804 2741.8 74 .67146 .46931 .13972 '37-95 .42101 2636.4 0.75 9.65381 0.45062 2.12207 132.46 340336 25314 76 6355 .43202 .10376 126.99 38505 2426.9 77 .61646 .41348 .08471 121.54 .36600 2322.7 .78 79 .59662 57590 39502 .37662 .06487 .04416 1 1 6. 1 1 110.70 .34616 32545 2219.0 2115.7 0.80 9-55423 0.35829 2.02249 105-31 3-30378 2012.7 .81 53 I 5 .34001 1-99975 1 99-943 .28104 1910.0 .82 5 75 8 .32180 .97584 94.589 25713 1807.7 83 .84 -48235 455 6 4 30363 .28552 -95061 .92389 89.250 83.926 .23190 .20518 1705.7 1603.9 0.85 9.42725 0.26745 I - 8 955 I 78.615 3.17680 1502.4 .86 39695 .24943 .86521 73-3I7 .14650 1401.2 .87 36445 23*45 .83271 68.032 .11400 1300.2 .88 .32940 21350 .79766 62.757 07895 1199.4 .89 29!35 19559 7596i 57492 3.04090 1098.7 0.90 9.24972 0.17771 1.71797 52.236 2.99926 998.31 .91 .20374 .15986 .67200 46.989 95329 898.03 .92 i5 2 39 .14203 .62065 41.750 .90194 797.89 93 .09423 .12423 .56249 36.516 .84378 697-88 94 9.02714 .10645 49539 31.289 .77668 597.98 0.95 8.94783 0.08868 1.41609 26.067 2.69738 498.17 .96 .85082 07093 3 I 9Q7 20.848 .60036 398.44 97 .72580 .05319 .19406 I5-633 47535 298.78 .98 .54965 -03S45 .01791 10.421 .29920 199.16 99 .24859 .01773 0.71684 5.21007 1.99813 99-571 1.00 oo ; o.ooooo 00 o.ooooo oo o.ooo il 1 SMITHSONIAN TABLES. 62 TABLE 32. GAMMA FUNCTION, Value of log JT- ^dx + 10. Values of the logarithms + 10 of the " Second Eulerian Integral " (Gamma function) S. log n)-|-ic for values of between i and 2. When has values not lying between i and 2 the value of the ft nction can be readily calculated from the equation T(w-f-i) = I\) = ( i) . . . ( r)T(n r). n 1 2 3 4 5 6 7 8 9 1OO 9-99 97497 95001 925*2 90030 87555 85087 82627 80173 77727 I.OI 75287 72855 7043 68011 65600 63*96 60798 58408 56025 53648 1.02 5 I2 79 48916 46561 44212 41870 39535 37207 34886 32572 30265 1.03 1.04 27964 05334 25671 03108 23384 21104 98677 18831 9647* 16564 94273 4305 92080 12052 89895 09806 87715 07567 5544 1.05 9-9883379 81220 79068 76922 74783 72651 70525 68406 66294 64188 i. 06 62089 59996 579*o 55830 5375,7 5*690 49630 47577 4553 43489 1.07 4M55 39428 37407 35392 33384 3*382 29387 27398 254*5 23439 i. 08 21469 19506 17549 *5599 13655 mn 29785 07860 P.5M*. 04029 1.09 02123 00223 98329 96442 9456i 92686 90818 88956 87100 81256 1.10 9.9783407 81570 7973 s 779*4 76095 74283 72476 70676 68882 67095 i. n 65313 63538 61768 60005 58248 56497 54753 530*4 51281 49555 1. 12 47834 46120 44411 42709 4*013 39323 37638 3596o 34288 32622 1.13 30962 29308 27659 26017 24381 22751 21126 19508 17896 16289 I.I4 14689 13094 09922 08345 06774 05209 03650 02096 00549 1.15 9.9699007 9747 i 95941 944*7 92898 9*386 89879 88378 86883 85393 1.16 83910 82432 80960 79493 78033 76578 75*29 73686 72248 70816 1.17 .69390 67969 66554 63742 62344 60952 59566 58*85 56810 l.lo 55440 54076 52718 5*366 50019 48677 4734* 46011 ' 44687 43368 1.19 42054 40746 39444 38147 36856 35570 34290 33016 3*747 30483 1.20 9.9629225 27973 26725 25484 24248 23017 21792 20573 *935 8 18150 1. 21 16946 15748 14556 '3369 12188 IIOI I 08675 06361 1.22 05212 04068 02930 01796 00669 99546 98430 973*8 96212 95*** 1.2 3 594015 92925 91840 90760 89685 88616 87553 86494 8544* 84393 1.24 ' 83350 82313 81280 80253 79232 78215 77204 76198 74201 1.25 9.9573211 72226 71246 70271 69301 68337 67377 66423 65474 6453 1.26 1.27 63592 54487 62658 53604 61730 52727 60806 5*855 59888 50988 58975 50126 58067 49268 57*65 48416 56267 47570 55374 46728 1.28 45891 45059 44232 434*0 42593 41782 40975 40173 39376 38585 1.29 37798 37oi6 36239 35467 347oo 33938 32429 31682 30940 1.30 9-9530203 29470 28743 28021 27303 26590 25883 25180 24482 23789 1.31 23100 22417 21739 21065 20396 19732 19073 18419 17770 17125 1.32 16485 '5850 15220 *4595 *3975 *3359 12748 12142 1 1 541 10944 i-33 10353 09766 09184 08606 08034 07466 06903 06344 0579* 05242 i-34 04698 04158 03624 03094 02568 02048 01532 OIO2I 00514 00012 1.35 9-94995 * 5 99023 98535 98052 97573 97100 96630 96166 95706 95251 1.36 94800 94355 939*3 93477 93044 92617 92*94 9*776 91362 90953 9549 90149 89754 89363 88977 88595 88218 87846 874/8 87II5 I'js 86756 86402 86052 85707 85366 85030 84698 84371 84049 S373I i-39 83417 83108 82803 82503 82208 81916 81630 81348 81070 80797 1.40 9.9480528 80263 80003 79748 79497 79250 79008 78770 78537 78308 1.41 78084 77864 77648 77437 7723 77027 76829 76636 76446 76261 1.42 76081 75905 75733 75565 75402 75243 75089 74939 74793 74652 i-43 745'5 74382 74254 74*30 74010 73894 73783 73676 73574 73476 1.44 73382 73292 73207 73*25 73049 72976 72908 72844 72784 72728 Legendre's "Exercises de Calcul Integral," tome SMITHSONIAN TABLES. TABLE &2 (continued). GAMMA FUNCTION. N 1 2 3 4 5 6 7 8 9 1.45 9.9472677 72630 72587 72549 72514 72484 72459 72437 72419 72406 1.46 72397 72393 72392 72396 72404 72416 72432 72452 72477 72506 1.47 72539 72576 72617 72662 72712 72766 72824 72886 72952 73022 1.48 73097 73175 73258 73345 73436 7353 1 73630 73734 73841 73953 1.49 74068 74188 743 1 2 74440 74572 74708 74848 74992 75 ! 4i 75293 1.50 9.9475449 75610 75774 75943 76116 76292 76473 76658 76847 77040 l -5 l 77237 774"- 77642 77851 78064 78281 78502 78727 78956 79189 1.52 79426 79667 79912 80161 80414 80671 80932 81196 81465 81738 i-53 i-54 82015 84998 82295 85318 82580 85642 82868 85970 83161 86302 83457 86638 83758 86977 84062 87321 84370 87668 84682 88019 1.55 9.9488374 88733 89096 89463 89834 90208 90587 90969 9 r 355 91745 1.56 92139 92537 92938 93344 93753 94166 94583 95004 95429 95 8 57 l >57 96289 96725 97165 97609 98056 98508 98963 99422 99885 00351 i-58 i-59 500822 05733 01296 06245 01774 06760 02255 07280 02741 07803 03230 08330 03723 08860 04220 09395 04720 09933 05225 J 0475 1.60 9.9511020 11569 I2I22 12679 13240 13804 M372 14943 J 55 T 9 16098 1.61 16680 17267 17857 18451 19048 19649 20254 20862 21475 22091 1.62 22710 23333 23960 24591 25225 25863 26504 27149 27798 28451 1.63 29107 29766 30430 31097 3*767 32442 33120 338oi 34486 35 X 75 1.64 35867 36563 37263 37966 38673 39383 40097 40815 41536 42260 1.65 9.9542989 43721 44456 45*95 4593 s 46684 47434 48187 48944 49704 1.66 50468 5 I2 36 52007 52782 5356o 54342 55 I2 7 559*6 56708 5754 1.67 58303 59106 59913 60723 61536 62353 63174 63998 64825 65656 1.68 66491 67329 68170 69015 69864 70716 7i57i 7243 73293 74159 1.69 75028 759oi /6777 77657 78540 79427 80317 81211 82108 83008 1.70 9.9583912 84820 85731 86645 87563 88484 89409 90337 91268 92203 1.71 93 HI 94083 95028 95977 96929 97884 98843 99805 00771 01740 1.72 602712 03688 04667 05650 06636 07625 08618 09614 10613 11616 i-73 12622 13632 14645 15661 16681 17704 18730 19760 20793 21830 1.74 22869 23912 2 4959 26009 27062 28118 29178 30241 31308 32377 1.75 9-963345I 34527 35607 36690 37776 38866 39959 41055 42155 43258 1.76 44364 45473 46586 47702 48821 49944 51070 52199 5333 1 54467 i-77 55606 56749 57894 59043 60195 6135 62509 63671 64836 66004 1.78 67176 68351 69529 70710 71895 73082 74274 75468 76665 77866 1.79 79070 80277 81488 82701 83918 85138 86361 87588 88818 90051 1.80 9.9691287 92526 93768 95 OI 4 96263 975'5 98770 00029 01291 02555 1.81 703823 05095 06369 07646 08927 IO2II 11498 12788 14082 15378 1.82 16678 17981 19287 20596 21908 23224 24542 25864 27189 28517 1.83 29848 31182 32520 33860 35204 36551 379oo 39254 40610 41969 1.84 43331 44697 46065 47437 48812 50190 5'57i 52955 54342 55733 1.85 9.9757126 58522 59922 61325 62730 64139 6555 1 66966 68384 69805 1.86 71230 72657 74087 75521 76957 78397 79839 81285 82734 84186 1.87 1.88 85640 800356 87098 01844 88559 03335 90023 04830 91490 06327 92960 7 827 94433 0933 i 95909 10837 97389 12346 98871 !3 8 59 1.89 : 5374 16893 18414 J9939 21466 22996 24530 26066 27606 29148 1.90 9.9830693 32242 33793 35348 36905 38465 40028 41595 43 l6 4 44736 1.91 46311 47890 4947 i 5 I0 55 52642 54232 55825 5742i 59020 60621 1.92 62226 63834 65445 67058 68675 70294 71917 73542 75 J 7o 76802 i-93 1.94 78436 9493 s 80073 96605 81713 98274 83356 99946 SJ002 01621 86651 03299 88302 04980 91614 08350 9J2U5 10039 1.95 9.9911732 13427 !5 I2 5 16826 18530 20237 21947 23659 25375 27093 1.96 28815 30539 32266 33995 35728 37464 39202 40943 42688 44435 1.97 46185 47937 49693 5H5 1 53213 54977 56744 58513 60286 62062 1.98 63840 65621 67405 69192 70982 72774 7457 76368 78169 79972 i-99 81779 83588 85401 87216 89034 90854 92678 9454 96333 98165 SMITHSONIAN TABLES. 6 4 TABLE 33. ZONAL SPHERICAL HARMONICS. Degrees P, p, p, p. PS p. * 1 O + I.OOOO + I.OOOO + I.OOOO + I.OOOO + I.OOOO + I.OOOO + I.OOOO I .9998 9995 .9991 9985 9977 .9968 9957 2 9994 .9982 9963 9939 9909 .9872 9830 3 .9986 9959 .9918 9863 9795 .9714 .9620 4 .9976 9927 9854 975 .9638 9495 9329 's + 0.9962 + 0.9886 + 0.9773 + 0.9623 + 0.9437 + 0.9216 + 0.8962 6 9945 .9836 .9674 9459 .9194 .8881 .8522 7 9925 9777 9557 .9267 .8911 .8492 .8016 8 9903 9709 9423 .9048 .8589 .8054 7449 9 .9877 9633 9273 .8803 .8232 7570 .6830 10 + 0.9848 + 0.9548 + 0.9106 + 0.8532 + 0.7840 + 0.7045 + 0.6164 ii .9816 9454 8923 .8238 7417 .6483 .5462 12 .9781 9352 .8724 .7920 .6966 .5891 47 3 1 13 9744 .9241 .8511 .7582 .6489 5273 .3980 14 9703 .9122 .8283 .7224 5990 4635 .3218 15 + 0.9659 + 0.8995 + 0.8042 + 0.6847 + 0.5471 + 0.3983 + 0.2455 16 .9613 .8860 7787 6454 4937 3323 .+ -1700 7 95 6 3 .8718 75 T 9 .6046 4391 .2661 + .0961 18 .9511 .8568 .7240 .5624 3836 .2002 + .0248 19 9455 .8410 .6950 .5192 .3276 1353 -433 20 -f 0-9397 + 0.8245 + 0.6649 + 0.4750 + 0.2715 + 0.0719 0.1072 21 9336 .8074 6338 .4300 .2156 + .OI06 .1664 22 .9272 7895 .6019 3845 .1602 .0481 .2202 23 .9205 .7710 .5692 3386 .1057 -1038 .2680 24 9I3S 75*8 5357 .2926 0525 - -1558 3094 25 + 0.9063 + 0.7321 + 0.5016 + 0.2465 + 0.0009 O.2O4O 0.3441 26 .8988 .7117 .4670 .2007 .0489 .2478 3717 27 .8910 .6908 4319 *553 .0964 .2869 .3922 28 .8829 .6694 3964 .1105 -1415 .3212 4053 2 9 .8746 .6474 .3607 .0665 - -1839 3502 30 + 0.8660 + 0.6250 + 0.3248 + 0.0234 0.2233 0.3740 0.4102 31 8572 .6021 .2887 -0185 2595 3924 .4022 3 2 .8480 .5788 2527 -059* .2923 4053 .3877 33 .8387 5551 .2167 .0982 .3216 .4127 .3671 34 .8290 53 10 .1809 -1357 3473 .4147 .3409 35 + 0.8192 + 0.5065 + 0.1454 0.1714 0.3691 0.4114 0.3096 36 .8090 .4818 .1102 .2052 3871 .4031 2738 37 .7986 45 6 7 0755 .2370 .4011 .3898 2 343 38 .7880 43 I 4 .0413 .2666 .4112 3719 .1918 39 7771 4059 .0077 .2940 .4174 3497 .1470 40 + 0.7660 + 0.3802 0.0252 0.3190 0.4197 0.3236 0.1006 41 7547 3544 0574 .3416 .4181 2939 -0535 42 743 1 3284 .0887 .3616 .4128 .2610 .0064 43 73H 3023 .IIQI 379 1 .4038 2255 + .0398 44 7193 .2762 .1485 3940 3914 .1878 + .0846 45 + 0.7071 + 0.2500 0.1768 0.4063 0.3757 0.1484 + 0.1271 46 .6947 2238 .2040 .4158 .3568 .1078 .1667 47 .6820 1977 .2300 .4227 335 .0665 .2028 48 49 .6691 .6561 .1716 .1456 2547 .2781 .4270 .4286 3105 .2836 -0251 + .0161 2350 .2626 50 + 0.6428 + 0. 1 1 98 0.3002 0.4275 0.2545 + 0.0564 + 0.2854 SMITHSONIAN TABLES. * Calculated by Mr. C. E. Van Orstrand for this publication. TABLE ^ (continued). ZONAL SPHERICAL HARMONICS. I Degrees PI P 2 P 3 P 4 PS p PT 5 + 0.6428 + 0.1198 0.3002 0.4275 0.2545 + 0.0564 + 0.2854 5 1 .6293 .0941 .3209 4239 2235 0954 303 1 52 6157 .0686 .3401 .4178 .1910 .1326 3 '54 53 .6018 .0433 3578 .4093 1571 .1677 .3221 54 1 5878 .0182 3740 3984 .1223 .2002 3234 1 55 + 0-5736 0.0065 0.3886 -0.3852 0.0868 + 0.2297 + 0.3191 56 5592 .0310 .4016 .3698 .0509 .2560 3095 57 5446 .0551 4I3 1 3524 .0150 .2787 .2947 58 5299 ,0788 .4229 3331 + .0206 .2976 .2752 59 S'S .1021 .4310 3"9 + .0557 3125 .2512 60 + 0.5000 0.1250 0-4375 0.2891 + 0.0898 4 0.3232 + 0.2231 61 .4848 .1474 4423 .2647 .1229 .3298 .1916 62 4695 .1694 4455 .2390 1545 3321 1572 63 4540 .1908 447 1 .2121 .1844 332 .1203 64 4384 .2117 .4470 .1841 .2123 .3240 .0818 65 + 0.4226 0.2321 0.4452 O.T552 + 0.2381 + 0.3138 + 0.0422 66 .4067 .2518 .4419 .1256 .2615 .2997 + .0022 67 3907 .2710 4370 0955 .2824 .2819 -0375 68 3746 .2895 4305 . -0651 3005 .2606 -0763 69 3584 374 .4225 0344 3158 .2362 -"35 70 + 0.3420 0.3245 0.4130 0.0038 + 0.3281 + 0.2089 0.1485 71 3256 .3410 .4021 + .0267 3373 .1791 .1808 72 .3090 .3568 .3898 .0568 3434 .1472 .2099 73 .2924 3718 .3761 .0864 3463 .1136 2352 74 .2756 .3860 .3611 "53 .3461 .0788 2563 75 + 0.2588 0-3995 0.3449 + 0.1434 + 0.3427 + 0.0431 0.2730 76 .2419 4122 3275 1705 3362 + .0070 .2850 77 .2250 .4241 .3090 .1964 .3267 .0290 .2921 78 .2079 4352 .2894 .2211 3143 .0644 .2942 79 .1908 4454 .2688 2443 .2990 .0990 .2913 80 4-0.1736 0.4548 0.2474 + 0.2659 + 0.2810 0.1321 0.2835 Si .1564 4633 .2251 .2859 .2606 1035 .2708 82 .1392 .4709 .2020 .3040 2378 .1927 2536 83 .1219 4777 1783 3203 .2129 .2193 .2321 84 .1045 .4836 1539 3345 .1861 .2431 .2067 II + 0.0872 .0698 0.4886 .4927 0.1291 .1038 + 0.3468 + 0.1577 .1278 0.2638 .2810 0.1778 .1460 87 0523 4959 .0781 .3648 .0969 .2947 .1117 88 89 0349 0175 .4982 4995 .0522 .0262 3704 3739 .0651 .0327 345 3105 0755 .0381 90 + o.oooo 0.5000 o.oooo + 0.3750 + o.oooo 0.3125 o.oooo SMITHSONIAN TABLES. 66 TABLE 34. CYLINDRICAL HARMONICS OF THE OTH AND 1ST ORDERS Values when n = o and i of the Bessel function J n (x) Ji(x) /'(*) = dJo(x) dx X /(*) /i 00 X /<*) /(*) X Jo(x) /!(*) X Jo(x) Ji(x) .00 unity zero .50 .938470 .242268 1.00 .765198 .440051 1.60 .511828 557937 .01 999975 .005000 5i .936024 246799 .01 .760781 .443286 5i .506241 559315 .02 .999900 .010000 52 933534 .251310 .02 756332 .446488 52 .500642 560653 03 999775 .014998 53 .930998 255803 03 751851 .449658 53 .495028 561951 .04 .999600 .019996 54 .928418 .260277 .04 747339 452794 54 .489403 .563208 .05 999375 .024992 .55 925793 .264732 1.05 .742796 455897 1.55 .483764 .564424 .06 .999100 .029987 56 .923123 .269166 .06 .738221 .458966 56 .478114 .565600 .07 998775 034979 57 .920410 27358i .07 7336i6 .462OOI 57 472453 566735 .08 .998401 .039968 58 .917652 277975 .08 .728981 .465003 58 .466780 .567830 .09 .997976 .044954 59 .914850 282349 .09 .724316 .467970 59 .461096 568883 .10 .997502 .049938 .60 .912005 .286701 1.10 .719622 .470902 1.60 455402 569896 .11 .996977 .054917 .61 .909116 .291032 .11 .714898 .473800 .61 .449698 .570868 .12 .996403 .059892 .62 .905184 295341 .12 .710146 .476663 .62 443985 571798 13 995779 .064863 63 .903209 .299628 13 705365 .479491 63 .438262 .572688 .14 .995106 .069829 .64 .900192 303893 .14 .700556 .482284 .64 432531 573537 .15 994383 .074789 .65 .897132 308135 1.16 .695720 .485041 1.65 .426792 .574344 .16 .993610 .079744 .66 .894029 312355 .16 .690856 .487763 .66 .421045 575IH i? .992788 .084693 67 .890885 316551 17 685965 .490449 67 .415290 575836 .18 .991916 .089636 .68 .887698 .320723 .18 .681047 .493098 .68 .409528 .576520 .19 .990995 .094572 .69 .884470 .324871 .19 .676103 .495712 .69 .403760 577163 .20 .990025 .099501 .70 .881201 .328996 1.20 .671133 .498289 1.70 397985 577765 .21 .989005 .104422 7i .877890 333096 .21 .666137 .500830 7i .392204 .578326 .22 987937 .109336 72 874539 337170 .22 .661116 .503334 .72 .386418 578845 23 .986819 .114241 73 .871147 .341220 2 3 .656071 .505801 73 .380628 579323 .24 .985652 .119138 74 .867715 345245 .24 .651000 .508231 74 .374832 57976o .25 .984436 .124026 .75 .864242 .349244 1.26 .645906 .510623 1.75 369033 580156 .26 .983171 .128905 76 .860730 3532i6 .26 .640788 .512979 76 363229 580511 .27 .981858 133774 77 .857178 357i63 27 635647 .515296 77 357422 .580824 .28 .980496 .138632 .78 853587 .361083 .28 .630482 .517577 78 351613 .581096 .29 .979085 .143481 79 .849956 364976 .29 625295 .519819 79 .345801 581327 .30 .977626 .148319 .80 .846287 .368842 1.30 .620086 .522023 1.80 339986 581517 3i .976119 153146 .81 .842580 .372681 3i .614855 .524189 .81 334170 .581666 32 974563 .157961 .82 .838834 .376492 32 .609602 .526317 .82 328353 581773 33 .972960 .162764 83 835050 380275 33 .604329 .528407 83 322535 .581840 34 .971308 167555 84 .831228 .384029 34 .599034 .530458 .84 .316717 581865 .35 .969609 172334 .85 .827369 .387755 1.35 593720 .532470 1.85 .310898 .581849 36 .967861 .177100 .86 823473 391453 36 .588385 .534444 .86 .305080 58i793 37 .966067 .181852 87 .819541 395I2I 37 583031 -536379 87 .299262 .581695 38 .964224 .186591 .88 8i557i .398760 38 577658 .538274 .88 .293446 58i557 39 962335 .191316 .89 .811565 .402370 39 .572266 .540131 .89 .286631 58i377 .40 .960398 .196027 .90 .807524 405950 1.40 .566855 .541948 1.90 .281819 581157 .41 .958414 .200723 .91 .803447 .409499 .41 .561427 .543726 .91 .276008 .580896 .42 .956384 .205403 .92 799334 .413018 42 55598i -545464 .92 .270201 .580595 43 .954306 .210069 93 .795186 .416507 43 .550518 .547162 93 .264397 .580252 44 .952183 .214719 94 .791004 .419965 44 .545038 .548821 94 .258596 .579870 .45 .950012 219353 .95 .786787 423392 1.45 539541 .550441 1.95 .252799 .579446 .46 947796 .223970 .96 782536 .426787 .46 .534029 .552020 .96 .247007 578983 47 945533 .228571 97 778251 4,30151 47 528501 .553559 97 .241220 .578478 48 .943224 233154 .98 773933 433483 .48 .522958 .555059 .98 235438 577934 49 .940870 .237720 99 .769582 436783 .49 .517400 .556518 99 .229661 577349 .50 .938470 .242268 1.00 .765198 .440051 1.50 .511828 .557937 2.00 .223891 576725 SMITHSONIAN TABLES. TABLE 34 (continued). CYLINDRICAL HARMONICS OF THE OTH AND IST ORDERS- Ji(x) = J(*). I 3.831706 -.402759 2 7-OI5587 + .300116 3 10.173468 - . 249705 4 13.323692 +.218359 5 16.470630 - . 196465 6 19.615859 +.180063 7 22 .760084 -.167185 8 25.903672 + .156725 9 29.046829 . 148011 10 32.189680 +. 140606 ii 35.332308 -.134211 12 38.474766 + .128617 13 41.617094 -.123668 14 44-7593*9 +.119250 15 47.901461 -.115274 Higher roots may be obtained as under (a). NOTES, y = J n (x) is a particular solu- tion of BessePs equation, The general formula for J n (x) is ^_(-i)^- Mto o or when is an integer and T fv\ 2H T ( J n+l\XJ J n \- and 7 T / \ SMITHSONIAN TABLES ^ ' J_ n (^)=(-l)/nW. Tables 35 to 36 are based upon Gray and Matthews' reprints from Dr. Meissel's tables. See also Reports of British Associa- tion, 1907-1916. TABLE 37. ELLIPTIC INTEGRALS. *JT IT Values of I 2 (1 sin 2 0sin 2 4>) 2 "cty This table gives the values of the integrals between o and n / 2 of the function (i sin 2 0sin 2 <) ues of the modulus corresponding to each degree of 6 between o and 90. d$ for different val- e n d* ir z (i sin 2 0sin 2 <)*aty e X7T ,. 2 d$ f *( sin 2 * >ne of symmetry. The mass of a unit of volume is w. Body. Axis. Weight. Moment of Inertia Io. Square of Ra- dius of Gyra- tion pj. Sphere of radius r Diameter 4 v,r* 8*wr& 2^2 3 15 5 Spheroid of revolution, po- lar axis 2a, equatorial di- Polar axis 4*war* Sirwar* 2r2 ameter 2r 3 5 5 Ellipsoid, axes 2^, 2b, 2c Axis 2a 4-irwabc 4-irwabc ( 2 -f c 2 - ) ^ 2 -ff2 3 ?S 5 Spherical shell, external ra- dius r, internal r' Diameter ^Tn^r* r' 8 ) STTIV^ r' & ) fl^j 3 IS Ditto, insensibly thin, ra- dius r, thickness dr Diameter ,^-dr 8mvr*dr 2r 2 3 3 Circular cylinder, length 20, radius r Longitudinal axis 2a 2wr* irwar* ^2 2 Elliptic cylinder, length 2a, Longitudinal inua6c(P+t?) 3 2 +r 2 transverse axes 2b, 2c axis 2a 2 4 Hollow circular cylinder, length 2a, external ra- dius r, internal r' Longitudinal axis 20. 2irwa(r 2 r" 2 ) m ^ r 2 +r v 2 Ditto, insensibly thin, thick- Longitudinal Axwardr 49Va**tfr r 2 ness dr axis 20 Circular cylinder, length 2a, radius r Transverse diameter 2-jrwar 2 ra/^ 2 (3r2+ 4 02) r z a 2 4 + 3 6 Elliptic cylinder, length 2a, Transverse -> mva&f(y z -}-4a z ) i^ 4 *~ 3 Ditto, insensibly thin, thick- Transverse 4 2 r 2 a 2 ness dr diameter 4-mvar r 3 a ' 2+ 3 Rectangular prism, dimen- sions 2a, 2b, 2c Axis 20. Swabc 8zvat><:(t>' 2 -\-c 2 ) b 2 +c 2 3 3 Rhombic prism, length 2a, diagonals 2b, 2c Axis 2a Afivabc z-wabc^+c 1 } 3 b 2 +c 2 6 Ditto Diagonal 2b qwabc 2wabc(c' i -\-2a' i ) c 2 a 2 3 6 + 3 (Taken from Rankine.) For further mathematical data see Smithsonian Mathematical Tables, Becker and Van Orstrand (Hyperbolic, Circular and Exponential Functions); Functionentafeln, Jahnke und Emde (xlgx, Roots of Transcendental Equations, a -j- bi and re 1 **, Exponentials, Hyperbolic Functions, /x f*oo t*~x du, I - du, I du, Fresnel Integral, Gamma Function, Gauss Integral J X J Oo -^= I f-x^dx, Pearson Function e-^v I si , Elliptic Integrals and Functions, Spherical and Cylindrical Functions, etc.). For further references see under Tables, Mathematical, in the nth ed. Encyclopaedia Britannica. See also Carr's Synopsis of Pure Mathematics and Mellor's Higher Mathematics for Students of Chemistry and Physics. SMITHSONIAN TABLES- TABLE 39. yj INTERNATIONAL ATOMIC WEIGHTS. VALENCIES. The International Atomic Weights are quoted from the report of the International Committee on Atomic Weights (Journal American Chemical Society, 39.42, p. 9, 1920). Substance. Symbol. Relative atomic wt. Oxygen = 16. Valency. Substance. Symbol. Relative atomic wt. Oxygen =16. Valency. Aluminum Al 27.1 3- Mercury Hg 200.6 I, 2. Antimony Sb 1 20. 2 3>5- Molybdenum Mo 96.0 4,6. Argon A 39-9 o. Neodymium Nd 144-3 3- Arsenic As 74.96 3' 5- Neon Ne 2O.2 o. Barium Ba J 37-37 Nickel Ni 58.68 2,3- [ation^ Bismuth Bi 208.0 3> 5- Niton (Raeman- Nt. 222.4 Boron B 10.9 3- Nitrogen N 14.008 3. 5- Bromine Br 79.92 i. Osmium Os 190.9 6,8. Cadmium Cd 112.40 2 . Oxygen O 16.00 2. Caesium Cs 132.81 I. Palladium Pd 106.7 2,4- Calcium Ca 40.07 2. Phosphorus P 31.04 3,5- Carbon C 12.005 4- Platinum Pt 195.2 2, 4- Cerium Ce 140.25 3' 4- Potassium K 39.10 I. Chlorine Cl 35-46 Praseodymium Pr 140.9 3- Chromium Cr 52.0 2, 3, 6. Radium Ra 226.0 2. Cobalt Co 5 8 -97 2, 3- Rhodium Rh 102.9 3. Columbium Cb 93-1 5. Rubidium Rb 85-45 I. Copper Cu 63-57 I, 2. Ruthenium Ru 101.7 6,8. Dysprosium Dy 162.5 3- Samarium Sa 150.4 3- Erbium Er 167.7 3- Scandium Sc 3- Europium Eu 152.0 3- Selenium Se 79-2 2, 4, 6. Fluorine F 19.0 i. Silicon Si 28.3 4- Gadolinium Gd 3. Silver A g 107.88 i. Gallium Ga 70.1 3. Sodium Na 23.00 i. Germanium Ge 72-5 4- Strontium Sr 87.63 2. Glucinum Gold Gl Au 9.1 197.2 2. e I, 3. Sulphur Tantalum S Ta 32.06 181.5 2, 4, 6. 5. Helium He 4.00 O. Tellurium Te 127-5 2, 4, 6. Holmium Ho l6 3-5 3- Terbium Tb 159.2 3- Hydrogen H 1.008 Thallium Tl 204.0 1.3- Thorium Th 232.15 4- Indium In 114.8 3- Iodine I 126.92 I. Thulium Tm 168.5 3- Iridium Ir I 93- 1 4- Tin Sn 118.7 2, 4- Iron Fe 2, 3. Titanium Ti 48.1 " 4- Krypton Kr 8^92 * O 0. Tungsten W 184.0 6. Uranium U 238.2 4,6. Lanthanum La 139.0 3- Lead Pb 207.20 2, 4. Vanadium V 51.0 3' 5- Lithium Li 6.94 I. Xenon Xe 130.2 0. Lutecium Lu 175- 3. Ytterbium Yb I 73-'5 3- Magnesium Manganese Mg Mn 24.32 54-93 2 2, 3. 7- Yttrium Zinc Yt Zn 89-33 6 5-37 3- Zirconium Zr 90.6 4- SMITHSONIAN TABLES. 7 '2 TABLE 40. VOLUME OF A CLASS VESSEL FROM THE WEIGHT OF ITS EQUIVALENT VOLUME OF MERCURY OR WATER. If a glass vessel contains at / C, P grammes of mercury, weighed with brass weights in air at 760 mm. pressure, then its volume in c. cm. at the same temperature, /, : V= PR = P^> at another temperature, / lf : V = PA\ = P pjd 1 1 + 7 (*i /) } p = the weight, reduced to vacuum, of the mass of mercury or water which, weighed with brass weights, equals i gram ; d = the density of mercury or water at /C, and 7 = o.ooo 025, is the cubical expansion coefficient of glass. Temper- ature t WATER. MERCURY. R. R lt ^ = 10. Rl, *, = 20. R. *^=, o. R lt ti = 20. 1.001192 I.OOI443 I.OOI693 0.0735499 0.0735683 0.0735867 I "33 1358 I6O9 5633 5798 5982 2 1092 1292 1542 5766 59*4 6098 3 1068 1243 H93 5900 6029 6213 4 1060 I2IO I46O 6033 6144 6328 5 1068 "93 1443 6l6 7 6259 6443 6 1.001092 1131 1.001192 1206 I.OOI442 ' 0.0736301 6434 0.0736374 6490 0.0736558 8 1184 1234 M85 6568 6605 6789 9 1252 1277 6702 6720 6904 10 '333 1584 6835 6835 7020 ii 1.001428 i.oor4O3 I.OOI653 0.0736969 0-0736951 0.0737135 12 1536 1486 1736 7103 7066 7250 13 1657 1582 I8 3 2 7236 7181 7365 14 1790 1690 1940 7370 7297 7481 IS J 935 1810 2060 754 7412 7596 16 1.002092 1.001942 I.OO2I93 0.0737637 0.0737527 0.0737711 17 2261 2086 2337 7771 7642 7826 18 2441 2241 2491 795 7757 7941 19 2633 2407 2658 8039 7872 8057 20 2835 2584 2835 8172 7988 8172 21 1.003048 1.002772 1.003023 0.0738306 0.0738103 0.0738288 22 3271 2970 3220 8440 82 1 S 8403 23 354 3178 3429 8573 8333 8518 24 3748 3396 3647 8707 8449 8633 25 4001 3624 3875 8841 8564 8748 26 1.004264 1.003862 I.004II3 0.0738974 0.0738679 0.0738864 27 28 4537 4818 41 10 4366 4361 46l6 9108 9242 8794 8910 8979 9094 2 9 5110 4632 4884 9376 9025 9210 30 54io 4908 5159 95 10 9140 9325 Taken from Landolt, Bornstein, and Meyerhoffer's Physikalisch-Chemische Tabellen. SMITHSONIAN TABLES. TABLES 41-42. REDUCTIONS OF WEIGHINGS IN AIR TO VACUO. TABLE 41. 73 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 M S (i/d i/d,) where 5 = the density (vvt. of i ccm in grams = 0.0012) of the air during the weighing, d the density of the body, d t that of the weights. 5 for various barometric values and humidities may be determined from Tables 153 to 155. The following table is computed for 8 = 0.0012. The corrected weight = M + kM/iooo. Density of body weighed d. Correction factor, k. Density of body weighed d. Correction factor, k. Pt. Ir. Brass Quartz or weights weights Al. weights d 1 =2i.s. 8.4. 2.65. Pt. Ir. Brass weights weights ^=21.5. 8.4. Quartz or Al. weights 2.65. . 5 4-2-34 + 2.26 4- i-95 1.6 + 0.69 + 0.61 4-0.30 .6 4- .94 + 1.86 4- 1-55 1.7 + -65 4- -56. 4- -25 7 4- .66 i +I.S7 + 1.26 1.8 + .62 4- -52 + .21 75 4- -55 + 1.46 4-I-I5 1.9 4- .58 4- -49 + .18 .80 + .44 + 1.36 4-1-05 2.O 4- -54 + .46 + .15 .85 + .36 + 1.27 + 0.96 2-5 4- -43 + .34 + .03 .90 + .28 4-I-I9 + .88 3- 4- -34 + .26 .05 95 + .21 + 1.12 + .8! 4.0 + .24 + .16 .15 1. 00 + .14 + 1. 06 4- -75 6.0 + .14 + .06 -25 .1 + 1.04 +0.95 + -64 8.0 + .09 + .01 -30 .2 + 0.94 + .86 4- -55 1 0.0 + .06 .02 -33 3 4- -87 + .78 4- -47 15.0 4- -03 .06 -37 4 5 + .80 + -75 4- -71 + .66 + .40 4- -35 2O.O 22.0 + .004 .001 .08 .09 -39 .40 TABLE 42.- Reductions of Densities in Air to Vacuo. (This correction may be accomplished through the use of the above table for each separate weighing.) If s is the density of the substance as calculated from the uncorrected weights, S its true den- sity, and L the true density of the liquid used, then the vacuum correction to be applied to the uncorrected density, s, is 0.0012 (i s/L). Let W s = uncorrected weight of substance, Wi = uncorrected weight of the liquid displaced by the substance, then by definition, s = LW s /Wi. Assuming D to be the density of the balance of weights, W s {i +0.0012 (i/S i/D)}and Wi {i +0.0012 (i/L i/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 i cc. of air is 0.0012 gram). Ws{r + 0.0012 (i/S i/D) } Then the true density S = L. Wl {i + 0.0012 (i/L i/D) } But from above W s /W T j = s/L, and since L is always large compared with 0.0012, S 5 = 0.0012(1 s/L). The values of 0.0012 (i s/L) for densities up to 20 and for liquids of density I (water), 0.852 (xylene) and 13.55 (mercury) follow : (See reference below for discussion of density determinations). Density of substance s. Corrections. Density of substance s Corrections. WaTer. L = 0.852 Xylene. L = '3-55 Mercury. L=i Water. L='S.SS Mercury. 0.8 + O.OO024 _ II. O.OI2O + 0.0002 0.9 + .OOOI2 _ 12. .0132 + .OOOI i. O.OOOO O.OOO2 + O.OOII T 3- .0144 O.OOOO 2. .OOI2 .OOl6 + .0010 14. .01 s6 O.OOOO 3- 4- .OO24 .0036 .0030 + .0009 .0044 + .0008 g .0168 .0180 .OOOI .0002 5- .0048 .0058 + -0008 17. .0192 .0003 6. .OO6O .0073 + .0007 18. .0204 .OOO4 7. .OO72 .0087 + .0006 19. .0216 .OOO5 8. .0084 .OIOI + .0005 20. .0228 .OOO6 9- .0096 .0115 + .0004 ; 10. .0108 .0129 + .0003 SMITHSONIAN TABLES. Johnston and Adams, J. Am. Chem. Soc. 34, p. 563, 1912. J A TABLE 43. MECHANICAL PROPERTIES. * Compiled from various sources by Harvey A. Anderson, C.E., Assistant Engineer Physicist, U. S. Bureau of Standards. The mechanical properties of most materials vary between wide limits; the following figures are given as being representative rather than what may be expected from an individual sample. Figures denoting such properties are commonly given either as specification or experimental values. Unless otherwise shown, the values below are experimental. Credit for information included is due the U. S. Bureau of Standards; the Am. Soc. for Testing Materials; theSoc. of Automotive Eng.; the Motor Transport Corps, U. S. War Dept.; the Inst. of Mech. Eng.; the Inst. of Metals; Forest Products Lab.; Dept. of Agriculture (Bull. 556); Moore's Materials of Engineering; Hatfield's Cast Iron; and various other American, English and French authorities. The specified properties shown are indicated minimums as prescribed by the Am. Soc. for Testing Materials, U. S. Navy Dept., Panama Canal, Soc. of Automotive Eng., or Intern. Aircraft Standards Board. In the majority of cases, specifications show a range for chemical constituents and the average value only of this range is quoted. Corresponding average values are in general given for mechanical properties. In gen- eral, tensile test specimens were 12.8 mm (0.505 in.) diameter and 50.8 mm (2 in.) gage length. Sizes of compressive and transverse specimens are generally shown accompanying the data. All data shown in these tables are as determined at ordinary room temperature, averaging 20 C (68 F.). The properties of most metals and alloys vary considerably from the values shown when the tests are con- ducted at higher or lower temperatures. The following definitions govern the more commonly confused terms shown in the tables. In all cases the stress referred to in the definitions is equal to the total load at that stage of the test divided by the original cross-sectional area of the specimen (or the corresponding stress in the extreme fiber as computed from the flexure formula for transverse tests). Proportional Limit (abbreviated P-limit). Stress at which the deformation (or deflection) ceases to be proportional to the load (determined with extensometer for tension, compressometer for compression and deflectometer for transverse tests). Elastic Limit. Stress which produces a permanent elongation (or shortening) of o.ooi per cent of the gage length, as shown by an instrument capable of this degree of precision (determined from set readings with extensometer or compressometer). In transverse tests the extreme fiber stress at an appreciable permanent deflection. Yield Point. Stress at which marked increase in deformation (or deflection) of specimen occurs without in- crease in load (determined usually by drop of beam or with dividers for tension, compression or transverse tests). Ultimate Strength in Tension or Compression. Maximum stress developed in the material during test. Modulus of Rupture. Maximum stress in the extreme fiber of a beam tested to rupture, as computed by the empirical application of the flexure formula to stresses above the transverse proportional limit. Modulus of Elasticity (Young's Modulus). Ratio of stress within the proportional limit to the corre- sponding strain, as determined with an extensometer. Note: All moduli shown are obtained from tensile tests of materials, unless otherwise stated. Brinell Hardness Numeral (abbreviated B. h. n.). Ratio of pressure on a sphere used to indent the material to be tested to the area of the spherical indentation produced. The standard sphere used is a 10- mm diameter hardened steel ball. The pressures used are 3000 kg for steel and 500 kg for softer metals, and the time of application of pressure is 30 seconds. Values shown in the tables are based on spherical areas computed in the main from measurements of the diameters of the spherical indentations, by the following formula: B. h. n. = P -f- irtD = P -h irD(D/2 - P = pressure in kg, / = depth of indentation, D = diameter of ball, and d = diameter of indentation, all lengths being expressed in mm. Brinell hardness values have a direct relation to tensile strength, and hardness determinations may be used to define tensile strengths by employing the proper conversion factor for the ma- terial under consideration. Shore Scleroscope Hardness. Height of rebound of diamond pointed hammer falling by its own weight on the object. The hardness is measured on an empirical scale on which the average hardness of martensitic high carbon steel equals 100. On very soft metals a " magnifier" hammer is used in place of the commonly used "universal" hammer and values may be converted to the corresponding "universal" value by multi- plying the reading by $. The scleroscope hardness, when accurately determined, is an index of the tensile elastic limit of the metal tested. Erichsen Value. Index of forming quality of sheet metal. The test is conducted by supporting the sheet on a circular ring and deforming it at the center of the ring by a spherical pointed tool. The depth of impression (or cup) in mm required to obtain fracture is the Erichsen value for the metal. Erichsen standard values for trade qualities of soft metal sheets are furnished by the manufacturer of the machine corresponding to various sheet thicknesses. (See Proc. A. S. T. M. 17, part 2, p. 200, 1917.) Alloy steels are commonly used in the heat treated condition, as strength increases are not commensurate with increases in production costs for annealed alloy steels. Corresponding strength values are accordingly shown for annealed alloy steels and for such steels after having been given certain recommended heat treat- ments of the Society of Automotive Engineers. The heat treatments followed in obtaining the properties shown are outlined on the pages immediately following the tables on steel. It will be noted that considerable latitude is allowed in the indicated drawing temperatures and corresponding wide variations in physical prop- erties may be obtained with each heat treatment. The properties vary also with the size of the specimens heat treated. The drawing temperature is shown with the letter denoting the heat treatment, wherever the information is available. TABLE 44. MECHANICAL PROPERTIES. TABLE 44. Ferrous Metals and Alloys Iron and Iron Alloys. 75 Metal. Grade. 14 1 Ultimate 1 strength. 1 1 Sjj sa Ultimate 1 strength. I .s E ^ fciE.S o9 M wS,^ Reduct. 1 in area. I Hardness. Brinell at 3000 kg Sclero- scope. Tension- kg/mm 2 Tension lb/in 2 Per cent. Iron: Electrolytic* (remelt) : as forged . . . annealed 900 C. Gray castt(i9 mm diam. bars) .... Malleable cast, American (after Hatfield) 34-o 12.5 indet. fi4-o <3i-5 ,19:0 {28.0 fiQ-5 122.5 29-5 II.O 48.0 25.0 66.0 5i-o 35-5 12.5 48.0 22.5 54-5 37-5 38.5 27.0 {17.5 120.5 (24-5 (40.0 |29-5 145-5 40.8 (34-o (37.0 3i-5 24-5 53-5 38.0 74.0 64-5 38.5 24-5 54-5 37-5 60.5 49.0 48,500 l8,OOO indet. | 20,000 (45,000 ,27,000 {40,000 ( 28,000 (32,000 41,800 16,000 68,100 35,800 94,000 72,900 50,700 17,600 68,200 31,800 77,700 53,4oo 55,ooo 38,000 ( 25,000 (38,000 (35,000 (57,000 ,42,000 {65,000 58,000 ( 48,000 (53,000 45,200 34,900 76,300 54,2oo 105,000 91,600 54,7oo 34,900 77,5oo 53,4oo 86,000 69,800 33-0 520 negh M5-0 < 4-5 / 6.0 { 2.0 21.6 (40.0 (30.0 35-o 53-o 37-o 50.0 6.0 24.0 26.0 60.0 2I.O 51.0 28.0 27.0 83.0 87.0 gible {15-0 t 4-5 e 6.O \ 2.0 U5-o ^35-0 78.0 81.5 82.0 90.6 7-5 25.1 84-3 93-5 76.4 85-3 74-7 55-5 95 t 75 t ( 100 (150 ~ 18 {24 1 40 {25 ( 3 European (after Am. Malleable Castings Ass.) (run of 24 successive heats, 1919)1 Commercial wrought . . Silicon alloys |! Si 0.01: as forged. . . (Melted in vacuo) ann. 970 C (Note: C max. o.oi per cent) Si 1.71 : as forged annealed 970 C Si 4.40 1 as forged annealed 970 C Aluminum alloy s^ Al 0.00 : as forged (Melted in vacuo) ann. 1000 C (Note: C max. o.oi per cent) Al 3.08 : as forged annealed 1000 C Al 6.24 I as forged annealed 1000 C .6.7 0.204 Composition, approximate: Electrolytic, C 0.0125 per cent; other impurities less than 0.05 per cent. Cast, gray: Graphitic, C 3.0, Si 1.3 to 2.0, Mn 0.6 to 0.9, S max. o.i, P max. 1.2. A. S. T. M. Spec. A48 to 18 allows S max. o.io, except S max. 0.12 for heavy castings. Malleable: American " Black Heart," C 2.8 to 3.5, Si 0.6 to 0.8, Mn max. 0.4, S max. 0.07, P max. 0.2. European " Steely Fracture," C 2.8 to 3-5, Si p.6 to 0.8, Mn 0.15, S max. 0.35, P max. 0.2. Compressive Strengths [Specimens tested: 25.4 mm (i in.) diam. cylinders 76.2 mm (3 in.) longj. Electrolytic iron 56.5 kg/mm 2 or 80,000 lb/in 2 . Gray and malleable ca^t iron 56.5 to 84.5 kg/mm 2 or 80,000 to 120,000 lb/in 2 . Wrought iron, approximately equal to tensile yield point (slightly above P-limit). Density: Electrolytic iron 7.8 g/cm 3 or 487 lb/ft 3 Malleable iron 7.6 g/cm 3 or 474 lb/ft j Cast iron 7.2 g/cm 3 or 449 lb/ft 3 Wrought iron 7.85 g/cm 3 or 490 lb/ft 3 Ductility: Normal Erichsen values for good trade quality sheets, 0.4 mm (0.0156 in.) Thickness, soft annealed. Depth. mm in. Sheet metal hoop iron, polished 9.5 0.374 Charcoal iron tinned sheet 7.5 0.295 Second quality tinned sheet Modulus of elasticity in tension and compression: Electrolytic iron .... 17,500 kg/mm 2 or 25,000,000 lb/in 2 Cast iron 10,500 kg/mm 2 or 15,000,000 lb/in 2 Modulus of elasticity in shear: Electrolytic iron 7030 kg/mm 2 or 10,000,000 lb/in 2 Wrought iron Scleroscope hardness values shown are as determined with the Shore Universal hammer. Strength in Shear: Electrolytic (remelt) Commercial wrought P-limit 8.4 kg/mm 2 or 12,000 lb/in 2 P-limit Ultimate strength 21.1 kg/mm 2 or 30,000 lb/in 2 Ultimate strength. , Transverse strength, from flexure formula: Gray cast iron Modulus of rupture, 33.0 kg/mm 2 or 47,000 lb/in 2 "Arbitration Bar," 31.8 mm (ij in.) diameter, or 304.8 mm (12 in.) span; minimum central load at rup- ture 1130 to 1500 kg (2500 to 3300 lb.); minimum central deflection at rupture 2.5 mm (o.i in.), (A. S. T. M. Spec. A 48-18). * Properties of Swedish iron (impurities less than i per cent) approximate those of electrolytic iron, t These two values of B. h. n. only are as determined at 500 kg pressure, t U. S. Navy specifies minimum tensile strength of 14.1 kg/mm 2 or 20,000 lb/in 2 . Averages for a U. S. foundry. [| From T. D. Yensen, University of Illinois, Engr. Exp. Station, Bulletin No. 83, 1915 (shows Si 4.40 as alloy of maximum strength). ^ From T. D. Yensen, University of Illinois, Engr. Exp. Station, Bulletin No. 95, 1917. SMITHSONIAN TABLES. Malleable iron.. Wrought iron. . . 17,500 kg/mm 2 or 25,000,000 lb/in 2 17,500 kg/mm 2 or 25,000,000 lb/in 2 Cast iron 8450 .kg/mm 2 or 12,000,000 lb/in 2 7030 kg/mm 2 or 10,000,000 lb/in 2 2 1. 1 kg/mm 2 or 30,000 lb/in 2 35.0 kg/mm 2 or 50,000 lb/in 2 jfo TABLES 45-46. MECHANICAL PROPERTIES OF MATERIALS- TABLE 45. Carbon Steels ' Commercial Experimental Values. S. A. E. (Soc. of Automotive Eng.. U. S. A.) classification scheme used as basis for steel groupings. First two digits S. A. E. Spec. No. show steel group number, and last two (or three in case of five figures) show carbon content in hundredths of one per cent. The first lines of properties for each steel show values for the rolled or forged metal in the annealed or nor- malized condition. Comparative heat-treated values show properties after receiving modified S. A. E. heat treatment as shown below (Table 46). The P-limit and ductility of cast steel average slightly lower and the ultimate strength 10 to 15 per cent higher than the values shown for the same composition steel in the annealed condition. Tiie properties of rolled steel (raw) are approximately equal to those shown for the annealed con- dition, which represents the normalized condition of the metal rather than the soft annealed state. The data for heat-treated strengths are average values for specimens for heat treatment ranging in size from to i in. diameter. The final drawing or quenching temperature for the properties shown is indicated in degrees C with the heat treatment letter, wherever the information is available. In general, specimens were drawn near the lower limit of the indicated temperature range. Metal. S.A.E. spec. no. Nominal contents per cent. S.A.E. heat treat- ment. I p!< Ultimate 1 strength. 1 J PH Ultimate 1 strength. 1 ' S H 31" Reduct. 1 in area. Hardness. Brinell (5) 3000 kg. o ^ Hardness. PH 3 *"* PH Brinell (0)3000 kg Sclero- scope. Tension kg/mm 2 Tension lb/in 2 Compression kg/ mm 2 Compression Ib/in 2 Semi-steel: Graph. C 2. 85 \ Comb. C o. 76 / Graph. C 2. 92 \ Comb. Co. 60 j 7-9 4-2 19.8 14.9 11,200 6,000 28,200 21,200 24-3 18.3 72.6 61.4 34,500 26,000 103,000 87,300 176 170 - Tension specimens 12.7 mm (0.5 in.) diameter, 50.8 mm (2 in.) gage length; elongation and reduction of area negligible. Compression specimens 20.3 mm (0.8 in.) diameter, 61.0 mm (2.4 in.) long; failure occurring in shear. Tension set readings with extensometer showed elastic limit of 2.1 kg/mm 2 or 3000 lb/in 2 . Modulus of elasticity in tension 9560 kg/mm 2 or 13,600,000 lb/in 2 . SMITHSONIAN TABLES. TABLE 51. Steel-wire Rope Specification Values. 79 Cast steel wire to be of hard crucible steel with minimum tensile strength of 155 kg/mm 2 or 220,000 Ib/in* and minimum elongation of 2 per cent in 254 mm (10 in.). Plow steel wire to be of hard crucible steel with minimum tensile strength of 183 kg/mm 2 or 260,000 lb/in 2 and minimum elongation of 2 per cent in 254 mm (io in.). Annealed steel wire to be of crucible cast steel, annealed, with minimum tensile strength of 77 kg/mm 2 or 110,000 lb/in 2 and minimum elongation of 7 per cent in 254 mm (io in.). Type A: 6 strands with hemp core and 19 wires to a strand (= 6 X 19), or 6 strands with hemp core and 18 wires to a strand with jute, cotton or hemp center. Type B: 6 strands with hemp core, and 12 wires to a strand with hemp center. Type C: 6 strands with hemp core, and 14 wires to a strand with hemp or jute center. Type AA: 6 strands with hemp core, and 37 wires to a strand (= 6 X 37) or 6 strands with hemp core and 36 wires to a strand with jute, cotton or hemp center. Description. Diameter. Approx. weight. Minimum strength. mm in. kg/m Ib/ft kg Ib. Galv. cast steel, Type A .... 9-5 12.7 25-4 38.i 9-5 12.7 25-4 38.1 9-5 12.7 25-4 38.i 25-4 41-3 9-5 12.7 25-4 36.5 9-5 T2.7 25-4 4i-3 f I l I I If J I l| I if 1 I If 0.31 0-55 2.23 5.06 0-35 0.58 2-23 5-28 0.25 0.42 1.68 3-94 i-59 4-35 0.31 o-55 2-23 4.66 o-33 0.58 2-35 6.18 O. 21 0-37 I.SO 3-40 O. 22 -39 1.50 3-55 0.17 0.28 1-13 2.65 1.07 2.92 0.21 0-37 1-50 3-i3 O. 22 -39 1.58 4-15 3,965 6,910 27,650 63,485 3,840 7,410 27,650 59,735 2,995 5,210 20,890 47,965 18,825 5i,575 4,690 8,165 32,675 69,140 4,540 8,750 32,250 83,010 8,740 15,230 60,960 139,960 8,460 16,330 60,960 131,690 6,600 11,500 46,060 105,740 41,500 113,700 10,340 18,000 72,040 152,430 10,000 19,300 71,100 183,000 u a a a a a a a a a a n a it n Galv. cast steel, Type A A it a n t( a Galv. cast steel, Type B u a a a n Galv. cast steel, Type C Galv. plow steel, Type A a a a u a a a a a a Galv. plow steel, Type AA. . a a a a a a a tt a a .... TABLE 52. Plow Steel Hoisting Rope (Bright). (After Panama Canal Specification No. 302, 1912.) Wire rope to be of best plow steel grade, and to be composed of 6 strands, 19 wires to the strand, with hemp center. Wires entering into construction of rope to have an elongation in 203.2 mm or 8 in. of about 2? per cent. Diameter.^ Spec, minimum strength. Diameter. Spec, minimum strength. mm in. kg Ib. mm in. kg Ib. 9-5 f 5,215 11,500 38.1 if 74,390 164,000 12.7 ^ 9,070 20,000 50.8 2 127,000 280,000 19.0 f 20,860 46,000 63.5 ** 207,740 458,000 25-4 I 34,470 76,000 69.9 2f 249,350 550,000 TABLE 53. Steel-wire Rope Experimental Values. (Wire rope purchased under Panama Canal Spec. 302 and tested by U. S. Bureau of Standards, Washington, D. C.) Description and analysis. Diameter. Ultimate strength. Ultimate strength (net area). mm in. kg Ib. kg/mm 2 lb/in 2 Plow Steel, 6 strands x 19 wires C 0.90, S 0.034, P 0.024, Mn 0.48, Si 0.172 . . . . 50.8 69.9 82.6 82.6 2 2f 3l 3* 137,900 314,800 392,800 425,000 304,000 694,000 866,000 937,ooo 129.5 I5I.2 132.2 142.5 184,200 214,900 187,900 202,400 Plow Steel, 6 strands X 25 wires C 0.77, S 0.036, P 0.027, Mn 0.46, Si 0.152 . . . Plow Steel, 6 x 37 plus 6 x 19 C 0.58, S 0.032, P 0.033, Mn 0.41, Si 0.160 Monitor Plow Steel, 6 x 61 plus 6 x 19, C 0.82, 80.025, P 0.019, Mn 0.23, Si 0.169 Recommended allowable load for wire rope running over sheave is one fifth of specified min. strength. SMITHSONIAN TABLES. So TABLES 54-55. TABLE 54. Aluminum. Density 1& E Z^ JM 1 2jS II '"I- te C c tjd Hardness. Metal, approx. composition, Condition. or weight. PH g| A S' J2 6^ W ft *C ^ *n per cent. gm per cm ? Ib.per ft* Tension, kg/mm 2 Tension, lb./in 2 Per cent. |8 ^ OQ ALUMINUM: Av. Al 99.3 Imp., Fe and Si. . . Cast, sand at 700 C 2-57 160.5 6.0 to 8.0 to 8,500 to 12,000 to 29 to 36 to 25 to 4 to Cast, sand and 7-0 9.8 10,000 14,000 15 22 26 5 heat treated Ann. 500 C, air 8. 9 to 12,600 to 28 to 30 to 25 to 4 to cooled Cast, chill Sheet, ann 2-57 2.69 2.70 2.70 2.70 160.5 168.0 168.5 168.5 168.5 6.0 6.0 14.0 15.0 21.0 9-6 9.0 9-0 21.0 23-0 28.0 9,000 8,500 20,000 22,000 30,000 13,600 13,000 13,500 30,000 33,000 40,000 18 20.0 23-0 4.0 6.0 22 25. c 25.0 35-0 50.0 27 26 S 5 14 Sheet, hard Bars, hard Wire, hard Compressive strength: cast, yield point 13.0 kg/mm 2 or 18,000 lb/in 2 ; ultimate strength 47.0 kg/mm 2 or 67,000 lb/in 2 . Modulus of elasticity: cast, 6900 kg/mm 2 or 9,810,000 lb/in 2 at 17 C. TABLE 55. Aluminum Sheet. (a) Grade A (Al min. 99.0) Experimental Erichsen and Scleroscope Hardness Values. [From tests on No. 18 B. & S. Gage sheet rolled from 6.3 mm (0.25 in.) slab. Iron Age v. 101, page 950]. Heat treatment annealed. Thickness, mm Indentation, mm Scleroscope hardness. None (as rolled) 08 6 83 @ 200 C, 2 hours @ 300 C, 2 hours @ 400 C, 2 hours @ 200 C, 30 min .09 .07 .08 8.86 10. 17 9.40 8.0 4-5 4-5 ii 8 @ 400 C, 30 min .08 9.80 4-5 (6) Specification Values. (i) Cast: U. S. Navy 49 Al, July i, 1915; Al min. 94, Cu max. 6, Fe max. 0.5, Si max. 0.5, Mn max. 3. Minimum tensile strength 12.5 kg/mm 2 or 18,000 lb/in 2 with minimum elongation of 8 per cent in 50.8 mm (2 in.). (2) Sheet, Grade A: A. S. T. M. 25 to i8T; Al min. 99.0; minimum strengths and elongations. Gage, sheet thicknesses. Temper, No. Tensile strength. Elong. in 50.8 mm or 2 in. (B.&S.) mm in. kg/mm 2 lb/in 2 per cent. 12 tO .052 to 0.0808 to i Soft, Ann. 8.8 12,500 30 Sheets of temper No. 1 6 incl. 293 .0509 2 Half-hard 12.5 18,000 1 i to withstand being 3 Hard 15. 5 22,000 4 bent double in any di- 17 to .152 to .0453 to i Soft, Ann. 8.8 12,500 20 rection and hammered 22 incl. 643 .0253 2 Half-hard 3 Hard 12.5 17-5 18,000 2^,000 5 2 flat; temper No. 2 to bend 180 about radius 23 to 26 incl. 574 to .404 .0226 to .0159 i Soft, Ann. 2 Half-hard 8.8 12.5 12,500 18,000 10 5 equal to thickness with- out cracking. I 3 Hard 21.0 30,000 2 NOTE. Tension test specimen to be taken parallel to the direction of cold rolling of the sheet. SMITHSONIAN TABLES. TABLE 66. ALUMINUM ALLOY. 8l Density ~ If S 1 *' p db E i a Hardness. or weight. ^3 ,S K 'S v c oo *~ Alloy, approx. Condition, 5* PH 5~ 3 2>^" P4*o composition per cent per cent. reduction. ^ cL gm/ cm 3 ft' Tension, kg/mm 2 Tension, lb/in 2 per cent. |8 t/2 <" Aluminum Copper . Cast, chill.... _ 5-3 10.5 7,5oo 15,000 24.0 34-0 _ _ Al 98 Cu i Imp. max. i Rolled, 70% . . 19.0 21.0 27,000 30,000 4.0 Al 96 Cu 3 Imp. max. i Cast, chill.... Rolled, 70%.. ~ ~ 8.1 25-0 HI 11,500 35,ooo 19,500 41,000 I2.O 5-5 2I.O Al 94 Cu 5 Imp. max. i Cast, chill Rolled, 70% . . IO.O 23-0 15-0 27.0 14,500 33,ooo 21,500 38,000 7-o 6.0 14.0 A192 Cu8: Alloy No. Cast, sand 2.88 1 80 7-7 to 10.5 to 1 1 ,OOO tO 1 5 ,000 to 4.0 to 3-5 to 50 to 13 to 12 10.5 16.2 15,000 23,000 None None 65 18 Al 90-92 Cu 7-8.5 Imp. max. 1.7 Cast* 2.9 181 12.7 18,000 I.O Copper, Magnesium.. Cast at 700 C. 3- 2 tO 9.6 to 4,500 to 13,600 to 2.0 to 0.5 to 74 to 17 tc Al 9.52 Cu 4.2 Mg 0.6 4.6 13.3 6,500 18,900 o o 74 18 Ann. 500 C.. . 4-6 17.3 6,500 24,900 3-0 I.O 80 21 Duralumin or 178 f Ann 2.8 174 25-0 42.0 35,100 59,500 21. 1 29-5 Alloy Al 94 Cu 4 Mg \ Rolled 70%. . . 53-o 56.0 75,400 79,600 4-0 13-2 0.5 1 Rolled heat tr'd t 23.4 39-O 33,400 55,300 25.5 26.0 . Copper, Manganese . . Al 96 Cu 2 Mn 2 Cast, chill Rolled, 20 mm - IO.O 19.0 14.0 27.0 14,300 27,100 20,300 38,200 5-o 16.0 28.0 ~ Al96Cu3Mni Cast, chill. ... H-3 19.0 16,200 27,000 14.0 Naval Gun Factory. . . ( Cast, sand. . . . 2.8 I 75 14.0 20,000 12.0 Al 97 Cu 1.5 Mn i.. . . (Forged 14.0 19.0 i9,5oo 27,800 I2.O 47-o Al 94 Cu max. 6 Mn max. 3 Minimum J. . . 12.7 l8,OOO 8.0 Copper, Nickel, Mg Cast at 700 C. 3-5 to 17.9 to 5,000 to 25,500 to 6.0 to 8.5 to 54 to 9 to Al 93-5 Cu 3.5 Ni 1.5 Mg i Mn 0.5 Copper, Nickel Mn... Cast at 700 C. ~ 9-8 23.2 14-5 tO 14,000 33,000 20,600 to i-S 6.0 to I.O II.O tO 86 50 to 25 9 to Al 94.2 Cu 3 Ni 2 Mn 0.8 21.4 30,500 I.O 2.0 9 1 27 Magnesium: Magnalium Al 95 Mg 5 Cast, sand 2.5 156 5-6 15-5 8,000 22,000 7.0 8-5 Al 77-98, Mg 23-2.. . Cast, chill 2.410 1 50 to 29.5 to 42,000 to 2.57 160 145-0 64,000 Cast, chill. ... 4.0 II.O 5,8oo 14,900 21.0 36.0 Nickel Al 97 Ni 2 Drawn, cold . . 14.0 16.0 19,700 22,700 13-0 37-0 Rolled, hot. . . 8.0 13.0 1 1 ,900 18,200 28.0 52.0 Cast, chill 6.0 15.0 j 9,000 21,700 9-0 II.O Al95Ni S Drawn, cold. . 16.0 20.0 22,90O 27,000 8.0 24.0 Rolled, hot . . . 9.0 16.0 13,500 22,300 22.0 36.0 Nickel Copper: Al 93.5 Ni 5.5 Cu i . . Cast, chill 7.0 17.0 10,700 24,800 6.0 8.0 Al 91.5 Ni 4.5 Cu 4. . Cast, chill 7.0 18.0 9,900 25,200 4.0 5-o Al 92 Ni 5.5 Cu 2 / Drawn, cold. . \Rolled, hot... ~ ~ 22.0 13-0 27.0 22.0 31,700 18,200 37,800 31,500 8.0 16.0 15-0 24.0 ~ ~ Zinc, Copper: Al 88.6 Cu 3 Zn 8.4. . Cast at 700 C. 4-7 I8. 5 6,700 26,300 8.0 7-5 So 10 Ann. 500 C. . _ _ 4-4 20.2 6,200 28,800 8.0 7-5 50 IO Al 81.1 Cu 3 Zn 15.9. Cast at 700 C. 3-1 193 9.8 24.7 14,000 35,ioo 2.O 2.0 74 15 Ann. 500 C... 9.8 29.0 14,000 41,200 4.0 4.0 70 US * Specification Values: Alloy " No. 12": A. S. T. M. B26-i8T, tentative specified minimums for aluminum, copper, t Quenched in water from 475 C. after heating in a salt bath. Modulus of elasticity for Duralumin averages 7000 kg/mm 2 or 10,000,000 lb/in 2 . t Specification values: Aluminum castings; U. S. Navy 49 Al, July i, 1915 (Impurities: Fe max. 0.5, Si max. 0.5). SMITHSONIAN TABLES. 82 TABLES 57-59 MECHANICAL PROPERTIES. TABLE 57. Copper. Metal and approx. composition. Per cent. Condition. Density or weight. P-limit. 1 Ultimate 1 strength. 1 1 Ultimate I strength. 1 .a g^ bis'i ! ssr Reduct. I in area. Hardness. & is si gm/ cm 8 lb/ ft* Tension, kg/mm 2 Tension, lb/in 2 Per cent. Copper: 00.9: electrolytic Cu 99.6 Ann. 2oc 3 C. 8.89 8.85 8.89 8.90 555 552 m 6.0 7.0 14.0 mdet. 26.0 27.0 18.0 35-o 25.0 35-0 47-3 21.9 33-0 8,500 10,000 20,000 indet. 37,000 38.000 25,000 50,000 35,000 50,000 67,400 31,200 46,800 50.0 20.O 5-0 50.0 9.0 0.8 24-5 4-3 50.0 60.0 8.0 60.0 64.5 76.0 70.5 40 so 94 42 l 6 18 Cast f Hard, 40% reduct \ Ann. at 500 C. . . Drawn cold, 50% reduct Rolled . . Cu 99.6 No Ann. (96% re- duction). .... . . Ann. 750 C after drawing cold . . . Drawn hot (64% reduction) Cu 99.9 1 * Wire drawn cold from 3.18 mm (0.125 in.) to 0.64 mm (0.025 in.) Bull. Am. Inst. Min. Eng., Feb., 1919. t Wire drawn at 150 C from 0.79 mm (0.031 in.) to 0.64 mm (0.025 in.) (Jeffries, loc. cit.). Compression, cast copper, Ann. 15.9 mm (0.625 in.) diam. by 50.8 mm (2 in.) long cylinders. Shortened 5 per cent at 22.0 kg/mm 2 or 31,300 lb/in 2 load. 10 " " 29.0 kg/mm 2 " 41,200 lb/in 2 20 " " 39.0 kg/ mm 2 " 55,400 lb/in 2 ' Shearing strength, cast copper 21.0 kg/mm 2 or 30,000 lb/in 2 Modulus of elasticity, electrolytic 12,200 kg/mm 2 or 17,400,000 lb/in 2 cast 7,700 kg/ mm 2 or 11,000,000 lb/in 2 " " drawn, hard 12,400 kg/mm 2 or 17,600,000 lb/in 2 TABLE 58. Rolled Copper Specification Value. Specification values: U. S. Navy Dept., 4?C2, minimums for rolled copper, Cu min. 99.5 Description, temper and thickness. Tensile strength. Elong. in 50.8 or 2 in. per cent. kg/mm 2 lb/in 2 Rods, bars, and shapes: Soft Hard: to 9. 5 mm (f in.) incl 21.0 35-0 31-5 28.0 24-5 21.0 tO 28.O 24-5 30,000 50,000 45,ooo 40,000 35,ooo 30,000 to 40,000 35,ooo 25 10 12 IS 20 25 to 25 18 Hard: 9.5 mm to 25.4 mm (i in.) Hard: 25 . 4 mm to 50. 8 mm (2 in.) Hard: over 50 8 mm (2 in ) Sheets and plates: Soft Hard TABLE 59. Copper Wire Specification Values. Specific Gravity 8.89 at 20 C (68 F). Copper wire : Hard Drawn (and Hard-rolled flat copper of thicknesses corresponding to diameters of wire) Specification values. (A. S. T. M. BI-IS, and U. S. Navy Dept., 22\V3, Mar. i, 1915-) Diameter. Minimum tensile strength. Maximum elongation, per cent in 254 mm (10 in.). mm in. kg/mm 2 lb/W 11.68 .460 34-5 49,000 2-75 10.41 9.27 .410 365 35-9 37-1 51,000 52,800 3-25 .80 8.25 .325 38.3 54,5oo .40 7-34 .289 39-4 56,100 17 6.55 .258 40-5 57,600 .98 5-82 .229 41-5 59,000 79 in 1524 mm (60 in.) 5.18 .204 42.2 60,100 2 4 .62 .182 43-0 61,200 .18 i .12 .162 43-7 62,100 .14 .66 .144 44-3 63,000 .09 25 .128 44.8 63,700 .06 .90 .114 45-2 64,300 .02 59 .102 45-7 64,900 .00 3i .091 46.0 65,400 97 .06 .O8l 46.2 65,700 95 83 .072 46.3 65,900 .92 .63 .064 46.5 66,200 .00 45 057 46.7 66,400 .89 30 .051 46.8 66,600 87 .14 045 47-0 66,800 .86 .02 .040 47-1 67,000 85 P-limit of hard-drawn copper wire must average 55 per cent of ultimate in table, and 60 per cent of tensile strength for smaller sizes. tensile strength for four largest sized wires SMITHSONIAN TABLES. TABLES 60-63. MECHANICAL PROPERTIES. TABLE 60. Copper Wire Medium Hard-drawn. (A. S. T. M. 62-15) Minimum and Maximum Strengths. Tensile strength. Minimum. Maximum. minimum per cent mm in. kg/mm 2 lb/in kg/mm 2 lb/in II .70 0.460 29-5 42,000 34-5 49,OOO 3-75 6-55 .258 33-o 47,000 38.0 54,000 2.50 in i524mm (60 in.) 4.12 .162 34-5 49,000 39-5 56,000 -is 2-59 . IO2 35-5 50,330 40.5 57,330 1.04 1.02 .040 37-o 53,ooo 42.0 60,000 0.88 Representative values only from table in specifications are shown above. P-limit of medium hard-drawn copper averages 50 per cent of ultimate strength. TABLE 61. Copper Wire Soft or Annealed. (A. S. T. M. 83-15) Minimum Values. Diameter. Minimum tensile strength. Elongation in 254 mm (10 in.), per cent. mm ill. kg/mm 2 lb/h* n. 70 to 7.37 0.460 to 0.290 25-5 36,000 35 7 . 34 to 2 . 62 0.289 to o. 103 26.0 37,000 30 2- 59 to 0.53 O.IO2 tO O. 02 1 27.0 38,500 25 0.51 to o . 08 O.O2O tO O.OO3 28.0 40,000 2O NOTE. Experimental results show tensile strength of concentric-lay copper cable to approximate 90 per cent of combined strengths of wires forming the cable. TABLE 62. Copper Plates. (A. S. T. M. Bn-i8) for Locomotive Fire Boxes. Specification Values. Minimum requirements. Tensile strength. Elong. in 203.2 mm (8 in.), per cent. kg/mm* lb/in Copper, Arsenical, As 0.25-0.50 Impurities, max. 0.12 22.0 21 .O 31,000 30,000 35 30 Copper, Non-arsenical: Impurities, max. 0.12 NOTE. Copper to be fire-refined or electrolytic, hot-rolled from suitable cakes. TABLE 63. Copper Alloys. The general system of nomenclature employed has been to denominate all simple copper- zinc alloys as brasses, copper-tin alloys as bronzes, and three or more metals alloys composed primarily of either of these two combinations as alloy brasses or bronzes, e.g., "Zinc bronze" for T.I. S. Government composition " G " Cu 88 per cent, Sn 10 per cent, Zn 2 per cent. Alloys of the third type noted above, together with other alloys composed mainly of copper, have been called copper alloys, with the alloying elements other than minor impurities listed as modifying copper in the order of their relative percentages. In some instances, the scientific name used to denote an alloy is based upon the deoxidizer used in its preparation, which may appear either as a minor element of its composition or not at all, e.g., phosphor bronze. Commercial names are shown below the scientific names. Care should be taken to specify the chemical composition of a commercial alloy, as the same name frequently applies to widely varying compositions. SMITHSONIAN TABLES. TABLE 64. MECHANICAL PROPERTIES OF MATERIALS- TABLE 64. Copper-zinc Alloys or Brasses; Tin Alloys or Bronzes. Metal and Density or weight. j || 1 || fj3 IS Hardness. composition, Condition. * 5ts * 11 ssr K. M O QJ gm cm 3 Ib ft 3 Tension, kg/mm 2 Tension , lb/in 2 Per cent. la If Brass : Sand cast 20.0 29,000 22 Cu 90 Zn iof. . Cold rolled, hard Cold rolled, soft. 8.7 543 39-0 26.0 55,000* 37,000* 4: 70 60 47 20 10 Cu 80, Znao {. Cu 70, Zn 30. . Cu66Zn34Std. sheet Sand cast Cold rolled, hard Cold rolled, soft. Sand cast / Cold rolled, hard \ Cold rolled, soft. 8.6 8.4 8.5 8.4 537 524 530 524 25-0 53-0 29.0 28.0 42.0 34-0 35,000 75,ooo* 42,000* 40,000 60,000 48,000 * 3 l> 50* 32 85 85 75 46 45 28 12 26 12 Cu 60, Zn 40.. . Muntz metal. . . Sand cast Cold rolled, hard U 522 15-5 32.2 49.0 21,800 45,000 45,8oo 70,000 15 30 22 50 Bronze : Cu 97.7, Sn 2.3. /Cast \Rolled 6.0 7.6 19-5 34- 8,500 10,800 28,000 48,000 20 55 75 ICast or gun Cu 90, Sn 10. . . bronze or bell 8.78 548 7-2 23.0 10,300 33,ooo 10 23 metal Cu 80 Sn 20 Cast 881 Cu 70, Sn 30. . . Cast 8.84 552 1-4 5-o 2,000 7,000 o.S Compressive Strengths, Brasses: Cu 90, Zn 10, cast 21.0 kg/mm 2 or 30,000 lb/in 2 Cu 80, Zn 20, cast 27.4 kg/mm 2 or 39,000 lb/in 2 Cu 70, Zn 30, cast 42.0 kg/mm 2 or 60,000 lb/in 2 Cu 60, Zn 40, cast 52.5 kg/mm 2 or 75,000 lb/in 2 Cu 50, Zn 50, cast 77.0 kg/mm 2 or 110,000 lb/in 2 Modulus of elasticity, cast brass, average 9100 kg/mm 2 or 13,000,000 lb/in 2 Erichsen values: Soft slab, 1.3 mm (0.05 in.) thick, no rolling, depth of impression 13.8 mm (0.55 in.). Hard sheet, 1.3 mm, rolled 38% reduction, depth of impression 7.3 mm (0.29 in.). Hard sheet, 0.5 mm, rolled 60% reduction, depth of impression 3.7 mm (0.15 in.). Compressive Ultimate Strengths, Cast Bronzes: Cu 97.7, Sn 2.3 to 24.0 kg/mm 2 or 34,000 lb/in 2 Cu 90, Sn 10 to 39.0 kg/mm 2 or 56,000 lb/in 2 Cu 80, Sn 20 to 83.0 kg/ mm 2 or 118,000 lb/in 2 Cu 70, Sn 30 to 105.0 kg/mm 2 or 150,000 lb/in 2 Specification value, A. S. T. M., B 22-18 T, for specimen = cylinder 645 sq. mm (i sq. in.) area, 25.4 mm (i in. > long. Cu 80, Sn 20: minimum Compressive elastic limit = 17.0 kg/mm 2 or 24,000 lb/in a Modulus of elasticity for bronzes varies from 7000 kg/mm 2 or 10,000,000 lb/in 2 to 10,000 kg/mm 2 or 15,500,00^ lb/in 2 * Values marked thus are S. A. E. Spec, values. (See S. A. E. Handbook, Vol. I, p. i3a, rev. December, 1913. t Red metal. t Low brass or bell metal. A. S. T. M. Spec. Big-iST requires B.h.n. of 51-65 kg/mm 2 @ 5000 kg pressure for 70: 30 annealed sheet brass. FOOT NOTES TO TABLE 65, PAGE 85. *Tensilite, Cu6?, Zn 24, Al 4.4, Mn 3.8, P o.oi compressive P-limit: 42.2 kg/mm 2 or 60,000 lb/in 2 and 1.33 per cent set for 70.3 kg/mm 2 or 100,000 lb/in 2 load. t Compressive P-limit 20.0 to 28.2 kg/mm 2 or 28,500 to 40,000 lb/in 2 t Compressive ultimate strength 54.5 kg/mm 2 or 77,500 lb/in 2 Compressive P-limit 4.2 kg/mm 2 or 6000 lb/in 2 and 40 per cent set for 70.3 kg/mm 2 or 100,000 lb/in 2 ^ Modulus of elasticity 9840 kg/mm 2 or 14,000,000 lb/in 2 , || Values are for yield point. ** Minimum values for ingots. ft Rolled manganese bronze (U. S. N.) Cu 57 to 60, Zn 40 to 37, Fe max. 2.0, Sn 0.5 to 1.5; 2.9 per cent increase for thickness 25.4 mm (i in.) and under. it Ni 9 per cent, B.h.n. = 130 as rolled; B.h.n. = 50 as annealed at 930 C. U. S. Navy Dept. Spec. 468 3a, June i, 1917: German silver Cu 60 to 67, Zn 18 to 22, Ni min. 15, no mechanical requirements. For list of 30 German silver alloys, see Braunt, " Metallic Alloys," p. 314, "best" (Hiorns), " hard Sheffield," Cu 46, Zn 20, Ni 34. Platinoid Cu 60, Zn 24, Ni 14, W i to 2; high electric resistance alloy with mechanical properties as nickel brass. HII Specification Values, Naval Brass Castings, U. S. Navy, 466 lob, Dec. i, 1917 for normal proportions Cu 62, Zn 37, Sn i, min. tensile strength 17.5 kg/mm 2 or 25,000 lb/in 2 with 15 per cent elongation in 50.8 mm (3 in.). SMITHSONIAN TABLES. TABLE 65. MECHANICAL PROPERTIES. TABLE 65. Copper Alloys Three (or more) Components. tf J If I .1 pi Jg Hardness. Alloy and approx. composition Condition. V * If PH SI 5 S)^' OS'o () per cent. it to O 4> gm per cm ID per ft* Tension, kg/ mm 2 Tension, lb/in 2 Per cent. 1! PQ 1! Brass, Aluminum. . Cast Cu 57,Zn42, Al i . . 40.0 57,000 50.0 Cu s S Zn 41 Al 4. - 6o.O 85,400 16.5 Cu62'.9, Zn 33.3,'A 3.8.1 56.2 80,000 Cu 70.5, Zn 26.4, Al Alum., Manganese.. 3.lJ Cast, tensilite* 13-4 33-0 19,000 47,000 50.0 Cu64, Zn 29, Al3.i Mn 2.5, Fe 1.2.. . 21. 1 68.8 30,000 98,000 16.0 17.0 130 Alum., Vanadium.. . Cu 58.5, Zn 38.5, Al 1.5, V 0.03 Cold drawn . . . 35-6 57-0 50,600 81,400 12.0 14.0 Iron: Cu 56, Zn 41.5, Fe i. Cast 50.7 to 72,000 to 35-o to 35-0 to 109 to 59-2 84,000 22.O 25-0 119 Aich's Metal Cu6o,Zn38.2,Fei.8 Cast 8.42 526 40.3 57,300 Delta Metal r 7 F f Cast, sand.. . 31-7 45,ooo 10.0 CU 57, ^ n 42, re i.. \ Rolled, hard . . 42.2 60,000 17.0 Cu6s,Zn30, Fes.. Rolled hard... 45-5 65,000 Iron, Tin: Cu56.s,Zn40,Fei.5, Cast 23.2 to 49- 2 tO 33, ooo to 70,000 to 35-0 to 35-o to 104 to Sn i.of 26.0 52.8 37,ooo 75,ooo 20.0 22.0 119 Sterro metal: Cu 55, Zn 42.4 Fe 1.8, Sn 0.8 f Cast < Forged ( Hard drawn . . 8.4 525 42.5 53-6 58.5 - 60,500 76,200 83,100 - = = Lead or Yellow brass Cast 8-5 53i 23.2 to 33,000 to 30.0 to 35-O tO ___ 27-5 39,ooo 26.0 30.0 Cu 60 to 63.5, Zn 35 / Sheet ann 25-5 42,000 50.0 to 33-5, Pb 5 to 3. Lead, Tin or \Sheethard.... 42.9 61,000 30.0 Red brass Cast 8.6 535 II. 21.0 16,000 30,000 17.0 19.0 7-o Cu83,Zn7,Pb6,Sn4 Cu 78,Zn9.s, Pb 10, Sn 2 .... Cast 8.87 554 8.4 18.6 12,000 26,500 22. 24.9 Yellow brass: Cu 70, Zn 27, Pb 2, Sn i Cast 8.4 524 7-4 20.7 10,500 29,500 25-0 28.5 53-0 Manganese or Man- ganese bronze Cu 58, Zn 39, Mn Cast, sand U . . 8.3 520 21. 1 tO 49.2 to 30,000 to 70,000 to 30.0 to 3 2.0 to 109 to i8to 0.05 24-6 52.7 35,000! 1 75,ooo 22.0 25.0 119 19 (Sn, Fe, Al, Pb.) Cast, chill .... 22-5 tO 26.0| | 52.7 to 563 32,000 to 3 7, oool | 75, ooo to 80,000 32.0 to 25-0 34.0 to 28.0 119 to 130 i8to 22 Cu 60, Zn 39 Mn, Rolled 8.3 520 31-5 52-5 45,000 75,ooo 25-0 28.0 3O tr Specification values: U. S. Navy, 46 B i6a** 49.2 70,000 20.O U.S.N., 4 6B i 5 a Rolledft 2 4 .6 49-2 ?5,ooo 70,000 3O.O Manganese Vana- dium: Cu 58.6, Zn 38.5, Al Cold drawn . . . 5-6 57-0 50,600 81,400 I2.O 14.0 1.5 Mn 0.5, V 0.03. Nickel: Nickel sil- ver, Cu 60.4, Zn 31.8, Ni 7.7 Cast 1.5 53 0.8 25.3 15,400 36,000 .O.5 ,2.0 46 German silver, Cu 61.6, Zn 17.2, Ni 21. i 8.7 544 3-2 28.8 18,800 40,900 28.5 25.1 80 Cu 60.6, Zn 11.8, Ni 27.3 8.8 547 16.7 37-6 23,700 53,500 32.O 31.4 67 Fine wire: CusS.Zn 24,Nii8 Drawn hard . . 8-5 530 105.5 50,000 Nickel silver tt Nickel Tungsten : Tin: Cu6i,Zn38,Sni... Naval brass, as above Cast, sand Ann. after roll- II. 30.0 15,700 42,600 29-6 32.0 ing 26.0 43-5 37,000 62,000 25.0 37-0 Tobin bronze: as be- Cast .8.3 518 17.6 42.2 25,000 60,000 low Cu 58.2, Zn 39.5 Sn 2.3. Rolled . . 8.4 5 2 4 38.0 56.0 54,000 79,000 35.O 40.0 Cus5,Zn43, Sn 2 Castllll .... 48.4 68,900 48.0 70.0 """" For Footnotes see page 84. SMITHSONIAN TABLES. 86 TABLE 65 (continued). MECHANICAL PROPERTIES. TABLE 65. Copper Alloys Three (or more) Components. Alloy and approx. composition per cent. Condition. Density or weight. 1 .d J fc Ultimate 1 strength. 1 d H eu l! S ^ ti fc c Coo"" Iff Reduct. I of area. 1 Hard- Sfi Brinell(oi 500 kg. % "> gm per cm 3 8.8 9.1 8.9 8.6 Ib. !? r Tension, kg/mm* Tension, Ib/in 2 Per cent. Brass, Tin (continued): Rods:* o to 12.7 mm ($ in.) 12.7 to 25.4 mm (i in.) over 25.4 mm (in.) diam.. Shapes, all Plates to 12.7 mm (i in.) over 12.7 mm ( in.) thick Tubing (wall thickness) o to 3.2 mm (1 in.) 3.2 to 6.4 mm (J in.) Cold drawn See Cu. Al Castt Cast / Cast, sand . \Cast, chill.. Cast CastH CastU Cast 549 570 555 535 19.0 18.3 17.6 iS-7 19-3 17.6 21. 1 19-7 I8. 3 56.5 15.8 13-4 to 16.2 10.9 12.8 I I.O 13.8 13-4 tO 14.1 10.5 9.0 9.2 8.1 28.0 II. 2 tO I4.I 4a.IHl 28.I|||| ax.zlHI 17-6111! 42.2 40.8 38.0 39-4 38.7 39-4 42.2 38.7 35-1 64.5 38.7 IS-S 21. 1 tO 2 4 .6 22.1 24.7 21.0 18.8 21. 1 tO 2 4 .6 21.8 tO 26.0 21.4 19.1 28.6 27.9 46.0 21.8 to 24.6 56.2 42.2 38.7 63.2 3S-i 27,000 26,000 25,000 22,400 27,500 25,000 30,000 28,000 26,000 80,000 22,500 19,000 to 23,000 15,500 18,200 16,000 19,600 19,000 to 20,000 I5,OOO 12,800 13,100 II.SOO 40,000 16,000 to 20,000 60,000 40,000 III 30,000 III 25,ooo|||| 60,000 58,000 54,000 56,000 SS.ooo 56,000 60,000 55,ooo 50,000 92,000 SS.ooo 22,000 30,000 to 35,ooo 31,400 35,200 30,000 26,800 30,000 to 35,000 3 1, ooo to 37,000 30,400 27,200 40,700 39,700 65,000 31,000 to 35,000 80,000 60,000 SS.ooo 90,000 50,000 35-o 40.0 40.0 30.0 32.0 35-o 28.0 32.0 35-0 "5 25.0 20.0 tO 15-0 13-5 4-5 6.0 II iS.oto 15-0 20.0 tO 16.0 4.0 25.0 32.0 31.0 30.0 6.0 to 10.0 I2.O 20.O 25.0 25.0 To ber cold radii todi 29.0 26.0 to 18.0 12.0 3-5 3-5 "5 24.0 to 22.0 3-3 28.0 31-0 Requir bend throi abou us ec thick d i2< aboi s equ amete 65 to 70 II 65 50 to 55 57 to 59 72 to 77 ed col igh is t rad lual ( ness. 3 It al r. 12 8.0 ii 37 .0 i - o Vanadium : Victor bronze, V 0.03, Cu 58.6, Zn 38.5, Al 1.5, Fe i.o U. S. Navy f 49 Bib.... Bronze, Aluminum Lead: Cu 89, Sn 10, Pb i Cu 88, Sn 10, Pb 2 Cu 80, Sn 10, Pb 10 Lead, Phosphor: Cu 80, Sn 10, Pb 10, P trace Lead Zinc, Red brass: Cu8i, Sn7,Pbg, Zn3 Cu 88, Sn 8, Pb 2, Zn 2 Lead, Zinc Phosphor: Cu 73.2, Sn 11.3, Pb 12.0, Zn 2.5.P i Cast**.... Cast Casttt Casttt Rolled Cast Cast . . . . Manganese : Cu88, Snio, Mn 2 Nickel, Zinc: Cu88, Sns,Nis,Zn2(i)... Cu8g, Sn4,Ni 4 ,Zn3(2)... Phosphor : Cu 95 Sn 4 9 P o i CuSg, Sn 10.5, P 0.5. ...... Cu 80, Sn 20, P max. i Rods and bars up to 12.7 mm (i in.) (minimum) over 12.7 mm to 25.4 mm (i in.) over 25.4 mm (i in.) Sheets and plates spring temper Medium temper tfronze, Phosphor: spring wiri, hard-drawn or hard-rolled (U. S. Navy Spec. 22 Ws, Dec. i, 1915)- Cug^, Sn min. 4.5, Zn max 0.3, Fe max. o.i, Pb max. 0.2, P 0.05 to 0.50; max. along, in 203 mm (8 in.) = 4 per cent. Min. tensile Diameter (group limits). Diameter (group limits). Min. tensile strength. kg/mm 2 Ib/in 2 mm in. kg/mm" Ib/in' .0 .0 135,000 125,000 to 6. 35 109.52 100.250 to 0.375 77.5 iio,oco 74.0 105,000 Over 1.59 mm to 3.17 mm (0.125 in.). . 88 * Specification Values, Rolled Brass, Cu 62, Zn 37, Sn i, min. properties after U. S. Navy Spec., 1918. t Specification Values: Jan. 3, 1916, Vanadium Bronze Castings, Cu 61, Zn 38, Sn max. i (inch V). Mimima. I Compressive P-limit 15.5 kg/mm 2 or 22,000 Ib/in 2 5 Compressive P-limit 10.5 kg/mm 2 or 15,000 Ib/in 2 and 28 per cent set for 70 kg/mm 2 or 100,000 Ib/in 2 [I Ultimate compressive strength, 54.2 kg/mm 2 or 77,100 Ib/in 2 (Cu 76, Sn 7, Pb 13, Zn 4). If Compressive P-limit 8.8 to 9.1 kg/mm 2 or 12,500 to 13,000 Ib/in 2 , and 34 to 35 per cent set for 70 kg/mm 2 ** Compression: ultimate strength 49.5 kg/mm 2 or 70,500 Ib/in 2 tt Modulus of Elasticity: (i) 12,200 kg/mm 2 or 17,300,000 Ib/in 2 ; (2) 10,500 kg/mm 2 or 14,000,000 Ib/in 2 it Compressive P-limit 17.6 to 28.1 kg/mm 2 or 25,000 to 40,000 Ib/in 2 and 6 to 10 per cent set for 70 kg/mm* or 100,000 Ib/in 2 load. Specification Values: U. S. Navy 46 B sc, Mar. i, 1917, Cu 85 to oo, Sn 6 to n, Zn max. 4: Cast, Grade i. Im- purities max. 0.8; min. tensile strength 31.6 kg/mm 2 or 45,000 Ib/in 2 with 20 per cent elong. in 50.8 mm (2 in.). t Grade 2. Impurities max. 1.6; min. tensile strength 21.1 kg/mm 2 or 30,000 Ib/in 2 with 15 per cent elong. in 50.8 mm (2 in.). Specification Values: U. S. Navy 468 i^b, Mar. i, 1916, Cu min. 94. Sn min. 3.5, P 0.50, rolled or drawn. Fill Minimum yield points specified: for P-limits assur"" ^6 per cent o( V! Uu =hown. SMITHSONIAN TABLES. TABLE 65 (continued). MECHANICAL PROPERTIES. TABLE 65. Copper Alloys Three (or morel Components. ." tO 'g g |? 'c fi ijjjj 3s Hardness. Alloy and approx. composition. Condition. 1! PH m | fe If h* fijj (3) per cent. . 3J? i V gm per cm 3 ID. per in 3 Tension, kg/mm 2 Tension, Ib/in 2 Per cent. It Bronze : Silicon Cast 46.0 65,000 Cu 70, Zn 29.5, Si 0.5 . . Zinc*Comp. "G" Drawn, hard. . Cast 8.6 535 8.6 74.0 27.4 12,200 IDS, 000 38,900 25.0 21.0 64 13 Admiralty gun metal . . Comm'c'l range Castt 5.6 to 8.4 22.5 to 26.7 8, ooo to 12,000 32,000 to 38,000 25.0 to IO.O 25.0 to 12.0 65 to 75 10 to 20 Spec, values Cast (mins.). . . 21. 1 30,000 14.0 Cu88, Sn8,Zn4 Castt 8.5 530 7-7 27-5 1 1, OOO 39,200 30.5 24.0 58 II Cu8s,Sni3,Zn2 Cast 26.7 38,000 2.5 2-5 25 Zinc, Lead Cu90,Sn6.5,Zn2,Pbi.s Cast .. 8.4 to 23*0 to 12,000 to 34,000 to 3 S o to 34.0 to 50 to Rods and bars || up to II. 2 28.1 16,000 40,000 25.0 26.0 60 12.7 mm ( in.) 28.1 56.2 40,000 80,000 30.0 Required to bend over 12.7 mm to 25.4 cold through mm (i in.) 26.4 52.7 37,500 75,000 30.0 1 20 about ra- over 25. 4 mm (i in.). . Shapes,! | all thicknesses ~ 2 4 .6 26.4 50.7 52.7 35,000 37,500 72,000 75,000 30.0 30.0 dius equal to thickness. Sheets and plates,! |o to 12.7 mm (5 in.) 27-4 54-8 39,000^ 78,000 30.0 " over 12.7 mm (in.).. 26.4 52.7 37,500 75,000 30.0 " AluminumTin : Cu88.5, Alio.4, Sni.2 Aluminum Titanium: Cast, chill.... 26.0 48.0 36,700 68,000 4-5 5-5 !8 9 32 (Cast** 13-9 52.0 19,800 74,ooo 19-5 23-7 IOO 25 Cugo, Al 10 \ Quench, 1 800 C.... 29.0 74.0 40,500 105,200 I.O 0.8 262 Cu 89, Al 10, Fe i Cast ft 7-58 473 14.1 to 45-7 to 20,000 tO 65,000 to 30.0 to 30.0 to 93 to 25 to I 7 .6 56.2 25,OOO 80,000 20.0 20.0 IOO 26 Lead: Cu 71.9, Pb 27.5, Sn 0.5 Cast 4.2 to 6,000 to 3.0 to 4. 2 tO 4.6 6,600 3-2 6.7 Nickel, Aluminum: Cu82.i,Nii4.6, Al 2.5, Zno. 7 Cu85,Sns,Zn5,Pbs. Forged . . . - 44-5 10.5 to 90.0 19-0 to 63,300 1 5,000 to 128,000 27,000 to IO.O 20.0 tO 12.0 2O.O tO 50 to - Cast 3 A 23.2 19,000 33,000 16.0 15.0 62 Cu 83,Sn 14, Zn 2, Pb i Cast 10.5 to 16.2 to 15,000 to 23, ooo to 4.0 to 4.0 to 20 13-4 19.0 19,000 27,000 0.5 0-5 24 Zinc, Phosphor (" Non Gran") Cu86, Sn n,Zn3, Ptr. Cast 13-0 25.0 19,000 35,000 9.0 Vanadium, See Brass, Vanadium. Copper, Aluminum or Aluminum Bronze: Cuoo, Al 10 Cast, sand ||||. 7-5- 468- 3-9 to 51.1 to 19,800 to 7 2, 700 to 28.8 to 30.0 to 102 tO 25 to 7-45 465 23-3 60.0 33,200 85,500 21.7 22.4 106 26 CU92.5, Al 7.2 Rolled, and 7.0 37.5 9,600 53,500 91.0 72.9 81 19 ann. Aluminum, Iron or Sill- Wrought 9.8 59-3 14,000 84,400 "5 man bronze Cast 8.1 55-5 11,500 78,850 14.5 - __ __ t Cu 86.4, Al 9.7, Fe 3.9.. Cast, sand.. 14.0 54-0 20,000 77,000 24.5 25-0 IOO _ f Quenched 850 C. Cu 88.5, Al 10.5, Fe i.o. drawn i 700 C.... 28.0 65.0 40,000 92,000 14.0 18.5 140 : * Gov't. Bronze: Cu 88, Sn 10, Zn 2 (values shown are averages for 30 specimens from five foundries tested at the Bureau of Standards). t Compressive P-limit 10.5 kg/mm 2 or 15,000 lb/in 2 with 29 per cent set for 70 kg/mm 2 or 100,000 lb/in 2 load. t Values from same series of tests as first values for " 88-10-2, averages for 26 specimens from five foundries tested at Bureau., of, Standards. Compressive P-limit 9.1 kg/mm 2 or 13,000 lb/in 2 with 34 per cent set for 70 kg/mm 2 or 100,000 lb/in 2 load. || Specification mimmums: U. S. Navy 46817, Dec. 2, 1918, for hot-rolled aluminum bronze, Cu 85 to 87, Al 7 to 9, Fe 2.5 to 4.5. Specification values under P-limit are for yield point. f Two and six tenths per cent increase in strength up to 762 mm (30 hi.) width. ** Compressive P-limit: cast, 14.1 kg/mm 2 or 20,000 lb/in 2 with 11.4 per cent set at 70 kg/mm 2 or 100,000 lb/in* ft Compressive P-limit: cast, 12.7 to 14.1 kg/mm 2 or 18,000 to 20,000 lb/in 2 with 13 to 15 percent set at 700 kg/mm* or 100,000 lb/in 2 load. tt Modulus of elasticity 14,800 kg/mm 2 or 21,150,000 lb/in 2 Compressive P-limit 8.4 kg/mm 2 or 12,000 lb/in 2 with 36 per cent set for 70.3 kg/mm 2 , or 100,000 lb/in 2 load. II II High values are after Jean Escard " L 'Aluminum dans L'Industrie," Paris, 1918. Compressive P-limit 13.5 kg/mm 2 or 19,200 lb/in 2 with 13.5 per cent set for 70.3 kg/mm 2 or 100,000 lb/in 2 load. SMITHSONIAN TABLES. 88 TABLE 66. MECHANICAL PROPERTIES- TABLE 66. Miscellaneous Metals and Alloys. Metal or alloy. Approx. composition, per cent. Condition. Density [ or weight. 1 *j h Ultimate 1 strength. 1 P-limit. Ultimate 1 strength. 1 .5 g_ f' .B ? ~, wST |l aS'o Hard- ness. Brinell @ "too ktr. l| ^ gm per cm 8.8 8.9 iQ-3 17.2 11.38 11.40 10.5 1-7 i? 8.7 8.9 12. 1 21.5 10.5 10.57 16.6 7-3 lb. S Tension, kg/mm 2 Tension, lb/in 2 Per cent. * Cobalt, Co 99.7 . . Cast S5o 556 1203 i73 710 711 6s"s 1 06 I0( 5i8 543 555 755 1342 655 660 1035 456 2.8 i67** 12.6 21.2 SS-i 28.3 22.8** 28.1** 21. 1 I.I 23.1 26.0 18.0 26.0 45-8 102.0 1.3 2.; i. 2. 4-5 21.0 23. 26.7 29.9 46.0 64.7 53-4 109.0 49-3 73-8 64.8 112.5 45-7 56.2 45-7 27.0 37-3 24.6 28.1 36-0 77.0 91.0 2.8 3-7 7.0 IO.2 9.1 8.6 IO.I 4,000 23,800 ** 17,000 30,100 78,400 40,300 32,500** 40,000 ** 30,000 i, 600 33,ooo 37,000 25,000 37,ooo 65,100 145,000 i,78o 3,300 2,420 3,130 6,400 30,000 33,ooo 38,000 42,500 65,000 92,000 76,000 155,000 70,000 104,000 92,200 160,000 65,000 80,000 65,000 39,ooo 53,ooo 35,ooo 40,000 51,200 109,500 130,000 4,000 5,300 10,000 14,500 13,000 12,200 14,300 25.0 5-7 II.O II.O 35-0 18.0 31-3 46.3 25.0 32.0 15-0 18.0 50.0 35-0 1.9 1.6 41.0 8.0 6.1 20.0 61.7 7O.2 1-5 1-3 81.0 41.0 121 48 8 76 83 59 14 20 2 35 21 27 24 13 32 8 Gold, Au 100 /Cast \ Drawn hard Drawn hard Drawn hard Cast { Rolled hard.... j Drawn soft .... [ Drawn hard .... Cast Copper, Au go, Cu 10 Copper, Silver, Au 58, Cu 30 Ag 12 ,ead, Pbf (Comm'c'l.) Antimony iPbgs.5,Sb4.5 Magnesium, Mg. < Drawn hard Cast Wrought, aim. . . Wrought, com Rolled hard, " Rolled ann. ' Drawn hard, D = 1.65 mm or 0.065 in /Cast. . Nickel, Ni 98.5 Ni 99.95. . Nig8 <; Ni . ft. Ni Copper, iron, manganese or Monel metal: Ni 67, Cu 28, Fe 3, Mn 2 . Ni 66, Cu 28, Fe 3-S, Mn 2-5 Ni7i,Cu27, Fe2 46 Mia || \Rolled Wrought Drawn hard Cast, minimums. Rolled, min., rods \ and bars 11.. .. I Rolled, mini- < mum, sheets [ and plates. . . . Drawn hard. . . . Drawn hard ... . Drawn ann Cast 46 Mybll II Palladium, Pd Platinum, Pt Silver, Ag 100 Copper, Ag 75, Cu 25.... Tantalum, Ta Tin, Sn 99.8ft Antimony, Copper, Zinc (Britannia Metal): Sn8i,Sbi6, Cua.Zni. Zinc, Aluminum, etc. (aluminum solder): Sn63,Zni8, Al 13, Cu 3, Sb 2, Pb i Sn62, Znis,Alu,Pb 8, Cu 3 ,Sbi Zinc, aluminum: Sn 86, Zn 9, Al 5 Aluminum, zinc, cad- mium: Sn 78, Al 9, Zn 8, Cd 5 . Drawn hard. . . . Drawn hard. . . . Drawn hard. . . . f Cast Rolled [ Drawn hard Cast Cast Cast, chill Cast, chill Antimony: Modulus of Elasticity 7960 kg/mm 2 or 11,320,000 lb/in 2 (Bridgman). *Compressive strength: cast and annealed, 86.0 kg/mm 2 or 122,000 lb/in 2 . Comm'c'l. comp., C 0.06, cast, tensile, ultimate, 42.8 kg/mm 2 or 61,000 lb/in 2 , with 20 per cent elongation in 50.8 or 2 in. Compression, ultimate 123.0 kg/mm 2 or 175,000 lb/in 2 Stellite, Co 59.5, Mo 22.5, Cr 10.8, Fe 3.1, Mn 2.0, Co.g, Si 0.8. Brinell hardness 512 at 3000 kg. t Modulus of elasticity, cast or rolled, 492 kg/mm 2 or 700,000 lb/in 2 ; drawn hard 703 kg/mm 2 or 1,000,000 lb/in 2 I For compressive test data on lead-base babbitt metal, see table following zinc. Modulus of elasticity 15,800 kg/mm 2 or 22,500,000 lb/in 2 . || Specification values, U. S. Navy, Monel metal, Ni min. 60, Cu min. 23, Fe max. 3.5, Mn max. 3.5, C + Si max. 0.8, Al max. 0.5. 1 Values shown are subject to slight modifications dependent on shapes and thicknesses. ** Values are for yield point. tt Compressive strength: cast, 4.5 kg/mm 2 or 6,400 lb/in 2 Modulus of elasticity: cast av. 2,810 kg/mm 2 or 4,000,000 lb/in 2 ; rolled av. 401.0 kg/mm 2 or 5,700,000 lb/in 2 SMITHSONIAN TABLES. TABLE 67. MECHANICAL PROPERTIES. TABLE 67. Miscellaneous Metals and Alloys. (a) TUNGSTEN AND ZINC. Metal or alloy Density or weight. 1 +J-C ! If -ji Sg |s Hardness. approx. Condition. fc p &s W <) comp. per cent. gm per cm 3 Ib. per ft 3 Tension, kg/mm- Tension, lb/in 2 Per cent P II (J u (/) * Ingot sintered, D = 5.7 mm or 0.22 in. 18.0 1124 12.7 _ 18,000 0.0 0.0 _ Swaged rod, D = 0.7 mm or 0.03 in. 151.0 215,000 4.0 28.0 Drawn hard, Tungsten, W99-2* I D = 0.029 mrn or - - - 415.0 164.0 500,000 233,5oo 3-2 65.0 14.0 - Swaged and drawn hot 97.5%reductionf.. . Same as above and equiaxed at 2oooC in Hzt 118.0 168,000 0.0 o.o _ Cast 7-o 437 (I mpurities Pb, Fe ind Cd) Coarse crystalline. . . . 2.8 to 4,000 to 42 to 8 to Fine crystalline 8.4 12,000 48 10 Zinc, Zn: Rolled (with grain or direction of rolling) . _ _ 2.0 19.0 2,900 2 7 ,000 _ Rolled (across grain or direction of rolling) . 4-1 25-3 5,8oo 36,000 Drawn hard M 443 7-o 10,000 * Commercial composition for incandescent electric lamp filaments containing thoria (ThCh) approx. 0.75 per cent after Z Jeffries Am. Inst. Min. Eng. Bulletin 138, June, 1918. f After Z Jeffries Am. Inst. Min. Eng. Bulletin 149, May, 1919. t Ordinary annealing treatment makes W brittle, and severe working, below recrystallization or equiaxing tempera- ture, produces ductility W rods which have been worked and recrystallized are stronger than sintered rods. The equiaxing temperature of worked tungsten, with a s-min. exposure, varies from 2200 C for a work rod with 24 per cent reduction, to 1350 C ior a fine wire with 100 per cent reduction. Tungsten wire, D = 0.635 rnm or 0.025 in. Compression on cylinder 25.4 mm (i in.) by 65.1 mm (2.6 in.), at 20 per cent deformation: For spelter (cast zinc) free from Cd, av. 17.2 kg/mm 2 or 24,500 lb/in 2 . For spelter with Cd 0.26, av. 27.4 kg/mm 2 or 39,000 lb/in 2 . (See Proc. A. S. T. M., Vol. 13, pi. 19.) Modulus of rupture averages twice the corresponding tensile strength. Shearing strength: rolled, averages 13.6 kg/mm 2 or 194,000 lb/in 2 . Modulus of elasticity: cast, 7,750 kg/mm 2 or 11,025,000 lb/in 2 Modulus of elasticity, rolled, 8450 kg/mm 2 or 12,000 ooo lb/in 2 . (Moore, Bulletin 52, Eng. Exp. Sta. Univ. of 111.) (6) WHITE METAL BEARING ALLOYS (BABBITT METAL). A. S. T. M. vol. xviii, I, p. 491. Experimental permanent deformation values from compression tests on cylinders 31.8 mm (ij in.) diam. by 63.5 mm (2$ in.) long, tested at 21 C (70 F.) (Set readings after removing loads.) Permanent deformation @ 21 C Hardness. Al- loy No per cent. temp. Weight. @ 454 kg = i ooo Ib. @ 2268 kg = 5000 Ib. @ 4536 kg = 10,000 Ib. _-CJ .S M JJO 88 Sn Sb Cu Pb C F. g/cm 3 lb./ft 3 mm in. mm in. mm in. @ @@ Tin Base. i 91 o 4.5 4-5 440 824 7-34 4S8 0.000 o.oooo 0.025 O.OOIO 0.380 0.0150 28.6 12.8 2* 89.0 7-5 3 432 808 7-39 46! .000 .0000 .038 .0015 305 .0120 28.^ 12.7 3 8.S.3 8.3 8.3 491 916 7.46 465 .025 .0010 .114 .0045 .180 .0070 34-4 15.7 4 75-0 12.0 3-o IO.O 360 680 7-52 469 .013 .0005 .064 .0025 .230 .0090 29.6 12.8 5 65.0 15-0 2.0 18.0 350 66 1 7-75 484 .025 .0010 .076 .0030 .230 .0000 29.6 n.8 Lead Base. 6 2O.O 15.0 i-5 6 3 .S 337 638 9-33 582 .038 .0015 .127 .0050 457 .Ol8o 24-3 ii. i 7 IO.O 15-0 75-0 329 625 9-73 607 .025 .0010 .127 .0050 .583 .0230 24.1 11.7 8 5-0 15-0 80.0 329 625 10.04 627 .051 .0020 .229 .0090 1-575 .0620 20.9 10.3 9 5-o IO.O 85.0 319 616 10.24 640 .102 .0040 305 .0120 2.130 .0840 19-5 8.6 10 2.O 15.0 83.0 325 625 10.07 629 .025 .0010 254 .0100 3.910 1540 17.0 8.9 ii 15.0 85.0 325 625 10.28 642 .025 .0010 254 .0100 3.020 .1190 17.0 9.9 12 IO.O 90.0 334 634 10.67 666 0.064 0.0025 0.432 0.0170 7.240 0.2850 14-3 6.4 * U S. Navy Spec. 46M2b (Cu 3 to 4.5, Sn 88 to 89.5, Sb 7.0 to 8.0) covers manufacture of anti-friction-metal castings. > Composition W.) NOTE. See also Brass, Lead (yellow brass), Brass, Lead-Tin (Red Brass); Bronze, Phosphor, etc., under Copper alloys SMITHSONIAN TABLES. TABLE 68. MECHANICAL PROPERTIES. TABLE 68. Cement and Concrete. (a) CEMENT. CEMENT: Specification Values (A. S. T. M. Cg to 17, Cio to 09, and Cg to i6T). Minimum strengths based on tests of 645 mm 2 (i in 2 ) cross section briquettes for tension, and cylinders 50.8 mm (2 in.) diameter by ioi.6mm (4 in.) length for compression. Mortar, composed of i part cement to 3 parts Ottawa sand by volume; specimens kept in damp closet for first 24 hours and in water from then on until tested. Cement Specific Tension. Age, Compression. (1:3 mortar tested). gravity. days. . . kg/mm 2 Ib/in* kg/mm 2 lb/in 2 Std. Portland. 3.10 7 o. 16 2OO 0.85 1,200 White Portland 3-07 28 .24 300 1.60 2,000 Natural Av. . . 2.85 7 3 5 Natural 28 0.09 125 (b) CEMENT AND CEMENT MORTARS. CEMENT AND CEMENT MORTARS. Bureau of Standards Experimental Values. Corn- pressive Strengths of Portland cement mortars of uniform plastic consistency. Data from tests on 50.8 mm (2 in.) cubes stored in water. Sand: Potomac River, representative con- crete sand. Cement. Sand. Water, Age, days. Compressive strength. Proportions by volume. per cent. kg/mm 2 Ib/itf I 30.0 7 4. 2O 5,970 28 6.40 9,120 I i 16.0 7 3.10 4,440 28 4-75 6,750 I 2 13-6 7 2 05 2,900 28 3.10 4,440 I 3 13-9 7 I 25 1,780 28 2 05 2,890 I 9 15 . i 7 O. 10 1 20 28 c 15 200 NOTE. (From Bureau of Standards Tech. Paper 58.) Neat cement briquettes mixed at plastic consistency (water 21 per cent) show 0.52 kg/mm 2 or 740 lb/in 2 tensile strength at 28 days' age; i Cement: 3 Ottawa sand-mortar briquettes, mixed at plastic consistency (water 9 per cent) show 0.28 kg/mm 2 or 400 lb/in 2 tensile strength at 28 days' age. SMITHSONIAN TABLES. TABLE 68 (continued). MECHANICAL PROPERTIES. (c) CONCRETE . CONCRETE: Compressive strengths. Experimental values for various mixtures. Results compiled by Joint Committee on Concrete and Reinforced Concrete. Final Report adopted by the Committee July i, 1916. Data are based on tests of cylinders 203.2 mm (8 in.) diameter and 406.4 mm (16 in.) long at 28 days age. American Standard Concrete Compressive Strengths. Aggregate. Units. Mix. 1:4* 1:6 Granite, trap rock Gravel, hard limestone and hard sandstone . . Soft limestone and soft sandstone. . Cinders. kg/mm 2 lb/in 2 kg/mm 2 lb/in 2 kg/mm 2 lb/in 2 kg/mm 2 lb/in 2 2-3 2.1 3000 2 2OO 0.6 800 2.O 2800 1.8 2500 1800 700 2 2OO 1-4 200O I.I 1500 0.4 600 1800 i.i 1600 0.8 1 200 0.4 500 i .o 1400 0.9 1300 0.7 1000 o-3 400 NOTE. Mix shows ratio of cement (Portland) to combined volume of fine and coarse aggregate (latter as shown). Committee recommends certain fractions of tabular values as safe working stresses in reinforced concrete design, which may be summarized as follows: Bearing, 35 per cent of Compressive strength; Compression, extreme fiber, 32.5 per cent of Compressive strength; Vertical shearing stress 2 to 6 per cent of Compressive strength, depending on reinforcing; Bond stress, 4 and 5 per cent of Compressive strength, for plain and deformed bars, respectively. Modulus of Elasticity to be assumed as follows: For concrete with strength. Assume modulus of elasticity. kg/mm 2 lb/in 2 kg/mm 2 lb/in 8 up to 0.6 0.6 to 1.5 1-5 tO 2 . over 2 . o up to 800 8OO tO 2200 2200 tO 2900 over 2900 530 1400 2IOO 750,000 2,OOO,OOO 2,500,000 3,000,000 (See Joint Committee Report, Proc. A. S. T. M. v. XVII, 1917, p. 201.) EDITOR'S NOTE. The values shown in the table above are probably fair values for the Compressive strengths of concretes made with average commercial material, although higher results are usually obtained in laboratory tests of specimens with high grade aggregates. Observed values on 1:2:4 gravel concrete show moduli of elasticity up to 3160 kg/mm 2 or 4,500,000 lb/in 2 and Compressive strengths to 4.2 kg/mm 2 or 6000 lb/in 2 Tensile strengths average 10 per cent of values shown from Compressive strengths. Shearing strengths average from 75 to 125 per cent of the Compressive strengths; the larger percentage representing the shear of the leaner mixtures (for direct shear, Hatt gives 60 to 80 per cent of crushing strength) . Compressive strengths of natural cement concrete average from 30 to 40 per cent of that of Portland cement concrete of the same proportioned mix. Transverse strength: modulus of rupture of i : 2\ : 5 concrete at i and 2 months, equal to one sixth crushing strength at same age (Hatt). Weight of granite, gravel and limestone, 1:2:4 concretes averages about 2.33 g/cm 3 or 145 lb/ft 3 ; that of cinder concrete of same mix is about 1.85 g/cm 3 or 115 lb/ft 3 Concrete, 1:2:4 Mix, Compressive Strengths at Various Ages. Experimental Values: one part cement, two parts Ohio River sand and four parts of coarse aggregate as shown. Compressive tests made on 203.2 mm (8 in.) diameter cylinders, 406.4 mm (16 in.) long. (After Pitts- burgh Testing Laboratory Results. See Rwy Age, vol. 64, Jan. 18, 1918, pp. 165-166.) Coarse aggregate. Unit. Age. 14 days. 30 days. 60 days. 180 days. Gravel Limestone Trap rock Granite Slag No. i SlasNo. 2.. kg/mm 2 lb/in 2 kg/mm 2 lb/in 2 kg/mm 2 lb/in 2 kg/mm 2 lb/in 2 kg/mm 2 lb/in 2 kg/mm 2 lb/in 2 i-3S 1921 1.24 1758 1-45 2063 1.49 2122 *-75 2484 i-37 1941 1.61 2294 i-53 2174 1.67 2386 1.61 2292 2.16 3075 1.78 2525 2.06 2925 2-35 3343 2.36 2.14 3043 2-37 3365 2.06 2930 2.67 3798 3-n 4426 3-39 4819 2.92 3-38 4803 2.64 3753 NOTE. Maximum and minimum test results varied about 5 percent above or below average values shown above. SMITHSONIAN TABLES. 92 TABLE 69. MECHANICAL PROPERTIES. TABLE 69. Stone and Clay Products. (a) STRENGTH AND STIFFNESS OF AMERICAN BUILDING STONES.* Stone. Weight, average. Compression. Ultimate strength. Flexure. Modulus of rupture. Shear. Ultimate strength. Flexure, modulus of elasticity. Average. si Average. to II 30 50 IOO 55 Average. Range per cent. Average. Range per cent. ! * 1 1 <& 1 H & c g 1 I ^ M I. 60 O.QO I.OO I. 2O { .c 1 I SO M lb/in Granite. . . Marble. . . Limestone Sandstone. 2.6 2-7 2.6 2.2 165 170 1 60 135 14.20 8.85 6.30 8.80 20,2OO 12,600 9,000 12,500 25 25 95 5 !-i5 1.05 0.85 1.05 1600 ISOO I20O 1500 2300 I3OO 1400 I7OO 20 25 45 45 5300 5750 5900 2300 7,500,000 8,200,000 8,400,000 3,300,000 25 50 65 IOO * Values based on tests of American building stones from upwards of twenty-five localities, made at Watertown (Mass.) Arsenal (Moore, p. 184). Each value shown under "Range" is one half the difference between maximum and minimum locality averages expressed as a percentage of the average for the stone. (b) STRENGTH AND STIFFNESS OF BAVARIAN BUILDING STONE.* Stone. Weight, average. Compression. Ultimate strength. Flexure. Modulus of rupture. Shear. Ultimate Strength.! Flexure. Modulus of elasticity. Average. Range per cent. Average. 8>g u o *l 5 45 55 Average. || g" P4 a Average. -|! r/ S & M 1 1 fco J4 "h > 5 *h I "is ja 1C M I.OO 0-45 0.6O 0.50 .Is jQ kg/mm 2 Ib/irf Granite. . Marble t Limestone Sandstone 2.66 2.16 2.48 2.30 165 135 155 145 13.70 5.60 8.10 8.10 19,500 8,000 11,500 11,500 5 15 5 75 0. 9 0.30 I. 10 o-45 1300 450 1550 650 1420 62O 870 680 o 50 20 35 1600 3450 2350 2500 2,300,000 4,900,000 3,350,000 3,550,000 30 90 35 * Values based on careful tests by Bauschinger, " Communications," Vol. 10. t Shearing strength determined perpendicular to bed of stone, j Values are for Jurassic limestone. GENERAL NOTES. i. Later transverse strength (flexure) tests on Wisconsin building stones (Johnson's "Materials of Construction," 1918 ed., p. 255) show moduli of rupture as follows: Granite, 1.90 to 2.75 kg/mm 2 or 2710 to 3910 lb/in 2 ; limestone, 0.80 to 3.30 kg/mm 2 or 1160 to 4660 lb/in 2 ; sandstone, 0.25 to 0.95 kg/mm 2 or 360 to 1320 lb/in 2 . 2. Good slate has a modulus of rupture of 4.90 kg/mm 2 or 7000 lb/in 2 (loc. cit., p. 257). SMITHSONIAN TABLES. TABLE 69 (continued). MECHANICAL PROPERTIES- TABLE 69. Stone and Clay Products. 93 (c) STRENGTHS OF AMERICAN BUILDING BRICKS.* Brick description. Absorption average per cent. Compression. Min. ult. strength. Flexure. Min. modulus rupture. kg/mm 2 Vb/vf kg/mm 2 Ib/in* Class A (Vitrified) 5 12 18 3-50 2-45 1 .40 1.05 5000 3Soo 2OOO I5OO 0.65 0.40 0.30 O. 2O QOO 600 400 300 Class B (Hard burned) Class C (Common firsts) Class D (Common) * After A. S. T. M. Committee C~3, Report 1913, and University laboratories' tests for Committee C~3 (Johnson, p. 281). (d) STRENGTH IN COMPRESSION OF BRICK PIERS AND OF TERRA-COTTA BLOCK PIERS. Tabular values are based on test data from Watertown Arsenal, Cornell University, U. S. Bureau of Standards, and University of 111. (Moore, p. 185). Brick or block used. Mortar. Compression.* Av. ult. strength. kg/mm 2 lb/in 2 Vitrified brick Pressed (face) brick Pressed (face) brick. i part P.f cement : 3 parts sand .... i part P. cement : 3 parts sand i part lime : 3 parts sand i part P. cement : 3 parts sand i part lime : 3 parts sand i-95 1.40 I. 00 0.70 0.50 2. IO 2800 200O 1400 1000 700 3000 Common brick Common brick Terra-cotta brick. . . i part P. cement : 3 parts sand * Building ordinances of American cities specify allowable working stresses in com- pression over bearing area of 12.5 per cent (vitrified brick) to 17.5 percent (common brick) of corresponding ultimate compressive strength shown in table. t P. denotes Portland. (e) STRENGTH OF COMPRESSION OF VARIOUS BRICKS. Reasonable minimum average compressive strengths for other types of brick than building brick are noted by Johnson, "Materials of Construction," pp. 289 ff., as follows: Brick. kg/mm 2 lb/in 2 sand-lime .- . 2 IO 3OOO sand-lime (German) . . . I ^"? 2180 (av 255 tests) paving 5 60 8000 acid-refractor v o 70 IOOO silica-refractory . . . I AO 2OOO The specific gravity of brick ranges from 1.9 to 2.6 (corresponding to 120 to 160 lb/ft 3 ). Building tile: hollow clay blocks of good quality, minimum compressive strength: 0.70 kg/mm 2 or 1000 lb/in 2 . Tests made for A. S. T. M. Committee C-io (A. S. T. M. Proc. XVII, I, p. 334) show compressive strengths ranging from 0.45 to 8.70 kg/mm 2 or 640 to 12,360 lb/in 2 of net section, corresponding to 0.05 to 4.20 kg/mm 2 or 95 to 6000 lb/in 2 of gross section. Recommended safe loads (Marks, "Mechanical Engineers' Handbook," p. 625) for effective bearing parts of hollow tile: hard fire-clay tiles 0.06 kg/mm 2 or 80 lb./in 2 ; ordinary clay tiles 0.04 kg/mm 2 or 60 lb/in 2 ; porous terra- cotta tiles 0.03 kg/mm 2 or 40 lb/in. 2 The specific gravity of tile ranges from 1.9 to 2.5 corresponding to a weight of 120 to 155 lb/ft 3 . SMITHSONIAN TABLES. 94 TABLE 70. MECHANICAL PROPERTIES. TABLE 70. Rubber and Leather. (a) RTJBBER, SHEET.* Ultimate strength. Ult. elongation. Set| Grade. Longitudinal.f Transverse. Longit. Transv. Longit. Transv. kg/mm 2 lb/in* kg/mm 2 lb/in* per cent. per cent. I I.Q2 2730 l.8l 2575 630 640 II . 2 7-3 2 i-45 2070 1-43 2030 640 670 6.0 5-0 3 0.84 1200 0.89 1260 480 555 22.1 I6. 3 4 1.30 1850 I .20 1700 410 460 34-o 24.0 5 0.48 6 9 0.36 5io 320 280 27-5 25.0 6 0.62 880 0.48 690 315 3i5 34-3 25-9 * Data from Bureau of Standards Circular 38. f Longitudinal indicates direction of rolling through the calendar. t Set measured after 300 per cent elongation for i minute with i minute rest. The specific gravity of rubber averages from 0.95 to 1.25, corresponding to an average weight of 60 to 80 lb/ft 3 . Four-ply rubber belts show an average ultimate tensile strength of 0.63 to 0.65 kg/mm 2 or 890 to 930 lb./in 2 (Benjamin), and a working tensile stress of 0.07 to o.n kg/mm 2 or 100 to 150 lb./in 2 is recommended (Bach). (6) LEATHER, BELTING. Oak tanned leather from the center or back of the hide: Minimum tensile strengths of belts f single 2.8 kg/mm 2 or 4000 lb./in 2 (Marks, p. 622) \ double 2.5 kg/mm 2 or 3600 lb./in 2 Maximum elongation for one hour application of J single 13.5 per cent 1.6 kg/mm 2 or 2250 lb./in 2 stress \ double 12.5 percent. Modulus of elasticity of leather varies from an average value of 12.5 kg/mm 2 or 17,800 lb/in 2 (new) to 22.5 kg/mm 2 or 32,000 lb./in 2 (old). Chrome leather has a tensile strength of 6.0 to 9.1 kg/mm 2 or 8500 to 12,900 lb/in 2 . The specific gravity of leather varies from 0.86 to 1.02, corresponding to a weight of 53.6 to 63.6 lb./ft 3 . SMITHSONIAN TABLES. TABLE 71. MECHANICAL PROPERTIES. 95 TABLE 71. Manila Rope. Manila Rope, Weight and Strength Specification Values. From U. S. Government Stand- ard Specifications adopted April 4, 1918. Rope to be made of manila or Abaca fiber with no fiber of grade lower than U. S. Govern- ment Grade I, to be three-strand,* medium-laid, with maximum weights and minimum strengths shown in the table below, lubricant content to be not less than 8 nor more than 12 per cent of the weight of the rope as sold. Approximate diameter. Circumference. Maximum net weight. Minimum breaking strength. mm in. mm in. kg/m Ib/ft. kg Ib. 6-3 i 4 19.1 1 0.029 0.0196 320 700 7-9 A 25-4 I 0.044 0.0286 540 1,2.00 9-5 t 28.6 li 0.061 o . 0408 660 i,45o ii. i A 3i-8 li- 0.080 0.0539 790 i,750 ii. 9 If 34-9 it 0.095 0.0637 950 2,100 12.7 i 38-1 i* o. 109 0-0735 I, IIO 2,450 14-3 A 44-5 T 3 * 4 0.153 o. 1029 1,430 3,15 15-9 f 50.8 2 0-195 0.1307 1,810 4,000 19. i .3 4 57-2 2| 0.241 0.1617 2,220 4,900 20. 6 H 63-5 2* 0.284 o. 1911 2,680 5,900 22.2 7 8 69.9 af 0.328 0.2205 3,i7o 7,000 2S-4 I 76.2 3 0-394 o . 2645 3,720 8,200 27.0 *A 82.6 3* 0-459 o . 3087 4,3io 9,5oo 28.6 ii 88.9 3* 0-525 0.3528 4,990 11,000 31-8 ii 95-2 3f 0.612 0.4115 5,670 12,500 33-3 IT 5 101 .6 4 0.700 0.4703 6,440 14,200 34-9 it 108.0 4t 0.787 0.5290 7,260 16,000 38-1 ii H4-3 4l 0-875 0.5879 7,940 17,500 39-4 iA 120.7 44 0.984 0.6615 8,840 19,500 41.2 if 127.0 5 1.094 0.7348 9,750 21,500 44-5 if 140.0 5* 1.312 0.8818 n,55o 25,500 50.8 2 152-4 6 I-576 1.059 13,610 30,000 52.4 2& 165.1 6* 1.823 1.225 15,420 34,000 57-2 a* 177-8 7 2.144 1.441 17,460 38,500 63.5 2* 190 5 ?i 2.450 1.646 19,730 43,5oo 66.7 2f 203.2 6 2-799 1.881 22,220 49,000 73-o 2f 215-9 8* 3-I36 2.107 24,940 55,ooo 76.2 3 228.6 9 3-543 2.381 27,670 61,000 79-4 si 241-3 9i 3-936 2.645 30,390 67,000 82.5 si 254.0 10 4-375 2.940 33,no 73,ooo * Four-strand, medium-laid rope when ordered may run up to 7 % heavier than three-strand rope of the same size, and must show 95 % of the strength required for three-strand rope of the same size. SMITHSONIAN TABLES MECHANICAL PROPERTIES. TABLE 72. Hardwoods Grown in U. S. (Metric Units). Common and botanical name. Specific gravity, oven-dry, based on Static bending. Impact bend- ing. Compression. Shear Ten- sion. Hardness. 1 1? Modulus of elasticity, kg/mm 2 5 04 II rt 3 si fi S| Parallel to grain. Perpendicular to grain P-limit, kg/mm 2 8 "3 ^ 12- s Load to i imbed 11.3 mm d. ball vol. when green. vol. oven- dry. *! J .*}" I s PH Modulus of rupture, Ib/in 2 Modulus of elas- ticity i ooo X Ib/in 2 % pi Parallel to grain. 1 Perpendicular to grain, P-limit Ib/in"- 1 oti Perpendicular to grain, ult. st. Ib/in 2 Green. Air- dry. P- limit. lb/ft !* Ib/irf 1 2 11 13 14 15 Alder, red (Alnus oregona) Ash, black (Fraxinus nigra) Ash, white (forest grown). (Fraxinus americana) Ash, white (2d growth) . . (Fraxinus americana) Aspen (Populus tremuloides) Basswood (Tilia americana) Beech Wash. Mich, and Wis. Ark. and W. Va. N. Y. Wis. Wis. and Pa. Ind. and Pa. Wis. and Pa. Wis. Tenn. and Wis. Pa. Md. and Tenn. Mo. Tenn. Tenn. Wis. Wis. and Pa. Cal. La. Mo. Mo. O., Miss., Pa. and W. Va. Tenn. Tenn. Tenn. Mo. and Ind. La. Wis. Ind., Pa. and Wis. Cal. Ark., La., Ind. and Tenn. Ark., La. and Ind Mo. Tenn. Ind. and Tenn. Ky. 98 83 43 40 107 103 62 72 68 104 55 122 III 80 62 50 88 79 97 81 63 60 82 62 40 63 117 66 60 62 84 68 58 64 83 81 46 53 46 51 47 41 55 51 58 46 46 55 49 So 65 54 52 70 56 50 61 64 57 62 58 Oi 62 46 56 71 64 62 63 38 52 58 28 34 40 46 27 26 44 38 45 27 36 30 29 33 54 45 35 54 34 36 46 51 40 49 49 47 35 34 44 56 45 47 53 28 35 39 3800 2600 4900 6lOO 29OO 27OO 4500 2900 4600 2900 4200 3100 29OO 4200 4 800 4600 3600 7600 4200 3700 5200 5900 3400 5800 8800 56OO 360O 3100 5OOO 6300 3700 4700 5600 320O 3300 5400 6500 6000 9100 10800 5300 5000 8 ,oo' 5800 8600 5400 8000 5600 5300 7400 8800 9500 6900 1 1 200 7300 6800 9800 1 1 000 6500 8400 13800 10200 6800 5800 9IOO 10600 7700 8300 10000 5600 6500 9500 1170 IO2O 1350 1640 840 1030 1240 IOIO 1540 970 1310 930 IOIO 1560 1180 1190 1030 20IO IO50 1150 1370 1570 900 920 1850 1290 IIIO 940 1480 1340 1290 1250 1370 I2IO 1060 I42O 8000 7200 11700 13800 6900 6200 10400 7800 11700 7300 IO20O 7900 7200 9300 7IOO IIOOO 8 loo 14200 oooo 1 0000 12300 14400 8900 IO200 18300 11800 8800 6800 1 2 100 II200 IO4OO 10700 I2IOO 8000 8800 II900 2650 1620 3230 3820 1620 1710 2550 1650 2760 1960 2940 2040 1770 2760 2870 2290 4870 2760 2360 3040 3430 1970 6280 3320 2200 1950 3120 4050 2330 2990 3030 2 OOO 2390 360O 310 430 800 790 200 210 610 300 450 270 440 380 240 410 1030 750 390 I02O 590 460 9 60 1000 610 IIIO 1430 1420 570 460 75o 1480 730 830 IIIO 310 450 600 770 870 1260 1600 620 610 I2IO 790 IIIO 760 1130 800 680 990 1520 1270 920 1550 1190 1070 1480 1320 1130 1670 1760 1660 1040 1050 1380 1700 1 1 20 I25O 1470 790 1000 1220 390 490 620 790 180 280 760 380 480 430 570 430 410 440 660 560 640 600 Sio 680 610 770 930 610 560 770 970 740 770 770 460 630 570 (Fagus atropunicea) Birch paper (Betula papyri/era) Birch, 3'ellow (Betula lutea) Butternut (Juglans cinerea) Cherry, black (Prunus serotina) Chestnut (Castanea dentata) Cottonwood (Populus deltoides) Cucumber tree (Magnolia acuminata) Dogwood (flowering) .... (Cornus florida) Elm, cork (Ulmus racemosa) Elm white (Ulmus americana) Gum, blue (Eucalyptus globulus) Gum, cotton (Nyssa aquatica) Gum, red (Liquidambar styracifiua) Hickory pecan (Hicoria pecan) Hickory, shagbark (Hicoria ovata) Holly, American (Ilex opaca) Laurel, mountain (Kalmia latifolia) Locust black (Robinia pseudacacia) Locust, honey (Gledilsia triacanlhos) Magnolia (evergreen) (Magnolia joetida) Maple silver (Acer saccharinum) Maple, sugar (Acer saccharum) (Quercus chrysolepsis) Oak red (Quercus rubra) Oak, white (Quercus alba) Persimmon (Diospyros virginiana) Poplar, yellow (Liriodendron tulipifera] (Platanus occiJentalis) Walnut, black (Juglans nigra) NOTE. Results of tests on sixty-eight species; test specimens, small clear pieces, 2 by 2 inches in section, 30 bending; others, shorter. Tested in a green condition. Data taken from Bulletin 556, Forest Service, U. S. Dept. containing data on 130,000 tests. See pages 97 and 99 for explanation of columns. SMITHSONIAN TABLES. inches long tor of Agriculture, MECHANICAL PROPERTIES. TABLE 75. Conifers Grown in U. S. (English Units). 99 Common and botanical name. Locality where grown. Moisture content, j green, per cent. Weight. Static bending. Impact lending. Compression. Shear. Ten- sion. 1 J2" I Modulus of rupture, Ib/in 2 Modulus of elas- ticity looo X Ib/in 2 1 f& Parallel to grain Perpendicular to grain, P-limit Ib/in 2 fe 2 ! Green. Air- dry. Perpendicula grain, ult. st. 1 P- limit. 3* -53 1* !~ Ib/ftP Ib/in 2 r 1 2 3 4 5 6 7 8 9 11 13 14 15 Cedar, incense (Libocedrus decurrens) Cedar Port Orford Cal. and Ore. Ore. Wash, and Mont. Wis. ^a. and Mo. Ore. and Wash. Wis. Wash, and Ore. VIont. and Wyo. VIont. and Ore. Ore. Cal. Tenn. and Wis. Wash. VIont. and Wash. Fla. 1 08 52 39 55 87 102 117 36 38 94 41 156 105 71 58 47 70 65 47 54 85 64 123 58 95 74 43 53 52 44 45 39 27 28 48 47 45 38 34 44 31 56 48 41 48 53 54 39 5 42 54 50 50 39 46 39 34 33 47 54 24 3i 23 21 30 27 25 34 32 27 26 26 29 29 37 45 39 28 43 34 35 37 26 30 28 27 28 26 38 45 3900 3900 3300 2600 4000 3900 3000 5000 3600 3600 34oo 3000 4200 3400 4600 5600 4400 3000 5400 3700 37oo 45oo 3300 3Soo 3100 3400 3400 3000 4200 6500 6200 6800 5200 4200 6800 6300 4900 7800 6400 6100 5700 6000 6700 6100 75oo 8800 7500 55oo 8700 6400 6700 8000 5300 5700 5200 5300 5700 SSoo 7200 IOIOO 840 1500 950 640 1190 1300 960 1580 1180 1300 1280 1130 1120 1190 1350 1630 1380 1080 1630 1380 1 1 20 1450 970 1330 1010 IO7O 1 1 80 1180 1240 990 7300 9300 7100 5300 8000 7800 6900 9400 9100 8100 7900 7200 7900 7800 9400 11300 9500 7200 10800 7500 9100 1 1 200 6700 7600 6700 6500 7200 7000 7800 13100 2870 3970 2500 1420 3100 2380 222O 3400 2520 2680 2370 26lO 2710 2290 3250 3950 2870 2100 3840 2470 2100 3650 2340 2770 2080 2370 2360 2280 3010 34^3 460 380 3io 290 470 320 210 530 450 340 310 440 500 350 560 590 550 310 600 360 510 4 80 350 300 340 310 350 330 480 1040 830 880 720 620 820 670 610 910 880 700 700 730 880 810 920 1030 900 690 1070 780 950 800 710 710 680 640 770 780 860 1620 280 240 2IO 240 280 240 i So 200 350 230 | I 180 260 263 260 2. S3 2QD 280 220 2QO igo 3SO 330 270 250 280 rfg 220 2.SO 260 450 (Chamaecyparis law- soniana) Cedar western red (Thuja plicata) Cedar, white (Thuja occidentalis) (Taxodium distichum) Fir, amabilis (Abies amabilis) Fir balsam (Abies balsamea) Fir, Douglas (i) (Pseudntsuga taxifolia) Fir Douglas (2) (Pseudotsuga taxifolia') (Abies grandis) (Abies nobilis) Fir, white (Abies concolor) Hemlock (eastern) (Tsuga canadensia) Hemlock (western) (Tsuga heterophylla) (Larix occidentalis) Pine Cuban (Pinus heterophylla) Pine, loblolly (Pinus taeda) Pine, lodgepole ?la., N. anc S. Car. Col., Mont, and Wyo. Fla., La. anc Miss. Wis. Tenn. Ark. and La. Cal. Mont. Col., Mont., Ariz., Wash and Cal. Wis. N H and (Pinus contorta) (Pinus palustris) Pine, Norway (Pinus resinosa) Pine pitch (Pinus rigida) (Pinus cchinata) (Pinus lambcrtiana) (Pinus monticola) Pine, western yellow .... (Pinus pondcrosa) Pine white (Pinus slrobus) (Picea rubcns) Spruce, Sitka (Picca sitchensis) Tenn. Wash. Wis. Wash. (Larix laricina) Yew western (Taws brevifolia) COLUMN NOTES (continued). (7) recommended allowable working stress (interior construction): I tabular value; experi- mental results on tests of air-dry timber in small clear pieces average 50 per cent higher; kiln-dry, double tab alar values; (1 repeated falls of so-lb. hammer from increasing heights; 11-12, 2O3.2-mm (8 in.) long specimen* loader! on ends with deformations measured in a i52.4-mm (6 in.) gage length; (12) allowable working stress \ tabular crushing strength; (13) iS2.4-mm (0 in.) long block loaded on its side with a central bearing area of 2s8o.6-mm 2 (4 in 2 ) allowable working stress, j tabular value. (14) so.8-mm by 50 8-mm (2 in.) projecting lip sheared from block; allowable working stress, J tabular value; (15) 63.5-mm (2^ in.) specimen with 25.4-mm (i in.) free loaded length; allowable working stress, J tabular value. (16-17) for values in Ibs. multiply values of metric tables by 2.2. SMITHSONIAN TABLES. 100 TABLES 76-77. ELASTIC MODULI- TABLE 76. Rigidity Modulus If to the four consecutive faces of a cube a tangential stress is applied, opposite in direction on adjacent sides, the modulus of rigidity is obtained by dividing the numerical value of the tangential stress per unit per sq. mm.) by the number representing the change of angles on the non-stressed faces, measured in radians. Substance. Rigidity Refer- Substance. Rigidity Modulus. Refer- ence. . 335 2 5 80 355 37'5 37oo 1240 4060 2450 4780 4-i3 445 4664 2850 3950 5210 6706 7975 6940 8108 755 1710 7820 4359 '4 ! 5 ; 10 II 5 * 5 j 10 19 5 14 5 '5 10 , 7 6 H 5 5 ii Quartz fibre 2888 2380 2960 2650 2566 2816 8290 7458 8070 7 8 7 2 173 '543 3880 3820 6630 6220 235 2730 1770 1280 1190 2290 2O 21 5 10 16 ii 16 15 5 ii 5 i9 5 J 9 16 2 3 23 23 23 ii it "i UM Silver cast, 6oCu+ 12 Sn . ith, slowly cooled . . Bronze, cast, 88Cu+ 12 Sn. ti " hard-drawn .... : Steel " cast '* cast, coarse gr. . . . " silver- i Tin, cast M Zinc u Glass . ... M .esium, cast .... 1'hosphor bronze .... Granite Marble . . Slate References 1-16, see Table 48. 21 Boys, Philos. Mag. (5) 30, 1890. Ann. 28, 1886. 22 Thomson, Lord Kelvin, i. 1 6, 1829. 23 Gray and Milne. 19 K .ttingen, 1886. 24 Adams-Coker, Carnegie Publ. No. 46, 20 Threlfall, Philos. Mag. (5) 30, 1890. 1906. TABLE 77. -Variation of the Rigidity Modulus with the Temperature. * = n<> ( i a/ ft/' 2 yt' 4 }, where / = temperature Centigrade. Substance. Me aio /3io* yio" Authority. ^ . 21 S 8 48 3 2 Pisati, Nuovo Cimento, t 34, 1879. Copper 3200 3972 455 2716 36 2 3 47 Kohlrausch-Loomis, Pogg. Ann. 141. Pisati, loc. cit. 1 ff 572 28 K and L, loc. cit. 1 8108 206 19 1 1 Pisati, loc. cit. *' 6940 48} 12 _ K and L, loc. cit. . . Silver . 1 1 1 387 -8 ii I'i^ati, loc ( 41 cit. H 8290 i7 59 -9 * = is ('(/! 5)1; Horton, Philos. Trans. 204 A, 1905. - per (com- mercial) Iron 4-37* 26 8.45 a =.00039 .00038 .00029 .00026 Platinum Gold Silver i Aluminum 6.46* 2-45 2.67 2-55 a = .0001 2 .00031 .00048 i .00148 Tin i. Lead o. Cadmium 2. Quartz 3. 50* a =.00416 So .00 1 64 31 .0058 DO .00012 SMITHSONIAN TABLC*. * Modulus of rigidity in io dynes per sq. cm. TABLES 78-81 . TABLE 78. Interior Friction at Low Temperatures. IOI C is the damping coefficient for infinitely small oscillations; T, the period of oscillation in sec- onds; N, the second modulus of elasticity. Guye and Schapper, C. R. 150, p. 963, 1910. Substance ... ... Cu Ni \u Pd Pt Ona T\7 Length of wire in cm . 22.5 22.2 22.3 22.2 23.0 17.2 17-3 Diameter in mm 643 .411 .609 553 .812 .601 .612 100 C C 24.1 I -34 27-5 1.67 2.98 55-8 _ T 2. 3 8lS 3 . 83 i s 3.0IOS 2.579 i . 1435 i.8o8s Nxio- 11 .... 3-32 7-54 2-55 5-08 5-77 2.71 oC C 5-88 .417 4.82 1.25 4.60 7.19 4.69 T 2.336s 3-754S 2.9695 2.5715 i 133s I-759S I . 4085 Nxio- 11 .... -195 C C .... 3-45 3-64 7-85 .556 2.62 6.36 5.12 744 3-02 2.87 1.64 2.26 1.02 T 2.2748 3-577S 2.9025 2.5525 I. HIS 1.6945 1.4255 Nxio- 11 .... 3.64 8.65 2.74 5-19 6.10 3.18 2.20 TABLE 79. Hardness. Agate 7. Brass 3-4. Iridosmium 7. Sulphur r -5- 2 -5 Alabaster 1.7 Caiamine . 5. Iron 4-5. Stibnite 2. Alum 2-2.5 Calcite 3. Kaolin i. Serpentine 3-4. Aluminum 2. Amber 2-2.5 Copper 2.5-3. Corundum 9. Loess (o) 0.3 Magnetite 6. Silver 2 -5-3- Steel 5-8.5 Andalusite 7.5 Diamond 10. Marble 3-4. Talc i. Anthracite 2.2 Dolomite 3.5-4- Meerschaum 2-3. Tin 1.5 Antimony 3.3 Feldspar 6. Mica 2.8 Topaz 8. Apatite 5. Flint 7. Opal 4-6. Tourmaline 7.3 Aragonite 3.5 Fluorite 4. Orthoclase 6. Wax (o) 0.2 Arsenic 3.5 Galena 2.5 Palladium 4.8 Wood's metal 3. Asbestos 5. Garnet j. Phosphorbronze 4. Asphalt 1-2. Augite 6. Glass 4.5-6.5 Gold 2.5-3. Platinum 4.3 Platin-iridium 6.5 Barite 3.3 Graphite 0.5-1. Pyrite 6.3 Beryl 7.8 Gypsum 1.6-2. Quartz 7. Bell-metal 4. Hematite 6. Rock-salt 2. Bismuth 2.5 Hornblende 5.5 Ross' metal 2.5-3.0 Boric acid 3. Iridium 6. Silver chloride 1.3 From Landolt-Bbrnstein-Meyerhoffer Tables : Auerbachs, Winkleraann, Handb. der Phys. 1891. TABLE 80. Relative Hardness of the Elements. C IO.O Ru 6-5 Cu 3- Au 2-5 Sn 1.8 Li 0.6 B 95 Mn Sb Te 2-3 Sr 1.8 P 0.5 Cr 9.0 Pd 4.8 Al 2.9 Cd 2.O Ca '5 K -5 Os 7.0 Fe 4-5 Ag 2-7 S 2.0 Ga i-S Na 0.4 Si 7.0 Pt 4-3 Bi 2.5 Se 2.0 Pb '5 Rb Ir 6.5 As 3-5 Zn 2-5 Mg 2.0 In 1.2 Cs 0.2 Rydberg, Zeitschr. Phys Chem 33, 1900 TABLE 81. Ratio, p, of Transverse Contraction to Longitudinal Extension under Tensile Stress. (Poisson's Ratio.> Metal Pb Au Pd Pt Ag Cu Al Bi Sn Ni Cd Fe P o-45 0.42 o-39 o-39 0.38 o-35 0-34 o-33 0-33 0.31 0.30 0.28 From data from Physikalisch-Technischen Reichsanstalt, 1907. p for: marbles, 0.27; granites, 0.24; basic-intrusives, 0.26; glass, 0.23. Adams-Coker, 1906. SMITHSONIAN TABLES. 102 TABLE 82. ELASTICITY OF CRYSTALS. The formulae were deduced from experiments made on rectangular prismatic bars cut from the crystal. These bars were subjected to cross bending and twisting and the corresponding Elastic Moduli deduced. The symbols a /3 y, o, /J, y, and cu /3 -y., represent the direction cosines of the length, the greater and the less transverse dimensions of the prism witn reference to the principal axis of the crystal. E is the modulus for extension or compression, and 1 is the modulus for torsional rigidity. The moduli are in grams per square centimeter. ;te. 10* -g- = i6.i 3 + i8. 5 i0' + 10.427* 4- ;( 3 8.7<;0 V 4 i 5-2i7-' I0 io -^- = 69. 5 2a* 4- 1 1 7.66)8' -f- 1 16.467' -f 2(20. 1 60V -f 85.297-^ + 1 27.350^) Beryl (Emerald). io^ u -g- = 4.325 sin'9 4 4.619 cos 4 ? 4 13.328 sin 2 cos-?) io 10 -Y- = 1 5.00 3.675 cos 4 4> 2 1 7-536 cos-p cos-9i Fluorite. lo io -JT = ^'OS 6-26 (a< 4 ! 4 7*) ~Y = 58-04 5 - 08 (/B V' + 7'- -f '-'-) Pyrite. Ig= 5.08 - 2.24 (a 1 4 0' 4- 7 1 ) io 10 -^- = 18.60 1 7.95 (0V 4 7'a- 4 0-0^) Rock salt. ^- = 33-48 9.66 (a 4 4 4 4 7 l ) Io io -^- = 1 54-58 77-28 (0 V 4 7 '- 4 o-0 ') Sylvite. ^p- = 7S- 1 48-2 (o 4 + 0*4 7 4 ) io 10 - = 306.0 192.8 (0V 4 7- a- 4 a-0') where 0j . 2 are the angles which the length, breadth, and thickness of the specimen make with the principal axis of the crystal. ' Topaz. io 10 -^- io 10 =4-34' a 4 4 3-46o0 4 4 3-77 17 4 4 2 (3.8 79 0V+ 2.8567-^4 2.39^0-) 4 .88a* 4 16.540* 4 I6-457 4 + 3O-890V 4 4O.8cy)rV 4 43-5i-0- Quartz. ^ = 1 2.734 ( I yi)* 4 1 6.693 ( ' 7-)7 J 4 9-7057 4 8.46007 ( 3B -' 0-^) 15_ := ,9.665 + 9-060742 4 22.98 4 7'-7i- ~ 16.920 [(70H- 07i) (3a, - 00i) - 0, 7 , These formulx are taken from Volt's papers (Wied. Ann. vols. 31, 34, and 35). SMITHSONIAN TABLES. TABLE 83. ELASTICITY OF CRYSTALS. I0 3 Some particular values of the Elastic Moduli are here given. Under E are given moduli for extension or compression in the directions indicated by the subscripts and explained in the notes, and under T the moduli for torsional rigidities round the axes similarly indicated. Moduli in grams per sq. cm. (a) ISOMETRIC SYSTEM.* Substance. E a E, E,. T Authority. Fluorite 1473 X 10 1008 X io 6 910 X io 6 345 X io 6 Voigt.t Pvrite 3530 X 4I9X 1C 6 2530 X io 6 349 X io 6 2310 X io 6 303 X io 6 1075 X io' J I29X io 6 M Rock salt . . . " . 403 x IO 6 339 X io 6 Koch.J Sylvite 401 X IO 6 209 X 10 ' Sodium chlorate 372 X 405 x 1$ 196 X io 6 319 X io 6 655 X lo- 5 Voigt. Koch. Potassium alum . . 181 X 1 06 i99Xio Beckenkamp. Chromium alum 161 X I0 177 X io 6 " Iron alum . . . . I86X IO 6 ((>) ORTHORHOMBIC SYSTEM.|| Substance. E, E, i E, E, | E S E, Authority. 1'arite Topaz 620 X io e 2304 X io fi 540 X 2890 X IO 6 IO 6 959 X io 6 2652 X io 6 I 376 X io 6 1 702 X io 6 2670 X io 6 2893 X 10 740 X io 3180 X io 6 Voigt. M Substance. T lf -t,, T 13 = T 31 T..-T,, Authority. Barite Topaz 283 X io 6 1336X106 293 Xio 6 I353X io 6 121 X IO 6 II04X io 6 Voigt. In the MONOCLINIC SYSTEM, Coromilas (Zeit. fiir Kryst. vol. i) gives Gypsum \ mi 1 = 887X106 at n = 313 x io 6 at 21.9 to the principal axis. 75.4 Mica [ Em u = 2213 X io 6 in the principal axis. IE. n = 1554 x io 6 at 45 to the principal axis. In the HEXAGONAL SYSTEM, Voigt gives measurements on a beryl crystal (emerald). The subscripts indicate inclination in degrees of the axis of stress to the principal axis of the crystal . E = 2165 X io 6 , E 46 = I796X io 6 , E 90 =23i2 X io 6 , TO = 667 X io 6 , T 90 = 883X io 6 . The smallest cross dimension of the prism exp< mmented on (see T able 82), was in the principal axis for this last case. In the RHOMBOHEDRAL SYSTEM, Voigt has measured quartz. The subscripts have the same meaning as in the hexagonal system. E = 1030X10, E_ 45 =1305X106, E +4 5 = 850X10, E 90 = 785X10, To = 508 X io 6 , T 90 = 348 X io 6 . Baumgarten^T gives forcalcite E == 501 X io'\ E_ 45 = 441 X io' 1 , E + 45 = 772 X io 6 , E 9 o = 79 X io r> . * In this system the subscript a indicates that compression or extension takes place along the crystalline axis, and distortion round the axis. The subscripts b and c correspond to directions equally inclined to two and normal to the third and equally inclined to all three axes respectively. f Voigt, " Wied. Ann." 31, p. 474, p. 701, 1887; 34, p. 981, 1888; 36, p. 642, 1888. J Koch, " Wied. Ann." 18, p. 325, 1882. Uecketikamp, "Zeit. fiir Kryst." vol. io. li The subscripts i, 2, 3 indicate that the three principal axes are the axes of stress; 4, 5. 