NRLF 
 
PHYSICAL AND CHEMICAL CONSTANTS 
 
RECENTLY PUBLISHED 
 
 NEW IDEAS ON INORGANIC CHEMISTRY. By Dr. 
 A. WERNER, Professor of Chemistry in the University of 
 Zurich. Translated, with the Author's sanction, from the 
 second German edition, by EDGAR PERCY HEDLEY, 
 Ph.D., A.R.C.Sc.I. 8vo, 7*. &/. net. 
 
 THE RELATIONS BETWEEN CHEMICAL CONSTI- 
 TUTION AND SOME PHYSICAL PROPERTIES. 
 By SAMUEL SMILES, D.Sc., Fellow of University College, 
 and Assistant Professor of Organic Chemistry at University 
 College, London University. Crown 8vo, 14^. 
 
 NEW REDUCTION METHODS IN VOLUMETRIC 
 ANALYSIS. A Monograph. By EDMUND KNECHT, 
 Ph.D., M.Sc.Tech., F.I.C., Professor of Technological 
 Chemistry at the Victoria University of Manchester, and 
 EVA HIBBERT, Demonstrator in Chemistry, Municipal 
 School of Technology, Manchester. Crown 8vo, 3^. net. 
 
 A HISTORY OF THE THEORIES OF AETHER AND 
 ELECTRICITY, from the Age of Descartes to the Close 
 of the Nineteenth Century. By E. T. WHITTAKER, Hon. 
 Sc.D. (Dublin), F.R.S., Royal Astronomer of Ireland. 
 8vo, I2j. &/. net. 
 
 ANALYTICAL MECHANICS, comprising the Kinetics and 
 Statics of Solids and Fluids. By EDWIN H. BARTON, 
 D.Sc. (Lond.), F.R.S.E., A.M.I.E.E., Professor of 
 Experimental Physics, University College, Nottingham. 
 8vo, los. 6d. net. 
 
 ELEMENTS OF MECHANICS. With numerous Examples, 
 for the use of Schools and Colleges. By GEORGE W. 
 PARKER, M.A., of Trinity College, Dublin. With 116 
 Diagrams and Answers to Examples. 8vo, 4*. 6d. 
 
 A HISTORY OF THE CAVENDISH LABORATORY, 
 1871-1910. With 3 Portraits in Collotype and 8 other 
 Illustrations. 8vo, 'js. 6d. net. 
 
 LONGMANS, GREEN, AND CO. 
 
 LONDON, NEW YORK, BOMBAY, AND CALCUTTA 
 
.TABLES OF 
 
 PHYSICAL AND 
 CHEMICAL CONSTANTS 
 
 AND SOME MATHEMATICAL FUNCTIONS 
 
 BY 
 
 G. W. C. KAYE 
 
 B.A. (CANTAB.), D.Sc. (LOND.), A.R.C.Sc. (LOND.) 
 
 THE NATIONAL PHYSICAL LABORATORY ; LATE SUB-LECTOR IN PHYSICS, TRINITY COLLEGE, 
 
 CAMBRIDGE 
 
 AND 
 
 T. H. LABY 
 
 B.A. (CANTAB.) 
 
 PROFESSOR OF PHYSICS, WELLINGTON, N.Z. ; FORMERLY EXHIBITION OF 1851 SCHOLAR; 
 JOULE STUDENT ; AND RESEARCH EXHIBITIONER, EMMANUEL COLLEGE, CAMBRIDGE 
 
 LONGMANS, GREEN, AND CO. 
 
 39 PATERNOSTER ROW, LONDON 
 NEW YORK, BOMBAY, AND CALCUTTA 
 1911 
 
 All rights reserved 
 
C 
 
 
PREFACE 
 
 THE need for a set of up-to-date English physical and chemical tables 
 of convenient size and moderate price has repeatedly impressed us during 
 our teaching and laboratory experience. We have accordingly attempted 
 in this volume to collect the more reliable and recent determinations of 
 some of the important physical and chemical constants. 
 
 To increase the utility of the book, we have inserted, in the case of 
 many of the sections, a brief resiwnt containing references to such books 
 and original papers as may profitably be consulted. 
 
 Every effort has been made to keep the material up to date ; in many 
 cases a full reference to the original paper is given, while, failing such 
 reference, the year of publication is almost always indicated. 
 
 The scope of the volume calls for little comment on our part. We 
 have dipped a little into Astronomy, Engineering, and Geology in so far 
 as they border on Physics and Chemistry. It will be noticed that con- 
 siderable space has been allotted to Radioactivity and Gaseous lonization : 
 it is hoped that the collection of data, which we believe to be the first 
 of the kind, will be of assistance to the numerous workers in a field whose 
 phenomenal and somewhat transitional growth is a little dismaying from our 
 present point of view. 
 
 Attention has been paid to the setting and accuracy of the mathe- 
 matical tables ; these are included merely to facilitate calculations arising 
 out of the use of the book, and limitations of space have cut out all but 
 a few of the more essential functions. The convenience of the student 
 of the newer physics has been studied by the inclusion of a table of values 
 of t~ * reduced from Newman's original results. 
 
 It is remarkable in how few cases the physical properties of pure, 
 commonly occurring chemical compounds are known with accuracy : the 
 task of augmenting (not always with discrimination) already overburdened 
 families of organic compounds receives much greater attention. 
 
 For many of the constants which date from before 1905 we are glad 
 to acknowledge our indebtedness to the very complete and accurate 
 Physikalisch-Chemische Tabellen of Landolt Bornstein and Meyerhoffer 
 (indicated throughout by L.B.M.). 
 
 235470 
 
vi PREFACE 
 
 We began this book while at the Cavendish Laboratory, Cambridge, 
 and Dr. G. A. Carse shared in its inception. To Mr. G. F. C. Searle, 
 F.R.S., we feel we owe much for his encouragement and suggestions when 
 the scope of the book was under consideration. We record gratefully the 
 help of a number of friends who have seen the proof-sheets of sections 
 dealing with subjects with which their names are associated. Dr. J. A. 
 Harker, F.R.S., and Mr. R. S. Whipple read the sections, on Thermometry ; 
 Mr. F. E. Smith revised the account of Electrical Standards, and Mr. C. C, 
 Paterson that of Photometry ; Mr. A. Campbell criticized the section on 
 Magnetism ; and Professor Callendar, Principal Griffiths, and Dr. Chree 
 have elucidated various points in Heat and Terrestrial Magnetism. 
 
 We owe thanks to Dr. Glazebrook for his permission to utilize the 
 values of a number of constants recently determined at the National 
 Physical Laboratory. Finally, we are greatly indebted to Mr. E. F. F. 
 Kaye, M.Sc., who has given us valuable assistance in preparing the 
 manuscript and revising the proof-sheets. 
 
 It was decided to keep the volume within reasonable limits, partly for 
 the reader's convenience, and partly with the hope that the task of 
 subjecting it to frequent revision in the future might not be impossible. 
 We have consequently had to pick and choose our data, and it is scarcely 
 likely that, our selection will meet every individual requirement. That 
 some sections are inadequately treated we fully realize, and we shall be 
 very glad to receive suggestions and to be informed of any mistakes 
 which, despite every care, have eluded us. 
 
 G. W. C. K. 
 T. H. L. 
 
 September, 1911. 
 
CONTENTS 
 
 PAGES 
 
 GENERAL PHYSICS, ASTRONOMY, ETC i 43 
 
 HEAT 44 _ 66 
 
 SOUND :"... 6768 
 
 LIGHT 6980 
 
 ELECTRICITY 81 88 
 
 MAGNETISM 8993 
 
 RADIOACTIVITY AND GASEOUS IONIZATION 94108 
 
 CHEMISTRY 109128 
 
 MATHEMATICAL TABLES 129147 
 
 INDEX 149153 
 
ATOMIC WEIGHTS 
 
 INTERNATIONAL ATOMIC WEIGHTS FOR 1911 
 
 = 16 
 
 (See F. W. Clarke, "A Recalculation of the Atomic Weights," 1910) 
 
 Element. 
 
 Symbol. 
 
 Atomic 
 Weight. 
 
 Element. 
 
 Symbol. 
 
 Atomic i 
 Weight. 
 
 Aluminium - 
 
 Al 
 
 27-1 
 
 Neodymium 
 
 Nd 
 
 I44'3 
 
 Antimony 
 
 Sb 
 
 I20'2 
 
 N f*nn 
 
 Ne 
 
 20-2 
 
 
 Argon .... 
 
 A 
 
 39-88 
 
 Nickel ... 
 
 Ni 
 
 58-68 
 
 Arsenic .... 
 
 As 
 
 74-96 
 
 Niobium t 
 
 Nb 
 
 93-5 
 
 Barium .... 
 
 Ba 
 
 I37'37 
 
 Nitrogen 
 
 N 
 
 14-01 
 
 Beryllium* * 
 
 Be 
 
 9-1 
 
 Osmium 
 
 Os 
 
 190-9 
 
 Bismuth * 
 
 Bi 
 
 208 "o 
 
 Oxygen .... 
 
 
 
 1600 
 
 Boron .... 
 
 B 
 
 iro 
 
 Palladium * 
 
 Pd 
 
 106-7 
 
 Bromine 
 
 Br 
 
 79-92 
 
 Phosphorus 
 
 P 
 
 31-04 
 
 Cadmium 
 
 Cd 
 
 II2'40 
 
 Platinum 
 
 Pt 
 
 195-2 
 
 Caesium 
 
 Cs 
 
 132-81 
 
 Potassium 
 
 K 
 
 39-10 
 
 Calcium * 
 
 Ca 
 
 40-09 
 
 Praseodymium 
 
 Pr 
 
 140-6 
 
 Carbon .... 
 
 C 
 
 12-00 
 
 Radium .... 
 
 Ra 
 
 226-4 
 
 Cerium .... 
 
 Ce 
 
 I40-25 
 
 Rhodium - * - 
 
 Rh 
 
 102-9 
 
 Chlorine 
 
 Cl 
 
 35'46 
 
 Rubidium - - 
 
 Rb 
 
 85H5 
 
 Chromium * 
 
 Cr 52-0 
 
 Ruthenium 
 
 Ru 
 
 101-7 
 
 Cobalt .... 
 
 Co 
 
 58-97 
 
 Samarium . 
 
 Sa 
 
 I50'4 
 
 Copper .... 
 
 Cu 
 
 63-57 
 
 Scandium 
 
 Sc 
 
 44-1 
 
 Dysprosium - 
 
 Dy 1625 
 
 Selenium - - - 
 
 Se 
 
 79-2 
 
 Erbium .... 
 
 Er 
 
 167-4 
 
 Silicon .... 
 
 Si 
 
 28-3 
 
 Europium - 
 
 Eu 
 
 I52'0 
 
 Silver .... 
 
 Ag 
 
 107-88 
 
 Fluorine* 
 
 F 
 
 I9-0 
 
 Sodium .... 
 
 Na 
 
 23-00 
 
 Gadolinium 
 
 Gd 
 
 157 3 
 
 Strontium 
 
 Sr 
 
 87-63 
 
 Gallium .... 
 
 Ga 
 
 69-9 
 
 Sulphur* 
 
 S 
 
 32-07 
 
 Germanium 
 
 Ge 
 
 72'5 
 
 Tantalum 
 
 Ta 
 
 i8ro 
 
 flnlri 
 
 Au 
 
 197-2 
 
 Tellurium * * 
 
 Te 
 
 127-5 
 
 
 Helium .... 
 
 He 
 
 3-99 
 
 Terbium 
 
 Tb 
 
 159-2 
 
 Hydrogen 
 
 H 
 
 i -008 
 
 Thallium 
 
 Tl 
 
 204*0 
 
 Indium .... 
 
 In 
 
 114-8 
 
 Thorium 
 
 Th 
 
 232-0 
 
 Iodine .... 
 
 1 
 
 126*92 
 
 Thulium - 
 
 Tm 
 
 168-5 
 
 Iridium .... 
 
 Ir 
 
 I9VI 
 
 Tin . 
 
 fin 
 
 IIQ'O 
 
 
 Fe 
 
 -7 J 
 
 55-85 
 
 Titanium 
 
 ^7 n 
 
 Ti 
 
 x y w 
 4 8-I 
 
 
 LC H u fit r\ n . 
 
 Kr 
 
 82-9 
 
 Tungsten 
 
 W 
 
 184-0 
 
 
 Lanthanum - 
 
 La 
 
 I39'0 
 
 Uranium - 
 
 U 
 
 238-5 
 
 Lead . 
 
 Ph 
 
 207*10 
 
 \ / ^ KI r^ rl 1 1 VM 
 
 
 <i"o6 
 
 Lithium .... 
 
 M^ M 
 
 Li 
 
 6-94 
 
 vanadium * 
 Xenon .... 
 
 Xe 
 
 130-2 
 
 Lutecium . 
 
 Lu 
 
 174-0 
 
 Ytterbium- 
 
 Yb 
 
 172*0 
 
 Magnesium 
 
 Mg 
 
 24-32 
 
 Yttrium .... 
 
 Y 
 
 890 
 
 Manganese * 
 
 Mn 
 
 "?4'93 
 
 Zinc 
 
 7n 
 
 6c-?7 
 
 Mercury . . Hg 
 
 */T^ -7*J 
 
 200-0 
 
 Zirconium > 
 
 Ml 
 
 Zr 
 
 **3 j/ 
 
 9O-6 
 
 Molybdenum 
 
 Mo 
 
 96-0 
 
 
 
 
 * Beryllium or Glucinum (Gl). t Niobium or Columbium (Cb). 
 
ATOMIC WEIGHTS 
 
 THE ELEMENTS IN THE ORDER OF ATOMIC WEIGHTS 
 
 i 
 
 Atomic 
 Weight. Fir8t lsolated by 
 
 Date. 
 
 1 
 
 N 
 
 Wei^ht. First isolated b y 
 
 Date. 
 
 
 
 
 
 
 CO 
 
 
 
 
 H 
 
 I -008 
 
 Cavendish 
 
 1766 
 
 Mo 
 
 96*0 
 
 Hjelm 
 
 1790 
 
 He 
 
 3*99 
 
 Ramsay & Cleve * 
 
 1895 
 
 Ru 
 
 101*7 
 
 Claus 
 
 1845 
 
 Li 
 
 6-94 
 
 Arfvedson 
 
 1817 
 
 Rh 
 
 102-9 
 
 Wollaston 
 
 1803 
 
 Be 
 
 9-1 
 
 Wohler ?nd Bussy 
 
 1828 
 
 Pd 
 
 1067 
 
 Wollaston 
 
 1803 
 
 B 
 
 iro 
 
 Gay- Lussac & Thdnard 
 
 1808 
 
 Ag 
 
 107*8 
 
 
 
 P. 
 
 C 
 
 1200 
 
 
 
 P. 
 
 Cd 
 
 112-40 
 
 Stromeyer 
 
 1817 
 
 N 
 
 14*01 
 
 Rutherford 
 
 1772 
 
 In 
 
 114-8 
 
 Reich and Richter 
 
 1863 
 
 
 
 1600 
 
 Priestley and Scheele 
 
 1774 
 
 Sn 
 
 119*0 
 
 
 
 P. 
 
 F 
 
 19-0 
 
 Moissan 
 
 1886 
 
 Sb 
 
 I2O'2 
 
 Basil Valentine 
 
 i5centy. 
 
 Ne 
 
 20*2 
 
 Ramsay and Travers 
 
 1898 
 
 1 
 
 126-92 
 
 Courtois 
 
 1811 
 
 Na 
 
 23-00 
 
 Davy 
 
 1807 
 
 Te 
 
 I27-5 
 
 v. Reichenstein 
 
 1782 
 
 Mg 
 
 24-32 
 
 Liebig and Bussy 
 
 1830 
 
 Xe 
 
 I30-2 
 
 Ramsay and Travers 
 
 1898 
 
 Al 
 
 27-1 
 
 Wohler 
 
 1827 
 
 Cs 
 
 I32-8I 
 
 BunsenandKirchhoff 
 
 1861 
 
 Si 
 
 28-3 
 
 Berzelius 
 
 1823 
 
 Ba 
 
 I37-37 
 
 Davy 
 
 1808 
 
 P 
 
 3 1 '04 
 
 Brand 
 
 1674 
 
 La 
 
 I39-0 
 
 Mosander 
 
 1839 
 
 S 
 
 32-07 
 
 
 
 P. 
 
 Ce 
 
 140*25 
 
 Mosander 
 
 1839 
 
 Cl 
 
 35-46 
 
 Scheele 
 
 1774 
 
 Pr 
 
 140*6 1 Auer von Welsbach 
 
 1885 
 
 K 
 
 39-10 
 
 Davy 
 
 1807 
 
 Nd 
 
 144*3 
 
 Auer von Welsbach 
 
 1885 
 
 A 
 
 39-88 
 
 Rayleigh & Ramsay 
 
 1894 
 
 Sa 
 
 150-4 
 
 L. de Boisbaudran 
 
 1879 
 
 Ca 
 
 40-09 
 
 Davy 
 
 1808 
 
 Eu 
 
 152*0 
 
 Demargay 
 
 1901 
 
 Sc 
 
 44-1 
 
 Nilson and Cleve 
 
 1879 
 
 Gd 
 
 1573 
 
 Marignac 
 
 1886 
 
 Ti 
 
 48-1 
 
 Gregor 
 
 1789 
 
 Tb 
 
 159-2 
 
 Mosander 
 
 1843 
 
 V 
 
 51-06 
 
 Berzelius 
 
 1831 
 
 Dy 
 
 162-5 
 
 U. &D. 
 
 1907 
 
 Cr 
 
 52-0 
 
 Vauquelin 
 
 1797 
 
 Er 
 
 167-4 
 
 Mosander 
 
 1843 
 
 Mn 
 
 54'93 
 
 Gahn 
 
 1774 
 
 Tm 
 
 168-5 
 
 Cleve 
 
 1879 
 
 Fe 
 
 55-85 
 
 
 
 P. 
 
 Yb 
 
 172*0 
 
 Marignac 
 
 1878 
 
 Ni 
 
 58-68 
 
 Cronstedt 
 
 1751 
 
 Lu 
 
 174-0 
 
 Urbain 
 
 1908 
 
 Co 
 
 58-97 
 
 Brand 
 
 1735 
 
 Ta 
 
 181*0 
 
 Eckeberg 
 
 1802 
 
 Cu 
 
 63-57 
 
 
 
 P. 
 
 W 
 
 184-0 
 
 Bros. d'Elhujar 
 
 1783 
 
 Zn 
 
 65-37 
 
 Ment. by B.Valentine 
 
 I5centy 
 
 Os 
 
 190-9 
 
 Smithson Tennant 
 
 1804 
 
 Ga 
 
 69-9 
 
 L. de Boisbaudran 
 
 1875 
 
 Ir 
 
 193-1 
 
 Smithson Tennant 
 
 1804 
 
 Ge 
 
 72-5 
 
 Winkler 
 
 1886 
 
 Pt 
 
 195-2 
 
 
 
 i6centy. 
 
 As 
 
 74-96 
 
 Albertus Magnus 
 
 I3centy 
 
 Au 
 
 197-2 
 
 
 
 P. 
 
 Se 
 
 79*2 Berzelius 
 
 1817 
 
 Hg 
 
 200*0 
 
 Md. byTheophrastus 
 
 300 B.C. 
 
 Br 
 
 79-92 Balard 
 
 1826 
 
 TI 
 
 204*0 
 
 Crookes 
 
 1861 
 
 Kr 
 
 82-9 Ramsay and Travers 
 
 1898 
 
 Pb 
 
 207-IO 
 
 Mentd. by Pliny 
 
 P. 
 
 Rb 
 
 85*45 Bunsen and Kirchhoff 
 
 1861 
 
 Bi 
 
 208 -o 
 
 Mtd. by B. Valentine 
 
 1 5 centy. 
 
 Sr 
 
 87-63 
 
 Davy 
 
 1808 
 
 Ra 
 
 226-4 
 
 Curies and Bemont 
 
 1902 
 
 Y 
 
 89-0 
 
 Wohler 
 
 1828 
 
 Th 
 
 232*0 
 
 Berzelius 
 
 1828 
 
 Zr 
 
 90*6 
 
 Berzelius 
 
 1825 
 
 U 
 
 238-5 
 
 Peligot 
 
 1841 
 
 Nb 
 
 93'5 
 
 Hatchett 
 
 1801 
 
 
 
 
 
 P., Prehistoric; * Lockyer (in sun), 1868 ; U. & D., Urbain & Demenitroux. 
 
C.G.S. UNITS 
 
 C.G.S. UNITS AND DIMENSIONS 
 
 References: Mach, "Science of Mechanics;" Everett, ''C.G.S. System of 
 Units ; " Maxwell " Theory of Heat." 
 
 The metric standards of length and mass are kept at the International Bureau of 
 Weights and Measures in the Pavilion de Breteuil, Sevres, near Paris. The Bureau 
 is jointly maintained by the principal civilized governments as members of the Metric 
 Convention. The use of metric weights and measures was legalized in the United 
 Kingdom in 1897. 
 
 LENGTH 
 
 Unit the centimetre, i/roo of the international metre, which is the distance, 
 at the melting-point of ice, between the centres of two lines engraved upon the 
 polished "neutral web" surface of a platinum-iridium bar of a nearly X-shaped 
 section, called the International Prototype Metre. 
 
 The alloy of 90 Pt, 10 Ir used (also for the International Kilogramme) has not a large expan- 
 sion coefficient (see p. 53), is hard and durable, and was artificially aged. Pt-Ir copies of this 
 metre, called National Prototype Metres, were made at the same time, and distributed by 
 lot about 1889 to the different governments. The international metre is a copy of the 
 original Borda platinum standard the metre des archives. This was intended to be one ten- 
 millionth of the quadrant from the equator to the pole through Paris, and was legalized in 
 J 795 by the French Republic. But as the value of a quadrant came to be more accurately 
 determined, and moreover is changing, the actual bar constructed was made the standard.* 
 
 The international prototype metre has been measured (1894 and 1907) in terms of the wave- 
 lengths of the cadmium rays (see p. 75), and equals 1,553,164-1 wave-lengths of the red ray 
 in dry air at 15 C. (H. Scale) and 760 mm. pressure. (See Michelson's "Light Waves," 
 
 1903-) 
 
 References : Guillaume, "La Convention du Metre," and Chree, Phil. Mag., 1901. 
 
 MASS 
 
 Unit the gramme, i/iooo of the International Prototype Kilogramme, 
 
 which is the mass of a cylinder of platinum-iridium. 
 
 The international kilogramme is a copy of the original Borda platinum kilogramme the kilo- 
 gramme des archives which was intended to have the same mass as that of a cubic decimetre of 
 pure water at the temperature of its maximum density. More exact measurements revealed the 
 incorrectness of the relation (see p. 10), and so the kilogramme was subsequently defined as above. 
 
 As with the metre, Pt-Ir copies of the international standard National Prototype Kilo 
 grammes have been distributed to the different governments. 
 
 TIME 
 
 Unit the second, which may be defined simply as 1/86,164-09 of a sidereal 
 day. For all practical purposes the sidereal day may be regarded as the period 
 of a complete axial rotation (360) of the earth with respect to the fixed stars.f 
 
 The second is usually defined as 17(24 x 60 x 60) of a mean solar day, i.e. 
 1/86,400 of the average value of the somewhat variable interval (the apparent 
 solar day) between two successive returns of the sun to the meridian (see p. 15). 
 
 Strictly, the sidereal day is the interval between two successive transits of the first point 
 of Aries J across any selected meridian. The true period of rotation of the earth is actually- 
 about i/ioo second longer than the sidereal day ; the difference arises from the slow and con- 
 tinual change of direction (" precession ") of the earth's axis in space. 
 
 A tropical or solar year is the average interval between two successive returns of the sun 
 to the first point of Aries ; it is found to equal 365-2422 mean solar days. Our modern 
 (Julian) calendar assumes that in 4 successive civil years, 3 consist of 365 days, and I of 366 ; 
 the average thus being 365-25 days. The Gregorian correction (that century years are not to 
 count as leap years unless divisible by 400) reduces this value to 365*2425 mean solar days, 
 and thus the average civil year is a close approximation to a tropical year. 
 
 * According to the latest estimates, the mean meridian quadrant = 10,002,100 metres 
 (see p. 13). 
 
 f Tidal friction is retarding the rotation of the earth, so that the above (sidereal) definition 
 of the second, while practically justified, is theoretically not quite perfect. 
 
 \ The first point of Aries is that one of the two nodes of intersection of the ecliptic and the 
 celestial equator where the sun (moving in the ecliptic) crosses the equator from south to north 
 (at about March 21). The ecliptic is the apparent yearly track of the sun in a great circle on 
 the celestial sphere. 
 
 Neglecting small irregularities, this is true also for any star. 
 
BRITISH UNITS 
 
 A sidereal year is the time interval in which the sun appears to perform a complete revolu- 
 tion with reference to the fixed stars ; if. it is the time in which the earth describes one sidereal 
 revolution round the sun. Owing to precession, a sidereal year is longer than a tropical year. 
 
 h. m. s. 
 
 Mean solar day = 24 o o = 86,400 sees. 
 
 Sidereal day = 23 56 4*0906 = 86, i64'O9o6 sees. 
 
 Tropical year = 365*2422 mean solar days. 
 Sidereal year =365-2564 ,, (epoch 1900). 
 = 366*2564 sidereal days. 
 
 Reference : Newcomb, " Astronomy." 
 
 BRITISH IMPERIAL STANDARDS. 
 
 (From information supplied by Major MacMahon, F.R.S., Board of Trade, 
 
 Standards Office.) 
 
 According to the Weights and Measures Act, 1878, the yard is the distance, 
 at 62 F., between the central transverse lines in two gold plugs in the bronze 
 bar, called the Imperial Standard Yard, when supported on bronze rollers 
 in such manner as best to avoid flexure of the bar. 
 
 The defining lines are situated at the bottom of each of two holes, so as to be in the medium 
 plane of the bar, which is of i inch square section and 38 inches long. Its composition is 32 Cu, 
 I 5 Sn, 2 Zn. Copper alloys are now known not to be suitable for standards of length, and in 1902 a 
 Pt-Ir X -shaped copy of the yard was made. 
 
 The pound is the weight in vacuo of a platinum cylinder called the imperial 
 standard pound. 
 
 The imperial standard yard and pound are preserved at the Standards Office 
 of the Board of Trade, Old Palace Yard. A number of official copies have beer- 
 prepared, and are in the custody of the Royal Society, the Mint, Greenwich Ob- 
 servatory, and the Houses of Parliament. 
 
 The gallon contains 10 Ibs. weight of distilled water weighed in air against 
 brass weights at a pressure of 30 inches, and with the water and the air at 62 F. 
 
 [NOTE. No mention is made in the Act of the density of the brass weights, or 
 of the humidity of the air.] 
 
 BRITISH AND METRIC EQUIVALENTS 
 
 The present legal equivalents are those legalized by the Order in Council of 
 May 19, 1898, and derived at the International Bureau of Weights and Measures, by 
 Benoit in 1895 in the case of the yard and the metre, and by Broch in 1883 for 
 the pound and the kilogramme. (See 7'rav. et Mdm. du Bur. Intl.) tomes iv., 1885, 
 and xii., 1902.) 
 
 Imperial Standard. International Prototype. (Reciprocal.) 
 
 I yard *9 14399 metre 1-093614 
 
 i pound "45359243 kilogramme 2*2046223 
 
 [NOTE. The yard is defined at 62 F., the metre at o C] 
 
 DERIVED C.G.S. UNITS AND STANDARDS 
 
 GENERAL AND MECHANICAL UNITS 
 
 Area : Unit the square centimetre. 
 
 Volume : Unit the cubic centimetre (c.c.). The metric unit is the litre, 
 now defined as the volume of a kilogramme of pure, air-free water at the tem- 
 perature of maximum density (see p. 22) and 760 mm. pressure (Proces Verbait.v, 
 1901, p. 175). The litre was originally intended to be i cubic decimetre or 1000 
 c.cs. ; the present accepted experimental relation is that i kilogramme of water at 
 4 C. and 760 mm. pressure measures iooo'o27 c.cs. (see p. 10). 
 
 Density -. Unit grammes per c.c. Specific gravity expresses the density 
 of a substance relative to that of water, and is objectionable in requiring two tem- 
 peratures to be stated. 
 
5 
 
 DERIVED C.G.S. UNITS 
 
 Velocity : Unit i cm. per second. Angular Velocity : Units i radian 
 (57-296) per sec. ; i revolution per sec. 
 
 Acceleration : Time rate of alteration of velocity. Unit (i cm. per sec.) per 
 sec. Angular Acceleration : Units i radian per sec. 2 ; i revolution per sec. 2 
 
 Momentum : Mass multiplied by velocity. Unit i gm. cm. sec." 1 . 
 
 Moment of Momentum: Momentum multiplied by distance from axis of 
 reference. Unit i cm. 2 gm. sec." 1 . 
 
 Moment of Inertia : 2;;z^ 2 , where m is the mass of any particle of a body, 
 and d its distance from the axis of reference. Unit- i cm. 2 gm. (see p. 16). 
 
 Angular Momentum : Moment of inertia multiplied by angular velocity 
 round axis of reference. Unit i cm. 2 gm. sec." 1 . 
 
 Porce : Measured by the acceleration it produces in unit mass. Unit the 
 dyne = cm. gm./sec. 2 Gravitational unit the weight of i gram g dynes. 
 
 Couple, Torque, Turning Moment : Force multiplied by distance from 
 point of reference. Uniti dyne cm. 
 
 Work : Force multiplied by distance through which point of application of 
 force moves in direction of force. Unit the erg = i dyne cm.; i joule = io 7 ergs. 
 [i calorie = 4/18 joules]. Gravitational unit weight of i gm. X i cm. = g dyne 
 cms. = g ergs. 
 
 Energy : Measured by the work a body can do by reason of either (i) its 
 motion Kinetic Energy (= mv 2 /2) or (2) its position Potential Energy. 
 Unit the erg. (See "Work.") i Board of Trade Unit = i kilowatt hour = 
 3-6 x io 6 watt-sees. 
 
 Power : Work per unit time. Unit i erg per sec. i watt = io 7 ergs 
 per sec. i joule per sec. i volt-ampere, i kilowatt = 1*34 horse-power. 
 
 Pressure, Stress: Force per unit area. Unit i dyne per cm. 2 i megabar 
 = io 6 dynes per cm. 2 = 750 * ir.m. mercury at o C., lat. 45, and sea-level (g 980-6). 
 i atmosphere = 760 mm. mercury at o C., lat. 45, and sea-level = 759'4 mm. 
 mercury at o C. in London = 1-0132 x 10 dynes per cm. 2 = 147 Ibs. per inch 2 
 = 0-94 ton per foot 2 . * Correct to f part in 5QOO> 
 
 Elasticity : Ratio of stress to resulting strain. Unit i dyne per cm. 2 , since 
 the dimensions of a strain are unity. 
 
 HEAT UNITS 
 
 Temperature : The melting-point of pure ice under i atmosphere is defined as 
 o C., and the boiling-point of water under i atmosphere as 100 C. This funda- 
 mental interval is divided into 100 parts by use of the constant-volume hydrogen 
 thermometer (see p. 44) ; each part is a degree Centigrade. Dimensions of tem- 
 perature are not required, as it is defined independently of mass, length, and time. 
 
 Heat : Dynamical unit the erg. Thermal unit the calorie = heat required 
 to raise the temperature of i gramme of water from / C. to (/ + i) C. The 
 2O calorie (/ = 20) = 4-180 x io 7 ergs. The 15 calorie (/ = 15) = 4-184 x 
 io 7 ergs. The mean calorie (= i/ioo heat required to raise i gramme of water 
 from o to 100 C.) = 4*184 x io 7 ergs, (see pp. 55, 56). i watt-minute 14-3 
 calories. The large calorie = 1000 calories. 
 
 Gas Constant R., in pv RO/m, where p is the pressure, v the volume, 
 9 the absolute temperature of a gram-molecule (i.e. m grams) of a gas of 
 molecular weight m. For i gram-molecule of an ideal gas of density p, 
 
 _, p-vm p m 1*0132 x io 6 x 22412 
 
 R = - - - = -. ; - = 83*15 x 10 ergs per grm. (Berthelot, 
 
 see p. 1 06). This value is a constant for all ideal gases. To derive R for i gram 
 of a gas, this figure should be divided by the molecular weight (oxygen = 16) 
 of the gas. R has the dimensions of a 'specific heat in dynamical units. 
 
 ELECTRICAL AND MAGNETIC UNITS 
 
 Reference:]. J. Thomson, "Mathematical Theory of Electricity and Mag- 
 netism." The fundamental basis of the electrostatic [system of units is the repulsive 
 force between two quantities of like electricity. In the electromagnetic system the 
 repulsion between two like magnetic poles is taken as the basis. 
 
 The electromagnetic system (or one based on it) is universally employed in 
 electrical engineering ; the electrostatic is used only in certain special cases. 
 
 ELECTROSTATIC UNITS 
 
 Quantity or Charge: Unit that quantity which placed i cm. distance 
 from an equal like quantity repels it with a force of I dyne. 
 
ELECTRICAL UNITS 
 
 Current : Unit Unit quantity flowing past a point in unit time. 
 
 Potential Difference and Electromotive Porce : Unit that P.D. which 
 exists between two points when the work done in taking unit quantity from one point 
 to the other is i erg. 
 
 Capacity: Unit the charge onla conductor which is at unit potential ; or 
 in the case of a condenser, when its plates are at unit P.D. 
 
 Dielectric Constant, Inductivity, or Specific Inductive Capacity of 
 a medium is the ratio of the capacity of a condenser having the medium as 
 dielectric, to the capacity of the same condenser with a vacuum as dielectric (p. 84). 
 
 ELECTROMAGNETIC UNITS 
 
 Magnetic Pole Strength or Quantity : Unit that quantity which, placed 
 i cm. distance from an equal like quantity, repels it with a force of i dyne. 
 
 Magnetic Force or Field Strength: Unit the force which acts on unit 
 magnetic pole. 
 
 Magnetic Moment of magnet = pole strength x length of magnet. 
 
 Intensity of Magnetization = magnetic moment per unit volume. 
 
 Permeability of a medium is the ratio of the magnetic induction in the 
 medium to that in the magnetizing field (p. 89). 
 
 Susceptibility: Unit intensity of magnetization per unit field (p. 89). 
 
 Electric Current : Unit that current which produces unit magnetic force 
 at the centre of a circle of radius 2* cms. 
 
 Quantity = current x time. 
 
 Potential and E.M.F. : Unit that P.D. which exists between two points 
 when the work done in taking unit quantity from one point to the other is i erg. 
 
 Electrostatic Capacity = quantity/potential difference. 
 
 Resistance = potential difference/resulting current. (Ohm's law is assumed.) 
 
 Conductance : Reciprocal of resistance. 
 
 Specific Resistance : Resistance per unit area per unit length (p. 81). 
 
 Conductivity : Reciprocal of specific resistance. 
 
 Coefficient of Self-induction of a circuit is the E M.F. produced in it by 
 unit time-rate of variation of the current through it. 
 
 Coefficient of Mutual Induction of two circuits is the E.M.F. produced 
 in one by unit time-rate of variation of the current in the other. 
 
 PRACTICAL ELECTRICAL UNITS 
 
 At an International Conference on Electrical Units and Standards held in 
 London, October, 1908, it was resolved that 
 
 1. The magnitudes of the fundamental electrical units shall, as heretofore, Le 
 determined on the electromagnetic system of measurement with reference to the 
 centimetre, gramme, and second (c.g.s.). These fundamental units are (i) the Ohm, 
 the unit of electrical resistance, which has the value io 9 c.g.s. ; (2) the Ampere, 
 the unit of electric current, which has the value lo" 1 c.g.s. ; (3) the Volt, the 
 unit of electromotive force, which has the value io 8 c.g.s. ; (4) the Watt, the unit 
 of power, which has the value io 7 c.g.s. [For absolute electrical units, see p. 8.] 
 
 2. As a system of units representing the above, and sufficiently near to them 
 to be adopted for the purpose of electrical measurements, and as a basis for 
 legislation, the Conference recommends the adoption of the International Ohm, 
 the International Ampere, and the International Volt. 
 
 3. The Ohm is the first primary unit. The International Ohm is defined 
 as the resistance offered to an unvarying electric current by a column of mercury 
 a* o C., 14*4521 grammes in mass, of a constant cross-section, and of a length 
 of 106*300 cms. 
 
 4. The Ampere is the second primary unit. The International Ampere 
 is defined as the unvarying electric current which, when passed through a solution 
 of nitrate of silver in water, in accordance with authorized specification, deposits 
 silver at the rate of 'ooi 1 1800 gramme per second. 
 
 5. The International Volt is defined as the electrical pressure which, when 
 steadily applied to a conductor whose resistance is one International Ohm, will 
 produce a current of one International Ampere. 
 
 6. The International Watt is defined as the energy expended per second by 
 an unvarying electric current of one International Ampere under an electric pressure 
 of one International Volt. 
 
DIMENSIONS OF UNITS 
 
 
 
 DIMENSIONS 
 
 OF UNITS 
 
 The dimensions in terms of length, mass, and time are denoted by the indices 
 
 given under L, M, and T. Thus the dimensions of power are L 2 MT~ 3 . 
 
 MECHANICAL AND HEAT UNITS 
 
 Quantity. 
 
 L. M. T. 
 
 Quantity. 
 
 L. M. T. 
 
 Quantity. 
 
 L. M. T. 
 
 Length . . 
 
 I O O 
 
 Momentum 
 
 i i i 
 
 Strain . . . 
 
 000 
 
 Mass . . . 
 
 I 
 
 Moment of mo- 
 
 
 Elasticity . . 
 
 I 12 
 
 Time . . . 
 
 Angle . . . 
 
 I 
 000 
 
 mentum . . 
 Moment of in- 
 
 2 I-I 
 
 Compressibility 
 Viscosity . . 
 
 I -1 2 
 -I I-I 
 
 Surface . . . 
 
 2 O O 
 
 ertia f . . 
 
 2 I 
 
 Diffusion . . 
 
 2 O-I 
 
 Volume . . . 
 
 300 
 
 Angular mo- 
 
 
 Capillarity . . 
 
 I 2 
 
 Density . . . 
 
 3 i o 
 
 mentum . . 
 
 2 I I 
 
 Temperature . 
 
 000 
 
 Velocity . . . 
 
 I I 
 
 Force . . . 
 
 I -2 
 
 Heat* . . . 
 
 2 I -2 
 
 Angular vel. . 
 
 I 
 
 Couple, Torque 
 
 2 2 
 
 Thermal Con- 
 
 
 Acceleration . 
 Angular accele- 
 
 I 2 
 
 Work, Energy 
 Power . . . 
 
 2 2 
 
 2 -3 
 
 ductivity* . 
 Entropy* . . 
 
 i i -3 
 
 2 I -2 
 
 ration . . . 
 
 02 
 
 Pressure, Stress 
 
 I 2 
 
 
 
 ELECTRICAL AND MAGNETIC UNITS 
 
 v, the ratio of the electromagnetic to the electrostatic unit of quantity, is usually 
 taken as 3 x io 10 , and is a pure number (p. 69). (See Riicker, Phil. Mag., 22, 1889.) 
 
 Unit. 
 
 
 Dimensions. 
 
 Relations. 
 
 Sytn- 
 
 Tinl 
 
 E.S. Unit. 
 
 E.M. 
 
 Unit. 
 
 E.S.U. 
 
 
 001. 
 
 
 
 
 
 
 PrapHral TTm't 
 
 
 L. 
 
 M. T * 
 
 L. M. 
 
 T. it. 
 
 E.M.U. 
 
 -tictuLiodi unit. 
 
 
 
 
 
 
 
 . 
 
 
 
 
 
 
 
 
 
 
 E.M.U. E.S.U. 
 
 Electrical 
 
 
 
 
 
 
 
 
 
 
 Charge or quan- 
 
 
 
 
 
 
 
 
 
 tity . . . 
 
 . 
 
 e 
 
 a 
 
 -1 1 
 
 i \ 
 
 o J 
 
 l/i 
 
 coulomb 
 
 = io^ 1 =3x io 9 
 
 Resistance . 
 
 , 
 
 R 
 
 i 
 
 I I 
 
 I - 
 
 - 1 i 
 
 
 ohm 
 
 = io 9 i x io~~ n 
 
 Current . . 
 
 . 
 
 i 
 
 f 
 
 J-2 1 
 
 \ \ ~ 
 
 - i J 
 
 ijv 
 
 ampere 
 
 = 10-1 =3 xio 9 
 
 Potential or 
 
 
 
 
 
 
 
 
 
 
 E.M.F. . . 
 
 . 
 
 E 
 
 i 
 
 2 I - o 
 
 \- 
 
 ~ 2 ? 
 
 V 
 
 volt 
 
 = io 8 = 1/300 
 
 Electric field 
 
 
 F 
 
 -i 
 
 1 - I 1 
 
 \\~ 
 
 -2 | 
 
 V 
 
 (volt/cm.) 
 
 
 
 Conductivity . 
 
 
 K 
 
 
 
 I I 
 
 2 
 
 I I 
 
 \lv* 
 
 " recipro- 
 
 = io~ 9 = 9 xio n 
 
 
 
 
 
 
 
 
 
 cal ohm " 
 
 
 Capacity . . 
 
 j 
 
 C 
 
 i 
 
 I 
 
 I 
 
 2 I 
 
 I/V 2 
 
 micro- 
 
 = io~ 15 =9X io 5 
 
 
 
 
 
 
 
 
 
 farad t 
 
 
 
 Self and mutual) 
 induction . / 
 
 LjM 
 
 i 
 
 21 
 
 I 
 
 I 
 
 V* 
 
 jhenry 
 \ cm. 
 
 = I0 9 
 J 
 
 i-t^jo-* 
 
 Dielectric con- 
 
 
 
 
 
 
 
 
 
 
 stant f . . 
 
 
 k 
 
 
 
 I 
 
 2 
 
 2 I 
 
 I/V 2 
 
 
 
 
 
 -- 
 
 Magnetic 
 
 
 
 
 
 
 
 
 
 
 
 Pole strength 
 
 
 m 
 
 1 
 
 ^ O j 
 
 f *-i i 
 
 V 
 
 
 
 
 
 
 
 Flux (total lines) 
 
 N 
 
 1 
 
 i o | 
 
 i i- 
 
 - I | 
 
 I/V 
 
 maxwell 
 
 = I 
 
 = 3xio 10 
 
 Force ; field 
 
 
 
 
 
 
 
 
 
 
 
 strength 
 
 . 
 
 H 
 
 i 
 
 | 2 J 
 
 i- \ - 
 
 -i-ir 
 
 ilv 
 
 gauss 
 
 = 1 
 
 = 3 x io 10 
 
 Induction . . 
 
 . 
 
 B 
 
 - 
 
 2 ~2 
 
 -H- 
 
 -i 1 
 
 V 
 
 gauss 
 
 = I =XIO~ 10 
 
 Intensity of mag- 
 
 
 
 
 
 
 
 
 
 
 netization . 
 
 , 
 
 I 
 
 f 
 
 i -i 
 
 -U- 
 
 -i -| 
 
 V 
 
 
 
 
 
 
 
 Permeability . 
 
 
 P- 
 
 2 
 
 21 
 
 O 
 
 I 
 
 V* 
 
 
 
 
 
 
 
 * In dynamical units. 
 
 t Specific in'ductive capacity. J io~ 6 farad. 
 
 Example : To find the number (n) of ergs per sec. in a horse-power (33,000 ft.-lbs. per min.). 
 
 Dimensions of power = L 2 MT~ 3 = LT -1 [Force] 
 
 
 ft. 
 
 3,000 
 cm 
 
 {min.V 1 Ib. weight 
 
 33,000 x 30 
 
 ^ x 453'6 x 981 
 
 O 
 
 sec. / " dyne 
 
 60 
 
 = 7-46 X io 9 ergs per sec. = 746 watts. 
 
8 
 
 ELECTRICAL UNITS 
 
 ABSOLUTE DETERMINATIONS OF ELECTRICAL UNITS 
 
 See Baillehache, " Unites Electriques," Paris, 1909, and the " Report of the London 
 Conference " (p. 6). The appendix to this report (is sued separately, 9</.) gives full 
 particulars as to the realization of the ampere and ohm, together with the specifica- 
 tion of the Weston normal (cadmium) cell. 
 
 THE OHM 
 
 The mean value 1O6'29 cms. of Hg of i sq. mm. cross-section at o C. may be 
 taken as a measure of the present experimental value of the true ohm, which is equal 
 to io 9 E.M. (c.g.s.) units. Compare the international ohm (p. 6). A new determi- 
 nation of the ohm is in progress at the National Physical Laboratory. 
 
 cm./0. 
 
 Method. 
 
 Observer. 
 
 cm./0. 
 
 Method. 
 
 Observer. 
 
 106-28 
 
 106-22 
 I06'32 
 
 Spinning disc 
 
 >J 5> 
 
 Mean result 
 
 Rayleigh, 1882 
 Rayleigh and 
 Mrs. Sedg- 
 wick, 1883 
 Rowland, 1887 
 
 106-29 
 
 106-32 
 106-27 
 
 Induced dis- 
 charge 
 Spinning disc 
 
 (McGill ap- 
 paratus) 
 
 Glazebrook, '88 
 
 V. Jones, 1894 
 Ayrton and V. 
 Jones, 1897 
 
 The 1884 "legal" ohm = -9972 intl. ohm; the B.A. ohm = -9866 intl. ohm. 
 
 THE AMPERE 
 
 The electrochemical equivalent of silver is given in milligrams per coulomb 
 (i ampere for i sec.) = lo^ 1 E.M. unit of quantity. Mean = '0011 1826gm. cou- 
 lomb. Compare th'e international ampere (p. 6). 
 
 mg. Ag. 
 
 Method. 
 
 Observer. 
 
 mg. Ag. 
 
 Method. 
 
 Observer. 
 
 1-11828 
 
 1-11827 
 
 Dynamometer 
 
 Current 
 weigher 
 
 Kohlrausch, '84 
 Corrected 1908 
 Smith, Mather, 
 and Lowry, 
 
 1-11821 
 1-11829 
 
 Dynamometer 
 j> 
 
 Janet, Laporte, 
 de la Gorce, 
 1909 
 Do, 1910 
 
 
 
 1907 
 
 
 
 
 E.M.F. OF WESTON CELL 
 
 The electromotive force (E) of the Weston (cadmium) cell in volts (io 8 . E M. 
 units) as realized from one of the accepted specifications. The now (1911) accepted 
 international value of E is 1*0183 international volts (see p. 6) at 20 C. 
 Temperature coefficient. Over the range o to 40, Wolff (1908) obtained 
 for the E.M.F. at t- 
 
 E t = 30 -oooo4o6(/ 20) - 9*5 x io 7 (/ 2o) 2 . 
 
 E at 20. 
 
 Method. 
 
 Observer. 
 
 E at 20^. 
 
 Method. 
 
 Observer. 
 
 1-0185 
 1*01822 
 1-01841 
 1-01869 
 
 !Intl. ohm and 
 dynamo- 
 meter 
 Intl. ohm and 
 current weigher 
 
 Guthe, 1906 
 Guillet,i9o8 
 Pellat, 1908 
 Janet, Laporte, 
 Jouaust, 1908 
 
 1*01820 
 1-01834 
 
 Intl. ohm and 
 current weigher 
 
 Intl. ohm and 
 intl. ampere 
 
 Ayrton, Mather, 
 and Smith, 1908 
 
 Jaeger and v. 
 Steinwehr, 1909 
 
 The E.M.F. of the Clark cell = 1*433 volts at 15 C. It diminishes by about 
 I "2 parts in 1000 for i C. rise of temp. 
 
CONVERSION FACTORS 
 
 BRITISH INTO METRIC CONVERSION FACTORS 
 
 Conversion factors based on the relations given on p. 4. g is taken as 981 
 
 cm.-sec.~ 2 . Reciprocals are given for converting metric into British measure. 
 
 British. 
 
 Metric. 
 
 (Reciprocal.) 
 
 British. 
 
 
 Metric. 
 
 (Reciprocal.) 
 
 Length 
 
 
 
 Force 
 
 
 
 
 
 i inch 
 
 2-5400 cm.* 
 
 *3937 t 
 
 i poundal 
 
 = 
 
 13,825 dynes 
 
 7*233 X io- 5 
 
 i yard = 
 
 9144 metre* 
 
 1-0936 
 
 i pound wgt. = 
 
 
 4*45 x io 6 
 
 2*247 x io~ 6 
 
 i mile = 
 
 1*6093 km. 
 
 6214 
 
 
 
 
 dynes 
 
 
 Area 
 
 
 
 Pressure 
 
 
 
 
 i sq. inch = 
 
 6*45 i6sq cm. 
 
 i55of 
 
 i Ib./sq. inch = 
 
 68,971 
 
 1*45 x io~ 5 
 
 Volume 
 
 
 
 
 
 
 dynes/cm/ 
 
 
 cubic inch = 
 
 16-387 c.c. 
 
