None
If the observed time of oscillation of a magnet or pendulum be t, with an arc of oscillation of a degrees, kt must be subtracted from the observed value in order to reduce the time to that of an infinitely small oscillation (63). a. O** 1 2 3 4 5 6 7 8 9 10" k. a. k. a. 20" 21 22 23 24 26 26 27 28 29 30" k. a. 30" 31 32 33 34 35 36 87 38 39 40" k. 0-00000 000 002 004 008 012 ow 023 030 039 0-00048 0 2 2 4 4 B 6 7 9 9 10' 11 12 13 14 15 ^ W 17 18 19 20* 0*00048 058 069 080 098 107 188 154 172 0-00190 10 11 11 13 14 15 16 16 18 18 0*00190 210 230 251 . 274 297 322 347 373 400 0*00428 20 20 21 23 23 25 26 26 27 28 0*00428 457 487 • 518 550 583 •616 651 686 728 0-00761 29 30 31 32 33 d3 35 35 37 38 TABLE 21 A. Reduction of Deflection e observed on a Divided Scale when the Distance from the Mirror is A Scale-divisions (49). By subtracting the number in the Table the scale-reading becomes proportional to the angle of deflection. The corrections for the tangents are equal to ^, for the sines to |^, of the numbers given. A. e=60. 100. 150. 200. 250. 800. 850. 400. » 450. 500. 1000 0 04 0-33 1*11 2*60 5 02 8-54 13*33 19*5 27-1 86*8 1200 0*03 0*23 0-77 1-82 3*53 6-03 9-45 13-9 19-6 26-2 1400 0*02 0*17 0-57 1-34 2-61 4-47 7-03 10-4 14-6 19-7 1600 0*02 0*13 0*44 1*03 2-00 3-44 5*43 8-0 11-3 15-4 1800 0*01 0*10 0-35 0*82 1-59 2*73 4*30 6*4 9-0 12-3 2000 0-01 0*08 0-28 0*66 1*29 2-22 3*51 5*21 7-37 10-05 2200 0 01 0-07 0-23 0*55 1*07 1*83 2*91 4*32 6*12 8-35 2400 0*01 0*06 0*19 0*46 0-90 1-54 2*45 3*64 5*16 7*05 2600 0 01 0*05 0*16 0*39 0*77 1-32 2*09 3*11 4*42 6 08 2800 0*01 0*04 0*14 0*34 0-66 1-14 1*81 2-69 3-82 5*21 3000 0 00 0 04 0-12 0-29 0-58 0-99 1-58 2-85 3*33 4*55 3200 0*00 0*03 Oil 0*26 0-51 0*87 1*38 2 07 2-93 4*01 8400 0-00 0*03 0*10 0-23 0-45 0-77 1-23 1*83 2*60 3-56 3600 0*00 0*03 0 09 0*21 0*40 0-69 1-10 1*64 2-82 3-18 3800 0-00 0 02 0*08 0*18 0-36 0*62 0*98 1*47 2-09 2-86 4000 0-00 0*02 0*07 017 0-32 0-56 0*89 1-83 1-88 2-58 TABLES 447 TABLE 2 IB. For the Rkduction of Observations of the Oscillations OF A " DAMPED ** Magnet Needle (61 and 78.) T and a = Time and amplitude of oscillation for ratio of damping k, r and a=the corresponding time and amplitude without damping. Then T/r=VlTA5pand a/ai=e^''**°"''/^=A:'^'- *»""''/^- x=log k. Aslognat i*. A:=io^=e^ J. 1/r.tan -l r/A. Vl+At/,r«. 0-00 0^0000 1^000 1-0000 1^0000 •01 •0280 1-028 1^0000 1^0116 •02 •0461 1-047 1^0001 1-0231 •08 •0691 1-072 1-0002 1 -0347 •04 •0921 1-096 1 -0004 1-0463 •05 •1161 1^122 1-0007 1-0678 •06 •1882 1-148 1-0010 1-0694 •07 ■1612 1176 1 0013 1-0811 •08 •1842 1-202 1-0017 10927 •09 •2072 1-230 1 -0022 1-1044 •10 •2308 1-259 1 -0027 1-1160 •11 •2588 1-288 1^0032 1-1277 •12 •2763 1^318 1 0089 1-1398 •18 -2993 1^849 1-0046 1-1510 •14 •3224 1 ^880 1 0062 1 1626 •16 •8454 1^418 1 -0060 1-1748 •16 •3684 1^445 1^0069 1 -1869 •17 •3914 1-479 1 -0077 1-1976 •18 •4145 1-614 1 -0087 1-2091 •19 •4376 1-549 1-0097 1 -2208 •20 •4605 1-586 1 0107 • 1 -2324 •21 •4836 1-622 1-0118 1-2440 •22 •6066 1-660 1-0130 1-2665 •23 •5296 1-698 1-0142 1-2670 •24 •6626 1-788 1^0166 1-2785 •25 •5756 1-778 1^0167 1-2900 •26 •6987 1-820 10180 1-8014 •27 •6217 1-862 1 -0194 1*8128 •28 •6447 1-905 1 -0208 1 -3242 •29 •6677 1-950 1^0228 1-3856 •80 •6908 1-996 1*0239 1-3469 •31 •7188 2-042 1 •0-265 1'3582 •82 •7868 2-089 1 -0271 1 -8694 •88 •7599 2138 1-0288 1 -3806 •84 •7829 2-188 1 -0306 1 -3918 •35 •8059 2-289 1 -0324 1-4029 •86 •8289 2-291 1 ^0342 1-4140 •37 •8520 2-344 1-0361 1 -4260 •38 •8750 2-399 1 •0381 1 -4860 '89 •8980 2-456 1^0401 1 -4469 •40 •9210 2-512 1-0421 1 -4578 •41 •9441 2^670 1-0442 1-4686 •42 •9671 2-630 1-0468 1 -4794 •43 0-9901 2-692 1-0485 1 -4901 •44 1-0131 2-754 1-0507 1^6008 PHYSICAL UKASDREUENTS I 3 1 i 1 ' 1 ^ 0-217 213 209 204 200 19S 192 188 184 180 177 -b 0-216 211 207 203 169 165 161 187 183 180 176 Id 0-215 210 206 201 197 164 190 186 181 178 174 Pliis 2S2ISS •- |lis5 SSsSSS - 0-211 207 202 198 194 190 186 181 178 174 170 i isssss gsgssg TABLES 449 TABLE 22a. — Horizontal Intensity in the United States FOR 1885, in C.M.G. units. , North Latitude. LoNoiTDDB West from Qbebnwioh. 