6 that the axe; are in the three principal planes at angles of 45 to the corresponding axes. IT Baumgarten, " Poj-g. Ann." 152, p. 369, 1879. SMITHSONIAN TABLES. TABLES 84-86. COMPRESSIBILITY OF GASES. TABLE 84. Relative Volumes at Various Pressures and Temperatures, the volumes at O 8 C and at 1 atmosphere being taken as 1 000 000. Oxygen. Air. Nitrogen. Hydrogen. Aim. 99-5 i99-5 99-4 200. 4 99.S i99.6 99.3 200. 5 100 200 3 00 400 5 600 700 800 900 9265 4570 3208 2629 2 3 I2 2115 1979 1879 1800 7000 4343 3830 3 2 44 2867 26lO 2417 2268 6283 4900 4100 3570 3 202 2929 2718 973 5050 3658 3036 2450 2288 2168 2070 7360 S^o 4170 3565 3180 2904 2699 2544 9430 6622 5240 4422 3883 3502 3219 3000 9910 5'95 3786 3142 2780 2543 2374 2240 2149 7445 53 01 4265 3655 2775 2616 9532 6715 533' 4515 3973 3589 330 3085 5690 4030 3207 2713 2387 2149 1972 I8 3 2 7567 5286 4M7 3462 3006 2680 2444 2244 9420 6520 575 4210 3627 3212 2900 2657 IOOO 1735 2151 1992 2415 2828 2068 1720 2093 Amagat: C. R. m, P- 871, 1890; Ann. chim. phys. (6) 29, pp. 68 and 505, TABLE 85, Ethylene. pv at o C and i atm. = I. Atm. 10 20 30 40 60 80 100 i37-5 i 9 8.5 4 6 . 0.562 0.684 . . . _ _ _ _ 4 8 0.508 50 0.176 O.42O O.629 0.731 0.814 0-954 1.077 1.192 1-374 1.652 52 0.240 O.598 - 0.229 0.56l - - - ~ c6 O.22/ 0.524 100 O.3IO o-33 i 0.360 0.403 0.471 0.668 0.847 1.005 1.247 1.580 150 2OO 300 0.441 0.365 0.8o6 o-459 0.385 0.827 0.485 0.610 0.852 o-S^ 0.638 0.878 0.551 0.669 0.649 0-744 0.972 0.776 0.838 1.048 0.924 0.946 1.133 1.178 1.174 1.310 1.540 1-537 1.628 5 00 IOOO 1.2,6 2.289 1.280 2.321 1.308 2-354 2'. 3 8 7 1.367 2.422 I-43I 2-493 1.500 2.566 1.578 2.643 1.721 2-798 1.985 Amagat, C. R. m, p. 871, 1890; 116, p. 946, 1893. TABLE 86. Relative Gas Volumes at Various Pressures. The following table, deduced by Mr. C. Cochrane, from the PV curves of Amagat and other observers, gives the relative volumes occupied by various gases when the pressure is reduced from the value given at the head of the column to i atmosphere: Gas. (Tcmp.= x6C.). Relative volume which the gas will occupy when the pressure is reduced to atmospheric from " Perfect " gas I atm. I I 50 atm. 50 48.5 50-5 50.9 52.3 69.0 100 atm. 100 93.6 100.6 101.8 105.2 107.9 477* 120 atm. 1 2O III. 3 120.0 I2I-9 128.6 485* 150 atm. ISO 136.3 147.6 150.3 161.9 498* 200 atm. 2OO 176.4 190.8 194.8 212.6 218.8 515* Hydrogen \ir Oxygen Oxygen (ato C.) * Carbon dioxide is liquid at pressures greater than 90 atmospheres. SMITHSONIAN TABLES. TABLES 87-89. COMPRESSIBILITY OF GASES. TABLE 87. Carton Dioxide. 10 Pressure in Relative values of pv at mercury. l8.2 35-' 40,2 50.o 60. o 70. o 8o.o 90 .0 I00.0 30 liquid 2 3 60 2460 259 ; 2730 2870 2995 3120 3225 1725 I 9 00 2145 i 2330 2525 2685 2845 2980 80 62 S 750 825 1200 1650 1975 2225 2440 2635 no 825 93 980 1090 1275 i 1550 1845 ! 2105 2325 140 1 020 1 1 20 1175 1250 1360 1525 1715 ! J 95 2160 170 I2IO 1310 1360 1430 1520 1645 1780 i J975 2135 200 1405 1500 1550 1615 1705 ; 1810 1930 2075 2215 230 T 59 1690 1730 1800 1890 1990 2090 2210 2340 260 1770 1870 1920 1985 2O7O 2166 2265 2375 2490 290 1950 2060 2IOO 2I7O 226O 2340' 2440 2550 2655 3 20 2i35 2240 2 280 2360 2440 2525 2620 2725 2830 Relative values of pv ; pv at o C. and i atm. = i. 10 20 1 30 40 i 60 80 100 137 198 258 5 0.105 0.114 0.680 0-775 0-75 0.984 1.096 1. 206 .380 100 0.202 0.213 0.229 0.255 0.309 0.661 0.8 7 3 1.030 259 1.582 1.847 150 0.295 0.309 0.326 0.346 0.377 0-485 0.681 0.878 -I.S9 1.530 1.818 300 0-559 0.578 0-599 0.623 0.649 0.710 0.790 0.890 .108 1.493 1-820 500 0.891 0.913 0.938 0.963 0.990 1.054 I.I24 I.2OI 362 1.678 IOOO 1.656 1.685 I.7I6 1.748 1.780 1.848 I. 9 2I 1.999 " Araagat, C. R. in, p. 871, 1890; Ann. chim. phys. (5) 22, p. 353, 1881; (6) 29, pp. 68 and 405, 1893. TABLE 88. Compressibility of Gases. p.v. (\ atm.) i vfi M E^gjX sis* Reference. 1 Substance. o d 1 Pressure, megabars. *N-o I^X li rs Reference. 1 Acetone 14 20 20 23 500 I OOC III 61 C.2 9 I j Ethyl ether, ct'd.. tt tt ti Ethyl iodide... 20 20 2O I, OOO I2,OOO 2OO 61 10 81 I I 16 M 4.O I ^ OOO 9 I M 2O 4.OO 60 16 ;Yrnyl alcohol Id. 27 88 IO a 2O *;oo 64 i iso... 2O 2OO 84 1 6 a 2O 1,000 co i " iso... 20 2O 400 70 61 16 i (c Gallium 20 IO 12,000 200 8 7 C 7 i 6 i. n ti 20 2O 1,000 I ^ OOC 46 8 i i Glycerine Hexane 15 o 5 200 22 117 12 16 4.O I "> OOO 8 i 20 4.00 01 16 Benzene 17 80 2 3 Kerosene 20 C.OO c; i 2O ?OO 77 16 u 20 I, OOO AC i u 2O 4OO 6? 16 tt 20 I2,OOC 8 i Bromine ^6* 16 ll 12 OOO 8 I 3 14 2O 4.OO CJ 16 Mercury 20 3OO VQ"> 7 Butyl alcohol, iso.. " iso.. " iso.. " iso.. iso.. ." I s0 ' ' Carbon bisulphide. . it n ti Carb. tetrachloride. a n lo 2O 20 20 20 2O 16 20 2O 2O 20 2O 8 200 400 500 I, OOO 12,000 21 50C 1,000 12,000 200 AOO 97 81 64 56 46 8 86 57 48 6 86 7* 2 16 16 i i i 10 i i i 16 16 M (4 Methyl alcohol. . . . u ( a u it it it tt Nitric acid Oils: Almond Castor 22 22 22 15 2O 20 2O 2O 2O O 15 I r 500 I, OOO 12,000 23 200 400 500 I,OOO I2,OOO 17 5 r 3-97 3-9i 2-37 103 95 80 65 54 8 32 53 46 8 | 8 10 16 16 i j i U T -> ~ : 12 Chloroform tt 2O 2O 200 4OO 83 70 16 16 Linseed Olive 15 I ^ 5 5i 12 12 Dichlorethylsulfidc . Ethyl acetate 32 3^ I 3 I, OOO 2,000 2? 34 24 jO"? 5 5 IO Rape-seed Phosph. trichloride . 2O IO 2O 250 ^oc 59 71 0} 15 II I M tt it tt Ethyl alcohol a n 2O 20 14 23 2D 2OO 400 23 500 I, OOO 90 75 100 63 CA 16 16 10 i i it tt Propyl alcohol, n. . . " n... " (n?) 2D 20 20 2O 2O 1,000 12,000 2OO 400 sOO 47 S 77 67 65 I I 16 16 i tt n Ethyl bromide. . it it tt 20 2O 20 2O 12,000 200 40O COQ 8 IOO 82 70 i 16 16 " (n?). " (n?). Toluene 20 20 20 2O 1,000 12,000 2OO 4OO 47 7 74 64 i i 16 it. it tt it it 2O 2O 1,000 12,000 54 8 Turpentine Water 20 2O 13 74 4-) 15 ii Ethyl chloride. ICT 2 3 i ^i IO 2O 2OC 43 it) 2O rOO IO2 a 2O 4OO 41 if. it 2O I OOO 66 a 2O 50C 59 4 it it 2O I2,OOO 8 u 4O 50C P 4 Ethyl ether. . 2< 2T. 1 88 IO tt 4O IOOO 33 4 a it 2O ?OC 84. i tt 4O 12,000 9 4 Xylene, meta it tt 20 2O 200 4OO 69 60 16 i 16 For references, see page 108. IITHSONIAN TABLES. loS I ABLE 93. COMPRESSIBILITY OF SOLIDS. If I" is the volume of the material under a pressure P megabars and Vo is the volume at atmospheric pressure, then the compressibility = (i/l'o) (dV/dP). Its unit is cmVmegadynes (reciprocal megabars). io 6 //3 is the bulk modu- lus in absolute units (dynes/cm 1 ). The following values of /8, arranged in order of increasing compressibility, are for P = o and room temperature, i megabar = io dynes = 1.013 kg/cm 2 = 0.987 atmosphere. Substance. Compres- sion per unit vol. per mega- bar X io Bulk modulus. dynes/cm 1 X 10* Reference. Substance. Compres- sion per unit vol. per mega- bar X io Bulk modulus. dynes/cm 2 Xio' 2 Reference. Tungsten Boron Silicon Platinum 0.27 0-3 32 .38 53 :8 .60 7 75 .84 .89 99 03 33 39 74 89 09 17 3-7 3-0 3-1 -3 .2 9 I .67 4 33 .19 .12 .12 .OI 0.97 0.75 0.72 0-57 0.53 0.48 0.46 I 2 I 2 i 3 5 I, 2 Plate glass Lead 23 .27 3 4 7 9 3-0 3-0 3-1 4.12 4-5 5-7 7-4 9-0 9-2 12. O 12.9 13-0 IS.6 20.5 31-7 40.0 61.0 0-45 0.44 0.43 0.42 0-37 0-34 0.33 0.33 0.32 0.24 0.22 O.I7S 0.135 0. Ill 0.109 0.083 0.078 0.077 0.064 0.049 O.032 0.025 0.016 I 2 Thallium. Antimony Quartz... ...;.... Nickel Molybdenum .... Tantalum Palladium Magnesiui Bismuth . Graphite. Silica glas Sodium ch Arsenic . . Calcium . Potassium Lithium . . Phosphorv Selenium . Sulphur.. Iodine . . . Sodium . . Phosphoru Potassium Rubidium Calcium . n i Gold . loride . . . chloride is (red)'.'. s (white) Pyrite Copper Brass Chromium Silver. . . Mg. silicate, crys. Aluminum Calcite Zinc. Tin Gallium Cadmium NOTE. Winklemann, Schott, and Straulel (Wied Ann. 61, 63, 1897, 68, 1899) give the following coeffi- cients (among others) for various Jena glasses in terms of the volume decrease divided by the increase of pressure expressed in kilograms per square millimeter: No. Glass. Compres- sibility. 1 Xo. Glass. Compres- sibility. 665 .. 7520 5800 4530 3790 2154 S 208 500 S 196 Kalible Heavies Very H Tonerdl silicat 3660 1209 Barytbo 16 Nutnmk 278 'osilicat tBleisilicat. eavy Bleisili( sorat with s< . 3550 e 3470 ilkzinksilicat :at )dium, baryt The following values in cm 2 /kg of io X Compressibility are given for the corresponding temperatures by Griineisen, Ann. der Phys. 33, p. 65, 1910. Al 191, 1.32; 17, 1.46; 125, 1.70. Fe 190, 0.61; 18, 0.63; 165, 0.67. Cu 191, 0.72; 17, 0.77; 165, 0.83. Ag 191, 0.71; 16*, 0.76; 166, 0.86. Pt 189, 0.37; 17, 0.39; 164, 0.40. Pb 191, (2.5); 14, (3.2). References to Table 92, p. 107: (1) Bridgman, Pr. Am. Acad. 49, i, 1913; (2) Roentgen, Ann. Phys. 44, i, 1891; :;tni-l'al;izzo, Mem. Acad. Lin. 3, 18, 1883; :^'man, Pr. Am. Acad. 48, 341, 1912; (s) Adams, Williamson, J. Wash. Acad. Sc. 9, Jan. 19, 1919; (6) Richards, Boyer, Pr. Nat. Acad. Sc. 4, 389, 1918; (7) Richanl-,, J. Am. Ch. Sex:. 37, 1646, 1915; \m. Acad. 47, 381, 1911; (9) Amagat, C. R. 73, 143, 1872; do) Amagat, C. R. 68, 1170, 1869; (n) Amagat, Ann. chim. phys. 29, 68, 505, 1893; (12) de Metz, Ann. Phys. 41, 663, 1890; (13) Adams, Williamson, Johnston, J. Am. Chem. Soc. 41, 27, 1919; (14) Colladon, Sturm, Ann. Phys. 12, 39, 1828; (15) Quincke, Ann. Phys. 19, 401, 1883; (16) Richards el al. J. Am. Ch. Soc. 34, 988, 1912. References to Table 93, p. 108: (1) Adams, Williamson, Johnston, J. Am. Ch. Soc. 41, 39, tpXJK (2) Richards, ibid. 37, 1646, 1915; (3) Bridgman, Pr. Am. Acrid. 44, 279, 1909; 47, 366, 1911; (4) Adams, Williamson, unpublished; (5) Richards, Boyer, Pr. Nat. Acad. Sc. 4, (6-) Voigt, Ann. Phys. 31, 1887; 36, 1888. 5, 1918; SMITHSONIAN TABLES. TABLE 94. SPECIFIC GRAVITIES CORRESPONDING TO THE BAUME SCALE. The specific gravities are for i5.56C (6oF) referred to water at tLe same temperature as unity For specific gravities less than unity the values are calculated from the formula : Degrees Baume = 140 Specific Gravity 130. For specific gravities greater than unity from: Degrees Baume = 145 - Specific Gravity Specific Gravities less than i. 0.00 0.01 O.O2 0.03 0.04 0.05 0.06 0.07 O.o8 O.OQ Specific i Gravity. Degrees Baume'. 0.00 1 03-33 99-5 1 95.81 92.22 88.75 85.38 82.12 78.95 75.88 72.90 .70 7O.OO 67.18 6444 61.78 59-19 56.67 54-21 51.82 49-49 47-22 .80 45.00 42.84 40-73 38.68 36-67 34-7 J 32.79 30.92 29.09 27-30 .90 23-85 22.17 20.54 18.94 17-37 15-83 M-33 12.86 11.41 1. 00 IO.OO Specific Gravities greater than i. o.oo 0.0 1 0.02 0.03 0.04 0.05 ! 0.06 ' 0.07 0.08 0.09 Specific i Gravity. Degrees Baume. .OO O.OO 1.44 2.84 4.22 5.58 6.91 8.21 9.49 10.74 11.97 .IO 13.18 14-37 15-54 16.68 17.81 18.91 20.00 21.07 22.12 2 3- r 5 .20 24.17 25.16 26.15 27.11 28.06 29.00 29.92 30-83 31-73 32.60 30 .40 4M3 48.33 54.38 59-71 6444 34.31 42.16 48.97 54-94 60.20 64.89 35^5 42.89 49.60 55-49 60.70 65.33 35-98 43.60 50.23 56.O4 61.18 65.76 36.79 44-3 1 50.84 56.58 61.67 66.20 37-59 45.00 51-45 57-12 62.14 66.62 38.38 45-68 52.05 57.65 62.61 39.16 46.36 52-64 58-17 63.08 39-93 47-03 53-23 58.69 63-54 40.68 47-68 53-8o 59-20 63-99 SMITHSONIAN TABLES. I10 TABLE 95, DENSITY IN GRAMS PER CUBIC CENTIMETER OF THE ELEMENTS, LIQUID OR SOLID. N. B. The density of a specimen may depend considerably on its state and previous treatment. Element. Physical State. drams per cu. cm.* Tempera- ture c.t Authority. Aluminum commercial h'd d'n 2.70 20 Wolf, Bellinger, 1910 M Antimony wrought vacuo-distilled 2.65-2.80 6.618 2O Kahlbaum, 1902. " ditto-compressed 6.691 2O < amorphous 6.22 Herard. Argon liquid 1.3345 -I8 3 Baly-Donnan. " I-4233 189 '' " Arsenic crystallized 5-73 M amorph. br.-black 3-70 Geuther. .. yellow 3-88 Linck. Barium 3-78 Guntz. Bismuth solid 9.70-9.90 electrolytic 9-747 Classen, 1890. vacuo-distilled 9.781 2O Kahlbaum, 1902. liquid IO.OO 271 Vincentini-Omodei. ' solid 9.67 271 .. Boron crystal 2-535 Wigand. .1 amorph. pure 2-45 Moissan. Bromine liquid 3.12 Richards-Stull. Cadmium cast 8.54-8.57 wrought 8.67 M vacuo-distilled 8.648 2O Kahlbaum, 1902. M solid 8-37 318 Vincentini-Omodei. " liquid 7-99 318 Caesium 1-873 2O Richards-Brink. Calcium 1-54 Brink. Carbon diamond 3-52 Wigand. ' graphite 2.25 << Cerium electrolytic 6.79 Muthmann- Weiss. " pure 7.02 Chlorine liquid '507 -33-6 1 )rugman-Ramsay. Chromium 6.52-6.73 " pure 6.92 20 Moissan. Cobalt 8.71 21 Tilden, Ch. C. 1898. Columbium 8.4 15 M uthmann-W'eiss. Copper cast annealed ^r 8 - 95 2O Bellinger, 1911 wrought hard drawn 8.85-8.95 20 vacuo-distilled 8.9326 2O Kahlbaum, 1902. ditto-compressed 8.9376 2O " " liquid 8.217 Roberts- Wrightson. Erbium 4-77 St. Meyer, Z Ph. Ch. 37. Fluorine . liquid 1.14 2OO Moissan-Dewar. Gallium 5-93 2 3 de Boisbaudran. Germanium 546 20 Winkler. Glucinum 1.85 Humpidge. Gold cast '9-3 " wrought '9- 33 " vacuo-distilled 18.88 20 Kahlbaum, 1902. 14 ditto-compressed 19.27 20 Helium Hydrogen liquid liquid 0.15 0.070 -269 252 Onnes, 1908. Dewar, Ch. News, 1904. Indium 7.28 ' Richards. To reduce to pounds per cu. ft. multiply by 62.4. t Where the temperature is not given, ordinary atmospheric temperature is understood. Compiled from Clarke's Constants of Nature, Landolt-Bornstein-MeyerhofTer's Tables, and other sources. Where no authority is stated, the values are mostly means from various sources. SMITHSONIAN TABLES. TABLE P5 (continued). Ill DENSITY IN GRAMS PER CUBIC CENTIMETER OF THE ELEMENTS, LIQUID OR SOLID. Element. Physical State Grams per cu. cm.* Tempera- ture c.t Authority. Iridium 22.42 17 Deville-Debray Iodine 4.940 2O Kichards-Stull Iron pure 7-85-7.88 K gray cast 7-03-7-I3 " white cast 7-58-7-73 wrought 7.80-7.90 ' liquid 688 Roberts-Austen steel 7.60-7.80 Krypton liquid 2.16 146 Ramsay-Travers Lanthanum 6.15 Muthmann- Weiss Lead vacuo-distilled 11.342 20 Kahlbaum, 1902 M ditto-compressed u-347 2O it II solid 11.005 3^5 Vincentini-Omodei M liquid 10.645 3-5 " " " 11 10.597 400 Day, Sosman, Hostetter, " " 10.078 850 1914 Lithium o-534 20 Richards-Brink, '07 Magnesium 1.741 Voigt Manganese 7.42 Prelinger Mercury liquid I3-596 o Regnault, Volkmann M I3-546 20 M 13.690 38.8 Vincentini-Omodei " solid M-I93 38.8 Mallet " " i4-3 8 3 1 88 Dewar, 1902 Molybdenum 9.01 Moissan Neodvmium 6.96 Muthmann- Weiss Nickel 8.60-8.90 Nitrogen liquid 0.810 195 Baly-Donnan, 1902 it " 0.854 205 " " " Osmium 22.5 Deville-Debray ! Oxygen liquid 1.14 184 Palladium 12.16 Richards-Stull Phosphorus \ white 1.83 " red 2.2O " metallic 2-34 15 Hittorf Platinum 21.37 20 Richards-Stull Potassium 0.870 20 Richards-Brink, '07 M solid 0.851 62.1 Vincentini-Omodei a liquid 0.830 62.1 i< Praesodymium 6-475 Muthmann- Weiss Rhodium 12.44 Holborn Henning Rubidium Ruthenium '532 I 2. 06 20 o Richards- Brink, '07 Toby Samarium 7-7-7-8 Muthmann- Weiss Selenium 4-3-48 Silicon cryst. 2.42 20 Richards-Stull-Brink " amorph. 2 -35 15 Vigoroux Silver cast 10.42-10.53 wrought 10.6 vacuo-distilled 10.492 20 Kahlbaum, 1902 ditto-compressed 10.503 20 . u liquid 9-5 1 Wrightson Sodium 0.9712 20 Richards-Brink, '07 solid 0.9519 97.6 Vincentini-Omodei liquid 0.9287 97.6 " " 1.0066 188 Dewar Strontium 2.50-2.58 Matthie 57 Cedar Cherry 0.49-0.57 0.70-0.90 30-35 43~5 6 Mahogany, Honduras " ' Spanish 0.66 0.85 4i 53 Cork 0.22-0.26 14-16 Maple 0.62-0.75 39-47 I )ogwood 0.76 47 Oak 0.60-0.90 37-5 6 Ebony '11-1.33 69-83 Pear-tree 0.61-0.73 38-45 Kim 0.54-0.60 34-37 Plum-tree 0.66-0.78 41-49 Fir or Pine, American Poplar 0-35-0-5 22-31 White 0-35-0.50 22-31 ! Satinwood 0-95 59 Larch Pitch 0.50-0.56 0.83-0.85 31-35 52-53 Sycamore Teak, Indian 0.40-0.60 0.66-0.88 24-37 4i-55 Red 0.48-0.70 3-44 " African 0.98 61 Scotch 0-43-0.53 27-33 Walnut 0.64-0.70 40-43 Spruce Yellow 0.48-0.70 0.37-0.60 30-44 2 3-37 Water gum Willow I.OO 0.40-0.60 62 24-37 Greenheart 0.93-1.04 58-65 * Where the temperature is not given, ordinary atmospheric temperature is understood. SMITHSONIAN TABLES. TABLE 97. DENSITY IN GRAMS PER CUBIC CENTIMETER AND POUNDS PER CUBIC FOOT OF VARIOUS SOLIDS. N. B. The density of a specimen depends considerably on its state and previous treatment ; especially is this the case with porous materials. Material. Grams per Pounds per Material. Grams per Pounds per cu. cm. cu. foot. cu. cm. cu. foot. Agate 2.5-2.7 156-168 Gum arabic 1.3-1.4 80- 85 Alabaster : Gypsum 2-3I-2.33 144-145 Carbonate 2.69-2.78 168-173 Hematite 4-9-5-3 J 306-330 Sulphate 2.26-2.32 I4I-I45 Hornblende 3- I8 7 Albite Amber 2.62-2.65 I.o6-I.Il 163-165 66- 69 Ice Ilmenite 0.917 4-5-5- 57-2 280-310 Amphiboles 2.9-3.2 180-200 Ivory 1.83-1.92 114-120 Anorthite 2.74-2.76 171-172 Labradorite 2.7-2.72 168-170 Anthracite 1.4-1.8 87-112 Lava : basaltic 2.8-3.0 I75~ l8 5 Asbestos 2.O-2.8 125-175 trachytic 2.0-2.7 125-168 Asphalt I.I-I-5 69- 94 Leather : dry 0.86 54 Basalt 2.4-3.1 150-190 greased i. 02 64 Beeswax 0.96-0.97 60- 6 r Lime : mortar 1.65-1.78 103-111 Beryl 2.69-2.7 168-168 slaked 1.3-1.4 81- 87 Biotite 2.7-3.1 170-190 Limestone 2.68-2.76 167-171 Bone 1.7-2.0 106-125 Litharge : Brick 1.4-2.2 87-137 Artificial 9-3-9-4 580-585 Butter 0.86-0.87 53- 54 Natural 7.8-8.0 490-500 Calamine 4-1-4-5 255-280 Magnetite 4-9-5-2 306-324 Caoutchouc 0.92-0.99 57-62 Malachite 3-7-4- i 231-256 Celluloid i-4 7 Marble 2.6-2.84 160-177 Cement, set 2.7-3.0 170-190 Meerschaum 0.99-1.28 62- 80 Chalk 1.9-2.8 118-175 Mica 2.6-3.2 165-200 Charcoal : oak o.57 35 Muscovite 2.76-3.00 172-225 pine 0.28-0.44 1 8- 28 Ochre 3-5 218 Chrome yellow 6.00 374 Oligoclase 2.65-2.67 165-167 Chromite 4-32-4-57 270-285 Olivine 3-27-3-37 204-210 Cinnabar 8.12 57 Opal 2.2 137 Clay 1.8-2.6 122-162 Orthoclase 2.58-2.61 161-163 Coal, soft 1.2-1.5 75- 94 Paper 0.7-1.15 44- 72 Cocoa butter 0.89-0.91 56- 57 1 Paraffin 0.87-0.91 54- 57 Coke 1.0-1.7 62-105 \ Peat 0.84 5 2 Copal 1.04-1.14 65- 7 1 Pitch 1.07 67 Corundum 3.9-4.0 245-250 Porcelain 2-3-2.5 I43- 1 5 6 Diamond : Porphyry 2.6-2.9 162-181 Anthracitic 1.66 104 Pyrite 4-95-5- * 309-318 Carbonado 3-oi-3-25 188-203 Quartz 2.65 165 Diorite 2.52 157 Quartzite 2-73 170 Dolomite 2.84 177 Resin 1.07 67 Ebonite 1.15 72 Rock salt 2.18 136 Emery 4.0 250 Rutile 6.00-6.5 374-406 Epidote 3- 2 5-3-5 203-218 Sandstone 2.14-2.36 I34-H7 Feldspar 2-55-2-75 159-172 Serpentine 2.50-2.65 156-165 Flint 2.63 164 Slag, furnace 2.0-3.9 125-240 Fluorite 3.18 198 Slate 2-6-3.3 162-205 Gamboge 1.2 75 Soapstone 2.6-2.8 162-175 Garnet 3- 1 5-4- 3 197-268 Starch 1.53 95 Gas carbon 1.88 117 Sugar 1.61 100 Gelatine 1.27 1 80 Talc 2.7-2.8 168-174 Glass : common 2.4-2.8 150-' 7 5 Tallow 0.91-0.97 57- 60 flint 2-9-5-9 180-370 Topaz 3-5-3-6 219-223 Glue 1.27 80 Tourmaline 3-0-3-2 190-200 Granite 2.64-2.76 165-172 Zircon 4.68-4-70 292-293 Graphite 2.30-2.72 144-170 SMITHSONIAN TABLES. TABLE 98. DENSITY IN GRAMS PER CUBIC CENTIMETER AND POUNDS PER CUBIC FOOT OF VARIOUS ALLOYS. Alloy. Brasses: Yellow, 7oCu + 3Zn, cast 8.44 527 rolled 8.56 534 " " drawn 8.70 542 Red, 9oCu + loZn 8.60 536 White, 5oCu+5oZn 8.20 511 Bronzes: goCu-fioSn 8.78 548 S5Cu+i5Sn 8.89 555 8oCu-p-2oSn 8.74 545 75Cu-j-25Sn 8.83 551 German Silver: Chinese, 26-3Cu-|- 36.6Zn-f- 36.8Ni . . . 8^30 518 Berlin (i) 52Cu + 26Zn-f22Ni .... 8.45 527 " (2) 59Cu-f 3oZn -f uNi .... 8.34 520 " (3) 63Cu + 3oZn -f 6Ni . . . . 8.30 518 Nickelin 8.77 547 Lead andTin: 87.sPb+ i2.5Sn . . . . . . . 10.60 661 i6Sn 10.33 6 44 10.05 627 9-43 588 J-3 Sn 8 -73 545 Bismuth, Lead, and Tin : 53Bi + 4oPb -f 7Cd .... 10.56 659 Wood's Metal: 5oBi+ 25Pb+ i2.5Cd+ i2.5Sn .... 9.70 605 Cadmium and Tin : 32Cd + 68Sn 7.70 480 Gold and Copper: 98 Au + 2Cu 18.84 u?6 " " " o,6Au -j- 4Cu J 8-36 1145 94Au-f-6Cu 17.95 ll20 92Au-f-8Cu 17.52 1093 ox>Au 4- loCu 17.16 1071 88Au-j~ I2 Cu 16.81 1049 86 A u + 14^11 16.47 I02 7 Aluminum and Copper: ioAl-f-9oCu 7.69 480 " " 5A1 -j- 95^u 8.37 522 3Al-f 97 Cu 8.69 542 Aluminum and Zinc : 91 Al -\-gZn 2.80 175 Platinum and Iridium : 9oPt+ioIr. ... . . 21.62 1348 8Pt+ i Sir 21.62 1348 66.67 Pt + 33-33lr 21.87 !3^4 5Pt + 95lr 22.38 1396 Constantmn : 6oCn 4- 4ONi 8.88 554 Nfagnalium: 7oAl -j- 3Mg 2.0 125 Manganin : 84Cu + i2Mn -|- 4Ni 8.5 530 Platinoid: German silver -j- little Tungsten 9.0 560 Grams per cubic centimeter. Pounds per cubic toot. SMITMSOM TABLES. TABLES 99-100. TABLE 99.-DENSITIES OF VARIOUS NATURAL AND ARTIFICIAL MINERALS. (See also Table 97.) Name and Formula. Density grams Sp.Vol. cc. per erence. 1 Name and Formula. Density grams Sp. Vol. cc. per 1 K per cc. gram. 2 per cc. gram. " K Pure compounds, all at Feldspars : 2 5 C Magnesia, MgO 3-603 2775 , Albite glass, NaAlSi 3 O 8 art. 2 -375 4210 6 Lime, CaO 3-306 3025 2 Albite cryst., NaAlSi 3 O 8 Forms of SiO 2 : art. 2.597 .3851 Quartz, natural 2.646 3779 " Anorthite glass, " artificial 2.642 3785 " CaAl 2 Si 2 O 8 , art. 2.692 37 * 5 Cristobalite, artificial 2.319 43 * 2 " Anorthite cryst, Silica glass 2.2O6 4533 u CaAl 2 Si 2 O 8 , art. 2-757 .3627 Forms of Al 2 SiO 5 : Soda anorthite, Sillimanite glass 2 -53 395 3 NaAlSiO 4 , art. 2.563 .3902 7 Sillimanite cryst. 3.022 3309 Borax, glass, Na 2 B 4 O 7 2. 3 6 .423 6 Forms of MgSiO 3 : " cryst. " 2.27 440 /8 Monoclinic pyroxene 3- 183 .3142 5 Fluorite, natural, CaF 2 a Orthorhombic pyroxene 3-i66 3 T 59 (20) 3.180 3*45 8 /3' Monoclinic amphibole " (NH 4 ) 2 S0 4 (30) ^765 .5666 9 7' Orthorhombic amphi- bole Glass 2.849 2 -735 3510 3656 K 2 S0 4 (30) KC1, fine powder (30) Forms of ZnS : 2.657 1.984 3764 .5040 Forms of CaSiO 3 : Sphalerite, natural* 4.090 .2444 10 a (Pseudo-wollastonite) (Wollastonite) 2.904 2.906 3444 3441 2 Wurtzite, artificialt Greenockite, artificial 4.087 4.820 2447 .2075 Glass 2.895 3454 " Forms of HgS : Forms of Ca 2 SiO 4 : Cinnabar, artificial 8.176 .1223 " o calcium-orthosilicate 3.26 37 ii Metacinnabar, artifi- )8 3-27 306 M cial 7.58 .132 7 " 2.965 337 11 ff " Minerals : Lime-alumina compounds : Gehlenite, from Velar- 3CaO A1 2 O 3 3.029 33 01 3 den a 3-3 33 n CaO*3A)A 2.820 3546 Spurrite, from Velardena, CaO Al,0 3 3CaO 5A1 2 O 3 2.972 3365 M 2Ca 2 Si0 4 CaCO 3 Hillebrandite, from Vel- 3-005 .3328 M 3CaO 5A1 2 O 3 , unstable ardena, form 3-4 3 2 9 " CaSiO 3 'Ca(OH) 2 2.684 3726 ( Forms of MgSiO 3 CaSiO 3 : Diopside, natural, cryst. 3.258 .3069 4 Pyrite, natural, FeS, Marcasite, natural, FeS 2 5-OI2 4-873 '995 2052 10 artificial, " glass 3-265 2.846 3063 35*4 * Only 0.15% Fe total impurity. t Same composition as Sphaler- ite. References: i, Larsen 1909; 2, Day and Shepherd; 3, Shepherd and Rankin, 1909; 4, Allen and White, 1909; 5, Allen, Wright and Clement, 1906; 6, Day and Allen, 1905; 7, Washington and Wright, 1910; 8, Merwin, 1911 ; 9, Johnston and Adams, 1911 ; 10, Allen and Crenshaw, 1912; II, Wright, 1908. All the data of this table are from the Geophysical Laboratory, Washington. TABLE 10O.-DENSITIES OF MOLTEN TIN AND TIN-LEAD EUTECTIC. Temperature Molten tin 37 pts. Pb, 63, Sn.* 2 5 0C. 6.982 8.01 1 300 6-943 7-965 400 6.875 7-879 500 6.814 7.800 600 6-755 7-731 900 6.578 1200 6-399 1400 6.280 1600 6.162 * Melts at 181. Day and Sosman, Geophysical Laboratory, unpublished. For further densities inorganic substances see table 219. organic 220. SMITHSONIAN TABLES. TABLES 101-102. WEIGHT OF SHEET METAL. TABLE 101. Weight ol Sheet Metal. (Metric Measure.) This table gives the weight in grams of a plate one meter square and of the thickness stated in the first column. Thickness in thou- sandths of Iron. Copper. Brass. Aluminum. Platinum. Gold. Silver. a cm. 1 78.0 89.0 85.6 26.7 215.0 193.0 105.0 2 156.0 178.0 I7I.2 53-4 430.0 386.0 2IO.O 3 4 234.0 312.0 267.0 356.0 256.8 342.4 80. i 1 06.8 6450 860.0 579-0 772.0 315.0 42O.O 5 390.0 445-0 428.0 133-5 1075.0 965.0 525-0 6 468.0 534-0 513.6 160.2 1290.0 1 1 58.0 630.0 7 546.0 623.0 599.2 186.9 1505.0 I35 1 - 735-0 8 624.0 712.0 684.8 213.6 1720.0 1544.0 840.0 9 7O2.O 801.0 770.4 240.3 1935-0 1737.0 945-0 10 780.0 890.0 856.0 267.0 2150.0 1930.0 1050.0 TABLE 102. - Weight of Sheet Metal. (British Measure.) Iron. Copper. Brass. Aluminum. Platinum. in Mils. Pounds per Sq. Foot. Pounds per Sq. Foot. Pounds per Sq. Foot. Pounds per Sq. Foot. Ounces per Sq. Foot. Pounds per Sq. Foot. Ounces per Sq. Foot. 1 .04058 .04630 .04454 .01389 .2222 .1119 1.790 2 3 .08116 .12173 .09260 .13890 .08908 ' ^3363 .02778 .04167 4445 .666 7 .2237 3356 3-579 5-369 4 .16231 .18520 .17817 05556 .8890 -4474 7.158 5 .20289 .23150 .22271 .06945 I.III2 5593 8.948 6 24347 .27780 .26725 -08334 J-3335 .6711 10.738 7 .28405 .32411 3II79 .09723 1-5557 .7830 12.527 8 3 2 463 37041 35 6 34 .11112 1.7780 .8948 14.3*7 9 .36520 .41671 .40088 .I25OI 2.0OO2 1.0067 1 6.106 10 .40578 .46301 44542 .13890 2.2224 1.1185 17.896 Gold. Silver. Thickness in Mils. Troy Ounces per Sq. Foot. Grains per Sq. Foot. Troy Ounces per Sq. Foot. Grains per Sq. Foot. 1 1.4642 702.8 0.7967 382.4 2 2.9285 MOW I -5933 764-8 3 4.3927 2108.5 2.3900 II47.2 4 5-0570 2811.3 3.1867 1529.6 5 7.3212 35M-2 3-9833 1912.0 6 8.7854 4217.0 4.7800 2294.4 7 10.2497 4919.8 5'5767 2676.8 8 9 II-7I39 13.1782 5622.7 6325-5 6-3734 7.1700 3059-2 3441.6 10 14.6424 7028.3 7.9667 3824.0 SMITHSONIAN TABLES. TABLE 103. 117 DENSITY OF LIQUIDS. Density or mass in grams per cubic centimeter and in pounds per cubic foot of various liquids. Liquid. Grams per cubic centimeter. Pounds per cubic foot. Temp. C. Acetone . .... Alcohol, ethyl .... methyl .... Aniline . .... Penzene . .... Bromine . .... Carbolic acid (crude) * .... 0.792 0.807 0.810 1-035 3.187 0.950-0.965 T 2O "? 49-4 50-4 50-5 64.5 56.1 199.0 59.2-60.2 80 6 20 o 15 I 480 02 ^ 18 O 8C.7 r-j c IOO Ether O 7^6 OoO ^r Q o o 660 69 A I O A 1 O Glycerine 1.260 o 87=; 78.6 ZA 6 IOO Miik ..::.: : Naphtha (wood) ...... Naphtha (petroleum ether) .... Oils : Amber Anise-seed Camphor Castor ..... 1.028-1.035 0.848-0.810 0.665 0.800 0.096 0.910 0060 64.2-64.6 52.9-50.5 41.5 49.9 62.1 56.8 60 * 15 15 16 1C i 041 06 65 -66 2C, 002^ C7 7 je o 926 j/ / 57 8 16 Creosote ...... Lard Lavender . . . . . Lemon ...... Linseed (boiled) Neat's foot Olive 1.040-1.100 0.920 0.877 0.844 0.942 0.913-. 917 o 918 64.9-68.6 57-4 54.7 11:1 57.0-57-2 C7 -3 15 II 16 15 1C Palm ...... Ooo^ ^6 ; JC o 650 3 U O 40 6 o o 62^ ?8 o 2C. Peppermint Petroleum (light) .... Pine Poppy Rapeseed (crude) .... (refined) .... 0.90-. 92 0.878 0.795-0-805 0.850-0.860 0.924 0.915 0.913 o 055 50-57 54-8 49.6-50.2 53.0-54.0 57.7 57-1 57-0 CQ 6 25 15 15 15 15 1C cc 25 O QIO =7.7 30 i< Train or Whale . Turpentine. .... Valerian . .... Wintergreen .... Pyroligneous acid .... Water . . .... 0.906 0.918-0.925 0.873 0.965 1.18 0.800 I.OOO 56.5 57.3-57.7 54.2 60.2 74. 49-9 62.4 00 15 16 16 25 4 SMITHSONIAN TABLES. Il8 TABLE 104. DENSITY OF PURE WATER FREE FROM AIR. O TO 41 C. [Under standard pressure (76 cm), at every tenth part of a degree of the international hydrogen scale from o to 41 C, in grams per milliliter J ] De- crees Tenths of Degrees. Mean Differ- Sentl- ences. rrade. 1 2 3 4 5 6 7 8 9 I 3 4 0.9998681 9267 9679 9922 I.OOOOOOO 8747 93^5 9711 9937 *9999 8812 9363 9741 *" 51 88 7 q 9408 9769 9962 *9992 8936 9452 9796 9973 *9986 8996 9494 9821 998i *9979 9053 9534 9844 (#88 * 99 70 9 I0 9 9573 9 866 9994 * 99 6o 9 i6 3 9 6io 9887 9998 *9947 9 2l6 9645 9905 *0000 *9934 4- 59 4- 24 1 5 0.999 9919 9902 9884 9864 9842 9819 9795 9769 9742 9713 - 24 6 9682 9650 9617 9582 9545 9507 94 68 9427 9385 934i 39 8 9296 8764 9249 8703 9201 8641 9151 8577 9100 8512 9048 8445 8994 8377 8308 8237 8823 8165 El 9 8091 8017 7940 7863 7784 7704 7622 7539 7455 7369 81 10 7282 7*94 7105 7014 6 9 2I 6826 672 9 6632 6533 6432 9 q n 6 33 r 6228 6124 6020 59 1 3 5805 5696 5586 5474 5362 108 12 5248 5*32 5016 4898 4780 4660 4538 4415 4 2 9 I 4166 121 13 4040 3912 3784 3523 339 r 3257 3122 2 9 86 2850 133 2 7 I2 2572 2431 2289 2147 2003 1858 1711 i5 6 4 1416 145 15 1266 1114 0962 0809 0653 0499 0343 0185 0026 * 9 865 156 16 0.998 9705 9542 9378 9214 ^48 8881 8713 8544 8373 8202 168 1 7 8029 7856 7681 7505 7328 715 6 9 7i 6791 6610 6427 178 18 6244 6058 5873 5686 5498 5309 5"9 4927 4735 4541 190 i 1 9 4347 4152 3955 3757 3558 3358 3158 2955 2752 2549 200 20 2343 2137 1930 1722 1511 1301 IOC)O 0878 0663 0449 211 21 0233 0016 *9799 * 95 8o *9359 * 9 i 39 *8 9 i 7 *86 94 *847O *82 4 5 221 22 0.997 8019 7792 7564 73351 7104 6873 6641 6408 6173 5938 232 2 3 5702 5466 5227 4^8 4747 4506 4264 4021 3777 2 4 2 24 3286 3039 2790 2541 2291 2040 1788 1535 1280 1026 252 i * 6 0770 0.9968158 7892 0255 7624 *9997 *9736 7356 7087 * 9 476 6817 * 9 2I4 6545 *8 95 i 6273 *8688 6000 *8 4 2 3 5726 26l 271 ' 27 28 2 9 2652 0.995 976i 5^6 2366 94 66 4898 2080 9171 4620 8$ 4342 1505 8579 4062 1217 8282 3782 9 28 7983 3500 0637 7684 3218 0346 7383 2935 0053 7083 280 30 6780 6478 6174 5869 5564 5258 495 4642 4334 4024 37 31 37H 3401 * 3 89 2776 2462 2147 1832 I 5 I 5 1198 0880 315 32 0561 0241 *9599 +9276 *8954 *8 3 o 4 *7979 *7653 324 33 0-994 7325 6997 6668 6338 6007 5676 5345 5011 4678 4343 332 34 4007 3671 3335 2997 2659 2318 1978 1638 I2 9 6 0953 340 35 0610 0267 *9922 *957 6 *923o *888 3 *8534 *8i86 * 7 8 37 * 74 86 347 36 0.9937136 6784 6432 6078 5725 5369 5 OI 4 4658 43oi 3943 37 355 3226 2866 2505 2144 1782 1419 1055 o6 9 i 0326 362 i 38 0.9929960 9593 9227 8859 8490 8120 775 1 7380 7008 6636 370 39 6263 5890 5516 5140 4765 4389 4011 3 6 34 3255 2876 377 40 2497 2116 1734 1352 097! 0587 0203 * 9 8i8 *9433 *947 -384 41 0.991 8661 1 According to P. Chappuis, Bureau international des Poidt et Mesures, Travaux et Mdmoires, 13; 1907. SMITHSONIAN TABLES. TABLE 105. 1 19 VOLUME IN CUBIC CENTIMETERS AT VARIOUS TEMPERATURES OF A CUBIC CENTIMETER OF WATER FREE FROM AIR AT THE TEMPERATURE OF MAXIMUM DENSITY. TO 4O C. Hydrogen Thermometer Scale. Temp. .0 .1 .2 3 4 5 .6 7 .8 9 1.000132 125 118 112 1 06 IOO 095 089 084 079 I 073 069 064 059 055 051 047 043 039 35 2 032 029 026 023 020 018 016 013 on 009 3 008 006 005 OO4 003 002 OOI OOI 000 000 4 000 000 oo(9 OOI OOI 002 003 OO4 005 007 5 008 OIO OI2 014 016 018 02 1 023 026 O2Q 6 032 035 039 042 046 050 054 5 8 062 066 7 070 075 080 085 090 095 101 1 06 112 118 8 124 130 J 37 142 149 156 162 169 I 7 6 184 9 191 198 206 214 222 230 238 2 4 6 254 263 10 ii 272 367 281 377 388 398 308 409 420 327 43 337 441 347 453 464 12 476 487 499 511 522 534 547 559 584 13 596 609 623 636 649 661 6 75 688 702 7i5 14 729 743 757 772 7 86 800 815 830 844 859 15 873 890 905 920 935 95 1 967 983 998 015* 16 1.001031 047 063 080 097 "3 130 147 164 182 17 198 216 2 33 252 269 287 35 3 2 3 34i 358 18 378 396 41 c 433 45 2 490 5 10 548 !9 568 588 606 626 646 667 687 707 728 748 20 769 790 811 832 853 874 895 916 938 96o 21 98! 002* 024* 046* 068* 091* 113* 135* 158* 181* 22 23 1.002203 436 226 459 249 483 271 57 295 556 342 58i 364 605 389 629 412 654 24 679 704 729 754 779 804 829 854 879 90S 2 5 932 958 983 OIO* 036* 061* 088* 115* 141* 1 68* 26 1.003195 221 248 275 302 330 357 384 412 439 27 467 495 523 55 579 607 6 35 663 692 720 28 749 776 806 836 865 922 981 Oil* 29 1.004041 069 IOO 129 160 189 220 250 280 310 3 34, 371 403 432 464 494 5 26 557 588 619 3 1 651 682 7*3 744 777 808 840 872 9 "> I s"* pi-lQ^Vv SrClo + 6H 2 O 1.027 1.053 .1.082 1. 1 ytj I. Ill I.O42 1.174 1.242 1-317 ._ J 5. u BaClo . . . BaCl 2 +2H 2 1.045 I -35 1.094 1.075 1.147 1.119 I.2O5 I.I66 1.269 I.2I7 1-273 - - 21. u Schiff. CuClo . . . 1.044 1.091 1.155 1. 221 I.29I 1.360 1-527 _ _ I7>5 Franz. NiCl 2 . . . 1.048 1.098 1-157 1.223 1.299 ~L _ _ !7-5 HgCl 2 . . . Fe 2 Cl 6 . . . PtCl 4 . . . . 1.041 1.041 1.046 1.092 1.086 1.097 1.130 I - I 53 I.I79 I.2I4 1.232 1.285 1.290 1.362 1.413 1.546 T -545 1-785 1.668 20. Men dele jeff. Hager. Precht. SnCl 2 +2H 2 O 14 -j- 5H 2 O 1.032 1.029 1.067 1.058 1.104 1.089 1. 122 I.I85 I-I57 1.229 I - I 93 1.329 1.274 1.444 1-365 1.580 1.467 15- Gerlach. LiBr .... I -33 1.070 i. in I-I54 1.202 1.252 1.366 1.498 J 9-5 Kremers. KBr .... 1-035, 1-073 1.114 I-I57 1.205 L254 1.364 _ " NaBr . . . 1.038 1.078 1.123 I.I72 1.224 1.279 1.408 !-5 6 3 - 19-5 u MgBr 2 . . . rf f t 1.041 1.085 1.135 I.I89 1-245 1.308 1.449 1.623 _ J 9-5 u ZnBr 2 . . . CdBr 2 . , CaBr 2 . . . BaBr 2 . . . 1.043 1.041 1.042 1.043 1.088 1.087 1.090 1.144 I - I 39 I-I37 1.142 1.202 I.I97 I.I92 I.I99 1.263 1.258 2.250 I.26o 1.328 I -3 2 7 J-473 1.479 *-4S9 1.483 1.648 1.678 1.639 1.683 1.873 1 9-S 19-5 u a SrHro KI ". . . . I.il . . 1.043 1.036 1.089 1.076 1.077 i. 080 1.089 1.140 1.118 1. 122 I.I26 I.I38 I.IgS 1.164 I.I7O I.I 77 I.I94 1.200 1.216 1.222 1.232 1-253 '328 1.269 1.278 1.292 1.316 1.489 T -394 1.412 1.430 1.467 1.693 1-544 T -573 1.598 1.648 1-953 1.732 1-775 i. 808 1-873 19-5 19-5 19-5 19.5 u Nal . . . . ZnI 2 . . . 1.038 1.043 CdI 2 . . i. 086 I.I 3 6 I.I 9 2 I.25I ,. 3 , 7 1.474 1.678 _ I95 u Mjil-j. . . . CaI 2 .... - . . . BaI 2 .... 1.041 1.042 i .043 1.043 i. 086 1.088 1.089 1.089 I.I38 I.I40 I.I92 I.I96 I.I98 I.I99 1.2 5 2 1.258 1.260 1.263 1.318 '319 1.328 '33 1 1.472 1-475 1.489 1-493 1.666 1.663 1.693 1.702 1.908 r -953 1.968 1 9-S 19-5 19-5 NaClO 8 . . . '035 1.039 1.068 i. 08 1 1.106 1.127 I-I45 I.I76 I.I88 1.229 JJ33 1.329 - - 19-5 19.5 u KXO;; . . . 1.031 1.064 1.099 1 - 1 3S _ _ _ _ Gerlach. NaNO, . . . AgNO, . . . 1.031 1.044 1.065 1.090 I.IOI 1.140 1.140 1.180 '255 1.222 I. 3 22 1.479 1.416 1-675 1.918 20.2 Schiff. Kohlrausch. * Compiled from two papers on the subject by Gerlach in the " Zeit. fur Anal. Chim.," vols. 8 and 27. SMITHSONIAN TABLES. TABLE 108 (continued). DENSITY OF AQUEOUS SOLUTIONS. I2 3 1 Weight of the dissolved substance in 100 parts by weight of the solution. U Substance. d Authority. i 5 10 15 20 25 30 4 o so 60 H NH 4 N0 3 . . Zn(N0 3 ), . . . 1.020 1.048 I.O4I 1.095 .063 .146 .085 .2OI .107 263 '3 1 -325 1.178 1.456 1.229 1.282 17-5 Gerlach. Franz. Zn(N0 3 ) 2 + 6H 2 O Ca(N0 3 ) 2 . . . 1-037 1.054 1-075 .118 "3 .162 .211 .178 .260 1.250 1.367 1.329 1.482 1.604 14. 17-5 Oudemans. Gerlach. Cu(NO 3 ) 2 . . . 1.044 1.093 -143 203 .263 .328 1.471 - - 17-5 Franz. Sr(N0 3 ) 2 . . . 1.039 1.083 .129 .179 - - - - - 19-5 Kremers. Pb(N0 3 ) 2 . . . 1.043 I.09I 143 .199 .262 332 - 17.5 Gerlach. Cd(N0 3 ) 2 . . . 1.052 1.097 .150 .212 .283 355 r -53 6 1-759 - 17.5 Franz. Co(N0 3 ) 2 . . . 1.045 1.090 137 .192 .252 .318 1.465 17-5 " Ni(N0 3 ) 2 . . . 1.045 1.090 137 .192 .252 .318 1.465 - - 17-5 " Fe 2 (N0 3 ) 6 . . . 1.039 1.076 .117 .I60 .210 .261 T -373 1.496 1-657 17-5 n Mg(NO 3 ) 2 +6H 2 O Mn(NO 3 ) 2 +6H 2 I.OI8 I.O25 1.038 1.052 .000 .079 .082 .108 .105 .138 .129 .169 1.179 1-235 1.232 1-307 1.386 21 8 Schiff. Oudemans. K 2 C0 3 .... 1.044 1.092 .141 .192 -245 300 1.417 1-543 - 15 Gerlach. K 2 CO 3 + 2H 2 O . 1.037 I.O72 .no .150 .191 233 1.320 1.415 1.511 15- Na 2 CO 3 ioH 2 O . I.OI9 1.038 057 .077 .098 .118 - - - 15- " (NH 4 ) 2 S0 4 . . 1.027 i-55 .084 IT 3 .142 .170 1.226 1.287 - 19. Schiff. Fe 2 (S0 4 ) 3 . . . 1.045 1.096 .150 .207 .270 .336 1.489 - - 18. Hager. FeSO 4 -|-7H 2 O . 1.025 T -53 .081 .in .141 .173 1.238 17.2 Schiff. MgSO 4 .... 1.051 1.104 .161 .221 .284 - - - - 15 Gerlach. MgS0 4 +7H 2 O. I.O25 1.050 -075 .101 .129 '55 1.215 1.278 - 15- " Na 2 S0 4 +ioH 2 O I.OI9 1.039 59 .O8l .102 .124 15. " CuSO 4 + 5H 2 O . I.03I 1.064 .098 T 34 .173 .213 18. Schiff. MnSO 4 -f- 4H-)O . 1.031 1.064 1.099 .135 .174 .214 1.303 1.398 J 5- Gerlach. ZnS0 4 -f 7H 2 . 1.027 1-057 1.089 .122 .156 .191 1.269 1-443 20.5 Schiff. Fe 2 (S0 4 ) 3 .K 2 SO 4 + 2 4 H 2 . . I.O26 1.045 i. 066 1.088 1. 112 1.141 17.5 Franz. 1 Cr 2 (S0 4 ) 8 -K 2 SO 4 -|- 24H 2 O . . 1.016 1.033 1.051 1-073 1.099 1.126 1.188 1.287 J-454 17-5 M MgS0 4 + K 2 SO 4 + 6H 2 O . . . 1.032 i. 066 I.IOI I.I38 - - - - - 15. Schiff. (NH 4 ) 2 S0 4 + FeS0 4 + 6H 2 O 1.028 1.058 1.090 1. 122 I-I54 1.191 - - - 19- M K 2 Cr0 4 .... 1.039 1.082 1.127 I.I74 1.225 1.279 !-397 - - x 9-5 II K 2 Cr 2 O 7 . . . 1.035 1.071 1.108 - _ - - - - 19-5 Kremers. Fe(Cy) 6 K 4 . . . 1.028 1.059 1.092 I.I26 - - - - - Schiff. Fe(Cy) 6 K 3 . . . Pb(C 2 H 3 2 ) 2 + 1.025 T - 53 1.070 I.II3 ~ ~ -~ 13 7H 2 O r 071 1.064 I. IOO T T "37 I 177 i. 220 1.71 s 1.426 _ I C. Gerlach. 2 NaOH + As 2 O 5 ' **// * j j A 'T- ** ^ 3 -f- 24H 2 O . . i. 020 1.042 1. 066 1.089 I.II4 1.140 1.194 - - 14. Schiff. 5 10 is 20 30 40 60 80 ICO SO* O4O 1.084 I7-> 179 1.^77 1.789 1.1:64 1.840 _ I C. Brineau. SO 2 OI7 1.028 CM C of ^ / / *. o^y J^T _ o 4- Schiff. O77 1.069 4i 141 1.217 1.422 i so6 _ 1C. Kolb. C 4 H 6 6 .... .O2I 1.047 .070 L -4 L .096 1.150 .207 T" '- - D 15- Gerlach. C^ F T O 018 1.038 _ -O O7Q 1. 127 .170 1.277 _ _ 15. *' Cane sugar . . . I.OI9 1.039 .060 **/ y .082 .1 _ j I.I29 .178 / o 1.289 _ _ M HC1 I.O2S I.OSO .07 S .101 I.I SI .2OO _ _ 15. Kolb. HBr ^~ j I O7S ^ w j O7 7 **/ j .is8 J I.2S7 376 _ _ _ 14. Topsoe. HI ... 1 - w j j I. O77 -""Y j O77 .118 .165 ** Jf 1.271 Of .400 _ _ _ 13. " H 2 SO 4 . . w *)/ T O72 .w/ / .069 .106 . 1 4S * / 1.223 .707 I. SOI 1.772 1.838 15. Kolb. T O4O .082 I 7 1 1j 174 1.277 J 1 J / 3 17.5 Stolba. P 2 5 * .... l'35 1.027 .077 057 l -/ .119 .086 ' * / *T .167 .119 *"/ o v'i88 -3~85 .264 1.676 1.438 : - ^7-5 15- Hager. Schiff. HNO 8 . . '. T 028 1.056 .088 .119 I.l84 .250 1.373 1.459 1.528 I c. Kolb. C 2 H 4 Oo T OO7 I.OI4 .021 .028 I.04I .052 i. 068 .055 .5. Oudemans. 124 TABLE 1O9. DENSITIES OF MIXTURES OF ETHYL ALCOHOL AND WATER IN CRAMS PER MILLILITER. The densities in this table are numerically the same as specific gravities at the various temperatures in terms of water at 4 C. as unity. Based upon work done at U. S. Bureau of Standards. See Bulletin Bur. Stds. vol. 9, no. 3 ; con- tains extensive bibliography ; also Circular 1-9, 1913. Per cent C,H 8 OH by weight Temperatures. 10 C. 15 C. 20 C. 25 C. 30 C. 35 C. 4 o C. 0-99973 0.99913 0.99823 0.99708 0.99568 0.99406 0.99225 I 785 725 636 5 20 379 217 034 2 602 542 453 336 194 031 .98846 3 426 365 275 J $ 7 014 .98849 663 4 2 5 8 195 .98984 .98839 6 7 2 485 5 008 032 .98938 817 670 5 01 3 11 6 .98946 .98877 780 656 57 335 142 7 80 1 729 627 500 347 172 8 660 584 478 346 189 009 808 9 524 442 33* 193 031 .97846 641 10 393 304 187 043 97875 685 475 ii 267 171 047 97897 723 527 312 12 I4 I 041 .97910 753 573 '1 13 026 .97914 775 6ti 424 216 .96989 H .97911 790 643 472 278 063 829 '5 800 669 5'4 334 133 .96911 670 16 692 552 387 199 .96990 760 5 12 '7 583 433 259 062 844 607 35 2 18 473 129 .96923 697 452 189 '9 363 191 .96997 782 547 294 023 20 252 068 864 639 395 34 95856 21 *39 .96944 729 495 242 95973 687 22 024 818 592 348 087 809 516 23 .96907 689 453 199 .95929 643 343 24 787 SS 8 312 048 769 476 168 11 665 539 424 287 168 020 .95895 738 607 442 306 94991 810 11 406 268 144 .95867 710 576 410 272 098 94955 774 3 29 125 844 548 241 .94922 590 248 30 95977 686 382 067 74i 403 55 3 1 823 524 212 .94890 557 214 .93860 3 2 665 038 709 37 02 1 662 33 502 1 86 .94860 5 2 5 180 93825 461 34 334 Oil 679 337 .93986 626 257 35 162 .94832 494 146 79 425 05 1 36 .94986 650 306 .93952 59 r 221 .92843 % 805 620 464 273 114 939 '9 756 556 016 .92808 634 422 39 43 i 079 720 353 .92979 597 208 40 238 .93882 518 148 770 385 .91992 4' 42 43 042 .93842 6 39 682 478 271 3 r 4 107 .92897 .92940 729 558 344 128 170 .91952 733 774 554 33 2 44 433 062 685 301 .91910 5*3 108 45 226 .92852 472 692 291 .90884 g 017 .92806 593 640 426 21 I 257 041 .91823 .91868 649 429 472 250 028 069 .90845 621 660 434 207 49 379 9*995 604 208 .90805 396 .89979 50 162 776 384 .90985 580 168 750 SMITHSONIAN TABLES. T ABLE 1O 9 (">''"*) 125 DENSITY OF MIXTURES OF ETHYL ALCOHOL AND WATER IN CRAMS PER MILLILITER. Per cent |C 2 H B OH by weight Temperature. 10 C. 15 C. 20 C. 25 C. 30 C. 35 C. 40 C. 5 0.92162 0.91776 0.91384 0.90985 0.90580 0.90168 0.89750 51 9 I 943 555 160 7 6o 353 .89940 5 1 9 723 333 .90936 534 o 2 710 288 53 502 IIO 711 307 .89896 479 056 54 279 .90885 485 079 667 248 .88823 P 55 .90831 659 433 258 031 .89850 621 437 206 016 .88784 589 356 57 607 207 .89803 392 .88975 552 122 58 .89980 574 162 744 3^9 .87888 59 54 752 344 88931 5 12 085 653 60 .89927 523 "3 699 278 .87851 417 61 698 293 .88882 466 044 615 1 80 62 468 062 650 2 33 .87809 379 86943 63 2 37 .88830 417 .87998 574 142 705 64 006 597 183 763 337 .86905 466 65 66 .88774 . 364 130 .87948 527 291 100 .86863 667 429 227 .85987 67 68 308 074 .87895 660 477 241 054 .86817 625 387 190 .85950 747 69 .87839 424 004 579 148 710 266 70 602 187 .86766 340 .85908 470 025 72 365 127 .86949 710 527 287 100 .85859 667 426 228 .84986 .84783 540 73 .86888 470 047 618 184 743 297 74 648 229 .85806 376 .84941 500 053 75 408 .85988 564 134 698 257 .83809 ;6 77 1 68 .85927 747 55 322 079 .84891 647 455 211 013 .83768 564 78 685 262 .84835 .8 39 66 523 S 74 79 442 018 590 J 58 720 . 277 .82827 80 I97 .84772 344 .8391 1 473 029 578 81 .84950 525 096 664 224 .82780 329 82 702 277 .83848 4i5 .82974 53 83 453 028 599 164 724 279 .81828 84 203 .83777 348 .82913 473 027 576 85 -8395 * 525 095 660 220 .81774 322 86 697 271 .82840 405 .81965 519 067 87 441 014 583 148 7 08 262 .80811 88 181 82754 3 2 3 .81888 448 003 552 89 .82919 492 062 626 186 .80742 291 90 654 227 .81797 362 .80922 478 028 91 36 .81959 529 094 JJ 211 .79761 92 114 688 257 .80823 34 .79941 49 i 93 94 .81839 5 61 134 .80983 705 549 272 in .79835 669 393 220 .78947 i 278 .80991 .80852 566 424 138 .79991 706 555 271 114 .78831 670 99 698 399 094 274 79975 670 .79846 547 243 415 117 .78814 .78981 684 382 542 247 77946 100 .77806 507 100 .79784 360 78934 506 075 641 203 SMITHSONIAN TABLES. TABLE 110. DENSITIES OF AQUEOUS MIXTURES OF METHYL ALCOHOL, CANE SUGAR, OR SULPHURIC ACID. 1'er cent by weight of substance. Methyl Alcohol. Cane Sugar. 20 Sulphuric Acid. D^C. Per cent by weight of substance. Methyl Alcohol. D^ C. Cane Sugar. 20 Sulphuric Acid. O I 0.99913 .99727 0.998234 1. 002 1 20 0.99823 1.00506 50 0.91852 91653 1.229567 1.235085 '39505 1.40487 2 99543 1.006015 1.01178 52 9'45' 1.240641 1.41481 3 99370 1.009934 1.01839 53 .91248 1.246234 1.42487 4 .99198 I.OI388I 1.02500 54 .91044 1.251866 1.43503 5 .99029 1.017854 1.03168 55 .90839 '257535 1.4453 6 .98864 I.02I855 1.03843 56 .90631 1.263243 1.45568 7 .98701 1.025885 1.04527 57 .90421 1.268989 1.46615 8 98547 1.029942 1.05216 58 .90210 1.274774 1.47673 9 98394 1 .034029 1.05909 59 .89996 1.280595 1.48740 10 .98241 1.038143 I.0660 9 60 .89781 1.286456 1.49818 ii .98093 1.042288 1.07314 61 89563 1.292354 1.50904 12 97945 1.046462 1.08026 62 .89341 1.298291 I.5I999 13 X ** .97802 1.050665 1.08744 63 .89117 1.304267 1.53102 .97660 1 .054900 1.09468 64 .88890 1.310282 I.542I3 1C .97518 1.059165 1.10199 65 .88662 I.3I6334 '55333 16 97377 1.063460 1.10936 66 88433 1.322425 1.56460 '7 97237 1.067789 1.11679 67 .88203 1.328554 '57595 18 .97096 1.072147 1.12428 68 .87971 '334722 1.58739 19 96955 I.076537 I - I 3 I 83 69 87739 1.340928 1.59890 20 .96814 1.080959 ''3943 70 875 7 1.347174 1.61048 21 22 23 24 .96673 96533 .96392 .96251 1.085414 1 .089900 1.094420 1.098971 1.14709 1.15480 1.16258 1.17041 7' 72 73 74 .87271 87033 .86792 .86546 I.353456 I.359778 1.366139 I-372536 1.62213 1.63384 i .64560 1.65738 11 .96108 95963 I-I03557 I.I08I75 1.17830 1.18624 76 .86300 .86051 1.378971 1.385446 1.66917 1.68095 27 I.II2828 1.19423 77 .85801 '391956 1.69268 28 15668 I.II75I2 1.20227 78 8555' '398505 '70433 29 955'8 I.I2223I 1.21036 79 .85300 1.405091 '.71585 3 .95366 1.126984 1.21850 80 .85048 1.411715 1.72717 3 2 95213 .95056 I.I3I773 1.136596 1.22669 1.23492 81 82 .84794 .84536 1.418374 1.425072 1.73827 1.74904 33 .94896 I.I4I453 1.24320 83 .84274 1.431807 '75943 34 94734 1.146345 1-25154 84 .84009 I-438579 1.76932 35 94570 1.15127? 1.25992 85 83742 1.445388 1.77860 36 .94404 1.156238 1.26836 86 .83475 1.452232 1.78721 37 .94237 1.161236 1.27685 87 .83207 I.459II4 1.79509 38 .94067 1.166269 1.28543 88 82937 1.466032 1.80223 39 .93894 1.171340 1.29407 89 .82667 1.472986 1.80864 40 .93720 1.176447 1.30278 90 .82396 1.479976 1.81438 4' 93543 1. 181592 I -3 II 57 9' .82124 1.487002 1.81950 42 93365 1.186773 1.32043 92 .81849 1.494063 1.82401 43 93'85 I.I9I993 1.32938 93 .81568 1.501 158 1.82790 44 .93001 1.197247 '33843 94 .81285 1.508289 ' -83 1 1 5 45 92815 1.202540 '34759 95 .80999 '5'5455 1.83368 46 .92627 1.207870 96 80713 1.522656 1.83548 47 .92436 1.213238 1.36625 97 .80428 1.529891 1.83637 48 .92242 1.218643 '37574 98 .80143 1.537161 1.83605 49 .92048 1.224086 '38533 99 79859 1.544462 50 .91852 1.229567 L39505 100 79577 1.551800 (i) Calculated from the specific gravity determinations of Doroschevski and Rozhdestvtnski at '5 /'5 C. ; J. Knss., 1'hys. Chem. Soc., 41, p. 977, 1909. According to Dr. F. I'lato; Wiss. Abh. der K. Normal-Eichungs-Kommission, 2, p. 153, 1900. Dr. Domke's table; Wiss. Abh. der K. Normal-Eichungs-Kommission, Calculated from 5, p. 131, 1900. SMITHSONIAN TABLES. All reprinted from Circular 19, U.S. Bureau of Standards, 1913. TABLE 111. DENSITY OF GASES 127 The following table gives the density as the weight in grams of a liter (normal liter) of the gas at o C, 76 cm pressure and standard gravity (sea-level, 45 latitude), the specific gravity referred to dry, carbon-dioxide-free air and to pure oxygen, and the weight in pounds per cubic foot. Dry, carbon-dioxide-free air is of remarkably uniform density; Guye, Kovacs and Wourtzel found maxi- mum variations in the density of only 7 to 8 parts in 10,000. For highest accuracy pure oxygen should be used as the standard gas for specific gravities. Observed densities are closely propor- tional to the molecular weights. Gas. Formula. Weight of normal liter in grams. Specific gravity. Pounds per cubic foot. Refer. Air = i 02= i Air C 2 H 2 NH 3 A Br 2 C4Hio C0 2 CO C1 2 C 2 N 2 C 2 H 6 C 2 H4 F 2 He HBr HCI HF H 2 H 2 S Kr CH4 CH 3 C1 C 2 H 6 Ne N 2 NO N 2 O 2 CsH 8 H 2 S0 2 X I . 2930 I.I79I 0.7708 1.7809 7.14 2-594 1.9768 I . 2504 3-221 f 0.41 to \o. 9 6 2.323 1-3562 1.2609 1.70 0.1785 3.616 1.6398 0.922 0.08987 1.538 3.708 0.7168 2.304 2. IIO 0.9002 1.2507 1.3402 1-9777 1.42905 2.0196 0.593 2.9266 5.851 I.OOOO 0.9119 0.5961 1-3773 5-52 2.006 1.5289 0.9671 2.491 / 0.32 to 10.74 1.797 1.0489 0.9752 i-3i 0.1381 2-797 1.2682 0.713 0.06950 1.189 2.868 Q-5544 1.782 1.632 0.6962 0.9673 1.0365 1.5296 1.1052 1.5620 0.462 2.2634 4.525 o . 9048 0.8251 0-5394 i . 2462 5.00 1.815 1-3833 0.8750 2.254 / o . 29 to 10.67 1.626 0.9490 0.8823 1.19 0.1249 2.530 1-1475 0.645 0.06289 1.076 2.595 0.5016 t. 6x2 1-477 0.6299 0.8752 0.9378 1-3839 I.OOOO 1.4132 0.418 2.0479 4.094 0.08072 0.07361 0.04812 O.linS 0.446 0.1619 0.12341 0.07806 O.2OII / '0.026 to \ o . 060 0.1450 0.08467 0.07872 0.106 0.01115 0-2257 0.10237 0.0576 0.005610 0.09602 0-2315 0-04475 0.1438 0.1317 0.05620 0.07808 0.08367 0.12347 0.089214 0.12608 0.0373 0.18270 0.3653 I 2 3 3 4 4 3 3 3 4 5 2 6 14 4 3 8 9 3 7 5 10 10 7 3 3 3 n 12 13 3 7 Acetylene Ammonia Argon Bromine Butane Carbon dioxide Carbon monoxide Chlorine Coal gas Cyanogen Ethane Ethylene Fluorine Helium Hydrobromic acid Hydrochloric acid Hydrofluoric acid Hydrogen Hydrogen sulphide Krypton Methane . . ]Methyl chloride Methyl ether Neon Nitrogen Nitric oxide Nitrous oxide Oxygen Propane Steam at 100 C Sulphur dioxide Xenon References: (i) Guye, Kovacs, Wourtzel, Jour. chim. phys., 10, p. 332, 1912; (2) Stahrfoss, Arch. Sc. phys. et nat., IV, 28, p. 384, 1909; (3) Guye, Jour. chim. phys., 5, p. 203, 1907 (contains review of best determinations and indicates most proba- ble values); (4) Computed; (5) Baume and Perrot, Jour. chim. phys., 7, p. 369, 1909; (6) Moissan, C. R., 138, 1904; (7) Watson, Jour. Chem. Soc., 97, p. 833, 1910; (8) Thorpe, Hambley, Jour. Chem. Soc., 53, p. 765, 1888; (9) Morley, Smithsonian Con- tributions to Knowledge, 1895; (10) Baume, Jour. chim. phys., 6, p. i, 1908; (n) Ger- mann, Jour, of Phvs. Chem., 19, p. 437, 1915; (12) Timmermans, C. R., 158, p. 789, 1914; (13) Peabody's Steam Tables, 1909; (14) Taylor, Phys. Rev., 10, p. 653, 1917. SMITHSONIAN TABLES. 128 TABLE 112. VOLUME OF CASES, Values ol 1 + .00367 *. The quantity i + .00367 t gives for a gas the volume at < when the pressure is kept constant, or the pressure at ( when the volume is kept constant, in terms of the volume or the pressure at o. (t) This part of the table gives the values of i -f .00367 1 for values of t between o and 10 C. by tenths of a degree. (1) This part gives the values of i + .00367 / for values of / between 90 and 4- 1990 C. by 10 steps. These two parts serve to give any intermediate value to one tenth of a degree by a sim- ple computation as follows : In the () table find the number corresponding to the nearest lower temperature, and to, this number add the decimal part of the number in the (a) table which corresponds to the difference between the nearest temperature in the (*) table and the actual temperature. For example, let the temperature be 682. 2 : We have for 680 in table (6) the number .... 3-495 60 And for 2.2 in table (a) the decimal .00807 Hence the number for 682.2 is 3-53 6 7 (0) This part gives the logarithms of i + .00367 1 for values of t between 49 and + 399 C. by degrees. (d) This part gives the logarithms of i -+-.00367 / for values of t between 400 and 1990 C. by 10 steps. (a) Values of 1 + .00367 / for Values of / between and 10 G. by Tenths of a Degree. t 0.0 0.1 0.2 0.3 0.4 1. 00000 1.00037 1.00073 I.OOIIO 1.00147 I .00367 .00404 .00440 .00477 .00514 2 .00734 .00771 .00807 .00844 .00881 3 .OIIOI .01138 .01174 .01211 .01248 4 ..01468 01505 .01541 .01578 .01615 5 1.01835 1.01872 1.01908 I.OI945 1.01982 6 7 .02202 .02569 .02239 .02606 .02275 .02642 .02312 .02679 .02349 .02716 8 .02936 .02973 .03009 .03046 .03083 9 03303 03340 03376 03413 .03450 1 0.5 0.6 0.7 0.8 0.9 i 1.00184 .00550 1.00220 .00587 1.00257 .00624 1.00294 .00661 1.00330 .00697 2 .00918 .00954 .00991 .01028 .01064 3 4 .01284 .01652 .OI32I .01688 01358 .01725 01395 .01762 .01431 .01798 5 6 1.02018 .02386 1.02055 .02422 1.02092 .02459 1.02129 .02496 1.02165 .02532 7 .02752 .02789 .02826 .02863 .02899 8 9 .03120 .03486 03I5 6 03S 2 3 03193 03560 .03290 03597 .03266 03633 SMITHSONIAN TABLES. TABLE 112. {continued). VOLUME OF GASES. I2 9 (b) Values of 1 t .00367 1 lor Values of t between 90 and -f 1990 0. by 10 Steps. t 00 10 20 30 40 000 I.OOOOO 0.96330 0.92660 0.88990 0.85320 4000 100 2OO 300 4OO 1. 00000 1.36700 1.73400 2.IOIOO 2.46800 1.03670 1.40370 1.77070 2.13770 2.50470 1.07340 1.44040 1.80740 2.17440 2.54140 I.IIOIO 1.47710 1.84410 2.2IIIO 2.57810 1.14680 1.51380 1.88080 2.24780 2.61480 500 600 700 800 900 2.83500 3.20200 3.56900 3.93600 4.30300 2.87170 3.23870 3.60570 3.97270 4-33970 2.90840 3-2754 3.64240 4.00940 4.37640 2.94510 3.3I2IO 3.67910 4.04610 44I3IO 2.98180 3.34880 3.71580 4.08280 4.44980 1000 IIOO 1200 1300 1400 4.67000 5.03700 5.40400 5.77100 6. 1 3800 4.70670 5-07370 5.44070 5.80770 6.17470 4-7434 5.11040 5-4774 5.84440 6.21140 4.78010 5.I47IO S-SMio 5.88110 6.24810 4.81680 5.18380 5.55080 5.91780 6.28480 1500 1600 1700 1800 1900 6.50500 6.87200 7.23900 7.60600 7.97300 6.54170 6.90870 7.27570 7.64270 8.00970 6.57840 6.94540 7.31240 7.67940 8.04640 6.61510 6.98210 7.34910 7.71610 8.08310 6.65180 7.01880 7.38580 & 2000 8.34000 8.37670 8.41340 8.45010 8.48680 * 50 60 70 80 90 ooo 0.81650 0.77980 0.74310 0.70640 0.66970 +000 TOO 200 300 400 1.18350 J-SSQS 1.91750 2.28450 2.65150 1.22020 1.58720 1.95420 2.32120 2.68820 1.25690 1.62390 1.99090 2.35790 2.72490 1.29360 1.66060 2.02760 2.39460 2.76160 I-33030 1.69730 2.06430 2.43130 2.79830 5OO 600 700 800 900 3.01850 3-3855 3-75 2 5o 4.11950 4.48650 3-0552 ' 34222O 3.78920 4.15620 4.52320 3.09190 3-4589 3.82590 4.19290 4-5599 3.12860 3-49560 3.86260 4.22960 4.59660 3-I6530 3-53230 3-89930 4.26630 4-63330 1000 IIOO 1 200 1300 1400 4-85350 5.22050 5- 5 8 7 5 5-9545 6.32 1 50 4.89020 5.25720 5.62420 5.99120 6.35820 4.92690 5-2939 5.66090 6.02790 6.39490 4.96360 5-336o 5.69760 6.06460 6.43160 5.00030 5-36730 5-7343 6.10130 6.46830 1500 1600 1700 1800 1900 6.68850 7-555 7.42250 7.78950 8.15650 6.72520 7.09220 745920 7.82620 8.19320 6.76190 7.12890 7-4959 7.86290 8.22990 6.79860 7.16560 7-5326o 7.89960 8.26660 6.83530 7.20230 7-56930 7.93630 8.30330 2000 8-52350 8.56020 8.59690 8.63360 8.67030 SMITHSONIAN TABLES. 1 3 o TABLE 112 (continued). VOLUME OF (c) Logarithms of 1 + .00367 t lor Values t 1 2 3 4 Mean diff. per degree. 40 1931051 1.929179 1.927299 1.925410 7-9235I3 1884 30 947546 945744 943934 .942117 1805 20 .966892 .965169 .963438 .961701 959957 1733 10 .983762 .982104 .980440 978769 .977092 1667 O o.oooooo .998403 .996801 .995192 993577 1605 4-0 0.000000 0.001591 0.003176 0.004755 0.006329 1582 10 .015653 .017188 .018717 .020241 .02 1 760 1526 20 .030762 032244 033721 03 5 i 93 .036661 1474 3 .045362 .046796 .048224 .049648 .051068 1426 40 .059488 .060875 .062259 .063637 .065012 1381 50 0.073168 0.074513 0.075853 0.077190 0.078522 1335 60 .086431 087735 .089036 .090332 .091624 1299 70 .099301 .100567 .101829 .103088 .104344 I2 59 80 .11 1800 .113030 .114257 .115481 .116701 1226 90 .123950 .125146 .126339 .127529 .128716 1191 100 0.135768 0.136933 0.138094 0.139252 0.140408 1158 110 .147274 .248408 .149539 .150667 I 5 I 793 1129 120 .158483 .159588 .160691 .161790 .162887 IIOI 130 .169410 .170488 i7 I 5 6 3 .172635 173705 1074 140 .180068 .181120 .182169 .183216 .184260 1048 150 0.190472 0.191498 0.192523 o.i93545 0.194564 1023 160 .200632 .201635 .202635 203634 .204630 IOOO 170 180 .210559 .220265 .211540 .221224 .212518 .222180 . -213494 .223135 .214468 .224087 976 956 190 229759 230697 231633 .232567 .233499 935 200 0.239049 0.239967 0.240884 0.241798 0.242710 916 2IO .248145 .249044 .249942 .250837 25I73 1 897 2 2O 230 257054 .265784 257935 .266648 .258814 .267510 259692 .268370 .260567 .269228 878 861 2 4 274343 .275189 .276034 .276877 .277719 844 250 0.282735 0.283566 0.284395 0.285222 0.286048 828 260 .290969 .291784 292597 .293409 .294219 8^3 270 280 .299049 .306982 .299849 .307768 308552 .301445 .309334 .302240 310115 784 290 314773 .315544 3*63*4 3 i 7083 3 17850 769 300 0.322426 0.323184 0.323941 0.324696 0.325450 756 310 320 329947 337339 .330692 .338072 33'435 338801 332178 339533 33 2 9 J 9 .340262 743 730 33 340 3446o8 351758 345329 .352466 346048 353^74 .346766 .353880 .347482 354585 719 707 350 0.358791 0.359488 0.360184 0.360879 0-361573 696 360 365713 366399 .367084 .367768 .368451 684 370 372525 373201 373875 374549 375221 674 390 379233 385439 379898 .386494 .380562 387148 .381225 .387801 .381887 388453 664 654 SMITHSONIAN TABLES. TABLE 112 (continued). CASES. of t between 49 and +399 0. by Degrees. 1 5 6 7 8 9 Mean diff. per degree. 40 1.921608 1.919695 ^917773 7.915843 1.913904 1926 30 20 .940292 .958205 .938460 .95 6 447 .936619 .954681 .934771 .952909 .932915 .951129 1845 1771 10 .975409 973719 .972022 .970319 .968609 1699 o .991957 .990330 .988697 .987058 .985413 1636 + 0.007897 0.009459 0.011016 0.012567 0.014113 1554 10 .023273 .024781 .026284 .027782 .029274 1500 20 .038123 .039581 .041034 .042481 .043924 145 30 40 .052482 .066382 053^93 .067748 .055298 .069109 .056699 .070466 .058096 .071819 1402 1359 50 60 0.079847 .092914 0.081174 .094198 0.082495 .095486 0.083811 .096765 0.085123 .098031 1315 I28l 70 105595 .106843 .108088 .109329 .110566 1243 80 .117917 .119130 .120340 .121547 .122750 1210 90 .129899 .131079 .132256 13343 .134601 II 75 100 0.141559 0.142708 0.143854 0.144997 0.146137 1144 no .152915 .154034 155151 .156264 - 1 5737 5 ia 120 .163981 .164072 .166161 .167246 .168330 1087 130 .174772 .175836 .176898 .177958 .179014 1060 140 .185301 .186340 187377 .188411 .189443 1035 150 0.195581 0.196596 0.197608 0.198619 0.199626 IOII 1 60 .205624 .206615 .207605 .208592 .209577 988 170 215439 .216409 .217376 218341 .219304 966 1 80 .225986 .226932 .227876 .228819 946 190 .234429 235357 .236283 .237207 .238129 925 200 0.243621 0.244529 0.245436 0.246341 0.247244 906 210 .252623 2 535 12 .254400 .255287 .256172 887 2 2O .261441 .262313 .263184 .264052 .264919 870 230 .270085 .270940 .271793 .272644 273494 853 240 .278559 .279398 .280234 .281070 .281903 836 250 260 0.286872 .295028 0.287694 .295 8 35 0.288515 .296640 0.289326 .297445 0.290153 .298248 820 805 270 .303034 .303827 .304618 305407 .306196 790 280 290 .310895 .318616 3 Il6 73 3 T 938 1 .312450 .320144 .313226 .320906 .314000 .321667 7 6 763 300 0.326203 0.326954 0.327704 0.328453 0.329201 750 310 333659 334397 335 J 35 .335871 .336606 737 320 .340989 34I7I5 .342441 343 I 64 .343887 724 330 .348198 .348912 .349624 .350337 .351048 7i3 340 355289 35599 1 356693 357394 358093 701 350 360 370 380 0.362266 .369132 .375892 .382548 0.362957 .369813 .376562 383208 0.363648 370493 377232 .383868 0.364337 371171 .377900 384525 0.365025 .371849 378567 385183 690 678 668 658 39 .389104 .389754 390403 .391052 .391699 648 SMITHSONIAN TABLES. 132 TABLE 112 (continued). VOLUME OF GASES. (d) Logarithms of 1 + .00367 / for Values of t between 400 and 1990 0. by 10 Steps. t 00 10 20 30 40 400 0-392345 0.398756 0.405073 0.411300 0.417439 500 0452553 0.458139 0.463654 0.469100 0.474479 600 .505421 510371 .515264 .520103 .524889 700 552547 556990 .561388 .565742 .570052 800 900 595055 633771 .599086 .637460 603079 .641117 607037 .644744 .610958 .648341 1000 0.669317 0.672717 0.676090 0.679437 0.682759 IIOO .702172 705325 708455 7"563 .714648 1 200 732715 735655 738575 74M75 744356 1300 .761251 .764004 .766740 769459 .772160 1400 .788027 .790616 .793190 795748 .798292 1500 1600 0.813247 .837083 0.815691 839396 0.818120 .841697 0.820536 0.822939 .846263 1700 .839679 .861875 .864060 .866234 .868398 1800 1900 .881156 .901622 .883247 .903616 .885327 .905602 .887398 .907578 .889459 909545 t 50 60 70 80 90 400 0.423492 0.429462 0.435351 0.441161 0.446894 500 600 0.479791 .529623 0.485040 534303 0.490223 538938 0.495350 .543522 0.500415 .548058 700 800 574321 .614845 582734 .622515 .626299 .590987 .630051 900 .651908 655446 658955 .662437 .665890 1000 IIOO 0.686055 .717712 0.689327 720755 0-692574 .723776 0.695797 .726776 0.698996 729756 1 200 .747218 .750061 .752886 755692 .758480 1300 1400 774845 .800820 777514 803334 .780166 .805834 .782802 .808319 .785422 .810790 1500 1600 1700 1800 0.825329 .870550 .891510 0.827705 .850781 .872692 893551 0.830069 .853023 .874824 .895583 0.832420 855253 876945 .897605 0.834758 857471 .879056 .899618 1900 .911504 913454 915395 .917327 .919251 SMITHSONIAN TABLES. TABLES 113-114. 133 RELATIVE DENSITY OF MOIST AIR FOR DIFFERENT PRESSURES AND HUMIDITIES. TABLE 113. Values of ^, from h = 1 to h = 9, for the Computation of Different Valuei of the Ratio of Actual to Normal Barometric Pressure. This gives the density of moist air at pressure h in terms of the same air at normal atmosphere pres- sure. When air contains moisture, as is usually the case with the atmosphere, we have the following equation for pressure term: h=B 0.378^, where e is the vapor pressure, and B the corrected barometric pressure. When the necessary psychrometric observations are made the value of e may be taken from Tabl* 189 and then 0.3782 from Table 115, or the dew-point may be found and the value of 0.378* taken from Table 115. h h 760 1 2 3 0.0013158 .0026316 .0039474 4 I 0.0052632 .0065789 .0078947 7 8 9 0.0092105 .0105263 .0118421 EXAMPLES OF USE OF THE TABLE. To find the value of when h = 754.3 760 h =: 700 gives .92105 50 ' .065789 4 .005263 vJ .000395 754-3 -992497 To find the value of when h 5.73 760 k = 5 gives .0065789 .7 ' ; .0009210 .03 " .0000395 5-73 .0075394 TABLE 114. Values of the logarithms of * Q for values of h between 80 and 340. Values from 8 to 80 may be got by subtracting i from the characteristic, and from 0.8 to 8 by subtracting 2 from the characteristic, and so on. h Values of log A. 760 1 2 3 4 5 6 7 8 9 80 90 T.O2228 07343 7.02767 .07823 7.03300 .08297 7.03826 .08767 7.04347 .09231 7.04861 .09691 7.05368 .10146 7.0587 1 .10596 7.06367 .11041 7.06858 .11482 100 1.11919 1.12351 7.12779 7.13202 7.13622 7.14038 7.14449 7.14857 7.15261 7.15661 no .16058 .16451 .16840 .17226 .17609 .17988 .18364 18737 .19107 19473 120 .19837 .20197 20555 .20909 .21261 .21611 .21956 .22299 .22640 .22978 130 140 23313 .26531 .23646 .26841 23976 .27147 24304 27452 .24629 27755 .24952 28055 2^273 28354 25591 .28650 25907 .28945 .26220 .29237 150 160 1.29528 3 2 33! 1.29816 .32601 7.30103 .32870 7.30388 33 J 37 7.30671 33403 7.30952 33667 7.31231 33929 7.31509 .34190 7.31784 34450 7.32058 34707 170 1 80 .34964 37446 .35218 .37686 35471 .37926 .35723 .38164 35974 .38400 .36222 38636 .36470 38870 .36716 .39128 .36961 39334 37204 39565 190 39794 .40022 .40249 .40474 .40699 .40922 .41144 41365 41585 .41804 200 1.42022 7.42238 7.42454 7.42668 7.42882 7.43094 7.43305 7.43516 7.43725 7-43933 2IO .44141 44347 44552 44757 .44960 .45162 45364 45565 .45764 45963 220 2 3 .46161 .48091 .46358 .48280 .46^4 .48467 46749 48654 46943 .48840 47137 .49025 47329 .49210 47521 49393 .47712 49576 .47902 4975 s 240 .49940 .50120 .50300 50479 .50658 50835 .51012 .51188 5 I 3 6 4 51539 250 i-S'713 7.51886 7.52059 7.52231 7.52402 7.52573 7.52743 7.52912 7.53081 7.53249 260 534i6 53583 53749 S39I4 54079 .54243 54407 54570 54732 .54894 270 55055 .55216 55376 55535 55694 55852 .56010 .56167 56 ?2 56479 o o 280 290 .56634 .58158 .58308 .56944 58457 57097 57250 58753 57403 .58901 57555 .59048 .57707 .59194 57858 59340 .58008 .59486 300 1.59631 T -59775 7.59919 7.60063 7.60206 7.60349 7.60491 7.60632 7.60774 7.60914 3*o 61055 .61195 61334 61473 .61611 .61750 .61887 .62025 .62161 .62298 320 .62434 .62569 .62704 .62839 .62973 63107 .63240 63373 63506 .63638 330 340 .63770 .65067 .63901 .65194 .64032 65321 .64163 65448 .64293 65574 .64423 .65701 64553 .65826 .64682 65952 .64810 .66077 64939 .66201 SMITHSONIAN TABLES. 34 TABLE 114 (contimud). DENSITY OF AIR. Values of logarithms of -J- for values of h between 350 and 800. /* Values of log A. 6 760 1 2 3 4 5 6 7 8 9 350 7.66325 7.66449 7.66573 7.66696 7.66819 7.66941 7.67064 7.67185 7.67307 7.67428 3 6o 67549 .67669 .67790 .67909 .68029 .68148 .68267 .68385 .68503 .68621 370 68739 .68856 68973 .69090 .69206 .69322 69437 69553 .69668 .69783 69897 .70011 .70125 .70239 70352 70465 .70577 .70690 .70802 .70914 390 7*025 .71136 .71247 71358 .71468 7*578 .71688 .71798 .71907 .72016 400 7.72125 7.72233 7.72341 7.72449 7.72557 7.72664 7.72771 7.72878 7.72985 7.73091 410 73*97 73303 .73408 735*4 .73723 .73828 73932 .74036 74*40 420 74244 74347 74450 74553 ^4655 7475 s .74860 .74961 75063 75*64 43 440 .76264 76362 .75467 .76461 75567 76559 76657 .75768 .76755 .75867 .76852 75967 .76949 .76066 .77046 .76165 77*43 450 7.77240 7-77336 777432 7.77528 7.77624 7.77720 7.77815 7.77910 7.78005 7.78100 460 .78194 .78289 78383 .78477 78570 .78664 .78757 78850 78943 79036 470 480 .79128 .80043 .79221 80133 793*3 .80223 79405 80313 79496 .80403 .79588 80493 .79770 .80672 .79861 .80761 79952 .80850 490 .80938 .81027 .81115 .81203 .81291 .81379 .81467 .81554 .81642 .81729 500 7.8i8i6 7.81902 7.81989 7.82075 7.82162 7.82248 7.82334 7.82419 7.82505 7.82590 5* .82676 .82761 .82846 .82930 83015 .83099 .83184 .83268 83352 83435 520 .835*9 .83602 .83686 .83769 .83852 .83935 .84017 .84100 .84182 .84264 53 84346 .84428 84510 .84591 .84673 .84754 84833 .84916 .84997 .85076 540 .85158 85238 853*9 85399 85479 .85558 85638 857*7 85797 .85876 550 7.85955 7.86034 7.86113 7.86191 7.86270 7.86348 7.86426 7.86504 7.86582 1.86660 560 86737 .86815 .86892 .86969 .87047 .87*23 .87200 .87277 87353 .87430 570 .87506 87582 87658 87734 .87810 .87885 .87961 .88036 .88111 .88186 580 590 .88261 .89004 88336 .89077 .88411 .89151 .88486 .89224 .88560 89297 .88634 89370 .88708 89443 .88782 .895*6 .88856 .89589 38? 600 7.89734 7.89806 7.89878 7.89950 7.90022 7.90094 7.90166 7. 9 02 3 8 7.90309 7.90380 610 .90452 90523 .90594 .90665 90735 .90806 90877 90947 .91017 .91088 620 .91158 .91228 .91298 9*367 9*437 9*507 9*576 9*645 9*7*5 .91784 630 9*853 .91922 .91990 92059 .92128 .92196 .92264 92333 .92401 .92469 640 92537 .92604 .92672 .92740 .92807 92875 .92942 93009 .93076 93*43 650 7.93210 7.93277 7-93343 7.93410 7.93476 7-93543 7.93609 7.93675 7-9374* 7.93807 660 670 .93873 .94526 93939 9459* .94004 94656 .94070 94720 94*35 9475 .94201 94849 .94266 949*3 9433* .94978 94396 .95042 .94461 .95106 680 95*70 95233 95297 9536* 95424 95488 9555* 956*4 95677 9574* 690 .95804 .95866 .95929 .95992 96055 .96117 .96180 .96242 96304 .96366 700 7.96428 7.96490 7.96552 7.96614 7.96676 7.96738 7.96799 7.96861 7.96922 7.96983 710 97044 .97106 .97167 .97228 .97288 97349 974*o 9747* 9753* 97592 720 97652 977*2 97772 97832 .97892 9795* .98012 .98072 .98132 .98191 730 .98251 983*0 98370 .98429 .98488 .98547 .98606 .98665 .98724 .98783 740 .98842 .98900 98959 .99018 .99076 99*34 99*93 .99251 99309 99367 750 7.99425 7.99483 7.99540 7.99598 7.99656 7-997*3 7.99771 7.99828 7.99886 7-99942 760 o.ooooo 0.00057 o.ooi 14 0.00171 0.00228 0.00285 0.00342 0.00398 0.00455 0.00511 770 .00568 .00624 .00680 00737 .00793 .00849 .00905 .00961 .01017 .01072 780 .01128 .01184 .01239 .01295 0135 .01406 .01461 .01516 .01571 .01626 790 .01681. 01736 .01791 .01846 .01901 01955 .02010 .02064 .02119 .02173 SMITHSONIAN TABLES. TABLES 115-116. TABLE 115. - Values of 0.378e.* This table gives the humidity term 0.3786, which occurs in the equation 5 = 6 135 760 = 8 -^- for the calculation of the density of air containing aqueous vapor at pressure e; do is the density of dry air at normal temperature and barometric pressure, B the ob- served barometric pressure, and h = B 0.3 78^, the pressure corrected for humidity. For values of ', see Table 113. Temperatures are in degrees Centigrade, and pressures in milli- meters of mercury. Dew point. Vapor pressure (ice). 0.378e Dew point. e Vapor pressure (water). 0.378* Dew point. Vapor pressure (water). 0.378* C mm mm C mm mm C mm mm -50 0.029 O.OI 4-58 i-73 30 31-86 12.0 -45 0.054 O.O2 I 4.92 1.86 31 33-74 12.8 -40 0.096 O.O4 2 5-29 2.OO 32 35-70 J 3-5 -35 o. 169 O.O6 3 5-68 2.15 33 37-78 14-3 -30 -25 0.288 0.480 O.II 0.18 4 5 6. 10 6-54 2.31 2.47 H 39-95 42.23 16.0 24 0-530 0.20 6 7.01 2.66 36 44.62 16.9 23 0.585 0.22 7 7.51 2.84 37 47-13 17-8 22 0.646 o. 24 8 8.04 3-04 38 49.76 18.8 21 -20 o. 712 0.783 0.27 0.30 18 8.61 9. 21 3-25 3.48 39 40 52-51 55-40 19.8 20.9 19 0.862 0-33 ii 9-85 3.72 41 58.42 22.1 18 0.947 0.36 12 10.52 3-98 42 61.58 23-3 17 .041 0-39 13 II. 24 4-25 43 64.89 24.5 16 .142 0-43 14 11.99 4-53 44 68-35 25.8 -15 .252 o-47 15 12.79 4.84 45 71.97 27.2 14 373 0.52 16 5.16 46 75-75 28.6 13 503 0-57 17 14-54 5-50 47 79.70 30.1 12 .644 0.62 18 15.49 5-85 48 83-83 31-7 II .798 0.68 16.49 6.23 49 88.14 33-3 -10 .964 0.74 20 17-55 6.63 50 92.6 35-o 9 2.144 0.81 21 18.66 7.06 51 97-3 36.8 8 2.340 0.88 22 19.84 7-50 52 IO2. 2 38.6 7 2-550 0.96 23 21.09 7-97 53 107.3 40.6 6 2.778 05 24 22.4O 8-47 54 II2.7 42.6 -5 3-025 14 25 23.78 8-99 55 118.2 44-7 4 3.291 .24 26 25.24 9-54 56 I24.O 46.9 3 3-578 35 27 26.77 10. 12 57 130.0 49-1 2 3.887 47 28 28.38 10.73 58 136.3 I 4. 220 4.580 .60 73 29 30 30.08 31-86 n-37 12.04 8 142. 8 149.6 54-0 56-5 * Table quoted from Smithsonian Meteorological Tables. TABLE 116. Maintenance of Air at Definite Humidities. Taken from Stevens, Phytopathology, 6, 428, 1916; see also Curtis, Bui. Bur. Standards, 11, 359, 1914; Dieterici, Ann. d. Phys. u. Chem., 50, 47, 1893. The relative humidity and vapor pressure of aqueous vapor of moist air in equilibrium conditions above aqueous solutions of sul- phuric acid are given below. Density of acid sol. Relative humidity. Vapor pressure. Density of acid sol. Relative humidity. Vapor pressure. 20 C 30 C 20 C 30 C mm mm mm mm .OO 100. 17.4 31-6 30 58.3 IO. I 18.4 05 97-5 17.0 30.7 35 47.2 8-3 15-0 . IO 93-9 I6. 3 29.6 .40 37-i 6-5 11.9 15 88.8 15-4 28.0 50 18.8 3-3 6.0 . 20 80.5 14.0 25-4 .60 8-5 i-5 2-7 25 70.4 12. 2 22. 2 .70 3-2 0.6 1.0 SMITHSONIAN TABLES. 136 TABLE 117. PRESSURE OF COLUMNS OF MERCURY AND WATER, British and metric measures. Correct at o C. for mercury and at 4 C. for water. METRIC MEASURE. BRITISH MEASURE. Cms. of Hg. Pressure in grams per sq. cm. Pressure in pounds per sq. inch. Inches of Hg. Pressure in grams per sq. cm. Pressure in pounds per sq. inch. 1 I3-5956 0.193376 1 34-533 0.491174 2 27.1912 0.386752 2 69.066 0.982348 3 40.7868 0.580128 3 103.598 1.473522 4 54.3824 0.773504 4 138-131 1.964696 5 67.9780 0.966880 5 172.664 2.455870 6 81.5736 1.160256 6 207.197 2.947044 7 95.1692 1-353632 7 241.730 3.438218 8 108.7648 1.547008 8 276.262 3.929392 9 122.3604 1.740384 9 310.795 4.420566 10 I35-9560 1.933760 10 345'328 4.911740 Cms. of H,0. Pressure in grams per sq. cm. Pressure in pounds per sq. inch. Inches of H 2 0. Pressure in grams per sq. cm. Pressure in pounds per sq. inch. 1 I 0.0142234 1 2-54 0.036127 2 2 0.0284468 2 S .08 0.072255 3 3 0.0426702 3 7.62 0.108382 4 4 0.0568936 4 10.16 0.144510 5 5 0.0711170 5 12.70 0.180637 6 6 0.0853404 6 15.24 0.216764 7 7 0'0995638 7 17.78 0.252892 8 8 0.1137872 8 20.32 0.289019 9 9 O.I280I06 9 22.86 0.325147 10 10 0.1422340 10 25.40 0.361274 SMITHSONIAN TABLES. TABLE 118. REDUCTION OF BAROMETRIC HEIGHT TO STANDARD TEMPERATURE.' Corrections for brass scale and English measure. Corrections for brass scale and metric measure. Corrections for glass scale and metric measure. Height of barometer in inches. a in inches for temp. F. Height of barometer in mm. a in mm. for temp. C. Height of barometer in mm. a in mm. for temp. C. 150 0.00135 400 0.0651 50 0.0086 16.0 .00145 410 .0668 100 OI72 17.0 .00154 420 .0684 / .0258 '7-5 18.0 18.5 19.0 19-5 .00158 .00163 .00167 .00172 .00176 430 440 460 470 .0700 .0716 .0732 .0749 .0765 200 2 5 3 00 35 0345 .0431 0517 .0603 200 20.5 O.OOlSl .00185 480 490 .0781 .0797 400 45 500 0.0689 0775 .0861 21.0 .00190 500 0.0813 520 .0895 21.5 .00194 510 .0830 540 .0930 22.0 .00199 520 .0846 560 .0965 22.5 .00203 530 .0862 580 .0999 23.0 .OO2O8 540 .0878 23-5 .OO2I2 550 .0894 600 0.1034 560 .0911 610 .1051 24.0 O.OO2I7 570 .0927 620 .1068 24-5 .OO22I 580 0943 630 .1085 25.0 .00226 590 .0959 640 .1103 25-5 26.0 .00231 .00236 600 0.0975 650 660 .II2O "37 26.5 .00240 610 .0992 27.0 .00245 620 .1008 670 0.1154 27-5 .00249 630 .1024 680 .1172 640 .1040 690 .1189 28.0 0.00254 650 .1056 700 .1206 28.5 .00258 660 1073 710 .1223 29.0 .00263 670 .1089 720 .1240 29.2 .00265 680 .1105 730 .1258 29.4 .00267 . 690 .1121 29.6 .00268 740 0.1275 29.8 .00270 700 O.II37 75 .1292 30.0 .00272 710 1154 760 .1309 720 .1170 770 1327 30.2 0.00274 730 .1186 780 1344 3-4 .00276 740 .I2O2 790 .1361 30.6 .00277 75 .1218 800 1378 30-8 .00279 760 I2 35 31.0 31.2 .00281 .00283 770 780 .1267 850 900 o. 1 464 3M .00285 790 .1283 95 .1639 31.6 .00287 800 .1299 IOOO 1723 1 *The height of the barometer is affected by the relative thermal expansion of the mercury and the glass, in the case of instruments graduated on the glass tube, and by the relative expansion of the mercury and the metallic inclosing case, usually of brass, in the case of instruments graduated on the brass case. This relative expansion is practically proportional to the first power of the tem- perature. The above tables of values of the coefficient of relative expansion will be found to give corrections almost identical with those given in the International Meteorological Tables. The numbers tabulated under a are the values of a in the equation //> = Hf a (/'/) where Ht is the height at the standard temperature, Ht' the observed height at the temperature/', and a (t' /) the correction for temperature. The standard temperature is o C. for the metric system and 28. 5 F. for the English system. The English barometer is correct for the temperature of melting ice at a temperature of approximately 28.s F., because of the fact that the brass scale is graduated so as to be standard at 62 F., while mercury has the standard density at 32 F. EXAMPLE. A barometer having a brass scale gave H ' = 765 mm. at 25 C. ; required, the cor- responding reading at o C. Here the value of a is the mean of .1235 and .1251, or .1243 ; . . a(t' t) = .1243 X 25 = 3.11. Hence ff = 765 3.1 1 -= 761.89 N. B. Although a is here given to three and sometimes to four significant figures, it is seldom worth while to use more than the nearest two-figure number. In fact, all barometers have not the same values for a, and when great accuracy is wanted the proper coefficients have to be deter- mined by experiment. SMITHSONIAN TABLES. 138 TABLE 119. REDUCTION OF BAROMETER TO STANDARD GRAVITY. Free-air Altitude Term. Correction to be subtracted. The correction to reduce the barometer to sea-level is (gi g)/g X B where B is the barometer reading and g and |i the value of gravity at sea-level and the place of observation respectively. The following values were computed for free-air values of gravity gi (Table 565). It has been customary to assume for mountain stations that the value of gi = say about J the free-air value, but a comparison of modern determinations of gi in this country shows that little reliance can be placed on such an assumption. Where gi is known its value should be used in the above correction term. (See Tables 566 and 567. Similarly for the latitude term, see succeeding tables, the true value of g should be used if known; the succeeding tables are based on the theoretical values, Table 565.) Height Observed height of barometer in millimeters. above Si g sea-level. 400 450 500 550 600 650 700 7*50 800 meters. IOO 0.031 Correction in mm to be subtracted for .02 .02 .02 200 0.062 height above sea-level in first column and .04 05 05 _ 300 0.093 barometer reading in the top line. .07 .07 07 400 0.123 .09 .10 .IO 500 0.154 _. MM . .11 .12 13 MM MM 600 0.185 .12 13 .14 _ 700 0.216 .14 15 .16 800 0.247 .16 .18 .19 _ 000 0.278 .18 . 20 . 22 1000 0.309 .18 .19 .20 .22 .24 IIOO 0-339 .19 .21 .22 .24 I2OO 0.370 .21 23 .24 .26 1300 0.401 ^ .22 24 .26 29 MM MM 1400 0.432 24 .26 .28 31 1500 0.463 .24 .26 .28 30 33 1600 0.494 25 .28 30 32 1700 1800 0.525 0.555 :3 30 31 32 34 34 .36 .020 .0463 I5OOO IOOO 0.586 30 33 36 39 .OI9 .0447 14500 2000 0.617 .28 31 34 38 .41 .021 .019 .0432 14000 2IOO 0.648 30 33 36 .40 .021 .018 .04l6 13500 220O 0.679 3i 35 .38 .41 .O2O .017 .O40I 13000 230O 0.710 32 .36 .40 43 .021 .019 .017 .0386 12500 24OO 0.740 34 .38 .42 45 .021 .018 .Ol6 .0370 12000 2500 0.771 31 35 39 43 47 .O2O .Ol8 015 0355 II500 26OO 0.802 33 37 .41 .021 .019 .017 .015 0339 IIOOO 27OO 0.833 34 .38 .42 .O2O .018 .Ol6 .014 .0324 10500 2800 0.864 35 .40 44 .OI9 .017 015 013 .0308 1 0000 2OOO 0-895 .36 .41 .46 .020 .018 .Ol6 015 013 .0293 9500 3000 0.926 .38 .42 47 .019 .017 .Ol6 .014 .012 .O278 9000 3100 0-957 39 44 .018 .Ol6 015 .013 .0262 8500 3200 0.988 .40 .46 .017 -015 .OI 4 .012 .0247 8000 3300 1.019 .42 47 .017 .016 .014 013 .O23I 7500 3400 1.049 43 .48 .016 015 .013 .012 .0216 7000 3500 1.080 44 49 .015 .014 .012 .Oil .0200 6500 3600 i. in 45 .014 013 .Oil .0185 6000 3700 1.142 .46 .013 .012 .Oil .0170 5500 3800 1. 173 .48 .012 .Oil .Oil .OIO 0154 5000 3900 1.204 49 .Oil .010 .010 .0139 4500 4000 1.235 50 .010 .009 .009 .0123 4000 .008 .008 .007 .007 Corrections in in. to be .OO92 3000 .006 -005 .005 .0041 subtracted for height above .0062 20OO .003 .003 .003 sea-level in last column and .O03I IOOO barometer reading in bot- tom line. feet. 30 28 26 24 22 20 18 16 J 4 Height Observed height of barometer in inches. above sea-level. SMITHSONIAN TABLES. TABLE 1 2O. REDUCTION OF BAROMETER TO STANDARD GRAVITY.* METRIC MEASURES. From Latitude o e to 45, the Correction is to be Subtracted. '39 Lati- tude 520 540 560 580 600 620 640 660 680 700 720 740 760 780 mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. nun* mm. mm. 1-39 1-45 1-50 1-55 1.61 1.66 1.71 1.77 1.82 -!.8 7 1-93 -1.98 2.04 2.09 5 1-37 .42 1.48 1-53 - .58 1.64 -1.69 -74 -79 1.85 .90 ri.95 2.OO 2.06 6 1.36 .42 1.47 1.52 57 1.63 1.68 73 78 1.83 .89 1.94 99 2.04 7 1-35 .40 1.46 I-5I 56 1.61 1.66 .72 77 1.82 87 1.92 .98 2.03 8 1-34 3^ 1.44 1.49 55 i. 60 1.65 70 75 1. 80 85 1.91 .96 2.01 9 1-33 .38 1-43 1.48 53 1.58 1.63 .68 73 1.78 .84 1.89 94 1.99 10 I-3I - .36 1.41 -1.46 -51 1.56 1.61 .66 -7i 1.76 .81 -1.86 .92 .97 II 1.29 34 i-39 1.44 49 i-54 i-59 .64 .69 1.74 79 1.84 .89 .94 12 1.27 32 1-37 1.42 47 1.52 i-57 .62 67 1.72 76 1.81 .86 .91 13 1.25 30 i-35 1.40 45 1.50 1-54 59 .64 1.69 74 1.78 83 .88. 14 1.23 .28 1-33 1.38 .42 1.47 1.52 56 .61 1.66 7i i.- 75 .80 85 15 1. 21 .26 1.30 1.35 .40 1.44 j.49 -54 - -58 1.63 - -67 1.72 -77 - .81 16 I.I9 .23 1.28 1.32 37 1.41 1.46 50 55 i. 60 .64 1.69 73 .78! 17 1.16 .20 1.25 1.29 34 1.38 1-43 47 52 1.56 .60 1.65 .69 .74 18 1. 13 .18 1.22 1.26 .31 1-35 1-39 44 .48 1.52 57 1.61 .65 70, 19 1. 10 15 I.I9 1.23 .27 1.32 1.36 .40 44 1.48 53 i-57 .61 65 20 1.07 1. 1 1 I.I6 1.20 .24 1.28 1.32 .36 .40 1.44 -49 -1-53 -57 - .61 21 1.04 1. 08 1. 12 1.16 .20 1.24 1.28 32 36 .40 44 1.48 52 56; 22 I. 01 I. OS 1.09 1.13 .16 i. 20 1.24 .28 32 36 .40 1.44 .48 51 23 0.98 1. 01 1.05 1.09 13 1.16 1.20 .24 .28 3i 35 i-39 43 46 24 0.94 0.98 1. 01 1.05 .08 I. 12 1.16 19 .23 .27 30 1-34 37 -4i 25 0.90 0.94 0.97 1. 01 .04 1.08 1. 1 1 .15 .18 .22 -25 1.29 -32 .36; 26 0.87 0.90 0.93 0.97 .00 1.03 1.07 .10 .13 17 .20 1.23 .27 30. 27 0.83 0.86 0.89 0.96 0.99 i. 02 05 .08 .12 15 1.18 .21 .24 28 0.79 0.82 0.85 o.88| 0.91 0-94 0.97 .00 1.03 .06 .09 1. 12 * .18 29 0.75 0.78 0.81 0.84 0.86 0.89 0.92 0.95 0.98 .OI .04 1.07 .IO .12 30 31 0.71 0.67 0.74 0.69 0.76 0.72 0.79 0.82 0.74 0.77 0.85 0.80 0.87 0.82 0.90 0.85 0.93 0.87 0.95 0.90 0.981 i. oi O.92 0.95 1.04 0.08 .06 .00 32 0.62 0.65 0.67 0.70 0.72 9-74 0.77 0.79 0.82 0.84 0.86 0.89 0.91 0.04 33 0.58 0.60 0.63 0.65 0.67 0.69 0.72 0.74 0.76 0.78 0.80 0.83 0.85 0.87 34 0.54 0.56 0.58 o.6oj 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 o-79 0.81 35 0.49 0,51 0-53 -HJ.55 0.57 0.59 0.61 0.63 0.64 0.66 0.68 O.7O 0.72 0.74 36 0.45 0.46 0.48 0.50 0-52 0.53 o.55 0-57 0.58 0.60 0.62 0.64 0.65 0.67 37 0.40 0.42 o.43 0.45 0.46 0.48 0.49 0.51 0.52 0-54 0.56 0-57 0-59 0.60 38 0.36 0.37 0.38 O.40 O.4I 0.42 0.44 0-45 0.46 0.48 0.49 0.51 0.52 0-53 39 0.31 0.32 0-33 0-34 0.36 o.37 0.38 0.39 0.40 0.42 0-43 0.44 0-45 0.46 40 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 o. 34 0.35 0.36 0.37 0.38 0-39 41 0.21 O.22 0.23 O.24 0.25 0.26 0.26 0.27 0.28 0.29 0.30 0.30 0.31 0.32 42 0.17 0.17 0.18 O.I9 0.19 0.20 O.2I O.2I 0.22 O.22 0.23 O.24 0.24 0.25 43 0.12 0.12 0.13 0.13 O.I4 0.14 0.15 0.15 0.16 0.16 0.16 0.17 0.17 0.18 44 O.07 0.07 0.08 0.08 0.08 0.08 0.09 0.09 0.09 O.IO O.IO O.IO O.IO O.II 45 j 0.02 O.O2 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.030.03 0.03 0.03 0.04 " Smithsonian Meteorological Tables.' SMITHSONIAN TABLES 140 TABLE 121. REDUCTION OF BAROMETER TO STANDARD GRAVITY.* METRIC MEASURES. From Latitude 46* to 90", the Correction is to be Added. Lati- tude. 520 540 560 580 600 620 640 660 680 700 720 740 760 780 mm. mm. mm. iniii. mm. mm. mm. mm. mm. mm. mm. mm. mm. mm* 45 0.02 O.O2 O.O3 0.030.030.03 O.O3 O.O3 0.03 0.03 0.03 O.O3 O.O3 0.04 46 +O.02+O.03 +0.03 +0.03+0.03+0.03 +0.03 +0.03 +0.03 +0.03 +0.03 +0.03 +0.04 +0.04 47 O.O7 0.08 0.08 0.08 0.08 0.09 0.09 0.09 0.09 0.10 0.10 0.10 O.IO O.II 48 O.I2 0.12 0.13 0.13 0.14 0.14 0.15 0.15 0.16 0.16 0.17 0.17 0.18 0.18 49 0.17 0.17 o. 18 0.19 0.19 0.20 0.21 O.2I 0.22 0.23 0.23 O.24 0.25 0.25 50 0.22 O.22 0.23 0.24 0.25 0.26 0.26 0.27 0.28 0.29 0.30 0.31 0.31 0.32 51 +0.26 +0.27 +0.28 +0.29 +0.30 +0.31 +0.32 +0.33 +0.34 +0.35 +0.36 +0-37 +0.38 +0.39 52 0.31 0.32 0.33 0.34 0.36 0-37 0.38 0-39 O.4O 0.42 0.43 0.44 0.45 0.46 53 0.36 0.37 0.38 0.40 0.41 O.42 0-44 0.45 0.46 0.48 0.49 0.51 0.52 0-53 54 0.40 0.42 o.43 0.45 0.46 0.48 0-49 0.51 0.52 o.54 0.56 .057 0.59 0.60 55 0-45 0-46 0.48 0.50 0.52 0-53 0.55 0-57 0.58 0.60 0.62 0.64 0.65 0.67 56 +0.49 +0.51+0.53 +0.55 +0-57 +0-59 +0.60 +0.62 +0.64 +0.66 +0.68 + 0./0 +0.72 +0-74 57 0.54! 0.56^ 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 58 0.58' 0.60 0.62 0.65 0.67 0.69 0.71 0.74 0.76 0.78 0.80 0.82 0-85 0.87 59 0.62 0.65 0.67 0.69 0.72 o-74 o-77 o.79 0.81 0.84 0.86 0.89 0.91 o-93 60 0.66 0.69 0.72 0.74 0.77 o-79 0.82 0.84 0.87 0.89 0.92 0-94 o-97 I.OO 61 +0.71+0-73 +0.76 +0.79 +0.81 +0.84 +0.87 +0.89 +0.92 +0-95 +0.98 + I.OO +1.03 +1.06 62 0.74 0.77 0.80 0.83 0.85 0.88 0.91 o-94 0-97 .00 1.02 1.05 i. 08 i. ii 63 0.78 0.81 0.85 0.88 0.91 0.94 o-97 I.OO 1-03 .06 1.09 1. 12 1-15 1.18 64 0.82 0.85 0.89 0.92 0-95 0.98 .01 1.04 i. 08 .11 I.I4 1. 17 1.20 1-23 65 0.86 0.89 o-93 0.96 0-99 1.03 .06 1.09 1-13 .16 I.I9 1.22 1.26 1.29 66 +0.90+0.93 +0.97 + 1.00 +1.04 +1-07 + .10 + 1.14 + 1.17 + .21 + 1.24 + 1.28 + I.3I + 1-35 67 0-93 0-97 I.OO .04 i. 08 .11 15 1.18 1.22 25 1.29 1-33 1.36 1.40 68 0.97 I.OO 1.04 .08 i. ii .15 .19 1.23 1.26 30 1-34 1-37 I.4I i-45 69 I.OO 1.04 i. 08 .11 I-I5 .19 23 1.27 I-3I 34 1.38 1.42 1.46 1.50 1.03 1.07 i. ii 15 1.19 23 27 i-35 39 1-43 1.47 i-55 71 + 1.06 + I.IO + 1.14 + .18 + 1.22 + .26 +1.31 + I.35 + 1-39 + I-43 +1-47 + I-5I + 1-55 + 1.59 72 1.09 I 13 1.17 .22 1.26 30 i-34 1.38 1.42 1.47 i . 51 i-55 i-59 1.63 73 74 I. 12 1. 14 1. 10 1.19 1.20 1.23 3 1.29 1-32 ia i-37 1,41 1.42 i-45 1.46 1-50 1.50 i-54 '55 1-58 I -50 1-63 1.63 1.67 1.67 1.72 75 1.17 I. 21 1.26 .30 i-35 39 1-44 1.48 1-53 1-57 1.62 1.66 1.71 i-75 76 +1.19 + 1.24 + 1.28 + -33 + 1.37 + -42 + L47 + 1.51 +1.56 + 1.60 + 1.65 + 1.70 + 1-74 + 1.79 77 1. 21 1.26 I.3I 35 1.40 45 .49 1.54 1.59 1.63 1.68 1.73 1.77 1.82 78 1.23 1.28 1.33 38 1.42 47 52 1-57 1.61 .66 71 1.76 i. 80 1.85 79 1.25 1.30 1-35 .40 1-45 49 54 i-59 1.64 .69 .73 1.78 1.83 1.88 80 1.27 1.32 1-37 .42 1-47 51 56 1.61 1.66 71 .76 1.81 1.86 1.90 81 +1.29 + 1.33 + 1.38 + -43 + 1.48 + .53 + .58 + 1.63 + 1.68 + .73 + .78 + 1.83 +1.88 + 1-93 82 83 1.30 i. 31 1.35 1.36 1.40 1.41 '.46 1.50 I.5I 1 .60 .61 1.65 1.67 1.70 1.72 .75 77 .80 .82 1.85 1.87 1.90 1.92 1-95 1.97 84 1.32 1-37 1-42 .48 1-53 .58 1.63 1.68 i-73 .78 .83 1.88 1.98 85 1-33 1.38 1.43 49 1-54 .59 1.64 1.69 1-74 79 .84 1.90 1-95 2.OO 90 + 1.35 + 1.41 + 1.46 + 1.51+1.56 + 1.61 + 1.67+1.72 + 1-77 + 1.82 + 1.87 +I.93 +1.98 +2.03 SMITHSONIAN TABLE*. " Smithsonian Meteorological Tables." TABLE 122. REDUCTION OF BAROMETER TO STANDARD GRAVITY. 41 ENGLISH MEASURES. From Latitude o* to 45, the Correction is to be Subtracted. Lati- tude. 19 20 21 22 23 24 25 26 27 28 29 30 Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. 0.051 0.054 0.056 0.059 0.062 0.064 O.O67 0.070 0.072 0.075 0.078 O.OSO 5 0.050 0.053 0.055 0.058 0.061 0.063 0.066 0.069 0.071 0.074 0.077 0.079 6 0.050 0.052 0.055 0.058 O.OOO 0.063 0.066 O.068 0.071 0.073 0.076 0.075 7 0.049 0.052 0.055 0.057 O.O60 O.062 0.065 o.o68i 0.070 0.073 0.075 O.O7fi 8 O.O49 0'052 0.054 0.057 0.059 O.062 0.064 0.067 0.070 0.072 0.075 0.077 9 0.048 0.051 0.054 0.056 0.059 0.061 0.064 0.066 0.069 0.071 0.074 0.076 10 0.048 0.050 0.053 0.055 0.058 O.O60 0.063 -0.066 0.068 0.071 0.073 0.076 ii 0.047 0.050 0.052 0.055 0.057 0.060 O.O62 0.065 0.067 0.070 0.072 O.O75 12 0.047 O.O49 0.051 0.054 0.056 0.059 0.061 0.064 0.066 0.069 0.071 0.07] 13 0.046 0.048 0.051 0.053 0-055 0.058 0.060 0.063 0.065 0.068 0.070 0.072 14 0.045 0.047 0.050 0.052 0.055 0.057 0.059 0.062 0.064 0.066 0.069 0.071 15 0.044 0.047 0.049 0.051 0.053 0.056 0.058 0.060 0.063 0.065 0.067 0.070 16 0.043 0.046 0.048 0.05O 0.052 0.055 0.057 0.059 0.062 0.064 0.066 0.068 17 0.042 0.045 0.047 0.049 0.051 0.053 0.056 0.058 0.060 0.062! 0.065 0.067 18 0.041 0.044 0.046 0.048 0.050 0.052 0.054 0.057 0.059 0.061 0.063 0.065 19 0.040 0.042 0.045 0.047 0.049 0.051 0-053 0.055 0.057 0.059 0.062 O.O6^ 20 0.039 0.041 0.043 0.045 0.047 0.050 0.052 0.054 0.056 0.0580.060 O.o62 21 0.038 0.040 O.O42 0.044 0.046 0.048 0.050 0.052 0.054 0.056 0.058 o.ooo 22 0.037 0.039 O.04I 0.043 0.045 0.047 0.049 0.050 0.052 0.054 0.056! 0.05* 23 0.036 0.038 0.039 0.041 0.043 0.045 0.047 0.049 0.051 0.053 0.054! 0.056 *4 0.034 0.036 0.038 0.040 0.042 0.043 0.045 0.047 0.049 0.051 0.052 0.054 25 -0.033 0.035 0.037 0.038 0.040 0.042 0.043 0.045 0.047 0.049 0.050 0.052 26 0.032 0.033 0.035 0.037 0.038 0.040 0.042 0.043 0.045 0.047 0.048} 0.050 27 0.030 0.032 0.033 0.035 0.037 0.038 0.040 0.041 0.043 0.045 0.046; 0.048 28 0.029 0.030 0.032 0.033 0.035 0.036 0.038 0.039 0.041 0.043 0.044 0.046 29 0.027 0.029 0.030 0.032 0.033 0.035 0.036 0.037 0.039 0.040 0.042 0.043 30 0.0261 0.027 0.029 0.030 0.031 0.033 0.034 0.035 0.037 0.038 0.040; 0.041 3i 0.024 O.020 0.027 0.028 0.030 0.031 0.032 0.033 0.035 0.036 0.037 0.038 32 0.023 O.O24 0.025 0.026 0.028 0.029 0.030! 0.031 0.032 o 034 0.035 0.036 33 O.O2I O.O22 0.023 0.025 0.026 0.027 0.028 0.029 0.030 0.031 0.032 0.034 34 O.O2O 0.021 O.O22 0.023 0.024 0.025 0.026 0.027 0.028 0.029 0.030 0.031 35 O.OlS -0.019 O.02O O.02I 0.022 0.023 0.024 0.025 0.026 0.027 0.027 0.028 36 0.016 O.OI7 O.OlS O.OI9 O.020 O.02I 0.022 0.022 0.023 0.024 0.025! 0.026 37 0.015 0.015 0.016 0.017 0.018 O.OI9 O.OI9 O.O20 O.O2I O.O22 O.O22 0.023 38 0.013 O.OI4 O.OI4 0.015 0.016 0.016 O.OI7 0.018 0.018 O.OI9 O.O2O 0.020 39 O.OII O.OI2 0.012 O.OI3 0.014 0.014 O.OI5 0.015 0.016 0.017 O.OI7 0.018 40 0.010 O.OIO O.OII O.OII 0.012 0.012 O.OI3 0.013 0.014 O.OI4 0.015 0.015 41 0.008! 0.008 0.009 O.O09 0.009 O.OIO O.OIO O.OII O.OII 0.012 O.OI2J O.OI2 42 0.006 0.006 O.OO7 O.OO7 0.007 0.008 0.008 O.OOS O.O09 0.009 0.009 0.010 43 0.004 0.005 O.O05 0.005 0.005 0.005 O.OO6 o.oo6i 0.006 o.oooj 0.007 0.007 44 0.003 0.003 0.003 0.003 0.003 0.003 0.003 o . 004 o . 004 0.004 0.004 0.004 45 O.OOI O.OOI O.OOIi- O.OOI O.OOI O.OOI O.OOI ! O.OOI O.OOI O.OOI, O.OOI O.OOI Smithsonian Meteorological Tables.' SMITHSONIAN TABLES. 1 4 2 TABLE 123. REDUCTION OF BAROMETER TO STANDARD GRAVITY.* ENGLISH MEASURES. From Latitude 46 to 90 the Correction is to be Added. 'Lati- tude. 19 20 21 22 23 24 25 26 27 28 29 30 Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. 45 O.OOI O.OOI O.OOI O.OOI O.OOI O.OOI O.OOI O.OOI O.OOI O.OOI O.OOI O.OOI 46 +0.001 +0.001 +O.OOI +0.001 +0.001 +0.001 +O.OOI +O.OOI +O.OOI +0.001 +O.OOI +O.OOI 47 0.003 0.003 0.003 O.OO3 0.003 0.003 0.003 0.004 0.004 0.004 0.004 0.004 48 0.004 0.005 0.005 O.OO5 0.005 0.006 O.OO6 O.OO6 0.006 0.006 0.007 0.007 49 0.006 o.octf 0.007 O.OO/ O.OO7 0.008 0.008 0.008 0.009 0.009 0.009 O.OIO 50 0.008 0.008 0.009 O.O09 O.OIO O.OIO O.OIO O.OII O.OII 0.012 O.OI2 O.OI2 51 +O.OIO+O.OIO +O.OII +O.OII + 0.012 +O.OI2 +0.013 +0.013 +0.014 +O.OI4 +0.015 +0.015 52 O.OII 0.012 O.OI2 0.013 O.OI4 O.OI4 0.015 0.015 0.016 0.016 O.OI7 O.OlS 53 0.013 0.014 O.OI^ 0.015 0.016 0.016 0.017 0.018 O.OlS 0.019 O.O2O O.O2O 54 0.015 0.015 0.016 O.OI7 0.018 O.OI9 0.019 O.O2O 0.021 O.O22 O.O22 O.O23 55 0.016 O.OI7 0.018 O.OI9 O.020 0.021 O.O2I O.O22 0.023 0.024 0.025 O.O26 56 +0.018 +0.019 +O.O2O +O.O2I +O.022 +0.023 +O.O24 +O.O24 +0.026+0.026+0.027 +0.028 57 O.020 O.O2I O.O22 0.023 O.O24 O.O25 O.O26 0.027 0.028 0.029 0.030 0.031 58 O.O2I O.O22 0.023 0.025 0.026 O.O27 0.028 O.029 0.030 0.031' 0.032 0.033 59 0.023 0.024 0.025 0.026 O.O28 O.O29 0.030 0.031 0.032 0.033 0.035 0.036 60 0.024 0.026 O.027 0.028 0.029 0.031 0.032 0.033 0.034 0.036 0.037 0.038 61 +0.026 +0.027 +0.028 +0.030 + 0.031 +0.033 +0.034 +0.035 +0.037 +0.038 +0.039 +0.041 62 0.027 0.029 0.030 O.O32 0.033 0.034 0.036 0.037 0.039 0.040 o . 042 o . 043 63 0.029 0.030 0.032 0.033 0.035 0.036 0.038 0.039 0.041 0.042 0.044 0.045 64 0.030 0.032 0.033 0.035 0.036 0.038 0.040 0.041 0.043 0.044 0.046 0.047 65 0.031 0.033 0.035 0.036 0.038 0.040 0.041 0.043 0.045 0.046 0.048 0.050 66 +0.033 +0.034 +0.036 +0.038 +0.040 +0.041 +0.043 +0.045 +o . 047+0 . 048;+ . 050 +0.052 67 0.034 0.036 0.038 0.039 0.041 0.043 0.045 0.047 0.048' 0.050 0.052 0.054 68 0.035 0.037 0.039 0.041 0.043 0.045 0.046 0.048 0.050' 0.052 0.054 0.056 69 0.036 0.038 0.040 0.042 0.044 0.046 0.048 0.050 0.052 0.054! 0.056 0.058 70 0.038 0.040 0.042 0.044 0.046 0.048 0.050 0.052 0.053 0.055 0.057 0.059 71 +0.039 +0.041 +0.043 +0.045 +0.047 +0.049 +0.051 +0.053 +0.055 +0.057 +0.059 +0.061 72 0.040 0.042 0.044 0.046 0.048 0.050 0.052 0.054 0.057 0.059 0.061 0.063 73 0.041 9.043 0.045 0.047 0.049 0.052 0.054 0.056 0.058 O.o6o 0.062 0.064 74 0.042 0.044 0.046 0.048 0.051 0.053 0.055 0.057 0.059 0.062 0.064 0.066 75 0.043 0.045 0.047 0.049 0.052 0.054 0.056 0.058 0.061 0.063 0.065 0.067 76 77 +0.044 0.044 +0.046+0.048 0.047 0.049 +0.050 0.051 +0.053 0.054 +0.055 0.056 +0.057 0.058 +0.060 0.061 +0.062 0.063 +0.064 0.065 0.066 0.068 0.069 0.070 78 0.045 0.047 0.050 0.052 0-055 0.057 0.059 0.062 0.064 O.066 0.069 0.071 79 0.046 0.048 0.051 0.053 0-055 0.058 0.060 0.063 0.065 0.067 O.070 0.072 80 0.046 0.049 0.051 0.054 0.056 0.059 0.061 0.063 0.066 0.068 0.071 0.073 81 +o.047,+o.o49 +0.052 +0.054 +0.057 +0.059 +0.062 +0.064 +0.067 +0.069 +0.072 +0.074 82 0.047 0.050 0.052 0.055 0.057 0.060 0.062 0.065 0.067 0.070 0.072) 0.075 83 0.048 0.050 0.053 0.056 0.058 0.061 0.063 0.066 o.o68| 0.071 0.073 0.076 84 0.048 0.051 0.053 0.056 0.059 0.061 0.064 0.066 0.069 0.071 0.074 0.076 85 0.049 0.051 0.054 0.056 0.059 0.061 0.064 0.067 0.069 0.072 0.074 0.077 90 4-0.049+0.052 +0.055 +0.057 +o . 060+0 . 062+0 . 065 +0.068 +0.070+0.073 +0.075+0.078 SMITHSONIAN TABLES. * " Smithsonian Meteorological Tables." TABLES 124-125. TABLE 124. Correction oi the Barometer for Capillarity.* 143 i. METRIC MEASURE. HEIGHT OF MENISCUS IN MILLIMETERS. Diameter of tube 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 in mm. Correction to be added in millimeters. 4 0.83 1.22 i-54 1.98 2-37 _ _ _ 47 0.65 0.86 1.19 i-45 i. 80 6 .27 41 .56 0.78 0.98 1. 21 i-43 - 7 .18 .28 .40 53 .67 0.82 0.97 '13 9 .20 15 .29 .21 38 .28 .46 33 .56 .40 65 .46 0.77 52 10 '5 .20 .25 .2 9 33 37 n .IO .14 .18 .21 .24 27 12 - - .07 .10 13 15 .18 .19 13 " .04 .07 .10 .12 13 .14 2. BRITISH MEASURE. HEIGHT OF MENISCUS IN INCHES. Diameter of tube .01 .02 .03 .04 .05 .06 . .07 .08 in inches. Correction to be added in inches. J 5 0.024 0.047 0.069 0.092 0.116 _ _ _ .20 .Oil .022 033 045 059 0.078 - 2 5 .006 .OI2 .019 .028 037 .047 0.059 - 30 35 .40 .004 .008 .005 .004 .008 .006 .018 .012 .008 .023 .015 .010 .029 .018 .012 035 .022 .014 O.O42 .026 .Ol6 45 5 - .003 .002 .005 .004 .007 .005 .008 i .010 .006 1 .006 .012 .007 55 : " .001 .002 .003 .004 005 .005 * The first table is from Kohlrausch (Experimental Physics), and is based on the experiments of Mendelejeff and Gutkowski (Jour, de Phys. Chem. Geo. Petersburg, 1877, or Wied. Beib. 1877). The second table has been calcu- lated from the same data by conversion into inches and graphic interpolation. TABLE 125. Volume of Mercury Meniscus in Cu. Mm. Height of Diameter of tube in mm. meniscus. '4 '5 16 17 18 19 20 21 22 23 24 mm. 1.6 T 57 185 214 245 280 318 356 398 444 492 54i 1.8 2.O 2.2 2.4 2.6 181 206 233 262 291 211 240 271 303 338 244 2 7 8 3*3 35 388 281 3i9 358 400 444 320 362 406 454 503 362 409 459 5" 565 407 400 5S 573 633 455 5'3 574 639 706 7 708 782 704 781 862 694 776 859 948 Scheel und Heuse, Annalen der Physik, 33, p. 291, 1910. SMITHSONIAN TABLES. 144 TABLE BAROMETRIC PRESSURES CORRESPONDING TO THE TEMPERATURE OF THE BOILING POINT OF WATER. Useful when a boiling-point apparatus is used in the determination of heights. Copied from the Smithsonian Meteorological Tables, 4th revised edition. (A) METRIC UNITS. Tem- jeraturc. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 c mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. 80 355-40 356.84 358.28 359-73 36I.I9 362.65 364.11 365.58 367.06 368.54 81 82 370.03 385-16 37L52 386.70 373-01 388.25 374.51 389-80 376.02 39L36 377-53 392.92 379-05 394-49 380.57 396.06 382.09 397-64 383.62 399-22 83 400.8l 402 . 40 404 . oo 405.61 407.22 408.83 410.45 4I2.O8 413.71 415-35 84 416.99 418.64 420.29 421-95 423.61 425.28 426.95 428.64 430.32 432-01 85 433-71 435-41 437-12 438.83 440.55 442 . 28 444-01 445-75 447-49 449-24 86 450.99 452-75 454.51 456.28 458.06 459.84 461.63 463-42 465.22 467.03 8? 468.84 470.66 472.48 474.31 476.14 477-99 479.83 481.68 483.54 485.41 88 487.28 489.16 491.04 492.93 494.82 496.72 498.63 500.54 502.46 504.39 89 506.32 508.26 5I0.2O 512.15 514.11 516.07 518.04 520.01 521-99 523-98 90 91 92 525.97 546.26 567.20 527.97 548.33 509.33 529.98 550.40 571-47 53L99 552.48 573-61 534-01 554.56 575.76 536.04 556.65 577.92 538.07 558.75 580.08 540.11 560.85 582.25 5f .15 562.96 584.43 544-21 565.08 586.61 93 588.80 591.00 593-20 595.41 597.63 599.86 602 . 09 604.33 606.57 608.82 94 611.08 613.35 615-62 617.90 620.19 622.48 624.79 627.09 629.41 63L73 95 634.06 636 . 40 638.74 641.09 643.45 645-82 648.19 650.57 652.96 655.35 96 657.75 66o.l6 662.58 665.00 667.43 669.87 672.32 674.77 677.23 679.70 97 682.18 684.66 687.15 689-65 692.15 694.67 697.19 699.71 702.25 704.79 98 707.35 709.90 712.47 715.04 717.63 720 . 22 722.81 725-42 728.03 730.65 99 733.28 635.92 738.56 741.21 743.87 740-54 749-22 75I-90 754-59 757-29 100 760.00 762.72 765-44 768.17 770.91 773-66 776.42 779.18 78i.95 784.73 (B) ENGLISH UNITS. Tem- perature- .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 F. Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. 185 17.075 I7.IT2 17.150 I7.I87 17.224 17.262 I7.300 17.337 17-375 17.413 186 17.450 17.488 17.526 17.564 17.602 17-641 17-679 17.717 17.756 17.794 187 17.832 17.871 17.910 17.948 17.987 18.026 18.065 I8.I04 18.143 I8.I82 188 18.221 l8.26l 18.300 18.340 18.379 18.419 18.458 18.498 18.538 18.578! 189 18.618 18.658 18.698 18.738 18.778 18.818 18.859 18.899 18.940 i8.980 ( 190 19.021 19.062 I9.IO2 I9.I43 19.184 19-225 19.266 19.308 19.349 19.390 191 I9-43I 19.473 19.514 19.556 19.598 19.639 I9.68I 19.723 19.765 19.807 192 19-849 19.892 19-934 19.976 20.019 20.061 20. 104 20.146 20.189 20.232 193 20.275 20.318 20.361 20.404 20.447 20.490 20.533 20.577 20.62O 20.664 194 20.707 20.751 20.795 20.839 20.883 20.927 20.971 21.015 21.059 21.103 195 21.148121.192 21.237 21.282 21.326 21.371 2I.4l6 21.461 21.506 2I.55I 196 21. 597 121.642 21.687 21-733 21.778 21.824 21.870 21.915 21.961 22.007 197 22.053 22.099 22.145 22.192 22.238 22.284 22.331 22.377 22.424 22.471 198 22.517 22.564 22.611 22.658 22.706 22.752 22.80O 22.847 22.895 22.942 199 22.990 23.038 23.085 23.133 23.181 23.229 23.277 23.325 23-374 23.422 200 23.470 23oI9 23.568 23.616 23.665 23-714 23 - 763 23.812 23.861 23.910 201 23-959 24.009 24.058 24.108 24.157 24.207 24.257 24.307 24-357 24.407 202 24-457 24.507 24.557 24.608 24-658 24.709 24.759 24.810 24-861 24.912 203 24-963 25.014 25.065 25.116 25.168 25.219 25.271 25.322 25-374 25.426 204 25.478 25.530 25.582 25.634 25.686 25-738 25.791 25.843 25.948 205 206 26.001 26.534 26.054 26.587 26.107 26.641 26.160 26.695 26.213 26.749 26.266 26.803 26.319 26.857 26.373 26.912 26.426 26.966 26.480 27.021 207 208 209 27.075 27 . 626 28.185 27.130 27.681 28.242 27.184 27.737 28.298 27.239 27-793 28.355 27.294 27.848 28.412 27.349 27.904 28.469 27.404 27.960 28.526 27.460 28.0l6 28.583 27.515 28.073 28.640 27.570 28. 129 28.697 210 28.754 28.812 28.869 28.927 28.985 29 . 042 29.100 29.158 29.216 29-275 211 29-333 29.391 29.450 29.508 29.567 29.626 29.685 29.744 29.803 29.862 212 29.921 29.981 30.040 30.100 30.159 30.219 30.279 30-339 30 . 399 30.459 213 30.519 30 . 5^O 30.640 30.701 .30.761 30.822 7O &ft7 7r nnc IT orVi TABLE 127. 145 DETERMINATION OF HEIGHTS BY THE BAROMETER. Formula of Babinet : Z = C C (in meters) = 16000 fi -f- iil+J)~j metric measures. I- 1000 -I In which Z = difference of height of two stations in feet or meters. 0) B barometric readings at the lower and upper stations respectively, corrected for all sources of instrumental error. t , t =r air temperatures at the lower and upper stations respectively. Values of C. ENGLISH MEASURES. METRIC MEASURES. i ('<> + *). C LogC H'o + 4 C LogC Fahr. Feet. Cent. Meters. 10 49928 4.69834 10 '5360 4.18639 15 505H 70339 8 15488 .19000 6 15616 J 9357 20 5 I0 94 4.70837 4 T 5744 .19712 25 5 l6 77 71330 2 15872 .20063 30 52261 4.71818 16000 4.20412 35 52844 .72300 + 2 16128 20758 4 16256 .2IIOI 40 53428 4.72777 6 16384 .21442 45 54011 .73248 8 16512 .21780 50 54595 4737I5 10 16640 4.22IIC 55 55178 .74177 12 16768 .22448 H 16896 .22778 60 5576i 474633 16 17024 .23106 65 5 6 344 75085 18 17152 2343 1 70 56927 4-75532 20 17280 4-23754 75 575 11 75975 22 17408 .24075 80 58094 4.76413 24 26 17664 24393 .24709 85 58677 .76847 28 17792 .25022 90 59260 4-77276 30 17920 4-25334 95 59844 .77702 3 2 18048 25643 34 18176 2595 100 60427 4.78123 36 18304 .26255 Values only approximate. Not good for great altitudes. A more r ccurate formula with corresponding tables may be found in Smithsonian Meteorological Tables. SMITHSONIAN TABLES. 146 TABLE 128. VELOCITY OF SOUND IN SOLIDS. The velocity of sounds in solids varies as VE/P, where E is Young's Modulus of elasticity and p the density. These constants for most of the materials given in this table- vary through a somewhat wide range, and hence the numbers can only be .taken as rough approximations to the velocity which may be obtained in any particular case. When temperatures are not marked, between 10* and 20 is to bo understood. Substance. Temp. C. Velocity in meters per second. Velocity in feet per second. Authority. Metals: Aluminum o 5104 16740 Masson. Brass .... _ 3500 11480 Various. Cadmium .... - 2307 7570 Masson. Cobalt .... - 4724 15500 11 Copper .... 2O 356 11670 Wertheim. " .... IOO 3290 IO8OO H " .... 200 2950 9690 u Gold (soft) 20 1743 5717 " " (hard) 2IOO 6890 Various. Iron and soft steel 5OOO 16410 Iron ..... 2O r j -JQ 16820 Wertheim. IOO 5300 17390 "..... 200 4720 15480 " " cast steel . 20 4990 16360 " " '' " 2OO 4790 I57IO " Lead 2O 1227 4026 M Magnesium Nickel .... - 46O2 4973 I5IOO 16320 Melde. Masson. Palladium .... 3K5 10340 Various. Platinum .... 2O 2690 8815 Wertheim. . IOO 2570 8437 " " .... 200 2460 8079 u Silver .... 2O 2610 8553 " " .... IOO 2640 8658 Tin - 2500 8200 Various. Zinc - 3700 I2I40 Various: Brick .... _ f 3 6 52 11980 Chladni. Clay rock Cork .... : 3480 500 II42O 1640 Gray & Milne. Stefan. Granite .... Marble .... - 395 3810 12960 12500 Gray & Milne. tt Paraffin .... 15 1304 4280 Warburg. Slate .... Tallow .... 16 45 10 390 14800 1280 Gray & Milne. Warburg. Tuff 2850 9350 Gray & Milne. Glass 1 from - 5000 16410 Various. I to 6000 19690 M Ivory .... Vulcanized rubber ) 3 OI 3 54 9886 177 Ciccone & Campanile. Exner. (black) J 5 I O2 " (red) . o 69 226 " " " " . 70 34 III u Wax .... 17 880 2890 Stefan. Woods : Ash, along the fibre . 28 441 4670 145 M Wertheim. " across the rings '390 4570 " along the rings - 1260 4140 Beech, along the fibre " across the rings . _ 3340 1840 10960 6030 t " along the rings Elm, along the fibre _ 1415 4120 4640 13516 " " across the rings 1420 4665 " along the rings Fir, along the fibre . _ 1013 4640 3324 15220 " Maple " . . 4110 13470 Oak - 3850 12620 Pine " Poplar Sycamore " - 3320 4280 4460 10900 14050 14640 SMITHSONIAN TABLES. TABLE 129. VELOCITY OF SOUND IN LIQUIDS AND GASES. For gases, the velocity of sound^V^r/P, where P is the pressure, p the density, and 7 the ratio of specific heat at constant pressure to that at constant volume (see Table 253). For moderate tem- perature changes V t = V d + at) where 0=0.00367. The velocity of sound in tubes increases with the diameter up to the free-air value as a limit. The values from ammonia to methane inclusive are for closed tubes. Substance. Temp. C. Velocity in meters per second. Velocity in feet per second. Authority. Liquids : Alcohol, 9$% . 12.5 1241. 4072. Dorsing, 1908. it 20.5 1213- 3980. " Ammonia, cone. 16. 1663- 5456- 't Benzol 17- 1166. 3826. a Carbon bisulphide . 15- 1161. 3809. Chloroform iS- 983- 3225. " Ether iS- 1032. " NaCl, 10% sol. iS- 1470. 4823. < " 15% ". 15- 1530. 5020. " 20% " . 15- 1650. 54I4- u Turpentine oil. IS- 1326. 4351- " Water, air-free 13- 1441. 4728. " < 19. 1461. 4794- 11 < a 31. 1505- 4938. " ' Lake Geneva 9- 1435- 4708. Colladon-Sturm. ' Seine river . 15- 1437- 4714. Wertheim. < < < 30. 1528. 5013. 11 < 60. 1724. 5657- " Explosive waves in water : Guncotton, 9 ounces . 1732. 5680. 1 Threlfall, Adair, " 10 " . 1775- 5820. L 1889, see Bar- 18 " . 1942. 6372- ton's Sound, p. 64 " . . 2013. 6600. J 518. Gases : Air, dry, CO 2 -free 0. 33L78 1088.5 Rowland. " 0. 331-36 1087.1 Violle, 1900. " CO 2 -free . 0. 33I.9 2 1089 o Thiesen, 1908. i atmosphere . 0. 33L7 1088. Mean. 25 " . . 0. 332.0 1089. " (Witkowski). 50 " . . 0. 334-7 1098. ' 100 " . o. 350.6 1150. - . 20. 344- 1129. . 100. 386. 1266. Stevens. . 500. 553- 1814. ' . 1000. 700. 2297. Explosive waves in air: Charge of powder, 0:24 gms. 3-80 " 17.40 45-6o 336. 500. 93i- 1 102. 1640. 3060. 4l60. 1 Violle, Cong. In- tern. Phys. i, J 243, 1900. Ammonia . 0. 415. I36l. Masson. Carbon monoxide 0. 337- 1 1106. Wullner. " " 0. 337-4 1107. Dulong. " dioxide . 0. 258.0 846. Brockendahl, 1006. " disulphide 0. 620. Masson. Chlorine 0. 206.4 677- Martini. (i 0. 205-3 674- Strecker. Ethylene 0. 314- 1030. Dulong. Hydrogen . 0. 1269.; 4165- " " 0. 1286.4 4221. Zoch. Illuminating gas 0. 490.4 1609. < Methane 0. 432. 1417. Masson. Nitric oxide 0. 325- 1066. ' Nitrous oxide . 0. 261.8 859- Dulong. Oxygen 0. 317-2 1041. '* Vapors : Alcohol 0. 230.6 756. Masson. Ether 0. 179.2 588. '' Water . 0. 401. 1315- i< tt IOO. 404.8 1328. Treitz, 1903. ti 130. 424.4 1392. 148 TABLES 13O-131. MUSICAL SCALES, The pitch relations between two notes may be expressed precisely (i) by the ratio of their vibra- tion frequencies; (a) by the number of equally-tempered semitones between them (E- b.); also, les conveniently, (3) by the common logarithm of the ratio in (i); (4) by the lengths of the two portions of the tense string which will furnish the notes; and (5) in terms of the octave as unity. The ratio in (4) is the reciprocal of that in (i); the number for (5) is 1/12 of that for (2); the number for (a) is nearly 40 times that for (3). Table 130 gives data for the middle octave, including vibration frequencies for three standards of pitch: A a =435 double vibrations per second, is the international standard and was adopted by the American Piano Manufacturers' Association. The "just-diatonic scale" of C-major is usually deduced, following Chladni, from the ratios of the three perfect major triads reduced to one octave, thus: 4:5:6 4:5:6 4:5:6 F A C E (I B D 16 20 24 30 36 45 54 24 27 30 32 36 40 45 48 Other equivalent ratios and their values in E. S. are given in Table 131. By transferring D to the left and using the ratio 10 : 12 : 15 the scale of A-minor is obtained, which agrees with that of C-major except that D = 26 2/3. Nearly the same ratios are obtained from a series of harmonics beginning with the eighth; also by taking 12 successive perfect or Pythagorean fifths or fourths and reducing to one octave. Such calculations are most easily made by adding and subtracting intervals expressed in E. S. The notes needed to furnish a just major scale in other keys may be found by successive transpositions by fifths or fourths as shown in Table 131. Disregarding the usually negligible differ- ence of 0.02 E. S., the table gives the 24 notes to the octave required in the simplest enharmonic organ; the notes fall into pairs that differ by a comma, 0.22 E. S. The line " mean tone " is based on Dom Bedos* rule for tuning the organ (1746). The tables have been checked by the data in Ellis' Helmholtz's "Sensations of Tone." TABLE 130. Interval. Ratios. Logarithms. Number of double Vibrations per second. Note. Just. Tem- pered. Just. Tem- pered. Just. Tem- pered. Just. Just. Just. Tem- pered- Tem- pered. Tem- pered E. S. E. S. c, o. I.OO 1. 00000 .0000 .00000 256 264 258-7 258.7 261.6 271-1 i 1.05926 .02509 274.0 277.2 287.3 o 2.04 2 1. 125 1.12246 05115 .05017 288 297 291.0 290.3 293-7 304-3 3 1.18921 07526 307-6 3.i 322.4 3-86 4.98 4 S 1.25 i-33 1.25992 1.33484 .09691 .12494 .10034 12543 320 341.3 330 352 323-4 344.9 325-9 345-3 329-6 349-2 341-6 361.9 6 1.41421 15051 365.8 370-0 383-4 7.02 7 1.50 1.40831 .17609 .17560 384 396 388 387-5 392.0 406.2 8 1.58740 20069 410.6 415-3 430.4 A, 8.84 9 1.67 1.68179 .22185 22577 426.7 440 431- 1 435-0 440.0 456.0 10 1.78180 .25086 460.9 446.2 483.1 B, 10.88 II 1.875 1.88775 .27300 27594 480 495 485-0 488.3 493-9 511.8 c* 12. OO 12 2.OO 2.00000 .30103 30103 512 528 5I7.3 517-3 523-2 542.3 TABLE 131. Key of c D E F G A B C 7 *s C3 1.14 0.92 3.18 2.96 4-78 6.12 5-9 8.16 7-94 9.98 9.76 12.02 II.80 6 " FS 1.14 2.96 5-00 6.12 8.16 9.98 II.IO 0.92 2.74 4.78 5-90 7-94 9.76 10.88 c " B^s 1.14 2.96 4.08 6.12 7-94 9.98 j ' II.IO 5 o.g2v 2.74^ 3. So/ 5-9 5.68^ 7-94 7.72^ Lit II.IO > 10.88 7 J 2 " D o.9> 2.04- 5 . 9 0v 7-02v / 9.06 < 10.88- J I # G o.cxy 2.04^ 3.86 v f 5-9' ^7.02 v / 9.06' io.88 v '12.00 C * o.oo* 2.04^ 3 86^ 4.98 7.02 / 8.84^ S lo-SS 1 " 12.00 i !> F v' 0.00' 1.82 3.86 4.98, 7.02 8.84^ 9.96 12.00 2 i>S Bt> 0.00 1.82 2.94 4.98 6.80 8.84 9.96 I2.OO 3" E? -.22 1.82 2.94 4-98 6.80 7.92 9.96 11.78 4" A? -.22 0.90 2.94 4.76 6.80 7.92 9.96 11.78 5 " 1)7 -.22 0.90 2.94 4.76 5.88 7.92 9-74 11.78 6 " G? 0.90 2.72 4.76 5-88 7.92 9-74 10.86 7" c? 0.90 2.72 3-84 5.88 770 9-74 10.86 Harmonic Series 8 0.0 U) 9 2.04 (a!? 8 ) IO 3.86 / 2, \ \4-70/ it 5-51 12 7-02 / 25 \ V7-73/ 8.41 '4 9.69 15 10.88 it 12.00 Cycle of fifths O.O 1.14 2.04 3.18 4.08 5-22 6.12 7-02 8.16 9.06 IO.2O II.IO 12.24 Cycle of fourths Mean tone O.O O.O 0.90 0.76 1. 80 '93 2.94 3-" 3.86 4.98 5-3 5.88 5-79 6.78 6-97 7 .92 7.72 8.82 8.90 9.96 IO.O7 10.86 10.83 11.76 I2.OO Equal 7 step O.O 1.71 3-43 5-M 6.86 8.57 IO.29 12.00 SMITHSONIAN TABLES. TABLES 132-135. MISCELLANEOUS SOUND DATA. TABLE 132. A Fundamental Tone, Its Harmonics (Overtones) and the Nearest Tone of the Equal-tempered Scale. I4Q No. of partial i 2 4 5 6 8 Q 10 Frequency 129 259 388 Si? & 776 1030 I2O? Nearest tempered note C c ig C F G B? D E Corresponding frequency 129 259 388 517 652 775 922 1293 No. of partial II 12 13 14 15 16 1^ 18 20 Frequency 1423 1552 1681 1811 1940 2069 2328 2586 Gb G G# Bi> s c r# D D/ Corresponding frequency 1463 1550 1642 1843 1953 2O69 2192 2323 NOTE. Overtones of frequencies not exact multiples of the fundamental are sometimes called inharmonic partials. TABLE 133. Relative Strength of the Partials in Various Musical Instruments. The values given are for tones of medium loudness. Individual tones vary greatly in quality and, therefore, in loudness. Instrument. Strength of partials in per cent of total tone strength. i 2 3 4 5 6 7 8 9 10 II 12 Tuning fork on box . . Flute 100 66 26 2 12 36 6 24 25 2 26 II 4 9 4 10 i? 35 6 10 29 3 7 12 27 35 5 4 8 i 14 o 3 ii o | 2 2 18 3 15 ] I 5 6 i i Violin, A string Oboe Clarinet Trombone 6 4 3 2 i TABLE 134. Characteristics of the Vowels. The larynx generates a fundamental tone of a chosen pitch with some 20 partials, usually of low intensity. The particular partial, or partials, most nearly in unison with the mouth cavity is greatly strengthened by resonance. Each vowel, for a given mouth, is characterized by a particular fixed pitch, or pitches, of resonance corresponding to that vowel's definite form of mouth cavity. These pitches may be judged by whispering the vowels. It is difficult to sing vowels true above the corresponding pitches. The greater part of the energy or loudness of a vowel of a chosen pitch is in those partials reinforced by resonance. The vowels may be divided into two classes, the first having one char- acteristic resonance region, the second, two. The representative pitches of maximum resonance of a mouth cavity for selected vowels in each group are given in the following table. Vowel indicated by italics in the words. Pitch of maxi- mum resonance. Vowel indicated by italics in the words. Pitch of maxi- mum resonance. father, far, guard raw, fall, haul . . 910 732 mat, add, cat pet feather, bless 800 and 1840 691 and 1953 461 488 and 2461 gloom, move, group 326 bee, pique, machine 308 and 3100 TABLE 135. Miscellaneous Sound Data. Koenig's temperature coefficient for the frequency (n) of forks is nearly the same for all pitches. n t o(i o.opoii* C), Ann. d. Phys. 9, p. 408, 1880. Vibration frequencies for continuous sound sensations are practically the same as for continuous light sensation, 10 or more per second. Helmholtz' value of 32 per sec. may be taken as the flicker value for the ear. Moving pictures use 16 or more per sec. For light the number varies with the intensity. Pitch limits of voice: 60 to 1200 vibrations per second. Piano pitch limits: 27.2 to 4138.4 v. per sec. (over 7 octaves). Organ pitch limits: 16 (32 ft. pipe), sometimes 8 (64 ft.) to 4138 (ij in.) (9 octaves). Ear can detect frequencies of 20,000 to 30,000 v. per sec. Koenig, by means of dust figures, measured sounds from steel forks with frequencies up to 90,000. The quality of a musical tone depends solely on the number and relative strength of its partials (simple tones) and probably not at all on their phases. The wave-lengths of sound issuing from a closed pipe of length L are *L, 4^/3, 4^/5, etc., and from an open pipe, 2L, 2L/2, 2L/3, etc. The end correction for a pipe with a flange is such that the antinode is 0.82 X radius of pipe beyond the end; with no flange the correction is 0.57 X radius of pipe. The energy of a pure sine wave is proportional to n*A 2 ; the energy per cm 3 is on the average 2pir*U*A-/\' 1 ; the energy passing per sec. through i cm* perpendicular to direction of propagation is 2pir*U 3 A*/\*; the pressure is \(y + i) (average energy per cm 3 ); where n is the vibration number per sec., X the wave-length, A the amplitude, V the veloc- ity of sound, p the density of the medium, J the specific heat ratio. Altberg (Ann. d. Phys. n, p. 405, 1903) measured sound-wave pressures of the order of 0.24 dynes/cm 2 = 0.00018 mm Hg. SMITHSONIAN TABLES. 1 S TABLES 1 36-137. TABLE 136. Aerodynamics. KINETICS OF BODIES IN RESISTING MEDIUM. The differential equation of a body falling in a resisting medium is diifdt = g ku*. The ve- locity tends asymptotically to a certain terminal velocity, V '= \/g/&- Integration gives u = V- tanh (gt/Y), x = " log cosh (gt/T) if w = x = / = o. When body is projected upwards, du/df = g &u 2 , and if u is velocity of projection, then tan" 1 u/V = tan" 1 (u Q /Y) -gtlV, x = (V*/2g) log (V* + u *) (V* + 2 ). The particle comes to rest when / = (V/g) tan" 1 (u /V) and x = (P/2g) log (i - o 2 /7 2 ). For small velocities the resistance is more nearly proportional to the velocity. Stokes' Law for the rate of fall of a spherical drop of radius a under gravity g gives for the velocity, t>, where a and p are the densities of the drop and the medium, t] the viscosity of the medium. This depends on five assumptions: (i) that the sphere is large compared to the inhomogeneities of the medium; (2) that it falls as in a medium of unlimited extent; (3) that it is smooth and rigid; (4) that there is no slipping of the medium over its surface; (5) that its velocity is so small that the resistance is all due to the viscosity of the medium and not to the inertia of the latter. Because of 5, the law does not hold unless the radius of the sphere is small compared with rj/vp (critical radius). Arnold showed that a must be less than 0.6 this radius. If the medium is contained in a circular cylinder of radius R and length Z,, Ladenburg showed that the following formula is applicable (Ann. d. Phys. 22, 287, 1907, 23, 447, 1908): 2 ga 2 ((7 - p) __ 9 i?(i + 2.40./R) (i -f- 3.