5Jeui ||ark Hate (^allege of Agriculture JVt (Cornell Jlmuermtii Jthaca. N. 1. library Cornell University Library QD 65.W45 Che mi ca.ca^jonub.es a . a j|o < Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924002979767 CHEMICAL CALCULATION TABLES FOR LABORATORY USE BY HORACE L. WELLS Professor of Analytical Chemistry and Metallurgy in the Sheffield Scientific School of Yale University SECOND EDITION, REVISED WITH A DOUBLE THUMB-INDEXED LOGARITHM TABLE Reprinted and Corrected for the 1920 Atomic Weights NEW YORK JOHN WILEY & SONS, Inc. Lonpon; CHAPMAN & HALL, Limited 1920 Copyright, 1903, BY HENRY HOLT & CO. Copyright, 1919, by HORACE L. WELLS <3> 1 *oS~7 Stanbope pttu P. H. Gl ISO N COMPANY BOSTON, U.S.A. PREFACE This book of tables for every day use in the chemical laboratory is a revision and modification of my "Tables for Chemical Calculations" published about 16 years ago, and now out of print. The changes in our official atomic weights have made necessary a complete revision of most of the tables. A new table for facilitating the calculation of percentage compositions of organic compounds has been added, while, in order to make the book more compact and thus more con- venient for its chief uses, several of the smaller, less important tables have been omitted, while the matter relating to the explanation of the tables and the illus- tration of their uses has been either left out or much changed and abbreviated. The table of logarithms of numbers has been provided with a double thumb- index which is believed to be a novel and useful device. With this improvement one can turn from any place in the table to any other reference, backward as well as forward, by practically a single motion, since all indices are visible from every part of the table. The greatest care has been used to secure accuracy in the data by the duplica- tion, at least, of their derivation, with a complete verification after the plates were cast. There is no doubt that accurate calculation is exceedingly important in con- nection with quantitative analysis and other kinds of chemical work, and it is believed that these tables will be of assistance in avoiding errors of calculation, as well as in making the work more rapid and less laborious than is often the case. H. L. W. vi CONTENTS PAOB Introduction 1 TABLE I. Atomic Weights 3 II. Gravimetric Factors 4 III. Formula-Weights 11 IV. Indirect Analyses -. 17 V. Reduction of Gas-Volumes to 0° and 760 mm 18 VI. Calculation of Percentage of Nitrogen from the Gas-Volume 19 VII. Barometer Corrections for Temperature 20 VIII. Multiples for Organic Compounds 21 IX. Constants for Molecular-Weight Determinations 22 X. Weights and Measures 23 Notes on the Use of Logarithms 24 XI. Logarithms of Numbers 25 CHEMICAL CALCULATION TABLES INTRODUCTION Five-place logarithms have been adopted in this book because they are satis- factory in usually introducing no inherent errors of calculation into the results obtained from the four-figure and five-figure numbers frequently used as data in chemical computations. It is true that four-place logarithms will give amply accurate results for a great deal of analytical work, but as these are liable to give incorrect fourth figures in some cases the longer logarithms are to be preferred for general use. It is easy to use these with the conveniently indexed table here supplied, and they have the additional advantage that, since usually only four figures at the most are significant in the results of analytical work, these can be taken from the nearest logarithm without the trouble of interpolating for a fifth figure. Computers should appreciate, and apply in carrying out their figures, the effects upon their results of the apparent errors of the approximate numbers employed. For general guidance in this matter the following rule may be given: Take as a basis the smallest number of apparently reliable figures in any of the approximate numbers used by multiplication and division (not including addi- tion and subtraction) in producing the result. Then, if the number used for the basis begins with a smaller figure than does the result, the number of figures to be preserved in the result will usually be equal to the basis, while if the reverse is true in regard to the first figures the number of figures to be considered significant in the result will usually be one more than the basis. It should be borne in mind that zeros at the end of decimals may be apparently reliable. For example: a. 23.00-- X 2.5417 -- = 58.46— (not 58.5 nor 58.459) 6.0.0089— X 0.16598— =0.00148-- (not 0.0015 nor 0.001475) c. 0.2301 -- -5- 2.5600 -- =0.08988-- (not 0.0899 nor 0.89883) d . 0018 i g X 0.8034 (factor) X 100 = 1.6500 g (substance) This rule is by no means an absolute one, and it should be modified according to judgment. For instance, in the example d given above, since 88 is so much larger than the 18 from which it is derived, it might well be preferred to call the result 0.09%. In some cases it is desirable to preserve a very uncertain last figure, while in other instances it is best to omit it, but it is very bad practice to report more than one evidently uncertain figure, or to leave off or fail to calculate one or more apparently accurate ones. Attention may be called here to the im- portance of adding a unit to the preceding figure when a figure greater than 5 is left off. 1 2 CHEMICAL CALCULATIONS For a more extensive discussion of the use of approximate numbers in calcu- lations, the author's "Text Book of Chemical Arithmetic" may be referred to. In order that accidental errors of calculation may be avoided it is recommended that entirely independent duplications of all calculations should be carried out, for mistakes are not always discovered by simply looking over the work. In Tables II and III the logarithms are generally given, for the sake of uni- formity, as though the atomic weights were exact, instead of approximate, num- bers. For instance, a five-place logarithm is given for the atomic weight of boron, 11.0 — , just as though it were known to be 11.000. This feature need cause no trouble as far as the gravimetric factors are concerned, since the latter are practically always more accurate than the data to which they are applied, and hence they need not be considered in deciding upon the significant figures of the results of ordinary calculations. The numerical formula weights in Table III in some cases have an uncertain last figure. Hg 200.6 For example, in the addition S 32.06 232.66 the last figure in the sum is uncertain because it has been obtained by addition to an unknown (plus or minus) figure. It has been preferred in most cases to retain such uncertain figures, since leaving them off and giving, for instance, HgS as 232.7 would be liable to decrease the accuracy of such formula-weights. In using these numbers for calculations it will usually make no difference whether or not the final figures are apparently accurate, but a glance at the atomic weights will show which is the case. The student should observe that many of the numerical factors in Table II, when multiplied by 100, give percentages of constituents, and that they may often be conveniently used in this way. For example, NaCl — > Na = 0.39444 shows that NaCl contains 39.44% of Na and 60.56% of CI. Since the factor 0.39444 is derived from 23.00 — , its last figure is uncertain and has not been used in giving the percentages (compare the rule previously given) . It should be stated that the value 0.0012510 g. was adopted in Table VI as the weight of 1 cc. of nitrogen gas at 41° latitude, instead of the value 0.0012514 g. at 45° because the former latitude is more suitable for general reference in the United States, but that the change makes a difference of only about one part in 3000 and is entirely inappreciable in nitrogen determinations by the Dumas method. ATOMIC WEIGHTS Table I. ATOMIC WEIGHTS.* O = 16. Aluminium Al 27 . 1 Antimony Sb 120.2 Argon A 39.9 Arsenic As 74.96 Barium Ba 137 . 37 Beryllium (Glucinum) ... Be 9.1 Bismuth Bi 208.0 Boron B 10.9 Bromine Br 79 . 92 Cadmium Cd 112.40 Caesium Cs 132.81 Calcium. . . : Ca 40.07 Carbon C 12.005 Cerium Ce 140 . 25 Chlorine CI 35.46 Chromium Cr 52 . Cobalt Co 58.97 Copper Cu 63.57 Dysprosium Dy 162.5 Erbium Er 167.7 Europium Eu 152.0 Fluorine F 19.0 Gadolinium Gd 157.3 Gallium Ga 70.1 Germanium Ge 72. 5 Gold Au 197.2 Helium He 4.00 Holmium Ho 163 . 5 Hydrogen H 1.008 Indium In 114.8 Iodine I 126.92 Iridium Ir 193 . 1 Iron Fe 55.84 Krypton Kr 82. 92 Lanthanum La 139 . Lead Pb 207.20 Lithium Li 6.94 Lutecium Lu 175 . Magnesium Mg 24.32 Manganese Mn 54.93 Mercury Hg 200.6 Molybdenum Mo 96.0 Neodymium Nd 144.3 Neon Ne 20.2 Nickel Ni 58.68 Niobium (Columbium) . . Nb 93 . 1 Niton Nt 222.4 Nitrogen. N 14.008 Osmium Os 190.9 Oxygen O 16.00 Palladium Pd 106.7 Phosphorus P 31 .04 Platinum Pt 195.2 Potassium K 39. 10 Praseodymium Pr 140 . 9 Radium Ra 226.0 Rhodium Rh 102.9 Rubidium Rb 85.45 Ruthenium Ru 101 . 7 Samarium Sm 150.4 Scandium Sc 44. 1 Selenium Se 79.2 Silicon Si 28.3 Silver Ag 107.88 Sodium Na 23 . 00 Strontium Sr 87.63 Sulphur S 32.06 Tantalum Ta 181.5 Tellurium Te 127.5 Terbium Tb 159.2 Thallium Tl 204.0 Thorium Th 232.15 Thulium Tm 168.5 Tin Sn 118.7 Titanium Ti 48.1 Tungsten W 184.0 Uranium U 238.2 Vanadium V 51.0 Xenon X 130.2 Ytterbium Yb 173.5 Yttrium Yt 89.33 Zinc Zn 65.37 Zirconium Zr 90 . 