IC-NRLF B M OEb llfi Q D 65 M7 1913 CHEM UCTION TABLES MOORE THE usrjfet ^ UtKlLlV LIBRARY vumsmcx JAMOMHA f\I LOGARITHMIC REDUCTION TABLES FOR STUDENTS OF ANALYTICAL CHEMISTRY BY CHAKLES J. MOORE, Pn.D. (VIRGINIA) AUSTIN TEACHING FELLOW IN .MA ANrKD ANALYTICAL CHEMISTRY IN HARVARD UNIVERSITY GINN AND COMPANY BOSTON NEW YORK CHICAGO LONDON COPYRIGHT, 1913, BY CHARLES J. MOORE ALL EIGHTS RESERVED 913.7 GINN AND COMPANY PRO- PRIETORS BOSTON U.S.A. M7 TO THE MEMORY OF MY DEVOTED MOTHER THIS LITTLE VOLUME IS DEDICATED PREFACE These tables are intended primarily for students of analytical chemistry. My aim has been to produce a book adapted to the needs of the beginner, and, at the same time, to arrange the material in such a way that it may be conveniently used by advanced students and chemists. In discussing logarithms I realize I have encroached on foreign territory, but, in my experience as a teacher, I have known many students who were unfamiliar with the use of logarithms, and who were unwilling to acquaint themselves with the subject unless it be presented as a part of their present work. The subject ie important for any one to know who has many arith- metical computations to make, and I hope that a sufficient number will profit by the explanations to justify me in including them. , The tables contain the most recent trustworthy values to be found in the literature. These values and their logarithms have been checked three times in order to eliminate possible errors. I have used freely Landolt-Bornstein's Physikalisch-chemische Tabellen, Ostwald-Luther's Physiko-chemische Messungen, and many original articles. C. J. MOORE CAMBRIDGE, MASSACHUSETTS CONTENTS TABLE PAGE I. ATOMIC WEIGHTS OF THE ELEMENTS AND THEIR LOGARITHMS . 3 II. MULTIPLES OF THE ATOMIC WEIGHTS OF COMMON ELEMENTS AND TIIKIK LOGARITHMS 5 III. MOLECULAR WEIGHTS OF COMMON COMPOUNDS AND THEIR LOGA- RITHMS 7 IV. MULTIPLES OF THE MOLECULAR WEIGHTS OF SOME COMMON COM- POUNDS AND OF THE WEIGHTS OF A FEW RADICALS TOGETHER WITH THEIR LOGARITHMS 10 V. REDUCTION OF COMPOUNDS FOUND TO CONSTITUENTS SOUGHT BY MULTIPLICATION 11 VI. REDUCTION OF BAROMETRIC READINGS TO '. . . 16 VII. GEOGRAPHICAL LATITUDE, ELEVATION, AND GRAVITY OF SOME IMPORTANT CITIES 17 VIII. REDUCTION OF BAROMETRIC READINGS TO NORMAL GRAVITY . . 18 IX. CAPILLARY DEPRESSION OF MERCURY 19 X. TENSION OF AQUEOUS VAPOR 20 XL REDUCTION OF WATER PRESSURE TO MERCURY PRESSURE . . .21 XII. REDUCTION OF THE VOLUME OF GASES TO NORMAL PRESSURE . 22 XIII. REDUCTION OF THE VOLUME OF GASES TO 0C 25 XIV. REDUCTION OF THE VOLUME OF GASES SATURATED WITH AQUEOUS VAPOR TO 0, NORMAL PRESSURE, AND DRY 28 XV. OBSERVED DENSITY AND THE WEIGHT OF A LITER OF SOME COM- MON GASES 30 XVI. DENSITY OF DRY ATMOSPHERIC AIR AT 760 MM. PRESSURE AND TEMPERATURES RANGING FROM TO 35 31 XVII. APPARENT WEIGHT OF A CUBIC CENTIMETER OF WATER AND THE VOLUME OF AN APPARENT GRAM OF WATER AT TEMPERATURES FROM 10 TO 25 34 XVIII. SPECIFIC VOLUME OF WATER AT TEMPERATURES FROM TO 35 . 35 XIX. DENSITY OF WATER AT TEMPERATURES FROM TO 35 ... 36 XX. THE PROPORTION BY WEIGHT OF ABSOLUTE ALCOHOL IN 100 PARTS OF SPIRITS OF DIFFERENT SPECIFIC GRAVITIES, AND THE PROPOR- TION BY VOLUME OF ABSOLUTE ALCOHOL IN 100 VOLUMES OF SPIRITS OF DIFFERENT SPECIFIC GRAVITIES 37 vii viii CONTENTS TABLE PAGE XXL SPECIFIC GRAVITY OF SOLUTIONS OF AMMONIUM HYDROXIDE . 38 XXII. SPECIFIC GRAVITY OF SOLUTIONS OF HYDROCHLORIC ACID . . 38 XXIII. CONSTANT BOILING SOLUTION OF HYDROCHLORIC ACID ... 39 XXIV. SPECIFIC GRAVITY OF NITRIC ACID 40 XXV. SPECIFIC GRAVITY OF SULPHURIC ACID 41 XXVI A~} CORRECTIONS FOR THE EXPOSED THREAD OF MERCURY THER- XXVI B) MOMETERS . 43, 44 XXVII. FIXED POINTS OF THE THERMOMETRIC SCALE 44 XXVIII. CORRECTIONS FOR Loss OF WEIGHT IN AIR 45 XXIX. TABLE OF LOGARITHMS TO Six PLACES OF DECIMALS .... 46 EXPLANATIONS OF THE PRECEDING TABLES 65 DISCUSSION OF LOGARITHMS AND DIRECTIONS FOR USING THE TABLE OF LOGARITHMS . 73 LOGARITHMIC REDUCTION TABLES TABLE I THE ATOMIC WEIGHTS OF THE ELEMENTS AND THEIR LOGARITHMS Symbol Atomic weight Logarithm Aluminum Al 27.1 .432 969 Antimony Sb 119.86 .078 674 Argon A 39.9 .600 973 Arsenic As 74.95 .874 772 I Jarium Ba 137.36 .137860 Bismuth Bi 208.0 .318063 Boron B 11.0 .041 393 Bromine Br 79.909 .902 596 Cadmium Cd 112.41 .050 805 Caesium Cs 132.80 .123 198 Calcium Ca 40.07 .602 819 Carbon C 12.00 .079 181 Cerium Ce 140.24 .146 872 Chlorine Cl 35.454 .549 665 Chromium Cr 52.00 .716003 Cobalt Co 58.96 .770 557 Columbium Cb 93.5 .970 812 Copper Cu 63.57 .803 252 Dysprosium Py 162.5 .210853 Erbium Er 167.4 .223 755 Europium Eu 152.0 .181 844 Fluorine F 19.0 .278 754 Gadolium Gd 157.3 .196 729 Gallium Ga !69.9 .844 477 Germanium Ge 72.5 .860338 Glucinum Gl 9.1 .959 041 Gold Au 197.2 .294 907 Helium He 4.0 .602060 Hydrogen H 1.0078 .003 375 Indium In 114.8 .059942 Iodine I 126.91 .103 496 Iridium Ir 193.1 .285 782 Iron Fe 55.83 .746 868 Krypton Kr 81.8 .912 753 Lanthanum La 139.0 .143 015 Lead Pb 207.07 .316117 Lithium Li 6.939 .841 297 Lutecium Lu 174.0 .240 549 Magnesium Mg 24.32 .385 964 Manganese Mn 54.92 .739 731 a. TABLE I (CONTINUED) Symbol Atomic weight Logarithm Mercury Molybdenum Neodymium Neon Hg Mo Nd Ne 200.61 96.0 144.26 20.0 .302 353 .982 271 .159 146 .301 030 Nickel Ni 58.67 .768 416 Nitrogen Osmium N Os 14.01 190.9 .146438 .280 806 Oxygen Palladium Pd 16.000 106.7 .204 120 .028 164 Phosphorus Platinum P Pt 31.03 195.0 .491 782 .290035 Potassium K 39.091 .592 077 Praseodymium Kadium Pr Ra 140.6 225.95 .147 985 .354012 Rhodium Rh 102.9 .002415 Rubidium Rb 85.44 .931661 Ruthenium Ru 101.7 .007 321 Samarium Sa 150.4 .177248 Scandium Sc 44.1 .644 439 Selenium Se 79.2 .898 725 Silicon Si 28.3 .451 786 Silver Sodium Ag Na 107.87 22.993 .032 901 .361 595 Strontium Sr 87.613 .942 569 Sulphur Tantalum S Ta 32.07 181.5 .506 099 .258877 Tellurium Te 127.5 .105 510 Terbium Tb 159.2 .201 943 Thallium Tl 204.0 .309 630 Thorium Th 232.40 .366 236 Thulium Tu 168.5 .226 600 Tin Sn- 119.0 .075 547 Titanium Ti 48.1 .682 145 Tungsten Uranium w u 184.0 238.40 .264 818 .377 306 Vanadium V 51.2 .709 270 Xenon Xe 128.0 .107210 Ytterbium Yb 172.0 .235 528 Yttrium Y 89.0 .949 390 Zinc Zn 65.36 .815312 Zirconium Zr 90.6 .957 128 TABLE II SECOND TO SEVENTH MULTIPLES OF THE ATOMIC WEIGHTS OF COMMON ELEMENTS AND THEIR LOGARITHMS 2 log 3 log 4 log Aluminum 54.2 733 999 81.3 910090 108.4 035 029 Antimony 239.72 379704 359.58 555 796 479.44 680 734 Arsenic 149.90 175 802 224.85 351 892 299.80 476 832 Barium 274.72 438 890 412.08 614 982 549.44 739 920 Bismuth 416.0 619093 624.0 795 185 832.0 920 123 Boron 22.0 342 423 33.0 518514 44.0 643 453 Bromine 159.818 203 626 239.727 379 717 319.636 504656 Cadmium 224.82 351 835 337.23 527 927 449.64 652 865 Calcium 80.14 903 849 120.21 079 941 160.28 204879 Carbon 24.00 380211 36.00 556 303 48.00 681 241 Chlorine 70.908 850 695 106.362 026 787 141.816 151 725 Chromium 104.00 . 017033 156.00 193 125 208.00 318063 Cobalt 117.92 071 588 176.88 247 679 235.84 372618 Copper 127.14 104 282 190.71 280374 254.28 405 312 Fluorine 38.0 579784 57.0 755 875 76.0 880 814 Gold 394.4 595 937 591.6 772 028 788.8 896 967 Hydrogen 2.0156 304 405 3.0234 480 496 4.0312 605 434 Iodine 253.82 404 526 380.73 580617 507.64 705 556 Iron 111.66 047 898 167.49 223 989 223.32 348 928 Lead 414.14 617 147 621.21 793 238 828.28 918177 Lithium 13.878 142 327 20.817 318418 27.756 443 357 Magnesium 48.64 686994 72.96 863 085 97.28 988024 Manganese 109.84 040 760 164.76 216852 219.68 341 790 Mercury 401.22 603 383 601.83 779 474 802.44 904413 Molybdenum 192.0 283 301 288.0 459 392 384.0 584331 Nickel 117.34 069 446 176.01 245 537 234.68 370476 Nitrogen 28.02 447 468 42.03 623 559 56.04 748498 Oxygen 32.000 505 150 48.000 681 241 64.000 806 181 Phosphorus 62.06 792 812 93.09 968903 124.12 093 842 Platinum 390.0 591 065 585.0 767 156 780.0 892 095 Potassium 78.182 893 107 117.273 069 198 156.364 194 137 Silicon 56.6 752 816 84.9 928 908 113.2 053 846 Silver 215.74 333 930 323.61 510022 431.48 634 961 Sodium 45.986 662 626 68.979 838717 91.972 963 655 Strontium 175.226 243 598 262.839 419 690 350.452 544 628 Sulphur 64.14 807 129 96.21 983 220 128.28 108 159 Tin 238.0 376577 357.0 552 668 476.0 677 607 Titanium 96.2 983 175 144.3 159 266 192.4 284 205 Tungsten 368.0 565 848 552.0 741 939 736.0 866 878 Uranium 476.8 678 336 715.2 854 428 953.6 979 366 Zinc 130.72 116343 19608 292 433 261.44 417372 TABLE II (COXTIXUED) 5 log 6 log 7 log Aluminum 135.5 131 939 162.6 211 121 189.7 278 067 Antimony 599.30 777 644 719.16 856 826 839.02 923 772 Arsenic 374.75 573 742 449.70 652 923 524.65 719 869 Barium 686.80 836 830 824.16 916012 961.52 982 958 Bismuth 1040.0 017033 -1248.0 096 215 1456.0 163 161 Boron 55.0 740 363 66.0 819 544 77.0 886491 Bromine 399.545 601566 479.454 680 747 559.363 747 694 Cadmium 562.05 749 775 674.46 828 956 786.87 895 903 Calcium 200.35 301 789 240.42 380971 280.49 447 917 Carbon 60.00 778151 72.00 857333 84.00 924 279 Chlorine 177.270 248 635 212.724 327816 248.178 394 763 Chromium 260.00 414973 312.00 494 155 364.00 561 101 Cobalt 294.80 469 528 353.76 548 709 412.72 615 656 Copper 317.85 502 222 381.42 581 404 444.99 648 350 Fluorine 95.0 977 724 114.0 056 905 133.0 123 852 Gold 986.0 993 877 1183.2 073 058 1380.4 140 005 Hydrogen 5.0390 702 344 6.0468 781 526 7.0546 848 472 Iodine 634.55 802 466 761.46 881 647 888.37 948 594 Iron 279.15 445 838 334.98 525 019 390.81 591 966 Lead 1035.35 015 087 1242.42 094 269 1449.49 161 215 Lithium 34.695 540 267 41.634 619 448 48.573 686 395 Magnesium ] 21.60 084 934 145.92 164 115 170.24 231 062 Manganese 274.60 438 701 329.52 517881 384.44 584 828 Mercury 1003.05 001323 1203.66 080 504 1404.27 147451 Molybdenum 480.0 681 241 576.0 760 422 672.0 827369 Nickel 293.35 467 386 352.02 546 567 410.69 613514 Nitrogen 70.05 845 408 84.06 924589 98.07 991 536 Oxygen 80.000 903090 96.000 982 271 112.000 049 218 Phosphorus 155.15 190 752 186.18 269 933 217.21 336 880 Platinum 975.0 989 005 1170.0 068 186 1365.0 135 133 Potassium 195.455 291 047 234.546 370 228 273.637 437 175 Silicon 141.5 150 756 169.8 229 938 198.1 296 884 Silver 539.35 731 870 647.22 811052 755.09 877 998 Sodium 114.965 060 566 137.958 139 747 160.951 206 694 Strontium 438.065 641 538 525.678 720 720 613.291 787 667 Sulphur 160.35 205 069 192.42 284-250 224.49 351 197 Tin 595.0 774517 714.0 853 698 833.0 920 645 Titanium 240.5 381 115 288.6 460296 336.7 527 243 Tungsten 920.0 963 788 1104.0 042 969 1288.0 109 916 Uranium 1192.0 076 276 1430.4 155457 1668.8 222 404 Zinc 326.80 514282 392.16 593 463 457.52 660 410 TABLE III MOLECULAR WEIGHTS OF COMMON COMPOUNDS AND THEIR LOGARITHMS Mol.wt. log Mol. wt. log AgBr 187.779 273 647 Cr0 3 100.00 000 000 AgCN 133.88 126 716 Cr0 4 116.00 064 458 AgCl 143.324 156319 Cu 2 143.14 155 761 Agl 234.78 370661 CuO 79.57 900 749 As"NO 169.88 230 142 Cu 2 S 159.21 201 970 A1 2 0, 3 102.2 009451 CuS 95.64 980 640 A1 2 (S0 4 ) 3 .18H 2 666.69 823 924 CuS0 4 159.64 203 142 AsA 197.90 296446 CuS0 4 -5H 2 249.72 397 453 AsO 229.90 361 539 FeC0 3 115.83 063 821 2 5 As0 3 122.95 089 729 FeCl 2 .4H 2 198.80 298416 As0 4 138.95 142 859 FeCL 162.19 210 024 As 2 S 3 246.11 391 130 FeO 71.83 856 306 As/ 6 310.25 491 712 Fe 2 0_ 159.66 203 196 BA 1 70.0 845 098 FeP0 4 150.86 178574 BaC0 3 197.36 295 259 FeS 87.90 943 939 BaCL 208.27 318627 FeS0 4 151.90 181 558 BaCl 2 -2H 2 244.30 387 923 FeS0 4 -7H 2 278.01 444060 BaCr0 4 253.36 403 738 HBO, 62.0 792 392 Ba(N0 3 ) 2 261.38 417273 HBr 80.917 908 040 BaO 153.36 185 712 HCH0 2 46.02 662947 Ba(OH) 2 8 H 2 315.50 498999 HC 2 H 3 2 60.03 778 368 BaS0 4 233.43 368 157 H,C,0 4 90.02 954 339 BaSiF 6 279.66 446630 H 2 C 2 4 -2H 2 126.05 100543 BjA 464.0 666518 H 2 C 4 H 4 6 150.05 176236 BLS 512.2 709 440 H 3 C 6 H 5 T .H 2 210.08 322 323 cd, 44.00 643 453 HC1 36.462 561 840 C. 7 88.00 944 483 HC10 4 100.462 002 002 3 60.00 778151 H s CrA 218.02 338 496 CaC0 8 100.07 000304 H 2 00 4 118.02 071 956 CaCl 2 110.98 045245 HF 20.0 301 030 CaCL.6H a O 219.07 340 583 HI 127.918 106932 CaO 56.07 748731 HNO 63.02 799478 CaS0 4 136.14 133 986 H 2 3 18.0156 255649 CaS0 4 2 H 2 172.17 235 958 H 34.0156 531 678 CdO 128.41 108599 H PO 98.05 991 448 CdS 144.48 159 808 H 2 Pt(Jl 6 409.7 612 466 CdS0 4 208.48 319064 H 2 S 34.09 532 627 CoO 74.96 874 830 H 2 S0 3 82.09 914290 CoS0 4 155.03 190416 H 2 S0 4 98.09 991 625 CoS0 4 7 H 2 281.14 448 923 Hg 2 Cl 2 472.13 674 062 Cr A 152.00 181 844 HgCl 2 271.52 433 802 TABLE III (CONTINUED) Mol.wt. log Mol.wt. log KA1(S0 4 ) 2 -12H 2 KA1SLO, KBr 474.5 279.1 119.000 676 236 445 760 075 547 NH 4 C1 (NH 4 ) 2 Fe(S0 4 ) 2 -6HO NH 4 Fe(S0 4 ) 2 .12H 2 53.50 392.14 482.19 728 354 593 441 683 218 KCN 65.10 813 581 NHOH 35.05 544 688 138.13 74.545 140 288 872 419 (NH 4 ) 3 P0 4 (Mo0 3 ) 12 (NH 4 ) 2 PtCl 6 1877.2 443.8 273511 647187 KC10 3 122.545 088 296 (NH 4 ) 2 S0 4 132.15 121067 KC10 4 138.545 141 591 NaAlSi 3 8 263.0 419 956 K Co(NO ) 452.29 655417 Na B 202.0 305 351 K 2 Cr0 4 194.18 288 205 Na 2 BX-10H 2 382.1 582 177 K 2 Cr 2 O. 294.18 468 613 NaBr 7 102.902 012 424 KCr(S0 4 ) 2 -12H 2 K 3 Fe(CN) 6 499.42 329.15 698466 517394 NaC 2 H 3 2 .3H 2 Na 2 C0 3 136.06 105.99 133 730 025 265 K 4 Fe(CN) 6 368.24 566131 Na 2 C0 3 -10H 2 286.14 456579 KI 166.001 220111 NaCl 58.447 766 762 KI0 3 214.001 330416 Na 2 O 2 7 2 H 2 298.02 474 245 KMn0 4 158.01 198 685 NaHCO 84.00 924 279 KNO 85.10 929 930 Na 9 HP0 4 .12H 2 358.24 554 174 KN0 3 101.10 004751 NaHSO 4 120.07 079 435 KNaC 4 H 4 6 -4H 2 282.18 450 526 NaNO 69.00 838 849 K 2 94.182 973 968 NaN0 3 85.00 929 419 KOH 56.099 748 955 3 61.986 792 294 K 2 PtCl 6 K 2 S0 4 485.9 174.25 686 547 241 173 Na 2 2 NaOH 77.986 40.00 892017 602060 MgC0 3 84.32 925 931 Na 2 S 2 -5H 2 248.20 394 802 MgCl 2 .6H 2 203.32 308 180 Na 2 S0 3 .7H 2 252.17 401 693 MgO 40.32 605 521 Na 2 S0 4 142.06 152472 Mg P 222.70 347 720 Na 2 S0 4 .10H 2 322.21 508 139 M g sd 4 7 120.39 080590 u 2 4 2 74.67 873 146 MgS0 4 -7H 2 246.50 391 817 NiS0 4 154.74 189 603 MnC0 3 114.92 060 396 NiS0 4 -7H 2 280.85 448 474 MnO 70.92 850 769 N0 3 62.01 792 462 Mn 2 3 157.84 198 217 PCL 137.39 137955 Mn 3 4 228.76 359 380 PBr 3 270.76 432 585 Mn0 2 86.92 939 120 P 28 110.06 041630 M n ^ 7 MnS 283.90 86.99 453 165 939 469 2 o ?K 142.06 95.03 152472 977 861 MnS0 4 150.99 178948 PbC0 3 267.07 426 625 MnS0 4 -4H 2 223.05 348 402 PbCl 2 277.98 444014 NH 17.03 231215 PbCr0 4 323.07 509 297 NH 18.04 256 237 Pb(N0 3 ) 2 331.09 519946 (NH 4 ) 2 C 2 4 .H 2 142.10 152 594 PbO 223.07 348441 TABLE III (CONTINUED) Mol.wt. log Mol.wt. log PbS 239.14 378652 SnO 135.0 130334 PbSO, 303.14 481 643 Sn0 2 151.0 178977 PtCl. 336.8 527372 SrCO 147.61 169 116 S0 2 64.07 806655 Sr(NO) 211.63 325 577 S0 3 80.07 903 470 SrO 103.613 015 414 S0 4 96.07 982 588 Sr(OH) 2 -8H 2 265.754 424 480 Si0 2 60.3 780317 SrS0 4 183.68 264 062 Si0 3 76.3 882 525 ZnCd 125.36 098 159 SiO. 92.3 965 202 ZnO 81.36 910411 SnCl 2 189.9 278 525 ZnS 97.43 988693 SnCl 2 -2H,0 225.9 353916 ZnS0 4 7 H 2 287.54 458 698 SnCl 4 260.8 416 308 10 TABLE IV SECOND TO FIFTH MULTIPLES OF THE MOLECULAR WEIGHTS OF SOME COMMON COMPOUNDS AND OF THE WEIGHTS OF A FEW RADICALS TOGETHER WITH THEIR LOGARITHMS 2 log 3 log 4 log 5 log AgBr 375.558 574677 563.337 750 768 751.116 875 707 938.895 972617 AgCl 286.648 457349 429.972 633 440 573.296 758379 716.620 855 289 Agl 469.56 671 691 704.34 847 782 939.12 922 721 1173.90 069631 A10 204.4 310481 306.6 486572 408.8 611511 511.0 708421 Ba(OH) 2 342.75 534977 514.13 711073 685.50 836007 856.88 932920 Ba(OH) 2 .8H 2 631.00 800029 946.50 976 121 1262.00 101059 1577.5 197 969 C0 2 88.00 944483 132.00 120574 176.00 245 513 220.00 342 423 CO 120.00 079181 180.00 255 273 240.00 380211 300.00 477121 CaO 112.14 049 761 168.21 225 852 224.28 350 791 280.35 447 701 Cr 304.00 482 874 456.00 658965 608.00 783904 760.00 880814 Cub 3 159.14 201 779 238.71 377871 318.28 502 809 397.85 599 719 FeO 143.64 157275 215.46 333 367 287.28 458305 359.10 555215 Fe 2 3 319.28 504172 478.92 680263 638.56 805 202 798.20 902112 HCHO 92.03 963 929 138.05 140036 184.06 264959 230.10 361917 HC H 120.06 079398 180.09 255 490 240.13 380446 300.15 477338 H C 180.03 255 345 270.05 431 444 360.06 556375 450.10 653 309 H 2 C 2 4 -2H 2 252.09 401556 378.14 577653 504.19 702 594 630.25 799513 H C H 300.09 477251 450.14 653348 600.19 778 289 750.25 875 206 H 3 C 6 H 5 7 -H 2 420.16 623415 630.23 799499 840.31 924 440 1050.2 021 293 HC1 72.924 862 870 109.385 038958 145.847 163 898 182.31 260810 HNO 126.04 100 508 189.05 276577 252.07 401 521 315.10 498 448 H 2 36.0312 556700 54.0468 732 828 72.0614 857 724 90.0780 954619 H 2 S0 4 196.17 292 633 294.26 468 731 392.34 593 663 490.45 690 595 K 2 188.364 274998 282.546 451089 376.728 576028 470.910 672938 KOH 112.198 049985 168.296 226074 224.395 351013 280.49 447925 MgO 80.64 906551 120.96 082 642 161.28 207 581 201.60 304491 NH 3 34.07 532372 51.10 708421 68.13 833 338 85.15 930 185 NH 4 36.08 557267 54.12 733 358 72.16 858297 92.30 965 207 NH 4 OH 70.1 845 718 105.15 021 809 140.20 146 748 175.25 243 658 N0 3 124.02 093 492 186.03 269583 248.04 394 522 310.05 491 432 Na 2 C0 8 211.97 326274 317.96 502372 423.94 627304 529.95 724 235 NaOH 80.002 903100 120.002 079 188 160.003 204 128 200.00 301 030 OH 34.0156 531 678 51.0234 707 769 68.0312 832 708 85.039 929618 p o 4 190.06 278 891 285.09 454982 380.12 579921 475.15 676831 -P 9 O, 284.12 453 502 426.18 629 593 568.24 754 532 710.30 851442 s6 2 5 128.14 107685 192.21 283 776 256.28 408715 320.35 505 625 S0 3 160.14 204 500 240.21 380 591 320.28 505 530 400.35 602 440 S0 4 192.14 283 618 288.21 459 709 384.28 584 648 480.35 681 558 Si0 2 120.6 081 347 180.9 257439 241.2 382377 301.5 479 287 Si0 3 152.6 183 555 228.9 359646 305.2 484585 381.5 581 495 SiO 184.6 266232 276.9 442 323 369.2 567 262 461.5 ' 664172 TABLE V 11 REDUCTION OF COMPOUNDS FOUND TO CONSTITUENTS SOUGHT BY MULTIPLICATION Sought Found Factor log Ag AgBr .57445 759 254 AgCl .75 263 876 582 Al Al .53 033 724 548 As As,o' .75 745 879 356 AsX .65 202 814 263 As A .60908 784 672 AsS. .48316 684 090 MgNH.AsO..H,0 Mg 2 As 2 7 .37601 .48 270 575 200 683 684 As 2 3 As 2 6 .86081 934 907 As 2 S 3 .80411 905316 -A-S j^r .63 787 804734 MgNH.AsO -H 2 .49 641 695 844 As 2 5 Mg 2 As 2 7 As 2 S 3 .63 728 .93 413 804 328 970 409 As0 3 As 2 S 3 .99914 999629 AsO AsS 1.12917 052 759 Ba BaO 8 .89 568 952 148 BaC0 3 BaCr0 4 .69 599 .54213 842 601 734 103 BaSO. BaSiF 6 .58 844 .49117 769 703 691 230 BaO BaC0 3 .77 706 890453 BaSO, .65 698 817555 Bi WA .89 655 952 575 Bi 2 S 3 .81217 909645 B .31 428 497 325 KBF .08 723 940 666 Br AgBr .42 555 628 949 C CaCO. .27 273 .43 969 435 728 643 149 CaO .78473 894 722 MgO 1.09 127 037 932 C 3 Ca CO CaCO 3 1.36363 .40 042 134698 602515 CaO .71 464 854088 CaS0 4 .29 433 468 833 CaC0 3 CaO 1.78473 251 573 CaSO. .73 505 866318 CaO C0 2 1.27432 105 278 12 TABLE V (CONTINUED) Sought Found Factor log CaO CaC0 3 .56031 748 427 CaSO, .41 186 614 745 Cd CdO .87 540 942 206 CdS .77 803 890 997 CdSO, .53919 731 741 CdO CdS .88 877 948 791 CdS0 4 .61 593 789 535 Cl Ag .32 867 516764 Cl AgCl .24 737 393 346 Co CoO .78 655 895 727 CoS0 4 .38031 580 141 2CoS0 4 -3K 2 S0 4 .14159 151041 2CoK (NO.) -3H 2 .12300 089 922 CoO Co 1.27137 104273 CoS0 4 .48 352 684 414 2CoS0 4 -3K 2 S0 4 2CoS0 4 K 3 (N0 2 ) 6 -3H 2 .18002 .15 638 255 314 194 195 Cr BaCr0 4 .20 524 312 265 Cr () .68421 835 189 PbCr0 4 .16096 206 706 Cr BaCr0 4 .29 997 477076 PbCr0 4 .23 524 371517 Cr0 3 BaCrO, .39 470 596 262 Cr 2 3 1.31 579 119186 PbCi0 4 .30 953 490 703 Cr0 4 BaCrO, .45 784 660 710 Cr 1.52631 183 644 PbCrO, .35 905 555 161 Cu CuO .79 892 902 503 CuS .79857 902312 CuO Cu 1.25 169 097 497 Cu 2 S .99 956 999 809 F CaF 2 .48 662 687 189 SiF 4 .72 866 862 530 Fe FeA" .69 