*a/) As the spheres diminish in size the medium behaves as if inhomogeneous because of its molec- ular structure, and the velocity becomes a function of I/a, where / is the mean free path of the molecules. Stokes' formula should then be modified by the addition of a factor, viz.: 2 trap ( . I v\ = - - (ff - p) < i + (0.864 + o.2ge-*-*S w*)) - (See chapter V, Millikan, The Electron, 1917 ; also Physical Review 15, p. 545, 1920.) TABLE 137. Flow of Gases through Tubes.* When the dimensions of a tube are comparable with the mean free path (Z) of the molecules of a gas, Knudsen (Ann. der Phys. 28, 75, 199, 1908) derives the following equation correct to 5% even when D/L = 0.4: Q, the quantity of gas in terms of PV which flows in a second through a tube of diameter Z>, length /, connecting two vessels at low pressure, difference of pressure PI, equals (P% P\)/W\/p where p is the density of the gas at one bar (i dyne/cm 2 ) = (mo- ular weight)/(83.i5 X io 6 7") and IV' which is of the nature of a resistance, = 2-394I//Z? 3 + 3-I84/Z? 2 . The following table gives the cm 3 of air and Hat i bar which would flow through dif- ferent sized tubes, difference of pressure i bar, room temperature. / = icm. D = icm. W = 5.58 Q, cm 8 of air, 5200. cm 3 of J? 2 , 19700. 10 i 27.1 1070. 4050. i o.i 2710. 10.7 40.5 10 o.i 24300. i. 20 3.60 Knudsen derives the following equation, equivalent to Poiseuille's at higher, and to the above at lower pressures : Q = (P z -Pi) {aP + b (i + iP)/(i + f Z P)} where a = irD 4 /i2Si ) S (Poiseuille's constant) ; b = i/^\/p, (coefficient of molecular flow) ; c^ = \/~p Z)/i)-, and r 2 = 1.24 \/p D!I\ ; T? = viscosity coef- ficient. The following are the volumes in cm 3 at i bar, 2OC, that flow through tube, D = i cm, / = locm, /'.,- j\ = i bar, average pressure of /'bars: P = io. Q = 13,000,000. P = 5. Q = 1026. P = i. Q = 1044. cm 3 100. 2,227. 4- 1024. o.i 1065. IO. 1,058. 3. 1025. O.QI IO7O. When the velocity of flow is below a critical value, /^(density, viscosity, diameter of tube), the stream lines are parallel to the axis of the tube. Above this critical velocity, V c , the flow is tur- bulent. F e = ki7 pr for small pipes up to about 5 cm diameter, where K is a constant, and r the tube radius. \Vhcn these are in cgs units, k is io 3 in round numbers. Below F c the pressure drop along the tube is proportional to the velocity of gas flow ; above it to the square of the velocity. * See Dushman, The Production and Measurement of High Vacua, General Elec. Rev. 23, p. 493, 1920 SMITHSONIAN TABLES. TABLES 138-139. AERODYNAMICS. TABLE 138. Air Pressures upon Large Square Normal Planes at Different Speeds through the Air. The resistance F of a body of fixed shape and presentation moving through a fluid may be written F = pl?V*f(LV/v) in which p denotes the fluid density, v the kinematic viscosity, L a linear dimension of the body F the speed of trans- lation. In general / is not constant, even for constant conditions of the fluid, but is practically so for normal impact on a plane of fixed size. In the following, p is taken as 1.230 g/l (.0768 lbs./ft 3 ). The mean pressure on thin square plates of i.i m 2 (12 ft 2 ), or over, moving normally through air of standard density at ordinary transportation speeds may be written P =.oo6ov 2 for P in kg per m 2 and v in km per hour or P = 0032-11* for P in Ibs. per ft 2 and v in miles per hour. The following values are computed from this formula. For smaller areas the correction factors as given in the succeeding table (Table 139) derived from experiments made at the British National Physical Laboratory, may be applied. Units: the first of each group of three columns gives the velocity; the second, the corresponding pressure inkg/m 2 when the first column is taken as km per hour; the third in pds/ft 2 when in miles per hour. Veloc- ity. Pressure. Veloc- ity. Pressure, Veloc- ity. Pressure. Veloc- ity. Pressure. Metric. English. Metric. English. Metric. English. Metric. English. 10 .60 0.32 40 9.60 5-12 70 29.4 15-7 IOO 60.0 32.0 ii 73 o.39 4^ 10.09 5.38 71 30.2 16.1 101 61.2 32.6 12 .86 0.46 42 10.58 5-6 4 72 16.6 102 62.4 33-3 13 14 .01 .18 ;fj 43 44 11.09 ii. 6 5-92 6.20 73 74 32' 32.8 17.0 17-5 103 104 63.7 64.9 33-9 34-6 16 35 54 .82 JS 12. I 12.7 6.48 6.77 11 33-7 34-7 18.0 18.5 105 106 66.1 67.4 35-3 36.0 17 73 .92 47 13-3 7.07 77 35-6 19.0 107 68.7 36.6 18 94 .04 48 13-8 78 36.5 19-5 108 70.0 37-2 19 17 .16 49 14.4 7.68 79 37-4 20.0 109 7i-3 38.0 20 .40 .28 50 15-0 8.00 80 38.4 20.5 no 72.6 38.7 21 65 .41 Si 15-6 8.32 8l 39-4 21.0 in 73-9 39-4 22 .90 55 52 16.2 8.65 82 40.3 21.5 113 75-3 40.1 23 3-17 .69 53 16.9 8-99 83 41-3 22.0 "3 76.6 40.9 2 4 3.46 .84 54 17.5 9-33 84 42.3 22.6 "4 78.0 41.6 25 26 3-75 4-06 .00 .16 18.1 18.8 9.68 10.04 8s 86 43-3 44.4 23-1 23-7 "5 116 79-3 80.8 42.3 43-1 27 4-37 33 57 19-5 10.40 87 45-4 24.2 117 82.1 43-7 28 4.70 51 58 20.2 10.76 88 46.4 2 4 .8 118 83.5 44-6 29 5-05 .69 59 20.9 11.14 89 47-5 25-4 119 84-9 45-3 30 5-40 .88 60 21.6 11-52 90 48. 6 25-9 120 86.4 46.1 31 5-77 3-o8 61 22.3 11.91 49-7 26.5 121 87.8 46.8 32 6.14 3-28 62 23.0 12.3 92 50.8 27.1 123 89-3 47-6 33 6.54 3-48 63 23.8 12.7 93 51-9 27-7 123 90.8 48.4 34 6-93 3-70 64 2 4 .6 I3-I 94 53-0 28.3 124 92.2 49-2 11 7-35 7-74 3-92 4-15 65 66 3:S 13-5 13-9 54-2 28.9 29-5 IS 93-7 95-3 50.0 50.8 37 8.22 4.38 67 26.9 14.4 97 56 5 30.1 127 96.8 51-6 38 8.66 4.62 68 27.7 14.8 98 57-6 30-7 128 98.4 52.5 39 9.12 4-87 69 28.6 15-2 99 58.8 31-4 129 98.7 53-2 TABLE 139. Correction Factor for Small Square Normal Planes. The values of Table 138 are to be multiplied by the following factors when the area of the surface is less than about I m 2 (12 ft 2 ). Metric. English. Area, m 2 Factor. Area, m- Factor. Area, ft 2 Factor. Area, ft 2 Factor 0.03 O.IO 0.50 0.845 0.859 0.884 5-o 6.0 7-o 0.969 0-975 0.979 0.03 0. 10 0.50 0.842 0-857 0.884 S-o 6.0 7-0 0.968 0-973 0.977 0-75 I.OO 0.890 0.898 8.0 9-o 0.984 0.989 0.75 I.OO 0.889 0.896 8.0 9.0 0.981 0.986 2.00 0.919 IO.O 0-993 2.OO 0.917 IO.O 0.990 3-00 0.933 II. 0.999 3-00 0.930 II. 0.994 4.00 0.950 12.0 I. 000 4.00 0-943 12.0 I. 000 SMITHSONIAN TABLES. 152 TABLES 140-14J. AERODYNAMICS. TABLE 140. Effect of Aspect Ratio upon Normal Plane Pressure (Eiffel). The mean pressure on a rectangular plane varies with the "aspect ratio," a name introduced by Langley to denote the ratio of the length of the leading edge to the chord length. The effect of aspect ratio on normally moving rectangular plates is given in the following table, derived from Eiffel's experiments. Aspect ratio. I. 00 I.OO i-5 1.04 3.00 1.07 6.00 I. 10 IO.OOO 1.145 14.60 1.25 20.00 i-34 30.00 1.40 41.500 1-435 50.00 i-47 Pressure on rectangle Pressure on square TABLE 141. Ratio of Pressures on Inclined and Normal Planes. The pressure on a slightly inclined plane is proportional to the angle of incidence a, and is given by the formula P a = c-P 9 o-a. The value of c, which is constant for incidences up to about 12, is given for various aspect ratios. The angle of incidence is taken in degrees. Aspect ratio - . 3 0.0360.0430.050 4 0-053 5 0.057 6 0.061 7 0.065 8 0.070 9 0.075 10 0.080 Value of c. . TABLE 142. Skin Friction. The skin friction on an even rectangular plate moving edgewise through ordinary air is given by Zahm's equation, or F(pds./ft.2) o. 00030 U(m 2 ))- 93 { nkm/hr.)} 1 - 86 in metric units 0.0000082 \A (ft. 2 ) }- 93 { 7(ft./sec.) } 1 i 86 , where A is the surface area and V the speed of the plane. The following table gives the friction per unit area on one side of a plate. Speed. Skin friction. Kg per sq. m. Plane. Speed. Skin friction. Lbs. per sq. ft. Plane. km/hr. i m long. 32 m long. miles/hr. ft/sec. i ft. long. 32 ft. long. 5 0.0059 0.0047 5 7-3 . 00033 o . 00026 10 0.0217 0.0171 10 14-7 O. 001 2 I o . 00095 15 o . 0464 o . 0364 15 22. O 0.00258 0.002O2 20 0.079 0.062 20 29-3 0.00439 0.00345 25 0. 122 0.095 25 36.7 0.0068 0.00530 30 o. 169 0.133 30 44-o o . 0094 O.OO74 40 0.288 0.225 40 58-7 0.0160 O.OI25 So 0-439 0.346 50 73-3 0.0244 O.OI92 00 0.616 0.482 60 88.0 0.0342 0.0268 70 80 0.82 i. 06 0.64 0.83 70 80 102.7 II7-3 0.0455 0.0587 0.0357 0.0461 90 i-3i 1.03 90 132.0 0.073 0.0572 IOO 1.58 1.24 IOO 146.7 0.088 0.069 no 1.89 1.49 no 161. 2 o. 105 0.083 120 2.20 1-73 1 20 175-8 O. 122 0.096 125 2-39 1.87 125 183.4 - I 33 o. 104 130 2.56 2.01 130 190.5 o. 142 O. 112 135 2.68 2. IO 135 197.8 0.149 o. 117 140 2.94 2.31 140 205.4 o. 164 0.128 US 3 15 2.47 145 212.5 0.175 0.137 150 3-37 2.6 5 !50 220.0 0.188 0.147 SMITHSONIAN TABLES. TABLES 143-145. AERODYNAMICS. The following tables, based on Eiffel, show the variation of the resistance coefficient K, with the angle of impact i, the aspect (ratio of leading edge to chord length), shape and velocity V in the formula tf(kg/m 2 ) = KS(m 2 )fF(m/sec.)} 2 The value of K for km/hour would be 0.77 times greater. TABLE 143. Variation of Air Resistance with Aspect and Angle. Size of plane. Aspect. Values of i. Max. ratio. 6 10 20 | 30 40 45 60 75 Value. . Values of Ki /Kto. 15 x 90 cm 15 X45 cm 25 x 25 cm 30 x 15 cm 45 x 15 cm I I 2 3 6 9 .07 . II . 20 .26 31 37 45 13 . 21 36 43 50 58 .62 .40 51 .80 .91 77 .70 73 0.67 0.89 1.24 0.72 0.77 0.78 0.80 0.92 I. 20 I.I7 0.79 0.84 0.84 0.85 I. 08 I . 22 I. 08 0.82 0.88 0.88 0.88 1.07 i. 06 1.03 0.90 0.94 o-93 0.94 1.03 1.02 1.02 0-97 0.99 0.98 0.99 1.07 1.22 1.46 0.91 0.77 0.69 60 45 38 20 20 IS 90 x 15 cm 90 x 10 cm Cylinder, base JL to wind: Diameter of base, 30 cm Diameter of base, 15 cm Cylinder, base Cylinder, base TABLE 144. Variation of Air Resistance with Shape and Size. Length, o cm iR* 2R* *R* 6R* SR* o cm K = .0675 .068 .055 .050 K= .066 .066 .055 .051 .051 .0515 to wind: diameter base, 15 cm, length, 60 cm K = .040 to wind: diameter base, 3 cm, length, 100 cm K = .060 .059 Cone, angle 60, diam. base, 40 cm, point to wind, solid K = .032 Cone, angle 30, diam. base, 40 cm, point to wind, solid K = .021 Sphere, 25 cm diam. K = .on Hemisphere, same diam., convex to wind K = .021 Hemisphere, same diam., concave to wind K = .083 Sphero-conic body, diam., 20 cm, cone 20, point forward K = .010 Sphero-conic body, diam., 20 cm, cone 20, point to rear K = .0055 Cylinder, 120 cm long, spherical ends to wind K = .012 The wind velocity for the values of this table was 10 m/sec. Tables 143 and 144 were taken from "The Resistance of the Air and Aviation," Eiffel, trans- lated by Hunsaker, 1913. * In the case of these cylinders the percentages due to skin friction are 2, 3, 6, 8, n and 16 per cent respectively, excluding the disk. TABLE 145. Variation of Air Resistance with Shape, Size and Speed. This table shows the peculiar drop in air resistance for speeds greater than 4 to 12 meters per second. Another change occurs when the velocity approaches that of sound. Values of K. 1 Speed, m/sec. 4 6 8 10 12 14 16 20 32 Sphere, 16. 2 cm diameter 033 .030 .028 .027 .024 .009 .0095 .OIO .on Sphere, 24.4 cm diameter .025 .025 .O2I 013 .OIO .010 .010 .OIO .OIO Sphere, 33 cm diameter .023 .017 .OI2 .010 .OIO .OIO .on .012 .012 Concave cup, 25 cm diameter .090 .090 .089 .087 .087 .088 .089 095 . IOO Convex cup, 25 cm diameter 027 .022 .021 .022 .022 .021 .020 .019 .018 Disk, 25 cm diameter .071 .070 .070 .070 .070 .070 .070 .070 .068 Cylinder cm element _L to wind, d = 15 cm, I = 15.0 043 .042 037 .030 025 .022 .021 .022 .022 element JL to wind, 30 30.0 045 .032 .027 .023 .024 .025 .025 .025 .023 element _L to wind, 15 7.5 .035 034 .032 .031 .031 -031 .030 .030 .030 element _L to wind, 15 12.0 038 -037 .036 .032 .030 .028 .027 .025 .025 element _L to wind, 15 22.5 .042 .041 .038 034 .031 .028 .025 .022 .O2O element || to wind, 15 105.0 .069 .061 057 055 053 .052 051 .051 .050 Spherical ends, 15 120.0 .024 .022 .019 .018 .018 .Ol8 .017 .Ol6 015 Taken from "Nouvelles Recherches sur la resistance de 1'air et 1'aviation," Eiffel, 1914. SMITHSONIAN TABLES. 154 TABLES 146-148. TABLE 146. -Friction. The required force F necessary to just move an object along a horizontal plane =.fN where N is the normal pressure on the plane and f the " coefficient of friction." The angle of repose * (tan * = F/N) is the angle at which the plane must be tilted before the object will move from its own weight. The following table of coefficients was com- piled by Rankine from the results of General Morin and other authorities and is sufficient for ordinary purposes. Material. / I// + Wood on wood, dry .2 5 -. 5 4.00-2.00 14.0-26.5 " " " soapy .20 5.00 "S Metals on oak, dry 5o-.6o 2.00-1.67 26.5-31.0 " " " wet .24-. 26 4- 17-3- 8 5 ^S-M-S " " " soapy ...... .20 5.00 "5 " " elm, dry ..'.... .20-.25 5.00-4.00 11.5-14.0 Hemp on oak, dry 53 1.89 28.0 " " " wet 33 3.00 18.5 Leather on oak . . . . 27-. l8 q.70-2.86 I C.O IQ C " " metals, dry */ %J" 56 Of *w 179 j- w y*j 2 9-5 " " " wet 36 278 2O.O " " " greasy 23 4-35 I 3 .0 " " " oily T 5 6.67 8-5 Metals on metals, dry .15-. 20 6.67-5.00 8.5-11.5 "wet 3 3-33 16.5 Smooth surfaces, occasionally greased . continually greased . .07-.08 .05 14.3-12.50 20.00 4.0-4.5 3- " best results .... .O3-.O36 33-3-27-6 175-2.0 Steel on agate, dry * .20 5.00 TI -5 " " " oiled* .107 9-35 6.1 Iron on stone Wood on stone .30-70 About .40 3-33-1-43 2.50 167-35.0 22.O Masonry and brick work, dry .... .60-70 1.67-1.43 33-o-35-o '' " " damp mortar 74 J -35 36-5 " on dry clay 5 1 1.96 27.0 " " moist clay Earth on earth dry sand, clay, and mixed earth . " " " damp clay 33 .25-1.00 38-75 I.OO 3-oo 4.00-1.00 2-63-1-33 I.OO 18.25 14.0-45.0 21.0-37.0 45-o " " " wet clay 3 1 3- 2 3 17.0 " " " shingle and gravel .81-1. ii 1.23-0.9 39.0-48.0 * Quoted from a paper by Jenkin and Ewing, " Phil. Trans. R. S." vol. 167. In this paper it is shown that in cases where " static friction " exceeds " kinetic friction " there is a gradual increase of the coefficient of friction as the speed is reduced towards zero. TABLE 147, -Lubricants. The best lubricants are in general the following: Low temperatures, light mineral lubricating Very great pressures, slow speeds, graphite, soapstone and other solid lubricants. Heavy ssures slow speeds ditto and lard, tallow and other greases. Heavy pressures and high speeds, sperm oil, castor oil, heavy mineral oils. Light pressures, high spee/s, sperm, refined |etleum .rape, cot tonsced. Ordinary machinery, lard oil, tallow oil, heavy mineral oils and the eavier vegetable oils. Steam cylinders, heavy mineral oils, lard, tallow. Watches and delicate iisms, clarified sperm, neat's-foot, porpoise, olive and light mineral lubricating oils. TABLE 148. -Lubricants For Cutting Tools. Material. Turning. Chucking. Drilling. Tapping Milling. Reaming. Tool Steel, Soft Steel, Wrought iron Cast iron, brass Copper Glass dry or oil dry or soda water dry or soda water dry dry turpentine or kerosene oil or s. w. soda water soda water dry dry oil oil or s. w. oil or s. w. dry dry oil oil oil dry dry lard oil lard oil lard oil dry mixture Mixture = X crude petroleum, % lard oil. Oil = sperm or lard. Tables 147 and i^quoted from "Friction and Lost Work in Machinery and Mill Work," Thurston, Wiley and Sons. SMITHSONIAN TABLES. TABLES 149-151. VISCOSITY. TABLE 149. Viscosity of Fluids and Solids. 155 The coefficient of viscosity of a substance is the tangential force required to move a unit area of a pkne surface with unit speed relative to another parallel plane surface from which it is separated by a layer a unit thick of the sub- stance. Viscosity measures the temporary rigidity it gives to the substance. The viscosity of fluids is generally meas- ured by the rate of flow of the fluid through a capillary tube the length of which is great in comparison with its diameter. The equation generally used is , the viscosity, Virgd*t X28Q0 + X) where y is the density (g/cm 3 ), d and / are the diameter and length in cm of the tube, Q the volume in cm* discharged in / sec., X the Couette correction which corrects the measured to the effective length of the tube, h the average head in cm, m the coefficient of kinetic energy correction, mf/g, necessary for the loss of energy due to turbulent in distinc- tion from viscous flow, g being the acceleration of gravity (cm/sec/sec), v the mean velocity hi cm per sec. (See Tech- nologic Paper of the Bureau of Standards, 100 and 112, Herschel^igi 7-1918, for discussion of this correction and X.) The fluidity is the reciprocal of the absolute viscosity. The kinetic viscosity is the absolute viscosity divided by the density. Specific viscosity is the viscosity relative to that of some standard substance, generally water, at some definite temperature. The dimensions of viscosity are ML~ l T~ l . It is generally expressed in cgs units as dyne-seconds per cm 2 or poises. The viscosity of solids may be measured in relative terms by the damping of the oscillations of suspended wires (see Table 78). Ladenburg (1006) gives the viscosity of Venice turpentine at 18.3 as 1300 poises; Trouton and Andrews (1904) of pitch at o, 51 X io 10 , at 15, 1.3 X to 10 ; of shoemakers' wax at 8, 4.7 X io 6 ; of soda glass at 575, ii X io 12 ; Deeley (1908) of glacier ice as 12 X io 13 . TABLE 150. Viscosity of Water in Centipoises. Temperature Variation. Bingham and Jackson, Bulletin Bureau of Standards, 14, 75, 1917. Vis- Vis- Vis- Vis- Vis- Vis- Vis- c. cosity. C. cosity. C. cosity. C. cosity. C. cosity. C. cosity. C. cosity. cp cp cp cp cp cp cp o .7921 10 .3077 20 1.0050 30 0.8007 40 0.6560 50 0.5494 60 0.4688 i .7313 ii .2713 21 0.9810 3i 0.7840 41 0.6439 Si 0.5404 65 0.4355 2 .6728 12 .2363 22 0.9579 32 0.7679 42 0.6321 52 0.5315 70 0.4061 3 .6191 13 .2028 23 0.9358 33 0.7523 43 o. 6207 53 0.5229 75 0.3799' 4 5674 14 .1709 24 0.9142 34 0-7371 44 0.6097 54 0.5146 80 0.3*65 | .5188 .4728 IS 16 .1404 .1111 25 26 0.8937 0.8737 35 36 0.7225 0.7085 45 46 0.5988 0.5883 55 56 0.5064 0.4985 85 00 0-3355 0.3165 7 .4284 17 .0828 27 0.8545 37 0.6947 47 0.5782 57 0.4907 95 0.2994 8 .3860 18 0559 28 0.8360 38 0.6814 48 0.5683 S8 0.4832 IOO 0.2838 9 .3462 19 .0299 29 0.8180 39 0.6685 49 0.5588 59 0.4759 153 0.181* * de Haas, 1894. Undercooled water: 2.10, 1.33 cp; 4.70, 2.12 cp; 6.20, 2.25 cp; 8.48, 2.46 cp; 9.30, 2.55 cp; White, Twining, J. Amer. Ch. Soc., 50, 380, 1913. TABLE 151. Viscosity of Alcohol-water Mixtures in Centipoises. Temperature Variation. Percentage by weight of ethyl alcohol. c. o IO 20 30 39 40 45 50 60 70 80 90 IOO o .792 3-3II 5.3I9 6.94 7-25 7.14 6-94 6.58 5-75 4.762 3-6oo -732 -773 5 10 519 .308 577 .179 4.065 3.I6S 5-29 4-05 5.62 4-39 5-59 4-39 5-50 4-35 5-26 4.18 4-63 3-77 3-906 3-268 3-125 2.710 309 .101 .623 .466 15 .140 .792 .6l8 3-26 3-52 3-53 3-Si 3-44 3.14 2.770 2.309 .802 -332 20 .005 538 .183 2.71 2.88 2.91 2.88 2.87 2.67 2.370 2.008 .610 .200 25 .894 .323 .815 2.18 35 2-35 2-39 2.40 2.24 2.037 1.748 .424 .006 30 .801 .160 553 .87 .00 2.02 2.02 2.02 1-93 1.767 I.53I .279 .003 35 .722 .006 332 .58 71 1.72 1.73 1.72 1.66 1-529 1-355 .147 .914 40 .656 .907 .160 .368 473 1.482 1-495 1.499 1.447 1-344 1.203 035 834 45 599 .812 .015 .189 .284 1.289 1-307 1.294 1.271 1.189 1.081 939 .764 50 549 734> .907 .050 .124 1.132 1.148 I- 155 1.127 1.062 0.968 .848 .702 60 70 .469 .406 .609 514 :& 0.834 0.683 0.885 0.725 0.893 0.727 0.907 0.740 0.913 0.740 0.902 0.729 0.856 0.695 0.789 0.650 .704 089 -592 -504 80 356 430 505 0.567 0.598 0.601 0.609 0.612 o. 604 SMITHSONIAN TABLES. Same authority as preceding table. 156 TABLES 162-164. VISCOSITY. TABLE 152. Viscosity and Density of Sucrose in Aqueous Solution. See Scientific Paper 298, Bingham and Jackson, Bureau of Standards, 1917, and Technologic Paper 100, Herschel, Bureau of Standards, 1917. -ity in centipoises. Density d*. Tempera- ture. Per cent sucrose by weight. Per cent sucrose by weight. 20 40 60 20 40 60 0C .7921 3.804 14-77 238. 0.99987 . 08546 I . 18349 - 29560 5 .5188 3-154 11.56 156. 0.99999 . 08460 I . l8l92 .29341 10 3077 2.652 9-794 109.8 0-99973 08353 I. l8O2O .29117 15 .1404 2.267 7.468 74-6 0.99913 .08233 I.I7837 . 28884 20 .0050 I .960 6. 200 56-5 0.99823 . 08094 I.I7648 . 28644 30 0.8007 1-504 4-382 33.78 0.99568 .07767 I.I72I4 . 28144 40 0.6560 I-J93 3-249 21.28 0.99225 .07366 I.I6759 .27615 5 0-5494 0.970 2-497 14.01 0.98807 .06898 I.I6248 .27058 60 0.4688 0.808 1.982 9-83 0.98330 .06358 LI5693 I . 26468 70 0.4061 0.685 i. 608 7-15 80 0-3565 0.590 1-334 5-40 Densities due to Plato. TABLE 153. Viscosity and Density of Glycerol in Aqueous Solution (20 C). % Glycerol. * Den- sity. g/cm Viscos- ity in centi- poises. roo X Kine- matic viscos- ity. Gfyc- erol. Den- sity, g/cm' Viscos- ity in centi- poises. ioo X Kine- matic viscos- ity. Git erol. Den- sity. g/cnV Viscos- ity in centi- poises. ioo X Kine- matic viscos- ity- 5 1.0098 I.lSl 1.170 35 -0855 3-II5 2.870 65 1.1662 I4-5I 12.44 10 1.0217 1.364 1-335 40 .0989 3-79 1 3-450 70 1.1797 21.49 l8.22 15 1-0337 1.580 I-529 45 .1124 4.692 4.218 75 1.1932 33-71 28.25 20 1.0461 1.846 r-765 50 .1258 5.908 5.248 80 I . 2066 55-34 45-86 25 1.0590 2.176 2-055 55 1393 7.664 6.727 85 I. 2201 102.5 84.01 30 1.0720 2.585 2.411 60 .1528 10.31 8-943 90 1-2335 207.6 168.3 The kinematic viscosity is the ordinary viscosity in cgs units (poises) divided by the density. TABLE 154. Viscosity and Density of Castor Oil (Temperature Variation). c B x / 1 Kinematic 1 '-ity. ! C ft I! 1U C i! Q M >. Kinematic 1 1 viscosity. 1 C is '7s ,J5 Kinematic 1 viscosity. 1 5 .9707 37.6 38.7 14 9645 16.61 17.22 23 -9583 7.6; 8.00 32 .9520 3-94 4.14 6 .9700 34.5 35-5 15 .9638 15-14 15-71 24 9576 7.06 7-37 33 9513 3-65 3.84 7 .9693 31-6 32.6 16 9631 13.80 M-33 25 9569 6.51 6.80 34 .9506 3-40 3.58 8 .9686 28.9 29.8 17 .9624 12.65 13-14 26 9562 6.04 6-32 35 9499 3.16 3-33 9 .9679 26.4 27-3 18 .9617 11.62 12.09 27 9555 5-6i 5.87 36 .9492 2.94 3.10 10 .9672 24.2 25.0 19 .9610 10. 71 11.15 28 .9548 5-21 5-46 37 9485 2.74 2.89 ii .9665 22.1 22.8 20 .9603 9.86 10. 27 29 9541 4-8<> 5.08 38 .9478 2.58 2.72 12 .9659 20. I 20.8 21 9596 9.06 9-44 30 9534 4-51 4-73 39 .9471 2.44 2.58 13 .9652 18.2 18.9 22 9589 8-34 8.70 9527 4.21 4-42 40 9464 2.31 2-44 1 Tables 153 and 154, taken from Technologic Paper 112, Bureau of Standards, 1918. Glycerol data due to Archbutt, Deeley and Gerlac}r, Castor Oil to Kahlbaum and Raber. See preceding table for definition of kinematic viscosity. Archbutt and Deeley give for the density and viscosity of castor oil at 65.6 C, 0.9284 and 0.605, respectively; at 100 C, 0.9050 and 0.169. SMITHSONIAN TABLES. TABLE 155. VISCOSITY OF LIQUIDS- Viscosities are given in cgs units, dyne-seconds per cm 2 , or poises. 157 Liquid. C Viscosity. Refer- ence. Liquid. C Viscosity. Refer- ence Acetaldehyde 0. 10. 0.00275 0.00252 0.00231 i i i * Dark cylinder *" Extra L. L." 37-8 IOO.O 37 8 7-324 0.341 10 IO Air Aniline -192.3 o. 00172 o. 04467 2 3 Linseed .925 $ IOO.O 0.451 10 Bismuth 60. 285 0.0156 o. 0161 3 4 -922 914 50. 0.176 9 ?6e o 0146 Olive 9195 i x8 Copal lac Glycerine 22. 2 8 4.80 4-2 2 I 15- 1-075 ii 14 3 13.87 6 " 9065 3 tt 20.3 26 5 8.30 4. 94 6 6 " .9000 40. 5 0.363 o 258 ii 8o.3i%H 2 O.. 6 4 .05%H 2 0.. 49-79%H 2 0.. 8-5 8.5 8.5 i . 02 1 O.222 o. 092 6 6 6 tRape '.'.'.'.'.'.'.'.'.'. 70. 15-6 37-8 0.124 i.n8 0.422 ii 10 IO Hydrogen, liquid Menthol, solid liquid 14.9 34-9 0. 0001 I 2 X 1012 0.069 2 7 7 g (another) (another) IOO.O 15.6 IOO.O 0.080 1.176 0.085 IO 10 10 o. 20. o. 01661 0.01547 o 01476 4 4 " " .915 " .906 t Sperm 50.0 90.0 15.6 0.206 0.078 9 IO ii O8 37 8 o 185 11 ii Oils: 299. 0.00975 4 Paraffins: Pentane 21 . O o 0026 12 Dogfish-liver . 923 J. . . " .918.... " .908.... 30. 50. 0.414 0. 211 o 080 9 9 Hexane Heptane Octane 23-7 24.0 22. 2 0.0033 0.0045 o 0053 12 12 12 Linseed .925 " 922 30. 0.331 9 Nonane 22.3 0.0062 12 " .914 QO. O.O?! 9 Undecane 22.7 0.0095 12 * Spindle oil . 885 .... IS.6 37 8 0-453 o 162 10 Dodecane Tridecane 23-3 23.3 0.0126 o OI 55 12 12 * Light machinery IOO.O 0.033 10 Tetradecane Pentadecane 21.9 22.0 0.0213 0.0281 12 12 . 907 t is 6 I 138 22. 2 o 0359 12 * Light machinery .... 37 8 0.342 IO Phenol.. 18.3 o. 1274 13 9O.O o 0126 13 * " Solar red" engine. . 15 6 1 . 915 IO Sulphur 170. 320.0 14 37 8 o 496 IO 180. 550.0 14 ii ii ii o 058 187. 560 o 14 *" Bayonne" engine.. 15.6 37 8 2.172 o S72 IO 200. 25O. 500.0 104.0 14 14 * " IOO.O 0.063 IO 300. 24.0 14 * " Queen's red " engine 15 6 2 995 IO 340. 6.2 14 37 8 380. . 5 14 * " Galena " axle oil . IOO.O IS 6 0.070 4 366 10 420. 448. :S 14 14 * ii ii < ?7 g t Tallow 66. . 176 IO * Heavy machinery. . . IS 6 6 606 IO IOO. .078 10 37 8 280. .0168 4 * Filtered cylinder. . . . 37.8 2 .406 IO 357- .0142 4 IOO O o 187 389- .0131 4 * Dark cylinder 37-8 IOO.O 4.224 0.240 10 10 * American mineral oils; based on water as .01028 at 20 C. t Based on water as per ist footnote. J Densities. References: (i) Thorpe and Rodger, 1894-7; (2) Verschaffelt, Sc. Ab. 1917; (3) Wijkander, 1879; (4) Plus*. Z. An. Ch. 93, 1915; (5) Metz, C. R. 1903; (6) Schottner, Wien. Ber. 77, 1878, 79, 1879; (7) Heydweiller, W. Ann. 63, 1897; (8) Koch, W. Ann. 14, 1881; (9) White, Bui. Bur. Fish. 32, 1912; (10) Archbutt-Deeley, Lubrication and Lubricants, 1912; (n) Higgins, Nat. Phys. Lab. n, 1914; (12) Bartolli, Stracciati, 1885-6; (13) Scarpa, 1903-4; (14) Rotinganz, Z. Ph. Ch. 62, 1908. SMITHSONIAN TABLES. j t-g TABLE 166. VISCOSITY OF LIQUIDS- Compiled from Landolt and Bornstein, 1912. Based principally on work of Thorpe and Rogers, 1894-97. Viscosity given in centipoises. One centipoise = o.oi dyne-second per cm 2 . Liquid. Viscosity in centipoises. Formula. oC 10 C 20 C 30 C 40 C 50 C 70 C 100 C Acids: Formic Acetic Propionic CH 2 2 C 2 H4O 2 C 3 H 6 2 C.H802 C 4 H 8 2 CH 4 C 2 H 6 CsHeO C 3 H 8 C 3 H 8 C^oO C 4 H 10 C 5 H 12 C 5 H 12 C 6 H 6 C 7 H 8 C 8 H 10 C 8 H 10 CgHio C 8 Hio C 2 H 5 Br C 3 H 7 Br C 3 H 7 Br C 3 H 5 Br C 2 H4Br Br C 3 H 7 C1 C 3 H 5 C1 C 2 H 4 C1 CHCla CC14 C 4 H 10 C 4 H 10 C 6 H 12 C 6 H 14 C 2 H 4 2 C 3 H 6 C 3 H 6 2 Cjls0 2 CH 3 I C 2 H 6 I C 3 H 7 I C 3 H 6 I C 5 H 12 CsHi 2 CeHi 4 C 6 H 14 C 7 H 16 C 7 H 16 C 8 His CS 2 C 4 H 10 S solid solid 1.521 2.286 1.887 0.817 1.772 2-145 3-883 4-565 5.186 8.038 ii. 129 8-532 0.906 0.772 0.877 1. 105 0.806 solid 0.487 0.651 0.611 0.626 2.438 i. 267 0.442 0.413 1.132 0.706 !-35i 0.294 0-314 0.402 o-544 0.436 0.510 0.484 0.582 0.606 0.727 0-944 0.936 o. 289 0.284 0.401 0.376 0.524 0.481 o. 706 0.438 0.563 2.248 2.247 solid .289 .851 .568 .690 .466 70S 2.918 3.246 3-873 5-548 7-425 6.000 0.763 0.671 o. 761 0.937 0.702 0.738 0.441 0.582 0-545 0.560 2.039 I. 120 0.396 0-372 0.966 0-633 I.I38 0.268 0.285 0.360 0.479 0.391 0-454 0-43 1 0.512 0.548 0.654 0-833 0.826 0.262 0.256 0.360 0-338 0.465 0.428 0.616 0.405 0.501 1-783 1.784 I. 222 I. IO2 1-540 I.3I8 0.596 I . 200 1.363 2. 256 2.370 2.948 3.907 5.092 4-342 0.654 0.590 0.669 0.810 O.62O 0.648 0.402 0.524 0.489 0.504 I.72I 1.005 0-359 0-337 0.838 0-571 0-975 0-245 0.260 0.324 0.425 o-355 0.408 0.388 0-455 0.500 0.592 0-744 0-734 o. 240 0.234 0.326 0.306 0.416 0.384 0.542 0.376 0.450 1.487 .460 .040 .960 304 .129 .520 .003 .168 779 757 2.267 2.864 3-594 3.207 0.567 0.525 0-594 o. 709 0-552 0-574 0.368 0-475 0-443 0.458 1-475 0.911 0.326 0.307 0.736 o-5i9 0.848 0.223 0.237 0.294 0.381 0-325 0.369 o-352 0.407 0.460 0.540 0.669 0.660 o. 220 o. 296 0.279 0-375 0-347 0.483 0-352 0.407 1.272 1.219 0.905 0.845 I. 1 2O 0.980 0.456 0.834 0.914 1.405 I-33I 1.782 2. 122 2.6O7 2.415 0.498 0.471 0.531 0.627 0.497 0.513 0-433 0.403 0.419 1.286 0.830 0.299 0.282 0.652 0-474 0.746 0.268 0-344 0.336 0.320 0.367 0.424 0-495 0.607 0-597 0.271 0.254 0.341 0.315 0-433 0.330 0.369 I.07I 1.036 0.796 0-752 0-975 0.862 0.403 o. 702 0.763 .130 .029 .411 .611 937 .851 0.444 0.426 0.479 0.560 0.451 0.463 0-397 0.368 0.384 1.131 o. 761 0.584 0-435 0.662 0.245 0.311 0.308 0.293 0-333 0.456 0.552 0-544 0.248 0.233 0.310 0.288 0.391 0.338 0.926 .780 631 .607 .760 683 .510 553 .760 .646 930 359 354 397 458 375 383 338 328 903 479 534 .279 391 .466 .458 .262 243 -324 .287 .728 549 465 459 551 .501 -540 527 .610 .632 .278 .310 352 . 296 .300 .678 371 365 252 Butyric i-Butyric . Alcohols: Methyl . . Ethyl * ... Allyl Proovl 1U K7 i-Propyl. . Butyric i-Butyric Amyl, op. act Amyl, op. inact. Aroma tics: Benzene Toluene Ethylbenzole Orthoxylene . Metaxylene Paraxylene Bromides- Ethyl Propyl i-Propyl. . . . Allyl Ethylene Bromine. . . Chlorides: Propyl Allyl Ethylene Chloroform . . . Carbon-tetra Ethers: Diethyl Methyl-propyl Ethyl-propyl . . Dipropyl Esters: Methylformate . . . Ethylformate Methylacetate Ethylacetate Iodides: Methyl Ethyl Propyl Allyl Paraffines: Pentane i-Pentane. .me . . i-Hexane Heptane i-Heptane Octane Sulphides: Carbon di-. . . . Kthyl Turpentine f SMITHSONIAN TABLES. Bureau of Standards, see special table, f Glaser. TABLE 157. VISCOSITY OF SOLUTIONS. 159 This table is intended to show the effect of change of concentration and change of temperature on the viscosity of solutions of salts in water. The specific viscosity X 100 is given for two or more densities and for several tem- peratures in the case of each solution, /u. stands for specific viscosity, and t for temperature Centigrade. Salt. Percentage by weight of salt in solution. Authority* BaCl 2 7-60 _ 77-9 10 44.0 30 35-2 5p _ _ Sprung. " 15.40 86.4 " 56.0 39-6 - " " 24-34 - 100.7 u 66.2 M 47-7 M - - " Ba(NO 3 ) 2 2. 9 8 1.027 62.0 15 5" 25 42.4 35 34-8 45 Wagner. : 5-24 1.051 68.1 54-2 44.1 36-9 " CaCl 2 I5-I7 - 1 10.9 10 7i-3 3 50-3 5 - _ Sprung. " 31.60 272.5 M 177.0 " 124.0 " - " " 39-75 - 670.0 " 379-o " 245-5 " - - M " 44.09 - - 593-1 " 363-2 M - - * Ca(NO 3 ) 2 '7-55 1.171 93-8 15 74-6 25 60.0 35 49-9 45 Wagner. " 30.10 1.274 144.1 " 112.7 4 * 90.7 " 75- 1 " u 40.13 1.386 242.6 u 217.1 M 156-5 u 128.1 " " CdCl 2 11.09 1.109 77-5 I5 60.5 2 5 49.1 35 40.7 45 " 16.30 1.181 88.9 " 70-5 " 57-5 47-2 " M 24.79 1.320 104.0 " 804 " 64.6 " 53-6 " " Cd(NO 3 ) 2 7.81 1.074 61.9 15 50.1 25 41.1 35 34-o 45 u u 15.71 I-I59 71.8 58.7 M 48.8 41-3 " " 22.36 1.241 85.1 u 69.0 " 57-3 " 47-5 " " CdS0 4 7.14 i. 068 78.9 15 61.8 25 49-9 35 4i-3 45 " 14.66 1-159 96.2 " 72.4 58.1 48.8 " " 22.OI 1.268 120.8 u 91.8 " 73-5 " 60. i " " CoCl 2 7-97 1.081 83.0 15 65.1 25 53-6 35 44-9 45 ' 14.86 22.27 1.161 1.264 1 1 1. 6 161.6 85.1 126.6 73-7 101.6 85^6 M Co(NO 3 ) 2 8.28 1-073 74-7 15 9 25 48.7 35 39-8 45 H " 15.96 1.144 87.0 .2 55-4 44-9 " " 24-53 1.229 110.4 u .0 " " 59- i M H CoSO 4 7.24 14.16 21.17 i. 086 I - I 59 1.240 86.7 117.8 193.6 y 68. 7 95-5 146.2 25 55-o 76.0 113.0 35 6i l 7 89.9 45 M H CuCl 2 I2.OI 1.104 87.2 y 67.8 25 55.1 35 45-6 45 11 21-35 1.215 121.5 95-8 77-o 63-2 44 u u 33-03 178.4 14 137.2 M 107.6 " 87.1 M Cu(N0 3 ) 2 18.99 1.177 97-3 y 76.0 25 61.5 35 51.3 45 ft " 26.68 1.264 126.2 98.8 80.9 68.6 tk " H 46.71 '536 382.9 " 283.8 " 215-3 " 172.2 " " CuSO 4 6-79 1-055 79-6 y 61.8 25 49-8 35 41.4 45 " M 12.57 1.115 98.2 74.0 " 59-7 " 52-0 " 17.49 1.163 124.5 u 96.8 " 75-9 61.8 HC1 8.14 1-037 71.0 y 57-9 25 48-3 35 40.1 45 M u 16.12 1.084 80.0 66.5 56.4 48.1 " M " 23.04 1.114 91.8 " 79-9 M 65-9 " 56-4 HgCl 2 0.23 3-55 1.002 I -33 76.75 IO 58-5 59-2 20 46.8 46.6 3f 38-3 38.3 40 U SMITHSONIAN TABLES. i6o TABLE 157 (continued). VISCOSITY OF SOLUTIONS, Salt. Percentage by weight of salt in solution. Density - t * Authority. HN0 8 8-37 1.067 66.4 15 54-8 2 5 45-4 35 37-6 45 Wagner. " 12.20 I.IIO 69-5 " 57-3 u 47-9 " 40.7 " " " 28.31 1.178 80.3 " 65.5 " 54-9 " 46.2 " " H 2 S0 4 7.87 1.065 77-8 15 61.0 25 50.0 35 41.7 45 u I5-50 1.130 95.1 < 75-o <( 60.5 u 49-8 " 23-43 1.200 122.7 u 95-5 " 77-5 " 64-3 M " KCi IO.23 - 70.0 10 46.1 30 33.1 50 _ _ Sprung. 22.21 70.0 " 48.6 M 36.4 " - " KBr 14.02 _ 67.6 IO 44.8 3? 32.1 5 _ _ M .. 23.16 66.2 " 44-7 33-2 M _ _ " 34.64 66.6 M 47-o " 35-7 H - - " KI 8.42 - 69.5 IO 44-o 3 fci-3 50 _ _ H I7.OI 65-3 u 42.9 " _ H " 33-03 61.8 " 42.9 " 32-4 " _ _ " " 45-98 67.0 M 45-2 " 35-3 " _ _ < " 54-oo - 68.8 U 48.5 u 37-6 " - - " KC10 3 3-51 - 71.7 IO 44-7 30 3i-5 50 _ _ u 5-69 ~ * 45-o 31-4 - - " KNO 3 6.32 _ 70.8 10 44.6 3 31.8 5 _ _ u M 12.19 68.7 " 44.8 3 2 -3 " _ _ U " 17.60 - 68.8 H 46.0 " 33-4 " - - M K 2 SO 4 5- T 7 - 77-4 IO 48.6 3p 34-3 50 _ _ m 9-77 81.0 " 52.0 3 6 -9 u - - * K 2 Cr0 4 "93 _ 75-8 10 62.5 3f 41.0 4p _ _ 19.61 85.3 " 68.7 47-9 _ _ n 24.26 1-233 97.8 " 74-5 " _ _ Slotte. 32.78 109.5 " 88.9 " 62.6 It - - Sprung. K 2 Cr 2 O 7 4.71 6.97 1.032 1.049 72.6 73-i 10 55-9 5-4 20 45-3 45-5 3? 37-5 37-7 4p Slotte. LiCl 776 - 96.1 10 59-7 30 41.2 5 _ _ Sprung. '3-9 1 ~ 21.3 75-9 " 52.6 " 26.93 229.4 " 142.1 " 98.0 " - - " Mg(N0 8 ) 2 18.62 34-19 1. 102 I.2OO ^99.8 IS 81.3 164.4 25 66.5 132.4 35 56.2 109.9 45 Wagner. 39-77 1.430 3 x 7-o M 250.0 " 191.4 " 158.1 " " MgS0 4 4-98 - 96.2 10 59-o 3f 40.9 50 _ _ Sprung. it 9-5 19.32 - 30-9 1O2.2 77-7 166.4 53-o 1 06.0 _ _ I MgCr0 4 2^86 1.089 1.164 "3 67.1 10 84.8 I2 5-3 20 67.4 99-0 3f 55-o 79-4 40 Slotte. 27.71 I.2I7 232.2 " 172.6 " 133-9 " 06.6 " u MnCl 2 8.01 1.096 1.196 92.8 30-9 y 71.1 104.2 25 57-5 84.0 35 48.1 68.7 45 Wagner. 30-33 J-337 56-3 M 193.2 " T 55- " 23-7 M H 40.13 *-453 37-3 393-4 300.4 " 48.5 " M SMITHSONIAN TABLES. TABLE 157 VISCOSITY OF SOLUTIONS. 161 Salt. Percentage by weight of salt in solution. Density. M t fi t M i M t Authority. Mn(N0 3 ) 2 18.31 29.60 49-31 1.148 1.506 96.0 167-5 396.8 \s 76.4 126.0 301.1 2 } ii 64-5 104.6 22I.O 35 5^.6 88.6 188.8 45 tt Wagner. < MnS0 4 u "45 18.80 22.08 I.I47 I.2 5 I 1.306 129.4 228.6 661.8 15 U 98.6 172.2 474.3 2 u 5 78.3 I37-I 347-9 35 63-4 107.4 266.8 45 M NaCl 7-95 I4-3 1 - 82.4 94 .8 10 U 52.0 60. 1 30 31.8 36-9 5 - - Sprung. " 23.22 - r&3 u 79-4 " 47-4 " - - M NaBr 9-77 18.58 - L 5 : 6 6 IO 48.7 53-5 30 34-4 38.2 So - - " 27.27 95-9 " 61.7 " 43-8 " - - (( Nal 8.83 - 73-i 10 46.0 3f 324 5 _ _ H M 17-15 35-69 _ 73-8 86.0 47-4 55-7 M 33-7 40.6 : : u " 55-47 - 157-2 M 96.4 " 66.9 " - - " NaClO 3 11.50 _ 78.7 IO 50.0 3f 35-3 5 _ _ M " 20.59 88.9 " 56.8 40.4 - " 33-54 - - I2I.O " 75-7 " 53- " - - NaNO 3 7-25 _ 75-6 IO 47-9 3f 33-8 5f _ _ " I2 -35 81.2 " 51.0 36.1 _ _ ( 18.20 - 87.0 " 55-9 " 39-3 " - - " u 3i-55 121. 2 76.2 " 53-4 M - - * Na 2 SO 4 4.98 - 96.2 IO 59-o 3f 40.9 5f _ _ M " 9-50 130.9 77-7 53-o (< 14.03 187.9 " 107.4 " 71.1 M _ " " 19.32 - 302,2 " 166.4 " 106.0 " - - " Na 2 CrO 4 5.76 1.058 85.8 10 66.6 2O 53-4 3 43-8 4 ? Slotte. 10.62 14.81 1. 112 1.164 103-3 127-5 79-3 97.1 63-5 77-3 < 52-3 63.0 M NH 4 C1 3-67 _ 71-5 IO 45- 3? 3i-9 5 _ _ Sprung. 8.67 69.1 45-3 32.6 - " 15.68 67-3 M 46.2 " 34-o " - " " 23-37 - 67-4 " 47-7 M 36.1 " - - " NH 4 Br J 5-97 _ 6 5 .2 IO 43-2 3 3 T -5 5 - _ 11 2 5-33 62.6 " 43-3 32.2 " - < " 36.88 - 62. 4 44-6 " 34-3 M - - NH 4 N0 3 5-97 - 69.6 10 44-3 3 31.6 5f - " 12.19 66.8 " 44-3 3'-9 - " " 27.08 67.0 " 47-7 " 349 M - - H .< 37-22 49-83 - 71.7 81.1 51.2 63-3 38.8 48.9 : : M M (NH 4 ) 2 S0 4 8.ro - 107.9 10 52-3 30 37-o 5 - - < " r 5-94 I 20. 2 " 60.4 - 43-2 " - - II 25-51 : 148.4 74-8 54-i SMITHSONIAN TABLES. 162 TABLE 157 (continued). VISCOSITY OF SOLUTIONS, Salt. Percentage by weight of salt in solution. Density. M t * t /A ' M t Authority. (NH 4 ) 2 Cr0 4 10.52 1-063 79-3 10 62.4 20 _ _ 42-4 40 Slotte. H 19-75 28.04 1. 120 I-I73 88.2 IOI.I 70.0 80.7 M 00.8 3? 48.4 56.4 - M M (NH 4 ) 2 Cr 2 7 6.85 1.039 72-5 10 56.3 20 45-8 30 38.0 40 " " 13.00 1.078 72.6 " 57-2 " 46.8 u 39-i " M u 19-93 I.I26 77-6 It 58.8 " 48.7 " 40.9 " NiCl 2 11.45 I.I09 90.4 15 70.0 2 5 r ? .r 35 48.2 45 Wagner. " 22.69 1.226 140.2 " 109.7 " 87.8 " 72-7 '' * " 30.40 1-337 229.5 " 171.8 " 139-2 " 111.9 u " Ni(N0 8 ) 2 16.49 1.136 90.7 15 70.1 25 j7-4 35 48.9 45 " 30.01 1.278 T 35- 6 M 105.9 " 85.5 ' 70.7 M M " 40-95 1.388 222.6 M 169.7 M 128.2 " 152.4 " M NiS0 4 10.62 1.092 94-6 iS 73-5 25 60. i 35 49-8 45 M " 18.19 1.198 154-9 119.9 99-5 75-7 M n 25-35 i-3H 298-5 " 224.9 " 173-0 " 1524 " U Pb(N0 8 ) 2 17-93 1.179 74.0 15 59-' 2 5 48-5 35 40-3 45 32-22 1.362 91.8 72.5 M 59-6 M 50.6 M Sr(N0 3 ) 2 10.29 i. 088 69-3 15 56.0 25 45-9 35 39- 1 45 U M 21.19 1.124 87-3 69.2 57-8 48.1 u " M 32-61 i -37 116.9 H 93-3 M 76.7 " 62.3 " " ZnCl 2 '5-33 1.146 93- 6 15 727 2 5 57-8 35 48.2 45 H u 23-49 1.229 111.5 86.6 ii 69.8 u 57-5 U ii 33-78 1-343 iS 1 -? 117.9 U 90.0 u 72.6 M " Zn(N0 3 ) 2 I5 . 95 1.115 80.7 15 64-3 25 52.6 35 43-8 45 H H 30.23 44-5 1.229 1-437 104.7 167.9 it 85.7 130.6 U (I 69.5 105.4 57-7 87-9 ZnSO 4 7.12 1.106 97.1 IS 79-3 25 62.7 35 51.5 45 u 16.64 1.195 156.0 u 118.6 94-2 ii 73-5 " 23.09 1.281 232.8 i?7-4 135-2 u 108.1 SMITHSONIAN TABLts. TABLE 158. SPECIFIC VISCOSITY.* I6 3 Dissolved salt. Normal solution. J normal. \ normal. normal. Authority. >> 5 1 \l C/T >> 1 Specific viscosity. >, 1 4) >> 4ri *U O 0) U * , i Q u >> si n Acids : C1 2 O 3 . . 1.0562 I.OI2 1.0283 1.003 1.0143 I.OOO 1.0074 0.999 Reyher. HC1 . . . 1.0177 1.067 1.0092 1.034 1.0045 1.017 1.0025 1.009 M HC1O 3 . . 1.0485 1.052 1.0244 1.025 I.OI26 1.014 1.0064 1. 006 " HNO 3 . . 1.0332 1.027 I.OI68 I.OII 1.0086 1.005 1.0044 1.003 " H 2 SO 4 . . 1.0303 I.OOXD 1.0154 1.043 1.0074 I. O2 2 1-0035 1. 008 Wagner. Aluminium sulphate 1.0550 1.406 1.0278 I.I78 1.0138 I.082 1.0068 1.038 a Barium chloride . . 1.0884 I.I23 1.0441 L057 I.O226 I.O26 I.OII4 1.013 u " nitrate . . 1.0518 1.044 1.0259 I. O2 1 1.0130 1. 008 u Calcium chloride . 1.0446 1.156 I.02I8 1.076 1.0105 1.036 1.0050 1.017 " nitrate . , 1.0596 I.II7 1.0300 1-053 1.0151 1.022 1.0076 1.008 u Cadmium chloride . 1.0779 I-I34 1.0394 1.063 1.0197 1.031 1.0098 I.O2O " nitrate 1.0954 I.I65 1.0479 1.074 1.0249 1.038 I.OII9 I.OI8 " sulphate . 1.0973 1.348 1.0487 I-I57 1.0244 1.078 I.OI20 I -33 Cobalt chloride . . 1.0571 I.2O4 1.0286 1.097 1.0144 1.048 1.0058 1.023 M " nitrate . . 1.0728 I.I66 1.0369 1-075 1.0184 1.032 1.0094 1.018 " " sulphate . . 1.0750 1-354 1-0383 1.160 I.OI 9 3 1.077 I.OIIO 1.040 " Copper chloride . . 1.0624 1.205 I-03I3 1.098 1.0158 1.047 1.0077 1.027 " nitrate . . r - 755 1.179 1.0372 1.080 1.0185 I.O4O 1.0092 1.018 " " sulphate 1.0790 1-358 1 .0402 1.160 1.0205 I.OSO I.OI03 1.038 " Lead nitrate . . . 1.1380 I.IOI 0.0699 1.042 *-35* I.OI7 I.OI75 1.007 ti Lithium chloride 1.0243 1.142 1.0129 i. 066 i .0062 I.03I I.OO3O I.OI2 " " sulphate 1-0453 1.290 1.0234 i-i37 1.0115 1.065 1.0057 1.032 " Magnesium chloride i-i375 I.2OI i. oi 88 1.094 1.0091 1.044 1.0043 I. O2 1 M " nitrate . 1.0512 I.I7I 1.0259 1.082 1.0130 1.040 1.0066 1.020 " " sulphate 1.0584 !-3 6 7 1.0297 1.164 1.0152 1.078 1.0076 1.032 Manganese chloride 1-0513 1.209 1.0259 1.098 1.0125 1.048 1.0063 I.O23 K " nitrate . 1.0690 1.183 1-0349 1.087 1.0174 1.043 1.0093 1.023 " sulphate 1.0728 1.364 1-0365 1.169 1.0179 1.076 1.0087 1.037 Nickel chloride . > 1.0591 1.205 1.0308 1.097 1.0144 1.044 1.0067 1. 02 1 " nitrate . . . I -755 1.180 1.0381 1.084 1.0192 I.O42 1.0096 I.OI9 " " sulphate . . 1.0773 1.361 1.0391 1.161 1.0198 1-075 I.OOI7 1.032 " Potassium chloride . 1.0466 0.987 .0235 0.987 1.0117 0.990 1.0059 0-993 64 " chromate 1.0935 1.113 0475 I -53 1.0241 I.O22 I.OI2I I.OI2 || " nitrate . 1.0605 0-975 0305 0.982 1.0161 0.987 1.0075 0.992 " sulphate i .0664 1.105 0338 1.049 1.0170 I. O2 1 1 .0084 1.008 Sodium chloride . . 1.0401 1.097 .0208 1.047 1.0107 1.024 I.OO56 I.OI3 Reyher. " bromide . . 1.0786 1.064 .0396 1.030 1.0190 I.OI5 I.OIOO 1.008 M " chlorate . 1.0710 1.090 0359 1.042 1.0180 I.O22 1.0092 1. 01 2 " nitrate . . Silver nitrate . . . 1-0554 1.1386 1.065 1.058 .0281 .0692 1.026 i. 020 1.0141 1.0348 I.OI2 1. 006 1.0071 1.0173 I.OO7 I.OOO Wagner. Strontium chloride . i .0676 1.141 33 6 1.067 1.0171 1.034 1.0084 1.014 u nitrate . 1.0822 1.115 .0419 1.049 1.0208 1.024 1.0104 I.OII Zinc chloride . . . 1.0590 1.189 .0302 1.096 1.0152 1-053 1.0077 1.024 " nitrate . . . 1.0758 1.164 .0404 i. 086 1.0191 1.039 1 .0096 1.019 " sulphate. . . 1.0792 1.367 1.0402 i-i73 1.0198 1.082 1.0094 1.036 * In the case of solutions of salts it has been found (vide Arrhennius, Zeits. fur Phys. Chem. vol. i, p. 285) that the specific viscosity can, in many cases, be nearly expressed by the equation /u. =:MI"> where fx t is the spec for a normal solution referred to the solvent at the same temperature, and n the number of gramme molecules solution under consideration. The same rule may of course be applied to solutions stated in percentages gramme molecules. The table here given has been compiled from the results of Reyher (Zeits. fur Phys. Lhem. vol. 2, p. 749) and of Wagner (Zeits. fur Phys. Chem. vol. 5, p. 3') and illustrates this rule. The numbers are all i SMITHSONIAN TABLES. 164 TABLE 159. VISCOSITY OF GASES AND VAPORS- The values of /A given in the table are io 6 times the coefficients of viscosity in C. G. S. units. Substance. Temp. M Refer- ence. Substance. Temp. Refer- ence. 18.0 -21.4 0.0 15-0 99.1 182.4 302.0 66.8 78.4 97-4 82.8 116.9 108.4 82.9 0.0 20. 0.0 14-7 17.9 99-7 183-7 o. 19.0 100. O 16.9 -20.7 0. 15-0 99.1 182.4 302.0 0.0 20.0 o.o 20. o o.o 17-4 61.2 o.o 78. 163.9 173-3 180.7 220.3 255-9 299-3 135- 142. 142. 162. 143- 144. 160. 96. 108. 210.4 220.8 224.1 273-3 322.1 70. 79- 118. 92.4 129.4 142. 145-7 186.1 222.1 268.2 163.0 184.0 128.7 147.0 95-9 102.9 189.0 68.9 I 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 5 5 5 5 5 10 6 6 i 2 10 2 2 2 2 10 4 4 4 i i 3 i Ether 16.1 36-5 0. 72-3 o.o 0.0 15-3 66.6 184.6 20. 6 o.o 15- 99-2 182.4 302.0 i5-o 270.0 300.0 330-o 360.0 390.0 20.0 0.0 15-0 302.0 44-0 -2i-5 o. 10.9 53-5 o. 0. o. 15-4 53-5 o.o 16.7 IOO.O 15. 73-2 79-3 93-5 216.0 96.1 189.1 196.9 234.8 269.9 81.9 86.7 88.9 105-9 121.5 139.2 246. 489- 1 532- 1 582. t 627. f 671-t 120. I 98.8 105.2 213.9 232. 156-3 166. 170.7 189.4 179. 138- 189. 195-7 215-9 90.4 96.7 132.0 222. i I 4 3 2 5 5 5 5 2 IO 2 2 2 2 II 8 8 8 8 8 4 2 2 2 3 7 10 7 7 IO 10 IO 7 7 i i 9 ii \ r * Ethyl chloride. . . . Ethyl iodide Ethylene Helium a Alcohol, Methyl. . . . Alcohol Ethyl n n Hydrogen u ll it Krypton Alcohol, Propyl, norm Alcohol, Isopropyl. . Alcohol, Butyl, norm . Alcohol, Isobutyl. . . Alcohol, Tert. butyl. \mmonia Mercury Yreon u u i i ( Methane Benzene Methyl chloride . . . u u u it Methyl iodide. . . . Nitrogen i i Carbon bisulphide . . Carbon dioxide < < Carbon monoxide. . . Chlorine u Nitric oxide Nitrous oxide. . . . Oxygen a n Chloroform it Water Vapor a. a n Xenon Ether i Puluj, Wien. Ber. 69 (2), 1874. 9 Meyer-Schumann, Wied. Ann. 13, 1881. 2 Breitenbach, Ann. Phys. 5, 1901. io Jeans, assumed mean, 1916. 3 Steudel, Wied. Ann. 16, 1882. n Rankine, 1910. 4 Graham, Philos. Trans. Lond. 1846, III. 12 Vogel (Eucken, Phys. Z. 14, 1913). For 5 Schultze, Ann. Phys. (4), 5, 6, 1901. summaries see: Fisher, Phys. Rev. 24, 6 Schumann, Wied. Ann. 23, 1884. 1904; Chapman, Phil. Tr. A. 211, 7 Obermayer, Wien. Ber. 71 (2a), 1875. 1911; Gilchrist, Phys. Rev. i, 1913. 8 Koch, Wied. Ann. 14, 1881, 19, 1883. Schmidt, Ann. d. Phys. 30, 1909. * Gilchrist's value of the viscosity of air may be taken as the most accurate at present avail- able. His value at 20.2 C is 1.812 x io~ 4 . The temperature variation given by Holman (Phil. Mag. 1886) gives p = 1715.50 x io~ 7 (i + .oo275/ - .00000034/2). See Phys. Rev. i, 1913. MilHkan (Ann. Phys. 41, 759, 1913) gives for the most accurate value f* t = 0.00018240 - 0.000000493(23-0 when (23>*>i2) whence ju 20 = 0.0001809 0.1%. For // he gives 0.0001711. fThe values here given were calculated from Koch's table (Wied. Ann. 19, p. 869, 1883) by the formula /z = 489 [i 4- 746(/ 270)]. SMITHSONIAN TABLES. TABLE 160. VISCOSITY OF GASES- Variation of Viscosity with Pressure and Temperature. 165 According to the kinetic theory of gases the coefficient of viscosity ju = i(pc/), p being the density, c the average velocity of the molecules, / the average path. Since / varies inversely as the number of molecules per unit volume, pi is a constant and JJL should be independent of the density and pressure of a gas (Maxwell's law). This has been found true for ordinary pressures; below -fa atmosphere it may fail, and for certain gases it has been proved untrue for high pres- sures, e.g., CO 2 at 33 and above 50 atm. See Jeans, " Dynamical Theory of Gases." c depends only on the temperature and the molecular weight; viscosity should, therefore, increase with the pressures for gases, c varies as the Vr, but fj, has been found to increase much more rapidly. Meyer's formula, juj = jUo(i + at), where a is a constant and /A> the viscosity at o C, is a convenient approximate relation. Sutherland's formula (Phil. Mag. 31, 1893). is the most accurate formula in use, taking in account the effect of molecular forces. It holds for temperatures above the critical and for pressures following approximately Boyle's law. It may be thrown into the form T = KT^/fj, C which is linear in terms of T and T^/JJL, with a slope equal to K and the ordinate intercept equal to C. See Fisher, Phys. Rev. 24, 1907, from which most of the following table is taken. Onnes (see Jeans) shows that this formula does not represent Helium at low temperatures with anything like the accuracy of the simpler formula The following table contains the constants for the above three formulae, T being always the absolute temperature, Centigrade scale. Gas. C K Xio' a * Gas. C K X io 7 a 11- Air 124 150 _ .754 Hydrogen 72 66 .69 Argon 172 206 .819 Krypton 1 88 Carbon mo- Neon 2<2 noxide ... 102 J 35 .00269 74 Nitrogen 1 10 143 .00269 74 Carbon dioxide 240 158 .00348 .98 Nitrous oxide, Chloroform. . . 454 159 N 2 O 313 172 00345 93 Ethylene. 226 1 06 OO^^O Oxygen 1^1 176 79 Helium 80 148 .683 Xenon 252 Helium .647 *The authorities for n are: Air, Rayleigh; Ar, Mean, Rayleigh, Schultze; CO, CO 2 , X_>, N 2 O, von Obermayer; Helium, Mean, Rayleigh, Schultze; 2d value, low temperature work of Onnes; H 2 , O 2 , Mean, Rayleigh, von Obermayer. SMITHSONIAN TABLES. 1 66 TABLE 161. DIFFUSION OF AN AQUEOUS SOLUTION INTO PURE WATER. If k is the coefficient of diffusion, dS the amount of the substance which passes in the time dt t at the place x, through q sq. cm. of a diffusion cylinder under the influence of a drop of concen- tration del dx, then gives the gram-molecules per liter. -. dx k depends on the temperature and the concentration. The unit of time is a day. Substance. c ,o k tf Substance. . k Ii Bromine . O.I 12. 0.8 i Calcium chloride 0.864 8.5 0.70 4 Chlorine . 12. 1.22 t< if 1.22 9- 0.72 44 Copper sulphate II 17- o-39 2 " ' 4 . . O.O6O 9- 0.64 44 Glycerine M IO.I4 o-357 3 44 44 . 0.047 9- 0.68 44 Hydrochloric acid . " 19.2 2.21 Copper sulphate 17- 0.23 2 Iodine II 12. (0.5) i 44 " o-95 17- 0.26 it Nitric acid ft 1 9-S 2.07 2 u ii 0.30 17- o-33 ' 4 Potassium chloride . " 1 7-S 1.38 2 44 " 0.005 17. o-47 " hydroxide ft '3-5 1.72 2 Glycerine 2/8 10.14 0-354 3 Silver nitrate . fl 12. 0.985 2 44 . . 6/8 10.14 0-345 " Sodium chloride " 15.0 o-94 2 44 ... 10/8 10.14 0.329 it Urea " 14-8 0.97 3 44 ... 14/8 10.14 0.300 " Acetic acid O.2 0.77 4 Hydrochloric acid . 4.52 n-5 2-93 4 Barium chloride " 8. 0.66 4 u u 3.16 ii. 2.67 ii Glycerine " IO.I 3-55 3 it t< 0-945 n. 2.12 4 ' Sodium actetate it 12. 0.67 5 it it 0.387 n. 2.02 44 44 chloride u 15.0 o-94 2 t it O.2CO ii. 1.84 " Urea it 14-8 0.969 3 Magnesium sulphate 2.18 5-5 O.28 4 Acetic acid 1.0 12. 0.74 6 ti if 0.541 5-5 0.32 it Ammonia it I 5- 2 3 J -54 7 it t 3-23 10. 0.27 it Formic acid " 12. o-97 7 it ii O.4O2 10. 0-34 Glycerine Hydrochloric acid . " IO.I4 12. 0-339 2.09 I Potassium hydroxide 0-75 0-49 12. 12. .72 .70 6 Magnesium sulphate " 7- 0.30 4 it it 0-375 12. .70 Potassium bromide . *' 10. I-I 3 8 44 nitrate . 3-9 I 7 .6 0.89 2 44 hydroxide . Sodium chloride t. 12. 15.0 1.72 0.94 6 2 44 : 1.4 o-3 I 7 .6 I 7 .6 .IO .26 ii a u u '4-3 0.964 3 u ii O.O2 I 7 .6 .28 " " hydroxide . it 12. i.i i 2 sulphate o-95 19.6 0.79 " iodide it 10. 0.80 8 if tt 0.28 19.6 0.86 it Sugar* . " 12. 0.254 6 ft ii 0.05 19.6 o-97 " Sulphuric acid " 12. 1. 12 6 if n O.O2 19.6 I.OI " Zinc sulphate . tt 14-8 0.236 Q Silver nitrate . 3-9 12. o-535 " Acetic acid 2.0 12. 0.69 5 " 44 0.9 12. 0.88 " Calcium chloride it IO. 0.68 8 u ti O.O2 12. I -35 " Cadmium sulphate . Hydrochloric acid . u 19.04 12. 0.246 2.21 I Sodium chloride 2/8 4/8 14-33 14-33 1.013 3 Sodium iodide ti 10. O.9O 8 41 " 6/8 J 4-33 0.980 2 Sulphuric acid " 12. 1.16 6 it u 10/8 J 4-33 0.948 " Zinc acetate 41 18.05 0.210 9 " " . 14/8 !4-33 0.917 14 " " . 44 0.04 0.120 9 Sulphuric acid 9-85 18. 2-36 2 Acetic acid 3- 12. 0.68 " 4-85 18. 1.90 " Potassium carbonate 10. 0.60 8 it ii 2.85 18. i. 60 ii " Jiydroxide it 12. 1.89 6 II ft 0.85 1 8. i-34 " Acetic acid 4-0 12. 0.66 6 <4 " -35 18. 1.32 Potassium chloride.- 14 10. 1.27 8 If II 0.005 18. 1.30 " i Euler, Wied. Ann. 63, 1897. 5 Kawalki, Wied. Ann. 52, 1894; 59, 1896. 2 Thovert, C. R. 133, 1901 ; 134, 1902. 6 Arrhenius, Zeitschr. Phys. Chem. 10, 1892. 3 Heimbrodt, Diss. Leipzig, 1903. 7 Abegg, Zeitschr. Phys. Chem. n, 1893. 4 Scheffer, Chem. Ber. 15, 1882; 16, 1883; 8 Schuhmeister, Wien. Ber. 79 (2 , 1879. Zeitschr. Phys. Chem. 2, 1888. 9 Seitz, Wied. Ann. 64, 1898. Compiled from Landolt-Bornstein-Meyerhoffer's Physikalisch-chemische Tabellen. SMITHSONIAN TABLES. TABLE 162. DIFFUSION OF VAPORS. 167 Coefficients of diffusion of vapors in C. G. S. units. The coefficients are for the temperatures given in the table and a pressure of 76 centimeters of mercury.* Vapor. Temp. C. o 7ft for vapor diffusing into hydrogen. kt for vapor diffusing into air. kt for vapor diffusing into carbon dioxide. Acids : Formic .... a O.O 65.4 84-9 0.5I3I 0.7873 0.8830 O.I3I5 0.2035 0.2244 0.0879 0.1343 0.1519 Acetic .... O.O 0.4040 0.1061 0.0713 u 65.5 O.62II 0.1578 0.1048 Isovaleric .... 98.5 O.O 0.7481 0.2II8 0.1965 0-0555 O.I32I 0.0375 . 98.0 0-3934 0.1031 0.0696 Alcohols : Methyl .... O.O 0.5001 0-1325 O.o88o i< 25.6 0.6015 0.1620 0.1046 i4 49.6 0.6738 0.1809 0.1234 Ethyl ..'.'. O.O 0.3806 0.0994 0.0693 . 40.4 0.5030 0.1372 0.0898 . 66.9 0.5430. 0-1475 O.IO26 Propyl .... 0.0 0-3I53 0.0803 0.0577 66.9 0.4832 0.1237 0.0901 . . . 83-5 0-5434 - I 379 0.0976 Butyl .... 0.0 0.2716 0.068 1 0.0476 , 99.0 ' 0.5045 0.1265 0.0884 Amyl .... O.O 0.2351 0.0589 0.0422 99.1 0.4362 0.1094 0.0784 Hexyl .... 0.0 0.1998 0.0499 0-0351 99.0 0.3712 0.0927 0.0651 O.O O 2Q4.O O O7 ?I O O?27 19.9 \j.^^\j 0.3409 U.U/^l 0.0877 \_.W^./ 0.0609 45-0 0-3993 O.IOII 0.0715 Carbon disulphide .... O.O 0.3690 0.0883 0.0629 . 19.9 0-4255 O.IOI5 0.0726 it 32.8 0.4626 O.II2O 0.0789 Esters : Methyl acetate . 0.0 0.3277 0.0840 0.0557 i( 20.3 0.3928 O.IOI3 0.0679 Ethyl .' ! O.O 46.1 0-2373 0.3729 0.0630 0.0970 0.0450 0.0666 Methyl butyrate . 0.0 0.2422 0.0640 0.0438 Q2.I 0.4308 O.II39 0.0809 Ethyl ! ! O.O 0.2238 0.0573 0.0406 96.5 0.4112 0.1064 0.0756 " valerate O.O 0.2050 0.0505 0.0366 . 97.6 0.3784 0.0932 0.0676 Ether O.O - 0.2060 0.0775 OXKC2 H 19.9 v *^ ;/ 0.3410 0.0893 J-3 0.0636 Water 0.0 0.6870 0.1980 0.1310 " 49-5 I.OOOO 0.2827 o.iSir . 92.4 1.1794 Q-345 1 0.2384 * Taken from Winkelmamrs papers (Wied. Ann. vols. 22, 23, and 26). The coefficients for o were calculated by Winkelmann on the assumption that the rate of diffusion is proportional to the absolute temperature. According to the investigations of Loschmidt and of Obenneyer the coefficient of diffusion of a gas, or vapor, at o C. and a pressure of 76 centimetres of mercury may be calculated from the observed coefficient at another temperature and pressure by the formula k Q = k T \-A) where T is temperature absolute and / the pressure of the gas. The exponent n is found to be about 1.75 for the permanent gases and about 2 for condensible gases. The following are examples: Air CO 2 , = 1.968; CO 2 N,O, =a.psj CO, H, =i. 74 2; CO O, 1.785.: H nii's results, as given in the above table, se z=i,755? O N, =i.792. Winkelma diffusing into air, hydrogen or carbon dioxide. SMITHSONIAN TABLES. seem to give about 2 for vapors T 68 TABLES 163-164. DIFFUSION OF GASES, VAPORS, AND METALS. TABLE 168. Coefficients of Diffusion for Various Oases and Vapors.* Gas or Vapor diffusing. Gas or Vapor diffused into. Temp. c. Coefficient of Diffusion. Authority. Air o o o o o o o o o o o o o o o o o o o o o 8 18 18 0.661 0.1775 0.1423 0.1360 0.1405 O.I3H 0-5437 0.1465 0.0983 O.I 802 0.0995 0.1314 o.ior 0.6422 0.1802 0.1872 0.0827 0.3054 0.6340 0.53^4 0.6488 -4593 0.4863 0.6254 0-5347 0.6788 0.1787 - l 3S7 0.7217 o. 1 7 1 o 0.4828 0.2390 0.2475 0.8710 Schulze. Obermayer. Loschmidt. Waitz. Loschmidt. Obermayer. Loschmidt. Stefan. Obermayer. Loschmidt. Obermayer. Stefan. ii Obermayer. i ti Loschmidt. Obermayer. Loschmidt. Guglilemo. Carbon dioxide .... FOR GASES IN WATER. Temperature Centigrade. t Carbon dioxide. CO, Carbon monoxide. CO Hydrogen. H Nitrogen. Nitric oxide. NO Nitrous oxide. N,0 Oxygen. 1.797 0-0354 0.02 1 10 0.02399 0.0738 1.048 0.04925 5 10 I.4IJO 1.185 03 ! 5 .0282 .02022 .01944 02134 .01918 .0646 .0571 0.8778 0-7377 04335 .03852 '5 I.OO2 .0254 .01875 .01742 0515 0.6294 03456 20 O.OXd .0232 .01809 01599 .0471 0-5443 03137 2 5 0.772 .0214 01745 .01481 .0432 .02874 3 .0200 .01690 .01370 .0400 .02646 40 0.506 .0177 .01644 OII95 0351 - .02316 5 .0161 .Ol6o8 .01074 3 1 5 .02080 100 0.244 .0141 .Ol6oO .OIOII .0263 .01690 Temperature Centigrade. t Air. Ammonia. NH 3 Chlorine. Cl Ethylene. C 2 H 4 Methane. CH 4 Hydrogen sulphide. H 2 S Sulphur dioxide. S0 2 0.02471 1174.6 3-036 0.2563 0.05473 4-371 79-79 5 .02179 971-5 2.808 2I 53 .04889 3-965 67.48 10 01953 840.2 2.585 1837 .04367 3.586 56-65 15 .01795 7J6.0 2.388 .1615 03903 3-233 47.28 20 .01704 683.1 2.156 .1488 03499 2.905 39-37 25 610.8 1.950 ~ .02542 2.604 32-79 ABSORPTION COEFFICIENTS, a t , FOR GASES IN ALCOHOL, G>H 5 OH. T* Centigrade. t Carbon dioxide. C0 2 Ethylene. Methane. Hydrogen. C 2 H 4 CH 4 H Nitrogen. Nitric oxide. NO Nitrous oxide. N 2 O Hydrogen Sulphur sulphide, dioxide. H 2 S S0 2 4.329 3-595 0.5226 0.0692 0.1263 0.3161 4.190 17.89 328.6 5 3.891 3.323 .5086 .0685 .1241 .2998 3-838 14.78 251.7 IO '5 20 25 3-5H 3-199 2.946 2,756 3.086 .4953 -0679 2.882 .4828 .0673 2-713 -4710 .0667 2.578 .4598 .0662 .1228 .1214 .I2O4 .1196 .2861 .2748 2659 -2595 3-525 3-215 3-015 2.819 II. 99 190.3 9-54 144-5 7.41 114.3 5.62 99.8 iis table contains the volumes of different gases, supposed measured at o C. and 76 centimeters' pressure, which it volume of the liquid named will absorb at atmospheric pressure and the temperature stated in the first column. The numbers tabulated are commonly called the absorption coefficients for the gases in water, or in alcohol, at the temperature t and under one atmosphere of pressure. The table has been compiled from data published by Bohr & Bock, Bunsen, Carius, Dittmar, Hamberg, Henrick, Pagliano & Kmo, Raoult, Schbnfeld, Setschenow, and Winkler. The numbers are in many cases averages from several of these authorities. OTE. The effect of increase of pressure is generally to increase the absorption coefficient. The following is approximately the magnitude of the effect in the case of ammonia in alcohol at a temperature of 23 C. : ( P ~ 45 cms. 50 cms. 55 cms. 60 cms. 65 cms. ' 033 =: 69 74 7g g 4 gg According to Setschenow the effect of varying the pressure from 45 to 85 centimeters in the case of carbonic acid in water is very small. SMITHSONIAN TABLES. TABLES 17O-172. CAPILLARITY. -SURFACE TENSION OF LIQUIDS/ 173 TABLE 170. -Water and Alcohol In Contact with Air. TABLE 172. -Solutions of Salts In Water, t Surface tension in dynes per centimeter. Surface tension in dynes per centimeter. Surface tension in dynes Salt in solution. Density. Temp. Tension n dynes per cm. Temp. Temp. c/. Temp. timeter. Water. Ethyl alcohol. Water. affl. Water. BaCl 2 CaClo 1.2820 1.0497 15-16 15-16 8l.8 77-5 5 10 75-6 74-9 74-2 23-5 2 3 .I 22.6 40 45 5 70.0 2O.O 19-5 19.1 80 85 90 64-3 63-6 62.9 HC1 1-2773 1.1190 1.0887 1 9 19 2O 20 95- 90.2 73-6 74-5 15 20 25 30 35 73-5 72.1 71.4 70.7 22.2 21.7 21-3 20.8 20.4 & 65 70 75 67.8 67.1 66.4 65-7 65.0 18.6 18.2 17-8 '7-3 16.9 95 100 62.2 61.5 KC1 MgCl 2 1.0242 1.1699 I.IOII 1.0463 L2338 1.1694 2O 15-16 15-16 15-16 15-16 15-16 i ^ 16 m so. i 78.2 90.1 85.2 78 o NaCl 1.1932 20 a I.I074 20 80.5 1.0360 20 77.6 NH 4 C1 1.0758 16 84.3 TABLE 171. -Miscellaneous Liquids in Contact with Air. 1-0535 I.028I 16 16 81.7 78.8 SrCl 2 T 11 T A i c 1 6 8 c ft Liquid. Surface Authority. I.I2O4 15-16 79-4 Temp. C tension in dynes K 2 C0 3 1.0567 '3575 15-16 15-16 77-8 90.9 per cen a 1.1576 15-16 81.8 timeter. "Mo CT} i .0400 15-16 77-5 1.1329 14-15 79-3 Aceton .... Acetic acid . Amyl alcohol . . Benzole .... 1 6.8 17.0 I 5 .0 15.0 23-3 30.2 24.8 28.8 Ramsay-Shields. Average of various. KNO 3 M 1.0605 1.0283 1.1263 1.0466 14-15 14-15 14 14 77.8 77-2 78.9 77-6 Butyric acid . . iq.o 28.7 M NaNO 3 1.3022 12 83-5 Carbon disulphide 20.0 Chloroform . . 20.0 Ether 20.0 3- 5 28.3 18.4 Quincke. Average of various. CuSO 4 1.1311 I-I775 1.0276 12 15-16 15-16 80.0 78.6 77-o ; Glycerine . . . 17.0 63.14 Hall. H 2 SO 4 1.8278 15 63.0 ? Hexane . . . . 0.0 21.2 Schiff. 1-4453 15 79-7 M ' 68.0 14.2 it 1.2636 15 79-7 Mercury .... Methyl alcohol . Olive oil .... 1 8.0 15.0 2O.O 520.0 24.7 34.7 Average of various. K 2 S0 4 MgS0 4 1.0744 1.0360 1.2744 15-16 15-16 15-16 78.0 77-4 83.2 Petroleum . Propyl alcohol 2O.O 5 .8 25-9 2 5-9 Magie. Schiff. Mn 2 SO 4 i. 0680 1.1119 15-16 15-16 77.8 79.1 M M 97.1 18.0 M " 1.0329 15-16 77-3 Toluol .... i q.o 29.1 ZnS0 4 1-3981 15-16 83-3 n 18 9 M M 1.2830 15-16 80.7 Turpentine . 2I.O 2 s: 5 Average of various. H 1.1039 15-16 77-8 * This determination of the capillary constants of liquids has been the subject of many careful experiments, but the results of the different experimenters, and even of the same observer when the method of measurement is changed, do not agree well together. The values here quoted can only be taken as approximations to the actual values for th liquids in a state of purity in contact with pure air. In the case of water the values given by Lord Rayleigh from the wave length of ripples (Phil. Mag. 1890) and by Hall from direct measurement of the tension of a flat film (Phil. Mag. 1893) have been preferred, and the temperature correction has been taken as 0.141 dyne per degree centigrade. The values for alcohol were derived from the experiments of Hall above referred to and the experiments on the effect of temperature made by Timberg (Wied. Ann. vol. 30). The authority for a few of the other values given is quoted, but they are for the most part average values derived from a large number of results published by different experimenters. f From Volkmann (Wied. Ann. vol. 17, p. 353). For more recent data see especially Harkins, J. Am. Ch. Soc., 39, p. 55, 1917 (336 liquids), and 42, p 702, 2543, 1920. SMITHSONIAN TABLFS J 74 TABLES 173-176. TENSION OF LIQUIDS. TABLE 173. -Surface Tension of r Liquid. Specific gravity. Surface tension in dynes per cen- timeter of liquid in contact with Air. Water. Mercury. Water . I.O ?ia 1.4878 0.7906 0.9136 0.8867 7977 1. 10 1.1248 75-o 5 '3-0 3-5 (31-8) (24.1) 34-6 28.8 29.7 (72.9) 69.9 o.o 392.0 41.7 26.8 18.6 "5 (28.9) (392) (387) (415) 3 6 4 317 241 271 (392) 429 Mercury ........ Bisulphide of carbon Kthyl alcohol Olive oil Turpentine ........ Petroleum ........ Hyposulphite of soda solution .... TABLE 174. - Surface Tension of Liquids at Solidifying Point, t Substance. Tempera- ture of solidifi- cation. Cent. Surface tension in dynes per centimeter. Substance. Tempera- ture of solidifi- cation. Cent. Surface tension in dynes per centimeter. Platinum 2OOO I6 9 I Antimony 432 249 Gold .... I2OO 1003 Borax .... IOOO 216 Zinc .... 360 877 Carbonate of soda IOOO 2IO Tin .... 2 3 Chloride of sodium _ 116 Mercury 40 588 Water .... 87-9J Lead .... 330 457 Selenium 217 71.8 Silver .... IOOO 427 Sulphur III 42.1 Bismuth 26< 1390 Phosphorus . 43 42.0 Potassium 58 37 T Wax .... 68 34.1 Sodium 90 i s s TABLE 175. Tension of Soap Films. Elaborate measurements of the thickness of soap films have been made by Reinold and Rucker.y They find that a film of oleate of soda solution containing i of soap to 70 of water, and having 3 per cent of KNO 3 added to increase electrical conductivity, breaks at a thickness varying between 7.2 and 14.5 micro-millimeters, the average being 12.1 micro- millimeters. The film becomes black and apparently of nearly uniform thickness round the point where fracture begins. Outside the black patch there is the usual display of colors, and the thickness at these parts may be estimated from the colors of thin plates and the refractive index of the solution. When the percentage of KNO 3 is diminished, the thickness of the black patch increases. For example, KN() :J =3 i 0.5 o.o Thickness = 12.4 13.5 14.5 22.1 micro-mm. A similar variation was found in the other soaps. It was also found that diminishing the proportion of soap in the solution, there being no KNQs dissolved, increased the thickness of the film. i part soap to 30 of water gave thickness 21.6 micro-mm. I part soap to 40 of water gave thickness 22.1 micro-mm. i part soap to 60 of water gave thickness 27.7 micro-mm. i part soap to 80 of water gave thickness 29.3 micro-mm. Qa,.,^c ,u.i-. ,1 ..... m K vui. zo, inn 5 ; wnn me exception ot those in brackets, which were not corrected by bout Jo^C ' 3re somewhat too high, for the reason stated by Worthington. The temperature was t Quincke, " Pogg. Ann." vol. 13?, p. 661. It will be observed that the value here given on the authority of Quincke is much higher than his subsequent measurements, as quoted above, give. " Proc. Roy. Soc." 1877, and " Phil. Trans. Roy. Soc." 1881, 1883, and 1893. NOTE. Quincke points out that substances may be divided into groups in each of which the ratio of the surface tension to the dens.ty ,. nearly constant. Thus, ,f this ratio for mercury be taken as unit, the ratio for the bromides and iodides is about a half : that of the nitrates, chlorides, sugars, and fats, as well as the metals, lead, bismuth, and antimony, about i : that of water, the carbonates, sulphates, and probably phosphates, and the metals platinum, gold, silver, cadmium, tin, and copper, 2 ; that of zinc, iron, and palladium, 3; and that of sodium, 6. SMITHSONIAN TABLES. VAPOR PRESSURE. TABLE 176. Vapor Pressure of Elements. 175 Hydrogen. Oxygen. Nitrogen. Argon. Xenon. Krypton. H scale. mm H scale. mm T mm K mm K mm K mm 20.4IK 20.22 19-93 19.41 18.82 I8.I5 17.36 16.37 14-93 800 7 6o 700 600 500 400 300 2OO IOO 9 o.6oK 90. 10 89.33 87.91 86.29 84-39 82.09 79.07 . 800 760 700 600 500 400 300 200 77-33K 76-83 76-65 75-44 74-03 72-39 70.42 67.80 63-65 7 6o. 7I4.5 700. 600. 500. 400. 300. 2OO. IOO. 155-6, 139.0 137-8 136.8 123.1 87.8 86.5 85-5 83-8 82.6 8l. 7 77-3 J.O2OO. 2325I- 21334- 20700. [0313. 821.2 704.5 633-4 524-3 465.0 410. 1 215.0 287.7 273-3 255-6 254.0 252.6 248.7 244.2 239-7 237-4 23L4 183.2 44112 3I50I 21967 21512 19984 I8I53 15868 I397I 13505 IH34 2O20 210.5 206.4 204. I 201.5 2OI.O 197.9 170.9 II2.7 88.6 84.2 41245 37006 34693 31621 30837 28808 11970 387 17-4 9- Travers, Sen- ter, jaque- rod, 1902-3. Travers, Jaque- rod, 1902-5. Fischer, Alt, 1902. Ramsay, Travers, Zs . phys. Ch. 38, rooi. Chlorine. Bromine. Iodine. Copper. Silver. C Pressure. C mm C mm C Atme. C Atme. + 146. +100. +50. + 20. O. 20. -33-6 -40. -50- -60. -70. -80. -85- -88. 93 . 50 atm. 41 . 70 atm. 14. 70 atm. 6.62 atm. 3.66 atm. i . 84 atm. 760. mm 560. mm 350. mm 210. mm 118. mm 62.5 mm 45- mm 37-5 mm +58.75 56.3 51-95 46.8 40.45 33-05 23-45 16.95 8.20 -5-05 -7.0 -8.4 12. O -16.65 7 6o 700 600 500 400 300 2OO 150 IOO 50 45 40 30 20 +55 5o 45 40 35 30 25 15 o 3.084 2.154 1.498 1.025 0.699 0.469 0.305 0.131 0.030 2310 2180 1980 1.0 0.338 O.I3I5 1955 1780 1660 I.O 0.346 0.1355 Lead Bismuth. C Atme. C Atme. 2100 1870 1525 1420 1320 II. 7 6-3 I.O o.35o 0.138 2060 1950 1740 1420 1310 1 200 16.5 n. 7 6-3 I.O 0.338 0.134 Baxter, Hick- ey, Holmes, J. Am. Ch Soc. 1907. . Zinc. Tin. Knietsch, W. Ann. 1890. Cu to Sn, Greenwood, Pr. Roy. Soc. 83A, 1910; Zs. ph. Ch. 76, 1911. Ramsay, Young J. Ch. Soc. 1886. C Atme. C Atme. 1510 1280 1230 II2O 53-o 21-5 ii. 7 6.3 2270 2100 1970 I.O 0-345 0.133 TABLE 177. Vapor Pressure and Rate of Evaporization K Mo mm W mm Evaporation rate. g/cm 2 /sec. Platinum. Mo W K mm g/cm 2 /sec. 1800 2OOO 2200 2400 2600 2800 3000 3200 3500 o.o 8 643 0.06789 o . 04396 0.021027 0.0160 0.1679 3890 \ 760 mm / 0.011645 o . 09849 0.07492 0.05151 0.04286 0.03362 0-02333 0.0572 0.010863 O.O7IOO o . 06480 O.04I20 0.03179 0.02l8l o. 012114 0.010144 0.09798 0.07236 0.06429 0.05523 0.04467 0.03769 1000 I20O I4OO I60O I800 2000 4l80 0.017324 O.Oi2lH o. 09188 o . 07484 0.05350 0.03107 760 mm 0.019832 O.Ou26o 0.011401 o . 09966 0.07667 0.05195 Langmuir, MacKay, Phys. Rev. 2, 1913; 4, 19*4- Order of vacuum, o. ooi-mm. p = K.T~^e~^o/RT dynes/cm 2 . Egerton, Phil. Mag. 33, p. 33, 1917. Zn, X = 3.28 x io 4 ; K = 1.17 x io 14 Cd, X = 2.77 X io 4 ; K = 5.27 X io 13 Hg, X = i. 60 x io 4 ; =3.72 X io 13 (Plnudsen) SMITHSONIAN TABLES. 1 7 6 TABLE 178. VAPOR PRESSURES, The vapor pressures here tabulated have been taken, with one exception, from Regnault's results The vapor pressure of Pictefs fluid is given on his own authority. The pressures are in centimeters of mercury. Tem- pera- ture Cent. Acetone. C 8 H 6 Benzol. C 6 H 6 Carbon bisul- phide. CS, Carbon tetra- chloride. ecu Chloro- form. CHC1 8 Ethyl alcohol. C 2 H 6 Ethyl ether. C 4 H 10 Ethyl bromide. C 2 H 5 Br Methyl alcohol. CH 4 Turpen- tine. C 10 H 6 25 _ _ 4.41 .41 _ 20 _ .c8 4-73 "98 - 33 6.8 9 5.92 63 - 15 - .88 6.16 i-35 - g 8-93 7.81 93 10 1.29 7-94 1.85 65 11.47 10.15 1.35 5 - 1.83 10.13 2.48 - .91 I 4 .6l 13.06 1.92 _ 2 -53 12.79 3-29 5-97 1.27 18.44 16.56 2.68 .21 5 _ 3-42 1 6.00 4-32 1.76 23.09 20.72 3-69 10 _ 4.52 19.85 5.60 10.05 2.42 28.68 25-74 5-oi .29 15 _ 5 89 24.41 7.17 _ 3-3 35.36 3 1.6 9 6.71 20 17.96 7 : 5 6 29.80 9.10 16.05 4-45 43.28 38.70 8.87 44 25 22.63 9-59 36.11 n-43 20.02 5-94 52.59 46.91 1 1. 60 - 3 28.10 12.02 43-46 14.23 24-75 7-85 6348 56.45 15.00 .69 35 34-52 14-93 51-97 17-55 30-35 10.29 76.12 67.49 19.20 - 40 42.OI 18.36 61-75 21.48 36.93 '3-37 90.70 80.19 24-35 i. 08 45 50-75 22.41 72.95 26.08 44.60 17.22 107.42 94-73 30.61 50 62.29 27.14 85-71 3M4 53-50 21.99 126.48 111.28 38.17 1.70 55 72.59 32.64 100.16 37-63 63-77 27.86 148.11 130-03 47.22 So 86.05 39-oi 116.45 44-74 7 c CA K 35-02 172.50 151.19 57-99 2.65 65 70 101.43 118.94 46-34 54-74 1 34-7 5 1 55-2 1 52-87 62.11 104.21 43-69 54-n 199.89 230.49 174-95 201.51 70.73 85-71 4.06 75 138.76 64.32 177.99 72-57 121.42 66-55 264.54 231.07 103.21 - 80 161.10 75- ! 9 203.25 84-33 140.76 81.29 302.28 263.86 123.85 6.13 85 9 186.18 214.17 87.46 101.27 231.17 261.91 97-5 1 112.23 162.41 186.52 98.64 118.93 343-95 389-83 300.06 339-89 147.09 174.17 9.06 95 245.28 116.75 296.63 128.69 213.28 142.51 440.18 205.17 100 279-73 134.01 332-51 146.71 242.85 169.75 495-33 431.23 240.51 13.11 105 no 317.70 359-40 153.18 174-44 372.72 416.41 166.72 188.74 275-40 311.10 201.04 236-76 555-62 621.46 483.12 539-40 280.63 325-96 18.60 "5 405.00 197.82 463-74 212.91 350.10 277-34 693-33 600.24 376.98 - 1 20 454.69 223.54 514-88 239-37 392.57 323-17 771.92 665.80 434.18 25-70 125 508.62 231.71 569-97 268.24 438.66 374-69 _ 736.22 498.05 - 130 '35 566.97 629.87 282.43 3^-85 629.16 692-59 299.69 333-86 542.25 432-30 496.42 811.65 892.19 569-13 647-93 34-90 140 697.44 352-07 760.40 370.90 600.02 567-46 977.96 733-71 46.40 391.21 832.69 411.00 661.92 645.80 830.89 150 '55 - 433-37 478.65 909.59 454.31 501.02 728.06 798.53 731-84 825.92 - 936-13 60.50 68.60 160 - 527-14 55 I -3 I 873.42 77-5 165 170 - 568.30 634.07 - 605.38 663.44 952.78 - - - - - SMITHSONIAN TABLES. TABLE 178 (continued). VAPOR PRESSURES. 177 Tem- pera- ture, Centi- grade. Ammonia. NH 3 Carbon dioxide. C0 2 Ethyl chloride. CjH 8 Cl Ethyl iodide. C 2 H 5 I Methyl chloride. CH 3 C1 Methylic ether. C 2 H 6 Nitrous oxide. NjO Pictet's fluid. 44C0 2 2 by weight Sulphur dioxide. so, Hydrogen sulphide. 30 86.61 - 11.02 - 57-90 57-65 - 58.52 28.75 - 25 110.43 1300.70 14.50 - 7J.78 71.61 1569.49 67.64 37.38 374-93 20 139.21 1514.24 18.75 88.32 88.20 1758.66 74.48 47.95 443.85 '5 10 I73-65 214.46 I758-25 2034.02 23.96 30.21 _ 107.92 130.96 107.77 130.66 1968.43 2200.80 89.68 101.84 60.79 76.25 5*9-65 608.46 5 264.42 2344.13 37.67 - 157.87 J57-25 2457.92 121.60 94.69 706.60 318.33 2690.66 46.52 4.19 189.10 187.90 2742.10 139.08 116.51 820.63 5 383-03 3075.38 56-93 5-41 225.11 222.90 3055-86 167.20 142.11 949.08 10 457-40 3499-86 69.11 6.92 266.38 262.90 3401.91 193.80 J7I-95 1089.63 15 543.34 3964-69 83.26 8.76 313.41 307-98 3783.I7 226.48 206.49 1244.79 20 638.78 4471.66 99.62 II.OO 366.69 358.60 4202.79 258.40 246.20 1415.15 25 30 747.70 870.10 5020.73 5611.90 118.42 139.90 13.69 16.91 426.74 494.05 415.10 477.8o 4664.14 5 i 70.85 297.92 291.60 343-18 1601.24 1803.53 35 1007.02 6244.73 164.32 20.71 569.11 6335-9 383.80 401.48 2002.43 40 11 59- 53 6918.44 191.96 25.I7 - 434.72 467.02 2258.25 45 1328.73 7631.46 223.07 30.38 478.80 540.35 249543 50 1515-83 - 257-94 36.40 - - _ 521.36 622.00 2781.48 & 1721.98 1948.21 : 266.84 340.05 43-32 51.22 : : * 712.50 812.38 3069-07 3374-02 65 2196.51 - 387.85 - - - - 922.14 3696.15 70 2467.55 440.50 - - - 4035.32 75 2763.00 _ 498.27 _ _ _ _ _ _ _ 80 3084.31 - 561.41 - - - - - - - 85 3433-09 630.16 - 90 3810.92 704.75 95 4219.57 785.39 - - - 100 4660.82 - 872.28 - - - - - - - SMITHSONIAN TABLES. i 7 8 TABLES 179-18O. VAPOR PRESSURE, TABLE 179. Vapor Pressure of Ethyl Alcohol.* i 1 2 3 4 5 6 7 8 9 Vapor pressure in millimeters of mercury at o C. 10 20 30 40 70 12.24 23-78 44.00 78.06 I33-70 220.00 350-30 541.20 13.18 $6 82.50 140.75 230.80 366.40 564.35 27.94 49-47 87.17 148.10 242.50 383-10 588.35 15.16 28.67 52-44 92.07 155.80 253-80 400.40 613.20 16.21 30.50 97-21 163.80 265.90 638'95 3244 58.86 102.60 172.20 278.60 437.00 665.55 18.46 34-49 62.33 108.24 181.00 291.85 456.35 693.10 19.68 36-67 65.97 114.15 190.10 305-65 476.45 721.55 20.98 38.97 69.80 120.35 199.65 3*9-95 751.00 22.34 41.40 209.60 334.85 518.85 781.45 From the formula log/ = a -j- ba* + cf? Ramsay and Young obtain the following numbers.f ! 10 20 30 40 50 60 70 80 90 Vapor pressure in millimeters of mercury at o C. IOO 200 12.24 1692.3. 22182. 23-73 43-97 3223.0 32196- 78.11 4318.7 38389- 13342 5686.6 219.82 7368.7 350.21 9409.9 540.91 11858. 811.81 14764. 1186.5 18185. TABLE 180. Vapor Pressure of Methyl Alcohol, t o 1 2 3 4 5 6 7 8 9 E H Vapor pressure in millimeters of mercury at o C. 10 gr 31.6 57.o 33-6 60.3 35-6 63.8 37-8 67-5 40.2 71.4 42.6 75-5 45-2 79-8 47-9 84-3 50.8 89.0 20 94-o 99-2 104.7 1 10.4 116.5 122.7 129.3 136.2 143-4 151.0 30 40 '& 158.9 259-4 409-4 624.3 167.1 271.9 427.7 650.0 175-7 285.0 446.6 676.5 184.7 2 98-5 466.3 703.8 194.1 312.6 486.6 732.0 203.9 327.3 5077 761.1 214.1 342.5 529-5 791.1 224.7 358.3 552-0 822.0 235-8 374-7 575-3 247-4 391-7 599-4 * This table has been compiled from results published by Ramsay and Young (Jour. Chem. Soc. vol. 47, and Phil. Trans. Roy. Soc., 1886). t In this formula := 5.0720301 ; log b 2.6406131 ; log c = 0.6050854 ; log a = 0.003377538; log 0= 1.99682424 _15o _aoo 0.25 6 6 6 7 8 8 9 IO II 12 13 14 15 17 18 2O 32 050 II 12 n 14 iS 17 18 2O 21 23 25 28 . 30 34 37 40 64 0.75 17 18 21 23 25 27 3 32 35 38 42 46 5 55 00 96 1.00 1.25 1.50 1.75 22 2 4 27 30 33 36 38 42 26 3 2 39 45 28 35 42 49 3 53 33 36 42 45 50 54 58 63 40 49 42 47 54 58 64 70 75 82 51 56 61 64 70 76 76 84 92 Eg 98 6? 84 IOO 74 92 80 too 2.00 44 48 S2 56 61 66 72 79 86 93 mm, -1 -2 - 2.25 49 53 S8 63 69 75 81 $9 96 - 2.50 2.75 55 59 60 65 65 7i 70 77 76 84 83 90 91 ioo 99 3.50 3.75 77 82 83 89 90 98 97 - 3.00 66 71 78 84 92 ioo - - - 4.00 88 95 3.25 71 77 84 91 99 _ _ - 4.25 93 IOO - 3.50 77 83 9 98 ~ ~~ ~ ~~ ~ 4.50 99 ~ " Vapor Air Temperatures, dry bulb, Centigrade. mm. 1 2 3 40 8 o 60 70 go 9 10= 11= 12 13= 14 18 16 17 Igo 190 20 0.5 ii 10 9 Q 8 8 7 7 6 6 5 5 5444 4 3 333 1.0 22 2O 19 18 16 15 14 13 !3 12 II IO 10 9 8 8 7 7 7 6 6 1.5 33 3i 28 27 2S 23 22 2O 19 18 16 15 14 13 13 12 ii IO 10 9 9 2.0 44 4i 38 35 33 29 27 25 23 22 2O 19 18 17 16 15 14 13 12 12 2.5 55 5i 47 44 38 36 33 3i 29 27 26 24 22 21 2O 18 17 16 15 14 3.0 66 61 57 S3 49 46 43 40 3 8 35 33 3i 29 27 25 24 22 21 20 18 17 3.5 4.0 4.5 5.0 77 71 66 88 81 76 99 92 85 - - 95 62 88 74 83 6 1 77 50 47 44 57 54 50 65 60 56 72 67 63 47 H 38 36 44 4i 49 46 55 5i 34 3i 29 28 3 8 3 6 34 3 2 43 40 38 36 48 45 42 39 20 3 33 37 24 28 3 1 35 23 21 2O 26 2 2 3 29 28 26 33 3i 29 5.5 _ _ _ 97 qi 8s 79 74 69 64 60 56 53 49 46 43 41 38 36 34 32 6.0 _ _ _ qq Q2 86 80 75 70 66 6 1 58 54 51 47 44 42 39 37 34 e* e 93 87 81 76 71 6? 62 58 55 51 48 41: 42 40 37 7.0 7.5 - - - - _ ioo 94 85 - ,00 94 82 88 77 72 82 77 67 63 59 55 72 67 63 59 52 55 49 52 46 43 40 49 46 43 8.0 _ _ _ _ ioo 94 88 82 77 72 67 63 S9 56 52 49 46 p K OQ Q-7 87 82 76 72 67 63 <;? ?2 AQ Q O yy 98 g-> 86 81 76 71 67 6^ cq re c.2 Q ? O7 q T 85 80 75 7O 66 62 c8 s s inn 06 qo 84. 7q 74 6n 76 y 67 6^ J.J..U So ST 78 74 6q jL2.ll q6 QO J.O.U O7 91 86 So JL4.U 1 K f\ Q7 Q" 7 86 98 g" JLo.U 17.0 q8 SMITHSONIAN TABLES. 1 88 TABLE 190 (continued). RELATIVE HUMIDITY, Vapor Pressure Air Temperatures, dry bulb, Centigrade. 80 21 82 23 24 26 26 27 28 29 30 31 32 33 34 35 36 37 38 3 39 40 C 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 6 5 12 II 17 16 2 3 22 29 27 34 3J 40 38 46 43 5 2 49 69 65 75 ?o So 76 55544443 10 10 9 8 8 8 7 7 15 14 14 13 12 ii ii 10 20 19 18 17 16 15 14 13 33333322222 66655554444 10 9988776665 13 12 ii ii 10 10 9 9 8 8 7 25 24 31 29 36 34 41 38 46 43 5i 48 56 53 61 58 66 62 71 67 2 3 21 20 27 26 24 32 30 28 3 6 34 3 2 41 38 36 45 43 40 50 47 44 54 5i 48 63 60 56 19 18 17 23 21 20 26 25 24 3 29 27 34 32 30 38 36 34 42 39 37 45 43 40 49 46 44 53 50 47 16 15 14 13 13 12 ii ii 19 18 17 16 15 14 14 13 22 21 20 19 l8 17 l6 15 25 24 23 21 20 19 l8 17 29 27 25 24 23 22 20 19 86 8i 76 72 68 64 60 57 92 87 82 77 72 68 64 60 98 92 87 81 77 72 68 64 - 97 92 86 81 77 72 68 - - 97 91 86 81 76 72 - - - 96 90 85 80 76 - 95 89 84 79 - -- - - ioo 94 88 83 ----- 98 92 87 ------ 96 91 - ioo 94 -------98 53 50 57 54 61 57 64 60 68 64 71 67 75 7i 78 74 82 77 85 81 89 84 93 87 96 91 ioo 94 32 30 28 27 35 33 3 1 29 38 36 34 32 4i 39 37 35 44 42 40 37 48 45 42 40 51 48 45 43 54 5 r 48 45 57 54 5 1 48 60 57 54 5 1 63 60 57 53 6 7 63 59 56 70 66 62 59 73 69 65 62 76 72 68 64 25 24 23 21 28 26 25 24 30 29 27 26 33 31 29 28 35 33 32 30 38 36 34 32 4i 3 8 36 34 43 41 38 36 46 43 4 1 39 48 45 43 4i 51 48 45 43 53 5 48 45 56 53 50 47 58 55 S 2 49 61 57 54 5 1 79 75 71 67 63 60 56 54 83 78 74 70 66 62 59 56 86 81 76 72 68 65 61 58 89 84 79 75 71 67 63 60 92 87 82 78 73 69 65 62 10 10 9 12 12 II 14 13 J 3 16 15 15 18 17 16 20 19 18 22 21 20 24 23 22 26 25 24 28 27 26 3 29 27 3 2 3 1 29 34 33 3 1 37 35 33 39 36 35 4i 38 36 43 40 38 45 42 40 47 44 42 49 46 44 51 48 46 53 50 47 55 52 49 57 54 5i 59 56 53 30 --------- 95 90 85 80 76 72 68 64 61 58 55 31 ---------- 98 93 88 83 78 74 70 66 63 60 56 32 ---------- - 96 91 86 81 77 72 69 65 62 33 -----_--__ - 99 93 88 84 79 75 71 67 63 34 __---__-__ - - Q 6 91 86 81 77 73 69 65 62 35 ------ 99 94 89 84 79 75 7* 67 64 36 __________ - - - 96 91 86 81 77 73 69 66 37 ---_----__ - - - 99 94 89 84 79 75 71 67 38 ---_----__ - - - - 96 91 86 81 77 73 69 39 --------__ ____ 99 93 88 83 79 75 40 -___--____ _____ 9 6 9 o868i7773 41 _________ _____ 98 93 88 83 79 75 42 _________ _ _ _ _ _ I00 95 90 85 81 77 43 -------___ ______ 97 92 87 83 78 --------- ______ 99 94 89 84 80 45 --_--__-__ _______ 96 91 86 82 46 -____________ 99 93 88 84 47 _---______ ________ 95 90 86 48 ---------- ________ 97 93 87 __________ ________ 99 94 89 50 __----____ _________ 96 91 51 ---_____ __________ 98 93 52 - 95 54 55 MITHSONIAN TABLES. TABLES 190 (concluded), jgj. TABLE 190 (concluded). Relative Humidity. (Data from 20 to 60 C. based upon Table 185). 189 Vapor Air Temperatures, dry bulb, Centigrade. Pressure. mm. 40 41 42 43 44 45 46 47 48 49 60 51 52 53 54 66 56 67 58 59 60 5 10 9 18 9 8 17 16 8 15 7 15 7 14 7 6 T 3 6 12 6 II 5 ii 5 10 5 10 5 9 4 9 I '3 4 8 4 7 4 3 7 7 15 27 26 24 23 22 21 20 18 17 16 15 15 14 *3 12 12 ii 10 10 20 36 34 33 3 1 2 9 28 26 25 24 23 22 21 20 19 18 17 16 15 15 14 13 25 45 43 4i 39 37 35 33 3 1 3 28 27 26 24 23 22 21 20 19 1 8 18 17 30 35 40 is 4 72 5 1 49 60 57 68 65 46 g 44 5 ?- 42 49 56 40 46 53 38 44 50 36 42 48 34 40 45 43 41 29 34 39 28 33 37 27 2 5 3 34 3 2 23 27 3 1 22 26 29 21 20 2 5 23 28 27 45 8l 77 73 69 66 63 59 57 54 5 1 49 4 6 44 42 40 38 36 35 33 3 2 3 50 90 86 81 77 73 70 66 63 60 57 54 5 1 49 47 44 42 40 38 37 35 33 55 99 94 89 85 81 76 73 69 66 62 59 57 54 5I 49 46 44 42 40 39 37 60 - - 98 93 88 83 Z 9 75 72 68 65 62 60 56 53 5 1 48 46 44 42 40 65 WJf\ IOO 95 90 86 82 oo 78 o . 74 Q_ 67 so 61 Ar 55 5 2 50 48 46 43 I\J 75 - - - - - 97 92 99 oo 94 54 90 oO 85 76 76 81 72 77 DO 74 6 5 70 67 64 58 5 1 55 49 47 53 50 80 - - - - - - _ IOO 96 9 1 86 82 78 75 7i 68 64 62 59 56 54 85 90 ~ _ _ ~ : : 97 92 97 87 93 84 88 79 84 11 72 76 69 73 65 69 62 66 60 57 63 60 95 - mm. 67 58 59= 60 _ _ _ 98 94 89 84 80 77 73 70 67 64 100 - 125 9 6 92 88 8 4 - - - - 98 93 89 .85 81 77 73 70 67 105 - 130 IOO 95 9 1 87 _ _ _ _ _ _ 98 93 89 85 81 77 74 70 110 135 99 95 9 - - - - 98 93 89 85 81 77 74 115 - 140 - 98 94 - 97 93 88 84 81 77 120 _ 145 97 92 88 84 80 97 125 150 96 9 2 88 84 IOO TABLE 191. Relative Humidity. This table gives the relative humidity direct from the difference between the reading of the dry (t C.) and the wet (t! C.) thermometer. It is computed for a barometer reading of 76 cm. The wet thermometer should be ventilated about 3 meters per second. From manuscript tables computed at the U.S. Weather Bureau. Depression of wet-bulb thermometer, t -^ . t 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.6 5.0 6.6 -15 90 9i 72 62 53 44 35 25 16 7 _ _ _ _ _ _ _ -12 92 85 77 69 62 54 47 39 32 25 7 - - - -9 94 88 81 75 70 62 56 50 44 39 23 9 - - - -6 -3 95 96 89 85 87 80 82 74 ?8 69 64 59 54 49 74 69 66 61 57 36 46 25 36 13 26 2 17 7 ~ ~ 96 92 89 8S 81 78 74 71 67 64 55 46 38 2 9 21 13 6 +3 97 94 87 84 81 78 75 72 69 62 54 46 40 32 25 18 0.5 1.0 1.5 2.0 2.5 3.0 G 3.5 4.0 4.5 60 6.0 7.0 8.0 9.0 10. 11. 12. +3 92 84 76 69 62 54 46 40 32 25 12 _ _ _ _ _ +6 94 80 73 66 60 54 47 41 35 23 1 1 - - - - +9 94 88 82 76 70 65 59 53 48 42 32 22 12 3 - - - + 12 94 89 84 78 73 68 63 58 53 48 38 30 21 12 4 - + 15 95 90 8S 80 ?6 71 66 62 58 53 44 36 28 20 13 4 - + 18 95 90 86 82 78 73 69 65 61 57 49 42 35 27 20 13 6 +21 96 9 1 87 83 79 75 71 67 64 60 53 46 39 32 26 9 13 + 24 96 9 2 88 85 81 77 74 7 66 63 56 49 43 37 3 T 26 21 +27 96 93 90 86 82 79 76 72 68 65 59 S3 47 4i 36 31 26 +30 0.6 93 90 86 82 79 76 73 70 67 61 55 44 39 35 3 +33 96 93 90 86 83 80 77 74 7i 68 63 57 S2 47 42 37 33 +36 +39 97 97 93 94 90 87 88 84 85 81 78 75 72 70 82 79 76 74 71 64 66 57 61 54 56 5 52 45 47 4i 36 43 39 SMITHSONIAN TABLES. TABLES 192-193. CORRECTION FOR TEMPERATURE OF EMERGENT MERCURIAL THERMOMETER THREAD- When the temperature of a portion of a thermometer stem with its mercury thread differs much from that of the bulb, a correction is necessary to the observed temperature unless the instrument has been calibrated for the experimental conditions. This stem correction is pro- portional to nft(T - /), where n is the number of degrees in the exposed stem, ft the apparent coefficient of expansion of mercury in the glass, T the measured temperature, and / the mean temperature of the exposed stem. For temperatures up to 100 C, the value of is for Jena i6i" or Greiner and Friedrich resistance glass, 0.000159, for Jena 59"', 0.000164, and when of unknown composition it is best to use a value of about 0.000155. The formula requires a knowl- edge of the temperature of the emergent stem. This may be approximated in one of three ways: (1) by a "fadenthermometer" (see Buckingham, Bulletin Bureau of Standards, 8, p. 239, 1912); (2) by exploring the temperature distribution of the stem and calculating its mean tempera- ture; and (3) by suspending along the side of, or attaching to the stem, a single thermometer. Table 192 is taken from the Smithsonian Meteorological Tables, Tables 193-195 from Rimbach, Z. f. Instrumentenkunde, 10, p. 153, 1890, and apply to thermometers of Jena or resistance glass. TABLE 192. Stem Correction for Centigrade Thermometers. Values of o.oooissn(T f). (T-t). n 10 20 30 40 S 60 70 80 10 C O.O2 0.03 0.05 O.O6 0.08 0.09 O. II O. 12 20 0.03 0.06 0.09 O. 12 o. 16 o. 19 O. 22 0.25 30 0.05 0.09 0.14 o. 19 0.23 0.28 0-33 0-37 40 0.06 O. 12 o. 19 0.25 0.31 0.37 0-43 0.50 50 0.08 o. 16 0.23 0.31 0-39 0.46 0-54 O.62 60 O.O9 o. 19 0.28 0-37 0.46 0.56 0.65 0.74 70 O. II 0.22 0-33 0-43 0-54 0.65 o. 76 0.87 80 O. 12 0.25 0-37 0.50 0.62 0.74 0.87 0.99 90 O.I4 0.28 0.42 0.56 o. 70 0.84 0.98 I. 12 IOO o. 16 0.31 0.46 O.62 0.78 o-93 I. 08 1.24 TABLE 193. Stem Correction for Thermometer of Jena Glass (0 to 360 C). Degree length 0.9 to i.i mm; / = the observed temperature; t' = that of the surrounding air i dm. away; n = the length of the exposed thread. Correction to be added to the reading /. n /- /' 70 80 90 100 120 140 160 180 200 220 10 O.OI O.OI 0.03 0.04 0.07 O. IO 0.13 0.17 o. 19 O. 21 2O 0.08 O. 12 o. 14 o. 19 0.25 0.28 0.32 0.40 0.49 o-54 30 0.25 0.28 0.32 0.36 O.42 0.48 0-54 0.66 0.78 0.87 40 0.30 o-35 0.41 0.48 O.6O 0.67 0.77 0.92 1. 08 1.20 50 0.41 0.46 0.52 o-59 0.79 0.89 0.98 1.16 1.38 i-53 60 0.52 0.60 0.68 0.79 0-99 I. II 1.23 1.46 1.70 1.87 70 0.63 0.74 0.85 0.98 I. 2O 1.32 1-45 1.70 1.99 2. 21 80 0.75 0.87 I.OI i-i5 1-38 i-53 1.70 1.98 2.29 2-54 90 0.87 0.99 I.I3 1.28 1.62 1.82 1.94 2.25 2.60 2.89 IOO 0.98 I. 12 1.29 1.47 1.82 2.03 2. 20 2-55 2.92 3-24 1 20 1.88 2.28 2.49 2.68 3-i3 3-59 3-96 140 2-75 2.97 3.22 3-75 4.24 4-69 160 - 3-35 3-80 4-35 4.92 5-45 180 4-37 4-99 5-63 6,22 200 5.68 6-34 6.98 2 2O 7-05 7.82 1 SMITHSONIAN TABLES TABLES 194, 195. CORRECTION FOR TEMPERATURE OF MERCURY IN THERMOMETER STEM (continued). TABLE 194. - Stem Correction lor Thermometer of Jena Glass (0-360 0). Degree length i to 1.6 mm.; /=the observed temperature; /= that of the surrounding air one dm. away ; ;/ = the length of the exposed thread. CORRECTION TO BE ADDED TO THERMOMETER READING.* t V 70 80 90 100 120 140 160 180 200 220 n 10 20 O.O2 O.I 3 0.03 0.15 0.05 0.18 0.07 O.22 O.I I 0.29 0.17 0.38 O.2I 0.46 0.27 0-33 0.6 1 0.38 0.67 10 20 30 40 0.24 -35 0.28 0.41 o-33 0.48 0-39 0.56 0.48 0.68 0-59 0.82 0.70 0.94 0.78 1.04 0.88 1.16 0.97 1.28 3 40 50 0.47 0.53 0.62 0.72 0.88 1.03 I.I7 I. 3 , 1.44 i-59 50 60 0-57 0.66 0.77 0.89 1.09 1.25 1.42 1.58 1.74 1.90 60 70 0.69 0.79 0.92 1. 06 1.30 1.47 1.67 1.86 2.04 2.23 70 80 0.80 0.91 1.05 1. 21 1.52 1.71 1.94 2.15 2-33 2-55 80 90 0.91 1.04 1.19 1.38 i-73 1.96 2.2O 2.42 2.64 2.89 90 IOO 1.02 1.18 1.56 1.97 2.18 2-45 2.70 2.94 3-23 IOO IIO - - - I. 7 8 2.19 2-43 2.70 2.98 3.26 3-57 no 120 - - - I. 9 8 2-43 2.69 2-95 3-26 3-58 3-9 2 1 20 130 _ _ _ _ 2.68 2.94 3-20 3.56 3.89 4.28 130 140 2.92 3.22 3-47 3.86 4.22 4.64 140 I 5 - 3-74 4-15 4-.S6 5.01 J 5 160 - 4.00 4.46 4.90 5-39 160 170 1 80 - - - - - - 4.27 4-54 4.76 5-07 5-24 5-59 5-77 6.15 170 1 80 190 200 - - - - - : 5-70 5-95 6.30 6.54 6.94 190 200 210 _ _ _ _ _ _ _ - 6.68 7-35 210 220 7.04 7-75 220 * See Hovestadt's " Jena Glass" (translated by J. D. and A. Everett) for data on changes of thermometer zeros. TABLE 195. Stem Correction lor a so-called Normal Thermometer of Jena Glass (0-100 0). Divided into tenth degrees ; degree length about 4 mm. CORRECTION TO BE ADDED TO THE READING f. t t' 30 35 40 45 50 55 60 65 70 75 80 85 IO 20 0.04 O.T2 0.04 0.12 0.05 0.13 0.05 0.14 0.05 0.15 0.06 0.16 0.06 0.17 0.07 0.18 O.o8 0.19 0.09 O.2O O.IO O.22 O.IO 0.23 30 O.2I 0.22 0.23 0.24 0.25 0.25 0.27 0.29 0.31 0.33 o-35 0.37 40 70 0.28 0.36 0-45 O.29 0.38 0.48 0.31 0.40 0.51 o-33 0.42 o-53 0-35 0.44 o-55 0-37 0.46 0-57 0.66 0-39 0.48 0.60 0.69 0.41 0.50 0.03 0.71 0-43 i& o-75 0-45 -57 0.69 0.8 1 0.48 0.61 0-73 0.87 0.51 0.65 0.78 0.92 80 90 _ _ _ _ 0.76 0.8 1 0.92 0.87 0.99 ^ I.OO 1. 06 1. 20 IOO _ 1. 10 1.18 L_ 1.34 SMITHSONIAN TABLES. IQ2 TABLES 196-199. THERMOMETERS. TABLE 196. Oas and Mercury Thermometers. If /H, /M, 'cos, 'i6, 69, 'T, are temperatures measured with the hydrogen, nitrogen, carbonic acid, lu > 59 m > and " verre dur " (Tonnelot), respectively, then , H _ / T = *~r^ E 0-61859 + 0.004735 1./ 0.00001 1 577-' 2 ]* [0.33386+ 0.0039910.^ 0.000016678.^]*. [0.67039 -j- 0.0047351. / o.ooooi 1 577-' 2 ]t 0.31089 + 0.0047351-' * Chappuis ; Trav. et Mem. du Bur. internal, des Poids et Mes. 6, 1888. t Thiesen, Scheel, Sell; Wiss. Abh. d. Phys. Techn.Reichanstalt,2, 1895; Scheel; Wied. Ann. 58, 1896; D. Mech. Ztg. 1897. TABLE 197. t H - t l6 ( Hydrogen -16 m ). 1 2 3 4 5 6 7 8 9 .000 -.007 -OI 3 .019 -025 -.031 .036 .042 047 -.051 IO .056 -.061 -.065 .069 .073 .077 .080 .084 .087 .090 20 093 -.096 -.098 .101 .103 -.105 .107 .109 .no .112 3 "3 .114 .115 .116 .117 .118 .119 .119 .119 .I2O 40 .120 .120 .I2O .I2O .119 .119 .Il8 . 1 1 8 .117 .Il6 g 90 .103 -.087 .058 .030 "5 .101 .081 .056 .027 .114 .099 .078 053 .024 "3 .097 .076 .050 .021 .Ill -.096 .074 .048 .018 .110 .094 .071 .045 .015 .109 -.092 -.069 .042 .012 .107 .090 .066 .039 .009 .106 -.087 .064 ' .036 .006 .IO4 -.08 5 .O6l 033 .003 IOO .OOO TABLE 198. t H 1 69 (Hydrogen- 59 m ). ,o 2 3 4 5 6 7 8 9 .000 -.003 .006 .009 .011 -.014 .016 .018 .020 .022 IO 20 30 .024 035 .038 -.02| .036 037 .027 -036 .037 .028 037 .037 .030 037 037 .031 -.037 .036 .032 .038 .036 035 034 .038 035 035 .038 034 40 034 033 .032 .032 .031 .030 .029 .028 .028 .027 50 .026 .025 .024 .023 .022 .021 .O2O .OI9 .Ol8 .017 60 .016 .015 .015 .OI4 .013 ! .OI2 .Oil .OIO .009 .008 70 .008 .007 .006 .005 .005 .004 .003 .003 .002 .OOI 80 .001 .001 .000 .000 + .001 + .OOI + .00 1 + .002 +.002 + .002 90 +.002 + .002 + .002 + .OO2 + .002 + .002 + .OOI + .001 + .001 .000 IOO .000 TABLE 199. (Hydrogen - 16 1 "), (Hydrogen 69" 1 ). -5 10 -15 20 -25 -30 -35 ta tie t H t 6 9 +0.04 +0.02 +0.08 +0.04 +O.I 3 +0.07 + O.I 9 +0.10 +0.25 +0.14 +0. 3 2 +0.18 +0.40 +0.2 3 All compiled from Landolt-Bornstein-Meyerhoffer's Physikalisch-chemische Tabellen. SMITHSONIAN TABLES. TABLES 2OO, 2O1 . AIR AND MERCURY THERMOMETERS. TABLE 200. IAIR t 16 . (Air IB.) 00. ,o 2 3 4 5 6 7 8 9 O .000 .006 .012 .017 .022 .027 -.032 .037 .041 .045 IO ^.049 53 X .O6l -.065 .068 .071 .074 .077 .080 20 -.083 .086 .089 .091 .093 .095, .097 .099 .IOI .102 3 .103 .104 .105 .I06 .107 .I08 .109 .IIO .IIO .110 40 .110 .110 .Ill .Ill .110 .110 .110 .109 -'.109 .108 5 .107 .107 .106 .105 .IO4 .103 .102 .101 .100 .098 60 -.096 -95 .093 .092 .090 .088 .086 -.084 .082 .080 70 .078 .076 .074 .072 .070 -.067 -.065 .062 .060 057 80 .054 .052 .049 .047 .044 .041 39 -.036 034 .031 90 .028 .025 .023 .O2O .017 .014 .on .009 .006 .003 IOO .000 +.003 4-.oo6 +.008 + .011 + .014 +.017 +.019 +.022 + .025 no +.028 +.030 +.033 + .035 | +.038 + .041 +.043 +.046 + .0 4 8 + -O$O 120 +'53 +055 +057 -j_.o6o +.062 + .06 4 +.066 +.068 + .070 + .072 130 +.074 +.076 +.078 +.080 +.081 + .08 3 +.084 +.086 + .08 7 140 I 5 +.090 +.098 +.091 +.098 +.092 +.098 +093 +.099 +.094 +.099 + 095 + .099 +.096 +.098 +.096 + .097 + .097 +.097 1 60 170 +.097 +.084 +082 +095 +.080 +.094 +.078 +.093 +.076 + .092 + 073 +.090 +.071 +!o68 + .065 + .086 + .062 180 +.059 +.055 +.052 +.048 +.045 + .041 +037 +033 + .028 + .023 190 +.019 +.014 +.009 +.004 .OOI .007 .013 .019 .025 .031 200 .038 .045 .051 .058 .066 .073 .080 .088 -.096 lOq 2IO -"3 .122 .130 1 39 .148 .158 .168 .177 -.187 -.198 2 2O .208 .219 .230 .241 .252 .264 275 -.287 .300 .312 2 3 325 .338 '351 -365 -.378 392 .407 .421 43 6 450 240 .466 .481 497 529 546 -.562 579 597 .614 2 5 -.632 .650 .668 .687 -.706 725 745 -.76; -.785 -.80 5 260 .825 .846 -.867 .889 .911 933 955 .978 I.OOI I.O25 270 1.048 I.O72 1.096 1. 121 1.146 1.171 1.196 1.222 1.248 1.274 280 1.301 -I. 3 28 -1.356 1.384 1.412 1.440 1.469 -1.498 1.528 -I. q 5 8 290 -1.588 1.618 1.649 -1.680 1.711 1-743 1.776 1. 808 1.841 1.874 3 00 -1.908 Note: See Circular 8, Bureau of Standards relative to use of thermometers and the various precautions and corrections. TABLE 201. tAiR t B9 . (Air 69 m .) c. 1 2 3 4 5 6 7 8 9 IOO .000 .000 .000 .OOO .000 .000 .000 .000 .000 .OOO no .000 .000 .000 .OOI .OOI .001 .001 .001 .OO2 .OO2 120 130 .002 .004 .002 .004 .002 .005 .OO2 .005 .002 .006 -.003 .006 .003 1 .003 .006 ; .007 .004 .007 .004 .008 140 .008 .008 .009 .009 .010 .010 .Oil .Oil .012 .OI2 150 .013 .013 .014 .015 .016 .016 .016 .017 .018 .019 160 .019 .020 .021 .O2I .022 .023 .024 .025 .026 .027 170 .028 .029 .030 .031 .032 033 .034 .035 037 .038 1 80 190 039 .052 .040 .053 .041 055 -.043 .056 .044 .057 045 .059 .046 .060 -062 .049 .064 .051 -.066 200 .067 SMITHSONIAN TABLES. 194 TABLES 202-2O4. GAS, MERCURY, ALCOHOL, TOLUOL, PETROLETHER, PENTANE, THERMOMETERS. TABLE 202. t !i tji (Hydrogen-Mercury). Temper- ature, C. Thurincer Glass.* Verre dur. Tounelot.t Resistance Glass.* English Crystal Glass.* Choisv-le- Roi.* I22 m* Nitrogen Thermometer. TB T M .t CO 2 Ther- mometer. TH-T 0(v t o o o c o O .OOO .000 .000 .000 .OOO .000 .000 .OOO IO 075 .0^2 .066 .008 .007 .005 .006 .025 20 .085 .108 .001 .004 .006 .010 .043 3 .'56 .102 -I3 1 +.017 + .004 .002 .Oil 054 40 .168 .107 .140 +037 + .014 + .OO I .Oil 059 .166 .150 .103 .090 '35 .119 +057 +.073 + .025 + 033 + .004 + .008 .009 .005 059 53 70 .124 .072 .095 +.079 + .037 + .009 .OOI .044 80 .088 .OCO .068 + .070 + .032 + .007 + .OO2 .031 90 .047 -.026 .034 +.046 + .022 + .006 + .003 .016 100 .000 .000 .000 .000 .000 .000 .OOO .000 * Schlosser, Zt. Instrkde. ai, 1901. t Chappuis, Trav. et mem. du Bur. Intern, des Poids et Mas. 6, TABLE 203. Comparison of Air and High Temperature Mercury Thermometers. Comparison of the air thermometer with the high temperature mercury thermometer, filled under pressure and made of 59 UI glass. Air. 59 m . Air. 59 m . o 0. 375 3854 100 100. 400 412.3 200 200.4 425 440.7 3 00 304.1 450 469.1 325 35 330.9 358.1 475 500 498.0 527-8 Mahlke, Wied. Ann. 1894. TABLE 204. Comparison of Hydrogen and Other Thermometers. Comparison of the hydrogen thermometer with the toluol, alcohol, petrolether, and pentane ther- mometers (verre dur). Hydrogen. Toluol* Alcohol I.* Alcohol II.* Petrolether.t Pentane.J o o o O 0.00 O.OO 0.00 _ O.OO IO 20 -8.54 16.90 9-31 18.45 9.44 18.71 9-03 17.87 3 25.10 27.44 -27.84 26.55 40 -50 60 33- r 5 41.08 48.90 36.30 45-05 53-71 -36.84 45-74 54-55 42.6 35-04 43-36 5 r -5 70 -56.63 62.31 63.31 59.46 IOO _ 80.2 82.28 150 - _ _ 1 13.0 116.87 200 ~ 140.7 146.84 * Chappuis, Arch. sc. phys. (3) 18, 1892. t Holborn, Ann. d. Phys. (4) 6, 1901. I Rothe, unpublished. All compiled from Landolt-Bornstein-Meyerhoffer's Physikalisch-chemische Tabellen. SMITHSONIAN TABLES. TABLES 2O5-2O7. TABLE 205. Platinum Resistance Thermometers. Callendar has shown that if we define the platinum temperature, pt, by pt = ioo<{ (R R ) /(Rioo Ro) } , where R is the observed resistance at t C., R that at O, R 100 at 100, then the re- lation between the platinum temperature and the temperature t on the scale of the gas thermo- meter is represented by t pt = S-{ t/ 100 i }-t/ioo where 8 is a constant for any given sample of platinum and about 1.50 for pure platinum (impure platinum having higher values). This holds good between 23 and 450 when 5 has been determined by the boiling point of sulphur (445.) See Waidner and Burgess, Bui. Bureau Standards, 6, p. 149, 1909. Also Bureau reprints 124, 143 and 149. TABLE 206. Thermodynamic Temperature of the Ice Point, and Seduction to Thermodynamic Scale. Mean = 273.13 C. (ice point). For a discussion of the various values and for the corrections of the various gas thermometers to the thermodynamic scale see Buckingham, Bull. Bureau Standards, 3, p. 237, 1907. Scale Corrections for Gas Thermometers. Temp. c. Constant pressure = 100 cm. Constant vol., p = 100 cm, t = OC He H N He H N 240 _ + 1.0 .. +0.02 +0.18 _ 200 +0.11 . + .26 + .01 + .06 ICO -f .04 + -03 +0.40 .OOO + .OIO +0.06 5 + .OI2 + .02 + .12 .000 + .004 + .02 + 25 .003 .003 .020 .000 .OOO .006 + 50 -003 -003 -025 .000 .OOO .OO6 + 75 -003 -003 .017 .000 .OOO .OO4 + 150 -j- 200 + -007 + .01 + .01 + .02 + .04 + .11 + .000 .000 + .001 + .002 + .01 + -04 + 45 +0.04 + -5 o.oo +O.OI + .2 + 1000 +0.3 + 1-7 -f- 7 + 15 +3- + 1-3 See also Appendix, p. 438. TABLE 207. Standard Points for the Calibration of Thermometers. Substance. Point. Atmos- phere. Crucible. Temperatures. Nitrogen Scale. Thermodynamic. Water Naphthalene Benzophenone Cadmium boiling, 760 mm. melting or solidifv. air air graphite IOO.OO 2 1 8.0 305-85l 320.8 - -O.I -O.2 100.00 218.0 305-9 320.9 Zinc < (t ' " " 4I9-3 - r-3 419.4 Sulphur Antimony Aluminum boiling, 760 mm. melting or solidify, solidification CO 2 graphite 444-4 5 : 629.8 - 658.5 - -O.I Io.5 -0.6 444.55 630.0 658.7 Silver Cold melting or solidify. ( U " H it 960.0 - 1062.4 - -0.7 1 0.8 vJOltl t( H II 1082.6 \ -0.8 Copper Li 2 SiO 8 melting air platinum I20I.O = - I.O Diopside, pure Nickel melting or solidify. H and N magnesia and Mg. aluminate I39I.2 - I 2.0 Cobalt i " magnesia 1489.8 - -2.0 Palladium < < air " 1549.2 - - 2.O Anorthite, pure melting " platinum 1549-5 ~ I 2.O Platinum 1 . ^B mOSOSSm :5-* M ^^^i * Thermoelectric extrapolation, t Optical extrapolation, m^v anH Vi3Soo) Sublimes. Potassium. . . 62.3 Cerium. . . . 640 Praseodymium. 940 (Muthmann- Weiss.) Chlorine. . . -101.5 (Olszewski.) Radium 700 Rhodium J 95o (Mendenhall-Inger- Chromium . 1615 B urgess- Wai ten- soll.) berg. Rubidium . . . 38 Cobalt 1480 B urgess- Walten- Ruthenium. . 2450? berg. Samarium. . . 1300-1400 (Muthmann- Weiss.) Scandium. . . ? Copper. . . . 1083 * 3 Mean, Holborn- Selenium. . . . 217-220 Day, Day- Silicon 1420 Adjusted. Clement. Silver 960.5 Adjusted. Erbium Sodium 97-5 Fluorine. . . -223 (Moissan-Dew- Strontium. . . Between Ca and Ba? ar.) [S 112. 8 Various Forms. See Sulphur. . j Sit 119. 2 Landolt-Bornstein. [S,-io6.8 Gallium . . . 30.1 Germanium 958 Tantalum. . . 2900 Adjusted from Waid- Gold 1063 . o Adjusted. ner-Burgess = 2910. Helium. . . . <-2 7 I Hydrogen. . -259 Tellurium. . . 452 Adjusted. Indium. . . . 155 (Thiel.) Thallium.... 302 Iodine 113 s R H n CTP * T T 1 T T v* T*Vi/-kWM w 7 AA7n rrpnHnror A ,5 o Ixcvllgc . 112 1 1 j) . A 11 Ori urn . . . . ^ I 7OO V. \\ til LLI1 UUI^. < >36o. Black, sublimes, Engel, C. R. 96. 1883. << 280-310 - Yellow, sublimes. Barium Boils in vacuo, Guntz, 1903. Bismuth 1420-1435 1430. Barus, 1894; Greenwood, 1. c. Boron Volatilizes without melting in electric arc. Bromine 59-63 61 . i Thorpe, 1880; van der Plaats, 1886. Cadmium 778. Berthelot, 1902. Caesium - 670. Rufr-Johannsen. Carbon - 3600. Conputed, Violle, C. R. 120. 1895. " Volatilizes without melting in electric oven. Moisson. Chlorine - -33-6 Regnault, 1863. Chromium - 2200. Greenwood, Ch. News, 100, 1909. Copper 2100-2310 2310. I.e. Fluorine Helium -I8 7 . -267. Moisson-Dewar, C. R. 136, 1903. Computed, Tracers Ch. News, 86, 1902. Hydrogen 252.5-252.8 252.6 Mean. Iodine >200. Iron _ 2450. Greenwood, 1. c. Krypton - 151-7 Ramsay, Ch. News, 87, 1903. Lead - I525- Greenwood, 1. c. Lithium - 1400. Ruff-Johannsen, Ch. Ber. 38, 1905. Magnesium 1 120. Greenwood, 1 c. Manganese - 1900. " " Mercury 357- Crafts; Regnault. Molybdenum - 3620. Langmuir, Mackay, Phys. Rev. 1914. Neon 239- Dewar, 1901. Nitrogen 195.7-194.4 IPS- Mean. Oxygen 182.5-182.9 182.7 " Ozone - 119. Troost. C. R. 126, 1898. Phosphorus 287-290 288. Platinum - 39io. Langmuir, Mackay, Phys. Rev. 1914. Potassium 667-757 712. Perman; Ruff-Johannsen. Rubidium 696. Ruff-Johannsen. Selenium 664-694 690. Silver 1955- Greenwood, 1. c. Sodium 742-757 750. Perman ; Ruff-Johannsen. Sulphur 444.7-445 444-7 Mean. Tellurium Deville-Troost, C. R. 91, 1880. Thallium _ 1280. v. Wartenberg, 25 Anorg. Ch. 56, 1908 Tin _ 2270. Greenwood, 1. c. Tungsten - 5830. Langmuir. Phys. Rev. 1913. Xenon - 109.1 Ramsay, Z. Phys, Ch. 44. 1903. Zinc 916-942 930. SMITHSONIAN TABLES. 200 TABLES 216-218. TABLE 216. Effect of Pressure on Melting Point. Substance. Melting point at i kg/sq. cm Highest experimental pressure: kg/sq. cm dt/dp at i kg/sq. cm. At (observed) for 1000 kg/sq. cm Reference F -38.85 en. 7 I2,OOO 2,800 O . 005 I I 0.0136 5-1* 13-8 I 2 \ ' 97.62 I2,OOO 0.00860 +12. 3t 4 Bi . . 271.0 I2,OOO -0.00342 -3- 5t- 4 Sn . . . 231 .9 2,000 0.00317 3- 1 ? 3 Bi Cd Pb 270.9 320.9 327.4 2,OOO 2,OOO 2,OOO -0.00344 o . 00609 0.00777 -3-44 6.09 7-77 3 3 3 * A / (observed) for 10,000 kg/sq. cm is 50.8. fNa melts at 177.5 at 12,000 kg/cm 2 ; K at 179-6; Bi at 218.3; Pb a obtains melting point for tungsten as follows: i atme, 3623 K- 8, 3594; 18, 3572; 28, 3564. Phys. Rev. 1917. References: (i) P. W. Bridgman, Proc. Am. Acad. 47, pp. 391-96, 416-19, 1911; (2) G. Tammann, Kristallisieren und Schmelzen, Leipzig, 1903, pp. 98-99; (3) J. Johnston and L. H. Adams, Am. J. Sci. 31, p. 516, 1911; (4) P. W. Bridgman, Phys. Rev. 6, i, 1915. A large number of organic substances, selected on account of their low melting points, have also been investigated: by Tammann, loc. cit.; G. A. Hulett, Z. physik. Chem. 28, p. 629, 1899; F. Korber, ibid., 82, p. 45, 1913; E. A. Block, ibid., 82, p. 403, 1913; Bridgman, Phys. Rev. 3, 126,1914; Pr. Am. Acad. 51, 55, 1915; 51,581,1916; 52,57,1916; 52,91,1916. The results for water are given in the following table. TABLE 217. Effect of Pressure on the Freezing Point of Water (Bridgman*). Pressure: t kg/sq. cm Freezing point. Phases in Equilibrium. I O.O Ice I liquid. I,OOO -8.8 Ice I liquid. 2,000 20. 15 Ice I liquid. 2,115 22. O Ice I ice III liquid (triple point). 3,000 18.40 Ice III liquid. 3,530 -17.0 Ice III ice V liquid (triple point). 4,000 -13-7 Ice V liquid. 6,000 - 1.6 Ice V liquid. 6,380 + 0.16 IceV iceVI- liquid (triple point). 8,000 12.8 IceVI liquid. 12,000 37-9 Ice VI liquid. 16,000 57-2 Ice VI liquid. 20,000 73-6 Ice VI liquid. * P. W. Bridgman, Proc. Am. Acad. 47, pp. 441-558, 1912. t i atm. - i . 033 kg/sq. cm. TABLE 218. Effect of Pressure on Boiling Point. * Metal. Pressure. C j Metal. Pressure. C Metal. Pressure. C Bi 10. 2 cm Hg. 1 200 Ag 26.3 cm Hg. 1780 Pb 20 . 6 cm Hg. 1410 Bi 25.7 cm Hg. 1310 Cu 10.0 cm Hg. 1980 Pb 6.3 atme. 1870 Bi 6.3 atme. 1740 Cu 25.7 cm Hg. 2180 Pb 11.7 atme. 2100 Bi 11.7 atme. i95o Sn 10. i cm Hg. 1970 Zn 11.7 atme. 1230 Bi 16.5 atme. 2060 Sn 26. 2 cm Hg. 2IOO Zn 21.5 atme. 1280 Ag 10.3 cm Hg. 1660 Pb 10.5 cm Hg. 1315 Zn 53 . o atme. 1510 * Greenwood, Pr. Roy. Soc., p. 483, 1910. SMITHSONIAN TABLES. TABLE 219. 2OT DENSITIES AND MELTING AND BOILING POINTS OF INORGANIC COMPOUNDS- Substance. Chemical formula. Density, about 20 C Melting point C Authority. 1 Boiling point Pres- sure mm Authority. 1 1 Aluminum chloride nitrate oxide Ammonia Ammonium nitrate sulphate . . . phosphite. . Antimony trichloride. . . pentachloride Arsenic trichloride Arsenic hydride A1C1 3 A1(N0 3 ) 3 + 9 H 2 A1 2 O 3 NH 3 NH 4 NO 3 (NH4) 2 S0 4 NH 4 H 2 P0 3 SbCl 3 SbCl 6 AsCla AsH 3 4.00 1.72 1.77 3-06 2-35 2.20 190. 72.8 2050. -75- I6 5 . 140. 123. 73- 3- -18. 113 ^ 2 28 3 4 5 ii 8 6 183.^ I34-* -33-5 210.* 150.* 223. 102. 130.2 CJ4. g 752 7 6o 7 6o 68 760 760 I 7 14 23 6 Barium chloride nitrate . . BaCl 2 Ba(NO 3 ) 2 3-86 ^. 24 960. C7C. ii 2 4 " perchlorate .... Bismuth trichloride .... Boric acid Ba(C10 4 ) 2 BiCl 3 H 3 BO 3 4-56 i .46 55- 232-5 185. 10 440. 760 " anhydride Borax (sodium borate).. Cadmium chloride B 2 3 Na 2 B 4 O 7 CdCl 2 1.79 2.36 4O^ 577- 741- 560. 27 2< ooo =*= Q " nitrate Calcium chloride chloride .... Cd(NO 3 ) 2 + 4H 2 O CaCl 2 CaCl 2 + 6H 2 O 2.45 2.26 1.68 59-5 774-o 29. 6 2 132. 760 4 " nitrate Ca(NO 3 ) 2 2.36 499- 24 , " nitrate. . Ca(NO 3 ) 2 + 4H 2 O 1.82 42 .3 ?6 132.* 11 oxide CaO 2 . 7 2570. 28 Carbon tetrachloride . . . trichloride " monoxide ecu C 2 C1 6 CO 1-59 1-63 -24. 184. 207. 22 6 76.7 190. 760 760 23 6 " dioxide CO 2 i ^6 C7. 7 -80. subl. disulphide . . . CS 2 i 26 no. 13 46. 2 760 Chloric (per) acid Chlorine dioxide HC10 4 + H 2 O C1O 2 1.8* 5- -76. 15 3 9-9 731 21 Chrome alum KCr(SO 4 ) 2 + i2H 2 O i 83 89. 16 nitrate Cr 2 (NO 3 ) 6 + i8H 2 O 37- 2 I7O. 760 2 Chromium oxide Cobalt sulphate Cupric chloride Cr 2 3 CoS0 4 CuCl 2 5-04 3-53 2 Q^ 1990. 97- 498. 28 16 9 880.* * Cuprous chloride .... Cu 2 Cl 2 7 7 421 . I OOO =*= 760 9 Cupric nitrate Cu(NO 3 ) 2 + 3H 2 O 2 H.> 80. .613 8l. -85. Villard. Allylene Ethylacetylene . . . v_x 2 * i*2 C 3 H 4 C 4 H 6 1 10. 130. -23.5 +8. Bruylants, Kutsche- roff, and others. Propylacetylene . . . C 6 H 8 _ _ - 48.-50. Bruylants, Taworski. Butylacetylene . . . Oenanthylidene . CeHio CyH^ _ _ " 68.-70. loo.-ior. Taworski. Beilstein, and oth- ers. ' Caprylidene .... C 8 Hi 4 0. 0.771 - I33--J34- Behal. Undecylidene .... CnHao .- 2IO.-2I5- Bruylants. Dodecylidene . . . CigHaa 9- .810 9- 105.* Krafft. Tetradecylidene . Hexadecylidene . . . Ci 4 H 26 CieH 3 o + 6.5 20. .806 .804 + 6-5 20. 160* a Octadecylidene . . . Ci 8 H 34 3- .802 30- 184.* " (d) Monatomic alcohols : C, z H 2W _j_ I OH. Methyl alcohol . . . CH 3 OH o. 0.8 1 2 97- 66. Ethyl alcohol .... C 2 H 5 OH 0. .806 -114. 78. Propyl alcohol . . . C 3 H 7 OH o. .817 -127. 97- From Zander, " Lieb. Butyl alcohol .... C 4 H 9 OH o. .823 117. Ann." vol. 224, p. 85, Amyl alcohol .... C 6 H U OH o. .829 - 138. and Krafft, " Ber." Hexyl alcohol . . . C 6 H 13 OH 0. 833 : 57- vol. 16, 1714, Heptyl alcohol . . . C 7 H 15 OH o. .836 l~36. 176. " 19, 2221, ( )ctyl alcohol .... C 8 H 17 OH o. 839 ' 18. J 95- ' 23, 2360, Nonyl alcohol . . . C 9 H 19 OH o. .842 5- 213. and also Wroblew- Decyl alcohol . . . CioHaiOH + 7- 839 + 7- 231. . ski and Olszewski, Dodecyl alcohol . . . Ci 2 H 2 5OH 24. .831 24. 143* " Monatshefte," Tetradecyl alcohol . . Ci 4 H 2 gOH 38- .824 38- 167* vol. 4, p. 338. Hexadecyl alcohol . . Ci C H 33 OH 5- .818 5- 190.* Octadecyl alcohol . . Ci 8 H 37 OH 59- .813 59- 211.* (e) Alcoholic ethers : C W H 2JI+2 O. Dimethyl ether . . . C 2 H C O _ _ _ -2 3 .6 Erlenmeyer, Kreich- baumer. Diethyl ether .... C 4 H 10 4- Q-73 1 117 + 34-6 Regnault, Olszewski. Dipropyl ether . . . C 6 H 14 0. 763 90.7 Zander and others. 1 >i-iso-propyl ether . . C 6 H 14 o. 743 _ 69. " Di-n-butyl ether . . . C 8 H 18 0. .784 - 141. Lieben, Rossi, and others. c-butvl ether . . C 8 H 18 21. .756 _ 121. Kessel. I)i-iso-butyl " . . C 8 H 18 T 5- .762 _ 122. Reboul. I)i-iso-amyl " . . CioHaaO 0. 799 - 1 70.-I 75. Wurtz. Di-sec-hexyl " . . C 12 H 20 O - - 203--208. Erlenmeyer and Wanklyn. I)i-norm-octyl " . . C 16 H 84 17- .805 - 280.-282. Moslinger. (f) Ethyl ethers : C W H 2W+2 O. Ethyl-methyl ether . . C 8 H 8 0. 0.725 _ II. Wurtz, Williamson. " propyl ' . . < r,H,,<> 20. -739 _ 63--64- Chancel, Briihl. " is<>-prnpyl ether . C C H,,0 o. 745 _ 54- Markownikow. " norm-butyl ether C,H,;O o. .769 _ 92. Lieben, Rossi. " iso-butyl ether . CeH l4 75 1 78.-8o. Wurtz. " iso-amyl ether C 7 Hi6O 18. .764 _ 112. Williamson and others. " norm-hexyl ether " norm-heptyl ether C 8 H 18 CfHsoO 1 6. .790 - '34--I37- 165. Lieben, Janeczek. Cross. " norm-octy! ether * jiI I'jsO 17- 794 1 82.-! 84. Moslinger. * Boilingpofat (inder 15 mm. pressure. t Liquid at n. C. and 180 atmospheres' pressure (Cailletet). SMITHSONIAN TABLES. 205 TABLE 220 (concluded). DENSITIES AND MELTING AND BOILING POINTS OF SOME ORGANIC COMPOUNDS. (g) MISCELLANEOUS. Substance Chemical formula. Density and temperature. Melting point C BoilinR point C Authority. Acetic acid CH 3 COOH 1.115 o I6. 7 118.5 Young, '09 Acetone CH 3 COCH 3 0.812 o -94.6 56.1 Aldehyde C 2 H 4 O 0.806 o I2O. +20. 8 Aniline CeHsNH, i . 038 o -8. 183.9 Beeswax 0.96 =fc 62. Benzoic acid C 7 H 6 2 I-2Q3 4 121. 249. Benzene C 6 H 6 o 870 20 ? 48 80.2 Richards Benzophenone . . . (C 6 H 5 ) 2 CO w ^ / V i . 090 50 O T'*-' 48- 305-9 Holborn- Henning Butter 0.86-7 7O =*= Camphor C 10 H 16 O 0.99 10 o v 176. 209. Carbolic acid .... C 6 H 5 OH 1 . 060 2 1 43- 182. Carbon bisulphide CS 2 1.292 o -no. 46. 2 " tetrachlor- ide . CCL, 1.582 21 T.Q 76 7 Young Chlorbenzene .... C 6 H 5 C1 I. Ill 15 O ' -40. / w * / 132. V """O Chloroform CHC1 3 12^7 O -65 61.2 Cyanogen . . . C 2 N 2 / 3<. 21 . Ethyl bromide . . . C 2 H 5 Br i-45 15 OO -117. 38.4 chloride . . . CoH 5 Cl 0.918 8 -141 .6 14- " ether C 4 H 10 0.736 o -118. 34-6 " iodide C 2 H 5 I 1-944 14 72. Formic acid HCOOH i . 242 o 8.6 100.8 Gasolene 0.68 70-90 Glucose CHO(HCOH) 4 CH 2 OH 1-56 146. Glycerine C 3 H 8 3 i . 269 o 20. 290. lodof orm CHI 3 4.01 25 119. Lard 29 Methyl chloride. . CH 3 C1 0.992 -24 -103.6 -24.1 Methyl iodide CH 3 I 2.285 15 -6 4 . 42.3 Naphthalene .... C 6 H 4 -C4H 4 1-152 15 80. 218. Holborn- Henning Nitrobenzene .... C 6 H 5 2 N I. 212 7.5 5- 211. Nitroglycerine . . . C 3 H 5 N 3 9 I. 60 Olive oil 0.92 20 =*= 300 * Oxalic acid C 2 H 2 4 - 2 H 2 1.68 I9O. 1 Paraffin wax, soft. 38-52 350-390 " hard 52-56 390-430 Pyrogallol C 6 H 3 (OH) 3 i . 46 40 133- 293- Spermaceti o o"; i^ 45 =t Starch CeHioOs vo o 1.56 none Sugar, cane CwHaOu 1.588 20 160. Stearine (C 1S H 35 2 ) 3 C 3 H 6 0.925 65 7i- Tallow, beef 0.94 15 27-38 " mutton . . 0-94 15 32-41 Tartaric acid .... C 4 H 6 6 1-754 170. Toluene CcHsCHs 0.882 oo -92. 110.31 Richards Xylene (o) C 6 H 4 (CH 3 ) 2 0.863 20 -28. 142. " (m) C 6 H 4 (CH 3 ) 2 0.864 20 54- 140. " (P). C 6 H 4 (CH 3 ) 2 0.861 20 J 5- I 3 8. SMITHSONIAN TABLES- 206 TABLES 221-223. MELTING-POINTS, TABLE 221. Melting-point of Mixtures. Metals. Melting-points, C. Reference. 1 Percentage of metal in second column. o% 10% 30% 30% 40% 50% 60% 70% 80% 90% 100% Pb. Sn. 326 295 2 7 6 262 240 220 190 I8 5 200 216 232 i Bi. 322 290 179 '45 126 168 205 268 7 Te. 322 710 790 880 917 760 600 480 -410 425 446 8 Ag. Ni. 328 460 360 545 420 590 400 620 370 650 330 70S 290 775 250 8 4 2OO 90S 130 959 96 9 Cu. 326 870 920 925 945 95 955 985 1005 1020 1084 2 Sb. 326 250 275 330 395 440 490 525 560 600 632 16 Al. Sb. 650 750 840 925 945 950 970 1000 1040 1010 632 17 Cu. 650 630 600 560 540 580 610 755 930 1055 1084 18 Au. 655 675 740 800 855 9'5 970 1025 1055 675 1062 10 Ag. 650 625 615 600 590 5 8o 575 570 650 750 954 1 7 Zn. 654 640 620 600 580 560 530 510 475 425 419 ii Fe. 653 860 1015 1 1 10 "45 "45 1220 1315 1425 1500 'SIS 3 Sn. 650 645 ' 635 625 620 605 590 57 54o 232 '7 Sb. Bi. 632 610 590 575 555 54 5 20 470 405 330 268 16 Ag. 630 595 57 545 520 500 505 545 680 850 959 9 Sn. 622 600 570 525 480 430 395 350 310 255 232 19 Zn. 632 555 S'o 540 570 565 540 525 S'o 470 419 17 Ni. Sn. '455 1380 1290 1200 "35 1290 1305 1230 1060 800 232 17 Na. Bi. 96 425 520 590 645 690 720 73 7'5 570 268 13 Cd. 96 125 185 245 285 325 33 34 360 390 322 13 Cd. Ag. 322 420 520 610 700 760 805 850 895 940 954 I 7 XI. 321 300 285 270 262 258 245 230 210 235 302 M Zn. 322 280 270 295 3*3 327 34 355 370 390 419 ii Au. Cu. 1063 910 890 895 95 925 975 IOOO IO25 1060 1084 4 Ag. 1064 1062 1061 1058 1049 1039 1025 1006 982 963 5 Pt 1075 1125 1 100 1250 1320 1380 1455 '53 1610 1685 1775 20 K. Na. 62 '7-5 IO 3-5 5 ii 26 4 1 58 77 97-5 15 Sf Cu Ni. 62.5 1080 '33 1180 .65 188 205 9 215 I IO 220 135 240 162 280 265 305 301 13 Ag! 1082 1035 1240 990 1290 945 I32O 910 870 8 3 788 814 875 I 455 9 6o * 7 9 Sn. 1084 1005 890 755 725 680 630 580 53 440 232 12 Zn. 1084 1040 995 930 900 880 820 780 700 580 419 6 Ag. Zn. 959 850 755 75 690 660 630 610 57 505 419 1 1 Sn. 959 870 630 55 495 450 420 375 300 232 9 Na. Hg. 96.5 90 80 70 60 45 22 55 95 215 13 1 Means, Landolt-Bornstein-Roth Tabellen. 2 Friedrich-Leroux, Metal. 4, 1907. 3 Gwyer, Zs. Anorg:. Ch. 57, 1908. 4 Means, L.-B.-R. Tabellen. 5 Roberts- Austen Cliem. News, 87, 2, 1903. 6 Shepherd J. ph. ch. 8, 1904. 7 Kapp, Diss., Konigsberg, 1901. 8 Fay and Gilson, Trans. Am. Inst. Min. Eng. Nov. 9 Heycock and Neville, Phil. Trans. iSgA, 1897. 10 " " I94A, 201, 1900. ii Heycock and Neville, J. Chem. Soc. 71, 1897. Phil. Trans. 202A, i, 1903. 13 Kurnakow, Z. Anorg. Chem. 23, 439, 1900. 14 30, 86, 1902. 15 30, 109, 1902. 16 Roland-Gosselin, Bui. Soc. d'Encour. (5) i, 1896. 17 Gautier, " " " (5) i, " 18 Le Chatelier, " " " (4) 10, 573, 1895. 19 Reinders, Z. Anorg. Chem. 25, 113, 1896. 20 Erhaid and Schertel, Jahrb. Berg-u. Hiittenw- Sachsen. 1879, 17. TABLE 222. Alloy ol Lead, Tin, and Bismuth. Per cent. Lead . . . Tin Bismuth. . . . 32.0 '5-5 52-5 25.8 .9.8 54-4 25.0 5-o 60.0 43-o 14.0 43-o 33-3 33-3 33-3 10.7 23.1 66.2 50.0 33-o 17.0 35-8 52.1 12. 1 20. o 60.0 20.0 70.9 9.1 20.0 Solidification at 96 IOlO 2 5 -- 128 145 148 161 181 l82 234 Charpy, Soc. d'Encours, Paris, 1901. TABLE 223. - Low Melting-point Alloy. I J er cent Cadmium .... Tin .... 10.8 IO.2 I 4 .8 13-1 17 8 6.2 7-' 6-7 Lead . . Bismuth .... 50.1 50-4 52.2 48.8 34-4 50.0 39-7 53-2 43-4 49-9 Solidification at 65-5 67-5 68.5 68.5 76.5 89-5 95 Drewitz, Diss. Rostock, 1902. All compiled from Landolt-Bornstein-Meyerhoffer's Physikalisch-chemische Tabellen. SMITHSONIAN TABLES. TABLE 224. 2.OJ TRANSFORMATION AND MELTING TEMPERATURES OF LIME-ALUMINA- SILICA COMPOUNDS AND EUTECTIC MIXTURES. The majority of these determinations are by G. A. Rankin. (Part unpublished.) Substance. CaSi0 3 . CaSiO 3 . Ca 2 Si0 4 . Ca 3 Si 2 O 7 . Ca 3 SiO 5 . Ca 3 Al 2 6 . Ca 5 Al 6 Oi4 CaAL0 4 . Al 2 Si0 5 . CaAl 2 Si 2 O 8 Ca 2 A] 2 SiO7 Ca 3 Al 2 SiO 8 CaO A1 2 O 3 SiO 2 48.2 48.2 51.8 51.8 35- 35- 35- 41.8 73.6 26.4 62.2 37-8 47-8 52.2 - 354 64.6 2 t 8 Hi 36.6 20. i 40.8 37.2 5-9 3-9 37-i 43-3 22.0 18.2 Transformation. Melting a to ft and reverse Melting 7 to )8 and reverse & to a and reverse Dissociation into Ca 2 SiO 4 and liquid Dissociation into Ca 2 SiO 4 and CaO Dissociation into CaO and liquid Melting Melting Melting Melting Melting Melting Dissociation into Ca 2 SiO 4 + Ca 2 Al 2 SiO 7 and liquid . . Temp. I 540 2 I2OO -\-2 2130 -4^10 675 5 I42O -j-2 1475 5 1335 5 EUTECTICS. EUTECTICS. Crystalline Phases. %CaO A1 2 3 Si0 2 Melting Temp. Crystalline Phases. %CaO A1 2 O 3 SiO 2 Meltin Temp. CaSiO 3 ,SiO 2 Ca,SiO 3 j 3CaO,2SiO 2 I Ca,SiO 4 j CaO. j Al 2 Si0 5) SiO 2 Al 2 SiO 5 ,Al 2 O 3 CaAl 2 Si 2 O 8 1 CaSiO 3 ] CaAl 2 Si 2 O 8 1 Si0 2 j CaAl 2 Si 2 O 8 i SiO 2 ,CaSiO 3 \ Ca 2 Al 2 SiO 7 i Ca 2 Si0 4 A1 2 3 CaAl 2 Si 2 O 8 j CaAl 2 Si 2 O 8 I Al 2 Si0 5 ,SiO 2 j Ca 2 Al 2 SiO 7 i Ca 3 AlioOi 8 J CaoAl 2 SiO 7 j CaAl 2 4 Ca 2 Al 2 SiO 7 CaAl 2 O 4 Ca 3 Al 10 18 CaAl 2 Si 2 O 8 I Ca 2 Al 2 Si0 7 j Ca 2 Al 2 SiO 7 ; Ca 3 Si 2 7 CaSi0 3 Ca 2 Al 2 Si0 7 CaSi0 3 j 37- 54-5 67.5 - - '3- 64. 34-i 10.5 23.2 49.6 !9-3 9.8 35- 37-8 37-5 30.2 47.2 45-7 18.6 19-5 14.8 23-7 39-3 19.8 50.8 5 2 -9 S3- 2 36.8 1 1.8 13.2 63- 45-5 32-5 87. 36. 47-3 70. 62. 26.7 41.4 70.4 14.2 9-3 9-3 33- 41. 41.1 1436 2065^ 1610 1810 1299 1359 1165 '545 1547 1345 '55 2 1512 1505 1385 1310 1316 CaAl 2 Si 2 O 8 Ca 2 Al 2 SiO 7 CaSiO 3 CaAl 2 Si 2 O 8 Ca 2 Al 2 SiO 7 A1 2 3 Ca 2 SiO 4 a 2 SiO 4 ) aAl 2 O 4 a 5 A! 6 Oi 4 ) 38. 20. 42. 2 9-2 39- 3 1 - 8 49-5 43-7 6.8 1265 1380 1335 QUINTUPLE POINTS. Ca 2 Al 2 Si0 7 Ca 3 Si0 7 Ca 2 SiO 4 Ca 2 Al 2 SiO 7 Ca 2 Si0 4 CaAl 2 O 4 CaAl 2 Si 2 O 8 A1 2 3 Al 2 SiO 6 48.2 11.9 39.9 Ca 2 Al 2 SiO 7 A1 2 3 48.3 42. 9-7 15-6 36-5 47-9 31.2 44.5 24.3 1335 1512 1475 QUADRUPLE POINTS. 