6 * This is the International Table for 1920. GRAVIMETRIC FACTORS Table II. GRAVIMETRIC FACTORS. Aluminium, 27.1 Given. AI2O3 Al 2 AIPO4 Sought. Al 2 AI2O3 (i)Al 2 3 Antimony, 120.2 Sb 2 4 Sb 2 4 Sb 2 4 Sb 2 Sb 2 3 Sb 2 6 Sb 2 S 3 Sb 2 S 3 Sb 2 S3 Sb 2 Sb 2 3 Sb 2 5 Arsenic, 74.96 Sb 2 Sb 2 As 2 S 3 Sb 2 3 Sb 2 6 As 2 As 2 S 3 As 2 S 3 As 2 S 3 As 2 3 As 2 B (2)As0 4 As 2 S 6 Mg 2 As 2 7 Mg 2 As 2 7 As 2 As 2 As 2 3 Mg 2 As 2 07 Mg 2 As 2 07 Ag 3 As0 4 As 2 B (2)As0 4 As Barium, 137-37 As 2 As 2 BaS0 4 As 2 3 As 2 6 Ba BaS0 4 BaCr0 4 BaCr0 4 BaO Ba BaO BaC0 3 BaC0 3 Ba Ba BaO BaO Bismuth, 208.0 Bi 2 3 BiOCl BiOCl Bi 2 Bi (i)Bi 2 3 Multiply by Factor. N. Log. .5303 .72 455 1.886 .2754s .4184 , .62 156 .7898 .9475 1.0526 .89 749 •97 656 .02 225 .7142 .8569 .9519 .85 384 •93 291 .97 860 1.1997 1.3328 .6092 .07 907 .12 476 .78 475 / .8042 .9343 1.1293 •90 538 •97 047 .05 281 .4833 .4827 .6373 .68419 .68 372 •80 435 .7403 .8949 .1620 .86 944 •95 178 .20 962 1.3202 1.5336 .5885 .12 063 .18572 •76 973 .6570 .5422 .6053 .81 758 •73 413 .78 198 .6960 .7770 1.1165 .84 260 .89 045 .04 785 .8965 .8017 .8942 •95 257 .90 399 .95 142 GRAVIMETRIC FACTORS Given. Sought. Multiply by Factor. N. Log. B12S3 Bi 2 S 3 Bi 2 Bi 2 Bi 2 3 Bi 2 3 .8122 .9059 1.1154 .90 967 •95 710 •04 743 Boron, 10.9 Bromine, 79.92 B 2 3 B 2 AgBr B 2 B 2 3 Br .3123 3.202 .42556 .49 460 •50 540 .62 896 AgBr Br— CI Br— CI HBr Br AgBr .43092 1.7976 4.2241 .63 440 .25 469 •62 573 Cadmium, 112.40 Br CdO CdS (1)0 Cd Cd .1001 .8754 .7781 .00 043 .94 220 .89 102 Caesium, 132.81 CdS Cd CS2SO4 CdO CdO Cs 2 .8888 1.1424 .7344 .94 882 .05 780 •86 593 Calcium, 40.07 Cs 2 PtCl 6 Cs 2 CaO Cs 2 Cs 2 Ca .3943 1.0602 .71465 •59 587 .02 540 .85 409 CaO CaSO-4 CaS0 4 CaC0 3 Ca CaO 1.7848 .2944 .4119 •25 159 .46 886 .61 477 CaC0 3 CaCOs Ca Ca CaO CaO .4004 .5603 1.3993 .60 250 .74 840 •14 59i Carbon, 12.005 Ca CaO BaC0 3 CaC0 3 CaS0 4 C0 2 2.4975 2.4279 .2229 •39 750 .38 523 .34 820 CaC0 3 C0 2 C C0 2 C C0 2 .4397 .2728 3.6656 .64318 •43 586 .56414 Chlorine, 35.46 co 2 AgCl AgCl C0 3 CI HC1 1.3636 .24738 .2544 .13 468 •39 337 •40 555 - Ag CI AgCl CI (i)0 (1)0 .3287 .2256 .05581 .51 680 •35 335 •74 672 GRAVIMETRIC FACTORS Given. Sought. Multiply by Factor. N. Log. Chromium, 52.0 Cr 2 3 Cr 2 3 PbCr0 4 Cr 2 (2)Cr0 3 Cr .6842 1 .3158 .1609 .83 519 .11919 .20 653 PbCr0 4 PbCr0 4 Cr 2 (|)Cr 2 8 CrOa Cr 2 3 .2351 .3094 1.462 •37 134 •49 053 .16481 Cobalt, 58.97 Cr C0SO4 C03O4 Cr0 3 Co Co 3 1.923 .3804 .7343 .28 400 .58 022 .86 589 Copper, 63.57 Co CuO Cu CoO Cu CuO 1.2713 .7989 1.2517 .10 426 .90 250 .09 750 Cu 2 S Cu 2 S CuSCN Cu 2 (2)CuO Cu .7986 .9996 .5226 .90 234 •99 984 .71817 Cyanogen, 26.013 CuSCN AgCN Ag CuO CN CN .6541 .1943 .2411 .81 567 .28 843 .38225 Fluorine, 19.0 Hydrogen, 1.008 CaF 2 SiF 4 H 2 F 2 F 4 H 2 .4867 .7287 .1119 .68 730 .86 253 .04 884 Iodine, 126.92 Agl Pdl 2 I— CI I I 2 I .5405 .7041 1.3877 •73 283 .84 760 .14230 Iron, 55.84 I— CI Fe 2 3 Fe 2 3 Agl Fez (2)FeO 2.5672 .6994 .8998 .40 947 .84 473 .95 415 Fe 2 3 FeS Fe (2)FeS 2 Fe FeO 1.5025 .6353 1.2865 .17 682 .80 296 .10 942 Lead, 207.20 Fe 2 PbS0 4 PbS0 4 Fe 2 3 Pb PbO 1.4298 .6833 .7360 .15 527 .83 458 .86 688 PbS0 4 PbCr0 4 PbCr0 4 PbS Pb PbO .7890 .6411 .6906 .89 706 .80 692 .83 922 GRAVIMETRIC FACTORS Given. Sought. Multiply b N. y Factor. Log. PbS PbS PbCl 2 Pb PbO Pb .8660 .9329 .7450 •93 752 .96 982 .87216 Lithium, 6.94 PbO Pb Li 2 S0 4 Pb PbO Li 2 .9283 1.0772 .1263 .96 770 .03 230 .10 123 Li 2 S0 4 Li 3 P0 4 Li 2 Li 2 Li 3 Li 2 .2718 .1797 2.153 •43 422 .25 455 •33 299 Magnesium, 24.32 Mg 2 P 2 7 Mg 2 P 2 7 Mg 2 P 2 7 Mg 2 (2) MgO (2)MgC0 3 .2184 .3621 .7572 •33 923 •55 879 •87 923 MgS0 4 MgS0 4 MgO Mg MgO Mg .2020 .3349 .6032 •30 54i •52 497 .78 044 Manganese, 54.93 MgO Mg Mn 2 P 2 7 MgC0 3 MgO Mn 2 2.0914 1.6579 .3869 .32 044 .21 956 .58 761 Mn 2 P 2 7 ' M113O4 Mna0 4 (2)MnO (3)Mn (3)MnO .4996 .7203 .9301 .69 863 •85 749 .96851 MnS MnS MnS0 4 Mn MnO Mn .6315 .8154 .3638 .80 034 .91 136 .56 086 MnSO-4 MnO Mn MnO Mn0 2 MnO .4698 1.2256 1.2913 .67188 .08 834 .11 102 Mercury, 200.6 Mn HgS HgS . Mn0 2 Hg HgO 1.5826 .8622 .9310 .19936 •93 56i .96 894 HgCl HgCl Hg Hg HgO HgO .8498 .9176 1.0798 .92 931 .96 264 •03 333 Molybdenum, 96.0 Nickel, 58.68 Mo0 8 PbMoO, NiS0 4 Mo MoO» Ni .6667 .3922 .3792 .82 391 •59 346 .57 889 GRAVIMETRIC FACTORS Given. Sought. Multiply by Factor. N. tog. NiO Ni Nitrogen, 14.008 NH 4 C1 Ni NiO N .7858 1.2727 .2618 .89 529 .10 471 .41 803 NH 4 C1 NH4CI (NH 4 ) 2 PtCl6 NH 3 NH4 (2)N .3184 . .3372 '.06310 .50 291 .52 789 .80 000 (NH 4 ) 2 PtCl 6 (NH 4 ) 2 PtCl 6 (NH 4 ) 2 PtCl 6 (2)NH 3 (2)NH 4 (2)NH 4 C1 .07671 .08126 .2410 .88 487 .90 985 .38 196 Pt Pt Pt (2)N (2)NH 3 (2)NH 4 .1435 .1745 .1848 .15 693 .24 181 .26 679 N NH 3 N NH 3 N (§)(NH 4 ) 2 1.216 .8225 1.859 .08 488 .91 S12 .26 926 N N N (§)(NH 4 ) 2 S0 4 (i)N 2 6 N0 3 4.716 3.855 4.427 .67 362 .58 608 .64 607 N N Phosphorus, 31.04 Mg 2 P 2 7 N0 2 NO P2 3.284 2.142 .2787 •5i 645 •33 086 .44 519 Mg 2 P 2 7 Mg 2 P 2 7 FePO* P 2 6 (2)P0 4 a)P 2 o 6 .6379 .8534 .4708 .80 477 •93 "7 .67 287 U 2 P 2 0n P 2 6 P 2 P 2 6 p 2 P 2 6 .1989 .4369 2.289 .29 854 .64 042 •35 958 Platinum, 195.2 (NH 4 ) 2 PtCl 6 Potassium, 39.10 KC1 KC1 Pt K (|)K 2 .4396 .52441 .63170 .64 306 .71 967 .80051 K 2 S0 4 K 2 S0 4 K 2 PtCl 6 K 2 K 2 K 2 .44876 .54056 .1609 .65 201 • 73 285 .20 643 K 2 PtCl 8 KjPtClg KC10* K 2 (2)KC1 K .1938 .3067 .2822 .28 727 .48 676 .45 054 GRAVIMETRIC FACTORS Given. KCIO4 KCIO4 K Sought. (i)K 2 KCl (i)K 2 Multiply by Factor. N. Log. .3399 .53 138 .5381 .73 087 1.2046 .08084 Rubidium, 85.45 Rb 2 S0 4 Rl^PtCU Rb Rb 2 Rb 2 (i)Rb*0 .6402 .2952 1.0936 .80 629 .47017 .03 887 Selenium, 79.2 Silicon, 28.3 Se Se Si0 2 Se0 2 Se0 3 Si 1.4040 1.6060 .4693 •14 737 .20 576 .67 147 Si0 2 Si0 2 Si0 2 Si0 3 (i)Si 2 7 Si0 4 1.265 1.398 1.531 .10 220 ■14 55i .18488 Silver, 107.88 Si AgCl AgCl Si0 2 Ag (§)Ag 2 2.131 .75262 .80842 .32 853 .87 657 .90 764 AgBr Agl Ag2 Ag Ag AgjO .57444 .45945 1.0742 •75 924 .66 224 .03 107 Sodium, 23.00 NaCl NaCl Na 2 S0 4 Na (|)Na 2 Na 2 .39344 .53028 .32381 •59 487 •72 450 .51 029 NE2S04 NaaCOa NasCOs Na 2 Na 2 Na 2 .43644 .43394 .58487 .63 992 •63 743 .76 706 Strontium, 87.63 Na SrS0 4 SrS0 4 (i)Na20 Sr SrO 1.3478 .4770 .5642 • 12 963 .67 856 •75 140 SrC0 3 SrC0 3 Sr Sr SrO SrO .5936 .7019 1.1826 •77 346 .84 630 .07 284 Sulphur, 32.06 BaS0 4 BaS0 4 BaS0 4 s so 2 so 3 . 13734 .27443 .34298 .13 780 •43 843 •53 526 BaS0 4 BaSO* S so 4 H 2 S0 4 S0 2 .41151 .42015 1.9981 .61 438 .62 340 .30 063 10 GRAVIMETRIC FACTORS Given. Sought. Multiply by Factor. N. Log. Tellurium, 127.5 S s Te S0 3 H 2 S0 4 Te0 2 2.4972 3.0591 1.2510 •39 746 .48 560 .09 725 Thallium, 204.0 Te Til Tl 2 PtCl 8 Te0 3 Tl Tl 2 1.3765 .6165 .5000 •13 877 .78 990 .69 899 Thorium, 232,15 Tin, 1 18.7 Tl 2 Th0 2 Sn0 2 T1 2 Th Sn 1.0392 .8789 .7877 .01 671 •94 392 .89 634 Titanium, 48.1 Tungsten, 184.0 Sn Ti0 2 W0 3 Sn0 2 Ti W 1.2696 .6005 .7931 .10366 •77 852 •89 933 Uranium, 238.2 Vanadium, 51.0 U 3 8 U 3 8 V 2 6 u 3 (3)U0 2 v 2 .8481 .9620 .5604 •92 844, .98319 •74 853 Zinc, 65.37 v 2 V ZnO v 2 o 6 vo 4 Zn 1.784 2.255 .8034 •25 147 •35 313 .90 492 ZnS ZnS Zn 2 P 2 7 Zn ZnO Zn 2 .6710 .8352 .4289 .82 669 •92 177 •63 237 Zirconium, 90.6 Zn 2 P 2 7 Zn ZrQ 2 (2)ZnO ZnO Zr .5339 1.2447 .7390 •72 745 .09 508 .86 864 FORMULA = WEIGHTS 11 Table III. FORMULA = WEIGHTS Formula. Weight. Log. Formula. Weight. Log. Ag 107.88 .03 29I4 B 10.9 •03743 Ag2 215.76 •33 397 B 2 21.8 •33846 Ag3 323.64 .51 007 B 2 3 69.8 .84386 Ag 3 As0 4 462.60 .66 521 AgBr 187.80 •27 370 Ba 137.37 •13 789 AgCN 133.89 .12 676 BaC0 3 197.375 •29 530 AgCl 143.34 • 15637 BaCl 2 208.29 .31 867 Agl 234.80 .37070 BaCl 2 -2H 2 244.32 .38 796 AgI0 3 282.80 •45 148 BaCr0 4 253.37 .40 376 AgN0 3 169.89 .23 017 Ba(N0 3 ) 2 261.39 .41 729 Ag 2 231.76 •36 504 BaO 153.37 ■18574 |Ag 2 115.88 .06 401 Ba0 2 169.37 .22 884 Ag 3 P0 4 418.68 .62 188 Ba0 2 -8H 2 313.50 .49 624 Ag e S 247.82 •39 4M Ba(OH) 2 -8H 2 315.51 .49 901 BaS0 4 233.43 .36816 Al 27.1 •43 297 Ala AICI3 A1C1 3 -6H 2 54.2 133.48 241.58 •73 400 .12 542 .38306 Be BeO 9.1 25.1 •95 904 •39 967 A1K(S0 4 ) 2 -12H 2 474.51 .67 623 Bi 208.0 .31 806 .61 909 A1NH 4 (S0 4 ) 2 -12H 2 453.45 •65 653 Bi 2 416.0 AlNa 3 F 6 210.10 •32 243 Bi 2 3 464.0 .66 652 A1 2 3 102.2 .00 945 *Bi 2 3 232.0 .36 549 §A1 2 3 51.1 .70 842 BiOCl 259.46 .41 407 A1P0 4 122.14 .08 686 Bi(OH) 2 N0 3 304.02 .48 291 A1 2 (S0 4 ) 3 342.38 •53 451 Bi 2 S 3 512.18 .70 942 A1 2 (S0 4 ) 3 -18H 2 666.67 .82 391 As 74.96 .87 483 Br 79.92 .90 266 Asi! 149.92 .17586 Br 2 159.84 .20 369 AsCl 3 181.34 .25 850 Br 3 239.76 •37 978 As 2 3 197.92 .29 649 Br 4 319.68 .50 472 §As 2 3 98.96 •99 546 Br 6 399.60 .60 163 iAs 2 3 49.48 .69 443 Br 6 479.52 .68 081 As 2 5 229.92 .36 158 §As 2 B 114.96 .06 055 C 12.005 .07 936 As0 4 138.96 .14 289 c 2 24.01 •38 039 As 2 8 277.92 •44 392 CH 3 15.03 .17 696 As 2 S 3 246.10 •39 i" CH 4 16.04 .20 520 As 2 S B 310.22 •49 167 C 2 H 2 26.03 •41 547 C 2 Hs 29.05 •46315 Au 197.2 .29491 CeHe « 78.08 .89 254 AuCl 3 -2H 2 339.61 •53 098 12 FORMULA = WEIGHTS Formula. Weight. C2H3O2 59.03 C4H4O6 148.05 CN 26.013 CNS 58.07 CO 28.005 co 2 44.005 co 3 60.005 c 2 o 4 88.01 CON 2 H 4 60.05 cs 2 76.13 Ca 40.07 CaC 2 64.08 CaC0 3 100.08 CaCl 2 110.99 CaCl 2 -6H 2 219.09 CaCl 2 126.99 CaF 2 78.07 CaO 56.07 Ca(OH) 2 74.09 Ca 3 (P0 4 ) 2 310.29 CaS0 4 136.13 CaS0 4 -2H 2 172.16 CaSiOs 116.37 Cd 112.40 CdCO, 172.41 CdCl 2 -2H 2 219.35 Cd(N0 3 ) 2 -4H 2 308.48 CdO 128.40 CdS 144.46 CdS0 4 208.46 CdS0 4 -2fH 2 256.50 Ce 140.25 CezOa 328.50 Ce0 2 172.25 CI 35.46 Cl 2 70.92 Cl 3 106.38 CL, 141.84 CI5 177.30 Cle 212.76 CIO 51.46 Log. 77 107 .17041 .41 519 .76 397 .44 724 64 350 77818 94 453 77 853 88156 60 282 80 672 00035 04528 34062 10 377 89248 74 873 86976 49 177 13 396 23 593 06 584 05077 23657 34 "4 48 922 10857 15 975 31903 40 909 14 690 51654 23 616 54 974 85077 02 686 15 180 24871 32789 71 147 Formula. Weight. Log. CIO3 83.46 .92 148 C10 4 99.46 •99 765 C1 2 6 150.92 •17 875 C1 2 7 182.92 .26 226 Co 58.97 •77 063 CoCl 2 -6H 2 237.99 •37 656 Co(N0 3 ) 2 -6H 2 291.08 .46 401 CoO 74.97 .87 489 Co 3 4 240.91 .38 186 CoS0 4 155.03 .19 041 CoS0 4 -7H 2 281.14 .44 892 Cr 52.0 .71 600 Cr 2 104.0 .01 703 Cr 2 3 152.0 .18 184 Cr0 3 100.0 .00 000 Cr0 4 116.0 .06 446 Cr 2 7 216.0 •33 445 Cs 132.81 .12323 Cs 2 265.62 .42 426 CsAl(S0 4 ) 2 -12H 2 568.22 •75 452 CsCl 168.27 .22 601 Cs 2 281.62 .44 966 Cs 2 PtCl, 673.58 .82 839 Cs 2 S0 4 361.68 •55 833 Cu 63.57 .80 325 Cu 2 127.14 .10428 CuCl 99.03 •99 577 CuCl 2 134.49 .12 869 CuCU^HjO 170.52 •23 177 Cul 190.49 •27 987 CuFeS 2 183.53 .26371 Cu(N0 3 ) 2 -6H 2 295.68 •47 082 CuO 79.57 .90 075 Cu 2 143.14 ■ 15 576 Cu 2 S 159.20 .20 194 CuSCN 121.64 .08 508 CuS0 4 159.63 .20 311 CuS0 4 -5H 2 249.71 •39 744 Fe 55.84 •74 695 Fe» 111.68 .04 798 FORMULA = WEIGHTS 13 Formula. Weight. Log. Formula. Weight. Log. Fe 3 167.52 .22 406 Hg 200.6 •30 233 FeC0 3 115.85 .06 390 Hg(CN) 2 252.63 .40 248 FeCU 162.22 .21 OIO HgCl 236.06 •37 302 FeCl 3 -6H 2 270.32 •43 188 HgCl 2 271.52 •43 380 Fe(NH 4 ) 2 (S0 4 ) 2 -6H 2 392 . 