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1O38

SMITHSONIAN

PHYSICAL TABLES

PREPARED BY

THOMAS GRAY

THIRD REVISED EDITION

^sS^C^^S^tf \\

CITY OF WASHINGTON

PUBLISHED BY THE SMITHSONIAN INSTITUTION

1904

Iknicherbocfecr press, flew JlJoch

ADVERTISEMENT TO REVISED EDITION.

THE edition of the Smithsonian Physical Tables issued in 1896 having
become exhausted, a careful reexamination of the original work has been made
at my request by the author, Professor Gray, and the few changes found neces-
sary have been made in the plates.

S. P. LANGLEY,

Secretary,

SMITHSONIAN INSTITUTION,
WASHINGTON CITY, October jo, /<?97>

ADVERTISEMENT TO SECOND REVISED EDITION.

THE revised edition of the Smithsonian Physical Tables issued in 1897
having become exhausted, and the demand continuing, a second revised
edition is now issued. The author, Professor Gray, has again examined the
work and made a few corrections in the plates, table 283 in particular being
rewritten to agree with the recent report of the International Committee on
Atomic Weights.

S. P. LANGLEY,

Secretary.

SMITHSONIAN INSTITUTION,
WASHINGTON CITY, January^ 1903.

ADVERTISEMENT TO THIRD REVISED EDITION.

The second revised edition of the Smithsonian Physical Tables issued in
January, 1903, having become exhausted, and the demand for the work
continuing, a third revised edition is now published, in which the author
has made a few corrections to agree with the latest researches.

S. P. LANGLEY,

Secretary.
SMITHSONIAN INSTITUTION,

WASHINGTON CITY April, 1904.

7452

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 was pub-
lished in 1852. A second edition was issued in 1857, and a third edition, with
further amendments, in 1859. Though primarily designed for meteorological
observers reporting to the Smithsonian Institution, the tables were so widely
used by physicists that, after twenty-five years of valuable service, the work was
again revised and a fourth edition was published in 1884. In a few years the
demand for the tables exhausted the edition, and it appeared to me desirable to
recast the work entirely, rather than to undertake its revision again. After care-
ful consideration I decided to publish a new work in three parts — Meteorologi-
cal Tables, Geographical Tables, and Physical Tables — each representative of
the latest knowledge in its field, and independent of the others, but the three
forming a homogeneous series. Although thus historically related to Dr. Guyot's
Tables, the present work is so entirely changed with respect to material, arrange-
ment, and presentation that it is not a fifth edition of the older tables, but essen-
tially a new publication.

The first volume of the new series of Smithsonian Tables (the Meteorological
Tables) appeared in 1893, and so great has been the demand for it that a second
edition has already become necessary. The second volume of the series (the
Geographical Tables), prepared by Prof. R. S. Woodward, was published in 1894.
The present volume (the Physical Tables), forming the third of the series, has
been prepared by Prof. Thomas Gray, of the Rose Polytechnic Institute, Terre
Haute, Indiana, who has given to the work the results of a wide experience.

S. P. LANGLEY, Secretary.

PREFACE.

IN the space assigned to this book it was impossible to include, even approxi-
mately, all the physical data available. The object has been to make the tables
easy of reference and to contain the data most frequently required. In the
subjects included it has been necessary in many cases to make brief selections
from a large number of more or less discordant results obtained by differ-
ent experimenters. I have endeavored, as far as possible, to compile the tables
from papers which are vouched for by well-known authorities, or which, from
the method of experiment and the apparent care taken in the investigation, seem
likely to give reliable results.

Such matter as is commonly found in books of mathematical tables has not
been included, as it seemed better to utilize the space for physical data. Some
tables of a mathematical character which are useful to the physicist, and which
are less easily found, have been given. Many of these have been calculated for
this book, and where they have not been so calculated their source is given.

The authorities from which the physical data have been derived are quoted on
the same page with the table, and this is the case also with regard to explanations
of the meaning or use of the tabular numbers. In many cases the actual numbers
given in the tables are not to be found in the memoirs quoted. In such cases
the tabular numbers have been obtained by interpolation or calculation from the
published results. The reason for this is the desirability of uniform change of
argument m the tables, in order to save space and to facilitate comparison of
results. Where it' seemed desirable the tables contain values both in metric and
in British units, but as a rule the centimetre, gramme, and second have been used
as fundamental units. In the comparison of British and metric units, and quan-
tities expressed in them, the metre has been taken as equal to 39.37 inches,
which is the "legal ratio in the United States. It is hardly possible that a series

IV PREFACE.

of tables, such as those here given, involving so much transcribing, interpolation,
and calculation, can be free from errors, but it is hoped that these are not so
numerous as to seriously detract from the use of the book.

I wish to acknowledge much active assistance and many valuable suggestions
during the preparation of the book from Professors S. P. Langley, Carl Barus,
F. W. Clarke, C. L. Mees, W. A. Noyes, and Mr. R,. E. Huthsteiner. I am also
under obligations to Professors Landolt and Bornstein, who kindly placed an
early copy of their " Physikalisch-Chemische Tabellen " at my disposal.

THOMAS GRAY.

ROSE POLYTECHNIC INSTITUTE,

TERRE HAUTE, IND., July 13, 1896.

TABLE OF CONTENTS.

PAGE

Introduction on units of measurement and conversion factors xv

Units of measurement, general discussion xv

Dimension formulae for dynamic units xvii

" " " heat units xxiii

" of electric and magnetic units, general discussion xxv

" formulae in electrostatic system . xxvi

" " " electromagnetic system xxix

Practical units of electricity, legalization of xxxiii

TABLE

1. Formula:! for conversion factors :

(a) Fundamental units 2

(b) Derived units 2

I. Geometric and dynamic units 2

II. Heat units 3

III. Magnetic and electric units 3

2. Equivalents of metric and British imperial weights and measures :.

(1) Metric to imperial 5

(2) Multiples, metric to imperial 6

(3) Imperial to metric 7

(4) Multiples, imperial to metric 8

3. Tables for converting U. S. weights and measures :

(1) Customary to metric 9

(2) Metric to customary 10

4. Factors for the conversion of lengths n

5. " " " " " areas u

6. " " " " " volumes 12

7. " " " " capacities 12

8. " " • " " masses 13

9. " " " " moments of inertia 13

10. " " " " " angles 14

11. " " " " " times 14

12. " " " " " linear velocities 15

13. " " " " " angular velocities 15

14. "' " '" " momentums. 16

15. " " " " moments of momentum ........ 16

Vi TABLE OF CONTENTS.

16. Factors for the conversion of forces ............. 17

17. " linear accelerations ........ 17

18. " angular accelerations ....... 18

19. " linear and angular accelerations .... 18

20. " stress or force per unit of area, gravitation

units ............ 19

21. " " power, rate of working, or activity, gravi-

tation units .......... 19

22. " " " " " work or energy, gravitation units ... 20

23. " " film or surface tension ....... 20

24. " " power, rate of working or activity, absolute

units ............ 21

25. " work or energy, absolute units ....21

26. " " " " " stress or force per unit of area, absolute

units ............ 22

27. " " " " film or surface tension, absolute units . . 22

28. " " " " " densities ............ 23

29. " specific electrical resistance ..... 23

30. " " " " " electrolytic deposition ....... 24

31. " " " " " heat units ........... 24

32. " " " " " thermometer scales ........ 25

33. " " " " electric displacement and other quantities

of dimensions M* L~* ...... 25

34. " " " " " surface density of magnetization and other

quantities of dimensions M* L~^ ... 26

35. " " " " " intensity of magnetization and other quan-

tities of dimensions M* L5 ..... 26

36. " " " " electric potential a.nd other quantities of

dimensions M* iJ ........ 27

37. " " " " " magnetic moment and other quantities of

dimensions M* L* ........ 27

jc fi—x

38. Values of - - (hyperbolic sines) for values of x from o to 5 ... 28

2

^, I _ y.

39. - (hyperbolic cosines) for " ... 29

40. Logarithms of ~ « " « « .......... 30

41. « of - " " " .......... 31

2

42. Values of e* and ^"x and their logarithms ........... 32

43. " " e** and tr* " " " ..... ...... 33

44. " " <£' and ^* " " ...... ..... 34

45. " " anf- " ........... 34

46. " " e* and e~x fractional values of x . . . 35

47. Probability of errors of observation . ............ 35

48. " " " " " ............. 36

49- Values of 0.6745^

50. " " °.6745V/,7(^ 37

51- " "

52. " « 0.8453 , - ....... •.....,,..... 37

n — i

53. " " the logarithm of the gamma function T(n) for values of n

between i and 2 3&

54. " " the first seven zonal harmonics from 0 = o° to # = 90° . . . 40

55. " " log M/4TrVaal for facilitating the calculation of the mutual

inductance between two coaxial circles 42

for different values of 6 with the loga-

« |V(i — sin^sinV)**

rithms of these integrals ............ 43

57. Cross section and weight of copper, iron, and brass wire of different

diameters, British units ................ 44

58. Cross section and weight of copper, iron, and brass wire of different

diameters, metric units ................ 4$

59. Cross section and weight in various units of aluminium wires of differ-

ent diameters ............ ....... 48

60. Cross section and weight in various units of platinum wires of different

diameters ..................... 5°

61. Cross section and weight in various units of gold wires of different

diameters ..................... 52

62. Cross section and weight in various units of silver wires of different

diameters ..................... 54

63. Weight, in grammes per square metre, of sheet metal ...... 56

64. " " various British units, of sheet metal ......... 57

65. Size, weight, and electrical constants of copper wire according to Brown

and Sharp's gauge and British measure ........... 58

66. Same data as 65, but in metric measure ........... 60

67. " " " " but British standard wire gauge ........ 62

68. " " " 67, but in metric measure ........... 64

69. " " " 65, but Birmingham wire gauge ......... 66

70. " " " 69, but in metric measure ........... 68

71. Strength of materials :

(a) Metals and alloys ................. 70

(£) Stones and bricks ................. 70

(c) Timber ........ ' ............ 70

72. Composition and physical properties of steel ...... .... 71

73. Effect of the reduction of section produced by rolling on> the strength of

bar iron ..................... 72

74. Effect of diameter on the strength of bar iron ......... 72

i/ 111 TABLE OF CONTENTS.

75. Strength of copper-tin alloys (bronzes) 73

76. " copper-zinc alloys (brasses) 73

77. " " copper-zinc-tin alloys 73

78. Moduli of rigidity 74

79. Young's modulus of elasticity • '•••• 75

80. Effect of temperature on rigidity 76

81. Values of Poisson's ratio 76

82. Elastic moduli of crystals, formulae 77

83. " " " " numerical results . 78

84. Compressibility of nitrogen at different pressures and temperatures . 79

85. " " hydrogen " " " " " . 79

86. " " methane "

79

87. " ethylene " . 79

88. " " carbon dioxide" " " " value of/?/ 80

89. " " " " " « "values of

the ratio p"v/p\Vi ...*.... 80

90. " air, oxygen, and carbon monoxide at different pres-

sures and ordinary temperature 80

91. " sulphur dioxide at different pressures and tempera-

tures 8 1

92. " ammonia at different pressures and temperatures . 81

93. and bulk moduli of liquids 82

94- " " " " " solids 83

95. Density of various solids 84

96. " " " alloys 85

97. " " " metals 86

98. " « " woods 87

99. " " " liquids 88

100. " " " gases 89

101. " " aqueous solutions of salts 90

102. " " " water between o° and 32° C 92

103. Volume of water at different temperatures in terms of its volume at

temperature of maximum density 93

104. Density and volume of water in terms of the density and volume at

4° C 94

105. " " mercury at different temperatures 95

1 06. Specific gravity of aqueous ethyl alcohol 96

107. Density of aqueous methyl alcohol • 97

108. Variation of density of alcohol with temperature 98

109. Velocity of sound in air, principal determinations of 99

no. " " " " solids 100

in. " " " liquids and gases 101

112. Force of gravity at sea level and different latitudes ., 102

113. Results of some of the more recent determinations of gravity .... 103

114. Value of gravity at stations occupied by U. S. C. & G. Survey in 1894 . 104

115. Length of seconds pendulum for sea level and different latitudes . .104

116. Determinations of the length of the seconds pendulum 105

TABLE OF CONTENTS. IX

117. . Miscellaneous data as to .the earth and planets . . . . . . . . . 106

118. Aerodynamics : Data for wind pressure and values of J*"m Pa = fa P^ 108
iig. " Data for the soaring of planes 109

120. Terrestrial magnetism, total intensity no

121. " secular variation of total intensity no

122. " " dip in

123. " " secular variation of dip in

124. " " horizontal intensity .... 112

125. " " secular variation of horizontal intensity . . .112

126. " " formulae for value and secular variation of dec-

lination 113

127.. " " secular variation of declination (eastern stations) 114

128. " " " " " " (central stations) 115

129. . " " " " " " (western stations) 116

130. " " position of agonic line in 1800, 1850, 1875,

and 1890 117

131. " " date of maximum east declination at various

stations 118

132. Tables for computing pressure of mercury and of water, British and

metric measures 119

133. Reduction of barometric height to standard temperature ..... 120

134. Correction of barometer to standard gravity, British and metric mea-

sures 121

135. Reduction of barometer to latitude 45°, British scale 122

136. " " " " " " metric scale 123

137. Correction of barometer for capillarity, metric and British measures . 124

138. Absorption of gases by liquids 125

139. Vapor pressures 126

140. Capillarity and surface tension, water and alcohol in air 128

141. miscellaneous liquids in air . . . .128

142. " aqueous solutions of salts 128

143. " " liquids in contact with air, water, or

mercury 129

144. liquids at solidifying point 129

145. " " " thickness of soap films . . . . . .129

146. Colors of thin plates, Newton's Rings 130

147. Contraction produced by solution of salts 131

148. " " " dilution of solutions 134

149. Coefficients of friction 135

150. Specific viscosity of water at different temperatures 136

151. Coefficients of viscosity for solutions of alcohol in water 137

152. Specific viscosity of mineral oils 137

153. " " " various " 137

154. " " " various liquids 138

155. " temperature variation 139

156. " " " solutions, variation with density and temperature . 140

157. " " " " atomic concentrations 144

X TABLE OF CONTENTS.

158. Specific viscosity of gases and vapors 145

159. " " formulae for temperature variation . . . .146

160. Diffusion of liquids and solutions of salts into water 147

161. " vapors 148

162. " gases and vapors 149

163. Isotonic coefficients and lowering of the freezing-point 150

164. Osmotic pressure f$o

165. Pressure of aqueous vapor (Regnault) 13,1

1 66. " " " " (Regnault and Broch) 154

167. Weight in grains of aqueous vapor in a cubic foot of saturated air . . 155

168. " " grammes of " " " metre of " " . . 155

169. Pressure of aqueous vapor at low temperatures r<j6

170. Hygrometry, vapor pressure in the atmosphere 157

171. clew-points 158

172. Values of 0.378^ in atmospheric pressure equation h=B — 0.378^ . .160

173. Relative humidity 160

174. Table for facilitating the calculation of ^760 r62

175. Logarithms of 7^/760 for values of h between 80 and 800 162

176. Values of 1-^.0036"}?:

(a) For values of /between o° and 10° C. by tenths 164

(/;) " " " / " — 90° and +1-990° C. by tens 165

(r) Logarithms for / " — 49° and +399° C. by units 166

(ti) " " " t " 400° and 1990° C. by tens 168

177. Determination of heights by barometer 169

178. Barometric pressures corresponding to different temperatures of the

boiling-point of water :

(a) British measure 170

(b) Metric measure ifi

179. Rowland's standard wave-lengths in arc and sun spectra . . . . .172

180. Wave-lengths of the Fraunhofer lines ^,5

181. Various determinations of the velocity of light 176

182. Photometric standards 176

183. Solar energy and its absorption by the terrestrial atmosphere . . . .177

184. The solar constant '77

1-85. Index of refraction of glass :

(a) Fraunhofer's determinations 178

(b) Bailie's " '7<s

(c) Hopkinson's " '7s

(d) Mascart's " • 17^

(e) Langley's " *79

(/) Vogel on effect of temperature

Of) Muller « « « «

1 86. Indices of refraction for various alums 180

187. " " " " metals and metallic oxides :

(a) Kundt's experiments 181

(ft) Du Bois and Ruben's experiments 181

(f) Drude's experiments 181

TABLE OF CONTENTS. XI

188. Index of refraction of rock salt, various authorities 182

jgg. " " " " sylvine 182

igo. " " " " fluor-spar . . . . . . <. 183

igi. " " " " various monorefringents ....,..,. 184

ig2. " " " " Iceland spar 185

!g3. " " " " quartz 186

ig4. " " " " various uniaxial crystals 187

jgg. " " " " " biaxial crystals 187

ig6. " " " " solutions of salts and acids :

(a) Solutions in water 188

(b) Solutions in alcohol J88

(f) " " potassium permanganate 188

igj. Index of refraction of various liquids 189

ig8. " " " " gases and vapors 190

199. Rotation of plane of polarized light by solutions 191

200. " " " " " " " sodium chlorate and by quartz . 191

201. Lowering of freezing-points by salts in solution 192

202. Vapor-pressures of solutions of salts in water 194

203. Raising of boiling-points by salts in solution 196

204. Thermal conductivity of metals and alloys 197

205. " various substances 198

206. " " " water and solutions of salts 198

207. " organic liquids 198

208. " " " gases 198

209. Freezing mixtures 199

210. Critical temperatures, pressures, volumes, and densities of gases. . . 200

211. Heat of combustion 201

212. " " combination 202

213. Latent heat of vaporization 204

214. '' " " fusion 206

215. Melting-points of chemical elements 207

216. Boiling-points of 207

217. Melting-points of various inorganic compounds 208

218. Boiling-points of 210

219. Melting-points of mixtures 211

220. Densities, melting-points, and boiling-points of some organic com-

pounds :

(a) Paraffin series 212

(I)} Olefine series 212

(f) Acetylene series 212

(a) Monatomic alcohols ' . . 213

(<?) Alcoholic ethers 213

(/) Ethyl ethers -> . •- 213

221. Coefficients of linear expansion of chemical elements 214

222. " miscellaneous substances . . . .215

223. " cubical expansion of crystalline and other solids . . .216

224. « " " " " liquids 217

Xll TABLE OF CONTENTS.

225. Coefficients of cubical expansion of gases .218

226. Dynamical equivalent of the thermal unit 210

227. " " " " " « historical table .220

228. Specific heat of water, descriptive introduction 222

228. Specific heat of water . .222

229. Ratio of specific heats of air, various determinations 223

230. Specific heats of gases and vapors . 224

231. Vapor pressure of ethyl alcohol 22e

232. " " " methyl " 225

233. Vapor pressures and temperatures of various liquids :

(a) Carbon disulphide .226

(£) Chlorobenzene .- .226

(^) Bromobenzene . 226

(</) Aniline 226

(e) Methyl salicylate k 227

(/) Bromonaphthaline 227

(g) Mercury 22?

234. Thermometers, comparisons of mercury in glass and air thermometers 228
235- comparison of various kinds with hydrogen thermometer 229

236. " " " " " air thermometer . . 229

237. change of zero due to heating (Jena glass) 230

238. " " " " " " " (various kinds of glass) . 230

239. " " " " " " " effect of composition of

glass 231

240. slow change of zero with time 231

241. correction for mercury in stem 232

242. Emissivity of polished and blackened surfaces in air at ordinary pres-

sures 234

243. Emissivity of polished and blackened surfaces in air at different pres-

sures 234

244. Constants of emissivity from various substances to vacuum .... 235

245. Effect of absolute temperature of surface on the emissivity, constants

of bright and blackened platinum wire 235

246. Radiation of bright platinum wire to copper envelope across air of dif-

ferent pressures 236

247. Effect of pressure on radiation at different temperatures 236

248. Properties and constants of saturated steam, metric measure .... 237

249. " " « " " " British measure .... 238

250. Ratio of the electrostatic to the electromagnetic unit of electricity, dif-

ferent determinations of • 243

251. Dielectric strength :

(a) Medium air and terminals flat plates < . 244

(b) " " " " balls of different diameter .... 244

(c) balls comparison of the results of dif-

ferent observers 244

252. Dielectric strength of gases, effect of pressure on 245

253. " " "- various substances 245

TABLE OF CONTENTS. Xlll

254. Data as to electric battery cells :

(a) Double fluid batteries • • • 246

(b) Single fluid batteries . . . ' '. 247

(c) Standard cells 247

(d) Secondary cells ... 247

255. Thermoelectric power of various metals and alloys . . . . .248

256. " " " " alloys 249

257. Thermoelectric neutral point of various metals relative to lead . . . 249

258. Specific heat of electricity for metals ' . 249

259. Thermoelectric power of metals and solutions -250

260. Peltier effect, Jahn's experiments . . 250

261. " " Le Roux's " 250

262. Conductivity of three-metal and miscellaneous alloys ...... 251

263. " " alloys 252

264. Specific resistance of metallic wires, various dimension units . . . .254

265. " " " metals, various authorities 255

266. " " " " and alloys at low temperatures 256

267. Effect of elastic and permanent elongation on resistance of metallic

wires 258

268. Resistance of wires of different diameter to alternating currents . . . 258

269. Conductivity of dilute solutions proportional to amount of dissolved salt 259

270. Electrochemical equivalent numbers and densities of approximately nor-

mal solutions 259

271. Specific molecular conductivities of solutions 260

272. Limiting values of specific molecular conductivities 261

273. Temperature coefficients of dilute solutions 261

274. Various determinations of the ohm, the electrochemical equivalent of

silver and the electromotive force of the Clark cell . 262

275. Specific inductive capacity of gases 263

276. " " " " solids 264

277. " " " " liquids 265

278. Contact difference of potential, solids with liquids and liquids with

liquids in air 266

279. Contact difference of potential, solids with solids in air 268

280. Potential difference between metals in various solutions ..... 269

281. Resistance of glass and porcelain at different temperatures .... 270

282. Relation between thermal and electrical conductivities :

(a) Arbitrary units 271

(b) Values in c. g. s. units . . . 271

(c) Berget's experiments 271

(</) Kohlrausch's results 271

283. Electrochemical equivalents and atomic weights of the chemical ele-

ments . 272

284. Permeability of iron for various inductions 274

285. Permeability of transformer iron :

(a) Specimen of Westinghouse No. 8 transformer 274

(*) " " "6 " ....... 275

XIV TABLE OF CONTENTS.

(c) Specimen of Westinghouse No. 4 transformer 275

(ft} " Thomson-Houston 'i 5oo-watt transformer . . . . 275

286. Composition and magnetic properties of iron and steel 276

287. Permeability of some specimens in Table 286 278

288. Magnetic properties of soft iron at o° and 100° C . 278

289. " " " steel at o° and 100° C. . 278

290. " " " cobalt at 100° C 279

291. " " " nickel at 100° C 279

292. " " magnetite 279

293. " Lowmoor wrought iron in intense fields . . .279

294. " " Vicker's tool steel in intense fields 279

295- " Hadfield's manganese steel in intense fields . . 279

296. Saturation values for different steels 279

297. Magnetic properties of very weak fields 280

298. Dissipation of energy in the cyclic magnetization of magnetic substances 280
299- " £" " " " " " cable transformers . 280

300. " " " " " " « various substances . 281

301. " " transformer cores . 282

302. " " various specimens of

soft iron . . . 283
Magneto-optic rotation, Verdet's constant 284

303. " in solids 285

304. " " " liquids 286

305. " " solutions of acids and salts in water . . . 288

306. " " " " " salts in alcohol 290

307. " in hydrochloric acid 290

308. " " "gases 291

309. Miscellaneous values of Verdet's and Kundt's constants 291

310. " " susceptibility for liquids and gases .... 292

311. Kerr's constants for iron, nickel, cobalt, and magnetite 292

312. Effect of magnetic field on the electric resistance of bismuth (initial

resistance of one ohm for zero field and various temperatures) . . 293

313. Effect of magnetic field on the electric resistance of bismuth (initial

resistance one ohm for zero field and temperature zero Centigrade) 293

314. Specific heat of various solids and liquids 294

315. Specific heat of metals 296

INTRODUCTION.

UNITS OF MEASUREMENT AND CONVERSION FORMULAE.

Units. — The quantitative measure of anything is a number which expresses the
ratio of the magnitude of the thing to the magnitude of some other thing of the
same kind. In order that the number expressing the measure may be intelligi-
ble, the magnitude of the thing used for comparison must be known. This leads
to the conventional choice of certain magnitudes as units of measurement, and
any other magnitude is then simply expressed by a number which tells how many
magnitudes equal to the unit of the same kind of magnitude it contains. For
example, the distance between two places may be stated as a certain number of
miles or of yards or of feet. In the first case, the mile is assumed as a known
distance ; in the second, the yard, and in the third, the foot. What is sought for
in the statement is to convey an idea of the distance by describing it in terms of
distances which are either familiar or easily referred to for comparison. Similarly
quantities of matter are referred to as so many tons or pounds or grains and so
forth, and intervals of time as a number of hours or minutes or seconds. Gen-
erally in ordinary affairs such statements appeal to experience ; but, whether this
be so or not, the statement must involve some magnitude as a fundamental quan-
tity, and this must be of such a character that, if it is not known, it can be readily
referred to. We become familiar with the length of a mile by walking over dis-
tances expressed in miles, with the length of a yard or a foot by examining a yard
or a foot measure and comparing it with something easily referred to, — say our
own height, the length of our foot or step, — and similarly for quantities of other
kinds. This leads us to be able to form a mental picture of such magnitudes
when the numbers expressing them are stated, and hence to follow intelligently
descriptions of the results of scientific work. The possession of copies of the
units enables us by proper comparisons to find the magnitude-numbers express-
ing physical quantities for ourselves. The numbers descriptive of any quan-
tity must depend on the intrinsic magnitude of the unit in terms of which it is
described. Thus a mile is 1760 yards, or 5280 feet, and hence when a mile is
taken as the unit the magnitude-number for the distance is i, when a yard is taken
as the unit the magnitude-number is 1760, and when afoot is taken it is 5280.
Thus, to obtain the magnitude-number for a quantity in terms of a new unit when
it is already known in terms of another we have to multiply the old magnitude-
number by the ratio of the intrinsic values of the old and new units ; that is, by
the number of the new units required to make one of the old.

XVI INTRODUCTION.

Fundamental Units of Length and Mass. — It is desirable that as few dif-
ferent kinds of unit quantities as possible should be introduced into our measure-
ments, and since it has been found possible and convenient to express a large
number of physical quantities in terms of length or mass or time units and com-
binations of these they have been very generally adopted as fundamental units.
Two systems of such units are used in this country for scientific measurements,
namely, the British and the French, or metric, systems. Tables of conversion
factors are given in the book for facilitating comparisons between quantities ex-
pressed in terms of one system with similar quantities expressed in the other. In
the British system the standard unit of length is the yard, and it is defined as fol-
lows : "The straight line or distance between the transverse lines in the two gold
plugs in the bronze bar deposited in the Office of the Exchequer shall be the gen-
uine Standard of Length at 62° F., and if lost it shall be replaced by means of its
copies." [The authorized copies here referred to are preserved at the Royal
Mint, the Royal Society of London, the Royal Observatory at Greenwich, and the
New Palace at Westminster.]

The British standard unit of mass is the pound avoirdupois, and is the mass of
a piece of platinum marked " P. S. 1844, i lb.," which is preserved in the Exchequer
Office. Authorized copies of this standard are kept at the same places as those
of the standard of length.

In the metric system the standard of length is defined as the distance between
the ends of a certain platinum bar (the metre des Archives] when the whole bar is
at the temperature o° Centigrade. The bar was made by Borda, and is preserved
in the national archives of France. A line-standard metre has been constructed
by the International Bureau of Weights and Measures, and is known as the Inter-
national Prototype Metre. This standard is of the same length as the Borda stand-
ard. A number of standard-metre bars which have been carefully compared with
the International Prototype have lately been made by the International Bureau of
Weights and Measures and furnished to the various governments who have con-
tributed to the support of that bureau. These copies are called National Proto-
types.

Borda, Delambre, Laplace, and others, acting as a committee cf the French
Academy, recommended that the standard unit of length should be the ten mil-
lionth 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 metre bar was made
by Borda. The metre is not now defined as stated above, but as the length of
Borda's rod, and hence subsequent measurements of the length of the meridian
have not affected the length of the metre. ^

The French, or metric, standard of mass, the kilogramme, is the mass of a
piece of platinum also made by Borda in accordance with the same decree of the
Republic. It was connected with the standard of length by being made as nearly
as possible of the same mass as that of a cubic decimetre of distilled water at
the temperature of 4° C., or nearly the temperature of maximum density.

As in the case of the metre, the International Bureau of Weights and Measures

INTRODUCTION. XV11

has made copies of the kilogramme. One of these is taken as standard, and is
called the International Prototype Kilogramme. The others were distributed in
the same manner as the metre standards, and are called National Prototypes.

Comparisons of the French and British standards are given in tabular form
in Table 2 ; and similarly Table 3, differing slightly from the British, gives the
legal ratios in the United States. In the metric system the decimal subdivi-
sion is used, and thus we have the decimetre, the centimetre, and the millimetre as
subdivisions, and the dekametre, hektometre, and kilometre as multiples. The
centimetre is most commonly used in scientific work.

Time. — The unit of time in both the systems here referred to is the mean
solar second, or the 86,4ooth part of the mean solar day. The unit of time is
thus founded on the average time required for the earth to make one revolution
on its axis relatively to the sun as a fixed point of reference.

Derived Units. — Units of quantities depending on powers greater than unity
of the fundamental length, mass, and time units, or on combinations of different
powers of these units, are called "derived units." Thus, the unit of area and of
volume are respectively the area of a square whose side is the unit of length and
the volume of a cube whose edge is the unit of length. Suppose that the area of
a surface is expressed in terms of the foot as fundamental unit, and we wish to
find the area-number when the yard is taken as fundamental unit. The yard is
3 times as long as the foot, and therefore the area of a square whose side is a
yard is 3 X 3 times as great as that whose side is a foot. Thus, the surface will
only make one ninth as many units of area when the yard is the unit of length as
it will make when the foot is that unit. To transform, then, from the foot as old
unit to the yard as new unit, we have to multiply the old area-number by 1/9, or by
the ratio of the magnitude of the old to that of the new unit of area. This is the
same rule as that given above, but it is usually more convenient to express the
transformations in terms of the fundamental units directly. In the above case,
since on the method of measurement here adopted an area-number is the product
of a length-number by a length-number the ratio of two units is the square of the
ratio of the intrinsic values of the two units of length. Hence, if / be the ratio
of the magnitude of the old to that of the new unit of length, the ratio of the cor-
responding units of area is P. Similarly the ratio of two units of volume will be
T3, and so on for other quantities.

Dimensional Formulae. — It is convenient to adopt symbols for the ratios
of length units, mass units, and time units, and adhere to their use throughout ;
and in what follows, the small letters, /, tn, /, will be used for these ratios. These
letters 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 /, #/, / are known, and the
powers of /, m, and / involved in any particular unit are also known, the factor for
transformation is. at once obtained. Thus, in the above example, the value of/
was 1/3 and the power of /involved in the expression for area is /2; hence, the
factor for transforming from square feet to square yards is 1/9. These factors

XV111 INTRODUCTION.

have been called by Prof. James Thomson "change ratios," which seems an
appropriate term. The term " conversion factor " is perhaps more generally
known, and has been used throughout this book.

Conversion Factor. — In order to determine the symbolic expression for the
conversion factor for any physical quantity, it is sufficient to determine the degree
to which the quantities length, mass, and time are involved in the quantity. Thus,
a velocity is expressed by the ratio of the number representing a length to that
representing an interval of time, or L/T, an acceleration by a velocity-number
divided by an interval of time-number, or L/T2, and so On, and the correspond-
ing ratios of units must therefore enter to precisely the same degree. The fac-
tors would thus be for the above cases, ///and ///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

is the dimensional equation for energy, and ML"T~2 is the dimensional formula
for energy.

In general, if we have an equation for a physical quantity

Q = CL"M"T,

where C is a constant and LMT represents length, mass, and time in terms of one
set of units, and we wish to transform to another set of units in terms of which

the length, mass, and time are LyM/T1,, we have to find the value of ' '' ' which

L M. i

in accordance with the convention adopted above will be ltmft, or the ratios of
the magnitudes of the old to those of the new units.

Thus Ly = L/, Mt = Mm, Ty = T/, and if Qy be the new quantity-number

Qy^CL/'MyTy*

or the conversion factor is /WT, a quantity of precisely the same form as the
dimension formula LaM*Tc.

We now proceed to form the dimensional and conversion factor formulas for
the more commonly occurring derived units.

1. Area. — The unit of area is the square the side of which is measured by
the unit of length. The area of a surface is therefore expressed as

S = CLa,

where C is a constant depending on the shape of the boundary of the surface
and L a linear dimension. For example, if the surface be square and L be the
length of a side C is unity. If the boundary be a circle and L be a diameter
C = 7r/4, and so on. The dimensional formula is thus L2, and the conversion
factor 72.

2. Volume. — The unit of volume is the volume of a cube the edge of which
is measured by the unit of length. The volume of a body is therefore expressed as

INTRODUCTION. XIX

V = CL3,

where as before C is a constant depending on the shape of the boundary. The
dimensional formula is L3 and the conversion factor /*.

3. Density. — The density of a substance is the quantity of matter in the unit
of volume. The dimension formula is therefore M/V or ML~8, and conversion
factor w/~3.

Example. — The density of a body is 150 in pounds per cubic foot: required
the density in grains per cubic inch.

Here m is the number of grains in a pound = 7000, and / is the number of
inches in a foot= 12 ; .'. w/~3 = 7ooo/i23 = 4.051. Hence the density is 150 X
4.051 =607.6 in grains per cubic inch.

NOTE. — The specific gravity of a body is the ratio of its density to the density of a standard
substance. The dimension formula and conversion factor are therefore both unity.

4. Velocity. — The velocity of a body at any instant is given by the equation

7' = Si or velocity is the ratio of a length-number to a time-number. The di-
aT

mension formula is LT"1, and the conversion factor lt~l.

Example. — A train has a velocity of 60 miles an hour : what is its velocity in
feet per second ?

Here /= =5280 and ^ = 3600 ; .-. /t~l — = — r .467. Hence the velo-

3600 30

city = 60 X 1-467 = 88.0 in feet per second.

5. Angle. — An angle is measured by the ratio of the length of an arc to the
length of the radius of the arc. The dimension formula and the conversion
factor are therefore both unity.

6. Angular Velocity. — Angular velocity is the ratio of the magnitude of the
angle described in an interval of time to the length of the interval. The dimen-
sion formula is therefore T"1, and the conversion factor is t~*.

7. Linear Acceleration. — Acceleration is the rate of change of velocity or

j = — • The dimension formula is therefore VT"1 or LT~8, and the conversion
dt

factor is //~2.

Example.' — A body acquires velocity at a uniform rate, and at the end of one
minute is moving at the rate of 20 kilometres per hour : what is the acceleration
in centimetres per second per second ?

Since the velocity gained was 20 kilometres per hour in one minute, the accel-
eration was 1 200 kilometres per hour per hour.

Here/=iooooo and / = 36oo; /. //~'2= 100 ooo/36oo2 = . 00771, and there-
fore acceleration r=. 007 7 1 X 1200 = 9.26 centimetres per second.

8. Angular Acceleration. — Angular acceleration is rate of change of angu

XX INTRODUCTION.

lar velocity. The dimensional formula 13 thus angular velocity Qr ^ and thg
conversion factor /~2.

9. Solid Angle. — A solid angle is measured by the ratio of the surface of
the portion of a sphere enclosed by the conical surface forming the angle to the
square of radius of the spherical surface, the centre of the sphere being at the

vertex of the cone. The dimensional formula is therefore or i, and hence

it

the conversion factor is also i.

10. Curvature. — Curvature is measured by the rate of change of direction of
the curve with reference to distance measured along the curve as independent

variable. The dimension formula is therefore an^ e or Lr1, and the conversion

length

factor is 7"1.

n. Tortuosity. — Tortuosity is measured by the rate of rotation of the tan-
gent plane round the tangent to the curve of reference when length along the

curve is independent variable. The dimension formula is therefore ,an^ e or

length

L"1, and the conversion I actor is l~l.

12. Specific Curvature of a Surface. — This was defined by Gauss to ber
at any point of the surface, the ratio of the solid angle enclosed by a surface
formed by moving a normal to the surface round the periphery of a small area
containing the point, to the magnitude of the area. The dimensional formula is

therefore - — or L~2, and the conversion factor is thus /~2.
surface

13. Momentum. — This is quantity of motion in the Newtonian sense, and is,
at any instant, measured by the product of the mass-number and the velocity-
number for the body.

Thus the dimension formula is MV or MLT"1, and the conversion factor mll~l.

Example. — A mass of 10 pounds is moving with a velocity of 30 feet per sec-
ond : what is its momentum when the centimetre, the gramme, and the second are
fundamental units ?

Here tn = 453-59* /=3°-48, and / = i ; .-. mlt'1 — 453. 59 X 3°-48 = 13825.
The momentum is thus 13825 X 10 X 30 = 4147500.

14. Moment of Momentum. — The moment of momentum of a body with
reference to a point is the product of its momentum-number and the number
expressing the distance of its line of motion from the point. The dimensional
formula is thus MI/T"1, and hence the conversion factor is ni?*t~l.

15. Moment of Inertia. — The moment of inertia of a body round any axis
is expressed by the formula 2/wr2, where m is the mass of any particle of the body

INTRODUCTION. XXI

and r its distance from the axis. The dimension formula for the sum is clearly
the same as for each element, and hence is ML2. The conversion factor is there-
fore ml1.

16. Angular Momentum. — The angular momentum of a body round any
axis is the product of the numbers expressing the moment of inertia and the
angular velocity of the body. The dimensional formula and the conversion fac-
tor are therefore the same as for moment of momentum given above.

17. Force. — A force is measured by the rate of change of momentum it is
capable of producing. The dimension formulae for force and " time rate of
change of momentum " are therefore the same, and are expressed by the ratio
of momentum-number to time-number or MLT~2. The conversion factor is thus

NOTE. — When mass is expressed in pounds, length in feet, and time in seconds, the unit force
is called the poundal. When grammes, centimetres, and seconds are the corresponding units the
unit of force is called the dyne.

Example. Find the number of dynes in 25 poundals.

Here m = 453-59» l = 3°-48, and /= i ; .'. m/r*= 453.59 X 30.48= 13825
nearly. The number of dynes is thus 13825 X 25 = 345625 approximately.

18. Moment of a Couple, Torque, or Twisting Motive. — These are dif-
ferent names for a quantity which can be expressed as the product of two numbers
representing a force and a length. The dimension formula is therefore FL or
ML2T~2, and the conversion factor is

19. Intensity of a Stress. — The intensity of a stress is the ratio of the num-
ber expressing the total stress to the number expressing the area over which the
stress is distributed. The dimensional formula is thus FL~2 or ML^T"2, and the
conversion factor is

20. Intensity of Attraction, or " Force at a Point." — This is the force of
attraction per unit mass on a body placed at the point, and the dimensional for-
mula is therefore FM~* or LT~2, the same as acceleration. The conversion fac-
tors for acceleration therefore apply.

21. Absolute Force of a Centre of Attraction, or " Strength of a Cen-
tre." — This is the intensity of force at unit distance from the centre, and is there-
fore the force per unit mass at any point multiplied by the square of the distance
from the centre. The dimensional formula thus becomes FL2M-1 or L8T~2. The
conversion factor is therefore /3/~2.

22. Modulus of Elasticity. — A modulus of elasticity is the ratio of stress
intensity to percentage strain. The dimension of percentage strain is a length
divided by a length, and is therefore unity. Hence, the dimensional formula of a
modulus of elasticity is the same as that of stress intensity, or ML~JT~2, and the
conversion factor is thus also

XX11 INTRODUCTION.

23. Work and Energy. — When the point of application of a force, acting on
a body, moves in the direction of the force, work is done by the force, and the
amount is measured by the product of the force and displacement numbers. The
dimensional formula is therefore FL or ML2T~2.

. The work done by the force either produces a change in the velocity of the body
or a change of shape or configuration of the body, or both. In the first case it
produces a change of kinetic energy, in the second a change of potential energy.
The dimension formulae of energy and work, representing quantities of the same
kind, are identical, and the conversion factor for both is m/'2t~*.

24. Resilience. — This is the work done per unit volume of a body in distort-
ing it to the elastic limit or in producing rupture. The dimension formula is there-
fore ML2T~2L~3 01 ML~lrr~2, and the conversion factor mt~lr2.

25. Power, or Activity. — Power — or, as it is now very commonly called, ac-
tivity — is defined as the time rate of doing work, or if VV represent work and P power

P = -— - . The dimensional formula is therefore WT"1 or ML2T~8, and the con-
at

version factor *w/2/~3, or for problems in gravitation units more conveniently flt~l,
where f stands for the force factor.

Examples, (a) Find the number of gramme centimetres in one foot pound.

Here the units of force are the attraction of the earth on the pound * and
the gramme of matter, and the conversion factor is./?, where/" is 453.59 and /is
30.48.

Hence the number is 453-59 X 30.48 = 13825.

(b} Find the number of foot poundals in i oooooo centimetre dynes.
Here m = i/453-59» /= I/3°-48, and t= i ; .'. w/V~2 = 1/453-59 X 3Q-482,
and io*ml*r* = 107453.59 X 30.48*= 2.373.

(c) If gravity produces an acceleration of 32.2 feet per second per second, how
many watts are required to make one horse-power ?

One horse-power is 550 foot pounds per second, or 550 X 32.2 = 17710 foot
poundals per second. One watt is io7 ergs per second, that is, io7 dyne centi-
metres per second. The conversion factor is /w/2/"8, where m = 453.59, /= 30.48,
and /= i, and the result has to be divided by io7; the number of dyne centime-
tres per second in the watt.

Hence, 17710 *»/V78/io7= 17710 X 453-59 X 3o.482/io7= 746.3.

(//) How many gramme centimetres per second correspond to 33000 foot
pounds per minute ?

The conversion factor suitable for this case is/7/"1, where/" is 453-59, / is 30.48,
and / is 60.

Hence, 33000 lf~l= 33000 X 453-59 X 30.48/60= 7604000 nearly.

* It is important to remember that in problems like that here given the term "pound" or
" gramme " refers to force and not to mass.

INTRODUCTION. XX111

HEAT UNITS.

1. If heat be measured in dynamical units its dimensions are the same as those
of energy, namely ML'2T~2. The most common measurements, however, are
made in thermal units, that is, in terms of the amount of heat required to raise
the temperature of unit mass of water one degree of temperature at some stated
temperature. This method of measurement involves the unit of mass and some
unit of temperature, and hence if we denote temperature-numbers by ® and their
conversion factors by 6 the dimensional formula and conversion factor for quan-
tity of heat will be M0 and mO respectively. The relative amount of heat com-
pared with water as standard substance required to raise unit mass of different
substances one degree in temperature is called their specific heat, and is a simple
number.

Unit volume is sometimes used instead of unit mass in the measurement of
heat, the units being then called thermometric units. The dimensional formula
is in that case changed by the substitution of volume for mass, and becomes L3®,
and hence the conversion factor is to be calculated from the formula /80.

For other physical quantities involving heat we have : —

2. Coefficient of Expansion. — The coefficient of expansion of a substance
is equal to 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 is inversely as the mag-
nitude of the unit of temperature. Hence the dimensional and conversion-factor
formula; are ®-1 and 0"1.

3. Conductivity, or Specific Conductance. — This is the quantity of heat
transmitted per unit of time per unit of surface per unit of temperature gradient.
The equation for conductivity is therefore, with H as quantity of heat,

_L2T
L

and the dimensional formula — — = -— , which gives mt~lt~l for conversion factor.

Li 1

In thermometric units the formula becomes L/'T"1, which properly represents
diffusivity. In dynamical units H becomes ML'2T~2, and the formula changes to
MLT"8®"1. The conversion factors obtained from these are t*t~l and mlt~*Q~l
respectively.

Similarly for emission and absorption we have —

4. Emissivity and Immissivity. — These are the quantities of heat given
off by or taken in by the body per unit of time per unit of surface per unit dif-
ference of temperature between the surface and the surrounding medium. We
thus get the equation

EL2®T = H = M®.

The dimensional formula for E is therefore ML"2!'"1, and the conversion factor

XXIV INTRODUCTION.

mf"2t~l. In thermometric units by substituting /8 for m the factor becomes //""*,.
and in dynamical units int~a&~1.

5. Thermal Capacity. — This is the product of the number for mass and
the specific heat, and hence the dimensional formula and conversion factor are
simply M and m.

6. Latent Heat. — Latent heat is the ratio of the number representing the
quantity of heat required to change the state of a body to the number represent-
ing the quantity of matter in the body. The dimensional formula is therefore
MG/M or ®, and hence the conversion factor is simply the ratio of the tempera-
ture units or H. In dynamical units the factor is T2/"2.*

7. Joule's Equivalent. — Joule's dynamical equivalent is connected with
quantity of heat by the equation

ML2T-2=JH or JM®.

This gives for the dimensional formula of J the expression L'^T"2®"1. The conver-
sion factor is thus represented by f*t~26~l. When heat is measured in dynamical
units J is a simple number.

8. Entropy. — The entropy of a body is directly proportional to the quantity
of heat it contains and inversely proportional to its temperature. The dimen-
sional formula is thus M®/® or M, and the conversion factor is m. When heat is
measured in dynamical units the factor is w/2/"2^"1.

Examples, (a) Find the relation between the British thermal unit, the calorie,,
and the therm.

Neglecting the variation of the specific heat of water with temperature, or de-
fining all the units for the same temperature of the standard substance, we have
the following definitions. The British thermal unit is the quantity of heat required
to raise the temperature of one pound of water i° F. The calorie is the quan-
tity of heat required to raise the temperature of one kilogramme of water i° C.
The therm is the quantity of heat required to raise the temperature of one gramme
of water i° C. Hence : —

(1) To find the number of calories in one British thermal unit, we have

^ = •45399 and 0 = $ J •'• *»0= -45399 X 5/9 = -25199-

(2) To find the number of therms in one calorie, w— 1000 and 0=i;

/. m6 •=• 1000.

It follows at once that the number of therms in one British thermal unit is
1000 X .25199 = 251.99.

(b) What is the relation between the foot grain second Fahrenheit-degree and
the centimetre gramme second Centigrade-degree units of conductivity ?

The number of the latter units in one of the former is given by the for-

* It will be noticed that when 0 is given the dimension formula L2T-'2 the formulae in thermal
and dynamical units are always identical. The thermometric units practically suppress mass.

1 NTRODUCTION. XXV

mula ml~lrlb°, where m = . 064799, /= 30.48, and /= i, and is therefore^:
.064799/30.48 = 2.126 X io~8.

(f) Find the relation between the units stated in (#) for emissivity.

In this case the conversion formula is ml~*t~l, where ml and / have the
same value as before. Hence the number of the latter units in the former is
0.064 799/3°-48a = 6.975 X io~5.

(d) Find the number of centimetre gramme second units in the inch grain
hour unit of emissivity.

Here the formula is w/"2/"1, where m = 0.064 799> /=2-54, ar>d ^ = 3600.
Therefore the required number is 0.064 799/2-542 X 3600 = 2.790 X io~b.

(e) If Joule's equivalent be 776 foot pounds per pound of water per degree
Fahrenheit, what will be its value in gravitation units when the metre, the
kilogramme, and the degree Centigrade are units ?

The conversion factor in this case is .,_, or I0~~l, where / — .3048 and
0-1 = 1.8 ; .'. 776 X .3048 X 1.8 =425.7.

(/) If Joule's equivalent be 24832 foot poundals when the degree Fahren-
heit is unit of temperature, what will be its value when kilogramme metre
second and degree-Centigrade units are used ?

The conversion factor is /7~20~', where /= .3048, t = i, and 0~l = 1.8 ;

.-. 24832 x pr*ff-l = 24832 x .3048' x 1.8 = 4152.5. ^

In gravitation units this would give 4152.5/9.81 =423.3.

ELECTRIC AND MAGNETIC UNITS.

There are two systems of these units, the electrostatic and the electromagnetic
systems, which differ from each other because of the different fundamental suppo-
sitions on which they are based. In the electrostatic system the repulsive force
between two quantities of static electricity is made the basis. This connects force,

quantity of electricity, and length by the equation f=a ^ft, where f is force, a a

quantity depending on the units employed and on the nature of the medium, g and
qt quantities of electricity, and / the distance between q and qt. The magnitude of
the force f for any particular values of ^, qt and / depends on a property of the
medium across which the force takes place called its inductive capacity. The in-
ductive capacity of air has generally been assumed as unity, and the inductive
capacity of other media expressed as a number representing the ratio of the induc-
tive capacity of the medium to that of air. These numbers are known as the spe-
cific inductive capacities of the media. According to the ordinary assumption,
then, of air as the standard medium, we obtain unit quantity of electricity when
in the above equation q-=.qt, and/, a, and / are each unity. A formal definition
is given below.

In the electromagnetic system the repulsion between two magnetic poles or

XXVI INTRODUCTION.

quantities of magnetism is taken as the basis. In this system the quantities force,
quantity of magnetism, and length are connected by an equation of the form

where m and mt are in this case quantities of magnetism, and the other symbols
have the same meaning as before. In this case it has been usual to assume the
magnetic inductive capacity of air to be unity, and to express the magnetic induc-
tive capacity of other media as a simple number representing the ratio of the in-
ductive capacity of the medium to that of air. These numbers, by analogy with
specific inductive capacity for electricity, might be called specific inductive capac-
ities for magnetism. They are usually called permeabilities. ( Vide Thomson,
" Papers on Electrostatics and Magnetism," p. 484.) In this case, also, like that
for electricity, the unit quantity of magnetism is obtained by making m = mt, and
f, a, and / each unity.

In both these cases the intrinsic inductive capacity of the standard medium is
suppressed, and hence also that of all other media. Whether this be done or not,
direct experiment has to be resorted to for the determination of the absolute val-
ues of the units and the relations of the units in the one system to those in the
other. The character of this relation can be directly inferred from the dimen-
sional formula:; of the different quantities, but these can give no information as to
the relative absolute values of the units in the two systems. Prof. Riicker has
suggested (Phil. Mag. vol. 27) the advisability of at least indicating the exist-
ence of the suppressed properties by putting symbols for them in the dimensional
formulae. This has the advantage of showing how the magnitudes of the different
units would be affected by a change in the standard medium, or by making the
standard medium different for the two systems. In accordance with this idea, the
symbols K and P have been introduced into the formulae given below to represent
inductive capacity in the electrostatic and the electromagnetic systems respectively.
In the conversion formulae k and/ are the ordinary specific inductive capacities
and permeabilities of the media when air is taken as the standard, or generally
those with reference to the first medium taken as standard. The ordinary for-
mulae may be obtained by putting K and P equal to unity.

ELECTROSTATIC UNITS.

i. Quantity of Electricity. — The unit quantity of electricity is defined as
that quantity which if concentrated at a point and placed at unit distance from an
equal and similarly concentrated quantity repels it, or is repelled by it, with unit
force. The medium or dielectric is usually taken as air, and the other units in ac-
cordance with the centimetre gramme second system.

In this case we have the force of repulsion proportional directly to the square
of the quantity of electricity and inversely to the square of the distance between
the quantities and to the inductive capacity. The dimensional formula is there-
fore the same as that for [force X length2 X inductive capacity]1 or
and the conversion factor is

INTRODUCTION. XXV11

2. Electric Surface Density and Electric Displacement. — The density
of an electric distribution at any point on a surface is measured by the quantity
per unit of area, and the electric displacement at any point in a dielectric is mea-
sured by the quantity displaced per unit of area. These quantities have therefore
the same dimensional formula, namely, the ratio of the formulae for quantity of
electricity and for area or MiL~JT~1K4, and the conversion factor »/-/~-/~U'5.

3. Electric Force at a Point, or Intensity of Electric Field. — This is
measured by the ratio of the magnitude of the force on a quantity of electricity at
a point to the magnitude of the quantity of electricity. The dimensional formula
is therefore the ratio of the formulae for force and electric quantity, or

''

which gives the conversion factor //r/"5/"1^"*.

4. Electric Potential and Electromotive Force. — Change of potential
is proportional to the work done per unit of electricity in producing the change.
The dimensional formula is therefore the ratio of the formulae for work and elec-
tric quantity, or

M L'21 - M1J jrj^j— J

M'UT-'K* ~
which gives the conversion factor m*Pf~lk~-.

5. Capacity of a Conductor. — The capacity of an insulated conductor is
proportional to the ratio of the numbers representing the quantity of electricity in
a charge and the potential of the charge. The dimensional formula is thus the
ratio of the two formulae for electric quantity and potential, or

_ T v
'-'-' ~

which gives tk for conversion factor. When K is taken as unity, as in the ordinary
units, the capacity of an insulated conductor is simply a length.

6. Specific Inductive Capacity. — This is the ratio of the inductive cap?c-
ity of the substance to that of a standard substance, and hence the dimensional
formula is K/K or i.*

7. Electric Current. — Current is quantity flowing past a point per unit of
time. The dimensional formula is thus the ratio of the formulae for electric quan-
tity and for time, or

and the conversion factor m*l*t~zk*.

* According to the 'ordinary definition referred to air as standard medium, the specific inductive
capacity of a substance is K, or is identical in dimensions with what is here taken as inductive ca-
pacity. Hence in that case the conversion factor must be taken as I on the electrostatic and as
/"V2 on the electromagnetic system.

XXV111 INTRODUCTION.

8. Conductivity, or Specific* Conductance. — This, like the corresponding
term for heat, is quantity per unit area per unit potential gradient per unit of time.
The dimensional formula is therefore

__ y-iK or _ electric quantity

•,., area X potential gradient X time

The conversion factor is t~lk.

9. Specific* Resistance. — This is the reciprocal of conductivity as above
defined, and hence the dimensional formula and conversion factor are respec-
tively TK"1 and tk~l.

10. Conductance. — The conductance of any part of an electric circuit, not
containing a source of electromotive force, is the ratio of the numbers represent-
ing the current flowing through it and the difference of potential between its ends.
The dimensional formula is thus the ratio of the formulae for current and poten-
tial, or

from which we get the conversion factor lt~lk.

1 1 . Resistance. — This is the reciprocal of conductance, and therefore the
dimensional formula and the conversion factor are respectively L/^TKT1 and

EXAMPLES OF CONVERSION IN ELECTROSTATIC UNITS.

(a) Find the factor for converting quantity of electricity expressed in foot grain
second units to the same expressed in c. g. s. units.

By (i) the formula is m*flt~lfc, in which in this case ;// = 0.0648, /== 30.48, / =
i, and k= \ ; .'. the factor is o.o6485 X 30.48* = 4.2836.

(b) Find the factor required to convert electric potential from millimetre milli-
gramme second units to c. g. s. units.

By (4) the formula is ///W"1^"-, and in this case m — o.ooi, /= o. :, /= i, and
k-=.\\ .'. the factor =»o.ooii X o. i5 = o. 01.

(e) Find the factor required to convert from foot grain second and specific in-
ductive capacity 6 units to c. g. s. units.

By (5) the formula is Ik, and in this case /— 30.48 and k = 6 • .*. the factor
= 30.48 X 6= 182.88.

* The term "specific.," as used here and in 9. refers conductance and resistance to that between
the ends of a bar of unit section and unit length, and hence is different from the same term in
specific heat, specific inductivity, capacity, etc., which refer to a standard substance.

INTRODUCTION. XXIX

ELECTROMAGNETIC UNITS.

As stated above, these units bear the same relation to unit quantity of magne-
tism that the electric units do to quantity of electricity. Thus, when inductive
capacity is suppressed, the dimensional formula for magnetic quantity on this sys-
tem is the same as that for electric quantity on the electrostatic system. All quan-
tities in this system which only differ from corresponding quantities defined above
by the substitution of magnetic for electric quantity may have their dimensional
formulae derived from those of the corresponding quantity by substituting P
for K.

i. Magnetic Pole, or Quantity of Magnetism. — Two unit quantities of
magnetism concentrated at points unit distance apart repel each other with unit
force. The dimensional formula is thus the same as for [force X length2 X in-
ductive capacity] or M^IJT"1?-, and the conversion factor is

2. Density of Surface Distribution of Magnetism. — This is measured
by quantity of magnetism per unit area, and the dimension formula is therefore
the ratio of the expressions for magnetic quantity and for area, or MiL~JT~1Pi,
which gives the conversion factor

3. Magnetic Force at a Point, or Intensity of Magnetic Field. — The
number for this is the ratio of the numbers representing the magnitudes of the
force on a magnetic pole placed at the point and the magnitude of the magnetic
pole.

The dimensional formula is therefore the ratio of the expressions for force and
magnetic quantity, or

and the conversion factor m^l~^t~lp~^.

4. Magnetic Potential. — The magnetic potential at a point is measured by
the work which is required to bring unit quantity of positive magnetism from zero
potential to the point. The dimensional formula is thus the ratio of the formula
for work and magnetic quantity, or

1UT 2^-2

— M4LJT

which gives the conversion factor

5. Magnetic Moment. — This is the product of the numbers for pole
strength and length of a magnet. The dimensional formula is therefore the pro-
duct of the formulae for magnetic quantity and length, or M^UT"1?', and the con-
version factor nfil*-t~lp1-.

6. Intensity of Magnetization. — The intensity of magnetization of any por-
tion of a magnetized body is the ratio of the numbers representing the magni-

XXX INTRODUCTION.

tude of the magnetic moment of that portion and its volume. The dimensional
formula is therefore the ratio of the formula; for magnetic moment and volume, or

L8
The conversion factor is therefore i

7. Magnetic Permeability,* or Specific Magnetic Inductive Capacity.
— This is the analogue in magnetism to specific inductive capacity in electricity.
It is the ratio of the magnetic induction in the substance to the magnetic induc-
tion in the field which produces the magnetization, and therefore its dimensional
formula and conversion factor are unity.

8. Magnetic Susceptibility. — This is the ratio of the numbers which repre-
sent the values of the intensity of magnetization produced and the intensity of the
magnetic field producing it. The dimensional formula is therefore the ratio of
the formulae for intensity of magnetization and magnetic field or

or P.

The conversion factor is therefore/, and both the dimensional formula and con-
version factor are unity in the ordinary system.

9. Current Strength. — A current of strength c flowing round a circle of
radius r produces a magnetic field at the centre of intensity 2-^cjr. The dimen-
sional formula is therefore the product of the formulae for magnetic field intensity
and length, or M-L-T-1P~-, which gives the conversion factor m*l't~lp~*.

10. Current Density, or Strength of Current at a Point. — This is the
ratio of the numbers for current strength and area. The dimensional formula
and the conversion factor are therefore M*JLr*T~1P~~l and

11. Quantity of Electricity. — This is the product of the numbers for cur-
rent and time. The dimensional formula is therefore M^L-T"1?"5 X T= M-L*P~^
and the conversion factor w1/4/"*.

12. Electric Potential, or Electromotive Force. — As in the electrostatic
system, this is the ratio of the numbers for work and quantity of electricity. The
dimensional formula is therefore

ML2T~2
M*L»P-»

and the conversion factor

* Permeability, as ordinarily taken with the standard medium as unity, has the same dimension
formula and conversion factor as that which is here taken as magnetic inductive capacity. Hence
for ordinary transformations the conversion factor should be taken as i in the electromagnetic and
in the electrostatic systems.

INTRODUCTION. XXXI

13. Electrostatic Capacity. — This is the ratio of the numbers for quantity
of electricity and difference of potential. The dimensional formula is therefore

± — I/-*!??-1.

s i c— '' ni —

and the conversion factor / V2/"1.

14. Resistance of a Conductor. — The resistance of a conductor or elec-
trode is the ratio of the numbers for difference of potential between its ends and
the constant current it is capable of producing. The dimensional formula is
therefore the ratio of those for potential and current or

= LT-aP.

The conversion factor thus becomes //"*/, and in the ordinary system resistance
has the same conversion factor as velocity.

15. Conductance. — This is the reciprocal of resistance, and hence the dimen-
sional formula and conversion factor are respectively L^TP"1 and l~ltp~l.

16. Conductivity, or Specific Conductance. — This is quantity of electric-
ity transmitted per unit of area per unit of potential gradient per unit of time.
The dimensional formula is therefore derived from those of the quantities men-
tioned as follows : —

L

The conversion factor is therefore l~'ltp~\

17. Specific Resistance. — This is the reciprocal of conductivity as defined
in 15, and hence the dimensional formula and conversion factor are respectively
L2T-'P and Prlp.

18. Coefficient of Self-induction, or Inductance, or Electro-kinetic In-
ertia. — These are for any circuit the electromotive force produced in it by unit
rate of variation of the current through it. The dimensional formula is therefore
the product of the formulae for electromotive force and time divided by that for
current or

,, _ X T = LP.

The conversion factor is therefore Ip, and in the ordinary system is the same as
that for length.

19. Coefficient of Mutual Induction. — The mutual induction of two cir-
cuits is the electromotive force produced in one per unit rate of variation of the
current in the other. The dimensional formula and the conversion factor are
therefore the same as those for self-induction.

XXxii INTRODUCTION.

20. Electro-kinetic Momentum. — The number for this is the product of
the numbers for current and for electro-kinetic inertia. The dimensional formula
is therefore the product of the formulae for these quantities, or M^UT"1?^ X LP
= MJL!T-1PJ, and the conversion factor is w5/1/"1/-.

21. Electromotive Force at a Point. — The number for this quantity is
the ratio of the numbers for electric potential or electromotive force as given in
12, and for length. The dimensional formula is therefore M^UT"2?*, and the
conversion factor wW~^J.

22. Vector Potential. — This is time integral of electromotive force at a
point, or the electro-kinetic momentum at a point. The dimensional formula
may therefore be derived from 21 by multiplying by T, or from 20 by dividing
by L. It is therefore M^T"1?*, and the conversion factor m*fit~lfi.

23. Thermoelectric Height. — This is measured by the ratio of the num-
bers for electromotive force and for temperature. The dimensional formula is
therefore the ratio of the formulae for these two quantities, or M-lJT"2?4®""1, and
the conversion factor *&flf~*jP$~l.

24. Specific Heat of Electricity. — This quantity is measured in the same^
way as 23, and hence has the same formulae.

25. Coefficient of Peltier Effect. — This is measured by the ratio of the
numbers for quantity of heat and for quantity of electricity. The dimensional
formula is therefore

and the conversion factor

EXAMPLES OF CONVERSION IN ELECTROMAGNETIC UNITS.

(a) Find the factor required to convert intensity of magnetic field from foot
grain minute units to c. g. s. units.

By (3) the formula is m^l~^~l/>~\ and in this case m = 0.0648, /= 30.48, / =
60, and/ = i ; .'. the factors = 0.0648* X 30.48^ X 6o~l = 0.00076847.

Similarly to convert from foot grain second units to c. g. s. units the factor is
0.0648- X 30-48"-' = 0.046 108.

(£) How many c. g. s. units of magnetic moment make one foot grain second
unit of the same quantity ?

By (5) the formula is 7/r/*/"1/*, and the values for this problem are m — 0.0648,
/ = 30.48, / = i, and/ = i ; .'. the number = 0.0648* X $o-4&* = i3°5-6-

(f) If the intensity of magnetization of a steel bar be 700 in c. g. s. units, what
will it be in millimetre milligramme second units ?

INTRODUCTION. XXX111

By (6) the formula is wV*/"1/4, and in this case m = 1000, /= 10, /= i, and
p = i • .*. the intensity = 700 X 1000- X i°- = 70000.

(//) Find the factor required to convert current strength from c. g. s. units to
earth quadrant io~n gramme and second units.

By (9) the formula is wV5/"1/"4, and the values of these quantities are here m =
ion, /= io~9, /—i, and/ = i ; .'. the factor = io*i X io~§= 10.

(<?) Find the factor required to convert resistance expressed in c. g. s. units into
the same expressed in earth-quadrant io~u grammes and second units.

By (14) the formula is lt~lp, and for this case /= io~9, /= i, and / = i ;
.'. the factor = io~9.

(/) Find the factor required to convert electromotive force from earth-quadrant
io~n gramme and second units to c. g. s. units.

By (12) the formula is #zV§/~^% and for this case m = io~n, /= io9, t= i,
and/ — i ; .'. the factor = io8.

PRACTICAL UNITS.

In practical electrical measurements the units adopted are either multiples or
submultiples of the units founded on the centimetre, the gramme, and the second
as fundamental units, and air is taken as the standard medium, for which K and P
are assumed unity. The following, quoted from the report to the Honorable the
Secretary of State, under date of November 6th, 1893, by the delegates repre-
senting the United States, gives the ordinary units with their names and values
as defined by the International Congress at Chicago in 1893 : —

" Resolved, That the several governments represented by the delegates of this
International Congress of Electricians be, and they are hereby, recommended to
formally adopt as legal units of electrical measure the following : As a unit of re-
sistance, the international ohm, which is based upon the ohm equal to io9 units of
resistance of the C. G. S. system of electro-magnetic units, and is represented
by the resistance offered to an unvarying electric current by a column of mercury
at the temperature of melting ice 14.4521 grammes in mass, of a constant cross-
sectional area and of the length of 106.3 centimetres.

" As a unit of 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 accom-
panying specifications,* deposits silver at the rate of 0.001118 of a gramme per
second.

* " In the following specification the term ' silver voltameter ' means the arrangement of appara-
tus by means of which an electric current is passed through a solution of nitrate of silver in water.
The silver voltameter measures the total electrical quantity which has passed during the time of
the experiment, and by noting this time the time average of the current, or, if the current has been
kept constant, the current itself can be deduced.

" In employing the silver voltameter to measure currents of about one ampere, the following
arrangements should be adopted : —

XXXIV INTRODUCTION.

" As a unit of electromotive force, the international -volt, which is the electro-
motive force that, steadily applied to a conductor whose resistance is one interna-
tional ohm, will produce a current of one international ampere, and which is rep-
resented sufficiently well for practical use by ISSf °f tne electromotive force
between the poles or electrodes of the voltaic cell known as Clark's cell, at a tem-
perature of 15° C., and prepared in the manner described in the accompanying
specification.*

" As a unit of quantity, the international coulomb, which is the quantity of elec-
tricity transferred by a current of one international ampere in one second.

"As a unit of capacity, the international farad, which is the capacity of a con-
denser charged to a potential of one international volt by one international cou-
lomb of electricity. t

" As a unit of work, the joule, which is equal to io7 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.

" As a unit of power, the watt, which is equal to io7 units of power in the c. g. s.
system, and which is represented sufficiently well for practical use by the work
done at the rate of one joule per second.

" As the unit of induction, the henry, which is the induction in a circuit when
the electromotive force induced in this circuit is one international volt, while the
inducing current varies at the rate of one ampere per second.

"The Chamber also voted that it was not wise to adopt or recommend a stand-
ard of light at the present time."

By an Act of Congress approved July i2th, 1894, the units recommended by
the Chicago Congress were adopted in this country with only some unimportant
verbal changes in the definitions.

By an Order in Council of date August 23d, 1894, the British Board of Trade
adopted the ohm, the ampere, and the volt, substantially as recommended by
the Chicago Congress. The other units were not legalized in Great Britain.
They are, however, in general use in that country and all over the world.

"The kathode on which the silver is to be deposited should take the form of a platinum bowl
not less than io centimetres in diameter and from 4 to 5 centimetres in depth.

"The anode should be a plate of pure silver some 30 square centimetres in area and 2 or 3,
millimetres in thickness.

" This is supported horizontally in the liquid near the top of the solution by a platinum wire
passed through holes in the plate at opposite corners. To prevent the disintegrated silver which
is formed on the anode from falling on to the kathode, the anode should be wrapped round with
pure filter paper, secured at the back with sealing wax.

"The liquid should consist of a neutral solution of pure silver nitrate, containing about 15 parts
by weight of the nitrate to 85 parts of water.

" The resistance of the voltameter changes somewhat as the current passes. To prevent these
changes having too great an efftct on the current, some resistance besides that of the voltameter
should be inserted in the circuit. The total metallic resistance of the circuit should not be less
than io ohms."

* " A committee, consisting of Messrs. Helmholtz, Ayrton, and Carhart, was appointed to pre-
pare specifications for the Clark's cell. Their report has not yet been received."

•f The one millionth part of the farad is more commonly used in practical measurements, and is
called the microfarad.

PHYSICAL TABLES

TABLE 1 .

FUNDAMENTAL AND DERIVED UNITS.

(a) FUNDAMENTAL UNITS.

Name of Unit.

Symbol.

Conversion Factor.

Length.
Mass.

L
M

/
m

Time.

T

t

Temperature.
Electric Inductive Capacity.
Magnetic Inductive Capacity.

(H)

K
P

6
k
/

(fr) DERIVED UNITS.

/. Geometric

and Dynamic Units.

Name of Unit.

Conversion Factor.

Area.
Volume.

: , /2
/8

Angle.
Solid Angle.
Curvature.

\

I

I
/-1

Tortuosity.
Specific curvature of a surface.
Angular velocity.
Angular acceleration.
Linear velocity.
Linear acceleration.

l~l

!-*

r1
/r2
irl
ir'2

Density.
Moment of inertia.

m /-»

mr

Intensity of attraction, or " force at a point."
Absolute force of a centre of attraction, or " strength \
of a centre." )
Momentum.

/r2
/8/-2

m I r1

Moment of momentum, or angular momentum.
Force.

m r2 r1

m / r2

Moment of a couple, or torque.
Intensity of stress.
Modulus of elasticity.
Work and energy.
Resilience.

m /2 r2
m l~l r'2
m 1-* t -
m /2 ra
mf-lt '2

Power or activity.

m r2 r3

SMITHSONIAN TABLES.

FUNDAMENTAL AND DERIVED UNITS.

TABLE 1

//. Heat Units.

Name of Unit.

Conversion Factor.

Quantity of heat (thermal units).

" " (thermometric units).

" " (dynamical units).

Coefficient of thermal expansion.
Conductivity (thermal units).

" (thermometric units), or diffusivity,

" (dynamical units).

Emissivity and imissivity (thermal units).

" " (thermometric units).

" " (dynamical units).

Thermal capacity.
Latent heat (thermal units).

" " (dynamical units).
Joule's equivalent.

Entropy (heat measured in thermal units).
" ( " " dynamical units).

m l~l r1

m /r3 b~l
m /~2 t~l

6~l

m
m

e

I2
m

r r2 e-1

///. Magnetic and Electric Units.

Name of Unit.

Conversion factor
for electrostatic
system.

Conversion factor
for electromag-
netic system.

Magnetic pole, or quantity of mag- )

netism. >

Density of surface distribution of (^

magnetism. j

Intensity of magnetic field.
Magnetic potential.
Magnetic moment.
Intensity of magnetisation.
Magnetic permeability.
Magnetic susceptibility and mag-)

netic inductive capacity. |

Quantity of electricity.
Electric surface density and electric )

displacement. )

Intensity of electric field.
Electric potential and e. m. f.
Capacity of a condenser.
Inductive capacity.
Specific inductive capacity.
Electric current.

I* r2 #

?*/*

w* /-» r1
m* /» r1 K
ik
k

SMITHSONIAN TABLES.

TABLE 1 .

FUNDAMENTAL AND DERIVED UNITS.

///. Magnetic and Electric Units.

Conversion factor

Conversion factor

Name of Unit.

for electrostatic

for electromag-

system.

netic system.

Conductivity.

f—\ fa

/-//->

Specific resistance.

t k~l

/a t~l p

Conductance.

I t~l k

l~l t p~l

Resistance.

/-> tk~l

I t~l p

Coefficient of self induction and )
coefficient of mutual induction. j

l~l /2 k~l

IP

Electrokinetic momentum.

td> /J k~*

m^ /» t~l p^

Electromotive force at a point.

JI 1 . I 7 1
t t k

nr> /5 /~2/}

Vector potential.

m- t~* k~^

WJ /'' t~l'jffr

Thermoelectric height and specific )

i /5 /-I /,-! fi-l

j ., 2 j . j

heat of electricity. )

m

m / / /

Coefficient of Peltier effect.

nt r* t fc+ 0

•w*

SMITHSONIAN TABLES.

TABLE 2.

EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS
AND MEASURES.*

(I) METRIC TO IMPERIAL

LINEAR MEASURE.

MEASURE OF CAPACITY.

i millimetre (mm.) I 0.03937 in.
(.001 m.) )

I millilitre (ml.) (.001 J i •
«• , / = 0.00103 cub. in.

i centimetre (.01 m.) = 0.39371 "
i decimetre (.1 m.) = 3-93708 "

i centilitre (.01 litre) = ? ~ 070., -n

(39-37079 "

I METRE (m.) . . = < 3.28089917 ft.

( i-093633°6yds-

(

i decilitre (.1 litre) . . = 0.17608 pint,
i LITRE (1,000 cub. )

1 ^oTiT6 1 ' ' = I0'936;53 "

centimetres or i > = 1.76077 pints,
cub. decimetre) )

i hectometre J ,<

i dekalitre (10 litres) . --= 2.20097 gallons.

(100 m.) | -' ' ~

; i hectolitre (100 " ) .= 2.75121 bushels.

i kilometre i = 0.62138 mUe.

i kilolitre (i,ooo " ) .= 3.43901 quarters.

i myriametre / x «,,»o~ M
\ t . . = 0.21302 miles.
(10,000 m.) )

i microlitre . . . . = o.ooi ml.

i micron . . . .= o.ooi mm.

APOTHECARIES' MEASURE.

i cubic centi- ) C 0.03527 fluid ounce,
metre ('i— ^ 0.28219 fluid drachm,
gramme w't) ) f I5-43235 grains weight.

SQUARE MEASURE.

i cub. millimetre = 0.01693 minim.

i sq. centimetre . . = 0.15501 sq. in.

AVOIRDUPOIS WEIGHT.

i sq. decimetre 1 .
(100 sq. centm.) ) -* •> Dy

i milligramme (mgr.) . = 0.01543 grain.

i sq. metre or centi- / ) 10.76430 sq. ft.
are (loosq. dcm.) J J 1.19603 sq. yd.

i centigramme (.01 gram )= 0.15432 "
i decigramme (.1 " )= 1.54324 grains.

i ARE (100 sq. m.) = 119.60333 sq. yds.

I GRAMME — IS-43235 "

i hectare (100 ares )
or 10,000 sq. m.) \ = 2-47"5 acres.

I dekagramme (logram.) = 5.64383 drams,
i hectogramme ( i oo " ) = 3.5273907.

( 2.20462125 Ib.

I KILOGRAMME (l,000" ) = < 15432.34874

( grains.

CUBIC MEASURE.

i myriagramme(iokilog.)= 22.04621 Ib.

i quintal (loo " )= 1.96841 cwt.

i cub. centimetre )

I millier or tonne I __ 0.^420591 ton.

(c.c.) (1,000 cubic £ = 0.06103 cub. in.

millimetres) )

i cub. decimetre )

TROY WEIGHT.

(c.d.) ( i, ooo cubic > = 61.02705 " "

centimetres) ;

( 0.03215073 oz. Troy.

I CUB. METRE ) j 35.31658074 Cub. ft.

I GRAMME . . = 1 0.64301 pennyweight.

f ' 5-43235 grains.

APOTHECARIES' WEIGHT.

! 0.25721 drachm.

o 77162 scruple.

i S-43235 grains.

NOTE. — The METRE is the length, at the temperature of o° C., of the platinum-indium bar deposited with the
Board of Trade.

The present legal equivalent of the metre is 39'37079 inches, as above stated. If a brass metre is, however,
compared, not at its legal temperature (o° C. or 32° F^), but at the temperature of 62° F., with a brass yard at the
temperature also of 62° F., then the apparent equivalent of the metre would be nearly 39 '382 inches.

The KILOGRAMME is the weight in vacuo at o° C. of the platinum-indium weight deposited with the Board of

T^^Ja

Trade

e.

The LITRE contains one kilogramme weight of distilled water at its maximum density (4° C.), the barometer being
at 760 millimetres.

* Quoted from sheets issued in 1890 by the Standard Office of the British Board of Trade.
SMITHSONIAN TABLES.

TABLE 2.

EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS
AND MEASURES.

(2) METRIC TO IMPERIAL

LINEAR MEASURE.

MEASURE OF CAPACITY.

I

2

3
;4

Is

\6

8
9

Millimetres
to
inches.

Metres
to
feet.

Metres
to
yards.

Kilo-
! metres to
miles.

Litres
to
pints.

Dekalitres
to
gallons.

Hectolitres
to
bushels.

Kilolitres
to
quarters.

0-03937079
0.07874158
0.11811237
O.I57483I6
6.19685395

0.23622474

0.27559553
0.31496632

0-354337"

3.28090
6.56180
9.84270
13.12360
16.40450

19.68540
22.96629
26.24719
29.52809

1.09363
2.18727
3.28090

4-37453
5-46817

6.56180

7-65543
8.74906
9.84270

0.62138
1.24276
1.86415

248553
3.10691

3.72829 ;
4.34968
4.97106

5-59244 !

I

2

3

! 4
5
6

8
9

1.76077

3-52I54
5.28231
7.04308
8.80385

10.56462

12.32539
14.08616
15.84693

2.20097
4.40193
6.60290
8.80386
11.00483

13.20580
1 5.40676
17.60773
19.80870

2.75121
5.50242
8.25362
11.00483

1 3-7 5604

16.50725
19.25846
22.00966
24.76087

3-43901
6.87802
10.31703
13.75604
I7-I9505

20.63406
24.07307
27.51208
30.95110

SQUARE MEASURE.

WEIGHT (AVOIRDUPOIS).

I

2

' 3
4

: s

6

8
! 9

Square
centimetres

Square
metres to

Square
metres to

Hectares

Milli-
grammes
to
grains.

Kilogrammes
to grains.

Kilo-
grammes
to
pounds.

Quintals
to
hundred-
weights.

inches.

feet.

yards.

0.15501
0.31001
0.46502
0.62002
0-77503

0.93004
1.08504
1.24005

1 -39 505

10.76430
21.52860
32.29290
43.05720
53-82I50

64.58580
75-35010
86.11439
96.87869

1.19603
2.39207
3.58810
4.78413
5.98017

7.17620
8.37223
9.56827
10.76430

2.47114 I
4.94229
7-4I343
9.88457

12.35572

14.82686
17.29800
19.76914
22.24029

I

2

3
4
5
6

8
9

0.01543
0.03086
0.04630
0.06173
0.07716

0.09259

o. 1 0803

0.12346
0.13889

15432.34874
30864.69748
46297.04622
61729.39496
77161.74370

92594.09244
108026.44118
123458.78992
138891.13866

2.20462
4.40924
6.61386
8.81849
II.O23H

I3-22773
I5-43235
17.63697
19.84159

1.96841
3.93682

5-90523
7.87364
9.84206

11.81047
13.77888

I5-74729
17.71570

CUBIC

MEASURE.

APOTHB-
CARIKS' ;
MEASURE.

AVOIRDUPOIS
(cont.)

TROY WEIGHT.

APOTHE-
CARIES'
WEIGHT.

Cubic
decimetres
to cubic
inches.

Cubic
metres to
cubic
feet.

Cubic
metres to
cubic
yards.

Cub. cen-
timetres
to fluid
drachms.

\
2

3
4
5
6

8
9

Milliers or
tonnes to
tons.

Grammes
to ounces
Troy.

Grammes
to penny-
weights.

Grammes
to

scruples.

1

2

3
4
.5
6

J

9

61.02705
122.05410
183.08115
244.10821
305- I 3526

366.16231
427.18936
488.21641
549.24346

35-3I658
70.63316
105.94974
141.26632
176.58290

211.89948
247.21607
282.53265
317.84923

1.30802
2.61604
3.92406
5.23209
6.54011

7.84813

9- 1561 5
10.46417
11.77219

0.28219
0.56438
0.84657 i
1.12877 I
1.41096 !

I-693I5

1-97534
2-25753
2-53972

0.98421
1.96841
2.95262
3.93682
4.92103

5-90524
6.88944

7.87365
8.85785

0.032 1 5

0.06430
0.09645
0.12860
0.16075

0.19290
0.22506
0.25721
0.28936

0.64301
1.28603
1.92904
2.57206
3.21507

3.85809
4.50110
5.14412
S-787I3

0.77162

I-54323
2.31485
3.08647
3.85809

4.62970
5.40131
6.17294
6-94455

SMITHSONIAN TABLES.

TABLE 2.

EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS
AND MEASURES.

(3) IMPERIAL TO METRIC.

LINEAR MEASURE.

MEASURE OF CAPACITY.

, ( 25.39954113 milli-

gill — 1.41983 decilitres.

pint (k gills) . J . . = 9.56793 litre.

i inch ..... ^ metres.

i foot ((2 in.) . . = 0.30479449 metre.

quart j( 2 pints)' . . = ^.13586 litres.

i YARD (3 ft.) . L= 0.91438348 "

GALLON (4 quarts) = 4-54345797 "

i pole (5! yd.) . . = 5.02911 metres.

peck (2 galls.) . . = 9.08692 "

i chain (22 yd. or )
100 links) \= 2°'Il644

bushel (8 galls.) . = 3.63477 dekalitres,
quarter (8 bushels) = 2.90781 hectolitres.

i furlong (220 yd.) — 201.16437 "

1 :

.,,,,, ( 1.60931493 kilo-
i mile (1,760 yd.) . = metres.

AVOIRDUPOIS WEIGHT.

SQUARE MEASURE.

• I 64.79895036 milli-

- , { 6.41:137 sq. cen-
i square inch . . = j *&£„£.

t. i \ 9.28997 sq. deci- !
I sq.ft. (I44sq..n.) = j V m^/es.

( grammes,
dram — i 77185 grammes.

ounce (16 dr.) . . = 28.34954 "
POUND (16 oz or » = 0.4535926s kil
7,000 grains) J

I SQ. YARD (9 Sq. ft.) = j °' metre';1"' SC*'

stone ( 14 Ib.) . . =: 6.35030

i perch (30* sq. yd.) = j '5- Wsq. me-

i rood (40 perches) — i 10.11678 ares,
i ACRE (4840 sq. yd.) = 0.40467 hectare.

quarter (28 Ib.) .= 12.70059
hundredweight t j 50.80238 "
(ii2lb.) 1) ~( 0.50802 quintal.
iton(2ocwt.) .' .= J 1-01604754 millier
j or tonne.

i sq. mile (640 acres) = \2^^^12 heC"

••-I i i ;

TROY WEIGHT.

CUBIC MEASURE.

, :-- - i !

i cub. inch= 16.38617589 cub. centimetres.

, , / 01 i 0.02832 cub. metre,
. cub. foot ( 1728 } \ *i b

cub-'"-) f \ decimetres.

grains avoir-l ° \ = 3I-IO35° grammes,
i penny weight .( |4 ( _ ,
grains) j

i CUB. YARD (27 I —07641:1342 cub. metre.

NOTE, -j- The Troy grain is of the same weight as

cub. ft.) J

the Avoirdupois grain.

,', j .., .. |

1 ...

APOTHECARIES' MEASURE.

i :

APOTHEC'ARIES' WEIGHT.

i gallon (8 pints ;or j . fi ..
1 60 fluid ounces) } ~ 4-5434O
I fluid ounce, f 3 i j 28.39661 cubic
(8 drachms) ) ~ \ '. centimetres.

! ' i

i ounce (8 drachms) = 31.10350 grammes,
i drachii, 3 i ( 3 scfu- j cc
pies) J^ 3-86794

i fluid drachm, f 3 1 j 3-5495^ cubic

pie. y ^ j

(60 minims) \ \ centimetres.

i scrupje, 91 (20 / __ 'jQcnR "
crrains) \

i minim, ni (0.91146 i _ \ 0.05916 cubic

grain weight) | • . } centimetres.

NOTE. — The Apothecaries' ounce is of the same

weight as the Troy ounce. The Apothecaries'

NOTE. — The Apothecaries' gallon is of the same

jrrain is also of the' same weight as the Avoirdupois

capacity as the Imperial gallon.

grain.

NOTE. — The YARD is the length at 62° 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 <he Board of Trade.

The GALLON contains 10 Ib. weight of distilled water at the temperature of 62° Fahr., the barometer being at
30 inches. The weight of a cubic inch of water is 252.286 grains.

SMITHSONIAN TABLES.

TABLE 2.

EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS
AND MEASURES.

(4) IMPERIAL TO METRIC.

r

LINEAR MEASURE.

MEASURE OF CAPACITY.

Inches
to
millimetres.

Feet
to
metres.

Yards
to
metres.

Miles
to kilo-
metres.

Quarts
to
litres.

Gallons
to
litres.

Bushels
to
dekalitres.

Quarters
to
hectolitres.

I

2

3

4
5
6

8
9

25-39954II3
50.79908226
76.19862340
101.59816453
126.99770566

I52-39724679
177.79678792
203.19632906
228.59587019

0.30479
0.60959
0.91438
1.21918
1 -52397
1.82876
2-I3356
2-43835

2-743I5

0.91438
1.82877

2-743'S
3.65753
4-57I92

5-48630
6.40068

7 -3 r 5°7
8.22945

1.60931
3.21863
4.82794
6.43726
8.04657

9-65589
11.26520
12.87452
14.48383

I

2

3
4
5
6

8
9

1.13586
2.27173
3-40759
4-54346
5-67932
6.81519

7-95'°5
9.08692
10.22278

4-54346
9.08692

I3-63037
18.17383
22.71729

27.26075
31.80421
36.34766
40.89112

3-63477
7-26953
10.90430
I4-53907
18.17383

21.80860

25-44336
29.07813
32-7I290

2.90781

5-8I563
8.72344
11.63125
I4-53907

17.44688
20.35469
23.26250
26.17032

SQUARE MEASURE.

WEIGHT (AVOIRDUPOIS).

Square
inches
to square
centimetres.

Square
feet
to square
decimetres.

Square
yards to
square
metres.

Acres to
hectares.

Grains to
milligrammes.

Ounces to
grammes.

Pounds Hundred-
tp kilo- weights to
grammes, quintals.

I

3
4
5
6

7
8

9

6-45I37
12.90273
19.35410
25.80547
32-25683

38.70820

45- ! 5957
51.61094
58.06230

9.28997

18.57994
27.86990

37-I5987
46.44984

55-7398I
65.02978

74-3 ! 974
83.60971

0.83610
1.67219
2.50829

3-34439
4.18049

5.01658
5.85268
6.68878
7-52487

0.40467
0.80934
1.21401
1. 61868
2.02336

2.42803
2.83270

3-23737
3-64204

I

3

4
5
6

8
9

64- 79895036
129.59790072
194.39685109
259.19580145

323-99475l8'
388.79370218
453-59265255
518.39160291
583-I9055327

28.34954
56.69908
85.04862
113.39816
141.74770

170.09724
198.44679
226.79633
255-I4587

0.45359 0.50802
0.90719 1.01605
1.36078 1.52407
1.81437 2.03209
2.26796 2.54012

2.72156 3.04814

3-I75,l5 3-556I7
3.62874 4.06419
4.08233 4.57221

CUBIC MEASURE.

APOTHE-
CARIES'
MEASURE.

AVOIRDUPOIS
(cont.).

TROY WEIGHT.

APOTHE-
CARIES'

WEIGHT.

Cubic
inches
to cubic
centimetres.

Cubic feet
to
cubic
metres.

Cubic
yards
to cubic
metres.

Fluid
drachms
to cubic
centi-
metres.

Tons to
milliers or
tonnes.

Ounces to
grammes.

Penny-
weights to
grammes.

Scruples
to
grammes.

I

2

3
4
5
6

8
9

16.38618

32-77235

49- ! S8 53
65-54470
81.93088

98.31706

"4-70323
I3[.o8o4i

I47-47558

0.02832
0.05663
0.08495
0.11326
0.14158

0.16989
0.19821
0.22652
0.25484

0.76451
1.52903
2.29354
3.05805
3.82257

4.58708

5-35I59
6.1l6ll

6.88062

3-54958
7.09915
10.64873
14.19831
17.74788

21.29746
24.84704
28.39661
31.94619

I

2

3
4
5
6

8
9

1.01605
2.03210
304814
4.06419
5.08024

6.09629

7-II233
8.12838

9- '4443

31.10350
62.20699

93- 3 '049
124.41398

i55-5I748

186.62098
217.72447
248.82797
279-93 '47

I-555I7

3-''035
4.66552
6.22070
7-77587

9-33 ' °5
10.88622
12.44140
13-99657

1.29598
2.59196
3.88794
5.18391
6.47989

777587
9.07185
10.36783
11.66381

SMITHSONIAN TABLES.

TABLE 3.
TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES."

(I) CUSTOMARY TO METRIC.

LINEAR.

CAPACITY.

Inches
to

Feet to

Yards to

Miles

Fluid
drams to

Fluid
ounces

Quarts to

Gallons to

millimetres.

metres.

metres.

kilometres.

or cubic

to

litres.

litres.

centimetres.

I

25.4001

0.304801 ;

0.914402

1-60935

I

3-70

29-57

0.94636

3-78543

2

50.8001

0.609601 1.828804

3.21869 i

2

7-39

59-15

1.89272

7.57087

3

76.2002

0.914402 , 2.743205

4.82804

3

11.09

88.72

2.83908

11.35630

4

IOI.6OO2

I.2I92O2 ; 3.657607

6-43739

4

14.79

Il8.29

3-78543

15.14174

5

127.0003

1.524003 4-572009

8.04674 i

5

18.48

147.87

4-73E79

18.92717

6

152.4003

1.828804 5.486411

9.65608 I

6

22.18

177-44

S-M' 5

22.71261

8

177.3004
203.2004

2.133604 6.400813

2-43^405 7-3 '52 1 5

11.26543 ;
12.87478

8

25.88
29-57

2O7.O2
236.59

6.62451
7.57087

26.49804
30.28348

9

228.6005

2.743205 8.229616

14.48412

9

33-27

266.16

8-51723

34.06891

SQUARE.

WEIGHT.

Square
inches to
square cen-
timetres.

Square feet
to square
decimetres.

Square
yards to
square
metres.

Acres to
hectares.

Grains to
milli-
grammes.

Avoirdu-
pois ounces
to
grammes.

Avoirdu-
pois pounds
to kilo-
grammes.

Troy
ounces to
grammes.

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

0.90719

62.20696

3

!9-355

27.871

2.508

1.2141 ,

3

194.3968

85.0486

1.36078

93-3I044

4

25.807

37- 161

3-344

1.6187

4

259-I957

113.3981

1.81437

124.41392

5

32.258

46.452

4.181

2.0234 ,

5

323-9946

141.7476

2.26796

I55.5I740

6

38.710

55-742

5-oi7

2.4281

6

388.7935

170.0972

2.7-2156

186.62088

7

45.161

65.032

5.853

2.8328

7

453-5924

198.4467

3-I75'5

217-72437

8

51.613

74-323

6.689

3-2375

8

5l8-39I4

226.7962

3-62874

248.82785

9

58.065

83-613

7-525

3.6422

9

583-1903

255-H57

4.08233

279-93 '33

CUBIC.

Cubic

Cubic

inches to

yards to

Bushels to

i Gunter's chain = 20.1168 metres.

cubic cen-

cubic

hectolitres.

timetres.

metres.

i sq. statute mile = 259.000 . hectares.

i fathom — 1.829 metres.

I

2

16.387

32-774

0.02832
0.05663

0.765
1.529

0.35239 !
0.70479

i nautical mile = 1853.25 metres.

3

49.161

0.08495

2.294

1.05718

i foot = 0.304801 metre.

4
5
6

65.549
81.936

98.323

0.11327
0.14158

0.16990

3.058
3-823
4.587

1.40957 |
1.76196

2.11436 !

i avoir, pound = 453.5924277 gramme.
1 5432-35639 grains = i.ooo kilogramme.

7

114.710

0.19822

5-352

2.46675

S

131.097

0.22654

6.II6

2.81914

i 9

147.484 0.25485

6.881 3.17154 ;

The only authorized material standard of customary length i«s the Troughton scale belonging to the United States
Office of Standard Weights and Measures, whose length at 59°.62 Fahr. conforms to the British standard. The yard
in use in the United States is therefore equal to the British yard.

The only authorized material standard of customary weight is the Troy pound of the Mint. It is of brass of un-
Jinown density, and therefore not suitable for a standard of mass. It was derived from the British standard Troy
pound of 1758 by direct comparison. The British Avoirdupois pound was also derived from the latter, and contains
7,000 grains Troy.

The grain Troy is therefore the same as the grain Avoirdupois, and the pound Avoirdupois in use in the United
States is equal to the British pound Avoirdupois.

The British gallon = 4.54346 litres.

The British bushel = 36.3477 litres.

The length of the nautical mile given above and adopted by the U. S. Coast and Geodetic Survey many years
ago, is defined as that of a minute of arc of a great circle of a sphere whose surface equals that of the earth (Clarke's
Spheroid of 1866).

* Quoted from sheets issued by the United States Office of Standard Weights and Measures.
SMITHSONIAN TABLES.

9

TABLE 3.

TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES.

(2) METRIC TO CUSTOMARY.

LINEAR.

CAPACITY.

Millilitres

or cubic

Centi-

.

Deca-

Hecto-

Metres to

Metres to

Metres to

Kilometres

centi-

litres to

litres

litres

inches

feet.

yards.

to miles, j

metres

fluid

to

to

to fluid

ounces.

gallons.

bushels.

drams.

I

39-3700

3.28083

1.093611

0.62137

I

0.27

0-338

1.0567

2.6417

2.8377

2

78.7400

6.56167

2.187222

1.24274 i

2

0-51

0.676

2.1134

5.2834

5-6755

3

118.1100

9.84250

3.280833

1.86411

3

0.8 1

I.OI4

3.1700

7.9251

8-5I32

4

157.4800

13- I 2333

4-374444

2.48548

•1

1. 08

1-353

4.2267

10.5668

I 1.8510

5

196.8500

16.40417

5.468056

3.10685 |

5

'•35

1.691

5-2834

13.2085

14.1887

6

236.2200

19.68500

6.561667

3.72822

6

1.62

2.029

6.3401

I 5.8502

17.0265

8

275.5900
314.9600

22.96583
26.24667

7-655278
8.748889

4-34959
4.97096 1

8

1.89

2.16

2.367
2.705

7.3968
8-4535

18.4919
21.1336

1 9.8642
22.7019

9

354-3300

29.52750

9.842500

5-59233

9

2.43

3-043

9.5101

23-7753

25-5397

SQUARE.

WEIGHT.

Square

Square

Square

Milli-

Kilo-

Hecto-

Kilo-

centimetres

metres to

metres to

Hectares i

grammes

grammes

gra

mines

grammes

to square

square

square

to acres.

to

to

to <

unces

o pounds

inches.

feet.

yards.

grains.

grains.

avoirdupois.

avoirdupois.

I

0.1550

10.764

1.196

2-47' :

i

0.01543

I5432-36

3

•S274

2.20462

2

0.3100

21.528

2.392

4-942 |

! 2

0.03086

30864.71

7.0548

4.40924

3

0.4650

32.292

3-588

7-4I3

3

0.04630

46297.07

10.5822

6.61387

4

O.62OO

43-055

4.784

9.884

4

0.06173

61729.43

14

.1096

8.81849

5

0.7750

53-8'9

5.980

'2-355 i

5

0.07716

77161.78

'7

6370

11.02311

6

0.9300

64.583

7.176

14.826 1

6

0.09259

92594.14

21

1644

'3-22773

7

1.0850

75-347

8.372

17.297 I

7

o. 1 0803

1 08026.49

24.6918

8

1.2400

86. 1 1 1

9-568

19.768 i

8

0.12346

123458.85

28

2192

17.63698

9

1-3950

96.875

10.764

22.239

9

o. 1 3889

138891.21

3'

7466

19.84160

CUBIC.

WEIGHT.

Cubic

Cubic

Cubic

Cubic
metres to i
cubic

Quintals to
pounds av.

Milliers or
onnes to pounds

Kilogrammes
to ounces

to cubic

to cubic

cubic

inches.

inches.

feet.

yards.

I

0.06 1 o

61.023

35-3'4

1.308

I 220.46

2204.6

32.1507

2

O.I22O

122.047

70.629

2.616

2 440.92

4409.2

64.3015

3

0.1831

183.070

'05.943

3.924 j

3 661.39

661-

;-9 96.4522

4

0.2441

244.094

141.258

5-232

4 881.85

88ii

•5

1 28.6030

5

0.3051

305.117

176.572

6.540

5 1102.31

11023.1

160.7537

6

0.3661

366. 1 40

211.887

7.848

6 1322.77

13227.7

192.9044

7

0.4272

427.164

247.201

9-156

7 1543-24

I 5432.4

225.0552

8

0.4882

488.187

282.516

10.464

8 1763-70

17637.0

257.2059

9

0.5492

549-210

3I7-830

11.771

9 1984.16

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 q parts of the former to i of the latter metal. From one of these a cer-
tain number of kilogrammes were prepared, from the other a definite number of metre bars. These standards of
weight and length were intercompared, without preference, and certain ones were selected as International prototype
standards. The others were distributed by lot, in September, 1880, to the different governments, and are called
National prototype standards. Those apportioned to the United States were received in 1890, and are kept in the
Office of Standard Weights and Measures in Washington, D. C.

The metric system was legalized in the United States in 1866.

The International Standard Metre is derived from the Metre des Archives, and its length is defined bv the dis-
tance between two lines at o° Centigrade, on a platinum-iridium bar deposited at the International Bureau of Weights
and Measures.

The International Standard Kilogramme is a mass of platinum-iridium deposited at the same place, and its
weight in vacuo is the same as that of the Kilogramme des Archives.

The litre is equal to a cubic decimetre, and it is measured by the quantity of distilled water which, at its maximum
density, will counterpoise the standard kilogramme in a vacuum, the volume of such a quantity of water being, as

nearly as has been ascertained, equal to a cubic decimetre.
SMITHSONIAN TABLES.

10

CONVERSION FACTORS.

TABLES 4, 5.

IJ

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12

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TABLES 18, 1 9.

CONVERSION FACTORS.

|

u

w

i

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BOO — OO NO _
— co - poO

PI rt- ON PI T
O PI rv M ^r

B

1 — 1 PO O 1 PI l rt-

)imensions rr A>

.§ %•
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er min.

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tv, Q\ in rv. in

pj o **• •* PO

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per min., p

6

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per sec.
per min.

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rv, o ""i N fv!

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XXX X

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SMITHSONIAN TABLES.

18

TABLES 2O, 21

CONVERSION FACTORS.

1

i

r^NO ON PI •^-
T roo\ O ro
CO PI LOO CC

NO LO •— O O

tt

-1-IP1 OlPI O

Dimensions =:

Centimetres of
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6

to

"o o o
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ro ~ PI ro O

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f

|

3

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ON O CO - Q "">
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at o° Cei

6

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3

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5

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cent

d

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6

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SMITHSONIAN TABLES.

TABLES 22, 23.

CONVERSION FACTORS.

I

•8
|

I

pi

s,.

t

*

_1

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fO — OO OO O
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2O

CONVERSION FACTORS.

X

§

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SMITHSONIAN TABLES.

21

TABLES 26, 27.

CONVERSION FACTORS.

g

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"o'o'o •

"rt

"S

XXX

3

^

H r"AO co

0

&

PI CO PI

0.

CO '030

SMITHSONIAN TABLES.

22

TABLES 28, 29.

CONVERSION FACTORS.

OO O •"I'O

a

B

S3

j

T}- PI \o O
l^^O "^ O

t^ ^t" PI t^^H

POO T CN°

55

8

PO PI T)- IO

ja

|OIN -|ro

|

d

'71* *?

1

O.

O O O O

=
Q

I

E

6

£

XXXXH

S
O

•-• \O i~*~ ON

PI ~ pj PO

ui)

PO ^foo •^~

OO t^t ON PO

VO if* O ON

0

O t^ "~>Q PI

u

.-

J

^ O TCW O
r^vo oo '*•

.H •

too d PO pJ

3

7 K <*

£

C

o

XXX

"12

"

O ON O ON

O

*1- O O OO
O ""i O P<

LO o O "^

LTi TJ- K- PI

CO Lr> O PO

"1 f ONOO

i ""

t

i-l

CNO O 10 to

CO I-;. •- »0

3

7 T 7 T

S.

0 O 0 O

•3

o

xx.xx

c

3
0
ft

ON d ""> t^

PJ 1^ CO PJ

\O OO PI -i

CO t^ TT\£)

1

J

OO ^\O _O
r^j PO ON ON

U

• . •

f

bo PM ^" •""

3

t «- 7 -

2L

b ^oo

•o

o

X XXX

c

PI rH o r^ ^

3

r^ o toco

O

CO CO OO PI

cu

to PI ^5 TJ-

PO i^* T}~ PI

"— •- PI vd

PI to r^ PI

CO 'I- PO PI

^§

i

vO -^- ON PI
O vO O to\o
OO — Pi vO

£ ~

^H ^^

1|

'b'b'b^b

t> 5

1— 1 hri M* M

— 5

XXXX

c 8

6

f^ O ON tovo
ON r^co vo

H 3

to r-~ — ON

- OO O O

.y

ON r^ •" •— '

\^

^S

tj;

OO PO ON ON

3

O

.'

M

O to O O

O*kM. M M

il

rt u

^o **

d
c

51

'o'b'o'o

c

si

XXXX

i

£

T3

§

6
2

r^x ON "^ Tt*_J
O to P] PI "^

O ^ PO PO

u

»• CO P< N

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tOO ON

S

Jj

to § ® ON

•!-» ^^

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d PO « i»o

o ^

t

u "

o o o

U II

c II

23

3 .

6

XX X

oo c< O H oo
••d" en O ON

B

ON N- O to

O

U

pTIS ^

*

a

0

E

$

CC O O C>

vO — O O ^o
ON to o ON

PO ••* o co

3^

l« pi I-N3

o "

7 « 7 T

O O 0 O

V ||

Mb* »• M

|3

3

6

XX XX
oo N H o so

T3

CN ^-" O to

§

-f -<f q oq

u

N i- ~ r~.

PO PI PI PI

•d

^

tOQ OC 00 PO

>"-*

1-5

PI CCZC t*,.

,«|

IPO |poi-<i-toc

u c

7 T T t

o o o o

2 II

X XXX

33

^i

J^ t*^ r^~ PO

C

IP ir? 2"

3

t**. O O to

*

Sf

r-^ ON ON ON
OO — - O

•t- o o -

1?

o

to O O ON

°.s

« 7 '?

0 0 O

§ «

X XX

sS-

6

H PI rf Tj- Tf

T3

f^t

OO OO OO "1

•"• 00 CO CO

a

S 8 8 2"

vo T}- TJ- ro j

SMITHSONIAN TABLES.

TABLES 3O, 31

CONVERSION FACTORS.

s

d

a

f

A\*o oo "

3

H

oo tor^

' ir>\O t^

i

|fOI~lN

S.

£

TT"V ;

1

222

1

: J

>i:xx

fr*"} O ~;

l^jt

^

CN Q '

?53

0* ""> O

vO « ^

!/•>"•> OO

•d

j

o* oq PI

c
o

|tf O HH

D

I

J

§

H -o

i

*!/ MI

2

j

^K X

0

3

feH^

££ s

i

Hn

LOO ro

1

« ro
£-.' N ^*"

3

ico i~ d

.S

:

E

1
Ti T i

-o

0,0

5
o
0.

i

X X
•if r^\O

f N Tj-
08 w N

S •

t^, M M

{ ) O oo O

O « 'f

•o

N IM CN

a

S

|

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\

j

1

'

c« W

i .

O O Q

c

)

HN 1-4

I

O

j

.- j f^ rovO
r " VO f1' Q

O ro tii

•

a

M

ro COM
i-o ro r^ !

1:

J

ro **o ir^o

•J

cJ

?.p i

I

C

bio

T3

«rt

s

i 1

0 O

'

O

6

d

XX

^1 n OH
*O \Q *^

.

O O O

I

y, :

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r^ f*^ .co

•

.ti -

,

lO 5~t D

I

Dfih

dicft d

i

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j

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2

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X

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6
%

M N H ^O

roro oo
oo OS >o

[j

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ro en «

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4

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s'i

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u

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g> ;

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d
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SMITHSONIAN TABLES.

TABLES 32, 33,

CONVERSION FACTORS.

TABLE 32. — Conversion Factors for Expression of Temperatures.

Dimension =

Centigrade.

Fahrenheit.*

Reaumur.

No.

|

Log.

No.

Log.

No.

Log.

1
5-55556 X lo-1
1.25000

0

1.744727
0.096910

I.8OOOO
1
2.25000

0.255272
0 ;
0.352182

8.00000 X IO"1
4-44444 X iQ-1

7.903090

1.647817
0

* The zero of the Fahrenheit scale is 32° below the freezing point of water.

In many of the derived units for the measurement of physical quantities, the
unit of time may be taken as constant, because it is seldom that any other unit
than the second is used. This is the case, in particular, for the electric and
magnetic units. Tables 33-37 below, giving the factors for the conversion of
units depending on different dimensional equations in M and L from one set
of fundamental units to another, will be found sufficient for almost all cases.

TABLE 33. — Electric Displacement, etc.

Dimensions = M^L -T™.

Foot Grain
Second Units.

Metre Gramme
Second Units.

Centimetre Gramme or ) Second
Millimetre Milligramme ) Units.

No.

Log.

No.

Log.

No.

Log.

1
6.61058 X to-1
6.61058 X io2

0

1.820240
2.820240

i-5'273
i.ooooo X io3

0.179760
0
3.000000

I.5I273XIO-3
I.OOOOO X IO~3

1

3.179760

3.000000
0

SMITHSONIAN TABLES.

TABLES 34, 35.

CONVERSION FACTORS.

£

I

Ml

0

vC 0 0

x X

—

§

i-<

o o o

"s

II

.11

O ~ N

1

1?

U -

u O

o^

c
E

JOT

6

XX
o\ o o H

Q

a

121

08 8

\o o o

£8 8

*

J?§° °

£

••"

o o o

'

C x

iril- IN

Si

T 7 T

1

£3

00 0

SOT

01

U

o

XX X

O^ Q ^ O

\

O O O

\O O O

g

loll

£2
E'™

\O O O

l« «l«

25

V r—;

7 7

£§

0 00

• SOT

6

X XX

O^rH O O

° §8

4- « -

3

ro ro m

c-'

d I— I"

P

7

+-i *^

O 0

If

XX

OT

6

on c» oo

N

a'

_H
II

i

£

i

Hf

Dimensions

Millimetre M
Second I

o
Z

C6cb'o
XXX

o o o

"1" 9 9

ri o O

t

I

c •

re .;;

^

d - IN

1

i?

0 I

N

? o

1

OJ

^

X X

1

0

*

oo O H O

s

^r O O

c

- " -

1

n 0 O

1

A

1° §

1

E 2

1-1

S i§il

IO

CO

<*5

H

C-o

7 7 T

m

o> -

0 00

2

£ 8

t-^ H- H-

2

*cn

6

X XX

*yf

oo H O O

1 §§

i

0 fl fl M
*•* U~> U~l LO

C .^;

oq oo oq

•O

Vfo

§8

U- <u

c«

o

XX

IO U~l U~>

SMITHSONIAN TABLES.

26

CONVERSION FACTORS.

TABLES 36, 37.

s '

<S80

M

0)

1

|

ro O O

"s

« •

^•0 3)

IJ

•2'H

c

S

0

"S

*£) ^> ^

'at

£ g

H-t H-. HH

3

1*

6

XXX

ON o o H

s

00* O O
f> O O

•<i- « «

E
c to

bo

c

OO O O

1

It

o o o

1

ll

d

XX X

•S

o

«

J£§ 0

fc

oo o o

o

5

^- ~

H

00 00

l
S

A
o

ro O O

H

_q

c "c

IfJ iroivd

§

T ? T

H

01 C

0 00

i; o

>-< t-« NH

**

6

X XX

fO 00

00 O O

'3'£

i

M M N

o o

o g

M M

fa "

X X

w

6

rH

^t" "!t* ^"

ro ro to

ro to to

CO

-••

-I--

41

1

1

00 O O
i/~j O O Q

a

1!

55

iiS,5

d

^?

2 "2 2

>-. O

g

•*-• CJ

jj

Jc/3

6

XXX

5

i

ty~) O O

ti

co O Q

MO O

OO O O

o

D

E

*"*

i— O O

p .

ro- |4

<L>

00 T

*-• g

°o o o

E 8

'H w

0

XX X

u

*

\c~ o 8

>-O Q O

O O O

ITS «

CO O Q

M

OO O O°

0

LOQ o O

hj

« 80

E £

Ir-i |M |i>>

S'c

r 7 t

t§

O 0 O

6

X XX

£* § §

!? °-

i

® or oc oo

OO CO OO

c^2

"^f^rtO

ll

T T

*c

o o o

c c

Nl tar M

XXX

in

6

H ^o co co

*

C Q 0

a c- 5%

i/ \r LO

*^

SMITHSONIAN TABLES.

TABLE 38.

HYPERBOLIC FUNCTIONS.*

Hyperbolic sines. Values of

1

X

0

1

2

3

4

5

6

7

8

9

0.0

o.oooo

O.OIOO

O.O2OO

0.0300

0.0400

0.0500

0.0600

0.0701

0.080

0.0901

O.I

.1002

.1 IO2

.120^

.1304

.1405

.1506

.1607

.170^

.1810

.1911

0.2

.ZOf

.21 15

.22l£

.2320

.2423

.2526

.2629

•2733

•2837

.2941

°-3

•3045

•3 '5°

•3255

-336o

.3466

,•3572

.3678

•3785

.3892

.4000

0.4

,.4108

.4216

•4325

•4434

•4543

•4653

•4764

•4875

.4986

.5098

0.5

0.5211

o-5324

0.5438

o-SSS2

0.5666

0-5782

0.5897

O.J6OK

0.6131

0.6248 '

0.6

.6367

.6485

.6605

.6725

.6846

.6967

.7090

^7213

•7336

.7461 i

0.7

.7586

.7712

.7838

.7966

.8094

.8223

•8353

.8484

.8615

.8748

0.8

.8881

.9015

.9150

19286

•9423

.9561

-9700

^9840

.9981

/.OI22

0.9

1.0265

i .0409

1-0554

1.0700

1.0847

1.0995

1.1144

1,1294

1.1446

I.I598

1.0

1.1752

1.1907

I.2O6j

I.222O

1-2379

1-2539

1.2700

I.2862

1.3025

I.3I90

i.i

•3356

•3524

•3693

•3863

•4035

.4208

.4382

•455s

•4735

•49H

1.2

•5095

.5276

.5460

•5645

•5831

.6019

.6209

.6400

•6593

.6788

!-3

.6984

.7182

-7381

•7583

.7786

.7991

.8198

.8406

.8617

.8829

1.4

•9043

•9259

•9477

.9697

.9919

2.0143

2.0369

2.0597

2.0827

2.1059

1.5

2.1293

2.1529

2.1768

2.2008

2.2251

2.2496

2-2743

2-2993

2.3245

2.3499

1.6

•3756

.4015

.4276

•4540

.4806

•5075

•5346

•5620

.5896

.6175

i-7

.6456

.6740

.7027

•73'7

.7609

•79°4

.8202

•8503

.8806

.9112

1.8

.9422

•9734

3.0049

3-0367

3.0689

3-1013

3- '340

3.1671

3.2005

3-234I

1.9

3.2682

3-3025

•3372

.3722

.4075

•4432

.4792

•5'56

•5523

•5894

2.0

3.6269

3.6647

3.7028

3-74M

3-7803

3.8196

3-8593

3-8993

3-9398

3.9806

2.1

4.0219

4.0635

4.1056

4.1480

4.1909

4-2342

4-2779

4-3221

4.3666

4.4117

2.2

4-4571

4-503°

4-5494

4.5962

4.6434

4.6912

4-7394

4.7880

4-8372

4.8868

2-3

4-9370

4.9876

5-0387

5-0903

5-1425

5-*95l

5-2483

5.3020

5-3562

5.4109

2.4

5.4662

5.5221

5-5785

5-6354

5.6929

5-75JO

5-8097

5.8689

5.9288

5.9892

2.5

6.0502

6.1118

6.1741

6.2369

6.3004

6-3645

6.4293

6.4946

6.5607

6.6274

2.6

6.6947

6.7628

6-8315

6.9009

6.9709

7.0417

7.1132

7-1854

7-2583

7-33!9

2.7

7.4063

7.4814

7-5572

7-6338

7.7112

7-7894

7.8683

7.9480

8.0285

8.1098!

2.8

8.1919

8.2749

8.3586

8.4432

8.5287

8.6150

8.7021

8.7902

8.8791

8.9689

2-9

9.0596

9.1512

9-2437

9-3371

9-43 1 5

9-5268

9.6231

9.7203

9.8185

9-9I77

3.0

10.018

10.119

IO.22I

10.324

11.429

"•534

11.640

11.748

11.856

1 1 .966

*i

11.076

11.188

11.301

11.415

11 -530

12.647

12.764

12.883

12.003

12.124

3-2

12.246

12.369

12.494

12.620

12.747

12.876

1 3.006

I3-I37

13.269

J3-403

3-3

13-538

I3-674

13.812

r3-95i

14.092

14-234

14-377

14.522

14.668

14.816

3-4

14.965

15.116

15.268

15.422

15-577

1 5-734

I5-893

16.053

16.214

16.378

3.5

16.543

16.709

16.877

17.047

17.219

I7-392

i7-567

17-744

17-923

18.103

3-6

18.285

18.470

18.655

18.843

1 9-033

9.224

19.418

19.613

19.811

2O.OIO

3-7

20. 2 II

20.415

20.620

20.828

21.037

21.249

21.463

21.679

21.897

22.117

3-8

22-339

22.564

22.791

23.020

23.252

23.486

23.722

23.961

24.202

24.445

3-9

24.691

24.939

25.190

25.444

25.700

25.958

26.219

26.483

26.749

27.018

4.0

27.290

27.564

27.842

28.122

28.404

28.690

28.979

29.270

29.564

29.862

4-i

30.162

30-465

30-772

31.081

3J-393

3I-709

32.028

32-350

32-675

33-004

4.2

33-336

33-67I

34.009

34-351

34-697

35.046

35-398

35-754

36-113

36.476

4-3

36-843

37-214

37-588

37.966

38.347

38.733

39.122

39-5'5

39-9 1 3

40.314

4-4

40.719

41.129

41.542

41.960

42.382

42.808

43-238

43-673

.4. 1 I 2

44-555

4.5

45.003

45-455

45.912

46.374

46.840

47-3"

47.787

48.267

48-752

49.242

4.6

49-737

50-237

50.742

5r-252

5' -767

2.288

52.813

53-344

53.880

54.422

4-7

54.969

55.522

56.080

56-643

57-213

7.788

58-369

58-955

59.548

60.147

4.8

60.751

61.362

61.979

62.601

63-231

63.i-66

64.508

65- '57

65.812

66.473

4-9

67.141

67.816

68.498

69.186

69.882

0.584

7I-293

72.010

72-734

3-465

* Tables 38-41 are quoted from " Des Ingenieurs Taschenbuch," herausgegeben vom Akademischen Verein (Htitte).
SMITHSONIAN TABLES.

28

HYPERBOLIC FUNCTIONS.

Hyperbolic cosines. Values of

TABLE 39.

•

0

1

2

3

4

5

6

7

8

9

0.0

I.OOOO

1. 000 1

I.OOO2

1.0005

i. 0008

1.0013

1.0018

1.0025

1.0032

1.0041

O.I

.0050

.0061

.0072

.0085

.0098

.0113

.0128

.0145

.0162

.0181

0.2

.0201

.0221

.0243

.0266

.0289

.0314

.0340

.0367

•0395

•0423

o-3

•0453

.0484

.0516

•0549

.0584

.0619

.0655

.0692

.0731

,0770

0.4

.Obi I

.0852

.0895

•0939

.0984

.1030

.1077

.1125

•"74

.1225

0.5

I.I276

1.1329

i 1-1383

1.1438

1.1494

I.I551

1.1609

1.1669

1.1730

1.1792

0.6

•1855

.1919

.1984

.2051

.2119

.2188

.2258

•2330

.2402

.2476

o-7

•2552

.2628

.2706

.2785

.2865

.2947

•3030

•3"4

•3 '99

.3286

q.8

•3374

•3464

•3555

•3647

•3740

•3835

•3932

.4029

.4128

.4229

0.9

•4331

^4434

•4539

.4645

•4753

.4862

•4973

.5085

.5199

•53H

1.0

1.5431

!-5549

1.5669

1-5790

I-59I3

1.6038

.6164

1.6292

i 6421

1-6552

i.i

.6685

.6820

.6956

•7093

•7233

•7374

•75'7

.7662

.7808

•7956

1.2

.8107

.8258

.8412

.8568

•8725

.8884

•9045

.9208

•9373

•9540

'•3

.9709

.9880

2.0053

2.0228

2.0404

2-0583

2.0764

2.0947

2.1132

2.1320

1.4

2.1509

.1700

.1894

.2090

.2288

.2488

.2691

.2896

•3103

•33'2

1.5

2.3524

2-3738

2-3955

2.4174

2-4395

2.4619

2.4845

2-5073

2-5305

2-5538

1.6

•5775

.6013

•6255

.6499

.6746

•6995

•7247

.7502

.7760

.8020

i-7

.8283

•8549

.8818

.9090

•9364

.9642

.9922

3.0206

3.0492

3.0782

1.8

3-I075

3-'37J

3.1669

3.1972

3.2277

3-2585

3.2897

.3212

•3530

.3852

1.9

•4177

.4506

.4838

•5'73

•55^

•5855

.6201

•6551

.6904

.7261

2.0

3.7622

3-7987

3-8355

3-8727

3-9103

3-9483

3.9867

4.0255

4.0647

4.1043

2.1

4-1443

4.1847

4.2256

4.2668

4-3085

4.3507

4-3932

4.4362

4-4797

4-5236

2.2

4-5679

4.6127

4.6580

4-7037

4-7499

4.7966

4-8437

4.8914

4-9395

4.9881

2-3

5-0372

5.0868

5- '370

5.1876

5.2388

5-2905

5-3427

5-3954

5-4487

5.5026

2-4

5-5569

5.6119

5.6674

5-7235

5.7801

5-8373

5-8951

5-9535

6.0125

6.0721

2.5

6.1323

6.1931

6-2545

6.3166

6-3793

6.4426

6.;o66

6.5712

6-6365

6.7024

2.6

6.7690

6.8363

6.9043

6.9729

7-0423

7.1123

7.l83i

7.2546

7.3268

7-3998

2.7

7-4735

7-5479

7.6231

7.6990

7.7758

7-8533

7-9136

7.0106

8.0905

8.1712

2.8

8.2527

8-3351

8.4182

8.5022

8.5871

8.6728

8-7594

8.8469

8-9352

9.0244

2.9

9. 1 1 46

9.2056

9.2976

9-3905

9.4844

9-5791

9.6749

9.7716

9.8693

9.9680

3.0

10.068

10.168

10.270

10-373

10.476

10.581

10.687

10.794

10.902

1 1. Oil

3-1

II. 121

12-233

"•345

"•459

"•574

11.689

1 1. 806

11.925

12.044

12.165

3-2

I2.2S;

13.410

1 2-534

12.660

12.786

12.915

13.044

I3-I75

I3-307

13.440

3-3

'3-575

14.711

13.848

I3-987

14.127

14.269

14.412

14.556

14.702

14.850

3-4

14.999

15.149

15.301

1 5-455

15.610

15.766

15-924

16.084

16.245

16.408

3.5

16-573

i6.739

16.907

17.077

17.248

17.421

I7-596

17.772

I7-95I

18.131

3-6

18-313

18.497

18.682

18.870

19.059

19.250

19.444

19.639

19.836

20.035

3-7

20.236

20.439

20.644

20.852

21.061

21.272

21.486

21.702

21.919

22.139

3-8

22.362

22.586

22.813

23.042

23-273

23-507

23-743

23.982

24.222

24.466

3-9

24.711

24-959

25.210

25-463

25.719

25-977

26.238

26.502

26.768

27.037

4.0

27.308

27.582

27.860

28.139

28.422

28.707

28.996

29.287

29.581

29.878

4.1

30.178

30.482

30.788

31.097

31.409

3I-725

32.044

32-365

32.691

33019

4.2

33-351

33-686

34.024

34-366

34-7"

35.060

35-412

35-768

36.127

36.490

4-3

36.857

37-227

37.601

37-979

38.360

38.746

39- '35

39-528

39-925

40.326

4-4

40-732

41.141

41-554

41.972

42-393

42.819

43-250

43.684

44-123

44.566

4.5

45.014

45.466

45-923

46-385

46.851

47-321

47-797

48.277

48.762

49-252

4.6

49-747

50.247

50-752

51.262

5r-777

52.297

52-823

53-354

53-890

54-43 !

4-7

54-978

55-531

56.089

56.652

57.221

S7-796

58.377

58-964

59-556

60.155

4.8

60.759

61.370

61.987

62.609

63-239

63.874

64.516

65.164

65.819

66.481

4.9

67.149

67.823

68.505

69.193

69.889

7.9-591

71.300

72.017

72.741

73-472

SMITHSONIAN TABLES.

29

TABLE 40.

HYPERBOLIC FUNCTIONS.

Common logarithms -j- 10 of the hyperbolic sines.

X

0

1

2

3

4

5

6

7

8

9

0.0

8.

oooo

3011

4772

6022

6992

7784

8455

9036

9548

O.I

•^0007

0423

0802

1152

1475

1777

2060

2325

2576

2814

0.2

3°39

3254.

3459

3656

3844

4025

4199

4366

4528

4685

o-3

4836

4983

S'25

5264

5398

5529

5656

5781

5902

6020

0.4

9.6136

6?49

635s)

6468

6574

6678

6780

6880

6978

7074

0.5

9.7169

7262

7354

7444

7533

7620

7707

7791

7875

7958

0.6

8039

8119

8199

8277

8354

843 l

8506

8581

8655

8728

0.7

8800

8872

8942

9012

9082

9150

9218

9286

9353

94ig

0.8

9485

9550

9614

9678

9742

9805

9868

993°

9992

0053

0.9

10.0114

0174

0234

0294

°353

0412

0470

0529

0586

0644

1.0

10.0701

0758

0815

0871

0927

0982

1038

i°93

1148

1203

i.i

1257

1311

J365

1419

1472

J525

1578

1631

1684

1736

1.2

1788

1840

1892

1944

1995

2046

2098

2148

2199

2250

'•3

2300

2351

2401

2451

2501

2551

2600

2650

2699

2748

1.4

2797

2846

2895

2944

2993

3041

3090

3138

3186

3234

1.5

10.3282

3330

3378

3426

3474

352i

3569

3616

3663

37"

1.6

3758

3805

3852

3899

3946

3992

4039

4086

4132

4'79

i-7

4225

4272

43i8

4364

4411

4457

45°3

4549

4595

4641

1.8

4687

4733

4778

4824

4870

4915

4961

5007

5052

5098

1.9

SM3

5188

5234

5279

5324

5370

5415

5460

55°5

555°

2.0

iQ-5595

5640

5685

573°

5775

5820

5865

5910

5955

5999

2.1

6044

6089

6i34

6178

6223

6268

6312

6357

6401

6446

2.2

6491

6535

6580

6624

6663

6713

6757

6802

6846

6890

2-3

6935

6979

7023

7067

7112

7156

7200

7244

7289

7333

2.4

7377

7421

7465

7509

7553

7597

7642

7686

773°

7774

2.5

10.7818

7862

7906

795°

7994

8038

8082

8126

8169

8213

2.6

8257

8301

8345

8389

8433

8477

8521

8564

8608

8652

2.7

8696

8740

8784

8827

8871

8915

8959

9C°3

9046

9090

2.8

9i34

9178

9221

9265

9309

9353

9396

9440

9484

9527

2.9

9571

96i5

9658

9702

9746

9789

9833

9877

9920

9964

3.0

11.0008

0051

0095

0139

0182

0226

0270

0313

°357

0400

3-1

0444

0488

°53 i

°575

0618

0662

0706

0749

0793

0836

3-2

0880

0923

0967

IOII

1054

1098

1141

1185

1228

1272

3-3

1316

1359

1403

1446

1490

1533

1577

1620

1664

1707

3-4

1751

1794

1838

1881

1925

1968

2OI2

2056

2099

2143

3.5

11.2186

2230

2273

2317

2360

2404

2447

2491

2534

2578

3-6

2621

2665

2708

2752

2795

2839

2882

2925

2969

3012

3-7

3056

3°99

3H3

3186

323°

3273

3317

336o

3404

3447

3-8

349i

3534

3578

3621

3665

3708

3752

3795

3838

3882

3-9

3925

3969

4012

4056

4099

4H3

4186

4230

4273

4317

4.0

11.4360

4403

4447

449°

4534

4577

4621

4664

4708

4751

4.1

4795

4838

4881

4925

4968

5012

5°55

5°99

5M2

5186

4.2

5229

5273

53l6

5359

5403

5446

5490

5533

5577

^620

4-3

5664

5707

575°

5794

5837

5881

5924

5968

6011

So55

4.4

6098

6141

6185

6228

6272

6315

6359

6402

6446

6489

4.5

11.6532

6576

6619

6663

6706

675°

6793

6836

6880

6923

4.6

6967

7010

7°54

7097

7141

7184

7227

7271

73M

7358

4-7

7401

7445

7488

7531

7575

7618

7662

7705

7749

7792

4.8

7836

7879

7922

7966

8009

8053

8096

8140

8183

8226

4.9

8270

83U

8357

8400

8444

8487

8530

8574

8617

8661

SMITHSONIAN TABLES.

UNIVERSITY
or

HYPERBOLIC FUNCTIONS.

Common logarithms of the hyperbolic cosines.

TABLE 41

X

0

1

2

3

4

5

6

7

8

9

0.0

o.oooo

oooo

0001

OOO2

0003

0005

0008

001 1

0014

0018

O.I

OO22

0026

0031

0037

0042

0049

0055

•_ 0062

0070

0078

O.2

0086

0095

0104

OII4

0124

0134

0145

• 0156

0168

0180

o-3

0193

0205

0219

0232

0246

0261

0276

0291

0306

0322

0.4

°339

0355

0372

0390

0407

0426

0444

0463

0482

0502

0.5

O.O522

0542

0562

0583

0605

0626

0648

0670

0693

0716

0.6

0/39

0762

0786

0810

0835

0859

0884

0910

0935

0961

0.7

0987

1013

1040

1067

1094

1122

"49

"77

1206

1234

0.8

1263

1292

1321

1350

1380

I4IO

1440

1470

1501

J532

0.9

1563

1594

1625

1657

1689

1721

J753

1785

1818

1851

l.O

0.1884

1917

1950

1984

2018

2051

2086

21 2O

2154

2189

i.i

2223

2258

2293

2328

2364

2399

2435

2470

2506

2542

1.2

2578

2615

2651

2688

2724

276l

2798

2835

2872

2909

i-3

2947

2984

3022

3059

3097

3'35

3'73

3211

3249

3288

1.4

3326

3-365

3403

3442

348i

352o

3559

3598

3637

3676

1.5

0-37i5

3754

3794

3833

3873

3913

3952

3992

4032

4072

r.6

4112

4i52

4192

4232

4273

43'3

4353

4394

4434

4475

i-7

4515

4556

4597

4637

4678

4719

4760

4801

4842

4883

1.8

4924

4965

5006

5048

5089

5f30

5172

5213

5254

^

5296

1.9

5337

5379

542i

5462

5504

5545

5587

5629

5671

5713

2.0

0-5754

5796

rS->Q

5°3°

5880

5922

5964

6006

6048

6090

6132

2.1

6i75

6217

6259

6301

6343

6386

6428

6470

6512

6555

2.2

6597

6640

6682

6724

6767

6809

6852

6894

6937

6979

2-3

7022

7064

7107

7150

7192

7235

7278

7320

7363

7406

2-4

7448

7491

7534

7577

7619

7662

7705

7748

7791

7833

2.5

0.7876

7919

7962

8005

8048

8091

8i34

8176

8219

8262

2.6

8305

8348

8391

8434

8477

8520

8563

8606

8649

8692

2-7

8735

8778

8821

8864

8907

8951

8994

9°37

9080

9123

2.8

9166

9209

9252

9295

9338

9382

9425

9468

95"

9554

2.9

9597

9641

9684

9727

9770

9813

9856

9900

9943

9986

3.0

i .0029

0073

0116

oi59

O2O2

0245

0289

0332

°375

0418

3-1

0462

0505

0548

0591

0635

0678

0721

0764

0808

0851

3-2

0894

0938

0981

1024

1067

MM

"54

"97

1241

1284

3-3

1327

!37i

1414

1457

I5OI

1544

1587

1631

1674

1717

3-4

1761

1804

1847

1891

1934

1977

202 1

2064

2107

2151

3.5

1.2194

2237

2281

2324

2367

2411

2454

2497

2541

2584

3-6

2628

2671

2714

2758

2801

2844

2888

2931

2974

3018

3-7

3061

3105

3H8

3^1

3235

3278

3322

3365

3408

3452

3-8

3495

3538

3582

3625

3669

3712

3755

3799

3842

3886

3-9

3929

3972

4016

4059

4103

4146

4189

4233

4278

4320

4.0

1-4363

4406

445°

4493

4537

4580

4623

4667

4710

4754

4.1

4797

4840

4884

4927

497i

5014

5057

5101

5'44

5188

4.2

5231

5274

53i8

536i

5405

5448

5492

5535

5578

5622

4-3

5665

5709

5752

5795

5839

5882

5926

5969

6012

6056

4-4

6099

6143

6186

6230

6273

63l6

6360

6403

6447

6490

4.5

I-6533

6577

6620

6664

6707

^751

6794

6837

6881

6924

4-6

4-7

6968
7402

7011
7445

7055
7489

7098
7532

7141
7576

7185
7619

7228
7662

7272
7706

73r5
7749

7358
7793

4.8

7836

7880

7923

7966

8010

8053

8097

8140

8184

8227

4-9

8270

8314

8357

8401

8444

8487

853i

8574

8618

8661

SMITHSONIAN TABLES.

TABLE 42.

EXPONENTIAL FUNCTIONS.

Values of <•* and ol e-* and their logarithms.

Values of e* and e~x for values of x intermediate to those here given may be found by adding or subtracting the
values of the hyperbolic cosine and sine given in Tables 38-39.

X

*•-*

log^

X

t*

log ex

OB

e-*

log e-x

0.1

1.1052

0-04343

5.1

164.03

2.21490

0.1

0.90484

^•95657

2

1.2214

08686

2

181.27

25833

2

81873

9I3M

3

J-3499

13029

3

200.34

30176

3

74082

86971

4

14910

17372

4

221.41

345'9

4

67032

82628

5

1.6487

21715

5

244.69

38862

5

60653

78285

0.6

1.8221

0.26058

5.6

270.43

2.43205

0.6

0.54881

1.73942

7

2.0138

30401

7

298.87

47548

7

49659

69599

8

2-2255

34744

8

330-3o

51891

8

44933

65256

9

2.4596

39087

9

365-04

56234

9

40657

60913

I.O

2.7183

43429

6.0

403-43

60577

I.O

36788

56570

1.1

3.0042

0.47772

6.1

445-86

2.64920

1.1

0-33287

1.52228

2

3.3201

52II5

2

492-75

69263

2

30119

47885

3

4

3-6693

4.0552

56458
60801

3

4

545-57
601.85

73606
77948

3
4

27253
24660

43542
39199

5

4.4817

65M4

5

665.14

82291

5

22313

34856

1.6

4-953°

0.69487

6.6

735-10

2.86634

1.6

0.20190

T-305!3

7

5-4739

73830

7

812.41

90977

7

18268

26170

8

6.0496

78173

8

897-85

95320

8

16530

21827

9

6.6859

82516

9

992.27

99663

9

'4957

17484

2.0

7.3891

86859

7-o

1096.63

3.04006

2.O

13534

i3Mi

2.1

8.1662

0.91202

7.1

I2I2.O

3-08349

21

0.12246

1.08798

2

9.0250

95545

2

1339-4

12692

2

11080

04455

3

9.9742

99888

3

1480.3

'7035

3

10026

OOII2

4

11.0232

1.04231

4

1636.0

21378

4

09073

2.95769

5

12.1825

08574

5

1 808.0

25721

5

08208

91426

2.6

13-463

1.12917

7.6

1998.2

3.30064

2.6

0.074274

5.87083

7

14.880

17260

7

2208.3

34407

7

067205

82740

8

16.445

21602

8

2440.6

38750

8

060810

78398

9

18.174

25945

9

2697.3

43093

9

055023

74055

3-o

20.086

30288

8.0

2981.0

47436

3-o

049787

69712

3.1

22.198

1-34631

81

3294-5

3-5J779

3.1

0.045049

2.65369

2

24-533

38974

2

3641.0

56121

2

040762

6lO26

3

27.113

43317

3

4023.9

60464

3

036883

56683

4

29.964

47660

4

4447-1

64807

4

033373

52340

5

33-"5

52003

5

4914.8

69150

5

030197

47997

3.6

36.598

i . 56346

8.6

5431-7

3-73493

3.6

0.027324

2.43654

7

40.447

60689

7

6002.9

77836

7

024724

393'i

8

44.701

65032

8

6634.2

82179

8

022371

34968

9

49.402

69375

9

7332-0

86522

9

020242

30625

4.0

54-598

• 73718

9.0

8103.1

90865

4.0

018316

26282

4.1

60.340

1.78061

9.1

8955-

3.95208

4.1

0.016573

2.21939

2

66.686

82404

2

9897-

995 5 !

2

014996

'7596

3

73.700

86747

3

10938.

4.03894

3

013569

13253

4

81.451

91090

4

12088.

08237

4

012277

08910

5

90.017

95433

5

13360.

12580

5

011109

04567

4.6

99.48

1-99775

96

14765.

4.16923

4.6

0.010052

2.00225

7

109-95

2.04118

7

16318.

21266

7

009095

3.95882

8

121.51

08461

8

18034.

25609

8

008230

91 539

9

I34-29

12804

9

19930.

29952

9

007447

87196

5-o

148.41

'7147

IO.O

22026.

34295

S-o

006738

82853

SMITHSONIAN TABLES.

EXPONENTIAL FUNCTIONS.

TABLE 43.

Value oi e*2 and e- *" and their logarithms.

The equation to the probability curve is y =: ,
negative, between zero and infinity.