3CaO.2SiO 2 2CaO.Si0 2 55-5 44-5 H75 The accuracy of the melting-points is 5 to 10 units. Geophysical Laboratory. See also Day and Sosman, Am. J. of Sc. xxxi, p. 341, ign. SMITHSONIAN TABLES. 2O8 TABLE 225. LOWERING OF FREEZING-POINTS BY SALTS IN SOLUTION. In the first column is given the number of gram-molecules (anhydrous) dissolved in 1000 grams of water; the second contains the molecular lowering of the freezing-point ; the freezing-point is therefore the product of these two columns. After the chemical formula is given the molecular weight, then a reference number. rt M 13 M -<* i ** M g. mol. looo g. H,O Molecul Lowerii; g. mol. . looog H 2 O Molecul Lowerir g. mol. looo g. H 2 O 1! g. mol. 1! looo g. H 2 O Pb(N0 3 ).>, 331-0: I, 2. 0.0500 347 0.4978 2.02 MgCU, 95.26: 6, 4- 0.000362 5-5 .1000 3-42 .8112 2.OI O.OIOO 5 fl .001204 5-3 .2000 3-32 I-5233 2.28 .0500 4-98 .002805 5-J7 .500 3-26 BaCL,, 208.3: 3,6, 13. .1500 4-96 .005570 4 97 1. 000 3-14 0".00200 5-5 .3000 5.186 01737 4.69 LiNO ;( , 69.07 : 9. .00498 5-2 .6099 5-^9 5 OI 5 2.99 0.0398 3-4 .OIOO KC1, 74.60: 9, 17-19. Ba(NO ; ,),, 261.5 : .1671 3-35 .O2OO 4-95 0.02910 3-54 0.000383 X> 5-6 .4728 3-35 .04805 4.80 .05845 3-46 .001259 5.28 1.0164 3-49 .100 4.69 .112 3-43 .002681 5-23 A1 2 (S0 4 ) 3 , 342-4 : 10. .2OO 4.66 3139 341 .005422 0.0131 5-6 .500 4.82 .476 3-37 .008352 5.04 .0261 4-9 .586 5-03 I.OOO 3.286 Cd(N0 3 ) 2 , 236.5: 3. .0543 4-5 750 5.21 1.989 3-25 0.00298 .00689 5-25 .217 4-03 3-83 CdCl,, 183.3: 3,14- 0.00299 5.0 3.269 NaCl, 58.50: 3, 20 3-25 12, 16. .01997 .04873 5.18 5-15 CdS0 4 , 208.5: i, ii. 0.000704 3.35 .00690 .0200 4.8 4.64 0.00399 .OIOOO 3-7 AgNO 3 , 167.0 : 4, 5- .002685 3-05 4.11 .0221 3-55 0.1506 3-3f .01151 2.69 .0818 3.93 04949 3-5 1 .5001 2.96 .03120 2.42 .214 3-39 .I08l 348 .8645 2.87 1473 2 538 9 5-30 5-5 0.00992 0455 3-7 3-5 750 2.87 .000843 3-'5 CaCL, m.o: 5, 13-16. .09952 3-53 1. 000 2.66 .002279 3-3 O.OIOO e.i .2474 3-5 NaN0 3 , 85.09: 2,6,7 i .006670 2-79 .05028 4-85 .5012 3.61 O.OIOO 3-6 j .01463 2.59 .1006 4-79 7939 3-7 1 .0250 3-46 .1051 2.28. 577 5-33 BaBr 2 , 297.3: , 4 . .0500 3-44 2074 1.95 .946 5-3 O.I 00 5- 10 .2000 3-345 .4043 1.84 2.432 8.2 .150 4.9 .500 3-24 .8898 1.76 11.5 .2OO 5.00 5o>5 3-30 i MgSO 4 , 120.4: i, 4, n. 3-829 14.4 50 5.18 1. 000 3.1 5 0.00067 5 3-29 0.0478 S- 2 AlBr.,, 267.0: 9. 1.0030 3-03 '. .002381 3.10 153 4.91 0.0078 1.4 NH 4 NO 3 , 80.11 : 6, 8. \ .01263 2.72 33 1 5-i5 0559 1.2 O.OIOO .0250 3-6 : 3-50 ; .0580 .2104 2.65 2-23 .612 .998 5-47 6-34 .1971 4355 1.07 1.07 i Hausrath, Ann. Phys. 9, 1902. ii Kahlenberg, . Phys. Ch. <;, 1901. 2 Leblanc-Noyes, Z. Phys. Ch. 6, 1890. 12 Abegg, Z. Phys. Ch. 20, 1896." i Jones, Z. Phys. Ch. ii, 1893. 4 Raoult, Z. Phys. Ch. 2, 1888. 5 Arrhenius, Z. Phys. Ch. 2, 1888. 6 Loomis. Wk-d. Ann. 57, 1806. 7 Jones, Am. Chem. J. 27, 1902- 8 Jones-Caldwell, Am. Chem. J. 25, 1901 9 Biltz, Z. Phys. Ch. 40, 1^2. 10 Jones-Mackay, Am. Chem. J. 19, '897. 13 Jones-Getman, Am. Ch. J. 27, 1902. 14 Jones-Chambers, Am. Ch. J. 23, 1900. 15 Loomis, Wied. Ann. 60, 1897. 16 Roozeboom, Z. Phys. Ch. 4, 1889. 17 Raotilt, Z. Phys. Ch. 27, 1898. 18 Roloff, Z. Phys. Ch. 18, 1895. iO Kistiakowsky, Z. Phys. Ch. 6, 1890. _ . ,, . 20 Loomis, \Vied. Ann. 51, 1894. Compiled from Landolt-Bomstein-Meyerhoffer's Physikalisch-chemische Tabellen. SMITHSONIAN TABLES- TABLE 225 (continued). 2O9 LOWERING OF FREEZING-POINTS BY SALTS IN SOLUTION (continued). U JS 5* *" M ~^~ mol. "s -r g. mol. 3.H U g. mol "g-c g. mol. *~ w h looo g. H,O 11 looo g. H 2 O II 1000 g. H 2 O IJ 1000 g. H,0 Jj CdBr 2 , 272.3 : 3, 14. KOH, 56.16: i, 15, 23. Na.,SiO 3 , 122.5: 15. 0.472 2.20 0.00324 5 fl 0.00352 0.01052 6.4 944 2.27 .00718 4.6 .00770 3-59 .05239 5-86 1.620 2.60 .03627 .0719 3-84 3-39 .O2OO2 .05006 3-44 3-43 .1048 .2099 5.28 4-66 (COOH) 2 , 90.02 : O.OIOO2 4, '5- 3-3 .1122 ' 3.18 .1001 3-42 5233 3-99 .02005 3-*9 .220 2.96 .2003 3 - 4 2 4 HC1, 36.46 : .05019 3.03 440 2.76 230 3-5 '-3, 6, 13 18, 22. s .1006 281 .800 CuBr,, 223.5 : 9- 0.0242 2-59 - T O -465 3-57 CH ;J OH, 32.03 : 24, 25. o.oioo 1.8 0.00305 .00695 .OIOO *P 3-6 .2022 .366 .648 "j 2.64 2.56 2.T. .0817 5.1 2255 5.27 .6003 5.89 CaBr.,, 200.0: 14. 0.0871 5.1 .1742 5.18 .3484 5.30 .5226 5.64 MgBr.,, 184.28 : 14. 0.0517 5.4 .103 5.16 .207 5.26 .0301 .2018 1.046 3-4i 6.200 C 2 H 5 OH, 46.04: I, 12, 17 O.OOO4O2 .004993 .0100 .02892 .0705 .1292 1.82 1.811 1.86 1.88 1.944 24-27 i67 J.Si 1.707 1.85 1.829 .01703 .0500 .1025 .2000 .3000 .464 .516 1.003 1.032 1.500 2.000 2.U5 3-OOO 3-59 3-59 3-57 3.612 3-68 3-79 3-95 4.10 4.42 4-97 4-52 6.03 C 3 H 5 (OH) 3 , 92.06 O.O2OO .I008 .2031 535 2.40 5-24 (C 2 H 5 ) 2 0, 74-08: O.OIOO .0201 .1011 .2038 J 24,25. 1.86 1.86 1.85 1.91 1.98 2.13 '1.6' 1.67 1.72 1.702 5 T 7 KBr, 119.1 : 9, 21. 0.0305 vo 3.61 .2024 5252 1.0891 1.832 1.834 1.826 3-053 4.065 4^57 4.90 5-67 6.19 Dextrose, 180.1 : 24, 30. 0.0198 1.84 .0470 1.85 .1850 .6801 .250 500 3-49 3-30 3-78 3.56 1.760 3.901 7.91 1 1. 1 1 1.83 1.92 2.O2 2.12 HN0 3 , 63.05 : 3, 13, 15. 0.02004 3-55 05015 3-50 .0510 1.71 .1326 1.87 .4076 . 1.894 I.IO2 1.921 Levulose, 180.1 : 24, 25. Cdlo, 366.1 : 3, 5, 22. 18.76 I.8l .1004 3.48 O.O2OI 1.87 O.OO2 1 .^S'-/' 4-5 0.0173 1. 80 .1059 3-53 .2050 1.871 .00020 _ /- 4.0 .0778 1.79 .2015 3-45 554 2.01 .O2O62 .04857 3-52 2.70 K 2 CO 3 , 138.30 : 6 O.OIOO 250 .500 3-50 3.62 1.384 2.77 2.32 3-04 .1360 2-35 .0200 4-93 I.OOO 3.80 Ci 2 H 22 O n , 342.2: i 24, 26. 333 2.13 .0500 4.71 2.000 4.17 0.000332 1.90 .684 2.23 .100 4-54 3-000 4.64 .001410 1.87 .888 2.51 .200 4-39 H 3 P0 2 , 66.0: 29. .009978 1.86 KI, 166.0 : 9, 2. Na 2 CO 3 , 106.10 : 6 0.1200 2.90 .O2OI i.SS 1 0.0651 3-5 O.OIOO 5- T .2542 2.75 .1305 1.88 .2782 .6030 3-50 3-42 .O2OO .0500 4-93 4.64 I.07I 2-59 2-45 H 2 S0 4 , 98.08 : 13, 20, 31-3 V 1.003 3-37 .IOOO 4.42 H 8 P0 8 ,8a.o: 4,5. O.OO46I 4.8 SrI 2 , 341.3: 22. .2OOO 4.17 0.0745 3.0 .OIOO 4.49 0.054 5 >l0 Na.,SO 3 , 126.2 : 28 .1241 2.8 .O2OO 4-32 .108 S- 2 0.1044 4.51 .2482 2.6 .0461 4.10 .216 5-35 3397 3-74 I.OO 2.39 .100 3-96 327 5-52 .7080 3-38 H 3 PO, 98.0 : 6, 22. .2OO 3-85 NaOH, 40.06: 15. Na,HPO 4 , 142.1: 22, 29. O.OIOO 2.8 .400 3-98 O.O2OO2 3-45 "o.oiooi 5-o .0200 2.68 I.OOO 4.19 .05005 3-45 .02003 4.84 .0500 2.49 1.500 4-96 .IOOI 3-41 .05008 4.60 .1000 2.36 2.000 5.65 .2000 3-407 .1002 4-34 .2000 2.25 2.500 6-53 1-20 See page 217. 21 Sherrill, Z. Phys. Ch. 43, 1903. 22 Chambers-Frazer, Am. Ch. J. 23, 1000. 23 Noyes-Whitney, Z. Phys. Ch. 15, 1894. 24 Loomis, Z. Phys. Ch. 32, 1900. 25 Abegg, Z. Phys. Ch. 15, 1894. 26 Nernst-Abegg, Z. Phys. Ch. 15, 1894. SMITHSONIAN TABLES. 27 Pictet-Altschul, Z. Phys. Ch. 16, 1895. 28 Barth, Z. Phys. Ch. 9, 1892. 29 Petersen, Z. Phys. Ch. n, 1893. 30 Roth, Z. Phys. Ch. 43, 1903. 31 Wildermann, Z. Phys. Ch. 15, 1894. 32 Jones-Carroll, Am. Ch. J. 28, 1902. 33 Jones-Murray, Am. Ch. J. 30, 1903. 210 TABLE 226. RISE OF BOILING-POINT PRODUCED BY SALTS DISSOLVED IN WATER.* This table gives the number of grams of the salt which, when dissolved in 100 grams of water, will raise the boil- ing-point by the amount stated in the headings of the different columns. The pressure is supposed to be 76 centimeters. Salt. 1C. 2 3 4 5 7 10 15 20 25 BaCl 2 +2H 2 O . i 5.0 3 1 - 1 47-3 63.5 (71-6 g ives 4 5 rise of temp . CaCl 2 0.0 "5 16.5 2I.O 25.0 32.0 4i-5 55-5 69.0 84-5 Ca(N0 3 ) 2 + 2H 2 . I2.O 25-5 39-5 53-5 68.5 IOI.O 152-5 240.0 331-5 443-5 KOH 4-7 9-3 17.8 17.4 20.5 26.4 34-5 47-o 57-5 67-3 KC>H 3 O 2 . 6.0 I2.O 1 8.0 24-5 31.0 44.0 63-5 98.0 134.0 I7I-5 KC1 9 .2 I6. 7 23-4 29.9 36.2 48.4 (57.4 gives a rise of 8. 5) K 2 C0 3 "5 22. 5 32.0 40.0 47-5 60.5 78.5 W3-S 127-5 I 5 2 -5 KClOg 13.2 2 7 .8 44.6 62.2 KI . 15.0 3O.O 45-o 60.0 74.0 99-5 134. 185.0 (220 gives i8.5) KXO 3 15.2 3 I.O 47-5 64-5 82.0 120.5 188.5 338-5 K 2 C 4 H 4 6 + |H 2 . 18.0 36.0 S4-o 72.0 90.0 126.5 182.0 284.0 K.\uC 4 H 4 O 6 . 17-3 34-5 Si-3 68.1 84.8 119.0 171.0 272.5 390.0 510-0 KNaC 4 H 4 O 6 + 4H 2 O 25.0 53-5 84.0 118.0 157-0 266.0 554-0 SS'o.o LiCl .... 3-5 7.0 IO.O 12.5 15.0 20.0 26.0 35-o 42-5 50.0 LiCl + 2H 2 O . 6.5 13.0 19-5 26.0 32.0 44-o 62.0 92.0 123.0 160.5 MgCl 2 -f 6H 2 O . MgSO 4 +7H 2 O II.O 4i-5 22.O 87.5 138.0 44.0 196.0 55- 262.0 77.0 I IO.O 170.0 241.0 334-5 NaOH 4-3 8.0 "3 14-3 17.0 22.4 30.0 41.0 51.0 60. i NaCl .... 6.6 12.4 17.2 21.5 25-5 33-5 (40.7 gives 8.8rise) NaNO 3 9.0 18.5 28.0 38.0 48.0 68.0 99-5 156.0 222.O NaC 2 H 3 2 -f 3H 2 O . 14.9 30.0 46.1 62.5 79-7 118.1 194.0 480.0 6250.0 Na 2 S 2 O 3 . 14.0 27.0 39-o 49-5 59-o 77.0 104.0 152.0 214.5 311.0 Na 2 HP0 4 . 17.2 34-4 5'-4 68.4 85-3 Na 2 C 4 H 4 6 + 2H 2 O . 21.4 44-4 68.2 93-9 121.3 183.0 (237-3 gives 8.4 rise) Na 2 S 2 O 3 + 5H 2 O 23.8 50.0 78.6 108.1 139-3 216.0 400.0 1765.0 Na 2 C0 3 -f ioH 2 . 34-i 86.7 177.6 3 6 9-4 1052.9 Na 2 B 4 O 7 + ioH 2 O . 39- 93- 2 254.2 898.5 (5555-5 gives 4-5 rise) NH 4 C1 6.5 12.8 19.0 24.7 29.7 39-6 56.2 88.5 NH 4 NO 3 . IO.O 2O.O 30.0 41.0 52-0 74-o 108.0 172.0 248.0 337-o (NH 4 ) 2 SO 4 154 3 O.I 44.2 58.0 71.8 99-i (115.3 gives 108.2) SrCl 2 + 6H 2 O . Sr(\0 3 ) 2 . . . 20.0 24.0 4O.O 45- 60.0 63.6 81.0 81.4 103.0 97.6 150.0 234.0 524.0 C 4 H 6 6 . . . r.,ll.-0 4 4- 2lI 2 C 6 H 8 7 4- H 2 17.0 I9.O 29.0 34-4 40.0 58.0 52.0 62.0 87.0 70.0 86.0 116.0 87.0 II2.O 145.0 123.0 169.0 208.0 177.0 262.0 320.0 272.0 540.0 553-o 374-0 1316.0 952-0 484.0 50000.0 Salt. 40 60 80 100 120 140 160 180 200 240 CaCl 2 . . . 137.5 222.O 314.0 KOH . . . 92.5 I2I.7 152.6 185.0 219.8 263.1 312.5 375.0 444.4 623.0 NaOH . . 93.5 NH 4 NO a . . 682.0 1 50.8 230.0 I37O.O 24OO.O 345-c 4Q9Q.O 526.3 8C47.0 800.0 00 J 333-o 2353.0 6452.0 - C 4 H 6 O fl . . 980.0 3774-0 infinity gives 170) * Compiled from a paper by Gerlach, " Zeit. f. Anal. Chem." vol. 26. SMITHSONIAN TABLES. TABLE 227. 211 FREEZING MIXTURES.* Column i gives the name of the principal refrigerating substance, A the proportion of that substance, B the proper- tion of a second substance named in the column, C the proportion of a third substance, D the temperature of the substances before mixture, E the temperature of the mixture, /''the lowering of temperature, G the temperature when all snow is melted, when snow is used, and H the amount of heat absorbed in heat units (small calories when A is grams). Temperatures are in Centigrade degrees. Substance. A B C D E F G H NaC 2 H 3 O 2 (cryst.) 35 H 2 O-ioo _ 10.7 4-7 154 _ _ NH 4 C1 . 30 " " 18.4 _ NaNO 3 . 75 " " 13.2 5.3 I8. 5 _ Na 2 S 2 O 3 (cryst.) . no " " - 10-7 8.0 18.7 - - KI. 140 " " - 10.8 11.7 22.5 - CaCl (cryst.) 250 11 U - 10.8 12.4 23.2 _ _ NH 4 N0 8 60 " " 13.6 -13.6 27.2 _ (NH 4 ) 2 S0 4 . . 2 5 " 5 NH 4 NO 3 -25 26.0 - - NH 4 C1 . 2 5 u " " 22.0 CaCl 2 . 25 tt " " - - 20.0 _ _ KN0 3 . 2 5 U it NH 4 Cl-25 - 2O.O _ _ Na 2 SO 4 2 5 u u u u _ _ I9.O _ _ NaNO 3 . 2 5 .< - - 17.0 _ - K 2 SO 4 . 10 Snow 100 1.9 0.9 _ Na 2 CO 3 (cryst.) . 20 u u _ 2.O 1.0 _ _ KN0 8 . 13 U U - -2.8 S 1.85 - - CaCl 2 . 3 u - IO-9 9-9 ' NH 4 C1 . NH 4 N0 3 25 45 ;; : z -I5-4 16.75 14.4 x 5-75 : : NaN0 3 . 5 u u ~ 17-75 16.75 ~ - NaCl . 33 U - 21.3 20.3 - - " 1.097 37-0 36.0 37.0 o.o " 1.26 36.0 35-o 30.2 17.0 H 2 SO 4 +H 2 O (66.i%H 2 S0 4 ) ;; 1-38 " 4^32 - 35-0 30.0 25-0 34-o 29.0 24.0 25.0 12.4 7.0 27.0 133-0 273.0 7.92 - 2O.O 19.0 3- 1 553-0 " 13.08 - I 16.0 15.0 2.1 967.0 " 0.35 o 0.0 52.1 " 49 - 19.7 49-5 " .61 - 39-0 40-3 CaCl 2 + 6H 2 O - .70 " .81 _ o _ _ 54-9t 40-3 30.0 46.8 " 1-23 - - - 21.5 88.5 " 2.46 o - 9.0 192.3 " 4-92 - - -. 4.0 392-3 Alcohol at 4 j 77 " 73 CO 2 solid _ 30.0 72.0 _ _ _ Chloroform . - U (( - - 77.0 - - - Ether . - 77.0 Liquid SO 2 . _ " " _ _ 82.0 - - _ H 2 0-. 75 - 20 5.0 - - 33-o 94 20 4.0 21.0 " " 10 4.0 34-o " " 5 4.0 40.5 Snow " _ o 4.0 _ 122.2 NH 4 N0 3 . H 2 O-i.20 ~ 10 14.0 - - , 17.9 Snow " - 14.0 - - 129.5 H 2 O-i.3i ro 17.5! - 10.6 Snow " _ o 17.5! _ I 3 I -9 H 2 O-3.6i ~ 10 8.0 - - 0.4 Snow " 8.0 327.0 * Compiled from the results of Cailletet and Colardeau, Hammerl, Hanamann, Moritz, Pfanndler, Rudorf, and Tollinger. t Lowest temperature obtained. SMITHSONIAN TABLES. 212 TABLE 228. CRITICAL TEMPERATURES, PRESSURES, VOLUMES, AND DENSITIES OF GASES.* 6 = Critical temperature. P = Critical pressure in atmospheres. = Critical volume referred to volume at o and 76 centimeters pressure. d = Critical density in grams per cubic centimeter. a, b, Van der Waals constants in (p + ~^) ( v ~ b ) = l + at ' Substance. e P <*> d a X io 6 b X io 8 Observer Air ... 140.0 39-0 _ _ 257 1560 , Alcohol (C 2 H 6 O) . 243.6 62.76 0.00713 0.288 2407 3769 2 - (CH 4 0) . 239.95 78.5 I8 9 8 2992 3 Ammonia 130.0 115.0 - - 79 8 1606 4 Argon . 117.4 52.9 259 1348 5 Benzene 288.5 47-9 0.305 3726 5370 Bromine 302.2 0.00605 1.18 1434 2O2O 6 Carbon dioxide 31.2 73- 0.0044 0.46 717 1908 - " monoxide . 141.1 35-9 275 1683 7 disulphide 273- 72.9 0.0090 - 2316 3430 8 Chloroform . 260.0 54.9 2930 445 9 Chlorine Ether '. ! '. 141.0 146.0 197.0 83-9 93-5 35-77 0.01584 0.208 "57 1063 3496 2259 2050 6016 4 10 ii " ... 194.4 35- 61 0.01344 0.262 3464 6002 3 Ethane . 32.1 49.0 1074 2848 12 Ethylene Helium . < 268.0 5 1 - 1 2.3 _ ~ 886 5 2533 700 ' Hydrogen " chloride . 240.8 5 I - 2 5 14. 86.0 _ _ 42 692 880 1726 15 52-3 86.0 _ 0.6 1 I73 1 4 " sulphide . 1 00.0 88.7 - - 888 1926 i Krypton 62.5 54-3 - 462 1776 5 Methane 81.8 54-9 - - 376 1557 " 95-5 50.0 357 1625 4 Neon < 205.0 29. - 5^3 Nitric oxide (NO) . 93-5 71.2 - - 257 1160 i Nitrogen 146.0 35-o 0.44 259 1650 i " monoxide (N 2 0) 35-4 75- 0.0048 0.41 720 1888 4,17 Oxygen . Sulphur dioxide 118.0 T 55-4 50.0 78-9 0.00587 0.6044 0-49 273 1316 1420 2486 i 9,17 Water . 358.1 0.001874 0.429 6 . 374- 217-5 " 1089 1362 16 (1) Olszewski, C. R. 98, 1884; 99, 1884; 100, 1885; Beibl. 14, 1890; Z. Phys. Ch. 16, 1893. (2) Ramsay-Young, Tr. Roy. Soc. 177, 1886. (3) Young, Phil. Mag. 1900. (4) Dewar, Phil. Mag. 18, 1884 ; Ch. News, 84, 1901. (5) Ramsay, Travers, Phil. Trans. 16, 17, 1901. (6) Nadejdme, Beibl. 9, 1885. (7) Wroblewski, Wied. Ann. 20, 1883 ; Stz. \Vien. Ak. 91, 1885. (8) Batelli, 1890. (9) Sajotschewsky, Beibl. 3, 1879. (io) Knietsch, Lieb. Ann. 259, 1890. (n) Batelli, Mem. Torino (2), 41, 1890. (12) Cardozo, Arch. sc. phys. 30, 1910. (13) Kamerlingh-Onnes, Comno. Phys. tab. Leiden, 1908, 1909, Proc. Amst. n, 1908, C. R. 147, 1908. (14) Olszewski, Ann. Phys. 17, 1905. (15) Ansdell, Chem. News, 41, 1880. (16) Holborn, Baumann Ann. Phys. 31, 19101 (17) Cailletet, C. R. 102, 1886; 104, 1887. 'Abridged for the most part from Landolt and Bornstein's "Phys. Chem. Tab." SMITHSONIAN TABLES. TABLE 229. CONDUCTIVITY FOR HEAT, METALS AND ALLOYS- 213 The coefficient k is the quantity of heat in small calories which is transmitted per second through a plate one centimeter thick per square centimeter of its surface when the difference of tempera- ture between the two faces of the plate is one degree Centigrade. The coefficient k is found to vary with the absolute temperature of the plate, and is expressed approximately by the equation k t = & [i + a.(t - Jo)]. o is the conductivity at t Q , the lower temperature of the bracketed pairs in the table, kt that at temperature /, and a is a constant, kt in g-cal. per degree C per sec. across cm cube = 0.239 x k t in watts per degree C per sec. across cm cube. Substance ,c *i a i> (j *aj C Substance. /C ftl a ji Aluminum -160 0.514 _ I Mercury .... o 0.0148! ' 18 0.480 u 50 0.0189; +.o55 7 ' IOO 0.492 + . 0030 2 Molybdenum 17 0.346 -.0001 6 * 200 o. 545 Nickel -160 O. 120 i * .... 400 o. 760 + . OO2O 3 i 18 W. X A.\f o. 1420 2 | .... 500 600 0.885 I.OI +.0014 3 o IOO 0.1425! 0.1380 j -.00032 3 Antimony .... IOO 0.0442 1 o 0^06 f .OOIO4 4 200 7OO 0.1325 I o 060 f -.00095 3 Bismuth -186 ^ov^ j o. 025 / w IOOO ^. wuy j o 064. ! tt 18 o. 0194 1 I2OO W . WVJlf. I o ot;8 I -.00047 3 IOO 0.0161 / -.0021 2 Palladium. . . 18 ^O / 0.1681 ! Brass -160 0.181 I it IOO w ' * W *-'O V 0.182 / +.0010 2 " 17 o. 260 I Platinum. . . . 18 0.1664! " , yellow. . o o. 204 +.0024 4 M IOO 0.1733 / + . 0005 I 2 " ,red.... o o. 246 +.0015 4 Pt 10% Ir .. 17 0.074 +.O002 6 Cadmium, pure -160 0.239 i Pt 10 % Rh . 17 0.072 +.0002 6 u 18 0.222 1 O Platinoid... . 18 0.060 i Constantan. . . IOO 18 0.215; 0.0540! - . 00038 2 Potassium. . . 5-o 57-4 0.232! 0.216 / -.0013 8 (60 Cu+4o Ni) IOO 0.0640/ +.00227 2 Rhodium. . . . 17 0.210 -.OOIO 6 Copper,* pure . -160 18 IOO 1.079 0.918! o . 908 J -.00013 I 2 Silver, pure. . -160 18 IOO 0.998 1.006! 0.992 J -.00017 i 2 German silver. 0.070 +.0027 4 Sodium 5-7 \ 0.321! 3 Gold 17 o . 705 .00007 6 u 88.1 0.288J . OO I 2 Graphite 17 0.037 +.0003 6 Tantalum. . . 17 0.130 .0001 6 Iridium 17 o. 141 - . 0005 8 " 1700 0.174 9 Iron,f pure . . . 18 IOO o. 161 ! 0.151 J - . 0008 2 M 1900 2 IOO 0.186! 0.198? +.00032 9 Iron, wrought. -160 18 0.152 0.144! . 00008 I 2 Tin... O IOO o.i55 I 0.145 J -.00069 4 * . IOO O.I43/ ,pure.... -160 o. 192 i " steel, i% 18 0.108 1 C ......... IOO o. 107 / -.0001 2 Tungsten. . . . 17 0.476 -.0001 6 Lead, pure -160 0.092 I n 18 IOO 0.083! 0.081 / .0001 2 Tungsten 1600 2OOO 0.249! 0.272 f +.00023 10 Magnesium. . . oto/ IOO) 0.376 4 M 2400 2800 0.294! 0-3I3J +.00016 10 Manganin .... 160 0.035 I Wood's alloy 0.319 7 " (8 4 CU+ 4 18 0.0519! Zinc, pure. . . -160 0.278 i Nii2Mn) TOO 0.0630) + . 0026 2 " 18 0.2653! -.00016 2 IOO 0.2619 / References: (i) Lees, Phil. Trans. 1908; (2) Jaeger and Diesselhorst, Wiss. Abh. Phys. Tech. Reich. 3, 1900; (3) Angell, Phys. Rev. 1911; (4) Lorenz; (5) Macchia, 1907; (6) Barratt, Pr. Phys. Soc. 1914; (7) H. F. Weber, 1879; (8) Hornbeck, Phys. Rev. 1913; (9) Worthing, Phys. Rev. 1914; (10) Worthing, Phys. Rev. 1917. * Copper: 100-197 C, k t = 1.043; 100-268, 0.969; 100-370, 0.931; 100-541, 0.902 (Her ing; for reference see next page). flron: 100-727 C, kt = 0.202; 100-912, 0.184; 100-1245, 0.191 (Hering). SMITHSONIAN TABLES. 214 TABLES 230-231. CONDUCTIVITY FOR HEAT. TABLE 230. Thermal Conductivity at High Temperatures. (See also Table 229 for metals; k in gram-calories per degree centigrade per second across a centimeter cube.) Tempera- I Tempera- jj Material. ture, k K Material. ture, k s C 8 C ! Amorphous carbon . . . 37-163 .028-. 003 Brick: Carborundum 150-1200 .0032-. 027 3 170-330 240-523 .027-. 004 .020-. 003 Building \ Terra-cotta / 15-1100 .0018-. 0038 3 283-597 .on-. 004 Fire-clay .... 125-1220 .003 2-. O054 3 100-360 .089 Gas-retort . . . 100-1125 .0038 3 100-751 .124 Graphite .... 300-700 .024 3 100-842 .129 Magnesia .... 50-1130 .002 7~. 007 2 3 Graphite (artificial) . . . 100-390 .338 Silica 100-1000 .002 -.0033 3 100546 -324 Granite 100 .0045. OO5O 4 100-720 .306 200 .0043-. 0097 4 100-914 .291 500 .0040 4 302830 .162 Limestone 40 .0046. OO57 4 2800-3200 .002 100 .003 9-. 0049 4 90-110 55-- 45 350 .0032-. 0035 4 180-120 .44-. 34 Porcelain (Sfevres) . . 165-1055 .0030-. 0047 3 500-700 .31-. 22 Stoneware mixtures . 70-1000 .0029-. 0053 3 References: (i) Hansen, Tr. Am. Electrochem. Soc. 16, 329, 1909; (2) Hering, Tr. Am. Inst. Elect. Eng. 1910; (3) Bui. Soc. Encouragement, in, 879, 1909; Electroch. and Met. Ind. 7, 383, 433, 1909; (4) Poole, Phil. Mag. 24, 45, 1912; see also Clement, Egy, Eng. Exp. Univers. 111. Bull. 36, 1909; Dewey, Pro- gressive Age, 27, 772, 1909; Woolson, Eng. News, 58, 166, 1907, heat transmission by concretes; Richards, Met. and Chem. Eng. n, 575, 1913. The ranges in values under i do not depend on variability in ma- terial but on possible errors in method; reduced from values expressed in other units. TABLE 231. Thermal Conductivity of Various Substances. Substance, temperature. kt Refer- ence. Substance, temperature. kt Refer- ence. Aniline BP 183 C., 160 .000112 .010 .012 .00050 .OOOSI .0022 .00013 .004 .00028 093 .025 .OO25 .OOIlS .0028o .00324 .OOOSl .OOI7O .OOlSl .00077 0053 .0066 .0050 .038 .0103 .00029 .0047 to .0056 .0018 .0063 .0044 i 2 3 4 4 5 5 5 5 5 5 5 5 i 6 i i 5 5 4 6 6 6 6 Naphthalene MP 79 C., 160 Naphthalene M P 79 C. , o .0013 .00081 .00068 .00062 .00106 .00065 .00062 .00039 .0025 .0586 .0173 0133 .0325 .0167 .0150 .00033 .00037 .00045 .00093 .0055 .00012 :SB .00026 .0012 .0037 .0037 .00070 .00022 .00087 5 5 S 5 5 5 5 5 6 6 6 6 7 7 5 8 9 Naphthol /3, MP 122 C., -160.. Naphthol, o Carborundum Concrete, cinder ... . Nitrophenol, MP 114 C., 160 Nitrophenol o stone Diatomaceous earth Paraffin MP 54 C., 160 Paraffin, o Earth's crust Fire-brick Porcelain Fluorite, o. Glass* window crown, ojiri, 190 Quartz || to axis o CrOWn, O3472, crown OUT! 100.. Rock salt, o Rock salt, 30 Rubber, vulcanized, 160 Rubber, o h'vy flint OIM, 190 h'vy flint ois, o h'vy flint OIM, 100. . . Glycerine, 160 Sand, white dry Granite Ice 160 Iceland spar, 190 Iceland spar o . Limestones, calcite ) Marbles dolomite j . Mica Flagstone J to cleavage Micaceous || to cleavage Vulcanite References: (i) Lees, Tr. R. S. 1905; (2) Lorenz; (3) Norton; (4) Hutton, Blard; (5) Eucken, Ann. d. Phys., 1911; (6) Herschel, Lebour, Dunn, B. A. Committee, 1879; (7) Tansson, 1904; (8) Melmer, 1911; (9) Stefan. SMITHSONIAN TABLES. TABLE 232. 215 THERMAL CONDUCTIVITIES OF INSULATING MATERIALS. Conductivity in g-cal. flowing in i sec. through plate i cm thick per cm 2 for i C difference of temperature. Material. Conduc- tivity. Density. g/cm3 Remarks. Air o 00006 Horizontal layer heated from above Calorox o 000076 o 064 Fluffy finely divided mineral matter Hair felt o 000085 O 27 Keystone hair o 000003 O 3O Felt between layers of bldg paper Pure wool o 000084 O IO7 Firmly packed o 000084 O IO2 a a ii u o . 000090 O OOOIOI 0.061 O O3O Loosely packed. Very loosely packed Cotton wool O OOOIO Firmly packed Insulite O OOOIO2 I O Pressed wood-pulp rigid fairly strong Linofelt o 000103 o 18 Vegetable fibers between layers of paper Corkboard (pure) Eel grass 0.000106 O OOO I I 0.18 O 2 ^ soft and flexible. Inclosed in burlap. Flaxlinum o 000113 o 18 Vegetable fibers firm and flexible Fibrofelt o 000113 o 18 Rock cork o 000119 o 33 Rock wool pressed with binder, rigid. Balsa wood O OOOI2 O 12 Very light and soft. Waterproof lith. . . . o 00014 o. 27 Rock wool, vegetable fiber and binder, not Pulp board Air cell \ in. thick Air cell i in. thick Asbestos paper 0.00015 0.000154 0.000165 0.00017 0.14 o. 14 o. 50 flexible. Stiff pasteboard. Corr. asbestos paper with air space. 11 11 U <( Fairly firm, but easily broken. Infusorial earth, block . . Fire-felt, sheet O.OOO2O o 000205 0.69 0.42 Asbestos sheet coated with cement, rigid. Fire-felt, roll O.OOO22 0.68 Soft, flexible asbestos. Three-ply regal roofing. . Asbestos mill board .... Woods, kiln dried: Cypress O.OOO24 O.OOO29 O.OOO23 0.88 0.97 0.46 Flexible tar roofing. Pressed asbestos, firm, easily broken. White pine O.OOO27 0.50 Mahogany Virginia pine Oak 0.00031 0.00033 O.OOO'K o-5S 0-55 0.61 Hard maple 0.00038 o. 71 Asbestos wood, sanded. . 0.00093 1.97 Asbestos and cement, very hard, rigid. Dickinson and van Dusen, Am. Soc. Refrigerating Eng. J. 3, Sept. 1916. SMITHSONIAN TABLES. 2l6 TABLES 233-234. CONDUCTIVITY FOR HEAT. TABLE 233. Various Substances. kt is the heat in gram-calories flowing in i sec. through a plate I drop in temperature. cm. thick per sq. cm. for iC Substance. Asbestos fiber .... 85% magnesia asbestos . Cotton . . Eiderdown Lampblack, Cabot number 5 Quartz, mesh 200 .... Poplox, popped Na 2 SiO 3 . Wool fibers . Density, 0.201 .216 .021 .IOI .0021 .109 193 1.05 0.093 .015 .054 .192 500 100 500 100 500 500 200 500 .00019 .00016 .00017 .000111 .000071 .00015 .000046 .000074 .000107 .00024 .000091 .000160 .000118 .000085 .000054 Substance. Asbestos paper . . Blotting paper . . . Portland cement . . Cork, t,oC . . . Chalk Ebonite, t, 49 . . . Glass, 'mean . . . Ice. ...... Leather, cow-hide " chamois . . Linen Silk ....... Caen stone, limestone Free stone, sandstone 0.00043 .00015 .00071 .0007? .0020 .00037 .002 .0057 .00042 .00015 .OOO2I .000095 .0043 .0021 Authority. Lees-Chorl- ton. Forbes. \ H, L, D, J see p. 205. Various. Neumann. I Lees-Chorl- ton. [ H, L, D. Left-hand half of table from Randolph, Tr. Am. Electroch. Soc. XXI ., p. 550, 1912 ; k t (Randolph's values) is mean conductivity between given temperature and about ioC. Note effect of compression (density). The following are from Barratt Proc. Phys. Soc., London, 27, 81, 1914- Substance. Brick, fire . Carbon, gas Ebonite . . Fiber, red Glass, soda Silica, fused . Density. '73 1.42 1.19 1.29 2.59 2.17 at 2oC. at iooC. .00110 .0085 .00014 .00112 .00172 00237 .00109 .0095 .00013 .00119 .00182 .00255 Substance. Boxwood . Greenheart Lignumvitae Mahogany Oak. . . Whitewood Density. 0.90 1.08 1.16 -55 0.65 0.58 at 2oC. at iooC. .00036 .00112 .OOO6O .00051 .00058 .00041 .00041 .00110 .00072 .00060 .00061 .00045 The following values are from unpublished data furnished by C. E. Skinner of the Westinghouse Co., Pitts- burgh, Penn. They give the mean conductivity in gram-calories per sec. per cm. cube per C. when the mean temperature of the cube is that stated in the table. Resistance in thermal ohms (watts/inch 2 /inch/C.) = 10.6 conductivity. Substance. Grams, per cm 3 . Conductivity. 00 C. 200 C. 300 C. 400 C. 500 C Safe temp. Air-cell asbestos Cork, ground Diatomit Infusorial earth, natural . " " h'd pressed blocks Magnesium carbonate .... Vitnbestos 0.232 .168 .326 .506 .321 450 .362 0.00034 .00015 .00028 .00034 .00030 .00023 .00049 0.00043 .00019 .00032 .00032 .00029 .00025 .00066 0.00050 .00037 .00040 .00033 .00025 .00079 0.00042 .00036 .00090 0.00046 320 i Ho 6cx) 400 300 600 TABLE 234. Water and Salt Solutions. Substance. c. k, Authority. Solution in water. Density. C. k t Authority. ( 0.00150 Goldschmidt, 'n. CuS0 4 .160 4-4 o.ooi 18 H. F. Weber. Water \ ( 1 1 25 20 .00147 .00136 .00143 { Lees, '98. Milner, Chattock, '98 KC1 NaCl .026 .T 7 8 '3- 4-4 26.3 .001 i 6 . 00 I 15 00135 Graetz. H. F. Weber. H 2 S0 4 .054 20.5 .00126 { Chree. ** .180 21. .TXM30 ZnS0 4 '34 4-5 .00118 } H. F. Weber. .136 4-5 SMITHSONIAN TABLES. TABLES 235-237. TABLE 235. Thermal Conductivity of Organic Liquids. Substance. C kt Ji ( Substance. C kt Substance. C C kt 1 Acetic acid Alcohols: methyl. . . ethyl amyl Aniline 9-i5 ii ii 0-15 .03472 .0352 .0346 03345 .03434 Q3333 i 2 2 3 I Carbon disulphide. Chloroform Ether 0-15 Q-iS 25 13 13 .03387 .03288 03303 .0368 03355 .03325 3 I I 2 5 5 Oils: olive. 25 o 03395 .03425 03349 .0344 01343 4 4 3 2 3 " castor Glycerine Oils: petroleum. . . turpentine. . Vaseline Xylene Benzene References: (i) H. F. Weber; (2) Lees; (3) Goldschmidt; (4) Wachsmuth; (5) Graetz. TABLE 236. Thermal Conductivity of Gases. The conductivity of gases, kt = 1(97 S)l*Cv, where 7 is the ratio of the specific heats, C P /C V , and fj. is the viscosity coefficient (Jeans, Dynamical Theory of Gases, igi6). Theoretically kt should be independent of the density and has been found to be so by Kundt and Warburg and others within a wide range of pressure below one atm. It increases with the temperature. Gas. rc kt Ref. Gas. tC kt Ref. Gas. tC kt Ref. Air*... At CO C02 -191 O 100 -183 o IOO -78 0.0000180 0.0000566 0.0000719 0.0000142 0.0000388 o . 0000509 0.0000542 0.0000219 0.0000332 C0 2 C 2 H 4 He H 2 CH4 IOO -193 IOO -192 IOO 0.0000496 0.0000395 0.000146 0.000344 o . 000398 0.000133 0.000416 o . 000499 0.0000720 4 i 4 Hg N 02 NO NzO 203 191 o IOO 191 IOO 8 o 0000185 0.0000183 0.0000568 0.0000718 0.0000172 0.0000570 0.0000743 o . 000046 0.0000353 3 4 References: (i) Eucken, Phys. Z. 12, 1911; (2) Winkelmann, 1875; (3) Schwarze, 1903; (4) Weber, 1917. * Air: k = 5.22 (io~ B ) cal. cm -1 sec.- 1 deg. C" 1 ; 5.74 at 22; temp. coef. = .0029 ; Hercus-Laby, Pr. R. Soc. 190, 1919. TABLE 237. Diffusivities. The diffusivity of a substance = A 2 = k/cp, where k is the conductivity for heat, c the specific heat and p the density (Kelvin). The values are mostly for room temperatures, about 18 C. Material. Diffusivity. Material. Diffusivity. Aluminum o 826 Coal o 002 o 139 Concrete (cinder) 0.0032 o 0678 Concrete (stone) ... 0.0058 Concrete (light slag) o 006 o 467 Cork (ground) 0.0017 Ebonite O.OOIO Gold i 182 o 0057 o 173 Granite 0.0155 Ice O.OII2 Lead O.OO92 o 883 Marble (white) 0.0090 o 0327 Paraffin . 0.00098 Nickel. 0.152 o. 240 Rock material (earth aver.) Rock material (crustal rocks) O.OIlS 0.0064 o 243 Sandstone 0.0133 Silver i 737 Snow (fresh) . O.OO33 Tin o. 407 Soil (clay or sand, slightly damp) 0.005 Zinc o. 402 Soil (very dry) . . . 0.0031 Air o 179 Water O.OOI4 Asbestos (loose) 0.0035 Wood (pine, cross grain) 0.00068 Brick (average fire) 0.0074 Wood (pine with grain) 0.0023 Brick (average building) . . 0.0050 Taken from An Introduction to the Mathematical Theory of Heat Conduction, Ingersoll and Zobel, 1913. SMITHSONIAN TABLES. 2l8 TABLE 238. LINEAR EXPANSION OF THE ELEMENTS- In the heading of the columns / is the temperature or range of temperature; C is the coefficient of linear expansion; A\ is the authority forC; M is the mean coefficient of expansion between o and 100 C; a and are the coefficients in the equation It = fc(i + at + /8t 2 ), where lo is the length at o C and It the length at t C; At is the authority for a, ft, and J/. See footnote for Molybdenum and Tungsten. Substance. t CX io ,ll M X 10^ a X io< 0X108 A Aluminum 40 o 2313 I O. 222O 2 600 3 191 to +16 0.1835 4 .23536 .OO7O7 5 Antimony: || to axis _L to axis 40 40 0.1692 0.0882 I I Mean. 40 o. 1152 I o. 1056 .0923 .OI32 6 Arsenic 40 o 0559 I Bismuth: || to axis 40 o. 1621 I _L to axis 40 O.I 208 I Mean . , . 40 o. 1346 I o. 1316 .1167 .OI49 6 Cadmium 40 o . 3069 I 0.3159 .2693 .0466 6 Carbon: Diamond 40 0.0118 I Gas carbon Graphite 40 40 0.0540 0.0786 I I .0055 .00l6 13 Anthracite 40 o 2078 I Cobalt 40 o. 1236 I Copper 40 0.1678 I 0.1666 .1481 .Ol85 6 191 to -|-i6 o 1409 4 . 16070 .00403 5 Gold 40 o. 1443 i o. 1470 1358 .0112 6 170 o 117 15 40 o 4170 I . . Irirlium Iron: Soft . I 4 8 40 0.088 O I2IO 16 i 0.090 16 Cast i Cast IQI to +16 o oS^o 4 Wrought . 18 to 100 7 . 11705 .005254 8 Steel i 09173 .008336 8 Steel annealed Lead 40 40 0.1035 i i 0.1089 .1038 2 73 .0052 .OO74 9 6 Lead (cast) Magnesium . . . 40 i o 261 16 Nickel 40 i 13460 .003315 8 16 Osmium 40 i Palladium 40 11670 .OO2l87 8 Platinum 40 i 08868 .001324 8 Potassium . 0-50 Ruthenium 40 i Selenium . . 40 o 3680 _ 12 Silicon Silver 40 18270 . OO4793 8 o 189 1 6 2 26 Sulphur: Cryst. mean Tellurium. .. 40 0.6413 i 1.180 o ^68? 12 Tin 3 ,. 6 Zinc ? o. 2290 6 Zinc (cast) 97 References: (i) Fizeau; (2) Calvert, Johnson and Lowe; (3) Chatelier; (4) Henning; (5) Dittenberger; (6) Matthiessen; (7) Andrews; (8) Holborn-Day; (9) Benoit; (10) Pisati and De Franchis; (n) Hagen; (12) Spring; (13) Day and Sosman; (14) Griffiths; (15) Dorsey; (16) Griineisen. Tungsten: (L - Lo)/Lo = 4.44 X io~(r - 300) + 45 X io~"(r - 300)" + 2.20 X io~ l3 (T - 300)'. Lo = length at 300 K. Coefficient at 300 K = 4.44 X io~*; 1300 K, 5.19 X IQ-; 2300 K, 7.26 X ie>-. Worthing, Phys. Rev. 1917- Molybdenum: Li = L*(i + 5.151 X io~ + 0.00570** X io-), for 19 to -142 C; 0.00138* X io-J, for io 8 Jto + 305 C; Schad and Hidnert, Phys. Rev. 1919. The Holborn-Day and Sosman data are for temperatures from 20 to 1000 C. SMITHSONIAN TABLES Lo(i+ s.oi/X 10-0 The Dittenberger, o to 600 C. TABLE 239. LINEAR EXPANSION OF MISCELLANEOUS SUBSTANCES. 2IQ The coefficient of cubical expansion may be taken as three times the linear coefficient. / is the temperature or range of temperature, C the coefficient of expansion, and A. the authority. Substance. 1 CX io A. Substance. t CX io A. Brass: Cast Wire o-ioo 40 o-ioo 16.6-100 16.6-350 16.6-957 40 0-80 16.7-25-3 4-29 25.3-35.4 o-ioo 50-60 o-ioo 191 to + 16 20 20 to i 7 8 o-ioo 12-39 15-100 0-16 16-38 38-4Q 40 0.1875 0.1930 i 783-- 193 0.1859 0.1906 0.1844 0.2116 0.1737 0.1782 0.1713 o. 1708 0.657-0.686 0.770 0.1523 0.842 o. 1950 0.1836 0.1523 0.1552 0.0833 0.0828 0.0891 0.0897 0.0954 0.0788 0.081 0.058 0.424 1.983 0.51 0.2631 * 0.0544 0.2508 0.238 0.181 0.117 1.0662 i 3030 4.7707 0.0884 i i 2 3 4 5 5 5 3 6 6 2 7 1 8 4 4 I 9 10 10 II II 12 12 13 14 IS 6 6 i 16 i 18 18 3 Platinum -silver: I Pt + 2Ag o-ioo 20-700 1000-1400 0-80 100 to + 16 0-80 190 to + 16 16 to 500 16-1000 $ -160 o-ioo 16.6-254 0-18 o-ioo 2.34 10-26 26-31 31-43 43-57 o 1523 0.0413 0-0553 0.0797 0.0521 0-1337 0.0026 0.0057 0.0058 o . 4040 0.691 0.300 0.1933 0.0832 0.0836 0.0472 0.0937 0.0773 'l 2 0.6300 0.0800 0.0951 0.0257 o . 0649 0.0565 0.0361 0.0638 0.0492 0.0541 0.0658 0.614 0.325 0-443 0.404 0.484 0-544 0-341 0.484 2.300 3.120 4.860 15.227 4 19 20 6 21 6 13 26 26 3 27 27 i 8 8 8 8 8 5 22 5 23 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 25 25 25 25 Porcelain Bayeux. . Quartz: Parallel to axis . . . Perpend, to axis... Quartz glass Rock salt...'..'.'.'.'.' Rubber, hard Speculum metal Topaz: Parallel to lesser horizontal axis. . . Parallel to greater horizontal axis. . . Parallel to vertical axis 71.5 Cu4- 27.7 Zn + o.aSn + o.sPb.. . 71 Cu + 29 Zn. Bronze: 3 Cu + i Sn 86.3 Cu + 9.7' Sn + 4 Zn - 6 Cu + l/hard Ef + |U Caoutchouc Constantan Ebonite Tourmaline: Parallel to longi- tudinal axis Parallel to horizon- tal axis Type metal Vulcanite Fluor spar: CaFi .... Gold-platinum: 2 Au + i Pt Gold-copper: 2 Au + i Cu Glass: Tube Wedgwood ware. . . Wood: Parallel to fiber: Ash Beech Plate Crown (mean) Chestnut Elm Mahogany Maple Oak Flint Jenather-|i6 IU \ mometer 1 normal / 59 m -... Gutta percha Ice Pine Walnut Across the fiber: Beech Chestnut Elm Iceland spar: Parallel to axis Perpendicular to axis Lead-tin (solder) 2 Pb 4- i Sn Mahogany Maple Oak... Magnalium Pine..' Walnut Marble Wax: White Paraffin Platinum-indium 10 Pt + i Ir References: (i) Smeaton. (8) Pfaff. (15) Mean. (2) Various. (9) Deluc. (16) Stadthagen. (3) Fizeau. (10) Lavoisier and Laplace. (17) Frohlich. (4) Matthiessen. (u) Pulfrich. (18) Rodwell. (5) Daniell. (12) Schott. (19) Braun. (6) Benoit. (13) Henning. (20) Deville and Troost. (7) Kohlrausch. (14) Russner. (21) Scheel. (22) Mayer. 23) Glatzel. 24) Villari. 25) Kopp. 26) Randall. (27) Dorsey. SMITHSONIAN TABLES. 32O TABLE 24O. CUBICAL EXPANSION OF SOLIDS, If v z and v\ are the volumes at / 2 and t\ respectively, then 7/2 = ^(1 + C&t), C being the coefficient of cubical expansion and A/ the temperature interval. Where only a single temperature is stated C represents the true coefficient of cubical expansion at that temperature.* Substance. t or A/ CX io Authority. Antimony O-IOO 0.3167 Matthiessen Beryl . . . O-IOO O.OICK Pfaff Bismuth O-IOO 0.^048 Matthiessen Copper Diamond .... O-IOO 40 0.4998 O.OK4 Fizeau Emerald . 40 0.0168 Galena O IOO 0. q q8 Pfaff Glass, common tube . . " hard O-IOO O-IOO 0.276 0.214 Regnault it " Jena, borosilicate 59 I1I . . . pure silica . . . Gold 2O-IOO 0-80 O-IOO 0.156 0.0129 0.4411 Scheel Chappuis Matthiessen Ice . ->o 1 1.1250 Brunner Iron O IOO O 7CCO Dulong and Petit Lead Paraffin O-IOO 20 0.8399 588 Matthiessen Russner Platinum ... O-IOO J.UU o ^65 Dulong and Petit Porcelain, Berlin . . . Potassium chloride . . nitrate . . " sulphate . . Quartz 20 O-IOO O-IOO 20 O IOO 0.0814 1.094 1.967 1-0754 o ^840 Chappuis and Marker Playfair and Joule Tutton Pfaff Rock salt co-6o 121 ''O Pulfrich Rubber .... 20 487 Silver O IOO t+.u/ o cS^i Sodium 'O ^-y^j 1 2 I T.6)A Stearic acid }> 8 4.C c * i jU4 C r Sulphur, native . . . Tin .... JJ' 45-i i3- 2 -5-3 O IOO 2.23 06889 Zinc O-IOO o 8928 (i * For tables of cubical expansion complete to 1876, see Clark's Constants of Nature, Smithsonian Collections, 280. SMITHSONIAN TABLES. TABLE 241. 221 CUBICAL EXPANSION OF LIQUIDS. If V is the volume at o then at t the expansion formula is V t = V (i + at + ftfl + 7/ 8 ). The table gives values of a, and y and of C, the true coefficient of cubical expansion, at 20 for some liquids and solutions. A/ is the temperature range of the observation and A the authority. Liquid. u a lo 3 /3io YIO* Cl 3 at 20 A Acetic acid 1 Acetone i Alcohol : Amyl Ethyl, 30% by vol. . . " 50% " " 99-3% " - " 500 atmo. press. . " 3000 " " . Methyl Benzene ....... 16-107 0-54 15-80 18-39 o-39 27-46 0-40 0-40 0-61 11-81 o-59 18-25 17-24 34-60 0-50 0-50 0-76 0-63 -15-38 o-33 O-IOO o-33 16-25 36-157 24-120 0-29 11-40 0-30 0-30 9-106 o-33 1.0630 1.3240 0.9001 0.2928 0.7450 I.OI2 0.866 0.524 1.1342 1.17626 1.06218 0.07878 0.42383 1.13980 0.940 0.581 1.18384 1.10715 1-51324 0-4853 0.4460 0.18182 0.6821 1.4646 0.2695 0.8340 0.8994 0.3640 0-3599 0.2835 0-5758 0.9003 0.06427 0.12636 3.8090 0.6573 10.790 1.85 2.20 1.3635 1.27776 1.87714 4.2742 0.8571 L37065 0.89881 4.66473 2.35918 0.4895 0.215 0.0078 1.1405 3-93 I 9 2.080 0.10732 1.396 1.237 1.258 2.580 0.432 1-9595 8.5053 1.0876 0.87983 1.18458 11.87 0.730 0.8741 0.80648 0.30854 1.91225 1:35*35 1.74328 4.00512 0.4446 0.44998 6.7900 1.071 1.487 0.902 1. 12 I.I99 1-237 I.I32 0.250 0.458 I.2I8 1.236 -*73 1.656 0-505 o-455 0.18186 0.721 i. 608 0-353" 1.090 0-955 0.414 0.410 0.387 0-558 0-973 0.207 3 3 4a 6 6 6 i i 5* 5 a 2 7 7 4* i i 4 b 4b 4a 8 9 U 10 M 7 n 12 9 9 9 Ib 13 1 Calcium chloride : 5.8% solution . . . 40.9% " 1 Carbon disulphide . . . 500 atmos. pressure 3000 " Carbon tetrachloride , . ' Chloroform .... 1 Ether Hydrochloric acid : 33.2% solution .... Mercury Qlj-yg oil Pentane Potassium chloride : 24.3% solution .... Phenol . ; Petroleum : Density 0.8467 .... Sodium chloride : 20.6% solution .... Sodium sulphate : 24% solution .... Sulphuric acid : 10.9% solution .... IOO O% Turpentine Water AUTHORITIES. i. Amagat: C. R. 105, p. 1120; 1887. 9. Marignac: Lieb. Ann., Supp. VIII, p. 335; 2. Thorpe : Proc. Roy. Soc. 24, p. 283; 1876. 1872. 3. Zander: Lieb. Ann. 225, p. 109; 1884. 10. Spring: Bull. Brux. (3) 3, p. 331 ; 1882. 4. Pierre: a. Lieb. Ann. 56, p. 139; 1845. n. Pinette : Lieb. Ann. 243, p. 32; 1888. b. Lieb. Ann. 80, p. 125; 1851. 12. Frankenheim : Pogg. Ann. 72, p. 422; I 5. Kopp : a. Lieb. Ann. 94, p. 257; 1855. 1847. b. Lieb. Ann. 93, p. 129; 1855. 13. Scheel: Wiss. Abh. Reichsanstalt, 4, p. i; 6. Reel-enamel : Sitzber. bayr. Ak. p. 327, 2 1903. Abt. ; 1866. 14- Thorpe and Jones: J. Chem. Soc. 63, 7. Drecker : Wied. Ann. 34, p. 952 ; 1888. p. 273 ; 1893. 8. Emo: Ber. Chem. Ges. 16, 1857; 1883. SMITHSONIAN TABLES. 222 TABLE 242. COEFFICIENTS OF THERMAL EXPANSION, Coefficients of Expansion of Gases. Pressures are given in centimeters of mercury. Coefficient at Constant Volume. Coefficient at Constant Pressure. Coeffi- X Coeffi- CJ Substance. Pressure cm. cient X j Substance. Pressure cm. cient X 1 IOO. c2 100. *; Qg Air ... .6 37666 i Air ... 7 6. 3671 3 . 1.3 37172 " . 2 57- 3693 ii IO.O .36630 " " 0-IOO . 100. 1 .36728 2 " ... 25-4 .36580 " Hydrogen o-ioo IOO.O .36600 " " ... 75-2 .36660 " "... 200 Atm. H2 9 " 0-IOO . 100. 1 36744 2 "... 400 " | .29 s " ... 76.0 .36650 3 "... 600 " .261 . 2OO.O .36903 it 800 " .242 " " ... 2OOO. .38866 " Carbon dioxide 76. 3 " ... IOOOO. 4100 it " 0-20 51.8 .37128 2 Argon . ( urbon dioxide 76.0 .3668 .36856 4 3 " o-40 " 0-IOO 51.8 51.8 .37100 3773 It " " 1.8 36753 i " 0-20 99-8 .37602 " 5.6 .36641 1C " 0-IOO 99-8 37410 M 74-9 37264 " " 0-20 '37-7 37972 0-20* 51-8 .36985 2 " 0-IOO 37/03 o-40 51.8 it o- 7 .5 2621. .1097 6 0-IOO 51-8 .36981 it " 64- 1 00 2621. 6574 " 0-20 99-8 37335 " Carbon monoxide . 76. .3669 3 0-IOO 99.8 .37262 Nitrous oxide 76. 3719 " 0-IOO Carbon monoxide . IOO.O 76. '16667 i Sulphur dioxide . it ( 76. 98. 3903 3980 *' Helium . 56.7 .3665" 4 O- T I Q 76. .4187 10 Hydrogen i6-i32 " !lT .0077 .3328 025 1.3623 6 i w *<- ! i/o r\r*v 76. 76. .4189 .4071 tt 47 .3656 " VapOl QO.^QQO 76. 3938 ii 93 .37002 i 0-2 47 76. 3799 ii . II. 2 s .36548 " 76.4 .36504 " 0-IOO Nitrogen 13- 13 2 IOO.O .06 .36626 2 .3021 6 Thomson has given, Encyc. Brit. " Heat," the following for the calculation of the ex- 0-20 0-IOO 53 100.2 IOO.2 ~>f\ .3290 36754 2 pansion, E, between o and iooC. Expansion is to be taken as the change of volume under constant pressure : Oxygen u-i32 . x ?o"! 3 20 ' 70. .007 ci .4161 6 .3984 M 7871 Hydrogen, E = .3662(1 .00049 F/z/), Air, E = .3662( i .0026 V/v), Oxygen, h = .3662(1 .0032 F/z>), (i O '7668; 8 Nitrogen, E = . 3662(1 .0031 F/z>), ! 18^5 j' J ' J0 .> .36600 CO 2 = .3662(1 .0164 V/v). Nitrous oxide Sulph'r dioxide SOs 75-9 76. 76. .36681 3676 3845 2 V/v is the ratio of the actual density of the gas at o C to what it would have at o C and i Atm. pressure. i Meleander, Wied. Beibl. 14, 1890; Wied. 5 Chappuis, Arch. sc. phys. (3), 18, 1892. Ann. 47, 1892. 6 Baly- Ramsay, Phil. Mag. (5), 38, 1894. 2 Chappuis, Trav. Mem. Bur. Intern. Wts. 7 Andrews, Proc. Roy. Soc. 24, 1876. Meas. 13, 1903. 8 Meleander, Acta Soc. Fenn. 19, 1891. 3 Regnault, Ann. chim. phys. (3)5, 1842. 9 Amagat, C. R. in, 1890. 4 Keunen-Randall, Proc. R. Soc. 59, 1896. 10 Him, Theorie mec. chaleur, 1862. SMITHSONIAN TABLES. TABLE 243. SPECIFIC HEAT OF THE CHEMICAL ELEMENTS- 223 Element. Range * of temperature, C Specific heat. Refer- ence. Element. Range * of temperature, Specific heat. Refer- ence. Aluminum . 240. 6 0092 45 Cobalt 500 18 190 o 0889 45 IOOO 18 73-O 190 46 182 to +15 0822 " IQO tO 82 .1466 47 15-100 . 1030 << 76 to i 1962 47 Copper t . 249.5 0035 <( +16 to +100 +16 to +304 .2122 $ 48 -22 3 185 .0208 O?32 lo -250 .1428 2089 " -6 3 + 25 .0865 46 " IOO .2226 2382 " 76 84 0937 OO^8 51 500 IOO " 16-100 2122 4 362 .0997 51 Antimony 15 0489 900 1259 IOO 0503 15-238 .O95I 43 ti 181 to 13 0868 Arsenic, gray O IOO O822 3 23100 Arsenic, black Barium Bismuth o-ioo l85 tO +20 -186 o .0861 .068 .0284 O3OI 3 4 I Gallium, liquid. . . solid Germanium Gold. . . 12 tO 113 12-23 o-ioo 185 to +20 .080 -079 0737 03? 22 22 23 75 20-IOO 0309 .O3O2 6 7 Indium . . . o-ioo o ioo .O3IO 0570 24 13 " fluid 280380 8 Q^ge Boron o-ioo 307 9 191 to 80 998 0454 49 76 to o 1677 47 Iridium 186 to +18 O282 26 Bromine, solid 78 tO 20 .0843 10 18-100 .O323 26 solid 192 to 80 .0702 49 Iron 223 .0176 46 fluid 13-45 . IO7 ri -163 .O622 46 Cadmium 223 .O308 46 < -63 . 0961 46 173 0478 46 < +37 IO92 46 ; ;::::::::: -73 21 IOO 0533 0551 0570 46 2 2 cast wrought 20-100 15-100 IOOO I 2OO .1189 .1152 I080 27 28 28 Caesium Calcium 200 300 0-26 l8S tO +20 0-181 0594 .0617 .0482 157 I7O 2 2 12 4 13 wrought hard-drawn . . hard-drawn. . 500 0-18 20-IOO 185 tO +20 O tO +2OO .176 .0986 .1146 .0958 1175 28 29 29 4 53 Carbon, graphite. . . 191 to 79 76 to o 0573 I2 SS 47 47 ' o to +300 o to +400 .1233 .1282 53 53 :: :: ::: -50 +11 977 .114 .160 467 14 14 14 ' ::::::::::::: o to +500 o to +600 o to +700 .1338 .1396 .1487 53 53 53 1730 5 52 ' o to +800 .1597 53 / -244 . 005 50 < o to +900 .1644 53 Acheson \ 186 027 50 o to +1000 *557 53 Carbon, diamond . . . 50 .0635 47 tO +1100 .1534 53 Cerium +n 985 o 100 .113 459 0448 47 47 15 Lanthanum Lead o-ioo 250 236 .0448 0143 0217 IS 46 46 Chlorine, liquid .... 0-24 2262 16 193 .0276 46 Chromium 2OO 0666 17 i 73 .0295 46 17 , 15 0299 < IOO II2I 17 i IOO .0311 2 600 185 to +20 .1872 086 17 " ' fl u 'id 300 310 0338 2 3 *When one temperature is given, the "true" specific heat is indicated, otherwise the "mean" specific heat. 1 0.3834 + o.ooo2o(/ 25) intern, j per g degree = 0.0917 + 0.000048 (* 25) cabo per g degree. (Griffith, 1913-) SMITHSONIAN TABLETS. 224 TABLE 243 (continued). SPECIFIC HEAT OF THE CHEMICAL ELEMENTS- Element. Range * of temperature, ^ Refer- ence. Element. Range * of temperature, Specific heat. Refer- ence. Lead 90 2IO 18-100 16-256 191 tO SO 78 to o -75 to +19 100 o So IOO IQO 185 to +20 60 325 625 20-IOO -i88to -79 79 to +15 60 325 20-IOO IOO IOO -77 to -42 36 to 3 185 to +20 85 IOO 250 185 tO +20 60 475 20 tO IOO 185 to +20 IOO 300 500 1000 18-100 19-98 -i86to +18 o-ioo 0-1265 -5 1 13-36 186 to +20 -186 to +18 IOO 200 500 750 IOOO 1300 2O-IOO 20-500 20-IOOO 20-1300 0.0312 0.0334 0.0310 0.0319 0.521 0.595 0.629 0.5997 0.7951 0.9063 I . 0407 1.3745 O.222 0.2492 0.3235 0-4352 0.2 4 92 0.0820 o. 1091 0. I2II 0.1783 O.I2II 0.0979 o. 1072 O.H43 0.0329 0.0334 0.032 0.03346 0.0328 0.03284 0.03212 0.062 0.0647 0.0750 o . 0647 0.092 o. 1128 o. 1403 0.1299 0.1608 0.109 0.0311 0.0528 0.0592 0.0714 o. 1829 O.2O2 0.178 0.0293 0.0275 O.0330 0.0349 0.0365 O.038I 0.0400 0.0319 0.0333 0.0346 0.0359 Si 51 43 43 47 47 47 31 3i 3i 3i 31 4 7 7 7 7 49 49 49 49 49 31 31 31 47 47 4 32 32 2 2 4 7 7 7 4 18 18 18 18 26 10 26 24 24 33 33 4 26 34 35 35 35 35 35 35 35 35 35 Potassium 191 to 80 78 too 185 to +20 10-97 o-ioo -188 to +18 185 to +20 -39 8 +57-1 232 -238 -213 173 +8 o-ioo 23 IOO 500 17-507 800 007-1100 185 tO +20 191 to 83 -77 to o 223 -183 -188 to +18 o-54 0-52 119-147 185 tO +20 I4OO 188 to +18 15-100 185 tO +20 20-100 O-IOO 196 to 79 76 to +18 21-109 250 IIOO 185 tO +20 o-ioo 185 tO +20 o-ioo IOOO 2000 2400 0-98 -IOO -243 193 -153 20-100 IOO 300 o-ioo 0.1568 0.1666 o. 170 0.0580 0.0802 0.0611 0.068 0.123 o. 1360 0.1833 o. 2029 0.0146 0.0307 0.0447 0.0540 0.0560 0.0559 0.05498 0.05663 0.0581 0.05987 0.076 0.0748 0.253 0.243 0.276 0.152 0.219 0.137 0.1728 o. 1809 0.235 0.033 0.043 0.047 0.0483 0.038 0.0326 0.0276 0.0486 0.0518 0.0551 0.05799 0.0758 0.082 0.1125 0.036 0.0336 0-0337 0.042 0.045 0.028 O.H53 0.0144 0.0625 0.0788 0.0931 0.0951 o. 1040 o . 0660 47 47 4 25 13 36 4 14 14 14 46 46 46 46 46 13 2 2 34 43 18 18 4 47 47 46 46 36 33 33 2 4 36 37 4 3 26 26 30 18 18 4 39 4 40 52 52 52 41 4 46 46 46 27 2 2 42 (i Rhodium Lithium Rubidium Ruthenium Selenium Silicon . . , ;;;; Silver . '. i Magnesium H i< 4I Manganese ; ::::::::::: 4 'fluid!!!!!! Sodium " i Mercury, sol " lici tl Sulphur rhombic . " monoclin. liquid . . . Tantalum Molybdenum Nickel '.'.'.:: Tellurium " crys. . . Thallium Thorium Tn cast ' fluid ' fluid Osmium Palladium Titanium Phosphorus, red. . . yellow, yellow. Platinum Tungsten lt ::::::::: Vanadium Zinc " M ii :: ::::::::: M M Zirconium * When one temperature is given, the "true" specific heat is indicated, otherwise the "mean" specific heat. See page 226 for references. SMITHSONIAN TABLES. TABLE 244. HEAT CAPACITIES. TRUE AND MEAN SPECIFIC HEATS. AND LATENT HEATS AT FUSION. 225 The following data are taken from a research and discussion entitled "Die Temperatuiv Warmeinhaltskurven der technisch wichtigen Metalle," Wiist, Meuthen und Durrer, For- schungsarbeiten herausgegeben vom Verein Deutscher Ingenieure, Springer, Heft 204, 1918. (a) There follow the constants of the equation for the heat capacity: W = a + bt + cf 2 ; for the mean specific heat: 5 = at~ l + b + ct; and for the true specific heat: s' - b + ict\ also the latent heats at fusion. (See also Table 243, pp. 223-224.) Ele- ment. Tempera- ture range. a b c X io La- tent heat. cal./g Ele- ment. Tempera- ture range. C a b cXio La- tent heat cal./g. Cr 0-1500 o. 10233 33-47 _ Ag 0-961 _ 0.05725 5.48 26.0 Mo 0-1500 0.06162 10.99 961-1300 53-17 0.00710 28.30 W 0-1500 0.03325 1.07 - Au 0-1064 0.03171 1.30 15-9 Pt 0-1500 0.03121 3-54 - 1064-1300 26.35 0.01420 8.52 Sn 0-232 0.06829 13.8. Cu 0-1084 o. 10079 3.05 41.0 232-1000 14-33 0.07020 -18.30 1084-1300 130.74 -.04150 65.6 Bi 0-270 0.03141 5-22 IO.2 Mn 0-1070 0.12037 25.41 36.6 270-1000 10.31 0.03107 5-41 II3O-I2IO -7.41 0.17700 24.14* Cd 0-321 0.05550 6.28 10.8 1230-1250 3-83 o. 19800 32I-IOOO 6.30 0.06952 6-37 Ni 0-320 o. 10950 52.40 56.1 Pb 0-327 0.03591 -11.47 5-47 330-1451 0.41 0.12931 O.II 1-33* 327-1000 6.07 0.02920 3-30 1451-1520 50.21 0.13380 Zn 0-419 0.08777 43.48 23.0 Co 0-950 0.09119 40.77 58.2 419-1000 14-34 0.13340 16. 10 1100-1478 22.OO o.i 1043 14-57 14.70* Sb 0-630 0.05179 3.00 38.9 1478-1600 57-72 o. 14720 630-1000 39-42 0.05090 2.96 Fe 0-725 o. 10545 56.84 49-4 Al 0-657 O. 222OO 38.57 94.0 785-919 -I.6 3 0.1592 6. 5 6* 657-1000 102.39 0.21870 24.00 919-1404 18.31 0.14472 0.05 6.67* 1405-1528 -77-18 o. 21416 1.94* 1528-1600 70.03 0.15012 * Allotropic heat of transformation: Mn, 1070-1130; Ni, 320-330; Co, 950-1100; Fe, 725-785; 9*9 * i; 1404-5 * 0.5. (b) TRUE SPECIFIC HEATS. c Pb Zn Al Ag Au Cu Ni Fe Co Quartz. oC 0-0359 0.0878 O. 222O 0.0573 0.0317 0.1008 0.1095 0.1055 0.0912 100 0.0336 0.0965 o. 2297 0.0583 0.0320 o. 1014 0.1200 O.II68 0.0993 0.2372 2OO 0.0313 o. 1052 0.2374 0.0594 0.0322 O. IO2O 0.1305 o. 1282 0.1073 0.2416 300 0.0290 O.II39 0.2451 0.0605 0.0325 o. 1026 0.1409 0.1396 0.1154 o. 2460 4OO 0.0266 o. 1226 0.2529 0.0616 0.0328 0.1032 0.1294 0.1509 0.1235 0.2504 500 0.0259 0.1173 o. 2606 0.0627 0.0330 o. 1038 0.1294 0.1623 0.1316 0.2548 600 0.0252 o. 1141 0.2683 0.0638 0.0333 0.1045 0.1294 0.1737 0.1396 0.2592 700 0.0246 o. 1109 0.2523 0.0649 0.0335 O.I05I 0.1295 0.1850 0.1477 0.2636 800 0.0239 o. 1076 0.2571 0.0660 0.0338 0.1057 0.1295 0.1592 0.1558 0.2680 9OO 0.0233 o. 1044 o. 2619 0.0671 0.0341 0.1063 0.1295 0.1592 0.1639 0.2724 1000 0.0226 O. IOI2 0.2667 0.0637 0.0343 o. 1069 0.1295 0.1448 0.2768 IIOO o . 0694 0.0329 o. 1028 o. 1296 0.1448 0.1424 0.2812 I2OO 0.0750 0.0346 0.1159 0.1296 0.1448 0.1454 0.2856 1300 0.0807 0.0364 o. 1291 o. 1296 0.1449 0.1483 o. 2900 . 1400 o. 1296 0.1449 0.1512 0.2944 I5OO 0.1338 o. 2142 0.1472 0.2988 I6OO 0.1501 0.1472 For more elaborate tables and for all the elements in upper table, see original reference. SMITHSONIAN TABLES. 226 TABLE 245. ATOMIC HEATS (60 K). SPECIFIC HEATS (60 K). ATOMIC VOLUMES OF THE ELEMENTS. The atomic and specific heats are due to Dewar, Pr. Roy. Soc. SgA, 168, 1913. Ele- ment. Specific heat -223 C. Atomk heat -22 3 C Atomic volume Ele- ment Specific heat 223 C. Atomic heat -223 C Atomic volume. Ele- ment. Specific heat - 223 C. Atomic heat -223C. Atomic volume. Li o. 1924 1-35 13-0 Cr 0.0142 0.70 7.6 Sn 0.0286 3-41 20.3 Gl 0.0137 0.125 4-9 Mn 0.0229 1.26 7-4 Sb 0.0240 2.89 18.2 B O.O2I2 0.24 4-5 Fe 0.0175 0.98 7-i I 0.0361 4-59 25.7 C* 0.0137 o. 16 5-i Ni 0.0208 1.22 6-7 Te 0.0288 3-68 21.2 ct 0.0028 0.03 3-4 Co 0.0207 I. 22 6.8 Cs 0.0513 6.82 71.0 Na O.I5I9 3-50 23-6 Cu 0.0245 1.56 7-i Baf 0.0350 4.80 36.6 Mg 0.0713 1.74 14.1 Zn 0.0384 2.52 9.2 La 0.0322 4.60 22.6 Al 0.0413 I. 12 IO.O As 0.0258 1.94 15-9 Ce 0.0330 4.64 20.3 Sit 0.0303 0.86 14.2 Se 0.0361 2.86 18.5 W 0.0095 i-75 9 .8 Si 0.0303 0.77 11.4 Br 0.0453 3-62 24.9 Os 0.0078 1.49 8-5 P Rb 0.0711 6.05 55-8 Ir 0.0099 1.92 8.6 yel. 0.0774 2.40 17.0 Srlf 0.0550 4.82 34-5 Pt 0.0135 2.63 9.2 P Zr 0.0262 2.38 21.8 Au 0.0160 3-i6 IO. 2 red 0.0431 1-34 13-5 Mo 0.0141 1.36 9-3 Hg 0.0232 4-65 14.8 S 0.0546 i-7S 16. Ru 0.0109 i. ii 9.0 Tl 0.0235 4-80 17.2 Cl 0.0967 3-43 24.6 Rh 0.0134 1.38 8-5 Pb 0.0240 4.96 I8. 3 K 0.1280 S-oi 44-7 Pd 0.0190 2.03 9.2 Bi 0.0218 4-54 21.3 Ca 0.0714 2.86 25-9 Ag 0.0242 2.62 10.2 Th 0.0197 4-58 21. I Ti O.O2O5 0.99 10.7 Cd o . 0308 3-46 13.0 U 0.0138 3-30 12.8 * Graphite. f Diamond. Fused. Crystallized. Impure. References to Table 243: (1) Bontschew. (2) Naccari, Atti Torino, 23, 1887-88. (3) Wigand, Ann. d. Phys. (4) 22, 1907. (4) Nordmeyer-Bernouli, Verh. d. phys. Ges. 9, 1907; 10, 1908. (5) Giebe, Verh. d. phys. Ges. 5, 1903. (6) Lorenz, Wied. Ann. 13, 1881. (7) Stiicker, Wien. Ber. 114, 1905. (8) Person, C. R. 23, 1846; Ami. d. chim. (3) 21, 1847; 24, 1848. (9) Moisson-Gautier, Ann. chim. phys. (7) 17, 1896. (10) Regnault, Ann. d. chim. (3) 26, 1849; 63, 1861. (n) Andrews, Pog. Ann. 75, 1848. (12) Eckardt-Graefe, Z. Anorg. Ch. 23, 1900. (13) Bunsen, Pogg. Ann. 141, 1870; Wied. Ann. 31, 1887. (14) Weber, Phil. Mag. (4) 49, 1875. (15) Hillebrand, Pog. Ann. 158, 1876. (16) Knietsch. (17) Adler, Beibl. 27, 1903. (18) Pionchon, C. R. 102-103, 1886. (19) Tilden, Phil. Trans. (A) 201, 1903. (20) Richards, Ch. News, 68, 1893. (21) Trowbridge, Science, 8, 1898. (22) Berthelot, Ann. d. chim. (5) 15, 1878. (23) Pettersson-Hedellius, J. Pract. Ch. 24, 1881. (24) Violle, C. R. 85, 1877; 87, 1878. (25) Regnault, Ann. d. chim (2) 73, 1840; (3) 63, 1861. (26) Behn, Wied. Ann. 66, 1898; Ann. d. Phys. (4) i, 1900. SMITHSONIAN TABLES. (27) Schmitz, Pr. Roy. Soc. 72, 1903. (28) Nichol, Phil. Mag. (5) 12, 1881. (29) Hill, Verh. d. phys. Ges. 3, 1901. (30) Spring, Bull, de Belg. (3) u, 1886; 29, 1895. (31) Laemmel, Ann. d. Phys. (4) 16, 1905. (32) Barnes-Cooke, Phys. Rev. 16, 1903. (33) Wiegand, Fort. d. Phys. 1906. (34) Tilden, Pr. Roy. Soc. 66, 1900; 71, 1903; Phil. Trans. (A) 194, 1900; 201, 1903. (35) White, Phys. Rev. 12, 436, 1918. (36) Dewar, Ch. News, 92, 1905. (37) Kopp, Phil. Trans. London, 155, 1865. (38) Nilson, C. R. 96, 1883. (39) Nilson-Pettersson, Zt. phys. Ch. i, 1887. (40) Mache, Wien, Ber. 106, 1897. (41) Bliimcke, Wied. Ann. 24, 1885. (42) Mixter-Dana, Lieb Ann. 169, 1873. (43) Magnus, Ann. d. Phys. 31, 1910. (44) Harper, Bull. Bureau of Stds. n, p. 259, 1914. (45) Nernst, Lindemann, 1910, 1911. (46) Nernst, Dewar. (47) Kosef, Ann. d. Phys. 36, 1911. (48) Magnus, Ann. d. Phys. 31, 1910. (49) Estreicher, Straniewski, 1912. (50) Nernst, Ann. d. Phys. 36, 395, 1911. (51) King, Phys. Rev. n, 1918. (52) Worthing, Phys. Rev. 12, 1918. (53) Harker, Pr. Phys. Soc. London, 19, 703, 1905; Fe .01; C .02; Si .03; S .04; P, Mn trace. TABLES 246-247. TABLE 246. Specific Heat of Various Solids. 227 Solia. Temperature C. Specific heat. Au- thority. Alloys : Bell metal Brass, red " yellow 80 Cu + 20 Sn 88.7CuH-ii.3Al German silver . Lipowitz alloy : 24-97Pb + 10. 13 Cd +5O.66BI + 14.24 Sn .... << 15-98 14-98 20-IOO 0-100 5-50 100-150 0.0858 .08991 .08831 .0862 . 10432 .09.464 0345 .0426 R L R Ln T M Rose's alloy: 27.5 Pb +48.9 Bi +23.6 Sn . Wood's alloy: 25.85 Pb'-f 6.99 Cd + 52.43 Bi + i4.73Sn . (fluid) Miscellaneous alloys : 17.5 Sb + 29-9 Bi-f- i8.7Zn + 33.9Sn 37.1 Sb+62.9Pb 39.9Pb + 6o.iBi " (fluid) 77-20 20-89 5-50 100-150 20-99 10-98 16-99 144 7cg 0356 .0552 .0352 .0426 05657 .03880 03165 .omoo S u M R P 63.7Pb + 36.3Sn 46.7Pb + 53-3Sn 63 8Bi -|-36.2Sn 12-99 10-99 20-QQ .04073 .04507 04001 R 46.9 Bi +53-1 Sn Gas coal Glass, normal thermometer :6"i .... French hard thermometer .... " crown ... " flint .... . 20-99 20-1040 19-100 10-50 10-50 .04504 3 I 45 .161 . 117 W z H M Ice . _!88 252 . 146 D .28^ _!8 78 463 {< India rubber (Para) ...... , ' ?-IOO .481 GT Mica 20 . 10 Paraffin 20- +3 .3768 R W 19 |-20 0-20 .60^0 fluid Vulcanite Woods .... 35-40 60-63 20-100 20 .622 .712 3312 3-7 B AM TABLE 247. Specific Heat of Water and of Mercury. Specific Heat of Water. Specific Heat of Mercury. Temper- ature,C. Barnes. Rowland. Barnes- Regnault. Temper- ature,C. Barnes Barnes- Regnault. Temper- ature,C. Specific Heat. Temper- ! ature,C. Specific Heat. -s oiSS _ _ 60 0.9988 0.9994 0.03346 i 90 0.03277 .0091 1.0070 i .0094 65 9994 i .0004 5 .03340 i IOO .03269 + 5 .0050 1.0039 1.0053 70 1. 000 1 1.0015 10 .03335 no .03262 10 .0020 i. 0016 1.0023 80 1.0014 1.0042 15 .03330 120 .03255 IS .0000 I.OOOO 1.0003 90 1.0028 1.0070 20 03325 130 .03248 20 0.9987 .9991 0.9990 IOO 1.0043 I.OIOI 25 .03320 j 140 .03241 25 .9978 .9989 .9981 120 1.0162 30 03316 ; 150 .0324 30 9973 .9990 .9976 140 - 1.0223 35 ; .03312 170 .0322 35 .9971 .9997 .9974 1 60 1.0285 40 .03308 190 .0320 40 9971 1.0006 .9974 ISO 1.0348 50 .03300 210 .0319 45 9973 1.0018 .9976 200 1.0410 60 .03294 50 9977 1.0031 .9980 220 - i .0476 70 .03289 - - 55 .9982 1.0045 .9985 1 80 .03284 Barnes's results : Phil. Trans. (A) 199, 1902; Phys. Rev. 15, 1902; 16, 1903. (H thermometer.) Bousjfteld, Phil. Trans. A 211, p. 199, 1911. Barnes-Rcgnault's as revised by Peabody ; Steam Tables. The mercury data from o C to 80, Barnes-Cooke ( H thermometer); from 90 to 140, mean of Winklemann, Naccari and Milthaler (air thermometer); above 140, mean of Narcari and Milthaler. 228 TABLES 248-260. TABLE 248. Specific Heat of Various Liquids. Liquid. Temp. c. Spec. heat. Au- thority. Liquid. Temp. Spec. heat. Au- thority. Alcohol ethyl -20 4 5-10 15-20 15 30 50 IO 40 65 -15 + 20 -20 + 20 -20 O + 20 12-15 12-14 13-17 53 65 0.5053 0.548 . 648 O.SQO 0.601 0.514 0.520 0.529 0.340 0.423 o.'482 0.764 0-775 0.787 0.695 0.712 0.725 0.651 0.663 0.676 0.848 0.951 0.975 0.464 0.482 R G H-D t DMG i i Pa B Ethyl ether 15-50 18 18 18 18 18 18 80-85 90-95 14 28 5-4 6.6 21-58 17-5 17-5 17-5 IO 65 85 20-52 20-52 0.529 0.576 0.876 0-975 0.942 0.983 0.791 0.978 0.396 0.409 0.350 0.362 0-434 0.438 0.471 0.387 0.411 o. 511 0.980 0.938 0.903 0.364 0.490 0-534 0.842 0.952 R E TH u (1 B (i A u W HW u W R Pa M (( H-D Ma fi Glycerine ... < KOH + 3oH 2 O '. " -j- 100 " NaOH + 5oH 2 O Anilin " + 100 " n NaCl + ioH 2 O " +200" Naphthalene, C 10 H 8 Benzole C 6 H 6 " C 6 H 6 Nitrobenzole CaClj, sp. gr. 1.^14 u U It " I.2o'.'. citron olive sesame turpentine " j 26 Petroleum ii U CuSo 4 + 50 H 2 O Sea water, sp. gr. 1.0043. ; ' 1-0235. " " " " 1.0463. Toluol CeHs + 200 " 4- 400 " Diphenylamine, Ci 2 HnN . . . u ft ZnSO4 + 50 HoO " + 200" References: (A) Abbot; (B) Batelli; (E) Emo; (G) Griffiths; (DMG) Dickinson, Mueller, and George; (H-D) de Keen and Deruyts; (Ma) Marignac; (Pa) Pagliani; (R) Regnault; (Th) Thomsen; (W) Wachsmuth; (Z) Zouloff; (HW) H. F. Weber. TABLE 249. Specific Heat of Liquid Ammonia under Saturation Conditions. Expressed in Calories^ per Gram per Degree C. Osborne and van Dusen, Bui. Bureau of Standards, 1918. Temp. C o I 2 3 4 5 6 7 8 9 -40 .062 .061 .060 059 .058 .058 057 .056 055 055 -30 .070 .069 .068 .067 .066 065 .064 .064 .063 .062 -20 .078 .077 .076 075 .074 .074 073 .072 .071 .070 -10 .088 .087 .086 -08 5 .084 .083 .082 .081 .080 .079 - .099 .098 .097 .096 .094 093 .092 .091 .090 .089 + o .099 .100 .101 .103 . 104 .105 .106 .108 .109 .110 + 10 . 112 113 .114 .116 .117 .118 . 120 . 122 .123 .125 + 20 .126 .128 .129 131 .132 134 .136 137 139 .141 +30 .142 .144 .146 .148 .ISO .152 154 .156 1.158 .160 +40 .162 .164 .166 I. 169 .171 173 .176 .178 1.181 .183 TABLE 250. Heat Content of Saturated Liquid Ammonia. Heat content = H = + pv, where is the internal or intrinsic energy. Osborne and van Dusen, Bui. Bureau of Standards, 1918. Temperature . . . H = e + pv -50 -53-8 -40 -43-3 -30 -32-6 -20 -21.8 -10 -II. o.o + 10 +11. 1 + 20 + 22. 4 +30 -33-9 +40 -45-5 +50 -57-4 SMITHSONIAN TABLES TABLES 251-252. SPECIFIC HEATS OF MINERALS AND ROCKS. TABLE 251. Specific Heat of Minerals and Rocks, 229 Substance. Tempera- ' ture C. Specific Heat. Refer- 1 ence. Substance. Tempera- ture C. Specific Heat. Refer- ence. Andalusite O-IOO 0.1684 , Rock-salt 13-45 0.219 6 Anhydrite, CaSO 4 O-IOO 1753 I Serpentine . 16-98 .2586 2 Apatite .... 15-99 .1903 2 Siderite 9-98 J 934 4 Asbestos 20-98 195 3 Spinel . 15-47 .194 6 Augite .... 20-98 3 Talc . 20-98 .2092 3 Barite, BaSO 4 10-98 .1128 4 Topaz . ; . O-IOO .2097 i Beryl .... X 5~99 .1979 2 Wollastonite *9~S* .178 6 Borax, Na 2 B 4 O 7 fused 16-98 .2382 4 Zinc blende, ZnS . O-IOO .1146 i Calcite, CaCO s . 0-50 .1877 r Zircon . 21-51 .132 6 " " . . O-IOO .2005 i Rocks : " " . 0-300 .2204 i ' Basalt, fine, black I2-IOO .1996 6 Cassiterite SnO 2 . 16-98 0933 4 " " " 20-470 .199 9 Chalcopyrite Corundum !5~99 9-98 .1291 .1976 2 4 i 470-750 .243 750-880 .626 9 9 Cryolite, Al. 2 F 6 .6NaF . 16-99 .2522 2 880-1190 .323 9 Fluorite, CaF 2 2154 4 Dolomite . 20-98 .222 3 Galena, PbS . O-IOO .0466 5 Gneiss 17-99 .196 10 Garnet .... 16-100 .1758 2 " 17-213 .214 10 Hematite, Fe 2 O 3 . 15-99 .1645 2 Granite I2-IOO .192 7 Hornblende . 20-98 .1952 3 Kaolin 20-98 .224 3 Hypersthene 20-98 .1914 3 Lava, Aetna 23-IOO .201 ii Labradorite . 20-98 3 " " . 31-776 -259 ii Magnetite 18-45 .156 6 " Kilauea . 25-100 .197 ii Malachite, Cu 2 CO 4 H 2 O *5-99 1763 2 Limestone . 15-100 .216 12 Mica (Mg) . 20-98 .2061 3 Marble O-IOO .21 " (K) . . . 20-98 .2080 3 Quartz sand 20-98 .191 3 Oligoclase 20-98 .2048 3 Sandstone . .22 Orthoclase 15-90 .1877 2 Pyrolusite, MnC>2 . Quartz, SiO 2 (i < 17-48 12-100 35 400-1200 1737 .2786 305 6 I 8 8 i Lindner. 6 Kopp. n Bartoli. 2 Oeberg. 7 Joly. 12 Morano. 3 Ulrich. 8 Pionchon. 4 Regnault. 9 Roberts-Austen, Riicker. 5 Tilden. 10 R. Weber. Compiled from Landolt-Bornstein-Meyerhoffer's Physikalisch-chemische Tabellen. TABLE 252. Specific Heats of Silicates. Silicate. Mean specific heats. o Cto True specific heats, at 100 500 900" 1400* o'C 100* 500 1000* 1300* Albite .... .1948 2363 .2561 __ .178 .211 .269 .294 _ " glass . .1977 .24IO .2640 Amphibole, Mg. silicate .2033 .2461 .2661 .2731* .185 .219 .279 .304 - glass . .2040 .2474 Andesine 1925 .2330 2525 _ - - .265 - - " glass 1934 .2615 _ _ _ _ Anorthite .1901 .2296 02481 .2674 .1/4 .205 .260 .286 .318 glass .1883 .230=1 _ Cristobal! te . .1883 i- .2426 .2568 .2680 _ - - - - Diopside .... .1924 .2314 .2500 .26o4t .176 .207 .262 .284 - glass . . 1939 2332 Microcline .1871 .2262 .2450 _ .171 .201 .258 .279 glass . .1919 .2321 2514 .2508* .176 .206 .264 .299 - Pyroxene .2039 .2484 Quartz .... . 1868 2379 .2596 . 2640* .168 .204 .294 2~8 5 - Silica glass .1845 .2302 .2512 - .166 .202 .266 .29 - Wollastonite . _ _ 2344 [ _ glass .1852 .2206 - - _ - - - " pseudo . .1844 .2170 .2324 .2448 .171 .197 243 .262 .272 ; to-i25o; Taken from White, Am. J. Sc. 47, i, 1919. 230 TABLE 253. SPECIFIC HEATS OF GASES AND VAPORS. Substance. Range of temp. C Sp. ht. constant pres- sure. Authority. Range of temp. C Mean ratio of specific heats. Cp/Cv. Authority. Acetone QHeO 26-IIO -30 fio O-2OO 20-440 20-630 20-800 108-220 101-223 23-100 27-200 20-90 34-115 35-180 116-218 83-228 -28- +7 15-100 11-214 23-99 26-198 86-190 i6-343 27-118 28-189 69-224 25-111 13-100 22-214 -28- +9 12-198 2I-IOO 2O-2O6 18-208 O-2OO 20-440 20-630 2O-8OO 13-172 27-67 27-150 27-280 I6-2O7 26-103 27-206 13-207 20-440 20-630 I6-2O2 IOO 180 0.3468 0.2377 0-2375 0.2366 0.2429 0.2430 0-4534 0.4580 0.5202 0.5356 0.1233 o. 2990 0.3325 0-3754 0.0555 0.1843 0.2025 0.2169 0.2425 o. 2426 0.1596 0.1125 0.1441 0.1489 0.4797 0.4280 o. 1940 0.1867 3 3996 3 4090 3 . 4100 0.2451 0.5929 0.2438 0.2419 o. 2464 0.2497 0.2317 1.625 1.115 0.65 0.2262 0.2126 o. 2241 0.2175 o. 2240 0.2300 0.1544 0.4655 0.421 0.51 Wiedemann. Regnault. Holborn and Austin. Regnault. Regnault. Wiedemann. 14 Dittenberger. Wiedemann. n Regnault. it n a Wiedemann. u Regnault. Strecker. Wiedemann. ii Regnault. Wiedemann. Strecker. Regnault. a Wiedemann. Regnault. Regnault. Regnault. Holborn and Austin. a Regnault. Berthelot and Olger. Regnault. Wiedemann. u Regnault. Holborn and Austin. Regnault. Thiesen. 2O -79-3 -79-3 500 53 IOO IOO IOO o 20 60 99-7 20-388 4-1 1 o IOO 3-67 o 22-78 99.8 42-45 I2-2O 2O IOO 4-16 19 3 IO 11-30 19 IOO 5-14 16-34 78 94 IOO 19 1.4011 1.405 2-333 .828 399 133 134 .256 3172 1.2770 1.667 1.403 1.403 1.105 1-293 1 2995 1.3003 1.403 1-395 1.205 1-336 I. IO2 I.I50 I.O29 I.O24 1.64 1.389 I.40O 1.4080 I.4I9 1.324 1.666 1.666 1.316 1.642 1.41 1.405 1-394 i-3i 1.311 i. 272 i-3 2 4 1-3977 1.256 1.274 i-33 1-305 1.666 Moody. Koch, 1907. " 200 atm Si ii it Fiirstenau. Jaeger. Stevens. n Wullner. a Niemeyer. Pagliani. (4 Stevens. Strecker. Lummer and Pringsheim. Moody, 1912. Wullner. Beyme. Martini. Beyme. Stevens. Miiller. Low, 1894. Mean, Jeans. Strecker. u Lummer and Pringsheim. Hartmann. Capstick. Ramsay, '12. Kundt and Warburg. Miiller. Ramsay, '12 Cazin. Masson. (i Natanson. Wullner. Leduc, '98. Lummer and Pringsheim. Miiller. Beyme. Jaeger. Makower. Ramsay,' 12. Air " Alcohol, 'C 2 H 6 OH.! < CH 3 OH Ammonia Benzene. CH| a Bromine Carbon dioxide, CO 2 . . < i3i5/> I026p 343P 496^ 651* &04p 9 62P 3i3/> S03P 7 8i/> 7&SP 1235^ 937 P 70 253P i6 9 p 332p 13.30 12.4V 12. Op Il.&P n.6v ii. 4P it. Si 11.45 12. 2P ii. 8v ii. 6p tt.sp ii. 4V 1 2. OP II. Op 10. Op 10. ip 9. 6v 10. 2V 3.2&V 3.26P S-io/> Alcohols: Methyl, 1 CH4O C 2 HeO CaHsO C4HioO C5H 12 C 2 H6O C4H 10 CsHsO CH.02 C 2 H 4 02 CsHeOz C4H80J CjHsO, CeHioOs CizHzoOio CaHsOa CeHeO C^HzzOn CeHioCH CioHuO CO(NH) 2 nop 32jp 483^ ^ 1$. 5o6p 62p 2IOP 3(&p 525P 330/> 680 414 397 735 '82 1353 152 5 3i* 7.10* 8.00^ 8.68 8.96* 7.6o* 8.92* 8-43* i-357 3-49 4.965 3:S 4.S8. J:S 3-9SP 4-23 9.02p 2.53 Ethane, g Ethyl 1 Propane g i-Butane, g n-butyl, 1 .... Amyl 1 n-Hexane, 1 n-Heptane 1 Ethers: Dimethyl g n-Octane, 1 Dekane, 1 Diethyl v defines: Ethylene, g Ethyl-methyl, v Acids: Formic 1 Propylene, g i-Butylene, g Amylene 1 Acetic, 1 Hexylene, 1 Acetylene, g n-butyric, 1. < Lactic, 1 .... Trimethylene, g Benzene, 1 Cellulose s Naphthalene, 1 Toluene, 1 Phenol, 1 Chloroform, v Sugar, cane, s Starch s Carbon disulphide 1 Methyl-chloride, g Ethyl-chloride, v Thymol, 1. . Urea 1 v, p, following the heats of combustion, signify at constant volume and pressure respectively. When re- ferred to constant pressure, the values are 0.58 Kg-cal. greater (at about 18 C) for each condensed gaseous molecule. The values are means from various observers. The combustion products are gaseous COt, liquid water, etc. I TABLE 262. Heat of Combustion Miscellaneous. Substance. Small calories perg substance. Reference. 1 Substance. Small calories perg substance. Reference. 1 Asphalt 9530 9200 8080 8100 7860 7900 590 1290 5700 8100 9500 5900 33900 1582 6080 9500 9300 9400 i 2 2 3 3 5 4 2 2 2 2 Oils: petroleum: crude 11500 IOOOO IO200 9500 IOOOO 11140 10340 8400 22OO 2240 9500 4170 4210 3990 4420 2 2 2 6 I 6 2 I 8 8 8 8 Butter light heavy diamond Copper (to CuO) Paraffin (to COz, HiiO 1) Paraffin (to COz, HizO g) Pitch Dynamite, 75% Egg white of Sulphur rhombic Fats, animal Sulphur, monoclinic Tallow Woods- beech 13% HzO Hydrogen Iron (to FezOs) birch 12% HO oak 13% HzO Oils: cotton-seed lard pine 12% HO olive References: (i) Slossen, Colburn; (2) Mean; (3) Berthellot; (4) Roux, Sarran; (5) Thomsen; (6) Stoh- mann; (7) Gibson; (8) Gottlieb. SMITHSONIAN TABLES 242 TABLE 263. HEAT VALUES AND ANALYSES OF VARIOUS TYPES OF FUEL- (a) COALS. Coal. .ignite f Low grade. \ High grade b-bitu- Low jzrade. minous i High grade itu- f Low grade, minous \ High gni.U- emi-bitu- ( Low grade minous \ Highgrade mi-anthracite thra- I Low grade, cite 1 High grade en I Low grade, coke I High grade 38.81 33 38 22.71 15-54 11.44 3-42 I: 7 * 2.07 2.76 3-33 1. 92 1.14 I! 25-48 27-44 34.78 33-03 33-93 34.36 U.5 14-57 9.81 2.48 27.29 29.62 36.60 46.06 43.92 58.83 75.5 78.20 78.82 82.07 84.28 88.87 94-66 8.42 9-56 5-91 5-37 10.71 3-39 7-3 3-97 9-30 12.69 9.12 8.99 3-57 0.97 0-94 0.29 0.58 4-94 0:58 0.99 0.54 1-74 0-54 0.60 1.18 o. 69 7.09 6.77 6.14 5-89 5-39 5-25 4-58 4.76 3-62 2.23 3-08 37-45 4I-3I 52.54 60.08 60.06 77-98 80.65 84.62 80.28 79.22 8i.35 0.50 0.67 1-03 1-05 1.02 1.29 1.82 1.02 1.47 0.68 0.79 45-57 4-75 34-09 27-03 17.88 11.51 4.66 5-09 3-59 4-64 5.o6 s, 3526 3994 5"5 5865 6088 7852 7845 8166 7612 6987 7417 7946 8006 6347 7189 9207 10557 10958 14121 14699 13702 12577 I335I 14300 14410 PEATS AND WOOD (air dried). Vol. hydro- carbon. Fixed carbon. Ash. Sul- phur. Hydro- gen. Carbon. Nitro- gen. Oxygen. Calories per gram. B.T.U.' per pound. Peats: Franklin Co., N. Y.. . Sawyer Co., Wis Woods: Oak, dry Birch, dry Pine, dry 67.10 56.54 28.99 27.92 3-Qi 15-54 0.37 0.29 0.37 0.15 0.29 5-93 4.71 6.02 6.06 6. 20 57-17 51.00 50.16 48.88 50.31 5726 4867 4620 4771 5085 10307 8761 8316 8588 9153 (c) LIQUID FUELS. Fuel. Specific gravity at 15 C. Calories per gram. British thermal units per pound. Petroleum ether Gasoline Kerosene Fuel oils, heavy petroleum or refinery residue Alcohol, fuel or denatured with 7 to 9 per cent water and denaturing material .684-. 694 .710-. 730 .790-. 800 .960-. 970 .8196-. 8202 I22IO-I2220 11100-11400 IIOOO-II200 I0200-I050O 6440-6470 21978-21996 19980-20520 I9800-20I60 18360-18900 II592-U646 (d) GASES. Gas. Natural gas, Cal Natural gas, Pa Natural gas, France Coal gas, low grade Coal gas, high grade Water gas, low tfrade Water gas, high grade 34-So 57-2 52.88 36.4 28.80 18.8 2.16 23.2 C 2 H 2 45_8 9-50 "llumi- i ants. 1.70 0.8 3-47 14.05 C02 0.58 O. 20 2.00 3-02 CO 10.40 3-20 36.8 19.1 O.I 0.40 1-15 N 2 0.90 0.90 0.48 14. 20 18.0 4.69 3-08 Cal. per m" 8339 12635 9364 6151 3736 2642 6140 B.T.U per cu. ft. 937 1420 1052 657 399 283 657 CiH. Data from the Geological Survey, Poole's The Calorific Power of Fuels, and for natural gas from Snelline (Van Nostrand s Chemical Annual). SMITHSONIAN TABLES. TABLE 264. CHEMICAL AND PHYSICAL PROPERTIES OF FIVE DIFFERENT CLASSES OF EXPLOSIVES. 243 Explosive. Specific gravity. i Number of large calories developed 1 by i kilogram of the explosive. | Pressure developed in own volume after elimination of surface in- fluence. Unit disruptive charge by ballistic pendulum. Rate of detonation. Cartridges i J in. diam. Duration of flame from 100 grams 1 of explosive. Length of flame from 100 grams. Cartridge ij in. transmitted explo- 1 sion at a distance of Products of combustion from 200 grams; gaseous, solid, and liquid, respectively. Ignition occurred in 4% fire damp & 1 coal dust mixture with 3* s o h ,gs Js'S 1 1 c i O O (A) Forty-per-centnitro- glycerin dynamite (B) FFF black blasting powder (C) Permissible explo- sive; nitroglycerin class (D) Permissible explo- sive; ammonium nitrate class (E) Permissible explo- sive; hydrated class 1.22 1.25 I.IO 0.97 i-54 I22I.4 789.4 760.5 992.8 6lO.6 8235 4817 59 12 7300 6597 227* 374t 458* 301* 279* 434* 4688 469.41 3008 3438 2479 -358 925. .471 -483 -338 24.63 54.32 27.79 25.68 17.49 12 4 I 3 88.4 79-7 '4-5 1544 126.9 4-i II 103.9 65.1 15-4 89.8 27-5 75-5 86,1 56.0 33-o 25 25 IOOO 800 Over IOOO Chemical Analyses. (A) Moisture 0.91 39.68 42.46 13-58 3-37 0.80 70.57 17-74 10.89 7.89 24.02 36-25 9.20 21.31 0.97 0.36 (D) (E) Moisture Ammon Sulphur Starch Wood p Poisono Mangaru Sand VToisture Nitrogly Ammon SanH 0.23 83.10 0.46 2.61 1.89 2.54 2.64 6.53 2.-U 30-85 9-94 Il7 $ 11.98 7.64 8.96 6.89 19.65 Nitroglycerin lum nitrate Calcium carbonate ulp js ma ise pe (B) Moisture roxide Sodium nitrate Charcoal (C) Moisture cerin um n itrate Nitroglycerin Sodium nitrate Coal Wood pulp and crude fibre from arauis Clay . Ammonium sulphate Zinc sulphate (7 HO) Potassium sulphate Starch Calcium carbonate . Magnesium " . . * One pound of clay tamping used. t Two pounds of clay tamping used. t Rate of burning. Cartridges if in. diam. || For 300 grammes. Compiled from U. S. Geological Survey Results, " Investigation of Explosives for use in Coal Mines, 1909." SMITHSONIAN TABLES. 244 TABLES 265-268. TABLE 265. - Additional Data on Explosives. Explosive. (Ref. Young, Nature, 102, 216, 1918.) Vol. gas per gin cc = V Calories per g=0 Coefficient = QV -i- IOOO Coefficient GP = i Calculated Temperature Q/C C, sp. ht. gases = 0.24 fiunpnwr|er cc 280 738 207 i 2240 C 74 1 1652 1224 6 6880 Nitrocellulose, 13% Nj 923 931 859 4-3 3876 Cordite, Mk. I. (NG, 57; NC, 38; Vaseline, 5) Cordite, MD (NG, 30; NC,6s; Vaseline, 5).. . Ballistite (NG, 50; NC, 50; Stabilizer, 5) .... Picric acid (Lyddite) 871 888 817 877 1242 1031 1349 810 1082 915 IIO2 7IO 5-2 4-4 5-3 3-4 SI7S 4225 5621 3375 Shattering power of explosive = vol. gas per g X cals./g X Vd X density where Vd is the velocity of detonation. Trinitrotoluene: Vd = 7000 m/sec. Shattering effect = .87 picric acid. Amatol (Ammonium nitrate + trinitrotoluene, TNT): Vd = 4500 m/sec. Ammonal (Ammonium nitrate, TNT, Al): 1578 cal/g; 682 cc gas; Vd = 4000 m/sec. Sabulite (Ammonium nitrate, 78, TNT 8, Ca silicide 14): about same as ammonal. TABLE 266. Ignition Temperatures Gaseous Mixtures. Ignition temperature taken as temperature necessary for hot body immersed in gas to cause ignition; slow com- bination may take place at lower temperatures. McDavid, J. Ch. Soc. Trans, in, 1003, 1917. Gases were mixed with air. Practically same temperatures as with Cfe (Dixon, Conrad, loc. cit. 95, 1909). Benzene and air 1062 C Ether and air . . . 1033 C 878 Ethylene and air CO and air 931 Hydrogen and air 747 TABLE 267. Time of Heating for Explosive Decomposition. Temperature C. 170 1 80 190 200 220 Ignition temperature. Time. sec. cec. sec. sec. sec. ct ct n 600 190 170 870 160 n n n iQS *l 60 165 100 340 n n 130 "67 60 240 n n 45 90 21 56 50 ISO 590 n 23 25 9 18 30 00 480 440 |300 300 590 900 450 Smokeless powder B Celluloid Pyroxylin Collodion cotton Celluloid * Safety matches Parlor matches Cotton wool . n, failure to explode in twenty minutes. * The decomposition of nitrocellulose in celluloid commences at about 100 C; above that the heat of decomposition may raise the mass to the ignition point if loss of heat is prevented. Above 170, decomposition occurs with explosive violence as with nitrocellulose. Rate of combustion is 5 to 10 times that of poplar, pine, or paper of the same size and conditions. t Measured by contact with porcelain tube of given temperature. Average. J Measured by contact with molten lead. Average. Taken from Technologic Paper of Bureau of Standards, No. 98, 1917. TABLE 268. Flame Temperatures. Measures made with optical pyrometer by F6ry, J. de Phys. (4) 6, 1907. Alcohol, with NaCl I 7 05C 1900 C Bunsen flame, i air 1812 2458 Bunsen Same, full air. 1871 Illuminating gas-oxygen MOO Cooper-Hewuf Hg '.I'.'.'.'.'.'.'.'.'.'.'. 35OO SMITHSONIAN TABLES. TABLE 269. 245 THERMO-CHEMISTRY. CHEMICAL ENERGY DATA. The total heat generated in a chemical reaction is independent of the steps from initial to final state. Heats of formation may therefore be calculated from steps chemically impracticable. Chemical symbols now represent the chemical energy in a gram-molecule or mol{ + +37-5 Na+ +57-3 Ni + + + 16.0 Mg++ + 108.8 AsO 4 [-215.0 Br +28.2 BrOj + II-2 CO 3 + 160.8 Cl- +39-1 10,- +55-8 I0 4 - +46.5 OH - + 54.4 PO 4 h 298.0 S 2 3 +138-6 Cu + + 16.0 Mn + + + 50.2 CIO + 26.0 S 2 8 +278.2 Cu-f 15-8? Pb + + + 4-0 C10 3 + 23.4 S 4 O 6 +260.8 Fe + + +22.2 Fe + + + 9-3 Rb + + 625.0 Sn + + + +3-3 C10 4 38.7 HC0 3 +163.0 S0 3 +151-0 SO 4 +214.0 H+ o.o Sr + + +119-6 HP0 2 +143-9 Se -35.6 Hg+ 19-8 T1+ +1.7 HPO, +229.6 SeO 3 +119.6 K+ +61.8 Zn++ +35-0 HP0 4 +304.8 SeO 4 +144-8 Li + + 62.8 HS +1.2 Te -34.8 NO 2 + 27.0 Te0 3 +77.0 N0 3 - +48.9 Te0 4 +98.4 I- +13,1 S 12.6 TABLE 271. Heats of Neutralization in Kilogram-Calories, The heat generated by the neutralization of an acid by a base is equal, for each gram-molecule of water formed, to 13.7 Kg. cal. plus the heat produced by the amount of un-ionized salt formed, plus the sum of the heats produced in the completion of the ionizations of the acid and the base. (See also p. 209). Base. HCl.aq HNO 3 .aq H,SO 4 .aq HCN-aq CH 3 COOH. aq H 2 .C0 3 -aq KOH aq 13-7 I 3 .8 15-7 2-9 13-3 10. 1 NaOH aq 13-7 13-7 2.9 T 3-3 10.2 NH 4 OH aq 12.4 I2 -5 14.5 12.0 8. i Ca(OH) 2 aq 14.0 '3-9 I 5 .6 3- 2 *34 9-5 1 Zn(OH) 2 aq 9.9 9-9 II.7 8.1 8.9 5-5 |Cu(OH) 2 aq 7.5 7-5 9 .2 ~~ 6.2 TABLE 272. Heat of Dilution, H 2 S0 4 . In Kilogram-calories by the dilution of one gram-molecule of sulphuric acid by m eram-mole- cules of water. m . . . . Kg. Cal. . . 6.38 2 9.42 3 11.14 5 13.11 *9 16.26 49 16.68 ?l* 199 17.06 399 17.31 1599 o. 17.86 SMITHSONIAN TABLES. 2 47 TABLES 273-275. RADIATION CONSTANTS. TABLE 273. Radiation Formula and Constants for Perfect Radiator. (exclusive of convection losses) at the tem J = ff ( T /4) ( Stef an-Boltzmann) ; where C / / 273 120 6< 10 m + 12 787 +34 1059 +56 1400 220 I 110 84 8 588 + 14 808 +36 1087 143 2IO 2 IOO 107 6 606 + 16 831 +18 I]tI 5 +60 1470 200 3 90 4 62 S + 18 855 +40 H45 +70 1650 190 5 80 JQC 2 643 +20 879 +42 1174 +80 1850 180 9 70 201 662 + 22 93 +44 1204 +90 2070 170 60 245 +2 682 + 24 928 +46 1234 + 100 2310 160 19 5 294 +4 701 + 26 953 +48 +2OO 5960 ISO 27 40 350 +6 722 1 +28 979 + 50 1298 + IOOO 3I3XI0 8 140 38 30 4l6 +8 744 +30 1005 +52 I 33 +2OOO 3I8XIO* 130 50 20 488 + 10 765 +32 1032 +54 1363 + 5OOO 921 Xio 6 TABLE 275. Values of JA for Various Temperatures Centigrade. Ekholm, Met. Z. 1902, used ^ = 8346 and C 2 = 14349, and for the unit of time the day. For 100, the values for JA have been multiplied by 10, for the other temperatures by TOO. A T 100 C 30 C 15 C oC 30 C 80 C A 100 C 30 C 15 C oC 30 C 80 C 2 I o ?8 5" 2961 2.SS7 2I7S 1491 623 3 80 41 18 7 i o 19 2626 2281 19 S4 1363 594 4 469 So8 272 *38 27 i 20 386 2329 2034 17 S4 1242 I 1047 1526 1777 3464 1085 2296 628 M S4 172 493 8 39 21 22 337 295 2068 1840 1816 1622 1574 MI3 1129 1026 527 494 7 1768 4954 348i 2353 93 i I0 5 23 2S9 1639 1448 1270 931 460 8 1810 SQ28 435 2 3088 1372 203 24 228 1462 !298 1141 846 428 9 10 ii 12 1724 1398 1225 6382 6386 6127 S7I2 4834 4979 4833 4633 3646 378i 3798 3676 1730 1971 2098 2114 316 426 520 592 y 28 30 202 I 79 142 114 1307 1170 947 771 1165 1047 850 696 1028 926 757 623 768 698 482 398 369 317 272 13 1063 5222 4300 3467 2090 640 40 44 3" 285 259 209 I 3 14 918 792 4713 4220 3930 3SS6 3215 2944 2004 1889 666 673 20 10 146 77 135 72 124 66 102 55 38 16 683 3759 2674 1760 663 80 4 27 25 24 20 14 17 59 3340 2862 2417 1626 649 IOO 2 12 II 10 9 7 i SMITHSONIAN TABLES. 248 TABLE 276. BLACK-BODY SPECTRUM INTENSITIES (J\). Values of J\ using for Ci, 0.23 X io, Ct, 14350., X in M- W the figures given for J\ are plotted in cms as ordi- nates to a scale of abscissae of i cm to i M. then the area in cm' between the smooth curve through the resulting points and the axis of abscissae is equivalent to the radiation in calories per sec. from i cm* of a black body at the correspond- ing temperature, radiating to absolute zero. The intensities when radiating to a body at a lower temperature may be obtained by subtracting the intensities corresponding to the lower temperature from those of the higher. Ihe nature of the black-body formula is such that when \7' is small, a small change in Ct produces a great change in /A; e.g., when Ci/Xr is 100 or 10, the change is 100 and 10 fold respectively; as Xr increases, the change becomes proportional; e.g., when Ct/ Xr is less than 0.05, the change in /* is proportional to the change in 62. X 50 K. 100 K 150 K 200 K. 250 K. 273 K. 300 K. 373 K. 400 K. 500 K. 600 K. I.O .0583 .OJ72 .0176 .0201 .O18I .0161 .0112 .01124 .0831 .0538 i . 5 i .O142 .O172 .0133 .0117 .0102 .o 8 8 .0749 .0558 .03143 2.0 .0191 .0182 .0185 .on? .091 .0911 .O7I2 .0513 .0546 .03168 .00184 2-5 .O47I .Ottl .0142 .0103 .O7IO .077 .0646 .0419 .0450 .0397 .0066 3.0 .O409 .0196 .0115 .082 .061 8 .069 0545 .03102 .03242 .00265 .0131 3-5 .OJ44 .0163 .0102 .072 .0613 .055 .0420 .0329 .03620 .00482 .0189 4.0 .0306 .0142 .094 .0614 .0552 .0418 0457 .0360 .00115 .00690 .0229 5-0 .0143 .0111 .0714 .0517 .0430 .048 .0321 .00134 .00226 .00952 .0249 6.0 .01019 .0105 .0514 .058 .048 .0318 .0341 .00195 . 00301 .01001 .0224 7-o .01883 .096 .0.6 .0419 .0315 .0330 0359 .00225 .00328 .00925 .0186 8.0 .01672 -085 .0518 .0436 .0322 -0339 .0371 .00232 .00321 . 00801 .0149 9.0 .01422 .0718 .0538 0454 .0327 0345 .0377 .00220 .00295 .00672 .0118 10. -01331 0754 .0565 .0471 .0330 .0348 .0378 .00201 .00262 .00554 .00929 12.0 OllIS .0624 .0413 .0494 .0331 .0347 .0370 .00157 .00196 00374 .00585 14.0 .01021 .o 6 6i .0418 . O4IO2 .0329 .0341 .0358 .00117 .00144 .00254 .00380 16.0 .0914 .0611 .0422 .04IOO .0325 .0334 .0546 .0387 .00105 .00176 .00254 18.0 0957 .0517 .0424 .0492 .0321 .0328 .03368 .03653 .03760 .00124 .00176 20. o . O8l6 .0522 .0424 .0482 .0317 .03224 .03200 03493 03575 .03902 .00125 25.0 0897 .0530 .0421 0457 .O3I22 .03131 .03164 .03258 -03295 .03439 '.03589 30.0 .0726 .0532 .0416 .0438 .0466 .0479 .0497 .03146 .03164 .03237 .03311 40.0 .0769 .0526 .059 .0418 .04282 0433 .04391 04558 .04620 .04858 .O3IIO 50.0 0795 .0518 .0551 .0592 .O4I50 .04158 .04184 04255 .04281 .04381 .04482 75-0 .0787 .0*67 .0515 .0524 .05338 . 05383 - 05436 .05580 . 05634 .05834 .04103 IOO.O 0755 .0629 0657 .0588 .05119 .05134 .03150 .05197 .05214 .05277 .05342 800 1000 1500 2000 3000 4000 5000 6000 8000 10000 20000 K. K. K. K. K. K. K. K. K. K. K. O.I _ _ _ 0.0226 0.01115 0.0624 0.0331 0.038 IS- 540. 710000. O.2 0.087 O.OOI2 0.46 iS-4 184. 3660. 22100. 820000. 0-3 0.0315 0.44 24.2 263. 1310. 9640. 31000. 3820000. 0.4 0.0145 5-75 US- 690. 2280. 10300. 25600. 180000. 0-5 0.172 20.6 226. 952. 2400. 8400. 17800. 92300. 0.6 .0548 0.014 0-757 40.8 301. 1000. 2240. 6290. H950. 51460. o-7 .0540 .0468 0.064 1-93 59-2 328. 925. 1860. 4590. 8110. 30700. 0.8 .0651 .00045 0.180 3-58 321. 800. 1490. 3350. 5620. 19400. 0.9 0434 .00183 0.378 5-35 77-3 295. 671. 1177. 2470. 3980. 12820. I.O .00015 .00538 0.645 7.06 77.8 262. 554- 928. 1842. 2880. 8800. i-S 0775 .0848 2.07 10. 25 52.2 122. 2IO. 309. 527- 758. 1980. 2.0 .0367 .221 2.43 8.19 29.0 57-6 90.2 125. 198. 275- 668. 2-5 .0719 305 2.IO 5-68 16.4 29-5 43-9 58.9 90.1 121.9 284. 3-0 .0964 320 1.64 3.82 9.66 16.4 23-7 31-1 46.4 61.9 140.7 3.5 .1050 .296 1.22 2.60 6.02 9.84 13-8 17-9 26.3 34-7 77-3 4.0 .1027 .256 0.007 1. 80 3.90 6.20 8-59 II. O 15-9 20.9 45-9 5-o .0839 .178 0.511 0.923 1.84 2.81 3-8i 4.81 6.84 8.89 I9-I5 6.0 .0629 .119 0.302 0.514 0.973 1-45 1-935 2.42 3-40 4-39 9-34 7-0 0459 .O8ll 0.188 0.307 0.560 0.820 1.165 1.348 1.88 2.41 5-09 8.0 0335 .0562 0.122 0.194 0.344 0.498 653 0.808 1.20 1-43 3-00 9.0 .0247 .0398 0.0824 0.128 0.223 0.319 .416 0.513 0.709 0.90 1.87 10. .0184 .0288 0.0575 0.0880 0.151 0.214 .278 0.342 0.470 0.598 1.24 12. .01072 .Ol6o 0.0304 0.0553 0.0757 0.107 1373 0.168 0.230 0.292 0.602 14-0 16.0 .00660 .00425 .0096 .00606 0.0175 0.0108 0.0256 0.0155 0.0421 0.0253 0.0587 0.0350 0754 .0448 0.0921 0.0546 0.125 0.0742 0.159 0.0938 0.326 0.192 18.0 .00285 .00400 0.00697 0.00997 0.0160 0.0221 .0282 0.0344 o . 0466 0.0585 0.120 20. O .00198 .00275 0.00470 0.00668 0.01068 0.0147 .01868 0.0227 0.0307 0.0388 0.0789 25.0 .00000 .OOI22 0.00203 0.00284 0.00448 O.OO6I2 .00777 o . 00941 0.0127 0.0160 0.0325 30.0 .03464 .03619 O.OOIOI 0.00141 O. 00220 0.00299 .00378 0.00455 0.00616 0.00775 0.0157 40.0 .03159 .03209 0.03334 0.03459 O.O37IO 0.03960 .00121 0.00146 0.00197 0.00247 0.00498 50.0 .04684 .04888 0.03140 0.03191 0.03294 0.03397 .03500 0.03603 0.03808 O.OOIOI 0.00204 75-o .04144 .04184 0.04286 0.04387 0.04591 0.04794 0.04997 0. 03120 o. 03161 0.03201 o . 03406 IOO.O .05470 .05598 0.05919 0.04124 0.04188 0.04252 0.04317 0.04381 0.04510 0.04639 0.03128 See Forsythe, J. Opt. Soc., 4,331, 1920, relative values, 0.4 to 0.76 ju. (steps o.oi /.), 12 temperatures, 1000 to 5000 K. SMITHSONIAN TABLES. TABLES 277-278. RADIATION EMISSIVITIES- TABLE 277. Relative Emissive Powers for Total Radiation. 249 Emissive 600 + C. Ka of black body = i. Receiving surface platinum black at 25 C; oxidized surfaces oxidized at 1 and Overholzer, Phys. Review, 2, p. 144, 1913. Temperature, Deg. C. 200 400 600 Silver O.O20 O.O60 O.II3 0.180 O.2IO 0.369 0.4II 0.521 0.568 0.610 0.631 0.643 0.790 I. CO 0.030 0.086 O.IIO 0.153 0.185 0.424 0-439 0-547 0.568 0.600 0.710 0.788 I.OO 0.038 O.IIO 0.192 0.190 0.478 0.463 0.570 0.568 0.589 0.777 0.787 I.OO Platinum (i ) Oxidized zinc Oxidized aluminum Calorized copper, oxidized. . Cast iron Oxidized nickel Oxidized monel Calorized steel, oxidized Oxidized copper. . . Oxidized brass Oxidized lead Oxidized cast iron Oxidized steel Black body Remark: For radiation properties of bodies at temperatures so low that the radiations of wave-length greater than 20 n or thereabouts are important, doubt must exist because of the possible and perhaps probable lack of blackness of the receiving body to radiations of those wave-lengths or greater. For instance, see Table 379 for the transparency of soot. TABLE 278. Emissivities of Metals and Oxides. Emissivities for radiation of wave-length 0.55 and 0.65 ft. Burgess and Wallenberg, Bui. Bureau of Standards, n, 591, 1914. In the solid state practically all the metals examined appear to have a negligible or very small temperature coeffi- cient of emission for X = 0.55 and 0.65 /j, within the temperature range 20 C to melting point. Nickel oxide has a well-defined negative coefficient, at least to the melting point. There is a discontinuity in emissivity, for X = 0.65 p at the melting point for some but not all the metals and oxides. This effect is most marked for gold, copper, and silver, and is appreciable for platinum and palladium. Palladium, in addition, possesses for radiation a property analogous to suffusion, in that the value of emissivity (X = 0.65 /*) natural to the liquid state may persist for a time after solidification of the metal. The Violle unit of light does not appear to define a constant standard. Article con- tains bibliography. Metals. Cu Ag Au Pd Pt Ir Rh Ni Co Fe Mn Ti ex, 0.55 ju solid 0.55 /i liquid. . 0.65 n solid. . . liquid . . . 0.38 0.36 O. IO 0.15 0-35 0.35 0.04 0.07 0.38 0.38 0.14 0.22 0.38 0.33 0.37 0.38 0-33 0.38 0.30 0.29 0.29 0.30 0-44 0.46 0.36 0.37 0.36 0.37 0-37 0.37 0.59 0-59 0-75 0.75 0.63 0.65 Metals Zr Th Y Er Be Cb V Cr Mo W U eX, 0.55 n solid.... liquid. . . 0.65 /J, solid.. . liquid 0.32 0.30 0.36 0.36 0.40 0.35 0.35 0.30 o.SS 0.38 o. 61 0.81 0.61. 0.61 0.61 0.49 0.40 0.29 0-35 0.32 0-53 0-39 0-39 0.43 0.40 0.39 0-77 0.54 0.34 Oxides: 0.65/1 NiO C03O4 FC304 Mn 3 04 TiOa ThOa YzOs BeO CbOx V 2 0, Crrf), UiO e\ solid. 0.89 o 77 0.63 o. 52 o. 57 0.61 0.37 0.71 0.69 0.60 o. 30 liquid 0.68 0.63 0.53 0.47 0.51 0.69 0.31 SMITHSONIAN TABLES. 250 TABLES 279-281. RADIATION EMISSIVITIES. TABLE 279. Relative Emissivities of Metals and Oxides. Emissivity of black body taken as 100. True temperature C. 500 600 700 800 900 1000 1100 1200 Ref. 60 FeO.4o FeiOj = Fe heated in air X = Total = 0.65 n 85 85 86 87 98 87 97 88 95 88 93 89 92 i i NiO X = ..Total = 0.65 fji - 54 62 98 68 96 72 94 75 92 Si 88 86 87 2 2 Platinum: True temp. C App.* temp. C Total emiss. Pt o 3-i 100 4-0 200 300 4OO 5.1 6.1 7.0 500 8.0 750 10.3 1000 486 12.4 1200 630 14.0 1400 780 15-5 1600 930 16.9 1700 1005 17-5 3 3 3 Tungsten: True temp. K (abs.) X = 0.467 X = 0.665 200 Si- 8 48.2 600 50.8 47.2 1000 49-8 46.3 1400 48.9 45-3 1800 47-9 44-3 2200 47.0 43-3 2600 46.0 42.4 3000 45-0 41.4 3400 44.1 40.4 3800 39 5 4 4 4 * As observed with total radiation pyrometer sighted on the platinum. References: (i) Burgess and Foote, Bui. Bureau of Standards, 12, 83, 1915; (2) Burgess and Foote, loc. cit. ii, 41, 1914; (3) Foote, loc. cit. n, 607, 1914; (4) Worthing, Phys. Rev. 10, 377, 1917. TABLE 280. Temperature Scale for Tungsten. Hyde, Cady, Forsythe, J. Franklin Inst. 181, 418, 1916. See also Phys. Rev. 10, 395, 1917. The color temperature temperature of black body at which its color matches the given radiation. Lumens/ watt Color temperature. Black-body temperature. True temperature. True temperature. True- color. True brightness. i 1763 K. 1627 K. 1729 K. 1700 12 100 2 1917 1753 1875 1800 20 "5 3 2025 1840 1976 1900 26 128 4 2109 1909 2056 2OOO 31 142 5 2179 1967 2125 2100 36 158 6 2237 2017 2184 22OO 39 175 7 2290 2062 2238 23OO 41 191 8 2338 2102 2286 2400 43 208 9 2383 2140 2332 10 2425 2174 2373 TABLE 281. Color minus Brightness Temperatures for Carbon. Hyde, Cady, Forsythe, Phys. Rev. 10, 395, 1917. Brightness temp. K Color brightness 1600 1700 1800 IQOO 2000 2100 ,0 2200 SMITHSONIAN TABLES. TABLES 282, 283. COOLING BY RADIATION AND CONVECTION. 251 TABLE 282. - At Ordinary Pressures. According to McFarlane* the rate of loss of heat by a sphere placed in the centre of a spherical enclosure which has a blackened surface, and is kept at a constant temperature of about 14 C, can be expressed by the equations e .000238 + 3.06 X io6* _ 2.6 X io V, when the surface of the sphere is blackened, or e = .000168 -{- 1.98 X io 6 t 1.7 X io s/ 2 , when the surface is that of polished copper. In these equa- tions, e is the amount of heat lost in c. g. s. units, that is, the quantity of heat, small calories, radiated per second per square centimeter of surface of the sphere, per degree differ- ence of temperature t, and t is the difference of temperature between the sphere and the enclosure. The medium through which the heat passed was moist air. The following table gives the results. Differ- ence of tempera- ture t Value of e. Ratio. Polished surface. Blackened surface. 5 .000178 .000252 .707 IO .000186 .000266 .699 15 .000193 .OOO279 .692 20 .OOO2OI .000289 .695 25 .OOO2O7 .000298 .694 30 .000212 .000306 .693 35 .000217 .000313 .693 40 .OOO22O .000319 693 45 .000223 .000323 .690 5 .OOO225 .000326 .690 55 .000226 .000328 .690 60 .OOO226 .000328 .690 TABLE 283. -At Different Pressures. Experiments made by J. P. Nicol in Tail's Labo- ratory show the effect of pressure of the en- closed air on the rate of loss of heat. In this case the air was dry and the enclosure kept at about 80 C. Polished surface. Blackened surface. I et t et PRESSURE 76 CMS. OF MERCURY. 63.8 .00987 6l.2 .01746 57-1 5-5 .00862 .00736 50.2 41.6 .01360 .01078 44.8 .00628 34-4 .00860 40.5 .00562 27-3 .00640 34-2 29.6 .00438 .00378 20.5 00455 23.3 .00278 - - .00210 " " PRESSURE 10.2 CMS. OF MERCURY. 67.8 .00492 62.5 .01298 61.1 00433 57-5 .01158 55 .00383 53-2 .01048 49-7 .00340 47-5 .00898 44.9 .00302 43-o .00791 40.8 .00268 28.5 .00490 PRESSURE i CM. OF MERCURY. 65 .00388 62.5 .01182 60 .00355 57-5 .01074 5 .00286 54-2 .01003 40 .00219 41.7 .00726 30 .00157 37-5 .00639 23-5 .00124 34-o 27-5 .00569 .00446 24.2 .00391 SMITHSONIAN TABLES. * " Proc. Roy. Soc." 1872. t " P.roc. Roy. Soc." Edinb. 1869. See also Compan, Annal. de chi. et phys. 26, p. 526. 252 TABLES 284, 285. COOLING BY RADIATION AND CONVECTION. TABLE 284. Cooling of Platinum Wire In Copper Envelope. Bottomley gives for the radiation of a bright platinum wire to a copper envelope when the space between is at the highest vacuum attainable the following numbers : r = 4o8 C., et 378.8 X ID-*, temperature of enclosure 16 C. ^=505 C., ft= 726.1 X lo- 4 , " " 17 C. It was found at this degree of exhaustion that considerable relative change of the vacuum produced very small change of the radiating power. The curve of relation between degree of vacuum and radiation becomes asymp- totic for high exhaustions. The following table illustrates the variation of radiation with pressure of air in enclosure. Temp, of enclosure 16 C., * = 4 o8 C. Temp, of enclosure 17 C., t 505 C. Pressure in mm. et Pressure in mm. et 740. 8137.0 X ID-* 0.094 1688.0 X io-* 440. 7971.0 053 1255-0 140. 7875- -034 1 1 26.0 42. 4- 0.444 7591.0 6036.0 2683.0 .013 .0046 .00052 920.4 831-4 767.4 .070 034 .012 1045.0 727-3 539- 2 .00019 Lowest reached ) but not measured ) 746.4 726.1 " .0051 436.4 .00007 378.8 TABLE 285. Effect of Pressure on Loss of Heat at Different Temperatures. The temperature of the enclosure was about 15 C. The numbers give the total radiation in therms per square cen- timeter per second. Pressure in mm. Temp, of wire in C. About IO.O I.O 0.25 0.025 o.i M. 100 0.14 O.I I 0.05 O.OI 0.005 2OO .31 .24 .11 .02 0055 300 50 38 .18 .04 .OIO5 400 75 53 25 07 .025 5OO .69 33 .13 055 6OO 85 45 2 3 700 37 .24 800 - - - .56 .40 1 900 ~ - .61 NOTE. An interesting example (because of its practical importance in electric light- ing) of the effect of difference of surface condition on the radiation of heat is given on the authority of Mr. Evans and himself in Bottomley's paper. The energy required to keep up a certain degree of incandescence in a lamp when the filament is dull black and when it is " flashed " with coating of hard bright carbon, was found to be as follows : Dull black filament, 57.9 watts. Bright " " 39.8 watts. SMITHSONIAN TABLES. TABLES 286-287. TABLE 286. Conduction of Heat across Air Spaces (Ordinary Temperatures). 253 Loss of heat by air from surfaces takes place by radiation (dependent upon radiating power of surface; for small temperature differences proportional to temperature difference; follows Stefan-Boltzmann formula, see p. 247) conduction, and convection. The two latter are generally inextricably mixed. For horizontal air spaces, upper surface' warm, the loss is all radiation and conduction; with warm lower surface the loss is greater than for similar vertical space. Vertical spaces: The following table shows that for spaces of less than i cm width the loss is nearly proportional to the space width, when the radiation is allowed for; for greater widths the increase is less rapid, then reaches a maxi- mum, and for yet greater widths is slightly less. The following table is from Dickinson and van Dusen, A. S. Refrigerat- ing Engineers J. 3, 1916. HEAT CONDUCTION AND THERMAL RESISTANCES, RADIATION ELIMINATED, AIR SPACE 20 CM HIGH. Heat conduction. Thermal resistance. Cal./hour/cmV C. Same units. space, cm. Temperature difference. Temperature difference. 10 15 20 25 10 15 20 25 o.S 0.46 0.46 0.46 0.46 2.17 2.17 2.17 2.17 I.O i-5 0.24 O. IOO 0.24 o. 172 0.24 0.182 0.24 0.192 4-25 6.25 4.20 5.8o 4-15 5-50 4.10 5-20 2.O 0.161 0.178 0.200 0.217 6. 20 5.6o 5.00 4.60 3-0 0.172 0.196 0.208 o. 217 5-80 5-io l&o 1.60 Variation with height of air space: Max. thermal resistance 20 cm high; 8.9 at 2.5 cm, 60 cm high. 4.0 at 1.4 cm air space, 10 cm high; 6.0 at 1.6 cm, TABLE 287. Heat Convection in Air at Ordinary Temperatures. In very narrow layers of air between vertical surfaces at different temperatures the convection currents, in the main, flow up one side and down the other, with eddyless (stream-line) motion. It follows that these currents trans- port heat to or from the surfaces only when they turn and flow horizontally, from which fact it follows, in turn, that the convective heat transfer is independent of the height of the surface. It is, according to the laws of eddyless flow, proportional to the square of the temperature difference, and to the cube of the distance between the surfaces. As the flow becomes more rapid (e.g., for a 20 difference and a distance of 1.2 cm) turbulence enters, and the above relations begin to change. For the dimensions tested, convection in horizontal layers was a little over twice that in vertical. Taken from White, Physical Review, 10, 743, 1917. Heat Transfer, in the Usual C.G.S. Unit, i.e., Calories per Second per Degree of Thermal Head per Square Cm of Flat Surface, at 22.8 Mean Temperature. Where two values are given, they show the range among determinations with different methods of getting the tem- perature of the outer plate. It will be seen that the value of the convection is practically unaffected by this difference of method. 1 Thermal head. 8 mm gap. 12 mm gap. 24 mm gap. Total. Convection. Total. Convection. Total. Convection. 0.99 - . ooo 083 9 \ . ooo 084 8 J .000 065 1.98* / .000 109 \ no . ooo 084 o \ .000 085 2 J .000 OOO ooo I 4 4-Q5 . OOO III .000 001 / .000 086 6 \ 88 i .000 002 003 !) .000 090 over .000 025 9.89 19.76 f .000 112 I "3 .000 116 .000 003 003 .000 007 .000 093 7 95 2 / .000 107 7 \ 109 4 . OOO OIO .000 on .000 024 026 .000 106 .000 126 over .000 040 over . ooo 060 SMITHSONIAN TABLES. 254 TABLE 288. CONVECTION AND CONDUCTION OF HEAT BY GASES AT HIGH TEMPERATURES-' The loss of heat from wires at high temperatures occurs as if by conduction across a thin film of stationary gas adhering to the wire (vertical and horizontal losses very similar). Thickness of film is apparently independent of temperature of wire, but probably increases with the temperature of the gas nd vanes with the diameter of the wire according to the formula b-logb/a = 28, where B = constant for any gas, b = diameter of film, a, of wire. The rate of convection (conduction) of heat is the product of two factors, one the shape factor, s, involving only a and B, the other a function d> of the heat conductivity of the gas. If W = the energy loss in watts/cm, then W = s(i). s may be found from the relation kdt. where A is the heat conductivity of the gas at temperature T in calories/cm C. i at that of the atmosphere. The following may be taken as the conductivities of the corresponding gases at high temperatures: For hydrogen air... mercury vapor k = 28 X * = 4-6 X * = 2.4 X iQ-V;r{i/(i + .ooo2T)/(i + 77^)} + .ooo2T)/(i + To obtain the heat loss: B may be assumed proportional to the viscosity of the gas and inversely proportional to the density. For air (see Table 289(6)) B may be taken as 0.43 cm; for Hz, 3.05 cm; for Hg vapor as 0.078. Obtain s from section (a) below from a/B; then from section (b) obtain i for the proper temperatures; the loss will IN WATTS PER CM AS FUNCTION OF ABSOLUTE TEMP. (K.). rK. Hz Air Hg rK. H 2 Air Hg o.oooo o.oooo _ 1500 4.787 0.744 0.1783 100 0.0329 0.0041 1700 5-945 0.931 0.228 200 0.1294 0.0168 1900 7-255 1.138 0.284 300 0.278 0.0387 2IOO 8-655 1-363 0-345 400 0.470 0.0669 230O 10. 18 i. 608 0.411 500 0.700 0.1017 0.0165 2500 11.82 1.871 0.481 700 I. 261 0.189 0.0356 27OO 13-56 o.556 900 1.961 0.297 0.0621 2900 15-54 0.636 I IOO 1300 2.787 3.726 0.426 0.576 0.0941 o.i333 3IOO 3300 17.42 19-50 0.719 0.807 1500 4.787 0-744 0.1783 3500 21.79 0.898 SMITHSONIAN TABLES. * Langmuir Physical Review, 34, p. 401, 1912. TABLE 289. HEAT LOSSES FROM INCANDESCENT FILAMENTS- (a) WIRES OF PLATINUM SPONGE SERVED AS RADIATORS (TO ROOM-TEMPERATURE SURROUND- INGS). HARTMAN, PHYSICAL REVIEW, 7, p. 431, 1916. Diameter wire, cm. (A) Observed heat losses in watts per cm. Absolute temperatures. 900 IOOO 1100 1200 1300 1400 1500 1600 1700 I800 I90O 2000 o . 0690 0.0420 0.0275 0.0194 1.70 1-35 I. 12 0.9-2 2.26 1-75 1.40 I- 15 3.01 2.26 1.76 i-39 3-88 2.84 2.23 1.74 4.92 3-53 2-73 2. 12 6.18 4.29 3-23 2-54 7-70 5-33 3-91 3-04 9-63 6.60 4-67 3-64 12.15 8.25 5-72 4-32 15-33 10.20 7-00 5-10 19 25 12.45 8.64 6. 10 23-75 14-75 10.45 7-35 (B) Heat losses corrected for radiation, watts per cm (A-C). o . 0690 0.0420 0.0275 0.0194 O.QI 0.87 0.80 0.70 i. 05 1.02 0.92 0.81 1-23 1.17 1-05 0.89 1.36 i-3i 1.22 1-03 1-45 1.42 1-35 i.iS i-Si 1-45 1-37 1-23 1-54 1-57 1.46 1.31 1.66 1.76 i-So 1.40 2.OO 2.08 1.67 1.47 2.56 2-43 I.9I I-5I 2:g I'll 4-30 3-26 2.70 1.88 (C) Computed radiation, watts per cm, a =5.61 X io~ u .* o . 0690 o. 0420 0.0275 0.0195 0-79 0.48 0.32 0. 22 I. 21 0-73 0.48 0-34 1.78 1.09 0.71 0.50 2.52 i-53 I. 01 0.71 3-47 2. II 1.38 0.97 4.67 2.84 1.86 1.31 6.16 3-74 2-45 1-73 7-97 4.84 3-17 2.24 IO.I5 6.17 4-05 2.85 12.77 7-77 5-09 3-59 15-85 9-65 6.32 4.46 19-45 11.85 7-75 5-47 (D) Conduction loss by silver leads, watts per cm. 0.0420 0.0275 0.0195 0.42 0.18 0.06 0.46 O.2I 0.08 0.49 0.28 0.08 0.61 0.35 0.09 0-75 0.43 O.II 0.88 0.48 O. 12 I. CO 0.55 0.14 1.07 o.S7 0.15 *-J 0.60 O.22 I. 22 0.67 0.23 (E) Convection loss by air, watts per cm. 0.0420 0.0275 0.0195 0.45 O.62 0.64 0.56 0.71 0-73 0.68 o.77 0.81 o. 70 0.87 0.94 0.67 0.92 1.04 0.57 0.89 i. ii 0-59 0.91 1.17 o. 69 0.93 1-25 0-95 1.07 1.29 I. 21 1.24 1.30 * This value is lower than the presently (1919) accepted value of 5.72. (b) WIRES or BRIGHT PLATINUM 40-50 CM LONG SERVED AS RADIATORS TO SURROUNDINGS AT 300 K. LANGMUIR, PHYSICAL REVIEW, 34, p. 401, 1912. Diameter wire, cm. 0.0510 0.02508 0.01262 0.00691 0.00404 Observed energy losses in watts per cm. Absolute temperatures. 0.22 0.17 0.13 0.12 O.II 700 0.52 0-39 0.31 0.29 0.24 900 0.90 0.68 0-53 0.48 0.41 1.42 1.02 0.79 0.72 0.61 1300 2.03 i-45 i. ii o.99 0.84 1500 2.89 2.00 I. 4 6 1-33 1.14 1700 4.10 2.68 i-95 1.79 1-54 1900 5-65 3-55 2.71 2.48 2.13 Energy radiated in watts per cm.' 1 0.0510 0.02508 0.01262 0.00691 0.00404 0.002 o.ooi o. ooi 0.000 0.000 0.013 0.007 0.003 0.002 O.OOI 0.049 0.024 O.OI2 0.007 0.004 0.137 0.067 0.034 0.019 O.OII 0.323 0.159 0.080 0.044 0.026 0.67 0-33 0.17 0.09 0.05 1.25 0.62 0.31 0.17 O. 10 2.15 1. 06 0.53 0.29 0.17 ' Convection " losses in watts per cm. 0.0510 0.02508 0.01262 0.00691 o . 00404 0.22 O.I? 0.13 0.12 O.II 0.51 0.38 0-31 0.29 0.24 0.85 0.66 0.52 0.47 0.41 1.28 0-95 0-75 0.70 0.60 1.71 1.29 1.03 0-95 0.81 2.22 1.6 7 1.29 1.24 1.09 2.85 2.06 1.6 4 1.62 1.44 3-50 2.49 2.18 2.19 1.96 Thickness of theoretical conducting air film. 0.0510 0.02508 0.01262 0.00691 0.00404 Means. 0.28 0.30 0.42 0.31 0.27 0.31 0.42 0.32 0.43 0.37 0-33 0-37 0.44 0.38 0.43 0-39 0.33 0.41 0.49 0.40 0.47 0.42 0.36 0.45 0.56 0.43 0.56 0-49 0.37 0.45 0.69 0.47 0.47 0.49 0.36 0.56 o.47 0.26 0.25 0.38 Means. 0-34 0-43 0.54 0-37 0.41 to. 43 * Computed with a = 5.32, black -body efficiency of platinum as follows (Lummer and Kurlbaum): 492 K. 0.039; 654, 0.060; 795, 0.075; 1108, 0.112; 1481, 0.154; 1761 K., 0.180. For significance of last group of data, see next page. , 0.075; t Weighted mean. SMITHSONIAN TABLES. 256 TABLES 290-291. THE EYE AND RADIATION- Definitions: A meter-candle is the intensity of illumination due to a standard candle at a meter distance. The millilambert (o.ooi lambert) measures the brightness of a perfectly diffusing (according to Lamberts cosine law) surface diffusing i lumen per cm j . A brightness of 10 meter-candles equals i millilambert. o.ooi ml corresponds roughly to night exteriors, o.i, to night interiors, 10 ml to daylight interiors and 1000, to daylight exteriors. A bright- ness of 100,000 meter-candles Is about that of a horizontal plane for summer day with sun in zenith, 500, on a cloudy day, 4, ist magnitude stars just visible, 0.2, full moon in zenith, .001, by starlight; in winter the intensity at noon may drop about $. TABLE 290. Spectral Variation of Sensitiveness as a Function of Intensity. Radiation is easily visible to most eyes from 0.330 ft (violet) to 0.770 M (red). At low intensities near threshold values (gray, rod vision) the maximum of spectral sensibility lies near 0.503 /J. (green) for 90% of all persons. At higher intensities after the establishment of cone vision, the max. shifts as far as 0.560 u. See Table 297 for more accurate values of sensitiveness after this shift has been accomplished. The ratio of optical sensation to the intensity of energy increases with increasing energy more rapidly for the red than for the shorter wave-lengths (Purkmje phenomenon); i.e., a red light of equal intensity to the eye with a green one will appear darker as the intensities are equally lowered. This phenomenon disappears above a certain intensity (above 10 millilamberts). Table due to Nutting, Bulletin Bureau of Standards. The intensity is given for the spectrum at 0.535/1 (green). Intensity (meter-candles) = Ratio to preceding step = .00024 .00225 9.38 .0360 16 -575 16 2.30 4 9.22 4 36.9 4 147.6 4 590-4 4 Wave-length, X. Sensitiveness. 0.430/11 0.081 0.093 0.127 0.128 0.114 0.114 0.450 0-33 0.30 0.29 0.31 0.23 0.175 0.16 . 0.470 0.63 o.SQ 0.54 0.58 0.51 0.29 0.26 0.23 0.400 0.96 (0.89) (0.76) (0.89) (0.83) 0.50 0-45 0.38 0-35 0.505 I.OO I.OO I.OO I.OO 0.99 (0.76) 0.66 0.61 0.54 0.520 0.88 0.86 0.86 0.94 0.99 (0.85) 0.85 0.85 0.82 0.535 0.61 0.62 0.63 0.72 0.91 (0.98) 0.98 0.99 0.98 0-555 0.26 0.30 0-34 0.41 0.62 0.84 0-93 0.97 0.98 0-575 0.074 O.IO2 0.122 0.168 (0-39) (0.63) (0.76) (0.82) (0.84) 0.590 0.025 0-034 0.054 0.091 0.27 0.49 0.61 0.68 0.69 0.605 0.008 0.012 O.024 0.056 0.173 0-35 (o.45) 0-54 0-55 0.625 0.004 0.004 O.OII 0.027 0.098 o. 20 0.27 0.35 0-35 0.650 0.000 0.000 O.OO3 0.007 0.025 0.060 0.085 O.I22 0.133 0.670 X, maximum sensitiveness 0.000 0.503 0.000 0.504 O. OOI 0.504 0.002 0.508 0.007 0.513 0.017 0-530 0.025 0.541 0.03O 0.543 0.030 0.544 TABLE 291. Threshold Sensibility as Related to Field Brightness. The eye perceives with ease and comfort a billion-fold range of intensities. The following data were obtained with the eye fully adapted to the sensitizing field, B, the field flashed off, and immediately the intensity, T, of a test spot (angular size at eye about 5) adjusted to be just visible. This table gives a measure of the brightness, T, necessary to just pick up objects when the eye is adapted to a brightness, B. Intensities are indicated log intensities in milli- lamberts. Blanchard, Physical Review, n, p. 81, 1918. Log B 7 - 6.0 5.0 4.0 3 .0 2 O I O O O + 1 + -> o +3 o / Log T white 5 81 4 87 _L O 2 o \T/B..' i 5 o 38 13 068 0018 0018 Log T blue 6 *8 e 82 ^ A6 2 l8 I 62 Log T green . . 6 42 5 62 2 60 2 O8 I 62 Log T, yellow 5 47 5 17 4 61 I 62 Log T, red 4- 2 7 4 oo -2 96 SMITHSONIAN TABLES. TABLES 292-295. THE EYE AND RADIATION. TABLE 292. He tero chroma tic Threshold Sensibility. 257 The following table shows the decrease in sensitiveness of the eye for comparing intensities of different colors. The numbers in the body of the table correspond to the line marked T/B of Table 291. The intensity of the field was probably between 10 and 100 millilamberts (25 photons). Comparison color. 0.693 ju o . 640 [i 0-575 M o.SOSM 0-475 M 0-430M Standard color: red yellow green 0.693 M 0-575 M o. 505 /j. 0.044 0.174 O. 211 0.088 o. 160 o 180 0.165 0.032 o 138 0.180 0.166 0.197 0.174 0.150 0.134 blue 0.475 M 0.168 0.180 0.130 0.130 0.068 0.142 TABLE 293. Contrast or Photometric Sensibility. For the following table the eye was adapted to a field of o.i millilambert and the Sensitizing field flashed off. A neutral gray test spot (angular size at eye, 5 X 2.5) the two halves of which had the contrast indicated (\ transparent, $ covered with neutral screen of transparency = contrast indicated) was then observed and the brightness of the transparent part measured necessary to just perceive the contrast after the lapse of the various times. One eye only used, natural pupil. Blanchard, Physical Review, n, p. 88, 1918. Values are log brightness of brighter field in millilamberts. Time in seconds. I 2 5 IO 20 40 60 Contrast' o oo 80 3 47 3 82 4 3O 4 60 4 89 0.39 o 67 - .63 40 -3.36 3 .00 -3-58 3. 13 3-74 3 22 -3.85 3 21 3-97 3 33 -4-06 3 46 -4-23 3 48 o 87 IO 2 46 2 49 2 48 2 55 2 67 0.97 . 20 1. 57 -1.67 1.69 1-59 -1.63 I 73 TABLE 294. Glare Sensibility. When an eye is adapted to a certain brightness and is then exposed suddenly to a much greater brightness, the latter may be called glaring if uncomfortable and instinctively avoided. Observers naturally differ widely. The data are the means of three observers, and are log brightnesses in millilamberts. The glare intensity may be taken as roughly 1 700 times the cube root of the field intensity in millilamberts. Angle of glare spot, 4. Blanchard, Physical Review, loc. cit. Log. field... Log. glare. . . -6.0 1-35 4.0 1.90 2.O 2.60 1.0 2.00 0.0 3.28 + 1.0 3.60 2.O 3-00 3-0 4.18 4.0 4.48 TABLE 295. Rate of Adaptation of Sensibility. This table furnishes a measure of the rate of increase of sensibility after going from light into darkness, and the values were obtained immediately from the instant of turning off the sensitizing field. Both eyes were used, natural pupil, angular size of test spot, 4.9, viewed at 35 cm. Blanchard, loc. cit. Retinal light persists only 10 to 20 m when one has been recently in darkness, then in a dimly lighted room; it persists fully an hour when a subject has been in bright sunlight for some time. A person who has worked much in the dark "gets his eyes" quicker than one who has not, but his final sensitiveness may be no greater. Sensitizing field. Logarithmic thresholds in millilamberts after osec. i sec. 2 sec. 5 sec. 10 sec. 20 sec. 40 sec. 60 sec. 5 min. 3omin. 60 min. White o i ml .79 .20 - .60 - .00 - .82 - .69 - .6l -32 -3-82 -2.99 -2.30 -1.66 3-92 -4.08 -3-84 -2.69 -4-13 3-27 - -53 .00 - .36 -39 - -17 - .98 -4.50 3-79 -3.08 -2.46 4.91 -4-82 4.41 -3-37 4-75 4-15 -3-54 -2.64 5-27 S-ii -4-65 -3-57 -4.96 4-51 3-94 -2.88 5-53 -5-26 -4.78 -3-65 -5-i6 -4.82 4-31 3-20 -5-68 5-43 5-02 -3.73 3-32 -5-06 -4.61 -3-84 -5.81 -5.56 -5-09 -3-8o -5-68 -5-52 5-22 -4.76 -6.23 -5.80 -5-39 4.02 -5-91 -5-86 -5-83 -5-77 -6.06 6.04 6.01 -5-97 10. o ml 100 o ml . . Blue o.i ml Green o.i ml Yellow o i ml Red o . i ml SMITHSONIAN TABLES. 2^8 TABLES 296-298. THE EYE AND RADIATION. TABLE 296. Apparent Diameter of Pupil and Flux Density at Retina. Flashlight measures of the pupil (both eyes open) viewed through the eye lens and adapted to various field intensi- ties. For eye accommodated to 25 cm, ratio apparent to true pupil, 1.02, for the unaccommodated eye, 1.14. The pupil size varies considerably with the individual. It is greater with one eye dosed; e.g., it was found to be for o.oi miUilambert, 6.7 and 7.2 mm; for 0.6 ml, 5.3 and 6.5; for 6.3 ml, 4.1 and 5.7; for 12.6 ml, 4.1 and 5.7 mm for both and one eye open respectively for a certain individual. At the extreme intensities the two values approach each other. The ratio of the extreme pupil openings is about A, whereas the light intensities investigated vary over i ,ooo,ooo-fold. (Blanchard and Reeves, partly unpublished data.) FLM Diameter, mm Effective millilamberts. Observed. (1.14/1.02) XObs. area, mm 2 lumens per mm 2 O.OOOOI 8 8.96 64 8.4 X io- O.OOI O.I ti 8.51 7.28 57 42 7 . 6 X io-"> 5-6 Xio-s 10 4-0 4-48 16 2.1 X io- IOOO 2.07 2-35 4-3 5-8 X io-5 TABLE 297. Relative Visibility of Radiation. This table gives the relation between luminous sensation (light) and radiant energy. The results of two methods are given: one from measures of the direct equality of brightness, which some consider the true method, as more direct, but criticized because of the difficulty of judging heterochromatic light (Hyde, Forsythe, Cady, A. J. 48, 87, 1918, 29 observers); the other (Coblentz, Emerson, Bui. Bureau of Standards, 14, 219, 1917, 130 observers) depends on the disappearance of flicker when two lights of different color and intensity are alternated rapidly. Color has a lower critical frequency than brightness and disappears first. Data determined for intensities above Purkinje effect. See Table 290. Ratio of light unit Oumen) to energy unit (watt) at 0.5511, 0.00162 (Ives, Coblentz, Kingsbury). Visibility. Visibility. Visibility. Visibility. Visibility. X X X X X M M M M M HFC CE HFC CE HFC CE HFC CE HFC CE .40 .049 .010 .48 138 125 56 995 -998 .64 154 .194 72 .0374 .0397 .41 .0362 .017 49 .216 .194 57 944 .968 -65 .094 "5 73 .0336 .0348 42 .0041 .024 50 328 3i6 58 .855 .898 .66 051 .0645 74 .0318 .0328 43 .0115 .029 -Si 515 503 59 735 .800 .67 .026 0338 75 .049 .0320 44 .022 033 52 .698 .710 .60 .600 .687 .68 .0125 .0178 76 .045 .036 .041 53 -847 .862 .61 464 557 .69 .0062 .0085 .46 055 056 54 .968 954 .62 341 .427 .70 .0031 .0040 47 .087 .083 55 .996 994 -63 .238 .302 71 .0015 .00203 TABLE 298. Miscellaneous Eye Data. Light passing to the retina traverses in succession (a) front surface of the cornea (curvature, 7.9 mm); (b) cornea (equivalent water path for energy absorption, .06 cm); (c.) back surface cornea|(curv., 7.9 mm); (d) aqueous humour (equiv. HjO, .34 cm, n = 1.337); M front surface lens (c, 10 mm); (/ ) lens (equiv. HjO, .42 cm, n 1.445); (s) back surface lens (c., 6mm); (h) vitreous humour (equiv. HjO, 1.46 cm, n = 1.337). An equivalent simple lens has its principal point 2.34 mm behind (a), nodal point 0.48 mm in front of (g), posterior principal focus 22.73 mm behind (a), anterior principal focus 12.83 mm. in front of (a), curvature, 5.125 mm. At the rear surface of the retina (.15 mm thick) are the rods (30 X 2ju) and cones (10 (6 outside fovea) fj, long). Rods are more numerous, 2 to 3 between 2 cones, over 3,000,000 cones in eye. Macula lutea, yellow spot, on temporal side, 4 mm from center of retina, long axis 2 mm. Central depression, fovea centralis, .3 mm diameter, 7000 cones alone present, 6 X 2 or 3ju. In region of dis- tinct vision (fovea centralis) smallest angle at which two objects are seen separate is 50" to 70" = 5.65 to 5-I4M at retina; 50 cones in 100/1 here; 4/1 between centers, 3^1 to cone, i/x to interval. Distance apart for separation greater as depart from fovea. No vision in blind spot, nasal side, 2.5 mm from center of eye, 15 mm in diam. Persistence of vision as related to color (Allen, Phys. Rev. n, 257, 1900) and intensity (Porter, Pr. Roy. Soc. 70, 313, 1912) is measured by increasing speed of rotating sector until flicker disappears: for color, .4/1, .031 sec.; .45**, .020 sec.; .SM, 015 sec.; .57^1, .012 sec.; .68/Lt, .014 sec.; .76^1, .018 sec.; for intensity, .06 meter-candle, .028 sec.; i me, .020 sec.; 6 me, .014 sec.; 100 me, .010 sec; 142 me., .007 sec. Sensibility to small differences in color has two pronounced maxima (in yellow and green) and two slight ones (extreme blue, extreme red). The sensibility to small differences in intensity is nearly independent of the intensity (Fechner's law) as indicated by the following data due to Konig: 7//o 1,000,000 100,000 10,000 IOOO 100 50 10 5 I O.I 7o in me dl/I, white .60 n .036 .019 .024 .018 .016 .018 .020 .030 .028 .032 .038 .048 .061 059 .103 .123 .212 377 .00072 .0056 50M .018 .018 .024 .025 .036 .049 .080 .133 .00017 018 040 049 .074 .137 .00012 SMITHSONIAN TABLES. TABLE 299. PHOTOMETRIC DEFINITIONS AND UNITS. Luminous flux, F = radiant power according to visibility, i.e., capacity to produce sensation of light. Unit, the lumen = flux emitted in a unit solid angle (steradian) by point source of one candle power. Visibility, A\ , of radiation of wave-length X = ratio luminous flux to radiant power (energy) producing it. Mean visibility, K m , over any range of X or for whole visible spectrum of any source = ratio total flux (lumens) to total radiant power (erg/sec, or watts). Luminous intensity, 7, of (approximate) point source = solid angle density of luminous flux in direction considered = dF/du or F/u if intensity is uniform. o> is the solid angle. Unit, the candle. Illumination on surface is the flux density on the surface = dF/dS or F/S when uniform. 