 0610 
 
 5 J 
 
 ? = 
 
 70*31 
 
 01422 
 
 cubic foot = 
 
 28*317 litre 
 
 03531 
 
 
 
 
 gm./cm. 2 
 
 
 pint 
 
 5682 litre 
 
 17598 
 
 i ton/sq. inch = 
 
 
 1*545 x io 8 
 
 6'47X io~ 9 
 
 gallon = 
 
 4-5460 litre*]: 
 
 2200 \ 
 
 
 
 
 dynes/cm. 2 
 
 
 Mass- 
 
 
 
 3 
 
 , = 
 
 
 1*575 
 
 6349 
 
 grain 
 
 "0648 gram 
 
 15-432 
 
 
 
 
 k. gm./mm. 2 
 
 
 oz. (avoir.) = 
 i lb. = 
 
 28*350 grams 
 4536 k. gm. 
 
 03527 
 2-2046 
 
 Work 
 
 i ft. -pound = 
 
 
 i'356joules 
 
 7373 
 
 i ton = 
 
 ioi6k. gm.|| 
 
 039842 
 
 "PflVVVfVM 
 
 
 
 
 
 Density 
 
 i Ib./cub. ft. = 
 
 01602 
 
 62-43 
 
 JL \JWw4T 
 
 i horse-power = 
 
 
 746 k.watt. 
 
 134 
 
 
 gm./cm. 3 
 
 
 Heat 
 
 
 
 
 
 Velocity 
 
 I mile/hour = 
 
 44-70 cm./sec. 
 
 02237 
 
 i B. Th. unit \ 
 (lib., iF.)/- 
 
 252*00 calories 
 
 00397 
 
 MISCELLANEOUS DATA 
 
 CONVENIENT APPROXIMATE RELATIONS 
 
 British. 
 
 U.States. 
 
 
 i yard = i metre, less 10% 
 
 i yd ) 
 
 fi yard 
 
 !i mm. = io 3 metre 
 i micron, M= lo^ 6 
 
 2 Ibs. = i k. gram, 
 
 at U 
 
 at 
 
 uu=io- Q 
 
 2 galls. = io litres, 
 
 62F.) 
 
 l59-6F. 
 
 _ 
 
 iA.U. = io- 10 
 
 i ton = (} tonr \ e ,1 less 2% 
 
 i lb. = 
 
 i lb. 
 
 i mil=io" 3 inch 
 
 ((1000 .gm.)) 
 
 i gal. = 
 
 1*20 gal. 
 
 
 SOME BRITISH WEIGHTS AND MEASURES 
 
 MATHEMATICAL 
 
 Useful in photography, etc. 
 
 Number. Log.ofNumber. 
 
 The avoirdupois, troy, and apothecaries 
 
 
 
 
 grain are the same in weight. 
 
 IT 
 
 3-141592654 -49715 
 
 lb. (avoir.) = 7000 grains =454 grams 
 
 7T 2 
 
 9*869604401 '99430 
 
 oz. = 437! =28*3 
 
 I/IT 
 
 318309886 1*50285 
 
 oz.(troy) = ] 
 
 
 1772453851 -24857 
 
 oz.(apothe-> = 480 =31'! 
 
 i radian 
 
 57-2Q5 
 
 78 175812 
 
 caries)] 
 
 i " -017453 radian 2*24188 
 
 fl drachm 3 = 60 minims = 3'55c.cs. 
 
 e 
 
 2718281828 "43429 
 
 fl. oz. =8 fl. drachms = 28-41 
 
 loge io 
 
 2-302585 -36222 
 
 pint = 20 fl. ozs. = 568 
 
 
 
 
 A 10% solution is 
 
 
 
 Multifilv 
 
 i grain in io minims of solution 
 
 2 o convert ' ~ v '^ '* 
 
 i oz. (avoir.) io fl. ozs. 
 
 Common into hyperbolic logs, 2-3026 
 
 2 oz. i pint 
 
 Hyperbolic common '4343 
 
 * Correct to i part in a million. t Correct to 3 
 
 parts in a million. 
 
 % Owing to the definition of the gallon (see p. 4), this number is dependent 
 
 on assumed buoyancy and temperature corrections. 
 
 
 
 i joule = io 7 ergs. || 
 
 i tonne : 
 
 = looo k. gm. 
 
10 
 
 MISCELLANEOUS DATA 
 
 M ISCELLAN EOUS DATA continued. 
 
 BRITISH COINAGE 
 
 NAUTICAL 
 
 I nautical or geographical mile 
 = mean length of i' lat. 
 
 Coin. Weight. Diameter. 
 
 sovereign 8 grams less '15% 2*18 cm. 
 penny \ oz. (avoir.) 1*2 inch 
 halfpenny \ ro 
 farthing ^ . '8 
 
 6080 feet ri5i mile 
 i knot = i nautical mile/hour 
 i fathom = 6 feet 
 i point = uj 
 
 British. Continental. 
 
 10 Centigrade = 50 Fahrenheit, 
 
 whence the following is convenient for 
 transforming room temperatures : 
 
 5 (/ F. - 50) = 9 (' C. - 10) 
 
 Million. . . io 6 io 6 
 Billion . . . io 12 2 x io 6 
 Trillion . . io 18 3 x io 6 
 
 VOLUME OF A KILOGRAMME OF PURE WATER 
 
 At 4C. and 760 mm. Values recalculated by Benoit. (Trav. et Mem. Bur. Intl., 14, 
 1910.) (See p. 4.) 
 
 Observer. c.cs. 
 
 Observer. c.cs. 
 
 Lefevre-Geneau and Fabbroni, 1799 . iooo'03o 
 Schuckburgh and Kater, 1798 and 1821 999-525 
 Svanberg and Berze"lius, 1825 . . . 999710 
 Stampfer, 1831 iooo'25o 
 
 Chancy 1893 . . ... looo'i^o 
 
 Guillaume 1904 . . . 1000*029 
 
 Chappuis, 1907 iooo'027 
 de Ldpinay, Benoit, and Buisson, 
 
 1907 IOCO'028 
 
 Kupffer, 1842 1000 '069 
 
 DENSITIES OF GASES 
 
 Supplementary to p. 26. Densities in grams per litre at o C., 760 mm., 
 sea-level, and lat. 45. 
 
 Gas. gms./litre. Observer. 
 
 Gas. gms./litre. Observer. 
 
 1 
 
 He . -1782 Watson, J.C.S., 1910 
 Ne . -9002 
 Kr . 3708 Moore 1908 
 Xe . 5-851 
 
 Ra, Em. 9727 Gray & Ramsay, P.R.S. 
 1910 
 CH 4 7168 Baume & Perrot, C.R., 
 1909 
 
 C.R., Compt. Rend.; J.C.S., Jonrn. Chem. Soc.; P.R.S., Proc. Roy. Soc. 
 
 PRESSURE COEFFICIENTS OF PV 
 
 Pressure coefficient, m, of pv for gases at i atmosphere and constant tempe- 
 rature ; p is the pressure in atmospheres, and v is the volume, m --' s, , ; 
 
 m is a measure of the deviation of the gas from Boyle's law. 
 Air, m = '00191, Regnault. 
 
 H! m = +'772 } Cha PP uis > Rayleigh, Leduc, and Sacerdote. 
 
II 
 
 GRAVITY 
 
 VALUES OF GRAVITY ("g") LONGITUDE AND LATITUDE 
 Helmert's formula connecting "gravity" with latitude and height is 
 g 980*617 2*593 cos 2A. ~ -ooo3o86H, where \ is the latitude, H is the height 
 in metres above sea-level, and 980-617 cms./sec. 2 is the value of g attributed 
 to lat. 45 and sea-level. The values of g calculated by this formula are for most 
 places in fair agreement with the observed values. Some discrepancy is found 
 in the vicinity of large mountain ranges, such as the Himalayas. 
 No absolute standard determination of g has been made in England for many 
 years, but comparisons have been made with Potsdam and Sevres. For relative 
 measurements, the relation dg -0226 d*& is useful, where N is the number of 
 vibrations which a pendulum makes in a mean solar day of 86,400 mean time 
 seconds. The length (/) of the " seconds " pendulum (i.e. 2 sees, period) = ^/ir 2 
 = -101321^-. /varies from 99*094 cms. at the equator to 99*620 cms. at the pole. 
 See Helmert's " Hohere Geodasie," " Die Grosse der Erde," 1906, and " Die 
 Schwerkraft im Hochgebirge," Clarke's "Geodesy," 1880, Sir Geo. Darwin's "Tides 
 and Kindred Phenomena," Fisher's " Physics of the Earth's Crust," and for recent 
 aspects of the subject, the reports to the triennial International Geodetic Conferences 
 (...1906, 1909...), and the reports of the U.S. Geodetic Survey. (See also p. 13.) 
 
 Place. 
 
 Longitude 
 E. or W. of 
 Greenwich. 
 
 Latitude (A). 
 
 Height (H) 
 above Sea- 
 level. 
 
 " s " 
 (calculated). 
 
 Pole 
 
 o // 
 
 2 6 38 W 
 4 4 W 
 48 W 
 5 56 W 
 i 54 W 
 2 35 W 
 o 5 41 E 
 3 10 W 
 6 15 W 
 6 40 32 W 
 2 58 45 W 
 i 34 56 W 
 3 ii 3 W 
 3 12 18 W 
 4 17 12 W 
 000 
 o 18 46 W 
 i 33 15 W 
 2 57 37 W 
 
 20 II W 
 
 o 10 23 W 
 
 o 7 57 W 
 
 2 14 2 W 
 
 i 36 53 W 
 i 8 45 W 
 i 15 39 W 
 4 9 W 
 i 6 12 W 
 
 2 48 W 
 
 o 5 50 E 
 
 2 28 10 W 
 
 26 40 E 
 
 O / II 
 
 90 o o 
 
 O 
 
 57 8 58 N 
 
 52 25 N 
 53 13 N 
 54 37 N 
 52 28 N 
 51 28 N 
 52 12 52 N 
 51 28 N 
 53 20 35 N 
 53 23 13 N 
 56 27 26 N 
 54 46 6 N 
 55 55 28 N 
 55 18 48 N 
 55 52 3i. N 
 51 28 38 N 
 51 28 6 N 
 53 48 30 N 
 53 24 19 N 
 51 25 20 N 
 5i 29 54 N 
 51 31 27 N 
 53 27 53 N 
 54 58 50 N 
 52 57 10 N 
 5i 45 34 N 
 
 50 22 N 
 
 50 48 3 N 
 56 20 N 
 53 23 2 N 
 53 50 40 N 
 
 29 o S 
 
 metres. 
 21 
 
 28 
 
 7t 
 
 |t 
 
 134 
 
 244 
 46 
 
 47 
 
 Si 
 5i 
 
 10 
 
 H 
 28 
 
 39 
 
 m 
 
 65 
 
 5 
 114 
 
 cms./sec. 2 
 983*210* 
 978*024 * 
 
 981*68 
 981*28* 
 98l*35* 
 981*47* 
 981*28* 
 981*20* 
 981*254 
 98r20* 
 98136 
 98r|6 
 981-62 
 981-48* 
 9 8l-54 
 98I-45 
 981-56 
 981-184 
 98r200 
 98r38 
 98135 
 981-195 
 981-19 
 981-19 
 981-37 
 981-48 
 
 98r3I 
 981*20 
 981-IO* 
 981-14 
 981-62* 
 98136* 
 98I-37 
 
 979-24* 
 
 Equator 
 
 British Isles- 
 Aberdeen (Univ.)J .... 
 Aberystwith 
 
 Bangor . 
 
 Belfast ... 
 
 Birmingham . 
 
 Bristol 
 
 Cambridge (Univ. Obs.) . . 
 Cardiff 
 
 Dublin (Trin. Coll.) . . . 
 (R.C.S) .... 
 Dundee (Univ. Coll.) % . . 
 Durham 
 
 Edinburgh 
 
 Eskdalemuir (Obs.) . . . 
 Glasgow (Univ.) % .... 
 Greenwich (Obs.) .... 
 Kew (Obs.) 
 
 Leeds ( Univ.) % .... 
 
 Liverpool (Univ.) J. . . . 
 London (Natl. Phys. Lab.) 
 (Univ., S. Kens.) . 
 (Univ. Coll.)t . . 
 Manchester (Univ.)^ . . . 
 Newcastle (Armstrong Coll.) 
 Nottingham (Univ. Coll.) % . 
 Oxford (Radcliffe Obs.) . . 
 Plymouth . . . 
 
 Portsmouth .... 
 
 St. Andrews (Univ.) . . . 
 Sheffield (Univ. Obs.) . . . 
 Stonyhurst (Obs.) .... 
 Africa 
 Bloemfontein . . . 
 
 
 11 No correction has been applied for height above sea-level. t Ground floor. 
 \ Physics laboratory. Teddington. || Second floor. 
 
12 
 
 GRAVITY 
 
 Place. 
 
 Longitude 
 E. or W. of 
 Greenwich. 
 
 Latitude (A). 
 
 Height (H) 
 above Sea- . ,?.., 
 level. (calculated). 
 
 Africa (contit.) 
 Cairo (Observatory) . . . 
 Cape Town . - - 
 
 / // 
 
 31 17 14 E 
 18 29 E 
 30 40 E 
 28 7 E 
 57 33 9 E 
 
 76 37 W 
 71 4 W 
 87 38 W 
 71 7 46 W 
 
 77 52 22 W 
 
 73 34 39 W 
 73 59 9 W 
 75 9 37 W 
 74 39 22 W 
 71 13 8 W 
 90 12 17 W 
 79 23 40 W 
 77 3 59 W 
 72 55 8W 
 
 72 48 56 E 
 88 21 30 E 
 114 10 28 E 
 80 14 54 E 
 
 138 35 8 E 
 153 i 36 E 
 144 58 32 E 
 115 52 E 
 151 12 23 E 
 174 46 37 E 
 
 13 19 E 
 10 43 23 E 
 12 34 40 E 
 6 9 H E 
 4 29 3 E 
 
 2 20 14 E 
 
 2 13 10 E 
 13 3 59 E 
 12 28 53 E 
 30 18 22 E 
 16 20 21 E 
 8 33 4E 
 
 O 1 II 
 
 30 4 38 N 
 33 56 S 
 29 40 S 
 26 ii S 
 20 5 39 S 
 
 39 18 N 
 42 21 N 
 41 52 N 
 
 42 22 48 N 
 
 18 24 51 N 
 45 30 17 N 
 40 43 49 N 
 39 57 8 N 
 40 20 58 N 
 46 48 21 N 
 38 38 4 N 
 43 39 36 N 
 38 56 32 N 
 
 41 19 22 N 
 
 18 53 45 N 
 22 32 54 N 
 22 18 13 N 
 13 4 8 N 
 
 34 55 39 S 
 27 28 S 
 37 49 53 S 
 3i 57 S 
 33 5i 4i S 
 41 18 i S 
 
 52 31 N 
 59 54 44 N 
 55 4i 13 N 
 46 ii 59 N 
 52 9 20 N 
 48 50 ii N 
 48 49 53 N 
 52 22 56 N 
 4i 53 54 N 
 59 56 30 N 
 48 12 47 N 
 47 22 40 N 
 
 metres. 
 
 33 
 
 1 2 
 
 1753 
 
 55 
 
 23 
 33 
 251 
 
 24 
 69 
 
 57 
 96 
 36 
 
 65 
 70 
 171 
 107 
 
 102 
 
 32 
 
 10 
 
 6 
 
 33 
 7 
 
 430 
 42 
 28 
 H 
 44 
 43 
 
 30 
 25 
 H 
 374 
 6 
 
 59 
 70 
 
 94 
 59 
 3 
 
 468 
 
 cms. /sec." 
 979-32 
 979-64 
 979-29 * 
 978-49 
 978-63 
 
 980-10 
 980-37 
 980-26 
 980-37 
 978-52 
 980-64 
 980*20 
 980-15 
 980-20 
 980*76 
 979-99 
 980-46 
 980*097 
 980-28 
 
 978-57 
 978-76 
 978-76 
 978-29 
 
 979-68 
 979-12 
 979-97 
 979-47 
 979-63 
 980-27 
 
 981-287 
 981-90 
 981-56 
 980-61 
 981-26 
 980-95 
 980-95 I 
 981-249 
 980-32 
 981-91 
 980-91 * 
 980*69 
 
 Durban 
 
 
 Johannesburg (L 
 Mauritius (Roy. 
 America 
 Baltimore (Mete 
 Boston (Meteoro 
 Chicago (Meteor 
 Harvard, Camb. 
 Jamaica (Monteg 
 Montreal (McGil 
 New York (Ruth 
 Philadelphia (Ob 
 Princeton (NJ.) 
 Quebec (Obs.) 
 St. Louis (Obs.) 
 Toronto (Obs ) 
 
 Jniv. Coll.) . 
 Alf. Obs.) . 
 
 arol. Stn.) . 
 1. Stn.) . . 
 ol. Stn.) . . 
 (Obs.) . . 
 o Bay Obs.) 
 lObs.) . . 
 fd. Obs.) . 
 s.) ... 
 
 
 Washington (Bui 
 Yale, New Have 
 Asia- 
 Bombay (Obs.) 
 Calcutta (Surv. C 
 Hong Kong (Ob 
 Madras (Obs.) 
 Australasia- 
 Adelaide (Obs) 
 
 . of Stands.) 
 a (Obs.) . 
 
 )ffice) '. ! 
 
 5.). . . . 
 
 
 Brisbane (Obs.) 
 Melbourne (Obs.) .... 
 Perth - 
 
 Sydney (Obs.) 
 Wellington (Obs 
 Europe- 
 Berlin (Reichsan 
 Christiania (Obs 
 Copenhagen (Ob 
 Geneva (Obs.) 
 Leyden (Obs.) 
 Paris (Obs.) . 
 
 
 ), N.Z. . . 
 stalt) t 
 s.). . . . 
 
 
 
 (Bureau Ii 
 Potsdam (Astror 
 Rome (Coll. Obs 
 St. Petersburg (f 
 Vienna (Impl. O 
 Zurich (Poly. Ob 
 
 itl.)t . . 
 . Inst.) . . 
 .) . . . 
 
 icad. Obs.). 
 bs.) . . . 
 s.). . . . 
 
 * No correction applied for height above sea-level. t Charlottenburg. J Sevres. 
 
 DISTANCES ON THE EARTH'S SURFACE 
 
 (See Ball's " Spherical Astronomy," 1909.) 
 
 Miles per degree of Miles per degree of 
 
 At T ot A A A - 
 
 Miles per degree of 
 Lat. 
 Longitude. Latitude. 
 
 Longitude. 
 
 JKI .km, m 
 Latitude. Longitude Latitude. 
 
 69-15 
 10 68-11 
 20 65-01 
 80 59'94 
 
 68*69 40 53'05 69-00 60 34*66 69-21 
 68-70 45 48'99 69-05 70 23-73 69-32 
 68-77 50 44'54 69-10 80 12-05 69-38 
 68-88 55 3975 69-16 90 o 69-39 
 
13 
 
 THE EARTH 
 
 SIZE AND SHAPE OF THE EARTH 
 
 The spheroid of revolution which most nearly approximates 
 following dimensions : [i 
 
 to the earth, has the 
 kilom. = -6214 mile.] 
 
 Observer. Equatorial radius, a. 
 
 Polar radius, b. 
 
 Ellipticity, (a fy/a. 
 
 Bessel, 1841 . . . 6,377,397 metres 
 Clarke, 1866 . . . 8,206 
 1880 ... 8,249 
 Helmert, 1906 * . 8,200 
 U.S. Survey, 1906 1 ! 8,388 
 
 6,356,079 metres 
 584 
 515 
 818 ,, 
 
 909 
 
 1/299*2 
 1/295*0 
 
 1/293*5 
 1/298*3 
 1/297*0 
 
 * "Die Grosse der Erde." 
 t "The Figure of the Earth," 1909, and Supplement, 1910; U.S. Coast and Geodetic 
 Survey. 
 
 MEAN DENSITY OF THE EARTH 
 
 (See Poynting's " Mean Density of the 
 Earth," 1893.) 
 
 su 
 
 The mean equate 
 solar parallax (Hin 
 1909) 
 
 Whence mean dista 
 from earth to sun 
 
 Mean time taken 
 light to travel fr 
 sun to earth 
 
 N 
 
 rial ] 
 ks, > = 8"*8o7 
 j 
 f 1*494 x io 11 
 nee) J metres 
 |~"| 9*282 x io 7 
 [ miles 
 by) 
 om [=498*2 sees. 
 
 Observer. Density. 
 
 Common Balance Method. 
 
 Povntinff 1878 T4Q3 
 
 Richarz and Krigar-Menzel, 
 
 1898 5'505 
 Torsion Balance Method. 
 
 Cavendish 1798 . . 5*45 
 
 MOON 
 
 Mean distance froml _ (60*27 x earth's 
 earth to moon / ~ \ radius 
 Mass of the moonj _((i/8r53) x 
 (Hinks, 1909) )\ earth's mass 
 Inclination of moon's 1 o> // 
 orbit to ecliptic /~* 
 
 Boys, Phil. Trans., 1895 . . 5*527 
 Braun 1896 . . . 5*527 
 
 Eotvos 1896 . . ... 5*534 
 
 
 Mean density of surface . . . 2*65 
 
 Mean polar quad- j = IO]002)Ioometres * 
 
 Volume of earth = 1*082 X io 21 metres 3 * 
 Mass of earth = 5*98 x io 27 grams f 
 = 5'87X io 21 tons 
 Area of land =i*45 x io 18 cm. 2 
 Area of ocean =3*67 X io 18 cm. 2 
 
 Me ocean d ( e Cay)} = 3-5x.o : c m . 
 
 Volume of ocean =1*41 x io 24 cm. 3 
 Mass of ocean = 1*45 x io 24 grms. 
 
 Constant of Gravitation (G in law 
 
 of attraction) = 6*658 x io~ 8 c.g.s. 
 
 Obliquity of the Ecliptic to the 
 
 equator = 23 27' 4"*O4 in 1909, subject 
 to a small fluctuation by nutation, and a 
 slow continuous decline of 46"*84 per 
 century. 
 
 Constant of aberration of a star 
 is theoretically equal to (Earth's orbital 
 velocity)/(velocity of light) = 20" '43 "'03 
 (Renan and Ebert, 1905). 
 
 Constant of precession, i.e. annual 
 precessional increase of the longitude of 
 a star = 5o"*2564 + "*ooo2225/, where /is 
 the interval in years from 1900 (New- 
 comb). 
 
 * Mean of Helmert and U.S. Survey, 
 t Using Boys' and Braun's result for 
 density. 
 
14 
 
 SOLAR SYSTEM 
 
 ELEMENTS OF THE SOLAR SYSTEM 
 
 8"*8o6 is taken as the equatorial horizontal solar parallax from the observations of 
 the asteroid Eros in 1900-1 ; 5*527 is adopted as the Earth's mean density (Boys, 
 1895 ; Braun, 1896). The constants for Mercury are those adopted by Stroobant 
 and Backland (1909). The value of the mass of Jupiter is that obtained by Cookson 
 (1908). The time of rotation of Venus is that suggested by Hansky and Stefanik 
 (1907). (See Newcomb's" Spherical Astronomy "and Ball's "Spherical Astronomy.") 
 
 Name. 
 
 Sun . . 
 Mercury 
 Venus . 
 Earth . 
 Mars . . 
 Jupiter . 
 Saturn . 
 Uranus . 
 Neptune 
 
 Equatorial Semi-diameter. 
 
 Angular.* Miles. Earth = 
 
 16 ri8 
 
 8 '40 
 8-80 
 4-68 
 
 i 
 
 2475 
 34-28 
 36-56 
 
 432,890 
 1387 
 3783 
 
 2108 
 43850 
 38170 
 15440 
 16470 
 
 109-2 
 
 350 
 955 
 
 I '000 
 
 532 
 
 iro6 
 9-63 
 3-90 
 4-15 
 
 Mass 
 Earth = 
 
 329,390 
 
 '34 
 >-8i8 
 
 I -000 
 
 106 
 
 3H'5o 
 
 94-07 
 
 14-40 
 
 1672 
 
 Mean Density. 
 
 Gravity 
 at Surf. 
 Earth i Water = i Earth = i 
 
 25 
 
 88 
 
 >'94 
 roo 
 071 
 
 25 
 
 *I2 
 
 24 
 23 
 
 4-86 
 5'20 
 
 5-527 
 3-90 
 
 1-36 
 63 
 
 1-34 
 1-28 
 
 27-61 
 
 28 
 
 >'9i 
 roo 
 
 38 
 
 2-57 
 
 I'OI 
 
 95 
 97 
 
 No. of 
 
 Satellites. J 
 
 o 
 o 
 
 2(D) 
 
 8(7 D; i R) 
 io( 9 D;iR) 
 
 4W 
 
 i (R) 
 
 Name. 
 
 Sun . . 
 
 Mercury. 
 Venus 
 Earth . 
 Mars . . 
 Asteroids 
 Jupiter . 
 Saturn . 
 Uranus . 
 Neptune 
 
 ' " d h m 
 
 7 i5t 25 9 7 
 
 23 40 (?) 
 
 23 27 823 56 4-09 
 
 24 52 24 37 2274 
 
 3 5 I 9 56 
 26 49 10 15 + 
 
 13? 
 
 27 
 
 
 Semi-major Axis of Orbit. 
 
 Sidereal Period. 
 
 Earth = i. 
 
 3870986 
 7233315 
 
 I -0000000 
 
 1-523688 
 
 2-55 to 2*85 
 5-202803 
 
 9-538844 
 19-19098 
 30' 07067 
 
 Bode's Law 
 
 4 = (0+4) 
 
 52 = (48 +4) 
 1 00 = (96 + 4) 
 196=3(192 + 4) 
 
 Millions Mean Julian 
 of Miles. Solar Days. Tears. 
 
 36-0 
 6 7 '2 
 92-9 
 141-6 
 237 to 265 
 
 483-3 
 
 886-2 
 
 1782-8 
 
 2793-5 
 
 87-9693 
 224-7008 
 365-2564 
 686-9797 
 
 ! 10759-20 
 30586-29 
 60187-65 
 
 24 
 
 62 
 
 roo 
 
 1-88 
 
 11-86 
 29-46 
 
 8374 
 164-78 
 
 Name. 
 
 Mercury. 
 Venus . 
 Earth . 
 Mars . . 
 Jupiter . 
 Saturn . 
 Uranus . 
 Neptune 
 
 EUipticity of 
 
 Planet. 
 
 1/298-3 
 
 1/270 ? 
 
 I/I7 
 
 i/9 
 i/95 ? 
 
 Mean Daily 
 
 Motion in 
 
 Orbit. 
 
 5 
 
 36 7'7 
 
 59 8-2 
 
 31 26-5 
 
 4 59'i 
 
 2 0-5 
 
 42-2 
 
 21-5 
 
 Longitude of 
 Perihelion |j 
 
 75 53 59 
 130 9 50 
 101 13 15 
 334 13 7 
 
 12 36 20 
 
 90 48 32 
 
 169 2 56 
 
 43 45 20 
 
 Longitude of 
 
 Ascending 
 
 Node.f 
 
 Inclination 
 of Orbit to 
 Ecliptic. 
 
 47 8 45 
 75 46 47 
 
 ooo 
 
 48 47 9 
 99 26 42 
 
 112 47 12 
 
 73 29 25 
 
 130 40 44 
 
 7 o 10 
 3 23 37 
 
 000 
 
 I 51 I 
 
 1 18 42 
 
 2 29 39 
 
 46 22 
 
 1 46 45 
 
 Eccentricity 
 of Orbit.** 
 
 "205614 
 006821 
 '016751 
 093309 
 048254 
 "056061 
 047044 
 008533 
 
 * This is the angle subtended by the semi-diameter at a distance equal to the Earth's 
 mean distance from the Sun. 
 
 t The inclination of the plane of the Sun's equator to the plane of the ecliptic.' 
 
 J D means direct ; R, retrograde. 
 
 The ellipticity = (a fy/a, where a is the major axis and b the minor axis of the spheroid 
 of revolution. The value given for the Earth is Helmert's (p. 13). 
 
 || Perihelion is the point in the orbit nearest the Sun. Longitude is the angular distance 
 from the first point of Aries (see p. 3), measured along the ecliptic. 
 
 ^f A node is one of the two points at which a planet's orbit intersects the plane of the 
 ecliptic. At the ascending node^the planet passes from south to north of the ecliptic. 
 
 ** The eccentricity = V( 2 2 )/tf, where a and b are the major and minor axes of the orbit. 
 
15 
 
 THE STARS 
 
 EQUATION OF TIME 
 
 ( + ) means that the equation of time has to be added as a correction to the 
 apparent solar time (i.e. sundial time) to give the mean solar or clock time (see p. 3). 
 (M) = maximum or minimum. The values below vary by a few seconds from year 
 to year. 
 
 Date. 
 
 Equation of 
 time. 
 
 Date. 
 
 Equation of 
 time. 
 
 Date. 
 
 Equation of 
 time. 
 
 Date. 
 
 Equation of 
 time. 
 
 Jan. i 
 
 16 
 Feb. i 
 
 12 
 
 Mar. i 
 
 16 
 
 + 3 ii 
 + 933 
 + 1337 
 + i425(M) 
 + 12 34 
 + 8 51 
 
 April i 
 
 16 
 
 May I 
 
 M 14 
 
 June i 
 '5 
 
 m. s. 
 
 +4 i 
 o o 
 
 -257 
 
 -349W 
 -227 
 o o 
 
 July i 
 26 
 
 Aug. 1 6 
 
 Sept. i 
 16 
 
 Oct. i 
 
 + 332 
 
 + 6 i8(M) 
 
 + 4 ii 
 o o 
 
 - s \ 
 
 10 10 
 
 Oct. 16 
 
 Nov. 3 
 
 16 
 
 Dec. i 
 
 12 
 
 25 
 
 14 20 
 
 -i62i(M) 
 15 10 
 
 io 56 
 
 -615 
 
 o o 
 
 PARALLAXES OF STARS 
 
 The proper motion of a star is its real change of place arising from the actual 
 motion of the star itself. 
 
 The annual parallax is the angle between the direction in which a star 
 appears as seen from the earth and the direction in which it would appear if it 
 could be observed from the centre of the sun. 
 
 A light-year is the distance that light travels in one year (see p. 69). 
 
 Star and Magnitude. 
 
 a Centauri ('2) . . . . 
 21185 Lalande (7*5) . . 
 6 1 Cygni (4-8) . . . . 
 Sirius (1*4) . . . . 
 
 Procyon (-5) 
 
 Altair (-9) 
 
 Aldebaran (ri) . . . 
 
 Capella (-2) 
 
 Vega (-I). . . . . . 
 
 1830 Groombridge (6*4) . 
 
 Polaris (2-1) 
 
 Arcturus ('2) . . . . 
 
 Proper motion 
 per year. 
 
 37 
 7'3 
 5-2 
 
 i'3 
 
 i '3 
 
 7 
 
 '2 
 
 '4 
 
 '4 
 
 7'0 
 
 O'O 
 
 2-3 
 
 Annual 
 parallax. 
 
 75 'oi 
 48 -02 
 
 37 -02 
 *37 '01 
 
 31 
 
 28 -02 
 17 '02 
 12 -02 
 12 '02 
 10 '02 
 07 'Q2 
 O24 
 
 Distance. 
 
 Sun's dist. = i Light-years 
 
 28 x io 6 
 
 '43 
 56 
 
 56 
 69 
 
 74 
 
 17 
 17 
 
 2'0 
 3 -0 
 
 87 
 
 4*4 
 6-8 
 8-8 
 
 8.0 
 O 
 
 II 
 
 12 
 
 22 
 27 
 27 
 
 33 
 
 47 
 
 140 
 
 SYSTEMATIC MOTIONS OF THE STARS 
 
 The apparent proper motions of the stars 
 show drifts in two directions. The assigned 
 positions of the apices of these directions 
 are: 
 
 Computer. 
 
 Kapteyn, 1904 
 Eddington . 
 Dyson . . . 
 
 Stream I. 
 
 R.A. Dec. 
 
 85 
 90 
 94 
 
 Stream II. 
 
 B.A. Dec. 
 
 260 
 292 
 
 -48 
 -58 
 
 -74 
 
 STANDARD TIMES 
 
 Referred to Greenwich time. 
 
 Gt. Britain,France,Hol-j 
 land, Belgium, Spain / 
 
 Ireland 
 
 Austria, Denmark, Ger- 
 many, Italy, Norway, 
 Switzerland .... 
 
 British South Africa, 
 Egypt, Turkey . . 
 
 Japan 
 
 Australia j 
 
 New Zealand .... 
 Canada and United \ 
 States I 
 
 Greenwich 
 
 time 
 25m.25s.fst. 
 
 i hour fast 
 
 i^ or 2 hours 
 
 fast 
 
 9 hours fast 
 8, 9, or io 
 
 hours fast 
 
 "i 
 4, 5, 6, 7, or 8 
 hours slow 
 
16 
 
 SCREWS 
 
 SCREWS 
 
 It is customary for British metal screws, of ]-inch diameter and above, to have a 
 Whitworth thread, for smaller sizes a British Association thread. In the Whitworth 
 thread the angle between the slopes is 55, in the B.A. thread 47'S . 
 
 The pitch is the distance between adjoining crests (say) of the same thread measured 
 parallel to the axis of the screw. It is the reciprocal of the number of turns per inch or 
 mm. as the case may be. The full diameter is the maximum over-all diameter. 
 
 Micrometer screws are made with some multiple or sub-multiple of 100 threads 
 to the inch or mm. 
 
 " Woodscrews " of iron or brass are numbered as follows : No. 4 has a diameter 
 of | inch, each succeeding number adding ^ inch to the diameter of the screw : this 
 applies to all lengths. The length of countersunk screws is measured over all ; that of 
 round-headed screws, from under the head. [i inch = 25*4 mm.] 
 
 STANDARD WHITWORTH. 
 
 Full di- 
 ameter 
 
 inch. 
 
 If 
 
 If 
 
 Ii 
 It 
 
 I 
 
 
 
 H 
 
 Threads 
 to inch 
 
 S 
 
 6 
 6 
 7 
 
 8 
 
 9 
 10 
 
 Fall di- Threads 
 ameter . to inch 
 
 inch. 
 I 
 
 H 
 A 
 
 10 
 
 II 
 II 
 
 12 
 12 
 
 18 
 
 20 
 
 BRITISH ASSOCIATION. 
 
 No. 
 
 Full di- 
 ameter. 
 
 Pitch. 
 
 mm. 
 
 6-0 
 5'3 
 47 
 
 2'8 
 
 2-5 
 
 2'2 
 
 mm. 
 
 ro 
 
 81 
 
 "73 
 66 
 
 '59 
 '53 
 48 
 
 '43 
 
 as * 
 
 mm. 
 I'9 
 
 i'7 
 
 I '2 
 
 1*0 
 
 *9 
 
 "19 
 70 
 
 "39 
 
 '35 
 
 25 
 23 
 
 21 
 19 
 17 
 
 No. 
 
 Full di- 
 ameter. 
 
 Pitch. 
 
 mm. ! 
 62 
 
 '54 
 4 8 
 42 
 '37 
 '33 
 29 
 
 25 
 
 14 
 '12 
 'II 
 10 
 
 09 
 08 
 07 
 
 M = mass of body. 
 
 MOMENTS OF INERTIA 
 (See A. M. Worthington, " Dynamics of Rotation." London.) 
 
 Body. 
 
 Uniform thin rod (length /) 
 
 Rectangular lamina (sides 
 
 a and b) 
 
 Circular lamina (radius r) 
 
 Solid cylinder (radius r ; 
 length /) 
 
 Hollow cylinder (external 
 and internal radii R and r ; 
 length /) 
 
 Solid sphere (radius r) 
 
 Hollow sphere (external and 
 internal radii R and r) 
 
 Anchor ring (mean radius 
 of ring R ; radius of cross- 
 section r) 
 
 Axis of rotation. 
 
 I' (i) Through centre, perpendicular to 
 length 
 (2) Through end, perpendicular to 
 length 
 
 (1) Through centre of gravity, per- 
 
 pendicular to plane 
 
 (2) Through centre of gravity, 
 
 parallel to side b 
 
 (1) Through centre, perpendicular to 
 
 plane 
 
 (2) Any diameter 
 
 (1) Axis of cylinder 
 
 (2) Through centre of gravity, per- 
 
 pendicular to axis of cylinder 
 
 (1) Axis of cylinder 
 
 (2) Through centre of gravity, per- 
 
 pendicular to axis 
 
 Through centre 
 Through centre 
 
 (1) Through centre, perpendicular 
 
 to plane of ring 
 
 (2) Any diameter 
 
 Moment of inertia. 
 
 Mf 
 
 
 M. 
 
 R 2 + 
 
 T 
 
 R a + 
 
 M (J'RT^ 
 M' 
 
 M 
 
17 
 
 VOLUME CALIBRATION 
 
 VOLUME CALIBRATION OF VESSELS BY WATER OR MERCURY 
 
 Volume content of vessel at / C. = V t = Vf t v t = w t (f), where 
 
 w t = observed weight in grams (against brass weights in air) of contained water 
 
 (or mercury) at / C. 
 
 W, = weight of such liquid in vacua (i.e. corrected for buoyancy in air). 
 v t volume of i gram of liquid at t C. 
 
 (/") is a factor which introduces the buoyancy and specific volume corrections. 
 The following table of values of the factor (/) is based on tables on pp. 19 and 22. 
 
 Temp. (/) of weighing 
 
 10 C. 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 Value of ( H 2 O . 
 factor (/)\Hg . 
 
 1-00133 
 
 073683 
 
 1*00143 
 
 073697 
 
 1-00154 
 073710 
 
 roo i 66 
 073724 
 
 1-00179 
 073737 
 
 1-00193 
 
 073750 
 
 1*00209 
 073764 
 
 1*00226 
 073777 
 
 Temp. (/) of weighing 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 25 
 
 Value of JH,O . 
 factor (/)lHg . 
 
 1*00244 
 
 073790 
 
 1*00263 
 073804 
 
 1-00283 
 073817 
 
 1-00305 
 073831 
 
 1-00327 
 073844 
 
 i '003 50 
 073857 
 
 1*00375 
 073871 
 
 1*00400 
 073884 
 
 The above gives the volume content V t of the vessel at the temperature of weighing, 
 / C. At any other temperature, /', the volume V t , = V t {i + y(t' - /)} = V 4 (F), where 
 I 7 is the coefficient of cubical expansion of the material of the vessel. Values of the 
 ; factor (F) for glass vessels (7 = -000025) ar e tabulated below. 
 
 iY - /) 
 
 2C. 
 
 4 
 
 6 
 
 8 
 
 -2C. 
 
 -4 
 
 -6 
 
 -8 
 
 Value of factor(F) 
 
 1-00005 
 
 roooio 
 
 1*00015 
 
 1*00020 
 
 99995 
 
 99990 
 
 99985 
 
 99980 
 
 Example. Weight of water contained in a vessel at 10 C. = 10 grams : thence 
 } volume of vessel at 10 C. = 10 x 1*00133 c.cs. The same vessel, if of glass, would 
 contain at 16 C , 10 x 1-00133 x 1*00015 - 10*0148 c.cs. 
 
 CAPILLARITY CORRECTIONS OF MERCURY COLUMNS 
 
 The height of the meniscus and the value of the capillary depression depend on 
 the bore of the tubing, on the cleanliness of the mercury, and on the state of the walls 
 of the tube. The correction is negligible for tubes with diameters greater than about 
 25 mms. The table below gives the amount of the correction (which has to be added 
 to the height) for various diameters of glass tubing and meniscus heights. (Mendeldeff 
 and Gutkowsky, 1877. See also Scheel and Heuse, Ann. d. Phys., 33, 1910.) 
 
 Bore 
 
 Height of meniscus in mms. 
 
 Bore 
 
 Height of meniscus in mms. 
 
 nf 
 
 
 nf 
 
 
 tube. 
 
 *4 
 
 6 
 
 8 
 
 10 
 
 1-2 
 
 1-4 
 
 16 
 
 1-8 
 
 tube. 
 
 *8 
 
 1-0 
 
 1-2 
 
 1-4 
 
 1-6 
 
 1-8 
 
 mm. 
 
 4 
 
 mm. 
 "S3 
 
 mm. 
 1*22 
 
 mm. 
 
 1 '54 
 
 mm. 
 1*98 
 
 mm. 
 
 2*37 
 
 mm. 
 
 mm. 
 
 mm. 
 
 mm. 
 
 9 
 
 mm. 
 *2I 
 
 mm. 
 28 
 
 mm. 
 
 '33 
 
 mm. 
 *40 
 
 nun. 
 
 46 
 
 mm. 
 52 
 
 b 
 
 '47 
 
 6 5 
 
 86 
 
 ri9 
 
 r 45 
 
 I *80 
 
 
 
 
 
 10 
 
 'IS 
 
 20 
 
 <2 5 
 
 *2 9 
 
 33 
 
 '37 
 
 6 
 
 27 
 
 MI 
 
 *Sb 
 
 78 
 
 Q8 
 
 1*21 
 
 I '43 
 
 
 
 11 
 
 *IO 
 
 14 
 
 *i8 
 
 *2I 
 
 24 
 
 27 
 
 V 
 
 18 
 
 28 
 
 40 
 
 'S3 
 
 67 
 
 82 
 
 97 
 
 1*13 
 
 12 
 
 07 
 
 io 
 
 13 
 
 'IS 
 
 18 
 
 19 
 
 8 
 
 "~"" 
 
 *2O 
 
 29 
 
 3* 
 
 46 
 
 56 
 
 65 
 
 '77 
 
 13 
 
 04 
 
 07 
 
 *IO 
 
 '12 
 
 13 
 
 H 
 
IS 
 
 BAROMETRY 
 
 REDUCTION OF BAROMETER READINGS TO C. 
 
 Corrected height 
 
 ;/3 - V , 
 (I + Bt)l 
 
 and temperature of the barometer, = -0001818 (Regnault), the coefficient of cubical 
 expansion of mercury; o = -0000085, the coefficient of linear expansion of glass, 
 or -0000184 for brass. Hydrogen temperature scale. (After Broch, Inter. Bur. 
 Weights and Measures.) 
 
 (In standard English barometry the mercury is reduced to 32 F., and the 
 scale to 62 F. In the table below, both are reduced to the ice point.) 
 
 Temp. (/). 
 
 Correction in mms. to be subtracted. 
 
 GLASS SCALE. 
 
 BRASS SCALE. 
 
 Unconnected height in mms. 
 
 Unconnected height in mms. 
 
 700 
 
 720 
 
 740 
 
 760 
 
 780 
 
 700 
 
 720 
 
 740 
 
 760 
 
 780 | 
 
 2C. 
 4 
 6 
 8 
 
 mm. 
 24 
 4 8 
 
 73 
 
 97 
 
 25 
 '49 
 75 
 99 
 
 26 
 'Si 
 
 77 
 
 I'02 
 
 26 
 'S3 
 79 
 1-05 
 
 27 
 
 '54 
 81 
 i -08 
 
 mm. 
 23 
 46 
 6 9 
 91 
 
 24 
 
 '47 
 71 
 
 '94 
 
 24 
 48 
 72 
 '97 
 
 25 
 50 
 74 
 '99 
 
 25 
 '5 1 
 76 
 
 I'O2 
 
 10 
 
 I -21 
 
 1-25 
 
 1-28 
 
 1-31 
 
 i-35 
 
 I-I 4 
 
 1-17 
 
 I'2I 
 
 1-24 
 
 1-27 
 
 12 
 14 
 16 
 18 
 
 i'45 
 1-69 
 
 i*94 
 2-18 
 
 1-49 
 
 174 
 1-99 
 2-24 
 
 I'53 
 I'79 
 2-05 
 2-30 
 
 $ 
 
 2'10 
 2-36 
 
 1-62 
 
 1-89 
 2-16 
 2'43 
 
 i'37 
 i -60 
 1-82 
 2-05 
 
 1-41 
 
 1-64 
 1-88 
 
 2'II 
 
 i'45 
 1-69 
 
 i'93 
 2-17 
 
 1-49 
 
 173 
 
 1-98 
 2-23 
 
 I'53 
 178 
 2-03 
 2-29 
 
 20 
 
 2-42 
 
 2-49 
 
 2- 5 6 
 
 2-62 
 
 2-69 
 
 2-28 
 
 2'34 
 
 2-41 
 
 2-47 
 
 2'54 
 
 22 
 24 
 26 
 28 
 
 2-66 
 2-90 
 
 3M4 
 
 3-38 
 
 273 
 2-98 
 
 3'23 
 3'47 
 
 2'8l 
 
 3'o6 
 3-32 
 3*57 
 
 2-89 
 3-I5 
 3'4I 
 3^7 
 
 2*96 
 3'23 
 3'5o 
 
 377 
 
 2-51 
 
 273 
 2-96 
 
 3'i9 
 
 2-58 
 2*1 
 
 3 '04 
 3-28 
 
 2-65 
 2-89 
 3^3 
 3*37 
 
 2-72 
 2-97 
 3-21 
 3'46 
 
 279 
 3^5 
 3^0 
 
 3'55 
 
 30 
 
 3-62 
 
 372 
 
 3-83 
 
 3'93 
 
 4'03 
 
 3-4i 
 
 3'5i 
 
 3'6i 
 
 37i 
 
 3'80 
 
 32 
 34 
 
 3-86 
 4-10 
 
 3 '97 
 
 4-21 
 
 4-08 
 4'33 
 
 4-19 
 
 4'45 
 
 4*30 
 4'57 
 
 3-64 
 
 3-87 
 
 374 
 3'98 
 
 3-85 
 4-09 
 
 3'95 
 4-20 
 
 4-05 
 
 4-3I 
 
 REDUCTION OF BAROMETER READINGS TO LAT. 45 AND SEA-LEVEL 
 
 
 for "gravity." The corrections below result from the variation of "^-" with 
 latitude and height above sea-level (see p. n). The barometer correction for 
 
 TJ 
 
 latitude = ,-(C), has to be subtracted from the temperature corrected barometer 
 reading // for latitudes between o and 45 ; and added for latitudes from 45 to 90. i 
 
 Latitude 
 
 
 90 
 
 mm. 
 
 i -97 
 
 5 
 85 
 
 1-94 
 
 10 
 80 
 
 1-85 
 
 15 
 
 75 
 
 20 
 70 
 
 25 
 65 
 
 170 
 
 1-51 1-27 
 
 30 35 40 
 60 55 50 
 
 98 
 
 67 
 
 34* 
 
 45 
 
 45 ! 
 
 The " gravity correction " of the barometer for height above sea-level amounts 
 to about "13 mm. of mercury per 1000 metres above sea-level. The correction has 
 to be subtracted from the observed reading. 
 
 * London, "45. 
 
19 
 WEIGHINGS : 
 
 GAS VOLUMES 
 
 REDUCTION 
 
 OF WEIGHINGS TO VACUO 
 
 
 
 
 
 
 
 
 
 
 The buoyancy correction = 
 
 Mcr(i/A i/p) = M>, where M is the apparent mass 
 
 in grams of the body in 
 
 air, <r is the density of air (= "0012) in grams per c.c., A is 
 
 the density of the body, p is the density of the weights. The correction is true 
 
 ^ 4% I 
 
 for the following limits : 
 
 740 mm. press., 1 to 22 ; 760 mm., 8 to 29 ; 
 
 780 
 
 mm., 
 
 15 to 35. If the correction 
 
 is required more accurately, multiply the value of k 
 
 given below by 0-7-0012, 
 
 where 
 
 <r' is the true density of the air for the temp, and 
 
 press, at the time of the weighing (for o-', see p. 25). The corrections for quartz 
 
 weights are the same as 
 
 for Al. 
 
 + means cor", to be added to weight. 
 
 (See L.B.M.) 
 
 Density 
 
 **.f < D^i* 
 
 Correction Factor (k) in 
 
 Milligms. Density 
 
 Correction Factor (k} in Milligms. 
 
 oi uoay 
 weighed 
 
 Brass wgts. 
 
 Pt 
 
 wgts. 
 
 of Body 
 Al wgts. weighed 
 
 Brass wgts. 
 
 Pt wgts. 
 
 A 
 
 I wgts. 
 
 A. 
 
 p = 8-4. 
 
 P = 
 
 21*5. 
 
 p = 2 65. A. 
 
 p = 8-4. 
 
 p = 21*5. 
 
 P = 2-65. 
 
 5 
 
 + 2-26 
 
 + 
 
 2 '34 
 
 + '95 1*6 
 
 + -6i 
 
 + '69 
 
 H 
 
 .-30 
 
 55 
 
 4- 2*04 
 
 _j_ 
 
 2-13 
 
 + 73 1-7 
 
 + 56 
 
 + '65 
 
 H 
 
 - * 2 5 
 
 6 
 
 + 1-86 
 
 _j- 
 
 '94 
 
 + '55 1-8 
 
 + 52 
 
 + 62 
 
 H 
 
 - -21 
 
 65 
 
 + 170 
 
 _!_ 
 
 79 
 
 + '39 1-9 
 
 + '49 
 
 + 58 
 
 H 
 
 -18 
 
 7 
 
 + '57 
 
 -If. 
 
 66 
 
 + -26 2 
 
 + 46 
 
 + '54 
 
 -\ 
 
 -'15 
 
 75 
 
 + -46 
 
 4- 
 
 '55 
 
 + -15 2'5 
 
 + '34 
 
 + '43 
 
 + 03 
 
 8 
 
 + -36 
 
 + 
 
 '44 
 
 + -05 3 
 
 + 26 
 
 + '34 
 
 
 - 'OS 
 
 85 
 
 + -27 
 
 -j- 
 
 36 
 
 + -96 3'5 
 
 + *2O 
 
 + 29 
 
 
 - -ii 
 
 9 
 
 + -19 
 
 4. 
 