', where x may have any value, positive or

ar

<f-rs

log ex*

e-x"-

log e-x*

0.1

I.OIOI

0.00434

0.99005

7.99566

O

1.0408

01737

96079

98263

3

1.0904

03909

9 '393

96091

4

I-I735

06949

85214

93051

5

1.2840

10857

77880

89143

0.6

M333

0.15635

0.69768

1.84365

7

1.6323

21280

61263

78720

8

1.8965

27795

52729

72205

9

2.2479

35178

44486

64822

I.O

2.7183

43429

36788

56571

1.1

3-3535

0-52550

0.29820

1.47450

2

4.2207

62538

23693

37462

3

5-4I95

73396

18452

26604

4

7-0993

85122

14086

14878

5

9.4877

97716

10540

02284

1.6

1.2936 X 10

1. 11179

0.77306 X IO"1

2.88821

7

1-7993

255'i

55576 "

74489

8

2-5534

40711

39l64

59289

9

3.6996 "

56780

27052

43220

2.0

5-4598

73718

18316 "

26282

2.1

8.2269

1.91524

0.12155 "

2.08476

2

1.2647 X 10-

2.10199

79070 X i or*

3.89801

3

I-9834 "

29742

50418 "

70258

4

3-1735 "

50154

3I511

49846

5

5.1802

7M34

i9304

28566

2.6

8.6264 "

2-93583

0.11592 "

3.06417

7

1.4656 X io3

3.16601

68233 X 10-3

4.83400

8

2.5402 "

40487

39367

595!3

9

4.4918

65242

22263

3475s

3-o

8.1031

90865

12341

09135

3.1

1.4913 X io*

4-17357

0.67055 X io~4

5-82643

2

2.8001 "

44718

3^r3

55283

3

5.2960 "

72947

18644

27053

4

1.0482 X io5

5.02044

95402 X io-6

6.97956

5

2.0898

32011

47851

67989

3.6

4.2507 «

5.62846

0.23526 "

6-37I54

7

8.8205

94549

"337

05451

8

1.8673 X io<5

6.27121

53554 X 10-6

7.72879

9

4.0329

60562

24796

39438

4.0

8.8861

94871

11254

05129

4.1

1.9976 X io7

7.30049

0.50062 X io-"

' 5.69951

2

4.5809

66095

21829 "

33905

3

1.0718 X io8

8.0301 1

933°3 X ID"8

9.96989

4

2-5583 "

40796

39088 "

59204

5

6.2297

79447

16052 "

20553

4.6

1.5476 X io9

9.18967

0.64614 X io~9

10.81033

7

3.9228 "

59357

25494

40643

8

1.0143 X io10

10.00615

98595 X io-*>

"•99385

. 9

2.6755 "

42741

37376 "

57259

S-o

7.2005

85736

13888

14264

SMITHSONIAN TABLES.

33

TABLE 44.

EXPONENTIAL FUNCTIONS.

TT _*ae

Values of 0**and£ * and their logarithms.

0

IT

e**

\o§e**

e **

ir

}oge~^z

1

2- '933

0.34109

0.45594

1.65891

2

4.8105

.68219

.20788

.31781

3

1.0551 X 10

1.02328

.94780 X icr1

2.97672

4

2.3141

-36438

.43214

•63562

5

5-Q754

•70547

•19703

•29453

6

1.1132 X iQ2

2.04656

0.89833 X 10-2

3-95344

7

2.4415

.38766

.40958

.61 234

8

5-3549

.72875

.18674

.27125

9

1.1745 X lo3

3.06985

.85144 X ID"3

4-93OI5

10

2.5760

.41094

.38820

•58906

11

5.6498 "

3.75204

0.17700 "

4.24796

12

1.2392 X 10*

4-09313

.80699 X TO"4

5.90687

'3

2.7168

.43422

•36794

•56578

14

5.9610 "

•77532

.16776

.22468

15

1.3074 X id5

5.11641

.76487 X IO-5

6.88359

16

2.8675 "

S-45751

0.34873 "

6.54249

17

6.2893 «

.79860

.I59OO

.20140

18

1-3794 X io«

6.13969

.72495 X io-«

7.86031

r9

3-0254

.48079

•33053

.51921

20

6.6356 "

.82189

.1 5070

.17812

TABLE 45.

EXPONENTIAL FUNCTIONS.

V>r V»r

Values of & * x and f- * and their logarithms.

X

v"*

e *

v**
Iog0*

V*

0--T-*

V;

\oge -•*

1

1.4429

0.19244

0.64203

1.807 56

2

2.4260

.38488

.41221

.61512

3

3-7786

•57733

.26465

.42267

4

5-8853

.76977

.16992

.23023

5

9.1666

.96221

.10909

•03/79

6

14.277

1.15465

0.070041

2-84535

7

22.238

•34709

.044968

•65291

8

34.636

•53953

.028871

.46047

9

53-948

•73I9»

.018536

.26802

10

84.027

.92442

.OI IQX)!

•07558

11

130.87

2.11686

0.0076408

3.88314

12

203.85

.30930

.0049057

.69070

13

3I7-5°

•5OI74

.0031496

.49826

'4

494.52

.69418

.OO2O222

.30582

15

770.24

.88663

.0012983

•11337

16

1199.7

3.07907

0.00083355

4.92093

17
18

1868.5
2910.4

.27151
•46395

.00053517
.00034360

.72849
•53605

'9

20

4533-1
7060.5

.65639
.84883

.OOO22O6O
.00014163

•34361
.15117

SMITHSONIAN TABLES.

34

EXPONENTIAL FUNCTIONS.

Value of <••' and e~* and their logarithms.

TABLE 46.

1

X

ex

log ex

«-*

log e-*

1/64

1.0157

0.00679

0.98450

1.99321

1/32

•0317

•OI357

.96923

.98643

1/16

.0645

.02714

•93941

.97286

I/IO

.1052

•04343

.90484

•95657

i/9

•"75

.04825

.89484

•95175

1/8
i/7

I-I33I
•!536

0.05429
.06204

0.88250
.86688

144571

•93796

1/6

.1814

.07238

.84648

.92762

i/5

.2214

.08686

.81873

•$*3M

i/4

.2840

.10857

.77880

.89143

i/3

I-3956

0.14476

0-7 i 653

^•85524

1/2

.6487

.21715

.60653

.78285

3/4

2.1170

•32572

•4/237

.67428

i

•7183

•43429

.36788

•56571

5/4

3-4903

•54287

.28650

•45713

3/2

4.4817

0.65144

0.22313

1.34856

7/4

5-7546

.76002

•1/377

.23998

2

7-3^91

.86859 .

•13535

.13141

9/4

9.4877

.97716

.10540

.02284

5/2

12.1825

1.08574

.08208

2.91426

TABLE 47.
LEAST SQUARES.*

2 Chae

Values of P — -.- e-('<x*>*d(hx)

vVo

This table gives the value of P, the probability of an observational error having a value positive or negative equal
to or less than x when h is the measure of precision, P = -^ | e-(itx)1 d(hx)

cision,P=~= C'

Jo

lur

1

2

3

4

5

6

7

8

9

10

0.0

.01128

.02256

•03384

.04511

•05637

.06762

.07886

.09008

.10128

.11246

O.I

.12362

•13476

•MS8?

•15695

.16800

.17901

.18999

.20094

.21184

.22270

0.2

•23352

.24430

•25502

.26570

•27633

.28690

.29742

.30788

.31828

•32863

o-3

•3389T

•34913

•35928

.36936

•37938

•38933

•33921

.40901

.41874

.42839

0.4

•43797

•44747

.45689

.88623

.47548

.48466

•49375

•50275

.51167

•52050

0.5

.52924

•5379°

.54646

•55494

•56332

.57162

•57982

.58792

•59594

.60386

0.6

.61168

.61941

.62705

•63459

.64203

.64938

.65663

.66378

.67084

.67780

o-7

.68467

.69143

.69810

.70468

.71116

•71754

.72382

.73001

.73610

.74210

0.8

.74800

•75381

•75952

•76514

.77067

,77610

.78144

.78669

.79184

.79691

0.9

.80188

.80677

.81156

.81627

.82089

.82542

.82987

•83423

•83851

.84270

1.0

.84681

.85084

.85478

.85865

.86244

.86614

.86977

•87333

.87680

.88020

.1

•88353

.88679

.88997

.8930cS

.89612

.89910

.90200

.90484

.90761

.91031

.2

.91296

•91553

.91805

.92051

.92290

.92524

.92751

•92973

.93190

.93401

•3

.93606

.93807

.94001

.94191

•94376

•94556

•9473 i

.94902

.95067

.95229

•4

•95385

•95538

.95686

.95830

•95970

.96105

.96237

•96365

.96490

.96610

1.5

.96728

.96841

.96952

•97059

.97162

.97263

•97360

•97455

•97546

•97635

.6

.97721

.97804

.97884

.97962

.98038

.981 10

.98181

.98249

•98315

•98379

•7

.98441

.98500

•98558

.98613

.98667

.98719

.98769

.98817

.98864

.98909

.8

•989.52

.98994

•99035

.99074

.99111

.99147

.99182

.99216

.99248

.99279

•9

.99309

•99338

.99366

•99392

.99418

•99443

.99466

.99489

.99511

•99532

* Tables 47-52 are for the most part quoted from Howe's " Formula; and Methods used in the application of Least
Squares."

SMITHSONIAN TABLES.

35

TABLE 48.

LEAST SQUARES.

This table gives the values of the probability P, as defined in last table, corresponding to different values of
x I r where r is the " probable error." The probable error r is equal to 0.476947 h.

X

r

0

1

2

3

4

5

6

7

8

9

0.0

.00000

.00538

.01076

.01614

.02512

.02690

.03228

.03766

•04303

.04840

O.I

•05378

.05914

.06451

.06987

•07523

.08059

•08594

.09129

.09663

.10197

0.2

.10731

. i i 264

.11796

.12328

.12860

J339'

.13921

.14451

.14980

•15508

o-3

.16035

.16562

.17088

.17614

.18138

.18662

.19185

.19707

.20229

•20749

0.4

.21268

.21787

.22304

.22821

•23336

.23851

.24364

.24876

•25388

.25898

0.5

.26407

.26915

.27421

.27927

.28431

•28934

•29436

.29936

•30435

•3°933

0.6

•31430

•31925

•32419

.32911

•33402

•33892

•3438o

.34866

•35352

•35835

0.7

•363^

.36798

•37277

•37755

•38231

•38705

•39178

•39649

.401 1 8

.40586

o.S

.41052

.41517

.41979

.42440

.42899

•43357

•43813

•44267

.44719

.45169

0.9

.45618

.46064

.46509

.46952

•47393

•4/832

.48270

48605

•49139

•49570

1.0

.50000

.50428

•50853

•5I277

.51699

.52119

•52537

•52952

•53366

•53778

.1

.54188

•54595

.55001

•55404

.55806

•56205

.56602

.56998

•57391

•57782

.2

.58171

•58558

•58942

•59325

•59705

.60083

.60460

.60833

.61205

•6i575

•3

.61942

.62308

.62671

.63032

•63391

•63747

.64102

•64554

.64804

•651 52

•4

.65498

.65841

.66182

.66521

.66858

•67193

.67526

.67856

.68184

.68510

1.5

.68833

•69155

.69474

.69791

.70106

.70419

.70729

.71038

•71344

.71648

.6

.71949

.72249

.72546

.72841

•73134

•73425

•73714

.74000

.74285

•74567

•7

.74847

•75I24

.75400

•75674

•7-5945

.76214

.76481

.76746

.77009

.77270

.8

•77528

•77785

.78039

.78291

•78542

.78790

•79036

.79280

•79522

.79761

•9

•79999

.80235

.80469

.80700

.80930

.81158

•81383

.81607

.81828

.82048

2.0

.82266

.82481

.82695

.82907

.83117

•83324

•83530

•83734

•83936

•84137

2.1

•84335

•84531

.84726

.84919

.85109

.85298

.85486

.85671

•85854

.86036

2.2

.86216

.86394

.86570

.86745

.86917

.87088

•87258

.87425

•87591

•87755

2-3

.87918

.88078

•88237

•88395

.88550

•88705

.88857

.89008

•89157

.89304

2-4

.89450

•89595

.89738

.89879

.90019

•90157

.90293

.90428

.90562

.90694

2.5

.90825

.90954

.91082

.91208

•91332

.91456

•91578

.91698

.91817

•9!935

2.6

.92051

.92 1 66

.92280

•92392

•92503

.92613

.92721

.92828

•92934

•93038

2.7

•93i4i

•93243

•93344

•93443

•93541

•93638

•93734

•93828

.93922

.94014

2.8

.94105

.94195

.94284

•94371

.94458

•94543

.94627

.94711

•94793

.94874

2.9

•94954

•95033

.95111

•95^7

.95263

•95338

•95412

•95484

•95557

.95628

0

1

2

3

4

5

6

7

8

9

3

.95698

.96346

.96910

•97397

.97817

.98176

.98482

•98743

.98962

.99147

4

.99302

•9943 r

•99539

99627

.99700

.99760

.99808

.99848

•99879

•99905

5

.99926

•99943

.99956

.99966

•99974

.99980

•99985

.99988

.99991

•99993

TABLE 49.

LEAST SQUARES.

Values of the factor 0.6745\/-^.
\n— 1

This factor occurs in the equation e, = o.6745"V/ 3- for the probable error of a single observation, and other

similar equations.

n =

1

2

3

4

5

6

7

8

9

00

0.6745

0.4769

0.3894

0.3372

0.3016

0.2754

0.2549

0.2385

10

0.2248

0.2133

.2029

.1947

.1871

.1803

.1742

.1686

.1636

.1590

20

•1547

.1508

..1472

•1438

.1406

•1377

•1349

•!323

.1298

.1275

30

.1252

.1231

.1211

.1192

.1174

•1157

.1140

.1124

.1109

.1094

40

.1080

.1066

•'053

.1041

.1029

.1017

.1005

.0994

.0984

.0974

50

0.0964

0.0954

0.0944

0.0935

0.0926

0.0918

0.0909

0.0901

0.0893

0.0886

60

. .0878

.0871

.0864

•o857

.0850

•0843

.0837

.0830

.0824

.0818

70

.0812

.0806

.0800

•0795

.0789

.0784

•0778

•0773

.0768

.0763

80

•0759

.0754

.0749

.0745

.0940

.0736

•0731

.0727

.0723

.0719

90

•0715

.0711

.0707

.0703

.0699

.0696

.0692

.0688

.0685

.0681

SMITHSONIAN TABLES.

LEAST SQUARES.

Values of the factor 0.6745A/ * ,
\ «(n— 1)

TABLE SO.

/'V 2
, — — for the probable error of the arithmetic mean.
, «(«— i)

It —

1

2

3

4

5

6

7

8

9

00

0.4769

0.2754

0.1947

0.1508

0.1231

0.1041

0.0901

0.0795

10

0.07 1 1

0.0643

.0587

.0540

.0500

.0465

•0435

.0409

.0386

•0365

, 20

.0346

.0329

.0314

.0300

.0287

.0275

.0265

.0255

.0245

.0237

30

0.0229

O.O22I

0.0214

0.0208

O.O2OI

0.0196

0.0190

0.0185

0.0180

0.0.175

40

.0171

.0167

.0163

.0159

•0155

.0152

.0148

.0145

.0142

.0139

5°

.0136

.0134

.0131

.0128

.OI26

.0124

.0122

.0119

.0117

.0115

TABLE 51,

LEAST SQUARES.

Values of the factor 0.8453\/ — ^-=-. .

\ n(n—l)

This factor occurs in the equation e. = 0.8453 r7= ; for the probable error of a single observation.

»»(« — i)

n —

1

2

3

4

5

6

7

8

9

00

o.S9?8

0.34 5 i

0.2440

0.1890

0.1543

0.1304

0.1130

0.0996

10

0.0891

0.0806

.0736

.0677

.0627

.0583

.0546

•0513

.0483

.0457

20

, -0434

.0412

•°393

.0376

.0360

•0345

•0332

.0319

.0307

.0297

30

0.0287

0.0277

0.0268

0.0260

0.0252

0.0245

0.0238

0.0232

0.0225

O.O22O

40

.0214

.0209

.0204

.or99

.0194

.0190

.0186

.0182

.0178

.0174

50

.0171

.0167

.0164

.0161

.0158

•oi55

.0152

.0150

.0147

.0145

LEAST SQUARES.

TABLE 52.

Values of 0.8453

- .
— 1

This table gives the average error of the arithmetic mean wlien the probable error is one.

»l =

1

2

3

4

5

6

7

8

9

00

0.4227

0.1993

O.I22O

0.0845

0.0630

0.0493

0.0399

0.0332

10

0.0282

0.0243

.0212

.0188

.0167

.0151

.0136

.0124

.0144

.0105

20

.0097

.0090

.0084

.0078

.0073

.0069

.0065

.0061

.0058

•0055

30

0.0052

0.0050

0.0047

0.0045

0.0043

0.0041

0.0040

0.0038

0.0037

0.0035

40

.0034

•0033

.0031

.0030

.OO29

.0028

.0027

.0027

.0026

.0025

5°

.0024

•

.0023

.0023

.0022

.0022

.0021

.0020

.0020

.0019

.0019

SMITHSONIAN TABLES.

37

TABLE 53.

GAMMA FUNCTION.*

Value of log

/"»
'.( e-**-1

Jo

tlx + 10.

Values of the logarithms -f 10 of the " Second Eiilerian Integral " (Gamma f

c

unction) I

Jo

or log r(«)

for values of n between i and 2. When « has values not lying between i and 2 the value of the function can be
readily calculated from the equation T(«+i) rr «I\«) = «(«— i) . . . (n—r)T(n—r).

n

0

1

2

3

4

5

6

7

8

9

1.00

9-99

97497

95001

92512

90030

87555

85087

82627

80173

77727

I.OI

75287

72855

7043°

68011

65600

63196

60799

58408

56025

53648

1.02

51279

48916

46561

44212

41870

39535

37207

34886

32572

30265

1.03

27964

25671

23384

21104

I8§31

16564

14305

12052

09806

07^67

1.04

°5334

03108

00889

98677

96471

94273

92080

89895

87715

81544

1.05

9-9883379

81220

79068

76922

74783

72651

70525

68406

66294

64188

i. 06

62089

59996

579'o

55830

53757

51690

49630

47577

45530

43489

1.07

41469

39428

37407

35392

333»4

31382

29387

27398

25415

23449

i. 08
1.09

21469
02123

19506
00223

17542
98329

15599
96442

13655
9456i

11717
92686

m

07860
89856

05941
87100

04029 !
852^0 i

1.10

9.9783407

81570

79738

779f4

76095

74283

72476

70676

68882

67095

i. ii

653^

63538

61768

60005

58248

56497

54753

53014

51281

49555

1. 12

47834

46120

44411

42709

41013

39323

3/638

3596o

34288

32622

I-I3

30962

29308

27659

26017

24381

22751

21126

19508

17896

16289

I.I4

14689

i3094

"505

09922

08345

06774

05209

03650

02096

00549

1.15

9.9699007

9747 i

95941

94417

92898

91386

89879

88378

86883

85393

1.16

83910

82432

80960

79493

78033

76578

75129

73686

72248

70816

1.17

69390

67969

66554

65J45

63742

62344

60952

59566

58185

56810 |

1.18

55440

54076

52718

51366

50019

48677

47341

46011

44867

43368

1.19

42054

40746

39444

38i47

36856

35570

34290

33016

3!747

30483

1.20

9.9629225

27973

26725

25484

24248

23017

21792

20573

19358

18150

1. 21

16946

15748

'4556

13369

12188

IIOI I

09841

08675

07515

06361 |

1.22

05212

04068

02930

01796

00669

99546

98430

973!8

96212

95111

1.23

594015

92925

91840

90760

89685

88616

87553

86494

85441

84393

1.24

83350

82313

81280

80253

79232

78215

77204

76198

75197

74201

1.25

9-95732"

72226

71246

70271

69301

68337

67377

66423

65474

6453°

1.26

63592

62658

61730

60806

59888

58975

58067

57i65

56267

55374

1.27

54487

53604

52727

51855

50988

50126

49268

48416

47570

46728

1.28

45891

45059

44232

434io

42593

41782

40975

40173

39376

38585

1.29

37798

37016

36239

35467

34700

33938

33i8i

32439

31682

30940

1.30

9-9530203

29470

28743

28021

27303

26590

25883

25180

24482

23789

'•31

23100

22417

21739

21065

20396

19732

19073

18419

17770

17125

1.32

16485

r585o

15220

'4595

'3975

J3359

12748

12142

11540

10944

'•33

10353

09766

09184

08606

08034

07466

06903

06344

05791

05242

i-34

04698

04158

03624

03094

02568

02048

01532

OI02I

00514

OOOI2

1.35

9-94995I5

99023

98535

98052

97573

97100

96630

96166

95706

95251

1.36

94800

94355

93913

93477

93°44

92617

92194

91776

91362

90953

i-37

90549

90149

89754

89363

88977

88595

88218

87846

87478

87"5

1.38

86756

86402

86052

85707

85366

85030

84698

84371

84049

83731

*-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

77230

77027

76829

76636

76446

76261 !

1.42

76081

75905

75733

75565

75402

75243

75089

74939

74793

74652 i

1-43

745'5

74382

74254

7413°

74010

73894

73783

73676

93574

73746

1.44

73382

73292

73207

73^5

73049

72976

72908

72844

72784

72728

* Quoted from Carr's " Synopsis of Mathematics," and is there quoted from Legendre's "Exercises de Calcu)
Integral," tome ii.

GAMMA FUNCTION.

TABLE 53.

•

0

1

2

3

4

5

6

7

8

9

1.45

9.9472677

72630

72587

72549

725M

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

73°22

1.48

73097

73175,

73258

73345

73436

73531

73630

73734

73841

73953

1.49

74068

74188

74312

74440

74572

74708

74848

74992

75Hi

75293

1.50

9-9475449

75610

75774

75943

76116

76292

76473

76658

76847

77040

1.51

77237

77438

77642

77851

78064

78281

78502

78727

78956

79189

1.52

79426

79667

79912

80161

80414

80671

80932

81196

81465

81738

x-53

82015

82295

82580

82868

83161

83457

83758

84062

84370

84682

1.54

84998

853'8

85642

85970

86302

86638

86977

87321

87668

88019

1.55

9.9488374

88733

89096

89463

89834

90208

90587

90969

91355

9J745

1.56
r-57

92139
96289

92537
96725

92938
97165

93344
97609

93753*
98056

94166
98508

94583
98963

95004
99422

95429
99885

95857
00351

1.58

500822

01296

01774

02255

02741

03230

03723

04220

04720

05225

i-59

05733

06245

06760

07280

07803

08330

08860

09395

09933

10475

1.60

9.9511020

11569

I2I22

12679

13240

13804

14372

14943

*55i9

16098

1.61

16680

17267

17857

18451

19048

19650

20254

20862

21475

22091 |

1.62

22710

23333

23960

24591

25225

25863

26504

27149

27798

28451 !

1.63

29107

29767

30430

31097

31767

32442

33J20

338oi

34486

35!75

1.64

35867

36563

37263

37966

38673

39383

40097

40815

41536

42260

1.65

9.9542989

43721

44456

45T95

45938

46684

47434

48187

48944

49704

1.66

50468

5I236

52OO7

52782

5356o

54342

55127

559l6

56708

575°4

1.67

58303

59106

59913

60723

61536

62353

63174

63998

64826

65656

1.68

66491

67329

68170

69015

69864

70716

7I57I

7243°

73293

74159

1.69

75028

759oi

76777

77657

78540

79427

80317

81211

82108

83008

1.70

9.9583912

84820

85731

86645

87536

88484

89409

90337

91268

32203

1.71

93J4i

94083

95O28

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

i-74

22869

23912

24959

26009

27062

28118

29178

30241

3 '308

32377

1.75

9-963345I

34527

35607

36690

37776

38866

39959

41055

42155

43258

1.76

44364

45473

46586

47702

48821

49944

51070

52200

53331

54467

i-77

55606

56749

57894

59043

60195

61350

62509

63671

64836

66004

1.78

67176

68351

69529

70710

71895

73082

74274

75468

76665

77866

1.79

79070

80277

81488

82701

83198

85138

86361

87588

88818

90051

1.80

9.9691287

92526

93768

95OI4

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

3386o

35204

36551

37900

39254

40610

41969

1.84

43331

44697

46065

47437

48812

50190

5'57i

52955

54342

55733

185

9.9757126

58522

59922

61325

62730

64140

65551

66966

68384

69805

1.86

71230

72657

74087

75521

76957

78397

79839

81285

82734

84186

1.87

85640

87098

88559

90023

91490

92960

94433

959JO

97389

98871

1.88

800356

01844

03335

04830

06327

07827

0933 !

10837

12346

'3859

1.89

!5374

16893

18414

19939

21466

22996

24530

26066

27606

29148

1.90

9.9830693

32242

33793

35348

36905

38465

40028

41595

43 164

44736

1.91

46311

47890

4947 i

51055

52642

54232

55825

57421

59020

60622

1.92

62226

63834

65445

67058

68675

70294

71917

73542

75170

76802

i-93

78436

80073

8i7'3

83356

85002

86651

88302

§295_7

91614

93275

1.94

94938

96605

98274

99946

01621

03299

04980

06663

08350

10039

1.95

9.9911732

13427

'5I25

16826

18530

20237

21947

23659

25375

27093

1.96

28815

30539

32266

33995

35728

37464

39202

40943

42688

44435

1.97
1.98

46185
63840

47937
65621

49693
67405

S'451
69192

53213
70982

54977
72774

56744
7457°

$&

60286
78169

62062
79972

1.99

81779

83588

85401

87216

89034

90854

92678

94504

96333

98165

SMITHSONIAN TABLES.

39

TABLE 54.

ZONAL HARMONICS.*

The values of the first seven zonal harmonics are here given for every degree between 6 = 0° and 6 = go°.

e

Zl

Z2

Z3

Z4

Z5

Z»;

z-

0°

I.OOCO

I.OOOO

I.OOOO

I.OOOO

I.OOOO

I.OOOO

I.OOOO

1°

0.9998

09995 :

0.9991

0.9985

0.9977

09967

0.9955

2

•9994

.9982

•9963

•9939

.9909

.9872

.9829

' 3

.9986

•9959

.9918

•9863

•9795

•9713

.9617

4

.9976

.9927

•9854

•9758

•9638

•9495

•9329

5

.9962

.9886

•9773

.9623

•9437

.9216

.8961

6°

•9945

.9836

.9674

•9459

.9194

.8881

.8522

7

•9925

•9777

•9557

.9267

.8911

.8476

.7986

8

•99°3

.9709

•9423

.9048

•8589

.8053

.7448

9

.9877

•9633

•9273

.8803

.8232

•7571

.6831

10

.9848

•954^

.9106

•8532

.7840

•7045

.6164

11°

.9816

•9454

•8923

.8238

•7417

.6483

.5461

12

•9/8i

•9352

•8724

.7920

.6966

.5892

•4732

13

•9744

.9241

.8511

•7582

.6489

•5273

•394°

14

•9703

.9122

.8283

.7224

•5990

•4635

.3219

15

•9659

•8995

.8042

.6847

•5471

.3982

•2454

16°

.9613

.8860

•7787 '

.6454

•4937

•3322

.1699

i7

•9563

.8718

-75*9

.6046

•439 r

.2660

.0961

18

•9511

.8568

.7240

.5624

•3«36

.2002

.0289

19

•9455

.8410

.6950

.5192

.3276

•1347

—•0443

20

-9397

.8245

.6649

•475°

.2715

.0719

— .1072

21°

•9336

.8074

•6338

.4300

.2156

.0107

—.1662

22

.9272

•7895

.6019

•3845

.1602

— .0481

— .2201

23

•9205

.7710

.5692

•3386

•1057

-.1038

—.2681

24

•9135

.7518

•5357

.2926

•0525

—•1559

—•3°95

25

.9063

•7321

.5016

.2465

.0009

—•2053

—•3463

26°

.8988

.7117

.4670

.2007

— .0489

—.2478

—•3717

27

.8910

.6908

•43 i 9

•r553

—.0964

—.2869

—.3921

28

.8829

.6694

•3964

.1105

—.1415

—.3211

—.4052

29

.8746

.6474

.3607

.0665

-.1839

— -35°3

—.4114

3°

.8660

.6250

•3248

.0234

—•2233

—•3740

— .4101

31°

.8572

.6021

.2887

—.0185

—•2595

—•3924

— .4022

32

.8480

.5788

•2527

—.0591

—.2923

—.4052

-.3876

33

.8387

•5551

.2167

—.0982

—.3216

— .4126

—•3670

34

.8290

•53!°

.1809

— -!357

—•3473

—.4148

—•3409

35

.8192

.5065

•1454

—.1714

—.3691

—.4115

—.3096

36°

.8090

.4818

.1102

—.2052

—•3871

—.4031

-.2738

37

.7986

•4567

•0755

—.2370

— .4011

-.3898

—•2343

38

.7880

•43 1 4

.0413

—.2666

— .4112

—•3719

—.1918

39

•7771

•4059

.0077

—.2940

— .4174

—•3497

—.1469

40

.7660

.3802

— .0252

—.3190

—.4197

—•3234

—.1003

41°

•7547

•3544

—.0574

—.3416

—.4181

-.2938

—•0534 •

42

•7431

.3284

—.0887

-.3616

—.4128

— .2611

— .0065

43

•73H

•3°23

— .1191

—•3791

—.4038

—•2253

•°395

44

•7193

.2762

-.1485

—•3940

—•39'4

—.1878

.0846

45

.7071

.2500

—.1768

— .4062

—•3757

-.1485

.1270

* Calculated by Prof. Perry (Phil. Mag. Dec. 1891). See also A. Gray, "Absolute Measurements in Electricity
and Magnetism," vol. ii., part 2.

SMITHSONIAN TABLES.

40

ZONAL HARMONICS.

TABLE 54.

1

Zl

Z.j

Z3

Z4

Z5

Z6

Z7

46°

0.6947

0.2238

— .2040

-.4158

-•3568

—.1079

0.1666

47

.6820

.1977

— .2300

—.4252

—•335°

—.0645

•2054

48

.6691

.1716

—•2547

—.4270

— -3105

— .0251

•2349

49

.6561

.1456

—.2781

—.4286

-.2836

.0161

.2627

5°

.6428

.1198

—.3002

—•4275

—•2545

•0563

.2854

51°

.6293

.0941

—.3209

—4239

—•2235

.0954

•3°3!

52

•6'57

.0686

—.3401

-.4178

— .1910

.1326

•3!53

53

.6018

•0433

—•3578

—•4093

—•1571

.1677

.3221

54

55

.5878 .
•5736

.0182
— .0065

—•3740
—.3886

-•3984
-•3852

— .1223
—.0868

.2002
.2297

•3234
•3'9i

56°

•5592

—.0310

— .4016

-.3698

— .0510

•2559

•3°95

57

•5446

—•0551

—•4I31

—•3524

— .0150

•2787

.2949

58

.5299

—.0788

—.4229

— -3331

.0206

.2976

.2752

£9

•5'5°

— .1021

—.4310

— -3"9

•°557

•3125

.2511

60

.5000

—.1250

—•4375

—.2891

.0898

•3232

.2231

61°

.4848

—.1474

—•4423

—.2647

.1229

.3298

.1916

62

.4695

—.1694

—•4455

—.2390

•1545

•3321

•i57i

63

•4540

— .1908

—.4471

.2121

.1844

•3302

.1203

64

•4384

—.2117

—.4470

—.1841

.2123

.3240

.0818

65

.4226

—.2321

—•4452

— -1552

•2381

•3138

.0422

66°

.4067

-.2518

—.4419

— .1256

.2615

.2996

.0021

67

•3907

— .27IO

—•4370

—•0955

.2824

.2819

— -°37S

68

•3746

—.2896

—•43°5

— .0650

•3005

.2605

—.0763

69

•3584'

— -3°74

—.4225

—•0344

•3158

.2361

—•"35

70

.3420

—•3425

—.4130

—.0038

•3281

.2089

—.1485

71°

•3256

—.3410

— .4021

.0267

•3373

.1786

—.1811

72

.3090

-•3568

-.3898

.0568

•3434

.1472

— .2099

73

.2924

-•37i8

—•376i

.0864

•3463

.1144

—•2347

74

.2756

-.3860

—.361 1

•"53

•346i

.0795

—•2559

75

.2588

—•3995

—•3449

•1434

•3427

.0431

—.2730

76°

.2419

—.4112

—•3275

•1705

•3362

.0076

—.2848

77

.2250

—.4241

—.3090

.1964

.3267

—.0284

—.2919

78

.2079

—•4352

-.2894

.2211

•3*43

— .0644

—•2943

79

.1908

—•4454

—.2688

•2443

.2990

—.0989

—.2913

80

•1736

—.4548

—.2474

.2659

.2810

—.1321

-•2835

81°

.1564

—•4633

—.2251

.2859

.2606

— 1635

—.2709

82

.1392

—.4709

— .2020

.3040

•2378

— .1926

—•2536

«3

.1219

—•4777

— -1783

•3203

.2129

—.2193

—.2321

84

.1045

-.4836

— -'539

•3345

.1861

—.2431

— .2067

85

.0872

—.4886

—.129!

•3468

•1577

-.2638

— -J779

86°

.0698

—.4927

—.1038

•3569

.1278

—.2811

— .1460

87

•0523

—•4959

—.0781

.3648

.0969

—.2947

—.1117

88
89

•0349
•0175

-.4982
—•4995

— .0522
— .0262

•3704
•3739

.0651
.0327

—•3045
— -3I05

—•0735
—.0381

90

.ocoo

— .5000

— .0000

•375°

.0000

—•3125

— .0000

SMITHSONIAN TABLES.

TABLE 55.

MUTUAL INDUCTANCE.*

M
Values of log — -T=-

M

Table of values of log — y — - for facilitating the calculation of the mutual inductance M of two coaxial circles of

radii a, a', at distance apart b. The table is calculated for intervals of & in the value of cos—' { i —

I \a — a' )•* + o* >

from 60° to 90°.

1

0'

6'

12'

18

24

30'

36'

42'

48'

54'

60°

^•4994783

5022651

5050505

5078345

5106173

5^3989

5161791

5189582

5217361

5245128

61

5272883

5300628

5328361

5356084

5383796

5411498

5439!90 5466872

5494545

5522209

62

5549864

5577510

5605147

5632776

5660398

5688011

5715618

5743217

5770809

5798394

63

5825973

5853546

5881113

590867 5

5936231

5963782

5991322

6018871

6046408

6073942

64

6101472

6128998

6156522

6184042

6211560

6239076

6266589

6294101

6321612

6349121

65°

1.6376629

6404137

6431645

6459153

6486660

6514169

6541678

6569189

6596701

6624215

66

6651732

6679250

6706772

6734296

6761824

6789356

6816891 6844431

6871976

6899526

67

6927081

6954642

6982209

7009782

7037362

7064949

7092544

7120146

7H7756

7175375

68

7203003

7230640

7258286

7285942

7313609

7341287

7368975

7396675

7424387

7452111

69

7479848

7507597

753536i

7563^8

7590929

7618735

7646556

7674392

7702245

7730114

70°

1.7758000

7735903

7813823

7841762

7869720

7897696

7925692

7953709

7981745

8009803

7i

8037882

8065983

8094107

8122253

8150423

8178617

8206836

8235080

8263349

8291645

72

8319967

8348316

8376693

8405099

8433534

8461998

8490493

8519018

8547575

8576164

73

8604785

8633440

8662 i 29

8690852

8719611

8748406

8777237

8806106

8835013

8863958

74

8892943

8921969

8951036

8980144

9009295

9038489

9067728

9097012

9126341

9I557I7

75°

1.9185141

9214613

9244U5

9273707

9303330

9333005

9362733

9392515

9422352

9452246

76

9482196

9512205

9542272

9572400

9602590

9632841

9663157

9693537

9723983

9754497

77

9785079

98I5731

9846454

9877249

9908118

9939062

9970082

oooi i8T

0032359

006361?

78

0.0094959

0126385

0157896

0189494

0221181

0252959

0284830

0316794

0348855

0381014

79

0413273

0445633

0478098

0510668

0543347

0576136

0609037

0642054

0675187

0708441

80°

0.0741816

07753'6

0808944

0842702

0876592

0910619

0944784

0979091

1013542.

1048142

81

1082893

1117799

1152863

1188089

1223481

1259043

1294778

1330691

1366786

1403067

82

1439539

1476207

I5I3075

i55OI49

i 587434

1624935

1662658

1700609

1738794

1777219

83

1815890

1854815

1894001

'933455

1973184

2013197

2053502

2094108 2135026

2176259

84

2217823

2259728

2301983

2344600

2387591

2430970

2474748

2518940

2563561

2608626

85°

0.2654152

27001 56

2746655

2793670

2841221

2889329

2938018

2987312

3037238

3087823

86

3 '39097

3191092

3243843

3297387

335^62

3407012

3463184

3520327

3578495

3637749

87

3698153

3759777

3822700

3887006

3952792

4020162

4089234

4160138

4233022

4308053

88

4385420

4465341

4548064

4633880

4723127

4816206

4913595

5015870

5123738

5238079

89

5360007

5490969

5632886

5788406

5961320

6157370

6385907

6663883

7027765

7586941

* Quoted from Gray's " Absolute Measurements in Electricity and Magnetism," vol. ii., p. 852.

SMITHSONIAN TABLES.

42

ELLIPTIC INTEGRALS.

Values of

t HU-!
Jo

This table gives the values of the integrals between o and ir/2 of the function (i — sin'Osin2^)
ues of the modulus corresponding to each degree of 0 between o and 90.

TABLE 56.

for different val-

e

p d*

/•IT
1 *(i sin^sin^)1^

Ja

e

X* ^

I B(i— sin*0sin*$)J<#

JQ (i— sin20sin2<£$

(i— sin2esin20)*

Number.

Log.

Number.

Log.

Number.

Log.

Number.

Log.

0°

1.5708

0.196120

1.5708

0.196120

45°

1.8541

0.268127

I-35°6

0.130541

i

5709

I96I53

5707

196087

6

8691

271644

3418

i 27690

2

5713

196252

5703

195988

7

8848

275267

3329

124788

3

5719

196418

5697

195822

8

9011

279001

3238

121836

4

5727

196649

5689

r9559i

9

9180

282848

3H7

118836

5°

I-5738

0.19694?

1.5678

0.195293

50°

I -9356

0.2868 1 1

1-3055

0.115790

6

5751

197312

5665

194930

i

9539

290805

2963

112698

7

5/67

197743

5649

194500

2

9729

295101

2870

109563

8

5785

197241

5632

194004

3

9927

299435

2776

106386

9

5805

198806

5611

193442

4

2-0133

3°3fpi

2681

103169

10°

1.5828

0.199438

I-5589

0.192815

55°

2-0347

0.308504

1.2587

0.099915

i

5!l4

200137

5564

192121

6

0571

313247

2492

096626

2

5882

200904

5537

191302

7

0804

318138

2397

093303

3

59'3

201740

55°7

190537

8

1047

323182

2301

089950

4

5946

202643

5476

189646

9

1300

328384

2206

086569

15°

1.5981

0.203615

1-5442

0.188690

60°

2.1565

o.333'53

I.2III

0.083164

6

6020

204657

5405

187668

i

1842

339295

2015

079738

7

6061

205768

5367

186581

2

2132

345020

I92O

076293

8

6105

206948

5326

185428

3

2435

350936

1826

072834

9

6151

208200

5283

184210

4

2754

357053

1732

069364

20°

1.6200

0.209522

1-5238

0.182928

65°

2.3088

0.363384

1.1638

0.065889

i

6252

210916

5'9i

181580

6

3439

369940

*545

062412

2

6307

212382

5*41

180168

7

3809

376736

1453

058937

3

6365

213921

5090

i 7869 i

8

4198

383787

1362

055472

4

6426

215533

5°37

177150

9

4610

391112

1272

052020

25°

1.6490

0.217219

1.4981

0.175545

70°

2.5046

0-398730

1.1184

0.048589

6

6557

218981

4924

173876

i

5507

406665

1096

045183

7

6627

220818

4864

172144

2

5998

4M943

1OII

041812

8

6701

222732

4803

170348

3

6521

423596

0927

038481

9

6777

224723

4740

168489

4

7081

432660

0844

035200

30°

1.6858

0.226793

1.4675

0.166567

75°

2.7681

0.442176

i .0764

0.031976

i

6941

228943

4608

164583

6

8327

452196

0686

028819

2

7028

231173

4539

162537

7

9026

462782

0611

025740

3

7119

233485

4469

160429

8

9/86

474008

0538

022749

4

7214

235880

4397

158261

9

3.0617

485967

0468

019858

35°

1.7312

0.238359

1.4323

0.156031

80°

3- '534

o'.498777

i .0401

0.017081

6

74iS

240923

4248

153742

i

2553

512591

0338

014432

7

7522

243575

4171

I5I393

2

3699

527613

0278

011927

8

7633

246315

4092

148985

3

5004

544120

0223

009584

9

7748

249146

4013

146519

4

6519

562514

0172

007422

40°

1.7868

0.252068

i-393i

0.143995

85°

3-83I7

0.583396

1.0127

0.005465

i

7992

255085

3849

141414

6

4.0528

607751

0086

003740

2

8122

258197

3765

138778

7

3387

637355

0053

002278

3

8256

261406

3680

136086

8

7427

676027

0026

OOII2I

4

8396

264716

3594

1 33 340

9

5-4349

735192

0008

OOO326

45°

1.8541

0.268127

1.3506

0.130541

90°

oo

00

I.OOOO

SMITHSONIAN TABLES.

43

TABLE 57.

BRITISH UNITS.

Cross sections and weights of wires.

This table gives the cross section and weights in British units of copper, iron, and brass wires of the diameters
given in the first column. For one tenth the diameter divide section and weights by 100. For ten times the
diameter multiply by 100, and so on.

^c

il

5

Area of
cross
section
in
Sq. Mils.

Copper — Density 8.90.

Iron — Density 7.80.

Brass — Density 8.56.

Pounds
per Foot

Log.

Feet per
Pound.

Pounds
per Foot.

Log.

Feet pe
Pound.

Pounds
per Foot.

Log.

Feet per
Pound.

10

78.54

.000303

4.48150

3300-

.0002656

4.42420

3765.

.0002915

4.46458

343 '•

II

95-03

0367

•56429

2727.

03214

.50697

3112.

03527

54735

2836.

12

113.10

0436

.63986

2291.

03825

•58257

2615.

04197

62295

2383-

13

132.73

0512

•70939

1953-

04488

.65208

2228.

04926

69246

2030.

M

'53-94

0594

•77376

I683.

05206

.71646

1921.

057I3

75684

1750-

15

176.71

.000682

4.83368

1467.

.0005976

4-77637

167^,

.0006558

4.81675

J525-

16

201.06

0776

.88974

1289.

06799

•83244

1471.

07461

.87282

1340.

17

226.98

0876

.94240

1142.

07675

.88510

'3°3-

08423

.92548

1187.

18

25447

0982

.99205

1018.

08605

•93475

1162.

09443

•975'3

1059.

J9

283-53

1094

3.03902

914.

09588

.98171

1043.

.0010522

3.02209

950-

20

314.16

.OOI2I2

3-08357

825.1

.OOIO62

3.02626

941.4

.001166

3.06664

857-7

21

346-36

J336

.12594

748.3

II7I

.06864

853-8

1285

.10902

778.0

22

380.13

1467

.16634

681.8

1286

.10904

777-8

1411

.14942

708.9

23

4I5-48

1603

.20496

623.8

1405

.14766

711.7

1542

.18804

648.6

24

452.39

1746

.24192

572-9

J530

.18463

653-7

1679

.22500

595-7

25

490.87

.001894

3-27738

528.0

001660

3.22008

602.4

001822

3.26046

549-o

26

530.93

2046

.31146

488.1

1795

•25415

557-0

1970

•29453

5°7-5

27

572.56

2209

•34423

452.6

1936

•28693

5!6-5

2125

•32731

470.6

28

6i5.75

2376

•37583

420.9

2082

•31852

480.3

2285

•35890

437-6

29

660.52

2549

.40630

392-4

2234

.34900

447-7

2451

•3893«

408.0

30

706.82

.002727

3-43575

366.7

002390

3-37845

418.4

002623

3.41882

381.2

3i

754-77

2912

.46424

343-4

2552

•40693

391.8

2801

•44731

357-0

32

804.25

3103

.49181

322.2

2720

•4345°

367-7

2985

.47488

33 5- i

33

855-30

3300

•51854

303-0

2892

.46123

345-8

3'74

.50161

3I5-1

34

907.92

3503

•54446

285-4

3070

.48716

325-7

3369

•52754

296.8

35

962.11

003712

3.56964

269.4

003253

3-5I233

3°7-4

003570

3-5527I

280.1

36

1017.88

4927

.59412

254.6

3442

.5368.

290.5

3777

•57719

264.7

37

1075.21

4149

.61791

241.0

3636

.56061

275-0

3990

.60098

250.6

38

1134.11

4376

.64108

228.5

3844

.58476

260.2

4218

.62514

237-1

39

1194.59

4609

.66364

216.9

4040

.60633

247.6

4433

.64671

/•
225.6

40

1256.64

004849

3.68563

206.2

004249

3-62833

235-3

004664

3.66871

214.4

4i

1320.25

5094

.70708

196.3

4465

•64977

224.0

4900

.69015

204.1

42

1385.44

5346

.72801

187.1

4685

.67070

213-5

5r4i

.71108

'94-5

43

1452.20

5603

•74845

178.5

4911

.69114

203.6

5389

•73r52

185.6

44

1520.53

5867

.76842

170.4

5M2

.71111

'94-5

5643

•75149

177.2

45

1590-43

006137

378793

162.9

005378

3-73063

185.9

005902

3.77101

169.4

46

1661.90

6412

.80703

'55-9

5620

.74972

177.9

6167

.79010

162.1

47

'734-94

6694

.82569

149.4

5867

.76840

170.5

6438

.80878

'55-3

48

1809.56

6982

.84399

143-2

6119

.78669

163.4

6715

.82706

148.9

49

1885.74

7276

.86289

137-4

6377

.80459

156.8

6998

.84497

142.9

50

1963.50

007576

3-87945

132.0

006640

3.82214

150.6

007287

3.86252

T37-2

51

2042.82

7882

.89664

126.9

6908

•83934

144.8

758i

.87972

I3I-9

52

2123.72

8194

•91352

I22.O

7181

.85621

139.2

7881

.89659

126.9

53

2206.18

8512

•93005

U7-5

7460

•87275

i34-o

8187

•91313

I22.I

54

2290.22

8837

.94630

II3.2

7744

.88899

129.1

8499

•92937

117.7

55

2375-83

009167

3.96223

I09.I

008034

3-90493

124.5

008817

3-94531

II3-4

SMITHSONIAN TABLES.

44

TABLE 57,

BRITISH UNITS.

Cross sections and weights of wires.

c

E'l
.2^
Q

Area of
cross
section

in
Sq. Mils.

Copper — Density 8.90.

Iron — Density 7.80.

Brass — Density 8.56.

Pounds
per Foot.

Log.

Feet per
Pound.

Pounds
per Foot.

Log.

Feet per
Pound.

Pounds
per Foot.

Log.

Feet per
Pound.

55

2375-83

.009167

3.96223

109.1

.008034

3-90493

124.5

.008817

3-9453 '

"3-4

56

2463.01

09504

.97789

105.2

08329

.92058

1 20. 1

09140

.96096

109.4

57

2551.76

09846

_-99325

IOI.6

08629

•93595

"5-9

09470

•97633

105.6

58

2642.08

10195

98.1

08934

.95106

111.9

09805

_-99'44

IO2.O

59

2733-97

10549

.02320

94-8

09245

.96591

108.2

10146

2.00629

98.6

60

2827.43

.01091

2.03782

91.66

.00956

3.98050

104.59

.01049

2.02088

95-30

61

2922.47

1128

.05216

88.68

0988

.99486

101.19

1085

•03524

92.21

62

3019.07

1165

.06628

85.84

IO2I

2.00898

97-95

1 1 2O

.04936

89.25

63

3"7-25

1203

.08019

83.14

1054

.02288

94.87

"57

.06326

86.45

64

3216.99

1241

.09386

80.56

I088

.03656

91.83

"94

.07694

83-77

65

33l8-3r

.OI 280

2.10732

78.11

.OII22

2.05003

89.12

.01231

2~.o9O4i

8l.2I

66

3421.19

1320

.12061

75-76

"57

.06329

86.44

1270

.10367

78.76

67

3525-65

1360

•13367

73-51

1192

•07635

83.88

1308

.11673

76.43

68

3631-68

1401

•14655

7i-36

1228

.08922

81.42

1348

.12960

74-20

69

3739-28

1443

•i5924

69.30

1264

.10190

79.09

1388

.14228

72.06

70

384845

.01485

2.17174

67-34

.01302

2.11451

76.82

.01429

2.15489

70.00

71

3959-19

1528

.18404

65.46

1339

.12672

74.69

1469

.16710

68.06

72

4071.50

1571

.19618

63-65

1377

.13887

72.63

*5»

•17925

66.19

73

4185.39

1615

.20817

61.92

1415

•15085

70.66

1553

.19123

64.38

74

4300.84

1660

.22000

60.26

1454

.16267

68.76

1596

.20304

62.66

75

4417.86

.01705

2.23165

58.66

.01494

2.17432

66.95

.01639

2.21460

61.01

76

4536.46

'751

•243 1 7

57-13

1534

•18583

65.19

1684

.22621

59-40

77

4656.63

1797

•25453

55-65

'575

.19718

63-5°

!728

•23756

57-87

78

4778.36

1844

.26574

54-23

1616

•20839

61.89

1773

.24877

56.39

79

4901.67

1892

.27681

52-87

1658

.21946

60-33

1819

.25974

54-99

80

5026-55

.01939

2.28769

5r-56

.01700

2.23038

58-83

.01865

2.27076

53-6 1

1 8l

5 ! 53-oo

1988

.29848

50-29

1743

.24117

57-39

1912

.28155

52.29

82

5281.02

2038

.30914

49.07

1786

•25183

56.00

1960

.29221

51-03

83

5410.61

2088

.31966

47.90

1830

.26236

54-66

2OO8

•30274

49.80

84

5541-77

2138

.33006

46.77

1874

.27276

53-36

2057

•313H

48.63

85

5674.50

.02189

2-34034

45-67

.01919

2.28304

52.11

.O2IO6

2.32342

47-49

86

5808.80

2241

•35050

44.62

1964

.29320

50.91

2156

•33358

46-39

87

5944-68

2294

•36054

43.60

2OIO

•30324

49-75

22O6

•34362

45-33

88

6082.12

2347

•37047

42.61

2057

•3'3i7

48.62

2257

•35355

44-3°

89

6221.14

2400

.38028

41.66

2IO4

.32298

47-54

2309

•36336

43-31

90

6361.73

•02455

2.38999

40.74

.02151

2.33269

46.49

.02360

2.37297

42-37

9i

6503.88

2509

•39958

39-85

2199

.34228

45-47

2414

.38266

41-43

92

6647.61

2565

.40908

38-99

2248

•35178

44.49

2467

.39216

40-54

93

6792.91

2621

.41847

38-15

2297

.36116

43-54

252I

.40154

32'o7

94

6939.78

2678

•42775

37-35

2347

•37046

42.61

2575

.41084

38-83

95

7088.22

•02735

2.43694

36.56

.02397

2-37965

41.72

.02630

2.42003

38.02

96

7238.23

2793

.44604

35-8i

2448

.38874

40.86

2686

.42912

37-37

97

7389.81

2851

.45404

35-07

2499

•39775

40.02

2742

.43812

36.46

98

7542.96

2910

•46395

34-36

2551

.40665

39.20

2799

•44703

35-72

99

7697.69

2970

•47277

33-67

2603

•41547

38.42

2857

•45585

35-oi

lioo

7853-98

.03030

2.48150

33-oo

.02656

2.42420

37.65

.02915

2.46458

34-31

SMITHSONIAN TABLES.

45

TABLE 58.

METRIC UNITS.

Cross sections and weights of wires.

This table gives the cross section and the weight in metric units of copper, iron, and brass wires of the diameters
given in the first column. For one tenth the diameter divide sections and weights by 100. For ten times the
diameter multiply by 100, and so on.

, E

Copper — Density 8.90.

Iron — Density 7.80.

Brass — Density 8.56.

o a

1

a <n

§

1

V

.

B

.

"* .fl

^O O

S t

</) £

S 0

</> £

£ 6

5-3
a °

I?

|||

Log.

£ * s

rt % ^u

Log.

JsJ

1 * S

rt «J u

Log.

a h 1

5 0.2

Q "•

< *

0 S

§~0

0 S

S 0

0 S

S 0

10

78.54

0.06990

2.84448

14.306

0.06126

2.78718

16.324

0.06723

2.82756

14.874

ii

95-03

.08458

.92725

11.823

.07412

.86996

13.492

.08135

.91034

12.293

12

113.10

.10065

1.00285

9-935

.08822

•94556

"•335

.09681

•98594

10.330

13

132-73

.11813

•07236

8.465

.10353

1.01506

9-659

.11362

1-05544

8.80 1

14

153-94

.13701

•13674

7-299

.12008

•07945

8.328

•I3I77

.11983

7.589

15

176.71

°-I573

7.19665

6.358

0.1378

7.13936

7-255

0-1513

7.17974

6.6n

16

201.06

.1789

.25272

5.588

.1568

.19542

6.376

.1721

•23580

5.810

17

226.98

.2020

•30538

4.951

.1770

.24808

5-648

•1943

.28846

5-J47

18

254-47

.2265

•35503

4-4I5

.1985

•29773

5.038

.2178

•338"

4-591

'9

283-53

.2523

.40199

.2212

.34469

4.522

.2427

•38507

4.120

20

314.16

0.2796

7.44654

3-577

0.2450

7.38925

4.081

0.2689

7.42963

3-7I9

21

346.36

•3083

.48892

.244

.27O2

.43162

3-7oi

.2965

.47200

•373

22

380.13

•3383

•52932

2.956

.2965

.47203

•373

•3254

.51241

•073

23

415.48

.3698

•56794

.704

.3241

.51064

.086

•3557

•55103

2.812

24

452-39

.4026

.60490

.484

•3529

•54761

2-834

.3872

•58799

•582

25

490.87

0.4369

7.64036

2.289

0.3829

7.58306

2.612

0.4202

7.62344

2.380

26

530-93

•4725

•67443

.116

4141

.61713

•415

•4545

•65751

.200

27

572.56

.5096

.70721

1.962

.4466

.64992

•239

.4901

.69030

.040

28

615.75

.5480

•73880

.825

.4803

.68150

.082

•5271

.72188

1.897

.29

660.52

•5879

.76928

.701

•S»5*

.71198

1.941

•5654

•75236

.769

30

706.86

0.6291

7.79872

1.590

o-55'4

7.74143

1.814

0.6051

7.78181

1.653

31

754-77

.6717

.82721

•489

.5887

.76991

.699

.6461

.81029

•548

32

804.25

•7158

.85478

•397

.6273

•79749

•594

.6884

•83787

•453

33

855-30

.7612

.88151

.6671

.82421

•499

•7321

.86459

.366

34

907.92

.8081

.90744

[238

.7082

.85014

.412

.7772

.89052

.287

35

962.11

0.856

7.93261

1.168

0.7504

7.87531

1-333

0.8236

7.91570

1.214

36

1017.88

.906

•95709

.104

•7939

.89979

.260

•8713

.94017

.148

37

1075.21

•957

.98088

.045

.8387

•92359

.192

.9204

•96397

.087

38

1134.11

I.OI2

0.00504

0.988

.8866

•94775

.128

•9730

•98813

.028

39

1194.59

•063

.02661

.941

.9318

.96931

•073

1.0230

0.00969

0.978

40

1256.64

1.118

0.04861

0.894 1

0.980

7.99131

i .0200

1.076

0.03169

0.9296

42

1320.25
I385-44

•'75
•233

.07005
.09098

.8511
.8110

1.030
.081

0.01275
.03368

0.9711
.9254

.130
.186

•05313
.07406

.8849
•8432

43

1452.20

.292

.11142

•7738

.133

.05412

.8828

•243

.09450

.8044

44

1520-53

•353

•I3I39

•7389

.186

.07409

.8432

.302

.11447

•7683

45

1590.43

1.415

0.15091

0.7065

1.241

0.09361

0.806 1

1.361

0.13399

0-7345

46

1661.90

•479

.17000

.6761

.296

.11270

•7714

•423

•15308

.7029

47

'734-94

•544

.18868

.6476

•353

•13138

•7389

.485

.17176

•6734

48

1809.56

.611

.20696

.6209

.411

.14967

.7085

•549

.19005

.6456

49

1885.74

.678

.22487

•5958

.471

.16758

•6799

.614

.20796

.6195

50

1963.50

1.748

0.24242

0.5722

r.532

0.18513

0.6530

i. 68 1

0.22551

0-5950

51

2042.82

.818

.25962

•5500

•593

.20232

.6276

•753

•24371

•5705

52

2123.72

.890

.27649

.5291

.657

.21919

•6037

.818

•25957

53

2206.18

•964

•29303

•5093

.721

•23574

.5811

.888

.27612

•5295

54

2290.22

2.038

.30927

.4906

.786

•25197

•5598

.960

•29235

.5101

55

2375.83

2.114

0.32521

0.4729

1-853

0.26791

0.5396

2.034

0.30829

0.4917

SMITHSONIAN TABLES.

46

TABLE 58.

METRIC UNITS.

Cross sections and weights of wires.

3 0

J2

"

Copper — Density 8.90.

Iron — Density 7.80.

Brass — Density 8.56.

0 .

B

V

I

•

8

V

'" £

*o §

6 •

s s

g

v S

1 "I

W'S

1 hi

Log.

- o> E

! *•£

« i> t;

Log.

h " 6

" D. 2

111

Log.

Q »

< "

o&S

Sfto

o S

S 0

0 °"S

iao

55

2375.83

2.114

0.32521

•4729

'•853

0.26791

•5396

2-034

0.30829

.4917

56

2463.01

.192,'

.34086

.4562 I

.921

•28356

•5205

.108

•32394

•4743

57

2551.76

.271

•35623

•4403 .

.990

.29893

.5024

.184

•3393 i

•4578

58

2642.08

•351

-37134

•4253

2.061

•31404

.4852

.262

•35442

.4422

59

2733-97

•433

.38618

.4112

.132

.32889

.4689

•340

.36927

•4273

60

61

2827.43
2922.47

2.516
.601

0.40078
.41514

•3974
•3845

2.205
.280

0-34349
•35784

•4534
•4387

2.420
•502

0.38387
•39823

.4132
•3997

62

3019.07

.687

.42926

.3722

•355

•37196

.4246

-584

•41235

.3869

63

3117.25

•774

.44316

.3604

•431

•38587

•4"3

.668

.42625

•3748

64

3216.99

.863

.45684

•3493

•5°9

•39954

•3985

.760

.44092

•3623

65

3318.31

2-953

0.47031

•3386

2.588

0.41301

.3864

2.840

0-45339

•3521

66

3421.19

3-°45

•48357

.3284

.669

.42627

•3747

.929

.46665

•3415

67

3525-65

.138

•49663

•3187

.750

•43933

•3636

3.018

•47971

•33*3

68

3631.68

.232

•5°95°

•3094

•833

.45220

•3530

.109

.49258

•3217

69

3739-28

.328

.52218

•3005

.917

.46488

•3429

.201

.50526

•3I24

70

3848.45

3426

0-53479

.2919

3-oo3

0-47749

•3330

3-295

0.51787

•3035

71

3959-19

.524

.54700

.2838

.088

.48970

•3238

•389

.53008

.2951

72

4071.50

.624

•55915

.2759

.176

•50185

.485

•54223

.2869

73

4185.39

-725

•57"3

•2685

.265

'5'363

•3063

'583

•55421

.2791

74

4300.84

.828

.58294

.2612

•355

.2981

.682

.56603

.2716

75

4417.86

3-932

0.59460

•2543

3-446

0-53731

.2902

3.782

0-57769

.2644

76

4536.46

4-037

.60611

•2477

•538

.54881

.2826

.883

.58919

•2575

77

4656.63

.144

.61746

.2413

.632

.56017

•2753

.986

.60056

.2509

78

4778.36

•253

.62867

•2351

•727

•57137

.2683

4.090

.61175

•2445

79

4901.67

.362

•63974

.2292

•823

.58244

.2615

.177

.62283

•2394

80

5026.55

4-474

0.65066

•2235

3.921

0.59336

•2550

4-303

0.63375

•2324

81

5153.00

•586

.66145

.2180

4.019

.60415

.2488

.411

•64454

.2267

82

5281.02

.700

.67211

.2128

.119

.61481

.2428

.521

•65519

.2212

83

5410.61

.815

.68264

.2077

.220

.62534

•2369

.631

.66572

.2159

84

5541-77

•932

•69304

.2027

•323

•63574

•2313

•744

.67612

.2108

85

5674-50

5-05°

0.70332

.1980

4.426

0.64602

.2259

4.857

0.68640

•2059

86

5808.80

.170

•71348

•!934

•531

.65618

.2207

.972

.69656

.2OI I

87

5944-68

.291

•72352

.1890

•637

.66622

.2157

5.089

.70660

.1965

88

6082.12

•413

•73345

.1847

•744

.67615

.2108

.206

•71653

.1921

89

6221.14

•537

•74326

.1806

•852

.68596

.2061

•325

•72634

.1878

90

6361.73

5.662

0.75297

.1766

4.962

0.69567

.2015

5.446

0.73605

.I836

91

6503.88

.788

.76256

.1728

5-073

.70527

.1971

.567

•74565

.1796

92

6647.61

.916

.77206

.1690

.185

.71476

.1929

.690

•7SV4

•1757

93

6792.91

6.046

.78144

.1654

.298

.72414

.1887

.815

•76452

.1720

94

6939.78

.176

•79074

.1619

•413

•73344

•1847

.940

•77382

.1683

95

7088.22

6.309

0-79993

•1585

5-529

0.74263

.1809

6.068

0.78301

.1648

96

7238-23

•442

.80902

.1552

.646

•75173

.1771

.196

.79211

.1614

97

7389.81

•577

.81802

.1520

.764

.76073

•1735

•326

.801 1 1

.1581

98

7542.96

•713

.82693

.1490

.884

.76964

.1670

•457

.81002

.1549

99

7697.69

.851

•83575

.1460

6.004

•77846

.1665

•589

.81884

.1518

100

7*53.5*

6.990

0.84448

•I431

6.126

0.78718

.1632

6-723

0.82756

.1487

SMITHSONIAN TABLES.

47

TABLE 59.

BRITISH AND METRIC UNITS.

Cross sections and weights of wires.

The cross section and the weight, in different units, of Aluminium wire of the diameters given in the first column.
For one tenth the diameter divide sections and weights by 100. For ten times the diameter multiply by 100,
and so on.

a

E5

23
Q

Area of

cross
section
in
Sq. Mils.

Aluminium — Density 2.67.

Pounds
per
Foot.

Log.

Feet
per
Pound.

Ounces
per

Foot.

Log.

Feet
per
Ounce.

Grammes
per
Metre.*

Log.

Metres
per
Gramme.

10

78.54

.0000909

5.95862

IIOOO.

.001455

3.16274

687.5

.02097

2.32160

47.69

ii

95-03

OIIOO

4.04139

9091.

01760

•24551

602.4

•02537

•40437

39-41

12

113.10

01309

.11699

7638.

02095

.32111

477-4

.03020

•47997

33-"

13

132.73

01536

.18650

6509.

02458

.39062

406.8

•03544

•54948

28.22

14

153-94

01782

.25088

5612.

02851

•45500

350.8

.04110

.61386

24-33

15

176.71

.OOO2O45

4.31079

4889.

.003273

3-5H9I

305.6

.04718

2-67377

21.19

16

2OI.O6

02327

-36685

4297.

03724

•57097

268.5

.05368

.72984

18.63

i?

226.98

02627

.41952

3876.

04204

.62364

237-9

.06060

.78250

16.50

18

254-47

02946

•46917

3395-

04713

.67329

212.2

.06794

•83215

14.72

19

283.53

03282

•5I6I3

3047-

05251

.72025

190.4

.07570

.87911

13.21

20

314.16

.0003636

4.56068

2750.

.005818

3.76480

I7I.9

.08388

2.92366

11.922

21

346.36

04009

.60306

2494.

06415

.80718

!55-9

.09248

.96604

10.813

22

380.13

04400

•64346

2273.

07040

.84758

142.0

.IOI49

1.00644

9-853

23

415.48

04809

.68208

2079.

07697

.88630

129.9

.11093

.04506

9.014

24

452-39

05237

.71904

1910.

08378

.92316

119.4

.12079

.08202

8.279

25

490.87

.0005682

4-7545°

1760.

.00909

3.95862

IIO-OO

.1311

1.11748

7.030

26

53°-93

06147

.78867

1627.

0983

.99269

101.70

.1418

•i5'55

7-054

27

572.56

06628

.82135

1509.

1060

2.02547

94-30

.1529

•i8433

6.541

28

615.75

07127

•85293

1403.

1140

•05705

87.69

.1644

.21592

6.083

29

660.52

07646

.88341

1308.

1223

•08753

81.75

.1764

.24640

5.670

30

706.86

.0008182

4.91 286

1222.

.01309

2.11698

76.39

.1887

1.27584

5-299

31

754-77

08737

-94134

"45-

1398

.14546

71.54

.2OI5

•30433

4.962

32

804.25

09309

.96892

1074.

1489

•17304

66.89

.2147

•33I9°

-657

33

855-30

09900

•99565,

IOIO.

1584

•19977

63- '3

.2284

•35863

•379

34

907-92

10509

3.02158

952-

1681

.22570

59-47

.2424

•38456

.125

35

962.11

.OOIII4

3.04675

897.9

.01782

2.25087

56.12

•2569

7.40973

3-893

36

1017.88

1178

.07123

848.8

1885

•27535

53-05

.2718

•43421

.680

37

1075.21

1245

.09502

803.5

1991

.29914

50.22

.2871

.45800

•483

38

1134.11

I3l6

.11918

760.0

2105

.32329

47-5°

•3035

.48216

•295

39

1194.59

1383

•14075

723.2

•34487

45-20

.3190

•50373

•'35

4O

1256.64

.001455

3.16275

687.5

.02327

5.36687

42.97

•3355

r-52573

2.980

4i

1320.25

1528

.18419

654-4

2445

•38831

40.90

•3525

•54717

.837

42

1385.44

1004

.20512

623.6

2566

.40924

38.97

•3699

.56810

.704

43

1452.20

1681

.22556

594-9

2690

.42968

37-i8

-3877

•58854

•579

44

1520-53

1760

•24552

568.2

2816

.44964

35-51

.4060

.60851

•463

45

1590.43

.001841

3.26504

543-2

.02946

2.46916

33-95

.4246

7.62803

2-355

46

1661.90

1924

.28413

519.8

3078

.48825

32.49

•4437

.64712

•254

47

1734-94

2008

.30281

498.0

3213

•50693

31. 12

.4632

.66580

•'59

48

1809.56

2095

.32110

477-4

3351

.52522

29.84

.4832

.68408

.070

49

1885.74

2183

•33901

458.1

3492

•54313

28.63

•5035

.70199

1.986

50

1963.50

.002273

3-35656

440.0

•03636

2.56068

27-50

•5243

i"-7i954

1.907

51

2042.82

2365

•37376

422.9

3783

.57788

26.43

•5454

•73674

•833

S2

2123.72

2458

•39063

406.8

•59475

25-42

.5670

•7536i

.764

53

2206.18

2554

.40717

394-2

4086

.61129

24.47

.5891

.77015

.698

54

2290.22

2651

•42341

377-2

4242

•62753

23-57

.6115

.78639

•635

55

2375-83

.002750

3-43934

363-6

.04400

2.64346

22.73

•6343

7.80233

1.576

* Diameters and sections in terms of thousandths of a centimetre.

SMITHSONIAN TABLES.

48

TABLE 59.

BRITISH AND METRIC UNITS.

Cross sections and weights of wires.

c

ll

.E2

Q

Area of
cross
section
in
Sq. Mils.

Aluminium — Density 2.67.

Pounds
per
Foot.

Log.

Feet
per
Pound.

Ounces
per
Foot.

Log.

Feet
per
Ounce.

Grammes
per
Metre.*

Log.

Metres
per
Gramme.

55

2375-83

.002750

3-43934

363-6

.04400

2.64346

22-73

0-6343

1.80233

1-5/6

56

2463.01

2851

.45500

350-8

.04562

.65912

21.92

.6576

.81798

•521

57

255J-76

2954

•47037

338.6

.04726

.67449

21. l6

.6813

•83335

.468

58

2642.08

3058

.48547

327.0

.04893

.68959

20.44

•7054

.84846

.418

59

2733-97

3l65

.50032

316.0

.05063

.70444

J9-75

.7300

•86331

•370

60

2827.43

.003273

3.51492

305-5

.05236

2.71904

19.10

0-7549

1.87790

1-325

61

2922.47

3383

.52928

295.6

•05413

•73340

18.48 i

•7803

.89226

.282

62

3019.07

3495

•54340

286.2

•05591

•74752

17.88

.8061

.90638

.241

63

3"7-2S

3608

•55730

277.1

•05773

.76142

17.32

•8323

.92028

.201

64

3216.99

3724

.57098

268.5

•05958

•775'o

16.78

8589

•93396

.164

65

33l8-3i

.003841

3-58445

260.3

.06146

2.78857

16.27

0.8860

^•94743

I.I29

66

3421.19

3960

•59771

252-5

.06336

.80183

I5-78

•9*35

.96069

•095

67

3525-65

4081

.61077

245.0

.06530

.81489

tS-V

•9413

•97375

.062

68

3631.68

4204

.62364

237-9

.06726

•82777

14.87

.9697

.98662

.031

69

3739-28

4328

.63632

231.0

.06925

.84044

14.44

.9984

.99930

.OO2

70

3848.45

.004456

3-64893

224.4

.07129

2-85305

14.03

1.028

0.01191

0.9730

7i

3959-19

4583

.66114

218.2

•07333

.86526

13.64

•057

.02412

.9460

72

4071.50

47i3

•67328

212.2

•07541

.87740

13.26

.087

.03627

.9199

73

4185.39

4845

.68526

206.4

•0/751

.88938

12.90

.117

.04825

.8949

74

4300.84

4978

.69708

2OO-9

.07965

.90120

12-55

.148

.06006

.8708

75

4417.86

.005114

3.70874

195-5

.08182

2.91286

12.22

1.180

0.07172

0.8477

76

4536.46

5251

.72025

190.4

.08402

•92437

II.OX)

.211

-08323

.8256

77

4656.63

5390

.73160

185-5

.08624

•93572

1 1. 60

•243

•09458

.8043

78

4778.36

5531

.7428.

180.8

.08850

•94693

11.30

.276

•10579

.7838

79

4901.67

5674

•75387

176.2

.09078

•95799

1 1. 02

•309

.11686

.7641

80

5026.55

.005818

3.76480

I7I.9

.09309

2.96892

10.742

1.342

0.12778

0.7451

81

5i53-oo

5965

•77559

167.6

.09544

.97971

10.479

-376

•^857

.7268

82

5281.02

6113

.78625

I63.6

.09781

•99037

IO.224

.4IO

.14923

.7092

83

5410.61

6263

.79678

159-7

.IOO2I

1.00090

9-979

•445

•15976

.6922

84

5541-77

6415

.80718

155-9

.IO264

.01130

9-743

.480

.17016

•6757

85

5674-5o

'.006568

3.81746

152.2

.IO5I

1.02158

9-5*5

1.515

0.18044

0.6600

86

5808.80

6724

.82762

148.7

.1076

•03174

9-295

•551

.19060

.6448

8?

5944-68

6881

.83766

M5-3

.IIOI

.04178

9.082

-587

.20064

.6300

88

6082.12

7040

.84758

142.0

.1126

.05170

8.878

.624

.21057

•6158

89

6221.14

7201

.85740

138.9

.1152

.06152

8.679

.661

.22038

.6O2O

90

6361-73

.007364

3.86710

135-8

.1178

1.07122

8.488

1.699

0.23009

0.5887

9i

6503.88

7528

.87670

132.8

.1205

.08082

8.302

•737

.23968

•5759

92

6647.61

7695

.88619

130.0

.1231

.09031

8.122

•775

.24918

•5634

93

6792.91

7863

•89558

127.2

.1258

.09970

7-949

.814

.25856

•55H

94

6939-78

8033

.90487

124.5

.1285

.10899

7.780

•853

.26786

•5397

95

7088.22

.008205

3.91407

121.9

•1V3

1.11819

7.617

1.893

0.27705

0.5284

96

7238-23

8378

.92316

119.4

•1341

.12728

7-459

•933

.28614

•5*74

97

7389.81

8554

.93216

116.9

.1369

.13628

7-307

•973

•295!4

.5068

98

7542.96

8731

.94107

114.5

•1397

•I45J9

7-158

2.014

.30405

.4965

99

7697.69

8910

•94989

1 1 2.2

.1426

.15401

7-oi5

•055

.31287

.4865

100

7853-98

.009091

3.95862

IIO.O

•1455

1.16274

6-875

2.097

0.32160

0.4769

SMITHSONIAN TABLES.

* Diameters and sections in terms of thousandths of a centimetre.

49

TABLE 6O.

BRITISH AND METRIC UNITS.

Cross sections and weights of wires.

The cross section and the weight, in different units, of Platinum wire of the diameters given in the first column.
For one tenth the diameters divide sections and weights by 100. For ten times the diameter multiply by 100,
and so on.

c

II

Q

Area of
cross
section
in
Sq. Mils.

Platinum — Density 21.50.

Pounds
per
Foot.

Log.

Feet
per
Pound.

Ounces
per
Foot.

Log.

Feet
per
Ounce.

Grammes
per

Metre.*

Log.

Metres
per
Gramme.

10

78.54

.0007321

4.86455

1366.0

.01171

2.06867

85-38

0.1689

7.22753

5.922

i

95-°3

008858

•94732

1 1 29.0

.01417

•i5J44

70.56

.2043

.31030

4.894

12

113.10

01054

3.02292

948.6

.01687

.22704

59-29

.2432

•38590

4-II3

13

i32-73

01237

.09243

808.3

.01979

•29655

50.52

.2854

•45541

3-504

14

153-94

01435

.15681

696.9

.02296

.36093

43-56

•33'°

•5I979

3-021

15

176.71

.001647

3.21672

607.1

.02635

2.42084

37-95

0-3799

7.57970

2.632

16

201.06

01874

.27278

533-6

.03005

.47790

33-27

•4323

•63576

2.311

17

226.98

02II6

•32544

472-7

•03385

•52956

29-54

.4880

.68843

2.049

18

•254-47

02372

•37509

421.6

•03795

•57921

26-35

•5471

.73808

1.828

*9

283-53

02643

.42206

378.4

.04228

.62618

23-65

.6096

.78504

1.640

20

314.16

.002928

3.46661

341-5

.04685

2-67073

21.34

0.6754

7.82959

1.481

21

346-36

03228

.50898

309.7

•05165

.71310

19.36

•7447

.87197

•343

22

380.13

03543

•54939

282.2

.05669

•75351

17.64

-8i73

•91237

.224

23

415.48

03873

.58801

258.2

.06196

•79213

16.14

•8933

•95099

.119

24

452-39

04217

.62497

237.2

•06747

.82909

14.82

.9726

•98795

.028

25

490.87

.004575

3.66042

218.6

.07321

2.86454

13.66

1.055

0.02341

0.9475

26

530-93

04949

•69449

202. i

.07918

.89861

12.63

.142

.05748

.8760

27

572.56

05324

.72628

187.8

•08539

.93140

11.71

.231

.09026

.8124

28

615.75

05739

-75886

174.2

.09183

.96298

10.89

•324

.12184

•7553

29

660.52

06157

•78934

162.4

.09851

.99346

10.15

.420

.15232

.7042

30

706.86

.006589

3.81879

151.8

.1054

1.02291

9.486

1.520

0.18177

0.6 c;8o

31

754-77

07035

.84727

142.1

.1126

•OS1 39

8.884

•623

.21025

.6i62

32

804.25

07496

.87485

'33-4

.1199

.07897

8-338

•729

•23783

•5783

33

855-30

07972

•90157

125.4

.1276

.10569

7.840

•839

.26456

•5438

34

907.92

08463

.92750

118.2

•1354

.13162

7-385

•952

.29049

•5123

35

962. 1 1

.008968

3.95268

111.52

•'435

T. 1 5680

6.97.0

2.069

.031566

0.4834

36

1017.88

09488

•97715

105.41

.1518

.18127

6.588

.188

.34014

•4569

37

1075.21

IOO22

2.00095

99.78

.1604

.20507

6.236

.312

•36393

•4326

38

1134.11

"0595

.02511

94.38

.1695

.22923

5-899

•444

.38809

.4092

39

1194.59

11134

.04668

89.81

.1782

.25080

5-6i3

•568 •

.40966

.3893

40

1256.64

.01171

2.06867

85-38

.1874

1.27279

5-336

2.702

0.43166

0.3701

4i

1320.25

1231

.09011

81.26

.1969

•29423

5-079

•839

•453°9

•3523

42

I385-44

1291

.11104

77-44

.2066

•3i5l6

4.840

•979

•47403

•3346

43

1452.20

1354

.13148

73-88

.2166

•3356o

4.617

3.122

•49446

•3203

44

i52o.53

1417

•J5'45

70.56

.2268

•35557

4.410

.269

•5!443

•3059

45

1 590.43

.01482

2.17097

67.46

•2372

7-37509

4.216

3-4I9

0-53395

0.2924

46

1661.90

1549

.19006

64.56

.2478

.39418

4-035

•573

•55304

.2799

47

1734-94

1617

.20874

61.84

.2587

.41286

3-865

•73°

•57172

.2681

48

1809.56

1687

.22703

59-29

.2699

•43" 5

3-705

.891

.59001

.2570

49

1885.74

1758

•24494

56.89

.2812

.44906

3-556

4-054

.60792

.2467

50

1963.50

.01830

1.26249

54-64

.2928

1.46661

3-4I5

4.222

0.62547

0.2369

S1

2042.82

1904

.27969

52-52

•3°47

.48381

3.282

•392

.64267

.2277

52

2123.72

1979

•29655

50-52

.3167

.50067

3- '57

•566

•65954

.2190

53

2206.18

2056

•31310

48.63

.3290

.51722

3-039

•743

.67608

.2108

:54

2290.22

2135

•32933

46.84

•3415

•53345

2.928

•924

.69232

.2031

55

2375.83

.02214

2-34527

45.16

•3543

7-54939

2.822

5.108

0.70825

0.1958

SMITHSONIAN TABLES.

Diameters and sections in terms of thousandths of a centimetre.
50

TABLE 6O.

BRITISH AND METRIC UNITS.

Cross sections and weights of wires.

I

a
'" «

I*

(5

Area of
cross
section
in
Sq. Mils.

Platinum — Density 21.50.

Pounds
per
Foot.

Log.

Feet
per
Pound.

Ounces
Foot.

Log.

Feet
per
Ounce.

Grammes
per

Metre.*

Log.

Metres
per
Gramme.

55

2375-83

.02214

2.34527

45.16

0-3543

^•54939

2.822

5.108

0.70825

.1958

56

2463.01

2296

.36092

43-56

•3673

.56504

.722

•295

.72390

.1888

57

2551.76

2378 '

•37630

42.04

.3806

.58042

.628

.486

•73928

.1823

58

2642.08

2463

.39140

4O.6l

•3940

•59552

•538

.680

•7543s

.1760

59

2733-97

2548

.40625

39-24

.4077

.61037

•453

.878

•76923

.1701

60

2827.43

.02635

2.42085

37-94

0.4217

1.62497

2.372

6.079

0.78383

.1645

61

2922.47

2724

•43521

36-71

•4358

•63933

.294

-283

.79819

.1592

62

3019.07

2814

•44933

35-54

.4502

•65345

.221

.491

.81231

•1541

63

3II7-25

2906

•46323

34-42

.4649

•66735

•151

.702

.82621

.1492

64

3216.99

2999

.47691

33-35

.4798

.68103

.084

.917

.83989

.1446

65

33r8.3i

•03093

2.49037

32-33

0.4949

1.69449

2.O2I

7-134

0.85336

.1402

66

3421.19

3^9

•50363

3i-36

.5102

.70775

1.960

•356

.86662

.1360

67

3525-65

3286

.51670

30-43

•5258

.72082

.902

.580

.87968

.1319

68

3631.68

3385

•52956

29-54

.5416

•73368

.846

.808

•89255

.1281

69

3739-28

3485

•54224

28.69

•5577

.74636

•793

8.039

•90523

.1244

70

3848-45

.03588

2-55485

27.87

o.574i

1.75897

1.742

8.276

0.91 784

.1208

7i

3959- 1 9

3690

•56706

27.10

.5904

.77118

.694

•5'2

.93004

•"75

72

4071.50

3795

.57921

26.35

.6072

•78333

•647

•754

.94219

.1142

73

4185.39

3901

•59H9

25-63

.6242

•79531

.602

•999

•95417

.nil

74

4300.84

4009

.60301

24-95

.6414

.80713

•559

9.247

.96599

.1081

75

4417.86

.04118

2.61467

24.28

0.6589

1.81879

1.518

9.498

0.97765

.10528

76

4536.46

4228

.62617

23-65

•6765

.83029

.478

9-753

.98916

•10253

77

4656.63

4340

•63753

23.04

•6945

.84165

•440

IO.OI2

1.00051

.09988

78

4778.36

4454

.64874

22.45

.7126

.85286

•403

10.273

.01172

•09734

79

4901.67

4569

.65980

21.89

•73JO

.86392

.368

10-539

.02278

.09489

80

5026.55

.04685

2.67073

21.34

0.7496

1.87485

'•334

10.81

I-0337I

.09253

81

5 ! 53-oo

4803

.68152

20.82

.7685

.88564

.301

11.08

.04450

.09026

82

5281.02

4922

.69217

20.32

.7876

.89629

.270

"•35

.05516

.08807

83

5410.61

5043

.70270

19.83

.8069

.90682

•239

11.63

.06568

.08596

84

5541-77

5165

.71310

19.36

.8265

.91722

.210

11.91

.07609

•08393

85

5674.50

.05289

2.72338

18.91

0.8463

1.92750

1.182

I2.2O

1.08637

.08197

86

5808.80

54H

•73354

18.47

.8663

•93766

•154

12.49

.09652

.08007

87

5944.68

5541

•74358

18.05

.8866

.94770

.128

12.78

.10657

.07807

88

6082.12

5669

•75351

17.64

.9070

•95763

.102

I3.08

.11649

.07647

89

6221.14

5799

•76333

17.25

•9278

•96745

.078

<3-37

.12631

-0/477

90

6361-73

•0593o

2.77303

16.86

0.9487

7.97715

1.0541

13.68

1.13601

.07311

9i

6503.88

6062

.78263

16.50

.9699

.98675

.0310

1:3-98

.14561

.07152

92

6647.61

6196

.79212

16.14

.9914

.99624

.0087

T4-29

•^Sto

.06997

93

6792.91

6332

.80151

15-79

1.0130

0.00563

0.9871

14.60

. 1 6449

.06847

94

6939.78

6469

.81080

15.46

•0350

.01492

.9661

14.92

•17378

.06702

95

7088.22

.06607

2.81999

I5-X4

1.057

0.02411

0.9460

15.24

1.18298

.06562

96

7238.23

6747

.82909

14.82

.079

.03321

.9264

15-56

.19207

.06426

97

7389.81

6888

.83809

14.52

.102

.042.21

.9074

15.89

.20107

.06294

98

7542.96

7031

.84700

14.22

•125

.05112

.8890

l6.22

.20998

.06166

99

7697.69

7175

.85582

J3-94

.148

.05994

.8711

16-55

.21880

.06042

100

7853-98

.07321

2.86455

13.66

1.171

0.06867

0.8538

16.89

1.22753

.05922

* Diameters and sections in terms of thousandths of a millimetre.

SMITHSONIAN TABLES.

TABLE 61 .

BRITISH AND METRIC UNITS.

Cross sections and weights of wires.

The cross section and the weight, in different units, of Gold wire of the diameters given in the first column.
For one tenth the diameters divide sections and weights by 100. For ten times the diameter multiply by 100
and so on.

£

Is

J5

Area of
cross
section
in

Sq. Mils.

Gold — Density 19.30.

Troy
Ounces
per Foot.

Log.

Feet
per Troy
Ounce.

Grains
per
Foot.

Log.

Feet
per
Gram.

Grammes
per

Metre.*

Log.

Metres
per
Gramme.

10

78.54

.00958

3.98152

104-35

4.600

0.66276

.2174

0.1516

1.18065

6-597

ii

95-03

.01 1 60

2.06429

86.24

5-566

•74553

.1797

.1834

.26342

5-452

12

II3.TO

.01380

.13989

7246

6.624

.82114

.1510

•2l83

.33902

4.581

U

r32-73

•01657

.21940

60.34

7-774

.89064

.1286

.2562

•40853

3-904

14

153-94

.01878

.27378

53-24

9.016

•95503

.1109

.2971

•47291

3-366

15

176.71

.02 1 56

2.33369

46.38

10-35

1.01493

.09662

0.341 1

1.53282

2.932

16

2OI.O6

•02453

•38976

40.76

11.78

.07100

.08492

.3880

.58888

•577

17

226.98

.02770

.44242

36.11

13.29

.12366

.07522

.4381

.64154

.283

18

254-47

.03105

.49207

32.21

14.90

•I7331

.06710

•49"

.69119

.036

19

283-53

.03460

•53903

28.90

1 6.6 1

.22027

.ODO22

•5472

.738l6

1.827

20

314.16

•03833

2.58358

26.09

18.40

1.26482

•05435

0.6063

1.78271

1.649

21

346.36

.04226

.62596

23.66

20.29

.30720

.04939

.6685

.82509

.496

22

380.13

.04638

.66636

21.56

22.26

•3476r

.04492

•7337

.86549

•363

23

415.48

•04954

.69498

20.18

24-33

.38622

.04109

.8019

.90411

.248

24

452-39

.05520

.74194

18.12

26.50

.42319

•03774

•8731

.94107

•M5

25

490.87

.05990

2.77740

16.70

28.75

1.45865

.03478

0.9474

1.97652

'•0555

26

530-93

.06478

.81147

15-44

31.10

.49271

.03216

1.0247

0.01059

0-9759

27

572.56

.06986

.84425

I4-31

33-53

•52549

.02982

.1050

•04338

9050

28

6'5-75

•07513

.87584

13-31

36.06

•55708

•02773

.1884

.07496

.8415

29

660.52

.08060

.90632

12.41

38.69

.58756

.02585

.2748

.10544

.7844

30

706.86

.08625

2-93577

"•594

41.40

1.61701

.02415

1.364

0.13489

0-733°

31

754-77

.09210

.96425

10.858

44.21

.64549

.02262

•457

•16337

.6912

32

804.25

.09813

.99182

10.190

47.10

.67306

.02123

•SS2

.19095

.6442

33

855-30

.10436

1.01855

9.582

50.09

.69979

.01996

.651

.21768

.6058

34

907.92

.11078

.04448

9.027

S3-i8

•72572

.01881

•752

.24360

•5707

35

962.11

.1174

1.06965

8.518

56.35

1.75089

.01775

1-857

0.26878

0-5385

36

1017.88

.1242

.09413

8.051

59.62

•77537

.01677

•965

•29325

.5090

37

1075.21

.1312

.11792

7.622

62.97

•79917

.01588

2.070

•3^05

.4830

38

1134.11

.1387

.14208

7.210

66.58

.82332

.01502

.194

.34121

•4558.

39

"94-59

.1458

•16365

6.861

69.97

.84489

.01429

.306

•36278

•4337

40

1256.64

•1533

1.18565

6.521

73.60

1.86689

•OI359

2.425

0.38478

0.4123

4i

1320.25

.1611

.20709

6.207

77-33

.88833

.01293

•548

.4062 1

•3924

42

I385-44

.1691

.22802

5-9I5

81.14

.90926

.01232

.674

•42715

•3740

43

1452.20

.1772

.24846

5-643

85.05

.92970

.01176

.803

•44758

•3568

44

!520.53

•1855

.26843

5-390

89.06

•94967

.01123

•935

•46755

.3408

45

1590.43

.1941

1.28795

5-T53

93-15

1.96919

•010735

3.070

0.48707

0.3258

46

1661.90

.2028

.30704

4-931

97-34

.98828

.010273

.207

.50616

.3118

47

1734-94

.2117

•32572

4.724

roi.oi

2.00696

.009842

-348

.52484

.2986

48

1809.56

.2208

.34400

4-529

105.99

•02525

•009435

.492

•54313

.2863

49

1885.74

.2301

.36191

4-346

110.45

•043 i 5

.009054

•639

.56104

.2748

50

1963.50

.2396

1.37946

4.174

115.0

2 06070

.008696

3-790

0.57859

0.2639

51

2042.82

•2493

.39666

4.012

119.6

.07790

.008358

•943

•59579

•2537

52

2123.72

.2591

•41353

3-859

124.4

•09477

.008039

4.099

.61265

.2440

53

2206.18

.2692

.43007

3-7I5

129.2

.11131

.007739

.258

.62920

•2349

54

2290.22

•2795

.44631

3-578

134-1

•12755

•007455

.420

•64543

.2262

55

2375-83

.2899

1.46225

3-449

139.2

2.14349

.007186

4.585

0.66137

0.2181

SMITHSONIAN TABLES.

* Diameters and sections in terms of thousandths of a centimetre.
52

TABLE 61

BRITISH AND METRIC UNITS.

Cross sections and weights of wires.

c

Eg
.2 ^»

o

Area of
cross
section

Sq. Mils.

Gold — Density 19.30.

Troy
Ounces
per
Foot.

Log.

Feet
per Troy
Ounce.

Grains
per
Foot.

Log.

Feet
per
Grain.

Grammes
per
Metre.*

Log.

Metres
per
Gramme.

55

2375-83

.2899

1.46225

3-449

139.2

2.14349

.007186

4.585

0.66137

.2l8l

56

2463.01

•3005

•47790

•327

144-3

.15914

6932

4-754

.67702

.2104

$1

255^76

•3U4

•49327

.212

149.5

•I745t

6691

4-925

.69240

•2031

58

2642.08

.3224

.50838

.IO2

154-7

.18962

6462

5-099

•70/50

.1961

59

2733-97

•3336

•52323

2.998

1 60. 1

.20447

6245

5-277

•72235

.1895

60

2827.43

•3450

7.53782

2.899

165.6

2.21906

.006039

5-457

0.73695

•1833

61

2922.47

•3566

.55218

.804

I7I.2

•23342

5842

5.640

•7S131

•1773

62

3019.07

.3684

.56630

.715

176.8

•24754

5655

5.827

•76543

.1716

63

3"7-25

.3804

.58020

.629

182.6

.26144

5477

6.016

•77933

.1662

64

3216.99

•3925

•59388

.548

188.4

.27512

5307

6.209

•79301

.l6ll

65

3318.31

.4049

1.60735

2.470

194.4

2.28859

.005145

6.404

0.80647

.1561

66

3421.19

•4175

.62061

•395

200.4

.30185

4991

6.603

•8i973

.1514

67

3525-65

.4302

•63367

•324

206.5

•3»49'

4843

6.805

.83280

.1470

68

3631.68

•443 '

.64654

•257

212.7

•327/8

4701

7.010

.84566

.1427

69

3739-28

•4563

•65922

.192

219.0

.34046

4566

7.217

•85835

.1386

70

3848-45

•4697

1.67183

2.129

225-5

2.35307

•004435

7.429

0.87096

.1346

7i

3959-19

.4831

.68404

.070

231.9

.36528

4312

7.641

.88316

.1309

72

4071.50

.4968

.69619

.013

238.4

•37743

4195

7.858

•89531

•1273

73

4185.39

•5I07

.70817

1.958

245.1

.38941

4079

8.078

.90729

.1238

74

4300.84

•5248

.71998

•905

251.9

.40123

3970

8.301

.91911

.I2O4

75

4417.86

•5391

1.73164

1-855

258.8

2.41288

.003865

8.526

0.93077

•"73

76

4536-46

•5535

•74315

.807

265.7

•42439

3764

8-755

.94227

.1142

77

4656.63

.5682

•75450

.760

272.7

•43574

3666

8.987

•95363

.1113

78

4778.36

•5831

•76571

•715

279.9

.44695

3573

9.222

.96484

.1084

79

4901.67

.5981

.77678

.672

287.1

.45801

3483

9.460

.97590

•1057

80

5026.55

•6i33

1.78770

1.630

294.4

2.46894

.003401

9.701

0.98683

.10308

81

5 r 53-oo

.6288

.79849

•590

301.8

•47973

33'3

9-945

.99762

•10055

82

5281.02

•6444

•80915

•552

309-3

.49039

3233

10.192

1.00828

.09812

f3

5410.61

.6602

.81968

•5*5

316.9

.50092

3I56

10.442

.01880

-09577

84

5541-77

.6762

.83008

•479

324.6

•5"32

3081

10.696

.02921

.09349

85

5674.50

.6924

7.84036

1.444

332-4

2.52160

.003009

10.95

1.03948

.09131

86

5808.80

.7088

.85052

.411

340.2

•53J76

2939

II. 21

.04964

.08919

87

5944.68

•7254

.86056

•379

348.2

.54180

2872

11.47

.05969

.08716

88

6082.12

.7421

.87049

•347

356.2

•55!73

2807

11-74

.06961

.08519

89

6221.14

•7591

.88030

•3»7

364-4

•56i54

2744

I2.OI

•07943

.08328

90

6361.73

•7763

1.89001

1.288

372-6

2-57125

.002684

12.28

1.08913

.08145

9i

6503.88

•7936

.89960

.260

380.9

.58085

2625

12-55

.09873

.07967

92

6647.61

.8m

.90910

•233

389-3

•59034

2568

I2.83

.10822

.07794

93

6792.91

.8291

.91858

.206

397-9

•59972

25J3

13.11

.11761

.07628

94

6939.78

.8468

.92778

.181

406.5

.60902

2460

13-39

.12690

.07466

95

7088.22

.8649

7.93697

1.156

415.2

2.61821

.002409

13.68

1.13609

.07310

96

7238.23

.8832

.94606

.132

423-9

.62731

2359

'3-97

.14519

.07158

97

7389.81

.9017

•955°7

.109

432.8

•63631

2310

14.26

•I54I9

.07011

98

7542.96

.9204

•96397

.086

441.8

.64521

2263

14.56

.16310

.06869

99

7697.69

•9393

•97279

.065

45°-9

.65403

2218

14.86

.17192

.06731

100

7853-98

•9583

7.98152

1.043

460.0

2.66276

.002174

15.16

1.18065

.06597

* Diameters and sections in terms of thousandths of a centimetre.

SMITHSONIAN TABLES.

53

TABLE 62.

BRITISH AND METRIC UNITS.

Cross sections and weights of wires.

The cross section and the weight, in different units, of Silver wire of the diameters given in the first column. For
one tenth the diameters divide the section and weights by 100. For ten times the diameter muliply by 100, and
so on.

_c

is

Q

Area of
cross
section
in
Sq. Mils.

Silver — Density 10.50.

Troy
Ounces
per Foot.

Log.

Feet

per Troy
Ounce.

Grains
Foot.

Log.

Feet

Pe.r
Grain.

Grammes
per

Metre.*

Log.

Metres
per
Gramme.

10

78.54

.005214

3-7I7I5

191.79

2-503

0-39839

•3996

0.08247

2.91628

12.126

ii

95-03

.006308

•79992

I58.52

3.028

.48117

•3302

.09978

.99905

IO.O22

12

113.10

.007508

•87553

I33-I9

3.604

•55677

•2775

.11876

1.07465

8.420

'3

132.73

.008811

•94503

"3-49

4.229

.62627

.2364

•13937

.14416

7-175

14

153-94

.010219

2.00942

97.86

4.905

.69066

.2039

.16164

.20854

6.186

15

176.71

.01173

2.06932

85.24

5-63I

0.75057

.1776

0.1855

7.26845

5-389

16

2OI.O6

•01335

•12539

74.92

6.407

.80663

.1561

.2111

•32452

4-737

i7

226.98

.01507

.17805

66.37

7.233

.85929

.1383

•2383

•37718

4.196

18

254-47

.01689

.22770

59.20

8.109

.90894

•1233

.2672

.42683

3-743

19

283-53

.01882

.27466

S3-1 3

9-034

•95590

.1107

•2977

•47379

3-359

20

314.16

.02086

2.31921

47-95

IO.OI

1.00046

.09990

0.3299

i"-5'834

3-031

21

346.36

.02299

•36159

43-49

11.04

.04283

.09060

•3637

.56072

2.750

22

380.13

.02523

.40200

39-63

12.11

.08324

.08256

•3991

.60112

•505

23

415.48

.02758

.44061

36.26

13.24

.12186

••07553

•4363

•63974

.292

24

452-39

.03003

•477S8

32-99

14.42

.15882

.06937

•4750

.67670

.105

25

490.87

•03259

2.51303

30.69

15.64

1.19427

.06425

0.5154

1.71216

1.940

26

530.93

•03525

•54710

28.37

16.92

.22834

.05911

•5575

•74623

•794

27

572.56

.03801

.57988

26.31

18.24

.26113

.05481

.6012

.77901

.663

28

6'5-75

.04088

.61147

24.46

19.62

.29271

.05097

.6465

.81059

•547

29

660.52

•04385

.64195

22.81

21.05

•32319

•047 5 *

•6935

.84108

.442

30

706.86

.04692

2.67140

21.31

22.52

I-35264

.04440

0.7422

1.87052

1-347

31

754-77

.05010

.69988

19.96

24.05

.38lI2

0.4158

•7925

.89900

.262

32

804.25

•05339

•72745

i8-73

25-63

.40870

0.3902

•8445

.92658

.184

i 33

855-30

.05678

.75418

17.61

27.25

•43542

0.3669

.8981

•95331

•"3

34

907.92

.06027

.78011

16.59

28.93

•46135

0.3457

•9533

.97924

.049

35

962.11

.06387

2.80528

15.66

30.66

1.48653

.03262

I.OIO

0.00441

0.9899

36

1017.88

.06757

.82976

14.80

32-43

.51100

.03083

.069

.02889

•9356

37

1075.21

.07138

•85356

14.01

34.26

•53480

.02919

.129

.05268

.8857

: 38

1134.11

.07546

.87772

13-25

36.22

•55896

.02761

.194

.07684

.8378

; 39

1194.59

.07930

.89928

12.61

38.06

•58052

.02627

•254

.09841

•7973

40

1256.64

.08342

2.92128

11.99

40.04

1.60252

.02497

i-3r9

0.12041

0-7579

41

1320.25

.08764

•94272

11.41

42.07

.62396

.02377

.386

.14185

•7213

42

'385-44

.09197

•96365

10.87

44-15

.64489

.02265

•455

.16278

•6874

1 43

1452.20

.09640

.98409

10-37

46.27

•66533

.02161

•525

.18322

•6558

, 44

1520.53

.10094

1.00406

9.91

48.45

•68530

.02064

•597

.20318

•6263

45

1590.43

.1056

1.02358

9.471

50.68

1.70482

•01973

1.670

0.22270

0.5988

46

1661.90

•"93

.04267

9.065

52.96

•72391

.01888

•745

.24179

•5731

; 47

1734-94

.1152

.06135

8.683

55.28

•74259

.01809

.822

.26047

.5489 i

! 48

1809.56

.i2di

.07964

8.325,

57-66

.76088

•01734

.900

.27876

•5263

49

1885.74

.1252

•09755

7.988

60.09

•77879

.01664

.980

.29667

.5050

50

1963-5°

•1303

1.11509

7.672

62-57

1.79634

.01598

2.062

0.31422

0.4850

! 5i

2042.82

•1356

.13229

7-374

65.09

•81354

•01536

.145

•33M2

.4662

; 52

2123.72

.14110

.14916

7-P93

67-67

.83040

.01478

.230

.34829

.4484

53

2206.18

•1465

.16570

6.828

70.30

.84695

.01422

.316

•36483

•43 » 7

54

2290.22

.1520

.18194

6.578

72.99

.86328

.01370

•405

.38107

.4158

55

2375-83

•1577

T.I9788

6.340

75.70

1.87912

.01321

2-495

0.39700

0.4009

* Diameters and sections in terms of thousandths of a centimetre.
SMITHSONIAN TABLES.

54

TABLE 62.

BRITISH AND METRIC UNITS.

Cross sections and weights of wires.

B
'" £

Ei
.2^5

O

Area of
cross
section
in
Sq. Mils.

Silver — Density 10.50.

Troy
Ounces
per Foot.

Log.

Feet
per Troy
Ounce.

Grains

Fool.

Log.

Feet
per
Grain.

Grammes
per

Metre.*

Log.

Metres
per
Gramme.

55

2375-83

0.1577

T.I9788

6.340

75-70

1.87912

.01321

2.495

0.39700

0.4009

56

2463.01

•1635

•21353

.116

78.48

.89477

1274

.586

.41266

•3867

57

255'-76

.1694

.22890

5-903

81.31

.91014

1230

•679

.42803

•3732

58

2642.08

•1754

.24401

./OI

84.19

•92525

1188

•774

•443 '4

.3605

59

2733-97

.1815

.25886

.510

87.12

.94010

1148

.871

•45798

•3484

60

2827.43

0.1877

1.27346

5-328

90.09

1.95470

.OHIO

2.969

0.47258

0.3368

61

2922.47

.1940

.28781

•155

93.12

.96906

1074

3.069

.48694

•3259

62

3019.07

.2004

•3° "93

4.990

96.20

.98318

1040

.170

.50106

•3*55

63

3"7-25

.2069

•31584

-832

99-33

.99708

1007

•273

.51496

•3°55

64

3216.99

.2136

•32951

•683

102.51

2.01075

0975

-378

.52864

.2961

65

33I8-3I

0.2203

1.34298

4-540

105-7

2.02422

.009457

3-484

0.54211

0.2870

66

3421.19

.2271

•35624

•403

109.0

.03748

09173

•592

•55537

.2784

67

3525-65

.2340

•3693°

•273

112.3

.05054

08903

.702

•56843

.2701

1 f

3631.68

.2411

.38217

.148

"5-7

.06341

08642

.813

•58130

.2622

69

3739-28

.2482

•39485

.029

119.1

.07609

08393

.926

•59398

•2547

70

3848.45

0.2555

1.40746

3-9I3

122.7

2.08870

.008153

4.042

0.60659

0.2474

7i

3959-19

.2628

.41967

.805

126.2

.10091

07926

•157

.61880

.2406

72

4071.50

.2703

.43182

.700

129.7

.11306

07708

•275

.63094

•2339

73

4185.39

.2778

.44380

•599

133-4

.12504

07498

•395

.64293

•2275

74

4300.84

•2855

.45560

.502

137-0

.13686

07297

.516

•65474

.2214

75

4417.86

0.2933

1.46728

3.410

140.8

2.14852

.007104

4-639

0.66640

0.2156

76

4536.46

.3011

-•47878

.321

144.6

.16002

06918

•763

.67791

.2099

77

4656.63

.3091

.49014

•235

148.4

.17138

06739

.889

.68926

.2045

78

4778.36

•3!72

•50134

.152

!52-3

.18258

06568

5.017

.70047

•!993

79

4901-67

•3254

.51241

•073

156.2

•19365

06402

.147

•7"53

•!943

80

5026.55

0-3337

1-52333

2.997

160.2

2.20458

.006243

5.278

0.72246

0.1895

81

5153-0°

.3421

•53412

•923

164.2

•21537

06090

.411

•73325

.1848

82

5281.02

.3506

•54478

.852

168.3

.22602

05942

•545

•74391

.1803

83

5410.61

•3592

•55531

-784

172.4

•23655

05800

.681

•75444

.1760

84

5541-77

•3679

•56571

.718

176.6

•24695

05663

.819

.76484

.1719

85

5674-50

0.3767

T- 57 599

2-655

180.8

2.25723

•005531

5-958

0.77512

0.1678

86

5808.80

•3856

•58615

•593

185.1

.26739

05403

6.099

.78528

.1640

87

5944-68

•3946

.59619

•534

189.4

•2/743

05279

.242

•79532

.1602

88

6082.12

.4038

.60612

•477

193-8

.28736

05160

.386

.80524

.1566

89

6221.14

.4130

•6i593

.421

198.2

.29717

05045

•532

.81506

•I531

90

6361-73

0.4223

1.62564

2.368

202.7

2.30688

•004933

6.680

0.82476

0.1497

9»

6503.88

•43 '8

•63524

.316

207.2

.31648

04825

.829

•83436

.1464

92

6647.61

•4413

•64473

.266

2II.8

•32597

04721

.980

.84385

•r433

93

6792.91

.4509

.65411

.218

216.4

•33535

04620

7-132

.85324

.1402

94

6939.78

.4607

•66341

.171

221. 1

•34465

04522

.287

.86254

•1372

95

7088.22

0.4705

7.67260

2.125

225.9

2.35384

.004428

7-443

0.87173

0.1344

96

7238.23

.4805

.68170

.081

230.6

•36294

04336

.600

.88082

.1316

97

7389.81

.4906

.69070

.038

235-5

•37194

04247

•759

.88982

.1289

98

7542.96

.5007

.69961

1.997

240.4

-38085

04161

.920

.89873

.1263

99

7697.69

.5110

.70842

•957

245-3

.38967

04077

8.083

•90755

•1237

100

7853-98

0.5214

^•71715

1.918

250-3

2-39839

•003996

8.247

0.91628

0.1213

Diameters and sections in terms of thousandths of a centimetre.

SMITHSONIAN TABLES.

55

TABLE 63.

WEIGHT OF SHEET METAL.

•a

o o o o o

O 0 O 0 0

i

3

"~> O "1 O "~>

O i- •- PI P)
1-1 N CO TJ- u->

O 10 O "i O
roro ^r TJ- LO

vo t^oo a\ o

O O 0 O O

O 0 0 0 O

"3

O

rovo O\ M 1O
O\OO t^. r^vO
1-1 n to r^ ON

oo >- •* t^ o

LO "Trt- ro ro
1-1 f) 10 r^ O\

|

0 0 O O O

O O O O O

_c

rt

s

10 O ""i o ""^
— ro ^vO t-».
N ^vO OO O

M

o "1O m O
O\ O M to »o
M in t-v c\ 1-1

1

r^ ^t1 1-1 OO "i

ri ON^O ro O

'i

3
<

VO roo O no

N "TOO O CO

O \D <-OO r^
\O OO — TfO
"i « M pi M

en

VO N OO Tf O

VO N oo •* O

2

PQ

uO — \O N OO

oo t^ VD T)- ri
i-i N ro -f

fOCN •<*• O O
•• ONOO r^ LO
w> 100 t^oo

^

O O 0 O O

o o o o o

a
o
U

ONSO r^vo "^
OO I-^vO "^ -<J-

1-1 M <""> Tf

Tt ro PI •- O
n PI — O ON
,«">\O t^OO OO

j

o o o o o

O O O 0 O

o

OO VO rf N O
r^ u-i ro « Cs
1-1 N ro ro

OO O ^ PI O
VO rj- ri O OO
T}- "1\O f^ 1^.

J:
.-

H

S=J§

BJ'S-

c" 8*3

H N d*t »o

<O t^OO O\O

SMITHSONIAN TABLES.

TABLE 64,

WEIGHT OF SHEET METAL.

&.«

•*OO N \O O

•^•oo PI VO O

cfa

* 'Scr
* 0«

I

N IO t^ ON M

CO \O •* f) 11
co t^ — ""> ON

rfvO CNH •*•

ON 1^ to Tj- PI

P) xO O -^-OO
P) p» n roro

s !i

V [t,

r^ f*5 O t^ fO

vO fO O vO c*5

ON ON CNCO 30

t^ LT) CO ^ OS

O t^. rf Q r^

O vO PO O O
oo r~» r^ r^\O
r^ LO ro n ON

3 *

0^

O I- c^ roro

Tj- to>o r^ r^

u .

0.0

oo t~» "i ro P>

O oo t^. «o PO

3*"

2 a-
* OM

•ri

N ^X« - -4-

000--
t^ Tf « cx3 "1
1-1 N o ro

r^ ON PI tooo

n •• PI PI PI

PI ON^O ro O
TT •* tovo r-.

3 *~
.1

Ufa

N «O t^ O N

TJ-OO fi r>. >-i
\O PI ON ""> N

't ON rooo ro

Tf t~» O\ PI •*

VOON rooo N
00 •* — r^ TJ-
r-^ PI r^ — vO

3 *
Ow

« N rj- to r^

00 O i ro •*

t_

b«

« -

O CN CNOO OO
ON I^-vO ^0 Tf
t^ 10 ro «- CN

oo t^ t^-vo vo
PO PJ « O ON
t^ 10 PO n OO

^ So-

i-c COlO t^OO

O P) -^-vO r^

I 0"

2 N

•O&H

CM^VO •>!• fo
— ro to t^ Q\

i N m Tt to

1-4 PI ro TJ- 10

" O oo r^ to

i- PO -^-vO OO
r^oo ON O -
vO r^oo O 1-1

If

n n

u

a-g
ft*

PI to r^ o P)

PI rj-\o ON n

10 r^ O N •*
PO tooo O PI
ro to r^ o PI
PO to z^ O P<

S § o-
.2 C^

n

H M H PI N

S J; .

| ?1
f*

0 *

O\OO t^VO to
oo r^\O to TJ.
ro r^ ~ to o\
« PI ^- "",0
O O O O O

Tt- POP) w O

ro PI n O ON
ror^ — tooo

OO ON - Pi ro
O O •" — «

i£M

8 ^°
2 •§£

M 1*

-too ror^ i-
to 6 O « r^
Tt CN r^.OO PI
•S-OO ror^ P»
O o — « N

tO ON rJ-OO N
PI r^ rooo ^t-
r^ M vO O to
VO - too •*
P) PO ro TJ- •^>

&™

s.«
1 I*

U o °*

0 0 O O 0

f}O ON N tO

vO Pi OO "^ «
••f ON <T)OO PO
O O — « PI

— — — —
OO « •* t^ O
r^ rf O vO PO
t^ PI r^- n vO

(2M

k
0.3

a <n 0

0 ^fc

0 ?

00 \O rO« ON
to— r^ rooo
O I » PI PI

"3-00 PI \O O

O 0 H H- P)

t-^ toro O OO
T)- o vO PI t^
ro T(- T)- toio
Ti-oo P» vO O
PI N ro ro •>*•

£«

I

ijd

2 "S

H N rO1*"1

tO t^OO ONO

SMITHSONIAN TABLES.

57

TABLE 65.

SIZE, WEIGHT, AND ELECTRICAL

Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers
Size and Weight.

Gauge
Number.

Diameter in
Inches.

Square of
Diameter
(Circular
Inches).

Section in*
Sq. Inches.

Pounds
Foot.

Log.

Feet
per
Pound.

0000

0.4600

0.2116

O.l662

0.6412

T.8O7OI

1.560

OOO

.4096

.1678

.1318

.5085

.70631

1.967

oo

.3648

.1331

.1045

•4033

.60560

2.480

0

•3249

•T055

.0829

•3 '98

.50489

3.127

1

0.2893

0.08369

0.06573

0.2536

1.40419

3-943

2

.2576

.06637

•05213

.2011

•30348

4.972

3

.2294

.05263

.04134

•'595

.20277

6.270

4

.2043

.04174

.03278

.1265

.10206

7.905

5

.1819

•03310

.02600

.1003

.00136

9.969

6

0.1620

0.02625

0.02062

0.07955

2.90065

12.57

7

-1443

.02082

-01635

.06309

•79994

I5-85

8

.1285

.01651

.01297

.05003

.69924

19.99

9

•"44

.01309

.OIO28

.03968

•59853

25.20

10

.1019

.01038

.00815

.03146

.49782

3I-78

11

0.09074

0.008234

0.006467

0.02495

2.39711

40.08

12

.08081

.006530

.005129

.01979

.29641

50-54

13

.07196

.005178

.004067

.01569

.19570

63.72

14

.06408

.004107

.003225

.01 244

.09499

80.35

15

.05707

•003257

.002558

.00987

3-99429

101.32

16

0.05082

0.002583

O.OO2O28

0.007827

3-89358

127.8

I7

.04526

.002048

.001609

.006207

.79287

161.1

18

.04030

.001624

.001276

.004922

.69217

203.2

19

.03589

.001288

.OOIOI2

.003904

.59146

256.2

20

.03196

.OOIO2I

.OOO8O2

.003096

.49075

323-1

21

0.02846

o.oooSioi

0.0006363

0.002455

3-39004

408.2

22

•02535

.0006424

.0005046

.001947

.28934

S'3-6

23

.02257

.0005095

.0004001

.001544

.18863

647.7

24

.02010

.0004040

.0003173

.001224

.08792

816.7

25

.01790

.0003204

.0002517

.000971

4.98722

1029.9

26

0.01594

0.0002541

0.0001996

0.0007700

4.88651

1298.

27

.01419

.0002015

.0001583

.0006107

.78580

1638.

28

.01264

.0001598

.OOOI255

.0004843

.68510

2065.

29

.01126

.0001267

.0000995

.0003841

•58439

2604.

30

.01003

.0001005

.0000789

.0003046

.48368

3283-

31

0.008928

0.00007970

O.OOOO626o

0.0002415

4.38297

4140.

32

.007950

.00006321

.00004964

.0001915

.28227

5221.

33

.007080

.00005013

.00003937

.0001519

.18156

6583.

34

.006304

.00003975

.OOOO3I22

.0001205

.08085

8301.

35

.005614

.00003152

.00002476

.0000955

5.98015

10468.

36

0.005000

0.00002500

0.00001963

0.00007576

5-87944

13200.

37

•004453

.00001983

.OOOOI557

.00006008

•77873

16644.

38

.003965

.00001372

.OOOOI235

.00004765

.67802

20988.

39

.003531

.00001247

.OOOOO979

.00003778

•57732

26465.

40

.003145

.00000989

.00000777

.00002996

.47661

33372-

SMITHSONIAN TABLES.

TABLE 65.

CONSTANTS OF COPPER WIRE.

according to the American Brown and Sharp Gauge. British Measure. Temperature o° C. Density 8.90.

Electrical Constants.

Resistance and Conductivity.

Gauge
Number.

Ohms
per

Foot.

Log.

Feet
Ohm.

Ohms
per
Pound.

Pounds
per
Ohm.

0.00004629

5-6655I

2l6oi.

0.00007219

13852.

OOOO

.00005837

.76622

17131.

.00011479

87I2.

OOO

.00007361

.86693

13586.

.00018253

5479-

oo

.00009282

.96764

10774.

.00029023

3445-

0

O.OOOII7O

4-06834

8544.

0.000461 5

2166.8

1

.0001476

.16905

6775-

.0007338

1362.8

2

.OOOl86l

.26976

5373-

.OOII668

857-0

3

.0002347

.37046

4261.

.0018552

539-o

4

.0002959

.47117

3379-

.0029499

339-o

5

0.0003731

4.57188

2680.

0.004690

213.22

6

.0004705

.67259

2125.

.007458

134.08

7

•0005933

•77329

1685.

.011859

84.32

8

.0007482

.87400

1337.

.018857

53-03

9

.0009434

•97471

1060.

.029984

33-35

10

O.OOIIOX)

3-0754I

840.6

0.04768

20.973

11

.001500

.17612

666.6

.07581

13.191

12

.001892

.27683

528-7

.12054

8.296

13

.002385

•37753

419.2

.19166

5.218

H

.003008

.47824

332-5

.30476

3-281

15

0-003793

3-57895

263.7

0.4846

2.0636

16

.004783

.67966

209.1

•7705

1.2979

17

.006031

.78036

165.8

1.2252

0.8162

18

.007604

.88107

I3I-5

1.9481

•5*33

19

.009589

.98178

104.3

3.0976

.3228

20

O.OI2O9

2.08248

82.70

4.925

0.20305

21

.01525

•18319

65-59

7.832

.12768

22

.01923

.28390

52-01

I2-453

.08030

23

.02424

.38461

41.25

19.801

.05051

24

•03057

•48531

32.71

31.484

.03176

25

0.03855

2 <86o^

25-94

50.06

0.019976

26

.04861

.68673

20.57

79.60

.012563

27

.06130

•78743

16.31

126.57

.007901

28

.07729

.88814

12.94

201.26

.004969

29

.09746

.98885

10.26

320.01

.003125

30

0.1229

1.08955

8.137

508.8

0.0019654

31

.155°

.19026

6.452

809.1

.0012359

32

.1954

.29097

5.117

1286.5

.0007773

33

.2464

.39168

4.058

2045-6

.0004889

34

•3I07

.49238

3.218

3252.6

.0003074

35

0.3918

7.59309

2.552

5172.

0.0001934

36

.4941

.69380

2.024

8224.

.0001216

37

.6230

.79450

1.605

13076.

.0000765

38

.7856

.89521

• 1-273

20792.

.0000481

39

.9906

.99592

1.009

33060.

.0000303

40

SMITHSONIAN TABLES.

59

TABLE 66.

SIZE, WEIGHT, AND ELECTRICAL

Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers
Size and Weight.

Gauge
Number.

Diameter in
Centimetres.

Square of
Diameter
(Circular
Cms.).

Section in
Sq. Cms.

Grammes
per
Metre.

Log.

Metres
per
Gramme.

OOOO

1.1684

I-3652

1.0722

954-3

2.97966

0.001048

OCO

.0405

.0826

0.8503

756.8

.87896

.001322

OO

0.9266

0.8586

•6743

600. 1

.77825

.OOl666

o

.8251

.6809

•5343

475-9

•67754

.OO2 1 OI

1

0.7348

0.5400

0.4241

377-4

2.57684

0.002649

2

•6544

.4282

•3363

299-3

•47613

.003341

3

.5827

•3396

.2667

237-4

•37542

.004213

4

.5,89

.2693

.2115

188.2

•27472

.005312

5

.4621

.2136

.1677

M9-3

.17401

.006699

6

0.4115

0.16936

0.13302

118.39

2.07330

0.00845

7

.3665

•I343»

.10549

93.88

1.97259

.01065

8

.3264

.10651

.08366

74-45

.87189

•01343

9

.2906

.08447

.06634

59-04

.77118

.01694

10

.2588

.06699

.05261

46.82

.67047

.02136

11

0.2305

0.05312

0.04172

37-13

1.56977

0.02693

12

•2°53

.04213

•03309

29.45

.46906

.03396

i.3

.1828

•03341

.02624

23-35

•36835

.04282

H

.1628

.02649

.02081

18.52

.26764

.05400

15

.1450

.02101

.01650

14.69

.16694

.06809

16

0.12908

O.OI6663

0.013087

11.648

1.06623

0.0859

17

.11495

.013214

.010378

9-237

0.96552

.1083

18

.10237

.OIO479

.008231

7-325

.86482

•!365

19

.09116

.008330

.006527

5.809

.7641 1

.1721

20

.08118

.006591

.005176

4.607

.66340

.2171

21

0.07229

0.005227

0.004105

3-653

0.56270

0-2737

22

.06438

.004145

.003255

2.898

.46199

•345°

23

•05733

.003287

.002582

2.298

.36128

•4352

24

.05106

.002607

.002047

1.822

.26057

.5488

25

•04545

.OO2O67

.001624

1.445

•15987

.6920

26

0.04049

0.0016394

0.0012876

1.1459

0-05916

0.873

27

.03606

.OOI3OOI

.OOIO2 I I

.9088

1.95845

I. TOO

28

.03211

.OOIO3IO

.0008098

.7207

•85775

I.388

29

.02859

.0008176

.0006422

•57i5

•75704

1.750

30

.02546

.0006484

.0005093

•4532

•65633

2.2O6

31

0.02268

0.0005142

0.0004039

0-3594

l"-55562

2.782

32

.02019

.0004078

.0003203

.2850

.45492 -

3-508

33

.01798

.0003234

.0002540

.2261

•35421

4.424

34

.01601

.0002565

.OOO2OI4

•!793

•25350

5-578

35

.01426

.OOO2O34

.0001597

.1422

.15280

7-034

36

0.01270

O.OOOl6l3

0.0001267

0.1127

1.05209

8.87

37

.01131

.0001279

.0001005

.0894

2.95138

IT.I8

38

.01007

.0001014

.0000797

.0709

.85068

I4.IO

39

.00897

.0000804

.0000632

.0562

•74997

I7.78

40

•00799

.0000638

.0000501

.0446

.64926

22.43

SMITHSONIAN TABLES.

60

TABLE 661

CONSTANTS OF COPPER WIRE.

according to the American Brown and Sharp Gauge. Metric Measure. Temperature o° C. Density 8.90.

Electrical Constants.

Resistance and Conductivity.

Gauge
Number.

Ohms
per

Metre.

Log.

Metres
per
Ohm.

Ohms
per
Gramme.

Grammes
per
Ohm.

0.0001519

4.18150

6584.

o.ooooooi 592

6283000.

OOOO

.0001915

.28221

5221.

.0000002531

395IOOO.

OOO

.0002415

.38191

4141.

.0000004024

2485000.

00

.0003045

.48362

3284.

.0000006398

I 563000.

0

0.0003840

4-58433

2604.

0.000001017

982900.

1

.0004842

•68503

2065.

.OOOOOl6l8

618200.

2

.0006106

•78574

1638.

.000002572

388800.

3

.0007699

.88645

1299.

.000004090

244500.

4

.0009709

.98715

1030.

.000006504

I 53800.

5

O.OOI224

3.08786

816.9

0.00001034

96700.

6

.001544

.18857

647.8

.00001644

60820.

7

.001947

.28928

5*3-7

.00002615

38250.

8

.002455

.38998

407.4

.00004157

24050.

9

.003095

.49069

323-1

.00006610

15130.

10

0.003903

3-59I40

256.2

O.OOOIO5II

95T4-

11

.004922

.692JO

203.2

.00016712

5984.

12

.006206

.79281

161.1

.00026574

3763-

13

.007826

.89352

127.8

.00042254

2367.

14

.009868

•99423

101.3

.00067187

1488.

13

0.01244

2.09493

80.37

0.0010683

936.1

16

.01569

.19564

6373

.0016987

588.7

17

.01979

•29635

50-54

.0027010

370.2

18

.02495

•39705

40.08

.0042948

232-8

19

.03146

.49776

31-79

.0068290

146.4

20

0.03967

2.59847

25.21

0.010859

92.09

21

.05002

.69917

19.99

.017266

57-92

22

.06308

.79988

15.85

.027454

36.42

23

•07954

.•90059

12.57

•043653

22.91

24

.10030

i .001 30

9-97

.069411

11.88

25

o. 1 2647

T.IO2OO

7.907

0.11037

9.060

26

.15948

.202-f

6.270

•17549

5.698

27

.201 10

•30342

4-973

.27904

3-584

28

•25358

.40412

3-943

.44369

2.254

29

•3r976

.50483

3-I27

•70550

1.417

30

0.4032

1.60554

2.480

I.I2I8

0.8914

31

.5084

.70624

1.967

1-7837

.5606

32

.6411

.80695

1.560

2.8362

.3526

33

.8085
1.0194

.90766
0.00837

1-237
0.981

4.5097
7.1708

.2217
•1394

34
35

1-2855

0.10907

0.7779

11.376

0.08790

36

1.6210

.20978

.6169

18.130

•05516

37

2.0440

.31049

.4892

28.828

.03469

38

2-5775

.41119

.3880

45-838

.02182

39

3.2501

.51190

.3076

72.885

.01372

40

SMITHSONIAN TABLES.

61

TABLE 67.

SIZE, WEIGHT, AND ELECTRICAL

Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers
Size and Weight.

Gauge
Number.

Diameter
in Inches.

Square of
Diameter
(Circular
Inches).

Section
in Sq. Inches.

Pounds
per Foot.

Log.

Feet
per Pound.

7-0

0.500

0.2500

0.1963

0.75760

1.87944

1.320

6-0

.464

•2153

.1691

•65243

•81453

I-583

5-o

0.432

0.1866

0.1466

0.56554

^•7 5247

1.768

4-0

.400

.1600

•1257

.48486

.68562

2.062

3"°

•372

.1384

.1087

.41936

.62258

2.385

2-O

.348

.1211

.0951

.36699

.56466

2.725

O

•324

.1050

.0825

.31812

•50259

3- '43

1

0.300

0.09000

0.07069

0.27274

1-43574

3-667

2

•f6.

.07618

.05983

.23084

•36332

4-332

3

.06350

.04988

.19244

.28430

5.196

4

.232

•C5382

.04227

.16310

.21246

6.131

5

.212

.04494

•03530

.13620

•'3417

7-342

6

0.192

0.03686

0.02895

O.III7I

1.04810

8-95

7

.176

.03098

•02433

.09387

2.97252

10.65

8

.I60

.02560

.O2OIO

•07758

.88974

12.89

9

.144

.O2O74

.01629

.06284

.79822

15.91

10

.128

.01638

.01287

.04965

.69592

20.14

11

0.1 16

0.013456

0.010568

0.04078

2.61041

24.52

12

.104

.Olo8l6

.008495

•03278

•51557

30.51

13

.092

.008464

.006648

.02565

.40907

38-99

.080

.006400

.005027

.01939

.28768

5I-56

'5

.072

.005184

.004071

.01571

.19616

63.66

16

0.064

0.004096

0.003217

O.OI24I2

2.09386

80.6

17

.056

.003136

.002463

.009503

3-97787

105.2

18

.048

.002304

.OOlSlO

.006982

.84398

I43-2

19

.040

.OOI6OO

.001257

.004849

.68562

206.2

20

.036

.OOI296

.OOIOl8

.003927

.59410

254-6

21

0.032

O.OOIO24O

0.0008042

0.003103

3.49180

322-3

22

.028

.0007840

.0006157

.002376

•3758i

420.9

23

.024

.0005760

.0004524

.001746

.24192

572-9

24

.022

.0004840

.0003801

.001467

.16634

681.8

25

.020

.OOO4OOO

.0003141

.001212

.08356

824.9

25

0.0180

O.OOO324O

0.0002545

O.OOOgSiS

4.99209

1018.

27

.0164

.OOO269O

.OOO2 1 1 2

.OOO8I5I

.91119

1227.

28

.0148

.OOO2I9O

.OOOI728

.0006638

.82202

1506.

29

.0136

.OOOl85O

.0001453

.0005605

.74858

1784-

30

.0124

.OOOI538

.0001208

.0004660

.66834

2146.

31

0.0116

0.00013456

0.00010568

O.OOO4O78

4.61041

2452.

32

.0108

.00011664

.OOOO9l6l

•0003535

•54835

2829.

33

.0100

.OOOIOOOO

.00007854

.0003030

.48150

3300.

34

.0092

.00008464

.00006648

.0002565

.40907

3899.

35

.0084

.00007056

.00005542

.0002138

.33006

4677.

36

0.0076

0.00005776

0.00004536

O.OOOI75O

4-243I3

57I3-

37

.0068

.00004624

.00003632

.OOOI4O4

•I4752

7120.

38

.0060

.00003600

.OOOO2827

.OOOIOgi

.03780

9167.

39

.0052

.00002704

.00002 1 24

.00008 i 9

s-g^s1

I22OO.

40

.0048

.00002304

.OOOOlSlO

.0000682

•84398

14660.

41

0.0044

0.00001936

O.OOOOI52I

0.00005867

5.76840

17050.

42

.0040

.00001600

.OOOOI257

.00004849

.68562

2O62O.

43

.0036

.00001296

,OOOOrOl8

.00003927

.59410

25460.

44

.0032

.00001024

.00000804

.00003103

.49180

32230.

45

.0028

.00000784

.00000616

.00002381

.37681

41990.

46

0.0024

0.00000576

0.00000452

0.00001746

5.24192

57290.

47

.0020

.00000400

.000003 i 4

.OOOOI2I2

.08356

82490.

48

.0016

.00000256

.00000201

.OOOOO776

6.88974

I289OO.

49

.0012

.00000144

.00000113

.00000436

.63986

229200.

50

.0010

.00000100

.00000079

.00000303

.48150

330000.

SMITHSONIAN TABLES.

62

CONSTANTS OF COPPER WIRE.

according to the' British Standard Wire Gauge. British Measure. Temperature o° C. Density 8.90.

Electrical Constants.

TABLE 67.

Resistance and Conductivity.

Gauge
Number.

Ohms per Foot.

Log.

Feet per Ohm.

Ohms per Pound.

Pounds per Ohm.

0.00003918

5-5931°

25520.

0.000051719

'9335-

7-0

.00004550

•65799

21980.

.000069736

14339-

6-0

0.00005249

5.72006

19050.

0.0000928 1

'0775-

5-°

.OOOo6t22

.78691

1633°.

.00012627

7920.

4-0

.00007078

.84994

14130.

.00016880

5924-

3-°

.00008089

.90787

12360.

.OOO22O4O

4537-

2-0

.00009331

.96994

10720.

.00029333

3409-

O

O.OOOIO88

4.03679

9188.

0.0003991

2505.8

1

.OOOI286

.10921

7777-

.0005570

1795-2

2

.0001 543

.18823

6483.

.0008015

1247.7

3

.0001820

.26005

5495-

.OO 1 1 1 58

896.2

4

.0002180

•33836

4588.

.OOI6OO2

624.2

5

0.0002657

442443

3763-

0.0023786

420.4

6

.0003162

.50000

3162.

.0033688

296.9

7

.0003826

.58279

2613.

.0049323

202.7

8

.0004724

.67430

2117.

.0075176

I33-°

9

.0005979

.77661

1673-

.0084978

117.7

10

0.0007280

4.862 1 1

'373-6

0.017853

56-013

11

.0009056

.95696

1 104.2

.027631

36.191

12

.0011573

3-06345

864.1

.045 1 2 I

22.163

'3

.0015305

.18485

6534

.078927

12.669

14

.0018896

•27636

529.2

.I2O282

8.314

15

0.002391

3-37867

418.1

0.19267

5.1902

16

.003124

.49465

320.2

.32868

3-C423

i7

.004252

•62855

235-2

.60893

1.6423

18

.006122

.78691

'63-3

1.26268

0.7919

'9

.007558

.87842

132-3

1.92451

.5196

20

0.00957

198073

104.54

3.0827

0-32439

21

.01249

2.09671

80.04

5-2599

.19011

22

.01701

.23061

58.80

9.7429

.10264

23

.02024

.30618

49.41

I3.7988

.07246

24

.02506

.38897

39-91

2O.2O28

•0495 i

25

0.03023

2.48048

33-o8

30-792

0.032478

26

.03642

•56134

27.46

56-254

.017778

27

.04472
.05296

•65051
•72395

22.36
18.88

67-373
94.488

.014843
.010583

28
29

.06371

.80419

15.70

136.724

•007314

30

0.07449

2.87211

13.42

182.68

0.005474

31

.08398

.92418

11.91

237-59

.004209

32

.09796

.99103

IO.2I

323-25

.003094

33

•"573

1.06345

8.64

451.21

.002216

34

-13883

.14247

7.2O

649.25

.001 540

35

0.16959

7.22940

5-897

968.9

0.0010321

36

.21184

.32601

4720

1508.3

.0006630

37

.27210

•43473

3-675

2494.2

.0004009

38

.36226

•55902

2.760

4421.0

.0002262

39

•42515

.62855

2-352

6089.3

.0001642

40

0.5060

1.70412

1.976

8624.

0.00011596

41

.6122

.78691

•633

12627.

.00007919

42

•7558

.87842

.323

19245.

.00005196

43

.9566

•98073

.045

30827.

.00003244

44

1.2494

0.09671

O.8OO

52468.

.00001906

45

1.7006

0.23061

0.5880

97429.

0.000010264

46

2.5059

.38897

•3991

2O2O28.

.000004950

47

3.8264 .

.58279

•2613

493232-

.000002027

48

6.8025

' -83267

.1470

I55885I.

.000000642

49

9.7956

.99103

-IO2I

323245L

.000000196

50

SMITHSONIAN TABLES.

TABLE 68.

SIZE, WEIGHT, AND ELECTRICAL

Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers
Size and Weight.

Gauge
Number.

Diameter in
Centimetres.

Square of
Diameter
(Circular
Cms.).

Section in
Sq. Cms.

Grammes
per Metre.

Log.

Metres
per Gramme.

7-0

1.2700

1.6129

1.267

1127.4

3.05209

0.000887

6-0

.1786

.3890

.091

970.9

2.98719

.001032

5-°

1-0973

1.2040

0.9456

841.6

2.92512

O.OOI 1 88

4-0

.0160

•0323

.8107

721.6

•85827

.00 1 386

3-°

0.9449

0.8928

.7012

624.1

.79524

.OOl6o2

2-O

.8839

•7815

.6136

546.3

•73741

.001831

0

.8230

•6773

•5319

484.4

.68524

.002064

1

0.7620

0.58065

0.4560

405.9

2.60839

0.002464

2

.7010

•49157

•3858

343-6

•53607

.002910

3

.6401

.40970

.3218

286.4

•45695

.003492

4

•5893

•34725

.2727

242.7

.38512

.004 1 2O

5

•5385

.28996

.2277

202.7

.30682

.004934

6

0.4877

0.23783

0.18679

166.25

2.22075

0.006015

7

•4470

.19984

.15696

139.69

.14517

.007159

8

.4064

.16516

•1^973

"5-45

.06239

.008662

9

•3658

•13378

.10507

93- 5 1

1.97087

.010694

10

•3251

.10570

.08302

73-89

.86857

•013533

11

0.2946

O.o868l

O.o68l8

60.68

1.78307

0.01648

12

.2642

.06978

.05480

48.78

.68822

.02051

13

•2337

.05461

.04289

38-17

•S8'72

.02620

H

.2032

.04129

•03243

28.86

•46033

•03465

«S

.1829

•03344

.02627

23-38

.36881

.04278

16

0.16256

0.026426

0.020755

18.514

1.26751

0.05401

17

.14224

.020233

.015890

14.142

•I5°53

.07071

18

.12192

.014865

.011675

10.390

.01663

.09625

19

.10160

.010323

.008107

7.216

0.85827

.13858

20

.09144

.008361

.006567

5-845

.76675

.17109

21

0.08128

0.006606

0.005188

4.618

0.66445

0.2165

22

.07 1 1 2

.005058

.003972

3-536

•54847

.2828

23

.06096

.003716

.002922

2.598

•4'457

•3850

24

•05588

.003123

.002452

2.183

•33899

.4581

25

.05080

.00258 1

.002027

1.804

.25621

•5544

26

0.04572

0.0020903

0.0016417

1.4625

0.16509

0.6838

27

.04166

.0017352

.0013628

.2129

.08384

.8245

28

•03759

.0014132

.OOI 1099

0-9878

1.99467

1.0123

29

•03454

.0011922

.0009363

•8333

.92083

.2000

3°

.03150

.0009920

.0007791

•6934

.84099

.4422

31

0.02946

0.00o868l

0.0006818

0.6068

7.78307

1.648

32

.02743

.0007525

.0005910

.5260

.72100

1.901

33

.02540

.0006452

.0005067

.4510

•65415

2.217

34

•02337

.0005461

.0004289

•3817

.58172

2.620

35

.02134

.0004552

•0003575

.3182

.50271

3-143

36

O.OI930

0.0003726

0.0002927

0.2605

1.41578

3-839

37

.01727

.0002983

.0002343

.2090

•3i9i7

4.784

38

.01524

.0002323

.0001824

.1623

.21045

6.160

39

.01321

.0001746

.0001370

.1219

.08616

8.201

40

.01219

.0001486

.0001167

.1039

.01663

9.625

41

0.01118

0.0001249

0.0000982

0.0873

2.94105

"•45

42

.01016

.0001032

.0000813

.0722

.85827

13.86

43

.00914

.0000836

.0000656

.0584

•76675

17.11

44

.00813

.0000661

.0000519

.0462

.66445

21.65

45

.00711

.0000506

.0000397

•0354

.54847

28.28

46

0.00610

0.00003716

0.0000292

0.0260

2.41457

38-5

47

.00508

.00002581

.OOOO2O3

.0180

.25621

55-4

48

.00406

.00001652

.0000129

.0115

.06239

cS6.6

49

.00305

.00000929

.0000073

.0065

3.81251

154.0

50

.00254

.00000645

.0000051

.0045

.65415

221.8

SMITHSONIAN TABLES.

64

CONSTANTS OF COPPER WIRE.

according to the British Standard Wire Gauge. Metric Measure. Temperature o° C. Density 8.90.

Electrical Constants.

TABLE 68.