14 •59 344 Hgl 2 454.44 .65 748 FeNH 4 (S0 4 ) 2 -12H 2 482.19 .68 322 HgO 216.6 •33 566 FeO 71.84 .85 637 HgS 232.66 .36 672 Fe 2 3 159.68 .20325 |Fe 2 3 79.84 .90 222 I 126.92 •10353 Fe 3 4 231.52 •30 459 h 253.84 .40 456 FeS 87.90 •94 399 I3 380.76 .58 065 FeS 2 119.96 .07 904 I 4 507.68 •70 559 FeS0 4 -7H 2 278.01 .44 406 I5 634.60 .80 250 Ie 761.52 .88 168 H 1.008 .00 346 I2O5 333.84 •52 354 H 2 2.016 .30 449 IO, 174.92 .24 284 H 3 3.024 .48 058 I0 4 190.92 .28 085 H 4 4.032 .60 552 H 5 5.040 .70 243 K 39.10 .59218 H 6 6.048 .78 161 K 2 78.20 .89 321 H 3 B0 3 62.02 •79 253 K 3 117.30 .06 930 HBr 80.93 .90 811 K, 156.40 .19 424 HC 2 H 3 2 60.04 •77 844 KA1(S0 4 ) 2 -12H 2 474.51 .67 625 HCN 27.021 •43 171 KBr 119.02 .07 562 HC0 2 H 46.02 .66 295 KBr0 3 167.02 .22 277 H 2 C 2 4 90.03 •95 439 KGN 65.11 .81 367 H 2 C 2 4 -2H 2 126.06 .10 058 K 2 C0 3 138.21 .14 054 §[H 2 C 2 4 -2H 2 0] 63.03 •79 955 KC1 74.56 .87 251 H 2 C 4 H 4 06 150.07 .17 629 2KC1 149.12 • 17 354 HC1 36.468 .56 192 KC10 3 122.56 .08 835 HCIO4 100.47 .00 204 KC10 4 138.56 .14 164 HF 20.01 .30 125 K 2 Cr0 4 194.20 .28 825 HI 127.93 .10 697 K 2 Cr 2 7 294.20 .46 864 HKC0 3 100.11 .00 048 £K 2 Cr0 7 49.033 .69 049 HN0 3 63.016 •79 945 KCr(S0 4 ) 2 -12H 2 499.41 .69 846 HNaC0 3 84.01 •92 433 K 3 Fe(CN) 6 329.22 •51 749 HNa 2 P0 4 12H 2 358.24 •55 4i8 K»Fe(CN)« 368.32 .56 622 HO 17.008 .23 065 K 4 Fe(CN) 6 -3H 2 422.37 .62 569 H 2 18.016 .25 565 KHC0 3 100.11 .00 048 H 2 2 34.02 •53 173 KI 166.02 .22 016 H 3 P0 4 98.06 •99 149 KI0 3 214.02 •33 045 H 2 S 34.08 •53 250 |KI0 3 35.67 •55 230 H 2 S0 4 98.08 .99 158 KMn0 4 158.03 .19874 §H 2 S0 4 49.04 •69 055 2KM11O4 316.06 •49 977 H 2 SiFa 144.32 .15 933 1 *KMn0 4 31.606 •49 977 14 FORMULA = WEIGHTS Formula. Weight. Log. Formula. Weight. Log. KN0 2 85.108 .92 997 Mo 96.0 .98 227 KN0 3 101 .108 .00 478 Mo0 3 144.0 .15836 KNaC 4 H 4 6 4H 2 282.22 •45 059 MoS, 160.1 •20 439 K 2 94.20 •97 405 > §K 2 47.10 .67 302 N 14.008 .14 638 KOH 56.11 •74 904 N 2 28.016 .44 741 K 2 PtCl 6 486.16 .68 678 NH 2 16.024 .20 477 §K 2 PtCl 6 243.08 •38 575 NH 3 17.032 .23 126 KSCN 97.17 •98 754 NH 4 18.040 .25 624 K 2 S0 4 174.26 .24 120 (NH 4 ) 2 36.080 •55 727 2K2SO4 87.13 •94 017 NH 4 A1(S0 4 )2-12H 2 453.45 .65 653 K2S1F5 220.5 •34 341 (NH 4 ) 2 C 2 4 -H 2 142.11 .15 261 N2ILCO 60.05 •77 853 Li 6.94 .84 136 NH 4 C1 53.500 •72 835 Li 2 13.88 .14239 NH 4 Fe(S0 4 ) 2 -12H 2 482.19 .68 322 Li 2 C0 3 LiCl 73.89 .86 859 (NH 4 ) 2 Fe(S0 4 )2-6H 2 392.14 •59 344 42.40 •62 737 NH 4 NaHP0 4 4H 2 209.15 .32 046 Li 2 29.88 •47 538 (NH 4 ) 2 52.08 .71 667 §Li 2 14.94 •17 435 NH 4 OH 35.05 .54 466 Li 3 P0 4 115.86 •06 393 NH 4 N0 3 80.05 •90 335 Li 2 S0 4 109.94 .04 116 (NH 4 ) 2 PtCl 6 444.04 .64 742 Mg 24.32 •38 596 NH 4 SCN 76.11 .88 146 Mg 2 As 2 7 310.56 .49214 (NH 4 ) 2 S0 4 132.14 .12 103 MgC0 3 84.325 .92 596 N 2 ■ 44.016 .64 361 MgCl 2 -6H 2 203.34 .30 822 NO 30.008 .47 724 MgO 40.32 .60 552 N0 2 46.008 .66 283 Mg 2 P 2 7 222.72 •34 776 N0 3 62.008 .79 245 MgS0 4 120.38 .08 055 N 2 3 76.016 .88 091 MgS0 4 -7H 2 246.49 •39 180 N 2 5 108.016 .03 348 MgSi0 3 100.62 .00 268 |N 2 6 54.008 •73 245 Mn 54.93 •73 981 Na 23.00 •36 173 Mn 2 109.86 .04 084 Na 2 ' 46.00 .66 276 M11CO3 114.94 .06 047 Na 3 AlF 6 210.1 •32 243 MnCl 2 4H 2 197.91 .29 647 Na 2 B 4 7 201.6 .30 449 MnO 70.93 .85 083 Na 2 B 4 O 7 -10H 2 O 381.76 .58 179 Mn 2 3 157.86 .19828 NaBr 102.92 .01 250 Mn 3 4 228.79 •35 944 NaC 2 H 3 2 82.03 •9i 397 Mn0 2 86.93 •93 917 NaC 2 H 3 2 -3H 2 136.08 •13 379 Mn 2 7 221.86 .34 608 Na 2 C0 3 106.005 •02 S33 Mn 2 P 2 7 283.94 ■45 323 Na 2 CO 3 -10H 2 O 286.17 •45 662 MnS 86.99 •93 947 NaHC0 3 84.01 •92 433 M11SO4 , 150.99 •17895 NaCl 58.46 .76 686 MnS0 4 4H 2 223.05 •34 840 NaC10 3 106.46 .02 719 MnS0 4 -7H 2 277.10 .44 264 NaC10 4 122.46 .08 799 FORMULA = WEIGHTS 15 Formula. Weight. Log. Formula. Weight. Log. NaF 42.0 .62 325 Pb 207.20 •31 639 Na 2 HP0 4 -12H 2 358.24 •55 4 I 8 Pb(C 2 H 3 2 ) 2 -3H 2 379.32 •57 900 NaHSOs 104.07 •?i 733 PbC0 3 267.21 .42 686 NaHSO, 120.07 •07 943 PbCl 2 278.12 •44 423 Nal 149.92 .17 586 PbCr0 4 323.20 •50 947 NaN0 2 69.008 .83 890 Pb(N0 3 ) 2 331.22 .52 012 NaNO s 85.008 .92 946 PbO 223.20 •34 869 Na 2 62.00 •79 239 Pb0 2 239.20 •37 876 |Na 2 31.00 •49 136 Pb 3 4 685.60 .83 607 Na 2 2 78.00 .89 209 PbS 239.26 •37 887 NaOH 40.006 .60 217 PbS0 4 303.26 .48 181 NaP0 3 102.04 .00 877 Na4P 2 7 266.08 .42 501 Pd 106.7 .02 816 Na 2 S 78.06 .89 243 Pdl 2 360.54 •55 696 Na2S0 4 Na 2 SO 4 10H 2 O NaAO^HaO 142.06 322.22 248.20 •15247 .50816 •39 480 Pt PtCl« PtCU 195.2 337.04 407.96 .29 048 .52 768 .61 062 Ni 58.68 .76 849 NiCl 2 -6H 2 237.70 •37 603 Rb 85.45 •93 1.7 1 Ni(N0 3 ) 2 -6H 2 290.80 •46 359 RbAl(S0 4 ) 2 -12H 2 520.86 .71 672 NiO 74.68 .87 320 RbCl 120.91 .08 246 NiS 90.74 •95 780 Rb 2 186.90 .27 161 NiS0 4 154.74 .18 960 Rb 2 PtCl 6 578.86 •76 257 NiS0 4 -6H 2 262.84 .41 969 Rb 2 S0 4 266.96 .42 645 NiS0 4 -7H 2 280.85 .44 848 S 32.06 .50 596 Ni(NH 4 ) 2 (S0 4 ) 2 -6H 2 394 . 98 •59 658 s 2 64.12 .80 699 16.00 .20 412 SCN 58.073 •76 397 o 2 32.00 •50 515 so 2 64.06 .80 659 3 48.00 .68 124 so 3 80.06 .90 342 o 4 64.00 .80618 so 4 96.06 .98 254 5 o 6 OH 80.00 96.00 17.008 .90 309 .98 227 .23 065 Sb 2Sb 120.2 240.4 .07 990 •38 093 SbCl 3 226.58 •35 522 P 31.04 .49 192 SbCl 5 297.50 •47 349 P2 62.08 •79 295 Sb 2 3 288.4 .46 000 PCI3 137.42 .13 805 |Sb 2 3 144.2 •15897 PCU 208.34 •3i 877 Sb 2 6 320.4 •50 569 P2O5 142.08 .15 253 |Sb 2 5 160.2 .20 466 §P 2 5 71.04 .85 150 Sb 2 4 304.4 .48 344 PO4 95.04 •97 79i SbOCl 171.7 •23 477 2P0 4 190.08 .27 894 Sb0KC 4 H 4 6 -iH 2 332.36 .52 161 P2O3 110.08 .04 171 Sb 2 S 3 336.6 .52711 P2O7 174.08 .24 075 Sb 2 S B 400.7 .60 282 16 FORMULA = WEIGHTS Formula. Weight. Log. Formula. Weight. Log. Se 79.2 .89 873 Th 232.4 .36 624 Se0 2 111.2 .04 6lO Th0 2 264.4 .42 226 Se0 3 127.2 .10 449 Ti 48.1 .68 215 Si 28.3 ■45 179 Ti0 2 80.1 •90 363 Si 2 56.6 •75 282 SiF 4 104.3 .01 828 TI 204.0 •30 963 SiF 6 142.3 .15 320 T1C1 239.46 •37 923 Si0 2 60.3 .78 032 Til 330.92 •5i 973 Si0 3 76.3 .88 252 T1N0 3 266.01 .42 490 Si0 4 92.3 .96 520 Tl 2 PtCI 6 815.96 .91 167 Si 3 Og 212.9 .32 818 U 238.2 •37 694 Sn 118.7 .07 445 uo 2 270.2 •43 169 SnCl 2 189.62 .27 789 U 3 8 842.6 .92 362 SnCl 2 -2H 2 225.65 ■35 344 U0 2 (C 2 H 3 2 ) 2 -2H 2 424.30 .62 767 SnCU 260.54 .41 587 U0 2 (N0 3 ) 2 -6H 2 502.32 .70 098 SnO 134.7 •12 937 U 2 P 2 0u 714.48 •85 399 Sn0 2 150.7 .17 811 V 51.0 •7o 757 SnS 150.76 .17828 V 2 6 182.0 .26 007 SnS 2 182.82 .26 203 W 184.0 .26 482 Sr 87.63 •94 265 W0 3 232.0 •36 549 SrC0 3 147.64 .16 920 SrCl 2 -6H 2 266.65 .42 594 Zn 65.37 .81 538 Sr(N0 3 ) 2 211.65 .32 562 ZnC0 3 125.38 .09 823 SrO 103.63 .01 549 ZnCl 2 136.29 .13 446 Sr(OH) 2 -8H 2 265.77 .42 450 ZnO 81.37 .91 046 SrS0 4 183.69 .26 409 ZnS 97.43 .98 869 Z11SO4 161.43 .20 798 Te 127.5 •10 551 ZnS0 4 -7H 2 287.54 .45 870 Te0 2 159.5 .20 276 Te0 3 175.5 .24 428 Zr 90.6 •95 713 Te0 3 -3H 2 229.55 .36 088 Zr0 2 122.6 .08 849 H 2 18.016 ■25 565 13H 2 234.21 .36 961 2H 2 36.032 •55 668 14H 2 252.22' .40 178 3H 2 54.048 •73 278 15H 2 270.24 •43 175 4H 2 72.064 •85 77i 16H 2 288.26 •45 978 5H 2 90.08 •95 463 17H 2 306.27 .48 611 6H 2 108.10 •03 383 18H 2 324.29 .51 094 7H 2 126.11 .10 075 19H 2 342.30 •53 441 8H 2 144.13 •15 875 20H 2 O 360.32 •55 668 9H 2 162. 14 .20 989 21H 2 378.34 ■57 788 10H 2 O 180.16 .25 565 22H 2 396.35 .59 808 11H 2 198.18 .29 706 23H 2 414.37 .61 739 12H 2 216. 19 •33 484 24H 2 432.38 .63 587 INDIRECT ANALYSES 17 Table IV. INDIRECT ANALYSES. Mixture. a. AgBr Agl AgBr Agl NaCl KC1 NanSO-4 K 2 S0 4 NasSQ LijSO, '« J R^PtCU CsiiPtCle Determined. 6. Loss by fusing in chlorine Loss by fusing in chlorine. CI BaS0 4 BaS0 4 Rb 2 S0 4 CszSO, Formula. AgBr = 2.5496 a - 6.5454 6 (log .40 647) (log .81 594) Agl = - 1.5496 a + 6.54546 (log .19 022) (log .81 594) Br = 1.0850 a -2.7855 6 (log .03 543) (log -44 490) I = - .83758 a + 3.5380 b (log .92 303) (log .54 876) NaCl = - 3.6310 a + 7.6348 b (log .56 003) (log .88 280) ' KC1 = 4.6310 a -7.6348 b (log .66 567) (log .88 280) Na2S0 4 = - 4.4108 a + 3.2928 6 (log .64 452) (log .51 756) K 2 S0 4 = 5.4108 a - 3.2928 b (log -73 326) (log .51 756) Na2S0 4 = 4.4228 a - 2.0830 b (log .64 570) (log .31 869) Li a S0 4 = - 3.4228 a + 2.0830 b (log -S3 438) (log .31 869) Rb 2 S0 4 = 3.2682 a - 6.0866 b (log .51 43i) (log .78 437) Cs 2 S0 4 = - 3.2682 a + 7.0866 b (log .51 431) (log .85 044) Note. — This table is given to show a few convenient formulas for calculating the results of indirect analyses in cases where two transformations occur together. The formulas themselves may be readily derived from the proper factors by the use of algebra. For instance, for the third pair of formulas given above we have: NaCl + KC1 = o, and .60656 NaCl + .47559 KC1 = 6, and the solution of these simultaneous equations gives the formulas. Of the formulas given in the table, the first two pairs represent a process that has been fre- quently employed, and is capable of giving good results. The student should be warned, how- ever, against the use of most of the methods of complex indirect determination, except for the purpose of obtaining approximate results, because the errors in the determinations are largely increased in the final results. For example, the formulas indicate that an error of one part in 100 in the determination of chlorine in a mixture of NaCl and KC1 would produce errors of 7.6 parts in 100 in the calculated amounts of the salts. 18 REDUCTION OF GAS-VOLUMES TABLE V. REDUCTION OF GAS-VOLUMES TO 0° AND 760 MM. Vol. at o° and 760 mm = v. F. (h—w). v— v uiume < ji gas \yvj , 760(1+. 003670' «= Temperature of gas (C.°); h= Barometer-height, corrected, (mm); w= Tension of aqueous vapor (mm). t". Log F* w. t°. Log F* w. .11 919 4.6 15 .09 592 12.7 0.5 .11839 4.8 15.5 •09 5*7 13.1 1 .11 760 4.9 16 .09441 13.5 1.5 .11 681 5.1 16.5 .09 366 13.9 2 .11 602 5.3 , 17 .09 291 14.4 2.5 •" 5 2 3 5.5 17.5 .09 216 14.9 3 • 11 444 5.7 18 .09 141 15.3 3.5 •1136S 5.9 18.5 . 09 067 15.8 4 .11 286 6.1 19 .08 992 16.3 4.5 .11 208 6.3 19.5 .08918 16.8 5 .11 129 6.5 20 .08843 17.4 5.5 ■ 11 051 6.7 20.5 .08 769 17.9 6 •10 973 7.0 21 .08 695 18.5 6.5 .10895 7.2 21.5 .08 621 19.0 7 .10817 7.5 22 •08 547 19.6 7.5 .10740 7.7 22.5 .08474 20.2 8 .10 662 ' 8.0 23 . 08 400 20.9 8.5 •10585 8.3 23.5 .08327 21.5 9 10508 8.5 24 ■08 253 22.2 9.5 10430 8.8 24.5 .08 180 22.8 10 10 354 9.1 25 .08 107 23.5 10.5 10 277 9.4 25.5 .08 034 24.2 11 10 201 9.8 26 .07 961 25.0 11.5 10 124 10.1 26.5 .07 888 25.7 12 10 048 10.4 27 .07 816 26.5 12.5 09 972 10.8 27.5 •°7 743 27.3 13 09 896 11.1 28 .07 671 28.1 13.5 09 820 11.5 28.5 •07 599 28.9 14 09 744 11.9 29 .07 527 29.7 14.5 09668 12.3 29.5 ■07 455 30.6 30 •07 383 31.5 * The characteristic of all the logarithms is —3. CALCULATION OF PERCENTAGE OF NITROGEN 19 Table VI. CALCULATION OF PERCENTAGE OF NITROGEN FROM THE GAS-VOLUME. v.F. (h - w) %N = 8 -- Volume of nitrogen (cc) . factor (table) = ; - 001251 °X 100 Q00 g. H 2 + 30 g. KOH = 23.1% KOH) '760(1+ .00367 4) h = Height of barometer, corrected (mm). w = Tension of aqueous vapor (mm). S = Weight of substance (g). t = Temperature of gas (C. c ). 23.1% KOH H 2 0. 23.1% KOH. H 2 0. t°. Log. F* w. w. t". Log F* w. w. .21 645 3.7 4.6 15.5 ■ 19 243 10.5 13.1 0.5 •21565 3.8 4.8 16 .19 167 10.8 13.5 1 .21 486 3.9 4.9 16.5 .19 092 11.2 13.9 1.5 .21 407 4.1 5.1 17 .19 017 11.5 14.4 2 .21 328 4.2 5.3 17.5 . 18 942 11.9 14.9 2.5 .21 249 4.4 5.5 18 .18867 12.3 15.3 3 .21 170 4.5 5.7 18.5 ■18793 12.7 15.8 3.5 .21 091 4.7 5.9 19 .18718 13.1 16.3 4 .21 012 4.9 6.1 19.5 .18 644 13.5 16.8 4.5 • 20 934 5.0 6.3 20 .18569 13.9 17.4 5 .20855 5.2 6.5 20.5 .18495 14.4 17.9 5.5 .20 777 5.4 6.7 21 .18 421 14.8 18.5 6 . 20 699 5.6 7.0 21.5 • 18 347 15.3 19.0 6.5 .20 621 5.8 7.2 22 .18273 15.8 19.6 7 ■ 20 543 6.0 7.5 22.5 . 18 200 16.3 20.2 7.5 . 20 466 6.2 7.7 23 .18126 16.8 20.9 8 .20388 6.4 8.0 23.5 • 18 053 17.3 21.5 8.5 . 20 311 6.6 8.3 24 .17979 17.8 22.2 9 • 20 234 6.8 8.5 24.5 .17 906 18.4 22.8 9.5 .20 156 7.0 8.8 25 •17833 18.9 23.5 10 . 20 080 7.3 9.1 25.5 .17 760 19.5 24.2 10.5 . 20 003 7.6 9.4 26 .17 687 20.1 25.0 11 .19927 7.8 9.8 26.5 .17614 20.7 25.7 11.5 .19850 8.1 10.1 27 •I7S42 21.3 26.5 12 •19 774 '8.3 10.4 27.5 .17469 21.9 27.3 12.5 .19 698 8.6 10.8 v 28 •!7 397 22.6 28.1 13 .19 622 8.9 11.1 28.5 • I 7 325 23.3 28.9 13.5 .19546 9.2 11.5 29 •17 253 24.0 29.7 14 .19470 9.5 11.9 29.5 .17 181 24.7 30.6 14.5 19 394 9.8 12.3 30 .17 109 25.4 31.5 15 .19318 10.1 12.7 Note.