932 844 678 FeS 3 .63511 802 851 FeO Fe 1.28663 109 455 FeA .89 977 954 133 Fe Fe 1.42995 155 322 H 2 H 2 .11 188 048 756 HBr AgBr .43 092 634 393 HC1 AgCl .25 440 405 521 TABLE V (CONTINUED) 13 Sought Found Factor log HI Agl .54 484 736 271 HKO NH 4 C1 1.17794 071 124 (NH 4 ) 2 PtCl 6 .28 400 453 321 Pt .64 635 810 473 H 2 S0 4 BaS0 4 Hg. 2 Cl 2 HgS .42 021 .84 981 .86217 623 468 929 321 935 594 Hg 2 Hg 1.03 988 016 982 HgO Hg 1.07 976 033 326 I Agl .54 055 732 835 PdI 2 .70 408 847621 K KC1 .52 439 719658 K 2 PtCl 6 .16090 206 560 K Pt .40 093 603 072 K 2 SO .44868 651934 KC1 K PtCl .30 683 486 902 Pt .76457 883 414 K 2 KC1 .63 171 800519 KNO_ .46579 668187 K 2 PtCl 6 .19383 287 421 Pt .48 298 683 933 K 2 S0 4 .54 050 732 795 T7" Qf~\ J\-JO\J. BaS0 4 .74648 873 016 Li Li 2 .46 449 666975 Li CO .18 784 273 800 Li 3 P0 4 .17 967 254 483 Li 2 S0 4 .12622 101 131 Li 2 Li 2 C0 3 .40 441 606 825 Li 3 P0 4 .38 682 587 506 Li 2 S0 4 .27 174 434 156 Mg MgO .60317 780 443 MgC0 3 Mg 2 P 2 7 MgO .21 839 2.09 127 339 235 320410 Mg 2 P 2 7 .75 718 879 199 MgO Mg 2 P 2 7 .36 207 558 792 Mn MnO .77439 888 962 Mn 2 8 .69 590 842 544 Mn 3 4 .72 023 857472 Mn 2 P 2 7 .38 690 587 596 MnS .63 134 800 262 MnS0 4 .36373 560 783 MnO MnS .81 527 911 300 14 TABLE V (CONTINUED) Sought Found Factor log MnO MnS0 4 .46 970 671 821 N NH .82 266 915 223 (NH 4 ) 2 PtCl 6 .06 314 800 281 Pt .14 369 157433 NH N 1.21556 084 777 NH 4 C1 (NH 4 ) 2 PtCl 6 .31 832 .07 675 502 861 885 058 Pt .17466 242 210 NH 4 NH 4 C1 .33 720 527 883 3 (NH 4 ) 2 PtCl 6 NHC1 .08 130 1.15 907 910080 064 108 (NH 4 ) 2 PtCL .27 945 446 305 Pt .63600 803 457 Na _IM ct~ V-J .74 187 870331 NaCl .39340 594 833 NaN0 3 .27051 432 176 Na 2 S0 4 .32371 510153 NaCl Na 2 S0 4 .82 285 915 320 Na 2 NaCl .53 028 724 502 NaNO .36 462 561 845 Na SO .43 634 639 822 Na 2 S0 4 BaS0 4 .60 858 784 315 Ni NiO .78572 895 270 NiO Ni 1.27271 104 730 P P 2 5 .43 686 640 340 Mg P O .27 867 445 092 (NH 4 )^0 4 .12Mo0 3 .01 653 218271 P 2 g Ag 3 P0 4 .16 967 229 601 (NHlP0 4 -12MoO a (U0 2 ) 2 P 2 7 .63 790 .03 784 .19872 804752 577931 298251 P0 4 Mg 2 P 2 7 .85 344 931 171 Pb (NH 4 ) 2 P0 4 -12Mo0 8 PbCr0 4 .05 062 .64094 704 350 806 820 PbO .92 827 967 676 Pb0 2 .86 615 937 592 PbS .86 589 937 465 PbO PbSO. PbCr0 4 .68 309 .69047 834474 839 144 PbS .93 280 969 789 PbS0 4 .73 586 866798 PbS PbS0 4 .78 888 897009 TABLE V (CONTINUED) 15 Sought Found Factor log Pt NaCl 1.66818 222 243 s BaSO. .13 738 137 942 As 2 S .39 092 592 090 S0 3 - Ba0 4 .34 302 535 313 so BaSO. .41 156 614431 Sb Sb 2 8 .83 317 920 734 Sb 2 4 .78 928 897 230 Sb 2 S 8 .71360 853 455 SbS .59919 777 568 Sb 2 8 Sb 2 4 .94 732 976 496 Sb 2 S 8 .85 649 932 721 sb!s! .71 917 856 834 Si si6 2 5 .46932 671 469 Si0 8 Si0 2 1.26534 102 208 SiO Si0 2 1.53068 184 885 Si 2 7 Si0 2 1.39800 145 510 Sn Sn0 2 .78 808 896570 SnO SnO, .89 404 951 357 Sr SrCO, .59 354 773 453 SrO .84 558 927 155 SrS0 4 .47 699 678 507 SrO SrC0 8 .70 194 846 298 SrS0 4 .56 409 751352 Ti Ti0 2 .60 050 778512 U U0 2 .88 166 945 299 W w 3 o 3 8 .84 820 .79310 928 497 899330 Zn ZnO .80 334 904901 ZnS .67 084 826619 ZnO ZnS .83 506 921 718 ZnS ZnO 1.19752 078 282 16 TABLE VI REDUCTION OF BAROMETRIC READINGS TO (For temperatures above zero the corrections are negative and for temperatures below zero positive.) Temper- ature Glass Scale Brass Scale 740 mm. 750 mm. 760 mm. 770 mm. 780 mm. 740 mm. 750 mm. 760 mm. 770 mm. 780 mm. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1 13 13 13 13 14 12 12 12 13 13 2 26 26 26 27 27 24 25 25 25 25 3 38 39 39 40 41 36 37 37 38 38 4 51 52 53 53 54 48 49 50 50 51 5 0.64 0.65 0.66 0.67 0.68 0.60 0.61 0.62 0.63 0.64 6 77 78 79 80 81 72 73 74 75 76 7 0.90 0.91 0.92 0.93 0.95 85 86 0.87 0.88 0.89 8 1.02 1.04 1.05 1.07 1.08 0.97 0.98 1.99 1.01 1.02 9 15 17 18 20 21 1.09 1.10 12 13 15 10 1.28 1.30 1.31 1.33 1.35 1.21 1.22 1.24 1.26 1.27 11 41 43 45 46 48 33 35 36 38 40 12 53 56 58 60 62 45 47 49 51 53 13 66 69 71 73 75 57 59 61 63 65 14 79 81 84 1.86 1.89 69 71 73 76 78 15 1.92 1.94 1.97 2.00 2.02 1.81 1.83 1.86 1.88 1.91 16 2.05 2.07 2.10 13 16 1.93 1.96 1.98 2.01 2.03 17 17 20 23 26 29 2.05 2.08 2.10 13 16 18 30 33 36 39 43 17 20 23 26 29 19 43 46 49 53 56 29 32 35 38 41 20 2.56 2.59 2.62 2.66 2.69 2.41 2.44 2.47 2.51 2.54 21 68 72 76 79 83 53 56 60 63 67 22 81 85 2.89 2.92 2.96 65 69 72 76 79 23 2.94 2.98 3.02 3.06 3.10 77 81 84 2.88 2.92 24 3.06 3.11 15 19 23 2.89 2.93 2.97 3.01 3.05 25 3.19 3.23 3.28 3.32 3.36 3.01 3.05 3.09 3.13 3.17 26 32 36 41 45 50 13 17 21 26 30 27 45 49 54 59 63 25 29 34 38 42 28 57 62 67 72 77 37 41 46 51 55 29 70 75 80 85 3.90 49 54 58 63 68 30 3.83 3.88 3.93 3.98 4.03 3.61 3.66 3.71 3.75 3.80 31 3.95 4.01 4.06 4.11 17 73 78 83 3.88 3.93 32 4.08 14 19 25 30 85 3.90 3.95 4.00 4.05 33 21 26 32 38 43 3.97 4.02 4.07 13 18 34 33 39 45 51 57 4.09 14 20 25 31 35 4.46 4.52 4.58 4.65 4.71 4.21 4.26 4.32 4.38 4.43 TABLE VII 17 GEOGRAPHICAL LATITUDE, ELEVATION, AND GRAVITY (REFERRED TO 45 AND SEA LEVEL) OF SOME IMPORTANT CITIES Latitude Height above sea level m. Gravity log Baltimore, Met. 39 18' 23. 0.9 994 705 999 770 Berlin, New Obs. 52 30' 16.7" 37.00 1.0006736 000292 Bonn, Obs. 50 43' 45.0" 61.92 1.0005054 000219 Boston, Met. 42 21' 38. 0.9 997 438 999 889 Brussels, Old Obs. 50 51' 10.7" 56. 1.0005179 000225 Cambridge, Eng., Obs. 52 12' 5 1.6" 28. 1.0006504 000282 Cambridge, Mass., Harvard Obs. 42 22' 47.6" 24. 0.9 997 509 999892 Cincinnati, Obs. 39 8' 19.5" 263. 0.9 993 803 999731 Dublin, Dunsink Obs. 53 23' 13.1" 86. 1.0007365 000320 Freiberg 47 59' 40" 270.6 1.0001907 000083 Gottingen, Obs. 51 31' 48.2" 159.2 1.0005478 000 238 Greenwich, Obs. 51 28' 38.1" 47. 1.0005783 000251 Heidelberg, Obs. 49 23' 54.9" 113.6 1.0003688 000 160 Kopenhagen, Obs. 55 41' 12.9" 14. 1.0009602 000317 London, Camden Sq., Met. 51 32' 30" 34. 1.0005881 000 255 Madrid, Obs. 45 27' 59.2" 120. 1.0000053 000 002 Montreal, McGill Col. Obs. 45 30' 17.0" 57. 1.0000287 000012 New Haven, Yale Obs. 41 19' 22.3" 32. 0.9 996 521 999 848 New Orleans, Met. 29 58' 16. 0.9 986 721 999423 New York, Rutherford Obs. 40 43' 48.5" 96. 0.9 995 774 999817 Paris, Nat. Obs. 48 50' 11.2" 59. 1.0 003 345 000145 Philadelphia, Obs. 39 57' 7.5" 36. 0.9 995 254 999 794 Prag, Obs. 50 5' 15.8" 197. 1.0004053 000 176 Quebec, Obs. 46 48' 20.8" 70. 1.0001446 000063 St. Louis, Obs. 3838 / 3.6" 171. 0.9993611 999 722 San Francisco, Davidson Obs. 3 7 4 r 28.0" 47.2 0.9 993 272 999 708 Strassburg, New Obs. 48 35' 0.3" 144.66 1.0002845 000124 Washington, Georgetown Hts. Obs. 38 55' 14. 7" 285. 0.9993537 999 719 Zurich, Obs. d. Polyt. 47 22' 40" 468.24 1.0000718 000031 18 TABLE VIII REDUCTION OF BAROMETRIC READINGS TO NORMAL GRAVITY (From Landolt-Bornstein) A. REDUCTION TO 45 LATITUDE (From to 45 the correction is always negative, and from 45 to 90 positive.) Barometric Readings in mm., corrected for Temperature Latitude 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 Latitude mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. mm. 1.66 1.68 1.71 1.74 1.76 1.79 1.81 1.84 1.86 1.89 1.92 1.94 1.97 1.99 2.02 90 5 63 66 68 71 73 76 79 81 84 86 89 91 94 96 1.99 85 10 56 58 61 63 65 68 70 73 75 78 80 83 85 87 90 80 15 44 46 48 50 53 55 57 59 61 64 66 68 70 73 75 75 20 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 70 25 1.07 1.08 1.10 1.12 1.13 1.15 1.17 1.18 1.20 1.22 1.23 1.25 1.27 28 30 65 30 0.83 0.84 0.85 0.87 0.88 0.89 0.91 0.92 0.93 0.95 0.96 0.97 0.98 1.00 1.01 60 35 57 58 58 59 60 61 62 63 64 65 66 66 67 0.68 0.69 55 40 29 29 30 30 31 31 31 32 32 33 33 34 34 35 35 50 45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 45 B. REDUCTION TO SEA LEVEL (These corrections are all negative.) Height above sea level 772. Barometric Readings in mm., corrected for Temperature Height above sea level 772. 620 772772. 640 mm. 660 mm. 680 mm. 700 mm. 720 mm. 740 mm. 760 mm. 780 mm. 100 0.01 0.01 0.01 0.01 0.02 100 200 0.03 03 03 03 03 0.03 200 300 04 04 04 04 04 300 400 0.05 05 05 06 06 06 400 500 06 07 07 07 07 0.07 500 600 08 08 08 08 09 600 700 0.09 09 09 10 10 10 700 800 10 10 11 11 11 0.12 800 900 0.11 0.12 0.12 0.12 0.13 900 1000 0.12 0.13 0.13 0.13 0.14 0.14 1000 1100 13 14 14 15 15 0.16 1100 1200 15 15 16 16 16 1200 1300 16 16 17 17 18 1300 1400 17 18 18 19 0.19 1400 1500 18 19 19 20 1500 1600 19 20 21 21 1600 1700 21 21 22 0.23 1700 1800 22 23 23 1800 1900 0.23 0.24 0.25 1900 2000 0.24 0.25 2000 TABLE IX 19 CAPILLAKY DEPRESSION OF MERCURY (Interpolated by F. Kohlrausch from Mendelejeff and Gutkowsky.) Height of Meniscus in mm. Diameter of tube 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 mm. mm. mm. mm. mm. mm. mm. mm. mm. 4 0.83 1.22 1.54 1.98 2.37 5 47 0.65 0.86 1.19 1.45 1.80 6 27 41 56 0.78 0.98 1.21 1.43 7 18 28 40 53 67 0.82 0.97 1.13 8 20 29 38 46 56 65 0.77 9 15 21 28 33 40 46 52 10 15 20 25 29 33 37 11 10 14 18 21 24 27 12 07 10 13 15 18 19 13 04 07 10 12 13 14 20 TABLE X TENSION OF AQUEOUS VAPOR OVER WATER EXPRESSED IN TERMS OF NORMAL MERCURY UNITS (Taken from Landolt-Bornstein. Observations by Regnault.) Degrees Hydrogen Scale. Tenth Degrees .0 772/77. .1 777771. .2 777777. .3 771772. .4 777777. .5 772772. .6 777772. .7 772777. .8 mm. .9 772772. 4.579 4.612 4.646 4.679 4.713 4.747 4.782 4.816 4.851 4.886 1 4.921 4.957 4.992 5.028 5.064 5.101 5.137 5.174 5.211 5.248 2 5.286 5.324 5362 5.400 5.438 5.477 5.516 5.555 5.595 5.635 3 5.675 5.715 5.755 5.796 5.837 5.878 5.920 5.961 6.003 6.046 4 6.088 6.131 6.174 6.217 6.261 6.305 6.349 6.393 6.438 6.483 5 6.528 6.574 6.620 6.666 6.712 6.759 6.806 6.853 6.901 6.949 6 6.997 7.045 7.094 7.143 7.192 7.242 7.292 7.342 7.392 7.443 7 7.494 7.546 7.598 7.650 7.702 7.755 7.808 7.861 7.914 7.968 8 8.023 8.077 8.132 8.187 8.243 8.299 8.355 8.412 8.469 8.526 9 8.584 8.642 8.700 8.759 8.818 8.877 8.937 8.997 9.057 9.118 10 9.179 9.240 9.302 9.364 9.427 9.490 9.553 9.616 9.680 9.745 11 9.810 9.875 9.940 10.006 10.072 10.139 10.206 10.274 10.342 10.410 12 10.479 10.548 10.617 10.687 10.757 10.828 10.899 10.970 11.042 11.114 13 11.187 11.260 11.333 11.407 11.481 11.556 11.631 11.706 11.782 11.859 14 11.936 12.013 12.091 12.169 12.247 12.326 12.406 12.486 12.566 12.647 15 12.728 12.810 12.892 12.974 13.057 13.141 13.225 13.309 13.394 13.480 16 13.565 13.651 13.738 13.825 13.913 14.001 14.090 14.179 14.269 14.359 17 14.450 14.541 14.632 14.724 14.817 14.910 15.003 15.097 15.192 15.287 18 15.383 15.479 15.575 15.672 15.770 15.858 15.967 16.066 16.166 16.266 19 16.367 16.469 16.571 16.673 16.776 16.8SO 16.984 17.088 17.193 17.299 20 17.406 17.513 17.620 17.728 17.837 17.947 18.057 18.167 18.278 18.390 21 18.503 18.616 18.729 18.844 18.959 19.074 19.190 19.307 19.424 19.542 22 19.661 19.780 19.900 20.021 20.142 20.264 20.386 20.510 20.634 20.758 23 20.883 21.010 21.137 21.264 21.393 21.522 21.652 21.782 21.913 22.045 24 22.178 22.311 22.446 22.581 22.716 22.853 22.990 23.128 23.266 23.406 25 23.546 23.686 23.828 23.970 24.113 24.257 24.401 24.547 24.693 24.839 26 24.987 25.135 25.284 25.434 25.584 25.736 25.888 26.041 26.195 26.349 27 26.505 26.661 26.818 26.976 27.134 27.294 27.454 27.615 27.777 27.939 28 28.103 28.267 28.432 28.599 28.766 28.933 29.102 29.271 29.442 29.613 29 29.785 29.958 30.132 30.307 30.482 30.659 30.836 31.015 31.194 31.374 30 31.555 31.737 31.919 32.103 32.288 32.473 32.660 32.847 33.036 33.225 31 33.416 33.607 33.799 33.992 34.187 34.382 34.578 34.775 34.973 35.172 32 35.372 35.573 35.775 35.978 36.182 36.387 36.593 36.800 37.008 37.217 33 37.427 37.638 37.851 38.064 38.278 38.493 38.710 38.927 39.146 39.365 34 39.586 39.807 40.030 40.254 40.479 40.705 40.933 41.161 41.390 41.621 35 41.853 42.085 42.319 42.554 42.791 43.028 43.266 43.506 43.747 43.989 TABLE XI 21 REDUCTION OF WATER PRESSURE TO MERCURY PRESSURE (Calculated from the following : temperature of the water 4, of the mercury ; density of the water 1, of the mercury 13.59545) (Thiesen and Schul. Z. S. f . Instrk. 18, 138) Water Mercury Water Mercury Water Mercury Water Mercury Water Mercury 10 0.74 50 3.68 90 6.62 130 9.56 170 12.50 11 81 51 75 91 69 131 64 171 58 12 88 52 82 92 77 132 71 172 65 13 0.96 53 90 93 84 133 78 173 72 14 1.03 54 3.97 94 91 134 86 174 80 15 10 55 4.05 95 6.99 135 9.93 175 87 16 18 56 12 96 7.06 136 10.00 176 12.95 17 25 57 19 97 13 137 08 177 13.02 18 32 58 27 98 21 138 15 178 09 19 40 59 34 99 28 139 22 179 17 20 1.47 60 4.41 100 7.36 140 10.30 180 13.24 21 54 61 49 101 43 141 37 181 31 22 62 62 56 102 50 142 44 182 38 23 69 63 63 103 58 143 52 183 46 24 77 64 71 104 65 144 59 184 53 25 84 65 78 105 72 145 67 185 61 26 91 66 85 106 80 146 74 186 68 27 1.99 67 4.93 107 87 147 81 187 75 28 2.06 68 5.00 108 7.94 148 89 188 83 29 13 69 08 109 8.02 149 10.96 189 90 30 2.21 70 5.15 110 8.09 150 11.03 190 13.98 31 28 71 22 111 16 151 11 191 14.05 32 35 72 30 112 24 152 18 192 12 33 43 73 37 113 31 153 25 193 20 34 50 74 44 114 39 154 33 194 27 35 57 75 52 115 46 155 40 195 34 36 65 76 59 116 53 156 47 196 42 37 72 77 66 117 61 157 55 197 49 38 79 78 74 118 68 158 62 198 56 39 87 79 81 119 75 159 69 199 64 40 2.94 80 5.88 120 8.83 160 11.77 200 14.71 41 3.02 81 5.96 121 90 161 84 300 22.07 42 09 82 6.03 122 8.97 162 92 400 29.42 43 16 83 10 123 9.05 163 11.99 500 36.78 44 24 84 18 124 12 164 12.06 600 44.13 45 31 85 25 125 19 165 14 700 51.49 46 38 86 33 126 27 166 21 800 58.84 47 46 87 40 127 34 167 28 900 66.20 48 53 88 47 128 41 168 36 1000 73.55 49 60 89 55 129 49 169 43 TABLE XII REDUCTION OF THE VOLUME OF GASES TO NORMAL PRESSURE (This table contains the values of where h = 500 to 839 mm.) t \)\) (Landolt-Bb'rnstein) h mm. h 760 log 6 760 h nun. h 760 10g 4 h mm. h 760 log 6 760 500 0.65 789 818153 540 0.71 053 851 582 580 0.76316 882 616 501 0.65 921 9024 541 184 2382 581 447 3360 502 0.66 053 819 893 542 316 3187 582 579 4110 503 184 820 753 543 447 3984 583 711 4 858 504 316 1618 544 579 4786 584 842 5599 505 447 2475 545 711 5586 585 0.76974 6344 506 579 3337 546 842 6378 586 0.77 105 7083 507 711 4198 547 0.71 974 7176 587 237 7825 508 842 5049 548 0.72 105 7965 588 368 8561 509 0.66974 5906 549 237 8760 589 500 889 302 510 0.67 105 826 755 550 0.72 368 859 547 590 0.77 632 890041 511 237 7608 551 500 860 338 591 763 0773 512 368 8454 552 632 1128 592 0.77 895 1510 513 500 829304 553 763 1911 593 0.78026 1682 514 632 % 830 152 554 0.72 895 2698 594 158 2973 515 763 0993 555 0.73 026 3478 595 289 3701 516 0.67 895 1838 556 158 4262 596 421 4432 517 0.68 026 2675 557 289 5039 597 553 5163 518 158 3517 558 421 5820 598 684 5886 519 289 4351 559 553 6600 599 816 6614 520 0.68421 835 189 560 0.73 684 867373 600 0.78 947 897 336 521 553 6027 561 816 8151 601 0.79 079 8061 522 684 6856 562 0.73 947 8921 602 211 8786 523 816 7689 563 0.74 079 869 695 603 342 899 503 524 0.68 947 8515 564 211 870 468 604 474 900 225 525 0.69 079 839346 565 342 1234 605 605 0940 526 211 840 175 566 474 2005 606 737 1660 527 342 0996 567 605 2768 607 0.79868 2373 528 474 1822 568 737 3536 608 0.80000 3090 529 605 2640 569 0.74 868 4296 609 132 3806 530 0.69 737 843 463 570 0.75 000 875 061 610 0.80 263 904515 531 0.69 868 4278 571 132 5825 611 395 5229 532 0.70 000 5098 572 263 6582 612 526 5936 533 132 5916 573 395 7343 613 658 6647 534 263 6727 574 526 8097 614 789 7352 535 395 7542 575 658 8855 615 0.80 921 8061 536 526 8349 576 789 879 606 616 0.81 053 8769 537 658 9161 577 0.75 921 880 362 617 184 909470 538 789 849 966 578 0.76 053 1 116 618 316 910 176 539 921 850 775 579 184 1864 619 447 0875 TABLE XII (CONTINUED) 23 h mm. h 760 log 6 760 h mm. h 760 iogA 6 760 h mm. h 760 icgA 6 760 620 0.81 579 911 578 660 0.86 842 938 730 700 0.92 105 964 283 621 711 2281 661 0.86 974 939 389 701 237 4905 622 842 2976 662 0.87 105 940043 702 368 5522 623 0.81 974 3676 663 237 0701 703 500 6142 624 0.82 105 4370 664 368 1352 704 632 6761 625 237 5067 665 500 2008 705 763 7375 626 368 5759 666 632 2663 706 0.92 895 7992 627 500 6454 667 763 3312 707 0.93 026 8604 628 632 7148 668 0.87 895 3964 708 158 9220 629 763 7836 669 0.88026 4611 709 289 969 830 630 0.82 895 918528 670 O.SS 158 945 262 710 0.93 421 970 445 631 0.83 026 9214 671 289 5907 711 553 1058 632 158 919 904 672 421 6555 712 684 1665 633 289 920 588 673 553 7203 713 816 2277 634 421 1275 674 684 7845 714 0.93 947 2883 635 553 1962 675 816 8491 715 0.94 079 3493 636 684 2642 676 0.88 947 9131 716 211 4102 637 816 3327 677 0.89 079 949 775 717 342 4705 638 0.83 947 4005 678 211 950418 718 474 5312 639 0.84079 4688 679 342 1056 719 605 5914 640 0.84211 925 369 680 0.89 474 951 697 720 0.94 737 976 520 641 342 6044 681 605 2332 721 0.94 868 7120 642 474 6723 682 737 2972 722 0.95 000 7724 643 605 7396 683 0.89 868 3605 723 132 8327 644 737 8073 684 0.90000 4243 724 263 8924 645 0.84 868 8744 685 132 4879 725 394 979 521 646 0.85 000 929 419 686 263 5510 726 526 980 122 647 132 930 093 687 395 6144 727 658 0721 648 263 0761 688 526 6773 728 789 1316 649 395 1432 689 658 7406 729 0.95 921 1914 650 0.85 526 932 098 690 0.90 789 958 033 730 0.96 053 982511 651 658 2768 691 0.90921 8664 731 184 3103 652 790 3437 692 0.91 053 9294 732 316 3698 653 0.85 921 4099 693 184 959919 733 447 4289 654 0.86053 4766 694 316 960547 734 579 4883 655 184 5427 695 447 1 170 735 710 5471 656 316 6091 696 579 1796 '736 842 6064 657 447 6750 697 711 2421 737 0.96 974 6655 658 579 7413 698 842 3041 738 0.97 105 7242 659 711 8074 699 974 3665 739 237 7832 24 TABLE XII (CONTINUED) h mm. h 760 log 760 h mm. h 760 log 760 h mm. h 760 10g 4 740 0.97 368 988 416 780 1.02 632 Oil 283 820 1.07 895 033 001 741 500 9005 781 763 1837 821 1.08026 3529 742 632 989 592 782 1.02 895 2394 822 158 4059 743 763 990 175 783 1.03026 2947 823 289 4584 744 0.97 895 0761 784 158 3504 824 421 5 113 745 0.98 026 1341 785 289 4054 825 553 5642 746 158 1926 786 421 4609 826 684 6166 747 289 2505 787 553 5163 827 816 6693 748 421 3088 788 684 5712 828 1.08 947 7215 749 553 3670 789 816 6264 829 1.09 079 7741 750 0.98 684 994 247 790 1.03947 016812 830 1.09211 038 267 751 816 4827 791 1.04079 7363 831 342 8787 752 0.98 947 5403 792 211 7914 832 471 9299 753 0.99079 5982 793 342 8459 833 605 039 831 754 211 6560 794 474 9008 834 737 040 353 755 342 7133 795 605 019552 835 1.09 868 0871 756 474 7710 796 737 020 100 836 1.10000 1393 757 605 8281 797 1.04868 0643 837 132 1913 758 737 8856 798 1.05 000 1 189 838 263 2430 759 0.99 868 999 426 799 132 1 735 839 395 2949 760 1.00000 000000 800 1.05 263 022 276 761 1.00 132 0573 801 395 2820 762 263 1 141 802 526 3359 763 392 1699 803 658 3902 764 526 2278 804 789 4441 765 658 2848 805 1.05921 4982 766 789 3413 806 1.06053 5523 767 1.00 921 3982 807 184 6059 768 1.01 053 4549 808 316 6598 769 184 5112 809 447 7134 770 1.01316 005 678 810 1.06 579 027 672 771 447 6239 811 711 8209 772 579 6804 812 842 8742 773 710 7364 813 1.06974 9278 774 842 7927 814 1.07 105 029 809 775 1.01 974 8489 815 237 030 345 776 1.02 105 9047 816 368 0875 777 237 009 608 817 500 1408 778 368 010 164 818 632 1941 779 500 0724 819 763 2470 TABLE XIII 25 REDUCTION OF THE VOLUME OF GASES TO 0C. This table contains the logarithms of the values of 1 + 0.003670 1 where t to 149. t log t log t log t log 0.0 000000 4.0 993671 8.0 987433 12.0 981 284 0.1 999 839 4.1 3513 8.1 7277 12.1 1130 0.2 9683 4.2 3359 8.2 7 125 12.2 0980 0.3 9523 4.3 3200 8.3 6969 12.3 0826 0.4 9 362 4.4 3042 8.4 6813 12.4 0672 0.5 9202 4.5 2884 8.5 6657 12.5 0518 0.6 9 045 4.6 2730 8.6 6505 12.6 0368 0.7 8885 4.7 2572 8.7 6350 12.7 0215 0.8 8725 4.8 2414 8.8 6194 12.8 980062 0.9 8569 4.9 2260 8.9 6043 12.9 979 912 1.0 998 409 5.0 992 103 9.0 985 888 13.0 979 759 1.1 8249 5.1 1945 9.1 5732 13.1 9606 1.2 8093 5.2 1 792 9.2 5581 13.2 9457 1.3 7934 5.3 1634 9.3 5425 13.3 9304 1.4 7774 5.4 1477 9.4 5270 13.4 9150 1.5 7618 5.5 1323 9.5 5 119 13.5 9002 1.6 7458 5.6 