5 is the area of the surface. Units, meter-candle, foot-candle, phot, lux. (Lux = one lumen per m 2 ; phot => one lumen per cm 2 .) Brightness, b, of element of surface from a given point = dl/dS cos 0, where 6 is the angle between normal to surface and line of sight. Unit, candles per cm 2 . Normal brightness, 60 = dl/dS = brightness in direction normal to surface. Unit, the lambert. Specific luminous radiation, E' = luminous flux density emitted by a surface, or the flux emitted per unit of emissive area, expressed in lumens per cm 2 . For surfaces obeying Lam- bert's cosine law, E' = TT& O . The lambert, the cgs unit of brightness, is the brightness of a perfectly diffusing surface radiat- ing or reflecting one lumen per cm 2 . Equivalent to a perfectly diffusing surface with illumina- tion of one phot. A perfectly diffusing surface emitting one lumen per ft 2 has a brightness of 1.076 millilamberts. Brightness in candles per cm 2 is reduced to lamberts by multiplying by ir. A uniform point source of one candle emits 4?r lumens. One lumen is emitted by .07958 spherical candle power. One lumen emitted per ft 2 = 1.076 millilamberts (perfect diffusion). One spherical candle power emits 12.57 lumens. One lux = i lumen incident per m 2 = .0001 phot = .1 milliphot. One phot = i lumen incident per cm 2 = 10,000 lux = 1000 milliphots. One milliphot = .001 phot = .929 foot-candle. One foot-candle = i lumen incident per ft 2 = 1.076 milliphots = 10.76 lux. One lambert = i lumen emitted per cm 2 of a perfectly diffusing surface. One millilambert = .929 lumen emitted per ft 2 (perfect diffusion). One lambert = .3183 candle per cm 2 = 2.054 candles per in 2 . One candle per cm 2 = 3.1416 lamberts. One candle per in 2 = .4968 lambert = 486.8 millilamberts. Adapted from 1916 Report of Committee on Nomenclature and Standards of Illuminating Engineering Society. See Tr., Vol. u, 1916. SMITHSONIAN TABLES. 26O TABLES 300-302. TABLE 300. Photometric Standards. No primary photometric standard has been generally adopted by the various governments. In Germany the Heiner lamp is most used ; in England the Pentane lamp and sperm candles are used ; in France the Carcel lamp is preferred; in America the Pentane and Hefner lamps are used to some extent, but candles are more largely employed in gas photometry. For the photometry of electric lamps, and generally in accurate photometric work, electric lamps, standardized at a national standardizing institution, are commonly employed. The " International candle " is the name recently employed to designate the value of the candle as maintained by cooperative effort between the national laboratories of England, France, and America; and the value of various photometric units in terms of this international candle is given in the following table (taken from Circular No. 15 of the Bureau of Standards). i International Candle = i Pentane Candle. i International Candle = i Bougie Decimale. i International Candle = i American Candle. I International Candle = i.n Hefner Unit, i International Candle = 0.104 Carcel Unit. Therefore i Hefner Unit = 0.90 International Candle. The values of the flame standards most commonly used are as follows : 1. Standard Pentane Lamp, burning pentane 10.0 candles. 2. Standard Hefner Lamp, burning amyl acetate 0.9 candles. 3. Standard Carcel Lamp, burning colza oil 9.6 candles. 4. Standard English Sperm Candle, approximately .... i.o candles. TABLE 301. Intrinsic Brightness of Various Light Sources. Barrows. Ives & Luckiesl . National Electric Lamp Association. C.P.perSq. In. of surface of light. C. P. per Sq. In. of surface of light. C. P. per Sq. Mm. of sur- face of light. C. P. per Sq. In. of surface of light. Sun at Zenith . 600,000 _ _ 600,000 Crater, carbon arc . 200,000 84,000 130. 200,000 Open carbon arc . 10,000-50,000 - 10,000-50,000 Flaming arc . 5,000 - _ 5,000 Magnetite arc . - 4,000 6.2 - Nernst Glower . 800-1,000 (ii5v.6amp. d.c.) 3,010 4-7 (1.5 W.p.C.) 2,200 Tungsten incandescent, 1.15 w. p. c- _ 1,000 Tungsten incandescent, 1.25 w. p. c- 1,000 1,000 1.64 875 Tantalum incandescent, 2.0 w. p. c. 750 580 0.9 75 Graphitized carbon filament, 2.5 w p c 625 *7CO 1.2 625 UA Carbon incandescent, 3.1 w. p. c. u^;> 480 485 0-75 480 Carbon incandescent, 3.5 w. p. c. 375 400 0.63 375 Carbon incandescent, 4.0 w. p. c. 300 325 O.5O Inclosed carbon arc (d. c.) 100-500 _ 100-500 Inclosed carbon arc (a. c.) - - - 75-200 Acetylene flame (i ft. burner) . Acetylene flame () ft. burner) 75-100 53-o 33-o 0.082 0.057 75-100 Welsbach mantle 20-25 3^-9 0.048 20-50 Welsbach (mesh) 56.0 0.067 Cooper Hewitt mercury vapor lamp 16.7 14.9 0.023 '7 Kerosene flame 4-8 9.0 O.OI4 3-8 Candle flame . 3-4 3~4 Gas flame (fish tail) 3-8 2.7 0.004 3-8 Frosted incandescent lamp 4-8 2-5 ;irbon-dioxide tube lamp 0.6 - - 0-3-I-75 Taken from Data, 1911. TABLE 302. Visibility of White Lights. Range. Candle Power. 1 2 i sea-rr.ile=: 1855 meters .... 0.47 0.41 i 6 1 5 " " | 11.8 10. 1 Paterson and Dudding. * Deutsche Seewarte. i micro-calorie through i cm. at i m. =0.034 sperm candle = 0.0385 Hefner unit (no diaphragm) =. 0.043 Hefner unit (diap. 14 X 50 mm.). Coblentz Bui. B. of S., u, p. 87, 1914. SMITHSONIAN TABLES. TABLES 303-305. 2OI BRIGHTNESS OF BLACK BODY. CROVA WAVE-LENGTH. MECHANICAL EQUIVALENT OF LIGHT. LUMINOUS INTENSITY AND EFFICIENCY OF BLACK BODY- The values of L, the luminous intensity, are given in light watts/steroradian/cm 2 of radiating surface = (I/TT) J^ V^E^dX, where V^ is the visibility of radiation function. Mechanical equivalent. The unit of power is the watt; of lumininous flux, the lumen. The ratio of these two quan- tities for light of maximum visibility, X = 0.556 ,K the stimulus coefficient Vm; its reciprocal is the (least) mechanical equivalent of light, i.e., least since applicable to radiation of maximum visibility. A better term is umi lent of radiation o maximum visibility." One lumen =0.001496 watts (Hyde, Forsythe, Cady); or i w tion of maximum visibility (X = 0.556 n) = 668 lumens. White light has sometimes bee i denned as that emitted by a black body at 6000 K. The Crova wave-length for a black body is that wave-length, X, at which the luminous intensity varies bv the same fractional part that the total luminous intensity varies for the same change in temperature TABLE 303. Brightness, Crova Wave- length of Black Body, Mechanical Equivalent of Light.* TABLE 304. Luminous, Total Intensity and Radiant Luminous Efficiency of Black Body.* Tap Bright- ness, candles per cm 2 Crova wave- length, M Mech. equiv. watts per/. T, degrees absolute. Luminous intensity L watt/cm 2 Total intensity 340 8-75 275 Open arc, d.-c., series 6.6 325 2,920 11.15 305 Tungsten series 6.6 75 626 12.0 .384 Flame arc, a.-c., inclined electrodes 8.0 374 3.9*0 9-55 .405 Inclosed arc, d.-c., series Luminous arc, d.-c., multiple 6.6 4.0 475 440 3.315 2,870 14.32 15-32 459 547 Tungsten, multiple Nernst, a.-c., 3-glo\ver 0.545 i. 87 60 414 475 2,160 12.6 19.2 i Nernst, d.-c., 3-glower 1.87 414 2,160 19.2 .90 Inclosed arc, a.-c., series 7-5 480 2,410 19.9 2.05 Inclosed arc, a.-c., series 6.6 425 2,020 21.3 2.193 Tantalum, d.-c., multiple 40 199 21. 1 2.31 Tantalum, a.-c., multiple 40 199 21. 1 2.504 Carbon, 3.1 w. p. c., multiple 49.6 1 66 2 9 .9 3-24 Carbon, 3.5 w. p. c., series 6.6 2IO 626 33-6 3-47 Carbon, 3.5 w. p. c., multiple 56 1 66 33-7 3-5 Inclosed arc, d.-c., multiple 5- 55 i535 35-8 3.66 Inclosed arc, d.-c., multiple 3-5 385 1,030 37-4 3-84 Inclosed arc, a.-c., multiple 6.0 430 1,124 38.3 3-94 Inclosed arc, a.-c., multiple 4.0 285 688 41.4 4.265 Ives, Phys. Rev., V, p. 390, 1915 (see also VI, p. 332, 19*5); computed assuming z lumen = 0.00159 watt. Commercial Rating Lumens per Watt. Luminous Watts Flux -f- Watts In- put or True Efficiency. Open flame gas burner Bray 6' high pressure 0.22 O.OOO35 Petroleum lamp .26 .OOO4 Acetylene i.o liters per hour .67 .0011 Incandescent gas (low pressure) .350 lumens per B. t. u. per hr. 1.2 .0019 Incandescent gas (high pressure) .578 lumens per B. t. u. per hr. 2.0 .0031 Nernst lamp 4.8 .0076 Moore nitrogen vacuum tube Carbon incandescent (treated filament) 22O-v. oo-cycle, 113 ft. 4-watts per mean hor. C. P. 5.21 2.6 .0083 .0041 Tungsten incandescent (vacuum) 1.25 watts per hor. C. P. 8. .013 Carbon arc, open arc 9.6 amp. clear globe 1 1.8 .019 Mazda, type C 5oo-watt multiple .7 w. p. c. jr. .024 Mazda, type C 600 C. P. -20 amp. .5 w. p. c. 19.6 .031 Magnetite arc, series 6.6 amp. direct current 21.6 034 Glass mercury arc 40-70 volt; 3.5 amperes 23. .036 Quartz mercury arc Enclosed white flame carbon arc 174-197 volt ; 4.2 amperes 10 ampere, A. C. 267 .06 7 .042 " " 6.5 ampere, D. C. 35-5 057 Open arc " inclined 10 ampere, A. C. 29. .046 Enclosed ye low flame carbon arc 10 ampere, D. C. 10 ampere, A. C. 27.7 3M .044 050 t <( l< U 6.5 ampere, D. C. 34-2 54 Open arc, " , inclined 10 ampere, A. C. .066 10 ampere, D. C. 44-7 .071 TABLES 307-309. PHOTOGRAPHIC DATA. TABLE 307. Numerical Constants Characteristic of Photographic Plates. 263 Abscissae of figure are log E = leg // (meter- candles-seconds); Ordinates are densities, D = i/T ; E exposure = / (illumination in meter-can- dles) X t seconds; D, the density of deposit = i/T, where T is the ratio of the transmitted to incident intensity on de- veloped plate. * = inertia = intercept straight line portion of curve on log E axis. S = speed = (some constant)/ i; y gamma = tangent of angle a. L = latitude = projected straight line portion of characteristic curve on log E axis, expressed in ex- posure units = Anti log (b a). The curve illustrates the characteristic curve of a photographic plate. 2B- 24 X ^. ?n / 16 / 1 ? / b Q t- 2 -L- --- -*l 4 i i J 7 \ ^ 0^" ty a -*- \ \ . 4 > u 0. 6 b 9 1 2 1 i> 1 a 2 1 2 4 2 8 30 TYPICAL CHARACTERISTIC CURVE otf PHOTOGRAPHIC PLATE. TABLE 308. Relative Speeds of Photographic Materials. The approximate exposure may be obtained when the intensity of the image on the plate is known. Let L be the intensity in meter-candles; E, the exposure in seconds; P, the speed number from the following table; then E = i,35o,ooo/(L X P) approximately. Plate. Relative speed . Paper. Relative speed. Extremely high speed 100 ooo High speed 75,000 Slow enlarging Medium speed 60 ooo Rapid high contrast 6 < Medium speed high contrast Process, slow contrast 10,000 Rapid gas-light contrasty Lantern plate 3,000 Professiona i 25 TABLE 309. Variation of Resolving Power with Plate and Developer. The resolving power is expressed as the number of lines per millimeter which is just resolvable, the lines being opaque and separated by spaces of the same width. The developer used for the comparison of plates was Pyro-soda; the plate for the comparison of developers, Seed Lantern. The numbers are all in the same units. Huse, J. Opt. Soc. America, July, 1917. Plate. Albumen. Resolution. Process. Lantern . Medium High speed. speed. Resolving power 125 81 67 62 35 27 Developer . Resolving power. Developer. Resolving power. Developer. Resolving power. Pyro-caustic 77 Pyrocatechin 62 Amidol 51 Glycin 00 Pyro-metol 62 Process hydroquinone. . 5 64 Eikon.-hydroquinone 61 Ortol 49 Pyro 64 61 Rodinal 49 MQ25 64 Caustic hydroquinone. . 57 X-ray powders. . . 49 Metol 6l Eikonogen 57 Edinol 47 Nepera 62 Kachin 54 SMITHSONIAN TABLES. 264 TABLES 310-311. PHOTOGRAPHIC DATA- TABLE 310. Photographic Efficiencies of Various Lights. Source. Visual efficiency. Lumens per watt. Photographic efficiency. (a) (b) Ordinary plate. Ortho- chromatic plate. Pan- chromatic plate. Ordinary plate. Ortho- chromatic plate. Pan- chromatic plate. Sun 150 0.7 0.07 0.045 40 35 37 12 29 9 12 18 1 ,n 21.6 8.9 ii 23 100 181 8 18 600 218 324 126 257 % 106 23 25 33 37 56 64 1 08 316 IOO 155 28 500 195 275 112 234 177 1070 "5 32 35 41 45 62 68 99 354 IOO 130 8 165 249 104 "5 165 744 82 42 45 50 53 7 76 106 273 IOO 0.14 0.037 0.053 158 50 79 10 52 ii 62 12 0.37 o.Sl 1.74 2.41 6.1 8.9 1:1 47 IOO 0.21 O.O4O 0.086 I 3 2 46 68 10 45 II 86 14 0.52 0.74 2.2 3-0 6.8 9.8 5-2 7-3 54-2 IOO 0.24 0.042 0.13 99 39 62 8.5 2.O IO 60 10 0.68 0-95 2.7 3-5 7-7 II. 5-6 7-9 42 Sky Acetylene (screened) Pentane. . . . Mercury arc, quartz "Nultra" glass " crown glass. Carbon arc ordinary " white name " enclosed Carbon arc, " Artisto " Magnetite arc. . . Carbon glow-lamp Carbon glow-lamp Tungsten vacuum lamp vacuum lamp nitrogen lamp nitrogen lamp " blue bulb blue bulb. . Mercury arc (Cooper Hewitt).. . (a) Relative efficiencies based on equal illumination. (b) Relative efficiencies based on equal energy density. Taken from Jones, Hodgson, Huse, Tr. 111. Eng. Soc. 10, p. 963, 1915. TABLE 311. Relative Intensification of Various Intensifies. Bleaching solution. Blackening solution. Reference Intensi- fication. Mercuric bromide Amidol developer Ammonia Amidol developer Schlippe's salt Sodium sulphide Sodium stannate Sodium stannate Sodium sulphide Paraminophenol developer HgBr2 solution (Monckhoven sol. A).* Bleach according to Ben- nett; blackener.* Piper.* Debenham, B. J., f p. 186, '17. B. J. Almanac.* B. J. Almanac.* Desalme, B. J.,t p. 215, '12. Ordinary sepia developer. Hgl2 according to Bennett. i. IS i. IS 1-45 2.50 2.28 3-50 2.05 1-93 1-33 1-23 Mercuric chloride . . . Potassium bichromate -f- hydro- chloric acid . Mercuric iodide Lead ferricyanide Uranium formula Potassium permanganate + hydro- chloric acid Cupric chloride Potassium ferricyanide + potassium bromide Mercuric iodide See Nietz and Huse, J. Franklin Inst. March 3 1918. ' B. J. Almanac, see annual Almanac of British Journal of Photography t B. J. refers to British Journal of Photography. SMITHSONIAN TABLES. TABLE 312. WAVE-LENGTHS OF FRAUNHOFER LINES. 265 For convenience of reference the values of the wave-lengths corresponding to the Fraunhofer lines usually designated by the letters in the column headed " index letters," are here tabulated separately. The values are in ten millionths of a millimeter, on the supposition that the D line value is 5896.155. The table is for the most part taken from Rowland's table of standard wave- lengths. Index Letter. Line due to Wave-length in centimeters X io. Index Letter. Line due to Wave-length in centimeters X io. A !o 7621.28* 7594.06* G !c F : 4308.081 4307-907 a - 7164.725 g Ca 4226.904 B o 6870. 182 t h or H g H 4102.000 C or H a H 6563.045 H Ca 3968.625 a O 6278.303 f K Ca 3933-825 Di Na 5896.155 L Fe 3820.586 D 2 Na 5890.186 M Fe 3727.778 D 8 He 5875.985 N Fe 3581.349 Ei I" 5270.438 P Fe Fe 344LI55 3361.327 E 2 Fe 5269.723 Q Fe 3286.898 bi Mg Mg 5183.791 5172.856 R !" 3181.387 3'79-453 bg i Fe 5169.220 5169.069 5167.678 Si) sj Fe Fe Fe 3100.787 3100.430 3100.046 (Mg 5 i 6 7. 497 s Fe 3047-725 F or Hp H 4861.527 T Fe 3020.76 d Fe 4383-721 t Fe 2994-53 G' or H y H 4340.634 U Fe 2947.99 f Fe 4325-939 * The two lines here given for A are stated by Rowland to be: the first, a line " beginning at the head of A, outside edge"; the second, a "single line beginning at the tail of A." t The principal line in the head of B. $ Chief line in the a group. See Table 321, Rowland's Solar Wave-lengths (foot of page) for correction to reduce these values to standard system of wave-lengths, Table 314. SMITHSONIAN TABLCB. 266 TABLES 313-316. STANDARD WAVE-LENGTHS. TABLE 313. Absolute Wave-length * of Red Cadmium Line in Air, 760 mm. Pressure, 15* C. 6438.4722 Michelson, Travaux et Mem. du Bur. intern, des Poids et Mesures, 1 1, 1895. 6438.4700 Michelson, corrected by Benoit, Fabry, Perot, C. R. 144, 1082, 1907. 6438.4696 (accepted primary standard) Benoit, Fabry, Perot, C. R. 144, 1082, 1907. * ID Angstroms. 10 Angstroms = i MM = io~* mm. TABLE 314. International Secondary Standards. Iron Arc Lines in Angstrdms, Adopted as secondary standards at the International Union for Cooperation in Solar Research (transactions, 1910). Means of measures of Fabry-Buisson (i), Pfund (2), and Eversheim (3). Re- ferred to primary standard = Cd. line, A. = 6438.4696 Angstroms (serving to define an Angstrom). 76o mm., I5C. Iron rods, 7 mm. diam. length of arc, 6 mm.; 6 amp. for \ greater than 4000 Angstroms, 4 amp. for lesser wave-lengths ; continuous current, -{- pole above the , 220 volts ; source of light, 2 mm. at arc's center. Lines adopted in 1910. Wave-length. Wave-length. Wave-length. Wave-length. Wave-length. Wave-length. Wave-length. 4282.408 4547.853 4789.657 5083.344 5405.780 5615.661 6230.734 4315.089 4375-934 4592.658 4602.947 4878.225 4903-325 5110.415 5167.492 5434.527 5455-614 5658.836 5763.013 6265.145 6318.028 4427.314 4466.556 4647-439 4691.417 4919.007 5OOI.88I 5192.363 523 2 -957 5497-522 5506.784 6027.059 6065.492 6335-34I 6393.612 4494-572 453I-I55 4707.288 4736.786 5012.073 5049.827 5266.569 5371-495 5569-633 5586.772 6137.701 6191.568 6430.859 6494.993 TABLE 315. International Secondary Standards. Iron Arc Lines in Angstroms. Adopted in 1913. (4) Means of measures of Fabry-Buisson, Pfund, Burns and Eversheim. Wave-length. Wave-length. Wave-length. Wave-length. Wave-length. Wave-length. Wave-length. 3370.789 3399-337 3606.682 3640.392 3753.615 3805.346 3906.482 3907.937 4076.642 4118.552 4233-6I5 5709.396 6750.250 58577 59 Ni 3485-345 35 I 3-82i 3676.313 3677.629 3843.261 3850.820 3935.818 3977746 4134.685 4147.676 6546.250 6592.928 5892.882 Ni 3556.881 3724.380 3865.527 4021.872 4191.443 6678.004 (i) Astrophysical Journal, 28, p. 169, 1908; (2) Ditto, 28, p. 197, 1908; (3) Annalen der Physik, 30, p. 815, 1909. See also Eversheim, ibid. 36, p, 1071, 1911 ; Buisson et Fabry, ibid, 38, p. 245, 1912 ; (4) Astrophysical Journal, 39, p, 93, 1914, TABLE 316. Neon "Wave-Lengths. In- tensity. Wave length. In- tensity. Wave length. In- tensity. Wave length. In- tensity. Wave length. In- tensity. Wave length. 5 3369.004 5 3515.192 2 5820.155 4 6217.280 5 6717.043 6 34I/.906 8 3520.474 10 5852.488 7 6266.495 8 6929 . 468 6 3447.705 4 3593-526 6 5881.895 4 6304.789 3 7024.049 6 3454.197 4 3593.634 8 5944-834 8 6334.428 9 7032.413 5 3400.526 5 3000.170 4 5975-534 8 6382.991 3 7059.III 4 5 3464.340 3466.581 5 8 3633.664 5330.779 4 7 6029.997 6374.338 10 9 6402.245 6506.528 5 8 7I73.939 7245.167 6 3472.578 7 534L096 g 6096.163 4 6532.883 6 7438.902 4 | 3498.067 6 5400.562 9 6143.062 5 6598.953 5 7488.885 4 3501.218 4 5764.419 5 6163.594 8 6678.276 5 7535.784 International Units (Angstroms). Burns, Meggers, Merrill, Bull. Bur. Stds. 14, 765, 1918. SMITHSONIAN TABLES. TABLE 317. TERTIARY STANDARD WAVE-LENGTHS. IRON ARC LINES. For arc conditions see Table 314, p. 266. For lines of group c class 5 for best results the slit should be at right angles to the arc at its middle point and the current should be reversed several times during the exposure. Wave-lengths. Class. Inten- sity. Wave-lengths. Class. Inten- sity. Wave-lengths. Class. Inten- ! sity. #2781.840 4 4337-052 b3 5 5332.909 M 2 #2806.985 7 4369-777 b3 3 534L032 34 5 * 28 3 I -559 3 4415.128 bi 8r 5365.404 ai 2 #2858.341 3 4443.198 b3 3 5405.780 a 6 #2901.382 4 4461.658 a 3 4 5434.528 a 6 #2926.584 5 4489.746 *3 3 5473-9I3 a 4 #2986.460 #3000.453 3 4 4528.620 4619.297 C4 7 4 5497-5 2 ! 5501.471 a a 4 4 4 4786.811 C 4 3 5506.784 a 3 #3100.838 2 4 8 7i-33i C 5 8 J5535-4I9 a 2 #3154.202 4 4890.769 C 5 7 5563.612 b 3 #3217.389 A. " >? 4 4 4924.773 4939-685 a a 3 3 5975-352 6027.059 b b 2 3 #3307.238 *3347-932 4 4 4973- "3 4994.133 a a 2 3 6065.495 6136.624 b b 4 5 #3389.748 3 5041.076 a 3 6I57-734 b 4 #3476.705 5 5041.760 a 4 6165.370 b 3 #3506.502 *3553-74i 5 5051.641 5079.227 a a 4 3 6I73-345 6200.323 b b 4 4 #3617.789 6 5079-743 a 3 6213.44! b 5 #3659.521 5 5098.702 a 4 6219.290 b #3705.567 6R j 5 I2 3-7 2 9 a 4 6252.567 , b 6 #3749.487 8R 5127.366 a 3 6254.269 b 4 #3820.430 8R 5150.846 a 4 6265.145 b 5 *3 8 59-9*3 7R 5151.917 a 3 6297.802 b 4 #3922.917 6R l 5194.950 a 5 6335-342 b 6 #3956-682 6 5202.341 a 5 6430.859 b 5 #4009.718 5 5216.279 a 6494.992 b 6 #4062.451 4 5227.191 a 4 8 14132.063 bi 7 5242.495 a 3 t4 1 7 5-639 b 4 5270.356 34 8 14202.031 bi 7 r 53 28 -043 ai 7 14250.791 7 S3 28 - 537 34 4 * Measures of Burns. f Means of St. John and Burns. t Means of St. John and Goos. Others are means of measures by all three. References : St. John and Ware, Astrophysical Journal, 36, 1912; 38, 1913; Burns, Z. f. wissen. Photogj. 12, p. 207, 1913, J. de Phys. 1913, and unpub- lished data; Goos, Astrophysical Journal, 35, 1912; 37, 1913. The lines in the table have been selected from the many given in these references with a view to equal distribution and where possible of classes a and b. For class and pressure shifts see Gale and Adams, Astrophysical Journal, 35, p. 10, 1912. Class a: "This involves the well-known flame lines (de Watteville, Phil. Trans. A 204, p. 139. 1904), i.e. the lines relatively strengthened in low-temperature sources, such as the flame of the arc, the low-current arc, and the electric furnace. (Astrophysical Journal, 24, p. 185, 1906, 30, p. 86, 1909, 34, p. 37, 1911, 35, p. 185, 1912.) The lines of this group in the yellow-green show small but definite pressure displacements, the mean being 0.0036 Angstrom per atmosphere in the arc." Class b: "To this group many lines belong; in fact all the lines of moderate displacement under pressure are assigned to it for the present. These are bright and symmetrically widened under pressure, and show mean pressure displacements of 0.009 Angstrom per atmosphere for the lines in the region \ 5975-6678 according to Gale and Adams. Group c contains lines showing much larger displacements. The numbers in the class column have the following meaning : I, synv metrically reversed ; 2, unsymmetrically reversed ; 3, remain bright and fairly narrow under pres- sure ; 4, remain bright and symmetrical under pressure but become wide and diffuse ; 5, remain bright and are widened very unsymmetrically toward the red under pressure." For further measures in International units see Kayser, Bericht iiber den gegenwartigen Stand der Wellenlangenmessungen, International Union for Cooperation in Solar Research, 1913. For further spectroscopic data see Kayser's Handbuch der Spectroscopie. SMITHSONIAN TABLES, 2 68 TABLE 318. REDUCTION OF WAVE-LENGTH MEASURES TO STANDARD CONDITIONS- The international wave-length standards are measured in dry air at 15 C, 76 cm pressure. Density variations of the air appreciably affect the absolute wave-lengths when obtained at other temperatures and pressures. The follow- ing tables give the corrections for reducing measures to standard conditions, viz.: o = Xo(no no') (d do)/do in ten-thousandths of an Angstrom, when the temperature t C, the pressure B in cm of Hg, and the wave-length X in Angstroms are given; n and d are the indices of refraction and densities, respectively; the subscript o refers to standard conditions, none, to the observed; the prime ' to the standard wave-length, none, to the new wave-length. The tables were constructed for the correction of wave-length measures in terms of the fundamental standard 6438.4696 A of the cadmium red radiation in dry air, 15 C, 76 cm pressure. The density factor is, therefore, zero for 15 C and 76 cm, and the correction always zero for A = 6438 A. As an example, find the correction required for X when meas- ured as 3000.0000 A in air at 25 C and 72 cm. Section (a) of table gives (d do)/do = .085 and for this value of the density factor section (b) gives the correction to X of .0038 A. Again, if X, under the same atmospheric condi- tions, is measured as 8000.0000 A in terms of a standard X' of wave-length 4000.000 A, say, the measurement will reauire a correction of (0.0020 + 0.0008) = +.0028 A. Taken from Meggers and Peters, Bulletin Bureau of Stand- ards, 14, p. 728, 1918. TABLE 318 (a). 1000 X (d-do)/do. Bern 60.0 62.S 65.0 67.5 70 71 72 73 74 75 76 77 78 9C 192 -160 -126 -92 -59 - 4 6 -32 -19 -s +8 + 22 +35 +48 n 200 -167 133 100 -67 -53 -40 -27 -13 + 13 +27 +40 13 -206 172 -139 -106 -73 -60 -46 -33 20 7 +6 + 20 +33 IS 211 -178 145 112 -79 -66 -S3 -39 -26 -13 +13 +26 17 -216 -184 -ISI -118 -86 -73 -60 -47 34 21 -8 +5 +19 i 19 222 -189 -156 -124 -92 -79 -66 -53 -40 27 -14 -j +12 21 227 -iQS -I6 3 -130 -98 -85 -72 -59 -46 -33 21 -8 +5 23 232 200 -168 -136 104 91 -78 -65 52 40 27 -14 I 25 -238 -206 -174 -143 in -98 -85 -72 -60 -47 -34 22 -9 27 -243 211 -179 -148 -116 104 -91 -78 -66 53 40 -28 -15 2Q -2 4 8 -216 -185 -154 122 -109 97 -84 72 59 -46 -34 21 31 -253 222 -100 -159 -128 -116 -103 -91 -78 -66 -54 41 -29 33 -258 -227 -196 .-165 -134 121 -109 -97 -84 -72 -59 47 34 35 -262 231 200 170 139 127 114 IO2 90 77 -65 53 41 TABLE 318 (b). 8 = Xo(no-no')(d-do)/c?o, in Ten-thousandth Angstroms. Wave-lengths in Angstroms. iooo X d -do 2000 2500 3000 3500 4000 4500 5000 SSoo 6000 6500 7000 7500 8000 9000 1 0000 do Corrections in ten-thousandth Angstroms. -260 -259 -166 -116 -8 4 61 44 30 18 8 +1 +Q +17 + 24 +37 +50 -240 -239 154 \. -io 7 -7 8 -S 7 -4 c -25 5 -17 7 +1 +9 +16 + 22 +35 +46 220 -219 -141 -9 8 -7 i 5 2 3' -2t IS +1 +8 +14 + 20 +42 200 -199 -128 -89 -65 -47 -34 -23 -14 -6 +1 +7 +13 +19 +29 +38 -180 -179 115 80 58 42 30 21 -13 -6 +1 +6 + 12 +17 +26 +34 160 -159 10 ! -7 i -S 2 -3 i -2 7 ic ii 5 +1 +6 + 10 +15 + 23 +31 -140 120 -139 -119 90 62 45 3 77 54 39 2 3 24 16 io 3 20 14 8 4 4 C +9 +8 +13 +n + 20 +17 +27 +23 100 100 64 45 32 24 17 12 7 3 +0 +4 +7 +9 +14 +19 -80 -80 Si 36 26 -19 14 9 6 2 +0 +3 +s +7 + 12 + 15 -60 -60 -31 I -i 7 i 9 i i K n r 4 2 +0 + 2 +4 +6 +9 40 -40 -26 -18 -13 -9 -7 -5 - 3 I +0 +i +3 +4 +6 +8 CD 20 -13 -9 -6 -5 -3 -2 -i I +i +1 + 2 +3 +4 o o o o o o o o o o + 20 + 20 +13 +9 +6 +S +3 +2 +i +1 o I 2 2 3 4 +40 +40 +26 +18 +13 +9 +7 +5 ' +3 +1 -I 3 4 -6 -8 SMITHSONIAN TABLES. TABLE 319. SPECTRA OF THE ELEMENTS- 269 The following figure gives graphically the positions of some of the more prominent lines in the spectra of some of the elements. Flame spectra are indicated by lines in the lower parts of the panels, arc spectra in the upper parts, and spark spectra by dotted lines. Na K CS] Rti T1 In I I Hg lamp Co Ni Cu vacuo arc Ag I I Zn M arc Sn H He violet X-blue*r8reen-*yellowX-,orange* red i I i i i i I i i i i IV i i i I I i i i I i i ii I i i i i I i The following wave-lengths are in Angstroms. Na 5889.965 Rb 4202 Cu 4023 Mg 5168 5895.932 4216 4063 5173 K 4044 5648 5105.543* 5184 4047 5724 5153-251* 5529 5802 6207 5218.202* Sn 4525 7668 6299 5700 5563 7702 Tl 5351 5782.090* 5589 Li 4132 In 4102 5782.159* 5799 4602 45" Ag 4055 6453 6104 Hg 4046.8 4212 H 3970 6707.846* 4078.1 4669 4102 Cs 4555 4358.3 5209.081* 4340 4593 4916.4 5465.489* 4861 5664 4959-7 5472 6563 5945 5460.742* 5623 He 3I87.743' 6011 5769.598* Zn 4680. 138* 3888.646' 6213 5790.659* 4722.164* 4026.189' 6724 6152 4810.535* 4471.477' 6974 6232 4912 47x4.1431 4925 4921.929- 6103 5015.675" For other elements, see Kayser's Handbuch der Spectroscopie. * Fabry and Perot. t Merrill. 6362.345* 5875- 6i8f 6678. I49t 7065. i 88f SMITHSONIAN TABLES. 270 TABLE 320. SPECTRUM LINES OF THE ELEMENTS- Table of brighter lines only abridged from more extensive table compiled from Kayser and containing 10,000 lines (Kayser's Handbuch der Spectroscopie, Vol. 6, 1912). Wave- lengths, inter- Ele- Intensities. Wave- lengths, inter- Ele- Intensities. Wave- lengths, inter- Ele- Intensities national ment. national ment. national ment. Ang- stroms. Arc. Spark. Tube. Ang- stroms. Arc. Spark Tube. Ang- stroms. Arc. Spark. Tube. 3802.98 Nb 15 4 _ 3968.48 Ca 30 40 _ 4116.50 V IS S _ 08.21 I 10 72.01 Eu 20 20 18.48 Pr IS 10 10.73 Nh 10 20 74-71 Er IS 5 23.24 La 10 IS 14-45 Ra 20 2O 76.85 Tb 20 IO z8. 3 Y IS 8 Eu 20 2O 80.43 Br ,^_ 10 28.70 I L - 10 22.15 Rh 12 15 81.68 Em 15 28.91 Rh 15 10 28.47 Rh 12 IO 81.89 Tb IS 10 29-75 Eu So So 29-35 Mg IS 8 82.60 Y 12 12 30.42 Gd IS 10 32.30 Mg 2O IO 88.00 Ny 50 2O 35-29 Rh 12 10 36-83 Zr 15 _ 88.52 La 10 IS 35-80 Os IS S 38.29 S 8 10 91.13 Zr 8 12 37-13 Nb 12 4 38.29 Mg 2O 10 98.96 Zr 8 12 39-74 Nb IS 4 45-45 47.98 Co Tm 10 IS IS 10 4000.47 05-50 Tb 15 15 12 IO ~ 42.86 43-14 Y Pr IS 15 8 10, ~ 48-75 Tb IS IS 05-73 V 20 45-12 S IO 51.02 Cl 10 08.73 Pr 12 8 49-20 Zr 10 15 56.50 Rh IO 12 19.62 Pb 12 10 51-12 Er 15 4 58.29 Ni 20 8 22.70 Cu IS 10 52.63 Nb IS 5 60.86 Cl S 10 23-35 V 20 53-11 S IO 64.11 Mo 20 IO 23-71 Se 12 8 58.62 A IO 71-65 La 8 15 25.1 F 10 61.83 Ar 10 20 73-07 Co 10 12 30.80 Mn 18 8 62. 70 S 10 74.16 Tb 15 IS 31.70 La - 8 IS 63.64 Nb IS 10 76.66 Lu IS 10 33-03 Ga IO 30 64.66 Nb 12 5 88.64 He _ 10 33.06 Mn 15 8 66.43 Em 20 88.96 Nh IS 10 34-48 Mn IS 8 68.14 Nb 15 S 91.01 Nh 20 15 35-62 V 20 69.0 Se 10 10 94-09 Co IO IS 41-43 Mn 12 8 72.05 Ga IS 20 94-22 Pd IS 15 42-92 La 8 15 77-53 Y 12 20 96.36 Er IS 6 44-iS K 20 10 79.04 Ge 20 97.63 I 10 45-45 Nh 20 10 79-43 Pr 15 10 3900.53 Ti 15 10 45.82 Fe 6 15- 80.04 X 20 02.95 Mo IS 8 46.00 Dy 12 4 84.25 Lu 20 15 05.5 Si IS 4 46.6 Se 4 10 89.52 Pr IS 10 06.34 Er IS 10 17.21 K 20 10 90.91 Nb IS 9 07.14 Eu 30 20 48.73 Mn II 6 4200.65 A 10 07.52 Sc 12 6 55-53 Ag 50 6 01.82 Rb 20 IS 11.85 Sc IS 6 57-84 Pb 30 20 . 03-23 Em 10 14.26 Br 10 58-97 Nb IS 10 05.04 Eu 50 30 14.94 22.52 Sc X 12 __ 10 62.75 62.83 Cu Pr IS 12 IO 8 ~ 05-32 06.72 Nb Pr IS 15 4 12 25-43 Tb IS 10 63-47 Gd 20 08.96 Zr 12 30.51 Eu So So 77-3/4 La IO 12 11.14 Rh 15 IO 31. 10 33.67 I Ca 40 So 10 77-37 77-75 Y Sr IS So S 50 11.69 14-74 Dy Nb 12 12 S - 39-55 Tb IS 10 77-97 Dy 12 II IS-S2 Sr 30 30 40.07 I __ 10 78.79 ^ . ^,_ 10 15.56 Rb 20 10 _ __ 40.47 Rb IS 79-73 Nb IS 6 17-95 Nb IS 44-68 Dy 12 10 80.62 Ra 12 10 _ 21. 08 I __ 10 45-33 10 86.70 La 10 15 23.OO Pr IS 12 49.10 La 12 20 92.68 V IS 25.34 Pr IS 12 50.35 Y 12 12 99-80 V 20 26.56 Ge 7 So 51.01 X 10 4100.74 Pr IS 12 26.72 Ca 20 10 51-95 V IS 00.97 Nb 20 6 38.21 X 10 58.22 Zr 8 15 01.82 In 20 12 41.04 IT 12 IO 58.66 Pd 15 10 02.40 Y 12 8 44.34 Rb 15 58.85 Rh 15 12 03-4 F 10 45-2 Pb 20 66.23 67.59 Nb X 12 10 09.78 11.80 V V IS 20 10 45.38 46.3 X F 10 30 3968.40 Dy IS 12 4112-03 Os 12 4 4246.85 Sc IS 2O SMITHSONIAN TABLES. TABLE 320 (continued). SPECTRUM LINES OF THE ELEMENTS- 271 Wave- lengths, Intensity. Wave- lengths, Intensity. Wave- lengths, Intensity. inter- Ele- inter- Ele- inter- Ele- national ment. national ment. national ment. Ang- stroms. Arc. park. Tube. Ang- stroms, l Arc Spark. Tube. Ang- stroms. Arc. park. 'ube. 4253-61 54-34 S Cr 12 12 10 4477-77 81.17 Br Mg 20 10 4994-13 5035-36 Lu Ni 20 12 10 54.42 Nh 15 8 96.43 Pr 15 10 53-30 W 12 12 59-69 Bi 20 98.76 Pt 12 10 5135.08 Lu IS 60.84 Ob IS 5 4510-15 Pr 12 IO 56. 20 Sr 20 7 "* 06 Kr 10 22-59 Eu 20 20 i I. 19 I . 10 74.80 Cr 12 10 24.74 Sn 10 20 63.78 Pd IS 86.97 La 10 12 54-97 Cr 15 72.68 Mg 15 IS 4301.11 Nb 12 5 55-52 Ru 10 12 83.60 Mg 20 20 O2. 12 Bi 15 72-74 H 10 64.51 Cr 12 8 02.28 Y 12 73-09 Nb 12 5 5206.05 Cr 12 9 O3.6l Nd 20 10 74-26 I IO 08.42 Cr 12 10 05-49 Sr 10 20 85.47 X 10 09.08 Ag 30 20 05.78 Pr 15 10 89.35 Dy IS 5 24.70 W 12 12 07.92 Fe 6 15 94-09 Eu 30 20 56.95 Sr 20 6 08. I Em 10 4603 . 03 X 10 92.23 X ^ IO 09 . 63 Y 12 12 06.77 Nb 12 10 95-62 Pd IS 14.11 Sc 12 12 07-34 Sr 30 20 5330.65 O 10 19.60 Kr IO 09. 22 Em 10 32.01 Br IO 25-77 25.78 Nd Fe 'i 5 15 24.28 35.40 X Em IS 15 32.8 35-14 Sn s 20 2O 26.36 30.47 Nb X 12 15 27.29 27.98 Eu H 20 IS IO 50.49 52.86 Ny 20 IO 20 33-77 La 12 12 33-86 H 10 60.59 Mo IS 12 40.67 Ra IS 10 34-02 H 10 69.85 Se IO 43- 69 Cl s 10 44-11 Sm 15 74-08 Se -^ IO 48.01 A IO 46.16 Cr 12 10 95-27 Pd 12 49- 65 Em 15 48.66 Ni 15 54I9.I9 X IO 55. 47 Kr IO 61.92 Eu 20 IS 64-5 I IO 65.58 Br 4 10 66.65 I 10 65-49 Ag 30 2O 68.30 O 10 71.24 X 10 76.69 Lu 20 IO 74-5 1 Sc 10 12 72.12 Nb 12 10 76.91 . Ni 12 IO 74.81 Rh 15 12 75-36 Nb 12 8 80.95 Sr 20 IO 74-94 Y 15 20 80.138 Zn 10 20 . 96.78 I IO 79- 24 V 30 30 80.74 Em 10 5504-26 Sr 20 79-77 Zr IO 12 82.18 Ra 20 IS 06.51 Mo 20 IS 81.66 Mo 12 6 . 87.80 Zr 7 12 14-71 W 20 20 82.8 Se 8 10 4704-93 Br IS 10 21.80 Sr 20 83.55 Fe 10 20 . 08.26 I 10 33-01 Mo IS 12 84.73 V 20 30 14.42 Ni IS 8 42.78 Pd 12 86.9 Pb 20 22.164 Zn 10 20 56.49 Ny IS 89.98 V 2O 20 22.54 Bi 10 2O 62.5 Sn 30 93-17 X 10 30.86 Se 10 70.46 Mo IS IO 95- 24 V 15 10 38.12 Tl IS 89.2 Sa 2O 95-74 98.03 X Y 10 15 10 85-49 94.48 Br Cl ~ 10 20 10 10 5608.9 20.64 Pb As 12 IO 4401 . 54 Ni IS IS 4806.68 I 10 25-64 I 10 04.75 Fe 8 15 08.23 I 10 51-34 As IO 08.50 V 15 20 09-97 Cl 9 10 62.93 Y 12 08.83 Pr 12 10 __ 10.534 Zn 10 20 70.05 Pd IS ~- 10.09 I 10 11.83 Sr IS 8 98.54 V IS IS 11.71 Mo 12 6 19.28 Mo 12 S75I.40 Mo IS 20.46 24.36 Os Sm IS 2O IO 10 25-93 32.07 Ra Sr IS IS 10 6 99-4 5813-63 Sa Ra 20 IS 29.23 Pr IS 12 40.6 Se 4 10 52.49 Ne IS 34.26 35-58 37.23 I Eu Nb 20 12 2O 8 10 44-32 44-8 50-49 X Se I 6 IO 10 10 57-76 58.27 7S-64 Ni Mo He IS 12 8 10 42.56 46.6 Pt F 12 5 20 54-89 83-71 Y Y IO 12 IS 20 ~ 88.33 89-96 Mo Na IS 20 IO 20 48.11 X _ 10 4900.13 Y IO 20 95 93 Mo IS 10 5I-56 53-00 59-8 4462.21 Nd Em X 10 IS 10 10 20 ii-7 24.0 57-41 4962.27 Zn Zn 10 10 IS 15 20 20 - 95-93 5928.82 6090. 22 6121.80 Na Mo V H 20 15 IS 2O IS IS 10 NOTE. This table, somewhat unsatisfactory in its abridged form, is included with the hope to occupy its space later with a better table; e.g., no mercury lines appear since the scale of intensity used in the original tabl< in the intensity of all mercury lines falling below the critical value used m this table. SMITHSONIAN TABLES. 272 TABLE 321. STANDARD SOLAR WAVE-LENGTHS. ROWLAND'S VALUES. Wave-lengths are in Angstrom units (io~ 7 mm.), in air at 20 C and 76 cm. of mercury pressure. The intensities run from I, just clearly visible on the map, to 1000 for the H and K lines; below I in order of faintness to oooo as the lines are more and more difficult to see. This table contains only the lines above 5. N indicates a line not clearly defined, probably an undissolved multiple line ; s, a faded appear- ing line; d, a double. In the "substance" column, where two or more elements are given, the line is compound ; the order in which they are given indicates the portion of the line due to each element ; when the solar line is too strong to be due wholly to the element given, it is represented, Fe, for example; when commas separate the elements instead of a dash, the metallic lines coin- cide with the same part of the solar line, Fe, Cr, for example. Capital letters next the wave-length numbers are the ordinary designations of the lines. A indi- cates atmospheric lines, (wv), due to water vapor, (O), due to Oxygen. Wave- length. Substance. Inten- sity. Wave-length. Substance. Inten- sity. Wave- length. Sub- stance. Inten- sity. 3037.5103 3047.7255 Fe Fe 10 N 20 N 3372-947 3380.722 Ti-Pd Ni 10 d? 6N 3533-345 3536-709 Fe Fe 6 7 3053-530 S 7 d? 3414.911 Ni 15 354I-237 Fe 7 Mn, Ni IO 3423.848 Ni 3542.232 Fe 6 3057-552S 3059.2125 Ti, Fe Fe 20 20 3433-7I5 3440.7623 ) Q Ni, Cr Fe 8d? 20 3555-079 3558.6725 Fe Fe I 3067.3693 Fe 8 3441.1555 j Fe 15 3565-535S Fe 20 3073.091 Ti,- 6Nd? 3442.118 Mn 6 3566-522 Ni IO 3078.7695 Ti, - 8d? 3444.0203 Fe 8N 3570.2735 Fe 20 3088.1453 Ti 7 d? 3446.406 Ni *S 3572-014 Ni 6 3134.2305 Ni, Fe 8 3449-583 Co 6d? 3572-712 Se, - 6 3188.656 - Fe 6d? 3453-039 Ni 6d? 3578.832 Cr IO 3236.7033 Ti 7 9 3458.601 Ni 8 3581.3495 Fe 3 3239.170 Ti 7 3461.801 Ni 8 3584.800 Fe ' 6 3242.125 Ti, - 8 3462.950 Co 6 3585-105 Fe 6 3243.189 -, Ni . 6 3466.0155 Fe 6 3585-479 Fe 7 3247-6885 Cu 10 3475-5945 Fe IO Fe 6 3256.021 3267.8348 Fe? V 6 6 3476.8495 3483.923 Fe Ni 8 6d? 3587-130 3587-370 Fe Co 8 7 3271.129 Fe 6 3485493 FeCo 6 3588.084 Ni 6 3271.791 3274.0965 Ti, Fe Cu 6d? IO 3490.7335 3493.H4 Fe Ni 10 N 10 N 3593-636 3594.784 Cr Fe I 3277.482 Co-Fe 7 d? 3497-9825 Fe 8 3597-854 Ni 8 3286.898 3295.9513 Fe Fe,Mn 7 N 6 3500.9965 3510.466 Ni Ni 6d? 8 3605.4795 3606.8385 Cr Fe 6 3302.5108 Na 6 3512.785 Co 6 3609.0085 Fe 20 3315.807 3318.1603 Ni Ti 7 6 d? 35I3-965S 3515-206 Fe Ni 7 12 3612.882 Ni Fe 6d? 6 3320.391 Ni 7 3519.904 N 7 3618.9193 Fe 20 3336.820 Mg 8N 352i.4ios Fe 8 36I9-539 Ni 8 3349-597 Ti 7 3524-677 Ni 20 3621.6125 Fe 6 3361.327 Ti 8 3526.183 Fe 6 3622.1475 Fe 6 3365-908 Ni 6 3526.988 Co 6 3631.6053 Fe 15 3366.311 Ti, Ni 6d? 3529.964 Fe-Co 6 3640.5353 Cr-Fe 6 3369-7I3 Fe, Ni 6 3533-I56 Fe 6 3642.820 Ti 7 Corrections to reduce Rowland's wave-lengths to standards of Table 314 (the accepted standards, 1913). Temperature 15 C, pressure 760 mm. " The differences "(Fabry-Buisson-arc-iron) (Rowland-solar-iron)" lines were plotted, a smooth curve drawn, and the following values obtained : Wave-length 3000. 3100. 3200. 3300. 3400. 3500. 3600. 3700. Correction .106 .115 .124 .137 .148 .154 .155 .140 H. A. Rowland, " A preliminary table of solar-spectrum wave-lengths," Astrophysical Journal, 1-6, 1895-1897. SMITHSONIAN TABLES. TABLE 321 (continued). 273 STANDARD SOLAR WAVE-LENGTHS. ROWLAND'S VALUES. Wave-length. Substance. Inten- sity. Wave-length. Substance. Inten- sity. Wave-length. Substance. Inten- sity. 3647-9885 Fe 12 3826.0278 Fe 20 4045-975S Fe 3 365I-247 Fe,- 6 3827.980 Fe 8 4055.7015 Mn 6 3651.614 Fe 7 3829.5015 Mg IO 4057.668 7 3676.457 Fe, Cr 6 383I-837 Ni 6 4063.7595 Fe 20 3680.0695 Fe 9 3832.4505 Mg 15 4068.137 Fe-Mn 6 3684.2585 Fe 7 d? 3834.364 Fe 10 4071.9085 Fe 15 3685-339 Ti lod? 3838.4355 Mg-C 2 5 4077.8855 Sr g 3686.141 Ti-Fe 6 3840.5805 Fe-C 8 4i02.oooH5 H, In 4 oN 3687.6105 Fe 6 384LI95 Fe-Mn IO 4121.4775 Cr-Co 6d? 3689.614 Fe 6 3845.606 C-Co 8d? 4128.251 Ce-V,- 6d 3701.234 Fe 8 3850.118 Fe-Cr 10 4132.235 Fe-Co 10 3705.7085 Fe 9 3856.5245 Fe 8 4137.156 Fe 6 3706.175 Ca, Mn 6d ? 3857.805 Cr-C 6d? 4140.089 Fe 6 3709.3895 Fe 8 3858.442 Ni 7 4144.038 Fe 1C 3716.5915 Fe 7 3860.0555 Fe-C 20 4167.438 g 3720.0845 Fe 40 3865.674 Fe-C 7 4187.204 Fe 6 3722.6925 Ni 10 3872.639 Fe 6 4i9 I -595 Fe 6 3724.526 Fe 6 3878.152 Fe-C 8 4202.1985 Fe 8 3732.5455 Co-Fe 6 3878.720 Fe 7Nd? 4226.9O4sg Ca 20 d? 3733-469S Fe- 7 d? 3886.4345 Fe '5 4233.772 Fe 6 3735.0145 Fe 40 3887.196 Fe 7 4236.112 Fe 8 3737.2815 Fe 3 3894.211 - 8d 4250.2875 Fe 8 3738.466 6 3895-803 Fe 7 4250.9455 Fe 8 3743-508 3745-7I7S Fe-Ti Fe 6 8 3899-850 3903.090 Fe Cr, Fe, Mo 10 4254.5055 4260.6405 Cr Fe 8 IO 3746.0585 Fe 6 3904.023 8d 4271.9345 Fe 15 3748.4085 Fe IO 3905.6605 Si 12 4274.9585 Cr 7 d? 3749.6315 Fe 20 3906.628 Fe 10 4308.08 1 sG Fe 6 3753-732 Fe-Ti 6d? 3920.410 Fe 10 4325-939S Fe 8 3758.3755 3759.447 Fe Ti i2d? 3923.054 3928.0755 Fe Fe I2d? 8 4376.1075 H Fe 20N 6 3760.196 Fe 5 393045 Fe 8 4383.7205 Fe 15 3761.464 Ti 7 3933-523 8N 4404.9275 Fe 10 3763.9455 3765.689 Fe Fe 10 6 3933-825SK 3934.108 Ca Co, V-Cr IOOO 8N 4442.510 Fe Fe 8 6 3767.3415 3775.717 Fe Ni 8 7 3944.1605 3956.819 Al Fe T | 4447.8925 4494.7385 Fe Fe 6 6 3783.6745 Ni 6 3957-I77S Fe-Ca 7 d? 4528.798 Fe 8 3788.0465 Fe 9 3961.6745 Al 20 4534.139 Ti-Co 6 3795- M7S 3798.6555 Fe Fe 6 3968.350 39 68.625sH - Zr Ca 6N 700 4549.808 4554.21 is Ti-Co Ba 6d? 8 3799-693S 3805.4865 Fe Fe 6 3968.886 3969.413 Fe 6N 10 4572.1565 4603. 1 26 Ti- Fe 6 6 3806.865 ! Mn-Fe 8d? 3974.904 Co-Fe 6d? 4629.5215 Ti-Co 6 3807.293 Ni 6 3977.8915 Fe 6 4679.0275 Fe 6 3807.681 V-Fe 6 3986.9035 6 4703.1775 Mg IO 3814.698 _ 8 4005.408 Fe 7 4714.5995 Ni 6 3815.9875 Fe 15 4030.9185 Mn lod? 4736-963 Fe 6 3820.5865!, 3824.59 1 Fe-C Fe 2 I 4033.2245 4034.6445 Mn Mn 8d? 6d 4754.2255 4783.6135 Mn Mn I Corrections to reduce Rowland's wave-lengths to standards of Table 314 (the accepted standards, 1913). Temperature 15 C, pressure 760 mm. : Wave-length 3600. 3700. 3800. 3900. 4000. 4100. 4200. 4300- 44o. 4S- 4600. 4700. 4800. Correction .155 .140 .141 .144 .148 .15* .156 .161 167 .172 .176 ".179 .179. SMITHSONIAN TABLES. 274 TABLE 321 (continued). STANDARD SOLAR WAVE-LENGTHS. ROWLAND'S VALUES. Wave-length. Substance. Inten- sity. Wave-length Substance Inten- sity. Wave-length. Sub- stance. Inten- sity. 486l.527sF 4890.9483 "I T Fe 30 I 5948-7653 5985.0403 Si Fe 6 6 6593.1613 H Fe 40 4891.683 Fe 8 6003.2393 Fe 6 6867.45736 A(0) 6d? 4919.1743 Fe 6 6008.7853 Fe 6 6868.336 ) A(0) 6 4920.685 4957-785S Fe Fe 10 8 6013.7153 6oi6.86is Mn Mn 6 6 6868.478 J S 6869.1423 A(0) A(0) 6 7 5050.0083 Fe 6 6022.0163 Mn 6 6869.3533 A(0) 6 ci67.497sb4 Mg 15 6024.2813 Fe 7 6870.1 1 6 I A(0) 7 1 A 5171.7783 Fe 6 6065.7093 Fe 7 6870.249 J s A(0) 7 ) 5172.8563^2 Mg 20 6102.3923 Fe 6 6871.1803 A(0) 8 5183.7913^ Mg 30 6102.9373 Ca 9 6871.5323 A(0) 10 5233.1223 Fe 7 6108.3343 Ni 6 6872.4863 A(0) ii 5266.7383 Fe 6 6122.4343 Ca 10 6873.0803 A(0) 12 5269-723SE ! Fe 5283.8023 Fe 8d? 6 6136.8293 6137.915 Fe Fe 8 7 6874.0373 6874.8993 A(0) A(0) 12 5324.3733 Fe 7 6141.9383 Fe,Ba 7 6875.8303 A(0) *3 5328.236 Fe 8d? 6i55-35o 7 6876.9583 A(0) *3 5340.121 Fe 6 6162.3903 Ca 6877.8823 A(0) 12 534I-2I3 Fe 7 6169.2493 Ca 6 6879.2883 A(0) 12 5367.6693 Fe 6 6169.7783 Ca 7 6880.1723 A(0) 6 5370.1663 Fe 6 6170.730 Fe-Ni 6 6884.0763 A(0) 10 5383-578s Fe 6 6i9 T -393 s Ni 6 6886.000s A(0) II 5397-344S Fe 7 d? 6191.7793 Fe 9 6886.9903 A(0) 12 5405.9893 Fe 6 6200.5273 Fe 6 6889.1923 A(0) 1 3 5424.2903 Fe 6 6213.6443 Fe 6 6890.1513 A(0) 14 5429.911 Fe 6d? 6219.4943 Fe 6 6892.6183 A(0) 14 5447.1303 Fe 6d? 6230.9433 V-Fe 8 6893.5603 A(0) 15 5528.6413 Mg 8 6246.5353 Fe 8 6896.2893 A(0) 14 5569-848 Fe 6 6252.7733 -Fe 7 6897.2083 A(0) 15 5573-075 Fe 6 6256.5723 Ni-Fe 6 6900.1993 A(0) 14 5586.991 Fe 7 6301.718 Fe 7 6901.1173 A(0) 15 5588.985s Ca 6 6318.239 Fe 6 6904.3623 A(0) 14 5613.8773 5688.4363 Fe Na 6 6 6335-554 6337048 Fe Fe 6 7 6905.2713 6908.7833 A(0) A(0) 14 571 1.3133 Mg 6 6358.898 Fe 6 6909.6763 A(0) 1 3 5763.2183 Fe 6 6393.8203 Fe 7 6913.4483 A(0) ii 5857.6743 Ca 8 6400.2173 Fe 8 69I4-337S A(0) ii 5862.5823 Fe 6 6411.8653 Fe 7 6918.3703 A(0) 9 5890.18630-2 Na 3 6421.5703 Fe 7 6919.2503 A(0) 9 5896-155 DI Na 20 6439.2933 Ca 8 69 2 3-553 s A(0) 9 5901.6823 A(wv) 6 6450.0333 Ca 6 6924.4273 A(0) 9 5914.4303 -,A(wv) 6 6494.0043 Ca 6 7 I 9 I -755 A,- 6N 5919.8603 A(wv) 7 6495- 2I 3 Fe 8 7206.692 - A 6 5930.4063 Fe 6 6546.4793 Ti-Fe 6 Corrections to reduce Rowland's wave-lengths to standards of Table 314 (the accepted standards, 1913). Temperature 15 C, pressure 760 mm. : Wave-length 4800. 4900. 5000. 5100. 5200. 5300. 5400. 550. 5600. 5700. 5800. Correction .179 .176 .173 .170 .166 .171 .212 .217 .218 .213 .209 Wave-length 5800. 5900. 6000. 6100. 6200. 6300. 6400. 6500. Correction .209 .209 .213 .214 .213 .210 .209 .210. SMITHSONIAN TABLES. 6600. 6700. 6800. TABLE 322 SPECTRUM SERIES 275 In the spectra of many elements and compounds certain lines or groups of lines (doublets, triplets, etc.) occur in orderly sequence, each series with definite order of intensity (generally decreasing with decreasing wave-length), pres- sure effect, Zeeman effect, etc. Such series generally obey approximately a law of the form I - / _ N = X (m + RP ' where v is the wave-number in vacuo (reciprocal of the wave-length X) generally expressed in waves per on; m is a variable integer, each integer giving a line of the series; L is the wave number of the limit of the series (m = ); N, the "Universal Series Constant"; and R is a function of m, or a constant in some simple cases. Balmer's formula (1885) results if L = N/n*, where n is another variable integer and R = o. Rydberg's formula (1889) makes R a constant, and L is not known to be connected with N. Other formulae have been used with more success. Mogendorff (1906) requires R = constant/^, while Ritz (1003) has R = constant/wt*. Often no simple formula fits the case; either R must be a more complex function of m, or the shape of the formula is incorrect. Bohr's theory (see also Table 515) gives for Hydrogen If = {2ir*me*(M + m)}/MA, where e and m are the charge and mass of an electron, M the atomic weight, and h, Planck's constant. The best value for N is 109678.7 international units (Curtis, Birge, Astrophys. J. 32, 1910). The theory has been elaborated by Som- merfeld (Ann. der Phys. 1916), and the present indications are that N is a complex function varying somewhat from element to element. Among the series (of singles, doublets, etc.), there is apt to be one more prominent, its lines easily reversible, called the principal series, P(m). With certain relationships to this there may be two subordinate series, the first generally diffuse, D(m), and another, S(m). Related to these there is at times another, the Bergmann series B(m). m is the variable integer first used above and indicates the order of the line. The following laws are in general true among these series: (i) In the P(m) the components of the lines, if double, triple, etc., are closer with increasing order; in the subordinate series the distance of the components (in vibration number) remains constant. (2) Further, in two related D(m) and S(m), Av (vibration number difference) remains the same. (3) The limits (L) of the subordinate series, D(m) and S(m), are the same. (4) Av of the subordinate series is the same Av as for the first pair of the corresponding P(m). (5) The limits (L) of the components of the doublets (triplets, etc.) of the P(m) are the same. (6) The difference between the vibration numbers of the end of the P(m) and of the two corresponding subordinate series gives the vibration number of the first term of the P(m). The first line of the S(m) coincides with the first line of the P(m) (Rydberg-Schuster law). ther inform i the following tables, based greatly upon L>unz's Die benengesetze der JLimenspeiura, IJiss., Tubingen, 1911, wmcn has also appeared in book form, Hirzel, Leipzig. The following gives a schematic arrangement of the various series of a family in accordance with some of the above laws: Let {m, a, a} = N/(m + a + a/m 2 ) 2 ; VP(m) = \m, p, IT); VD(m) = \m, d, d)' VS(m) = \m t s, ff) and VB(m) = {m, b, /3); V originally referred to the variable part of the formula; when m takes a specific value, it becomes a constant term, viz. FS(i). Then a single line system is represented as follows: P'(m) = FS'(i) - VP'(mY, Vfa) = FP'(i) - FZX(f); S'(m) = FP'(i) - VS'(mY, [B'(m) = VD'(i) - VB'(m)}. A system of double lines would be represented as follows: P\"(m) = VS"(i) VPi"(mY, Di"(m) = FP"(i) VD"(mY, P 2 "(m) = F5"(i) - VP 2 "(mY, D 2 "(m) = FP"(i) - VD"(mY, Si"(m) = FP!"(i) - VS"(mY, {Bi"(m) = FZ>"(i) - VB"(m)}; S 2 "(m} = FP 2 "(i) - VS"(mY, \B 2 "(m) = VD"(i) - F-B"(m)). And similarly for a series of triplets, etc. Series Spectra of the Elements. The ordinary spectrum of H contains 3 series of the same kind: one in the; Schu- mann region, v = N(*/i 2 l /n?),n, 2, 3 . . .; one in the visible, v = N( l /2* V 2 ), n, 3, 4, 5- ', and one in the infra- red, v = N^/Z? V 2 ), n,4,s,6. . .He has three systems of series, one " enhanced," including the Pickering series formerly supposed to be due to H. The next two tables give some of the data for other elements. 2,66 1 0.5>u 0.3^ A 1 GUI 3|45 oo 2| 3|4|5||oo 21 3l4l5||oo| D(m) 5000 10000 20'000 30t)00 SEHIES SYSTEM or POTASSIUM. SMITHSONIAN TABLES. 276 TABLES 323-324. SPECTRUM SERIES. TABLE 323. Limits of Some of the Series. Pi (0) -&<*) Bl(0) *-, = Si (oo ) , P|(00) Z>,(oo) = S,(oo) *., W H 48,764 27,429 12,186 48,764 27,419 12,186 48,744 27,429 12,186 He 32,031 27,173 12,204 38,453 1 29,221 \ 29,222 12,208 - Li 43,484 28,581 12,202 Na *4i,445 24,472 24,489 12,274 - - K 35,oo6 21,963 22,020 13,471 - Rb 33,685 20,868 21,106 14,330 - Cs 31,407 19,674 20,228 16,809 16,907 - - Cu 62,306 3i,523 3i,77i 12,372 12,366 - Ag - - 61,093 30,621 31,542 12,351 - 39,752 Mg 26,613 ? ? ? 20,467 39,793 13,707 39,8i3 Ca 27,5io ? 60,423 60,646 28,929 17,761 33,983 < 34,089 28,929 28,950 49,353 34,142 28,964 Sr 25,745 - 55,029 55,830 31,026 31,420 27,605 27,705 45,895 31,607 27,766 Ba \ 51,616 ? ? ? 48,318 For the series of Zn, Cd, Hg, Al, Sn, Tl, O, S, Sn, see original reference. *48 lines have been measured in this series from 16,956 to 41,417. TABLE 324. First Terms of Some of the Series. Vibration Number Differences of Pairs A**, and Triplets A^i, A*>2. For the P(m) and the S (m) is given only the first or second term, since the term with index o may be omitted as coinciding with the first term of the S(m) or P(m) respectively. Consequently the numbers always proceed from greater to smaller wave-lengths. Which is the common line can always be recognized from the vibration numbers. See figure on the preceding page. The vibration differences can be obtained from Table 323. w BH o ., * < sw B(i) A, An A, H 21,334 15,233 9,871 5332 (6654 26,106 19,346 He I He 4,857 , 13,970 13,729 5348 Mg 6650 26,086 19,326 6,720 Na 17 9,231 I I7,"4 I 17, "8 14,149 14,148 5351 Ca [6650 26,045 20,495 19,285 19,828 _ K Rb 58 237 ~ Li 14,903 16,379 12,301 5347 ",763 25,414 22,153 Cs 552 Ma 16,973 12,215 7 782 25,191 Cu 249 16,956 12,198 7,766 54 ( 5036 5,oi9 16,381 21,834 921 K Rb Cs Cu Ag 13,043 12,985 12,817 12,579 ",733 11,178 30,783 30,535 30,472 30.551 8,552 8,493 6,776 6,538 3,32i 2,767 19,158 19,191 18,271 8,040 7,983 7,552 7,315 7,357 6,803 12,601 12,352 13,003 12,083 6592 7437 9972 9875 5495 5439 Sr Ba 5020 [5012 5,125 5,177 19,390 9,959 9,159 3,842 3,655 3,260 12,176 io,493 16,329 16,223 23,715 14,721 14,533 14,139 21,952 20,261 21,820 21,799 20,591 20,533 20,435 Sr Ba Zn Cd In Tl 223 801 1690 872? 2484? 112 2213 7793 106 394 878 389 1171 4632 20 52 187 370 190 542 1769 Mg 35,760 35,668 35,831 35,739 34,135 34,043 13,894 13,523 O S 3-7 18.2 2.1 II. I 12,645 Se 45 SMITHSONIAN TABLES. TABLES 325-326. TABLE 325. Index of Refraction of Glass. Indices of refraction of optical glass made at the Bureau of Standards. 277 nces o reraction of optical glass made at the Bureau of Standards. Correct probably to o ooooi The com position given refers to the raw material which went into the melts and does not therefore refer to the comoosition of the finished glass. Melt. 123 241 135 116 188 151 163 76 Wave-length. Ordinary crown. Borosili- cate crown. Barium flint. Light barium crown. Light flint. Dense barium crown. Medium flint. Dense flint. Hg 4046 . 8 Hg 4078.1 H 4340-7 -53189 53147 .52818 -53817 -53775 -53468 .58851 58791 58327 I-5QI37 i . 59084 i . 58698 i . 60507 i . 60430 i . 59860 63675 .63619 .63189 -65788 -65692 64973 69005 .68894 .68079 Hg 4358.6 H 4861.5 Hg 4916.4 .52798 .52326 .52283 53450 .53008 52967 . 58299 . 57646 .57587 1.58674 1.58121 1.58071 1.59826 i . 59029 i - 58958 .63163 . 62548 .62492 .64931 63941 63854 .68030 .66911 .66814 Hg 5461 . o .51929 52633 57105 1.57657 i . 58380 - 62033 63143 .66016 Hg 5769.6 Hg 5790-5 51771 .51760 . 52484 52475 56894 .56881 1-57473 i 5746o 1.58128 1.581*2 .61829 .61817 62834 .62815 .65671 . 65650 Na 5893 . 2 Hg 6234-6 5I7I4 -51573 -52430 .52297 .56819 56634 1.57406 1.57242 1.58038 1.57818 .61756 .61576 62725 .62458 65548 .65250 H 6563.0 .51458 .52188 . 56482 1.57107 1-57638 .61427 .62241 .65007 Li 6708.2 K 7682.0 .51412 .51160 -52145 .51908 56423 . 56100 1.57054 1.56762 1-57567 1.57183 .61369 . 61047 62157 .61701 64913 .64405 (Percentage composition) SiOz 67.0 64. 2 53-7 48.0 53-9 37-0 45-6 39-0 Na 2 O 12.0 9.4 i-7 2.0 I.O 3-4 3-0 K20 5-0 8.3 8.3 6.1 7-6 2.7 4-1 4.0 BzOs 3-5 II. 2.7 4.0 5-o BaO 10.6 6.1 14-3 29-5 47-0 ZnO i-5 2-5 IO.O 7-7 As 2 3 0.4 0.4 i-4 0.3 CaO i .0 2.O ^_ 3-0 4-o PbO 16.7 35-2 44-0 49.0 Sb 2 3 I.O TABLE 326. Dispersion of Glasses of Table 325. Melt. 123 241 135 116 188 151 163 76 D 1-51714 1.52430 1.56819 i.574o6 i . 58038 1.61756 1.62725 1.65548 r-*c 0.00868 0.00820 0.01164 0.01014 0.01391 O.OII2I 0.01700 0.01904 WjT) I 48 8 56 6 55 * 36.9 34- 4 *-c D n f 0.00612 0.00578 0.00827 0.00715 0.00991 0.00792 0.01216 0.01363 n F n G r 0.00492 o . 00460 0.00681 0.00577 o . 0083 i 0.00641 0.01032 0.01168 n D -n c 0.00256 0.00242 0.00337 o . 00299 0.00400 0.00329 0.00484 0.00541 i SMITHSONIAN TABLES. 278 TABLES 327-329. INDEX OF REFRACTION FOR GLASS. TABLE 327. - Glasses Made by Schott and Gen, Jena. The following constants are for glasses made by Schott and Gen, Jena : A , c D, F, o, are the indices of refraction in air for A=o.76S2/i, 0=0.6563/1, D=o.5S93, F=o.486i, G / = 0.4341. z/=( D I)/(F c). Ultra-violet indices: Simon, Wied. Ann. 53, 1894. Infra-red: Rubens, Wied. Ann. 45, 1892. Table is revised from Landolt, Bornstein and Meyerhoffer, Kayser, Hand- buch der Spectroscopie, and Schott and Gen's list No. 751, 1909. See also Hovestadt's "Jena Glass." Catalogue Type = 0546 0381 Oi8 4 Ol02 Oi6 5 S57 Designation = Zinc-Crown. Higher Dis- persion Crown. Light Silicate Flint. Heavy Silicate Flint. Heavy Silicate Flint. Heaviest Sili- cate Flint. Melting Number:= 1092 1151 45' 469 500 163 v = 60.7 51.8 41.1 33-7 27.6 22.2 . f Cd 0.2763^ 56759 _ _ _ _ _ S Cd .2837 56372 - - - i Cd .2980 55723 5793 .65397 - - M Cd .3403 54369 .55262 .63320 .71968 85487 - * Cd .3610 53897 .54664 .61388 70536 .83263 ~ rt H .4340^. .52788 53312 59355 .67561 .78800 1-94493 *O H .4861 .52299 52715 56515 .66367 .77091 1.91890 1 Na .5893 .51698 .52002 57524 .64985 75'30 1.88995 H .6563 .51446 S^JZ 57 II 9 .64440 .74368 1.87893 . M K .7682 5"43 .51368 .56669 .63820 73530 1.86702 '_J .8oo/m 5'3 S'3 1 5659 6373 7339 1.8650 *0 1.200 .5048 .5069 5585 .6277 7215 1.8481 1. 600 .5008 .5024 5535 .6217 7 l 5 l 1.8396 S 2.000 .4967 4973 5487 .6171 .7104 1.8316 2.400 - 544 .6131 " 1.8286 Percentage composition of the above glasses : O 546, SiO 2 , 65.4; K 2 O, 15.0; Na 2 O, 5.0; BaO, 9.6; ZnO, 2.0; Mn 2 O 3 , o.i ; As 2 O 3 , 0.4; B 2 3 , 2.5. 0381, SiO 2 , 68.7; PbO, 13.3; Na 2 O, 15.7; ZnO, 2.0; MnO 2 , o.i ; As 2 O 5 , 0.2. O 184, SiO 2 , 53.7 ; PbO, 36.0; K 2 O, 8.3; Na 2 O, i.o; Mn 2 O 3 , 0.06; As 2 O 3 , 0.3. O 102, SiO 2 , 40.0; PbO, 52.6; K 2 O, 6.5; Na 2 O, 0.5; Mn 2 O 3 , 0.09; As 2 O 5 , 0.3. O 165, SiO 2 , 29.26; PbO, 67.5; K 2 O, 3.0; Mn 2 O 3 , 0.04; As 2 O 3 , 0.2. S 57, SiO 2 , 21.9; PbO, 78.0; As 2 O 5 , o.i. TABLE 328. Jena Glasses. No. and Type of Jena Glass. D for D *D I Specific Weight. O 225 Light phosphate crown . . O 802 Boro-silicate crown .... UV 3 199 Ultra-violet crown . . . 0227 Barium-silicate crown . . . O 114 Soft-silicate crown .... O 608 High-dispersion crown . . UV 3248 Ultra-violet flint . . . . O 381 High-dispersion crown . . O 602 Baryt light flint 5*59 .4967 5035 5399 5151 5149 5332 .5262 .5676 .5686 5398 5710 .5900 6235 .6489 7174 7541 .9170 i .9626 .00737 0765 0781 0909 0910 0943 0964 1026 1072 1 IO2 1142 1327 1438 1599 1919 2434 2743 4289 4882 70.0 64-9 64-4 59-4 56.6 54-6 55-4 5'-3 53- 51.6 47-3 43-0 41.1 39-1 33-8 29.5 27-5 21.4 19.7 .00485 0504 0514 0582 0577 595 0611 0644 0675 0712 0711 0819 0882 9965 1152 1439 1607 245i 2767 00515 0534 0546 0639 0642 0666 0680 0727 0759 0775 0810 0943 IO22 1142 1372 1749 1974 3109 3547 .00407 0423 0432 05'4 0521 0543 0553 0596 0618 0629 0669 0791 0861 0965 1180 IS* 1 i73o 2808 3252 2.58 2.38 2.41 2.73 2-55 2.60 2-75 2.70 3-12 2.83 2.87 3 .r6 3-28 3.67 3.87 4-49 4-78 6.or 6-33 S 389 Borate flint O 154 Ordinary light flint .... Oi8 4 " "".... O 748 Baryt flint O 41 " " O 165 " . S 386 Heavy flint TABLE 329. Change ol Indices of Refraction for 1 C in Units of the Fifth Decimal Place. No. and Designation. Mean Temp. C D F G' AH 100 n S 57 Heavy silicate flint . . . O 154 Light silicate flint . . . 58.8 58.4 1.204 0.225 1.447 0.261 2.090 0-334 2.810 0.407 0.0166 0.0078 0327 Baryt flint light .... O 225 Light phosphate crown 58.3 58.1 0.008 0.202 0.014 0.190 0.080 o.i 68 0-137 0.142 0.0079 0.0049 SMITHSONIAN TABLES. Pulfrich, Wied. Ann. 45, p. 609, 1892. TABLES 330-332. INDEX OF REFRACTION, TABLE 330. Index of Refraction of Rock Salt In Air. 279 44 . Obser- ver. * n. Obser- ver. 4* n. Obser- ver. 0.185409 1.89348 M 0.88396 .534011 L 5-8932 .516014 P .204470 .291368 1.76964 1.61325 .. .972298 .98220 532532 532435 ii P 6.4825 5^5553 .513628 L P .358702 1-57932 " 1.036758 .531762 L u 5 '3467 L .441587 1.55962 " 1.1786 .530372 P 7.0718 .51 1062 P .486149 1.55338 above. #2=3.866619 M s = 5569.7 1 5 A 3 2 = 3292-47 SMITHSONIAN TABLES. 280 TABLES 333-336. INDEX OF REFRACTION. TABLE 333. -Index of Refraction of Fluorite in Air. MM) n Obser- ver MM) Obser- ver MM) M Obser- ver. 0.1856 1.50940 S I -4733 1.42641 P 4.1252 1.40855 P .19881 .21441 1.49629 1.48462 u 1.6206 1.42596 1.42582 M 4.4199 4.7146 L40559 .40238 .22645 1.47762 M 1.7680 1.42507 M 5.0092 .39898 u 25713 1.46476 " I-9I53 1-42437 " 5-3036 39529 32525 34555 .39681 1.44987 1.44697 1.44214 M 1.9644 2.0626 2.1608 1.42413 1-42359 1.42308 5-5985 5-8932 6.4823 .39142 .38719 37819 .48607 I-437I3 P 2.2IOO 1.42288 " 7.0718 .36805 " 58930 .65618 .68671 1-43393 1.43257 1.43200 P S 2-3573 2.5537 2.6519 1.42199 1.42088 1.42016 ,, 7.6612 8.2505 8.8398 35680 34444 33079 M M .71836 i. 43 T 57 M 2.7502 1.41971 9.4291 .31612 " .76040 1.43101 " 2.9466 1.41826 " 51.2 3.47 RA .8840 1.42982 P 3- '430 1.41707 " OI.I 2.66 " 1.1786 1.42787 " 3-2413 1.41612 " 00 2.63 S 1.3756 1.42690 '. 3-5359 I.4I379 M733 1.42641 3-8306 1.41120 References under Table 331. where a' 2 = 2.03882 Ai' 2 = 0.007 706 * = 0.003 1 999 /== 0.0000029 1 6 ^ = 6.c 6.09651 J/ 2 =o.oo6i3 A, 2 = 0.00884 71/3=5114.65 A r 2 = 1260.56 Aj, = 0.0940;* (P) TABLE 334. Change of Index of Refraction for 1C in Units of the 5th Decimal Place. C line, 1.220; D, 1.206; F, 1.170; G, 1.142. (PI) TABLE 335. -Index of Refraction of Iceland Spar (CaCO :t ) in Air. *GO o Obser- ver. A (^) n e Obser- ver. A (/a) * Obser- ver. 0.198 _ 1.5780 M 0.508 1.6653 1.4896 M 0.991 1.6438 1.4802 C .200 1.9028 '5765 " 533 1.6628 1.4884 .229 J . 6 393 1.4787 .208 1.8673 IJ664 1.6584 1.4864 u 307 1.6379 1.4783 .226 I.8l3O 1.5492 643 1.6550 1.4849 " 497 1.6346 1-4774 .298 1.7230 LS'Si C .6 S 6 1.6544 1.4846 " .682 1-6313 - -340 .361 I./008 1.6932 1.5056 1.5022 M C .670 .760 1.6537 1.6500 1.4843 1.4826 < -749 .849 1.6280 1.4764 .4IO 1.6802 1.4964 .768 1.6497 1.4826 M .908 _ M757 4 32 I.6755 1-4943 M ! .801 1.6487 1.4822 Q 2.172 1.6210 .486 1.6678 1.4907 -905 1.6458 1.4810 2.324 1-4739 C Carvallo, J. de Phys. (3), g, 1900. M Martens, Ann. der Phys. (4) 6, 1901, 8, 1902. P Paschen, Wied. Ann. 56, 1895. PI Pulfrich, Wied. Ann 45, 1892. RA Rubens-Aschkinass, Wied. Ann. 67, 1899. S Starke, Wied. Ann. 60, 1897. TABLE 336. Index of Refraction of Nltroso-dimethyl aniline. (Wood.) A n A n A n A n A n 0.497 2.140 1 0.525 J-945 0.584 8l5 0.636 1.647 0.713 I.7I8 .50 2.II4 536 1.909 .602 .796 .647 I-758 73 L7I3 .506 .508 .516 2.074 2.025 1.985 546 | :g 1.879 1.857 1.834 .611 .620 .627 '.778 .769 .659 .669 .696 1-75 1-743 1-723 749 763 1.709 1.697 Nitroso-dimethyl-aniline has enormous dispersion in yellow and green, metallic absorption in violet. See Wood. Phil. Mag. 1903. SMITHSONIAN TABLES. TABLES 337-338. INDEX OF REFRACTION. TABLE 337. Index of Refraction of Quartz (S10 2 ). 281 Wave- length. Index Ordinary Ray. Index Extraordinary Ray. Tempera- ture C. Wave- length. Index Ordinary Ray. Index Extraordinary Ray. Tempera- ture C. fk M 0.185 193 1.67582 .65997 1.68999 67343 18 0.656 .686 1.54189 .54099 1.55091 .S4998 18 < .198 .206 .65090 .64038 .66397 .65300 .760 1.160 53917 53 2 9 .54811 H .214 .63041 .64264 .969 .5216 _ .219 .62494 63698 " 2.327 5!5 6 _ .231 .61399 .62560 .84 539 _ 257 .59622 .60712 " 3.18 4944 _ .274 340 5 8 75 2 .56748 .59811 57738 M 3 4799 4679 Rubens. - .396 .55815 56771 4.20 4569 _ .410 55650 .56600 " 5.0 .417 _ .486 .54968 .55896 6.45 .274 _ 0.589 1.54424 1-55334 U 7.0 1.167 ~ Except Rubens' values, means from various authorities. TABLE 338. Indices of Refraction for various Alums.* r> u Index of refraction for the Fraunhofer lines. i Q EH a B c D E i F Q Aluminium Alums. -ffAl(SO 4 ) 2 +i2H 2 O.t Na NH 3 (CH 3 ) K 1.667 1.568 J-735 17-28 7-17 14-15 1.43492 45 or 3 .45226 143563 .45062 45303 I-43653 45177 45398 1.43884 .45410 45645 1.44185 .45691 45934 1.44231 45749 .45996 1.44412 .45941 .46181 1.44804 46363 Rb Cs NH 4 1.852 1.961 1.631 7-21 15-25 15-20 45232 45437 .45509 .45328 45517 45599 45417 .45618 45693 .45660 .45856 45939 45955 .46141 .46234 -45999 .46203 .46288 .46192 .46386 .46481 .46618 .46821 46923 Tl 2.329 10-23 .49226 493 1 7 49443 .49748 .50128 .50209 50463 .51076 Chrome Alums. J?Cr(SO 4 ) 2 +i2H,O.t Cs K 2.043 1.817 6-12 6-17 1.47627 .47642 1-47732 4773 s 1-47836 .47865 1.48100 48137 1.48434 .48459 1.48491 48513 1.48723 48753 1.49280 .49309 Rb 1.946 12-17 .47660 47756 .47868 .48151 .48486 .48522 48775 49323 NH 4 1.719 7-18 .47911 .48014 .48125 .48418 .48744 .48794 .49040 49594 Tl 2.386 9-25 .51692 51798 5 I 923 .52280 .52704 52787 53082 53808 Iron Alums. /?Fe(SO 4 ) 2 +i2H 2 O.t K i. 806 7-1 1 1.47639 1.47706 1.47837 1.48169 1.48580 1.48670 1.48939 1.49605 Rb 1.916 7-20 .47700 47770 .47894 .48234 .48654 .48712 .49003 .49700 Cs 2.061 20-24 .47825 .47921 .48042 .48378 .48797 .48867 .49136 49818 NH 4 1.713 7-20 47927 .48029 .48150 .48482 .48921 .48993 .49286 .49980 Tl 2-385 *S~*7 .51674 .51790 5 J 943 52365 52859 52946 .53284 .54112 * According to the experiments of Soret (Arch. d. Sc. Phys. Nat. Geneve, 1884, 1888, and Comptes Rendus, 1885). t JR stands for the different bases given in the first column. For cither alums see reference on Landolt-Bornstein-Roth Tabellen. SMITHSONIAN TABLES. 282 TABLE 339. INDEX OF REFRACTION. Selected Monorefringent or Isotropic Minerals. The values are for the sodium D line unless otherwise stated and are arranged in the order of increasing indices. Selected by Dr. Edgar T. Wherry from a private compilation of Dr. E. S. Larsen of the U. S. Geological Survey. Mineral. Formula. Index of refraction, X = 0.589^. Villiaumite NaF 3NaF. 3 LSF.2AlFi SiOi-nHiO CaF, KjO.Al203.4SO3.24HiO 3Na 2 0. 3 AljO v 6Si0 2 . 2 NaCl SiO 2 Na 2 O.Al 2 3 . 4 SiO 2 .2H 2 O 5Na 2 0. 3 Al 2 3 .6Si0 2 . 2 S0 3 Like preceding + CaO 4Na 2 0. 3 Al.,0 3 .6Si0 2 .Na 2 S 6 K 1 O.Al 2 O s . 4 Si0 2 2 Cs 2 0. 2 Al 2 O 3 .9SiO 2 . H 2 O NaCl Al,0,.nH,0 3 FeA.2As 2 6 . 3 K 2 0.sH 2 O MgO.AliOs 3(Ca, Mg, MnJO.AszOs MgO 3CaO.Al 2 O 3 .3SiO 2 3 (Mn, Fe)O.3BeO.3SiO2.MnS 3MgO.A)3.3SiOj 3 Ca0 3 .(Al, Fe) 2 03. 3 Si02 (Mg, Fe)O.Al 2 3FeO.Al2O3.3SiO 2 FeO.AlzOs ZnO.AlzOs 3 MnO.Al2O3.3SiOj CaO 3CaO.Cr 2 O3.3SiO 2 3CaO.Fe 2 O 3 .3SiO 2 6CaO.3T a2 O5.CbOF 3 CuCl Contains CaO, Ce 2 Os, TiO2, etc. 3 CaO.(Fe, Ti) 2 O 3 .3(Si, Ti)O 2 PbO.CuCl 2 .H 2 (Mg, Fe)0.(Al, Cr)^ 2Bi 2 Os.3SiO2 AgCl Contains Hg, NH, Cl, etc. FeO.CrzOs SbzOs Ag(Br, Cl) MnO NiO sCaO^TiO^SbsOs CuI. 4 AgI AgBr Contains CaO, FeO, TiO^ etc. Cul (Zn, Fe, Mn)O.(Fe, Mn)sOa (Zn, Fe)S CaO.TiOz C HgO. 2 HgCl MnS 2 MnS CuzO .328 -339 . 406-1 . 440 434 456 483 .486 .487 .400 495 .496 .500 500 S2S 544 570 .676 .723 727 .736 .736 739 745 755 .763 770 .778 .800 =*= .800 =*= .811 .830 .838 .857 925 930 .960-2.000 .980 .050 .050 .050 .061 .065 .070 .087 .i|o* .160 . 18 (Li light) .200 . 2CO 253 -330 346 .360 (Li light) .370-2.470 .380 .419 . 490 (Li light) .690 (Li light) . 700 (Li light) .849 Cryolithionite Opal Fluorite Alum Sodalite Cristobalite Analcite Sylvite Noselite Hauynite Lazurite . . . Leucite Pollucite Halite Bauxite Pharmacosiderite Spinel Berzeliite Periclasite Grossularite Helvite. Pyrope Arsenolite Hessonite Pleonaste Almandite Hercynite Gahnite Spessartite . . . Lime . . Uvarovite Andradite Microlite Nantokite Pyrochlore . Schorlomite Percy lite Picotite Eulytite Cerargyrite Mosesite . Chromite.. . Senarmontite Embolite Manganosite Bunsenite Lewisite Miersite Bromyrite . Dysanalite Marshite Franklinite Sphalerite Perovskite Diamond . tglcstonite. Hauerite Alabandite . . Cuprite SMITHSONIAN TABLEC- TABLE 340. INDEX OF REFRACTION. Miscellaneous Monorefringent or Isotropic Solids. 283 Substance. Spectrum line. Index of refraction. ; Authority. Albite glass D Amber Ammonium chloride D D .546 Mtihlheim Grailich Anorthite glass D t;7cc Asphalt . D 635 E L Nichols o 6?ou 621 Bell metal D 0052 Beer Boric Acid melted c D < F Borax melted c ,, D 4630 < F <4 Camphor D 532 Kohlrausch D 5462 Mtihlheim Canada balsam D 53O Mean Ebonite . red .66 Ayrton Perry Fuchsin A 03 B *9 ii c 33 < G 97 < ii H 32 Gelatin, Nelson no. i " various D D 530 1.5 6-1.534 Jones, 1911 Gum Arabic red .480 Jamin red .514 Wollaston Obsidian D i . 4821 . 496 Various Phosphorus D .1442 Gladstone, Dale Pitch . . red .531 Wollaston Potassium bromide D S593 Topsoe, Christiansen " chlorstannate. . . . D 6574 iodide D .6666 Resins: Aloes Canada balsam red red .619 .528 Jamin Wollaston Colophony . . . red 548 Jamin Copal.... Mastic red red .528 535 Wollaston Peru balsam Selenium . . . D A 593 61 Baden Powell Wood B 68 C 73 D 93 ft Sodium chlorate D 5150 Dussaud Strontium nitrate D 5667 Fock SMITHSONIAN TABLES. 284 TABLE 341. INDEX OF REFRACTION. Selected Uniaxial Minerals. The values are arranged in the order of increasing indices for the ordinary ray and are for the sodium D line unless otherwise indicated. Selected by Dr. Edgar T. Wherry from a private compilation of Dr. Esper S. Larsen of the U. S. Geological Survey. Mineral. Formula. Index of refraction. Ordinary ray. Extraordinary ray. (a) UNIAXIAL POSITIVE MINERALS. Ice HzO MgFj CuO.SiO2. 2 H 2 O 2CaO.Al2O3.sSiO2.6H2O (Ca, Na 2 )O.Al203.4Si0 2 .6H2O 2 KCl.FeCl 2 . 2 H 2 2Na 2 O.3AlsO3.6SiO 2 .7H 2 O KzO.SCaO.ieSiO^^H^ Si0 2 FeTOs.sSOa.gHzO MgO.HiKD KXX3AlzO3.4SO3.6H20 S(Mg, Fe)O.Al 2 03.3SiO 2 . 4 H 2 O 2Fe 2 O3.P 2 O 5 .i2H 2 O 6Na 2 O.6(Ca, Fe)O.2o(Si, Zr)O 2 .NaCl CuO.SiO^H^ 2 BeO.Si0 2 2CeOF.Ca0.3CO 2 2 ZnO.SiO 2 2(Ca, Mn, Fe)O.(Al, Fe)(OH, F)O. 2 SiO 2 Y203.P.05 2oCuO.SO3. 2 CuCl 2 . 2 oH 2 O BaO.TiO 2 .3SiO 2 6PbO. 4 (Ca, Mn)O.6SiO 2 .H2O CaO.WOs ZrO 2 .Si0 2 CaO.MoOs HgCl SnOa ZnO PbO.PbCh.COz Pb0. 2 PbCl 2 Agl FeO.(Ta, CbJzOs ZnS 6eO.S\xtO 3 . 5 TiOi CdS TiOz CSi HgS 309 378 .460 475 .480 .488 .490 535 * 5-44 550 559 572 576 582 .606 654 654 .676 .694 .716 .721 .724 757 .910 .918 .923 .967 973 997 .008 .114 .130 .210 .270 .356 450 .506 .6l6 654 854 313 39 570 =t .486 .482 -500 502 537 =*= 553 556 580 592 -579 645 .611 .707 .670 757 723 '.816 746 .804 945 934 .968 .978 .650 093 .029 .140 .210 .220 . 420 (Li light) 378 .510 (Li light) 529 903 697 3-201 Sellaite Chrysocolla Laubanite Chabazite Douglasite Hydronephelite . Apophyllite Quartz . Brucite Alunite ... . Cacoxenite Eudialite Phenacite Parisite Willemite Vesuvianite Connellite Benitoite Scheelite Zircon Powellite Calomel Cassiterite Z incite Phosgenite Penfieldite lodyrite Tapiolite Wurtzite Derbylite Greenockite Rutile Moissanite (b) UNIAXIAL NEGATIVE MINERALS. Chiolite Hanksite 2 NaF.AlF 3 iiNa 2 O.gSO 3 .2CO 2 .KCl 3CaO.C0 2 .Si0 2 .S0 3 .isH 2 eMgO.Ali-Os.CCk.isHiiO 4 Na 2 O.Ca0.4Al 2 03.2C0 2 . 9 Si0 2 .3H 2 O K 2 O.4CaO. 2 Al 2 O3.24Si0 2 .H 2 O KaO.AliO.2SiOi AhOs.C^Og.iSHzO "Ma" = sNa^.sAhOs.iSSiO^NaCl N a2 O.Al203.2Si0 2 349 .481 507 512 524 532 537 539 539 542 .342 .461 .468 .498 .496 529 533 5ii 537 538 Thaumasite Hydrotalcite . . Milarite Kaliophilite Mellite Marialite Nephelite SMITHSONIAN TABLES. TABLES 341-342. INDEX OF REFRACTION. TABLE 341 (Continued). Selected Uniaxial Minerals. 285 Mineral. Formula. . . Index of refraction. Ordinary ray. Extraordinary ray. (6) UNIAXIAL NEGATIVE MINERALS (continued). Wernerite Beryl MeiMai 3BeO.Al 2 O 3 .6SiO2 CuO.2UO3.P 2 O 6 .8H 2 O "Me" = 4 CaO. 3 Al 2 3 .6SiO2 Contains NazO, CaO, AhOs, SiO 2 . etc. 9Ca0.3P 2 O5.Ca(F, Cl) 2 CaO.C0 2 2CaO.Al 2 O 3 .SiO 2 Contains Na 2 O, FeO, AbOa, B 2 O3, SiC% etc. CaO.MgO.2CO 2 MgO.CO 2 MnO.H 2 O A1 2 O 3 ZnO.CO 2 MnO.CO 2 K 2 O. 3 Fe 2 O3.4SO 3 .6H 2 O FeO.C0 2 9Pb0.3P 2 O 5 .PbCl 2 3PbO. 2 Si0 2 9Pb0. 3 As 2 5 .PbCl2 PbO.PbCl 2 PbO.W0 3 (MR, Fe)O.TiO 2 9 Pb0. 3 V 2 5 .PbCh PbO.MoOs Ti0 2 PbO 3Ag 2 S.As 2 S 3 3Ag 2 S.Sb 2 S 3 Fe 2 3 578 .581 =*= 592 1.597 .634 634 .658 .669 .669* .682 .700 .723 .768 .818 .818 .820 .875 .050 .070 135 '5 .269 -310 354 .402 554 665 979 3.084 3.220 551 : .560 .629 631 .486 -658 .638=*= 503 509 .681 .760 .618 595 715 635 .042 .050 .118 .040 .182 950 .299 . 304 (Li light) 493 . 535 (Li light) .711 ' .881 " " .940 ' Torbernite Meionite Melilite Apatite ... Calcite Gehlenite Tourmaline Dolomite Magnesite Pyrochroite Corundum . ; Smithsonite ; Rhodochrosite Jai'osite Siderite Pyromorphite Barysilite. Mimetite Matlockite Stolzite Geikielite Vanadinite. . . Wulfenite. Octahedrite Massicotite Proustite Pyrargyrite Hematite TABLE 342. Miscellaneous Uniaxial Crystals. Crystal. Spectrum line. Index of refraction. Authority. Ordinary ray. Extraordinary ray. Ammonium arseniate NH^HisAsO^ D D D D Li D F D C D D D F D C D .5766 .6588 .769 .308 297 -539 .5762 .5674 5632 457 -586 447 5173 5109 .5078 .614 5217 .6784 .760 313 304 541 5252 5179 .5146 .466 .336 453 4930 .4873 .4844 599 T. and C* Mean Osann Meyer Kohlrausch T. and C. Mean T. and C. Martin Benzil (CeH&CO) 2 Corundum, A1 2 O 3 , sapphire, ruby Ice at 8 C Ivory . Sodium arseniate Na3AsO4 i2H 2 O :t nitrate NaNOs " phosphate NasPO4 i2H 2 O Nickel sulphate NiSO4 6H 2 O it Topsoe and Christiansen. SMITHSONIAN TABLES. 286 TABLE SiS. INDEX OF REFRACTION. Selected Biaxial Minerals. The values are arranged in the order of increasing /3 index of refraction and are for the sodium D line, except where noted. Selected by Dr. Edga; T. Wherry from private compilation of Dr. Esper S. Larsen of the U. S. Geological Survey. 1 Mineral. Formula. . Index of refraction. n a 5 my (a) BIAXIAL POSITIVE MINERALS. Stercorite N a2 O. (NH4)2O.P2O5.9H2O AhOs.SOa.gHjO SiO 2 Na 2 O.SO 3 KCl.MgCl 2 .6H 2 O Al 2 3 .3Sa.i6H20 FeO.S03.7H 2 Na 2 O.Al 2 3 . 3 SiO 2 . 2 H 2 O K 2 O.S0 3 (NH4) 2 O.2MgO.P 2 5 .i2H 2 O CaO.Al 2 O3.6SiO 2 .3H 2 O (Na, Ca)O.Al 2 03.2Si0 2 .3H 2 (K 2 , Ba)O.A]2O 3 .5SiO 2 .5H 2 O Li^.AlzOs.SSiCfe 2 CaO.P 2 5 .H 2 2 MgO.P 2 05.7H2O CaO.S0 3 .2H 2 fNHOiO.SO. "Ab" = Na 2 O.Al 2 O 3 .6SiO 2 4Mg0. 3 C0 2 . 4 H 2 3Al2O 3 .2P2O 6 .I2(H 2 O, 2 HF) MgO.S0 3 .H 2 2Fe 2 3 .sS0 3 .i8H 2 O CaO.C 2 a.H 2 Als04.Ps06.4lW) Ab2Ans A1 2 C>3.3H 2 O 3 M g O.P 2 05.M g F 2 CaO.S0 3 2CaO.3B 2 O 3 .sH 2 O Na 2 O.Al 2 3 .P 2 6 .(H 2 O, 2 HF) 3 FeO.P 2 5 .8H 2 Na 2 O.4CaO.6SiO 2 .H!!O 2 ZnO.Si0 2 .H 2 4MgO.2Si0 2 .Mg(F, OH) 2 Cu0. 3 Al 2 3 .2P 2 6 .9H 2 O 2 A10F.Si0 2 SrO.SOs 2CaO.Al 2 O3.3Si0 2 .H 2 O BaO.SO 3 MgO.Si0 2 Al 2 O 3 .SiO 2 2MgO.SiO 2 MgO.Si0 2 2BeO.AbQt.3SiOt.Hi0 3 MnO.P 2 5 .MnF 2 Li 2 O.Al 2 Os.4SiO 2 CaO.MgO.2SiO 2 2 (Mg, Fe)O.Si0 2 Li 2 O.2(Fe, Mn)O.P 2 O 5 439 459 .469 464 .466 474 .471 .480 494 495 .498 497 503 504 515 514 .520 521 525 527 525 523 530 .491 551 559 :$ 594 579 595 .614 .609 .610 . 619 .622 .616 .636 633 .638 .635 650 .652 .050 .660 .664 .662 .688 441 464 470 474 475 476 478 .482 495 496 499 503 505 .510 .518 519 523 523 529 530 534 535 543 555 558 5 ^ 566 570 576 592 .603 603 .606 .617 .619 .620 .620 .624 .626 .637 .042 .642 .651 653 655 .660 .666 .671 .680 .688 .469 470 473 485 494 483 .486 493 497 504 505 525 508 5i6 525 533 530 533 536 540 595 650 582 568 .587 .582 .614 .614 .615 633 634 636 639 .650 .627 .631 649 .648 657 653 .670 .658 .671 .672 .676 .694 .699 .692 Tridymite Thenardite Camallite Alunogenite Natrolite Arcanite Struvite Heulandite Thomsonite Petalite Gypsum Albite Wavellite Kieserite Whewellite . Variscite . . Labradorite Gibbsite Wagnerite Anhydrite Colemanite Fremontite Vivianite Pectolite Calamine Chondrodite Topaz Cefestite Prehnite Barite . . Anthophyllite Sillimanite Forsterite Enstatite Euclasite Triplite Spodumenite Diopside Olivine Triphylite SMITHSONIAN TABLES. TABLE 343 (continued). INDEX OF REFRACTION. Selected Biaxial Minerals. 287 Mineral. Formula. Index of refraction. *a nft n y (a) BIAXIAL POSITIVE MINERALS (continued). Zoisite 4 CaO.3Al 2 O3.6Si02.H 2 O Fe 2 O3.P 2 Oa.4H 2 O A1 2 03.H 2 2FeO.5Al 2 O3.4SiO2.H 2 O BeO.AhQj 3 CuO. 2 C0 2 .H 2 Fe 2 O 3 .As 2 Oo.4H 2 O 4 CuO.As 2 6 .H 2 O PbO.SOs CaO.TiOz.SiOz As 2 Os s PbClz MnO.WOs Mn 2 O 3 .H 2 O PbO.WOs 2PbO.PbCl 2 (Fe, Mn)O.Ta 2 Os (Fe, Mn)O.W03 PbO.CrOs 2Fe 2 O3..3TiO 2 Sb 2 Os.Ta 2 Oo HgO Ti0 2 PbO .700 .710 .702 .736 747 730 .765 772 -877 .000 .871 950 .200 .170 .240 .270 .240 .260 .310 .310 .380 374 370 583 Sio .702 .710 .722 .741 748 758 774 .810 .882 .907 .920 043 .217 .220 .240 .270 .270 320 .360 370 390 .404 500 .586 .6lO 1.706 '1-745 :3 :g 797 .863 894 034 .010 .240 .260 -320 530 (Li) 300 310 .430 (Li) .460 (Li) . 660 (Li) .420 (Li) '650 (Li) .741 .710 Diasporite Staurolite Chrysoberyl Azurite Scorodite Olivenite Anglesite . Titanite Claudetite Sulfur Cotunnite Huebnerite. . . Manganite Raspite Mendipite Tantalite Wolframite Crocoite Pseudobrookite Stibiotantalite ... Montroydite Brookite Lithargite. . . (b) BIAXIAL NEGATIVE MINERALS. Mirabilite Thomsenolite Na 2 O.SO3.ioH 2 NaF.CaF 2 .AlF 3 .H 2 O Na 2 O.C0 2 .ioH 2 O K 2 O.A1 2 O 3 .4SO 3 .24H 2 O MgO.SO3.?H 2 O B 2 O3.H 2 Na 2 O.2B 2 O 3 .ioH 2 O ZnO.SOs.7H 2 MgO.Al 2 O3.4Sa.22H 2 O Na 2 O.MgO.2SOs.4H 2 O 3 Na 2 O. 4 C0 2 .5H 2 Na 2 O.CO 2 .H 2 (Ca, Na 2 )O.Al 2 O 3 .6SiO 2 .sH 2 O K 2 O.N 2 5 MgO.S0 3 .KC1.3H 2 Na 2 O.CaO.2CO 2 .sH 2 CaO.Al 2 O 3 .3SiO 2 .3H;!O CaO.AhOs^SiCMHiiO K^.AhOt.esiCb Same as preceding (Na, K) 2 O.Al 2 3 .6SiO 2 Na 2 O.Ca0. 2 S03 4(Mg, FeX>-4AijO*.ioSiO^H<0 CuO.SOi.sHzO Ab 4 An 394 .407 405 430 433 340 447 457 .476 .486 .410 .420 494 334 494 444 512 513 .518 522 523 SIS 534 .516 539 -396 .414 425 452 455 456 470 .480 .480 .488 492 495 498 505 505 516 519 524 .524 .526 529 532 538 539 543 398 415 .440 458 .461 459 472 .484 483 489 542 .518 500 .506 .516 523 519 525 526 530 531 -536 540 .546 547 Natron Kalinite Sassolite Borax . '. Goslarite Pickeringite Bloedite Trona Thermonatrite Stilbite Niter Gaylussite Scolecite Laumontite Orthoclase Anorthoclase Glauberite . Chalcanthite Oligoclase SMITHSONIAN TABLES. 288 TABLE 343 (continued). INDEX OF REFRACTION. Selected Biaxial Minerals. Mineral. Formula. Index of refraction. "a /J y (b) BIAXIAL NEGATIVE CRYSTALS (continued). Bervllonite NaiO.2BeO.P205 Al203.2SiO2.2H20 K2O. 4 (Mg, Fe)0. 2Al2a.6SiOj.HjO CaO.2UO3.P2Os.8H2O "An" = CaO.Al 2 03.2SiOj L a2 03.3C02. 9 H20 AliOs^SiOj-HzO 3MgO. 4 SiO2.H20 3ZnO.P 2 O s .4H20 K20.3Al203.6SiOj.2H2O Al 2 03.P20 5 .2LiF Al 2 03.3SiOj.2(K,Li)F K20.6MgO.Al 2 03.6SiO2.2HjO Ca0.3Mg0. 4 SiO 2 Ca0.3(M g) Fe)O. 4 SiOj CaO.SiO2 (Fe, Mg)O.Al 2 03.P20 5 .H2O CaO.B 2 O3.2SiO2 Na 2 0. 2 FeO.Al2O3.6SiOj AhOs.SiOj Contains Na 2 O, MgO, FeO, Si0 2 , etc. 2 CaO. 2 SiO2.B2O3.H 2 O 3CoO.As 2 5 .8HjO CaO.MgO.SiOj SrO.COj BaO.COj CaO.C0 2 6(Ca, Mn)O.2Al 2 03.B 2 03.8SiO 2 .H 2 O 8Al 2 03.B 2 03.6Si0 2 .H 2 Al 2 Os.SiO 2 4Ca0.3(Al, Fe) 2 03.6SiOj.HjO 3 CuO.CuCl 2 .3H 2 O 2FeO.SiO 2 2(Pb, Cu)O.Sa.HjO 2CuO.CO2.HjO 2 PbO.S0 3 4PbO.S03.2COj.HjO PbO.COz PbCh.PbO.HjO PbO.PbClj ZrOj Fe 2 03.H 2 O 2Fe 2 O3.3H 2 O in part FejOs.HjO SbjOs 2FejO3.HjO in part AsS Hg 2 OCl (Tl, Ag) 2 S.PbS.2AsjS 3 SbjSs 552 .561 541 553 576 520 552 539 572 561 579 .560 .562 .609 .611 .616 .603 .632 .621 .632 .629 .625 .626 .651 .520 529 -531 .678 .678 .712 .729 .831 .824 .818 -655 -930 .870 .804 .077 .040 .130 930 .170 .210 .ISO 450 4 60 350 3.078 3-194 .558 .563 574 575 584 .587 -588 .589 590 590 593 !e is .029 .632 .634 .638 .638 .642 & 3 .661 .662 .667 .676 .682 .685 .686 .720 -754 .861 .864 .866 875 990 .000 .076 .116 .150 .190 .210 .290 350 350 550 590 . 040 3-176 4-303 .561 565 574 577 -588 .613 .600 589 590 594 -597 -605 .606 635 .636 .631 639 .636 .638 643 .653 .669 .699 .668 .667 -677 .686 .688 .689 .728 .768 .880 .874 -909 .909 .020 .010 .078 .158 .150 .200 510 .310 350 (Li) 350 - 550 (Li) .610 (Li) . 670 (Li) 3-188 4.460 Kaolinite Biotite ... . Autunite Anorthite Lanthanite. . . Pyrophyllite . . Talc Hopeite Muscovite Amblygonite . Lepidolite . . Phlogopite Tremolite. . Actinolite Wollastonite Lazulite . Danburite Glaucophanite Andalusite Hornblende Datolite Erythrite Monticellite Strontianite. \Yitherite Aragonite Axinite Dumortierite Cyanite Epidote Atacamite Fayalite Caledonite Malachite Lanarkite . Leadhillite Cerussite Laurionite Matlockite Baddeleyite Lepidocrocite Limonite Goethite Valentinite Turgite Realgar Terlinguaite Hutchinsonite Stibnite SMITHSONIAN TABLES. TABLES 344-345. INDEX OF REFRACTION. TABLE 344. Miscellaneous Biaxial Crystals. 289 Crystal. Spectrum line. .. Index of refraction. Authority. "a /3 "y Ammonium oxalate, (NH4) 2 C 2 O4.H 2 O. . . Ammonium acid tartrate, (NH4)H(C4H 4 O6) D D D D D D D D Cd, 0.226/4 H, 0.656/1 D D red D F D C yellow D D red Tl D Li D F D C i.438i 1.5188 5697 4932 5390 495 432 .4990 4307 .7202 6873 3346 .4976 4932 .4911 .6610 .5422 5397 5379 4953 4620 4568 4544 1-5475 .5614 .581 6935 4977 5435 501 455 5266 4532 738o 7254 .722 5056 4992 .4946 .4928 -526 555 6994 5332 5685 5667 5639 5353 4860 4801 4776 i 5950 1.5910 7324 .5089 .526 .461 5326 4584 8197 7305 .5064 .5029 .4980 4959 7510 5734 .57i6 5693 .6046 .4897 .4836 .4812 Brio T. and C * Cloisaux Liweh Schrauf Grailich Genth Means Borel Dufet T. and C. Mallard Schrauf T. and C. Groth Dufet Brio Calderon Means T. and C. Ammonium tartrate, (NH^C^Oe Antipyrin, CnH^NOz Citric acid, CeHsO.I^O. . . Codein, Ci8H 21 N03.H 2 Magnesium carbonate, MgCOs.3H 2 O. . . . sulphate, MgSO4. 7 H 2 O Potassium bichromate, K2Cr2O? chromate, K2CrO< nitrate, KNO 3 .............. sulphate, K2SO4 Racemic acid, C4H 6 O6.H 2 O Resorcin, CeH6O2 Sodium bichromate, Na 2 Cr 2 O7.2H 2 O acid tartrate, NaH(C4H4O6).2H 2 O Sugar (cane), Ci2H 2 2Oii Tartaric acid, C4H 6 O 6 (right-) Zinc sulphate ZnSCu 7H 2 O it * Topsoe and Christiansen. TABLE 345. Miscellaneous Liquids (see also Table 346), Liquefied Gases, Oils, Fats and Waxes. Substance. Temp. C Index for D o. 589/4. Refer- ence. Substance. Temp Index for D o. 589/4- Refer- ence. Liquefied gases: Br 2 Cls CO 2 15 14 15 18 6 18.5 -190 16.5 -90 15 -181 IS- 16.5 10 16.5 iS-5 IS 20 20 15-5 IS 15.5 27 20 IS-S 659 367 i9S 325 .180 384 -205 325 330 194 . 221 350 252 :9 .4728-1.4753 . 4799-1 4803 . 47-1 . 48 . 5301-1 . 5360 .4587 .4790-1.4833 4737-1-4757 .4757-1.4768 .460-1.467 .4702-1.4720 a b b b b b c b c b c b b b b d e e e d e d e e d Oils: Lavendar Linseed Maize Mustard seed. . . Neat's foot Olive 20 IS 15-5 iS-5 IS I 5 ' 5 60 15-5 20 15-5 25 15-5 25 15.5 15.5 15-5 15-5 19 40 40 75 84 40 40 60 . 464-1 466 .4820-1.4852 4757-1-4768 .4750-1.4762 . 4695-1 47o8 .4703-1-4718 4510 .4723-1.4731 .464-1-468 4770 .4677 .4748-1.4752 4741 4742 .4760-1.4775 .4665-1-4672 4739 503 4649 4552-1.4587 4398-1.4451 4520-1.4541 4560-1.4518 4584-1-4601 4510 e e d d e d d d e d e d e d e e d e e e e e e e e C 2 N 2 C 2 H 4 H 2 S N 2 NH 3 NO N 2 O 2 SO 2 Palm Peanut Peppermint Poppy Porpoise. . . . Rape (Colza) .... Seal HC1 HBr HI.. Soja bean Sperm Sunflower Oils: Almond Castor Citronella. . . . Clove Cocoanut. . . . Cod liver Cotton seed . . Croton Eucalyptus . . Lard Tung Whale Fats and Waxes: Beef tallow Beeswax Carnauba wax. . . . Cocoa butter Lard Mutton tallow . . . References: (a) Martens; (b) Bleekrode, Pr. Roy. Soc. 37, 339, 1884; (c) Liveing, Dewar, Phil. Mag., 1892-3; (d) Tolman, Munson, Bui. 77, B. of C., Dept. Agriculture, 1905; (e) Seeker, Van Nostrand's Chemical Annual. For the oils of reference d, the average temperature coefficient is 0.000365 per C. SMITHSONIAN TABLES. TABLE 346. INDEX OF REFRACTION. Indices of Refraction of Liquids Relative to Air. Substance. Den- sity. Temp. Indices of refraction. Author- ity. 0.397M 0-4.UM 0.486/4 0.589JU D 0.656^1 C Acetaldehyde, CHjCHO. 0.780 0.791 i. 022 0.794 0.808 0.800 0.804 0.880 1.487 1-293 1.263 1.591 1.090 1.512 1.489 0.728 0-715 1.109 i. 219 i. 260 0.660 0.679 3-318 0.962 I.OI2 0.707 0.92 0.99 0.99 I. 06 1.05 O.92 .7 7 0.87 0.625 i. 060 I.O2I O.9IO 0.982 20 20 20 20 20 20 20 20 20 2O 20 20 20 20 20 14.9 20 20 20 20 2O 20 23-3 20 20 98.4 22.4 I5-I I5-I 21.4 20 10 22.5 23-5 O 10.6 20.7 I5 i 40.6 82.7 16.6 20 20 40 80 1-3399 1.7289 I-7I75 1.6994 i.4<* 1.8027 I . 6084 I . 7039 1.6985 i 4939 I.49I3 1-3435 1-3444 1.34" 1-3332 3394 .3678 .6204 3362 3773 .3700 . 0004 -3938 5236 .0007 .7041 .6920 .6748 .4729 .6679 .4679 -458 .4200 .3607 .0006 -395 .3804 .4828 -3836 4059 5439 .4097 1-5775 1-3645 1-5684 1.5816 1.5170 i - 3404 I-34I3 i.338o 1.3302 -3359 -3639 .6041 3331 3739 .3666 .0004 .3901 .5132 .0006 .6819 .6688 -6523 .4676 .6470 .4624 -4530 .4160 .3576 . 0006 -392 -3764 .4784 3799 .4007 .7692 . 0007 .6031 .4046 .4847 -5743 5647 5623 -6389 .6314 .6508 -4825 4644 .4817 4793 .3610 5558 .5356 .5659 -5386 .5070 3372 .338o 3349 .3270 i^O^tf ^ISO^ 5863 -3290 3695 3618 . 0004 .3854 .5012 .0006 6582 6433 .6276 .4607 .6245 4557 .4467 .4108 .3538 .0006 -3853 -37I4 -4730 3754 3945 7417 . 0007 5823 5239 4007 .4782 5572 5475 .6104 .6026 .6188 4763 4573 4744 4721 .3581 5425 .5485 4955, *^3S3Q .3338 -3307 3230 -3298 -3573 5793 .3277 .3677 3605 . 0004 .3834 4965 .0006 .6495 -6336 .6182 4579 .6161 4530 4443 .4088 -3515 .0006 3830 -3693 .4706 3734 -3920 7320 .0006 5746 .5198 3987 4755 .5508 -5410 5391 .6007 5930 .6077 4738 4545 4715 .4692 -3570 5369 -5174 5419 .5228 .4911 -3312 -33I9 .3290 -3313 la Means ib Means 2 i Means 3 4 id 1C 1C Means te Means la 5 1C 1C Means if 1C ic 6 I 5 7 I 6 6 ! le 11 li ih 10 Means Acetone, CHsCOCHs. . . Aniline, CaHs.NHj. . Alcohol, methyl, CHs.OH. . . " ethyl CiH6.OH " dn/dt n-propyl CjH 7 .OH Benzene, C B H 6 " CH, dn/dt Bromnaphthalene, Ci H 7 Br. . . . Carbon disulphide, CSt " tetrachloride,' CCU . . . Chinolin, C 9 H 7 N Chloral, CCb.CHO Chloroform, CHCU Decane, CioH Ether, ethyl, C2H 5 .O.C 2 H B " dn/dt Ethyl nitrate, C 2 Hs O NOj Formic acid, H.COiH Glycerine, CsHsOs Hexane, CHsCCH^CHs . '. . Hexylcae, CH3(CH 2 ) 3 CH.CH 2 . . Methyl iodide, CHsI " dn/dt Naphthalene, CioHs. . . . Nicotine, GoHuN? Octane, CH3(CHz) 8 CHs Oil, almond. .. . anise seed bitter almond cassia cinnamon olive rock turpentine Pentane, CHafCH^aCHs. '. . Phenol, CeHsOH Styrene, CsHsCH.CHa. Thymol, CioHi4O. . . Toluene, CHs.CeHs Water, H 2 O. . " " References: i, Landolt and Bornstein (a, Landolt; b, Korten; c, Briihl; d, Haagen; e, Landolt, Jahn; f, Nasini, Bernheimer; g, Eisenlohr; h, Eykman; i, Auwers, Eisenlohr); 2, Korten; 3, Walter; 4, Ketteler; 5, Landolt; 6, Olds; 7, Baden Powell; 8, Willigen; 9, Fraunhofer; 10, Briihl. SMITHSONIAN TABLES. TABLE 347. INDEX OF REFRACTION. Indices of Refraction relative to Air lor Solutions of Salts and Adds. 291 Substance. Indices of refraction for spectrum lines. Density. Temp. C G D F *v H Authority. (a) SOLUTIONS IN WATER. Ammonium chloride 1.067 27 C -05 I-3770: 1 -37936 I-38473 1 -39336 Willigen. Calcium chloride 39^ 29-75 -3485C .4400C 3 S^ S^ 44279 355'5 44938 .36243 46001 ti .215 22. Q 3941 1 39652 40206 41078 " 143 25-8 37152 37369 37876 .38666 " Hydrochloric acid . Nitric acid .... I.I66 359 20.75 18.75 1.40817 39893 141109 .40181 1.41774 40857 142816 41961 (4 Potash (caustic) . . Potassium chloride . 416 normal II.O solution 40052 .34087 40281 34278 .40868 .34719 1.35049 41637 Fraunhofer. Bender. " " double normal .34982 35 J 79 35645 35 994 i " triple normal 35831 .36029 36512 -36 890 it Soda (caustic) . . Sodium chloride . . 1.376 .189 21.6 18.07 1.41071 1.41334 1.41936 37789 -38322 1.38746 142872 Willigen. Schutt. " .109 18.07 3575 1 35959 -36442 .36823 M 35 18.07 .34000 .34I9 1 .34628 34969 1 Sodium nitrate . . Sulphuric acid . . .811 22.8 I8. 3 1.38283 43444 1-385 436 I-39I34 44168 140121 44881 Willigen. M " .632 18,3 42227 42466 42967 43 694 u " .221 36793 .37009 .37468 .38 " " .028 18.3 33663 .33862 34285 34938 < Zinc chloride . . . i-359 26.6 1-39977 1.40222' 140797 141738 ( . .209 264 37292 37515 .38026 .38845 (b) SOLUTIONS IN ETHYL ALCOHOL. Ethyl alcohol . . . 0.789 25-5 I -3579 I '359 7 I 1,36 39S - 1.37094 Willigen. " 932 27.6 .35372 35556 3S 986 .36662 ' Fuchsin (nearly sat- urated) . . - 16.0 .3918 398 .361 3759 Kundt. Cyanin (saturated) . 16.0 3831 3705 3821 M NOTE. Cyanin in chloroform also acts anomalouslv ; for example, Sieben gives for a 4.5 For j per cent, solution AU= i-4593> P-B= ^4695, HF (green) = 14514, PG (blue) = 14554. i 9.9 per cent, solution he gives JJ. A = 14902, /t f (green) = 14497, /io(blue) = 14597. (c) SOLUTIONS OF POTASSIUM PERMANGANATE IN WATER.* Wave- length Spec- trum Index for Index for Index for Index for Wave- ength Spec- trum Index for Index for Index for Index for X 10. Hue. i % sol. 2 % sol. 3 % sol. 4 % sol. n cms. Xio". line. i % sol. 2 % SOI. 3 % sol. 4 % sol. 68. 7 B 1.3328 1-3342 _ L3382 Si.6 _ 1.3368 I-3385 _ _ 65.6 C 3335 -3348 1.3365 339 r 50-0 - 3374 .3383 L3386 1.3404 6l. 7 3343 3365 3381 .3410 48.6 F 3377 - .3408 594 3354 3373 3393 .3426 48.0 3395 3398 3413 58-9 D 3353 3372 3426 46.4 3397 .3402 .3414 3423 56.8 3362 3387 3412 3445, 44-7 3407 3421 .3426 3439 55-3 3366 3395 3417 3438 434 3417 3452 52-7 E 3363 42.3 3431 3442 3457 .3468 52.2 3362 -3377 .3388 SMITHSONIAN TABLES. * According to Christiansen. 292 TABLE 348. INDEX OF REFRACTION. Indices of Refraction of Gases and Vapors. A formula was given by Biot and Arago expressing the dependence of the index of refraction of a gas on pressure and 0_! p temperature. More recent experiments confirm their conclusions. The formula is n t i = /"A"' ere n t is the index of refraction for temperature /, for temperature zero, a the coefficient of expansion of the gas with temperature, and/ the pressure of the gas in millimeters of mercury. Fpr air see Table 349. (a) Indices of refraction. Spectrum 10 s (n-i) Spectrum io (n-i) Wave- (n-i ) io. line. Air. line. Air. length. Air. 0. N. H. A .2905 M 2993 .4861 .2951 .2734 .3012 .1406 B .2911 N 3003 .5461 .2936 2/17 -299 s .1397 C .2914 o 3 OI 5 5790 .2930 .2710 1393 D .2922 P 3 2 3 .6563 .2919 .2698 .2982 .1387 E 2 933 Q 303 1 .4360 .2971 .2743 co 2 .1418 F 2943 R 3043 .5462 2937 .2704 .4506 .1397 G .2962 S 353 .6709 .2918 .2683 .4471 T 38S II .2978 T .3064 6.709 .2881 .2643 -4804 .1361 K .2980 U 3075 8.678 .2888 .2650 .4579 .1361 L .2987 First 4, Cuthbertsons ; the rest, Koch, 1909. (V) The following are compiled mostly from a table published by Briihl (Zeits. fur Phys. Chem. vol. 7, pp. 25-27). The numbers are from the results of experiments by Biot and Arago, Dulong, Jamin, Ketteler, Lorenz, Mascart, Chappius, Rayleigh, and Riviere and Prytz. When the number given rests on the authority of one observer the name of that observer is given. The values are for o Centigrade and 760 mm. pressure. Substance. Kind of light. Indices of refraction and authority. Substance. Kind of light. Indices of refraction and authority. Acetone Ammonia D white I.OOIO79-I.OOIIOO i .00038 1 - 1 . 00038 5 Hydrogen . . white D .000138-1.000143 .000132 Burton. Argon . D D 1.000373-1.000379 1.000281 Rayleigh. Hydrogen sul- ( phide . . | D D .000644 Dulong. .000623 Mascart. Benzene D 1.001700-1.001823 Methane . . . white .000443 Dulong. Bromine D 1.001132 Mascart. u D .000444 Mascart. Carbon dioxide white D i . 000449- l 0004 50 1.000448-1.000454 Methyl alcohol . Methyl ether . D D .000549-1.000623 .000891 Mascart. Carbon disul- j white 1.001500 Dulong. Nitric oxide . . white .000303 Dulong. phide D 1.001478-1.001485 " u D .000297 Mascart. Carbon mon- ( oxide . . j white white 1.000340 Dulong. 1.000335 Mascart. Nitrogen . . . M white D .000295-1.000300 .000296-1 .000298 Chlorine white 1.000772 Dulong. Nitrous oxide . white .000503- i.ooocoy D 1.000773 Mascart. u D .000516 Mascart. Chloroform . . D 1.001436-1.001464 Oxygen white .000272-1.000280 Cyanogen . white 1.000834 Dulong. D .000271-1.000272 " . D 1.000784-1.000825 Pentane . D .001711 Mascart. Ethyl alcohol . Ethyl ether . . D D 1.000871-1.000885 1.001521-1.001544 Sulphur dioxide white D .000665 Dulong. .000686 Ketteler. Helium D 1.000036 Ramsay. Water . white .000261 Jamin. Hydrochloric j white 1.000449 Mascart. . . D 1.000249-1.000259 acid . D i .000447 " SMITHSONIAN TABLES. 293 INDEX OF REFRACTION. TABLE 349. Index of Refraction of Air (15C, 76 cm). Corrections for reducing -wave-lengths and frequencies in air (15 C, 76 cm) to vacua. The indices were computed from the Cauchy formula (n i)io 7 = 2726.43 + i2.288/(A*X io~ 8 ) +0.35557 (A 4 X icr 16 ). For o C and 76 cm the constants of the equation become 2875.66, 13.412 and 0.3777 respectively, and for 30 C and 76 cm, 2589.72, 12.259 and 0.2576. Sellmeier's formula for but one absorption band closely fits the observations: n 2 = i + 0.0005 73 78A 2 /(X 2 595260). If n i were strictly proportional to the density, then (n-i V ( i)t would equal i + at where a should be 0.00367. The following values of a were found to hold: A o.Ss/i o.75/i 0.65/1 0.55/1 0.45/4 0.35/1 0.25;* a 0.003672 0.003674 0.003678 0.003685 0.003700 0.003738 0.003872 The indices are for dry air (0.05 % CO 2 ). Corrections to the indices for water vapor may be made for any wave- length by Lorenz's formula, + 0.000041 (m/jfo), where m is the vapor pressure in mm. The corresponding frequencies in waves per cm and the corrections to reduce wave-lengths and frequencies in air at 15 C and 76 cm pressure to vacuo are given. E.g., a light wave of 5000 Angstroms in dry air at 15 C, 76 cm becomes 5001.391 A in vacuo; a frequency of 20,000 waves per cm correspondingly becomes 19994.44. Meggers and Peters, Bui. Bureau of Standards, 14, p. 731, 1918. Fre- Vacuo Fre- Vacuo Wave- Dry air Vacuo quency correction Wave- Dry air Vacuo quency correction length, (n-i) X io 7 correction or X in air waves per cm for :- in air A .e-r, (n - i) X io* correction for A in air waves per cm i . for -r in air A Ang- stroms. 15 C 76 cm (n\ - X). Add. i X /I A \n\ \) ' Ang- stroms. 15 C 76 cm (n\ - A) Add. i A GariD in air. Subtract. in air. Subtract. 2000 3256 651 50,000 16.27 55oo 2771 524 18,181 5-04 2100 3188 670 47,619 15-18 5600 2769 551 17,857 4-94 2200 3132 689 45,454 14.23 5700 2768 -578 17,543 4.85 2300 2400 3086 3047 710 73i 43,478 41,666 13-41 12.69 5800 59oo 2766 2765 .604 .631 17,241 16,949 ta 2500 3014 754 40,000 12.05 6000 2763 .658 16,666 4.60 2600 2986 776 38,461 11.48 6100 2762 .685 i6,393 4-53 2700 2800 2962 2941 800 824 37,037 35,714 10.97 10.50 6200 6300 2761 2760 .712 739 16,129 15,873 1:3 2900 2923 848 34,482 10.08 6400 2759 .766 15,625 4-3i 3000 2907 .872 33,333 9.69 6500 2758 .792 15,384 4.24 3100 3200 2893 2880 .897 .922 32,258 31,250 9-33 9.00 6600 6700 2757 2756 .819 .846 14,925 4.18 4.11 3300 2869 947 30,303 8.69 6800 2755 -873 14,705 4-05 3400 2859 .972 29,411 8.41 6900 2754 .900 14,492 3-99 3500 2850 .998 28,571 8.14 7000 2753 -927 14,285 3-93 3600 2842 .023 27,777 7100 2752 954 14,084 3.88 3700 2835 .049 27,027 7.66 7200 2751 .981 13,888 3-82 3800 2829 075 26,315 7-44 73oo 275i .008 13,698 3-77 3900 2823 .101 25,641 7-24 7400 2750 035 13,513 3-72 4000 2817 .127 25,000 7.04 75oo 2749 .062 13,333 3-66 4100 2812 153 24,390 6.86 7600 2749 .089 13,157 3-62 4200 2808 179 23,809 6.68 7700 2748 .116 12,987 3-57 4300 4400 2803 2799 .205 .232 23,255 22,727 6.52 6.36 7800 7900 2748 2747 143 .170 12,820 12,658 3-52 3.48 4500 2796 .258 22,222 6.21 8000 2746 .197 12,500 3-43 s 4600 2792 .284 21,739 6.07 8100 2746 .224 12,345 3-39 4700 4800 4900 2789 2786 2784 311 338 .364 21,276 20,833 20,4O6 5-93 5-8o 5.68 8250 8500 8750 2745 2744 2743 .265 332 .400 12,121 11,764 11,428 3-33 3-23 3-13 5000 5100 5200 5300 2781 2779 2777 2775 391 .417 444 .471 20,OOO 19,607 19,230 18,867 5-56 5-45 5-34 5-23 9000 9250 9500 9750 2742 2741 2740 2740 .468 536 .604 .671 11,111 10,810 10,526 10,256 3-05 2.96 2.88 2.81 5400 2773 497 I8,5l8 5-13 IOOOO 2739 739 10,000 2.74 SMITHSONIAN TABLES. 294 TABLES 350-352. MEDIA FOR DETERMINATIONS OF REFRACTIVE INDICES WITH THE MICROSCOPE. TABLE 350. -Liquids, n D (0.689,*) = 1.74 to 1.87. In 100 parts of methylene iodide at 20 C. the number of parts of the various substances in- dicated in the following table can be dissolved, forming saturated solutions having the permanent refractive indices specified. When ready for use the liquids can be mixed by means of a dropper to five intermediate refractions. Commercial iodoform (CHI 3 ) powder is not suitable, but crys- tals from a solution of the powder in ether may be used, or the crystalized product may be bought. A fragment of tin in the liquids containing the SnI 4 will prevent discoloration. CHI S . SnI 4 . AsI 8 . SbI 3 . s. na at 20. 12 1.764 25 'ZS 2 5 12 1. 806 3 6 1.820 40 27 27 11 7 1.826 1.842 35 3i 3i 14 16 8 8 10 IO 38 TABLE 351. Resin-like Substances, n D (0.589,*) =1.68 to 2.10. Piperine, one of the least expensive of the alkaloids, can be obtained very pure in straw-colored crystals. When melted it dissolves the tri-iodides of arsenic and antimony very freely. The solutions are fluid at slightly above 100 and when cold, resin-like. A solution containing 3 parts antimony iodide to one part of arsenic iodide with varying proportions of piperine is easier to manipulate than one containing either iodide alone. The following table gives the necessary data concerning the composition and refractive indices for sodium light. In preparing, the constituents, in powder of about i mm. grain, should be weighed out and then fused over, not m, a low flame. Three-inch test tubes are suitable. Per cent Iodides. oo. 10. 20. 30. 40. 50. 60. 70. 80. Index of refraction 1.683 1.700 1.725 i-75 6 I -794 1.840 1.897 1.968 2.050 TABLE 352. Permanent Standard Resinous Media, n D (0.589^) = 1.546 to 1.682. Any proportions of piperine and rosin form a homogeneous fusion which cools to a transparent resinous mass. The following table shows the refractive indices of various mixtures. On account of the strong dispersion of piperine the refractive indices of minerals apparently matched with those of mixtures rich in this constituent are 0.005 to o.oi too low. To correct this error a screen made of a thin film of 7 per cent antimony iodide and 93 per cent piperine should be used over the eye-piece. Any amber-colored rosin in lumps is suitable. Per cent Rosin. oo. IO. 20. 3- 40. 5- 6 . 7 o. 80. 90. 100. Index of refraction 1.683 1.670 I-657 1.643 I.6 3 I 1.618 1.604 1.590 i-575 1.560 r-544 All taken from Merwin, Jour. Wash. Acad. of Sc. 3, p. 35, 1913. SMITHSONIAN TABLES. 295 TABLE 353. OPTICAL CONSTANTS OF METALS. TABLE 353. Two constants are required to characterize a metal optically, the refractive index, n and the absorption index, k, the latter of which has the following significance : the amplitude of a wave after travelling one wave-length, A 1 measured in the metal, is reduced in the ratio 1 i :e 2** or for any distance d, i : e - -jp. for the same wave-length measured in air this ratio becomes i : e ^~ - k nk is sometimes called the extinction coefficient. Plane polarized light reflected from a polished metal surface is in general elliptically polarized because of the relative change in phase between the two rectangular components vibrating in and perpendicular to the plane of incidence. For a certain angle, <;> (principal incidence) the change is 90 and if the plane polarized incident beam has a certain azimuth ^ (Principal azimuth) circularly polarized light results. Approximately, (Drude, Annalen der Physik, 36, p. 546, 1889), k = tan 2$ ( i cot 2 <) and n = For rougher approximations the factor in parentheses may be omitted. R = computed per- centage reflection. (The points have been so selected that a smooth curve drawn through them very closely indicates the characteristics of the metal.) Metal. A * 5 Computed. Authority. n k nk R Cobalt 0.231 6 4 3'' 2939 1. 10 1.30 '43 32. Minor. 275 70 22 29 59 1.41 1.52 2.14 46. 11 .500 77 5 3i 53 1-93 3-72 66. " 650 79 o 3i 25 2-35 1.87 4.40 69. Ingersoll. I.OO 81 45 29 6 3.63 1.58 5-73 73- " 1.50 83 21 26 18 5.22 1.29 6-73 75- " 2.25 8 3 4 8 26 5 5-65 1.27 7.18 76. " Copper .231 65 57 26 14 1.05 1.45 29. Minor. 347 65 6 28 16 1.19 1.23 1.47 32- " .500 70 44 33 46 1. 10 2.13 2-34 56. " .650 74 16 V 30 0.44 7-4 3-26 86. Ingersoll. .870 78 40 84 4 42 30 42 30 0-35 0.83 II. 11.4 3.85 9.46 91. 96. ',! 2.25 85 13 42 30 1.03 11.4 II.7 97- " 4.00 87 20 42 30 1.87 11.4 21.3 Forst.-Fre'ed. 5-50 88 oo 3-i6 9.0 28.4 it " Gold I.OO 81 45 44 oo 0.24 28.0 6.7 tt H 2.00 85 30 43 5 6 0.47 26.7 12.5 " " 3.00 87 05 43 5 0.80 24-5 19.6 " " 5-00 88 15 43 25 1.81 i S.i 33- il Iridium I.OO 82 10 29 X 5 3-85 1. 60 6.2 4< K 2.00 83 10 29 40 4-30 1.66 7.1 " 3-00 81 40 30 40 3-33 1.79 6.0 K Nickel 5.00 0.420 79 oo 72 20 32 20 3i 42 227 1.41 2.03 1.79 4.6 2-53 54- Tool. 0.589 76 i 3 1 4 1 1.79 1.86 3-33 62. Drude. 0.750 78 45 32 6 2.19 1.99 4-36 70. Ingersoll. I.OO 80 33 32 2 2.63 2.00 5.26 74- " Platinum 2.25 I.OO 84 21 75 3 33 30 37 3-95 1.14 2-33 3.25 9.20 3-7 85. Forst.-Fre'ed. 2.OO 74 30 39 So 0.70 5.06 3-5 " " 3-00 73 50 41 oo 0.52 6.52 3-4 " S-oo 72 oo 42 10 -34 9.01 3-t < Silver 0.226 62 41 22 l6 1.41 0.75 i. ii 18. Minor. 293 63 14 18 56 0.62 0.97 '7- " 316 52 28 15 38 1-13 0.38 0-43 4- " 332 52 i 37 2 0.41 1.61 0.65 32- N 395 66 36 43 6 0.16 12.32 1.91 87. " .500 72 31 43 29 0.17 17.1 2-94 93. " .589 75 35 43 47 0.18 20.6 3.6 4 95- " 750 79 26 44 6 0.17 30.7 5-6 97- Ingersoll. I.OO 82 o 44 2 0.24 29.0 6.96 98. 11 1.50 84 42 43 48 0-45 23-7 10.7 98. 1 2.25 3-oo 86 18 87 10 43 34 42 40 0.77 1.65 19.9 12.2 '5-4 20.1 99. Fbrst.-Fre'ed. 4.50 88 20 41 10 4-49 7-42 33-3 " " Steel 0.226 66 51 28 17 1.30 1.26 1.64 35- Minor. 257 68 35 28 45 i. 3 8 1.35 1.86 40. " 325 69 57 3 9 *37 I.S3 2.09 45- " .500 75 47 29 2 2.09 1.50 3-14 57- " .650 1.50 7748 81 48 27 9 28 51 2.70 3-7 1 '33 i-55 3-59 5-75 59- 73- Ingersoll. 2.25 83 22 30 36 4.14 1.79 7-4 1 80. Drude, Annalen der Physik und Chemie, 39, p. 481, 1890; 42, p. 186, 1891; 64, p. 159, 1898. Minor, Annalen der Physik, 10, p. 581, 1903. Tool, Physical Review, 31, p. i, 1910. Ingersoll, Astrophysical Journal, 32, p. 265, 1910; Fbrsterling and Freedericksz, Annalen der Physik, 40, p. 201, 1913. SMITHSONIAN TABLES. 296 TABLES 354-355. OPTICAL CONSTANTS OF METALS. TABLE 354. Metal. A. n. k. R. Ref. Metal. A. n. k. R. Ref. Al* 0.589 1.44 5-32 83 I Rh* 0-579 i-54 4.67 78 3 Sb.* Bi.tJ 589 white 3-4 2.26 4.94 70 I 2 Se.J .400 .490 2.94 3.12 2.31 1.49 44 35 5 5 Cd* 589 1.13 5.01 85 I .589 2-93 0-45 2 5 5 Cr.* 579 2.97 4.85 70 3 .760 2.60 0.06 20 Cb* 579 1. 80 2.II 41 3 Si* 589 4.18 0.09 38 6 Au.t 257 0.92 I.I4 28 4 1.25 3-67 0.08 33 6 .441 1.18 1.8 5 42 4 2.25 3-53 0.08 31 6 .589 0.47 2.8 3 82 4 Na. (liq.) .589 .004 2.61 99 i I. crys. Ir.* Fe. 589 579 -257 3-34 2.13 I.OI 30 11 4 3 4 Ta.* Sn* W.* 579 589 579 1.48 2.76 2.31 5-25 2.71 44 82 49 3 i 3 441 1.28 1.37 28 4 V* 579 3-03 3-51 58 3 589 i-S" 1.63 33 4 Zn* 257 0-55 0.61 20 4 Pb* .589 2.01 3-48 62 i .441 o-93 3.19 73 4 Mg* 589 0-37 4.42 93 i 589 1-93 4.66 74 4 Mn* 579 2.49 3^9 64 3 .668 2.62 5.08 73 4 Hg. (liq.) '.326 0.68 2.26 66 4 44 i I.OI 1.62 3-42 4.41 74 4 4 A = wave-length, n = refraction index. 668 1.72 4.70 77 4 k = absorption index, R = reflection. Fd* Pt.t 579 257 44 l 1.62 1.17 1.94 3-41 1.65 3.16 I 3 4 4 (i) Drude, see Table 205; (2) Kundt, prism used, Ann. der Physik und Chemie, 34, p. 477, 36, p. 824, 1889; (3) v. Wartenberg, Verh. 2.63 2.QI 59 cq 4 4 deutsch. Physik. Ges. 12, p. 105, 1910; (4) Meier, Annales der Physik, 10, p. 581, 1903; Ni* 275 .441 .589 7 1.09 1.16 1.30 1.23 1.97 jy 24 25 43 t 4 4 4 (5) Wood, Phil. Mag. (6), 3, 607, 1902 ; (6) Ingersoll, see Table 205. * solid, t electrolytic, J prism, deposited as film in vacuo. TABLE 355. Reflecting Power of Metals. (See page 298.) Wave- A length 4 c/: o u o U s* A g A z A K A S c CO c N M Per cents. 5 72 46 _ 76 34 38 _ _ 49 57 _ .6 53 24 73 48 77 32 45 49 .8 S4 2S 74 5- 81 29 64 48 S6 60 I.O 2.0 82 II 8 7 2 67 72 27 3S 78 87 74 77 o2 li 84 28 28 78 90 5 52 54 61 62 8S 61 69 80 92 4.0 92 68 96 81 48 94 84 90 88 92 28 57 72 93 79 97 7-o 96 71 9 S 93 54 95 9 1 93 94 94 28 94 68 81 88 98 10.0 98 72 98 97 59 96 94 97 9S 28 84 96 98 12.0 98 99 97 96 95 97 95 : 85 96 99 Coblentz, Bulletin Bureau of Standards, 2, p. 457, 1906, 7, p. 197, 1911. The surfaces of some of the samples were not perfect so that the corresponding values have less weight. The methods for polishing the various metals are described in the original articles. The following more recent values are given by Coblentz and Emerson, But Bur. Stds. 14,0. 207, 1917; Stellite, an exceedingly hard and untarnish- able alloy of Co, Cr, Mo, Mn, and Fe (C, Si, S, P) was obtained from the Haynes Stellite Co, Kokomo, Indiana. Wave-length, fi, .15 .20 .30 .50 .75 i.oo 2.00 3.00 4.00 5.00 9.00 Tungsten, - - - .50 .52 .576 .900 . 9 43 -9^8 . 9 53 .32 .42 .50 .64 .67 .689 .747 .792 .825 .848 .880 SMITHSONIAN TABLES. TABLES356-358.-THE REFLECTION OF LIGHT. 297 According to Fresnel the amount of light reflected by the surface of a transparent medium i / A i D\ l i sin 2 (/' r) - tan 2 (/ r) ) = i (4 + } = - \ sin -2 (/ - _|_ r ) + tan 2 (/-fr) 5 ' 1S amount polarized in the plane of inci- dence ; B is that polarized perpendicular to this ; i and r are the angles of incidence and refraction. TABLE 356, Light reflected when i = or Incident Light is Normal to Surface. . l(A+B). n. i (^ + -ff). . iU + ^). n. KA+B^\ 1. 00 0.00 4 2.78 2.O u. ii 5- 44.44 1. 02 1.05 0.01 0.06 .6 4.00 5-33 2.25 2-5 14.06 18.37 5-83 10. 5O.OO 66.67 I.I 1.2 0.23 0.83 :I 6.72 8.16 2.75 3- 22.89 25.00 100. oo 96.08 IOO.OO i-3 1.70 9 9-63 4. 36.00 TABLE 357. Light reflected when n is near Unity or equals 1 + dn. A T> A _ B \ IP flu mft (A + B). A+B I.OOO I.OOO I.OOO O.O 5 1.015 .985 I.OOO 1.5 10 1.063 I.OOI 6.2 15 1.149 .862 I.OO5 14-3 20 1.282 752 .017 26.0 2 5 1.482 .612 .047 41.5 30 1.778 .444 .III 60.0 35 2.221 .260 .240 79.1 40 2.904 .088 496 94-5 45 4-000 .000 2.OOO IOO.O 50 5.857 .176 3.016 94-5 9-239 1.081 5.160 79.1 60 I6.OOO 4.000 10.000 60.0 65 70 3L346 73-79 12.952 42.884 22.149 57.98I 41.5 26.0 75 222.85 167.16 195.00 14-3 80 1099.85 971.21 I0 35-53 6.2 85 1 733 -64 16808.08 17069.36 1.5 90 oo 00 00 0.0 TABLE 38. Light reflected when n = 1.55. i. r. A. B. dA.\ dB.t I (A+B). A-B m A+B' o / O O.O 4-65 4-65 0.130 0.130 4-65 0.0 5 3 J 3-4 4.70 4.61 .131 .129 4-65 I.O 10 6 25.9 4.84 4-47 135 .126 4.66 4.0 IS 9 36-7 5-09 4.24 .141 .121 4.66 9.1 20 12 44.8 5-45 3-92 .150 "4 4.68 16.4 25 15 49-3 5-95 3-50 .161 .105 4-73 25.9 18 49-1 6.64 3.00 .175 .094 4.82 37-8 35 40 21 43-1 24 30.0 7-55 8.77 2.40 i-75 .191 .210 8i .066 4.98 5.26 S'-7 66.7 45 27 8.5 10.38 1.08 233 .049 5-73 81.2 5 29 37- * 12.54 0.46 .263 .027 6.50 92-9 55 3i 54-2 15-43 0.05 303 .007 7-74 99-3 60 33 58-1 19-35 0.12 .342 -.013 9-73 98.8 65 35 47- 24.69 ''3 375 .032 12.91 91.2 70 37 J9- 1 31.99 4.00 .400 .050 18.00 77-7 75 38 32.9 42.00 10.38 .410 .060 26.19 61.8 80 39 26.8 55-74 23-34 .370 -.069 39 54 41.0 82 30 39 45-9 64.41 34-04 .320 -.067 49.22 30.8 85 o 39 59- 49-03 .250 .061 61.77 20.6 86 o 40 3.6 79.02 56.62 .209 -055 67.82 16.5 87 o 40 6.7 83.80 65.32 .163 -.046 74- 5 6 12.4 88 e 40 8.9 88.88 75-3 .Il8 .036 82.10 8.3 89 o 40 10.2 94.28 86.79 .063 .022 90.54 4-' 90 o 40 10.7 IOO.OO IOO.OO .000 .000 IOO.OO O.O Angle of total polarization = 57 10^.3, A = 16.99. * This column gives the degree of polarization. t Columns 5 and 6 furnish a means of determining A and B for other values of . They represent the change in these quantities for a change of of o.ox. Taken from E. C. Pickering's " Applications of Fresnel's Formula for the Reflection of Light." SMITHSONIAN TABLES. TABLES 359-36O. REFLECTING POWER OF METALS. TABLE 359, Perpendicular Incidence and Reflection. (See also Tables 352-355.) The numbers give the per cents of the incident radiation reflected. i j 1 a i _ cTI" !' i ^ | I 1 x-< 1 Wave-length, , ilver-backed G ercury-backed 1 lach's Magnali 6gA 1+ Z iM les-Schiineman + 34^ + *^. ss' Speculum 1\ 68.2CK + 3I.8.S Nickel. trolytically De t ^ if 11 1 Copper. 'omtnercially F & 11 ^*^> Gold. trolytically De Brass. ( Trowbridge | 1 N C/3 a m sd o 3 ^ ^ S 4j 3 MR N ^ 0) .i _ _ 67.0 35-8 29-9 37-8 _ 32-9 25-9 33-8 38-8 _ 34-i ' .288 70.6 37-1 37-7 42.7 35*0 24.3 38.8 34.0 21.2 305 - i A - - 72.2 37-2 41.7 44-2 37-2 25-3 39-8 31.8 9.1 .316 .326 _ _ 75-5 39-3 - 45-2 - 40-3 24.9 41.4 28.6 - 14.6 338 - - 46.5 - 55-5 - _ 81.2 43-3 51.0 4 8.3 45-o 27-3 43-4 27.9 - 74-5 385 - - 83.9 44-3 49.6 - 47-8 28.6 45-4 27.1 - 81.4 .420 45 85"? 72^8 83.3 83-4 47.2 49.2 56.4 60.0 56.6 59-4 4 - 8 54-4 32.7 37-0 51.8 54-7 29-3 33- 1 - 86.6 9-5 .500 86.6 70.9 83-3 49-3 63-2 60.8 53-3 54-8 43-7 584 47.0 - 9i-3 55 88.2 71.2 82.7 48.3 64.0 62.6 59-5 54-9 477 61.1 74.0 92.7 .600 88.1 69.9 83.0 47-5 64-3 64.9 83-5 55-4 71.8 64.2 84.4 - 92.6 .650 .700 89.1 89.6 71-5 72.8 82.7 83-3 5i-5 54-9 65-4 66.8 66.6 68.8 89.0 90.7 56.4 57-6 80.0 83.1 66.5 69.0 88.9 92-3 " 94-7 95-4 .800 _ _ 84-3 63.1 _ 69.6 _ 58.0 88.6 70.3 94-9 _ 96.8 I.O 84.1 69.8 70-5 72.0 63.1 90.1 72.9 97-o '5 85.1 79.1 75-o 78.6 _ 70.8 93-8 77-7 97-3 - 98.2 2.O 86.7 82.3 80.4 83-5 76.7 95-5 80.6 96.8 9I.O 97-8 3- - - 87.4 854 86.2 88.7 - 83.0 97.1 88.8 - 93-7 98.1 4.0 - - 88.7 87.1 88.5 91.1 - 87.8 97-3 91-5 96.9 95-7 98.5 5 >o 89.0 87-3 89.1 94.4 89.0 93-5 97-o 95-9 98.1 7.0 90.0 88.6 90.1 94-3 92.9 98.3 95-5 98.3 97.0 98.5 9.0 90.6 90.3 92.2 95-6 92.9 98.4 95-4 98.0 97-8 98.7 I I.O 90.7 90.2 92.9 95-9 94.0 98.4 95-6 98.3 96.6 98.8 14.0 " 92.2 90.3 93- 6 97.2 " 96.0 97-9 96.4 97-9 " 98.3 Based upon the work of Hagen and Rubens, Ann. der Phys. (i) 352, 1000; (8) r, 1902; (n) 873, 1903. Taken partly from Landolt-Bbrnstein-Meyerhoffer's Physikalisch-chemische Tabellen. TABLE 360. Percentage Diffuse Reflection from Miscellaneous Substances. Lamp-blacks. i 21 jj Wave- length /* i & c. E- ll Acetylene $i x ^ Green lea\ Lead oxid 1 < Zinc oxide 15 Lead carbonate a < Black veh Black felt. Red brick *.6o 3-2 25. 52, 84. 82. 89. is- 1.8 14. 30. 95 3-4 i-3 I.I 0.6 '3 I.I 88. 86. 75- 93. 21. 4-4 3.3 1.3 9 .8 1.2 1.4 SI- 21. 8. 18. 29. 3-7 8.8 3-8 1-3 1.2 1.6 2.1 26. 2. 3- ,S- II. 2-7 12. 24.0 4-4 3-o 4.0 2.1 5-7 4-2 IO. 6. 5- 7> *Not monochromatic (max.) means from Coblentz, ]. Franklin Inst. 1912. Bulletin Bureau of Standards, 9, p. 283, 1912, contains many other materials. SMITHSONIAN TABLES. TABLES 361-362. REFLECTING POWER OF PIGMENTS- TABLE 361. Percentage Reflecting Power of Dry Powdered Pigments. 299 Taken from "The Physical Basis of Color Technology," Luckiesh, J. Franklin Inst., 1917. The total reflecting power depends on the distribution of energy in the illiuninant and is given in the last three columns for noon sun, blue sky, and for a 7.9 lumens/ watt tungsten filament. Spectrum color. Vio- let. Blue. Green. Yellow. Orange. Red. i i Ii Wave-length in /z 0.44 0.46 0.48 0.50 0.52 0-54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 fj American vermilion .... 8 6 ,> 5 6 6 9 ii 24 39 S3 61 66 65 14 12 12 Venetian red 5 5 S 6 7 12 19 24 28 30 32 32 10 13 Tuscan red Indian red . . I 7 7 8 8 8 8 12 II 16 15 18 18 20 20 22 22 23 23 24 24 10 IO 9 12 II Burnt sienna Raw sienna 12 13 13 13 18 6 26 9 3."> 14 43 18 46 20 46 21 45 23 44 24 45 25 43 II 33 9 30 13 37 Golden ochre Chrome yellow ochre. . . 22 8 22 9 23 7 27 7 40 10 53 19 63 30 71 46 74 62 3 11 Ii 72 80 33 29 63 40 Yellow ochre 20 2O 21 24 32 42 53 OS 6 4 61 00 59 59 59 49 40 S3 Chrome yellow medium. 5 5 6 8 18 48 66 75 78 79 81 8! 81 81 54 So 63 Chrome yellow light. . . . 13 13 18 30 56 82 88 89 90 89 88 8? 85 84 76 70 82 Chrome green light .... Chrome green medium. . 10 7 10 7 14 10 23 21 26 21 23 17 20 13 17 ii 14 9 II 7 1 8 6 7 6 6 5 19 14 19 14 18 12 Cobalt blue 59 67 58 49 38 35 23 15 ii IO IO 10 ii IS 7 20 IO 25 17 16 7 18 IO 1 TABLE 362. Infra-red Diffuse Percentage Reflecting Powers of Dry Pigments. i Wave- length in n 8 9 rj 1 6 i PL, 1 S 1 g N 1 I White lead paint. IZn oxide paint. 0.60* 3 27 52 26 74 70 84 86 82 86 85 86 88 85 76 68 0-95 * 4 24 45 41 88 86 84 93 89 79 72 4-4 14 is 33 5i 30 34 41 21 47 8 16 22 23 29 ii 8.8 13 5 26 4 ii 5 20 7 3 2 4 5 10 4 24.0 6 4 8 IO 9 10 7 6 10 5 9 6 5 7 9 * Non -monochromatic means from Coblentz, Bui. Bureau Standards 9, p. 283, 1912. For the REFLECTING (and transmissive) power of ROUGHENED SURFACES at various angles of incidence see Gorton, Physical Review, 7, p. 66, 1916. A surface of plate glass, ground uniformly with the finest emery and then silvered, used at an angle of 75, reflected 90 per cent at 4M, approached 100 for longer waves, only 10 at m, ess than 5 in the visible red and approached o for shorter waves. Similar results were obtained with a plate of rock salt for transmitted energy when roughened merely by breathing on it. In both cases the finer the surface, the more suddenly it cuts off the short waves. SMITHSONIAN TABLES. 3 oo TABLES 363-365. REFLECTING POWER. TABLE 363. Reflecting Power of Powders (White Light). Various pure chemicals, very finely powdered and surface formed by pressing down with glass plate. White (noon light) light. Reflection in per cent. Nutting, Jones, Elliott, Tr. 111. Eng. Soc. 9, 593, 1914. Aluminum oxide 83 . 6 Barium sulphate 81 . i Borax . . Magnesium carbonate 86 . 6 (block) 88.0 Sodium chloride 78.1 Sodium sulphate 77. Starch. . Borax 81.6 Magnesium oxide 85.7 Starch 80.3 Boric acid 83.2 Rochelle salt 79-3 Sugar 87.8 Calcium carbonate 83 . 8 Salicylic acid 81.1 Tartaric acid 79 . i Citric acid 81.5 Sodium carbonate 81 TABLE 364. Variation of Reflecting Power of Surfaces with Angle. Illumination at normal incidence, i J watt tungsten lamp, reflection at angles indicated with normal. 111. Eng. Soc., Glare Committee, Tr. 111. Eng. Soc. n, p. 92, 1916. Angle of observation. i 3 5 10 15 30 45 60 Magnesium carbonate block 0.88 0.80 0.78 0.76 0.69 "-3 0.29 0-23 0.83 4-Q 0.69 II- 3 0.29 0.22 0.69 11.3 0.29 0.21 0.78 0.88 0.80 0.78 0.76 0.69 0.31 0.29 o. 20 0.72 4-55 0.88 0.80 0.78 0.76 0.69 0. 22 0.27 o. 19 0.62 3-86 0.87 0.80 0.78 0.76 0.69 0. 21 0. 20 o. 16 0.49 3-03 0.83 0-77 0.78 o.73 0.68 0. 20 O.I 4 O.II 0.28 0.78 0.72 o.7S o. 76 0.70 0.66 o. 20 0.13 0. II 0.21 0.42 0.68 0.66 0.72 0.67 0.64 0.18 0.12 O.I2 o. 16 0.35 Magnesium oxide Matt photographic paper White blotter Pot opal, ground. . . . Flashed opal, not ground Glass, fine ground Glass, course ground Matt varnish on foil ... .... Mirror with ground face The following figures, taken from Fowle, Smithsonian Misc. Col. 58, No. 8, indicate the amount of energy scattered on each side of the directly reflected beam from a silvered mirror; the energy at the center of the reflected beam was taken as 100,000, and the angle of incidence was about 3. Angle of reflection, 3 Energy o' 100,000 8' 600 10' 244 15' 146 20' 107 30' 66 45' 33 60' 22 100' It Wave-length of max energy of Nernst lamp used as source about 2/t. TABLE 365. Infra-red Reflectivity of Tungsten (Temperature Variation). Three tungsten mirrors were used, a polished Coolidge X-ray target and two polished flattened wires mounted in evacuated soft-glass bulbs with terminals for heating electrically. Weniger and Pfund, J. Franklin Inst. Wave- length Absolute reflec- tivity at room Per cent increase in reflectivity in going from room temperature to in At- in per cent. 1377 K 1628 K 1853 K 2056 K 0.67 Si +6.0 +7-4 +8.7 +9-8 0.80 55 +8.2 1.27 70 o.o o.o o.o 0.0 1.90 83 -6.6 -8.2 -9.6 II. 2.00 85 -7-5 -9.3 10. 