None
vz 1 — • n *180- n 100-n 50 2500 7-071 0-0200 0-873 1000 61 2601 7-141 0-0196 0-890 1-041 52 2704 7-211 0-0192 0-908 1-083 58 2809 7-280 0-0189 0-925 1-128 54 2916 7-348 0-0185 0-942 1-174 55 8025 7-416 0-0182 0-960 1-222 56 8136 7-483 0-0179 0-977 1-278 57 3249 7-650 0-0175 0-995 1-326 58 3364 7-616 0-0172 1-012 1-381 59 8481 7-681 0-0169 1-030 1-439 60 3600 7-746 0-0167 1-047 1-600 61 3721 7-810 0-0164 1-065 1-664 62 8844 7-874 0-0161 1-082 1-632 6S 3969 7-937 0-0159 1-100 1-703 64 4096 8-000 0-0156 1117 1-778 65 4225 8-062 0-0154 1134 1-857 66 4356 8-124 0-0152 1-152 1-941 67 4489 8-185 0-0149 1-169 2-030 68 4624 8-246 0-0147 1-187 2-125 69 4761 8-307 0-0145 1-204 2-226 70 4900 8-367 0-0148 1-222 2-333 71 5041 8-426 0-0141 1-239 2-448 72 5184 8*485 0 0139 1-267 2-571 73 5329 8-544 0-0137 1-274 2-704 74 5476 8-602 0-0136 1-292 2-846 75 5625 8-660 00133 1-309 3-000 76 5776 8-718 0-0132 1-326 3-167 77 5929 8-775 0-0130 1-344 3-348 78 6084 8-832 0-0128 1-361 3-645 79 6241 8-888 0-0127 1-379 3-762 80 6400 8-944 0-0125 1-896 4-00 81 6561 9-000 0-0123 1-414 4-26 82 6724 9 065 0-0122 1-431 4-56 83 6889 9-110 0-0120 1-449 4-88 84 7066 9-165 0-0119 1-466 6-26 85 7225 9-220 0-0118 1-484 5-67 86 7396 9-274 0-0116 1-601 6-14 87 7569 9-327 00115 1-518 6-69 88 7744 9-881 0-0114 1-536 7-33 89 7921 9-484 0-0112 1-563 8-09 90 8100 9-487 00111 1-671 9-00 91 8281 9-539 0-0110 1-588 10-11 92 8464 9-692 0-0109 1-606 11-50 93 8649 9-644 0-0108 1-623 13-29 94 8836 9-695 0-0106 1-641 15-67 95 9025 9-747 0-0105 1-668 19-0 96 9216 9-798 0-0104 1-676 24-0 97 9409 9-849 0-0103 1-693 82-3 98 9604 9-899 0-0102 1-710 49 0 99 9801 9-960 0-0101 1-728 99-0 100 10000 10-000 0-0100 1-746 00 2 II 466 PHYSICAL MEASUREMENTS TABLE 38. Logarithms to 4 Places. N. Ift 0 1 2 8 4 5 6 7 8 0 Diff. 42^ 0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 11 0414 0453 0492 0531 0569 0607 0646 0682 0719 0755 38 12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 35 13 1139 1173 1206. 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 8 0 1 2 8 4 5 6 7 8 9 Diir. TABLES 467 TABLE ZS—amiinued. Logarithms to 4 Places. N. 65 0 1 2 8 4 6 6 7 8 0 IMff. 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 4 Diff. 0 I 2 8 4 6 G 7 8 9 468 PHYSICAL MEASUREMENTS TABLE 38—continvsd. Logarithms to 4 Places. 100 0 1 2 8 4 b 6 7 8 9 Diff. 00000 0043 0087 0130 0173 0217 0260 0303 0346 0389 43 101 00432 0475 0518 *0661 0604 0647 0689 0732 0775 0817 43 102 00860 0903 0945 0988 1030 1072 1115 1157 1199 1242 42 103 01284 1326 1368 1410 1452 1494 1586 1578 1620 1662 42 104 01703 1745 1787 1828 1870 1912 1953 1995 2036 2078 42 106 02119 2160 2202 2243 2284 2325 2366 2407 2449 2490 41 106 02531 2572 2612 2653 2694 2735 2776 2816 2857 2898 40 107 02938 2979 3019 3060 3100 3141 3181 3222 3262 3302 40 108 03342 3383 3423 3463 3503 3543 3583 3628 3663 3703 40 109 03743 3782 3822 3862 3902 3941 3981 4021 4060 4100 40 110 N. 04139 4179 4218 4258 4297 4336 4376 4415 4454 4493 39 Diff. 0 1 2 8 4 5 6 7 8 9 TABLE 39. Trioonohetrical Functions. 