1166 9.6 4963 13.6 8848 1.7 7304 5.7 1008 9.7 4808 13.7 8695 1.8 7137 5.8 0850 9.8 4 653 13.8 8542 1.9 6984 5.9 0697 9.9 4502 13.9 8393 2.0 996824 6.0 990540 10.0 984 347 14.0 978 240 2.1 6664 6.1 0383 10.1 4 192 14.1 8087 2.2 6509 6.2 0231 10.2 4041 14.2 7938 2.3 6350 6.3 990073 10.3 3887 14.3 7786 2.4 6191 6.4 989 916 10.4 3732 14.4 7634 2.5 6032 6.5 9759 10.5 3577 14.5 7481 2.6 5877 6.6 9607 10.6 3426 14.6 7333 2.7 5718 6.7 9450 10.7 3271 14.7 7180 2.8 5559 6.8 9293 10.8 3117 14.8 7028 2.9 5404 6.9 9141 10.9 2967 14.9 6880 3.0 995 244 7.0 988983 11.0 982 813 15.0 976 727 3.1 5086 7.1 8828 11.1 2658 15.1 6575 3.2 4931 7.2 8675 11.2 2507 15.2 6427 3.3 4772 7.3 8519 11.3 2353 15.3 6274 3.4 4614 7.4 8362 11.4 2199 15.4 6122 3.5 4459 7.5 8210 11.5 2049 15.5 5974 3.6 4301 7.6 8054 11.6 1895 15.6 5822 3.7 4142 7.7 7897 11.7 1 741 15.7 5665 3.8 3984 7.8 7741 11.8 1587 15.8 5517 3.9 3829 7.9 7588 11.9 1437 15.9 5370 2(3 TABLE XIII (CONTINUED) t log t log t log t log 16.0 975 229 20.0 969 238 24.0 963 339 28.0 957519 16.1 5067 20.1 9089 24.1 3192 28.1 7373 16.2 4919 20.2 8943 24.2 3048 28.2 7236 16.3 4768 20.3 8794 24.3 2900 28.3 7095 16.4 4616 20.4 8644 24.4 2753 28.4 6941 16.5 4465 20.5 8495 24.5 2606 28.5 6795 16.6 4318 20.6 8350 24.6 2462 28.6 6654 16.7 4166 20.7 8200 24.7 2315 28.7 6508 16.8 4015 20.8 8051 24.8 2167 288 6363 16.9 3867 20.9 7905 24.9 2024 28.9 6221 17.0 973 717 21.0 967 756 25.0 961 876 29.0 956 076 17.1 3565 21.1 7606 25.1 1 729 29.1 5931 17.2 3418 21.2 7461 25.2 1586 29.2 5789 17.3 3267 21.3 7313 25.3 1440 29.3 5644 17.4 3116 21.4 7164 25.4 1293 29.4 5499 17.5 2968 21.5 7019 25.5 1 150 29.5 5358 17.6 2817 21.6 6870 25.6 1003 29.6 5213 17.7 2666 21.7 6721 25.7 0856 29.7 5068 17.8 2516 21.8 6572 25.8 0709 29.8 4923 17.9 2369 21.9 6427 25.9 0566 29.9 4783 18.0 972 219 22.0 966 279 26.0 960419 30.0 954 638 18.1 2068 22.1 6130 26.1 0272 30.1 4493 18.2 1922 22.2 5986 26.2 960 130 30.2 4353 18.3 1771 22.3 5837 26.3 959 983 30.3 4208 18.4 1620 22.4 5689 26.4 9837 ' 30.4 4063 18.5 1470 22.5 5541 26.5 9690 30.5 3918 18.6 1323 22.6 5396 26.6 9548 30.6 3778 18.7 1173 22.7 5248 26.7 9402 30.7 3634 18.8 1022 22.8 5099 26.8 9255 30.8 3489 18.9 0876 22.9 4955 26.9 9113 30.9 3349 19.0 970 726 23.0 964 807 27.0 958 966 31.0 953 205 19.1 0575 23.1 4658 27.1 8820 31.1 3060 19.2 0430 23.2 4514 27.2 8678 31.2 2920 19.3 0280 23.3 4366 27.3 8532 31.3 2776 19.4 970 130 23.4 4218 27.4 8387 31.4 2632 19.5 969 981 23.5 4074 27.5 8245 31.5 2492 19.6 9829 23.6 3926 27.6 8099 31.6 2348 197 9682 28.7 3778 27.7 7953 31.7 2204 19.8 9534 23.8 3630 27.8 7806 31.8 2060 19.9 9388 23.9 3487 27.9 7664 31.9 1920 TABLE XIII (CONTINUED) 27 t log t log t log t log 32.0 951 776 35 947518 70 900700 110 852 726 32.1 1632 36 6114 71 899 433 111 1592 32.2 1492 37 4702 72 8170 112 850 461 32.3 1349 38 3303 73 6912 113 849 333 32.4 1205 39 1905 74 5656 114 8208 32.5 1061 75 4405 115 7085 32.6 0922 76 3156 116 5965 32.7 0778 77 1912 117 4849 32.8 0635 78 0671 118 3736 32.9 0495 79 889 434 119 2625 33.0 950351 40 940513 80 888 200 120 841 517 33.1 0208 41 939 125 81 6970 121 840412 33.2 950 069 42 7741 82 5743 122 839 309 33.3 949 926 43 6363 83 4519 123 8210 33.4 9783 44 4988 84 3 299 124 7113 33.5 9643 45 3618 85 2083 125 6019 33.6 9500 46 2252 86 880 869 126 4928 33.7 9358 47 930 891 87 879 660 127 3839 33.8 9215 48 9 534 88 8453 128 2754 33.9 9075 49 8181 89 7250 129 1671 34.0 948 932 50 926832 90 876 050 130 830 591 51 5487 91 4854 131 829513 52 4147 92 3661 132 8438 53 2810 93 2471 133 7365 54 1478 94 1284 134 6295 55 920150 95 870 101 135 5228 56' 918 826 96 868 920 136 4164 57 7506 97 7743 137 3102 58 6189 98 6570 138 2043 59 4877 99 5399 139 820 986 60 913 569 100 864 231 140 819932 61 2265 101 3067 141 8880 62 910964 102 1906 142 7831 63 909 668 103 860 748 143 6784 64 8375 104 859 593 144 5741 65 7087 105 8441 145 4699 66 5801 106 7292 146 3660 67 4520 107 6146 147 2623 68 3243 108 5003 148 1589 69 1969 109 3863 149 0558 28 TABLE XIV REDUCTION OF THE VOLUME OF GASES SATURATED WITH AQUEOUS VAPOR TO 0, NORMAL PRESSURE, AND DRY (1 + 0.003070^)700 (V is the volume of the gas, p the uncorrected barometric pressure read on a glass or wooden scale, p barometric pressure corrected for temperature, h the maximum tension of aqueous vapor, t the temperature. This table contains the logarithms of (1 + 0.008670*) 760 where p varies from 730 to 780 and t from 12 to 24.) (Landolt-Bornstein) t p=730 log Differ- ence for 10mm. p = 740 log Differ- ence for 10mm. p=750 log Differ- ence for 10mm. p=760 log Differ- ence for 10mm. p=770 log Differ- ence for 10mm. p = 780 log 12.0 95663 599 96262 591 96 853 584 97437 575 98012 568 98 580 12.2 622 600 222 591 813 583 396 576 97972 568 540 12.4 582 599 181 592 773 583 356 576 932 568 500 12.6 541 600 141 592 733 583 316 576 892 568 460 12.8 501 599 100 592 692 584 276 576 852 568 420 13.0 95460 600 96060 592 96652 584 97236 ' 576 97812 568 98380 13.2 419 600 96019 592 611 584 195 576 771 569 340 13.4 378 601 95979 592 571 584 155 576 731 569 300 13.6 337 601 938 592 530 584 114 577 691 568 259 13.8 296 601 897 592 489 584 073 577 650 569 219 14.0 95 256 600 95856 592 96448 585 97033 576 97609 570 98179 14.2 214 601 815 592 407 585 96992 577 569 569 138 14.4 173 601 774 592 366 585 951 577 528 569 097 14.6 131 601 732 593 325 585 910 577 487 570 057 14.8 090 601 691 593 284 585 869 577 446 570 016 15.0 95048 602 95650 593 96243 585 96828 577 97405 570 97 975 . 15.2 95007 601 608 593 201 585 786 578 364 570 934 15.4 94965 601 566 594 160 585 745 578 323 570 893 15.6 923 602 525 593 118 586 704 577 281 570 851 15.8 881 602 483 594 077 585 662 578 240 570 810 16.0 94839 602 95441 594 96035 585 96620 578 97198 571 97 769 16.2 797 602 399 594 95993 586 579 578 157 570 727 16.4 755 602 357 594 951 586 537 578 115 571 686 16.6 712 603 315 594 909 586 495 578 073 571 644 16.8 670 602 272 595 867 586 453 579 032 570 602 TABLE XIV (CONTINUED) 29 t p = 730 log Differ- ence for 10mm. p = 740 log Differ- ence for 10mm. p = 750 log Differ- ence for 10mm. p = 760 log Differ- ence for 10mm. p = 770 log Differ- ence for 10mm. p = 780 log 17.0 94627 603 95230 594 95824 587 96411 579 96990 571 97561 17.2 585 602 187 595 782 587 369 578 947 572 519 17.4 542 603 145 595 740 586 326 579 905 572 477 17.6 499 603 102 595 697 587 284 579 863 571 434 17.8 456 603 059 595 654 587 241 580 821 571 392 18.0 94413 603 95 016 596 95612 587 96 199 579 96778 572 97 350 18.2 370 603 94973 596 569 587 156 580 736 571 307 18.4 326 604 930 596 526 587 113 580 693 572 265 18.6 283 604 887 596 483 587 070 580 650 572 222 18.8 239 604 843 596 439 588 027 580 607 573 180 19.0 94196 604 94800 596 95396 588 95984 580 96564 573 97137 19.2 152 604 756 597 353 588 941 580 521 573 094 19.4 108 605 713 596 309 588 897 581 478 573 051 19.6 064 605 669 596 265 589 854 580 434 573 97007 19.8 020 605 625 596 221 589 810 581 391 573 96964 20.0 93975 606 94 581 597 95178 588 95766 581 96347 574 96921 20.2 931 605 536 597 133 589 722 582 304 573 877 20.4 886 606 492 597 089 589 678 582 260 573 833 20.6 842 606 448 597 045 589 634 582 216 574 790 20.8 797 606 403 598 001 589 590 582 172 574 746 21.0 93752 606 94358 598 94 956 590 95546 581 96127 575 96702 21.2 707 606 313 598 911 590 501 582 083 574 .657 21.4 662 606 268 598 866 591 457 582 96039 574 613 21.6 616 607 223 598 821 591 412 582 95994 575 569 21.8 571 607 178 598 776 591 367 582 949 575 524 22.0 93 525 607 94132 599 94 731 591 95322 583 95 905 575 96480 22.2 479 608 087 599 686 591 277 583 860 575 435 22.4 433 608 94041 599 640 591 231 583 814 576 390 22.6 387 608 93 995 600 595 591 186 583 769 576 345 22.8 341 60S 949 600 549 591 140 584 724 575 299 23.0 93295 608 93903 600 94503 591 95094 584 95678 576 96254 23.2 248 609 857 600 457 592 049 583 632 577 209 23.4 202 608 810 601 411 592 95003 584 587 576 163 23.6 155 609 764 600 364 592 94956 585 541 576 117 23.8 108 609 717 601 318 592 910 585 495 576 071 24.0 93061 609 93670 601 94271 593 94864 584 95448 577 96025 30 TABLE X\ 7 OBSERVED DENSITY AND THE WEIGHT OF A LITER OF SOME COMMON GASES UNDER THE FOLLOWING CONDITIONS : AND 760 MM. PRESSURE AT SEA LEVEL AND 45 LATITUDE. AIR = 1 Substance Density Wt. 1 liter in grams at sea level and 45 lat. log Observer Acetylene 0.92 1.1620 065 206 Berthelot Air 1.00 1.2928 111532 Leduc "1 Mean Lord Rayleigh J value Ammonia 0.5971 0.7621 882 012 Leduc Argon 1.379 1.782 250 908 Ramsay and Travers Bromine f 5.5243 1 \ at 227.92 J 7.1426 853 856 Jahn Carbon dioxide 1.52909 1.9652 293 407 Lord Rayleigh Carbon monoxide 0.96716 1.2506 097 118 Lord Rayleigh Chlorine 2.491 3.1666 500 593 Leduc Ethane 1.075 1.3421 127 785 Kolbe Ethylene 0.9852 1.2520 097 604 Saussure Hydrogen 0.06926 0.09004 954435 Regnault Hydrogen sulphide 1.1895 1.5230 182700 Leduc Hydrobromic acid 2.71 3.6163 558 265 Lowig Hydrochloric acid 1.2692 1.6283 211 734 Leduc Hydriodic acid 4.3757 5.7106 756 682 Thomson Methane 0.5576 0.7160 854 913 Thomson Methyl ether 1.617 2.0567 313171 Dumas and Peligot Nitrogen 0.96737 1.2542 098 367 Lord Rayleigh Nitrogen dioxide 1.0372 1.3417 127 655 Leduc Nitrogen monoxide 1.5301 1.9688 294 202 Leduc Oxygen 1.10535 1.4292 155 093 Lord Rayleigh Sulphur dioxide 2.2639 2.8611 456 533 Leduc TABLE XVI 31 DENSITY OF DRY ATMOSPHERIC AIR AT 760 MM. PRESSURE AND TEMPERATURES RANGING FROM TO 35 Values of d t . rfi0 = .0012928 \ 1 + .003670 1) t dt, 760 log t dt, 760 log t dt, 760 log 0.0 0.0 012 928 111531 4.0 0.0012741 105 204' 8.0 0.0012559 098 955 0.1 12923 1363 4.1 12736 5033 8.1 12 555 8817 0.2 12919 1229 4.2 12732 4897 8.2 12550 8644 0.3 12914 1061 4.3 12728 4760 8.3 12 546 8505 0.4 12909 0893 4.4 12723 4590 8.4 12541 8332 0.5 12904 0724 4.5 12 718 4419 8.5 12537 8194 0.6 12900 0590 4.6 12713 4248 8.6 12532 8020 0.7 12895 0421 4.7 12709 4111 8.7 12528 7882 0.8 12890 0253 4.8 12704 3941 8.8 12524 7743 0.9 12885 110084 4.9 12700 3804 8.9 12519 7570 1.0 0.0 012 SSI 109 950 5.0 0.0012695 103 633 9.0 0.0012515 097431 1.1 12876 9781 5.1 12690 3462 9.1 12511 7292 1.2 12871 9612 5.2 12686 3325 9.2 12506 7118 1.3 12867 9477 5.3 12681 3154 9.3 12501 6945 1.4 12862 9309 5.4 12677 3017 9.4 12497 6806 1.5 12857 9140 5.5 12672 2845 9.5 12492 6632 1.6 12853 9005 5.6 12 668 2708 9.6 12488 6493 1.7 12848 8 836 5.7 12663 2537 9.7 12484 6354 1.8 12843 S667 5.8 12659 2399 9.8 12479 6180 1.9 12 838 8497 5.9 12654 2228 9.9 12475 6041 2.0 0.0012834 108 362 6.0 0.0 012 649 102 056 10.0 0.0012470 095867 2.1 12829 8193 6.1 12645 1919 10.1 12466 5727 2.2 12824 S024 6.2 12640 1747 10.2 12462 5588 2.3 12820 7888 6.3 12636 1610 10.3 12457 5414 2.4 12815 7719 6.4 12631 1438 10.4 12453 5274 2.5 12 810. 7549 6.5 12627 1300 10.5 12448 5 100 2.6 12806 7414 6.6 12622 1 128 10.6 12444 4960 2.7 12801 7244 6.7 12618 0991 10.7 12440 4820 2.8 12797 7108 6.8 12613 0818 10.8 12435 4646 2.9 12792 6939 6.9 12609 0681 10.9 12431 4506 3.0 0.0 012 787 106 769 7.0 0.0012604 100 508 11.0 0.0 012 426 094331 3.1 12783 6633 7.1 12600 0371 11.1 12422 4192 3.2 12778 6463 7.2 12595 0198 11.2 12418 4052 3.3 12773 6293 7.3 12591 100060 11.3 12413 3877 3.4 12769 6157 7.4 12586 099 888 11.4 12409 3737 3.5 12764 5987 7.5 12582 9750 11.5 12404 3562 3.6 12759 5817 7.6 12577 9577 11.6 12400 3422- 3.7 12755 5681 7.7 12573 9439 11.7 12396 3282 3.8 12750 5510 7.8 12 568 9266 11.8 12391 3106 3.9 12746 5374 7.9 12564 9128 11.9 12387 2966 32 TABLE XVI (CONTINUED) t dt, 760 log t dt, 760 log t dt> 760 log 12.0 0.0012383 092 826 16.0 0.0012211 086751 20.0 0.0012044 080 770 12.1 12378 2651 16.1 12207 6609 20.1 12040 0627 12.2 12374 2510 16.2 12203 6467 20.2 12036 0482 12.3 12370 2370 16.3 12198 6289 20.3 12032 0338 12.4 12365 2194 16.4 12194 6146 20.4 12028 0193 12.5 12361 2054 16.5 12190 6004 20.5 12023 080 013 12.6 12357 1913 16.6 12186 5861 20.6 12019 079 868 12.7 12352 1737 16.7 12181 5683 20.7 12015 9724 12.8 12348 1597 16.8 12177 5540 20.8 12011 9579 12.9 12344 1456 16.9 12173 5398 20.9 12007 9435 13.0 0.0 012 339 091 280 17.0 0.0012169 085 255 21.0 0.0 012 003 079 290 13.1 12335 1139 17.1 12 165 5112 21.1 11999 9145 13.2 12331 0998 17.2 12160 4934 21.2 11995 9000 13.3 12326 0822 17.3 12156 4791 21.3 11991 8855 13.4 12322 0681 17.4 12152 4648 21.4 11987 8711 13.5 12318 0540 17.5 12148 4505 21.5 11982 8529 13.6 12313 0364 17.6 12144 4362 21.6 11978 8384 13.7 12309 0223 17.7 12139 4183 21.7 11974 8239 13.8 12305 090 082 17.8 12135 4040 21.8 11970 8094 13.9 12301 089 940 17.9 12131 3897 21.9 11966 7949 14.0 0.0 012 296 089 764 18.0 0.0012127 083 753 22.0 0.0011 962 077 804 14.1 12292 9623 181 12123 3610 22.1 11958 7659 14.2 12288 9481 18.2 12119 3467 22.2 11954 7513 14.3 12283 9305 18.3 12114 3288 22.3 11950 7368 14.4 12279 9163 18.4 12110 3144 22.4 11 946 7223 14.5 12275 9022 18.5 12 106 3001 22.5 11942 7077 14.6 12270 8845 18.6 12102 2857 22.6 11938 6932 14.7 12266 8703 18.7 12098 2714 22.7 11934 6786 14.8 12262 8561 18.8 12094 2570 22.8 11930 6640 14.9 12258 8420 18.9 12089 2390 22.9 11926 6495 15.0 0.0012253 088 242 19.0 0.0012085 082 247 23.0 0.0011922 076 349 15.1 12249 8101 19.1 12081 2103 23.1 11918 6203 15.2 12 245 7959 19.2 12077 1959 23.2 11914 6058 15.3 12241 7817 19.3 12073 1815 23.3 11 910 5912 15.4 12236 7640 19.4 12069 1671 23.4 11906 5766 15.5 12232 7498 19.5 12065 1527 23.5 11902 5620 15.6 12228 7355 19.6 12060 1347 23.6 11898 5474 15.7 12224 7213 19.7 12 056 1 203 23.7 11894 5328 15.8 12219 7036 19.8 12052 1059 23.8 11889 5 145 15.9 12215 6894 19.9 12048 0915 23.9 11885 4999 TABLE XVI (CONTINUED) 33 t dt, 760 log t <*t, 760 lOg t dt, 760 log 24.0 0.0011881 074 853 28.0 0.0011 723 069 039 32.0 0.0011569 063 296 24.1 11877 4707 28.1 11 719 8891 32.1 11 566 3183 24.2 11873 4 561 28.2 11 716 8779 32.2 11562 3033 24.3 11 869 4414 28.3 11712 8631 32.3 11558 2883 24.4 11865 4268 28.4 11708 8483 32.4 11554 2732 24.5 11861 4121 28.5 11 704 8334 32.5 11550 2582 24.6 11857 3975 28.6 11700 8186 32.6 11547 2469 24.7 11853 3828 28.7 11696 8037 32.7 11 543 2319 24.8 11849 3682 28.8 11692 7889 32.8 11539 2168 24.9 11846 3572 28.9 11688 7740 32.9 11535 2018 25.0 0.0011842 073 425 29.0 0.0011684 067 592 33.0 0.0011531 061 867 25.1 11838 3278 29.1 11681 7480 33.1 11528 1 754 25.2 11834 3132 29.2 11677 7331 33.2 11524 1603 25.3 11830 2985 29.3 11673 7183 33.3 11520 1453 25.4 11826 2838 29.4 11 669 7034 33.4 11516 1302 25.5 11822 2691 29.5 11 665 6885 33.5 11513 1 189 25.6 11818 2544 29.6 11661 6736 33.6 11509 1038 25.7 11814 2397 29.7 11657 6587 33.7 11505 0887 25.8 11810 2250 29.8 11654 6475 33.8 11501 0736 25.9 11806 2103 29.9 11650 6326 33.9 11497 0585 26.0 0.0011802 071 956 30.0 0.0011646 066177 34.0 0.0011494 060471 26.1 11 798 1808 30.1 11642 6028 34.1 11490 0320 26.2 11794 1661 30.2 11638 5878 34.2 11486 0169 26.3 11790 1514 30.3 11634 5729 34.3 11483 060055 26.4 11786 1366 30.4 11630 5580 34.4 11479 059 904 26.5 11782 1219 30.5 11627 5468 34.5 11475 9753 26.6 11778 1072 30.6 11 623 5318 34.6 11471 9601 26.7 11 774 0924 30.7 11619 5 169 34.7 11468 9488 26.8 11 770 0777 30.8 11615 5019 34.8 11464 9336 26.9 11 768 0703 30.9 11611 4870 34.9 11460 9185 27.0 0.0011762 070 481 31.0 0.0011607 064720 35.0 0.0011456 059033 27.1 11 759 0370 31.1 11 603 4570 27.2 11 755 0223 31.2 11600 4458 27.3 11751 070075 31.3 11 596 4308 27.4 11747 069 927 31.4 11592 4158 27.5 11743 9779 31.5 11588 4009 27.6 11739 9631 31.6 11 585 3896 27.7 11 735 9483 31.7 11 581 3746 27.8 11 731 9 335 31.8 11 577 3596 27.9 11727 9187 31.9 11 573 3446 34 TABLE XVII (Ostwald-Luther. Physiko-chemische Messungen) Degrees C. Apparent weight of a cc. of water log Volume of an apparent gram of water log 10 .9986 999392 1.0014 .000 608 11 85 9348 15 0651 12 84 9305 16 0694 13 83 9261 17 0738 14 82 9218 18 0781 15 81 9174 19 0824 16 79 9087 21 0911 17 77 9000 23 0998 18 76 8956 24 1041 19 74 8869 26 1 128 20 72 8782 28 1214 21 70 8695 30 1301 22 67 8565 33 1431 23 65 8477 35 1517 24 63 8390 37 1604 25 60 8259 40 1734 TABLE XVIII 35 SPECIFIC VOLUME OF WATER (Thiesen, Scheel, and Diesselhorst, Wiss. Abh. d. Phys. Techn. Reichsanst. 3, 69) Hydrogen Scale Tenth Degrees Degrees 1 2 3 4 5 6 7 8 9 1.000132 126 119 113 107 101 095 089 084 079 1 073 069 064 059 055 051 047 043 039 035 2 032 029 026 023 020 018 016 013 Oil 009 3 008 006 005 004 003 002 001 001 000 000 4 000 000 000 001 001 002 003 004 005 007 5 008 010 012 014 016 018 021 023 026 029 6 032 035 039 042 046 050 054 058 062 066 7 071 075 080 085 090 096 101 107 112 118 8 124 130 137 143 149 156 163 170 177 184 9 192 199 207 215 223 231 239 247 256 264 10 273 282 291 300 309 319 328 338 348 358 11 368 378 388 399 409 420 431 442 453 464 12 476 487 499 511 522 534 547 559 571 584 13 596 609 622 635 648 661 675 688 702 715 14 729 743 757 772 786 800 815 830 844 859 15 874 890 905 920 936 951 967 983 999 *015 16 1.001 031 048 064 081 098 114 131 148 165 183 17 200 218 235 253 271 289 307 325 343 361 18 380 399 417 436 455 474 493 513 532 . 551 19 571 591 610 630 650 671 691 711 732 752 20 773 794 815 836 857 878 899 921 942 964 21 985 *007 *029 *051 *073 *0% *118 *140 *163 *186 22 1.002 208 231 254 277 300 324 347 370 394 418 23 441 465 489 513 538 562 586 611 635 660 24 685 710 735 760 785 810 835 861 886 912 25 938 964 990 *016 *042 *068 *094 *121 *147 #174 26 1.003 201 227 254 281 308 336 363 390 418 445 27 473 501 529 556 585 613 641 669 698 726 28 755 783 812 841 870 899 928 957 987 *016 29 1.004046 075 105 135 165 194 225 255 285 315 30 346 376 407 437 468 499 530 561 592 623 31 655 686 717 749 781 812 844 876 908 940 32 972 *005 *037 *070 *102 *135 *167 *200 *233 *266 33 1.005 299 332 365 399 432 465 499 533 566 600 34 634 668 702 736 771 805 839 874 908 943 35 978 *013 *047 *OS2 *118 *153 *188 *223 *259 #294 36 TABLE XIX DENSITY OF WATER (Thiesen, Scheel, and Diesselhorst, Wiss. Abh. d. Phys. Techn. Reichsanst. 