Resistance and Conductivity.

Gauge
Number.

Ohms per Metre.

Log.

VIetres per Ohm.

Ohms per Gramme.

Grammes per Ohm.

O.OOOI2S6

4.10907

7779-

O.OOOOOOII4O

8770000.

7-o

.0001493

•I7398

6699.

.0000001537

6504000.

6-0

O.OOOI722

4.23605

5814.

0.0000002046

4887000.

5-o

.OOO2OO9

.30289

4979-

.0000002784

3592000.

4-0

.0002322

•36593

4306.

.0000003721

2687000.

3^>

.0002653

•42376

3769-

.0000004857

2059000.

2-0

.0003061

.48592

3266.

.0000006319

1 583000.

O

0.0003571

4-55277

2801.

0.0000008798

1137000.

1

.0004218

.62510

237i-

.0000012275

814700.

2

.0005061

.70421

1976.

.0000017671

565900.

3

.000597 1

.77604

1675-

.0000024600

406500.

4

.0007151

•85434

1398.

.0000035279

283500.

5

0.0008718

4.94041

1147.1

0.0000052-44

190700.

6

.0010375

3.01 599

963-9

.000009350

107000.

7

.0012554

.09877

796.6

.000010874

91960.

8

.0015499

.19029

645.2

.000016573

60340.

9

.0019615

.29259

509.8

.000026547

37670.

10

0.002388

3-378io

418.7

0.00003936

25410.

11

.002978

•47295

335-8

.00006092

16420.

12

.003796

•57934

263.4

.00009945

10060.

'3

.005022

.70083

199.1

.00017398

5748.

M

.006199

•79235

161.3

.00026518

3771-

15

0.007846

3-89465

127.45

0.0004238

2359-6

16

.010248

2.01064

97.58

.0007246

1380.1

17

.013949

•14453

71.69

.0013425

744-9

18

.O2OO86

.30289

49-79

.0027837

359-2

19

.024798

•3944'

40.32

.0042428

235-7

20

0.03138

2.49671

31.86

0.005398

185.25

21

.04099

.61270

24-39

.011594

86.25

22

•05579

•74659

17.92

.021479

46.56

23

.06640

.82217

15.06

.030421

32-87

24

.08034

.90495

12.45

-044539

22.45

25

0.09919

2.99647

10.082

0.06782

14-745

26

.11949

1-07733

8.369

.09851

10.151

27

.14672

.16649

6.8 1 6

•M853

6.732

28

•I739I

•24034

5-750

.20869

4.792

29

.2O9OI

.32017

4.784

.30142

3-3i8

3°

0.2388

7.37810

4.187

0.3936

2.5407

31

•2755

.44017

3.629

•5238

1.9091

32

•3214

.50701

3.112

.7126

1-4033

33

•3797

•57944

2.634

•9947

1.0053

34

•4555

.65846

2.196

I-43I3

0.6987

35

0.5564

^•74539

1-7973

2.136

0.46816

36

.6950

.84200

.4388

3-333

.30003

32

.8927

.95070

.1202

7.019

.14247

38

1.1885

0.07 501

0.8414

9-747

.10260

39

•3949

•!4453

.7169

13-424

.07449

40

i. 660

O.22OII

0.6024

19.01

0.05260

41

2.009

.30289

•4979

27.84

•03592

42

2.480

•39441

, ..- -4033

42-43

•02357

43

3-I38

.49671

.3186

67.96

.01471

44

4-099

.61270

.2440

1 1 5-94

.00863

45

5-579

0.74659

0.1792

210.4

0.004753

46

8.034

.90495

.1245

445-4

.002245

47

12-554 «

1.09877

.0797

1087.4

.000920

48

22.318

' .34865

.0448

3436-7

.000291

49

3^-138

.50701

.0311

7126.3

.000140

50

SMITHSONIAN TABLES.

TABLE 69.

SIZE, WEIGHT, AND ELECTRICAL

Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers
Size and Weight.

Gauge
Number.

Diameter
in Inches.

Square of
Diameter
(Circular
Inches).

Sections in
Sq. Inches.

Pounds
per
Foot.

Log.

Feet
per
Pound.

OOOO

0-454

o 2061

0.16188

0.6246

1.79561

1.601

ooo

•425

.1806

.14186

•5474

.73828

1.827

oo

.380

.1440

•11341

•4376

.64107

2.285

o

•340

.1 156

.09079

•35°3

•54446

2.855

1

0.300

O.O9OOO

0.07069

0.2727

M3574

3.666

2

.284

.08065

•06335

.2444

.38814

4.091

3

•259

.06708

.05269

•2033

.30810

4.919

4

.238

.o'5664

.04449

.1717

•23465

5.826

5

.220

.04840

.03801

.1467

.16634

6.8 1 8

6

0.203

o.o4r2i

0.03237

0.12488

1.09649

8.008

7

.180

.03240

.02545

.09818

2.99204

10.185

8

.165

.02723

.02138

.08250

.91647

I 2.1 21

9

.148

.02190

.01720

.06638

.82202

I 5-065

10

•134

.01796

.01410

.05441

•73571

18-379

11

O.I 2O

0.014400

0.011310

0.04364

2.63986

22.91

12

.109

.011881

.009331

.03600

•55635

27.77

13

.095

.009025

.007088

•02735

•43695

36.56

H

.083

.006889

.005411

.02088

•3J965

47.90

15

.072

.005184

.004072

.01571

.19616

63.65

16

0.065

0.004225

0.0033183

0.012803

2-10733

78.10

17

.058

.003364

.0026421

.010194

.00835

98.IO

18

.049

.00240!

.0018857

.007276

3.86189

137.44

19

.042

.001764

.0013854

.005346

.72800

187.06

20

•035

.001225

.0009621

.003712

•56963

269.40

21

0.032

0.001024

0.0008042

0.003103

3.49180

322.3

22

.028

.000784

.00061 58

.002376

.37581

420-9

23

.025

.000625

.0004909

.001894

•27738 -

528.0

24

.022

.000484

.0003801

.001467

.16634

681.8

25

.O2O

.000400

.0003142

.OOI 21 2

.08356

824.9

26

O.OlS

0.000324

0.0002545

O.OOOgSiS

4.99204

1018.

27

.Ol6

.000256

.000201 i

.0007758

.88974

1289.

28

.014

.000196

.0001539

.OOO594O

•77375

1684.

29

-013

.000169

.0001327

.OOO5I2I

.70939

J953-

30

.OI2

.000144

.0001131

.0004364

.63986

2292.

31

O.OIO

O.OOOIOO

0.00007854

0.00030304

4.48 1 50

33°o-

32

•00,9

.00008 1

.00006362

.00024546

.38998

4074.

33

.008

.000064

.00005027

.00019395

.28768

5156-

34

.007

.000049

.00003848

.00014849

.17169

6734-

35

.005

.000025

.0000 i 963

.00007576

5-87944

13200.

36

0.004

0.000016

0.00001257

0.00004849

5.68562

20620.

SMITHSONIAN TABLES.

66

TABLE 69.

CONSTANTS OF COPPER WIRE.

according to the Birmingham Wire Gauge. British Measure. Temperature o° C. Density 8.90.

Electrical Constants.

Resistance and Conductivity.

Gauge
Number.

Ohms
per
toot.

Log.

Feet
per
Ohm.

Ohms
per
Pound.

Pounds
per
Ohm.

0.00004752

5.67692

21040.

0.0000761

13140.

OOOO

.00005423

•73425

18440.

.0000991

10090.

OOO

.00006784

.83146

14740.

.OOOI 550

6451.

OO

.00008474

.92807

1 1 800.

.0002419

4'34-

O

0.0001088

4.03679

9188.

0.0003991

2505.8

1

.0001214

.08439

8234.

.0004969

2012.5

2

.0001460

.16443

6848.

.0007183

1392.2

3

.0001729

.23788

5783-

.OOIOO74

992.6

4

.0002024

.30618

4941.

.0013799

724-7

5

0.0002377

4.37604

4207.

0.001903

525-26

6

.0003023

.48048

3308.

•003079

324-76

7

.0003598

.55606

2779.

.004361

229.30

8

.0004472

•65051

2236.

.006737

148.43

9

•0005455

.73682

I833-

.010025

99-75

10

0.0006802

4.83267

1470.2

0.01559

64.148

11

.0008245

.91618

1212.9

.02290

43.670

12

.0010854

3-03558

921.3

.03969

25-195

'3

.0014219

.15287

703-3

.06811

14.682

14

.0018896

.27636

529.2

.12028

8.314

'5

0.002318

3 36520

43r-3

o.iSir

5-5225

16

.002980

•47417

335-6

•2923

3.4211

17

.004080

.61064

245-1

.5607

I-7835

18

•005553

•74453

1 80. i

1.0388

0.9627

19

.007996

.90289

125.1

2.1541

•4643

20

0.009566

3-98073

104.54

3-083

0.32439

21

.012494

2.09671

80.04

5-259

.19015

22

.015709

•I95I5,

63.66

8-275

.12085

23

.020239

.30618

49.41

13-799

.07246

24

.024489

.38897

40.83

20.203

.04950

25

0.02887

2.46048

34-64

29.41

0.034006

26

.03826

.58279

26.13

49-32

.020275

27

.04998

.69877

2O.OI

84.14

.011885

28

•05796

•76314

I7-25

113,18

.008835

29

.06802

.83266

14.70

155.88

.006415

30

0.09796

2.99103

IO.2O9

323-2

0.0030936

31

.12095

1.08254

8.269

492.7

.0020290

32

.15306

.18485

6-533

789.2

.0012671

33

.19991

.30083

5.002

1346-3

.0007420

34

.39182

•59309

2-552

5171.9

.0001933

35

O.6I222

7.78691

1.663

12627.

0.00007920

36

SMITHSONIAN TABLES.

TABLE 70.

SIZE, WEIGHT, AND ELECTRICAL

Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers
Size and Weight.

Gauge
Number.

Diameter in
Centimetres.

Square of
Diameter
(Circular
Cms.).

Section in
Sq. Cms.

Grammes
Metre.

Log.

Metres
per
Gramme.

OOOO

I-'532

1.3298

1.0444

929-5

2.96826

0.001076

000

.0795

•l653

.9152

814.6

.91093

.OOI228

00

0.9652

0.9316

•73'7

651.2

.81372

.001536

o

.8636

.7458

.5858

521-3

.71711

.001918

1

0.7620

0.5806

0.4560

405-9

2.60839

0.002464

2

.7214

.5216

.4087

363-7

.56079

.002749

3

•6579

.4328

•3399

302.5

.48075

.003306

4

.6045

•3655

.2870

255-4

.40730

.003915,

5

•5588

•3I23

.2452

218.3

•33899

.004581

6

0.5156

0.2659

0.20881

185.84

2.26914

0.005381

7

.4572

.2090

.16417

146.11

.16469

.006844:

8

.4191

•1756

•!3795

122.78

.08912

.008145

9

' -3759

•1413

.11099

98.78

1.99467

.010124;

10

•3404

•1158

.09098

80.98

.90836

.012349,

11

0.3048

0.09290

0.07297

64-94

1.81251

0.01540

12

.2769

.07665

.06160

54-83

.73900

.01824 •

13

.2413

.05823

•04573

40.70

.60960

.02457

H

.2108

.04445

.03491

3 '-°7

•49231

.03219

15

.1829

•03345

.02627

23-43

.36981

.04268 :

16

0.16510

0.027258

0.021409

19.054

1.27998

0.05248

17

•I4732

.021703

.017046

15.171

.iSlOI

•06592

18

.12446

.015490

.012166

10.828

•03454

•09235

19

.10668

.011381

.008938

7-955

0.90065

•12571

20

.08890

•007903

.006207

5-524

.74229

.18103

21

0.08128

0.006606

0.005189

4.618

0.66445

0.2165

22

.07 I I 2

.005058

•003973

3-536

•54847

.2828

23

.06350

.004032

.003167

.45003

•3547

24

.05588

.003123

.002452

2.1 83

•33899

.4581

25

.05080

.002581

.002027

I.8O4

.25621

•5544 ,

26

0.04572

0.0020903

0.0016418

I.46ll

0.16469

0.6844

27

.04064

.0016516

.0012972

•1J545

.06239

.8662

28

•03556

.0012645

.0009932

0.8839

1.94641

T-i3!3 '

29

.03302

.0010903

.0008563

.7621

.88204

.3122 |

3°

.03048

.0009290

.0007297

.6494

.81251

•5399 ;

31

0.02540

0.0006452

0.0005067

0.4510

1.65415

2.217

32

.02286

.0005226

.0004104

•3653

•56263

2-738

33

.02032

.0004129

.0003243

.2886

•46033

3-465

34

.01778

.0003161

.0002483

.22IO

•34435

4-525

35

.OI27O

.0001613

.0001267

.1127

.05209

8.870

36

O.OIOI6

0.0001032

0.0000811

O.O722

2.85827

13.861

SMITHSONIAN TABLES.

68

TABLE 70.

CONSTANTS OF COPPER WIRE.

according to the Birmingham Wire Gauge. Metric Measure. Temperature o° C. Density 8.90.

Electrical Constants.

Resistance and Conductivity.

Gauge
Number.

Ohms
per
Metre.

Log.

Metres
per
Ohm.

Ohms
per
Gramme.

Grammes
per
Ohm.

0.0001559

4.19290

6414.

0.0000001677

5962000.

OOOO

.0001779

.25024

5620.

.OOOOOO2 I 84

4578000.

OOO

.OOO2226

•34745

4493-

.0000003418

2926000.

00

.0002780

.44406

3597-

.0000005333

1875000.

o

0.0003571

4-55277

2800.

0.0000008798

II37OOO.

1

.0003985

.60038

2510.

.0000010955

9:2800.

2

.0004791

.68041

2087.

.00000:5837

631400.

3

.0005674

•75386

'763-

.OOOOO2221O

450200.

4

.0006640

.82217

1506.

.0000030420

328700.

5

0.0007799

4.89202

1282.2

0.000004196

238300.

6

.0009257

•99647

1080.3

.000006789

147300.

7

.0011804

3.07205

847.2

.000009615

: 04000.

8

.0014672

.16649

681.6

.000014853

67330-

9

.0017898

.25280

558.7

.OOOO22IO3

45240.

10

0.002232

3.34865

448.1

0.00003437

29:00.

11

.002643

.42216

378.3

.00004822

20740.

12

.003561

.55157

280.8

.00008749

"43°-

13

.004665

.66886

214.4

.000:50:6

6660.

14

.006185

•79135

161.7

.00026396

3789-

15

0.007607

3.88119

131.46

0.0003992

2504.9

16

•009553

.98016

104.68

.0006297

1588.0

17

•013385

2.12662

74-71

.0012362

808.9

:8

.018219

.26052

54.89

.OO220X)2

436.6

19

.026235

.41888

38.12

.0047489

2:0.6

20

0.03138

2.49671

31.86

0.006796

147.14

21

.04099

.61270

24-39

.0:1594

86.25

22

.05142

•71113

19.45

.018243

54.82

23

.06640

.82217

15.06

.030421

32-87

24

.08034

•90495

12.45

•044539

22.45

25

0.09919

2.99647

10.08

0.06789

I4-731

26

.12583

1.09877

7-947

.:o874

9-:96

27

.16397

.21476

6.099

•18550

5-391

28

.19016

•279'3

5-259

.24951

4.008

29

.22I38

•34865

4-5J7

•34367

2.910

30

0.3214

7.50701

3.112

0.7126

1.4032

31

.3968

•59853

2.520

1.0862

0.9206

32

.5022

.70083

1.991

I-7398

.5748

33

•6559

.81682

1.525

2.9861

•3349

34

1.2855

0.10907

0.778

11.4020

.0877

35

2.0086

0.30289

0.498

27.8370

0.0359

36

SMITHSONIAN TABLES.

69

TABLE 71.

STRENGTH OF MATERIALS.'

(a) METALS.

Name of metai. TESTS''*1.1

Aluminium wire .

"20000— 1 nnnn

Brass wire, hard drawn 50000-150000
Bronze, phosphor, hard drawn 110000-140000
" silicon " " 95000-115000
Copper wire, hard drawn 60000-70000

" wire, hard drawn
" " annealed
Lead, cast or drawn

. . . . 8OOOO-I2OOOO
. . . . 50000-60000
2600-3300

Platinum t wire

......... 50000

Steel, mild, hard drawn .
" hard " "

. . IOOOOO-20OOOO
I5OOOO-33OOO

......... 22OOO-3OOOO

(b) STONES AND BRICKS.

Resistance to crush-
Name of substance. ing in pounds
per sq. in.

Basalt

. . . . . . . . . l8oOO-27OOO

•?oo-i qoo

, . • . . . . . : . •. 17000-26000

......... 4500-8000

Slate . . .

. ' . . . . . . . 11000-30000

(r) TIMBER.

Tensile strength Resistance to
Name of wood. in pounds per crushing in
sq. in. pounds per sq. in.

Ash ....

. . . . . t . IIOOO— 2IOOO 6000-9000

Beech
Birch . .
Chestnut .
Elm ....

. . . . . IIOOO-lSoOO 9OOO-IOOOO
. . . , . . . I2OOO-l8oOO 5OOO-7OOO
IOOOO-I3OOO 4OOO-6OOO

Hackberry ~. .
Hickory . . .
Maple . . .
Mulberry . . .
Oak, burr .
" red .
" water
" white
Poplar
Walnut .

10000-16000
15000-25000 7OOO-I2OOO
8OOO-I2OOO 6OOO-8OOO
8OOO-I4OOO
I5OOO-2OOOO 7000-10000
13000-18000 5OOO-7OOO
I2OOO-l6oOO 4000-6000
20OOO-25OOO 6000-9000
• IOOOO-I5OOO 5OOO-8OOO
8OOO-I4OOO 4OOO-8OOO

in other than the ordinary inch pound units.

t On the authority of Wertheim.

t The crushing strength of cast iron is from 5.5 to 6.5 times the tensile strength.

NOTBS. — According to Boys, quartz fibres have a tensile strength of between 1 16000 and 167000 pounds per square
inch.

Leather belting of single thickness bears from 400 to 1600 pounds per inch of its breadth.

SMITHSONIAN TABLES.

PHYSICAL PROPERTIES OF STEEL.*

TABLE 72.

Percentages of

^_

1

!§

c

3

u

T>

bo

3

•&8

Z m

I.

-5>8

{J

1

0 ?

o"5

P.

a 2,

" 6

et,

o -
o .£s

if

|

s.

P.

Si.

C.

Mn.

Cu.

Co.

Ni.

Sb.

c ^

1 -

y'2 :='S

C

la

1*

1+

n

l:i

o

3

.004

.014

•145

•257

.O2O

.OO2

.008

.OIO

216

379

246

9-5 Io6

30-9

.009

.084

.,63

.009

.020

.023

.021

.016

252

434

260

12.3

129

32.6

.Oil

.109

.168

.042

.051

.028

.028

•044

276

481

234

17.4

"9

27-5

.027

.247

.216

.036

.072

.027

.048

.070

322

529

243

24.7

117

24.9

.014

.029

•037

.161

.121

.OOI

trace

trace

317

534

277

18.4

15'

32.0

trace

•039

.084

•234

.000

.014

.036

•057

•"5

260

605

250

15.6

no

20.8

.008
.056

•034

•0/3
.007

.316
•r39

.064
.165

.008
•364

.016
.076

.023
.107

419

478

649
687

263

26 1

37-9
46-3

130

I IO

22.3

18.1

.004

.024

.087

•447

.072

.005

.018

.023

461

755

271

46.0

124

18.6

.058

.128

.013

.254

•341

•278

.045

.065

487

785

293

55-o

91

'5-5

066

.099

.016

.326

•525

.306

.054

.078

549

793

255

58.0

38

5.6

.002

.022

.123

•595

.124

.001

.007

.006

480

828

267

42-7

151

2I.O

.008

.062

.071

•447

493

.007

.040

.065

484

859

284

38.2

'74

22-7

.041

•I25

.028

•355

•404

•253

.049

.102

543

880

254

55-9

49

6.7

.062

.138

.018

•39°

•584

•344

•073

.no

565

953

259

73-7

44

5.6

.002

.020

.096

.652

.061

.030

.007

.018

5*0

955

269

50.2

112

13-7

.002

.026

.164

•935

.099

.004

.018

.016

557

957

278

65-3

123

1 6.6

•043

.104

.074

.756

•465

•346

.052

.120

652

IOIO

237

94.6

14

1-7

.028

.065

.028

.690

•459

.022

.000

.COO

516

1 022

285.

55.6

37

4.6

.003

.031

.204

•929

.129

.007

.013

.OIO

590

1050

284

62.1

148

16.0

.038

.092

.070

•387

•625

.210

.050

•"5

631

I I 12

279

83.2

135

13-7

.001

•015

.150

.971

.074

.003

.003

.015

555

II7I

262

65.6

99

9.9

.000

.019

.192

1.105

.226

.001

.002

.004

668

1254

272

82.7

93

9.0

.014

.063

•043

.681

.625

•038

.COD

.000

614

1288

260

82.2

108

9-9

STKEL CONTAINING CHROMIUM.

trace

.020

.116

.461

.027

trace

.000

.612 Cr.

370

810

275

28.3

I IO

15-6

.001

.019

.136

•454 -023

.000

.OOO

.921 Cr.

495

915

287

44-8

157

19.1

trace

.007

.154

.639 .050

.008

trace

1.044 Cr.

500

967

281

56.1

25

3-5

—

—

.600 —

—

—

2. 200 Cr.

675

1030

—

—

—

19.9

—

—

—

1. 100 j —

—

—

4.000 Cr.

1770

1778

~

~

~~

7-5

STEEL CONTAINING TUNGSTEN.

_

_

.09

1.99

.19

7.81 per cent tungsten .

1464

o.o

—

—

•OS

2.06

2.66

6.73 " "

—

760

—

—

— o.o

Same after heating to dull red and quenching in oil

—

940

—

—

— o.o

.21

i. 20

•35

6.45 per cent tungsten .

1900

— 0.75

STEEL CONTAINING MANGANESE.

.06

.08

•37

.72

9.8

\ one test
; another te

—

1065
1 190

—

—

—

22.O
28.9

st . . . .

* The samples here given are arranged in the order of ultimate strength. The table illustrates the great com-
plexity of the problem of determining the effect of any given substance on the physical properties. It will be noticed
that the specimens containing moderately large amounts of copper are low in ductility, — that high carbon or high sum
of carbon and manganese generally gives high strength. The first specimen seems to indicate a weakening effect
of silicon when a moderate amount of carbon is present. It has to he remembered that no table of this kind proves
much unless nearly the same amount of work has been spent on the different specimens in the process of manufacture.
Most of the lines give avenges of a number of tests of similar steels. The table has been largely compiled from the
Report of the Board on Testing Iron and Steel, Washington, 1881, and from results quoted in Howe's " Metallurgy
of Steel."

t The strengths and elasticity data here given refer to bar or plate of moderate thickness, and are in pounds per
square inch. Mild steel wire generally ranges in strength between 100000 and 200000 pounds per square inch, with
an elongation of from 8 to 4 per cent. Thoroughly annealed wire does not differ greatly in strength from the data
given iii the table unless it has been subjected to special treatment for the purpose of producing high density and
fine-grained structure. Drawing or stretching and subsequent rest tend to increase the Young's Modulus.

SMITHSONIAN TABLES. 7 I

TABLE 73.

ELASTICITY AND STRENGTH OF IRON.*

Area of cross sec-

tion of the bar in
percentage of the
area of the cross
section of the

Relative values of
ultimate strength.

Relative values of
the stress at the
yield point.

pile.

I

125

194

2

112

I/O

3
4

5
7

I O6
IO4

I°3
IOI

144
140

130
II4

The variation of the yield point is not
regular, and seems to have been much
affected by the temperature of rolling.

10

TOO

IOO

15

98

92

TABLE 74.

APPROXIMATE VARIATION OF THE STRENGTH OF BAR IRON, WITH
VARIATION OF SECTION. t

Diameter
in inches.

Strength per sq.
in. in pounds.

Total strength of
bar.

Diameter
in inches.

Strength per sq.
in. in pounds.

Total strength
of bar.

2.2

59000

224000

I.I

543°0

52000

2.1

58500

203000

1.0

54000

42OOO

2.O

58000

182000

0.9

53700

34000

1-9

57600

163000

0.8

533°0

2/000

1.8

57100

145000

o-7

53000

2OOOO

i-7

56700

129000

0.6

52700

I49OO

1.6

56300

113000

o-5

52400

10300

i-5

55900

99000

0.4

52100

66OO

1.4

555°0

85000

o-3

51900

3700

i-3

55100

73000

0.2

51600

l6OO

1.2

54700

62OOO

O.I

51300

4OO

* This table was computed from the results published in the Report of the U. S. Board on Testing Iron and Steel,
Washington, 1881, and shows approximately the relative effect of different amounts of reduction of section from the
pile to the rolled bar. A reduction of the pile to 10 per cent of its original volume is taken as giving a strength of
loo, and the others are expressed in the same units.

t The strength o£ bar iron may be taken as ranging from 15 per cent above to 15 per cent below the numbers here
given, which represent the average of a large number of tests taken from various sources.

NOTES. — The stress at the yield point averages about 60 per cent of the ultimate strength, and generally lies be-
tween 50 and 70 percent. The variation depends largely on the temperature of rolling if the iron be otherwise fairly
pure.

According to the experiments of the U. S. Board for Testing Iron and Steel, above referred to, a bar of iron which
has been subject to tensile stress up to its limit of strength gains from 10 to 20 per cent in strength if allowed to rest
free from stress for eight days or more before breaking. The effect of stretching and subsequent rest in raising the
elastic limit and tensile strength was discovered by Wbhler, and has been investigated by Bauschinger, who shows
that the modulus of elasticity is also raised after rest. The strengthening effect of stretching with rest, or continuous
very slowly increased loading, has been rediscovered by a number of experimenters.

SMITHSONIAN TABLES.

TABLES 75-77.

EFFECT OF RELATIVE COMPOSITION ON THE STRENGTH OF ALLOYS
OF COPPER, TIN, AND ZINC.*

TABLE 75. — Copper-Tin Alloys. (Bronzes.)

TABLE 76. — Copper-Zinc Alloys. (Brasses.

_,

tte

c

"o

0

V b/J

.— c

•o 'a

'£ c

gj

_c

Ml ^

B?

c £

el

M u

fl

C

H w

£a

CJ w

I =*

i *

fc! ="

".5

l-i

ii O

0.

$

Pounds per square inch.

0,

IOO

oo

28000

14000

42000

8.

44

95

5

3IOOO 17000

46000

10.

4i

90

IO

290OO 2IOOO

54000

4-

31

85

15 33000

26000

74000

1.6

24

80

20

32000 28000 , 124000

o-5

14

75

25

18000

1 8000

150000

o.o

8

70

30

6500

6500

143000

o.o

2

65

35

2800

2800

75000

0.0

4

•M

O

"o

u wi

173 c

H

c

c a

3

- —

H •"

V O

5"

fe S

"'1

^" -

£

OH

Pounds per square inch.

AH

IOO

O

2/OCO

14000

41000

7

95

S

28OOO

I2OOO

28000

12

90

IO

30000

IOOOO

29000

18

8S

15

32OOO

9000

33000

25

80

20

34000

8000

39000

33

75

25

37000

9000

46000

38

70

30

4IOOO

IOOOO

54000

38

6S

35

46000

13000

63000

33

60

40

49OOO

17000

74000

55

4S

440OO

2OOOO

90000

10

5°

SO

3OOOO

24OOO

116000

4

45

55

I4OOO

14000

126000

o

TABLE 77. — Copper-Zinc-Tin Alloy s.§

Percentage of

Tensile

Percentage of

Tensile

strength

strength

Copper.

Zinc.

Tin.

in pounds
per sq. in.

Copper.

Zinc.

Tin.

in pounds
per sq. in.

45

50

5

I5OOO

25

5

45OOO

50

45

5

5OOOO

20

IO

44OOO

So

40

10

15000

70

'5

15

37000

f43

••>

65000

IO

20

30000

cc

I 40

5

62OOO

5

25

24000

1-35

IO

32500

20

5

45OOO

1 30

15

15000

J'5

10

45000

37

3

6OOOO

75

I10

15

43000

60

35

5

52500

I 5

20

4IOOO

30

10

4OOOO

(J5

5

45000

L 2O

20

IOOOO

80

i I0

10

' 45000

30

5

50000

( 5

15

47500

65

4

25
2O

IO

15

42000
30000

85

\'l

5

10

43500
46500

'5

20

1 8000

90

5

5

42OCO

10

25

I2OOO

* These tables were compiled from the results published by the U. S. Board on Testing of Metals. The numbers
refer to unwrought castings, and are subject to large variations for individual specimens.

t The crushing strengths here given correspond to 10 per cent compression for those cases where the total com-
pression exceeds that amount.

t For crushing strength, 10 per cent compression was taken as standard.

§ This table covers the range of triple combinations of these three metals which contain alloys of useful strength
and moderate ductility. The weaker cases here given, and those lying outside the range here taken, are generally weak
and brittle. The absolute strength may of course be varied by the method of fusing and casting, and certainly can be
greatly increased by working. The object of the table is to show relative values, and to give an idea of the strength of
sound castings of these alloys.

SMITHSONIAN TABLES.

73

TABLE 78.

ELASTIC MODULI.

Rigidity Modulus.*

Modulus of Rigidity.

Substance.

Pounds per

Grammes per

Authority.

square inch

square centi-

-^ 10".

metre -p JO°.

Metals : —

Aluminium

3.4-4.8

241-335

Thomsont-Katzenelsohn.

Brass and Bronze wire

4.6-5.8

320-410

Various.

Copper, drawn .

5.6-6.7

393-473

Thomson.!

" "...

5-o

352

Katzenelsohn.

German silver

6.2

432

"

" " ' .

7-i

496

Gray.

Gold, pure . ...

5-6

395

Katzenelsohn.

""....

4.0

281

Thomson.!

Iron, soft . . . -.;•.•

9.6

671

Wertheim.

" drawn . . .

10-14

700-800

Various.

Platinum . . . . ( ... '

8.9

622

Thomson.!

" . . .

9-4

663

Tisati.

Silver . ,. , . .

3-8

270

Thomson.!

" . . ' . . .

3-6

256

Pisati.

" . . . . .

3-8

265

Baumeister.

Steel, cast .

10.6

746

XVertheim.

" " . - .

11.8

829

Pisati.

Tin

2.2

J54

Kiewiet.

Zinc . . .

5-1

360

Thomson.!

" . . •- .

5-4

382

Kiewiet.

Glass . . . . ' .

3-3

235

Wertheim.

" .......

3-9

273

Kowalski.

Stone : —

Clay rock . . .

2-5

177

1

Granite . -.. .

1.8

128

Gray

Marble . . .

i-7

119

&

Slate

3-2

229

Milne.

Tuff .....

i-5

1 02

J

Wood . . . . .

.I-.I7

7-12

Gray.

* The modulus of rigidity as used in this table may be shortly defined by the following equation : —

Modulus of rigidity - Intensity of tangential stress.
Distortion in radians.

To interpret the equation imagine a cube of the material, to four consecutive faces of which a tangential stress of
uniform intensity is applied, the direction of the stress being opposite on adjacent faces. The modulus of rigidity is
the number obtained by dividing the numerical value of the tangential stress per unit of area by the number repre-
senting the change of the angles on the nonstressed faces of the cube measured in radians,
t Lord Kelvin.

SMITHSONIAN TABLES.

74

ELASTIC MODULI.

Young's Modulus.-

TABLE 79.

Substance.

Young's Modulus.

Authority.

Pounds per
square inch
-=- io8.

Grammes per
square centi-
metre -^- 10°.

Metals : —
Brass and bronze, cast ....

8.6-10
14-17

16-18
17-20

12-14

18
8-1 7 1
24-3°

2.2-2.9
14
17
23-26

22

1 0-10.7

23-30*
27-30

16
12-14

2.2-3.6
8.6-11.4
7-10

4-7
5-9

$

2.7

0.85

I.O-2.2

600-700
IOOO-I2OO
II5O-I25O
1052
I2O9-I4OO
813-980

55O-I2OO
I70O-2IOO

I 56-200

979
1176
1600-1700

'SB2
700-7.50
1600-2100
1900-2100

870-960
160
151-255
600-800
500-700

416
400
686
189
60
70-154

Various.

Wertheim.
Various.

Wertheim.
Various.

Wertheim.

Various.
Wertheim.
Various.

Various.
Wertheim.
Various.

Beetz.
Various.

Gray
&
Milne.

Various.

Copper, drawn . . . . .'""';
" annealed . . . , .
German silver, drawn . . . •
Gold, drawn . . . . . .

" wrought . . .
Iron wire . . ...
Lead, cast or drawn . .
Palladium, soft .....
hard .....
Platinum, drawn ....
soft . ' . ...
Silver, drawn
Steel . ..... ...
" hard drawn . . .".,..
Tin
Zinc . .
Bone . . . . . . abt.

Glass ........
Ice . . . . . . .

Stone : —

Granite

Tuff .......
Whalebone abt.
Wood

* The Young's Modulus of elasticity is used in connection with elongated bars or wires of elastic material. It is
the ratio of the number representing the longitudinal stress per unit of area of transverse section to the number rep-
resenting the elongation per unit of length produced by the stress, or : —

Young's Modulus = Inte,nsity of »Q"giti.dinal stress.
Elongation per unit length.

In the case of an isotropic substance the Young's Modulus is related to the elasticity of form (or rigidity modulus)
and the elasticity of volume (or bulk modulus) in the manner indicated in the following equation : —

£•— 9"*_

where K is Young's Modulus, n the rigidity modulus and k the bulk modulus.

The bulk modulus is the ratio of the number expressing the intensity of a uniform normal stress applied all over
the bounding surface of a body (solid, liquid or gas) to the number expressing the change of volume, per unit volume,
produced by the stress.

t The modulus for cast iron varies greatly, not only for different specimens, but in the same specimen for different
intensities of stress. It is diminished for tension stress by permanent elongation.

t See also Table 72. ,

SMITHSONIAN TABLES.

75

TABLES 80, 81 .

ELASTIC MODULI.

TABLE 80. —Variation of the Rigidity oi Metals with Temperature.*

The modulus of rigidity at temperature / is given by the equation nt = «0 (i -)- at + #2 -f- yf).

Metal.

no

a

0

y

Authority.

Brass

320 X io6

— .000455

— .00000136

_

K. & L.

Copper .

265 X io1
397 X IOH

— .002158

— .0027 1 6

— .00000048
-f .00000023

— .0000000032
— .0000000047

Pisati.

• . .

390 X xo15

— .000572

— .OOOOOO28

—

K. & L.

Iron

694 X io6

— .000483

.OOOOOO I 2

—

"

" . • .

811 X io«

— .000206

— .OOOOOOI9

-)- .00000000 1 1

Pisati.

Platinum .

663 X 10°

— .0001 1 1

— .OOOOOO50

-f- .0000000008

«

Silver

257 X io6

— .000387

.00000038

— .00000000 1 1

"

Steel . . .

829 X io'J

— .000187

— .00000059

-f- .0000000009

«

TABLE 81. — Ratio p of Transverse Contraction to Longitudinal Extension under Tensile Stress

(Poisson's Ratio).

Name of substance.

Range of the
value of p.

Mean
of each
range.

Final
mean.

Authority.

Brass

0.340-0.500

0.469 ]
0.420

Everett.
Baumeister.

! ! ! ' '.'','-

—

0.387

0-325 f

o-357

Kirchhoff.
Mallock.

. . . . *

— —

0-3'5 i

Wertheim.

" ......

— —

0.226 J

Littmann.

Copper

— —

0.348 |

Mallock.

" ......

0.224-0.441

o-332 i

0.340

Thomson.

Iron

— —

0.310]

Everett.

* .

— —

0.253 I

Mallock.

" ......

0.250-0.420

0.304 f

0.277

Baumeister.

0.214-0.268

o-243 J

Littmann.

Lead

— —

0-375

o-375

Mallock.

Steel, hard . . ' .

0.293-0.295

0.294 )

Kirchhoff.

" " '.'.'.'.'.

0.275-0.328
0.266-0.303

0.294 >
0.296 )

0.295

Okatow.
Schneebeli.

" soft

— —

0.304 ]

Okatow.

'.'.'.'.'.

0.306 !
0-253 f

0.299

Schneebeli.
Mallock.

.

— —

0-333 J

Goetz & Kurz.

Zinc . . ....

0.180-0.230

0.205

0.205

Mallock.

_. .

It

Ivory

— —

about

0.309
0.500

M

Paraffin ......

u

Cork . . . . ,

—

0.000

i)

Caoutchouc (for small extensions)

0.370-0.640

0-505 I
0.500!

0.502

j Rontgen. .
( Amagat.

Jelly . . ...

~~

0.500

0.500

Maurer.

Katzenelsolin gives the following values, together with the percentage variation S between o° and 100° C.

Substance. p

5

Aluminium . . . . . . . . . . . OIT

I C 7

Brass .......... 04^

1 Q

German silver 0.33

3-4

Gold ............ 017

2 C

Iron ............ 027

•J 7

Platinum ......... . rvtfi

r r

Silver

o-37

12.2

* According to the experiments of Kohlrausch and Loomis (Pogg. Ann. vol. 141), and of Pisati (N. Cim.fo) vols. 4,5).
SMITHSONIAN TABLES.

76

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, a, j3, y, and o« 0, V2 represent the direction cosines of the length, the greater and the less transverse
dimensions of the prism with reference to the principal axis of the crystal. E is the modulus for extension or
compression, and T is the modulus for torsional rigidity. The moduli are in grammes per square centimetre.

Harite.
io10
-p- = 16.130* + 18.51/3' + 10.427* + 2(38.79/3V2 -r 1 5-2i7-er + 8.88a-j82)

lfj_ — 6g.52a4 + 1 17.66/8' +]i 16.467* + 2(20.i6/3-V + 85-297?a2+ i27.35a-02)

Beryl (Emerald).

io10

-rr- =4.325 sin'0 -j- 4.619 cos4^ -j- 13.328 sin2^ cos2?

rr

10

io —

-rp- = I 5-00 3.67 5 COS*02 — 1 7- 536 COS2? COS29i

Fluor spar.

-— = 13.05 — 6.26 (a* + j8l + 7*)

^- = 58.04 — 50.08 (/3V2 + y-a- + a2)82)

Pyrites.

^- = 5.08 — 2.24 (a4 + 0' + 7*)

^ = 18.60 — 17.95 (fl'V + r«'2 + «'2)82)

Rock salt.

^ = 33.48 - 9.66 (a* + P + T4 )

^r- = I 54.58 — 77.28 (0V2 + 7'2«- +«'202)
Sylvine.

where <j> <t>i fa are the angles which
the length, breadth, and thickness
of the specimen make with the
principal axis of the crystal.

-^- = 306.0 — 192.

Topaz.
io10
-^ —4.341 a4 + 3.46oj8* + 3.7717*+ 2 (3.879/3 V+ 28. 567V+ 2.39a^2)

io10

-T = I4.88a» + 16.54)8* + i6.4574 + 30.89j8V2 + 4P&9ry*a* + 43-5i«2)82

Quartz.

io10

-g- = 12.734 (i — 72)2+ 16.693(1 — 72)72 + 9.7057* — 8.460/37 (3o2 — )82)

io10

-- = 19.665 + 9-060722 + 22-9847'V2 — 16.920 [(7/3 + 07i) (3««i — ^3i) — £27-2)]

* These formulae are taken from Voigt's papers (Wied. Ann. vols. 31, 34, and 35).
SMITHSONIAN TABLES.

77

TABLE 83.

ELASTICITY OF CRYSTALS.

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.

(a) REGULAR SYSTEM.*

Substance.

Authority.

Fluor spar
Pyrites . .
Rock salt .

Sylvine . .

Sodium chloride
Potash alum .
Chrome alum
Iron alum .

1473 X l°6
3530 X io6
416 X io6
403 X io6
401 X io6
372 X io6
405 X io6
181 X io6
161 X io6
186 X io6

1008 X io6
2530 X io6
346 X io6
339 X io6
209 X io6
196 X io6
319 X to6
199 X io6
177 X io6

910 X io6

2310 X io6

31 1 X io6

345 X io6

1075 X io6

129 X io6

655 X

Voigt.t

Koch.J

Voigt.
Koch.
Beckenkamp.§

(b) RHOMBIC SYSTEM.||

Substance.

Barite
Topaz

620 X io6
2304 X io6

540 X io6
2890 X io6

959 X io6
2652 X io6

376 X io6
2670 X io6

702 X io6
2893 X io°

740 X io6
3180 X io6

Authority.

Voigt.

Substance.

T, . = T,

Authority.

Barite
Topaz

283 X io6
I336X io6

293 X io6
I353X io6

121 X IO6

1104 X io6

Voigt.

In the MONOCLINIC SYSTEM, Coromilas (Zeit. fur Kryst. vol. i) gives

( £ =887 X io6 at 21.9° to the principal axis.
Lrypsum <

( Ena,, = 1X106 at 7.4°

313X

22I3

1554 X io6 at 45° to the principal axis.

75.4
**• j Emai = 22I3 X Io6 i" tne principal axis.

( Enun =

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.

£0 = 2165X106, E45 = 1 796 X io6, E90 = 23i2X io6,
TO = 667X106, T»o = 883X106. The smallest cross dimension of the
prism experimented on (see Table 82), was in the principal axis for this last case.

In the RHOMBOHEDRIC SYSTEM, Voigt has measured quartz. The subscripts have the
same meaning as in the hexagonal system.

£0=1030X106, E_45 = i305X io6, £+45 = 850 X io6, £90=785X106,

To = 508 X io6, T90 = 348 X io6.
Baumgarten IT gives for calcspar

£0=501X106, E_45 = 44i Xio6, E+45 = 772X io6, E90 = 79° X io6.

* In this system the subscript ,T 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.

t Voigt, " Wied. Ann." vol. 31, 34-35.

% Koch, " Wied. Ann." vol. 18.

§ Beckenkamp, "Zeit. fur Kryst." vol. io.

|| The subscripts i, 2, 3 indicate that the three principal axes are the axes of stress; 4, 5, 6 that the axes of stress
are in the three principal planes at angles of 45° to the corresponding axes.

H Baumgarten, " Pogg. Ann." vol. 152.

SMITHSONIAN TABLES.

78

TABLES 84-87.

COMPRESSIBILITY OF CASES."

These tables give the relative values of the product pv for different pressures and temperatures, and hence show the
departure from Boyle's law. The pressures are in metres of mercury, or in atmospheres, the volume being
arbitrary. The temperatures are in centigrade degrees.

TABLE 84.— Nitrogen.

TABLE 85. — Hydrogen.

Pressure in

Relative values of pv at —

metres of

1

mercury.

. 7°. 7

30°. i

5°0-4

7S°-5

100°. I

30

274 S

287 S

3080

3330

3575

60

2740

287 S

3100

3360

3610

IOO

2790

2930

3 '70

344 S

3<595

140

2890

3040

327 s

3SSQ

3820

180

3OI.S

3i So

3390

3675

3950

220 .

3 HO

328S

3SP

3820

4090

260 ,

3290

3440

36«S

397 S

4240

300

34 So

3600

3840

413°

4400

320

3525

3<>75

39'5

4210

4475

Pressure in

Relative values of fv at —

metres of

mercury.

i7°-7

4°°-4

60°. 4

8i°.i

100°. I

£

2830
2885

3045
3110

3235

329 S

343°

3Soo

3610

3680

IOO

2Q8S

3200

3400

3620

378o

140

3080

3lOO

3500

371°

3880

180

3I8S

3420

3620

3830

4010

220

32QO

3S20

372 s

393°

4110

260

3400

3025

3*3°

4040

4220

300

3Soo

3730

3935

4140

4325

320

355°

378o

399°

4200

43*5

TABLE 86. - Methane.

Pressure in

Relative values of pv at —

metres of

mercury.

i4°-7

29°-5

4o°.6

60°. i

79°-8

100°. I

3°

2580

2745

2880

3100

_

_

60

2400

2590

2735

2995

3230

3460

IOO

2275

2480

2640

2935

3180

3435

140

22OO

2480

2055

2940

3190

3460

180

2360

2560

2730

3OI5

3260

3525

220

2510

2690

2840

3I25

3300

3625

TABLE 87. - Ethylene.

Pressure in

Relative values of pv at —

metres of

mercury.

16^.3

20°.3

30°. I

4o°.o

So°.o

6o°.o

70°. o

79°-9

89°-9

I00°.0

3°

1950

2055

2220

2410

2580

2715

2865

2970

3090

3225

60

810

900

II9O

1535

1875

2IOO

2310

25OO

2680

2860

90

1065

i"5

H95

!325

1510

I7IO

1930

2l6o

2375

2565

1 2O

I325

1370

1440

1540

1660

1780

1950

2115

2305

2470

IS0

1590

1625

I60X>

1785

1880

1990

2125

2250

2390

2540

180

1855

1890

1945

2035

2130

2225

2340

245°

256S

2700

2IO

21 IO

2145

2200

2285

2375

2470

2570

2680

2790

2910

240

2360

2395

245°

2540

2625

272O

2810

2910

3015

3I25

270

26lO

2640

27IO

2790

2875

2965

3060

3150

3240

3345

300

2860

2890

2960

3040

3I25

3215

3300

3380

3470

356o

320

3035

3065

3'25

3200

3285

3375

3470

3545

3625

37io

* Tables 84-89 are from the experiments of Aciagat; " Ann. de chim. et de phys.," 1881, or " Wied. Bieb.," 1881,
p. 418.

SMITHSONIAN TABLES.

79

TABLES 88-90.

COMPRESSIBILITY OF CASES.

TABLE 88. — Carbon Dioxide.

Relative values of pv at —

Pressure in

metres of

mercury.

l8°.2

3S°-i

40^.2

5o°.o

6o°.o

70°.o

8o°.o

90°.o

100°.0

3°

liquid

2360

2460

2590

2730

2870

2995

31 20

3225

5°

-

1725

1900

2145

2330

2525

2685

2845

2980

80

625

750

8:5

I2OO

1650

*975

2225

2440

2635

110

825

93°

980

IO9O

1275

J55°

1845

21OS

2325

140

1 020

1 1 20

"75

I250

1360

1525

17*5

'95°

2160

170

I2IO

1310

1360

143°

1520

1645

1780

!975

2I35

2OO

1405

1500

155°

1615

1705

1810

193°

2075

2215

230

1590

1690

1730

I8OO

1890

1990

2090

22IO

2340

260

1770

1870

1920

1985

2070

2166

2265

2375

2490

290

1950

2060

2IOO

2I7O

2260

2340

2440

255°

2655

320

2135

2240

2280

2360

2440

2525

2620

2725

2830

TABLE 89. -Carbon Dioxide.*

Value of the ratio pv lp\v\ at —

Pressure in

atmospheres.

5o°

100°

200°

2S0°

0.725

1.0037

1. 002 1

I.OOO9

1.0003

1.440

1.0075

1 .0048

I.OO25

I.OOI5

2.850

1.1045

1.0087

I.OO4O

I.OO2O

TABLE 90. — Air, Oxygen, and Carbon Monoxide at Temperature between 18° and 22 .

The pressure p is in metres of mercury ; the product pv is simply relative.

Air.

Oxygen.

Carbon monoxide.

P

pv

/

PV

P

PV

2407

26968

24.07

26843

24.06

27147

34-9°

26908

34-89

26614

34-91

27102

45-24

26791

-

-

45-25

27007

55-3°

26789

55-50

26185

55-52

27025

64.00

26778

64.07

26050

64.00

27060

72.16

26792

72.15

25858

72.17

27071

84.22

26840

84.19

25745

84.21

27158

101.47

27041

101.46

25639

101.48

24420

1 33-89

27608

133-88

25671

I33-90

28092

177.60

28540

177-58

25891

177.61

29217

214.54

29585

214.52

26536

214.54

30467

250.18

30572

-

-

250.18

31722

304.04

32488

303-03

28756

304.05

339'9

* Similar experiments made on air showed the ratio pv t
\ Amagat, " Compte Rendu," 1879.

SMITHSONIAN TABLES.

80

to be practically constant.

TABLES 91 , 92.

RELATION BETWEEN PRESSURE, TEMPERATURE AND
VOLUME OF SULPHUR DIOXIDE AND AMMONIA.*

TABLE 91. — Sulphur Dioxide.

Original volume 100000 under one atmosphere of pressure and the temperature of the experi-
ments as indicated at the top of the different columns.

c
£8

Corresponding Volume for Ex-
periments at Temperature —

Pressure in Atmospheres for
Experiments at Temperature —

£

58°.o

99°-6

l83°2

58°.o

99°.6

l83°.2

10

8560

9440

_

12

6360

7800

-

IOOOO

-

9.60

-

H

16
18

4040

6420
53'0
4405

-

9000
8000

9.60
10.40

Jo-35
1185

_

20

-

4030

-

7000

"•55

i3-05

-

24
28

:

3345
2780

3180

6000

12.30

14.70

-

32

-

2305

2640

5000

13-15

16.70

—

36

-

2260

4000

14.00

20.15

-

40

5°

:

H5°

2040
1640

3500

14.40

23.00

-

60

-

-

1375

3000

-

26.40

29.10

70

-

-

1130

2500

-

30-15

33-25

80
90

:

I

93°

790

2OOO

-

35-20

40.95

IOO

-

-

680

1500

-

39.60

55-2°

1 20

-

-

545

IOOO

-

-

76.00

140
160

-

-

43°
325

500

—

—

117.20

TABLE 92. — Ammonia.

Original volume 100000 under one atmosphere of pressure and the temperature of the experiments as
indicated at the top of the different columns.

.5

£ o

Corresponding Volume for Ex-
periments at Temperature —

Pressure in Atmospheres for Experiments
at Temperature —

£

46°.6

99^.6

i83°.6

3°°.2

46°.6

99°-6

i83°.o

10

9500

_

_

IOOOO

8.85

9.50

_

12.5

15
20

7245
5880

7635
6305
4645

4875

9000
8000

9.60
IO.4O

10.45
11.50

12.00

—

25

-

3560

3835

7000

II.O5

13.00

13.60

-

3°

;

2875

3185

6000

II.80

14-75

15-55

-

35
40

45

-

2440
2080

1795

2680

2345
2035

5000
4000

12.00

1 6.60

18.35

1 8.60
22.70

19.50

24.00

5°

-

1490

1775

3500

—

18.30

25.40

27.20

55

-

1250

'590

3000

-

-

29.20

3'-5°

60

—

975

1450

2500

-

-

34-25

37-35

"0

80

1245
1125

2OOO

-

-

41-45

45-5°

90

-

-

1035

1500

-

-

49-70

58.00

IOO

950

IOOO

59-65

93.60

^. * From the experiments of Roth, " Wied. Ann." vol. n, 1880.

SMITHSONIAN TABLES.

81

TABLE 93.

COMPRESSIBILITY AND BULK MODULI OF LIQUIDS.

Liquid.

Temp.

\*>*

Compression
per unit vol-
ume peratmo.
X 10".

Pressure or
range of pres-
sure in at-
mospheres.

Authority.

Calcu ated values of
bulk modulus in —

Grammes
per sq. cm.

Pounds
per sq. in.

Acetone ....

14

no

8-7-35-4

Amagat ....

94XI05

1.34 Xio5

Benzene ....

16

90

8.12-37.2

" ....

115 ||

1.64 "

' ....

15-4

87.I

1-4

Pagliani & Palazzo

1.69 «

' ....

50.1

III

1-4

"

93 ;;

1.32 "

Carbon bisulphide

0

78

—

Colladon & Sturm

1.89 "

i 11

15

62.6

—

Quincke ....

1*65 «

2-35 '

• 11

15.6

87.2

8-35

Amagat ....

119 "

1.69 '

' "

IOO

174

8-35

" ....

59 "(

1.84 '

Chloroform . . .

8-5

62.5

1.267

Grassi

2.15 '

9.2

62.6

4.247

165 "

2.35 '

Ether

r
12

64.8

168

T" TV
1.309

8-10

u

"j

'I9

61

2.26 '
0.87 "

Amagat . .

QQ

rrr

•* o^

18.6 "

0.26 "

u

00

Jjj
521

8.6- id 5

u

19.8 "

0.28 "

u

61

0 j
IOO

8.57-22.l9

it

14.4 "

(f

*J

6l

8.t;7 — 74.77

it

OT-'T-
1<\.1 "

0.50 '

11

*j

25.4

IQO

J/ OT" J J
8.46-74.22

u

JJ J

O 77 *

Ethyl alcohol . .

•** J'T-
10

3f**

94-5

^^ tr^/ J*T*"*^

1-2

Colladon & Sturm

109 "

w./ /

U H

12

71 1

T A pfa

Tait

I4O "

2.OO '

" '. '.

/ j'j
101

8.5-37.12

Amagat ....

i ^^.i
I O2 "

i-45 '

" " . .

28

86

I 5O-2OO

Barus ....

120

1.71

K u

28

81

I 5O-400

" ....

I27

1.81 '

« u

65

no

I5O-2OO

" ....

94

i-34

it it

65

IOO

I 5O-4OO

' ....

103

1.47

" " . .

IOO

168

150-200

' ....

61

0.87 '

" " . .

IOO

132

I5O-4OO

' ....

78

i. it '

" " . .

185

320

I5O-2OO

' . . . '.

32

0.46 '

" " . .

185

274

I5O-3OO

' ....

38

o-54 '

" " . .

185

245

I5O-4OO

" ....

42

0.60

" " . .

310

4200

150-200

(i

2-5

0.036 '

" " . .

310

2 2OO

150-300

" ....

4-7

0.067 '

" " . .

310

1530

I5O-4OO

" ....

6.7

0.095 '

Ethyl chloride . .

12.8

156

8.53-I3-9

Amagat ....

66.3

0.94

" " . .

12.8

I5l

8.53-36.45

" ....

68.5

0.97

" " . .

61.5

256

12.65-34.36

it

40-3

0.57

" " . .

99

510

12.79-19.63

" ....

20.3

0.29

u 11

99

495

12.79-34.47

" ....

20.9

0.30 '

Glycerine . . .

Quincke ....

411.2

5-85 '

Mercury ....

o

1-38

1-30

Colladon & Sturm

3058.0

43-5

" ....

o

3-92

Amagat ....

2629.0,

37-4 '

Methyl alcohol .

11. C.

I.OI2

Grassi . .

1 14.5

i. 61 '

J-j
11-5

91.1

7.513

1 11. i

"j
: 1.61

" " '. '.

J j
IOO

221

8-68-37.32

Amagat . . • . .

* ^O' *

046.3

. 0.66 '

Nitric acid . . .

20.3

338.5

'-32

Colladon & Sturm

030.2

0.43

Oils : Almond . .

17

55-19

Quincke ....

i§7-7

2.67

• Olive . . .

20.5

63.3-

" ....

163.0

2.32

Paraffine

14.84

62.69

De Metz ....

164.5

2.34 '

Petroleum .

16.5

69.58

Martini ....

148.3

2.1 1

Rock . . .

19.4

74^8

Quincke ....

138.4

1-97 '

Rape seed .

20.3

59-61

" . . • . . .

174-3

2.48 '

Turpentine .

19.7

79.14

it

130-7

1.86 •'

Sulphur dioxide .

o

302.5

1-16

Colladon & Sturm

0344

0-49

Toluene ....

IO

79

—

De Heen. . .- *]

I30-7

1.86

Xylene ....

10

73-8

140.0

1.99 «

SMITHSONIAN TABLES.

82

TABLE 93.

COMPRESSIBILITY AND BULK MODULI OF LIQUIDS.

^ —

c , g

£ 8

Calculated values of

•If-

o £.5

bulk modulus in —

Liquid.

£•£ v

3 ° c m

Authority.

ss 5"o

& M'U "

Grammes

Pounds

u*lx

«£il It

per sq. cm.

per sq. in.

Water sea

i •>

44*

I

Tait

274.8 X IO5

7.14 X IO5

12

47*

I

22O.O "

< (i

0

49.65

1-24

Colladon & Sturm .

208.0 "

2.96 "

« «

176

4^ o

Amagat

241. 1 "

"I A'i "

'

O

5°-3

i-5

Pagliani & Vincentini

206.0 '

2-93 "

' "

10

47.0

'-5

"

22O.O "

3-13 '

' '•

20

44-5

-5

"

232.0 "

3-3° '

' "

3°

42.5

-5

"

243.2 '

3.46 "

< K

40

40.9

-5

"

253-1

3.60 «

' "

5°

39-7

-5

a

260.1

3-70 '

< "

60

38-9

-5

it

265.0 "

3-77 '

' "

70

39-o

-5

u

264.3 "

3.76 "

' "

80

39-6

«

260.8 "

3.71

1 "

90

40.2

-5

"

257-3 "

3.66 "

IOO

41.0

-5

252.4 '

3-59 "

TABLE 94.

COMPRESSIBILITY AND BULK MODULI OF SOLIDS.

Solid.

Compression
per unit vol-
ume per atmo.
X io«.

Authority.

Calculated values of
bulk modulus in —

Grammes
per sq. cm.

Pounds
per sq. in.

Crystals : Barite

1-93
0.747
1. 2O
I.I4
2.67
4.2t
7-45t
0.61
0.113

i. 02
2.76
0.68
2.2-2.9

Voigt . .

Amagat .
Buchanan
Amagat .

535 X io«
1384 "
860 "
906 "

387 "
246 '

1694 "
9140 "
1090 '
1 202 "

IOI2 "

374 "
1518 "
405 "

7.61 X i o6

19.68 "
12.24 "
12.89 "
5-5° "

3-5° '
i-97 '
24.11
130.10 "
15.48 "
17.10 '
14.41

21.61 "
5.76 «

Beryl

Fluorspar

Pyrites

Quartz

Rock salt . ....

Sylvine

Topaz

Tourmaline
Brass

Copper

Delta metal

Lead

Steel

Glass

* Tait finds for fresh water the value .0072 (i —0.034 />) and for sea water .00666 (i — 0.034/0 where/ is the pres-
sure in tons per square inch. The range of variation of p was from i to 3 tons.

t Rbntgen and Schneider by piezometric experiments obtained 5.0 X io~ « for rock salt and 5.6 X io~ * for sylvine
(Wied. Ann., vol. 31).

SMITHSONIAN TABLES.

TABLE 95.

DENSITY OR MASS IN GRAMMES PER CUBIC CENTIMETRE AND POUNDS
PER CUBIC FOOT OF VARIOUS SOLIDS.*

Substance.

Grammes
per cubic
centimetre.

Pounds
per cubic
foot.

Substance.

Grammes
per cubic
centimetre.

Pounds
per cubic
foot.

Agate . . . »>

2.5-2.7

156-168

Gas carbon .

1.88

119

Alabaster :

Glass :

Carbonate

2.69-2.78

168-173

Common .

2.4-2.8

i S0-' 75

Sulphate .

2.26-2.32

141-145

Flint

2.9-4.5

180-280

Alum, potash . ..•

1-7

1 06

Glauber's salt

1.4-1.5

87-93

Amber . . .[

1.06-1.11

66-69

Glue ....

1.27

80

Anthracite . . • • .1

1.4-1.8

87-112

Gneiss . " .

2.4-2.7

150-168

Apatite . . .:

3.16-3.22

197-201

Granite . ... ..

2-5-3-0

156-187

Aragonite . . . .'

3-o

I87

Graphite . * 'Z

1.9-2.3

120-140

Arsenic . ' . .

5-7-5-72

356-358

Gravel . , .

94-112

Asbestos . . .;

2.O-2.8

I25-i/5

Gray copper ore

4-4-5-4

275-335

Asphaltum . . .•_

I.I-I.2

69-75

Green stone

2.9-3.0

180-185

Barite . . / . J

4-5

281

Gum arable . , .

1.3-1.4

80-85

Basalt

2.7-3.1

168-193

Gunpowder :

Beeswax . . .

0.96-0.97

60-6 1

Loose

0.9

56

Bole . . . ..

2.2-2.5

137-156

Tamped . . .

1-75

109

Bone ....

1.7-2.0

106-125

Gypsum, burnt . .

1.81

!'3

Boracite . . .

2.9-3.0

181-187

Hornblende . ..

3-o

187

Borax . . ...

i. 7-1 .8

106-112

Ice . ,-••/.*

0.88-0.91

55-57

Borax glass .

2.6

162

Iodine . .

4-95

309

Boron

2.68-2.69

167-168

Ivory ... ..

1.83-1.92

114-120

Brick . .

2.O— 2.2

125-137

Kaolin . . J

2.2

J37

Butter ....

0.86-0.87

53-54

Lava :

Calamine .

4-1-4-5

255-280

Basaltic .

2.8-3.0

I75-18S

Calcspar .

2.6-2.8

162-175

Trachytic

2.O-2.7

125-168

Carbon.

Lead acetate .

2.4

J5o

See Graphite, etc.

Leather:

Caoutchouc

0.92-0.99

57-62

Dry .. . -,

0.86

54

Celestine

3-9

243

Greased .

i. 02

64

Cement :

Lime :

Pulverized loose

1.15-1.7

72-105

Mortar

1.65-1.78

103-1 i i

Pressed .

1.85

H5

Slaked

1.3-1.4

81-87

Set .
Cetin ....

2.7-3.0
0.88-0.94

168-187
55-59

Lime . . . - ..
Limestone . . .

2.3-3.2
2.46-2.86

144-200
154-178

Chalk . . ...

i .9-2.8

118-175

Litharge :

Charcoal :

Artificial .

9-3-9-4

580-585

Oak

o-57

35

Natural .

7.8-8.0

489-492

Pine

0.28-0.44

!7-5-27-5

Magnesia .

3-2

200

Chrome yellow .

6.00

374

Magnesite . .

3-°

I87

Cinnabar

8.12

5°7

Magnetite . . .

4.9-5.2

306-324

Clay ....

1.8-2.6

122-162

Malachite . . ..3

3-7-4-1

231-256

Clayslate

2.8-2.9

175-180

Manganese :

Coal, soft .

1.2-1.5

75-94

Red ore .

3-46

216

Cobaltite

6-4-7-3

400-455

Black ore . - f*

3-9-4-1

243-256

Cocoa butter
Coke ....

0.89-0.91
1.0-1.7

56-57
62-105

Marble . . "
Marl . . : .

2.5-2.8
1.6-2.5

157-177

100-156

Copal ....

1.04-1.14

65-71

Masonry

1.85-2.3

116-144

Corundum . . <. .

3.9-4.0

245-250

Meerschaum

.99-1.28

61.8-79.9

Diamond

3-5-3-6

220-225

Melaphyre .

2.6

162

Anthracitic

1.66

104

Mica ....

2.6-3.2

165-200

Carbonado

3-01-3-25

188-203

Mortar

1.75

109

Diorite . . . ;

2.8-3.1

I75~I93

Mud ....

1.6

102

Dolomite . . .

3.8-2.9

175-181

Nitroglycerine

1.6

99

Earth, dry .

1.6-1.9

100-120

Ochre ....

3-5

218

Ebonite . . .'•

i-'S

72

Opal ..*<.!

2.2

137

Emery . . »,

4.0

250

Orpiment . . . •

3-4-3-5

212-218

Epsom salts :

Paper ....

0.7-1.15

44-72

Crystalline

1.7-1.8

I06-II2

Paraffin

0.87-0.91

54-57

Anhydrous

2.6

162

Peat ....

0.84

52

Feldspar ... .

2.53-2.58

158-161

Phosphorus, white

1.82

114

Flint . . .

2.63

164

Pitch ....

1.07

67

Fluor spar .

3.14-3.18

196-198

Porcelain

2-3-2-5

I43~r 56

Gabronite . .. .

2.9-3.0

I8I-I87

Porphyry .

2.6-2.9

162-181

Gamboge ...

1.2

75

Potash

2.26

141

Galena

7-3-7-6

460-470 '

Pyrites

4-9-5-2

306-324

Garnet

3-6-3-8

230-335 ;

Pyrolusite .

3-7-4-6

231-287

SMITHSONIAN TABLES.

* For metals, see Table 97.
84

DENSITY OF VARIOUS SOLIDS.

TABLE 95.

Substance.

Giammes
per cubic
centimetre.

Pounds
per cubic
foot.

Substance.

Grammes
per cubic
centimetre.

Pounds
per cubic
foot.

Pumice stone

0.37-0.9

23-56

Soapstone, Steatite

2.6-2.8

162-175

Quartz

2.65

165

Soda :

Resin ....

1.07

67

Roasted .

2-5

156

Rock crystal

2.6

162

Crystalline

i-45

90

Rock salt

2.28-2.41

142-150

Spathic iron ore

3-7-3-9

231-243

Sal ammoniac

1.5-1 6

94-100

Starch

x-53

95

Saltpetre

1.95-2.08

122-130

Stibnite

4.6-4.7

287-293

Sand :

Strontianite

3-7

Dry ....

1.40-1.65

87-103

Syenite

2.6-2.8

162

Damp . . /.

1.90-2.05

119-128

Sugar ....

1.61

IOO

Sandstone .

2.2-2.5

1 37-i S6

Talc .

2-7

168

Selenium

4.2-4.8

262-300

Tallow-

.91 -.97

570-605

Serpentine .

2.43-2.66

152-166

Tellurium .

6.38-6.42

398-401

Shale . . .

2.6

162

Tile ....

1.4-2.3

87-143

Silicon

2.0-2.5

125-156

Tinstone

6.4-7.0

399-437

Siliceous earth .

2.66

166

Topaz

3-5-3-6

219-223

Slag, furnace

2-5-3-0

156-187

Tourmaline

2.94-3.24

183-202

Slate ....

2.6-2.7

162-168

Trachyte

2.7-2.8

168-175

Snow, loose

0.125

7-8

Trap ....

2.6-2.7

162-170

TABLE 96.

DENSITY OR MASS IN GRAMMES PER CUBIC CENTIMETRE AND POUNDS
PER CUBIC FOOT OF VARIOUS ALLOYS (BRASSES AND BRONZES).

Alloy.

Grammes
per cubic
centimetre.

Pounds
per cubic
foot.

Brasses : Yellow, 7oCti -)- 3oZn, cast

8.44

527

" " rolled

8.56

534

drawn .....

8.70

542

Red, goCu -f- roZn

8.60

536

White, 5oCu + 5oZn

8.20

5"

Bronzes: goCu + loSn

8.78

548

8sCu + isSn

8.89

555

8oCu -j- 2oSn

8.74

545

75Cu -j- 25Sn

8.83

551

German Silver: Chinese, 26-3Cu -(- 36.6Zn + 36.8 Ni .

8.30

5'S

Berlin (i) 52Cu -f- 26Zn -f 22Ni ....

8.45

527

" " " (2) 59Cu -j- 3oZn -j- uNi .

8.34

520

" (3) 63Cu + 30211 + 6Ni ....

8.30

5i8

" " Nickelin

8.77

547

Lead and Tin: 87_5Pb -f- i2-5Sn

1 0.60

661

' " 84?b + i6Sn

iQ-33

644

' " 77.8Pb + 22.2Sn

10.05

627

' « 63.7Pb + 36-3«n

9-43

588

46.7Pb+ 53-3Sn

8-73

545

" 30-5Pb + 69.5811

8.24

5'4

Bismuth, Lead, and Tin : ^Bi + 4oPb -f 7Cd ....

10.56

659

Wood's Metal: 5oBi + 25Pb + i2-5Cd + 12.5811 . . .

9.70

605

Cadmium and Tin : 32Cd-f- 68Sn .......

7.70

480

Gold and Copper : g8Au -(- 2Cu

18.84

1176

' ' " g6Au + 4Cu

18.36

"45

' ' " 94 Au -j- 6Cu

17-95

1 1 20

92Au -f 8Cu

17.52

1093

' ' " goAu -4- ioCu

17.16

1071

88Au -f i2Cu

1 6.8 1

1049

' ' " 86Au -j- i4Cu

16.47

1027

Aluminium and Copper : loAl + ox»Cu

7.69

480

5A1 + 95Cu

8-37

522

3A1 + 97Cu *

8.69-

542

Aluminium and Zinc : grAl -(- gZn ......

2.80

'75,

Platinum and Iridium : goPt + iolr

21.62

1348

85?! + islr ;''

21.62

1348

66.67 Pt + 33-33 lr . . . - . '••'

21.87

i364

5Pt + 95lr

22.38 ,

1396

SMITHSONIAN TABLES.

TABLE 97.

DENSITY OR MASS IN GRAMMES PER CUBIC CENTIMETRE AND
POUNDS PER CUBIC FOOT OF THE METALS.*

When the value is taken from a particular authority that authority is given, but in most cases the extremes or average

from a number of authorities are given.

r

Metal.

Physical state.

Grammes per
cubic centi-
metre.

Pounds per
cubic foot.

d

d
H

Authority.

Aluminium . . .

Cast . . .

2.56-2.58

160-161

" ...

Wrought . .

2.65-2.80

165-175

Antimony . . .

Solid . . .

6.70-6.72

418-419

" ...

Amorphous .

About 6.22

388

Barium ....

—

3.75-4.00

234-250

Solid . . .

Q.7O— O OO

605-618

sp/w3fty

9-673

604

271

) Vincentini and

" ....

Liquid . . .

10.004

624

271

) Omodei.

Cadmium . . .

Cast . . .

8.54-8.57

533-535

" ....

Wrought . .

8.670

54i

" ....

Solid . . .

8.366

522

318

I Vincentini and

" ....

Liquid . . .

7.989

498

318

) Omodei.

Caesium ....

—

1.88-1.90

117

Calcium ....

—

1.580

98.6

Cerium ....

—

6.62-6.72

475-482

Chromium . . .

—

6.52-6.73

407-420

Cobalt ....

Cast . .

8.50-8.70

530-542

" ....

Wrought . .

9.100

563

Columbium . .

Liquid . . .

7.10-7.40

443-462

Copper ....

Cast . . .

8.80-8.95

549-5S8

" ....

Wrought . .

8.85-8.95

552-558

" ....

Liquid . . .

8.217

S'3

Roberts & Wrightson.

Didymium . . .

—

6.540

408

Gallium ....

—

5-930

3?o

24

Lecoq de Boisbaudran.

Germanium . .

—

5.460

34i

2O

Winkler.

Glucinium . . .

—

1.86-2.06

116-127

Gold

Cast . . .

19.26-19.34

1202-1207

" ....'.

Wrought . .

I9-33~I9-34

1207

Indium ....

—

7.27-7.42

454-463

Iridium ....

—

21.78-22.42

i 359-1 399

Iron

Gray cast .

7.O?-7.I -J

4 ^Q— 44 ^

White cast

/ O / J

7. C8-7.71

Toy *t*Tj
477-482

11

Wrought .

/ .J / / J

7.80—7.00

t/ j *f-'*-
48^—40"?

it

Liquid .

j >*J^f 1 .*~J^

6.880

*T^J T^J

42Q

Roberts & Wrightson.

Lanthanum

6.05-6.16

^ S

377-384

Hildebrand & Norton.

Lead

Cast

1 1 . "?4O

708

2/1

Reich.

Wrought . .

o^

11.360

f ***

7OQ

^•T-

24.

ii

Solid . . .

1 1.005

/ s

686

T"

•?2t;

I Vincentini and

it

Liquid .

10.64^

664

J^J

32C

) Omodei.

Lithium ....

V-T J

0.590

39

-J

Magnesium . .

—

1.69-1.75

105-109

Manganese . . .

—

6.86-8.03

428-501

" ...

—

Av. abt. 7.4

462

Mercury ....

—

J3-596

848

Molybdenum .

—

8.40-8.60

524-536

Nickel ....

—

8.30-8.90

S'7-555

Osmium ....

—

21.40-22.40

1335-1398

Palladium .

—

1 1. 00-12.00

686-749

Platinum

—

2I.2O-2I.7O

i322-i354

Potassium . . .

Solid . . .

0.86-0.88

54-55

" ...

Solid . . .

0.8510

53-7

62.1

\ Vincentini and

Rhodium . . .

Liquid .

0.8298

II.OO-I2.IO

686^755

62.1

J Omodei.

Ruthenium . . .

—

II.OO-II.40

686-711

Silver ....

Cast. . . .

10.40-10.50

649-655

'* ....

Wrought . .

•0.55-10.57

658-659

Liquid . . .

9.500

593

Roberts & Wrightson.

* This table has been to a large extent compiled from Clark's " Constants of Nature," and Landolt & Bornstein's
" Phys. Chem. Tab."

t When the temperature is not given, ordinary atmospheric temperature is to be understood.

SMITHSONIAN TABLES.

86

TABLE 97.

DENSITY OR MASS IN GRAMMES PER CUBIC CENTIMETRE AND
POUNDS PER CUBIC FOOT OF THE METALS.

Metal.

Physical state.

Grammes per
cubic centi-
metre.

Pounds per
cubic foot.

f
U
n.

H

Authority.

Sodium ....

«

Strontium . . .
Thallium . . .
Tin

Solid . . .
Liquid . . .
At boiling pt.

Cast. . . .

0.97-0.99
0.9519
0.9287
0.7414
2.50-2.58
II.8-II.9
7.2QO

605-618

59-4
58.0

46.3
156-161
736-742

4CC

97.6
97-6

) Vincentini and
) Omodei.
Ramsay.
Matthieson.

Matthieson.

«

Wrought .

7.7OO

4CC

„

Crystallized .

6.Q7—7.l8

AT. c-448

„

Solid . . .

7.1871;

4C4

226

) Vincentini and

(i

Liquid .

6.988

f.

4 TO

226

) Omodei.

Titanium t . • •
Thorium J . . .
Tungsten . . .
Uranium . . .
Zinc

Cast . . .

5-300
9.4-IO.I
I9.I2O
18.33-18.65
7.O4—7.l6

341

587-630

"93
1143-1163

470-447

Roscoe.

M

\Vrought .

7-IQO

440

M

Liquid .

6.480

404

Roberts & Wrightson.

Zirconium . . .

4.140

258

Froost.

TABLE 98.

MASS IN GRAMMES PER CUBIC CENTIMETRE AND IN POUNDS PER
CUBIC FOOT OF DIFFERENT KINDS OF WOOD.

The wood is supposed to be seasoned and of average dryness.

Wood.

Grammes
per cubic
centimetre.

Pounds
per cubic
foot.

Wood.

Grammes
per cubic
centimetre.

Pounds
per cubic
foot.

Alder ' .

0.4 •'-o 68

26-42

Greenheart

O.Q7— I.O4

c8-6i;

Annie .

0.66-0.84

4I-C2

Hazel

O.6o-O.8o

77—4Q

Ash

0.65—0.85

4O- C7

Hickory

O.6O-O.Q7

77- c8

Basswood. See Linden.

Iron-bark

I.O7

64

Beech . . . • i •

O.7O-O.QO

47— C.6

1 Laburnum

O.Q2

57

084

52

Lancewood

O.68— I.OO

42—62

Birch : .

O.CI-O.77

72-48

i Lignum vitae . . • .

I.I7—I.77

77-87

Box

O.QC— I.l6

CO— 72

Linden or Lime-tree .

0.72-0. CQ

20—^7

Bullet tree . . . '-.

1.05

yj~/<-
6c

Locust

0.67-0.71

A2— AA

Butternut
Cedar

0.38

O.4O-O. C7

24
70—71;

Mahogany, Honduras .
" Spanish .

0.56
0.85

35

C7

Cherry • .

O.7O-O.QO

47— Co

Maple

0.62—0.7 c

70-47

Cork

O.22-O.26

^j T*

14—16

Oak

0.60-0.90

-27— c6

Ebony

I.I I — 1-33

60-87

Pear-tree

0.61-0.73

78-4C

Elm

0.54—0.60

74—77

Plum-tree . .

0.66-0.78

41— 4Q

Fir or Pine, American

Poplar

0. 7 C— O. S

22—71

White

O 1 C— O CO

22—71

Satinwood

O QC

CO

Larch .

o 50—0 56

71—7?

o 40—0 60

24—77

Pitch . .
Red . .
Scotch

0.83-0.85
0.48-0.70

O.47— O. C7

52-S3
3°-44

27—77

Teak, Indian ....
'• African ....
Walnut

0.66-0.88
0.98
0.64—0.70

41-55

61

4O— 47

Spruce .

o 48—0 70

7O— 44

Water gum

I OO

^^T^J
62

O 77— O 60

27—77

Willow

o 40—0 60

24—77

* When the temperature is not given, ordinary atmospheric temperature is to be understood.

t The density of titanium is inferential, and actual determination a year or two ago gave a lower value.

t The lower value for thorium represents impure material.

SMITHSONIAN TABLES.

TABLE 99.

DENSITY OF LIQUIDS.

Density or mass in grammes per cubic centimetres and in pounds per cubic foot of various liquids.

Liquid.

Grammes per
cubic centimetre.

Pounds per
cubic foot.

Temp. C.

Acetone

0.792

49-4

0°

Alcohol, ethyl

0.791

49.4

0

" methyl .......

0.810

5°-5

o

" proof spirit

0.916

57-2

o

Anilin ........

1-035

64-5

o

Benzene ........

0.899

56.1

0

Bromine

3-187

199.0

0

Carbolic acid (crude)

0.950-0.965

59.2-60.2

15

Carbon disulphide ......

1.293

80.6

15

Chloroform

1.480

92-3

18

Ether . . . •'.••• • ' •

0.736

45-9

o

Glycerine

1.260-

78.6

o

Mercury

13-596

836.0

o

Naphtha (wood)

0.848-0.810

52-9-5o-5

o

Naphtha (petroleum ether)

0.665

4i-5

15

Oils: Amber

o.Soo

49.9

15

Anise-seed .......

0.996

61.1

16

Camphor

0.910

56.8

—

Castor

0.969

60.5

15

Cocoanut .......

0.925

57-7

15

Cotton seed »

0.926

60.2

16

Creosot .......

1.040-1.100

64.9-68.6

15

Lard . . .

0.920

57-4

15

Lavender . .' . . . .

0.877

54-7

16

Lemon .......

0.844

52-7

16

Linseed (boiled) . . . . . -'.

0.942

58.8

IS

Mineral (lubricating) . . . •. '<

0.900-0.925

56.2-57.7

20

Olive . . . . . . . • .

0.918

57-3

15

Palm ........

0.905

56-5

15

Pine ........

0.850-0.860

53.0-54.0

15

Poppy *..•••

0.924

57-7

—

Rapeseed (crude) .....

0.915

57-i

15

O.QI^

1:7.0

I c

Resin .......

**r J

0-955

3 «•
59-6

J

15

Train or Whale ......

0.918-0.925

57-3-57-7

15

Turpentine . ... . .

0.873-

54-2

16

Valerian . . . ".'''.. * .

0.965

60.2

16

Petroleum . . . .'•*". .

0.878

54-8

0

(light). . ....', .'

0.795-0.805

49.6-50.2

15

Pyrol igneous acid ......

0.800

49-9

o

Sea water ........

1.025

64.0

15

Soda lye . ... . .'

I.2IO

75-5

17

Water .........

I.OOO

62.4

4

SMITHSONIAN TABLES.

TABLE IOO

DENSITY OF CASES.

The following table gives the specific gravity of gases at o° C. and 76 centimetres pressure relative to air at o° and
76 centimetres pressure, together with their mass in grammes per cubic centimetre and in pounds per cubic foot.

GM.

Sp.'gr.

Grammes per
cubic centimetre.

Pounds per
cubic fooi.

Air . . . .. ' . . . . r-

1. 000

o.ooi 293

0.08071

Ammonia -. . . . \. »

o-597

0.000770

0.04807

Carbon dioxide . . . . • . •.

1.529

0.001974

0.12323

Carbon monoxide ........

0.967

O.OOI234

0.07704

Chlorine .

2.422

0.003133

0-19559

( from
Coal gas }
(to

0.340
0.450

O.OOO42I

0.000558

0.02628
0.03483

Cyanogen .

i. 806

0.002330

0.14546

Hydrofluoric acid

2.370

0.002937

0-I8335

1. 2 SO

o.ooi 61 6

0.10088

0.0696

0.000090

0.00562

Hydrogen sulphide . . .

I.I9I

0.001476

0.09214

O. CCQ

0.000727

0.04 <; T.8

Nitrogen . . . . . ...

0.972

0.001257

0.07847

Nitric oxide, NO .

1.039

0.001343

0.08384

1. 527

0.001970

0.12298

Oxygen .

1.105

0.001430

0.08927

Sulphur dioxide . . . . . . ~~

2.247

0.002785

0.17386

Steam at 100° C

0.469

0.000581

0.03627

SMITHSONIAN TABLES.

89

TABLE 1O1.

DENSITY OF AQUEOUS SOLUTIONS.*

The following table gives the density of solutions of various salts in water. The numbers give the weight in
grammes per cubic centimetre. For brevity the substance is indicated by formula only.

Substance.

Weight of the dissolved substance in 100 parts by weight of
the solution.

u

d

E

H

Authority.

5

10

15

20

25

3°

40

5°

60

K2O ....

1.047

1.098

I-I53

1.214

1.284

1-354

!-503

1.659

1.809

IS-

Schiff.

KOH . . .

1.040

1.082

I.O27

1.076

1.229

1.286

I.4IO

L538

1.666

"

Na2O . . .

1-073

1.144

1.218

1.284

!-354

1.421

L557

1.689

1.829

J5-

"

NaOH . . .

1.058

1.114

I.l69

1.224

1.279

1.331

1.436

!-539

1.642

'5-

"

NH3 ....

0.978

0.949

0.940

0.924

0.909

0.896

-

16.

Carius.

NH4C1 . . .

I.OI5

1.030

1.044

1.058

1.072

_

_

_

_

I5.

Gerlach.

KC1 ....

I O7I

1.065

I OQQ

1. 175

I C

t.

NaCl. . . .

T 035

I.O72

i. no

- J J

1.191

1 _>•

f C

H

LiCl ....

I.O29

l.\Jj £.
1.057

1.085

1.116

1.147

1.181

1.255

_

_

1 j-

15-

«

CaCl2 . . .

1.041

I. 086

1.132

1.181

1.232

1.286

1.402

-

-

"

CaCl2 + 6H2O

I.OI9

I.O4O

1. 06 1

1.083

1.105

1.128

1.176

1.225

1.276

18.

Schiff.

A1C13 . . .

I.O35

I.O72

I. Ill

1.153

1.196

1.241

1.340

-

-

!5-

Gerlach.

MgCl2 . . .

I.O4I

1.085

1.130

1.177

1.226

1.278

-

-

"

MgCl2+6H2O

I.OI4

I.O32

1.049

1.067

1.085

1.103

1.141

1-183

1.222

24.

Schiff.

ZnCl2 . . .

1.043

1.089

!-i35

1.184

1.236

1.289

1.417

1-563

1-737

'9-5

Kremers.

CdCl2 . . .

1.043

1.087

1.138

1.193

1.254

1-319

1.469

t.653

1.887

19-5

"

SrCl2. . . .

T O44

I.OQ2

1. 147

1.198

1.257

1. 721

_

__

—

I c.

Gerlach.

SrC)2 + 6H2O

I.O27

y

!-°53

i!o82

i. in

1.042

**O
I.I74

1.242

1.317

_

J
'5-

BaCl2 . . .

1.045

1.094

1.147

1.205

1.269

-

-

-

-

"

BaCl2-f-2H2O

1-035

1-075

1.119

1.166

1.217

1-273

-

-

-

21.

Schiff.

CuCl2 . . .

1.044

1.091

1.155

1. 221

1.291

1.360

1.527

_

_

!7-5

Franz.

NC12 ....

i 048

1.098

I.I 57

1.227

I 2QQ

__

__

tt

HgCl2 . . .

1.041

1.092

j/

tj

'_

-

_

_

-

20.

Mendelejeff.

Fe2Cl6 . . .

1.041

i. 086

1.130

I.I79

1.232

I.29O

1-413

r-545

1.668

'7-5

Hager.

PtCl4. . . .

T O46

I.OQ7

I.I 57

I.2I4

I 2o 5

1.362

i ^d.6

I'recht.

SnCl2+2H2O

1.032

y /
1.067

DO
I.IO4

I-I43

I.I85

1.229

1.329

1-444

1.580

15-

Gerlach.

SnCl4-r-5H2O

1.029

1.058

1.089

1. 122

I-I57

I-I93

1.274

1-365

1.467

15-

u

LiBr ....

!-°33

1.070

I. Ill

I-I54

I.2O2

1.252

1.366

1.498

-

19.5

Kremers.

KBr ....

1-035

1-073

I.II4

I-I57

1.205

1.254

1.364

-

19.5

"

NaBr . . .

1.038

1.078

I.I23

I.I72

1.224

1.279

1.408

1-563

-

195

"

MgBr2 . . .

1.041

1.085

I-I35

I.I89

1.245

1.308

1.449

1.623

_

19-5

»

ZnBr2 . . .

1.043

1.091

I.I94

I.2O2

1.263

1.328

1-473

1.648

1-873

"

CdBr2 . . .

1.041

1. 088

I-I39

I.I97

1.258

i-324

1.479

1.678

-

19-5

"

CaBr2 . . .
BaBr2 . . .

1.042
1.043

1.087
1.090

1-137
1.142

I.I92
1-199

2.250
I.26O

i-3'3
1.327

1.459
1.483

1.639
1.683

-

19.5
19-5

'

SrBr2 . . .

1.043

1.089

1.140

I.I98

I.26O

1-328

1.489

1.693

1-953

19-5

«

KI ....

i 076

1.076

1.118

1.164

1.2 1 6

1.269

1.732

1 0.5

t

Lil ....

1.036

1.077

1. 122

I.I70

1.222

1.278

1.412

!-573

1-775

*y j

19-5

'

Nal ....

i 078

1. 080

I.I26

I.I77

I 272

1.292

I .4^0

i. 808

IQ.5

<

ZnI2 . . .

1.043

1.089

1.138

I.I94

1-253

1.366

1.418

1.648

1.873

y j
19-5

'

CdI2 ....

1.042

1. 086

1.136

I.I92

I.25I

i-3i7

1-474

1.678

_

19-5

«

Mfflo

i 041

1. 086

I.I 77

I.IQ2

I 2 C'7

1.318

I A72

1.666

I Q I 7

IQ. t;

<*

CaI2 ....

T O42

1. 088

i'i J/

y
I.IQO

1.258

I.7IQ

'TV •

1.663

I.QOS

y j
10. C

u

SrI2 ....

1.043

1.089

I.I4O

y

1.198

I.26o

* o y
1.328

1.489

1.693

•y^-'

'•953

x j

19-5

"

BaI2 ....

T QA.1

1.089

I.I4I

I.IQQ

I "•( i "

i-33'

¥ AC\~i

1.702

1.968

IQ.5

**

NaClOs . . .

1-035

1. 068

1.106

yy

I.I88

1.233

1.329

y j
19-5

»

NaBrO3 . . .

1.039

I.oSl

1.127

1.176

1.229

1.287

-

-

19.5

(t

KNO3 . . .

1.031

1.064

1.099

1-135

-

-

-

-

15.

Gerlach.

NaNO3 . . .

1.031

1.065

I.IOI

1.140

I.lSo

1.222

1. 717

1.416

-

20. 2

Schiff.

AgNG-3 - - -

1.044

1.090

1.140

I.I95

1.255

1.322

1.479

1.675

1.918

15-

Kohlrausch.

' Compiled from two papers on the subject by Gerlach in the " Zeit. fiir Anal. Chim.," vols. 8 and 27.
SMITHSONIAN TABLES.

90

DENSITY OF AQUEOUS SOLUTIONS.

TABLE 101

Substance.

Weight of the dissolved substance in 100 parts by weight of
the solution.

CJ
d.

I

Authority.

5

10

15

20

25

30

4°

5°

60

NH4N03 . . .
ZnN03 . . . .
ZnNO3+6H2O .
Ca(NO3)2 • • •
Cu(N03)2 . . -
Sr(N03)2 . . .
Pb(N03)2 . . .
Cd(N03)2 . . .
Co(N03)2 . . .
Ni(N03)2 . , .

Fe2(N03)6 • • •
Mg(N03)2+6H20
Mn(N03)2+6H2O
K2CO3 ....

I.O2O
1.048

I-°37
1.044

r-Q39

1.043

1.052

1.045
1.045

1.039
1.018

1.025

1. 044

I.04I
I.O95
1.054

1-075
1.093

1.083
1.091
1.097
1.090
I.O9O

1.076
1.038
1.052
1.092
I.O72

1.038

!-o55
1.096

i -°53
1.104

1.050
1.039
1.064
1.064
1.057

1.045

1-033
i. 066

1.058
1.082

1.071
1.059
1-053

1.064
1.042

1.062
1.146

1.118

1-143

1.129

1-143

1.150

1-137
1-137
1.117

1. 060

1.079

1.141

I. IIO

1-057
1.084
1.150
1.081

I.M.I

I-07S
1.059
1.098
1.099
1.089

1. 066
1.051
I.IOI

1.090
1.127

1.108
1.092

1.145

I.IOO

1.066

1.085

I.2OI
I.II3
I.I62
1.203

I.I79
I.I99
1. 212
I.I92
I.I92

1.160

1.082
I.IOS
I.I92
I.I5O

1-077
I.II3
I.2O7
I. Ill
1. 221

r.ioi

1.081
1-134

i-'3S

1. 122
1. 088

i-°73

1-138

1. 122
I.I74

I.I26
I-I79

I-I37
1.089

1.107
1.263

1. 211
1.263

1.262
1.283
1.252
1.252

I.2IO
I.IO5
I.I38

1-245
I.I9I

1.098
I.I42
1.270
I.I4I
1.284

I.I29
I.IO2

I-I73
I.I74
1.156

1. 112
1.099

I-I54
1.225

I.I77
I.II4

1.131

1-325
1.178
1.260
1.328

I-332

1-355
1.318
1.318

1.261
1.129
1.169
1.300
1-233
1.118
1.170
i-336
i-i73

i-iSS
1.124
1.213
1.214
1.191

1.141
1.126

1.191
1.279

i. 220
1.140

1.178
1.456
1.250

I-367
I.47I

1-536
1.465
1.465

1-373
1.179

1-235
1.417
1.320

1.226
1.489
1.238

1.215

1-303
1.269

1.188
1-397

i-3i5
1.194

1.229

i-597
1.329
1.482

1-759

1.496
1.232
i-3°7
1-543
1-415

1.287

1.278

I-398
i-35i

1.287
1.426

1.282
1.604

1-657
1.386
1.511

1-443
1-454

17-
17-
14.
17-
17-
19.
17-
17-
17-
17-

X7-S

21

8
15
IS-

15-

IQ.

17.2

15

15-
15.

15-

20.5

17-5
17-5
15-

19.

19-5

19-5
15-
13

15-
14.

15-

4-
15-
iS-
IS-

17-5

!S-
14-
13-

'5-

17-5
r7-5
iS-
iS-
15-

Gerlach.
Franz.
Oudemans.
Gerlach.
Franz.

Kremers.
Gerlach.
Franz.

ci

Schiff.
Oudemans.
Gerlach.

«

Schiff.
Hager.
Schiff.
Gerlach.
u

Schiff.
Gerlach.
Schiff.

Franz.
u

Schiff.
«

Kremers.
Schiff.

Gerlach.
Schiff.

Brineau.
Schiff.
Kolb.
Gerlach.

u

Kolb.
Topsoe.

Kolb.

Stolba.
Hager.
Schiff.
Kolb.
Oudemans.

K2CO3 + 2H20 .
Na2CO3ioH2O .
(NH4)2S04 . .
Fe2(S04)3 . . .
FeS04 + 7.H2O .
MgSO4 ....

1-037

1.019

1.027

1.045

1.025
i.om

MgSO +7H2O .
Na2So4-(- ioH2O
CuS04+5H20 .
MnS04 + 4H20 .
ZnSO4+7H2O .

Fe2(SO)3+K2S04
+ 24H2O . . .
Cr2(SO)3-t-K2SO4
+ 24H20 . .
MgSO4 + K2SO4
+ 6H20 . . .
(NH4)2S04 +
FeSO4 + 6H2O
1 K2CrO4 ....

1.025
1.019
1.031
1.031
1.027

1.026
1.016
1.032
1.028

I.OT.Q

K2Cr2O7 . . .
Fe(Cy)6K4 . . .
Fe(Cy)6K3 . . .
Pb(C2H302)2 +
3H2O ....

1-035
1.028
1.025

I. Oil

2NaOH + As2O5
+ 24H2O . .

SO8

I.O2O

5

10

15

20

3°

4o

60

80

ICO

I. O4O

1.084
1.028
1.069
1.047
1.038

1.039

1.050

1-073
1.077
1.069

I.082
1.077
1.057
1.056
I.OI4

1.132

1.045

2.104
1.070

1.058

1. 060

1-075

1.114
1.118
1.106

1.127
1.119
i. 086
i. 088
i. 02 1

.179
.063
.141

.oq6
.079

.082
.101

.158
.165
•145

.174

.167

.119
.119
1.028

1.277

I.2I7
I.I5O
I.I23

I.I29
I.ISI

1-257
I.27I
1.223

1-273
I.27I

i88
1.184
1.041

1.389

1.294
1.207
1.170

1.178

i. 200
i-376
1.400

i-3°7

1-385
1.264
1.250
1.052

1.564
1.422

1-273
1.289

1.501

1.676
1.438
1.373

1.840
1.506

1-732

1-459
1-075

1.838

1.528
1-055

SO2

I.OIl

N2O5

I.O'?'?

C4HfiOB .

1. 02 1

C6H8O7 ....

1.018

Cane sugar . .
HC1

.019

.025

HBr . . . ; .

o-35
•O17

HI

H2S04 ...... .

H2SiFl6
P2O5

.032
.040

•O"??

P205 + 3H20. .
HNO

.027
.028

.007

SMITHSONIAN TABLES.

TABLE 1O2.

DENSITY OF WATER AT DIFFERENT TEMPERATURES BETWEEN Oc

AND 32° C.*

The following table gives the relative density of water containing air in solution, — the maximum density of water
free from air being taken as unity. The correction required to reduce to densities of water free from air are given
at the foot of the table. For all ordinary purposes the correction may be neglected. The temperatures are for the
hydrogen thermometer.

Temp. C.

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9

— 0

0.9998742

8678

8613

8547

8478

8408

8336

8263

8188

8111

+ o

0.9998742

8804

8864

8922

8979

9035

9088

9140

9191

9240

I

9287

9332

9376

9419

9460

9499

9536

9572

9607

9640

2

9671

9701

9729

9755

9780

9803

982*

9846

9864

9881

3

9897

9911

99^3

9934

9944

9952

9958

9963

9966

9968

4

9968

9966

9964

9959

9953

9946

9933

9927

9915

9901

5

0.9999886

9870

9852

9833

9812

9790

9766

9740

97H

9685

6

9656

9625

9592

955s

9522

9485

9446

9407

9365

9322

7

9278

9232

9185

9137

9087

9035

8982

8928

8873

88n;

8

8758

8697

8636

8J73

8509

8443

8376

8308

8238

8167

9

8095

8021

7946

7791

7712

7631

7549

7466

738i

10

0-9997295

7208

7119

7029

6937

6844

6750

6654

6558

6459

ii

6360

6259

6i57

6053

5949

5842

5735

5626

55'6

5405

12

5292

5178

5063

4947

4829

47 10

4590

4468

4345

4221

J3

4096

3969

3841

3712

358i

345°

33'7

3182

3°47

2910

14

2772

2633

2493

235'

2208

2064

1919

1772

1624

H75

15

0.9991325

"74

IO2I

0867

0712

°556

0399

0240

0080

9919

16

17

89757
8071

7594
7896

9429
7720

9264
7543

9097
7365

8929
7185

8760
7004

8589
6823

8418
6640

8245
6456

18

6270

6084

5897

5/o8

55i8

5328

5'36

4943

4749

4553

19

4357

4160

396l

3762

356i

3359

3*57

2953

2748

2542

20

21

0-9982335

0205

4126
9987

1917
9767

1707
9546

1496
9325

1283
9102

1070
8878

o855
8653

0640
8427

0423
8200

22

77972

7744

75'4

7283

7051

6818

6584

6340

6114

5877

23

5639

5400

5160

4920

4678

4435

4191

3947

3701

3455

24

3207

2959

2709

2459

2208

1956

1702 •

1448

"93

0937

25

0.9970681

0423

0164

9904

9644

93~S2

9120

8857

8592

81^7

26

68061

7794

7527

7258

6988

6718

6447

6i75

59° J

5628

27

5353

5°77

4801

4523

4245

3966

3686

3405

3I24

2841

28

2558

2274

1989

!7Q3

1416

1 129

0840

°55'

0261

9971

29

59679

9387

9094

8800

8505

8209

8913

7616

73i8

7019

30

0.9956720

6419

6118

5816

55H

5210

4906

4601

4296

3989

3i

3682

3374

3066

2756

2446

2135

1823

1511

1198

0884

If we put D't for the density of water containing air and D, for the density of water free
from air, we get the following corrections on the above table to reduce to pure water : —

t= 0123456789 10

io7(D,:-D't) = 25 27 29 31 32 33 33 34 34 33 32

t= 11 12 13 14 15 16 17 18 19 20 — 32

io7(D,-D't)= 31 29 27 25 22 19 16 12 4 negligible.

* This table is given by Marek in :l Wied. Ann.," vol. 44, p- 1721 l89'-
SMITHSONIAN TABLES.

92

TABLE 103.

VOLUME IN CUBIC CENTIMETRES AT VARIOUS TEMPERATURES OF A
CUBIC CENTIMETRE OF WATER AT THE TEMPERATURE OF MAXI-
MUM DENSITY.*

The water in this case is supposed to be free from air. The temperatures are by the hydrogen thermometer.

Temp. C.

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9

0°

1.000127

120

114

108

1 02

096

091

086

080

°75

I

070

066

061

057

052

048

044

040

037

033

2

030

027

024

02 1

019

017

014

012

OIO

009

3

007

006

004

003

002

002

OOI

OOI

ooo

ooo

4

ooo

OOO

OOI

OOI

OOI

OO2

003

OO4

005

007

5

1.000008

010

012

014

016

018

020

023

026

029

6

032

035

038

041

045

049

°53

057

06 1

065

7

069

074

079

084

089

094

099

I05

no

116

8

122

128

'34

141

M7

154

160

167

174

181

9

189

196

204

211

219

227

235

244

252

260

10

I.OOO269

278

287

296

305

314

324

334

343

353

n

363

373

383

394

405

415

426

437

448

459

12
13

471
591

482

494
616

629

l\l

529

655

668

566
695

578
709

14

722

736

750

765

779

794

809

823

838

853

15

1. 000868

884

899

9*4

930

945

961

977

993

609

16

1025

042

058

075

091

108

125

142

159

'7

194

211

229

247

265

283

301

3'9

338

356

18

374

393

412

43 i

45°

469

488

5°7

527

546

19

566

585

605

625

645

666

686

707

727

748

20

1.001768

Z§2

810

8ji

§52

874

§25

916

238

960

21

981

003

025

047"

069

092

114

137

159

TS2

22

2205

228

251

274

297

320

343

367

39 *

414

23

438

462

486

5ID

534

559

583

607

632

657

24

682

707

732

757

782

807

833

858

884

910

25

1.002935

961

987

014

040

666

002

"9

146

172

26

3199

226

253

280

307

335

362

389

417

445

27

472

500

55*-*

584

612

641

669

697

726

28

754

783

812

841

870

899

928

957

987

016

29

4045

075

105

'34

164

194

224

254

284

3'5

30

1.004345

375

406

436

467

498

529

560

59I

622

32

653
971

684
003

716
036

748
068

780

IOI

811
133

843

166

199

22Z
231

239
264

33

5297

330

363

396

43°

463

497

53°

564

597

34

631

665

699

733

767

801

835

870

904

939

35

[-005973

ooS

642

077

TTT

146

1ST

217

^52

m

* The table is quoted from Landolt and Bernstein's " Physikalische Chemie Tabellen," and depends on experi-
ments by Thiesen, Scheel, and Marek.

SMITHSONIAN TABLES.

93

TABLE 1O4.

DENSITY AND VOLUME OF WATER.*

The mass of one cubic centimetre at 4° C. is taken as unity.

Temp. C.

Density.

Volume.

Temp. C.

Density.

Volume.

— 10°

0.998145

1.001858

25°

0.99712

1.00289

— 9

8427

1575

26

687

3M

— 8

8685

i3!7

27

660

34i

— 7

8911

1089

28

633

368

— 6

9118

0883

29

605

396

— 5

0.999298

1.000702

30

0.99577

1.00425

— 4

9455 '

0545

31

547

455

— 3

9590

0410

32

5'7

486

— 2

9703

0297

33

485

5^8

I

9797

0203

34

452

551

0

0.999871

1.000129

35

0.99418

1.00586

I

9928

0072

36

383

621

2

9969

0031

37

347

657

3

9991

0009

38

310

694

4

i .000000

0000

39

273

732

5

0.999990

I.OOOOIO

40

0-99235

1.00770

6

9970

0030

4i

197

809

1

9933
9886

0067
0114

42
43

158
118

849
889

9

9824

0176

44

078

929

10

0.999747

1.000253

45

0.99037

i .0097 1

ii

9655

0345

46

8996

014

12

9549

0451

47

954

°57

13

9430

0570

48

910

IOI

H

9299

0701

49

865

148

15

0.999160

1.000841

50

0.98820

1.00195

16
i7

9002
8841

0999

1160

g

582
338

439
691

18
19

8654
8460

1348
1542

65

70

074
7794

964

256

20

0.998259

1.001744

75

0.97498

1.00566

21

8047

'957

80

194

887

22

7826

2177

85

6879

221

23

7601

2405

90

556

567

24

7367

2641

95

219

93 1

25

0.997120

1.002888

100

0.95865

1.00312

SMITHSONIAN TABLES.

* Rossetti, " Berl. Her." 1867.

94

TABLE 105.

DENSITY OF MERCURY.

Density or mass in grammes per cubic centimetre, and the volume in cubic centimetres of one gramme
of mercury. The density at o° is taken as 13.5956,* and the volume at temperature t is Vt =
V0(i+ .000181792*+ 175 X lo-'^-f 35116 X jo-1;i*3).t

Temp. C.

Mass in
grammes per
cub. cm.

Volume of
i gramme in
cub. cms.

Temp. C.

Mass in
grammes per
cub. cm.

Volume of
i gramme in
cub. cms.

— 10°

13.6203

0.0734195

30°

13.5218

0-0739544

— 9

6178

4329

3i

5'94

9678

— 8

6153

4463.

32

5169

9812

— 7

6129

4596

33

5M5

9945

— 6

6104

473°

34

5120

40079

— 5

13.6079

0.0734864

35

13.5096

0.0740213

— 4

^SS

4997

36

507!

0346

— 3

6030

5i3i

37

5047

0480

— 2

6005

5265

38

5022

0614

— I

598l

5398

39

4998

0748

0

'3- 5956

0-0735532

40

13-4974

0.0740882

I

2

593i
59°7

5666
5800

£

473i
4488

2221
356l

3

5882

5933

70

4246

4901

4

S8S7

So

4005

6243

5

I3-5833

0.0736201

90

I3-3764

0.0747586

6

5808

6334

100

3524

8931

7

5783

6468

no

3284

50276

8

5759

6602

1 20

3045

1624

9

5734

6736

130

2807

2974

10

I3-5709

0.0736869

140

13.2569

0-0754325

ii

5685

7003

150

233 !

5679

12

5660

7137

1 60

2094

7035

13

5635

7270

170

1858

8394

14

5611

7404

180

l62I

9755

15

I3-5586

0-0737538

190

I3-I385

0.0761 1 20

16

5562

7672

200

II5O

2486

17

5537

7805

2IO

0915

3854

18

55'3

7939

2 2O

0680

5230

19

5488

8073

230

0445

6607

20

I3-5463

0.0738207

240

13.0210

0.0767988

21

22

5439
54M

8340
8474

250
260

12.9976
9742

9372
70760

23

5390

8608

270

9508

1252

24

5365

8742

280

9274

3549

25

!3-534i

0.0738875

290

12.9041

0.0774950

26

53' 6

9009

300

8807

6355

27

5292

9M3

310

8573

7765

28

5267

0277

320

8340

9180

29

5243

9411

330

8l07

80600

30

13.5218

0-0739544

340

12.7873

0.0782025

350

7640

3455

360

7406

4891

* Marek, " Trav. et Mem. du Bur. Int. des Poids et Mes." 2,
,t Broch, 1. c.

SMITHSONIAN TABLES.

95

TABLE 1O6.

SPECIFIC GRAVITY OF AQUEOUS ETHYL ALCOHOL.

(a) The numbers here tabulated are the specific gravities at 60° F., in terms of water at the same tempera-
ture, of water containing the percentages by weight of alcohol of specific gravity .7938, with reference to the
same temperatures.*

til

" a *
fVoxi

0

1

2

3

4

5

6

7

8 9

Specific gravity at 15°. 56 C. in terms of water at the same temperature.

0

10
20

30
40

50

60
70
80
90

1. 0000
.9841
.9716
.9578
•9396

0.9184
.8956
.8721
.8483
.8228

.9981
.9828

•9703
.9560
•9376

.9160
.8932
.8696

•8459
.8199

•9965
.9815
.9691
•9544
•9356

•9135
.8908
.8672

.8434
.8172

•9947
.9802
.9678
.9528
•9335

•9"3

.8886
.8649
.8408
.8145

•993°
•97»9
.9665
.9511
•93 i 4

.9090
.8863
.8625
.8382
.8118

.9914
•9778
•9652
•9490
.9292

.9069

.8840
.8603

•8357
.8089

.9898
.9766
•9638
.9470
.9270

.9047
.8816
.8581

•833'
.8061

.9884

•9753
.9623

•9452
.9249

.9025
•8793
•8557
•8305
.8031

.9869 .9855
.9741 .9728
•9609 .9593
•9434 -9416
.9228 .9206

.9001 .8979
.8769 .8745
.8533 .8508
•8279 .8254
.8001 -7969

(b) The following are the values adopted by the " Kaiserlichen Normal-Aichungs Kommission." They are
based on Mendelejeff's formula, t and are for a cohol of specific gravity .79425, at 15-' C., in terms of water
at 15° C. ; temperatures measured by the hydrogen thermometer.

II

h^
fl*

""rt *
(X'o^1

0

1

2

3

4

5

6

7

8

9

Specific gravity at 15° C. in terms of water at the same temperature.

0

10
20

30
40

50

60
70
80
90

1. 00000

•98393
.97164

•95770

•93973

0.91865
89604
87265
84852
82304

.99812
.98262
.97040
.95608
•93773

.91644

•89373
.87028
.84606
.82036

.99630

•98135
.96913

•95443
•93570

.91421
.89141
.86789

•84358
.81763

•99454
.98010
.96783
•95273
•93365

.91197
.88909
.86550
.84108
.81488

.99284
.97888
.96650
.95099
•93157

.90972
.88676
.86310

•83857
.81207

.99120
•97768

•96513
.94920
.92947

.90746
.88443
.86070
.83604
•80923

•98963
.97648

•96373
•94738
•92734

.90519
.88208
.85828

•83349
.80634

.98812

•97528
.96228

•94552
.92519

.90292
.87974
.85586
.83091
•80339

.98667
.97408
.96080

•94363
.92303

.90063
•87738
.85342
.82832
.80040

.98528
.97287

•95927
.94169
.92088

.89834
.87502
.85098
.82569
•79735

(c) The following values have the same authority as the last ; the percentage of a cohol being given by volume
instead of by weight, and the temperature 15°. 56 C. on the mercury in Thuringian glass thermometer; the
specific gravity of the absolute alcohol being .79391.

Percentage
of alcohol
by volume.

0

1

2

3 4

5

6

7

8

9

Specific gravity at is°.s6 C. in terms of water at same temperature.

0

10

20

3°
40

50

60
70
80
90

I.OOOOO
.98657
.97608
.96541

•95'85

0-93445
•9 13 58
.89010

.86395
.83400

.99847
•98543
•97507
.96421
.95029

•9325°
•9" 34
.88762
.86116
.83065

.99699
.98432
.97406
.96298
.94868

•93052
.90907
.88511

•85833
.82721

•99555
.98324

•97304
.96172
.94704

.92850
.90678
.88257

•85547
•82365

.99415
.98218
.97201
.96043
•94536

.92646

.90447
.88000
.85256
.81997

.99279
.98114
.97097
.95910
•94364

•92439
.90214
.87740
.84961
.81616

.99147
.9801 1
.96991

•95773
.94188

.92229
.89978

•87477
.84660
.81217

.90019
.97909
•96883
•95632
.94008

.92015
.89740
.87211

•84355
.80800

•98895,
.97808
.96772

•95487
.93824

.91799
.89499

•86943
.84044

•80359

.98774
.97708
.96658

•9&£

•93636

.91580
.89256
.86670
.83726
.79891

* Fownes, " Phil. Trans. Roy. Soc." 1847.
t " Pogg. Ann." vol. 138, 1869.

SMITHSONIAN TABLES.

96

DENSITY OF AQUEOUS METHYL ALCOHOL.

TABLE 1O7.

Densities of aqueous methyl alcohol at o° and 15.56 C., water at 4° C. being taken as 100000. The numbers in the
columns a and b are the coefficients in the equation pt = p0 — at — 6C where pt is the density at temperature t.
This equation may be taken to hold between o° and 20" C.

Percent-

Density

Density

Percent-

Density

Density

age of

at

at

a

b

age of

at

at

a

CH40.

0° C.

,50.S6C.

CH4O.

o°C.

.5°-56 C.

0

i

99987
99806

99907
99729

— 6.0
— 5-4

0.705
•694

50

92873
92691

91855
91661

65.41
66.19

2

99631

99554

-4-8

.681

52

92507

91465

66-95

3

99462

99382

— 3-9

.670

53

92320

91267

67.68

4

99299

99214

•659

54

92130

9IO66

68.39

5

99M2

99048

— 2.2

0.648

55

91938

90863

69.07

6

98990

98893

1.2

•634

56

91742

90657

69.72

7

98843

98726

— 0.2

.621

57

91544

90450

70-35

8

98701

98569

+ 0-9

.609

58

9' 343

90239

70.96

9

98563

98414

2.1

•596

59

9U39

9OO26

71-54

1O

98429

98262

3-3

0.581

60

90917

89798

71.96

ii

98299

9811 1

4.8

•569

61

90706

89580

72-37

12

98171

97962

6.2

•552

62

90492

89358

72.91

13

98048

97814

7-8

•536

63

90276

89133

73-45

M

97926

97668

9-5

•5*9

64

90056

88905

73-98

15

97806

97523

II.O

0.500

65

89835

88676

74-51

16

97689

97379

12.5

.480

66

89611

88443

75-05

17

97573

97235

14-5

.461

67

89384

88208

75-57.

18

97459

97093

1 6.2

•440

68

89154

87970

76.10

19

97346

96950

,8.3

.420

69

88922

87714

76.62

20

97233

96808

2O.O

0.398

70

88687

87487

77-M

21

97120

96666

22.2

•373

71

88470

87262

77.66

22

97007

96524

24-3

•350

72

88237

87021

78.18

23

96894

96381

26.4

.321

73

88003

86779

78.69

24

96780

96238

29.0

.291

74

87767

86535

79.20

25

96665

96093

3J-3

0.261

75

87530

86290

79-71

26

96549

95949

33-8

.230

76

87290

86042

80.22

27

96430

95802

36-0

.191

77

87049

85793

80.72

28

96310

95655

38.8

.151

78

868c6

85542

81.23

29

96187

95506

41.1

.106 ,

79

86561

85290

8i-73

Equation pt — Po — <rf

80

86314

85035

82.22

81

86066

8y177O

Q fj — fy

30

96057

95367

44-36

82

85816

°4// y

84521

83.21

3r

95921

95211

45-66

83

85564

84262

83.70 .

32

95783

95053

46.93

84

85310

84001

84.19

33

95643

94894

48.17

34

95500

94732

49-39

85

85055

83738

84-67

86

84798

83473

85.16

35

95354

94567

50.58

87

84539

83207

85-64

36

95204

94399

51-75

6

88

84278

82938

86.12

37

95051

94228

52.89

3

89

84015

82668

86.59

38

94895

94055

54-01

is?

39

94734

93877

55-10

"Hb

90

83751

82396

87.07

c

91

83485

82123

87-54

40

94571

93697

56.16

•

92

83218

81849

88.01

41

94400

57-20'

4|

93

82948

81572

88.48

42

94239

93335

58.22

£

94

82677

81293

88.94

43

94076

93155

59-20

<u

44

939H

92975

60.17

f*

95

82404

81013

89.40

96

82129

80731

89.86

45

93744

92793

61.10

97

81853

80448

90.32

46

93575

92610

62.01

98

81576

80164

90.78

47

• 93403,

92424

62.90

99

81295

79872

91.23

48

93229

92237

63.76

49

93052

92047

64.60

100

81015

79589

91.68

* Quoted from the results of Dittmar & Fawsitt, "Trans. Roy. Soc. Edin." vol. 33.
SMITHSONIAN TABLES.

97

TABLE 108.

VARIATION OF THE DENSITY OF ALCOHOL WITH TEMPERATURE.

(a) The density of alcohol at f-1 in terms of water at 4° is given * by the following equation :

dt •=. 0.80025 — 0.0008340^ — oooooo 2t)P.
From this formula the following table has been calculated.

Density or Mass in grammes per cubic centimetre.

0

10
20
3°

.80625
.79788

•78945
.78097

.80541
.79704

.78012

.80457
.79620

•78775
.77927

.80374

•79535
.78691
.77841

.80290

•79451
.78606

•77756

.80207

•79367
.78522
.77671

.80123
.79283
•78437
•77585

.80039
.79198

•78352
.77500

.79956
.79114
.78267
•774H

.79872
.79029
.78182
•77329

(b) Variations with temperature of the density of water containing different percentages of alcohol. Water

at 4° C. is taken as unity, t

Percent-
age of
alcohol by
weight.

Density at temp. C.

Percent-
age of
alcohol by
weight.

Density at temp. C.

25

3°
35
40

45
50

0.99988

•99'35
.98493

•97995
.97566

0.97115
.96540
.95784
•94939
•93977

0.92940

099975
•99"3
.98409
.97816
.97263

0.96672
.95998
•95'74
•94255
•93254

0.92182

0.99831
.98945

•97527
.96877

0.96185
•95403
•945H
•935H
•92493

0.91400

0-99579
.98680

•97892
.97142
.96413

0.95628
•94751

.92787
.91710

0.90577

50

II

65
70

75

80

85
90

95
1OO

0.92940
.91848
.90742

•89595
.88420

0.87245
.86035
.84789
.83482
.82119

0.80625

0.92182
.91074

•89944
.88790
.87613

0.86427
.85215
.83967
.82665
.81291

0.79788

0.91400

•90275
.891 29
.97961
.86781

0.85580
.84366

•83U5
.81801

•80433
0.78945

0.90577
.89456

.87125
•85925

0.84719

•83483
.82232
.80918
•79553

0.78096

* Mendelejeff, " Pogg. Ann." vol. 138.

t Quoted from Landolt and Bomstein, " Phys. Chem. Tab." p. 223.

SMITHSONIAN TABLES.

98

TABLE 109.

VELOCITY OF SOUND IN AIR.

Rowland has discussed (Proc. Am. Acad. vol. 15, p. 144) the principal determination of the velocity of sound in
atmospheric air. The following table, together with the footnotes and references, are quoted from his paper.
Some later determinations will be found in Table in, on the velocity of sound in gases.

IJ

i

L

A

•d
|

3 °

Irs

.i. ° u
hi

PI o > i £

ll

ii§

fj

"o °

3-d
£ v

2 £

2
o

JJ ='«
>> . ^

<u *a

i-

o-s-c^.
"S-O £

>, " c S

i 5

S3

JO O

£"

"5 rt

«^

(A <U

£

|

11

8

oo c

-2°o

oljCj"^

E o

0(2

P

F

>2

>2

"3 «o
> £ °

(2°

i

2

1738
1811

France . .
Dusseldorf

40

5°-7°-5 C-

172.56 T.

332.9m.
333-7 "

-

332.6m.
332-7

2
2

3

1821

India . . <

1 20

70

83°-95 F.
79°-9 F.

1149.2 ft.
1 131.5 ft.

333-oc
329.6°

: }

330-9

2

4

1822

France . .

3°

i5°.9C.

340.89 m.

331.36

-

330-8

4

5

1822

Austria . .

88

9°.4 C.

-

332.96

-

332-5

3

6

7

1823
1824-5

Holland j
Port Bowen

22 Shots

14 "
51

u°.6C.
n°.oC.e

-38° F. to +33° F-

340-37
339-27

333-62
332.62
332-27r

332.82"
331.91"

7
i

8

1839

—

5°. 5 to 9° C.

336-50

332. 2O»

—

33J-8

i

9

10

1844
1868*

Alps . . .
France . .

34
149

8°.i7 C.
2° to 20° C.

338-oi

332-11

332-37
330-71

-

4
10

General mean deduced by Rowland, 331.75.

Correcting for the normal carbonic acid in the atmosphere, this becomes 331.78 metres
per second in pure dry air at o° C.

REFERENCES.

1 French Academy : " Mem. de 1'Acad. des Sci." 1738, p. 128.

2 Benzenburg : Gibberts's " Annalen," vol. 42, p. i.

3 Goldingham : " Phil. Trans." 1823, p. 96.

4 Bureau of Longitude : " Ann. de Chim." 1822, vol. 20, p. 210 ; also, " CEuvres d'Arago,"

" Mem. Sci." ii. i.

5 Stampfer und Von Myrbach : " Pogg. Ann." vol. 5, p. 496.

6 Moll and Van Beek : " Phil. Trans." 1824, p. 424.

7 Parry and Foster : " Journal of the Third Voyage," 1824-5, Ap

1828, p. 97.

8 Savant: " Ann. de Chim." ser. 2, vol. 71, p. 20. Recalculated.

9 Bravais and Martins : " Ann. de Chim." ser. 3, vol. 13, p. 5.
10 Regnault: " Rel. des Exp." iii. p. 533.

p. 86 ; " Phil. Trans."

a I believe that I calculated these reduced numbers on the supposition that the air was rather more than
half saturated with moisture.

b Reduced to o° C. by empirical formula,

c Wind calm.

d Moll and Van Beek found 332.049 at o° C. for dry air. They used the coefficient .00375 to reduce. I
take the numbers as recalculated by Schroder van der Kolk.

* An error of 0.21° C. was made in the original. See Schroder van der Kolk, " Phil. Mag." 1865.

f Corrected for wind by Galbraith.

g Recalculated from Savart's results.

* This is given as 1864 in Rowland's table. The original paper is in " Me'm. de 1'Institut," vol. 37, 1868.

SMITHSONIAN TABLES.

99

TABLE 110.

VELOCITY OF SOUND IN SOLIDS.

The numbers given in this table refer to the velocity of sound along a bar of the substance, and hence depend on the
Young's Modulus of elasticity of the material. The elastic constants of 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 be understood.

Substance.

Temp. C.

o

Velocity in
metres per
second.

Velocity in
feet per
second.

Authority.

Metals: Aluminium . - .

_

5104

16740

Masson.

Brass ....

-

3500

11480

Various.

Cadmium

-

2307

7570

Masson.

Cobalt ....

-

4724

15500

"

Copper ....

2O

3560

1 1670

Wertheim.

"

100

3290

10800

"

"

2OO

2950

9690

"

Gold (soft) .

2O

1743

5717

"

ii

IOO

1720

5640

«

" ....

2OO

1735

5691

"

Gold (hard) .

-

2IOO

6890

Various.

Iron and soft steel

-

5OOO

16410

"

Iron ....

20

5 '3°

16820

Wertheim.

" ....

IOO

53°o

17390

u

" ....

2OO

4720

15480

"

" cast steel

20

4990

16360

"

" " " .

IOO

4920

16150

"

" " " . .

2OO

4790

15710

"

Magnesium .

—

4602

15100

Melde.

Nickel ....

—

4973

16320

M asson.

Palladium

—

3t5°

10340

Various.

Platinum

20

2690

8815

Wertheim.

" ...

IOO

2570

8437

"

" ...

2OO

2460

8079

"

Silver ....

20

2610

8553

"

" ....

IOO

2640

8658

"

«

20O

2480

8127

"

Tin '..'..

-

2500

8200

Various.

Zinc ....

-

3700

12140

"

Various : Brick ....

-

3652

11980

Chladni.

Clay rock

-

348o

1 1420

Gray & Milne.

Granite

-

395°

12960

"

Marble

-

3810

12500

><

Slate ....

-

4510

14800

"

Tuff ....

-

2850

9350

u

Glass . . jf™

—

5000
6000

16410
19690

Various.

Ivory ....

-

3013

9886

Ciccone & Campanile.

Vulcanized rubber [

0

54

177

Exner.

(black) $

5°

31

I O2

"

" (red) .

o

69

226

"

« a «

7°

34

III

"

Woods : Ash, along the fibre

4670

i53'o

Wertheim.

" across the rings .

—

1390

4570

"

" along the rings

-

1260

4140

"

Beech, along the fibre .

-

3340

10960

"

" across the rings

-

1840

6030

i

" along the rings

-

1415

4640

<

Elm, along the fibre

-

4120

I35J6

'

" across the rings .

-

1420

4665

'

" along the rings

-

1013

3324

'

Fir, along the fibre . '

-

4640

15220

"

Maple

-

4110

13470

"

Oak

-

3850

12620

u

Pine

-

332o

10900

u

Poplar

-

4280

14050

n

Sycamore

4460

14640

«

SMITHSONIAN TABLES.

IOO

TABLE 1 1 1

VELOCITY OF SOUND IN LIQUIDS AND CASES.

Substance.

Temp. C.
o

Velocity in
metres per
second.

Velocity in
feet per
second.

Authority.

Liquids: Alcohol . ...

8.4

1264

4148

Martini.

" ....

23

1160

3806

Wertheim.

Ether ....

o

"59

3803

"

Oil of turpentine

24

1212

3977

"

. Water ( Lake Geneva)

9

H35

4708

Colladon & Sturm.

" (from Seine river)

15

1437

47M

Wertheim.

ii ii it it

3°

1528

5OI3

"

--«- <i ii ii

60

1724

5657

"

Water ....

3-9

Martini.

. .

13-7

1437

47H

"

H

25.2

1457

4780

"

Gases: Air .....

o

333

1092

Dulong.

0

33 ' -6

1087

Wertheim.

.

o

333

1092

Masson.

.....

o

33°-7

1085

Le Roux.

.

0

1089

Schneebeli.

.

o

332-5

1091

Kayser.

.

o

33' -9

1089

Wullner.

.

o

33r-7

1088

Blaikley.

o

33 ' -2

1086

Violle & Vautier.

— 10.9

326.1

1070

Greely.

—25-7

317.1

1040

"

-37-8

3°9-7

1016

1 002

u

0

332-4

1091

Stone.

Ammonia . . . .

o

4i5

1361

Masson.

Carbon monoxide

o

337-1

1106

Wullner.

11 «

o

337-4

1107

Dulong.

" dioxide .

0

261.6

858

"

Carbon disulphide

o

189

606

Masson.

Chlorine ....

0

206.4

677

Martini.

" ....

o

2°5-3

674

Strecker.

Ethylene ....

o

3H

1030

Dulong.

Hydrogen ....

0

1269.5

4165

"

" ....

0

1286.4

4221

Zoch.

Illuminating gas .

o

490.4

1609

"

Methane ....

o

422

1385

Masson.

Nitric oxide

0

325

1066

"

Nitrous oxide

o

261.8

859

Dulong.

Oxygen ....

0

3'7-2

1041

"

Vapors : Alcohol ....

0

230.6

756

Masson.

Ether ....

o

179.2

588

"

Water ....

o

401

1315

"

96

410

1345

SMITHSONIAN TABLES.

101

TABLE 112.
FORCE OF GRAVITY FOR SEA LEVEL AND DIFFERENT LATITUDES.

This table has been calculated from the formula ^, = ^45 [i — .002662 cos2<£],* where <t> is the latitude.

Lati-
tude <t>.

ff

in cms. per
sec. per sec.

Log.

0

in inches per
sec. per sec.

Log.

a

in feet per
sec. per sec.

Log.

0°

977.989

2-990334

385-034

2-585498

32.0862

1.506318

5

8.029

0352

.050

5517

.0875

6336

10

.147

0404

.096

5570

.0916

6388

'5

•339

0490

•173

5655

•0977

6474

20

.600

0605

•275

5771

.1062

6590

25

978.922

2.990748

385.402

2.585914

32.1168

1.506732

3°

9.295

0913

-548

6079

.1290

6898

31

•374

0949

.580

6114

.1316

6933

32

•456

0985

.6l2

6150

•1343

6969

33

•538

IO2I

.644

6187

•1370

7005

34

979.622

2.991059

385-677

2.586224

32.1398

!• 507043

35

.707

IO90

•7"

6262

•1425

7080

36

i9,3

"35

•745

6300

.1454

7119

37

.880

H73

•779

6339

.1490

7167

38

.968

1212

.813

6377

.I5II

7196

39

980.057

2.991251

385-849

2.586417

32-I540

1.507236

40

.147

1291

.884

6457

•1570

7275

4i

•237

1331

.919

6496

.1607

7325

42

•327

1372

•955

6537

.1630

7356

43

.418

I4II

.990

6577

.1659

7395

44

980.509

2.991452

386.026

2.586617

32.1688

I-507436

4£

.600

1492

.062

6657

.1719

7476

46

.691

'532

.098

6698

.1748

75i6

47

.782

1573

•134

6738

.1778

7557

48

•873

1613

.170

6778

.1808

7597

49

980.963

2.991653

386.205

2.586818

32.1838

!• 507637

5°

i-°53

1693

.241

6858

.1867

7677

Si

•143

1732

.276

6898

.1896

77i6

52

.231

1772

•311

6937

.1924

7756

53

.3,8

1810

•345

6975

•'954

7794

54

981.407

2.991849

386 380

2.587014

32-1983

1 -507833

55

•493

1887

.414

7053

.2011

7871

56

•578

1925

•447

7090

.2039

7909

57

.662

1962

.480

7127

.2067

7946

58

•744 :

1998

•513

7164

.2094

7983

59

981.825

2.992034

386.545

2.587200

32.2121

1.508018

60

•903

2070

•576

7235

.2147

8054

65

2.278

2234

•723

7400

.2276

8229

70

.600

2377

.849

7542

•2375

8361

75

.861

2492

•952

7657

.2460

8476

80

983-053

2.992577

387.028

2.587742

32-2523

1.508561

85

.171

2629

.074

7794

.2562

8613

90

.210

2646

.090

7812

•2575

8631

* The constant .002662 is based on data given by Harkness (Solar Parallax and Related Constants, Washington
1891).

The force of gravity for any latitude 0 and elevation above sea level h is verv nearly expressed by the equation

^ =*45(i --002662 cos 2*) [i-2|(i-2l)],

where R is the earth's radius, 5 the density of the surface strata, and A the mean density of the earth. When S~o
we get the formula for elevation in air. For ordinary elevations on land is nearly J, which gives for the correction
at latitude 45° for elevated portions of the earth's surface

f«-4= 980-6 X-5| - ,225.75 ^ in dynes.

4/C 4/t

5*-

h .

— 386.062 X 1- = 482.562 in inch pound units.
4A /?

_i /

= 32.1719 X -^5= 40.2149^- in poundals.

4/f K

This gives per 100 feet elevation a correction of

.00588 dynes )

.00232 inch pound units > diminution,
oooiq^ poundals )

SMITHSONIAN TABLES. IO2

GRAVITY.

TABLE 1 13.

In this table the results of a number of the more recent gravity determinations are brought together. They serve to
show the degree of accuracy which may be assumed for the numbers in Table 112. In general, gravity is a little
lower than the calculated value.for stations far inland and slightly higher on the coast line.

Place.

Latitude.

N. +, S. — .

Elevation
in metres.

Gravity in dynes.

Refer-
ence.

Observed.

Reduced to
sea level.

Singapore

1° if
-7 56
— 7 57
-8 49

— IO OO

13 04

— 15 55
— i5 57
20 43
20 52
20 56
21 18
32 23
— 33 52
— 33 56
35 4i
— 36 S2
37 20
37 20
37 47
37 47
38 53
39 54
39 58
40 27
40 28-
40 44
40 46
41 49
42 49
45 31

46 12
46 12

46 57
47 23
48 50
51 28
52 3°
54 34
55 59
56 28
57 03
57 07
58 18
59 1°
59 32

14

686
46

2

18

IO

533
3001

3
i'7
3

2

43
ii
6

43
1282
1282
114
114

IO

1645

122

651
348.
II
1288
I65

45°

IOO

405
405
572
466
67

7
49
6
o

8

12

5
5
4

978.07
978.24
978.08
978.14
978.36
978.16
978.66
978.52
978.27
978.85
978.90
978.96

979-75
979.67
979.61

979-94
979.67
979.64
979.68

979-95
980.02
980.10
979.68
980.12
980.08
980.09
980.26
979.82

980.34
980.34
980.73
980.58
980.60
980.61
980.67
980.96
981.20
981.26
981.45
981.49
981.59
981.68
981.66

981-73
981.81
981.82

978.07
978.24
978.21

978.15
978.36
978.16
978.66
978.58
978.84
978.85
978.92
978.96

979-7,5
979.68
979.61

979-94
979.68
979.89
979.92

979-97
980.04
980.10
979.98
980.14
980.20
980.15
980.26
980.05

980-37
980.42
980.75
980.64
980.66
980.69
980.74
980.97
981.20
981.27
981.45
981.49
981.59
981.68
981.66

98i-73
981.81
981.82

I
2

2
2

3
2

2
2
3

3
3
3

2
I
2
I
I

4

5
4
5
4

6
6
4

5
5
7

9
9
9
8
8
8
4
4
4
4
^
4
4
4

Georgetown, Ascension ....
Green Mountain, Ascension . . .
Loanda, Angola

Caroline Islands

Bridgetown, Barbadoes ....
Jamestown, St. Helena ....
Longwood, " ....
Pakaoao, Sandwich Islands . . .
Lahaina, " "...
Haiki, " "...
Honolulu, " "...
St. Georges, Bermuda ....
Sidney, Australia

Cape Town

Tokio, Japan .

Auckland, New Zealand ....
Mount Hamilton, Cal. (Lick Obs.)

San Francisco, Cal

« 11 «

Washington, D. C.*

Denver, Colo

York, Pa

Ebensburgh, Pa

Allegheny, Pa

Hoboken, N. J. . . ...

Salt Lake Citv, Utah

Chicago, 111

Pampaluna, Spain ....

Montreal, Canada

Geneva, Switzerland

Berne, "

Zurich, " ....

Paris, France

Kew, England . . ....

Berlin, Germany . . .

Port Simpson B C .

Burroughs Bay, Alaska ....
Wrangell, " ....
Sitka, " ....
St. Paul's Island, " ....
Juneau, " ....
Pyramid Harbor, " ....
Yakutat Bay, " ....

I Smith : " United States Coast and Geodetic Survey Report for 1884," App. 14.
2 Preston : " United States Coast and Geodetic Survey Report for 1860," App. 12.
3 Preston : Ibid. 1888, App. 14.
4 Mendenhall : Ibid. 1891, App. 15.
5 Defforges : " Comptes Rendus," vol. 118, p. 231.
6 Pierce : " U. S. C. and G. S. Rep. 1883," App. 19.
7 Cebrian and Los Arcos : " Comptes Rendus des Seances de la Commission Perma-
nente de 1'Association Geodesique International," 1893.
8 Pierce: " U. S. C. and G. S. Report 1876, App. 15, and 1881, App. 17."
9 Messerschmidt : Same reference as 7.

* In all the values given under references 1-4 gravity at Washington has been taken at 980. 100, and the others
derived from that by comparative experiments with invariable pendulums.
SMITHSONIAN TABLES.

103

TABLE 1 14.

SUMMARY OF RESULTS OF THE VALUE OF GRAVITY (</) AT STATIONS
IN THE UNITED STATES, OCCUPIED BY THE U. S. COAST AND
GEODETIC SURVEY DURING THE YEAR 1894.*

Station.

Latitude.

Longitude.

Elevation.

a

observed.

Atlantic Coast.

0 1 II

O 1 II

Metres.

Dynes.

Boston, Mass. . . . . ..

42 21 33

71 03 50

22

980.382

Cambridge, Mass. ....

42 22 48

7i 07 45

14

980.384

Princeton, N. J. . » . .

40 20 57

74 39 28

64

980.164

Philadelphia, Pa

39 57 06

75 ii 40

16

980.182

Washington, C. & G. S. .

3^ 53 r3

77 oo 32

. M

980.098

Washington, Smithsonian. . *

38 53 20

77 oi 32

10

980. toot

Appalachian Elevation.

Ithaca, N. Y

42 27 04

76 29 oo

247

980.286

Charlottesville, Va

38 02 01

78 30 16

1 66

979.924

Deer Park, Md. ....

39 25 02

79 '9 5°

770

979.921

Central Plains.

Cleveland, Ohio ».

41 30 22

81 36 38

2IO

980.227

Cincinnati, Ohio ....

39 08 20

84 25 20

245

979.990

Terre Haute, Ind. . . . .. !

39 28 42

87 23 49

I51

980.058

Chicago, 111

4i 47 25

87 36 °3

182

980.264

St. Louis, Mo

38 38 03

90 12 13

J54

979.987

Kansas City, Mo. ....

39 05 5°

94 35 21

278

979.976

Ellsworth, Kan. .....

38 43 43

98 13 32

469

979.912

Wallace, Kan

38 54 44

101 35 26

1005

979.741

Colorado Springs, Col.

38 5° 44

104 49 02

1841

979.476

^Q 4O "?6

104. c6 cc

1618

Q7Q. CQC

Rocky Mountains.

jy t^ O

1 ^-t J^ J 3

^j

y/ y-jVj

Pike's Peak, Col. ....

1.8 co 20

105 02 02

42cn

O78.O4O

Gunnison, Col. .....

o jw

38 32 33

i 06 56 02

t~yj
2340

y/ *-"vH
979.328

Grand Junction, Col.

39 04 °9

108 33 56

1398

979.619

Green River, Utah ....

38 59 23

i 10 09 56

1243

979.622

Grand Canyon, Wyo.

44 43 !6

no 29 44

2386

979.885

Norris Geyser Basin, Wyo.

44 44 09

i 10 42 02

2276

979-936

Lower Geyser Basin, Wyo.

44 33 21

no 48 08

22OO

979.918

Pleasant Valley, Jet., Utah

39 5° 47

in oo 46

2191

979.498

Salt Lake City, Utah

40 46 04

i" 53 46

1322

979.789

TABLE 1 15.

LENGTH OF SECONDS PENDULUM AT SEA LEVEL FOR DIFFERENT

LATITUDES, t

ri

= i!

c

c H

c

1

•2

- o>

n

ti

SI'S

b«

"S

if

c t;

tub

— !->
||

bO

2

"l §

M 0

_)

>-)

J

S

If

,3

_i

O

J

0

99.0910

1.996034

39.0121

1.591200

50

99.4014

1-997393

39-1344

1-592558

5

.0950

6052

•0137

1217

ss

•4459

7587

.1520

2753

10

.1079

6104

.0184

1270

60.