65" 70' 75" 80* 85' 90* 95' 100' 106' 110' 115' 120' 125' 0 0 0 • e e o • e • 0 •  •280 34 • • ■ • •• ■ • • •246 -252 •252 •267 •263 •268 •269 •272 •274 35 • • • • ■ ■ •230 •238 •244  •256 •258 38 > • • • •• •209 •213 •215 •222 •227 •234 •242 •246 •249 •252 39 • ■ ■ • • • •195 •205 •208  •233 •237 •240 •242 41 ■ • • •182 •184 •189 •192 •196 •203 •212 •220 •226 •231 •235 •238 42 • • • •174 •176 •180 •185 •187 •196 •204 •218 •219 •224 •230 •233 43 •163 •165 •168 •172 •174 •178 •187 •196 •206 •213 •218 •223 •228 44 •158 •158 •159 •161 •166. TABLE 23. — West Decunation. North Latitude. LonRlttule East from Greenwich. 6' 135 14-3 14-7 c* 1 8' 0* 10' 11^6 ir9 123 ir i-r 10^7 11-0 11-1 . 13- 10^3 10-4 10^4 45'' 50 55 13-1 13^8 14-4 12^7 13-3 14^0 12^4 12-9 13^4 12-0 12^4 12-8 11-1 11-4 11-7 14' 10^1 9-9 9 6 15' 9^5 9-4 8-6 10' 9-1 8-9 8-3 17- - lb' 19' 7^6 7-5 7-2 20' 2r 22' 64 6 0 6-6 45" 50 55 8-6 8-4 8-0 8-1 8-0 7^7 7-2 7-0 6^7 6^8 6-5 6-2 2a 450 PHYSICAL MEASUREMENTS o 00 CO o I 09 I S> i 1 1 r1 «>9« • rH04 C4 1 1 1 O to CO to • • ■ • kO tx> o» oo " r-l 1-4 rH C^ .1111 00 O lO o «o ■ ■ « • • o « "* t*-o>  06 « O <N -«*  •••••• C^ 00 A rH  *•••■ o w w 1-t o CO ua  • ■ I I I r O I** ; ft • ■ ■ ^H  1 u »^ (H S £ ? o a *< S: C5 S «: CO rf . «i "^ ^ "^ "• " rf et q) o f^ ^ g «* " .a 2 ^ 1 1I 8 * «^ TABLES 451 TABLE 24. — Inclination. North Uitltude. Longitude Bast trom Greenwich. North Latitude. Longitude East firom- Greenwich. 5* 10- 15' 20' 6' 10' 16' 20' 45° 46 47 48 49 50 62-4 8-1 8-8 4-6 6-3 6-0 61-6 2-3 3 1 3-9 47 6-5 61-0 1-8 2-6 8-3 4-1 5-0 60-5 1-4 2-3 8-0 8-8 4-5 51 52 53 54 55 66-6 7-2 7-9 8-5 9-2 66-1 67 7-3 8-0 87 657 6-4 7-0 77 8-4 65-2 6-1 6-8 7-5 8-1 TABLE 24a. — ^Incunation in the United States for 1885. gi 0 25 LONOITUDB Wbst ntOM GRRXNWICn. 86' 70" 76" 80* 1 85' 90' 05'  -6 • 52-6 e 61-8  29 • • ■ • • ■ • • ■ 60*4 59-3 58-5 677 57-1 66*a 55-2 54-0 30 • • • ■ • • • ■ • 61-4 60-6 59-8 59 0 58-3 57-4 56-4 66-1 31 ■ • • ■ ■ > • • • 62-5 617  63-8  587 35 • « • • * ■ 66-8 667 66 0 65-4 64-5 687 62-8 61-8 607 60-7 36 • ■ « • • ■ 68-1 68-0 67 1 66-3 657 647 63-8 62-8 617 60-8 37 • « • ft • 1 69-0 687 68-1 67-6 66-8 66-8 64-9 63-9 62-8 61-9 38 • • « 70-0 69-5 69-3  65-8 64-8 64-0 62-7 40 • • • • ■ ■ 717 71-5 71-2 70-3 697 69-0 68-0 66-8 657 647 68-5 41 • • ■ • • ■ 72-8 72-4 72-0 71-8 70-8 70-0 68-9 67-8 66-6 65-6 64-3 42 t • • 73-2 73 -5 73 0 72-8 72-4 71-9 71-1 69-9 68-8 67-6 66-5 65-1 43 • • • 73-9 74-1 73-9 73-6 73-2 727 71-9 70-9 697 68-6 67-8 66-1 44 74-6 74-8 75-0 74-5 74-1 73-6 727 71-8 70-7 69-5 68-4 67-1 45 74-8 75-4 75-6 757 75-4 75-0 74-4 73-5 72-6 71-5 70-4 69-4 68 0 46 75-8 76-1 76-4 76-4 76*3 76-9 75-2 74-4 73-4 72-8 71-2 70-3 68-9 47 767 76-6 77-3 77-1 77-0 767 75-9 75-2 74-2 73-1 71-9 70-9 69-8 48 77-5 77-2 B • ■ 77-9 78-0 77-4 767 75-9 75-0 73-8 727 71-6 70-8 49 • ■ ■ • • • 78-8 78-8 78-2 77-6 767 757 747 73-4 72-3 717 50 • « • ■ • « • • • 797 797 79-0 78-3 77-5 76-5 75-4 74-3 73-1 72-6 The thick figures represent a region of no annual change (in 1885). 452 PHYSICAL MEASUREMENTS TABLE 25. — Conductivity of some Metals. Most of the figures are only approximate. Resifitance increases at mean temperature for a rise of l"* in mercury . . about 0-00090 of the whole in pure solid metals . about 0*004 „ „ In Qerman silver, the temperature-coefficient varies from + 0*00024 to 0*0006. This may be approximately estimated as 1-1 0000th of the conductivity as referred to mercury. Good " nickelin " 0*00023. The resistance of alloys of 88% Cu with 12% Mn, as well as of 84Cu, 4Ni, and 12Mn (" Manganin "), and 60Cu with 40Ni ("Con- stantin"), is at mean temperatures almost independent of variations (Feussner and Lindeck). 