- - The table is based on Lord Rayleig h's weight of nitrogen, at latitude 41° and se level, 0.0012510 g. The characteristic of all the logarithms is —4. 20 BAROMETER CORRECTIONS Table VII. BAROMETER CORRECTIONS. For Temperature. Grlass Scale (Bunsen). Brass Scale (Delcros). mm. to be deducted. mm. to be deducted. f. Reading f. Reading. 700 720 740 760 780 700 720 740 760 780 1 0.120 0.123 0.127 0.130 0.133 1 0.113 0.116 0.119 0.123 0.126 2 0.2 0.2 0.3 0.3 0.3 2 0.2 0.2 0.2 0.3 0.3 8 0.4 0.4 0.4 0.4 0.4 3 0.3 0.4 0.4 0.4 0.4 4 0.5 0.5 0.5 0.5 0.5 4 0.5 0.5 0.5 0.5 0.5 5 0.6 0.6 0.6 0.7 0.7 5 0.6 0.6 0.6 0.6 0.6 6 0.7 0.7 0.8 0.8 0.8 6 0.7 0.7 0.7 0.7 0.8 7 0.8 0.9 0.9 0.9 0.9 7 0.8 0.8 0.8 0.9 0.9 8 1.0 1.0 1.0 1.0 1.1 8 0.9 0.9 1.0 1.0 1.0 9 1.1 1.1 1.1 1.2 1.2 9 1.0 1.0 1.1 1.1 1.1 10 1.2 1.2 1.3 1.3 1.3 10 1.1 1.2 1.2 1.2 1.3 11 1.3 1.4 1.4 1.4 1.5 11 1.2 1.3 1.3 1.4 1.4 12 1.4 1.5 1.5 1.6 1.6 12 1.4 1.4 1.4 1.5 1.5 IS 1.6 1.6 1.7 1.7 1.7 13 1.5 1.5 1.6 1.6 1.6 H 1.7 1.7 1.8 1.8 1.9 U 1.6 1.7 1.7 1.7 1.8 15 1.8 1.8 1.9 2.0 2.0 15 1.7 1.8 1.8 1.8 1.9 16 1.9 2.0 2.0 2.1 2.1 16 1.8 1.9 1.9 2.0 2.0 17 2.0 2.1 2.2 2.2 2.3 17 1.9 2.0 2.0 2.1 2.] 18 2.2 2.2 2.3 2.3 2.4 18 2.0 2.1 2.2 2.2 2.3 19 2.3 2.3 2.4 2.5 2.5 19 2.1 2.2 2.3 2.3 2.4 20 2.4 2.5 2.5 2.6 2.7 20 2.3 2.3 2.4 2.5 2.5 21 2.5 2.6 2.7 2.7 2.8 21 2.4 2.5 2.5 2.6 2.7 22 2.6 2.7 2.8 2.9 2.9 22 2.5 2.6 2.6 2.7 2.8 23 2.8 2.8 2.9 3.0 3.1 28 2.6 2.7 2.8 2.8 2.9 u 2.9 3.0 3.0 3.1 3.2 n 2.7 2.8 2.9 2.9 3.0 25 3.0 3.1 3.2 3.3 3.3 25 2.8 3.0 3.1 3.0 3.2 26 3.1 3.2 3.3 3.4 3.5 26 2.9 3.1 3.1 3.2 3.3 27 3.2 3.3 3.4 3.5 3.6 27 3.1 3.2 3.2 3.3 3.4 28 3.4 3.4 3.5 3.6 3.7 28 3.2 3.3 3.3 3.4 3.5 29 3.5 3.6 3.7 3.8 3.9 29 3.3 3.4 3.5 3.6 3.7 80 3.6 3.7 3.8 3.9 4.0 80 3.4 3.5 3.6 3.7 3.8 Notes on Densities of Gases and Vapors. — The molecular weight in grams of any gas or vapor has a volume of 22.4 liters at 0° and 760 mm. Hence: Mol. wt. = 22.4 X wt. of 1 liter in grams, and Wt. of 1 liter in grams. = mol. yrt. -5- 22.4. In most cases the values derived from these formulas do not correspond precisely with the observed values, but they suffice for most practical purposes. For instance, the volume of 32 g. of oxygen is 22.390 instead of 22.4 1., and in other cases there is still greater variation. It happens that the relation between grams and liters is practically the same as that be- tween ounces, avoirdupois and cubic feet, hence: Wt. of 1 cu. ft. in ounces, av. = mol. wt. -f- 22.4. The density of air corresponds to a mean molecular weight of 29, or more precisely 28.95 when compared with O2 as 32. Hence the molecular weight of a gas or vapor divided by 29 gives its density compared with air at the same temperature and pressure. 1 1. air at 0° and 760 mm. = 1.2928 g. MULTIPLES FOR ORGANIC COMPOUNDS ' Table VIII. MULTIPLES FOR ORGANIC COMPOUNDS. H H 2 H 3 H 4 H 6 H 6 H 7 H 8 H 9 Hio H u H12 H13 H w H15 Hl6 H17 His H19 H20 H21 H22 H23 H24 H25 H26 H27 H28 H29 H30 H31 H32 H33 H34 H35 H36 H37 H38 H39 H40 Number. 1.008 2.016 3.024 4.032 5.040 6.048 7.056 8.064 9.072 10.08 11.09 12.10 13.10 14.11 15.12 16.13 17.14 18.14 19.15 20.16 21.17 22.18 23.18 24.19 25.20 26.21 27.22 28.22 29.23 30.24 31.25 32.26 33.26 34.27 35.28 36.29 37.30 38.30 39.31 40.32 Log. Number. Log. Number. Log. 00346 C 12.005 .07 936 N 14.008 .14 638 30 449 C 2 24.01 •38 039 N 2 28.016 •44 741 48058 C 3 36.02 • 55 654 N 3 42.024 .62 350 60552 C 4 48.02 .68 142 N 4 56.036 •74 847 70243 c 6 60.03 •77 837 N 5 70.040 •84 535 78 161 c 6 72.03 •85 75i N 6 84.048 .92 453 84856 c 7 84.04 .92 449 N 7 98 .056 .99 147 90655 c 8 c 9 96.04 108.05 .98 245 .03 362 N 8 112.064 .04 947 95 770 S 32.06 •50 596 00 346 C10 120.05 •07 936 S 2 64.12 .80 699 04 493 Cu 132.06 .12 077 S 3 96.18 .98 308 08 279 C12 144.06 • 15854 S 4 128.24 .10 802 11 727 C13 156.07 •19 332 S 6 160.30 .20 493 14 953 C14 C16 168.07 180.08 .22 549 •25 546 S 6 192.36 .28 412 17 955 CI 35.46 •54 974 20763 C16 192.08 .28 348 Cl 2 70.92 ■85 077 23 401 Cl7 204.09 .30 982 Cl 3 106.38 .02 686 25864 C18 216.09 •33 463 cu 141.84 .15 180 28 217 Cl9 228.10 •35 8i3 CI 5 177.30 .24 871 30 449 C20 C21 240.10 252.11 •38 039 •40 159 Cl 6 212.76 •32 789 32 572 Br 79.92 .90 266 34 596 C22 264.11 •42 179 Br 2 159.84 .20 369 36 511 C23 276.12 .44 no Br 3 239.76 •37 978 38364 C24 C25 288.12 300.13 •45 957 •47 731 Br 4 319.68 •50 472 40 140 I 126.92 • 10353 41 847 C26 312.13 •49 433 I 2 253.84 .40 456 43 489 C27 324.14 •51 073 Is 380.76 .58 065 45 056 C28 C29 336.14 348.15 .52 652 •54 177 L 507.68 •70 559 46583 On 176 •24 551 48058 C30 360.15 •55 648 o 12 o 13 192 208 .28330 49 485 16 .20 412 .31 806 50866 2 32 •50515 o 14 224 •35 025 52 192 o 3 48 .68 124 o 16 240 .38 021 53 491 04 64 .80618 Oie 256 .40 824 54 753 5 80 .90 309 O17 272 •43 457 55 979 o 6 96 .98 227 o 18 288 •45 939 57 I7i 7 112 .04 922 o 19 304 .48 287 58320 o 8 128 .10 721 O20 320 •50515 59 450 9 144 .15836 021 336 •52 634 60 552 O10 160 .20 412 022 352 •54 654 22 CONSTANTS FOR MOLECULAR-WEIGHT DETERMINATIONS TABLE IX. CONSTANTS FOR MOLECULAR-WEIGHT DETERMINATIONS. (The constants are taken from Ostwald-Luther " Physiko-Chemische Messungen.") © The formula is M = K -rj, where M is the molecular weight of the dis- solved substance, s its weight in grams, L the weight of the solvent in grams, d the observed change in temperature, and K is the constant, which depends upon the nature of the solvent. By Depression of Freezing-point. Solvent. Water Benzole Naphthaline Phenanthrene Phenol Glacial acetic acid Nitrobenzole P. toluidine Solvent. Ethyl ether Benzole Chloroform Carbon bisulphide Glacial acetic acid Ethyl alcohol Ethyl acetate Acetone Water Ethylene bromide Aniline Phenol Melts at. i A.- N. Log. 0° 1850 .2672 5.5 5000 .6990 80 7000 .8451 96 12000 .0792 39 7500 ■87SI 17.7 3900 •59" 5.3 7000 .8451 42.5 5100 .7076 •ILING-POINT. , K.- Soils at. N. Log. 35° 2160 334S 80 2610 4166 61 3590 55Si 46 2350 37" 118 2530 4031 78 1170 0682 75 2680 4281 56 1720 2355 100 510 7076 132 6450 8096 182 3220 5°79 132 3040 4829 WEIGHTS AND MEASURES 23 Table X. WEIGHTS AND MEASURES. Length. Multiply by Factor. Given. Sought. N. Log. Inches Centimeters 2.540 40483 Centimeters Inches .39370 59 517 Feet Meters .30480 48 402 Meters Feet 3.2808 Si 598 Miles Kilometers 1.6093 20665 Kilometers Miles Area. .62137 79 335 Sq. Inches Sq. Centimeters 6.4516 80 967 Sq. Centimeters Sq. Inches . 1550 19033 Sq. Feet Sq. Meters .09290 96803 Sq. Meters Sq. Feet Volume. 10.764 03 197 Cu. Inches Cu. Centimeters 16.387 21 450 Cu. Centimeters Cu. Inches .06102 78 55o Cu. Feet Cu. Meters .02832 45 20 5 Cu. Meters Cu. Feet Capacity, 35.314 54 795 U. S. Fluid Ounces Cu. Centimeters 29.574 • 47 091 Cu. Centimeters U. S. Fluid Ounces .03381 52909 U. S. Quarts Liters .94635 97 605 Liters U. S. Quarts 1.0567 02395 U. S. Gallons Liters 3.7854 57812 Liters U. S. Gallons Weight. .26417 42 188 Grains Grams .06480 81 157 Grams Grains 15.432 18843 Ounces, troy- Grams 31.103 49 281 Grams Ounces, troy .03215 5° 7*9 Ounces, av. Grams 28.350 45 255 Grams Ounces, av. .03527 •54 745 Pounds, av. Grams 453.59 65667 Kilograms Pounds, av. 2.2046 34 333 24 NOTES ON THE USE OF LOGARITHMS NOTES ON THE USE OF LOGARITHMS. In these tables the "characteristics" of the logarithms, or the figures before their decimal points which fix the decimal points of the numbers, have been omitted, because in ordinary chemical calculations it is usually easier to find the positions of the decimal points by simple inspection of the numbers employed than by the use of characteristics. For example, suppose we have; .4693 g. AgCl (log .67145) to be multiplied by the factor which gives the amount of chlorine in it, .24738 (log .39336). The addition of the logs gives the log .06481, corresponding to the numerical figures 11610. Now by inspection, since .24738 is nearly \, or since .4693 is nearly §, it is evi- dent that the result must be not far from J of .4693 or \ of .24738, so that the deci- mal point must be placed to correspond; that is, .11610. Now if we divide the amount of chlorine by the weight of substance taken for analysis, say .2603 g. (log .41547) we have .06481 - .41547 = .64934, corresponding to the number .44601, the decimal point of which is found by inspection, since the result must be about 4 times .11610. Multiplying this by 100 we find 44.60% of chlorine. The fifth figure in this result is an uncertain one because it is derived from the datum .2603 ; hence it is best not to report it. In this case the trouble of interpolating for a fifth figure might have been avoided by taking four figures corresponding to the nearest logarithm. By the use of a co-logarithm (i.e., 1 — log) of the division the preceding calcu- lation may be made by a single addition: AgCl, .4693 log .67145 Factor, .24738 log .39336 Substance, .2603 1 - log .58453 .64934 -» 44.60% An inspection of the numbers employed above shows the position of the decimal point. The result could not possibly be 4.460%. The student who is not skilful in the use of logarithms should practice multipli- cations and divisions with numbers giving known results until he acquires pro- ficiency. The easily remembered logarithm of 2, which is .30103, is often of considerable assistance in calculations. For instance, the logarithm of the atomic weight of Mg, 24.32, is .38596; hence the log of 2 Mg is .68699 and that of § Mg is .08493. LOGARITHMS OF NUMBERS FIVE-PLACE TABLE WITH DOUBLE THUMB-INDEX (26) 1 .000 - 26 LOGARITHMS OF NUMBERS. N. 1 2 3 4 5' 6 7 8 9 P.P. 100 oo ooo 043 087 130 173 217 260 3°3 346 389 101 43 2 475 5i8 56i 604 647 689 732 775 817 1 4 4 4 102 86o 903 945 988 *o30 1=072 *ii5 *i57 *i99 *242 2 9 9 8 103 oi 284 326 368 410 452 494 53 6 578 620 662 3 13 13 13 104 703 745 787 828 870 912 953 995 *°3<5 *°7 8 4 5 6 18 17 17 105 02 119 160 202 243 284' 325 3 66 407 449 490 26 26 25 106 S3i 572 612 653 694 735 776 816 857 898 V 3 1 3° 29 107 938 979 *oi9 *o6o *IOO 1=141 *i8i *222 *262 *3° 2 8 35 34 34 108 °3 342 383 423 463 503 543 583 623 663 7°3 9 4° 39 38 109 743 782 822 862 902 941 981 *02I *o6o *IOO 110 04 139 179 218 258 297 33 6 37 6 415 454 493 111 53 2 57i 610 650 689 727 766 805 844 883 1 41 40 39 4 4 4 8 8 8 112 922 961 999 *o 3 8 *°77 *n5 * I 54 *I92 *23I *269 ?, 113 05 3° 8 346 385 423 461 5°o 538 576 614 652 3 12 12 12 114 690 729 767 805 843 881 918 956 994 1=032 4 5 6 16 16 16 21 20 20 25 24 23 115 06 070 108 145 183 221 258 296 333 37i 408 116 446 483 52i 558 595 633 670 7°7 744 78i 7 29 28 27 117 819 856 «93 93° 967 1=004 *o4i *o78 *ii5 *i5i 8 33 32 31 118 07 188 225 262 298 335 372 408 445 482 5i8 9 37 36 35 119 555 59i 628 664 700 737 773 809 846 882 120 918 954 990 *02 7 *o63 *°99 **35 *i7i *207 *243 121 08 279 314 35° 386 422 458 493 529 565 600 I 38 37 36 4 4 4 8 7 7 11 11 11 122 636 672 707 743 778 814 849 884 920 955 ?, 123 991 *026 *o6i 1=096 *I 3 2 *l67 *202 *237 *272 1=307 3 124 09 342 377 412 447 482 517 552 587 621 656 4 5 6 15 15 H 19 19 18 23 22 22 125 691 726 760 795 830 864 899 934 968 1=003 126 10 037 072 106 140 175 209 243 278 312 346 7 27 26 25 127 380 4i5 449 483 517 551 585 619 653 687 8 30 30 29 128 721 755 789 823 857 890 924 958 992 1=025 9 34 33 32 129 11 059 °93 126 160 193 227 261 294 327 361 130 394 428 461 494 528 561 '594 628 66l 694 131 727 760 793 826 860 893 926 959 992 1=024 1 35 34 33 4 3 3 7 7 7 132 12 057 090 123 15C 189 222 254 287 320 352 •}, 133 385 418 45° 483 516 548 58l 613 646 678 3 11 10 10 134 710 743 775 808 840 872 9°5 937 969 *OOI 4 5 14 14 13 18 17 17 135 13 °33 066 098 130 162 194 226 258 290 322 6 21 20 20 136 354 38b 418 45° 481 5i3 545 577 609 640 7 25 24 23 137 672 704 735 767 799 830 862 8Q3 925 956 8 28 27 26 138 988 *oi9 *o5i *082 *H4 *i45 *i7<> *2o8 *239 1=270 9 3 2 3 1 3° 139 14 301 333 3 6 4 395 426 457 489 520 55i 582 140 613 644 675 706 737 768 799 829 860 891 141 922 953 983 *oi4 *°45 ♦076 *io6 **37 *i68 1=198 1 32 31 3D 3 3 3 6 6 6 142 15 229 2 S9 290 320 35i 381 412 442 473 5°3 a 143 534 5<>4 594 625 055 685 7i5 746 776 806 3 10 9 9 144 836 866 897 927 957 987 *oi7 *°47 *°77 1=107 4 5 6 .13 12 12' 145 16 137 167 197 227 256 286 316 346 376 406 16 16 15 19 r 9 l8 . 