.4876

7770

.1683

2935

15

.1265

6190

.O26l

1356

6S

•5255

7935

.1832

3100

20

.1529

6306

•0365

1471

70

•558i

8077

.1960

3242

25

99-1855

1.996448

39-0493

1.591614

75

99^845

1.998192

39.2065

1-593358

30

.2234

6614

.0642

1779

80

.6040

8277

.2141

•3442

35

.2651

6796

.0806

1962

8S

.6160

8329

.2188

•3494

40

.3096

6991

.0982

2157

90

.6200

8347

.2204

•3512

45

•3555

7192

.1163

2357

* G. R. Putnam, Phil. Soc. of Washington, Bull. vol. xiii.

t Taken as standard. The other values were obtained from this by means of invariable pendulums,
t Calculated from force of gravity table by the formula l = g] ir-. For each 100 feet of elevation subtract 0.000596
centimetres, or 0.000235 inches, or .0000196 feet.

SMITHSONIAN TABLES.

IO4

TABLE 116.

LENGTH OF THE SECONDS PENDULUM.*

Date of
determi-
nation.

IJj.i
1^1

Range of latitude included by
the stations.

Length of pendulum in metres
for latitude <t>.

Correspond-
ing length
of pendulum
forlat. 45°.

Refer-
ence.

1799

15

From + 67° 05' to — 33° 56'

0.990631 -}- -005637 sin2 9

0-99345°

I

1816

31

" +74° 53' —5i° 2 1'

0.990743 + -005466 sin'2 ^

0.993976

2

1821

8

" +38° 40' -60° 45'

0.990880 -f- -00534° sin2 <{>

0-99355°

3

1825

25

" +79°50/ —i 2° 59'

0.990977 -j- -005142 sin'2<t>

0.993548

4

1827

4i

" + 79° So' — 51° 35'

0.991026-)- .005072 sin2<t>

0.993562

5

1829

5

o° o' -f 67° 04'

0-990555 + -0° 5679 sin2 $

0-993395

6

1830

49

' + 79° S1' — 5l0 35'

0.991017 -f- .005087 sin'2®

0.993560

7

1833

' — —

0.990941 -j- .005142 sin2?

0.993512

8

1869

5'

' + 79° 5o' - 51° 35'

0.990970 -j- .005185 sin2 9

Q-9935 54t

9

1876

73

. • +79° 50' -62° 56'

0.991011 + -005105 sin'20

°-993563

10

1884

123

' +79° 5°' —62° 56'

0.990918 -j- .005262 sin2 9

0-993549

ii

Combining th<

* above results

0.990910 -f- .005290 sin'2 9

0-993555

12

In 1884, from the series of observations used by Ur. Fischer, Dr. G. W. Hill 1S found
/= 0.9927148 metre

+ 0.0050890 p~4 (sin2 0 — |

51')

-- 0.0000979 p~4 cos2 0 cos (2w' +29° 04')

— 00001355 p~5 (sin3^ — f sin )0

+ 0.0005421 p~5 (sin2^ — |) cos $ cos («' + 217°

-j- 0.0002640 p~5 sin (f> cos2 <}> cos (2ta + 4° 49')

-j- 0.0001248 p~5 cos8 <j> cos (30)' -j- 1 10° 24')

-j- 0.0001489 p-6 (sin4 <t> — f sin2 <j> + ^)

-j- 0.0007386 p~6 (sin3 0 — f sin <j>) cos <j> cos («' -(- 3° 02')

-f- 0.0002175 p~8 (sin2 <j> — |) cos2 <t> cos (2«' -f 262° 17')

-j- 0.0003126 p~6 sin <t> cos3 ^ cos (30*' + 148° 20')

-f- 0.0000584 p~6 cos4 0 cos (40)' + 248° 19')

where <f> is the geocentric latitude, «' the geographical longitude, and p a factor, varying
with the latitude, such that the radius of the earth at latitude <t> is ap where a is the equa-
torial radius of the earth.

1 Laplace : "Traite de Mecanique Celeste," T. 2, livre 3, chap. 5, sect. 42.

2 Mathieu : " Sur les experiences du pendule;" in " Connaissance des Temps 1816,"
Additions, pp. 314-341, p. 332.

3 Biot et Arago : "Recueil d'Observations geodesiques, etc." Paris, 1821, p. 575.

4 Sabine : " An Account of Experiments to determine the Figure of the Earth, etc., by
Sir Edward Sabine." London, 1825, p. 352.

5 Saigey : " Comparaison des Observations du pendule a diverses latitudes ; faites par
MM. Biot, Kater, Sabine, de Freycinet, et Duperry ; "in " Bulletin des Sciences Mathe-
matiques, etc.," T. i, pp. 31-43, and 171-184. Paris, 1827.

6 Pontecoulant : " Theorie analytique du Systeme du monde," Paris, 1829, T. 2, p. 466.

7 Airy : " Figure of the Earth ; " in " Encyc. Met." 2d Div. vol. 3, p. 230.

8 Poisson : " Traite de Mecanique," T. i, p. 377 ; " Connaissance des Temps," 1834,
pp. 32-33 ; and Puissant : " Traite de geodesic," T. 2, p. 464.

9 Unferdinger: "Das Pendel als geodatisches Instrument;" in Grunert's "Archiv,"
1869, p. 316.

10 Fischer : " Die Gestalt der Erde und die Pendelmessungen ; " in " Ast. Nach." 1876,
col. 87.

11 Helmert : "Die mathematischen und physikalischen Theorieen der hbheren Geo-
dasie, von Dr. F. R. Helmert," II. Theil. Leipzig, 1884, p. 241.

12 Harkness.

13 Hill, Astronomical paper prepared for the use of the "American Ephemeris and
Nautical Almanac," vol. 3, p. 339.

* The data here given with regard to the different determinations which have been made of the length of the
seconds pendulum are quoted from Harkness (Solar Parallax and its Related Constants, Washington, 1891).
t Calculated fr«m a logarithmic expression given by Unferdinger.

SMITHSONIAN TABLES.

105

TABLE 1 -?7.

MISCELLANEOUS DATA WITH REGARD TO THE EARTH AND PLANETS.*

Length of the seconds pendulum at sea

level = 7 = 39.01 2540 + 0.208268 sin2 0 inches.

= 3.251045 -f- 0.017356 sin2 <j> feet.
= 0.9909910 + 0.005290 sin- <j> metres.
Acceleration produced by gravity per sec-
ond per second mean solar time . . =^=32.086528 -{- 0.171293 sin2 <p feet.

= 977.9886 + 5.2210 sin2 <j> centimetres.

Equatorial semidiameter . . . . =« = 20925293 -j- 409.4 feet.

= 3963.124 -j- 0.078 miles.
= 6377972-!- 124.8 metres.

Polar semidiameter ..... =£ = 20855590-!- 325.1 feet.

= 3949.922 -I- 0.062 miles.
= 6356727 -j- 99.09 metres.

One earth quadrant =393775819-)- 4927 inches.

= 32814652 -j- 410.6 feet.
= 62 1 4.896 -J- 0.078 miles.
= 10001816 -J- 125.1 metres.

Flattening =a—t = l

a 300.205 -j- 2.964

Eccentricity = — = 0.006651018.

Difference between geographical and geocentric latitude = 0 — 0'

= 688.2242" sin 2 0 — 1. 1482" sin 4 <j> -f- 0.0026" sin 6 ty.

Mean density of the Earth = 5.576 ^ 0.016.
Surface density of the Earth = 2.56 -j- 0.16.

Moments of inertia of the Earth ; the principal moments being taken as A, B, and C,
and C the greater :

C— A i

— 7: — = 0.00326521 = — 7 ;

C 306.259

C — A = 0.001064767 Ed1 ;
A = B = 0.325029 Eaz ;
C = 0.326094 Ea* ;
where E is the mass of the Earth and a its equatorial semidiameter.

Length of sidereal year = 365.2563578 mean solar days ;

= 365 days 6 hours 9 minutes 9.314 seconds.

Length of tropical year

= 365.242199870 — 0.0000062124 — — mean solar days ;

= 365 days 5 hours 48 minutes ( 46.069 — 0.53675 — — ) seconds.
Length of sidereal month

= 27.321661 162 — 0.00000026240 — — days ;

= 27 days 7 hours 43 minutes f 11.524 — 0.022671 - — j seconds.
Length of synodical month

= 29.530588435 — 0.00000030696 — — days ;

= 29 days i? hours 44 minutes ( 2.841 —0.026522 — — j seconds.
Length of sidereal day = 86164.09965 mean solar seconds.

N. B. — The factor containing t in the above equations (the epoch at which the values of
the quantities are required) may in all ordinary cases be neglected.

* Harkness, " Solar Parallax and Allied Constants."
SMITHSONIAN TABLES.

106

TABLE 117,
MISCELLANEOUS DATA WITH REGARD TO THE EARTH AND PLANETS.

MASSES OF THE PLANETS.

Reciprocals of the masses of the planets relative to the Sun and of the mass of the Moon
relative to the Earth :

Mercury =8374672-!- 1765762.
Venus = 408968 -[- 1874.
Earth* =327214-^-624.
Mars = 3093500 J- 3295.
Jupiter = 1047.55 zt °-2a
Saturn = 350 1.6^ 0.78.
Uranus = 22600 ± 36.
Neptune = 18780 -J- 300.

Moon =81.068-1-0.238.

Mean distance from Earth to Sun = 92796950 -J- 59715 miles ;

= 149340870^-96101 kilometres.

Eccentricity of Earth's orbit = e\

= 0.016771049 — 0.0000004245 (/ — 1850) — 0.000000001367 (— — ) .

\ loo /

Solar parallax = 8.80905" -j- 0.00567".
Lunar parallax = 3422.54216" -J- 0.12533".

Mean distance from Earth to Moon = 60.2693 r 5 -J- 0.002502 terrestrial radii;

= 238854.75 -J- 9.916 miles ;
= 384396.01 ^- 15.958 kilometres.

Lunar inequality of the Earth = L = 6.52294" -[- 0.01854".

Parallactic inequality of the Moon = Q = 124.95126" J- 0.08197".

Mean motion of Moon's node in 365.25 days=/t= —19° 21' 19.6191" + 0.14136" * °°.

Eccentricity and inclination of the Moon's 0^1 = ^2 = 0.054899720.

Delaunay's y = sin \ I— 0.044886793.
/ = 5° 08' 43-3546".

Constant of nutation = 9.22054" -|- 0.00859" + 0.00000904" (t — 1850).
Constant of aberration = 20.45451" J- 0.01258".

Time taken by light to traverse the mean radius of the Earth's orbit

= 498.00595 -j- 0.30834 seconds.

Velocity of light = 186337.00 -{- 49.722 miles per second.

= 299877.64 -[- 80.019 kilometres per second.

* Earth + Moon.
SMITHSONIAN TABLES.

lO/

TABLE 1 18.

AERODYNAMICS.

The pressure on a plane surface normal to the wind is for ordinary wind velocities expressed by

where k is a constant depending on the units employed, w the mass of unit volume of the air,
a the area of the surface and v the velocity of the wind.* Engineers generally use the table of
values of P given by Smeaton in 1759. This table was calculated from the formula

P==. 00492 z/'2

and gives the pressure in pounds per square foot when v is expressed in miles per hour. The
corresponding formula when v is expressed in feet per second is

/)=.OO228z/2.

Later determinations do not agree well together, but give on the average somewhat lower
values for the coefficient. The value of w depends, of course, on the temperature and the baro-
metric pressure. Langley'st experiments give kw=. 00166 at ordinary barometric pressure and
10° C. temperature.

For planes inclined at an angle a less than 90° to the direction of the wind the pressure may
be expressed as Pa = FaPw

Table 118, founded on the experiments of Langley, gives the value of fa for different values of
a. The word aspect, in the headings, is used by him to define the position of the plane relative to
the direction of motion. The numerical value of the aspect is the ratio of the linear dimension
transverse to the direction of motion to the linear dimension, a vertical plane through which is
parallel to the direction of motion.

TABLE 118.— Values of Fa In Equation Pa = PaP9o.

Plane 30 in. X 4.8 in.

Plane 12 in. X 12 in.

Plane 6 in. X 24 in.

Aspect 6 (nearly).

Aspect i.

Aspect J.

a

Fm

a

*;

a

Fa

0°

o.oo

0°

o.oo

0°

O.OO

5

0.28

5

0.15

5

0.07

10

0.44

10

0.30

TO

0.17

IS

0.55

15

0.44

15

0.29

20

0.62

20

o-57

20

o-43

25

0.66

25

0.69

25

0.58

3°

0.69

3°

0.78

30

0.71

35

0.72

35

0.84

40

0.74

40

0.88

—

-

45

0.76

45

0.91

-

-

50

0.78

50

-

-

-

* The pressure on a spherical surface is approximately 0.36 that on a plane circular surface of the same diameter
as the sphere ; on a cylindrical surface with axis normal to the wind, about 0.5 that on a rectangular surface of length
equal to the length, and breadth equal to the diameter of the cylinder.

t The data here given on Professor Langley's authority were communicated by him to the author.

SMITHSONIAN TABLES.

108

TABLE 1 1 9.

AERODYNAMICS.

On the basis of the results given in Table 118 Langley states the following condition for the
soaring of an aeroplane 76.2 centimetres long and 12.2 centimetres broad, weighing 500 grammes,
— that is, a plane one square foot in area, weighing i.i pounds. It is supposed to soar in a
horizontal direction, with aspect 6.

TABLE 119. - Data for the Soaring of Planes 76.2 X 12.2 cms. weighing 500 Grammes, Aspect 6.

Weight of planes of like

Inclination

Soaring speed •».

Work expended per minute
(activity).

form, capable of soaring
at speed v with the ex-
penditure of one horse

to the hori-

power.

zontal a.

Metres per
sec.

Feet per
sec.

Kilogramme
metres.

Foot
pounds.

Kilogrammes.

Pounds.

2°

20.0

66

24

174

95-o

209

5

I5.2

5°

41

297

55-5

122

10

I2.4

4i

65

474

34-8

77

15

II. 2

37

86

623

26.5

58

3°

10.6

35

17S

1268

13.0

29

45

II. 2

37

33°

2434

6.8

'5

In general, if p = — - —
area

Soaring speed v—\ £ - —

V k Fg. cos a

Activity per unit of weight =v tan a

The following data for curved surfaces are due to Wellner (Zeits. fur Luftschifffahrt, x., Oct.
1893).

Let the surface be so curved that its intersection with a vertical plane parallel to the line of
motion is a parabola whose height is about ^ the subtending chord, and let the surface be
bounded by an elliptic outline symmetrical with the line of motion. Also, let the angle of incli-
nation of the chord of the surface be a, and the angle between the direction of resultant air
pressure and the normal to the direction of motion be )8. Then ft < a, and the soaring speed is

-, while the activity per unit of weight =z>tan /3.

k />a cos j3'

The following series of values were obtained from experiments on moving trains and in the
wind.

Angle of inclination a = —3° o° +3° 6° 9° 12°

Inclination factor Fa= 0.20 0.50 0.75 0.90 i.oo 1.05

tanj8= o.o i 0.02 0.03 0.04 o.io 0.17

Thus a curved surface shows finite soaring speeds when the angle of inclination a is zero or even
slightly negative. Above a= 12° curved surfaces rapidly lose any advantage they may have for
small inclinations.

SMITHSONIAN TABLES.

109

TABLES 12O, 121.

TERRESTRIAL MAGNETISM.

TABLE 120. - Total Intensity of the Terrestrial Magnetic Field.

This table gives in the top line the total intensity of the terrestrial magnetic field for the longitudes given in the first
column and the latitudes given in the body of the table. Under the headings 13, 13.5, and 13.75 there are some-
times several entries for one longitude. This indicates that these lines of total force cut the same longitude line
more than once. The isodynamic lines are peculiarly curved and looped north of Lake Ontario. The values are
for the epoch January i, 1885, and the intensities are in British and C. G. S. units.

Longi-
tude*

10.5
or

11. 0

or

11.5

or

I2.O

or

12.5

or

13.0 or .5994

13.5 or .6225

13.75 or .6340

.4841

.5072

•53°i

•5533

•5764

67

o

o

0

0

o

o

O

0

o

o

o

o

0

44-5

5-5

68

/iX •>

43- l

70

-

-

-

-

—

41.9

-

-

-

-

-

-

—

72

—

-

-

-

-

40.6

-

-

-

-

-

-

-

75

if\ ->

3°-7

76

_

_

_

_

_

36-4

_

44-7

_

_

_

_

_

77

-

-

-

-

-

36.0

-

43-6

45-4

-

-

-

-

78

-

22.6

24-5

-

-

34-i

—

43-3

45-2

-

—

-

-

80

-

22.8

24-5

27.9

31.2

35- !

-

43-9

44-6

-

-

-

-

81

-

22.8

24-5

27.1

31.2

35-5

-

41.4

41.9

44-3

45-8

-

—

82

_

22.8

24.6

26.4

3!-3

35-5

_

4F.2

42.1

43-6

45-8

-

-

83

—

22.7

24.8

26.6

31.2

35-2

-

41.0

46.2

—

-

-

-

85

19.6

22.2

25.0

27.9

30.8

34-4

-

40.8

47.6

-

-

45-5

46.1

86

19.8

22-3

-

28.3

30.6

35-3

-

41.1

48.0

-

-

45.2

47-4

87

2O.O

22.5

-

28.6

3°-4

35-5

-

41.9

48.4

-

-

43-2

47-7

90

2O. I

22.5

-

29.9

3i-9

36.6

-

41.6

49.1

-

-

43-2

48.2

92

2O. I

22-3

-

29-3

33-3

37-4

-

41.7

50.2

-

-

44-7

48.2

95

20.0

22-3

-

28-3

33-i

37-2

-

41.2

-

-

-

43-7

-

IOO

2O.O

22.8

-

30.0

34-i

39-o

-

41.4

-

-

-

42.7

-

105

21.7

24.4

-

33-1

36.1

39-8

-

43-6

-

-

-

44-8

-

110

23.2

26.9

31.2

34-4

37-7

41.6

-

45.2

-

-

-

47.0

-

"5

-

29.1

31.8

36.2

40.1

44-5

-

-

-

—

-

-

-

120

-

3°-7

34-7

37-8

42-3

46.4

-

- .

-

-

-

-

-

124

39-6

44.2

TABLE 121. —Secular Variation of the Total Intensity.

Values in British units of total intensity of terrestrial magnetic force at stations given in the first column and epochs
January i of the years given in the top line.

Station.

1840

1845

1850

18S5

1860

1865

1870

1875

1880

1885

Cambridge . .
New Haven .
New York
Sandy Hook .
Albany . .

13.48
13-47
'3-56
13-7°
13.68

13-33

13.40

'3-Si
13-59
'3-65

13.21

'3-25
'3-39
I3-36
I3-72

13.22
13.11

'3-27
I3-I7
13.80

13-37
13.20

'3-32
13-23
13-87

13-45
13-33
I3-36
13-35
13-93

13-49
I3-4I
'3-36
13.40
13.92

13-39
I3-4I
I3-31
13-39
13.82

I3-T4
13.29

i3-!9
I3-30
13.61

12.79

13-OS

12.99

I3-I3

I3-27

Philadelphia .
Baltimore .
Washington .
Toronto . .
Cleveland

!352
'3-56
13-43
14.03

13-85

13-44
1345
13-36
!3-93
I3-78

'3-45
1338
'3-31
13-95
I3-76

13-47
13-37
'3-34
I3-9I
12.75

I3-5I
13-44
13-39
1382

I3-78

13-55
13.46
I3-42
13.82

I3-83

I3-58
13.48
I3-42
13-77
13.84

13-57

13.48

I3-38
I3-78
13.81

'3-49
I3-38
13.29
I3-78
13-74

!3-25
13.22
13.20
13-76
13.61

Detroit . . .

13-85

13.80

i3-7i

13.68

I3-72

'3-75

13-76

I3-78

13-73

13.62

* Tables 120-125 have been compiled from a very full discussion of the magnetic dip and intensity for the United
States and adjacent countries, given in Appendix 6 of the Report of the United States Coast and Geodetic Survey
for 1885. Later Reports of the survey have been consulted, particularly in connection with the extrapolation of the
values of horizontal intensity to 1890 and 1895, but most of the data are taken from Mr. Schott's Appendix to the 1885

SMITHSONIAN TABLES.

IIO

TERRESTRIAL MAGNETISM.

TABLES 122, 123.

TABLE 122. — Values of the Magnetic Dip.

This table gives for the epoch January i, 1885, the values of the magnetic dip, stated in first column, corresponding
to the longitudes given in the top line and the latitudes given in the body of the table. Thus, for longitude 95°
and latitude 30° the dip was 59° on January i, 1885. The longitudes are west of Greenwich. For positions above
the division line in the table the dip was increasing, and for positions below that line decreasing, in 1885.

Dip.

Longitudes west of Greenwich.

66°

70°

75°

80°

85°

90°

95°

I003

105°

IIO°

.15°

120°

124°

o

o

o

0

0

0

o

o

0

0

o

o

O

0

44

-

-

-

-

-

17.9

18.4

19.1

19.6

-

-

-

-

45

-

-

-

-

-

18.7

19.2

19.8

20.3

•-

_

_

_

6

-

-

-

-

-

19.2

19.8

20.6

21. 1

-

-

-

-

7

—

-

-

—

-

2O.O

20.S

21.2

21.8

-

-

-

—

8

-

-

17.9

-

-

20-5

21.2

21-9

22-5

23-3

-

-

-

9

-

-

I8.7

-

-

21.2

21.9

22.6

23.2

24.0

-

-

-

50

-

-

-

-

21.4

22.1

22.7

23-5

24.1

24.7

_

-

_

i

-

-

-

-

22.2

22.8

23.6

24-3

24.8

25-5

-

-

-

2

-

-

—

22.4

23.0

23-7

24.4

25.1

25.6

26.3

27.4

-

-

3

—

-

-

23-3

23-9

24-5

25.2

25-9

26.5

27.1

28.2

-

-

4

-

-

-

24.0

24.7

25-3

26.O

26-7

27.2

28.1

29.0

-

-

55

-

-

-

24.8

2S-S

26.1

26.8

27-5

28.1

28.9

29.9

-

_

6

-

-

24.7

25.6

26.3

26.9

27.5

28.1

28.9

29.7

30.6

-

-

7

-

-

-

26.4

27.1

27.7

28.3

28.9

29.7

30.6

3M

-

-

8

-

-

-

27-3

27.9

28.5

29.1

29.8

30-5

3M

32-3

-

-

9

-

-

-

28.0

28.7

29.4

30.0

30.6

31-5

32-4

33-3

34-4

-

60

-

-

-

28.6

29.6

30.2

30.8

3J-5

32-4

33-4

34-3

,W

-

i

-

-

-

29.9

30-3

3°-9

3'-7

32-4

33-3

34-2

35-3

.36.2

-

2

-

-

-

30.6

y>3

3*-9

32-5

33-3

34-3

35-2

36.3

37-i

-

3

-

-

-

31.6

32.0

32-7

33-6

34-2

35-2

36.2

37-i

38.1

39-°

4

-

-

-

32-7

33-2

33-6

34-5

35-2

36.1

37-2

38.1

39-o

40-3

65

-

-

-

33-5

34-o

34-6

35-5

36.2

37-i

38-2

39-2

40-3

4i-5

6

-

-

—

34-3

35-o

35-8

36-5

37-2

38.1

39-2

40.3

4«-5

42.5

7

-

-

35-1

35-3

35-9

36.6

37-2

38.2

39-i

40.2

41.4

42-5

43-6

8

-

-

35-8

36.0

36.6

37-5

38.2

39-2

40.0

41.2

42.4

43-6

44-7

9

-

-

37-o

37-5

37-6

38-5

39-2

40.0

41.2

42.2

43-5

44-6

45-7

70

-

-

38.0

38.5

39-o

39-6

40.4

41.0

42-1

43-3

44-5

456

46.9

i

-

-

39-i

39-5

39-8

40.7

41.1

41.8

43-2

44-3

45-7

47-2

47-9

2

-

-

40.4

40-3

40.9

41.6

42.1

43-i

44-3

45-5

47.1

48.6

49-2

3

-

41.7

41.2

41.9

42.2

42-7

43-4

44-4

45-5

46.9

48.6

50.0

4

43-5

43- i

42.9

43- !

43-4

43-9

44-5

45-6

46.7

48-3

49-7

-

-

75

44.9

44-5

44-3

44.0

44-5

45-°

45-7

46.7

48.0

49-5

51.0

-

_

6

45-7

45-9

45-5

45-4

45-5

46.1

47.1

48.2

49-5

5°-7

—

—

7

47-3

47-6

46.7

46.9

47.0

47-4

48-3

49-4

50.6

-

-

-

8

-

-

-

48.2

48.0

48.8

49-7

50-7

51-8

-

-

-

-

9

-

-

-

49-3

49-3

-

51.0

5*-9

-

-

-

-

-

80

-

-

-

50.4

5°-4

-

-

-

-

-

-

-

-

TABLE 123. — Secular Variation of the Magnetic Dip.

Values of magnetic dip at stations given in the first column, and epochs, January i, of the years given in the top line.

Station.

1840

1845

1850

1855

1860

1865

1870

1875

1880

1885

Cambridge .

74.25

74.29

74-35

74-40

74-42

74.38

74.26

74.02

73-65

73- 1 2

New Haven

73-47

73-51

73-56

73-6i

73-64

73.62

73-54

73..18

73-"

72.72

New York .

72-75

72-73

72.75

72.78

72.80

72./8

72.71

72-56

72.31

71-93

Sandy Elook

72.63

72.61

72-63

72.66

72.68

72.66

72.59

72-44

72.19

71.81

Albany . .

74-75

74.80

74-88

74-96

75.02

75.02

74-95

74-77

74.46

73-99

Philadelphia

71.99

72.02

72.08

72-15

72.20

72.21

72.16

72.02

71.77

71-38

Baltimore .

71-74

71.66

71.66

71.69

71-74

71.77

71.76

71.67

71.48

71.16

Washington

71-39

71-39

71-38

7I-36

7J-32

71.25

7«-i3

71.00

70.80

70-55

Toronto . .

75.28

75-25

75-32

75-39

75-4'

75-35

75-27

75-20

75-03

74.88

Cleveland .

73-22

73-!9

73-21

73-24

73.28

73-29

73-27

73-i8

73-°3

72-78

Detroit . .

73-61

73-61

73-63

73-66

73-68

73-69

73-67

73.60

73-47

73-28 ,

SMITHSONIAN TABLES.

Ill

TABLES 124, 125.

TERRESTRIAL MAGNETISM.

TABLE 124. — Horizontal Intensity.

This table gives, for the epoch January i, 1885, the horizontal intensity, H, corresponding to the longitudes in the top
line and the latitudes in the body of the table. At epoch 1885 the force was increasing for positions above the
division line, and was decreasing for positions below the division line.

H
in British
units.

Longitudes west of Greenwich. ,

H
inC.G.S.
units.

65°

7°°

75°

80°

85°

90°

o

95°

100°

,05°

110°

1.5°

120°

124°

2.50

2-75
3-°°
3-25
3-5°

3.75

4.00
4-25
4-5°
4-75

5.00

5-25
5-5°

I75
o.oo

6.25

6.50

6-75
7.00

7-25

0

o

o

°

o
An 8

o

0

o

o

°

°

o

.1153

.1268

•1383
.1498
.1614

1729

.1844
•1959
•2075
.2190

.2305

.2422

•2536
.2651
.2766

.2881

.2997
.3112
.3228
•3343

48.3

45-5
43-2

47-3
45-6
43-8

42.2
40.7

46.6

45-5
43-6

42.5
41.2
39-6
38.1
36-6

35- *

48-5
47-2
45-8
44-o

42.6

4J-5
40.2

38-7
37-4

35-8
34-6

33-o
31.0
28.8

27-4
25.8
23.6

20.8

48.8
47.6
46.1
44.6

43-2
42.1
40.4

39-2
37-6

36.2

,"?5'2

49.8
48.5
46.7
45.I

43-6
42.4
41.0

39-7
38-4

49-1

47.6

45-8

44.6

43-4
41.8

40.4

5O.I
48.5

47-2

45-8
44.6
43-°
41.6

47-3
45-7
44-2
42.8

48.4
46.8

454
43-8
42.0

40-3

37-7

36.7
34-8
32.3

28.4
26.1
24.0

21.2

49.4

48.7
47-0

45-2
43-6

41.9
39-6

37-7
35-6
33-6

49.6
47.6

45-7
44-2

42.6
39-8
37-4

47-7
46-3
44.6
42.8

41.1
39-2
37-2
35-2
33-i

3i-i
28.6

39-i

37-8
35-9
34-5
32-7
31.0

29.8
27.7

22.8
19.9

39-9

38.5
37-o

35-3
33-6
31.6

29.9
28.0

23.0
20.3

41.0

39-3

38.0

36-3
34-7
3i-9

28.2

23.2
20.5

36-9
35-4

33-8
32.1

3°-3
28.1
27-3

22.5
I9-S

33-8
32.2
30.6

29.2

27-3

22.1

24.1
18.2

TABLE 125. — Secular Variation of the Horizontal Intensity.

Values of the horizontal intensity, H, in British units, for stations given in first column and epochs given in top line.
The values for 1890 and 1895 have been extrapolated from the values up to 1885. The epochs are for January i of
the different years given.

Station.

1840

1845

1850

1855

1860

1865

1870

1875

1880

1885

1890

1895

Cambridge . .

3-66

3.61

3-56

3-55

3-59

3.62

3.66

3-68

3-70

3-71

3-73

3-74

New Haven . .

3-83

3.80

3-75

3-7°

3-72

3-76

3.80

3-83

3.86

3-87

3-87

3-86

New York . .

4.02

4.01

3-97

3-93

3-94

3-95

3-97

3-99

4.01

4-03

4-05

4.07

Sandy Hook

4.09

4.06

3.99

3-92

3-94

3-98

4.01

4.04

4.07

4.10

4-i3

4.16

Albany . . .

3.60

3.58

3-58

3-58

3-58

3.60

3-6i

3-63

3-64

3-66

3-67

3-69

Philadelphia

4.18

4.15

4.14

4-13

4-13

4.14

4.16

4.19

4.22

4-23

4.24

4.24

Baltimore . .

4-25

4-23

4.21

4.20

4.21

4.21

4.22

4.24

4-25

4.27

4.28

4-3°

Washington

4.28

4.26

4-25

4.26

4.29

4-3i

4-33

4-35

4-37

4-39

4.41

4.42

Toronto . . .

3-56

3-54

3-53

3-51

3-48

3-49

3-5°

4.52

3-56

3-58

4.60

4.61

Cleveland . .

4.00

3-98

3-97

3-96

3-96

3-97

3-98

3-99

4.01

4-03

4-05

4.07

Detroit . . .

3-9i

3-89

3-86

3-85

3-85

3-86

3-87

3-89

3-90

3-92

3-93

3-94

San Diego . .

6.12

6.19

6.22

6.25

6.26

6.24

6. 20

6.15

6.10

6.07

6.04

6-03

Santa Barbara .

5-87

5-93

5-94

5-95

5-0

5-95

5-94

5-92

5.88

5.84

5.80

5-77

Monterey . .

5-63

5-71

5-75

5-77

5-76

5-75

5-72

5.69

5-66

5-65

5-64

5-63

San Francisco .

5-49

5-54

5-56

5-57

5-59

5-59

5-58

5-54

5-51

5-49

5-47

5-45

Fort Vancouver

4.44

4.51

4-55

4-56

4.58

4-58

4-57

4.56

4-54

4-53

4-52

4.52

SMITHSONIAN TABLES.

112

TERRESTRIAL MAGNETISM.

TABLE 126.

Secular Variation of Declination in the Form of a Function of the Time for a Number of Stations.

More extended tables will be found in App. 7 of the United States Coast and Geodetic Survey Report for 1888, from
which this table has been compiled. The variable m is reckoned from the epoch 1850 and thus— t — 1850.

Station.

Latitude.

West
longitude.

The magnetic declination (D) expressed as
a function of time.

(a) Eastern Series of Stations.

St. Johns, N. F. . ... .

0 1

47 34-4

0 /

52 41.9

O O 0

21.94+ 8.89 sin (1.05 m + 63.4)*

Quebec, Canada ....

46 48.4

71 14-5

14.66+ 3.03 sin (1.4 m -- 4.6)

+ 0.61 sin (4.0 m + 0.3)

Charlottetown, P. E. I.

46 14.0

63 27.0

'5-95 + 7-78 sin (1.2 m + 49.8)

Montreal, Canada

45 30-5

7334-6

11.88+ 4.17 sin (1.5 m — 18.5)

+ 0.36 sin (4.9 m + 19.0)

Bangor, Me. ....

44 82.2

6846.9

13-86+ 3.55 sin (1.30*7 + 8.6)

Halifax, N. S

44 39.6

63 35-3

16.18+ 4.53 sin (i.oom + 46.1)*

Albany, N. Y.

42392

73 45-8

8.17 + 3.02 sin (1.44 m — 8.3)

Cambridge, Mass.

42 22.9

71 07.7

9.54 + 2.69 sin (1.30 m + 7.0)

+ 0.18 sin (3.20 m + 44.0)

New Haven, Conn.

41 18.5

72 55-7

7-78+ 3.11 sin (1-40 m — 22.1)

New York, N. Y.

40 42.7

7400.4

7.04+ 2.77 sin (1.30 m — 18.1)

+ 0.14 sin (6-3ow + 64.0)

Harrisburg, Pa. . . .

40 15.9

70 52.6

2.93+ 2.98 sin (1.50 /» + 0.2)

Philadelphia, Pa. ...

39 56-9

7509.0

5.36+ 3.17 sin (1.50 m — 26.1)

+ 0.19 sin (4-oow/ + 14.6)

Washington, D. C.

38 53-3

77 00.6

2-73+ 2-57 sin (1.45 m — 21.6)

+ 0.14 sin (12.00 m + 27)

Cape Henry, Va.

36 55-6

76 00.4

2.42+ 2.25 sin (1.47 m — 30.6)

Charleston, S. C. . .

32 46.6

70 55-8

— 1.82+ 2.75 sin (1.40 m — 1 2.1)*

Paris, France . . .

48 50.2

t 2 2O.2

6-479 4~ 16.002 sin (0.765 m + 1 18.77)

+ [0.85 — 0.35 sin (0.69/2)] sin [(4.04

+ 0.0054 // + .000035 «2)wJt

St. George's Town, Bermuda

32 23.0

64 42.O

6.95 + 0.0145 m + 0.00056 »/2 *

Rio de Janeiro, Brazil . : .

— 22 54.8

4309-5

2.19 + 9.91 sin (0.80 m — 10.4)*

(6) Central Series of Stations.

York Factory, B. N. A. . • .

56 59-9

92 26.O

7.34+16.03 sin (i.io m — 97.9)

Fort Albany, B. N. A. . ; .

52 22.0

8238.0

J5-78+ 6.95 sin ( i. 20 m — 99.6)*

Sault Ste Marie, Mich. . ,.

46 29.9

84 20.1

1.54 + 2.70 sin (1.45 m — 58.5)

Toronto, Canada . . ;.

43 39-4

7923.5

3.60 + 2.82 sin (1.40 m — 447)

+ 0.09 sin (9.30 m + 136)

+ 0.08 sin (19.00 m + 247)

Chicago, 111

41 50.0

87 36-8

— 3-77 + 2.48 sin (1.45 m — 62.5)

Cleveland, Ohio . '. .

41 30.4

81 41.5

0.47 + 2.39 sin (1.30 m — 14.8)

Denver, Colo

39 45-3

104 59.5

— 15.30 + o.oi i m + 0.0005 m2

Athens, Ohio .i . .

39 I9-°

82 02.0

— 1.51 + 2.63 sin (1.40 m — 24.7)

Cincinnati, Ohio . ' .

39 °8-4

84 25.3

— 2.59+ 2.43 sin (1.42^ — 37.9)

St. Louis, Mo.
New Orleans, La. ...

38 38.0
29 52.2

9O 12.2
9003.9

— 5.91 + 3.00 sin (1.40 m — 51.1)*
— 5.20 + 2.98 sin ( i .40 m — 69.8)

Key West, Fla

24 33-5

81 48.5

— 4.31 + 2.86 sin 11.30 m — 23.9)

Kingston, Port Royal, Jamaica .

i7 55-9

76 50.6

— 3-8 1 + 2.39 sin (i.io m — 10.6)

(£) Stations on the Pacific Coast, etc.

City of Mexico, Mex.

19 26.0

9911.6

— 5-34 + 3- 28 sin (i. oom— 87.9)*

Cerros Island, Lower Cal., Mex.

28 04.0

115 12.0

— 7.40 + 4.61 sin (1.05 tn — 107.0)

San Francisco, Cal. '. .' |.

37 47-5

122 27.3

— 13.94 + 2.65 sin (1.05 m — 135.5)

Vancouver, Wash. . . ;.

45 37-5

12239.7

— 17-93 + 3-12 sin (1.35 w — '34-i)

Sitka, Alaska ....

57 02.9

135 '9-7

— 25.79 + 3.30 sin (1.30 m — 104.2)

Port Etches, Alaska . . • J.

60 20.7

. 146 37-6

— 23.71 + 7.89 sin (1.35 m — 80.9)

Petropavjovsk, Siberia . . i .

530..0

ti58 43.0

— 3-35 + 2.97 sin ( i .30 m + 1 2. 2)

* Approximate expression. t East longitude.

t Compiled from a series of observations extending back to 1541. The primary wave follows the sum of the con-
stant and first periodic term closely. The period seems to be about 470 years. In the expression for the secondary
wave n = t — 1700.

SMITHSONIAN TABLES.

TABLE 127.

TERRESTRIAL MAGNETISM.

Secular Variation of the Declination. — Eastern Stations.*

Station.

1800

1810

1820

1830

1840

1850

1860

1870

1880

1890

1900

o

o

o

o

o

o

o

0

o

o

0

St. Johns, N. F. . .

23-5

25.0

26.5

28.0

29.0

29.9

35-°

30.8

30.8

3°-5

29.9

Quebec, Canada . .

12. 1

12.1

12.3

12.9

13.8

14.9

16.0

16.9

17.4

!7-5

'7-5

Charlottetown,

P. E. I. ....

_

_

_

I Q. -I

2O.7

2I.Q

22.8

21.4

21.7

21 7

2T •?

Montreal, Canada .

8.0

7-8

7-9

y j

8.4

^.w. /

94

y
10.7

I2.O

•"j"fr
13.0

~ O'/

I3.8

^•Jv
14.4

J J
15.0

Eastport, Me. . . .

13.2

I4.O

14.8

15.6

16.4

I7.I

I7.8

I8.3

18.7

18.9

19.0

Bangor, Me. . . .

10.9

II.4

12.1

12.8

13.6

144

IS'2

15-9

16,5

16.9

17-3

Halifax, N. S. . . .

15-9

I6.7

17.4

lS.2

18.9

19.4

19.9

2O-3

2O.6

2O-7

20.7

Burlington, Vt. . .

7-3

7.2

7-5

8.1

8.9

9-7

10-3

I I.O

11.9

12.8

!3-5

Hanover, N. H. . .

5-8

6.0

6-5

7.2

7-9

8.8

9-8

10.8

11.7

12-5

!3-!

Portland, Me. . . .

8.5

8.9

9-5

IO.I

10.8

1 1.6

12-3

13.0

13-6

I4.I

14.4

Rutland, Vt. . . .

6-3

6.2

6.5

6.9

7.6

8-5

94

10.4

"•3

12-3

13.0

Portsmouth, N. H. .

74

7-7

8.1

8.7

9-5

10.3

n. i

11.9

12.7

l3-3

J3-7

Chesterfield, N. H. .

6.0

6.4

7-o

7-7

8-5

94

10.3

11.2

I2.O

12.6

Newburyport, Mass.

7-3

7-6

8.1

8.6

9-3

1 0.0

10.7

11.4

12.0

12-5

12.8

Williamstown,.Mass.

5-7

5-9

6-3

6.8

74

8.1

8.8

9.6

10-3

IO-9

11.4

Albany, N. Y. . .

-

5-4

5-8

6-3

7-o

7-7

8-5

9.2

9-9

10-5

10.9

Salem, Mass. . . .

6-3

6.6

7-2

7-9

8.7

9.6

10.6

11.5

12.3

13.0

13-S

Oxford, N. Y. . . .

3-o

3-1

34

3-9

4-5

S-1

5-9

6.6

74

8.0

8.6

Cambridge, Mass. .

7-i

7-5

8.0

8.6

9-3

1 0.0

10.6

II. 2

1 1.6

11.9

12.0

Boston, Mass. . . .

6.9

7-3

7.8

8.4

9.0

9-7

10.3

10-9

"•5

11.9

12.2

Provincetown, Mass.

7.2

7-7

8.2

8.9

9.6

10.2

10.9

"•5

I2.O

12.4

12.6

Providence, R. I. . .

6-5

6-5

6.7

7-3

8.2

9-2

9.8

10.2

10.8

1 1.6

12. 1

Hartford, Conn. . .

S-2

5-2

5-5

5-8

6.2

6.8

74

8.0

8.6

9.2

9.8

New Haven, Conn. .

4-7

4-7

5-°

54

5-9

6.6

7-3

8.1

8.8

9-5

IO.I

Nantucket, Mass.

6.8

7-2

7-7

8.7

9.0

9.6

IO.I

10.6

I I.O

"•3

II.5

Cold Spring Harbor,

N. Y

4-7

4-9

S-2

5-6

6.1

6.7

7-3

7-9

8.4

8.9

9-3

New York, N. Y. .

4-3

4-5

4.6

S-o

5-6

6-3

6.9

74

7-9

8.5

9.1

Bethlehem, Pa. . .

2.6

2-3

2-3

2-5

2.9

3-5

4.2

5-°

5-8

6.7

74

Huntingdon, Pa. . .

I.O

0.8

0.9

i.i

!-5

2.1

2.7

3-5

4.2

4.9

5-6

New Brunswick,

N.J

2-5

2-9

34

4.0

4-7

5-3

6.0

6.6

7-i

7-5

7-9

Jamesburg, N. J. . .

3-1

3-i

34

3-8

4-3

4-9

5-6

6-3

7.0

7.6

8.2

Harrisburg, Pa. . .

0.0

o-3

0.8

1.4

2.2

2.9

3-7

44

5-o

5-5

5-8

Hatboro, Pa. . . .

1.8

2.O

2-5

3-o

3-7

4-3

5.0

5-7

6.7

7.6

8.0

Philadelphia, Pa. .

2.1

2.2

2.4

2.9

34

4.1

4-7

54

6.2

7.0

7-7

Chambersburg, Pa. .

-o-3

—0-5

—0-3

O.2

o-7

1.4

2.O

2-7

34

4.2

5-°

Baltimore, Md. . .

0.6

0-7

0.9

1.2

1-7

2.3

2-9

3-5

4.2

4-7

5-2

Washington, D. C. .

0.2

O.2

0.4

0-7

i.i

i.o

2-5

2-9

3-7

4-3

4.6

Cape Henlopen, Del.

0.8

0-9

i.i

!-5

2.O

2.6

2.4

4.1

4.9

5-6

6.2

Williamsburg, Va. .

— O.2

—o-3

— O.2

0.0

0.4

0.9

1.5

2.1

2-7

3-3

3-9

Cape Henry, Va. .

0.2

O.2

O;2

0.5

0.8

i-3

1.8

2-4

2-9

3-5

. 3-9

New Berne, N. C. .

— 1.9

— 1.9

—1.6

— 1.2

—0.7

0.2

o-5

I.I

i-7

2-3

2.7

Milledgeville, Ga. .

—S-o

—5-3

-5.6

-5-6

—5-5

—5-3

— s-°

—4-5

—4.0

-34

—2.7

Charleston, S. C.

—4-5

—4-4

—4.0

-3-6

—3-°

—2.4

—i-7

— i.i

—0.4

O.I

o-5

Savannah, Ga. . .

—47

—4-7

—4-2

-3-8

—3-3

—2-7

— 2.1

— 1.4

—0.9

Paris, France . . .

22.6

22.3

21.9

21.8

21.8

20.9

19.1

17-5

16.6

15.1

St. George's Town,

B. I

m

60

60

60

71

*7 C

7 O

8 d

Rio de Janeiro, Bra-

u.y

u.y

u.y

"

/•b

/•y

o.^

zil ..... .^

C A

A C

7 A

—-2.2

f> f\

f\ A

1.8

31

A C

c»

J'T

4-5

J-4

u.y

O.4

•*

4- 5

5-°

* This table gives the secular variation of the declination since the year 1800 for a series of stations in the Eastern
States and adjacent countries. Compiled from a paper by Mr. Schott, forming App. 7, Report of the United States
Coast and Geodetic Survey for 1888. The minus sign indicates eastern declination.

SMITHSONIAN TABLES.

114

TABLE 1 28.

TERRESTRIAL MAGNETISM.

Secular Variation of the Declination. — Central Stations.*

Station.

1800

1810

1820

1830

1840

1850

I860

1870

1880

1890

1900

York Factory, Brit.

N. A

O.I

—2.5

—4-7

-6-5

-7-8

-8-5

—8.6

—8.2

—7-2

-5-6

-3-6

Fort Albany, Brit.

N. A

134

I 2. 1

10.9

IO.O

9-3

8.9

8.8

9.1

9.6

10.3

11.4

Duluth, Minn. .

j

Superior City, Wis.

r-

~

—

~*

*"*

-9.8

— IO.O

— IO.I

— IO.I

—9.9

-9-5

Sault Ste. Marie,

Mich

— o. t;

— O.Q

— i.i

—1.6

— i.o

—0.8

— O.T

O.2

0.8

I.C

2.2

Pierrepont Manor,

j

v.y

J

j

N. Y

_

_

2.6

3.0

1-5.7

A. e

C.A

6.^

7.2

8.0

8.8

Toronto, Canada .

_

-

0.8

J /

'•3

T" .}

1.6

j"r

2.2

3

2-7

/

3-6

4.1

4.8

Grand Haven, Mich.

-

-

—5.0

—5.2

—5-2

—4-9

—4-4

—2.7

—i-5

Milwaukee, Wis. .

-

-

—7-4

-6.9

6.2

—5-4

—4-5

-3-6

Buffalo, N. Y. . .

O.2

0.2

0.4

0.8

i-3

2.O

2.8

3-7

4-5

5-3

6.0

Detroit, Mich. . .

—3-2

— 3-1

— 2.9

—2-5

2.1

—1.6

I.O

—0.4

O.I

0.6

0.9

Ypsilanti, Mich.

—4-1

-3-6

—3-o

2.2

—1.4

—0.6

O.2

0.9

i-5

1.9

Erie, Pa

— °-5

-o-5

—0.4

0.4

0.9

1.6

2-3

3-°

3-6

4.2

Chicago, 111. . . .

—6.2

-6-3

—6.2

—6.0

-5.6

—5-1

-4.6

—4.0

—3-3

Michigan City, Ind.

-

-

-

-5.6

—5-4

—5-0

-4.6

—4.0

—3-5

—2.9

—2-3

Cleveland, Ohio

—1.9

—i-7

— 1-5

— i.i

—0.6

—O.I

0.4

0.9

1.4

1.9

2-3

Omaha, Neb. . .

—12.5

—12.6

— 12.6

—12.4

— 12.0

—11.5

— 10.9

IO.2

—9-5

-8-7

Beaver, Penn. . .

— I.I

—'•3

— 1-2

— I.I

—0.8

— o-3

O.2

0.9

!-5

2.2

2.8

Pittsburg, Pa. . .

-

-

-

O.2

0.7

i-3

1.9

2-5

3-1

3-5

Denver, Colo. . .

-

-

—

-

-

—'5-1

—14.9

—14.5

—14.1

Marietta, Ohio . .

_

—2.9

—2.8

—2.7

—2-3

—1.9

— !-3

—0.6

O.I

0.8

1.4

Athens, Ohio .

—4.1

—4.1

—3-9

-3-6

— 3-1

—2.6

2.O

—1.4

—0.7

— O.I

0.4

Cincinnati, Ohio .

—4-9

—5.0

—5.0

-4-8

—4-5

—4.1

-3-6

—3-0

—2.4

—1.8

—'•3

St. Louis, Mo. .

—8.9

—8.6

—8.2

—7-7

—7-i

-6.4

-5.6

—4-9

Nashville, Tenn. .

—

-

-6.7

-6.9

—6.9

-6.7

-6-3

-5-8

-5-1

—4-4

-3-6

Florence, Ala. . .

-

-6-5

-5-6

-6.5

-6.4

—6.1

— 5-7

—5-3

-4.8

—4-3

-3-8

Mobile, Ala. . .

-5-8

-6-3

-6.7

—7.0

—7-1

—7.0

— 6.7

-6.4

-5-8

—5-2

-4.6

Pensacola, Fla. . .

—6.8

—7.2

—7-5

-7-6

—7-4

—7.1

—6.6

—6.0

—5-3

-4-6

-3-8

New Orleans, La. .

—7-i

-7.6

—8.0

-8.1

— 8.2

—8.0

—7-7

—7-2

-6.6

—5-2

San Antonio, Texas

—

-

-9.8

— IO.I

—10.3

— 10.2

IO.I

-9-7

—9-3

—8.7

—8.1

Key West, Fla. .

-

-

-6.9

-6-5

-6.0

—5-5

-4.8

—4-2

-3-6

—3-°

—2.4

Havana, Cuba . .

—7.0

-6.9

—6.6

-6-3

-5-8

—5-3

-4.8

—4.2

-3-6

—3-0

—2-5

Kingston, Port

Royal, Jamaica .

—6.0

-5-8

—5-5

—5-i

—4-7

—4-3

-3<8

—3-3

—2.9

—2-5

2.1

Barbadoes, Car. Isl.

—3-4

—3-0

—2-5

2.O

— 1-5

—0.9

—0.4

O.I

o-5

0.9

1.2

Panama, New Gra-

nada ....

—7-9

-7-8

-7.6

—7-3

—7.0

-6.7

-6-3

—5-9

—5-5

—5-0

-4.6

* This table gives the secular variation of the declination since the year 1800 for a series of stations in the Central
States and adjacent countries. The minus sign indicates eastern declination. Reference same as Table 127.

SMITHSONIAN TABLES.

TABLE 129.

TERRESTRIAL MAGNETISM.

Secular Variation of the Declination. — Western Stations. •

Station.

1800

1810

1820

1830

1840

1850

1860

1870

1880

1890

1900

o

o

o

o

o

o

o

o

o

o

o

Acapulco, Mex. ....

7 6

8.1

8.c

8 7

80

80

87

8.5

8.1

7 6

7T

Vera Cruz, Mex

/ w

8.6

9.0

" J

9-3

**•-/

9-3

u.y
9-2

o.y
8.9

o./

8.4

7.0

/.u
6.2

.,1

5-3

City of Mexico, Mex. . .

7-5

7-9

8.2

8-5

8.6

8.6

8.5

84

8.1

7.8

7-4

San Bias, Mex. .....

7-i

7.8

8.4

8.9

9-3

9.4

9.4

9-3

9.0

8-5

7-9

Cape San Lucas, Mex. . .

6.2

6.9

7.6

8-3

8.8

9.2

9-5

9.6

9.6

9-4

9.0

Magdalen a Bay, L. Cal. .

6.6

7-4

8.2

8.9

9-5

IO.O

10.3

10.5

10.5

10.3

IO.O

Ceros Island, Mex. . .' .

9.0

9.8

10.5

II.O

"•5

1 1.8

12.0

12.0

11.9

1 1.6

II.2

El Paso, Mex. . ,. .

-

12.3

12.5

12.4

12.3

11.9

11.4

San Diego, Cal. . . .: .

IO.3

10.8

114

II.O

12.7

12.7

I7.O

I T..2

J-3-7

1 1 1

17 •»

Santa Barbara, Cal. . . .

• w\?

n.6

12.3

* *«t

12.9

V

13-4

*•• o

*3-9

**/

14-3

*o
14.6

*O*r

14.8

JO
14.8

1 j-j
14.8

1 J--
14.6

Monterey, Cal. ....

12.3

12.9

13.4

r3-9

14.4

14.9

J5-3

1 6.6

15-9

1 6.0

16.1

San Francisco, Cal. . . .

13.6

14.1

14.5

15.0

iS-4

15.8

16.1

16.3

16.5

16.6

1 6.6

Cape Mendocino ....

'5-1

15.6

16.0

16.5

16.9

17.2

17.4

17.6

17.7

17.7

17.6

Salt Lake City, Utah . .

-

-

16.0

16.4

1 6.6

1 6.6

16.3

!5-7

Vancouver, Wash. . . .

16.8

'7-5

18.2

18.9

19.6

20.2

20.6

20.9

21.0

2I.O

20.8

Walla Walla, Wash. . .

_

_

_

_

_

20-4

20.8

2I.O

21. 1

21.0

20.8

Cape Disappointment,

Wash

17.7

18.2

187

IO 2

19.8

2O 1

20.8

21.2

21.6

21.8

2T O

Seattle, Duwanish Bay,

/ /

!<_»./

ly. ^

•**J

f*t'y

Wash

_

_

_

_

_

21. 1

21.8

22.1

22. T

22.2

22.1

Port Townsend, Wash.

18.1

1 8.8

19.6

20-3

20.9

"1-O
21.4

21.7

21.8

21-5

21. 1

Nee-ah Bay, Wash. . . .

18.3

18.9

19.6

20-3

21.0

21.6

22.1

22.5

22-7

22.7

22.6

Nootka, Vancouver Island
Captain's and Iliuliuk Har-

19.6

20. i

20.7

21.3

22.O

22.5

23.0

23-5

23.8

23-9

24.0

bors, Unilaska Island .

19-3

19.6

19.7

19.8

19.7

19.7

19-5

19-3

18.9

1 8.6

18.2

Sitka, Alaska

26.4

27.1

278

28.1

28.7

2Q.O

20. 1

2Q.O

28.8

28.4

^7 O

St. Paul, Kadiak Island .

*\Mf

25-5

*/ *A

26.4

*/ •*J

27.0

•*"O

27-3

*'«-'•/

27.4

— y.w

27.1

^.y. «

26.6

^.y.w

25-9

25.0

23-9

"/•y
22.7

Port Mulgrave, Yakutat

Bay, Alaska

27.8

29.2

7O A

11 2

11 7

->i 8

11. A

7O.7

2O 7

28.4

26.8

Port Etches, Alaska . . .

*/•**

27.8

29-3

Jw"+

3°-4

ji.i
31.2

J1'/
31.6

O*'°

3!-5

J"1

31.0

J***/

30.1

*yv

28.8

27-3

25-5

Port Clarence, Alaska . .

-

26.6

27.0

26.9

26.4

25-6

24.4

22.9

21.2

'9-5

Chamisso Island, Kotze-

bue Sound

_

_

ii. i

11 1

•31. 1

-?o t;

29.6

28 1

26.8

2C ^

->-j r

Petropavlovsk, Kamchatka,

i}***

J1-J

Jl *

JUO

mf'J

•y«

~OO

Siberia

c 7

52
.^

A 7

A T

1 A

2 7

2.1

1 r

I .O

O 7

O £

0 •/

*•/

*T *

j-4

••/

1-J

**/

(J.ij

* This table gives the secular variation of the declination since the year 1800 for a series of stations in the Western
States and adjacent countries. The declinations are all east of north. Reference same as Table 127.

SMITHSONIAN TABLES.

116

TABLE 13O.

TERRESTRIAL MAGNETISM.

Agonic Lines.*

The line of no declination is moving westward in the United States,
and east declination is decreasing west of, while west declination is
increasing east of the agonic line.

Lat. N.

Longitudes of the agonic line for the years —

1800

1850

1875

1890

o

0

o

o

o

25

-

-

-

75-5

3°

-

-

-

78.6

35

-

76.7

79.0

79-9

6

75-2

77-3

79-7

80.5

7

76-3

77-7

80.6

82.2

8

76.7

78.3

81.3

82:6

9

76.9

78.7

81.6

82.2

40

77-o

79-3

81.6

82.7

i

77-9

80.4

81.8

82.8

2

79.1

81.0

82.6

83-7

3

179-4

81.2

83.1

84-3

4

79-8

-

83.3

84.9

45

1 -

-

83.6

85.2

6

-

-

84.2

84.8

7

-

-

85.1

854

8

-

-

86.0

85-9

9

—

—

86.5

86.3

* Reference same as Table 127.

SMITHSONIAN TABLES.

I!/

TABLE 131 .

TERRESTRIAL MAGNETISM.

Date of Maximum East Declination.*

This table gives the date of maximum east declination for a number of
stations, beginning at the northeast of the United States and ex-
tending down the Atlantic coast to New York and west to the Pacific.

Station.

Date.

Halifax.t N. S. . . .

1714

Eastport, Me. . . ' .

17 C7

Bangor, Me

1 1 JJ
1774

Portland, Me. ....

1779

Boston, Mass. ....

1780

New Haven, Conn.

I8OO

New York, N. Y

1784

Jamesburg, N. J.

1802

Philadelphia, Pa

1802

Pittsburg, Pa. ....

1808

Cincinnati, Ohio ....

l8l4

Florence, Ala. ....

1821

l822

Nashville, Tenn

1834

Chicago, 111. .....

I83I

Denver, Colo. ....

1839

Salt Lake, Utah ....

1873

Vancouver, Wash.

I883

Cape Mendocino, Cal. . «

1886

San Francisco, Cal. . . .

1893

* Reference same as Table 127.

t The opposite phase of maximum west declination is now located
at Halifax.

SMITHSONIAN TABLES.

118

TABLE 132.

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 grammes per
sq. cm.

Pressure
in pounds per
sq. inch.

Inches of
Hg.

Pressure
in grammes per
sq. cm.

Pressure
in pounds per
sq. inch.

1

I3-S956

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

latop

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

I-353632

7

241.730

3.438218

8

108.7648

1.547008

8

276.262

3.929392

9

122.3604

1.740384

9

3<o-795

4.420566

10

I35-9560

I-933760

10

345-328

4.911740

Cms. of
HjO.

Pressure
in grammes per
sq. cm.

Pressure
in pounds per
sq. inch.

Inches of
H,O.

Pressure
in grammes per
sq. cm.

Pressure
in pounds per
sq. inch.

1

I

0.0142234

1

2-54

0.036227

2

2

0.0284468

2

5.08

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

i5-24

0.216764

7

7

0.0995658

7

17.78

0.252892

8

8

0.1137872

8

20.32

0.289019

9

9

0.1280106

9

22.86

0.325147

10

10

0.1422340

10

25.40

0-361274

SMITHSONIAN TABLES.

119

TABLE 133.

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 o£
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

IOO

.0172

17.0

.00154

420

.0684

!5°

.0258

«7-5

.00158

43°

.0700

2OO

•°345

18.0

.00163

440

.0716

2SO

.0431

18.5

.00167

45°

.0732

300

•0517

19.0

.00172

460

.0749

35°

.0603

19.5

.00176

470

.0765

;. 480

.0781

400

0.0689

200

0.00181

49°

.0797

45°

•0775

20.5

.00185

500

.0861

2I.O

.00190

500

0.0813

520

.0898

21-5

.00194

5W

.0830

540

•0934

22.O

.00199

520

.0846

560

.0971

22-5

.00203

53°

.0862

580

.1007

23.0

.00208

540

.0878

23-5

.00212

55°

.0894

GOO

0.1034

560

.0911

610

.1051

24.0

0.00217

570

.0927

620

.1068

24-5

.00221

i 580

•0943

630

.1085

25.0

.00226

i, 590

.0959

640

.1103

25-5

.00231

650

.1120

26.0

.00236

600

0.0975

660

•"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

73°

.1258

29.4

.00267

690

.1121

29.6

.00268

740

0.1275

29.8

.00270

700

O.II37

75°

.1292

30.0

.00272

710

•"54

760

.1309

j 720

.1170

770

, -1327

30.2

0.00274

73°

.1186

780

•1344

3°-4

.00276

740

.I2Q2

790

.1361

30.6

.00277

75°

.I2r8

800

•1378

30.8

.06279

i 760

•I235

1

31.0

.00281

! 77°

.1251

850

0.1464

31.2

i .00283

780

.1267

900

•1S51

3.M

.00285

i 790

.1283

950

.1639

31.6

.00287

8OO

.1299

IOOO

.1723

. * 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 an<} 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 temperature. The above tables of values of

lemperaiuie ui «tpfjiuAiiii<ttciy ma .5 r., DCGBUVC ifi me idci
at 62° F., while mercury has the standard density at 32° F.

EXAMPLE. — A barometer having a brass scale gave t/ = 76$ mm. at 25° C. ; required, the corresponding
reading at o° C. Here the value of a is the mean of .1235 ar>d .1251, or .1243; .'. a (t1 — t) = .1243 X 25 = 3.11.
Hence //0 = 765 — 3.11 — 761.89.

N. B. — Although o 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 determined by experiment.

SMITHSONIAN TABLES.

1 2O

TABLE 134.

CORRECTION OF BAROMETER TO STANDARD GRAVITY.

Height

Observed height of barometer in millimetres.

above sea

level in

metres.

400

450

500

55°

600

650

700

750

800

IOO

.014

.015

.016

200

.028

.030

.032

300

Correction in millime-

.041

.044

.047

400

tres for elevation above

•°55

•°59

.063

500
600

sea level in first column
and height of barometer
in top line.

.064

.077

.068
.082

.oy "?

.078

7OO

.OOX)

.096

.102

800

.103

.109

.117

900

.115

.123

•T3'

IOOO

.108

.118

.128

•137

.146

I IOO

.118

.130

.141

.150

1200

.129

.142

•154

.164

1300

.140

•153

.166

.178

I4OO

•'51

.165

.I79

.191

I5OO

.147

.162

.176

.191

.205

I600

•' 57

.172

.188

.204

I7OO

.167

.183

.200

.217

l8oo
I90O
2OOO
2IOO
22OO
2300
24OO

.176
.185
.194
.203
.212

•177
.187
.196
.206
.216
.226
.236

.194
.204
•215
.226

•237
.248

•259

.212
.224

•235
.247

•259
.271
.283

•230
.242
.255

i-345
.291

•340
.292
.244
.196
.149

1.245
1.203
.162
.I2O
.088
.046
.004

15000
14500
14000
13500
13000
12500

12000

25OO

.195

.220

•245

.270

•295

•237

.101

.962

II5OO

27OO
2800
20X)0
3OOO
3IOO
3200

•203
'211
.219
.227
•235
•243
.251

.229
.238

•247
.256
.265
.274
.283

•255
.265

.294

I.O5O

•984
.918

•3IS

.196
.136
.076
.Ol6

•957

.184
.130
.076

.022
.969

•915
.861

•053
.005

•957
•909
.861
.813
•765

.920
.879
•837

•795
•753

I IOOO
10500
lOOOO

9500

9000
8500
8000

3300
3400

•259
.267

.292
.201

1.077
1.005

.787

.721

.897
•837

.807

•753

7500

7000

35°°

^83

•3°9

•934
.862

.655
.789

•777
.718

.700

6500
6000

3700
3800
3900
4OOO

.291
.299
•307
•314

•779
.701
.623

.790
.718
.646
•574

•724
.658

•592
.526

.658
•598

5500

5000

4500

4000

•5°3
.419

•545
.467

•389

•503
•43 !
•359

.461

•395

Corrections in hundredths
of an inch for elevation above
sea level in last column and

3500
3000
2500

.269

•335
•251

•233

.287
.215

height of barometer in bottom
line.

2OOO
I5OO

.192

.179

.167

•155

IOOO

.096

.OOX)

.084

.078

500

32

3°

28

26

24

22

20

18

16

14

Height

above sea

level in

Observed height of barometer in inches.

feet.

SMITHSONIAN TABLES.

121

TABLE 135.

REDUCTION OF BAROMETER TO STANDARD GRAVITY.*

Reduction to Latitude 45 . — English Scale.

N. B. From latitude o" (o 44° the correction is to be subtracted.
From latitude 90° to 46° the correction is to be added.

Latitude.

Height of the barometer in inches.

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°

90°

0.051

0.053

0.056

0.059

0.06 1

0.064

0.06/

0.069

0.072

0.074

0.077

0.080

5

85

0.050

0.052

0-055

0.058

O.o6o

0.063

0.066

0.068

O.O7I

0-073

0.076

0.079

6

84

.049

.052

•055

•057

.060

.062

.065

.068

.070

•073

.076

.078

7

83

.049

.052

•054

•057

•059

.062

.065

.067

.070

.072

•075

.077

8

82

.049

.051

•054

.056

•059

.061

.064

.067

.069

.072

.074

.077

9

81

.048

.051

•°53

.056

.058

.061

.063

.066

.068

.071

•073

.076

10

80

0.048

0.050

0-053

0.055

0.058

O.o6o

0.063

0.065

0.068

0.070

0.073

0.075

ii

79

.047

.049

.052

.054

•057

•°59

.062

.064

.067

.069

.072

•074

12

78

.046

.049

.051

•054

.056

.058

.061

.063

.066

.068

.071

•073

'3

77

•045

.048

.050

•053

•055

.057

.060

.062

.065

.067

.069

.072

14

76

.045

.047

•049

.052

•054

.056

.059

.06:

.063

.066

.068

.071

15

75

0.044

0.046

0.048

0.051

0.053

0.055

0.058

O.O6O

0.062

0.065

0.067

0.069

16

74

•043

•045

•047

.050

.052

•054

.056

•059

.061

.063

.065

.068

17

73

.042

•044

.046

.049

.051

•053

•055

•057

.060

.062

.064

.066

18

72

.041

•043

•045

.047

.050

.052

•054

.056

.058

.060

.062

.065

'9

7'

.040

.042

.044

.046

.048

•050

.052

.055

.057

.059

.061

.063

20

70

0.039

0.041

0.043

0.045

0.047

0.049

0.051

0-053

0.055

0.057

0.059

0.06 1

21

69

.038

.040

.042

•044

.045

•047

.049

.051

•053

•055

•057

•°59

22

68

.036

.038

.040

.042

.044

.046

.048

.050

.052

•054

.056

•057

23

67

•°35

•037

•039

.041

•043

.044

.046

.048

.050

.052

.054

•055

24

66

•034

.036

•037

•039

.041

•043

.045

.046

.048

.050

.052

•053

25

65

o-033

0.034

0.036

0.038

0.039

0.041

0.043

O.O44

0.046

0.048

0.050

0.051

26

64

031

•033

•034

.036

•038

•039

.041

•043

.044

.046

.048

.049

27

63

.030

.031

•033

•034

.036

.038

•039

.041

.042

.044

•045

.047

28

62

.028

.030

.031

•033

•034

.036

•037

•039

.040

.042

•043

•045

29

61

.027

t.028

.030

.031

.032

•034

•035

•037

.038

•039

.041

.042

30

60

0.025

0.027

0.028

0.029

0.031

0.032

0-033

0.035

0.036

0.037

0.039

O.040

31

59

.024

.025

.026

.027

.029

.030

.031

.032

•034

•°35

.036

•037

32

58

.022

.023

.025

.026

.027

.028

.029

.030

.032

•033

•034

•035

33

57

.021

.022

.023

.024

.025

.026

.027

.028

.029

.030

.031

.032

34

56

.OI9

.020

.O2I

.022

.023

.024

.025

.026

.027

.028

.O2Q

.030

35

55

0.017

0.018

O.Oig

O.O2O

O.O2I

O.O22

0.023

O.O24

O.O25

0.025

O.O26

O.027

36

54

.Ol6

.016

.017

.018

.019

.020

.O2I

.021

.022

•023

.024

.025

37

53

.OI4

.015

.015

.Ol6

.017

.018

.018

.OI9

.O2O

.O2I

.021

.022

38

52

.012

.013

.014

.OI4

.015

.015

.Ol6

.017

.017

.018

.Dig

.019

39

5i

.Oil

.Oil

.OI2

.OI2

.013

.013

.014

.OI4

.015

.015

.Ol6

.017

40

50

O.OO9

0.009

O.OIO

O.OIO

O.OII

O.OII

O.OI2

O.OI2

O.OI2

0.013

0.013

O.OI4

4'

49

.007

.007

.008

.008

.009

.009

.OO9

.OIO

.OIO

.OIO

.Oil

.Oil

42

48

.OO5

.006

.006

.006

.006

.007

.007

.007

.008

.008

.008

.008

43

47

.OO4

.004

.004

.004

.004

.004

.005

.OO5

.005

.005

.005

.co6

44

46

;002

.002

.002

.002

.002

.002

.002

.002

.003

.003

.003

.003

SMITHSONIAN TABLES.

* " Smithsonian Meteorological Tables," p. 58.
122

TABLE 136.
REDUCTION OF BAROMETER TO STANDARD GRAVITY.*

Reduction to Latitude 45°. —Metric Scale.

N. B. — From latitude o° to 44° the correction is to be subtracted.
From latitude 90° to 46° the correction is to be added.

Latitude.

Height of the barometer in millimetres.

520

S6o

600

620

640

660

680

700

720

740

760

780

mm.

mm.

mm.

mm.

mm.

mm.

mm.

mm.

mm.

mm.

mm.

nun.

0°

90°

I.38

1.49

1. 60

1.65

1.70

I.76

1.81

1.86

1.92

1.97

2.O2

2.08

5

85

1.36

1.47

•57

1.63

.68

x-73

1.81

1.84

1.89

1-94

•99

2.04

6

84

J-35

1.46

•56

i. 61

•67

1.72

1.78

1.82

1.87

i-93

.98

2.03

7

83

i-34

i-45

•55

.60

•65

1.70

1.77

1.81

1.86

1.91

.96

2.01

8

82

•54

•59

.64

1.69

1.76

1.79

1.84

1.89

•94

2.OO

9

81

1.32

1.42

•52

•57

.62

1.67

1.74

i-77

1.82

1.87

.92

1-97

10

80

1.30

1.40

.50

•55

.60

1.65

1.70

i-75

i. 80

1.85

.90

1-95

ii

79

1.28

1.38

.48

•53

•58

1.63

1.68

1.73

1.78

1.83

.88

'•93

12

78

1.26

1.36

.46

•51

.56

i. 60

1.65

1.70

1.75

i. 80

•85

1.90

13
14

77
76

1.24

1.22

i-34
1.32

•44
.41

.48
.46

•53

•5°

1-58

'•55

1.63
i. 60

1.67
1.65

1.72
1.69

i-77
1-74

.82
•79

1.87
1.83

15

75

1. 2O

1.29

•38

•43

.48

1.52

i-57

1.61

1.66

1.71

•75

i. 80

16

74

I.I7

1.26

•35

.40

•44

1.49

t-54

1-58

1.63

1.67

•72

1.76

17

73

*•*&

1.24

•32

•37

.41

1.45

1.50

i-54

i-59

1.63

.68

1.72

18

72

1. 12

1. 21

.29

•34

•38

1.42

1.46

I-5I

'•55

i-59

.64

1.68

19

I.O9

I.I7

.26

•3°

•34

1.38

i-43

1.47

1.51

i-55

•59

1.64

20

70

1. 06

I.I4

.22

.26

•3i

r-35

i-39

i-43

1.47

1.51

i-55

i-59

21

69

1.03

I. II

.19

•23

•27

1-31

i-35

1-38

1.42

1.46

1.50

1.54

22

68

I.OO

1.07

•15

.19

.23

1.26

1.30

i-34

1.38

1.42

.46

1.49

23

67

0.96

I.O4

.11

.18

1.22

1.26

1.29

1.33

'•37

.41

1.44

24

66

•93

I.OO

1.07

.10

.14

1.18

I.2I

1.25

1.28

1.32

•35

i-39

25

65

0.89

0.96

1.03

i. 06

.10

I-I3

1.16

I.2O

1.23

1.27

•3°

1-33

26

64

•85

•92

0.98

i. 02

.05

1. 08

i. ii

I-I5

1.18

I.2I

•25

1.28

27

63

.81

.88

•94

0.97

.00

1.03

i. 06

I.IO

"3

1. 16

.19

1.22

28

62

•77

•83

.89

.Q2

0.95

0.98

I.OI

1.04

1.07

I.IO

.13

1.16

29

61

•73

•79

•85

.87

.90

•93

0.96

0.99

i. 02

1.04

.07

I.IO

30

60

0.69

0-75

0.80

0.83

0.85

0.88

0.91

0.94

0.96

0.98

I.OI

1.04

31

59

•65

.70

•75

•77

.80

.82

•85

.87

.90

.92

0.95

0.97

32

58

.61

•65

.70

.72

•75

•77

•79

.82

.84

.86

.89

.91

33

57

.56

.61

.65

.67

.69

.71

•74

.76

•78

.80

.82

.84

34

56

.52

•56

.60

.62

.64

.66

.68

.70

.72

•74

.76

.78

35

55

0.47

0.51

o-55

0.56

0.58

0.60

0.62

0.64

0.66

0.67

0.69

0.71

36

54

•43

.46

•49

.51

•53

•54

•56

•58

•59

.61

•63

.64

! 37

53

-38

.41

•44

•45

•47

.48

•5°

•51

•53

•54

.56

•57

38

52

•33

.36

•39

.40

.41

•43

•44

•45

.46

.48

•49

.50

39

51

.29

•33

•34

•35

•37

•38

•39

.40

.41

.42

•43

40

50

0.24

0.26

0.28

0.29

0.30

0.31

0.31

0.32

0.33

0.34

o-3<;

0.36

41

49

.19

.21

.22

•23

.24

.24

•25

.26

•27

.27

.28

•29 ,

42

48

.14

.16

•17

•17

.18

.18

.19

.19

.20

.21

.21

.22

43

47

.10

.10

.11

.12

.12

.12

.13

.13

.13

.14

.14

.14

44

46

.05

•05

.06

.06

.06

.06

.06

.07

.07

.07

.07

SMITHSONIAN TABLES.

* " Smithsonian Meteorological Tables," p. 59.
123

TABLE 137.

CORRECTION OF THE BAROMETER FOR CAPILLARITY.*

i. METRIC MEASURE.

HEIGHT OF MENISCUS IN MILLIMETRES.

Diameter
of tube

04

0.6

0.8

1.0

1.2

1.4

1.6

1.8

in mm.

Correction to be added in millimetres.

4

0.83

1.22

i-54

1.98

2-37

_

_

_

5

•47

0.65

0.86

I.IQ

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

"3

8

-

.20

.29

•3!

.46

•56

•65

o-77

9

-

•'5

.21

.28

•33

• 40

.46

•52

10

-

-

•!5

.20

.25

.29

•33

•37

ii

—

-

.10

.14

.18

.21

•24

•27

12

-

-

.07

.10

•r3

•'5

.18

.19

J3

.04

.07

.10

.12

•'3

.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 hundredths of an inch.

•J5

2.36

4.70

6.86

9-23

11.56

_

_

_

.20

1. 10

2.20

3.28

4-54

5-94

7.85

-

-

•25

o-55

1.20

1.92

2.76

3.68

4.72

5.88

-

•3°

•36

o-79

1.26

1.77

2.30

2.88

3-48

4.20

•35

•51

0.82

i-i5

1.49

1.85

2.24

2.65

.40

-

.40

.61

0.81

i. 02

1.22

1.42

1.62

•45

-

•32

•Si

0.68

0.83

0.96

1-15

•50

-

-

.20

•35

•47

.<6

.64

0.71

•55

.08

.20

•31

.40

•47

•52

* 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. 1867). The second table has been calcu-
lated from the same data by conversion into inches and graphic interpolation.

A number of tables, mostly based on theoretical formulae and the capillary constants of mercury in glass tubes in
air and vacuum, were given in the fourth edition of Guyot's Tables, and may be there referred to. They are not
repeated here, as the above is probably more accurate, and historical matter is excluded for convenience in the use
of the book.

SMITHSONIAN TABLES.

124

TABLE 138.

ABSORPTION OF CASES BY LIQUIDS.*

ABSORPTION COEFFICIENTS, at, FOR GASES IN WATER.

Temperature

Centigrade.

1

Carbon
dioxide.
C02

Carbon
monoxide.
CO

Hydrogen.
H

Nitrogen.

Nitric
oxide.
NO

Nitrous
oxide.
N2O

Oxygen.

O

1.797

0-0354

O.O2IIO

0.02399

0.0738

I

305

0.04925

5

1.450

•03 * 5

.O2O22

.02134

.0646

I

095

•04335

IO

I.I

8S

.0282

.01944

.01918

•0571

0.920

.03852

15

I.OO2

.0254

.01875

.01742

•OS'S

0.778

•03456

20

O.9OI

.0232

.Ol8O9

.01599

.0471

0.670

•°3'37

25

0.772

.0214

. -01745

.01481

.0432

-

.02874

30

.0200

.01690

.01370

-

-

.02646

40

0.506

.0177

.01644

.01195

-

-

.02316

50

.Ol6l

.01608

.01074

—

—

.02080

IOO

0.244

.01600

.01011

—

—

.01690

Temperature
Centigrade.
t

Air.

Ammonia.
NH3

Chlorine.
Cl

Ethylene.
C2H4

Methane.
CH4

Hydrogen
sulphide.
H2S

Sulphur
dioxide.
SO2

O

0.0247 !

1174.6

3-036

0.2563

0-05473

4-371

79-79

5

.02179

971-5

2.8o8

•2I53

.04889

96s

67.48

IO

•01953

840.2

2.585

•1837

.04367

3-586

56-65

IS

•01795

756.0

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, at, FOR GASES IN ALCOHOL, C,H5OH.

Centigrade. Carbon

. dioxide.
C02

Ethylene.
C.H4

Methane. Hydrogen.
CH4 H

Nitrogen.

N

Nitric
oxide.
NO

Nitrous
oxide.
N20

Hydrogen Sulphur
sulphide, dioxide.
H2S SO,

o 4-329

3-595

0.5226 0.0692

o. 1 263

0.3161

4.190

17.89 328.6

5 3-891

3-323

.5086 .0685

.1241

.2998

3.838

14.78 251.7

10 3.514

3.086

•4953 -0679

.1228

.2861

3-525

11.99 r9°-3

IS 3-'99

20 2.946
25 2.756

2.882

2-713
2.578

.4828 .0673
.4710 .0667
.4598 .0662

.1214
.1204
.1196

.2748
.2659
•2595

3-215
3-015
2.819

9.54 144.5
7.41 114.5
5.62 99.8

* This table contains the volumes of different gases, supposed measured at o° C. and 76 centimetres' pressure, which
unit 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 & Emo, Raoult, Schonfeld, Setschenow, and Winkler.
The numbers are in many cases averages from several of these authorities.

NOTE. — 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.
I 0,3 = 69 74 79 84 88

According to Setschenow the effect of varying the pressure from 45 to 85 centimetres in the case of carbonic acid in
water is very small.
SMITHSONIAN TABLES.

• 125

TABLE 139.

VAPOR PRESSURES.

The vapor pressures here tabulated have been taken, with one exception, from Regnault's results.
The vapor pressure of Pictet's fluid is given on his own authority. The pressures are in centimetres o(
mercury.

Tem-
pera-
ture
Cent.

Acetone.
C3H60

Benzol.
C6He

Carbon
bisul-
phide.
CS2

Carbon
tetra-
chloride.
CC14

Chloro-
form.
CHC18

Ethyl
alcohol.
C2H60

Ethyl
ether.
C4H100

Ethyl
bromide.
C2H5Br

Methyl
alcohol.
CH40

T 1
Turpen-
tine.
CioH6

—25°

_

_

_

_

_

_

_

4.41

.41

_

— 20

-

•58

4-73

.98

-

•33

6.89

5.92

•63

-

—IS

-

.88

6.16

i-35

-

.51

8-93

7.81

•93

-

—10

—

1.29

7-94

1.85

-

.65

11.47

10.15

'•35

-

—5

-

1.83

10.13

2.48

-

.91

14.61

13.06

1.92

-

0

_

2-53

12.79

3-29

_

1.27

18.44

16.56

2.68

.21

5

—

3-42

16.00

4-32

—

1.76

23.09

20.72

3-69

-

10

-

4-52

19.85

5-6o

-

2.42

28.68

25-74

5-oi

•29

IS

—

5-89

24.41

7.17

-

3-30

35-36

31.69

6.71

20

17.96

7-56

29.80

9.10

16.05

4-45

43.28

38.70

8.87

•44

25

22.63

9-59

36.11

"•43

20.02

5-94

52-59

46.91

1 1. 60

_

3°

28.10

I2.O2

43-46

14.23

24-75

7-85

63-48

5645

15.00

.69

35

34-52

H-93

5r-97

17-55

30-35

10.29

76.12-

67-49

19.20

40

42.01

I8.36

6i-75

21.48

36.93

13-37

90.70

80.19

24-35

i. 08

45

5°-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

53-5°

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

-

60

86.05

39-01

116.45

44-74

75-54

35-02

172.50

151.19

57-99

2.65

65

101.43

46.34

134-75

52.87

88.97

43-69

199.89

174-95

70.73

70

118.94

54-74

155.21

62.11

104.21

54.11

230.49

201.51

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-I9

203.25

84.33

140.76

81.29

302.28

263.86

123-85

6.13

85

186.18

87.46

231.17

97-51

162.41

98.64

343-95

300.06

147.09

90

214.17

101.27

261.91

112.23

186.52

118.93

389-83

339-89

174.17

9.06

95

245.28

116.75

296.63

128.69

213.28

142.51

440.18

383-55

205.17

—

100

279.73

134.01

332-5T

146.71

242.85

169.75

495-33

43I-23

240.51

13.11

I05

3*7-70

i53-i8

372-72

166.72

275.40

201.04

555.62

483.12

280.63

-

no

359-40

174.14

416.41

188.74

311.10

236-76

621.46

539-40

325-96

1 8.60

"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

251.71

569-97

268.24

438.66

374.69

_

736.22

498.05

-

130

566.97

282.43

629.16

299.69

488.51

432-30

-

811.65

569-13

34-90

'35

629.87

3I5-85

692.59

333-86

542.25

496.42

-

892.19

647-93

-

140

697.44

352-07

760.40

370.90

600.02

567-46

-

977.96

733-71

46.40

M5

391.21

832.69

411.00

661.92

645.80

—

-

830.89

-

150

_

433-37

909.59

4 54-3 '

728.06

73L84

_

-

936-I3

60.50

«ss

-

478.65

501.02

798-53

825.92

-

-

68.60

160

-

527-I4

-

55i-3i

873.42

-

—

—

-

77-50

165

-

568.30

-

605.38

952.78

-

-

-

-

-

170

634.07

663.44

SMITHSONIAN TABLES.

126

TABLE 139.

VAPOR PRESSURES.

Tem-
pera-
ture,
Centi-
grade.

Ammonia.
NH3

Carbon
dioxide.
CO3

Ethyl
chloride.
C,HSC1

Ethyl
iodide.
C2H6I

Methyl
chloride.
CH3C1

Methylic
ether.
C,H80

Nitrous
oxide.
N2O

Pictet's
fluid.
64SOo-|-
44CO2 by
weight

Sulphur
dioxide.
SO2

Hydrogen
sulphide.
HtS

—30°

86.61

-

1 1. 02

-

57-9°

57-65

-

58.52

28.75

-

—25

1 10.43

1300.70

14.50

_

71.78

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

443^5

— 15
— 10

I73-6S
214.46

1758.25
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-I3

37-67

-

157.87

'57-25

2457.92

121.60

94-69

706.60

0

3I8-33

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

6i.n

6.92

266.38

262.90

3401.91

193.80

I7I-95

1089.63

15

20

543-34
638.78

3964.69
4471.66

83.26
99.62

8.76
II.OO

3I3-4i
366.69

307-98
358.60

3783-I7
4202.79

226.48
258.40

206.49
246.20

1244.79
1415-15

25

747-7°

5020.73

118.42

13.69

426.74

415.10

4664.14

297-92

291.60

1601.24

30

870.10

5611.90

139.90

16.91

494.05

477.80

5170.85

338.20

343-i8

1803.53

35

1007.02

6244.73

164.32

20.71

569.11

-

6335-98

383.80

401.48

2002.43

40

"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

2495-43

50

^s-Ss

-

257-94

36.40

-

-

-

521-36

622.00

2781.48

55

1721.98

-

266.84

43-32

-

-

-

712.50

3069.07

60

1948.21

—

340.05

51.22

—

-

—

-

812.38

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

-

-

-

-

-t

-

-

90

3810.92

-

704-75

—

—

-

-

—

-

—

95

4219.57

-

785-39

—

—

-

-

-

-

-

100

4660.82

-

872.28

-

-

-

-

-

-

-

SMITHSONIAN TABLES.

127

TABLES 14O-142.

CAPILLARITY. -SURFACE TENSION OF LIQUIDS.*

TABLE 140. —Water and Alcohol in Contact with Air.

TABLE 142. — Solutions ol Salts in
Water, t

Surface tension
in dynes per
centimetre.

Surface tension
in dynes per
centimetre.

o c 1

Surface
tension
in dynes

Salt in
solution.

Density.

Temp.
C.°

Tension
in dynes
per cm.

Temp.

Temp.
C.

Temp.
C.

per cen-
timetre.

Water.

Ethyl
alcohol.

Water.

Ethyl
alcohol.

Water.

BaCl2
fifi

1.2820

1.0497

15-16
15-16

8l.8

77-5

\^a\^\2

^jS11

'9

95-°

0°

75-6

23-5

40°

7O.O

2O.O

80°

64-3

"

1-2773

19

90.2

5

74-9

23.I

45

69-3

19-5

85

63.6

HC1

1.1190

20

73-6

IO

74.2

22.6

5°

68.6

19.1

90

62.9

1.0887

20

74-5

15

20

73-5
72.8

22.2
21-7

55
60

67.8

67-r

18.6
18.2

95

IOO

62.2
61.5

KC1

1.0242

1.1699

20
15-16

75-3
82.8

25
30

35

72.1
71.4
70.7

21.3
20.8
2O-4

65
70

75

66.4
65-7
65.0

17.8

'£'3
16.9

j

MgCl,

I.1OII

1.0463

1-2338
i . 1 694

15-16
15-16
15-16
15-16

1C T (~\

80. i

78.2
90.1
85.2

-u o

NaCl

1.0362
1.1932

20

7<3.O
85.8

"

1.1074

20

80.5

"

1.0360

20

77.6

NH4C1

1.0758

16

84-3

TABLE 141.

— Miscellaneous Liquids in Contact with Air.

"

r-°535

16

81.7

<<

1.0281

16

78.8

Liquid.

SrCl2

1.3114

15-16

85.6

Surface

"

1.1204

15-16

79-4

Temp.
C.°

tension
in dynes

Authority.

K2C08

i .0567
1-3575

15-16
15-16

77-8
90.9

timetre.

"

1.1576

15-16

81.8

"

i .0400

15-16

77-5

Na2CO3

1.1329

14-15

79-3

Aceton . . . .

14.0

25.6

Average of various.

"

1.0605

14-15

77-8

Acetic acid . . .

17-0

30.2

"

"

1.0283

14-15

77.2

Amyl alcohol .

I5.0

24.8

"

KNO3

1.1263

14

78.9

Benzene .

15.0

28.8

"

"

i .0466

14

77-6

Butyric acid . .

I5.0

28.7

"

NaNO3

1.3022

12

83-5

Carbon disulphide

2O.O

3°-5

Quincke.

"

1.1311

12

80.0

Chloroform . . .

2O.O

28.3

Average of various.

CuS04

I-I775

15-16

78.6

Etht

r .

2O.O

18.4

H

"

1.0276

i ;-i6

77.O

Glycerine

17.0

63.14

Hall.

H2S04

1.8278

3

*s

/ / v

63.0?

Hexane . .

o.o

21.2

Schiff.

"

J-4453

15

79-7

"

68.0

14.2

"

"

1.2636

15

79-7

Mercury ....

2O.O

470.0

Average of various.

K2S04

1.0744

15-16

78.0

Methyl alcohol

15.0

24.7

"

"

1.0360

15-16

77-4

Olive oil .

.

2O.O

34-7

"

MgS04

1.2744

15-16

83.2

Petroleum . . .

20.0

25-9

Magie.

"

i. 0680

15-16

77-8

Propyl alcohol . .

5-8

25-9

Schiff.

Mn2SO4

1.1119

15-16

79.1

"

' . .

97.1

18.0

"

"

1.0329

15-16

77-3

Toluol ....

15.0

29.1

"

ZnSO4

1.3981

15-16

833

"

109.8

18.9

"

(i

1.2830

15-16

80.7

Turpentine . . .

2I.O

28.5

Average of various.

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 the
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 o. i4i 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.

t From Volkmann (Wied. Ann. vol. 17, p. 353).

SMITHSONIAN TABLES.

128

TENSION OF LIQUIDS.

TABLE 143. —Surface Tension of Liquids.41

TABLES 143-145.

Liquid.

Specific
gravity.

Surface tension in dynes per cen-
timetre of liquid in contact with —

Air.

Water.

Mercury.

1.0

13-543
1.2687
1.4878
0.7906
0.9136
0.8867

9-7977

I.IO

1.1248

75-o
5 '3-o
30-5
(3i-8)
(24.1)
34-6
28.8
29.7

(729)
69.9

O.O
392.0
41.7
26.8

18.6
11.5

(28.9)

(392)

(3?7)
(415)
364

31?
241

271
(392)
429

Mercury . . ...

Ethvl alcohol . . . • . . •

Turpentine . ...
Petroleum .....•••
Hydrochloric acid ......
Hyposulphite of soda solution ....

TABLE 144. — Surface Tension of Liquids at Solidifying Point, t

Tempera-

Surface

Tempera-
ture of

Surface

Substance.

solidifi-
cation.
Cent.0

tension in
dynes per
centimetre.

Substance.

solidifi-
cation.
Cent.0

tension in
dynes per
centimetre.

Platinum

2OOO

1691

Antimony

432

249

Gold ....

I2OO

1003

Borax ....

IOOO

216

Zinc ....

360

877

Carbonate of soda

IOOO

2IO

Tin ....

230

599

Chloride of sodium

-

116

Mercury

—40

588

Water ....

o

87.9J

Lead

33°

457

Selenium

217

71.8

Silver ....

IOOO

427

Sulphur

III

42.1

Bismuth
Potassium

•9

1390
37i

Phosphorus .
Wax . .

§

42.0
34-i

Sodium

90

258

TABLE 145. — Tension of Soap Films.

Elaborate measurements of the thickness of soap films have been made by Reinold and
Rucker.|| They find that a film of oleate of soda solution containing i of soap to 70 of
water, and having 3 per cent of KNOs added to increase electrical conductivity, breaks at
a thickness varying between 7.2 and 14.5 micro-millimetres, the average being 12.1 micro-
millimetres. 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 (vide Newton's rings, Table 146).

When the percentage of KNOs is diminished, the thickness of the black patch increases.
For example, KNOs =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 KNO3 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.

* This table of tensions at the surface separating the liquid named in the first column and air, water or mercury
as stated at the head of the last three columns, is from Quincke's experiments (Pogg. Ann. vol. 130, and Phil. Mag.
1871). The numbers given are the equivalent in degrees per centimetre of those obtained by Worthington from
Quincke's results (Phil. Mag. vol. 20, 1885) with the exception of those in brackets, which were not corrected by
Worthington ; they are probably somewhat too high, for the reason stated by Worthington. The temperature was
about 20° C.

t Quincke, " Pogg. Ann." vol. 135, p. 661.

i 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.

II " Proc. R«y. Soc.'^iS??, 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 density is nearly constant. Thus, if 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.

I2Q

TABLE 146.

NEWTON'S RINGS.

Newton's Table of Colors.

The following table gives the thickness in millionths of an inch, according to Newton, of a plate of air, water, and
glass corresponding to the different colors in successive rings commonly called colors of the first, second, third.
' etc., orders.

Color for re-
flected light.

Color for
transmitted
light.

Thickness in

Color for re-
flected light.

Thickness in

millionths of an

millionths of an

0

inch for —

1

6

Color
for trans-
mitted
light.

inch for —

|

i

c

a

to

.S3

rt

a

«

•

*

*

O

£

5

I.

Very black

o-S

0.4

O.2

Yellow . .

Bluish

Black . .
Beginning

White . .

I.O

0.75

0-9

Red.

green

27.1
29.0

20-3
21-7

17-5
18.7

of black .
Blue . .

Yellowish

2.O

l-S

''

3

Bluish red

—

32.0

24.0

20.7

red . .

2-4

1.8

!.

<

IV.

Bluish

White .

Black . .

5-2

3-9

3-4

green .

—

24.0

2 5-

5

22.0

Yellow .

Violet .

5-3

4.6

Green

Red .

35-^

5

22-7

Orange

—

l'.o

6.0

4.2

Yellowish

Red. .

Blue . .

9.0

6.7

5-8

green .

—

36.0

27.0

23.2

Red.

Bluish

II.

Violet .

White .

1 1.2

3-4

7-2

green

3

30.2

26.O

Indigo .

—

12.8

9.6

8.4

Blue .

Yellow .

14.0

10.5

9.0

V.

Greenish

Green .

Red . .

15.1

"•3

9-7

blue . .

Red .

46.0

34-

(

39-7

Yellow .

Violet

16.3

12.2

10.4

Red.

—

52-5

39-4

34-o

Orange

—

17.2

13.0

"•3

Bright red

Blue . .

18.2

J3-7

11.

s

VI.

Greenish

Scarlet .

—

19.7

14.7

12.7

blue . .

—

58.7

46

38.0

Red.

—

65.0

48.7

42.0

III.

Purple .

Green

2 I.O

'5-7

'3-5

Indigo .

—

21. 1

17.6

14.2

VII.

Greenish

Blue .

Yellow .

23.2

17-5

15.

i

blue . .

—

72.0

53-

a

45.8

Green .

Red . .

25.2

18.6

16.2

Reddish

white

—

7'-

0

57-

-

49-4

The above table has been several times revised both as to the colors and the numerical

values. Professors Reinold and Rucker, in their investigations on the measurement

of the

thickness of soap films, found it necessary to make new determinations. They give a shorter
series of colors, as they found difficulty in distinguishing slight differences of shade, but
divide each color into ten parts and tabulate the variation of thickness in terms of the tenth

of a color band. The position in the band at which the thickness is given and the order of
color are indicated by numerical subscripts. For example : RI 5 indicates the red of the first

order and the fifth tenth from the edge furthest from the red edge of the spectrum
thicknesses are in millionths of a centimetre.

The

1

Color.

Posi-

Thick-

1

Color.

Posi-

Thick-

1

Color.

Posi-

Thick-

6

tion.

ness.

6

tion.

ness.

6

tion.

ness.

I.

Red* .

RI c

28.4

Red* .

Rss

76-5

VI.

Green .

G60

141.0

Bluish

Green*

GG B

147.9

II.

Violet .

V25

30-5

red* .

BR35

8l.5

Red . .

RGO

154.8

Blue . .

B25

35-3

Red* .

Re 5

162.7

Green .

G2 5

40.9

IV.

Green .

G4 o

84.1

Yellow *

Y25

45-4

"

G45

89-3

VII.

Green .

G7 o

170.5

Orange *

025

49.1

Yellow

Green*.

G7 5

178.7

Red . .

R26

52.2

green *

YG45

96.4

Red . .

RTO

186.9

Red* .

R46

105.2

Red* .

RV 5

193.6

III.

Purple .

P3 5

55-9

Blue . .

Bso

57-7

V.

Green .

GS o

III.9

VIII.

Green .

Gg o

200.4

Blue* .

B35

60.3

Green*.

Gg 5

II8.8

Red . .

Rg o

211.5

Green .

G3 6

65.6

Red . .

Rso

126.0

Yellow *

Yg 6

71.0

Red* .

Rfi5

'33-5

* The colors marked are the same as the corresponding colors in Newton's table.
SMITHSONIAN TABLES.

130

CONTRACTION PRODUCED BY SOLUTION.*

TABLE 147.

Across the top of the heading are given the formulas of the salt dissolved, its molecular weight (M. W. ), and the den-
sity of the salt, with the authority for that density.

Grammes of
the salt in
loo of water.

Observed
volume.

Calculated
volume.

Per cent
of
contraction.

Grammes of
the salt in
loo of water.

Observed
volume.

Calculated
volume.

Per cent
of
contraction.

KaO.

NaOH.

M. W. = 47.02. Density = 2.656 (Karsten).

M. W. = 39.95. Density = 2. 130 (Filhol ).

(Hager.)

(Schiff.)

4.702

99.88

101-77

1.86

3-995

99-4

101.88

2-43

9.404
14.106
18.808
23-5IO
28.212

99-92
I00.l8
I00.6o
IOI.2O
IO2.OO

103.55
105-32
107.09
108.86
110.64

4.20
4.88
6.06
7.04
7-81

7-990
11.985
15.980

19-975
23.970

99-4
99.6

IOO.2

100.8
101.7

103-75
105.63
107.50
109.38
111.26

4.19

6.79
7.84
8-59

32.914
37.616
42.318
47-02O
70.530

IO2.9O
103.90
104.96

106.10

II2.2O

112.41
114.18
115.96

"7-73
126.59

8.46
9.01
9.80
9.88
"•37

27.965
31.960

35-955
39-950

102.7

103.8

105.0

1 06. 2

"3-4

"3-13
115.01
116.88
118.76
128.14

9.22

9-75
10.17
10.58
11.50

79-934

114.88

130.14

"•73

79.900

121. 2

I37-52

11.87

119.850

138.6

156.28

11.31

159.800
199.750

156.6
174-8

I75-04
193.80

10.54
9.80

KOH.

239.970

193.6

212.56

8.92

M. W. — 56. Density — 2.044 (Filhol).

(Schiff.)

5-6

IOI.2

102.74

1.50

II. 2

IO2.6

105.48

2-73

NH3.

1 6.8

104.0

108.22

3-90

M. W. = 17. Density = 0.616 (Andreef).

28.0

105.4
106.8

113.70

6.07

(Carius.)

33-6

108.4

116.44

6.91

39-2

IIO.O

119.18

7.70

1-7

102.5

102.76

0.25

44-8

111.6

121.92

8.46

3-4

105.0

105.52

0.49

5°-4

113.2

124.66

9.19

5-1

107.4

108.28

• 0.8 1

56.0

115.0

127.40

9.72

6.8

109.8

1 1 1 .04

1. 12

84.0

124.2

141.10

11.98

8.5

II2.2

113.80

I.4I

II2.O

134.6

154.80

'3-05

10.2

II4.6

116.56

1.68

168.0

157-6

182.20

13-50

II.9

II7.O

119.32

'•95

224.0

181.8

209.60

13.26

I3.6

1194

I22.O8

2. 2O

15-3

I2I.8

1 24.84

2-44

17.0

124.2

127.60

2.66

25-5

135-8

141.40

3-96

NasO.

34-o

147-3

155.20 '

5-°9

M. W. =30.97. Density = 2. 805 (Karsten).

51.0

169.7

182.80

7.17

(Hager.)

3-097

99.01

IOI.IO

2.07

6.194
9.291
12.388

98.26
97.76
97-45

IO2.2I
103.31
IO442

3-86
5-37
6.67

NH4C1.
M. W. = 53.38. Density = 1.52 (Schroeder).

1 5-405

97.29

IO^. %f2

7.00

18.582
2 1 .679

97-23
97-32

106.63
107.73

8.8 1
9.66

(Gerlach.)

24.776

97-55

108.83

10-37

5-338

103.7

103.51

0.18

27.873

97.84

109.94

II.OO

10.676

107-5

107.02

0-45

30.970

98.20

111.04

11.56

16.014

III-5

110.54

0.87

46.455.

100.94

116.56

13.40

21.352

"5-3

114.05

1. 10

52.649

102.30

118.77

13-87

26.690

119.2

117.56

1.40

* The table was compiled from a paper by Gerlach (Zeits. fur Anal. Chem. vol. 27).
SMITHSONIAN TABLES.

TABLE 147.

CONTRACTION PRODUCED BY SOLUTION.

Grammes of
the salt in
100 of water.

Observed
volume.

Calculated
volume.

Per cent
of
contraction

Grammes of
the salt in
100 of water.

Observed
volume.

Calculated
volume.

Per cent
of
contraction.

KC1.

M. W. = 74.41. Density = 1.945 (Clarke).

BaCl2.
M. W. = 207.54. Density=3.7S (Schroeder).

(Gerkch.)

(Gerlach.)

7.441
14.882
22.323

102.8
105.8
108.9

103.83
107.65
111.48

o-99
1.72
2.31

!0-377
20.754

3I-I3I

IOI.6
102.9
104.9

102.77

105-53
108.30

I.I4
2.50
3-'4

NaCl.
M. W. = 58.36. Density = 2.150 (Clarke).

KI.
M. W. = 166.57. Density = 3.07 (Clarke).

(Gerlach.)

( Kremers. )

S-836
11.672
17.508

23-344
-29.180

IOI-7

103-7
105.8
107.9
IIO.I

102.71

105-43
108.14

110.86
113.58

o-99
1.64
2.16
2.67
• 3.06

16.657

33-3H
49.971
66.628

83.285

104.5
109.3
114.2
Iig.I
124.0

105-39
110.77
116.18
121.57
1 26.97

0.85

i-34
1.70

2. 2O

2-34

LiCl.

M. W. = 42. Density = 1.980 (Gerlach).

KC1O3.
M. W. = 122.29. De isity = 2.33i (Clarke).

(Kremers.)

(Gerlach.)

6.114

102-3

102.62

0.314

4-2
8.4
12.6

16.8

2I.O
42.O

101.9
103.8
105.8
107.8
IIO.O

120.7

102.14
104.28
106.42
108.56
1 10.70
121.40

0.24
0.46
0.58
0.70
0.63
0.58

KN03.
M. W. = 100.93. Density = 2.092 (Clarke).

(Gerlach.)

CaCl2.
M. W. = i 10.64. Density = 2.216 (Schroeder).

5.046
10.093
20.186

101.90
104.84
108.40

102.41
104.83
109.65

0.50

o-79
1.14

(Gerlach.)

NaNOs.
M. W. = 84.88. Density= 2.244 (Clarke).

S-S32
11.064
16.596
22.128
27.660
33-192
66.384

IOI.2
IO2.2

103.5
104.8
106.3
IO8.O

118.6

102.50
104.99
107.49
109.99
112.48
114.98
129.96

1.26
2.66

3-7i
4.72

5-50
6.07
8.74

(Kremers.)

8.488
16.976
42.440
84.880

102-9
1 06. 1

116.2

134-3

103.78
107.56
118.91

137.82

0.85
1.36
2.28

2-55

SrCI2.
M. W. = 157.94. Density = 3.05 (Schroeder).

NH4
79.90. Dens

N08.

oeder).

(Gerlach.)

(Gerlach.)

7-895
I5-790
23.685

3I-580

39-475

101.4

102.5
104.0

I05-S
107.2

102.59
105.17
107.76
110.34
112.93

1.16
2-55
3-43
4-39
5-07

7.990
15.980

39-950
79.900

104.6
109.3
124.4
149.8

104.59
109.18
122.96
145.92

0.076
O.I 06
1.170
2.66o

SMITHSONIAN TABLES.

132

CONTRACTION PRODUCED BY SOLUTION.

TABLE 147.

Grammes of
the salt in
100 of water.

Observed
volume.

Calculated
volume.

Per cent
of
contraction.

Grammes of
the salt in
loo of water.

Observed
volume.

Calculated
volume.

Per cent
of
contraction.

Ca(NOs)2.
M. W. = 163.68. Density = 2.36 (Clarke).

Na,COs.
M. JV. = 105.83. Density 2.476 (Clarke and Schroeder).

(Gerlach.)

(Gerlach.)

1-637

3-274
4.910
6.547
8.184
16.368

32-736
49.104
65-472
81.840

100.45
100.90

101-35
101.85
102.30
104.70
109.90

"5-55
121.50
127.65

100.69
101.39
IO2.o8
102.77

103-47
106.94
113.87
I 2O.8l

127.74

134.68

0.24
0.48
0.72
0.90

I-I3
2.09

3-49

4-35
4.89

5-22

5.292
10.582
I5-875

IOO.OO
100.44

101.06

102.14
104.27
106.41

2.09
3.68
5-03

K2S04.
M. W. — 173.90. Density 2.647 (Clarke).

(Gerlach.)

Ba(N03)2.
M. W. = 260.58. Density = 3.23 (Clarke).

8.695

101.94

103.29

1.30

(NH4)2S04.
M. W. = 131.84. Density 1.762 (Clarke).

(Gerlach.)

2.6o6
5.212
7.817

100.5
IOI.O
101.5

100.81
101.61
102.42

0.30
0.60
0.90

(Schiff.)

6.592
13.184
19.776
26.369
65.920

102.92
105.96
109.20
1 1 2.60
135.20
I54-50

10374
107.48
112.26
114.97
I37-42
I56-I3

0.792
1.418
I.82I
2.060
1.615
1.044

Sr(N03)..
M. W. =210.08. Density = 2.93 (Clarke).

(Gerlach.)

FeSO4.
M. W. = 151.72. Density 2.99 (Clarke).

2.IIO
4.22O
6.329

8-439
10.549
21.098
42.196
63.294

100.48
100.95
101.40
101.95
102.45
104.95
IIO.2O
Il6.I5

100.72
101.44
102.16
102.88
103.60
107.20
114.40
121.60

0.24
0.48
0-74
O.gO
I. II
2.IO

3-67
4.48

*

7.586
15.172
22.758
3°-344

100.52
101.30
102.40
103.70

102.54
105.07
107.61
110.15

1.97

3-59
4.84

5-85

Pb(N03)2.
M. W. = 165.09. Density =. 4.41 (Clarke).

MgS04.
M. W. = 197.6. Density 2.65 (Clarke).

(Gerlach.)

16.509
33-018

82-545

102.4
105.1
114.0

103-74
107.49
118.72

1.29
2.22

3-97

*

5.988
11.976
17.964
23-952

100.13
100.40
101.26

IO2.IO

102.26
104.52
106.78
109.04

2.08

3-94
5.16
6.36

K.C03.
1' M. W. 137.93- Density 2.29 (Clarke and Schroeder). 1

(Gerlach.)

Na,SO4.
M. W. r= 141.80. Density = 2.656 (Clarke).

6.897

13-793
20.689
27.586
68.965

96-S51

100.96
102.22
103.78
105.44

118.20
128.10

103.01
106.02
109.08
112.05
130.12
142.16

1.99

3-59
4.82

5-90
9.16
9.89

(Gerlach.)

7.09
14.18

100.96
IO2.26

102.67
105-34

1.67
2.92

SMITHSONIAN TABLES.

* Authority not given.

133

TABLE 147.

CONTRACTION PRODUCED BY SOLUTION.

Grammes of
the salt in
100 of water.

Observed
volume.

Calculated
volume.

Per cent
of
contraction.

Grammes of
the salt in
100 of water.

Observed
volume.

Calculated
volume.

Per cent

of
contraction.

ZnSO4.
M.W. = 160.72. Density 3.49 (Clarke).

KC2H3O2.
M. W. = 97.90. Density = 1.472 (Gerlach).

*

(Gerlach.)

8.036
16.072
24.108 i
32.144
40.180

100.06
100.44
lOI.oS
101.90
I O2.86

102.30
104.61
106.91
109.21
111.51

2.19
3-98

5-45
6.69
7.76

9-79
19.58

48.95
97.90

105.2
110.5

127-3
156.4

106.65

"3-30
133.26
166.51

I.36
2-47
4-47
6.07

K2C4H4O6.
M. W. = 225.72. Density 1.98 (Gerlach).

A12K2(S04)4.
M. W. = 128.99. Density = 2.228 (Clarke).

(Gerlach.)

(Gerlach.)

6.450

100.58

IO2.OX>

2.25

22.572

45- '44
67.716
90.288
112.860

I35-432
1 58.004

1 08.8
118.3
128.2

138.7
149.2

J59-7
170.6

111.39
122.79
134.18
I45-58
156.97
168.36
179.76

2-33
3'66
4.46
4-73
4-95
5-i5
5.10

NaC-jHsOj.
M. W. = 81.85. Density = 1.476 (Gerlach).

(Gerlach.)

8.185
16.360

104.1
108.3

105-55
111.09

i-37
2.51

PKCoHsO,),.
M. W. i= 162.06. Density 3.251 (Schroeder).

M.W.

Na,C<

H406.
snsity 1.83 (Gerlach).

(Gerlach.)

(Gerlach.)

16.206
32.412
81.030

104.7
109.5
124.6

104.98
109.96
124.91

0.27
0.42
0.25

19.362
38.724

1 06.6
114.2

110.57
121.15

3-59

5-74

TABLE 148.

CONTRACTION DUE TO DILUTION OF A SOLUTION.!

The first column gives the name of the salt dissolved, the second the amount of the salt required to produce saturation
and the third the contraction produced by mixing with an equal volume of water.

Parts of an-

Parts of an-

Water with equal volume
of saturated solution of

hydrate salt
dissolved by

Contraction
when mixed.

Water with equal volume
of saturated solution of

hydrate salt
dissolved by

Contraction
when mixed.

following salts.

100 parts of

Per cent.

following salts.

100 parts of

Per cent.

H2O at 10° C.

H2Oat 10° C.

KC1 ...

3r-97

0.325

NH4NO3 . . ,

185.00

0.772

K2SO4

IO.IO

0.082

CaCl2 •

63-30

I-I35

KNO3 .

20.77

0.144

BaCl2 .

33-30

0.235

K2C03

88.72

2.682

MgS04 . .

30-50

0.677

NaCl .

35-75

0.490

ZnSO4 .

48.36

0.835

Na2SC>4 . •

8.04

0.107

FeS04 . . T

19.90

0.327

NaNO3

84.30

0-975

A12K2(S04)4

4-99

0.033

Na2CO3

16.66

0.206

CuSO4 •

20.92

0.2 1 8

NH4C1

36.60

0-273

Pb(N03)2 .

48.30

0.228

(NH4)2S04 . .

1.302

SMITHSONIAN TABLES.

* Authority not given.

t R. Broom, " Proc. Roy. Soc. Edin." vol. 13, p. 172.

134

TABLE 149.

FRICTION.

The following table of coefficients of friction f and its reciprocal i/f, together with the angle of friction or angle of
repose <£, is quoted from Rankine's "Applied Mechanics." It was compiled by Rankine from the results of
General Morin and other authorities, and is sufficient for all ordinary purposes.

Material.

/

I//

*

1

Wood on wood, dry ......

•25--50

4.00-2.00

14.0-26.5

" " " soapy

.20

5.00

11.5

Metals on oak, dry

.5o-.6o

2.00-1.67

26.5-31.0

" " " wet

.24-. 26

4.17-3.85

13-5-14-5

" " " soapy

.20

5.00

"•5

" " elm, dry

.2O-.25

5.00-4.0Q

11.5-14.0

Hemp on oak, dry

•53

1.89

28.0

" " " wet

•33

3.00

18.5

Leather on oak

.27-.38

3.70-2.86

15.0-19.5

" " metals, dry ......

.56

1.70

2Q.C

" '' " wet

.36

&

S J

20.O

" " " greasy . . .

•23

4-35

I3.0

" " " oily

•15

6.67

8-5

.1 ?— .20

6.67—5.00

8.5-ii.q

" " " wet ......

•3

3-33

"•3 »**3

16.5

Smooth surfaces, occasionally greased .

.O7-.o8

14.3-12.50

4.0-4.5

" continually greased .

.05

20.00

3-o

" " best results ....

•Q3-.036

33-3-27-6

i-7 5-2-0

Steel on agate, dry *

.20

5.00

"•5

" " " oiled*

.107

9-35

6.1

Iron on stone

.30-70

3-33-1-43

16.7-35.0

Wood on stone

About .40

2.50

22.O

Masonry and brick work, dry ....

.60-. 70

1.67-1.43

33-0-35-°

" '• " " damp mortar

•74

!-35

36-5

" on dry clay

•51

1.96

27.0

" " moist clay

•33

3.00

18.25

Earth on earth

.25-1.00

4.00-1.00

14.0-45.0

" " " dry sand, clay, and mixed earth .

•38-75

2-63-1.33

21.0-37.0

" " " damp clay .....

I. CO

I.OO

45.0

" " " wet clay

•31

3-23

17.0

" " " shingle and gravel

.8i-i.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.

SMITHSONIAN TABLES.

135

TABLE 150.

VISCOSITY.

The coefficient of viscosity is the tangential force per unit area of one face of a plate of the
fluid which is required to keep up unit distortion between the faces. Viscosity is thus measured
in terms of the temporary rigidity which it gives to the fluid. Solids may be included in this
definition when only that part of the rigidity which is due to varying distortion is considered.
One of the most satisfactory methods of measuring the viscosity of fluids is by the observation
of the rate of flow of the fluid through a capillary tube, the length of which is great in compari-
son with its diameter. Poiseuille * gave the following formula for calculating the viscosity coef-

ir/lf^s
ficient in this case : /*= .,, , , where h is the pressure height, r the radius of the tube, s the

density of the fluid, v the quantity flowing per unit time, and / the length of the capillary part of
the tube. The liquid is supposed to flow from an upper to a lower reservoir joined by the tube,
hence h and / are different. The product hs is the pressure under which the flow takes place.
Hagenbach t pointed out that this formula is in error if the velocity of flow is sensible, and sug-
gested a correction which was used in the calculation of his results. The amount to be sub-

z>2
tracted from h, according to Hagenbach, is -= — , where g is the acceleration due to gravity.

V--S
Gartenmeister \ points out an error in this to which his attention had been called by Finkener,

and states that the quantity to be subtracted from h should be simply — ; and this formula is

S

used in the reduction of his observations. Gartenmeister's formula is the most accurate, but all
of them nearly agree if the tube be long enough to make the rate of flow very small. None of the
formulae take into account irregularities in the distortion of the fluid near the ends of the tube,
but this is probably negligible in all cases here quoted from, although it probably renders the
results obtained by the " viscosimeter " commonly used for testing oils useless for our purpose.
The term " specific viscosity " is sometimes used in the headings of the tables ; it means the
ratio of the viscosity of the fluid under consideration to the viscosity of water at a specified
temperature.

TABLE 150. — Specific Viscosity of Water at different Temperatures relative to Water at 0° C.

Authorities.

Absolute

Temp.

Mean

value in

inC°.

value.

C. G. S.

Poiseuille.

Graham.

Rellstab.

Sprung.

Wagner.

Slotte.

units.

0

IOO.O

IOO.O

IOO.O

IOO.O

IOO.O

IOO.O

IOO.O

IOO.O

o.oi78§

5

85.2

84.4

84.8

85-3

84-9

- ,*s

-

84.9

0.0151

10

73-5

73-6

72.9

73-5

73-2

-

-

73-3

0.0131

15

64-3

63-5

63.7

63.0

63-9

63-9

—

637

0.0113

20

56.7

56.0

56.0

55-5

56.2

56.2

5°4

56.2

O.OIOO

25

_

49-5

50-5

48.7

50-5

50-3

-

49-9

0.0089

3°

45-2

44-7

45-°

45.0

45.2

44.6

45-2

45.0

0.0080

35

40.2

41.1

40.0

40.8

40.3

-

40.5

0.0072

40

-

36.8

37-o

37-2

37-o

36.7

36.9

36.9

0.0066

45

-

33-9

33-9

34-5

34-o

34-5

—

34-2

0.006 1

50

30.8

3"

3"

31.2

3J-3

3i-7

-

31.2

0.0056

*"Comptes rendus,'' vol. 15, 1842. " Mdm. Serv. Etr." 1846.

t " Pogg. Ann." vol. log, 1860.

t " Zeits. fiir Phys. Chim.'; vol. 6, 1890.

§ The value 0.0178 is taken from a paper by Crookes (Phil. Trans. R. S. L. 1886), where the coefficient is given as
|t = o.oi7793i/', where P— ' = i +.0336793 T-\- .0002209936 7'2, where T is the temperature of the water in degrees
Centigrade. The numbers in the table were calculated not from the formula but from the numbers in the column
headed " mean value."
SMITHSONIAN TABLES.

136

TABLES 151-153.

VISCOSITY.

TABLE 151. - Solution of Alcohol in Water.*
Coefficients of viscosity, in C. G. S. units, for solution of alcohol in water.

Percentage by weight of alcohol in the mixture.

Temp.

C.

o

8.21

16.60

34.58

43-99

S3.36

75-75

87-45

99.72

0°

O.OlSl

0.0287

0-0453

0.0732

0.0707

0.0632

0.0407

0.0294

O.OlSo

5

.0152

.0234

•035 l

.0558

•°552

.0502

•0344

•0256

.0163

10

.0131

•0195

.0281

•0435

.0438

.0405

.0292

.0223

.0148

15

20

.0114
.OIOI

.0165
.0142

.0230
.0193

•0347
.0283

•0353
.0286

•0332
.0276

.0250
.0215

.0195
.0172

.0134
.OI22

25

0.0090

0.0123

0.0163

0.0234

0.0241

O.O232

0.0187

O.OI52

O.OIIO

3°

.OOSI

.0108

.0141

.0196

.0204

.0198

.0163

•0135

.0100

35

.0073

.0096

.OI22

.0167

.0174

.0171

.0144

.0120

.0092

40

.0067

.0086

.0108

.0143

.0150

.0149

.0127

.OIO7

.0084

45

.006l

.0077

.0095

.0125

.0131

.0130

.0113

.0097

.0077

SO

0.0056

0.0070

0.0085

O.OIO9

0.0115

O.OII5

O.OIO2

0.0088

0.0070

55

.0052

.0063

.0076

.0096

.0102

.OIO2

.OOgi

.0086

.0065

60

.0048

.0058

.0069

.0086

.0091

.0092

.0083

.0073

.0060

The following tables (152-153) contain the results of a number of experiments in the viscosity of mineral oils derived
from petroleum residues and used for lubricating purposes.t

TABLE 152. -Mineral Oils.

be

Sp. viscositv. Water at

.

o -

20° C. — i.

C'

|t

If

0

°c.

°c

20° C.

50° C.

100° C.

•93'

243

274

_

11.30

2-9

.921

216

246

-

7-31

2-5

.906

189

208

-

3-"45

.921

163

190

_

27.80

2.8

.917

132

168

-

-

2.6

•904
.891

170

207
182

8.65
4-77

2-65
1.86

'•3

.878

108

148

2-94

1.48

•«55

42

45

1.65

-

-

•905

165

202

_

3.10

r-5

.894
.866

90

270
224

7-60
2.50

3.60
1.50

TABLE 153. — Mineral Oils.

Oil.

tj,

C

Q

fj

|i

K
°C.

w

F

°c.

*****

«S||
|?J

%r^~2
> '"•«

Cylinder oil . .

.917

227

274

191

Machine oil . .

.914

213

260

IO2

Wagon oil . .

•9*4

148

182

80

" " . .

.911

157

187

70

Naphtha residue

.910

134

162

55

Oleo-naphtha

.910

219

2S7

121

" "

.904

20 r

242

66

" "

.894

184

222

26

Oleonid . . .

.884

185

2I7

28

best

quality

.881

1 88

224

20

Olive oil ...

.916

_

_

22

Whale oil . .

.879

-

-

9

•875

* This table was calculated from the table of fluidities given by Noack (Wied. Ann. vol. 27, p. 217), and shows a
maximum for a solution containing about 40 per cent of alcohol. A similar result was obtained for solutions of acetic
acid.

t Table 152 is from a paper by Engler in Dingler's " Poly. Jour." vol. 268, p. 76, and Table 153 is from a paper by
Lamansky in the same journal, vol. 248, p. 29. The very mixed composition of these oils renders the viscosity a very
uncertain quantity, neither the density nor the flashing point being a good guide to viscosity.

t The differenj groups in this table are from different residues.

SMITHSONIAN TABLES.

137

TABLE 154.

VISCOSITY.

This table gives some miscellaneous data as to the viscosity of liquids, mostly referring to oils and paraffins. The

viscosities are in C. G. S. units.

Liquid.

G.%

Coefficient
of
viscosity.

Temp.
Cent. °

Authority.

Ammonia . . . ...

0.0160

II.9

Poiseuille.

0.0149

14-5

"

O.OIII

2O.O

Gartenmeister.

Glycerine . . .

42.20

2.8

Schottner.

**

25.18

8.1

ti

u

1^87

1A. 1

n

"

*.>"/

8.30

"to

20.3

«

4-94

26.5

"

Glycerine and water .

94.46

7-437

8-5

if

" "...

80.31

i. 02 1

8-5

"

" "...

64.05

O.222

8-5

"

•

49-79

0.092

8-5

it

Glycol . . . .

O.O2I9

o.o

Arrhenius.

O.Ol84

— 20

Koch.

O.OI7O

0.0

.

0.0157

2O.O

"

„

O.OI22
O.OIO2

IOO.O
2OO.O

tt

"

0.0093

300.0

"

0.1878

2O.O

Gartenmeister.

Olive oU

0.0

Reynolds.

Paraffins : Decane

O.OO77

22-3

Bartolli & Stracciati.

Dodecane .

O.OI26

23-3

" "

Heptane

O.OO45

24.0

tt ft

Hexadecane

0.0359

22.2

ii a

Hexane

0.0033

23-7

if if

Nonane

O.OO62

22.3

II !<

Octane

O.OO53

22.2

If It

Pentane

O.OO26

21 O

14 II

Pentadecane

0.028l

22.O

If II

Tetradecane

0.0213

21.9

II If

Tridecane .

0.0155

23-3

II <l

Undecane .

OOO95

22.7

If II

Petroleum (Caucasian) . .

OOIOX)

17-5

Petroff.

Rape oil

25-3

O.O

O. E. Meyer.

it it

7 8 c

IO.O

**

« «

i '63

2O.O

»

•

0.96

30.0

* Calculated from the formula ft = .017 — .000066*+ 00000021^ — .0000000002 $& (vide Koch, Wied. Ann. vol. 14.
p. i).

t Given as 1=3. 2653 e--yiKT, where T is temperature in Centigrade degrees.

SMITHSONIAN TABLES.

138

TABLE 1 55.

VISCOSITY.

This table gives the viscosity of a number of liquids together with their temperature variation. The headings are
temperatures in Centigrade degrees, and the numbers under them the coefficients of viscosity in C. G. S. units.*

Liquid.

Temperatures Centigrade.

Authority.

10°

to9

3o°

40°

50°

Acetone

.004."?

.OOV)

.0036

.OOT.2

.0028

Pribram & Handl.

Acetates : Allyl . . .

^^TO
.0068

•?:
.OOOI

.0054

,WJ —

.0049

.0044

u

Amyl . ,i .

.0106

.0089

.0077

.0065

.0058

u

Ethyl . . .

.OO5I

.0044

.0040

.0035

.0032

"

Methyl . . .

.OO46

.OO4I

.0036

.0032

.0030

u

Propyl . . .

.0066

.0059

.0052

.0044

.0039

H

Acids : t Acetic . . .

.0150

.OI26

.0109

.0094

.0082

"

Butyric . . .

.OI96

.0163

.0136

.0118

.0102

Gartenmeister.

Formic . . .

.0231

.0184

.0149

.0125

.0104

"

Propionic . .

.0125

.0107

.0092

.0081

.0073

Rellstab.

" . .

.0139

.0118

.OIOI

.0091

.0080

Pribram & Handl.

Salicylic . . .

.0320

.O27I

.0222

.0181

.0150

Rellstab.

Valeric . . .

.O27I

.O22O

.0183

•OI55

.0127

«

Alcohols : Allyl ....

.0206

.0163

.0128

.0103

.0083

Pribram & Handl.

Amyl . . .

.O65I

.0470

•0344

•0255

.0196

u «

Butyl . . .

.0424

.0324

.0247

.0190

.0150

" "

Ethyl . . .

.0150

.OI22

.0102

.0085

.0072

Gartenmeister.

Isobutyl . .

.O58O

.0411

.0301

.0223

.0170

u

Isopropyl . .

•0338

.0248

.0185

.0140

.0108

"

Methyl . . .

.0073

.OO02

.0054

.0047

.0041

"

Propyl . . .

.0293

.0227

.0179

.0142

.0115

"

Aldehyde

.ocny

•OO'?7

_

_

Rellstab.

Aniline

^^j/

• WJf

.0440

.07 1 Q

.0241

.0189

Wijkander.

Benzene

.0071

>wtf bfv

.0064

3 y

.00 ^s

.W.f.1

.0048

.004"?

Benzoates : Ethyl . . .

»"*/O

.0265

.0217

j j

.0174

w ^

.0146

"VLTj
.OI24

Rellstab.

Methyl . .

.0231

.0196

.0160

.0134

.OII5

"

Bromides : Allyl . . .

.0061

.0053

.0048

.0045

.0041

Pribram & Handl.

Ethyl . . .

.0043

.0037

.0035

—

-

" "

Ethylene . .

.0169 ,

.0149

—

-

« .<

Carbon disulphide . .

-

.0036

.0035

.0034

—

Wijkander.

Carbon dioxide (liquid) .

.0008

.0007

.0005

-

Warburg & Babo.

Chlorides : Allyl . . .

.0039

.0036

•0033

—

-

Pribram & Handl.

Ethylene . .

.0083

.0072

.0063

.0056

<>

Chloroform

.0064

.00 S7

.0052

.0046

.OO4 "?

u

Ether

^T-
.OO26

^^J/

.002 "?

.0021

.Wif.^

u

Ethyl sulphide ....

.0048

.V^/_J

.0043

.0039

•°°35

.0032

u

Iodides : Allyl ....

.0080

.0072

.0065

.0059

•0053

"

Ethyl ....

.0064

.0057

.0052

.0048

.OO44

X

Metaxylol

.OO7i;

.0066

.0058

.OOC2

OOA7

u

Nitro benzene ....

••'*'/ J

.0203

.0170

.0144

.ww^/
.0124

«

" butane ....

.0119

.0103

.0089

.0078

.OO09

"

" ethane

.0080

.0071

.0064

OOC7

.OO52

M

" propane ....

.0099

.WW/ 1
.OO87

.0077

A**j/

.0068

.OO6l

«

" toluene ....

•0233

.0190

.0159

.0136

"

Propyl aldehyde . . .

.0047

.OO4I

.0036

•°°33

-

« u

Toluene

.0068

.0059

.0052

.0047

.OO42

u «

* Calculated from the specific viscosities given in Landolt & Boernstein's " Phys. Chem. Tab." p. 289 et seq., on
the assumption that the coefficient for water at o° C. is .0178.
t For inorganic acids, see Solutions.

SMITHSONIAN TABLES.

139

TABLE 156.

VISCOSITY OF SOLUTIONS.

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, p stands for specific viscosity, and t for temperature Centigrade.

Salt.

Percentage
by weight
of salt in
solution.

Density.

M

t

M

t

V-

t

M

/

Authority.

BaCl2

7.60

_

77-9

10

44-o

3f

35-2

5f

Sprung.

"

15.40

-'

86.4

"

56.0

39-6

-

-

'•

"

24-34

-

100.7

*'

66.2

H

47-7

"

-

-

"

Ba(N03)2

2.98

1.027

62.0

15

51.1

25

42-4

35

34-8

45

Wagner.

5-24

1.051

68.1

54-2

"

44.1

36-9

"

CaCl2

I5-I7

-

110.9

IO

7i-3

30

50-3

5f

_

_

Sprung.

"

31.60

-

272.5

"

177.0

"

124.0

-

-

"

"

39-75

-

670.0

"

379-o

"

245-5

"

-

-

"

<4

44.09

-

-

-

593-1

"

363-2

"

-

-

"

Ca(NO»)8

17-55

I.I7I

93-8

15

74.6

25

60.0

35

49-9

45

Wagner.

"

30.10

1.274

144.1

"

112.7

"

90.7

"

75-i

"

"

"

40.13

1.386

242.6

'*

217.1

'56-5

**

128.1

"

"

CdCl2

11.09

1.109

77-5

15

60.5

25

49.1

35

40.7

45

u

"

16.30

i.iSi

88.9

70-5

57-5

47-2

"

"

24.79

1.320

104.0

80.4

"

64.6

**

53-6

**

"

Cd(N03)2

7.81

1.074

61.9

15

50.1

25

41.1

35

34-o

45

H

"

i5-7i

!-!59

71.8

58-7

**

48.8

4i-3

"

"

22.36

1.241

85.1

u

69.0

**

57-3

"

47-5

"

«

CdS04

7.14

i. 068

78.9

15

61.8

25

49-9

35

4i-3

45

«

"

14.66

i-'SJ

96.2

72-4

58.1

48.8

«

**

22.01

1.268

120.8

«

91.8

**

73-5

"

60. i

"

**

CoCl2

7-97

1.081

83.0

'5

65.1

25

53-6

35

44-9

45

"

"

14.86

1.161

in.6

85.1

73-7

58.8

"

<(

22.27

1.264

161.6

"

126.6

"

101.6

"

85-6

"

"

Co(N08)2

8.28

!-°73

74-7

15

57-9

25

48.7

35

39-8

45

«

"

15.96

1.144

87.0

55-4

44-9

"

"

24-53

1.229

110.4

**

88.0

**

7i-5

"

59-i

"

M

CoSO4

7.24

i. 086

86.7

15

68.7

25

55-o

35

45-1

45

«

"

14.16

I-I59

117.8

95-5

76.0

61.7

(i

"

21.17

1.240

193.6

**

146.2

"

113.0

**

89.9

**

CuCl2

J2.OI

1.104

87.2

15

67.8

25

55-1

35

45-6

45

H

*'

21-35

1.215

121.5

95-8

77-o

63.2

"

33-03

i-33i

178.4

*'

137-2

**

107.6

**

87.1

(i

"

Cu(N03)2

18.99

1.177

97-3

15

76.0

25

61-5

35

5*-3

I5

"

"

26.68

1.264

126.2

98.8

80.9

68.6

"

"

46.71

!-536

382.9

"

283-8

**

215-3

**

172.2

**

*'

CuSO4

6.79

'•055

79.6

15

61.8

25

49.8

35

41.4

45

"

*'

12-57

1.115

98.2

74-o

"

59-7

52.0

"

"

17.49

1.163

124.5

"

96.8

"

75-9

"

61.8

"

"

HC1

8.14

1-037

71.0

'5

57-9

25

48-3

35

40.1

45

«

"

16.12

1.084

80.0

66.5

56-4

48.1

"

H

»

23.04

1.114

91.8

**

79-9

«

65-9

56-4

"

«

HgCl2

0.23

1.023

_

_

58-5

2O

46.8

3f

38-3

40

•

•

3-55

'•033

76.75

10

59-2

46.6

38-3

<(

SMITHSONIAN TABLES.

140

VISCOSITY OF SOLUTIONS.

TABLE 156

Salt.

Percentage
by weight
of salt in
solution.

Density.

•

t

*

t

r

t

-

'

Authority.

HNOg

8-37

.067

66.4

15

54-8

25

45-4

35

37-6

45

Wagner.

"

12.2O

.116

69-5

57-3

"

47-9

"

40.7

"

"

" •

28.31

.178

80.3

65-5

**

54-9

"

46.2

u _

H2S04

7.87
I5-50

.065
.130

77-8
95- r

15

61.0
75-o

25

50.0
60.5

35

41.7
49-8

45

It

" •

23-43

.2OO

122.7

"

95-5

77-5

M

64-3

KC1

10.23
22.21

-

70.0
70.0

IO

46.1
48.6

3°

36-4

5°

- •

-

Sprung.

KBr

I4.O2

_

67.6

IO

44.8

3?

32.1

50

_

_

«

"

23.16

-

66.2

"

44-7

33-2

"

—

-

"

"

-

66.6

"

47.0

35-7

"

—

-

**

KI

8.42

_

695

IO

44.0

30

31.3

So

-

_

«

"

17.01

-

65.3

"

42.9

3M

"

—

-

"

"

33-03

-

61.8

"

42.9

"

32-4

"

-

-

"

«

45.98

54-oo

-

63.0
68.8

"

45-2
48-5

«

35-3
37-6

«

-

-

!!

KC1O3

3-51

-

71.7

10

44-7

30

31.5

5°

-

-

«

**

5-69

—

—

"

45.0

**

3M

-

-

"

KN03

6.32

-

70.8

IO

44-6

3°

31.8

5°

-

_

»

"

12.19

-

68.7

"

44-8

32-3

-

—

"

" :

17.60

-

68.8

"

46.0

"

33-4

**

-

-

"

K2S04

5-!7

-

77-4

10

48.6

3p

34-3

5°

-

-

"

**

9-77

-

81.0

"

52.0

36-9

-

—

"

K2CrO4

"•93

_

75-8

IO

62.5

30

41.0

40

_

_

«

"

19.61

-

85-3

"

68.7

"

47-9

"

-

—

"

"

24.26

1.233

97-8

"

74-5

"

"

-

-

Slotte.

-

32.78

-

109.5

88.9

"

62.6

"

-

-

Sprung.

K2Cr2O7

4.71

1.032

72.6

IO

55-9

20

45-3

3f

37-5

40

Slotte.

"

6.97

1.049

73-'

11

56-4

"

45-5

37-7

"

LiCl

7-76

-

96.1

IO

59-7

3°

41.2

5°

_

_

Sprung.

"

I3-9I

-

121.3

"

75-9

52.6

-

-

"

a

26.93

-

229.4

"

142.1

"

98.0

*"

-

-

H

Mg(N03)2

18.62

I.IO2

99-8

15

81-3

25

66.5

35

56.2

45

Wagner.

"

34-19

1.200

213.3

164.4

132.4

109.9

"

"

**

39-77

1.430

3!7-o

"

250.0

'*

191.4

**

158.1

"

"

MgS04

4.98

-

96.2

IO

59-o

30

40.9

50

-

-

Sprung.

"

9.50

-

130.9

"

77-7

"

53-o

"

-

—

"

«

19.32

-

302.2

166.4

106.0

"

-

-

"

MgCrO4

12.31

1.089

111.3

10

84.8

20

67.4

30

55-o

40

Slotte.

" •

21.86

.164

167.1

"

125-3

"

99-0

79-4

"

u

"

27.71

.217

232-2

"

172.6

"

133-9

M

1 06.6

"

"

MnCl2

8.01

.096

92.8

'S

71.1

25

57-5

35

48.1

45

Wagner.

" ••

15-65

.196

130.9

104.2

"

84.0

68.7

"

"

30-33

•337

256.3

**

193-2

*

155-°

"

123-7

"

"

40.13

•453

537-3

393-4

300.4

246.5

SMITHSONIAN TABLES.

141

TABLE 1 56.

VISCOSITY OF SOLUTIONS.

Salt.

Percentage
by weight
of salt in
solution.

Density.

M

• t

n

/

M

t

t>-

t

Authority.

Mn(NO3)2

18.31

1.148

96.0

\s

76.4

25

64-5

35

55-6

45

Wagner.

"

29.60

•323

167.5

126.0

104.6

88.6

"

ti

49-3 »

.506

3968

301.1

**

221.0

"

188.8

"

«

MnSO4

"•45

.147

129.4

15

98.6

25

78-3

35

63-4

45

«

"

1 8.80

.251

228.6

"

172.2

I37-I

107.4

"

"

22.08

.306

661.8

<(

474-3

"

347-9

**

266.8

"

"

NaCl

7-95

_

82.4

10

52.0

30

31.8

5°

-

_

Sprung.

"

I4-31

-

94-8

"

60. i

36-9

-

-

"

"

23.22

-

128.3

"

79-4

**

47-4

**

-

-

*'

NaBr

9-77

_

75-6

10

48.7

3°

34-4

5°

_

_

«

"

18.58

-

82.6

"

53-5

38.2

-

-

"

a

27.27

-

95-9

61.7

43-8

"

-

-

*'

Nal

8.83

_

73- J

IO

46.0

3°

32-4

5°

-

_

«

"

17-iS

-

73-8

"

47-4

33-7

"

-

-

"

"

35-69

—

86.0

"

55-7

"

40.6

"

-

-

"

"

55-47

-

157-2

"

96.4

H

66.9

-

-

"

NaClO3

11.50

_

78.7

IO

50.0

3°

35-3

5°

-

_

«

"

20.59

—

88.9

"

56.8

"

40-4

"

-

-

"

"

33-54

-

I2I.O

«

75-7

»

53-o

"

-

-

NaNOs

7-25

_

75-6

IO

47-9

3°

33-8

5°

-

-

U

M

I2-35

—

81.2

"

51.0

"

36.1

"

-

-

"

"

18.20

-

87.0

"

55-9

"

39-3

"

-

-

"

u

31-55

—

121. 2

u

76.2

«

53-4

"

—

—

"

Na2SO4

4.98

-

96.2

IO

59-o

3°

40.9

5°

-

-

"

«

9.50

-

130.9

"

77-7

"

53-°

"

-

-

**

II

14.03

—

I87.9

"

107.4

"

71.1

"

-

-

"

"

I9-32

-

302.2

"

166.4

"

1 06.0

-

-

**

Na2CrO4

5-76

1.058

85.8

IO

66.6

20

53-4

3°

43-8

40

Slotte.