25% nickel-copper ("patent nickel") has the temperature - coefficient + 0 *0002 ; 20% platinum - silver + 0 -00033. Compare note, p. 273. The resistance of carbon diminishes with the temperature. The temperature-coefficient averages about 0*0002 to 0*0008. The resistance of a wire of Im length, and q section is = o;l/q ohm, or = 8,1/q Siem, 8 = 1*06. <r and k=\J8. The numbers are for pure soft metaL Hardness, and especially impurities, lessen the conductivity. Specific Hesistauce. Conduc- A m. mm. 2- wire has the tivity as At 18". resistance compared. to Mercury In ohms. In Siem. units. atO. Silver ..... o = q-oi6 « = 0-017 A; = 69 Copper 0-0172 0*0182 65 Gold. 0-023 0*024 41 Zinc 0-063 0-067 15 Iron. 009-0-15 0*10-0-16 6-10 Steel. 0-15-0-43 0*16-0*46 2-6 Platinum 0*14 0-15 6-6 Lead. 0-21 0*22 4-6 Antimony 0-45 0-48 21 Mercury 0-958 1-016 0*984 Bismuth 1-2 1*2 0-8 Gas-carbon. 50-0 50-0 0-02 Brass. 0-07 -0-09 0*07-0-10 10-14 20% Platinum-silver 0-20 0-21 4*8 German-silver 0-16-0-40 0-17-0-42 2-4-6 Nickelin 0-42 0-44 2*3 40% Nickel-copper ■ . I 0-48 0-51 2-0 12% Manganese-copper. 0-34 0-36 2-8 30% Manganese-copper. 1-08 1-14 0-9 TABLES 453 TABLE 26. Electrical Conductivity of some Salts and Acids in Aqueous Solution at 18° referred to Mercury at 0°. (ZnSO^ according to Beetz ; KCl, NaCl, NH4CI, and HNO, accord- ing to Grotian and Kohlrausch ; the others according to the author's observations.) Compare Pogg, Ann. clix. 257, and Wied. Ann, vi. 37. By the percentage is meant the weight of the dissolved sub- stance in 100 parts of the solution. The salts are anhydrous. k is the conductivity at 18°, M the increase of hiorV temperar ture, in percents of K^g. Solu- tion. KCl. NaCl. NH4CI. Na2804. KRO4. MgSO*. CUSO4. Jt.l07 Ale t.107 Ak fc.lO^ AA- Jt.lO' Afc Jk.lO! ' Afc Jt.107 Afc kAW Ak 6% 64 2-0 63 2-2 86 2*0 38 2-4 43 2-2 24 2-3 18 2-2 10 127 1-9 113 2-1 166 1-9 64 2-5 81 2-0 39 2-4 30 2-2 15 189 1-8 153 2-1 242 1-7 83 2-6 ■ • « ■ • • 45 2-5 39 2-3 20 250 17 183 2-2 315 1-6 • « • « • •  HCl. H2SO4. KI. ZnSO^. AgNOs. KHO. At. 107 Ak Jt.l07 Ak k.\(fl Ak k.W Ak fc.107 Ak k,W At kl(P Ak 6% 241 1-50 369 1-59 195 1-21 32 2 1 18 2-3 24 2-2 161 1-9 10 431 1-45 590 1-57 366 1-28 64 2-0 30 2-3 44 2-2 295 1-9 15 573 1-40 698 1-56 508 1-36 98 1-9 39 2-3 64 2-2 399 1-9 20 665 1-38 713 1-55 611 1-45 136 1-8 43 2-4 81 2-1 468 2-0 25 720 1-38 677 1-54 671 1-54 175 1-8 44 2-6 99 2-1 506 21 30 734 1-39 620 1-53 691 1-62 215 1-7 41 3 0 116 2-1 508 2-3 35 719 1-43 553 1-52 678 1-70 257 1-6 33 4-0 131 2-1 477 2-4 40 686 1-49 483 ■ • • 636 1-78 296 1-5 • ■ • 146 2-1 422 2-7 50 590 1-6 • • « • • • 505 1-93 367 1-4 • a > 173 2-1 ■  297 per cent Sp. gr. 1*185 HCl 717 at 18-3 „ 1-092 H2S04 692 at 30*4 „ „ 1-224 KHO 510 at 28 „ II 1 "-^74 MgS04 46 at 17 „ 1-183 ZnS04 44-2 at 23*5 „ „ 1-286 454 PHYSICAL MEASUREMENTS TABLE 26a- — Resistances of Metals (J. C. Maxwell). '^ In the following Table B is the resistance in ohms of a column 1 meter long, and 1 ffram weight, at 0" C. ; and r is the resistance in centimeters per second of a cube of 1 centimeter, according to the experiments of Matthiessen." Percentage Incre- Specific Gravity. JZ. r. ment of Resistance fori' Cat 20*0. Silver 10-60 hard drawn 0-1689 1609 0-377 ^?r : 8-96 „ 0-1469 1642 0-388 19-27 0-4160 2164 0-866 Lead 11-391 pressed 13-596 liquid 2-257 19847 0-387 Mercury. 