3, Hydrogen Scale Tenth Degrees Degrees 1 2 3 4 5 6 7 8 9 0.999 868 874 881 887 893 899 905 911 916 922 1 927 932 936 941 945 950 954 957 961 965 2 968 971 974 977 980 982 985 987 989 991 3 992 994 995 996 997 998 999 999 *000 *000 4 1.000000 000 000 *999 *999 *998 *997 *996 *995 *993 5 0.999 992 990 988 986 984 982 979 977 974 971 6 968 965 962 958 954 951 947 943 938 934 7 929 925 920 915 910 904 899 893 888 882 8 876 870 864 857 851 844 837 830 823 816 9 808 801 793 785 778 769 761 753 744 736 10 727 718 709 700 691 681 672 662 652 642 11 632 622 612 601 591 580 569 558 547 536 12 525 513 502 490 478 466 454 442 429 417 13 404 391 379 366 353 339 326 312 299 285 14 271 257 243 229 215 200 186 171 156 141 15 126 111 096 081 065 050 034 018 002 *986 16 0.998 970 953 937 920 904 887 870 853 836 819 17 801 784 766 749 731 713 695 677 659 640 18 622 603 585 566 547 528 509 490 471 451 19 432 412 392 372 352 332 312 292 271 251 20 230 210 189 168 147 126 105 083 062 040 21 019 *997 *975 *953 *931 *909 *887 *S64 *S42 *819 22 0.997 797 774 751 728 705 682 659 635 612 588 23 565 541 517 493 469 445 421 396 372 347 24 323 298 273 248 223 198 173 147 122 096 25 071 045 019 *994 *968 *941 *915 *SS9 *S63 *836 26 0.996 810 783 756 730 703 676 648 621 594 567 27 539 512 484 456 428 400 372 344 316 288 28 259 231 202 174 145 116 087 058 029 000 29 0.995 971 941 912 882 853 823 793 763 733 703 30 673 643 613 582 552 521 491 460 429 398 31 367 336 305 273 242 211 179 148 116 084 32 052 020 *988 *956 *924 *892 *859 *S27 *794 *762 33 0.994 729 696 663 630 597 564 531 498 464 431 34 398 364 330 296 263 229 195 161 126 092 35 058 023 *989 *954 *920 *885 *850 *815 *7SO *745 TABLE XX 37 THE PROPORTION BY WEIGHT OF THE PROPORTION BY VOLUME OF ABSOLUTE ALCOHOL IN 100 PARTS ABSOLUTE ALCOHOL IN 100 VOL- OF SPIRITS OF DIFFERENT SPE- UMES OF SPIRITS OF DIFFERENT CIFIC GRAVITIES (Fownes) SPECIFIC GRAVITIES (Gay-Lussac) 100 100 100 vol. vol. vol. Per cent Per cent Per cent spirits spirits spirits Sp. G. at 15.5 of real alco- Sp. G. at 15.5 of real alco- Sp. G. at 15.5 of real alco- Sp. G. at 15 con- tain vol. of real Sp. G. at 15 con- tain vol. of real Sp. G. at 15 con- tain vol. of real hol hol hol alco- alco- alco- hol hol hol .9991 0.5 .9511 34 .8769 68 .9985 1 .9594 35 .8932 69 .9981 1 .9490 35 .8745 69 .9970 2 .9581 36 .8907 70 .9965 2 .9470 36 .8721 70 .9956 3 .9567 37 .8882 71 .9947 3 .9452 37 .8696 71 .9942 4 .9553 38 .8857 72 .9930 4 .9434 38 .8672 72 .9929 5 .9538 39 .8831 73 .9914 5 .9416 39 .8649 73 .9916 6 .9523 40 .8805 74 .9898 6 .9396 40 .8625 74 .9903 7 .9507 41 .8779 75 .9884 7 .9376 41 .8603 75 .9891 8 .9491 42 .8753 76 .9869 8 .9356 42 .8581 76 .9878 9 .9474 43 .8726 77 .9855 9 .9335 43 .8557 77 .9867 10 .9457 44 .8699 78 .9841 10 .9314 44 .8833 78 .9855 11 .9440 45 .8672 79 .9828 11 .9292 45 .8508 79 .9844 12 .9422 46 .8645 80 .9815 12 .9270 46 .8483 80 .9833 13 .9404 47 .8617 81 .9802 13 .9249 47 .8459 81 .9822 14 .9386 48 .8589 82 .9789 14 .9228 48 .8434 82 .9812 15 .9367 49 .8560 83 .9778 15 .9206 49 .8408 83 .9802 16 .9348 50 .8531 84 .9766 16 .9184 50 .8382 84 .9792 17 .9329 51 .8502 85 .9753 17 .9160 51 .8357 85 .9782 18 .9309 52 .8472 86 .9741 18 .9135 52 .8331 86 .9773 19 .9289 53 .8442 87 .9728 19 .9113 53 .8305 87 .9763 20 .9269 54 .8411 88 .9716 20 .9090 54 .8279 88 .9753 21 .9248 55 .8379 89 .9704 21 .9069 55 .8254 89 .9742 22 .9227 56 .8346 90 .9691 22 .9047 56 .8228 90 .9732 23 .9206 57 .8312 91 .9678 23 .9025 57 .8199 91 .9721 24 .9185 58 .8278 92 .9665 24 .9001 58 .8172 92 .9711 25 .9163 59 .8242 93 .9652 25 .8979 59 .8145 93 .9700 26 .9141 60 .8206 94 .9638 26 .8956 60 .8118 94 .9690 27 .9119 61 .8168 95 .9623 27 .8932 61 .8089 95 .9679 28 .9096 62 .8128 96 .9609 28 .8908 62 .8061 96 .9668 29 .9073 63 .8086 97 .9593 29 .8886 63 .8031 97 .9657 30 .9050 64 .8042 98 .9578 30 .8863 64 .8001 98 .9645 31 .9027 65 .8006 99 .9560 31 .8840 65 .7969 99 .9633 32 .9004 66 .7947 100 .9544 32 .8816 66 .7938 100 .9621 33 .8980 67 .9528 33 .8793 67 .9608 34 .8956 68 38 TABLE XXI SPECIFIC GKAVITY OF SOLUTIONS OF AMMONIUM HYDROXIDE AT 15 C. (Lunge and Wiernik, Zeit. f. angew. Chem., 1889, 181) Sp. G. Mf in vacuo Per cent NH 3 grams 1 liter contains NH 3 grams Sp. G. at"' in vacuo Per cent NH 3 grams 1 liter contains NH 3 grams Sp. G. atr in vacuo Per cent NH 3 grams 1 liter contains NH 3 grams 1.000 .00 0.0 0.960 9.91 95.1 0.920 21.75 200.1 0.998 .45 4.5 958 10.47 100.3 918 22.39 205.6 996 .91 9.1 956 11.03 105.4 916 23.03 210.9 994 1.37 13.6 954 11.60 110.7 914 23.68 216.3 992 1.84 18.2 952 12.17 115.9 912 24.33 221.9 990 2.31 22.9 950 12.74 121.0 910 24.99 227.4 988 2.80 27.7 948 13.31 126.2 908 25.65 232.9 986 3.30 32.5 946 13.88 131.3 906 26.31 238.3 984 3.80 37.4 944 14.46 136.5 904 26.98 243.9 982 4.30 42.2 942 15.04 141.7 902 27.65 249.4 980 4.80 47.0 940 15.63 146.9 900 28.33 255.0 978 5.30 51.8 938 16.22 152.1 898 29.01 260.5 976 5.80 56.6 936 16.82 157.4 896 29.69 266.0 974 6.30 61.4 934 17.42 162.7 894 30.37 271.5 972 6.80 66.1 932 18.03 168.1 892 31.05 277.0 970 7.31 70.9 930 18.64 173.4 890 31.75 282.6 968 7.82 75.7 928 19.25 178.6 888 32.50 288.6 966 8.33 80.5 926 19.87 184.2 886 33.25 294.6 964 8.84 85.2 924 20.49 189.3 884 34.10 301.4 962 9.35 89.9 922 21.12 194.7 882 34.95 308.3 TABLE XXII SPECIFIC GRAVITY OF SOLUTIONS OF HYDROCHLORIC ACID AT 15 C. (Lunge and Marchlewski, Zeit. angew. Chem., 1891, 135) Sp. G. atL- in vacuo 100 pts. by wt. contain grams HC1 1 liter contains grams HC1 Sp. g. atr in vacuo 100 pts. by wt. contain grams HC1 1 liter contains grams HC1 Sp. G. .tv in vacuo 100 pts. by wt. contain grams HC1 1 liter contains grams HC1 1.000 0.16 1.6 1.070 14.17 152 1.140 27.66 315 1.005 1.15 12.0 1.075 15.16 163 1.145 28.61 328 1.010 2.14 22.0 1.080 16.15 174 1.150 29.57 340 1.015 3.12 32.0 1.085 17.13 186 1.155 30.55 353 1.020 4.13 42.0 1.090 18.11 197 1.160 31.52 366 1.025 5.15 53 .095 19.06 209 1.165 32.49 379 1.030 6.15 64 .100 20.01 220 1.170 33.46 392 1.035 7.15 74 .105 20.97 232 1.175 34.42 404 1.040 8.16 85 .110 21.92 243 1.180 35.39 . 418 1.045 9.16 96 .115 22.86 255 1.185 36.31 430 1.050 10.17 107 .120 23.82 267 1.190 37.23 443 1.055 11.18 118 .125 24.78 278 1.195 38.16 456 1.060 12.19 129 .130 25.75 291 1.200 39.11 469 1.065 13.19 141 .135 26.70 303 TABLE XXIII 39 CONSTANT BOILING SOLUTION OF HYDROCHLORIC ACID (Hulett and Bonner, Jour. Am. Chem. Soc., 31, 390) Grams constant Barometric Per cent boiling distillate pressure HC1 containing 1 mol HC1 770 20.218 180.390 760 20.242 180.170 750 20.266 179.960 740 20.290 179.745 730 20.314 179.530 The easiest and most accurate method of preparing standard solutions of hydrochloric acid is to weigh out a definite amount of the constant boiling solution of hydrochloric acid and dilute this to a certain volume. The con- stant boiling solution is obtained by diluting the concentrated hydrochloric acid of the laboratory with an equal volume of water. Distill from a retort or distilling flask connected with a condenser. When three fourths has been distilled off, change the receiver and collect as much of the remainder as is desirable. The last fraction is the constant boiling solution, and if the barometric pressure is noted, the exact weight of this solution which when diluted to a liter yields a normal solution can be ascertained by reference to the table. 40 TABLE XXIV SPECIFIC GRAVITY OF NITRIC ACID AT 15 C. (Lunge and Rey, Zeit. angew. Chem., 1891, 165) Specific gravity at 15 in vacuo 100 pts. by wt. contain grams HN0 3 1 liter contains grams HN0 3 Specific gravity at^in vacuo 100 pts. by wt. contain grams HN0 3 1 liter contains grams HN0 3 Specific gravity at ^ in vacuo 100 pts. by wt. contain grams HN0 3 1 liter contains grams HN0 3 1.000 0.10 1 1.205 33.09 399 1.410 67.50 952 1.005 1.00 10 1.210 33.82 409 1.415 68.63 971 1.010 1.90 19 1.215 34.55 420 1.420 69.80 991 1.015 2.80 28 1.220 35.28 430 1.425 70.98 1011 1.020 3.70 38 1.225 36.03 441 1.430 72.17 1032 1.025 4.60 47 1.230 36.78 452 1.435 73.39 1053 1.030 5.50 57 1.235 37.53 463 1.440 74.68 1075 .035 6.38 66 1.240 38.29 475 1.445 75.98 1098 .040 7.26 75 1.245 39.05 486 1.450 77.28 1121 1.045 8.13 85 1.250 39.82 498 1.455 78.60 1144 .050 8.99 94 1.255 40.58 509 1.460 79.98 1168 .055 9.84 104 1.260 41.34 521 1.465 81.42 1193 1.060 10.68 113 1.265 42.10 533 1.470 82.90 1219 1.065 11.51 123 1.270 42.87 544 1.475 84.45 1246 1.070 12.33 132 1.275 43.64 556 1.480 86.05 1274 1.075 13.15 141 1.280 44.41 568 1.485 87.70 1302 1.080 13.95 151 1.285 45.18 581 1.490 89.60 1335 1.085 14.74 160 1.290 45.95 593 1.495 91.60 1369 1.090 15.53 169 1.295 46.72 603 1.500 94.09 1411 1.095 16.32 179 1.300 47.49 617 1.501 94.60 1420 1.100 17.11 188 1.305 48.26 630 1.502 95.08 1428 1.105 17.89 198 1.310 49.07 643 1.503 95.55 1436 1.110 18.67 207 1.315 49.89 656 1.504 96.00 1444 1.115 19.45 217 1.320 50.71 669 1.505 96.39 1451 1.120 20.23 227 1.325 51.53 683 1.506 96.76 1457 1.125 21.00 236 1.330 52.37 697 1.507 97.13 1464 1.130 21.77 246 1.335 53.22 710 1.508 97.50 1470 1.135 22.54 256 1.340 54.07 725 1.509 97.84 1476 1.140 23.31 266 1.345 54.93 739 1.510 98.10 1481 1.145 24.08 276 1.350 55.79 753 1.511 98.32 1486 1.150 24.84 286 1.355 56.66 768 1.512 98.53 1490 1.155 25.60 296 1.360 57.57 783 1.513 98.73 1494 1.160 26.36 306 .365 58.48 798 1.514 98.90 1497 1.165 27.12 316 .370 59.39 814 1.515 99.01 1501 1.170 27.88 326 .375 60.30 829 1.516 99.21 1504 1.175 28.63 336 .380 61.27 846 1.517 99.34 1507 1.180 29.38 347 .385 62.24 862 1.518 99.46 1510 1.185 30.13 357 .390 63.23 879 1.519 99.57 1512 1.190 30.88 367 1.395 64.25 896 1.520 99.67 1515 1.195 31.62 378 1.400 65.30 914 1.200 32.36 388 1.405 66.40 933 TABLE XXV 41 SPECIFIC GRAVITY OF SULPHURIC ACID AT 15 C. (Lunge, Isler and Naef, Zeit. angew. Chem., 1890, 131) Sp. G. at f in vacuo 100 pts. by wt. contain grams H 2 S0 4 1 liter contains grams H 2 S0 4 Sp. G. at ^ in vacuo 100 pts. by wt. contain grams H 2 S0 4 1 liter contains grams H 2 S0 4 Sp. G. at^in vacuo 100 pts. by wt. contain grams H 2 S0 4 1 liter contains grams H 2 S0 4 1.000 .09 1 1.225 30.48 373 1.450 55.03 798 1.005 .83 8 1.230 31.11 382 1.455 55.50 808 1.010 1.57 16 1.235 31.70 391 1.460 55.97 817 1.015 2.30 23 1.240 32.28 400 1.465 56.43 827 1.020 3.03 31 1.245 32.86 409 1.470 56.90 837 1.025 3.76 39 1.250 33.43 418 1.475 57.37 846 1.030 4.49 46 1.255 34.00 426 1.480 57.83 856 1.035 5.23 54 1.260 34.57 435 1.485 58.28 865 1.040 5.96 62 1.265 35.14 444 1.490 58.74 876 1.045 6.67 71 1.270 35.71 454 1.495 59.22 885 1.050 7.37 77 1.275 36.29 462 1.500 59.70 896 1.055 8.07 85 1.280 36.87 472 1.505 60.18 906 1.060 8.77 93 1.285 37.45 481 1.510 60.65 916 1.065 9.47 102 1.290 38.03 490 1.515 61.12 926 1.070 10.19 109 1.295 38.61 500 1.520 61.59 936 1.075 10.90 117 1.300 39.19 510 1.525 62.06 946 1.080 11.60 125 1.305 39.77 519 1.530 62.53 957 1.085 12.30 133 1.310 40.35 529 1.535 63.00 967 1.090 12.99 142 1.315 40.93 538 1.540 63.43 977 1.095 13.67 150 1.320 41.50 548 1.545 63.85 987 1.100 14.35 158 1.325 42.08 557 1.550 64.26 996 1.105 15.03 166 1.330 42.66 567 1.555 64.67 1006 1.110 15.71 175 1.335 43.20 577 1.560 65.08 1015 1.115 16.36 183 1.340 43.74 586 1.565 65.49 1025 1.120 17.01 191 1.345 44.28 596 1.570 65.90 1035 1.125 17.66 199 1.350 44.82 605 1.575 66.30 1044 1.130 18.31 207 1.355 45.35 614 1.580 66.71 1054 1.135 18.96 215 1.360 45.88 624 1.585 67.13 1064 1.140 19.61 223 1.365 46.41 633 1.590 67.59 1075 1.145 20.26 231 1.370 46.94 643 1.595 68.05 1085 1.150 20.91 239 1.375 47.47 653 1.600 68.51 1096 1.155 21.55 248 1.380 48.00 662 1.605 68.97 1107 .160 22.19 257 1.385 48.53 672 1.610 69.43 1118 .165 22.83 266 1.390 49.06 682 1.615 69.89 1128 .170 23.47 275 1.395 49.59 692 1.620 70.32 1139 .175 24.12 283 1.400 50.11 702 1.625 70.74 1150 .180 24.76 292 1.405 50.63 711 1.630 71.16 1160 .185 25.40 301 1.410 51.15 721 1.635 71.57 1170 .190 26.04 310 1.415 51.66 730 1.640 71.99 1181 .195 26.68 319 1.420 52.15 740 1.645 72.40 1192 .200 27.32 328 1.425 52.63 750 1.650 72.82 1202 .205 27.95 337 1.430 53.11 759 1.655 73.23 1212 .210 28.58 346 1.435 53.59 769 1.660 73.64 1222 1.215 29.21 355 1.440 54.07 779 1.665 74.07 1233 1.220 29.84 364 1.445 54.55 789 1.670 74.51 1244 TABLE XXV (CONTINUED) SPECIFIC GRAVITY OF SULFURIC ACID AT 15 C. (Lunge, Isler and Naef, Zeit. angew. Chem., 1890, 131) Sp. G. atV 5 m vacuo 100 pts. by wt. contain grams H 2 S0 4 1 liter contains grams H 2 S0 4 Sp. G at^in vacuo 100 pts. by wt. contain grams H 2 S0 4 1 liter contains grams H 2 S0 4 Sp. G. at in vacuo 100 pts. bywt. contain grams H 2 S0 4 1 liter contains grams H 2 S0 4 1.675 74.97 1256 1.775 83.90 1489 1.831 92.30 1690 1.680 75.42 1267 1.780 84.50 1504 1.832 92.52 1695 1.685 75.86 1278 1.785 85.10 1519 1.833 92.75 1700 1.690 76.30 1289 1.790 85.70 1534 1.834 93.05 1706 1.695 76.73 1301 1.795 86.30 1549 1.835 93.43 1713 1.700 77.17 1312 1.800 86.90 1564 1.836 93.80 1722 1.705 77.60 1323 1.805 87.60 1581 1.837 94.20 1730 1.710 78.04 1334 1.810 88.30 1598 1.838 94.60 1739 1.715 78.48 1346 1.815 89.05 1621 1.839 95.00 1748 1.720 78.92 1357 1.820 90.05 1639 1.840 95.60 1759 1.725 79.36 1369 1.821 90.20 1643 1.8405 95.95 1765 1.730 79.80 1381 1.822 90.40 1647 1.8410 97.00 1786 1.735 80.24 1392 1.823 9P.60 1651 1.8415 97.70 1799 1.740 80.68 1404 1.824 90.80 1656 1.8410 98.20 1808 1.745 81.12 1416 1.825 91.00 1661 1.8405 98.70 1816 1.750 81.56 1427 1.826 91.25 1666 1.8400 99.20 1825 1.755 82.00 1439 1.827 91.50 1671 1.8395 99.45 1830 1.760 82.44 1451 1.828 91.70 1676 1.8390 99.70 1834 1.765 82.88 1463 1.829 91.90 1681 1.8385 99.95 1838 1.770 83.32 1475 1.830 92.10 1685 TABLE XXVI A 43 CORRECTIONS FOR THE EXPOSED THREAD OF MERCURY THERMOMETERS (Landolt-Bornstein) np(T-t) n is the length of exposed thread expressed in terms of the thermometer graduations, /3 the apparent coefficient of expansion of mercury in glass. T the temperature read off, t, the mean temperature of the exposed thread. For temperatures lower than 100 /3 varies from ^V o to srW' depending on the glass, and for higher temperatures the fraction is somewhat smaller. T V THERMOMETERS, GRADUATED FROM TO 100 (Length of degrees about 4 mm.) T t = 30 35 40 45 50 55 60 65 70 75 80 85 n=10 .05 .05 .05 .05 .05 .05 .05 .05 .1 .1 .1 .1 20 .1 .1 .15 .15 .15 .15 .15 .20 .2 .2 .2 .25 30 .2 .2 .25 .25 .25 .25 .25 .3 .3 .35 .35 .35 40 .3 .3 .3 .35 .35 .35 .4 .4 .45 .45 .5 .5 50 .35 .4 .4 .4 .45 .45 .5 .5 .55 .55 .6 .65 60 .45 .5 .5 .55 .55 .55 .6 .65 .65 .7 .75 .8 70 .65 .7 .7 .75 .8 .85 .9 80 .75 .8 .85 .95 1.0 1.1 90 .9 1.0 1.1 1.1 1.2 100 1.1 1.2 1.3 1.3 44 TABLE XXVI B THERMOMETERS GRADUATED FROM TO 360 (Length of degrees 1 to 1.6 mm.) T-t = 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 72 = 10 0. .05 .05 .05 .1 .1 .1 .15 .2 .2 .2 .25 .3 .35 .35 .40 20 .15 .15 .2 .2 .25 .3 .3 .4 .45 .45 .5 .55 .55 .60 .65 .65 30 .25 .3 .35 .4 .45 .5 .55 .6 .65 .7 .75 .8 .85 .9 .95 .95 40 .35 .4 .5 .55 .6 .7 .75 .8 .90 .95 1.0 1.0 1.1 1.2 1.2 1.3 50 .45 .55 .6 .7 .8 .9 .95 1.0 1.1 1.2 1.2 1.3 1.4 1.4 1.5 1.6 60 .55 .65 .75 .9 1.0 1.1 1.2 1.2 1.3 1.4 1.5 1.6 1.7 1.7 1.8 1.9 70 .7 .8 .9 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.9 2.0 2.1 2.2 80 .8 .9 1.0 1.2 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 90 .9 1.0 1.2 1.4 1.6 1.7 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.8 2.9 100 1.0 1.2 1.3 1.6 1.8 2.0 2.1 2.2 2.3 2.4 2.6 2.7 2.8 2.9 3.1 3.2 110 1.8 2.0 2.2 2.3 2.4 2.5 2.7 2.8 3.0 3.1 3.3 3.4 3.6 120 2.0 2.2 2.4 2.6 2.7 2.8 2.9 3.1 3.3 3.4 3.6 3.7 3.9 130 2.4 2.7 2.8 2.9 3.0 3.2 3.4 3.6 3.7 3.9 4.1 4.3 140 2.7 2.9 3.1 3.2 3.3 3.5 3.7 3.9 4.0 4.2 4.4 4.6 150 3.5 3.7 4.0 4.1 4.3 4.6 4.8 5.0 160 3.7 4.0 4.2 4.5 4.7 4.9 5.1 5.4 170 4.0 4.3 4.5 4.8 5.0 5.2 5.5 5.8 180 4.3 4.5 4.8 5.1 5.3 5.6 5.9 6.1 190 5.4 5.6 5.9 6.2 6.5 200 5.7 6.0 6.3 6.6 6.9 210 6.3 6.7 7.0 7.3 220 6.7 7.0 7.4 7.7 TABLE XXVII FIXED POINTS OF THE THERMOMETRIC SCALE (Transition temperatures) H. Scale Na 2 Cr0 4 - 10H 2 - Na CrO 6H 2 19.5251 Na 2 00 4 . lOHtO Na 2 Cr0 4 4H 2 19.987 I Richards and Kelley Na 2 Cr0 4 . 6H 9 - Na 2 Cr0 4 4H 2 25.90 J Na 2 C0 8 - 10H 2 - Na 2 C0 3 7H 2 32.00 1 Na 2 C0 3 . 10H 2 - Na 2 C0 3 - H 2 32.96 I Wells and McAdam Na 2 C0 3 7H - Na 2 C0 3 H 2 35.37 J Na 2 S0 4 NaBr . 10H 9 2H 2 "0 - Na 2 S0 4 -NaBr 32.3831 50.674 J Richards and Wells MnCl 2 . 4H 2 - MnCl 2 .2H 2 58.089 Richards and Wrede TABLE XXVIII 45 CORRECTIONS FOR LOSS OF WEIGHT IN AIR The following table, calculated by Kohlrausch, contains corrections, C, expressed in milligrams, to be added algebraically to each gram of apparent weight of a substance, the specific gravity of which is S. S C S C S C 0.7 + 1.57 2.0 + 0.458 9 -0.009 0.8 + 1.36 2.5 + 0.337 10 - 0.023 0.9 + 1.19 3.0 + 0.257 11 - 0.034 1.0 + 1.06 3.5 + 0.200 12 - 0.043 1.1 + 0.95 4.0 + 0.157 13 - 0.050 1.2 + 0.86 4.5 + 0.142 14 - 0.057 1.3 + 0.78 5.0 + 0.097 15 - 0.063 1.4 + 0.71 5.5 + 0.075 16 - 0.068 1.5 + 0.66 6.0 + 0.057 17 - 0.072 1.6 + 0.61 6.5 + 0.042 IS - 0.076 1.7 + 0.56 7-0 + 0.029 19 - 0.080 1.8 + 0.52 7.5 + 0.017 20 - 0.083 1.9 + 0.49 8.0 + 0.007 The following values are of constant use in revising the atomic weights of the elements by means of their halides. Vacuum correction per apparent gram Ag _ 0.000031 gram AgBr + 0.000041 gram AgCl +0.000075 gram Agl + 0.000071 gram Brass weights Glass Specific gravity 8.3 2.5 Vacuum correction per apparent gram. - 0.000145 + 0.000335 TABLE XXIX LOGARITHMS OF NUMBERS (From 1 to 10,000) N. log N. log N. log N. log 1 0.000000 26 1.414973 51 1.707570 76 1.880814 2 0.301030 27 1.431364 52 1.716003 77 1.886491 3 0.477121 28 1.447158 53 1.724276 78 , 1.892095 4 0.602060 29 1.462398 54 1.732394 79 1.897627 5 0.698970 30 1.477121 55 1.740363 80 1.903090 6 0.778151 31 1.491362 56 1.748188 81 1.908485 7 0.845098 32 1.505150 57 1.755875 82 1.913814 8 0.903090 33 1.518514 58 1.763428 83 1.919078 9 0.954243 34 1.531479 59 1.770852 84 1.924279 10 1.000000 35 1.544068 60 1.778151 85 1.929419 11 1.041393 36 1.556303 61 1.785330 86 1.934498 12 1.079181 37 1.568202 6? 1.792392 87 1.939519 13 1.113943 38 1.579784 63 1.799341 88 1.944483 14 1.146128 39 1.591065 64 1.806181 89 1.949390 15 1.176091 40 1.602060 65 1.812913 90 1.954243 16 1.204120 41 1.612784 66 1.819544 91 1.959041 17 1.230449 42 1.623249 67 1.826075 92 1.963788 18 1.255273 43 1.633468 68 1.832509 93 1.968483 19 1.278754 44 1.643453 69 1.838849 94 1.973128 20 1.301030 .. 45 1.653213 70 1.845098 95 1.977724 21 1.322219 46 1.662758 71 1.851258 96 1.982271 22 1.342423 47 1.67209S 72 1.857333 97 1.986772 23 1.361728 48 1.681241 73 1.863323 98 1.991226 24 1.380211 49 1.690196 74 1.869232 99 1.995635 25 1.397940 50 1.698970 75 1.875061 100 2.000000 REMARK. In the following table, in the nine right-hand columns of each page, where the first or leading' figures change from 9's to O's, asterisks are introduced instead of the O's, to catch the eye, and to indicate that from thence the two figures of the logarithm to be taken from the second column stand in the next line below. TABLE XXIX (CONTINUED) 4T N. 1 2 3 4 5 6 7 8 9 D. 100 000000 0434 0868 1301 1734 2166 2598 3029 3461 3891 432 101 4321 4751 5181 5609 6038 6466 6894 7321 7748 8174 428 102 8600 9026 9451 9876 *300 *724 1147 1570 1993 2415 424 103 012837 3259 3680 4100 4521 4940 5360 5779 6197 6616 419 104 7033 7451 7868 8284 8700 9116 9532 9947 *361 *775 416 105 021189 1603 2016 2428 2841 3252 3664 4075 4486 4896 412 106 5306 5715 6125 6533 6942 7350 7757 8164 8571 8978 408 107 9384 9789 *195 *600 1004 1408 1812 2216 2619 3021 404 108 033424 3826 4227 4628 5029 5430 5830 6230 6629 7028 400 109 7426 7825 8223 8620 9017 9414 9811 *207 *602 *998 396 110 041393 1787 2182 2576 2969 3362 3755 4148 4540 4932 393 111 5323 5714 6105 6495 6885 7275 7664 8053 8442 8830 389 112 9218 9606 9993 *380 *766 1153 1538 1924 2309 2694 386 113 053078 3463 3846 4230 4613 4996 5378 5760 6142 6524 382 114 6905 7286 7666 8046 8426 8805 9185 9563 9942 *320 379 115 060698 1075 1452 1829 2206 2582 2958 3333 3709 4083 376 116 4458 4832 5206 5580 5953 6326 6699 7071 7443 7815 372 117 8186 8557 8928 9298 9668 **3S *407 *776 1145 1514 369 118 071SS2 2250 2617 2985 3352 3718 4085 4451 4816 5182 366 119 5547 5912 6276 6640 7004 7368 7731 8094 8457 8819 363 120 079181 9543 9904 *266 *626 *987 1347 1707 2067 2426 360 121 082785 3144 3503 3861 4219 4576 4934 5291 5647 6004 357 122 6360 6716 7071 7426 7781 8136 8490 8845 9198 9552 355 123 9905 *258 *611 *963 1315 1667 2018 2370 2721 3071 351 124 093422 3772 4122 4471 4820 5169 5518 5866 6215 6562 349 125 6910 7257 7604 7951 8298 8644 8990 9335 9681 **26 346 126 100371 0715 1059 1403 1747 2091 2434 2777 3119 3462 343 127 3804 4146 4487 4828 5169 5510 5851 6191 6531 6871 340 128 7210 7549 7888 8227 8565 8903 9241 9579 9916 *253 .338 129 110590 0926 1263 1599 1934 2270 2605 2940 3275 3609 335 130 113943 4277 4611 4944 5278 5611 5943 6276 6608 6940 333 131 7271 7603 7934 8265 8595 8926 9256 9586 9915- *245 330 132 120574 0903 1231 1560 1888 2216 2544 2871 3198 3525 328 133 3852 4178 4504 4830 5156 5481 5806 6131 6456 6781 325 134 7105 7429 7753 8076 8399 8722 9045 0268 9690 **12 323 135 130334 0655 0977 1298 1619 1939 2260 *SO 2900 3219 321 136 3539 3858 4177 4496 4814 5133 5451 5769 6086 6403 318 137 6721 7037 7354 7671 7987 8303 8618 8934 9249 9564 315 138 9879 *194 *508 *S22 1'136 1450 1763 2076 2389 2702 314 139 143015 3327 3639 3951 4263 4574 4885 5196 5507 5818 311 140 146128 6438 6748 7058 7367 7676 7985 8294 8603 8911 309 141 9219 9527 9835 *142 *449 *756 1063 1370 1676 1982 307 142 152288 2594 2900 3205 3510 3815 4120 4424 4728 5032 305 143 5336 5640 5943 6246 6549 6852 7154 7457 7759 8061 303 144 8362 8664 8965 9266 9567 9868 *168 *469 *769 1068 301 145 161368 1667 1967 2266 2564 2863 3161 3460 3758 4055 299 146 4353 4650 4947 5244 5541 5838 6134 6430 6726 7022 297 147 7317 7613 7908 8203 8497 8792 9086 9380 9674 9968 295 148 170262 0555 0848 1141 1434 1726 2019 2311. 