 28 
 
 + *88 4 
 
 + 16 
 
 + 24 
 
 
 -I 5 
 
 95 
 
 + -12 
 
 -j_ 
 
 21 
 
 + -81 5 
 
 + 10 
 
 
 ) 
 
 
 - -21 
 
 1 
 
 + -06 
 
 4- 
 
 '4 
 
 + 75 6 
 
 + 06 
 
 + *i< 
 
 1 
 
 
 - '25 
 
 I'l 
 
 + '95 
 
 4- 
 
 4 
 
 + -64 8 
 
 + '01 
 
 + 09 
 
 
 - '30 
 
 1-2 
 
 + -86 
 
 4. 
 
 '94 
 
 + '55 10 
 
 -02 
 
 + 06 
 
 
 - '33 
 
 1-3 
 
 + 78 
 
 + 
 
 8 7 
 
 + '47 15 
 
 -06 
 
 + "03 
 
 
 - '37 
 
 1-4 
 
 + 71 
 
 4- 
 
 80 
 
 + -40 20 
 
 '08 
 
 + '004 
 
 
 - '39 
 
 1-5 
 
 + -66 
 
 + 
 
 75 
 
 + '35 22 
 
 - -09 
 
 'OOI 
 
 -40 
 
 REDUCTION OF GASEOUS 
 
 VOLUMES TO AND 760 MMS. 
 
 PRESSURE 
 
 Corrected volume v 
 
 = {v/(i + 00367/)} .//76o, where z>, /, and p are the 
 
 observed volume, temp., 
 
 and pressure (in mms. of mercury) of the gas 
 
 respectively. 
 
 g = 980-62 cms. per sec 2 . 
 
 The 
 
 coefficient '00367 observed by Regnault. 
 
 
 
 Values of (1 + -00367*). 
 
 Temp. (/). 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 0C. 
 
 I '0000 
 
 1-0037 
 
 1*0073 
 
 I "OIIO 
 
 1-0147 
 
 1-0183 
 
 I 'O22O 
 
 1-0257 
 
 1-0294 
 
 1*0330 
 
 10 
 
 0367 
 
 0404 
 
 0440 
 
 0477 
 
 0514 
 
 0550 
 
 0587 0624 
 
 0661 
 
 0697 
 
 20 
 
 0734 
 
 0771 
 
 0807 
 
 0844 
 
 0881 
 
 0917 
 
 0954 
 
 0991 
 
 1028 
 
 1064 
 
 30 
 
 no: 
 
 1138 
 
 1174 
 
 I2II 
 
 1248 
 
 1284 
 
 1321 1358 
 
 1395 
 
 1431 
 
 40 
 
 1468 
 
 1505 
 
 
 1578 
 
 1615 
 
 1651 
 
 1688 1725 
 
 1762 
 
 1798 
 
 50 
 
 1835 
 
 1872 
 
 1908 
 
 1945 
 
 1982 
 
 2018 
 
 2055 2092 
 
 2129 
 
 2165 
 
 60 
 
 2202 
 
 2239 
 
 2275 
 
 2312 
 
 2349 
 
 2385 
 
 2422 2459 
 
 2496 
 
 2532 
 
 70 
 
 2569 
 
 2606 
 
 2642 
 
 2679 
 
 2716 
 
 2752 
 
 2789 ! 2826 
 
 2863 
 
 2899 
 
 80 
 
 2936 
 
 2973 
 
 3009 
 
 3046 
 
 3083 
 
 3119 
 
 3156 : 3103 
 
 3230 
 
 3266 
 
 90 
 
 333 
 
 3340 
 
 3376 
 
 3413 
 
 3450 
 
 3486 
 
 3523 1 356o 
 
 3597 
 
 3633 
 
 100 
 
 3670 
 
 3707 
 
 3743 
 
 3780 
 
 3817 
 
 3853 
 
 3890 j 3927 
 
 3964 
 
 4000 
 
 110 
 
 4037 
 
 4074 
 
 4110 
 
 4H7 
 
 4184 
 
 4220 
 
 4257 4294 
 
 4331 
 
 4367 
 
 ! Values of p/760 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Press, (p). 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 Q 
 
 9 
 
 700 mm. 
 
 9211 
 
 9224 
 
 9227 
 
 9250 
 
 9263 
 
 9276 
 
 9289 -9303 
 
 9316 
 
 9329 
 
 710 
 
 9342 
 
 '9355 
 
 9368 
 
 9382 
 
 '9395 
 
 9408 
 
 9421 -9434 
 
 '9447 
 
 9461 
 
 i 720 
 
 9474 
 
 9487 
 
 9500 
 
 "95 I 3 
 
 9526 
 
 '9539 
 
 9553 -9566 
 
 '9579 
 
 "9592 
 
 730 
 
 9605 
 
 9618 
 
 9632 
 
 9 6 45 
 
 9658 
 
 9671 
 
 9684 -9697 
 
 9711 
 
 "9724 
 
 740 
 
 9737 
 
 9750 
 
 9763 
 
 9776 
 
 9789 
 
 9803 
 
 9816 -9857 
 
 "98 
 
 42 
 
 9855 
 
 750 
 
 9868 
 
 9882 
 
 9895 
 
 9908 
 
 9921 
 
 9934 
 
 '9947 
 
 9961 
 
 '9974 
 
 7 J J 
 
 9987 
 
 ! 760 
 
 I'OOOO 
 
 1-0013 
 
 1*0026 
 
 1-6039 
 
 1-0053 
 
 1-0066 
 
 1*0079 1*0092 
 
 I-OI05 
 
 1-0118 
 
 770 
 
 1-0132 
 
 1*0145 
 
 1-0158 
 
 1-0171 
 
 i 0184 
 
 1-0197 
 
 1*0211 1*0224 
 
 1-0237 
 
 1*0250 
 
20 
 
 DENSITIES 
 
 DENSITIES OF THE ELEMENTS 
 
 Average densities of liquid and solid elements in grams per c.c. at ordinary temperatures 
 unless otherwise stated. For gaseous densities see p. 26. The density of a specimen may 
 depend considerably on its state and previous treatment, e.g. the density of a cast metal is 
 increased by drawing, rolling, or hammering. See Koppel in L.B.M. 
 
 Element. 
 
 Density. 
 
 Element. 
 
 Density. 
 
 Element. 
 
 Density. 
 
 Aluminium . . 
 Antimony . . 
 Argon (liq.) . . 
 Arsenic . . . 
 Barium . . . 
 Beryllium . . 
 
 . 2-65 
 . 6-62 
 . i-4/-i85 
 - 573 
 375 
 i'93 
 9*80 
 
 Indium .... 
 Iodine .... 
 Iridium .... 
 Iron (pure) . . . 
 Krypton (liq.) 
 Lanthanum . . . 
 Lead 
 
 7-12 
 
 4'95 
 22-41 
 7-86 
 2-16 
 6-12 
 
 I I "^7 
 
 Samarium . 
 Scandium . . . 
 Selenium, amorph . 
 cryst. . 
 liq. . . 
 Silicon .... 
 Silver 
 
 7'8 
 
 (?) 
 4'8 
 
 4'5 
 4-27 
 c. 2-3 
 
 JO'C 
 
 Boron . . 
 
 2-5 (?) 
 
 Lithium .... 
 
 1 * j/ 
 
 "Ml 
 
 Sodium .... 
 
 'Q7i 
 
 Bromine . . . 
 Cadmium . . 
 Caesium . . . 
 Calcium . . . 
 Carbon 
 Diamond . . 
 Graphite . . 
 Cerium . . . 
 Chlorine (liq.) . 
 Chromium . . 
 Cobalt . . . 
 
 . 3-102/25 
 . 8-64 
 . 1-87 
 1-55/29 
 
 3'52 
 . 2-3 
 . 6-68 
 , 2-49/0 
 . 6-50 
 . 8-6 
 
 Magnesium . . . 
 Manganese . . . 
 Mercury (see p. 22) 
 Molybdenum . . 
 Neodymium . . 
 Neon (liq.) . . . 
 Nickel .... 
 Niobium .... 
 Nitrogen (liq.) 
 Osmium .... 
 Oxygen Clio/) . 
 
 174 
 7*39 
 I3'56/I5 
 8-6 
 6-96 
 
 (?) 
 8-9 
 1275 
 
 79/-I96 
 22-5 
 
 I'27/ 2^? 
 
 Strontium . 
 Sulphur, rhombic 
 monoclinic 
 amorphous 
 liquid 1 1 3 
 Tantalum . . . 
 Tellurium . . . 
 Terbium .... 
 Thallium . . . 
 Thorium .... 
 Tin ... 
 
 2-54 
 2-07 
 1-96 
 1-92 
 1-81 
 16-6 
 6-25 
 
 (?) 
 11-9 
 11-3 
 
 7'2Q 
 
 Copper . . . 
 Erbium . . . 
 Fluorine (liq.) . 
 Gadolinium . . 
 Gallium . . . 
 Germanium . . 
 Gold 
 
 8-93 
 . 477 (?) 
 . i-ii/-i87 c 
 (?) 
 5*95 
 5'47 
 
 . IQ*^2 
 
 Palladium . . . 
 Phosphorus, red . 
 yellow 
 Platinum . . . 
 Potassium . . . 
 Praseodymium 
 Radium .... 
 
 1 1-4 
 2'20 
 I-8 3 
 2r50 
 862 
 6-48 
 f ? ) 
 
 Titanium . . . 
 Tungsten . . . 
 Uranium . . . 
 Vanadium . . . 
 Xenon (liq.) . . 
 Ytterbium . . . 
 Yttrium 
 
 I7-I8-8 
 I8'7 
 5'5 
 3'5 
 (?) 
 
 r8(?> 
 
 Helium (liq ) 
 
 I5/B.P. 
 
 Rhodium 
 
 12'A.A. 
 
 Zinc 
 
 7*1 
 
 1 Hydrogen (liq.) 
 
 55 5J 
 
 . -07/B.P. 
 086/M.P. 
 
 Rubidium . . . 
 Ruthenium . . . 
 
 1-532 
 I2'3 
 
 Zirconium . . 
 
 4^5 
 
 The densities of the alkali metals Li, Na, K, Rb, Cs are due to Richards and Brink, 1907 ; of He at 
 268'6, Onnes, 1908; of W, Gin. 1908; of Ta, Nb, and Th, von Bolton, 1905, 1907, 1908; of Ca, 
 Goodwin, 1904 ; of Rh and Ir, Holborn, Henning, and Austin, 1904 ; of Br, Andrews and Carlton, 1907. 
 
 DENSITIES OF COMMON SUBSTANCES 
 
 Average densities in grams per c.c. at ordinary temperatures. For densities of acids, 
 alkalies, and other solutions, see pp. 23 et seq . ; of "chemical compounds," p. 109 ; of gases, 
 p. 26 ; of other minerals, p. 126. 
 
 Substance. 
 
 Density. 
 
 Substance. 
 
 Density. 
 
 Substance. Density. 
 
 Metals & Alloys 
 
 Iron, cast . . . 
 wrought . . 
 wire . . . 
 Steel . . . 
 
 7-1-77 
 7-8-7-9 
 77 
 7-7-7-9 
 8-4-8-7 
 r.8-4 
 8-7-8-9 
 
 8-96 
 
 1772 
 
 Coins (English) 
 silver . . 
 Constantan (Eu- \ 
 reka)||. . . / 
 German silver 1 . 
 Gunmetal . . . 
 Magnalium ** . . 
 Manganin ft 
 Phosphor bronze \\ 
 Platinoid . . . 
 Pt (90), Ir (10). . 
 
 10-31 
 8-88 
 
 8-9 
 8-0-8-4 
 
 C. 2 
 
 8-5 
 8-7-8-9 
 c. 9 
 21-62 
 
 Woods (seasoned). 
 
 Ash ; mahogany . 
 Bamboo .... 
 Beach ; oak ; teak 
 Box 
 Cedar . 
 
 6-8 
 
 c. -4 
 7 -- 9 
 9-1-1 
 S--6 
 
 ri-i'3 
 i -2-1-3 
 
 6-7 
 '5-7 
 '4-' 5 
 
 Brass (ordy.) * . . 
 Brass weights . . 
 Bronze (Cu, Sn) . 
 Coins (English) 
 bronze f . 
 goldj . . 
 
 Ebony .... 
 Lignum vita: . . 
 Pitchpine ; walnut 
 Red pine (deal) . 
 White pine . . . 
 
 * c. 66 Cu, 34 Zn. f 95 Cu, 4 Sn, i Zn. \ 91^ Au, 8} Cu. 92,1 Ag, i\ Cu. j| 60 Cu, 40 Ni. 
 1 60 Cu, 15 Ni, 25 Zn. '* c. 70 Al, 30 Mg. ft 84 Cu, 12 Mn, 4 Ni. \\ 92!, Cu, 7 Sn, \ P. 
 Described as German silver with a little tungsten. 
 
21 
 
 DENSITIES 
 
 DENSITIES OF COMMON SUBSTANCES (.contd.') 
 
 Substance. 
 
 Density. 
 
 Substance. Density. 
 
 Substance. 
 
 Density. 
 
 Minerals, etc. 
 
 Agate ; slate . . 
 Asbestos .... 
 board 
 i Carbon (see above^ 
 Charcoal .... 
 Coal .... 
 
 2-5-27 
 3-0 
 
 T2 
 
 3-'6 
 1-2-1-5 
 1-4-1-8 
 1-0-17 
 1-9 
 4-0 
 
 2'5-3 
 2-5-2-8 
 
 C. 2 
 
 *4-'9 
 2-66 
 
 2*21 
 2-07 
 2-6 3 
 
 2-2-2-3 
 
 Liquids. 
 
 Glycerine . . . 
 Methylated spirit . 
 Milk . . . 
 
 1-26 
 83 
 c. 1-03 
 85 
 '97 
 '9 1 -'93 
 90--92 
 
 *9i ~'93 
 c.'S 
 68-72 
 i '01-1-05 
 87 
 ro8 
 
 ri 
 1-8-2-0 
 i '4 
 
 22-'26 
 
 1-8 
 
 Gelatine .... 
 Glass, flint . . . 
 crown ; j 
 window / 
 Jena . . . 
 Ice (Roth, 1908), o c 
 (Vincent,'o2),o 
 Indiarubber. . . 
 Ivory 
 Leather .... 
 Paper ..... 
 
 1-27 
 2-9-4 5 
 
 2-4-2-6 
 
 (see p. 74.) 
 9168 
 9160 
 92-'97 
 1-8-1-9 
 85-1 
 7-n 
 c. ri 
 2-2-2-4 
 c. ri 
 i '45 
 
 C. '12 
 I'02 
 
 S7--88 
 8S--93 
 9 5--96 
 c. r8 
 
 C. I'O 
 
 Naphtha .... 
 Oil, castor . . . 
 linseed . . . 
 lubricating . 
 olive ; palm . 
 paraffin . . 
 
 Ppfrnl 
 
 anthracite . 
 Coke .... 
 
 1 Gas carbon . . . 
 Emery .... 
 Granite .... 
 ; Marble .... 
 Masonry .... 
 Pumice (natural) . 
 Quartz .... 
 Silica, fused 
 transparent 
 translucent . 
 Sand (silver) . . 
 Sandstone ; kaolin 
 
 Sea-water . . . 
 Turpentine . . . 
 Vinegar .... 
 
 Miscellaneous. 
 Amber .... 
 Bone . 
 
 Pitch ... 
 Porcelain . . . 
 Resin . . . . . 
 
 Red fibre. . . . 
 Snow (loose) . . 
 Tar 
 
 Wax, soft paraffin . 
 hard 
 white ; bees- 
 sealing . . 
 soft red . . 
 
 Celluloid. . . . 
 Cork ... 
 
 Ebonite .... 
 
 DENSITY DETERMINATION CORRECTIONS 
 
 In the determination of the density of a body by weighing in water, the true density 
 (corrected for air buoyancy and water density) is given by A(D <r)+ <r, where A is the 
 uncorrected density of the body, D is the density of the water, and <r is the density of the 
 air. The table below gives the correction to be applied to A. D is taken as "9992 (correct 
 to i part in 2000 between 10 and 18 C., see p. 22) and <r as -0012 (see p. 25). means 
 that the correction has to be subtracted from A. (See Stewart and Gee, " Practical Physics," 
 vol. i.) 
 
 Corr. 
 
 0-5 
 1-0 
 1-5 
 2-0 
 2-5 
 3-0 
 3-5 
 
 0002 
 
 ooo8 
 0018 
 0028 
 0038 
 
 0048 
 
 0058 
 
 4-0 
 4-5 
 5-0 
 5-5 
 6-0 
 6-5 
 7-0 
 
 Corr. 
 
 0068 
 0078 
 0088 
 0098 
 0108 
 0118 
 0128 
 
 7-5 
 7-8 
 7-9 
 8-0 
 8-1 
 8-2 
 8-3 
 
 Corr. 
 
 0138 
 0144 
 0146 
 0148 
 0150 
 0152 
 0154 
 
 Corr. 
 
 8-4 
 8-5 
 8-6 
 8-7 
 8-8 
 8-9 
 9-0 
 
 0156 
 0158 
 0160 
 0162 
 0164 
 0166 
 0168 
 
 9-5 
 10-0 
 11-0 
 12-0 
 13-0 
 140 
 15-0 
 
 Corr. 
 
 -0178 
 -0188 
 -0208 
 - -0228 
 -0248 
 -0268 
 -0288 
 
 16-0 
 17-0 
 180 
 19-0 
 20-0 
 210 
 22-0 
 
 Corr. 
 
 -0308 
 -0328 
 -0348 
 -0368 
 -0388 
 
 -0408 
 -0428 
 
 DENSITY OF DAMP AIR 
 
 The density of damp air may be derived from the expression <r = oy(H o'378/)/H, 
 where crj is the density of dry air at a pressure H mms. (see p. 25), H is the barometric 
 height, and/ is the pressure of water-vapour in the air. 
 
 HYDROMETERS 
 
 Common : Density = degrees/iooo. 
 
 Ban me : Density at 15 = i44"3/( H4'3 - Baume' degrees). 
 
 Twaddell : Density - i + (Twaddell degrees/2Oo). 
 
 Sikes : One degree = a density interval of '002 on the average. 
 
22 
 
 DENSITIES 
 
 DENSITY OF WATER 
 
 In grams per millilitre.* Pure air-free water under i atmos. Temps, on const. -vol. 
 
 H. scale. Water has a maximum density at 3'98 (Chappuis, 1897 ; Thiesen, Scheel 
 and Diesselhorst ; De Coppet, 1903). The temp. (/,) of maximum density at different 
 
 pressures (p], measured in atmos., is given by t m 3*98 -0225^ 
 
 i). 
 
 
 The specific volume is the reciprocal of the density. For reciprocals, see p. 136. 
 
 (See Chappuis, Trav. et Me"m. 
 
 Bur. Intl., 13, 1907 ; and Scheel, L.B. 
 
 M.) 
 
 
 For density of ice see p. 21 
 
 ; of steam, p. 26. [* i litre = 1000-027 c.cs.] 
 
 Density 
 
 of water at - 10 - -998 15; at - 5 = '99930. 
 
 
 Temp. 
 
 
 
 2 
 
 4 
 
 6 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 0C. 
 
 99987 
 
 '99997 
 
 i -ooooo -99997 -99988 
 
 '99973 
 
 '99953 
 
 99927 
 
 99897 
 
 99862 
 
 20 
 
 99823 
 
 9978o 
 
 99732 
 
 99681 -99626 
 
 995 6 7 
 
 99505 '99440 
 
 99371 
 
 9930 
 
 40 
 
 9922 
 
 9915 
 
 9907 
 
 9898 -9890 
 
 9881 
 
 9872 -9862 
 
 9853 
 
 9843 
 
 60 
 
 9832 
 
 9822 
 
 9811 
 
 -9801 -9789 
 
 9778 
 
 9767 
 
 '9755 
 
 '9743 
 
 9731 i 
 
 80 
 
 9718 
 
 9706 
 
 9693 
 
 9680 -9667 
 
 9653 
 
 9640 
 
 9626 
 
 9612 
 
 9598 
 
 100 
 
 9584 
 
 
 
 
 
 951 
 
 
 
 
 
 
 Density at 150 = 
 
 = '917 ; at 200 = -863 ; at 250 = 79 ; at 300 
 
 = -70. 
 
 
 DENSITY OF MERCURY 
 
 In grams per c.c. Hydrogen scale of temp. For reciprocals, see p. 136. 
 
 (See 
 
 Chappuis, Trav. et 
 
 Mtm. Bur. Intl., 13, 1907 ; and Scheel, 1905, 
 
 L.B.M. 
 
 
 Temp. 
 
 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 
 13 
 
 I3 
 
 13 
 
 13 
 
 13 
 
 13 
 
 13 
 
 13 
 
 13 
 
 13 
 
 -20C. 
 
 20 
 
 6450 
 
 5955 
 5462 
 
 "6400 
 5905 
 5413 
 
 '6351 
 5856 
 
 5364 
 
 6301 
 5806 
 
 6251 
 
 '5757 
 5266 
 
 6202 
 
 5708 
 5217 
 
 6152 
 
 5659 
 5168 
 
 6103 
 5609 
 
 6053 
 5070 
 
 6004 
 
 '55" 
 5022 
 
 40 
 
 4973 
 
 4924 
 
 4875 
 
 4826 
 
 4778 
 
 4729 
 
 4680 
 
 4632 
 
 4583 
 
 '4534 
 
 60 
 80 
 
 4486 
 
 4001 
 
 '4437 
 '3953 
 
 4389 
 3904 
 
 4340 
 3856 
 
 4292 
 3808 
 
 4243 
 
 '3759 
 
 '37" 
 
 4146 
 3663 
 
 4098 
 3615 
 
 4050 
 3566 
 
 
 
 
 20 
 
 40 
 
 60 
 
 80 
 
 100 
 
 120 
 
 140 
 
 160 
 
 180 
 
 100 
 
 13-3518 
 
 13-304 
 
 13-257 
 
 13-209 
 
 13-162 
 
 13-115 
 
 13-068 
 
 13-021 
 
 12-974 12-927 
 
 -300 
 
 12-881 
 
 12-834 
 
 12-787 
 
 12-740 
 
 
 
 
 
 
 
 
 
 
 
 
 
 DENSITY OF 
 
 ETHYL ALCOHOL, C 2 H 5 OH . Aq 
 
 
 
 In grams per c.c. 
 
 % indicates grams of C 2 H 5 OH in 100 grams of aqueous 
 
 solution. Hydrogen scale of temp. (Calculated by E. W. Morley 
 
 from Mende- 
 
 le'eflf's Observations, Jour. Am. Chem. Soc., Oct. 1904.) 
 
 
 
 
 At 17 C. 
 
 
 
 % 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 9988 
 
 9969 
 
 '995 * 
 
 '9933 
 
 9916 
 
 9899 
 
 9884 
 
 9869 
 
 9854 
 
 9840 
 
 10 
 
 9826 
 
 9813 
 
 9800 
 
 9787 
 
 '9775 
 
 9762 
 
 9750 
 
 '9737 
 
 9725 
 
 '9713 
 
 20 
 
 9700 
 
 9687 
 
 9674 
 
 9661 
 
 9647 
 
 9633 
 
 9619 
 
 9604 
 
 9589 
 
 '9573 
 
 30 
 
 '9557 
 
 '9540 
 
 9524 
 
 9506 
 
 9489 
 
 9470 
 
 9452 
 
 '9433 
 
 9414 
 
 '9394 
 
 40 
 
 '9375 
 
 '9354 
 
 '9334 
 
 *93 i 3 
 
 9292 
 
 9271 
 
 9250 
 
 9228 
 
 9207 
 
 9185 
 
 50 
 
 9163 
 
 9140 
 
 9118 
 
 9096 
 
 9073 
 
 9051 
 
 9028 
 
 9005 
 
 8982 
 
 8959 
 
 60 
 
 8936 
 
 8913 
 
 8890 
 
 8867 
 
 8843 
 
 8820 
 
 8797 
 
 8773 
 
 8749 i 
 
 8726 
 
 70 
 80 
 
 8702 
 8461 
 
 8678 
 8436 
 
 8655 
 8411 
 
 8631 
 8386 
 
 8607 
 8361 
 
 8582 
 
 '8558 
 8310 
 
 8534 
 8285 
 
 8510 ' 
 8259 
 
 8485 
 8232 
 
 90 
 
 8206 
 
 8179 
 
 8152 
 
 8124 
 
 8096 
 
 8068 
 
 8039 
 
 8010 
 
 7980 
 
 7950 
 
 100 
 
 7919 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 For other temperatures, interpolate from the above and the following : 
 
 
 
 At 22 C. 
 
 
 
 I o%, -9978; 10%, -9813 ; 20%, -9678 ; 30%, '9526 ; 40%, '9338 ; 50%, '9122; 60%, 
 
 8895 ; 
 
 70%, -8660; 80%, -8417; 00%, -8162; 100%, 7876. 
 
23 
 
 DENSITIES: ACIDS 
 
 DENSITY OF HYDROCHLORIC ACID, HCI . Aq 
 
 Grams per c.c. at 15 
 
 C. (Lunge and Marchlewski, 189 
 
 I.) 
 
 
 Grams HCI in ! 
 
 
 Grams HCI in 
 
 I Grams HCI in 
 
 
 
 i Dens. 
 
 
 
 Dens. 
 
 
 
 Dens. 
 
 Dens. 
 
 100 gm. 
 
 1 litre Change 
 
 *__ 1 1 O 
 
 Dens. 
 
 100 gm. 
 
 1 litre 
 
 Change 
 
 fnr 1 1 
 
 Dens. 
 
 100 gm. 
 
 1 litre Change 
 
 *v- _1_ 1 o 
 
 
 of Solution. 
 
 1UT n: A . 
 
 
 of Solution. 
 
 
 
 of Solution. 
 
 
 I'Ol 
 
 2-14 
 
 22 
 
 00016 
 
 08 
 
 16-15 
 
 174 
 
 00035 
 
 1-15 
 
 29-6 
 
 340 
 
 00052 
 
 1-02 
 
 
 42 
 
 00019 
 
 09 
 
 18-1 
 
 197 
 
 00038 
 
 1-16 
 
 31-5 
 
 366 
 
 00054 
 
 1-03 
 
 6-15 
 
 64 
 
 OOO2I 
 
 10 
 
 20*0 
 
 220 
 
 '00040 
 
 1-17 
 
 33*5 
 
 392 
 
 00056 
 
 1-04 
 
 8-16 
 
 8S 
 
 00024 
 
 11 
 
 21-9 
 
 243 
 
 00043 
 
 1-18 
 
 35'4 
 
 418 
 
 00058 
 
 1-05 
 
 10*17 
 
 107 
 
 00027 
 
 ' * 12 
 
 23-8 
 
 267 
 
 00045 
 
 1* 19 
 
 37' 2 
 
 443 
 
 00059 
 
 1-06 
 
 12-19 
 
 129 '00030 
 
 13 
 
 257 
 
 291 
 
 '00048 
 
 1-20 
 
 
 469 
 
 00060 
 
 1-07 
 
 14-17 
 
 152 -00032 
 
 14 
 
 27-7 
 
 315 '00050 
 
 
 
 
 
 
 
 DENSITY OF 
 
 NITRIC ACID, HNO 3 . Aq 
 
 Grams per c.c. at 1 5 C. % N 2 O 5 = '857 x % 
 
 HNO 3 by weight. (Lungeand Key, 1891.) 
 
 
 Grams HN0 3 in 
 
 Dens. 
 
 
 Grams HNO, in i 
 J i Dens. 
 
 Grams HNO in 
 3 Dens. 
 
 Dens. 
 
 100 gm. 
 
 1 litre 
 
 Change 
 
 fivr 1 1 
 
 Dens. 
 
 100 gm. 
 
 1 litre Change 
 
 4V,,- J^ 1 
 
 Dens. 
 
 100 gm. 
 
 1 litre Change 
 
 * 110 
 
 
 of Solution. 
 
 
 
 of Solution. 
 
 
 
 of Solution. 
 
 1-02 
 1-04 
 
 370 
 
 7-26 
 
 38 
 
 75 
 
 OOO22 
 '00028 
 
 1-22 
 1-24 
 
 m 
 
 430 
 
 475 
 
 OOOSO 
 00086 
 
 1-42 
 1-44 
 
 69-8 
 
 747 
 
 991 -00137 
 
 1075 '00143 
 
 | 1-06 
 
 10-7 
 
 "3 
 
 00034 
 
 1-26 
 
 41*3 
 
 521 
 
 00091 
 
 1-46 
 
 80-0 
 
 1168 -00149 
 
 1-08 
 
 
 151 
 
 00040 
 
 1-28 
 
 44 "4 
 
 568 
 
 00097 
 
 1-48 
 
 86-0 
 
 1274 -00154 
 
 1-10 
 
 17-1 
 
 188 
 
 00045 
 
 1-30 
 
 47'5 
 
 617 
 
 00103 
 
 1-50 
 
 94-1 
 
 1411 -00160 
 
 1-12 
 
 2O'2 
 
 227 
 
 00051 
 
 1-32 
 
 50-7 
 
 669 
 
 00109 
 
 1-504 
 
 96*0 
 
 1444 "00161 
 
 1-14 
 
 23-3 
 
 266 
 
 00057 
 
 1-34 
 
 
 725 
 
 '00114 
 
 1-508 
 
 97'5 
 
 1470 -00162 
 
 1-18 
 
 26*4 
 
 306 
 
 '00062 
 
 1-36 
 
 57'6 
 
 783 
 
 'OOI2O 
 
 1-512 
 
 
 1490 -00163 
 
 1-18 
 
 29*4 
 
 347 
 
 00068 
 
 1-38 
 
 6i\3 
 
 846 
 
 00126 
 
 1-516 
 
 99 -2 
 
 1504 '00164 
 
 1-20 
 
 
 388 
 
 00074 
 
 1-40 
 
 65-3 
 
 914 
 
 00132 
 
 1-520 
 
 997 
 
 1515 -00166 
 
 DENSITY OF SULPHURIC ACID, H 3 SO 4 . Aq 
 
 i Grams per c. 
 
 c.ati5C. %SO 3 = '8i6x%H 2 SO 4 by weight. (Lunge and I sler, 1895.) 
 
 Density. 
 
 Grams H 2 S0 4 in 
 
 
 
 Grams H 2 S0 4 in 
 
 Grams H2S0 4 in 
 
 100 gm. 1 litre 
 
 Density. 
 
 100 gm. 
 
 1 litre 
 
 Density. 
 
 100 gm. 
 
 1 litre 
 
 of Solution. 
 
 
 of Solution. 
 
 
 of Solution. 
 
 02 
 
 
 3'Q3 
 
 31 
 
 1-44 
 
 54' i 
 
 779 
 
 1-822 
 
 90-4 
 
 1647 
 
 '04 
 
 
 5-96 
 
 62 
 
 1-46 
 
 
 ;6'o 
 
 817 
 
 1-824 
 
 90-8 
 
 1656 
 
 06 
 
 
 8-77 
 
 93 
 
 1-48 
 
 57'8 
 
 856 
 
 1-826 
 
 91-2 
 
 1666 
 
 08 
 
 ii 60 
 
 I2 5 
 
 1-50 
 
 597 
 
 896 
 
 1-828 
 
 91-7 
 
 1676 
 
 10 
 
 U'lS 
 
 158 
 
 1-52 
 
 61-6 
 
 93 6 
 
 1-830 
 
 92 i 
 
 1685 
 
 12 
 
 i 
 
 7-01 
 
 191 
 
 1-54 
 
 
 53-4 
 
 977 
 
 1-832 
 
 92-5 
 
 1695 
 
 14 
 
 19-61 
 
 223 
 
 1-56 
 
 65-1 
 
 1015 
 
 1-834 
 
 c 
 
 )3'o 
 
 1706 
 
 16 
 
 22-19 
 
 257 
 
 1-58 
 
 66-7 
 
 1054 
 
 1-836 
 
 93'8 
 
 1722 
 
 18 
 
 24-76 
 
 292 
 
 1*60 
 
 68-5 
 
 1096 
 
 1-838 
 
 94-6 
 
 1739 
 
 1-20 
 
 2 7'3 
 
 328 
 
 1'62 
 
 70-3 
 
 H39 
 
 1-840 
 
 ( 
 
 )5'6 
 
 1759 
 
 1-22 
 
 29-8 
 
 3 6 4 
 
 1-64 
 
 72-0 
 
 1181 
 
 
 
 
 
 1-24 
 
 32-3 
 
 400 
 
 1-66 
 
 73'6 
 
 1222 
 
 1-8405 
 
 95 '9 
 
 1765 
 
 1-26 
 
 3 
 
 4*6 
 
 435 
 
 1-68 
 
 75'4 
 
 1267 
 
 1-8410 
 
 97-0 
 
 1786 
 
 1'28 
 
 36-9 
 
 472 
 
 1-70 
 
 77-2 
 
 1312 
 
 1-8415 
 
 977 
 
 1799 
 
 1-30 
 
 39-2 
 
 5 10 
 
 1-72 
 
 78-9 
 
 
 1-8410 
 
 c 
 
 >8'2 
 
 1808 
 
 1-32 
 
 4 
 
 i'5 
 
 548 
 
 1-74 
 
 807 
 
 1404 
 
 1-8405 
 
 987 
 
 1816 
 
 1-34 
 
 437 
 
 586 
 
 1-76 
 
 82 4 
 
 
 1-8400 
 
 99-2 
 
 1825 
 
 1-36 
 
 4 
 
 5'9 
 
 624 
 
 1*78 
 
 84-5 
 
 1504 
 
 1-8395 
 
 99*4 
 
 1830 
 
 1-38 
 
 4 
 
 8-0 
 
 662 
 
 1-80 
 
 86-9 
 
 
 1-8390 
 
 997 
 
 1834 
 
 1-40 
 
 50-1 
 
 702 
 
 1-81 
 
 1 
 
 $8-3 
 
 1598 
 
 1-8385 
 
 99'9 
 
 1838 
 
 1-42 52-1 
 
 740 
 
 1-82 
 
 90*0 
 
 I6 39 
 
 
 
 
 
24 
 
 DENSITIES: ALKALIES 
 
 DENSITY OF AMMONIA, NH 4 HO . Aq 
 ('.rams per c.c. at 15 C. 
 
 Grains NH, in j 
 
 Dens. 
 
 Dens. 100 gm. 1 litre' Change 
 forl r 
 of Solution 
 
 996 
 992 
 988 
 984 
 980 
 976 
 972 
 968 
 964 
 960 
 
 1-84 
 2-80 
 3'8o 
 4-80 
 5-80 
 6-80 
 7-82 
 8 '84 
 9-91 
 
 18-2 
 
 277 
 
 37-4 
 47-0 
 56-6 
 66 i 
 
 757 
 85-2 
 
 00019 
 
 "OOO2O 
 00021 
 OOO22 
 00023 
 00024 
 '00025 
 '00026 
 OOO27 
 00029 
 
 i Grams NH, in 
 
 Dens. 
 
 Dens. 100 gm. 1 litre Change 
 forl 
 
 956 
 952 
 948 
 944 
 940 
 936 
 932 
 928 
 924 
 920 
 
 of Solution. 
 
 11-03 
 12-17 
 
 I3-3I 
 14-46 
 
 I5'63 
 16-82 
 18-03 
 19-25 
 20-49 
 21-75 
 
 105-4 
 II5-9 
 126-2 
 
 136-5 ', 
 146-9 
 
 I57-9 
 168-1 
 178-6 
 189-3 
 
 2OO'I 
 
 00031 
 00033 
 00035 
 00037 
 00039 
 00041 
 '00042 
 00043 
 00045 
 00047 
 
 Grams NH 3 in 
 
 Dens. 
 
 Dens. 100 gm. 1 litre Change 
 fordbl . 
 of Solution. 
 
 916 
 912 
 908 
 904 
 900 
 896 
 892 
 888 
 884 
 880 
 
 210-9 
 
 22I"9 
 
 23-03 
 
 24'33 
 
 25-65 | 232-9 
 
 26-98 I 243-9 
 
 28-33 255-0 
 
 29-69 
 
 31-05 
 
 32-50 
 
 34-10 
 
 35-70 
 
 2-0 
 277-0 
 288-6 
 301-4 
 3H-2 
 
 00049 
 00051 
 00053 
 00055 
 00057 
 00059 
 00060 
 "00062 
 00064 
 
 -coo66 
 
 DENSITY OF SODIUM HYDROXIDE, NaHO . Aq 
 
 Grams per c.c. at 18 C. The percentages indicate grams of NaOH in 100 grams 
 of solution. (Bousfield and Lowry, 1905.) 
 
 % Density. 
 
 9986 
 
 I'OIOO 
 
 1-0213 
 
 I -0324 
 I-Q435 
 1-0545 
 1-0656 
 i -0766 
 1-0877 
 1-0987 
 
 Density. 
 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 
 1098 
 
 I20S 
 
 1429 
 1540 
 1650 
 1761 
 1871 
 1982 
 2092 
 
 '_ 
 
 Density. 
 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 
 2202 
 2312 
 
 '2422 
 2532 
 2641 
 
 2751 
 
 2860 
 2 9 68 
 3076 
 3184 
 
 % Density. 
 
 30 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 
 3290 
 3396 
 3502 
 3605 
 3708 
 3811 
 
 3913 
 4014 
 
 "4"5 
 4215 
 
 40 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 48 
 49 
 
 Density. 
 
 -43H 
 4411 
 4508 
 4604 
 4699 
 "4794 
 4890 
 
 4985 
 5080 
 
 '5 J 74 
 
 DENSITY OF SODIUM CARBONATE, Na 2 CO 3 . Aq 
 Grams per c.c. at 15 C. (Lunge.) 
 
 Density. 
 
 1-007 
 1-014 
 1-022 
 1-029 
 1-036 
 1-045 
 1-052 
 
 Grams Na ,CO , in 
 100 gm. I 1 litre 
 
 of Solution. 
 
 67 
 
 i'33 
 2-09 
 2-76 
 
 3'43 
 4-29 
 
 6-8 
 
 I3-5 
 21-4 
 
 28-4 
 
 35*5 
 44*8 
 52-0 
 
 Density. 
 
 Grams Na,C0 3 in 
 
 100 gm. I 1 litre 
 
 of Solution. 
 
 1-060 
 1-067 
 1-075 
 1-083 
 1-091 
 1-100 
 1-108 
 
 S7i 
 
 6'37 
 7-12 
 
 7-88 
 8-62 
 
 9'43 
 10*19 
 
 60-5 
 68-0 
 76-5 
 
 85-3 
 
 94'0 
 
 103-7 
 
 112-9 
 
 Density. 
 
 1-116 
 1-125 
 1-134 
 1-142 
 1-152 
 
 Grams Na .CO, in 
 100 gm. I 1 litre 
 
 of Solution. 
 
 10-95 
 11-81 
 12 61 
 13-16 
 14-24 
 
 I22'2 
 I32-9 
 I43-0 
 
 Change of density per i C. (o to 30), o to 7 % = '0002 ; 1 1 to 20 % = '0004. 
 
 DENSITY OF CALCIUM CHLORIDE, CaCI 2 . Aq 
 
 Grams per c.c. at I7'9 C. The percentages indicate grams 01" anhydrous CaCL 
 in 100 grams of solution. (Pickering, 1894.) 
 
 % Density. 
 
 1-007 
 1*024 
 1-041 
 1-058 
 1-076 
 
 11 
 13 
 15 
 17 
 19 
 
 Density. 
 
 1-094 
 
 1-131 
 1-150 
 1-169 
 
 21 
 23 
 25 
 27 
 29 
 
 Density. 
 
 1-189 
 1-209 
 1-229 
 1-250 
 
 1-272 
 
 31 
 33 
 35 
 37 
 
 Density. 
 
 1-294 
 1-316 
 I-338 
 1-361 
 I-384 
 
 % Density. 
 
 41 
 43 
 
 1-406 
 1-429 
 
25 
 
 DENSITIES: SOLUTIONS, AIR 
 
 DENSITIES OF SOME AQUEOUS SOLUTIONS 
 
 Grams per c.c. 
 
 at 1 8 
 
 C. 
 
 The indicated % is the number of grams of anhydrous 
 
 substance in 100 grams of solution. (Kohlrausch, " ] 
 
 Prakt. Phys.") 
 
 Substance. 
 
 5% 
 
 10% 
 
 15% 
 
 20% 
 
 25% 
 
 Substance. 
 
 5% 
 
 10% 
 
 15% 
 
 20% 
 
 NaCl . 
 
 1-034 
 
 071 
 
 109 
 
 148 
 
 1*190 
 
 MgS0 4 . 
 
 050 
 
 1*104 
 
 160 
 
 '220 
 
 1 NaNO 3 
 
 1-033 
 
 068 
 
 105 
 
 144 
 
 1-185 
 
 Bad, . 
 
 044 
 
 1-093 
 
 -147 
 
 204 
 
 NaA . 
 
 1-025 
 
 051 
 
 078 
 
 105 
 
 1-132 
 
 NH 4 C1. 
 
 '014 
 
 1*029 
 
 "043 
 
 057 
 
 H 3 P0 4 . 
 
 i -027 
 
 054 
 
 083 
 
 114 
 
 1-145 
 
 CuSO 4 . 
 
 051 
 
 1*107 
 
 167 
 
 230 
 
 ZnSO 4 . 
 
 1-051 
 
 107 
 
 167 
 
 232 
 
 1*305 
 
 KC1 . . 
 
 031 
 
 1*064 
 
 098 
 
 "133 
 
 ! Fed 3 . 
 
 1-130 
 
 175 
 
 226 
 
 278 
 
 
 KNO S . 
 
 030 
 
 1*063 
 
 097 
 
 I-I33 
 
 SrCl 2 . 
 
 1-044 
 
 093 
 
 146 
 
 202 
 
 1*256 
 
 K 2 SO 4 . 
 
 039 
 
 ro8r 
 
 
 
 
 MgCl 2 . 
 
 1-042 
 
 ro86 
 
 130 
 
 I 7 6 
 
 1*225 
 
 K 2 Cr 9 O 7 
 
 -035 
 
 1*072 
 
 1-109 
 
 
 
 Substance. 
 
 5% 
 
 10% 
 
 15% 
 
 20% j 25% 30% 35% 
 
 40% 
 
 45% 
 
 50% 
 
 KBr. . 
 
 1*035 
 
 073 
 
 114 
 
 1-157 -204 1-254 -307 
 
 1*365 
 
 1*429 
 
 
 
 KI . . 
 
 1*036 
 
 076 
 
 120 i.'iql 
 
 5 "218 1*273 '33 2 
 
 1-397 
 
 1*468 
 
 i"545 
 
 | K 2 C0 3 . 
 
 044 
 
 091 
 
 140 
 
 1-191 
 
 244 1-299 -356 
 
 1*415 
 
 1*477 
 
 1*541 
 
 1 LiCl. . 
 
 027 
 
 056 
 
 085 
 
 i-ii- 
 
 147 i'i8i '217 
 
 i* 
 
 255 
 
 
 
 
 
 
 CdSO 4 . 
 
 049 
 
 103 
 
 161 i '224 
 
 1. '295 1-372 -457 
 
 
 
 
 
 
 
 
 AgN0 3 . 
 
 042 
 
 089 
 
 1-140 l'l$t 
 
 > -255 1*321 -394 
 
 1*477 
 
 1*570 
 
 1*674 
 
 PbA 2 . 
 
 1*036 
 
 07 s 
 
 1-118 1-162 
 
 , 1*212 1*265 1-322 
 
 i -386 
 
 
 
 
 
 Sugar*. 
 
 i *oi 8 
 
 039 
 
 ro6o 
 
 i i -081 
 
 1*104 1*128 1*152 
 
 
 177 
 
 i '203 
 
 1-230 
 
 * 60%, 
 
 1*287 ; [75%, 1*380 (supersaturated)]. 
 
 DENSITY OF DRY 
 
 AIR AT DIFFERENT TEMPERATURES AND 
 
 PRESSURES 
 
 Grams per c.c 
 
 . ; pressures in mm. 
 
 of mercury at o C. lat. 
 
 45 ; g - 
 
 = 980*62 cms. 
 
 per sec. 2 . These densities are calculated by the expression 
 
 001293 
 
 H 
 f 760' 
 
 (i + 
 
 
 It 
 
 where "001293 is 
 
 due to Leduc, 1898 
 
 , and Rayleigh, 1893 (p. 26) ; and '00367 to 
 
 Regnault. For density 
 
 of damp air, 
 
 see p. 21. 
 
 
 
 
 
 
 
 Pressure in Millimetres (H). 
 
 Temp. (/). 
 
 710 
 
 720 
 
 730 
 
 740 
 
 750 
 
 760 
 
 770 
 
 780 
 
 0C. 
 
 001208 
 
 001225 
 
 001242 
 
 001259 
 
 001276 
 
 001293 
 
 001310 
 
 001327 
 
 2 
 
 001199 
 
 001216 
 
 001233 
 
 001250 
 
 001267 
 
 001284 
 
 001300 
 
 001317 
 
 4 
 
 001190 
 
 001207 
 
 001224 
 
 001241 
 
 001258 
 
 001274 
 
 001291 
 
 001308 
 
 6 
 
 001182 
 
 001199 
 
 001215 
 
 001232 
 
 001248 
 
 001265 
 
 001282 
 
 001298 
 
 8 
 
 001173 
 
 001190 
 
 001207 
 
 001223 
 
 001240 
 
 001256 
 
 001273 
 
 001289 
 
 10 
 
 001165 
 
 001182 
 
 001198 
 
 001214 
 
 001231 
 
 001247 
 
 001264 
 
 001280 
 
 12 
 
 001157 
 
 001173 
 
 001190 
 
 001206 
 
 'OOI222 
 
 001238 
 
 001255 
 
 001271 
 
 14 
 
 001149 
 
 001165 
 
 001181 
 
 001197 
 
 OOI2I4 
 
 001230 
 
 001246 
 
 001262 
 
 16 
 
 001141 
 
 001157 
 
 001173 
 
 001189 
 
 001205 
 
 OOI22I 
 
 001237 
 
 001253 
 
 18 
 
 001133 
 
 001149 
 
 001165 
 
 001181 
 
 OOII97 
 
 OOI2I3 
 
 001229 
 
 001245 
 
 20 
 
 001125 
 
 001141 
 
 001157 
 
 001173 
 
 OOII89 
 
 001205 
 
 001220 
 
 001236 
 
 22 
 
 001118 
 
 001133 
 
 001149 
 
 001165 
 
 001181 I '001196 
 
 'OOI2I2 
 
 001228 
 
 24 
 
 ooi no 
 
 001126 
 
 001141 
 
 001157 
 
 001173 | -ooi i 
 
 88 
 
 'OOI2O4 
 
 001220 
 
 26 
 
 001103 
 
 001118 
 
 001134 
 
 001149 
 
 001165 'ooi i 80 
 
 OOII96 
 
 OOI2II 
 
 28 
 
 001095 
 
 OOIIII 
 
 001126 
 
 001142 
 
 OOII57 
 
 OOII73 
 
 OOII88 
 
 OOI2O3 
 
 30 
 
 001088 
 
 001103 
 
 001119 
 
 001134 
 
 OOII49 
 
 ooii 
 
 65 
 
 ooi 180 
 
 OOII95 
 
26 
 
 GASEOUS DENSITIES 
 
 DENSITIES OF GASES 
 
 Only those gases for which accurate density determinations have been made are 
 included in this table (see also p. 10). Other gases will be found in the table below. 
 For density of air under different temperatures and pressures, see p. 25. 
 
 Densities are in grams per litre (1000*027 c.cs. ; see p. 10) at o C. under 
 760 mm. of mercury at o C. and lat. 45 (g = 980-62), Le. under a pressure of 
 i 'oi 323 x io 6 dynes per sq. cm. (After P. A. Guye, Chem. News, 1908.) 
 
 Gas. 
 
 Air 
 
 Oxygen, O 2 .... 
 
 Hydrogen, H 2 ... 
 Nitrogen, N 2 . . . . 
 
 Argon, A 
 
 Nitrous oxide, N 2 O 
 Nitric oxide, NO . . 
 Ammonia, NH 3 . . . 
 Carbon monoxide, CO . 
 Carbon dioxide, CO 2 . 
 Hydrochloric acid, HC1 
 Sulphur dioxide, SO 2 . 
 
 Density and Observer. 
 
 .9777 R. ; i 
 1-3429 L. ; 1-3402 Gr. ; 
 077 19 L.; 077085 P.D.; 
 1-2501 L. ; 1-2504 R. 
 1-9763 L. ; 1-9769 R. i ' 
 1-6407 L. ; 1*6397 Gr. 
 2-9266 L. ; 
 
 J. ")V^_J. XV 
 
 1-9769 R. ; I 
 1-6397 Gr. ; 
 2-9266 J.P. ; 
 
 1-42900 M. ;\ 
 
 P. ' / 
 
 0*089873 M. 
 2507 Gr. 
 