9 -12.3 2.90 92 -7.7 -9-4 ii. i -12.5 4-00 93 12.5 See also Weniger and Pfund, Phys. Rev. 15, p. 427, igig. SMITHSONIAN TABLES. TABLE 366. TRANSMISSIBILITY OF RADIATION BY DYES- 301 Percentage transmissions of aqueous solutions taken from The Physical Basis of Color-Technology Luckiesh J Franklin Inst. 184, 1917. Spectrum color Violet. Blue. Green. Yellow. Orange. Red. Wave-length in p 44 .46 .48 So .52 .54 56 .58 .60 .62 .64 .66 .68 .70 Carmen ruby opt Amido naphthol red 6 i i 4 80 69 IS 15 17 2 4 35 3 28 2 77 58 s 89 :a 83 77 84 . 92 21 89 50 . 81 84 7 39 25 3 7 I 2 3 i 70 34 51 40 I I I I 36 62 4 7 39 69 49 64 12 20 29 57 31 32 6 14 40 63 84 89 60 56 23 9 71 76 75 5i 18 6 3i 13 9i 84 69 59 79 66 88 78 8 2 83 64 28 2 71 45 76 68 i 23 i 4 13 14 12 3 4 6 i 2 6 i 31 32 48 7 52 3 2 20 48 91 7 43 84 i 58 96 4 53 77 i i 43 84 18 74 91 10 82 88 90 21 30 36 52 23 4 70 60 37 8 i 57 39 19 26 17 7 24 34 40 41 13 i 92 92 89 51 38 28 i 69 60 46 26 7 i 21 31 76 65 46 48 35 24 44 27 17 52 27 9 44 26 19 13 2 50 33 26 4 i 53 13 25 II 22 2 38 10 47 12 34 i 54 14 82 67 82 75 86 23 53 43 60 97 98 96 96 i 31 97 97 82 83 43 88 91 94 96 97 60 84 92 93 29 16 13 2 4 i 2 I 32 14 80 67 18 9 32 20 7 4 ~8 IS 9 14 19 3 2 I 22 15 10 6 23 27 34 I - 4 18 4 38 75 56 96 98 90 95 96 44 54 63 39 54 65 78 88 90 86 95 96 55 72 84 ii 35 55 8? 93 92 96 97 98 87 90 90 91 95 96 2 23 50 82 92 96 67 75 81 98 98 98 96 96 96 70 79 80 97 97 97 84 85 86 95 96 97 3 27 64 95 95 95 95 96 96 721 41 52 36 19 5 3 i i 4 12 7 5 I 2 6 I 2 I 4 i 557 36 56 74 2 4 8 73 93 97 13 42 75 55 90 98 83 96 96 49 70 84 27 79 97 3 37 49 60 92 96 96 98 98 08 96 96 96 73 78 82 72 77 79 91 92 92 96 96 96 88 90 92 65 68 69 92 92 92 98 98 08 90 90 90 97 98 98 7i 79 79 96 96 96 85 86 87 98 98 98 96 96 96 81 81 81 97 97 97 86 87 87 97 97 97 85 93 93 96 96 95 2 23 64 12 50 = j 5 ~ 6 ~ ^ 21 49 73 33 18 37 60 41 64 72 4 16 40 6 42 78 14 29 53 81 88 92 16 25 45 97 97 97 92 93 94 98 98 98 93 ii 23 96 95 94 96 96 96 i 13 23 97 97 96 26 63 89 Erythrosine Hematoxyline Alizarinered Acid rosolic (pure) Rapid filter red Aniline red fast extra A Pinatype red fast Eosine Rose bengal Cobalt nitrate Tartrazine Chrysoidin Aurantia Aniline yellow phosphine Fluorescein Aniline yellow fast S Methyl orange indicator Uranine Uranine naphthaline Orange B naphthol Safranine Martius gelb Naphthol yellow Potassium bichromate, sat . . . Cobalt chromate Naphthol green Brilliant green Malachite green Saurgriin Methylengriin Aniline green naphthol B Neptune green Cupric chloride Turnbull's blue Victoria blau . . .... Prussian blue (soluble) Wasser blau Resorcine blue Toluidin blau Patent blue Dianil blue Filter blue Aniline blue, methyl Magenta Gentiana violet .... Rosazeine Iodine (dense) Rhodamine B Acid violet Cyonine in alcohol "... Xylene red Methyl violet B For the infra-red transmission (to 1 2/x) and reflection powers of a number of aniline dyes, see Johnson and Spence, Phys. Rev. 5, p. 349, 1915. SMITHSONIAN TABLES. 3O2 TABLES 367-369. TRANSMISSIBILITY OF RADIATION BY JENA GLASSES. TABLE 367. Coefficients, a, in the formula It = ha*, where h is the Intensity before, and It after, transmission through the thickness t. Deduced from observations by Muller, Vogel, and Rubens as quoted in Hovestadt's Jena Glass (English translation). Coefficient of transmission, a. Unit t=i dm. 375 M 39 M .400 M .434 M .436 , 455 M 477 M 503 M .580^1 .677 fi O 340, Ord. light flint O 102, HVy silicate flint .388 456 .02 S .614 .569 .680 .463 .502 .566 ft .880 .700 .880 .782 .878 .828 939 794 93. Ord. ~ -7H .807 .899 .871 903 943 O 203, " " crown .583 S8} .695 .667 .806 .822 .860 .872 .872 903 O 598, (Crown) - -797 .770 77' .776 .818 .860 Unit t=i cm. 0.7 V- 0,5, I.I M 1.4 f- 1.7 n 2.0 M 2-3 M M, 2. 7 /A 2.9 >x 3.., S 204, Borate crown S 179, Med. phosp. cr. I.OO 99 94 95 .90 .90 .85 .84 .81 .67 .69 49 1 .2Q .18 - O 1 143, Dense, bor. sil. cr. .98 - 97 - 95 93 .00 .84 71 47 27 O 1092, Crown 99 96 95 99 .99 .91 .82 71 .60 .48 .29 O 1151, " .08 99 99 .98 94 .90 79 75 45 3 2 O 451, Light flint O 469, Heavy " I.OO I.OO _ I .98 99 ? .92 98 .84 97 .78 .90 :%& 34 50 500, " " S 163, " I.OO I.OO - I.OO 98 - I.OO 99 - I.OO 99 99 .92 94 74 78 TABLE 368. Note : With the following data, / must be expressed in millimeters ; i. e. the figures as given give the transmissions for thickness of I mm. No. and Type of Glass. Wave-length in /m. Visible Spectrum. Ultra-violet Spectrum. .644 /a 578 M .546 M 509 M .480 M 436, 405, 384, .361, 340, 332M 309 M .280^ F38i5 Dark neutral 35 35 37 35 34 30 T 5 .06 F45I2 Red filter 94 05 F2745 Copper ruby .72 39 47 47 45 43 43 F43I3 Dark yellow .98 97 93 83 .09 F435I Yellow .98 97 .96 93 44 i.S F4937 Bright yellow F 4930 Green filter I.O 17 I.O 50 I.O 64 99 .62 74 44 .40 3i .28 .22 .18 .14 .06 F3873 Blue filter .18 5 73 .69 59 .36 .10 F 3654 Cobalt glass, transparent for outer red IS 44 .8s I.O I.O I.O I.O I.O .58 F 3653 Blue, ultraviolet F 37 28 Didymium, str'g bands 99 .72 99 .96 .11 95 .65 .96 I.O 99 I.O 99 I.O .89 I.O .89 I.O 77 .81 -54 .18 This and the following table are taken from Jenaer Glas fiir die Optik, Liste 751, 1909 TABLE 369. - Transmlsslblllty by Jena Ultra-violet Glasses. No. and Type of Glass. Thickness. 0-397 M 0.383 M. 0.361 ft 0.346 fj. 0.325 M 0.309 M 0.280 M UV 3199 Ultra-violet i mm. 2 mm. I.OO 0.99 I.OO 0.99 I.OO 0.99 I.OO 0.97 I.OO 0.90 0-95 0-57 0.56 < i dm. 0-95 o-95 0.89 0.70 0.36 UV 3248 " i mm. I.OO I.OO I.OO I.OO 0.98 0.91 o-35 (i 2 mm. 0.98 0.98 0.98 0.92 0.78 0.38 (( U i dm. 0.96 0.87 0.79 0.45 0.08 SMITHSONIAN TABLES. TABLE 370. TRANSMISSIBILITY OF RADIATION BY GLASSES- 303 The following data giving the percentage transmission of radiation of various substances, mostly glasses, are selected from Spectroradiometric Investigation of the Transmission of Vari- ous substances, Coblentz, Emerson and Long, Bui. Bureau Standards, 14, p. 653, 1918. Glass or substance, manufacturer. Thick- ness, mm Transmission per cents. Wave-lengths in p.. o-5 I.O i.S 2.0 2.5 3.0 3-s 4.0 4-5 S-o Purple fluorite 4.98 .007 .24 IO IO 1.95 5-9 3-i8 3-55 i-55 2.88 2.2 3-43 5-n 2.6 i-5 2-43 2.58 6.36 3-70 3-23 2. II 4-43 1.96 1.98 2.04 2.04 1.58 22 34 O o 90 80 12 50 52 55 90 50 72 59 76 3 8 4i 83 73 50 5o 60 83 50 90 75 i 4 i 2 O 74 o o 23 9 1 92 o 86 76 9i 2 3 43 63 o 64 70 89 62 90 60 2 53 23 4 i 43 i 15 24 60 9 1 9i o 91 80 91 47 i 2 44 37 o o 72 72 89 67 91 82 6 79 53 12 63 2 50 60 74 9i 2 90 4 91 82 9 1 48 i i 46 ii 76 65 75 68 87 75 13 83 68 19 10 79 3i 61 75 78 88 83 ii 89 81 90 48 i i 46 o 40 2 IO 15 35 23 6 25 20 ii 3 36 ii ii 45 45 42 6 1 5i 30 70 57 o 47 o 33 i IO 3 13 4 7 9 9 4 5 27 5 i 20 13 2O 8 2 3 35 20 52 60 o 48 o 36 o o I 7 4 7 o 8 6 6 28 4 2 20 12 25 12 27 II 38 25 51 62 O 48 o 7 o o 2 I o o o o o I I 7 2 5 3 7 2 10 62 O O 48 o o o o o o o o o o o o o o o o o Gold film on Crooke's glass. . . " " " crown glass Molybdenite Cr 2 (SO 4 )3.i8H 2 O Chrome alum, 10 g to 100 g H 2 CoCl 2 , 10 g to 100 g H 2 O GLASSES: Copper ruby, flashed Pyrex Corning Noviol, B, Corning, yellow . . . Novieweld3, Corning, dk-yellow Gi7ioN green Corning Gi74J, Corning, heat abs'b'g. . Gs&4 Corning blue . . . . . Gi72BWs. Corning, red-purple Crookes' A A. O. Co " sage green 30, A. O. Co Lab. 58, A. O. Co Fieurzal B, A. O. Co Akopos green, J. K. O. Co Manufacturers: Corning Glass Works, Corning, N. Y.; A. O. Co., American Optical Co., Southbridge, Mass.; J. K. O. Co., Julius King Optical Co., New York City. For other glasses see original reference. See also succeeding table, which contains data for many of the same glasses. SMITHSONIAN TABLES. 304 TABLE 371. TABLE 371. Transmission of the Radiations from a Gas-filled Tungsten Lamp, the Sun, a Magnetite Arc, and from a Quartz Mercury Vapor Lamp (no Globe) through Various Substances, especially Colored Glasses. Color. Trade name. Source.* Thick- ness in mm Transmission, per cent. Gas- filled tung- sten. Quartz mercury vapor.f Mag- netite arc.t Solar radia- tion. Greenish-yellow Smoky green Yellow-green Fieuzal, B Fieuzal, 63 Fieuzal, 64 Euphos Euphos, B Akopos green Hallauer, 65 Hallauer, 64 G 124, IP Noviweld, 30% Noviweld, shade 3 Noviweld, shade 4$ Noviweld, shade 6 Noviweld, shade 7 Saniweld, dark G34 Noviol, shade A Noviol, shade B Noviol, shade C Ferrous No. 30 No. 61 Lab. No. 59 Gi2 4 JA Smoke, C Smoke, D Crookes, A Crookes, B Pfund Pfund Lab. No. 58 Lab. No. 57 Shade C Electric smoke G 55 A 62 Shade D G 5 3 G i 7 i-IZ 0584 G 172 BW 5 Gs8s Selenium Flashed Window Crown Mica Mica Water A. O. C. F. H. E. . F. H. E. B. S. B. &L. J. K. B. S. F. H. E. C. G. W. C. G. W. C. G. W. C. G. W. C. G. W. C. G. W. B. S. J. K. C. G. W. C. G. W. C. G. W. C. G. W. A. O. C. A. 0. C. A. O. C. C. G. W. B. &L. B. &L. A. O. C. A. O. C. A. 0. C. A. O. C. A. O. C. A. 0. C. A. O. C. A. O. C. C. G. W. B. &L. C. G. W. C. G. W. C. G. W. C. G. W. C. G. W. C. G. W. Schotts B. S. B. S. B. S. B. S. B. S. B. S. 2.04 i. 80 1.65 3-27 3-12 i.sS 2.36 1.35 2.81 2.14 2. 20 2.20 2.17 2.17 3-12 1-32 3-57 2.00 2.88 2.0O 1-95 2.10 1-93 *-S3 2.26 2-45 1.97 2.OO iTsS 2.00 2. II 1.89 2.85 2.09 2-51 3-21 3-75 4-93 3-13 2.90 3-22 1.85 1.56 1-30 0.09 10. 71.6 75-5 50.7 78.9 78.8 84.6 70.3 S8. 7 0.4 S-i 3-4 1.6 0.9 0.8 Si- 6 78.1 56.9 74-1 S-3 82.7 3-7 i Ill 75-7 2.6 83.3 82.8 36.6 17.4 37-6 2.9 46.6 24.9 72.4 35-8 67.8 69.4 34-2 26.9 34-3 22.0 25-0 24.7 29-5 17-7 25-9 0. 2 7-8 4-2 I. 2 0.4 0. 2 IS-2 10.6 17.0 32.2 I7-S 28.6 17.3 21- S 3L2 16.0 46.1 32.0 7.2 1-3 40.0 Si-9 44-3 2.2 17.0 20.7 3-9 41.7 25.2 26.5 34-0 7-9 4~8 59-5 64.9 35-4 43-1 }54-0 46.0 SS-o 53-0 59-0 2.7 0.8 O. 2 43-Q 56.0 ii. 5 12.5 52.0 39-0 64.0 1.2 66 39 48 63 72 64 74 55 9 O.Q 5 47 81 75 72 17 72 19 60 1 69 12 88 79 ii 16 4i 48 46 82 92 " " Amber. . . . Orange Yellow Sage green Yellow-green Blue-green Black Neutral tint Gold plate " (darker).. Colorless Amethyst. Purple Blue Blue, dark Blue-green Blue-green, pale .... Red-purple Blue-purple Red Colorless Brown Colorless Clear *A. O. C., Amer. Optical Co., Southbridge, Mass.; C. G. W., Corning Glass Works, Corning, N. Y.; B. & L., Bausch & Lomb, Rochester, N. Y.; J. K., Julius King Optical Co., New York City; F. H. E., F. H. Edmonds, optician, Washington, D. C.; B. S., Bureau of Standards; scrap material, source unknown. t Infra-red radiation absorbed by quartz cell containing i cm layer of water. Taken from Coblentz-Emerson & Long, Bui. Bureau Standards, 14, 653, 1918. J Transmission of i cm cell having glass windows. SMITHSONIAN TABLES. TABLE 372. TRANSMISSIBILITY OF RADIATION. Transmissibility of the Various Substances of Tables 330 to 338. 305 Alum : Ordinary alum (crystal) absorbs the infra-red. Metallic reflection at 9.05/1 and 30 to 40/4. Rock-salt : Rubens and Trowbridge (Wied. Ann. 65, 1898) give the following transparencies for a i cm. thick plate in % : X % 9 10 12 13 14 IS 16 17 18 19 20.7 23-7/* 99-5 99-5 99-3 97.6 93-i 84.6 66.1 51.6 27.5 9.6 0.6 0. Pfliiger (Phys. Zt. 5. 1904) gives the following for the ultra-violet, same thickness : 280/1/1, 95.5% 231, 86%; 210, 77%; 186, 70%. Metallic reflection at 0.110/1, 0.156, 51.2, and 87/1. Sylvite : Transparency of a i cm. thick plate (Trowbridge, Wied. Ann. 60, 1897). X 9 IO II 12 U 14 '5 16 17 18 19 20.7 23-7M % 100. 98.8 99.0 99-5 99-5 97-5 95-4 93-6 92. 86. 76. 58. 1 S- Metallic reflection at 0.114,1*, 0.161, 61.1, 100. Fluorite : Very transparent for the ultra-violet nearly to o.i/i. Rubens and Trowbridge give the following for a i cm. plate (Wied. Ann. 60, 1897) : X 8* 9 IO ii 12/1 % 84.4 54-3 16.4 I.O O Metallic reflection at 24/4, 31.6, 40/1. Iceland Spar: Merritt (Wied. Ann. 55, 1895) gi yes the following values of k in the formula i = i e- kd (d in cm.) : For the ordinary ray : X 1. 02 1-45 1.72 2.07 2. II 2.30 2-44 2-53 2.60 2.6 5 2.741* k o.o o.o 0.03 0.13 0.74 1.92 3.00 1.92 1. 21 1.74 2.36 X 2.83 2.90 2-95 3-04 3-30 3-47 3.62 3.80 3.98 4-35 4-52 4.83M k 1.32 0.70 i. 80 4-71 22.7 19.4 9.6 1 8.6 00 6.6 14-3 6.1 For the extraordinary ray : X 2-49 2.87 3.00 3-28 3.38 3-59 3.76 3-90 4.02 4.41 4-67M k 0.14 0.08 0-43 1.32 0.89 1.79 2.04 1.17 0.89 1.07 2.40 X k 4.91 5-4 5-34 5-50/* 1.25 2.13 4.41 12.8 Quartz : Very transparent to the ultra-violet ; Pfliiger gets the following transmission values for a plate i cm. thick : at 0.222/1, 94.2%; 0.214, 92 ; 0.203, 8 3-6; 0.186, 67.2%. Merritt (Wied. Ann. 55, 1895) gi ves tne following values for k (see formula under Iceland Spar) : For the ordinary ray : X 2.72 2.8 3 2-95 3-7 3- T 7 3-38 3-67 3 .82 3-96 4.12 4-5M k 0.20 0.47 o-57 0.31 O.2O O.I 5 1.26 1.61 2.04 3-4i 7-30 For the extraordinary ray X 2.74 2.89 3.00 3.08 3-26 3-43 3-52 3-59 3.64 3-74 3-9i 4.19 4.36M k o.o o.n -33 0.26 O.I I 0.51 0.76 1.88 1.83 1.62 2.22 3-35 8.0 For X>7 /*, becomes opaque, metallic reflection at 8.50/1, 9.02, 20.75-24.4/1, then trans- parent again. The above are taken from Kayser's " Handbuch der Spectroscopie," vol. iii. SMITHSONIAN TABLES. 306 TABLES 373-374. TRANSMISSIBILITY OF RADIATION, TABLE 373. - Color Screens. The following light-filters are quoted from Landolt's " Das optische Drehungsvermogen, etc." 1898. Although only the potassium salt does not keep well it is perhaps safer to use freshly prepared solutions. Thick- Grammes of Optical cen- Color. ness. Water solutions of substance tre of band. Transmission. in 100 c.cm. M Red 20 2O Crystal-violet, 560 Potassium monochromate 0.005 IO. 0.6659 j begins about 0.718)1*. { ends sharp at 0.639/4. Yellow 2O Nickel-sulphate, NiSO^aq. 3- 0.5919 0.614-0.574^, M 15 Potassium monochromate 10. Green 15 2O Potassium permanganate Copper chloride, CuCla.2aq. 0.025 60. 0-533 0.540-0.505/1 Bright j blue ) 20 20 20 Potassium monochromate Double-green, SF Copper-sulphate, CuSO^aq. 10. O.O2 15- 0.4885 j 0.526-0.494 and | 0.494-0.458/4 Dark ( 2O Crystal-violet, 5BO 0.005 0.4482 0.478-0.410/4 blue \ 2O Copper sulphate, CuSO^aq. IS- TABLE 374. - Color Screens. The following list is condensed from Wood's Physical Optics : Methyl violet, 4R - (Berlin Anilin Fabrik) very dilute, and nitroso-dimethyl-aniline transmits 0.365/1. Methyl violet + chinin-sulphate (separate solutions), the violet solution made strong enough to blot out 0.4359;*, transmits 0.4047 and ,0.4048, also faintly 0.3984. Cobalt glass + aesculin solution transmits 0.4359/4. Guinea green B extra (Berlin) -j- chinin sulphate transmits 0.4916/1. Neptune green (Bayer, Elberfeld) + chrysoidine. Dilute the latter enough to just transmit 0.5790 and 0.5461 ; then add the Neptune green until the yellow lines disappear. Chrysoidine + eosine transmits 0.5790/4. The former should be dilute and the cosine added until the green line disappears. Silver chemically deposited on a quartz plate is practically opaque except to the ultra-violet region 0.3160-0.3260 where 90% of the energy passes through. The film should be of such thickness that a window backed by a brilliantly lighted sky is barely visible. In the following those marked with a * are transparent to a more or less degree to the ultra-violet-. * Cobalt chloride: solution in water, absorbs o.$o-.$3/j.; addition of CaCl2 widens the band to 0.47-. 50. It is exceedingly transparent to the ultra-violet down to 0.20. If dissolved in methyl alcohol -(- water, absorbs O-5O-.53 and everything below 0.35. In methyl alcohol alone 0.485- 0.555 and below 0.40/4. Copper chloride: in ethyl alcohol absorbs above 0.585 and below 0.535 > m alcohol -f- 50% water, above 0.595 and below 0.37/4. Neodymium salts are useful combined with other media, sharpening the edges of the absorption bands. In solution with bichromate of potash, transmits O-535-.565 and above 0.60/4, the bands very sharp (a useful screen for photographing with a visually corrected objective). Praseodymium salts : three strong bands at 0.482, .468, .444. In strong solutions they fuse into a sharp band at 0.435-. 4^5M- Absorption below 0.34. Picric acid absorbs 0.36-42/4, depending on the concentration. Potassium chromate absorbs O.4O--35, O-3O-.24, transmits 0.23/4. * Potassium permanganate: absorbs 0.5 5 5-. 50, transmits all the ultra-violet. Chromium chloride : absorbs above 0.57, between 0.50 and .39, and below 0.33/4. These limits vary with the concentration. Aesculin : absorbs below 0.363/4, very useful for removing the ultra-violet. * Nitroso-dimethyl-aniline : very dilute aqueous solution absorbs O.49-.37 and transmits all the ultra-violet. Very dense cobalt glass -j- dense ruby glass or a strong potassium bichromate solution cuts off everything below 0.70 and transmits freely the red. Iodine': saturated solution in CS 2 is opaque to the visible and transparent to the infra-red. SMITHSONIAN TABLES. TABLES 375, 376. TRANSMISSIBILITY OF RADIATION. TABLE 375. -Color Screens. Jena Glasses. 307 Kind of Glass. Maker's No Color. Region Transmitted. Thick- ness. mm. J Copper-ruby . . 2728 Deep red .... Only red to O.6/* .... I 1 la Gold-ruby . 459 111 Red . ... j Red, yellow ; in thin layers also / 2 2a 3 4 4a 4b Uranium . . . Nickel . . . . Chromium . . u Green copper . . 454 111 455 UI 440 111 4 i4 m 433 m 43 1 i Bright yellow . . . \ Bright yellow, fluo- / resces. Bright yellow-brown Yellow-green . . . Greenish-yellow . . Green 1 blue and violet, l Red, yellow, green to E b ; in ) j thin layer also blue J ( Red, yellow, green (weakened), ) | blue (very weakened) J Yellowish-green Red, green; from 0.65-. 50/4 . . . id n. 10. 5- 6 Chromium . Copper chromium 432 436'" Yellow-green . . . Grass-green . . . Yellowish-green, some red . . . 2 ~3 2-5 8 Green-filter . . 437 m 4tf m Dark green .... Green (in thin sheets some blue) . Green 5- 5- 10 Copper . . . . 2742 Blue, as CuSO 4 . . Green, blue, violet c-i2 ii Blue-violet . . 447 m Blue, as cobalt glass 12 i< < Cobalt . . 424 111 Blue ( Blue, violet, blue-green (weak- ) I ened), no red Blue violet extreme red 2-5 13 14 i ^ Nickel .... Violet .... Gray 450 111 452 m 44d ln Dark violet .... Violet (G-H), extreme red ... Violet (G-H), some weakened . . V 7-J 13 M 44 q" 1 f nizable color J All parts of the spectrum weakened 0.1-3 See " Uber Farbglaser fur wissenschaftliche und technische Zwecke," by Zsigmondy, Z. fur In- strumentenkunde, 21, 1901 (from which the above table is taken), and " Cber Jenenser Licht- filter," by Grebe, same volume. (The following notes are quoted from Everett's translation of the above in the English edition of Hovestadt's " Jena Glass.") Division of the spectrum into complementary colors : 1st by 2728 (deep red) and 2742 (blue, like copper sulphate). 2nd by 454"' (bright yellow) and 447'" (blue, like cobalt glass). 3rd by 433'" (greenish-yellow) and 424'" (blue). Thicknesses necessary in above: 2728, 1.6-1.7 mm.; 2742, 5; 454, 16; 447 IU , 1.5-2.0; 433"', 2.5-3.5; 424 1 ", 3 mm. Three-fold division into red, green and blue (with violet) : 2728, 1.7 mm. ; 414'", 10 mm.; 447"', 1.5 mm., or by 2728, 1.7 mm. ; 436'", 2.6mm. ; 447'", 1.8 mm. Grebe found the three following glasses specially suited for the additive methods of three-color projection : 2745, red ; 438"', green; 447"', blue violet ; corresponding closely to Young's three elementary color sensations. Most of the Jena glasses can be supplied to order, but the absorption bands vary somewhat in different meltings. See also "Atlas of Absorption Spectra," Uhler and Wood, Carnegie Institution Publications, 1907. TABLE 376. Water. Values of a in I = I e ftd , d in c. m. I ; I, intensity before and after transmission. Wave-length /*, .186 193 .200 .210 .220 .230 .240 .200 .300 .415 a .0688 .0165 .009 .OO6l .0057 .0034 .0032 .0025 .0015 .00035 Wave-length /z, 43 45 .487 .500 550 .600 .650 .865 945 a .00023 .0002 .0001 .O002 .0003 .OOl6 .0025 .272 .206 538 First 9; Kreusler, Drud. Ann. 6, 190.1; next Ewan, Proc. R. Soc. 57, 1894, Aschkinass, Wied Ann. 55, 1895; last 3, Nichols. Phys. Rev. i, i. See Rubens, Ladenburg, Verb. D. Phys. Ges.,p. 19, 1909, for extinction coefs., reflective power and index of refraction, i /* to 18 /*. SMITHSONIAN TABLES. 3 o8 TABLE 877. TRANSMISSION PERCENTAGES OF RADIATION THROUGH MOIST AIR. (For bodies at laboratory temperatures; for transmission of shorter -wave energy, see Table 553.) The values of this table will be of use for finding the transmission of energy through air containing a known amount of water vapor. An approximate value for the transmission may be had if the amount of energy from the source be- tween the wave-lengths of the first column is multiplied by the corresponding transmission coefficients of the subse- quent columns. The values for the wave-lengths greater than i8ju are tentative and doubtful. Fowle, Water-vapor Transparency, Smithsonian Misc. Collections, 68, No. 8, 1917; Fowle, The Transparency of Aqueous Vapor, Astro- physical J. 42, p. 394, 1915. Range of wave-lengths. Precipitable water in centimeters. M M .001 .003 .006 .01 03 .06 . 10 25 50 I.O 2.0 6.0 IO.O o.rstoi.o _ _ _ IOO 99 99 98 97 95 93 90 83 78 i.o 1.25 99 99 98 97 95 92 89 85 74 69 i-2S i. 5 96 92 84 80 66 57 5i 44 3i 28 1.5 2.0 98 97 94 88 79 73 70 66 60 57 *2 3 06 92 8? 84 77 70 64 3 4 95 88 84 ?8 72 66 63 *4 92 83 76 ?i 65 60 53 5 6 95 82 75 68 56 Si 47 35 6 7 85 54 50 3i 24 8 4 3 2 o 7 8 94 84 76 68 57 46 35 16 IO 2 8 - 9 100 IOO IOO 99 98 96 94 65 t9 1 100 IOO IOO IOO IOO IOO IOO IOO IOO IOO IOO tio n 100 IOO IOO IOO IOO IOO IOO IOO IOO IOO IOO II 12 IOO IOO IOO IOO IOO 99 98 96 95 93 . 12 13 100 IOO IOO IOO 99 99 97 86 82 *I3 14 IOO IOO IOO 99 97 94 90 80 60 * 14 is 96 93 80 75 50 15 o o o *i5 16 70 55 40 o o o o 16 17 . 50 20 o 17 18 25 10 o o 18 oo 98 94 89 82 45 * These places require multiplication by the following factors to allow for losses in COa gas. Under average sea-level outdoor conditions the COz (partial pressure per cu. m. Paschen gives 3 times as much for indoor conditio 2ju to 3)U, for 2 grams in m 2 path (95); for 140 grams in m 2 = 0.0003 atmos.) amounts to about 0.6 gram us. path (93); ' (70); more CO 2 no further effect: 4 " 5 " " " " " " (93); " " " " " 13 "14, slight allowance to be made; 14 " 15, 80 grams in m 2 path reduces energy to zero; 15 " 16, " " t These places require multiplication by 0.90 and 0.70 respectively for one air mass and 0.85 and 0.65 for two air masses to allow for ozone absorption when the radiation comes from a celestial body. In the above table italicized figures indicate extrapolated values. F. Paschen gives (Annalen d. Physik u. Chemie, 51, p. 14, 1894) the absorption of the radiation from a blackened strip at 500 C by a layer 3.? centimeters thick of water vapor at 100 C and atmospheric pressure as follows: Wave-length ................. Percentage absorption ......... 2 . 20-3 . 80 5-33-7-67M 94 94-13 The following table, due to Rubens and Aschkinass (Annalen d. Physik u. Chemie, 64, p. 598, 1898), gives the Wave-length Percentage absorption Wave-length I4-3M Percentage absorption 43 SMITHSONIAN TABLES. 35 I5-7M 6S 16.0/4 52 80 2O.O/J IOO 39 TABLES 378-379. REFLECTION AND ABSORPTION OF LONG-WAVE RADIATIONS- TABLE 378. Long- wave Absorption by Gases. Unless otherwise noted, gases were contained in a 20 cm long tube. Rubens, Wartenberg, Verb. d. Phys. Ges. 13, P- 7Q6, IQU. g Percentage absorption. g Percentage absorption. Gas D B Long X, Kg lamp. Gas o 1 LongX. Hg lamp. S 23M 52/i Fil- K 23M 52/i IlO/i Fil- CM tered, fe tered, 3UM 3I4M H 2 ... ?6 IOO IOO IOO 99 6 IOO 99-5 IOO 98.5 IOO 97-6 NHa... CH 4 . . . 76 7 6 83.1 o-S 99-2 99 2 43-3 IOO 66.7 IOO Br 2 .. 20 IOO IOO IOO IOO IOO C 2 H 2 . . . 76 99-5 87 4 97-3 97-9 IOO SO^. 76 22.6 76.9 12.7 6 4.8 C 2 H... 76 99 96.4 92.8 IOO IOO CO 2 76 IOO IOO IOO. IOO IOO CS 2 . . . . 26 97-8 IOO IOO 99-5 IOO CO... H 2 S.. 7 6 76 IOO 99 6 IOO ii. 6 94-1 J-4 92.1 10.3 91.6 21.4 C 2 H 6 O . C | to 25 parts of 1 H 2 SO 4 and 100 f parts H 2 O . . J ( i part H 2 SO 4 to ) ( 12 parts H 2 O . [ 2.00 ( i part H 2 SO 4 to ( I 12 parts H 2 O . ( ( 12 parts K 2 Cr 2 O 7 ( ( to 100 parts H 2 O J 2.03 Daniell* . ( i part H 2 SO 4 to ) ] 4 parts H 2 O . } Copper ( Saturated solution ) I ofCuSO 4 +sH 2 O J 1. 06 ( i part H 2 SO 4 to ( 1 1 2 parts H 2 O . j M I.O9 < ( 5% solution of / \ ZnS0 4 + 6H 2 0( ( < 1.08 ( < ( i part NaCl to J 1 4 parts H 2 O . f M 1.05 Grove . . ( i part H 2 SO 4 to J ( 1 2 parts H 2 O . ) Platinum Fuming HNO 8 . . i-93 it < Solution of ZnSO 4 HNO 3 , density 1.33 1.66 < ( H 2 SO 4 solution, ) \ density 1.136 .) Concentrated HNO 3 i-93 M ( H 2 SO 4 solution, J I density 1.136 . ( HNOa, density 1.33 1.79 M ( H 2 SO 4 solution, ( | density 1.06 . ) 1.71 ( ( H 2 SO 4 solution, ) I density 1.14 . J < HNOa, density 1.19 1.66 ( H 2 SO 4 solution, ) ( density 1.06 . ) < ( 1.61 "... < NaCl solution . . < " density 1.33 1.88 Marie Davy < < ( i part H 2 SO 4 to ) I 12 parts H 2 O ( Carbon ( Paste of protosul- ) < phate of mercury ^ ( and water . . . ) 1.50 Partz . . ( < Solution of MgSO 4 " Solution of K 2 Cr 2 O 7 2.06 * The Minotto or Sawdust, the Meidinger, the Callaud, and the Lockwood cells are modifications of the Daniell, and hence have about the same electromotive force. SMITHSONIAN TABLES. TABLE 383 (continued}. 313 COMPOSITION AND ELECTROMOTIVE FORCE OF VOLTAIC CELLS. Name of cell. Negative pole. Solution. Positive pole. E. M. F. in volts. (b) SINGLE FLUID CELLS. Leclanche . . . Chaperon . . . Edison-Lelande . Chloride of silver Law Amal. zinc Zinc . . i Amal. zinc u Zinc . . ( Solution of sal-ammo- \ I niac C f Carbon. Depolari- ] I zer : manganese 1 1 peroxide with j [ powdered carbon j ( Copper. Depolar- ( ) izer : CuO . . . ) ( Silver. Depolari- ( zer: silver chl'ride Carbon .... M < M Cadmium . . . Copper .... 1.46 0.98 0.70 1.02 i-37 i-3 i .08 2.OI 0-34 0.98 ( Solution of caustic 1 notash . 1 23 % solution of sal- ) ( ammoniac . . . . J I C J " " ( ipJznO,ipt.NH 4 Cn I 3 pts. plaster of paris, 1 j 2 pts. ZnCl2,and water J [ to make a paste . . J ( Solution of chromate | of potash .... ( 12 parts K 2 Cr 2 O 7 + 25 parts H 2 SO 4 -j- ( 100 parts H 2 O . . ( i part H 2 S0 4 -f I 12 parts H 2 O + ( ipartCaS0 4 . .) H 2 O Dry cell (Gassner) Poggendorff . . J. Regnault . . . Jolta couple . . (c) STANDARD CELLS. Weston normal . Clark standard . jCadmi'm) j am'lgamj Zinc | am'lgam \ ( Saturated solution of ) 1 CdS0 4 f ( Saturated solution of ) j ZnS0 4 ( Mercury. Depolarizer: paste of Hg 2 SO 4 and CdS0 4 . . . . ( Mercury. Depolarizer: paste of Hg 2 SO 4 and ZnSO 4 .... 1.0183* at 20 C 434 at 15 C (d) SECONDARY CELLS. Lead accumulator Regnier (i) . . . " (2). . . Main . ... Lead . . Copper . Amal. zinc Amal. zinc Iron . . ( H 2 SO 4 solution of ) } density i.i . . . J CuSO 4 + H 2 SO 4 . . ZnSO 4 solution . . . H 2 SO 4 density ab't 1. 1 KOH 20 % solution . PbO 2 . . 2.2f ( 1.68 to 1 0.85, av- ( erage 1.3. 2.36 2.50 ( i.i, mean of full ( discharge. " inH 2 SO 4 . A nickel oxide . Edison .... *The temperature formula is E,= E 20 0.0000406 (t 20) 0.00000095 (t 20 ) 4-0-0000000 1 (t ao). t The value given for the Clark cell is the old one adopted by the Chicago International Electrical Congress in 1893. The temperature formula is E t = E 15 0.00119 (t 15) 0.000007 (t 15)*. t F. Streintr gives the following value of the temperature variation at different stages of charge : at E. M. F. dE/dtXio 1.9223 140 1.9828 228 2.0031 335 2.0084 285 2.010$ 2 55 2.2070 73 Dolezalek gives the following relation between E. M. F and acid concentration : Per cent H,SO 4 64.5 52.2 35.3 21.4 5.2 E.M.F., oC 2.37 3.25 2.10 2.00 1.89 SMITHSONIAN TABLES. 3'4 TABLE 384. CONTACT DIFFERENCE OF Solids with Liquids and Temperature of substances E s cL c 3 u C 1 2 1 C H 1 (.01 .269 ( -285) ( - I0 5 Distilled water . 1 to .148 171 ) to > 177 \ to I -17 .100 .1/1 I 1 ( -345; *// (+156 Alum solution : saturated / at 16 q C. . . ( - .127 -.653 139 .246 -.225 536 Copper sulphate solution : ) sp. gr. 1.087 at r6.6 C. ) - .103 - - - - - Copper sulphate solution : ) saturated at 15 C. . . ) - .070 - - - - - Sea salt solution : sp. gr. ( 1.18 at 20.5 C. . . . J - 475 -.605 - .856 334 -.565 Sal-ammoniac solution : ) saturated at 15. 5 C. . [ Zinc sulphate solution : sp. j gr. 1.125 at i6.9 C. . . f ; -396 -.652 -.189 059 3 6 4 -637 -.238 Zinc sulphate solution :[ saturated at I5.3 C. . \ -43 One part distilled water + ) 3 parts saturated zinc > _ _ _ _ _ _ -444 sulphate solution . . . ) Strong sulphuric acid in distilled water : i to 20 by weight . . . - - - _ - - 344 i to 10 by volume . . . ( about > t -35 1 i to 5 by weight .... - - - - - - (.01 ) 5 to i by weight .... to - - .I2O - 25 - (3-0) ( -55 ) ( .72 j ^ ^ Concentrated sulphuric acid { to > 1.113 _ ! to to > _. _ (85) ( 1.252 1.6 ) Concentrated nitric acid _ _ .672 _ _ Mercurous sulphate paste . - _ _ _ _ _ Distilled water containing ) trace of sulphuric acid ( - - - - - .241 * Everett's " Units and Physical Constants: " Table of SMITHSONIAN TABLES TABLE 384 (continued). POTENTIAL IN VOLTS. Liquids with Liquids in Air.* during experiment about 16 C. i u o o> |o g J I 1 c " || 1^ : 5. T -s 11 Is 1 3 B 1 1 - ll "C 11 P. ! r 2 t: 2 1 || 1 i 5 E 3 c. s N * N * i+ V) .IOO .231 .047 .164 Alum solution: saturated at i6.s C ~ .014 ~ ~ " ~ Copper sulphate solution : sp. gr. 1.087 at i6.6 C. - - - - - - .000 - - - Copper sulphate solution : ) saturated at 15 C. . . [ - - - 043 - - - .095 .102 - Sea salt solution : sp. gr. 1.18 at 20. 5 C. . . . - 435 - - - - - - - - Sal-ammoniac solution : { saturated at 15. 5 C. . j - 348 - - - - - - - - Zinc sulphate solution : ) sp. gr. 1.125 at l6 9 C - J Zinc sulphate solution : / saturated at 15. 3 C. . ( -.284 - - .200 - .095 - - - One part distilled water + ) 3 parts saturated zinc > .102 sulphate solution . . ) Strong sulphuric acid in distilled water : i to 20 by weight . . . o i to 10 by volume . . . -35 8 i to 5 by weight .... .429 5 to i by weight .... Concentrated sulphuric acid .848 .010 - 1.298 1.456 1.269 - 1.699 - - Concentrated nitric acid Mercurous sulphate paste . 4/5 Distilled water containing 1 078 trace of sulphuric acid . ) Ayrton and Perry's results, prepared by Ayrton. SMITHSONIAN TABLES. TABLE 385. DIFFERENCE OF POTENTIAL BETWEEN METALS IN SOLUTIONS OF SALTS. The following numbers are given by G. Magnanini * for the difference of potential in hundredths of a volt between zinc in a normal solution ot sulphuric acid and the nieials named at the head of the different columns when placed in the solution named in the first column. The solutions were contained in a U-tube, and the sign of the differ- ence of potential is such that the current will flow from the more positive to the less positive through the ex- ternal circuit. Strength of the solution in gram molecules per liter. Zinc.f Cadmium. t Lead. Tin. Copper. I Silver. No. of molecules. Salt. Difference of potential in centivolts. 0-5 H 2 SO 4 O.O 36.6 5 J -3 100-7 121.3 I.O NaOH 32.1 19-5 3'-8 O.2 80.2 95-8 I.O KOH 42.5 '5-5 32.0 1.2 77.0 104.0 0.5 Na 2 SO 4 1.4 35-6 50.8 51-4 IOI-3 120.9 I.O Na 2 S 2 8 5-9 24.1 45-3 45-7 38.8 64.8 I.O KNO 3 ii.Sj 31 . 9 42.6 3 1 - 1 8l.2 !05-7 I.O NaNO 8 "-5 32-3 51.0 40-9 95-7 114.8 0.5 K 2 Cr0 4 2 3-9t 42.8 41.2 40.9 94.6 I2I.O 0.5 K 2 Cr 2 O 7 72.8 DI.I 78.4 68.1 123.6 132.4 K 2 S0 4 1.8 34-7 51.0 40.9 95-7 II4.8 0.5 (NH 4 ) 2 S0 4 0-5 37-r. 53-2 57-6* 101.5 125-7 0.25 K 4 FeC 6 N 6 6.1 33.6 50-7 41.2 -t 8 7 .8 0.167 KeFe 2 (CN)i2 4 I.O 80.8 81.2 130.9 110.7 124.9 I.O KCNS 1.2 32.5 52.8 52-7 52-5 72.5 I.O NaNOg 4-5 35-2 50.2 49-o 103.6 104.6? 0.5 Sr(N0 8 ) 2 14.8 38-3 50.6 48.7 103.0 1 1 9-3 0.125 Ba(N0 8 ) 2 21.9 39-3 52.8 109.6 121.5 I.O KN0 8 t 35-6 47-5 49-9 104.8 115.0 0.2 KClOa 1510$ 39-9 53-8 57-7 105-3 120.9 0.167 KBrO 8 13-20* 40.7 5|-3 5-9 111.3 120.8 I.O NH 4 C1 2.9 324 5 i. 3 5-9 81.2 101.7 I.O KF 2.8 22.5 41.1 50.8 61.3 61.5 I.O NaCl Si- 2 5-3 80.9 101.3 I.O KBr 2-3 3 T -7 47.2 52-5 736 82.4 I.O KC1 32.1 51.6 52-6 81.6 107.6 o-5 NaaSOa 8.2 28.7 41.0 31.0 68.7 103.7 -II NaOBr 18.4 41.6 73- 1 70.6 J 89.9 99-7 I.O C 4 H 6 6 5-5 39-7 61.3 54-4 104.6 123.4 0.5 C 4 H 6 6 4.1 61.6 57-6 110.9 125.7 0.5 C 4 H 4 KNaO 7-9 31-5 51-5 42-47 100.8 119.7 * " Rend, della R. Ace. di Roma," 1890. t Amalgamated. t Not constant. After some time. II A quantity of bromine was used corresponding to NaOH = i. SMITHSONIAN TABLES. TABLE 386. THERMOELECTRIC POWER. 317 The thermoelectric'power of a circuit of two metals is the electromotive force produced by one decree C difference of temperature between the junctions. The thermoelectric power varies with the temperature, thus: thermoelectric power = Q = dE/dt = A + Bt, where A is the thermoelectric power at o C, B is a constant, and / is the mean tem- perature of the junctions. The neutral point is the temperature at which dE/dt = o, and its value is A/B. When a current is caused to flow in a circuit of two metals originally at a uniform temperature, heat is liberated at one of the junctions and absorbed at the other. The rate of production or liberation of heat at each junction, or Peltier effect, is given in calories per second, by multiplying the current by the coefficient of the Peltier effect. This coefficient in calories per coulomb = QT/y, in which Q is in volts per degree C, T is the absolute temperature of the junction, and 3F = 4.19. Heat is also liberated or absorbed in each of the metals as the current flows through portions of varying temperature. The rate of production or liberation of heat in each metal, or the Thomson effect, is given in calories per second by multiplying the current by the coefficient of the Thomson effect. This coefficient, in calories per coulomb = BTd/3, i n which B is in volts per degree C, T is the mean absolute temperature of the junctions, and 6 is the differ- ence of temperature of the junctions. (BT) is Sir W. Thomson's "Specific Heat of Electricity." The algebraic signs are so chosen in the following table that when A is positive, the current flows in the metal considered from the hot junction to the cold. When B is positive, Q increases (algebraically) with the temperature. The values of A , B, and thermoelectric power in the following table are with respect to lead as the other metal of the thermoelectric circuit. The thermoelectric power of a couple composed of two metals, i and 2, is given by subtracting the value for 2 from that for i; when this difference is positive, the current flows from the hot junction to the cold in i. In the following table, A is given in microvolts per degree, B in microvolts per degree per degree, and the neutral point in degrees. The table has been compiled from the results of Becquerel, Matthiessen and Tait; in reducing the results, the electromotive force of the Grove and Daniell cells has been taken as 1.95 and 1.07 volts. The value for constantan reduced from results given in Landolt-Bornstein's tables. The thermoelectric p are given by Becquerel in the reference given below. :tric powers of antimony and bismuth alloys Substance. A Microvolts. B Microvolts. Thermoelectric power at mean temp, of junctions (microvolts). Neutral point ~ B Author- ity. 20 C 50 C Aluminum 0.76 -11.94 +2.63 +I.34 +2.80 +17-15 + 2.22 -21.8 -83.57 -3-04 +0.0039 0.0506 +0.0424 +0.0094 +O.OIOI 0.0482 0.0000 -0.0094 0.0506 +0.2384 0.0506 -0.68 +6.0 + 22.6 +26.4 -12.95 13.56 97.0 89.0 65.0 45-0 +3.48 22 + 1.52 +O.IO +3-8 0.2 +3-0 +16.2 +17-5 o.oo + 2.03 +5.9 -0.413 -2278 0.56 14.47 -12.7 +4-75 +2-45 +8.9 19-3 +1.81 +7-30 +14-74 + 12. IO +9.10 0.00 +I.7S 3-30 -15-50 -24-33 +195 -"^36 -62 -143 C-T 7 7D +356 +T 3 6 [-"431] T M T B M T B S' M T M S T M B T S MB B T Antimony, comm'l pressed wire.. . axial " equatorial Argentan Arsenic Bismuth, comm'l pressed wire. . . . pure " crystal, axial equatorial Cadmium. . . fused Cobalt CoDoer commercial Gold ' pianoforte wire Lead Molybdenum Nickel " (-18 to 175) SMITHSONIAN TABLES. 318 TABLES 386 (continued). -387.-THERMOELECTRIC POWER. TABLE 386. Thermoelectric Power (continued). Substance. A Microvolts. D Microvolts. Thermoelectric power at mean temp, of junctions (microvolts). Neutral point f\ Au- thority. 20' C. So-C. B' Palladium .... Phosphorus (red) . 6.18 +2-57 0.60 +7.90 +5-90 +6.15 + 2.12 + 11.27 0.43 +2-32 0.0355 0.0074 0.0109 +O.OO62 0.0133 +0.0055 +0.0147 0.0325 +0.0055 +0.0238 -6. 9 +29.9 + 0.9 + 2.42 .8l8 +8.03 +5-63 +6.26 +807. +2.41 +3.00 + 10.62 2.6 +500. + 160. +0.8 +0.1 0.33 2.0 +2.79 +3-7 -7.96 + 2.20 I- 15 +0.94 2.14 +8.21 +5-23 +6.42 +2.86 +2.18 +9.65 +0.33 0.16 +3.51 174 347 55 [1274] 444 [-1118] 144 347 78 -^98 T M T B T M T M B T H H H M T T M ' (hardened) . (malleable) . ' wire ' another specimen Platinum-iridium alloys: 85%Pt+i5%Ir . . 90%Pt + io%Ir . . ,95% Pt+ 5% IT . . Selenium Silver (pure hard) . " wire .... Steel Tantalum .... Tellurium /3 . a .... Thallium Tin (commercial) . Tungsten ' pure pressed . B Ed. Becquerel, "Ann. de Chim. et de Phys." [4] vol. 8. S. Bureau of Standards. M Matthiesen, "Pogg. Ann." vol. 103, reduced by Fleming Jenkin. T Tait, "Trans. R. S. E." vol. 27, reduced by Mascart. H Haken, Ann. der Phys. 32, p. 291, 1910. (Electrical conductivity of Te/3 = o.o4, Tea 1.7 e. m. units.) Swisher, igi/. TABLE 387. Thermoelectric Power of Alloys, The thermoelectric powers of a number of alloys are given in this table, the authority being Ed. Becquerel. The/ are relative to lead, and for a mean temperature of 50 C. In reducing the results from cc the thermoelectric power of lead to copper was taken as 1.9. :opper as, a reference metal, Substance. Relative quantity. Thermoelec 1 tricpower in 1 microvolts. 1 Substance. Relative j quantity. [ Thermoelec- 1 trie power in 1 microvolts. 1 Substance. Relative ' quantity. ! Therraoelec- 1 trie power in 1 microvolts. 1 Antimony Cadmium 806) 22 7 Antimony Zinc 2 ) I > 43 Bismuth Antimony J! -5M Antimony Cadmium Zinc 4) 2 > I ) 146 Tin Antimony Cadmium Sj 35 Bismuth Antimony !l 63.2 Antimony Cadmium Bismuth Antimony Zinc Antimony Zinc Bismuth 806) 121 ) 806? 806) 406 > 121 ) 137 95 8.1 Zinc Antimony Tellurium Antimony Bismuth Antimony Iron 3) 4 i \ 10.2 8.3 Bismuth Antimony Bismuth Antimony Bismuth Tin Bismuth Selenium "1 12 | I ) 10 I 68.2 66.9 60 24.5 Antimony 4l Antimony 8 / 1.4 Cadmium 2! ?/: Magnesium i ) Bismuth 12 ) Lead 7\ nr* i r , i 7 Antimony 8 1 0.4 Zinc 1 ' 3 1 - 1 Zsinc 1 J Lead i ) Bismuth 12 I Antimony Cadmium H Bismuth - -43-8 Arsenic I j 46.0 Zinc i r 40 Bismuth 2 ) Bismuth 1 ( f<3 Tin ij i Antimony i C 33-4 Bismuth sulphide I J Go. I Tatti TABLE 388. TABLES 388, 389. Theimoelectrlc Power against Platinum. One junction is supposed to be at oC; + indicates that the current flows from the o junction into the platinum. The rhodium and indium were rolled, the other metals drawn.* Tempera- ture, C. Au. Ag. 9o%Pt-f IO%Pd. IO%Pt+ 90%Fd. Pd. 90%Pt+ io%Rh. 9%Pt+ io%Ru. Ir. Rh. -185 0.15 0.16 O.I I +0.24 +0.77 _ 0.53 0.28 0.24 80 + 100 -0-31 +0.74 -0-30 +0.72 0.09 +0.26 4-0.15 0.19 4-0-39 0.56 -0-39 +0.73 0.32 +0.65 0.31 +0.65 + 2OO + 1.8 + 1-7 +0.62 0.31 1. 20 + '5 + I.C + 300 +3.0 + 1.0 0-37 2.O 4-2-3 + 2.6 +2.5 + 2.6 + 400 +4-5 +4-5 + 1-5 0-35 2.8 +3-2 +3-6 +3-6 +3-7 + 5 00 +6.1 +6.2 + 1.9 o.i 8 -3.8 +4-6 +4-8 45.i + 600 + 700 +7-9 4-9-9 +8.2 + 10.6 +2.4 +2.9 +0.12 +0.61 -4.9 6-3 S:! 4-5-7 +6.9 +6.1 +7.6 +6.5 +8.1 +800 +900 + I2.O 4-13-2 +16.0 # + 1.2 +2.1 -7-9 9.6 + 7 .2 +8. 3 +8.0 +9-2 +9.1 + 10.8 +9-9 + 11.7 + IOCO + 1100 + i6Jf is +3-i +4.2 -"5 ~ 1 3-S + 10.6 + 10.4 + 11.6 + 12.6 + 13-7 + 15.8 +(1300) 4~ T 3 l + '4-2 + 18 6 +20.4 +(1500) " " " " * + 15-6 + 16.9 +23-' +25.6 * Holborn and Day. TABLE 389. Thermal B. M. F. of Platinum-Rhodium Alloys Against Pure Platinum, In Millivolts.* 10 p. ct. t i p. ct. 5 P- ct. Low. High. Stan- dard. 15 p. ct. 20 p. Ct. 30 p. ct.t 40 p. ct.t loop. Ct.t 100 O T O c c 0.6^ 0.64 0.64 o 6<; 06? 2OO O J." 7 i 18 I 4.1 I 4^ I 4^ i <;o J C I 300 0.63 1.85 2.28 2.32 2.32 2.41 .... 2-34 2.45 O* 2-57 400 0.84 2.53 3 .2I 3 .26 3.25 3-45 3-50 3-50 3.64 3-76 500 1.05 3.22 4.17 4-23 4.23 4-55 4 .60 4-74 493 5-08 60O 700 ' 2 S i-45 3.92 4.62 ci6 6.19 5-24 6.28 is 5-71 6.94 h 6.06 7-49 6.31 7.80 6. 55 8.1 4 800 i.6 S 5-33 7-25 7-35 7-33 8.23 8.60 9.01 9-37 9.87 900 i.8 S 6.05 8-35 8.46 8.43 9-57 10.09 10.67 11.09 11-74 IOOO 2.05 6.79 9-47 9.60 9-57 10.96 11.65 12.42 12.94 1374 I 100 2.25 7-53 10.64 10.77 10.74 12.40 13.29 14-33 14.99 M.87 I2OO 2-45 8.29 11.82 11.97 "93 13-87 14.96 16.39 17-13 I8.IO I3OO I4OO 2.65 2.86 9.06 9.82 13.02 14.22 13.18 14-39 i3- J 3 14-34 I5-38 16.98 16.65 18.39 18.51 20.67 I9-5 1 21-73 20.46 3 06 i S 61 T C C C 18 41 -o i c 3-00 1663 i68-> 1 5-ii T A 7 C IQ Q4. T QO flMf 2 11.31 1781 18 03 17 QC 21 47 2~i nc 3-4 I /.j ~ c < _ T Aa 18 70 18 61 T> 11 ^4 s ^ I 75S 3-5 1.2.44 10-49 ~-.J l -4OJ * Carnegie Institution, Pub. 157, 1911. t Holborn and Day, mean value, 1899. t Holborn and Wien, 1892. SMITHSONIAN TABLES. 3'20 TABLES 390-391. THERMOELECTRIC PROPERTIES: PRESSURE EFFECTS- TABLE 390. Thermoelectric Power; Pressure Effects. The following values of the thermoelectric powers under various pressures are taken from Bridgman, Pr. Am. Acad. Arts and Sc. 53, p. 269, 1018. A positive emf means that the current at the hot junction flows from the uncompressed to the compressed metal. The cold junction is always at o C. The last two columns give the constants in the equation E = thermoelectric force against lead (o to 100 C) = (At + BP) X io~ volts, at atmospheric pressure, a positive emf meaning that the current flows from lead to the metal under consideration at the hot junction. Metal. Thermo-electric force, volts X io Formula coefficients. Pressure, kg/cm 2 2000 4000 ! 8000 12,000 Temperature, C 50 100 50 100 50 100 20 50 100 A B Bit.. Znf. . 53,000 6,200 4.930 2,040 2,850 2,190 1,810 1,190 C Jg 456 +292 70 a 123 -84 -156 85,000 14,100 10,870 7,120 5,950 4,380 3,600 2,530 i, 680 1,870 1,670 1,050 1,052 584 IOI 140 +87 232 -167 -348 110,000 13,000 9,380 4,620 5,800 4,400 3,600 2,360 1,500 1,720 590 920 905 +580 91 +187 +58 242 -181 > 316 185,000 28,500 20,290 14,380 11,810 8,800 7,3io 4,990 3,400 3,720 3,250 2,120 2,051 i, 216 294 278 +165 452 -362 -692 255,000 26,100 17,170 10,960 ii,53o 8,630 7,370 4,690 3,230 3,350 5,300 i, 860 i,79i 1,124 32 375 +70 -489 -395 630 425,000 58,100 37,630 28,740 23,790 17,690 14,350 10,120 7,190 7,190 5,820 4,210 3,974 2,420 929 555 +292 -894 -791 1,360 185,000 14,400 8,780 6,680 6,750 5,ooo 3,88o 2,700 i, 880 +1,900 990 +880 +990 + ^ +146 -182 -308 -259 -352 452,000 38,500 23,750 19,180 17,200 12,970 11,030 7,050 5,140 4,950 220 28l 2,627 1,616 312 562 + 10 719 -648 937 710,000 87,400 52,460 45,56o 35,470 26,520 21,570 15,140 11,440 10,560 7,680 6,330 5,76o 3,546 1,962 833 +390 1,314 1,296 2,061 74.42 +3 047 + 1.659 + 12.002 -34.76 ,-5-496 3 092 +1-594 17.61 + 2.556 +16.18 +2.899 +2-777 0.416 +5-892 +0.230 +1.366 -0.095 -17.32 + .0160 -.00495 -. 00134 l + .1619 - 0397 .01760 -.01334 + .01705 .0178 + .00432 -.00892 + . 00467 s + .00483 + . 00008 4 + .02167 6 .00067 + .000414* + . 00004 . 0390 j TU ::::: Cd t Constantant . . . Pd* Pt*.. wt Ni*.. Ag* IFef. Pbl. Au* Cu t. . . Alt Mo t Snt... Manganin t. . .. Mgf.. ........ Cot * Identical wire of Table 398. t Another wire of same sample, t Different sample. Results too irregular for interpolation for values at other temperature and pressures; see original article, (i) .0556/ 8 ; (2) .0486/ 3 , annealed ingot iron; (3) .O5I66/ 3 ; (4) .out*; (5) . 0425/8; (6) .041 12/ 3 . TABLE 391. Peltier and Thomson Heats; Pressure Effects. They refer itive if heat is absorbed by the positive The following data indicate the magnitude of the effect of pressure on the Peltier and Thomson heats. to the same samples as for the last table. The Peltier heat is considered positive if heat is absorbed by current from the surroundings on flowing from uncompressed to compressed metal. A positive 2477 2537 .02596 7 3-66 10.55 .03948 .0,190 .0 2 28 4 o 2 379 .02569 .0,664 2758 .02853 .02948 9 2.91 6.634 .0,151 .0,301 .0,452 .02603 02754 .03904 .0106 .0121 .0136 .0151 II 2.30 4.172 27 I 9 .0,959 .0120 .0144 .0168 .0192 .0216 .0240 13 1-83 2.624 .0,381 .0,762 .0114 .0152 .0191 .0229 .0267 .0305 .0343 .0381 15 1.45 1.650 .o 2 6o6 .0121 .0182 .0242 0303 .0364 .0424 .0485 0545 .0606 1.038 .0,963 .0193 .0289 .0385 .0482 .0578 .0674 .0771 .0867 .0963 |M .912 .6527 0153 .0306 .0460 .0613 .0766 .0919 .1072 .1226 .1379 .1532 21 723 .4105 .0244 .0487 -0731 .0974 .1218 .1462 .1705 .1949 .2192 .2436 23 573 .2582 .0387 775 .1162 .1549 .1936 .2324 .2711 .3098 3486 .3873 25 27 .455 .361 .1624 .1021 .0616 .0979 .1232 .1959 .1847 .2938 3 3079 .4897 3695 5877 .4310 .6856 .4926 .7835 5542 .8815 .6158 9794 29 .286 .0642 .'557 3"4 .4671 .6228 .7786 9343 1.090 1.246 1.401 1-557 3 1 .227 .0404 .2476 .4952 .7428 .9904 1.238 1.486 1-733 I.gSl 2.228 2.476 33 .180 0254 3937 .7874 I. ill 1-575 1.968 2.362 2.756 3-I50 3-543 3-937 35 .'43 .0160 .6262 1.252 1.879 2-505 3-131 3-757 4-383 5.009 5-636 6.262 37 .113 .0100 .9950 1.990 2-985 3.980 4-975 5-97 6.965 7.960 8-955 9-95 39 40 .090 joSo .0063 .0050 '583 1.996 3.166 3.992 4.748 5.988 7.984 9.980 9-497 11.98 1 1. 08 13-97 12.66 15-97 14-25 17.96 19.96 SMITHSONIAN TABLES. TABLE 397. RESISTIVITY OF METALS AND SOME ALLOYS- 323 The resistivities are the values of pin the equation R = pl/s, where R is the resistance in microhms of a length / cm of uniform cross section s cm 1 . The temperature coefficient is a in the formula Rt = R\i + M|- The information of column 2 does not necessarily apply to the temperature coefficient. See also next table for tempera- ture coefficients o to 100 C. Substance. Remarks. Tempera- ture, C Microhm- cm Refer- ence. Temperature coefficient. t, * Refer- ence. Advance Aluminum see constantan see p. 334 c.p. liquid drawn liquid solid \ liquid / 99.57 pure see constantan 99 . 8 pure 60% Cu, 40% Ni annealed hard -drawn electrolytic pure very pure, ann'ld see constantan 18% Ni 99. 9 pure pure, drawn 99.9 pure see constantan 20. -189. 100. o. + 100. 400. 20. -190. +860. 0. 18. 100. 20. -160. 18. 100. 318. -187. 0. 27. 30. 20. 0. 20. 2O. 20. 20. 20. -206. + 205. 400. 20. 20. 0. 20. -I8 3 . 0. 20. 194-5 o. -186. o. + 100. 2.828 0.64 1% 3-86 8.0 4i-7 10. S 120. 35- 119.0 160.2 7- 2.72 7-54 9.82 34-1 S-2S 19. 22. 2 36.6 4.6 2.6 87. 9-7 49- 1.724 1.77 0.144 2.92 4.10 1.692 92. Sa- te' 0.68 2. 22 2.44 3-77 8.37 1.92 o.io 8.3 i 3 3 3 3 3 5 6 1 9 9 S 10 9 9 II 12 II 13 13 14 IS 16 5 i i? i? 3 18 5 12 5 17 ii 9 17 19 20 20 20 18 25 IOO 500 20 2O 20 2O 2O 12 25 IOO 200 500 20 see col. 2 IOO 400 IOOO 20 2O 20 loo ann'ld 500 IOOO + 0039 + .0034 + .0040 + .0050 + .0036 + .004 + .002 + .0038 + .0036 + .0007 + .000008 + .OO0002 .000033 .000020 + .OO0027 + 00393 + .00382 + .0038 + .0042 + .0062 + .000l6 + .0004 + .0034 + .0025 + 0035 + .0049 2 4 4 4 S S 5 5 14 S 4 4 4 4 4 5 5 4 4 4 5 5 5 4 4 4 H Antimony . Arsenic Bismuth Brass Cadmium ;; Caesium Calcium Calido Chromium Climax Cobalt Constantan Copper Eureka Excello German silver Gold (( la la... Ideal Iridium SMITHSONIAN TABLES. 324 TABLE 397 (continued). RESISTIVITY OF METALS AND SOME ALLOYS- Substance. Remarks. Tempera- ture, G Microhm- cm Refer- ence, Temperature coefficient. t, a Refer- ence. Iron. . . 99 -98% pure pure, soft E. B. B. B.B. Siemens-Martin manganese 35% Ni, "invar." piano wire temp, glass, hard ' , yellow " ,blue " , soft cold pressed solid liquid free from Zn pure 84Cu,i2Mn,4Ni solid liquid drawn pure 20. '-ft? o. +98.5 196.1 400. 20. 2O. 20. 2O. 20. 0. O. 0. 0. o. 20. -183. -78. o. +90.4 196.1 318. -187. 0. 99.3 230. 20. -I8 3 . -78. O. +98.5 400. 20. 20. -183.5 102-9 -50-3 39-2 -36.1 o.o 50. IOO. 2OO. 350. 20. 2O. 2O. 20. -182.5 -78.2 0. 94 9 400. 10. 0.652 5-32 8.85 17.8 21.5 43-3 10.4 It. g 18. 70. 81. n. 8 45-7 27. 20.5 iS-9 22. 6. 02 14.1 20.4 28.0 36.9 94- 1-34 8-55 12.7 45-2 4.6 I.OO 2.97 4-35 5-99 II. 9 5.o 44. 95 783 6.97 15-04 21.3 25-5 80.6 94.07 98.50 103.25 114.27 135-5 5-7 42. IOO. 7-8 1.44 4-31 6-93 11. i 60.2 5 17 17 17 17 17 3 5 5 5 5 22 23 23 23 23 23 5 17 17 i? 17 17 24 12 12 12 25 5 17 17 17 17 3 IS S 5 17 17 17 17 17 17 27 24 24 24 5 5 5 28 28 28 28 3 20 25 IOO 500 IOOO 20 see col. 2 + .0050 + .0062 + .0052 + .0068 + .0147 + .0050 + .005 + .004 + .003 + .001 + .0032 + .0016 +.0033 + .0039 + .0043 + .004 + .0038 + .0050 + .0045 + .0036 + .0100 + .000006 .000000 .000042 . 00005 2 .000000 .0001 1 + .00089 +.00088 + .0033 + .0034 + .0048 + .O020 ^.0004 .006 + .0062 + .0043 + .0043 + .0030 + .0037 5 21 4 4 4 4 5 5 5 5 23 23 23 5 2 5 24 4 4 4 4 4 26 4 4 4 5 5 5 24 4 4 4 4 i i i steel o see col. 2 o see col. 2 20 18 20 o 25 IOO 500 600 12 25 IOO 250 475 500 20 Rt = Rod + . 00089* + .OOOOOI/ 2 ) 25 IOO IOOO 20 20 20 o 25 IOO 500 IOOO M M 11 M Lead M " M Lithium j Magnesium < Manganese Manganin Mercury i< M < Molybdenum N Monel metal Nichrome Nickel SMITHSONIAN TABLES. TABLE 397 (continued). RESISTIVITY OF METALS AND SOME ALLOYS. 325 Substance Remarks. Tempera- ature, C Michrom- cm Refer- ence. Temperature coefficient. t. Refer, ence. Osmium very pure wire solid liquid 99. 98 pure electrolytic solid liquid pure 1000 K 1500 K 2000 K 3000 K 35oo K trace Fe liquid 20. 20. -I8 3 . -78. o. 08.5 20. 203 . 1 -97-5 0. IOO. 400. -75- o. 55- -186. 78.3 o. IOO. -190. o. 35- 40. 20. 18. -183. -78. o. 98.15 192.1 400. -180. -75- o. A 20. 20. 19.6 -183. -78. 0. 98.5 20. 20. -184. -78. o. 91 -45 20. 727. 1227. 1727. 2727. 3227. -183. -78. 0. 92.45 191-5 440. 60.2 ii. 2.78 7.17 10.21 13-79 IO. 2.44 6.87 10.96 14.85 26. *:? 8.4 0.70 3.09 l 9 6.60 2-5 ii. 6 13-4 19.6 58.* .629 390 .021 .468 .062 .608 3-77 I.O 2.8 4.3 5-4 10.2 24.8 IS-S 200,000 4-08 ii. 8 17.60 24.7 47- ii. 5 If o.o 13-0 18.2 3-2 5.51 25.3 41.4 59.4 98.9 118. 1.62 3-34 5-75 8.00 10.37 37-2 3 5 17 17 17 17 5 17 17 17 17 3 13 13 13 20 20 20 20 13 13 13 13 2 17 17 17 17 17 3 13 13 13 13 13 8 17 17 17 17 S 5 17 17 17 IT- IS 29 29 29 29 29 29 17 17 17 17 17 7 20 o 20 2O 25 IOO 500 20 2O 20 IS Soo 1000 20 + 0033 + 0035 + .003 + .0037 + .0038 + .0030 + .0036 + .0044 + .0031 -j-.OOOOI +.0042 +.0045 + .0057 + .0089 + 0037 S 21 5 21 5 4 4 4 5 5 5 2 4 4 5 Palladium. ii I i Platinum ii ii M Potassium Rhodium " Rubidium n Silicium. . Silver ii and temperature /. The average coefficient is the total change of resistance between o and 12,000 kg/cm 1 divided by 12,000 and the resist- ance at atmospheric pressure and -the temperature in question. Table taken from Proc. Nat. Acad. 3, p. n, 1917. For coefficients at intermediate te.nperatures and pressures, see more detailed account in Proc. Amer. Acad. 52, p. 573, 1917. Sn, Cd, Zn, Kahlbaum's "K " grade; Tl, Bi, electrolytic, high purity; Pb, Ag, Au, Cu, Fe, Pt, of exceptional purity. Al better than ordinary, others only of high grade commercial purity. Average temperature coefficient o to 100 C Pressure coefficients. Instantaneous coefficient. Average coefficient o to 12,000 kg/cm 2 AtoC At 100 C At okg At 12,000 kg okg 12,000 kg o kg 12,000 kg Ato At 100 In. + .00406 .00447 .00517 .00424 .00421 .00416 00434 .004074 .003968 . 004293 .004873 .003657 .006206 .003178 .003868 . 004336 .002973 .003219 . 00390 * .00473 + . 00438 -.oo6 3 t + .00383 .00441 .00499 .00418 .00412 .00420 00435 .004069 . 003964 .004303 .004855 .003676 .006184 .003185 .003873 . 004340 .002967 .003216 .00403 + .00395 .041226 .041044 .041319 .041063 .041442 .040540 .040416 .040358 .040312 .O4020I .040158 .040094 .040241 . 040198 .040198 .040133 .040149 . 0401 28 .04055 + .041220 + .04154 .03129 .041016 . 040936 .041180 .040837 .041220 .040425 .040365 .040321 .040286 .O40I79 .04OI42 .040081 .040218 .O4OI9O .040l8l .040126 .040139 .040121 + .041064 + .040213 .041510$ .041062 .041456 .041106 .041483 .040524 .040397 040355 .040304 .040184 .040163 .040076 .040247 .040189 .040190 .040130 .040153 .040130 +.040768 +.04152 .041072 + .040973 .041200 .040887 041237 .040407 040373 .040331 .040292 040175 .040156 .040070 .040230 .040187 .040182 .040125 .040147 .040123 + .040723 + .04i895 .O4IO2I .04O920 .041151 .040894 .041212 .040470 .O40382 040333 .040287 .040183 .040147 .040087 .040226 .040190 .040187 .040129 040143 .040123 .04055 + .041220 + .042228 -.041131 I .040951 .041226 .040927 .041253 . 040454 .040377 .040336 .040292 .040177 .040158 .040073 .040235 .040186 .040184 .040126 .040149 . 040126 + .040768 + .041980 Sn Tl . Cd Pb Zn Al Ag Au Cu ... Ni... Co Fe Pd Pt Mo... Ta W Mg Sb Bi... Te .... * tO 20. t o to 24. J Extrapolated from 50. Extrapolated from 75. Additional data from P. Nat. Acad. Sc., 6, 505, 1920. Data are 10,000 x mean pressure coefficient, o 12,000 kg, and 10,000 x instantaneous pressure coefficient at o kg. 1 = liquid ; s = solid. Li, s, o +.0772 + .068 Ca. o Li, 1, 240 +.093 + .093 Sr, Na, s,o .345 .663 1I-, s,o Na, 1,200 .436 .922 Hg, 1 25 K, s, 25 - .604 1.86 Ga, s, o K, 1, 165 .8o 9 a 1.68 Ga, 1, 30 + ..06 + .680 .236b .219 .0247 0531 + .502 334 -.064 Ti, o Zr, o Bi, 1, 275 W, o La, o P, black, o .00!? .0040 .ioic 0135 -0331 .81 - .004 -123 .014 -039 2.OO a, o - 9,000 kg; b, 7,640 - 12,000 kg; c, o - 7,000 kg. The Ga, Na, K, Mg, Hg, Bi, W, P, of exceptional purity. TABLE 399. Resistance of Mercury and Manganin under Pressure. Mercury, pure and free from air and with proper precautions, makes a reliable secondary electric-resistance pres- sure gage. For construction and manipulation see "The Measurement of High Hydrostatic Pressure; a Secondary Mercury Resistance Gauge," Pr. Am. Acad. 44, p. 221, 1919. Pressure, kg/cm 2 500 IOOO 1500 2000 2500 3OOO 4000 5000 6000 6500 R(p 75) 0.9186 I. 0000 I.OOOO 1.0970 0.9055 0.9836 0.9854 1.0770 0.8930 0.9682 0.9716 1.0580 0.8818 0-9535 0.9588 i . 0400 0.8714 0.9394 0.9462 1.0230 0.8582 0.9258 0.9342 I.OO70 0.8478 O.9I28 o. 9228 0.9908 0.8268 0.8882 0.9010 0.9614 0.8076 0.8652 0.8806 0.9342 0.7896 0.8438 0.8616 0.9086 0.7807 0-8335 0.8527 0.8966 R(i> 2$ e ) R(p 125) * This line gives the Specific Mass Resistance at 25, the other lines the specific volume resistance. The use of mercury as above has the advantage of being perfectly reproducible so that at any time a pressure can be measured without recourse to a fundamental standard. However, at o C mercury freezes at 7500 kg/cm 2 . Man- ganin is suitable over a much wider range. Over a temperature range o to 50 C the pressure resistance relation is linear within i/io per cent of the change of resistance up to 13,000 kg/cm 2 . The coefficient varies slightly with the sample. Bridgman s samples (German) had values of (AR/pR ) X io from 2295 to 2325. These are + instead of , as with most of the above metals. See "The Measurement of Hydrostatic Pressure up to 20,000 Kilograms per Square Centimeter." Bridgman, Pr. Am. Acad. 47, p. 321, 1911. SMITHSONIAN TABLES. TABLE 4OO. 327 CONDUCTIVITY AND RESISTIVITY OF MISCELLANEOUS ALLOYS. TEMPERATURE COEFFICIENTS. Conductivity in mhos or = 7(=7o(l _ fl/ + &/2) and resi , tivity in microhma _ cm Metals and alloys. Composition by weight. 7o aXio " ! < 3 Gold-copper-silver . 58.3 Au + 26.5 Cu+ 15.2 Ag 66.5 Au+ i5.4Cu + 18.1 Ag 7-58 6.83 574* 13.2 I 14.6 I 7.4Au + 78.3Cu+ 14.3 Ag 28. c6 1830$ 3.6 i Nickel-copper-zinc . \ 6.57Zn by volume . . .J 4.92 444 20.3 i Brass Various 12. 2-15. 12. 16 1-2X10 6.4-8.4 2 8.2 3 1 hard drawn . 70.2 Cu + 29.8Zn .... 1 annealed . " " 14-35 - ^m ^ 7.0 3! German silver . Various 7_e f6o.i6Cu + 25.37Zn+ "} O 33- 2 ( * j 14-03 Ni + .30 Fe with trace [ l^of cobalt and manganese . J 3-33 360 30. 4 Aluminum bronze . _ 7-5-8.5 5-7Xio 2 12-13 2 Phosphor bronze . _ 10-20 - 5-10 2 Silicium bronze . . - - - 41 - 2.4 5 Manganese-copper . 30 Mn + 70 Cu .... 1 .00 40 IOO Nickel-manganese- . copper .... 3 Ni + 24 Mn + 73 Cu . . 2.10 30 48. 4 "i8.46Ni+6i.63Cu + Nickelin . i9.67Zn + o.24Fe + 3sl 300 33. 4 , 0.19 Co + o.iSMn . . .J '25.1 Ni + 74.4iCu + Patent nickel . . o.42Fe + o.23Zn + 2.92 190 34- 4 .0.13 Mn + trace of cobalt J r 53-28Cu + 25.3iNi+ ] Rheotan .... 16.89 Zn + 4.46 Fc + 1.90 410 53- 4 o 37 Mn . . . J Copper-manganese- iron . 91 Cu +7.1 Mn + 1.9 Fe 4.08 1 20 20. 5 Copper-manganese- 70 . 6 Cu + 23 . 2 Mn + 6.2 Fe . *T * y 1 -^ ' 22 T"~ O Copper-mangancse- / / * iron 69.7 Cu + 29.9 Ni + 0.3 Fe 2.60 i ^n 7$R ~ Manganin 84 Cu + 12 Mn + 4 Ni . 2-3 6 44- 2 Constantan 6oCu + 4oNi . ... 2.04 8 *iQ 1 Matthiessen. 3 W. Siemens. 5 VanderVcn. 7 Feussner. 2 Various. 4 Feussner and Lindeck. 6 Blood. 8 Jaeger-Diesselhorst. *f t k b X io'=924, 93, 7280, 51, respectively. SMITHSONIAN TABLC*. 328 TABLE 401. CONDUCTING POWER OF ALLOYS. This table shows the conducting power of alloys and the variation of the conducting power with temperature.* The values of C were obtained from the original results by assuming silver =: j- mhos. The conductivity is taken as C t = C (i at-^-At 2 ), and the range of temperature was from o to 100 C. The table is arranged in three groups to show (i) that certain metals when melted together produce a solution which has a conductivity equal to the mean of the conductivities of the components, (2) the behavior of those metals alloyed with others, and (3) the behavior of the other metals alloyed together. It is pointed out that, with a few exceptions, the percentage variation between o"- and 100 can be calculated from tha formula P = P e -^ where/ is the observed and /' the calculated conducting power of the mixture at 100 C., and P e is the calculated mean variation of the metals mixed. Weight % Volume % c Variation per 100 C. 10* b X 10 j of first named. Observed. Calculated. GROUP i. Sn 6 Pb 77.O4 83.96 7.C7 890 8670 30.18 2Q.67 Sn 4 Cd 82.41 Q.l8 4080 11870 28.89 3O.O7 SnZn 78.06 77.71 7880 8720 30.12 70.16 PbSn 64 11 6 do 5780 84^0 2Q. IO 24 76 2C 06 16 16 7780 8OOO 2986 y , 2Q 67 SnCd4 23-05 23.50 13-67 j/ oij 3850 9410 29.08 30.25 CdPb 6 7-37 10-57 5.78 3500 7270 27-74 27.60 GROUP 2. Lead-silver (Pb2oAg) . Lead-silver (PbAg) . 95-05 48.97 94.64 46.90 5.60 8.03 3630 1960 7960 3100 28.24 19.96 7-73 Lead-silver (PbAg 2 ) . 3244 30.64 13.80 1990 2600 I7-3 6 10.42 Tin-gold (Sn t2 Au) . . 77-94 90.32 5-20' 3080 6640 24.20 14.83 " " (SngAu) . . 59-54 79-54 , 3-03 2920 6300 22.0X) 5-95 Tin-copper .... 92.24 80.58 93-57 83.60 7-59 8.05 3680 333 8130 6840 28.71 26.24 19.76 H-57 " " t . . . . " t. . . . " t . . . . 12.49 10.30 9.67 14.91 12.35 II.OI 5-57 6.41 7.64 m 691 1185 34 5.18 6.60 3-99 4.46 5-22 " " t . 4.96 6.02 12.44 995 705 9-25 7-83 " t . . . . 1.15 1.41 39-41 2670 5070 21.74 20-53 Tin-silver 91.30 96.52 7.81 3820 8190 3O.OO 23-3I 53-85 75-51 8.65 3770 8 55 29.18 11.89 Zinc-copper t . . . 36.70 42.06 13-75 1370 1340 12.40 11.29 t . . . 25.00 29-45 13-70 1270 1240 11-49 10.08 t . . . 16.33 23.61 13-44 1880 1800 1 2.80 I2.3O t . . . 8.89 10.88 29.61 2040 3030 17.41 1742 " t . . . 4.06 5-03 38.09 2470 4IOO 20.61 20.62 NOTE. Barus, in the " Am. Jour, of Sci." vol. 36, has pointed out that the temperature variation of platinum alloys containing less than 10% of the other metal can be nearly expressed by an equation y =: nt, where y is the temperature coefficient and x the specific resistance, m and n being constants. If a be the temperature coefficient at o C. and j the corresponding specific resistance, J (a + m)=n. For platinum alloys Barus's experiments gave m .000194 and n = .0378. For steel m = .000303 and n = .0620. Matthiessen's experiments reduced by Barus gave for Gold alloys nt =r .000045, n .0072 1. Silver m .000112, n=z .00538. Copper " m = .000386, n .00055. * From the experiments of Matthiessen and Vogt, " Phil. Trans. R. S." v. 154. t Hard-drawn. SMITHSONIAN TABLES. TABLES 401 (continued) -402. TABLE 401. Conducting Power ol Alloys. 329 GROUP 3. Alloys. Weight % Volume % C 10* a X io 6 X io Variation per 100 C. of first named. Observed. Calculated. Gold-copper t . . . " " t . . . 99-23 90-55 98-36 81.66 35-42 10.16 2650 749 4650 21.87 7.41 23.22 7-53 Gold-silver t . . . . " '' * .... t '. ! '. '. < u % 87-95 87.95 64.80 64.80 79-86 79.86 52.08 52.08 13.46 13.61 9.48 9-51 1090 1140 673 721 793 1160 246 495 10.09 10.21 6-49 . 6.71 9.65 959 6.58 6.42 " t . . . . 31-33 19.86 13.69 885 8.2 3 . 8.6? " u * .... 3*33 19.86 13-73 908 641 8-44 8.31 Gold-copper t . . . 34-83 19.17 12.94 864 570 8.07 8.18 " t . . . 1.52 0.71 53-2 3320 7300 25.90 25.86 Platinum-silver t . . 33-33 19.65 4.22 330 208 3.10 3.21 " t . . 9.81 5-05 11.38 774 656 7.08 7-2^ " t . . 5.00 2-51 19.96 1240 1150 11.29 u.88 Palladium-silver t 25.00 23-28 5-38 324 154 3-40 4.21 Copper-silver t . . . 98.08 98.35 56-49 3450 7990 26.50 27.30 " t . . . 94.40 95-17 51.93 3250 6940 25-57 25-41 " t '. . . 76.74 77.64 44.06 303 6070 24.29 21.92 " t . . . 42-75 46.67 47.29 2870 5280 22.75 24.00 " t . . . 7.14 8.25 50.65 2750 436o 23-17 25-57 " t . . . 1-3 1 50-3 4120 8740 26.51 29-77 Iron-gold t . . . . 13-59 27-93 i-73 3490 7010 27-92 14.70 " " t . . . . 9.80 21. 18 1.26 2970 1220 17-55 11.20 " " t- ...... 4.76 10.96 1.46 487 103 3-84 13.40 Iron-copper t . . . 0.40 0.46 24-51 1550 200X) 13-44 I4-03 Phosphorus-copper t 2.50 _ 4.62 476 I 45 - - " t 0-95 14.91 1320 1640 - - Arsenic-copper t 5-40 - 3-97 516 989 - - " t . . 2.80 _ 8.12 736 446 " t trace 38-52 2640 4830 ; * Annealed. t Hard-drawn. TABLE 402. Allowable Carrying Capacity of Rubber-covered Copper Wires. (For inside wiring Nat. Board Fire Underwriters' Rules.) B-f S Gage 18 16 14 12 10 8 6 5 4 3 1 o 00 0000 Amperes 3 6 12 17 24 33 46 54 65 7 6 90 107 I2 7 150 2IO 500,000 circ. mills, 390 amp.; 1,000,000 c. m., 650 amp.; 2,000,000 c. m., 1,050 amp. For insulated al. wire, capacity =84% of cu. Preece gives as formula for fusion of bare wires I = ad*, whered=diam. in inches, a for cu. is 10,244; al., 7585; pt.,5172; German silver, 5230; platinoid, 4750; Fe, 3148; Pb., 1379; alloy 2 pts. Pb., i of Sn., 1318. SMITHSONIAN TABLES. 33 TABLE 403. RESISTIVITIES AT HIGH AND LOW TEMPERATURES. The electrical resistivity (p, ohms per cm. cube) of good conductors depends greatly on chemical purity. Slight con- tamination even with metals of lower p may greatly increase p. Solid solutions of good conductors generally have higher p than components. Reverse is true of bad conductors. In solid state allotropic and crystalline forms greatly mod- ify p. For liquid metals this last cause of variability disappears. The + temperature coefficients of pure metals is of the same order as the coefficients of expansion of gases. For temperature resistance (t, p) plot at low temperatures the graph is convex towards the axis of t and probably approaches tangency to it. However for extremely low temper. atures (Junes finds very sudden and great drops in p. e.g. for Mercury, p, 5^ 54 -77-6 1.564 .696 -150. .567 359 -IOO. .916 .608 - 77-8 3-97 .691 -50. 1.813 .806 -IOO. .904 573 -76.8 1.040 .600 4.04 -703 0. 2.247 I.OO -5- 1.240 .786 -50. 1. 212 -80 5 o. 5-75 1.00' IOO. 2-97 1-32 0. 1-578 1.00 o. 1.506 I.OO IOO. 7-95 -38 200. 3-83 1.70 IOO. 2.28 1-44 IOO. 2.15 1-43 300. 13-25 2.30 500. 6.62 2.94 200. 2.96 1.88 200. 2.80 1.86 415. 17.00 2.96 750. 9-35 4.16 500. 5.08 3-22 400. 3.46 2.30 427. 37-30 IOOO. 12-54 5.58 750. 7.03 4-46 750. 6.65 4-42 450. 37.08 6.46 1063. 13-50 6.01 1000. 9.42 5-97 960. 8.4 500. 36.60 6.36 1063. 30.82 '3-7 1083. IO.2O 6-47 960. 76.6 II.O 000. 35-90 6.23 1200. 32.8 14.6 1083. 2I.3O 13-5 IOOO. 77.07 a 3 700. 33.60 6./Q 1400. 35-0 15.8 1200. 22.30 14.1 1200. 19.36 12.9 800. 35 oo 6 ig 1500. 37-0 16.3 1400. 23.86 15.1 1400. 21.72 14.4 850. 35-74 6.21 1500. 24.62 15-0 1500. 23.0 15-3 Mercury. Potassium. Sodium. Iron. C. Pt P_t C Pt ft C Pt Pt C Pt Pt PO PO PO PO -200. 5-38 .057 -200. 1.720 .246 -200. 0.605 '-37 -252.7 0.01 I .0010 -I 5 0. 10.30 .109 -I 5 0. 2.654 379 -150. 1-455 330 -200. 2.27 .212 -IOO. 15.42 .164 -100. 3-724 -532 -IOO. 2.380 541 -192.5 .844 .079 -50. 21.4 .227 -50- 5.124 732 -50. 3-365 -764 -loo. 5.92 554 1 -30. 07.7 975 o. 7.OOO I.OO 0. 4.40 I.OOO - 75-i 6-43 .602 o. 94-1 I.OOO 20. 7.II6 1.016 20. 4.873 1.107 - 50- 8.15 763 50. 08.3 1-045 60. 8.790 1.256 93-5 6.290 1.429 - o. 10.68 I.OO IOO. 103.1 7.096 65. 13-40 1.914 IOO. 9.220 2.095 IOO. 16.61 1 -554 200. 114.0 1.212 IOO. 15-31 2.187 120. 9.724 2.209 200. 24-50 2.293 300. 127.0 1-350 1 20. 76.7O 2.386 140. 10.34 2-349 400. 43-29 4.052 Manganin. German Silver. Constantan. 90%Pt. 10% Rh. Pt Pt Pt Pt c. Pt PO C. Pt PO Pt PO c. Pt PO -200. 37-8 974 -200. 27.9 .930 -200. 42.4 .961 -200. 14.49 .685 -I 5 0. 38.2 985 -150. 28.7 957 -I 5 0. 975 -I 5 0. 16.29 .770 -IOO. 38.5 .992 -IOO. 29-3 977 -IOO. 43-5 .986 -IOO. .8.05 854 -50- 38.7 997 -50. 29-7 .000 -5- 43-9 995 - 5- 19.66 93 0. 38.8 i.ooo o. 30.0 I.OOO o. 44.1 l.COO o. 21.14 I.OOO IOO. ^8 9 1.003 IOO. 33-i 1.103 IOO. 44-6 1. 012 IOO. 24.20 1.145 400. 38.3 .987 400. 44.8 I.OI6 . Au. below o, Niccolai, Lincei RenH. (5), i6,p. 757,906, 1907; above, Northrnp, Jour. Franklin Inst. 177, p- 85, 1914. Cu. below, Niccolai, 1. c. above, Northrup, ditto, 177. p. i, 1914. Ag. below, Niccolai, I.e. above Northrup, ditto, 178, p. 85, 1914. Zn. below, Dewar, Fleming, Phil. Mag. 36, p. 271, 1803 ; above, Northrup, 175, p. 153, 1913. Hg. below Dewar, Fleming, Proc. Roy. Soc. 66, p. 76, IQOO; above, Northrupi see Cd. K. below Guntz, Broniewski, C. R. 147, p. 1474, 1008, 148, p. 204, looo- Above, Northrnp, Tr. Am. Electroch. Soc. p. 185, 1911. Na, below, means, above, see K. Fe., Manganin, Constantan. Niccolai, I.e. German Silver, 90% Pt. 90% Rh., Dewar and Fleming Phil. Mag. 36, p. 271, 1893. SMITHSONIAN TABLES. TABLE 4O3 (continue^. RESISTIVITIES AT HIGH AND LOW TEMPERATURES. (Ohms per cm. cube unless stated otherwise.) Platinum. Lead. Bismuth. Cadmium. Pt Pt Pt Pt Po C. Pt c. Pt Po C. Pt Po -265. 0.10 .0092 -252.9 0.59 .0298 -200. 34-8 314 -252-9 0.17 .0218 -253- -233- -'53- - 73- '5 7^2 .014 .049 .378 .708 -203. -192.8 -103. - 75-8 4.42 5-22 n.8 '3-95 223 .264 598 705 -1 5 0. -IOO. - 50. 0. 55-3 75-6 94-3 110.7 499 .683 .852 I.OO -200. -190.2 -.83.1 -139.2 1.66 2.OO 2.22 3.60 214 .258 .286 464 o. 1 1.05 i.oo - 53- 15-7 .792 "7- 120.0 1.083 -IOO. A s, .619 100. 14.1 1.28 o. .9.8 I.OO 100. 156.5 '43 0. 7-75 I.OO 200. 17.9 1.62 100. 27.8 1.403 200. 214.5 J-937 300. 16.50 2.13 400. 800. ?5 4 40-3 2.30 3-65 2OO. 3'9- 38.0 50.0 1.919 2.52 259. 263. 267.0 127-5 2.41 c 1.150 325. 350. 4-35 4-33 1000. 47 -o 4-25 333- 95 - 4.80 300. 128.9 1.164 400. ?? ?o 4-35 I2OO. 52-7 4-77 400. 98.3 4 .qb 500. 139-9 1.263 500. 35 12 1400. 1600. 58.0 63.0 5-25 5-7 600. 800. 107.2 116.2 5-41 5-86 700. 750. 150.8 J53-5 1.361 1.386 700. 35-78 4.62 Tin. Carbon, Graphite.* Fused silica. Alundum cement. P Pt Pt_ PO o C . p in ohms, cm. cube. C. p = megohms cm. c. p in ohms cm. cube. -200. 2.60 .199 Carbon Graphite 15. >2oo,ooo,ooo. 20. >9Xo -100. 7-57 .580 O. 0.0035 0.00080 230. 20,000,000. 800. 30800. o. 13-05 I.OO 500. .0027 .00083 300. 200,000. 900. 13600. 200. 20.30 i-55 1000. .0021 .00 .87 350. 30,000. 1000. 7600. 225. 22.00 169 1500. .0015 .00090 450. 800. 1 100. 6500. 235. 47 .bo 3-^3 2000. .0011 .ooioo 700. 30. 1200. 2300. 750. dl.22 4.6 9 2500. .0009 .001 1 850. about 20. 1600. 190. Pt. low, Nernst, 1. c. high, Pirrani, Ber. Dentsch. Phvs. Ges. 12, p. 305, Pb. low, Schimank, Nernst, 1. c. high. Northrup, see Zn. Bi. low, means, high, Northrup, see Zn. Cd. low, Euchen, Gehlhoff, Verh. Deutsch. Phys. Ges. 14, p. 169, 1912, high, Northrup, see Zn. Sn. low, Dewar, Fleming, high, Northrup, see Zn. Carbon, graphite, Metallurg. Ch. F.ng. 13, p. 23, 1915. Silica, Campbell, Nat. Phys. Lab. n, p. 207, 1914. Alundum, Metallurg. Ch. Eng. 12, p. 125, 1914. * Diamond 1030 C, p >io 7 ; 1380, 7.5 X IC)5 v - Wartenberg, 1912. TABLE 404. Volume and Surface Resistivity of Solid Dielectrics. The resistance between two conductors insulated by a solid dielectric depends both upon the surface resistance and the volume resistance of the insulator. The volume resistivity, p, is the resistance between two opposite faces of a cen- timeter cube. The surface resistivity, s') mils. Gage No. 7-0 490.0 12.4 500. 7-0 6-0 461.5 11.7 464. 6-0 5-0 430.5 10.9 432. S-o 4-0 460. TI.7 393-8 10.0 400. 454. 4-0 3-o 2-0 410. 365. 10.4 9-3 362.5 33i.o 9-2 8.4 372. 348. 425. 380. 3-o 2-O o i 2 325. 289. 258. 8.3 7-3 6-5 306.5 283.0 262.5 7-8 7.2 6-7 227. 219. 324. 300. 276. 340. 300. 284. I 2 3 229. 5.8 243-7 6.2 212. 252. 259. 3 4 204. 5-2 225.3 5-7 207. 232. 238. 4 5 182. 4.6 207.0 5-3 204. 212. 220. 5 6 162. 4-1 192.0 4-9 2O I. 192. 203. 6 7 144- 3-7 177.0 4-5 199. 176. I 80. 7 8 128. 3-3 162.0 4.1 197. 1 60. I6 S . 8 9 U4. 2.91 148.3 3-77 194- 144- I 4 8. 9 10 102. 2.59 135.0 3-43 191. 128. 134. 10 II 91. 2.30 120.5 3-06 188. 116. 120. II 12 81. 2.05 105.5 2.68 185. 104. 109. 12 13 72. 1.83 9i.5 2.32 182. 92. 95. 13 14 64. 1.63 80.0 2.03 180. 80. 83. 14 15 57- 1.45 72.0 1.83 178. 72. 72. IS 16 Si- 1.29 62.5 1-59 175. 64. 65- 16 17 45- US 54-0 1-37 172. 56. 58. 17 18 40. 1.02 47.5 1. 21 168. 48. 49* || 19 36. 0.91 41.0 1.04 164. 40. 42. 19 20 32. .81 34-8 0.88 1 6 1. 36. 35- 20 21 28.5 .72 31-7 .81 157- 32. 32. 21 22 25-3 .62 28.6 .73 155. 28. 28. 22 33 22.6 57 25.8 .66 153- 24- 25. 23 24 20.1 Si 23.0 .58 151. 22. 22. 24 25 17.9 45 20.4 .52 148. 20. 2O. 75 26 IS.9 .40 18.1 .46 146. 18. 1 8. 26 27 14.2 36 17.3 .439 M3. 16.4 1 6. 27 28 12.6 32 16.2 .411 139. 14.8 14. 28 29 11.3 .29 15-0 .381 134. 13-6 13- 29 30 10.0 .25 14.0 .356 127. 12.4 12. 3O 31 8.9 .227 13.2 335 120. 1 1. 6 10. 31 32 8.0 .202 12.8 .325 "5- 10.8 9- 32 33 7-1 .ISO 11.8 .300 112. 10. 8. 33 34 35 6-3 5.6 .160 .143 10.4 9.5 .264 .241 no. 1 08. :: 7- 5- 34 35 36 S-o .127 9.0 .229 106. 7.6 4* 36 37 4-5 .113 8.5 .216 103. 6.8 37 38 4.0 1OI 8.0 .203 101. 6.0 38 39 3-5 .090 7-5 .191 99. 5-2 39 40 3-1 .080 7.0 .178 97. 4.8 40 4i 6.6 .168 95- 4-4 41 42 6.2 .157 92. 4.0 42 43 6.0 .152 88. 3-6 43 44 5.8 .147 85. 3-2 44 45 5-5 .140 Si. 2.8 45 46 5.2 .132 79. 2-4 46 47 5-0 .127 77- 2.0 47 48 4.8 .122 75- 1.6 48 49 4.6 .117 72. 1.2 49 50 4-4 .112 69- I.O So * The Steel Wire Gage is the same gage which has been known by the various names: " Washburn and Moen," " Roeb~ ling," "American Steel and Wire Co.'s." Its abbreviation should be written "Stl. W. G. r " to distinguish it from " S. W. G.," the usual abbreviation for the (British) Standard Wire Gage. f The American Wire Gage sizes have been rounded off to the usual limits of commercial accuracy. They are giren to four significant figures in Tables 410 to 413. They can be calculated with any desired accuracy, being based upon a simple mathematical law. The diameter of No. oooo is denned as 0.4600 inch and of No. 36 as 0.0050 inch. The ratio of any diameter to the diameter of the next greater number \l = 1. 1229322. Taken from Circular No. 31. Copper Wire Tables, U.S. Bureau of Standards which contains more complete tables. SMITHSONIAN TABLES. 334 TABLES 4-07-413. WIRE TABLES. TABLE 407 Introduction. Mass and Volume Resistivity of Copper and Aluminum. The following wire tables are abridged from those prepared by the Bureau of Standards at the request and with the cooperation of the Standards Committee of the American Institute of Elec- trical Engineers (Circular No. 31 of the Bureau of Standards). The standard of copper resist- ance used is " The Internationa! Annealed Copper Standard "as adopted Sept. 5, 1913, by the International Electrotechnical Commission and represents the average commercial high-conduc- tivity copper for the purpose of electric conductors. This standard corresponds to a conductivity of 58. Xio- 6 cgs. units, and a density of 8.89, at 20 C. In the various units of mass resistivity and volume resistivity this may be stated as 0.15328 ohm (meter, gram) at 20 C. 875.20 ohms (mile, pound) at 20 C. 1.7241 microhm-cm, at 20 C. 0.67879 microhm-inch at 20 C. 10.371 ohms (mil, foot) at 20 C. The temperature coefficient for this particular resistivity is 020 = 0.00393 or cto = 0.00427. The temperature coefficient of copper is proportional to the conductivity, so that where the con- ductivity is known the temperature coefficient may be calculated, and vice-versa. Thus the next table shows the temperature coefficients of copper having various percentages of the standard con- ductivity. A consequence of this relation is that the change of resistivity per degree is constant, independent of the sample of copper and independent of the temperature of reference. This re- sistivity-temperature constant, for volume resistivity and Centigrade degrees, is 0.00681 michrom- cm., and for mass resistivity is 0.000597 ohm (meter, gram). The density of 8.89 grams per cubic centimeter at 20 C., is equivalent to 0.32117 pounds per cubic inch. The values in the following tables are for annealed copper of standard resistivity. The user of the tables must apply the proper correction for copper of other resistivity. Hard-drawn copper may be taken as about 2.7 per cent higher resistivity than annealed copper. The following is a fair average of the chemical content of commercial high conductivity copper: Copper 99.91% Sulphur 0.002% Silver. . 03 Iron 002 Oxygen 052 Nickel Trace Arsenic 002 Lead " Antimony 002 Zinc " The following values are consistent with the data above : Conductivity at o C., in c.g.s. electromagnetic units 62.969 X io~ & Resistivity at o C., in michroms-cms 1.5881 Density at o C 8.90 Coefficient of linear expansion per degree C 0.000017 " Constant mass " temperature coefficient of resistance at o C 0.00427 The aluminum tables are based on a figure for the conductivity published by the U.S. Bureau of Standards, which is the result of many thousands of determinations by the Aluminum Company of America. A volume resistivity of 2.828 michrom-cm., and a density of 2.70 may be considered to be good average values for commercial hard-drawn aluminum. These values give: Mass resistivity, in ohms (meter, gram) at 20 C 0.0764 " " (mile, pound) at 20 C 436. Mass per cent conductivity 200.7% Volume resistivity, in michrom-cm. at 20 C 2.828 in microhm-inch at 20 C i.i 13 Volume per cent conductivity 61.0% Density, in grams per cubic centimeter 2.70 Density, in pounds per cubic inch 0.0975 The average chemical content of commercial aluminum wire is Aluminum 99-57% Silicon 0.29 Iron 0.14 SMITHSONIAN TABLES. TABLES 408, 409. COPPER WIRE TABLES. TABLE 408. -Temperature Coefficients of Copper for Different Initial Temperatures (Centtfrade) and Different Conductivities. 335 Ohms (meter, gram) at 20 C. Per cent conductivity. a I5 20 2 S a 3 o 050 0.161 34 .ISQ66 95% 96% 0.004 03 .00408 0.003 80 .003 85 0.003 73 00377 0.003 67 .00370 0.003 60 .00364 0.003 36 00330 .158 02 157 53 97% 97-3% .004 13 .00414 .00389 .003 90 .003 8 1 .003 82 003 74 00375 .00367 .003 68 .00342 003 43 .15640 .15482 98% 99% .004 17 .004 22 .00393 .003 97 .00385 .00389 .00378 .003 82 OC3 71 003 74 00345 .00348 .153 28 .151 76 100% 101% .004 27 .00431 .004 01 .00405 .003 93 .00397 .00385 .003 89 .00378 .00382 003 5 * 00355 NOTE. The fundamental relation between resistance and temperature is the following: Rt = R tl (i+a ti [t-tJ), where a^ is the "temperature coefficient," and t^ is the "initial temperature" or "temperature of reference." The values of a in the above table exhibit the fact that the temperature coefficient of copper is proportional to the conductivity. The table was calculated by means of the following formula, which holds for any per cent conductivity, n, within commercial ranges, and for centigrade temperatures, (n is considered to be expressed decimally: e.g., il percent conductivity =: 99 per cent, n = 0.99.) + (/! 20) n (0.00393) TABLE 409, -Reduction of Observations to Standard Temperature. (Copper.) Temper- ature C. Corrections to reduce Resistivity to 20 C. Factors to reduce Resistance to 20 C. Temper- ature C. Ohm (meter, gram). Microhm cm. Ohm (mile, pound). Microhm inch. For 96 per cent con- ductivity . For 98 per cent con- ductivity. For 100 per cent con- ductivity. o 5 10 +0.011 94 + .008 96 + .005 97 +0.1361 + .1021 + .0681 + 68.20 + Si-iS + M-io +0.053 58 + .040 1 8 4- .026 79 ix4i6 i. 0600 1.0392 1.0834 1.0613 1.0401 X '2 S 2 1.0626 1.0409 5 10 ii 12 13 + .00537 + .004 78 + .004 18 + .0612 + -0544 + .0476 + 30.69 + 27.28 + 23.87 f .024 ii + -021 43 + .01875 1-0352 1.0311 1.0271 1-0359 1.0318 1.0277 1.0367 1-0325 1.0283 ii 12 13 14 15 16 + .003 58 + .002 99 + .002 39 + .0408 + -0340 + -0272 + 20.46 + 17-05 + 13-64 + .016 07 + .013 40 + .010 72 1.0232 1.0192 I- oi 53 1.0237 1.0196 1.0156 1.0242 1.0200 I.OIOO 14 ii \\ 19 + .001 79 + .001 19 + .000 60 + .0204 + -0136 + .0068 + 10.23 + 6.82 + 3-41 + .00804 + -00536 + .00268 1.0114 1.0076 1.0038 1.0117 1.0078 1.0039 I.OII9 1.0079 1.0039 17 18 19 20 21 22 o .000 60 .001 19 - .0068 .0136 3-41 - 6.82 o .002 68 - .00536 1. 0000 0.9962 -9925 1. 0000 0.9962 9924 1 .0000 0.0961 .9922 20 21 22 23 24 25 - .001 79 .002 39 - .00299 .0204 .0272 .0340 10.23 13.64 17.05 .008 04 .010 72 .013 40 .9888 .9851 9815 .9886 .9848 .9811 .9883 .9845 .9807 23 24 25 26 11 - .003 58 .004 18 .004 78 .0408 .0476 - -0544 20.46 - 23.87 27.28 .016 07 .018 75 - .021 43 9779 9743 .9707 9774 9737 .9701 .9770 9732 .9695 26 27 28 29 30 35 - -00537 -005 97 .008 96 .0612 ' - .0681 .1021 30.69 - 34.10 51-15 .024 ii .026 79 .040 1 8 .9672 .9636 .9464 .9665 .9629 9454 .9658 .9622 9443 29 30 35 40 45 50 .on 94 -014 93 - .017 92 .1361 .1701 .2042 - 68.20 - 85.25 102.30 - -053 58 - .06698 - .08037 .9298 .9138 .8983 .9285 .9122 .8964 .9271 9105 .8945 40 45 50 55 60 65 .020 OO .023 89 .02687 - .2382 - .2722 .3062 -119-35 -136.40 -153-45 - -093 ?6 .107 16 .120 56 .8833 .8689 8549 .8812 .8665 .8523 .8791 .8642 .8497 g 65 70 75 .029 86 - .03285 - -3403 -3743 -170.50 -187-55 -133 95 -147 34 .8413 .8281 8385 .8252 .8358 .8223 70 75 SMITHSONIAN TABLES. 336 TABLE 410. WIRE TABLE, STANDARD ANNEALED COPPER, American Wire Gage (B. A S.)- English Units. ENGLISH. Gage No. Diameter in Mils. at 20 C. Cross-Section at 20 C. Ohms per 1000 Feet.* Circular Mils. Square Inches. oC ( = 3*F) 20 C ( = 68F) 50 C (=i23F) 75 C ( = 1670 F) oooo ooo 00 460.0 409.6 364.8 211 600. 167800. 133 loo. 0.1662 .1318 .1045 0.045 J 6 .056 95 .071 81 0.049 01 .061 80 077 93 0.054 79 .06909 .087 12 0.059 61 .075 16 .09478 o I 2 324-9 289.3 257.6 105 500. 83690. 66370. .08289 065 73 . .052 13 09055 .1142 .1440 .09827 .1239 1563 .1099 1385 1747 .1195 i5 7 .1900 3 4 5 229.4 204.3 181.9 5 2 640. 41 740. 33100. .041 34 .032 78 .02600 .1816 .2289 .2887 .1970 .2485 3*33 .2203 .2778 .3502 .2396 .3022 .3810 6 8 162.0 144-3 128.5 26250. 20 820. 16 510. .020 62 -01635 .01297 .3640 -4590 .5788 3951 .4982 .6282 .4416 5569 .7023 .4805 .6059 .7640 9 10 ii 114.4 101.9 90.74 13090. 10 380. 8234. .01028 .008155 .006 467 .7299 .9203 1.161 .7921 .9989 1.260 .8855 I.II7 1.408 9633 1.215 1-532 12 13 14 80.8 1 71.96 64.08 6530. 5*78. 4107. .005 129 .004 067 .003225 1.463 1.845 2.327 1-588 2.003 2.525 1-775 2.239 2.823 I-93 1 2.436 3.071 3 17 57-07 50.82 45.26 32$7. 2583. 2048. .002 558 .002 028 .001 609 2-934 3.700 4.666 3.184 4.016 5.064 3-560 4.489 5.660 3-873 4.884 6.158 18 '9 20 40.30 35-9 31.96 1624. 1288. IO22. .001 276 .OOI OI2 .000 802 3 5.883 7.418 9-355 6.385 8-051 10.15 7-138 9.001 IJ -35 7765 9.792 12.35 21 22 23 28.45 25-35 22-57 SlO.I 642.4 509-5 .000 636 3 .000 504 6 .0004002 11.80 14.87 18.76 12.80 16.14 20.36 14-31 18.05 22.76 15-57 19.63 24.76 24 3 20.10 17.90 15.94 404.0 320.4 254-1 0003173 .000251 7 .000 199 6 23-65 29.82 37.61 25.67 32-37 40.81 28.70 36.18 45-63 31.22 39-36 49.64 27 28 29 14.20 12.64 11.26 2OI.5 159.8 126.7 .0001583 .000 125 5 .00009953 47-42 59.80 75-40 5M7 64.90 81.83 57-53 72-55 91.48 62.59 78.93 99-52 30 3 1 32 10.03 8.928 7-95 IOO-5 79.70 63.21 .000 078 94 .000 062 60 .000 049 64 95.08 119.9 151.2 103.2 130.1 164.1 "5-4 145-5 183.4 123.5 158.2 199-5 33 34 35 7.080 6-305 5-615 50.13 39-75 3I-52 .000 039 37 .000 031 22 .OOO O24 76 190.6 240.4 33- 1 206.9 260.9 329.0 231-3 291.7 367.8 251.6 3I7-3 400.1 36 ^ 5.000 4-453 3-965 25.00 19.83 1572 .00001964 .00001557 .000012 35 382.2 482.0 607.8- 414.8 659.6 463-7 584.8 737-4 504-5 636.2 802.2 39 40 3-531 3-145 12.47 9-888 .000009793 .000 007 766 766.4 966.5 831.8 1049. 929.8 "73- IOI2. 1276. * Resistance at the stated temperatures of a wire whose length is 1000 feet at 20 C. SMITHSONIAN TABLES. ENGLISH. TABLE 41O (continued}. WIRE TABLE, STANDARD ANNEALED COPPER American Wire Gage (B. & a.). English Units (confined). 337 % Diameter in Mils, at 20 C. Pounds per 1000 Feet. Feet per Pound. Feet per Ohm.* o C (=32 F) 20 C (=68 F) 50 C (=I22F) 75 C (=.67 F) 0000 ooo 00 460.0 409.6 364.8 640.5 507-9 402.8 1.561 1.968 2.482 22 140. 17 560. 13 930. 2O 400. 16 180. 12 830. 18 250. 14 470. ii 480. 16 780. 13 300. 10 550. I 2 324.9 289.3 257-6 3'9-S 253-3 200.9 3-130 3-947 4-977 II 040. 8758. 6946. 10 180. 8070. 6400. 9103. 7219. 5725. 8367. 6636. 5262. 3 4 5 229.4 204.3 I8I.9 159-3 126.4 100.2 6.276 7.914 9.980 5508. 4368. 3464. 5075- 4025. 3192. 4540- 3600. 2855- 4I73- 3309. 2625. 6 162.0 M4-3 128.5 79.46 63.02 49.98 12.58 15-87 2O.OI 2747. 2179. 1728. 2531. 2007. 1592. 2264. 1796. 1424. 2081. 1651. 1309. 9 10 ii 114.4 IOI-9 90.74 39.63 31-43 24.92 25-23 31.82 4O.I2 1370. I08 7 . 861.7 1262. 1001. 794.0 1129. 895-6 710.2 1038. 823.2 652.8 12 J 3 14 80.81 71.96 64.08 19.77 15.68 12.43 50-59 63.80 80.44 683.3 541-9 429.8 629.6 499-3 396.0 563-2 446.7 354-2 5177 410.6 325-6 II i? 57-07 50.82 45.26 9.858 7.8l8 6.200 IOI-4 127.9 161.3 340.8 270.3 214-3 314.0 249.0 J 97-5 280.9 222.8 176.7 258.2 204.8 162.4 18 19 20 40.30 35.89 31.96 4.917 3-899 3.092 203.4 256.5 3234 I7O.O 134.8 106.9 156.6 124.2 98.50 I4O.I III. I 88.ii 128.8 I02.I 80.99 21 22 23 28.46 25-35 22.57 2.452 1-945 1.542 407.8 514.2 648.4 84.78 67.23 53-32 78.11 61.95 49-13 69.87 55-41 43-94 64-23 50-94 40.39 24 3 20. i o 17.90 '5-94 1.223 0.9699 .7692 817.7 1031. I3OO. 42.28 33-53 26.59 38.96 30.90 24.50 34.85 27.64 21.92 32.03 25.40 20.15 27 28 29 14.20 12.64 11.26 .6100 .4837 3836 1639. 2067. 2607. 21.09 16.72 13.26 '9-43 I5-4I 12.22 I7-38 I3-78 10.93 15.98 12.67 IO.O5 30 31 32 10.03 8.928 7-95 .3042 .2413 1 9 1 3 3287. 4I45- 5227. 10.52 8.341 6.614 9.691 7.685 6.095 8.669 6-875 5-452 7.968' 6.319 5.0II j 33 34 35 7.080 6-305 5-6i5 .1517 .1203 .095 42 6591. 8310. 10 480. 5-245 4.160 3-299 4-833 3-833 3.040 4.323 3-429 2.719 3-974 i 3-I52 : 2-499 36 9 5.000 4-453 3-965 .075 68 .060 01 .047 59 13 210. 16 660. 21 OIO. 2.616 2.075 1.645 2.4II I.9I2 I.5l6 2.156 1.710 1.356 1.982 *-572 i 1.247 39 40 3-53' 3-M5 .037 74 .029 93 26 5OO. 33 4io. 1-305 1-035 I.2O2 0-9534 1-075 0.8529 0.9886 .7840 Length at 20 C. of a wire whose resistance is i ohm at the stated temperature*. SMITHSONIAN TABLES. 33 O TABLE 410 (continued). WIRE TABLE, STANDARD ANNEALED COPPER (continued). American Wire Gage (B. A S. >. English Units (continued). ENGLISH, Gage No. Diameter in Mils at 20 C. Ohms per Pound. Pounds per Ohm. oC. ( = 3 2F.) 20 C. ( = 6SF.) 50 C. (=.22F.) 20 C. ( = 68 F.) oooo 000 00 460.0 409.6 364.8 o.ooo 070 51 .OOO II2I .000 1783 o.ooo 076 52 .000 1217 .000 1935 o.ooo 085 54 .000 1360 .000 2163 13070. 8219. 5169. O I 2 324.9 289.3 257.6 .000 2835 .000 4507 .000 7166 .000 3076 .000 4891 .000 7778 .000 3439 .000 5468 .000 8695 325L 2044. 1286. 3 4 5 229.4 204.3 181.9 .001 140 .001 812 .002 881 .001 237 .001 966 .003 127 .001 383 .002 198 003 495 808.6 508.5 319.8 6 i 162.0 144-3 128.5 .004 581 .007 284 .on 58 .004 972 .007 905 .012 57 005 558 .008838 .014 05 2OI.I 126.5 79-55 9 10 ii 114.4 101.9 90.74 .018 42 .029 28 .046 56 .01999 .031 78 05 53 .022 34 035 53 .056 49 50-03 3'-47 19.79 12 13 14 80.8 1 71.96 64.08 .074 04 .1177 .1872 .080 35 .1278 .2032 .08983 .1428 .2271 12.45 7.827 4.922 ;i 17 57-07 50.82 45.26 .2976 4733 7525 -323 -5136 .8167 .3611 5742 .9130 3.096 1.947 1.224 18 19 20 40.30 35*9 31.96 1.197 1.903 3-025 1.299 2.065 3-283 1.452 2.308 3.670 0.7700 4843 .3046 21 22 23 28.46 25-35 22.57 4.810 7.649 12. l6 5.221 8.301 13.20 5.836 9.280 14.76 J 9i5 .1205 075 76 24 3 2O. I O 17.90 15-94 19-34 30.75 48.89 20.99 33-37 53.06 23.46 37-31 59-32 .047 65 .029 97 .01885 3 29 14.20 12.64 11.26 77-74 123.6 196.6 84.37 134.2 213-3 94.32 150.0 238-5 .on 85 .007 454 .004 688 30 3i 32 10.03 8.928 7.950 312.5 497-0 790.2 339-2 539-3 857.6 379-2 602.9 958.7 .002 948 .001 854 .001 166 33 34 35 7.080 6-305 5-615 1256. 1998. 3*77- 1364. 2168. 3448. iSH 2424. 3854. ooo 7333 .000 4612 .000 2901 36 ! % 5.000 4-453 3-965 5051- 8032. 12 770. 5482. 8717. 13860. 6128. 9744. 15490. .000 1824 .000 1147 .000072 15 39 40 3-531 3-145 20 310. 32 290. 22 040. 35 040- 24 640. 39 170- .000 045 38 .000 028 54 SMITHSONIAN TABLES. METRIC. TABLE 411. WIRE TABLE, STANDARD ANNEALED COPPER. American Wire Gage (B. & S.) Metric Units. 339 Diameter Cross Section Ohms per ] Uloroeter." Gage No. in mm. at 20 C. in mm. 1 at 20 C. oC. 20 C. 50 C. 75 C. 0000 11.68 107.2 0.1482 0.1608 0.1798 0.1956 OOO 10.40 85.03 .1868 .2028 .2267 .2466 oo 9.266 6743 2356 2557 .2858 .3110 o 8.252 53-48 .2971 .3224 .3604 .3921 I 7.348 42.41 3746 .4066 4545 4944 2 6-544 .4724 5127 .6235 3 5.827 26.67 5956 .6465 .7227 .7862 4 5 5.189 4.621 21.15 16.77 75" .9471 .8152 1.028 91 1 3 1.149 .9914 1.250 6 4.115 I 3-3 1.194 I.2Q6 1.449 1-576 7 3-665 1.506 1.634 1.827 1.988 8 3.264 8.366 1.899 2.o6l 2.304 2.506 9 2.906 6.634 2-395 2-599 2.905 3.161 10 2.588 5.261 3.020 3-277 3-663 3.985 ii 2.305 4.172 3.807 4.132 4.619 5-025 12 2-053 3-309 4.801 |.2I I 5-825 6-337 \4 .828 .628 2.624 2.081 6.054 7-634 6-57 1 8.285 7-345 9.262 7.991 10.08 15 .450 1.650 9.627 10.45 n.68 12.71 16 .291 1.309 12.14 13.17 14-73 16.02 .150 1.038 1 6.6 1 18.57 20.20 18 1.024 0.8231 19.30 20.95 23.42 25.48 1 9 0.9116 6527 24-34 26.42 29-53 32.12 20 .8ll8 5 X 76 30.69 33-3 1 37-24 40.51 21 .7230 .4105 38.70 42.00 46.95 51.08 22 23 6438 5733 32^5 .2582 48.80 61.54 52-96 66.79 59-21 74.66 6441 81.22 24 25 .5106 4547 .2047 .1624 77.60 97.85 84.21 106.2 94.14 118.7 IO2.4 I29.I 26 .4049 .1288 123.4 133-9 149.7 162.9 27 .3606 .1021 155-6 168.9 188.8 203.4 28 .3211 .080 98 196.2 212.9 238.0 258.9 29 .2859 .064 22 247.4 268.5 300.1 326.5 3 2546 .050 93 3"-9 338.6 378.5 4II.7 3 2 .2268 .2019 .040 39 .032 03 393-4 496.0 426.9 538.3 477-2 601.8 519.2 654.7 33 34 'I&ol .025 40 .020 14 625.5 788.7 678.8 856.0 758.8 956.9 825.5 IO4I. 35 :! 4 26 015 97 994-5 1079. 1207. I313- 3 6 .1270 .012 67 1254- 1361- 1522. I6 55- 3 .1131 .1007 .010 05 .007 967 1581. 1994. 1716. 2164. 1919. 2419. 2087. 2632. 39 40 .089 69 .079 87 .006 318 .005 oio 2514- 2729. 3441- 3847. 33*9- 4185. Resistance at the stated temperatures of a wire whose length is i kilometer a SMITHSONIAN TABLES, 340 TABLE 411 (continued). WIRE TABLE, STANDARD ANNEALED COPPER (continued). American Wire Gage (B. & S.) Metric Units (continued). METRIC, Gage No. Diameter in mm. at 20 C. Kilograms per Kilometer. Meters per Gram. Meters per Ohm.* oC. 20 C. 50 C. 75 C. oooo 000 00 11.68 10.40 9.266 953-2 755-9 599-5 o.ooi 049 .001 323 .001 668 6749. 5352. 4245- 6219. 4932. 39II- 5563. 4412. 3499. 5"3. 4055. 3216. o I 2 8.252 7.348 6-544 475-4 377-0 299.0 .002 103 .002 652 003 345 2117. 3102. 2460. 195 1 ' 2774. 2200. 1745. 2550. 2O22. 1604. 3 4 5 5.827 5.189 4.621 237.1 188.0 149.1 .004 217 .005 318 .006 706 1679. I33J. 1056. 1547- 1227. 972.9 1384. 1097. 870.2 1272. 1009. 799-9 6 I 4-IIS 3.665 3.264 118.2 93-78 74.37 .008 457 .010 66 -013 45 ^ 7 ' 3 664.0 526.6 771-3 611.8 485.2 690.1 547-3 434-0 634-4 53- i 399-o 9 10 ii 2.906 2.588 2.305 58.98 46.77 37.09 .016 96 .021 38 .026 96 417.6 33L2 262.6 384-8 305-1 242.0 344-2 273.0 216.5 316.4 250.9 199.0 12 U M 2.053 1.828 1.628 29.42 23-33 18.50 .03400 .042 8 7 .054 O6 208.3 165.2 131.0 191.9 152.2 120.7 171.7 136.1 1 08.0 157.8 125.1 99.24 \l I? 1.450 1.291 1.150 14.67 11.63 9.226 .068 16 085 95 .1084 103.9 82.38 65.33 95-71 75-90 60.20 85.62 67.90 53-85 78.70 62.41 49.50 18 19 20 I.O24 0.9116 .8ll8 7.317 5-803 4.602 1367 1723 .2173 51.81 41.09 32.58 47-74 37-86 30.02 42.70 33-86 26.86 39.25 31-13 24.69 21 22 23 .7230 .6438 5733 3-649 2.894 2.295 .2740 3455 4357 25.84 20.49 16.25 23.81 1 8.88 14.97 21.30 16.89 13-39 19.58 15-53 12.31 24 25 26 .5106 4547 .4049 1.820 1.443 1.145 .5494 .6928 .8736 I2.8 9 10.22 8.105 11.87 9.417 7.468 10.62 8.424 6.680 9-764 7-743 6.141 11 29 .3606 .3211 .2859 0.9078 .7199 .5709 1. 102 1.389 1.752 6.428 5-97 4.042 5.922 4.697 3-725 5.298 4.201 3-332 4.870 3.862 3.063 30 31 32 : 2 2 ^ 6 .2019 .4527 3590 .2847 2.2O9 2.785 3-512 3.206 2.542 2.OI6 2-954 2.342 1.858 2.642 2.095 1.662 2.429 1.926 i.5 2 7 33 34 35 .1798 .1601 .1426 .2258 .1791 .1420 4.429 5.584 7.042 1. 006 1.473 1.168 0.9265 1.318 1.045 0.8288 1. 211 0.9606 .7618 36 % .1270 .u 3 i .1007 .1126 .08931 .070 83 8.879 1 1. 2O 14.12 0.7974 .6324 5015 7347 .5827 .4621 .6572 .5212 .4133 .6041 .4791 -3799 39 40 .08969 .079 87 .056 17 .044 54 17.80 22.45 3977 3'54 .3664 .2906 .3278 .2600 3 OI 3 .2390 * Length at 20 C. of a wire whose resistance is i ohm at the stated temperatures. SMITHSONIAN TABLES. METRIC. TABLE 411 {continued). WIRE TABLE, STANDARD ANNEALED COPPER (continued). American Wire Gage (B. & S.). Metric Units (continued). Gage No. Diameter in mm. at 20 C. Ohms per Kilogram. Grams per Ohm. oC. 20 C. 50 C. 20 C. oooo ooo 00 11.68 10.40 9.266 o.ooo 155 4 .OOO 247 2 .000 393 o o.ooo 168 7 .000 268 2 .000 426 5 o.ooo 188 6 .000 299 9 .000 476 8 5 928 ooo. 3 728 ooo. 2 344000. 2 8.252 7-348 6-544 .000 624 9 .000 993 6 .001 580 .OOO 678 2 .001 078 .001 715 .000 758 2 .001 206 .001 917 i 474 ooo. 927 300. 583 200. 3 4 5 5.827 5.189 4.621 .002 512 003 995 .006352 .002 726 004 335 .006 893 .003 048 .004 846 .007 706 366800. 230 700. 145 100. 6 8 4-ii5 3.665 3.264 .010 10 .016 06 -025 53 .010 96 017 43 .027 71 .012 25 .019 48 .030 98 91 230. 57380. 36080. 9 10 ii 2.906 2.588 2-305 .04060 .064 56 .1026 .044 06 .070 07 .1114 .049 26 078 33 .1245 22 690. I 4 2 7 0. 8976. 12 !3 14 2-053 1.828 1.628 .1632 2 595 .4127 .1771 .2817 4479 .1980 3M9 .5007 56.45 355- 2233- 11 17 1.450 1.291 1.150 .6562 1.043 1.659 .7122 1.132 1.801 7961 1.266 2.013 1404. 883.1 555-4 18 !9 20 1.024 0.9116 .8118 2.638 4.194 6.670 2.863 $ 3-201 3.089 8.092 349-3 219.7 138-2 21 22 23 .7230 .6438 -5733 1 0.60 16.86 26.81 11.51 18.30 29.10 12.87 20.46 32.53 86.88 54.64 34.36 24 S .5106 4547 .4049 42.63 67.79 107.8 46.27 73-57 117.0 51.73 82.25 130.8 21.61 13-59 8.548 27 28 2 9 .3606 .3211 .2859 171.4 272.5 433-3 1 86.0 295.8 470.3 207.9 33- 6 5 2 5-7 5-376 3-381 2.126 3 3 1 32 .2546 .2268 .2019 689.0 1096. 1742. 747-8 1189. 1891. 836.0 1329. 2114. 1-337 0.8410 .5289 33 34 35 'S 8 ..i6oi .1426 2770. 4404. 7003. 3006. 4780. 7601. 336i- 44- 8497- .3326 .2092 .1316 36 % .1270 .1131 .1007 11140. 17710. 28150. 1 2090. 19220. 30560. i35io. 21480. 34i6a .08274 .052 04 032 73 39 40 .08969 .079 87 44770. 71180. 48590. 77260. 543 10 ' 86360. .020 58 .01294 SMITHSONIAN TABLES. 342 TABLE 412. -ALUMINUM WIRE TABLE, Hard-Drawn Aluminum Wire at 20 C. (or, 68 F.). American Wire Gage (B. & S.). English Units. ENGLISH. Gage No. Diameter in Mils. Cross Section. Ohms per 1000 Feet. Pounds per looo Feet. Pounds per Ohm. Feet per Ohm. Circular Mils. Square Inches. oooo 460. 212 OOO. 0.166 0.0804 195- 2420. 12 400. OOO 410. 168 ooo. .132 .IOI 154- 1520. 9860. 00 365. 133000. .105 .128 122. 957- 7820. 325. 106000. .0829 .l6l 97-o 602. 62OO. 2 2!: 83700. 66400. .0657 .0521 3 76.9 61.0 379- 238. 4920. 3900. 3 4 22 9 . 204. 52 600. 41-700. .0413 .0328 .408 48.4 38-4 150. 94.2 3090. 2450. 5 182. 33 I0 - .0200 .514 30-4 59-2 I950- 6 162. 26 300. .O2O6 .648 24.1 37-2 1540. 7 144. 20 800. .0164 .817 19.1 23-4 I22O. 8 128. 1 6 500. .0130 1.03 15.2 14.7 970. 9 114. 13 100. .0103 1.30 I2.O 9.26 770. 10 102. 10 400. .008 15 1.64 9-55 5-83 610. ii 91. 8230. .00647 2.07 7-57 3-66 484. 12 81. 6530. .005 I 3 2.61 6.00 2.30 384- 13 72. 5180. .004 07 3-29 4.76 i.45 34- 64. 4110. .003 2 3 4.14 378 0.911 241. I5 57- 3260. .002 56 5.22 2.99 573 191. 16 51- 2580. .002 03 6.59 2-37 .360 152. 17 45- 2050. .001 61 8.31 1.88 .227 1 20. 18 40. 1620. .001 28 10.5 1.49 143 95-5 19 20 36. 32. 1290. IO2O. .001 01 .000 802 13.2 16.7 1.18 0-939 .0897 .0564 75-7 60.0 21 28.5 810. .000 636 2I.O 745 355 47.6 22 25-3 642. .000 505 26.5 591 .0223 37-8 23 22.6 509- .000400 33-4 .468 .0140 29.9 24 20.1 404. .000 317 42.1 371 .008 82 2 3-7 11 17.9 15.9 320. 254- .000 252 .000 200 I 3 ' 1 67.0 295 234 005 55 .003 49 1 8.8 14.9 27 14.2 202. .000 158 84.4 .185 .002 19 11.8 28 12.6 1 60. .000 126 1 06. .147 .001 38 9-39 2 9 "3 127. .000 099 5 134- .117 .000868 745 30 1 0.0 101. .000 078 9 169. .0924 .000 546 5-9 1 31 32 8.9 8.0 79.7 63.2 .000 062 6 .000 049 6 213. 269. 0733 .0581 .000 343 .000 216 4.68 3-72 33 7.1 50.1 .000 039 4 339- .0461 .000 136 2-95 34 6-3 39-8 .OOO 031 2 428. 3 6 5 .000 085 4 2-34 35 5.6 3 r -5 .000 024 8 540. .0290 .000 053 7 1.85 36 5-o 4-5 25.0 19.8 .000 019 6 .000 015 6 681. 858. .0230 .0182 .000 033 8 .OOO O2 I 2 1.47 1.17 3 8 4.0 iS-7 .000 012 3 1080. 0145 .000 013 4 0.924 39 3-5 12.5 .000009 79 1360. .0115 .000 008 40 .733 40 3-i 9-9. .000 007 77 1720. ' .0091 .000 005 28 .581 SMITHSONIAN TABLES. METRIC. TABLE 413. -ALUMINUM WIRE TABLE. Hard-Drawn Aluminum Wire at 20 0. American Wire Gage (B. & S.) Metric Units. 343 Gage No. Diameter in mm. Cross Section in mm. 2 Ohms per Kilometer. Kilograms per Kilometer. Grams per Ohm. Meters per Ohm. 0000 II.7 107. 0.264 289. I 100 000. 3790. ooo 10.4 85.0 333 2 3 0. 690 ooo. 3010. oo 9-3 67.4 .419 182. 434 ooo. 2380. 8-3 53-5 .529 144. 273 ooo. 1890. I 7-3 42.4 .667 114. 172 ooo. 1500. 2 6.5 33-6 .841 90.8 108 ooo. 1190. 3 5-8 26.7 1. 06 72.0 67 900. 943. 4 5-2 21.2 i-34 57- 1 42 700. 748. 5 4-6 1 6.8 1.69 45-3 26 900. 593- 6 4.1 13-3 2.13 35-9 1 6 900. 470. 7 3-7 10.5 2.68 28.5 10 600. 373- 8 3-3 8-37 3.38 22.6 6680. 296. 9 10 n 2.91 2-59 2.30 S3 4.17 4.26 & 17.9 14.2 "3 4200. 2640. 1660. X 148. 12 2.05 3-3 1 8-<55 8.93 1050. 117. IT 1.83 2.62 10.8 7.08 657. 92.8 14 1.63 2.08 13.6 5.62 413- 73-6 I5 i.45 1.65 17.1 446 260. 584 16 1.29 I-3 1 21.6 3-53 164. 46-3 17 'IS 1.04 27-3 2.80 103. 36-7 18 1.02 0.823 344 2.22 64.7 29.1 19 O.gi 653 43-3 1.76 40.7 23-1 20 .81 .518 54-6 I.4O 25.6 18.3 21 .72 .411 68.9 I. II 16.1 14.5 22 23 .64 57 .326 .258 86.9 no. 0.879 .697 IO.I 6.36 11.5 24 5 1 .205 138. 553 4.00 7.24 25 45 .162 174. 438 2.52 5-74 26 ^ 3 .40 .129 220. 348 1.58 4-55 3 36 3 2 .102 .0810 277. 349- .276 .219 *3 3.61 2.86 29 .29 .0642 440. 173 394 30 3' 32 25 .227 .202 .0509 .0404 .0320 555- 700. 883. 138 .109 .0865 .248 .156 .0979 i. 80 143 '13 33 34 35 .ISO .160 143 .0254 .O20I .Ol6o i no. 1400. 1770. .0686 0544 .0431 .0616 .0387 .0-44 0.899 712 565 36 .127 .0127 2230. 0342 T 53 448 TI 3 .0100 2820. .0271 .00903 355 38 .101 .0080 355- .0215 .00606 .2 2 39 40 .090 .080 .0063 .0050 4480. 5640. . .0171 . .00381 .002 40 .223 177 ^^"i^"""* SMITHSONIAN TABLES. 344 TABLES 414-415. TABLE 414. Ratio of Alternating to Direct Current Resistances for Copper Wires. This table gives the ratio of the resistance of straight copper wires with alternating currents of different frequencies to the value of the resistance with direct currents. Diameter of Frequency/ = wire in millimeters. 00 100 IOOO 10,000 100,000 1,000,000 0.05 _ _ _ _ *I.OOI O.I * .001 1.008 0.25 .003 1.247 o-S * .001 .047 2.240 I.O .008 .503 4.19 2.O .001 .120 .756 8.10 3- .006 437 4.00 12.0 4- .021 .842 5.24 17.4 5- * .001 .047 . 240 6.49 19.7 7-5 .001 .002 .210 3-22 7.50 29.7 10. .003 .008 .503 4.IQ 12.7 39-1 IS- .016 .038 .136 6.14 18.8 20. .044 .120 .756 8.10 25.2 . 25- 105 .247 3.38 10. I 28.3 40. 474 .842 5.24 17.4 100. 3-31 4.19 13.7 39-i Values between i.oop and i.ooi are indicated by *i.poi. The values are for wires having an assumed conductivity of 1.60 microhm-cms; for copper wires at room tempera- tures the values are slightly less than as given in table. The change of resistance of wire_other than copper (iron wires excepted) may be calculated from the above table by taking it as proportional to d^///p where d diameter,/ the frequency and p the resistivity. If a given wire be wound into a solenoid, its resistance, at a given frequency, will be greater than the values in the table, which apply to straight wires only. The resistance in this case is a complicated function of the pitch and radius of the winding, the frequency, and the diameter of the wire, and is found by experiment to be sometimes as much as twice the value for a straight wire. TABLE 415. Maximum Diameter of Wires for High-frequency Alternating-to-direct-current Resistance Ratio of 1.01. Frequency -f- io 6 . . . . O.I O.2 0-4 0.6 0.8 I.O 1.2 1-5 2.0 3-0 Wave-length, meters 3000 I5OO 750 500 375 300 250 200 150 IOO Material. Diameter in centimeters. Copper o 006 bilver .0345 o C)o8o Gold Platinum .1120 0.0793 0.0560 0.0457 0.0396 0-0354 0.0323 0.0290 .0250 0.0205 Mercury .264 0.187 0.132 .1080 0.0936 0.0836 0.0763 0.0683 .0591 0.0483 Manganin Constantan German silver .1784 .1892 1942 0.1261 0.1337 0.1372 0.0892 0.0946 0.0970 .0729 .0772 .0792 .0631 .0664 .0692 0.0564 0598 .0515 .0546 .0560 0.0488 0.0500 0399 0423 0434 0.0325 0.0345 0.0354 Graphite 765 0-541 0.383 312 .271 242 221 0.197 171 0.140 Carbon 60 o 801 t-66 r 6 ,c Iron n *= 1000 . y 00263 0.00186 0.00131 00108 0.00094 0.00083 0.00076 0. 00p68 0.00059 0.00048 /x = 500 00373 0.00264 0.00187 00152 0.00132 o. 00118 O.OOIOS 0.00096 o . 00084 0.00068 p. = loo 00838 0.00590 0.00418 00340 0.00295 0.00264 O.O024I 0.00215 0.00186 0.00152 Bureau of Standards Circular 74, Radio Instruments and Measurements, 1918. SMITHSONIAN TABLES. TABLE 416. ELECTROCHEMICAL EQUIVALENTS- 345 Every gram-ion involved in an electrolytic change requires the same number of coulombs or ampere-hours of elec- tricity per unit change of valency. This constant is 96.404 coulombs or 26.804 ampere-hours per gram-hour (a Fara- day) corresponding to an electrochemical equivalent for silver of o.ooi 11800 gram sec" 1 amp" 1 . It is to be noted that the change of valence of the element from its state before to that after the electrolytic action should be considered. The valence of a free, uncombined element is to be considered as o. The same current will electrolyze "chemically equivalent" quantities per unit time. The valence is then included in the "chemically equivalent" quantity. The fol- lowing table is based on the atomic weights of 1917. Element. II CJ > Mg coulomb. Coulombs per mg Grams per amp.- hour. Element. Change of 1 1 valency. | Mg per coulomb. Coulombs per mg Grams per amp.- hour. 10 682 Nickel o 6081 Chlorine. . . Copper .'. '.'. I 3 5 7 .'3675 .1225 0735 .0525 .6588 .3294 2.721 8.164 13.606 19-05 1.518 3.036 1.3229 0.4410 o . 2646 0.1890 2.3717 i 1858 Oxygen . . Platinum . 2 3 2 4 2 0.3041 0.2027 0.08291 0.04145 1.0115 o 5057 3.289 4-933 12.062 24.123 0.0887 .0946 .7208 2085 .1492 .641 821 Gold .044 0.4893 7-357 it 6 0.3372 2.966 214 Hydrogen Lead .6812 .010459 *473 1.468 5-728 o. 4657 2.452 0.037607 7 . 7302 Potassium . . Silver Sodium I i 0.4052 1.1180 o . 2384 2.468 0.89445 4 195 -459 .0248 8581 07 }6 o 9314 3 8651 Tin 2 o 6151 I 626 u .5368 1.8628 I .9326 4 0.3075 3.252 . IO7 Mercury .0789 0394 0.4810 0.9620 7.484 3-742 Zinc 2 0.3387 2-952 .2IQ4 The electrochemical equivalent for silver is p.ooi 11800 g sec" 1 amp" 1 . (See p. xxxvii.) For other elements the electrochemical equivalent = (atomic weight divided by change oi valency) times 1/96494 g/sec/amp. or g/coulomb. The equivalent for iodine has been determined at the Bureau of Standards as 0.0013150 For a unit change of valency for the diatomic gases Brs, Cb, Fz, Hj, Nz and Oz there are required 8.619 coulombs/cm 3 o C, 76 cm (0.1160 cm 3 /coulomb) 2.394 ampere-hours//, o C, 76 cm (0.4177 //ampere-hour). NOTE. The change of valency for Oa is usually 2, etc. SMITHSONIAN TABLES. 346 TABLES 417, 418. CONDUCTIVITY OF ELECTROLYTIC 'SOLUTIONS. This subject has occupied the attention of a considerable number of eminent workers in molecular physics, and a few results are here tabulated. It has seemed better to confine the examples to the work of one experimenter, and the tables are quoted from a paper by F. Kohl- rausch,* who has been one of the most reliable and successful workers in this field. The study of electrolytic conductivity, especially in the case of very dilute solutions, has fur- nished material for generalizations, which may to some extent help in the formation of a sound theory of the mechanism of such conduction. If the solutions are made such that per unit volume of the solvent medium there are contained amounts of the salt proportional to its electro- chemical equivalent, some simple relations become apparent. The solutions used by Kohlrausch were therefore made by taking numbers of grams of the pure salts proportional to their elec- trochemical equivalent, and using a liter of water as the standard of quantity of the solvent. Tak- ing the electrochemical equivalent number as the chemical equivalent or atomic weight divided by the valence, and using this number of grams to the liter of water, we get what is called the normal or gram molecule per liter solution. In the table, m is 'used to represent the number of gram^ molecules to the liter of water in the solution for which the conductivities are tabulated. The conductivities were obtained by measuring the resistance of a cell filled with the solution by means of a Wheatstone bridge alternating current and telephone arrangement. The results are for 18 C., and relative to mercury at o C., the cell having been standardized by filling with mercury and measuring the resistance. They are supposed to be accurate to within one per cent of the true value. The tabular numbers were obtained from the measurements in the following manner : Let KI 8 = conductivity of the solution at 18 C. relative to mercury at o C. A7 8 = conductivity of the solvent water at 18 C. relative to mercury at o C. Then K^ J^ = k 1(t = conductivity of the electrolyte in the solution measured. - = ^ = conductivity of the electrolyte in the solution per molecule, or the " specific 0V molecular conductivity." TABLE 417. Value of A- IH for a few Electrolytes. This short table illustrates the apparent law that the conductivity in very dilute solutions is proportional to the amount of salt dissolved. l KC1 NaCl AgN0 3 KC 2 H 3 2 K 2 S0 4 MgS0 4 0.0000 1 1.2*6 I.O24 1.080 0-939 T - 2 75 1.056 O.OOOO2 2.434 2.056 2.146 1.886 2-532 2.104 0.00006 7.272 6.162 6.462 5.610 7-5 2 4 6.216 O.OOOI 12.09 10.29 10.78 9-34 12.49 10.34 TABLE 418. Electro-Chemical Equivalents and Normal Solutions. The following table of the electro-chemical equivalent numbers and the densities of approximately normal solutions of the salts quoted in Table 419 may be convenient. They represent grams per cubic centimeter of the solution at the temperature given. Salt dissolved. Grams per liter. m Temp. C. Density. Salt dissolved. Grams per liter. m Temp. Density. KC1 . 74-59 I.O 15.2 1-0457 K 2 S0 4 87.16 I.O 18.9 1.0658 NH 4 C1 . . NaCl . . . 53-55 58.50 I.OOO9 I.O 18.6 18.4 1.0152 .0391 |Li 2 SO 4 . 71.09 55-09 I.OOO3 1.0007 18.6 18.6 1. 0602 1.0445 LiCl . . . 42.48 I.O 18.4 .0227 |MgSO 4 . 60.17 1.0023 18.6 1-0573 iBaCl 2 . . 104.0 I.O 1 8.6 .0888 ^ZnSO 4 80.58 I.O 5-3 1.0794 |ZnCl 2 . . KI. . . . 68.0 165.9 I.OI2 I.O 15.0 1 8.6 .0592 .1183 CuS0 4 . 79-9 69.17 I.OOI 1. 0006 18.3 1.0776 1.0576 KNO 8 . . 101.17 I.O 1 8.6 .0001 ^NagCOs . 53-04 I.O 17.9 1.0517 NaNO 8 . . 85.08 I.O 18.7 1.0542 KOH . . 56.27 1.0025 1 8.8 1.0477 AgNO 8 . . 169.9 65.28 I.O HC1 . . HN0 8 . . 36-51 63-13 1.0041 1.0014 18.6 18.6 I.Ol6l 1.0318 KCTOj, 61.29 -5 18.3 1.0367 iH 2 S0 4 . 49.06 1. 0006 18.9 1.0300 KC 2 H 8 O 2 . 98.18 1.0005 1 8.6 1 .0467 SMITHSONIAN TABLE*. * " Wied. Ann." vol. 26, pp. 161-226, 1885. TABLE 419. 347 SPECIFIC MOLECULAR CONDUCTIVITY /x : MERCURY = 1O 8 . Salt dissolved. w 10 5 3 I 0.5 O.I .05 .03 .01 K 2 S0 4 . . _ _ _ _ 672 736 897 959 1098 KC1 827 919 958 1047 1083 1107 "47 KI . ... 7/0 900 968 997 1069 IIO2 1123 1161 NH 4 C1 . - 752 825 907 948 1035 1078 IIOI 1142 KNO 3 . 572 752 839 983 1037 1067 1122 |BaCl 2 . - - 487 658 725 86 1 904 939 IOO6 KC1O 3 . 799 927 (976) 1006 I0 53 ^BaN 2 Oe 531 755 828 (870) 95 1 |CuS0 4 . AgN0 8 . . . - 35i 150 448 2 4 I 635 288 728 424 886 479 936 (966! 675 1017 ZnSO 4 . - 82 I 4 6 249 302 43 i 500 51:6 685 j;MgS0 4 . - 82 270 330 474 532 587 715 vNa 2 SO 4 . . - i - 475 559 734 784 828 906 NaCl 2 ! .' ! 60 180 398 280 528 $ 757 865 817 897 (920) 9'5 962 NaNO 3 . KC 2 H 3 2 3 240 381 617 594 694 671 817 784 855 820 841 879 I |Na 2 C0 3 660 1270 2|4 1560 427 1820 1899 682 2084 2343 799 2515 899 2855 C 2 H 4 O . o-5 2.6 5-2 12 19 43 62 79 132 HC1 ... 600 1420 2010 2780 3 OI 7 3244 3330 3369 34i6 HNO 3 . 610 1470 2O7O 2770 2991 3225 3289 33 2 8 3395 1H 3 P0 4 . . . KOH . 148 423 160 990 170 2OO I7l8 250 1841 43 1986 540 2045 620 2078 790 2124 NH 3 2.4 3-3 8.4 12 31 43 50 92 Salt dissolved. .006 .002 .001 .0006 .0002 .0001 .00006 .00002 .00001 iK 2 S0 4 . 1130 n8r 1207 1220 1241 1249 1254 1266 1275 KC1 ". . '. 1162 1185 "93 "99 1209 1209 1212 I2I 7 1216 KI . 1176 "97 1203 1209 1214 1216 1216 1216 1207 NH 4 C1 . "57 1180 1190 "97 I2O4 I2O9 1215 1209 1205 KN0 3 . 1140 "73 1180 1190 "99 I2O7 I22O 1198 1215 |BaCl 2 . 1031 1074 1092 IIO2 1118 1126 "33 "44 1142 KClOg . 1068 1091 IIOI IIO9 1119 1122 1126 "35 1141 ^BaN 2 O 982 1033 1054 1066 1084 1096 IIOO 1114 1114 |CuS0 4 . 740 873 95 987 1039 1062 1074 1084 1086 AgN0 3 . I0 33 1068 1069 1077 1078 1077 1073 1080 !nSO 4 744 861 919 953 IOOI 1023 1032 1047 1060 ^IgSO 4 . 773 88 1 935 967 1015 1034 1036 1052 1056 ^a 2 SO 4 933 980 998 1009 1026 1034 1038 1056 1054 aCl 2 '. 939 976 979 998 994 1008 1004 1014 1020 1018 IO29 1029 1031 1027 1033 1028 1036 1024 NaN0 3 . 921 942 952 956 966 975 970 972 975 KC 2 H 3 O 2 891 913 919 923 933 934 935 943 *Na 2 CO 3 956 1010 1037 1046 988 874 790 715 697* |H 2 S0 4 . 3001 3240 3316 3342 3280 3"8 2927 2077 M'3* C 2 H 4 . 170 283 380 470 796 995 "33 1304* HC1 3438 3455 3455 3440 3340 3 i 7 o 2968 2057 1254* HN0 3 . 342i 858 3448 945 968 3408 977 3285 920 3088 837 2863 746 1904 497 "44* 402* ko 8 H 4 .' .' ! 2141 2140 2110 2074 1892 1689 M74 845 747* NH 3 116 190 260 330 500 610 690 700 560* * Acids and alkaline salts show peculiar irregularities. SMITHSONIAN TABLES. 34-8 TABLES 420, 421. LIMITING VALUES OF JJL. TEMPERATURE COEFFICIENTS. TABLE 420.- Limiting Values of p. This table shows limiting values of /* =: .10* for infinite dilution for neutral salts, calculated from Table 271. Salt. P Salt. pi Salt. M Salt. M iK 2 S0 4 . 1280 |BaCl 2 . 1150 iMgS0 4 . 1080 iH 2 S0 4 . 3700 KC1 . . . 1220 iKClO 8 . 1150 iNa 2 SO 4 . 1060 HC1 . . 3500 KI . . . I22O BaN 2 6 . 1 1 20 iZnCl . . 1040 HNO 3 . . 35 NH 4 C1 . . I2IO iCuSO 4 . IIOO NaCl . . 1030 H 3 P0 4 . IIOO KN0 8 . . I2IO AgNO 3 . 1090 NaN0 8 . 980 KOH , . 2200 - - iZnSO 4 . 1080 K 2 C 2 H 8 O 2 940 iNa 2 CO 8 . I4OO If the quantities in Table 420 be represented by curves, it appears that the values of the specific molecular conductivities tend toward a limiting value as the solution is made more and more dilute. Although these values are of the same order of magnitude, they are not equal, but depend on the nature of both the ions forming the electrolyte. When the numbers in Table 421 are multiplied by Hittorf's constant, or o.oooii, quan- tities ranging between 0.14 and o.io are obtained which represent the velocities in milli- metres per second of the ions when the electromotive force gradient is one volt per millimetre. Specific molecular conductivities in general become less as the concentration is in- creased, which may be due to mutual interference. The decrease is not the same for different salts, but becomes much more rapid in salts of high valence. Salts having acid or alkaline reactions show marked differences. They have small specific molecular conductivity in very dilute solutions, but as the concentration is in- creased the conductivity rises, reaches a maximum and again falls off. Kohlrausch does not believe that this can be explained by impurities. H3PO 4 in dilute solution seems to approach a monobasic acid, while H 2 SO 4 shows two maxima, and like HsPO 4 approaches in very weak solution to a monobasic acid. Kohlrausch concludes that the law of independent migration of the ions in media like water is sustained. TABLE 421. -Temperature Coefficients. The temperature coefficient in general diminishes with dilution, and for very dilute solutions appears to approach a common value. The following table gives the temperature coefficient for solutions containing o.oi gram mole- cule of the salt. Salt. Temp. Coeff. Salt. Temp. Coeff. Salt. Temp. Coeff. Salt. Temp. Coeff. KC1 . . . O.O22I KI . . . 0.0219 iK 2 S0 4 . 0.0223 1K 2 C0 8 . . 0.0249 NH 4 C1 . . NaCl . . LiCl. . . *BaCl 2 . . |ZnCl 2 . . *M g Cl 2 . 0.0226 0.0238 0.0232 0.0234 0.0239 O.O24I KN0 8 . . NaNO 8 . . AgN0 8 . . |Ba(NO a ) 2 KC1O 3 . . KC 2 H 8 O 2 . 0.0216 0.0226 0.0221 0.0224 O.O2I9 0.0229 !Na 2 S0 4 . iLi 2 S0 4 . iMgS0 4 . IZnSOs iCuS0 4 . 0.0240 0.0242 0.0236 0.0234 0.0229 4Na 2 CO 3 . . 0.0265 KOH . , HC1 . . . HNO 8 . . . *H 2 S0 4 . . 0.0194 0.0159 0.0162 0.0125 *H 2 S0 4 ) for m = .001 f 0.0159 SMITHSONIAN TABLES. TABLE 422, 349 THE EQUIVALENT CONDUCTIVITY OF SALTS, ACIDS AND BASES IN AQUEOUS SOLUTIONS. In the following table the equivalent conductance is expressed in reciprocal ohms. The con- centration is expressed in milli-equivalents of solute per litre of solution at the temperature to which the conductance refers. (In the cases of potassium hydrogen sulphate and phosphoric acid the concentration is expressed in milli-formula-weights of solute, KHS( ) 4 or I I :! l'( ) 4 , per liter of solu- tion, and the values are correspondingly the modal, or "formal," conductances.) Except in the cases of the strong acids the conductance of the water was subtracted, and for sodium acetate, ammonium acetate and ammonium chloride the values have been corrected for the hydrolysis of the salts. The atomic weights used were those of the International Commission for 1905, referred to oxygen as 16.00. Temperatures are on the hydrogen gas scale. Concentration in gram equivalents, looo liter reciprocal ohms per centimeter cube Equivalent conductance in : ; gram equivalents per cubic centimeter Substance. Concen- 1 tration. 1 Equivalent conductance at the following C temperatures. 18 25 50 75 100 128 156 218 281 306 Potassium chloride . 130.1 (152.1) (232.5) (321-5) 414 (519) 625 825 1005 1 1 20 < 2 126.3 146.4 393 588 779 930 I008 10 122.4 141-5 215.2 295.2 377 470 560 741 874 9IO (4 <( 80 "3-5 342 498 638 723 720 (( ( IOO II2.O 129.0 194-5 264.6 336 415 490 Sodium chloride . . 109.0 - - 362 555 760 970 I080 " " 2 105.6 - 349 534 722 895 955 " " IO 102.0 _ 336 5 11 685 820 860 " " . . 