H

10.62

1. 112

I03-3

"

79-3

"

63-5

*'

52-3

"

"

"

14.81

1.164

127-5

"

97.1

"

77-3

«

63.0

"

"

NH4C1

3-67

_

7i-5

IO

45-°

3°

3i-9

5°

_

-

Sprung.

H

g.67

—

69.1

"

45-3

32.6

"

-

-

u

M

15.68

-

67-3

"

46.2

"

34-o

"

-

-

(1

"

23-37

-

67.4

"

47-7

"

36.1

"

-

— '

"

NH4Br

15-97

_

65.2

10

43-2

3°

3i-5

5°

• '-. !'

•-

(t

«

25.33

—

62.6

"

43-3

32.2

M

-

—

((

«

36.88

—

62.4

"

44-6

34-3

"

—

—

NH4NO3

5-97

_

69.6

IO

44-3

30

31.6

5°

— ';

-

»

"

12.19

-

66.8

"

44-3

"

3i-9

"

-

-

(t

"

27.08

-

67.0

"

47-7

"

349

"

-

-

"

«

37-22

-

7i-7

"

51.2

"

38.8

«

~

-

'"

(i

49-83

-

81.1

"

63-3

H

48.9

"

—

—

"

(NH4)SS04

8.10

_

107.9

10

52-3

3°

37-o

5°

-

-

«

H

15.94

-

120.2

"

60.4

u

43-2

"

-

-

II

25-51

148.4

74-8

54-i

H

SMITHSONIAN TABLES.

142

VISCOSITY OF SOLUTIONS.

TABLE 1 56.

Salt.

Percentage
by weight
of salt in
solution.

Density

u

/

M

t

*

/

M

/

Authority.

(NH4)2CrO4

10.52

1.063

79-3

10

62.4

20

_

_

42-4

40

Slotte.

«'

19-75
28.04

I.I2O
•I-I73

88.2

IOI.I

«

7O.O
80.7

*

6a8

3°

48.4
56-4

«

(NH4)2Cr207

6.85

1.039

72.5

IO

56-3

20

45-8

3f

38.0

40

«

*;

13.00

1.078

72.6

"

57-2

"

46.8

39- *

"

"

**

19-93

I.I26

77-6

"

58.8

--

48.7

"

40.9

"

ii

NiCl2

"•45

1.109

90.4

15

70.0

25

57-5

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

"

"

Ni(NO3)2

16.49

1.136

90.7

15

70.1

25

57-4

35

48.9

45

«

"

30.01

1.278

135-6

"

105.9

70.7

"

"

40.95

1.388

222.6

"

169.7

«

128.2

a

152.4

"

"

NiSO4

10.62

1.092

94.6

15

73-5

25

60. i

35

49-8

45

.«

"

18.19

1.198

154-9

"

119.9

99-5

M

75-7

"

25-35

1-3*4

298.5

«

224.9

M

i73-o

'*

152.4

u

"

Pb(N08)2

'7-93

1.179

74-0

\S

59-i

25

48-5

35

40-3

45

«

32.22

1.362

91.8

72.5

d

59.6

50.6

"

Sr(N08)2

10.29

1.088

69-3

»5

56.0

25

45-9

35

39-i

45

.<

"

21.19

1.124

87-3

69.2

d

57-8

48.1

"

"

32.61

i-307

116.9

M

93-3'

76.7

U

62.3

**

"

ZnCl2

15-33

23-49

1.146
1.229

93-6
111.5

IS

72.7
86.6

25

57-8
69.8

35

48.2
57-5

45

H

"

33-78

1-343

151.7

«

117.9

«

90.0

«

72.6

"

"

Zn(N03)2

'5-95

1.115

80.7

'5

64-3

25

52.6

35

43-8

45

»

"

30-23

1.229

104.7

"

85.7

"

69-5

57-7

u

"

44.50

1-437

167.9

"

130.6

«

105.4

"

87-9

**

«

ZnSO4

7.12

1.106

97.1

15

79-3

25

62.7

35

5T-5

45

««

"

16.64

I-I95

156.0

118.6

94-2

73-5

"

23.09

1.281

232.8

<>

177-4

«

135-2

108.1

SMITHSONIAN TABLES.

TABLE 157.

SPECIFIC VISCOSITY.*

Dissolved salt.

Normal solution

J normal.

J normal.

^ normal.

Authority.

:*,

Q

Q

Specific
viscosity.

>>
1

0 >>

tc.t:

IS

t/3'S

>,

c
Q

Specific
viscosity.

>,

c
P

Specific
viscosity.

Acids : ClgOs . .

T T / • 1

1.0562

I.OI2

1.0283

1.003

1.0143

I.OOO

1.0074

0-999

Kevher.

ilLI .

T T f\ f \

1.0177

1.067

1 .0092

1.034

1.0045

I.OI7

1.0025

1.009

" .

HClUa . .

1.0485

I.O52

1.0244

1.025

1.0126

1.014

1 .0064

i. 006

If

HNOg . .

II C f \

1.0332

I.O27

I.OI68

I.OI I

1.0086

1.005

1.0044

1.003

"

1120U4 .

1.0303

I.OgO

1.0154

1.043

1.0074

1.022

1-0035

1.008

Wagner.

Aluminium sulphate
Barium chloride . .

I-0550
1.0884

1.406
I.I23

1.0278
1.0441

1.178
r-057

1.0138

1.0226

I.082
I.O26

1.0068
I.OII4

1.038
1.013

"

" nitrate . .
Calcium chloride

1.0446

1.156

1.0518
1.0218

1.044
1.076

1.0259
1.0105

I. O2 1
1.036

1.0130
1.0050

i. 008
1.017

«

" nitrate .

1.0596

I.II7

1.0300

J-053

1.0151

1.022

1.0076

1.008

"

Cadmium chloride .

1.0779

'•134

1.0394

1.063

1.0197

I.03I

1.0098

i. 020

'"

" nitrate

1.0954

1.165

1.0479

1.074

1 .0249

1.038

1.0119

1.018

it

sulphate .

1-0973

1.348

1.0487

1.157

1.0244

1.078

I.OI2O

r-°33

"

Cobalt chloride . .

1.0571

I.2O4

1.0286

1.097

1.0144

1.048

1.0058

1.023

"

" nitrate . .

1.0728

I.I66

1.0369

1-075

1.0184

1.032

1 .0094

1.018

"

" sulphate . .

1.0756

2-354

1-0383

1.160

1.0193

J.077

I .OIIO

1.040

"

Copper chloride . .

1.0624

1.205

1-0313

1.098

1.0158

1.047

1.0077

1.027

«

" nitrate . .

i-0755

1.179

1.0372

1.080

1.0185

I.O4O

1.0092

1.018

"

" sulphate

i .0790

'•35»

1 .0402

1.160

1.0205

I. O8O

1.0103

1.038

«

Lead nitrate . . .

1.1380

I.IOI

0.0699

1.042

I-®3S1

I.OI7

1.0175

1.007

"

Lithium chloride

1.0243

1,142

1.0129

i. 066

1 .0062

I.03I

1 .0030

I.OI 2

"

" sulphate

1-0453

1.290

1.0234

i-i37

1.0115

1.065

1.0057

1.032

"

Magnesium chloride

I-I375

1. 201

1.0188

1.094

1 .009 1

1.044

1.0043

I. O2 1

«

" nitrate .

1.0512

I.I7I

1.0259

1.082

1.0130

I.O4O

1. 0066

I.O2O

«

" sulphate

1.0584

I-367

1.0297

1.164

1.0152

1.078

1.0076

1.032

«

Manganese chloride

1.0513

I.2O9

1.0259

1.098

1.0125

1.048

1.0063

1.023

"

nitrate .

1.0690

I.l83

1.0349

1.087

1.0174

1.043

1.0093

I.O23

"

'" sulphate

1.0728

1.364

1-0365

1.169

1.0179

1.076

1.0087

1-037

"

Nickel chloride . .

1.0591

I.2O5

1.0308

1.097

1.0144

1.044

1 .0067

I. O2 1

H

" nitrate . . .

r-°755

I.lSo

1.0381

1.084

1.0192

1,042

1 .0096

I.OI9

"

" sulphate .

1-0773

1.361

1.0391

1.161

1.0198

1-075

1.0017

1.032

"

Potassium chloride .

1.0466

0.987

1-0235

0.987

1.0117

0.990

1.0059

0-993

"

" chromate

1-0935

I.II3

1-0475

1-053

1.0241

I.O22

I.OI2I

I.OI2

"

" nitrate .

1.0605

Q-975

1-0305

0.982

I.Ol6l

0.987

1.0075

0.992

«

" sulphate

1.0664

1.105

1-0338

1.049

1.0170

I. O2 1

I.OO84

1.008

"

Sodium chloride . .

1.0401

1.097

1 .0208

1.047

1.0107

I.O24

1.0056

I.OI3

Reyher.

" bromide . .

1.0786

1.064

1.0396

1.030

1.0190

I.OI5

I.OIOO

1. 008

"

" chlorate

1.0710

1.090

r-°359

1.042

1.0180

I. O2 2

1.0092

I.OI 2

"

" nitrate .

1-0554

1.065

1.0281

1.026

1.0141

I.OI2

1.0071

I.OO7

u

Silver nitrate . . .

1.1386

1.058

1.0692

i. 020

1.0348

I. OO6

1.0173

I.OOO

Wagner.

Strontium chloride .

1.0676

1.141

1-0336

1.067

1.0171

1.034

1.0084

I.OI4

«

" nitrate .

1.0822

1.115

1.0419

1.049

1. 0208

I.O24

1.0104

I. OH

"

Zinc chloride . . .

1.0509

1.189

1.0302

1.096

1.0152

I-°53

1.0077

I. «O24

"

" nitrate . .

1.0758

1.164

t .0404

i. 086

1.0191

1-039

1.0096

I.OI9

"

" sulphate . . .

1.0792

1-367

1.0402

i-i73

1.0198

1.082

1.0094

1.036

u

* 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 /n=r/ij™, where ^ is the specific viscosity
for a normal solution referred to the solvent at the same temperature, and n the number of gramme molecules in the
solution under consideration. The same rule may of course be applied to solutions stated in percentages instead of
gramme molecules. The table here given has been compiled from the results of Reyher (Zeits. filr Phys. Chem. vol. 2,
p. 749) and of Wagner (Zeits. fur Phys. Chem. vol. 5, p. 31) and illustrates this rule. The numbers are all for 25° C.

SMITHSONIAN TABLES.

144

TABLE 158.

VISCOSITY OF CASES AND VAPORS.

The values of f* given in the table are ib6 times the coefficients of viscosity in C. G. S. units.

Substance.

Temp.

Authority.

Substance.

Temp.

^C.

"

Authority.

Acetone ....

1 8.0

78

Puluj.

Carbon dioxide .

12.8

147

Schumann.

" ''

IOO.O

208

"

Air

O.O

172

Thomlinson.

o.o

168

Obermeyer.

Carbon monoxide

o.o

163

Obermeyer.

a

16.7

18-?

Puluj.

* ***/

. J

Chlorine . . .

o.o

129

Graham.

Alcohol : Methyl .

66.8

135

Stendel.

" ...

2O.O

147

"

Ethyl .

78.4

142

"

Normal

Chloroform . .

17.4

103

Puluj.

propyl

97-4

142

H

Ether ....

16.0

73

"

Isopropyl

82.8

162

"

Normal

Ethyl iodide . .

73-3

216

Stendel.

butyl

116.9

H3

"

Methyl " . . . .

44.0

232

"

Isobutyl

108.4

144

"

Tertiary

Mercury ...

270.0

489

Koch.*

butyl

82.9

160

"

M

300.0

536

M

Ammonia . . .

o.o

.96

Graham.

r ! '

360.0

627

«

" ...

2O.O

108

"

" .

390.0

671

**

Benzene ....

I9.O

79

Schumann.

Water ....

0.0

90

Puluj.

" ....

IOO.O

118

"

" ....

16.7

97

"

" ....

IOO.O

132

L. Meyer &

Carbon disulphide

16.9

99

Puluj.

Schumann.

* The values here given were calculated from Koch's table (Wied. Ann. vol. 19, p. 869) by the formula
/— 270)].

SMITHSONIAN TABLES.

145

TABLE 159.

COEFFICIENT OF VISCOSITY OF CASES.

The following are a few of the formulae that have been Riven for the calculation of the coefficient of viscosity of gases

for different temperatures.

Gas.

Value of ft.

Authority.

Air

Un ( I -1- .OO27 Z 1 t — .OOOOOO"14. t2)

Holman

.OOOI72 (I -|- OO2/3 t)

O. E. Meyer.

u

.0001687 (i 4- .00274. /)

Obermeyer.

Carbon dioxide . .

u u

/*o(i + .003725* — .00000264 *2 + . 00000000417 /3)
.0001414 (I + .00348^)

Holman.
Obermeyer.

Carbon monoxide .

.0001630 (l -J- .00269 ')

"

Ethylene ....

.0000966 (I -f .00350^)

"

Ethylene chloride

.0000935 (I + .0038 It)

«

Hydrogen ....

.0000822 (I -f -OO249 /)

ii

Nitrogen ....

.0001635 (l -f- .00269 «')

"

Nitrous oxide (N2O)
Oxygen

.0001408 (l + .00345^)
.0001873 (l -f- .00283 1)

"

SMITHSONIAN TABLES.

146

TABLE 160.
DIFFUSION OF LIQUIDS AND SOLUTIONS OF SALTS INTO WATER.

The coefficient of diffusion as tabulated below is the constant which multiplied by the rate of change of concentration
in any direction gives the rate of flow in that direction in C. G. S. units. Suppose two liquids diffusing into each
other, and let p be the quantity of one of them per unit volume at a point A , and p' the quantity per unit volume at
an adjacent point S, and x the distance from A to B. Then if jr is small the rate of flow from A towards B is
equal to k (p — P')/JC, where k is the coefficient of diffusion. Similarly for solutions of salts diffusing into the sol-
vent medium, p and p' being taken as the quantities of the salt per unit volume. The results indicate that k depends
on ihe absolute density of the solution. Under c will be found the concentration in grammes of the salt per loo cu.
cms. of the solution ; under « the number of gramme-molecules of water per gramme-molecule of salt or of acid or
other liquid.

Substance.

c

n

fcXIO7

Temp. C.

Authority.

Ammonia .....

- •

16.0

123

4-5

Scheffer.*

" .....

-

85.0

123

4-5

"

Ammonium chloride .

23

-

10.0

Schuhmeister.t

11 U

61.0

152

J7-5

Scheffer

Barium chloride ....

-

46.0

76

8.0

u

Calcium chloride

-

13.0

83

9.0

"

.

—

297.0

74

9.0

"

U (I

-

384.0

79

9.0

"

" " ...

IO

-

79

IO.O

Schuhmeister.

Cobalt chloride ....

10

-

53

IO.O

.14

Copper "

10

—

5°

IO.O

"

Copper sulphate
Hydrochloric acid

10

"

24
267

IO.O

o.o

It

Scheffer.

" ...

-

9.8

2^5

0.0

*

.

-

14.1

'95

0.0

"

.

—

27.1

176

o.o

"

" "...

-

129-5

161

o.o

"

" "...

—

7 "*

3°9

II.O

"

" "...

-

27.6

245

II.O

>t

" "...

-

69.4

234

II.O

"

" "...

—

108.4

213

II.O

"

Lead nitrate ....

-

136.0

76

I2.O

"

" " ....

—

5'4-o

82

I2.O

"

Lithium chloride

14

_

81

10.0

Schuhmeister.

" bromide

20

-

93

IO.O

"

" " ...

38

—

IOO

IO.O

"

" iodide ....

-

93

IO.O

«

Magnesium sulphate .

10

-

32

IO.O

"

" "...

-

45-°

32

5-5

Scheffer.

« u

-

184.0

37

5-5

"

(I II.

-

30.0

3'

IO.O

"

" "...

-

248.0

39

IO.O

"

Potassium chloride

-

32.0

98

7.0

II

" "...

-

107.0

1 06

7.0

"

a u

10

-

127

IO.O

Schuhmeister.

U 11

3°

-

147

IO.O

"

" bromide .

10

-

13'

IO.O

"

...

3°

—

144

IOO

"

" iodide ...

10

-

130

IO.O

"

" ...

3°

-

'45

IO.O

"

" "...

90

-

168

IO.O

"

nitrate

15

-

93

10.0

"

sulphate .

'3

-

87

IO.O

"

Sodium chloride

10

-

97

IO.O

"

" " ...

3°

-

106

IO.O

u

" bromide

3°

_

99

IO.O

*

" iodide ^

.15

-

93

IO.O

"

...

3°

—

IOO

IOO

"

" nitrate .....

10

-

69

IO.O

"

"- carbonate

13

-

IO.O

"

" sulphate

IO

-

76

IO.O

"

Nitric acid . .. '., ^

-

2-9

225

9.0

Scheffer.

' . . . . n

—

$3

234

9«o

*'

" .

-

35-o

206

9.0

"

" " . . . . ^

-

436.0

200

9,0

"

. Sulphuric acid „

-

1 8.8

124

8.0

«<

"• ""•

_

125.0

8-5

"

a u '
....

-

686.0

132

9.0

"

" . . . .

-

0.5

1/50,

13.0

"

11 1C

35-o

144

13.0

ii

* " Z. fiir Phys. Chem." 2, p. 390.
SMITHSONIAN TABLES.

t " Wien. Akad. Ber." vol. 79, 2. Abth. p. 603.

147

TABLE 161.

DIFFUSION OF CASES AND VAPORS.

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 centimetres of mercury.*

Vapor.

Temp. C.

0

kt for vapor
diffusing into
hydrogen.

kt for vapor
diffusing into
air.

kt for vapor
diffusing into
carbon dioxide.

Acids : Formic . . ' . .

0.0

0.5131

0-I3I5

0.0879

65.4

0.7873

0.2035

0-I343

.

84.9

0.8830

0.2244

0.1519

Acetic ....

0.0

0.4040

0.1061

0.0713

... .' .

65.5

O.02II

0.1578

0.1048

u
Isovaleric ....

98.5

o.o

0.7481
0.2II8

0.1965
0-0555

0.1321
0-0375

' ' .' '

98.0

0-3934

0.1031

0.0696

Alcohols : Methyl . . ...

0.0

0.5001

0.1325

0.0880

" • . . .

25.6

0.6015

0.1620

0.1046

•

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

0-543°

0.1475

. O.IO26

Propyl . .

o.o

o-3 1 53

0.0803

0.0577

66.9

0.4832

0.1237

0.0901

83-5

0-5434

o.i379

0.0976

Butyl . . .

0.0

0.2716

0.068 1

0.0476

. .

99.0

0-5045

o. 1 265

0.0884

Amyl ....

0.0

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

Benzene ......

o.o

0.2940

0.0751

0.0527

tt

19.9

0.3409

0.0877

0.0609

45.0

0-3993

O.IOII

0.0715

Carbon disulphide ....

0.0

0.3690

0.0883

0.0629

.

19.9

0.4255

0.1015

0.0726

« n

32.8

0.4626

O.II2O

0.0789

Esters : Methyl acetate .

0.0

0-3357

0.0852

0.0572

" .

20.3

0.3928

O.IOI3

0.0679

. Ethyl

o.o

0-2373

0.0630

0.0450

" "...

46.1

0.3729

O.O97O

0.0666

Methyl butyrate .

o.o

0.2422

0.0640

0.0438

• " "...

92.1

0.4308

O.II39

0.0809

Ethyl "...

0.0

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 ......

0.0

0.2960

0-0775

0.0552

. .

19.9

0.3410

0.0893

0.0636

Water . . .

0.0

0.6870

0.1980

0.1310

" . . . ...

49-5

I.OOOO

0.2827

0.1811

92.4

1.1794

0-3451

0.2384

* Taken from Winkelmanivs 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 kK-=kT(— °) T-, where T is temperature absolute and / the pressure of the gas. The

\ / / ft

exponent « is found to be about 1.75 for the permanent gases and about 2 for condensible gases. The following
are examples : Air — CO3, «=i.c)68; CO» — N2O, « = 2.o5; CO2 — H, «=ri.742; CO — O, «=ri.785: H — O,
«=r 1.755; O — N, «= 1.792. Winkelmann's results, as given in the above table, seem to give about 2 for vapors
diffusing into air, hydrogen or carbon dioxide.

SMITHSONIAN TABLES.

148

TABLE 162.
COEFFICIENTS OF DIFFUSION FOR VARIOUS CASES AND VAPORS.*

Gas or vapor diffusing.

Gas or vapor diffused into.

Temp.
C-.

<a&'.: -**-*

Air .

Carbon dioxide .

O

0.1343 Obermayer.

" . . .

Oxygen .

0

0.1775

"

Carbon dioxide . . .

Air . .

O

0.1423

Loschmidt.

a u

"

O

0.1360

Waitz.

" "...

Carbon monoxide

0

0.1405

Loschmidt.

" "...

" " . .

0

0.1314

Obermayer.

" "...

Ethylene ., .

O

o.i 006

u

" "...

Hydrogen

O

0-5437

"

" "...

Methane

O

0.1465

"

" "

Nitrous oxide

0

0.0983

Loschmidt.

" **"*•

Oxygen

O

0.1802

"

Carbon disulphide

Air ....

0

0.0995

Stefan.

Carbon monoxide

Carbon dioxide

O

01314

Obermayer.

" " . .

Ethylene

O

0.1164

"

" " .

Hydrogen

O

0.6422

Loschmidt.

" " . .

Oxygen

O

0.1802

(i "

" " . .

" ...

O

0.1872

Obermayer.

Ether ....

Air ....

O

0.0827

Stefan.

, . .[

Hydrogen

0

0.3054

"

Hydrogen .

Air . .

O

0.6340

Obermayer.

" • • •

Carbon dioxide .

O

o-5384

••' "

" ....

" monoxide

O

0.6488

"

" ....

Ethane ....

O

0-4593

u

" ....

Ethylene

0

0.4863

u

" ....

Methane . . .

O

0.6254

"

" ....

Nitrous oxide

O

0-5347

"

"

Oxygen

0

0.6788

"

Nitrogen ....

Oxygen

O

0.1787

«

Oxygen ....

Carbon dioxide

O

°-I357

"

" ....

Hydrogen

0

0.7217

Loschmidt.

Sulphur dioxide

Nitrogen
Hydrogen

O
O

0.1710
0.4828

Obermayer.
Losehmidt.

Water

Ai'r . . . .

8

0.2390

Guglielmo.

" ....

" ....

18

0.2475

"

Hydrogen

18

0.8710

* Compiled for the most part from a similar table in Landolt & Boernstein's " Phys. Chem. Tab."
SMITHSONIAN TABLES.

149

TA3LE 163.

OSMOSE.

The following table given by H. de Vries* illustrates an apparent relation between the isotonic coefficient t of solu-
tions and the corresponding lowering of the freezing-point and the vapor pressure. The freezing-points are taken
on the authority of Raoult, and the vapor pressures on the authority of Tammann. t

Substance.

Formula.

Isotonic
' coefficient
X 100.

Molecular
lowering of
the freezing
point X 100.

Molecular
lowering of
the vapor
pressure

X IOOO.

Glycerine

C3H803

• I78

171

Cane sugar ....

Ci2H22On

1 88

185

_

Tartaric acid . . .

C4H606

202

J95

188

Magnesium sulphate . ' ,

MgS04

196

192

156

Potassium nitrate . .

KNO3

300

308

267

Sodium nitrate .

NaNOg

300

337

296

Potassium chloride . .

KC1

287

336

3'3

Sodium chloride .

NaCl

3°5

351

33°

Ammonium chloride .

NH4C|:

300

348

3*3

Potassium acetate

KC2Hg()2

300

345

33 1

Potassium oxalate

K2C204

393

45°

37 2

: Potassium sulphate

K2S04

392

39°

351

Magnesium chloride .

MgCJ2

433

488

5'3

Calcium chloride . .

CaCl2

433

466

TABLE 164.

OSMOTIC PRESSURE.

The following numbers give the result of Pfeffer's § measurement of the magnitude of the osmotic pressure for a one
per cent; sugar solution. The result was found to agree with' that of an equal molecular solution of hydrogen.
The value for the hydrogen solution is given in the third column of the table.

. Temperature
C.

Osmotic pressure
: in atmospheres.

0.649(1 +.00367 4

6.8

0.664

0.665

J3-7

0.691

0.68 1

14.2

0.671

0.682

'5-5

0.684

0.686

22.O

0.721

0.701

32.0

0.716

0.725

36.6

0.746

o-735

' "Zeits. fur Phys. Chem." vol. 2, p. 427.

t The isotonic coefficient is the relative value of the molecular attraction of the different salts for water or the
relative value of the osmotic pressures for normal solutions. In the above table the coefficient for KNO3 was taken
as 3 arbitrarily and the others compared with it. The concentrations of different salts which give equal osmolic pres-
sures are called by Tammann and others isosmotic concentrations; they are sometimes called isotonic concentrations.
The reciprocals of the numbers of molecules in the isotonic concentrations are called by De Vries the isotonic coeffi-
cients.

t See also Tammann, " Wied. Ann." vol. 34, p. 315.

§ Winkelmann's " Handbuch der Physik," vol. i, p. 632.

SMITHSONIAN TABLES.

TABLE 165.
PRESSURE OF AQUEOUS VAPOR, ACCORDING TO RECNAULT.

The last four columns were calculated from the data given in the second column and the density of mercury.

«

cr

£

~

i*

fd

5f

" Er

i

i

q

i*

i_ .

CT

~ &

$

Jj

- u

s

ftj:

V-

3

••£

£

U

•
.. y

°" u

a1"

°~ 3

...G

iC

; o

U Jj

v P

ft

U "

o ft

o

o

<u p

:- 'r

V S"

o

O.

E

H

£-5
££

™ 0

o

c"S

3 C
1*

•i

«~
OH

a o

s-
£

ft

I

ft

5 6
jj'o

£

£•=
O

"O .C
§ C

jr

i E

1°

3 §
M 5

ft

£

H

0

4.60

6.254

O.OSOX)

0.181

0.0061

32.0

40

54.91

74-653

1.061

2.162

0.072

104.0

i

4-94

6.716

.0955

.194

.0065

3*8

41

57-91

78.678

1. 121

2.280

.076

105.8

2

5-3°

7.2061 .1025

.209

.0070

35-6

42

61.01

82.947

1.216

2.404

.080

107.6

3

5-69

7-736

.1100

.224

.0075

37-4

43

64-35

87.488

1.244

2-533

.085

109.4

. 4

6.10

8.291

.1180

.240

.0080

39--

44

67.79

92.165

1.312

2.669

.089

III. 2 j

5

6-53

8.878

0.1263

0.257

0.0086

41.0

45

71-39

97-059

1.381

2.811

0.094

II3-0

6

7.00

9-5 '7

•'354

.276

.0092

42.8

46

75-16

102.184

1.454

2-959

.099

H4.8

i 7

7-49

10.183

.1452

•295

.0099

44-6

47

79.09

107.528

'•530

3-"4

.104

II6.6

8

8.02

10.904

.316

.0107

46.4

48

83.20

"3-"5

1.609

3-276

.109

II8.4

9

8-57

11.651

• 1657

•338

.0114

48.2

49

87.50

118.962

1.692

3-444

.115

I2O.2

10

9.17

12.467

0-1773

0.361

O.OI2

500

50

91.98

125.05

1.78

3.62

O.I2I

122 0

ii

9-79

I3-310

.1893

.386

.013

51.8

51

96.66

131.42

1.87

3.81

.127

123.8

12

10.46

14.207

.2023

.412

.OI4

53-6

52

101.54

138.04

1.96

4.00

.134

125.6

13

11. 16

I5-I73

.2158

•439

.015

55-4

53

106.64

144.98

2.06

4.20

.140

1274

; **

11.91

16.192

•2303

.469

.Ol6

57-2

54

111.95

152.20

2.17

4.41

.147

129.2

15

12.70

17.266

0.2456

0.500

O.OI7

590

55

117.48

I59-72

2.27

4-63

0.155

I3I-0

16

'3-54

18.408

.2618

•533

-Ol8

60.8

56

123.24

167-55

2-39

4.85

.163

132.8

17

14.42

19.605

.2789

.568

.Oig

62.6

57

129.25

'75-72

2.50

5-09

.170

1346

18

15-36

20.883

.2970

.605

.O2O

64.4

58

135-5'

184-23

2.62

5-33

.178

136.4

19

16-35

22.229

.3162

.644

.022

66.2

59

142.02

193.08

2.75

5-59

.187

138.2

20

21

17-39

18.50

23-643
25.152

0-3363

•3577

0.685
.728

0.023

.024

68.0
69.8

60

61

148.79
I55-84

202.29
211.87

.2.88
3.01

5-86
6.14

0.196
.205

I4O.O

I4I.8

22

19.66

26.729

.3802

•774

.O26

71.6

62

163.17

221.84

6.42

.215

143.6

23

20.89

28.401

.4040

.822

.028

73-4

63

170.79

232.20

3-30

6.72

.225

1454

24

22.18

30-I55

.4289

•873

.029

75-2

64

178.71

242.97

3-46

7.04

•235

147-2

25

23-55

32.018

0-4554

0.927

0.031

77.0

65

186.95

254.17

3.62

7-36

0.246

149.0

26

24.99

33-975

.984

•°33

78.8

66

195.50

265.79

3-78

7.70

•257

i £0.8

27

26.51

36.042

.5126

1.044

•034

80.6

67

204.38

277.87

3-95

8.05

.267

152.6

28

28.10

38.204

•5434

.106

•037

82.4

68

213.60

290.40

8.41

.281

154-4

; 29

29.78

40.488

•5759

.172

•039

84.2

69

223.17

303-4I

4-32

8-79

•494

156.2

30

31-55

42.894

0.6101

1.242

O.O42

86.0

70

233.09

316.90

4-51

9.18

0.306

1580

31

45-423

.6461

•315

•044

87.8

71

243-39

330.90

4-71

9-58

•320

159.8

32

35-36

48.074

.6838

•392

•047

89.6

72

254.07

345-42

4.91

IO.OO

•334

161.6

33

37-4i

50.861'

•7234

•473

.049

91.4

73

265.15

360.49

5.12

10.44

•349

163.4

34

39-57

53-798

•7655

•558

•°52_>

93-2

74

276.62

376.08

5-35

10.89

•364

165.2

35

41.83

56.870

0.810

1.647

0-055

950

75

288.52

392.26

5-58

"•36

0.380

167.0

36

44.20

60.093

•855

.740

.058

96.8

76

300.84

409.01

5.82

11.84

•396

1 68.8

37

46.69

63.478

•903

.838

.061

98.6

77

313.60

426.36

6.06

12-35

.414

170.6

38

49-30

67.026

•954

.941

•065

100.4

78

326.81

444-32

6.32

12.87

•430

172.4

39

52.04

70.752

1.007

2.049

.068

IO2.2

79

340.49

462.93

6.58

13.40

.448

174.2

SMITHSONIAN TABLES.

TABLE 165.

PRESSURE OF AQUEOUS VAPOR, ACCORDING TO RECNAULT.

d-

»

a1

C/J

D

c

if

" .

t

JL

E

Jj

g

1 *

£ i

t

"y >,

i

_£

U

S-i:

I/I OJ

11

a..

a;

f

U

o

3

<U P

Q.

~{j

»4

£

Q.

•

II

E °*-
S =
g 5J

•vj:

l|

||

C.

0

1

<"•*,

£ °

E-S

I§

C~U
O-"

11

11

a.
E

H

£•

o

{£

£

£

H

£

O

PL,

£

£

r-1

80

354-64

482.15

6.85

13.96

0.446

176.0

120

1491.28

2027.48

28.85

58.71

1.962

248.0

8l

369.29

502.07

7.14

14-54

.486

177.8

121

«539-25

2092.70

29.78

60.6 1

2.025

249.8

82

384.44

522.67

7-44

15.14

.506

179.6

122

1588.47

2159.62

30-73

62.54

.091

251.6

83

400.10

543.96

7-74

1575

.526

181.4

123

1638.96

2228.26

64-53

.157

253-4

84

416.30

565-99

8.05

16.39

•548

183.2

124

1690.76

2298.69

32.70

66.56

.225

255-2

85

433-04

588.74

8-37

17.01;

0.570

185.0

125

1743-88

2370.91

33-72

68.66

2.295

257.0

86

45°-34

612.26

8.71

17-73

•593

186.8

126

1 798.35

2444.96

34-78

70.80

.366

258.8

87

468.22

636.57

9-°5

18.43

.616

188.6

127

1854.20

2520.89

35-86

73-0°

•43°

260.6

88

486.69

661.68

9.41

19.16

.640

180.4

128

1911.47

2598.76

75-25

•5i5

262.4

89

505-76

687.61

9.78

19.91

.665

192.2

129

1970.15

2678.54

38-11

77-57

.592

'264.2

90

525-45

714.38

10.16

^20.69

0.691

194.0

130

2030.28

2760.29

39.26

79-93

2-671,

266.O

91

545-78

740-31

10.56

21.49

.719

195.8

131

2091.94

2844.12

40.47

82.36

•753

267.8

92

566.76

770.54

10.95

22.31

.746

197.6

132

2155.03

2929.89

41.68

84.84

.836

269.6

93

588.41

799.98

r i .38

23- r 7

•774

199.4

2219.69

3017.80

42.93

87-39

.921

"•271.4

94

610.74

830.34

11.81

24.04

.804

201.2

134

2285.92

3107.85

44.21

89.99

3.008

273.2

95

633.78

861.66

12.26

24-95

0-834

203.0

135

2353-73

3200.04

45-52

92.67

3-097

275.0

96

657-54

893.97

12.71

25.89

.865

204.8

136

2423.16

329443

46.87

95-39

.188

276.8

97

682.03

927.26

I3-J9

26.85

•897

206.6

J37

2494.23

3391.06

48.24

98.19

.282

278.6

98

707.28

961.59

13.68

27-85

•931

208.4

138

2567.00

3489.99

49-65

101. 06

-378

280.4

99

733-3'

996.98

14.18

28.87

•965

21O.2

139

2641.44

359L29

51.06

103.99

•476

282.2

100

760.00

1033.26

14.70

29.92

1. 000

212.0

140

2717.63

3694.78

52-55

106.99

3-576

284.0

IOI

787-59

1070.78

I5-23

31.01

.036

213.8

141

2795-57

3800.75

54-07

110.06

.678

285.8

102

8 1 6.01

1109.41

'5-79

32.13

•074

215.6

142

2875-30

3909.14

55.60

113.20

-783

287.6

103

845.28

1149.21

'6-35

33-28

.112

217.4

143

2956.86

4020.03

57-i6

116.41

.890

289.4

IO4

875-4I

1190.17

16.94

34-46

.152

219.2

144

3040.26

4I33-42

58.79

1 19.69

4.000

291.2

105

906.41

1232.32

T7-53

35-69

I-I93

22 1. 0

145

3I25-55

4249^7

60.44

123.05

4-i 13

293.0

106

938-31

1275.69

18.15

36-94

•235

222.8

146

3212.74

4367.91

62.13

1 26.48

.227

294.8

107

971.14

1320.32

18.78

38-23

.278

224.6

147

33OI-87

4489.09

63.86

129.99

•344

296.6

1 08

1004.91

1366.24

19.44

39-56

.322

226.4

148

3392.98

4612.96

65.62

I33-58

•464

298.4

109

1039.65

1413.47

20. 1 1

40-93

•368

228.2

149

3486.09

4739-55

67.41

'37-25

.587

300.2

110

'075-37

1462.03

20.80

42.34

I.4I5

230.0

150

3581.2

4868.9

69.26

141.0

4.712

302.0

in

1 1 1 2.09

1511-97

21.51

4378

•463

231.8

15'

3678-4

5001.1

71.14

144.8

.840

303-8

112

1149.83

1563.26

22.24

45-25

.513

233.6

'52

3777-7

5136.1

73.06

148.7

.971

305-6

"3

1188.61

1615.99

22.99

46.80

.564

2354

3879.2

5275-0

75-02

152-7

5.104

307-4

114

1228.47

1670.18

23.76

48.37

.6l6

237.2

154

3982.8

5414.8

77.03

156.8

.240

309.2

115

1269.41

1725.84

24-55

49.98

1.670

2390

155

4088.6

5558.6

79.07

161.0

5-38o

3II.O

116

i3ii-47

1783.02

25-37

51-63

.726

240.8

156

4196.6

5705.5

81.22

165.2

.522

3I2.8

117
118

1354.66
1399.02

1841.74

1902.05

26.20
27.06

53-34
55.08

.782
.841

242.6
244.4

158

4306.9
4419.5

5855-5
6008.5

83.29
85-47

169.6
174.0

.667
.815

314.6
316.4

119

1444-55

1963-95

27.94

56.87

.OXII

246.2

159

4534-4

6164.7

87.69

178.5

.966

318.2

SMITHSONIAN TABLES.

152

TABLE 165.
PRESSURE OF AQUEOUS VAPOR, ACCORDING TO RECNAULT.

c
U

it

i

o-i

£
S

L

£

...c

1

fa

c
U

b

ST

M

g1

g

I

"~ 3

.. J3

"re
fa

o

V "

V p

Cu

11 "

a, a.

o

o

V Jj

c c

&

V V

2f£

o

0.

i I

E-s
E -

"H-g

= £

i!

Q,

o.

5 E

£ c

i-g

II

11

D.

1

""o

Is

C "•"

ju'o

S rt

a

E

Ji'o

- =
o —

g'o

£«

E

01

H

£

0

£

£

H

H

0,

O

A

0,

£

H

160

161

4651.6
4771-3

6324.2
6486.8

89.96

92.27

I83.I
187.9

6. 1 20

6.278

320.0

321.8

195

196

10519.6
10746.0

14302.7
1 4609.8

203.43
207.81

414.1
423.'

13.842
14-139

3830

162

4893.4

6652.8

94.63

192.7

6-439

323.6

197

10975.0

I492I.2

212.25

432.1

14.441

3866

163

5017.9

6822.2

97.04

197.6

6.603

3254

198

11209.8

I 5240.4

216.77

441.3

14.749

388.4

164

6994.9

99.50

202.6

6.770

327.2

199

11447.5

155635

221.37

450.7

1 5.062

390.2

165

5274-5

7171.1

IO2.OI

2077

6.940

329.0

200

1 1 689.0

15891.9

226.04

460.1

15-380

392.0

166

5406.7

7350-7

104.56

212-9

7.114

330-8

2OI

11934.4

16225.5

230.79

469.8

1 5-703

393 tS

167

5541-4

7533-9

IO7.l8

218.2

7.291

332-6

2O2

12183.7

16564.7

235.61

479-7

16.031

395-6

168

5678.8

7720.7

109.84

223.6

7-472

334-4

203

12437.0

16908.8

240.54

489.6

16.364

397-4

169

5818.9

7911.1

112-53

229.1

7.656

336-2

2O4

12694.3

I7257-3

245-49

499-8

16.703

399-2

170

5961-7

8105.2

115.29

234.1

7.844

338.0

205

12955-7

17614.0

250-53

510.1

17.047

401.0

171

6107.2

8303-1

ii8.ii

240.4

8.036

339-8

206

13221.1

17974.9

255-67

520.5

I7-396

402.8

172

6255-5

8504.7

120.98

246.3

8.231

341.6

207

13490.8

18341.5

260.88

53'-2

'7-75'

404.6

173

6406.6

8710.2

123.90

252.2

8.430

343-4

208

13764.5

'87I3-7

266.18

541.9

18.111

406.4

174

6560.6

8919.5

126.87

258-3

8.632

345-2

209

14042.5

19091.6

27I-55

552-9

18.477

408.2

175

6717.4

9132.8

129.91

264.5

8.839

347-°

210

14324.8

19475.4

277.01

564.1

18.848

410.0

176

6877.2

9350-0

133-0°

270.8

9.049

348-8

211

14611.3

19864.9

282.58

575-3

19.226 41 I.b

177

7040.0

9571-3

136-15

277.2

9.263

350-6

212

14902.2

20260.5

288.21

586.7

I9.6o8|413.6

178

7205.7

9796.6

1 39-3 5

283.7

9.481

3524

21;

15*97.5

20661. c

293.92

598.3

19.997

415.4

7374-5

10026.1

142.62

290.3

9-703

354-2

214

15497.2

21069;

299.72

610.2

20.391

417.2

180

7546.4

10259.7

M5-93

297.1

9.929

356.o

215

15801.3

21482.8

305-57

622.1

20.791

4190

181

7721.4

10497.7

149.32

304.0

10.150

357-8

216

16109.5

21902.4

3"-57

634.2

21.197

420.8

182

7899-5

10739.9

I52-77

311.0

10.394

359-6

217

16423.2

22328.3

317.62

646.6

21.690

422.6

183

8080.8

10986.4

156-32

3I8.I

10.633

361.4

218

1 6740.9

22760.;

323.78

659.1

22.O27

424.4

184

8265.4

"237.3

1 59.84

3254

10.876

363-2

219

17063.;

23198.6

330-o i

671.8

22.452

426.2

185

8453-2

11490.0

163.47

332-3

11.123

365-0

220

17390.4

23643.2

336-30

684.7

22.882

4280

1 86

187

8644.4
8838.8

11752-5
12016.9

167.17
170.94

340-3
348.0

1 1 -374
11.630

366.8
368.6

221

222

17722.1

18058.6

24094.3
24551.8

342.70
349-21

6977
711.0

23-76M43'-6

1 88

9036.7

12285.9

174.76

355-8

11.885

370-4

223

18399.9

25015.8

355-8'

724.4

24.210433.4

189

9238.0

12559.6

178.65

363.7 12.155

372.2

224

18746.1

25486.4

362.50

738.0

24.666^435.2

190

9442.7

12837.9

182.61

371-8

12.425

374-0

225

19097.0

25963-5

369.29

75'-9

25.128437.0

191

9650.9

13121.0

186.63

380.0

12.690

375-8

226

19452.9

26447.4

376.17

765.8

25-596

438-8

192

9862.7

13408.9

190.72

388.312.977

377-6

227

19813.8

26938.0

383-15

780.9

26.07 '

440.6

'93

10078.0

13701.7

194.88

396.8 13.261

379-4

228

20179.6

27435-4

390.22

794-5

26.552

442.4

194

10297.0

I3999.4

I99-I3

405.4 13.549

381.2

229

20550.5

27939.6

397-40

809.0

27.040

444-2

SMITHSONIAN TABLES.

153

TABLE 166.

PRESSURE OF AQUEOUS VAPOR, ACCORDING TO BROCH.*

Temp.
°C.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

—28

0.46

0-45

0.44

0.43

0-43

0.42

0.41

0.40

0.40

o-39

—26

°-55

0-54

°-53

0.52

0.51

0.50

0.50

0.49

0.48

0.47

—24

0.66

0.65

0.64

0.63

0.62

0.61

0.60

0.58

o-57

0.56

22

0.79

0.78

0.77

0-75

0.74

o-73

0.71

0.70

0.69

0.68

2O

0.94

o-93

0.91

0.90

0.88

0.87

085

0.84

0.82

0.8 1

—18

1. 12

1. 10

i. 08

1. 06

1.05

1.03

.01

0.99

0.98

0.96

— 16

1.32

1.30

1.28

1.26

1.24

1.22

.20

l.lS

1.16

1.14

—14

1.56

1-54

1.51

1.49

1.46

1.44

.42

1-39

T-37

'•35

12

1.84

1.81

1.78

i-75

1.72

1.69

.67

1.64

1.61

1-59

— IO

2-1.5

2.12

2.08

2.05

2.O2

J-99

.96

i-93

1.90

1.87

—8

2-51

2.48

2-44

2.40

2.36

2-33

2.29

2.26

2.22

2.19

—6

2-93

2.89

2.84

2.80

2.76

2.72

2.67

2.63

2-59

2-55

—4

3-4'

3-36

3-31

3-26

3-21

3.16

3-"

3-07

3-03

2.98

— 2

3-95

3^9

3-84

3-78

3-72

3-67

3-62

3-56

3-51

3-46

— O

4-57

4-5°

4-44

4-37

4-31

4-25

4.19

4-13

4.07

4.01

+0

4-57

4.64

4.70

4-77

4.84

4.91

4-98

5-°5

5.12

5.20

2

5-27

5-35

5-42

5-50

5-58

5.66

5-74

S.S2

5-90

5-99

4

6.07

6.15

6.24

6-33

6.42

6.51

6.60

6.69

6.78

6.88

• 6

6.97

7.07

7,17

7.26

7.36

7-47

7-57

7.67

7.78

7.88

8

7-99

8.10

8.21

8-32

8-43

8-55

8.66

8.78

8.90

9.02

10

9.14

9.26

9-39

9-5,1

9.64

9-77

' 9-9°

10.03

10.16

10.30

12

10-43

10-57

10.71

20.85

10.99

11.14

11.28

"•43

11.58

"•73

14

n.88

12.04

12.19

'2-35

12.51

12.67

12.84

1300

13-17

13-34

16

'3-51

13.68

13.86

14.04

14.21

14.40

14.58

14.76

14.95

iS-H

18

15-33

15-52

!5-72

15.92

16.12

16.32

16.52

16.73

16.94

17-15

20

I7-36

17-58

17.80

18.02

18.24

18.47

18.69

18.92

19.16

T9-39

22

19.63

19.87

20. 1 1

20.36

20.61

20.86

21. II

21-37

21.63

21.89

24

22.15

22.42

22.69

22.96

23-24

23-52

23.80

24.08

24-37

24.66

26

24.96

25-25

25-55

25.86

26.16

26.47

26.78

27.10

27.42

27.74

28

28.07

28.39

28.73

29.06

29.40

29.74

30.09

3°-44

30-79

3i-i5

30

3I-5I

31-87

32.24

32.61

32.99

33-37

33-75

34-14

34-53

34-92

32

35-32

35-72

36-13

36.54

36-95

37-37

37-79

38.22

38-65

39.08

34

39-52

39-97

40.41

40.87

41.32

41.78

42.25

42-72

43-19

43-67

36

44.16

44-65

45-J4

45-64

46.14

46.65

47.16

47-68

48.20

48.73

38

49.26

49.80

50.34

50.89

5M4

52.00

52-56

53- 1 3

53-70

54.28

40

42

54-87
61.02

55-46
6r.66

56.05
62.32

56-65
62.98

57.26
63.64

57.87
64.31

5849
64.99

I9'!1

65.67

59-74
66.36

60.38

67.05

44

67.76

68.47

69.18

69.90

70.63

71-36

72.10

72-85

73.60

74.36

46

75-13

75-91

76.69

77-47

78.27

79.07

79.88

80.70

81.52

82-35

48

83.19

84.03

84.89

85-75

86.6 1

87.49

88.37

89.26

90.16

91.06

50

91.98

92.90

93-83

94-77

95-71

96.66

97-63

98.60

99-57

100.56

S2

101.55

102.56

103-57

104.59

105.62

106.65

107.70

108.76

109.82

110.89

54

111.97

113.06

114.16

115.27

116.39

117.52

118.65

119.80

120.95

122.12

56

123.29

124.48

125.67

126.87

1 28.09

129.31

130-54

J3I-79

I33-04

I34-30

58

135.58

136.86

138.15

139.46

140.77

142.10

143-43

144.78

146.14

I47-51

60

148.88

150.27

151.68

I53-09

'54-51

155-95

157-39

158.85

160.32

161.80

62

163.29

164.79

166.31

167.83

1 69-37

170.92

172.49

174.06

i75-65

177-25

64

178.86

180.48

182.12

i83-77

185-43

187.10

188.79

190.49

192.20

1 93-93

66

195-67

197.42

199.18

200.96

202.75

204.56

206.38

208.21

210.06

211.92

68

21379

215.68

217.58

219.50

221.43

223.37

225-33

227.30

229.29

231.29

* This table is based on Renault's experiments, the numbers being taken from Rroch's reduction of the obser-
vations (Trav. et Mem. du Bur. Int. des Poids et Me>. torn. i). The numbers differ very slightly from those of
Regnault (see Table 165). The direct measurements of Marvin given in Table 169 show that .the numbers in this
table

le are high for temperature below zero centigrade.
SMITHSONIAN TABLES.

154

TABLE 166.
PRESSURE OF AQUEOUS VAPOR, ACCORDING TO BROCH.

Temp.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

70

233-3I

235-34

237-39

239-45

241.52

243.62

245-72

247.85

249.98

252.14

72

254-30

256.49

258.69

260.91

263.14

265-38

267.65

269.93

272.23

274-54

74

276.87

279.21

281.58

283.95

286.35

288.76

291-19

293.64

296.11

298.59

76

301.09

303.60

306.14

308.69

311.26

3I3-85

316.45

3 '9-07

321.72

324-38

78

327-05

332-47

335-20

337-95

340-73

343-52

346.33

349.16

352-01

80 354.87

357-76

360.67

363-59

366.54

369-5I

372.49

375-50

378.53

381.58

82

384-64

387-73

390.84

393-97

397.12

400.29

403.49

406.70

409.94

4I3-J9

84

416.47

4I9-77

423.09

426.44

429.81

433- '9

436.60

440.04

443-49

446.97

86

450.47

454.00

457-54

461.11

464.71

468.32

471.96

475-63

479-32

483-03

88

486.76

490.52

494-3'

498. 1 2

501.95

505.81

509.69

513-6°

5*7-53

521.48

90

52547

529.48

533- 5 1

537-57

541-65

545-77

549.90

554-07

558.26

562.47

92

566.71

570.98

575-28

579-6i

583.96

588.33

59274

597-17

601.64

606.13

94

610.64

615.19

61976

624.37

629.00

633.66

638.35

643.06

647.81

652-59

96

657.40

662.23

667.10

672.00

676.00

681.88

686.87

691.89

696.93

702.02

98

707-I3

712.27

7I7-44

722.65

727.89

733- '6

738.46

743.80

749- i 7

754-57

100

760.00

76,47

770-97

776.50

782.07

787.67

-

-

-

-

TABLE 167.

WEIGHT IN GRAINS OF THE AQUEOUS VAPOR CONTAINED IN A CUBIC
FOOT OF SATURATED AIR.*

Temp.

°F.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

70

80

9.0

—10

0356

0.340

0-324

0.309

0.294

0.280

0.267

0.254

0.242

0.230

— °

0.564

0.540

0.516

0-493

0.471

0.450

0.430

0.411

0.391

0-373

+0

0.564

0.590

0.617

0.645

0.674

0.705

0-735

0.767

O.8OI

0.837

10

0.873

c.gio

0.950

0.991

1-033

1.077

1. 122

1.169

1.217

1.268

20

1.321

J-374

143°

1.488

1-549

i.6n

I-675

1-743

1.812

1.882

3°

1.956

2.034

2-113

2.194

2.279

2.366

2-457

2.550

2.646

2-746

40

2.849

2-955

3.064

3-*77

3-294

3-4I4

3-539

3-667

3.800

3-936

50

4.076

4.222

4-372

4.526

4-685

4.849

5.016

5-I9I

5-370

5-555

60

5-745

5-941

6.142

6-349

6-563

6.782

7.009

7.241

7.480

7.726

70

7.980

8.240

8.508

8.782

9.066

9-356

9-655

9.962

10.277

10.601

80

10.934

11.275

11.626

11.987

12.356

12.736

13.127

13.526

13-937

14-359

90

14.790

15-234

1 5.689

16.155

16.634

17.124

17.626

18.142

18.671

19.212

100

19.766

20-335

20.917

21.514

22.125

^ 2.7 50

23.392

24.048

24.720

25.408

IIO

26.112

26.832

27.570

28.325

29.096

29.887

TABLE 1 68.

WEIGHT IN GRAMMES OF THE AQUEOUS VAPOR CONTAINED IN A
CUBIC METRE OF SATURATED AIR.

Temp.
°C-

0.0

1-0

2.0

3.0

4.0

50

6.0

70

8.0

9.0

—20

1.078

0.992

0.913

0.839

0.770

0.706

0.647

0-593

0.542

0.496

— ro

2.363

2.192

2.032

1.882

1.742

1.611

1.489

1-375

1.269

1.170

— o

4.835

4-5I3

4.211

3.926

3-659

3407

3-!7i

2-949

2.741

2-546

+0

4.835

5-!76

5-538

5.922

6.330

6.761

7.219

7-703

8.215

8-757

10

9-330

9-935

10-574

11.249

11.961

12.712

'3-505

1 4-339

i 5.218

16.144

20

17 n8

i8;i43

19.222

20-355

21.546

22.796

24.109

25.487

26.933

28.450

30

30-039

3'-7°4

33-449

35-275

37- '87-

39-187

41.279

43-465

45-751

48.138

SMITHSONIAN TABLES.

* See " Smithsonian Meteorological Tables," pp. 132-133.

TABLE 169.

PRESSURE OF AQUEOUS VAPOR AT LOW TEMPERATURE.*

Pressures are given in inches and millimetres of mercury, temperatures in degrees Fahrenheit and degrees Centigrade.

(a) Pressures in inches of mercury ; temperatures in degrees Fahrenheit.

Temp. F.

o°.o

1°.0

2°.0

3°.0

4°.0

6°-0

6°.0

7°.0

8°.0

9°.0

—50°

—40

—3°
— 20

10

—0

+o

IO

20

30

O.OO2I
.0039
.0069
.0126
.O222

0.0383

•0383
.0631
.1026
.1641

0.0019

.0037

.0065
.0119
.0210

0.0263

.0403
.0665-
.1077
.1718

0.0018
.0035
.0061
.0112
.0199

0.0244
.0423
.0699
.1130
.1798

0.0017
•0033
.0057
.0106
.0188

0.0225
.0444

•0735
.1185

0.0016
.0031
.0054
.0100
.0178

0.0307
.0467
.0772
.1242

0.0015
.0029
.0051
.0094
.0168

0.0291
.0491
.0810
.1302

0.0013
.0027
.0048
.0089
.0159

0.0275

•0515
.0850

•1365

0.0013
.0026
.0046
.0083
.0150

0.0260
.0542
.0891
.1430

O.OOI2
.OO24
.0044
.0078
.OI4I

O.O247
.0570.

•0933
.1497

O.OOII

.0022
.0041

.0074
•0133

0.0234

.0600

.0979
.1568

(to) Pressures in millimetres of mercury ; temperatures in degrees Fahrenheit.

Temp. F.

o°.o

1°.0

2°.0

3°.0

4°.0

5°.0

6°.0

7°.0

8°.0

9°.0

—50°

—40
_3o
— 20

— IO

—0°

+o

10

20

30

0.053

.100

.176
.319

•564
0.972

.972

1.603

2.607

4.169

0.049

.094

.165

.301

•534

0.922
1.023
1.688
2-735
4-364

0.046
.089

•155
.284

•505

0.873
1-075
1.776
2.869
4.568

0.043
.084
.146
.268
.478

0.826
1.129
1.867
3.009

0.040
.079
.138

•253

.452

0.781
1.186
1.961
3-155

0.037
.074
.130

•239

.427

0.738
1.246
2.058
3-3°7

0.034
.069
.123
.225
•403

0.698
1.309
2.158
3-466

0.032
.065
.117

.212

.384

0.661
I-376
2.262

3-631

0.030
.061
.1 II
.199
-358

0.627
1.447
2.371
3-803

0.028

•057
.105
.187
•338

0-595
r-523
2.486
3.982

(0) Pressures in inches of mercury ; temperatures in degrees Centigrade.

Temp. C.

o°.o

1°.0

2°.0

3°.0

4°.0

B°.0

6°.0

7°.0

8°.0

9°.0

—0°

— IO

— 20

—30
—40

0.1798

.0772
.0307

.OI 12

.0040

0.1655
.0706
.0278
.0101
.0036

0.1524
.0645
.0252
.0091
.0032

0.1393

.0588
.0229
.0082
.0029

0.1290

•0537
.0208
.0073
.0025

0.1185
.0491
.0188
.0065

.0022

0.1091
.0449
.0171
.0059
.0020

0.0998
.0411
•0153
•0°53
.0017

0.0916

•0375
.0138
.0048
.0015

0.0842
.0341
.0124
.0044
.0013

(d) Pressures in millimetres of mercury ; temperatures in degrees Centigrade.

Temp. C.

o°.o

1°.0

2°.0

3°.0

4°.0

5°.0

6°.0

7°-0

8°.0

9°.0

—0°

IO

— 20

—3°
—40

4.568

1.961

0.781

0.284

O.IOO

4.208
1.794
0.706
0.256
0.090

3-875
I-637
0.641
0.231
0.081

3-565
1-493
0-583
0.207
0.072

3-277

'•363

0.528
0.185
0.064

3.009
1.246
0.478
0.165
0.057

2.767
1.140
0.432
0.148
0.050

2-534
1.044
0.389

o-i33
0.044

2.327
0.952
0-350

O.I 21
0.039

2.138
0.864
o-3 r 5

O.I 10

0.034

* Marvin's results (Ann. Rept. U. S. Chief Signal Officer, 1891, App. 10).
SMITHSONIAN TABLES.

I56

TABLE 1 7O.
PRESSURE OF AQUEOUS VAPOR IN THE ATMOSPHERE.

This table gives the vapor pressure corresponding to various values of the difference t — ^ between the readings of
dry and wet bulb thermometers and the temperature i1, of the wet bulb thermometer. The differences / — /t are
given by two-degree steps in the top line, and t^ by degrees in the first column. Temperatures in Centigrade
degrees and Regnault's vapor pressures in millimetres of mercury are used throughout the table. The table was
calculated for barometric pressure B equal to 76 centimetres, and a correction is given for each centimetre at the
top of the columns.*

«1

53-

2

4

6

8

10

12-

14

16

18

20

Difference per
i°of*-ft

Corrections for
B per centi-
metre, t

.013

.026

.040

•°53

.066

.079

.092

.106

.119

• 132

—10

1.96

0.96

0 100

—9

2.14

1.14

0.14

O.IOO

—8

2-33

i-33

o-33

O.IOO

—7

2-53

i-53

o-53

c. x&tnple.

O.IOO

—6

2.76

1.76

0.76

t-t^— 7.2

O.IOO

— 5

tfj — 1O.O

3.01

2.OI

I.OO

.5=74-5

O.IOO

—4

3.28

2.28

1.27

0.27

Tabular number=r 6.12 — 6X.ioi= 5.51

O.IOO

I ~3

m

2-57

1.56

0.56

Correctioa for B= 1.5 X .048 . . — .07

O.IOO

— 2

3.88

2.88

1.87

0.87

Hence we get/ . . . = 5.58

O.IOO

— I

4.22

3.22

2.21

1. 21

O.2I

O.IOO

0

4.60

3.60

2-59

i-S9

o-59

O.IOO

I

4-94

3-93

2.92

1.92

0.92

O.IOO

2

5-3°

4.29

3-29

2.28

1.28

0.27

O.IOO

3

5.69

4.68

3.68

2.67

1.66

0.66

O.IOI

4

6.10

5-09

4.09

3.08

2.07

1.06

0.05

O.IOI

5

6-53

5-52

4:5i

3-5°

2.49

1.48

0.48

O.IOI

6

7.00

5-99

4.98

3-97

2.96

i-95

0.94

O.IOI

7

7-49

6.48

5-47

4-45

3-44

2-43

1.42

0.41

O.IOI

8

8.02

7.01

5-99

4.98

3-97

2.96

1.94

0-93

O.IOI

9

8.57

7-56

6-54

5-53

4.51

3-50

2-49

1.48

0.46

O.IOI

10

9.17

8.16

7.14

6.12

5-' r

4.09

3.08

2.07

1. 06

0.05

O.IOI

ii

9-79

8.77

7-76

6-74

5-73

4.71

3-69

2.68

1.66

0.64

0.102

12

10.46

9-44

8-43

7.41

6-39

5-37

4-36

3-34

2.32

1.30

0.28

O.I O2

13

ii. 16

10.14

9.12

8.10

7.09

6.07

5-°5

4-03

3.01

1.99

o-97

O.I O2

14

11.91

10.89

9-87

8.85

7-83

6.8 1

5-79

4-77

3-7i

2.69

1.67

0.102

15

12.70

11.68,

10.66

9.64

8.62

7.60

6.58

5-56

4-54

3-52

2-50

O.I O2

16

!3-54

12.52

11.50

10.47

9-45

8-43

7.41

6-39

5-37

4-35

3-33

O.I O2

17

14.42

13.40

12.37

11.35 10-33

9-3'

8.28

7.26

6.24

5.22

4.20

0.102

18

I5-36

U.34

'3-3*

12.29 11.26

10.24

9.21

8.19

7.17

6.15

5-!3

O.I O2

'9

16.35

'5-33

14.30

13.27

12.25

11.22

10.20

9.17

8.15

7-i3

6.1 1

O.I O2

20

17-39

16-37

15-34

H-31

13.28

12.26

IK23

10.21

9.18

8.15

7.12

0.103

21
syy

18.50
19.66

17.47
18.63

16.45
17.60

15.42 14.39
l6-57 ; iS-54

J3-36
H-51

!2.33

13.48

11.31
12.46

10.28
"•43

9-25
10.40

8.22

9-37

0.103
0.103

23

20.89

19.86

18.83

; 17-80

16.77

15-74

14.71

13.68

12.66

11.63

1 0.60

0.103

24

22.18

21.15

20.12

19.09

18.05

17.02

15-99

14.96

13-94

12.91

11.88

0.103

25

23-55

22.52

21.49

20.45

19-43

18.39

17-36

16-33

15-3°

14.27

13-24

0.103

26

24-99

23.96

22.92

21.89

20.86

19.82

18.79

17.76

i6-73

I5-70

14.67

0.103

27

26.51

25.48

24.44

23-40

22.37

21-34

20.30

19.27

18.24

17.21

16.18

0.103

28

28.10

27.07

26.03

24.99

23.96

22.92

21.89

20.85

19.82

18.79

17.76

0.103

29

29.78

28.75

27.71

26.67

25-63

24.59

23-56

22.52

21.49

20.46

19-43

0.103

30

3T-55

30-51

29.47

28.43

27.40

26.36

25.32

24.29

23.25

22.22

21. 18

0.104

31

33-4i

32-37

31-33

30.29

29.25

28.22

27.18

26.14

25.10

24.07

23-03

0.104

32

35-36

34-32

33-28

32.24

3'-2i

30-17

29.13

28.09

27.05

26.OI

2497

0.104

33

37-41

36-37

35-33

34-29

33-25

32.22

31.18

3°- J4

29.10

28.06

27.02

0.104

34

39-57

38-53

37-48

36-44

35-40

34-36

33-32

32.28

3I-24

30.20

29.16

0.104

35

41.83

40.79

39-74

38.70

37.66

36.62

35-68

34-64

33-6o

32-56

31-52

0.104

36

37

44.20
46.69

43.16
45-65

42.11
44.60

41.07
43-56

40-03
42.52

3S-99
41.48

37-95
40.44

36.90
39-39

35-86
38-35

34.82

37-31

3378
36.27

0.104
0.104

38

49-3°

48.26

47.21

46-17

45- ! 3

44.08

43-04

41.99

40.95

39-91

38.87

0.104

39

52-94

51.00

49-95

48.91

47-86

46.82

45-77

44-73

43-78

42-74

41.69

0.105

* The table was calculated from the formula /=/i —0.00066 £(f—(t) (i +0.00115^) (Ferrel, Annual Report
U. S. Chief Signal Officer, 1886, App. 24).

I When B is less than 76 the correction is to be added, and when B is greater than 76 it is to be subtracted.

SMITHSONIAN TABLES.

157

TABLE 171.

DEW-

The first column of this table gives the temperatures of the wet bulb thermometer, and the top line the difference
the table. The dew-points were computed for a barometric pressure of 76 centimetres. When the barometer differs
and the resulting number added to or subtracted from the tabular number according as the barometer is below or

I

*—/!=!

Z

3

4

5

6

7

8

Dew-points corresponding to the difference of temperature given in the above line and the
wet-bulb thermometer reading given in first column.

57/55 =

.04

.11

.22

49

— 10

— 13.2

— 17.9

— 9

I2.O

1 6.0

— 22.O

— 8

10-7

14-3

194

— 7

9-5

12.7

I7.I

— 24.0

— 6

8-3

1 1.2

14.9

20.3

87/85 =

03

.06

.11

.18

•31

43

— 5

— 9-7

— 12-9

— 17-5

— 24-5

— 4

6.0

8-3

II. I

14.8

20.1

— 3

4.8

6.9

9.4

12.6

1 6.8

— 23-4

2

3-6

5-5

7-8

10.5

13.9

18.9

— i

2-5

4.2

6.2

8.5

"•5

iS-4

— 21.0

87/55 =

.02

.04

.07

.10

.14

.19

.26

38

0

— 1.3

— 2.9

-4-8

— 6.8

— 9-3

— 123

_,6.5

— 22.9

i

0.3

3-5

5-3

7.6

IO.2

13-S

18.3

2

+ 0.6

0.7

2.2

3-9

6.1

8-3

n. i

14.7

3

1.7

+ O.2

I.O

2.6

4.6

6.4

8.9

11.9

4

2.8

1.4

0.0

1.3

3-1

4-7

6.9

9.4

57/55 =

.02

•03

05

.07

.09

.11

14

.18

5

3-8

2.6

+ 1.2

— O.I

-1.6

— 3-2

— 5-0

— 7.1

6

4-9

3-7

2-5

+ i.i

0.2

3-3

5-2

7

6.0

4.9

3-7

2.4

+ I.I

o-3

1.8

3-4

8

7.0

6.0

4-9

3-7

2-5

4- i.i

°-3

1.8

9

8.1

7.1

6.1

5-°

3-9

2.6

+ 1.2

O.I

87/85 =

.01

.02

•03

°5

.06

.08

.10

.12

10

9.1

8-3

7-3

6-3

5-2

4.1

2.8

+ 1.5

ii

10.2

9-3

8.4

7-5

6-5

S-5

4-3

3.1

12

II. 2

10.4

9.6

8.7

7-8

6.8

5-8

- 4-7

-13

12.3

-"•5

10.7

9.9

9.1

8.2

7-2

6.2

14

13-3

12.6

11.9

ii. i

10.3

9-°5

8.6

7.6

5 7/85 =

.01

.02

•03

.04

.06

07

08

15

144

J3-7

13.0

12.3

ii-5

10.8

9-9

9.1

16

IS-4

14.8

14.1

12.7

I2.O

10.5

17

16.4

15.8

'5-2

14.6

13-9

13.3

12.6

1 1.8

18

17.5

16.9

16.3

15-7

15.1

14-5

13.8

13.1

19

I8.5

18.0

17.4

16.9

16.3

14.4

8 7/85 =

005

.01

.015

.02

.027

•033

04

•°5

20

19-5

19.0

18.5

1 8.0

17.4

16.9

16.3

iS-7

21

20-5

20.1

19.6

19.1

18.6

18.1

I7-S

17.0

22

21.6

21. 1

20.7

20. 2

19.7

19.2

18.7

18.2

23

22.6

22.2

21.7

21-3

20.8

20.4

19.9

19.4

24

23.6

23.2

22.8

224

22.O

21.5

21. 1

2O.6

87/85 =

005

.01

015

.02

.025

•03

•035

.04

25

24.6

24.2

23-9

23-5

23.1

22.7

22.2

21.8

26

25-6

25-3

24.9

24-5

24-2

23.8

23-4

23.0

27

26-7

26.3

26.O

25.6

25-3

24.9

24-5

24.1

28

27.7

27-3

27.0

26.7

26.4

26.0

25-7

25-3

29

28.7

28.4

28.1

27.8

27.4

27.1

26.8

26.4

87/85 =

.003

.OO6

.01

-013

.OI7

.019

.022

.026

30

29.7

29.4

29.1

28.8

28.5

28.2

27.9

27.6

3'

3°-7

3°-5

30.2

29.9

29.6

29-3

29.0

28.7

32

31.7

31-5

31.2

3°-9

3°-7

3°-4

3O.I

29.8

33

32.8

32-5

32.2

32.0

3*-7

3I-S

31.2

30-9

34

33-8

33-5

33-3

33-°

32.8

32-5

32.3

32.0

8 7/85 =

003

.005

008

.010

.013

.016

.Oig

.021

35

34-8

34-5

34-3

34.1

33-8

33-6

33-4

33.1

36

35-8

35-5

35-3

35- i

34-9

34-6

34-4

34-2

37

36.8

366

36.2

36.0

35-7

35-5

35-3

38

37-8

37-6

37-4

37-2

37-o

36.8

36.6

36-4

39

38.8

38.6

38-2

38.0

37-9

37-6

37-5

SMITHSONIAN TABLES.

I58

TABLE 171 .
POINTS.

between the dry and the wet bulb, when the dew-point has the values given at corresponding points in the body ol
from 76 centimetres the corresponding numbers in the lines marked &T/&B are to be multiplied by the difference;
or above 76. See examples.

*

*-<, = 9

10

11

12

13

14

15

Dew-points corresponding to the difference of temperature given in the above line and the
wet-bulb thermometer reading given in first column.

1 1

EXAMPLES.

(i) Given £= 72, /]=: 10, t — /i = 5.

Then tabular number for tt — 10 and t — ^1 = 5 is 5.2
Also 76 — 72 = 4 and 5 '/'/«#=. 06.

.'. Correction =10.06 X 4= .... .24

Hence the dew-point is 5.44

(2) Given .5 = 71.5, /, — 7,/ — /1=:8.

Then, as above, tabulated number =: . . 3.4

2

Correction = 0. 15 X4 5— 67

Dew-point = 4.07

57755 =

•45

.67

0

i

2

2O.O

3

I5.8

— 22.2

4

12.4

16.8

5 7755 =

23

29

•37

•44

•54

.66

•72

5

— 19.8

— 13-1

— 17.7

6

7-4

IO.I

13-4

— 18.1

7

5-3

7-6

IO.I

'3-5

-18.3

8

3-3

5-2

7-4

10. 1

I3-S

-18.3

9

1.6

3-2

5-1

7.2

9-9

— 17.2

5 7755 =

.14

17

.20

.22

25

.29

•36

10

o.o

— 1-3

— 3-°

— 4-7

— 6.8

— 9-4

— 12.5

ii

+ 1.8

+ 0-3

I.O

2.6

4-3

6-3

8.8

12

3-5

2.2

+ 0.8

0.6

2.1

3-7

5-7

13

5.1

3-9

2-7

~\~ !-3

O.I

1.6

3-1

>4
57755 =

6.7
.09

5-6
.11

4-5

.12

3-3
.14

.16

+ 0.5
.18

0.9

.20

15

8.2 '

7-2

6.2

5.1

3-9

2-7

_|_ I.T

16

9.6

8.7

7-8

6.8

5-8

4-7

3-5

17

I I.O

IO.2

9.4

8-5

7-5

6-5

5-5

18

12.4

II.7

10.9

IO.I

9.2

8-3

7-4

'9

13.8

I3-1

12.4

1 1.6

10.8

I O.O

9.1

87755 =

.06

.07

.08

.09

.10

.11

•13

20

15.1

14-5

13-8

12.4

1 1.6

10 8

21

16.4

15-8

15.2

M-S

'3-9

13.2

12.5

22

17.6

17.1

16.5

15-9

'5-3

14.7

14.0

23

18.9

18.4

17.9

17-3

1 6.8

16.2

I5-7

24

20. 1

19.6

19.2

18.7

18.1

17.6

17.0

57755 =

•045

05

.06

.06

.07

.08

.09

25

21.4

20.9

20.4

2O.O

'9-5

19.0

18.5

26

22.6

22.1

21.7

21-3

20.8

20.3

19.9

27

23-7

234

22.9

22-5

22.1

21.7

21.2

28

24.9

24-5

24.2

23.8

23-4

23.0

22.6

29
57755 =

26.1
031

25-7
•035

25.4
.041

25.0
.047

24.6
•°53

24.2
.06

23-9
.07

30

27.2

26.9

26.6

26.2

25-9

25-5

25.2

31

28.4

28.1

27.8

27.4

27.1

26.8

26.4

32

29.5

29.2

28.9

28.6

28.3

28.0

27.7

33

30-7

30-4

30.1

29.8

29.5 •

29.2

28.9

34
57755 =

31.8
.024

3I-S
.027

31.2
.029

30-9
032

3°-7
°37

3°-4
037

3O.I
.04

35

32.9

32.6

32-4

32.1

31.8

31-6

36

34-0

33-7

33-5

33-3

33-o

32.8

32-5

3£ *

t-i

34-9

34-6

34-4

34-2

33-9

33-7

38

. -2

35-9

35-7

35-5

35-3

35-1

34-8

39

37-3

37-i

36-8

36-6

36-4

36.2

36.0

SMITHSONIAN TABLES.

159

TABLE 172.

VALUES OF 0.378e.*

This table gives the humidity term 0.3781?, which occurs in the equation fr=L — = So~ — °'3 for the calcu-

760 760

lation of the density of the dry air in a sample containing aqueous vapor at pressure e ; So is the density at normal
barometric pressure, B the. observed barometric pressure, and h the pressure corrected for humidity. For values

of — see Table 174. Temperatures are in degrees Centigrade, and pressures in millimetres of mercury.

Dew-
point

Vapor
pressure.
e

0.3786.

Dew-
point.

Vapor
pressure.
«

0.378 e.

Dew-
point.

Vapor
pressure.
e

0.3786.

— 30°

0.38

0.14

0

4-57

1-73

30°

3I-5I

11.91

— 29

.42

.16

i

4.91

1.86

3'

33-37

12.61

— 28

.46

•17

2

5-27

1.99

32

35-32

13-35

— 27

•5°

.19

3

5.66

2.14

33

37-37

14-13

— 26

•55

.21

4

6.07

2.29

34

39-52

14.94

— 25

0.61 '

0.23

5

6.51

2.46

35

41.78

'5-79

— 24

.66

.25

6

6.97

2.63

36

44.16

16.69

— 23

•73

.28

7

7-47

2.82

37

46.65

17-63

22

•79

•30

8

7-99

3.02

38

49.26

18.62

21

.87

•33

9

8-55

3-23

39

52.00

19.66

— 20

0.94

0.36

10

9.14

3-45

40

54-87

20.74

— 19

1.03

•39

ii

9-77

3-69

4i

57-87

21.86

— 18

.12

.42

12

10.43

3-94

42

61.02

23.06

— 17

.22

.46

13

11.14

4.21

43

64.31

24.31

— 16

•32

•So

14

11.88

4-49

44

67.76

25.61

— 15

1-44

0.54

15

12.67

4-79

45

7I-36

26.97

— 14

•|6

•59

16

I3-5I

5-"

46

75-'3

28.40

— 13

.69

.64

17

14.40

5-44

47

79.07

29.89

12

.84

.70

18

T5-33

5-79

48

83.19

3i-45

— I I

•99

•75

19

16.32

6.17

49

87.49

33-07

— 10

2.15

0.81

20

I7-36

6.56

50

91.98

34-77

— 9

•33

.88

21

18.47

6.98

Si

96.66

36-54

— 8

•5'

•95

22

19.63

7.42

52

. 101.55

38.39

— 7

.72

1.03

23

20.86

7.89

53

106.65

40.31

— 6

•93

.11

24

22.15

8-37

54

111.97

42.32

— 5

3-'6

1.19

25

23.52

8.89

55

"7-52 .

44.42

— 4

.41

.29

26

24.96

9-43

56

123.29

46.60

3

.67

•39

27

26.47

IO.OI

57

129.31

48.88

•95

•49

28

28.07

10.61

58

I35-58

51.25

— i

4-25

.61

29

29.74

11.24

59

142.10

53-71

* This table is quoted from " Smithsonian Meteorological Tables," p. 225.
SMITHSONIAN TABLES.

1 60

TABLE 173.

RELATIVE HUMIDITY.*

This table gives the humidity of the air, for temperature t and dew-point d in Centigrade degrees, expressed
in percentages of the saturation value for the temperature t.

Depression of
the dew-point.
t — d

Dew-point (d).

Depression of
the dew-point.
t — d

Dew-point (d).

— 10

o

+ .0

+ 20

+3°

-,0

0

+ ,0

+ 20

+ 30

C.

C.

o°.o

IOO

IOO

IOO

IOO

IOO

8°.0

54

57

60

62

64

O.2

98

99

99

99

99

8.2

54

56

59

61

63

0.4

97

97

97

98

98

8.4

53

56

58

60

63

0.6

95

96

96

96

97

8.6

52

55

57

60

62

0.8

94

94

95

95

96

8.8

5i

54

57

59

61

1.0

92

93

94

94

94

9.0

51

53

56

58

61

1.2

9i

92

92

93

93

9.2

5°

S3

55

58

60

1.4

9°

90

91

92

92

9-4

49

52

55

57

59

1.6

88

89

90

91

91

9.6

48

51

54

56

59

1.8

8?

88

89

90

90

9.8

48

51

53

56

58

20

86

87

88

88

89

10.0

47

So

53

55

57

2.2

84

85

86

87

88

10.5

45

48

5i

54

2.4

83

84

85

86

87

II.O

44

47

49

52

2.6

82

83

84

85

86

"•5

42

45

48

51

2.8

80

82

83

84

85

12.0

4i

44

47

49

3.0

79

81

82

83

84

12.0

39

42

45

48

3-2

78

80

81

82

83

13.0

38

4i

44

46

3-4

77

79

80

81

82

'3-5

37

40

43

45

3-6

76

77

79

80

82

14.0

35

38

4i

44

3-8

75

76

78

79

81

14.5

34

37

40

43

4.0

73

75

77

78

80

15.0

33

36

39

42

4.2

72

74

76

77

79

15-5

32

35

38

40

4.4

71

73

75

77

78

16.0

31

34

37

39

4-6

70

72

74

76

77

16.5

3°

33

36

38

4.8

69

7i

73

75

76

17.0

29

32

35

37

5.0

68

70

72

74

75

17.5

28

31

34

36

5-2

67

69

7i

73

75

1 8.0

27

3°

33

35

5-4

66

68

70

72

74

18.5

26

29

32

34

5.6

65

67

69

7i

73

19.0

25

28

3i

33

5.8

64

66

69

70

72

»9-5

24

27

3°

33

6.0

63

66

68

70

7i

20.0

24

26

29

32

6.2

62

65

67

7i

2I.O

22

25

27

6.4

61

64

66

68

70

22.O

21

23

26

6.6

60

63

65

67

23.0

19

22

24

6.8

60

62

64

66

68

24.0

18

21

23

7.0

59

61

63

66

68

25.0

17

19

22

7-2

58

60

63

65

67

26.0

16

18

21

7-4

57

60

62

64

66

27.0

15

17

20

7.6

56

59

61

63

65

28.0

H

16

19

7.8

.55

58

60

63

65

29.0

'3

15

18

8.0

54

57

60

62

64

3O.O

12

14

17

* Abridged from Table 45 of " Smithsonian Meteorological Tables."
SMITHSONIAN TABLES.

TABLES 174, 175.

DENSITY OF AIR FOR DIFFERENT PRESSURES AND HUMIDITIES.

TABLE 174. — Values of h , from h = l to h = 9, for the Computation of Different Values of the Ratio
760

of Actual to Normal Barometric Pressure.

Tl

iis gives the density of air at pressure h in terms of the density at normal atmosphere pressure. When the air
contains moisture, as is usually the case with the atmosphere, we have the following equation for the dry air
ure : A=£ — 0.378?, where e is the vapor pressure, and B the observed barometric pressure corrected for
erature. When the necessary observations are made the value of e may be taken from Table 1 70, and then

press
tempe

0.378? from Table 172, or the dew-point may be found and the value of 0.378^ taken from Table 172.

h

h
760

1

3

0.0013158
.0026316
.0039474

4

0.0052632
.0065789
.0078947

7

8
9

0.0092105
.0105263
.0184210

EXAMPLES OF USE OF THE TABLE.

T.

To find the value of — when h =: 754.3
760

h •=. 700 gives .92105
50 ' .065789
4 .005263

-3 " .000395

754-3 -992497

To find the value of — when h = 5.73
760

k =r 5 gives .0065789
•7 .0007895

.03 " .0000395

5-73

.0074079

TABLE 175. —Values of the logarithms of /( for values of h between 80 and 340.

760

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

0

i

2

3

4

5

6

7

8

9

80

T.O2228

1.02767

1.03300

7.03826

7.04347

7.04861

7.05368

7.0587 1

7.06367

7.06858

90

•07343

.07823

.08297

.08767

.09231

.09691

.10146

.10596

.1 1041

. 1 1 482

100

7.11919

1.12351

7-12779

7.13202

7.13622

7.14038

7.14449

7.14857

7.15261

7.15661

110

.16858

.16451

.16840

.17226

.17609

.17988

.18364

•18737

.19107

•19473

1 20

•19837

.20197

•20555

.20909

.21261

.21611

.21956

.22299

.22640

130

•23313

.23646

•23976

.24304

.24629

•24952

•25273

•25591

•25907

.26220

140

•26531

.26841

.27147

•27452

•27755

.28055

•28354

.28650

•28945

.29237

ISO

1.29528

1.29816

1.30103

7.30388

7.30671

7.30952

7.31231

7.31509

7.31784

7.32058

160

•32331

.32616

.32870

•33!37

•33403

•33667

•33929

.34190

•3445°

•34/07

170

.34964

.35218

•35471

•35723

•35974

.36222

.36470

.36716

.36961

•37204

1 80

•37446

•37686

•37926

•38164

.38400

•38636

.38870

.39128

•39334

•39565

190

•39794

.40022

.40249

.40474

.40699

.40922

.41144

•41365

•41585

.41804

200

7.42022

1.42238

7.42454

7.42668

7.42882

7.43694

M33°5

7-435 T 6

7.43725

7-43933

2\O

.44141

•44347

•44552

•44757 i -44960

.45162

.45364

•45565

.45764

•459%

22O

.46161

.46358

.46^4

•46749

•46943

•47137

•47329

•47521

.47712

.47902

2JO

.48091

.48280

.48467

.48654

.48840

.49025'

.49210

•49393

•49576

.49758

240

.49940

.50120

.50300

.50479

.50658

•50835

.51012

.51188

•51364

•S'539

250

1-517*3

1.51886

7.52059

7.52231

7.52402

7-52573

7.52743

7.52912

7.53081

7.53249

2<X>

•53416

•53583

•53749

•539M

•54079

•54243

•54407

•54570

•54732

.54894

2;tO

•55055

•552i6

•55376

•55535

•55694

•55852

.56010

.56167

•56323

•56479

280

•56634

•56789

.56944

•57097

•57250

•57403

•57555

•57707

.57858

.58008

290

•58158

.58308

•58457

.58605

•58753

.58901

.59048

•59'94

•59340

.59486

300

7.59631

7-59775

7.59919

7.60063

7.60206

7.60349

7.60491

7.60632

7.60774

7.60914

310

.61055

•61195

•6i334

•6i473

.61611

.61750

.61887

.62025

.62161

.62298

320

.62434

.62569

.62704

•62839

•62973

.63107

.63240

.63373

.63506

•63638

33°

.63770

.63901

.64032

.64163

.64293

.64423

•64553

.64682

.64810

.64939

340

.65067

.65194

•65321

.65448

•65574

.65701

.65826

•65952

.66077

.66201

SMITHSONIAN TABLES.

l62

TABLE 175.

DENSITY OF Am.

Values oi logarithms of — for values of h "between 350 and 800.
760

h

Values of log —.
760

0

1

2

3

4

5

6

7

8

9

35O

1.66325

1.66449

7.66573

7.66696

7.66819

7.66941

7.67064

7.67185

7.67307

7.67428

360

•67549

.67669

.67790

.67909

.68029

.68148

.68267

.68385

.68503

.68621

37°

.68739

.68856

•68973

.69090

.69206

.69322

•69437

•69553

.69668

.69783

380

.69897

.70011

.70125

.70239

•70352

.70465

•70577

.70690

.70802

.70914

390

.71025

.71136

.71247

•71358

.71468

.71578

.71688

.71798

.71907

.72016

400

T.72I25

1.72233

7.72341

7.72449

7-72557

7.72664

7.72771

7.72878

7.72985

1.73091

410

•73'97

•73303

.73408

•735H

•736i9

•73723

.73828

•73932

.74036

.74140

420

.74244

•74347

•7445°

•74553

•74655

•7475s

.74860

.74961

•75063

•75l64

43°

•75265

•75366

•75467

•75567

.75668

•75768

•75867

•75967

.76066

.76165

440

.76264

.76362

.76461

•76559

•76657

•76755

.76852

.76949

.77046

•77143

450

1.77240

7.77336

7.77432

7.77528

7.77624

7.77720

7-778I5

7.77910

7.78005

7.78100

460

.78194

.78289

•78383

•78477

•78570

.78664

•78757

.78850

•78943

.79036

470

.79128

.79221

•793'3

•79405

•79496

.79588

.79679

.79770

.78961

•79952

480

.80043

•80133

.80223

•80313

.80403

.80493

.80582

.80672

.80761

.80850

49°

.80938

.81027

.81115

.81203

.81291

•81379

.81467

•81554

.81642

.81729

500

T.8i8i6

1.81902

7.81989

7.82075

7.82162

7.82248

7.82334

7.82419

7.82505

7.82590

510

.82676

.82761

.82846

.82930

•83015

.83099

.83184

.83268

•83352

•83435

520

$3$*9

.83602

.83686

.83769

.83852

•83935

.84017

.84100

.84182

.84264

53°

.84346

.84428

.84510

.84591

.84673

•84754

•84835

.84916

•84997

.85076

540

.85158

.85238

•853!9

•85399

•85479

•85558

.85638

•85717

•85797

.85876

550

7.85955

1.86034

7.86113

7.86191

7.86270

7.86348

7.86426

7.86504

7.86582

7.8666o

560

.86737

.86815

.86892

.86969

.87047

.87123

.87200

.87277

•87353

.87430

5/0

.87506

.87282

.87658

•87734

.87810

.87885

.87961

.88036

.88111

.88186

580

.88261

.88336

.88411

.88486

.88560

.88634

.88708

.88782

.88856

.88930

590

.89004

.89077

.89151

.89224

.89297

.89370

.89443

.89516

.89589

.89661

600

1.89734

1.89806

7.89878

7.89950

7.90022

7.90094

7.90166

7.90238

7.90309

7.90380

610

.90452

.90523

.90594

.90665

•90735

.90806

.90877

.90947

.91017

.91088

620

.91158

.91228

.91298

•91367

•9!437

.91507

.91576

.91645

.91715

.91784

630

•91853

.91922

.91990

.92059

.92128

.92196

.92264

•92333

.92401

.92469

640

•92537

.92604

.92672

.92740

.92807

•92875

.92942

.93009

.93076

•93 '43

650

1.93210

1.93277

7-93343

7.93410

7.93476

7-93543

7.93601

^93675

7-93741

7.93807

660

•93873

•9393°

.94004

.94070

•94135

.94201

.94266

•94331

.94396

.94461

670

.94526

.94591

•94656

.94720

•94785

•94849

•949J3

•94978

.95042

.95106

680

•95!7o

•95233

•95297

•9536i

•95424

.95488

•95551

.95614

•95677

•95741

690

.95804

.95866

•95929

•95992

•96055

.96117

.96180

.96242

.96304

.96366

700

7.96428

1.96490

7-96552

7.96614

7.96676

7.96738

7.96799

7.96861

7.96922

7.96983

710

.97044

.97106

.97167

.97228

.97288

•97349

.97410

•97471

•97 531

.97592

720

.97652

•977 1 2

.97772

•97832

.97892

•979 5 1

.98012

.98072

.98132

.98191

73°

.98251

.98310

.98370

.98429

.98488

•98547

.98606

.98665

.98724

.98783

740

.98842

.98900

•98959

.99018

.99076

•99134

•99J93

.99251

.99309

•99367

750

1.99425

1.99483

7.99540

7.99598

7.99656

^•997 1 3

7.99771

7.99828

7.99886

7.99942

760

o.ooooo

0.00057

0.00114

0.00171

0.00228

0.00285

0.00342

0.00398

0.00455

0.00511

77°

.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.

163-

TABLE 176.

VOLUME OF PERFECT CASES.

Values of 1 + .00367 1.

The quantity i -f- -00367 i gives for a perfect gas the volume at t° 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°.

(a) This part of the table gives the values of i + .00367 1 for values of / between o°
and 10° C. by tenths of a degree.

(b) This part gives the values of i +.00367; for values of t between — 90° and + 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 (6) 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 (6) table and the actual temperature. For example, let the
temperature be 682°. 2 :

We have for 680 in table (6) the number .... 3.49560
And for 2.2 in table (a) the decimal . .... .00807

Hence the number for 682.2 is 3-50367

(0) This part gives the logarithms of i -f- . 00367* for values of / between — 49° and

+ 399° C. by degrees.

(fl) This part gives the logarithms of i -f- .00367 1 for values of / between 400° and 1990°
C. by 10° steps.

(a) Values of 1 + .00367 / for Values of / between 0° and 10° C. by Tenths
of a Degree.

t

0.0

0.1

0.2

0.3

0.4

0

1. 00000

1.00037

1.00073

I.OOIIO

I.OOI47

I

.00367

.00404

.00440

.00477

.00514

2

.00734

.00771

.00807

.00844

-0088r

3

.OIIOI

.01138

.01174

.OI2II

.OI248

4

.01468

•01505

.01541

.01578

.Ol6l5

5

1.01835

1.01872

1.01908

1.01945

I.OI982

6

.02202

.02239

.02275

.02312

.02349

7

.02569

.02606

.02642

.02679

.02716

8

.02936

.02973

.03009

.03046

.03083

9

•03303

•03340

•03376

•03413

•03450

t

0.5

0.6

0-7

0.8

09

0

1.00184

I.OO22O

1.00257

1 .00294

i .00330

i

.00550

.00587

.00624

.00661

.00697

2

.00918

.00954

.00991

.01028

.01064

3

.01284

.01321

•OI358

•01395

.01431

4

.01652

.01688

.01725

.01762

.01798

5

1.02018

I.O2O55

1.02092

1.02129

1.02165

6

.02386

.02422

.02459

.02496

.02532

7

.02752

.02789

.02826

.02863

.02899

8

.03120

•03156

•03193

.03290

.03266

9

.03486

•03523

.03560

•03597

•03633

SMITHSONIAN TABLES.

164

TABLE 176.

VOLUME OF PERFECT CASES.

(b) Values of 1 -f . 00367 1 for Values of t between —90° and + 1990° C. by

10 Steps.

t

00

10

20

30

40

—000

I.OOOOO

0.96330

0.92660

0.88990

0.85320

4000

too
200
300
400

I.OOOOO

1.36700
1.73400

2.IOIOO

2.46800

1.93670
1.40370
1.77070
2.13770
2.50470

1.07340
1 .44040
1.80740
2.17440
2.54140

I.IIOIO

1.44710

1.84410

2.21 IIO

2.57810

1.14680

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
3.27540
3.64240
4.00940
4.37640

2.94510
3.31210
3.67910

4.04610

4.41310

2.98180
3.34880
3-7I580
4.08280
4.44980

1000

IIOO

1 200
1300
1400

4.67000

5.03700

5.40400

5.77100

6.13800

4.70670
5.07370
5.44070
5.80770
6.17470

4-74340
5.11040
5-47740
5.84440
6.21140

4.78010
5.14710
5.51410

5.88110
6.24810

4.81680
5.18380
5-55080
5.91780
6.28480

15OO

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
7.6/940
8.04640

6.61510
6.98210

7.34910

7.71610

8.08310

6.65180
7.01880
7.38580
7.75280
8.11980

2000

8.34000

8.37670

8.41340

8.45010

8.48680

t

50

60

70

80

90

-000

0.81650

0.77980

0.74310

0.70640

0.669/0

+000

IOO
200

300
400

1.18350

1 -55050
1.91750

2.28450
2.65150

I.22O2O
1.58720
1-95420
2.32I2O
2.6882O

1.25690
1.62390
1.99090
2-55790
2.72490

1.29360
1.66060
2.02760
2.39460
2.76160

I-33030
1.69730
2.06430

2-43 J 3°
2.79830

500

600
700
800
900

3.01850

3-38550
3-75250
4.11950

4.48650

3.05520
342220
3.78920
4.15620
4.52320

3.09190
3.45890
3.82590
4.19290
4-55990

3.12860
3-4956o
3.86260
4.22960
4.59660

3-16530

3-53230
3-89930
4.26630

4-63330

1000

IIOO

1 200
1300
1400

•4-85350

5.22050

5-58750
5-95450
6.32150

4.89020
5.25720
5.62420
5.99I2O
6.35820

4.92690
5.29390
5.66090
6.02790
6.39490

4.96360
5-33o6o
5.69760
6.06460
6.43160

5.00030
5-36730
5-73430
6.10130
6.46830

1500

1600
1700
1800
1900

6.68850

7-05550
7.42250
7.78950

8.15650

6.72520
7.O922O
7.45920
7.82620
8.19320

6,76190
7.12890
7.49590
7.86290
8.22990

6.79860
7.16560
7-53260
7.89960
8.26660

6.83530

7.20230
7.56930

7-93630
8.30330

2000

8.52350

8.56O2O

8.59690

8.63360

8.67030

SMITHSONIAN TABLES.

I65

TABLE 176

VOLUME OF

(c) Logarithms of 1 + .00367 ' for Values

t

0

1

2

3

4

Mean diff.
per degree.

— 40

1931051

1.929179

1.927299

1.925410

^•9235'3

1884

— 3°

•949341

•947546

•945744

•943934

.942117

1805

20

.966892

.965169

•963438

.961701

•959957

J733

IO

.983762

.982104

.980440

.978769

.977092

1667

O

0.000000

.998403

.996801

.995192

•993577

1605

+ 0

o.oooooo

0.001591

0.003176

0.004755

0.006329

1582

IO

•015653

.017188

.018717

.020241

.021760

1526

20

.030762

•032244

. .033721

•°35193

.036661

1474

3°

.045362

.046796

.048224

.049648

.051068

1426

40

.059488

.060875

.062259

.063637

.065012

1381

50

0.073168

0.0745 ^3

0-075853

0.077190

0.078522

1335

60

.086431

•087735

.089036

•090332

.091624

1299

70

.099301

.100567

.101829

.103088

.104344

*259

80

.111800

.113030

.114257

.115481

.116701

1226

90

.123950

.125146

.126339

.127529

.128716

1191

100

0.135768

0.136933

0-138094

0.139252

0.140408

1158

no

.147274

.248408

•149539

.150667

•I5'793

1129

120

.158483

.159588

.160691

.161790

.162887

IIOI

130

.169410

.170488

•'715.63

.172635

•173705

1074

140

.180068

.181120

.182169

.183216

.184260

1048

150

0.190472

0.191498

0.192523

0.193545

0.194564

1023

160

.200632

.201635

.202635

.203634

.204630

1000

170

.210559

.211540

.212518

•2 1 3494

.214468

976

180

.220265

.221224

.222180

•223135

.224087

956

190

.229959

.230697

•231633

•232567

•233499

935

200

0.239049

0.239967

0.240884

0.241798

0.242710

916

210

.248145

.249044

.249942

.250837

•25I731

897

220

•257054

•257935

.258814

.259692

.260567

878

230

.265784

.266648

.267510

.268370

.269228

861

240

•274343

.275189

.276034

.276877

.277719

844

250

0.282735

0.283566

0.284395

0.285222

0.286048

828

260

.290969

.291784

.292597

.293409

.294219

813

270

.299049

.299849

.300648

.301445

.302240

798

280

.306982

.307768

.308552

•309334

•3IOII5

784

290

•314773

•315544

•3!63H

•3I7o83

•3 17850

769

300

0.322426

0.323184

0.323941

0.324696

0-32545°

756

310

•329947

.330692

•331435

•332178

•3329i9

743

320

•337339

.338072

•338803

•339533

.340262

73°

33°

.344608

•345329

•345048

.346766

.347482

719

340

•35T758

.352466

•353!74

.353880

•354585

707

350

o.35879i

0.359488

0.360184

0.360879

0-361573

696

360

•365713

•366399

.367084

.367768

.368451

684

370

•372525

,373201

•373875

•374549

•375221

674

380

•379233

,379898

.380562

.381225

.381887

664

390

•385439

.386494

.387148

.387801

•388453

654

SMITHSONIAN TABLES.

166

TABLE 176.

PERFECT CASES.

of t between —49° and +399° C. by Degrees.

t

5

6

7

8

9

Mean diff.
per degree.

— 40

1.921608

1.919695

1.917773

^•9! 5843

1.913904

1926

— 3°

.940292

.938460

.936619

•934771

.932915

I84S

20

.958205

.956447

.954681

.952909

.951129

1771

— 10

.975409

•973719

.972022

.970319

.968609

1699

O

.991957

.990330

.988697

.987058

•985413

1636

' + 0

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°

3°

.052482

•053893

.055298

.056699

.058096

1402

40

.066382

.067748

.069109

.070466

.071819

1359

50

0.079847

0.081174

0.082495

0.08381 1

0.085123

1315

60

.092914

.094198

.095516

.096715

.098031

I28l

70

•I°5595

.106843

.108088

.109329

.110566

1243

80

.117917

.119130

.120340

.121547

.122750

12IO

90

.129899

.131079

.132256

•133430

.134601

"75

100

0.141559

0.142708

0.143854

0.144997

0.146137

1144

no

•152915

•154034

•tSS'S1

.156264

•'57375

1115

1 20

.163981

.164072

.166161

.167246

.168330

1087

130

•174772

•175836

.176898

•177958

.179014

1060

!; 140

.185301

.186340

•187377

.188411

.189443

•035

150

0.195581

0.196596

0.197608

0.198619

0.199626

ion

160

.205624

.206615

.207605

.208592

.209577

988

170

•2 '5439

.216409

.217376

.218341

.219904

966

180

.225038

.225986

.226932

.227876

.228819

946

190

.234429

•235357

.236283

.237207

.238129

925

200

0.243621

0.244529

0.245436

0.246341

0.247244

906

2IO

.252623

•253512

.254400

.255287

.256172

887

2 2O

.261441

.262313

.263184

.264052

.264919

870

230

.270085

.270940

•271793

.272644

•273494

853

24O

.278559

.279398

.280234

.281070

.281903

836

250

0.286872

0.287694

0.288515

0.289326

0.290153

820

260

.295028

•295835

.296860

•297445

.298248

805

270

•303034

.303827

.304618

•305407

.306196

790

280

.310895

•3Il673

•3I245°

.313226

.314000

776

290

.318616

•3T938i

.320144

.320906

.321667

763

3OO

0.326203

0.326954

0.327704

0.328453

0.329201

75°

310

•333659

•334397

•335r35

•335871

.336606

737

320

.340989

•34I7I5

.342441

•343 * 64

.343887

724

33°

.348198

.348912

•349624

•350337

.351048

713

340

•355289

•355991

•356693

•357394

•358093

701

350

0.362266

0.362957

0.363648

0-364337

0.365025

690

360

.369132

.369813

•370493

•37'i7i

.371849

678

370

•375892

.376562

•377232

.377900

•378567

668

380

.382548

.383208

.383868

•384525

•385183

658

39°

.389104

•389754

•390403

.391052

.391699

648

SMITHSONIAN TABLES.

I67

TABLE 176.

VOLUME OF PERFECT CASES.

d Logailtluns of l .00367' for Values of / between 400 and 1990° C. by 10° Steps.

*

00

10

20

30

40

400

0-392345

0.398756

0.405073

0.411300

0.417439

500

0-452553

0.458139

0.463654

0.469100

0-474479

600

.505421

•5I037i

.515264

•520103

.524889

700
800

•552547
•595055

.556990
.599086

.561388
•603079

.565742
•607037

.570052
.610958

900

•633771

.637460

.641117

•644744

.648341

1000

0.669317

0.672717

0.676090

0.679437

0.682759

IIOO

.702172

•705325

•708455

•7"563

.714648

1200

•732715

•735655

•738575

•741745

•744356

1300

.761251

.764004

.766740

•769459

.772160

1400

.788027

.790616

.793190

•795748

.798292

15OO

0.813247

0.815691

0.818120

0.820536

0.822939

1600

.837083

•839396

.841697

.843986

.846263

1700

•859679

.861875

.864060

.866234

.868398

1800

.881156 .883247

.885327

.887398

.889459

1900

.901622

.903616

.905602

.907578

•909545

t

60

60

70

80

90

400

0.423492

0.429462

0-435351

0.441161

0.446894

5OO

0.479791

; 0.485040

0.490225

0-49535°

0.500415

600

.529623

•534305

•538938

•5435,22

.548058

700

•574321

•578548

•582734

.586880

.590987

800

.614845

.618696

•622515

.626299

.630051

900

.651908

.655446

•658955

.662437

.665890

1000

0.686055

0.689327

0.692574

0-695797

0.698996

IIOO

.717712

.720755

.723776

.726776

.729756

1 200

.747218

.750061

.752886

.755692

.758480

1300

.774845

•7775H

.780166

.782802

.785422

1400

.800820

•803334

.805834

.808319

.810790

1500

0.825329

0.827705

0.830069

0.832420

0.834758

1600

.848828

.850781

•853023

•855253

.857471

1700

.870550

\ .872692

.874824

.876945

.879056

1800

.891510

•89355 *

•895583

.897605

.899618

1900

.911504

•9*3454

•915395

•9'7327

.919251

SMITHSONIAN TABLES.

168

TABLE 17',

DETERMINATION OF HEIGHTS BY THE BAROMETER.

Formula of Babinet : Z = C -~

B0+B

C (in feet) = 52494 ft -\-fQ~T~ *~ &4 | English measures.
l_ 900 -I

C (in metres) = 16000 \ i + 2 ^ " ~*~ ' I metric measures.
L 1000 J

In which Z rr difference of height of two stations in feet or metres.
S0, B — barometric readings at the lower and upper stations respectively, corrected for all

sources of instrumental error.
/„, t := air temperatures at the lower and upper stations respectively.

Values of C.

ENGLISH MEASURES.

METRIC MEASURES.

i('o + >).

C

LogC

H'o + O-

C

LogC

Fahr.

Feet.

Cent.

Metres.

10°

49928

4.69834

—10°

15360

4.18639

15

5°5 "

•70339

—8

15488

.19000

—6

15616

•'9357

20

51094

4.70837

—4

15744

.19712

25

5l677

•7'33°

2

15872

.20063

3O

52261

4.71818

0

16000

4.20412

35

52844

.72300

+ 2

16128

.20758

4

16256

.2IIOI

40

53428

4-72777

6

16384

.21442

45

540II

•73248

8

16512

.21780

50

54595

4-737I5

10

16640

4.22II5

55

55178

•74177

12

16768

.22448

14

16896

.22778

60

5576i

474633

16

17024

.23106

65

56344

•75085

18

17152

•23431

70

56927

4-75532

20

17280

4-23754

75

575"

•75975

22

17408

.24075

24

17536

•24393

80

58094

4.76413

26

17664

.24709

85

58677

.76847

28

17792

.25022

90

59260

4.77276

30

17920

4-25334

95

59844

.77702

32

18048

•25643

34

18176

.25950

100

60427

4.78123

36

18304

.26255

SMITHSONIAN TABLES.

169

TABLE 178.

BAROMETRIC

Barometric pressures corresponding to different
This table is useful when a boiling-point apparatus is used

(a) British Measure.

Temp. F.

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9

185°

186

17-05
17.42

17.08
17.46

17.12
I7-50

17.16
17-54

17.20
17.58

I7-23
17.61

17.27
17.65

I7-3I
17.69

17-35
17-73

17-39
17-77

187

188

17.81

1 8. 20

17.84
18.24

17.88
18.27

17.92
18.31

17.96
18-35

18.00
18.39

18.04
18.43

18.08
18.47

18.12
18.51

18.16
18.55

189

190

18.59

19.00

18.63
19.04

18.67
19.08

18.71
19.12

18-75
19.16

18.79
19.20

18.83
19.24

18.87
19.28

18.91
19.32

18.95
19.36

191

192

19.41
19.82

19-45
19.87

19.49
19.91

J9-53
19-95

19-57
19.99

19.61

20.04

19.66

20.08

19.70

20. 1 2

19.74
20.17

19.78

20. 2 1

193

194

20.25
20.68

20.29
20.73

20.34
20.77

20.38
20.82

20.42
20.86

20-47
20.90

20. 5 r
20.95

20-55
20.99

20.60
21.04

20.64

21.08

195

196

21.13
21.58

21.17
21.62

21.22
21.67

21.26
21.71

21.30
21.76

21-35

21.80

21.39

21.85

21.44
21.89

21.48
21.94

21-53
21.99

197

198

22.03

22.50

22.08
22.54

22.12
22.59

22.17
22.64

22.22
22.69

22.26
22.73

22.31

22.78

22.36
22.83

22.40

22.88

22.45
22.92

199

200

22.97
23-45

23.02
23-50

23.07
23-55

23.11
23.60

23.16
23-65

23.21

23.70

23.26
23-75

23-31
23.80

23-36
23-85

23.40
23.89

201

202

23-94
24.44

23-99
24.49

24.04
24.54

24.09
24-59

24.14
24.64

24.19
24.69

24.24
24.74

24.29
24.80

24-34
24.85

24-39
24.90

203

204

24-95
25.46

25.00
25-52

25.05
25-57

25.10
25.62

25-I5
25.67

25.21
25-73

25.26
25.78

25-3I
25-83

25-36
25.88

25.41
25-94

205

206

25-99
26.52

26.04
26.58

26.IO
26.63

26.15
26.68

26.20
26.74

26.25
26.79

26.31
26.85

26.36
26.90

26.42
26.96

26.47
27.01

207

208

27.07
27.62

27.12

27.67

27.18
27-73

27.23
27.79

27.29
27.84

27-34
27.90

27.40
27-95

27-45
28.01

27-51
28.07

27.56
28.12

209

2IO

28.18
28.75

28.24
28.81

28.29
28.87

28.35
28.92

28.41
28.98

28.46
29.04

28.52
29.10

28.58
29.16

28.64
29.21

28.69
29.27

211

212

29-33
29.92

29-39
29.98

29-45
30.04

29.51
30.10

29-57
30.16

29.62
30.22

29.68
30.28

29.74
3°-34

29.80
30.40

29.86
30-46

SMITHSONIAN TABLES.

170

TABLE 178.

PRESSURES.

temperatures of the boiling-point of water.

in place of the barometer for the determination of heights.

(b) Metric Measure.*

Temp. C.

.0

.1

.2

.3

.4

.5

.6

.7

-8

.9

80°

354-6

356-I

357-5

359-Q

360.4

361.9

363-3

364.8

366.3

367.8

81

369-3

370.8

372.3

373-8

375-3

376.8

378.3

379-8

381-3

382.9

82

384-4

385-9

387-5

389.0

390.6

392.2

393-7

395-3

396.9

398-5

83

400.1

401.7

403-3

404.9

406.5

408.1

409.7

4"-3

413.0

414.6

84

416.3

417.9

419.6

421.2

422.9

424.6

426.2

427.9

4296

431-3

85

433-0

434-7

436-4

438.1

439-9

441.6

443-3

445- '

446.8

448.6

86

45°-3

452-1

453-8

455-6

457-4

459-2

461.0

462.8

464.6

466.4

87

468.2

470.0

471-8

473-7

475-5

477-3

479-2

481.0

482.9

484.8

88

486.6

488.5

490.4

492-3

494.2

496.1

498.0

499-9

501.8

503-8

89

505-7

507.6

509.6

5ii-5

5I3-5

5r5-5

5I7-4

5*9-4

521.4

5234

90

525-4

527-4

529-4

531-4

533-4

535-5

537-5

539-6

541.6

543-7

9i

545-7

547-8

549-9

551-9

554-0

556-?

558.2

560.3

562.4

564.6

92

566-7

568.8

57i-o

57 3- i

575-3

577-4

579-6

581.8

584.0

586.1

93

588.3

590-5

592.7

595-0

597-2

599-4

601.6

603.9

606. 1

608.4

94

610.7

612.9

615.2

617.5

619.8

622.1

624.4

626.7

629.0

631.4

95

633-7

636.0

638.4

640.7

643.1

645-5

647.9

650.2

652.6

655.0

96

657-4

659-9

662.3

664.7

667.1

669.6

672.0

674-5

677.0

679-4

97

681.9

684.4

686.9

689.4

691.9

694-5

697.0

699.5

702.1

704.6

98

707.2

709.7

712.3

714.9

7I7-5

720.1

722.7.

725-3

727.9

73°-5

99

733-2

735-8

738.5

741.2

743-8

746.5

749-2

. 751-9

754-6 «

• 757-3

100

760.0

762.7

765-5

7§8.2

770.9

773-7

776.5

779-2

782.0

784.8

SMITHSONIAN TABLES.

* Pressures in millimetres of mercury.

I/I

TABLE 179.

STANDARD WAVE-LENGTHS,

This table is an abridgment of the table published by Rowland (Phil. Mag. [5] vol. 36, pp 49-75). The first column
gives the number of the line reckoned from the beginning of Rowland's table, and thus indicates the number of
lines of the table that have been omitted. The second column gives the chemical symbol of the element repre-
sented by the line of the spectrum. The third column indicates approximately the relative intensity of the lines
recorded and also their appearance ; A" stands for reversed, d for double, ? for doubtful or difficult. The fourth
column gives tie relative " weights " to be attached to the values of the wave-lengths as standards. The last
column gives the values of the wave-lengths in Angstrom's units, i. e., in ten millionth* of a millimetre in ordinary
air at about 20-' C. and 760 millimetres pressure. When two or more elements are on the same line of the table
it indicates that they have apparently coincident lines in the spectrum for that wave-length. When two or more
lines are bracketed it means that the first one has a line coinciding with one side of the corresponding line in the
solar spectrum and so on in order. Lines marked A(o) and A(iw) denote lines due to absorption by the oxygen
or water vapor in the earth's atmosphere. The letters placed in front of some of the numbers in the first column
are the symbols of well-known lines in the spectrum. The footnotes are from Rowland's paper.

No. of
line.

Element.

Inten-
sity and
appear-
ance.

Weight.

Wave-
length (arc
spectrum).

No. of
line.

Element.

Inten-
sity and
appear-
ance.

Weight.

Wave-
lengih (arc
spectrum).

I

Sr

2

I

2152.912

"5

Fe

10 R

4

2937.020

4

Si

3

2

2210.939

117

Fe

IK

4

2954.058

7

Si

2

2

2218.146

121

Fe

8 R

12

2967.016

9

Al

4

2

2269.161

124

Fe

\2R

15

297335s

ii

Ca

20 R

3

2275.602

126

Fe

10 R

15

2983.689

14

Ba

20 R

I

2335.267

129

Fe

%R

18

2994.547

16

Fe

-

2

2348.385

J3*

Ca

\o R

3

2997-43°

19

Al

7

3

2373.213

Fe

8 R

IS

3001.070

22

Fe

2

2388.710

[36

Ca

\^R

3

3006.978

24

Ca

25 R

5

2398.667

141

Fe

6A3

15

3008.255

'51

Fe

25*

18

3020.759

29

Si

8

15

2435.247

163

Fe

20 R

13

3047.720

31

Si

3

10

2443.460

169

Fe

loR

15

3059.200

33«

37*

4O

Si
C
Bo

3

10

20

IO

15 ,

20

2478.661
24Q7.82I

(Sun
spectrum.)

i *fv

™*ry*

136

?

3

-

3005.160

51

Si

IS

7

2516.210

144

?

4

-

301 2-557

55

Si

9

10

2524.206

J54

?

5

7

3024475

59 1

Hg

50 R

2

2536.648

158

?

5

7

Al

10

5

2568.085

164

?

5

3050.212

6$

Mn

—

2

2593.810

171

Co

3

5

3061.930

•73

Si

5

7

2631.392

177

Fe?

4

6

3078.148

77

Fe

3

2720.989

187

?

2

9

3094-739

78

Ca

5

i

2721.762

197

Vat

5

9

3121.275

82

Fe

3

2742.485

20 1

-

3

5

3140.869

85

Fe

-

3

2756.427

203

Mn

i

5

3167.290

99

Mg

20 R

12

2795.632

207

Cr?

4

5

3188.164

102

Mg

20 A'

10

2802.805

209

Ti

4

5

3200.032

106

Fe

4

7

2832.545

211

Ti

3

6

3218.390

in

Mg

100 R

15

2852.239

215

Ti

4

3

3224.368

112

Si

15

12

2881.695 i 222

Cu

9

5

3247.680

* Seems to be the only single carbon line not belonging to a band in the arc spectrum. It was determined

to belong to carbon by the spark spectrum.

t This line appears as a sharp reversal, with no shading, in the spectra of all substances tried that contained

any trace of a continuous spectrum in the region.

t There is a faint line visible on the violet side.

SMITHSONIAN TABLES.

172

STANDARD WAVE-LENGTHS.

TABLE 179.

No. of
Line.

Element.

Inten-
sity and
appear-
ance.

Weight.

Wave-
length (sun
spectrum).

No. of
Line.

Element.

Inten-
sity and
appear-
ance.

Weight.

Wave-
length (sun
spectrum).

224

Va

4

IO

3267.839

409t

Fe?

10

3

4005.305

229

Na

6

6

5302.501

410

Fe

3

7

4016.578

235

Ti

5

IO

33l8-i63

417

Fe

20

7

4045.975

239

Zr

i

8

3356.222

420

Mn

5

J3

4055-70I

241

Fe

2

12

3389.887

422

Fe

15

7

4063.756

244

Fe

4

18

3406.955

424

Fe

4

H

4073.920

250

Co

4

IO

3455-3*4

428

Fe

2

8

4088.716

255

Co, Fe, Ni

4

IO

3478.001

431

Fe

4

M

4114.600

261

Fe

3

4

3500.721

434

Fe

3

17

4157.948

265

Co

5

IO

55*8487

436

Fe

3

20

4185.063

269

Fe

5

IO

3540.266

439

Fe

5

4

4202.188

274

1 Ti \
} Fe J

i,d?

12

3564.680

.T445
448

Ca

Cr i

10

IO

15

4226.892
4254.502

278

Fe

40

6

358i-344

45i

Fe

8

9

4271.924

279

Fe?

4

12

3583-483

456

?

4

14 i 4293-249

284

Fe

4

12

3597-92

( Ca

2 )

3 ' 4307-904

290

Fe

15

IO

3609.015

6462

) -

-></

3

4308.034

292

Fe

4

15

3612.217

( Fe

5)

10

4308.071

294

Fe

20

10

3618.924

/465

Fe

8

i5

4325.940

298

Fe

4

14

3623-332

467

Fe

3

17

4352-903

301

Fe

20

IO

3631.619

^47i

Fe

10

ii

4383721

3°7

Fe

IO

II

3647-995

473

Fe

8

ii | 4404-927

311

Fe

3

'3

3667-397

477

Ca

4

7

4425.609

( Co )

48ot

Fe

5

18

4447.899

3»3

Fef

6

13

3683.202

484

Fe

5

18

4494-735

f Va )

320

Fe

5

II

3707.186

49°

Ti

4

17

4508.456

324

Fe

5°

10

3720.086

493

Ba

7

8

4554-213

327

Fe

5

15

3732-542

496

Ti

6

14

4572.157

338

Fe

20

8

3789-633

500

Fe

4

20

4602.183

34i

Fe

15

7

3758-379

505

IS.}

5

!3

4629.515

348

Fe

3

15

378i.330

508

Fe

4

17

4643-645

355

Fe

3

15

3804-153

5"

Fe

6

12

4679.028

35«

Fe

30

4

3820.567

5J5

< Ni

4

12

4686.395

361

Fe

20

4

3826.024

5'8§

Mg

9

II

4703.180

369

Fe

5

8

3843.406

524

Mn

6

I

4783.601

37i

Fe

IO

3

3860.048

528

Mn

6

12

4823.697

375

C

7

3

3883.472

^"531-

H

15

5

4861.496

379

Fe

4

12

3897-599

537

Fe

7 :

4

4919.183

382
A- 387*

Ti
Ca

4
300

15

5

3924.669
3933-809

545

[£}

3

10

4973-274

39i

Al

10

7

3944-159

549

Fe

4

7

4994.316

393

Fe

4

15

3950.101

558

Ti

3

8

5020.210

397

Fe

3

ii

3960.429

561

Fe

5

12

5050.008

-#399

Ca

200

5

3968.620

564

Fe

4

H

5068.946

404

Fe, Ti

4

H

3981.914

567

Fe

2

9

5090.959

* This line is doubly reversed and spread out in broad shading for 6.000 to 7.000 on either side. In each

case the second reversal is slightly excentric with respect to the other, being displaced towards the red.

t Seven or eight lines, the brightest, and most of the others are due to iron.

J There is a faint side line towards the red.

', § This lin»is shaded towards the violet, probably due to a close side line.

,!

SMITHSONIAN TABLES.

173

TABLE 1 79.

STANDARD WAVE-LENGTHS.

Inten-

— —

No. of
Line.

Element.

sity anc
appear
ance.

Weight

Wave-
length (sun
spectrum).

No. of
Line.

Element.

sity and
appear-
ance.

Weight

Wave-
length (sun
spectrum).

570

Fe

2

II

5109.825

762

Fe

6

H

5930.410

575

Fe

4

9

51 27-53°

764

Si

6

H

5948.761

580

Fe

3

5

5141.916

770

Fe

6

7

5987.286

589

Fe

4

5162.448

774

Mn

6

6013.717

778

Fe

6

8

6024.280

(592

Mg

8)

3

5167.501

** I 593

-

-{d

7

5l67-572

782

Fe

7

13

6065.708

(594

Fe

6^

3

5167.686

786

Ca

6

9

6102.941

( 595

Fe

4)

3

5169.066

792

Ca

9

ii

6122.428

l>3 < 596

-

- > d

5

5169.161

797

Ca

10

9

6162.383

(597

Fe

4)

3

5169.218

804

Fe

8

10

6191.770

£2599

Mg

10

9

5172.671

808

Fe,Va

7

12

6230.946

bi 601

Mg

20

ii

5183.792

811

Fe

7

9

6252.776

610

Fe

4

10

52I5-352

815

Fe

5

II

6265.347

614

Fe

8

9

5233- * 24

822

Fe

7

7

6301.719

618

Fe

3

12

5253-649

827

Fe

6

12

6335-550

EZ 630*

Fe

8<t?

16

5269.722

834

Fe

7

9

6393.818

(631

Ca

*i

5270.448

838

Fe

7

10

64 1 1 .864

E\ < 632

-

-(d

12

5270.495

843

Ca

7

II

6439.298

(633

Fe

4)

5270.533

846

Ca

5

7

6471.881

639

Fe

6

II

5283-803

850

Fe

7

9

6495.209

643

Fe

4

10

5307-546

856

(Ti )

6

ii

6546.486

647

Fe

8

8

5324.373

£"858

H

30

13

6563.054

655

Fe

6

8

5367-670

863

Fe

5

ii

6593.161

659

Fe

6

ii

867

Ni

5

10

6643.482

662

Fe

7

M

5405.987

870

Fe

5

10

6678.232

668

Fe

7

9

5347-I30

877

Fe

4

12

6750.412

674

Fe

4

10

5463-493

879

Ni

4

9

6768.044

676

Ni

4

10

5477.128

883

Fe

3

8

6810.519

679

Fe

4

8

5501.685

886

Fe

3

6

6441.591

682

Mg

7

8

5528.636

#896

A(o)

12

6870.186

687

Fe

5

8

5569-848

911

A(o)

4

I3

6884.083

690

Ca

6

9

5588.980

925

A(o)

6

9

6909.675

695

Ca

4

4

5601.501

93 l

A(o)

4

9

6919.245

699t

Fe

2

12

5624-253

938

A(wv)

8

IO

6947.781

7oot

Fe, Va

4

M

5624.768

940

A(wv)

8

12

6956.700

706

Fe

s

9

5662.745

957

?

6

8

7035-I59

710

Na

6

7

5688.434

961

?

6

5

7122.491

717

Fe

5

10

573 i -973

969

A (wv)

10

5

7200.753

720

Fe

5

10

5753-342

977

A(wv)

15

4

7243.904

725

Cu?Co?

jd?

9

5782.346

984

A(ivv)

no

3

7290.714

732

Fe

5

7

5806.954

99°

?

7

2

7389.696

737 1

Ca

7

5857.672

99711

A(o)

4

7594-059

Z>3740§

He

-

—

5875-982

998

A(o)

10

5

7621.277

A 743

Na

15

20

5890.182

1004

A(o)

14

3

7660.778

A 745

Na

10

20

5896.154

IOIO

•?

4

i

7714.686

* Component about .088 apart on the photographic plate. It is an exceedingly difficult double.

t Lines used by Pierce in the determination of absolute wave-lengths.

t There is a nickel line near to the red.

§ This value of the wave-length is the result of three series of measurements with a grating of 20,000 lines

to the inch and is accurate to perhaps .02.

II Beginning at the head of A , outside edge.

SMITHSONIAN TABLES.

174

TABLE 18O.

WAVE-LENGTHS OF FRAUNHOFER LINES.

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 mil-
lionths of a millimetre on the supposition that the D line value is 5896.156. The table is for the most part taken
from Rowland's table of standard wave-lengths, but when no corresponding wave-length is there given, the number
given by Kayser and Runge has been taken. These latter are to two places of decimals.

Index letter.

Line due to —

Wave-length in
centimetres X io8.

Index letter.

Line due to —

Wave-length in
centimetres X io8.

(d

7621.277*

G' or H

II

4340.66 §

A

/

fo

7594-059*

fFe

4308.071

a

. -

7184.781

G

-

4308.034

B

u

6870.186!

lea

4307.904

C or Ha

ii

6563.054

g

Ca

4226.892

a

o

6278:289^:

h or Hg

II

4101.87

D,

Na

5896.154

H

Ca

3968.620

Do

Na

5890.182

K

Ca

3933-809

D3

He

5875.982

L

Fe

3820.567

fFe

5270.533

M

Fe

3727.763

Ei

-

5270.495

N

Fe

358I-344

ICa

5270.448

O

Fe

344I-I35

E2

Fe

5269.722

P

Fe

3361.30

bi

Mg

5183.792

Q

Fe

3286.87

b-2

Mg

5172.871

f Ca

3181.40

Ril

1

fFe

5169.218

( Ca

3l79-45

b3

\-

5169.161

Vl

Fe

3M4.58 (?)

1

IFe

5169.066

fFe

3100.779

Si

|

fFe

5167.686

3100.415

S2

I

b<

j -

5167.572

[Fe

3100.064

Ug

5167.501

s

Fe

3047.720

F or llft

H

4861.496

T

Fe

3020.759

d

Fe

4383.721

t

Fe

2994-542

f

Fe

4325-940

U

Fe

2947-993

* The two lines here given for A are stated by Rowland to be : the first, a line " beginning at the head of A, out-
side edge; " the second, a "single line beginning at the tail of A."
t The principal line in the head of B.
t Chief line in the a group.
§ Ames, " Phil. Mag." (5) vol. 30.

II Cornu gives 3179.8, which, allowing for the different value of the standard D line, corresponds to about 3180.3.
IT Cornu gives 3144.7, which would correspond to about 3145.2.

SMITHSONIAN TABLES.

175

TABLE 181.

DETERMINATIONS OF THE VELOCITY OF LIGHT, BY DIFFERENT

OBSERVERS.*

Wt. of

obser-

Date of
determi-
nation.

No. of

experi-
ments
made.

Method.

Interval
worked
across in
kilometres.

Velocity in
kilometres per
second.

Velocity in miles
per second.

Refer-
ence.

vation
as esti-
mated
by

Hark-

ness.

1849

-

Toothed wheel

8.633

31 5324

195935

I

O

1862

80

Revolving mirror

O.O2

298574 zt 204

1 85.527 ±127

2

I

1872

658

Toothed wheel

IO.3IO

298500 J- 995

l8548l-J-6l8

3

I

I874

546

"

22.91

300400 -±- 300

186662 J, 1 86

4

2

1879

too

Revolving mirror

0.6054

299910^-51

186357^31.7

5

3

1880

12

Toothed wheel

I 5-5510 )

301384-1-263

187273^164

6

I

148

Revolving mirror

5.1019

299709

186232

7

_

1880

to

39

" '"

74424

299776

186274

7

-

I

65

k<

7.4424

299860

186326

7

6

1882

23

!'

0.6246

299853 i 60

186322 -j- 37

8

3

Mean from all weighted measurements . .

299835 rk1 54

186310^-95.6

9

Mean from those having weights > i . . .

299893-1-23

186347 -j- 14.3

9

i Fizeau. " Comptes Rendus," 1849.

2 Foucault, "Recueil des travaux scientifiques," Paris, 1878.

3 Cornu, " Jour, de 1'Ecole Polytechnique," Paris, 1874.

4 Cornu, " Annales de 1'Observatoire de Paris," Memoires, tome 13, p. A. 298, 1876.

5 Michelson, " Proc. A. A. A. S." 1878.

6 Young and G. Forbes, " Phil. Trans." 1882.

7 Newcomb, "Astronomical Papers of the American Ephemeris," vol. 2, pp. 194, 201, and 202.
8 Michelson, " Astronomical Papers of the American Ephemeris," vol. 2, p. 244.

9 Harkness.

TABLE 182.

PHOTOMETRIC STANDARDS.'

Name of standard.

Violle
units.

Carcels.

Star

candles.

German
candles.

English
candles.

Hefner-
Alteneck
lamps.

Violle units |. . . : .

1. 000

2.08

16.1

16.4

18.5

18.9

Carcels . . . . . I .

0.481

1. 00

7-75

7.89

8.91

9.08

Star candles . . ...

O.O62

0.130

I.OO

1.02

J-'S

I.I7

German candles

0.061

0.127

0.984

I.OO

i-»3

'•'5

English candles

0.054

O.I 12

0.870

0.886

I.OO

I. O2

Hefner-Alteneck lamps . " .

0-°53

O.II4

0-853

0.869

0.98

I.OO

* Quoted from Harkness, " Solar Parallax," p. 33.

t This table, founded on Violle's experiments, is quoted from Paterson's translation of Palaz' " Industrial Pho-
tometry," p. 173-

t The Violle unit is sometimes called the absolute standard of white light. It is the quantity of light emitted
normally by one square centimetre of the surface of melted platinum at the temperature of solidification.

SMITHSONIAN TABLES.

176

TABLE 183.

SOLAR ENERGY AND ITS ABSORPTION BY THE EARTH ATMOSPHERE.

This -table gives some of the results of Langley's researches on the atmospheric absorption of solar energy.* The
first column gives the wave-length A, in microns, of the spectrum line, while the second and third columns give
the corresponding absorption, according to an arbitrary scale, for high and low solar attitudes. The fourth column,

' £, gives the relative values of the energy for the different wave-lengths which would be observed were there no

; terrestrial atmosphere.

A

<*1

(la

E

0*375

112

27

353 j

.400

235

63

683 >

•45°

424 1

140

1031 i

.500

570

225

1203

.600

621

3"

1083 i

.700

553

324

849

.800

372

246

5J9

.900

238

167

316

1. 000

235

167

309

THE SOLAR CONSTANT.

TABLE 184.

The " solar constant " is the amount of heat' per unit of area of normally exposed surface which, at the earth's mean

distance, would be received from the sun's radiation if there were no terrestrial atmosphere. The following table

; is taken from Langley's researches on the energy of solar radiation. t The first column gives the wave-length in

' microns. The second and third columns give relatively on an arbitrary scale a i upper and a lower limit to the

possible value of spectrum energy.

Spectrum

' Spectrum

Spectrum

Spectrum

Wave-

energy

i energy

Wave-

energy

energy

length.

(upper

i (lower

length.

(upper

(lower

limit).

limit).

limit)<

limit).

0^.530

203.9

122-5

I^.OOO

105.0

102.3

•375

196.6

IIO.O

I.2OO

78.2

6l.3

.400

242.2

139-1

I.4OO

65.I

J2-2

•45°

783.2

105.5

1. 6OO

48.0

45-o

.500

852.9

374-1

I.8OO

39-2

36-4

.600

5 "4-7

333-0

2.000

29.1

27.1

.700

3J7-7

255-4

2.2OO

19.4

17'5,

.800

173-9

167.3

2.400

7-o

6.8

The areas of the energy curves are respectively
The solar constants deduced from these areas are

149,060 and 95,933
3.505 and 2.630

Langley concludes that "in view of the,large limit of error we can adopt three calories as the mosf probable valuq
of -the solar constant," or that " at the earth's mean distance, in the absence of its absorbing atmosphere, the solar
rays would raise one gramme of water three degrees per minute, for each normally exposed square centimetre of its
surface."

* "Am. Jour, of Sci." vols. xxv., xxvii. , and xxxii.

t "Professional Papers of U. S. Signal Service," No. 15, 1884.

SMITHSONIAN TABLES.

TABLE 185.

INDEX OF REFRACTION FOR CLASS.

The table gives the indices of refraction for the Fraunhofer lines indicated in the first column. The kind of glass,
the density, and, where known, the corresponding temperature of the glass are indicated at the top of the different
columns. When the temperature is not given, average atmospheric temperature may be assumed.

(a) FRAUNHOFER'S DETERMINATIONS. (Ber. Munch. Akad. Bd. 5.)

Density
Temp. C.

li

C
D

£

F
G
If

Flint glass.

18^.75

1.62775
.62965

.64202
.64826
.66029
.67106

1.60204
.60380
.60849

•61453
.62004
.63077
.64037

Crown glass.

2.756

1-55477
•55593
•55908

.56674
•57354
•57947

2-535
'7°-5

I-52583
.52685

•52959

•533°!
•53605
.54166

•54657

•52530
.52798

•53*37
•53434
•53991
.54468

(b) BAILLE'S DETERMINATIONS. (Quoted from the Ann. du Bur. des Long. 193, p. 620.)

Flint glass.

Density
Temp. C.

B
C

1)
b,
K
G
H

1.5609
.5624
.5660

•5715
•5748
.5828
.5898

I-5659

•5675
•57 '5
•5776

•5902
•5979

3-24

22°.0

1.5766

•5783
.5822

•5887
•5924
.60l8

1.5966
.5982
.6O27
.6098

.6246
.6338

3-54
23°. 2

1.6045
.6062
.6109
.6183
.6225

•6335
.6428

3-63
i3°-7

1.6131
.6149
.6198
.6275
.6321

•6435
•6534

3-68
24°.o

1.6237

•6255
.6304
.6384
.6429

•6549
.6647

4.08
1 2°. 4

1.6771

•6795
.6858

•6959
.7019
.7171
.7306

5.00

22°.S

I.78OI

•7831
.7920
.8062
.8149

.8567

Crown glass. (Bailie, itiit.)

Density
Temp. C.

I

C

1)
in
F
G

H

1.5126

•5'34
.5160
.5198
.5222
.5278
•5323

2.50
17^.8

I-5244
•5254
.5280
•5320
•5343
•5397
•5443

1.5226
•5237
•5265
•5307
•5332
•5392
•5442

2.80

1-5157
.5166

•5192
•5234
•5256
•5313
.5360

1-5554
.5568
.5604
•5658
.5690

•5769
•5836

(c) HOPKINSON'S DETERMINATIONS. (Proc. Roy. Soc. vol. 26.)

Density =

Hard
crown.

2.486

Soft
crown.

Titani-
silicic
crown.

Flint glass.

2.866

3.206

3-659

3.889

A
B
C
D
E
b!
F

(G)
G
h

.5145

•520331
.520967

•523139
.527994

•528353
.530902

•532792

1.508956
.510916
.511904
.514591
.518010
.518686
.520996
.526207
•526595
•529359

I-539I55
•540255

•543249
.547088
.547852
•55047i
•556386
•556830
•559999
•562392

1.534067
•536450
•537673
.54101 i

•545306
.546166
.549121
•555863
•556372
.560010
.562760

1.568558
.570011
•574015
•579223!
.580271 I
.583886)
.592190
.592824

•597332
.600727

1.615701
.617484
.622414
.628895
.630204
.634748
.645267
.646068
.651840
.656219

1-639143
.642874
.644866
.650388

•657653
.659122
.664226
.676111
.677019

•683577
.688569

1.696531
.701060
.703478
.710201
.719114
.720924

•727237
.742063

•743204
.751464

•757785

N. B. — D is the more refrangible of the pair of sodium lines; (G) is the hydrogen line near G.

SMITHSONIAN TABLES.

I78

INDEX OF REFRACTION FOR GLASS.

TABLE 185.

(d) MASCART'S DETERMINATIONS. (Ann. Ch m. Phys.

(,8) LANGLEV'S DETERMINATIONS. (Silliman's Jour-

1868.)

nal, 27, 1884.)

Flint glass.

Crown glass.

Flint glass.

Density =:

3-615

3-239

2.578

Wave length

Index of

Temp. —

30'. o

26°.0

28^.0

in mm. X io(>.

refraction.

A

1.60927

1.57829

1.52814

2030

I-55I5

B

.61268

.58114

53011

1918

•5520

1870

•5535

C

.61443

.58261

•53"3

1810

•5544

D

.61929-

.58671

•53386

1580

•5572

1540

•55/6

E

.62569

•59197

•53735

1360

.5604

b4

.62706

•59304

•53801

1270

.5616

1130

•5636

F

.63148

•59673

•54037

940

.5668

G

.64269

.60589

.54607

910

•5674

890

.5678

H

.65268

.61390

55093

850

.5687

L

.65817

.62012

55349

815

.5697

760.1 =

= A

•57H

M

.66211

.62138

55531

656.2 = C

•5757

N

.66921

.62707

55853

588-9 =

= DI

•5798

516.7 =

- b4

.5862

O

•67733

•63341

56198

486.1 = F

.5899

P

•63754

56419

396.8 =

= HI

.6070

Q

.64174

56646

344-0 =

= U

.6266

(f) EFFECT OF

TEMPERATURE. (Vogel, Wied. Ann.

vo. 25.)

nt+ nt' = a(t — t>) -f ft (t — /')3,

where nt is the absolute index of refraction for

the

temperature /, and a and ft are constants. For tem-

peratures ranging from 12° to 260° Voge obtains the
following values of a and ft for the Fraunhofer lines

given at the tops of the columns.

*.

D Hp

Hy

White glass \

a.108 =

96
107

123 224

1 06 97

327

93

A

Flint glass j

a .TO* =

190

101

190 362

147 221

575

221

(g) EFFECT OF TEMPERATURE.

(Muller, Publ. d

Astrophys. Obs. zu Potsdam, 1885.)

Flint glass.

Crown glass.

Fraun-

hofer

line.

Density = 3.855.
Temp. C.=—i° to 24°.

Density = 3. 218.
Temp. C. = — 3° to 21°.

Density =r 2.522.
Temp. C. = — 5° to 23°.