146 435 4<>5 495 524 554 584 613 643 673 702 7 22 22 21 147 73 2 761 791 820 850 879 909 938 967 997 8 26 25 24 148 17 026 056 085 114 143 173 202 231 260 289 9 29 28 27 149 3i9 348 377 406 435 464 493 522 55i 580 IT. O 1 2 3 4 5 6 7 8 9 P.P. LOGARITHMS OF NUMBERS. 27 N. O 1 2 3 4 5 6 7 8 9 P. P> 150' 17 609 638 667 696 725 754 782 811 840 869 151 898 926 955 984 *°i3 *04i =•=070 *099 *i27 *is6 1 3 3 152 18 184 213 241 270 298 327 355 384 412 441 2 5 6 153 469 498 526 554 583 611 639 667 696 724 3 ? 8 154 752 780 808 837 865 893 173 921 201 949 229 977 *°°5 257 285 4 5 6 12 11 15 14 17 17 155 J 9 033 061 089 117 145 156 312 34° 368 396 424 45i 479 5°7 535 562 V 20 20 157 59° 618 645 673 700 728 756 783 811 838 8 9 23 22 26 25 158 866 893 921 948 976 *oo3 =•=030 ♦058 *o8s *ii2 159 20 140 167 194 222 249 276 548 303 575 33° 602 358 385 629 656 160 412 439 466 493 520 161 683 710 737 763 790 817 844 871 898 925 1 3 3 162 95 2 978 *oo5 *032 *°59 *o8 5 *II2 *i 39 *i6s *i92 2 5 5 163 21 219 245 272 299 325 352 378 4°5 43 * 458 3 S 8 164 484 5ii 537 564 59° 617 643 669 696 722 4 5 6 11 10 14 13 16 16 165 748 775 801 827 854 880 906 932 958 985 166 22 on °37 063 089 115 141 167 194 220 246 V 1 j 18 167 272 298 324 350 376 401 427 453 479 5°5 8 9 22 21 168 53 1 557 583 608 634 660 686 712 737 763 24 23 169 789 814 840 866 891 917 172 943 198 968 223 994 *oi9 249 274 25 1 170 23 045 070 096 121 147 171 300 325 35° 376 401 426 452 477 502 528 1 3 172 553 578 603 629 654 679 704 729 754 779 2 5 173 805 830 855 880 9°5 93° 955 980 *oo5 *030 3 8 174 24 °55 080 105 130 155 180 204 229 254 279 4 5 6 10 13 15 175 3°4 329 353 378 403 428 452 477 5°2 527 176 55i 576 601-^625 650 674 699 724 748 773 7 18 177 797 822 846 871 895 920 944 969 993 *° l8 8 9 20 178 25 042 066 091 "5 139 164 188 212 237 261 23 179 285 310 334 358 382 406 43 1 455 479 5°3 180 527 55i 575 600 624 648 672 696 720 744 181 768 792 816- 840 864 888 912 935 959 983 1 2 2 182 26 007 031 °55 079 102 126 150 174 198 221 2 5 5 183 245 269 293 316 34o 364 387 411 435 458 3 7 7 184 482 5°5 529 553 576 600 623 647 670 694 4 5 6, 1 1 1 3 9 2 12 ! i 14 185 717 74i 764 788 811 834 858 881 905 928 186 95i 975 998 *02I *045 *o68 *09i *ii4 *i38 *i6i V 1 7 16 187 27 184 207 231 254 277 300 323 346 37° • 393 8 9 1 i l8. 188 416 439 462 485 508 53 1 554 577 600 623 189 646 669 692 715 738 761 784 807 830 852 22 21 190 875 898 921 944 967 989 *OI2 *°35 ="058 *o8i 191 28 103 126 149 171 194 217 240 262 285 307 1 2 2 192 33° 353 375 398 421 443 466 488 5ii 533 2 * 4 193 556 578 601 623 646 668 69I 713 735 758 3 ? 6 194 780 803 825 847 870 892 914 937 959 981 4 5 6 1 1 ? 8 1 11 3 13 195 29 003 026 048 070 092 «S 137 159 181 203 196 226 248 270 292 314 336 358 380 403 425 7 8 9 1 5 15 3 17 D 19 197 447 469 491 513 535 557 579 601 623 645 2 198 <■' 667 688 710 73 2 754 776 798 820 842 863 199 885 907 929 95i 973 994 *oi6 *o 3 8 *o6o *o8i N. 1 2 ,3 4 5 6 7 8 9 P. P. 9 .954 1 .000 28 LOGARITHMS OF NUMBERS. N. 1 2 3 4 5 6 7 8 9 P.P. 200 3° io 3 "5 146 168 190 211 233 255 276 298 201 320 34i 363 384 406 428 449 47i 492 514 1 2 2 202 ' 535 557 578 600 621 643 664 685 707 728 2 4 4 203 75° 771 792 814 835 856 878 899 920 942 3 7 6 204 963 3 r J 75 984 197 *oo6 218 *027 239 *o48 260 ^069 *09i *II2 **33 *i54 4 5 6 9 8 11 11 •3 13 j 205 281 302 323 345 366 206 387 408 429 450 47i 492 513 534 555 576 7 '5 15 i 207 597 618 639 660 681 702 723 744 765 785 8 18 17 208 806 827 848 869 890 911 93 ! 952 973 994 9 20 19 209 3 2 015 222 °35 243 056 263 077 284 098 3°5 118- !39 160 181 201 210 325 346 366 387 408 211 428 449 469 490 5i° 53i 552 572 593 613 1 2 212 634 654 675 695 7i5 73<> 756 777 797 818 2 4 213 838 858 879 899 919 940 960 980 *OOI *02I 3 6 214 33 041 062 082 102 122 J 43 163 183 203 224 4 5 6 8 10 12 215 244 264 284 3°4 325 345 365 385 4°5 425 216 445 465 486 506 526 546 566 586 606 626 7 14 217 646 666 686 706 726 746 766 786 806 826 8 16 218 846 866 885 9°5 925 945 965 985 *oo5 *025 9 18 219 34 044 242 064 262 084 282 104 301 124 321 r 43 163 183 203 223 220 34i 361 380 400 420 221 439 459 479 498 5i8 537 557 577 596 616 1 2 222 635 655 674 694 7*3 733 753 772 792 811 2 4 223 830 850 869 889 908 928 947 967 986 *oo5 3 6 224 35 ° 2 5 218 044 238 064 257 083 276 102 295 122 141 160 180 199 4 5 6 8 10 11 225 3i5 334 353 372 392 226 411 43° 449 468 488 5°7 526 545 564 583 7 13 227 603 622 641 660 679 698 717 736 755 774 8 15 228 793 813 832 851 870 889 908 927 946 965 9 17 ! 229 984 3 6 *73 *oo3 192 *02I 211 *040 '229 *°59 248 *078 *°97 *n6 *i35 *i54 230 267 286 3°5 324 342 231 361 380 399 418 43 6 455 474 493 5" 53° 1 2 232 549 568 586 605 624 642, 661 680 698 717 2 4 233 736 754 773 791 810 829 847 866 884 9°3 3 5 234 922 37 107 940 125 959 144 977 162 996 181 *oi4 199 *°33 218 *°5* 236 *o7o 254 *o88 273 4 5 6 7 9 11 235 236 291 310 328 346 365 383 401 420 438 457 7 13 237 475 493 5" 53° 548 566 585 603 621 639 8 14 238 658 676 694 712 73 1 749 767 785 803 822 9 16 239 840 858 876 894 912 93 J 949 967 985 *°°3 240 38 021 °39 o57 o75 °93 112 130 148 166 184 241 202 220 238 256 274 292 310 328 346 364 1 2 242 382 399 4i7 435 453 47i 489 5°7 525 543 2 3 243 561 578 596 614 632 650 668 686 7°3 721 3 5 244 739 757 775 792 810 828 846 863 881 899 4 5 6 7 9 10 245 917 934 952 970 987 *°°5 *023 *04i •058 *o76 246 39 °94 in 129 146 164 182 199 217 235 252 7 12 247 270 287 305 322 34P 358 375 393 410 428 8 9 H 248 445 463 480 498 515 533 55° 568 585 602 15 i 249 620 637 655 672 690 707 724 742 759 777 ST. 1 2 3 4 5 6 7 8 9 P.P. LOGARITHMS OF NUMBERS. 29 N. 1 2 3 4 5 6 7 8 9 P.P. 250 39 794 811 829 846 863 881 8q8 9i5 933 95o 251 967 985 *002 *oi9 *°37 *o54 *o7i *o88 *io6 *I23 1 is 2 252 40 140 157 175 192 209 226 243 261 278 295 2 4 253 312 3 2 9 346 364 381 398 415 43 2 449 466 3 5 254 483 500 518 535 552 569 586 603 620 637 4 5 6 7 9 11 255 654 671 688 7o5 722 739 756 773 790 807 256 824 841 858 875 892 909 926 943 960 976 7 13 257 993 *OIO *027 *°44 *o6i *o78 *°95 *ni *I28 *i45 8 14 258 41 162 179 196 212 229 246 263 280 296 3 J 3 9 16 259 33° 347 3<>3 380 397 414 43° 447 464 481 260 497 5i4 53i 547 564 58i 597 614 631 647 261 664 681 697 7i4 73i 747 764 780 707 814 1 2 262 830 847 863 880 896 913 929 946 963 979 2 3 263 996 *OI2 *029 *Q45 *o62 *o78 *°95 *iii *I27 *I44 3 5 264 42 160 177 193 210 226 243 259 275 292 308 4 5 6 7 9 10 265 3 2 5 341 357 374 390 406 423 439 455 472 266 488 504 521 537 553 570 586 602 619 6 35 7 12 267 651 667 684 700 716 732 749 765 78i 797 8 '4 268 8i3 830 846 862 878 894 911 927 943 959 9 15 269 975 99I *oo8 *024 *o4o *os6 *072 *o88 *I04 *I20 270 43 136 152 169 185 201 217 233 249 265 28l 271 297 3*3 329 345 361 377 393 409 425 441 1 2 272 457 473 489 505 521 537 553 569 S84 600 2 3 273 616 632 648 664 680 696 712 727 743 759 3 5 274 775 791 807 823 838 854 870 886 902 917 4 5 6 6 8 10 275 933 949 965 981 996 *OI2 *028 *044 *°59 *°75 276 44 091 107 122 138 154 170 185 201 217 232 7 11 277 248 264 279 295 3" 326 342 358 373 389 8 9 13 278 404 420 43 6 45i 467 483 498 514 529 545 l A 2 .301 279 560 576 592 607 623 638 654 669 68 S 700 280 716 73 1 747 762 778 793 809 824 840 855 281 871 886 902 917 932 948 963 979 994 *OIO 1 2 3 282 45 ° 2 5 040 056 071 086 102 117 *33 148 163 . 2 3 .477 283 179 194 209 225 240 2 55 271 286 301 3*7 3 5 284 33 2 347 362 378 393 408 ' 423 439 454 469 4 5 6 6 8 9 285 484 500 5i5 53° 545 56i 576 591 606 621 4 286 637 652 667 682 697 712 728 743 758 773 7 11 .602 287 788 803 818 834 849 864 879 894 909 924 8 9 12 ,' 288 939 954 969 984 *ooo *oi5 *°3° *o45 *o6o *o75 '4 f -"*" 289 46 090 i°5 120 135 150 16S 180 195 210 225 14 5 290 240 255 270 285 300 3i5 33° 345 359 374 .698 291 389 404 419 434 449 464 479 494 509 523 1 1 292 538 553 568 583 598 613 627 642 657 672 2 3 6 293 687 702 716 73i 746 761 776 790 805 820 3 4 294 835 850 864 879 894 909 923 938 953 967 4 5 6 6 7 8 >ifo 295 982 997 *OI2 *026 *04i =1=056 *o7o •085 *IOO *H4 ' 7 296 47 i 2 9 144 159 173 188 202 217 232 246 261 7 8 9 10 297 276 290 3°5 3*9 334 349 3 6 3 378 392 407 13 .846 298 422 43 6 45i 465 480 494 5°9 524 538 553 299 567 582 596 611 625 640 654 669 683 698 8 N. O' 1 2 3 4 5 6 7 8 9 P.P. .903 9 .964 1 .000 30 LOGARITHMS OF NUMBERS. N. 1 jj 3 4 5 6 7 8 9 P.P. 300 47 7 12 727 741 756 770 784 799 813 828 842 301 857 871 885 900 914 929 943 958 972 986 1 2 302 48 001 oiS 029 044 058 073 087 IOI 116 130 2 3 303 144 159 173 187 202 216 230 244 259 273 3 5 304 287 302 316 330 344 359 373 387 401 416 4 5 6 6 8 9 305 43° 444 458 473 487 5oi 515 53° 544 558 306 572 586 601 615 629 643 657 671 686 700 7 11 307 714 728 742 756 770 78S 799 813 827 841 8 9 12 308 855 869 883 897 911 926 940 954 968 982 '4 309 996 *OIO *024 *o 3 8 *052 *o66 *o8o *°94 *io8 *I22 310 49 *3 6 150 164 178 192 206 220 234 248 262 311 276 290 304 318 332 346 360 374 388 402 312 415 429 443 457 471 48S 499 5i3 527 54 1 313 SS4 568 582 596 610 624 638 651 665 679 314 693 707 721 734 748 762 776 79o 803 817 14 315 831 845 859 872 886 900 914 927 941 955 2 3 316 969 982 996 *OIO *024 *o 3 7 *o5i *o65 *o79 *092 3 4 317 50 106 120 *M 147 161 174 188 202 21S 229 4 6 318 243 256 270 284 297 3" 325 338 352 365 5 6 7 8 9 7 8 10 11 319 379 393 406 420 433 447 461 474 488 501 320 ' 515 5 2 9 542 556 569 583 596 610 623 637 321 651 664 678 691 7°S 718 732 74S 759 772 13 322 786 799 813 826 840 853 866 880 893 907 323 920 934 947 961 974 987 *OOI *oi4 *028 *o4i 324 5* °SS 068 081 °95 108 121 135 148 162 175 325 188 202 215 228 242 255 268 282 295 308 326 322 335 348 362 37S 388 402 415 428 441 327 4SS 468 481 495 508 521 534 548 561 574 328 587 601 614 627 640 654 667 680 693 706 1 1 329 720 733 746 759 772 786 799 812 82s 838 2 3 4 3 4 5 330 851 865 878 891 904 917 93o 943 957 970 331 983 996 *oo9 *022 *Q35 *o 4 8 *o6i *o75 *o88 *IOI 5 7 332 52 114 127 140 *53 166 179 192 205 218 231 6 8 333 244 257 270 284 297 310 323 330 349 362 7 9 334 375 388 401 414 427 44o 453 466 479 492 8 9 10 12 335 5°4 5i7 530 543 556 569 582 595 608 621 336 634 647 660 673 686 699 711 724 737 75o 337 763 776 789 802 815 827 840 853 866 879 338 892 9°5 917 930 943 956 969 982 994 *oo7 339 53 ° 2 ° °33 046 058 071 084 097 no 122 135 340 148 161 J 73 186 199 212 224 237 250 263 341 275 288 301 3*4 326 339 352 364 377 39° 1 1 342 403 4i5 428 441 453 466 479 491 504 5i7 2 2 343 529 542 555 567 580 593 605 618 631 643 3 4 344 656 668 681 694 706 719 845 732 857 744 870 757 882 769 89S 4 5 6 5 6 7 345 782 794 807 820 832 346 908 920 933 945 958 970 983 995 *oo8 *020 7 8 347 54 t>33 045 058 070 083 o95 108 120 133 145 8 9 10 348 iS8 170 183 !95 208 220 233 245 258 270 349 283 295 307 320 332 345 357 37° 382 394 N. O 1 2 3 4 5 6 7 8 9 P.P. LOGARITHMS OF NUMBERS. 