57 '29 28-64 19 '08 11-30 11-43 B-614 8-144 2-904 2-747 2-60B 2-476 2-868 2-248 S'14fi 1-0000 0-9998 -9994 ■9988 -9976 ■9982 ■9945 '9926 '990S '9877 '9848 '9816 '9781 '9744 ■9703 ■9669 ■9813 -9563 -9611 '9456 !i INDEX AJ980LX7TB acceleration, 409 angle, 408 caliber, 74 conductivity, heat, 126 directive force, 410 electrostatic measure, 411 „ potential, 874 energy, 409 force, 409 galvanic measures, 417 heat, 409 kinetic energy, 410 magnetic measures, 413 magnetism of bar, 258 measure, KM.F., 334 mechanical measiires, 409 modulus of elasticity, 411 moment of inertia, 411 „ of rotation, 410 potential energy, 410 pressure, 409 resistance, 360 space, 408 surface, 408 system of measurement, 404 time, 408 unit of light, 206 velocity, 409 volume, 408 weighing, 38 work, 409 Absorption of light, 208 Accumulators, 275 Air thermometer, 92 Altitude of pole, 397 Altitudes, measurement, 393 Amalgamation of zinc, 269 Angle of optic axes, 201 of polarisation, 189 Angular aperture of objective, 188 measurement with mirror, 214 Apertometer, 188 Approximation formulae, 6, 10 Arc, infinitely small, 225 Area of coils, 363 Areometers, 45 Artificial horizon, 393 Afltatisation of needles, 234 Astronomical terms, 390 Atmospheric pressure, 76 Auguste's psychrometer, 109 Avogadro's law, 44 Babimbt's compensator, 209 Balance, ratio of arms, 36 sensitiveness, 34 testing and adjusting, 30 use of, 32 Ballistic galvanometer, 381 Barometer, 76 Barometric measurement heights, 78 Batteries, efficiency of, 274 galvanic, 268 internal resistance, 321 B.A. unit, 265 Beats, musical, 141 Bichromate battery, 269 Bifilar galvanometer, 285 magnetometer, 250 suspension, 226 variometer, 253 Boiling point of fluid, 104 of thermometer, 82 Bridge, Wheatstone's, 303 Bridge- wire, calibration, 311 Calculation by equal intervals, 16 numerical, 28 of corrections, 24 Caliber, absolute, of tube, 74 Calibration of electrometers, 375 of rheostat or bridge-wire, 309 of thermometer, 86 of tube, 73 Calomel cell, 269 Calorie, 111 Calorimeter, 111 ice. 111, 120 472 PHYSICAL MEASUBEMEKTS Calorimeter, vapour, 123 Capacity by weighing, 71 electric, 378 Capillarity, coefficient of, 143 Capillary electrometer, 372 Carbons for battery, 269 Cathetometer, 69 Circuits, divided, 274 Clark's normal cell, 269 Clock, rate of, 398 Coefficient of absorption of light, 208 of capillarity, 143 of expansion, 98 of friction in liquids, 146 of magnetic induction, 366 of torsion of magnet, 231 Coils, area of, 863 Colorimetry, 206 Commutator, 272, 300 Comparison of E.M.F., 328 of horizontal intensity, 266 Compass, magnetic, 239 Compensated magnetometer, 249 Condensers, 384 Conduction of heat, 124 Conductivity, absolute for heat, 126 Conductor, self-induction, 365 Constant errors, 2 Contact-comparator, 68 Contact measures, 68 Copper voltameter, 289 Correction of weights, 40 Corrections, calculation, 24 Crystals, angle of axes, 201 biaxial, 201 measurement of angles, 148 positive and negative, 200 unaxial, 198, 199 Current measure with rheostat, 292 Damped magnetic needles, 219, 344, 447 Damping, resistance by, 308 Daniell's battery, 269 Declination of terrest magnetism, 237 Deflection variometer, 264 Density, 43 and weight, 30 correction for temperature, 50 of gases, 53, 63 „ by time of escape, 64 of moist air, 54 of solids, 46 reduction to vacuo, etc., 48 vapour, 55 Derived currents, 267 Dew-point hygrometer, 108 Dielectric constant, 384 Differential galvanometer, 298 Diffraction gratings, 173 Dimensions, 407 Divided circuits, 267, 274 currents, 267 scale or rule, 65 Dividing engines, 66, 67 Double quartz