2603 2895 293 149 3186 3478 3769 4060 -4351 4641 4932 5222 5512 5802 291 N. 1 2 3 4 5 6 7 8 9 D. 48 TABLE XXIX (CONTINUED) N. 1 2 3 4 5 6 7 8 9 D. 150 176091 6381 6670 6959 7248 7536 7825 8113 8401 8689 289 151 8977 9264 9552 9839 *126 *413 *699 *9SS 1272 1558 287 152 181844 2129 2415 2700 2985 3270 3555 3839 4123 4407 285 153 4691 4975 5259 5542 5825 6108 6391 6674 6956 7239 283 154 7521 7803 80S4 8366 8647 8928 9209 9490 9771 **51 281 155 190332 0612 0892 1171 1451 1730 2010 22S9 2567 2846 279 156 3125 3403 3681 3959 4237 4514 4792 5069 5346 5623 278 157 5899 6176 6453 6729 7005 7281 7556 7832 8107 8382 276 158 8657 8932 9206 9481 9755 **29 *303 *577 *S50 1124 274 159 201397 1670 1943 2216 2488 2761 3033 3305 3577 3848 272 160 204120 4391 4663 4934 5204 5475 5746 6016 6286 6556 271 161 6826 7096 7365 7634 7904 8173 8441 8710 8979 9247 269 162 9515 9783 **51 *319 *5S6 *S53 1121 13S8 1654 1921 267 163 2121S8 2454 2720 2986 3252 3518 3783 4049 4314 4579 266 164 4844 5109 5373 5638 5902 6166 6430 6694 6957 7221 264 165 7484 7747 8010 8273 8536 8798 9060 9323 9585 9846 262 166 220108 0370 0631 0892 1153 1414 1675 1936 2196 2456 261 167 2716 2976 3236 3496 3755 4015 4274 4533 4792 5051 259 168 5309 5568 5826 60S4 6342 6600 6858 7115 7372 7630 258 169 7887 8144 8400 8657 8913 9170 9426 9682 9938 *193 256 170 230449 0704 0960 1215 1470 1724 1979 2234 2488 2742 254 171 2996 3250 3504 3757 4011 4264 4517 4770 5023 5276 253 172 5528 5781 6033 6285 6537 6789 7041 7292 7544 7795 252 173 8046 8297 8548 8799 9049 9299 9550 9800 **50 *300 250 174 240549 0799 1048 1297 1546 1795 2044 2293 2541 2790 249 175 3038 3286 3534 3782 4030 4277 4525 4772 5019 5266 248 176 5513 5759 6006 6252 6499 6745 6991 7237 7482 7728 246 177 7973 8219 8464 8709 8954 9198 9443 9687 9932 *176 245 178 250420 0664 0908 1151 1395 1638 1881 2125 2368 2610 243 179 2853 3096 3338 3580 3822 4064 4306 4548 4790 5031 242 180 255273 5514 5755 5996 6237 6477 6718 6958 7198 7439 241 181 7679 7918 8158 8398 8637 8877 9116 9355 9594 9S33 239 182 260071 0310 0548 0787 1025 1263 1501 1739 1976 2214 238 183 2451 2688 2925 3162 3399 3636 3873 4109 4346 4582 237 184 4818 5054 5290 5525 5761 5996 6232 6467 6702 6937 235 185 7172 7406 T641 7875 8110 8344 8578 8812 9046 9279 234 186 9513 9746 9980 *213 *446 *679 *912 1144 1377 1609 233 187 271842 3074 2306 2538 2770 3001 3233 3464 3696 3927 232 188 4158 4389 4620 4850 5081 5311 5542 5772 6002 6232 230 189 6462 6692 6921 7151 7380 7609 7838 8067 8296 8525 229 190 278754 8982 9211 9439 9667 9895 *123 *351 *57S *S06 228 191 281033 1261 1488 1715 1942 2169 2396 2622 2849 3075 227 192 3301 3527 3753 3979 4205 4431 4656 4882 5107 5332 226 193 5557 5782 6007 6232 6456 6681 6905 7130' 7354 7578 225 194 7802 8026 8249 8473 8696 8920 9143 9366 9589 9812 223 195 290035 0257 0480 0702 0925 1147 1369 1591 1813 2034 222 196 2256 2478 2699 2920 3141 3363 3584 3S04 4025 4246 221 197 4466 4687 4907 5127 5347 5567 5787 6007 6226 6446 220 198 6665 6884 7104 7323 7542 7761 7979 8198 8416 8635 219 199 8853 9071 9289 9507 9725 9943 *161 *378 *595 *S13 218 N. 1 2 3 4 5 6 7 8 9 D. TABLE XXIX (CONTINUED) 49 N. 1 2 3 4 5 6 7 8 9 D. 200 301030 1247 1464 1681 1S98 2114 2331 2547 2764 2980 217 201 3196 3412 3628 3844 4059 4275 4491 4706 4921 5136 216 202 5351 5566 5781 5996 6211 6425 6639 6854 7068 7282 215 203 7496 7710 7924 8137 8351 8564 8778 8991 9204 9417 213 204 9630 9843 **56 *26S *4S1 *693 *906 1118 1330 1542 212 205 311754 1966 2177 2389 2600 2812 3023 3234 3445 3656 211 206 3867 4078 4289 4499 4710 4920 5130 5340 5551 5760 210 207 5970 6180 6390 6599 6809 7018 7227 7436 7646 7854 209 208 8063 8272 8481 8689 8898 9106 9314 9522 9730 9938 208 209 320146 0354 0562 0769 0977 1184 1391 1598 1805 2012 207 210 322219 2426 2633 2839 3046 3252 3458 3665 3871 4077 206 211 4282 4488 4694 4899 5105 5310 5516 5721 5926 6131 205 212 6336 6541 6745 6950 7155 7359 7563 7767 7972 8176 204 213 8380 8583 8787 8991 9194 9398 9601 9805 ***s *211 203 214 330414 0617 0819 1022 1225 1427 1630 1832 2034 2236 202 215 2438 2640 2842 3044 3246 3447 3649 3850 4051 4253 202 216 4454 4655 4856 5057 5257 5458 5658 5859 6059 6260 201 217 6460 6660 6860 7060 7260 7459 7659 7858 8058 8257 200 218 8456 8656 8855 9054 9253 9451 9650 9849 **47 *246 199 219 340444 0642 0841 1039 1237 1435 1632 1830 2028 2225 198 220 342423 2620 2817" 3014 3212 3409 3606 3802 3999 4196 197 221 4392 4589 4785 4981 5178 5374 5570 5766 5962 6157 196 222 6353 6549 6744 6939 7135 7330 7525 7720 7915 8110 195 223 8305 8500 8694 8889 9083 9278 9472 9666 9860 **54 194 224 350248 0442 0636 0829 1023 1216 1410 1603 1796 1989 193 225 2183 2375 2568 2761 2954 3147 3339 3532 3724 3916 193 226 4108 4301 4493 4685 4876 5068 5260 5452 5643 5834 192 227 6026 6217 6408 6599 6790 6981 7172 7363 75^4 7744 191 228 7935 8125 8316 8506 8696 8886 9076 9266 9456 9646 190 229 9835 **25 *215 *404 *593 *7S3 *972 1161 1350 1539 189 230 361728 1917 2105 2294 2482 2671 2859 3048 3236 3424 188 231 3612 3800 3988 4176 4363 4551 4739 4926 5113 5301 188 232 5488 5675 5862 6049 6236 6423 6610 6796 6983 7169 187 233 7356 7542 7729 7915 8101 8287 8473 8659 8845 9030 186 234 9216 9401 9587 9772 9958 *143 *328 *513 *69S *SS3 185 235 371068 1253 1437 1622 1806 1991 2175 2360 2544 2728 184 236 2912 3096 3280 3464 3647 3831 4015 4198 4382 4565 184 237 4748 4932 5115 5298 5481 5664 5846 6029 6212 6394 183 238 6577 6759 6942 7124 7306 7488 7670 7852 8034 8216 182 239 8398 8580 8761 8943 9124 9306 9487 9668 9849 **30 181 240 380211 0392 0573 0754 0934 1115 1296 1476 1656 1837 181 241 2017 2197 2377 2557 2737 2917 3097 3277 3456 3636 180 242 3815 3995 4174 4353 4533 4712 4891 5070 5249 5428 179 243 5606 5785 5964 6142 6321 6499 6677 6856 7034 7212 178 244 7390 7568 7746 7923 8101 8279 8456 8634 8811 8989 178 245 9166 9343 9520 9698 9875 **51 *228 *405 *582 *759 177 246 390935 1112 1288 1464 1641 1817 1993 2169 2345 2521 176 247 2697 2873 3048 3224 3400 3575 3751 3926 4101 4277 176 248 4452 4627 4802 4977 5152 5326 5501 5676 5850 6025 175 249 6199 6374 6548 6722 6896 7071 7245 7419 7592 7766 174 N. 1 2 3 4 5 6 7 8 9 D. 50 TABLE XXIX (CONTINUED) N. 1 2 3 4 5 6 7 8 9 D. 250 397940 8114 8287 8461 8634 8808 8981 9154 9328 9501 173 251 9674 9847 **20 *192 *365 *538 *711 *SS3 1056 1228 173 252 401401 1573 1745 1917 2089 2261 2433 2605 2777 2949 172 253 3121 3292 3464 3635 3807 3978 4149 4320 4492 4663 171 254 4834 5005 5176 5346 5517 5688 5858 6029 6199 6370 171 255 6540 6710 6881 7051 7221 7391 7561 7731 7901 8070 170 256 8240 8410 8579 8749 8918 9087 9257 9426 9595 9764 169 257 9933 *102 *271 *440 *609 *777 *946 1114 1283 1451 169 258 411620 17S8 1956 2124 2293 2461 2629 2796 2964 3132 168 259 3300 3467 3635 3803 3970 4137 4305 4472 4639 4806 167 260 414973 5140 5307 5474 5641 5808 5974 6141 6308 6474 167 261 6641 6807 6973 7139 7306 7472 7638 7804 7970 8135 166 262 8301 8467 8633 8798 8964 9129 9295 9460 9625 9791 165 263 9956 *121 *286 *451 *616 *781 *945 1110 1275 1439 165 264 421604 1788 1933 2097 2261 2426 2590 2754 2918 3082 164 265 3246 3410 3574 3737 -3901 4065 4228 4392 4555 4718 164 266 4882 5045 5208 5371 5534 5697 5860 6023 61S6 6349 163 267 6511 6674 6836 6999 7161 7324 7486 7648 7811 7973 162 268 8135 8297 8459 8621 8783 8944 9106 9268 9429 9591 162 269 9752 9914 **75 *236 *398 *559 *720 *881 1042 1203 161 270 431364 1525 1685 1846 2007 2167 2328 2488 2649 2809 161 271 2969 3130 3290 3450 3610 3770 3930 4090 4249 4409 160 272 4569 4729 4888 5048 5207 5367 5526 5685 5844 6004 159 273. 6163 6322 6481 6640 6798 6957 7116 7275 7433 7592 159 274 7751 7909 8067 8226 8384 8542 8701 8859 9017 9175 158 275 9333 9491 9648 9806 9964 *122 *279 *437 *594 *752 158 276 440909 1066 1224 1381 1538 1695 1852 2009 2166 2323 157 277 2480 .263 7 2793 2950 3106 3263 3419 3576 3732 3889 157 278 4045 4201 4357 4513 4669 4825 4981 5137 5293 5449 156 279 5604 5760 5915 6071 6226 6382 6537 6692 6848 7003 155 280 447158 7313 7468 7623 7778 7933 8088 8242 8397 8552 155 281 8706 8861 9015 9170 9324 9478 9633 9787 9941 **95 154 282 450249 0403 0557 0711 0865 1018 1172 1326 1479 1633 154 283 1786 1940 2093 2247 2400 2553 2706 2859 3012 3165 153 284 3318 3471 3624 3777 3930 40S2 4235 4387 4540 4692 153 285 4845 4997 5150 5302 5454 5606 5758 5910 6062 6214 152 286 6366 6518 6670 6821 6973 7125 7276 7428 7579 7731 152 287 7882 8033 8184 8336 8487 8638 8789 8940 9091 9242 151 288 9392 9543 9694 9845 9995 *146 *296 *447 *597 *74S 151 289 460898 1048 1198 1348 1499 1649 1799 1948 2098 2248 150 290 462398 2548 2697 2847 2997 3146 3296 3445 3594 3744 150 291 3893 4042 4191 4340 4490 4639 47S8 4936 5085 5234 149 292 5383 5532 5680 5829 5977 6126 6274 6423 6571 6719 149 293 6868 7016 7164 7312 7460 7608 7756 7904 8052 8200 148 294 8347 8495 8643 8790 8938 9085 9233 9380 9527 9675 148 295 9822 9969 *116 *263 *410 *557 *704 *851 *99S 1145 147 296 471292 1438 1585 1732 1878 2025 2171 2318 2464 2610 146 297 2756 2903 3049 3195 3341 3487 3633 3779 3925 4071 146 298 4216 4362 4508 4653 4799 4944 5090 5235 5381 5526 146 299 5671 5816 5962 6107 6252 6397 6542 6687 6832 6976 145 N. 1 2 3 4 5 6 7 8 9 D. TABLE XXIX (CONTINUED) 51 N. 1 2 3 4 5 6 7 8 9 D. 300 477121 7266 7411 7555 7700 7844 7989 8133 8278 8422 145 301 8566 8711 8855 8999 9143 9287 9431 9575 9719 9863 144 302 480007 0151 0294 0438 0582 0725 0869 1012 1156 1299 144 303 1443 1586 1729 1872 2016 2159 2302 2445 2588 2731 143 304 2874 3016 3159 3302 3445 3587 3730 3872 4015 4157 143 305 4300 4442 4585 4727 4869 5011 5153 5295 5437 5579 142 306 5721 5863 6005 6147 6289 6430 6572 6714 6855 6997 142 307 7138 7280 7421 7563 7704 7845 7986 8127 8269 8410 141 308 8551 8692 8833 8974 9114 9255 9396 9537 9677 9818 141 309 9958 **99 *239 *380 *520 *661 *801 #941 1081 1222 140 310 491362 1502 1642 1782 1922 2062 2201 2341 2481 2621 140 311 2760 2900 3040 3179 3319 3458 3597 3737 3876 4015 139 312 4155 4294 4433 4572 4711 4850 4989 5128 5267 5406 139 313 5544 5683 5822 5960 6099 6238 6376 6515 6653 6791 139 314 6930 7068 7206 7344 7483 7621 7759 7897 8035 8173 138 315 8311 8448 8586 8724 8862 8999 9137 9275 9412 9550 138 316 9687 9824 9962 **99 *236 *374 *511 *64S *785 *922 137 317 501059 1196 1333 1470 1607 1744 1880 2017 2154 2291 137 318 2427 2564 2700 2837 2973 3109 3246 3382 3518 3655 136 319 3791 3927 4063 4199 4335 4471 4607 4743 4878 5014 136 320 505150 5286 5421 5557 5693 5828 5964 6099 6234 6370 136 321 6505 6640 6776 6911 7046 7181 7316 7451 7586 7721 135 322 7856 7991 8126 8260 8395 8530 8664 8799 8934 9068 135 323 9203 9337 9471 9606 9740 9874 *#*9 *143 *277 *411 134 324 510545 0679 0813 0947 1081 1215 1349 1482 1616 1750 134 325 1883 2017 2151 2284 2418 2551 2684 2818 2951 3084 133 326 3218 3351 3484 3617 3750 3883 4016 4149 4282 4414 133 327 4548 4681 4813 4946 5079 5211 5344 5476 5609 5741 133 328 5874 6006 6139 6271 6403 6535 6668 6800 6932 7064 132 329 7196 7328 7460 7592 7724 7855 7987 8119 8251 8382 132 330 518514 8646 8777 8909 9040 9171 9303 9434 9566 9697 131 331 9828 9959 **90 *221 *353 *4S4 *615 *745 *876 1007 131 332 521138 1269 1400 1530 1661 1792 1922 2053 2183 2314 131 333 2444 2575 2705 2835 2966 3096 3226 3356 3486 3616 130 334 3746 3876 4006 4136 4266 4396 4526 4656 4785 4915 130 335 5045 5174 5304 5434 5563 5693 5822 5951 6081 6210 129 336 6339 6469 6598 6727 6856 6985 7114 7243 7372 7501 129 337 7630 7759 7888 8016 8145 8274 8402 8531 8660 8788 129 338 8917 9045 9174 9302 9430 9559 9687 9815 9943 **72 128 339 530200 0328 0456 0584 0712 0840 0968 1096 1223 1351 128 340 531479 1607 1734 1862 1990 2117 2245 2372 2500 2627 128 341 2754 2882 3009 3136 3264 3391 3518 3645 3772 3899 127 342 4026 4153 4280 4407 4534 4661 4787 4914 5041 5167 127 343 5294 5421 5547 5674 5800 5927 6053 6180 6306 6432 126 344 6558 6685 6811 6937 7063 7189 7315 7441 7567 7693 126 345 7819 7945 8071 8197 8322 8448 8574 8699 8825 8951 126 346 9076 9202 9327 9452 9578 9703 9829 9954 **79 *204 125 347 540329 0455 0580 0705 0830 0955 1080 1205 1330 1454 125 348 1579 1704 1829 1953 2078 2203 2327 2452 2576 2701 125 349 2825 2950 3074 3199 3323 3447 3571 3696 3820 3944 124 N. 1 2 3 4 5 6 7 8 9 D. 52 TABLE XXIX (CONTINUED) N. 1 2 3 4 5 6 7 8 9 D. 350 544068 4192 4316 4440 4564 4688 4812 4936 5060 5183 124 351 5307 5431 5555 5678 5802 5925 6049 6172 6296 6419 124 352 6543 6666 6789 6913 7036 7159 7282 7405 7529 7652 123 353 7775 7898 8021 8144 8267 83S9 8512 8635 8758 8881 123 354 9003 9126 9249 9371 9494 9616 9739 9861 9984 *106 123 355 550228 0351 0473 0595 0717 0840 0962 1084 1206 1328 122 356 1450 1572 1694 1816 1938 2060 2181 2303 2425 2547 122 357 2668 2790 2911 3033 3155 3276 3398 3519 3640 3762 121 358 3883 4004 4126 4247 4368 4489 4610 4731 4852 4973 121 359 5094 5215 5336 5457 5578 5699 5820 5940 6061 6182 121 360 556303 6423 6544 6664 6785 6905 7026 7146 7267 7387 120 361 7507 7627 7748 7868 7988 8108 8228 8349 8469 8589 120 362 8709 8829 8948 9068 9188 9308 9428 9548 9667 9787 120 363 9907 **26 *146 *265 *385 *504 *624 *743 *863 *982 119 364 561101 1221 1340 1459 1578 1698 1817 1936 2055 2174 119 365 2293 2412 2531 2650 2769 2887 3006 3125 3244 3362 119 366 3481 3600 3718 3837 3955 4074 4192 4311 4429 4548 119 367 4666 4784 4903 5021 5139 5257 5376 5494 5612 5730 118 368 5848 5966 6084 6202 6320 6437 6555 6673 6791 6909 118 369 7026 7144 7262 7379 7497 7614 7732 7849 7967 8084 118 370 568202 8319 8436 8554 8671 8788 8905 9023 9140 9257 117 371 9374 9491 9608 9725 9842 9959 **76 *193 *309 *426 117 372 570543 0660 0776 0893 1010 1126 1243 1359 1476 1592 117 373 1709 1825 1942 2058 2174 2291 2407 2523 2639 2755 116 574 2872 2988 3104 3220 3336 3452 3568 3684 3800 3915 116 375 4031 4147 4263 4379 4494 4610 4726 4841 4957 5072 116 376 5188 5303 5419 5534 5650 5765 5880 5996 6111 6226 115 377 6341 6457 6572 6687 6802 6917 7032 7147 7262 7377 115 378 7492 7607 7722 7836 7951 8066 8181 8295 8410 8525 115 379 8639 8754 8868 8983 9097 9212 9326 9441 9555 9669 114 > 380 579784 9898 **12 *126 *241 *355 *469 *5S3 *697 *811 114 381 580925 1039 1153 1267 1381 1495 1608 1722 1836 1950 114 382 2063 2177 2291 2404 2518 2631 2745 2858 2972 3085 114 383 3199 3312 3426 3539 3652 3765 3879 3992 4105 4218 113 384 4331 4444 4557 4670 4783 4896 5009 5122 5235 5348 113 385 5461 5574 5686 5799 5912 6024 6137 6250 6362 6475 113 386 6587 6700 6812 6925 7037 7149 7262 7374 7486 7599 112 387 7711 7823 7935 8047 8160 8272 8384 8496 8608 8720 112 388 8832 8944 9056 9167 9279 9391 9503 9615 9726 9838 112 389 9950 **61 *173 *2S4 *396 *507 *619 *730 *842 *953 112 390 591065 1176 1287 1399 1510 1621 1732 1843 1955 2066 111 391 2177 2288 2399 2510 2621 2732 2843 2954 3064 3175 111 392 3286 3397 3508 3618 3729 3840 3950 4061 4171 4282 111 393 4393 4503 4614 4724 4834 4945 5055 5165 5276 5386 110 394 5496 5606 5717 5827 5937 6047 61-57 6267 6377 6487 110 395 6597 6707 6817 6927 7037 7146 7256 7366 7476 7586 110 396 7695 7805 7914 8024 8134 8243 8353 8462 8572 8681 110 397 8791 8900 9009 9119 9228 9337 9446 9556 9665 9774 109 398 9883 9992 *101 *210 *319 *428 *537 *646 *755 *S64 109 399 600973 1082 1191 1299 1408 1517 1625 1734 1843 1951 109 N. 1 2 3 4 5 6 7 8 9 D. TABLE XXIX (CONTINUED) 53 N. 1 2 3 4 5 6 7 8 9 D.. 400 602060 2169 2277 2386 2494 2603 2711 2819 2928 3036 108 401 3144 3253 3361 3469 3577 3$S6 3794 3902 4010 4118 108 402 4226 4334 4442 4550 4658 4766 4874 4982 5089 5197 108 403 5305 5413 5521 5628 5736 5844 5951 6059 6166 6274 108 404 6381 6489 6596 6704 6811 6919 7026 7133 7241 7348 107 405 7455 7562 7669 7777 7884 7991 8098 8205 8312 8419 107 406 8526 8633 8740 8847 8954 9061 9167 9274 9381 9488 107 407 9594 9701 9808 9914 **21 *128 *234 *341 *447 *554 107 408 610660 0767 0873 0979 1086 1192 1298 1405 1511 1617 106 409 1723 1829 1936 2042 2148 2254 2360 2466 2572 2678 106 410 612784 2890 2996 3102 3207 3313 3419 3525 3630 3736 106 411 3842 3947 4053 4159 4264 4370 4475 4581 4686 4792 106 412 4897 5003 5108 5213 5319 5424 5529 5634 5740 5845 105 413 5950 6055 6160 6265 6370 6476 6581 6686 6790 6895 105 414 7000 7105 7210 7315 7420. 7525 7629 7734 7839 7943 105 415 8048 8153 8257 8362 8466 8571 8676 8780 8884 8989 105 416 9093 9198 9302 9406 9511 9615 9719 9824 9928 **32 104 417 620136 0240 0344 0448 0552 0656 0760 0864 0968 1072 104 418 1176 1280 1384 1488 1592 1695 1799 1903 2007 2110 104 419 2214 2318 2421 2525 2628 2732 2835 2939 3042 3146 104 420 623249 3353 3456 3559 3663 3766 3869 3973 4076 4179 103 421 4282 4385 4488 4591 4695 4798 4901 5004 5107 5210 103 422 5312 5415 5518 5621 5724 5827 5929 6032 6135 6238 103 423 6340 6443 6546 6648 6751 6853 6956 7058 7161 7263 103 424 7366 7468 7571 7673 7775 7878 7980 8082 8185 8287 102 425 8389 8491 8593 8695 8797 8900 9002 9104 9206 9308 102 426 9410 9512 9613 9715 9817 9919 **21 *123 *224 *326 102 427 630428 0530 0631 0733 0835 0936 1038 1139 1241 1342 102 428 1444 1545 1647 1748 1849 1951 2052 2153 2255 2356 101 429 2457 2559 2660 2761 2862 2963 3064 3165 3266 3367 101 430 633468 3569 3670 3771 3872 3973 4074 4175 4276 4376 100 431 4477 4578 4679 4779 4880 4981 5081 5182 5283 5383 100 432 5484 5584 5685 5785 5886 5986 6087 6187 6287 6388 100 433 6488 6588 6688 6789 6889 6989 7089 7189 7290 7390 100 434 7490 7590 7690 7790 7890 7990 8090 8190 8290 8389 99 435 8489 8589 8689 8789 8888 8988 9088 9188 9287 9387 99 436 9486 9586 9686 9785 9885 9984 **S4 *183 *283 *3S2 99 437 640481 0581 0680 0779 0879 0978 1077 1177 1276 1375 99 438 1474 1573 1672 1771 1871 1970 2069 2168 2267 2366 99 439 2465 2563 2662 2761 2860 2959 3058 3156 3255 3354 99 440 643453 3551 3650 3749 3847 3946 4044 4143 4242 4340 98 441 4439 4537 4636 4734 4832 4931 5029 5127 5226 5324 98 442 5422 5521 5619 5717 5815 5913 6011 6110 6208 6306 98 443 6404 6502 6600 6698 6796 6894 6992 7089 7187 7285 98 444 7383 7481 7579 7676 7774 7872 7969 8067 8165 8262 98 445 8360 8458 8555 8653 8750 8848 8945 9043 9140 9237 97 446 9335 9432 9530 9627 9724 9821 9919 **16 *113 *210 97 447 650308 0405 0502 0599 0696 0793 0890 0987 1084 1181 97 448 1278 1375 1472 1569 1666 1762 1859 1956 2053 2150 97 449 2246 2343 2440 2536 2633 2730 2826 2923 3019 3116 97 N. 1 2 3 4 5 6 7 8 9 D. 54 TABLE XXIX (CONTINUED) N. 1 2 3 4 5 6 7 8 9 D. 450 653213 3309 3405 3502 3598 3695 3791 3888 3984 4080 96 451 4177 4273 4369 4465 4562 4658 4754 4850 4946 5042 96 452 5138 5235 5331 5427 5523 5619 5715 5810 5906 6002 96 453 6098 6194 6290 6386 6482 6577 6673 6769 6864 6960 96 454 7056 7152 7247 7343 7438 7534 7629 7725 7820 7916 96 455 8011 8107 8202 8298 8393 8488 8584 8679 8774 8870 95 456 8965 9060 9155 9250 9346 9441 9536 9631 9726 9821 95 457 9916 **11 *106 *201 *296 *391 *4S6 *5S1 *676 *771 95 458 660865 0960 1055 1150 1245 1339 1434 1529 1623 1718 95 459 1813 1907 2002 2096 2191 22S6 2380 2475 2569 2663 95 460 662758 2852 2947 3041 3135 3230 3324 3418 3512 3607 94 461 3701 3795 3889 3983 4078 4172 4266 4360 4454 4548 94 462 4642 4736 4830 4924 5018 5112 5206 5299 5393 5487 94 463 5581 5675 5769 5862 5956 6050 6143 6237 6331 6424 94 464 6518 6612 6705 6799 6892 6986 7079 7173 7266 7360 94 465 7453 7546 7640 7733 7826 7920 8013 8106 8199 8293 93 466 8386 8479 8572 8665 8759 8852 8945 9038 9131 9224 93 467 9317 9410 9503 9596 9689 9782 9875 9967 **60 *153 93 468 670246 0339 0431 0524 0617 0710 0802 0895 0988 1080 93 469 1173 1265 1358 1451 1543 1636 1728 1821 1913 2005 93 470 672098 2190 2283 2375 2467 2560 2652 2744 2836 2929 92 471 3021 3113 3205 3297 3390 3482 3574 3666 3758 3850 92 472 3942 4034 4126 4218 4310 4402 4494 4586 4677 4769 92 473 4861 4953 5045 5137 5228 5320 5412 5503 5595 5687 92 474 5778 5870 5962 6053 6145 6236 6328 6419 6511 6602 92 475 6694 6785 6876 6068 7059 7151 7242 7333 7424 7516 91 476 7607 7698 7789 7881 7972 8063 8154 8245 8336 8427 91 