13 071 96146 0-072 Gold 2, Silver 1 16*218 hard or annealed 1-668 10988 0 065 Selenium at 100° C. crystalline form • « • exioJ* 1-00 TABLE 26b, — ^Electromotive Force of Constant Batteries (J. C. Maxwell). Concentrated Solution of Daniell I. Amalgamated Zinc H2SO4+ 4 Aq CUSO4 Copper „ IL „ „ +12 Aq CUSO4 „ in. ,, „ + .. CuNO, Bunsen I. ,, » + IL .. M + ff Grove fi If f > + 4Aq HNO, Carbon sp. gr. 1*38 „ HNO, Pktinum Volt 1-079 0-978 1-00 1-964 1-888 1-956 TABLE 27. — Electro-chemical Equivalents. A current of 1 ampere =0*1 [cm. g. sec. ] = 10 [mm. mg. sec. ] decomposes or separates Mg. silver. Mg. copper. Mg. hydrogen. Mg. water. C.C mixed gases at 0" C. and 760 nun. In 1 sec. In 1 min. In 1 hr. 1-1181 67-09 4025 0-3284 19-70 1182 0-01039 0-623 37-41 0-0933 6-60 336 0-1740 10-44 626 TABLE 27a. — Comparison op Measures of Electric Current-Strength. A Carrent-Strength which is measured in Must be multiplied by the following Numbers to reduce it to Cubic Cm. Water Oases per Miuute. Mgr. Water per minute. Mgr. Copper per Minute. Mgr. Silver per Minute. Magnetic Measure Mm.* Mgr,* Sea Cub. Cm. Water Gases per min. Mgr. Water per Min. Mgr. Copper „ Mgr. Silver „ Magnetic Measure Mm.2 Mgr.i Sec. 1 -865 0-5294 0-1665 1054 0-6363 0-2839 0-0834 0-5653 1-889 8-522 0-2937 1-991 6-432 11-99 3-406 • « • 6-779 0-9484 1-769 0-6028 0-1476 • ■ • TABLES 455 TABLE 27b. — Molecular Conductivity klii of some Electro- lytes AT 18° G. in aqueous Bolution containing /a equivalents. [F. K., Wied. Ann. xxvl 195, 1885.] /i is the strength {>er liter in gram-equivalents ; coxnpare Table 8a. k is the conductivity as compared to mercury at 0° C. The limiting values are graphically extrapolated, as well as the bracketed values for acids, upon tiie hypothesis that the first observed conductivities are depressed by the impurity of the water. KCl. NaCl. HCl. *Ka804. iMgSO^. iHaS04. ADproxirnAte Limit- ing Value . .. 1230 1040 -1 [8550] 1290 4 [1100] [8800] /A = 0-0001 0-0002 0-0005 1215 1210 1201 1026 1021 1016 [8500] [3490] [3480] 1125 1240 1224 1034 1015 976 [3580] [3520] [3440] 0-001 0-002 0-005 1193 1185 1165 1008 999 981 3460 3455 3445 1207 1181 1140 935 881 790 [8850] 8250 3050 0-01 0-02 0-05 1147 1123 1083 962 938 897 3416 8890 8380 1098 1044 959 715 632 534 2860 2650 2840 0-1 0-2 0-5 1047 1009 958 865 826 757 8240 8140 8020 897 832 786 467 408 830 2090 1960 1900 1 2 5 917 864 • • • 696 604 898 2780 2340 1420 672 271  ■ • • • ■ • 655 147 80 TABLE 27c. — ^Electrical Potential and Striking Distance S IN Air. (From Bailie, Quincke, Bichat and Blondlot, Paschen, Freyberg.) R= Radius of ball in cm. V = Electrostatic potential in [cm. g. sec] 800 y. gives the potential in volts. s R ill cm. 8 R in cm. 1-0 0-5 8-0 1-0 0-5 8-0 cm. 0-02 0 04 0-06 0-08 0-1 0-2 0-8 V. 5-2 8-2 11-0 13-5 16 28 88 V.  0-6 0-7 0-8 0-9 1-0 V. 48 57 65 72 78 82 85 V. 48 57 66 75 88 91 97 V. 45 55 65 75 87 98 109 456 PHYSICAL MEASUREMENTS TABLE 28. — Units of the Absolute System of Measurement. Fundamental magnitudes : — Length l^ mass m, time L Each kind of magnitude is expressed in the form ^, m/*', ^ ; \fi, r, being the dimensions of the magnitude in respect to length, mass, and time. The unit of time is the second. Related units of length and mass are : dm,k,; cm,g. ; mm.mg. The numbers in the last column show the ratio N in which a unit increases by the change from mm,mg, to em.g.; or from cm.g. to dm.k. Quantities given in m7n.7ng. units (Gauss- Weber system) must therefore be divided by N to reduce them to cnug. The middle column contains the names of various imits in use, and the number of them which make up the corresponding em. g. unit. If we put 300 X 10 cm. sec, then the ratio Electromag. unit/Electrostat. unit for electnc quantity or current is t; ; for electric potential 1/v ; for electric capacity i^ ; and for electric resistance 1/t;^. X 0 0 r 0 N Angle ..... 1 Length .... 1 0 0 1 centimeter 10 Linear curvature. 1 0 0 10-^ Area of surface 2 0 0 10« Volume .... 3 0 0 10« Mass ..... 0 1 0 1 gram 10» Density .... -3 1 0 1 Time, period of oscillation 0 0 1 1 second 1 Velocity .... 1 0 -1 10 Angular velocity. 