 9774 G.P. 
 1-3402 G.D. 
 0-7708 G.P. 
 
 9768 G.P. 
 1-6398 G.G. 
 2-9266 B. 
 
 Accepted 
 density. 
 
 drains/litre. 
 1-2928 
 
 I-42900 
 
 0-08987 
 
 1-2507 
 
 1-7809 
 
 1-9777 
 
 r3402 
 
 0-7708 
 
 I-2504 
 
 1-9768 
 
 1-6398 
 
 2-9266 
 
 Density 
 rel. to 
 
 0-90469 
 1-00000 
 
 0-06289 
 
 0-87523 
 
 1-2463 
 
 1-3840 
 
 0-93786 
 
 0-5394 
 
 0-87502 
 
 1-3833 
 
 1-1475 
 
 2-0480 
 
 B., Berthelot ; G.D., Guye & Davila ; G.G., Guye & Gazarian ; G.P., Guye & 
 Pintza; Gr., Gray ; J.P., Jacquerod & Pintza : L., Leduc ; M., Morley ; P.O., 
 Perman & Davies ; R., Rayleigh ; Ra., Ramsay. 
 
 The densities below are all experimental values, and are relative to that of 
 oxygen (O 2 = 16) at o and 760 mms. at lat. 45 (see above). 
 
 Gas. 
 
 Acetylene, C 2 H 2 . . 
 Arsine, AsH 3 . . . 
 Boron fluoride, BF 3 . 
 Bromine, Br 2 <r.228C 
 Butane, C 4 H 10 . . . 
 Carbon oxychloride, 
 COC1 2 
 
 oxysulphide,COS 
 Chlorine, C1 2 . . . 
 
 monoxide, C1 2 O 
 
 dioxide, C1O 2 . 
 Cyanogen, C 2 N 2 . . 
 Ethane, C 2 H 6 . . . 
 Ethylamine, 
 
 C 2 H 5 NH 2 . . . . 
 Ethyl chloride, 
 
 C 2 H 6 C1 . . . . 
 Ethyl fluoride, C 2 H 5 F 
 Ethylene, C 2 H 4 . . 
 Fluorine, F 2 . . . . 
 
 Eel. 
 dens. 
 
 39*02 
 
 79-99 
 29*10 
 
 50-75 
 
 30-47 
 36-07 
 
 43-54 
 3374 
 26-16 
 
 I5-57 
 2277 
 
 32-13 
 24-62 
 14-27 
 18-97 
 
 Gas. 
 
 Helium, He . . . . 
 Hydrobromic acid, 
 
 HBr 
 
 Hydrofluoric acid, HF 
 Hydriodic acid, HI . 
 Hydrogen selenide, 
 
 H 2 Se 
 
 sulphide, H 2 S 
 
 telluride, H 2 Te 
 
 Krypton, Kr . . . 
 
 Methane, CH 4 (1909) 
 
 Methylamine, 
 
 CH 3 NH 2 . . . . 
 Methyl chloride, 
 
 CH 3 C1 
 
 Methyl ether, C 2 H 6 O 
 fluoride, CH 3 F 
 Methylene fluoride, 
 
 CH 2 F 2 
 
 Neon, Ne (1910) . . 
 
 Bel. 
 
 dens. 
 
 1-98 
 
 10-32 
 63-36 
 
 40-47 
 17-22 
 65-00 
 
 4I-5 
 8-03 
 
 15-64 
 
 25-06 
 23-41 
 17-67 
 
 26*21 
 10-82 
 
 Gas. 
 
 Nitrogen oxychloride, 
 NOC1 ..... 
 Nitrogen peroxide 
 (N 2 O 4 ) 26-7 C. 
 398 
 602 
 8O6 
 1001 
 1215 
 
 ,(NO 2 )154-O 
 , 1832 
 Phosphine, PH 3 . . 
 Phosphorus chloro- 
 fluoride, PC1 2 F 3 
 oxyfluoride, POF 3 
 pentafluoride, PP\ 5 
 trifluoride, PF 3 
 Propylene, C 3 H 6 
 
 Eel. 
 
 33-45 
 
 35-62 
 30-12 
 26-06 
 
 Silicon fluoride, SiF 4 
 
 Xenon, Xe 
 
 22' 
 
 22-73 
 
 17-58 
 
 78-19 
 
 53-29 
 65-01 
 
 52-I3 
 
 165-35 
 
 DENSITY OF SATURATED WATER VAPOUR 
 
 Densities in grams per litre under different pressures. (Zeuner, 1890.) 
 
 Atmos. 
 
 o 
 
 5 
 10 
 
 275 
 5-27 
 
 0-5 
 
 1 
 
 1-5 
 
 0-315 i 0-606 0-887 
 3-01 3-26 3-52 
 5-52 5-76 6-01 
 
 1-16 
 
 377 
 6-25 
 
 2-5 
 
 4-02 
 6-50 
 
 1-70 
 4-27 
 6-74 
 
 3-5 
 
 i-97 
 4-52 
 6*99 
 
 2-23 
 4-77 
 7-23 
 
 4-5 
 
 2-49 
 5-02 
 
27 
 
 ELASTICITIES 
 
 ELASTICITIES 
 
 Young's Modulus, or Longitudinal Elasticity, E in dynes per sq. cm. 
 Rigidity, Torsion Modulus, or Shear Modulus, n in dynes per sq. cm. 
 Volume Elasticity, Cubic Elasticity, or Bulk Modulus, k in dynes per sq. cm. 
 Compressibility (cubic), C = i/. 
 
 Poisson's Ratio, a- - lateral contraction per unit breadth/longitudinal extension per 
 unit length. For a homogeneous isotropic substance 
 
 n = , E N . O) ; <r = - I . . () ; k = -r-^ r . (V) 
 
 2(1 + <r) 2 3(1 - 2(t) 
 
 For an isotropic solid Poisson's Ratio must lie between +\ and I, but for some 
 materials it may, when deduced from E and ;/, exceed + 1. (See Searle's " Elasticity.") 
 
 1 megabar = i o 6 dynes per sq. cm. = '987 atmos. i/ roi 3 atmos. = the pressure measured 
 by 750*15 mms. of mercury at o C. sea-level, and latitude 45 = 749'66 mms. at o in London. 
 
 The elasticities of a substance depend considerably upon its history. The extent of the 
 agreement between the calculated and observed values of n and of <r below gives an indication 
 of the degree of isotropy of the metals used. (Griineisen, Reichsanstalt, A,nn. d. Phy., 1908.) 
 
 ELASTICITIES OF METALS 
 
 Metal at 18 C. 
 
 Young's 
 Modulus, E. 
 
 Rigidity, . 
 
 Foisson's Ratio, a. 
 
 Vol. 
 Elast. k. 
 
 Compress? 
 
 CTIPV 
 
 (see also below 
 and pp. 28, 29). 
 
 By static 
 method or 
 longl. vibns. 
 
 By oscilln, 
 method. 
 
 Calcd. by 
 formula (a). 
 
 Ob- 
 served. 
 
 Calcd. 
 by for- 
 mula (b). 
 
 Calcd. by 
 formula (c). 
 
 . pei 
 megabar 
 (calculated). 
 
 Aluminium (W) * . 
 
 7-05 x ro 11 
 
 2-67 x lo 11 
 
 2*63 X lo 11 
 
 '339 
 
 310 
 
 7-46 x lo 11 
 
 1-33 x io~ 6 
 
 Bismuth (C), pure . 
 
 3-19 
 
 
 
 1-20 
 
 "33 
 
 
 3'H 
 
 3-2 
 
 Cadmium (C), pure 
 
 4'99 
 
 
 
 1-92 
 
 30 
 
 
 
 4-12 
 
 2-4 
 
 Copper (W), pure . 
 
 12-3 
 
 4-55 
 
 4*55 
 
 '337 
 
 356 
 
 13-1 
 
 74 
 
 Gold (W), pure . 
 
 8-0 
 
 277 
 
 2-80 
 
 422 
 
 "495 
 
 1 6-6 
 
 60 
 
 Iron(W),-i%C. . 
 
 2I"3 
 
 
 8-31 
 
 280 
 
 
 16-1 
 
 63 
 
 Steel (W), i%C. . 
 
 20-9 
 
 8'12 
 
 8-12 
 
 287 
 
 287 
 
 16-4 
 
 62 
 
 Lead (C), pure . . 
 
 1-62 
 
 
 
 562 
 
 446 
 
 
 
 5-00 
 
 2'0 
 
 Nickel (W) t . 
 
 20'2 
 
 
 
 7-70 
 
 309 
 
 
 
 17-6 
 
 '57 
 
 Palladium (C), pure 
 
 II'3 
 
 5-11 
 
 4-04 
 
 '393 
 
 101 
 
 17-6 
 
 57 
 
 Platinum (C), pure 
 
 16-8 
 
 6'io 
 
 6-04 
 
 387 
 
 368 
 
 24-7 
 
 41 
 
 Silver (W), pure . 
 
 7-90 
 
 2-87 
 
 2-86 
 
 '379 
 
 369 
 
 io - 9 
 
 92 
 
 Tin (C), pure . . 
 
 5'43 
 
 
 
 2*04 
 
 '33 
 
 
 
 5-29 
 
 19 
 
 Bronze (C) J . . . 
 
 8 -08 
 
 3'43 
 
 2-97 
 
 358 
 
 177 
 
 9-52 
 
 1-05 
 
 Constantan (W) . 
 
 16-3 
 
 6-1 1 
 
 
 325 
 
 329 
 
 15*5 
 
 '65 
 
 Manganin (W) || . 
 
 12-4 
 
 4-65 
 
 4-65 
 
 329 
 
 329 
 
 12-1 
 
 83 
 
 (C) means cast; (W) worked. * -5% Fe, '4% Cu. f 97 % Ni > *'4% Co, i% Mn. 
 
 1 857% Cu, 7-2% Zn, 6-4% Sn. 60% Cu, 40% Ni. || 84% Cu, 12% Mn, 4% Ni. 
 
 The (experimental) results below are mostly for ordinary laboratory materials, chiefly wires. 
 
 Substance. 
 
 Young's Modulus, E. 
 
 Rigidity, n. 
 
 Volume Elast. k. 
 
 Poisson's Ratio, <r. 
 
 
 12*4 12*9 x lo 11 S. 
 
 -2'Q 4. X IO 11 S. 
 
 14-3 x lo 11 M 
 
 26 S. 
 
 Iron (wrought) . . . 
 (cast) .... 
 Steel ... 
 
 19-20 
 10-13 G. 
 
 IQ'C 2O*6 
 
 77-8-3 
 3*5-5-3 
 
 7*Q 8'Q 
 
 14-6 
 9-6 
 18-1 M 
 
 c.'2^ 
 
 23--3I 
 
 *2C "II 
 
 Zinc (i % Pb) . . . . 
 Brass (c. 66 Cu, 34 Zn) . 
 German silver * ... 
 Platinoid f 
 
 87 G. 
 97-10-2 
 1 1-6 S. 
 13-6 S. 
 
 3'8 
 f.5'5 
 
 4-3-47 
 r6o S. 
 
 10-65 M - 
 
 ^j JJ 
 21 
 
 34-:'40 
 
 37 
 '37 
 
 Phosphor bronze J . . 
 Quartz fibre .... 
 Indiarubber .... 
 Jena Glasses, Crowns . 
 Flints . 
 
 I2'0 S. 
 
 5-18 
 048--052 
 6-5-7-8 
 5 'o-6-o 
 
 4-36 s. 
 
 3-0 H. 
 00016 
 
 2-6-3-2 
 2*0-2-5 
 
 i'4 
 
 4-0-5-9 
 3-6-3-8 
 
 38 S. 
 *46-'49 Sc. 
 
 20--27 
 22-'26 
 
 (G.) Gruneisen, 1907. (H.) Horton, 1905. (M.) Mallock, 1905. (S.) Searle, 1900. 
 
 (Sc.) Schiller, 1906. * 60 Cu, 15 Ni, 25 Zn. t German silver with a little tungsten. 
 
 J 92-5 Cu, 7 Sn, -5 P. Pure Zn, 12*5 X lo 11 dynes/cm 2 . 
 
28 
 
 TENSILE STRENGTHS 
 
 ELASTICITIES (contd.) 
 
 Substance. 
 
 Iridium|j 
 
 Rhodiumj 
 
 Tantalum 
 
 Invar 
 
 9oPt,ioIr 
 
 Silk fibre 
 
 Spider 
 
 thread . 
 Catgut . 
 Ice (-2) 
 Quartz 
 
 (crystal) 
 Marble . 
 Oak . . 
 Deal . . 
 Mahogany 
 Teak . 
 
 Young's 
 Modulus, 
 
 E. 
 dynes/cm. 2 
 
 5'2Xio n (G.) 
 3-2 (G.) 
 
 18-6 (Bo.) 
 
 14-1 
 
 2TO 
 
 '3 
 
 32 
 
 28 
 
 6-8 
 2-6 
 i'3 
 
 "9 
 
 88 
 r66 
 
 (B.)S 
 
 Temperature coefficient o in 
 Blast, = Elast 15 |l - a (t - 15)} 
 
 At 15 C. 
 
 Aluminium 
 Copper . . 
 Gold . . 
 I ron . . 
 Steel . . 
 Platinum . 
 Silver . . 
 Tin ... 
 Brass . . 
 German sil ver 
 Phosphor-bronze 
 Quartz fibre! 
 
 a for E.* 
 
 I0~ 4 
 
 a for n f 
 
 2-4 
 98 
 
 7'5 
 
 37 
 
 13-5x10- 
 4-0 
 3'3 
 
 9 
 
 ro 
 
 4'5 
 
 6-5 
 
 Compressibility C. per 
 megabar (i.e. lO 6 dynes/cm. 2 ) 
 
 7-llC.; 200 SOOmegabars 
 
 (see also pp. 27, 29). 
 
 Aluminium 17 x 
 Copper .i -88 
 Gold . .! '80 
 Lead . .2-8 
 Magnesium 3-2 
 Platinum . "$6 
 Flint glass 3*0 
 Germ.glass 
 
 tubing . 2-57 
 Steel . 
 
 10" 
 
 (A.) 
 
 (Br.; 
 
 (A.) Amagat. (B.) Benton, 1907 and 1908. (Bo.) v. Bolton, 1905. 
 (Br.) Bridgman, 1909. (G.) Griineisen, 1907. * Wassmuth, 1906, and 
 Schaefer, 1902. f Horton, 1904 and 1905. \ Diminishes rapidly 
 with increasing load. Shows marked elastic fatigue. || Pure. 
 
 TENSILE STRENGTHS OF MATERIALS 
 
 Tenacities or breaking stresses in dynes per sq. cm. The elastic limit is always 
 exceeded before the breaking stress is reached. The process of drawing into wire 
 seems to strengthen the material, and the finer the wire the greater is the breaking 
 stress. (See Poynting and Thomson's " Properties of Matter.") 
 
 For crushing and shearing strengths, see Ewing's " Strength of Materials " or one 
 of the Engineering " Pocket-books.'-' For bursting strengths of tubing, see p. 39 ; for 
 tensile strengths of liquids, see p. 39. 
 
 To reduce to kilogrammes per sq. mm., it is sufficient to divide by io 8 ; to Ibs. per 
 sq. inch, divide by 7 X io 4 . * Along the grain. 
 
 Substance. 
 
 Aluminium, cast 
 
 rolled 
 
 Copper, cast 
 
 rolled 
 
 Iron, (a) cast 
 
 (b} wrought 
 
 (c) steel castings . . . 
 Mild steel (-2 %C) . 
 High carbon^ annld. . 
 (for springs) j temprd. 
 Tungsten or chrome 
 
 Ni steel, 5%; 12% . 
 
 Lead 
 
 Tin 
 
 Zinc, rolled 
 
 Brass (ordinary), f66Cu^cast 
 n \34ZnJrolled 
 
 Phosphor-bronze 
 
 Gun-metal (90 Cu, io Sn) . . 
 
 Soft solder 
 
 Glass 
 
 Ash,beech,oak,teak,mahogany* 
 
 Fir, pitch-pine * 
 
 Red or white deal * . 
 
 Tenacity. 
 
 dynes/cm. 
 
 io 9 
 
 9-1-5 
 
 I'2-I*9 
 
 2-0-2-5 
 
 8-2-3 
 
 2-9-4-5 
 
 2-3-7-0 
 
 4"3-4"9 
 7-0-7-7 
 9-3-10-8 
 
 11-12 
 
 6-2; 14 
 
 1-1-1-5 
 1-5-1-9 
 
 2'3-37 
 2-5-2-8 
 1-9-2-6 
 
 *3-'9 
 6-ri 
 4 --8 
 '3-7 
 
 Substance. 
 
 Tenacity. 
 
 White or yellow pine * ... 
 
 Leather belt 
 
 Hemp rope 
 
 Catgut 
 
 Spider thread 
 
 Silk fibre 
 
 Quartz fibre 
 
 WIRES. 
 
 Aluminium 
 
 Copper, hard drawn . . . 
 annealed .... 
 
 Gold 
 
 Iron (charcoal), hard drawn 
 
 annealed 
 
 Steel; (i) ordinary; (2)tempd. 
 
 pianoforte 
 
 Nickel 
 
 Platinum 
 
 Silver ... .... 
 
 Tantalum 
 
 Brass 
 
 Phosphor-bronze, hard drawn 
 German silver 
 
 dynes/cm. 2 
 2-'5 X IO 9 
 
 c. '3 
 
 '6-1-0 
 
 4-2 
 r8 
 26 
 
 C. 10 
 
 1-7-2*0 
 
 4-0-4-6 
 2-8-3-1 
 
 2-6 
 
 5-4-6-2 
 
 c. 4-6 
 
 f. II 515-5 
 18-6-23-3 
 
 5*3 
 3-3 
 2-9 
 
 4-2 
 
 3-1-3-9 
 6-9-10*8 
 4-6 
 
29 
 
 COMPRESSIBILITIES 
 
 COMPRESSIBILITIES OF ELEMENTS 
 
 Coefficient of compressibility C = ^ , where 5V is the change in volume of a 
 
 volume V under a change of pressure 5^ (temp, constant). 
 
 The values of C below are per megabar (i.e. io 6 dynes per sq. cm.). To express as 
 
 compressibility per atmosphere, increase C by ^ of its value. Room temp. Pressure 
 
 range, 100-500 megabars. Based on compressibility of mercury = "O 5 37i per megabar. 
 
 The results show a periodic relation with atomic weight. See also pp. 27, 28. 
 
 (Richards, Zeit. Phys. Chem.^ 61, 1907, and Journ. Chem. Soc., 1911.) 
 
 Element. 
 
 Al. 
 Sb. 
 As. 
 Bi. 
 Br. 
 Cd 
 Cs. 
 Ca. 
 
 1*3x10 
 2*2 
 
 4'3 
 
 2-8 
 5 r8 
 
 1-9 
 61 
 
 rs 
 
 C,diamond '5 
 graphite 3 
 
 Element. 
 
 Element. 
 
 Hg . 
 Mo . 
 Ni . 
 Pd . 
 P, red 
 
 white 
 Pt . 
 K. . 
 Rb . 
 Se 
 
 371 x io~ 6 
 
 26 
 
 27 
 
 38 
 
 9-0 
 20-3 
 
 21 
 
 31-5 
 40 
 
 i r8 
 
 Element. 
 
 Si. 
 
 Ag 
 
 Na 
 
 S . 
 
 Tl 
 
 Sn 
 
 Zn 
 
 16x10 
 
 84 
 15-4 
 12-5 
 
 2'6 
 
 17 
 
 1*5 
 
 COMPRESSIBILITIES OF LIQUIDS 
 
 C = compressibility per megabar (i.e. io 6 dynes per cm. 2 ). To express as com- 
 pressibility per atmosphere, increase C by g\y of its value. 
 
 As the pressure increases C becomes less. In general a rise in temperature 
 increases the Compressibility of a liquid ; but water, however, shows a minimum value 
 of C at about 50 C. (Amagat). The compressibility of a solution diminishes as the 
 concentration increases (see Poynting and Thomson's " Properties of Matter " and 
 Auerbach in L.B.M.). 
 
 Where the limits of pressure are not given, they are for Amagat, 8-37 atmos. ; for 
 Rontgen, 8 atmos. ; for Richards, 100-200 atmos. 
 
 Liquid. 
 
 Water, 1-25 atmos. (A.) 
 
 900-1000 (A.) 
 
 900-1000 (A.) 
 
 2500-3000 (A.) 
 
 Sea-water(Grassi,i85i) 
 
 Mercury . . . (A.) 
 
 ... (Ri.) 
 
 Methyl alcohol,CH 3 OH 
 
 (A.) 
 
 Ethyl alcohol 
 
 1-500 atm. (A.) 
 150-200 atm. (Ba.) 
 Propyl alcohol, 
 
 C 3 H 7 OH . . (R.) 
 
 Propyl alcohol iso- (R.) 
 
 Butylalcohcl.C 4 H 9 OH 
 
 (R.) 
 
 Butyl alcohol iso- (R.) 
 Amyl alcohol, 
 
 C 5 H U OH . . (R.) 
 Chloroform . . (Ri.) 
 
 Temp. 
 
 15 C. 
 
 15 
 198 
 
 14'2 
 
 20 
 15 
 
 14-7 
 
 
 310 
 
 17'7 
 17-8 
 
 17'4 
 17-9 
 
 17'7 
 20 
 
 Com p. C per 
 megabar. 
 
 48-9X 
 
 55'4 
 25-8 
 
 4 3'82 
 371 
 
 102*7 
 
 76 
 
 4147 
 
 95-8 
 101-7 
 
 96-8 
 
 89-4 
 9*4 
 
 Liquid. 
 
 Carbon tetrachloride 
 
 (Ri.) 
 
 Carbon bisulphide (A.) 
 
 Ether, 1-50 atmos. (A.) 
 
 900-1000 (A.) 
 
 (A.) 
 
 Methyl acetate . (A.) 
 
 Ethyl acetate . . (A.) 
 
 ,, bromide . (A.) 
 
 chloride . (A.) 
 
 Acetic acid, 1-16 atm. 
 
 (C. & S.) 
 
 Glycerine, C 3 H 5 (OH) 3 
 
 (QO 
 
 Olive oil ... (Q.) 
 Paraffin oil (de Metz, 
 
 1890) 
 
 Petroleum (Martini) . 
 Pentane, C 5 H 12 . (G.) 
 Benzene, C 6 H 6 . (R.) 
 Turpentine,C 10 H 13 (Q.) 
 
 Temp. 
 
 20 C. 
 15-6 
 
 
 
 198 
 14-3 
 13-3 
 99-3 
 15-2 
 
 20-5 
 20-5 
 
 14-8 
 
 16*5 
 
 20 
 
 17-9 
 
 19'7 
 
 Comp. C per 
 megabar. 
 
 89-6 X 
 
 85-9 
 145-2 
 
 64*2 
 142*2 
 
 95'8 
 1027 
 
 291-3 
 151-1 
 
 ICT 
 
 40-2 
 24-8 
 
 687 
 5H 
 90-8 
 78-14 
 
 (A.) Amagat, Comptes Rendus, 1884-93 ; (B.) Bartoli, 1896 ; (Ba.) Barus, 1891 ; (C. & S.), 
 Colladon and Sturm, 1827; (G.) Grimaldi, 1886; (Q.) Quincke, Wied. Ann., 19, 1883; (R.) 
 Rontgen, Wied. Ann., 44, 1891 ; (Ri.) Richards, 1907. 
 
30 
 
 VISCOSITIES 
 
 1 
 
 VISCOSITIES 
 
 Or LIQUIDS 
 
 
 If two parallel planes are at unit distance apart in a fluid 
 
 , and one of them is 
 
 
 moving in its own 
 
 plane 
 
 with unit velocity relatively 
 
 to the other plane, then the 
 
 
 tangential force exerted per unit area on each of the planes is equal to the viscosity. 
 
 
 The dimensions of a viscosity are ML" 1 *!""" 1 . 
 
 
 
 
 
 For the capillary-tube method of determining viscosities, Poiseuille's formula is, 
 
 
 Viscosity 
 
 n = -f 
 
 -VyT, where p is the 
 
 pressure difference 
 
 between the two ends of the 
 
 
 tube, r the radius of the tube, / its length, V the volume 
 
 of liquid delivered in a time /. 
 
 
 VISCOSITY 
 
 OF WATER 
 
 
 
 
 
 Determined 
 
 by an efflux method and corrected for kinetic energy of outflow. 
 
 
 (Hosking, Phil. 
 
 Mag., 1909, 1, 502 
 
 2, 260.) 
 
 
 Temp. 
 
 Viscosity. 
 
 Temp. 
 
 Viscosity. 
 
 Temp. Viscosity. 
 
 Temp. 
 
 Viscosity. 
 
 
 0C 
 
 c.g.s. 
 
 01793 
 
 20 C C. 
 
 '01006 
 
 50 C. '00550 
 
 90 C. 
 
 00316 
 
 
 5 
 
 01522 
 
 25 
 
 00893 
 
 60 
 
 00469 
 
 100 
 
 00284 
 
 
 10 
 
 01311 
 
 30 
 
 00800 
 
 70 '00406 
 
 124* 
 
 00223 
 
 
 15 
 
 01142 
 
 40 
 
 00657 
 
 80 
 
 00356 
 
 153* 
 
 00181 
 
 
 
 
 
 
 * 
 
 de Haas, 1894. 
 
 
 VISCOSITY OF MERCURY 
 
 (Koch, 1881.) 
 
 
 Temp. 
 
 -20C. 
 
 
 
 20 
 
 50 
 
 100^ 
 
 200 
 
 300 
 
 
 Viscosity (c.g.s.) 
 
 0186 
 
 0169 
 
 0156 
 
 0141 
 
 0122 
 
 *OIOI 
 
 0093 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 VISCOSITIES OF VARIOUS LIQUIDS (see Stockl in L.B.M.). 
 
 
 Substance. 
 
 oc. 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c.g.s. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Methyl alcohol, 
 
 CH 4 O 
 
 00813 
 
 00686 
 
 00591 
 
 00515 
 
 00450 
 
 00396 
 
 00349 
 
 
 
 
 j Ethyl 
 
 55 C 2 H 6 
 
 
 
 0177 
 
 0145 
 
 0119 
 
 00989 
 
 00827 
 
 00697 
 
 00591 
 
 00504 j 
 
 
 Propyl 
 
 
 ^ 3 H 8 
 
 o 
 
 0388 
 
 0292 
 
 0225 
 
 0178 
 
 0140 
 
 0113 
 
 00919 
 
 00757 ! 
 
 
 Isopropyl 
 
 
 
 . . 
 
 . 
 
 0456 
 
 0324 
 
 0237 
 
 0175 
 
 0133 
 
 0103 
 
 00804 
 
 00642 ! 
 
 
 | Ether (C 2 
 
 HA.O 
 
 , 
 
 . 
 
 00286 
 
 00258 
 
 00234 
 
 '00212 
 
 
 
 
 
 
 
 
 
 
 :. 
 
 
 Chloroform, CHC1 3 . 
 
 00700 
 
 00626 
 
 00564 
 
 '00511 
 
 00465 
 
 00426 
 
 00390 
 
 
 
 
 Carbon tetrachloride . 
 
 0135 
 
 0113 
 
 00969 
 
 00841 
 
 00738 
 
 00653 
 
 00583 
 
 00524 
 
 
 bisulphide . . 
 
 00429 
 
 00396 
 
 00367 
 
 00342 
 
 00319 
 
 
 
 
 
 
 
 
 dioxide 
 
 (liq.) 
 
 . 
 
 
 
 
 00085 
 
 '00071 
 
 00053 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Benzene, C 6 H 6 
 
 . . 
 
 
 00902 
 
 00759 
 
 00649 
 
 00562 
 
 00492 
 
 00437 
 
 00390 
 
 00351 
 
 
 Aniline, C 6 H 6 NH 2 . . 
 
 
 
 
 0655 
 
 0440 
 
 0319 
 
 0241 
 
 0189 
 
 0156 
 
 
 
 Glycerine, C 3 H 5 
 
 (OH) 3 
 
 46'0 
 
 2TO 
 
 8 
 
 5 
 
 3'5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Bromine 
 
 
 
 
 'O 
 
 r-KS 
 
 'Oil 
 
 T 
 
 *oo 
 
 "im 
 
 00898 
 
 
 ->o8r'7 
 
 
 *V7/lA 
 
 
 
 
 
 Turpentine, dens. = '87 
 
 0225 
 
 0178 
 
 0149 
 
 0127 
 
 0107 
 
 00926 
 
 00821 
 
 00728 
 
 
 Pentane (n), C 6 H 12 
 
 00283 
 
 00255 
 
 00232 
 
 00212 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Hexane (n), C 6 H U 
 
 00396 
 
 00355 
 
 00320 
 
 00290 
 
 00264 
 
 00241 
 
 00221 
 
 
 
 Formic acid, HCO 2 H 
 
 
 
 
 0224 
 
 0178 
 
 0146 
 
 0122 
 
 0103 
 
 0089 
 
 
 0077 
 
 
 Acetic acid, CH 3 
 
 C0 2 H 
 
 
 
 
 
 
 
 '0122 
 
 0104 
 
 '0090 
 
 0079 
 
 0070 
 
 
 0062 
 
 
 Propionic acid,C 3 H 6 O 2 
 
 0152 
 
 0129 
 
 'OHO 
 
 0096 
 
 0084 
 
 0075 
 
 0067 
 
 
 0060 
 
 
 Butyric 
 
 <- 
 
 4 H 8 C 
 
 )., 
 
 0228 
 
 0185 
 
 0154 
 
 0130 
 
 '01 1 2 
 
 0097 
 
 0085 
 
 
 0076 
 
 
 Isobutyric 
 
 
 
 
 
 0188 
 
 0157 
 
 0131 
 
 0113 
 
 0098 
 
 0086 
 
 '0076 
 
 
 0068 
 
 
 Methyl formate . . . 
 
 00429 
 
 00384 
 
 00347 
 
 00317 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ! Ethyl 
 
 1 
 
 . 
 
 
 00505 
 
 00448 
 
 00402 
 
 '00362 
 
 00328 
 
 00299 
 
 
 
 
 
 
 
 Methyl acetate . . . 
 
 00478 
 
 00425 ! '00381 
 
 00344 
 
 00312 
 
 00284 
 
 
 
 
 
 
 
 Machine oil, 
 
 c. 1/19 ; olive oil, "99/15; 
 
 paraffin oil, c. 
 
 02/19 ; 
 
 rape oil, 1-6/20. 
 
 
31 
 
 VISCOSITIES 
 
 RELATIVE VISCOSITIES OF SOME AQUEOUS SOLUTIONS 
 
 Strength of solutions i normal. Viscosities relative to that of water at same temp. 
 
 For a complete list, see Stockl in L.B.M., and Moore, Phys. Rev., 1896. 
 
 
 Substance. 
 
 Temp. 
 
 Eelative 
 Viscosity. 
 
 Substance. 
 
 Temp. 
 
 Relative 
 Viscosity. 
 
 Ammonia . 
 
 
 25 C. 
 
 I '02 
 
 Potassium chloride . 
 
 17 o. 
 
 6C. 
 
 98 
 
 Ammonium 
 
 chloride 
 
 17-6 
 
 
 98 
 
 Potassium iodide . . 
 
 17'6 
 
 91 
 
 Calcium chloride 
 
 20 
 
 
 1-31 
 
 Sodium hydrate . . 
 
 25 
 
 
 1-24 
 
 Hydrochloric acid . 
 
 25 
 
 
 i -07 
 
 Sulphuric acid . . . 
 
 25 
 
 
 ro9 
 
 VISCOSITIES OF SOLIDS 
 
 Venice turpentine * at 17'3, 1 300, c.g.s. Shoemaker's wax t at 8, 47 x 
 
 io 6 . c.g.s. 
 
 Pitch t at 0, 51 X io 10 ; at 15, J 
 
 3 x io 10 . Soda glass t at 575, 1 1 x io 12 ; 
 
 Glacier ice, 
 
 t 12 X io 13 . 
 
 710, 4 x io 10 . 
 
 * R. Ladenburg, 1906. 
 
 t 
 
 Trouton and Andrews, 
 
 1904. \ Deeley, 1908. 
 
 VISCOSITIES OF GASES AND 
 
 VAPOURS 
 
 
 
 Clerk Maxwell showed in 1860 that, on the basis of the kinetic 
 
 theory, the 
 
 coefficient of viscosity of a 
 
 gas 
 
 would be independent of the pressure, and would 
 
 vary as the 
 
 square root of 
 
 the absolute temperature 
 
 The first relation is true 
 
 except at very low pressures 
 
 ; the second deduction is not supported by experiment. 
 
 Of the formulas connecting 
 
 gaseous viscosity (T?) and temperature (/), 
 
 there are 
 
 the convenient but only approximate relation of O. 
 
 E. Meyer, t\ t - 
 
 = *7o 
 
 (i + /), 
 
 where a is a 
 
 const. ; and the less manageable but accurate formula of Sutherland 
 
 (Phil. Mag., 
 
 31, 1893), who, 
 
 by 
 
 taking account of the effects of molecular 
 
 forces in 
 
 bringing about collisions which otherwise would have been avoided, 
 
 derived the 
 
 expression 77 
 
 273 + C 
 
 ( 6 
 
 J , where 6 is the absolute temperature, 
 
 and C is 
 
 '-n* d + c ' 
 
 W 
 
 Sutherland's 
 
 constant. The 
 
 formula only holds for temps, above the 
 
 critical, and 
 
 for pressures such that Boyl 
 
 2's law is approximately obeyed. Sutherland's relation 
 
 
 
 
 
 K6 
 
 3/i! 
 
 
 is thus of the form (which lends itself to graphical treatment), 6 ~ 
 
 C, where 
 
 K is a constant. (See Fisher, Phys. Rev., 1907, 1909 et seq. ; O. E. Meyer's 
 
 " Kinetic 
 
 Theory of Gases ; " and Stockl 
 
 in L.B.M. For a bibliography of gaseous 
 
 viscosity, 
 
 see Pedersen, Phys. Rev., 25, 1907.) The values below are for dry gases. 
 
 
 iGas or Vapour. 
 
 Temp. 
 
 n- 
 
 Observer. 
 
 Gas or Vapour. 
 
 Temp. 
 
 * 
 
 Observer. 
 
 
 
 xio- e 
 
 
 
 
 
 X10-6 
 
 
 
 Air . . . 
 
 -21 C. 
 
 164 
 
 Breitenbach 
 
 Nitrogen 
 
 OC. 
 
 166 
 
 v.Obermayer 
 
 
 O 173 
 
 
 (1901) 
 
 (contd.} 
 
 11 
 
 171 
 
 (1876) 
 
 
 O 
 
 171 
 
 Hogg, 1905 
 
 
 54 
 
 190 
 
 55 55 
 
 
 
 
 170 
 
 G.&G.*ioo8 
 
 Helium 
 
 O 
 
 189 
 
 Schultze, '01 
 
 
 
 
 171 
 
 Fisher, 1909 
 
 
 15 
 
 197 
 
 
 55 
 
 
 15 
 
 181 
 
 Markowski 
 
 
 185 
 
 270 
 
 
 
 
 99-6 
 
 221 
 
 
 CI9P4) 
 
 Neon . . 
 
 15 
 
 312 
 
 Rankine, 7 io 
 
 
 302 
 
 299 
 
 Breitenbach 
 
 Argon . . 
 
 O 
 
 210 
 
 Schultze, '01 
 
 Hydrogen 
 
 -21 
 
 82 
 
 
 (1901) 
 
 
 15 
 
 221 
 
 
 
 
 
 
 
 86 
 
 
 55 5 
 
 
 184 
 
 322 
 
 
 
 
 15 
 
 89 
 
 
 5> 55 
 
 Krypton . 
 
 15 
 
 2 4 6 
 
 Rankine, 'io 
 
 
 99 
 
 1 06 
 
 
 55 55 
 
 Xenon . . 
 
 15 
 
 222 
 
 
 55 
 
 
 302 139 
 
 
 55 55 
 
 Chlorine . 
 
 
 
 129 
 
 Graham, '46 
 
 Oxygen 
 
 O 
 
 187 
 
 v.Obermayer 
 
 
 20 
 
 147 
 
 
 
 
 15 
 
 195 
 
 
 (1876) 
 
 Water(vap.) 
 
 O 
 
 90 
 
 Puluj, 1878 
 
 
 54 
 
 216 
 
 
 55 55 
 
 
 15 
 
 97 
 
 
 
 Nitrogen . 
 
 -21 
 
 157 
 
 
 5 55 
 
 
 100 
 
 132 
 
 M*.&S.i88i 
 
 * Grindley 
 
 and Gibson. 
 
 1 
 
 Kundt and Warburg. 
 
 Meyer and Schumann. 
 
32 
 
 VISCOSITIES 
 
 VISCOSITIES OF 
 
 GASES AND VAPOURS (contd.) 
 
 as or Vapour. 
 
 Temp. 
 
 . 
 
 Observer. 
 
 Gas or Vapour. 
 
 Temp. 
 
 . 
 
 Observer. 
 
 Mercury 
 
 OC. 
 
 xio- 
 162* 
 
 S. Koch, '83 
 
 Carbon 
 
 99 C. 
 
 xio- 
 1 86 
 
 Breitenbach 
 
 (vap.) 
 
 3OO 
 
 
 532 
 
 
 M 
 
 dioxide 
 
 3O2 
 
 
 268 
 
 j? 
 
 (1901) 
 
 
 380 
 
 
 656 
 
 
 
 Methane, 
 
 
 
 
 104 
 
 Graham, '46 
 
 N itrous 
 
 -21 
 
 
 125 
 
 v.Obermayer 
 
 CH 4 
 
 20 
 
 
 120 
 
 
 
 oxide 
 
 
 
 
 135 
 
 M 
 
 (1876) 
 
 Ethylene, 
 
 -21 
 
 
 8 9 
 
 Breitenbach 
 
 
 100 
 
 
 183 
 
 
 
 C 2 H 4 
 
 
 
 
 97 
 
 )5 
 
 (1901) 
 
 Nitric 
 
 O 
 
 
 165 
 
 Graham, '46 
 
 
 15 
 
 
 102 
 
 
 
 oxide 
 
 2O 
 
 
 1 86 
 
 
 
 
 
 99 
 
 3 
 
 128 
 
 w 
 
 
 Sulphur 
 dioxide 
 
 O 
 20 
 
 
 123" 
 138 
 
 
 
 Alcohol 
 
 (vap.) 
 
 
 17 
 
 
 83 
 89 
 
 Puluj, 1878 
 
 J) 
 
 Sulphuret* 
 hydrogen 
 
 O 
 20 
 
 
 130 
 
 
 3) 
 
 Ether (vap.) 
 
 78 
 O 
 
 1 R 
 
 
 142 
 6 9 
 
 5) 
 
 
 Cyanogen . 
 
 O 
 
 
 95 
 
 
 5J 
 
 
 JLO 
 
 36 
 
 
 73 
 
 7Q 
 
 " 
 
 
 Carbon 
 monoxide 
 
 2O 
 
 20 
 
 
 107 
 
 163 
 184 
 
 v.Obermayer 
 
 (1876) 
 
 Chloroform 
 (vap.) 
 
 W V 
 
 O 
 
 17-4 
 61 
 
 fv 
 
 99 
 103 
 189 
 
 Breitenbach 
 
 (1901) 
 
 M 51 
 
 Carbon 
 
 -21 
 
 
 129 
 
 Breitenbach 
 
 Benzene 
 
 
 
 
 69 
 
 Schumann 
 
 dioxide 
 
 
 
 
 139 
 
 
 
 (1901) 
 
 (vap.) 
 
 19 
 
 
 79 
 
 
 
 (1884) 
 
 
 15 
 
 
 146 
 
 V 
 
 
 
 
 100 
 
 
 118 
 
 n 
 
 n 
 
 
 
 * Extrapolated. 
 
 
 
 TEMPERATURE COEFFICIENTS OF VISCOSITY 
 
 Based largely on W. 
 
 J. Fisher's computations (ref. above). 
 
 
 Sutherland's 
 
 
 
 Sutherland's 
 
 
 Gas or Vapour. 
 
 Consts. 
 
 Meyer's 
 
 Gas or Vapour. 
 
 Consts. 
 
 Meyer's 
 
 
 C 
 
 K 
 
 
 
 C K 
 
 Const, a 
 
 Air . . . 
 
 124 
 
 iSoxio- 7 
 
 00273 
 
 Xenon .... 
 
 252 246 x io ' 
 
 
 
 
 Hydrogen . . . 
 
 72 
 
 66 
 
 
 
 Water (vap.) . . 
 
 72 
 
 
 
 Oxygen .... 
 
 127 
 
 175 
 
 00283 
 
 Carbon monoxide 
 
 102 135 , 
 
 00269 
 
 Nitrogen . . . 
 
 IIC 
 
 143 
 
 00269 
 
 dioxide . 
 
 240 158 , 
 
 00350 
 
 Helium .... 
 
 80 
 
 148 
 
 
 
 Nitrous oxide . . 
 
 
 00345 
 
 Neon ..... 
 
 56 
 
 220 
 
 
 
 Ethylene . . . 
 
 226 106 , 
 
 00350 
 
 Argon .... 
 
 170 
 
 207 
 
 
 
 Chloroform (vap.) 
 
 454 159 i 
 
 
 Krypton .... 
 
 1 88 
 
 240 
 
 . 
 
 
 
 
 SIZE, 
 
 VELOCITY, AND FREE PATH OF MOLECULES 
 
 p = density of gas in gms./c.c. 
 
 at o C. N = number of molecules of gas 
 
 per c.c. 
 
 and 76 cms. 
 
 at o C. and 76 cms. 
 
 
 / = i atmos. = 
 
 1*0132 X io 6 dynes/cm.- a = molecular diameter in cms. 
 
 6 = absolute temperature. 
 
 ;;/ = mass of a 
 
 single molecule (in 
 
 R = gas constant. 
 
 grams). 
 
 
 
 b b of Van der Waal's equation (p. 34). G = square root 
 
 of mean square mole- 
 
 k thermal conductivity of gas 
 
 (p. 52). cular vel. (cm./sec. at o C.). 
 
 c v = specific heat at const, volume (p. 58). n = mean molecular velocity (cm./sec.). 
 
 t] = viscosity of gas (p. 31). 
 
 L = length of mean free path in 
 
 cms. 
 
 Assuming a Maxwell-Boltzmann distribution of velocities 
 
 
 G = V< 
 
 MNw) = V^/P = V^Rfl 
 
 
 
 n = 4G/V/67T = *92iG 
 
 Collision 
 
 frequency = n/L = 5 x io n per sec. for O 2 
 
33 
 
 MOLECULES 
 
 SIZE, VELOCITY, AND FREE PATH OF MOLECULES (contd.) 
 
 MOLECULAR SIZE 
 
 The molecular diameter a- has been calculated by the following formulae : 
 
 1. The viscosity TJ of a gas is a function of the size of its molecules. 
 
 r, = 44 P n/(V'2Nir(7 2 ) . . . Jeans /. a- = {'o9i2/>G/(Ni)}* 
 
 2. The thermal conductivity, k r6i)c v = ' 
 
 .: <r = {'i46pGc 
 
 3. Van der Waal's, b = 2irNa 3 /^ .-. a- = {3#/(2irN)}i 
 
 4. Limiting density, i.e. density D of densest known form, a - {6p/(irDN))3 
 
 The values of p and r? used in calculating G and L below are given on pp. 26, 31. 
 The values of a- tabulated are mostly taken from Jeans' " Dynamical Theory of 
 Gases," or Rudorf (Phil. Mag., 1909, p. 795). Jeans takes N = 4 x io 19 , while in the 
 table following, the more recent value 275 x io 19 has been used. 
 
 Gas. 
 
 Hydrogen, H 2 . 
 
 Helium, He . 
 
 Nitrogen, N 2 . 
 
 Oxygen, O 2 . 
 
 Neon, Ne . . 
 
 Argon, A . . 
 
 Krypton, Kr . 
 
 Xenon, Xe . . 
 
 Chlorine, Cl . 
 
 Methane, CH 4 
 
 Ethylene, C 2 H 4 
 
 Carbon mon- 
 oxide, CO . 
 
 Carbon di- 
 oxide, CO 2 . 
 
 Ammonia,NH 3 
 
 Nitrous oxide, 
 N 2 O . . . 
 
 Nitric oxide, 
 NO . . . 
 
 Sulph. hydro- 
 gen, H 2 S . . 
 
 Sulph. dioxide, 
 S0 2 . . . 
 
 Hydrochloric 
 acid, HC1 . 
 
 Water, H 2 O . 
 
 G at C. 
 
 cm. /sec. 
 
 x io 4 
 13-11 
 
 4*93 
 4*6 1 
 5-61 
 
 2-86 
 2-28 
 3-07 
 6-48 
 4-88 
 
 4'93 
 
 6-28 
 
 476 
 
 4*44 
 3-22 
 
 4-30 
 7-08 
 
 Mean free 
 path, L. 
 
 cm. 
 
 18-3 x 
 28-5 
 
 9*44 
 
 9*95 
 
 I0'0 
 
 9*49 
 
 4'57 
 779 
 
 5*47 
 9-27 
 
 6-29 
 6-95 
 
 6'io 
 9 - o6 
 5-90 
 
 4'57 
 
 6-86 
 
 7-22 
 
 Molecular diameter <r deduced from 
 
 cm. 
 
 2-47 x io~ 8 
 
 2'l8 
 3-50 
 
 3*39 
 
 4*96 
 
 4'55 
 
 3-50 
 
 4'i8 
 
 4*27 
 
 4-09 
 
 cm. 
 2'40X 
 
 3'3I 
 
 3-1 1 
 
 4-68 
 
 3'3i 
 4-32 
 
 4-20 
 
 IQ- 
 
 2-30 
 3'53 
 
 2-86 
 
 2-92 x io 
 
 4-34 
 
 2-97 
 
 279 
 
 4*43 
 4'93 
 4-88 
 
 5'26 
 
 4H2 
 4-58 
 
 3'45 
 
 The formulae above assume the molecules to be spherical. Sutherland (Phil. 
 Mag., 1910), adopting his formula (see p. 31) for the variation of f\ with temp., obtains 
 the following values of <r. Unit, io~ 8 cm. 
 
 2-17 
 
 He 
 
 1*92 j 2'66 
 
 N 2 
 
 3*33 
 
 NO 
 
 CO C0 2 
 
 2-74 2-90 
 
 3'3i I 3*76 
 
34 
 
 CRITICAL DATA 
 
 CRITICAL DATA AND VAN DER WAAL'S CONSTANTS 
 
 Critical temperature, B e , is the highest temperature at which a gas can be 
 liquefied by subjecting it to pressure. 
 
 Critical pressure, / c , is the pressure (of gas and liquid) at the critical temperature. 
 
 Critical volume, v, is here defined as the ratio of the volume that a gas has at 
 the critical temp, and press, to that which it would have at o C. and 760 mms., i.e. it 
 is the volume of gas at O c and/ which at N.T.P. would have unit volume. Some 
 writers take the critical volume to be the specific volume (c.cs. per gram) at B c and p c . 
 
 Most of the characteristic equations of state which have been proposed for gases 
 take the form (p + a\v^)(v b) R0, where p is the pressure, v the volume, the 
 absolute temperature of the gas, and R is the "gas constant." a expresses the mutual 
 attraction of the molecules. The " covolume " b is proportional to the space occupied 
 by the molecules : O. E. Meyer takes b 4.4/2 (volume of molecules). Van der Waal 
 assumes a is constant : if this were true the constant volume and thermodynamic 
 scales of temperatures would agree they do not, however (see p. 44). Joule and 
 Thomson, Clausius, Amagat, and Berthelot, among others, regard a as a function 
 of 6 (e.g. a cc i/a), and b as constant. 
 
 Assuming with Van der Waal that a and b are constants, the equation can be 
 regarded as a cubic in 7', which has its three roots equal at the critical point, whence 
 a = 27R 2 C 2 /(64A), and b = R C /(8A). 
 
 The values of a and b below are largely from Rothe (L.B.M.). Taking pressures 
 in atmos., and the volume of the gas at o C. and I atmos. as i, R = pv\Q = 1/273. 
 In these units, b is in terms of the volume of the gas at o C. and i atmos. 
 
 Example. For CO 2 p c 73 atmos. and C = 273 + 31*1 = 304-1, whence 
 b = 304- 1 /(8 X 273 x 73) = -00191 of the volume of the gas at o C. and i atmos. 
 
 See Preston's " Heat," Nernst's " Theoretical Chemistry," Young's " Stoichio- 
 metry," Berthelot (Trav. et Mhn. Bur. Intl., 1907). * Indicates calculated values. 
 
 Substance. 
 
 Critical 
 
 Van der Waal's 
 
 Observer. 
 
 Temp. e c 
 
 Press.p c 
 
 Vol. v c 
 
 a. 
 
 b. 
 
 
 
 atmos. 
 
 
 
 
 
 Hydrogen 
 
 -234'5C. 
 
 20 
 
 00264* 
 
 00042 
 
 00088 
 
 Olszewski, '95 
 
 
 
 -118 
 
 CO 
 
 OTH 76* 
 
 "OO27^ 
 
 "00142 
 
 v.Wroblewski, '85 
 
 Nitro a en 
 
 1 1 O 
 
 146 
 
 5 
 33 
 
 vXs^\s 
 
 00517* 
 
 *> A '*/ j 
 
 0025^ 
 
 :cai&L 
 
 3? )) 
 
 
 Air 
 
 140 
 
 -3Q 
 
 '00468* 
 
 'OO" > s 7 
 
 "ooi 56 
 
 Olszewski, '84 
 
 
 -268 
 
 Jy 
 2'3 
 
 00299* 
 
 *^**3/ 
 
 '0000615 
 
 000995 
 
 Onnes, 1908 
 
 
 
 < 2IO 
 
 
 
 
 
 
 Argon 
 
 -II7-4 
 
 52-9 
 
 00404* 
 
 00259 
 
 00135 
 
 Ramsay and 
 
 
 Krypton . . 
 