477 8518 8609 8700 8791 8882 8973 9064 9155 9246 9337 91 478 9428 9519 9610 9700 9791 9882 9973 **63 *154 *245 91 479 680336 0426 0517 0607 0698 0789 0879 0970 1060 1151 91 480 681241 1332 1422 1513 1603 1693 1784 1874 1964 2055 90 481 2145 2235 2326 2416 2506 2596 2686 2777 2867 2957 90 482 3047 3137 3227 3317 3407 3497 3587 3677 3767 3857 90 483 3947 4037 4127 4217 4307 4396 4486 4576 4666 4756 90 484 4845 4935 5025 5114 5204 5294 5383 5473 5563 5652 90 485 5742 5831 5921 6010 6100 6189 6279 6368 6458 6547 89 486 6636 6726 6815 6904 6994 7083 7172 7261 7351 7440 89 487 7529 7618 7707 7796 7886 7975 8064 8153 8242 8331 89 488 8420 8509 8598 8687 8776 8865 8953 9042 9131 9220 89 489 9309 9398 9486 9575 9664 9753 9841 9930 **19 *107 89 490 690196 0285 0373 0462 0550 0639 0728 0816 0905 0993 89 491 1081 1170 1258 1347 1435 1524 1612 1700 1789 1877 88 492 1965 2053 2142 2230 2318 2406 2494 2583 2671 2759 88 493 2847 2935 3023 3111 3199 3287 3375 3463 3551 3639 88 494 3727 3815 3903 3991 4078 4166 4254 4342 4430 4517 88 495 4605 4693 4781 4868 4956 5044 5131 5219 5307 5394 88 496 5482 5569 5657 5744 5832 5919 6007 6094 6182 6269 87 497 6356 6444 6531 6618 6706 6793 6880 6968 7055 7142 87 498 7229 7317 7404 7491 7578 7665 7752 7839 7926 8014 87 499 8101 8188 8275 8362 8449 8535 8622 8709 8796 8883 87 N. 1 2 3 4 5 6 7 8 9 D. TABLE XXIX (CONTINUED) 55 N. 1 2 3 4 5 6 7 8 9 D. 500 698970 9057 9144 9231 9317 9404 9491 9578 9664 9751 87 501 9838 9924 **11 **9S *184 *271 *35S *444 *531 *617 87 502 700704 0790 0877 0963 1050 1136 1222 1309 1395 1482 86 503 1568 1654 1741 1827 1913 1999 2086 2172 2258 2344 86 504 2431 2517 2603 2689 2775 2861 2947 3033 3119 3205 86 505 3291 3377 3463 3549 3635 3721 3807 3893 3979 4065 86 506 4151 4236 4322 4408 4494 4579 4665 4751 4837 4922 86 507 5008 5094 5179 5265 5350 5436 5522 5607 5693 5778 86 508 5864 5949 6035 6120 6206 6291 6376 6462 6547 6632 85 509 6718 6803 6888 6974 7059 7144 7229 7315 7400 7485 85 510 707570 7655 7740 7826 7911 7996 8081 8166 8251 8336 85 511 8421 8506 8591 8676 8761 8846 8931 9015 9100 9185 85 512 9270 9355 9440 9524 9609 9694 9779 9863 9948 **33 85 513 710117 0202 0287 0371 0456 0540 0625 0710 0794 0879 85 514 0963 1048 1132 1217 1301 1385 1470 1554 1639 1723 84 515 1807 1892 1976 2060 2144 2229 2313 2397 2481 2566 84 516 2650 2734 2818 2902 2986 3070 3154 3238 3323 3407 84 517 3491 3575 3659 3742 3826 3910 3994 4078 4162 4246 84 518 4330 4414 4497 4581 4665 4749 4833 4916 5000 5084 84 519 5167 5251 5335 5418 5502 5586 5669 5753 5836 5920 84 520 716003 6087 6170 6254 6337 6421 6504 6588 6671 6754 83 521 6838 6921 7004 7088 7171 7254 7338 7421 7504 7587 83 522 7671 7754 7837 7920 8003 8086 8169 8253 8336 8419 83 523 8502 8585 8668 8751 8834 8917 9000 9083 9165 9248 83 524 9331 9414 9497 9580 9663 9745 9828 9911 9994 ** 77 83 525 720159 0242 0325 0407 0490 0573 0655 0738 0821 0903 83 526 0986 1068 1151 1233 1316 1398 1481 1563 1646 1728 82 527 1811 1893 1975 2058 2140 2222 2305 2387 2469 2552 82 528 2634 2716 2798 2881 2963 3045 3127 3209 3291 3374 82 529 3456 3538 3620 3702 3784 3866 3948 4030 4112 4194 82 530 724276 4358 4440 4522 4604 4685 4767 4849 4931 5013 82 531 5095 5176 5258 5340 5422 5503 5585 5667 5748 5830 82 532 5912 5993 6075 6156 6238 6320 6401 6483 6564 6646 82 533 6727 6809 6890 6972 7053 7134 7216 7297 7379 7460 81 534 7541 7623 7704 7785 7866 7948 8029 8110 8191 8273 81 535 8354 8435 8516 8597 8678 8759 8841 8922 9003 9084 81 536 9165 9246 9327 9408 9489 9570 9651 9732 9813 9893 81 537 9974 **55 *136 *217 *298 *378 *459 *540 *621 *702 81 538 730782 0863 0944 1024 1105 1186 1266 1347 1428 1508 81 539 1589 1669 1750 1830 1911 1991 2072 2152 2233 2313 81 540 732394 2474 2555 2635 2715 2796 2876 2956 3037 3117 80 541 3197 3278 3358 3438 3518 3598 3679 3759 3839 3919 80 542 3999 4079 4160 4240 4320 4400 4480 4560 4640 4720 80 543 4800 4880 4960 5040 5120 5200 5279 5359 5439 5519 80 544 5599 5679 5759 5838 5918 5998 6078 6157 6237 6317 80 545 6397 6476 6556 6635 6715 6795 6874 6954 7034 7113 80 546 7193 7272 7352 7431 7511 7590 7670 7749 7829 7908 79 547 7987 8067 8146 8225 8305 8384 8463 8543 8622 8701 79 548 8781 8860 8939 9018 9097 9177 .9256 9335 9414 9493 79 549 9572 9651 9731 9810 9889 9968 ** 47 *126 *205 *284 79 N. 1 2 3 4 5 6 7 8 9 D. 56 TABLE XXIX (CONTINUED) N. 1 2 3 4 5 6 7 8 9 D. 550 740363 0442 0521 0600 0678 0757 0836 0915 0994 1073 79 551 1152 1230 1309 1388 1467 1546 1624 1703 17S2 I860 79 552 1939 2018 2096 2175 2254 2332 2411 2489 25 68 2647 79 553 2725 2804 2882 2961 3039 3118 3196 3275 3353 3431 78 554 3510 3588 3667 3745 3823 3902 39SO 4058 4136 4215 78 555 4293 4371 4449 4528 4606 4684 4762 4840 4919 4997 78 556 5075 5153 5231 5309 5387 5465 5543 5621 5699 5777 78 557 5855 5933 6011 6089 6167 6245 6323 6401 6479 6556 78 558 6634 6712 6790 6868 6945 7023 7101 7179 7256 7334 78 559 7412 7489 7567 7645 7722 7800 7878 7955 8033 8110 78 560 748188 8266 8343 8421 8498 8576 8653 8731 8808 8885 77 561 8963 9040 9118 9195 9272 9350 9427 9504 9582 9659 77 562 9736 9814 9891 9968 **45 *123 *200 *277 *354 *431 77 563 750508 0586 0663 0740 0817 0894 0971 1048 1125 1202 77 564 1279 1356 1433 1510 1587 1664 1741 1818 1895 1972 77 565 2048 2125 2202 2279 2356 2433 2509 2586 2663 2740 77 566 2816 2893 2970 3047 3123 3200 3277 3353 3430 3506 77 567 3583 3660 3736 3813 3889 3966 4042 4119 4195 4272 77 568 4348 4425 4501 4578 4654 4730 4807 4883 4960 5036 76 569 5112 5189 5265 5341 5417 5494 5570 5646 5722 5799 76 570 755875 5951 6027 6103 6180 6256 6332 6408 6484 6560 76 571 6636 6712 6788 6864 6940 7016 7092 7168 7244 7320 76 572 7396 7472 7548 7624 7700 7775 7851 7927 8003 8079 76 573 8155 8230 8306 8382 8458 8533 8609 8685 8761 8836 76 574 8912 8988 9063 9139 9214 9290 9366 9441 9517 9592 76 ' 575 9668 9743 9819 9894 9970 **45 *121 *196 *272 *347 75 576 760422 0498 0573 0649 0724 0799 0875 0950 1025 1101 75 577 1176 1251 1326 1402 1477 1552 1627 1702 1778 1853 75 578 1928 2003 2078 2153 2228 2303 2378 2453 2529 2604 75 579 2679 2754 2829 2904 2978 3053 3128 3203 3278 3353 75 580 763428 3503 3578 3653 3727 3802 3877 3952 4027 4101 75 581 4176 4251 4326 4400 4475 4550 4624 4699 4774 4848 75 582 4923 4998 5072 5147 5221 5296 5370 5445 5520 5594 75 583 5669 5743 5818 5892 5966 6041 6115 6190 6264 6338 74 584 6413 6487 6562 6636 6710 6785 6859 6933 7007 7082 74 585 7156 7230 7304 7379 7453 7527 7601 7675 7749 7823 74 586 7898 7972 8046 8120 8194 8268 8342 8416 8490 8564 74 587 8638 8712 8786 8860 8934 9008 9082 9156 9230 9303 74 588 9377 9451 9525 9599 9673 9746 9820 9894 9968 **42 74 589 770115 0189 0263 0336 0410 0484 0557 0631 0705 0778 74 590 770852 0926 0999 1073 1146 1220 1293 1367 1440 1514 74 591 1587 1661 1734 1808 1881 1955 2028 2102 2175 2248 73 592 2322 2395 2468 2542 2615 2688 2762 2835 2908 2981 73 593 3055 3128 3201 3274 3348 3421 3494 3567 36iO 3713 73 594 3786 3860 3933 4006 4079 4152 4225 4298 '4371 4444 73 595 4517 4590 4663 4736 4809 4882 4955 5028 5100 5173 73 596 5246 5319 5392 5465 5538 5610 5683 5756 5829 5902 73 597 5974 6047 6120 6193 6265 6338 6411 6483 6556 6629 73 598 6701 6774 6846 6919 6992 7064 7137 7209 7282 7354 73 599 7427 7499 7572 7644 7717 7789 7862 7934 8006 8079 72 N. 1 2 3 4 5 6 7 8 9 D. TABLE XXIX (CONTINUED) 57 N. 1 2 3 4 5 6 7 8 9 D. 600 778151 8224 8296 8368 8441 8513 8585 8658 8730 8802 72 601 8874 8947 9019 9091 9163 9236 9308 9380 9452 9524 72 602 9596 9669 9741 9813 9885 9957 **29 *101 *173 *245 72 603 780317 0389 0461 0533 0605 0677 0749 0821 0893 0965 72 604 14)37 1109 1181 1253 1324 1396 1468 1540 1612 1684 72 605 1755 1827 1899 1971 2042 2114 2186 2258 2329 2401 72 606 2473 2544 2616 2688 2759 2831 2902 2974 3046 3117 72 607 3189 3260 3332 3403 3475 3546 3618 3689 3761 3832 71 608 3904 3975 4046 4118 4189 4261 4332 4403 4475 4546 71 609 4617 4689 4760 4831 4902 4974 5045 5116 5187 5259 71 610 785330 5401 5472 5543 5615 5686 5757 5828 5899 5970 71 611 6041 6112 6183 6254 6325 6396 6467 6538 6609 6680 71 612 6751 6822 6893 6964 7035 7106 7177 7248 7319 7390 71 613 7460 7531 7602 7673 7744 7815 7885 7956 8027 8098 71 614 8168 8239 8310 8381 8451 8522 8593 8663 8734 8804 71 615 8875 8946 9016 9087 9157 9228 9299 9369 9440 9510 71 616 9581 9651 9722 9792 9863 9933 *** 4 **74 *144 *215 70 617 790285 0356 0426 0496 0567 0637 0707 0778 0848 0918 70 618 0988 1059 1129 1199 1269 1340 1410 1480 1550 1620 70 619 1691 1761 1831 1901 1971 2041 2111 2181 2252 2322 70 620 792392 2462 2532 2602 2672 2742 2812 2882 2952 3022 70 621 3092 3162 3231 3301 3371 3441 3511 3581 3651 3721 70 ' 622 3790 3860 3930 4000 4070 4139 4209 4279 4349 4418 70 623 4488 4558 4627 4697 4767 4836 4906 4976 5045 5115 70 624 5185 5254 5324 5393 5463 5532 5602 5672 5741 5811 70 625 5880 5949 6019 6088 6158 6227 6297 6366 6436 6505 69 626 6574 6644 6713 6782 6852 6921 6990 7060 7129 7198 69 627 7268 7337 7406 7475 7545 7614 7683 7752 7821 7890 69 628 7960 8029 8098 8167 8236 8305 8374 8443 8513 8582 69 629 8651 8720 8789 8858 8927 8996 9065 9134 9203 9272 69 630 799341 9409 9478 9547 9616 9685 9754 9823 9892 9961 69 631 800029 0098 0167 0236 0305 0373 0442 0511 0580 0648 69 632 0717 0786 0854 0923 0992 1061 1129 1198 1266 1335 69 633 1404 1472 1541 1609 1678 1747 1815 1884 1952 2021 69 634 2089 2158 2226 2295 2363 2432 2500 2568 2637 2705 69 635 2774 2842 2910 2979 3047 3116 3184 3252 3321 3389 68 636 3457 3525 3594 3662 3730 3798 3867 3935 4003 4071 68 637 4139 4208 4276 4344 4412 4480 4548 4616 4685 4753 68 638 4821 4889 4957 5025 5093 5161 5229 5297 5365 5433 68 639 5501 5569 5637 5705 5773 5841 5908 5976 6044 6112 68 640 806180 6248 6316 6384 6451 6519 6587 6655 6723 6790 68 641 6858 6926 6994 7061 7129 7197 7264 7332 7400 7467 68 642 7535 7603 7670 7738 7806 7873 7941 8008 8076 8143 68 643 8211 8279 8346 8414 8481 8549 8616 8684 8751 8818 67 644 8886 8953 9021 9088 9156 9223 9290 9358 9425 9492 67 645 9560 9627 9694 9762 9829 9896 9964 **31 **9S *165 67 646 810233 0300 0367 0434 0501 0569 0636 0703 0770 0837 67 647 0904 0971 1039 1106 1173 1240 1307 1374 1441 1508 67 648 1575 1642 1709 1776 1843 1910 1977 2044 2111 2178 67 649 2245 2312 2379 2445 2512 2579 2646 2713 2780 2847 67 N. 1 2 3 4 5 6 7 8 9 D. 58 TABLE XXIX (CONTINUED) N. 1 2 3 4 5 6 7 8 9 D. 650 812913 2980 3047 3114 3181 3247 3314 3381 3448 3514 67 651 3581 3648 3714 3781 3848 3914 3981 4048 4114 4181 67 652 4248 4314 4381 4447 4514 4581 4647 4714 4780 4847 67 653 4913 4980 5046 5113 5179 5246 5312 5378 5445 5511 66 654 5578 5644 5711 5777 5843 5910 5976 6042 6109 6175 66 655 6241 6308 6374 6440 6506 6573 6639 6705 6771 6838 66 656 6904 6970 7036 7102 7169 7235 7301 7367 7433 7499 66 657 7565 7631 7698 7764 7830 7896 7962 8028 8094 8160 66 658 8226 8292 8358 8424 8490 8556 8622 8688 8754 8820 66 659 8885 8951 9017 9083 9149 9215 9281 9346 9412 9478 66 660 819544 9610 9676 9741 9807 9873 9939 ##*4 **70 *136 66 661 820201 0267 0333 0399 0464 0530 0595 0661 0727 0792 66 662 0858 0924 0989 1055 1120 1186 1251 1317 1382 1448 66 663 1514 1579 1645 1710 1775 1841 1906 1972 2037 2103 65 664 2168 2233 2299 2364 2430 2495 2560 2626 2691 2756 65 665 2822 2887 2952 3018 3083 3148 3213 3279 3344 3409 65 666 3474 3539 3605 3670 3735 3SOO 3865 3930 3996 4061 65 667 4126 4191 4256 4321 4386 4451 4516 4581 4646 4711 65 668 4776 4841 4906 4971 5036 5101 5166 5231 5296 5361 65 669 5426 5491 5556 5621 5686 5751 5815 5880 5945 6010 65 670 826075 6140 6204 6269 6334 6399 6464 6528 6593 6658 65 671 6723 6787 6852 6917 6981 7046 7111 7175 7240 7305 65 672 7369 7434 7499 7563 7628 7692 7757 7821 7SS6 7951 65 673 8015 8080 8144 8209 8273 833S 8402 8467 8531 8595 64 674 8660 8724 8789 SS53 8918 S9S2 9046 9111 9175 9239 64 675 9304 9368 9432 9497 9561 9625 9690 9754 9S18 9882 64 676 9947 ##H **75 *139 *204 *26S *332 *396 *460 *525 64 677 830589 0653 0717 0781 0845 0909 0973 1037 1102 1166 64 678 1230 1294 1358 1422 I486 1550 1614 1678 1742 1805 64 679 1870 1934 1998 2062 2126 2189 2253 2317 2381 2445 64 680 832509 2573 2637 2700 2764 2828 2892 2956 3020 3083 64 681 3147 3211 3275 3338 3402 3466 3530 3593 3657 3721 64 682 3784 3848 3912 3975 4039 4103 4166 4230 4294 4357 64 683 4421 4484 4548 4611 4675 4739 4802 4866 4929 4993 64 684 5056 5120 5183 5247 5310 5373 5437 5500 5564 5627 63 685 5691 5754 5817 5881 5944 6007 6071 6134 6197 6261 63 686 6324 6387 6451 6514 6577 6641 6704 6767 6830 6894 63 687 6957 7020 7083 7146 7210 7273 7336 7399 7462 7525 63 688 7588 7652 7715 7778 7841 7904 7967 8030 8093 8156 63 689 8219 8282 8345 8408 8471 8534 8597 8660 8723 8786 63 690 838849 8912 8975 9038 9101 9164 9227 9289 9352 9415 63 691 9478 9541 9604 9667 9729 9792 9855 9918 9981 **43 63 692 840106 0169 0232 0294 0357 0420 0482 0545 0608 0671 63 693 0733 0796 0859 0921 0984 1046 1109 1172 1234 1297 63 694 1359 1422 1485 1547 1610 1672 1735 1797 1860 1922 63 695 1985 2047 2110 2172 2235 2297 2360 2422 2484 2547 62 696 2609 2672 2734 2796 2859 2921 2983 3046 3108 3170 62 697 3233 3295 3357 3420 3482 3544 3606 3669 3731 3793 62 698 3855 3918 3980 4042 4104 4166 4229 4291 4353 4415 62 699 4477 4539 4601 4664 4726 4788 4850 4912 4974 5036 62 N. 1 2 3 4 5 6 7 8 9 D. TABLE XXIX (CONTINUED) 59 N. 1 2 3 4 5 6 7 8 9 D. 700 845098 5160 5222 5284 5346 5408 5470 5532 5594 5656 62 701 5718 5780 5842 5904 5966 6028 6090 6151 6213 6275 62 702 6337 6399 6461 6523 6585 6646 6708 6770 6832 6894 62 703 6955 7017 7079 7141 7202 7264 7326 7388 7449 7511 62 704 7573 7634 7696 7758 7819 7881 7943 8004 8066 8128 62 705 8189 8251 8312 8374 8435 8497 8559 8620 8682 8743 62 706 8805 8866 8928 8989 9051 9112 9174 9235 9297 9358 61 707 9419 9481 9542 9604 9665 9726 9788 9849 9911 9972 61 70S 850033 0095 0156 0217 0279 0340 0401 0462 0524 0585 61 709 0646 0707 0769 OS30 0891 0952 1014 1075 1136 1197 61 710 851258 1320 1381 1442 1503 1564 1625 1686 1747 1809 61 711 1870 1931 1992 2053 2114 2175 2236 2297 2358 2419 61 712 2480 2541 2602 2663 2724 2785 2846 2907 2968 3029 61 713 3090 3150 3211 3272 3333 3394 3455 3516 3577 3637 61 714 3698 3759 3820 3881 3941 4002 4063 4124 4185 4245 61 715 4306 4367 4428 4488 4549 4610 4670 4731 4792 4852 61 716 4913 4974 5034 5095 5156 5216 5277 5337 5398 5459 61 717 5519 5580 5640 5701 5761 5822 5882 5943 6003 6064 61 718 6124 61S5 6245 6306 6366 6427 6487 6548 6608 6668 60 719 6729* 6789 6850 6910 6970 7031 7091 7152 7212 7272 60 720 857332 7393 7453 7513 7574 7634 7694 7755 7815 7875 60 721 7935 7995 8056 8116 8176 8236 8297 8357 8417 8477 60 722 8537 8597 8657 8718 8778 8838 8898 8958 9018 9078 60 723 9138 9198 9258 9318 9379 9439 9499 9559 9619 9679 60 724 9739 9799 9859 9918 9978 **3S **9S *158 *21S *278 60 725 860338 0398 0458 0518 0578 0637 0697 0757 0817 0877 60 726 0937 0996 1056 1116 1176 1236 1295 1355 1415 1475 60 727 1534 1594 1654 1714 1773 1833 1893 1952 2012 2072 60 728 2131 2191 2251 2310 2370 2430 2489 2549 2608 2668 60 729 2728 2787 2847 2906 2966 3025 3085 3144 3204 3263 60 730 863323 3382 3442 3501 3561 3620 3680 3739 3799 3858 59 731 3917 3977 4036 4096 4155 4214 4274 4333 4392 4452 59 732 4511 4570 4630 4689 4748 4808 4867 4926 4985 5045 59 733 5104 5163 5222 5282 5341 5400 5459 5519 5578 5637 59 734 5696 5755 5814 5874 5933 5992 6051 6110 6169 6228 59 735 6287 6346 6405 6465 6524 6583 6642 6701 6760 6819 59 736 6878 6937 6996 7055 7114 7173 7232 7291 7350 7409 59 737 7467 7526 7585 7644 7703 7762 7821 7880 7939 7998 59 738 8056 8115 8174 8233 8292 8350 84 09 8468 8527 8586 59 739 8644 8703 8762 8821 8879 8938 8997 9056 9114 9173 59 740 869232 9290 9349 9408 9466 9525 9584 9642 9701 9760 59 741 9818 9877 9935 9994 **53 *111 *170 *228 *287 *345 59 742 870404 0462 0521 0579 0638 0696 0755 0813 0872 0930 58 743 0989 1047 1106 1164 1223 1281 1339 1398 1456 1515 58 744 1573 1631 1690 1748 1806 1865 1923 1981 2040 2098 58 745 2156 2215 2273 2331 2389 2448 2506 2564 2622 2681 58 746 2739 2797 2855 2913 2972 3030 3088 3146 3204 3262 58 747 3321 3379 3437 3495 3553 3611 3669 3727 3785 3844 58 748 3902 3960 4018 4076 4134 4192 4250 4308 4366 4424 58 749 4482 4540 4598 4656 4714 4772 4830 4888 4945 5003 58 N. 1 2 3 4 5 6 7 8 9 D. 60 TABLE XXIX (CONTINUED) N. 1 2 3 4 5 6 7 8 9 D. 750 875061 5119 5177 5235 5293 5351 5409 5466 5524 5582 58 751 5640 5698 5756 5813 5871 5929 5987 6045 6102 6160 58 752 6218 6276 6333 6391 6449 6507 6564 6622 6680 6737 58 753 6795 6S53 6910 6968 7026 7083 7141 7199 7256 7314 58 754 7371 7429 7487 7544 7602 7659 7717 7774 7832 7889 58 755 7947 8004 8062 8119 8177 8234 8292 8349 8407 8464 57 756 8522 8579 8637 8694 8752 8809 8866 8924 8981 9039 57 757 9096 9153 9211 9268 9325 9383 9440 9497 9555 9612 57 758 9669 9726 9784 9841 9898 9956 **13 **70 *127 *185 57 759 880242 0299 0356 0413 0471 0528 0585 0642 0699 0756 57 760 880814 0871 0928 0985 1042 1099 1156 1213 1271 1328 57 761 1385 1442 1499 1556 1613 1670 1727 1784 1841 1898 57 762 1955 2012 2069 2126 21S3 2240 2297 2354 2411 2468 57 763 2525 2581 2638 2695 2752 2809 2866 2923 2980 3037 57 764 3093 3150 3207 3264 3321 3377 3434 3491 3548 3605 57 765 3661 3718 3775 3832 3SS8 3945 4002 4059 4115 4172 57 766 4229 4285 4342 4399 4455 4512 4569 4625 4682 4739 57 767 4795 4852 4909 4965 5022 5078 5135 5192 5248 5305 57 768 5361 5418 5474 5531 5587 5644 5700 5757 5813 5870 57 769 5926 5983 6039 6096 6152 6209 6265 6321 63 78 6434 56 770 8S6491 6547 6604 6660 6716 6773 6829 6885 6942 6998 56 771 7054 7111 7167 7223 7280 7336 7392 7449 7505 7561 56 772 7617 7674 7730 7786 7842 7898 7955 8011 8067 8123 56 .773 8179 8236 8292 8348 8404 8460 8516 8573 8629 8685 56 774 8741 8797 8853 8909 8965 9021 9077 9134 9190 9246 56 775 9302 9358 9414 9470 9526 9582 9638 9694 9750 9806 56 776 9862 9918 9974 **30 **S6 *141 *197 *253 *309 *365 56 777 890421 0477 0533 0589 0645 0700 0756 0812 0868 0924 56 778 0980 1035 1091 1147 1203 1259 1314 1370 1426 1482 56 779 1537 1593 1649 1705 1760 1816 1872 1928 1983 2039 56 780 892095 2150 2206 2262 2317 2373 2429 2484 2540 2595 56 781 2651 2707 2762 2818 2873 2929 2985 3040 3096 3151 56 782 3207 3262 3318 3373 3429 3484 3540 3595 3651 3706 56 783 3762 3817 3873 3928 3984 4039 4094 4150 4205 4261 55 784 4316 4371 4427 4482 4538 4593 4648 4704 4759 4814 55 785 4870 4925 4980 5036 5091 5146 5201 5257 5312 5367 55 786 5423 5478 5533 5588 5644 5699 5754 5809 5864 5920 55 787 5975 6030 6085 6140 6195 6251 6306 6361 6416 6471 55 788 6526 6581 6636 6692 6747 6802 6857 6912 6967 7022 55 789 7077 7132 7187 7242 7297 7352 7407 7462 7517 7572 55 790 897627 7682 7737 7792 7847 7902 7957 8012 8067 8122 55 791 8176 8231 8286 8341 8396 8451 8506 8561 8615 8670 55 792 8725 8780 8835 8890 8944 8999 9054 9109 9164 9218 55 793 9273 9328 9383 9437 9492 9547 9602 9656 9711 9766 55 794 9821 9875 9930 9985 ** 39 **94 *149 *203 *258 *312 55 795 900367 0422 0476 0531 0586 0640 0695 0749 0804 0859 55 796 0913 0968 1022 1077 1131 1186 1240 1295 1349 1404 55 797 1458 1513 1567 1622 1676 1731 1785 1840 1894 1948 54 798 2003 2057 2112 2166 2221 2275 2329 2384 2438 2492 54 799 2547 2601 2655 2710 2764 2818 2873 2927 2981 3036 54 N. 1 2 3 4 5 6 7 8 9 D. TABLE XXIX (CONTINUED) 61 N. 1 2 3 4 5 6 7 8 9 D. 800 903090 3144 3199 3253 3307 3361 3416 3470 3524 3578 54 801 3633 3687 3741 3795 3849 3904 3958 4012 4066 4120 54 802 4174 4229 4283 4337 4391 4445 4499 4553 4607 4661 54 803 4716 4770 4824 4878 4932 4986 5040 5094 5148 5202 54 804 5256 5310 5364 5418 5472 5526 5580 5634 5688 5742 54 805 5796 5850 5904 5958 6012 6066 6119 6173 6227 6281 54 806 6335 6389 6443 6497 6551 6604 6658 6712 6766 6820 54 807 6874 6927 6981 7035 7089 7143 7196 7250 7304 7358 54 808 7411 7465 7519 7573 7626 7680 7734 7787 7841 7895 54 809 7949 8002 8056 8110 8163 8217 8270 8324 8378 8431 54 810 908485 8539 8592 8646 8699 8753 8807 8860 8914 8967 54 811 9021 9074 9128 9181 9235 9289 9342 9396 9449 9503 54 812 9556 9610 9663 9716 9770 9823 9877 9930 9984 **37 53 813 