0 0 -1 1 Acceleration 1 0 -2 10 Angiilar acceleration 0 0 -2 1 Force 1 1 -2 1 dyne 10* Moment of rotation, directive force .... 2 -2 10* Pressure .... -1 -2 10» Modulus elasticity - 1 -2 10« Capillary constant 0 -2 10* Coefficient internal friction -1 -1 10« Moment of inertia. 2 0 10** Work, energy, vis viva quantity of heat .... 2 1 -2 1 erg. 10* Number of oscillations, pitch. 0 0 -1 1 Index of refraction 0 0 0 1 Rotatory power -1 0 0 10-1 Electrostatic System. • Electric quantity. 3 i -1 J 1 0"* coulombs 10» Potential .... i 1 -1 300 volts 10» Capacity .... 1 0 0 J 10-" farads 10 Dielectric constant 0 0 0 1 Electric current f i -2 J lO-* am. 10» Resistance .... -1 0 1 9x10" ohm. 10-^ TABLES 457 TABLE 28— continued. ELECTRO-lfAGNETIC StSTEM Magnetic pole Magnetic potential Magnetism of bar. Magnetic intensity Spea Magnetism (vol.) Const, of magnetisation Electric current Current density Electric quantity. Electro-chemical equivalent Electro-magnetic force, potential Capacity Resistance Specific resistance. Current efl&ciency. El.  0 10 amperes 10 coulombs 10-« volte 10* farads 10-* ohm lO-*^ watts. N 10» 10^ 10* 10 10 1 10« 1 10» 10 10» 10-^ 10 lO'* 10* 10 TABLE 28b.— Birmingham Wire Gauge (Holtzapffel). WG. Diameter in inches. BWC 0 0-340 14 2 -284 16 4 -238 18 6 -203 20 8 -165 22 10 •134 24 12 -109 26 BWO. ^tchl" I BWG. 0 -083 28 •065 30 -049 32 •036 33 -028 34 -022 35 •018 36 Diameter in inches. 0-014 •012 •009 •008 •007 -005 •004 TABLE 28c. — Mean Specific Heats of Water and Platinum. Water (Regnault). Platinum (Pouillet). From 0" to 40' C. 1*0013 „ 0 „ 80 1-0035 „ 0 ,,120 1-0067 „ 0 „ 160 1-0109 „ 0 „ 200 1-0160 „ 0 „ 230 1-0204 From 0° to 100" C. 0-0335 „ 0 „ 300 0-0343 „ 0 „ 500 0-0352 „ 0 „ 700 0-0360 „ 0 „ 1000 0-0373 „ 0 „ 1200 0-0382 • 458 PHYSICAL MEASUREMENTS TABLE 29. — Symbols, Atomic Weight, Valence, and Specific Heat of some Elements. The Atomic Weight is the smallest proportion in which the element enters into combination ; hydrogen being taken as 1, or practically oxygen as 16. The Valence or Atomicity indicates the largest number of atoms of hydrogen or other univalent element which one atom usually replaces or combines with. In many cases the element acts as if its valence were less by 2 or 4 than that given. Equal quantities of electricity liberate e<iual valences. Specific EiecU multiplied by atomic weight is nearly constant for the same physical state in all elements. The JSleetro-negcUive elements, or those which in electrolysis appear at the positive pole or zincode, are printed in italics; the electro-positive, or those which appear at the native pole or platinode, in Roman type. The difference, however, is only one of degree. Name. Symbol. Atomic Weight, Valence. Specific Heat of Equal Farts. Aluminium Al 27-1 VL in. 0-202 Antimony Sb 120-3 V. 0-0508 Arsenic As 76-0 V. 0-0814 Barium Ba 137-0 IL Bismuth. Bi 208 0 V. o'-0308 Boron B 11-0 IV. 0-25 Bromine. Br 79-96 I. / 0-1060 Liquid 1 0-0843 SoUd Cadmium. Cd 112-1 IL 0-0548 Calcium Ca 40-0 IL Carbon C 12-0 IV. / 0-459 Charcoal \ 0-467 Diamond Chlorine. CI 86-45 I. 0*1210 Const press. Chromium Cr 62-2 VL 0-100 Cobalt. Co 59 0? VL 0-1070 Copper Cu 63-3 IL 0-0952 Mtwrine. F 19-0 I. Gold. Au 197-2 IIL 0-0324 Hydrogen. H 1-003 I. 0*4090 Const press. Iodine I 126-86 I. 0-0541 Iron. Fe 56-0 VI. IIL 0-1188 Lead Pb 206-9 IV. 0 0314 Lithium Li 7-03 I. 0-941 Magnesium Mg 24-4 IL 0-2499 Manganese Mn 55-1 VL IIL 0-122 Mercury. Hg 200-4 IL 0-0319 Solid Nickel. Ni 68-5 VL III. 0-108 Nitrogen. N 14-04 V. 0*2438 Const press. Oxygen 0 16 00 IL 0*2175 Const, press. Phosphorus P 31-0 V. 0-170-0-189 Platinum. Pt 194-8 IV. 0-0324 Potassium K 39 14 I. 0-166 Selenium. Se 79 1 VL 0-074-0-086 Silicon Si 28-4 IV. 0-203 Silver Ag 107-94 I. 0-0560 Sodium Na 23 06 I. 0*2934 Strontium. Sr 87-5 IL Sulphur. S 32-06 VL 