 -62-5 
 
 54'3 
 
 00532* 
 
 00462 
 
 00178 
 
 Travers, 1900 
 
 
 
 U'7 
 
 C7"2 
 
 "0060* 
 
 Oo8l8 
 
 QQ'>"3Q 
 
 
 Chlorine 
 
 / 
 146 
 
 .)/ 
 
 93 '5 
 
 006I5* 
 
 01063 
 
 (^K^-*^W 
 00205 
 
 Knietch, '90 
 
 
 Bromine . . . . 
 
 302 
 
 131* 
 
 00605 
 
 01434 
 
 00202 
 
 Nadejdine, '85 
 
 
 Water 
 
 365 
 
 194-6 
 
 00386 
 
 oi 1 8 
 
 00150 
 
 Battelli, '90 
 
 
 Hydrochloric acid . . 
 
 52'3 
 
 86 
 
 0052* 
 
 00697 
 
 00173 
 
 Dewar, 1884 
 
 Carbon monoxide . . 
 
 -141-1 
 
 35'9 
 
 00505* 
 
 00275 
 
 00168 
 
 v.Wroblewski, '83 
 
 Carbon dioxide . . . 
 
 3"i*i 
 
 73 
 
 0066 
 
 00717 
 
 OOI9I 
 
 Andrews, 1869 
 
 Carbon bisulphide . . 
 
 273 
 
 72-9 
 
 0090 
 
 '02316 
 
 00343 
 
 Battelli, 1890 
 
 Ammonia, NH 3 . . . 
 
 130 
 
 115*0 
 
 00481* 
 
 00798 
 
 00161 
 
 Dewar, 1884 
 
 Nitrous oxide, N 2 O 
 
 38-8 
 
 77'S 
 
 00436 
 
 00710 
 
 00184 
 
 Villard, 1894 
 
 Nitric oxide, NO . . 
 
 -93*5 
 
 71-2 
 
 00347* 
 
 00257 
 
 00116 
 
 Olszewski, '85 
 
 Nitrogen tetroxide,NO 2 
 
 171-2 
 
 147* 
 
 00413 
 
 00756 
 
 00138 
 
 Nadejdine, '85 
 
 Sulphuretted hydrogen 
 
 100 
 
 887 
 
 00578* 
 
 00888 
 
 00193 
 
 Olszewski, '90 
 
 Sulphur dioxide . . . 
 
 I55-4 
 
 78-9 
 
 00745* 
 
 01316 
 
 00249 
 
 Sajotschewsky,'78 
 
 Methane, CH 4 . . . 
 
 -95 5 
 
 50 
 
 00488* 
 
 00357 
 
 00162 
 
 Dewar, 1884 
 
 Acetylene, C 2 H 2 . . 
 
 36-5 
 
 61-6 
 
 0069* 
 
 00880 
 
 00230 
 
 Mackintosh, '07 
 
 Ethylene, C 2 H 4 . . . 
 
 10 
 
 51-7 
 
 00752* 
 
 00877 
 
 00251 
 
 Olszewski, '95 
 
 Ethane, C 2 H 6 . . . 
 
 34 
 
 50-2 
 
 00839* 
 
 01060 
 
 0028 
 
 ['86 
 
 Ethylalcohol,C 2 H 6 OH 
 
 243 
 
 62-7 
 
 OO7I 
 
 02407 
 
 00377 
 
 Ramsay & Young, 
 
 Ether (C 2 H 6 ) 2 . . . 
 
 197 
 
 35'8 
 
 0158 
 
 03496 
 
 00602 
 
 Battelli, '92 
 
 Chloroform, CHC1 3 . 
 
 260 
 
 54*9 
 
 0133 
 
 0293 
 
 00445 
 
 Sajotsche\vsky,'78 
 
 Aniline, C 6 H 5 NH 2 . . 
 
 425-6 
 
 5 2 '3 
 
 0183* 
 
 05282 
 
 00611 
 
 Guye& Mallet, '02 
 
 Benzene, C 6 H 6 . . . 
 
 288-5 
 
 47'9 
 
 0161* 
 
 03726 
 
 00537 
 
 Young, 1900 
 
35 
 
 DIFFUSION 
 
 DIFFUSION OF GASES 
 
 The Coefficient of diffusion, D, is the mass of the "diffusing" gas which crosses 
 unit area in unit time under unit concentration gradient : the dimensions of the coefficient 
 are cm. 2 sec.- 1 . D is inversely proportional to the total pressure of the two gases, and 
 roughly proportional to the square of their absolute temperature. Total pressure 
 I atmosphere. H 2 O. 2 implies that H 2 is diffusing into O 2 . 
 
 
 (See Meyer's "Km 
 
 etic Ineory of Gases," and v. Stemwehr in L.B.M.) 
 
 
 
 
 
 
 
 D into 
 
 Gases. 
 
 e c. D 
 
 Gases. 
 
 tC. D 
 
 Gas 
 
 (\Vinkelmann) 
 
 tC. 
 
 
 
 
 
 
 
 
 
 Air. 
 
 C0 2 
 
 H 2 
 
 H., 0, . 
 
 -677, 0. 
 
 CO U, . 
 
 
 
 642, L. 
 
 Formic acid . 
 
 
 
 131 
 
 088 
 
 113 
 
 H., O, . 
 
 -68 1, 0. 
 
 CO-C 2 H 4 
 
 O 
 
 ioi, O. 
 
 Acetic . . . 
 
 
 
 106 
 
 071 
 
 404 
 
 H, CH 4 
 
 O -625, O. 
 
 
 
 
 Propionic acid 
 
 
 
 082 
 
 058 
 
 'J26 
 
 H., CO . 
 
 -649,0. 
 
 CO, CO 
 
 
 
 131,0. 
 
 Butyric acid . 
 
 
 
 0^ 
 
 037 '201 
 
 H.,C0 2 . 
 H 8 C 2 H 4 
 
 o -538,0. 
 
 -483, 0. 
 
 C0 2 CO 
 CO, Air 
 
 o 
 
 
 
 141, L. 
 142, L. 
 
 Isobutyricacicl 
 Me. alcohol . 
 
 o 
 o 
 
 07 
 132 
 
 0471-271 
 088 -500 
 
 H 2 N a O 
 
 -535,0. 
 
 CO 2 CH 4 
 
 
 
 146,0. ; -16, L. 
 
 Et. . 
 
 o 
 
 '102 
 
 068 
 
 3/8 
 
 
 
 C0 2 2 . 
 
 o 
 
 18, L. 
 
 Propyl alcohol 
 
 
 
 080 
 
 os8 
 
 311 
 
 0,~ N, . 
 
 o -171,0. 
 
 CO 2 NoO 
 
 
 
 i, L. ; -15, O. 
 
 Butyl . 
 
 
 
 068 
 
 048 
 
 272 
 
 Da H., . 
 
 -722, L. 
 
 CO,-H 2 
 
 
 
 55, L. 
 
 , 
 
 99 
 
 126 
 
 088 
 
 504 
 
 H.,0 CO, 
 
 18 -155, G. 
 
 Air O 2 . 
 
 o 
 
 178, 0. 
 
 Benzene - 
 
 
 
 07 S 
 
 o^ 
 
 294 
 
 H 2 O Air 
 
 8 -239, G. 
 
 Air H., . 
 
 17 
 
 66, Sc. 
 
 Me. acetate . 
 
 O 
 
 084 
 
 056 
 
 328 
 
 H.,0 Air 
 
 15 -246, G. 
 
 
 
 
 Et. formate . 
 
 O 
 
 08 S 
 
 OS7 
 
 336 
 
 H 2 Air 
 
 18 -248, G. 
 
 CS 2 Air 
 
 
 
 i, S. 
 
 Et. acetate . 
 
 O 
 
 071 
 
 049 
 
 273 
 
 H 2 O Air 
 
 -203, H. 
 
 
 
 
 Et. butyrate . 
 
 O 
 
 057 
 
 041 
 
 224 
 
 
 1 
 
 
 
 
 Et.iso-butyrate 
 
 O 
 
 055 
 
 040 
 
 224 
 
 G., Guglielmo, 1884 ; H., Houdaille, 1896 ; L., Loschimdt, 1870 ; O., v. Obermaycr, 1887 ; 
 S., Stefan, 1879 ; Sc., Schulze, 1897. 
 
 DETERMINATION OF ALTITUDES BY THE BAROMETER 
 
 C* ( FT _ T T \ 
 
 Babinet's formula (Compt. RemL, 1850) is, Altitude - V. * , :, 2 r where E 1 = 
 
 **i + W 2 
 
 barometer reading at lower station, H 2 at upper station. If altitudes are in metres, and 
 barometric heights in mms., 
 
 C = 32(500 + A + 4) 
 | where / x and / 2 are the corresponding station temperatures ( C.). 
 
 In the table below the mean temperature, (^ + / 2 )/ 2 , is taken as 10 C., and the baro- 
 metric height at sea-level as 760 mm., so that altitudes are in metres above sea-level. 
 I The values are of course only approximate. Babinet's formula is not applicable to very 
 j great altitudes. 
 
 Altitude 
 
 
 
 100 200 ! 300 
 
 400 
 
 500 
 
 600 
 
 700 ' 800 
 
 900 
 
 metres. 
 
 
 1000 
 
 mm. 
 7 60 
 
 674 
 
 mm. mm. mm. 
 
 75 1 742 733 
 666 658 650 
 
 mm. 
 724 
 642 
 
 mm. 
 7 l6 
 635 
 
 mm. 
 707 
 627 
 
 mm. mm. 
 699 i 690 
 
 620 ! 612 
 
 mm. 
 682 
 60 5 
 
 THICKNESS OF THIN METAL FOIL 
 
 Approximate thickness of the thinnest beaten metal leaf at present commercially 
 obtainable. Unit io~ cm. 
 
 Metal. . 
 
 Al 
 
 Cu 
 
 Au 
 
 Pt 
 
 Ag 
 
 Dutch metal. 
 
 (Cigarette paper.) 
 
 Thickness 
 
 20 
 
 34 
 
 8 
 
 25 
 
 21 
 
 70 
 
 2500 
 
36 
 
 SURFACE TENSIONS 
 
 SURFACE TENSIONS 
 
 In dynes per cm. (A) 
 
 indicates liquid in contact with air, (V) indicates liquid in 
 
 contact with its vapour. 
 
 The surface tension of a liquid varies somewhat with the 
 
 age (and 
 
 contamination) of the surface. 
 
 
 
 
 Temperature variation. It follows from 
 
 Eotvos' 
 
 rule, that the surface 
 
 tension T at temp. / is approximately proportional 
 
 to (/ c /), where t c is the critical 
 
 temp., the constant of proportionality being much the same for chemically similar 
 
 substances. The surface tension at f e is zero. (For critical 
 
 temps, see p. 34.) 
 
 See Poynting and Thomson's " Properties of Matter," and Meyer in L.B.M. 
 
 WATER (/ c = 365 C.) 
 
 Surf. Tens. 
 T at 15 C. 
 
 Method. 
 
 Observer. 
 
 Temp. (/). 
 
 T./T,, 
 
 Temp. (t). 
 
 T,/r 15 
 
 dynes per cm. 
 
 
 
 
 
 
 
 72-8 (A) 
 74'3 (A) 
 
 Vibrating jet 
 Vibrating jet 
 
 Bohr., Phil. Trans., '09 
 Pedersen,/ 3 . Trans. ,'07 
 
 0C. 
 10 
 
 r030 
 
 roio 
 
 60 C 
 70 
 
 901 
 876 
 
 74'2 (A) 
 
 Capillary waves 
 
 Kalahne, Ann.d. Phy., 
 
 15 
 
 1OOC 
 
 ) 8O 
 
 851 
 
 73*8 (A) 
 
 Hanging drop 
 
 Sentis, 1897 ['02 
 
 20 
 
 990 
 
 9O 
 
 827 
 
 73'3 (A) 
 
 Tension of film 
 
 Hall, 1893 ['93 
 
 3O 
 
 970 
 
 100 
 
 80 
 
 74'3 (A) 
 
 Capillary waves 
 
 Rayleigh, Phil. Mag., 
 
 40 
 
 947 
 
 120 
 
 75 
 
 73*3 (A) 
 
 Capillary tube 
 
 Volkmann, 1895 
 
 50 
 
 925 
 
 140 
 
 70 
 
 7i'4(V) 
 77-6 (A) 
 
 Capillary tube 
 Pull on ring 
 
 Ramsay & Shields, '93 
 Weinberg, 1892 
 
 
 
 
 
 Ramsay 
 
 & Shields, '93 ; 
 
 Volk- 
 
 
 
 
 mann & .brunner 
 
 
 Substance. 
 
 
 Temp. (/). 
 
 Surf. 
 Tens. 
 
 Method. 
 
 Observer. 
 
 
 
 
 
 
 dynes 
 
 
 
 
 
 
 INORGANIC. 
 
 
 
 
 cm. 
 
 
 
 
 
 
 Cadmium 
 
 
 
 CO 2 
 
 Molten 
 
 6 93 
 
 Weight of drop 
 
 Quincke 
 
 
 Gold 
 
 
 A 
 
 1O7OC. 
 
 612 
 
 Curvature of drop 
 
 Heydweiller, '98 | 
 
 Lead 
 
 
 CO 2 
 
 335 
 
 477 
 
 Capillary waves 
 
 Grunmach 
 
 Mercury ( 
 
 T = T -'379') 
 
 A 
 
 17-5 
 
 TV J 
 
 547 
 
 Capillary tube 
 
 Quincke 
 
 
 Potassium 
 
 
 C 
 
 0. 
 
 58 
 
 364. 
 
 We 
 
 lirVif of f\r 
 
 rn 
 
 
 
 Sodium 
 
 
 CO 2 
 
 90 
 
 J^T 
 520 
 
 
 JJ 
 
 
 Sulphur (M.P. 115). . 
 
 A 
 
 16O 
 
 59( 
 
 Press, reqd.to bub- j 
 
 Zickendraht, '06 ; 
 
 
 
 / 
 
 t 
 
 25O 
 
 118 
 
 bl 
 
 f n i r frnm 
 
 rnr ! 
 
 and Qu 
 
 inrkp. 
 
 
 (B.P.) 
 
 A 
 
 445 
 
 441 
 
 tube thro' liquid) 
 
 '08 
 
 Liquid oxygen .... 
 
 A 
 
 -183 
 
 13-1 
 
 Capillary waves 
 
 Grunmach 
 
 1906 
 
 ,, nitrogen . . . 
 
 A 
 
 -196 
 
 8*5 
 
 
 
 
 
 
 
 1906 
 
 nitrous oxide . . 
 
 A 
 
 -89-4 
 
 26-3 
 
 
 
 
 n 
 
 1004 
 
 Nickel carbonyl,Ni(CO) 4 
 
 V 
 
 19-8 
 
 14-2 
 
 Capillary tube 
 
 Ramsay 
 
 and 
 
 
 
 
 
 
 
 
 
 
 Shields, 
 
 1893 
 
 Ammonia 
 
 soln. (d = '96) 
 
 A 
 
 15 
 
 647 
 
 Vibrating jet 
 
 Pedersen, 
 
 1907 
 
 Sulph- acidsol. (*/= 1*14) 
 
 A 
 
 15 
 
 74'4 
 
 9* 1) 
 
 1907 
 
 Other solns. (see below) 
 
 
 
 
 
 
 
 
 
 
 CARBON COMPOUNDS. 
 
 
 
 
 
 
 
 
 
 
 Acetone, (CH 3 ) 2 CO . . 
 
 V 
 
 16-8 
 
 23*3 
 
 Capillary tube 
 
 ( Ram say 
 
 and 
 
 
 
 V 
 
 78-3 
 
 15-9 
 
 
 
 
 
 \ Shields, 
 
 1893 
 
 Acetic acid, CH 3 CO 2 H . 
 
 V 
 
 20 
 
 23*5 
 
 
 , 
 
 
 
 
 
 
 
 V 
 
 300 
 
 1-16 
 
 
 
 
 u 
 
 M 
 
 Alcohol methyl, CH 4 O 
 
 V 
 
 2O 
 
 23 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 200 
 
 S* 2 
 
 
 
 
 
 
 
 ethyl,C 2 H 6 OH 
 
 V 
 
 20 
 
 22'0 
 
 
 } , 
 
 
 
 
 
 (T f = To - -002/) . . 
 
 V 
 
 15O 
 
 9'5 
 
 
 
 
 
 
 55 
 
 propyl (), 
 
 V 
 
 16*4 
 
 23-8 
 
 
 
 
 
 
 
 
 
 C 3 H 7 OH 
 
 V 
 
 78-3 
 
 187 
 
 
 
 
 
 ,, 
 
 Aniline, C 6 H 6 .NH 2 " . . 
 Benzene, C 6 H 6 . 
 
 A 
 
 A 
 
 15 
 17-5 
 
 43 'o 
 29-2 
 
 Vibrating jet 
 Capillary tube 
 
 Pedersen, 1907 
 Volkmann 
 
37 
 
 SURFACE TENSIONS 
 
 Substance. 
 
 CARBON COMPOUNDS. 
 
 (fO*t4.) 
 
 Butyric acid, C 3 H 7 CO 2 H 
 Carbon bisulphide . . 
 Carbon tetrachloride. . 
 
 Chloroform, CHC1 3 . . 
 Ether (ethyl), (C 2 H 5 ) 2 O . 
 (T, = T --ii5/) . . 
 Ethyl acetate, 
 
 CH 3 CO 2 C 2 H 5 
 Formic acid, HCOOH . 
 
 Olive oil (dJ2o = -91) . 
 Paraffin oil (d - '847) . 
 Propionic acid, C 3 H 6 O 2 
 
 Pyridine, C 5 H S N . . . 
 
 Toluene, C 6 H 6 .CH 3 . 
 Turpentine, C 10 H 16 . . 
 
 Temp. (/). 
 
 Surf. 
 Tens. 
 
 15 C. 
 132 
 
 19-4 
 
 46'1 
 
 20 
 25O 
 
 15 
 
 20 
 150 
 
 20 
 100 
 
 17 
 
 8O 
 
 20 
 
 25 
 
 16-6 
 132 
 
 17'5 
 
 91 
 
 15 
 
 15 
 
 dynes 
 
 cm. 
 267 
 164 
 336 
 29-4 
 257 
 
 16-5 
 2-9 
 23-6 
 14 
 
 37'5 
 30-8 
 
 32 
 
 26-4 
 
 26-6 
 
 'I' 5 
 367 
 
 26-5 
 28-8 
 27-3 
 
 Method. 
 
 Capillary tube 
 
 Curvature of drop 
 Capillary tube 
 
 Vibrating jet 
 Capillary tube 
 
 Observer. 
 
 (Ramsay and 
 \ Shields, 1893 
 
 Kaye, 1905 
 Jaeger, 1892 
 
 ("Ramsay and 
 V Shields, 1893 
 Magie, 1888 
 Frankenheim, '47 
 ("Ramsay and 
 \ Shields, 1893 
 (Dutoit and Fri- 
 \ derich, 1900 
 Pedersen, 1907 
 Kaye, 1905 
 
 SURF. TENSIONS OF SOLUTIONS 
 
 The surface tension of aqueous 
 salt solutions is generally greater 
 than that of pure water. Dorsey 
 (Phil. Mag., 1897) has shown 
 T,, = T + A . 
 
 T n is the surf. tens, of a sol. of 
 n gram equivalents per litre^ 
 T that of water at same temp. 
 
 Salt. 
 
 NaCl . , 
 KC1 . . . 
 
 4(Na 2 CO s ) 
 
 I(K 2 C0 3 ) . 
 |(ZnS0 4 ) . 
 
 171 
 
 2*00 
 177 
 
 r86 
 
 SURFACE TENSIONS AT INTER-LIQUID BOUNDARIES 
 
 Liquids at 20 C. 
 
 Water-benzene . . 
 chloroform f 
 ether . . . 
 olive oil J 
 paraffin oil . 
 Mercury-water . . 
 alcohol . 
 chloroform f 
 
 Surface 
 Tension T. 
 
 dynes/cm. 
 
 29'5 
 I2'2 
 206 
 
 427* 
 
 399 
 399 
 
 Obrerver. 
 
 Pockels, 1899 
 Quincke 
 
 Pockels, 1899 
 Gouy, 1908 
 Quincke 
 
 * Diminishes with time. 
 \ Density = '91. 
 
 t Density = I '49. 
 Density = 79. 
 
 ANGLES OF CONTACT BETWEEN GLASS AND LIQUIDS 
 
 Angles of contact vary largely with the freshness of the surfaces in contact. 
 
 Liquid. 
 
 Mercury . . 
 Water . . . 
 Water . . . 
 Methyl alcohol 
 Ethyl alcohol . 
 Ether . . . 
 Chloroform 
 
 Angle. 
 
 Observer. 
 
 5 2 40' 
 
 8-9 
 
 ot 
 
 
 
 
 1 6 
 
 Quincke 
 
 Wilberforce 
 
 Magie, '88 
 
 Liquid. 
 
 Acetic acid 
 Benzene 
 Paraffin oil 
 Turpentine 
 
 Angle. Observer. 
 
 
 26 
 
 17 
 
 Magie, '88 
 
 * For freshly formed drop, 41 5'. 
 t Glass quite clean. 
 
 The angle of contact of water against different metals varies between 3 and 11. 
 
 SIZE OF DROPS AND THICKNESS OF LIQUID FILMS 
 Reference may be made to the writings of J. J. Thomson ("Conduction of 
 Electricity through Gases"), C. T. R. Wilson, Laby (Phil. Trans. A, 1908), Reinold 
 Riicker (Phil. Trans., 1886), Lord Rayleigh, and Johonnot (Phil. Mag., 1906). 
 
38 
 
 HYGROMETRY 
 
 RELATIVE HUMIDITY AND DEW-POINT 
 
 Relative humidity = ' . ico, where [p] t is the actual pressure of water-vapour 
 
 at temperature /, and is equal to [pj (lj) , the saturated vapour- pressure at the dew- 
 point (dp} ; [/]* is the pressure of saturated vapour at /. For a table of saturated 
 water-vapour pressures, see p. 40. (See " Smithsonian Meteorological Tables.''') 
 
 Percentage relative humidities for different dew-points and dew-point depressions 
 are tabulated below. 
 
 Dew-point 
 
 O 
 
 + 10 
 20 
 30 
 
 Depression of dew-point = f 
 
 OC. 1 
 
 100 
 ICO 
 100 
 IOO 
 100 
 
 92 85 
 
 93 87 
 
 94 88 
 94 89 
 94 89 
 
 3 4 C 
 
 79 
 81 
 82 
 83 
 
 73 
 75 
 77 
 7 
 
 84 80 
 
 6? 
 70 
 72 
 74 
 75 
 
 6 I 7 C 
 
 62 
 
 65 
 68 
 70 
 71 
 
 58 
 61 
 64 
 66 
 68 
 
 8 9 10 12 14 16 18 
 
 53 
 57 
 60 
 
 49 
 53 
 56 
 58 
 64 61 
 
 46 
 50 
 53 
 55 
 
 57 
 
 39 
 44 
 47 
 49 
 52 
 
 34 
 38 
 4i 
 44 
 46 
 
 29 26 
 
 34 I 30 
 
 37 33 
 
 39 35 
 
 42 3 
 
 WET AND DRY BULB HYGROMETER 
 
 Apjohn (1835), August (1825), and others, by making various assumptions 
 (some of doubtful legitimacy), have derived formulas of the type 
 
 M, - Mr = AH(/ -/)[! + B(/ - /)] 
 
 where / is the temperature of the dry bulb, t w that of the wet, [p~\ t is the actual 
 pressure of water- vapour in the air (at temperature /), [ is the saturated vapour 
 pressure of water at the temperature (/ w ) of the wet bulb, H is the barometric 
 height, and A and B are constants. (See Preston's " Heat.") 
 
 The indications of this hygrometer are so dependent on its environment that for 
 most purposes B may be taken as zero, and H as constant, say 760 mms. 
 
 If H is measured in millimetres, and temperatures in Centigrade degrees, the 
 following values of A are suitable for the conditions mentioned : 
 
 A = -0007 if wet bulb is caused to swing for a short time. 
 
 A = '00075 in a Stevenson screen as used by Meteorological Office. 
 
 A = '0008 in open air with slight wind. 
 
 A = -0009 in open air with no wind. 
 
 A = 'ooi in a small closed room. 
 
 Rizzo (1897) takes A = '00075 and B = '008, and the table below is derived 
 by employing these values. [p~]* w can be got from the table of saturated vapour 
 pressures on p. 40, and thus the desired vapour pressure [p~\ t can be determined. 
 
 VALUES OF [p]* w - [p] t (Rizzo) 
 
 Barom. 
 Press. H. 
 
 770 
 760 
 750 
 730 
 700 
 670 
 
 770 
 760 
 750 
 73O 
 7OO 
 670 
 
 Difference of temperature of dry and wet bulb thermometers (/ - /,). 
 
 "57 
 56 
 *55 
 *54 
 
 52 
 50 
 
 *I2 
 II 
 
 08 
 03 
 '99 
 
 3 
 
 5 
 
 1-69 
 
 r6 7 
 r6 5 
 r6o 
 
 i'54 
 1-47 
 
 mm. 
 2-23 
 2-20 
 2M7 
 2*12 
 
 11 C. 12 
 
 578 
 
 5-26 
 5-03 
 
 6-26 
 6-iS 
 6-09 
 
 5*93 
 5-69 
 
 5'44 
 
 13 
 
 67 
 
 6-63 
 
 6-54 
 
 6-37 
 
 6-1 1 
 
 5-84 
 
 14 
 
 7-17 
 
 7-08 
 6-98 
 679 
 6-52 
 6-24 
 
 mm. 
 
 278 
 274 
 271 
 2-63 
 2-52 
 2-42 
 
 6 
 
 3-21 
 
 3-12 
 3-00 
 2-87 
 
 8 
 
 3-81 
 
 376 
 
 371 
 3-61 
 
 4*27 
 4'2I 
 
 4' 10 
 
 3-93 
 376 
 
 9 
 
 475 
 4'6 9 
 4-56 
 
 4'37 
 4-19 
 
 10 
 
 5-24 
 5-17 
 
 5'03 
 4-82 
 
 4-62 
 
 15 
 
 7-62 
 
 7-52 
 7*42 
 
 7-22 
 
 6-63 
 
 16 
 
 8-06 
 
 7'95 
 7-84 
 7-63 
 7-32 
 7-01 
 
 17 18 19 20 
 
 8-47 
 8-36 
 8-25 
 8-03 
 770 
 7'37 
 
 8-89 
 
 877 
 8-66 
 
 8-43 
 8-08 
 
 773 
 
 9-30 
 9-18 
 9-06 
 8-82 
 8-46 
 8-08 
 
 969 
 9-56 
 
 9'44 
 9-18 
 8-82 
 8-43 
 
39 
 
 HYGROMETRY 
 
 WET AND DRY BULB HYGROMETER (contd.} 
 GLAISHER'S FACTORS 
 
 Mr. Glaisher, in 1841-5, took many thousands of observations with the wet and dry 
 bulb hygrometer in Greenwich, India, and Toronto, and from simultaneous readings 
 of a Daniell's hygrometer (now recognized as being an untrustworthy instrument) 
 drew up a table of " factors." 
 
 The factor (/) at any dry-bulb reading is defined by 
 
 depression of dew-point = / t dp f(t /,) 
 
 the notation being as above. Glaisher's factors are employed by the Meteorological 
 Office and the Meteorological stations in this country. The hygrometer readings 
 are taken in a Stevenson screen, which is essentially a box with double louvred sides. 
 
 The factors for a range of dry-bulb temperatures are tabulated below. The 
 formula above yields the dew-point; and the saturated vapour pressure at the dew- 
 point gives the actual vapour pressure at t. For a table of saturated vapour 
 pressures, see p. 40. (See "The Observers' Handbook," Meteorological Office.) 
 
 Dry Bulb 
 Temp. (/). 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 - 1O C. 
 O 
 + 10 
 20 
 30 
 
 876 
 
 3-32 
 
 2 '06 
 179 
 1-65 
 
 873 
 
 2-8 1 
 
 2 '02 
 
 177 
 
 1-64 
 
 8-55 
 2-54 
 1-99 
 
 175 
 1-63 
 
 8-26 
 2-39 
 1-95 
 174 
 1-62 
 
 7-82 
 2-31 
 1-92 
 172 
 1-61 
 
 7-28 
 2-26 
 1-89 
 170- 
 i -60 
 
 6-62 
 
 2-21 
 I-8 7 
 I-6 9 
 I'59 
 
 577 
 2-17 
 r8 5 
 r68 
 1-58 
 
 4-92 
 2-13 
 1-83 
 1-67 
 1-57 
 
 4-04 
 
 2*10 
 
 r8i 
 r66 
 1-56 
 
 CHEMICAL HYGROMETER 
 
 The values below are grams of water vapour contained in a cubic metre (io 6 c.cs.) 
 of saturated air at / 60 mms. total pressure. Calculated from Regnault's observations. 
 
 Temp. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 Q 
 
 0C. 
 10 
 2O 
 3O 
 
 4-84 
 
 9'33 
 17-12 
 30-04 
 
 518 
 
 993 
 18 14 
 31-70 
 
 5 54 
 10-57 
 19-22 
 33*45 
 
 5-92 
 11-25 
 20-35 
 
 35 >2 7 
 
 6-33 
 11-96 
 21-54 
 37-18 
 
 6-76 
 1271 
 22-80 
 39^8 
 
 7-22 
 i35o 
 24-11 
 4i-3 
 
 7-70 
 
 14-34 
 25-49 
 
 43-5 
 
 8-21 
 15-22 
 26-93 
 45'8 
 
 876 
 16*14 
 28-45 
 48-2 
 
 TENSILE STRENGTHS OF LIQUIDS 
 
 Liquids perfectly free from air can sustain considerable tension without rupture, 
 e.g. water can withstand a tension of 5 atmospheres, alcohol 12, and strong sulphuric 
 acid 12 atmospheres. Extensions of volume of 08% for water, i'i % for alcohol, 
 and 17% for ether have been obtained. The volume elasticity (p. 29) of alcohol is 
 the same for extension as for compression. (See Worthington, Phil. Trans. A., 
 1892 ; Dixon, Proc. Roy. Dub. Soc., 1909 ; Berthelot, Ami. Chim. Phys., 3O, 1850 ; 
 Poynting and 'I homson's " Properties of Matter.") 
 
 BURSTING STRENGTHS OF GLASS TUBING 
 
 Bursting pressures in atmospheres for German soda glass tubing. Most glass- 
 tubing is in a state of considerable strain, and a factor of safety of not less than two 
 should usually be employed. (Roebuck, Phys. Rev., 1909 ; and Onnes and Braak, 
 Kon. Ak. Wet., Amsterdam, 1908.) Ordinary boiler water-gauge glasses stand 
 between 12 and 24 atmospheres. 
 
 Thickness 
 
 
 
 
 Bore. 
 
 
 
 
 of Wall. 
 
 1 mm. 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 1 mm. 
 2 
 3 
 4 
 
 atmos. 
 
 5/0 
 560 
 
 310 
 
 420 
 450 
 
 280 
 340 
 460 
 
 230 
 
 400 
 400 
 
 220 
 330 
 
 310 
 
 150 
 240 
 
 320 
 
 190 
 
 220 
 230 
 280 
 
40 
 
 VAPOUR PRESSURES 
 
 VAPOUR PRESSURES 
 
 Inter- and Extrapolation of Vapour Pressures. The Kirchhoff-Rankme- 
 Dupre* formula, log p A 4- B/0 + C log 0, where / is the vapour pressure, 6 the 
 absolute temperature, and A, 13, C are constants, is accurate and convenient (e.g. 
 see p. 41). For values of A, B, C, see Juliusburger, Ann. d. Phys., p. 618, 1900. 
 
 Ramsay and Young's Method. If two liquids, one at absolute temperature e 
 and the other at tf', have the same vapour pressure, the ratio 6/0', when plotted 
 against 0, gives a straight line. This method may be used to find roughly the 
 vap. press, of a substance at any temperature when only its boiling-point is known. 
 
 Interpolation by Logarithms. The curve of vapour pressure (/) against 
 temp. (/) is approximately hyperbolic, and thus log p plotted against / gives a 
 graph of slight curvature, which over 10 intervals of / may, for approximate work, 
 be regarded as a straight line : thus the following method of interpolation : 
 Example. Required vap. press, of water at 15, given 
 
 ,0 Jfj* '26i? =1 , 04 = logI27; ,, /atI5 c =I27> 
 
 actually it is I2'8. 
 
 20 C 
 
 VAPOUR PRESSURE OF ICE 
 
 In mms. of mercury at o C. ; g = 980-62 cms. per sec. 2 ; hydrogen (const, vol.) 
 scale of temps. (Scheel, and Heuse, Reichsanstalt Ann. d. Phys., 1909.) 
 
 Temp. . 
 
 Yap. press. 
 
 -50" C. -40 
 
 030 mm. '096 
 
 -30 
 
 288 
 
 -20 C 
 
 784 
 
 -10 
 
 -5 C 
 
 1-963 
 
 3-022 
 
 -2 
 
 3^85 4-579 
 
 (SATURATED) VAPOUR PRESSURE OF WATER 
 
 In mms. of mercury at o C. ; -=980-67 cms. per sec. 2 Thermodynamic 
 scale of temp, (see p. 44). From 20 to o the observations are due to Scheel 
 and Heuse (v. ice); from o to 50, to Thiesen and Scheel ; from 50 to 200, to 
 Holborn and Henning, Reichsanstalt (Ann. d. Phys., 26, 833, 1908). For vapour 
 
 pressures at temps, near 100 see also the table of boiling-points on next page. 
 Vap. press, at- 20 C., -960 mm.; -10 ,2'i6o; -5,3'i7i; -2, 3*958; -1, 4-25 8. 
 
 Temp. 
 
 oc. 
 
 10 
 20 
 30 
 
 40 
 60 
 80 
 
 100 
 
 120 
 140 
 160 
 180 
 
 200 
 
 4-579 
 9-205 
 
 3i-7i 
 
 
 149-2 
 355-1 
 760*0 
 
 1489 
 2709 
 4633 
 75H 
 11647 
 
 4-924 
 9-840 
 18-62 
 33'57 
 
 61-30 
 163-6 
 384-9 
 8I5-9 
 1586 
 2866 
 4874 
 7866 
 
 12142 
 
 5-290 
 10-513 
 1979 
 35'53 
 
 68-05 
 179-1 
 416-7 
 
 875-I 
 1687 
 3030 
 5124 
 8230 
 
 12653 
 
 3 
 
 5-681 
 11-226 
 
 2 1 "O2 
 37-59 
 
 6 
 
 75*43 
 I95-9 
 450-8 
 
 937-9 
 
 1795 
 3202 
 
 384 
 
 6-097 
 11-980 
 22-32 
 39-75 
 
 8 
 
 83-50 
 214-0 
 487-1 
 
 1004 
 1907 
 3j8i 
 5655 
 8999 
 
 6-541 
 12779 
 23-69 
 42-02 
 
 10 
 
 92-30 
 233-5 
 525-8 
 
 1074-5 
 2026 
 3569 
 5937 
 9404 
 
 6 
 
 7'on 
 13-624 
 
 25-I3 
 44-40 
 
 12 
 
 ioi'9 
 
 254-5 
 567'i 
 1149 
 2150 
 
 3764 
 6229 
 
 9823 
 
 14-517 
 
 26-65 
 
 46-90 
 
 14 
 
 112-3 
 277-1 
 6iro 
 
 1227 
 
 2280 
 3968 
 
 6533 
 10256 
 
 8-042 
 15-460 
 28-25 
 
 16 
 
 123-6 
 301-3 
 657-7 
 1310 
 
 2416 
 
 4181 
 
 6848 
 
 10705 
 
 8-606 
 16-456 
 
 29-94 
 52-26 
 
 327-2 
 707-3 
 1397 
 2560 
 4402 
 
 7i75 
 11168 
 
 (Battelli, 1892.) 
 
 Temp. . . 
 
 Vap. Press. 
 
 220 C. 240 260 280 
 
 1 7,380 mm. 
 
 300 320 340 
 
 25.170 3576o i 50,600 ! 67,620 I 88,340 113,830 141,870 
 
 Interpolate logs of vapour pressures as explained above. 
 
41 
 
 VAPOUR PRESSURES 
 
 BOILING-POINT OF WATER UNDER VARIOUS BAROMETRIC 
 
 PRESSURES 
 
 Hydrogen scale of temps. Pressures in mms. of mercury at o C. ; g 980*62 
 cms. per sec. 2 (Regnault's measurements ; reduced by Broch, 1881 ; recalculated 
 by Wiebe, 1893.) 
 
 Barometric 
 Height. 
 
 680 mm. 
 
 690 
 
 700 
 
 710 
 
 720 
 
 730 
 
 740 
 
 750 
 
 760 
 
 770 
 
 780 
 
 96-91 
 97-32 
 97-71 
 98-11 
 98-49 
 98-88 
 
 99'25 
 99-63 
 
 100-00 
 
 100-37 
 100-73 
 
 1 
 
 96-95 97-00 
 36 -40 
 
 98-14 
 
 53 
 
 91 
 
 99-29 
 
 67 
 
 100-03 
 
 40 
 
 76 
 
 79 
 98-18 
 
 57 
 
 '95 
 
 99*33 
 
 70 
 
 3 
 
 97-03 
 '44 
 83 
 
 98-22 
 61 
 '99 
 
 99-37 
 '74 
 100*07 IOOTI 
 
 '44 
 
 80 
 
 47 
 84 
 
 4 
 
 97-07 
 48 
 87 
 
 98-26 
 65 
 
 99-03 
 *4i 
 78 
 
 100-15 
 
 'Si 
 
 87 
 
 97-11 
 52 
 91 
 
 98-30 
 69 
 
 99-07 
 
 '44 
 
 81 
 
 100-18 
 
 '55 
 91 
 
 6 
 
 97-I5 
 50 
 '95 
 
 98-34 
 72 
 
 99-10 
 48 
 85 
 
 100-22 
 
 5 8 
 '94 
 
 97-20 
 
 ;59 
 98-38 
 
 76 
 
 99-14 
 52 
 89 
 
 100-26 
 
 62 
 
 98 
 
 8 
 
 97-24 
 63 
 
 98-03 
 42 
 80 
 
 99-18 
 56 
 '93 
 
 100-29 
 66 
 
 loroi 
 
 9 
 
 97-28 
 67 
 
 98-07 
 *45 
 84 
 
 99-22 
 
 59 
 96 
 
 100-33 
 69 
 
 101-05 
 
 VAPOUR PRESSURE OF MERCURY 
 
 In mms. of mercury at o C. Reduced from the observations of Hertz, Ramsay and 
 Young, Callendar and Griffiths, Pfaundler, Morley, Gebhardt, Cailletet, Colardeau, 
 Riviere. For interpolation from 1 5 to 270. 
 
 log/ = 15-24431 - 3623-932/0 - 2-367233 log e (A) 
 
 From 270 to 450 
 
 log/ = 1004087 - 3271-245/0 - 7020537 log e 
 ^ at the boiling-point = 13-6 mm. per degree (Laby, Phil. Mag., Nov., 1908). 
 
 Vap. 
 Tem P- Press. 
 
 mm. 
 
 C. -00016* 
 
 5 -00026* 
 
 10 -00043* 
 
 15 -00069 
 
 20 -00109 
 
 Vap. 
 Tem P- Press. 
 
 25 
 
 30 
 
 35 
 
 40 
 
 50 
 
 mm. 
 00l68 
 00257 
 00387 
 
 00574 
 0122 
 
 Temp. 
 
 Vap. 
 Press. 
 
 60 C 
 
 80 
 
 100 
 
 150 
 
 200 
 
 -0246 
 0885 
 276 
 
 2-88 
 
 17-81 
 
 Temp. 
 
 250 
 
 300 
 
 356-7 
 
 400 
 
 450 
 
 Vap. 
 
 Press. 
 
 248*6 
 760 
 566 
 | 3229 
 
 Temp. 
 
 Vap. 
 Press. 
 
 atmos. 
 
 500 8 
 
 600 22-3 
 
 700 50 
 
 800 102 
 
 880 162 
 
 * Extrapolated by formula A. 
 
 VAPOUR PRESSURE OF ETHYL ALCOHOL 
 
 Vap. press, in mms. of mercury at o C. Calculated by Bunsen from Regnault's 
 results (1862), which are in good agreement with the mean of those of Ramsay and 
 Young (1886), and Schmidt (1891). 
 
 Regnault, Vapour press, at -20, 3-34 mm.; at -10, 6-47 mm. 
 
 Temp. 
 
 0C. 
 10 
 20 
 30 
 
 12-73 
 24-08 
 44-0 
 78-4 
 
 13-65 
 
 25'59 
 46-7 
 
 27-19 | 
 
 15-59 
 28-9 
 
 49-5 ! 52-5 
 
 4 
 
 16-62 
 3o-7 
 
 557 
 
 i7'7 
 32-6 
 59'o 
 
 6 
 
 18-84 
 
 34'6 
 
 62-5 
 
 20*04 
 16-8 
 
 8 
 
 21-31 
 
 39-0 
 
 70-1 
 
 22-66 
 
 41-4 
 
 (Ramsay and Young, 1886.) 
 
 Temp. 
 Press. 
 
 30 C. ! 40 50 I 60 C 
 
 78-1 mm.' 133-4 219-8 350-2 
 
 70 C 
 
 80 C 
 
 54i 
 
 812 
 
 100 
 
 1692 
 
 120 
 
 3220 
 
 140 
 
 5670 
 
 160 
 
 9370 
 
 Interpolate logs of vapour pressures as explained on p. 40. 
 
42 
 
 VAPOUR PRESSURES 
 
 VAPOUR PRESSURES OF ELEMENTS 
 
 / = vapour pressure in mms. of mercury at o C. lat. 45 and sea-level (g - 980-62) (i.e. 
 i mm. Hg = 1333*2 dynes per sq. cm.). If followed by at., p is in atmospheres; 6 = absolute 
 temp. (A.) ; / = temp, in C. ; (j) solid ; (/) liquid. The thermometry is in many cases somewhat 
 dubious. 
 
 Interpolate logs of vapour pressures as explained on p. 40. 
 
 Argon .... 
 
 (Olszewski, 1895) 
 
 Argon 
 
 Krypton . . . . 
 Xenon . . . 
 (Ramsay & Travers) 
 
 Bromine 
 
 (Ramsay & Young, 1886) . 
 
 Chlorine 
 
 (Knietsch, 1890). . . . 
 
 Iodine (Baxter, Hickey, 
 & Holmes, 1907) . . . 
 
 Hydrogen (Travers & 
 Jaquerod, 1902) . . . . 
 
 Helium . . 
 
 (Onnes, 1908) 
 
 Mercury .... 
 
 Nitrogen (Baly, 1900 
 Fischer & Alt., 1902) 
 
 Oxygen (Jaquerod, Travers, 
 & Center, 1902) . . . 
 
 Phosphorus .... 
 
 (Schrotter, 1848) . . 
 
 Sulphur ( Ruff & Graff, '08 
 13., 1899; C., 1899) . 
 
 -121 C. - 
 
 50-6 at. 
 
 78'9 A. 
 110-5 A. 
 0148 c -9 A. 
 
 E> 300 mm. 
 
 t -16-6 C. 
 
 ? 20 mm. 
 
 ? 62-5 mm. 
 
 6c. 
 
 03 mm. 
 
 t-258-2C. 
 
 p IOO mm. 
 
 128-6 
 
 38-0 
 
 86-9 
 1213 
 163-9 
 
 760 
 
 120 
 30 
 -60 
 
 210 
 
 16~ 
 
 131 
 
 2567 
 
 200 
 
 -129-6 
 
 35-8 
 
 97-9 
 135-2 
 182-9 
 
 2000 
 
 -5-0 
 
 50 
 
 -40 
 
 560 
 
 30 
 
 469 
 
 2557 
 
 300 
 
 4 C '5A. 
 
 760 mm. 
 
 See p. 41. 
 
 0|1>2 -5A. 
 
 86 mm. 
 fl 79 1 A. 
 
 -134-4 -135-1 -136-2 
 29-8 29-0 27-3 
 
 107-3 155-6 = crit. 
 
 147-3 210-5 
 199-6 
 
 40,200 41,240 
 
 16 9 234 
 
 150 200 
 
 -20 
 
 I -84 at. 3-66 
 
 85 117 
 
 2O IOO 
 
 -255-0 -254-3-253-7 
 
 400 500 600 
 
 - I Neon (Travers 
 I & Jaquerod, '02) 
 
 I Ra. Emanation | 
 
 4000 
 8-2 
 
 IOO 
 
 -33-6 
 
 760 
 
 55 
 
 3-08 
 
 -138-3 -1391 
 
 25-3 23-7 
 temp. 
 
 = crit. temp. 
 287'8 = crit. temp 
 
 40-5 519 
 
 400 600 
 
 10 20 
 
 4-95 6-62 
 
 137 160 9 
 
 200 400 
 
 -253 2 -252 9 
 
 700 760 
 
 15-65A.(j)204(jn He 
 2'4 mm. 12-8 /Scale 
 
 | See p. 103. 
 
 587 
 
 760 
 
 30 
 
 8-75 
 
 185 3 
 
 760 
 
 H. Scale" 
 
 165 C. 
 
 1 20 mm. 
 
 50 C. 
 
 "0003 mm. 
 
 67-8 
 200 
 
 821 
 
 300 
 
 170 
 
 U3 
 
 100 
 
 0089 
 
 72-4 
 
 400 
 
 84-4 
 
 400 
 
 180 
 
 204 
 
 147 
 192 
 
 77-3 
 
 760 
 
 86-3 
 
 500 
 
 200 
 
 266 
 
 211 
 
 3-I4 
 
 80 
 1013 
 
 879 
 
 600 
 
 209 
 
 339 
 
 400 
 
 c. 372 
 
 83 
 
 1386 
 
 89-3 
 
 700 
 
 219 
 
 359 
 
 444-5 
 
 760 
 
 86 
 
 1880 
 
 901 
 
 760 
 
 226 
 
 393 
 
 89 
 
 2465 
 
 90-6 
 
 800 
 
 230 
 
 91 
 
 2916 
 
 11. Scale 
 
 2873 
 
 760 
 
 8t/5p = o'O9/mm. near 
 B.P. (see p. 50). 
 
 VAPOUR PRESSURES OF COMPOUNDS 
 
 For a complete list, see Schenck in L.B.M. 
 
 Hydrochloric acid 
 | (F., 1845 ; Ansdell, 
 
 '1880)! 
 
 t -73-3C. 
 5 1-8 at. 
 
 -45-5 
 
 6'3 
 
 -15 
 
 6-84 
 
 -233 
 12-8 
 
 -5 
 
 9'3 
 
 -39 
 
 23-1 
 
 
 
 10-8 
 
 40 
 
 29-8 
 
 10 
 
 14-3 
 10 
 
 2-26 
 
 9-2 
 
 33-9 
 30 
 
 237 
 20 
 
 3-24 
 
 138 
 
 37-7 
 
 50 
 
 36-6 
 
 30 
 
 4-52 
 
 220 
 
 457 
 60 
 44'4 
 
 40 
 
 6-15 
 
 334 
 
 58-8 
 
 70 
 
 53'i 
 50 
 
 8-19 
 
 Sulphuretted hydrogen . 
 ; (R., 1862) 
 
 t -25 C. 
 ? 4'93 at. 
 
 
 
 Sulphur dioxide .... 
 
 (Regnault, 1862) . . . 
 
 -30 C. 
 
 *39 at. 
 
 -20 
 
 63 
 
 -776 
 
 44-1 
 
 -10 
 
 TOO 
 
 
 
 i'53 
 
 Ammonia, NH 3 . . . . 
 (Brill, 1906) ..... 
 
 -80 C. 
 
 35 '2 mm. 
 
 -70-4 
 
 74'9 
 
 -64-4 
 116-0 
 
 ~20~ 
 
 23-1 
 
 -60-8 
 
 157-6 
 
 -54-4 
 
 239-5 
 
 36-1 
 
 -462 
 
 403-5 
 
 10 
 
 44-8 
 
 -398 
 
 568-2 
 
 20 
 
 55'3 
 
 -330 
 
 761 
 
 40 
 
 83-4 
 
 Nitrous oxide, N 2 O 
 
 (Cailletct, '78; R., 
 
 ''62) .' 
 
 -80 C. 
 
 i -9 at. 
 
 60 
 
 5^5 
 
 -40 
 iro 
 
 -10 
 
 28-9 
 
 Nitric oxide, NO 
 (Olszewski, 1885) 
 
 -176'5 C C 
 024 at. 
 
 . -167 
 
 182 
 
 -138 
 
 5*4 
 
 -129 
 
 10-6 
 
 -119 
 
 200 
 
 -110 
 
 31-6 
 
 -105 
 
 41-0 
 
 1009 
 49-9 
 
 -975 
 
 57-8 
 
 I Nickel carbonyl, NiCO 4 . 
 (D. & Jones, 1903). . . 
 
 t -9 C. 
 > 94- 3 mm. 
 
 -7 
 
 104-3 
 
 -2 
 
 129-1 
 
 
 
 I44-5 
 
 10 
 
 215 o 
 
 16 
 
 283-5 
 
 20 
 
 329-5 
 
 30 
 
 462 
 
 
 
 
 Interpolate logs 
 
 of vapour pressures as 
 
 explained on p. 
 