plate, 193 refraction, 198 weighing, 38 Dust figures, velocity of sound by, 138 Dynamo currents, 275 Dynamos, measurements on, 337 Earth inductor, 352, 361 Efficiency of batteries, 274 of dynamos, 339 Elasticity by bending, 133 by stretching, 128 by vibrations, 132 modulus of, 128 Electric capacity, 378 currents of short duration, 346 lamps, photometry of, 341 quantity, ele. mag., 348 thermometer, 378 waves, velocity of, 387 Electrodynamic balance, 285 Electrodynamometer, 283 Electrolytes, resistance, 316 Electromagnetic rotation of light, 344 Electrometers, calibration, 375 capillary, 372 quadrant, 369 sine, 369 various, 373 Electromotive force, 266 forces, small, 270 Electrostatip potential, absolute, 374 potentials, 369 quantity, 377 Electrostatics, 368 general methods, 368 Elliptically polarised light, 209 E.M.F., comparison of, 328, 378 in absolute measure, 334 of batteries, 454 short integral of^ 348 Empirical constants, 11 Equal intervals, calculation by, 16 Equations, solution of, 17 Errors of observation, 1 Expansion-coefficient, 98 Expansion of liquids, 100 Focal length of lens, 177 Focometer, 183 Fraunhofer lines, 156 Freezing point, 81, 101 of fluids, 101 of solutions, 103 Friction, coefficient oi^ in liquids, 146 INDEX 473 Galvanic batteries, 268 connections, 271 determination of magnetic field, 341 resistance, 264 resistance coils, 272 Galvanism, 264 Galvanometer, ballistic, 881 bifilar, 285 differential, 298 mirror, 282 resistance of, 324 Siemens's universal, 332 sine, 282 tangent, 276 torsion, 336 Galvanometers, efficiency of, 274 graduation, 293 various, 286 Gauss's method for linear equations, 21 Goniometer, 148 Graduation of current measures, 293 Great resistances, 387 Half-shadow polarimeter, 194 Heat, 81 conduction, 124 specific, 111 Heights by barometer, 78 Heterostatic arrangement, 369 Horizon, artificial, 393 Horizontal intensity, 240 galvanic measure of, 341 Humidity of air, 107 Hydrometers, 45 Nicholson's, 47 Hygrometer, absorption, 110 Hygrometry, 107 Hygroscopic bodies, 110 Hypsometry, 78 IcB calorimeter. 111, 120 Lliostatic arrangement, 371 Inclination, magnetic, 235 Induction coefficient, magnetic, 356 Inertia, moment of, 228 Influence of errors on result, 4 Insulation, 368 Interference refractor, 164 Internal resistance of battery, 321 Interpolation, 27 Jamin's compensator, 169 interference reftractor, 165 - Jolly's spring balance, 47 KLEMMSPANNUNQy 336 Latitude, 397 Least squares, 11 Lens, foKcal length, 177 Light, electromagnetic rotation, 344 wave-length, 173 Linear equations. Gauss's method for, 21 Liquids, expansion, 100 Logarithmic decrement, 219 Lummer-Brodhun prism, 205 Magnet, separation of poles, 262 temperature coefficient, 260 Magnetic compass, 239 declination, 237 field of bobbin, 275 fields, strong, 857 inclination, 235 induction coefficient, 356 intensity, horizontal, 240, 341 theodolite, 248 Magnetism, 233 absolute measure, 258 distribution in magnet, 359 Magneto-inductor, 355 Magnetometer, bifilar, 250 compensated, 249 Magnifying power of lens, 184 of microscope, 187 of telescope, 184 Mean error, 1, 16 Measurement of size, 65 Measures, contact, 68 Melting point, 101 Mercury, purification, 72 resistances, 315 Meridian of a place, 394 Microscope, measurement by, 66 Minimum deviation, 153 Mirror galvanometers, 