31 N. O 1 2 3 4 5 6 7 8 9 P.P. 350 54 407 419 432 444 456 469 481 494 506 518 351 53* 543 555 568 580 593 6 °5 6l 7 6 3° 6 42 1 1 352 654 667 679 691 704 716 728 741 753 765 2 3 353 777 790 802 814 827 839 851 864 876 888 3 4 354 900 913 925 937 949 962 974 986 998 *on 4 5 6 5 7 8 355 55 o 2 3 °35 047 060 072 084 096 108 121 133 356 i45 157 169 182 194 206 218 230 242 255 7 9 357 267 279 291 3°3 3*5 328 340 352 364 376 8 9 10 358 388 400 413 425 437 449 461 473 485 497 359 5°9 522 534 546 558 570 582 594 606 618 360 630 642 654 666 678 691 703 715 727 739 361 75i 763 775 787 799 811 823 835 847 859 362 871 883 «95 907 919 93 1 943 955 9 6 7 979 363 991 *oo3 *oi.s *o27 *038 ♦050 *o62 *o74 *o86 *098 364 56 no 122 *34 146 158 170 182 194 205 217 13 365 229 241 2 53 265 277 289 301 312 324 336 1 2 2 366 348 360 37 2 384 396 407 419 431 443 4SS 3 4 367 467 478 490 5° 2 5 r 4 526 538 549 561 573 4 5 368 585 597 608 620 632 644 656 667 679 691 5 6 369 703 7M 726 738 75° 761 773 785 797 808 6 7 8 7 8 10 370 820 832 844 855 867 879 891 902 914 926 371 937 949 961 972 984 996 *oo8 *oi9 *o3i *o43 9 11 372 57 °54 066 078 089 IOI 113 124 136 148 159 373 171 183 194 206 217 229 241 252 264 276 374 287 299 310 322 334 345 357 3 68 3 8 o 392 375 403 415 426 438 449 461 473 484 496 5°7 376 519 53° 542 553 565 576 588 600 611 623 377 634 646 657 669 680 692 703 715 726 738 378 749 761 772 784 795 807 818 830 841 852 1 1 379 864 875 887 898 910 921 933 944 955 9 6 7 2 3 4 2 3 4 380 978 990 *OOI *oi3 *024 *o35 *o47 *o58 *o7o *o8i 381 58 092 104 "5 127 138 149 161 172 184 195 5 6 382 206 218 229 240 252 263 274 286 297 309 6 7 383 320 33i 343 354 365 377 388 399 410 422 7 8 384 433 444 456 467 478 490 501 512 524 535 8 9 9 10 385 546 557 569 580 59 1 602 614 625 636 647 386 659 670 681 692 704 715 726 737 749 760 387 771 782 794 805 816 827 838 850 861 872 388 883 894 906 917 928 939 95o 961 973 984 389 995 *oo6 *oi7 *028 *040 ♦051 *o62 *o73 *o84 *095 162 173 184 195 207 390 59 lo6 118 129 140 151 391 218 229 240 251 262 273 284 295 306 318 1 1 392 3 2 9 34o 35i 3 62 373 384 395 406 417 428 2 2 393 439 45° 461 472 483 494 5°6 5*7 528 539 3 3 394 55° 56i 572 583 594 605 616 627 638 649 4 5 6 4 5 6 395 660 671 682 693 704 715 726 737 748 759 396 77° 780 791 802 813 824 835 846 857 868 7 7 397 879 890 901 912 923 934 945 956 9 66 977 8 9 8 398 988 999 *OIO *02I #032 *043 *o54 *o65 *o76 *o86 9 399 60 097 108 119 I30 141 152 163 173 184 195 N. 1 2 3 4 5 6 ' 7 8 9 P.P. 8 .903 9 .954 1 .000 32 LOGARITHMS OF NUMBERS. N. O 1 2 3 4 5 6 7 8 9 P.P. 400 6o 206 217 228 239 249 260 271 282 293 3°4 401 3 r 4 325 336 347 358 3 6 9 379 390 401 412 402 423 433 444 455 466 477 487 498 5°9 520 403 53i 54i 552 563 574 584 595 606 617 627 404 638 649 660 670 681 692 7°3 713 724 735 405 746 756 767 778 788 799 810 821 831 842 406 853 863 874 885 895 906 917 927 938 949 1 1 407 959 970 981 991 *002 *oi3 *023 *Q34 *Q45 *<>55 2 2 408 61 066 077 087 098 I09 119 r 3° 140 151 162 3 3 409 172 183 194 204 215 225 236 247 257 268 4 5 6 4 6 7 410 278 289 300 310 321 33 1 342 352 3&3 374 411 384 395 405 416 426 437 448 458 469 479 7 8 412 490 500 5" 521 532 542 553 563 574 584 8 9 9 413 595 606 616 627 637 648 658 669 679 690 414 700 711 721 73 1 742 752 763 773 784 794 415 805 815 826 836 847 857 868 878 888 899 416 909 920 93° 941 951 962 972 982 993 *°°3 417 62 014 024 °34 °45 °55 066 076 086 097 107 418 118 128 138 149 159 170 180 190 201 211 419 221 232 . 242 252 263 273 284 294 304 315 420 3 2 5 335 346 356 366 377 387 397 408 418 421 428 439 449 459 469 480 •490 5°o ?" 521 1 2 10 422 53i 542 552 562 572 583 593 603 613 624 423 634 644 655 66 5 675 68 5 696 706 716 726 3 3 4 5 6 424 737 747 757 767 778 788 798 808 818 829 4 5 6 425 839 849 859 870 880 890 900 910 921 93* 426 941 95i 961 972 982 992 *002 *OI2 *022 *°33 7 7 427 63 043 °53 063 073 083 094 I04 114 124 *34 8 8 428 144 i55 165 175 185 195 205 215 225 236 9 9 429 246 256 266 276 286 296 306 317 327 337 430 347 357 367 377 387 397 407 417 428 438 431 448 458 468 478 488 498 5°8 518 S28 5^8 432 548 558 568 579 589 599 609 619 629 6 39 433 649. 659 669 679 689 699 709 719 729 739 434 749 759 769 779 789 799 809 819 829 839 435 849 859 869 879 889 899 909 919 929 939 436 949 959 969 979 988 998 *oo8 *oi8 *028 *038 1 1 437 64 048 058 068 078 088 098 108 118 128 I 31 2 2 438 i47 157 167 177 I8 7 197 207 217 227 237 3 3 439 246 256 266 276 286 296 306 316 326 335 4 5 6 4 5 5 440 345 355 365 375 385 395 404 414 424 434 441 444 454 464 473 483 493 503 5i3 523 532 7 8 9 6 442 542 552 562 572 582 59i 601 611 621 631 7 8 443 640 650 660 670 680 689 699 709 719 729 444 738 748 758 768 777 787 797 807 816 826 445 836 846 856 86s 875 885 895 904 914 924 446 933 943 953 963 972 982 992 *002 *OII *02I 447 65 °3 X 040 050 060 070 079 089 099 108 Il8 448 128 I 37 147 157 167 176 186 I96 20s 2 J 5 449 225 234 244 2 54 263 273 283 292 302 312 N. 1 2 3 4 5 6 7 8 9 P.P. LOGARITHMS OF NUMBERS. 33 N. o 1 2 3 4 5 6 7 8 9 P.P. 450 65 3 21 33i 34i 350 360 3 6 9 379 389 398 408 451 418 427 437 447 456 466 475 485 495 5°4 452 5i4 523 533 543 55 2 562 57i 581 591 600 453 610 619 629 6 39 648 658 667 677 686 696 454 706 7i5 725 734 744 753 763 772 782 792 10 455 801 811 820 830 839 849 858 868 877 887 456 896 906 916 9 2 5 935 944 954 9 6 3 973 982 1 1 457 992 *OOI *OII *020 *°3° *°39 *049 *os8 *o68 *o77 2 3 4 2s 458 66 087 096 106 "5 124 134 J 43 153 162 172 3 4 5 i 6 7 8 459 181 191 200 210 219 229 238 247 257 266 5 6 7 8 460 276 285 295 3°4 3*4 3 2 3 332 34 2 35 1 361 461 37° 380 389 398 408 4i7 427 436 445 455 462 464 474 483 492 502 5" 521 53° 539 549 9 Q 463 558 567 577 586 596 605 614 624 633 642 464 652 661 671 680 689 699 708 717 727 736 465 745 755 764 773 783 792 801 811 820 829 466 839 848 857 867 876 885 894 904 913 922 467 93 2 941 95° 960 969 978 987 997 *oo6 *oi5 468 67 025 °34 °43 052 062 071 080 089 099 108 469 117 127 136 145 154 164 173 182 191 201 9 470 210 219 228 237 247 • 2 56 265 274 284 293 471 302 3" 321 33° 339 348 357 367 376 385 1 I 472 394 403 413 422 43 1 440 449 459 468 477 2 2 473 486 495 5°4 5i4 523 532 54i 550 560 569 3 4 5 6 7 g 3 474 578 587 596 605 614 624 6 33 642 651 660 4 5 5 6 7 8 475 669 679 688 697 706 7i5 724 733 74 2 75 2 476 761 770 779 788 797 806 815 825 834 843 477 852 861 870 879 888 897 906 916 925 934 9 478 943 952 961 970 979 988 997 *oo6 *oi5 *024 479 68 034 043 052 061 070 079 088 097 106 115 480 124 1 33 142 151 160 169 178 187 196 205 481 215 224 233 242 251 260 269 278 287 296 482 3°5 3i4 323 33 2 34i 35° 359 368 377 386 483 395 404 413 422 43 1 440 449 458 467 476 484 485 494 5° 2 5" 520 5 2 9 538 547 556 56S 8 485 574 583 592 601 610 619 628 637 646 655 486 664 673 681 690 699 708 717 726 73s 744 1 1 487 753 762 771 780 789 797 806 815 824 833 2 ' 488 842 851 860 869 878 886 895 904 913 922 3 4 5 6 7 8 9 2 489 93 1 940 949 958 966 975 984 993 *002 *OII 3 4 5 6 6 490 69 020 028 °37 046 °55 064 °73 082 090 O99 491 108 117 126 i35 144 i5 2 161 170 179 l88 492 197 205 214 223 232 241 249 258 267 276 7 493 285 294 302 311 320 329 338 346 355 3 6 4 494 373 381 39° 399 408 417 425 434 443 45 2 495 461 469 478 487 496 5°4 513 5 22 53i 539 496 548 557 566 574 583 592 601 609 618 627 497 636 644 653 662 671 679 688 697 705 714 498 7 2 3 73 2 740 749 758 767 775 784 793 801 499 810 819 827 836 845 854 862 871 880 888 sr. 1 2 3 4 5 6 7 8 9 P. P. 9 .964 1 .000 34 LOGARITHMS OF NUMBERS. N. O 1 2 3 4 5 6 7 8 9 P.P. 500 69 897 906 914 923 932 940 949 958 966 97s 501 984 992 *OOI *OIO *oi8 *027 *036 *°44 *o53 *o62 502 70 070 079 088 096 W 114 122 131 140 148 503 iS7 165 174 183 191 200 209 217 226 234 504 243 252 260 269 278 286 295 303 312 321 505 3 2 9 338 346 355 3 6 4 372 38! 389 398 406 506 4i5 424 432 441 449 458 467 475 484 492 1 507 S°i 509 5i8 526 535 544 552 56i 5°9 578 2 2 508 586 595 603 612 621 629 638 646 655 66 3 3 3 509 672 680 689 697 706 7i4 723 73 1 74° 749 4 5 6 4 5 5 510 757 766 774 783 791 800 808 817 825 834 511 842 851 859 868 876 88s 893 902 910 919 7 6 512 927 935 944 952 961 969 978 986 995 *°°3 8 7 513 71 012 020 029 °37 046 054 063 071 079 088 9 8 514 096 i°5 "3 122 130 *39 147 i55 164 172 515 181 189 198 206 214 223 231 240 248 257 516 265 273 282 290 299 3°7 315 324 332 34i 517 349 357 366 374 383 39i 399 408 416 425 518 433 441 45° 458 466 475 483 492 500 508 519 517 525 533 542 55° 559 567 575 5 8 4 592 520 600 609 617 625 634 642 650 659 667 675 521 684 692 700 709 717 725 734 742 75° 759 1 B 522 767 775 784 792 800 809 817 825 834 842 2 523 850 858 867 875 883 892 900 908 917 925 3 2 524 933 941 95° 958 966 975 983 991 999 *oo8 4 5 6 3 v 4 5 525 72 016 024 032 041 049 o57 066 074 082 090 526 099 107 "5 123 132 140 148 156 165 173 7 6 527 181 189 198 206 214 222 230 239 247 255 8 6 528 263 272 280 288 296 3°4 313 321 329 337 9 7 529 346 354 362 37o 378 387 395 403 411 419 530 428 43 6 444 452 460 469 477 485 493 5°i 531 5°9 5i8 526 534 542 '550 558 567 575 583' 532 59i 599 607 616 624 632 640 648 656 665 533 673 681 689 697 7°5 713 722 73° 738 746 534 754 762 770 779 787 795 803 811 819 827 535 835 843 852 860 868 876 884 892 900' 908 536 916 925 933 941 949 957 965 973 981 989 1 1 537 997 *oo6 *oi4 *022 *°3° *°38 *o46 *°54 *o62 *o7o 2 1 538 73 078 086 094 I02 in 119 127 135 143 !5i 3 2 539 159 167 175 I«3 191 199 207 215 223 231 4 5 6 3 4 4 540 239 247 255 263 272 280 288 296 3°4 3 12 541 320 328 336 344 352 360 368 37° 384 392 7 5 542 400 408 416 424 432 440 448 45° 464 472 8 9 6 6. 543 480 488 496 5°4 512 520 528 53° 544 552 544 560 568 576 584 592 600 608 616 624 632 545 640 648 656 664 672 679 687 695 703 711 546 719 727 735 743 751 759 767 775 783 79J 547 . 799 807 8i5 823 830 838 846 854 862 870 548 878 886 894 902 910 918 926 933 941 949 549 957 965 973 981 989 997 *oo5 ♦013 *020 *028 N. O 1 2 3 4 5 6 7 8 9 P.P. LOGARITHMS OF NUMBERS. 