B

1.643776 + .00000474 *

I-574359 + .00000324*

1.512588 — .00000043*

C
D

.645745 + .00000486 *
.651 193 -j- .00000495 /

.575828+ .00000333*
.579856 + .00000323 *

•51 3558 — -00000033*

.516149 + .OOOOOOI7 *

bi
F

.659632 + .00000710*
.664936 + .00000653 *

.586000 + .00000443 *
.589828 + .00000439 *

.520004 + .00000054 *
.522349 + .00000048 *

Hy

.676720 + .00000783 *

.598205 + .00000560 *

.527360 + .00000082 *

h

.684144 -f- .00000861 *

.603398 + .00000636 *

.520376 + .00000143 *

N. B. — The above examples on the effect of temperature give an idea of
effect, but are only applicable to the particular specimens experimented on.

the order of magnitude of that

SMITHSONIAN TABLES.

179

TABLE 186.

INDEX OF REFRACTION.

Indices of Refraction for the various Alums.*

*

o

Index of refraction for the Fraunhofer lines.

1

E
H

a

B

c

D

E

b

F

0

Aluminium Alums. /?Al(SO4)2+i2H2O.t

Na

1.667

17-28

1.43492

143563

I-43653

1.43884

1.44185

1.44231

1.44412

1.44804

NH3(CH3)

1.568

7-17

•45013

.45062

•45r77

.45410

.45691

•45749

.45941

•46363

K

I-73S

14-15

.45226

•45303

•45398

•45645

•45934

.45996

.46181

.46609

Rb

i.8S2

7-21

•45232

; -45328

•45417

.45660

••45955

•45999

.46192

.46618

Cs

1.961

15-25

•45437

•455!7

.45618

.45856

.46141

.46203

.46386

.46821

NH4

1.631

15-20

•45509

•45599

•45693

•45939

.46234

.46288

.4648 1

.46923

Te

2-329

10-23

.49226

•493 ! 7

•49443

.49748

.50128

.50209

•50463

.51076

Indium Alums, .ff In(SO4),+ i2H2O.t

Rb

2.065

3_n

1.45942

1.46024

1.46126

1.46381

1.46694

1.46751

1.46955

1.49402

Cs

2.241

17-22

.46091

.46170

.46283

.46522

.46842

.46897

.47105

.47562

NH4

2.01 1

17-21

.46193

•46259

•46352

.46636

•46953

•47015

•47234

. -4775°

Gallium Alums. ^Ga(SO4)24-i2H2O.t

Cs

2.II3

17-22

1.46047

1.46146

1.46243

1.46495

r. 4678 5

1.46841

1.47034

1.47481

K

.46118

.46195

.46296

.46528

.46842

.46904

•47093

.47548

Rb

1.962

13-15

.46152

.46238

•46332

.46579

.46890

.46930

.47126

.47581

NH4

1-777

15-21

.46390

.46485

•46575

•46835

.47146

.47204

.47412

.47864

Te

2-477

1 8-20

.50112

.50228

•50349

.50665

•5^57

•5"3i

•51387

.52007

Chrome Alums. /?Cr(SO4)2+i2H2O.t

Cs

2.043

6-12

1.47627

1-47732

1.47836

1.48100

1.48434

1.48491

1.48723

1.49280

K

1.817

6-! 7

.47642

•4773s

.47865

•48137

•48459

•48513

•48/53

.49309

Rb

1.946

12-17

.47660

•47756

.47868

.48151

.48486

.48522

•48775

•49323

NH4

1.719

7-18

.47911

.48014

.48125

.48418

•48744

.48794

.49040

•49594

Te

2-386

9-25

.51692

.51798

.52280

.52704

•52787

.53082

.53808

Iron Alums. -ffFe(SO4)2+i2H,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

•49838

NH4

I-7I3

7-20

.47927

.48029

.48 1 50

.48482

.48921

.48993

.49286

.49980

Te

2.385

15-17

j.5'674

•5^90

•5'943

•52365

•52859

.52946

.53284

.54112

* According to the experimenits of Soret (Arch. d. Sc. Phys. Nat. Geneve, i884, 1888, and Comptes Rendus, 1885).
t A" stands for the different bases given in the first column.

SMITHSONIAN TABLES.

1 80

TABLE 187.

INDEX OF REFRACTION.

Index of Refraction of Metals and Metallic Oxides.

(a) Experiments of Kundt * by transmission of light through metallic prisms of small angle.

Index of refraction for

Name of substance.

Red.

White.

Blue.

Silver ....

_

0.27

_

Gold ....

0-38

0.58

I.OO !

Copper t.

0-45

0.65

o-95

Platinum . /.

1.76

1.64

i-44

Iron . / .

1.81

1.73

1.52

Nickel ....

2.17

2.01

1.85

Bismuth ....

2.61

2.26

2.13

Gold and gold oxide

1.04

-

1.25

" " "

0.89

0-99

i-33

" t

— '

2.03

—

Bismuth oxide .

—

I.QI

-

Iron oxide

.

1.78

2.11

2.36

Nickel oxide

2.18

2.23

2-39

Copper oxide .

2.63

2.84

Platinum and platinum oxide .

3-31

3-29

2.90

•

4.99

4.82

4.40

(b) Experiments of Du Bois and Rubens by transmission of light through prisms of small angle.

The experiments were similar to those of Kundt, and were made with the same spectrometer.

Somewhat greater accuracy is claimed for these results on account of some improvements intro-

duced, mainly by Prof. Kundt, into the method of experiment. There still remains, however,
a somewhat large chance of error.

Index of refraction for light of the following color and wave-length.

Name of metal. Red (u^

" Red."

Yellow (D).

Blue (F).

Violet (G).

A = 67.1

A = 64.4

A = 58.9

A = 48.6

A = 43. .*

Nickel . . 2.04

193

1.84

1.71

'•54

Iron . . 3.12

3.06

2.72

2-43

2.05

Cobalt . . 3.22

3.10

2.76

2-39

2.IO

(0) Experiments of Drude.

The following table gives the results of some

of Drude's experiments. § The index of refrac-

tion is derived in this case from

the constants of elliptic polarization by reflection, and are for

sodium light.

Metal.

Index of
refraction.

! Meta .

Index of !
refraction,
j

Aluminium . ; .

1.44

Mercurv

'•73

Antimony . . . !

3-°4

Nickel

1,79

Bismuth . ' .

1.90

Platinum

2.06

Cadmium . : .

1-13

Silver ....

0.181

Copper . ...

0.641

Steel

2.41

Gold ....

0.366

Tin, solid . . . :

1.48

Iron . ...

2.36

" fluid . . . j

2.IO • .

Lead . ...

2.OI

Zinc . . . .1

2.12

Magnesium .1

o-37

^

* " Wied. Ann." voli 34, and " Phil Mag." (5) vol. 26.
t Wave-lengths A are in millionths of a centimetre.

t Nearly pure oxide.
§ " Wied. Ann." vol. 39.

SMITHSONIAN TABLES.

181

TABLES 188, 189.

INDEX OF REFRACTION.

TABLE 188. —Index of Refraction of Rock Salt.

Determined by Langlev.
Temp. 24° C.

Determined by Rubens and
Snow.

Determined by other authorities.

Line of
spec-
trum.

Wave-
length
in cms.
X io«.

Index of
refraction.

Line of
spec-
trum.

Wave-
length
in cms.
X 10".

Index of
refrac-
tion.

Line of
spec-
trum.

Index of
refraction.

Authority.

M

37-2?

1.57486

Hy

43-4

1.5607

Ha

1.54046

j

L

38.20

•57207

F

48-5

•553'

H0

•553'9

> Haagen at 20° C.

H2

39-33

.56920

D

58-9

•5441

Hy

.56056

)

HX

39.68

•56833

C

65.6

•5404

G

43-°3

•56133

75-5

•5370

Ha

I-54095

!Bedson and

V

48.61

•55323

79-o

•5358

H*

•55384

Carleton Williams

b4

S'-67

•54991

83-1

•5347

Hy

•52515

at I5°C.

bi

5I-83

•54975

87.6

•5337

. D!

57-89

.54418

92-3

•5329

B

1.53884

1

D2

58.95

.54414

97-8

•S321

C

.54016

1

C

65.62

•54051

I03-5

•53r3

D

•54381

iMiilheims.

B

68.67

•539'9

110.7

•5305

E

.54866

A

76.01

•5367

118.6

•5299

F

.55280

p a r

94-

•5328

127.7

•5293

i

"3-

•53°5

138.4

•5286

A

I-53663

1

v

139-

•5287

151.1

.5280

B \

•53918

n

132.

•5268

166.0

•5275

B i

•53902

184.5

.5270

C \

•54050

Determined by Baden Powell.

207.6

237.2
277.1

•5264
•5257
•5247

C \
M

•54032
.54418
.54400

Stefan at 17° and
22° C. The up-

B
C
D

-

1-5403
•5415
•5448

302.2

332.0
oj

369.0
415.0

•5239
•5230

•5217
•5208

H

Fi

.54901
.54882

•55324
•55304

per values are
at 17° and the
lower at 22° for
each line.

E

-

.5498

474-5

•5J97

G

.56129

F

-

•5541

554-0

.5184

° \

.56108

G

-

.5622

644.7

•5l63

H

.56823

H

.5691

830-7

•5138

H i

.56806

TABLE 189. — Index of Refraction of Sylvine (Potassium Chloride).

Determined by Rubens and Snow.

Determined by other authorities.

Wave-length
in cms. X 10".

Index pf
refraction.

Wave-
length in

Index of
refraction.

Line of
spec-

Index of
refraction.

Authority.

43-4 (Hy)

1.5048

145.8

1.4766

A

I-48377

48.6 (F)

.4981

160.3

•476l

B

•48597

58.9 (H)

.4900

478.1

4755

C

•48713

65-6 (C)

.4868

200.5

•4749

D

.49031

• Stefan at 20 C.

E

•49455

80.2

1.4829

229.1

1.4742

F

.49830

84-5

.4819

267.3

•4732

G

•50542

89-3

.4809

320.9

.4722

H

.51061

94-4

.4807

356.I

•4717

B

•4754

C

.4767

100.3
107.0

1-4795
.4789

4OO.I
457-7

1.4712

.4708

D
E

•4825
.4877

• Grailich.

U4-5

.4781

534-5

.4701

F

•4903

123.4

•4776

641.2

•4693

G

•5005

D

•4904

Tschermak.

1337

1.4771

802.2

1.4681

D

•493°

Groth.

SMITHSONIAN TABLES.

182

TABLE 1 9O.

INDEX OF REFRACTION.

Index of Refraction of Fluor Spar.

Determined by
Rubens and Snow.

Determined by
Sarasi n.

Determined by the
authorities quoted.

Wave-length
in cms.
Xio«.

Index
of
refraction.

Line
of
spectrum.

Wave-
length in
cms. X 10°.

Index
of
refraction.

Line
of
spectrum.

Index
of
refraction.

Authority.

43-4(Hy)

1-4393

A

76.040

1.431010

D

1-4339

Fizeau.

48-5(Fj

•4372

a

71.836

•43 r 57 5

58.9(D)

•4340

B

68.671

•431997

A

1.43003"

65.6(C)

•4325

c

65.618

•43257i

a

•43'53

80.7

•43°7

D

58.920

•433937

B

.43200

85.0

•43°3

F

48.607

•437051

c

•43250 •

Miilheims.

89.6

.4299

h

41.012

.441215

D

•43384

95-Q

.4294

H

39.681

•442137

E

•43551

100.9

.4290

Cd

36.090

•445356

F

.43696 .

107.6

.4286

u

34.655

.446970

115.2

.4281

"

34.0I5

•447754

B

1.43200

124.0

.4277

"

32-525

.449871

D

•43390

134-5

.4272

"

27.467

•459576

F

•43709 •

Stefan.

146.6

.4267

"

25-7I3

.464760

G

.43982

161.3

.4260

"

23-I25

.475166

H

.44204

179.2

.4250

"

22.645

.477622

201.9

.4240

"

21-935

.481515

Red

M33 j

DesCloi-

230-3

.4224

"

21.441

.484631

Yellow

•435 )

seaux.

268.9

.4205

Zn

20.988

.487655

322.5
403-5

.4174
.4117

«

20.610
20.243

.490406
.493256

Na

1.4324*)
-4342t )

Kohl-
rausch.

462.0

.4080

Al

19.881

.496291

538.0

.4030

"

19.310

.502054

646.0

.3960

H

18.560

.509404

807.0

.3780

* Gray at 23° C.
t Black at 19° C.

SMITHSONIAN TABLES.

183

TABLE 191.

INDEX OF REFRACTION.

Various Monorefringent or Optically Isotropic Solids.

Substance.

Line of
Spectrum.

Index of
Refraction.

Authority.

Agate (light color) . . .

red

1-5374

De Senarmont.

Ammonium chloride .....

D

1.6422

Grailich.

Arsenite .......

D

1-755

DesCloiseaux.

Barium nitrate

D

1.5716

Fock.

Bell metal . ! • . ,«

D

1.0052

Beer.

t * ' 1 " J

(Li

2.34165 )

Blende . .

{ Na

2.36923 1

Ramsay.

(Tl

2.40069 )

,

(C

1.46245]

Boric acid . . ...

fa

1-46303 1

( F

1.47024 1
1.51222 |

Bedson and
Carleton Williams.

!j)

1.51484 1

.

F

1.52068]

Camphor

D

i 1.5462

Kohlrausch.
Mulheims.

Diamond (colorless) . .

(red
} green

2.414 J
2.428 J

DesCloiseaux.

f B

2.46062 )

Diamond (brown)

< D

2.46986 [

Schratif.

' E

2.47902 )

Ebonite

D

1.6

Ayrtqn & Perry.

fA

1.73 ]

IB

1.81

•{ c

1.90 }-

\Verijicke.

i

I ~

i-3i

j

i . i

LH

i-54

l

Garnet (different varieties) . . . •

D

( 1.74 to /
/ 1.90 f

Variojus.

red

1.480

Jamiri.

Wollaston.

Hanyne . . . . ; .

D

1.4961

Tschifchatscheff.

Helvine . • .

D

1-739

Levy.& Lecroix.

Obsidian . ,

D

( 1.48210 )
} 1.486 J

Various.

Opal . . . ! . . . . .

D

i 1.406 (.
1 1-450 I

"i

Pitch .-...- j

red

Wollaston.

Potassium bromide !
" chlorstannate ....
" iodide ! .

D

1-5593 )
1-6574 I
1.6666 )

Topsoe and
Christiansen.

ii

2.1442

Gladstone & Dale. J

Resins : Aloes . i

red

T^T-
I.6I9

Jamiri.

Canada balsam

"

1.528

Wrollaston.

M

Jamiri.

Copal

«

1.528

" i P

Mastic . ! . ... . .1

"

1.535

Wollaston.

Peru balsam . . . .

D

i-593

Baderi Powell.

,:

fA

2-653 }

1

Selenium; vitreous ! i

i

JB

1C «

2-73° I
2.86 f

Sirks.'

ID

2.98 j

i

D

2 17^ )

, ;

Silver < chloride . ', . . . . . '

2.o6l

Wernicke.

( iodide . ! :

'

2.182 )

Sodalite \ blue '. ' ' ' ' '

1

1.4827 I

- .Q _ _ [

Feusner.

I clear like water ...

I-4833 I

*

I.CJ CQ

Dussaud.

Spinel

'

j j

DesCloiseaux.

Strontium nitrate

1.5667

Fock.

SMITHSONIAN TABLES.

184

TABLE 192.

INDEX OF REFRACTION.

Index of Refraction of Iceland Spar.

'.'he determinations of Carvallo, Mascart, and Sarasin cover a considerable range of wave-length, and are here given.
Many other determinations have been made, but they differ very little from those quoted.

Line of
spectrum.

Wave-
length in
cms. X IOB.

Index of refraction for —

Line of
spectrum.

Wave:
length in
cms. X 10*.

Index of refraction for —

Ordinary
ray.

Extraordi-
nary ray.

Ordinary
ray.

Extraordi-
nary ray.

Authority: Carvallo.

Authority : Sarasin.

-

2I5

-

1-4753

Cdi2

32-53

1.70740

1.50857

-

198

1.6279

-

Cd17

27.46

•74I51

.52276

-

177

-

.4766

Cd18

25-71

.76050

•53019

-

154

•6350

-

Cd23

23.12

.80248

•54559

; -

US

.6361

•4779

Cd24

22.64

.81300

.54920

, -

122

.6403

-

Cd25

21 -93

.83090

•555!4

A

i !

B

108

76.04
68.67

.6424
.65006
•65293

•44799
.48275
.48406

Cd26

21.43

.84580

•55993

Authority : Mascart.

. A

a
B

-

1.65013
.65162
.65296

1.48285
.48409

Authority : Sarasin.

A

76.04

1.65000

1.48261

a

71.84

•65156

•48336

C

-

.65446

.48474

B

68.67

.65285

.48391

D

-

.65846

.48654

Cdi

64-37

•65501

.48481

E

-

.66354

.48885

D

58.92

•65339

.48644

b4

-

.66446

-

Cd2

53-77

.66234

.48815

F

-

•66793

.49084

Cd3

S3-36

.66274

.48843

G

-.

.67620

•49470

Cd4

50.84

.66525

•48953

H

-

.68330

•49777

F

48.61

•66783

49079

L

-

.68/06

.49941

Ccl5

47-99

.66858

.49112

M

-

.68966

•50054

Cd6

46.76

.67023

.49185

N

-

.69441

•50256

Cd7

44.14

•67417

•49367

0

-

.69955

.50486

h

41.0.1

.68036

•49636

P

-

.70276

.50628

H

39-6fe

.68319

•49774

Q

_ !

.70613

.50780

; Cd9

36-op

.69325

.50228

R

-

•7"55

.51028

:' Cd10 •

34-65

.69842

•50452

S

-

.71580

-

Cdn

34.01

.70079

•50559

T

-

•71939

-

SMITHSONIAN TABLES.

I85

TABLE 1 93.

INDEX OF REFRACTION.

Index of Refraction of Quartz.

Line or wave-
length in cms.
X io6.

Index for —

Line
of

spectrum.

Index for —

Ordinary
ray.

Extraordinary
ray.

Ordinary
ray.

Extraordinary
ray.

Quincke (right-handed quartz).

B

I-53958

1.54780

c

cjoS?

C/1Q77

D

•54335

•55J99

Cdi

1.54227

I-55I24

E

.54649

•555°8

D

Cd2
Cd3

fA

•54419
•54655
•54675

•55335
•55573
•55595

F
G

.54868
•55241

•55758

.54825

•55749

Cd5
Cd6

•55014
•55104

•55943
.56038

Quincke (left-handed quartz).

Cd7

•55318

.56270

Cd9
Cd10
Cdn

•56348
.56617

•56744

•57599
•57741

B
C
I)

1.54022
.54092

1.54880

•54945
.55245

Cd12
Cd17
Cd18
Cd23

•57094
•58750
.59624
.61402

ft i ,4 1 f,

.58097
.59812
.60713
.62561

E
F
G

•54575
•54845
•55246

•55533
.55801

•56163

Cd26

.62502
.63040

.62992

•63705
.64268

Authority : Mascart.

£n27

•63569

•64813

Zn28
Zn2g
A130
A131
A132

.64041
.64566
.65070
.65990
.67500

.65308
•65852
.66410
.67410
.68910

A
a
B
C
D

1.53902
54018

•54099
.54188

•54423

1.54812

•549'9
.55002

•55095
•55338

E

.54718

• "5 56 T.6

b4

•54770

•55694

F

.54966

•55897

Authority : Rubens.

G

•55429

•56372

H

.55816

•56770

L

.56019

•56974

434(Hy)
48-5(F)
59-0(0)
65.6(0

1-5538

•5499
•5442
•5419
•5376

-

N
O
P

Q

R

•5615°
.56400
.56668
.56842

.57121
•5738r
•57659
.57822

•57998
•58273

90.4

.K1O4

_

97-9

•5353

_

106.7
T 17 A

•5342

-

Authority: Van der Willigen (left-handed quartz).

'30-5
146.8
167.9
*95-7

•5287
.5257
.5216

-

A
B
C

I-539M
•54097
•54185

1.54806
•54998
•55085

234.8

.5160

—

D
E

•54419

•54715

•55329
•55633

C r(Q r r

G

.55422

•55^55
•56365

H

.55811

•56769

SMITHSONIAN TABLES.

* For wave-lengths, see Tables 190 and 192.

1 86

INDEX OF REFRACTION.

TABLE 194. - Uniaxial Crystals.

TABLES 194, 195.

Substance.

Line of
spec-
trum.

Index of refraction.

Authority.

Ordinary
ray.

Extraordi-
nary ray.

Alunite (alum stone) . . . . - ..»'

D

T-573

1.592

Levy & Lacroix.

Ammonium arseniate .....

red

i-577

4.524

De Senarmont.

Anatase . •. ».-» >.'•-. .

D

2-5354

2-4959

Schrauf.

Apatite . ... . . .

D

1-6345

"

Benzil ........

D

1.6588

1.6784

DesCloiseaux

Beryl . " . ... . . . .

"I

1.589 to
1.570

1.582 to
1.566

/ Various.

Brucite . •/• . * ' ' * •

D

1.560

1.581

Kohlrausch.

Calomel .•/•••

red

1.96

2.60

De Senarmont.

Cinnabar

red

2.854

3-J99

DesCloiseaux.

Corundum (ruby, sapphire, etc.)

red j

1.767 to

1.769

1-759
1.762

* :

Dioptase .......

green

1.667

r-723

Emerald (pure) ......

green

1.584

1.578

"

Ice at— 8° C

D

1.309

i-3i3

Meyer.

Idocrase .......

Dl

1.719 to

1.717 to

> DesCloiseaux.

I

1.722

1.720

)

Ivory ........

D

'•539

i-54i

Kohlrausch.

Magnesite

D

1.717

I-5I5

Mallard.

Potassium arseniate

red

1.564

i-5i5

DesCloiseaux.

" " .....

red

'•493

1.501

De Sernamont.

Silver (red ore)

red

3.084

2.881

Fizeau.

Sodium arseniate

D

1.459

1.467

Baker.

" nitrate ......

D

i-5»7

J-336

Schrauf.

" phosphate

D

1.446

2.452

Dufet.

Strychnine sulphate .....

D

1.614

1.519

Martin.

Tin stone

D

1.997

2.093

Grubenman.

Tourmaline (colorless) ....

D

'•637

1.619

Heusser.

" (different colors)

°i

1.63310
1.650

1.616 to
1.625

1 Jerofejew.

Zircon (hyacinth)

red

1.92

1.97

De Senarmont.

1)

1.924

1.968

Sanger.

TABLE 195. -Biaxial Crystals.

Index of refraction.

Line of

.

Substance.

spec-
trum.

Minimum.

Interme-
diate.

Maximum.

Authority.

Anglesite

D

1.8771

1.8823

1.8936

Arzruni.

Anhydrite

D

I-5693

I-5752

1.6130

Miilheims.

Antipyrin

D

1.5101

1.6812

1.6858

Glazebrook.

Aragonite

D

I-530I

1.6816

1.6859

Rudberg.

Axinite

red

1.6720

1.6779

I.68IO

DesCloiseaux.

Barite ....

D

1.636

1-637

1.648

Various.

Borax

D

1.4467

1.4694

1.4724

Dufet.

Copper sulphate .

D

1.5140

1.5368

1-5433

Kohlrausch.

Gypsum . . .

D

1.5208

1.5228

1-5298

Miilheims.

Mica (muscovite) . ...

D

1 5601

I-5936

J-5977

Pulfrich.

divine ....

D

1.661

1.678

1.697

DesCloiseaux.

Orthoclase . . .

D

1.5190

!-5237

1.5260

"

Potassium bichromate .

D

1.7202

1.7380

1.8197

Dufet.

" nitrate

D

13346

1.5056

1.5064

Schrauf.

" sulphate

D

I-4932

1.4946

1.4980

Topsoe & Christiansen.

Sugar (cane)

D

'•5397

1.5667

1.5716

Calderon.

Sulphur (rhombic)

D

l-9S°S

2-0383

2.2405

Schrauf.

Topaz (Brazilian)

D

1.6294

1.6308

I-6375

Miilheims.

Topaz (different kinds)

DS

1.630 to
1.613

1.631 to
1.616

1.637 to
1.623

> Various.

Zinc sulphate

D

1.4568

1.4801

1.4836

Topsoe & Christiansen.

SMITHSONIAN TABLES.

I87

TABLE « 96.

INDEX OF REFRACTION.

Indices of Refraction relative to Air for Solutions of Salts and Acids.

Substance.

Indices of refraction for spectrum lines.

Authority.

Density.

Temp. C.

D

C

F

Hy

H

(a) SOLUTIONS IN WATFR.

Ammonium chloride

1 .067

27°-Q5

1 ^7703

I-37936

I-38473

I-39336

Willigen.

1

"

•025

29-75

•34850

•35050

•355r5

•36243

Calcium chloride

•398

25-65

.44000

.44279

.44938

.46001

."

"

.215

22.9

•394"

•39652

.40206

.41078

11

"

... ^*

•143

25.8

•37152

•37369

•37876

.38666

Hydrochloric acid .

I.I66

20.75

1.40817

1.41109

1.41774

1.42816

Nitric acid .

•359

18.75

•39893

.40181

.40857

.41961

Potash (caustic) . .

.416

II.O

.40052

.40281

.40

SoS

•41637

Fraunhofer.

Potassium chloride .

normal solution

•34087

.34278

•34719

I-35049

Bender.

"

double normal

.34982

•35179

•35645

•35994

"

a

"

triple normal

•35831

.36029

•36512

.36890

"

Soda |

caustic)

I-376

21.6

1.41071

I-4I3

34 1.41936

1.42872

Willigen.

Sodium chloride . .

.189

18.07

•37562

•377!

*9

.38322

1.38746

Schutt.

" .

"

.109

18.07

•35751

•35959

.36442

.36823

"

**

u

•035

18.07

.34000

•34I91

.34628

•34969

Sodium nitrate . '• .

1.358

22.8

1.38283

1 -38535

I-39I34

1.40121

Willigen.

Sulphuric acid . .

.811

I8.3

•43444

•43669

.44168

•44

«3

'

1 •

"

"

.632

I8.3

.42227

.42466

•42967

•43694

4

"

"

.221

I8.3

•36793

.37009

.37468

•38158

i

"

*'

.028

I8.3

•33663

.33862

•34285

•34938

t

Zinc chloride . . .

!-359

26.6

1-39977

1.40222

1.40797

-

1.41738

<

ii

.209

26.4

•37292

•375'5

.38026

-38845

4

(to) SOLUTIONS IN ETHYL

ALCOHOL.

Ethyl alcohol . . .

0.789

25-5

I-3579I

I-3597I

I-36395

-

I-37094

Willigen.

"

"

•932

27.6

•35372

•35556

•35986

.36662

Fuchsin (nearly sat-

urated) .

-

16.0

.3918

•398

.361

•3759

Kundt.

Cyanin (saturated) .

~v

16.0 '

•3831

•37°5

.3821

NOTK. — Cyanin in chloroform also acts anomalously

for example, Sieben gives for

a 4-5

per cent, solution /uu= 1.4593, M«= l-4^9^ Mp(greeit) = I-45I4» M« (blue) = i

•4554-

For a 9.9 per cent, solution he gives /x^= 1.4902, /tp(green) = 1.4497, /ir;(blue) = i

•4597-

(o) SOLUTIONS OF POTASSIUM PERMANGANATE IN WATER.*

Wave-
length

Spec-
trum

Index
for

Index
for

Index
for

Index
for

Wave-
length

Spec-i
trum :

Index
for

Index
for

Index
for

Index
for

in cms.
X io«.

Hue.

i % sol.

2 % SOI.

3 % sol.

4 % sol.

in cms.
X jo".

line. :

i % sol.

2 % sol.

3 % sol.

.4 % sol.

68.7

B

1.3328

1-3342

_

1.3382

5,.6

_ ;

1-3368

I-3385

_

_

65.6

C

•3335

•3348

'•3365l

•3391

50.0

-

•3374

•3383

1-3386

1.3404

6l.7

-

•3343

•3365

•338i

.3410

48.6

F

•3377

.3408

59-4

-

•3354

•3373

•3393 ,

.3426

48.0

-

•338i

•3395

•3398

•34'3

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

43-4

-

•3417

-

-

'34£o

52-7

E

•3363

-

42-3

-

•343 !

•3442

•3457

•3468

52.2

•3362

•3377

•3388

1

SMITHSONIAN TABLES.

* According to Christiansen.

188

TABLE 197.

INDEX OF REFRACTION.

Indices of Refraction of Liquids relative to Air.

Substance.

Temp.
C.

Index of refraction for spectrum lines.

Authority.

C

D

F

H7

H

Acetone ....

10°

1.3626

1.3646

1.3694

I-3732

_

Korten.

Almond oil ...

0

•4755

.4782

•4847

-

Olds.

Analin* ....

20

•5993

•5863

.6041

.6204

-

Weegmann.

Aniseed oil ...

21.4

.5410

•5475

.5647

-

-

Willigen.

"...

I5-I

.5508

•5572

•5743

-

1.6084

Baden Powell. .

Benzene t • • • •

IO

1.4983

1.5029

1.5148

-

1-5355

Gladstone.

.

21.5

•4934

•4979

•5°95

—

•53°4

"

Bitter almond oil .

20

•5391

•5623

•5775

Landolt.

Bromnaphtalin . .

20

.6495

.6582

.6819

.7041

.7289

Walter.

Carbon disulphide J

o

1-6336

I-6433

1.6688

1.6920

17175

Ketteler.

" "

20

.6182

.6276

•6523

.6748

.L994

"

" "

IO

.6250

•6344

•6592

.7078

Gladstone.

" "

!9

.6189

.6284

•6352

—

.7010

Dufet.

Cassia oil ....

IO

.6007

.6104

.6389

— '

•7039

Baden Powell.

u '*....

22.5

•5930

.6026

.6314

-

.6985

« u

Chinolin ....

20

1.6094

1.6171

1.6361

1.6497

_

Gladstone.

Chloroform . . .

IO

.4466

.4490

•4555

.4661

Gladstone & Dale.

" ...

3°

-

•4397

-

.4561

" "

" ...

20

•4437

.4462

•4525

-

Lorenz.

Cinnamon oil . .

23-5

.6077

.6188

.6508

-

-

Willigen.

Ether

I c

I.-5CC4

i. TI; 66

1.^606

i. -?68^

Gladstone & Dale.

1 J

I c

'•JJJ^

.7C77

• • j j""

JCOJ.

'Jp*****

,76j.I

1 j^'o
.-371-5

Kundt.

Ethyl alcohol

1 j

o

Jj/ J
•3677

•jjy-t
•3695

*JrMr*

•3739

•3773

•o/ * j

Korten.

" " . .

IO

•3636

•3654

.3698

•3732

-

"

" " . .

20

•3596

.3614

•3657

.3690

-

"

*' .

15

.3621

•3638

•3683

•3751

Gladstone & Dale.

Glycerine ....

20

1.4706

_

1.4784

1.4828

-

Landolt.

Methyl alcohol . .

15

•3308

1.3326

•3362

-

.3421

Baden Powell.

Olive oil ....

o

•4738

•4763

•4825

-

-

Olds.

Rock oil ....

o

•4345

•4573

.4644

—

—

«

Turpentine oil . .

10.6

M7I5

1.4744

1.4817

-

M939

Fraunhofer.

" " . .

20.7

.4692

.4721

•4793

—

•4913

Willigen.

Toluene ....

20

•49"

•4955

.5070

•5X7°

-

Bruhl.

Water§ ....

16

•33'8

•3336

•3377

•3409

-

Dufet

16

•33i8

•3337

•3378

•3442

Walter.

* Weegmann gives jtifl=: 1.59668 — .000518*. Knops gives /KF= 1.61500 — .00056*.
t Weegmann gives f*c = 1.51474 — .000665*. Knops gives HD= 1.51399 — .000644*.
t Wiillner gives fi^= 1.63407 — .00078*; i*-p= 1.66908 — .00082*; ^ = 1.69215 — .00085*.

§ Dufet gives /«./>= '-33397 — io—7 (125 * + 20.6** — .000435/3 — .oonj*4) between o° and 50°; and nearly the
same variation with temperature was found by Ruhlmann, namely, MB— !-33373 — '°~ 7 (20. 14 *2+. 000494 *«).

SMITHSONIAN TABLES.

189

TABLE 198.

INDEX OF REFRACTION.

Indices of Detraction 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

temperature. More recent experiments confirm their conclusions. The formula is nt— i =r — °— - - "-• where

i + 0/760

nt is the index of refraction for temperature t, na for temperature zero, a the coefficient of expansion of the gas
with temperature, and/ the pressure of the gas in millimetres of mercury. Taking the mean value, for air and
white light, of «0 — i as 0.0002936 and a as 0.00367 the formula becomes

.0002936 _ P .0002895 P_

i -j- .00367 t 1.0136 X io6 i + .00367 io°'

where P is the pressure in dynes per square centimetre, and t the temperature in degrees Centigrade.

(a) The following table gives some of the values obtained for the different Fraunhofer lines for air.

Spectrum

Index of refraction according to —

Spectrum Ind" l^™'1011

line.

Ketteler.

Lorenz.

Kayser & Runge.

Kayser & Runge.

A

1.0002929

1 .0002893

1.0002905

M 1.0002993

B

2935

2899

2911

N 3003

C

2938

2902

2914

O 3015

D

2947

2911

2922

E

29S8

2922

2933

P 1.0003023

Q 3031

F

1.0002968

1.0002931

1.0002943

R 3°43

G

2987

2949

2962

H

3°°3

2963

2978

S 1.0003053

K

b ' —

2980

T 3064

L

—

—

2987

u 3075

(b) The following data have been compiled 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 .

D

I.

OOIO79-I.OOIIOO

Hydrogen . .

white

1.000138-1.000143

Ammonia

white

1.000381-1.000385

"

white

1.000139-1.000143

i<

D

1.000373-1.000379

Hydrogen sul- j

D

1.000644 Dulong.

Argon . .

D

1.000281 Rayleigh.

phide . . 1

D

1.000623 Mascart.

Benzene .

D

1.001700-1.001823

Methane . . .

white

1.000443 Dulong.

Bromine .

D

i.

001152 Mascart.

"

D

1.000444 Mascart.

Carbon dioxide

white

i .000449-1 .000450

Methvl alcohol .

D

1.000549-1.000623

"

"

D

i .000448-1 .000454

Methyl ether .

D

1.000891 Mascart.

Carbon disul- {

white

i

001500 Dulong.

Nitric oxide .

white

1.000303 Dulong.

phide .

• )

D

1.001478-1.001485

D

1.000297 Mascart.

Carbon mon- \

white

1.000340 Dulong.

Nitrogen . . .

white

i .00029 5- 1 .000300

oxide .

• 1

white

i

000335 Mascart.

M

D

i .000296- r .000298

Chlorine .

white

< t.

000772 Dulong.

Nitrous oxide .

white

1.000503-1.000507

"

D

r

000773 Mascart.

" "

D

1.000516 Mascart.

Chloroform . .

D

1.001436-1.001464

Oxygen . . .

white

1.000272-1.000280

Cyanogen

white

1.000834 Dulong.

u

D

1.000271-1.000272

"

D

1.000784-1 .000825

Pentane . . .

D

1.001711 Mascart.

Ethyl alcohol .

D

1.000871-1.000885

Sulphur dioxide

white

1.000665 Dulong.

Ethyl ether . .

D

1.001521-1.001544

" "

D

i. 000686 Ketteler.

Helium .

D

1.000043 Rayleigh.

Water. . . .

white

1.000261 Jamin.

Hydrochloric $

white

1.000449 Mascart.

" . . . .

D

T .000249-1 .000259

acid . .

• 1

D

i

000447

SMITHSONIAN TABLES.

IQO

ROTATION OF PLANE OF POLARIZED LIGHT.

TABLE 1 99.

A few examples are here given showing the effect of wave-length on the rotation of the plane of polarization. The
rotations are for a thickness of one decimetre of the solution. The examples are quoted from Landolt & Born-
stein's " Phys. Chem. Tab." The following symbols are used : —

/=: number grammes of the active substance in 100 grammes of the solution.

c = " solvent "

g — " active " " cubic centimetre '

Right-handed rotation is marked + , left-handed—.

Line of

Wave-length
according to

Tartaric acid,* CuH6O6,
dissolved in water.

Camphor,* Ci0H16O,
dissolved in alcohol.

Santonin, t ClsHj8O3,
dissolved in chloroform.

spectrum.

Angstrom in

q = 50 to 95,

q = 50 to 95,

9=75 to 06.5,

cms. X io6.

temp. = 24" C.

temp. ~ 22.9° C.

temp. = 20° C.

B

68.67

— 140°. I +0.2085?

C

65.62

+ 2°. 748 + 0.09446?

38°. 549 — 0.0852?

— 149.3 +°-I555?

D

58.92

+ 1.950 + 0.13030?

51.945 — 0.0964?

— 202.7 + 0.3086 ?

E

52.69

+ 0.153 + 0.17514?

74-33'— o-1 343 '/

— 285.6 +0.5820?

DI

- -

- -

— 302-38 + o-6557 ?

D2

F
e

51.72
48.61
43-83

— 0.832 + 0.19147?
— 3-598 + 0.23977 ?
— 9.657 + 0.31437?

79-348 — 0.1451 ?
99.601 — 0.1912 ?
149.696 — 0.2346?

— 365-55 + 0.8284 ?
— 534.98+ 1.5240?

Santonin, t C];1H18O3, *
dissolved in alcohol.

Santonin, t Cj>;H18O3,

Santouicacid,t
C15H,o04,
dissolved in
chloroform.

Cane sugar,!
dissolved in

dissolved in
alcohol.

dissolved in
chloroform

temp. := 20° C.

c = 4.046.
temp. =

20° C.

c =13. 1-30.5.
temp. =

20° C.

(- = 27.192.
temp. =r 20° C.

p = io to 30.

B

68.67

— 110.4°

442°

484°

-49°

47°-56

C

65.62

— 118.8

5°4

549

— 57

52-70

D

58.92

— 161.0

693

754

— 74

60.41

E

52.69

— 222.6

991

1088

— 105

84.56

b,

5I-83

— 237-1

IO53

1148

112

-

b,

51.72

-

-

-

87.88

F

48.61

— 261.7

1323

1444

— '37

101.18

e

43-83

— 380.0

2OII

22OI

— 197

-

G

43-°7

-

-

-

-

131.96

g

42.26

"

238l

26lO

— 230

* Arndtsen, " Ann. Chim. Phys." (3) 54, 1858.

t Narini, " R. Ace. dei Lincei," (3) 13, 1882.

t Stefan, " Sitzb. d. Wien. Akad." 52, 1865.

ROTATION OF PLANE OF POLARIZED LIGHT.

TABLE 2OO.

Sodium chlorate (Guye, C. R. 108, 1889).

Quartz (Soret & Sarasin, Arch, de Gen. 1882, or C. R. 95, 1882).*

Spec-
trum
line.

Wave-
length.

Temp.
C.

Rotation
per mm.

Spec-
trum
line.

Wave-
length.

Rotation
per mm.

Spec-
trum
litie.

Wave-
length.

Rotation
per mm.

a

71.769

i5°.o

2°.o68

A

76.04

i2°.66S

Cd9

36.090

63°. 268

B

67.889

17.4

2.318

a

71.836

14.304

N

35.818

64-459

C

65-073

2O.6

2-599

B

68.671

15.746

Cdio

34-655

69.454

D

59.085

18.3

3.104

0

34.406

70.587

E

53-233

1 6.0

3.841

C

65.621

17.318

F

48.912

11.9

4.587

D2

58951

21.684

Cdn

34-015

72.448

G

45-532

IO.I

5-331

L>i

58.891

21.727

P

33.600

74-571

G

42.834

14.5

6.005

^

32.858

78.579

H

40.714

13-3

6.754

E

52.691

27-543

Cdi2

32.470

80.459

L

38.412 "

14.0

7-654

F

48.607

32-773

M

37-352

10.7

8.100

G

, 43-072

42.604

R

3!-798

84.972

N

35-544

12.9

8.861

Cdn

27.467

121.052

P

33-93 i

I2.I

9.801

h

41.012

47.481

Cd18

25-713

143.266

Q

32-34I

II-9

10.787

H

39.681

5I-I93

Cd23

23.125

190.426

R

30.645

I3.r

11.921

K

39-333

52-i55

T

29.918

12.8

12.424

Cd24

22.645

201.824

Cd17

28.270

r2.2

13.426

L

38.196

55-625

Cd25

21-935

220.731

Cd18

25-038

11.6

14.965

M

27.262

58.894

Cd2e

21.431

235-972

* The paper is quoted from a paper by Ketteler in " Wied. Ann." vol. 21, p. 444. The wave-lengths are for
the Fraunhofer lines, Angstrom's values for the ultra violet sun, and Cornu's values for the cadmium lines.

SMITHSONIAN TABLES.

IQI

TABLE 201.

LOWERING OF FREEZING-POINT BY SOLUTION OF SALTS.

Under P is the number of grammes of the substance dissolved in 100 cubic centimetres of water. Under C is the
amount of lowering of the freezing-point. The data have been obtained by interpolation from the results pub-
lished by the authorities quoted.

Substance and
observer.

P

c°

Substance and
observer.

P

c-

Substance and
observer.

P

C3

AgNOs

5

o-93

ZnSO4

i

O.IO

MgCl2

°-5

0.26

F. M. Raoult.*

10

1.71

F. M. Raoult.*

2

0.23

S. Arrhenius.t

I.O

°-53

15

2.38

3

0.36

'•5

0.81

20

2-97

4

o-49

2.O

1. 10

25

3-53

5

061

2-5

i-39

30

4.00

IO

1.23

1.69

35

4-43

15

1.85

3-5

2.00

40

4.80

20

2.50

4.0

2.32

45

5-15

25

4-5

2.65

5°

5-45

30

3-94

5-°

2.98

55

5-75

5-5

3-32

60

6.00

CuSO4

i

0.15

6.0

3-67

65

6.26

F. M. Raoult.*

2

0.29

3

0.40

BaCl2

o-5

O.II9

Ca(N03)2

i

0.28

4

0.51

Harry C. Jones.§

I.O

0.234

F. M. Raoult.*

2

0.56

5

0.62

1.5

0-344

3

0.84

6

0.72

2.O

0.450

4

1. 12

7

0.82

5

I.4O

8

0.92

SrCl2

o-5

0.17

10

2.78

9

i. 02

S. Arrhenius.t

I.O

o-34

15

4.26

10

1. 12

'•5

0.50

20

6.00

2.0

0.65

CdSO4

i

O.O9

2-5

0.80

Cd(N03)2

o-5

O.I 1 2

F. M. Raoult*

2

O.ig

3-o

o-95

Harry C. Jones. §

I.O

0.217

3

0.28

3-5

.12

4

0.38

4.0

.29

Na2S()4

i

0.28

5

0.48

4-5

•44

F. M. Raoult *

2

0.56

IO

I.OO

.60

3

0.84

15

i-54

5-5

-76

4

1. 12

20

2. 1 I

6.0

•93

5

I.4O

25

2-77

30

3-51

CuCl2 + 2H20

o-5

0.15

K2S04

0.5

0.14

35

4.40

S. Arrhenius.t

I.O

0.30

S. Arrhenius.

I.O

0.27

1.5

0.44

1.5

o-39

NaCl

0.5

0.32

2.O

0-58

2.O

0.51

S. Arrhenius.t

I.O

0.62

2-5

0.72

2-5

0.63

1.5

0.92

3-°

0.86

3-o

0.74

2.0

1.22

3-5

.00

3-5

4.0

0.85
0.96

2-5

1.52
1.82

4.0
4-5

.14
.29

4-5

1.07

5-°

•43

5-°

1.17

KC1

0.5

0.234

5-5

•57

5-5

.27

Harry C. Jones.}:

I.O

0.464

6.0

1.71

6.0

•37

1.5

0.693

6-5

1.85

6-5

•47

2.O

0.915

2.0

2.OO

7.0

•57

2.5

1.136

7-5

.67

3-°

!-359

CdCl2

o-5

O.I 2O

8.0

•77

Harry C. Jones.§

I.O

O.227

LiCl

o-5

o-45

1.5

0.322

MgSO4
F. M. Raoult.*

i

2

3

0.18

o-35
0.52

S. Arrhenius.t

I.O
2.O

0.89

i-34

1.78

CaCl2
S. Arrhenius.t

0.5

I.O

1.5

0.23
0.45

0.68

4

0.70

2-5

2-23

2.0

0.91

C

0.89

J
IO

2O

i-77
2.78
3.68

NH4C1
Harry C.Jones.}

0.5

I.O

0.326
0.644
0-957

2-5

3-o

3-5
4.0

1.14

1.37

1.61
1.85

SMITHSONIAN TABLES.

* In " Zeits. fur Physik. Chem." vol. 2, p. 48g, i!
t Ibid. vol. 2, p. 491, 1888.
Z Ibid. vol. ii, p. no, 1893.
§ Ibid. vol. ii, p. 529, 1893.

192

TABLE 2O1

LOWERING OF FREEZING-POINT BY SOLUTION OF SALTS.

Substance and
observer.

P

c-^

Substance and
observer.

P

C°

Substance and
observer.

P

C°

ZnCl2

0.5

0.185

Alcohol, C»H6O

O.I

0.044

H2S03

°-5

0.15

Harry C. Jones.*

I.O

0.348

Harry C. Jones.}

0.2

0.087

S. Arrhenius.t

I.O

0-30

o-3

0.129

»-5

o-45

CdBro

°-5

0.080

0.4

0.170

20

0.60

Harry C. Jones.*

I.O

0.142

o-S

0.212

2-5

0.75

i:5

0.195

I.O

O.4O2

3-o

0.90

2.0

0.248

3-5

1.05

2-5

0.300

4.0

1.20

3-°

0.352

4-5

i-35

Acetic acid,

O.I

0.034

5-o

1.50

CdI2

I

0.06

C2H402

0.2

0.067

5-5

1.65

S. Arrhenius.t

2

0.12

Harry C.Jones.}

o-3

O.O99

6.0

i. 80

3

O.ig

o-4

O.I3I

6-5

i-95

4

0.25

°-5

O.l62

7-o

2.IO

5

0.32

I.O

o-3 * 3

10

0.63

H2SO4

O.I

O.O44

'5

0.92

Harry C. Jones.}

O.2

0.088

20

1.22

°-3

O.I3I

25

!-52

P(OH)3

°-5

0.18

0.4

O.I72

S. Arrhenius.t

I.O

o-35

o-5

O.2I2

NaOH

O.I

O.O92

!-5

0.50

I.O

O.4O2

Harry C. Jones.}

O.2

0.178

2.O

0.65

o-3

O.2OO

H3P04

o-5

O.I4

0.4

0-337

S. Arrhenius.t

I.O

0.27

o-5

0.410

i-5

0.38

HI03

o-5

0.09

2.0

0.49

KOH

O.I

0.064

S. Arrhenius.t

I.O

0.18

2-5

O.6O

Harry C. Jones.}

O.2

0.126

i-5

0.27

3-o

0.70

0-3

0.189

2.O

o-35

3-5

0.80

0-4

0.252

2-5

o-44

4.0

O.OX)

o-5

0.312

3-o

0.52

0.6

0.370

3-5

0.61

Cane sugar.

0.5

0.030

0.7

0.430

4.0

0.69

F. M. Raoult.§

i.o

O.OOO

4-5

0.78

2.O

O.II8

NH4OH

0.05

0.028

5-°

0.86

3-°

0.176

Harry C. Jones.}

O.IO

0.056

4.0

0-234

0.15

0.084

5-o

O.292

0.20

0.113

IO.O

0.587

0.25

0.143

HC1

O.I

0.099

15.0

0.88 1

Harry C. Jones.|

O.2

0.198

2O.O

1.174

Na2CO8

O.I

0.048

°-3

0.296

25.0

1.465

Harry C. Jones.}

O.2

0.096

0.4

o-395

30.0

i-752

o-3

0.143

o-5

0-493

35-o

2.048

0.4

0.188

40.0

2-333

0.5

0.228

I.O

0.417

Glycerine.il

I.O

O.22

HNO3

O.I

0.06 1

S. Arrhenius.t

2.O

0-42

K2C03

O.I

0.039

Harry C. Jones.}

0.2

0.118

3-°

0.64

Harry C. Jones. }

0.2

0.078

0-3

0-175

4.0

0.87

o-3

0.116

0.4

0.232

50

I. II

0.4

0.152

0.5

0.285

6.0

i-34

0.5

0.187

0.6

o-33«

8.0

1.83

I.O

o-343

o-7

0.390

IO.O

2.32

12.0

,83

* In " Zeits. fiir Physik. Chem.'' vol. n, p. 529, 1883.
t Ibid. vol. 2, p. 491, 1888.
t Ibid. vol. 12, p. 623, 1893.
§ F. M. Raoult, C. R. 114, p. 268.

II 50% solution solidifies at — 31° C., according to Fabian, "Ding. Poly. Journ."vol. 155, p. 345. This gives an
average of .3 per gramme.

SMITHSONIAN TABLES.

193

TABLE 202.

VAPOR PRESSURE OF SOLUTIONS OF SALTS IN WATER.*

The first column gives the chemical formula of the salt. The headings of the other columns give the number of
gramme-molecules of the salt in a litre of water. The numbers in these columns give the lowering of the
vapor pressure produced by the salt at the temperature of boiling water under 76 centimetres barometnc pressure.

Substance.

0.5

1.0

2.0

3.0

4.0

5.0

6.0

8.0

10.0

A12(S04)3 - ' .

12.8

36-5

A1C13 ....

22.5

61.0

179.0

318.0

Ba(S03)2 . . .

6.6

'5-4

34-4

Ba(OH)2 . . /

12.3

22.5

39-o

Ba(N03)2 : ^. .-.

!3-5

27.0

Ba(C103)2 .

15-8

33-3

70.5

1 08. 2

BaCl2 ....

16.4

36.7

77.6

BaBr2 ....

1 6.8

38.8

91.4

I5O.O

204.7

Ca(S03)2 •

9-9

23.0

56.0

I O6.O

Ca(NO3)2 .

16.4

34-8

74.6

139-3

161.7

205.4

CaCl2 ....

17.0

39-8

95-3

1 66.6

24I-5

3I9-5

CaBr2.

!7-7

44.2

1,5.8

191.0

283-3

368.5

CdSO4

4.1

8.9

18.1

CdI2 ....

7.6

14.8

33- S

52-7

CdBr2.

8.6

17.8

36-7

55-7

8o.O

CdC12.

9.6

18.8

36-7

57-o

77-3

99-0

Cd(N03)2 . .

15.9

36.1

78.0

122.2

Cd(C103)2 .

i?-5

CoS04

5-5

10.7

22.9

45-5

CoCl2.

15.0

34-8

83.0

136.0

186.4

Co(N03)2 .

!7-3

39-2

89-0.

152.0

218.7

282.0

332-0

FeSO4

5-8

10.7

24.0*

42.4

H3BO3 . . .
H3P04

6.0
6.6

12.3
14.0

25.1
28.6

38.0
45-2

51.0
62.0

81.5

103.0

146.9

'89-5

H3As04 .

7-3

15.0

30.2

46.4

64.9

H2S04 . . .

12.9

26.5

62.8

104.0

148.0

198.4

247.0

343-2

KH2P04 .

IO.2

'9-5

33-3

47-8

60.5

73-1

85.2

KNO3.

10-3

21. 1

40.1

57-6

74-5

88.2

IO2.I

126.3

148.0

KC1O3

10.6

21.6

42.8

62.1

80.0

KBr03 . . .

10.9

22.4

45.0

KHSO4

10.9

21-9

43-3

65-3

85-5

107.8

129.2

170.0

KNOZ

n. i

22.8

44-8

67.0

90.0

110.5

I30-7

167.0

198.8

KC1O4

"•5

22-3

KC1 ....

12.2

24.4

48.8

74.1

100.9

128.5

152.2

KHCO2 .

II.6

23.6

59-o

77-6

104.2

132.0

1 6O.O

210.0

255-0

KI

12-5

25-3

52.2

82.6

1 1 2.2

Hi-S

I7I.8

225-5

278.5

K2C2O4 .

13-9

28.3

59-8

94.2

I3I.O

K2WO4

13-9

33-°

75-°

123.8

175-4

226.4

K2C03

144

31.0

68.3

i°5-S

I52.O

209.0

258.5

35°-°

KOH ....

15.0

29.5

64.0

99.2

I4O.O

181.8

223.0

309-5

387.8

K2CrO4

16.2

29.5

60.0

LiN03

12.2

25-9

55-7

88.9

122.2

'55-i

1 88.0

253-4

309.2

LiCl ....

I 2. 1

25-5

57-i

95-°

!32-5

J75-5

219.5

3"-5

393-5 1

LiBr ....

12.2

26.2

60.0

97.0

I4O.O

186.3

241.5

341-5

438.0 1

Li2S04

13-3

28.1

56.8

89.0

LiHSO4 .

12.8

27.0

57.0

93-o

130.0

1 68.0

Lil

13-6

28.6

64.7

105.2

J54-5

206.0

264.0

357-o

445-°

Li28iFl6 .

15-4

34-o

70.0

1 06.0

LiOH ....

J5-9

37-4

78.1

Li2CrO4

16.4

32-6

74.0

I2O.O

171.0

* Compiled from a table by Tamniann, " Me'm. Ac. St. Petersb." 35. No. 9,
Phys." ch. 2, 42, 1886.

SMITHSONIAN TABLES.

194

See also Referate, "Zeit. f.

TABLE 202.
VAPOR PRESSURE OF SOLUTIONS OF SALTS IN WATER.

Substance.

0.5 j 1.0

2.0

3.0

4.0

5.0

6.0

8.0

10.0

MgS04 . . . ,.

6.5

I2.O

24-5

47-5

MgCl2. . . .

1 6.8

39-o

100.5

183-3

277.0

377-Q

Mg(N03)2 . . ,

17.6

42.0

IOI.O

174.8

MgBr2

17.9

44-o

115.8

205-3

298.5

MgH2(S04)2 . .'".

18.3

46.0

116.0

MnSO4

6.0

10.5

21.0

Mn€l2. . * /I

15.0

34-o

76.0

122.3

167.0

209.0

NaHoPO4 . . /T

10.5

20.0

36-5

5i-7

66.8

82.0

96.5

126.7

157.1

NaHSO4 .' .

10.9

22.1

47-3

75.0

IOO.2

126.1

148.5

189.7

2-31-4

NaN03 -. . .

10.6

22.5

46.2

68.1

90-3

111.5

I3I-7

167.8

198.8

NaClO3 /"' . ".

10.5

23.0

48.4

73-5

98-5

123-3

147-5

196-5

223-5

(NaP03)6 . . .

H.6

NaOH . ; .

1 1.8

22.8

48.2

77-3

107-5

i39-i

172.5

243-3

314.0

NaNO2

1 1.6

24.4

50.0

75-o

98.2

122.5

146.5

189.0

226.2

NaHPO4 .

12.1

23-5

43-°

60.0

78.7

99.8

I22.I

NaHCO2 .

12-9

24.1

48.2

77-6

IO2.2

127.8

152.0

198.0

239-4

NaS04

12.6

25.0

48.9

74.2

NaCl ....

12.3

25.2

52.1

80.0

I II.O

143.0

176.5

NaBrO3

I2.I

25.0

54-i

81.3

108.8

136.0

NaBr ....

12.6

25'9

57-o

89.2

124.2

J59-5

'97-5

268.0

Nal ....

12.1

25.6

60.2

99-5

136-7

177-5

22I.O

301-5

370.0

Na4P2O7 .

13.2

22.0

Na2CO3 .

14-3

27-3

53-5

80.2

I II.O

Na2C2O4 . . .

M-5

30.0

65.8

105.8

146.0

Na2WO4 .

I4.8

33-6

7r.6

"5-7

162.6

Na3PO4

I6.S

30.0

52-S

(NaP03)3 •

17.1

36.5

NH4NO3 .

12.8

22.O

42.1

62.7

82.9

103.8

I2I.O

152.2

180.0

(NH4)2SiFl6

"•5

25.0

44-5

NH4C1

I2.O

237

45-1

69-3

94.2

118.5

138.2

179.0

213.8

NH4HSO4 .

II.5

22.O

46.8

71.0

94-5

118.

139.0

181.2

2 1 8.0

(NH4)2S04. . .

II.O

24.0

46.5

69.5

93-°

117.0

I4I.8

NH4Br

II-9

23-9'

48.8

74-i

99.4

121.5

M5-5

190.2

228.5

NH4I ....

12.9

2S.I

49-8

78-5

104.5

132-3

156.0

2OO.O

243-5

NiSO4

5-°

10.2

21.5

NiCl2 ....

16.1

37-o

86.7

147.0

212.8

Ni(N03)2 .

16.1

37-3

9i-3

156.2

235-o

Pb(N03)2 .

12.3

23-5

45-°

63.0

Sr(S03)2 . . .

7.2

20.3

47.0

Sr(N03)2 . . yj

15.8

31.0

64.0

97-4

i3M

\ SrCI2 . .

16.8

38.8

91.4

156.8

223.3

281.5

SrBr2 . . ' . .'-\

17.8

42.0

IOI.I

179.0

267.0

ZnS04 . . ' .1

4-9

10.4

21.5

42.1

66.2

ZnCl2 . . . t\

9.2

18.7

46.2

75-o

107.0

'53-o

195.0

Zn(N03)2 . . .'

16.6

39-o

93-5

157-5

223.8

SMITHSONIAN TABLES.

195

TABLE 2O3.

RISE OF BOILING-POINT PRODUCED BY SALTS DISSOLVED IN WATER.*

This table gives the number of grammes of the salt which, when dissolved in 100 grammes of water, will raise the
boiling-point by the amount stated in the headings of the different columns. The pressure is supposed to be 76
centimetres.

Salt.

i«c

2°

3°

4°

5"

7°

10°

15°

20°

25'

BaCl2 + 2H20 .

I

5.0

3I-1

47-3

63-5

(7I-6 g

ives 4°

.5 rise

of temi

'.)

CaCU . .

to

11.5

16.5

2I.O

25.0

32.0

4i-5| 55-5

69.0

84.5

Ca(NO3)2 + 2H2O .

I

2.0

25-5

39-5

53-5

68.5

98.7

152.51 2400

331-5

443-5

KOH

4-7

9-3

13.6

17.4

20.5

26.4

34-5 i 47-o

57-5

67-3

KC2H3O2 .

6.0

12.0

1 8.0

24.5

31.0

44-o

98.0

134.0

KC1 . .. . .

9-*

I6.7

23-4

29.9

36.2

48.4

(57.4 gives a rise of 8°. 5)

K2CO3

11.5

22.5

32.0

40.0

47-5

60.5

78.5

I03-5

127-5

J52-5

KC103

13.2

27.8

44-6

62.2

KI .

15.0

30.0

45-o

60.0

74-o

99-5

134.

185.0

(220 gives i8°.5)

KNO3

'5-2

3I.O

47-5

64-5

82.0

120.5

188.5

33»-5

K2C4H4O6 + ^H2O .

18.0

36.0

54-o

72.0

90.0

126.5

182.0

284.0

KNaC4H4O6 .

J7-3

34-5

5'-3

68.1

84.8

119.0

171.0

272.5

390.0

510.0

KNaC4H4O6 + 4H2O

25.0

53-5

84.0

118.0

I57-o

266.0

554-o

5510.0

LiCl' ....

3-5

7-o

IO.O

12.5

15.0

18.5

26.0

35-o

42.5

50.0

LiCl+2H2O .

6-5

13.0

»9-5

26.0

32.0

44.0

62.0

92.0

123.0

160.5

MgCl2 + 6H2O .

II.O

22.O

33.0

44.0

^55-o

77-o

I IO.O

170.0

241.0

334-5

MgSO4 -|- 7H2O

4

I.C

87-5

138.0

196.0

NaOH

4-3

8.0

"•3

H-3

17.0

22.4

30.0

41.0

51.0

60. i

NaCl ....
NaNO3

6.6
9.0

12.4
18.5

17.2
28.0

2I-5
38.0

25-5
48.0

&i

(40.7

99-5

jives 8°
156.0

.8 rise)

222.O

NaC2H3Oo + 3H.,O .

14.9

30.0

46.1

62.5

79-7

118.1

194.0

484.0

6250.0

Na2S203 . . .

14.0

27.0

39-o

49-5

59-o

76.0

104.0

147.0

214.5

302.0

NaoHPO4 .

17.2

34-4

5i-4

68.4

85-3

Na2C4H406 + 2H2O .

21.4

44-4

68.2

93-9

121.3

183.0

(237.3 gives 8°4 rise)

Na2S2O3 + 5^2O

23.8

50.0

78.6

108.1

139-3

2 1 6.0

400.0^

1765.0

Na2CO3 4- ioH2O .

34-i

86.7

177.6

369.4

1052.9

NaoB4O7 + ioH2O .

39-

93-2

254.2

898.5

(5555-5 gives 4°-5 rise)

NH4C1

6-5

12.8

19.0

24.7

29.7

39-6

56.2

88.5

NH4N03 .

IO.O

2O.O

30.0

41.0

52.0

74.0

io8>o

172.0

248.0

337-o

NH4SO4 .

iS-4

30.1

44-2

58.0

71.8

99.1

(115.3 gives

108.2)

SrCl3 4- 6H2O .

20.0

40.0

60.0

81.0

103.0

150.0

234.0

524.0

Sr(N08)a •

24.0

45-o

63.6

81.4

97.6

C4H606 .

17.0

34-4

52.0

70.0

87.0

123.0

177.0

273.0

374-0

484.0

C2H2O4 4- 2H20

I9.O

40.0

.62.0

86.0

II2.O

169.0

262.0

536-°

1316.0

50000.0

C6H807 + H20

29.0

58.0

87.0

1 1 6.0

145.0

208.0

320.0

553-o

952.0

Salt. 40°

60°

80°

100°

120 >

140°

160° 180° 200° 240°

CaCl2 . . . 137.5

222.0

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

150.8

230.0

345-o

526-3

800.0

1 333-0 2353.0 6452.0

NH4N03 . . 682.0

1370.0

2400.0

4099.0

8547.0

oo

C4H6Oe • • 980.0

3774-0

'infinity gives 170)

* Compiled from a paper by Gerlach, " Zeit. f. Anal. Chem." vol. 26.
SMITHSONIAN TABLES.

196

TABLE 2O4.

CONDUCTIVITY FOR HEAT.

Metals and Alloys.

The coefficient k is the quantity of heat in therms which is transmitted per second through a plate one centimetre
thick per square centimetre of its surface when the difference of temperature 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 ex-
pressed approximately by the equation kt=^k0 (i -f- at). In the table k0 is the value of kt for o° C., t the tempera-
ture Centigrade, and a a constant.

Substance. , t

fc,

a

0

Substance.

t

fct

6.

s

5

Aluminium . .

0-3435 I
•36l9 f

.0005356

I

Clay slate,
(Devonshire) .

.00272

6

Antimony . . . <

.0442 1
.0396 j

— .001041

I

Granite . . i .

i from
{ to

—

.00510

.00550

I6

Bismuth . . . <

.0177 1
.0164 )

— .000735

I

Slate :
along cleav- j from

_

.00550

u

Brass (yellow) . |

.2041 1
.2540 J

.002445

I

age .
across cleav-

to
from

_

.00650

.00315

I -

I 6

" <«*> ' '{ 100

.2460 i
.2827 f

.001492

I

age . . .
Marbles, in-

to

—

.00360

r

Cadmium . . . <

.2200 |
.2045 J

— .000705

I

cluding lime-
stone, cal-

from

_

.00470

U

( o

I.O4O5

.000039

2

c i t e, and

to

-

.00560

r

Copper . . . < o
( zoo

.7226 )

.000051

I

compact do-
lomite . .

German silver . <

.0700}
.0887 J

.002670

I

Micaceous flagstone :
along cleavage . .

_

.00632

6

( i o

! Iron . . . . <

| IOO

.1665 (
.1627 \

— .000228

I

across cleavage . .
Sand (white dry) . .

~

.00441

.00093

6
6

" (wrought) * < !

.2070 /

.1567 j
.0836 I

^~ .oooS(3i

3

Sandstone and i
hard grit<
(dry) . . .(

from
to

-

•00545
.00565

\6

' ' ( IOO

.0764 >

I

Serpentine

t i o

.0148 i

(Cornwall red) . .

-

.00441

6

Mercury . . . < 50

.0189 f

4

( O-IOO

.0201

.001267

2

Snow in compact

Magnesium . . o— 100

.7760

.000000

I

layers

_

.000 t;i

7

Steel (hard) . .

j^.
.0620

5

Plaster of Paris

-

.0013

/

6

" (soft) . .

.IIIO

-

5

Pasteboard .

—

.00045

8

Silver .... o

1.0960

-

4

Strawboard . .

-

.00033

8

rr- \ '. O

Tin . . <

.1528)
•1423 }

—.000687

i

Paraffin . . .

(

o

.00014
.00023

8
9

\ IOO

Wood's alloy

•0319 j.

-

4

(

IOO

.00168

9

2

Sawdust

.OOOI 2

8

'

Vulcanite . .

_

.00087

10

Vulcanized

from

-

.00034

6

rubber (soft) ) to

-

.OOO54

6

Wood, Fir :

parallel to axis . .

-

.0003

8

perpendicular

to

axis .

—.

.OOOO9

8

Wax (bees) . .

• •

-

.00009

8

AUTHORITIES.

i Lorenz. 3 J. Forbes. 5 Kohlrausch. 7 Hjeltstrom. 9 R. Weber.

2 Berget. 4 H. F. Weber. 6 H. L. & D.t 8 G. Forbes. 10 Stefan.

* A repetition of Forties's experiments by Mitchell, under the direction of Tail, shows the conductivity to increase
with rise of temperature. (Trans. R. S. E. vol. 33, 1887.)

t Herschel, Lebour, and Dunn (British Association Committee).
SMITHSONIAN TABLES.

197

TABLES 2O5-208.

CONDUCTIVITY FOR HEAT.

TABLE 205. — Various Substances. TABLE 206. — Water and Salt Solutions.

Au-

Substance.

t

*t

thor-

ity.

Carbon

o

. 00040 z

I

Cement ....

o

.000162

I

Cork

o

.OOO7 1 7

I

Cotton wool . . .

o

.OOOO43

I

Cotton pressed . .

-

.000033

I

Chalk

.OO2OOO

•7

Ebonite ....

49

.000370

2

Felt

o

.000087

I

Flannel ....

0

.000035

I

,-,, \ from . . .
Glass'jto. . . .

:

.0005 )
.0023 J

3

Horn

_

.000087

i

Haircloth ....

_

.000042

i

Ice .

:

.00223
.00568

i
4

j

Caen stone (build- |
ing limestone) . \

-

•00433

2

Calcareous sand- \

stone (freestone) j

.OO2 1 1

AUTHORITIES.

I G. Forbes. 3 Various.

2 H., L., & D.* 4 Neumann.

Au-

Substance.

Density.

t

*i

thor-

ity.

Water . .

_

_

.002

I

1

-

0

.OOI2O

2

'

-

9-15

.00136

2

• •

-

4

.OOI29

3

. .

-

30

.00157

4

~

18

.OOI24

5

Solutions in

water.

CuSO4 . .

1.160

4-4

.001 1 8

2

KC1 . . .

1.026

13

.00116

4

NaCl . . .

3,H%

10-18

.00267

6

H2S04 . .

•054

20.5

.00126

5

• •

.100

20.5

.00128

5

ZnSO4 . .

.180
•134

21

4-5

.00130
.00118

5

2

•

.136

4-5

.001 15

2

AUTHORITIES.

i Bottomlev. 4 Graetz.

2 H. F. Weber. 5 Chree.

3 Wachsmuth. 6 Winkelmann.

TABLE 207. — Organic Liquids.

TABLE 208. — Gases.

Substance.

t

kt

1

3

<

Acetic acid . . .

9-i S

.472

_

I

Alcohols : amyl .

9-'5

.328

-

I

ethvl .

9-15

•423

-

methyl

•495

-

\ Carbon disulphide

9-' 5

•343

-

Chloroform . . .

9-15

.288

-

Ether

Q— I C

^QT

Glycerine . . .

•637

O.I 2

2

Oils : olive . . .

-

•39.S

-

3

castor . .

-

.425

-

3

petroleum .

IJ

•3SS

.on

2

turpentine .

'3

•325

.0067

2

AUTHORITIES.

i H. F. Weber. 2 Graetz. 3 Wachsmuth.

Substance.

t

X 1000

a

Authority. 1

Air

o

Q
O
0

.568
.458

•499
•307

.00190
.00548

Ammonia . . .
Carbon monoxide
" dioxide .

Ethvlene . . .
Hydrogen . . .
Methane. . . .

0
0

7-8

•395

•327
.647

.00445
.00175

Nitrogen . . .
Nitrous oxide . .
Oxygen ....

7-8
7-8
7-8

•524
•350
•563

.00446

AUTHORITY.

i Winkelmann.

* Herschel, Lebour, and Dunn (British Association Committee).

SMITHSONIAN TABLES.

TABLE 209.

FREEZING MIXTURES.*

Column i gives the name of the principal refrigerating substance, A the proportion of that substance, B the propor-
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 tempera-
ture when all snow is melted, when snow is used, and // the amount of heat absorbed in heat units (therms when
A is grammes). Temperatures are in Centigrade degrees.

Substance.

A

B

C

D

E

F

G

H

NaC2H3O2 (cryst.)

»S

II2O-ioo

_

10.7

— 4-7

15-4

_

_

NII4C1 .

3°

" "

-

'3-3

— 5-i

18.4

-

-

NaN03.

'75

" "

-

13.2

— 5-3

18.5

—

—

Na2S2O3 (cryst.) .

I 10

« i<

-

10.7

— 8.0

18.7

-

-

KI.

140

« a

-

10.8

— 11.7

22.5

-

-

CaClo (cryst.)

250

" "

-

10.8

— 12.4

23.2

-

-

NH4N08 .'« .

60

" "

-

13.6

-13.6

27.2

—

-

(NH4)2S04 .

25

<" 5°

NH4NO3-25

26.0

-

-

NH4C1 .

25

" "

-

-

22.O

-

-

CaCl2 .

25

" "

" "

-

-

2O.O

-

-

KNO3 .

25

" "

NH4Cl-25

-

-

2O.O

-

-

Na2SO4

25

" "

" "

-

-

ig.O

-

-

NaNO3.

" "

" •'

-

-

17.0

-

-

KoSO4 .

10

Snow 100

-

—

— 1.9

0-9

—

Na2CO3 (cryst.) .

20

" "

-

—

2.O

1.0

-

-

KNO3 .

'3

u ii

-

—

-2.8S

1.85

-

-

CaCl2 .

3°

" "

-

—

10-9

9.9

-

-

NH4C1 .

25

" "

-

—

— 15-4

14.4

-

-

NH4N03

45

II II

-

—

— l6.75

'5-75

-

-

NaN03 .

50

" "

-

—

— 17-75

'6-75

-

-

NaCl .

33

« II

-

—

— 21-3

20.3

-

-

" 1.097

-

—

— 37-0

36.0

— 37-0

o.o

" 1.26

-

—

— 36.0

35-o

— 30.2

17.0

H2SO4+H2O
(66.i%H2S04)

" 1.38

2.52
4-32

-

—

— 35-°
— 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-°

" 13.08

-

—

— 16.0

15.0

2.1

967.0

o-35

- :,

o

-

-

0.0

52.1

•49

-

o

-

—

— 19.7

49-5

.61

-

0

-

-

— 39-0

40-3

CaCl2 + 6H2O -

.70
" .81

_

o
o

-

_

— 54-9t
— 40-3

30.0;
46.8

" 1-23

-

o

-

-

— 21.5

88.5

2.46

-

o

-

-

— 9.0

192.3

4.92

-

o

-

-

— 4.0

392-3

Alcohol at 4° I

77

" 73
CO2 solid

_

0

— 30.0
— 72.0

:

:

—

Chloroform .

-

" "

-

-

— 77.0

-

_

_

Ether .

-

" "

-

—

— 77-6

-

_

_

Liquid SO2 .

-

" "

-

-

— 82.0

-

-

_

i

H20-.7S

-

20

5-°

-

-

33-o

i

•94

-

20

— 4.0

-

-

21.0

i

" "

-

10

— 4.0

-

-

34-o

i

<* «

—

5

— 4.0

—

—

40.5

i

Snow "

-

o

— 4.0

—

-

122.2

NH4NO3 .

i

H2O-i.20

-

IO

— 14.0

-

~

l7-9

i

Snow "

-

o

— 14.0

-

_

I29-5;

i

H2O-i.3i

-

IO

-i7-5t

-

-

10.6

i

Snow "

-

o

— J7-5t

-

-

*y-9

i

H20-3.6i

-

IO

— 8.0

-

_

0.4

i

Snow "

o

— 8.0

327.0

* Compiled from the results of Cailletet and Colardeau, Hammer!, Hanamann, Moritz. Pfanndler, Rudorf, and
Tollinger.

t Lowest tejnperature obtained.

SMITHSONIAN TABLES.

199

TABLE 210.

CRITICAL TEMPERATURES, PRESSURES, VOLUMES, AND DENSITIES

OF CASES.*

6 = Critical temperature.

/'= Pressure in atmospheres.

<t>= Volume referred to air at o° and 76 centimetres pressure.

*/— Density in grammes per cubic centimetre.

Substance. •

e

P

<?>

d

Observer.

Air. \ . . . ,

— 140.0

39-°

Olszewski.

Alcohol (C2H6O) .

243.6

62.76

0.007 1 3

0.288

Ramsay and Young.

• • «

233-7

-

-

-

Jouk (lowest value

recorded).

" (CH40) . , ."

239-95

78.5

-

-

Ramsay and Young.

Ammonia ...»

130.0

115.0

_

_

Dewar.

Argon . ,

I2I.O

50.6

-

J-5

Olszewski.

288.5

47.0

0.0098 1

o -jc c

\T o u n GT •

Carbon dioxide . .

30.92

*T/ y
77

0.0066

U-JJ,5

Andrews.

" monoxide .

I4I.I

35-9

_•

_'

Wroblewski.

" disulphide .

277.7

78.1

-

-

Dewar.

Chloroform . . . ''-,

26O.O

54-9

-

-

Sajotschewski.

Chlorine ....

I4I.O

83-9

_

_

Dewar.

" ....

148.0

-

-

Ladenburg.

Ether

19.7

35-77

0.01584

0.208

Battelli.

" .....

1944

35-6'

0.01344

0.246

Ramsay and Young.

Ethylene ....

9-2

58.0

—

-

Van cier Waals.

•

I3.0

-

0.00569

0.21

Cailletet.

Hydrogen ....

— 220.0

2O.O

_

_

Olszewski.

" chloride

5I-25

86.0

-

-

• Ansdell.

X U

52-3

86.0

-

0.61

Dewar.

" sulphide

IOO.O

88.7

-

-

Olszewski.

Methane . . .

—81.8

54-9

-

-

"

....

—99-5

50.0

-

-

Dewar.

Nitric oxide (NO) .

—93-5

71.2

_

_

Olszewski.

Nitrogen ....

— 146.0

35-o

-

0.44

"

" ....

— 146.0

33-o

-

-

Wroblewski.

" monoxide (NgO)

354-o

75-o

-

-

Dewar.

Oxygen

—118.0

50.0

_

0.6044

Wroblewski.

Sulphur dioxide

155-4

78.9

-

-

Sajotschewski.

'• "...

157.0

-

-

-

Clark."

Water

K&I

_

0.001874

0.420

Nadejdine.

ii

*JJ

370.0

195-5

. ^ ,7

Dewar.

* Abridged for the most part from Landolt and Boernstein's " Phys. Chem. Tab."

NOTE. — Guldberg shows (Zeit. fur Phys. Chem. vol. 5, p. 375) that for a large number of organic substances the
ratio of the absolute boiling to the absolute critical temperature, although not constant, lies between 0.58 and 0.7, the
majority being between .65 and .7. Methane, ethane, and ammonia gave approximately 0.58. H,S gave .566, and
CS,, N,O, and O gave about .59.
SMITHSONIAN TABLES.

200

TABLE 21 1

HEAT OF COMBUSTION.

Heat of combustion of some common organic compounds.
Products of combustion, CO2 or SO2 and water, which is assumed to be in a state of vapor.

Substance.

Therms per
gramme of
substance.

Authority.

Acetylene .....

11923

Thomsen.

Alcohols : Amyl / .

8958

Favre and Silbermann.

Ethyl

7183

« « <i

Methyl

53°7

« <i «

Benzene . . . . . .

9977

Stohmann, Kleber, and Langbein.

Coals : Bituminous .

7400-8500

Various.

Anthracite

7800

Average of various.

Lignite ....

6900

"

Coke ....

7000

"

Carbon disulphide

3244

Berthelot.

Dynamite, 75% .

1290

Roux and Sarran.

Gas : Coal gas ....

5800-11000

Mahler.

Illuminating

5200-5500

Various.

Methane ....

13063

Favre and Silbermann.

Naphthalene

9618-9793

Various.

Gunpowder ....

720-750

«

Oils : Lard ....

9200-9400

«

Olive ....

9328-9442

Stohmann.

Petroleum, Am. crude

11094

Mahler.

" " refined .

11045

"

" Russian .

10800

«

Woods : Beech with 12.9% H2O

4168

Gottlieb.

Birch " 11.83 "

4207

H

Oak " 13.3 «

399°

«

Pine " 12.17 "

4422 .

"

SMITHSONIAN TABLES.

201

TABLE 212.

HEAT OF

Heat of combination of elements and compounds expressed in units, such that when unit mass of the substance is

units, which will be raised in temperature

Substance.

Combined
with oxygen
forms —

Heat
units.

Combined
with chlorine
forms —

Heat

units.

Combined
with sulphur
forms —

Heat
units.

tf

o

•£• •

3 •?
<-

Calcium ....

CaO

3284

CaCl2

4255

CaS

2300

I

Carbon — Diamond.

CO2

7859

-

-

2

" " . .

CO

2141

-

-

-

-

3

" — Graphite .

C02

7796

-

-

-

-

3

Chlorine ....

Cl20

— 254

—

-

-

-

i

Copper ....

Cu2O

321

CuCl

520

-

-

i

"

CuO

585

CuCljj

819

CuS

158

i

«

"

593

-

—

—

—

4

Hydrogen*

H2O

34154

HC1

22OOO

H2S

2250

3

«

"

34800

-

-

-

-

" • . . .

"

34417

-

-

-

-

6

Iron

FeO

!353

FeCl2

1464

FeSH2O

428

3

«

-

FeCl3

1714

—

-

3

Iodine ....

I205

177

-

-

-

Lead ....

PbO

243

PbCl2

4OO

PbS

98

Magnesium

MgO

6077

MgCl2

6291

MgS

3'9I

Manganese

MnOH2O

1721

MnCl2

2042

MnSH2O2

841

Mercury ....

Hg20

105

HgCl

206

-

-

" ....

HgO

153

HgCl2

310

HgS

84

Nitrogen*

N2O

-654

-

-

" ....

NO

— i54i

-

-

-

-

" ....

N02

— H3

-

-

-

-

Phosphorus (red)

P205

5272

-

-

-

-

" (yellow)

"

5747

-

-

-

-

7

" "

"

5964

-

—

-

-

i

Potassium

K20

1745

KC1

2705

K2S

1312

8

Silver ....

Ag20

27

AgCl

271

Ag2S

24

i

Sodium . .

Na2O

3293

NaCl

4243

Na2S

1900

8

Sulphur ....

S02

2241

-

-

-

-

i

" . . .

"

2165

-

-

-

-

2

Tin ......

SnO

573

SnCl2

690

-

-

4

"

-

SnCl4

1089

-

-

7

Zinc

ZnO

1185

-

-

—

—

4

ijH

ZnCl2

'495

~

~

i

Substance.

Combined
withS + Ot
to form —

Heat
units.

Combined
with N-f-Oa
to form —

Heat
units.

Combined
withC + O3
to form —

Heat

units.

.Author-
ity.

Calcium ....

CaSO4

7997

Ca(N03)2

5080

CaC03

6730

Copper ....

CuSO4

2887

Cu(N03)2

I3°4

—

-

Hydrogen

H2S04

96450

HNO3

41500

-

-

Iron .....

FeSO4

4208

Fe(NO3)2

2134

—

-

Lead ....

PbSO4

1047

Pb(N03)2

512

PbCO3

814

Magnesium

MgS04

12596

-

-

-

Mercury ....

—

-

-

-

-

Potassium

K2SO4

4416

KN03

306 r

K2CO3

3583

Silver ....

Ag2S04

776

AgN03

266

Ag2C03

561

Sodium .

Na2SO4

7119

NaNOs

4834

Na2CO3

5841

Zinc .....

ZnSO4

3538

~

~

"

AUTHORITIES.

i Thomsen. 3 Favre and Silbermann. 5 Hess. 7 Andrews.

2 Berthelot. 4 Joule. 6 Average of seven different. 8 Woods.

SMITHSONIAN TABLES.

* Combustion at constant pressure.
2O2

TABLE 212.

COMBINATION.

caused to combine with oxygen or the negative radical, the numbers indicate the amount of water, in the same
from o^ to i° C. by the addition of that heat.

In dilute solutions.

£
o

Substance.

Forms —

Heat
units.

Forms —

Heat
units.

Forms —

Heat

units.

|S

Calcium

CaOHfO

3734

CaCl2H2O

4690

CaS 4- H20

2457

i

Carbon — Diamond .

-

-

-

-

-

-

2

<> >i

-

-

-

-

—

-

3

" — Graphite .

-

-

-

-

-

-

3

Chlorine . . ./

-

-

-

-

-

-

i

Copper . . /

-

-

-

-

-

-

i

" .

—

—

—

—

—

—

i

" ...

-

-

-

-

-

- .

4

Hydrogen . • *'

_

••

~~

_

:

_

3

Iron . . .

FeO -f H2O

1 220*

FeCI2+H2O

1785

:

_

3

"

-

-

FeCl3

2280

-

-

3

Iodine

-

-

-

-

-

-

Lead ....

_

_

PbCl.2

368

-

-

Magnesium

MgO2H2

9°5°t

MgCl2

7779

MgS

4784

Manganese

-

-

MnCl2

2327

-

-

Mercury .

-

-

-

—

-

-

" ...

-

-

HgCl2

299

-

-

Nitrogen .

_

_

_

:

_

-

Phosphorus (red)

_

_

_

:

-

(yellow) .

-

-

-

-

-

-

7

" "

—

—

' —

—

—

—

i

Potassium .

K20

2 IIO*

KC1

2592

K2S

1451

8

Silver

—

—

—

—

—

—

i

Sodium

Na20

3375

NaCl

4190

Na2S

2260

8

Sulphur

-

-

—

—

—

i

Tin ....

_

_

SnCl2

691

:

-

7

"

-

-

SnCl4

1344

-

-

7

Zinc ....

-

-

-

—

-

-

4

" .

—

—

ZnCl2

'735

~

—

i

In dilute solutions.

0

Substance.

Forms —

Heat

units.

Forms —

Heat
units.

Forms —

Heat
units.

\*

Calcium . ( .

-

Ca(N03)2

5175

_

_

Copper
Hydrogen .
Iron ....

CuSO4
H2S04
FeS04

3150
IO53OO
42IO

Cu(N08)a
HNO8

Fe(N03)3

1310

2455°
2134

-

-

Lead ....

_

-

Pb(N08)a

475

-

-

Magnesium

MgS04

13420

Mg(N08)3

8595

-

-

Mercury .
Potassium .

K2S04

4324

Hg(N03)2
KN03

335
2860

_

_

Silver

Ag2S04

753

AgN03

216

-

-

Sodium

Na2SO4

7160

NaNO3

4620

Na2CO8

5995

Zinc ....

ZnSO4

3820

Zn(N03)2

2035

"

~

AUTHORITIES.

i Thomsen. 3 Favre and Silbermann. 5 Hess. 7 Andrews.

2 Berthelot. 4 Joule. 6 Average of seven different. 8 Woods.

SMITHSONIAN TABLES.

* Thomsen. t Total heat from elements.

203

TABLE 213.

LATENT HEAT OF VAPORIZATION,

The temperature of vaporization in degrees Centigrade is indicated by T ; the latent heat in calories per kilogramme
or in therms per gramme by H ; the total heat from o° C. in the same units by H'. The pressure is that due to
the vapor at the temperature 7".

Substance.

Formula.

T

H

HI

Authority.

Acetic acid . - .

C2H402

118°

84.9

-

Ogier.

Alcohol : Amyl . .

C5H120

131

120

-

Schall.

Ethyl .

C2H60

_

2O9

-

Favre and Silbermann.

. . .

"

78.1

205

255

Wirtz.

"

o

236

236

Regnault.

...

"

5°

264

"

...

"

IOO

-

267

"

"

150

-

285

"

Methyl . .

CH4O

64.5

2.67

307

Wirtz.

' . . .

"

o

289

289

Ramsay and Young.

' . . .

"

5°

—

274

" '

' . . .

"

IOO

-

246

ii i

' .' .

"

150

-

206

ii i

' . . .

"

200

—

152

11 i

' . . .

"

238.5

-

44-2

" '

Ammonia ....

NH3

7-8

294.2

-

Regnault.

" ....

"

ii

291.3

-

"

" ....

"

16

297.4

-

"

....

• "

17

296.5

-

"

Benzene ....

C6H6

80. i

92.9

127.9

Wirtz.

Bromine ....

Ba

88

45-6

-

Andrews.

Carbon dioxide, solid

CO2

_

_

138-7

Favre.

liquid .

"

— 25

72-23

-

Cailletet and Mathias.

ii u

"

o

57.48

-

u u i>

" " • I

"

12.35

44-97

-

Mathias.

" " . .

"

22.04

31.8

—

"

ii 11

"

29.85

14.4

-

"

. .

•

30.82

3-72

-

u

" disulphide

CS2

46.1

83.8

94.8

Wirtz.

" " .

II

0

90

90

Regnault.

" " . .

"

IOO

-

100.5

"

ii »

**

140

-

102.4

"

Chloroform .

CHC13

60.9

58-5

78.8

Wirtz.

Ether . ...

C4H100

34-5

88.4

107

«

" - .

"

34-9

9°-5

Andrews.

" • ' .

"

o

94

94

Regnault.

.....

"

5°

-

115.1

"

. .

11

120

-

140

"

Iodine . . . . .

I

-

2-95

-

Favre and Silbermann.

Sulphur dioxide . . .'

SO2

O

91.2

_

Cailletet and Mathias.

" " ...

"

3°

80.5

—

u 11 ii

ii u

"

65

68.4

—

u

Turpentine ....

C10H10

'59-3

74.04

-

Brix.

Water . .' '.

H20

IOO

535-9

_

Andrews.

u

IOO

637

Regnault.

SMITHSONIAN TABLES.

2O4

TABLE 2 13.

LATENT HEAT OF VAPORIZATION.*

Substance, formula, and
temperature.

/r= total heat from fluid at g° to vapor at f.
r = latent heat at A"1.

Authority.

Acetone,
C3H60,

- 3° to 14?°-

/= 140.5 + 0.36644 / — 0.000516 ft
*= '39-9 + 0.23356 / + 0.00055358/2
r = 139.9 — 0.27287 / + 0.0001571 ft

Kegnault.

Winkelmann.
«

Benzene,
CeHe,
7° to 215°.

1= 109.0 -f 0.24429^ — 0.0001315/3

Regnault.

Carbon dioxide,

CO*

— 25° to 31°.

t*= f 18.485 (31 — t) — 0.4707 (31 —ft)

Cailletet and
Mathias.

Carbon disulphide,
CS2,
— 6° to 143°.

/ = 9O.o + 0.14601 t — 0.000412 ft
/ = 8g-5 -j- 0.16993 / — 0.0010161 ft-{- 0.000003424 fl
r = 89.5 — 0.06530 1 — 0.0010976 ft -j- 0.000003424 fl

Regnault.
Winkelmann.

Carbon tetrachloride,
CC14,
8° to 163°.

/= 52.0 + o. 14625 / — 0.000172 ft
1 = 5 1 .9 4- o. 1 7867 t — 0.0009599 ft + 0.000003733 /*
r= 51.9 — 0.01931 t — 0.0010505 ft +' 0.000003733 fl

Regnault.
Winkelmann.

Chloroform,

CHClg,

— 5° to 159°.

1 = 67.0 -f- o.i 375 1
/ = 67.o-f- o.i47i6/ — 0.0000437 ft
r = 67.0 — 0.08519 / — 0.0001444 1'2

Regnault.

Winkelmann.
u

Nitrous oxide,
N2O,

— 20° tO 36°.

r*= 131.75 (36.4 — /) — 0.928 (36.4 — /)2

Cailletet and
Mathias.

Sulphur dioxide,
S02,
o° to 60°.

r = 91 .87 — 0.3842 t — 0.000340 ft

Mathias.

* Quoted from Landolt and Boernstein's " Phys. Chem. Tab." p. 350.
SMITHSONIAN TABLES.

205

TABLE 214,

LATENT HEAT OF FUSION.

This table contains the latent heat of fusion of a number of solid substances. It has been compiled principally from
Landolt and Boernstem's tables. C indicates the composition, '!' the temperature Centigrade, and H -the latent
heat.

Substance.

C

T

H

Authority.

Alloys: 30.5?!:) -f- 69.580 . '.

PbSn4

I83

17

Spring.

36.gPb -j- 6i.3Sn .

PbSn3

179

'5-5

"

63.7Pb + 36.3Sn .

PbSn

177-5

n.6

"

77.8Pb -j- 22.2Sn .

Pb2Sn

176-5

9-54

"

Britannia metal, 9811 -)- i Pb

-

236

28.0*

Ledebur.

Rose's alloy,

24Pb + 27-38n -f- 48.7Bi

-

98.8

6.85

Mazzotto.

tir it n I 2^.ol'l) — 1— I4.7ol1 I

Wood s alloy < f ^ • ,'• _i7. /^j (

-

75-5

8.40

"

Bromine . . . . . ;

Br

—7-32

16.2

Regnault.

Bismuth . '..-.-. i

Bi

266.8

12.64

Person.

Benzene . ' !.

CCH6

5-3

30-85

Fischer.

Cadmium .....

Cd

320.7

13-66

Person.

Calcium chloride

CaCl2 + 6H2O

28.5

40.7

"

Iron, Gray cast

-

2.3

Gruner.

White " ..-:"•

-

-

33

"

Slag

-

-

5°

"

Iodine .....

I

-

11.71

Favre and Silbermann.

Ice . . . - •

H2O

0

79.24

Regnault.

" . '. . ' . • . .

"

o

80.02

Bunsen.

" (from sea-water)

{H.O + 3.S3SI
J of solids j

-8-7

54-o

Petterson.

Lead ......

Pb

325

5-86

Rudberg.

Mercury

Hg

2.82

Person.

Naphthalene ....

79.87

35-62

Pickering.

Palladium ...

Pd *

(1500)?

36-3

Violle.

Phosphorus ....

P

40-05

4-97

Petterson.

Potassium nitrate

KNO3

333-5

48.9

Person.

Phenol . . .

C6H60

25-37

24-93

Petterson.

Paraffin I

-

52.40

Batelli.

Silver .....

Ag

999

21.07

Person.

Sodium nitrate . . .

NaNO3

64.87

"

Sodium phosphate

( Na2HP04 )
\ + I2H20 J

36.1

66.8

"

Spermaceti ....

-

43-9

36-98

Batelli.

Sulphur . . . . .

S

"5

9-37

Person.

Wax (bees) ....

• - .

61.8

42-3

"

Zinc - . - .

Zn

4I5-3

28.13

SMITHSONIAN TABLES.

* Total heat from o° C.

206

MELTING-POINT OF CHEMICAL ELEMENTS.

TABLE 215.

The melting-points of the chemical elements are in many cases somewhat uncertain, owing to the very different
results obtained by different observers. This table gives the extreme values recorded except in a few cases where
one observation differed so mucji from all others as to make its accuracy extremely improbable. The column
headed " Mean " gives a probable average value.

Range.

^

Range.

V

>

tm

Substance.

Min.

Max.

L'.lll

I

O

Substance.

Min.

Max.

Mean.

%

i

Aluminium .

("* O

6co.

C.°

850.

C.°
625.

Lithium . . .

C.

c..u

180.

13

Antimony .

425.

450-

435-

Magnesium .

75°-

800.

775-

»3

Arsenic . . .

bet. Sb anu Ag

I

Manganese .

-

1900.

14

Barium . . .

above that of cast iron

2

Mercury . .

— 38- 5t

—39-44

—39-04

Beryllium

below that of silver

3

Molybdenum .

above white heat

15

Bismuth . . .

266.8

269.2

268.1

Nickel . . .

1450.

1600.

1500.

Boron, amorph

melts in elect, arc

4

Osmium . .

-

2500.

16

Bromine . . .

—7.2

—7-3

—7-27

Nitrogen . .

—203.

—214.

—208.

Cadmium .; ^

3'5-

321.

318.

Palladium . .

'35°-

1950.

1600.

Caesium . . .

26.5

5

Phosphorus

44.2

44-4

44.25

Chlorine, liquid

-

-

— 1 02.

6

Platinum

1775-

22OO.

1900.

Chromium .

above that of platinum

7

Potassium .

55-

63-

60.

Cobalt . . .

1 500. 1 800.

1650.

Rhodium . .

2OOO.

16

Copper . . .

1050. 1330.

1 100.

Rubidium . .

-

38.5

Gallium . .

3°- ! 5

8

Ruthenium . .

-

-

I800.

Germanium

-

900.

9

Silenium . .

-

217.

17

Gold ....

1035-

1250.

1080.

Silicon

bet. cast iron and steel

7

Indium . . .

-

176.

10

Silver ....

916.

1040. 950.

Iodine . .

107.

115.

112.

Sodium . .

95-6

—97.6 97.6

Iridium .

1950. 1500.

2225.

Strontium . .

red heat

18

Iron (pure) .

1500. 1800.

J635-

Sulphur . . .

in.

1 20.

II5.I

" (white pig)

1050.

I ICO.

1075-

Tellurium . . 452.

525-

470.

" (gray pig)

noo. 2275.

1 200.

Thallium . . 288.

290.

289.

Steel ....

1300. 1400.

1360.

Tin .... 226.1;

235-

230.

" (cast) . .

- —

1375-

1 1

Tungsten . above that of manganese

'9

Lanthanum . .

between Sb and Ag

12

Zinc .... 400. 433.

4I5-

Lead ....

322.

335-

326.

i

1 Mallet. (i Olszewski, 1884. *> Winkler, 1867. u Carnelley, 1879.

2 Frey. ~ Deville, 1856. » Ledebur, 1881. 15 Buchholz. *» Wohler.

3 Debray. 8 Lecoq de Bois- 12 Hildebrand and 16 Pictet, 1879.

4 Despretz. baudran, 1876. Norton, 1875. n Hittorf, 1851.

5 Setterberg, 1882. 9 Winkler, 1886. 13 Bunsen. 18 Matthieson, 1855.

BOILING-POINT OF CHEMICAL ELEMENTS.

TABLE 216.

The column headed " Range " gives the extremes of the records found. Where the results are from one observer
the authority is quoted with date of publication.

Range.

i

i.

c

Range.

S

Min.

Max.

£

0

Min.

Max.

.S

O

Aluminium . .

abov

e white

heat

I

Nitrogen . . .

_

_

—194.4

8

Antimony . .

1470.

1700.

>535-

Oxygen . . . j — 181.

— 184.

-183.

Arsenic . . .

449-

45°-

2

Ozone .... -

-

— 106.

9

Bismuth .

1090.

1700.

1413-

Phosphorus . : 287.3

20X).

288.

Bromine . . .

59-27

63-05

62.08

Potassium . .

667.

725.

695.

Cadmium . .

720.

860.

779-

Selenium

664.

683.

67 S-

Chlorine . . .

-

- -

-31-6

3

Sodium . . .

742.

907.

82 S.

Iodine . .

over 200°

4

Sulphur . . .

447-

448.4

448.1

Lead ....

bet. 1450° and 1600°

5

Thallium . . .

1600.

1800.

1700.

Magnesium . .

-

• -

IIOO.

6

Tin ....

bet. 1450° and 1600°

Mercury k .. ;•

—

"•

357-

7

Zinc . .

891.

1040.

958-

1 Deville, 1854. 3 Regnault, 1863. 5 Carnellev, 1879. 7 Regnault, 1862. 9 Olszewski, 1887.

2 Cbnechy. * Stas, 1865. 6 Ditte, 1871. 8 Olszewski, 1884.

SMITHSONIAN TABLES.

207

TABLI 217.

MELTING-POINTS OF VARIOUS INORGANIC COMPOUNDS.*

Melting-points.

>,

Substance.

Chemical formula.

Particular

o

Date of

Min.

Max.

or average

1

publication.

values.

•*

Aluminium chloride .

A1C13

_

_

190.

I 1888

nitrate .

A1(N03)3 + 9H2O

-

-

72.8

2

1859

Ammonia ....

NH3

-

-

—75-

3

1875

Ammonium nitrate .

(NH4)N03

145.

1 66.

156.

" sulphate

(NH4)2S04

-

140.

4

1837

" phosphite

NH4H2PO3

-

-

123.

5

1887

Antimonietted hydrogen .

SbH3

-

- •

—91.5

6

1886

Antimony trichloride

SbCla

72.

73-2

72.8

-

-

" pentachloride .

SbCI5

—6.

7

I875

Arsenic trichloride .

AsCl3

-

-

— 18.

8

1889

Arsenietted hydrogen

AsH3

-

-

— "3-5

6

1884

Barium chlorate

Ba(C103)2

-

-

414.

9

1878

" nitrate

Ba(N03)2

-

-

593-

9

1878

" perchlorate .

Ba(C104)2

-

-

5°5-

10

1884

Bismuth trichloride .

BiC)3

22i;.

230.

227-5

ii

1876

Boric acid

H3B03

184.

1 86.

185.

9 i '878

" anhydride

B203

-

577-

9 1878

Borax (sodium borate)

Na2B407

-

-

561.

9 1878

Cadmium chloride .

CdCl2

-

-

9 1878

" nitrate

Cd(NO3)2 + 4H2O

—

-

59-5

2

l859

Calcium chloride

CaCl2

719.

723-

721.

9 1878

"

CaCl2 + 6H2O

28.

29.

28.5

- -

nitrate

Ca(N03)2

-

56i.

9 1878

"

Ca(NO3)2 -j- 4H2O

-

-

44-

2

1859

Carbon tetrachloride

CC14

_

_

—24.7

12

1863

trichloride .

C2C16

182.

187.

184.5

-

-

monoxide

CO

— 199.

—207.

203.

-

dioxide

CO2

-56.5

—57-5

—57-

3 '845

disulphide .

CS2

— no.

•3 '883

Chloric acid

HC1O4 + H2O

-

-

5°-

14

1 86 1

Chlorine dioxide

C102

—

-

-76.

3

1845

Chrome alum .

KCr(SO4)2+ i2H2O

-

-

89.

i ^ 1 884

Chrome nitrate . .<

Cr2(N03)6 + i8H20

-

-

37-

2 '859

Cobalt sulphate

CoSO4

96.

98.

97-

15! 1884

Cupric chloride

CuCl2

498.

9 i 1878

Cuprous "

Cu2Cl2

-

-

434-

9 1878

" nitrate

Cu(NO3)2 -f 2H2O

-

-

114.5

2 : 1859

Hydrobromic acid .

HBr

-

-

--86.7

Hydrochloric acid

HC1

-

-

—112.5

6

1884

Hydrofluoric acid

HF1

-

-

—92.3

6

1886

Hydroiodic acid

HI

-

-

—49-5

3

1845

Hydrogen peroxide .

H202

-

-

16

1818

" phosphide

PH3

r

-

— 132.5

6

1886

" sulphide .

H2S

-

-

—85.6

3

1845

Iron chloride

FeCl3

301.

3°7-

303-

-

" nitrate

Fe(N03)3 + 9H20

47.2

2

1859

" sulphate .

FeSO4 + 7H2O

-

-

64.

15

1884

Lead chloride .

PbCl2

498.

580.

526.

-

" metaphosphate

Pb(P03)2

800.

_9

1878

Magnesium chloride

MgCl2

-

-

708.

9

1878

" nitrate .

Mg(N03)2-f 6H2O

-

-

90.

2

1859

" sulphate

MgSO4 + 5H2O

-

-

54-

15

1884

Manganese chloride .

MnCl2 + 4H2O

- -

87-5,

17

-

nitrate .

Mn(NO3)2 + 6H2O

;

25-8

1859

sulphate .

MnSO4 + 5H2O

- -

54-

15

1884

Mercuric chloride

HgCl2

287. 293.

290.

"™

i Friedel and Crafts. 5 Araat. 9 Carnelley. 13 VVroblewski and Olszewski.

2 Ordway. 6 Olszewski. 10 Carnelley and O'Shea. 14 Roscoe.
3 Faraday. 7 Kammerer. n Muir. ' 15 Tilden. 17 Clark, "Const, of Nat."

4 Marchand. 8 Besson. 12 Regnault. 16 The'nard.

* For more extensive tables on this subject, see Carnelley's " Melting and Boiling-point Tables," or Landolt and
Boernstein's " Phys. Chem. Tab."

SMITHSONIAN TABLES.

208

TABLE 217.
MELTING-POINTS OF VARIOUS INORGANIC COMPOUNDS.

Melting-point.

>,

Substance.

Chemical formula.

Min

M.ax.

Particular
or

o

^

Date of pub-
lication.

probable

^

value.

Nickel carbonyl .

NiCO4

_

_

—25-

I

1890

' nitrate

Ni(NO3)2 + 6H20

-

—

56.7

2

1859

' sulphate . . .

NiSO4 -f 7H20

98.

IOO.

99.

3

1884

Nit 'ic acid . . .

HN03

-

—47-

4

1878

' anhydride . ...

N205

, -

-

30-

5

1872

' oxide * . . f

NO

' -

-

-16.7

6

1885

' peroxide . ({'• .

N204

-

-

— 10.14

7

1890

Nitrous anhydride

N.203

-

-

—82.

8

1889

" oxide

N20

-

-

—99-

9

18/3

Phosphoric acid (ortho)

H3P04

38.6

41.7

40-3

Phosphorous acid

H3P03

7O.I

74-

72.

-

-

Phosphorus trichloride

PC13

iu.8

10

1883

oxychloride

PClOg

-

-

— '-5

ii

1871

disulphide

PS2

296.

298.

297.

12

I879

pentasulphide .

P-2S5

274.

276.

275-

,13

I879

sesquisulphide

P4Sa

142.

167.

158.

trisulphide

P-2S3

290.

Ii4

1864

Potassium carbonate .

K2C03

834.

1150. ?

836.

-

' chlorate

KC103

334-

372.

354-

• " —

-

' perchlorate

KC104

610.

,•'5

1880

chloride

KC1

73°-

738.

734-

-

nitrate

KN03

327-

353-

340-

—

-

' acid phosphate .

KH2P04

96.

3

1884

' acid sulphate

KHS04

-

-

200.

16

1840

Silver chloride .

AgCl

450.

457-

453-

-

-

nitrate

AgN03

198.

224.

214.

—

-

nitrogenietted .

AgN3

250.

20

1890

perchlorate

AgC104

-

-

486.

18

1884

phosphate

Ag3P04

-

-

849.

'5

1878

metaphosphate

AgP03

-

—

482.

15

1878

sulphate .

AgoS()4

-

-

654.

15

1878

Sodium chloride .

NaCl

772.

960.

772-

-

" hydroxide

NaOH

-

60.

'7

1884

" nitrate

NaNO3

298.

33°-

3I5-

-

-

" chlorate .

NaClO3

302.

;I5

18/8

' perchlorate

NaClO4

-

-

482.

18

1884

' carbonate

Na2CO3

814.

920.

884.

-

-

' "...

Na2C03 + ioH2O

_

_

34-

3

1884

' phosphate

Na2HPO4-f-4H2O

35-

36-4

35-4

-

' metaphosphate

NaPO3

617-

15

1878

' pyrophosphate

Na4P207

-

—

888.

15

1878

' phosphite

(H2NaP03)2 + 5H20

-

-

42.

'9

1888

" sulphate .

Na2S04

861.

865.

863.

15

1878

" "...

Na2SO4 -f ioH2O

-

—

34-

3

1884

" hyposulphite .

Na2S203+5H20

45-

48.1

47-

-

Sulphur dioxide .

•so2

76.

79-

78.

-

_

Sulphuric acid

H2S04

10. 1

10.6

10.4

21

1884

" "...

I2H2S04 + H2O

—

-

—°-5

22

1853

" "...

H2S04 + H2U

7-5

8.5

8.

—

" (pyo) .

H2S207

35-

22

1853

Sulphur trioxide

S03

14.8

T5-

14.9

5

1876-1886

Tin, stannic chloride .

SnCl4

-

—33-

23

1889

" stannous "

SnCl2

_

_

250.

24

_

Zinc chloride

ZnCl2

-

-

262.

2 ^

1875

" " ...

ZnCl2 -f 3H2O

-

-

7-

26

1886

" nitrate . .• •

Zn(N03)2 + 6H2O

• -

-

36-4

3

1884

" sulphate

ZnSO4+7H2U

-

-

50.

3.

1884

i Mond, Langer & Quincke 10 Wroblewski & Olszewski. 15 Ornelley. 20 Curtius. 25 Braun.

2 Ordway. 6 Olszewski. n Gentlier & Michaelis. 16 Mitscherlich. 21 Mendelejeff. 26 Engel.

3 Tilden. • - 7 Ramsay. 12 Ramme. 17 Cripps. 22 Marignac.
4 Berthelot. 8 Birhaus. 13 V. & C. Meyer. 18 Carnelley & O:Shea. 23 Benson.

5 R. Weber. 9 Wills. 14 Lemoine. ' 19 Amat. 24 Clark, " Const, of Nat."

SMITHSONIAN TABLES.

* Under pressure 138 mm. mercury.
209

TABLE 218.

BOILING-POINTS OF INORGANIC COMPOUNDS. «

V

Boiling-point.

>,

Substance.

Chemical formula.

Particular

'C

o

Date of

Min.

Mix.

or aver-

—

publication.

age values.

<,

Airt ;. ; , j . ' . : .

_

_

_ •

— 192.2

I

1884

*' •' • • » T • . .

—

—

—

— I9I-4

2

1884

Aluminium chloridej . '; .

A1C13

-

-

207.5

3

1888

" nitrate . ,

A1(N03)3 + 9H20

-

-

134-

4

J859

Ammonia . . . !

NH3

—

-

—38.5

5

1863

Antimonietted hydrogen .

SbH3

_

— ' •

-i 8

2

1886

Antimony pentachloride § .

SbCl5

IO2.

103.

_

6

1889

trichloride .

SbC)3

2 1 6.

—3-5

220.

-

_

Bismuth trichloride

BiCl3

427.

441.

435-

5- 7

_

Cadmium chloride

CdClo

861.

954-

908.

10

1880

" nitrate

Cd(N03)2 + 4H2O

-

132.

4

l859

Calcium nitrate .

Ca(N03)2 + 4H20

-

-

132.

4

1859

Carbon dioxide .

CO2

-78.2

-80.

—79.1

1863-1880

" disulphide

CS2

46.

47-4

46.6

8,9

1880-1883

" monoxide . , .

CO

190.

— J93-

— *9l-S

2> I

1884

Chromic oxychloride .

CrO2Cl2

"5-9

118.

117.

_

_

Chromium nitrate

Cr2(N03)0+i8H20

-

I25-5

4

1859

Copper nitrate . . ' . ";

Cu(N03)2 + 3H20

-

-

170.

4

l859

Cuprous chloride

Cu2Cl2

954-

1032.

993-

10

1880

Hydrobromic acid || .

HBr

125.

I25-5

ii

1870

Hydrochloric acid

HC1

no.

12

'859

Hydrofluoric acid

HF

I25-

I25-5

_

13

1869

Hydroiodic acid .

HI

127.

II

1870

Iron nitrate

Fe(N03)3 + 9H20

-

-

I25-

4

'859

Magnesium nitrate

Mg(N03)2 + 6H20

-

-

143-

4

1859

Manganese chloride .

MnClo -f 4H2O

-

-

1 06.

14

nitrate

Mn(N()3)2 + 6H2O

-

-

I29-5

4

1859

Mercuric chloride

HgCl2

502.

3°7-

3°4-

Nickel nitrate . .

Ni(N03)2 + 6H2O

r36-7

4

1859

Nitric acid . . ..' ! .

HN03

-

—

86.

IS

1830

" anhydride . •

N205

45-

50.

-

16

1849

" oxide . . i .

NO

—'53-

2

1885

Nitrous anhydride . .

N203

— 10.

3-5

-

-

" oxide

N20

-87.9

—92.

—92.

-

-

Phosphorus trichloride

PC13

73-8

76.

75-

-

-

" sesquisulphide

P4-S3

380.

>7

1883

trisulphide ,

P2S3

-

-

490.

17

1886

pentasulphide

P2S5

518.

53°-

522.

-

" trioxide . ' .

P203

'73-

18

1890

Silicon chloride .

SiCl4

56.8

59-

58.

-

-

Sulphuric acid .

i2H2SO4+ H2O

338-

J9

'853

Sulphur trioxide

S03

46.

47-

46-3

" dioxide .

S02

—8.

— 10.5

-9.6

-

-

" chloride

S2C12

138.

144.

!39-

-

-

Tin, stannous chloride

SnCl2

606.

628.

617.

-

—

"• stannic "

SnCl4

-

-

II3-9

8

1876

Zinc chloride

ZnCl2

676.

73°-

7°3-

-

-

" nitrate

Zn(N03)2 + 6H2O

—

J31-

4

1859

I
I Wroblewski. 8 Thorpe. 15 Mitscherlich.

i 2 Olszewqki. 9 Friedburg. 16 Deville.

3 Friedel and Crafts. 10 Carnelley and Carleton-Williams. 17 Isambert.

4 Ordway. n Topsoe. 18 Thorpe and Ttitton.

5 Regnault. 12 Roscoe and Dittmar. 19 Marignac.

6 Anschiitz and Evans. 13 Gore.

7 Pictet. 14 Clark, "Const, of Nature."

* For a more complete table, see Clark's "Constants of Nature1' (Smithsonian Collections).

t Pressure 76 cm. t Pressure 2.64 atmos. § Pressure 68 mm. || Pressure 75.8 cm.

SMITHSONIAN TABLES.

2IO

TABLE 219,

MELTING-POINTS OF MIXTURES.

Metals
and
observer.

Atomic
ratio.

Percent
of metal. 1

Per cent
of metal.

***:

Metals
and
observer.

Atomic
ratio.

Per cent
of metal.

Per cent
of metal. 1

Per cent
of metal. 1

Per cent
of metal. 1

be .

C"1.

(jo

Pb

Sn

Cd

Sn

Pb

Bi

Pb4Sn

87.5

12-5

292.

Cd, Sn,

Cd4Sn5Pb5Bi10

10.8

14.2

24.9

50.1

65.5

Pb3Sn

84.0

16.0

283.

Pb

Cd3Sn4Pb4Bi8

10.2

14-3

25.1

50.4

67-5

Pb
and

Pb2Sn
PbSn

77-8

3^3

270.
235-

and

CdSn2Pb2Bi4
CdSnPbBi

7.0

14.8
13.8

26.0
24-3

48.8

68.5
68.5

Sn *

PbSn2

467

53-3

197.

PbSn3

36-9

63.1

181.

PbSn4

30-5

69.5

187.

Cd, Pb

CdPb3Bi4

Cd

Pb
39-7

Bi

53-2

_

89.5

Pb

Pb

Bi

and Bi 6

Cd2Pb7Bi8

6-7

43-4

49.9

-

95-0

and

PbaBig

27.2

72.8

125-3

Bi-

Sn

Pb

Bi

Cd

ca

Bi

Sn, Pb

25.0

25.0

50.0

-

95-°

and

CdBi4

21.2

78.8

146.3

and Bi7

—

18.8

31.2

50.0

95-o

Cd
and
Sn2

CdSn2

Cd
32.2

Sn
67.8

173-8

Zn, Pb
and Sn 8

-

Zn
4.2

Pb
26.9

Sn
68.9

-

168.

Sn
and

Sn3Bi4

Sn
29.8

Bi

70.2

136.4

Cu and
Zn

Cu

Zn

Bi*
Zn

Zn
83-3

Pb
16.7

205.

(white
brass) 9

50.0

50.0

912.

and

-

69.5

3°-5

190.

Ag

Au

Pb3

-

50.0

50.0

202.

-

IOO.

-

-

-

954-

A rr

' ; -

80.

20.

-

-

975-

Zn
and
Sb3

-

Zn
90.
82.

Sb

IO.

18.

236.
250.

§

and
Au10

!. -

60.
40.
20.

40.
60.
80.

-

-

995-
1 020.
1045.

—

—

IOO.

—

—

1075-

Pb

Pb

Sb

—

90.

IO.

240.

and
Sb3

-

82.

18.

260.

Au

Pt

—

IOO.

—

—

—

1075.

-

95-

5-

-

-

I IOO.

Na
and

_

Na

K

6.

_

90.
85-

IO.

15-

_

—

1130.
1 1 60.

K*

-

80.

20.

-

1190.

Ag

Cu

-

75-

25-

-

-

1220.

-

IOO.

-

1040.

-

70.

30.

-

-

I255-

-

92-5

7-5

931.0

-

65-

35-

-

-

1285.

-

82.1

17.9

886.0

-

60.

40.

-

-

1320.

-

79-8

2O.2

887.0

Au

-

55-

45-

-

-

J350-

-

77-4

22.6

858.0

and

-

-

-

1385-

Ag

_

75.0
71.9

25.0
28.1

850.0
870.5

Pt8

:

45-

40.

I

_

—

1420.
1460.

and

-

63.0

37-o

847.0

-

35-

65-

—

-

1495.

Cu5

-

60.0

40.0

857.0

-

70.

-

-

1535-

-

57-Q

43-°

900.0

-

25-

75-

-

-

1570-

-

54.1

45-9

920.0

-

20.

80.

-

—

1610.

-

50.0

50.0

941.0

-

15-

85-

-

-

1650.

-

45-9

54-i

961.0

-

IO.

90.

-

-

1690.

-

25.0

75-°

1 114.

-

5-

95-

-

-

i73°-

IOO.

'33°-

.

IOO.

"

"

1775-

i Pillichody, " Ding. Poly. Jour." vol. 162. 6 Von Hauer, " J. f. prakt. Ch." (i), 94, 436.
2 Ruclbers;, " Pogg. Ann." 71. 7 W. Spring, " Fort. d. Phys." 1875.

3 Ledebur, " Wied. Bieb." 5, 650, 1881. 8 Svanberp, " J. B. f. Ch." 1847-48.
4 Rosenfeld, " Ber. Chem. Ges." 1891. 9 Daniell, Bolley's " Hdb. f. ch. Techn." 8, 45.

5 W. Roberts, "Ann. Chem. et Phys." (5), 13, 118, 1878. 10 Erhard and Schutel, " Fort. d. Phys." vol. 35.

SMITHSONIAN TABLES.

* From Landolt and Boernstein's " Phys. Chem. Tab."

211

TABLE 220.

DENSITIES, MELTING-POINTS, AND BOILING-POINTS OF SOME
ORGANIC COMPOUNDS.

N. B. — The data in this table refer only to normal compounds.

Substance.

Formula.

Temp.

Den-
sity.

Melting-
point.

Boiling-point.

Authority.

(a) Paraffin Series : CWII2W_|_2.

Methane* . . .

CH4

-164.

0.415

—185.8

— 164.

Olszewski.

Ethanet ....

C2H6

-

-

-

-

Propane ....

C3H8

-

-

-

—25 to —30

Roscoe and Schorlemmer.

Butane ....

C4Hio

b

; .60

_

+ [

Butlerow.

Pentane ....

C5H12

17-

.626

-

+37-

Schorlemmer.

Hexane ....

CeHi4

17-

.663

-

+69.

"

Heptane ....

C7Hi6

o

.701

-

98.4

, Thorpe.

Octane ....

Cgllis

o

.719

-

l25-5

"

Nonane ....

CgH20

20.

.718

—5i-

150.

Krafft.

Decane ....

CioH22

20.

•73°

—3i-

Undecane . . .

CiiH24

—26.

•774

—26.

195.

Dodecane . . .

Cl2H.26

12.

•773

12.

214.

Tridecane . . .

CieH28

—6.

•775

—6.

234-

Tetradecane . .

Ci4H3o

+4-

•775

+4-

252-

Pentadecane .

C 15 H32

IO.

.776

+ 10.

270.

Hexadecane . .

Ci<jH34

1 8.

•775

18.

287.

Heptadecane . .

C'nHse

22.

•777

22.

3°3-

Octadecane . . .

Cisllss

28.

•777

28.

Nonadecane . .

Ci9ll4o

32-

•777

32-

33°-

Eicosane . . .

C2oH42

37-

.778

37-

2054

Heneicosane . .

C2lH44

40.

.778

40.

2154

Docosane . . .

C22H46

44-

.778

44-

2244

Tricosane . . .

C23H48

48.

•779

48.

2344

Tetracosane

C24HfiO

51-

•779

5'-

2434

Heptacosane .

C27H56

60.

.780

60.

2704

Pentriacontane .

Qu He4

68.

.781

68.

3°24

("V J_T

7O

781

7O

Tint

Penta-tria-contane

C35H?2

/U.

75-

./Ol

.782

/<J.

75-

Jlu'i

(b) Olefines, or the Ethylene Series: CWH2W.

Ethylene . . .

C2H4

_

_

— 169.

—103.

Wroblewski or Olszewski.

Propylene . . .

C3H6

-

-

-

Butylene

C4H8

— 13.5

0-635

—

i.

Sieben.

Amylone . .
Hexylene . . .

C5H10
C6Hi2

o

.76

:

J^

Wagner or Saytzeff.
Wreden or Znatowicz.

Heptylene . . .

C7Mi4

19.5

•703

-

Morgan or Schorlemmer.

Octylene . . .

C8Hic,

17-

.722

-

I22.-I23.

Moslinger.

Nonylene . . .

C9H18

-

—

—

X53-

Bernthsen, " Org. Chem."

Decylene . . .

C'i0H2o

-

-

-

'75-

" «• "

Undecylene

C 11 1 1,22

-

-

-

U It it

Dodecylene

Ci2H24

— 31-

•795

— 31-

964

Krafft.

Tridecylene . .

C 13H-26

233-

Bernthsen.

Tetraclecylene . .

Ci4H28

12.

•794

— 12.

1274

Krafft.

Pentadecylene

CinHgo

-

-

247.

Bernthsen.

Ilexaclecylene . .

Ci6H32

+4-

.792

+4-

'55-t

Krafft, Mendelejeff, etc.

Octadecylene . .

CisHse

18.

.791

1794

Krafft.

Eicosylene . . .

C.joH4o

-

-

Cerotene . . .

C27Hc4

,-

-

58-

-

Bernthsen.

Melene .....

C30H6o

"

62.

* Liquid at — n.° C. and 180 atmospheres' pressure (Cailletet).

+ 4.° " 46
t Boiling-point under 15 mm. pressure.

SMITHSONIAN TABLES.

212

TAZCE 22O,

DENSITIES, MELTING-POINTS, AND BOILING-POINTS OF SOME
ORGANIC COMPOUNDS.

Substance.

Chemical | Temp,
formula. 1 C°.

Specific
gravity.

Melting-
point.

Boiling-
point.

Authority.

(c) Acetylene Series : CWH2W_2.

Acetylene .

C H

Allylene

C3H4

Ethylacetylene . . .

C4HC

-

-

-

+ 18.

Bruylants, Kutsche-

roff, and others.

Propylacetylene . . .

C5H8

-

-

-

48.-50-

Bruylants, Taworski.

Butylacetylene . . J

CeHio

-

-

-

68.-/O.

Taworski.

Oenanthylidene . . .

C7Hi2

-

-

-

io6.-io8.

Bruylants, Behal,

and others.

Caprylidene ....

C8Hu

0.

0.771

-

I33-~I34-

Behal.

Undecylidene. . . .

CnH2o

-

-

2IO.-2I5-

Bruylants.

Dodecylidene . . .

CiaH^

— 9-

.810

— 9-

105.*

Krafft.

Tetradecylidene . . .

ci4H2;

+ 6.5

.806

+ 6.5

I34-*

" /

Hexadecylidene . . .

CieHgo

20.

.804

20.

1 00.*

"

Octadecylidene . . .

Ci8H34

30-

.802

30-

184.*

"

(d) Monatomic alcohols : CBH2W_|_,OH.

Methyl alcohol . . .

CHgOH

0.

0.8 1 2

_

66. '

Ethyl alcohol ....

C2H5OH

o.

.806

— 130.1

78.

Propyl alcohol . . .

C3H7OH

o.

.817

-

97-

From Zander, " Lieb.

Butyl alcohol ....

C4H9OH

0.

.823

-

117.

Ann." vol. 224, p. 85,

Amyl alcohol ....

C5HnOH

o.

.829

-

138.

and Krafft, "Ber."

Hexyl alcohol . . .

CGH13OH

o.

•833

-

vol. 16, 1714,

Heptyl alcohol . . .

C7H15OH

o.

.836

- -

170!

" 19, 2221,

Octyl alcohol . . . . i C8H17OH

o.

•839

-

195.

" 23, 2360,

Nonyl alcohol . . . C9Hi9OH

0.

.842

— 5-

213.

and also Wroblew-

Decyl alcohol . . . Ci0H2iOH

+ 7-

•839

+ 7-

231.

ski and Olszewski,

Dodecyl alcohol . . . CioH25OH

24.

.831

-4-

I43-*

" Monatshefte,"

Tetradecyl alcohol . . Ci4H2,,OH

38.

.824

38.

167.*

vol. 4, p. 338.

Hexadecyl alcohol . . CieH3sOH

50.

.818

190.*

Octadecyl alcohol . . Ci8H37OH

59-

.813

59-

211.*

(e) Alcoholic ethers : CwH2w_j_2O.

Dimethyl ether . . .

C2HC0

-

_

-

-23.6

Erlenmeyer, Kreich-

baumer.

Diethyl ether ....

C4H100

4-

0.731

-

+ 34-6

Regnault.

Dipropyl ether . . .

C6H140

o.

•763

—

90.7

Zander and others.

Di-iso-propyl ether .

, C6H140

0.

•743

-

69.

H

Di-n-butyl ether . . .

C8H180

o.

•784

-

141.

Lieben, Rossi, and

others.

Di-sec-butyl ether . .

C8H180

21.

.756

-•

121.

Kessel.

Di-iso-butyl " .' .

C8H180

I5-

.762

-

122.

Reboul.

Di-iso-amyl " ». .

CioH-^O

0.

•799

-

I70.-I 75.

Wurtz.

Di-sec-hexyl '' . .;

C12H260

-

-

-

2O3.-2O8.

Erlenmeyer and

Wanklvn.

Di-norm-octyl " . -.

C16H840

17-

•805

2SO.-282.

Moslinger.

(f) Ethyl ethers : C,,H2M+2O.

Ethyl-methvl ether .

C3H80

_

_

_

II.

Wurtz, Williamson.

propyl "

C5H120

20.

0-739

-

63--64-

Chancel, Briihl.

iso-propyl ether .

C5H120

0.

•745

-

54-

Markownikow.

norm-butyl ether

C6H140

o.

.769

-

92.

Lieben, Rossi.

iso-butyl ether

C6H140

-

•75r

-

78.-8o.

Wurtz.

iso-amyl ether

C7H160

18.

.764

-

112.

Williamson and

others.

norm-hexyl ether

C8H180

-

-

-

1 34.- 1 37.

Lieben, Janeczek.

nornj-heptyl ether

C9H200

1 6.

.790

-

iS^iS

Cross.

norm-octvl e'ther

C10H220

17-

•794

~

Moslinger.

* Boiling-point under 15 mm. pressure.

t Liquid at — n.° C. and 180 atmospheres' pressure (Cailletet).

SMITHSONIAN TABLES.

213

'ABLE 221.

COEFFICIENTS OF THERMAL EXPANSION.

Coefficients of Linear Expansion of the Chemical Elements.

In the heading of the columns T is the temperature or range of temperature, C the coefficient of linear expansion,
! Al the authority for C, JJ/the mean coefficient of expansion between o° and ico° C., a and /3 the coefficients in the
; equation /« = /„ (i + at-^-ftt-), where /<, is the length at o° C. and It the length at /° C., A, is the authority for a,
ft, and in.

Substance.

T

C
Xio*

A*

M
Xio*

a
X io«

ft

XlO«

/},

Aluminium

40
600

0.2313

•3*5°

Fizeau . . .
Les Chatelier.

O.222O

-

-

j Calvert, John-
| son and Lowe.

Antimony :

Parallel to cryst.

axis ....

40

.1692

Fizeau.

Perp. to axis

40

.0882

"

Mean ....

40

.1152

"...

.1056

.0923

.0132

Matthieson.

Arsenic ....

40

•°559

"

Bismuth :

Parallel to axis

40

.1621

M

Perp. to axis

40

.1208

M

Mean ....

40

.1346

" ...

.1316

.1167

.0149

Matthieson.

Cadmium . .

40

.3069

"...

•3'59

.2693

.0466

"

Carbon :

Diamond . . .

40

.0118

«'

Gas carbon . .

40

.0540

"

Graphite . . .

40

.0786

"

Anthracite . .

40

.2078

"

: Cobalt ....

40

.1236

"

Copper ....

40

.1678

"...

.1666

.1481

.Ol8S

Matthieson.

Gold . . . . .

AQ

.1 AA1

t(

I A 7O

nc8

.OI I 2

||

Indium ....

i\\j

40

T^H- j

.4170

"

.i^/VJ

-1 jy

Iron :

Soft ....

40

.1210

"

Cast ....

40

.IO6I

"

Wrought . . .

— i8to 100

.1 I4O

Andrews.

Steel ....

40

.IJ22-

-Fizeau.

" annealed

40

.1095

" ...

.1089

.1038

.OO52

Benoit.

Lead

40

.2924

*i

.27OQ

.0271

.OO74

Matthieson.

Magnesium . .

*t^
40

.2694

"

•*/ ^y

"?*i 3

• W/ .-J.

Nickel ....

40

.1279

"

Osmium . . .

40

.0657

"

Palladium . . .

40

.1176

"...

.1 IO4

.IOII

.0093

Matthieson.

Phosphorus . .

0-40

I-2S30

Pisati and De

Franchis.

Platinum . . .

40

.0899

Fizeau . . .

.0886

.0851

•0035

Matthieson.

Potassium . . .

0-50

.8300

Hagen.

Rhodium . . .

40

.0850

Fizeau.

Ruthenium . . .

40

.0960

"

Selenium . . .

40

.3680

• " ...

.6604

-

-

Spring.

Silicon ....

40

.0763

"

Silver ....

40

.1921

"...

•1943

.1809

•0135

Matthieson.

Sulphur :

Cryst. mean .

40

.6413

44

I.ISO

-

-

Spring.

Tellurium . . .

40

•1675

"...

.3687

-

-

"

Thallium . . .

40

.3021

"

Tin

40

• 2274

i<

.2296

.'"O'n

.206^

Matthieson.

Zinc

^
40

•-- J<t
.2918

«

.2Q76

~ *JJ
.2741

•wyj

O'*'?4

Tv^

yt v

•""/ T-'

•vr— J^

N. B. — The above table has been with a few exceptions compiled from the results published by Fizeau, " Comptes
Rendus," vol. 68, and Matthieson, " Proc. Roy. Soc.," vol. 15.

SMITHSONIAN TABLES.

2I4

TABLE 222.

COEFFICIENT OF THERMAL EXPANSION.

Coefficient of Linear Expansion for Miscellaneous Substances.

N. B. —The coefficient of cubical expansion may be taken as three times the linear coefficient. T is the temperature
or range of temperature, C the coefficient of expansion, and A the authority.

Substance.

T

CXio«

A

Substance.

T

CXio«

A

Brass :

Cast .

0-100°

0.1875

\

Platinum-silver:

Wire .

"

0.1936

I

lPt+2Ag

0-100°

0.1523

4

— r

/ "

.1783-. 1930

2

Porcelain

20-790

0.0413

16

7i-5Cu-f-27.7Zn-(-

" Bayeux .

1000-1400

0.0553

'7

o.3Sn-(-o.5Pb

40

0.1859

3

Quartz :

7iCu-f-29Zn

O-IOO

0.1966

4

Parallel to axis .

0-80

0.0797

6

Bronze :

Perpend, to axis .

"

0-1337

6

3Cu+iSn . ' .

166-100

0.1844

5

Speculum metal

O-IOO

0.1933

i

166-350

O.2I l6

5

Topaz :

" " .

16.6-957

0-1737

5

Parallel to lesser

86.3Cu+9.7Sn-(-

horizontal axis

"

0.0832

8

4Zn

40

0.1782

3

Parallel to greater

97.6Cu-|-2.2Sn-t-

horizontal axis

"

0.0836

8

o.2P, hard

0-80

O.I7I3

6

Parallel to verti-

" " " " soft

"

o. 1 708

6

cal axis

"

0.0472

8

Caoutchouc

-

.657-.6S6

2

Tourmaline :

"

16.7-25.3

0.770

7

Parallel to longi-

Ebonite .

25-3-35-4

0.842

7

tudinal axis

"

0.0937

8

Fluor spar : CaF2 .

O-IOO

0.1950

8

Parallel to hori-

German silver .

"

0.1836

8

zontal axis

"

0.0773

8

Gold-platinum :

Type metal

16.6-254

0.1952

5

2Au+iPt

"

0.1523

4

Vulcanite

0-18

0.6360

18

Gold-copper :

Wedgwood ware

O-IOO

0.0890

5

2Au-|-iCu

"

0.1552

4

Wood :

Glass :

Parallel to fibre :

Tube .

"

0.0833

i

Ash .

"

0.0951

19

"...

"

0.0828

9

Beech

2-34

0.0257

20

Plate .

"

0.0891

10

Chestnut .

0.0649

20

Crown (mean)

"

- 0.0897

10

Elm .

'

0.0565

2O

"

50-60

0.0954

ii

Mahogany

1

0.0361

2O

Flint .

"

0.0788

ii

Maple

1

0.0638

2O

Jena thermometer

Oak .

'

0.0492

2O

(normal)

O-IOO

0.081

12

Pine .

'

0.0541

20

«< « [.gill

"

0.058

12

Walnut .

1

0.0658

2O

Gutta percha .

20

1.983

'3

Across the fibre :

Ice .

-20 to -i

o-375

Beech

1

0.614

2O

Iceland spar :

Chestnut .

1

°-325

2O

Parallel to axis .

0-80

0.2631

6

Elm .

<

0.443

2O

Perpendicular to

Mahogany

'

0.404

20

axis

"

0.0544

6

Maple

i

0.484

2O

Lead-tin (solder)

Oak .

<

0-544

2O

2Pb+iSn

O-IOO

0.2508

i

Pine .

1

0.341

20

Paraffin . . . | 0-16

1.0662

IS

Walnut .

'

0.484

2O

"...

16-38

i . 3030

IS

Wax: White .

10-26

2.300

21

"

3^49

4.7707

15

"

26-31

3.120

21

Platinum-iridium

"

4.860

21

loPt+iIr

40

0.0884

3

' '

43-57

15.227

21

AUTHORITIES.

i Smeaton. 6 Benoit. , ii Pulfrich. 16 Braun. 21 Kopp.

2 Various. 7 Kohlrausch. 12 Schott. 17 Ueville and Troost.

3 Ffeeau. 8 Pfaff. 13 Russner. 18 Mayer.

4 Matthieson. 9 Deluc. 14 Brunner. 19 Glatzel.

5 Daniell. 10 Lavoisier and Laplace. 15 Rodwell. 20 Villari.

SMITHSONIAN TABLES.

215

TABLE 223.

COEFFICIENTS OF THERMAL EXPANSION.

Coefficients of Cubical Expansion of some Crystalline and other Solids.*
T= temperature or range of temperature, C= coefficient of cubical expansion, A = authority.

Substance.

T

C X io4

A

Antimony ....

O-IOO

0.3167

Matthieson.

Beryl . .

O-IOO

0.0105

Pfaff.

Bismuth . . • .

-

0.4000

Kopp.

Diamond .•

40

0.0354

Fizeau.

Emerald

40

0.0168

"

Fluor spar . i • »

14-47

0.6235

Kopp.

Garnet . « j

o-ioo

0.2543

Pfaff.

Glass, white tube

O-IOO

0.2648

Regnault.

" green tube

c-ico

0.2299

"

" Swedish tube . • .•

O-IOO

0.2363

•'

" hard French tube .

O-ICO

0.2142

"

" crystal tube

O-IOO

O.2IOI

"

" common tube .

O-I

0.2579

,i

" Jena

O-IOO

0-2533

Reichsanstalt.

Ice

— 20 to — i

1.1250

Brunner.

Iceland spar . . /

50-60

0.1447

Pulfrich.

Idocrase ....

o-ioo

0.2700

Pfaff.

Iron . . . .- . .•

O-ICO

0.3550

Dulong and Petit.

"

0-300

0.4410

i,

Magnetite, FesO4 . t

O-IOO

0.2862

Pfaff.

Manganic oxide, MnoOg

O-IOO

0.522

Playfair and Joule.

Orthoclase (adularia)

O-IOO

0.1794

Pfaff.

Porcelain . . • •'.••'

O-IOO

0.1080

Deville and Troost.

Quartz . . . .*

50-60

0.3530

Pulfrich.

Rock salt

50-60

I.2I2O

"

Spinel ruby . . .

40

0.1787

Fizeau.

Sulphur, rhombic . .

O-IOO

2.2373

Kopp.

Topaz - .

O-IOO

0.2137

Pfaff.

Tourmaline

6-100

0.2181

"

Zincite, ZnO

40

0.0279

Fizeau.

Zircon ....

o-ioo

0.2835

Pfaff.

* For more complete tables of cubical expansion, see Clarke's " Constants of Nature
(Smithsonian Collections), published iu 1876.

SMITHSONIAN TABLES.

2l6

TABLE 224.
COEFFICIENTS OF THERMAL EXPANSION.

Coefficients of Cubical Expansion of Liquids.

This table contains the coefficients of expansion of some liquids and solutions of salts. When not otherwise stated
atmospheric pressure is to be understood. 7* gives the temperature range, C the mean coefficient of expansion
for range T in decrees C., and AI the authority for C. a, ft, and y are the coefficients in the volume equation
z>t = vu (i -j- aJ + fli2 + y&), and /« the mean coefficient for range o°-ioo° C., and AI is the authority for these.

Liquid.

T

C
X 1000

A,

in

X ioo

o X looo

/3 X io«

yX io»

A.