282 Mixtures, specific heat by. 111 Modulus of elasticity, 128 of torsion, 136 Mohr's balance, 45 Moment ot inertia, 228, 411 of rotation, 247, 410 Monochord, 142 Multiplication method, 349 Musical note, number of vibrations in, 140 Nicholson's hydrometer, 47 Numerical aperture of objective, 188 calculations, 28 Ohm, 265 Ohm's laws, 264, 267 Ophthalmometer, 70 Optical rotating power, 190 telephone, 288 Oscillation period, 221 Parallelism of glass plate, 152 Period of oscillation, 221 474 PHYSICAL MEASUBEMENTS Photometry, 203 of coloured light, 206 of electric lamps, 341 Plane surfaces, testing, 177 Platinising silver, 270 Polarisation, angle of, 189 Polaristrobometer, 193 Polar separation, 233 Porous cells, 270 Position of equilibrium of needle, 218 Positive and negative crystals, 200 Potential difference, 328 in closed circuits, 335 terminal, 336 Potentials, electrostatic, 369 Probable error, 112 Psychrometer, 109 Purification of mercury, 72 Pyknometers, 45, 46 Quadrant electrometer, 369 Quantity of electricity, 346 ele. Stat., 377 Quartz wedge saccharimeter, 195 Radius of curvature, 174 Rate of clock, 398 Ratio of balance arms, 36 of damping, 219 Recoil method, 351 Reduction of scale to angular measure, 216 of weight to vacuo, 38 to infinitely small arc, 225 Refractive index, 150 by microscope, 157 determination, 152 Refractometer, 162 Resistance, absolute measure, 360 by damping, 308 by measuring currents, 297 coils, 272 comparison of uneqaal, 306 galvanic, 264 internal, of battery, 321 of copper wire, 265 of electrolytes, 316 of galvanometers, 324 of mercury, 315 very great, 387 Rheostat, 272 calibration, 309 Rotation of light, electromagnetic, 344 of polarisatiou, 190 Rule, divided, 65 Sacx)Parimetry, 190 Savart's plate, 193 Self-)induction of conductor, 365 Sensitiveness of balance, 34 / Separation of poles of magnet, 238, 262 Short integral of E.M.F., 348 Shunts, 264, 280 measurement of strong coirents by, 280 Siemens*s unit, 265 universal galvanometer, 332 Silvering glass, 215 Sflver voltameter, 289 Sine electrometer, 369 galvanometer, 282 Size, measurement of, 65 Solution of equations, 17 Sound, velocity, 138 Specific gravity, 43 of gases, 53, 63 of liquids, 44 of solids, 46 heat, 111 by cooling, 119 by galvanic method, 118 by ice-calorimeter, 120 by mixture, 113 by vapour-calorimeter, 123 inductive capacity, 384 rotation, 190 Spectrometer, 150 Spectrophotometer, 207 Spectrum analysis, 169 Spherometer, 68 Spring balance. Jolly's, 47 current balance, 288 Squares, least, 11 Stroboscope, 141 Surveying with compass, 239 Suspension, bifilar, 226 of magnets, 234 Swinging of balance, 32 of needle, 218 Syren, 141 Tangent galvanometer, 9, 276 Taring, weighing by, 38 Telephone, optical, 288 Temperature by'thermo-element, 97 calculation, 84 Temperature-coefficient of conductor, 813 magnet, 260 Tension of vapour, 105 Terminal potential difference, 386 Terrestrial magnetism, measurement, 240 Theodolite, 391 magnetic, 248 repeating, 394 Thermo-chemical measurements, 124 Thermo-elements, 97, 271 Thermometer, 81 air, 92 calibration, 86 Time from altitudes of sun, 399 Time measurement by short currents, 848 INDEX 475 Torsion galvanometer, 336 modnlns, 136 of suspended magnet, 231 Total reflection, 168 by spectrometer, 163 Total-reflectometer, 160 Uniaxial