910091 0144 0197 0251 0304 0358 0411 0464 0518 0571 53 814 0624 0678 0731 0784 0838 0891 0944 0998 1051 1104 53 815 1158 1211 1264 1317 1371 1424 1477 1530 1584 1637 53 816 1690 1743 1797 1850 1903 1956 2009 2063 2116 2169 53 817 2222 2275 2328 2381 2435 2488 2541 2594 2647 2700 53 818 2753 2806 2859 2913 2966 3019 3072 3125 3178 3231 53 819 3284 3337 3390 3443 3496 3549 3602 3655 3708 3761 53 820 913814 3867 3920 3973 4026 4079 4132 4184 4237 4290 53 821 4343 4396 4449 4502 4555 4608 4660 4713 4766 4819 53 822 4872 4925 4977 5030 5083 5136 5189 5241 5294 5347 53 823 5400 5453 5505 5558 5611 5664 5716 5769 5822 5875 53 824 5927 5980 6033 6085 6138 6191 6243 6296 6349 6401 53 825 6454 6507 6559 6612 6664 6717 6770 6822 6875 6927 53 826 6980 7033 7085 7138 7190 7243 7295 7348 7400 7453 53 827 7506 7558 7611 7663 7716 7768 7820 7873 7925 7978 52 828 8030 8083 8135 8188 82-40 8293 8345 8397 8450 8502 52 829 8555 8607 8659 8712 8764 S816 8869 8921 8973 9026 52 830 919078 9130 9183 9235 9287 9340 9392 9444 9496 9549 52 831 9601 9653 9706 9758 9810 9862 9914 9967 **1 9 **71 52 832 920123 0176 0228 0280 0332 0384 0436 0489 0541 0593 52 833 0645 0697 0749 0801 0853 0906 0958 1010 1062 1114 52 834 1166 1218 1270 1322 1374 1426 1478 1530 1582 1634 52 835 1686 1738 1790 1842 1894 1946 1998 2050 2102 2154 52 836 2206 2258 2310 2362 2414 2466 2518 2570 2622 2674 52 837 2725 2777 2829 2881 2933 2985 3037 3089 3140 3192 52 838 3244 3296 3348 3399 3451 3503 3555 3607 3658 3710 52 839 3762 3814 3865 3917 3969 4021 4072 4124 4176 4228 52 840 924279 4331 4383 4434 4486 4538 4589 4641 4693 4744 52 841 4796 4848 4899 4951 5003 5054 5106 5157 5209 5261 52 842 5312 5364 5415 5467 5518 5570 5621 5673 5725 5776 52 843 5828 5879 5931 5982 6034 6085 6137 6188 6240 6291 51 844 6342 6394 6445 6497 6548 6600 6651 6702 6754 6805 51 845 6857 6908 6959 7011 7062 7114 7165 7216 7268 7319 51 846 7370 7422 7473 7524 7576 7627 7678 7730 7781 7832 51 847 7883 7935 79S6 8037 8088 8140 9191 8242 8293 8345 51 848 8396 8447 8498 8549 8601 8652 8703 8754 8805 8857 51 849 8908 8959 9010 9061 9112 9163 9215 9266 9317 9368 51 N. 1 2 3 4 5 6 7 8 9 D. 62 TABLE XXIX (COXTIXUED) N. 1 2 3 4 5 6 7 8 9 D. 850 929419 9470 9521 9572 9623 9674 9725 9776 9827 9879 51 851 9930 9981 **32 **S3 *134 *185 *236 *287 *338 *389 51 852 930440 0491 0542 0592 0643 0694 0745 0796 0847 0898 51 853 0949 1000 1051 1102 1153 1204 1254 1305 1356 1407 51 854 1458 1509 1560 1610 1661 1712 1763 1814 1865 1915 51 855 1966 2017 2068 2118 2169 2220 2271 2322 2372 2423 51 856 2474 2524 2575 2626 2677 2727 2778 2829 2879 2930 51 857 2981 3031 3082 3133 3183 3234 3285 3335 3386 3437 51 858 34S7 3538 3589 3639 3690 3740 3791 3841 3892 3943 51 859 3993 4044 4094 4145 4195 4246 4296 4347 4397 4448 51 860 934498 4549 4599 4650 4700 4751 4801 4852 4902 4953 50 861 5003 5054 5104 5154 5205 5255 5306 5356 5406 5457 50 862 5507 5558 5608 5658 5709 5759 5809 5860 5910 5960 50 863 6011 6061 6111 6162 6212 6262 6313 6363 6413 6463 50 864 6514 6564 6614 6665 6715 6765 6815 6865 6916 6966 50 865 7016 7066 7117 7167 7217 7267 7317 7367 7418 7468 50 866 7518 7568 7618 7668 7718 7769 7819 7869 7919 7969 50 867 8019 8069 8119 8169 8219 8269 8320 8370 8420 8470 50 868 8520 8570 8620 8670 8720 8770 8820 8870 8920 8970 50 869 9020 9070 9120 9170 9220 9270 9320 9369 9419 9469 50 870 939519 9569 9619 9669 9719 9769 9819 9869 9918 9968 50 871 940018 006S 0118 0168 0218 0267 0317 0367 0417 0467 50 872 0516 0566 0616 0666 0716 0765 0815 0865 0915 0964 50 873 1014 1064 1114 1163 1213 1263 1313 1362 1412 1462 50 874 1511 1561 1611 1660 1710 1760 1809 1859 1909 1958 50 875 2008 2058 2107 2157 2207 2256 2306 2355 2405 2455 50 876 2504 2554 2603 2653 2702 2752 2801 2851 2901 2950 50 877 3000 3049 3099 3148 3198 3247 3297 3346 3396 3445 49 878 3495 3544 3593 3643 3692 3742 3791 3841 3890 3939 49 879 3989 4038 4088 4137 4186 4236 4285 4335 4384 4433 49 880 944483 4532 4581 4631 4680 4729 4779 4828 4877 4927 49 881 4976 5025 5074 5124 5173 5222 5272 5321 5370 5419 49 882 5469 5518 5567 5616 5665 5715 5764 5813 5862 5912 49 883 5961 6010 6059 6108 6157 6207 6256 6305 6354 6403 49 884 6452 6501 6551 6600 6649 6698 6747 6796 6845 6894 49 885 6943 6992 7041 7090 7140 7189 7238 7287 7336 7385 49 886 7434 7483 7532 7581 7630 7679 7728 7777 7826 7875 49 887 7924. 7973 8022 8070 8119 8168 8217 8366 8315 8364 49 888 8413 8462 8511 8560 8609 8657 8706 8755 8804 8853 49 889 8902 8951 8999 9048 9097 9146 9195 9244 9292 9341 49 890 949390 9439 9488 9536 9585 9634 9683 9731 9780 9829 49 891 9878 9926 9975 **24 **73 *121 *170 *219 *267 *316 49 892 950365 0414 0462 0511 0560 0608 0657 0706 0754 0803 49 893 0851 0900 0949 0997 1046 1095 1143 1192 1240 1289 49 894 1338 1386 1435 1483 1532 1580 1629 1677 1726 1775 49 895 1823 1872 1920 1969 2017 2066 2114 2163 2211 2260 48 896 2308 2356 2405 2453 2502 2550 2599 2647 2696 2744 48 897 2792 2841 2889 2938 2986 3034 3083 3131 3180 3228 48 898 3276 3325 3373 3421 3470 3518 3566 3615 3663 3711 48 899 3760 3808 3856 3905 3953 4001 4049 4098 4146 4194 48 W. 1 2 3 4 5 6 7 8 9 D. TABLE XXIX (CONTINUED) 63 N. 1 2 3 4 5 6 7 8 9 D. 900 954243 4291 4339 4387 4435 4484 4532 4580 4628 4677 48 901 4725 4773 4821 4869 4918 4966 5014 5062 5110 5158 48 902 5207 5255 5303 5351 5399 5447 5495 5543 5592 5640 48 903 5688 5736 5784 5832 5880 5928 5976 6024 6072 6120 48 904 6168 6216 6265 6313 6361 6409 6457 6505 6553 6601 48 905 6649 6697 6745 6793 6840 6888 6936 6984 7032 7080 48 906 7128 7176 7224 7272 7320 7368 7416 7464 7512 7559 48 907 7607 7655 7703 7751 7799 7847 7894 7942 7990 8038 48 908 8086 8134 8181 8229 8277 8325 8373 8421 8468 8516 48 909 8564 8612 8659 8707 8755 8803 8850 8898 8946 8994 48 910 959041 9089 9137 9185 9232 9280 9328 9375 9423 9471 48 911 9518 9566 9614 9661 9709 9757 9804 9852 9900 9947 48 912 9995 **42 **90 *13S *185 *233 *2SO *32S *376 *423 48 913 960471 0518 0566 0613 0661 0709 0756 0804 0851 0899 48 914 0946 0994 1041 1089 1136 1184 1231 1279 1326 1374 47 915 1421 1469 1516 1563 1611 1658 1706 1753 1801 1848 47 916 1895 1943 1990 2038 2085 2132 2180 2227 2275 2322 47 917 2369 2417 2464 2511 2559 2606 2653 2701 2748 2795 47 918 2843 2890 2937 2985 3032 3079 3126 3174 3221 3268 47 919 3316 3363 3410 3457 3504 3552 3599 3646 3693 3741 47 920 963788 3835 3882 3929 3977 4024 4071 4118 4165 4212 47 921 4260 4307 4354 4401 4448 4495 4542 4590 4637 4684 47 922 4731 4778 4825 4872 4919 4966 5013 5061 5108 5155 47 923 5202 5249 5296 5343 5390 5437 5484 5531 5578 5625 47 924 5672 5719 5766 5813 5860 5907 5954 6001 6048 6095 47 925 6142 6189 6236 6283 6329 6376 6423 6470 6517 6564 47 926 6611 6658 6705 6752 6799 6845 6892 6939 6986 7033 47 927 7080 7127 7173 7220 7267 7314 7361 7408 7454 7501 47 928 7548 7595 7642 7688 7735 7782 7829 7S75 7922 7969 47 929 8016 8062 8109 8156 8203 8249 8296 8343 8390 8436 .47 930 968483 8530 8576 8623 8670 8716 8763 8810 8856 8903 47 931 8950 8996 9043 9090 9136 9183 9229 9276 9323 9369 47 932 9416 9463 9509 9556 9602 9649 9695 9742 9789 9835 47 933 9882 9928 9975 *#21 **6S #114 *161 *207 *254 *300 47 934 970347 0393 0440 0486 0533 0579 0626 0672 0719 0765 46 935 0812 0858 0904 0951 0997 1044 1090 1137 1183 1229 46 936 1276 1322 1369 1415 1461 1508 1554 1601 1647 1693 46 937 1740 1786 1832 1879 1925 1971 2018 2064 2110 2157 46 938 2203 2249 2295 2342 2388 2434 2481 2527 2573 2619 46 939 2666 2712 2758 2804 2851 2897 2943 2989 3035 3082 46 940 973128 3174 3220 3266 3313 3359 3405 3451 3497 3543 46 941 3590 3636 3682 3728 3774 3820 3866 3913 3959 4005 46 942 4051 4097 4143 4189 4235 4281 4327 4374 4420 4466 46 943 4512 4558 4604 4650 4696 4742 4788 4834 4880 4926 46 944 4972 5018 5064 5110 5156 5202 5248 5294 5340 5386 46 945 5432 5478 5524 5570 5616 5662 5707 5753 5799 5845 46 946 5891 5937 5983 6029 6075 6121 6167 6212 6258 6304 46 947 6350 6396 6442 6488 6533 6579 6625 6671 6717 6763 46 948 6808 6854 6900 6946 6992 7037 7083 7129 7175 7220 46 949 7266 7312 7358 7403 7449 7495 7541 7586 7632 7678 46 N. 1 2 3 4 5 6 7 8 9 D. TABLE XXIX (CONTINUED) N. 1 2 3 4 5 6 7 8 9 D. 950 977724 7769 7815 7861 7906 7952 7998 8043 8089 8135 46 951 8181 8226 8272 8317 8363 8409 8454 8500 8546 8591 46 952 8637 8683 8728 8774 8819 8865 8911 8956 9002 9047 46 953 9093 9138 9184 9230 9275 9321 9366 9412 9457 9503 46 954 9548 9594 9639 9685 9730 9776 9821 9867 9912 9958 46 955 980003 0049 0094 0140 0185 0231 0276 0322 0367 0412 45 956 0458 0503 0549 0594 0640 0685 0730 0776 0821 0867 45 957 0912 0957 1003 104S 1093 1139 1184 1229 1275 1320 45 958 1365 1411 1456 1501 1547 1592 1637 1683 1728 1773 45 959 1819 1864 1909 1954 2000 2045 2090 2135 2181 2226 45 960 982271 2316 2362 2407 2452 2497 2543 2588 2633 2678 45 961 2723 2769 2814 2859 2904 2949 2994 3040 3085 3130 45 962 3175 3220 3265 3310 3356 3401 3446 3491 3536 3581 45 963 3626 3671 3716 3762 3807 3852 3897 3942 3987 4032 45 964 4077 4122 4167 4212 4257 4302 4347 4392 4437 4482 45 965 4527 4572 4617 4662 4707 4752 4797 4842 4887 4932 45 966 4977 5022 5067 5112 5157 5202 5247 5292 5337 5382 45 967 5426 5471 5516 5561 5606 5651 5696 5741 5786 5830 45 968 5875 5920 5965 6010 6055 6100 6144 6189 6234 6279 45 969 6324 6369 6413 6458 6503 6548 6593 6637 6682 6727 45 970 986772 6817 6861 6906 6951 6996 7040 7085 7130 7175 45 971 7219 7264 7309 7353 7398 7443 7488 7532 7577 7622 45 972 7666 7711 7756 7800 7845 7890 7934 7979 8024 8068 45 973 8113 8157 8202 8247 8291 8336 83S1 8425 8470 8514 45 974 8559 8604 8648 8693 8737 8782 8826 8871 8916 8960 45 975 9005 9049 9094 9138 9183 9227 9272 9316 9361 9405 45 976 9450 9494 9539 9583 9628 9672 9717 9761 9806 9850 44 977 9895 9939 9983 **2S **72 *117 *161 *206 *250 *294 44 978 990339 0383 0428 0472 0516 0561 0605 0650 0694 0738 44 979 0783 0827 0871 0916 0960 1004 1049 1093 1137 1182 44 980 991226 1270 1315 1359 1403 1448 1492 1536 1580 1625 44 981 1669 1713 1758 1802 1846 1890 1935 1979 2023 2067 44 982 2111 2156 2200 2244 2288 2333 2377 2421 2465 2509 44 983 2554 2598 2642 2686 2730 2774 2819 2863 2907 2951 44 984 2995 3039 3083 3127 3172 3216 3260 3304 3348 3392 44 985 3436 34SO 3524 3568 3613 3657 3701 3745 3789 3833 44 986 3877 3921 3965 4009 4053 4097 4141 4185 4229 4273 44 987 4317 4361 4405 4449 4493 4537 4581 4625 4669 4713 44 988 4757 4801 4845 4889 4933 4977 5021 5065 5108 5152 44 989 5196 5240 5284 5328 5372 5416 5460 5504 5547 5591 44 990 995635 5679 5723 5767 5811 5854 5898 5942 5986 6030 44 991 6074 6117 6161 6205 6249 6293 6337 6380 6424 6468 44 992 6512 6555 6599 6643 6687 6731 6774 6818 6862 6906 44 993 6949 6993 7037 7080 7124 7168 7212 7255 7299 7343 44 994 7386 7430 7474 7517 7561 7605 7648 7692 7736 7779 44 995 7823 7867 7910 7954 7998 8041 8085 8129 8172 8216 44 996 8259 8303 8347 8390 8434 8477 8521 8564 8608 8652 44 997 8695 8739 8782 8S26 8869 8913 8956 9000 9043 9087 44 998 9131 9174 9218 9261 9305 9348 9392 9435 9479 9522 44 999 9565 9609 9652 9696 9739 9783 9826 9870 9913 9957 43 N. 1 2 3 4 5 6 7 8 9 D. EXPLANATIONS OF THE PRECEDING TABLES TABLE I THE ATOMIC WEIGHTS OF THE ELEMENTS This table contains the most recent values of the atomic weights of the ele- ments, based upon the following standards : oxygen 16.000, silver = 107.87. There seems to be little doubt now that the atomic weight of silver is at least as low as 107.87, and for that reason all of those values which have been determined by means of silver are recalculated to this basis. The writer has ventured to give the atomic weights of a few elements to three places of decimals, but it must be remembered that the third place is obtained by averaging a large number of analyses, and, with two exceptions, it is not definitely known. However, in view of the fact that such excellent work has been done in revising the weights in these special cases, it seems probable that the values as recorded approach more closely the true values than would be the case if the third place were dropped. TABLES II-IV These tables contain the molecular weights * of common compounds, mul- tiples of the atomic weights of common elements, and of some common compounds. They are useful in calculating the amounts of substances which are chemically equivalent to given amounts of other substances. A few examples will illus- trate some of their uses : (1) Calculate the weight of hydrochloric acid which is exactly equivalent to 1.5 grams of sodium carbonate. Na 2 CO 3 + 2 HC1 = 2 NaCl + CO 2 + H 2 O. mol. wt. Na 2 CO 3 : mol. wt, HC1 x 2 : : 1.5 grains Na 2 CO 3 : x grams HC1. " mol. wt. HC1 x 2 x 1.5 = wt. HC1 required. mol. wt. Na 2 CO 3 * The accuracy of a molecular \veight is largely determined by the least accurate of the atomic weights which make it up. For example, it is useless to give the molecular weight of sulphuric acid to more than two places of decimals, although the atomic weight of hydrogen is known within a few units in the fourth place of decimals, and oxygen is the standard. 65 66 EXPLANATIONS OF THE PKECEDING TABLES log second multiple of the mol. wt. HC1 (Table IV) = 1.862870 log 1.5 (table of logarithms) = 0.17(3091 sum = 2.038901 log mol. wt. Na 2 C0 3 (Table III) = 2.025265 difference = 0.013696 The number of which 0.013696 is the logarithm is 1.03203, which is the weight of HC1 required. (2) What weight of silver must be dissolved in nitric acid and added to a solution containing two grams of barium chloride in order to precipitate exactly all of the chlorine? BaCl 2 + 2 AgN0 8 = 2 AgCl + Ba (N0 3 ) 2 . mol. wt. BaCl 2 : at. wt. Ag x 2 : : 2 grams BaCl 2 : x grams Ag. at. wt. Ag x 2 x 2 = wt. Ag required. mol. wt. BaCl 2 log second multiple at. wt. Ag (Table II) = 2.333930 log 2 (table of logarithms) = 0.301030 sum - 2.634960 log mol. wt. BaCl 2 (Table III) = 2.318627 difference = 0.316333 The number of which 0.316333 is the logarithm is 2.07172, which is the weight of silver required. (3) The atomic weights of many of the elements are most readily and accurately determined by preparing certain of their halides in a state of great purity, and then in a weighed sample of such material determining the exact weight of pure silver which is equivalent to the halogen. From such data the atomic weight of the element in question may be easily calculated by means of the tables. For example, let us take a special case which will illustrate the method : A weighed sample of phosphorus tribromide was treated in such a manner that the exact weight of silver equivalent to the bromine it contained was determined, and the weight of silver bromide formed was also determined. The atomic weights of bromine and silver being accurately known, we have only to calculate from the data the molecu- lar weight of phosphorus tribromide and subtract from it three times the atomic weight of bromine in order to obtain the atomic weight of phosphorus. Therefore we make the following proportion : wt. Ag : wt. PBr 3 : : at. wt. Ag x 3 : mol. wt. PBr g . EXPLANATIONS OF THE PRECEDING TABLES 67 In this calculation we need, in addition to the logarithms of the first two terms of the proportion, the logarithm of the third multiple of the atomic weight of silver, and the third multiple of the atomic weight of bromine, both of which are given in Table II. To calculate the same value from the weight of silver bromide formed, which incidentally serves as a check on the first value and also gives one a clear idea of the purity of the precipitate, we make the following proportion : wt. AgBr : wt. PBr 3 : : mol. wt. AgBr x 3 : mol. wt. PBr 3 . The third multiple of the molecular weight of silver bromide is given in Table IV. The tables are also useful in making standard solutions, especially those of certain normalities, as in many cases it is only necessary to shift the decimal point in the proper value in order to ascertain the weight of substance which a liter of the standard solution should contain. A normal solution contains in a liter of solution a gram molecular weight of substance reduced to a univalent basis. Two examples will serve to indicate the method of using the tables for this purpose. NOTE. It is scarcely necessary to call attention to the rule of decimal fractions, i.e. that to divide by 10 is equivalent to moving the decimal point one place to the left in the dividend ; that to divide by 100 is equivalent to moving the point two places to the left, etc. SOLUTIONS OF HYDROCHLORIC ACID OF CERTAIN NORMALITIES JV=mol. wt. (Table III). N _ mol. wt. __ mol. wt. x 5 ~2~~ 2 10 N mol. wt. mol. wt. x 2 55 10 N _ mol. wt. To~ 10 N_ _ mol. wt. __ mol. wt. x 4 25~ 25 100 N _ mol. wt. mol. wt. x 2 50 ~~ 50 100 N _ mol. wt. 100~ 100 (Table IV). (Table III). (Table IV). (Table IV). (Table III). 68 EXPLANATIONS OF THE PRECEDING TABLES SOLUTIONS OF SODIUM CARBONATE OF CERTAIN NORMALITIES N = moLwt. ^ mol.wt.x6 N mol. wt. mol. wt. /n N mol. wt. mol.wt. x 5 ,, T = =0= (Table IV). 10 2 x 10 100 N mol. wt. mol. wt. x 2 . 