 40. 
 
 
 i 
 
43 
 
 VAPOUR PRESSURES 
 
 VAPOUR PRESSURES OF COMPOUNDS (contd.} 
 
 Interpolate logs of vapour pressures as explained on p. 40. 
 
 Carbon dioxide . . . 
 
 (Zeleny & Smith, 1906) . 
 
 Carbon bisulphide . . . 
 
 (Regnault, 1862) . . . 
 
 2-5 mm. 
 
 119 
 
 657' 
 
 -65 (s) 
 
 2100 
 
 -56-4t-65(/) 
 
 3910 2508 
 
 40(/) 
 7510 
 
 14,830 
 
 -10 (/) 
 19,630 
 
 -20 C. 
 
 > 47*3 mm. 
 
 -10 
 
 79'4 
 
 
 
 128 
 
 10 
 
 198 
 
 20 
 
 298 
 
 40 
 
 618 
 
 60 
 
 1164 
 
 80 
 
 2033 
 
 100 
 
 3325 
 
 Chloroform, CHC1 3 . . . 
 (Regnault, 1862). . . . 
 
 20 C. 
 
 ) 160-5 mm. 
 
 -20 C. 
 
 > 9-8 mm. 
 
 -90 C. (s) 
 
 -69 at. 
 
 30 
 
 248 
 
 -10 
 
 18-47 
 -85 (s) 
 
 I'OO 
 
 
 
 26-5 
 
 1194 
 
 IOO 
 
 40 
 
 369 
 
 
 
 32-9 
 
 -81 
 
 1-25 
 
 10 
 
 45'4 
 
 50 
 
 535 
 10 
 
 56 
 
 -70 
 
 2-22 
 
 20 
 
 74-6 
 
 60 
 
 755 
 20 
 91 
 -50 
 
 5'3 
 
 70 
 
 1042 
 
 40 
 
 215 
 
 -23-8 
 
 13-2 
 
 80 
 
 1408 
 
 60 
 
 447 
 
 
 
 26-05 
 
 80 
 754 
 1750 
 600 
 
 90 
 
 1865 
 
 80 
 
 843 
 
 100 
 
 2429 
 
 Carbon tetrachloride, CC1 4 
 (R., 1862) 
 
 100 
 
 1467 
 
 Acetylene, C 2 H 2 .... 
 (Villard, 1895) .... 
 
 202 
 
 42-8 
 
 365 
 
 6r6(M.) 
 
 Benzene, C 6 H 6 .... 
 (Youn ? , 1889) .... 
 
 -10 C. 
 
 > 14-8 mm. 
 
 ) 50 mm. 
 
 40 
 
 181-1 
 
 60 
 
 389 
 
 100 
 
 1344 
 
 1808 
 700 
 
 120 
 
 2238 
 
 Aniline, C 6 H 5 NH 2 . . . 
 (Kahlbaum, 1898) . . . 
 
 138-7 
 
 200 
 
 151-5 
 
 300 
 
 1611 
 
 400 
 
 168-7 
 
 500 
 
 183-9 
 
 760 
 
 Bronmaphthalene . . . 
 C 10 H 7 Br (Ra. & Y., 1885) 
 
 ; 215 C. 
 ) 158-9 mm. 
 
 220 
 
 181-8 
 
 230 
 
 236-0 
 
 240 
 
 303 '4 
 
 250 
 
 386-4 
 
 260 
 
 487-4 
 
 270 
 
 608-8 
 
 275 
 
 677-9 
 
 2804 
 
 760 
 
 Me. alcohol, CH 3 OH . . 
 (R.,'62;Ra.&Y. ;Ri.,'86) 
 
 t -10 C. 
 ) 14*8 mm. 
 
 
 
 28-5 
 
 17 
 
 78-3 
 
 20 
 
 88-7 
 
 30 
 
 150 
 
 50 
 
 80 
 
 1238 
 
 120 
 
 4342 
 
 150 
 
 9361 
 
 n.propyl alcohol, t,C 3 H. OH 
 (Ra. & Y. ; S. ; Ri., '86) . 
 
 ; 0C. 
 3 3-9 mm. 
 
 10 
 
 7-8 
 
 17 
 12-4 
 
 30 
 
 28-2 
 
 40 
 
 60 
 
 157 
 
 80 
 
 389 
 
 100 
 
 843 
 
 120 
 
 1668 
 
 Iso-butyl alcohol f . . . 
 C 4 H OH(Ri.,'86; S., '91) 
 
 t 10 C. 
 
 > 4' I mm. 
 
 17 
 
 6-8 
 
 20 
 
 8-1 
 
 40 
 
 60 
 
 94-2 
 
 80 
 
 245 
 
 100 
 
 569 
 
 100 
 
 234 
 
 108 
 
 760 
 
 120 
 522 
 
 120 
 
 H95 
 
 Iso-amyl alcohol t . . . 
 C 5 H H OH(Ri., '86; S.,'9i) 
 
 c 17 C. 
 
 ) 178 mm. 
 
 30 
 
 4-68 
 
 40 
 
 9'33 
 
 50 
 
 17-4 
 
 60 
 
 32-0 
 
 80 
 93'3 
 
 130 
 
 Formic acid,f CH 2 O 2 . . 
 (S., 1891 ; K., 1898) . . 
 
 t 0C. 
 ) IO'2 mm. 
 
 10 
 
 18-4 
 
 30 
 
 2O'6 
 
 17 
 
 26-3 
 
 50 
 
 56-2 
 
 20 
 
 31-6 
 
 30 
 
 40 
 
 79'4 
 
 70 
 
 266 
 
 80 
 
 373 
 
 101 
 
 760 
 
 Acetic acid, f C,H 4 Oo . . 
 (Ra.Y.;Ri.,'86; S",'9i) 
 
 t 17 C. 
 
 p 9-8 mm. 
 
 70 
 
 133 
 
 90 
 
 288 
 
 110 
 
 582 
 
 130 
 10:8 
 
 150 
 
 1847 
 
 200 
 
 5905 
 
 Propionic acid,f C 3 H 6 Oo . 
 (Ri., '86 ; S., '91 ; K., '98) 
 
 t 15 C. 
 
 ) i -7 mm. 
 
 17 
 
 2'O 
 
 20 
 
 30 
 
 4'9 
 
 40 
 
 9-1 
 
 60 
 
 28-2 
 
 70 
 
 46-1 
 
 80 
 
 74'5 
 
 140 
 
 760 
 
 Butyric acid,t C 4 H 8 O 2 . 
 (Ra. & Y., '86; S. '91 ; K. '94) 
 
 t 17 C. 
 p -52 mm.* 
 
 r 17 c. 
 
 p -88 mm.* 
 
 t -20 C. 
 
 ) 67-7 mm. 
 
 20 
 
 66* 
 
 30 
 
 1-9 
 
 10 
 
 117-6 
 
 30 
 
 i '4 
 
 50 
 
 8-2 
 
 195 
 
 50 
 
 70 
 
 25-1 
 10 
 
 3C9 
 
 70 
 
 16-2 
 
 90 
 
 67-6 
 
 20 
 
 476 
 
 90 
 
 44*9 
 
 110 
 
 162 
 
 40 
 1029 
 
 110 
 
 in 
 
 130 
 
 347 
 
 60 
 
 1990 
 
 80 
 361 
 
 130 
 
 245 
 
 150 
 
 684 
 
 80 
 
 3497 
 
 150 
 
 497 
 
 153-5 
 
 760 
 
 100 
 
 5782 
 
 Iso-butyric acid,t C 4 H 8 O 2 
 1 (Ri.,'86;S.,'9i; K., '94) 
 
 Methyl formate t . . . 
 CHO 2 CH 3 (Y. &T., '93) . 
 
 Methyl butyrate f . . . 
 i C 4 H 7 2 .CH 3 (Y.&T.,' 93 ) 
 
 t -10 C. 
 p 3-55 mm. 
 
 
 7'3 
 
 10 
 
 13-8 
 
 20 
 
 24-5 
 
 40 
 
 69-2 
 
 60 
 
 167-5 
 
 100 
 
 701 
 
 
 
 Methyl isobutyrate t . . 
 
 C 4 H 7 O 2 .CH 3 (Y.&T., '93) 
 
 t -10 C. 
 
 5 6*22 mm. 
 
 
 
 12-15 
 
 10 
 
 22-4 
 
 20 
 
 38-9 
 
 40 
 
 1047 
 
 60 
 
 244 
 
 80 
 
 505 
 
 100 
 
 956 
 
 120 
 
 1660 
 
 Ethyl acetate f . . . . 
 C 2 H 3 2 .C 2 H 5 (Y.&T.,' 93 ) 
 
 t -20 C. 
 
 [> 6'5 mm. 
 
 -10 
 
 12-9 
 
 
 
 
 
 24-3 
 
 10 
 
 42-7 
 
 20 
 
 72-8 
 
 40 
 
 186 
 
 60 
 
 1 88-0 
 
 60 
 
 80 
 
 833 
 100 
 
 785 
 
 100 
 
 1515 
 
 120 
 
 1388 
 
 Ethyl propionate f . . . 
 C 3 H 5 2 .C 2 H 5 (Y.&T.,' 93 ) 
 
 t -10 C. 
 p 4-05 mm. 
 
 10 
 
 15-5 
 
 20 
 
 27-7 
 
 40 
 
 77'9 
 
 80 
 
 403-6 
 
 Propyl acetate t . . . . 
 i C 2 H 3 2 -C 3 H 7 (Y.&T.,'93) 
 
 t -10 C. 
 
 p 3*6 mm. 
 
 
 
 7 '4 
 
 10 
 
 '3*9 
 
 20- 
 
 25-1 
 
 40 
 
 70-8 
 
 60 
 172 
 
 80 
 
 373 
 
 JOO 
 
 724 
 
 120 
 
 1288 
 
 Ethyl ether, (C 2 H 5 ) 2 O 
 (Young, 1910) .... 
 
 t| -10 C. 
 
 P,II2'3 
 
 
 
 184-9 
 
 10 
 
 2QO-8 
 
 20 
 
 4398 
 
 40 
 
 921 
 
 60 
 
 1734 
 
 80 
 
 2974 
 
 100 
 
 4855 
 
 193-811 
 
 27,060 
 
 Interpolate logs 
 
 of vapour pressure as 
 
 explained on p. 
 
 40. 
 
 
 
 * Extrapolated, 
 t The vapour pressures here given have been graphically interpolated 
 Bodenstein ; C., Callendar ; D., Dewar ; F., Faraday ; K., Kahlbaum ; 
 Ra. and Y., Ramsay and Young ; Ri., Richardson ; i>., Schmidt ; Y. and 
 \ Triple point. || Critical temp. 
 
 from the observers' values. B., 
 M., Mackintosh; R., Regnault; 
 T., Young and Thomas. 
 
44 
 
 GAS THERMOMETRY 
 
 GAS THERMOMETRY 
 
 The standard thermometric scale of the International Committee of Weights 
 and Measures (1887) is that of the constant-volume hydrogen thermometer, the 
 hydrogen being taken at an initial pressure at o C. of 1000 mms. of mercury 
 measured at o C. sea-level and lat. 45 (= i'3i58 standard atmosphere). 
 
 THERMODYNAMIC TEMPERATURE OF THE ICE-POINT 
 
 Method. 
 
 From Joule-Thomson effect 
 Extrapolation to zero pressure 
 (see p. 54) 
 From Joule-Thomson effect 
 
 273-07 
 
 273-05 
 273-06 
 
 273-09 
 273-09 
 
 (273'I7) 
 273-25 
 273-14 
 
 Air. 
 
 273-19 
 273-27 
 
 C0 2 
 
 273-05 
 
 273-10 
 273-12 
 
 Computer. 
 
 Callendar, 1903 
 Berthelot and 
 
 Chappuis, 1907 
 Berthelot, 1907 
 Buckingham, 1908 
 Rose-Innes, 1908 
 
 General mean = 273- 13. 
 
 THERMODYNAMIC CORRECTIONS TO GAS SCALES OF TEMPERATURE 
 
 The corrections to both the constant-pressure (C.P.) and the constant-volume 
 (C.V.) scales are either (i) derived from characteristic equations of state (Callendar, 
 1903 ; Berthelot, 1907), or (2) in the case of the C.P. thermometer, computed from 
 the Joule-Thomson effect ; whence from these C.P. corrections and a knowledge of 
 the compressibility of the gas under different conditions the C.V. corrections can 
 be calculated. Chappuis (1907)* has experimentally compared the C.P. and C.V. 
 H. and N. thermometers each with mercury thermometers. The values below 
 are based on computations by Callendar (Phil. Mag., 1903), Berthelot* (from 
 Chappuis' data 1907), Onnes and Braak (1907 and 1908), Rose-Innes (Phil. Mag., 
 1908), and Buckingham (1908). t There is some divergence among the different 
 computations for hydrogen ; the agreement is much better in the case of nitrogen. 
 The thermodynamic correction to the C.V.H. thermometer is negligible, and with 
 nitrogen also at extreme temps, the correction is less than the error of working in 
 modern gas thermometry. The values for air are a little smaller than for nitrogen ; 
 for helium they are slightly larger than for hydrogen except at the lowest tempera- 
 tures, when the helium corrections are the smaller. New experiments on the Joule- 
 Thomson effect are needed, t ( + ) means that the correction has to be added to the 
 gas scale temperature to give the thermodynamic temperature. The correction is 
 proportional to the initial pressure of the gas in the thermometer. 
 
 * Trav. et Mem. Bureau Intl. 1907. t Bull. Bureau of Standards. 
 
 1 See Dalton, Proc. Konink. Akad. IVeten. Amsterdam^ April, 1909. 
 
 [908. 
 
 240 
 
 200 
 
 150 
 
 100 
 
 50 
 
 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 Const. Pressure Const. Volume 
 P = 1000 mm. ' P at = 1000 mm. 
 
 + -26 
 
 + -io 
 
 + -04 + -40 
 
 f -02 |+ *I2 
 
 
 
 -ooi ! -009 
 
 -002 -017 I "000 
 
 -003 '021 ! '001 
 
 - -003 - -023 I - -ooi 
 
 '003 -024 -ooi 
 
 '003 '022 -001 
 
 + -06 
 
 + *033 
 
 4- 'oio 
 
 + -005 
 
 -ooo 
 
 , 
 
 -os 
 
 -OO2 
 '004 
 "005 
 '006 
 -007 
 -006 
 
 tC. 
 
 70 
 
 80 
 
 90 
 
 100 
 
 200 
 
 300 
 
 400 
 
 450 
 
 600 
 
 800 
 
 1000 
 
 1200 
 
 Const. Pressure Const. Volume 
 P = 1000 mm. P at 0^ = 1000 mm. 
 
 003 i 
 
 002 ! 
 'OOI 
 
 
 
 '014 i 
 '034 i 
 07 (?) 
 
 "014 
 -Q 007 
 
 + -12 
 
 + '28 
 + -46 
 
 + I? 
 
 + 2-3 
 
 H, 
 
 -ooo 
 
 "OOO 
 
 
 
 + -004 
 
 + 'Oil 
 
 N 2 
 
 + -02 (?) 
 
 -"004 
 
 - '003 
 
 'OO2 
 
 
 
 + -04 ; 
 
 + '10 I 
 
 + -17! 
 
 + '19 I 
 
 + "5 
 + -7 
 -fro 
 
45 
 
 MERCURY THERMOMETRY 
 
 MERCURY THERMOMETRY 
 
 CORRECTIONS TO REDUCE MERCURY-IN-GLASS SCALE TEMPS. TO GAS SCALE TEMPS. 
 
 The values for the English Kew glass (which is a lead potash silicate) are due 
 to Harker (1906) ; the verre dur correciions are given by the International Bureau ; 
 those for the Jena glasses by Grutzmacher. The method at Kew is to determine 
 the ice-point correction before an observation is made. The other glasses have 
 their ice-point or zero depressions determined immediately after each temperature 
 reading. See Guillaume's "Thermometrie de Precision." Paris, 1889, and Chree's 
 "Notes on Thermometry," PhiL Mag. t 1898. The French glass, verre dur, is 
 used by Tonnelot of Paris. The normal glass, Jena 16'", may be known by the 
 presence of a thin violet line near the surface. Jena 59'" is a borosilicate (p. 74). 
 
 Temp. 
 
 -20 
 
 10 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 100 
 
 Kew Glass. 
 
 
 
 'OO 
 
 oo 
 
 +005 
 
 -f -oi 
 + 01 
 + 01 
 + 015 
 
 + 02 
 
 +025 
 
 
 Verre Dur. 
 
 '10 
 
 -II 
 
 -io 
 
 -09 
 -07 
 -05 
 
 Jena 16'". 
 
 
 
 -06 
 -09 
 *n 
 
 -12 
 'II 
 *IO 
 '08 
 '06 
 
 Jena 59'" 
 
 59'" 
 
 
 
 'O2 
 -04 
 '04 
 '04 
 
 -03 
 
 -02 
 -01 
 '00 
 '00 
 
 
 
 Temp. 
 
 110 
 
 120 
 
 130 
 
 140 
 
 150 
 
 160 
 
 170 
 
 180 
 
 190 
 
 200 
 
 250 
 
 300 
 
 Verre Dur. 
 
 *w ~ * \7 r* 
 
 +-o 4 
 + -06 
 + -07 
 + '07 
 + -06 
 + -03 
 o 
 
 - '04 
 
 - -09 
 
 Jena 16 
 
 ^N - '16" 
 
 -05 
 -07 
 -09 
 
 -08 
 
 -06 
 
 '02 
 '04 
 '63 
 
 Jena 59' 
 
 - 
 
 oo 
 
 'O2 
 -04 
 
 '39 
 
 . 
 
 17 
 4-1 
 
 DEPRESSION OF ZERO OF MERCURY THERMOMETERS 
 
 The values indicate the zero depressions after the thermometer has been heated 
 to the temp, stated. They have been determined by Guillaume, Thiesen, Schloesser, 
 and Bottcher because of the impossibility in practice of interrupting a series of 
 temperature measurements to take a number of zero readings (see above). 
 
 Temp. 
 
 10 C. 
 
 20 
 
 30 
 
 40 
 
 50 
 
 Verre Dur. Jena 16'". Jena 69'". 
 
 '008 
 017 
 027 
 037 
 048 
 
 on 
 017 
 
 024 
 031 
 
 "005 
 009 
 014 
 017 
 
 021 
 
 Temp. 
 
 60 C. 
 70 
 80 
 90 
 100 
 
 Verre Dur. ] Jena 16'". 
 
 Jena 59'", 
 
 -o6o 
 071 
 084 
 097 
 in 
 
 '039 
 048 
 
 057 
 066 
 077 
 
 024 
 027 
 030 
 033 
 035 
 
 STEM-EXPOSURE OR EMERGENT-COLUMN CORRECTION 
 
 The table below gives the (additive) "stem-exposure" correction for (i) the 
 ordinary solid-stem thermometer, and (2) the German pattern sleeve-thermometer, 
 which has a fine capillary in an outer glass tube. Both thermometers are of Jena 
 glass, with degree intervals about I mm. long. 
 
 / is the indicated temperature, and faux the temperature of an auxiliary thermo- 
 meter whose bulb is io cms. from and on a level with the mid-point of the exposed 
 stem. The auxiliary thermometer must be shielded from the source of heat. (See 
 Watson's " Practical Physics," and Rimbach, Zeit.f. Insf., 10, 1890.) 
 
 No. of 
 degree 
 divs. of 
 exposed 
 thread. 
 
 10 
 
 20 
 
 30 
 
 40 
 
 60 
 
 80 
 
 100 
 
 120 
 
 Solid Stem ; Scale on Stem. I Sleeve Thermometer; Enclosed Scale 
 
 t taux 
 
 70 C. 80 100 120 140 180 70 C. 
 
 u '02 
 
 13 
 
 24 
 
 '35 
 
 '57 
 
 80 
 
 I '02 
 
 -03 
 '15 
 
 28 
 HI 
 
 66 
 91 
 
 [18 
 
 -o 7 
 
 '22 
 
 '39 
 
 56 
 
 8 9 
 
 I'2I 
 
 I- 5 6 
 
 1-98 
 
 U.j, 
 
 29 
 
 48 
 
 68 
 1-09 
 1-52 
 1-97 
 2*43 
 
 38 
 
 59 
 
 82 
 
 1-25 
 
 1-71 
 
 2'l8 
 2-6 9 
 
 '2 7 
 
 78 
 I '04 
 I-58 
 2-15 
 270 
 
 '01 
 08 
 25 
 30 
 52 
 
 98 
 
 'OI 
 12 
 28 
 
 35 
 60 
 
 87 
 
 1*12 
 
 100 120 140 180 
 
 04 
 19 
 
 '79 
 
 25 
 
 42 
 
 60 
 
 99 
 
 1-38 
 
 1-82 
 
 2-28 
 
 28 
 
 48 
 
 67 
 
 I'll 
 
 2-03 
 2-49 
 
 4 
 
 66 
 
 92 
 -46 
 
 3-I3 
 
 No. of 
 degree 
 divs. of 
 exposed 
 thread. 
 
 10 
 
 20 
 
 30 
 
 40 
 
 60 
 
 80 
 100 
 120 
 
46 
 ELECTRICAL THERMOMETRY 
 
 PLATINUM THERMOMETRY 
 
 TO REDUCE PT-SCALE TEMPS. ('//) TO CONST. VOL. N-SCALE TEMPS. (0 
 
 Calendar's "difference formula "for the difference between the nitrogen-scale 
 temp. (/) and the Pt-scale temp, (tpf) is ttpt 8 /(/ ioo)io~ 4 , where 5 is close to 1-5. 
 Pt-scale temps, result from assuming a linear relation R/^ = R,,(i 4- o-tpt) between 
 temp, and the electrical resistance (R)of Pt ; a is the mean coefficient for the range 
 o to ioo. The " difference formula " gives the correction yielded by the truer 
 parabolic relation R/ = R (i -f a/ + J8/ 2 ). Pt thermometers should not be used 
 above i2ooC. (See Callendar, Phil. Mag., 1899, 1, p. 191 ; 2, p. 519, Camb. Sci. 
 Inst. Co.'s list "Technical Thermometry ; " and (for bibliography), Waidner and 
 Burgess, Bull. Bur. of Standards, 1909.) 
 
 8 = 1-50. (Marker, Phil. Trans., 1904.) 
 
 Pt Temps. 
 tpt. 
 
 
 
 20 
 
 40 
 
 60 
 
 80 
 
 100 
 
 120 
 
 140 
 
 160 
 
 180 
 
 
 r 
 
 t 
 
 r 
 
 t 
 
 * 
 
 t 
 
 r 
 
 t 
 
 f 
 
 t 
 
 -200 
 
 
 
 -i72- 9 
 
 -iS4'i 
 
 
 -u6-2 
 
 -97 c 'i3 
 
 -77"9 2 
 
 -58-6i 
 
 -39'i8 
 
 -i9-65 
 
 
 
 J 
 
 19-76 
 
 39*64 
 
 59*64 
 
 79-76 
 
 100 
 
 120-4 
 
 140-9 
 
 i6i'5 182-3 
 
 + 200 
 
 203-1 
 
 224-2 
 
 245-4 
 
 266-7 
 
 288-1 
 
 309*8 
 
 331-5 
 
 353-4 
 
 375-5 397*8 
 
 400 
 
 420*2 
 
 442-8 
 
 465-5 
 
 488-5 
 
 511-6 
 
 534*9 
 
 
 582-1 
 
 606 - o 630 'i 
 
 600 
 
 654'4 
 
 679-0 
 
 703-7 
 
 728-7 
 
 754-o 
 
 779*4 
 
 805-2 
 
 831-2 
 
 857-4 884-0 
 
 800 
 
 910-8 
 
 937'9 
 
 
 
 IO2I 
 
 1050 
 
 1078 
 
 1107 
 
 i U7 
 
 1167 
 
 1000 
 
 1197 
 
 1228 
 
 1259 
 
 1290 
 
 1323 
 
 1355 
 
 
 
 
 
 
 
 
 TO CALCULATE THE CHANGE At IN THE N-SCALE TEMP, (t) FOR A CHANGE OF +'01 IN 5 
 
 t 
 
 At 
 
 f 
 
 At 
 
 t 
 
 At 
 
 t At 
 
 t 
 
 At 
 
 t 
 
 At 
 
 -200 
 
 -o6o 
 
 -60 
 
 'OIO 
 
 80 
 
 'OO2 
 
 250 '038 
 
 600 
 
 '3o 
 
 950 
 
 o.g 
 
 -180 
 
 -050 
 
 -40 
 
 006 
 
 100 
 
 
 
 300 -060 
 
 650 
 
 36 
 
 1000 
 
 '9 
 
 -160 
 
 042 
 
 -20 
 
 002 
 
 120 
 
 'OO2 
 
 350 -088 
 
 700 
 
 42 
 
 1050 
 
 'O 
 
 -140 
 
 034 
 
 
 
 
 
 140 
 
 006 
 
 400 -120 
 
 750 
 
 "49 
 
 1100 
 
 j 
 
 -120 
 
 026 
 
 20 
 
 002 
 
 160 
 
 'OIO 
 
 450 -158 
 
 800 
 
 
 1150 
 
 2 
 
 -100 
 
 '020 
 
 40 
 
 '002 
 
 180 
 
 014 
 
 500 -20 
 
 850 
 
 "64 
 
 1200 
 
 "3 
 
 -80 
 
 014 
 
 60 
 
 '002 
 
 200 
 
 *O2O 
 
 550 -25 
 
 900 
 
 72 
 
 1250 
 
 *4 
 
 HIGH TEMPERATURES 
 
 (See Le Chatelier's " High Temperature Measurements ; " Waidner and Burgess, 
 Bull. Bureau of Standards, 1905 and 1907 ; Harker, Science Progress, 1911.) 
 
 For the measurement of high temperatures (say above 1200 C, which is about 
 the present upper experimental limit of the gas scale) the instruments in general 
 use are thermo-j unctions and optical or radiation pyrometers. Both involve extra- 
 polation. Thermo-couples have been used up to the temperature of the melting- 
 point of platinum (c. 1750). At high temperatures thermo-junctions yield rather 
 lower results than do optical pyrometers, e.g. see the M.P.'s of Pd and Pt on p. 49. 
 
 THERMO-ELEOTRIC THERMOMETRY 
 
 Temperature readings with thermo-couples are reduced by one of the 
 formulae : (a) E = a + bt + <r/ 2 , (b} E = mt n , or E = n log / + m , E being the 
 e.m.f. generated, and / the temperature of the hot junction, the cold junction 
 being at o. Up to about 1200 these formulae with suitable constants agree to 
 within 2 for the usual 10% (Pt, Pt - Rh) and (Pt, Pt - Ir) couples, but above 
 1200 formula (b} yields the higher results, e.g. see the melting-points of Pd and Pt 
 on p. 49. The thermo-e.m.f.'s of these Pt couples gradually diminish with pro- 
 longed heating. The values of the constants below are only average values. 
 
 E IN MICRO VOLTS (10~ 6 VOLT) 
 
 
 Couple. 
 
 a 
 
 b 
 
 c 
 
 n 
 
 ///' 
 
 Cold 
 
 junc- 
 tion 
 at o C. 
 
 Pt and (90 Pt, 10 Rh) . 
 Pt and (90 Pt, 10 Ir) . 
 Cu and Constantan f . 
 Cu and Fe . 
 
 -37* 
 -550* 
 
 o 
 
 8-1* 
 
 14-8* 
 
 
 
 lO'^J. 
 
 '0017* 
 0016* 
 
 '018^ 
 
 1-19 
 no 
 1-14 
 
 52 
 89 
 
 
 
 
 
 
 
 
 * These constants are not suitable for temperatures below 300. t ureka, 60 Cu, 40 Ni. 
 
47 
 
 THERMOMETRY 
 
 THERMO-ELECTRIC THERMOMETRY (contd.} 
 
 The following are the readings in micro-volts (io- 6 volt) determined at the 
 National Physical Laboratory for a Pt-Rh and a Pt-Ir couple, each having the cold 
 junction at o C. (Camb. Sci. Inst. Co.) 
 
 Couple. Temp. 50 100 150 200 250 | 300 ! 350 I 400 450 
 
 Pt 0C 
 
 and 500 
 
 (90 Pt, loRh) 1000 
 
 Pt 
 
 and 500 
 
 (90 Pt, io I r) 1000 
 
 o 
 
 377 
 880 
 
 o 
 
 737 
 1571 
 
 23 
 423 
 935^ 
 
 58 
 
 818 
 
 1657 
 
 470 
 991 
 
 125 
 
 899 
 1744 
 
 83 
 
 518 
 
 1048 
 
 195 
 
 981 
 
 1831 
 
 567 
 1106 
 
 268 
 1064 
 1919 
 
 158 
 
 617 
 1165 
 
 343 
 1147 
 
 2007 
 
 199 242 
 
 668 i 720 
 
 1225 1286 
 
 420 498 577 
 1231 1315 1400 
 2096 j 2185 | 2275 
 
 286 
 
 773 
 
 1348 
 
 826 
 
 657 
 
 1485 
 
 THERMO-E.M.F.'S AGAINST PLATINUM IN MICRO VOLTS (10-c VOLT) 
 
 One junction at o C. The current flows across the other junction from the 
 metal with the (algebraically) smaller value to the other metal. (See Watson's 
 " Physics " and Henning in L.B.M.) 
 
 Metal. - 190 ; + 100 
 
 Aluminium 
 Antimony . 
 Bismuth . 
 Cadmium . 
 Cobalt . . 
 Copper. . 
 Gold . . 
 Iron. 
 
 + 390 
 
 + 12300 | 
 60 
 
 200 
 1 2O 
 
 + 38o 
 +4700 
 
 6500 
 
 + 9 
 
 1520 
 + 740 
 + 730 
 
 2900 \c. + 1600 
 
 Metal. 
 
 Lead. . 
 
 Magne- 
 sium . 
 
 Mercury 
 
 Nickel . 
 
 Palla- 
 dium . 
 
 Silver , 
 
 - 190 + 100 
 
 + 2IO|-r- 410 
 + 330 + 410 
 
 o 
 
 + 2220 1640 
 
 + 790 
 140 
 
 - 5 60 
 + 710 
 
 Metal. 
 
 -190 
 
 .1+200 
 . 120 
 
 Tantalum 
 Tin . . 
 Zinc . . 
 Brass . . 
 Constantan*i 
 German sil- 
 verf. . . 
 ManganinJ 
 
 100 
 
 + 330 
 + 410 
 
 + 750 
 
 c.+ 400 
 
 -3440 
 
 C. 1000 
 
 + 570 
 
 * Eureka, 60 Cu, 40 Ni. f 60 Cu, 15 Ni, 25 Zn. J 84 Cu, 4 Ni, 12 Mn. 
 
 RADIATION AND OPTICAL THERMOMETRY 
 
 Most radiation thermometers use as a basis either (i) the Stefan-Boltzmann 
 law, E = K(0 4 4 ), where E is the total energy (of all wave-lengths) radiated by 
 a black body at absolute temp. to surroundings at absolute temp. , and K is a 
 const. (K = 53 x io~ 12 watts per cm. 2 per i see p. 65) ; or (2) Wien's equation con- 
 necting the temperature with the intensity of some particular wave-length of light 
 
 emitted (p. 65). The Wien equation is, Intensity I = ^A ~ ; v ~ ^', where A is the 
 wave-length, T is the " black body " temp, on the absolute scale, ^ and c 2 are 
 constants, and e is the base of the Napierian logarithms. Both equations give 
 results which agree very accurately with the gas scale over the calibrated range 
 o to I2OD C. Up to about 1500 radiation thermometers are, in practice, almost 
 always graduated empirically, usually against a thermo-couple. 
 
 The "black body" temperature of a radiating substance is the temperature at 
 which an ideal black body would emit radiation of the same intensity as that from 
 the substance, the radiation considered being of some particular wave-length. A 
 perfectly black body absorbs all the radiation which falls upon it ; it is destitute of 
 reflecting power. Coal, carbon, metals which when heated tarnish with a black 
 oxide, enclosed furnaces and muffles at a uniform temperature, all conform very 
 nearly to this definition. When a pyrometer is sighted upon a body which is not 
 "black," the temperature recorded the "black body" temperature will be lower 
 than the true temperature to an extent which increases with the reflecting power 
 of the body, e.g. if platinum and carbon have equal " black body " temperatures, 
 their actual temperatures may differ by 180 or so at 1500. 
 
 TEMPERATURE OF FIRE 
 
 Appearance . 
 
 Bed just 
 visible. 
 
 Dull Bed. 
 
 Cherry Bed. 
 
 Orange. 
 
 White. 
 
 Dazzling 
 White. 
 
 Temperature . 
 
 500 C. 
 
 c. 700 
 
 c. noo c 
 
 c. 
 
 c. 1500 
 
 For Standard temperatures for thermometer calibration, see p. 50, 
 
48 
 MELTING AND BOILING POINTS 
 
 MELTING AND BOILING POINTS OF THE ELEMENTS 
 
 For an account of temperature measurements, see p. 46. For melting and boiling points of 
 
 chemical compounds, see p. 109 ; of fats and waxes, see p. 50. 
 
 Element. 
 
 Melting 
 Point. 
 
 Observer. 
 
 Boiling 
 Point at 
 760 mms. 
 
 Observer. 
 
 Aluminium 
 
 657 C. 
 
 Holborn and Day, 1900 
 
 i8ooC. 
 
 Greenwood, 1909 
 
 Antimony . . 
 
 630 
 
 > 
 
 1440 Greenwood, 1909 
 
 Argon . . . 
 
 -188 
 
 Ramsay and Travers, 1901 
 
 -186 
 
 
 
 Arsenic . . 
 
 volatilizes 
 
 
 
 jsublimesj 
 I 450 / 
 
 
 Barium . . . 
 
 850 
 
 Guntz, 1903 
 
 
 
 
 
 Beryllium . . 
 
 c. 1430 
 
 Just and Mayer, 1909 
 
 
 
 
 
 Bismuth . . 
 
 269 
 
 Callendar, 1899 
 
 1420 
 
 Greenwood, 1909 
 
 Boron . . . 
 
 2000 tO 2500 
 
 Weintraub, 1909 
 
 /sublimes\ 
 I 3500 (?)/ 
 
 
 
 Bromine . . 
 
 -7'3 
 
 van der Plaats, 1886 
 
 63 
 
 van der Plaats, 1886 
 
 Cadmium . . 
 
 321 
 
 Holborn and Day, 1900 
 
 778 
 
 D. Berthelot, 1902 
 
 Caesium . . . 
 
 26*4 
 
 Eckardt and Graefe, 1900 
 
 670 
 
 Ruff & Johannsen, 1906 
 
 Calcium. . . 
 
 780 
 
 Ruff and Plato, 1903 
 
 
 
 
 
 Carbon . . . 
 
 4000 (?) 
 
 (Calculated) McCrae, 1906 
 
 
 
 
 
 Cerium . . . 
 
 623 
 
 Muthmann & Weiss, 1904 
 
 
 
 
 
 Chlorine . . 
 
 -102 
 
 Olszewski 
 
 -33'6 
 
 Regnault, 1863 
 
 Chromium . . 
 
 ( 1489 \ 
 
 ( not sharp / 
 
 Burgess, 1907 
 
 2200 
 
 Greenwood, 1909 
 
 Cobalt . . . 
 
 / J 4^4 
 I I49t 
 
 \ 
 Day & Sosman, 1910 / 
 
 
 
 
 
 Copper . . . 
 
 / 1084 * 
 I 1083 
 
 Holborn and Day, 1900 ) 
 Day and Sosman, 1910 / 
 
 2310 
 
 Greenwood, 1909 
 
 Erbium . . . 
 
 
 
 
 
 
 
 
 
 Fluorine . . 
 
 -223 
 
 Moissan and Dewar, 1903 
 
 -I8 7 
 
 Moissan & Dewar, 1903 
 
 Gallium . . 
 
 , 30-2 
 
 L. de Boisbaudran, 1876 
 
 
 
 
 
 Germanium . 
 
 900 (?) 
 
 Winkler, 1886 
 
 
 
 
 
 Gold .... 
 
 / 1063 
 \ 1062 f 
 
 Holborn and Day, 1901 | 
 Day and Sosman, 1910 / 
 
 2 53 (?) 
 
 
 
 Helium . . . 
 
 below 270 
 
 Onnes, 1908 
 
 - 268-6 
 
 Onnes, 1908 
 
 Hydrogen . . 
 
 -259 
 
 Travers, 1902 
 
 -2527 
 
 Travers, 1902 
 
 Indium . . . 
 
 155 
 
 Thiel, 1904 
 
 1000 (?) 
 
 
 
 Iodine . . . 
 
 H3 
 
 Lean & Whatmough, 1898 
 
 184-4 
 
 Drugmann & Ramsay, 'oo 
 
 Iridium . . . 
 
 2290 
 
 Mendenhall & Ingersoll, '07 
 
 255o(?) 
 
 
 
 Iron . . . .' 
 
 / I5 5 \ 
 \notdennitej 
 
 Burgess, 1907 
 
 2450 
 
 Greenwood, 1909 
 
 Krypton . . . 
 
 -169 
 
 Ramsay, 1903 
 
 -1517 
 
 Ramsay, 1903 
 
 Lanthanum . 
 
 810 
 
 Muthmann & Weiss, 1904 
 
 
 
 
 
 Lead. . . . 
 
 327 
 
 Holborn and Day, 1900 
 
 1525 
 
 Greenwood, 1909 
 
 Lithium . . . 
 
 1 86 
 
 Kahlbaum, 1900 
 
 >i4oo 
 
 Ruff Johannsen, 1906 
 
 Magnesium 
 
 633 
 
 Heycock and Neville, 1895 
 
 1 1 20 
 
 Greenwood, 1909 
 
 Manganese 
 
 ( 1207 } 
 \ not sharp / 
 
 Burgess, 1907 
 
 1900 
 
 Greenwood, 1909 
 
 Mercury . . 
 
 -38-80 
 
 Chappuis, 1900 
 
 3567 
 
 Callendar, 1899 
 
 Molybdenum . 
 
 >white heat 
 
 
 
 3200 (?) 
 
 
 
 Neodymium . 
 
 840 
 
 Muthmann & Weiss, 1904 
 
 
 
 
 
 Neon. . . . 
 
 
 
 
 
 -239 
 
 Dewar, 1901 
 
 Nickel . . . 
 
 / M35 
 I H52 1 
 
 Burgess, 1907 \ 
 Day and Sosman, 1910 / 
 
 2330 (?) 
 
 
 
 Niobium . . 
 
 1950 
 
 von Bolton, 1907 
 
 
 
 
 
 Nitrogen . . 
 
 -210-5 
 
 Fischer and Alt, 1903 
 
 -1957 
 
 Fischer & Alt, 1903 
 
 * In reducing atmosphere; 1062 in air. f Const, vol. N. thermometer. 
 
49 
 
 MELTING AND BOILING POINTS 
 
 MELTING AND BOILING POINTS OF THE ELEMENTS (contd.) 
 
 
 
 
 Boiling 
 
 
 Element. 
 
 Melting 
 
 Observer. 
 
 Point at 
 
 Observer. 
 
 
 Point. 
 
 
 760 nuns. 
 
 
 Osmium. . . 
 
 2200 C. 
 
 _ 
 
 _ 
 
 _ 
 
 Oxygen . . . 
 
 -235 
 
 
 
 -i82'9C. 
 
 Travers, 1902 
 
 Palladium * 
 
 
 Day and Sosman, 1910 
 
 2540 
 
 
 
 thermo-jn. (a) 
 
 1535 
 
 Holborn & Henning, 1905 
 
 
 
 
 
 optical therm. 
 
 * 
 
 1549 
 
 1545 
 
 Nernst & Wartenberg, 1906 
 
 
 
 ~ 
 
 
 1582 
 
 Holborn & Valentiner, 1907 
 
 
 
 
 
 thermo-jn. (a) 
 
 1530 
 
 Waidner & Burgess, 1907 
 
 
 
 
 
 11 [A 
 
 1543 
 
 ,, ,, 
 
 
 
 
 
 optical therm. 
 Phosphorus . 
 
 1546 
 
 Hulett, 1899 
 
 287" 
 
 Schrotter, 1848 
 
 Platinum * 
 
 
 
 
 
 thermo-jn. (a) 
 
 1710 
 
 Harker, 1905 
 
 2450 (?) 
 
 . 
 
 , (*) 
 
 1710 
 
 Holborn & Henning, 1905 
 
 
 
 
 
 optical therm. 
 
 1729 
 
 11 
 
 
 
 
 
 
 
 1750 
 
 Nernst & Wartenberg, 1906 
 
 
 
 
 
 i 
 
 1789 
 
 Holborn & Valentiner, 1907 
 
 
 
 
 
 thermo-jn. (a) 
 
 1706 
 
 Waidner & Burgess, 1907 
 
 
 
 
 
 >' \"/ 
 
 173 ^ 
 
 ,, ,, 
 
 
 
 
 optical therm. 
 Potassium . 
 
 1770 
 62-5 
 
 1909 
 Holt and Sims, 1894 
 
 / 758 
 I 667 
 
 Ruff & Johannsen, 1905 
 Permann, 1889 
 
 Praseodymium 
 
 940 
 
 Muthmann and Weiss, 1904 
 
 
 
 
 
 Rhodium . . 
 
 1907 Mendenhall & Ingersoll, '07 
 
 250x3 (?) 
 
 
 
 Rubidium . 
 
 38-5 
 
 Erdmann and Kothner, 1 896 
 
 696 
 
 Ruff & Johannsen, 1905 
 
 Ruthenium . 
 
 i9oo(?) 
 
 
 
 2520 (?) 
 
 
 
 Samarium . . 
 
 1350 
 
 
 
 
 
 
 
 Selenium . . 
 
 217 
 
 Saunders, 1900 
 
 690 
 
 Berthelot, 1902 
 
 Silicon . . . 
 
 I200(?) 
 
 
 
 3500 (?) 
 
 
 
 Silver . . . 
 
 / 962 t 
 
 I 960 t 
 
 Holborn and Day, 1900^ 
 Day and Sosman, 1910 / 
 
 1955 
 
 Greenwood, 1909 
 
 Sodium . . . 
 
 97'0 
 
 Kurnakow & Puschin, 1902 
 
 / 877 
 I 742 
 
 Ruff & Johannsen, 1905 
 Permann, 1889 
 
 Strontium . 
 
 9OO 
 
 
 
 
 
 
 
 
 
 
 (444*55 
 
 } Eumorfopoulos, 1908 
 
 
 ( IX 5 
 
 
 (c.p. air) 
 
 / (corrected, 1909) 
 
 Sulphur . . . 
 
 | rhombic 
 119 
 
 
 4447 
 
 (c.v. N) 
 
 j-Chappuis & Harker, 1902 
 
 
 Imonoclinic 
 
 
 444-53 
 (c.p. N) 
 
 Callendar, 1899 
 
 Tantalum . . 
 
 2910 
 
 Burgess, 1907 
 
 
 
 
 
 Tellurium . . 
 
 45 
 
 Matthey, 1901 
 
 1390 
 
 Deville and Troost, 1880 
 
 Thallium . 
 
 301 
 
 Kurnakow & Puschin, 1901 
 
 I280(?) 
 
 Wartenberg, 1907 
 
 Thorium . . 
 
 1690 
 
 Wartenberg, 1909 
 
 
 
 
 
 Tin .... 
 
 232 
 
 Heycock & Neville, 1895 
 
 2270 
 
 Greenwood, 1909 
 
 Titanium . . 
 
 c. 2500 
 
 
 
 
 
 
 
 Tungsten . . 
 
 f 3080 
 \ 2825 
 
 Burgess, 1907 \ 
 Wartenberg, 1907 / 
 
 3700 (?) 
 
 
 
 Vanadium . . 
 
 1620 
 
 
 
 
 
 
 
 Xenon . . . 
 
 140 
 
 Ramsay, 1903 
 
 -109 
 
 Ramsay, 1903 
 
 Zinc .... 
 
 4i8 % 
 
 Day and Sosman, 1910 
 
 918 
 
 Berthelot, 1902 
 
 Zirconium . . 
 
 c. 1300 
 
 ~ 
 
 " "" 
 
 ^ * 
 
 * See section on thermo-electric thermometers, p. 46, for meaning of (a) and (b). 
 
 t In reducing atmosphere ; 955 in air. J Const, vol. N. thermometer. 
 
50 
 
 STANDARD TEMPERATURES 
 
 STANDARD TEMPERATURES 
 
 Melting and boiling points of elements will be found on p. 48 ; of chemical 
 
 compounds, on p. 109. 
 
 B.P. = boiling point at 760 mm. ; M.P. = melting point ; T.P. = transition point. 
 
 Substance. 
 
 Temp. 
 
 Substance. 
 
 
 Temp. 
 
 Hydrogen .... B.P. 
 
 -253' 
 
 Zinc* 
 
 M.P. 
 
 419-4 
 
 Oxygen B.P. 
 
 -183 
 
 Sulphur * 
 
 B.P. 
 
 4447 
 
 Carbon dioxide ... B.P. 
 
 78*2 
 
 Aluminium .... 
 
 M.P. 
 
 657 
 
 Mercury M.P. 
 
 38*8 
 
 NaCl (Harker) . . 
 
 M.P. 
 
 801 
 
 Water . . M.P. 
 
 o 
 
 
 M P 
 
 1070 
 
 Na 2 S0 4 . ioH 2 O . . T.P. 
 
 32-383 
 
 Palladium (p. 49) . . 
 
 M.P. 
 
 1550 
 
 Water . . ... B.P. TOO 
 
 Platinum (p 49) 
 
 M P. 
 
 
 Naphthalene* . . . B.P. 
 
 218-0 
 
 Tin (Greenwood) . . 
 
 B.P. 
 
 2270 
 
 Tin* M.P. 
 
 2^ I Q 
 
 Arc t (W. & B.)t . . 
 
 
 3700 abs. 
 
 Benzophenone * . . B.P. 
 
 306*0 
 
 Arcf (Harker, '08) f . 
 
 
 
 3620 abs. 
 
 Cadmium* .... M.P. 
 
 321-0 
 
 Sun f (P. 66) . . . 
 
 
 
 5800 abs. 
 
 * Const, vol. N. scale, Waidner & Burgess, 1911 ; W. & B., Waidner & Burgess, 1904. 
 t Black body temperature. Positive crater. 
 
 EFFECT OF PRESSURE ON BOILING POINTS 
 
 S^/5/ is given as mm. Hg per degree C. for pressures not. very far removed from 
 760 mm. 
 
 The boiling point in absolute degrees C. of a substance under 760 mm. mercury 
 = -(760 /)(/ + 273), where c is a constant for the substance, and / is the B.P. in 
 degrees C. at the pressure p mm. The constant c is the same for chemically similar 
 substances. 
 
 (See Young, " Fractional Distillation.") 
 
 Substance. 
 
 8//8* 
 
 c 
 
 Substance. 
 
 8//8/ 
 
 c 
 
 Substance. 
 
 S//5/ 
 
 c 
 
 
 
 xio-" 
 
 
 
 xio- 6 
 
 
 
 xio- H 
 
 Hydrogen . . 
 
 2OO 
 
 
 
 CC1 4 .... 
 
 23 
 
 123 
 
 Benzene . . 
 
 23*5 
 
 121 
 
 Oxygen . . . 
 
 77 
 
 
 
 Pentane, n . . 
 
 25-8 
 
 125 
 
 Toluene . . . 
 
 217 
 
 120 
 
 Carbon dioxide 
 
 S5 
 
 
 
 Alcohol, methyl 
 
 29*6 
 
 100 
 
 Aniline . . . 
 
 19-6 
 
 112 
 
 Water . . . 
 
 27-2 
 
 99 
 
 ethyl . 
 
 30-3 
 
 94 
 
 Naphthalene . 
 
 17-1 
 
 IIQ 
 
 Mercury . . 
 
 13-6 
 
 118 
 
 amyl . 
 
 25 
 
 98 
 
 Benzophenone 
 
 is-i 
 
 
 Sulphur* . . 
 
 iro 
 
 114 
 
 Ether, ethyl . 
 
 26*9 
 
 121 
 
 Acetone . . . 
 
 26-4 
 
 H5 
 
 760) -o 4 52 (/ 76o) 2 , Harker & Sexton, 1908. 
 
 MELTING, FREEZING, AND BOILING POINTS OF FATS AND WAXES 
 
 At 760 mm. pressure. (See Lewkowitsch's treatise.) 
 
 Substance. 
 
 MF. 
 
 F.P. 
 
 Substance. 
 
 M.P. 
 
 F.P. 
 
 Substance. 
 
 M.P. 
 
 B.P. 
 
 Butter . . . 
 Lard . . . 
 Tallow, beef . 
 mutton 
 1] 
 
 c. 
 
 28-33 
 36-40 
 
 40-45 
 44-45 
 
 C. 
 20-23 
 27-30 
 
 27-35 
 36-41 
 
 Beeswax . . 
 Spermaceti . 
 Stearin . . 
 Naphthalene 
 
 C. 
 
 61-64 
 
 42-49 
 7 l-6 
 8o'o 
 
 c. 
 
 60-63 
 
 42-47 
 70 
 
 Paraffin wax, 
 Soft . . . 
 Hard . . 
 Olive oil . . 
 