Acetic acid ....
Acetone

• i6°-io70
0-54

— 1 5 to +80
0-80

0-39
18-39
0-40
0-40
—3810-1-70
11-81
— 7 to +60

18-25
17-24
—34 to +60
0-50
0-50
0-63
—1510+38

0-30
0-30
24-299

36-1 57
7-38
24-120

10-40
20-78

0-30
0-30
— 9 to +106

O-2OO

.866

•524

.940
•581

.992

I
I

I
I

2

.1433

-TJJ
.l6l6

•M33
•'385
.1168

.0506
.0510
.1468

•1399

.2150

•°534

.0489
•0933

.0742

.0572
•0477

•°539
•0577
.0899

.1039
.1067
.0611
.0627

.0489
.0799
.1051

1 .0630
1.3240

0.8900
1-0414
0.7450
0.2928

1.1856
1.1763
1.0382

0.0788
0.4238
1.1398

I.IO7I

i-5'32

0.4853

0.4460
0.0625
0.1818
0.6821

0.8340
0.8994
0.0213

0-3599

0.5408

0-5758
0.2835
0.9003
—.0658

0. 1 264
3.8090

0.6573
0.7836
1.850
17.900

I.5649
1-2775
I.7II4

4.2742
0.8571
1.3706

4.6647

2-3592
0.4895

0.430
8.710
O.OOOI75
1.1405

0.1073
1.396
10.462
2.516

1-075

0.864
5.160

J-959
8.507

1.0876
0.8798

1.1846
1.7168
0.730
11.87

O.gill
0.8065
0-5447

I.9I22

1-7433
4.0051

0.003512
—•539

0.4446
—6.769

3
3

4

I

6

4
5

4

7
7
4

4

4
8

9
9

10

ii

7

7

12
12

'3

14

9
9

12

9
9
5
15

Alcohol :
Amyl

Ethyl, sp. gr. .8095 .
" 50 % by volume

" 3°% : "

" 500 atmo. press.
" 3000 "
Methyl ....

Calcium chloride :
CaCl2, 5.8 % solution
CaCI2, 40.9 % " .
Carbon disulphide .
500 atmos. pressure .
3000 "
Chloroform ....
Ether

Glycerine

Hydrochloric acid :
HC1+6.25H20 . .
HC1 + 5oH2O . .
Mercury

Olive oil

Potassium chloride :
KC1, 2.5 % solution .
KC1, 24.3 % "
Potassium nitrate :
KN03, 5-3 % sol'n
KN03)2i.9% "
Phenol, C6H6O . . .
Petroleum

Sp. gr. 0.8467 . . .
Sodium chloride :
NaCl, i. 6% solution .
Sodium sulphate :
Na.2SO4, 24 % sol'n .
Sodium nitrate :
NaNO3, 36.2 % sol'n .
Sulphuric acid :
H2SO4 .....

H2SO4 + 5oH2O .
Turpentine ....
Water

AUTHORITIES.

i Amagat. 4 Pierre. 7 Decker. 10 Broch. 13 Pinette.
2 Barrett. 5 Kopp. 8 Emo. n Spring. 14 Frankenheim.
3 Zander. 6 Recknagel. 9 Marignac. 12 Nicol. 15 Scheel.

SMITHSONIAN TABLES.

217

TABLE 225.

COEFFICIENTS OF THERMAL EXPANSION.

Coefficients of Expansion of Gases.
The numbers obtained by direct experiment on the change of volume at constant pressure, EP, are separated in the

column of i atm. have been made for all pressures near to 76 centimetres of mercury. The other numbers in the
pressure columns are centimetres of mercury at o° C. and approx. 45° latitude, unless otherwise marked.

constant pressure.

pressure coumns are centmetres o mercury at o . an approx. 45 lattude, unless otherwise marked.
Thomson has given (vide Kncyc. Brit. art. "Heat") the following equations for the calculation of the expan-
sion, £, between o° and 100° C. of the gases named. Expansion is to be understood as change of volume under

£• = .3662(1— .00049 J/r°)
v 7'o '

£ = .3662(1 •+ .0026 —»}
v o '

E = .3662 (i -f .0032 — °)
i>0'

£• = .3662(1 +.0031 *>)
»o'

E — .3662 (1 + .0164 —°\
va>

where V0/va is the ratio of the actual density of the gas at o° C. to the density it would have at o° C. and one
atmosphere of pressure. The same experiments (Thomson & Joule, Trans. Roy. Soc. 1860), — which, together
with Regnault's data, led to these equations, — give for the absolute temperature of melting ice 2.731 times the
temperature interval between the melting-point of ice and the boiling-point of water under normal atmospheric
pressure.

Hydrogen .
Common air .
Oxygen . . .
Nitrogen
Carbon dioxide

Coefficient at constant volume.

Coefficient at constant pressure. t

Substance.

Pressure.

Ev
Xioo

o

€*

3 «
<'

Substance.

Pressure.

Sf

X 100.

Autlior-

itv.

Air . . . .

0.6

•3765

I

Air . . . .

76.

0.3671

3

"

1.6

•3703

" . . . ,

257-

0.3695

3

a

7.6

.3665

Hydrogen .

76-

0.36613

3

"

IO.O

•3663

"...

254-

0.36616

3

"

26.0

.3660

Carbon dioxide

76.

0.3710

3

"

37.6

.3662

" "

252.

0-3845

3

" . . . .

75.0

•3665

" " o°-64°

17.1 atm.

0-5136

6

"

76-83

.3670

2*

" 64°-! 00°

17.1 "

0.4747

6

"

11-15

.3648

3

" " o°-7.5°

24.81 "

0.7000

6

"

17-24

•3651

3

" " o°-64°

24.81 "

0.6204

6

"

37-51

•3658

3

" " 64°- 1 00°

24.81 "

0-5435

6

" . . . .

76 -

.3665

3

" o°-7.5°

34-49 "

1.0970

6

"

2OO

.3690

3

" o°-64°

34-49 "

0.8450

6

"

2OOO

.3887

3

" 0°-IOO°

34-49 "

0.6574

6

" . .

IOOOO

.4100

3

C'arbon monoxide

76.

0.3669

3

"

76

.3669

3*

Nitrous oxide .

76.

0-3719

3

" . . . .

76

-3671

4

Sulphur dioxide

76.

0-3903

3

"

i atm.

.3670

5*

" "

98.

0.3980

3

Carbon dioxide .

i "

.3706

5

Water vapor, o°-ii9°

i atm.

0.4187

7

" " . .

i "

.3726

i

" " o°-i4i°

i "

0.4189

7

' " . .

76-104

.3686

3

" 0°-l62°

i "

0.4071

7

ti «

174-234

•3752

3

" " 0°-200°

i "

o-3938

7

" "

793

.4252

3

" o°-247°

i "

0-3799

7

" oc-64° .

16.4 atm.

•4754

6

'• " 64°- 1 00°

16.4 "

.4607

6

" o°-64° .

25.87 "

•5728

6

AUTHORITIES. •

" 64°- 1 00°

25.87 "

.5406

6

" o°-64° .

33-53 "

•6973

6

i Melander. 5 Jolly.

" 64°-! 00°

33-53 "

•6334

6

2 Magnus. 6 Andrews.

Carbon monoxide

i "

.3667

3

3 Kegnault. 7 Hirn.

Hydrogen . .

i "

.3669

3

4 Rowland.

" ... ..__ . . _,_

i

•3656

5

Nitrogen . .

i "

.3668

3

Nitrous oxide

i "

.3676

3

" " ••"•).-••

i . "

•3707

5 .

Oxygen

i . "

•3674

5

Sulphur dioxide, SC>2 •

i . "

•3845 5

* Corrected by Mendelejeff to 45° latitude and absolute expansion of mercury. Rowland gets almost the same
correction on Regnault, using Wiillner's value of the expansion of mercury.

t The series of results at different pressures are given because, of their interest. The absolute values are a little
too low. (See preceding footnote.)

SMITHSONIAN TABLES.

218

TABLE 226.

DYNAMICAL EQUIVALENT OF THE THERMAL UNIT.

Rowland in his paper quoted in Table 227 has given an elaborate discussion of Joule's determinations and the cor-
rections required to reduce them to temperatures as measured by the air thermometer. The following table con-
tains the results obtained, together with the corresponding results obtained in Rowland's own experiments. The
variation for change of temperature in Rowland's result is due to the variation with temperature of the specific heat
of water.

Joule's value reduced

- u ^

to air thermometer

• 5£~rt _-

Date.

Method of experiment.

Temp,
of
water

Joule's
value.

and latitude of
Baltimore.

Row-
land's
value.

J-R.

||||

C.°

"S1"1 " I

A

Eng. units.

Met. units.

tf-oSK

1847

Friction of water .

15

781.5

787.0

442-8

427.4

+ 15-4

0

1850

«•>' .< ..

14

772.7

778.0

426.8

427-7

—0.9

IO

1850

" " mercury

9

772.8

779-2

427-5

428.8

'-3

2

1850

..

9

775-4

781.4

428.7

428.8

— O.I

2

1850

" " iron

9

7760

782.2

429.1

428.8

+0-3

I

1850

.« ..

9

773-9

780.2

428.0

428.8

—0.8

I

1867

Electric heating . .

1 8.6

-

-

428.0

426.7

+ i-3

3

1878

Friction of water .

14.7

772.7

776.1

425.8

427.6

—i.S

2

1878

" " "

12.7

774.6

778.5

427.1

428.0

—0.9

3

1878

" '•

'55

773-1

776.4

426.0

427-3

— '-3

5

1878

, "

14.5

767.0

770-5

422.7

427-5

-4.8

i

18-8

'• " "

'7-3

774.0

777-0

426.3

426.9

—0.6

i

From the above values and weights Rowland concludes as the most probable value
from Joule's experiments, at the temperature 14.6° C. and the latitude of Baltimore, 426.75,
and from his own experiments 427.52.

The mean of these results is 427.13 in metric units, or 778.6 in British units. Correct-
ing back for latitude, and to mercury thermometer, this gives about 774.5 for the latitude
of Manchester, instead of 772, as has been commonly used.

An elaborate determination recently made by Griffith and referred to in Table 227 gives
a value about one tenth of one per cent higher than Rowland's. Probably when a mer-
cury thermometer is involved in the measurements we may take 776 as the nearest whole
number in foot-pounds and British thermal units for the latitude of Manchester, and 777
for that of Baltimore. The corresponding values in the metric system will be 425.8 and
426.3, or in round numbers 426 for both latitudes.

The following quantities should be added to the equivalent of Baltimore to give the
equivalent at the latitude named : —

Latitude .... 0° 10° 20° 30° 40° 50° 60° 70° 80° 90°

Kilogramme-metres 0.89 0.82 0.63 0.34 0.08 — 0.41 — 0.77 — 1.06 — 1.26 — 1.33
Foot-pounds. . . 1.62 1.50 1.15 0.62 0.15 — 0.75 — 1.41 — 1.93 — 2.30 — 2.43

SMITHSONIAN TABLES.

219

TABLE 227.

MECHANICAL EQUIVALENT OF HEAT.

The following historical table of the principal experimental determinations of the mechanical equivalent of the unit of
heat has been, with the exception of the few determinations bearing dates later than 1879, taken from Rowland.*
The different determinations are divided into four groups, according to the method used. Calculations based on
the constants of gases and vapors as determined by others are not included in this table.

Method.

Observer.

Date.

Result.

Compression of air . . . .

Joule i

1845

443-8

Expansion " " . . . '•

Joule 1

i845

437-8

Experiments on steam engine . . .

Him 2

1857

413.0

" " " " . . . '

Him*

1860-1

420-432

(

443-6

Expansion and contraction of metals .

Edlund 3

1865 ]

430.1

(

428.3

" " " " "

Haga*

1881 j

437-8
428.1

Measurement of the specific volume of

vapor . . . . . •,

Perot 5

1886

424-3

Rumford '

1708

940 ft.-lbs.

Friction of water in tubes

Joule "

i / ye»
1843

424.6

' " " " calorimeter

Joule 1

l84S

488.3

' " " " "...

Joule 8

1847

428.9

' " " " "...

Joule 9

l850

423-9

' " mercury in "...

Joule 9

1850

424.7

' " plates of iron

Joule9

1850

425.2

" metals . . . . .

Him 2

1857

37 i -6

' " " in mercury calorimeter .

Favre 10

1858

413.2

' " " .....

Him2

1858

400-450

Boring " " .....

Him 2

1858

425.0

Water in balance a frotiement .

Him 2

1860-1

432.0

Flow of liquids under strong pressure

Him 2

i 860-1

432.0

Crushing of lead .....

Him2

1860-1

4250

Friction of metals .....

Puluj "

1876

426.6

Friction of water in calorimeter

Joule 12

1878

423-9

" " " " " , .

Rowland 13

1879

426.3

" " metals

Sahulka14

1890

427-5

Heating by magneto-electric currents

Joule ~

1843

460.0

Heat generated in a disc between the

f

43S-2

poles of a magnet . . . .

Violle 1S

1870 j

434-9

435-8

I

437-4

Flow of mercury under pressure

Bartoli 16

1880

428.4

Heat developed in wire of known abso- (
lute resistance \

Quintus Icilius,17
also Weber

} '857

399-7

Heat developed in wire of known abso- \
lute resistance }

Lenz
Weber

} 1859 |

396.4
478.2

Heat developed in wire of known abso-

lute resistance . . . . . !

Joule 18

1867

429-5

Heat developed in wire of known abso-

lute resistance . . . . . '

H. F. Weber 19

1877

428.15

Heat developed in wire of known abso-
lute resistance .....
Heat developed in wire of known abso-

Webster 2)

i885 ]

414.0 ergs per
gramme degree.

lute resistance . . . .- . "

Dieterici 21

1888

424.36

REFERENCES.

See opposite page.

SMITHSONIAN TABLES.

* " Proc. Am. Acad. Arts and Sci." vol. 15.
22O

MECHANICAL EQUIVALENT OF HEAT.

TABLE 227.

Method.

Diminishing the heat contained in a battery
when the current produces work

Diminishing the heat contained in a battery
when the current produces work . . .

Heat due to electrical current, electro-chemical
equivalent of water = .009379, absolute resist-
ance, electro-motive force of Daniell cell, heat
developed by action of zinc on sulphate of
copper ........

Heat developed in Daniell cell ....

Electromotive force of Daniell cell

Combination of electrical heating and mechan-
ical action by stirring water ....

Observer.

Joule 7

Favre ™
Weber,
Boscha,
Favre,

and
Silbermann

Joule
Boscha 23

Griffiths -*

Date.

1843

1858

1857

1859
1893

Result.

499.0
443-°

4I9-S

428.0

RKFERENCES.

1 Joule, " Phil. Mag." (3) vol. 26.

2 Him, " Theorie Mec. de la Chaleur," ser. i, 3me ed.

3 Edlund, " Pogg. Ann." vol. 114.

4 Haga, " Wied. Ann." vol. 15.

5 Perot, " Compt. Rend." vol. 102.

6 Rurnford, " Phil. Trans. Roy. Soc." 1798; Favre, " Compt. Rend." it

7 Joule, " Phil. Mag." (3) vol. 23.

8 Joule,

9 Joule,
10 Favre,

37-

Phil. Mag." (4) vol. 15.

n Pulnj,
12 Joule,

Compt. Rend." 1858 ;
Pogg. Ann." vol. 157.
Proc. Roy. Soc." vol. 27.

13 Rowland, " Proc. Am. Acad. Arts & Sci." vols. 15 & 16.

14 Sahulka, " Wied. Ann." vol. 41.

15 Violle, "Ann. de Chim." (4) vol. 22.

16 Bartoli, " Mem. Ace. Lincei," (3) vol. 8.

17 Quintus Icilius, " Pogg. Ann." vol. 101.

18 Joule, " Rep. Com. on Elec. Stand.," " B. A. Proc." 1867.

19 H. F. Weber, " Phil. Mag." (5) vol. ?.

20 Webster, " Proc. Am. Acad. Arts & Sci." vol. 20.

21 Dieterici, " Wied. Ann." vol. 33.

22 Favre, " Compt. Rend." vol. 47.

23 Boscha, " Pogg. Ann." vol. 108.

24 Griffiths, " Phil. Trans. Roy. Soc." 1893.

SMITHSONIAN TABLES.

221

TABLES 228, 229.

SPECIFIC HEAT.

Specific Heat of Water.

The specific heat of water is a matter of considerable importance in many physical measure-
ments, and it has been the subject of a number of experimental investigations, which unfortu-
nately have led to very discordant results. Kegnault's measurements, published in 1847,* show
an increase of specific heat with rise of temperature. His results are approximately expressed
by the equation

c = i -f- -0004 / -j- 0000009 f2<

which makes the specific heat nearly constant within the atmospheric range. A different equa-
tion was found from Regnault's results by Boscha, who thought the temperatures required cor-
rection to the air-thermometer. Regnault, however, pointed out that the results had already
been corrected. Jamin and Amaury t found, for a range from 9° to' 76° C., the equation

c = i -f- .001 1 / -)- .000001 2 13,

which nearly all the evidence available shows to be very much too rapid a change. Wiillner
gives, for some experiments of Munchhausen,}: the equation

c= i -j- .00030102 /
in vol. i, changed to

c= i -f .000425 1

in vol. 10, for a range of temperature from 17° to 64°. In 1879, experiments are recorded by
Stamo,§ by Henrichsen,|| and by Baumgarten,|| all of them giving large variation with temper-
ature.

In 1879, Rowland inferred from his experiments on the mechanical equivalent of heat that the
specific heat of water really passes through a minimum at about 30°, and he attempted to verify
this by direct experiment. The results obtained by direct experiments were not by any means
so satisfactory as those obtained from the friction experiment; but they also indicated that the
specific heat passed through a minimum, — but, in this case, at about 20° C. Further, direct
experiments were made in 1883, in Rowland's laboratory, by Liebig, using the same calorimetric
apparatus ; and these experiments also show a minimum at about 20° C.1T Since the publica-
tion of Rowland's paper a number of new determinations have been made. Gerosa gave, in
1881, a series of equations which show a maximum at 4°.4, then a minimum a little above 5° and
afterwards a rise to 24°! Neesen ** found a minimum near 30°, but got rather less variation than
Rowland. Rapp,tt taking the mean specific heat between o° and 100° as unity, gives the equa-
tion

c= 1.039925 — .007068 1-\- .0002 1 2 55/2 — .000001584^,

which gives a minimum between 20° and 30° and a maximum about 70°. Volten JJ gives an
equation which is even more extraordinary with regard to coefficients than the last, namely,

c = i — .0014625512 / -|- .0000237981 f2 — .000000 1 07 1 6 is,

which puts the minimum between 40° and 50°, and gives a maximum at 100°; which maximum
is, however, less than unity. Dieterici, in his paper on the mechanical equivalent of heat, dis-
cusses this subject ; but his own results being in close agreement with Rowland's, his table prac-
tically only extends Rowland's results through a greater range of temperature, assuming straight-
line variation to the two sides of the minimum. Bartoli and Stracciati §§ found a minimum at
about 30°; while Johanson in the same year gives a minimum at about 4° and then a rise about
12 times as rapid as that of Regnault. Griffiths |||| finds the equation

c = i — .0002666 (/" — 15)

to satisfy his experiments through the range from 15° to 26°. This agrees fairly well with Row-
land through the same range, and indicates that the minimum is at a temperature higher than
26°.

The following table gives the results of Rowland, Bartoli and Stracciati. and Griffiths. The
column headed " Rowland " has been calculated from Rowland's values of the mechanical equiv-
alent of heat at different temperatures, on the assumption that the specific heat at 1 5° is equal to
unity.

Me"m. de 1'Acad." vol. 21. t " Cqnipt. Rend.'' vol. 70, 1870.

' Wied. Ann." vols. i and 10. § " Wied. Reib." voi. 3.

' Wied. Ann." vol. 8.

Rowland, " Proc. Am. Acad." vol. 15, and Liebig, " Am. Jour, of Sci." vol. 26.
1 Wied. Ann." vol. 18, 1883.

tt ' Diss. Zurich." n " Wied. Ann." vol. 21, 1884.

§§ 'Wied. Beib." vol. 15, 1891. Illl "Phil. Trans." 1893.

SMITHSONIAN TABLES.

222

SPECIFIC HEAT.

TABLES 22« 229.

TABLE 228. — Specific Heat of Water.

Temp.
C.

Rowland.

Bartoli
• and
Stracciati.

Griffiths.

Temp.
C.

Rowland.

Bartoli
and

Stracciati.

Griffiths.

Dieterici.

Temp.
C.

Specific
heat.

0°

.0075*

1. 0066

_

19°

0.9984

0.9995

0.9989

0°

I. OOOO

, I

.0070*

1. 0060

-

20

0.9980

0.9995

0.9987

IO

0.9943

2

.0065*

•0054

-

21

0.9976

0.9995

0.9984

20

0.0893

3

.0060*

.0049

-

22

0-9973

0.9996

0.9981

30

0.9872

4

.0055*

.0043

-

23

0.9971

0.9996

0-9979

40

0.9934

5

.0050

.0038

-

24

0.9968

0.9998

0.9976

50

0.9995

6

.0045

•0033

-

25

0.9967

.OOOI

0-9973

00

.0057

7

.0040

.OO28

-

26

0.9965

.0003

0.9971

70

.OI2O

8

.0034

.0023

-

~7

0.9964

.0006

0.9967

80

.0182

9

.0029

.OOI9

-

28

0.9963

.OOIO

-

90

.0244

10

.0024

.0015

-

29

0.9962

.0014

-

100

.0306

ii

.0019

.OOI I

-

3°

0.0962

.0019

-

-

-

12

.0014

.OOO8

-

31

0.9963

I.OO24

-

_ , _

!3

.0009

.0005

-

32

0.9963

-

-

-

14

1.0005

.OOO2

-

33

0.9964

-

-

- -

15

1. 0000

.OOOO

1. 0000

34

0.9965

-

-

- -

16

0.9996

0.9998

0-9997

35

0.9966

-

-

-

17

0.9991

0.9997

0.9995

36

0.9967

-

-

-

18

0.9987

0.9976

0.9992

TABLE 229. - Specific Heat of Air.

The ratio of the specific heat at constant pressure to the specific heat at constant volume has been the subject of much
investigation, and more particularly so in the case of atmospheric air, on account of its interest in connection with
the velocity of sound. The following table gives the results of the principal direct determinations of this ratio for
air. It may be remarked that the methods most commonly employed have been modifications of that employed by
Clement and Desormes, and that the chances of error towards too small a ratio by this method are considerable.

Date.

Ratio.

Experimenters.

Some of these results are clearly too low ;

and hence neglecting all those that fall be-

I8l.2

•354

Clement and Desormes.

low 1.39 and giving equal weights to the

-

•374

Gay Lussac and Welter.

remainder we obtain, with a somewhat large

1853
1858

.249
.42 r
.4196

Delaroche and Berard.
Favre and Silbermann.
Masson.

probable error, the value 1.4070.
The values obtained indirectly from the

^59

.4025

Weisbach.

velocity of sound are undoubtedly much

1861

•3845

Him.

more accurate, judged either by the greater

1862
1863
1864

.41

•399
.41

Cazin.
Dupre.
Jamin and Richards.

ease of the experiment or by the better
agreement of the results. Assuming that

1864

•399

Tresca and Laboulaye.

the value 332 metres per second is good for

1869

.302

Kohlrausch.

the velocity of sound, the ratio of the specific

1873

4053

Rontgen.

heats must be near to 1.4063. Probably

1874
1883
1887

•3^
.4062

•384

Amagat.
Miiller.
Lummer.

1.4065 may be taken as fairly representing
present knowledge of the subject.

* Variation assumed uniform below 7 with same slope as from 7 to 5.
NOTE. — For specific heats of metals, solids and liquids, see pp. 294 to 296.

SMITHSONIAN TABLES.

223

TABLE 23O.

SPECIFIC HEAT.

Specific Heat of Gases and Vapors.

Substance.

Range of
temp. C.°

Sp. ht.
pressure
constant.

Authority.

Mean
ratio of
sp. hts.

Authority.

•o ^

"i ~ 8

3 Sri

Acetone

20-IIO

0-34/58

Wiedemann

_

_

".....

27-179

0.3740

" -

-

" » • ." . •

129-233

0.4125

Regnault

-

-

Air ...-.;

— 30 to -{- 10

0.23771

"

-

-

. .

0-100

0.23741

"

-

-

" , . . . .

O-2OO

c-23751

"

-

-

" , . ...

2O-IOO

0.2389

Wiedemann

-

-

" »..-..

mean

0.23788

-

1.4066

Various

0.1691

Alcohol, ethyl - . . »

108-220

0-4534

Regnault

1.136

( Jaeger
| Neyreneuf

0.3991

" methyl . . .

101-223

0.4580

"

-

-

Ammonia ....

23-100

0.5202

Wiedemann

-

-

" ....

27-200

o-5356

"

-

_

" . . . .

24-216

0.5125

Regnault

-

-

...»

mean

0.5228

-

'•31

j Cazin
\ Wiillner

0.3991

Benzene .....

34-H5

0.2990

Wiedemann

-

_

".....

35-180

0-3325

"

-

-

" . . . . ' ..

116-218

0-3754

Regnault

—

-

Bromine .....

83-228

0-0555

"

-

-

" . . .

19-388

0-0553

Strecker

1.293

Strecker

0.0428

Carbon dioxide

-28 to +7

0.1843

Regnault

-

" ...

15-100

0.2025

"

—

—

<. u

11-214

0.2169

"

-

-

. . ' ;'

mean

O.2OI2

-

1.300

j Ror.tgen
| Wiillner

0.1548

Carbon monoxide .

23-99

0.2425

Wiedemann

-

-

"

26-198

O.2426

«

1.403

I Cazin
\ Wiillner

0.1729

Carbon disulphide .

86-190

o. 1 596

Regnault

i. 200

Beyne

0.1330

Chlorine .....

13-202

O.I2IO

"

-

-

" ....

16-343

O.II25

Strecker

r-323

Strecker

0.0850

Chloroform ....

27-118

O.I44I

Wiedemann

-

28-189

0.1489

"

i.ic6

( Beyme
} M tiller

0.1346

Ether ...'...

69-224

0.4797

Regnault

-

-

''.....

27-189

0.4618

Wiedemann

-

-

"

25-11 i

0.4280

"

-

-

"

mean 0.4565

-

1.029

Miiller

0.4436

Hydrochloric acid .

22-214

0.1852

Regnault

-

-

" " .

13-100

o. 1 940

Strecker

i-395

Strecker

0.1391

Hydrogen ....

—28 to +9

3-3996

Regnault

-

" .

12-198

3.4090

"

-

-

" ....

2I-1OO

3.4100

Wiedemann

-

-

" '.'.-.

mean 3.4062

-

1.410

Cazin

2419

sulphide (H.2S) .

20-206

0.2451

Regnault

1.276

Miiller

0.1925

Methane .

18-208

0-59-9

"

1.316

"

0.4505

Nitrogen ....

O-2OO

0.2438

"

1.410

Cazin

0.1729

Nitric oxide (NO) .

13-172

0.2317

«

-

-

Nitrogen tetroxide (NCX>)

27-67

1.625

SBerthelot

-

-

" " "

27-150

1.115

and

-

" " "

27-280

0.650

Ogier

-

-

Nitrous oxide . ...

10-207

0.2262

Regnault

-

-

" " ...

26-F03

0.2126

Wiedemann

—

-

" " • .

27-206

0.2241

"

-

-

" " ...

mean 0.2214

-

1.291

Wiillner

•1715

Sulphur d-oxide (SOo) . ..

16-202

0.1544

Regnault

1.26

( Cazin )
) Miiller j

0.1225

Water . '.

128-217

0.4805

"

-

-

Macfarlane

.

100-125

0.3787

Gray

_

-

mean 0.4296

1

1.300

Various

0.3305

SMITHSONIAN TABLES.

224

TABLES 231 , 232.

VAPOR PRESSURE.

TABLE 231. —Vapor Pressure of Ethyl Alcohol.*

o

0^

1°

*>

3.

4°

5°

6°

7=

8-

9°

Vapor pressure in millimetres of mercury at o° C.

0°

10

20
30

40

50
60

70

12.24
23.78
44.00
78.06

I33-70

220.00

541.20

25-31
46.66

82.53

140.75
230.80
366.40
564-35

I4-I5
27.94

49-47
87.17

148.10
242.50
383-10
588.35

I5.l6
28.67
52-44
92.07

155.80
253.80
4OO.4O
613.20

16.21
30-50
55-56
97-21

163.80
265.90
418.35
638-95

'7-31
32-44
58.86
102.60

172.20
278.60
437-oo
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

69.80
120.35

199.65

3'995
497.25
751.00

22.34
41.40*

73-83
126.86

209.60

334-85
518.85

781-45

From the formula log/ = a -\- <V + <•'& Ramsay and Young obtain the following numbers.t

0

d,

1

0°

10° 2Q°

30 >

40°

50°

60°

70°

80°

90°

Vapor pressure in millimetres of mercury at o° C.

0°

100

200

12.24
1692.3
22182.

23-73
2359-8
26825.

43-97
3223.0
32196.

78.11

3S389-7

133.42
5686.6

455 »9-

219.82
7368.7

350-2I
9409.9

540.91
11858.

811.81
14764.

1186.5
18185.

TABLE 232. — Vapor Pressure of Methyl Alcohol.1

u

0°

1°

2°

3°

4°

5D

6°

7-

8°

9°

£

r*

Vapor pressure in millimetres of mercury at o° C.

0°

29.97

31.6

33-6

35-6

37-8

40.2

42.6

45-2

47-9

50.8

10

53-8

57.0

60.3

63.8

67.5

71.4

75-5

79-8

84-3

89.0

20

94-0

99-2

104.7

110.4

116.5

122.7

129.3

136.2

143-4

151.0

30

158.9

167.1

175-7

184-7

194.1

203.9

214.1

224.7

235-8

247-4

40

259.4

271.9

285.0

298-5

312.6

327-3

342-5

358-3

374-7

39 '-7

50

409.4

427-7

446.6

466.3

486.6

507.7

529-5

552.0

575-3

599-4

60

624.3

650.0

676.5

703-8

732.0

761.1

791.1

822.0

* 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 a=: 5.0720301 ; log£= 2.6406131 ; log c — 0.6050854 ; log a = 0.003377538; log /3 — 7.99682424
(c is negative).

i. Taken from a paper by Dittmar and Kawsitt (Trans. Roy. Soc. Edin. vol. 33).
SMITHSONIAN TABLES.

225

TABLE 233.

VAPOR PRESSURE.*

Carbon Bisulphide, Chlorobenzene, Bromobenzene, and Aniline.

Temp.

0°

1

2°

3°

4°

5°

6°

7° 8°

9°

(a) CARBON BISULPHIDE.

0°

127.90

I33-85

140.05

146.45

153.10

160.00

167.15

174.60

182.25

190.20

10

198.45

207.00

215.80

224-95

234.40

244.I5

254-25

264.65

275.40

286.55

20

298.05

309.90

322.10

334-70

347-70

361.10

374-95

389.20

403.90

419.00

3°

434.60

450.65

467-15

484.15

501.65

5 '9-65

538.15

557.I5

576.75

596.85

40

617.50

638.70

660.50

682.90

705.90

729.50

753-75

778.60

804.10

830-25

(b) CHLOROBENZENE.

20°

8.65

9.14

9.66

IO.2I

10.79

11.40

12.04

12.71

13.42

14.17

30

14.95

15-77

16.63

!7-53

18.47

19.45

20.48

21.56

22.69

23-87

40

25.10

26.38

27.72

29.12

30.58

32.10

33-69

35-35

37.08

38.88

50

40.75

42.69

44.72

46.84

49-05

5'-35

53-74

56.22

58.79

61.45

60

64.20

67.06

70.03

73-"

76.30

79.60

83.02

86.56

90.22

94.00

70

97.90

101.95

106.10

110.41

114.85

"9-45

124.20

129.10

I34-I5

139.40

80

1 44.80

150.30

1 56-05

161.95

168.00

174.25

181.70

187.30

194.10

201.15

90

208.35

215.80

223.45

231.30

239-35

247.70

256.20

265.00

274.00

283.25

100

292.75

302.50

3I2-50

322.80

333-35

344.15

355-25

366.65

378-30

390-25

no

402.55

415.10

427-95

441-15

454-65

468.50

482.65

497.20

512.05

527-25

1 20

542.80

558-70

575-05

59L70

608.75

626.15

643-95

662.15

680.75

699.65

130

718.95

738.65

758.8o

—

~

—

—

~

~

•"

(c) BROMOBENZENE.

40°

-

-

-

-

-

12.40

13.06

13-75

14.47

15.22

50

16.00

16.82

17.68

18.58

I9.52

20.50

21.52

22.59

23-71

24.88

60

26.10

27.36

28.68

30.06

3!-50

33-00

34-56

36.18

37-86

39.60

' 70
80

41.40
63.90

43.28
66.64

45.24
69.48

47.28
7242

49.40
75.46

51.60
78.60

53-88
81.84

56.25
85.20

58.71
88.68

61.26
92.28

90

96.00

99.84

103.80

107.88

112.08

116.40

120.86

125.46

130.20

I35-08

100

140.10

145.26

150.57

156.03

161.64

167.40

I73-32

179.41

185.67

192.10

110

198.70

205.48

212.44

219.58

226.90

234.40

242.10

250.00

258.10

266.40

1 20

274.90

283-65

292.60

301-75

3Io'^5

320.80

330-70

340.80

35i-i5

361.80

130
140

372.65
495.80

383-75
509.70

395- ^
523-90

406.70
538-40

418.60
553-20

430-75
568.35

443-20
583-85

455-90
599-65

468.90
6I5.75

482.20
632.25

150

649.05

666.25

683.80

701.65

7I9-95

738.55

757-55

776.95

796.70

816.90

(d) ANILINE. '

80°

1 8.80

19.78

20.79

21.83

22.90

24.00

25-'4

26.32

27.54

28.80

90

30.10

3J-44

32-83

34-27

35-76

37-30

38.90

40.56

42.28

44.06

1OO

IIO

45-90
68.50

47.80
71.22

49.78

74.04

51.84
76.96

53-98
79.98

56.20

83.10

58.50
86.32

60.88
89.66

63-34
93.12

65.88
96.70

1 20

100.40

104.22

108.17

112.25

116.46

1 20.80

125.28

129.91

134.69

139.62

130

144.70

149.94

155-34 160.90

166.62

172.50

178.56

184.80

191.22

197.82

140

204.60

211.58

218.76 226.14

233-72

241.50

249.50

257.72

266.16

274.82

150

283.70

292.80

302.15 311.75

321.60

33I-70

342-05

352-65

363-50

374.60

1 60

386.00

397.65

409.60 421.80

434-3°

447.10

460.20

473.60

487-25

501.25

170

515.60

530.20

545.20 560.45

576.10

592-05

608.35

625.05

642.05

659-45

180

677.15

695-30

71375 732-65

75I-90

77L50

* These tables of vapor pressures are quoted from results published by Ramsay and Young (Jour. Chem. Soc.
vol. 47). The tables are intended to give a series suitable for hot-jacket purposes.

SMITHSONIAN TABLES.

226

VAPOR PRESSURE.

Methyl Salicylate, Bromonaphthaline, and Mercury.

TABLE 233.

Temp.
C.

0°

1°

2°

r

4°

5°

60

7°

8°

9°

(e) METHYL SALICYLATE.

70°

2.40

2-58

2.77

2-97

3.18

3-40

3-62

3-85

4.09

4-34

80

4.60

4-87

5-15

5-44

5-74

6.05

6-37

6.70

7.05

7.42

90

7.80

8.20

8.62

9.60

9-52

9-95

10.44

10.95

11.48

12.03

100

12.60

13.20

13.82

14.47

15.15

I5-85

16.58

17-34

18.13

18.95

I IO

19.80

20.68

21.60

22-55

23-53

24-55

25.61

26.71

27.85

29.03

1 20

30-25

31.152

32-84

34.21

35-63

37-io

38.67

40.40

41.84

43-54

130

45-30

47.12

49.01

50.96

52-97

55-05

57-20

59-43

6i-73

64.10

140

66-55

69.08

71.69

74.38

77-15

80.00

82.94

85.97

89.09

92.30

150

95.60

99.00

102.50

106.10

109.80

113.60

"7-51

121-53

125.66

129.90

160

I34-25

138.72

M3-3'

148.03

152.88

157-85

162.95

168.19

I73-56

179.06

170

184.70

190.48

196.41

202.49

208.72

215.10

221.65

228.30

235-J5

242.15

180

249-35

256-70

264.20

271.90

279-75

287.80

296.00

304.48

321.85

190

330.85

340-05

349-45

359-05

368.85

378.90

389-15

399.60

410.30

421.20

2OO

432.35

443-75

455-35

467-25

479-35

491.70

504-35

517.25

530-40

543-8o

210

557-5°

571-45

585-70

600.25

61 5-05

630.15

645-55

661.25

677.25

693.60

22O

710.10

727.05

744-35

761.90

779-85

798.10

(f) BROMONAPHTHAUNB.

110°

3-6o

3-74

3-89

4.05

4.22

4.40

4-59

4-79

5.00

5-22

120

5-45

5-70

5-96

6.23

6.51

6.80

7.10

7.42

7-76

8.12

130

8.50

8.89

9.29

9.71

10.15

1 0.60

11.07

11.56

12.07

1 2.60

I4O

^S

I3-72

I4-31

14.92

»5-55

16.20

16.87

17-56

18.28

19.03

150

19.80

20.59

21.41

22.25

23.11

24.00

24.92

25.86

26.83

27.83

160

28.85

29.90

30.98

32.09

33-23

34-40

35-6o

36-83

38.10

39-41

170

40.75

42.12

43-53

44-99

46.50

48-05

49.64

51.28

52-96

54-68

180

56-45

58-27

60.14

62.04

64.06

66.10

68.19

70.34

72-55

74-82

190

77-iS

79-54

81.99

84.51

87.10

8975

92.47

95.26

98.12

101.05

200

104.05

107.12

110.27

113.50

116.81

120.20

123.67

127.22

130.86

J34-59

2IO
220

138.40
181.75

142.30
186.65

146.29
191.65

150-38
196.75

154.57
202.00

158.85
207-35

163.25
212.80

167.70
218.40

172.30
224-15

176-95
230.00

230

235-95

242.05

248.30

254.65

261.20

267-85

274-65

281.60

288.70

295-95

24O

303-35

310.90

318.65

326.50

334-55

342.75

351.10

359-65

368.40

377-30

250

386.35

395-60

405-05

414-65

424.45

434-45

444.65

455-oo

465.60

476.35

260

487-35

498.55

509.90

521-50

533-35

545-35

557-6o

570.05

582.70

595.60

270

608.75

622.10

635-70

649.50

663-55

677-85

692.40

707-15

722.15

737-45

(g) MERCURY.

270°

123.92

1 26.97

130.08

I33-26

136-50

139.81

143.18

146.61

I 50. 1 2

'53-70

280

157-35

161.07

164.86

168.73

172.67

176.79

180.88

185.05

189.30

1 93-63

290

198.04

202.53

207.10

211.76

216.50

221.33

226.25

231.25

241-53

300

246.81

252.18

257-65

263.21

268.87

274-63

280.48

286.43

292.49

208.66

310

3°4-93

3IT-3O

3J7-78

324-37

331-08

337-89

344.81

35I-85

359.00 ! 366.28

320

373-67

381.18

388.81

396.56

404.43

412.44

420.58

428.83

437-22

445-75

330

454-41

463.20

472. r 2

481.19

490.40

499-74

509.22

518.85

528.63

538.56

340

548.64

558-87

569-25

579-78

590.48

601.33

612.34

623.51

634-85

646.36

350

658.03

669.86

681.86

694.04

706.40

718.94

731-65

744-54

757-61

770.87

360

784-31

SMITHSONIAN TABLES.

227

TABLE 234.

AIR AND MERCURY THERMOMETERS.

Rowland has shown (Proc. Am. Acad. Sci. vol. 15) that, when o° and 100° are chosen for fixed points, the relation
between the readings of the air and the mercury in glass thermometers can be very nearly expressed by an equation

oftheform t=r-at(ia0-t)(6-t),

where t is the reading of the air thermometer and T that of the mercury one, a and b being constants. The smaller
a is, the more nearly will the thermometers agree at all points, and there will be absolute agreement for t — o or
loo or />.

Regnault found that a mercury thermometer of ordinary glass gave too high a reading between o° and 100°, and too
low a reading between iooj and about 245°. As to some other thermometers experimented on by Regnault,
little is recorded of their performance between o° and 100°, but all of them gave too high readings above i<xr',
indicating that below loo1- the mercury thermometer probably reads too low. Regnault states this to be the
case for a thermometer of Choisy le.Roi crystal glass, and puts the maximum error at from one tenth to two tenths
of a degree. Regnault's comparisons of the air and mercury thermometers and a comparison by Recknagel of a
mercury thermometer of common glass with the air thermometer are compared with the above formula by Rowland.
The tables are interesting as showing approximately the error to be expected in the use of a mercury thermom-
eter and the magnitude of the constants a and b for different glasses. They are given in the following Table.
Regnault's results above 100° C. compared with the formula /rr T — ai(ioo — t)(6—t), give for the constants a
and b the following values :

Cristal de Choisy Le Roi . «r= 0.00000032, £ — 0°.

Verre ordinaire . . . a = 0.00000034, ^ = 245°.

Verre vert .... a — 0.000000095, ^ — — 270°.*

Verre de Suede . . . a = 0.000000 14, 6=10°.

Common glass (Recknagel) a — 0.00000033, ^ = 290°.

(a) TEMPERATURES BETWEEN o° AND 100° C.

There are no observed results w ith which to compare the calculations for

the Choisv le Roi thermometer

through this range, and in the case of the vet-re ordinaire, the specimen for which the readings below 100°

are g veil was not the same as that used

ibove 100°, from which the constant

s a an

d b were caicul

ated. Row-

land shows that a = 0.00000044 and i= 260 give considerably better agreement.

Regnault's thermometers.

Recknagel's thermometer.

thermome-
ter.

Choisy

Verre ordinaire.

Calculated.

Observed.

Calculated.

O

OO.CO

00.00

00.00

OO.OO

OO.OO

.00

IO

10.00

IO.O7

-

IO.O8

10.08

.00

2O

19.99

—

20. 1 2

—

20.14

20.14

.OO

30

29.98

30.12

30.15

+•03

30.18

30.18

.OO

40

30-97

40.23

40.17

—.06

40.20

40.20

.00

50

49.96

50.23

;

50.17

—.06

50.20

50.20

.OO

60

59-95

60.24

60. 15

—.09

60. 1 8

60. 1 8

.OO

70

69.95

7O.22

7O.I2

.10

70.14

70.15

+ .OI

80

79.96

80.10

80.09

—.01

80.10

80. 1 1

+ .01

90

89.97

-

90.05

-

90.05

90.06

+ 01

IOO

I OO.OO

I OO.OO

r oo.oo

I OO.OO

I OO.OO

+ .0

(b) TEMPERATURES ABOVE 100° C., REGNAULT'S THERMOMETERS.

Air

Choisy le Roi.

Verre ordinaire.

Verre vert.

Verre de Suede.

ther.

Obs.

Calc.

Diff.

Obs.

Calc.

Diff.

Obs.

Calc.

Diff.

Obs.

Calc.

Diff.

IOO

I OO.OO

I OO.OO

+.00

I OO.OO

100.00

.00

I OO.OO

I OO.OO

.OO

I OO.OO

I OO.OO

.00

1 2O

1 20. 1 2

120.09

+-03

119-95

119.90

+-os

1 20.07

1 20.09

— .or

1 20.04

1 20.04

.00

140

140.29

140.25

+.04

r39-85

139.80

+-OS

140.21

140.22

— .01

140.11

140.10

+.01

160

160.52

160.49

+.03

159-74

159-72

+ .02

160.40

160.39

+ .01

160.20

160.21

— .01

180

l8o.8o

180.81

— .03

179-63

179.68

—.05

180.60

180.62

— .02

180.33

1 80. 14

— .or

2OO

201.25

201.28

— .01

199.70

199.69

+ .01

200.80

200.89 I — -°9

2OO. 50

200.53

—03

22O

221.82

221.86

—.04

219.80

219.78

+ .02

22 1. 2O

221.23

--03

220-7 S

220.78

— -°3

240

242.55

242.56

— .01

239.90

239.96

—.06

24 1 .60

241.63

—•03

241.16

241.08

+.08

26O

263.44

263.46

— .02

260.20

260.21

— .OI

262.15

262.09

+ .07

280

284.48

284.52

—.04

280.58

280.00

— .02

282.85

282.63

+ .2

i

300

305-72

305.76

—.04

301.08

301.12

—.04

320

327.20

—•°5

321.80

321.80

.OO

340

349-30

348.88

+.42

343-oo

342.64

+ -36

SMITHSONIAN TABLES.

* Misprinted f +] 270 in Rowland's paper.
228

TABLES 235, 236.
COMPARISON OF THERMOMETERS.*

Chappius gives the following equations for comparing glass thermometers:

iooo(7V— TH)-. 00543 doc— rm> ym + 1.412 x IO-HIOO— rm*) rm— 1.323 x K>-« (loo* —

1000 ( Tea, - TU) = -03S9 (>oo - Tm) Tm - o. 234 X io-« ( 100= - r««) 7V» - 0.5 u> X io~« (ioo» -
A^rr nitrogen ; //= hydrogen ; CO^ = carbon dioxide ; m = mercury.

TABLE 235. — Hydrogen Thermometer compared with others.

This table gives the correction which added to the thermometer reading gives the temperature by the hydrogen

thermometer.

Chappius's experiments, t

Marek's experiments.?

Tempera-

Mercury in glass.

ture by 1 Hard

thermom-
eter.

glass
mercury

Nitrogen
thermome-
ter.

dioxide
thermome-

Hard

French

Jena

. Thuringian glass.

inometer.

glass.

glass.

glass.

1830-40.

1888.

— 2O

+0.172

+O.OI4

+0.07 I

— IO

+0.0/3

+0.007

+0.032

C

o.ooo

O.OOO

O.OOO

0.000

O.OOO

O.OOO

O.OOO

o.ooo

IO

— 0.052

— 0.006

— 0.025

—0.044

— 0.060

— 0.056

—0.086

— 0.072

2O

— 0.085

— O.OIO

—0.043

—0.073

— O IOO

— 0.091

—0.149

— 0.125

3°

— O.I O2 I — O.OII

—0.054

— 0.091

—0.125

— O.IO9

— O.igi

—0.159

40

— 0.107 — o.oii

—0.059

— 0.098

—0.134

— O.I I I

—0.213

—0.178

5°

—0.103

— 0.009

—0.059

— 0.096

— 0.132

—0.103

— 0.216

—0.1 80

60

— 0.090

— 0.005

—0.053

— 0.086

— 0.118

—0.086

— O.2OI

—o.i 68

7°

— 0.072

— O.OOI

— 0.044

— 0.070

— 0.096

— 0.064

O.I7I

—0.143

So

— 0.050 ! +0.002

—0.030

— 0.050

— 0.068

— O.O4I

—0.127

— o.i 06

90

— 0.026 +0.003

— 0.016

— 0.026

—0.035

—0.018

— 0.069

— 0.058

IOO

o.ooo

o.ooo

o.ooo

O.OOO

o.ooo

O.OOO

o.oco

o.ooo

TABLE 236. — Air Thermometer compared with others.

This table gives the correction which added to the thermometer reading gives the temperature by the air thermometer.

Temperature
by air
thermome-
ter.

Mercury in
Thuringian
glass
thermometer
(Grommach §).

Mercury in Jena
glass thermome-
ter (Wiebe and
Boucher ||).

Temperature
by air
thermome-
ter.

Mercury in Jena
glass thermome-
ter (Wiebe and
Boucher ||).

Temperature
by air
thermome-
ter.

Baudin alcohol
tlu-rmometer
(.White t).

— 20

+0.03

+0-I53

130

— 0.07

0

— O.OOO

— IO

+O.O2

+0.067

140

— 0.09

—5

—0.144

O

o.oo

O.OOO

I50

— O.IO

IO

—0.382

10

—0.03

— 0.049

160

— O.IO

—'5

—0.704

20

— O.I I

—0.083

170

— 0.08

— 20

— I. IOO

3°

— O.I 2

—0.103

1 80

—006

—25

— 1-563

40

—0.08

O.I IO

190

O.O2

—30

—2.082

SO

-

— o. 1 07

200

+ 0.04

—35

—2648

54

— o 04

-

2IO

+ 0.1 1

—40

— 3-253

60

-

— 0.096

2 2O

+ 0.21

—45

-3.887

70

-

— 0.078

230

+0.32

-50

—4-54'

73

— 0.06

-

240

+ 0.46

—55

— 5.206

80

-

—0.054

250

+ 0.63

—60

-5.872

82

— 0.04

-

260

+0.82

-65

—6-531

90

-

—0.028

270

+ I-05

—70

— 7-!74

IOO

-

o.ooo

280

+ i-3°

—80

-8-371

I 10

-

—0.03

290

+ 1-58

—90

—9-392

1 20

—0.05

3OO

+ 1.91

— IOO

—10.163

* These two tables are taken with some slight alteration from Landolt and Boernstein's " Phys. Chem. Tab.'
t P. Chappius, "Trav. et Mem. du Bur. internal, des Poids et Mes." vol. 6, 1888.
t Marek, "Zeits. fiir Inst.-K." vol. 10, p. 283.

§ Grommach, " Metr. Beitr. heraus. v. d. Kaiser. Norm.-Aich. Comm." 1872.
II Wiebe und Bbttcher, " Zeits. fiir Inst. K." vol. 10, p. 233.
II White, " Proc. Am. Acad. Sci." vol. 21, p. 45.

SMITHSONIAN TABLES.

229

TABLE 237.

CHANCE OF THERMOMETER ZERO DUE TO HEATING.*

When a thermometer is used for measurements extending over a range of more than a few degrees, its indications are
generally in error due to the change of volume of the glass lagging behind the change of temperature. Some data
are here given to illustrate the magnitude of the change of zero after heating. This change is not permanent, but
the thermometer may take several days or even weeks to return to its i.ormal reading.

Kind of glass.

No. of
experi-
ment.

Maximum
temp, in
deg. cent.

Time at
maximum
temp, in
hours.

Normal Jena glass.

Thuringian
glass.

Composition of
Jena glass
used.

I.

II.

Depression of freezing-point.

I

290

5

I.O

I.O

2.1

ZnO 7 %

2

290

5

i-3

i-S

2.7

CaO 7 %

3

290

5

1.5

i-7

3-1

Na20 14.5 %

4

290

5

1.6

1.8

3-4

A1203 2.5%

5

290

5

i-7

1.9

3-6

B203 2 %

< 6,

290

5

1.8

2.0

3-7

Si02 67 %

7

290

25

2.O

2.2

4.2

TABLE 238.

CHANCE OF THERMOMETER ZERO DUE TO HEATING.

Description of thermometer.

Year of

Ratio of soda and potash
in the glass.

Depression of
zero due to
one hour's

heating to

Na20/K,0

K20/Na20

100° C.

Humboldt, No. 2 . ....

Before 1835

0.04

_

0.06

T. G. Greiner, Fj

1848

0.08

-

0.15

" F2 . . . .

1856

O.22

-

0.38

F3 .

1872

—

0.21

0.38

Ch. F. Geissler, No. 13 .

1875

-

0.26

0.40

G. A. Schultze, No. 3 ...

1875

-

0.24

0.44

Rapp's Successor, P'4

1878

0.83

0.65

* Allihn, " Zeits. fiir Anal. Chem." vol. 29, p. 385.

t W. Fresenius, "Zeits. fiir Anal. Chem." vol. 27, p. 189. See also, for this and following table, Wiebe in the
" Zeitschrift fiir Instrumentenkunde," vol. 6, p. 167, from which Fresenius quotes. The thermometer referred to i»
this table belonged to the Kaiserlichen Normal-Aichungs Commission.

SMITHSONIAN TABLES.

230

TABLE 239.

EFFECT OF COMPOSITION ON THERMOMETER ZERO.*

Jena Glasses.

Depression of

Descriptive
number.

Si2O

Na2O

K.O

CaO

AI203

B203

ZnO

zero due to
one hour's
heating to

100° C.

IV

70

_

13-5

I6.5

_

_

1

0.08

VIII

70

IS

15

-

-

-

0.08

XXII

66

14

14

6

-

-

-

1.05

XXXI

66

II. I

16.9

6

-

-

-

1.03

XVII111

69

15

10.5

-

5

-

-

1. 06

XX"1

70

7-5

7-5

IS

-

—

0.17

XIV"1

69

H

7

i

2

7

0.05

t XVI™

67.5

H

-

7

2-5

2

7

0.05

XVIII

52

o

9

3°

0.05

TABLE 240.

CHANCE OF ZERO OF THERMOMETER WITH TIME.

Closely allied to the changes illustrated in Tables 235-237 is the slow change of volume of the bulb of a thermometer
with age. The following short table shows the change for the normal Jena thermometer.J

Date of observation.

Thermometer
number. -

1886

1889

1890

Total
rise.

Rise of zero.

1O6

O.OO

°-3

0.04

0.04

108

O.OI

O.2

0.04

0.03

665

O.OI

o-3

0.05

0.04

667

O.O2

0.4

0.05

0.03

668

0.02

o-5

0.06

0.04

670

0.00

o-3

0.04

0.04

671

O.O5

0.9

0.09

0.04

672

0.05

O.o

0.08

0.03

SMITHSONIAN TABLES.

* Fresenius, " Zeits. fiir Anal. Chem." vol. 27, p. 189.

t Normal Jena glass.

Z Allihn, " Zeits. fiir Anal. Chem." vol. 29, p. 385.

231

TABLE 241.

CORRECTION FOR TEMPERATURE OF MERCURY IN THERMOMETER

STEM.*

/" = /— 0.0000795 » (P — *0> >n Fahrenheit degrees; 7':=/ — 0.000143 w (t1 — t), in Centigrade degrees. Where
7'= corrected temperature, * = observed temperature, /'= mean temperature of glass stem and mercury column,
n = the length of mercury in the stem in scale degrees.

(a) CORRECTION FOR FAHRENHEIT THERMOMETER

= value of 0.0000795 " (P — *)•

/'— t

10°

20 3

30J

40 3

50°

60°

70°

80°

90°

100°

10°

O.OI

O.O2

O.O2

0.03

0.04

0.05

0.06

0.06

0.07

0.08

20

O.O2

0.03

O.O5

0.06

0.08

O.IO

O.I I

0.13

0.14

0.16

3°

0.02

O.O5

0.07

O.IO

O.I 2

0.14

0.17

0.19

O.2I

0.24

40

0.03

O.O6

O.IO

0.13

0.16

0.19

O.22

o.

2S

0.29

0.32

50

O.O4

0.08

0. 12

0.16

0.20

0.24

0.28

0.32

0.36

0.40

60

o.o<;

O.IO

O.I4

0.19

0.24

0.29

o-33

0.38

043

0.48

70

0.06

O.I I

0.17

O.22

0.28

o-33

o-39

0-45

0.50

0.56

80

0.06

0.13

0.19

0.25

0.32

0.38

0-45

o.

Si

0-57

0.64

90

0.07

0.14

O.2I

O.29

0.36

0-43

0.50

o.

S7

0.64

0.72

IOO

0.08

0.16

0.24

0.32

0.40

0.48

0.56

0.64

O.72

0.79

110

0.09

0.17

O.26

o-35

0.44

0.52

0.61

0.70

0-79

0.87

1 20

O.IO

0.19

0.29

0.38

0.48

0-57

0.67

0.76

0.86

0.95

130

O.IO

0.21

0.3I

0.41

O.52

0.62

0.72

0.83

o-93

1.03

(b) CORRECTION FOR CENTIGRADE THERMOMETER

= value of 0.000143 n (t1 — f).

/' — t

10° 20° 30°

40 ^

50 60°

70

80°

10°

o.oi 0.03 0.04

O.o6

0.07 0.09

O.IO

O.I I

20

0.03 0.06 0.09

O.I I

0.14 0.17

O.2O

0.23

3°

0.04 0.09 o. 1 3

0.17

O.2I O.26

0.30

0-34

40

0.06 o. ii 0.17

0.23

0.29 0.^4

0.40

0.46

5°

O.O7 O.I4 O.2I

0.29

0.36 0.43

0.50

0-57

60

O.Og O.I7 O.26

o-34

0.43 .0.51

O.6o

0.69

70

O.IO O.2O 0.30

0.40

0.50 0.60

0.70

0.80

80

o.i i 0.23 0.34

0.46

0.57 0.69

O.8O

0.92

90

0.13 0.26 0.39

0.51

0.64 0.77

0.90

1.03

100

0.14 0.29 0.43

0.57

0.72 0.86

I

.00

1.14

N. B. — When f — /is negative the correction becomes additive.

SMITHSONIAN TABLES.

* " Smithsonian Meteorological Tables," p. 12.
232

TABLE 241.

CORRECTION FOR TEMPERATURE OF MERCURY IN THERMOMETER

STEM.

(c) CORRECTION TO BE ADDED TO THERMOMETER READING.*

t— i<

M

70°

80°

90°

100°

120°

140°

160°

180°

200°

220°

n

10°

O.O2

0.03

0.05

0.07

O.I I

0.17

0.21

0.27

o-33

0.38

10°

20

0.13

0.15

0.18

O.22

0.29

0.38

0.46

o-53

0.61

0.67

20

30
40

O.24

o-35

0.28
0.41

0.48

o-39
0.56

0.48
0.68

0.59
0.82

O./O
0.94

0.78
1.04

0.88
Mi

0.97
1.28

30
40

50

0.47

0.53

0.62

0.72

0.88

1.03

I.I7

i -i

1.44

i-59

50

60

0.57

o 66

0.77

0.89

.09

1.25

1.42

1.58

1.74

1.90

60

70

0.69

0.79

0.92

.06

' -3°

1.47

1.67

1.86

2.04

2.23

70

80

0.80

0.91

1.05

.21

•S2

1.71

1.94

2.15

2-33

2-55

80

9O

0.91

1.04

1.19

.38

•73

1.96

2.2O

2.42

2.64

2.89

90

TOO

i. 02

1.18

J-35

.56

•97

2.18

2.45

2.70

294

3-23

100

no

-

-

.78

2.19

2-43

2-70

2.98

3.26

3-57

no

1 20

-

-

-

.98

2-43

2.69

2-95

3.26

3-58

3-92-

120

130

-

-

-

2.68

2.94

3.20

356

3-89

4.28

130

140

-

-

-

-

2.92

3.22

3-47

3-86

4.22

4.64

140

150

-

-

-

-

—

3-74

4-'5

4-56

5.01

150

160

-

-

-

-

-

-

4.00

4.46

4.90

5-39

160

170

-

-

-

_

-

-

4.27

4.76

5-24

5-77

170

1 80

-

-

-

-

-

-

4-54

5.07

5-59

6.15

180

190

-

-

-

-

—

-

-

5-38

5-95

6-54

190

200

-

—

-

-

—

-

-

5-70

6.30

6.94

200 ;

210

-

-

-

-

-

-

-

-

6.68

7-35

210

220

7.04

7-75

220

* This table is quoted from Rimbach's results, "Zeit. fur Irtfetrumentenkunde," vol. 10, p. 153. The numbers
represent the correction made by direct experiment for thermometers of Jena glass graduated from o° to 360° C.,
the degrees being from i to 1.6 mm. long. The first column gives the length of the mercury in the part of the stem
which is exposed in the air, and the headings under t — t1 give the difference between the observed temperature and
that of the air.

SMITHSONIAN TABLES.

233

TABLES 242, 243.

EMISSIVITY.

TABLE 242. — Emissivity 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 io-6/ — 2.6 X io-V,
when the surface of the sphere is blackened, or

e — .000168 + 1.98 X io-°t — 1.7 X IO-8/2,

when the surface is that of polished copper. In these equa-
tions e is the emissivity in c. g. s. units, that is, the quantity
of heat, in therms, radiated per second per square centimetre
of surface of the sphere, per degree difference of tempera-
ture 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-
*

Value of e.

Ratio.

Polished surface.

Blackened surface.

5

.000178

.000252

.707

10

.OOOI86

.000266

.699

'5

.000193

.000279

.692

20

.OOO2OI

.000289

•695

25

.000207

.000298

.694

30

.OOO2 1 2

.000306

•693

35

.0002 i 7

.000313

•693

40

.000220

.000319

•693

45

.000223

.000323

.690

50

.000225

.000326

.690

55

.000226

.000328

.690

60

.000226

.000328

.690

TABLE 243.— Emissivity at Different Pres-
sures.

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 8° C.

1

Polished surface.

Blackened surface.

t

et

t

et

PRESSURE 76 CMS. OK MERCURY.

63.8

.00987

6l.2

.01746

57-i

.00862

5O.2

.01360

5°-5

.00736

41.6

.01078

44.8

.00628

34-4

.00860

40-5

.00562

27-3

.00640

34-2

.00438

20.5

.00455

29.6

.00378

-

-

23-3

.00278

-

—

1 8.6

.OO2IO

~

~

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-°

.00791

40.8

.00268

28.5

.00490

PRESSURE i CM. OF MERCURY.

65

.00388

62.5

.OI 182

60

•00355

57-5

.01074

5°
40

.00286
.00219

54-2
41.7

.01003
.00726

3°

.00157

37-5

.00639

23-5

.00124

34-o

.00569

-

-

27-5

.00446

24.2

.00391

SMITHSONIAN TABLES.

* " Proc. Roy. Soc." 1^72.

t " Eroc. Roy. Soc." Edinb. 1869.

234

TABLES 244, 245.
EMISSIVITY.

TABLE 244. - Constants of Emissivity.

The constants of radiation into vacuum have been determined for a few substances. The
object of several of the investigations has been the determination of the law of variation with
temperature or the relative merits of Dulong and Petit's and of Stefan's law of cooling.

Dulong and Petit's law gives for the amount of heat radiated in a given time the equation

H=Asae(at—i)

where A is a constant depending on the units employed and on the nature of the surface, s the
surface, a a constant determined by Dulong and Petit to be 1.0077, # the absolute temperature
of the enclosure, and t the difference of temperature between the hot surface and the enclosure.
The following values of A are taken from the experiments of W. Hopkins, the results being
reduced to centimetre second units, and the therm as unit of heat.

Glass . . . ;•';-' . •. .,4 = .00001327

Dry chalk /4 = . 00001195

Dry new red-sandstone A = .00001162

Sandstone (building) . ,<4 — .00001232

Polished limestone . . A = .00001263
Unpolished limestone

(same block) . . . A = .0001777

Stefan's law is expressed by the equation

where //and s have the same meaning as above, a is a constant, called Stefan's radiation con-
stant, T\ is the absolute temperature of the radiating body and 7g the absolute temperature of
the enclosure. Stefan's constant would represent, if the law held to absolute zero, the amount
of heat which would be radiated per unit surface from the body at i° absolute temperature to
space at absolute zero. The experiments of Schleiermacher, Bottomley, and others show that
this law approximates to the actual radiation only through a limited range of temperature.

Graetz * finds for glass

Schleiermacher f find for polished platinum wire

For copper oxide

7i = 400, T0 = o,tr = 1.0846 X IO"12
( 7\ = 1085, To = o, a- = o. 185 X io-12
7\— 1150, 7b = o, IT — 0.177 X io~12
T\ = 850, TO — o. <r = 0.600 X io-12
7\ = 1080, TO = o, <r = 0.701 X JO'1'2

TABLE 245. — Effect of Absolute Temperature of Surface.

The following tabular results are given by Bottomley. t The results of Schleiermacher were calculated from data given
in the paper above quoted. The temperatures /, are in degrees centigrade, and e is the emissivity or amount of
heat in therms radiated per square centimetre of surface per degree difference of temperature between the hot body
and the enclosure. The results are all for high vacuum.

Schleiermacher's results. Temperature of enclosure, o° C. ttti, t^e*, refer to
polished platinum wire, tge3 to blackened platinum wire.

Bottomley's results for
polished platinum, the
enclosures being at 15° C.

'i

«i

»«

C2

t,

«•.-(

*

e

'3°

21.6 X io-6

6S

14.5 X io-6

16

60.9 X io-6

302

65.05 X io-6

200

30.0 "

I IO

18.7 "

38

67.6 "

425

120.3 "

337

53-8 "

232

32.2 "

94

83-7 "

613

282.0 "

137.0 '

383

61.6 "

228

147.0

744

537-o "

826

3I5-° '

740

198.0 "

403

293.0

806

653-o

900

358.0 "

5«5

540.0

SMITHSONIAN TABLES.

* " Wied Ann." vol. u, p. 297.
t " Wied. Ann." vol. 26, p. 305.
t " Phil. Trans. Roy. Soc." 1887

235

TABLES 246, 247.

EMISSIVITY.

TABLE 246. — Radiation of Platinum Wire to 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 : —

/ = 4oS° C., «/=:378.8 X io~4, temperature of enclosure 16° C.
* =z 505° C., rf— 726.1 X io-4, " " 17° C.

It was found at this degree of exhaustion that considerable relative change of the vacuum produced very small
chinge 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 iu
enclosure.

Temp, of enclosure 16° C., ^ = 408-" C.

Temp, of enclosure 17° C., t — 505° C.

Pressure in mm.

et

Pressure in mm.

ct

740.

8i37.oX to-*

0.094

1 688.0 X io-*

440.

7971.0 "

•C53

• 1255.0 "

140.

7875.0 '

•034

1 1 26.0 '

42.

7591-0 '

.013

920.4 "

4-
0.444

6036.0 "
2633.0 "

.0046
.00052

831.4 "
767.4 "

.070

1045.0 "

.00019

746.4 '

•034

.012

727-3 "
539-2 '

Lowest reached )
but not measured [

726.1 "

.0051

436-4 '

.OOOO7

378.8 "

TABLE 247. — Effect of Pressure on Radiation at Different Temperatures.

The temperature of the enclosure was about 15° C. The numbers give the total radiation in therms per square cen-
timetre per second.

Pressure in mm.

Temp, of

wire in C-1.

About

IO.O

0.25

O.O23

o.i M.

100°

0.14

O.I I

0.05

o.or

0.005

2OO

•31

.24

.11

.02

.00 S5

300

•5°

•38

.18

.04

.0105

4OO

•75

•53

•25

.07

.025

5OO

-

.69

•33

.13

•055

6OO

-

•85

•45

•23

•J3

7OO

—

—

-

•37

.24

800

-

-

-

•56

.40

90O

"

~

"

.61

NOTK. — 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.

236

TABLE 248.

PROPERTIES OF STEAM.

Metric Measure.

The temperature Centigrade and the absolute temperature in degrees Centigrade, together with other data for steam
or water vapor stated in the headings of the columns, are here given. The quantities of heat are in therms or calo-

ries according as the gramme or the kilogramme is taken as the unit of mass.

d.

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J|0o

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£"0

£ tiS

H o^

Ill

OS II

Htt ..£ £ II -: c sL

usS!

0°

273

4.60

6.25

0.006

606.5

o.oo

606.5

31.07

575-4

575-4

210.66

2.732

5

278

6-53

8.88

.009

6o8.0

5.00

6030

3'-47

5/6-5 57i-5 '50-23

3-805

10

283

9.17

12.47

.012

609.5

I O.OO

599-5

31.89

577-7 567-7

108.51

5-231

15

288

12.70

17.27

.017

DILI

15.00

596.0

32-32

578-8 563.7

79-35

7.104

20

293

17-39

23.64

.023

612.6

2O.OI

592.6

32-75

579-8 559-8

78-72

9-532

25

298

23-55

32.02 0.031

614.1

25.02

589.1

33-20

580-9 ; 555-9

43-96

12.64

3°

303

3'-55

42.89 1 .042

615.6

3°.°3

585.6

33-66

582.0 552.0

33-27

16.59

35

308

41.83

56-87

.055

617.2

35-04

582.1

34.12

583.1 548.2

25-44

21.54

40

3'3

54.91

74.65

.072

618.7

40.05

587.6

34-59

584.1 544.1

19.64

27.70

45

97.06

.094

620.2

45-07

575-1

35.06

585.2

540.1

i5-3i

35-26

5°

323

91.98

125.0

O.I2I

621.7

50.09

57i-7

35-54

586.2

536-I

12.049

44-49

55

328

117.47

'59-7

.155

623.3

55- "

568.2

36.02

587-2

532-1

9.561

55-65

65

333

148.79

202.3

.196

624.8

60.13

564-7

36-51

588.3

528-1

7-653

69.02

65

338

186.94

254.2

.246

626.3

65.17

561.1

37-oo

524.2

6.171

84.94

70

343

233-08

316.9

-306

627.8

70.20

557-6

3748

590-4

520.2

5.014

103-75

75

348

288.50

392-3

0.380

629.4

75-24

554-1

37.96

591.4)516-2

4.102

125.8

80

353

354-62

482.1

.446

630.9

80.28

550-6

38.42

592.5 512.2

3-379

151.6

85

358

433-0°

588.7

•570

632.4

85-33

547-i

38.88

593.5 508.2

2.800

181.5

90

363

714.4

.691

633-9

90.38

543-6 39-33

594-6 ' 504.2

2-334

216.0

95

368

633-69

861.7

.834

635-5

95-44

540.0

39-76

595-7 , 500-3

J-957

255-7

100

373

760.00

I033-

I.OOO

637.0

100.5

536-5

40.20

596.8

496-3

1.6496

300.8

105

378

906.41

1232.

•193

638-5

105.6

533-o

40.63

597-9

492-3

I-3978

352-2

i Jo 383

1075.4

1462.

•415

640.0

no.6

5294

41.05

599.0 488.4

1.1903

410.3

1269.4

1726.

.670

641.6

"5-7

525-8

41.46

600. i

484.4

1.0184

475-6

1 20

393

I491-3

2027.

.962

643.1

120.8

522.3

41.86

601.2

480.4

0.8752

549-o

1 125

398

1743-9

2371-

2-295

644.6

125.9

518-7

42.25

602.4

476.5

0-7555

630.7

130

403

2030.3

2760.

2.671

646.1

131.0

S1S-1

42.63

603.5 4/2-5

0.6548

721.6

»35

408

2353-7

3200.

3-097

647-7

136.1

511.6

43.01

604.7 468.6

0.5698

822.3

140

4*3

2717.6

3695-

3-576

649.2

141.2

508.0

43-38

605.8 464.6

0-4977

933-5

H5

418

3l25-6

4249.

4-"3

650.7

146.3

504-4

43-73

607.0 460.7

0-4363

1055-7

150

423 7 $1.2

4869.

4.712

652.2

j51.5

500.8

44.09

608.2 456.7

0-3839

1190.

155 428

4088.6

5589.

5-38o

653-8

'56-5

497-2

44-43

609-3 452-8

0.3388

I336-

160

433

4651.6

6324.

6. 1 20

655-3

161.7

493-5

44.76

610.5 448.8

0.3001

1496.

165

438

5274.5

7171.

6.940

656.8

166.9

489.9

45-°9

611.7 444.8

0.2665

1669.

170

443

596i-7

8105.

7.844

658.3

172.0

486.3

45-40

6 1 2.9 {440.9

0-2375

1856.

175

448

6717.4

9*33-

8.839

659-9

177.2

482.7

45-7i

614.2

436-9

O.2I22

2059.

180

453

7546.4

10260.

9-929

661.4

182.4

479-o

46.01

6i5-4;433-o

O.IQXII

2277.

185

458

8453-2

11490.

11.123

662.9

187.6

475-3

46-30

616.6 ; 429.0

o. 1 708

2512.

190

463

9442-7

12838.

12.425

664.4

192.8

47i-7

46-59

617.9

425-0

0.1538

2763.

'95

468

10520.

14303-

13.842

666.0

198.0

468.0

46.86

619.1

421.1

0.1389

3031-

200

473

11689.

15892.

15.380

667.5

203.2

464-3

47-13

620.4

417.1

0.1257

33-8.

* Where A is the reciprocal of the mechanical equivalent of the thermal unit.

t =fL=^±AP^L- , internal-work pressure where ^ ^ ,aken }n ]itres tfce presgure is given square

z/ mechanical equivalent of heat

decimetre, and where v is taken in cubic metres the pressure is given per square metre, — the mechanical equivalent
being that of the therm and the kilogramme-degree or calorie respectively.

SMITHSONIAN TABLES.

237

TABLE 249.

PROPERTIES OF STEAM.

British Measure.

The quantities given in the different columns of this table are sufficiently explained by the headings. The abbrevia-
tion B. T. U. stands for British thermal units. With the exception of column 3, which was calculated for this
table, the data are taken from a table given by Dwelshauvers-Dery (Trans. Am. Sue. Mech. Eng. vol. xi.).

s. .

t

.•

.0

l.s

Sg

c-g

^ 3

-a
B

y

M O

.5 fj

rt

S."

8.-

its

re o c

c § c

4) A—

-lp

Ill

334)
••A O ^

»> Q.n>

sH

C- (-j

I'i

•s^l

«^

Is-jr?

illS

lyp

ffi

j) »ig

*.SS-

PM a

H-8

>§.£

£3R

K &pa

&M**

W-S-oW

h^'cW

>a.s

1

144

0.068

IO2.O

334-23

0.0030

70.1

980.6

62.34

1043.

1113.0

2

288

.136

126.3

173-23

.0058

94.4

961.4

64.62

IO26.

1120.4

3

432

.204

141.6

117.98

.0085

109.9

949-2

66.58

IOII.

1127.0

4

576

.272

I53-1

89.80

.01 1 1

121.4

940.2

67.06

1007.

1128.6

5

720

•340

162.3

72.50

.0137

I30-7

932.8

67.89

IOOI.

1131.4

6

864

0.408

170.1

61.10

0.0163

138.6

926.7

68.58

995-2

"33-8

7

1008

.476

176.9

53.00

.0189

145-4

92J-3

69.18

990-5

"35-9

8

II52

•544

182.9

46.60

.0214

I5I-5

916.5

69.71

986.2

"37-7

9

1296

.612

188.3

41.82

.0239

156.9

912.2

70.18

982.4

"39-4

10

1440

.680

193.2

37.80

.0264

161.9

908.3

70.61

979-0

1140.9

11

1584

0.748

197.8

34.61

0.0289

166.5

904.8

70.99

975-8

1142.3

12

1728

.816

2O2.O

31.90

.0314

170.7

901.5

71.34

972.8

"43-5

13

1872

.884

205.9

29.58

•0338

174-7

898.4

71.68

970.0

1 144.7

14

2016

•952

209.5

27-59

.0362

178.4

895.4

72.00

967-4

II45-9

'5

2160

i. 020

213.0

25-87

.0387

181.9

892.7

72.29

965.0

1146.9

16

2304

i. 088

216.3

24-33

0.0411

183.2

890.1

72.57

962.7

1147.9

17

2448

.156

219.4

22.98

•°435

188.4

887.6

72.82

960.4

1148.9

18

2592

.224

222.4

21.78

•0459

191.4

885-3

73.07

958.3

1 1 49.8

19

2736

.292

225.2

20.70

.0483

194-3

883.1

73-30

956-3

1 1 50.6

20

2880

.360

227.9

19.72

.0507

197.0

880.9

73-53

954-4

1151.4

21

3024

1.429

230.5

18.84

0-0531

199.7

878.8

73-74

952.6

1152.2

22

3168

•497

233-0

18.03

•0554

2O2. 2

876.8

73-94

950.8

u S3-0

23

3312

•565

235-4

17-3°

.0578

204.7

874.9

74-13

949.1

"53-7

24

3456

•633

237-7

16.62

.0602

2O7.O

873-1

74-32

947-4

"54-4

25

3600

.701

240.0

'5-99

.0625

209-3

871-3

74-Si

945-8

"55-1

26

3744

1.769

242.2

15.42

0.0649

2II-5

869.6

74.69

944-3

1155.8

27

3888

-837

244-3

14.88

.0672

2I3.7

867.9

74-85

942.8

1156.4

28

4032

•90S

246.3

14.38

.0695

215-7

866.3

75.01

941-3

"57-i

29

4176

•973

248.3

13.91

.0619

217-8

864.7

939-9

ii57-7

30

4320

2.041

25O.2

13.48

.0742

2197

863.2

75-33

938.5

"58-3

31

4464

2.109

252.1

l3-°7

0.0765

221.6

861.7

75-47

937-2

1158.8

32

4608

.177

253-9

12.68

.0788

223-5

860.3

75.61

935-9

1 1 59-4

33
34

4752
4896

•245
•313

255-7

257-5

12.32
11.98

•0835

225-3
227.1

858.9

857.5

75-76
75-89

934-6
933-4

1 1 59-9
1160.5

35

5040

.381

259.2

11.66

.0858

228.8

856.1

76.02

932.1

1161.0

36

5184

2-449

260.8

11.36

0.088 1

230-5

854.8

76.16

931.0

1161.5

37

5328

.517

262.5

11.07

.0903

232.2

853-5

76.28

929.8

1162.0

38

5472

•585

264.0

10.79

.0926

233-8

852-3

76.40

928.7

1162.5

39

5616

•653

265.6

10.53

.0949

235-4

851.0

76.52

927.6

1162.9

40

5760

.722

267.1

10.29

.0972

236.9

849.8

76.63

926.5

1163.4

41

5904

2.789

268.6

10.05

0.0995

238.5

848.7

76-75

9254

1163.9

42

6048

-857

270.1

9-83

.1018

239-9

847.5

76.86

9244

1164.3

43

6192

•925

27I-5

9.61

.1040

241.4

846.4

76.97

923.3

1164.7

44

6336

•993

272.9

9.41

.1063

242.9

845-2

77.07

922.3

1165.2

45

6480

3.061

274-3

9.21

.1086

244-3

844.1

77-18

921.3

1165.6

46

6624

3.129

275.6

9.02

0.1108

245-6

843.1

77.29

920.4

1 1 66.0

47

6768

.197

277.0

8.84

.1131

247.0

842.0

77-39

919.4

1 1 66.4

48

6912

.265

278.3

8.67

•"53

248.3

841.0

77-49

918.5

1166.8

49

7056

•333

279.6

8.50

.1176

249.7

840.0

77-58

1167.2

SMITHSONIAN TABLES.

238

TABLE 249.

PROPERTIES OF STEAM.

British Measure.

Pressure in
pounds per
square inch.

Pressure in
pounds per
square foot.

Pressure in
atmospheres.

1

B**

£X tu
if
HTS

Volume per
pound in
cubic feet.

Weight per
cubic foot
in pounds.

Heat of water
per pound in
B. T. U.

Internal latent
heat per pound
of steam in
B. T. U.

External latent
heat per pound
of steam in
B. T. U.

t Total latent
i heat per pound
: of steam in
! B. T. U.

Total heat per
pound of steam
in B. T. U.

50

7200

3.401

280.8

8-34

0.1198

251.0

839.0

77.67

916.6

1167.6

51

7344

.469

282.1

8.19

.1221

252.2

838.0

77.76

915-7

1 1 68.0

S2

7488

•537

283-3

8.04

•1243

253-5

837.0

77-85

914.9

1168.3

53

7632

.605

284.5

7.90

.1266

254-7

836.0

77-94

914.0

1168.7

54

7776

•673

2857

7.76

.1288

256.0

835-1

78.03

9i 3- »

1169.1

55

7920

3-741

286.9

7-63

O.I3IO

257-1

834.2

78.12

912-3

1169.4

56

8064

.801

288.1

7-5°

•1333

258.3

833-2

78.21

9"-5

1169.8

57

8208

.878

289.2

7-3«

•1355

259-5

832-3

78.29

910.6

II70.I

58

8352

.946

290.3

7.26

•1377

260.7'

83I-5

78.37

909.8

1170.5

59

8496

4.014

291.4

7.14

.1400

261.8

830.6

78.45

909.0

II7O.8

60

8640

4.082

292.5

7-03

O.I422

262.9

829.7

78-53

908.2

II7I.2

61

8784

.150

293.6

6.92

.1444

264.0

828.9

78.61

907-5

II7I-5

62
63

8928
9072

.218
.286

294.7
295.7

6.82
6.72

.1466

.1488

265.1
266.1

828.0
827.2

78.68
78.76

906.7
905-9

II7I.8
II72.I

64

9216

•354

296.7

6.62

.1511

267.2

826.4

78.83

905.2

1172.4

65

9360

4.422

297.8

6.52

0.1533

268.3

825.6

78.90

904.5

II72.8

66

9504

.490

298.8

6-43

•'555

269.3

824.8

78.97

903-7

"73-1

67

9648

.558

299.8

6-34

•1577

270.4

824.0

79.04

903.1

"73-4

68

9792

.626

300.1

6.25

•'599

271.4

823.2

79.11

902.3

II73-7

69

9936

.694

301.8

6.17

.1621

272.4

822.4

79.18

901.6

1174.0

70

10080

4.762

302.7

6.09

0.1643

273-4

821.6

79.25

900.9

"74-3

7i

10224

.830

3°3-7

6.00

.1665

274-3

820.9

7932

900.2

1174.6

72

10368

.898

304.6

5-93

.1687

275-3

820.J

79-39

899-5

1174.9

73

10512

.966

305-5

5-85

.1709

2/6.3

819.4

79-46

898.8

H75-1

74

10656

5-034

3°6-5

5-78

•1731

277.2

818.7

79-53

898.1

"75-4

75

10800

5.102

3°7-4

5-70

0-1753

278.2

817.9

79-59

897.5

"75-7

76

10944

.170

308.3

5-63

•1775

279.1

817.2

79-65

896.9

1176.0

77

11088

.238

309.2

5-57

.1797

280.0

816.5

79.71

896.2

1176.2

78

11232

.306

310.1

5-5°

.1818

280.9

815.8

79-77

895-6

1176.5

79

11376

•374

310.9

5-43

.1840

281.8

815.1

79-83

895.0

1176.8

80

11520

5-442

311.8

5-37

0.1862

282.7

814.4

79.89

894-3

1177.0

81

11664

.510

312.7

5-31

.1884

283.6

813.8

79-95

893-7

H77-3

82

11808

-578

3J3-5

5-25

.1906

284.5

813.0

80.01

893.1

1177.6

83

11952

.646

3I4-4

5-'9

.1928

285-3

812.4

80.07

892.5

1 177.8

84

12096

.714

3I5-2

5-*3

.1949

286.2

811.7

80.13

891.9

1178.0

85

12240

5.782

316.0

5-°7

0.1971

287.0

Sll.l

80.19

891.3

1178.3

86

11384

•850

316.8

5.02

•T993

287.9

810.4

80.25

890.7

1178.6

87

12528

.918

3J7-6

4.96

.2015

288.7

809.8

80.30

890.1

1178.9

88

12672

.986

318.4

4.91

.2036

289.5

809.2

80.35

889.5

1179.0

89

12816

6.054

319.2

4.86

.2058

290.4

808.5

80.40

888.9

"79-3

90

12960

6.122

320.0

4.81

0.2080

291.2

807.9

80.45

888.4

"79-5

9i

13104

.I9O

320.8

4.76

.2102

292.0

807.3

80.50

887.8

1179.8

92 i 13248

.258

321.6

4.71

.2123

292.8

806.7

80.56

887.2

1180.0

93

!3392

•327

322.4

4.66

•2145

293.6

806. 1

80.6 1

886.7

1180.3

94

13536

•396

323-I

4.62

.2166

294-3

805.5

80.66

886.1

1180.5

95

13680

6-463

323'9

4-57

0.2188

295.1

804.9

80.71

885.6

1180.7

96

13824

•S31

324.6

4-53

.2209

295-9

804.3

80.76

885.0

1180.9

97

I.396S

•599

325-4

4-48

•2231

296.7

803.7

80.8 1

884.5

1181.2

98

14112

• .667

326.1

4-44

.2252

297.4

803.1

80.86

884.0

1181.4

99

14256

•735

326.8

4.40

.2274

298.2

802.5

80.91

883.4

1181.6

SMITHSONIAN TABLES.

239

TABLE 249.

PROPERTIES OF STEAM.

British Measure.

"

g'S

•a

». E

CO

J:

i- S

S a

11

c

~ 3

0.5 .

.£ fe -S

oj £• O

i|

"«

8. j

0.3

*i .

"o S £>

«R.S .

1 is _

if-

'Soli'0

£ °. £ •

M C S

<U 3 3

(5S.ST

III

v P

H-o

III

'53 '.5 3

^ 5 o.

w a •

SaK

<v ~ ~ H

Slvrf

c s^H^

^ — —

-° o =

100

14400

6.803

327.6

4-356

0.2295

298.9

802.0

80.95

882.9

1181.8

IOI

14544

.871

328.3

.316

•2317

299.7

801.4

81.00

882.4

1182.1

IO2

14688

•939

329.0

.276

•2338

300.4

800.8

81.05

881.9

1182.3

103

14832

7.007

329.7

•237

•2360

30I.I

800.3

81.10

881.4

1182.5

104

14976

•075

330-4

.199

.2381

301.9

799-7

81.14

880.8

1182.7

105

15120

7-143

33, i

4.161

0.2403

302.6

799-2

81.18

880.3

1182.9

106

15264

.211

331-8

.125

.2424

303-3

798.6

81.23

879.8

1183.1

107

15408

.279

332-5

.088

.2446

3°4-0

798.1

81.27

879.3

1183.4

1 08
109

15696

•347
•415

333-2
333-8

•053
.018

•2467

.2489

3°4-7
3054

797-5
797.0

81.31
81.36

878.8
878.3

1183.6
1183.8

110

1 5840

7-483

334-5

3-984

0.2510

306.1

796.5

81.41

877.9

1184.0

in

15984

•551

335-2

•950

•2531

306.8

795-9

81.45

877.4

1184.2

112

16128

.619

335-8

.917

.2553

3°7-5

795-4

81.50

876.9

1184.4

"3

16272

.687

336.5

.885

•2574

308.2

794-9

8i-54

876.4

1184.6

114

16416

•757

337-2

•853

•2596

308.8

794-4

Si 58

875.9

1184.8

115

16560

7-823

337-8

3.821

0.2617

309-5

793-8

81.62

875.5

1185.0

116

16704

.891

338.5

.790

•2638

310.2

793-3

81.66

875.0

1185.2

1 17

16848

•959

339-'

.760

.2660

3I0.8

792.8

81.70

874.5

1185.4

118

16992

8.027

339-7

•730

.2681

3"-5

792-3

81.74

874.1

1185.6

119

17136

•095

340.4

.700

.2702

312.1

791.8

81.78

873.6

1185.7

120

17280

8.163

341.0

3-671

0.2724

312.8

791-3

81.82

873.2

1185.9

121
122

17424
17568

.231
•299

341.6
342.2

-643
.615

•2745
.2766

3I3-4
3'4-i

790.8
790-3

81.86
81.90

872.7

872.2

1186. i
1186.3

123

17712

-367

342-8

•587

•2787

3 '4-7

789-9

81.94

871.8

1186.5

124

17856

•435

343-5

.560

.2809

3I5-3

789.4

81.98

871.4

1186.7

125

18000

8-503

344-1

3-534

0.2830

316.0

788.9

82.02

870.9

1186.9

126

18144

•571

344-7

•507

.2851

316.6

788.4

82.06

870.5

1187.1

127

18288

•639

345-3

.481

.2872

3'7-2

787.9

82.09

870.0

1187.2

128

18432

.708

345-9

•456

.2893

3I7-8

787-5

82-13

869.6

1187.4

129

18576

.776

346.5

•431

.2915

318.4

787.0

82.17

869.2

1187.6

130

18720

8.844

347-1

3.406

0.2936

319.0

786.5

82.21

868.7

1187.8

'31

18864

.912

347-6

.382

•2957

3 '9-7

786.1

82.25

868.3

1188.0

132

19008

.980

348.2

•358

.2978

785.6

82.28

867.9

1188.1

133

19152

9.048

348.8

•334

.2999

320.9

785-1

82.32

867.5

1188.3

19296

.116

349-4

.310

.3021

321-5

784.7

82-35

867.0

1188.5

135

19440

9.184

349-9

3.287

0-3042

322.1

784.2'

82.38

866.6

1188.7

136

19584

.252

350-5

.265

•3063

322.6

783.8

82.42

866.2

1188.8

'37

19728

.320

•424

•3084

323-2

783-3

82.45

865.8

1189.0

138

19872

.388

351-6

.220

•3105

782.9

82.49

865.4

1 189.2

139

20016

•456

352.2

•'99

.3126

324-4

782.4

82.52

865.0

1 1 89.4

140

20160

9.524

352-8

3-r77-

0.3147

325-0

782.0

82.56

864.6

1 189.5

141

20304

•592

353-3

.156

.3168

781.6

82.59

864.2

1189.7

142

20448

.660

353-9

•135

.3190

326.1

781.1

82.63

863.8

1189.9

'43

20592

.728

354-4

.115

.3211

326.7

780.7

82.66

863.4

1 1 90.0

144

20736

.796

355-o

.094

•3232

327.2

780.3

82.69

863.0

1190.2

145

20880

9.864

355-5

3-074

0-3253

327-8

779-8

82.72

862.6

1190.4

146

21024

•932

356.0

•054

•3274

3284

779-4

82.75

862.2

1190.5

147

21168

IO.OOO

356.6

•035

.3295

328.9

779-0

82.79

86t.8

1190.7

148

21312

.068

357-1

.016

329-5

778-6

82.82

861.4

1190.9

149

21456

.136

357-6

•997

•3337

330-0

778.1

82.86

861.0

1191.0

SMITHSONIAN TABLES.

24O

TABLE 249.

PROPERTIES OF STEAM.

British Measure.

,

a

a —

c c

1*8

C

>- s

•SgJ

|S|

i i

c£

£._-

0.0

*i •

** o ^*

~ p . :

f Us .

5-^

s-c'tJ

s-gt!

s"H.

x £

S'S'y

•fi***-^

*o 5^

5 S re'2

£ £,!

~ o.«

•e'"1

tA — ?9

ii P fc

K 0

p •-,

,££.~ ~

r* ~"H

«J ~ SH

V <-, ~ £_ t

^ *-" *-' FH

*" — Q5

III

0 = 3
fill

II

H-S

111

£1!

KlLea

JS.S'cM

U « ""' .

c SJ2 •

fHLs

150

2l600

IO.2O4

358.2

2.978

0-3358

330-6

777-7

82.89

860.6

1191.2

151

21744

.272

358.7

.960

•3379

33I-I

777-3

82.92

860.2

1.91.3

J52

21888

•340

359-2

.941

-3400

331-6

776.9

82-95

859.9

1.91.5

22032

.408

359-7

•923

•3421

332.2

776.5 '

82.98

859-5

1.91.7

J54

22.76

•4/6

360.2

.906

•3442

332.7

776.1 j

83.01

859.I

1191.8

155

22320

10.544

360-7

2.888

0.3462

333-2

775-7 !

83.04

858.7

1.92.0

156

22464

.6.2

.871

•3483

333-8

775-3

83.07

858.3

1192.1

22608

.680

361 3

•854

•3504

334-3

774-9

83.10

858.0

1192.3

'58

22752

-748

362-3

.837

•3525

334-8

774-5

83-I3

857.6

.192.4

159

22896

.816

362.8

.820

•3540

335-3

774-1

83.16

857-2

1.92.6

160

23040

10.884

363-3

2.803

0-3567

335-9 .

773-7

83.19

856.9

1192.7

161

23184

•952

363-8

.787

.3588

336-4

773-3

83.22

856.5

1192.9

162

23328

1 1 .020

364-3

-771

•3609

336-9

7/2-9

83-25

856.1

1.93.0

163

23472

.088

364-8

•755

•3630

337-4

772.5

83.28

855.8

.193.2

164

236l6

•157

365-3

•739

•3650

337-9

772-1 ;

83-3I

855-4

i '93-3

165

23760

11.225

365-7

2.724

0.3671

338.4

77i-7

83-34

855-1

"93-5

166

23904

•293

366.2

.708

•3692

338.9

77'-3

83-37

8547

1.93.6

167

24048

.361

3667

•693

•3713

339-4

771.0

83-39

854.3

1.93.8

168

24192

•429

367.2

.678

•3734

339-9

770.6

83.42

854.0

' 193-9

169

24336

•497

367-7

.663

•3754

340-4

770.2

83-45

853.6

1.94.1

170

2448O

11-565

368.2

2.649

0-3775

340-9

769.8

83.48

853.3

11942

171

24624

•633

368.6

-634

•3796

341-4

769-4

83-5'

852.9

1194.4

172

24768

.701

369.1

.620

•3817

341-9

769..

83-54

852.6

1.94.5

173

24912

.769

369-6

.606

•3838

342.4

768.7

83-56

8522

1194.7

25056

-837

370.0

•592

•3858

342-9

768.3

83-59

851.9

1.94.8

175

252OO

11.0,05

370.5

2.578

0.3879

343-4

767.9

83.62

851.6

1194.9

176

25344

•973

371-0

•564

.3900

343-9

767-6

83.64

851.2

1195.1

177

25488

12.041

•550

.3921

344-3

767.2

83-67

850.9

1.95.2

178

25632

.109

371-9

•537

•3942

344-8

766.8

83-70

850.5

"954

179

25776

.177

372-4

524

.3962

345-3

766.5

83-73

850.2

"95-5

180

25920

12.245

372.8

2.5.0

0-3983

345-8

766.1

83-75

849.9

1195.6

181

26O64

•3'3

373-3

-497

.4004

346.3

765.8

83-77

849-5

1195.8

182

26208

.381

373-7

•485

.4025

346.7

765-4

83.80

849.2

H95-9

183

26352

•449

374-2

.472

.4046

347-2

765.0

83-83

848.9

1.96.1

184

26496

•51?

374-6

•459

.4066

347-7

764.7

83.86

848.5

1196.2

185

2664O

12.^85

37 5- !

2.447

0.4087

348.1

764-3

83.88

848.2

1196.3

1 86

26-84

•653

375-5

•434

.4108

348.6

764.0

83.90

847-9

1196.5

187

26928

.721

376.0

.422

.4129

349-1

763.6

83.92

847.5

1196.6

1 88

27072

•789

376.4

.410

.4150

349-5

763-3

83-95

847.2

1196.7

189

27216

.857

376.8

•398

.4170

350.0

762.9

83-97

846.9

1.96.9

19O

27360

12.925

377-3

2.386

0.4191

350-4

762.6

83-99

846.6

1197.0

IQI

27504

•993

377-7

•374

.4212

35°-9

762.2

84.02

846.3

1197.1

192

27648

13.06.

378.2

.362

•4233

35r-3

761.9

84.04

845-9

"97-3

'93

27792

.129

378.6

•351

•4254

351-8

761.6

84.06

845.6

1.97.4

194

27936

.197

379-0

•339

•4275

352.2

761.2

84.08

845-3

1197.5

195

2cSoSo

13-265

379-4

2-328

0.4296

3527

760.9

84.10

845.0

1197.7

196

28224

•333

379-9

•31?

.4316

353-1

760.5

84.13

844-7

1 197.8

197

28368

.401

380.3

.306

•4337

353-6

760.2

84.16

844-4

i .97.9

198

•285.2

.469

380.7

.295

•4358

354-0

.759-9

84.19

844.0

1198.1

199

28656

•537

381.1

.284

•4379

354-4

759-5

84.21

8437

1 198.2

SMITHSONIAN TABLES.

241

TABLE 249.

PROPERTIES OF STEAM.

British Measure.

«TJ

= "5

H3

>. B

.£ S*

u ft =

"v 2\°

•~J

!•

£

1st

-I*

^ S^J

II.S _

rt O c

C c C

&<?

3-§fi

S -~ D

3 ft

X <u

£ 'UV4~I

•SiTl'S

o o

c a. « .

= £•. rt

~ r^ S

"^ TJ

|||

III

« 2

el

H-0

£• a o

.if ° c

V J2 3
>3 0

!> o a

Baa

i 7s «*"*

>? sji^

o S^' •

Sg«

20

200

28800

13605

38l.6

2.273

0.4399

354-9

759-2

84.23

843.4

1198.3

2OI

28944

I3-673

382.0

.262

.4420

355-3

758.9

84.26

843.1

1 198.4

2O2

29088

I3-742

382.4

.252

.4441

355-8

758.5

84.28

842.8

1198.6

203

29232

13.810

382.8

.241

.4461

758.2

84-3°

842.5

1198.7

204

29376

13.878

383-2

.231

.4482

356'6

757-9

84-33

842.2

1198.8

205

29520

13.946

383.7

2.221

0.4503

357-1

757-5

84-35

841.9

1199.0

206

29664

14.014

384.I

.211

•4523

357-5

757-2

84-37

841.6

1199.1

207

29808

14.082

384.5

.201

•4544

357-9

756-9

84.40

841.3

1199.2

208

29952

14.150

384-9

.191

•4564

358-3

756.6

84.42

841.0

"99-3

209

30096

14.218

.l8l

.4585

358.8

756.2

84.44

840.7

1199.4

210

30240

14.386

3857

2.I7I

0.4605

359-2

755-9

84.46

840.4

1 1 99.6

211

30384

14.454

386.1

.162

.4626

359-6

755-6

84.48

840.1

1199.7

212

30528

14.522

386.5

.152

.4646

360.0

755-3

84.51

839.8

1199.8

213

30672

14.590

386.9

•143

.4666

360.4

755-0

84-53

839.5

1199.9

214

30816

14.658

387.3

•134

.4687

360.9

754-7

84-55

839.2

1 200. i

215

30960

14.726

387.7

2.124

0.4707

361-3

754-3

84-57

838.9

I2OO.2

216

31104

14.794

388.1

.115

.4727

361-7

754-0

84.60

838.6

1200-3

217

31248

14.862

388.5

,I06

•4748

362.1

753-7

84.62

838.3

I2OO-4

218

3 '392

14.930

388.9

.097

.4768

362.5

753-4

84.64

838.0

I2OO-5

219

31536

14998

.088

.4788

362.9

753-1

84.66

837-7

I2OO-7

SMITHSONIAN TABLES.

242

TABLE 250.

RATIO OF THE ELECTROSTATIC TO THE ELECTROMAGNETIC UNIT OF
ELECTRICITY (v) IN RELATION TO THE VELOCITY OF LIGHT.

Ratio of electrical units.

Reference.

Pate of
determina-
tion.

V

in cms. per sec.*

Determined by —

Publication.

Year.

1856

3.107 X io10

Weber & Kohlrausch .

Pogg. Ann.

1856

1868

2.842 X io10

Maxwell

Phil. Trans. .

1868

1869

2.808 X io10

i W. Thomson & King .

B. A. Report .

1869

1872

2.896 X io10

McKichan .

Phil. Trans. .

I872

I879

2.960 X ioi°

Ayrton & Perry .

Jour. Soc. Tel. Eng.

1879

I879

2.968 X io10

Hocken

B: A. Report .

I879

1880

2.955 X io10

Shida ....

Phil. Mag.

1880

1881

2.99 X io10t

Stoletow

Soc. de Phys. .

1881

1881

3.01 9 X io10

Klemencic .

Wien. Ber.

1884

1882

2.923 X io10

Exner ....

Wien. Ber.

1882

1883

2.963 X io10

J. J. Thomson

Phil. Trans. .

1883

1888

3.009 X io10

Himstedt

Wied. Ann. 35

1888

1889

2.981 X io10

Rowland

Phil. Mag.

1889

1889

3.000 X io10

Rosa ....

" " .

1889

1889

3.004 X io1''

W. Thomson

Phil. Mag.

1889

1890

2.995 X io10

J. J. Thomson & Searle

Phil. Trans. .

1890

* The results in this column correspond to a value of the B. A. ohm = .98664 X io9 cms. per sec. If we neglect
the first four determinations, and also that of Exner and Shida, because of their large deviation from the mean, the
remaining determinations give a mean value of 2. 9889 + .0137, a value which practically agrees with the best deter-
minations of the velocity of light. (Cf. Table 181.)
t Given as between 2.98 X io10 and 3.00 X io10.

SMITHSONIAN TABLES.

243

TABLE 251.

DIELECTRIC STRENGTH.

Difference of Electric Potential required to produce a Spark in Air.

(a) MEDIUM, AIR. ELECTRODE TERMINALS, FLAT PLATES.

Spark length

in
centimetres.

O.O[
0.02
O.O4
O.O7
O.IO
O.I4
O.2O
0.30
O.4O
0.50
0.60
0.80
I.OO

Difference of potential in volts required to produce a spark according to —

W. Thomson.1 De la Rue.2 MacFarlane.3 Bailie.4 Freyberg.5

79°
1340
1840
2940
4010

53°°

500
970
1900

4330

5740

762.0

10400

35_°7

5715

7818

9879

11925

13956
18006

4401

7653
10603

I343I
16341
19146
2S458
3*647

4344

7539
10671
13665
16293

19059
24465
28800

1 " Reprint of Papers on Elect, and Mag." p. 252. - " Proc. R. Soc." vol. 36, p. 151.

3 " Phil. Mag." vol. 10, 1880. 4 " Ann. de Chim. etde Phys." vol. 25, 1882.

5 " Wied. Ann." vol. 38, 1889.

(b) MEDIUM, AIR. ELECTRODE TERMINALS, BALLS OF DIAMETER d IN CENTIMETRES.

Experiments of Freyberg.

Spark length

in
centimetres.

d = o (points).

= 6.o

O.I
0.2

0-3
0-4
0.6

0.8

I.O
2.O

3720
4700
5300

6000
6900
8100

8600

IOIOO

13100

5050
8600

18400
19500
24600

30700

4660

9500

11700
14000

19300
23200

25800

35400

4560

8700
11600
14400
19500
24600
29000

8400

II200

14200

2CTOO
25800
29900

4530

7900

10500

I92OO
26OOO
3I6CO

From the above table it appears, as remarked by Freyberg, that for each length of spark there is a par-
ticular size of ball which requires the greatest difference of potential to produce the spark.

(c) COMPARISON OF RESULTS OF DETERMINATIONS, THE TERMINALS BEING BALLS.

Spark
length
in cms.

Difference of potential required to produce a spark in air according to —

Bailie.

Bichat and
Blondlot.'

Balls i centimetre diameter.

Paschen. Freyberg. Quincke.2

Balls 2 cms. diameter.

Bailie. Freyberg.

Balls 6 cms. diam.

•9
r.o

4590
8040
11190
13650
16410
19560
21690
23280
24030
24930

4200

8130

10860

14130

16800

19350
21030
23190
24540
25800

4860
8430
11670
14830
17760
20460
22640
24780

4660
9500
11670
13980
16800
19260
20970
23220
25110
25770

4830
8340
11670
14820
18030
20820
23670

4560
8700
"550
14400
17040
19470
22530
24630
27240
29040

4440
7920
11190
14010
16920
19980
22590
25770

4440

7680

10830

1350°
16530
19560
22620
26400
29220
33870

4530
7860
10470
12750
16410
19200
22590
26010
28770
31620

1 " Electricien," Aug. 1886.

2 " Wicd. Ann." vol. 19, 1883.

SMITHSONIAN TABLES.

244

TABLES 252, 253.
DIELECTRIC STRENGTH.

TABLE 252. — Effect of Pressure of the Gas on the Dielectric Strength.*

Length of spark is indicated by 7 in centimetres. The pressure is in centimetres of mercury at o° C.

Hydrogen.

Air.

Carbon dioxide.

7=0.2

7=0.4

7=o.6

7=0.2

7=0.4

7 = 0.6

7=0.2

7=0.4

/=o.6

2

5IO

606

-

819

I2O2

1536

II25

1446

1650

4

729

1017

1437

1140

1725

2289

I431 '

1971

23/3

6

945

i

333

1839

'455

2229

3012

'755

2484

8

1098

1572

2172

1740

2721

3684

2070

2913

3813 '

IO

1242

1806

2463

2004

3l86

4272

2355

3288

4278

15

1584

2376

333°

2664

4212

5736

2991

4227

5592

20

1866

2937

4020

3294

5205

70/4

37°5

5235

6801

25

2169

3444

4668

3816

6108

8346

4248

6l2O

8004

3°

2475

3957

533 i

4347

7O2O

9570

47°7

6921

9'47

35

2748

4407

5997

4845

7980

10797

5l63

7737

10293

40

3051

4863

6681

5349

8853

12009

5772

8543

"397 '

45

3339

5334

7347

9639

13224

6222

93°3

12483

5°

3606

5829

797i

•6288

I043I

14361

6489

10038

13557

55

2834

6294

8583

6711

II259

I544I

6789

10650

14610

60

4107

6747

9222

7i34

12084

16548

7197

"397

15702

65

4476

7197

9867

7569

12885

17688

7605

12114

16740

70

473 i

7629

10476

8016

I37IO

18804

8001

12816

17727 ]

75

4914

8031

11040

8487

19896

8388

13506

18705 .

Paschen deduces from the above, and also shows by separate experiments, that if the product of the pressure
of the gas and the length of spark be kept constant the difference of potential required to produce the spark

also remains constant.

In the following short table 7 is length of spark, P pressure, and V difference of potential, the unit being
the same as above. The table illustrates the potential difference required to produce a spark for different

values of tl.e product 1. P.

1. P.

Kfor H

V for Air.

I' for CO,

,/,

K for H

V for Air.

V for CO2

O.2

456

669

873

6.0

2481

4251

4443

0.4

567

837

II IO

IO.O

3507

6162

6198

0.6

660

996

1281

2O.O

5*35

10392

IOOII

I.O

846

1326

1599

30.0

8004

13448

13527

2.0

1427

2019

2271

45-0

11013

19848

18705

4-0

1884

3216

3468

TABLE 253. — Dielectric Strength (or Difference of Potential per Centimetre of Spark Length) of Different

Substances, in Kilo Volts, t

o ^

$£

•K-S

Substance.

% "

Substance.

Substance.

aj C
-=• V

v •-

o *

Q ">

Q "> ,

Air (thickness 5 mm.)

23.8

Beeswaxed paper .

54°-

Kerosene oil . . .

50.

Carbon dioxide " . .

22.7

Paraffined paper

360.

Oil of turpentine .

94- i

Coal gas " . .

'5-1

Paraffin (solid) . .

130.

Olive oil ....

82.

Hydrogen " . .

22.2

Paraffin oil ...

87-

Oxygen " . .

22-3

Paraffin (melted) .

56. :

1

i

SMITHSONIAN TABLES.

* Paschen.

t MacFarlane and Pierce, " Phys. Rev." vol. i, p. 165, 1893.

245

TABLE 254.
COMPOSITION AND ELECTROMOTIVE FORCE OF BATTERY CELLS

The electromotive forces given in this table approximately represent what may be expected from a cell in good work-
ing order, but with the exception of the standard cells all of them are subject to considerable variation.

(a) DOUBLE FLUID BATTERIES.

Name of
cell.

Negative pole.

Solution.

Positive
pole.

Solution.

K.M.F.
in voits.

Bunsen . .

Amalgamated zinc

j i part H2SO4 to /
1 12 parts H2O . J

Carbon

Fuming H2NOa

1.94

"

"

"

<«

HNO3, density 1.38

1.86

Chromate .

It U

' i2partsK2Cr2O7 1
to 25 parts of i
H2SO4 and 100 f
parts H2O . . J

«

( i part H2SO4 to }
\ 12 parts H2O . \

2.OO

«

„

$ i part H2SO4 to I
"( 12 parts H2O . {

H

( 12 parts K2Cr2O7 (
J to 100 parts H2O \

2.03

Daniell* .

«

( i part H2SO4 to J
( 4 parts H2O . }

Copper

( Saturated solution )
] ofCuSO4+5H2O(

1. 06

<< :

•«,

( i part H2SO4 to (
I 1 2 parts H2O . i

-

«

1.09

11

u «

( 5% solution of )
\ ZnSO4 + 6H2O (

«

ii

1. 08

It

(I II

j i part NaCl to }
( 4 parts H2O . (

"

H

1.05

Grove .

« 11

( i part H2SO4 to /
( 12 parts H2O . )

Platinum

Fuming MNO3 . .

i-93

. .

«

Solution of ZnSO4

"

HNO3, density 1.33

1.66

" . .

« «

( H2SO4 solution, |
( density 1.136 . )

"

Concentrated HNOg

i-93

" . j

a

( H2SO4 solution, I
\ density 1.136 . j

«

HNOa, density 1.33

i-79

« . j

.«

( H2SO4 solution, 1
j density 1.06 . )

«

«

1.71

u

„

( H2SO4 solution, )
\ density 1.14 . )

H

HNO3) density 1.19

1.66

(i

u u

( H2SO4 solution, \
I density 1.06 . j

«

.,

r.6i

u

« «

NaCl solution . .

"

" density 1.33

1.88

Marie Davy

,.

( i part H2SO4 to (
\ 12 parts H2O j

Carbon

C Paste of protosul- )
< phate of mercury >
( and water . . . ;

1.50

Partz . .

X • <

Solution of MgSO4

"

Solution of K2Cr2O7

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.

246

TABLE 254.
COMPOSITION AND ELECTROMOTIVE FORCE OF BATTERY CELLS.

Name of cell.

Negative
pole.

Solution.

Positive pole.

E. M. F.

in volts.

(V) SINGLE FLUID BATTEKIBS.

Leclanche . .

Chaperon . . .
Edison-Lelande .
Chloride of silver
Law

Amal. zinc
Zinc . .

Amal. zinc
Zinc . .

( Solution of sal-ammo- )
( niac ji

i Solution of caustic |
\ potash j

( 23 % solution of sal- )
1 ammoniac . . . J

15%
f ipt. ZnO,ipt.NH4Cl,l
1 3 pts. plaster of pan's, !
| 2pts.ZnCl2, and water j
[ to make a paste . . J
\ Solution of chromate 1
} of potash . . . . j
!I2 parts K2Cr2O7 + )
25 parts H2SO4 +
i oo parts H2O . . j
( i part H2SO4 + )
1 2 parts H2O -f
f i part CaSO4 . . )
H20

f Carbon surround- )
J ed by powdered
j carbon and perox- j
{ ide of manganese j

Copper and CuO

( Silver surrounded )
( by silver chloride J
Carbon ....

Cadmium . . .
Copper ....

1.46

0.98
0.70
I. O2

r-37
J-3
i. 08

2.OI

°34
0.98

Dry cell (Gassner)

Poggendorff . .
«

J. Regnault . . .
Volta couple . .

(C) STANDARD CELLS.

Kelvin, Gravity, )
Daniell . . . J

Clark standard .

Bailie & Ferry .
Gouy ....

Amal. zinc

j ZnSO4 solution, den- /
} sity 1.40 . . . . f

[ Mercurous sulphate in
paste with saturated
solution of neutral f
[ ZnSO4

( Electrolytic cop- )
< per in CuSO4 sol. ?
f density i.io . . )

Mercury ....

( Lead surrounded )
1 by powdered
( PbCl2 . . . .)

Mercury ....

C 1.072 [I
< — .00016
M^-i5)]

( i-434t'

^—.00077 j

((^-15)] !
,
f 0.50 tem-

| perature
•{ coeffic't
j about
[ .0001 1

( I-387 [f
< — .0002

( ('-«)]

( Zinc chloride, density i

1 I.I C7 . . (

( Oxide of mercurv in a 1
10 % sol. of ZnSO4 [
f (paste) )

Lodge's standard cell and Fleming's standard cell are, like the Kelvin cell above, modifications of the Dan-
iell zinc-zinc sulphate, copper-copper sulphate cell.

(d) SECONDARY CELLS.

Faure-Sellon- )
(Volckmar) . )

Regnier (i) . .

r (2) • •

Main ....

Lead . .

Copper .

Amal. zinc
Amal. zinc

( H2SO4 solution of )
( density i.i . . . J

CuSO4 + H2SO4 . .

ZnSO4 solution . . .
H2SO4 density ab't i.i

PbOo

2.2*

t 1.68 to
< 0.85, av-
( erage 1.3.
2.36
2.50

" in H2SO4 . .
«

* F. Streintz gives the following value of the temperature variation — - at different degrees of charge ;

E. M. F.

**/*x«,

E. M. F.

«/*x*

E. M. F.

«w~

1.9223 •

1.9828

140

228

2.0031
2.0084

335
285

2.0779
2.2070

130

73

2.0105

255

SMITHSONIAN TABLES.

247

TABLE 255.

THERMOELECTRIC POWER.

The thermoelectric power of a circuit of two metals at mean temperature t is the electromotive force in the circuit
for one degree difference of temperature between the junctions. It is expressed by dE j dt = A + Bt, when
dE / dt = o, t = — A / JS, and this the neutral point or temperature at which the thermoelectric power vanishes.
The ratio of the specific heat of electricity to the absolute value of the temperature t is expressed by — B for any
one metal when the oilier metal is lead. The thermoelectric power of different couples may be inferred from the
table, as it is the difference of the tabulated values with respect to lead, which is here taken as zero. The table
has been compiled from the results of Becquerel, Matthieson, and Tail. In reducing the results the electromotive
forces of the Grove's and the Daniell cells have been taken as 1.95 and 1.07 volts respectively.

Thermoelectric power

Neutral

Substance.

A

B X 10-"-

at mean temp, of
junctions (microvolts).

point
A

Author-
ity.

20° C.

.50° C.

B

Aluminium ....
Antimony, comm'l pressed wire

0.76

—°-39

0.68
—6.0

0.56

'95

T

M

" axial

—

—

2''. 6

_

_

"

" equatorial

-

-

-26.4

-

-

"

" ordinary .

-

-

• —17.0

-

-

E

1 1.94

c.o6

j -j Q r

14 47

^ ~/c

T

M

;)•'-"-'

-

12-7

_

B

Arsenic

—

-

13.56

-

M

Bismuth, comm'l pressed wire .

-

-

97.0

-

-

"

" pure " " .

-

-

89.0

-

-

"

" crystal, axial . . •

-

-

65.0

-

-

"

" equatorial

-

-

45-°

-

-

"

" commercial . .1

- '.

-

-

39-9

-

B

Cadmium ......

-2.63

—4.24

-3-48

—4-75

—62

T

" fused .

-

-

—2-45

-

15

Cobalt .....

-

-

22.

-

M

Copper

—1-34

—0.94

— 1.52

— i .81

— 143

T

" commercial .

—

—

O. IO

—

M

" galvanoplastic

-

-

-3-8

-

-

"

Gold

-

—

1.2

-

-

"

"

-2.80

— I.OI

3-D

—3-3°

—277

T

Iron ......

—17-15

4.82

— 1 6.2

—14.74

356

"

" pianoforte wire .

-

— r7-5

M

" commercial

-

-

12. IO

-

B

" "

- j

-

-

9-IO

• -

"

Lead

-

0.00

o.oo

0.00

-

—

j Magnesium ....

2.22

0.94

—2.03

— i-7S

236

T

Mercury .....

-

-

0.413

"M ,

" .....

-

-

-

3-3°

-

B

Nickel

-

-

-

^•S0

-

"

" (—18° to 175°)

21.8

5.06

22.8

24-33

-438

T

" (2500-300°) .

83-57

—23.84

-

"

(above 340°) .

3-°4

5.06

-

-

-

"

Palladium

6.18

3-55

6.9

7.96

—174

"

" .....

-

-

6.9

-

1!

Phosphorus (red)

-

-

—29.9

-

M

Platinum

-

-

—0.9

-

-

"

" (hardened)

—2-57

0.74

—2.42

2. 2O

347

T

" (malleable) .

0.60

1.09

8.82

I.I5

—55

"

" wire ....

-

-

-

—0.94

B

" another specimen

-

-

-

2.14

-

"

Platinum-indium alloys :

i

85% Pt -(- 15 % Ir

—7.90

— 0.62 j

-8.03

—8.21

—1274

T

9o%Pt+lo%Ir ., ..

—5-90

'•33

-5-63

— 5-23

444

"

95 % Pt -|- 5 % Ir • . •

-6.15

—0-55

—6.26

-6.42

— 1118 ,

"

Selenium .....

—807.

—

-

M

Silver .....

— 2.12 ;

—1-47

—2.41

—2.86

—144

T

" (pure hard)

—3.00

-

M

" wire .

—

_

_

—2.18

_

B

Steel . .'. . ...

— 11.27

3-25 '

— 10.62

— 9.65

347

T

Tellurium . • •».•-.

—502.

-

M

" . '

-

-

—429-3

-

B

Tin (commercial)

-

-

-

—°-33

-

"

" . .. . .

i

-

O.I

-

M

"

0-43

— 0.55

°-33

0.16

78

T

Zinc . . . .

—2.32

— 2.38

—2.79

— 3-51 :

-98

"

" pure pressed

-

- :

—3-7

-

M

B = Ed. Becquerel, " Ann. de Chim. et de Phys " [4] vol. 8. M =. Matthieson, " Pngg. Ann." vol. 103,
T = Tail, " Trans. R. S. E." vol. 27, reduced by Mascart. reduced by Fleming Jenkin.

SMITHSONIAN TABLES.

248

TABLE 256.

THERMOELECTRIC POWER OF ALLOYS.

The thermoelectric powers of a number of alloys are given in this table, the authority being Ed. Becquerel. They are
relative to lead, and for a mean temperature of 50° C. In reducing the results from copper as a reference metal,
the thermoelectric power of lead to copper was taken as — 1.9.

Substance.

Relative
quantity.

Thermo-
electric
power in
microvolts.

Substance.

Relative
quantity.

Thermo-
electric
power in
microvolts.

Antimony .
Cadmium .

806)
696)

227

Antimony .
Bismuth

11

8.8

Antimony .
Cadmium . . .

J

146

Antimony .
Iron ....

4[
1 )

2-5

Zinc . '-'.

I)

Antimony .

Si

Antimony .

806)

Magnesium

i\

1.4

Cadmium .
Bismuth . . x .

696 >
121 )

137

Antimony .
Lead ....

?!

—0.4

Antimony . . .

806)

f\ r

Bismuth . w

-

-43-8

Zinc ....

406 5

95

Bismuth

., )

Antimony .

806)

Antimony .

1 1,

—33-4

Zinc ....
Bismuth

406 [

121 )

8.1

Bismuth
Antimony .

ii

—51-4

Antimony .
Cadmium .

J

>-,£.

Bismuth
Antimony .

!l

—63.2

Lead ....
Zinc ....

;j

70

Bismuth
Antimony .

'?(

—68.2

Antimony .
Cadmium .

>

Bismuth . .
Antimony .

"i

—66.9

Zinc ....

i

46

Bismuth

2 )

Tin ....

• J

Tin . ...

if

60

Antimony .

Bismuth

10 (

Zinc ...

43

Selenium .

I (

—24-5

Tin ....

Bismuth

12 |

Antimony .

12)

Zinc ....

— 31-1

Cadmium .

10 >

35

Bismuth

12 /

'

Zinc ....

3)

Arsenic

— 46.0

Antimony .

IO I

Bismuth

j )

S-Q ,

Tellurium .

IO.2

Bismuth sulphide .

L!

OO.I

TABLE 257.
NEUTRAL POINTS WITH LEAD.*

Substance.

Temp.
C.

Substance.

Temp.
C.

Bismuth .

—580°

Zinc .

-95°

Nickel .

—424

Cadmium .

—59

Gold . .

-276

Platinum .

-56

Argentan

-238

Tin . . .

75

Cobalt .

—228

Rhodium .

132

Palladium

— 172

Ruthenium

136

Antimony

-I56

Aluminium

212

Silver . .

— 144

Magnesium

239

Copper .

—132

Iron . . .

356

TABLE 258.

SPECIFIC HEATS OF ELECTRICITY.t

The numbers are the coefficients B in the equation
jzf

—- = A + Bt, and have to be multiplied by the absolute

at

temperature T to give the specific heat of electricity. (See

also Table 255.)

Metal.

Sp.ht. of el.

Metal.

Sp. ht. of el.

T

r

Alumin-

Magnesium

— .00094

ium .

.00039

Nickel :

Antimony

.O222I

To 175° C. .

— .00507

Argentan

—.00507

250°-3IO° .

.00219

Bismuth .
Cadmium

—.01073
.00425

Above 340° .
Platinum (soft)

—•00351
— .00109

Cobalt .

— .OII4I

Palladium . .

— -00355

Copper .
Gold . .

.00094
.OOIOI

Rhodium . .
Rubidium . .

— .00113
— .00206

Iron . .

— .00481

Silver . .

.00148

Iridium .

.00000

Tin ....

.00055

Lead . .

.00000

Zinc ....

.00235

* Tail's " Heat," p. 180.

t Calculated from a table given by Tait by assuming the electromotive force of a Grove's cell — 1.95 volts.

SMITHSONIAN TABLES.

249

TABLE 259.

THERMOELECTRIC POWER OF METALS AND SOLUTIONS.*

Thermoelectric power of circuits, the two parts of which are either a metal and a solution of a salt of that metal or
two solutions of salts. The concentration of the solution was such that in 1000 parts of the solution there was
one half gramme equivalent of the crystallized salt. The circuit is indicated symbolically ; for example, Cu and
CuSO4 indicates that the circuit was partly copper and partly a solution of copper sulphate.

Thermoelec-

Substances forming circuit.

tric power in

Insoluble salts mixed with a solution of

microvolts.

the corresponding zinc or cadmium salts

for the purpose of acting as a conductor.

Cu and CuSC>4 .

754

The other part of the circuit was the metal

Zn and ZnSC>4
Cu and CuAc (acetate)
Pb and PbAc

760
660
176

of the insoluble salts. The results are com-
plex and of doubtful value.

Zn and ZnAc

693

Cd and CdAc .

5°3

Zn and ZnCl2 . ,
Cd and CdCl2 -

s

562
562

Substances forming circuit.

Thermoelectric
power in
microvolts.

Zn and ZnBr2

632

Zn and ZnI2 .

602

Cd and CdI2 ...

594

Ag and AgCl in ZnCl2

M3

Ag and AgCl in CdCl2

310

CuSO4 and ZnSO4 . .

40

Ag and AgBr in ZnBr2 . ;

327

CuAc and ZnAc .

8

Ag and AgBr in CdBr2

461

ZnAc and CdAc . . .

o

Ag and Agl in ZnI2 . .

414

CuAc and CdAc . ."

o

Ag and Agl in CdI2 .

unsuccessful

PbAc and ZnAc .

73

Hg and Hg2Cl2 in ZnCl2

680

PbAc and CdAc .

54

Hg and Hg2Cl2 in CdCl2 .-

673

PbAc and CuAc .

'33

Hg and Hg2Br2 in ZnBr2 .

650

ZnCl2 and CdCl2

9

Hg and Hg2Hr2 in CdBr2 .

815

ZnBr2 and CdBr2

15

Hg and Hg2I2 in ZnI2.

948

ZnI2 and CdI2 . . .

82

Hg and Hg2I2 in CdI2

891

TABLES 26O, 261.

PELTIER EFFECT.

TABLE 260. —Jahn's Experiments.!

Current flows from copper to metal mentioned.
Table gives therms per ampere per hour.

Metals.

Therms.

Cadmium

— 0.616

Iron ....

—3-6I3

Nickel ....

4.362

Platinum

0.320

Silver ....

—0.413

Zinc ....

^•585

CdtoCdSC-4

4.29

Cu to CuSC>4

—i-4

Ag to AgNOs .

7-53

Zn to ZnSC>4 . . ]

—2.14

TABLE 261. — Le Roux's Experiments.

Table gives therms per ampere per hour, and current flows
from copper to substance named.

Metals.

Therms.

Antimony (Becquerel's) §
(commercial) .

13.02
4.8

Bismuth (pure) . .
" (Becquerel's) || .

I9.I
25.8

Cadmium .....
German silver . .

iron . • .

0.46

2-47

2.C

Zinc ......

O 1Q

* Gockel, " Wied. Ann." vol. 24, p. 634.
t " Wied. Ann.'' vol. 34, p. 767.
t " Ann. de Chim. et de Phys.'' (4) vol. 10, p. 201.
'

SMITHSONIAN TABLES.

. . . . , . .

Becquerel's antimony is 806 parts Sb +406 parts Zn
I Becquerel's bismuth is 10 parts Bi -f- 1 part Sb.

121 parts Bi.

25O

TABLE 262.

CONDUCTIVITY OF THREE-METAL AND MISCELLANEOUS ALLOYS.

Conductivity Ct— C0 (i + at + bfl).

Metals and alloys.

Composition by weight.

&

a X io6

6X io9

C

S

Gold-copper-silver . /. .

58.3 Au 4- 26.5 Cu + 15.2 Ag

7.58

574

924

I

" " "... 66.5 Au 4- J5-4 Cu + 18.1 Ag

6.83

529

93

I

" . . . 7.4 Au + 78.3 Cu 4- 14-3 Ag

2806

1830

7280

1

( 12.84 Ni 4- io. so Cu 4- 1
Nickel-copper-zmc . . - j 6.5/Z,i b^volume . .(

4.92

444

5'

I

Brass . ' Various

I2.2-I5.6

1-2 X IO3

2

" hard drawn . . . 70.2 Cu + 29.8 Zn ....

12. l6

-

3

" annealed .... " . . . .

'4-35

-

—

3

German silver .... Various

3-5

-

-

2

( 6o.i6Cu 4- 25-37 Zn4- )

" .... ? 1 4.03 Ni 4- -30 l*'e with trace >

3-33

360

-

4

( of cobalt and manganese . )

Aluminium bronze . . • .

7-5-8-5

5-7 X io2

-

2

Phosphor bronze . ".- .

- - -

IO-2O

-

-

2

Silicium bron/e ....

41

_

_

e

Manganese-copper .

30 Mn 4~ 70 Cu

T-
I.OO

40

j
4

Nickel-mangane:-e-copper

3 Ni 4~ 24 Mn 4- 73 Cu . .

2.IO

—3°

-

4

( 18.46 Ni 4-6i. 63 Cu + }

Nickelin

•? 19.67 Zn 4~ 0.24 Fe 4"

-, QJ

•?oo

_

4

( 0.19 Co 4- o.iSMn . . .)

'

j

( 25.1 Ni4-744iCu4- J

Patent nickel .

? 0.42 Fe + 0.23 Zn 4-

2.92

190

_

4

( 0.13 Mn 4/ trace of cobalt )

-/

Rheotan ....

( 53.28 Cu 4- 25.31 Ni4- )
' 16.89 Zn 4- 4.46 Fe 4-

I.QO

410

4

Copper-manganese-iron .

;/
4.98

1 20

6

91 Cu 4" 7-1 Mn 4- i-9 Fe .

" " "

70.6 Cu + 23.2 Mn 4- 6.2 Fe

1.30

22

-

6

" " "

69.7 Cu -f 29-9 Ni 4- 36 Fe .

2.6O

1 2O

-

7

Temp. C.°

Manganin

84 Cu + i2Mn4-4Ni . .

2.33

25

IC-2O

8

J
14.

2O—1O

8

ii

4

T-

A

.v jw

10— m

8

41

*T
I

J O J

3 S — 40
40—41;

8
8

a

a

4

1

ttv H J

45 — 5^*

8

>i

.

.Q_rc

8

U 1

— 4

^-68

8

T

jj

1 Matthieson. 8 W. Siemens 5 Van der Ven. 7 Feusner.

2 Various. 4 Feusner and Lindeck. 6 Blood. 3 Lindeck.

SMITHSONIAN TABLES.

251

TABLE 263.

CONDUCTING POWER OF ALLOYS.

This table shows the conducting power of alloys and the variation of the conducting power with temperature.*

10°
The values of C0 were obtained from the original results by assuming silver = - — ~- mhos. The conductivity is

taken as Ct — C0 (i — at -\- fit*), 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 the

formula /' = /'c — where/ is the observed and /' the calculated conducting power of the mixture at 100° C.,
and P, is the calculated mean variation of the metals mixed.

Weight %

Volume %

Variation per 100° C.

of first named.

JO4

Observed.

Calculated.

GROUP i.

Sn6Pb

77.04

87.06

7.C7

7890

8670

70. 1 8

29.67

82.41

83.10

9.18

4O8O

I iSjO

28.89

7O.O7

SnZn

78.06

77.71

10.56

7880

8720

7O. I 2

J J
7O.l6

PbSn

64.13

6.4O

7780

8420

29.41

29.10

^A 76

16 06

16 16

7780

8OOO

29.86

2Q.67

SnCdi

27.O1;

27. CO

17.67

78 TO

2Q.o8

7O.2 ^

CdPb6

7.77

C.-78

7 TOO .

727O

27.74

27.60

GROUP 2.

Lead-silver (Pb2oAg) .

95-°5

94-64

5.60

3630

7960

28.24

19.96

Lead-silver (PbAg)

48.97

46.90

8.07

1960

3100

16-53

7-73

Lead-silver (PbAg2) .

32-44

30.64

13.80

1990

2600

I7-36

10.42

Tin-gold (Sni2Au) . .

77-94

90.32

5-20

3080

6640

24.2O

14.83

" " (Sn5Au) . .

59-54

79-54

3-03

292O

6300

22.9O

5-95

Tin-copper ....

92.24

93-57

7-59

3680

8130

28.71

19.76

" t . . . .

80.58

83.60

8.05

3330

6840

26.24

14-57

« t . . . .

12.49

14.91

5-57

547

294

S.l8

3-99

" t. . . .

10.30

'2-35

6.41

666

1185

5-48

4.46

" t. . . .

9.67

11.61

7-64

691

3°4

6.6O

5.22

" t . . . .

4.96

6.O2

12.44

995

705

9-25

7-83

" t - - • •

i-»5

1.41

39-41

2670

5070

21-74

20-53

Tin-silver

QI.7O

q6. C2

7.81

7820

8190

30.00

23.31

7C.CI

8.65

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

1 0.08

t . . .

16-53

23.61

13-44

1880

1800

12.80

12.30

" t . . .

8.89

10.88

29.61

2040

3°3°

17.41

17.42

" t . . .

4.06

5-03

38.09

2470

4100

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 — — — tit, where y is the

temperature coefficient and _r the specific resistance, in and n being constants. If a be the temperature coefficient at
o° C. and s the corresponding specific resistance, s (a -f- m) = n.

For platinum alloys Barus's experiments gave in — — .000194 ar>d " — -°378.

For steel m =r — .000303 and n = .0620.
Matthieson's experiments reduced by Barus gave for

Gold alloys m =. — .000045, n =r .00721.

Silver " m = — .000112, «=: .00538.

Copper " m =r — .000386, n rr .00055.

* From the experiments of Matthieson and Vogt, " Phil. Trans. R. S." v. 154.
t Hard-drawn.

SMITHSONIAN TABLES.

252

TABLE 263.

CONDUCTING POWER OF ALLOYS.

GROUP 3.

Alloys.

Weight %

Volume %

C0

IO4

rtX io6

6X 10°

Variation per 100° C.

of first named.

Observed.

Calculated.

Gold-copper t . . .

99-23

98-36

35.42

2650

4650

21.87

23.22

" t . . .

90.55

81.66

10.16

749

81

7.41

7-53

Gold-silver t . . . .

87.95

79-86

13.46

1090

793

10.09

9-65

" * . « •.

87.95

79-86

13.61

.1140

1160

10.21

9-59

" t . ! ! .'

64.80

52.08

9.48

673

246

6.49

6.58

" * ....

64.80

52.08

9.51

721

495

6.71

6.42

" t '.'.'.'.

31-33

19.86

13.69

885

53i

8.23

8.62

" * ....

3J-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-Q2

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-°5

11.38

774

656

7.08

7-25

t

5.00

2.51

19.96

1240

1150

11.29

11.88

Palladium-silver t • •

25.00

23.28

5-38

324

154

3-40

4.21

Copper-silvert • • •

98.08

98.35

56.49

3450

7990

26.50

27.30

t . - .

94.40

95-17

5J-93

3250

6940

25-57

25.41

t . . .

76.74

77.64

44.06

3°3°

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

4360

23.17

25-57

t - . .

I-31

'•53

5°-3°

4120

8740

26.51

29.77

Iron-gold t . . . .

13-59

27-93

i-73

349°

7010

27.92

14.70

" " t . . . .

9.80

21. 18

1.26

2970

1 220

17-55

1 1. 20

" " t . . . -

4.76

10.96

1.46

. 487

103

3-84

13.40

Iron-copper t ...

0.40

0.46

24.51

r55Q

2090

13-44

14.03

Phosphorus-copper t -

2.50

-

4-62

4/6

»45

-

-

" t .

0.95

-

14.91

1320

1640

—

-

Arsenic-copper t • •

5.40

_

3-97

5i6

989

-

-

" t . .

2.80

-

8.12

736

446

-

-

« t . .

trace

38-52

2640

4830

* Annealed.
SMITHSONIAN TABLES.

t Hard-drawn.

253

TABLE 264.

SPECIFIC RESISTANCE OF METALLIC WIRES.

This table is modified from the table compiled by Jenkin from Matthieson's results by taking the resistance of silver,
gold, and copper from the observed metre gramme value and assuming the densities found by Matthieson, namely,
10.468, 19.265, and 8.95.

Substance.

Resistance at o° C. of a
wire one cm. long, one
sq^cm. in section.

Resistance at o° C. of a
wire one metre long,
one mm. in diam. "

Resistance at o° C. of a
wire one metre long,
weighing one gramme.

Resistance at o° C. of a
wire one foot long,
nfon in. in diam.

Resistance at o° C. of a
wire one foot long,
weighing one grain.

Percentage increase of
resistance for i° C. in-
crease of temp, at 20° C. j

Silver annealed .

1.460 X JO"6

0.01859

•1523

8.781

.2184

0-377

" hard drawn . ,

1.585 «

0.02019

.1659

9-538

•2379

--

Copper annealed . . .

1.584 "

0.02OI7

.1421

9.529

.2037

0.388

" hard drawn .

1.619 "

O.O2O62

.1449

9.741

.2078

-

Gold annealed .

2.088 "

0.02659

.4025

12.56

•5771

0.365

" hard drawn

2.125 "

0.02706

.4094

12.78

.5870

-

Aluminium annealed .

2.906 "

0.03699

•0747

17.48

.1071

-

Zinc pressed . . .

5.613 "

0.07146

.4OI2

33-76

•5753

0-365

Platinum annealed . . .

9-035 "

O.II50

J-934

54-35

2.772

-

Iron

9-693 "

0.1234

•7551

58-31

1.083

-

Nickel "

12.43

0-1583

1-057

74.78

i-5i5

-

Tin pressed

13.18 "

0.1678

.9608

79.29

i-377

0-365

Lead "

19.14 "

0.2437

2.227

115.1

3-193

0.387

Antimony pressed

35-42 "

0.4510

2-379

213.1

3.410

0.389

Bismuth "

130.9

1.667

12.86

787-5

18.43

o-354

Mercury "

94.07

1.198

12.79

565-9

18.34

0.072

Platinum-silver, 2 parts Ag, )
i part Pt, by weight . )

24-33 "

0.3098

2.919

146.4

4.186

0.031

German silver . .

20.89 "

0.2660

1.825

125-7

2.617

0.044

Gold-silver, 2 parts Au, )
i part Ag, by weight . ;

10.84 "

0.1380

1.646 .

65.21

2-359

0.065

SMITHSONIAN TABLES.

254

TABLE 265.

SPECIFIC RESISTANCE OF METALS.

The specific resistance is here given as the resistance, in microhms, per centimetre of a bar one square centimetre in

cross section.

Substance.

Physical state.

Specific resistance.

Temp. C.

Authority.

Aluminium

_

2.9-4.5

O

Various.

Antimony .

-

35-4-45-8

O

"

"

Solid

182.8

Melting-point

De la Rive.

"

Liquid

129.2

"

"

"

-

137-7

860

"

Arsenic

/

• 33-3

o

Matthieson and

Vogt.

Bismuth .

Electrolytic soft

108.0

O

Van Aubel.

"

" hard

108.7

o

"

.

Commercial

110-268

o

Various.

Boron . .

Pulverized and com-

pressed

8 X io10

_

Moissan.

Cadmium .

-

6.2-7.0

-

Various.

"

Solid

16.5

3'8

Vassura.

"

Liquid

37-9

3i8

"

Gold . .

—

2.04-2.09

o

Various.

Calcium

-

7-5

1 6.8

Matthieson.

Cobalt . .

-

9.8

o

"

Copper . .

Commercial

1.58-2.20

0

Various.

Iron . . .

"

9.7-12.0

o

<>

"...

Electrolytic

II. 2

Ordinary

Kohlrausch.

"...

"

105.5

Red heat

"

"...

"

II4.8

Yellow heat

(i

"...

"

II8.3

Iron magnetic

heat

M

Steel. . .

Cast

I9.I

Ord. temp.

"

"...

"

85.8

Red heat

((

"...

"

1044

Yellow heat

II

"...