2^ = T^^--ToO-- (TableIV) - N mol.wt. ^mol.wt 50 2 x 50 100 N_ = mol. wt. ^ mol. wt. x 5 100 2 x 100 1000 TABLE V REDUCTION OF COMPOUNDS FOUND TO CONSTITUENTS SOUGHT BY MULTIPLICATION This table is intended to aid in calculations connected with the analysis of mineral substances, where it is so frequently necessary to determine a given substance in a state of combination different from that the proportionate amount of which we wish to know. If, for example, we wish to determine the amount of barium a given substance contains, we should probably pre- cipitate it and weigh it as barium sulphate and from this weight calculate the barium as follows : mol. wt. BaS0 4 : at. wt. Ba : : wt. BaSO 4 : wt. Ba. at ' Wt - Ba xwt.BaSO < = wt.Ba. mol. wt. BaS0 4 The constituent sought, in this case barium, is given in the first column of the table, and the state of combination in which it is convenient to determine the substance, barium sulphate, is given in the second column. On the same horizontal line with BaS0 4 a factor is given which is the quotient resulting from the division of the atomic weight of barium by the molecular weight of barium sulphate, so that it is only necessary to add to the logarithm of this factor the logarithm of the actual weight of barium sulphate in order to obtain the logarithm of the required weight of barium. From the above it is plain that the factors express the actual weight of substance sought, contained in, or equivalent to one gram of substance found ; that is, the first term of the proportion is reduced to unity, the second term EXPLANATIONS OF THE PBECEDING TABLES 69 is expressed by the factor, the third term is the weight of substance found. By multiplying the second and third terms together the product expresses the weight of substance sought. (2) In analyzing orthoclase feldspar the potassium and sodium are sepa- rated from the rest of the constituents and weighed together as chlorides. The potassium is then separated from the sodium in the usual manner and weighed as K. 2 PtCl 6 . It is customary to express the results of such analyses in percentages K 2 and Na. 2 0. From the weight of combined chlorides and the weight of K. 2 PtCl 6 the weights of K 2 and Na 2 are calculated as follows : mol. wt. K 2 PtCl 6 : chem. equiv. wt. K 2 O : : wt. K 2 PtCl 6 : wt. K 2 O. \vt. K 2 PtCl 6 x 0.19383 (factor) = wt. K 2 O. mol. wt. K 2 PtCl 6 : chem. equiv. wt. KC1 (2 KC1) : : wt."K 2 PtC! 6 : wt. KC1. wt. K 2 PtCl 6 x 0.30683 (factor) = wt. KC1. wt. of combined chlorides wt. KC1 = wt. NaCl. chem. equiv. wt. NaCl (2 NaCl) : mol. wt. Na 2 O : : wt. NaCl : wt. Na 2 O. wt. NaCl x 0.53028 (factor) = wt. Na 2 O. CALCULATION OF INDIRECT ANALYSIS Let us suppose that we have a mixture of a chloride and a bromide, and that we wish to determine the chlorine and the bromine. The weight of silver which is equivalent to the combined halogens is determined by the Volhard method. Then the precipitated AgCl and AgBr are collected and weighed together. Let x - wt. AgCl, and y = wt. AgBr. Then x + y = a (wt. of AgCl + AgBr), and i- x -\ y = b (wt. Ag equiv. to Cl and Br). AST Ag As ^ and * are constant quantities, we may represent them by k and k' respectively. The equations then become x + y - a, kx + k'y = b. Multiplying the first equation by k and subtracting the second from it in order to eliminate a*, we have kx + ky = ka, kx + k'y = 6, (k -k'}y = ka- 6, ka-b y = - 77- k k 70 EXPLANATIONS OF THE PRECEDING TABLES As k k' is a single constant we have y = p By substituting the value thus obtained for y in the first equation we have x = a value of y. wt. AgCl x 0.24737 = wt. Cl. wt. AgBr x 0.42555 = wt. Br. The values of - and - - are given in Table V under Ag and opposite Agl>r -A-gOi AgBr and AgCl respectively. TABLES VI-IX Normal atmospheric pressure is equal to the pressure exerted at sea level and 45 latitude by a vertical column of pure mercury 760 mm. long, the temperature of which is zero degrees C. Barometric readings made under ordinary conditions must be reduced to standard conditions ; that is, corrections must be applied for temperature, latitude, and elevation. Temperature corrections. In view of the fact that the cubical expansion of mercury is much greater than that of glass, and the length of the barometer scale also changes with the temperature, it is necessary to consider all of these factors in making the temperature corrections. However, these have been combined and the values are given in Table VI. Latitude corrections. Gravity at 45 latitude and sea level is considered normal. The values of this force in other latitudes as compared with the normal, taken as unity, are given in Table VII for a few important places. The length a barometric column of any latitude would have if it were acted upon by normal gravity may be calculated by multiplying the observed reading by that fraction which the force of gravity at the latitude in question is of normal gravity, or the proper correction may be taken from Table VIII, A. Elevation corrections. These are necessary, because gravity diminishes as we proceed from the center of gravity of the earth (Table VIII, B). Capillary depression corrections. Manufacturers of straight barometers make due allowance, in the adjustment of the scale, for capillary depression of the mercury ; and in U-shaped barometers and manometers the forces on the two surfaces compensate, provided the mercury is of uniform purity and the arms are of the same diameter. However, there are other purposes for which the values of the capillary depression of mercury may be needed, and they are given in Table IX. EXPLANATIONS OF THE PRECEDING TABLES 71 TABLES XII AND XIII REDUCTION OF GAS VOLUMES TO NORMAL CONDITIONS OF PRESSURE AND TEMPERATURE Boyle's Law. The volume of a given mass of any gas varies inversely as the pressure upon it, provided the temperature remains constant. If v represents the volume of a given mass of gas at 760 mm. pressure, and v l any other volume of the same mass at the pressure h, then 760 v = hv^ In order to calculate the volume any given amount of gas would have if it existed under normal pressure, we have only to add to the logarithm of the observed volume the logarithm of the value of = ' taken from Table XII. The sum will be the logarithm of the required volume. Moist gases are assisted in sustaining the pressure of the atmosphere by the partial pressure of water vapor. Therefore, in order to find the pressure which the gas itself is actually exerting (which is equal to the pressure under which it exists in equilibrium), we must subtract from the pressure of the atmosphere the aqueous tension. If the volume of a gas cannot be measured under exactly atmospheric pressure, it is frequently convenient to determine its pressure by measuring the difference between it and that of the atmosphere by means of an open arm manometer. The pressure of the atmosphere is then altered by the amount of this difference in order to ascertain the pressure under which the gas exists. The pressure which the gas alone exerts is represented by h of Table XII. Charles's Law. The volume of any gas increases by -^fa part of its vol- ume at C. for every degree its temperature increases. If V t is the volume of a gas at the temperature t, we have Vt = V + F x 0.00367* = F (l + 0.00367*); then F - The values of - are given in Table XIII for temperatures 1 -f- U.UUoo* t ranging from to 149. To calculate the volume a given amount of gas would have if its tempera- ture were reduced to zero, we have to add to the logarithm of the observed 72 EXPLANATIONS OF THE PRECEDING TABLES volume the logarithm of the value of Q0367 ( Table xni )> The sum will be the logarithm of the required volume. We may combine the expressions given above if we wish, as is usually the case, to reduce the volume to standard conditions of both pressure and tem- perature, thus FOP, reomm. = 4 x 1 + 0.00367 < X r '' *""" These reductions may be summed up as follows: Correct the barometric reading for temperature, latitude, and elevation. Subtract from the corrected reading the tension of aqueous vapor, and apply the manometer correction, if there be one. The result is the value represented by h. Add to the loga- rithm of the observed volume, the logarithm of (Table XII) and of j i \)\) T A AAQgrr ^ (Table XIII). The sum will be the logarithm of the required J. -f- U.UUobi t volume. TABLE XIV This table is intended to minimize the labor of reducing the volume of moist gases to normal conditions and dry. It is assumed that the temperature of the barometer and of the gas and water over which the gas is measured is the same. Under this condition the barometric reading is corrected for tem- perature, the tension of aqueous vapor subtracted, and the resulting value of combined with AAQ/T- ^ or certain combinations of temperature 4 oU 1 -j- U.UUoo^ t and pressure. Take from the table the logarithm corresponding to the temperature and approximate pressure. Interpolate to find the logarithm corresponding to the exact pressure, and add to it the logarithm of the observed volume of the gas. The sum will be the logarithm of the volume under normal conditions and dry. TABLE XV If one wishes to know the weight of an observed volume of gas, as in the analysis of nitrogenous organic substances by the Dumas method, the volume should be reduced to standard conditions, and then to the logarithm of this volume add the logarithm of the weight of one liter of the gas, taking care to express the volume read off as a fraction of a liter. EXPLANATIONS OF THE PRECEDING TABLES 73 TABLE XXVIII BUOYANCY OF AIR In view of the fact that the buoyant effect of the atmosphere changes considerably and often rapidly, it is necessary in work where great accuracy is required to reduce the apparent weight of a substance to a vacuum standard. If d is the weight of 1 cc. of air and v the volume of the object weighed, the true weight is w -\- vd, where w is the apparent weight. If the specific gravity of the substance is known, its volume is calculated by dividing its weight by the specific gravity. The error introduced by us- ing the apparent weight instead of the true weight in the expression v = - w s is negligible. Therefore the true weight of a substance is w -\ d. S If we wish to obtain absolute weighings, the same kind of correction must be applied to the weights. For brass weights (s = 8.3) the correction is 0.000145 per gram. This correction is negative and is to be subtracted from the calculated true weight of the substance. The true, absolute weight, then, of a substance weighed in air with brass weights is W Q = iv ( 1 + " - 0.000145 J . The values of d (Table XVI) are calculated for 760 mm. pressure. In work where the greatest accuracy possible is required, the value of d must be reduced to the existing condition of pressure ; namely, d x ^TT- In many instances, however, it is sufficiently accurate to consider d constant and equal to 0.0012 g. at room temperature. Under this condition the above expression becomes = w (l + ^j _ 0.000145^ = w (1 + c). (See Table XXVIII.) THE COMMON SYSTEM OF LOGARITHMS This system of logarithms is in general use because it greatly abridges numer- ical computation, and with due care arithmetical errors are largely eliminated. The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.* * The definition is based upon the assumption that there always exists a real number x which satisfies the equation b x = a, where a and b are positive numbers and b is greater than 1. 74 COMMON LOGARITHM S The base of the common system is 10, and since 10 = 1 10-! = 0.1 10 1 = 10 10- 2 = 0.01 10 2 = 100 10- 3 = 0.001 10 3 = 1000 10-4 = 0.0001 it follows from the definition of a logarithm that log 1 = log 0.1 = - 1 log 10 = 1 log 0.01 = - 2 log 100 = 2 log 0.001 = - 3 log 1000 = 3 log 0.0001 = 4 It is quite evident from the above table that the logarithms of all numbers between and 1 are negative and that the logarithms of all numbers greater than 1 are positive. NOTE. A negative number is considered as having no logarithm. We see also that the logarithm of any number between 1 and 10 is greater than and less than 1 ; thus log 2. 71 = 0.432969. The logarithm of any number greater than 10 and less than 100 is greater than 1 and less than 2 ; thus log 26. = 1.414973. It is plain that if a number is not an exact power of 10, its logarithm must consist at least in part of a decimal fraction. It is true that such logarithms can be expressed only approximately, but if the fractions are given to six places, they are sufficiently accurate for even the best atomic weight work. The integral part of a logarithm is called the characteristic, and the deci- mal part the mantissa. In the case just given 1 is the characteristic and .414973 the mantissa of the log 26. To find the characteristic of the logarithm of a number : (a) When the number is greater than unity, the characteristic of its log- arithm is one less than the number of digits to the left of the decimal point. Thus the characteristic of the logarithm of 46783.85 is 4. (b) When the number is less than unity, subtract from 9 the number of ciphers between the decimal point and the first significant figure, writing 10 after the mantissa. Thus the characteristic of the logarithm of 0.00089 is 6 with - 10 written after the mantissa : log 0.00089 = 6.949390 - 10. COMMON LOGAKITHMS 75 Some prefer to combine the two parts of such characteristics, writing the result as a negative characteristic, in which case it is one greater than the number of zeros preceding the first significant figure. The minus sign is written above the characteristic to show it applies only to it, for in construct- ing logarithmic tables it is convenient to make all mantissas positive even if the logarithm is a negative number. For example, log 1 = 0.602060 ; but since - .602060 = 1. + .397940, this may be written log = 1.397940 or 9.397940 10 with a positive mantissa. In order to avoid complications it is best to adhere to the first form of expression mentioned under (b) ; that is, when a logarithm has a negative characteristic to add 10 to and subtract 10 from it. For example, instead of writing the logarithm 1. + .397940, or 1.397940, we should write + 10 - 1. + .397940 - 10 = 9.397940 - 10. This is convenient when we wish to divide a logarithm by a number. Since man- tissas are always positive, it would not be correct to divide 1.397940 by 2, as we should confuse the positive and negative parts. If the form 9.397940 10 is used, the confusion is avoided, and the result of the division by 2 is 4.698970 5 = 1.698970, the actual logarithm resulting from the division. TABLE OF LOGARITHMS The great value of the common system of logarithms for the purposes of the analytical chemist is due to the fact that short tables can be constructed which contain the mantissas of the logarithms of all numbers from 1 or 100 to some given number, generally 1000 or 10,000, this being sufficient to cover all cases, and the characteristics can be determined by inspection. In order to use a table of logarithms one must know how to find the loga- rithm of any number, and how to take from the table the number which has a given logarithm, and also how to point the numbers off. To find from the table the logarithm of any number : (a) When the number consists of two significant figures. All of these numbers are given on the first page of the table in columns marked N. The logarithm of each number is placed opposite the number. (b) When the number consists of three or four significant figures. Find in the column of numbers the first three significant figures of the given number, then glance across the page along a horizontal line to the col- umn under the fourth figure of the given number ; four figures of the required mantissa are given at this point, to which two figures taken from the zero column must be prefixed. If the four figures of the required mantissa are T6 COMMON LOGARITHMS opposite a row of six figures in the zero column, the first two of the six are to be prefixed ; but if they are opposite only four figures in the zero column, the two figures to be prefixed will be found above, unless in passing back to the zero column asterisks be met with, in which case the two figures will be found immediately below the horizontal line in the zero column. Zeros should be written wherever asterisks occur. Characteristics are then prefixed in accordance with the rules already given. Examples : log 106 = 2.025306 log 1264 = 3.101747 log 2041 = 3.309843 log 2042 = 3.310056 log 2048 = 3.311330 (c) When the number consists of more than four significant figures. The mantissas of the logarithms of these numbers are not to be found in the table, but they can be easily calcuMted from values given in the table by a process of interpolation. The principle of proportional parts assumes that for a small change in a number there corresponds a proportional change in the logarithm. This is not strictly true, but the approximation is suffi- ciently close for most purposes. For example, required the log 521257. We find from the table log 5212 = 3.717004 and log 5213 = 3.717088. That is, an increase of one unit in the fourth figure produces an increase of .000084 in the logarithm. Therefore an increase of .57 of this unit will produce an increase in the logarithm equal to .57 x .000084, or .000048. Hence log 521257 = 5.717052. NOTE. In order to facilitate the process of interpolation it is customary to give the differences between the logarithms of consecutive numbers of four figures in a separate column. Such numbers are called tabular differences. In the table one number is given at the end of each horizontal line, and in each case it is nearly a mean of the differences of any two logarithms on the same line. It is intended that these numbers should serve only as a guide, and the last figure should be checked in every instance by glancing at the logarithms involved. The following rule is derived from the above : Place a decimal point after the fourth significant figure from the left, converting the given number into a whole number and a fraction, and this irrespective of any decimal point that may occur in the given number.* Find from the table the mantissa * Numbers with the same sequence of figures and which differ only in the position of the decimal point have the same mantissa, for one is the product of the other and an integral power of 10 ; hence their logarithms differ only by integers. Therefore the mantissa of the common logarithm of a number is independent of the decimal point. COMMOX LOGARITHMS 11 of the entire part and multiply the decimal part by the tabular difference ; add the product thus obtained to the mantissa of the entire part and prefix the proper characteristic, determined with respect to the position of decimal point in the original number. To find from the table the number which corresponds to a given logarithm : (a) Required the number the logarithm of which is 1.874772. We find this exact mantissa given in the table, and opposite in the column of numbers we find 749, the first three figures of the required number, and at the head of the column 5 the fourth figure. (&) Required the number the logarithm of which is 2.137860. The man- tissa of this logarithm is not given in the table, but it lies between the two mantissas .137671 and .137987, and the numbers corresponding to these are 1373 and 1374 respectively. The difference between the two mantissas taken from the table is 316, and the difference between the given mantissa and the smaller of the two taken from the table is 189 ; that is, an increase of 316 in the mantissa produces an increase of one unit in the corresponding number. Therefore an increase of 189 in the smaller of the two mantissas taken from the table will produce an increase of ^ff of a unit in the cor- responding number. Hence the required number is 137.359 nearly. The following rule is derived from the above : Search in the table for the mantissa of the given logarithm, and if it cannot be found, set aside the number corresponding to the next less mantissa. Sub- tract this mantissa from that of the given logarithm and divide the remainder by the tabular difference, carrying the division as far as desirable. Annex the quotient to the number set aside, and point off from the left one more integer figure than there are units in the characteristic of the given logarithm. If the characteristic is negative, the number is less than 1, and the number of zeros to be placed before the first figure is one less than the number of units in the characteristic. MULTIPLICATION BY LOGARITHMS Find from the table the logarithms of all the numbers to be multiplied together. Add these algebraically, remembering that negative signs apply only to the characteristic. The sum is the logarithm of the product. Thus multiply 27.1 by 119.86. log 27.1 = 1.432969 log 119.86 = 2.078674 3.511643 = log of product The number of which this is the logarithm is 3248.201. 78 EXPLANATIONS OF THE PEECEDING TABLES DIVISION BY LOGARITHMS Find the logarithm of the dividend and subtract from it the logarithm of the divisor. The difference is the logarithm of the quotient. The word " differ- ence " is used here in its algebraic sense. That is, if the characteristic of the logarithm of the divisor is negative, its sign must be changed ; but if that of the dividend is negative, it must be treated as a negative quantity. Let it be said once more that mantissas without exception are positive. 1. To divide 100.07 by 56.07. log 100.07 = 2.000304 log 56.07 = 1.748731 0.251573 = log of quotient The number of which this is the logarithm is 1.78473. 2. To divide 107.87 by 0.0187779. log 107.87 = 2.032901 log 0.0187779 = 2.273647 3.759254 = log of quotient The number of which this is the logarithm is 5744.5. 3. To divide 0.13736 by 153.36. log 0.13736 = 1.137860 log 153.36 = 2.185712 4.952148 = log of quotient The number of which this is the logarithm is .00089568. In regard to involution and evolution it is only necessary to say that the logarithm of any power of a number is obtained by multiplying the loga- rithm of the number by the exponent of the power, and that the logarithm of any root of a number is obtained by dividing the logarithm of the number by the index of the root. RETURN CHEMISTRY LIBRARY TO*- 1 00 Hildebrand Hall 642-3753 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS Renewable by telephone DUE AS STAMPED BELOW ro UNIVERSITY OF CALIFORNIA, BERKELEY FORM NO. 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