80 935 - - - 301 - 450 500 674 680 " " IOO 92.0 - 296 442 Silver nitrate . . . 115.8 - - - 367 - 570 780 965 1065 " " ... 2 II2.2 - - 353 - 539 727 877 935 < IO 108.0 _ . 337 57 673 790 818 2O I05.I _ _ - 326 - 488 639 < 40 IOI-3 _ _ 312 462 599 680 680 80 96.5 _ - - 294 - 432 552 614 604 " " IOO 94.6 _ 289 Sodium acetate . . 78.1 - - - 285 450 660 - 024 u 2 74-5 268 421 578 801 a a 10 71.2 253 396 542 702 Magnesium sulphate 80 O 63-4 114.1 _ _ 221 426 - 340 690 1080 ^_ 2 94-3 - - 3 02 377 260 10 76.1 - 234 241 '43 U 20 67.5 - 190 195 no " " 40 59-3 - - - 160 - 158 88 " " 80 52.0 ! - - - 136 - '33 75 " " IOO 49.8 - '3 - 126 Ammonium chloride 2OO 152.0 _ _ no (415) _ (fe) (841) _ (1176) 2 126.5 146.5 - - 399 - 601 801 1031 <4 \ I0 122.5 T T Q r 141.7 - 382 ~ 573 758 " 92? 828 Ammonium acetate . i 3 o II5.I (99.8) _ - - (338) - (523) " " 10 9T.7 - 300 456 - . 25 88.2 286 426 From the investigations of Noyes, Melcher, Cooper, Eastman and Kato; Journal of the American Chemical Society, 30, p. 335. 1908- SMITHSONIAN TABLES. 35 TABLE THE EQUIVALENT CONDUCTIVITY OF SALTS, ACIDS AND BASES IN AQUEOUS SOLUTIONS. Substance. C c Equivalent conductance at the following C temperatures. 18 25 50 75 100 128 156 218 281 306 Barium nitrate . . . O 116.9 _ _ 385 _ 600 840 II2O 1300 tt . tt 2 109.7 - 352 536 7i5 828 824 " "... 10 IOI.O 322 481 618 658 615 tt it 40 88.7 - _ - 280 - 412 57 53 448 " "... 80 81.6 - - - 258 - 372 449 430 it it IOO 79.1 249 Potassium sulphate . 132-8 - - - 455 - 715 1065 1460 1725 " 2 124.8 - 402 - 605 806 893 867 " " . . IO 115.7 - - - 365 - 537 672 687 637 ii it 104.2 - - - 455 545 .6- A A% 466 tr>f\ ft it 80 so IOO 97-2 95-o _ . _ _ 286 4*5 402 440 39 Hydrochloric acid . o 379-o - - - 850! - 1085 1265 1380 1424 " " . . 2 373-6 826 - 1048 I2I 7 X 33 2 '337 " " IO 368.1 _ _ 807 - 1016 1168 1226 1162 " " . . 80 353-o - - - 762 - 946 1044 1046 862 ii ii IOO 35-6 _ 754 _ 929 1006 Nitric acid .... o 377-o 421.0 570 706 826 945 ! 1047 (1230) - (1380) " . . . . 2 371-2 413.7 559 690 806 919 1012 1166 1156 " .... 10 406.0 548 676 786 893 978 " " 5 353-7 393-3 528 649 750 845 917 " .... IOO 346.4 385.0 516 6 3 2 728 817 880 454* Sulphuric acid ... o 383-0 (429) (590 (746) 891 (1041) 1176 1505 - (2030) "... 2 353-9 390.8 501 561 571 551 536 563 637 "... 10 309.0 337.0 406 435 446 j 460 481 533 "... 50 253-5 273-0 323 35 6 384 i 417 448 502 ' . . . IOO 233-3 251.2 300 336 369 404 435 483 - 474* ( 2 Potassium hydrogen \ sulphate ...}, Phosphoric acid . . i o 455-3 295-5 263.7 338.3 506.0 318.3 283.1 376 661.0 754 374.4 403 329-1 354 510 631 784 422 375 73 773 446 402 754 477 435 93 " " 2 283.1 3 TI -9 401 464 498 508 489 " " ' 10 203.0 222.0 273 ; 3 308 298 2/4 " " . . 50 I 2 7 132.6 157.8 \ 1 68.6 168 158 142 ti IOO 96-5 104.0 122.7 ! 129.9 128 I 120 108 Acetic acid .... (347-0) - - (773)! - (980) ("65) - (1268) " " IO 14.50 - 25-1 - 22.2 14.7 if it 3 8.50 14.7 1 - 13.0 8-65 tt (i 80 5.22 _ 9-5 ~ 8.00 5-34 it ii IOO 4-67 _ _ _ 8.10! - 4.82 - 1.57 Sodium hydroxide . ., ' 216.5 - - 594 - 835 1060 " ' 2 212. 1 - 814 . . 1 20 205.8 - 559 771 930 it i Barium hydroxide 50 200.6 222 256 389 - 540 - 738 873 (520) 645 (760) 847 ' . . . 2 215 359 4 59 1 ' ... j 10 207 235 342 449 548 664 722 ' . . . 50 Igl.I 215.1 308 399 478 549 i 593 "... IOO iSo.I 204.2 291 373 443 503 i 53i f o Ammonium hydrox-j 10 (238) 9-66 (271) (404) (526) (647) - 23.2 (764) (908) 22.3 (1141) 15.6 (1406) ide . . 1 IO c 66 mm 17 6 IOO 3 .io 3-62 5-35 6.70, 1 j.U 7-47 - 7.17 4.82 - i-33 * These values are at the concentration 80.0. SMITHSONIAN TABLES. TABLE 423. 351 THE EQUIVALENT CONDUCTIVITY OF SOME ADDITIONAL SALTS IN AQUEOUS SOLUTION. Conditions similar to those of the preceding table except that the atomic weights for 1908 were used. Substance. Concen- Equivalent conductance at the following C temperature. tration. 18 *5 5 75 100 .280 i 5 6P Potassium nitrate . . . 80.8 126.3 I45- 1 219 299 384 485 580 . 2 78.6 122.5 140.7 212.7 289.9 370.3 460.7 55 1 Potassium oxalate . . . 12.5 5 IOO 75-3 70.7 67.2 79-4 II7.2 109.7 104.5 134-9 126.3 120.3 M7.5 202.9 189.5 180.2 230 276.4 257-4 244.1 322 351.5 326.1 308.5 419 435-4 402.9 379-5 520.4 476.1 447-3 653 . . . 2 74-9 119.9 139.2 215.9 300.2 389.3 489.1 587 . I2. 5 69.3 1 1 1. 1 129.2 199.1 275-1 354.1 438.8 . . . 50 63 101 116.5 178.6 244.9 312.2 383-8 449-5 . IOO 59-3 94.6 109.5 167 227.5 288.9 353-2 4097 Calcium nitrate . . . 200 O 55-8 70.4 II2.7 102.3 130.6 '55 202 210.9 282 265.1 369 321.9 474 372.1 575 .' '. ! 2 I2. 5 5 66.5 61.6 55-6 I07.I H4.J IO2.6 191.9 176.2 157.2 266.7 244 216.2 346.5 314.6 276.8 438.4 394-5 343 529.8 473-7 405.1 . IOO 51-9 82.6 95.8 146.1 199.9 255-5 3'S-i 369-1 Potassium ferrocyanide . 2OO 48.3 98.4 76.7 159.6 88.8 185-5 2^' 4 184.7 403 234.4 527 288 334-7 it if "5 91.6 171.1 " " 2. 84.8 137 158.9 243.8 335.2 427.6 . I2 -5 71 II3-4 131.6 2OO.3 271 340 a 50 58.2 93-7 108.6 163.3 219.5 272.4 . IOO 53 84.9 98.4 I48.I 198.1 245 " 200 48.8 77-8 90.1 '35-7 180.6 222.3 . 400 45-4 72.1 83.3 124.8 1657 203.1 Barium ferrocyanide . . Calcium ferrocyanide . O 2 I2. 5 O 46.9 150 4^.8 146 176 86.2 56.5 171 277 127.5 83.1 271 393 166.2 107 386 521 202.3 129.8 512 " " 2 47.1 75.5 86.2 130 . I2 -5 31.2 49-9 57-4 " 24.1 38.5 44-4 64.6 81.9 " .* ; IOO 2OO 21.0 2O.6 35-1 32-9 40.2 37-8 58.4 55 m 84.3 77-5 u 4OO 20.2 32-2 54 67.5 76.2 Potassium citrate . . . 76.4 124.6 144-5 228 320 420 " ... o-5 1 20. i n 2 5 67.6 "5-4 109.9 134.5 128.2 2IO.I 198.7 293.8 276.5 381-2 357-2 " "... I2 -5 62.9 101.8 118.7 183.6 254.2 326 " ... 50 54-4 87.8 1 02. i 157-5 215-5 273 " ... IOO 50.2 80.8 93-9 143-7 196.5 247-5 " "... 300 43-5 69.8 I2 3-5 167 209.5 Lanthanum nitrate . . O 122.7 142.6 223 3*3 534 651 " " . . 2 68.9 1 1 0.8 128.9 200.5 279.8 363-5 549 " I2 -5 61.4 98.5 114.4 176.7 243-4 311.2 353.4 447-8 " " 5 54 86.1 99-7 '5 2 -5 207.6 261.4 3I5-8 357-7 it IOO 200 49.9 46 79-4 72.1 91.8 83-5 139-5 126.4 189.1 170.2 236.7 210.8 282.5 249.6 316.3 276.2 From the investigations of Noyes and Johnston, Journal of the American Chemical Society, 31, p. 287, 1909. SMITHSONIAN TABLES. 35 2 TABLES 424, 425. CONDUCTANCE OF IONS. - HYDROLYSIS OF AMMONIUM ACETATE. TABLE 424. -The Equivalent Conductance of the Separate Ions. Ion. 18 25 50 75 100 128 156 K. . 4O 4 646 74. c lie I CQ 206 263 -117 Na 40.4 26 47. c 50.9 82 116 155 203 249 NH 4 40. 2 64. S 74. c 115 159 207 26^ 319 Ac -12 Q C4.-2 03.5 IOI 143 1 88 24? 299 Ba . . . 77 55 2 65 1 04 149 200 767 122 *Ca 10 Si' 66 08 142 191 252 312 Jla TC 61 72 119 173 2^C, 312 388 Cl 4I.I 65.5 7C.C, 116 160 207 264 3l8 NO 8 4O.4 61.7 70.6 104 140 178 222 263 C 2 H 8 2 .... SO 4 20.3 41 34-6 68 2 40.8 70 6 7 I2C. 96 177 I 3 274 171 7Q-? 211 77O *C 2 4 |C 6 H 6 7 .... }Fe(CN) 6 .... H 39 36 58 240 63 2 60 95 ?I4 73 70 in 5 CQ s "3 i73 465 u '63 161 244 565 213 214 3 2I 644 275 722 336 777 OH . . IOC 172 102 o"> 204 j^j 760 4-10 C2C CQ2 From Johnson, Journ. Amer. Chem. Soc., 31, p. 1010, 1909. TABLE 425. Hydrolysis of Ammonium Acetate and lonlzatlon of Water. Temperature. Percentage hydrolysis. lonization constant of water. Hydrogen-ion concen- tration in pure water. Equivalents per liter. t I00 h K w Xio" C H Xio' - 0.089 0.30 18 (0-35) 0.46 0.68 25 - 0.82 0.91 IOO 4.8 48. 6.9 156 18.6 223. 14.9 218 52-7 461. 21.5 306 9i-5 168. 13.0 Noyes, Kato, Kanolt, Sosman, No. 63 Publ. Carnegie Inst., Washington. SMITHSONIAN TABLES. TABLES 426, 427. 353 DIELECTRIC STRENGTH. TABLE 426. Steady Potential Difference in Volts required to produce a Spark In Air with Ball Electrodes. Spark length, cm. J? = o. Points. /e = o.25 cm. /? = o. 5 cm. K=i cm. R = 2 cm. R 3 cm. *-. Plates. O.O2 _ _ 1560 1530 0.04 - - 2460 2430 2340 0.06 - 33 3240 3060 0.08 4050 3990 3810 O.I O.2 3720 4680 5010 8610 4740 8490 4560 8490 4560 8370 4500 7770 4350 7590 o-3 S3 10 III4O 11460 11340 III90 10560 10650 0.4 0.5 0.6 5970 6300 6840 14040 IS990 17130 14310 16950 19740 14340 17220 20070 14250 16650 20070 13140 16470 19380 16320 I9IIO 0.8 8070 18960 23790 24780 25830 26220 24960 I.O 8670 20670 26190 27810 29850 32760 30840 i-5 9960 22770 29970 37260 2.0 10140 2 t57 33060 45480 3- 11250 28380 4.0 I22IO 29580 5.0 13050 Based on the results of Bailie, Bichat-Blondot, Freyburg, Liebig, Macfarlane, Orgler, Paschen, Quincke, de la Rue, Wolff. For spark lengths from i to 200 wave-lengths of sodium light, see Earhart, Phys. Rev. 15, p. 163; Hobbs, Phil. Mag. 10, p. 607, 1905. TABLE 427, Alternating Current Potentials required to produce a Spark in Air with various Ball Elec- trodes. The potentials given are the maxima of the alternating waves used. Frequency, 33 cycles per second. Spark length. cm. K=i cm. R = i .92 ... .- R =10 ,- 0.08 3770 .10 4400 4380 433 4290 4245 4230 IS 5990 5940 5790 5800 57o .20 75 10 7440 734 7250 7320 733 25 9045 8970 8850 8710 8760 8760 0.30 10480 10400 10270 10130 IOl8o 10150 35 11980 11890 11670 11570 Il6lO 11590 .40 13360 13300 13100 12930 12980 12970 45 14770 14700 14400 14290 I 433 14320 50 16140 16070 15890 15640 15690 15690 0.6 18700 18730 18550 18300 18350 18400 7 21 35 21380 21140 20980 20990 2IOOO .8 0.9 23820 26190 24070 26640 23740 26400 23490 26130 23540 26110 23550 26090 I.O 28380 29170 28950 28770 28680 28610 1.2 1.4 32400 34100 38850 33790 38850 38580 33640 38620 33620 3580 1.6 38750 43400 43570 43250 43520 1.8 40900 - 48300 47900 2.0 42950 52400 Based upon the results of Kawalski, Phil. Mag. 18, p. 699, 1909. SMITHSONIAN TABLES. 354 TABLES 428. 429. DIELECTRIC STRENGTH. TABLE 428. Potential Necessary to produce a Spark In Air between more widely Separated Electrodes. I, Steady potentials. t < c i Steady potentials. S Ball electrodes. Cup electrodes. .c to c (/. 3 Ball electrodes. JJ s li ^ if Projection. EL C/3 2 s R=i cm. R-=2.scm. & 3 c R.= i cm. R=2.scm. 4.5 mm. i. 5 mm. -3 _ _ _ _ II280 6.0 61000 _ 86830 o-5 _ 17610 17620 - 17420 7.0 - 52000 0.7 - - 23050 - 22950 8.0 67000 52400 9O2OO I.O 1.2 I2OOO 30240 33800 31390 36810 31400 31260 36700 IO.O 12.0 73000 82600 74300 9 ! 93 933oo !-5 37930 443 10 - 445 10 14.0 92000 94400 2.0 292OO 42320 56000 56500 56530 I 5 .0 94700 2-5 3-o 40000 45000 46710 65180 71200 80400 68720 81140 1 6.0 2O.O IOIOOO 119000 ~ IOIOOO 3-5 753 92400 25.0 140600 4.0 48500 49100 78600 IOI700 103800 30.0 165700 4-5 81540 114600 35-o 190900 S-o 56500 50310 83800 - 126500 5-5 135700 This table for longer spark lengths contains the results of Voege, Ann. der Phys. 14, 1904, using alternating current it" electrodes, and the results with steady potential found in the recent very careful work of C. Miit- and "dull point ler, Ann. d. Phys. 28, p. 585, 1909. The specially constructed elec- trodes lor the columns headed " cup electrodes " had the form of a projecting knob 3 cm. in diame- ter and having a height of 4.5 mm. and 1.5 mm. respectively, attached to the plane face of the electrodes. These electrodes give a very satis- ?en the voltage iroughout the range studied. <3cm.> V ihese electrodes give a very s J factory linear relation between I spark lengths and the volt ' throughout the range studied. TABLE 429, - Effect of the Pressure of the Gas on the Dielectric Strength. Voltages are given for different spark lengths /. Pressure, cm. Hg. 7=0.04 /=o.o6 7=o.o8 7=0.10 7=0.20 l=o 30 7=0.40 7=0.50 2 _ _ _ _ 744 939 IIIO 1266 4 - 483 567 648 1015 '35 1645 J 9i5 6 582 690 795 1290 1740 2140 2 55 10 771 933 1090 1840 245 3015 358o 15 - IO6O 1280 1490 2460 3300 4080 4850 2 5 IIIO 1420 1725 2040 35o 4800 6000 7120 35 45 1375 1640 1820 2150 222O 2660 2615 3120 455 5475 .6270 7650 7870 9620 9340 11420 55 1820 2420 3025 36*0 6375 8950 11290 '3455 65 2040 2720 3400 4060 7245 I02IO 12950 15470 75 2255 3035 3805 4565 8200 II570 14650 1745 This table is based upon the results of Orgler, 1899. See this paper for work on other gases (or Landolt-Bornstein- Meyerhoffer). For long spark lengths in various gases see Voege, Electrotechn. Z. 28, 1907. For dielectric strength of air and CO 2 in cylindrical air condensers, see Wien, Ann. d. Phys. 29, p. 679, 1909. SMITHSONIAN TABLES, TABLES 430, 431. DIELECTRIC STRENGTH. TABLE 430. Dielectric Strength of Materials. Potential necessary for puncture expressed in kilovolts per centimeter thickness of the dielectric. Substance. Kilovolts per cm, Substance. l 2* * Substance. Kilovolts per cm. Ebonite .... 300-1100 Oils : Thickness. Papers : Empire cloth . . 80-300 Castor 0.2 mm. 190 Beeswaxed . . 770 paper . . Fibre . 45 20 I.O " Cottonseed 130 *7O Blotting . . . ISO Fuller board . . 200-300 Lard 0.2 " / U 140 iVl 3.11 1 1 1 3 . . . Paraffined . . 2 S 500 Glass Granite (fused) 300-1500 90 1.0 " Linseed, raw 0.2 " 40 '85 Varnished . . Paraffine : 100-250 Guttapercha . . . 80-200 I.O " 9 Melted . . . 75 Impregnated jute . 20 boiled 0.2 190 Melt, point. Leatheroid . . . Linen, varnished . 30-60 100-200 " I.O " Lubricating 80 5 Solid 43 47 350 400 Liquid air ... 40-90 Neatsfoot 0.2 " 200 52 230 Mica : Thickness. 1.0 " 9 70 450 Madras o.i mm. 1600 Olive 0.2 " 170 Presspaper . . . 45-75 1.0 " 300 I.O " 75 Rubber .... 160-500 Bengal o.i " 22OO Paraffin 0.2 " 215 Vaseline. . . . 90-130 1.0 " 700 1.0 " 160 Thickness. Canada o.i " 1500 Sperm, mineral 0.2 " 1 80 Xylenc 0.2 mm. 140 " 1.0 " 500 1.0 " 85 1.0 " 80 South America . I5OO " natural 0.2 " '95 Micanite . . . 400 I.O " 90 Turpentine 0.2 " 160 1.0 " no TABLE 431. Potentials in Volts to Produce a Spark In Kerosene. Electrodes Balls of Diam. d. Spark length. mm. 0.5 cm. i cm. 2 cm. 3 cm. 0.1 3800 3400 2750 2200 .2 7500 6450 4800 3500 3 10250 9450 7450 4600 4 11750 10750 9100 5600 i I305 14000 12400 !355 IIOOO 12250 8250 .8 15500 15100 13850 10450 I.O 16750 16400 15250 12350 Determinations of the dielectric strength of the same substance by different observers do not agree well For a dis- cussion of the sources of error see Mos'cicki, Electrotechn. Z. 25, 1904. For more detailed information on the dependence of the sparking distance in oils as a function of the nature of the electrodes, see Edmondson, Phys. Review 6, p. 65, 1898. SMITHSONIAN TABLES. 356 TABLES 432, 433. DIELECTRIC CONSTANTS. TABLE 432. - Dielectric Constant (Specific Inductive Capacity) of Gases. Atmospheric Pressure. Wave-lengths of the measuring current greater than 10000 cm. Gas. Temp. c Dielectric constant referred to Authority. Vacuum=i Air=i Air M 20 100 o o ICO o o o 145 1.000590 1.000586 1.00718 1.00290 1.00239 1.000946 1.000985 I.000600 1.000695 I.OOI3I 1.00146 1.00258 1.000264 1 .000264 1.000944 1.000953 I.OOII6 1.00099 1.00993 1.00905 1.00705 I.OOOOOO I.OOOOOO 1 .00659 1.00231 1.00180 1.000356 1.000399 I.OOOIOO 1.000109 1.00072 1.00087 1.00199 0.999674 0.999678 1.000354 1.000367 1.00057 1.00041 1.00934 1.00846 1 .00646 Boltzmann, 1875. KlemenCiC, 1885. Badeker, 1901. KlemenCic". Badeker. Boltzmann. KlemenCic". Boltzmann. KlemenCiC. Boltzmann. KlemenCic". Badeker. Boltzmann. KlemenclC. Boltzmann. KlemenCiC. Boltzmann. KlemenCiC. Badeker. KlemenCic'. Badeker. Ammonia . Carbon bisulphide . . . Carbon dioxide .... Carbon monoxide .... Ethylene Hydrochloric acid . . . Hydrogen Methane Nitrous oxide (N 2 O) . . (4 Sulphur dioxide .... < Water vapor, 4 atmospheres TABLE 433, Variation of the Dielectric Constant with the Temperature. For variation with the pressure see next table. If Z>0 = the dielectric constant at the temperature 6 C., Dt at the tempera- ture / C., and a and are quantities given in the following table, then D 9 = Dt [i a(/ 0) + 0(/ The temperature coefficients are due to Badeker. Gas. a /3 Range of temp. C. Ammonia . . 5-45 X io- 2.59 X icr 7 10 no Sulphur dioxide 6.19 X lo- 6 i. 86XIQ-7 IIO Water vapor . 1.4X10-* - US The dielectric constant of air at atmospheric pressure but with varying tem- perature may also be calculated from the fact that D i is approximately pro- portional to the density. SMITHSONIAN TABLES. TABLES 434, 435, DIELECTRIC CONSTANTS (continued). TABLE 434. Change of the Dielectric Constant of Oases with the Pressure. 357 Gas. Temper- ature, C. Pressure atmos. Dielectric constant. Authority. Air 19 II 15 15 2O 40 60 80 IOO 2O 60 so IOO 120 I4O 160 180 10 20 40 IO 20 40 I.OIOS 1.0218 1.0330 1.0439 1.0548 I.OIOI 1.0196 1.0294 1.0387 1.0482 1-0579 1.0674 1.0760 1.0845 1.008 1.020 1. 060 I.OIO 1.025 1.070 Tangl, 1907. Occhialini, 1905. it < Unde, 1895. H , a ;; M M It Carbon dioxide . . Nitrous oxide, NgO TABLE 435. Dielectric Constants of Liquids. A wave-length greater than 10000 centimeters is denoted by oo . Substance . Temp. Wave- length, cm. Dielectric constant. o . Substance. Temp. Wave- length, cm. Dielectric constant. j* Alcohol : Alcohol : Amyl . . . frozen 00 2.4 I Methyl . . 50 00 45-3 ' ... IOO " 30.1 I " . . o " 35- ' ... 50 " 23.0 I "... + 20 " 31.2 ' ... O " 17.4 I "... 17 75 33-2 , + 20 18 200 1 6.0 10.8 I 2 Propyl . . 120 60 oo 46.2 33-7 ' ... 18 73 4-7 2 "... O " 24.8 Ethyl . . . frozen oo 2.7 "... + 20 " 22.2 " ... 1 2O 1C 54.6 "... 15 75 12.7 2 " ... 80 " 44-3 Acetone . . . 80 00 33-8 5 it 40 35-3 28.4 " '.'.', O 15 I2OO 2O.6 ' 21.85 1 (i +20 17 200 25.8 24.4 2 Acetic acid 17 18 73 00 20.7 97 I " ... 75 23.0 2 " " . . '5 I2OO 10.3 6 M " 53 2O.6 3 " " 17 2OO 7.07 2 tt 4 8.8 3 " " 19 75 6.29 2 f* 0.4 5-0 4 Amyl acetate . 00 4.81 9 Methyl' .' .' frozen IOO 00 58.0 i Amylene . . 2. 2O 10 References on page 358. SMITHSONIAN TABLES. TABLE 435 (continued}. DIELECTRIC CONSTANTS OF LIQUIDS. A wave-length greater than 10000 centimeters is designated by oo Substance. Temp. Wave- length cm. Diel. const. ~ >, Substance. Temp. Wave- length cm. Diel. const. "5 >* !a.~ (frozen) Aniline .... 18 00 7-3 l6 || Nitrobenzol . . . 10 00 9-9 I Benzol (benzene) . 18 " 2.288 " . -5 " 42.0 " " " 19 73 2.26 2 . o " 41.0 " Bromine .... 2 3 84 3.18 12 . +*s " 37-8 " Carbon bisulphide 20 17 oo 73 2.626 2.64 13 2 . . . 30 18 y 36.45 II Chloroform . . . 18 00 5-2 II " ... 17 73 34-o 2 " ... 17 73 4-95 2 Octane .... 17 00 1.949 16 Decane .... 14 00 1.97 IO Oils: Decylene . . . 17 2.24 Almond . . . 20 00 2.83 18 Ethyl ether . . 80 00 7-05 5 Castor .... ii 14 4-67 19 ". . . . : 40 5-67 Colza .... 20 " 3- 11 20 4.68 u Cottonseed . . 14 M 3.10 21 (4 18 4.368 ii Lemon .... 21 * 2.25 22 44 41 20 4-30 13 Linseed 13 " 3-35 21 44 4 60 3-65 Neatsfoot . . . - U 3.02 2O " "... 100 3.12 " Olive .... 20 " 3-n 23 44 44 140 M 2.66 " Peanut . . . . ! 11.4 " 3-3 21 44 44 180 44 2.12 < Petroleum . . _ 2OOO 2-13 24 Crit. Petroleum ether 20 oo 1.92 2O 44 44 temp. || . Rape seed . . 16 " 2.85 21 192 1 53 Sesame . . . 134 3.02 M Formic acid . . 44 < Glycerine . . . 18 +2 (frozen) II 15 83 73 1 200 73 1200 4-35 19.0 62.0 58.5 56.2 14 2 6 2 6 Sperm .... Turpentine . . Vaseline . . . Phenol .... Toluene . . . 20 20 Js 4-i6 44 73 00 (I * 17 2.23 2.17 9.68 2-5 1 2.T.T, 20 25 2 5 ** 15 2OO 39.1 2 | V JJ u IQ 73 2.31 2 M X 5 8 7 ? 25-4 I C Meta-xylena . . . 18 00 II ii _ 0.4 2^6 J 4 . . . 17 73 2-37 2 TT T *7 OQ I ICAdilC Hydrogen perox- ) ide 4 6%inH 2 o} I 7 18 oo 75 8 4 .7 i? Water .... for temp, coeff. 18 17 oo 200 81.07 80.6 II 2 see Table 344. 17 74 8l. 7 " 17 38 83.6 i Abegg-Seitz, 1899. 10 Landolt-Jahn, ^892. 18 Hasenohrl, 1896. 2 Drude, 1896. ii Turner, 1900. 19 Arons-Rubens, 1892. 3 Marx, 1898. 12 Schlundt. 20 Hopkinson, 1881. 4 Lampa, 1896. 13 Tangl, 1903. 21 Salvioni, 1888. 5 Abegg, 1897. 14 Coolidge, 1899. 22 Tomaszewski, 1888. 6 Thwing, 1894. 15 v. Lang, 1896. 23 Heinke, 1896. 7 Drude, 1898. 16 Nernst, 1894. 24 Marx. 8 Francke, 1893. J 7 Calvert, 1900. 25 Fuchs. 9 Lowe, i'898. Addenda to Table 440, p. 361, Dielectric Constant of Rochelle Salt: The polarization of the Rochelle salt dielectric in an electric field is somewhat analagous to the behavior of the mag- netization of iron in a magnetic field, showing both saturation and hysteresis. The dielectric constant D depends on the initial and final fields and the hysteresis. Initial field, 765 v/cm.; Final field, 690 v/cm.; Average D (23 C), 40 765 153 205 765 -765 157 o 880 86 The last value may be fair value for ordinary purposes. The electrodes were tinfoil attached with shellac. The fieJd was applied perpendicular to the a axis. Like piezoelectric properties, the dielectric constant varies with different crystals. It depends on the temperature as follows : (field o to 880 v/cm) -70 C, D = 12; - 40 , 14; -20, 48; o, 174 ; +20, 88; +30, 52. (Data from Valesek, University of Minnesota, 1921.) SMITHSONIAN TABLES. TABLES 436, 437. DIELECTRIC CONSTANTS OF LIQUIDS {continued). TABLE 436. Temperature Coefficients of the Formula : 359 Substance. a Temp, range, C. Authority. Amyl acetate . . . Aniline . . . 0.0024 0.00351 O.OO106 0.000966 O.OOO922 0.00410 0.00459 O.OO57 0.00163 0.01067 0.00364 0.000738 O.OOO92 1 0.000977 0.004474 0.004583 0.00436 0.0008l7 0.0000087 O.OOOOOO6O O.OOOOI5 0.000026 0.0000072 O.OOOOOO46 O.OOOOII7 10-40 20-181 22-l8l 0-13 20-181 5-20 0-76 4-2 20-181 Lowe. Katz. Hasenohrl. Rate. Tangl. Ratz. Drude. Hasenohrl. Heinke, 1896. Hasenohrl. Ratz. Tangl. Heerwagen. Drude. Coolidge. Tangl. Benzene Carbon bisulphide . s 3 < j 1 1 Air . . IQI oo ! i.Aio I Nitrous oxide y 75 1.47-1.50 2 N 2 O 88 00 i-93 8 Ammonia . . . 34 75 21-23 3 ii ii 5 " 1.630 5 U 130 16.2 4 ii ii + 5 " i. 57s ii Carbon dioxide . 5 00 i-6o 8 1-583 5 ii ii Oxygen . . . + '5 182 II 1-520 1-491 it 9 ' " 4-iQ II 1-540 " ii " ' 1-465 8 Chlorine . . II 1-526 2.150 " Sulphur dioxide. 14.5 20 1 20 BO 1375 14.0 j . 20 II 2.030 it u .. 40 " 12.5 . II i-97o " ii ii 60 " 10.8 . + 10 " i-94o u ii ii 80 " 9-2 . II 2.08 6 ii ii IOO 4i 7.8 , + 14 IOO 1.88 4 ii ii 1 20 II 6.4 Cyanogen . . Hydrocyanic acid 23 21 84 2.52 about 95 7 Critical. . . . 140 154-2 II 4.8 2.1 Hydrogen sulph. IO CO 5-93 6 U ii 50 i " 4.92 ii . 90 376 i v. Pirani, 1903. 4 Coolidge, 1899. 7 Schlundt 1901. 2 Bahn-Kiebitz, 1904. 5 Linde, 1895. 8 Hasenohrl, 1900. 3 Goodwin-Thompson, 1899. 6 Eversheim, 1904. 9 Fleming-Dewar, 1896. SMITHSONIAN TABLES. 360 TABLES438, 439- DIELECTRIC CONSTANTS (continued). TABLE 438. -Standard Solutions for the Calibration of Apparatus for the Measuring of Dielectric Constants. Turner. Drude. Nernst. Substance. Diel. const, at 1 8. A= oo. Acetone in benzene at 19. A = 75 cm. Ethyl alcohol in water at 19.5. A= oo. Per cent by weight. Density 16. Dielectric constant. Temp, coefficient. 2.288 2.376 4.36' 7.298 10.90 27.71 36.45 81.07 Per cent by weight. Dielectric constant. Meta-xylene .... Ethyl ether .... Aniline Ethyl chloride . . . O-nitro toluene . . Nitrobenzene . . . Water (conduct. lo" 6 ) 20 40 60 80 100 0.885 0.866 0.847 0.830 0.813 0.797 2.26 5.10 8-43 I2.I 1 6.2 20.5 0.1% 0.4 0.6 100 90 80 70 00 26.0 29-3 Water in acetone at 19. A = 75 cm. O 20 40 60 80 100 0-797 0.856 0.903 0.940 0-973 0.999 20.5 31-5 43-5 57-0 70.6 80.9 vo 10 LO vo LO TJ- d d d o d d TABLE 439. -Dielectric Constants of Solids. Substance. Condi- tion. Wave- length, cm. Dielectric constant. 1* Substance. Condi- tion. Wave- length, cm. Dielectric constant. 1* Asphalt . . _ 00 2.68 , Temp. Barium sul- Iodine (cryst.) . 2 3 75 4.00 2 phate . . _ 75 IO.2 2 Lead chloride . Caoutchouc . _ oo 2.22 3 (powder) _ 4 2 2 Diamond . . - " I6. 5 i " nitrate _ u 16 2 " - 75 5-5 2 " sulphate . _ " 28 2 Ebonite . . - oo 2.72 4 " molybde- ii it 2.86 5 nate . . M 24 2 " 1000 2-55 6 Marble Glass * Density. (Carrara) _ 8-3 2 Flint (extra heavy) 4-5 00 9.90 7 Mica .... - 00 u 5.80-6.62 5 15 Flint (very Madras, brown _ ii 2.5-3.4 16 light) . . Hard crown Mirror . . 2.87 2. 4 8 6.61 6.96 6.44-7.46 7 7 5 green ruby . Bengal, yellow - 3-9-5-5 3 16 16 16 . _ " 5-37-5-90 8 " white . M 4.2 16 Lead (Pow- "* 600 5.42-6.20 8 " ruby . Canadian am- i 4-2-4-7 16 ell). . . 3-0-3-5 00 5-4-8-0 9 ber. . . . _ " 3- 16 Jena South America _ 5-9 16 Boron Barium . _ I 5-5-8-1 7.8-8.5 10 TO Ozokerite (raw) Paper (tele- - " 2.21 i Borosili- phone) - u 2.0 17 cate 6.4-7.7 i " (cable) . _ ii 2.0-2.5 i Gutta percha . - - 3-3-4-9 ii Paraffine . . Melting " 2.46 18 Temp. " . point. " 2.32 19 Ice .... -5 I2OO 2.85 12 " . . 44-46 ii 2.IO 20 " .'!.'! 18 190 5000 75 3.16 1.76-1.88 13 " ; ; 54-56 74-76 M ii 2.14 2.l6 20 20 References on p. 361, * For the effect of temperature, see Gray-Dobbie, Pr. Roy. Soc. 63, i8c " waye-length, see K. F. Lowe, Wied. Ann. 66, 1898.' SMITHSONIAN TABLES. 67, 1900. TABLES 439, 440. DIELECTRIC CONSTANTS (continued). TABLE 439. Dielectric Constanta of Solids (continued). 3 6i Substance. Condi- tion. Wave- length, cm. Diel. constant. f Substance. Condi- tion. Wave- length, cm. Did. constant. JU r Paraffine . . 47-6 6l 2.16 21 Sulphur 5 6.2 61 2.25 21 Amorphous - 00 3-98 i Phosphorus: " 75 2 Yellow . . - 75 3-60 2 Cast, fresh _ oo 4.22 I Solid . . . _ 80 4.1 22 < (i u 4-05 IS Liquid . . _ 80 3-85 22 " " _ 75 3-95 2 Porcelain: Cast, old . _ oo 3.60 18 Hard " " _ 75 3-9 2 (Royal B'l'n) - 00 5-73 15 ( near ) Seger " " . - " 6.6 1 '5 Liquid . ) melting- oo 3-42 I Figure " " . II 6.84 15 I point ) Selenium . . _ " 7-44 i Strontium " . . - 75 6.60 2 sulphate _ 75 "-3 2 " | oo 6.13 2 3 Thallium " 1000 6.14 2 3 carbonate _ 75 17 2 Shellac . . . 00 3.10 4 " nitrate . _ 75 16.5 2 " ... _ " 2-95-3-73 24 Wood dried " ... - " 25 ; Red beech . || fibres oo 4.83-2.51 - Amber . . . _ 2.86 18 (i ii Oak . . ! J_ " ii 7-73-3-63 4.22-2.46 : . . . -L " H 6.84-3-64 i v. Pirani, 1903. 10 Lowe, 1898. 18 Fallinger, 1902. 2 Schmidt, 1903. n (submarine-data). 19 Boltzmann, 1875. 3 Gordon, 1879. I2 Thwing, 1894. 20 Zietkowski, 1900. 4 Winklemann, 1889, 13 Abegg, 1897. 21 Hormell, 1902. 5 Elsas, 1891. 14 Behn-Kiebitz, 1904. 22 Schlundt, 1904. 6 Ferry, 1897. 15 Starke, 1897. 23 Vonwiller-Mason, 1907. 7 Hopkinson, 1891. 16 E. Wilson. 24 Wullner, 1887. 8 Arons-Rubens, 1891. 17 Campbell, 1906. 25 Donle. 9 Gray-Dobbie, 1898. TABLE 440. -Dielectric Constants of Crystals. Do, D/3, D-y are the dielectric constants along the brachy, macro and vertical axes respectively. Wave- Diel. const. Wave- Diel. const. O L. 2 , C U * -e x cm. _i_Axis. I Axis. 1* cm. Da DP Dy UNIAXIAL : RHOMBIC : Apatite .... Beryl . . 75 OO 9.50 7.8; 7.40 7 44 2 Aragonite . . . 00 75 9.14 9.80 7-68 6.55 4 I 7.IO 6.O; 7 Barite .... 00 6-97 10.09 7.00 4 M 7C C.C2 I 75 7.6 S I 2. 2O 7.70 i Calcite .... oo 8.49 7 J -S6 4 Celestite . . . 75 7.70 I8. 5 8.30 i Dolomite . . . Iceland spar . . Quartz .... 75 75 oo 8.78 7 .80 8.50 4.38 8.29 6.80 8.00 5.06 4.40 5 i i 4 6 Cerussite . . . MgSO 4 +7lU> K 2 SO 4 .... Rochelle salt* . Sulphur 75 00 n it 6.70 >St 23-2 6.05 5-08 6.92 192 8.28 4.48 8.89 4-77 i 7 7 I , IOOO 4.27 4.74 6 M 3.65 3 85 4.66 7 Ruby (Siam) . . Rutile (TiO 2 ) . . Tourmaline . . . 75 00 "3 '73 6-S4 4 i 4 Topaz .... " colorless . 75 75 3.62 6.65 6.25 3-85 6.70 6.54 4-66 6.30 644 i i 4 " ... 75 6-75 5-65 i Zircon .... 75 12.8 12.6 i See page 358. i Schmidt, 1903. 4 Fallinger, 1902, 1919. 7 Borel, 1893. 2 Starke, 1897. 5 v. Pirani, 1903. 8 Bolztmann, 1875. 3 Curie, 1889. 6 Ferry, 1897. SMITHSONIAN TABLES. 3 2 TABLE 441. WIRELESS TELEGRAPHY. Wave-Length in Meters, Frequency in periods per second, and Oscillation Constant LG in Microhenries and Microfarads. The relation between ihe free wave-length in meters, the frequency in cycles per second, and the capacity-inductance product in microfarads and microhenries are given for circuits between 1000 and 10,000 meters. For values between 100 and 1000 meters, multiply the columns for n by 10 and move the decimal point of the corresponding LC column two places to the left (divid- ing by 100); for values between 10,000 and 100,000, divide the n column by 10 and multiply the LC column by 100. The relation between wave-length and capacity-inductance may be relied upon throughout the table to within one part in 200. Example i : What is the natural wave-length of a circuit containing a capacity of o.ooi micro- farad, and an inductance of 454 microhenries ? The product of the inductance and capacity is 454 X o.ooi =0.454. Find 0.454 under LC ; opposite under meters is 1270 meters, the natural wave-length of the circuit. Example 2 : What capacity must be associated with an inductance of 880 microhenries in order to tune the circuit to 3500 meters ? Find opposite 3500 meters the LC value 3.45 ; divide this by 880, and the quotient, 0.00397, is the desired capacity in microfarads. Example 3 : A condenser has the capacity of 0.004 microfarad. What inductance must be placed in series with this condenser in order that the circuit shall have a wave-length of 600 meters ? From the table, the LC value corresponding to 600 meters is o.ioi. Divide this by 0.004, the capacity of the condenser, and the desired inductance is 25.2 microhenries. Meters. n LC Meters. n LC Meters. n LC 1000 3OO,OOO 0.281 1300 230,800 0.476 1600 187,500 0.721 IOIO 297,000 0.287 1310 229,000 0.483 1610 186,300 0.730 1020 294,100 ! 0.293 1320 227,300 0.490 1620 185,200 0-739 1030 291,300 0.299 '33 225,600 0.498 1630 184,100 0.748 IO4O 288,400 0.305 1340 223,900 0-505 1640 182,900 0.757 IO5O 285,700 0.310 J 350 222,200 0-5*3 1650 181,800 0.766 IO6O 283,600 0.316 1360 220,600 0.521 1660 180,700 0.776 1070 280,400 0.322 1370 218,900 0.529 1670 179,600 0.785 1080 277,800 0.328 1380 217,400 0-536 1680 178,600 0-794 logo 275,200 -335 1390 215,800 0.544 1690 177,500 0.804 IIOO 272,700 0.341 1400 214,300 0.552 1700 176,500 0.813 IIIO 270,300 0-347 1410 212,800 0-559 1710 175,400 0-823 1 120 267,900 -353 1420 2II,3OO 0.567 1720 174,400 0-833 1130 265,500 -359 143 2O9,8OO 0.576 1730 173,400 0.842 1140 263,100 0.366 1440 208,300 0.584 1740 172,400 0.852 1150 260,900 0.372 1450 2O6,9OO 0.592 1750 171,400 0.862 1160 258,600 o-379 1460 205,500 0.600 1760 170,500 0.872 1170 256,400 0.385 1470 2O4,IOO 0.608 1770 169,400 0.882 1180 254,200 0.392 1480 2O2,7OO 0.617 1780 168,500 0.892 1190 252,100 0-399 1490 2OI,3OO 0.625 1790 167,600 0.902 1200 250,000 0.405 1500 200,000 0-633 1800 166,700 0.912 I2IO 247,900 0.412 1510 198,700 0.642 1810 165,700 0.923 I22O 245,900 0.419 1520 197,400 0.650 1820 164,800 o-933 1230 243,900 0.426 1530 196,100 0.659 1830 163,900 0-943 1240 241,900 o-433 1540 194,800 0.668 1840 163,000 o-953 1250 240,000 0.440 J 55o 193,600 0.676 1850 l62,2OO 0.963 1200 238,100 0.447 1560 192,300 0.685 1860 161,300 o-974 1270 236,200 0-454 1570 I9I,IOO 0.694 1870 160,400 0.985 1280 234,400 0.461 1580 189,900 0.703 1880 159,600 -995 I20X) 232,600 0.468 i59o 188,700 0.712 1890 158,700 1. 000 Adapted from table prepared by Greenleaf W. Picard ; copyright by Wireless Specialty Apparatus Company, New jrk. Computed on basis of 300,000 kilometers per second for the velocity of propagation of electromagnetic waves. Yo SMITHSONIAN TABLES. TABLE 441 (concluded). WIRELESS TELEGRAPHY. Wave Length, Frequency and Oscillation Constant. 363 Meters. n LC Meters. n LC Metere. n LC I9OO 157,900 i 1.016 1 2800 IO7,IOO 2.21 7000 42,860 13-8 1910 157,100 1.026 2820 106,400 2.24 7100 42,250 14.2 1920 156,300 1-037 2840 105,600 2.27 7200 41,670 14.6 193 155,400 1.048 2860 104,900 2.30 73 41,100 15.0 I 94 1 54,600 1.059 2880 IO4,2OO 2-33 7400 40,540 15.4 !95 153,800 1.070 2900 103,400 2.37 75 4O,OOO I 5 .8 1960 153,100 I.oSl 2920 IO2,7OO 2.40 7600 39470 16.3 1970 152,300 1.092 2940 102,000 2-43 7700 38,960 16.7 1980 151,500 1.103 2960 101,300 2.47 7800 38,460 17.1 1990 1 50,800 I.1I4 2980 100,700 2.50 7900 37,980 I 7 .6 2OOO 150,000 I.I26 ' 3000 IOO,OOO 2-53 8000 37,5 1 8.0 2020 148,500 1.148 3100 96,770 2.70 8100 37,040 18.5 2040 147,100 I.I7I 3200 93,75 2.88 8200 36,59 18.9 2000 145,600 1.194 33 90,910 3-7 8300 36,140 19.4 2080 144,200 1.218 3400 88,240 3-26 8400 35,7i 19.9 2IOO 142,900 1.241 35 85,910 3-45 8500 35,29 20.7 2120 141,500 1.265 ! 3600 83,330 3-65 8600 34,880 20.8 2140 140,200 1.289 ! 3700 8 1 ,080 3-85 8700 34,480 21.3 2l6o 138,900 I -3 I 3 1 3800 78,950 s 4.06 8800 34,090 21.8 2180 137,600 1-338 39 76,920 4.28 8900 33,71 22. 3 2200 136,400 1.362 4000 75,000 4-5 9000 33,33 22.8 2220 135,100 1-387 4100 73, 1 7 4.73 9100 32,970 23.3 224O 133,900 i 1.412 4200 7i,43 4.96 9200 32,610 23.8 2200 2280 132,700 131,600 1.438 1.463 43 4400 69,770 68.180 5.20 545 93 9400 32,260 24-3 24.9 2300 2320 2340 130,400 129,300 128,200 1.489 '5*5 1.541 45 4600 47 66,670 65,220 63,83 5-7 5.96 6.22 95 9600 9700 3^59 3 I 2 5 3,93 25.4 25-9 26.5 ^T 2360 127,100 1.568 4800 62,500 6.49 9800 30,610 27.0 2380 126,000 1-594 4900 61,220 6.76 9900 3,3 10 27.6 24OO 125,000 1.621 5000 60,000 7.04 10000 30,000 28.1 2420 124,000 1.648 5100 58,820 7-32 2440 129,000 1.676 5200 57,69 7 .6l 2460 121,900 1.703 53 56,600 7-91 2480 121,000 1.731 54 55,560 8.21 2500 120,000 1-759 55 54,55 8.51 2520 119,000 1.787 5600 53,57 0.03 2540 : IlS.IOO 1.816 57 52,630 9.15 2560 117,200 1.845 5600 51,720 947 2580 116,300 1.874 59 50,850 9.81 j 26OO 1 1 5,400 1.903 6000 50,000 IO.I 262O II4,5OO 1.932 6100 49,180 KM 2640 1 1 3,6OO 1.962 6200 48,550 10.8 2660 II2,8OO 1.991 6300 47,620 I I.I 2680 111,900 2.02 6400 46,870 "-5 27OO 111,100 2.05 6500 46,150 11.9 2720 1 10,300 2.08 6600 45,45 12.3 2740 IO9,5OO 2. 1 1 6700 44,780 12.6 2760 108,700 2.14 6800 44,120 13.0 2780 107,900 2.18 6900 43,480 134 2800 107,100 2.21 7000 42,860 13-8 SMITHSONIAN TABLES. ^64 TABLES 442-443. TABLE 442. WIRELESS TELEGRAPHY. Radiation Resistances lor Various Wave-Lengths and Antenna Heights. The radiation theory of Hertz shows that the radiated energy of an oscillator may be repre- sented by E= constant (h'/A 2 ) I 2 , where h is the length of the oscillator, A, the wave-length and I the current at its center. For a flat-top antenna E == 1600 (h 2 / A 2 ) I 2 watts ; 1600 h 2 / A 2 is called the radiation resistance. (h = height to center of capacity of conducting system.) \^= 40 Ft. 60 Ft. 80 Ft. 100 Ft. 120 Ft. 160 Ft. 200 Ft. 300 Ft. 450 Ft. 600 Ft. 1200 Ft. Length A m ohm ohm ohm ohm ohm ohm ohm ohm ohm ohm ohm 200 6.0 134 24.0 37.0 S4-o 95.0 300 2-7 6.0 10.6 I6. 5 23.8 42.4 400 600 a66 34 1.5 6.0 2.7 9-3 4.1 134 6.0 2 3 .8 10.6 I6. 4 374 84.0 149.0 800 o-37 0.84 2 -3 34 6.0 9 .2 21.0 47-o 84.0 1000 I2OO 0.24 0.17 0.54 o-37 H 1.03 2.1 3 i 2.6 6.0 4.1 13-5 9-3 30.0 21.0 54-0 37-o 215.0 149.0 I5OO O.I I 0.24 0.42 0.66 o-9S 1.7 2.6 6.0 134 24.0 95-o 2000 0.13 0.24 0.37 0-54 o> 95 1.5 34 7-5 134 54-0 2500 3OOO 0.15 O.I I 0.24 0.17 o.34 0.24 0.61 0.42 S33 2.2 '5 4.8 34 8.6 6.0 34-0 24.0 4OOO 0.06 0.09 0.13 0.24 0.37 0.84 1.9 34 '34 5OOO 0.24 -53 1.20 2.2 8.6 6000 0.16 0-37 0.84 "5 6.0 7000 O.I 2 O.27 0.61 I.I 44 Austin, Jour. Wash. Acad. of Sci. i, p. 190, 1911. TABLE 443. THE DIELECTRIC PROPERTIES OF NON-CONDUCTORS. Phillips Thomas, J. Franklin Inst. 176, 283, 1913. Results of tests at unit area and unit thickness of dielectric. At 1000 cycles. Mica. Paper. Celluloid. Ice. Max. breakdown volts per cm. i o6Xio 6 O.7IXIO 6 I .O5XIO 6 onXio 6 Specific indue, capacity .... 4.00 4.OO 13.26 8640 Max. absorbable energy, watts-sec/cm 3 0.198 0.108 0.640 .00040 9O-angle of lead o 57' 3-Qi 2 10' 9.84 3 40' 48.3 I3 e 39' 1400 Equiv. resistance ohms/cm 3 Xio 11 . Conductivity per cm. cubeXicr 10 . . 2.56 1.02 0.207 .00722 Percent change in cap. per cycleXio 4 . 2.18 14.31 30.7 70.0 Percent change in resistance per cycle . 0.258 0.146 0.106 0.127 At 15 cycles. Specific inductive capacity .... 4.09 5-77 18.60 429.0 Max. absorbable energy, watt-sec/cm 3 . 0.203 0.126 0.90 O.OO2 Percent change in capacity per cycle . o.oo 0.306 1.74 i-59 On direct current. Conductivity per cm 3 .... 2 42XIO" 17 2.2/XIO- 1 - 7I.5XIO- 14 163. lo- 11 SMITHSONIAN TABLES. TABLE 444. MAGNETIC PROPERTIES. Unit pole is a quantity of magnetism repelling another unit pole with a force of one dyne; 47T lines of force radiate from it. M, pole strength; ^irM lines of force radiate from pole of strength M . H, field strength, = no. of lines of force crossing unit area in normal direction; unit =- gauss one line per unit area. M, magnetic moment, = Ml, where / is length between poles of magnet. /, intensity of magnetization or pole strength per unit area, = M/K = M/A where A is cross section of uniformly magnetized pole face, and V is the volume of the magnet. ^irM/A - 4717 = no. lines of force leaving unit area of pole. /, specific intensity of magnetism, = // p where p = density, g/cm 3 . , magnetic flux, = 4irM + HA for magnet placed in field of strength H (axis parallel to field). Unit, the maxwell. B, flux density (magnetic) induction, = /A = 4?r/ + H; unit the gauss, maxwell per cm. IA, magnetic permeability, = B/H. Strength of field in air-filled solenoid = H = UTT/IO) ni in gausses, * in amperes, w, number of turns per cm length. If iron filled, induction increased, i.e., no. of lines of force per unit area, B, passing through coil is greater than H; fj. = B/H. K, susceptibility; permeability relates to effect of iron core on magnetic field strength of coil; if effect be considered on iron core, which becomes a magnet of pole strength M and intensity of magnetism /, then the ratio I/H = (fj. i)/4 iris the magnetic susceptibility per unit volume and is a measure of the magnetizing effect of a magnetic field on the material placed in the field. fj. = 47TK +1. X, specific susceptibility (per unit mass) = K/p = J/H. X A > atomic susceptibility, = X X (atomic weight) ; XM = molecular susceptibility. / A , / M , similarly atomic and molecular intensity of magnetization. Hysteresis is work done in taking a cm 3 of the magnetic material through a magnetic cycle = flldl = (i/4ir)J*H dB. Steinmetz's empirical' formula gives a close approximation to the hysteresis loss; it is aB 1 ' 6 where B is the max. induction and a is a constant (see Table 472). The retentivity (B r ) is the value of B when the magnetizing force is reduced to zero. The reversed field necessary to reduce the magnetism to zero is called the coercive force (He). Ferromagnetic substances, ju very large, K very large: Fe, Ni, Co, Heusler's alloy (Cu 62.5, Mn 23.5, Al 14. See Stephenson, Phys. Rev. 1910), magnetite and a few alloys of Mn. n for Heusler's alloy, 90 to 100 for B = 2200; for Si sheet steel 350 to 5300. Paramagnetic substances, fJi>i, very small but positive, K = io~ 3 to io~*: oxygen, especially at low temperatures, salts of Fe, Ni, Mn, many metallic elements. (See Table 474.) Diamagnetic substances, jiecimer i gave th e fol- lowing results : 12300 | 67.5 595 1 I 972 1.6 TABLE 465. Magnetite. The following results are given by Du Bois * for a specimen of magnetite. H / [ B M 500 325 8361 I6. 7 IOOO 345 9041 9 .0 2OOO 35 10084 5-o I2OOO 35 20084 i-7 Professor Ewing has investigated the effects of very intense fields on the induction in iron and other metals.t The results show that the intensity of magnetization does not increase much in iron after the field has reached an in- tensity of looo c. g. s. units, the increase of induction above this being almost the same as if the iron were not there, that is to say, dBl dH is practically unity. For hard steels, and particularly manganese steels, much higher forces are required to produce saturation. Hadfield's manganese steel seems to have nearly constant susceptibility up to a magnetizing force of 10,000. The following tables, taken from living's papers, illustrate the effects of strong fields on iron and steel. The results for nickel and cobalt do not differ greatly from those given above. TABLE 466. Lowmoor Wrought Iron. H / B V- 3080 6450 10450 13600 16390 18760 18980 1680 1740 173 1720 1630 1680 173 24130 28300 32250 35200 36810 39900 40730 7.83 4-39 3-09 2-59 2.25 2.13 2.15 TABLE 467. Vlcker's Tool Steel. H / B M 6210 9970 I2I2O 14660 I 553 1530 1570 1550 1610 25480 29650 31620 3455 35820 4-IO 2.97 2.60 2.36 2.31 TABLE 468. -Hadlield's Manganese Steel. 1930 2380 335 5920 6620 7890 8, 10 in 187 191 2620 3430 4400 73 10 8970 10290 11690 14790 1.36 1.44 1.24 1.30 J-39 1.51 TABLE 469. Saturation Valnes for Steels of Different Kinds. i 7 B * I Bessemer steel containing about 0.4 per cent carbon . . Siemens-Marten steel containing about 0.5 per cent carbon 18000 1770 1660 88o 38860 2.16 3 Crucible steel for making chisels, containing about 0.6 per , _ onf . ^orKr-n 1 047 1480 38010 1.95 4 Finer quality of 3 containing about 0.8 per cent carbon . . 18330 1580 1440 38190 37690 2.08 1.92 i Crucible steel containing I per cent carbon Whitworth's fluid-compressed steel I 1590 38710 2.07 * " Phil. Mag." 5 series, vol. xxix, 1890. SMITHSONIAN TABLES. t " Phil. Trans. Roy. Soc." 1885 and 1889. 374 TABLES 47O-471. DEMAGNETIZING FACTORS FOR RODS. TABLE 470. ff= true intensity o* magnetizing field, H' = intensity of applied field, /= in- tensity of magnetization, H=H' .AY. Shuddemagen says : The demagnetizing factor is not a constant, falling for highest values of /to about 1/7 the value when unsaturated; for values of B (=^H~4ir/) less than 10000, N is approximately constant; using a solenoid wound on an insulating tube, or a tube of split brass, the reversal method gives values for TV which are considerably lower than those given by the step-by-step method ; if the solenoid is wound on a thick brass tube, the two methods prac- tically agree. Values of NX 10*. Cylinder. Ratio of Ballistic Step Method. Length to Diameter. Ellipsoid. Uniform Magneti- Magneto- metric Dubois. Shuddemagen for Range of Practical Constancy. zation. (Mann). Diameter. 0.158 cm. 0.3 1 75 cm. i.i 1 1 cm. 1.905 cm. 5 7015 _ 6800 10 2549 630 2 55 2l6o - - 1960 15 1350 280 1400 I2O6 1075 20 848 160 8 9 8 775 6 7 I 3 432 70 460 393 388 350 343 40 266 39 274 238 2 34 212 209 e 181 132 3 182 n8 116 lol 149 106 7 101 13 99 89 88 80 80 9.8 78 69 69 66 63 90 65 7-8 63 55 56 IOO 54 6-3 51.8 45 46 41 4 1 150 26 2.8 25.1 20 23 21 21 200 16 1.57 15.2 ii 12.5 II II 3 00 7-5 0.70 7-5 5* 4OO 4-5 2.8 C. R. Mann, Physical Review, 3, p. 359; 1896. H. DuBois, Wied. Ann. 7, p. 942 ; 1002. C. L. B. Shuddemagen, Proc. Am. Acad. Arts and Sci. 43, p. 185, 1907 (Bibliography). TABLE 471. Shuddemagen also gives the following, where B is determined by the step method and/f=//' KB. Ratio of Values of KX 10*. to Diameter. Diameter 0.3175 cm. Diameter i.i to 2.0 cm. 15 _ 8 5 .2 2O 53-3 25 - 36.6 30 30-9 27-3 40 18.6 16.6 50 12.7 1 1.6 60 9.25 8-45 80 IOO 3*66 5-05 3.26 I 5 1.83 1.67 SMITHSONIAN TABLES. TABLE 472. 375 DISSIPATION OF ENERGY IN THE CYCLIC MAGNETIZATION OF VARIOUS SUBSTANCES. C. P. Steinmetz concludes from his experiments* that the dissipation of energy due to hysteresis in magnetic metals can be expressed by the formula e = aB lA , where e is the energy dissipated and a a constant. He also concludes that the dissipation is the same for the same range of induction, no matter what the absolute value of the terminal inductions may be. His experiments show this to be nearly true when the induction does not exceed j- 1 5000 c. g. 8. units per sq. cm. It is possible that, if metallic induction only be taken, this may be true up to saturation ; but it is not likely to be found to hold for total inductions much above the satura- tion value of the metal. The law of variation of dissipation with induction range in the cycle, stated in the above formula, is also subject to verification.! Values of Constant a. The following table gives the values of the constant a as found by Steinmetz for a number of different specimens. The data are taken from his second paper. Number of specimen. Kind of material. Description of specimen. Value of 0. Iron .00^48 3 (( .00458 4 u .OO2o6 6 M Medium thickness tin plate .00425 Steel .00349 7 (i .00848 (l 9 {< ii u Same as 8 tempered in cold water .... .02792 12 a Tool steel glass hard tempered in water .07476 13 a " " tempered in oil .02670 14 u " " annealed .01899 15 " ' ) ( Same as 12, 13, and 14, after having been subjected ) ( .06130 16 " f ? to an alternating m. m. f. of from 4000 to 6000 > ] .02700 1 7 " ) r ampere turns for demagnetization . . . . ) ( -01445 ^ , . f~\ of "*-/-\T1 .01300 Io 19 " " " containing J % aluminium 01365 20 <( " " " " -J % " .01459 21 Magnetite . ( A square rod 6 sq. cms. section and 6.5 cms. long, ) 1 from the Tilly Foster mines, Brewsters, Putnam > ( County, New York, stated to be a very pure sample ) .02348 .OI22 ( Annealed wire, calculated by Steinmetz from ) .0156 2 3 24 | Ewing's experiments ) Hardened, also from Ewing's experiments .0385 25 Cobalt $ Rod containing about 2 % of iron, also calculated ) ] from Ewing's experiments by Steinmetz Consisted of thin needle-like chips obtained by .OI2O milling grooves about 8 mm. wide across a pile of thin sheets clamped together. About 30 % by vol- 26 Iron filings J ume of the specimen was iron. ] ist experiment, continuous cyclic variation of m. m. ) 0457 2cl experiment, 114 cycles per second [ 3d " 79~9 r cycles per second . .0396 0373 * " Trans. Am. Inst. Elect. Eng." January and September, 1892. t See T. Gray, " Proc. Roy. Soc." vol. Ivi. SMITHSONIAN TABLES. 376 TABLE 473. ENERGY LOSSES IN TRANSFORMER STEELS. Determined by the wattmeter method. Loss per cycle per cc = AB* -\-lni B'J, where B = flux density in gausses and n = frequency in cycles per second, x shows the variation of hysteresis with B between 5000 and 10000 gausses, and^y the same for eddy currents. Ergs per Gramme per Cycle. Watts per Pound at 60 Cy- cles and loooo Gausses. Thick- loooo Gausses. 5000 Gausses. C fcJQ Designation. ness. X y a 5,3 cm. Hyste- hi Hyste- S w* rT Hyste- resis. Total. resis. i^'S^g resis. 1^ ill Unannealed A 0.0399 ! 599 186 562 46 1.51 2. 02 0.00490 0.41 4-35 4.76 B .0326 1156 '34 384 36 1.59 1.89 00358 0.44 3-14 3-58 C .0422 1032 242 356 70 1.51 1.79 .00319 0.47 2.81 3.28 D .0381 1009 184 353 48 1.52 1 1.94 .00312 0.44 2.74 3-18 Annealed j E .0476 735 236 246 58 1.58 ! 2.02 .00227 0.36 2.OO 2.36 F .0280 666 100 220 27 i. 60 .88 .00206 0.44 1.81 2.25 G 0394 563 210 193 54 i-54 .96 .00174 ! 0.47 r -53 2.OO H* .0307 412 I 4 6 138-5 39 1.58 .00127 0.54 1. 12 1.66 J .0318 34 * 2O2 111.5 55 1.62 .88 .00105 0.70 0-93 63 k* .0282 394 124 130 3 2 1.61 .90 .00122 0.54 1.07 .61 L B .0346 0338 38i 354 184 2OO 125 116 50 57 1.61 1.61 .88 .81 .00118 .001 10 0.535 0.6 1 1-035 0.96 57 57 M 0335 372 I 7 8 127 46 1.55 95 .00115 0-55 I.OI .56 N .0340 3" 210 IO 5 56 1.62 .90 .00099 0.63 0.87 5 P 0437 334 l8 4 107 50 1.64 .88 .00103 0-34 0.91 25 Silicon steels Qt .0361 3J3 54 98 15 1.63 - .00094 0.14 0.825 0.965 R 3 '5 288 42 j 93 n 1.64 .00089 0.15 0.78 0-93 S .0452 278 72 90 18 1.63 _ .00086 0.12 o-755 0.875 T 0338 250 60 78 18 1.68 _ .00077 - r 8 0.68 0.86 U .0346 270 42 86 12 1.66 _ .00084 O- 1 2 0-735 0-855 V* .0310 25I-5 47 79 13 1.68 _ .00078 0.17 o.6 5 0-855 w* 0305 197 43 62.3 I2. 4 1.67 _ .00061 o.i 6 0-535 0.695 X .0430 200 65 64.2 16.6 1.65 - .00062 O.I2 0.545 0.665 1 | * German. t English. t In order to make a fair comparison, the eddy current loss has been computed for a thickness of 0.0357 cm. (Gage No. 29), assuming the loss proportional to the thickness. Lloyd and Fisher, Bull. Bur. Standards, 5, p. 453 ; 1909. Note. -For formula and tables for the calculation of mutual and self inductance see Bulletin Bureau of Standards, vol. 8, p. 1-237, 1912. SMITHSONIAN TABLES. 377 TABLE 474. MAGNETIC SUSCEPTIBILITY. If 31 is the intensity of magnetization produced in a substance by a field strength ft then the magnetic susceptibility H = 3I/*. This is generally referred to the unit mass; italicized figures refer to the unit volume. The susceptibility depends greatly upon the purity of the substai: pecially its freedom from iron. The mass susceptibility of a solution containing p per cent by weight of a water-free substance is, if H is the susceptibility of water, (p/ioo) H + (i p/ioo) HQ. Substance. HXio ! y Remark Substance. HXio Remarks Ag , O IQ 1 8 K.CO AgCl o 28 O.CO 1 O 20 Sol'n Air, i Atm .... -\-O.O24 1C Mb . . 4-0.38 ,0 Al 4-o.6c T* Mg f 0.04 -0 A1 2 K 2 (S0 4 ) 4 2 4 H 2 i.o Crys. MgSO 4 . , 4-Q-55 O JO IB A, i Atm .... 0.10 o Mn . . . 4-ii iX As O 1 rS MnPl Au W 'J O.IC 18 MnSO 4 122. 18 ,0 Sol'n B O.7 I 18 BaCl 2 O.7.6 20 NH 3 O.OOI 10 Be .... ~'J" -4-O.7Q T P Powd i ]y a Ln PT -0 Bi i 4 s ! Nad 4-O.SI Id Br O 78 18 NaoCOo 0.50 20 C, arc-carbon . . C, diamond . . . ~.j,_, 2.0 0.49 18 18 Na 2 CO 3 . 10 H 2 O . Nb O.I9 0.46 4-1 7 1 7 \l .rOWd. H CH 4 , i Atm.. . . -\-o.ooi 16 NiCl 2 T'J -1 dO 18 Snl'n 1 CO 2 , i Atm. . . . -\-O.OO2 16 NiSO 4 _L-. CS 2 .... 18 I o u - CaO . u '/ / ifi PowH 1 Qg 4~O.I2O 20 CaCl 2 CaCO 3 , marble . . V.^Y 0.40 0.7 X 9 P, white i P, red . . . . +0.04 0.90 O CO 20 20 Cd O 17 18 Pb CeBr 3 4.6.1 18 PbCl 2 POTO^ C1 2 , i Atm. . . . i "-j O. CQ 16 1 Pd - 2 5 4-c8 11 CoCl 2 w oy J-QO 18 Sol'n PrCl 3 i j- 1 [ I S Snl'n 1 CoBr 2 +47. 18 Pt T/3- -i- T T ,c CoI 2 1 1-" T < 1 ptpi. 1 -.!'_ CoSO 4 ..... 1 JJ- 4-C7. 4 ( Rh 4-i i 18 ool n i Co(N0 8 ) 2 .... y/' + =57- 18 (( IS O 4.8 18 Cr . -4-7 7 18 SO 2 i Atm if) CsCl . . . o ?8 17 Powd 1 Sb iS Cu . . . O OQ Se u.y4 i S CuCl 2 4-12. 2O Sol'n Si O.j- O I " 18 Crv; CuSO 4 . . 4-10 "O Sol'n SiO 2 Quartz CuS ... 4-o 16 17 Powd Glass r\ FeCl 3 4-oo 18 Sol'n Sn u o FeCl 2 4-QO 18 SrCl> i **yj o d" ''O Sol'n i FeSO 4 4-8- 20 < Ta 4-O O7 18 Fe 2 (N0 3 ) 6 . . . . FeCneK 4 .... FeCneK<} .... + 50. 0.44 4-Q I 18 Powd. Te . . . . Th Ti 0.32 4-0.18 -L-j i 20 18 18 He, i Atm. o 002 o Va 4-i c 18 H 2 , i Atm. o ooo 16 Wo J o IT o H 2 , 40 Atm. . o.ooo 16 Zn O. I C. 18 I H 2 O. O 7Q ''O ZnSO 4 O -1O I HC1 O8o "O Zr O.4C 18 H 2 SO 4 4-0 78 CH 3 OH -O 71 HNO 3 O 7O ''O C 2 H 5 OH O.SO He . O IQ 20 C 8 H 7 OH -o 80 i . : : : : - O A. "O C 2 H 6 OCoH 5 -o 60 20 In o i4- 18 CHClg o c;8 Ir W *3C + O I C 18 CH 078 K 20 4-7 7 KC1 O CO 20 Glycerine ' f o 64 22 KBr O 4O ''O Sn^ar O. C7 KI . o 38 "O Paraffin o <8 KOH O 3 C '^'J Sol'n Petroleum -O Ol K 2 S0 4 KMnO 4 .... V-JJ 0.42 4-2.0 20 Toluene .... \Vood -0.77 O.2-C KNO 3 O 77 20 Xylene 0.81 1 Values are mostly means taken of values given in Landolt-Bornstein's Physikalisch-chemischt Tabellen. dally Honda, Annalen der Physik ( 4 ), 32, 1910. SMITHSONIAN TABLES. See espe- 378 TABLE 4 75. MAGNETO-OPTIC ROTATION. Faraday discovered that, when a piece of heavy glass is placed in magnetic field and a beam of plane polarized light passed through it in a direction parallel to the lines of magnetic force, the plane of polarization of the beam is rotated. This was subsequently found to be the case with a large number of substances, but the amount of the rotation was found to depend on the kind of matter and its physical condition, and on the strength of the magnetic field and the wave-length of the polarized light. Verdet's experiments agree fairly well with the formula where c is a constant depending on the substance used, / the length of the path through the substance, // the intensity of the component of the magnetic field in the direction of the path of the beam, r the index of refraction, and A the wave-length of the light in air. If H be dif- ferent, at different parts of the path, IH is to be taken as the integral of the variation of mag- netic potential between the two ends of the medium. Calling this difference of potential z/, we may write Q = Av, where A is constant for the same substance, kept under the same physical conditions, when the one kind of light is used. The constant A has been called " Verdet's con- stant," * and a number of values of it are given in Tables 476-480. For variation with tempera- ture the following formula is given by Bichat : R = A'o (i 0.00104 / 0.000014/2), which has been used to reduce some of the results given in the table to the temperature corre- sponding to a given measured density. For change of wave-length the following approximate formula, given by Verdet and Becquerel, may be used : where p is index of refraction and A wave-length of light. A large number of measurements of what has been called molecular rotation have been made, particularly for organic substances. These numbers are not given in the table, but numbers proportional to molecular rotation may be derived from Verdet's constant by multiplying in the ratio of the molecular weight to the density. The densities and chemical formula are given in the table. In the case of solutions, it has been usual to assume that the total rotation is simply the algebraic sum of the rotations which would be given by the solvent and dissolved substance, or substances, separately; and hence that determinations of the rotary power of the solvent medium and of the solution enable the rotary power of the dissolved substance to be calculated. Experiments by Quincke and others do not support this view, as very different results are obtained from different degrees of saturation and from different solvent media. No results thus calculated have been given in the table, but the qualitative result, as to the sign of the rotation produced by a salt, may be inferred from the table. For example, if a solution of a salt in water gives Verdet's constant less than 0.0130 at 20 C., Verdet's constant for the salt is negative. The table has been for the most part compiled from the experiments of Verdet,t H. Becque- rcl,t Quincke, Koepsel,|| Arons,f Kundt,** Jahn.tt Schonrock.fJ Gordon, Rayleigh and Sidgewick,l||| Perkin,lT1F Bichat.*** As a basis for calculation, Verdet's constant for carbon disulphide and the sodium line D has been taken as 0.0420 and for water as 0.0130 at 20 C. * The constancy of this quantity has been verified through a wide range of variation of magnetic field by H. E. J. G. Du Bois (Wied. Ann. vol. ^ 5 ), p. 137, 1888. t ' Ann. de Chim. et de Phys." [3] vol. 52, p. r2g, 1858. $ ' Ann. de Chim. et de Phys." [5] vol. 12; " C. R." vols. 90, p. 1407, 1880, and 100, p. 1374, 1885. ' Wied. Ann." vol. 24, p. 606, 1885. ' Wied. Ann." vol. 26, p. 456, 1885. Wied. Ann." vol. 24, p. 161, 1885. * ' Wied. Ann." vols. 23, p. 228, 1884, and 27, p. 191, 1886. ' Wied. Ann." vol. 43, p. 280, 1891. $J 'Zeits. fur Phys. Chem." vol. n, p. 753, 1893. & ' Proc. Rov. Soc." 36, p. 4, 1883. ' Phil. Trans. R. S." 176, p. 343, 1885. * ' Jour. Chem. Soc." *** ' Jour, de Phys." vols. 8, p. 204, 1879, and 9, p. 204 and p. 275, 1880. SMITHSONIAN TABLES. TABLE 476. MAGNETO-OPTIC ROTATION. Solids. 379 Substance. Formula. Wave- length. Verdet's Constant. Minutes. Temp. C Authority. ZnS C PbB 2 O 4 Se Na 2 B 4 O 7 Cu 2 O A* 0.589 0.687 0.589 0.687 0.0095 0.2234 O.OI27 O.O6OO 0.4625 O.OI7O 0.5908 18-20 '5 15 '5 15 15 IS Quincke. Becquerel. M <; ( Blende Diamond .... Lead borate .... Selenium . . Sodium borate . . . Ziqueline (Cuprite) . . CaFl 2 0-2534 0.05989 20 Meyer, Ann. der 3655 435 .02526 .01717 u Physik, 30, 1909. .4916 .01329 .589 .00897 1. 00 .00300 2.50 .00049 3.00 .00030 Glass, Jena: Medium phosphate crn. 0.589 0.0161 18 DuBois, Wied. Ann. Heavy crown, 01143 . Light flint, 0451 Heavy flint 0500 < O.022O 0.0317 O.o6o8 51, 1894. " ' " 8161. . 0.0888 Zeiss, Ultraviolet o-3i3 0.0674 16 Landau, Phys. ZS. 0.405 .0369 M 9, 1908. 0.436 .O3II Quartz, along axis, i.e., Si0 2 0.2194 0.1587 20 Borel, Arch. sc. phys. plate cut 1 to axis 2 573 .1079 " 1 6, 1903. .3609 .04617 " .4800 02574 " .5892 .01664 6439 .01368 Rock salt . . . NaCl 0.2599 0.2708 20 Meyer, as above. .3100 .1561 (4 .4046 0775 " .4916 .0483 (t .6708 .0245 (( 1. 00 .01050 " 2.00 .00262 4.00 .00069 " Sugar, cane : along Ci 2 H 22 Oii 0.451 .0122 2O Voigt, Phys. ZS. 9, axis HA .'626 .0076 .0066 1908. axis HA 1 . . - 0.451 O.OI29 " 540 .0084 " .626 .0075 " Sylvite KC1 0.4358 0.0534 2O Meyer, as above. .5461 .6708 .0316 .O2OI2 M .00 .OIO5I " 1. 2O .00608 " 2.OO .OO2O7 " 4-00 .00054 SMITHSONIAN TABLES. 3 So TABLE 477. MAGNETO-OPTIC ROTATION. Liquids : Verdet's Constant for A. 0.589/i. Substance. Chemical formula. Density in grams per c. c. Verdet's constant in minutes. Temp. C Authority. Acetone C 8 H 6 0-7947 O.OII3 20 Jahn. Acids : Acetic Butyric C 2 H 4 2 C 4 H 8 2 1.0561 0.9663 .OIO5 .0116 21 y Perkin. " Formic CH 2 2 1.2273 .0105 " " Hydrochloric HCI 1.2072 .O224 " M " Hydrobromic HBr 1.7859 0343 " " " Hydroiodic HI 1-9473 OS'S " " Nitric HNOi 1.5190 .0070 13 < " Sulphuric H 2 SO 4 .0121 15 Becquerel. Alcohols : Amvl C 6 H n OH 0.8107 .0128 20 Jahn. Butyl C 4 H 9 OH 0.8021 .0124 ii Ethyl C 2 H 6 OH 0.7900 .0112 " Methyl CH 8 OH 0.7920 .0093 " Propyl C 8 H 7 OH 0.8042 .0120 u Benzene C 6 H 6 0.8786 .0297 * Bromides : Bromoform CHBr 8 2.902 r .0317 y Perkin. Ethyl C 2 H 5 Br 1.4486 .0183 u Ethylene C 2 H 4 Br 2 2.1871 .0268 " Methyl CHgBr I -733 I .0205 " Methylene CH 2 Br 2 2.4971 .0276 15 " Carbon bisulphide CS 2 0433 Gordon. X " .0420 18 Rayleigh. Chlorides : Amyl CHC1 0.8740 .0140 20 Jahn. " Arsenic AsCl 3 .0422 y Becquerel. " Carbon CC1 4 .0321 " Chloroform CHC1 3 1.4823 .0164 20 Jahn. Ethyl C 2 H 5 C1 0.9169 0.0138 6 Perkin. " Ethylene C 2 H 4 C1 2 1.2589 .0166 y " 1 Methyl CHgCl .0170 Fecquerel. Methylene CH 2 C1 2 i-33 61 .0162 Perkin. ' Sulphur bi- S 2 C1 2 393 Becquerel. Tin tetra SnCl 4 .0151 H ' Zinc bi- ZnCl 2 437 f M lodides : Ethyl C 2 H 6 I 1.9417 + .0296 t Perkin. Methyl CH 3 I 2.2832 0336 M Propvl C 3 H 7 I 1.7658 .0271 1 i Nitrates : Ethyl " Methyl C 2 H 6 O.NO a CH 8 O.NO 2 1.1149 1.2157 .0091 .0078 u < Propyl C 3 H 7 O.NO 2 1.0622 .0100 ( < Paraffins: Heptane C 7 H 16 0.6880 .0125 < " Hexane CH M 0.6743 / -r+j .0125 < " Pentane C 6 H 12 0.6332 .0118 < < Phosphorus, melted Sulphur, melted P S .1316 .0803 33 114 Becquerel. Toluene C 7 H 8 0.8581 .0269 28 Schonrock. Water, A = 0.2496 yu H 2 .1042 See Meyer, 0.275 .0776 Ann. der 0.3609 .0384 Physik, 30, 0.4046 .0293 1909. Meas- 0.500 .0184 ures by 0.589 .0131 Landau, 0.700 .0091 Siertsema, I.OOO .00410 Ingersbll. 1.300 .00264 Xylene CgHio 0.8746 .0263 27 Schonrock. SMITHSONIAN TABLES. TABLE 478. MAGNETO-OPTIC ROTATION. Solutions of acids and salts In water. Verdet's constant lor A = 0.589/i. 381 Chemical formula. Density, grams per c. c. Verdet's constant in minutes. Temp. * Chemical formula. Density, grams per c. c. Verdet's constant in minutes. Temp. * C 8 H 6 HBr u 0.9715 '3775 1.1163 0.0129 0.0244 0.0168 20 P LiCl MnCl 2 1.0619 1.0316 1.1966 0.0145 0.0143 0.0167 20 B HC1 I - I 573 O.O2O4 " If M 1.0876 o.oi 50 r " 1.0762 0.0168 " " HgCl 2 1.0381 0.0137 16 s HI 1.0158 I -957 0.0140 0.0499 " P NiCl 2 1.0349 1.4685 0.0137 0.0270 15 B 1-4495 0-0323 " 1.2432 0.0196 M 1.1760 O.O2O5 " M " J - I2 33 O.OI62 M M HNOi 1.3560 O.OIO5 " II KC1 i. 6000 0.0163 M ft NH 3 NH 4 Br 0.8918 1.2805 0.0153 O.O226 y ;; NaCl 1.0732 1.2051 O.OI45 O.OlSo 2O 15 B M 1.1576 0.0186 " " " 1.0546 0.0144 n BaBr 2 l -S399 1.2855 O.O2I5 0.0176 20 j SrC] 2 1.0418 1.1921 0.0144 O.OI62 " J CdBr 2 1.3291 0.0192 " " " 1.0877 0.0146 M it " 1. 1608 O.OI62 * " SnCl 2 1.3280 O.O266 15 V CaBr 2 1.2491 0.0189 " " " I.TII2 0.0175 " I - I 337 0.0164 M < ZnC] 2 1.2851 0.0196 U it KBr 1.1424 0.0163 " " I - I 595 0.0161 It < " 1.0876 0.0151 " " K 2 CrO 4 1.3598 0.0098 u < NaBr 1.1351 0.0165 " " K 2 Cr 2 O 7 1.0786 0.0126 SrBr 2 1.0824 1.2901 0.0152 0.0186 l< Hg(CN) 2 1.0638 1.0605 0.0136 0-0135 16 M S .. " 1.1416 0.0159 " If NH 4 I 1.5948 0.0396 15 P K 2 C0 8 Na 2 CO 8 1.1906 1. 1006 O.OI4O O.OI4O 2O M M 1.5109 1.2341 0-0358 0.0235 " NH 4 C1 1.0564 1.0718 0.0137 0.0178 15 V Cdl 1.5156 1.1521 0.0291 0.0177 2O M M BaCl 2 1.2897 0.0168 2O J KI 1.6743 0.0338 15 B " 1.1338 O.OI49 " " " I-3398 0-0237 '* CdCl 2 1.3179 0.0185 " " " 1.1705 0.0152 " u J - 2 755 0.0179 U a Nal I - I 939 O.O2OO " J H 1.1732 0.0160 " " 1.1191 0.0175 M II 0.0157 * NH 4 N0 8 1.2803 O.OI2I 15 P CaCI 2 1.1504 0.0165 M KN0 8 1.0634 O.OI3O 20 J u 1.0832 0.0152 " NaN0 8 I.III2 O.OI3I " " CuCl 2 1.5158 O.O22I 5 B U 2 O 3 N 2 O 6 2.0267 0.0053 M B " 0.0156 " ?> 1.1963 O.OII5 " M FeCl 2 M33 1 0.0025 5 " (NH 4 ) 2 S0 4 1.2286 O.OI4O 15 P " 1.2141 0.0099 M NH 4 .HSO 4 I.44I7 0.0085 u " 1.1093 O.OIlS " BaSO 4 I.I788 O.OI34 20 J Fe 2 Cl 6 I-6933 O.2O26 " M 1.0938 0.0133 M " I -53 I 5 O.IT4O u CdSO 4 1.1762 0.0139 w " " 0.0348 " M 1.0890 0.0136 " " u i.' 1 68? O.OOI5 " 14804 I.I762 0.0137 H " " 1.0864 O.O08 I " MnS0 4 I.244I 0.0138 " " " 1.0445 O.OII3 " K 2 SO 4 1-0475 0.0133 " u 1.0232 O.OI22 Na 2 SO 4 I. O66 1 0.0135 * J, Jahn, P, Perkin, V, Verdet, B, Becquerel, S, Schonrock; see p. 378 for references. SMITHSONIAN TABLES. TABLES 479, 48O. TABLE 479. -Magneto-Optic Rotation. Gases. Verdet's Substance. Pressure. Temp. constant in Authority. minutes. Atmospheric air . Carbon dioxide Atmospheric Ordinary u 6.83 X io- 6 13.00 " Becquerel. Carbon disulphide , Ethylene . - Nitrogen . , 74 cms. Atmospheric u 70 C. Ordinary 23.49 " 3448 " 6.92 " Bichat. Becquerel. Nitrous oxide . . . u (i 16.90 " Oxygen ... .. u u 6.28 ii Sulphur dioxide II ii 31-39 " u .. 246 cms. 20 C. 38.40 Bichat. See also Siertsema, Ziting. Kon. Akad. Watt., Amsterdam, 7, 1899; 8, 1900. Du Bois shows that in the case of substances like iron, nickel, and cobalt which have a variable magnetic susceptibility the expression in Verdet's equation, which is constant for substances of con- stant susceptibility, requires to be divided by the susceptibility to obtain a constant. For this expression he proposes the name " Kundt's constant." These experiments of Kundt and Du Bois show that it is not the difference of magnetic potential between the two ends of the medium, but the product of the length of the medium and the induction per unit area, which controls the amount of rotation of the beam. TABLE 480. Verdet's and Kundt's Constants. The following short table is quoted from Du Bois' paper. The quantities are stated in c. g. s. measure, circular measure (radians) being used in the expression of " Verdet's constant " and " Kundt's constant." Verdet's constant. Name of substance. Magnetic susceptibility. Wave-length of light Kundt's constant. Number. Authority. Cobalt . _ 6.44 X i o~ 5 3-99 Nickel . _ _ _ i 3- ! 5 Iron - _ - 6.56 2.63 Oxygen : I atmo. . Sulphur dioxide + 0.01 26 X io~ 5 0.0751 " 0.000179 X io~ 6 0.302 Becquerel. 5 .8 9 0.014 4.00 Water 0.0694 o-377 Arons 5-4 Nitric acid 0.0633 " -35 6 Becquerel. -5.6 Alcohol . 0.0566 " 0-330 De la Rive. -5.8 Kther. . 0.0541 " -3 r 5 " -5-8 Arsenic chloride Carbon disulphide . 0.0876 " 0.0716 " 1.222 1.222 Becquerel. Rayleigh. 14.9 17.1 Faraday's glass 0.0982 " 1.738 Becquerel. 17.7 SMITHSONIAN TABLES. TABLES 481 -483. TABLE 481. - Values of Eerr's Constant.* 383 Du Bois has shown that the rotation of the major axis of vibration of radiations normally reflected from a magnet is algebraically equal to the normal component of magnetization multiplied into a constant K. He calls this con- stant K, Kerr's constant for the magnetized substance forming the magnet. Color of light. Spectrum line. Wave- length in cms. X io Kerr's constant in minutes per c. g. s. unit of magnetization. Cobalt. Nickel. Iron. Magnetite. Red Li a D b F G 67.7 62.0 58.9 51-7 48.6 43-1 O.O2O8 0.0198 0.0193 0.0179 O.OlSo O.Ol82 0.0173 0.0160 0.0154 0.0159 0.0163 0.0175 0.0154 0.0138 0.0130 O.OIII O.OIOI 0.0089 +0.0096 +O.OI2O +0.0133 +0.0072 +0.0026 Red Yellow . . . Blue Violet . *H. E. J. G. Du Bois, " Phil. Mag." vol. 29. TABLE 482. Dispersion of Eerr Effect. Wave-length. o-SM I.OfJL i-SV- 2.0fi. 2-SK Steel . . . II 7 . l&. -14'. II'. -c/.o Cobalt . . . 9-5 "-S 9-5 II. -6. 5 Nickel . . . 5-5 4.0 o + 1-75 +3-o Field Intensity 10,000 C. G. S. units. (Intensity of Magnetization =r about 800 in steel, 700 to 800 in cobalt, about 400 in nickel). Ingersoll, Phil. Mag. u, p. 41, 1906. TABLE 483. - Dispersion of Eerr Effect. Mirror. Field (C. G. S.) 4ifx 44M .481* 52M .56* .60^ .64ft .66* Iron . . 21,500 .25 .26 .28 31 -36 .42 44 45 Cobalt . . 20,000 -36 35 34 35 35 35 35 -.36 Nickel . . I9,OOO .16 '5 13 13 .14 .14 .14 .14 Steel . . I9,2OO .27 .28 31 35 -.38 .40 44 45 Invar . . 19,800 .22 23 .24 2 3 2 3 .22 23 23 Magnetite l6,400 .07 .02 +.04 +.06 +.08 +.06 +04 +03 Foote, Phys. Rev. 34, p. 96, 1912. See also Ingersoll, Phys. Rev. 35, p. 312, 1912, for "The Kerr Rotation for Transverse Magnetic Fields," and Snow, 1. c. 2, p. 29, 1913, " Magneto-optical Parameters of Iron and Nickel." SMITHSONIAN TABLES. TABLES 484-486. RESISTANCE OF METALS. MAGNETIC EFFECTS. TABLE 484. Variation of Resistance of Bismuth, with Temperature, in a Transverse Magnetic Field. Proportional Values of Resistance. H -192 -135 100 -37 + 18 +60 + 100 + 183 o 0.40 0.60 0.70 0.88 1. 00 1. 08 25 .42 1.79 2000 1.16 0.87 0.86 0.06 .08 .11 .26 43 1. 80 4000 2.32 1.20 1. 10 .18 .21 .31 .46 1.82 6OOO 4.00 2 O6 1. 60 1.29 .30 32 39 1.85 8000 5-90 2.88 2.OO 1.50 43 42 .46 .57 1.87 1 0000 8.60 3.80 2-43 1.72 57 54 54 .62 1.89 I2OOO 10.8 4.76 2.93 71 67 .62 . 1.67 1.92 14000 12.9 5-82 3-50 2.16 87 .80 .70 1.73 1.94 I6OOO 18000 15-2 17-5 6.95 8. 15 4.11 4.76 2.38 2.60 2.02 2.18 1-93 2.06 .79 .88 1.80 1.87 1.96 1.99 20000 19.8 9-50 5-40 2.81 2.33 2.20 97 1.95 2.03 25OOO 30000 25-S 30.7 13-3 18.2 7-30 9-8 3.50 4.20 2.73 3.17 2.52 2.86 2.22 2. 4 6 2.10 2.28 2.09 2.17 35000 35-5 20.35 12.2 4.95 3.62 3-25 2.69 2-45 2.25 TABLE 485, Increase of Resistance of Nickel due to a Transverse Magnetic Field, expressed as % of Resistance at and H = 0. H -190 -75 +18 + 100 + 182 o +0 o 1000 +0.20 +0.23 +0.07 +0.07 +0.96 +0.04 2000 +0.17 +0.16 +0.03 +0.03 +0.72 0.07 30OO o.oo O.O5 -0.34 0.36 -0.14 0.60 4000 -0.17 -0.15 0.60 0.72 0.70 -I. IS . 6000 0.19 0.20 0.70 0.83 1.02 -1-53 8000 0.19 0.23 0.76 0.90 - -IS -1.66 1 0000 0.18 0.27 0.82 0.95 - .23 -1.76 I2OOO -0.18 0.30 0.87 I.OO .30 1.85 I40OO 0.18 0.32 0.91 - .04 - .37 -1.95 16000 -0.17 -0.35 -0.94 - .09 - .44 -2.05 18000 -0.17 -0.38 0.98 - .13 - -51 -2.15 200OO 0.16 -0.41 -1.03 - -17 -1.59 -2.25 25000 -0.14 -0.49 1. 12 - .29 -1.76 -2.50 30000 0.12 -0.56 1.22 -1.40 -1.95 2.73 35000 O.IO 0.63 -1.32 -i.SO -2.13 -2.98 F. C. Blake, Ann. der Physik, 28, p. 449; 1909. TABLE 486. Change of Resistance of Various Metals in a Transverse Magnetic Field. Room Temperature. Metal. Field Strength in Gausses. Per cent Increase. Authority. Nickel 1 0000 1.2 Williams, Phil. Mag. 9, 1905. ** " 1.4 Barlow, Pr. Roy. Soc. 71, 1903. 44 6000 i.o Dagostino, Atti Ac. Line. 17, 1908. " IOOOO 1.4 Grummach, Ann. der Phys. 22, 1906. Cobalt 41 0.53 Cadmium +0.03 Zinc * +0.01 Copper +0.004 Silver +0.004 Gold ' +0.003 Tin +O.002 Palladium +O.OOI Platinum ' +O.OO05 Lead " +O.O004. Tantalum +O.OOO3 Magnesium Manganin 6000 +O.OI +O.OI Dagostino, /. c. Tellurium ? +0.02 tO 0.34 Goldhammer, Wied Ann. 31. 1887. Antimony ? +0.02 tn o.T6oooo Antimony ... ... + O.Q '' O 22 4-2 1 4 Steel -I- OI 2 " O O^"? "O 07 1 f^. H"eusler alloy . . -j- OIO " O 0^6 -1-09 -{-007 " o on o 06 IOOO " I COO I 7O Cobalt -j-.ooi6 " o 0046 -4-o 01 r-l8oO " 24O -f39 4- r i Zinc 1 3 Cadmium + OQOC e T~ ! 3 .WUVJJJ5 -j- 00040 up to c o _l_ - Lead j- OOOOQ r O (?\ ^ 5 Tin OOOO3 - J. O C*\ Platinum ... ... OOO .00052 no to 270 18 German silver OOO^4. Gold 000^7 to 00071 Constantine .... OOOQ Manganese . OOOO1 OOO7 to OOI2 _}_ CO tO I 7O 1 Silver 0008 " ooi 5 ^4.6 " 4.7O J .OO2^ Magnesium .... . .00094 to 0035 Aluminum . 00076 " 00^7 Nickel OOJ.^ " O^d. -f-O O4 to O IQ -{-''OOO " QOOO r Carbon .017 4-c -l-IOO 4J? Bismuth ' Up to ID. 1 ' 3 ' +- 1 to 4.O . 1 "P up to 132000 -^''OO TABLE 488. Variation of Hall Constant with the Temperature. Bismuth. 1 Antimony. 8 H 182 -90 -23 4-11.5 4-100 H 186 79 o 4-21.5 4-58 IOOO 2OOO 3OOO 4000 5000 0000 62.2 49-7 45-8 42.6 40.1 28.0 25.0 22.9 21.5 20.2 18.9 l l' 16.0 12.9 12.7 12. 1 "5 II.O 10.6 7.28 7-17 7.06 6.95 6.84 6.72 0.263 0.252 0.245 0.249 0.243 02.35 0.217 0.21 1 O.2O9 0.203 Bismuth. 8 H 4-14.5 4-104 125 i I 89 a39 259 269 270 890 5.28 2.57 2.12 42 1.24 I. II 0.97 0.83 0.77* 1 Barlow, Ann. der Phys. 12, 1903. s Everdingen, Comm. Phys. Lab. Leiden, 58. * Traubenberg, Ann. der Phys. 17, 1005. * Melting-point. Both tables taken from Jahn, Jahrbuch der RadioactivitSt und Electronik, 5, p. 166; 1908, who has collected data of all observers and gives extensive bibliography. SMITHSONIAN TABLES. 386 TABLES 489-491. RONTGEN (X-RAYS) RAYS. TABLE 489. Cathode and Canal Rays. Cathode (negative) rays consist of negatively charged particles (charge 4.77 x io~ 10 esu, 1.591 x lo" 90 emu, mass, 9 x lo" 28 g or 1/1800 H atom, diam. 4 X 10 13 cm) emitted at low pressures in an electric discharge tube perpendicularly to the cathode (.*. can be focused) with velocities (io 9 to io 10 cm/sec.) depending on the acting potential difference. When stopped by suitable body they produce heat, ionization (inversely proportional to velocity squared), photo- graphic action, X-rays, phosphorescence, pressure. The bulk of energy Js transformed into heat (Pt, Ta, W may be fused). In an ordinary X-ray tube carrying io 3 ampere the energy given up may be of the order of 100 cal/m. Maximum thickness of glass or Al for appreciable transmission of high speed particles is .0015 cm. Maximum velocity V d with which a cathode ray of velocity F may pass through a material of thickness d is given by F 4 - F<* 4 = ad x io 40 ; a = 2 for air, 732 for Al and 2540 for Au, cm-sec, units (Whiddington, 1912). Cathode rays have a range of only a few millimeters in air. Canal (positive) rays move from the anode with velocities about io 8 cm/sec, in opposite direction to the cathode rays, carry a positive charge, a mass of the order of magnitude of the H molecule, cause strong ionization, fluorescence (LiCl fluoresces blue under cathode, red under canal ray bombardment), photographic action, strong pulverizing or disintegrating power and by bombardment of the cathode liberate the cathode rays. TABLE 490. Speed of Cathode Rays. The speed of the cathode particles in cm/sec, as dependent upon the drop of potential to which they owe the speed, is given by the formula v = 5.95 VE-io 7 . The following table gives values of 5.95 VE. Voltage IO 20 30 40 CO 60 7 80 oo IOO Velocity X io~ 7 . . . 18.8 26.6 32.6 37-6 42.1 46. 1 49.8 53-3 56.5 59-5 Voltage . IOO 200 *oo 400 (N - 3.5)2 where v is Rydberg's fundamental frequency (109,675 X the velocity of light) and N the atomic number, represents the data with considerable accuracy. The nuclear charge is obtained by Q = 2e(N - 3.5). Element. Atomic number. AU Element. Atomic number. AU Element. Atomic number. Au Bromine Krypton Rubidium .... Strontium. . . . Yttrium . . . 35 36 37 38 39 40 4i 42 .9179 .8143 .7696 .7255 .6872 6503 .6180 Ruthenium Rhodium . . Palladium. Silver 44 45 46 47 48 49 50 Si .5584 5324 5075 .4850 .4632 4434 .4242 .4065 Tellurium. . Iodine 52 53 54 55 56 57 58 .3896 3727 3444 3307 .3188 3073 Xenon Caesium . . . Barium. . . . Lanthanum Cerium. . . . Cadmium. . Indium .... Tin Zirconium. . . . ! Columbium . . Molybdenum. Antimony . SMITHSONIAN TABLES. 394 TABLES 600-502. - RADIOACTIVITY. Radioactivity is a property of certain elements of high atomic weight. It is an additive property of the atom, dependent only on it and not on the chemical compound formed nor affected by physical conditions controlling ordinary reactions, viz : temperature, whether solid or liquid or gaseous, etc. With the exception of actinium, radioactive bodies emit o, 0, or y rays, a rays are easily ab- sorbed by thin metal foil or a few cms. of air and are positively charged atoms of helium emitted with about 1/15 the velocity of light. They are deflected but very slightly by intense electric or magnetic fields. The $ rays are on the average more penetrating, are negatively charged particles projected with nearly the velocity of light, easily deflected by electric or magnetic fields and identical in type with the cathode rays of a vacuum tube. The y rays are extremely penetrating and non-deviable, analogous in many respects to the very penetrating Rontgen rays. These rays produce ionization of gases, act on the photographic plate, excite phosphorescence, produce certain chemical reactions such as the formation of ozone or the decomposition of water. All radio- active compounds are luminous evert at the temperature of liquid air. Table 506 is based very greatly on Rutherford's Radioactive Substances and their radiations (Oct. 1912). To this and to Landolt-Bornstein Physikalisch-chemische Tabellen the reader is re- ferred for references. In the three radioactive series each successive product (except Ur. Y, and Ra. C 2 ) results from the transformation of the preceding product and in turn produces the follow- ing. When the change is accompanied by the ejection of an a particle (helium, atomic weight = 4.0) the atomic weight decreases by 4. The italicized atomic weights are thus computed. Each pro- duct with its radiation decays by an exponential law ; the product and its radiation consequently depend on the same law. I = Ioe~ At where Io = radioactivity when t = O, I that at the time t, and A. the transformation constant. Radioactive equilibrium of a body with its products exists when that body is of such long period that its radiation may be considered constant and the decay and growth of its products are balanced. International radium standard : As many radioactivity measures depend upon the purity of the radium used, in 1912 a committee appointed by the Congress of Radioactivity and Electricity, Brussels, 1910, compared a standard of 21.99 m S- ^ P ure R a - chloride sealed in a thin glass tube and prepared by Mme. Curie with similar standards by Honigschmid and belonging to The Academy of Sciences of Vienna. The comparison showed an agreement of i in 300. Mme. Curie's standard was accepted and is preserved in the Bureau international des poids et mesures at Sevres, near Paris. Arrangements have been made for the preparation of duplicate standards for governments requiring them. TABLE 500. Relative Phosphorescence Excited by Radium. (Becquerel, C. R. 129, p. 912, 1899.) Without screen, Hexagonal zinc blende .... 13-36 With screen . .04 Diamond ...... 1.14 ii .01 it Double sulphate Ur and K . Calcium fluoride 1. 00 3 " : : 3 1 .02 The screen of black paper absorbed most of the a rays to which the phosphorescence was greatly due. For the last column the intensity without screen was taken as unity. The y rays have very little effect. TABLE 501. The Production of a Particles (Helium). (Geiger and Rutherford, Philosophical Magazine, 20, p. 691, 1910.) Radioactive substance (i gram.) a particles per sec. Helium per year. Uranium Uranium in equilibrium with products . Thorium " " . Radium ........ Radium hi equilibrium with products 2.37 X 10* 9.7 X io* 2.7 X io 4 3-4 X io> 13.6 X ioio 2.75 X io 5 cu. mm. n.o X io 5 " " 3.1 X io-6 " " 39 " " 158 " " TABLE 502. Heating Effect of Radium and Its Emanation. (Rutherford and Robinson, Philosophical Magazine, 25, p. 312, 1913.) Heating effect in gram-calories per hour per gram radium. a rays. rays. y rays. To*]. Radium .... Emanation Radium A ... Radium B -f C 25.1 28.6 30-5 39-4 4-7 6.4 25-1 28.6 30.5 50.5 Totals .... 123.6 4-7 6-4 134-7 Other determinations : Hess, Wien. Ber. 121, p. i, 1912, Radium (alone) 25.2 cal. per hour per gram. Meyer and Hess, Wien. Ber. 121, p. 603, 1912, Radium in equilibrium, 132.3 gram. cal. per o hour per gram. See also, Callendar, Phys. Soc. Proceed. 23, p. i, 1910; Schweidler and Hess, Ion. i, p. 161, 1909; Angstrom, Phys. ZS. 6, 685, 1905, etc. SMITHSONIAN TABLES. 395 TABLES 603-505. RADIOACTIVITY. TABLE 503. Stopping Powers of Various Substances for a Rays. s, the stopping power of a substance for the a rays is approximately proportional to the square root of the atomic weight, w. Substance H 2 Air 2 C 2 H 2 C 2 H 4 Al N 2 CO, CH 8 Br CS 2 Fe s ... .24 1.0 1.05 i. ii '35 1-45 1.46 1.47 2.09 2.18 2.26 Vw. . . .20 1.0 1.05 I.i; 1.44 1-37 1.52 1.51 2.03 1.95 1.97 Substance Cu Ni Ag Sn C.H. CH C 2 H 5 I CC1 4 Pt Au Pb s ... 2.43 2.10 2.46 2.2O 3-'7 2.74 & 3-37 3-53 ^ 3-'3 4.02 3-59 4.16 3-68 4-45 3-70 4.27 3-78 Bragg, Philosophical Magazine, n, p. 617, 1906. TABLE 504,- Absorption of Rays by Various Substances. /*, the coefficient of absorption for ft rays is approximately proportional to the density, D. Table 506 for n for Al. See Substance . . B C Na Mg Al Si P S K Ca fJL/D . . . . 4-65 4.4 4-95 S-i 5.26 5 '5 6.1 6.6 6-53 6.47 Atomic Wt. . ii 12 23 24.4 27 28 3i 32 39 40 Substance . . Ti Cr Fe Co Cu Zn Ar Se Sr Zr fJL/D .... 6.2 6.25 6.4 6.48 6.8 6.95 8.2 8.65 8-s 8-3 Atomic Wt. . 48 5 2 56 59 63-3 65.5 75 79 87.5 90.7 Substance . . Pd Ag Sn Sb I Ba Pt Au Pb U Ai/D . . . . 8.0 8.3 9.46 9.8 10.8 8.8 9.4 9-5 10.8 IO.I Atomic Wt. . 106 108 118 120 126 137 195 197 207 240 For the above data the rays from Uranium were used. Crowther, Philosophical Magazine, 12, p. 379, 1906. TABLE 506^- Absorption of 7 Rays by Various Substances. Substance. Density. Radium rays. Uranium rays. Th. D. Mcm)-i Meso. Tha M(cm)- 1 Range of thickness cm. /u (cm)- 1 IOOJA/D Mem)- 1 IOOM/D Hg . . Pb . . T 3-59 11.40 .642 495 4.72 4-34 .832 725 6.12 6.36 .462 .620 3 to 3-5 .0 " 7.9 Cu . . Brass . Fe Sn Zn 8.8 1 & 7.24 7.07 351 325 34 .281 .228 3-93 .416 392 .360 341 329 4.72 4.70 4.72 4.70 4-65 .294 .271 .250 .236 2 33 373 355 .316 35 .300 .0 " 7.6 .0 " 5.86 .0 " 7-6 o " 5-5 .0 " 6.0 Slate . Al 2.85 2.77 .118 .in 4.14 4.06 134 .130 4.69 4.69 .096 .092 .119 .0 " 9.4 .0 " II. 2 Glass . S . . . 2.52 1.79 .105 .078 4.16 4-38 .122 .092 4.84 5 .l6 .089 .066 3 .083 .0 " 11.3 .0 " 1 1. 6 Paraffin . .86 .042 4.64 043 5.02 .031 .050 .0 " 11.4 In determining the above values the rays were first passed through one cm. of Russell and Soddy, Philosophical Magazine, 21, p. 130, 1911. SMITHSONIAN TABLES. 396 TABLE 606. RADIOACTIVITY. P = 1/2 period = time when body is one half transformed. A = transformation constant (see previous page). The initial velocity of the a particle is deduced from the formula of Geiger V 3 = aR, where R = range and assuming the velocity for RaC of range 7.06 cm. at 20 is 2.06 X io cm per sec., i.e., v = 1.077^. 1 , , URANIUM-RADIUM GROUP. a rays. Atomic weights. 1/2 period, P Transforma- tion constants. x _ -6931 Rays. Range. 760""", 15 C Initial velocity. Kinetic energy. Whole no. of ions produced. cm cm per s Ergs. By an a particle. Uranium i . . . . Uranium Xi.. . Uranium X2. . . 238.2 234.2 234-2 5 X io y. 24.6 d. 1.15 m. 1.4 X io~ 10 y. .0282 d. .01 sec. flj-r 2.50 1-45 Xio .65 X 10-5 i . 26 X 10" Uranium 2 .... Uranium Y. . . . 234-2 23O . 2? io 6 yr. 1.5 d. 7 X io-7 y . .46d. a 2.90 1.53 Xio . 72 X 10-5 1.37 X 108 Ionium 230.2 io 5 yr. 7 . o X io 6 y. 3.11 i . 56 X io 8 75 XlO-6 1.40X10* Radium Ra Emanation . 226 222 1730 y. 3-8sd. . 00040 y. . 180 d. a+0 a 3-30 4.16 1.61 i-73 " 79 92 1.50 1.74 Radium A 218 3.0 m. .231 m. a 4-75 1.82 " I.OI 1.88 " Radium B 214 26.8 m. .0258 m. + 7 Radium Ci. . . . 214 19-5 m. .0355 m. a + /3 RaCz 210? 1.4 m. .495 m. Q ^_ , __ Radium C' 700000 s. a 6 94 2.o6Xio 9 I.3I X I0~ 8 2.37X108 Ra D, radio- lead 210 IS- 8y. . 044 y. slow/3 Ra E. 2IO 4 8* d. 14'? d S + T ___. Ra F. Polonium 210 136 d. .00510 d. a 3-84 1.68 X io .87 X io- 1.63 X TO* ACTINIUM GROUP. Actinium Radio- Act. . . . Actinium X ... A, 230? A A -4 19-5 d. 10. 2 d. 0355 d. .o68d. a? a 3-56 4. 26 i.6 4 X io 1.7 1.76 . 82 X 10-5 9 94 55X10* .8 79 Act. Emanation A -8 3.95. .1783. a 5-57 1.91 " I. 12 04 Actinium A. ... A - 12 .002 s. 350 s. a 6.27 1.98 I. 21 . 20 Actinium B.. . . A - 16 36 m. .0193 m. slow Actinium Ci. . . Actinium D . . . A - 16 A 20 2.1 m. 4.7 m. 33m. .147 a + 7 5-iS 1.85 Xio I . 05 X 10-5 1.94 X io 5 Actinium C'. . . A 20 a 6-45 2.00 " 1.23 THORIUM GROUP. Thorium Mesothorium i 232 228 1.3 X io 10 y. 5-3 X io-" .126 yr. a none 2.72 r . 50 X io . 69 X 10-5 1.32 X 105 Mesothorium 2 228 6.2 hr. .112 h. + 7 __. Radiothorium. . Thorium X.... 228 224 2 yr. 3-6 5 d. 347y- . 190 d. a 3-87 4-3 r . 70 X io i-75 .89 XlO- 5 94 I.66X 108 1.8 " Th. Emanation. 22O 54 sec. .0128 s. a 5-oo 1.85 " 1.04 1.9 " Thorium A. ... Thorium B 216 212 o. 14 sec. 10.6 h. 4-95 s. .0654 h. a + 7 5-70 1.94 I. IS 2.2 Thorium Ci . . . 212 60 m. .0118 m. a +0 4.80 i . 76 X io .95 X 10-6 i 8 X io 5 Thorium D.... 208 3.1 m. . 224 m. . Thorium C' . . . 212 iQ-u sec. 7 X 101 sec. a 8.6 2.22 X IO 9 i 53 X io-5 2.9 X 105 Potassium 39-1 ? P P Rubidium 85-5 ? ? * I I See The Constants of Radioactivity, Wendt, Phys. Rev. 7, p. 389, 1916. SMITHSONIAN TABLES. TABLE 606 (continued). RADIOACTIVITY. 397 fj. = coefficient of absorption for ft rays in terms of cms. of aluminum; Mlf of the y rays in cms of Al so that if /o is the incident intensity, J that after passage through d cms, / = Joe dp. URANIUM -RADIUM GROUP. /3 rays. 7 rays. Remarks. Absorption coefficient = n Velocity light = i Absorption coefficient = /xi Ur i 5io 14.4 300 200 13, 80, 890 13, S3 130 43 Wide range 52, .65 . 36 to . 74 .80 to .98 Wide range 24, .70, .140 354, 16, .27 230.40, .51 IIS 45, -99 Like Ra D 585 i gram U emits 2.37 X io a particles per sec. /9 rays show no groups of definite veloci- ties. Chemically allied to Th. Not separable from Ur i. Probably branch product. Exists in small quantity. Chemical properties of and non-separable from Thorium. Chemical properties of Ba. i gr emits per sec. in equilib. 13.6 X to 10 a par- ticles. Inert gas, density in H, boils -65 C, density solid 5-6, condenses low pres- sure 150 C. Like solid, has + charge, volatile in H. 400, in O about 550. Volatile about 400 C in H. Separated pure by recoil from Ra A. Volatile in H about 430, in O about 1000. Probably branch product. Separated by recoil from Ra C. Separated with Pb, not yet separable from it. Volatile below 1000. Separated with Bi. Probably changes to Pb. Volatile about 1000. UrXi UrXi... Ur 2... Ur Y Io Ra Ra Em RaA RaB RaCi Ra C2 RaD RaE... Ra F ACTINIUM GROUP. Act . . . 170 Very soft 28~ S 25, . 190 120,31, -45 .7 9 8 Probably branch product Ur series. Chemically allied to Lanthanum. Chemical properties analogous to Ra. Inert gas, condenses between 120 and 150. Analogous to Ra A. Volatile above 400. from the heat conductivity k, the specific heat at constant volume c v , {.itfpGcv/Nk}} (Laby and Kaye); a superior limit from the maximum density in solid and liquid states (Jeans, Sutherland, 1916) and an inferior limit from the dielectric constant D, [(D i)j/r.V}l or the index of refraction n, {(n 2 i)2/7r/vH. The table is derived principally from Dushman, I.e. 1 Gas. L X TO* (cm) Average free path.* Collision frequency. Q/L Xio- 20 C* lo' X Molecular diameters (cm): From L (vis- cosity) M From van der Waal's B From heat conduc- tivity Limiting Boltzmann. Meyer. Max density P Min. D or H oC 20 C 20 C 5-92 8.98 8.46 5.56 25-25 16.00 9-5 8~ S o 9-05 5-6 6.60 9.88 9-23 6.15 27-45 17-44 (14-7) 9.29 9-93 5-83 8-73 8.16 5-44 33-10 15.40 (I3.o) 8.21 8.78 9150 4000 5100 6120 4540 10060 5070 4430 2 97 2.88 3 19 1.90 2.40 2jj 3-08 2-94 3 12 3-23 2.6 S 2-34 (3-69) 3 oi 3 15 2.92 4-02 2.86 3 40 2-30 2.32 3 M 3-53 3-42 2 1 7 3-27 J:3 2.40 3 35 3 23 2.99 3-5S 2.66 74 90 92 ( '.70) 95 (I'll) Argon Carbon monoxide dioxide.. Helium Hydrogen Mercury Nitrogen Oxygen Xenon * Pressure = io 8 bars = io dynes -i- cm 1 = 75 cm Hg. SMITHSONIAN TABLES. 400 TABLES 513-514. TABLE 513. Cross Sections and Lengths of Some Organic Molecules. According to Langmuir (J. Am. Ch. Soc. 38, 2221, 1916) in solids and liquids every atom is chemically combined to adjacent atoms. In most inorganic substances the identity oi the molecule is generally lost, but in organic com- pounds a more permanent existence of the molecule probably occurs. When oil spreads over water evidence points to a layer a molecule thick and that the molecules are not spheres. Were they spheres and an attraction existed be- tween them and the water, they would be dissolved instead of spreading over the surface. The presence of the COOH, CO or OH groups generally renders an organic substance soluble in water, whereas the hydrocarbon chain decreases the solubility. When an oil is placed on water the COOH groups are attracted to the water and the hydrocarbon chains repelled but attracted to each other. The process leads the oil over the surface antil all the COOH groups are in contact if possible. Pure hydrocarbon oils will not spread over water. Benzene will not mix with water. When a limited amount of oil is present the spreading ceases when all the water-attracted groups are in contact with water. If weight w of oil spreads over water surface A , the area covered by each molecule is AM/wN where M is the molec- ular weight of the oil (O = 16), N, Avogadro's constant. The vertical length of a molecule / = M/apN = W/pA where p is the oil density and a the horizontal area of the molecule. Substance. Cross section in cm* X lo" / in cm (length) X 108 Substance. Cross section in cm 2 Xio" / in cm (length) Xio" Palmitic acid CisHsiCOOH . . 24 19 6 Cetyl alcohol CieHssOH 21 21 .9 Stearic acid CnHssCOOH 24 21.8 Myricyl alcohol CsoHeiOH 29 35- 2 Cerotic acid C 26 H 5 iCOOH Oleic acid Ci-HssCOOH . 18 29.0 10 8 Cetyl palmitate CuHsiCOOCieHss . Tristearin (CigHssOzjsCsHs 21 69 44-0 23 7 Linoleic acid CnHsiCOOH. . . 47 10. 7 Trielaidin (CisHssOz^CsHs 137 ii .9 Linolenic acid CnHwCOOH Ricinoleic acid CnH 3 2(OH)COOH.. . . 66 90 7.6 5-8 Triolein (CisHssO'^CsHs Castor oil (CnH32(OH)COO)3C3H 5 . Linseed oil (CnH3iCOO)3C 3 H5 145 280 143 II. 2 5-7 II. TABLE 514. Size of Diffracting Units in Crystals.^ The use of crystals for the analysis of X-rays leads to estimates of the relative sizes of molecular magnitudes. The diffraction phenomenon is here not a surface one, as with gratings, but one of interference of radiations reflected from the regularly spaced atomic units in the crystals, the units fitting into the lattice framework of the crystal. In cubical crystals {100} this framework is built of three mutually perpendicular equidistant planes whose distance apart in crystallographic parlance is dioo. This method of analysis from the nature of the diffraction pattern leads also to a knowledge of the structure of the various atoms of the crystal. See Bragg and Bragg, X-rays and Crystal Structure. 1918. Crystal. Elementary diffracting element. Side of cube. Molecules or atoms in unit cube. KC1 NaCl ZnS... Face-centered cube * cm 6.30 X io-8 5.56 X io-8 5 46 X io~ 4 molecules CaF 2 . . . " " " t a FeS 2 Fe ., ,, | 5.26 X io- 2 86 X io~ Al.. Face-centered cube 4 05 X 10" Na Ni Face-centered cube 2.76 X iQ- 3.52 X IQ- 2 4 * Each atom is so nearly equal in diffracting power (atomic weight) in KC1 that the apparent unit diffracting element is a cube (simple) of J this size. Elementary body -centered cube, atom at each corner, one in center; e.g., Fe, Ni (in part), Na, Li? Elementary face-centered cube, atom at each corner, one in center of each face; e.g., Cu, Ag, Au, Pb, Al, Ni (in part) , etc. Simple cubic lattice, atom in each corner. Double face-centered cubic or diamond lattice C (diamond); Si, Sb, Bi, As?, Te?. t Diamond lattice. J Cubic-holohedral. Cubic-pyritohedral. Metals taken from Hull, Phys. Rev. 10, p. 661, 1917 t See Table 528 for best values of calcite and rock-salt grating spaces. Note : (Hull, Science 52, 227, 1920). Ca, face-centered cube, side 5.56 A, each atom 12 neighbors 3.93 A distant. Ti, centered cube, cf. Fe, side 3.14 A, 8 neighbors 2.72 A. Zn, 6 nearest neighbors in own plane. 2.67 A, 3 above, 3 below, 2.92 A. Cd, cf. Zn, 2.98 A, 3.30 A. In, face-centered tetragonal, 4 nearest 3.24 A, 4 above, 4 below, 3.33 A. Ru, cf. Zn, 2.69 A, 2.64 A. Pd, face-centered cube, side 3.92 A, 12 neighbors. 2.77 A. Ta, centered cube, side 3.27 A, 8 neighbors 2.83 A. Ir, face-centered cube, side 3.80 A, 12 neighbors, 2.69 A (A =io~ 8 cm). Note : (Bragg, Phil. Mag. 40, 169, 1920). Crystals empirically considered as tangent spheres of diameter in table, atom at center of sphere. When lattice known allows estimation of dimensions of crystal unit. Table foot of next page (atomic numbers, elements, diameter in Angstroms, io- 8 cm). SMITHSONIAN TABLES. TABLE 515. 4OI ELECTRONS. RUTHERFORD ATOM. BOHR ATOM. MAGNETIC FIELD OF ATOM- References: Millikan, The Electron, 1917; Science, 45, 421, 1917; Humphreys. Science. 46, 273, 1917; Lodge Nature, 104, 15 and 82. 1919; Thomson, Conduction of Electricity through Gases; Campbell. Modern Electrical Theory; Lorentz, The Theory of Electrons; Richardson, The Electron Theory of Matter, 1914. Electron: an elementary + or unit of electricity. Free negative electron: (corpuscle, J. J. Thomson); mass = 9.01 X io-g - 1/1845 H atom, probably all of electrical origin due to inertia of self-induction. Theory shows that when speed of electron = i/io velocity of light its mass should be appreciably dependent upon that speed. If mo be mass for small velocity v, m be the transverse mass for v, v/( velocity of light) = /8, then m - mo(i /S 2 )^, Lorentz, Einstein; for/3 =0.01 o.io 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ml mo = 1.00005 1.005 1-02 1.048 1.091 1.155 1.250 1.400 1.667 2.2Q4 (Confirmed by Bucherer, Ann. d. Phys. 1909, Wolz, Ann. d. Phys. Radium ejects electrons with 3/10 to 98/100 velocity of light.) m, due to charge = 2E 2 /^a, E = charge, a = radius, whence radius of electron = 2 X io~ 13 cm = 1/50,000 atomic radius. Cf. (radius of earth)/ (radius of Neptune's orbit) = 1/360,000. Positive electron: heavy, extraordinarily small, never found associated with mass less than that of H atom. If mass all electrical (?) radius must be 1/2000 that of the electron. No experimental evidence as with electron, since high enough speeds not available. Penetrability of atom by /3 particle (may penetrate 10,000 atomic systems before it happens to detach an electron) and a particles (8000 times more massive than electron, pass through 500,000 atoms without apparent deflection by nucleus more than 2 or 3 times) shows extreme minuteness. Upper limit not larger than icr" cm for Au (heavy atom) or 10'", H (light atom) (Rutherford). Cf. (radius sun)/(radms Neptune's orbit) = 1/3000, but sun is larger than planets. (Hg atoms by billions may pass through thin-walled highly-evacuated glass tubes without impairing vacuum, therefore massive parts of atoms must be extremely small compared to volume of atom.) Rutherford atom: number of free + charges on atomic nuclei of different elements = approximately \ atomic weight (Rutherford, Phil. Mag. 21, 1911, deflection of a particles); Barkla concluded free electrons outside nucleus same in number (Phil. Mag. 21, 191 1, X-ray scattering). If mass is electromagnetic, then lack of exact equiva- lence may be due to overlapping fields in heavy crowded atoms, a sort of packing effect; the charge on U = 92, at. wt. = 238.5. Moseley (Phil. Mag. 26, 1912; 27, 1914) photographed and analyzed X-ray spectra, showing their exact similarity in structure from element to element, differing only in frequencies, the square roots of these frequencies forming an arithmetical progression from element to element. Moseley's series of increasing X-ray frequencies is with one or two exceptions that of increasing atomic weights, and these exceptions are less anomalous for the X-ray series than for the atomic -weight series. It seems plausible then that there are 92 elements (from H to U) built up by the addition of some electrical element. Moseley assigned successive integers to this series (see Table 531) known now as atomic numbers. Moseley's discovery may be expressed in the form i _ Ei A 2 i n 2 " , r Xi ~ Et* where E is the nuclear charge and A the wave-length. Substituting for the highest frequency line of W, \t = 0.167 X io~ 8 cm (Hull), 2 = 74 = Nw, and Ei = i, then Xi = highest possible frequency by element which has one + electron; Ai = 91.4 wtju. Now the H ultra-violet series highest frequency line = 91.2 my. (Lyman); i.e.. this ultra- violet line of H is nothing but its K X-ray line. Similarly, it seems equally certain that the ordinary Balmer series of H (head at 365 mfj.) is its L X-ray series and Paschen's infra-red series its M X-ray series. There may be other electrons on the nucleus (with corresponding -f- charges) since they seem to be shot out by radioactive processes. They may serve to hold the + charges together. He, atomic no. = 2, has 2 free -f- charges, at. wt. = 4; may imagine nucleus has 4 + electrons held together by 2 electrons, with 2 electrons outside nucleus. H has one + and one electron. The application of Newton's law to Moseley's law leads to Ei/Ez = ai/a\-, where the a's are the radii of the inmost electronic orbits, i.e., the radii of these orbits are inversely proportional to the central charges or atomic numbers. (Note: When an a particle (-f- charge = 2e) is emitted by a radioactive element, its atomic number decreases by 2, the emission of a charged particle increases its atomic number by i.) Bohr atom: (Phil. Mag. 26, i, 476, 857, 1913; 29, 332, 1915; 30, 394, 1915). The experimental facts and the law of circular electronic orbits limit the electrons to orbits of particular radii. \Vhen an electron is disturbed from its orbit, e.g., struck out by a cathode ray, or returns from space to a particular orbit, energy must be radiated. Ii gestive that the emission of a /3 ray requires a series of y ray radiations. H does not radiate unless ionized and then gives out a spectrum represented by Balmer's formula v = N(i/m" i/n 2 ) where v is the frequency, N, a constant, and i for all the lines in the visible spectrum has the value 2, , the successive integers, 3, 4. 5, . . .; if m = i and , 2,3,4,. ..Lyman's ultra-violet series results; if m =3,n. 4,5,6 Paschen's infra-red series. These con tions led Bohr to his atom and he assumed: (a) a series of circular non-radiating orbits governed as above; (b tion taking place only when an electron jumps from one to another of these orbits, the amount radiated and its frequency SMITHSONIAN TABLES. (This Table supplements Table 514). 3 Li 3.00 13 Al 2.70 25 Mn a. 95 t 3& Kr 2.35* 54 Xe 2.70* Gl 3 .o .4 Si .35 26 Fe 2.80 37 Rb 4-5 55 4-75 4 Gl 2.30 14 Si 6 C 1.54 16 S 7 N 1.30 .7 Cl . 8 O .30 18 A 9 F .35 19 ' 20 r e 2.00 J/ rww ^O" f/J 27 Co 2.75 38 Sr 3.90 56 Ba 4.20 28 Ni 2.70 47 Ag 3-55 ' Tl 4.50 .10 28 INI 2.70 47 "K -*-55 .05* 29 Cu 2.75 48 Cd 3.20 82 Pb 3-80 9 r ,.35 .v- .15 30 Zn 2.65 10 Ne 1.30* ' 20 Ca 3.40 33 As 2.52 11 Na 3.55 22 Ti 2.80 34 Se 2.3$ 52 2.65 12 Mg 2.85 24 Cr 2 .8ot 35 Br 2.38 53 I 2.80 * Outer electron shell. t Cr, "electronegative," 2.35; Mn, ditto, 2.35. Broughall (Phil. Mag. 41, p. 872, t 9 2i) computes in the same units from Van der Waal's constant " b " the diame- ters of He, N A, Kr, and^C as 2 7 3 , 2.6, 2.9, 3.1, and 3.4- These inert elements correspond to JW^g2 filled successive electron shells. The corresponding atomic numbers are 2, 10, 18, 36 and 54. for Langmu filled successive electron shells. The corresponding at see J. Am. Ch. Soc., p. 868, 1919, Science 54, p. 59, i9 21 4O2 TABLE 515 (continued). BOHR ATOM. MAGNETIC FIELD OF ATOM- being determined by kv = Ai At, h being Planck's constant and A\ and At. the energies in the two orbits; (c) the various possible circular orbits, for the case of a single electron rotating around a single positive nucleus, to be deter- mined by T = (i/2)rhn, in which r is a whole number, n is the orbital frequency, and T is the kinetic energy of rotation. The remarkable test of this theory is not its agreement with the H series, which it was constructed to fit, but in the value found for N. From (a), (b), and (c) it follows that N = (2T^e t E 2 m)/h 3 = 3-294 X lo 15 , within i/io per cent of the observed value (Science, 45, p. 327). The radii of the stable orbits = TW/4ir*me*, or the radii bear the ratios i, 4, 9, 16, 25. If normal H be assumed to be with its electron in the inmost orbit, then 20. = i.i X io~ 8 ; best determination gives 2.2 X io~ 8 . The fact that H emits its characteristic radiations only when ionized favors the theory that the emission process is a settling down to normal condition through a series of possible intermediate states, i.e., a change of orbit is necessary for radiation. That in the stars there are 33 lines in the Balmer series, while in the laboratory we never get more than 12, is easily explica- ble from the Bohr theory. Bohr's theory leads to the relationship v% v% = V L ( see x ' ra y tables) , Rydberg-Schuster law. /8 a a For further development, see Sommerfeld, Ann. d. Phys. 51, i, 1916, Paschen, Ann. d. Phys., October, 1916; Harkins, Recent work on the structure of the atom, J. Am. Ch. Soc. 37, p. 1396, 1915; 39, p. 856, 1916. Magnetic field of atom : From the Zeeman effect due to the action of a magnetic field on the radiating electron the strength of the atomic magnetic field comes out about ip 8 gauss, 2000 times the most intense field yet obtained by an electromagnet. A similar result is given by the rotation of a number of electrons, Aio 3 , where A is the atomic weight; for Fe this gives io 8 gauss. For other determinations, see Weiss (J. de Phys. 6, p. 661, 1907; 7, p. 249, 1908), Ritz (Ann. d. phys. 25, p. 660, 1908), Oxley (change of magnetic susceptibility on crystallization, Phil. Tr. Roy. Soc. 215, p. 95, 1915) and Merritt (fluorescence, 1915); Humphreys, "The Magnetic Field of an Atom," Science, 46, p. 276, 1917- SMITHSONIAN TABLES. TABLES 516-518. 43 Note: The phenomena of Electron Emission, Photo-electric Effect and Contact (Volta) Potential treated in the subsequent tables are extremely sensitive to surface conditions of the metal. The most consistent observations have been made in high vacua with freshly cut metal surfaces. TABLE 516. Electron Emission from Hot Metals. Among the free electrons within a metal some may have velocities great enough to escape the surface attraction. The number n reaching the surface with velocities above this critical velocity = N(RT/2irM)le~KT where N ** number of electrons in each cm 3 of metal, R the gas constant (83.15 X io erg-dyne), T the absolute temperature, M the atomic weight of electron (.000546, O = 16), v> the work done when a "gram-molecule" of electrons (6.06 X io electrons or 96,500 coulombs) escape. It seems very probable that this work is done against the attraction of the electron's own induced image in the surface of the conductor. When a sufficiently high + field is applied to escaping electrons so that none return to the conductor, then the saturation current has been found to follow the equation assuming N and w constant with the temperature; this is equivalent to the equation for n just given and is known as Richardson's equation. In the following table due to Langmuir (Tr. Am. Electroch. Soc. 29, 125, 1916) 12000 = satura- tion current per cm 2 for T = 2000 K; < = w/F - Rb/F = work done when electrons escape from metal in terms of equivalent potential difference in volts; F = Faraday constant = 96,500 coulombs. Metal. a amp/cm 2 b J?000 amp/cm 1 2 - ! (see Table 517 for significance of symbols), since the number of free electrons in different metals per unit volume is so nearly the same that RT log (N A /N g) may be neglected. The contact potentials may thus be calculated from photo- electric phenomena (see Table 517 for references). They are independent of the temperature. The following table gives a summary of values of in volts obtained from the various phenomena where an electron is torn from the attrac- tion of some surface. In the case of ionization potentials the work necessary to take an electron from an atom of metal vapor is only approximately equal to that needed to separate it from a solid metal surface. (a) THE ELECTRON AFFINITY OF THE ELEMENTS, IN VOLTS. Photo- Metal. Contact. (Henning.] Therinionic (Langmuir.] electric and contact. Photo- electric. (Richardson) Miscel- laneous. Single- line spectra. Adjusted mean. (Mifflkan.) Tungsten 4-52 4-52 Platinum 4-3 4-45 4.4? Tantalum 4 31 4- 3 Molybdenum 4.31 4- 3 Carbon. Silver 4-05 Copper. (4 o) Bismuth Tin 3 78 3-5 3-8 Iron ~ Rfi 3 2? Zinc Thorium 3.46 3.36 3-4 4.04 3-4 3-4 Aluminum 3-o6 2.8 Magnesium Titanium 2.63 3-2 4-35 2.7 Lithium _ 2-35 1.85 2-35 Sodium 1.82 2.1 2. II 1.82 (b) It should not be assumed that all the emf of an electrolytic cell is contact emf. Its emf varies with the elec- trolyte, whereas the contact emf is an intrinsic property of a metal. There must be an emf between the two electrodes of such a cell dependent upon the concentration of the electrolyte used. The following table gives in its first line the electrode potential e^ of the corresponding metals (in solutions of their salts containing normal ion concentration) on assumption of no contact emf at the junction of the metals. The second line, $ e h 3.7 volts, gives an idea of the electrode potentials (arbitrary zero) exclusive of contact emf. Metal Ag Cu Bi Sn Fe Zn Mg Li Na e h +0.80 +0.34 4-o. 20 O.IO -0-43 0.76 -i 55 -3-03 -2.73 4>- A -3.7 -0.40 +0.04 4-O.20 0. 20 -0-43 0.46 -0-55 -1.65 0.85 SMITHSONIAN TABLES. TABLES 620-631. IONIC MOBILITIES AND DIFFUSIONS. 405 The process of ionization is the removal of an electron from a neutral molecule, the molecule thus acquiring a result- ant -f charge and becoming a + ion. The negative carriers in all gases at high pressures, except inert gases, consist for the most part of carriers with approximately the same mobilities as the -f- ions. The negative electrons must, therefore, change initially to ions by union with neutral molecules. The mobility, U, of an ion is its velocity in cm/sec, for an electrical field of one volt per cm. The rates of diffusion, D, are given in cm 3 /sec. U = DP/Ne, where P is the pressure, N, the number of molecules per unit volume of a gas and e the electronic charge. Nature of the gas and the mobilities: (i) The mobilities are approximately proportional to the inverse sq. rts. of the molecular weights of the permanent gases; better yet when the proportionality is divided by the 4th root of the dielectric constant minus unity; (2) The ratio U + /U seems to be greater than unity in all the more electro- negative gases. Mobilities of Gaseous Mixtures: Three types: (i) Inert gases have high mobilities; small traces of electro- negative gases make values normal. (2) Mixed gases: lowering of mobilities is greater than would be expected from simple law of mixture. (3) Abnormal changes produced by addition of small quantities of electro-negative gases: e.g.: normal mobility 6 mm CzHsBr gave 6 mm CzHsI 10 mm CjHsOH " 9 mm CsHsO " U+ = 1.37 1-37 1-37 0.91 i IS U - Wellisch, Pr. Roy. Soc. 8zA, p. 500, 1009. Temperature Coefficient of Mobility: There is no decided change with the temperature. Pressure Coefficient of Mobility: Mobility varies inversely with the pressure in air from 100 to i/io atmosphere for ion, to i/iooo, for + ion; below i/io atmosphere all observers agree that the negative ion in air increases abnormally rapidly. Free Electrons: In pure He, Ar, and N, the negative carriers have a high mobility and are, in part at any rate, free electrons; electrons become appreciable in air at 10 cm pressure. TABLE 520. Ionic Mobilities. Dry gas. Mobilities. K i Observer. Dry gas. Mobilities. K i Observer. + - + - H He Ar N 6.70 5-09 1-37 1.27 1.36 0.81 0.74 1.40 7-95 6.31 i. 80 0.85 0.80 1.78 .000273 .000074 .000100 .000590 .000540 .000960 .00770 .000590 Zeleny Franck Zeleny Wellisch Mean Nitrous oxide Ethyl alcohol ecu Ethyl chloride 0.82 0.34 0.30 0.33 0.29 o. 29 0.30 0.17 0.90 0.27 0.31 0.31 0.31 0.28 0.31 O. IO .00107 .00940 .00426 .01550 .00742 .01460 .00870 Wellisch CO, NHa Air Ethyl ether Methyl bromide .... Ethyl formate Ethyl iodide Franck, Jahr. d. Rad. u. Elek. 9, p. 2. 1912; Wellisch, Pr. Roy. Soc. SaA, p. 500, 1009. The following values are from Yen, Pr. Nat. Acad. 4, 19 8. H 2 N 2 Air. S0 2 CoHi 2 CiH 6 C:H0 CjHiCl CHjI C-HJ u + 5-54 1-30 i-37 .412 .385 -363 . .507 .W .216 1.81 U - 8-45 i. 80 1.81 .414 451 -373 331 -U7 .220 1.81 U-/U+. i. S3 1.38 1.34 I. 00 1.17 i o;> 1.07 1.04 1.05 I. 00 TABLE 521. Diffusion Coefficients. The following table gives the observed and computed (D = sooUP/Ne = very nearly 0.023610 value* of the diffusion coefficients. The diffusion coefficients are given for some neutral molecules as actually determined for some gases into gases of nearly equal molecular weight. Table taken from Loeb, " The Nature of the Gaseous Ion, J. Franklin Inst. 184, p. 775, 1917. Gas diffused D II -4- D + lc r ions. into moK-t Computed. ved. Ar... Hz He No o. 706 73Q 5.09 6. 02 I. 20 o. 14; o i.\; Air Oi .178 1-35 0.0319 0.028 &::::::::::::: :: CO? N2 NzO CO .171 1.5-1.0 i >i 1.27 .82 .81 .0299 -0193 .019^ .oaj .oaj* CzHsOH COj o. 069? v} .00805 Air HzO Ethyl acetate Air 093 .246 :5i I-3S .0071 0319 - NHj NHa .190* 0.74 0174 * COs into COs. t Ethyl formate. J Estimated. SMITHSONIAN TABLES 4 o6 TABLES 522-524. COLLOIDS. TABLE 522. General Properties of Colloids. For methods of preparing colloids, see The Physical Properties of Colloidal Solutions, Burton, 1916; for general properties, see Outlines of Colloidal Chemistry, J. Franklin Inst. 185, p. i, 1918 (contains bibliography). The colloidal phase is conditioned by sufficiently fine division (i X icr 4 to io~ 7 cm). Colloids are suspensions (in gas, liquid, solid) of masses of small size capable of indefinite suspension; suspensions in water, alcohol, benzole, glyc- erine, are called hydrosols, alcosols, benzosols, glycerosols, respectively. The suspended mass is called the disperse phase, the medium the dispersion medium. Coiioms tall into 3 quite definite classes: ist, those consisting of extremely finely divided particles (Cu, Au, Ag, etc.) capable of more or less indefinite suspension against gravity, in equilibrium of somewhat the same aspect as the pases of the atmosphere, depending as in the Brownian movement upon the bombardment of the molecules of the medium: 2nd, those resisting precipitation (haemoglobin, etc.) probably because of charged nuclei and which maybe coagulated and precipitated by the neutralization of the charges; 3rd, colloidal as distinguished from the crystalloidal condition, the colloid being very slowly diffusible and incapable unlike crystalloids of penetrating membranes (gelatine, silicic acid, caramel, glue, white of egg, gum, etc.). Smallest particle of Au observed by Zsigmody (ultraraicroscope) i . 7 X lo"" 7 cm. visible in ordinary microscope about 2.5 X io~ 6 cm. " ultramicroscope, with electric arc 15 X io~ 7 cm. with direct sunlight i X io~ 7 cm. TABLE 523. Molecular Weights of Colloids. Determined from diffusion. Determined from freezing point Gum arabic Tannic acid (^22)* 1750 2730 Glycogen (162) * Tungstic acid (250) * ... 1625 1750 Egg albumen 7420 Gum 1800 Caramel 13200 Albumose 2400 (Due to Graham) Ferric hydrate (107) * oooo Egg albumen 14000 Starch (162) * 25000 * Formula weight. TABLE 524. Brownian Movement. The Brownian movement is a microscopically observed agitation of colloidal particles. It is caused by the bom- bardment of them by the molecules of the medium and may be used to determine the value of Avogadro's number. Perrin, Chaudesaignes. Ehrenhaft and De Broglie found, respectively, 70, 64, 63 and 64 X io 2 * as the value of this constant. The following table indicates the size and the dependence of this movement on the magnitude of the particles. Material. Diameter X io cm Medium. Temp. Velocity X 10* cm/sec. Observer. < Dust particles Gold 2.0 o 35 Water 20? none 200 Zsigmody Gold (i 280 a Gold Platinum Platinum 0.06 4 to .5 Acetone Water 18 20 700. 3900. 3200. Svedberg, 1906-9 Rubber emulsion Mastic IO. IO i? 20> 124. i 55 Henri, 1908 Gamboge 4- 5 ti 2O 2 . 4 Chaudesaignes, 1908. 2 13 it 3 4 The movement varies inversely as the size of the particles; in water, particles of diameter greater than 4^1 show no perceptible movement; when smaller than .I/JL, lively movement begins, while at 10 ntfj. the trajectories amount up to SMITHSONIAN TABLES. TABLES 525-527. 47 COLLOIDS. TABLE 525. Adsorption of Gas by Finely Divided Particles. See also p. 439 Fine division means great surface per unit weight. All substanct- tcn.l t., adsorb gas at surface, the more the higher the pressure and the lower the temperature. Since different gases vary in tin- adaption fractional separation n possible. Pt black can absorb 100 vols. Hz, 800 vols. On, Pd 3000 vols. H. In I'd. heated to 100, is used to remove Hz (higher temperature used for faster adsorption, will take more at lower temperature). Pt can dissolve several vols. of Hz, Pd, nearly TOO at ordinary temperatures; but it seems probable that the bulk of the 100 vols. of Hz taken by Pt and the 3000 by Pd must be adsorbed. In 1848 Rose found the density 21 to 22 for Pt foil but 26 for precipitated Pt. The film of adsorbed air entirely changes the behavior of very small particles. They flow like a liquid (cf. fog). With substances like carbon black as little as 5 per cent of the bulk is C; a liter of C black may contain 2.5 liters of air. Mitscherlich calculated that when CQz at atmospheric pressure, 12 C, is adsorbed by boxwood charcoal, it occu- pies 1/56 original vol. Apparent densities of gases adsorbed at low temperatures by cocoanut charcoal are of the T^T order (sometimes greater) as liquids. Cm 5 of Gas Adsorbed by a Cm 3 of Synthetic Charcoal (corrected to o C, 76 cm?) (Hemperl and Vater). C H 2 Ar N 2 02 CO CO 2 NO NjO Iff -185 7-3 19-5 284.7 12.6 92.6 21.0 107-4 632.2 25-4 122.4 26.8 139-4 697.0 83.8 568.4 103.6 231-3 109.4 330.1 CH, CzHe C 2 H 4 CzHi NHj H 2 S Cli SOj + 20 -78 41.7 174-3 119.1 275-5 139 2 360.7 135-8 488.5 197.0 213 .0 304 5 337-8 Cm 3 of Gas Adsorbed by a Cnv of Cocoanut Charcoal (corrected to o C, 76 cm) (Dewar). C He H2 N 2 O2 CO Ar -185 2 IS 4 135 15 18 155 230 21 100 12 I7S See Langmuir, J. Am. Ch. Soc. 40, 1361, 1918; Richardson, 39, 1829, 1916. TABLE 526. Heats of Adsorption. Adsorber. Amylene. 1 4> j M |3 S a 11 w *5 j 11 || 11 li u - % Carbon disulphidc. 1 a , * i I Fuller's earth * 57-1 30.2 27-3 21.8 17.2 13.4 10.9 10. S 8.4 4.6 4.6 4.2 3-9 Bone charcoal * 18.5 19 3 17.6 16.5 10.6 14.0 n. i 8.4 13-9 8.9 Kaolin * 78.8 27.6 24-5 20.4 15-7 9-9 99 94 7.2 Fuller's earth f .683 .684 .679 .611 .610 .621 .625 * Small calories liberated when i g of the adsorbent is added to a relatively large quantity of the liquid, t Volume adsorped from saturated vapor by i g of fuller's earth. Gurvich, J. Russ. Phys. Ch. Soc. 47, 805, 1915. TABLE 527. Molecular Heats of Adsorption and Liquefaction (Favre). Molecular heats of Molecular heats of Adsorber. Gas. adsorption. lique- faction. Adsorl>er. adsorption. lique- faction. Platinum H 2 46200 _ Charcoal IOOOO-IOOOO 5600 Palladium Charcoal H 2 NHs 18000 5000-8500 (5000) Hd HBt 020O-I0200 15200-15800 (3600) (4000) CO* 6800-7800 6250 HI 21000-23000 (4400) NzO 7100-10900 4400 SMITHSONIAN TABLES- 408 TABLES 528-529. TABLE 528. Miscellaneous Constants (Atomic, Molecular, etc.). Elementary electrical charge, charge on electron, i charge on a particle t = 4-774 * I0 ~ 10 esu ( M ) = 1.591 X io- 2 emu = i . 591 X io- coulomb Mass of .an electron i* = 9 . 01 X io~ 28 g Radius of an electron about 2 X io^ 13 cm Ratio elm, small velocities e/m = i. 766 X io 7 emu. g -1 Number of molecules per gram molecule or per gram molecular weight (Avogadro constant) N = 6.062 X io (M) Number of gas molecules per cm 3 , 76 cm, o C (Loschmidt's number) n = 2.705 X io 19 (M) Number of gas molecules per cm j , o C at i X io 6 bars 2 . 670 X io lj Kinetic energy of translation of a molecule at o C Eo 5 . 621 X io~ 14 erg (M) Constant of molecular energy, Eo/T - change of translational energy per C. . . e = 2.058 X io~ 16 erg/ 6 C (M! Mass of hydrogen atom : = i . 