 .1 
 
 38-52 
 52-56 
 
 C. 
 
 350-390 
 390-430| 
 c. 300 
 
51 
 
 THERMAL CONDUCTIVITIES 
 
 THERMAL CONDUCTIVITIES 
 
 The thermal conductivity, k, is given below as the number of (gram) calories 
 conducted per sq. cm. per sec. across a slab of the substance I cm. thick, having a 
 temp.-gradient of iC. per cm., i.e. calorie cm.' 1 sec." 1 temp." 1 . (See Callendar, 
 "Conduction of Heat," Encyc. Brit., and Winkelmann's " Handbuch der Physik," 
 III., 1906.) 
 
 METALS AND ALLOYS 
 
 k for most pure metals decreases with rise of temperature ; the reverse appears 
 to be true for alloys. If be the electrical conductivity and 8 the absolute temp., 
 then //(#) is very approximately a constant for pure metals. (See J. J. Thomson, 
 "Corpuscular Theory of Matter," and Lees, Phil. Trans., 1908.) The electrical 
 conductivity of the same specimen of many of the substances below will be found 
 on p. 8 1. 
 
 Substance. Temp. Cond.k. Observer. Substance. Temp. Cond.k. Observer. 
 
 Metals - 
 
 Aluminium 
 
 Antimony . 
 Bismuth . 
 
 Cadmium, pure 
 Copper, pure . 
 
 Gold " . . ! 
 Iron, pure . . 
 
 wrought 
 
 " t 
 cast t 
 
 steel|i% 
 
 | Lead, p ire 
 
 Magnesium 
 
 160 
 
 18 
 
 18 
 
 100 
 
 O 
 
 100 
 186 
 
 18 
 100 
 160 
 
 18 
 1OO 
 16O 
 
 18 
 100 
 
 18 
 100 
 
 18 
 
 100 
 
 16O 
 
 18 
 1OO 
 
 54 
 102 
 
 30 
 160 
 
 18 
 
 18 
 100 
 160 
 
 18 
 100 
 O to 
 10O 
 
 514 
 504 
 480 
 492 
 044 
 
 040 
 
 025 
 0194 
 
 0161 
 239 
 
 '222 
 
 216 
 
 [079 
 918 
 908 
 700 
 703 
 
 161 
 151 
 152 
 144 
 
 143 
 :ii4 
 in 
 149 
 113 
 115 
 108 
 107 
 092 
 083 
 082 
 
 \Lees, 
 }P.T., '08 
 J.&D, 
 
 1900 
 
 \Lorenz, 
 j 1881 
 M, 1907 
 J. & D, 
 
 1900 
 
 Lees, '08 
 J. & D, 
 
 1900 
 
 Lees, '08 
 J. & D, 
 
 1900 
 J. & D, 
 
 1900 
 J. & D, 
 
 1900 
 
 Lees, '08 
 J.&D, 
 
 1900 
 
 Callendar 
 
 Hall 
 \Lees, 
 
 1908 
 J. & D, 
 
 1900 
 
 Lees, '08 
 J. & D, 
 
 1900 
 Lorenz, 
 
 1881 
 
 Mercury . 
 
 > 
 
 
 
 Nickel . ! ! 
 
 . J97%\ 
 I Ni / 
 
 Palladium . . 
 
 
 
 Platinum . . 
 
 
 
 Silver, pure . 
 > 
 
 
 
 
 
 Tin, pure . . 
 
 
 
 
 
 Zinc, pure . . 
 
 Alloys- 
 Brass || . . . 
 
 
 Constantan } 
 
 (Eureka)!/ 
 German silver 
 
 J> S> 
 
 Manganin ** . 
 > 
 
 > 
 
 Platinoid . . 
 
 
 
 50 
 50 
 17 
 
 160 
 18 
 
 10O 
 18 
 
 1OO 
 18 
 
 1OO 
 
 16O 
 18 
 18 
 
 100 
 
 160 
 18 
 
 100 
 
 16O 
 18 
 
 1OO 
 
 160 
 17 
 18 
 
 1OO 
 O 
 
 100 
 
 160 
 18 
 
 100 
 18 
 
 0148 
 
 0189 
 
 0177 
 
 0197 
 
 129 
 
 142 
 
 138 
 
 168 
 
 182 
 
 166 
 
 173 
 998 
 
 *974 
 roo6 
 992 
 192 
 155 
 'MS 
 278 
 265 
 262 
 
 181 
 260 
 054 
 064 
 070 
 089 
 035 
 053 
 063 
 060 
 
 \ H. F. 
 JWeber,'79 
 A, 1864 
 R. W, '02 
 Lees, '08 
 .& D, 
 1900 
 J.&D, 
 1900 
 J.&D, 
 1900 
 Lees, 
 
 1908 
 
 J.&D, 
 
 1900 
 
 Lees, '08 
 
 .& D, 
 
 1900 
 
 Lees, '08 
 
 .&D, 
 
 1900 
 
 \Lees, 
 1908 
 
 &D, 
 
 1900 
 i Lorenz, 
 1881 
 
 Lees, '08 
 \]. & D, 
 1900 
 Lees, '08 
 
 2% C, 3% Si, i% Mn. 
 f 60 Cu, 40 Ni. 
 
 * 99% Al. f -i% C, -2% Si, -i% Mn. 
 
 3'5% C , 1-4% Si, -5% Mn. || 70 Cu, 30 Zn. 
 
 ** 84 Cu, 4 Ni, 12 Mn. 
 
 A, Angstrom ; J. & D, Jaeger & Diesselhorst ; M, Macchia ; R. W, R. Weber ; 
 P.T., Phil. Trans. 
 
52 
 
 THERMAL CONDUCTIVITIES 
 
 MISCELLANEOUS SUBSTANCES 
 
 The values below are mostly at ordinary temperatures. They must be regarded as rough 
 average values in the case of indifferent conductors. Nearly all liquids have very approxi- 
 
 mately the same conductivity, which in most cases appears to increase with temperature. 
 
 Substance. 
 
 k 
 
 Substance. 
 
 i 
 
 Substance. 
 
 i 
 
 Substance. 
 
 k 
 
 Glass- 
 Cilo wn ; window 
 Flint .... 
 Jena .... 
 Sqda .... 
 
 Woods (dry) 
 Mahogany . . 
 Oak, teak . . . 
 Pine, walnut . . 
 
 Miscellaneous 
 
 Asbestos paper . 
 Cardboard . . 
 Cement . . . 
 Cotton . . . 
 
 X I0~ 3 
 
 2-5, L. 
 
 2, L. 
 
 1-2, L. 
 
 i*3-r8 
 
 4, L. 
 
 6 
 
 '5 
 7, L. 
 
 '55, L- 
 
 Cotton wool . 
 Cork . . . 
 Earth's crust t 
 Ebonite . . 
 Felt . . . 
 Flannel . . 
 Gas carbon . 
 Graphite . . 
 Ice . . . . 
 Marble, white 
 Mica*. . . 
 Paper . . . 
 Paraffin wax . 
 Porcelain . . 
 Quartz, || axis 
 
 X I0~ 3 
 
 04 
 13, L. 
 4 
 42, L. 
 09 
 23, L. 
 
 10 
 12 
 
 5 
 7-1, L. 
 r8, L. 
 '3, L. 
 6,L. 
 2-5, L. 
 30, L. 
 
 Quartz, _[_axis 
 Rubber, Para 
 Sand . . . 
 Sawdust . . 
 Silicate cotton 
 Silk. . . . 
 Slate . . . 
 
 X I0~ 3 
 
 16, L. 
 
 45, L. 
 
 '12 
 
 19 
 
 22, L. 
 
 47, L- 
 
 Liquids 
 
 Alcohol, 25 . 
 Aniline, 12 . 
 Glycerine, 25 
 Paraffin oil, 1 7 
 Turpentine, 1 3 
 Vaseline, 25 
 
 X IO~ 4 
 
 4'3, L. 
 4' i 
 6-8, L. 
 
 3'5 
 
 3 
 
 Substance. 
 
 Temp. 
 
 Cond. k. 
 
 Obs. 
 
 Water . . . 
 
 17 
 2O 
 4 
 23*6 
 11 
 25 
 
 00131 
 00143 
 00138 
 00152 
 00147 
 00136 
 
 R.W.'o3 
 M.&C. 
 jH. F. 
 /Weber 
 \Lees, 
 / 1898 
 
 * Perp. to cleavage plane. t Average for igneous and sedimentary rocks ; see Brit. 
 Ass. Reports. L., Lees, 1892 & 1898 ; M. & C, Milner & Chattock, 1898 ; R. W., R. Weber. 
 
 GASES 
 
 In the case of a gas the thermal conductivity k = r6o3rjp, where 77 is the viscosity, and 
 c v the specific heat at constant volume. Stefan, and Kundt and Warburg have found, in agree- 
 ment with this formula, that k for air, hydrogen, etc., is constant between the pressures 76 cm. 
 ahd *i cm. k increases with the temperature. (See Meyer's " Kinetic Theory of Gases.") 
 
 Gas. 
 
 Temp. 
 
 Cond. k. 
 
 Gas. 
 
 Temp. 
 
 Cond. k. 
 
 Gas. 
 
 Temp. 
 
 Cond. k. 
 
 Gas. 
 
 Temp. 
 
 Cond. k. 
 
 
 C. 
 
 X I0~ 5 
 
 
 C. 
 
 X I0~ 6 
 
 
 C. 
 
 X I0~ 5 
 
 
 C. 
 
 X IO" 6 
 
 H 2 
 
 -15O 
 
 H7, E. 
 
 Air 
 
 
 
 5-22* 
 
 CO 
 
 7 
 
 5 -io,W. 
 
 N 2 O 
 
 
 
 3-50, W. 
 
 
 
 
 
 3 r8, E. 
 
 2 
 
 7 
 
 5-63, w. 
 
 C0 2 
 
 O 
 
 3-07, W. 
 
 
 
 1OO 
 
 5'o6,W. 
 
 
 
 
 
 31-9, G. 
 
 A 
 
 O 
 
 3-89, S. 
 
 >J 
 
 
 
 3-27, Sc. 
 
 NO 
 
 8 
 
 4'6o, W. 
 
 
 
 100 
 
 36-9, G. 
 
 CH 4 
 
 8 
 
 6-47, W. 
 
 M 
 
 100 
 
 5-06, Sc. 
 
 Hg 
 
 203 
 
 1-85, Sc. 
 
 He 
 
 
 
 33'9, S. 
 
 C 2 H 4 
 
 
 
 3'95 5 W. 
 
 NH 3 
 
 O 
 
 4-58, w. 
 
 
 
 
 N 2 
 
 7 
 
 5 -2 4 ,W. 
 
 CO 
 
 
 
 4-99, W. 
 
 M 
 
 100 
 
 7-09, W. 
 
 
 
 
 ; * Mean of five observers. E., Eckerlein, 
 
 iqoo; G., Graetz, 188; 
 
 ; S., Schwarze, 
 
 1^03 ; Sc., Schleiermacher, 1889 ; W., Winkelmann, 1875. 
 
 
 
 
 
 
 
 COEFFICIENTS OF LINEAR EXPANSION OF SOLIDS 
 
 To represent accurately over any considerable range the variation of 
 
 length 
 
 (/) with 
 
 temperature (/) requires for almost all solid substances a parabolic or cubic equation in /. 
 
 But if the temperature interval is not large, a linear equation // = /o(i 
 
 + a/) 
 
 may be 
 
 employed ; and this gives a definition of the mean coefficient of linear expansion 
 
 (a) over 
 
 that temperature range. The coefficient of cubical expansion = 30. 
 
 
 
 There is little point in tabulating coefficients of higher-powered terms of /, since for a 
 
 given specimen it is as a rule impossible without measurement to assume with any accuracy 
 
 anything more definite than the average value of even 
 
 the first power coefficient (a). 
 
 Except 
 
 in a few cases the linear coefficient as defined above 
 
 increases with the temperature. The 
 
 values of a subjoined are per degree C., and except when some temperature 
 
 s specified, for 
 
 a range round and about 20 C. Some substances expand irregularly, and extrapolation of a 1 
 
 may therefore be dangerous. Interpolation of a from the constituent metals must be employed 1 
 
 with caution in the case of alloys. (See Winkelmann's *' Handbuch der Physik," iii. 1906.) 
 
53 
 COEFFICIENTS OF EXPANSION 
 
 COEFFICIENTS OF LINEAR EXPANSION OF SOLIDS (fontd.) 
 
 Element. . Obs. 
 
 Element. 
 
 a. 
 
 Obs. 
 
 Element. a. 
 
 Obs. 
 
 i XIO" 6 
 
 
 Xio- 6 
 
 
 ! Xio~ 6 
 
 
 Aluminium i 25-5 V. '93 
 Antimony . 12 ! F. '69 
 
 Copper . . 
 Gold . . . 
 
 167 
 I3'9 
 
 V.'93 
 V.'93 
 
 Palladium . 1 117 
 Platinum . 8-9 
 
 S. '03 
 B. '88 
 
 Bismuth ... 157 j V. '93 
 
 Iridium . . 
 
 6-5 
 
 B. '88 
 
 Potassium . ! 83 
 
 H.'82 
 
 C. (diamond) i'2 ! F. '69 
 
 Iron (cast) . 
 
 I0'2 
 
 D. '02 
 
 Selenium, 40; 36*8 
 
 F. '69 
 
 (gas car- 
 
 (wrought) 1 1-9 
 
 H.D.'oo 
 
 Silver . . .| 18-8 
 
 V. '93 
 
 bon) . 5-4 : F. '69 
 
 Steel, 10-5 to 
 
 ir6 
 
 N.P.L. 
 
 Sulphur . . ; c. 70 
 
 
 
 (graphite) 1 7 '9 F - ' 6 9 
 
 Lead . . . 
 
 27-6 
 
 M. '66 
 
 Thallium, 40 30^2 
 
 F. '69 
 
 Cadmium . 28-8 M.'66 
 
 Magnesium . 25*4 
 
 V.' 93 
 
 Tin . . . 21-4 
 
 M. '66 
 
 Cobalt . .12-3 T. '99 
 
 Nickel . . 
 
 12-8 
 
 T.' 99 
 
 Zinc, 25'8 to , 26-3 
 
 N.P.L. 
 
 Substance. 
 
 Alloys- 
 Aluminium bronze . . . 
 Brass (ordy .) c. 66 Cu, 34 Zn 
 Bronze, 32 Cu, 2 Zn, 5 Sn 
 Constantan (Eureka), 60 
 
 Cu, 40 Ni 
 
 German silver, 60 Cu, 15 
 
 Ni,2 5 Zn, 50. : . . 
 Gunmetal (Admiralty) . . 
 Magnalium, 86 A1, 13 Mg 
 Nickel steel,* 10% Ni . 
 
 )1 '<~> )5 ' 
 
 30% 
 
 36% 
 
 (Invar f) 
 
 40% 
 5o% - 
 80% . 
 Phosphor bronze, 97*6 Cu, 
 
 2 Sn, -2 P 
 
 Platinum-indium, 90 Pt, 
 
 lolrj 
 
 Platinum - silver, 33 Pt, 
 
 67 Ag 
 
 Solder, 2 Pb, i Sn, 50 . 
 Speculum metal, 68 Cu, 
 
 32 Sn 
 
 Type metal, c. 135 . . . 
 
 Miscellaneous 
 Brick (Egyptian) . . . 
 Cement and concrete, loto 
 
 Ebonite 6410 
 
 Fluor spar, CaF 2 . . . 
 Glass, soft, 68 SiO 2 , 
 
 i4Na 2 O,7CaO 
 hard, 64 Si(_) 2 , 
 
 20 K 2 O, 1 1 CaO 
 
 17-0 
 18-9 
 177 
 
 17-0 
 
 18-4 
 
 18-1 
 
 24 
 
 13-0 
 
 19-5 
 
 I2'0 
 
 6-0 
 
 97 
 12-5 
 
 1 6-8 
 87 
 
 15 
 
 25 
 
 19*3 
 19 
 
 9*5 
 H 
 77 
 19 
 
 8-5 
 97 
 
 Obs. 
 
 N.P.L. 
 N.P.L. 
 B. '88 
 
 N.P.L. 
 
 Pf. '72 
 N.P.L. 
 St. '01 
 N.P.L. 
 N.P.L. 
 N.P.L. 
 
 N.P.L. 
 N.P.L. 
 N.P.L. 
 N.P.L. 
 
 B. '88 
 B. '88 
 
 Sm. 
 
 Sm. 
 Dl. 
 
 N.P.L, 
 
 F. '68 
 Sc. 
 Sc. 
 
 Substance. 
 
 Miscellaneous (contd.} 
 Glass, flint, 45 SiO 2 , 
 
 8 K 2 O, 46 PbO 
 
 Jena, 16'" (see p. 74) 
 
 59"' (see p. 74) 
 
 Verre dur (see p. 74) 
 
 Granite 
 
 Gutta-percha . . . . . 
 
 Ice, - 10 to o . . . . 
 
 Iceland spar, |l axis . . 
 
 _Laxis . . 
 
 Marble, white Carrara, 
 
 15, 1-4 to 
 
 black .... 
 
 Masonry . . . . 4 to 
 
 Paraffin wax, o-4o . . 
 
 Porcelain, Berlin . . . 
 
 xio 
 
 Obs. 
 
 *h 
 
 17 '/ 
 
 Sc. 
 
 o -100^ 
 
 Bayeux 
 
 Portland stone ... 
 Quartz (crystal), || axis 
 _L axis 
 Silica (fused), -80 too 
 oto3o' 
 o to loc 
 o to 1000 
 Sandstone . . . . 7 to 
 Slate 6 to 
 
 Woods (i) along grain 
 Beech ; mahogany . . . 
 
 Oak ; pine 
 
 (2) across grain 
 Beech ....... 
 
 Mahogany 
 
 Pine 
 
 57 J '96 
 7-2 C.'o 7 
 
 98 j Ru. '82 
 
 507 I Vn. '02 
 
 25-1 1 B. '88 
 
 -5-6 B. '88 
 
 3'5 
 4'4 
 7 
 
 -. 1 10 
 2-8 
 
 3'4 
 2-5 
 
 7*5 
 137 
 
 22 
 42 
 50 
 
 N.P.L. 
 
 S. '03 
 H.G.'oi 
 Bd. 'oo 
 
 T. '02 
 
 B. '88 
 B. '88 
 S. '07 
 C.'o 3 
 S. '07 
 
 54 R. 'lo 
 
 12 
 10 
 
 c. 3 VI. '68 
 c. 5 VI. '68 
 
 60 
 40 
 34 
 
 VI. '68 
 VI. '68 
 VI. '68 
 
 * See Guillaume's " Les Applications des Aciers au Nickel," 1904. f Invar is obtain- 
 able in three qualities, with a range of coefficients of ( '3 to + 2*5) X IO~ 6 at ordinary 
 temperatures. \ Used for international prototype metre (see p. 3). Used for Imperial 
 Standard Yard (see p. 4). B. Benoit ; Bd. Bedford ; C. Chappuis ; D. Dittenberger ; Dl. 
 Daniell ; F. Fizeau ; H. Hagen ; H.D. Holborn and Day; H.G. Holborn and Griineisen ; 
 M. Matthiessen ; N.P.L. National Physical Laboratory ; Pf. Pfaff; R. Randall ; Ru. Russner ; 
 S. Scheel; Sc. Schott ; Sm. Smeaton ; St. Stadthagen ; T. Tutton ; T.S.S. Thiesen, Scheel, 
 and Sell ; V. Voigt ; VI. Villari ; Vn. Vincent. 
 
54 
 COEFFICIENTS OF EXPANSION 
 
 COEFFICIENTS OF 
 
 CUBICAL EXPANSION OF 
 
 GASES 
 
 
 The volume coefficient, o, at constant pressure is defined by v t = 'o( r + a/) ; 
 
 the pressure coefficient, , at constant volume is defined by p t 
 
 = pj j _|_ t 
 
 3/), where 
 
 v t and p t are the volume and pressure respectively corresponding to /, the initial 
 volume and pressure (^o, /o) being measured at o C. The values of both o and ft 
 
 depend on the initial pressure 
 
 of the gas. If a gas obeys Boyle's law exactly, 
 
 a = ft. 
 
 
 
 
 Comparison of rarefied gas, H and absolute temperature scales. 
 
 By graphically or otherwise extrapolating a and ft to zero pressure, they become 
 
 equal (as we should expect, for 
 
 rarefied gases should behave 
 
 as ideal gases and 
 
 obey Boyle's l.iw), and we may write a = ft = y. For example, Berthelot finds from 
 
 Chappuis' data 
 
 
 
 
 For H 2 , mean y 
 
 = -00366207 = 1/273-07 (see p. 44) 
 
 N 2 , 7 
 
 = -00366182 = 1/273-09 (see p. 44) 
 
 Kelvin's absolute temperature scale agrees with the ideal gas scale, and there- 
 
 fore with the rarefied gas scale. Now, as will be seen below, for H 2 = y very 
 
 nearly, and thus the constant-volume hydrogen scale of temperature may justifiably j 
 
 be taken as closely approximating to the thermodynamic scale (see also p. 
 (See Bornstein and Scheel in L.B.M. ; Young's " Stoichiometry "; and 
 
 44)- 
 Berthelot 
 
 and Chappuis, Trav. et Mttm. du Bur. Intl., 1907.) 
 
 
 
 Gas. 
 
 Temp. 
 
 A- 
 
 a 
 
 Obs. 
 
 Gas. 
 
 Temp. 
 
 A- 
 
 ft 
 
 Obs. 
 
 I 
 
 AT CONSTANT PRESSURE. 
 
 AT CONSTANT VOLUME. 
 
 
 C. 
 
 cm. Hg. 
 
 
 
 C. 
 
 cm. Hg. 
 
 
 
 Air 
 
 o-ioo 
 
 lOO'I 
 
 0036728 
 
 0,1903 
 
 Air 
 
 
 
 58 
 
 0037666 
 
 M., 1892 
 
 ,, 
 
 O-IOO 
 
 76 
 
 3671 
 
 R., 1847 
 
 , 
 
 
 
 I'32 
 
 37172 
 
 ,, 
 
 H 2 
 
 O-IOO 
 
 100 
 
 36600 
 
 C., 1903 
 
 i 
 
 
 
 I0'0 
 
 36630 
 
 ?J 
 
 
 O-IOO 
 
 76 
 
 3661 
 
 R., 1847 
 
 
 
 
 17-24 
 
 36513 
 
 R., 1847 
 
 
 
 O-IOO 
 
 76 
 
 36609 
 
 R. M. 
 
 ! 
 
 
 
 76 
 
 36650 
 
 
 N 2 . 
 
 O-IOO 
 
 100 
 
 367313 
 
 C, 1903 
 
 , 
 
 o-ioo 
 
 lOO'I 
 
 36744 
 
 C., 1*903 
 
 . 
 
 O-IOO 
 
 139 
 
 367750; C., 1903 
 
 , 
 
 
 
 200 
 
 3690 
 
 R., 1847 
 
 . 
 
 
 
 200 atm. 
 
 434 
 
 A., 1890 
 
 , 
 
 
 
 2000 
 
 3887 
 
 
 
 . 
 
 
 
 1000 
 
 218 
 
 A., 1890 
 
 5 
 
 0-1067 
 
 23 
 
 36643 
 
 J. P. 
 
 2 
 
 
 
 100 
 
 486 
 
 A., 1890 
 
 H 2 . 
 
 O-IOO 
 
 52 
 
 36626 
 
 T. J., '02 
 
 CO. 
 
 
 
 76 
 
 3669 
 
 R., 1847 
 
 5) 
 
 O-IOO 
 
 70 
 
 366255 
 
 
 C0 2 
 
 O-2O 
 
 M'8 
 
 37128 
 
 
 
 O-IOO 
 
 100 
 
 366256 
 
 C., 1903 
 
 , . 
 
 0-40 
 
 37100 
 
 
 ,, . 
 
 O-IOO 
 
 109 
 
 36627 
 
 O, 1908 
 
 , . 
 
 O-IOO 
 
 77 
 
 37073 
 
 
 KT 2 . 
 
 O-IOO 
 
 53 
 
 36683 
 
 C, 1903 
 
 J 
 
 O-20 
 
 QQ 8 
 
 37602 
 
 
 . 
 
 O-IOO 
 
 79 
 
 36718 
 
 
 J 
 
 0-40 
 
 "7 " 
 
 37536 
 
 
 > 
 
 O-IOO 
 
 100 
 
 367440 
 
 j.J 
 
 
 O-IOO 
 
 J> 
 
 374io 
 
 
 2 
 
 O-IOO 
 
 66 
 
 36738 
 
 M.N.,'o3 
 
 , 
 
 0-20 , '7.7 
 
 37972 
 
 
 
 0-1067 
 
 18-23 
 
 36652 
 
 J.P. 
 
 J 
 
 0-40 
 
 37906 
 
 
 He 
 
 O-IOO 
 
 52 
 
 36627 
 
 T. J., '02 
 
 J 
 
 O-IOO 1 
 
 37703 
 
 
 M 
 
 O-IOO 
 
 70 
 
 366255 
 
 M 
 
 
 O-IOO 
 
 76 
 
 37282 
 
 R. M. 
 
 M 
 
 o-ioo 
 
 100 
 
 36616 
 
 O., 1908 I 
 
 N 2 O 
 
 
 
 76 
 
 3719 
 
 R., 1847 
 
 A . 
 
 
 
 51-7 
 
 3668 
 
 K. R, '96 
 
 NH y 
 
 0-50 
 
 76/1 c 
 
 3854 
 
 P.D.,'o6 
 
 CO 
 
 O-IOO 
 
 76 
 
 3667 
 
 R., 1847 
 
 S0 2 
 
 
 
 / / L J 
 
 76 
 
 3903 
 
 R.,i8 4 7 
 
 ,, 
 
 0-1067 23 
 
 36648 
 
 J.P. 
 
 
 / "~ 
 
 
 ^nft 
 
 _ _ __- 
 
 C I'X 
 
 26081 
 
 C~* T rw^'} 
 
 A., Amagat ; C., Chappuis; J. P., Jac- 
 querod & Perrot ; K. R., Kuenen & Randall ; 
 M., Melander ; M. N., Makower & Noble; 
 O., Onnes ; P. D., Perman & DavSes ; R., 
 Regnault ; R. M., Richards & Marks ; T. J., 
 Travers & Jacquerod. 
 
 rf f o 
 
 S0 2 
 
 0-20 
 
 o-ioo 
 0-1067 
 
 5 1 < 
 99-8 
 
 24 
 
 76 
 76 
 
 30901 
 
 37335 
 37262 
 
 36756 
 3676 
 345 
 
 "-) J 93 
 
 j. r'.' 
 
 R., 1847 
 R., 1847 
 
55 
 COEFFICIENTS OF EXPANSION 
 
 COEFFICIENTS OF CUBICAL EXPANSION OF LIQUIDS 
 
 As with solids (see p. 52), if the temperature 'interval is not large, a linear 
 equation v t = v (i + at) may be employed to show the relation between the volume 
 (zO of a liquid and its temperature (/). The mean coefficient (a) thus defined 
 increases in general with the temperature. The values of a subjoined are per C., 
 and for a range round 18 C. unless otherwise specified. 
 
 Liquid. Temp, range. 
 
 Mean Coefficient from C. to t C. 
 
 Observer. 
 
 Water 
 
 (see p. 22 
 and below) 
 Mercury 
 
 (see p. 22) 
 
 H scale. 
 
 17 to 4O 
 17 to 100 
 24 to 299 
 
 to 100 
 
 o :5 i3oi9/(/)- -0465769 4- -0586797^ - '077336/2 i Chappuis, '97 
 
 Density = i - ^^-^^ VV^T '^ i Thiesen, '03 
 
 466,700 / + 67 365 - / 
 
 Regnault, '47 
 
 (Broch) 
 Chappuis, '07 
 f Callendar & 
 Moss, Phil. 
 [ Trans., 191 1 
 
 00018179 
 
 00018169 'o 8 ::95 if + o a ii5/ 
 
 - 10 to 300 -ooo 1 805 5 5 + -o 7 1 244/ - 
 O to 2OO "00018006 + -o 7 2/, to i in 2000 
 
 Liquid. 
 
 Acetic acid . 
 
 Alcohol, me. . 
 ethyl 
 ,, amyl 
 
 Aniline . . 
 
 Benzene . . 
 
 CS 2 . . . 
 
 Chloroform . 
 
 x 10" 
 
 107 
 
 122 
 I 10 
 
 Q-5 
 
 O ^ 
 
 124 
 
 121 
 126 
 
 Liquid. 
 
 Ether, ethyl . 
 Ethyl bromide 
 Glycerine . . 
 Mercury (see 
 Methyl iodide 
 Oil, olive . . 
 paraffin . 
 
 X 10 E 
 
 163 
 
 137 
 
 50 
 
 above) 
 
 121 
 70 
 90 
 
 no 
 
 Liquid. 
 
 Pentane . . 
 
 Toluene . . 
 
 Turpentine . 
 
 Xylol(m) . 
 
 Water,5-io c 
 10-20 
 20-40 
 40-60 
 
 x io~ 
 
 159 
 109 
 
 94 
 101 
 
 5*3 
 
 15-0 
 30-2 
 45-8 
 
 Liquid. 
 
 Water, 60-80 
 
 Solutions 
 
 CaCl 2 , 5-8% . 
 
 40-9% 
 NaCl, 26% . 
 H 2 SO 4 , 100% 
 
 x 10" 
 
 587 
 
 25-0 
 45-8 
 43' 6 
 57 
 
 MECHANICAL EQUIVALENT OF HEAT 
 
 Joule's equivalent, J, is here given as the number of ergs equivalent to a calorie, 
 i.e. the heat required to raise i gram of water through 1 C. at some specified 
 temperature. The 15 calorie is about i part in icoo greater than the 2O 
 calorie. (See p. 56.) 
 
 See Griffith's "Thermal Measurement of Energy," 1901. 
 
 Observer. 
 
 Calorie. 
 
 Joule, 1843 
 
 Rowland, 1878. . . . 
 Griffiths, 1893 . . . . 
 Schuster and Gannon, 
 
 1894 
 
 Callendar and Barnes, 
 
 1899 
 
 N. scale 
 20 C. 
 20 
 20 
 
 Ergs. 
 
 X I0 7 
 
 4-169 
 4-180 
 4-184 
 
 4-181 
 
 4' 1 80 
 
 Observer. 
 
 Bousfield, Phil. Trans., 
 1911 
 
 Crdmieu & Rispail, 1908 
 
 Reynolds & Moorby, 
 1897 
 
 Barnes, 1909 (deduced) 
 
 Calorie. 
 
 N. scale 
 
 20 C. 
 
 
 Ergs. 
 
 Mean 
 Mean 
 
 x io 7 
 
 4'i75 
 4-185 
 
 4-184 
 4-185 
 
56 
 
 SPECIFIC HEATS 
 
 SPECIFIC HEAT OF WATER 
 
 Callendar and 
 
 Barnes (Phil, l^rans., 1902) used an electrical method of determining the 
 
 temperature variation of the specific heat of water. 
 
 The specific heats below are reduced by 
 
 Callendar (" Ency. Brit.," Art. " Calorimetry ") from their results ; they are relative to the specific 
 
 heat at 20 C. on the C.P. nitrogen scale. 
 
 The 20 calorie (see pp. 5 and 55) is adopted as 4-180 
 
 joules = 4' 1 80 X io 7 
 
 ergs, being the mean of the results of Rowland (1879) an d of Reynolds and 
 
 Moorby (reduced), 
 
 each of whom used 
 
 a mechanical method of determining "J." Thus the \ 
 
 values of J below do not rest on the values attributed to the electrical standards employed. 
 
 The specific heat of water is a minimum at 37'5 C. 
 
 
 The 15 calorie (according to Barnes, Proc. Roy. Soc., 1909) = 4*184 joules, assuming the 
 
 e.m.f. of the Clark cell at 15 C. = i'433o international volts. 
 
 The mean calorie (= T ^o f heat required to raise I gram of water from o to 100 C.) 
 
 ! = 4*185 joules (Barnes, 1909) ; = 4*184 joules (Reynolds and Moorby, 1897, corrected by Smith). 
 
 Temp Specific 
 heat. 
 
 Joules. 
 
 Temp. 
 
 Specific 
 heat. 
 
 Joules. 
 
 Tem P- ! taf 
 
 Joules. 
 
 
 
 
 
 
 
 
 -5C. 
 
 0158 
 
 4-246 
 
 45 C. 
 
 9983 
 
 4-I73 
 
 95 C. -0063 
 
 4 -206 
 
 
 
 0094 
 
 4-219 
 
 50 
 
 9987 
 
 4-175 
 
 100 -0074 
 
 4-211 
 
 5 
 
 0054 
 
 4-202 
 
 55 
 
 9992 
 
 4^77 
 
 120 -0121 
 
 4-231 
 
 10 
 
 0027 
 
 4-191 
 
 60 
 
 0000 
 
 4-180 
 
 140 -0176 
 
 4'254 
 
 15 
 
 QOII 
 
 4-184 
 
 65 
 
 0008 
 
 4-183 
 
 160 -0238 
 
 4-280 
 
 20 
 
 i-oooo 
 
 4-180 
 
 70 
 
 -0016 
 
 4-187 
 
 180 -0308 
 
 4-309 
 
 25 
 
 9992 
 
 4"i77 
 
 75 
 
 0024 
 
 4-190 
 
 200 -0384 
 
 4-34I 
 
 30 
 
 9987 
 
 4-I75 
 
 80 
 
 0033 
 
 4-194 
 
 220 -0467 
 
 4'376 
 
 35 
 
 9983 
 
 4-173 
 
 85 
 
 0043 
 
 4-198 
 
 
 
 40 
 
 9982 
 
 4*173 
 
 90 
 
 0053 
 
 4-202 
 
 
 
 SPECIFIC HEAT OF MERCURY 
 
 In terms of the gram calorie at I5'5 on the const, vol. H. scale. (Barnes and Cooke, Phys. 
 Rev., 15, 1902.) Mercury has a minimum specific heat at 140 C. (Barnes, Brit. Ass. Rep., 1909.) 
 
 Temp. C. 
 
 20 
 
 40 
 
 60 
 
 80 
 
 100 
 
 200 
 
 Spscific heat . '0335 
 
 0333 
 
 0331 
 
 0329 
 
 0328 
 
 (0327) 
 
 (-032) 
 
 SPECIFIC HEATS OF THE ELEMENTS 
 
 For gases, see p. 58. (See Waterman, 
 
 Phys. Rev., 1896, and Bornstein and Scheel in L.B.M.) 
 
 Substance. 
 
 Temperature. ' 
 
 Sp. 
 
 heat. 
 
 Observer. 
 
 Substance. 
 
 Temperature. 
 
 Sp. 
 heat. 
 
 Observer. 
 
 Aluminium . 
 
 -182 to 15 
 
 168 
 
 Tilden, 1903 
 
 Bromine, liqd. 
 
 13 to 45 
 
 107 
 
 Andrews, '48 
 
 
 15 to 185 
 
 219 
 
 ? 
 
 
 Cadmium * . 
 
 -186 to -79 
 
 050 
 
 Behn, 1900 
 
 
 600 j 
 
 282 
 
 Richards, '93 
 
 
 pure 
 
 18 to 99 
 
 '55 
 
 Voigt, 1893 
 
 Antimony . . 
 
 -18610-79-0462 
 
 Behn 
 
 , IQOO 
 
 Caesium . . 
 
 Oto26 
 
 048 
 
 E. & G., 1900 
 
 
 17 to 92 
 
 ot;o8 
 
 Gaede, 1902 
 
 Calcium . . 
 
 -185 to 20 
 
 157 
 
 N. 
 
 & B., 1906 
 
 Arsenic, cryst. 
 
 21 to 68 
 
 083 
 
 B. &W., 1868 
 
 
 
 to 100 
 
 149 
 
 Be., 1906 
 
 amorph. 
 
 21 to 65 -076 
 
 
 Carbon 
 
 
 
 
 
 
 Barium . . 
 
 -185 to 20 
 
 068 
 
 N. & B, 1906 
 
 Gas carbon . 
 
 24 to 68 
 
 204 
 
 B. & W., 1868 
 
 Beryllium . . 
 
 to 100 
 
 42^ 
 
 N. & P., 1880 
 
 Charcoal 
 
 Oto24 
 
 165 
 
 H.F.Weber,'75 
 
 Bismuth . . 
 
 -186 
 
 0284 
 
 Giebe, 1903 
 
 
 H 
 
 to 224 
 
 238 
 
 
 H 
 
 
 22 to 100 -0304 
 
 W., 
 
 1896 
 
 Graphite 
 
 -50 
 
 
 114 
 
 
 5) 
 
 Boron, amor. 
 
 to 100 
 
 307 
 
 M.&G., 1893 
 
 
 
 
 11 
 
 
 1 60 
 
 
 ,, 
 
 Bromine, solid 
 
 -78 to -20 
 
 084 
 
 Regnault, '49 
 
 
 
 
 202 
 
 
 297 
 
 
 " 
 
 * Contained Fe 
 
 and Zn. 
 
 
 
57 
 
 SPECIFIC HEATS 
 
 SPECIFIC HEATS OF THE ELEMENTS (contd.) 
 
 Substance. 
 
 Temperature 
 
 Sp. 
 heat 
 
 Observer. 
 
 Substance. 
 
 Temperature. 
 
 Sp. 
 
 heat. 
 
 Observer. 
 
 Carbon (contd.] 
 
 
 
 
 Palladium . . 
 
 -186 to 18 
 
 053 
 
 Behn, 1898 
 
 Graphite 
 
 977" C. 
 
 467 
 
 H.F.Weber,'75 
 
 
 18 to 100 
 
 059 
 
 >> 
 
 Diamond 
 
 -50 
 
 064 
 
 
 
 Phosphorus 
 
 
 
 
 >5 
 
 11 
 
 113 
 
 
 
 yellow 
 
 -78 to 10 
 
 17 
 
 Regnault, 1849 
 
 J> * 
 
 206 
 
 2/3 
 
 
 
 
 13 to 36 
 
 '202 
 
 Kopp, 1864 
 
 
 
 985 
 
 '459 
 
 
 
 ,, liquid 
 
 49 to 98 
 
 205 
 
 Person, 1847 
 
 Cerium . . . 
 
 to 100 
 
 045 
 
 H., 1876 
 
 red . 
 
 15 to 98 
 
 17 
 
 Regnault, 1853 
 
 Chlorine, liqd. 
 
 Oto24 
 
 226 
 
 Knietsch 
 
 Platinum . . 
 
 -186 to 18 
 
 '0293 
 
 Behn, 1898 
 
 I Chromium . 
 
 -200 
 
 067 
 
 Adler, 1903 
 
 
 18 to 100 
 
 0324 
 
 || 
 
 (i-4%Fe&Si) 
 
 
 
 104 
 
 }> 
 
 
 1230 
 
 '0461 
 
 Tilden, 1903 
 
 
 100 
 
 '112 
 
 
 
 Potassium . . 
 
 -78 to 23 
 
 166 
 
 Schiiz, 1892 
 
 
 400 
 
 133 
 
 j> 
 
 Rhodium . . 
 
 10 to 97 
 
 058 
 
 Regnault, 1862 
 
 Cobalt . . . 
 
 -182 to 15 
 
 082 
 
 Tilden, 1903 
 
 Ruthenium 
 
 to 100 
 
 06 1 
 
 Bunsen, 1870 
 
 
 15 to 100 
 
 103 
 
 
 
 Selenium, cryst 
 
 22 to 62 
 
 084 
 
 B. & W., 1868 | 
 
 
 15 to 630 
 
 123 
 
 55 
 
 amorph 
 
 18 to 38 
 
 095 
 
 jj 
 
 Copper . . . 
 
 -192 to 20 
 
 0798 
 
 Schmitz, 1903 
 
 Silicon, cryst. 
 
 -185 to 20 
 
 123 
 
 N. & B, 1906 
 
 
 20 to 100 
 
 0936 
 
 J5 
 
 
 57 
 
 183 
 
 H.F.Weber,'75 
 
 
 900 
 
 118 
 
 Le Verrier, '92 
 
 
 232 
 
 203 
 
 H 
 
 Didymium. 
 
 to 100 
 
 '046 
 
 H., 1876 
 
 Silver . . . 
 
 -186 to -79 
 
 0496 
 
 Behn, 1900 
 
 I Gallium, solid 
 
 12 to 23 
 
 079 
 
 B., 1878 
 
 
 15 to 100 
 
 056 
 
 B. & S., 1895 
 
 liquid 
 
 12 to 119 
 
 080 
 
 i 
 
 
 427 
 
 059 
 
 Tilden, 1903 
 
 1 Germanium . 
 
 to 100 
 
 074 
 
 N. & P., 1887 
 
 Sodium . . . 
 
 -185 to 20 
 
 234 
 
 N. & B., 1906 
 
 Gold. . . . 
 
 -185 to 20 
 
 035 
 
 N. & B., 1906 
 
 
 10 
 
 297 
 
 Bernini, 1906 
 
 
 18 to 99 
 
 0303 
 
 Voigt, 1893 
 
 
 128 
 
 *333 
 
 pj 
 
 Indium . . . 
 
 to 100 
 
 057 
 
 Bunsen, 1870 
 
 Sulphur 
 
 
 
 
 Iodine . . . 
 
 9 to 98 
 
 054 
 
 Regnault, 1840 
 
 rhombic 
 
 17 to 45 
 
 163 
 
 Kopp, 1865 
 
 Iridium . . . 
 
 -186 to 18 
 
 0282 
 
 Behn, 1898 
 
 liquid . 
 
 119 to 147 
 
 -235 
 
 Person, 1847 
 
 
 18 to 100 
 
 323 
 
 >> 
 
 Tantalum . . 
 
 -185 to 20 
 
 033 
 
 N. & B., 1906 
 
 Iron .... 
 
 -192 to 20 
 
 089 
 
 Schmitz, 1903 
 
 
 58 
 
 036 
 
 v. Bolton, 1905 
 
 
 20 to 100 
 
 119 
 
 j 
 
 Tellurium, crys. 
 
 15 to 100 
 
 048 
 
 Fabre, 1887 
 
 
 225 
 
 137 
 
 Stiicker, 1905 
 
 Thallium . . 
 
 -192 to 20 
 
 0300 
 
 Schmitz, 1903 
 
 
 to 1100 
 
 153 
 
 Marker, 1905 
 
 
 20 to 100 
 
 0326 
 
 M 
 
 Lanthanum . 
 
 to 100 
 
 045 
 
 H., 1876 
 
 Thorium . . 
 
 to 100 
 
 028 
 
 Nilson, 1883 
 
 Lead. . . . 
 
 -192 to 20 
 
 0293 
 
 Schmitz, 1903 
 
 Tin .... 
 
 -186 to -79 
 
 0486 
 
 Behn, 1900 
 
 
 20 to 100 
 
 0305 
 
 
 
 
 19 to 99 
 
 0552 
 
 Voigt, 1893 
 
 
 300 
 
 0338 
 
 Naccari, 1888 
 
 molten . 
 
 240 
 
 064 
 
 Spring, 1886 
 
 Lithium . . 
 
 Otol9 
 
 837 
 
 Be., 1906 
 
 Titanium . 
 
 -185 to 20 
 
 082 
 
 N. & B., 1906 
 
 
 to 100 
 
 1-093 
 
 u 
 
 
 to 100 
 
 JI 3 
 
 N. & P., 1887 
 
 Magnesium . 
 
 -186 to -79 
 
 189 
 
 Behn, 1900 
 
 
 to 440 
 
 162 
 
 H 
 
 
 18 to 99 
 
 246 
 
 Voigt, 1893 
 
 Tungsten . . 
 
 -185 to 20 
 
 036 
 
 N. & B., 1906 
 
 
 225 
 
 281 
 
 Stiicker, 1905 
 
 
 20 to 100 
 
 34 
 
 Gin, 1908 
 
 Manganese . 
 
 14 to 97 
 
 122 
 
 Regnault, 1862 
 
 Uranium . . 
 
 11 to 98 
 
 062 
 
 Regnault, 1840 
 
 Mercury . . 
 Molybdenum . 
 
 See preced 
 -185 to 20 
 
 n SP 
 063 
 
 N.& B., 1906 
 
 Vanadium . 
 
 Oto98 
 to 100 
 
 028 
 I5 
 
 Bliimcke, 1885 1 
 Mache, 1897 
 
 
 15 to 91 
 
 072 
 
 D. & G., 1901 
 
 Zinc .... 
 
 -192 to 20 
 
 084 
 
 Schmitz, 1903 
 
 Nickel . . . 
 
 -186 to 18 
 
 086 
 
 Behn, 1898 
 
 
 20 to 100 
 
 93 
 
 jt 
 
 
 18 to 100 
 
 109 
 
 if 
 
 
 300 
 
 104 
 
 Naccari, 1888 
 
 Osmium . . 
 
 19 to 98 
 
 031 
 
 Regnault, 1862 
 
 Zirconium . . 
 
 to 100 
 
 066 
 
 M.& D., 1873 
 
 B., Berthelot ; Be., Bernini ; B. & S., Bartoli & Stracciati ; B. & W., Bettendorff | 
 
 Wiillner ; D. & G., Defacqz & Guichard ; E. & G., Eckardt & Graefe ; H., Hillebrand ; M. 
 
 & D., Mixter & Dana ; M. & G., Moissan & Gautier ; N. & B., Nordmeyer & Bernouilli ; 
 
 N. & P., Nilson & Pettersson ; W., Waterman. 
 
58 
 
 SPECIFIC HEATS 
 
 SPECIFIC HEATS OF GASES AND VAPOURS 
 
 The values at const, pressure are, unless otherwise stated, all at atmospheric pressure, 
 heats given are calories per gram of gas per degree C. at the temp, stated. 
 
 The specific 
 
 Gas. 
 
 AT CONST 
 
 Air (dry) .... 
 it 5 .... 
 >> .... 
 
 5) .... 
 V ?) .... 
 
 70 atmos. 
 Argon . 
 
 Temp. Sp. ht. Observer. 
 
 ANT PRESSURE ( c/> ) 
 
 20 C. "2417 Swann, 1909 
 100 -2430 
 20-440 -2366 H. & A., 1905 
 20-98 -2372 Witkowski, 
 -102-17 -2372 1896 
 -50 -312 J 
 20-90 -123 D., 1897 
 3-402 Lussana, 1894 
 3788 
 -2350 * H. & H.,'o7 
 -200 -43 Alt, 1904 
 20-440 -2419 H. & A., 1905 
 20-800 -2497 
 -190 -347 Alt, 1904 
 16-343 -115 Strecker, '81 
 19-388 -055 '82 
 206-377 -034 
 23-99 -242 W., 1876 
 -2010 *H. & H., 07 
 20 '2020 Swann, 1909 
 
 100 -221 
 
 atmos. '2670 Lussana, '94 
 100 -4652';* H. & H., '07 
 
 Gas. 
 
 Ammonia, NH 3 . 
 Nitrous oxide, N 2 O 
 Nitric oxide, NO . 
 N. peroxide, NO., . 
 H.,S 
 CS 2 
 
 Temp. Sp. ht. 
 
 23 100 -520 
 26-103 ; -213 
 13-172 1 -232 
 27-67 1-625 
 20-206 i -245 
 86-190 -i 60 
 591 
 404 
 34-115 -299 
 27-118 -144 
 101-223 -458 
 108 220 -453 
 25-111 -428 
 179 249 -506 
 
 TANT VOLUME ( 
 
 -1715 
 f. 50 2-402 
 c. 55 -1650 
 2000 -0746 
 -175 
 100 -340 
 
 Observer. 
 
 iWkdemanl 
 1 1876 
 Regnault, '63 
 B. & 0., 1883 
 Regnault, '62 
 
 ?> 
 Lussana. '9$ 
 
 55 
 
 )Wiedemann, 
 
 1 i77 
 Regnault, '62 
 Regnault, '62 
 W., 1876 
 Regnault, '62 
 
 Jolv, 1891 
 
 ] 8 94 
 Pier, 1909 
 
 J? 
 >5 
 
 Methane, CH 4 . . 
 Ethylene C 2 H 4 . . 
 Benzene, C G H fi . . 
 Chloroform CHC1,. 
 Me. alcohol CH 4 O. 
 Et. alcohol C 2 H 6 O. 
 ether (C 2 H 5 ) 2 O. 
 Turpentine, C 10 H 16 
 
 AT CONS 
 
 Hydrogen . . . 
 30 atmos. 
 Nitrogen .... 
 (liq.) . . 
 Oxygen .... 
 
 " Oiq.) '. ' 
 Chlorine .... 
 Bromine .... 
 
 Air,t i atmos . . 
 Hydrogen j . . . 
 Carbon dioxide . 
 Argon ... 
 
 Carbon monoxide . 
 dioxide . . 
 > 
 >> 
 30 
 Water vapour . . 
 
 Nitrogen || . . . 
 Water vapour . . 
 
 B. & O., Berthelot & Ogier ; D., Dittenberger ; H. & / 
 * H. & H., Holborn (Nitrogen (0-1400), c 
 and Henning | C0 2 (0-1400), c 
 (Reichsanstalt). (Water vapour (100-1400 
 t Air, cv "1715 + '02788^ wherepis the density (gm./c.c 
 J H, cv diminishes with increasing density and falling ten 
 
 L., Holborn & Austin (Reichsanstalt) ; W., \YieJemann. 
 p - -2350 + -OOOOI9/ . 
 