0-163-0-178 Tin. Sn 118-1 IV. 0 0548-0-0562 Zinc. Zn 65-4 IL 0-0932-0-0955 TABLES 459 TABLE 30. Geographical Position and Height of some Places » ABOVE THE SeA. East longitude reckoned from Berlin is about 13*39 smaller, and from Ferro 17*66 larger than Greenwich. Aix-la-ChapeUe Amsterdam Basle .. Berlin .. Berne. Birmingham Bonn .. Boston Bremen Breslau Bmnswick Brussels Cambridge Cologne Copenhagen Carlsruhe. Cassel .. Dantzig. Darmstadt Dorpat Dresden Edinburgh Freiburg in B Giessen Glascow. Gottmgen. Greenwich HaUe .. Hamburg. Hanover. East vSnnffn North Height Green- wich. Lati- tude. above Sea. 6-1 50-78 160-200 4-9 52-37 • « • 7-6 47-56 260 18-4 52-50 40 7-4 46-95 650 -1-9 52-29 140-145 7-1 50-78 50 -70-0 42-87 • • ■ 8-8 53-08 • • • 17-0 51-11 180 10-5 52-27 100 4-4 50-85 90 0 1 52-20 • • • 7-0 50-94 40 12-6 55-69 ■ • » 8-4 49-01 120 9-6 51-82 160 18-7 54-85 • • • 87 49-87 140 26-7 58-38 50 13-7 51-04 100 -8-2 55-95 « • • 7-8 47-96 280 8-6 50-59 140 -4'3 55-85 • • • 9-9 51-58 180 0-0 61-48 ■ ■ • 12-0 51-49 100 10-0 58-56 • • • 9-7 52-88 70 Heidelberg Jena Innsbruck Kiel .. Konigsberg XjCOCIS. Madnd Marburg Milan. Montreal Munich MUnster New York Paris. Pesth. Philadelphia Prague. Rome. San Francisco Stockholm St Petersburg Strassburg Stuttgart .. Sydney Txibingen. Vienna Washington Wiirzburg. Zurich .. Boati^m North Height Qreen> lAti- above wich. tade. Sea. 8-7 49-41 100 11-6 50-94 160 11-4 47-27 570 10-2 54-84 • ■ • 20-5 54-71 • • • -1-5 58-78 60-100 12-4 51-84 100 -3-7 40-41 660 8-8 50-81 180-240 9-2 45-47 ISO -78-6 45-50 • ■ • 11-6 48-15 580 7-6 51-97 60 -74-0 40-71 • • • 2-8 48-88 60 191 47-50 70 -75-0 40-00 • ■ • 14-4 50-09 200 12-4 41-90 SO -122-4 37-77 • • • 18-1 59-84 • • • 80 3 59-94 • • • 7-8 48-58 150 9-2 48-78 270 151-1 88-85 • • • 9-1 48-62 820-880 16-4 48-28 180 -77-0 88-89 • • • 9-9 49-79 170 8-6 47-88 420-500 460 PHYSICAL MEASUREMENTS TABLE 31. Declination op the Sun, Equation of Tibie, and Sidereal Time for Mean Noon of 15° E. from Greenwich. (Central European " Unit Time.") Sidereal Time at Noon increases daily 3 min. 56-6 sec. =286*6 sec. Mean time of a place = Solar Time + Equation of Time. The figures in brackets 1 are for Leap Year. Declina- Differ- Equation of Time. Sidereal Declina- Differ- Eouation of Time. Sidereal Day. tion of the ence for Time at Day. tion of the ence for Time at San. Iday. Noon. Sun. Iday. Noon. Jan. o o m. 8. b> m. s. July o 0-068 0-102 0-136 0-164 0-194 0-222 m. s. h. m. s. 0 (1) -23-10 0-092 0-130 0-166 0-200 0-230 0-260 + 3 25 18 38 42 4 + 22-92 + 40 6 48 4 5 (6) -22-64 + 5 34 18 58 24 9 + 22-41 + 4 49 7 7 47 10 (11) - 21 -99 + 7 42 19 18 7 14 + 21-73 + 5 29 7 27 80 15 (16) -21-16 + 9 36 19 37 50 19 + 20-91 + 6 58 7 47 13 20 (21) -20-16 + 11 13 19 57 38 24 + 19-94 + 6 18 8 6 56 25 (26) -19-01 + 12 33 20 17 16 29 + 18-83 + 6 13 8 26 38 30 (31) -17-71 + 13 32 20 36 58 Aug. 0-248 0-272 0-294 0-314 0-830 0-346 Feb. 0-288 0-308 0-330 0-348 0-364 8 + 17-59 + 6 57 8 46 21 4 (5) - 16-27 + 14 10 20 56 41 8 + 16-23 + 6 27 9 6 4 9(10) 14 (15) -14-73 - 18-08 + 14 27 + 14 25 21 16 24 21 36 7 13 18 + 14-76 + 13-19 + 4 42 + 3 44 9 26 47 9 46 29 19 (20) -11-34 + 14 5 21 55 49 23 + 11-54 + 2 33 10 6 12 24 (25) - 9-52 + 13 28 22 15 32 28 + 9-81 + 111 10 24 65 March 1 - 7-65 0-874 0-384 0-890 0-394 0-394 0-394 0-390 + 12 36 22 36 15 Sept. 2 + 8-01 0-360 0-370 0-378 0-384 0-390 0-390 - 0 20 10 44 38 6 - 5-73 + 1131 22 54 58 7 + 6-16 - 1 69 11 4 21 11 - 3-78 + 10 15 23 14 41 12 + 4-27 - 8 41 11 24 8 16 - 1:81 + 8 52 23 34 23 17 + 2-35 - 6 26 11 43 46 , 21 + 0-16 + 7 23 23 54 6 22 + 0-40 - 7 12 12 8 29 26 + 2-13 + 5 52 0 13 49 27 - 1-65 - 8 66 12 23 12 31 + 4-08 + 4 19 0 33 32 Oct. 0-388 0-386 0-380 0-374 0-360 0-348 April 6 + 6-00 0-384 0-374 0-364 0-352 0-334 0-318 + 2 49 0 53 14 2 7 - 3-49 - 5-42 -10 34 -12 4 12 42 54 18 