crystals, 198, 199 Unit jar, 377 time, 391 Units, absolute or derived, 404 of galvanic resistance, 265 of heat. Ill Universal galvanometer, 332 Vacuo, reduction of weight to, 38 Vapour calorimeter, 123 density, 55 Dumas' method, 55 Gay-Lussac, Hofmann, 59 V. Meyer, 60 tension, 105 of solutions, 106 Variometer, bifiUr, 258 deflection, 254 Velocity of sound, 138 Verification of scale, divided rod, 66 Verniers, 66 Vibration form of light, 212 Vibrations in musical note, 140 Viscosity, 146 Voltameter, 288, 294, 341 copper, 289 silver, 289 water, 289 Volumenometer, 53 Water calorimeter, 111 voltameter, 289 Wave-length of light, 173 Weighing, absolute, 38 by oscillation, 32 by taring, 38 double, 38 Weight and density, 530 of observations, 4 reduction to vacuo, 3 Weights, correction of. 40 Wet-and-dry bulb thermometer, 109 Wheatetone's bridge, 303 Zinc, amalgamation of, 269 TABLES 28. Absoluts units, 456 10b. Absorption of gases, 435 10a. Aqueous solubilities, 435 27b. solutions, conductivity, 455 13. vapour, 438 13a. vapour tension, 439 37. Arc to absolute ang. measure, 464 21. infinitely small, 446 29. Atomic weights, 458 11. Baroubtbb, reduction, 436 12. heights by, 437 32. Beginning of year, 461 28b. Birmingham wire gauge, 457 13b. Boiling point of water, 439 16a. of other bodies, 441 17. Breaking strain of metals, 442 15. Capillary depression, 440 10. Conduction of heat, 435 25. Conductivity, elec. of metals, 452 26. of salts, etc., 453 3a. of solutions, 430 27 b. molecular, 455 21b. Damped needle, 447 23a. Declination, magnetic, America, 450 23. magnetic, Europe, 449 31. of sun, 460 1. Density of bodies, 427 6. of dry air, 432 1. of gases, 427 3, 3a. of solutions, 428, 430 4. of water, 431 28. Dimensions, 456 17. Elabtioitt of metals, 442 27. Electro-chemical equivalents, 454 3a. Electrolytic constants, 430 31. Equation of time, 460 9. Expansion coefficients, 434 19. Flame spectra, 443 10b. Oabes, absorption, 435 7. Gas volumes, reduction, 483 30. Geographical position of places, 459 8a. Gravity and pendulum, 434 16. Heats, specific, 440 29. of elements, 458 28c. of water and platinum, 457 2. Hydrometer scales, 427 13. Hygrometer, 438 12. Hypsometric, 437 12a. Inches to millimeters, 437 23, 23a. Inclination, magnetic, 451 \ 476 PHYSICAL MEASUREMENTS 20. Indices of refraction, 444 22, 22a. Intensity, horizontal, 448, 449 38. Logarithms, 466 22-24«. Maonbtism, terrest, 448-451 16a. Melting points, 441 15. Mercury, capillary dep., 440 14. vapour tension, 440 12a. Millimeters to inches, 437 17. Modulus of elasticity, 442 27h. Molecular conductivity, 455 18. Musical notes, vibrations, 442 20a. Nbwton*8 rings, 445 86. Numbers firaquently required, 463 8a. Pendulum, 484 28c. Platinum, sp. heat, 457 27c. Potential, electric, 455 33. 28c 5. 19, 19a. Spectra, 443 37. Squares, square roots, 464 35. Stars, mean place, 462 33. Snn*s radius, 461 29. Symbols, etc., of elements, 458 13a. Tensions of aq. vapour, 439 14. 3a. 39. of mercury vap., 440 Transference of ions, 430 Trigonometrical functions, 469 28. Units, absolute, 456 8. Vacuo, weight to, 434 17. Velocity of sound, 442 18. Vibrations of musical notes, 442 5. Volume, specific, of water, 431 19a. Wavs-lknoths in air, 443 87. Wheatstone-Kizchhoff bridge, 464 THE END r-:«.-A/,T' R. «L k. Ci^«KC. E^mrmw^ ^. 