"

"3-9

Nearly white

heat

(I

"...

Tempered glass hard

45.7 (i -f .00161*)

*

Barus and

Strouhal.

"...

' light yellow

28.9 ( i + .00244/1)

*

"...

' yellow

26.3 (i + .00280*)

*

"...

blue

20.5(1 + .00330*)

*

"...

light blue

18.4(1 +.00360*)

*

"...

' soft

15.9 (i + .00423*)

t

Iron . . .

Cast, hard

97.8

o

"...

" soft

74-4

o

Indium . .

-

8.38

o

Erhard.

Lead . .

—

18.4-19.6

0

Various.

Lithium

—

8.8

20

Matthieson.

Magnesium

-

4.1-5.0

o

Various.

Nickel . .

-

10.7-12.4

0

"

Palladium .

-

10.6-13.6

o

"

Platinum .

-

9-o-i5-5

o

"

Potassium .

-

25- l

0

Matthieson.

H

Fluid

50.4

IOO

"

Silver . .

_

i'S-i-7

o

Various.

Strontium .

-

25-!3

20

Matthieson.

Tellurium .

-

2.17 X io5

19.6

11

"

-

55-05

294

Vincentini and

Omodei.

Tin ...

-

9-53-"-4

o

Various.

" ...

-

9-53

0

Vassura.

" ...

Solid

20.96

226.5

"

" ...

Liquid

44- 56

226.5

"

Zinc . . .

—

5.56-6.04

o

—

**

, Solid

18.16

Melting-point

De la Rive.

• . .

Liquid

36.00

«

SMITHSONIAN TABLES.

255

TABLE 266.

RESISTANCE OF METALS AND

The electrical resistance of some pure metals and of some alloys have been determined by Dewar and Fleming and
increases as the temperature is lowered. The resistance seems to approach zero for the pure metals, but not for
temperature tried. The following table gives the results of Dewar and Fleming.*

When the temperature is raised above o° C. the coefficient decreases for the pure metals, as is shown by the experi-
experiments to be approximately true, namely, that the resistance of any pure metal is proportional to its absolute
is greater the lower the temperature, because the total resistance is smaller. This rule, however, does not even
zero Centigrade, as is shown in the tables of resistance of alloys. (Cf. Table 262.)

Temperature —

100°

20°

0°

— 80°

Metal or alloy.

Specific resistance in c. g. s. units.

Aluminium, pure hard-drawn wire .

4745

35°5

3161

-

Copper, pure electrolytic and annealed .

1920

M57

!349

-

Gold, soft wire ......

2665

2081

1948

1400

Iron, pure soft wire ...

13970!

9521

8613

-

Nickel, pure (prepared by Mond's process )
from compound of nickel and carbon > .
monoxide) )

19300

13494

12266

7470

Platinum, annealed .

10907

8752

8221

6i33

Silver, pure wire

2139

1647

1559

1138

Tin, pure wire

13867

10473

9575

. 6681

German silver, commercial wire

3572o

34707

34524

33664

Palladium-silver, 20 Pd + 80 Ag

15410

14984

14961

14482

Phosphor-bronze, commercial wire •» • . -

9071

8588

8479

8054

Platinoid, Martino's platinoid with I to 2% )
tungsten J

4459°

43823

43601

43022

Platinum-iridium, So Pt -f- 20 Ir . . .

31848

29902

29374

27504

Platinum-rhodium, 90 Pt -|- 10 Rh . . .

18417

14586

13755

10778

Platinum-silver, 66.7 Ag -f- 33.3 Pt .

27404

26915

26818

26311

Carbon, from Edison-Swan incandescent )
lamp }

-

4O46X io3

4092 X i o3

4I89XI03

Carbon, from Edison-Swan incandescent )
lamp }

3834X10*

3908 X i o3

3955X10*

4054Xio3

Carbon, adamantine, from Woodhouse and )
Rawson incandescent lamp \

6I68XIO*

6300X10'

6363X108

6495X108

* " Phil. Mag." vol. 34, 1892.

t This is given by Dewar and Fleming as 13777 for 96°. 4, which appears from the other measurements too high.
SMITHSONIAN TABLES.

256

TABLE 266.

ALLOYS AT LOW TEMPERATURES.

by Cailletet and Bouty at very low temperatures. The results show that the coefficient of change with temperature
the alloys. The resistance of carbon was found by Dewar and Fleming to increase continuously to the lowest

nients or Miiller, Benoit, and others. Probably the simplest rule is that suggested by Clausius, and shown by these
temperature. This gives the actual change of resistance per degree, a constant ; and hence the percentage of change
approximately hold for alloys, some of which have a negative temperature coefficient at temperatures not far from

Temperature =

— 100°

— 182°

-197°

Mean value of
temperature co-
efficient between
— 100° and

+ 100° C.*

Metal or alloy.

Specific resistance in c. g. s. units.

Aluminium, pure hard-drawn wire

1928

894

-

.00446

Copper, pure electrolytic and annealed .

757

272

178

431

Gold, soft wire

1207

604

-

375

Iron, pure soft wire

4010

1067

608

578

Nickel, pure (prepared by Mend's process )
from compound of nickel and carbon > .
monoxide) ;

6110

1900

-

538

Platinum, annealed

5295

2821

2290

34i

Silver, pure wire

962

472

-

377

Tin, pure wire

5671

2553

-

428

German silver, commercial wire

33280

32512

-

035

Palladium-silver, 20 Pd + So Ag .

14256

13797

-

039

Phosphor-bronze, commercial wire .

7883

737i

-

070

Platinoid, Martino's platinoid with i to 2% )
tungsten J

42385

4H54

-

025

Platinum-iridium, 80 Pt + 20 Ir

26712

24440

-

087

Platinum-rhodium, 90 Pt + 10 Rh .

9834

7134

-

312

Platinum-silver, 66.7 Ag + 33.3 Pt .

26108

25537

-

024

Carbon, from Edison-Swan incandescent ^
lamp $

42i8Xio3

4321 Xio3

-

-

Carbon, from Edison-Swan incandescent )
lamp ( '

4079X io3

4i8oXio3

-

031

Carbon, adamantine, from Woodhouse and (
Rawson incandescent lamp J '

6533 X i o3

-

-

029

* This is a in the equation R =. R0 (i -I- a/), as calculated from the equation a=: — — —

200 An

SMITHSONIAN TABLES.

257

TABLE 267.

EFFECT OF ELONGATION ON THE SPECIFIC RESISTANCE OF SOFT

METALLIC WIRES.*

Substance.

Increase of specific resistance for i % of elongation —

Permanent elongation.

Elastic elongation.

Copper . . . . * .
Iron ......
German silver ....

From .50 % to V6o %

" .70 " " .80 "
" -50 " " -55 "

From 2.5 % to 7.7 %
" 4.6 " " 4.8 "
" 0.7 " " i.o "

TABLE 268.

EFFECT OF ALTERNATING THE CURRENT ON ELECTRIC RESISTANCE,

This table gives the percentage increase of the ordinary resistance of conductors of different diameters
when the current passing through them alternates with the periods stated in the last column.t

Diameter in —

Area in —

Percentage increase of
ordinary resistance.

Number of
complete
periods per
second.

Millimetres.

Inches.

Sq. mm.

Sq. in.

IO

•3937

78.54

.122

Less than -fa

15

•5905

176.7

.274

2-5

20

.7874

314.16

.487

8

25

.9842'

490.8

.760

17-5

• So

40

'•575

1256

i-95

68

100

3937

7854

12.17

3.8 times

1000

39-39

785400

1217

35 times

9

•3543

63.62

.098

Less than y^y

134
18

.5280
.7086

MI-3

254-4

.218
•394

2-5

8

• 100

22.4

.8826

394

.611

17-5

7-75

•3013

47-2

.071

Less than T^W

11.61

iS-5

.4570
.6102

106

189

.164
.292

2-5

8

• 133

19.36

.7622

294

•456

'7-5

SMITHSONIAN TABLES.

* T. Gray, " Trans. Roy. Soc. Edin." 1880.
t W. M. Mordey, " Inst. El. Eng. London,"

258

TABLES 269, 27O.
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 grammes of the pure salts proportional to their elec-
trochemical equivalent, and using a litre of water as the standard 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 grammes to the litre of water, we get what is called
the normal or gramme molecule per litre solution. In the table, m is used to represent the
number of gramme molecules to the litre 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 JCl 8 — conductivity of the solution at 18° C. relative to mercury at o° C.

K™a = conductivity of the solvent water at 18° C. relative to mercury at o° C.

Then Jfia — K^9 = &la — conductivity of the electrolyte in the solution measured.

-is. = p = conductivity of the electrolyte in -the solution per molecule, or the "specific
m
molecular conductivity."

TABLE 269. —Value of /.-.. 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.

M

KC1

NaCl

AgN03

KC2H3O2

K2S04

MgS04

O.OOOOOI

1.216

1.024

I.oSo

0-939

1-275

1.056

0.00002

2.434

2.056

2.146

1.886

2.532

2.104

O.OOOO6

7.272

6.162

6.462

5.610

7-524

6.216

0.000 1

12.09

10.29

10.78

9-34

12.49

10.34

TABLE 270. — 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 271 may be convenient. They represent grammes per cubic centimetre of the solution
at the temperature given.

Salt dissolved.

Grammes
per litre.

nt

Temp.

Density.

Salt dissolved.

[Jrammes
per litre.

m

Temp.
C.

Density.

KC1 . . .

74-59

.O

15.2

•0457

JK2S04 .

87.16

1.0

18.9

1.0658

NH4C1 . .

53-55

.0009

18.6

.0152

iNa2SO4 .

71.09

I.OOO3

1 8.6

r.ooo2

NaCl . . .

58.50

.O

18.4

.0391

|Li2SO4 .

55-09

I.OOO7

18.6

1.0445

LiCl . . .

42.48

.O

18.4

.022?

iMgS04 •

60.17

1.0023

18.6

1-0573

JBaCl.2 . .

104.0

.0

1 8.6

.0888

£ZnS04 .

80.58

1.0

5-3

1.0794

JZnCla • •

68.0

.012

15.0

.0592

£CuS04 .

79-9

I.OOI

18.2

1.0776

KI . . . .

165.9

.O

18.6

1.1183

|K2C03 .

69.17

1. 0006

18.3

1.0576

KN03 . .

101.17

.O

1 8.6

1.0601

iNa,2C03 .

53-04

1.0

17.9

1.0517

NaNO3 . .

85.08

.O

18.7

1.0542

KOH . .

56-27

1.0025

1 8.8

1.0477

AgN08 . .

169.9

.O

-

-

HC1 . .

36-51

1.0041

18.6

1.0161

JBa(N08)2 .

65.28

o-5

-

-

HNO3 . .

63-13

1.0014

18.6

1.0318

KClO;i . .

61.29

o-5

18.3

1.0367

iH2S04 .

49.06

1. 0006

18.9

1.0300

KC2H802 .

, 98.18

1.0005

1 8.6

1.0467

SMITHSONIAN TABLES.

* " Wied. Ann." vol. 26, pp. 161-226.
259

TABLE 271.

SPECIFIC MOLECULAR CONDUCTIVITY /j. : MERCURY^ 1 O».

Salt dissolved.

»I= 10

5

3

I

0-5

O.I

•05

•03

.01

iKaS04 ,

_

_

_

_

672

736

897

959

1098

KC1

-

-

827

919

958

1047

1083

1107

"47

KI . ...

-

7/0

9OO

968

997

1069

IIO2

1123

1161

NH4C1 .

-

752

825

907

948

1035

1078

IIOI

1142

KNO3 .

-

572

752

839

983

J037

1067

1122

iBaC!2

_

_

487

658

725

86 1

904

939

1006

KClOa .

-

—

-'

799

927

(976)

1006

I053

iBa,,N,06

-

-

-

-

53 l

755

828

(8/0)

|-CuSO4 .

—

-

I5°

241

288

424

479

537

675

AgNOa . . .

-

351

448

635

728

886

936

1017

£ZnSO4 . . .

_

82

146

249

302

43 !

500

556

685

INagSoV •

_

82

151

270

475

33°
559

474
734

784

587
828

906

IZnCls . . .

60

1 80

280

5'4

601

768

817

851

9!5

NaCl . . .- ,:

-

398

528

695

757

865

897

(920)

962

NaN03 .

_

_

43°

617

694

817

855

877

907

KC2H302 . it

3°

240

594

671

784

820

841

879

|Na2CO3

254

427

510

682

751

799

899

£H«SO4 .

660

1270

1560

1820

1899

2084

2343

2515

2855

C2H4O .

0.5

2.6

S-2

12

19

43

62

79

132

HC1 . . ;

600

1420

2OIO

2780

3017

3244

3330

3369

34i6

HN03 .

610

1470

2O7O

2770

2991

3225

3289

3328

3395

iH'jPO4 .

148

160

170

2OO

250

43°

540

620

790

KOH .

423

990

1718

1841

1986

2045

2078

2124

NH3

°-5

2.4

3-3

8.4

12

3'

43

50

92

Salt dissolved.

.006

.002

.001

.0006

.0002

.0001

.00006

.00002

.00001

JK.S04 .

1130

1181

1207

1 220

1241

1249

1254

1266

1275

KC1

1162

1185

"93

"99

I2O9

1209

1212

1217

1216

KI .

1176

"97

1203

1209

1214

1216

1216

1216

1207

NH4C1 .

"57

1180

1190

"97

I2O4

1209

I2I5

1209

1205

KN08 .

1140

"73

1180

1190

"99

1207

I22O

1198

I2I5

|BaClo .

1031

1074

1092

IIO2

1118

1126

"33

"44

1142

KC108 .

1068

1091

I 10 1

1109

1119

1122

1126

"35

II4I

|Ba2NoOe

982

i°33

i°54

I066

1084

1096

IIOO

1114

III4

£CuSO~4 .

740

873

95°

987

i°39

IO62

1074

1084

1086

AgN03 . . .•

T°33

1057

1068

1069

1077

1078

1077

1073

1 080

|ZnSO4 .

744

86 1

919

953

IOOI

1023

1032

1047

IO6O

£MgSO4 .

773

88 1

935

967

1015

1034

1036

1052

1056

|Na2SO4

933

980

998

1009

1026

1034

1038

1056

1054

JZnCla .

939

979

994

1004

1 020

IO29

1031

1035

1036

NaCl . . .1

976

998

1008

1014

1018

IO29

1027

1028

IO24

NaNO3 . . .1

921

942

952

956

966

975

970

972

975

KC2HjjO2 . . ,

891

913

919

923

933

934

935

943

939

^NaoCOs . ..

956

IOIO

1037

1046

988

874

790

697*

^H2SO4 . i.

3001

3240

33 '6

3342

3280

3"8

2927

2077

1413*

C2H4O . . .;

170

283

380

470

796

995

"33

1328

1304*

HC1

3438

3455

3455

344°

3340

3i7o

2968

2057

1254*

HNO3 .

3427

3408

3285

3088

2863

1904

"44*

$H3PO4 .

858

945

968

977

920

837

746

497

402*

KOH

2141

2140

2110

2074

1892

1689

1474

845

747*

NH3

116

190

260

330

500

610

690

700

560*

SMITHSONIAN TABLES.

* Acids and alkaline salts show peculiar irregularities.
26O

TABLE 272.

LIMITING VALUES OF u.

This table shows limiting values of yu. = — . ID* for infinite dilution for neutral salts, calculated from Table 271.

Salt.

M

Salt.

^

Salt.

p

Salt.

/*

iK2SO4 .

1280

*BaCl2 .

1150

4MgS04 .

1080

iH2S04 •

3700

KCl . . .

1220

iKC!O3 .

1150

iNa2S04 .

1060

HCI ; ..?

3500

KI . . .

I22O

!BaN2O6 .

1 1 20

iZnCl . .

1040

HNO3 . .

3500

NH4C1. .

I2IO

£CuSO4 .

1 100

NaCl . .

1030

£H3P04 .

IIOO

KN03 . .

1210

AgN03 .

1090

NaNO3 .

980

KOH . .

22OO

-

-

iZnSO4 .

1080

K2C2H3O2

940

^NaoCOs .

1400

If the quantities in Table 271 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 272 are multiplied by Hittorf's constant, or o.ooon, quan-
tities ranging between 0.14 ando.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. HsPO4 in dilute solution seems to
approach a monobasic acid, while H2SO4 shows two maxima, and like H3PO4 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 273.

TEMPERATURE COEFFICIENT.

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 gramme mole-
cule of the salt.

Salt.

Temp.
Coeff

Salt.

Temp.
Coeff.

Salt.

Temp.
Coeff.

Salt.

Temp.
Coeff.

KCl . . .

O.O22I

KI . '. .

O.O2I9

iK2S04 .

0.0223

iK2C08 . .

0.0249

NH4C1 . .
NaCl . .
LiCl. . .
|BaCl2 . .
£ZnCl2 .
iMgCla .

0.0226
0.0238
0.0232
0.0234
0.0239
0.0241

KN03 . .
NaNO3 . .
AgN03. .
iBa(N03)2
KC103 . .
KC2H302 .

0.0216

0.0226
O.O22I
O.O224
O.O2I9
O.O229

iNa2SO4 .
|Li2SO4 .
pfgSO4 .
iZnSO3 .
iCuSO4 .

0.0240
0.0242
0.0236
0.0234
0.0229

iNa2CO3 . .

0.0265

KOH . . .
HCI . . .
HNO3 . . .
iH2S04 . .

0.0194
0.0159
O.OI62
0.0125

*H2S04 I
for m = .001 |

0.0159

SMITHSONIAN TABLES.

26l

TABLE 274.

VARIOUS DETERMINATIONS OF THE VALUE OF THE OHM, ETC.*

Observer.

Date.

Method.

Value of
B. A. U.

in ohms.

Value of 100
cms. of Hg
inB. A.U.

Value of
ohm in
cms.of Hg.

I

2

3

4

5
6

8
9

10

ii

12
12

13
14
IS

16
i?

18

!9

Lord Rayleigh
Lord Rayleigh
Mascart ....
Rowland . . .

Kohlrausch . .

Glazebrook . .
Wuilleumeier .
Duncan & Wilkes
Jones

1882
1883
1884
1887

1887

1882 to 1888
1890
1890
1891

1885
1888
1890

1884
1884

1885
1889

1883
1885

Rotating coil . .
Lorenz method . .
Induced current .
Mean of several
methods . . .
Damping of mag-
nets

.98651
.98677
.98611

.98644

.98660
.98665
.98686
.98634

(-95412)
•95374
•95349

•95338
•95352
•95355
•9534'

•95334
•95352
•95332
•95354

106.31
106.27
106.33

106.32

106.32
106.29
106.31
106.34
106.31

Induced currents .

Lorenz method . .
Lorenz method . .
Mean ....

An absolute de-
termination of re-
sistance was not
made. The value
.98656 has been
used.
Mean ....

Strecker ....
Hutchinson . .
Salvioni ....
Salvioni ....

H. F. Weber . .
H. F. Weber . .
Roti

•98653

106.31

-

106.32
106.30
106.33
106.30

•Q^IW

106.31

Induced current .
Rotating coil . .
Mean effect of in-
duced current .

Absolute measure-
ments compared
with German silver
wire coils issued
by Siemens or
Strecker.

I

1 05-37

106.16

105.89
105.98

106.24

106.03
105-93

Heinstedt . . .
Dorn

Wild

Damping of mag-
net

Damping of mag-
net

Lorenz ....

Lorenz method. .

The Board of Trade committee recommended for adoption the values .9866 and 106.3.
The specific resistance of mercury in ohms is thus .9407 X icr*.
Also i Siemens unit = .9407 ohm.
= .9535 B. A. U.
i ohm . . .= 1.01358 B. A. U.

The following values have been found for the mass of silver deposited from a solution
of silver nitrate in one second by a current of one ampere : —

Mascart, " J. de Physique," iii. 1884 . . 0011156
Rayleigh, " Phil. Trans." ii. 1884 ....... .0011179
Kohlrausch, " Wied. Ann." xxvii. 1886 0011183
T. Gray, " Phil. Mag." xxii. 1886 about t .001 1 18
Portier et Pellat, "J. de Physique," ix. 1890 ..... .0011192

The following values have been found for the electromotive force of a Clark cell at 15° C.
They have been reduced from those given in the original papers on the supposition that
i B. A. U. = .9866 ohm, and that the mass of silver deposited per second per ampere is
.001118 gramme.

Rayleigh, " Trans." ii. 1884 1-4345 volt.
Carhart ........... I.AIAO "

Kohle, " Zeitschrift fiir Instrumentenkunde," 1892 . . . 1.4341 "
Glazebrook and Skinner, " Proc. R. S." Ii. 1892 . . . 1.4342 "

* Abstract from the Report of the British Association Committee on Practical Standards for Electrical Measure-
ment, " Proc. Brit. Assoc." 1892.
t i .0000002 T. G.

SMITHSONIAN TABLES.

262

TABLE 275.

SPECIFIC INDUCTIVE CAPACITY OF CASES.

With the exception of the results given by Ayrton and Perry, for which no temperature record has been found,, the
values are for o° C. and 760 mm. pressure.

Gas.

Sp. ind. cap.

Authority.

Vacuum = i.

Air= I.

Air . . . . . . ~.

1.0015

I.OOOO

Ayrton and Perry.

. /,• ....

1.00059

I.OOOO

KlemenCiC.

• . ' . . ...

1 .00059

I.OOOO

Boltzmann.

Carbon disulphide ....

1.0029

1.0023

KlementiC.

Carbon dioxide, COg ....

1.0023

1.0008

Ayrton and Perry.

""....

1.00098

1 .00039

KlemenCic".

""....

1 .00095

1.00036

Boltzmann.

Carbon monoxide, CO ....

1.00069

I.OOOIO

KlemenCiC.

....

1 .00069

I.OOOIO

Boltzmann.

Coai gas (illuminating)

1.0019

1 .0004

Ayrton and Perry.

Hydrogen

1.0013

0.9998

Ayrton and Perry.

I.OOO26

0.99967

KlemenCiC.

I.OOO26

0.99967

Boltzmann.

Nitrous oxide, N2O ....

I. OOIl6

1.00057

KlemenCiC.

"

1 .00099

1.00040

Boltzmann.

Sulphur dioxide

1.0052

1.0037

Ayrton and Perry.

1.00955

1.00896

Klemenfif.

Vacuum 5 mm. pressure

I.OOOO

0.9985

Ayrton and Perry.

" o.ooi " " about .

1. 0000

0.94

Ayrton and Perry.

"

I.OOOO

0.99941

KlemenCif.

".......

I.OOOO

0.99941

Boltzmann.

SMITHSONIAN TABLES.

263

TABLE 276.

SPECIFIC INDUCTIVE CAPACITY OF SOLIDS (AIR^UNITY).

Substance.

Sp. ind. cap.

Authority.

Calcspar parallel to axis

7-5

Romich and Nowak.

" perpendicular to axis

7-7

" " "

Caoutchouc

2.12-2.34

Schiller.

vulcanized ....

2.69-2.94

"

Celluvert, hard gray ....

1.19

Elsas.

" " red . . . . ;

1.44

"

" black . . . . - .,

1.89

M

" soft red . . . . • ' . "

2.66

"

Ebonite . . . . . ' . ..

2.08

Rossetti.

" . . . .

3- r 5-3-48

Boltzmann.

"

2.21-2.76

Schiller.

" . ...

2.72

Winkelmann. '

" . . . - .

2.56

Wiillner.

" . . . . .

2.86

Elsas.

"

1.9

Thomson (from Hertz's vibrations).

Fluor spar . . . . .-'.'.

6.7

Romich and Nowak.

" " ......

6.8

Curie.

Glass,* density 2.5 to 4.5 . . . 1

5-10

Various.

Double extra dense flint, density 4.5 .

9.90

Hopkinson.

Dense flint, density 3.66

7-38

"

Light flint, " 3.20

6.70

M

Very light flint " 2.87

6.6 1

"

Hard crown " 2.485

6.96

"

Plate " - ...

8-45

M

Mirror

5.8-6.34

Schiller.

".......

6.46-7-57

Winkelmann.

".......

6.88

Donle.

"

6.44-7.46

Elsas.

Plate

3-3r-4-i2

Schiller.

".......

7-5

Romich and Nowak.

«

6.10

Wiillner.

Guttapercha

3-3-4-9

Submarine cable data.

Gypsum ;

6-33

Curie.

Mica '

6.64

KlemenCiC.

" .

8.00

Curie.

H

7.98

Bouty.

"........

5-66-5-97

Elsas.

"........

4.6

Romich and Nowak.

Paraffin _

2.32

Boltzmann.

" .......

1.98

Gibson and Barclay.

" ....... i

2.29

Hopkinson.

" quickly cooled translucent
" slowly cooled white .

1.68-1.92
1.85-2.47

Schiller.!

" .......

2.18

Winkelmann.

" .

1.96-2.29

Donle, Wiillner.

" fluid — pasty . . .

1.98-2.08

Arons and Rubens.

" solid

1-95

" " "

Porcelain ......

4-38

Curie.

Quartz, along the optic axis . . . ,

4-55

"

" transverse .

4-49

"

Resin . . . . . .

2.48-2.57

Boltzmann.

18 o

Hopkinson.

5-85

Curie.

Selenium

IO.2

Romich and Nowak.

Shellac .

3-10

Winkelmann.

....

3-67

Donle.

.......

2-95-3-73

Wiillner.

* The values here quoted apply when the duration of charge lies between 0.25 and 0.00005 of a second. J. J.
Thomson has obtained the value 2.7 when the duration of the charge is about i 725 X 10° of a second ; and this is
confirmed by Blondlot, who obtained for a similar duration 2.8.

t The lower values were obtained by electric oscillations of duration of charge about 0.0006 second. The larger
values were obtained when duration of charge was about 0.02 second.

SMITHSONIAN TABLES.

264

TABLE 276.
SPECIFIC INDUCTIVE CAPACITY OF SOLIDS (AIR = UNITY).

Substance.

Sp. ind. cap.

Authority.

Spermaceti ......
Sulphur

2.18
2.25
3.84-3.90
2.88-3.21
2.24
2. 04.

Rossetti.
Felici.
Boltzmann.
Wiillner.
J. J. Thomson.
Blondlot.

2.56

Trouton and Lilly.

TABLE 277.

SPECIFIC INDUCTIVE CAPACITY OF LIQUIDS.

Substance.

Sp. ind. cap.

Authority.

Alcohols :

Amyl

iS-'M

Cohn and Arons ; Tereschin.

Ethyi

24-27

Various.

Methyl

32-65

Tereschin.

Propyl .

22.8

"

Anilin . . -,

7-5

"

Benzene

1-93-2-45

Various.

" average about ....

2-3

at 5° C

2.1898

Negreano.

" 15° C

2-I534

"

" " 25° c

2.1279

"

" 40° C

2.1103

"

Hexane, between 11° and 13° C. .

1.859

Landolt and Jahn.

Octane, i3°.5-i4° C.

1-934

Decane, I3°5-I4°.2 C. .

1.966

Amylene, i5°-i6°.2 C.

2.2OI

Octylene, n°.5-i3°.6 C.

2-175

Decvlene, i6°-7 C.

2.236

Oils':

Arachid

3-1?

Hopkinson.

Castor .......

4.6-4.8

Various.

Colza

3-07-3- i 4

Hopkinson.

Lemon .......

2.25

Tomaszewski.

Neatsfoot ......

3-°7

Hopkinson.

Olive

3.08-3.16

Arons and Rubens ; Hopkinson.

Petroleum

2.02-2.19

Various.

Petroleum ether ....

1.92

Hopkinson.

Rape-seed

2.2-3.0

Various.

3.17

Hopkinson.

Sperm . . - .

3.02-3.09

Hopkinson ; Rosa.

Turpentine .....»,

2.15-2.28

Various.

Vaseline .

2.17

Fuchs.

Ozokerite . . . . . ~.

2.13

Hopkinson.

Toluene ......

2.2-2.4

Various.

Xylene . .

2.3-2.6

SMITHSONIAN TABLES.

265

TABLE 278.

CONTACT DIFFERENCE OF

Solids with Liquids and
Temperature of substances

1

1

C
0

•d

jj

i

o

u

0

"~

Jj

s

H

N

Mercury

092

.108

,«/0

.156

(.01

.269

'

(— -I05

Distilled water

< to

to

.148

.171

< to /

.177

< to
\ i\j

15

.100

•iT-w

•* / *

( -345)

• / /

(+•156

Alum solution : saturated [
at i6°.5 C }

—.127

—653

—•139

.246

— .225

—536

Copper sulphate solution : (

sp. gr. 1.087 at i6°.6 C. )

.103

Copper sulphate solution : )

saturated at 15° C. . . j

.070

Sea salt solution : sp. gr. /
1.18 at 20°.5 C. . . . (

-

—•475

— -605

-

—.•856

—•334

-•565

Sal-ammoniac solution : i
saturated at 15°. 5 C. . )

-

—•396

— .652

-.189

•°59

—.364

—•637

Zinc sulphate solution : sp. |
gr. 1.125 at i6°.9 C. . . (

-

-

-

-

-

-

-.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 i o by volume . . .

i about »
1 — -°3S >

-

-

-

-

-

-

i to 5 by weight ....

-

-

-

-

-

-

i.OI )

5 to i by weight ....

to >

-

-

— .I2O

-

—•25

-

3-°)

( -55)

( -72

r-3 )

Concentrated sulphuric acid

\ to (

1.113

-

) t0

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.

266

TABLE 278.

POTENTIAL IN VOLTS.

Liquids with Liquids In Air.*
during experiment about 16° C.

C

u

_o

J 0

1°'

ll

in

!<->

3°"

3 r*l

f GL,

a>o

T3

•• <>

V in

«z

w «o

JV «

'0

•o

a

rt

B "*

C *.

!«

1, ~

ss

'!.£

ra
_o

I

-

13

"o i!

•3-0

S»!

a -

•f-g

'•5 5

'c

_M .

J,

g

:=

6 3

S.3

36

"2 n

S.|

M
c

|.s

rt

fe

tn

3 —

C-*£

o a

c «

8-4-

o

»

%

5

< "

6 "

N "

Nw

0

GO

Mercury

Distilled water

.100

.164

Alum solution : saturated \

at i6°.5 C J

—

.OI4

~

~

~

•"

~

~

*~

"~"

Copper sulphate solution : )
sp. gr. 1.087 at i6°.6 C. }

-

-

-

-

-

-

.090

-

-

-

Copper sulphate solution : )
saturated at 15° C. . . J

-

-

-

—•043

-

-

-

•°95

.102

-

Sea salt solution : sp. gr. j
1.18 at 20°5 C. . . . J

-

—•435

-

-

-

-

-

-

-

-

Sal-ammoniac solution : j
saturated at I5°.5 C. . J

-

-•348

-

-

-

-

-

-

-

-

Zinc sulphate solution : \

sp. gr. 1.125 at i6°-9 C. )

Zinc sulphate solution : J
saturated at I5°.3 C. . )

-.284

-

-

.2OO

-

—•095

-

-

-

-

One part distilled water + )

3 parts saturated zinc >

-

—

—

—

—

— .102

—

—

-

-

sulphate solution . . )

Strong sulphuric acid in

distilled water :

i to 20 by weight . . .

-

-

-

-

-

-

-

-

-

-

i to 10 by volume . . .

-.358

-

-

-

-

-

-

-

-

-

i to 5 by weight ....

.429

-

-

-

-

-

-

-

-

-

5 to i by weight ....

-

— .016

-

-

-

-

-

-

-

-

Concentrated sulphuric acid

.848

-

-

1.298

1.456

1.269

-

1.699

-

-

Concentrated nitric acid

_

_

_

_

_

_

_

_

Mercurous sulphate paste .

-

-

•475

-

-

-

-

-

-

-

Distilled water containing )
trace of sulphuric acid . J

-

-

-

-

-

-

-

-

.078

Ayrton and Perry's results, prepared by Ayrton.
SMITHSONIAN TABLES.

267

TABLE 279.

CONTACT DIFFERENCE OF POTENTIAL IN VOLTS.

Solids with Solids in Air.*
Temperature of substances during the experiment about 18° C.

Carbon.

Copper.

Iron.

Lead.

Platinum.

Tin.

Zinc.

Zinc
amal-
gam.

Brass.

Carbon . . .

0

•370

.485

.858

•"3

•795

1.096!

i.2o8t

.414!

Copper . . .

—•37°

0

.146

.542

—.238

•456

•75°

.894

.087

Iron ....

-.485t

— .146

O

40 it

—•369

•3'3t

.6oof

•744t

— .064

Lead . . .

—.858

—•542

— .401

0

—.771

—.099

.210

•357t

—.472

Platinum . .

— .113!

.238

•369

.771

0

.690

.981

1.125!

.287

Tin ....

— -79St

—.458

—•3 '3

.099

— .690

0

.281

•463

—•372

Zinc ....

— i .096!

—•75°

— .600

— .216

-.981

.281

0

.144

—.679

" amalgam

— r.2o8t

-.894

—•744

— -357t

—1.125!

—•463

—.144

o

—.822

Brass . . .

—.414

—.087

.064

•472

-.287

•372

.679

.822

0

The numbers not marked were obtained by direct experiment, those marked with a dag-
ger by calculation, on the assumption that in a compound circuit of metals, all at the same
temperature, there is no electromotive force.
The numbers in the same vertical column are the differences of potential in volts between
the substance named at the top of the column and the substance named on the same line in.
the first column, when the two substances are in contact.

The metals used were those ordinarily obtained in commerce.

* Everett's " Units and Physical Constants." The table is from Ayrton and Perry's experiments, and was pre-
pared by Ayrton.
SMITHSONIAN TABLES.

268

TABLE 280.

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 of sulphuric acid and the metals 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
gramme molecules per
litre. x

Zinc.t

Cadmium. t

Lead.

Tin.

Copper.

Silver.

No. of
molecules.

Salt.

Difference of potential in centivolts.

°-5

H2S04

0.0

36.6

5!-3

5J-3

100.7

I2I-3

I.O

NaOH

— 32-1

19-5

31.8

O.2

80.2

95-8

1.0

KOH

—42.5

15-5

32.0

— 1.2

77-0

104.0

0.5

Na2SO4

1.4

35-6

50.8

5M

IOI.3

120.9

. i-o

Na2S2O3

—5-9

24.1

45-3

45-7

38.8

64.8

I.O

KNO3

11.8}

3J-9

42.6

31-1

8l.2

105-7

I.O

NaNO3

ii-S

51.0

40.9

95-7

114.8

°-5

K2CrO4

23-9J

23

41-2.

40.9

94.6

I2I.O

0.5

K2Cr2O7

72.8

61.1

78.4

68.1

123.6

I32-4

0.5

K2SO4

1.8

34-7

51.0

40.9

95-7

II4-8

°-5

(NH4)2S04

—0-5

37-i

53-2

57-6}

101.5

125.7

0.25

K4FeC«N6

—6.1

33-6

50-7

41.2

— t

87.8

0.167

Kf,Fe2(CN)8

4I.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

NaNO3

4-5

35-2

50.2

49.0

103.6

IO4.6?

°-5

SrN03

14.8

38-3

50.6

48.7

103.0

"9-3

0.125

Ba(N03)2

21.9

39-3

5*-7

52.8

109.6

121.5

I.O

KNQa

-t

35-6

47-5

49-9

104.8

115.0

O.2

KCK>a

i5-fc}

39-9

53-8

57-7

'05-3

120.9

0.167

KBrO3

13-20}

40.7

5'-3

5°-9

111.3

120.8

I.O

NH4C1

2.9

324

5T-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

—

3J-9

51.2

50-3

80.9

101.3

I.O

KBr

2-3

3»-7

47.2

52-5

73-6

82.4 •

I.O

KC1

32.1

51.6

52-6

81.6

107.6

0.5

NaaSOs

—8.2

28.7

41.0

31.0

68.7

103.7

-II

NaOBr

18.4

41.6

73- i

70.6}

89.9

99-7

I.O

C4H606

5-5

39-7

61-3

54-4§

104.6

123.4

°-5

C4H606

4.1

41-3

61.6

57-6

110.9

125.7

o-5

C4H4KNaO6

—7-9

3i-5

5I-S

42-47

100.8

119.7

* " Rend, della R. Ace. di Roma,'' 1890.

t Amalgamated.

t Not constant.

5 After some time.

II A quantity of bromine was used corresponding to NaOH = i.

SMITHSONIAN TABLES.

269

TABLE 281 .

VARIATION OF ELECTRICAL RESISTANCE OF CLASS AND PORCELAIN

WITH TEMPERATURE.

The following table gives the values of a, b, and c in the equation

log R =. a + 6t + ct2,

where R is the specific resistance expressed in ohms, that is, the resistance in ohms per centimetre of a rod one
square centimetre in cross section.*

No.

Kind of glass.

Density.

a

b

c

Range of
temp.
Centigrade.

I

Test-tube glass •> . . . ' .

-

13.86

—.044

.000065

0°-250°

2

"""...

2.458

14.24

—•°55

.OOOI

37-131

3

Bohemian glass . . •-'• f .

2-43

16.21

—•043

.0000394

60-174

4

Lime glass (Japanese manufacture) .

2-55

I3-H

—.031

— .OOOO2I

10-85

5

« a n a

2-499

14.002

— .025

— .00006

35-95

6

Soda-lime glass (French flask)

2-533

14.58

—.049

.000075

45-120

7

Potash-soda lime glass

2.58

16.34

—.0425

.0000364

66-193

8

Arsenic enamel flint glass

3-07

18.17

—•055

.000088

iQS-'SS

9

Flint glass (Thomson's electrometer
jar) . . . ...

3-I72

18.021

—.036

— .0000091

100-200

10

Porcelain (white evaporating dish) .

-

J5-65

— .042

.00005

68-290

COMPOSITION OF SOME OF THE ABOVE SP CIMENS OF GLASS.

Number of specimen =

3

4

5

7

8

«

Silica ... ...

61.3

57-2

70.05

75-65

54-2

55-18

Potash ...

22.9

21. 1

1.44

7.92

' 10.5

13.28

Soda . . ...

Lime, etc.

Lime, etc.

14.32

6.92

7.0

-

Lead oxide . . .

by diff.

by diff.

2.70

-

23-9

31.01

Lime

15.8

16.7

io-33

8.48

o-3

Q-35

Magnesia . . .

-

-

. r . '

0.36

O.2

0.06

Arsenic oxide . .

-

-

-

-

3-5

-

Alumina, iron oxide, etc.

-

-

i-45

0.70

0.4

0.67

SMITHSONIAN TABLES.

* T. Gray, "Phil. Mag." 1880, and " Proc. Roy. Soc." 1882.

270

TABLE 282.
RELATION BETWEEN THERMAL AND ELECTRICAL CONDUCTIVITIES.

That there is a close relation
between the thermal and the
electrical conductivities of
metal was shown experimen-
tally by Wiedemann and Franz
in 1853, and had been referred
to by Forbes, with whom a
difficulty arose with regard to
the direction of the variation
with temperature. The ex-
periments of Tail and his stu-
dents have shown that this
difficulty was largely, if not
entirely, due to experimental
error. The same relation has
been shown to hold for alloys
by Chandler Roberts and by
Neumann, This relation was

a. VALUKS IN ARBITKARY UNITS AT 15^ C.

Substance.

l^

*„

'l*
*15

Lead . .

7-93

4.569

i-74

Tin . . .

14.46

8.823

1.64

Zinc . . .

25-45

14.83

1.72

Copper . . 41.52

24.04

'•73

Iron, No. I

14.18

6.803

2.08

** i. ^

9.64

4.060

2-17

" 3

'3-75

6.565

2.09

denied by H. F. Weber, and
has been again experimentally
investigated and apparently
established by the experiments
of Kirchhoff and Hansemann,
of L. Lorenz, of F. Kohl-
rausch, and of Berget.

Putting /=: thermal conduc-
tivity, and k =r electrical con-
ductivity, Kirchhoff and
Hansemann find the values in
Table a. This table shows
iron to deviate considerably
from the other metals in the
relaiionship of the two con-
ductivities ; but this may possi-
bly be explained by its mag-
netic properties.

Lorenz 's results* show that the ratio // k for the different metals, except iron, is nearly constant for values
at o° and 100° C., but that the ratio is generally greater for poorly conducting substances. He shows that the

ratio ^ -T- ~£~ remains nearly constant for all metals examined, with the exception of iron, and has an aver-
age value, as shown by Table to, of about 1.37. He concludes that I / k— constant X 7", where T is the abso-
lute temperature.

In this table the values of / and k are given in c. g. s. units, and the metals are arranged in the order of
their heat conductivities. The same specimens were used for both the thermal and the electrical experiments.

b. VALUES IN C. G. S. UNITS.

Substances.

k0 X ior>

kloo X io5

Copper
Magnesium
Aluminium
Brass, red .
Cadmium .
Brass, yellow
Iron .
Tin .
Lead .

German silver
Antimony .
Bismuth .

0.7108
0.3760

0-3435
0.2460

O.22OO
0.2041
0.166;
0.1528
0.0836
0.0700
O.O442
0.0177

0.7226
0.3760
0.3619
0.2827
0.2045
0.2540
0.1627
0.1423
0.0764
0.0887
0.0396

0.016.1

45-74
24.47
22.46

15-75
14.41
12.62

10-37
9-346
5.141
3.766
2.199
0.929

33-82
17.50

10.18

I I.OO

6.628
6.524
3.602
3-632

1.522

0.633

1537
1529
1562

!527
1617
1605

1627
1858

2OII
I9OO

1-358
1.398

1.367
1.360

1.315

1.428
1-530

1-334
1.304

i-3J4
1.294

1-372

C. BERGET'S EXPERIMENTS^

The same specimens were used for both experiments. It will be seen that the ratio is nearly constant, but not

exactly so.

Substance.

k X io--

Substance.

X-X

Copper . .

Zinc . . .

Brass . .

Iron . . .

1.0405
0-303
0.2625
0.1587

V3

18.00

15-47
9.41

1.6

Tin . . .
Lead . .
Antimony
Mercury .

0.151
0.08 1 o
0.042

O.O2OI

8-33
5.06

2-47
i. 06

1.8
1.6
i-7
1.8

d. KOHLRAUSCH'S RESULTS.

An interesting confirmation of the relationship of the two conductivities has been furnished by F. Kohl-
rausch, who has shown that tempering steel causes equal proportional changes in the thermal and electrical
conductivities of the metal, thus leaving the ratio l/k unchanged by the process.^

Tempered steel
Soft steel

/= 0.062;
" = o.ni;

= 3.3; l/k = 0.019
=5-5; " =0.020

In the consideration of this subject it must be borne in mind that closely accurate values of thermal conduc-
tivity are very difficult to obtain, and hence fairly large variations are to be expected.

* " \Vied. Ann." vol. 13, p. 5q8.
t " Compt. Rend." vol. no, p. 76.

SMITHSONIAN TABLES.

I is in c. g. s. units and k in terms of mercury.

271

TABLE 283.

ELECTROCHEMICAL EQUIVALENTS AND INTERNATIONAL ATOMIC WEIGHTS.

With the exception of the value given for silver and that corresponding to valence 2 for copper, the electrochemical
equivalents given in this table have been calculated from the atomic weights and one or two of the more com-
mon apparent valences of the substance. The value given for silver is that which was adopted by the Inter-
national Congress of Electricians at Chicago in 1894. The number for silver is made the basis of the table ; the
other numbers, with the exception of copper, above referred to, are theoretical.

The International Atomic Weights are quoted from the report of the International Committee on Atomic Weights
(" Jour. Am. Chem. Soc.," vol. 25, p. 4).

Substance.

Symbol.

Relative
atomic wt.
Oxygen = 16.

Relative

aton.ic wt.
Hydrogen — i.

Electrochemical
Valence, equivalent in grammes
per coulomb X tooo

Aluminum . . .

Al

27.1

26.9

3

.0936

Antimony

Sb

1 20. 2

U9-3

3

.4150

4 ' , • .

* *

* *

* *

5

.2490

Argon ....

A

39-9

39-6

—

Arsenic . ..

As

75-0

74-4

3

.2590

"

"

"

5

.1554

Barium

Ba

137-4

136.4

2

.7116

Bismuth

Bi

208.5

206.9

3

.7199

" ...

"

"

"

5

.4319

Boron ....

B

ii.

10.9

3

.0380

Bromine

Br

79.96

79-30

i

.8283

Cadmium

Cd

112.4

in. 6

0

.5822

Caesium

Cs

133-

132.

I

1.3777

Calcium

Ca

40.1

39-8

2

.2077

Carbon

C

12. 0

11.91

4

.0311

Cerium

Ce

140.

139-

2

.7251

Chlorine

Cl

35-45

35.i8

1

.3672

Chromium . . .

Cr

52.1

5'-7

3

.1800

.

"

><

"

6

.0900

Cobalt . .

Co

59-0

5856

2

3056

" . . . . '

»

••

«•

3

.2038

Columbium .

Cb

94-

93-3

5

.1947

Copper

Cu

63.6

63.1

i

.6588

.

11

* *

"

2

.3290

Erbium

Er

166.

164.8

2

.8598

Fluorine

F

19.

18.9

I

.1968

Gadolinium .

Gd

156.

155

—

Gallium

Ga

70.

69-5

3

.2417

Germanium .

Ge

72.5

71.9

—

Glucinum

Gl

9.1

903

2

.0471

Gold . .

Au

197.2

195-7

3

.6809

Helium . .

He

4-

4-

—

Hydrogen . . .

H

1. 008

I.OOO

i

.0104

Indium . . . -

In

114.

113.1

3

.3936

Iodine . . . . '.

I

126.85

125 90

i

1.3140

Iridium . .

Ir

193.0

191-5

4

.4998

Iron ....

Fe

55-9

55-5

2

.2895

" . . - •• •

"

"

* *

3

.1930

Krypton . . . •'•

Kr

81.8

81.2

—

Lanthanum . . .

La

138.9

137 9

2

.7194

Lead . . . . ;

Pb

206.9

205.35

2

1.0716

Lithium . . ,

Li

7.03

6.98

I

.0728

Magnesium . . .

Mg

24.36

24.18

2

. 1 262

Manganese .

Mn

55-0

54-6

2

.2849

...

4

.1424

SMITHSONIAN TALCS.

272

TABLE 283.
ELECTROCHEMICAL EQUIVALENTS AND INTERNATIONAL ATOMIC WEIGHTS.

Substance.

Symbol.

Relative
atomic wt.
Oxygen = 16.

Relative
atomic wt.
Hydrogen — i.

Valence.

Electrochemical
equivalent in grammes
per coulomb X 1000

Mercury .

Hg

200.O

198.5

I

2.0/17

.

"

"

"

2

1-0359

Molybdenum

Mo

96.0

95-3

6

.I<J57

Neodymium

Nd

143.6

U^.S

—

Neon ....

Ne

20.

19.9

—

Nickel.

Ni

58.7

5S.3

2

.3040

.

* *

* l

*

3

.2O27

Nitrogen ...

N

1404

13-93

3

.0485

. - •

"

* *

"

5

.0291

Osmium .

Os

191.

189 6

6

.3297

Oxygen . . .

O

1 6 oo

15 88

2

.0829

Palladium

Pel

106.5

105-7

2

.5516

.

"

"

•'

5

.2206

Phosphorous

P

31.0

30.77

3

.IO/O

.

"

5

.0642

Platinum

Pt

1948

193-3

2

1.0098

.

**

1 *

M

4

•5049

Potassium

K

,39 15

38.86

I

.4055

Praesodymium

Pr

140.5

139-4

—

Radium

Rd

225.

223.3

—

Rhodium

Rh

103.0

102.2

3

.3556

Rubidium

Rb

854

84.8

i

.8846

Ruthenium .

Ru

101.7

ioo 9

4

.26J4

Samarium

Sm

150

148.9

Scandium

Sc

44.1

438

Selenium

Se

79-2

786

2

.4102

Silicon .-, .

Si

28.4

28.2

4

• 0735

Silver ....

Ag

107.93

107.12

i

i . 1 1 80

Sodium . . .

Na

2-3.05

22 68

i

.2388

Strontium

Sr

87.6

86.94

2

•4537

Sulphur

s

32 06

3'. 83

2

.1660

Tantalum

Ta

183.

181 6

5

-3791

Tellurium

Te

127.6

126.6

2

. 6609

Terbium

Tb

1 60.

158.8

Thallium

Tl

204 r

202.6

I

2.1142

Thorium

Th

232.5

230.8

2

1.2042

Thulium

Tm

171.

169 7

Tin ....

Sn

119.0

118.1

2

.6163

....

"

"

"

4

.3082

Titanium . .

Ti

48.1

47-7

4

.1246

Tungsten . . ^

W

184.

182.6

6

.3177

Urnaium

U

238.5

236.7

2

1-2353

" ...

>4

"

3

.8235

Vanadium . .

V

51.2

50.8

3

.1768

• - •• v

**

.

5

.1061

Xenon ....

Xe

128.

127.

—

Ytterbium

Yb

173-0

171.7

—

Yttrium . . .

Yt

89.0

88.3

2

.4610

Zinc ....

Zn

65-4

64.9

2

.3387

Zirconium , .' .

Zr

90.6

89.9

4

.2346

SMITHSONIAN TABLES.

273

TABLES 284, 285.

PERMEABILITY OF IRON.

TABLE 284. — Permeability of Iron Rings and Wire.

This table gives, for a few specimens of iron, the magnetic induction B, and permeability ft, corresponding to the
magneto-motive forces H recorded in the first column. The first specimen is taken from a paper by Rowland,*
and refers to a welded and annealed ring of " Burden's Best" wrought iron. The ring was 6.77 cms. in mean
diameter, and the bar had a cross sectional area of 0.916 sq. cms. Specimens 2-4 are taken from a paper by
Bosanquet.t and also refers to soft iron rings. The mean diameters were 21.5, 22.1, and 22.725 cms., and the
thickness of the bars 2.535, 1.295, and .7544 cms. respectively. These experiments were intended to illustrate the
effect of thickness of bar on the induction. Specimen 5 is from Ewing's book,t and refers to one of his own
experiments on a soft iron wire .077 cms. diameter and 30.5 cms. long.

Specimen 1

2

3

4

5

USAXB

B

*

B

V*

B

*

B

*

B

-

"S o J; = S

0.2

80

400

126

630

6s

325

8S

42 s

22

IIO

°-5

33°

660

377

7S4

224

448

214

428

74

148

o e : g =.=

I.O

145°

I4SO

1449

1449

840

840

885

88s

246

246

v ™ x = 3

2.0

4840

2420

4564

2282

3533

1766

2417

1208

95°

475

5-°

9880

1976

9900

1980

8293

1659

8884

1777

12430

2486

10.0

12970

1297

13023

1302

12540

1254

11388

1 139

15020

1502

2O.O

14740

737

14911

746

14710

73S

13273

664

15790

789

0 <u"2 s'2

50.0

16390

328

16217

324

16062

321

13890

278

IOO.O

17148

171

17900

179

14837

148

TABLE 285. — Permeability of Transformer Iron.§

This table contains the results of some experiments on transformers of the Westinghpuse and Thomson-Houston
types. Referring to the headings of the different columns, M\s the total magneto-motive force applied to the iron ;
M / 1 the magneto-motive force per centimetre length of the iron circuit : B the total induction through the mag-
netizing coil ; B / a. the induction per square centimetre of the mean section of the iron core ; M / B the magnetic
reluctance of the iron circuit; Bl/Ma the permeability of the iron, a being taken as the mean cross section of the
iron circuit as it exists in the transformer, which is thus slightly greater than the actual cross section of the iron.

(a) WESTINGHOUSE No. 8 TRANSFORMERS (ABOUT 2500 WATTS CAPACITY).

First specimen.

Second specimen.

M

T

. B

M

Bl

B

M

Bl

B

a

~B

Ma

B

a

B

Ma

2O

0-597

218X10'

1406

0.917 X io~*

2360

i6X to4

1032

1.25X10-*

'730

40

1.194

587 "

3790

0.68 1

3120

49 "

3*40

0.82 "

2640

60

1.791

878 "

5660

0.683 "

3180

82 "

5290

o-73 "

2970

80

2.338

1091 "

7040

0-734

2960

104 "

6710

0.77 "

2820

IOO

2.985

1219 "

7860

0.819

2640

118 "

7610

0.85 "

2560

120

3.#2

1330 "

8580

0.903 "

24TO

124 "

8000

0.97 "

2250

140

4.179

1405

9060

0-994

2186

131

8450

1.07

2036

160

4.776

'475

95'o

.090 "

2000

'35

8710

i.iS "

1830

180

5-373

1532

9880

.180 "

1850

140

9030

1.29 "

1690

200

5-970

1581

IO2OO

.270 "

1720

142 "

9160

1.41

1540

220

6.567

1618

10430

.360

1590

144

9290

••S3

1410

260

7.761

1692 "

IO9IO

•540

1410

SMITHSONIAN TABLES.

* " Phil. Mag." 4th series, vol. xlv. p. 151.

•t Ibid. 5th series, vol. xix. p. 73.

t " Magnetic Induction in Iron and Other Metals."

§ T. Gray, from special experiments.

274

TABLE 285.

PERMEABILITY OF TRANSFORMER IRON.

(to) WESTINGHOUSE No

. 6 TRANSFORMERS (ABOUT 1800 WATTS CAPACITY).

First specimen.

Second specimen.

M

T

B

M

Bl

B

M

Bl

B

a

B

Ma

B

a

B

Ma

20

0.62

I47XI03

1320

1. 36XIO-4

2140

2I5XI03

1940

0.93XIO-4

3*40

40

1.23

442

3980

0.91 '

3260

615

5540

0.64 "

4490

60

1.85

£?7

6280

0.86 •

339°

826

7440

0.72 "

4030

80

2.40

862

7770

0.93 '

3MO

986

8880

0.8 1 "

3590

too

3.08

949

8550

1.05 '

2770

1050

9460

0.95 "

3060

1 2O

3-7°

IOIO

9106

.19 '

245°

IIOO

9910

1.09

2670

140

4-3 1

1060

955°

•33 '

22IO

1140

10300

1.23 "

243°

160

4-93

1090

9820

•47 '

1990

1170

10500

*-37

2180

1 80

5-55

1 1 20

IOIOO

.61 '

1870

1190

10700

i-Si

1970

200

6.16

1150

10400

•74 '

l68o

—

~

(0) WESTINGHOUSE No. 4 TRANSFORMER
(ABOUT 1200 WATTS CAPACITY).

(d) THOMSON- HOUSTON 1500 WATTS TRANSFORMER.

M

B M

Bl

M

B

M

Bl

I

a

1

Ma

I

a

B

Ma

2O

0.69

i47Xio8

1470

1.36x10-4

2140

2O

0.42

70XI03

1560

2.86X10-*

373°

40

0.84

142

3160

2.81 "

3780

40

1.38

406 "

4066

0.98 '

•

2940

60

1.26

214

4770

2.8 1 "

3790

80

1.68

265

5910

3.02 "

3520

60

2.07

573 "

573°

1.05 '

*

2770

TOO

2.10

309

6890

3-24 '

3280

80

2.76

659 "

6590

1. 21 '

i

2390

120

160

2.52
3-36

348
408

7760
9IOO

3-45 '
3.92 "

3080

2710

2OO

4.20

456

IO2OO

4-39 '

2430

100

3-45

714 "

7140

I.4O '

2070

240

5-04

495

I 1000

4-87 •«

2190

280

5-88

524

11690

5-35 '

1990

1 20

4.14

748 "

7490

I. DO '

'

1810

320

6.72

55°

I227O

5.82 «

1820

360

7-S6

573

12780

6.29 "

1690

140

4-83

777 "

7770

1.80 '

*

1610

400

8.40

59i

I3I80

6.78 "

1570

440

9.24

5°4

13470

7.28 «

1460

275

TABLE 286.

COMPOSITION AND MAGNETIC

This table and Table 289 below are taken from a paper by Dr. Hopkinson * on the magnetic properties of iron and steel,
which is stated in the paper to have been 240. The maximum magnetization is not tabulated ; but as stated in the
by 4ir. " Coercive force" is the magnetizing force required to reduce the magnetization to zero. The ''demjig-
previous magnetization in the opposite direction to the " maximum induction " stated in the table. The "energy
which, however, was only found to agree roughly with the results of experiment.

Chemical analysis.

No.
of

Description of

Temper.

Test

specimen.

Total
Carbon.

Manga-
nese.

Sulphur.

Silicon.

Phos-
phorus.

Other
substances.

I

Wrought iron .

Annealed

_

_

_

_

_

2

Malleable cast iron .

"

-

—

-

—

-

-

3

Gray cast iron .

-

-

-

-

-

-

-

4

Bessemer steel .

-

0.045

O.2OO

0.030

None.

0.040

-

Whitworth mild steel

Annealed

0.090

0-153

o.o 1 6

"

0.042

-

6

" "

"

0.320

0.438

0.017

0.042

0.035

—

( Oil-hard-

7

j ened

~"

8

11 >'

Annealed

0.890

0.165

0.005

0.08 1

O.Oig

-

( Oil-hard-

'

u

9

l ened

T

10

Hadfield's manganese [
steel $ '

-

1.005

12.360

0.038

0.204

0.070

-

ii

Manganese steel

As forged

0.674

4-730

0.023

0.608

0.078

-

12

" " . .

Annealed

"

"

"

"

"

-

( Oil-hard-

'

tt

!3

\ ened

14

" " . »

As forged

1.298

8740

0.024

0.094

0.072

-

15

U «

Annealed

"

"

"

"

''

if\

((

( Oil-hard-

«

H

u

,(

IO

| ened

17

Silicon steel . . .

As forged

0.685

0.694

H

3438

0.123

_

18

" " .: .

Annealed

"

"

«

_

( Oil-hard-

19

| ened

~

20

Chrome steel ..

As forged

0-532

0-393

O.O20

0.220

0.041

0.621 Cr.

21

« «

Annealed

"

"

"

"

"

$ Oil-hard-

•

22

( ened

23

" " . .

As forged

0.687

0.028

"

0.134

0.043

1.195 Cr-

,24

" "...

Annealed

"

"

"

"

"

$ Oil-hard-

25

l ened

26

Tungsten steel .

As forged

1-357

0.036

None.

0.043

0.047

4.649 W. '

27

" "...

Annealed

"

"

«

"

"

"

! Hardened

28

" "...

in cold

"

«i

«

"

«

«

water

! Hardened

29

« '<

in tepid

"

"

"

"

«

«

water

3°

" " (French) .

$ Oil-hard-
/ ened

0.511

0.625

None.

O.O2I

0.028

3.444 W.

31

« «

Very hard

0-855

0.312

-

0.151

0.089

2-353 W.

32

Gray cast iron .

-

3-455

0-173

0.042

2.044

0.151

2.064 C.t

33

Mottled cast iron

-

2.581

0.610

0.105

1.476

0-435

1-477 C.t

34

White " " . .

-

2.036

0.386

0.467

0.764

0.458

35

Spiegeleisen .

4.510

7.970

Trace.

0.502

0.128

* Phil. Trans. Roy. Soc. vol. 176.
SMITHSONIAN TABLES.

t Graphitic carbon.

276

TABLE 286.

PROPERTIES OF IRON AND STEEL.

The numbers in the columns headed "magnetic properties" give the results for the highest magnetizing force used,
paper, it may be obtained by subtracting the magnetizing force (240) from the maximum induction and then dividing
netizing force ?1 is the magnetizing force which had to be applied in order to leave no residual magnetization after
dissipated" was calculated from the formula: — Energy dissipated == coercive force X maximum induction -^ IT.

No.
of
Test.

Description of
specimen.

Temper.

Specific
electri-
cal resis-
tance.

Magnetic properties.

Energy dis-
sipated per
cycle.

Maxi-
mum in-
duction.

Residual
induc-
tion.

Coer-
cive
force.

Demag-
netizive
force.

I

Wrought iron . . .

Annealed

.01378

18251

7248

2.30

_

J3356

2

Malleable cast iron .

"

03254

12408

7479

8.80

-

34742

3

Gray cast iron .

-

.10560

10783

3928

3.80

-

13037

4

Bessemer steel .

—

.01050

18196

7860

2.96

—

17137

5

Whitvvorth mild steel

Annealed

.OIO8O

19840

7080

1.63

-

10289

6

" "

"

.01446

18736

9840

6-73

-

40120

7

"

\ Oil-hard-
I ened

.01390

18796

11040

11.00

-

65786

S

" "

Annealed

.•°!559

l6l20

10740

8.26

-

42366

9

"

\ Oil-hard-
( ened

.01695

l6l2O

8736

19.38

-

99401

10

Hadfield's manganese (
steel \ '

-

.06554

3IO

-

-

'

IT

Manganese steel

'As forged

.05368

4623

22O2

23.50

37-13

34567

12

'' "

Annealed

.03928

10578

5848

33-86

46.10

"3963

I Oil hnrrl

T3

" " . .

1 Wll-lldl 1.1

( ened

•05556

4769

2158

27.64

, 40.29

41941

14

« n

As forged

.06993

747

-

-

-

t

15

ti a

Annealed

.06316

1985

540

24.50

50-39

15474

{ Oil-hard-

16

} ened

.07066

733

~

~

—

~

17

Silicon steel

As forged

.06163

15148

II073

9.49

I 2.6o

45740

18

" " ...

Annealed

.06185

14701

8149

7.80

10.74

36485

19

<i «

| Oil-hard-
J ened

.06195

14696

8084

12-75

17.14

596i9

i 20

Chrome steel .

As forged

.02016

15778

9318

12.24

13.87

6i439

1 21

a «

Annealed

.01942

14848

7570

8.98

12.24

42425

( Oil harrl

' 22

a a

1 \~tll— II dl LI

I ened

.02708

13960

8595

38-15

48.45

'69455

; 23

K i<

As forged

.01791

14680

7568

18.40

22.03

85944

; 24

« «

Annealed

.01849

13233

6489

15.40

19.79

64842

< Oil-hard-

25

n »

) ened

: -0303 5

12868

7891

40.80

56.70

167050

: 26

Tungsten steel .

As forged

.02249

I57i8

IOI44

15.71

17-75

78568

27

K «

Annealed

.02250

16498

IIOOS

'5-30

16.93

80315

( Hardened

28

" "...

| in cold

.02274

-

-

-

-

-

( water

C Hardened

29

<« «

< in tepid

.62249

15610

9482

30.10

34-70

149500

( water

i 3°

" (French) .

} Oil hard-
,\ ened

.03604

14480

8643

47.07

64.46

216864

' 31

" "...

Very hard

.04427

12133

68l8

51.20

70.69

197660

, 32

Gray cast iron .

-

.11400

9148

3l6l

13-67

I7-03

39789

; 33

Mottled cast iron

-

•;.o6286

10546

5108

12.24

-

41072

34

White " " . .

I -

.05661

9342

'5554

12.24

20.40

36383

35

Spiegeleisen

•

.10520

385

77

SMITHSONIAN TABLES.

277

TABLE 287.

PERMEABILITY OF SOME OF THE SPECIMENS IN TABLE 286.

This table gives the induction and the permeability for different values of the magnetizing force of some of the speei-
mens in Table 286. The specimen numbers refer to the same table. The numbers in this table have been taken
from the curves given by Dr. Hopkinson, and may therefore be slightly in error; they are the mean values for
rising and falling magnetizations.

Magnetiz-
ing force.
H

Specimen i (iron).

Specimen 8
(annealed steel).

Specimen 9 (same as
8 tempered).

Specimen 3
(cast iron).

B

M

B

M

B

/*

*

M

\

-

_

-

_

-

_

265

265

2

2OO

IOO

-

—

—

-

7OO

35°

3

-

-

-

-

-

-

1625

542

5

10050

2OIO

I525

300

75°

150

3000

600

IO

12550

1255

9000

900

1650

I6S

i^OOO

500

20

'455°

727

11500

575

5875

294

6000

300

30

15200

S°7

12650

422

9875

329

6500

217

40

15800

395

13300

332

11600

290

7IOO

177

5°

16000

320

13800

276

I2OOO

240

735°

149

70

16360

234

'435°

205

13400

191

7900

"3

100

16800

168

14900

M9

14500

145

8500

85

150

17400

116

15700

I05

I58OO

!°5

9500

63

200

17950

90

16100

80

l6lOO

80

10190

5i

TABLE 288.

MAGNETIC PROPERTIES OF SOFT IRON AT O

AND 1OO° C.

Soft iron at o° C.

Soft iron at 100° C.

H

.S

/

B

H

H

S

/

B

M

IOO

I8O.O

1408

17790

177.9

IOO

l8o.O

I4O2

17720

177.2

2OO

194-5

1521

19310

96-5

2OO

194.0

'5"

19190

96.0

4OO

208.0

1627

20830

52-1

4OO

207.0

1613

20660

51.6

7OO

215.5

1685

21870

31-2

700

213.4

1663

21590

29.8

IOOO

218.0

1705

22420

22.4

IOOO

215.0

1674

22040

21.0

1200

2,8.5

1709

22670

18.9

I2OO

215-5

1679

22300

1 8.6

TABLES 289.

MAGNETIC PROPERTIES OF STEEL AT Oc

AND 100° C.

Steel at o° C.

Steel at 100° C.

H

s

/

B

M

H

.s

/

B

f-

IOO

165.0

1283

16240

162.4

IOO

165.0

1278

16170

161.7

2OO

181.0

1408

17900

89-5

2OO

180.0

'395

17730

88.6

4OO

193.0

I5OO

19250

48.1

400

191.0

1480

19000

47-5

700

199-5

1552

20210

28.9

700

197.0

1527

I08oo

28.4

IOOO

203-5

I5«3

20900

2O.9

IOOO

199.0

!543

20380

20.4

I2OO

205.0

*595

2 1 24O

17.7

1500

203.0

'573

21270

14.2

375°t

2I2.O

1650

24470

6-5

3000

205-5

'593

23020

7-7

5000

208.0

1612

25260

5-1

* "Phil. Mag." 5 series, vol. xxix.

t The results in this and the other tables for forces above 1200 were not obtained from the ovoids above referred
to, but from a small piece of the metal provided with a polished mirror surface and placed, with its polished face nor-
mal to the lines of force, between the poles of a powerful electromagnet. The induction was then inferred from
the rotation of the plane of a polarized ray of red light reflected normally from the surface. (See Kerr's " Constants,''
P- 292-)

278

TABLES 29O-296.
MAGNETIC PROPERTIES OF METALS.

TABLE 290. — Cobalt at 100° C. TABLE 291. —Nickel at 100° 0.

H S

i

/ . B

M I

200

106

848

10850

54-2

300

116

928

11960

39-9

5OO

127

1016

13260

26.5

7OO

131

1048

13870

19.8

IOOO

!34

1076

14520

M-5

1500

I#

1104

15380

10.3

2500

J43

"44

16870

6-7

4000

r45

1164

18630

4-7

6coo

147

1176

20780

3-5

9000 ' 149

1192

23980

2.6

At o° C. this specimen gave the fol-

lowing results :

79°° | !54 | 1232

23380

3-o

H

S1

/

B

M

100

35-o

3°9

3980'

39-8

2OO

43-o

380

4966

24.8

3°°

46.0

406

5399

1 8.0

5OO

50.0

441

6043

I2.I

7OO

5!-5

454

6409

9-1

IOOO

53-o

468

6875

6.9

1500

56.0

494

7707

5-1

2500

58-4

5'5

8973

3-6

4000

59-o

520

10540

2.6

6oco

59-2

522

12561

2.1

9000

59-4

524

15585

i-7

I2OOO

59-6

526

18606

M

At o° C. this specimen gave the fol-

lowing results :

12300

67-5

595 1 '9782

1.6

TABLE 292. — Magnetite.

The following results are given by Du Bois * for a specimen of magnetite.

H

/

B

M

500
IOOO
2OOO
I2OOO

325

345
350
350

8361
9041
10084
20084

I6.7
9.0

5-o
i-7

TABLE 293. — Lowmoor
Wrought Iron.

TABLE 294. -Vicker's
Tool Steel.

TABLE 295. - Hadfleld's
Manganese Steel.

H

/

B

i

3080
6450
10450
13600
16390
18760
18980

1680
1740
1730
1720
1630
1680

'73°

24130
28300
32250
35200
36810
39900
40730

7-83
4-39
3-09
2-59
2.25
2.13
2.15

H

/

B

(M

6210
9970

I2I2O
14660
15530

1530

T570

!55o
1580
1610

25480
29650
31620

3455°
35820

4-IO

2-97
2.60
2.36
2.31

H

/

B

M

1930

ss

2620

1.36

2380

54

343°

1.44

3350

84

4400

•31

5920

III

73io

•24

6620

187

8970

•35

7800

191

10290

•3°

8390

263

'11690

•39

9810

396

14790

1.51

TABLE 296. —Saturation Values for Steels of Different Kinds.

H

/

B

1
M 1

I

3

15essemer steel containing about 0.4 per cent carbon . . .
Siemens-Marten steel containing about 0.5 per cent carbon
Crucible steel for making chisels, containing about 0.6 per
cent carbon

17600
18000

IQJ.7O

1770
1660

1480

39880
38860

38010

2.27 i
2.l6

I Qs

4

Finer quality of 3 containing about 0.8 per cent carbon ,
Crucible steel containing i per cent carbon

l833°
10620

1580

F44O

38190
-57600

2.08
I Q''

g

Whitxvorth's fluid-compressed steel

18700

I <%QO

78710

2 O7

—

* " Phil. Mag." 5 series, vol. xxix.

t " Phil. Trans. Roy. Soc." 1885 and

279

TABLE 297.

MAGNETIC PROPERTIES OF IRON IN VERY WEAK FIELDS.

The effect of very small magnetizing forces has been studied by C. Baur* and by Lord Kayleigli.t The following
short table is taken from Baur's paper, and is taken by him to indicate that the susceptibility is finite for zero values
of H and for a finite range increases in simple proportion to H. He gives the formula X.'= 15 -f- too H ', or /r=
15 ff -\- 100 H-. The experiments were made on an annealed ring of round bar 1.013 cms. radius, the ring haying
a radius of 9.432 cms. Lord Rayleigh's results for an iron wire not annealed give k=. 6.4 + 5.1 H, or / = 6.4 H
-(-5.1 ff~. The forces were reduced as low as 0.00004 c- &• s-> the relation of k to H remaining constant.

First experiment.

Second experiment.

H

k

/

H

k

.OI 580

16.46

2.63

.0130

'5-5°

.0308 1

17.65

5-47

.0847

18.38

.07083

23.00

'6-33

.0946

20.49

.13188

28.90

38.15

.1864

25.07

.2301 I

39.8l

91.56

.2903

32.40

.38422

5»-56

224.87

•3397

35-20

TABLES 298, 299.

DISSIPATION OF ENERGY IN CYCLIC MAGNETIZATION OF MAGNETIC

SUBSTANCES.

When a piece of iron or other magnetic metal is made to pass through a closed cycle of
magnetization dissipation of energy results. Let us suppose the iron to pass from zero magneti-
zation to strong magnetization in one direction and then gradually back through zero to strong
magnetization in the other direction and thence back to zero, and this operation to be repeated
several times. The iron will be found to assume the same magnetization when the same magne-
tizing force is reached from the same direction of change, but not when it is reached from the
other direction. This has been long known, and is particularly well illustrated in the permanency of
hard steel magnets. That this fact involves a dissipation of energy which can be calculated from
the open loop formed by ilie curves giving the relation of- magnetization to magnetizing force was
pointed out by Warburg J in 1881, reference being made to experiments of Thomson, § where such
curves are illustrated for magnetism, and to E. Cohn, || where similar curves are given for thermo-
electricity. The results of a number of experiments and calculations of the energy dissipajed
are given by Warburg. The subject was investigated about the same time by Ewing, who pub-
lished results somewhat later. If Extensive investigations have since been made by a number of
investigators.

TABLE 298.- Soft Iron Wire.

(From Swing's 1885 paper.)

Horse-

Total

Dissipation

power

induction

of energy

wasted per

per sq. cm.

in ergs per

ton at 100

B

cu. cm.

cycles per

sec.

2OOO

420

0.74

3000

800

1.41

4OOO

1230

2.18

5OOO

1700

3.01

6OOO

22OO

3-89

7000

2760

4.88

8OOO

345°

6.10

9000

4200

7-43

1 0000

5000

8.84

IIOOO

5820

10.30

I2OOO

6720

11.89

13000

7650

13-53

I4OOO

8650

I5-30

I5OOO

9670

17.10

* " Wied. Ann.'1 vol. xi.

t " Wied. Ann.:! vol. xiii. p. 141.

II " Wied. Ann." vol. 6.

Ml

SMITHSONIAN TABLES.

TABLE 299. — Cable Transformers.

Tliis table gives the results obtained by Alexander Siemens with one of
Siemens' cable transformers. The transformer core consisted of 900
soft iron wires i mm. diameter and 6 metres long.** The dissipation
of energy in watts is for 100 complete cycles per second.

Mean maxi-
mum induc-
tion density
in core.
B

Total ob-
served dis-
sipation of
energy in the
core in watts
per 1 12 Ibs.

Calculated
eddy current
loss in watts
per 112 Ibs.

Hysteresis
loss of
energy in
watts per
112 Ibs.

Hysteresis
loss of
energy in
ergs per
cu. cm.
per cycle.

IOOO

43-2

4

39-2

602

2OOO

96.2

16

80.2

I23! .

3000

158.0

36

I22.O

1874 ;

4OOO

231.2

64

I67.2

2566

5OOO

309-5

TOO

209.5

32'7

6000

390.1

144

246.1

3779

t " Phil. Mag." vo'- xxiii.
§ " Phil. Trans. Roy. Soc.'1 vol. 175.
IT " Proc. Roy. Soc." 1882, and " Trans. Roy. Soc." 18
P.roc. lust, of Elect. Eng." Loud., 1892.

280

TABLE 30O.

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 i' = a£1-6, where c 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 -^ 1500x3 c. g. s.
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.t

Values of Constant </.

The followii

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

a.

I

Iron .

Norway iron ........

.00227

'j

"

Wrought bar ........

.00326

3

"

Commercial ferrotype plate .....

.00548

4

"

Annealed .....

.00458

5

"

Thin tin plate

.OO286

6

"

Medium thickness tin plate .....

.00425

7

Steel .

Soft galvanized wire

.00349

8

" . • .

Annealed cast steel .......'

.00848

9

"

Soft annealed cast steel

.00457

10

"

Very soft annealed cast steel .....

.00318

ii

"

Same as 8 tempered in cold water ....

.02792

12

"

Tool steel glass hard tempered in water

.07476

'3

"

" " tempered in oil .....

.02670

'4

"

" " annealed .......

.01899

'5

" ' •)

( Same as 12, 13, and 14, after having been subjected J

( .O6l 30

16

"

? to an alternating m. m. f. of from 4000 to 6000 /

? .02700

i?

" ' '•$

f ampere turns for demagnetization . . . . )

( .01445 i

18

Cast iron .

Gray cast iron

.01300

'9

" " .

" " " containing J % aluminium

•01365

20

" "

'" " " *% - .

.01459

f A square rod 6 sq. cms. section and 6.5 cms. long, y

21

Magnetite .

< from the Tilly Foster mines, Brewsters, Putnam >

.02348

( County, New York, stated to be a very pure sample )

22

Nickel

Soft wire . . . . .

.OI22

$ Annealed wire, calculated by Steinmetz from )

23

) Ewing's experiments J

.0156

24

" ' .

Hardened, also from Ewing's experiments

.0385

25

Cobalt

Rod containing about 2 % of iron, also calculated j
) from Ewing's experiments by Steinmetz . . \

.OI2O

Consisted of thin needle-like chips obtained bv

milling grooves about 8 mm. wide across a pile of

thin sheets clamped together. About 30 % by vol-

26

Iron filings

ume of the specimen was iron,
ist experiment, continuous cyclic variation of m. m. (

O^ C*7

f. 1 80 cycles per second J

•°45/

2d experiment, 1 14 cycles per second

.0396

3d 79~9I cycles per second .

•0373

"Trans Am. Inst. Elect. Eng.'' January and September, 1892.
t See T. Gray, " Proc. Roy. Soc." vol. Ivi.

SMITHSONIAN TABLES.

28l

TABLE 3O1 .

DISSIPATION OF ENERGY IN THE CYCLIC MAGNETIZATION OF TRANS-
FORMER CORES.*

This table gives, for the most part, results obtained for transformer cores. The electromagnet core formed a closed
iron circuit of about 320 sq. cms. section and was made up of sheets of Bessemer steel about 1-20 inch thick. The
No. 20 transformer had a core of soft steel sheets about 7-1000 inch thick insulated from each other by sheets of
ihin paper. The cores of the other transformers were formed of soft steel sheets 15-1000 inch thick insulated from
each other by their oxidized surfaces only. The following are the particulars of the data given in the different
columns : —

Column i. Description of specimen.

2. The total energy, in joules per cycle, required to produce the magnetic induction given in column B

3. The energy, in joules per cycle, returned to the circuit on reversal of the magnetizing force.

4. The energy dissipaied, in joules per cycle, or the difference of columns 2 and 3.

5. 6, and 7. The quantities in columns 2, 3, and 4 reduced to ergs per cubic centimetre of the core.
B. The maximum induction in c. g. s. units per sq. cm.

1

2

3

4

5

6

7

B

6-5

0.9

5-6

1010

140

867

2660

24.4

2.6

21.8

3800

406

3400

6700,

66.8

10.4

56.4

10400

1620

8800

1 1600

81.4

15-4

66.0

12700

2400

10300

12700

Electromagnet . . . . •

96.6
126.2

21.8

38.2

74-8
88.0

15100
19700

3400
5960

11700
13700

14100
15200

i53-o

57-6

95-4

23900

8990

14900

15900

178.4

79.2

99.2

27800

12400

15500

16600

221.2

1 1 6.8

1044

34500

18300

16300

17240

275.6

168.0

107.6

42900

26200

16800

17420

'•31

0.30

1. 01

1435

328

1107

233°

4.65

I.IO

3-55

51 ro

I2IO

3900

4980

Westinghouse No 20

8.25

1.62

6.63

9060

1780

7280

6620

transformer . . . .

10.36

1.89

8.47

11350

2O7O

9280

7720

I 2. 2O

2.98

9.22

13440

3280

10160

8250

18.20

5-iS

13-05

19980

5660

14320

9690

0-45

0-055

0.400

875

I05

770

348o

Westinghouse No. 8
transformer, specimen i j

0.80
1.66

2.42

O.I O2

0.199

0.406

O.IOI

1.460

2.OIO

1544
3200
4650

196
380
780

1348
3870

5140

7570
9250

I

3-54

0-795

2.750

6820

'53°

5290

10940

0-399

0.046

o-353

768

88

680

3060

Westinghouse No. 8

0.820

0.085

o-735

1574

164

1410

4830

transformer, specimen 2

1-713

0.183

i-53o

3300

352

2948

7570

2.663

o-343

2.320

5120

660

4460

9270

f

0.488

0.062

0.426

1360

172

1188

4640

Westinghouse No. 6

0.814

0.096

0.718

2260

266

1994

6760

transformer, specimen i j

1.430

0.205

1.225

3980

570

34io

9370

I

2.OOO

0-33°

1.670

556o

918

4642

10950

f

O.722

O.IOO

0.622

2000

278

1722

7290

Westinghouse No. 6

1.048

0.164

0.884

2920

4^6

2464

9000

transformer, specimen 2 1

t-379

O.222

i-'57

3830

616

32I4

9990

I

i-73i

0.328

1.403

4810

912

3898

I I2IO

f

0-355

O.O44

0.311

1210

i52

1058

4540

Westinghouse No. 4

0.549

0074

0.475

1880

255

1625

CO2O

transformer .... 1

0.783

O.I26

0.657

2690

433

2257

7 '40

I

0970

0-175

0-795

3340

603

2737

7800

f

0.413

O.IO5

0.308

1930

490

1440

6150

Thomson-Houston 1500 j

0.68 1

O.lSg

0.492

3190

880

2310

8250

watt transformer . . j

1.207

0.389

0.8 1 8

5660

1830

3830

III IO

I

1-797

0.710

1.087

8420

332o

5100

13290

•* T. Gray, from special experiments ; see Table 285 for other properties.
SMITHSONIAN TABLES.

282

TABLE 3O2.

DISSIPATION OF ENERGY DUE TO MAGNETIC HYSTERESIS IN IRON.*

The first column gives the maximum magnetic induction B per square centimetre in c. g. s. units. The other col-
umns give the dissipation of energy in ergs per cycle per cubic centimetre for the iron specified in the foot-note

B

1

2

3

4

5

6

7

2OOO

400

420

53°

600

75°

930

IIOO

30OO

780

800

1050

1150

1350

1700

2150

4OOO

1200

1260

1670

1780

2030

2600

33°°

5OOO

1680

1770

2440

2640

2810

3800

4700

6000

22OO

2370

3r70

3360

3700

5200

6200

7000

2800

315°

4020

4300

4650

6600

7800

8OOO

343°

3940

5020

5300

5770

8400

9500

9OOO

4160

4800

• 6100

6380

6970

IOIOO

11400

IOOOO

4920

573°

7200

7520

8340

11800

13400

1IOOO

5800

6800

8410

8750

9880

13600

15600

I2OOO

6700

8000

9750

10070

"55°

15400

-

13000

7620

9200

1 1 200

11460

13260

17300

-

I4OOO

8620

10500

12780

13100

15180

-

-

I5OOO

973°

12150

14600

14900

17300

-

-

The iron for which data are given in columns i to 7 is described as follows : —
i. Very soft iron wire (taken from a former paper).
2,1. Sheet iron 1.95 millimetres thick ) almost alike.
2b. Thin sheet iron 0.367 millimetres thick »
3. Iron wire 0.975 millimetres diameter.
4. Iron wire of hedgehog transformer 0.602 millimetres diameter.
5. Thin sheet iron 0.47 millimetres thick.
6. Fine iron wire 0.2475 millimetres diameter.
7. Fine iron wire 0.34 millimetres diameter.

* Ewing and Klassen, " Phil. Trans. Roy. Soc." vol. clxxxiv. A, p. 1015.

283

TABLE 3O3.

MACNETO-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 ?', 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 303-310. For variation with tempera-
ture the following formula is given by Bichat : —

R = A>0 (i — 0.00104^ — O.OOOOI4/'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 : —

0, Mj'W— 0V

where /* 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 formulae 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-
rel,}: Quincke, § KoepselJ Arons,1[ Kundt,** Jahn,tt Sch6nrock,Jf Gordon, §§ Rayleigh and
Sidgevvick.lHI Perkin.llf 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

t

' Ann. de Chi

i. et de Phys." [3] vol. 52.

i

' Ann. de Chi

i. et de Phys." [5] vol. 12 ; " C. R." vols. 90 and 100.

§

' Wied. Ann.'

vol. 24.

II

' Wied. Ann.'

vol. 26.

if

' Wied. Ann.'

vol. 24.

**

' Wied. Ann.'

vols. 23 and 27.

tt

' Wied. Ann.'' vol 43.

»

' Zeits. fiir Pliys. Chem." vol. n.

§§

' Proc. Roy. Soc." 1883.

III!

' Phil. Trans. R. S." 1885.

iro

***

' Jour. Chem. Soc." vols. 8 and 12.
' Jour, de Phys." vols. 8 and 9.

SMITHSONIAN TABLES.

284

TABLE 3O3.

MAGNETO-OPTIC ROTATION.

Solids.

Substance.

Chemical
formula.

Density
or
grammes
per c. c.

Kind
of
light.

Verdet's
constant
in
minutes.

Temp. C.

Authority.

Amber

-

-

D

0.0095

18-20°

Quincke.

Blende

ZnS

-

"

0.2234

IS

Becquerel.

Diamond . . '. ,"• .

C

-

"

0.0127

"

«

Fluor spar ....

CaFl2

-

"

0.0087

«

u

Glass :

0.020"?

«

Faraday A ....

-

5-453

•

V.V*.VJ

0.0782

18-20

Quincke.

B . .
Flint .....

-

4.284

"

0.0649

0.0420

"

M

-

-

«

0.0325

15

Becquerel.

n

-

-

"

0.0416

"

M

" dense . , . .

-

-

"

0.0576

"

(«

. . . ,

-

-

"

0.0647

"

«

Plate . .. . . . • * *.

-

-

"

0.0406

18-20

Quincke.

Lead borate . . .

PbB204

-

"

0.0600

'5

Becquerel.

Quartz (perpendicular to axis)

-

-

"

0.0172

1 8-20

Quincke.

Rock salt «

NaCl

-

"

0-0355

'5

Becquerel.

Selenium ......

Se

-

B

0.4625

"

M

Sodium borate .

Na2B4O7

-

D

0.0170

"

«

Spinel (colored by chrome)

-

-

"

0.0209

"

»

Sylvine

KC1

-

"

0.0283

"

"

Ziqueline (suboxide of copper)

Cu2O

-

B

0.5908

"

M

SMITHSONIAN TABLES.

285

TABLE 304.

MAGNETO-OPTIC ROTATION.

Liquids.

Substance.

Chemical
formula.

Density
in
grammes
per c. c.

Kind
of
light.

Verdet's
constant
in
minutes.

Temp.
C.

Authority.

Acetone .....

C3H6O

O.7 Q47

D

o.oi 13

20

Jahn.

/ :XTV
0-7957

0.0115

15

Perkin.

".....

u

0.7947

"

0.0114

16

Schonrock.

Acids : (see also solutions in-

water)

Acetic

C2H4O2

I.O56l

«

0.0105

21

Perkin.

Butyric

C4H802

0.9663

"

O.OI 1 6

15

"

Formic

CH2O2

.2273

"

O.OIO5

15

"

Hydrochloric

HC1

.2O72

"

O.O224

15

"

" ...

a

—

"

O.O2O6

15

Becquerel.

Hydrobromic

HBr

•7859

"

0-0343

'5

Perkin.

Hydroiodic ....
Nitric

HI

HN03

•9473
.5190'

«

0.0513
0.0070

J5

!3

u

" (fuming)

"

"

O.OOSO

15

Becquerel.

Propionic ....

CgHgC^

09975

u

O.OIIO

15

Perkin.

Sulphuric ....

H2SO4

-

"

O.OI2I

15

Becquerel.

Sulphurous ....

H2S03

-

"

0.0153

15

"

Valeric ....

C5H10O2

O.Qd'lS

u

O.0 121

I c

Perkin.

Alcohols :

v :7TO

j

C6HUOH

_

K

O.OI3I

I C

Becquerel.

0.8107

"

0.0128

J

20

Jahn.

Butyl . .

C4H9OH

O.8O2 1

a

OOI24

20

u

u

O.OI24

15

Becquerel.

Ethyl . .

C2H5OH

0.7929

"

T^
O.OIO/

1 8-20

Quincke.

tt

*

O.79OO

**

O.OI 12

2O

Jahn.

It

<

O.7Q44

«

O.OII4

I c

Perkin.

«

«

/ ;/T^
0-7943

0

O.OII3

j

16

Schonrock.

Methyl

CH3OH

0.7915

"

O.OO94

18-20

Quincke.

a

*

O 7Q2O

"

0.0007

20

Jahn.

it

i

/ y~v

U

sj

o.oi 06

I S

Becquerel.

a

a

O.7966

u

0.0096

o
I c

Perkin.

«

a

0.7903

"

0.0096

J

21.9

Schonrock.

Octyl

C8H17OH

0.8296

"

0.0134

15

Perkin.

Propyl .....

C3II7OH

0.8050

tf

O.OI 2O

20.8

Schonrock.

" . .

tt

0.8082

"

O.OI 2O

15.0

Perkin.

"

a

-

"

0.0118

15

Becquerel.

i>

"

O.8O42

tt

O.OI 2O

20

Jahn.

Benzene . • . . . . •

CeHe

0.8786

«

0.0297

20

Jahn.

" .

«

-

"

0.0268

15

Becquerel.

" . ' . .

"

0.8718

It

0.0301

26.9

Schonrock.

Bromides :

Bromoform ....

CHBr3

2.9O2I

"

0.0317

15

Perkin.

Ethyl

C2H5Br

1.4486

"

0.0183

15

"

Ethylene ....

C2H4Br2

2.I87I

"

0.0268

15

"

«

"

2.1780

K

0.0269

20

Jahn.

Methyl

CH3Br

I-733I

"

0.0205

0

Perkin.

Methylene ....

C H2Br2

2.4971

"

0.0276

15

"

Octyl

C8H17Br

I.II70

"

0.0164

15

"

Propyl

C3H7Br

1.3600

"

0.0180

15

"

Carbon d 'sulphide .

CS2

1.2644

"

0.0441

18-20

Quincke.

"...

"

-

"

0.0434

O

( Becquerel,
i 1885.

" " . .

a

—

"

0.0433

0

Gordon.

i< a

"

-

H

0.0420

18

Rayleigh.

u a

"

-

tt

0.0420

18

Koepsel.

u

0.0439

O

Arons.

SMITHSONIAN TABLES.

286

TABLE 3O4.

MAGNETO-OPTIC ROTATION

Liquids.

Substance.

Chemical
formula.

Density
in
grammes
per c. c.

Kind
of
light.

Verdet's
constant
in
minutes.

Temp.
C.

Authority.

Chlorides:

Amyl . . . .

CHC1

0.8740

D

O.OI4O

20

Jahn.

Arsenic ....

As

-

"

0.0422

15

Becquerel.

Carbon ....

C

-

"

O.OI7O

15

"

" bichloride

ecu

-

"

0.0321

15

u

Chloroform . .

CHCU

1.4823

"

0.0164

20

Jahn.

«

u

1.4990

"

0.0166

15

Perkiri.

Ethyl .'.'.'..

C2H6C1

0.9169

"

0.0138

6

"

Ethylene ....

C2H4C12

1.2589

"

0.0166

15

«

"

"'

1.2561

"

0.0164

20

Jahn.

Methyl ....

CH3C1

-

"

0.0170

15

Becquerel.

Methylene ....

CH2d2

I-330I

a

0.0162

15

Perkin.

Octyl

C8H17C1

0.8778

"

0.0141

15

"

Phosphorus protochloride .

PC13

-

"

0.0275

15

Becquerel.

Propyl . . .

C3H7C1

0.8922

"

0-0135

15

Perkin.

Silicon ....

SiCl4

—

"

0.0275

15

Becquerel.

Sulphur bichloride

S2CI2

-

"

0.0393

15

"

Tin bichloride . . .

SnCU

—

"

0.0151

15

"

Zinc bichloride .

ZnCl2

-

"

0.0437

15

H

Iodides:

Ethyl . . '.

C2H5I

1.9417

"

0.0296

15

Perkin.

Methyl ....

CH3I

2.2832

"

0.0336

15

Octyl

C8Hi7l

•3395

"

0.0213

15

Propyl .....

C3H7I

.7658

u

0.0271

15

Nitrates :

Ethyl

C2H5O.NO2

•"49

"

0.0091

15

Ethylene (nitroglycol)

C2H4(N03)2

.4948

"

0.0088

IS

Methyl ....

CH3O.N02

•215?

"

0.0078

15

Propyl ....

C3H7O.N02

.0622

"

O.OIOO

15

Trinitrin (nitroglycerine) .

C3H5(N03)3

•5996

"

00090

15

Nitro ethane

C2H5N02

•0552

"

0.0095

15

Nitro methane .

CH3NO2

.1432

"

0.0084

15

Nitro propane

C3H5N02

.0100

"

O.OIO2

15

'

Paraffins :

Decane .

CioH22

0.7218

"

0.0128

23.1

Schonrock.

Heptane . . . .

C7H16

0.6880

*'

O.OI25

15

Perkin.

Hexane ....

C6H14

0.6580

"

O.OI22

22.1

Schonrock.

" ....

"

0.6743

"

O.OI25

15

Perkin.

Octane ....

CgHig

0.7011

"

0.0128

23.1

Schonrock.

Pentane . , '.

CsHi2

0.6196

"

c.oirt)

21. 1

"

" • .

"

0.6332

"

0.0118

15

Perkin.

Phosphorus (melted)

P

"

0.1316

33

Becquerel.

Sulphur (melted) .

S

-

M

0.0803

114

"

Toluene . . - .

C7H8

0.8581

"

0.0269

28.4

Schonrock.

'' ....

"

-

"

0.0243

IS

Becquerel.

Water

H2O

O QQQ2

<4

O.OI 7O

I r

«

i_>.yyy.i
0.9983

"

0.0131

18-20

Quincke.

" ....

"

0.9983

"

0.0132

20

Jahn.

Xylene . ....

CsHio

"

O.O22I

15

Becquerel.

0.8746

0.0263

27

Schonrock.

SMITHSONIAN TABLES.

287

TABLE 305.

MAGNETO-OPTIC ROTATION.

Solutions of Acids and Salts In Water.

Substance.

Cliemical
formula.

Density,
grammes
per c. c.

i Kind
of
light.

Verdet's
constant
in minutes

Temp.
C.

Authority.

Acetone . . .

C3H60

0.9715

D

O.OI29

20°

Jahn.

Acids :

Hydrobromic

HBr

'•7859

"

0-0343

y

Perkin.

" • •

"

1.6104

"

0.0304

"

• • • •

"

1-3775

"

0.0244

"

"

M

"

1.2039

'

0.0194

"

"

" "•••«,

"

1.1163

4

o.o 1 68

"

"

Hydrochloric .

HC1

1.2072

1

0.0225

*

"

" . • . .

"

1.1856

'

0.0219

*

"

. .

"

i-!573

'

0.0204

*

"

" ...

"

1.1279

'

0.0193

1

"

M

'

1.0762

'

o.o 1 68

•

"

>(

'

1-0323

"

0.0150

20

Jahn.

U

'

1.0158

"

0.0140

"

"

Hydriodic ....

HI

1-9473

u

0-0513

"

Perkin.

I-9057

"

0.0499

"

"

1.8229

"

0.0468

"

"

1.7007

"

0.0421

"

1-4495

"

0.0323

*

1.2966

"

0.0258

*

"

1.1760

1

0.0205

•

"

Nitric . . . v .

HNOs

1.5190

'

0.00 10

1

"

".....

"

1.3560

'

0.0105

'

"

Sulphuric + 3H2O .

H,S04

'

0.012 1

"

Becquerel.

NH3

0.8918

i

O OI C"2

I r

Perkin.

Bromides :

(J'U1 JJ

1 3

Ammonium . . ' '.

NH4Br

1.2805

'

O.O226

"

"

" ....

"

1.1576

1

o.o 1 86

"

"

Barium ....

BaBr2

1-5399

"

0.0215

2O

Jahn.

".....

"

i-2«55

"

0.0176

"

"

Cadmium ....

CdBr2

1.3291

"

0.0192

"

"

" ....

"

1. 1608

"

0.0162

"

"

Calcium ....

CaBr2

1.2491

"

0.0189

"

"

" ....

"

I-I337

"

0.0164

"

"

Potassium ....

KBr

1.1424

"

0.0163

"

"

" ....

"

1.0876

"

0.0151

"

"

Sodium ....

NaBr

1-135'

1.0824

<i

0.0165
0.0152

u

M

Strontium . . .

SrBr2

1.2901

"

o.o 1 86

"

'

" ....

"

1.1416

"

0.0159

"

'

Carbonate of potassium .

K2C03

1.1906

"

0.0140

20

'

" " sodium

Na2C03

1. 1006

ii

0.0140

"

'

it a ii _

"

1.0564

"

0.0137

"

'

Chlorides :

Ammonium (sal ammoniac)

NH4C1

1.0718

"

0.0178

t's

Verdet.

Barium ....

BaC'l2

1.2897

ii

0.0168

20

Jahn.

" ....

"

1-1338

"

0.0149

"

"

Cadmium . .

CdCl2

'•3179

"

0.0185

"

"

" ....

"

'•2755

M

0.0179

"

"

" r . .

M

1.1732

"

0.0160

"

u

.

.,

i-i53'

"

0.0157

"

"

Calcium . .

CaCl2

1.1504

"

0.0165

"

"

" . . . .

"

1.0832

"

0.0152

"

u

" ....

"

1.1049

"

0.0157

16

Schbnrock.

Copper . . .

CuCl2

1.5158

"

O.O22I

\S

Becquerel.

" ....

"

1.2789

"

o.o 1 86

"

U

1-1330

0.0156

SMITHSONIAN TABLES.

288

TABLE 305.

MAGNETO-OPTIC ROTATION.

Solutions of Acids and Salts in Water.

Substance.

Chemical
formula.

Density,
grammes
per c. c.

Kind
of
light.

Verdefs
constant
in minutes.

Temp.
C.

Authority.

Chlorides:

Iron ....

FeCl2

1-433'

D

0.0025

'5°

Becquerel.

'

1.2141

"

0.0099

"

"

/ »• •

'

1.1093

"

O.OIlS

''

"

'

i .0548

"

0.0124

"

"

(ferric)

Fe2Cl6

I-6933

"

— 0.2026

"

"

.

*

J-53'5

"

— 0.1140

"

ii

. >^r

1

1-323°

"

—0.0348

"

"

'

1.1681

"

— 0.0015

"

"

.

'

1.0864

a

O.OoSl

"

ft

..

"

1.0445

"

0.0113

"

ii

*

"

1.0232

"

O.OI22

"

11

Lithium

LiCl

1.0619

ii

O.OI45

20

Jahn.

" ...

"

1.0316

"

0.0143

"

"

Manganese .

MnCl2

1.1966

"

0.0167

15

Becquerel.

•

"

1.0876

"

O.OI5O

"

Mercury . . .

HgCl2

1.0381

"

0.0137

16

Schonrock.

•

"

1.0349

'

0.0137

"

"

Nickel ....

NiCl2

1.4685

'

0.0270

15

Becquerel.

.

"

1.2432

'

O.OI96

"

" • •

"

1-1233

'

O.OI62

"

ii

"

"

1.0690

1

0.0146

"

"

Potassium .

KC1

i. 6060

'

0.0163

"

ii

.

"

1.0732

'

0.0148

20

Jahn.

" ...

"

1.0418

'

O.OI44

"

"

Sodium

NaCl

1.2051

'

O.OlSo

15

Becquerel.

•

**

1.1058

'

0.0155

"

" ...

"

1.0546

'

O.OI44

"

"

" ....

"

1.0817

'

O.OI54

2O

Jahn.

ii

"

1.0418

'

O.OI44

"

"

Strontium .

SrCl2

1.1921

'

0.0102

"

"

" ...

"

1.0877

'

0.0146

"

"

Tin ....

SnCl2

1.3280

1

0.0266

15

Verdet.

**

"

1.1637

"

0.0198

"

"

I.III2

"

0.0175

it

Zinc ....

ZnCl2

1.2851

'

0.0196

"

" . . . .

"

i-r595

'

0.0161

"

Chromate of potassium .

K2CrO4

i-359«

1

0.0098

M

Bichromate of "

K->Cr2O7

1.0786

'

0.0126

"

Cyanide of mercury

Hy(CN)2

1.0638

'

0.0136

16

Schonrock.

" " "

"

1.0425

'

0.0134

"

"

" " "

"

1.0605

'

0.0135

"

"

Iodides :

Ammonium .

NH4I

1.5948

"

0.0396

15

Perkin.

" "...

"

1.5688

"

0.0386

"

11

<i

1.5109

<

0.0358

"

ii

a

a

1.2341

'

0.0235

"

"

Cadmium

Cdl

1-5156

'

0.0291

20

Jahn.

...

*

1.2770

'

0.0215

"

**

.

*

1.1521

'

0.0177

"

"

Potassium .

KI

1-6743

'

0.0338

i(5

Becquerel.

.

i-339«

'

0.0237

"

" ...

1.1705

"

0.0182

"

" . .

1.0871

"

0.0152

11

" . '

1.2380

"

O.O2II

20

Jahn.

...

1.1245

ii

O.OI74

"

Sodium . • . . '•

Nal

I-I939

"

0.0200

"

• , •

1.1191

H

0.0175

"

SMITHSONIAN TABLES.

289

TABLES 305-3O7.

MAGNETO-OPTIC ROTATION.

TABLE 305. — Solutions of Acids and Salts in Water.

Substance.

Chemical
formula.

Density,
grammes
perc. c.

Kind
of
light.

Verdet's
constant
in
minutes.

Temp.

Authority.

Nitrates :

Ammonium .

NH4NO3

1.2803

D

O.OI2I

IS

Perkin.

Potassium ....

KN03

1.0634

"

O.OI3O

20

Jahn.

Sodium ....

NaNO3

I.III2

"

O.OI3I

"

"

Uranium ....

U2O3.N2O5

2.O267

"

0.0053

"

Becquerel.

" ....

"

1.7640

"

0.0078

«

"

" ....

"

L3865

"

O.OIO5

"

"

" ....

"

I.I963

"

O.OII5

11

"

Sulphates :

Ammonium

(NH4)2S04

1.2286

"

O.OI4O

15

Perkin.

" (acid)

NH4.HSO4

I.44I7

'

0.0085

"

Barium ....

BaSO4

I.I788

i

0.0134

20

Jahn.

" • . . .

u

1.0938

'

0.0133

(1

'

Cadmium ....

CdSO4

I.I762

'

0.0139

ti

'

" • »

"

1.0890

i

0.0136

M

i

Lithium ....

Li2SO4

I.I702

«

0.0137

"

'

" ....

"

1.0942

'

0.0135

It

i

Manganese ....

MnSO4

I.244I

'

0.0138

U

'

" ....

"

I.I4I6

*

0.0136

U

i

Potassium ....

K2S04

1.0475

M

0.0133

u

i

Sodium ....

NaSO4

1.0661

M

0.0135

u

TABLE 306. - Solutions of Salts in Alcohol.

Substance.

Chemical
formula.

Density,
grammes
per c. c.

Kind
of
light.

Verdet's
constant
in
minutes.

Temp.

Authority.

Cadmium bromide . . .

CdBr2

1.0446

D

o.oi 59

2O

Jahn.

" " . «

«

0.9420

"

0.0140

Calcium "...

CaBr2

0.9966

u

0.0154

1

u 11

"

0.8846

"

0.0130

1

Strontium "...

SrBr2

0.9636

"

0.0140

<

" "...

H

0.8814

"

O.OI26

(

Cadmium chloride . .

CdCl2

0.8303

(i

O.OIlS

'

Strontium "

SrCl2

0-8313

"

O.OI 18

<

« «

"

0.8274

a

OOII7

<<

Cadmium iodide . .

CdI2

1.0988

(1

0.0199

"

u <«

0.9484

u

0.0156

«

TABLE 307. — Solutions in Hydrochloric Acid.

Substance.

Chemical
formula.

Density,
grammes
per c. c.

Kind
of
light.

Verdet's
constant
in
minutes.

Temp.
C.

Authority.

Antimony trichloride

SbCl3

2-4755

D

0.0603

15

Becquerel.

" " .

11

1.8573

"

0.0449

"

'•S^S

0.0347

"

I< II

"

1.3420

'

0.0277

Bismuth "

BiClg

2.0822

1

0.0396

11

it «

"

1-655°

'

0.0359

« «

«

1.4156

0.0350

SMITHSONIAN TABLES.

290

MAGNETO-OPTIC ROTATION.

Gases.

TABLE 308.

Verdet's

Substance.

Pressure.

Temp.

constant in

Authority.

minutes.

Atmospheric air

Atmospheric

Ordinary

6.83 X i o-6

Becquerel.

Carbon dioxide ....

13.00

Carbon disulphide ....

74 cms.

70° C.

23-49

Bichat.

Ethylene

Atmospheric

Ordinary

3448

Becquerel.

Nitrogen .....

6.92

"

Nitrous oxide . . . . . .

it

«

16.90

i(

Oxygen .

"

"

6.28

a

Sulphur dioxide ....

H

"

3r-39 '

it

it (4

246 cms.

20° C.

38.40

Bichat.

Du Bois discusses Kundt's results and gives additional experiments on nickel and cobalt.
He shows that in the case of substances like iron, nickel, and cobalt which have a variable mag-
netic 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 309.

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^ constant."

Verdet's constant.

Name of substance.

Magnetic
susceptibility.

Wave-length
of light

Kundt's
constant.

Number.

Authority.

Cobalt . .

_

_

_

6.44 X J0~5

3-99

Nickel

-

-

—

,

3-J5

Iron . . .: .

-

-

-

6.56

2.63

Oxygen : I atmo. .

-f- 0.0126 X io~5

0.000179 X icr6

Becquerel.

5.89

0.014

Sulphur dioxide

— 0.0751

0.302

14

— 4-OO

Water

— 0.0694

0-377

Arons

— 5-4

Nitric acid

— 0.0633

0-3S6

Becquerel.

-5-6

Alcohol . .

— 0.0566

0-330

De la Rive.

-5-8

Ether. .

— 0.0541

°-3 T 5

"

-S-8

Arsenic chloride

— 0.0876

1.222

Becquerel.

• — '4-9

Carbon disulphide .

— 0.0716

1.222

Rayleigh.

— 17.1

Faraday's glass

— 0.0982

1.738

Becquerel.

—17-7

SMITHSONIAN TABLES.

2QI

TABLE 310.

MAGNETIC SUSCEPTIBILITY OF LIQUIDS AND CASES.

The following table gives a comparison by Du Bois* of his own and some other determinations of the magnetic sus-
ceptibility of a few standard substances. Verdet's and Kundt's constants are in radians for the sodium line D.

Substance.

Verdet's
constant.

Faraday's
value
kX 10"

Becquerel's
value
/tXio6

Wahner's
value
k X io«

Water . . ...

3.77 X i o-6

— 0.69

—0.63

—0.536

Alcohol, C2H6O .

3-3° "

—0-57

—0.49

—0.388

Ether, C4H10O .

3-15 "

—0-54

-

—0.360

Carbon disulphide

12.22 "

— 0.72

—0.84

—0.465

Oxygen at i atmosphere . •;

0.00179"

0.13

0.12

-

Air at i atmosphere

0.00194 "

0.024

O.O25

-

Substance.

Quincke at 20° C.

Du Bois at is°C.

Density.

AXio6

Density.

k Xio«

Kundt's
constant.

Water .....

0.9983
0.7929

—0.815
— 0.660

0.9992
0.7963

—0.837
— 0.694

—4-5°
—4-75

Alcohol, C2H6O . . '

Ether, C4Hi0O . .

0.7152

— 0.607

0.7250

— 0.642

—4.91

Carbon disulphide

1.2644

—0.724

1.2692

—0.8 1 6

— 14.97

Oxygen at i atmosphere . <

-

-

0.00135

0.117

0.016

Air at i atmosphere . . j

-

-

O.OOI23

0.024

0.08 1

TABLE 31 1.

VALUES OF KERR'S CONSTANTS

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 10"

Kerr's constant in minutes per c. g. s. unit of magnetization.

Cobalt.

Nickel.

Iron.

Magnetite.

Red .

Li a

67-7

— 0.02o8

—0.0173

— o.oi 54

+0.0096

Red . . '

—

62.0

— O.O [ 98

— O.O 1 60

— 0.0138

+0.0120

Yellow . '.

D

58-9

— 0.0193

— O.OI54

— o.oi 30

+0.0133

Green .

b

51-7

— 0.0179

— 0.0159

— O.OI 1 1

+0.0072

Blue .

F

48.6

—0.0180

— 0.0163

— O.OIOI

+ O.OO26

Violet .

G

43- r

— 0.0182

—0.0175

— 0.0089

-

* " Wied. Ann." vol. 35, p. 163.
SMITHSONIAN TABLES.

t H. E. J. G. Du Bois, " Phil. Mag." vol. 29.

292

TABLES 312, 313.

EFFECT OF MAGNETIC FIELD ON THE ELECTRIC RE-
SISTANCE OF BISMUTH.*

TABLE 312. — Resistance One Ohm for Zero Field and Various Temperatures.

This table gives the resistance to the flow of a steady electric current when conveyed
across a magnetic field of the strength in c. g. s. units given in the first column if
the wire has a resistance of one ohm at the temperature given at the top of the col-
umn when the field is of zero strength.

Temp. C.—

0°

10°

18°

30°

50°

80°

Field.

Resistance.

OOO

.OOO

.000

I. OOO .OOO

.000

.OOO

IOOO

.018

.019

1.018 .017

.014

.007

2OOO

•045

.050

1.045 •°4I

•034

.015

3000

.088

.094

1.084 -°74

•055

.032

4000

•J35

•153

1.131

.118

.085

.050

5<X>O

.185

.214

1.183 -'56

•"3

•0/4

6OOO

.240

•273

1.242 | .202

.148

.100

7OOO
8000

•3°4
•365

•340

.406

1.295

r-35»

.258
-308

.190
•223

.127
•154

9000

•423

.467

1.417

•355

.266

.182

IOOOO

.480

•535

1.480

.409

•303

•203

15000

•743

•875

1.785

.665

•505

•343

2OOOO

2-507

2.087

1.927

•713

.490

25OOO

-

2.846

2-393

2.193

•93 i

.804

3OOOO

-

—

2.704

-

—

—

35°°°

—

-

3-03I

—

-

-

40000

3-369

TABLE 313. —Resistance One Ohm for Zero Field and Temperature Zero Cen-
tigrade.

This table gives the resistance in different magnetic fields and at different temperatures
of a wire, the resistance of which is one ohm at o° C., when the magnetic field is
zero. The current is supposed to be steady and to flow across the field.

Temp. C.=

0'

10°

18°

30°

50°

80°

Field.

Resistance.

oooo

1. 000

•037

1.072

•"5

.200

J-332

IOOO

I.OI8

•057

.091

.129

.217

I-34I

2000

1.045

.089

.118

•156

.241

'•352

3000

1. 088

•134

.162

.198

.266

1-375

4000

I-I35

.198

.210

.246

.302

i-397

5000

1.185

.260

•265

.290

•335

1.428

6000

1.240

•323

•327

•341

•379

1.464

7OOO

1.304

•392

•385

.404

.428

1.500

8000

^365

•458

•453

.460

.465

J-536

9000

1.423

•523

•5'5

•5°9

.520

'•573

IOOOO

1.480

•592

•583

•573

.562

1.610

15000

1-743

1.946

.907

.860

.805

1.784

2OOOO

—

2-295

2.243

2.148

2-055

1.980

25000

2.645

2.560

2.445

2.320

2-157

• Calculated from the results of J. B. Henderson's experiments,
SMITHSONIAN TABLES.

293

Phil. Mag." vol. 38, p. 488.

TABLE 314.

SPECIFIC HEATS OF VARIOUS SOLIDS AND LIQUIDS.4

SOLIDS.

Substance.

Temperature
in

Specific
heat.

Authority.

degrees C.

Alloys :

Bell metal .

15-98

0.0858

R

Brass, red

O

.08991

L

" yellow ........

O

.08831

"

8oCu-|-2oSn " .

14-98

.0862

R

88.7 Cu + 11.3 Al . . v .

2O-IOO

.10432

Ln

German silver .......

0-100

.09464

T

Lipowitz alloy : 24.97 Pb -f 10.13 Cd -f- 50.66 Bi

-j- 14.24 Sn

5-50

•°345

M

ditto

IOO-I50

.0426

"

Rose's alloy : 27.5 Pb -|- 48.9 Bi -)- 23.6 Sn .

—77-20

.0356

S

ditto

20-89

•°552

"

Wrood's alloy : 25.85 Pb + 6.99 Cd + 52-43 Bi +

14-73 Sn

5-5°

•0352

M

ditto (fluid)

100-150

.0426

"

Miscellaneous alloys :
17.5 Sb + 29.9 Bi + 18.7 Zn + 33.9 Sn

20-99

•05657

R

37.1 Sb + 62.9 Pb

10-98

.03880

M

39.9 Pb + 6o.iBi . . . . . . .

16-99

•03165

P

ditto (fluid) .

144-358

.03500

"

63.7 Pb -f- 36-3 Sn . . . . . - . ,.

12-99

.04073

R

46.7 Pb + 53.3 Sn • g

10-99

.04507

"

63.8 Bi 4- 36.2 Sn . . . • .

20-99

.04001

"

46.9 Bi +53.1 Sn . : . . . .

20-99

.04504

"

CdSn2 . .

—77-20

•°5537

"

Basalt .........

2O-IOO

.2O-.24

-

Calcspar

16-48

.206

K

Diamond . . . ...

—50-5

•0635

H W

.........

10.7

.1128

"

" .........

I4O.O

.2218

"

" . . . . . . . . ' .

2O6.O

•2733

"

" . • . ....

606.7

.4408

"

u

A^ c

A cXo

H

Gas coal . . . , . . .

20-1040

•3M5

_

Glass, crown . .

10-50

.161

H M

" flint

10-50

.117

"

" mirror . . . ....

10-50

.186

"

Gneiss .........

— 19-20

.1726

R W

'' .........

17-213

•2143

;'

Granite

O-IOO

.I9-.20

J& B

Graphite

—50-3

.1138

H W

" . ...

10.8

.1604

"

• . ; . ...

138-5

•2542

"

' .........

2OI.6

.2966

u

1 .........

641.9

•445°

"

',.........

977-0

.4670

"

16-1040

.310

D

REFERENCES.

A M — A. M. Mayer. B = Batelli. D = Dewar. E = Emo.

G & T = Gee & Terry. H & D = De Heen & Deruyts. H M = H. Meyer.

H W = H. F. Weber. J & B = Joly & Bartoli. K = Kopp.

L = Lorenz. Ln = Luginin. M = Mazotto. Ma=Marignac.

P= Person. Pa=Pagliani. Pn = Pionchon. R = Regnault.

R W == FLWeber. T = H. Tomlinson. Th = Thomsen. W = Wachsmuth.

* Condensed from more extensive tables given in Landolt and Bernstein's " Phys. Chem. Tab."

SMITHSONIAN TABLES.

294

TABLE 314.

SPECIFIC HEATS OF VARIOUS SOLIDS AND LIQUIDS.

Substance.

Temperature
in

Specific

Authority.

degrees C.

Gypsum

16-46

0.259

K

Ice

-78-0

.4627

R

" . . . . " . . ' . .

—30-0

•505

P

" . . . - . . . .

2I-I

.5017

"

India rubber (Para) . ...

?-IOO

.481

G&T

Marble, white . . . . . ' '. ^

16-98

.2158

R

gray . . . . ' . . . _ . .

23-98

.2099

"

Paraffin . . . . . ....

—20-3

.3768

R W

. . . • • * - .

— 19-20

•525'

"

. .

0-20

•6939

"

" .........

35-40

.622

B

fluid

6o-63

.712

"

Quartz . . . . ... . . . .

0

Pn

" .........

35°

.2786

"

" .........

400-1200

•305

«

Sulphur, cryst

17-45

.163

K

Vulcanite . . . ... . . . .

2O-IOO

•33'2

A M

LIQUIDS.

Alcohol, ethyl

— 20

0-5053

R

" " . . . . . . . . .

O

•5475

"

" "

40

.6479

"

" methyl ..'

5-io

.5901

"

« i<

15-10

.6009

u

Benzene

10

.3402

H&D

«

40

•4233

"

Ethyl ether . . *

O

.5290

R

Glycerine .........

'5-5°

•576

E

Oils, castor . . . .

-

•434

W

" citron . . . . .

5-4

.438

H W

" olive .........

6.6

.431

"

" sesame . . . . . . -^. .

—

•387

W

" turpentine . . . . . . .

0

.4106

R

Petroleum

21-58

•511

Pa

CuSO4+ 5oH2O " .

12-15

.848

"

<« 4. OOQ H2O . . . ...

12—14

.QCl

u

+ 400 H2O '.

I3-I7

7 J

•975

H

ZnSO4 + soH2O • ... .

20-52

.842

Ma

" + 200 HoO .

20-52

•95 2

"

KOH + 3oII2O . . . . .^ .

18

.876

Th

+ 200 H2O .

18 •

•975

"

NaOH + 50 H20 . . . ' .

18

.942

"

" + 100 H2O .......

18

•983

"

NaCl + ioH2U .

18

.791

"

+ 2coH2O . . . ....

18

.978

"

Sea water : density 1.0043

17-5

.980

"

" " " 1-0235 (about normal)

T7-5

•938

(<

1-0463

17-5

•903

REFERENCES.

A M = A. M. Maver. B — Batelli. D = Dewar. E = Emo.

G & T = Gee & Terry. H & D = De lleen & Deruyts. H M = H. Meyer.

H W = H. F. Weber. J & B = Joly & Bartoli. K = Kopp.

L = Lorenz. Ln = Luginin. M — Mazotto. Ma = Marignac.

P= Person. Pa=Pagliani. Pn = Pionchon. R = Regnault.

R W = R. Weber. T = H. Tomlinson. Th = Thomsen. W = Wachsmuth.

SMITHSONIAN TABLES.

295

TABLE 315.

SPECIFIC HEAT OF METALS.'

Metal.

Temperature
in

Specific

O

Metal.

Temperature
in

Specific

0

'degrees C.

heat.

3

degrees C.

heat.

1

Aluminium . .

2O

0.2135

N

Manganese

14-97

O.I2I7

R

" . .

IOO

.2211

"

Mercury : solid .

— 78 to — 40

.03192

M

u

2OO

.2306

1

20-50

•033' 2

W

"

300

.24OI

'

o

•03337

N

Antimony . . .

15

.04890

1

IOO

.03284

"

.

IOO

•05031

'

2OO

.03235

"

" ...

2OO

.05198

'

250

..03212

«

" ...

300

.05366

'

Nickel ....

14-97

.10916

R

Bismuth . . .

O

•03013

L

' ....

IOO

.11283

In

' ...

20-84

•0305

K

' ....

300

.14029

'

' fluid . .

280-380

•0363

P

' ....

500

.12988

'

Cadmium . . .

21

•0551

N

' ....

800

.1484

'

' ...

IOO.

.0570

"

' ....

IOOO

.16075

1

' ...

20O

.0594

"

Palladium . . .

O-IOO

.0592

V

' ...

300

.0617

"

" ...

0-1265

.0714

u

Calcium . . .

O-IOO

.1804

B

Platinum . . .

— 78-20

•03037

s

Chromium (?)

22-51

•09975

K

' ...

O-IOO

•0323

V

Cobalt ....

9-97

.10674

R

' ...

0-784

•°365

"

' ....

500

.14516

Pn

' ...

O-IOOO

•0377

«<

' ....

1000

.204

"

.

0-1177

.0388

"

Copper ....

o

.08988

L

' ...

1300

•03854

Pt

50

.09166

"

' ...

1400

.03896

"

17

.09244

N

' ...

itoo

.03980

"

....

IOO

.09422

"

Potassium . . .

—78.5-23

.1662

s

.

2OO

.09634

"

Silver ....

O-ICO

•0559

B

300

.09846

"

23

.05498

N

Gold . . . .

O-IOO

.0316

V

IOO

.05663

14

Indium . . .

O-IOO

•0323

"

2CO

•05877

"

" ...

0-1400

.0401

"

300

.06091

"

Iron

- I ?

IOQI

N

800

.076

Pn

* J
IOO

'lICI

fluid . .

907-1 ioo

/ w
.O748

',,

2OO

.I24Q

<.

Sodium ....

— 70.15—17

•v/ T^
.2870

s

u

•3.OO

& ^ty
.1-776

(|

/ ™ J /

—28-6

»JW

.2Q74

R

u

J***'

* 3f
.1764?

Pn

Tin .'..!!

— 78-20

:/O *

S

n

7OO

/ VT- J

/

o

.05368

L

u

/ *"*

720—1000

.218

a

«

«

IOOO-I2OO

.19887

«

<

75

0^641

a

Lead ....

—78-11

.03065

R

' fluid . . .

250-350

.0637

P

" ....

15

•02993

N

' " ...

250

•05799

I'll

" ....

IOO

.03108

"

' " ...

I IOO

.0758

"

u

2OO

O72J*

M

Zinc

O— IOO

QQ'J r

B

" fluid . . .

"UO

*o«c6

Sp

18

.0915

N

J
360

.04.006

F

,

IQO

.0951

Lithium

27— QQ

rw«f**2*W

.04.08

R

,

s

2OO

K

Magnesium

»/ yy

o

•y£r<*~r

.2456

L

. ,

•3.OO

.IO4O

7 1

.2 ^OQ

<

J~~

300-400

.122

LV

/ j

REFERENCES.

B = Bunsen. K = Kopp. L = Lorenz. LV = Le Verrier. N = Naccari.

P = Person. Pn = Pionchon. Pt = Pouillet. R = Regnault.

S = Schiiz. Sp= 'Spring. V = Violle. W = Winkelmann.

* Condensed from Landolt and Bbrnstein's " Phys. Chem. Tab."

SMITHSONIAN TABLES.

296

INDEX.

Al)sorption of gases by liquids 125

of solar energy by the atmosphere 177

Acceleration, angular and linear, conversion

factors for 17, 18

Activity, conversion factors for 19, 21

Aerodynamics ; data for the soaring of

planes 109

data for wind pressure 108

Agonic lines 117

Air, specific heat of 223

thermometer 228, 229

Alcohol, density of 96-98

vapor pressure of 126, 225

Alloys, electric conductivity of 251-253

electric resistance of 251-253, 256, 257

density of 85

specific heat of 294

strength of 73

thermal conductivity of 197

thermoelectric power of 248, 249

Alternating currents, resistance of wires for. 258

Alums, indices of refraction for 180

Angles, conversion factors for 14

Aqueous solutions, boiling-points of ....'... 196

vapor, density of 155

pressure of 151-154

Arc spectrum, wave-lengths in 172

Areas, conversion factors for 1 1

Atmosphere, pressure of vapor in 157

Atomic weights 272

Barometer, correction for capillarity 124

determination of heights by 169

reduction to latitude 45° 122, 123

reduction to sea level 121

reduction to standard temperature 120

Battery cells, composition and electromotive

force of 246, 247

Bismuth, electric resistance of, in magnetic

field 293

Boiling-point, of chemical elements 207

of various inorganic compounds 210

of various organic compounds 212

of water, barometric height correspond-
ing to 171

of water, effect of dissolved salts on. ... 196

Brick, strength of 70

British weights and measures, equivalents in
metric 7

Capacities, conversion factors for 12

Capacity, specific inductive 263-265

Capillarity, of aqueous solutions 128

correction of barometer for 1 24

of liquids as solidifying-point 129

of soap films 1 29

Capillarity (continued).

surface-tension of water and alcohol ... 128

various liquids 1 27

Carat, definition of 18

Cells, battery 246, 247

secondary 247

standard 247

Chemical elements, boiling and melting

points of 207

Cobalt, Kerr's constants of 291

magnetic properties of 279

Coefficients, isotonic 150

of diffusion 147, 149

of friction 135

of thermal expansion 214—218

of viscosity 137, 146

Color scale, Newton and Reinold and

Rucker 130

Combination, heat of 202

Combustion, heat of 201

Compressibility, of gases 79, 8 1

of liquids 82

of solids 83

Conducting power of alloys 251-253

Conductivities, molecular 260, 261

of electrolytes 259

thermal 197, 198

Contact, difference of potential 268

Conversion factor, definition of xviii

Conversion factors for acceleration, angular. . 18

acceleration, linear 17

activity 19, 21

angles 14

areas 1 1

capacities 12

densities 23

electric deposition 24

electric displacement 25

electric potential 27

electric resistance 23

energy 20, 2 1

film tension 20, 22

force 17

heat, quantities of 24

intensity of magnetization 26

length ii

masses 13

moment of inertia 13

moment of momentum 16

momentum 16

magnetic moment 27

magnetization, intensity of 26

magnetization, surface density of 26

power 19, 21

resistance, electric 23

stress 19, 22

temperatures 25

tension, film or surface 20

298

INDEX.

Conversion (continued).

time, intervals of 14

velocities 15

volumes 12

work 20, 21

Critical temperature of gases 200

Crystals, cubic expansion of 216

elastic constants of 78

formulae for elasticity of 77

refractive indices of 187

Cubic expansion, gases 218

liquids 217

solids 216

Cyclic magnetization, dissipation of energy
in 280-283

Declination, magnetic 1 13-1 18

Densities, of air, values of /i/?6o 162

alcohol 96-98

alloys and other solids 85

aqueous solutions 90

gases -. 89

liquids 88

mercury 95

metals 86

organic compounds 212

water 92-94.

woods 87

Density, conversion factors for 23

Dew-points, table for calculating 158

Diamonds, unit of weight for 13

Dielectric strength 244, 245

Diffusion of gases and vapors 149

liquids and solutions 147

Dilution of solution, contraction due to ... .134

Dimension formulae (see also Units) xvii

Dip, magnetic 1 1 1

Dynamic units, dimension formulas of xvii

formula? for conversion of 2

Dynamical equivalent of thermal unit 219

Earth, miscellaneous data concerning 106

Elasticity, moduli of 74~?8

Electric conductivity of alloys 251, 252

of metals 255

relation to thermal 271

constants of wires 58-68, 254

displacement .25

potential, conversion factors for 27

resistance, conversion factors for 23

resistance, effect of elongation on 258

units, conversion factors for 3

units, dimension formulae xxv

Electrochemical equivalents and atomic

weights 272

of solutions 259

Electrolytes, conductivities of 259

Electrolytic deposition, conversion factors for 24

Electromagnetic system of units xxix

Electromotive force of battery cells. . . .246, 247

Electrostatic system of units xxvi

Electrostatic unit of electricity, ratio of, to

electromagnetic 243

Elliptic integrals 43

Elongation, effect on resistance of wires. . . .258

Emissivity 234, 235

Energy, conversion factors for 20, 21

Equivalent, electrochemical 272

electrochemical of solutions 259

mechanical, of heat 220

Expansion, thermal 214, 218

Factors, conversion 1 1 -27

formulae for conversion 2, ^j

Film-tension, conversion factors for 20, 22

constants for 1 28, 1 29

Fluor spar, refractive index of 183

Formulae for conversion factors, dynamic

units 2

electric and magnetic units 3

fundamental units 2

geometric units 2

heat units 3

Formulas, dimension (see also Uttils}. .xvii-xxix

Force, conversion factors for 17

Force de cheval, definition of 19

Fraunhofer lines, wave-lengths of 175

Freezing mixtures 199

Freezing-point, lowering of, by salts 192

Friction, coefficients of 135

Functions, hyperbolic 2S~35

gamma 38

Fundamental units .2

Fusion, latent heat of 206

Gamma functions 38

Gases, absorption by liquids 125

compressibility of 79~8i

critical temperatures of >. 200

density and specific gravity of 89

expansion of 218

magnetic susceptibility of 292

magneto-optic rotation in 291

refractive indices of 190

specific heat of 224

thermal conductivity of 198

viscosity of 145, 146

volume of perfect (values of i -|- .00367 1)

164-168

Gauges, wire 58-68

Geometric units, conversion formulae for 2

Glass, electric resistance of 270

indices of refraction for 178, 179

Gravity, force of 102-104

Harmonics, zonal 40

Heat, conversion factors for quantities of . . . .24

latent heat of fusion 206

latent heat of vaporization 204

mechanical equivalent of 220

units, conversion factors for 24

dimension formulae for xxiii

formulae for conversion factors of . . . .3
Heats of combustion and combination. . 201, 202

Heights, determination by barometer 169

Humidity, relative iCi

Hydrogen thermometer 233

Hyperbolic cosines 29~3l

Hvperbolic functions . . 28-35

Hyperbolic sines 28-30

Hysteresis, magnetic 280-283

Iceland spar, refractive index of 185

Indices of refraction for alums 180

crystals 187

fluor spar i!" 5

gases and vapors 1 90

glass 17,", i/9

Iceland spar .' . . 185

liquids, various 189

metals and metallic oxides 181

monorefringent solids 184

INDEX.

299

Indices of refraction for alums (continued).

quartz 186

rock salt 182

solutions of salts 188

sylvine 182

Inductance, mutual 42

Integrals, elliptic .43

Intensity, horizontal, of earth's magnetic field

112

total, of earth's magnetic field no

Iron, elasticity and strength of 72

hysteresis in 280-283

magnetic properties of 274-283, 292

Isotonic coefficients 1 50

Jewels, unit of weight for 13

Joule's equivalent 220

Kerr's constant, definition and table of 292

Kilogramme, definition of xvi

Kundt's constants 291

definition of 291

Latent heat 204, 206

Least squares, various tables for 35, 37

Legalization of practical electric units. . . .xxxiv

Length, conversion factors for 1 1

Light, velocity of 176-243

rotation of plane of polarized 191

Linear expansion of chemical elements 214

of various substances 215

Liquids, absorption of gases by 125

compressibility and bulk moduli of 82

density of 88

magneto-optic rotation in 286, 287

magnetic susceptibility 292

refractive indices of 189

specific heat of 295

thermal conductivity of 197, 198

thermal expansion of 217

Lowering of freezing-point by salts 192

Magnetic field, effect of, in resistance of bis-
muth 293

moment, conversion factors for 27

permeability 274-280

properties of cobalt, manganese steel,

magnetite and nickel 279

properties of iron and steel 276

saturation values for steel 279

susceptibility of liquids and gases 292

units, conversion formulae for 3

dimension formulae for xxv

Magnetism, conversion factors for surface

density 26

terrestrial 1 10-1 18

Magnetization, conversion factors for inten-
sity of 26

Magnetite, Kerr's constant for 292

magnetic properties of 279

Magneto-optic rotation, general reference to

284

tables of 285-291

Masses, conversion factors for 13

Materials, strength of 7°~73

Measurement, units1 of xv

Mechanical equivalent of heat 220

Melting-points of chemical elements 207

Melting-points (continued).

of mixtures and alloys 211

of organic compounds 212

Mercury, density of 86

electric resistance of 255, 256

index of refraction 181

specific heat of 225

strength of 70

Metals, density of 86

electric resistance of 254-258

specific heat of 296

thermal conductivity of 197

Metals and metallic oxides, indices of refrac-
tion for 181

Metre, definition of xvi

Metric weights and measures —

equivalents in British .....* 5

equivalents in United States 10

Mixtures, freezing 199

Moduli of elasticity 74-83

Molecular conductivities 261, 262

Moments of inertia, conversion factors for. . . 13
Moment of momentum, conversion factor

for 16

Momentum, conversion factors for 13

Mutual inductance, table for calculating 42

Neutral-points, thermoelectric 249

Newton's rings and scale of colors 130

Nickel, Kerr's constants for 292

magnetic properties of 279

Ohm, various determinations of 262

Osmose and osmotic pressure 1 50

Pearls, unit of weight for 13

Peltier effect ... 250

Pendulum, length of seconds 104, 105

Permeability, magnetic 274-280

Photometric standards 176

Planets, miscellaneous data concerning 106

Poisson's ratio 76

Polarized light, rotation of the plane of 191

Potential, contact difference of 268

difference of, between metals in solu-
tions 269

electric, conversion factors for 27

Pound, definition of xvi

Power, conversion factors for 19, 21

Practical electrical units xxxiii

Pressure, barometric, for different boiling-
points of water 170, 171

critical, of gases 200

effect on radiation 236

of aqueous vapor 151-154

at low temperatures 156

in the atmosphere 1 57

of mercury column 119

osmotic 1 50

of vapors 126, 225-227

of wind 1 08

Probability, table for calculating 36

Quartz, fibres, strength of 70

refractive index of . . 186

Radiation, effect of pressure on 236

of inorganic compounds 2c8 ! Relative humidity 161

300

INDEX.

Resistance (see also Conductivity), electric.

of alloys 251-253, 256, 257

of electrolytes 259

of glass and porcelain 270

of metals and metallic wires 254-257

of wires, effect of elongation on 258

Rigidity, modulus defined 74

of metals 74

variation of, with temperature 76

Rotation, magneto-optic 284-291

Saturation values, magnetic, for steel 279

Seconds pendulum, length of 104, 105

Secondary batteries 247

Sections of wires 44~54> 58-68

Sheet metal, weight of 56, 57

Soaring of planes, data for 109

Solar constant 177

Solar spectrum, wave-length in 172

Solids, compressibility and bulk moduli of . . .83

density of 85

magneto-optic rotation in 284

Solution, contraction produced by 131-134

Solutions, aqueous, boiling-points of 196

density of 90

magneto-optic rotation in 288-290

refractive indices for . '. 188

specific heat of 224

Sound, velocity of, in air 99

in gases and liquids 101

in solids 100

Specific electrical resistance, conversion fac-
tors for 23, 254-256

Specific gravity (see also Density).

of aqueous ethyl alcohol 96

methyl alcohol 97

of gases 89

Specific heat of air 223

of gases and vapors 224

of metals 296

of solids and liquids 294, 295

of water 223

of water, formulae for 222

Specific inductive capacity 263-265

viscosity, aqueous solutions 144

oils 137

water 1 36

Spectra, wave-lengths in arc and solar 172

Standard cells 247

wave-lengths of light 172

Standards, photometric 176

Steel, physical properties of 71

Steam, properties of saturated 237

Steinmetz, constants for hysteresis of 281

Stone, strength of 70

thermal conductivity of 197

dielectric 244

Strength of materials 70-73

Stress, conversion factors for 19, 22

Surface-tension, constants of 128, 129

conversion factors for 20, 22

Sylvine, refractive index of 182

Temperature, conversion factors for 25

critical, of gases 200

Terrestrial magnetism, agonic lines 117

declination, data for maximum east at

various stations 1 18

dip and its secular variation for differ-
ent latitudes and longitudes 1 1 1

Terrestrial magnetism (continued).

horizontal intensity and its secular varia-
tion for different latitudes and longi-
tudes 112

secular variation of declination . . . . 1 13-116

Thermal conductivities 197, 198

relation to electrical 271

expansion, coefficients of 214-218

units, dynamic equivalent of 219

Thermoelectricity .248-250

Thermometer 228-233

air 228, 231

correction of, for mercury in stem 232

hydrogen 231

mercury in glass 229

zero change due to heating 229

zero, change of, with time 230

Timber, strength of 70

Time, unit of, defined xvii

Times, conversion factors for 14

Transformers, permeability of

iron in 274, 275, 280, 282

Units of measurement xv

dimension formulae for dynamic xviii

electric and magnetic xxv

electromagnetic xxix

electrostatic xxvi

fundamental .2

heat xxiii

practical, legalization of electric xxxiii

ratio of electrostatic to electromagnetic

243

United States weights and measures in
metric 9

Vapor, density of aqueous 155

diffusion of 149

pressure of 1 26, 225-227

pressure of aqueous 151-154

values of 0.378 e 160

pressure of, for aqueous solutions 194

refractive indices for 190

specific heats of 224

Vaporization, latent heat of 204

Velocity, angular and linear, conversion fac-
tors for 15

of light 176, 243

of sound 99, 101

Verdet's constants for alcoholic solution of

salts 290

aqueous solutions of salts 287

gases 291

hydrochloric acid solutions of salts 290

liquids and solids 285-287

and Kundt's constants 292

Viscosity, coefficient, definition of 136

coefficient of, for aqueous alcohol 137

for gases 1 46

for liquids 1 38

temperature effect on, for liquids 139

specific, for oils 137

for water 1 36

Volumes, conversion factors for 12

critical, of gases 200

Water, boiling-point for various barometric

pressures 170, 171

density of 92~94

specific heat of 222, 223

INDEX.

3OI

Water (continued).

thermal conductivity of 198

viscosity of 136

Wave-lengths of Fraunhofer lines 175

standard for arc and solar spectrum. . . . 172

Weights and measures —

British Imperial to Metric 7, 8

Metric to British Imperial 5, 6

Metric to United States 10

United States to Metric 9

Weights of sheet metal 56, 57

Weights of wires 44- 54

Wind, pressure of 108

Wire, gauges 58-67

Woods, densities of 88

Work, conversion factors for 20, 21

Yard, definition of ... .xvi

Young's moduli 75

modulus, definition of 75

Zonal harmonics 40

BSITY OF CALIFORNIA LIBRARY

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; K K *-