662 X to" 24 g (M) Radius of hydrogen molecule about : . io~ 8 cm Mean free path, ditto, 76 cm, o C, about Z, = i . 6 X io~ 6 cm/sec. Sq. rt. mean sq. velocity, ditto. 76 cm. o C G = 1.84 X 10* cm/ sec. Arithmetical average velocity, ditto. 76 cm. o C 12 = i . 70 X io 5 cm/sec. Average distance apart of molecules. 76 cm, o C = 3 X io~ 6 cm Boltzmann gas constant = constant of entropy equation = R/N = poVo/TN = (}) k = i .372 X io-" erg/ C Volume per mol(e) or gram-molecular weight of ideal gas, 76 cm, o C (i .01323 X io 6 bars) =22.412 liters Ditto, i X io bars, o C (75 cm Hg) = 22 . 708 liters Gas constant: PVm = RT. V m = vol. molec. wt. in g when P in g/cm 2 , V m in cm 3 R = 84. 780 g-cm/ C when P in atmospheres, Vm in liters R = o. 08204 /-atm/ C when P in dynes, Vm in cm 3 R =8.315 X io 7 ergs/ C Absolute zero = o Kelvin = 273.13 C i Mega bar (= Meteorological "bar") = io dynes/cm 2 = 1.013 kg/cm 2 =0.987 atmosphere Mechanical equivalent of heat, i g (20 C) cal = 4. 184 X io 7 ergs = 4. 184 Joules Faraday constant F = 96494 coulombs Velocity of light in vacuo c = 2. 99860 X io 10 cm/sec. Planck's element of action h = 6. 547 X xo"" 27 erg. sec. (M) Rydberg's fundamental frequency Vo = 3 . 28880 X io 15 sec." 1 Rydberg's constant. Vo/c N = 109678 . 7 \Vien's constant of spectral radiation ct = i. 4312 for X in cm (M) Stefan-Boltzmann constant of total radiation ;. Radial velocity km. i Achernar 0.6 B 5 I* 34-0'" -57 45' 0.094" 108 +0.051" -0.9 2 Aldebaran J. . . . 1. 1 K 5 4 30.2 + 16 18 0.203 160 +0.056 -0.2 +S5-I 3 Capellat t 0. 2 G 5 9-3 +45 54 0-437 1 68 +0.075 -0-5 +30.2 4 Rigel*f 0.3 B8 5 97 8 19 O.OOI 135 +0.007 5-5 + 22.6 I Betelgeuse t Canopus 0.6-1.2 -0.9 Ma F 5 49-8 6 21.7 + 7 23 -52 38 0.029 0.018 7 4 +0.019 +0.007 -2.7 -6.7 +21.3 + 20.8 1 7 Sinus* -1.6 A 6 40.7 16 35 1.316 204 +0.376 + 1.2 7-4 i 8 Procyon * 0.5 FS 7 34-1 +5 29 1.242 214 +0.309 +3-0 -3-5 9 Pollux . . I . 2 K 7 39-2 +28 16 o. 625 264 +o . 064 +0.2 +3-9 10 Regulus { 1-3 B8 10 3.0 + 12 27 0.247 269 +0.033 I.I -9.1 II a Crucis* I.I Bi 12 21. O -62 33 0.048 240 +0.047 -0.5 +7- 12 Crucis t I- 5 Bi 12 41. Q -59 9 0.056 240 +0.008 -4.0 + 13- 13 Spica t 1.2 B 2 13 19-9 -io 38 0.055 229 O.OI2 + 1.6 14 /8 Centauri t . . . 0-9 B! 13 56.8 59 53 0.041 219 +0.037 X-3 -7- 15 Arcturus 0. 2 K 14 II. I + 19 42 2.282 209 + 0-075 -0.5 39 16 a Centauri * 0.3 G 14 32.8 -60 25 3.680 281 +0-759 +4-7 -21.6 17 Antares 1 1 I. 2 Ma 16 23.3 26 13 0.034 192 +0.029 -1-5 3i 18 iQ Vega Altair O.I 0.9 A A 5 18 33-6 19 45-9 +38 41 +8 36 0.346 0.655 36 54 +0.091 +0.214 O.I + 2-5 -13-8 -33- 20 Deneb i-3 A2 20 38.0 +44 55 O.OOI 180 +O.002 -7.2 -4- 21 Fomalhaut i-3 A 3 22 52.1 -30 9 0.365 117 +0.138 + 2.0 +6.7 * Visual binary. t Spectroscopic binary. { Pair with common proper motion. Wide pair probably optical. Mass relative to sun of (7) is 3.1; of (8), 1.5; of (16), 2.0. For description of types, see Table 534 or Annals of Harvard College Observatory, 28, p. 146, or more concisely 56, p. 66, and 91, p. 5. The light ratio between successive stellar magnitudes is "V^ioo or the number whose logarithm is 0.4000, viz., 2.512. The absolute magnitude of a star is its magnitude reduced to a distance corresponding to o.i" parallax. TABLE 542. Wolf's Observed Sun-spot Numbers. Annual Means. Sun-spot number = k(io X number of groups and single spots observed + total number of spots in groups and single spots), k depends on condition of observation and telescope, equaling unity for Wolf with 3-in. telescope and power of 64. Wolf's numbers are closely proportional to spotted area on sun. 100 corresponds to about 1/500 of visible disk covered (umbras and penumbras). Periodicity: mean, 11.13, extremes, 7.3 and 17.1 years. Monthly Weather Review, 30, p. 171, 1002; monthly means, revised, 1749-1901; see A. Wolfer in Astronomische Mitteilungen and Zeitschrift fur Meteorologie, daily and monthly values. Year. i 2 3 4 5 6 7 8 9 1750 83 48 48 31 12 IO IO 32 48 j. 1760 63 86 61 45 36 21 // 38 70 106 1770 IOI 82 66 35 31 7 20 92 154 i jf> 1780 85 68 38 23 IO 24 83 132 I3 1 118 7790 90 67 60 47 41 21 16 6 4 7 1800 14 34 45 43 48 42 28 10 8 1 1810 o i 5 12 14 35 46 41 30 24 1820 1830 16 7 48 ,1 2 8 8 13 17 57 36 122 50 138 62 103 67 86 1840 63 37 24 it 15 40 62 98 124 96 1850 66 64 54 39 21 7 4 23 55 94 1860 96 77 59 44 47 30 16 7 37 1870 1880 139 32 ill 54 102 60 66 64 8 17 52 ii 25 12 u 3 7 6 6 1890 1900 7 IO 36 3 73 5 85 24 78 42 64 42 54 26 62 I 12 44 1910 19 6 4 10 46 55 99 78 NOTE: The sun's apparent magnitude is 26.5, sending the earth 00,000,000,000 times as much light as the star Aldebaran. Its absolute magnitude is +4-8. Ratio of total radiation of sun to that of moon about 100,000 to i 1 T , np i cv " " light " " " ' 400,000 to i / SMITHSONIAN TABLES. 416 TABLES 543-545. GEODETICAL AND ASTRONOMICAL TABLES. TABLE 543. Length, of Degrees on the Earth's Surface. Miles per degree Km. per degree Miles per degree Km. per degree At At Lat. L^t. of Long. of Lat. of Long. of Lat. of Lon^. of Lat. of Long. of Lat. 10 69.17 68.13 68.70 68.72 111.32 109.64 110.57 II0.60 S 39-77 34.67 6 9 .17 69.23 64.00 55.80 111.42 2O 3 65-03 59-9 6 68.79 63.88 104.65 96.49 110.70 110.85 65 70 29.32 2373 69.28 69.32 47.18 33.19 111.50 III.S7 40 4<5 49.00 68.99 69.05 85.40 78.85 111.03 III.I3 L 5 17.96 12.05 69-36 28.90 19.39 111.62 111.67 44-55 69.11 71.70 111.23 90 0.00 69.41 o.oo III.7O For more complete table see " Smithsonian Geographical Tables.' TABLE 544. Equation of Time. The equation of time when -f- is to be added to the apparent solar time to give mean time. When the place is not on a standard meridian (75th, etc.) its difference in longitude in time from that meridian must be subtracted when east, added when west to get standard time (75 th meridian time, etc.). The equation varies from year to year cyclically, and the figure following the -I- sign gives a rough idea of this variation. M. S. M. S. M. S. M. S. Jan. I t3 26-j f- T 4 Apr. i +4 2J - 7 July i +3 3'J :S Oct. i 10 12- U 8 Feb. i 9 2 5i r 9 - 4 15 May I +o 8 Z != 5 L 3 Aug. i t! 42 ^ +6 9^ L3 1=3 15 Nov. i 16 i 9 : : 6 I 2 Ma/i -f-14 20- + 12 34r j - 2 ~- 4 *5 June I 3 49d 2 28- - I = 3 Sept. I +4 24- -fo 2- tz5 -7 Dec. I 15 22 J -io 5 s: ^8 IS + 9 9a E 6 15 + 8 3 t 4 15 4 4iz L9 15 4 53d t-IO TABLE 545. Planetary Data. Body. Reciprocals of masses. Mean distance from the sun. K m . Sidereal period. Mean days. Equatorial diameter. Km. Inclination of orbit. Mean density. HoO = I Gravity at surface. Sun I. I39H07 1.42 28.0 Mercury 60000OO. S8xio 87-97 4842 7. 003 5-6l 0.4 Venus 408OOO. 108' 244.70 I2I9I 3-393 5-16 0.9 Earth * 329390. 149' 365-26 12757 5.52 I.OO Mars 3093500. 228 ' 686.98 6784 1.850 3-95 0.4 Jupiter 1047.35 778' 4332.59 142745 1.308 2.7 Saturn Uranus 3501.6 22869. 1426' 2869' 10759.20 30685.93 120798 49093 2.492 0-773 I '-3 1.2 1.0 Neptune 19700. 4495 " 60187.64 52999 1.778 1-30 1.0 Moon t 81.45 38 x io 4 27.32 3476 5-145 3-36 0.17 1 *Earth and moon, t Relative to earth. Inclination of axes: Sun 7. 25; Earth 23.45; Mars 24*.6; Tupiters'.i; Saturn 26. 8; Neptune 27.2. Others doubtful. Approximate rates if rotation: SunaSid; Moon27jd; Mercury 88d; Venus 225d; Mars 24"" 37"' ; Jupiter 9 h 55'" ; Saturn io h I4 m . SMITHSONIAN TABLE*. TABLES 646-648. ASTRONOMICAL DATA. 417 TABLE 546. Numbers and Equivalent Light of the Stars. The total of starlight is a sensible but very small amount. This table, taken from a paper by Chapman, shows that up to the 2oth magnitude the total light emitted is equivalent to 687 ist-magnitude stars, equal to about the hundredth rnrt of full moonlight. If all the remaining stars are included, following the formula, the equivalent addi- tion would be only three more ist-magnitude stars. The summation leaves off at a point whfcre each additional magni- tude is adding more stars than the last. But, according to the formula, between the 23d and 24th magnitudes there is a turning point, after which each new magnitude adds less than before. The actual counts have been carried so near this turning point that there is no reasonable doubt of its existence. Given its existence, the number of stars is probably finite, a conclusion open to very little doubt. All the indications of the earlier terms must be misleading if the margin between i and 2 thousand millions is not enough to cover the whole. (Census of the Sky, Sampson, Observ- atory, 1915-) Equivalent Equivalent Magnitude, m Number. number of ist- magnitude Totals to magnitude, m Magnitude, m Number. number of ist- magnitude Totals to magnitude, m stars. stars. -1.6. ... Sirius ii 9.0-10.0 174,000 69 380 6 10 o ii o . 426 ooo 68 448 II O 12 O 60 508 o.o-i.o. . . . 8 14 33 12.0-13.0 2,020,000 Si 559 1.0-2.0. . . . 2 . O~3 . .... 27 73 17 18 So 68 13.0-14.0 14.0-15.0 3,960,000 7,820,000 40 630 3.0-4.0. . . . 189 19 87 15.0-16.0 14,040,000 22 652 4-0-5.0.... 650 26 H3 16.0-17.0 25,400,000 16 668 5 . 0-6 . o .... 2,200 35 148 17.0-18.0 38,400,000 10 678 6 . 0-7 . o .... 6,600 42 190 18.0-19.0 54,600,000 6 684 56 246 76,000,000 3 687 8 . 0-9 . o .... 65,000 65 All stars fainter than 20.0 3 690 TABLE 547. - Albedos. The albedo, according to Bond, is defined as follows: "Let a sphere 5 be exposed to parallel light. Then its Albedo is the ratio of. the whole amount reflected from S to the whole amount of light incident on it." In the following table, m = the stellar magnitude at mean opposition; g = magnitude it would have at full phase and unit distance from earth and sun; ff = assumed mean semi-diameter at unit distance; p = ratio of observed brightness at full phase to that of a flat disk of same size and same position, illuminated and viewed normally and reflecting all the incident light according to Lambert's law; g depends on law of variation of light with phase; albedo = pq. Russell, Astrophysical Journal, 43, p. 173, 1916. Albedo of the earth: A reduction of Very's observations by Russell gives 0.45 in close agreement with the recent value of Aldrich of 0.43 (see Aldrich, Smithsonian Misc. Collections, 69, 1919). Object. m g ff P q Visual albedo. Color index. Photo- graphic albedo. Moon .... Mercury Venus -i -55 - -94 .12 -77 - -85 - .29 +0.89 +5-74 +7-65 +0.40 -0.88 0.06 -4.06 -1.36 -8.99 -8.67 -6.98 -7.06 2.40" 3-45 3-45 8-55 4.67 95-23 77-95 36.0 34-5 0.105 .164 .077 .492 139 375 .420 .42 49 0.694 0.42 0.72 .20 . ii S- S: 5: -S: 0.073 .069 055 59 '54 56: .63: -63: 73: +1.18 +0.78 +1.38 +0.50 + I.I2 0.051 .60 .090 73 = 0.47: Jupiter Saturn Uranus Neptune TABLE 548. Duration of Sunshine. Declination -23 27' 15 10 5 +5 +10 +15 + 20 + 23 27' ot sun: approx. date: Dec. 22. Feb. 9 Nov. 3. Feb. 23 Oct. 19. Mar. 8 Oct. 6. Mar. 21 Sept. 23- Sept. 10 Apr. 3. Apr. 1 6 Aug. 28. May i Aug. 13- May 20 Jan. 24. June 21 Latitude. h m h m h m h m h m h m h m h m h m h m o 12 07 12 07 12 07 12 07 12 07 12 07 12 07 12 07 12 07 12 07 II 32 ii 45 ii 53 12 00 12 07 12 14 12 21 12 29 12 36 12 43 20 10 55 II 22 ii 38 ii 53 12 07 12 22 12 37 12 52 13 08 13 20 30 10 13 10 57 II 21 ii 44 12 08 12 31 12 55 13 19 13 46 14 05 40 9 19 10 25 II 01 ii 35 12 O9 12 43 13 17 13 53 14 32 15 01 50 55 8 04 7 09 9 43 9 12 10 34 10 15 ii 23 ii 14 12 10 12 12 12 58 13 09 13 48 14 09 14 40 IS 13 15 38 16 26 16 23 17 23 60 5 5 2 8 34 9 52 ii 04 12 13 13 23 14 36 IS 57 17 31 18 52 6=; 3 34 7 39 9 19 10 50 12 16 13 43 IS IS 17 oi 19 19 22 03 70 6 10 8 31 10 29 12 19 14 II 16 15 18 50 75 2 37 7 04 9 '55 12 26 15 oo 1 8 05 80 3 10 8 46 12 38 16 44 For more extensive table, see Smithsonian Meteorological Tables. SMITHSONIAN TABLES- TABLES 649-552.-SOLAR ENERGY. TABLE 649. -The Solar Constant. Solar constant (amount of energy falling at normal incidence on one square centimeter per minute on body at earth's mean distance) = 1.932 calories == mean 696 determinations 190212. Apparently subject to variations, usually within the range of 7 per cent, and occurring irregularly in periods of a week qr ten days. Computed effective temperature of the sun : from form of black-body curves, 6000 to 7000 Absolute ; from Amax. = 2930 and max. = 0.470/11, 6230 ; from total radiation, J = 76.8xio- ia X T 4 , 5830 . TABLE 650. Solar spectrum energy (arbitrary units) and its transmission by the earth's atmosphere. Values computed from e n i= e a in , where e m is the intensity of solar energy after transmission: through a mass of air m ; m is unity when the sun is in the zenith, and approximately = sec. zenith distance for other positions (see table 5 5$) ', e =the energy which would have been ob- served had there been no absorbing atmosphere; a is the fractional amount observed when the sun is in the zenith. Transmission coef- Intensity Solar Energy. A {j b ^ ry ficients, a. M >. r j * *** i'l Mount Wilson. Washington. if - = '= u " S ~. " 2 s^ c ~ m i m = i 2 4 6 m= i 2 3 4 6 0.30 (.460) (.550) 54 30 25 II 2 i _ 32 .520 6*5 in 68 58 30 B 2 34 .580 .692 232 160 '35 78 26 9 .36 38 (.380) .635 .676 .562 302 354 278 192 239 122 162 49 74 20 34 i34 51 '9 7 3 .40 .46 .560 .090 .729 .809 .83-- .887 .768 .829 414 618 III 302 2 2O 428 117 206 62 205 232 426 130 294 73 203 41 140 67 SO .733 .862 .919 .850 606 557 522 450 334 248 441 323 237 17.4 94 .60 .779 .900 .940 .866 504 474 454 409 331 268 393 306 238 185 112 . -70 858 .950 .964 903 364 35i 346 329 297 268 312 268 230 197 J 45 .80 .886 ; .970 .976 915 266 260 2S8 250 235 221 236 209 185 ,64 145 1. 00 .922 .980 975 .941 1 66 162 163 160 154 147 J53 141 130 I2O 1 02 1.50 .938 .976* .965 .961 63 61 61* 60* ,S7* ss* 59 55 52 49 43 2.00 .912 .970* 932 .940 25 23 24* 23* 21* 19* 23 21 17 | Transmission coefficients are for period when there was apparently no volcanic dust in the air. * Possibly too high because of increased humidity towards noon. TABLE 551. The intensity of Solar Radiation in different sections of the spectrum, ultra-violet, visual infra-red. Calories. Wave-length. Mount Whitney. Mount Wilson. Washington. M /* m=o m= i 2 3 4 m= i 2 3 4 m = i 2 3 4 o.oo to 0.45 31 25 .19 .16 13 23 .16 .12 .09 13 .06 .04 .02 0.45 to 0.70 0.70 to oo o.oo to oo 7' .91 i-93 .67 3 .62 -85 1.66 t 1.56 54 .80 1.47 65 .69 i-57 11 I. 4 2 1.28 45 63 1.17 '35 .40 .62 1.08 3 57 .90 24 53 79 TABLE 552. - Distribution of brightness (Radiation) over the Solar Disk. (These observations extend over only a small portion of a sun-spot cycle.) Wave- length. M 0323 0.386 0-433 0.456 0.481 M 0.501 0-534 0.604 0.670 M 0.699 0.866 I.03I 1.225 M 1-655 2.097 3 0.00 0.40 13 338 312 456 423 486 5" 483 489 463 463 440 399 382 333 320 307 295 169 III 108 77.6 75-7 39-5 38-9 14.0 13-8 1 0.55 0.65 120 112 289 267 395 368 455 428 456 430 437 414 4'7 396 365 348 308 295 284 273 ,63 '59 103 73-8 72.2 38-2 37-6 13-6 13-4 I' 0.75 0.825 99 86 240 214 333 296 39 35' 394 358 3 8o 347 366 337 326 304 281 262 258 243 152 '45 99 94-5 69.8 67.1 36-7 35-7 13-1 12.8 1 0.875 0.92 f 64 1 88 163 266 233 3'7 277 324 290 323 286 3'2 281 284 259 247 227 229 212 38 If 5 64.7 61.6 34-7 33-6 12.5 12.2 fc 1 0.95 49 141 205 242 255 254 254 237 210 195 122 Si 58.7 32-3 II.7 Taken from vols. II and III and unpublished data of the Astrophysical Observatory of the Smithsonian Institution. Schwartzchild and Villiger : Astrophysical Journal, 23, 1906. SMITHSONIAN TABLES. TABLES 553-556. 419 ATMOSPHERIC TRANSPARENCY AND SOLAR RADIATION. TABLE 553. Transmission of Radiation Through Moist and Dry Air. This table gives the wave-length, A; a the transmission of radiation by dry air above Mount Wilson (altitude = 1730 m. barometer, 620 mm.) for a body in the zenith ; finally a correction fac- tor, a w , due to such a quantity of aqueous vapor in the air that if condensed it would form a layer i cm. thick. Except in the bands of selective absorption due to the air, a agrees very closely with what would be expected from purely molecular scattering. a w is very much smaller than would be correspondingly expected, due possibly to the formation of ions by the ultra-violet light from the sun. The transmission varies from day to day. However, values for clear days computed as fol- lows agree within a per cent or two of those observed when the altitude of the place is such that the effect clue to dust may be neglected, e.g. for altitudes greater than 1000 meters. If B=s the barometric pressure in mm., w, the amount of precipitable water in cm., then a B = a* 20 a*, w is best determined spectroscopically (Astrophysical Journal, 35, p. 149, 1912,37, p. 359, 1913) other- wise by formula derived from Ilann, w= 2-3e w io 2200 , e w being the vapor pressure in cm. at the station, h, the altitude in meters. See Table 377 for long-wave transmission. A (/*) a a\ v .360 (.660) 95 384 713 .960 413 .783 965 452 .840 .967 53 &s 977 I 574 905 974 .624 .929 .978 .653 938 .720 .970 .988 .986 .986 .990 1.74 .990 .990 Fowle, Astrophysical Journal, 38, 1913. TABLE 554. -Brightness of (radiation from) Sky at Mt. Wilson (1730 m.) and Flint Island (sea level). Zenith dist. of zone ..... ; o-ii; 15-35 35-50 So- 60 60-70 70-80 80-90 Sun. i o 8 X mean ratio sky/sun Mt. Wilson . Flint Island . 15 oo* IJ 5 400 122 520 128 610 150 660 700 210 720 4 6o ; Ditto X area of zone Mt Wilson 51.0 S 8.8 91-5 87.2 104.3 117.6 125.3 - ' 636 Flint Island . 3-9 17.9 22.5 21.4 29.2 35-3 80.0 210 Altitude of sun _ _ 5 15 25 35 47* 65 ; 82* Sun's brightness, cal. per cm. 2 per min. . _ - 533 .900 1-233 1.358 .4i3 T)ittn rm linriyontal surface 780 Mean brightness on normal surface sky X io 8 /sun Total sky radiation on horizontal cal. per cm. 2 - - 423 403 385 365 346 320 310 per m. ....... _ .056 . I IO .162 .189 .205 .226 .240 Total sun -f sky, ditto .102 343 .686 .969 1.246 1.581 i 1.747 * Includes allowance for bright region near sun. For the dates upon which the observation of the upper portion of table were taken, the mean ratios of total radiation sky/sun, for equal angular areas, at normal incidence, at the island and on the mountain, respectively, were 636 X 10 & and 210 X 10 8, on a horizontal surface, 305 X 10 *> and 77 > for the whole sky, at normal incidence, 0.57 and 0.20; on a horizontal surface 0.27 and 0.07. Annals of the Astro- physical Observatory of the Smithsonian Institution, vols. II and III, and unpublished researches (Abbot). TABLE 555. -Relative Distribution In Normal Spectrum of Sunlight and Sky-light at Mount Wilson. Zenith distance about 50. ^ ft )" M H /* C D b F Place in Spectrum 0.422 0-457 0.491 0.566 0.614 0.660 Intensity Sunlight 186 227 21 F 191 166 Intensity Sky-light 1194 986 701 395 23 I 174 Ratio at Mt. Wilson 642 4^5 309 187 121 105 102 '43 Ratio computed by Rayleigh Ratio observed by Kayleigh - - - 102 102 | 258 3 S TABLE 556. -Air Masses. See Table 174 for definition. Besides values derived from the pure secant formula, the tuHe contains those derived from various other more complex formula, taking into account the curva- ture of the earth, refraction, etc. The most recent is that of Bemporad. Zenith Dist. 20 40 60 70 75 80 85 88 Secant 1.00 1.064 1.305 2.000 2.924 3.864 5-76 11.47 P'orbes I.OO 1.065 1.306 T -995 2.902 v s o 5-57 IO.22 I8. 9 Bouguer Laplace Bemporad I.OO I.OO I.OO 1.064 '35 1.990 '993 1.995 2.900 2.899 2.904 3.805 5.56 10.20 5.56 10.20 5.60 ' IO-39 19.0 19.8 The Laplace and Bemporad values, Lindholm, Nova Acta R. Soc. Upsal. 3, 1913 ; the others, Radat metric, 1877. SMITHSONIAN TABLES. 420 TABLES 557-558. RELATIVE INTENSITY OF SOLAR RADIATION, TABLE 557. Mean Intensity ./ lor 24 hours of solar radiation on a horizontal surface at the top of the atmosphere and the solar radiation A , In terms of the solar radiation, t , at earth's mean distance from the son. RELATIVE MEAN VERTICAL INTENSITY (~7~r Motion of ' the sun ^ Date. in LATITUDE NORTH. . longi- AQ tude. 10 2O 30 40 50^ 00 70 80 90 Jan. 0.99 0.303 0.265 O.22O 0.169 0.117 0.066 0.018 I.O335 Feb. 31-54 .312 .282 .244 .200 .150 .100 .048 0.006 I.O288 Mar. \ 59.14 .320 303 .279 245 .204 .158 .108 .056 0.013 I.OI73 Apr. 89.70 3'7 3'9 .312 295 .269 235 195 .148 .101 0.082 1.0009 May 119.29 303 .318 330 329 .320 .302 .278 253 .255 .259 0.(>S4I flint 149.82 .287 31. s 334 345 349 345 337 344 .360 .366 O.97I4 July 179-39 283 .312 333 347 352 .351 345 .356 373 379 0.9666 Aug. 209.94 .294 .316 33 334 330 .318 .300 .282 295 .300 O.97O9 Sept. i 240.50 .310 .318 .316 305 .285 256 .220 .180 139 .140 0.9828 Oct. 270.07 3*7 .308 .289 .261 .225 .183 .135 .084 .ob S i 0-9995 Now. 300.63 .312 .286 251 .211 .164 .114 .063 .018 I.OI64 Dec. 330.19 34 .267 .224 175 .124 .072 .024 1.0288 Year.... 0.305 0.301 0.289 0.268 0.241 0.209 0-173 0.144 0-133 0.126 TABLE 558, Mean Monthly and Yearly Temperatures. Mean temperatures of a few selected American stations, also of a station of very high, two of very low temperature, and one of very great and one of very small range of temperature. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec. Year. i Hebron-Rama (Labr.) 20.9 -15-6 - 6.9 + 0.2 + 4-S + 7-6 + 8.0 . 0.8 6.2 16.2 5-2 2 Winnipeg (Canada) . 21.6 18.8 II. + 1.9 + 10.9 + 17.1 + 18.9 + 17.6 --ii. 6 + 4-1 -7.6 '5-7 + 0.6 3 Montreal 10.9 9.1 4-3 + 4-8 + 12.6+18.3 +20. S + 19-1 --14.7+ 7.8 0.2 7.1 + 5-5 4 Boston 2.8 2.2 + 1.2 f 7-1 +13.6+19.1 +21.8 +20.6 --16.9 + 11.1 + 4-8 -5 + 9-2 5 Chicago -4-8 2.9 + 1-2 4-7-9 + I 3-4 + I 9-7 +22.2 +21.6 --17.9+,,.! + 1-6 i-5 + 9.i 6 Denver 2. I -f- o.i + 1-8 + 8.3 +13.6+19.1 + 22.1 + 21.2 + 16.6+10.3 + 3-3 0.0+ 9.7 7 Washington + 0. 7 + 2.1 + S2 +11.7 + I7-7 +22.9 + 24.9 +21-7 + 19-9 +'3-4i+ 6.9 + 2.3+12.6 8 Pikes Peak l6. 4 I S .6 13-4 10.4 5-1 + 0.4 + 4-5 + 3-6 0.3 5.811.8 14.41 7.1 g St. Louis 0.8 + i.7 + 6.2 +H.4 +18.8 +24.0 +26.0 +24.9 +20.8 +14.2'+ 6.4 + 2.0+13.1 10 San Francisco -j-io. i +10.9 + 12.0 + 12.6 4-IJ.7 +M-7 + .4-6 + 14.8 +158 + 15-2 + . 3.5 + 10.8+13.2 ii Yuma . 12 New Orleans +12.3 -}-I2. I + u-9 +I4-S + 18.1 + .6.7 +21.0 4-20.6 fas-i +23-7 +29.4 +26.8 +33-1 +27.9 +32-6 +275 +29.1 +22.8+16.6 +25.7 + 21.01 + 15.9 + 13.3+22.3 + 13.1 +20.4 13 Massaua +2 S .6 +26.0 +27.1 +29.0 +.V. T +11. S +34-8 +34-7 +33-3 +31-71+29.0 +27-0+30.3 14 Ft. Conger (Greenl'd) 39- 40.1 33-5 25.3 10.0 + 0.4 + 2.8 + 1.0 9.0 22.730.9 33-4 20.0 15 Werchojansk 16 Batavia -51.0 +25-3 45-3 +254 32.5 +25-8 13.7 +26.3 + 2.0 +26.4 +12.3 +26.0 + '5-5 +25-7 + 10. 1 +25.9 + 2.5 iso 1 37.8 +26.3+26.4+26.2 47.0 16.7 +25.6+25.9 Lat., Long., Alt. respectively: (i) +58.5,63.o W, ; (2) +49.9, 97-r W, 2 3 3m.; (3) +45.5, 73-6 W, 57 m. ; (4) -[-42.3,71.1 W )3 8m.; (5) + 41 9, 87.6 W, 2 5 im.; (6) +39.7, 105.0 W, i6i 3 m.; (7) +38.9, 77-o W, 34 m.; (8) + 38.8, 105.0 W, 43 o8m. ; (9) + 38.6, 00.2 W, 1731".; (10) +37.8, 122.5 W, 4 7 m.; (n)+32. 7 , 114.6 W, 4 3 m. ; (12) +30.0, 90.1 W, i6m.; (13) + 15.6, 37.5 E, 901.5 (14) +81.7, 64.7 W.,; (15) +67.6, 133.8 E, i4om. ; (16) 6.2, 106.8 E, 7m. Taken from Hann's Lehrbuch der Meteorologie, 2 ! nd edition, which see for further data. Note: Highest recorded temperature in world = 57 C in Death Valley, California, July 10, 1913. Lowest recorded temperature in world = -68 C at Verkhoyansk, Feb. 1892. SMITHSONIAN TABLES. TABLES 559-561. THE EARTH'S ATMOSPHERE. TABLE 559. - Miscellaneous Data. Variation with Latitude. 421 Optical ev.dence of atmosphere's extent: twilight 63 km, luminous clouds 83, meteors 200, aurora 44-360. Jeans computes a density at 170 km of 2 X io 13 molecules per cm 3 , nearly all H (5% He); at 810 km, 3 X 10" molecule* per cm 3 abnost all H. When in equilibrium, each gas forms an atmosphere whose density decrease with altitude is independent of the other components (Dalton's law, HzO vapor does not). The lighter the gas, the smaller the decrease rate. A homogeneous atmosphere, 76 cm pressure at sea-level, of sea-level density, would be 7091 m high. Average sea-level barometer is 74 cm; corresponding homogeneous atmosphere (truncated cone) 7790 m, weighs (base, m) 10,120 kg; this times earth's area is 52 X io 14 metric tons or io~ 6 of earth's mass. The percentage by vol. and the partial pressures of the dry-air components at sea-level are: Nj, 78.03, 593.02 mm; Oi, 20.99, J59-52J A, 0.94, 7.144; COj, 0.03, 0.228; H2, o.oi, 0.076; Ne, p.ooi2, 0.009; He, 0.0004, 0.003 (Hann). The following table gives the varia- tion of the mean composition of moist air with the latitude (Hann). N 2 75-99 77-32 77.87 O 2 20.44 20.80 20.94 A, 0.92 0.94 Q-94 HiO 2.63 0.92 0.22 COl 0.02 O.O2 O.O3 soN 70 N TABLE 560. Variation of Percentage Composition with Altitude (Humphreys). Computed on assumptions: sea -level temperature 11 C; temperature uniformly decreasing 6 per km up to ii km, from there constant with elevation at 55. J. Franklin Inst. 184, p. 388, 1917. Height, km Argon. Nitrogen. Water vapor. Oxygen. Carbon dioxide. Hydrogen. Helium. Total pressure, mm 140 O.OI 99 15 0.84 0.0040 120 o. 19 98.74 1.07 0.0052 100 2.9S 0.05 O.II 95.58 1.31 0.0067 80 32-18 0.17 1.85 64.70 I. 10 0.0123 60 0.03 81.22 0.15 7.69 10.68 0.23 0-0935 5 0.12 86.78 O.IO io. 17 2.76 0.07 0.403 40 O. 22 86.42 0.06 12. 6l 0.67 0.02 1.84 30 0-35 84.26 0.03 15.18 O.OI 0.16 O.OI 8.63 20 0-59 81.24 0.02 18.10 O.OI 0.04 40.99 IS 0.77 79-52 O.OI 19.66 0.02 0.02 89-66 II 0.94 78.02 O.OI 20.99 O.O3 O.OI 168.00 5 0-94 77.89 0.18 20.95 0.03 O.OI 405- 0-93 77-08 I. 20 20.75 0.03 O.OI 760. TABLE 561. Variation of Temperature, Pressure and Density with Altitude. Average data from sounding balloon flights (65 for summer, 52 for winter data) made at Trappes (near Paris), Uccle (near Brussels), Strassburg and Munich. Compiled by Humphreys, 16 to 20 m chiefly extrapolated. Summer. Winter. Elevation, km Temp. C Pressure, mm of Hg. Density, dry air, g/cm 3 Temp. C Pressure, mm of Hg. Density, dry air, g/cm 1 20.0 51-0 44.1 0.000092 -57-0 39-5 0.000085 19.0 51-0 Si-5 .000108 57-0 46-3 .000100 18.0 51-0 60.0 .000126 -57-0 54-2 .000117 17.0 51-0 70.0 .000146 -57-0 63-5 .000137 16.0 51.0 81.7 .000171 57-0 74-0 .000160 15-0 -51-0 95-3 .000199 -57-0 87.1 .000187 14.0 -51-0 in. i .000232 -57-0 102. I .000220 13-0 51.0 129. 6 .000270 -57-o "9-5 .000257 12.0 -51.0 151-2 .000316 -57-0 140.0 .000301 II. -49-5 176. 2 .000366 57-0 164.0 000353 10. 45-5 205.1 .000419 -54-5 192.0 .000408 9.0 -37-8 237.8 .000470 -49-5 224.1 .000466 8.0 29.7 274-3 .000524 -43-0 260.6 .000526 7-0 22.1 314.9 . 000583 -35-4 301.6 .000590 6.0 IS-I 360.2 .000649 -28.1 347-5 .000659 5-0 -8.9 410.6 .000722 21.2 398.7 .000735 4.0 3-0 466.6 . 000803 -15-0 455-9 .000821 3-0 + 2.4 528.9 .000892 -9-3 5I9.7 .000915 2.5 +5-0 562.5 .000942 -6.7 554-3 .000067 2. O +7-5 598.0 .000990 -4-7 590.8 .001023 i-5 + 10.0 635.4 .001043 -3-0 629 6 .001083 1.0 + 12.0 674.8 .001100 1-3 670.6 .001146 0.5 + 14-5 716.3 .001157 0.0 71-4.0 .001215 0.0 + 15-7 760.0 .001223 +0.7 760.0 .001290 760 mm = 29.921 in. = 1013.3 millibars, i mm = 1.33322387 millibars, i bar = 1,000,000 dynes; this value, sanctioned by International Meteorological Conferences, is 1,000,000 times that sometimes used by physicists. SMITHSONIAN TABLES. 4 22 TABLES 562 563. TERRESTRIAL TEMPERATURES- TABLE 562. Temperature Variation over Earth's Surface (Hann). Temperatures C Mean ! Land Jan. Apr. July. Oct. Year. Range. temp. North pole -41.0 28.0 i.o -24.0 22.7 10.0 i. 7 +80 -32.2 22.7 + 2.0 -19.1 -17.1 34-2 I 7 20 70 00 -26.3 -16.1 -14.0. -2.8 7-3 14.1 9-3 +0.3 10.7 i.i 33-6 30.2 +0.7 4.8 e 50 -7.2 +5-2 17.9 6.9 +5-8 25-1 79 58 40 +5-5 I3-I 24.0 15- 7 14.1 18.3 14.1 45 30 20 14.7 21.9 20.1 25.2 27.3 28.0 21.8 26.4 20.4 25-3 12.6 6.1 21-3 25-4 43-5 31-5 + 10 25.8 27.2 27.0 26.9 26.8 1.4 27.2 24 Equator 26.5 26.6 25-7 26.5 26.3 0.9 27.1 22 10 26.4 25.9 23.0 25-7 25-5 3-4 25-8 20 20 25-3 24.0 19.8 22.8 23-0 5-5 24.0 24 30 21.6 18.7 14-5 18.0 18.4 7-1 19-5 20 40 iS-4 12.5 8.8 ii. 7 ix. 9 6.6 13-3 4 50 8.4 5-4 3-o 4.8 5-4 5-4 +6.4 2 60 3-2 -9-3 3-2 "S o.o 70 I. 2 21.0 12.0 19.8 1.3 71 80 South pole (-4-3) (-6.0) (-28.7) (-33-0) (-20.6) (-25.0) (24.4) (27.0) 100 (100) TABLE 563. Temperature Variation with Depth (Land and Ocean), Table illustrates temperature changes underground at moderate depths due to surface warming (read from plot for Tiflis, Lehrbuch der Meteorologie, Hann and Siiring, 1915). Below 20-30 m (nearer the surface in tropics) there is no annual variation. Increase downwards at greater depths, 0.03 =*= C per m (i per 35 m) 1. c. At Pittsburgh, 1524 m, 49.4, .0294 per m; Oberschlesien, 2003 m, 70, .0294 per m; or W. Virginia, 2200 m, 70, .034 per m (Van Orstrand). Mean value outflow heat from earth's center, 0.00000172 g-cal/cm 2 /sec. or 54 g-cal/cm 2 /year (39 Laby). Open ocean temperatures: Greatest mean annual range (Schott) 40 N, 4.2 C; 30 S, 5.1; but io*N, only 2.2; 50 S, 2.9. Mean surface temp, whole ocean (Kriimmel) 17.4; all depths, 3.9. Below i km nearly isothermal with depth. In tropics, surface 28; at 183 m, 11, 80% all water less than 4.4. Deep-sea (bottom) temps, range 0.5 to +2.6. Soundings in S. Atlantic: o km, 18.9; .25 km, 15; .5 km, 8.3; i km, 3.3; 3 km, 1.7; 4.5 km, 0.6. Temperature, centigrade. Depth, m Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec. , 4 10 14 21 29 32 32 24 16 9 4 o-S 4 4 9 13 18 23 26 28 24 18 12 6 I.O 6 6 8 12 15 20 24 26 23 18 14 IO i . 5 9 8 9 II 14 18 21 23 22 18 15 12 2.0 ii 10 IO II 16 19 21 21 18 16 14 3-0 14 12 12 II 13 14 16 17 18 18 17 15 4.0 15 13 12 12 12 14 16 16 17 17 16 5-0 IS 14 13 13 13 13 14 14 15 16 16 16 6.0 15 14 14 14 14 14 14 14 14 IS 15 IS SMITHSONIAN TABLES. TABLE 564. GEOCHEMICAL DATA. 423 Eighty-three chemical elements (86 including Po, Ac and UrX..,) are found on the earth. Besides the eight occur- ring uncombined as gases, 23 may be found native, Sb, As, Bi, L, Cu, Au, Ir, Fe, Pb?, Hg, Ni, Os, Pd, Pt, Rh, Ru, Se, Ag, S, Ta ?, Te, Sn ?, Zn ?. Combined the elements form about 1000 known mineral species. Rocks are in genera! aggregates of these species. Some few (e. g., quartzite, limestone, etc.) consist of one specie. We have some knowl- edge of the earth to a depth of 10 miles. This portion may be divided into three parts : the innermost of crystalline or plutonic rocks, the middle, of sedimentary or fragmentary rocks, the outer of clays, gravels, etc. 93% of it is solid mat- ter, f/,i liquid, and the atmosphere amounts by weight to 0.03% of it. Besides the 9 major constituents of igneous rock (see 7th col. of table) 3 are notable by their almost universal occurrence, TiO 2 , PaOg, and MnO. Bo, Gl, and Sc are also widely distributed. The density of the earth as a whole is 5.52 (Burgess); continental surface, 2.67 and outer 10 miles of crust, 2.40 (Harkness). Computed from average chernjcal composition: outer ten miles as a whole, 2.77; northern continents rvey, 1916; Washington, J. Franklin. Inst. 190, 2.73; southern, 2.76 ; Atlantic basin, 2.^3 ; Pacific basin, 2.88. Data of Geochemistry, Clarke, Bui. 616, U. S. Geological Su AVERAGE COMPOSITION OF KNOWN TERRESTRIAL MATTER. Average composition. Average composition of lithosphere. Atomic number and element. Litho- sphere, 93% Hydro- sphere, 7% Average includ- ing atmos- Igneous rocks. Compound. Igneous rocks, 95% Shale, 4% Sand- stone, o.75% Lime- stone, 0.25% Weighted average. phere. 8 O 47-33 85 . 79 46.43 47 29 SiOz 59.09 58.10 78.33 C IQ eg 77 14 Si 27.74 27.77 28.02 AhOa iS-35 15-40 4-77 O A V 0.81 ov * / / 14.89 13 Al 26 Fe 7-85 4-50 8.14 5.12 7.96 4-56 FC2G-3 FeO 3.08 3.80 4.02 2-45 1.07 30 54 2.69 3-39 30 Ca 3-47 0.05 3-63 3-47 MgO 3-49 2.44 1.16 7. 89 12 Mg 2.24 0.14 2.09 2.29 CaO 5-08 5-50 42-57 4.86 ii Na 19 K 2.46 2.46 1.14 0.04 2.85 2.60 2.50 2-47 Na 2 K 2 3-84 3-13 1.30 3.24 45 05 33 3-25 2.98 i H 0.22 10.67 0.127 o. 16 H 2 1.14 5.00 1.63 77 2.02 22 Ti 0.46 .629 .46 TiO 2 ... 1.05 .65 25 .06 77 6 C .19 O.O02 .027 13 ZrO 2 0.039 .02 17 Cl .06 2.07 .055 .063 C0 2 .102 2.63 5-03 41-54 70 35 Br 0.008 P 2 O 5 30 17 .08 04 .28 15 P . 12 - I3O .13 S. 53 .09 . IO 16 S . 12 .09 .052 .103 SG-3 ~6 4 07 05 03 56 Ba .08 .048 .092 Cl .056 .02 .06 25 Mn .08 .006 .078 F .078 09 38 Sr .02 .018 033 BaO 055 05 05 .09 7 N SrO .022 .04 9 F1 .IO .077 .10 MnO. . .125 05 .09 etc. 50 .in .091 NiO .025 .025 CivOa .056 05 VzOs. '.'.'.'.'.'. .032 .025 Li 2 .007 __ . .01 C .80 03 AVERAGE COMPOSITION OF METEORITES: The following figures give in succession the element, atomic number (bracketed), and the percentage amount in stony meteorites (Merrill, Mem. Nat. Acad. Sc. 14, p. 28, 1916). The "iron" meteorites contain a much larger percentage of iron and nickel, but there is a tendency to believe that with such meteorites the composition is altered by the volatilization or burning up of the other material in passing through the air. Note the greater abundance of elements of even atomic number (97.2 per cent). O (8) S (16) 36.53 i. 80 Fe (26) Ca (20) 23-32 1.72 Si (14) Al (13) 18.03 1-53 Mg (12) Ni (28) 13.60 1-52 Na (11) 1.64 Cr (24) 0.32 Mn (25) 0.23 K (19) 0.17 C (6) 0.15 Co (27) O. 12 Ti (22) O.II P ds) 0. II H (i) 0.09 Cu (29) O.OI Cl (17) 0.09 V (23) tr. Ru (44) tr. Pd (46) tr. Pt (78) tr. Ir (77) tr. SMITHSONIAN TABLES. 424 TABLE 666- ACCELERATION OF GRAVITY- For Sea Level and Different Altitudes. Calculated from U. S. Coast and Geodetic Survey formula, p. 134 of Special Publication No. 40 of that Bureau. g = 0.78039 (i + 0.005 294 sin 2 - 0.000007 sin 2 2 0)m g = 32-08783 (i + 0.005294 sin*. < -o. 000007 sin* 20) ft. Latitude cm/sec 1 log S ft/sec Latitude cm/ sec 2 ... ft./sec 2 5 978.039 2-9003562 9903735 32.0878 .0891 50 51 981.071 -159 2.9917004 9917394 32.1873 .1902 10 12 U .195 .262 340 .9904 .'5 4 9904552 .9004808 .0929 .0951 .0977 52 53 54 .247 .336 .422 .9917784 .9918177 .9918558 1931 .1960 .1988 U 16 17 978.384 430 .480 2.0905094 .9905298 .9905520 32.0991 .1007 .1023 a 57 981.507 .592 -675 2.9918934 .9919310 .9919677. 32.2016 .2044 . 2071 18 -532 .0905750 .1040 58 757 .9920040 .2098 .585 -9905985 .1057 59 .839 .9920403 -2125 20 978 641 2.9906234 32.1076 60 981.918 2.9920752 32-2151 21 .701 .9906500 .1095 61 995 .9921073 .2176 22 23 .763 .825 .9906775 . 9907050 .1116 .1136 62 63 982.070 145 .9921424 .9921756 . 2201 -2225 24 .892 . 9907348 .1158 64 .218 .9922079 .2249 25 978.960 2 . 9907649 32.1180 65 982.288 2.9922388 32.2272 26 979.030 . 990/960 .1203 66 356 .9922689 .2295 27 .101 .9908275 .1227 67 .422 .9922981 .2316 28 175 .9908603 .1251 68 487 .9923268 .2338 29 -251 .9908940 .1276 69 549 9923542 2358 30 979-329 2.9909286 32.1302 70 982.608 2.9923803 32.2377 31 .407 .9909632 1327 71 .665 .9924055 .2396 .487 . 9909987 .1353 72 .720 .9924298 .2414 33 -569 .9910350 1380 73 772 .9924528 2431 34 .652 .99IO7I8 .1407 74 .822 .9924749 .2 44 8 35 979-737 2.99II095 32.1435 75 982.868 2.9924952 32.2463 36 .822 .9911472 .1463 76 .912 9925147 .2477 37 .908 .1491 77 954 .9925332 .2491 38 995 .9912238 .1520 78 992 .9925500 2503 39 980.083 .9912628 1549 79 983-027 .9925655 2515 40 980.171 2.99I3OI8 32.1578 80 983-059 2.9925796 32.2525 .261 .0913417 . 1607 81 .089 .9925929 2535 42 350 .9913812 -1636 82 US . 9926043 -2544 43 .440 .9914210 .1666 83 139 .9926149 -2552 44 531 .9914613 .1696 84 .160 .9926242 .2558 8 980.621 .711 2.99I50II .9915410 32.1725 -1755 85 86 983-178 .191 2.9926321 .9926379 32-2564 .2569 47 .802 .9915814 -1785 87 .203 .9926432 .2572 48 .892 .9916212 .1814 88 .211 .9926467 2575 49 .98! .9916606 .1844 90 983.217 .9926494 2577 To reduce log g (cm. per sec. per sec.) to log g (ft. per sec. per sec.) add log 0.03280833 = 8.5159842 10. The standard value of gravity, used in barometer reductions, etc., is 980.665. It was adopted by the International Committee on Weights and Measures in 1901. It corresponds nearly to latitude 45 and sea-level. FREE-AIR CORRECTION FOR ALTITUDE. 0.0003086 cm/sec 2 /m when altitude is in meters. o . 000003086 ft/ sec 2 / ft when altitude is in feet. Altitude. Correction. Altitude. Correction. 200 m. 0.0617 cm/sec 2 200 ft. -0.000617 ft. /sec 2 300 .0926 300 . 000926 400 1234 400 .001234 500 000 1543 .1852 500 600 .001543 .001852 700 .2160 700 .002160 800 .2469 800 . 002469 000 2777 900 .002777 SMITHSONIAN TABLES- TABLE 566. GRAVITY. 425 The following more recent gravity determinations (Potsdam System) serve to show the accuracy which may be assumed for the values in Table 565, except for the three stations in the Arctic Ocean. The error in the observed gravity is probably not greater than o.oio cm/ sec 2 , as the observations were made with the half -second invariable pendulum, using modern methods. In recent years the Coast and Geodetic Survey has corrected the computed value of gravity for the effect of ma- terial above sea-level, the deficiency of matter in the oceans, the deficiency of density in the material below sea-level under the continents and the excess of density in the earth's crust under the ocean, in addition to the reduction for elevation. Such corrections make the computed values agree more closely with those observed. See special publica- tion No. 40 of the U. S. Coast and Geodetic Survey entitled, "Investigations of Gravity and Isostasy," by William Bowie, 1917; also Special Publication No. 10 of same bureau entitled, "Effect of Topography and Isostatic Compen- sation upon the Intensity of Gravity," by J. F. Hayford and William Bowie, 1912. Name. Latitude. Elevation, meters. Gravity, cm/sec 2 Observed. Reduced to sea-level. Refer- Kodaikanal, India 10 14' Ootacamund, India n 25 Madras, India 13 4 Jamestown, St. Helena 15 55 Cuttack, India 20 29 Amraoti, India 20 56 Sibbulpur, India 23 9 aya, India 24 48 Siliguri, India 26 42 Kuhrja, India 28 14 Galveston, Texas 29 18 Rajpur, India 30 24 Alexandria, La 31 19 St. Georges, Bermuda 32 21 McCormick, S. C 33 55 Shamrock , Texas 35 13 Cloudland, Tenn 36 6 Mount Hamilton, Cal 37 20 Kala-i-Chumb, Turkestan 38 27 Denver, Col 39 41 Hachinohe, Japan 40 31 Chicago, 111 41 47 Albany, N. Y 42 39 Florence, Italy 43 45 Minneapolis, Minn 44 59 Simplon Hospice, Switzerland 46 15 Fort Kent, Me 47 15 Sandpoint, Idaho 48 16 Medicine Hat, Canada 50 2 Field, Canada 51 24 Magleby , Denmark 54 47 Copenhagen , Denmark 55 41 St. Paul Island, Alaska 57 7 Fredericksvarn , Norway 59 o Christiania, Norway 59 55 Ashe Inlet, Hudson Strait 62 33 St. Michael, Alaska 63 28 Hatnarfjordr, Iceland 64 3 Niantilik, Cumberland Sound 64 54 Glaesibaer, Iceland 65 46 Sorvagen, Norway 67 54 Umanak, Greenland 70 40 Danes Island , Spitzbergen 79 46 Arctic Sea 84 12 Arctic Sea 84 52 Arctic Sea 85 55 2336 2254 6 10 28 342 447 no 118 198 3 1012 24 2 163 708 1890 1282 1345 1638 21 182 61 184 256 1998 1 60 637 664 1239 14 14 10 10 28 IS i 4 7 10 19 10 3 o o o 977-645 977-735 978.279 978.712 978.659 978.609 978.719 978.884 978.887 979.082 979.272 979.002 979.429 979.806 979.624 979-577 979-383 979.660 979.462 979.609 980.359 980.278 980.344 980.491 980.597 980.202 980.765 980.680 980.865 980.745 981.502 98i.559 981.726 981.874 981.927 982.105 982. 192 982.266 982.273 982.342 982.622 982.590 983-078 983-109 983-174 983-155 978.366 978.427 978.281 978.715 978.668 978.714 978.856 978.918 978.923 979-143 979-273 979.313 979-436 979.807 979.674 979-795 979.966 980.056 979.877 980.114 980.365 980.334 980.363 980.548 980.676 980.819 980.814 980.877 981.070 981.127 981 . 506 981-563 981.729 981.877 981-936 982 . no 982.192 982. 267 982.275 982.345 982.628 982.593 983.079 983.109 983.174 983.155 References: (i) Report i6th General Conference International Geodetic Association, London and Cambridge, 1909. 3d Vol. by Dr. E. Borrass, 1911; (2) U. S. Coast and Geodetic Survey, Special Publ. No. 40; * (3) U. S. Coast and Geodetic Survey, Report for 1897, Appendix 6.* * For references (2) and (3), values were derived from comparative experiments with invariable pendulums, the value for Washington being taken as 980.112. For the latter, Appendix 5 of the Coast and Geodetic Survey Report for 1901, and pages 25 and 244 of the 3d vol. by Dr. E. Borrass in 1911 of the Report of the i6th General Conference of the Intern. Geodetic Association, London and Cambridge, 1909. As a result of the adjustment of the net of gravity base stations throughout the world by the Central Bureau of the Intern. Geodetic Association, the value of the Wash- ington base station was changed to 980.112. SMITHSONIAN TABLES. 426 TABLE 567. ACCELERATION OF GRAVITY (0) IN THE UNITED STATES- The following table is abridged from one for 219 stations given on pp. 50 to 52, Special Publication No. 40, U. S. nirvey. The observed values depend on relative determinations and on adopted value of 980.112 for Washington (Toast and C.etxlctic Survey Office, see footnote, Table 566). There are also given terms necessary in reducing the theoretical value (Table 565) to the proper elevation (free-air) and to allow for topography and isostatic compensation by the Hayford method (see introductory note to Table 566). To a certain extent, the greater the bulk of material below any station, the less its average density. This phenomenon is knov. c compensation. The depth below sea-level to which this compensation extends is about 96 km. Below this depth any mass element is subject to equal (fluid) pressure from all directions. lion. Latitude. Longitude. Eleva- tion, meters. Observed cm/sec 2 Correction. Elevation, cm/sec 2 Topography and com- pensation, cm/sec 2 Key West. Fla 24 33-6' 29 57-0 30 17-2 31 46-3 32 43-3 32 47-2 33 30.8 33 36.5 33 45-0 34 43-1 34 45-0 35 8.8 35 13-8 35 35-8 35 57-7 36 5-3 36 6.2 37 20.4 37 32-2 37 47-5 38 38.0 38 50.3 38 50.7 38 56.3 38 54-7 38 59-4 39 8.3 39 I/- 8 39 28.7 39 40.6 39 57-1 40 4.0 40 21.0 40 27.4 40 46 . I 40 48-5 40 58.4 41 30.4 41 47-4 42 16.5 42 22.8 42 27.1 42 30.8 42 58.0 43 4-6 43 37-2 43 41-8 44 29.5 44 43-3 44 58.7 45 I I- 2 46 24.2 47 39-6 48 58.1 81 48.4' 90 4-2 97 44-2 106 29.0 114 37-0 79 56.0 86 48.8 91 12.2 84 23.3 76 39-8 92 16.4 90 3-3 80 50.8 IO5 12. I 83 55. 112 6.8 82 7.9 121 38.6 77 26.1 122 25.7 90 12.2 105 2.0 104 49.0 77 4-0 ioi 35-4 no 9.9 84 25.3 76 37-3 87 23-8 104 56.9 75 n. 7 80 43-4 74 39-5 80 0.6 in 53-8 73 57-7 117 43-8 81 36.6 87 36.1 71 48-5 71 7-8 76 29.0 94 II. 4 85 40.8 89 24.0 116 12.3 98 1.8 7i 34-3 no 29.7 93 13-9 67 16.9 105 50. 122 18.3 97 14-9 i 2 189 1146 M 6 179 44 324 I 89 80 228 1960 280 849 1890 1282 30 H4 154 4293 1841 103 1005 1243 245 30 151 1638 16 205 64 235 1322 38 1311 2IO 182 170 14 247 340 236 270 821 408 261 2386 256 38 7i8 58 243 978.970 979-324 979- 283 979.124 979.529 979.546 979-536 979.600 979-524 979.729 979-721 979-740 979-727 979.204 979-712 979.463 979.383 979.660 979.960 979-965 980.001 978.954 979-490 980.095 979-755 979-636 980.004 980.097 980.072 979-609 980.196 980.085 980.178 980.118 979-803 980.267 979-844 980.241 980.278 980.324 980.398 980.300 980.311 980.372 980.365 980.212 980.375 980.486 979.899 980.597 980.631 980.539 980.733 980.917 0.000 .001 .058 354 -.017 .002 -055 -.014 .100 .000 -.027 -.025 .070 -.605 -.086 -.262 -.583 396 -.009 -.035 .048 -1.325 -.568 -.032 -.310 -.384 .076 -.009 -.047 -.505 -.005 -.063 .020 -.073 -.408 .012 -.404 -.065 -.056 .052 .004 .076 -.105 --073 -.083 -.253 -.126 -.081 -.736 .079 .012 . 222 -.018 --075 +0.035 + .013 .001 + .OOI .010 +.016 + .011 + .005 + .014 +.036 + .001 + .OO2 + .015 + .017 .001 -.096 + .130 + .120 + .010 + 045 + .OOI +.187 .007 + .012 .000 - 043 + .002 + .006 + .001 .015 + .009 .003 + .013 .000 -.041 + .011 .004 .000 + 007 +.018 + -OIO + .005 + .002 + .003 + -003 .042 -.006 + .007 +.038 -.005 + .010 .020 . O2O -.009 New Orleans, La Austin, Tex. university El Paso, Tex Yuma, Ariz Charleston, S. C Birmingham, Ala Arkansas City, Ark Atlanta, Ga. capitol Beaufort, N. C Little Rock, Ark Memphis, Tenn Charlotte, N. C. , Las Vegas, N. Mex ' KnoxvUle, Tenn Grand Canyon, Ariz Cloudland,Tenn Mount Hamilton, Cal., Obs'y. Richmond, Va. . San Francisco, Cal St. Louis, Mo., university Pike's Peak, Col. . Colorado Springs, Col. ... Washington, D. C., Bur. St'ds. Wallace, Kans Green River, Utah Cincinnati, Ohio, obs'y Baltimore, Md., university. . . Terre Haute, Ind Denver, Co!., university obs'y. Philadelphia, Pa., university . Wheeling, W. Va. Princeton, N. J. . . . Pittsburg, Pa. . .'. Salt Lake City, Utah New York, N. Y., university. Winnemucca, Nev... Cleveland, Ohio '. Chicago, 111., university Worcester, Mass Cambridge, Mass, observatory Ithaca, N. Y., university . . . Fort Dodge, Iowa Grand Rapids, Mich Madison, Wis., university. . Boise, Idaho MitcheU, S. Dak. university. . Lancaster, N. H . Grand Canyon , Wyo Minneapolis, Minn. Calais, Me Miles City, Mont Seattle, Wash, university. . Pembina, N. Dak SMITHSONIAN TABLES. TABLES 668-569. 427 TABLE 568. Length of Seconds Pendulum at Sea Level and for Different Latitudes. Length Log. Length in Log. Length Log. Length in inches. inches. 99.0961 1.996056 39.0141 1.591222 So 99-4033 i . 997401 39.1351 1.592566 5 . IOOO . 996074 .0157 .591239 55 4475 997594 1525 .592760 10 . 1119 .996126 .0204 .591292 60 .4891 997776 .1689 . 592941 15 . 1310 .996210 .0279 -59I375 65 -5266 997939 .1836 593104 20 1571 .996324 .0382 .591490 70 5590 .998081 .1964 593246 25 99.1894 i . 996465 39.0509 1.591631 75 99.5854 1.998196 39.2068 i.59336i 30 .2268 .996629 .0656 .591794 80 .6047 .998280 .2144 . 593446 35 .2681 .996810 .0819 .591976 85 .6168 998332 .2191 593498 40 .3121 .997002 .0992 .592168 90 .6207 998350 . 2207 593515 45 -3577 .997201 .1171 592367 Calculated from Table 565 by the formula / = g/7T 2 . For each 100 ft. of elevation subtract 0.000953 cm or 0.000375 in. or 0.0000313 ft. This table could also have been computed by either of the following formu- lae derived from the gravity formula at the top of Table 565. / = 0.990961(1 + 0.005294 sin 2 0.000007 sin 2 20) meters / = 0.990961 + 0.005246 sin 2 0.000007 sin 2 20 meters / = 39.014135(1 + 0.005294 sin 2 0.000007 sin 2 20) inches. / = 39.014135 + 0.206535 sin 2 0.000276 sin 2 20 inches. TABLE 569. Miscellaneous Geodetic Data. Equatorial radius = a = 6378206 meters; 3963. 225 miles. Polar semi-diameter = b = 6356584 meters; 3949 . 790 miles. Reciprocal of flattening = -: = 295 . o Square of eccentricity = e 2 a 2 -i* = 0.006768658 6378388 =fc 1 8 meters; 3963-339 miles. 6356909 meters; 3949.992 miles. 297.0 =*= 0.5 0.0067237 0.0000120 Difference between geographical and geocentric latitude = ' = 688.2242" sin 20 1. 1482" sin 40 + 0.0026" sin 60. Mean density of the earth = 5.5247 =*= 0.0013 (Burgess Phys. Rev. 1902). Continental surface density of the earth = 2.67 \ TT i _ <;,> -icr> r>ar ttt Mean density outer ten miles of earth's crust = 2.40 ) Harkness - Se Constant of gravity, 6.66 X io~ 8 c.g.s. units. Rigidity = n = 8.6 X lo 11 c.g.s. units. \ A. A. Michelson, Astrophysical Journal, 39, Viscosity = e = 10.9 X io 16 c.g.s. units (comparable to steel), j p. 105, 1914. Moments of inertia of the earth; the principal moments being taken as A, B, and C, and C the greatest: C -A i 7: = 0.00326521 = ; C 306.259 C A = 0.001064767 13- SE 13.9 E 14. IE I4-3E 14. 4E 14. 4E 14. 6E I5-3E IS- 7E Mojave 12. 4E 12 .9 E 13- 4E 13- SE 14- 2E 14. 4E 14. 6E 14- 9E 14. 9E IS- IE IS.SE 16.3 E Modesto . . , 13- 8E 14.21 14- 7E IS- IE 15-5 E IS.SE 16. i E 16. i E 16. 2E i6.6E 17- 3E 17- 7E Redding IS- 6E 16. I E I6.6E 17. OE 17. 4E 17. SE I8.IE I8.2E I8.3E i8.7E 19. 4E I9-7E Colo. Pueblo __ 13- 7 E 13. SE 13 7 E 13 S E 13 . O E 12 . 8 E 13 . 3 E 13. 7 E Our.iv. . . __ IS O E IS 2 E IS . 2 E IS.OE 14 6 E 14. 6 E IS. I E IS 5 E Conn. Hartford 5-iW 5-SW 6.iw 6.8w 7-5W l. A S.iw 8.7W 9-4W ^ if 9.8w 10. 4W II.2W 12. IW Del. Dover i.6w i . 9\v 2-3W 2.8w 3-4W 4.0W 4-7W 5-3W S-9W 6. 5 w 7-2W 8.ow D. C. Washington.. . O.SE 0-3E 0.0 o.sw LOW i.7W 2. 4 W 3-OW 3-6W 4.2W 4-9W 5.6w Fla. Miami S-8E 5-7E S-3E 4 .9E 4-4E 3-9E 3-3E 2.7E 2.2E I.7E I-5E Bartow S-5E 5-4E 5-2E 4.8E 4-4 E 3-SE 3-2E 2.6E 2.1 E I.6E I.4E I-3E Jacksonville. . . S.OE S.OE 4-9E 4-6E 4 .2E 3-6E 3-OE 2. 4 E I.8E L3E LIE Tallahassee. . . 5-8E 5-SE 5-7E 5-SE 5-2E 4.8E 4.2E 3-6E 3-OE 2.SE 2. 4 E 2! 4 E Ga. Millen 4-9E 4 .8E 4 .6E 4-3E 3-9E 3-4E 2.?E 2.1 E I.SE 0-9E 0.7E 0-5E Americus S-9E 6.0E 5-9E S-6E 5-2E 4-7E 4-1 E 3-SE 2.9E 2. 4 E 2.2 E 2.2E Haw. Honolulu 9-4E 9-4E 9-SE 9.8E 10. I L IO-4E 10. 7 E J.I. I E Idaho Pocatello 17. 7E 17. 9E iS.OE I7-9E 17. SE I7-9E 18. s E iS.SE Boise iS.OE iS.SE iS.SE i8.6E iS.SE 19- SE 19. SE Pierce _ __ 2O. 2 E 2O. 6 E 21 O E 21.2 E 21. I E 21 . 2 E 21.4 E 22 . E 22. 2 E 111. Kankakee .... 6.6E 6.8E 6.8E 6.6E 5-8E S-3E 4.8E 4. IE 3-SE 3-3E 3- IE Ind. Rushville Indianapolis . . 7-7E S.OE 8.0E S-IE 8. IE S.OE 8.0E 4-7E 7 :sE 4-3E 7-4E 3-SE 7-OE 3-3E 6. 4 E 2.7E 5-7E 2.1 E 5-2E LSE 5- IE LIE 5. IE O.9E Iowa Walker 8.9E 9. IE 9.1 E 8.9E 8.6E 8.2E 7-SE 6.8E 6.2E 6.2E 6.2E Kans. Sac City Emporia IO. 4 E 10-7 E 10. SE 10. SE n-SE 10. SE II.4E 10.2 E II. 2 E 9.6E 10. SE 8.8E 10. 2 E 8. 4 E 9-9E 8.6E IO.I E 8.6E 10. 3E Ness City 12. 4E 12 .4 E 12. 2 E II. 9E II. 3 E II. 2 E II.4E II.7E Ky. Manchester. . . 3-SE 3-6E 3-4E 3- IE 2.8E 2.2E I.6E I.OE 0.3E O.3W o.6w o.8w Louisville 4 .8E Princeton | 6.8E 4-9E 6.9E 4.8E 6.9E 4 .6E 6.8E 4-3E 6.5E 3-8E 6.0E 3-2E S-SE 2.5E 4 .8E I.9E 4.2E I-SE 3-9E L3E 3-7E I.2E 3-SE La. Winfield 8.6E 8.9E 9.0E 9.0E 8.9E 8.6E 8.2E 7.6E 7.1 E 6.8E 7-OE 7-4E Me. Eastport 13. 9W 14. 7W IS-SW i6.3W I7.2W iS.ow iS.sw iS.Sw 19. ow 19- 3W 20. OW 21. OW Bangor > 1 1. 8w 12. 4 W 13- 2W 13. 9W 14. 7W IS-4W IS- 9W i6.4W i6.7W 17. iw i7.8w iS.Sw Md. Portland Baltimore 9-3W 9-9W LIW 10. 6w L4W II.2W I.QW ii.gw 2.4W 1 2 . 6W 3-iw 13. iw 3-8w 13. 6w 4.4W 14. iw S-OW 14- SW S-6w IS- 3W 6.3W 7.ow Mass. Boston 7-3W 7.8w 8. 4 W 9.iw 9.8w 10. sw II.OW I2.0W I2.6W 13. 4W 14. 4W Mich. Pittsfield Marquette S-7W 6.2W 6. 7 E 6. 7 W 6. 7 E 7-4W 6.SE S.iw 6. IE 8.7W 5-SE 9-3W 4-7E IO.OW 3-8E IO.4W 3-OE II.OW 2. 4 E n.8w 2. IE 12. 7W I.7E Minn. Lapeer Grand Haven. St. Paul E 2.6E 5. IE II.6E 2. 4 E S.OE ii. SE 2.1 E 4-8E II. QE I.6E 4-4E I.OE 3-SE II. 4E 0.3E 3- IE IO-9E o.sw 2. 4 E 10. 3E I.2W I.6E 9-SE i.8w LIE 8.9E 2-3W 7E 8.8E 2.8W 0.3 8. 7 E Marshall . II. 7E L6E II.4E II.OE 10.5 E 9.8E 9-3E 9-4E 9-4E Hibbing 10. SE 10. 7 E 10. SE 0.6E 10. 3 E 9-7E 9.0E 8.2E 7.6E 7-7E 7-SE Meridian... Vicksburg.... 7-3E 8.2E 7-4E 8. 4 E 13- OE 7-SE S.SE 3- IE 7-4E 8. 4 E 3-IE 7.2E. 8.2E 12. SE 6.9E S.OE 12.3 E 6. 5 E 7.6E II. 7E 5-9E 7. IE I.OE 5-2 E 6. 4 E 0. 4 E 4.8E 6.0E 0.6E 4-9E 6. IE 10. SE S-IE 6. 4 E SMITHSONIAN TABLES. TABLE 570. TERRESTRIAL MAGNETISM (continued). Secular Change of Declination (concluded'). 429 State. Station. 1810 1820 1830 1840 l8SO 1860 1870 1880 1800 1900 1910 1920 Mo. Hcrmajui _ Q.2E 9-3E Q.2E Q.OE 8. 7 E 8.3E 7-7E 7.0E 6. 5 E 6.5E 6.6E Sedalia Q.QE IO.OE IO.OE g.gE g.6E 9-3E 8. 7 E 8.0E 7.0E 7.8E S.OE Mont. Miles City 17. OE 17. SE 17. 7E 17. 4E I6.0E i6.gE I7-3E 17. 6E Lewis town. . . . IQ.5 E IQ.SE 2O. I E 20. IE 19. gE IQ.OE ig.6E 2O. I E 20-4 E Ovando 20. 4 E 20. 8 E 21. I E 21.2 E 21. 1 E 20. QE 21. I E 21. 6E 22. OE Nebr. Albion 12. 4E 12. 7 E 12. QE 12. QE 12. SE 12. SE 12. OE II. 4 E II. OE II. 2E II. 5 E Valentine I4.I E 14. IE 13. QE 13. 4 E 12. SE 12. 6E 12. SE 13- IE Alliance 15. 4E 15. 4 E IS- 3E 14. 8 E 14. 3E 14. 2 E 14. SE 14. SE Nev. Elko . . 17.3 E 17 . 6 E 17.7 E 17. 7 E 17 . 6 E 17. SE i8.4E iS.QE Hawthorne . . . l6. 2 E i6.6E i6.8E 17. OE 17. OE 17- 3E I8.0E l8. 4 E N. H. Hanover 7.iw 7-5W 8.2W S.QW 9-7W 10. sw II.IW n.6w I2.OW I2.6W 13- 2W 14. 2W N.J. Trenton 2.8W 3.IW 3-5W 4. iw 4-7W S-4W 6.ow 6.7W 7-2W 7-8w 8.6w 9-4W N. M. Santa Rosa . . . 12.7 E 12. SE 12. 7E 12. 4E 12. OE ii. gE 12. SE 12. gE Laguna 13. 4 E 1^.6 E I3-6E 13. 4E 13- OE 13- OE 13-6 E 14. IE N. Y Albany S-7W S.QW 6.4W 7.ow 7-Sw 8.5W Q.2W 10. OW 10. 3W 10. gw n.6w 12. SW Elmira 2.2W 2.4W 2.8w 3-3W 4.ow 4.8w 5-4W 6.3W 7-ow 7-SW 8.2W g.ow Buffalo I .OW I . IW T AW i . ow 2.4W 3 2W 3.8w 4. 7W 5 . 4\V Sow 6. sw 7 . 2W N. C. Newbern I.7E I.6E A . 4-W I-3E O.SE 0.3E O.^W LOW I.7W 2-3W . y w 2.gw 3-4W 4.0W Greensboro . . . 3-SE 3-4E 3- IE 2.7E 2.2E 1.61 I.OE 0.3E 0.3W o.8w I-3W i.Sw Asheville 4.2E 4 .2E 4.0E 3-6E 3-IE 2.6E 2.0E I.3E 0.7E 0.2E 0.2W o.sw N. D. Jamestown . . . 14. OE 14. 2 E 14. 2 E 14. OE 13- 7 E 13- 2 E 12.5 E 12. 2E 12. 4E 12. SE Bismarck i6.4E 16.3 E 16.1 E IS- 6E IS-OE 14. 7 E IS.OE IS- 2E Dickinson .... 17- 7E 17. 7E I7-5E 17. IE i6.SE 16.3 E i6.7E i6.gE Ohio Canton 2.3E 2. 2 E 2.0E I.7E I.2E 0.6E 0.0 o.7W I-3W I.QW 2.SW 3-iW Urbana 4-4E 4-4E 4-3E 4.0E 3-SE 3.0E 2.4E I.8E I.I E O.SE O.IE 0.3W Okla. Okmulgee .... IO.2 E IO. I E g.8E 9-5E g.iE 8. 7 E S.QE g.2E Enid __ II. 2E II. 2 E II. OE 10. 6E 10. 2 E Q.SE 10. I E 10. SE Ore. Sumpter IQ.3E I9-7E 2O. OE 20.2 E 2O. 2 E 2O. 4 E 21. 1 E 21. 4 E Detroit 16.7 E 17. 4E iS.OE i8.6E ig. 2 E ig.7E 2O. I E 20.3 E 20.5 E 20. SE 21. 6E 21. QE Pa. Wilkes-Barre. . 2.3W 2.5W 2.g\v 3.4W 4.ow 4-7W S-3W 6.ow 6.6w 7-2W 8.0W S.Sw Lockhaven. . . . I.4W i.SW I . QW 2.4W 3.ow 3-6w 4-3W S-ow 5-6w 6. 3 w 7-ow 7-7W Indiana 0.6E O.SE 0-3E O.IW o.7W i-3W 2.0W 2.6W 3-3W 3.gw 4.6w 5.2W P. R. San Juan I . OW 2.OW 3-4W R. I. Newport 6.6w 7.iw 7-7W 8.4W g.iw g.8w 10. 3W 10. 8w H.3W n.gw 1 2 . 7W 13. 7W S. C. Marion 3-4E 3-3E 3-OE 2.6E 2.1 E I.6E o.gE 0.3E O.4W LOW I.4W i.Sw Aiken 4.8E 4-7E 4-SE 4 .2E 3-7E 3-IE 2-SE I.QE I-3E 0.7E 0. 4 E O.I E S. D. Huron 13-2 E 13- 2E 13. OE 12. 7E 12. 3E II. 7E II. 2 E II. SE II. 7E Murdo IS.OE 14. gE I4-7E 14- 3 E I3-7E 13. 4E 13- 7 E 13. 9E Rapid City ... IO-4E i6.4E i6.3E IS-8E IS-3E IS- IE 15. 4E IS- 7E Tenn. Knoxville 3-8E 3-8E 3-6E 3-3E 2.QE 2. 4 E I.SE LIE O.SE o.o o.3W o.sw Shelbyville.... 6. 4 E 6.5E 6.4E 6.2 E S-9E 5-SE 4-9E 4-3E 3-7E 3-2E 3-OE 2.QE Huntingdon. . . 7-3E 7-4E 7-4E 7-3E 7.0E 6.6E 6. IE 5-SE 4.QE 4-4E 4-3E 4-4E Tex. Houston Q.OE g.2E 9-4E Q.4E 9-3E 8.QE 8. 4 E 7-9E 7-7E 8. IE 8.6E San Antonio . . 9-SE 9-7E g.8E 9-7E 9-5E Q.2E 8.yE 8.7E Q.2E 9-7E Pecos 10.7 E II. OE II. I E II. I E II. OE 10. SE IO.4E 10. 3E 10. 8 E II. 3E Wytheville.... 2.9E 2.QE 2.7E 2.4E 2.0E I.4E o.8E O.IE o.sw I.IW i.SW I.QW Wash. Wilson Creek.. 21.2 E 21. 6E 21. SE 21. QE 22.1 E 22:4E 23. OE 23. 3 E Seattle I8.QE IQ. SE 20.1 E 20. 7 E 21. 2E 21. 6E 22. OE 22. 2E 22. 4E 22. SE 23- SE 23. SE W. Va. Sutton I.QE I.8E I.6E I.2E O.SE 0.2E 0.4W I.IW i.8w 2.4W 2.gw 3-4W Wis. Shawamo 7-4E 7-4E 7-3E 7.0E 6-SE S.QE S.OE 4-3E 3-7E 3-4E 3- IE Floydada II . 2 E II. 3 E II . 2 E 10. QE 10. 4E 10.3 E 10. 7 E II. IE Utah Manti i6.4E 16.7 E i6.8E 16.7 E i6.4E i6.SE 17- IE 17- SE Vt. Rutland 6.6w 7.iw 7.6w 8.3W g.iw Q.8W 10. sw II.2W n.6w 12. IW 12. 8W 13- Sw Va. Richmond. . . . O.SE 0.6E 0.3E O.IW o.6w I.2W i.8w 2.5W 3-iw 3-7W 4-2W 4.QW Lynchburg.. . . I.6E I-5E I.3E O.gE O.SE O.IW o.7W I.4W 2.OW 2.6w 3-iw 3-7W Stanley 8.QE Q.OE Q.OE 8.8E 8. 4 E 7.8E 7. IE 6. 3 E S.8E 5-6E 5-4E Wyo. Douglas IS-8E I6.0E I6.0E 15. SE IS-3E IS.2E IS- 7E I6.0E Green River . . i6.8E 17. OE 17. OE i6.8E l6.5 E i6.6E I 7 . 2E 17- 5E SMITHSONIAN TABLES. 4.^0 TABLES 571 572. TERRESTRIAL MAGNETISM (continued). TABLE 571. Dip or Inclination. This table gives for the epoch January i, 1915. the values of the magnetic dip, /, corresponding to the longitudes Greenwich in the heading and the north latitudes in the first column. X 65 7 75 80 85 90 95 100 105 no "5 1 20 125 19 50-4 49-4 48-5 47.2 46.1 45-1 44-1 21 52.7 51.9 51-1 50.1 48.9 47-9 46.9 23 55-i 54 2 53-7 52.8 51-7 50.4 49-7 48.7 as 27 57-6 59-8 56.8 59-3 56-1 58.3 55-2 57-6 54-2 56.6 53.1 55-6 52.2 54-6 Si. a 53-6 50.1 52-4 29 61.9 6i.3 6o.| 59-7 58.9 57-9 56.8 55-8 54-6 53-8 31 33 35 = 63.6 65.4 67.2 63.8 65.6 67.3 63.4 65-3 67.2 62.8 64-7 66.6 62.0 64.0 66.1 61.1 63.1 65-3 60. i 62.4 64-3 59-0 61.2 63.2 i 62. 57-0 59-1 61.0 55-8 fc? - 37 gil 69.2 69.0 68.9 68.1 67.3 66.4 65.2 6 4 . 63.1 62.! 39 70.6 70.8 70.6 70. 6 70.0 69.2 68.3 67.3 66. 64.9 63-9 62.5 41 _ 72.2 72.3 72.5 72.2 71.7 71.0 70.1 69.0 68. 66.6 65.5 64.3 43 73.6 74.0 74.1 74.0 73-5 72.6 71.8 70.7 6o-7 68.4 67.2 65-9 45 47 74-3 75-6 74-9 76.3 ll'i 75-5 76.9 75-5 76.9 75-2 77.0 74-5 76.1 73-5 75-1 72.4 74-2 71-3 72.9 70.2 71.7 69.0 70.5 67.8 69-5 49 76.5 77-4 78.2 78-5 78.5 78-3 77-7 76.7 75-7 74-5 73-2 72.1 71.2 TABLE 572. Secular Change of Dip. Values of the magnetic dip for places designated by the north latitudes and longitudes west of Greenwich in the first two columns for January i of the years in the heading. The degrees are given in the third column and the minutes in the suceeding columns. Latitude. Long- itude. 1855 1860 1865 1870 1875 -1880 1885 I8 9 1895 1000 1905 1910 1915 25 80 55 + 32 32 31 29 26 23 18 18 22 31 43 73 108 25 no 49 + 14 26 36 45 52 61 67 74 82 92 IO2 116 132 30 83 60+ 66 70 73 74 73 67 57 51 53 61 78 101 126 30 IOO 57+ 4i 46 55 64 67 62 57 58 6s 74 8 7 103 I2O 30 "5 54+ 47 56 63 65 64 66 69 73 79 85 90 06 102 35 35 35 35 80 90 iS 120 66+ 65 + 62 + 59+ 67 67 56 68 61 59 67 53 61 64 46 47 61 55 39 45 60 45 34 39 59 36 28 39 61 3i 27 39 64 30 27 43 66 32 29 $ 57 66 55 i 8 72 66 40 75 7i + 82 82 78 73 65 55 43 33 27 24 24 29 36 40 90 70+ 30 31 34 37 36 32 29 26 25 26 30 38 48 40 105 67 + S6 S3 51 Si Si 52 S6 60 63 66 40 45 120 65 64+ 74+ 118 112 103 51 94 II 54 70 57 59 i 58 37 54 30 50 26 45 22 42 18 45 75 75 + 9i 87 83 78 73 6z 50 41 31 26 24 24 24 45 90 74+ 86 86 86 84 82 80 73 68 66 64 6s 68 72 45 105 72 + 30 28 27 26 26 25 25 24 45 49 122. 5 92 68+ 77+ & 44 79 47 78 50 76 50 74 49 74 8 44 66 40 6S 37 6^ g 3 21 60 49 120 72 + 27 25 24 23 22 21 20 20 19 17 12 06 SMITHSONIAN TABLES. TABLES 573-574. TERRESTRIAL MAGNETISM (continued). TABLE 673. Horizontal Intensity. 431 This table gives for the epoch January i, 1915, the horizontal intensity, H, expressed in cgs units, corresponding to the longitudes in the heading and the latitudes in the first column. X 4> 65 70 75 80 85 90 95 100 i5 110 "5 120 125 19 297 303 311 -3i6 .321 .325 325 21 .290 . 206 .303 .310 315 320 320 23 .283 .288 294 301 307 3" 3" 311 25 273 .281 .286 .292 .298 .302 303 303 304 27 .264 .271 .276 .281 .288 .292 295 .296 .297 29 31 - 237 253 .242 .258 .247 .265 254 .272 .260 .277 .266 .283 .272 .286 .276 .28 7 .279 .288 .280 .288 .280 ~ 33 .225 .230 .236 .242 .248 255 .259 .264 .270 .271 .272 35 .213 .217 .223 .232 235 .241 249 251 .256 .260 .263 37 .202 .205 .210 .213 .222 .227 234 .240 .244 .250 253 3Q 41 .191 .178 .193 .178 .196 .182 .200 .185 .206 .191 .212 .197 .218 .204 .226 .212 .232 .218 3 .242 .232 245 .236 43 .166 .166 .165 .171 .174 .182 .189 .198 .207 .214 .221 .227 ' 45 159 154 .153 153 155 .160 .167 .174 .185 .192 .202 .210 .216 47 .146 143 .139 .139 .141 .142 ISO 159 .168 .ISO .187 195 .202 49 135 .130 .126 -123 .123 .129 .136 .144 -153 .'164 .174 .182 .189 TABLE 574. Secular Change of 'Horizontal Intensity. Values of horizontal intensity, H, in cgs units for the places designated by the latitude and longitude in the first ^wo columns for January i of the years in the heading. u, Long. 1860 1865 1870 1875 1880 1885 1890 1895 1900 1905 1910 1915 o 25 80 .3086 3073 .3057 .3042 3025 .3008 .2990 .2970 .2949 .2917 .2870 .2810 25 no .3216 .3202 3187 .3168 .3153 3141 .3128 .3115 .3102 .3088 3063 .3030 30 83 2775 .2768 .2760 .2752 2743 .2732 .2720 .2705 .2686 .2658 .2614 .2560 30 IOO .2978 2959 .2941 .2924 .2908 '.2894 .2882 .2867 2847 .2817 .2780 30 "5 .2996 .2981 .2966 .2949 2934 .2922 .2910 .2899 .2890 .2880 .2863 .2840 35 80 .2367 .2362 2357 2355 2351 2347 .2340 2335 2325 .2306 .2272 .2230 35 90 .2460 .2460 2459 .2456 2453 2445 2435 .2418 .2387 2350 35 35 105 1 20 ~ * .2727 . 2619 .2714 .2607 .2702 .2598 .2690 .2589 .2679 .2582 .2670 .2572 .2663 .2559 .2657 2537 .2645 .2510 .2630 40 75 .1876 .1884 .1895 .1904 .1912 .1918 .1923 .1924 .1921 .1911 .1889 .i860 40 go .2080 .2076 .2073 .2070 .2069 .2068 .2066 .2062 .2054 .2042 .2019 .1990 40 105 .2269 .2263 .2258 .2254 .2250 .2245 .2237 .2227 .2210 . 2I9O 40 1 20 2439 .2430 .2422 .2416 .2409 .2402 .2396 .2390 .2381 .2370 45 65 .1504 1515 1527 1543 1557 .1568 1579 .1590 .1598 .1600 .1596 1590 45 75 .1487 .1490 .1497 .1508 .1518 .1529 .1540 .1548 .1552 1552 1543 1530 45 90 .1648 .1646 .1644 .1641 .1639 1637 .16^6 .1637 .1636 1633 .1620 .I60O 45 105 .1895 .1894 .1893 .1891 .1888 .1885 .1881 .1875 .1864 .1850 45 122.5 .2183 2175 .2166 .2158 .2148 .2140 .2134 .2130 .2128 .2128 .2125 .2I2O 49 92 1336 1334 .1330 1327 1325 1324 .1324 .1327 1330 .1^6 .1330 .1320 49 1 20 .1846 .1845 .1844 .1841 .1836 .1831 .1826 .1824 .1825 .1825 .1823 .1820 SMITHSONIAN TABLES. TABLES 575-576. TERRESTRIAL MAGNETISM (.continued). TABLE 575. Total Intensity. This Uble rives for the epoch January i. HJI.S. tin- values of the total intensity, F, expressed in cgs units corre- sponding to the longitudes in the heading ar.l tin- latitudes in the first column. X 65 70 75 80 85 90 95 100 105 110 120 125 10 .466 .469 465 .463 .461 453 _ : 21 .480 .482 483 479 477 .468 >3 495 492 497 .498 495 .488 .481 .471 25 27 509 513 531 513 525 512 .524 Sio .523 503 .517 494 509 .484 499 474 487 ' . 29 31 33 35 E 533 540 1 537 552 576 538 .556 .566 584 539 536 550 564 .533 .546 559 574 .522 .536 .548 557 ^528 543 549 497 514 528 -536 .488 .498 513 528 37 .566 577 .586 -592 595 .588 .585 572 561 552 541 39 _ 575 .587 590 .602 .602 597 590 586 575 -559 -550 531 582 585 .605 .605 .608 605 599 592 582 569 559 544 43 45 47 .588 .587 .588 .602 .607 .609 .602 .611 .613 .620 .619 .622 613 .626 .631 .609 625 .624 .605 .613 .618 599 .612 .617 597 599 .612 S8i 596 596 570 586 .584 556 572 577 49 .578 .596 .'616 .617 .617 .636 .638 .626 . 619 .614 .602 -592 587 TABLE 576. -Secular Change of Total Intensity. Values of total intensity, F, in cgs units for places designated by the latitudes and longitudes in the first two columns for January i of the years in the heading. Lat. Long. 1855 1860 1865 1870 1875 1880 1885 1890 1895 1900 1905 1910 1915 25 80 .5476 5453 5427 .5396 .5363 5324 5285 .5253 5227 .5208 .5178 .5160 .5131 25 no 4941 .4946 .4941 4933 .4914 .4906 .4900 .4889 .4884 4879 .4876 .4861 .4836 30 83 5758 5755 5749 5735 .5716 .5678 5625 .5584 5559 5549 5534 5510 5471 30 100 5608 5595 .5567 5523 5479 5455 5450 5444 5441 .5426 5399 30 "5 5219 .5216 5205 .5182 5149 5129 5114 .5101 594 .5092 -5086 .5068 5041 35 80 .6lOI .6000 6075 .6048 .6008 .5955 .5910 .5873 5856 .5838 5823 .5796 .5756 35 90 5993 5966 .5946 5914 5904 5885 .5868 .5861 5834 .5800 35 35 40 105 120 .6183 .6193 .6196 5457 .6204 .5720 .5428 .6190 5675 5401 .6160 5656 .5383 .6115 5636 5369 .6077 5634 5356 .6047 5630 5342 .0022 .5627 -5330 5991 5604 .5306 5948 5567 5276 .5892 40 00 .6236 .6240 .6246 .6233 .6209 .6190 .6169 6151 .6133 .6118 .6089 .6052 40 105 .6040 .6011 .5988 5978 .5967 5958 5955 5944 5912 5871 40 120 5739 5720 5709 5707 5692 .5676 5647 .5621 .5581 .5546 45 65 .6l6l .6x59 .6140 .6126 .6107 .6082 .6052 .6022 5994 5980 .5962 5923 .5875 45 75 .6369 6347 -6330 .6320 .6329 .6281 .6247 .6228 .6189 .6171 6157 .6121 .6070 45 90 6552 .6544 .6522 6495 .6474 .6415 6377 .6366 6349 6344 6315 .6264 45 105 .6296 .6276 .6261 .6245 .6232 .6206 .6170 .6n8 ! 45 122-5 .6037 .6019 .6010 .6000 .5978 5944 5913 5883 5855 5837 5820 .5784 5745 49 92 .6616 .6597 6578 .6540 .6508 .6498 .6448 .6421 .6427 .6424 .6426 .6380 6349 49 120 .6121 .6107 .6098 6083 .6061 6039 .6017 .6010 .6008 5997 5963 .5922 SMITHSONIAN TABLES- TABLES 577-578. TERRESTRIAL MAGNETISM (continued). TABLE 577. Agonic Line. 433 The line of no declination appears to be still moving westward in the United States, but, as the line of no annual change is only a short distance to the west of it, it is probable that the extreme westerly position will soon be reached. Lat N. Longitudes of the agonic line for the years 1800 1850 1875 1890 1905 1915 25 75-5 76.1 77-4 30 78.6 79-7 80.0 35 76.7 79.0 79-9 81.7 82.7 6 75- 2 77-3 79-7 80.5 82.8 84-4 7 76 3 77-7 80.6 82.2 83-5 84.0 8 76.7 78.3 81.3 82.6 83-6 84.1 9 76.9 78.7 81.6 82.2 83.6 83-9 40 77-o 79-3 81.6 82.7 84.0 84.3 i 2 77-9 79-i 80.4 81.0 81.8 82.6 82.8 83.7 84.6 84.8 85-1 85-3 3 79-4 81.2 83-1 84-3 85.0 85-4 4 79-8 83-3 84-9 85-S 85.8 45 83-6 85-2 86.0 86.2 6 84-2 84-8 86.4 86.3 7 85.1 85-4 86.4 86.6 8 86.0 85-9 86.5 87.2 9 86.5 86.3 87.2 88.0 TABLE 578. Mean Magnetic Character of Each Month in the Years 1906 to 1917.* Means derived from daily magnetic characters based upon the following scale: o, no disturbance; i, moderate disturbance, and 2, large disturbance. Year. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec. Year Mean. 1906 0.45 o. 90 0.68 0.63 0.58 0.56 o. 69 0.63 0.79 o-59 0-55 0.71 0.65 1907 0.69 0.83 0.58 o-SS 0.72 0.67 0:67 0.66 0.68 0.71 0.61 0.53 0.66 1908 0.64 0.71 0.87 0.68 0.82 0.66 0.49 0.77 0.89 0.53 0.60 0.47 0.68 1909 o. 76 0.63 0.79 0.49 0-S9 o-54 0.53 0.65 0.70 0.69 0.49 0.58 0.62 1910 0.58 0.71 0.81 0.68 0.72 0-53 0.55 0.81 0.80 0.96 0.77 0.76 0.72 1911 0.78 0.89 0.78 o. 76 0.70 0-53 0.61 0-53 0.50 0.59 0.49 0-45 0.63 1912 0.42 0.49 o-45 Q-45 o-47 0.47 0.41 0.49 0.47 0.46 0-45 0.43 0.46 1913 0.51 0-53 0-53 0-54 0-45 0-45 0.42 0.46 0.58 0.57 0.42 0.36 0.48 1914 0.46 0.50 0.62 0.50 0-37 0.52 0.61 0.61 0-53 0.64 0.60 0.46 0-54 1915 0-53 0.64 0.68 0.61 0.58 0.61 0.47 0.60 o.S9 0.77 0.82 o-54 0.62 1916 0.61 0.56 0.86 0.68 0.75 0.67 0.62 0-75 0.75 o. 76 0.83 0.65 0.71 1917 0.81 o. 69 0-59 0.63 0.66 0-55 0.61 0.85 0.61 0-74 0-53 0.72 0.67 * Compiled from annual reviews of the "Caractere magnetique de chaque jour" prepared by the Royal Meteoro- logical Institute of the Netherlands for the International Commission for Terrestrial Magnetism. The number of stations supplying complete data for the above years were respectively, 30, 32, 36, 38, 34, 39, 43, 42, 37, 35, 35, 35- Data from Sitka, Ekaterinburg, Stonyhurst, Wilhelmshaven, Potsdam-Seddin, De Bilt, Greenwich, Kew, Val Joyeux, Pola, Cheltenham, Honolulu, Bombay, Porto Rico, and Buitenzorg were employed for all of the years. SMITHSONIAN TABLES. 434 TABLE 573 ' RECENT VALUES OF THE MAGNETIC ELEMENTS AT MAGNETIC OBSERVATORIES. pilot l.y tin- Dop.irtmcnt of Terrestrial Magnetism, Carnegie Institution of Washington.) Latitude Longitude Middl of year. Magnetic elements. Declination Inclination Intensity (cgs units). Hor'l Ver'l. Total. Pavlovsk. . . O / 57 o.< N 56 50 N 55 5i N 55 47 N 55 19 N S3 Si N 5332N 52 23 N 52 17 N 52 i6N 52 06 N 51 56 N 51 48 N 51 29 N 51 28 N 51 28 N So 4 8N So 46 N 50 21 N 50 09 N 50 05 N 50 04 N 48 49 X 48 09 N 48 03 N 47 53 N 46 26 N 4452N 43 47 N 42 42 N 41 43 N 40 52 N 40 49 N 40 12 N 38 47 N 38 44 N 36 28 X 354IN .32 15 X 31 19 N 30 19 N 29 52 N 22 4 6 N 22 18 N 21 19 N 1 8 (6 X 18 38 N 18 09 N I436N 10 14 N 6 ii S 8 48 S 13 488 18 558 20 06 S 31 40 S 33 278 43 328 54 45 S J 60 45 S o / 30 29 E 135 20 W 60 38 E 12 27 E 49 08 E 3 12 W 2 28 W 8 ogE 13 04 E 13 01 E 104 16 E 5 ii E 10 15 W 10 20 E 7 14 E o 19 W o oo 4 21 E 16 14 E 18 55 E 5o 5 W 14 25 E 19 58 E 2 01 E ii 37 E 14 08 E 18 12 E 30 46 E 13 Si E 79 16 W 2 53 E 44 48 E 14 15 E o 31 E 8 25 W 95 10 W 76 50 W ' 6 12 W 139 45 E no 50 W 121 02 E 78 03 E 31 20 E 88 22 E 114 10 E 158 04 W 96 27 E 72 52 E 65 26 W 121 10 E 77 28 E 106 49 E 13 13 E 171 46 W 47 32 E 57 33 E 63 53 W 70 42 W 172 37 E 64 03 W} 42 32 W 1907 1916 1907 1915 1912 1913 1915 1911 1916 1916 1905 1914 1913 1905 1912 I9i5 1916 1911 1913 1908 1912 1912 1913 1913 1911 1904 1912 1910 1915 1916 1910 1913 IQII 1914 1915 1909 I9l6 1913 1912 I9l6 1909 1914 1913 1914 I9l6 I9l6 1914 1915 I9l6 I9II 1914 1912 1910 I9l6 1907 I9l6 1914 1909 1914 1906 1912 / i 09.9 E 30 24.0 E 10 35- 5 E 8 44-3 W 8 09.1 E 17 54-9 W 16 38.0 W ii 28.2 W 8 07.6 W 8 08.9 W i 58.1 E 12 22.6 W 20 19.6 W 10 40.3 W ii 39-4 W 15 18.4 W 14 46.9 W 13 13-9 W 6 58.2 W 6 12.3 W 17 24.2 W 7 50.3 W 5 03.3 W 13 59-2 W 9 23.8 W 9 02.4 W 6 17.5 W 3 35-9 W 7 39-o W 6 33-4 W 12 44.8 W 3 09.1 E 12 51.6 W 15 57-5 W 8 34.0 E 6 07.6 W 1451-7 W 5 03.4 W 13 44-4 E 2 59-6 W 2 18.8 E 2 17.0 W o 32.2 E o 13.8 W 9 43-8 E o 02.6 E o 40.6 E 3 19-4 W o 40.9 E i 17. i W o 47-3 E 16 12.3 W 9 59-9 E 9 29.7 W 9 47-6 W 8 40.4 E 13 57-9 E 16 44.8 E 15 41-6 E 4 46.5 E / 70 37-7 K 74 26.0 K 70 52.2 K 68 50. 6 N 69 17-3 M 69 37-3 N 68 41. 4 N 67 30.7 N 66 27. i N 66 24.1 N 70 25.0 N 66 46. 5 N 68 09. 2 N 66 56. 6 N 66 52. 8 N 66 oo. i N 66 26. 6 N 64 i8. 4 N 64 38. 9 N 63 06.2 N 62 26. 9 N 60 05 . i N 74 43-5 N 56 51. i N 56 11.7 N 57 47-5 N 58 34- 7 N 68 50. 2 N 70 49- 9 N 54 26 6 N 48 53. 7 N 59 26.1 N 45 34- 9 N 44 22.9 N 40 47 . 6 N 30 58.9 N 30 51. 8 N 39 29.2 N 23 06. i N 24 21. i N 50 56.7 N 16 i8.2N 4 ii. 2 N 31 19-48 35 32-2 S 29 54-5 S 54 05.7 S 52 54-68 25 41-5 S 29 57-2 S 67 59- 8 S 50 03.6 S 54 26. oS 1650 .1558 .1762 .1726 .1802 .1682 1734 .1811 .1870 1874 .2001 .l85I .1789 .1846 .1849 .I9O2 .l8oO 1974 .2063 .2IO6 .2171 .2217 1599 .2522 2330 2305 .2167 1934 .2494 .3000 .2706 3323 3316 -3003 3740 .37X6 .28 9 6 .3898 3637 .2315 .3820 3757 .3668 .2012 3536 2533 .2320 .2560 .2241 2717 2534 .4694 5592 .5081 4459 476S 4528 .4446 4375 .4290 .4289 5625 4314 4463 .4338 4332 4273 4312 4167 .4068 .4161 .3853 .5854 376i 3"6~98 3773 .5596 .5662 .3489 .3438 .4582 3391 3246 .2592 .2246 .2220 .2386 .1663 .1669 3470 .1117 0275 .2232 1437 .2034 3499 3069 1232 5546 3244 3544 4975 .5805 5378 4781 5094 4831 .4772 4735 .4680 .4680 5970 .4694 .4808 4714 4710 4677 4704 .4611 .4561 4693 4445 .6068 4528 4371 4422 .6001 .5889 .4289 4563 5322 4747 .4641 3967 .4363 .4328 3752 .4238 .4047 .4468 3981 3767 .4229 2473 .4080 4319 3847 .2841 5982 4231 4357 Sitka Katharinenhurg Rude Skov Kasan . . . EskdaJemuir. Stonvhurst Wilhelmshaven. . . Potsdam Scddin Irkutsk. De Bill Valencia Clausthal Bochum Kew. Greenwich . . . ! Uccle Hermsdorf Beuthen Falmouth.. . . Prague. . Cracow Val Toveux ... . Munich Kremsmiinster O'Gyalla (Pesth) Odessa Pola Agincourt (Toronto). . Tiffis Capodimontc Ebro (Tortosa)... Coimbra . . . Baldwin * Cheltenham.. . San Fernando. Tokio. . Tucson Lukiapang ** . Dehra Dun Helwan Barrackpore t Hongkong Honolulu Toungoo . Alibi,'.. Vieques Antipolo .... Kodaikanal \ Batavia-Buitenzorg. . . St. Paul de Loanda. . . Samoa (Apia) Tananarive Mauritius Pilar. . . i.-igo "Mchurch ar's Island.... Orcadas ^Baldwin Obs'y replaced by Tucson Obs'y, Oct. 1909; mean given for Jan -Oct '09 "Replaced Zi-ka-wei ObsV, 1908. f Observations discontinued Apr 26 ioi< I Provisumal values taken for position ol Port Cork, p. 298, American PracUcalNivigator, 1914 edition. SMITHSONIAN TABLES. APPENDIX. DEFINITIONS OF UNITS. ACTIVITY. Power or rate of doing work; unit, the watt. AMPERE. Unit of electrical current. The international ampere, "which is one-tenth of the unit of current of the C. G. S. system of electro-magnetic units, and which is represented sufficiently well for practical use by the unvarying current which, when passed through a solution of nitrate of silver in water, and in accordance with accompanying specifications, deposits silver at the rate of o.ooi 11800 of a gram per second." The ampere = i coulomb per second = I volt through I ohm = IO- 1 E. M. U. = 3 X 10 ' E. S. U.* Amperes = volts/ohms = watts/volts = (watts/ohms)*. Amperes X volts = amperes 2 X ohms = watts. ANGSTROM. Unit of wave-length = io- 10 meter. ATMOSPHERE. Unit of pressure. English normal =14.7 pounds per sq. in. ==29.929 in. = 760.18 mm Hg. 32 F. French " =760 mm of Hg. o = 29.922 in. = 14.70 Ibs. per sq. in. BAR. A pressure of one dyne per cm. 2 Meteorological " bar "= io tt dynes/cm 2 . BRITISH THERMAL UNIT. Heat required to raise one pound of water at its tem- perature of maximum density, i F. = 252 gram-calories. CALORIE. Small calorie = gram-calorie = therm = quantity of heat required to raise one gram of water at its maximum density, one degree Centigrade. Large calorie = kilogram-calorie = 1000 small calories = one kilogram of water rrised one degree Centigrade at the temperature of maximum density. For conversion factors see page 197. CANDLE, INTERNATIONAL. The international unit of candlepower maintained jointly by national laboratories of England, France and United States of America. CARAT. The diamond carat standard in U.-S. = 200 milligrams. Old standard = 205.3 milligrams = 3.168 grains. The gold carat : pure gold is 24 carats ; a carat is 1/24 part. CIRCULAR AREA. The square of the diameter = 1.2733 X true area. True area = 0.785398 X circular area. COULOMB. Unit of quantity. The international coulomb is the quantity of electricity transferred by a current of one international ampere in one second. = icr 1 E. M. U. = 3X io 9 E. S. U. Coulombs = (volts-seconds) /ohms = amperes X seconds. CUBIT = 18 inches. DAY. Mean solar day =1440 minutes = 86400 seconds = 1.0027379 sidereal day. Sidereal day = 86164.10 mean solar seconds. DIGIT. 3/4 inch ; 1/12 the apparent diameter of the sun or moon. DIOPTER. Unit of "power" of a lens. The number of diopters = the reciprocal of the focal length in meters. DYNE. C. G. S. unit of force = that force which acting for one second on one gram produces a velocity of one cm per sec. = ig -4- gravity acceleration in cm/sec./sec. Dynes = wt. in g X acceleration of gravity in cm/sec./sec. ELECTROCHEMICAL EQUIVALENT is the ratio of the mass in grams deposited in an electrolytic cell by an electrical current to the quantity of electricity. ENERGY. Sec Erg. ERG. C. G. S. unit of work and energy = one dyne acting through one centimeter. For conversion factors see page 197. FARAD. Unit of electrical capacity. The international farad is the capacity of a con- denser charged to a potential of one international volt by one international coulomb of electricity = io~* E. M. U. = 9 X io u E. S. U. The one-millionth part of a farad (microfarad) is more commonly used. Farads = coulombs/volts. * E. M. U.=C. G. S. electromagnetic units. E. S. TJ.=C. G. S. electrostatic units. APPENDIX. FOOT-POUND. The work which will raise one pound one foot high. For conversion factors see page 197. FOOT-POUNDALS. The English unit of work = f oot-pounds/g. For conversion factors see page 197. g. The acceleration produced by gravity. GAUSS. A unit of intensity of magnetic field = I E. M. U. = J X ionic 40<; metals Dilution,' beat of '(H 2 S6 4 ) .' .* ' 246 Dimensional formulae ... '* * Diopter . ?T.* .' ' ' ' n! P t "I?* 5 " 6 *;' ' '9 15 value, secular variation . 430 isK, distribution of brightness over sun's . 418 Distance earth to moon . sim : . ; : : : : 414 INDEX. 443 Distance of the stars, nebulae and clusters . . . .412 Dyes, transparency of .? ()I Dynamical equivalent of thermal unit 197 e (base of natural logarithms) *4 e (elementary electrical charge) 400 408 e/rn , and th"ir logarithms x=o to 10 . .c fractional 7T -o.i to 5.0 Xl to 20 55 ,. , e ~^ x , e ~~ 4 x=i to 20 ... 55 e'+e-* e*~ e ~ x an d their logarithms 41 2 2 Earth: atmospheric data 421 conductivity, thermal 422 degrees on, length of 410 elements, percentage composition 423 geochemical data 423 geodetical 424-427 moments of inertia 4 2 7 moon, distance of 4*4 rigidity 427 size of, shape of 4 2 7 spheroid constants 427 sun, distance of 4*4 temperatures 420, 422 viscosity 427 Efficiency of various lights 262 Elastic limit (see mechanical properties) .... 74 Elastic modulus of rigidity, temp, variation . . 100 Elasticity (see mechanical data) 74 crystals 102, 103 Young's modulus (see mechanical prop.) 74 Electrical charge, elementary 408 Electrical equivalents 3". Electrical units: international xxxyi standards .... xxxvm practical xxxvi Electric lights, efficiency of 262 Electric, triho-, series (frictional) 322 Electrochemical equivalents 345, 34 silver 345 Electrolytic conduction: ammonium acetate . . . .352 equivalent conductance 345~346 hydrolysis 352 ionic 352 ionization water . . . .352 solutions 345-346 spec, molecular . . . .347 limiting value (JL . . 348 temp, coef 348 Electro-motive force: accumulators 3*3 contact 314,316,404 Peltier 321 standard cells ...... 313 thermo-electric .... 317320 pres. effect . 320 voltaic cells 312-313 Weston normal xli Weston portable xliii Electromagnetic system of units xxxi Electromagnetic/electrostatic units =v . . . xxx, xxxvi Electrons: , + 401 affinity of elements 404 e/m 404 elementary charge 404 emission from hot bodies 403 ionization potentials 403 mass 408 photo-electric effect 403 radius 408 resonance potentials 403 work required to remove 403 Elements: atomic heats at 50 K 226 atomic numbers 409 atomic volumes 226 atomic weights (international) .... 71 boiling points 199 compressibility 108 conductivity electrical ...... 323-326 thermal 213 densities no earth's crust, occurrence in 423 PAGE Elements: evaporation rate, Mo, W, Pt 175 expansion, cubical (gaseous) 222 linear (solid) 218 hardness 73, 101 isotopes 410 latent heat of evaporation 233 melting points 198 meteorites, occurrence in 423 Peltier effect 317, 320322 periodic system 409-410 resistance, electrical 323-326 specific heats 223, 225 spectra 266-270 thermal conductivities 213 expansion 128, 222 thermo-electric powers 317,319 Thomson effect 317, 320 valencies 71 vapor pressures 175 Elementary electric charge 408 Elements, magnetic, at various observatories . . . 434 Elliptic integrals 69 Emanation (radioactive) 398 Emissivities, radiation 249, 250 Energy kinetic, definition 428 of molecule 408 Energy, minimum visible to eye 261 solar, data relating to 418420 of candle radiation 260 of sound waves 149 Entropy constant (Boltzmann) 408 Entropy of steam 234-240 Equation of time 41.6 Equilibrium radioactive 394 Equivalent, electrochemical 345-346 mechanical, of heat 197 Erg 435 Erichson values 73 Errors, probable 57~59 Ettingshausen effect 385 Eutectic mixtures, melting points 206, 207 Evaporation rate of, Mo, Pt, VV 175 Expansion, cubical: gases 222 liquids 221 solids 220 linear: elements 218 miscellaneous 219 Explosives: decomposition, ignition temp 244 miscellaneous 243-244 Exponential functions : see index under e 4155 diffusion integral 60 gudermanians 41 hyperbolic functions (nat) . 41 hyperbolic functions (logs) . 41 probability integral . . . 56-57 Eye: adaptation rate 257 color sensitiveness 256-258 contrast sensibility 257 Fechner's law 258 glare sensibility 257 heterochromatic sensibility 257 minimum energy visible 261 miscellaneous data 258 persistence of vision 258 pupil size for various intensities 258 Purkinje phenomenon 256 sensitiveness to light 256-258 small dif. of color, sensitiveness to 258 threshold sensitiveness 256 visibility of radiation, relative 258 Factorials: y function, n=i to 2 62 n!, n=i to 20 47 logs, n=i to 100 40 Falling bodies (Stokes* law) 150 Farad 3 1 l Faraday xliv, 311, 345 Faraday constant 408 Fechner's law 258 Ferromagnetism 365 Field, magnetic: earth's, components .... 428-434 metals, behavior of in . . . 365-377 resistance of metals in 384 rotation of plane of polarization . 378 thermo-galvanometric effects . . 385 Filaments, heat losses from 255 Flame temperatures 244 Fluidity 155 444 INDEX. PACE Foot pound 436 Fork, tuning, temperature coefficient 149 :ution, heat of, for elements 245, 246 ule: conversion .? dimensional, see introduction xxv least squares 59 Kraunhofer lines, solar, wave-lengths jo? Free path of molecules 399 Free zing mixtures 211 point, lowering of for salt solutions . . . 208 point of water, pressure effect 200 Frequencies, corresponding to wave-lengths .... 293 in air, reduction to vacuo 293 on, mechanical 154 internal of metals, temp, variation . . . 101 skin (air resistance) 152 Frictional electricity series 322 Functions: Bessel functions (roots, 68) ... 66-68 cylindrical harmonics 66-68 elliptic 69 exponential 48-56 gamma 62 hyperbolic 41 probability 56-58 trigonometric, circular ( ') 32 trigonometric, circular (radians) ... 37 zonal harmonics 64 Fundamental frequency (Rydberg) 408 Fundamental standards xxxiii units xxiii Fusion current for wires 329 Fusion, latent heat of 240 Gages, wire 333 Galvano-magnetic effects 385 Gamma function 62 Gas constant 408 Gas thermometry 192-194 Gases: absorption of by liquids 172 absorption of by water 170-171 absorption coef: long-wave radiation . . . 309 X-rays 389 compressibility 104 conductivity, thermal 217 critical data 212 densities 127 dielectric constants 356-361 strength 353~355 diffusion 168 ionic 405 expansion coefficients 222 expansion of 128-132 flow in tubes 150 ignition temperatures of mixtures 244 magnetic susceptibility 377 magnetic-optical rotation 382 refractive indices 292 Mnce (aerodynamical) 150153 solubility in water 170-171 sound, velocity of, in 147 specific heats (also c p /c,) 230 riscosity 164-165 volume, f (t, p) 104-106 f(t), 1+0.00367, logs . . . 128-132 x!v, 365 'm of units xxxv Ceochemical d;ita ' 42 ^ MC *,. .::::::: : : : : .; ^ Clare sensibility of eye ."257 Chases: refraction indices, American 277 Orman, temp. var. . . 278 tance electric, temp, var 332 transparency of 302-304, 306-307 Glass vessels, volume of 72 (.'ram-molecule, definition 43 r, of ralritc '. 4o g in constant 427 . acceleration of, altitude variation . . ! . 424 latitude variation .... 424 . . 425-420 iipciftc, see densities. Gudermanians ,, Gyration, radii of ..'.'.'.' .' ." .' 70 Hall effect, temperature variation 3 g- PAGE Hardness: (sec mechanical properties) 74. Hrinell test 74 elements 101 scleroscope test 74 Harmonics: cylindrical (Bessel) 66-68 roots, formulae . . 68 zonal 64 Heat: adsorption heats 407 atomic heats of elements 226 combination 245-246 combustion: explosives 243-244 fuels 242 gases 242 organic compounds 241 conductivity: metals (also high temp.) . . .213 gases 217,254 liquids 217 diffusivities 217 dilution, heat of, ILjSO* 246 formation 245-246 latent heat of fusion ". 240 vaporization, elements . . .233 Nil, 232 steam 234 various . . 232-233 pressure variation, NH 3 liq. . . 232 losses from incandescent wires 255 mechanical equivalent of 197 neutralization, H 2 SO,t 246 solution 246 specific: alloys 227 ammonia, liq 228 electricity 317 elements 233 gases 230 liquids 227-228 mercury 227 minerals, rocks 229 silicates 229 solids 227 true [elements, f(t)] 225 vapors 230 water 227 total [elements, f(t)] 225 treatment of steels 76 Heating effect, radium and emanation . . 194 Hefner unit ,260 Heights, barometric determination of 145 boiling point of water determination of . . 144 Helium, production, relation to radium 394 Henry xxxvii, xliv, 311 Heterochromatic sensibility of eye 257 Hertzen wave-lengths 4O 8 High-frequency electric resistance of wires .... 344 Horizontal intensity earth's field, 1915 . . . .431 secular var. . .431 Horse power 197 Humidity, relative: vapor-pressure and dry .... 187 wet and dry 189 Hydrogen: atomic data, mass, radius, etc 408 series spectra 275, 401 thermometer 192194 Hydrolysis of ammonium acetate 352 Hydrostatic pressures of Hg and HoO columns . .136 Hyperbolic functions, natural and logarithmic . . 41 Hysteresis 365 et seq, 3 75~376 Ice, allotropic modifications 200 freezing point, pressure effects 200 Ice-point, thermodynamic scale 195 Ignition temperatures gaseous mixtures 244 Incandescent filaments, heat losses 255 Inclination (dip) of magnetic needle, 1915 .... 430 secular var. . . 430 Index of refraction: air 293 alums 281 crystals, see minerals, etc. . 282-289 fats 289 fluorite, f(t) 280 gases and vapors 292 glass American 277 German f(t) 278 Iceland spar 280 liquefied gases 289 liquids 290 metals 296 minerals, isotropic 282 uniaxial 284 biaxial 2 86 IXDKX. 445 PAGE Index of refraction: miscellaneous, isotropic . . 283 uniaxial . . . 285 biaxial . . . 289 nitroso-dimthyl -aniline . . . 280 quartz 280 rock-salt, f(t) 279 salt solutions 291 silvine 279 solids, biaxial .... 286, 289 isotropic .... 282, 283 uniaxial .... 284, 285 standard media for microscope. 294 vapors 292 waxes 289 Induction, self 376 Inductive capacity, specific: crystals 361 gases, f(t. i) . . 356-357 liquids 357 liq. gases 359 solids 360 standard solutions . .360 Inertia, moments of 70 Inorganic compounds: boiling points 201 densities 201 melting points 201 soluibilities 169 Insulators: break-down potentials 364 dielectric properties . 364 resistance, thermal 214-216 electrical "... 331 Integral: diffusion 60 elliptic 69 formula 12 gamma function 62 probability 56-57,60 Intensity, horizontal, earth field, 1915 431 secular var. . . . 43 1 Intensity, total, earth field, 1915 . . 432 secular var 432 International candle standard 260 electric units xxxvi standards xxxvi ii standard radium 394, 398 standard wave-lengths .... 266267 Intrinsic brightness of various lights . . . Ionic charge diffusion mobilities lonization potentials Ions produced by a, /3, y rays work required to detach Ions, conductance of heat of formation Iron, magnetic properties (steels) . . . standard wave-lengths, international Isostacy Isotopes Joule Joule magnetic effect 260 401, 408 405 . 405 . '. 403 . . 398 403-404 . . 352 . . 246 365-376 266-267 . . 426 . . 410 197 365 K X-ray spectrum series 390 Kerr's constant, magneto-optic 383 Kinetic energy 436 molecular 408 Kundt's constant, magneto-optic 383 L X-ray series 39 r Lambert, definition 256, 259 Latent heat of fusion 240 Latent heat of pressure variation liq. ammonia . . . 232 Latent heat of vaporization: ammonia ..... 232 formulse 232 . 234 steam tables . various . . . Latitude correction to barometer of a few stations Least squares: formulse probability integral, arg, hx x/r inverse Q.6745VV (ni) 0.845 3 [i/Wn . . 231 139-142 420, 434 59 . . 56 57 . . 60 57 . . 58 . . 5S 58 Length, standards of xxxiv, 5 Light: eye, sensitiveness of to 256-258 flux, definition 259 intensities on various days 256 lambert, definition 256 least visible to eye 261 mechanical equivalent 261 photometric standards 260 units 259 polarized, reflection 295297 rotation of plane by substances . .310 rotation of plane, magnetic . 378383 reflection of: formulae 297 function of " n " 297 reflecting power: metals 295-298 pigments 299 powders 300 rough surfaces . . . . . 299 scattered light 300 temperature variation . . .300 sensitiveness of eye to 256258 transparency to: crystals 305 dyes 301 glasses, American . . 303304 Jena 302 water 307 velocity of 408, 414 wave-lengths: cadmium std. line 266 elements 269-271 Fraunhofer lines 265 solar, Rowland 272 Std. iron lines .... 266-267 Lights, brightness of various 260 color of various 261 efficiency of various electric 262 photographic efficiency of 264 visibility of white lights 260 Light-year 414 Limits of spectrum series 276 Linear expansion coefficients 218219 Liquids: absorption of gases by 172 Baume density scale 109 capillarity of 173 174 combustion heat, fuels 242 compressibilities 107 conductivity, thermal 217 contact emf 314-316 densities 115-117 mercury, f(t) 121 water, f(t) 118-120 dielectric constant 357360 strength 355 diffusion, aqueous solutions 166 expansion coefficients 221 expansion coefficients 221 fuels, combustion heats 242 magnetic optic rotation 380 magnetic susceptibility 377 potential dif. with substances .... 314-316 refractive indices 289291 sound velocity in i 47 specific heats 228 surface tensions 173174 thermal conductivity 217 expansion,, cubical 221 vapor pressures 175-187 viscosity, absolute 157-159 specific, solutions 163 Logarithms: standard 4-place : 26 1000 to 2000 24 anti-, standard 4-place 28 .9000 to i. oono Logarithmic functions 40 Longitudes of a few stations 420, 434 Long-wave transmissions 309 Loschmidt's number 408 Lowering of freezing points by salts 208 Lubricants for cutting tools 154 Lumen 259 Luminosity of black-body, f(t) 261 Lunar parallax 414 Lux 259 0.45 3 in i ...... 5 Leduc thermomagnetic effect ......... 385 Legal electrical units ........... xxxvli M X-ray spectrum . . Mache radioactivity unit Maclauren's theorem ' 39 o . 398 . 13 446 1NDKX. ftic field: atomic bismuth, resistance in ... Ettinghausen effect .... galvanometric effects . . . Hall effect Joule effect Leduc effect Nernst effect nickel, resistance in .... optical rotation polarization . 378 resistance (if metals in thermo-magnctic effects Villari effect Wiedemann effect Magnetic observatories, magnetic elements . . . . Magnetic properties: cobalt, o to 100 C. . . . Curie constant Curie point definitions demagnetizing factor for rods . diamagnctism, f(t) . . 365 ferro-cobalt alloy ferromagnetism hystersis 375 iron: 367 cast, intense fields pure soft, o and 100 C. . . very weak fields .... wrought magnetite, o, 100 C. . . magneto-strict ive effects . . magnet steel maxwell 311 nickel, o, 100 C paramagnetism, f(t) . . 365 permeability 365 saturation values for steels . steel: 367 energy losses . . magnet steel . . manganese steel saturation values . temperature effect . tool steel .... transformer steel . 371 weak fields Steinmetz constant .... susceptibility . . 365, 372 temperature effects . .371 Magnetism terrestrial: agonic line declination . . . dip inclination intensity, horizontal . . . total magnetic character yearly . . observatories, elements at . Magneto-optic rotation, gases Kerr constant Kundt constant liquids solids solutions Verdet's constant . . 378 Magnitudes, absolute stellar 415 stellar 415 sun Mass:. electronic, f(velocity) 401 fundamental standard hydrogen atom absorption coefficient for X-rays '. stellar Mathematical constants . . . physical Maxwell xlv, 311 Mean free path, H molecule .... Telocity H molecule Measures, weights: customary metric English metric 'al equivalent of heat . . . light .... Mechanical properties: definitions elastic limit . . Krichson value . hardness . . . . moduli . . VAGE . 403 . 384 , 385 385 . 385 , 365 . 385 , 385 . 384 -383 384 385 365 365 434 373 37-2 372 365 374 3/2 370 365 -376 -376 368 369 37i 370 373 373 365 370 ,365 373 . 372 , 37i 373 -376 376 370 373 373 -372 373 ,376 370 375 377 -373 425 420 422 422 423 424 4 2 5 426 382 383 383 380 379 38i -383 412 412 415 408 xxxiv 408 389 404 H 408 ,365 408 408 -10 5-7 197 261 74 74 74 74 74 PAGE il properties: definitions: modulus of rupture 74 proportional limit. ' 74 scleroscope . . . ultimate strength, eompr. tension yield point . . . alloys: aluminum brasses bronzes copper iron miscel. steel white metal . 74 74 74 74 8l 83-85 83-85 75-79 88-89 77 .89 aluminum: 80-8 1 alloys brick and brick piers .... 93 cement g o cement mortars 90 clay products 93 concrete 91 copper: ..." 82 brasses and bronzes 8385 wire 82-83 heat treatment for steels . . 76 iron: 75 alloys 75 leather belting 94 p-ratio extension/contraction. 101 rigidity moduli f(t) . . . . 100 rope, manila 95 steel-wire 79 rubber, sheet . 94 steel: 76 alloys 77 heat treatment for . . 76 semi- 78 wire 78 wire-rope 79 stone products 92 terra-cotta piers 93 tungsten 89 white metal 89 woods: conifers: English unit 99 metric unit . 97 hard: English unit . 98 metric unit . . 96 Melting points: alloys 206 elements 198 eutectics 207 inorganic compounds 201 lime-alumina-silica compounds . . 207 organic compounds 203 paraffins 203 pressure effect 200 water-ice, pressure effect .... 200 Meniscus, volume of mercury 143 Mercury: density and volume, 10 to 360" C. . 121 conductivity thermal, high temp 254 electric resistance standard xxxviii meniscus, volume of 143 pressure hydrostatic of columns 136 specific heat 227 thermometer 190-194 vapor pressure 180 Metals: conductivity, thermal 213 diffusion 168 potential differences, Volta .... 316,404 reflection of light by 295-296, 298 refraction indices 295-296 optical constants 295-298 resistivity, temperature coefficient .... 323 pressure effect 326 Volta emf 316,404 weight sheet metal 116 Metallic reflection 295-296, 298 Meteors, chemical composition 423 Meter-candle 256, 259 Metric weights and measures, equivalents . . . 5-10 Mho 436 INDEX. 447 PAGE Micron, fi 7, 436 Milky way, pole of 4'4 Minerals: densities 115 refractive indices: biaxial 286 isotropic 282 uniaxial 284 specific heats 229 Minimum energy for light sensation 261 Mixtures freezing 211 Mobilities, ionic 405 Moduli, see mechanical properties 74-i3 Mogendorf series formula 275 Moist air, density of I33-I35 maintenance of 135 transparency to radiation, .36 to 1.711. 411 to 2o/ti . . . 308 Molecular collision frequencies 399 conductivities: equivalent .... 349-352 specific 346-348 crystal units 400 diameters 399, 400 free paths 399 heats of adsorption 407 liquefaction 407 kinetic energy 408 magnitudes 399~4oo, 408 number in cm 3 , 76 cm, o C 48 gram -molecule 408 velocities 399 weights of colloids 406 Moments of inertia: earth 427 formulae ......... 70 Month 4i4, 436 Moon: albedo 41 7 distance from earth, parallax 4 T 4 radiation compared with sun's 407 Musical scale 148 tone quality 149 Mutual induction 37& Nernst thermomagnetic potential difference .... 385 Neutral points, thermoelectric 3*7 Neutralization, heat of 246 Nickel, Kerr's constants for 383 magnetic properties, o to 100 373 resistance in magnetic field 384 Nitrogen thermometer 192 Nitroso-dimethyl-aniline, refractive index 280 Nuclear charge, atomic 393, 4i Number of stars 417 Numbers atomic 409 X-ray spectra and .... 390-393 Numbers: magnetic character 433 sun-spot '....415 Nutation 4*4 Observatories, magnetic elements at 434 Ohm: xxxvii, xxxviii, 311 electrical equivalents 311 Oersted xlvi Oils, viscosity of 156, 157 Optical constants of metals 295 Optical rotation magnetic 378383 Optical thermometry 250 Organ pipes, pitch 149 Organic compounds: boiling points 203 densities 203 melting points 203 Organic salts, solubilities 170 Oscillation constants wireless telegraphy .... 362 times of wires, temperature variation . . 101 Overtones 149 Tf pi 14, 436 P-limit (proportional limit) 74 et seq. Parsec 414 Parallax, solar, lunar 414 stellar 412, 415 Paramagnetism 365 Partials (sound) 149 Particle, smallest visible 406 Peltier effect: 317, 321 pressure effect 320 Pendulum, second: formula; latitude variation . . 42? Penetration cathode rays 37 high speed molecules 387 Pentane candle 260 thermometer 194 Periodic system: Hackh 410 Mendelejeff 409 Permeability, magnetic 365 et seq. Persistence of vision 258 Petrol-ether thermometer 194 Phosphorescence (radio-active excitation) .... 394 Phot 259 Photoelectricity 403 Photographic data: intensification 264 lights, efficiencies 264 plate characteristics 263 resolving power 263 speeds various materials . . . 263 Photometric definitions, units 259 standards 260 Physiological constants of the eye 258 Pi (ir) 14,436 Pigments, reflecting powers f(X) 299 Pipes, organ: pitch 149 Pitch: 148 organ pipes 149 voice, limits 149 Planck's " h" 408 radiation formulae, Ci Co 247 Plane, air resistance to 150-152 Planetary data 416 Platinum resistance thermometer 195 thermoelectric thermometer 196 thermoelectric powers against 319 Poisson's ratio 101 Polonium radioactive series 39 8 Polarized light: reflection by 295-296, 297 rotation of plane 310 magnetic 378-383 Porcelain, resistance, f(t) 332 Positive rays 386 Potential (emf ) : accumulators 313 cells voltaic 312-313 contact 314,316,404 ionizing 403 Peltier 321 sparking, kerosene 355 various . . . . 353-355 resonance 403 standard cells 313 thermo-electric 317-320 pressure effect . . 320 Weston normal xli portable xliii Poundal 436 Precession 414 Pressure: air, on moving surfaces 150-152 barometric, reductions, capillarity . . . 143 gravity . . 138-143 temperature . . 137 boiling water 144 critical, gases 212 mercury columns 136 volume relations, gases 104 water columns 136 Pressure effect on boiling points 200 melting points 200 resistance electrical 326 thermoelectric powers 320 Pressure vapor: alcohol, methyl and ethyl .... 178 aqueous (steam tables 234) . 183-186 elements 175 mercury 180 salt solutions 181 water vapor (steam tables 234) 183186 various 176-181 Probable errors 56-50 Probability integral 56-57 inverse 60 Proportional limit (P-limit) 74 et seq. Pupil diameter 258 Purkinje phenomenon 256 Quality, tone Quartz: refraction indices . . . . transmission of radiation by 149 280 30$ 448 INDEX. PAGE R, gas constant 408 p, I'oisson's ratio I0 ' .ui 430 circular functions in terms of 37 Radiation: black-hody. formula? 247 f(X,T) -'47,^48 total, f(t) 247 candle 26 constants, L series of radiations 39 1 M series of radiations 392 monochromatic radiations 387 secondary radiations 387 spectra: absorption 393 K series 390 L series 391 M series 392 tungsten 392 wave-length and cathode fall .... 387 Roots of Bessel functions, ist and 2nd orders . . 68 Roots square 15 Rope, manilla, mechanical properties 95 steel wire, mechanical properties 79 Rotation of polarized light 310 magnetic .... 378-382 Rough surfaces, reflecting power 299 Rowland solar wave-lengths 272 Rupture, moduli of 74 et seq Rutherford atom 401 Kydherg constant 408 Rydberg series formula (spectrum) 275 a, Stefan-Boltzmann 247 Salt solutions: boiling point raising 210 conductivity thermal 216 freezing point lowering 208 vapor pressure . . . 181 Scales, musical 148 Scleroscope (hardness test) 74 Screens, color 306307 Second pendulum, formula 419 sea-level values, f(0) 419 Secohm xliv Secondary batteries 313 X-rays 387 Self induction 376 Sensation, Minimum energy of light for 261 Sensitiveness of eye to light and radiation . . 256-258 Series, mathematical 13 Series spectra: Balmer formula 401, 275 first terms 276 limits of 276 Morgendorff formula 275 Ritz formula 275 Rydberg formula 275 vibration differences 276 Sheet metal, weight of 116 Silver, electrochemical equivalent 345 Silver voltameter xl Silvine, refractive index 279 Sines, natural and logarithmic, circular 32 hyperbolic .... 41 Sky brightness 419 Skin friction, air resistance 152 Soap films 174 Solids: compressibility 108 contact potentials 314,316,404 densities 113 dielectric constants 360 expansion coefficients, cubical 227 linear .... 218-220 hardness 74 et seq, 101 magneto-optic rotation 379 refractive indices 277-289 resistance, electrical 323-344 velocity of sound 146 Verdet's constant 379 Solubility: gases in water 170 pressure effect . ... 171 salts in water, inorganic, f(t) . . . . 169 organic, f(t) 170 Solutions: boiling point raise by salts in .... 210 conductivity electrolytic 346-352 thermal 216 densities of aqueous 122 diffusion of aqueous 166 dielectric constant, calibration stds. . . 360 freezing points lowering by salts in ... 208 magneto-optic rotation by 381 PAGE Solutions: refractive indices 291 specific heats 228 surface tensions 173 vapor pressures 181 Verdet's constant 381 viscosities, specific 1 59, 163 Sound, velocity of: gases 147 liquids 147 solids 147 waves, energy of 149 Sparking potentials: air, alternating potentials . . 353 large spark-gaps, f(p) . . 354 steady potentials . . . .353 dielectrics 355 kerosene 355 Specific heat of electricity 317 Specific heats: ammonia, sat. liq 228 elements 223, 225, 226 gases, also c p /c r 230 liquids 228 mercury 227 minerals and rocks 229 rocks 229 silicates 229 solids 227 vapors 230 water 227 Specific gravities (see densities) 109135 conversion of Baume 109 Specific inductive capacities: crystals 361 gases, f(t,p) . . 356-357 liquids, f(t) . 357~359 solids 360 std. solutions . . . 360 Specific molecular conductivity 347-348 Specific resistance, see resistivity 323-326 Specific viscosity: 159, 163 Spectrum: black-body intensities 247, 248 elements, international units . . . 267, 270 eye sensitiveness, f(X) 256258 iron standards, international units . 266, 267 radium 398 series, limits, first terms, etc 276 solar: intensities of energy 418 Rowland wave-lengths 272 cor. to intern, scale . . 272 standard wave-lengths, intern, units. 266267 stellar 403 wave-lengths standards 266, 267 reduction to std. pressure. 268 X-ray: absorption 393 atomic numbers 390393 K series 390 L series 391 M series 392 tungsten 392 Speed of corpuscles 401 Spherical harmonics 64 Sputtering, cathodic ..." 386 Squares of numbers 15 Square roots of numbers 15 Squares, least, formulae and tables 56-59 Standard cells, emf of 313 radium, international 394 refractive media for microscope 294 resistance, mercury xxxviii temperature calibration points 195 wave-lengths: primary (international) . 266 secondary (international) . 266 tertiary (international) . . 267 reduction to std. pressure . 268 Standards: electrical, international xxxviii fundamental xxxiii photometric 260 Stars: brightness 413 densities 413 distances 412 equivalent ist magnitude 4*7 first magnitude data (positions, etc.) . . .415 Harvard classification 4" light, total 417 magnitudes, apparent and absolute 413 masses 413 motions 412 number of 417 parallax 415 45 INDEX. FACE Stars: size 4'3 spectra 4" temperatures, surface 4 11 velocities . . . .' 41*. 4*5 Steam tables *34 Steel: ma&netic properties 367-376 mechanical properties 7679 Stefan-Boltzmunn constant, and formula 247 Steinmetz magnetic constant 375 Stcllite. reflecting powers 150 Stem correction for thermometers 190-191 Stokes law for falling bodies 150 Stone, mechajiical properties 92 Storage batteries 3 '3 Strengths see mechanical properties 74~99 Sucrose, viscosities of solutions, f(t) 156 Sugar cane, densities aqueous solutions 126 Sulphuric acid, densities aqueous solutions .... 126 Sun: apex of solar motion 4" brightness 260 disk brightness distribution 418 distance to earth 4*4 Fraunhofer lines 265 magnitude, stellar 4*3 motion 4" numbers. Wolf's sun-spot 4*5 parallax 4*4 radiation compared to moon 4*4 constant (solar constant) 41 variation with month and latitude . . 420 spectrum: energy intensities 4 T ^ Fraunhofer lines 265 Rowland's wave-lengths 272 spot numbers, Wolf's 41 5 temperature 418 velocity 41 1 wave-lengths: Fraunhofer lines 265 Rowland's 272 Sunshine, duration of f (month, latitude) 417 Surface resistivities, solid dielectrics 331 Surface tensiens 173, 174 Susceptibility magnetic, definition 365 elements, etc 377 Tangents circular, nat. and log., f(, ') .... 32 f (radians) ... 37 hyperbolic, nat. and log 41 Taylor's series 13 Telegraphy, wireless: 362, 364 Temperature, black -body scale for W 250 brightness black body as function of. 261 brightness scale for C 250 color scale for W 250 critical gas constants 212 earth: f (altitude) 421 f(latitude) 422 monthly and yearly means . . 420 variation below surface . . . 422 flame temperatures 244 ignition, gaseous mixtures 244 standards xxxiv stellar 411 sun's 418 thermodynamic 195 zero absolute 195 Tensile strengths, see mechanical properties . . . 74-99 Tension, surface 173, 174 Tensions, vapor, see vapor pressures 175-186 Terrestrial magnetism: agonic line 425 declination 420 dip 422 inclination 422 intensity, horizontal . . . 423 total 424 magnetic character, yearly . 425 observatories, elements at . 426 Thermal unit, British 435 standard calorie 435 Thermal conductivity: alloys, metals 213 building materials . 215 earth 422 gases 217 high temperature 254 PAGE Thermal conductivity: insulators 214-216 high temp. 214 liquids 217 metals, high temper- ature 213 salt solutions . . . 216 water 216 Thermal diffusivities 217 Thermal expansion: cubical: gases 222 liquids 221 solids 220 linear: elements 218 miscellaneous .... 219 Thermal unit: British 435 calorie 435 dynamical equivalents ... 197 Thermo-chemistry: heat of combustion: carbon cpds . 241 coals . . . 242 cokes . . . 242 gases . . . 242 liquid fuels .242 miscellaneous . 24 1 peats . . . 242 heat of dilution, H 2 S0 4 .... 246 formation 245 ions 246 neutralization .... 246 Thermodynamical scale of temperature, ice-point . . 195 Thermoelectrical properties: (emf) alloys .... 318 platinum 319 elements . . . 317 Peltier . . 317, 321 pressure effects . 320 Thomson . 317, 320 Thermoelements, calibration of ^96 Thermogalvanometric effect 385 Thermomagnetic effects 385 Thermometry: absolute zero 195 air i6Hl o to 300 C .... 193 59 in > 100 to 200 C ... 193 59*11, high temperature ... 194 calibration points, standard . . . . 195 gas-mercury, formulae, comparisons 192-194 hydrogen 1 6Hi, o to 100 C . . 192 i6in, 59 _ 5 to 35 C 192 various 194 ice point 195 Kelvin scale 193 mercury cf with gas 190-194 platinum resistance 195 resistance electrical 195 stem corrections 190-191 thermodynamic scale, ice-point ... 195 thermo-electric, Cu-Constantan ... 196 Pt-PtRh 196 Thomson thermo-electric effect 317,320 Thorium radio-active group, constants of 396 Threshold sensitiveness of eye ^ . . . 256 Timber, strength of 96-99 Timbre (sound) 149 Time, equation of 416 Time, solar, sidereal 414 Time standards xxxiv Transformation constants of radio-active substances. 396 Transformation points of minerals 207 Transmissibility to radiation: air, moist . . . 308,419 atmospheric . . . .418 crystals, various . . . 306 dyes 301 glass, American . 303, 304 Jena .... 302 water 307 water-vapor . . 308, 419 Trigonometric functions : circular, ( ') nat., log. . 32 (radians), log . . 37 hyperbolic, nat., log. ... 41 Tribo-electric series 322 Tubes, flow of gas through 150 Tuning forks, temperature coefficients 149 Ultimate strengths of materials, see Mechanical. properties 74~99 INDEX. 451 Ynits of measurements, see Introduction ... electrical, absolute . . . international . legal . . . practical . . fundamental photometric radioactive work, transformation factors Uranium group of radio-active substances .... PAGE . xxiii . xxxv i . xxxvi xxxvii . xxxvi xxiii . 260 . 394 197 396 T, ratio electro-magnetic to static units . . xxx, xxxvi Vacuo, reduction of densities to 73 weighings to 73 Valencies of the elements 7 1 Van der Waal's constants 212 Vaporization, latent heat Of: 231 ammonia 232 elements, theoretical . 233 formula 232 steam tables . . . .234 Vapor pressure: alcohol ethyl 178 methyl 178 aqueous (see water below) . . 183, 234 carbon disulphide i79 elements *75 mercury 180 radium emanation ....... 398 salt solutions 181 various 179180 water: atmospheric via wet and dry sea-level . . . 186 other altitudes . 185 saturated 183 steam tables 234 Vapor, water; weight per m 3 and ft 3 185 Vapors: densities 127, 234 diffusion of 167, 168 heats of vaporization 231-239 heats specific 230 pressures, see vapor pressures .... 175186 refractive indices 292 specific heats 230 viscosities 164 water, transparency to radiation . . . 308, 419 Velocity of light 408, 414 molecules 399 sound, in gases 147 liquids 147 solids 146 stars 4H 412 sun 411 Verdet's constant (magneto- optic) 378-382 gases 382 liquids 380 solids 379 solutions, aqueous 381 Vessels, volume of glass, via Hg 72 Villari magnetic effect 365 Viscosity: air 164 alcohol ethyl, f(t, dilution) 155 castor oil, f(t) 156 centipoise, definition 155 definition 155 earth 427 gases, temperature and pressure var. 164-165 glycerol, dilution variation 156 liquids, f(t) 157-158 specific: solutions, f(dens., t) .... 159 atom. cone. 25 C. . 163 sucrose solutions, f(t, dilution) .... 156 vapors, f (p, t) 164-165 water, f(t) 155 Visibility of radiation 256-258 relative of various colors 256-258 white lights 260 Vision, distinct 258 persistence of 258 Voice, pitch limits of 149 Voltages: accumulators 313 contact 314, 316, 404 Peltier 321 standard cells 313 thermoelectric 317-320 pressure effect 320 voltaic cells 312-313 Weston normal xli Weston portable . xliii PAGE Voltaic cells; comp., emf: double fluid 312 secondary 313 single fluid 313 standard 313 storage 313 Voltameter, silver xl Volts, electrical equivalents 311 Volts, legal, international xli, 3 1 1 Volume atomic, 50 K 226 critical for gases 212 glass vessels, determination of 72 gases, f (p) 104-106 f(t) 128-132 mercury, 10 to +360 C 121 resistance of dielectrics 331 specific of elements 225 water, o to 40 C 119 10 to 250 C 120 Vowels, tone characteristics 149 Waal's (van der) constants 212 Water: boiling point, f(p) 144 density,f (t) o to 4iC, 10 to 25oC 118-120 solutions, ethyl alcohol 124 glycerol 156 methyl alcohol 126 sucrose 156 sugar (cane) 126 sulphuric acid 126 various . . . 122, 159-163 freezing point, f( pressure) 200 ionization of 352 melting point, f(p) 200 pressure (hydrostatic) of columns of ... 136 solutions: boiling points 210 densities, see water, density solu- tions . . 118-126, 156, 159-163 diffusion 166 electrolytic conduction . . 346-352 freezing points 208 viscosities 156, 159-163 specific heat 227 thermal conductivity : 216 transparency to radiation 307 vapor pressure 234239, 183184 vapor pressure of in atmosphere . . . 185189 viscosity, f(t) 155 volume, o to 40 C, 10 to 250 C. 119, 120 Water-vapor, determination in atmosphere, via wet and dry sea-level 186 various altitudes . . . . 185 relative humidity via wet and dry . . 189 dry and v.p. . . 187 in atmosphere, f (altitude) 421 transparency 308, 419 weight saturated per m 3 and ft 3 . . . 185 Watt xxxvii, xlv, 311 Wave-lengths: Angstrom, definition 266 cadmium red line 266 Crova 261 elements, international scale . . 267, 270 Fraunhofer solar lines ' 265 iron arc standards 266267 neon, international scale . . . . . 266 pipes (sound) 149 limits. Hertz, X, visible, etc. ... 408 Rontgen 390-393 Rowland solar 272 corrections to Intern X 272 solar, Fraunhofer lines 265 Rowland 272 standard pressure, correction to ... 268 standards: international primary . . 266 secondary 266-267 tertiary . . 267 vacuo, reduction to 293 wireless 362-364 X-ray 390-393 Waves, energy of sound 149 Weighings, reduction to vacuo 73 Weight sheet metal 116 Weights, atomic 71 Weights and Measures: customary to metric ... 5 metric to customary ... 6 metric to imperial .... 8 imperial to metric .... 10 miscellaneous 7 452 INDEX. PAGE Weston normal cell xli Weston portable cell xlili Wiedemaiui magnetic effect 365 Wind pressures 150-153 Wire gages, comparison 333 Wire, mechanical properties: copper 82-83 steel 78 sifi'l rope and cable . 79 Wire resistance, auxiliary table for computing . . . 322 Wire tables: aluminum, English measures .... 342 metric measures .... 343 see also 334 copper, English measures 336 metric measures 339 see also 334 temperature coefficients .334,335 reduc. to std. . .335 Wires, alternating-current resistance 344 carrying capacity of 329 high-frequency resistance 344 V.ires. .beat losses from incandescent, bright Pt. . 255 Pt sponge . 255 Wireless telegraphy: antennae resistances .... 364 wave-lengths, frequencies, oscil- lation constants 362 Wolf sun-spot numbers, 1750 to 1917 415 Woods: densities 96-99, 112 mechanical properties: conifers, Eng. units. 99 metric units 97 hard wds, Eng. units 98 metric units 96 Work, conversion factors , , 197 PAGE X-rays: 383-393 absorption coefficients (mass) 389 atomic numbers and spectra . . " . . 390-393 calcite grating space 408 cathode efficiencies 387 characteristic radiations 387 corpuscular radiation 387-388 crystals, diffraction with 401 energy relations 387 general radiations 387 heterogeneous radiations 387 homogeneous radiations 387 independent radiations 387 intensity 388 ionization 388 K series of radiations 390 L series of radiations 391 M series of radiations 392 monochromatic radiations 387 secondary radiations 387 spectra: absorption 393 K series 390 L series 391 M series 392 tungsten 392 wave-lengths 390-393 wave-lengths and cathode fall 387 Years 414, 437 \ early temperature means 420 Young's modulus, definition 74 values 74-103 Yield point (mechanical property) 74-103 Zero, absolute, thermodynamic scale 195 Zonal harmonics 64. bc fctoettfi&e press CAMBRIDGE . MASSACHUSETTS U . S . A DATE DUE SLIP OL I.I1IKAKV THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW Ql'i 7- | SEP 2 5 1942 US 2 ii 1946 1949 OGT 25 195" rtt Iiibrary of the University of California Medical