2 37 10 + 7-87 + 123 1 12 57 12 - 7-32 -13 24 13 22 20 15 + 9-69 + 04 1 32 40 17 - 9-19 -14 31 13 42 3 20 + 11-45 - 1 5 162 28 22 - 10-99 -16 23 14 1 45 26 + 13-12 - 2 4 2 12 5 27 - 12-73 -16 0 14 21 28 30 + 14-71 - 2 52 2 31 48 Nov. 0-330 0-312 0-288 0-266 0-236 0-206 May 5 10 + 16-19 + 17-57 0-296 0-276 0-250 0-224 0-196 0-164 - 3 27 - 3 48 2 51 81 3 11 14 1 6 11 -14-38 -15-94 -17-38 -16 18 -16 16 -16 52 14 41 11 15 0 54 15 20 37 15 + 18-82 - 3 58 3 30 57 16 -18-71 -16 7 16 40 19 20 + 19-94 - 3 45 3 50 39 21 -19-89 -14 2 16 0 2 25 + 20-92 - 3 23 4 10 22 26 -20-92 -12 86 16 19 45 80 + 21-74 - 2 49 4 30 5 Dec. 0-174 0-140 0-102 0-064 0-026 0-012 0-054 June 0-186 0-100 0-068 0-034 0-002 0-034 1 -21-79 -10 68 16 39 28 4 + 22-42 - 2 4 4 49 48 6 -22-49 - 8 54 16 59 10 9 + 22-92 - Ill 5 9 30 11 -23-00 - 6 40 17 18 63 14 + 23-26 - 0 10 5 29 13 16 -23-32 - 4 17 17 38 36 19 + 23-43 + 0 55 5 48 56 21 -23-45 - 149 17 58 19 24 + 23-43 + 20 6 8 39 26 -23-39 + 0 41 18 18 2 18 37 44 29 + 28-26 + 82 6 28 22 31 -23-12 I + 38 TABLES 461 TABLE 32. Correction Table for the Beginning of the Year. Tear. Correction. Year. Correction. 1891. + 0-151 1897. + 0-699 1892. + 0-909 1898. + 0-457 1893. + 0-667 1899. + 0-214 1894. + 0-425 1900. -0-028 1896. + 0-182 1901. -0-270 1896. + 0-941 1902. -0-512 TABLE 33. SuN*s Radius. Date. January 1 February 1 March 1. April 1. May 1 June 1 Radius. 0-272 0-271 0-269 0-267 0-265 0-263 Date. July 1. August 1. September October 1 November December ] Badias. 0-268 0-263 0-265 0-267 0-269 0-271 TABLE 34. Refraction at Different Altitudes. Altitude. Refhictlon. Altitude. Refhtction o 6. o 0 16 50. 0013 10. 0-09 60. 0-009 15. 0-06 70. 0 006 20. 0-04 80. 0 003 80. 0-028 90. 0-000 40. 0-019 462 PHYSICAL MEASUREMENTS TABLE 35. Mean Places of some Principal Stars for 189 30. Right Ascension. Yearly Variation. sec. + 3-37 Declination. Yearly Variation. + 19-8 a Cassiopeiffi hr. 0 min. 84 sec. 26-1 • 55 57 It 1 a Arietis-. 2 1 8-4 + 8-37 22 67 28 + 17-2 a Persei 8 16 41-0 + 4-26 49 28 48 + 18-1 a Tauri (Aldobaran) 4 29 46-8 + 8-44 16 17 37 + 7-5 a Aurigte (Capella) 6 8 47-1 + 4-43 45 53 19 + 4-0 a Ononis. 5 49 227 + 3-25 7 23 12 + 1-0 a CanU Majoiia (Sinus) 6 40 26-1 + 2-64 -16 84 11 - 47 a Geminomm (Castor) 7 27 46-2 + 3-84 32 7 22 - 7-6 a Canis Minoris (Procyon) 7 33 42-1 + 8-14 5 29 56 - 9-0 a Hydne. 9 22 19-8 * + 2-95 -8 11 42 -16-4 a Leonis (Regulus) 10 2 40-4 + 8-20 12 29 24 -17-5 a UraseMajoris. 10 67 7-4 + 376 62 19 48 -19-4 p Leonis. 11 43 86-1 + 3-06 15 10 18 -20-1 a Virginis (Spica) 13 19 83-3 + 315 -10 36 10 -18-9 a Bootis (Arctunis) 14 10 46-8 + 273 19 44 23 -18-9 a Coron© (Gomma) 15 80 9-5 + 2-54 27 4 30 -12-8 a Scorpii (Antares) 16 22 50-8 + 3-67 -26 11 40 - 8-8 a Ophiuchi 17 29 58-0 + 278 12 38 17 - 2-8 oLyr»(Vega). 18 33 18-9 + 2-03 38 41 3 + 3-2 a Aqnilee (Altair) 19 45 837 + 2-93 8 86 9 + 9-8 a Cygni. 20 37 47-1 + 2-04 44 53 58 + 127 a Piscis Australis (Fomal- 22 51 44*2 + 3-32 -30 11 22 + 19-0 naat) a Pegasi . . . • 22 59 25-8 + 2-98 14 87 47 + 19-3 a Ursfle Minoris (Polaris). 1 19 417 + 23-9 88 44 15 + 18-9 9 Ursse Minoris. 18 6 49-2 -19-5 86 36 44 + 0-6 TABLES 463 TABLE 36. Numbers frequently required. (The fractions in brackets are approximate values. ) x=8-1416 (V), ir«=9-8696, -=0-3183l, ^=7854, log. ir=0-497l499. Basis of natural logarithms e= 2*71 88 ; log. 0=0*43429. The modulus of natural logarithms M=l/log. «= 2*3026 ; log. M = '36222. The angle of which the arc is equal to the radiu8= 67**2958 =3487 '75' =206265*. Ratio of the probable to the mean error =0*6745 (|). 1 Paris foot =0*32484 meter (i^). 1 meter =3*0784 Paris feet. 1 Paris line =2*2588 mm. ()). 1 mm. =0*44330 Paris line. 1 Rhenish foot=0'31385 meter(H)- 1 meter =3*1862 Rhenish feet. 1 English foot =0-30479 „ (^)- 1 meter =3*2809 English feet 1 Geogr. mile =7*4204 kilom. (V). 