35 N. O 1 2 3 4 5 6 7 8 9 P.P. 550 74 036 044 052 060 068 076 084 092 099 107 551 "5 123 1 3 1 J 39 147 i55 162 170 178 186 552 194 202 210 218 225 233 241 249 257 265 553 273 280 288 296 3°4 312 320 327 335 343 554 35i 359 367 374 382 390 398 406 414 421 555 429 437 445 453 461 468 476 484 492 500 556 5°7 5i5 523 53i 539 547 554 562 57° 578 557 586 593 601 609 617 624 632 640 648 656 558 663 671 679 687 695 702 710 718 726 733 559 74i 749 757 764 772 780 858 788 865 796 873 803 881 811 889 s 560 819 827 834 842 850 561 896 904 912 920 927 935 943 95° 958 966 1 1 562 974 981 989 997 *oo5 *OI2 *020 *028 *°35 *°43 2 2 563 75 051 059 066 074 082 089 097 105 "3 120 3 2 564 128 136 i43 151 J 59 . , 166 243 174 251 182 2 59 189 266 197. 274 4 5 6 7 8 9 3 4 5 565 205 2.13 220 228 236 566 282 289 297 3°5 312 320 328 335 343 35i 6 6 7 567 358 366 374 381 389 3-97 404 412 420 427 568 435 442 45° 458 465 473 481 488 496 5°4 569 5" 5i9 526 534 542 549 557 565 572 58° 570 587 595 603 610 618 626 633 641 648 656 571 664 671 679 686 694 702 709 717 724 732 572 740 747 755 762 770 778 785 793 800 808 573 815 823 831 838 846 853 861 868 876 884 574 891 899 906 914 921 929 937 944 952 959 575 967 974 982 989 997 *oo5 *OI2 *020 *02 7 *°35 576 76 042 050 °57 065 072 080 087 095 103 no 577 118 125 i33 140 148 155 163 170 178 185 578 *93 200 208 215 223 230 238 245 253 260 579 268 275 283 290 298 3°5 3 1 3 320 328 335 7 ' 580 343 35° 358 365 373 380 388 395 4°3 410 581 418 425 433 440 448 455 462 47° 477 485 1 1 582 492 500 5°7 515 522 53° 537 545 552 559 2 1 583 567 574 582 589 597 604 612 619 626 634 3 2 584 641 649 656 664 671 678 686 693 701 708 4 5 6 3 4, 4 585 716 723 73° 738 745 753 760 768 775 782 586 790 797 805 812 819 827 834 842 849 856 7 8 9 5 6 6 587 864 871 879 886 893 901 908 916 923 93° 588 938 945 953 960 967 975 982 989 997 *oo4 589 77 012 019 026 034 041 048 056 063 070 078 590 085 °93 100 107 115 122 129 i37 144 151 591 159 166 173 181 188 195 203 210 217 225 592 232 240 247 254 262 269 276 283 291 298 593 3°5 3 J 3 320 327 335 342 349 357 364 37i 594 379 386 393 401 408 4i5 422 43° 437 444 595 45 2 459 466 474 481 488 495 5°3 5i° 517 596 525 S3 2 539 546 554 56i 568 576 583 59° 597 597 605 612 619 627 634 641 648 656 663 598 670 677 685 692 699 706 7i4 721 728 735 599 743 75o 757 764 772 779 78b 793 . 801 808 N. 1 2 3 4 5 6 7 8 9 P.P. 9 .964 1 .000 36 LOGARITHMS OF NUMBERS. N. 1 2 3 4 5 6 7 8 9 P. P. 600 77 8i5 822 830 837 844 851 859 866 873 880 601 887 895 902 909 916 924 931 938 945 952 602 960 967 974 981 988 996 *oo3 *OIO *oi7 *Q25 603 78 032 °39 046 °53 061 068 075 082 089 097 604 104 in 118 125 132 140 147 154 161 168 8 I 605 176 183 . T 9° 197 204 211 219 226 233 240 606 247 254 262 269 276 283 290 297 3°5 312 1 607 3*9 326 333 340 347 355 3 62 3^9 376 383 2 2 608 39° 398 405 412 419 426 433 440 447 455 3 2 609 462 469 476 483 490 497 5°4 512 5i9 526 4 5 6 3 4 5 610 533 54° 547 554 561 569 576 583 59° 597 611 604 611 618 625 633 640 647 654 661 668 7 6 612 675 682 689 696 704 711 718 725 732 739 8 6 613 746 7 53 760 767 774 781 789 796 803 810 9 7 614 817 824 831 838 845 852 859 866 873 880 615 888 895 902 909 916 923 -.930 937 944 95i 616 958 965 972 979 986 993 *ooo *oo7 *oi4 *02I 617 79 029 036 043 050 °57 064 071 078 085 092 618 099 106 "3 120 127 134 141 148 155 162 619 169 176 183 190 197 204 211 218 225 232 620 239 246 2 53 260 267 274 281 288 295 302 621 3°9 316 3 2 3 33° 337 344 351 358 3 6 5 372 1 1 622 379 386 393 400 407 414 421 428 435 442 2 1 623 449 45 6 463 470 477 484 49 * 498 5°5 511 3 2 624 5i8 5 2 5 532 539 546 553 56o 5^7 574 581 4 5 6 3 4 4 625 588 595 602 609 616 623 630 637 644 650 626 657 664 671 678 685 692 699 706 7i3 720 7 5 627 727 734 74i 748 754 761 768 775 782 789 8 6 628 796 803 810 817 824 831 837 844 851 858 9 6 629 865 872 879 886 893 900 906 9 1 3 920 927 630 934 941 948 955 962 9 6 9 975 982 989 996 631 80 003 010 017 024 030 037 044 051 058 065 632 072 079 085 092 099 106 113 120 127 *34 633 140 147 154 161 168 175 lg 2 188 195 202 634 209 216 223 229 236 243 250 257 264 271 635 277 284 291 298 3°5 312 318 325 332 339 636 346 353 359 366 373 380 387 393 400 407 1 637 414 421 428 434 441 448 455 462 468 475 2 1 638 482 489 496 502 5°9 5*6 523 53° 53& 543 3 2 639 55° 557 564 570 577 584 59* 59« 604 611 4 5 6 2 3 4 640 618 625 632 638 645 652 659 665 672 679 641 686 693 699 706 7*3 720 726 733 740 747 7 4 642 754 760 767 774 781 787 794 801 808 814 8 5 643 821 828 835 841 848 855 862 868 875 882 9 5 644 889 895 902 909 916 922 929 93 6 943 949 _ 645 956 9 6 3 969 976 983 990 .996 *oc>3 *OIO *oi7 646 81 023 030 °37 043 050 057 064 070 077 084 647 090 097 104 in 117 124 131 J 37 144 151 648 158 164 171 178 184 191 198 204 211 218 649 224 231 238 245 251 258 265 271 278 285 P P. N. O 1 2 3 4 5 6 7 8 9 LOGARITHMS OF NUMBERS. 37 N. 1 2 3 4 5 6 7 8 9 P.P. 650 8i 291 298 3°5 3" 3i8 325 33 r 338 345 35i 651 358 365 37i 378 385 39i 398 4°5 411 418 652 425 43i 438 445 45i 458 465 47i 478 485 653 491 498 5°5 5" 5i8 525 53i 538 544 55i 654 558 564 57i 578 584 59i 657 598 664 604 671 611 677 617 684 655 624 631 637 644 651 656 690 697 704 710 717 723 73° 737 743 75° 657 757 763 77° 776 783 790 796 803 809 816 658 823 829 836 842 849 856 862 86g 875 882 659 889 «95 902 908 9i5 921 928 935 941 948 660 954 961 968 974 981 987 994 *ooo *oo7 *oi4 661 82 020 027 °33 040 046 ' °53 060 066 °73 079 1 1 662 086 092 099 i°5 112 119 125 132 138 MS 2 1 663 151 158 164 171 178 184 191 197 204 210 3 2 664 217 223 230 236 243 249 256 263 269 276 4 5 6 3 4 4 665 282 289 295 302 308 3 IS 321 328 334 34i 666 347 354 360 367 373 380 387 393 400 406 7 5 667 4i3 419 426 432 439 445 452 458' 465 47i 8 6 668 478 484 491 497 5°4 5i° 5i7 523 53° 536 9 6 669 543 549 556 562 569 575 582 588 595 601 670 607 614 620 627 633 640 646 653 659 666 671 672 679 685 692 698 7°S 711 7i8 724 73° 672 737 743 75° 756 763 769 776 782 789 795 673 802 808 814 821 827 834 840 847 853 860 674 866 872 879 885 892 898 9°5 911 918 924 675 93° 937 943 95o 956 963 969 975 982 988 676 995 *OOI *oo8 *oi4 *020 *027 *°33 *040 *o46 *052 677 83 059 065 072 078 085 091 097 104 no 117 678 123 129 136 142 149 15s 161 168 174 181 679 187 *93 200 206 213 219 283 225 289 232 296 238 302 245 308 680 251 257 264 270 276 681 315 321 327 334 340 347 353 359 366 372 1 1 682 378 385 391 398 404 410 4i7 423 429 436 2 1 683 442 448 455 461 467 474 480 487 493 499 3 2 684 506 512 5i8 525 S3 1 537 544 5S° 556 563 4 5 6 2 3 4 685 569 575 582 588 594 601 607 613 620 626 686 632 639 645 651 658 664 670 677 683 689 7 4 687 696 702 708 715 721 727 734 740 746 753 8 9 5 688 759 7.65 771 778 784 790 797 803 809 816 5 689, 822 828 835 841 847 853 860 866 872 879 690 885 891 897 904 910 916 9 2 3 929 935 942 691 948 954 960 967 973 979 985 992 998 *oo4 692 84 on 017 023 029 036 042 048 °55 061 067 693 073 080 086 092 098 i°5 in 117 123 130 694 136 142 148 155 161 167 173 180 186 192 695 198 205 211 217 223 230 236 242 248 255 696 261 267 2 73 280 286 292 298 3°5 3 11 317 697 3 2 3 33° 33(> 342 348 354 361 367 373 379 698 386 392 398 404 410 417 423 429 435 442 699 448 454 460 466 473 479 485 491 497 5°4 N. 1 2 3 4 5 6 7 8 9 P.P. 9 .954 1 .000 38 LOGARITHMS OF NUMBERS. N. O 1 2 3 4 5 6 7 8 9 P. P. 700 84 5™ 5i6 522 528 535 54i 547 553 559 566 701 572 578 584 59° 597 603 609 615 621 628 702 634 640 646 652 658 665 671 677 683 689 703 696 702 708 7i4 720 726 733 739 745 75i 704 7S7 763 770 776 782 788 794 800 807 813 705 819 825 831 837 844 850 856 862 868 874 706 880 887 893 899 9°5 911 917 924 930 936 1 1 707 942 948 954 960 967 973 979 985 991 997 2 1 708 85 o°3 009 016 022 028 °34 040 046 052 058 3 2 709 065 071 077 083 089 °9S 101 107 114 120 4 5 6 3 4 4 710 126 132 138 144 150 156 163 169 i75 181 711 187 J 93 199 205 211 217 224 230 236 242 7 5 712 248 2 54 260 266 272 278 285 291 297 3°3 8 6 713 3°9 3i5 321 327 333 339 345 352 358 364 9 6 714 .37° 376 382 388 394 400 406 412 418 425 715 43i 437 443 449 455 461 467 473 479 485 716 491 497 503 5°9 5i6 522 S28 534 54o 546 717 552 558 564 57° 576 582 588 594 600 606 718 612 618 625 631 637 643 649 655 661 667 719 673 679 685 691 697 7°3 709 7i5 721 727 6 I 720 733 739 745 75i 757 763 769 775 781 788 721 794 800 806 812 818 824 830 836 842 848 1 722 854 860 866 872 878 884 890 896 902 908 2 1 723 914 920 926 932 938 944 95° 956 962 968 3 2 724 974 980 986 992 998 *oo4 *OIO *oi6 *02 2 *028 4 5 6 2 3 4 725 86 034 040 046 052 058 064 070 076 082 088 726 094 100 106 112 118 124 130 136 141 147 7 4 727 153 159 165 171 177 183 189 195 20I 207 8 9 5 728 213 219 225 231 237 243 249 255 26l 267 5 729 273 279 285 291 297 303 308 3*4 320 326 730 332 338 344 35° 356 362 368 374 380 386 731 39 2 398 404 410 4i5 421 427 433 439 445 732 45i 457 463 469 475 481 487 493 499 5°4 733 5io 5i6 522 528 534 54° 546 552 558 564 734 57° 576 581 587 593 599 60s 611 617 623 ' 735 629 635 641 646 652 658 664 670 676 682 736 688 694 700 7°5 711 717 723 729 735 741 1 1 737 747 753 759 764 77° 776 782 788 794 800 2 1 738 806 812 817 823 829 835 841 847 853 859 3 2 739 864 870 876 882 888 894 900 906 911 917 4 5 6 2 3 3 740 923 929 935 941 947 953 958 964 970 976 741 982 988 994 999 *oo5 *OII *oi7 *023 *029 *°35 7 4 742 87 040 046 052 058 064 070 °75 081 087 °93 8 9 4 743 099 i°5 in 116 122 128 i34 140 146 151 5 744 157 163 169 175 181 186 192 198 204 210 745 216 221 227 2 33 239 245 251 256 262 268 746 274 280 286 291 297 3°3 3°9 315 320 326 747 332 338 344 349 355 361 3^7 373 379 384 748 39° 396 402 408 413 419 425 43i 437 442 749 448 454 460 466 47i 477 483 489 495 500 N. O 1 2 3 4 5 6 7 8 9 P. P. LOGARITHMS OF NUMBERS. 