1 kilom. =0*13476 Geogr. mile. 1 English mile=l -60929 „ 1 kilom. =0*62138 English mile (f ). Half the major axis of the earth = 6378*2 kilometers. ,, minor ,, =6356"5 „ The mean semidiameter of earth = 6367 *4 , , Mean length of civil year, 865 days 5 hours 48*8 min. Sidereal day = mean day- 3 min. 55*9 sec =0*99727 mean day. Velocity of sound at 0' 0. in dry air =331. sec. Coefficient of expansion of gases 0*00367 (rfs). 1 grm. wt at 45* lat. =980*6 cm.g. sec.-*. 1 at pressures 1038 g.-wt /cm.' =1013200 cm.-^ g. sec.-'. 1 water gram, calorie =428 g. wt m = 42000000 cm.*g. sec,-'. Latent heat of water =79*9; of steam = 536 (1 lb. water 1' Fah.=772 foot- pounds.) Specific heat of air at constant pressure =0*237. Ratio of specific heats of air or H ; constant pressure to constant vol. = 1 '40. Capillary constant of water, 7 '8 ; alcohol, 2*3 ; mercury, 50 mg./mm. Ratio of molecular wt. to vapour density (air) = 28*9 ; to H = l. 1 liter H. at 0' C. and 760 mm. weighs 0*0896 g. Velocity of light in «icuo= 800000 km. /sec. Index of refraction of air = 1*00029. Wave-length of Na light (D. Fraunhofer) = 0*0005893 mm. A quartz plate 1 mm. thick rotates Na light 21**7. Ratio of electro-magnetic to electrostatic unit of electricity v= 300*10^ cm. /sec. 1 Ampere = 0*l cm.* g.* sec.-* el.-mag. =300x10' cm." g.« sec.-' el.-stat units/sec. = 1*1181 mg. Ag/sec. 1 Ohm = 10* cm. sec.-* eL-mag. = 1/9 x 10-" cm.-* sec. eL-stat = 1*068 m./mm.' Hg. 0* C. = 1014 B. A. units. 1 Volt = 10* cm.? g. ♦ sec.-" el.-mag. = 1/300 cm.* g.* sec.-* el.-stat. (Ger. legal Ohm and Volt see, p. 423.) Bunsen cell=l'9 ; Daniell=l*l to 1*2 ; Clark at 15*=1*433 volts. 1 Volt-ampere or Watt =0*102, kg.-wt m./sec. =0*24 water g. cal./sec. 464 PHYSICAL MEASUREMENTS TABLE 37. — Squares, Square Eoots, and Reciprocals. Conversion of degrees of Arc into absolute Angular Measure. Table for use with the Wheatstone-Kirchhoff Bridge. n. n>. V^ 1 n* liJO n 100-n 1 1 1-000 1-0000 0-0175 I 0-0101 2 4 1-414 0-6000 0-0349 0-0204 3 9 1-732 0-3333 0-0524 0-0309 4 16 2-000 0-2500 0-0698 0-0417 6 25 2-236 0-2000 0-0873 0-0526 6 36 2-449 0-1667 0-1047 0-0638 7 49 2-646 0-1429 0-1222 0-0763 8 64 2-828 0-1250 0-1396 0-0870 9 81 3 000 0-1111 0-1571 0-0989 10 100 3162 0-1000 0-1745 0-1111 11 121 3-317 0-0909 0-1920 0-1236 12 144 3-464 0-0833 0-2094 0-1364 13 169 3-606 0-0769 0-2269 0-1494 14 196 3-742 0-0714 0-2443 0-1628 15 225 8-873 0-0667 0-2618 0-1765 16 256 4-000 0-0625 0-2793 0-1905 17 289 4-123 0-0588 0-2967 0-2048 18 324 4-243 0-0556 0-3142 0-2195 19 361 4-359 0-0526 0-3316 0-2346 20 400 4-472 0-0500 0-3491 0-2500 21 441 4-583 0-0476 0-3665 0-2658 22 484 4-690 0-0455 0-3840 0-2821 23 529 4-796 0-0435 0-4014 0-2987 24 576 4-899 0-0417 0-4189 0-3158 25 625 5-000 0-0400 0-4363 0-3333 26 676 5-099 0-0385 0-4538 0-3514 27 729 5 196 0-0370 0-4712 0-3699 28 784 5-292 0-0357 0-4887 0-3889 29 841 5-385 0-0345 0-5061 0-4085 30 900 5-477 0-0333 0-5236 0-4286 31 961 5-568 0-0323 0-5411 0-4493 32 1024 5-657 0-0313 0-5585 0-4706 33 1089 5-745 0-0303 0-5760 0-4925 34 1156 6-831 0-0294 0-5934 0-6162 35 1225 5-916 0-0286 0-6109 0-588 36 1296 6-000 0-0278 0-6283 0-562 37 1369 6-083 0-0270 0-6458 0-587 38 1444 6-164 0-0263 0-6632 0*613 39 1521 6-245 0-0256 0-6807 0-639 40 1600 6-325 0-0250 0-6981 0-667 41 1681 6-403 0-0244 0-7156 0-695 42 1764 6-481 0-0238 0-7330 0-724 43 1849 6-557 0-0233 0-7505 0-754 44 1936 6-633 0-0227 0-7679 0-786 45 2025 6-708 0-0222 0-7854 0-818 46 2116 6-782 0-0217 0-8029 0-852 47 2209 6-856 0-0213 0-8203 0-887 48 2304 6-928 0-0208 0-8378 0-923 49 2401 7 000 0-0204 0-8552 0-961 50 2500 7-071 0-0200 0-87-27 1-000 TABLES 465 TABLE 37 — carUinued, — ^Squares, Square Roots, & Reciprocals. Conversion of degrees of Arc into absolute Angular Measure. Table for use with the Wheatstone-Kirchhoff Bridge. n. 1|2. 