39 K. O 1 3 3 4 5 6 7 8 9 P.P. 750 87 506 512 5i8 523 529 535 54i 547 552 558 751 5 6 4 57° 576 58i 587 593 599 604 610 616 752 622 628 6 33 6 39 645 651 656 662 668 674 753 679 685 691 697 7°3 708 7i4 720 726 73i 754 737 743 749 754 760 766 772 777 783 789 755 795 800 806 812 818 823 829 835 841 846 756 852 858 864 869 875 881 887 892 898 904 757 910 9i5 921 927 933 938 944 95° 955 961 758 967 973 978 984 99° 996 *OOI *oo7 *oi 3 *oi8 759 88 024 030 036 041 047 °53 058 064 070 076 760 081 087 °93 098 104 no 116 121 127 J 33 761 138 144 150 156 161 167 J 73 178 184 190 1 6 I 762 195 201 207 213 218 224 230 235 241 247 2 I 763 252 258 264 270 275 281 287 292 298 3°4 3 2 764 3°9 3i5 321 326 332 338 343 349 355 360 4 5 6 .2 3 4 765 366 372 377 383 389 395 400 406 412 417 766 423 429 434 440 446 45i 457 463 468 474 7 4 767 480 485 491 497 5°2 508 5i3 5i9 525 53° 8 5 768 536 542 547 553 559 564 57° 576 581 587 9 5 769 593 598 604 610 615 621 627 632 638 °43 770 649 655 660 666 672 677 683 689 694 700 771 7°5 711 717 722 728 734 739 745 75° 756 772 762 767 773 779 784 790 795 801 807 812 773 818 824 829 835 840 846 852 857 863 868 774 874 880 885 891 897 902 908 9*3 919 925 775 93° 93<5 941 947 953 958 964 969 975 981 776 986 992 997 *oo3 *oo9 *oi4 *020 *02 5 *°3i *°37 777 89 042 048 °53 o59 064 070 076 081 087 092 778 098 104 109 "5 120 126 131 137 143 148 779 i54 159 i65 170 176 182 187 193 198 204 780 209 215 221 226 232 237 243 248 254 260 781 265 271 276 282 287 2 93 298 304 310 3 r 5 1 2 5 782 321 326 332 337 343 348 354 360 365 37i 1 1 783 376 382 387 393 398 404 409 415 421 426 3 2 784 43 2 437 443 448 454 459 465 470 476 481 4 5 6 2 3 3 785 487 492 498 504 509 515 520 526 53i 537 786 542 548 553 559 564 570 575 581 586 592 7 4 787 597 603 609 614 620 625 631 636 642 647 8 4 788 653 658 664 669 675 680 686 691 697 702 9 5 789 708 713 719 724 73° 735 74i 746 752 757 - 790 763 768 774 779 785 790 796 801 807 812 791 818 823 829 834 840 845 851 856 862 867 792 873 878 883 889 894 900 9°5 911 916 922 793 927 933 938 944 949 955 960 966 971 977 794 982 988 993 998 *oo4 *oc>9 *oi5 *020 *026 *°3 r - 795 90 037 042 048 o53 °59 064 069 075 080 086 796 091 097 102 108 "3 119 124 I29 135 140 797 146 151 157 162 168 173 179 184 189 195 798 200 206 211 217 222 227 2 33 238 244 249 799 255 260 266 271 276 282 287 293 298 3°4 N. 1 2 3 4 5 6 7 8 9 P.P. 1 .000 • i 2 10 LOGARITHMS OF NUMBERS. .301 N. O 1 2 3 4 5 6 7 8 P.P. 3 800 90 309 3 J 4 320 325 33 1 336 342 347 352 358 •477 801 3 6 3 369 374 380 385 39° 39<> 401 407 412 802 417 423 428 434 439 445 45° 455 461 466 4 ■602 803 472 477 482 488 493 499 5°4 509 5i5 520 804 526 53* 536 542 547 553 558 5&3 569 574 805 580 585 590 596 601 607 612 617 623 628 806 634 687 6 39 693 644 698 650 7°3 655 709 660 666 671 725 677 73° 682 5 .698 807 7i4 720 736 808 741 747 752 757 763 768 773 779 784 789 809 795 800 806 811 816 822 827 832 838 843 810 849 854 859 865 870 875 881 886 891 897 6 811 902 907 9i3 918 924 929 934 940 945 95o 1 1 -.778 812 956 961 966 972 977 982 988 993 998 *oo4 2 1 813 91 009 014 020 025 030 036 041 046 052 °57 3 2 814 062 068 o73 078 084 089 094 100 i°5 no 4 5 6 2 3 4 7 815 116 121 126 132 i37 142 148 153 158 164 .845 816 169 i74 180 1 85 190 196 201 206 212 217 7 4 *s 817 222 228 233 238 243 249 254 2 59 265 270 8 9 5 8 .903 818 275 281 286 291 297 302 3o7 312 318 323 5 819 328 334 339 344 35° 355 360 365 37i 37<> 820 381 387 392 397 403 408 413 418 424 429 821 434 440 445 45° 455 461 466 47i 477 482 822 487 492 498 5°3 508 5i4 5i9 524 529 535 823 S4o 545 55i 556 56i 566 572 577 582 587 824 S93 598 603 609 614 619 624 630 635 640 825 645 651 656 661 666 672 677 682 687 6 93 826 698 7°3 709 714 719 724 73° 735 740 745 827 7Si 756 761 766 772 777 782 787 793 798 828 803 808 814 819 824 829 834 840 845 850 829 855 861 866 871 876 882 887 892 897 9°3 830 908 9 J 3 918 924 929 934 939 944 95° 955 831 960 965 971 976 981 986 991 997 *002 *oo7 1 1 832 92 012 018 023 028 °33 038 044 049 054 °59 2 1 833 065 070 °75 080 085 091 096 101 I06 in 3 2 834 117 122 127 132 137 143 148 153 158 163 4 5 6 2 ■ 3 3 835 169 174 179 184 189 195 200 205 2IO 215 836 221 226 231 236 241 247 252 257 262 267 7 4 837 273 278 283 288 293 298 3°4 3°9 314 3*9 8 4 838 3 2 4 33° 335 34° 345 35° 355 361 366 37 1 9 5 839 376 381 387 392 397 402 407 412 418 423 840 428 433 438 443 449 454 459 464 469 474 841 480 485 490 495 500 5°5 5" 5i6 521 526 842 53* 536 542 547 552 557 562 5<>7 572 578 843 S83 588 593 598 603 609 614 619 624 629 844 634 639 645 650 655 660 665 670 675 681 845 686 691 696 701 706 711 716 722 727 73 2 846 737 742 747 752 758 763 768 773 778 783 847 788 793 799 804 809 814 819 824 829 834 848 840 845 850 8.55 860 86 S 870 875 88l 886 849 891 896 901 906 911 916 921 927 932 937 N". O 1 2 » 4 5 6 7 8 9 P.P. LOGARITHMS OF NUMBERS. 41 N. 1 2 3 4 5 6 7 8 9 P. P. 850 92 942 947 952 957 962 967 973 978 983 988 851 993 998 *oc>3 *oo8 *oi3 *oi8 *024 *029 *°34 *039 852 93 044 049 054 •059 064 069 075 080 085 090 853 °9S 100 i°5 no "5 120 125 1 3 I 136 141 854 146 151 156 161 166 171 176 181 186 192 6 I 855 197 202 207 212 217 222 227 232 237 242 856 247 252 258 263 268 2 73 278 283 288 293 1 857 298 3°3 308 3*3 318 323 328 334 339 344 2 I 858 349 354 359 3 6 4 3 6 9 374 379 384 389 394 3 2 859 399 404 409 414 420 425 43° 435 440 445 4 5 6 2 3 4 860 45° 455 460 465 47° 475 480 485 490 495 861 50° 5°5 5io 5i5 520 526 53i 536 54i 546 7 4 862 55* 556 56i 566 57i 57° 58i 586 591 596 8 9 5 863 601 606 611 616 621 626 631 6^6 641 646 5 864 651 656 661 666 671 676 682 687 692 697 865 702 707 712 717 722 727 732 737 f42 747 866 75 2 757 762 767 772 777 782 787 792 797 867 802 807 812 817 822 827 832 837 842 847 868 852 857 862 867 872 877 882 887 892 897 869 902 907 912 917 922 927 932 937 942 947 870 . 95 2 957 962 .967 972 977 982 987 992 997 871 94 002 007 012 017 022 027 032 037 042 047 1 1 872 052 °57 062 067 072 077 082 086 091 096 2 1 873 lor 106 in 116 121 126 I 3 I 136 141 146 3 •2 874 151 156 161 166 171 176 181 186 191 196 4 5 6 2 3 i : 3 875 201 206 211 216 221 226 231 236 240 245 876 250 255 260 265 270 275 280 285 290 295 7 4 877 300 3°5 310 3i5 320 325 33° 335 34o 345 8 9 4 878 349 354 359 364 3 6 9 374 379 384 389 394 5 879 399 404 409 414 419 424 429 433 438 443 880 448 453 458 463 468 473 478 483 488 493 881 498 5°3 5°7 512 5i7 522 527 532 537 542 882 547 552 557 562 567 57i 57<> 58i 586 59i 883 59 6 601 606 611 616 621 626 630 635 640 884 64S 650 655 660 66 S 670 675 680 685 689 4 885 694 699 704 709 714 719 724 729 734 738 886 743 748 753 75« 763 768 773 778 783 787 1 887 792 797 802 807 812 817 822 827 832 836 2 1 888 841 846 851 856 861 866 871 876 880 885 3 1 889 890 895 900 9°5 910 9*5 919 924 929 934 4 5 6 2 2 2 890 939 944 949 954 959 963 968 973 978 983 891 988 993 998 *002 *oo7 *OI2 *oi7 *022 *027 1=032 7 3 892 95 °3 6 041 046 05I 056 061 066 07I 075 080 8 9 3 4 893 085 090 °95 IOO 105 IO9 114 119 124 129 894 134 J 39 143 148 153 158 163 168 173 177 895 182 187 192 IQ7 202 207 211 2l6 221 226 896 231 236 240 245 250 255 260 265 270 274 897 279 284 289 294 299 3°3 308 3*3 318 323 898 328 332 337 342 347 352 357 361 366 37i 899 376 381 386 390 395 400 4°5 410 415 419 N. O 1 2 3 4 5 6 7 8 9 P .P. 1 .000 40 2 ,_ .301 3 .477 4 .602 42 LOGARITHMS OF NUMBERS. 5 .698 6 i.778 7 ■ .845 • 8 .903 9 .954 X. O 1 2 3 4 5 6 7 8 9 ^M 900 95 424 429 434 439 444 448 453 458 463 468 i\ 901 472 477 482 487 492 497 5°i 506 5 11 5^ i 902 S2i 525 53° 535 54° 545 55° 554 559 564 m 903 569 574 578 583 .588 593 598 602 607 612 904 617 622 626 631 636 641 646 650 ft55 660 i 1 905 665 670 674 679 684 689 694 698 7°3 708 906 713 718 722 727 732 737 742 746 75 1 756 907 761 766 770 775 780 785 789 794 799 804 908 809 81, 818 82^ 828 8 S 2 831 842 «47 852 909 856 861 866 871 875 880 885 890 895 899 947 5 910 904 909 914 918 923 928 933 938 942 911 952 9S7 961 966 971 976 980 985 990 995 1 1 912 999 *oo4 *oo9 *oi4 *oi9 *023 *028 *o33 ♦038 *042 2 1 913 96 047 052 °57 061 066 071 076 080 085 090 3 4 5 6 7 8 g 2 914 °9S 099 104 109 114 118 123 128 *33 1 37 3 3 915 142 147 J 52 156 161 166 171 175 180 185 916 190 194 199 204 209 213 218 223 227 232 4 917 237 242 246 251 256 261 265 270 275 280 4 5 918 284 289 294 298 303 308 313 317 322 327 919 332 33 6 341 346 35o 355 360 3ft5 3 6 9 374 920 379 384 388 393 398 402 407 412 417 421 921 426 43 1 435 440 445 45° 454 459 464 468 922 473 478 483 487 492 497 5°i 506 5ii 5i5 923 520 525 53° 534 539 544 548 553 558 562 924 567 572 577 58i 586 591 595 600 605 609 925 614 619 624 628 6 33 638 642 647 652 656 926 661 666 670 675 680 68 S 689 694 699 7°3 927 708 713 717 722 727 73 1 73ft 74i 745 75° 928 755 759 764 769 774 778 783 788 792 797 929 802 806 811 816 820 825 830 834 839 844 930 848 853 858 862 867 872 876 881 886 890 931 895 900 904 909 914 918 923 928 93 2 937 1 932 942 946 95i 956 960 9ft5 970 974 979 984 2 1 933 988 993 997 *002 *oo7 *OII *oi6 *02I *°25 *°3o 3 1 934 97 °35 °39 044 049 °53 058 063 067 072 077 4 5 6 2 ! 2 ( 2 935 081 086 090 °95 100 104 109 114 118 123 936 128 132 137 142 146 151 155 160 165 169 7 3 937 174 179 183 188 192 197 202 206 211 216 8 3 938 220 225 230 234 239 243 248 2 53 257 262 9 4 939 267 271 276 280 285 290 294 299 3°4 308 940 3*3 317 322 327 33 1 33^ 34o 345 35o 354 941 359 3 6 4 3 68 373 377 382 387 39 1 396 400 942 4°5 410 414 419 424 428 433 437 442 447 943 45i 456 460 465 470 474 479 483 488 493 944 497 502 506 5ii Sib 520 525 529 534 539 945 543 548 552 557 562 566 571 575 58o 58S 946 589 594 598 603 607 612 617 621 626 630 947 635 640 644 649 653 658 663 667 672 676 948 681 685 690 695 699 704 708 713 717 722 949 727 73 1 736 740 745 749 754 759 763 768 - N. 1 3 3 4 5 6 7 8 9 P. P. LOGARITHMS OF NUMBERS. 43 N. o 1 3 4 5 6 7 8 9 P.P. 950 97 772 777 782 786 791 795 800 804 809 811 951 818 823 827 832 836 841 845 850 855 8^9 952 864 868 873 877 882 886 891 896 900 9°S 953 909 914 918 923 928 932 937 941 946 95° 954 955 959 964 968 973 978 982 987 991 996 955 98 000 005 009 014 019 023 028 032 °37 041 956 046 050 °55 °59 064 068 °73 078 082 087 957 091 096 100 i°5 109 114 118 123 127 132 958 J 37 141 146 150 155 159 164 168 i73 177 959 182 186 191 195 200 204 209 214 218 223 960 227 232 236 241 245 250 254 2 59 263 268 961 272 277 281 286 290 295 299 3°4 308 3*3 1 1 962 318 322 327 33 1 33 6 34o 345 349 354 358 2 1 963 3 6 3 367 372 376 381 385 39° 394 399 4°3 3 2 964 408 412 417 421 426 43° 435 439 444 448 4 5 6 2 3 3 965 453 457 462 466 47i 475 480 484 489 493 966 498 502 507 5" 5i6 520 525 529 534 538 7 4 967 543 547 552 556 561 5<>5 57° 574 579 583 8 4 968 * 588 592 597 60 r 605 610 614 619 623 628 9 5 969 632 637 641 646 650 655 659 664 668 673 970 677 682 686 691 695 700 704 709 7*3 717 971 722 726 73 1 735 740 744 749 753 758 762 972 767 771 776 780 784 789 793 798 802 807 973 811 816 820 82s 829 834 838 843 847 851 974 856 860 865 869 874 878 883 887 892 896 975 900 905 909 914 918 923 927 93 2 936 941 976 945 949 954 958 9 6 3 967 972 976 981 985 977 989 994 998 *oo3 *oc>7 *OI2 *oi6 *02I *°25 *029 978 99 034 038 043 047 052 O56 061 065 069 074 979 078 083 087 092 096 IOO i°5 I09 114 118 980 123 127 1 3 1 136 140 145 149 154 158 162 981 167 171 176 180 185 189 J 93 I98 202 207 1 4 982 211 216 220 224 229 2 33 238 242 247 251 2 983 255 260 264 269 273 277 282 286 291 295 3 1 984 300 3°4 308 3 I 3 3*7 322 326 33° 335 339 4 5 6 2 2 2 985 344 348 352 357 361 366 37° 374 379 383 986 388 392 39<5 401 4°5 410 414 419 423 427 7 3 987 432 43 6 441 445 449 454 45« 463 467 47i 8 3 988 476 480 484 489 493 498 502 506 5" 515 9 4 989 520 524 528 533 537 542 546 55° 555 559 990 564 568 572 577 58i 585 59° 594 599 603 991 607 612 616 621 625 629 634 638 642 647 992 651 656 660 664 669 673 677 682 686 691 993 695 699 704 708 712 717 721 726 73° 734 994 739 743 747 752 756 760 7&5 769 774 778 995 782 787 791 795 800 804 808 813 817 822 996 826 830 835 839 843 848 852 856 861 865 997 870 874 878 883 887 891 89b 900 904 909 998 9*3 917 922 926 93° 935 939 944 948 952 999 957 961 965 970 974 978 983 987 991 996 N". 1 2 3 4 5 6 7 8 9 P.P. 9 .964