 '=-20IO + -OCOG 74 2/--0 7 l8,' 'j^P- 
 
 , cp -4669 - -oooo 1 68/ + "0 7 44/ 2 
 CO,, c v '165 + "2125? + '34p 7 , p being density 
 p. || N, Cv = '175 -f- -00016^, / being the temp. 
 
 RATIO OF THE SPECIFIC HEATS FOR GASES AND VAPOURS 
 
 y = the ratio of the specific heat at constant pressure to that at constant volume, y is usually 
 determined directly by some method involving an adiabatic expansion, such as the determination 
 of the velocity of sound in the gas. From a knowledge of either (i) the pressure or (2) the 
 temperature immediately following an adiabatic expansion (Clement and Desormes, Lummer and 
 Pringsheim's methods respectively), y can be deduced from pv^f = const, or 6v* ~ x = const. 
 (See Capstick, ; ' Science Progress," 1895.) 
 
 Gas. 
 
 Temp. 
 
 0C. 
 
 
 310 
 
 5-14 
 
 
 y 
 
 1-63 
 1-667 
 
 c r66 
 1-666 
 
 1-402 
 1-401 
 i '40 1 
 1-414 
 
 Observer. 
 
 Gas. 
 
 Temp. y Observer. 
 
 M on atomic gases 
 Helium .... 
 Arson . 
 
 B. & G., 1907 
 Niemeyer, '02 
 
 K.&W., 1876 
 
 L. & P., 1898 
 Stevens, 1905 
 Makower. '03 
 Hartmann, '02 
 
 Air (dry) .... 
 
 5> .... 
 JJ )> .... 
 JJ )1 .... 
 )) .... 
 
 200 } 
 
 atmos. J 
 Hydrogen 
 ,, ... 
 Nitrogen .... 
 Oxygen .... 
 Carbon monoxide . 
 Nitric oxide, NO . 
 
 -402 Koch, 1907 
 -402 F., 1908 
 500 -399 
 900 -39 Knlahne, '03 
 -79'3 -405 Koch, 1907 
 "828 ' 
 -79-3 -333 
 -419 Hartmann, 0; 
 4 16 -408 L. & P., 1898 
 41 Cazin, 1862 
 5 14 -400 L. & P., 1898 
 401 Leduc, 1898 
 394 Masson 
 
 Neon . . . . ) 
 Krypton ... 
 Xenon . . . . j 
 Mercury vapour 
 
 Diatomic gases 
 1 Air (dry) .... 
 .... 
 
 ;> 5> .... 
 .... 
 
 15. & G., Behn & Geiger ; F. Fiirstenau ; K. & W. Kundt & Warburg ; L. & P., Lummer & Piingsheim. 
 
59 
 
 SPECIFIC HEATS 
 
 RATIO OF THE SPECIFIC HEATS FOR GASES AND VAPOURS (conti.) 
 
 Gas. 
 
 Triatomic gases 
 
 Ozone 
 
 Water vapour . 
 Carbon dioxide . . 
 
 Ammonia, NH 3 
 Nitrous oxide, N 2 O 
 |NitrogenjN 2 O 4 . . 
 peroxide/ NO., . . 
 H.,S. 
 
 Sulphur dioxide. < 
 
 Polyatomic gases 
 
 Methane, CH 4 . 
 Ethane, C 2 H,. . 
 Propane, C 3 H 8 . 
 
 Temp. 
 
 100 (?) 
 4-11 
 
 Observer. 
 
 1*29* Jacobs, 1905 
 1*305 Makower, '03 
 1-300 L. & P., 1898 
 1*306 Hartmann, '05 
 
 500 1-26 j F., 1908 
 
 20 
 150 
 
 16-34 
 500 
 
 1*336 Leduc, 1898 
 
 1*324: 
 
 1*172 Natanson, '85 
 
 i'3i 
 
 1*340! Capstick, '95 
 
 1*239; 
 
 1*26 | Miiller, 1883 
 
 F., 1908 
 
 T22 
 
 Capstick, '93 
 (Daniel & 
 | \ Pierron, '99 
 
 Gas. 
 
 Acetylene, C 2 H 2 
 
 Ethylene, C 2 H 4 . . 
 Benzene, C G H G . 
 
 55 . . . . 
 
 Chloroform, ) 
 
 CHC1 3 . . . j 
 
 CC1 4 
 
 Me. alcohol . . . 
 
 chloride 
 
 iodide . 
 
 Et alcohol . 
 
 bromide . 
 
 chloride . 
 
 ether . . 
 
 Acetic acid 
 
 Temp. 
 
 20 
 997 
 24-42 
 998 
 
 997 
 19-30 
 
 53 
 
 998 
 
 22-7 
 12-20 
 
 99-7 
 1365 
 
 Observer. 
 
 26 |M.& F., 1897 
 
 264 i Capstick, '95 
 40 Pagliani, '96 
 Stevens, '02 
 
 Miiller, 1883 
 Stephens, '02 
 Capstick, '95 
 
 105 
 
 no 
 
 150 
 
 130 
 
 256 I Stevens, '02 
 
 '274 Capstick, '93 
 
 '279 ! 55 
 '286 
 
 133 Jaeger, 1889 
 134 Stevens, '02 
 Capstick, '93 
 
 1 88 
 187 
 '024 
 
 '112 
 
 147 
 
 Low, 1894 
 Stevens, '02 
 
 Extrapolated; F., Fiirstenau; L. & P., Lummer & Pringshcim ; M. & F., Maneuvrier and Fournier. 
 
 SPECIFIC HEATS OF VARIOUS BODIES 
 
 In most cases, the specific heats given must only be regarded as rough average values. 
 
 Substance. i Temp, j Sp. ht. 
 
 Alloys- C. | 
 
 Brass, red . . -090 
 
 yellow . } -088 
 
 Eureka ... 18 I '098 
 (Constantan) 
 
 German silver . 0-100 j -095 
 
 Liquids- 
 
 Alcohol, amyl . 
 ethl . 
 
 methyl 
 Aniline * ... 
 Benzene . . . 
 
 Brine, ( 
 
 density 1*2 < 
 (Harker) 
 
 18 
 
 
 
 40 
 
 12 
 
 15 
 
 10 
 
 40 
 
 -20 
 
 
 
 15 
 
 '55 
 
 '547 
 
 648 
 
 *6o i 
 
 5H 
 
 340 
 
 423 
 
 69 
 
 71 
 
 72 
 
 Substance. 
 
 Ether, ethyl 
 Glycerine . . 
 Oil, olive . . 
 
 ,, paraffin 
 
 Sea-water . . 
 Toluene . . . 
 Turpentine . . 
 
 Miscel- 
 laneous 
 
 Asbestos . . 
 
 Basalt . . . 
 
 Ebonite . 
 Fluorspar, CaF 2 
 Glass, crown . 
 flint . 
 
 Temp. Sp. ht. 
 
 18 
 18-50 
 
 7 
 
 20-60 \ 
 
 17 
 18 
 18 
 
 20-100 
 20-100| 
 
 20-100 
 
 30 
 
 10-50 
 10-50 
 
 ;s6 
 
 47 
 
 51 to 
 54 
 "94 
 40 
 
 *42 
 
 *20 
 '20 tO 
 
 24 
 
 '33 
 '21 
 
 12 
 
 Substance. 
 
 Glass, Jena i6"'t 
 Jena 59'" t 
 
 Granite . . . 
 Ice. , . . . 
 Indiarubber 
 
 Marble, white . 
 
 Paraffin wax . 
 Porcelain $ . . 
 Quartz, SiO 2 . 
 
 Rocksalt/NaCi 
 Sand .... 
 Silica (fused) . 
 
 Temp. Sp. ht 
 
 18 
 18 
 
 20-100 
 
 -21 to 
 -1 
 
 15-100 
 
 18 
 0-20 
 
 19 
 19 
 
 "*i9to 
 
 w *20 
 
 > '5O2 
 
 1-48 
 f*2I tO 
 \*22 
 *6 9 
 
 15-1000 -255 
 
 
 
 350 
 18 
 
 20-100 
 15-200 
 15-800 
 
 174 
 279 
 
 '21 
 
 19 
 
 *2CO 
 
 248 
 
 * Griffiths, Phil. Mag., 1893. 
 
 t See p. 74. 
 
 \ Harker, 1905. 
 
 Greenwood, 1911 
 
LATENT HEATS 
 
 60 
 
 LATENT HEAT OF FUSION 
 
 The number of gram calories required to convert i gram of substance from solid 
 into liquid without change of temperature. 
 
 ICE 
 
 Temp. 
 
 6-5 C. 
 O 
 O 
 O 
 
 It. ht. 
 
 cals. 
 76-03 
 
 79'59 
 
 80'02 
 
 7977 
 
 Observer, etc. 
 
 Pettersson, 1881. 
 Regnault, 1843, corrected. 
 Bunsen, 1870, with ice calorimeter. 
 
 Smith, Phys. Rev., 1903 (in terms of 15 calorie = 4*184 joules, 
 taking Clark cell = 1*433 volts at I 5 C 0- 
 
 VARIOUS SUBSTANCES 
 
 Substance. Temp. 
 
 Elements- 
 Aluminium 
 
 Bismuth . . 
 
 Cadmium . . 
 
 Copper . . . 
 
 Lead . . . 
 
 Mercury . . 
 Palladium 
 
 Phosphorus . 
 
 657 
 269 
 321 
 
 327 
 1550 
 
 44 
 
 It. lit. 
 
 cals. 
 
 77 
 13 
 14 
 
 43 
 5 
 
 36 
 5 
 
 Substance. Temp. 
 
 Platinum . 
 Potassium 
 Silver . . 
 Sulphur . 
 Tin . . . 
 Zinc . . . 
 Compounds 
 NH 3 . . 
 
 1750 
 
 62 
 
 960 
 
 H5 
 232 
 418 
 
 -75 
 
 Lt.ht. 
 
 cals. 
 
 27 
 16 
 
 9 
 
 14 
 28 
 
 108 
 
 Substance. Temp. Lt.ht 
 
 NaNO 3 . 
 KN0 3 . . 
 H 2 S9 4 . . 
 Acetic acid 
 Benzene . 
 Glycerine . 
 Naphthalene 
 Xylene . . 
 
 339 
 10-3 
 
 4 
 5'4 
 
 8 
 
 16 
 
 cals. 
 63 
 
 47 
 24 
 44 
 30 
 42 
 
 35 
 39 
 
 LATENT HEAT OF VAPORISATION 
 
 Latent heats are given as the number of gram calories required to convert 
 i gram of substance from liquid into vapour without change of temperature. The 
 I latent heat of vaporisation vanishes at the critical temperature. 
 
 Trotitpn's Rule. The latent heat of vaporisation of i gramme molecule of a 
 liquid divided by the corresponding boiling point (on the absolute scale) is a 
 constant (C). C = 21 for substances of which both liquid and vapour are unassociated. 
 If the liquid is associated, C j> 21 (e.g. water, C = 26) ; if the vapour is associated, 
 C < 21 (e.g. acetic acid, C = 15). [See Nernst's "Theoretical Chemistry."] 
 
 STEAM 
 
 Regnault's equation connecting latent heat and temperature takes no account 
 of the temperature variation of the specific heat of water (see p. 56). The equation 
 gives values which are too large at low temperatures. The equations of Griffiths, 
 Henning, and Smith have been reduced and are here expressed in terms of the 
 15 calorie = 4*184 joules. Griffiths' and Smith's results rest further on an 
 attributed value of 1-433 volts for the e.m.f. of the Clark cell at 15 C. 
 
 See also next page. [The critical temp, of water is about 365 C.] 
 
 Observer. 
 
 Regnault, 1847 . 
 
 Griffiths, 1895 . 
 
 Henning, Ann. 
 d.Phys., 1906, 
 1909 . . . 
 
 Smith, Phys.\ 
 Rev., 1907 J 
 
 Temp, range 
 of ezpts. 
 
 Latent heat L ( at t C. 
 
 63-i 9 4 C. L t = 606-5 - -6 9 5/ 
 30 and 40 ; L t = 598*0 -6o5/ 
 3o-ioo { L( = 599'4 -'&>/, to'3 s % 
 
 ioo-i8o L t = 538-97 - -6428(/ - ioo) - - 
 L< = 597'2 - - 
 
 - ioo 
 
61 
 
 LATENT HEATS 
 
 LATENT HEAT OF STEAM (contd.) 
 
 In terms of 
 15 calorie. 
 
 Eegnault, Griffiths, i Joly, 
 1847. 1895. 1895. 
 
 606 f 
 
 598 1 
 
 537 
 
 537*5 1 
 
 540 
 
 Callendar, 
 
 * 
 
 595 t 
 
 540 
 
 Dieterici, ! Henning, 
 1905. 1906. 
 
 596-0 J 
 
 599 1 
 
 539-4 
 
 Smith, 
 1907. 
 
 597 1 
 
 539 1 
 
 Richards & 
 
 Matthews, 
 
 1911. 
 
 538-0 
 
 * From sp. ht. of steam experiments and total heat formula. 
 
 Reduced to mean calories (4-185 joules) ; Clark cell = 1*433 volts. 
 
 t Extrapolated. 
 
 By comparing L 100 (by steam calorimeter) with the mean specific heat of water between 12 and 100. 
 Callendar and Barnes' specific heat has been used (p. 56). 
 
 LATENT HEATS OF VAPORISATION OF VARIOUS SUBSTANCES 
 
 The values below are for pure substances, and are due to Young, Proc. Roy. Dublin Soc., 
 1910. The precise calorie employed is not stated. 
 
 Temp. 
 
 C. 
 
 
 
 20 
 
 40 
 
 60 
 
 80 
 
 100 
 
 120 
 
 140 
 
 160 
 
 180 
 
 200 
 
 220 
 
 240 
 
 260 
 
 280 
 
 Crit. \ 
 temp./ 
 
 SnCl 4 . | CC1 4 . 
 
 cals. 
 
 3176 
 
 30-54: 
 29'12j 
 27-69 
 26-29' 
 
 24'57: 
 22-82 
 
 20-86! 
 18-50 
 15-60 
 
 cals. 
 
 46-00 
 
 44'15 
 42-08 
 
 39-92 
 37-95 
 35-40 
 32-6l 
 29-45 
 25^6 
 20-07 
 10-43 
 
 3iS7 283' 
 
 Pent- 
 ane(). 
 
 cals. 
 
 84-3I 
 80-07 
 
 75-33 
 69-94 
 6 4 - 4 8 
 56-58 
 47-42 
 
 35' 01 
 24-68* 
 
 Methyl 
 
 Ethyl 
 
 Propyl 
 
 Ethyl 
 ether. 
 
 Alcohol. 
 
 cals. 
 289-2 
 284-5 
 277-8 
 269-4 
 259-0 
 246-0 
 232-0 
 
 216-1 
 
 198-3 
 
 177-2 
 151-8 
 
 112-5 
 
 cals. j 
 
 220*9 
 
 220-6 
 
 218-7 
 
 213-4 
 
 206-4 
 
 I97T 
 184-2 
 
 cals. 
 
 I73-0 
 164-0 
 
 cals. 
 
 87-54 
 82-83 
 
 I7I- 
 
 156-9, 
 I39-2 
 II6-6 
 
 88-2 
 40-3 
 
 142-4 
 129-0 
 Il6'3 
 IO2'2 
 
 33*5 
 
 240 | 243-! I 2637 i93-8 
 
 68-42 
 62*24 
 
 55-93 
 46-07 
 31-87 
 
 Methyl 
 
 Ethyl Propyl 
 
 Acetate. 
 
 cals. 
 
 94-07 
 
 88-39 
 8287 
 76-83 
 69-96 
 6roo 
 50-56 
 
 34-87 
 20-99* 
 
 cals. 
 
 8578 
 
 82-15 
 
 77-53 
 
 65-91 
 
 59-87 
 52-71 
 42-63 
 27-17 
 
 cals. 
 
 79-80 
 76-33 
 7I-84 
 67-66 
 62-80 
 
 57-23 
 5078 
 42-40 
 30-70 
 
 II-731I 
 
 Acetic 
 acid. 
 
 cals. 
 
 84-05 
 87-02 
 89-69 
 
 9!'59 
 92-32 
 
 94-38 
 91-83 
 
 89-63 
 87-71 
 85-55 
 82-02 
 78-18 
 72-26 
 63-48 
 
 32i-6 
 
 Ben- 
 zene. 
 
 cals. 
 
 95'45 
 91-41 
 86-58 
 82-82 
 78-94 
 74-62 
 68'8l 
 62-24 
 
 54-11 
 43-82 
 
 288-5 
 
 * At 190. f At 230. 
 
 At 190. At 230. 
 
 At 249 
 
 At 275 C. 
 
 Substance. 
 
 Mercury . 
 Sulphur 
 Phosphorus 
 Liquid H 2 . 
 >i 2 . 
 
 ii air . 
 
 Cl . 
 Bromine . 
 Iodine . 
 
 Temp 
 
 C. 
 
 358 
 
 3i6 
 
 287 
 
 188 
 
 22 
 
 58 
 
 174 
 
 Lt. ht. 
 
 cals. 
 
 68 
 362 
 130 
 123 
 
 58 
 
 67 
 46 
 24 
 
 Substance. 
 
 Liquid N 2 O 
 
 NH 3 
 C0 2 
 
 !', SO, 
 
 Me. formate 
 
 iodide . 
 
 Chloroform 
 
 Temp. 
 
 -20 
 o 
 
 22 
 
 -10 
 
 4 6 
 
 32' 
 
 42 
 
 O 
 
 Lt. ht. 
 
 cals. 
 
 6 7 
 
 341 
 
 57 
 
 96 
 
 85 
 
 uo'5 
 46 
 67 
 
 Substance. 
 
 Chloroform 
 
 Et. bromide . 
 propionate 
 
 iodide . . 
 formate 
 
 Am. alcohol . 
 
 Aniline . . . 
 
 Toluene 
 
 Turpentine . . 
 
 Temp. 
 
 C. 
 
 6i c 
 
 38 
 100 
 
 7i 
 50 
 
 in 
 159 
 
 Lt. ht. 
 
 cals. 
 58 
 60 
 
 79 
 47 
 98 
 
 120 
 104 
 
 84 
 70 
 
62 
 
 THERMOCHEMISTRY 
 
 
 THERMOCHEMISTRY 
 
 In thermochemistry the conservation of energy is assumed in accordance with 
 
 experiment, and consequently (i) if a cycle of chemical change takes place so that 
 
 the final state of the reacting substances is identical with the initial, then as much 
 
 heat is absorbed as is given out, i.e. the total heat of the reaction is zero ; (2) the 
 
 heat of reaction only depends on the initial and final states of the reacting sub- 
 
 stances, and not on the intermediate stages. The results below are affected by, but 
 
 have not been 
 
 corrected for, any changes in the accepted values of the atomic 
 
 weights since the experiments were carried out. 
 
 
 MOLECULAR HEAT OF FORMATION 
 
 The molecular heat of formation (H.F.) is the heat liberated when the 
 
 molecular weight in grams of a compound is formed from its elements. When 
 
 the state of aggregation of an element or compound is not given, it is the state 
 
 in which it occurs at room temperature and pressure. A minus sign before an 
 
 H.F. means that heat is absorbed in the building up of the compound. 
 
 Unit the gram calorie (at 15 to 20 C.) per gm. molecule of compound. Aq 
 
 = solution in a 
 
 large amount of water. The reactions are at constant pressure. 
 
 Example. - 
 
 -H.F. of CuSO 4 = 183,000 ; of CuSO 4 . Aq = 198,800. /. the heat 
 
 of solution of CuSO 4 = 198,800 - 183,000 = 15,800 cals. per gram mol. 
 
 (T., Thomsen, "Thermochemistry," trans, by Miss K. A. Burke ; B., Berthelot, 
 
 Ann. d. Chim. et d. P/iys., 1878 ; T.B., mean of both these observers' values. See 
 
 also Bottger in 
 
 L.B.M.) For organic compounds, see p. 64. 
 
 
 INORGANIC COMPOUNDS 
 
 Compound. 
 
 Mol. H.F. in 
 calories. 
 
 *- ; M :aS in 
 
 *** ; M S in 
 
 Non-Metals 
 
 X IO 3 
 
 
 X IO 3 
 
 
 XIO 3 
 
 HClgas . . 
 
 22'0,T. 
 
 CO 2 from \ 
 
 G7-i B T 
 
 NH 4 Cl.Aq . 72-4 
 
 HCl.Aq . . 
 
 39*3, T. 
 
 amorph. C / 
 
 97 J u - L ' 
 
 (NH 4 ) 2 SO 4 . 283, T.B. 
 
 HBr gas . . 
 
 8M, T. 
 
 CO, from \ 
 
 ^ fj n 
 
 (NH 4 ) 2 SO 4 .Aq 280-6 
 
 HBr.Aq . . 
 
 28-6, T. 
 
 diamond / **->'^ 
 
 NH 4 OH.Aq . 90, B. 
 
 HI gas. . . 
 
 -6-1, T.B. 
 
 B 2 O 3 ; amp. B. 
 
 273, B. 
 
 BaO .... 126, T. 
 
 HI.Aq . . 
 
 + 13-2, T.B. 
 
 SiO 2 Aq ; crys. 
 
 1 80, B. 
 
 Ba' v OH) 2 . . 217, T. 
 
 HF . . 
 
 + 38-5 
 
 As 2 3 . . [Si 155, T. 
 
 BaCl 2 . . . 197, T. 
 
 H 2 O liq. . . 
 
 68-4, T. 
 
 As,0 6 ... 219, T. 
 
 BaCl 2 Aq . . 
 
 I99' 1 , T - 
 
 M * * 
 
 69-0, B. 
 
 CC1 4 from fl ^ V-o 
 
 Bi 2 3 . . . 
 
 20 
 
 ., gas . . 
 
 58-1, B. 
 
 diamond / 
 
 /V| ** 
 
 BiCI 3 . . . 91, T. 
 
 H 2 2 .Aq. . 
 
 47-0 
 
 SbCl 3 solid . 
 
 9i'4,T. 
 
 Cd(OH) 2 . .] ^ ^ 
 
 H.S from \ 
 
 -T7 T 
 
 SbCl 5 liq. . 
 
 105, T. 
 
 Cd + + H,O ] 
 
 
 rhombic S. ./ 
 
 z /, j. . 
 
 CS 2 from ) 
 
 
 CdCl 2 . . . 
 
 93, T. 
 
 NH 3 . . . 
 
 12 
 
 diamond &>-i9, B. 
 
 CdS0 4 . . . 
 
 222, T. 
 
 AsH 3 . . . 
 SbH 3 . . . 
 
 - 3 67 
 
 -87, B. 
 
 rhombic S. .) 
 C 2 N 2 gas V R 
 
 CdSO 4 .8/3H 2 O| 
 on sol. in Aq / 
 
 + 2-66, T. 
 
 SiH 4 . . . 
 
 25 
 
 fromdiam.J 74 ' ^ 
 
 CdSO 4 . Aq . 
 
 2327, T. 
 
 SO 2 from "i 
 
 *i/-\ 
 
 H 2 SO 4 liq. . 
 
 193, T. 
 
 Cs 2 0. . . . 
 
 100 
 
 rhombic S. ./ 
 
 7 
 
 H 2 S0 4 .Aq ) 
 
 
 CaO . . . .) 
 
 131, T. 
 
 SO 3 liq. from j 
 
 
 from rhombic) 
 
 210, T. 
 
 ,, Moissan.f 
 
 H5 
 
 rhombic S. .) 
 
 103 
 
 S . . .] 
 
 
 Ca(OH)., 
 
 ^20 
 
 N 2 ... 
 
 -19 
 
 HNO 3 liq. . 
 
 4i'6,B. 
 
 x*^yv-r*Ayj ^ 
 
 CaC 2 . . . 
 
 * y 
 -7-25 
 
 NO . ... 
 
 -21-6, T. 
 
 HN0 3 .Aq . 
 
 49 
 
 CaCl 2 . . . ! 170, T. 
 
 N 2 3 . . . 
 
 NO 2 /22 . . 
 
 -21-4, B. 
 -17, B. 
 
 HCN gas 1 __ 
 from diam. / ? 
 
 CaCl 2 .Aq. . 
 CaSO 4 . . . 
 
 187-4, T. 
 318, T. 
 
 7150. . 
 
 -7 '6, B. 
 
 HCN liq. . -24-8 
 
 CaCO 3 . . . 
 
 270, T. 
 
 N 2 6 liq. . . 
 
 3'6, T. 
 
 H 3 PO 4 liq. . 302 
 
 Ca(N0 3 ) 2 . . 
 
 202, B. 
 
 P 2 O 5 solid . 
 
 369 
 
 
 
 CoO .... 
 
 64 
 
 P 2 O 6 . Aq . . 
 
 405 
 
 Metals 
 
 
 CoCl 3 . . . 
 
 76-5. T. 
 
 CO from } 
 
 ir\ T* 
 
 A1 2 3 . . . 
 
 38o, B. 
 
 CoSO 4 .7H 2 O 
 
 234, T. 
 
 amorph. C. ./ 
 
 29, 1. 
 
 A1C1 3 . . . 
 
 161 
 
 Co(N0 3 ),.6H 2 
 
 119, T. 
 
 CO from ) 
 
 _/:.. T) 
 
 Al 2 (S0 4 ) 3 .Aq 
 
 880 
 
 CuO. . . . 
 
 37'2, T. 
 
 diamond .f 
 
 2O I, 13. 
 
 NH 4 C1 . . 
 
 76-3, T.B. 
 
 CuCl 2 . . . 
 
 5 r6 
 
63 
 
 HEATS OF FORMATION 
 
 
 
 
 INORGANIC 
 
 COMPOUNDS (contd.^ 
 
 Compound. 
 
 Mol. H.F. in 
 calories. 
 
 Compound. 
 
 ttol. H.F. in 
 calories. 
 
 Compound. 
 
 Mol. H.F. in 
 calories. 
 
 Metals (contd.} 
 
 X 
 
 IO 3 
 
 
 
 X IO 3 
 
 
 
 
 X IO 3 
 
 CuS0 4 . 
 
 
 1183, T. 
 
 MgCl 2 . 
 
 . . 
 
 51, T. 
 
 AgCl . 
 
 . 
 
 29-2, T.B. 
 
 CuSO 4 . Aq 
 
 . 
 
 198-8 
 
 , T. 
 
 MgS0 4 . 
 
 
 502, T. 
 
 Na 2 . 
 
 . 
 
 91 
 
 to ioo 
 
 CuS0 4 .5H 2 \ j 
 on sol. in Aq ./. 
 
 MgSO 4 . Aq . 1322 
 MnO ... 91 
 
 NaHO . . . 
 NaHO.Aq . 
 
 102 
 112 
 
 3, T.B. 
 2, T.B. 
 
 AuBr 3 . 
 
 
 8.0 
 O 
 
 T. 
 
 MnCl, . 
 
 . . 112 
 
 NaCl . 
 
 . 
 
 97 
 
 8, T.B. 
 
 AuCl 3 . 
 
 . 
 
 23, T. 
 
 Hg 2 . 
 
 . 
 
 24-9 T. 
 
 NaNO 3 . 
 
 . 
 
 in, T.B. 
 
 FeO . . 
 
 .J 
 
 64-6 
 
 
 HgO . 
 
 . 
 
 
 Na 2 SO 4 . 
 
 a 
 
 328 
 
 1, T.B. 
 
 Fe 2 3 /4oo 
 
 .1 
 
 196 
 
 
 Hg 2 S0 4 
 
 . 
 
 75 
 
 Na 2 C0 3 
 
 . . 
 
 272, T.B. 
 
 Le Chatelier .J 
 
 
 
 HgCl . 
 
 . 
 
 
 SrO . . 
 
 . . 
 
 130, T.B. 
 
 FeSO t .7H O. 
 
 240 
 
 
 HgCl, . 
 
 . 
 
 53' 2 
 
 Sr(OH) 2 
 
 . 
 
 217, B. 
 
 FeSO 4 . Aq 
 
 * . 
 
 236 
 
 
 NiO . . 
 
 . 
 
 597 
 
 SrCl 2 . 
 
 . 
 
 185, T.B. 
 
 FeCl 3 . 
 
 
 96, T. 
 
 NiCl 2 . 
 
 . 
 
 74'5, T. 
 
 SrCl 2 .Aq 
 
 . 
 
 196, T. 
 
 PbO . . 
 
 
 50-3, T. 
 
 NiSO 4 .Aq . 2 
 
 .29, T. 
 
 T1 2 0. . 
 
 . 
 
 42 
 
 2, T. 
 
 PbO 2 . . 
 
 
 
 
 PtCl 4 . 
 
 . 
 
 59*4 
 
 T1CI . . 
 
 . 
 
 48-6, T. 
 
 PbCl 2 . 
 
 
 83, T. 
 
 K 2 O . . 
 
 1 
 
 97 
 
 T1 2 SO 4 . 
 
 . 
 
 221, T. 
 
 PbS0 4 . 
 
 , 
 
 216, T. 
 
 KHO . 
 
 . . 104, B.T. 
 
 SnO . . 
 
 . 
 
 70 
 
 Pb(NO 3 ), 
 
 , 
 
 105-5 
 
 
 KHO.Aq. . 117, B.T. 
 
 SnCl 2 . 
 
 . 
 
 81, T. 
 
 Pb(N0 3 ) 2 .Aq 
 
 97-9 
 
 
 KC1 . . 
 
 . . 106, B.T. 
 
 SnCl 4 . 
 
 . 
 
 128 
 
 Li 2 O . . 
 
 , 
 
 140 
 
 
 KC1 . Aq 
 
 . . 101-6, T. 
 
 ZnO . . 
 
 . 
 
 85-4, T. 
 
 LiOH . 
 
 . 
 
 in 
 
 
 KNO 3 . 
 
 . . |II 9 , B.T. 
 
 ZnCl 2 . 
 
 . 
 
 Q7 
 
 3, T.B. 
 
 LiCl . . 
 
 
 94, T. 
 
 K 2 SO 4 . 
 
 . . ! 34 4, T.B. 
 
 Zn(N0 3 ) 2 
 
 .Aq 
 
 132 
 
 
 LiCl.Aq . 
 
 
 102-4 
 
 
 Ag 2 . 
 
 
 5'9, T. 
 
 ZnSO 4 . 
 
 
 230-3, T.B. 
 
 Li,S0 4 . 
 
 f 
 
 334, T. 
 
 ,, 
 
 . ! 
 
 7, B. 
 
 ZnSO 4 .A 
 
 q 
 
 248-7 
 
 LiN0 3 . 
 
 . 
 
 112, T. 
 
 AgN0 3 . 
 
 
 
 287, T.B. 
 
 ZnSO 4 .7l 
 
 },o\ 
 
 ,/c 
 
 MgO . . . 
 
 
 
 H3, I 
 
 
 AgN0 3 .Aq . 
 
 23-3, T. 
 
 on sol. in Aq/ 4 
 
 
 MOLECULAR HEAT OF NEUTRALISATION 
 
 Unit the gram 
 
 calorie (at 15 to 20) 
 
 per gram molecule 
 
 of base. 
 
 Thus 
 
 KOH. Aq + HC1. Aq = KC1. Aq + H 2 O + 13,750 calories. Thomsen (= T.) ob- 
 
 served at 1 8 to 
 
 20 C., and the final dilution 
 
 was 3600 gms. (7200 
 
 for Na salts) per 
 
 gm. mol. of 
 
 base. Berthelot (= B.) used at least 2000 gms. of H 2 
 
 O per 17 gms. of 
 
 hydroxylion, HO. 
 
 Base. 
 
 HC1 
 
 HF 
 
 HN0 3 
 
 HCN 
 
 |H 2 S0 4 
 
 JH 2 C0 3 
 
 1H 3 P0 4 
 
 1 Oxalic. 
 
 
 X 
 
 IO 3 
 
 XIO 3 
 
 X IO 3 
 
 X IO 3 
 
 X IO 3 
 
 X IO 3 
 
 X IO 3 
 
 X IO 3 
 
 iNaOH . 
 
 I374.T.; 
 
 i6- 3 ,T. 
 
 I37,T.; 
 
 2-8 
 
 15-64, T. I io-i,T.; 
 
 14-8, T. 
 
 I3-8,T. 
 
 
 IT 
 
 7, B. 
 
 
 13*5, B. 
 
 
 10-2, B. 
 
 
 
 2NaOH . 
 
 
 
 
 
 
 
 
 3 r 3 8J,T. 2o-2, T. 
 
 27-1* T. 
 
 28- 3 ,T. 
 
 iLiOH . 
 
 13*85, T. 
 
 i6- 4 f 
 
 
 
 2-93 
 
 1 5-64, T. 
 
 
 
 
 iKOH . 
 
 137, T.; 
 
 16-1 
 
 13-8, T. 
 
 2-8, T. 
 
 1 57, T.B. 
 
 io-i, B. 
 
 
 
 i3'8,B. 
 
 
 iy 
 
 6, B. 
 
 
 
 
 
 
 
 
 iNH 4 OH. 
 
 
 , T. ; 
 
 15-2 
 
 12-3, T. 
 
 1*3, B 
 
 I4'3, T.B. 
 
 8-4, T. ; 
 
 13-5, B. 
 
 127 
 
 
 12-4, B. 
 
 
 
 
 5'3, B. 
 
 
 
 ^CaOH . 
 
 14-0, B. 
 
 18-4 1 
 
 13-9, B. 
 
 3*2 
 
 i 5 -6,T. 
 
 9'3,t T. ; 
 
 
 
 
 
 
 
 
 
 
 
 
 9-8,f B. 
 
 
 
 ASrOH . 
 
 13* 
 
 8,T. 
 
 17-8! 
 
 i3'9. B. 
 
 3'i5 
 
 15-4, T. 
 
 io-4,fT.B. 
 
 
 
 
 
 jBaOH . 
 
 13' 
 
 9, B. 
 
 16-1 
 
 
 3'i5 
 
 18-4, B.T. 
 
 ii-o,tT.B. 
 
 
 
 
 
 
 
 
 
 i3'9, B. 
 
 
 
 
 
 
 |Mg(OH) 2 
 
 IT 
 
 8,B. 
 
 15-2 
 
 13-8, T. 
 
 i'5 
 
 15-3, B.T. 
 
 8- 9 5,f B. 
 
 
 
 
 
 |Cu(OH) 2 
 
 7' 
 
 5, T. 
 
 
 7-6 
 
 
 9-2 
 
 * 
 
 
 ~ 
 
 * 3NaOH gives 
 
 34-0 X io 3 , T. f Base in solid state. I iH 2 SO 4 . iH 2 CO 3 . 
 
64 
 
 HEATS OF COMBUSTION 
 
 HEATS OF COMBUSTION AND FORMATION OF CARBON COMPOUNDS, COAL, ETC. 
 
 Molecular heats of formation (H.F.) of organic compounds are deduced from 
 their heats of combustion (H.C.), by subtracting the latter from the heat generated 
 on burning the carbon and hydrogen contained in the compound. Experimental 
 errors in the H.C. thus become magnified in the H.F. Heats of combustion 
 determined by Thomsen are for the vapour of the compound at 18 C. ; for the 
 liquid the H.C. and H.F. would be greater by the latent heat of evaporation. 
 Thomsen assumes H.F. of CO 2 from amorphous C as = 96,960 cal. ; of water as 
 68,360 cal. per gm. molecule. For H.F. of inorganic compounds, see p. 62. 
 
 The H.C. and H.F. of carbon compounds is an additive property (see 
 Thomsen's " Thermochemistry ") Berthelot's bomb calorimeter has been of con- 
 siderable importance in the modern experimental side of the subject. 
 
 Unit the gram calorie (at 15 to 20) per gram molecule. 
 
 Example. 16 gms. of methane, CH 4 , give out 212,000 gram calories of heat 
 when burnt at constant pressure, to water and CO 2 at 18 C. 
 
 (T., Thomsen, " Thermochemistry ; " B., Berthelot.) 
 
 Compound. 
 
 Methane, CH 4 . . 
 
 Ethane, C 2 H 6 . . . 
 Propane, C 3 H 8 . . 
 
 Acetylene, C 2 H 2 . . ./ 
 
 Ethylene, C 2 H 4 . . . 
 
 Benzene, C 6 H 6 . . . 
 
 Naphthalene, C, H 8 . 
 
 Toluene, C 7 H 8 . . . 
 
 Me. alcohol, CH 4 O . . 
 
 Me. chloride, CH 3 C1 . 
 
 Chloroform, CHC1 3 . . 
 
 Et. alcohol, C 2 H 6 . . 
 
 Et. ether, C 4 H 10 O . . 
 
 Et. chloride, C 2 H 5 C1 . 
 Acetic aldehyde, C 2 H 4 O 
 
 Formic acid, CH 2 O 2 . 
 
 Acetic acid, C 2 H 4 O 2 . 
 Propionic acid, C 3 H 6 O 2 
 
 Me. formate, C 2 H 4 O 2 . 
 
 H.C. H.F 
 
 X I0 3 
 2I2,T. 
 
 213, B. 
 370, T. 
 
 372, B 
 529, T. 
 
 3H 
 333, T. 
 799, T. 
 1239 
 
 177, T. 
 107, T. 
 340, T. 
 660, T. 
 334, T. 
 282, T. 
 69-4, T. 
 
 241, T. 
 
 x io 3 
 217 
 
 28-6 
 
 -47*8 
 
 -27 
 -12-5 
 
 -TS 
 
 22-6 
 24' I 
 
 58-5 
 70 
 30-7 
 487 
 
 95*9 
 105-3 
 109-4 
 
 89-4 
 
 Compound. 
 
 Me. acetate, C 3 H 6 O 2 . 
 Carb. bisulphide, CS 2 . 
 Methylamine, CH 6 N . 
 Dimethylamine, C 2 H 7 N 
 Aniline, C 6 H 7 N . . . 
 Pyridine, C 5 H 5 N. . . 
 Sugar, C l2 H 22 Oi,. . . 
 Illuminating gas per 
 
 cub. metre . . . 
 Coal (anthracite) 
 
 Coal (brown) . . . 
 
 Coke 
 
 Paraffin oil. . . . 
 
 Wood 
 
 Albumens- 
 Casein 
 
 Flesh 
 
 White of egg . . . 
 Yoke of egg . . . 
 Haemoglobin . . . 
 
 H.C. H.F. 
 
 XIO 3 
 
 399, T. 
 265, T. 
 258, T. 
 420, T. 
 838, T. 
 675, T. 
 1364 
 5-6 to 
 
 7-6 to 
 
 8-4 
 
 47 
 
 6-9 
 
 9-8 
 
 (3-9*0) 
 14-4 / 
 
 5-86 
 5-66 
 5-67 
 8-12 
 
 5'9 
 
 xro 3 
 967 
 -26 
 
 9' 5 
 
 12-7 
 
 -17-4 
 
 -19-4 
 
 per gm. 
 
 MOLECULAR HEAT OF DILUTION 
 
 The heat set free or absorbed on diluting a gram molecule of liquid with water is the 
 molecular heat of dilution: thus on diluting HC1 to (HC1, 300 H 2 O), 17,300 calories per 
 36-5 grams of HC1 are set free ; diluting 2NaCI, H 2 O( = 20) to (2NaCl, 1OOH 2 O) 
 absorbs 1060 cal. per 2 X 58*65 gm. of NaCl. Unit the gram calorie (at 15 to 20) per 
 gram molecule. (See Thomsen, " Thermochemistry.") 
 
 HC1 
 
 H 2 O 
 
 1 5-37 
 2u-36 
 5 14-96 
 50 17 i 
 300i73 
 
 HNO, 
 
 H 2 X 
 
 \ 
 
 5 
 10 7 
 
 H 2 S0 4 
 
 H 2 
 
 io 3 
 6-38 
 
 5 13 i 
 
 ._ 49i6 7 
 20746 199i7-i 
 320 7-491600 1 7'9 
 
 NaHO 
 n = 3 
 
 H 2 0x 
 
 H 2 O 
 
 13'! 
 72- 9 |3 
 
 5-8 
 2532619-5 
 2002- 94 110 
 
 2NaCl 
 n = 20 
 
 H 2 
 
 126 100 
 385 200 
 400 
 
 02 
 00 
 
 2NaN0 3 
 
 H 2 
 
 -i 06 50 
 
 -1-31 100 
 
 -i- 4 i200 
 
 400 
 
 Na.,SO, 
 
 Xio' H 2 O Xio : 
 
 -2-26100 -665 
 
 -3-86;40o|-i-38 
 -4-19800 -1-48 
 
 ZnCl 2 
 
 H 2 Xio 1 
 
 10 1-85 
 
 203-15 
 
 50 5-32 
 
 1006-81 
 
 4008-02 
 
 Zn(NO a ) 2 
 = 10 
 
 H 2 O Xio 1 
 
 15 -91 
 20 1-15 
 50 1-20 
 100 i n 
 200ro7 
 
 Heat developed on diluting NH 3 .H 2 O to NH 3 .2OoH 2 O (Berthelot). 
 
65 
 
 SOLAR CONSTANT 
 
 ENERGY AND WAVE-LENGTH OF FULL RADIATION 
 
 The radiation from a full or black body radiator depends both in quality and quantity 
 upon the temperature. The total energy radiated (of all wave-lengths), from unit area in 
 unit time, is given by Stefan's law, E = K0 4 , where K is Stefan's constant and 6 is the absolute 
 temperature (see Optical Pyrometry, p. 47, and below). 
 
 The dependence of the quality on the temperature is expressed by Wierts displacement 
 law, A m = const., where A m is the length of the particular waves which carry most of the 
 energy. Further, the energy E OT , carried by the waves of length A TO , varies as the 5th power 
 of the temperature (absolute) : E m 0~ 5 = const. 
 
 The energy (from unit area) radiated by some particular wave-length \ is expressed 
 
 accurately by Ex = Cx-5/(^/A - i) PlancKs formula 
 
 where C = '353 erg.-cm. 2 sec.- 1 , a = 1*445 cm.-deg., and e is the base of Napierian logs. 
 
 At low temperatures or for short wave-lengths (A0 <3 cm.-deg.) Planck's formula becomes 
 (to -8 % at least) EA = CA - 5 ^-a/A0 . . Wierts formula (see p. 47) 
 
 For long waves and high temperatures (A0 > 730 cm. deg.), we have (to i % at least) 
 
 E\ =C\-*ee- a /a RayleigWs formida 
 
 (See Preston's " Heat," 2nd edit. ; Kayser's " Spectroscopie," II. ; Lorentz's "Theory of 
 
 Electrons," 1910.) 
 
 WIEN'S DISPLACEMENT LAW 
 
 A m = const. = A. (See above), 
 measured in cms. 
 
 is 
 
 Total 
 
 STEFAN'S LAW 
 
 radiation from a full radiator 
 
 K0 4 (see above). K is in erg cm.-' 2 sec." 
 
 Observer. 
 
 2940 j Lunmer and Pringsheim, 1899 
 
 2888 | Paschen and Wanner, B. B,, 1899 
 
 2902 I Wanner, 1900 
 
 2940 Paschen, A. d. P., 1901 
 
 2890 | Rubens and Kurlbaum, A. d. P., 1901 
 
 5-32 x io~ 5 
 
 5'3 
 5'35 
 
 Observer. 
 
 Kurlbaum, A. d. P., 1898 
 Lummer and Pringsheim, A. d. P., 
 
 1901 
 
 Bauer and Moulin, C. /?., 1910 
 Valentiner, A. d. P., 1910 
 
 A. d. P., Ann. der Phys. ; B. B., Berlin Ber. ; C. R., Compt. Rend. 
 
 SOLAR CONSTANT AND TEMPERATURE OF SUN 
 
 The solar constant S is the energy received from the sun by the earth (at its mean 
 distance) per sq. cm. in unit time, corrected for the loss by absorption in the earth's 
 atmosphere. 
 
 The determination of the absorption loss is difficult ; it is best derived from simul- 
 taneous observations at high and low stations. 
 
 Langley and Abbot ("Smithsonian Reports," 1903 et seq.} give the following relation 
 between atmospheric absorption and wave-length : 
 
 Wave-length (A.U. = io- 8 cm.) 
 
 Fraction transmitted 
 
 4000 
 '49 
 
 6000 
 
 74 
 
 8000 
 
 85 
 
 10,000 
 
 12,000 
 
 91 
 
 If R is the energy radiated in unit time from a sq. cm. of the sun's surface, then 
 
 /earth's solar distance! 2 j 9 . 2 
 
 R = \ ----- sun'sTadius~~ * S = i 
 
 Assuming the sun to be a full or black body radiator, its " effective " absolute tempera- 
 ture 9 may be deduced either from (i) Stefan's law, R = K(0 4 - T 4 ), where K is Stefan's 
 constant (see above) and T is the earth's absolute temperature, or (2) Wien's displacement 
 law, 0\ m = const, (see above). 
 
 Langley and Abbot (ref. above) find the distribution of the energy of solar radiation 
 among the different wave-lengths (A) to be as follows : 
 
 Wave-length (A.U.) . . 
 
 Relative energy, E 
 
 400045005000550060007000^000 10,000 
 16 
 
 15-2 
 
 18-4 
 
 ir 
 
 8'8 
 
 5'4 
 
 12,000 
 
 14,500121,000 
 
 A for E max . = 4900 x io 8 cm. Taking Wien's displacement law to be 0A max . = "29, and 
 assuming the sun to be a full radiator, its temperature = 5920 absolute. 
 
 ! 
 
SOLAR CONSTANT 
 
 66 
 
 SOLAR CONSTANT AND TEMPERATURE OF THE SUN (contd.) 
 
 The values of S below are expressed in both (i) calories per min. per cm.' 2 , and 
 (2) watts per cm. a (i calorie per sec. = 4-18 watts). The sun's mean temp. 8 is in 
 degrees C. absolute. Abbot and Fowle find the solar constant varies by about 8 %. 
 (See Poynting and Thomson's "Heat;" Chree, Nature, 82, 2090; Report (1910) 
 of the International Union for Solar Research ; and "Smithsonian Reports.") 
 
 Solar Const. 
 
 cm/ 
 
 cm/ 
 
 2-25 
 
 2-38 
 1-925* 
 
 154 
 i66 
 
 -H6 
 
 146 
 134 
 
 Sun's 
 Temp. 
 
 Abs. 
 
 57/o c 
 
 5920 
 7060 
 5610 
 
 5630) 
 5360) 
 5630 
 59?ot 
 
 597ot 
 58 4 ot 
 
 Account. 
 
 Comparison with const, temp. Atmos. 
 
 absorp. taken as 29 % 
 Using Wien's displacement law (above) 
 Corner Grat, Switzerland 
 Natl. Phys. Lab., England. Atmos. 
 
 absorp. taken as 29 % 
 Mt. Blanc. Comparison with const, temp. 
 
 Atmos. absorp., 9 % with zenith sun 
 Mt. Blanc. Atmos. absorp., 3-4 % 
 Washington (sea-level) and Mt. Wilson 
 
 (6000 ft.) 
 
 Review of previous work 
 Mt. Wilson (6000 ft.) and Mt. Whitney 
 
 (14,500 ft.) 
 
 Observer. 
 
 Wilson, 1902 
 
 Langley & Abbot, '03 
 Scheiner, 1908 
 HarkerBlackie,'o8 
 
 (FeYy & Millochau 
 
 \Fe*ry, 1909 
 Millochau, 1909 
 Abbot & Fowle, '09 
 
 Bellia, 1910 
 Abbot, 1910 
 
 * Mean value for period 1904-9 (Nature, 1911). 
 
 t Calculated from S, taking Stefan's const, as 5-3 X io~ 12 watts cm.~ 2 sec." 1 deg.~ 4 . 
 
 THE CRYOSCOPIC CONSTANT 
 
 The cryoscopic constant, K, would be the depression of the freezing-point of a solvent 
 when the molecular weight in grams of any substance (which does not dissociate or asso- 
 ciate) is dissolved in 100 grams of the solvent, supposing the laws for dilute solutions held 
 for such a concentration (Raoult, 1882). Van't Hoff (1887) showed that K = R0 2 /(iooL), 
 where R = the gas constant (see p. 5), 6 the absolute freezing-point of the solvent, L its 
 latent heat of fusion in ergs. Example. For i gram-molecule of solute in 100 gms. of 
 water 
 
 K = 8-315 x io 7 x (273'i) 2 /(79'67 x 4-184 x 10) = 18-60 
 
 (See Whetham's " Theory of Solution," p. 149.) 
 
 (After Bruni., L.B.M.) 
 
 Solvent. 
 
 Water . . 
 
 H 2 SO 4 .H 2 O 
 SbCl 3 . . 
 Acetic acid 
 Aniline . 
 
 M. 
 pt. 
 
 Lat ht. 
 (cals.) 
 
 oCJ 79-6 
 
 8-4 
 73-2 
 
 17 
 -6 
 
 317, B. 
 I3'4, T. 
 437, Pe. 
 
 K 
 
 Calcd. Obsd. 
 
 50 
 174 
 
 ' 48, L. 
 ji84, T. 
 i 39, R- 
 I 57,A.R. 
 
 Solvent. 
 
 Benzene . 
 
 
 
 Formic acid 
 Phenol . . 
 p. Xylol . . 
 
 pt. 
 
 Lat. ht. 
 (cals.) 
 
 5C. 29-1, P. W. 
 5-5 3o'i, F. 
 57-4, Pe. 
 
 K 
 
 Calcd. Obsd 
 
 24-9, P.W 
 
 39'3, C. 
 
 53*3 
 51-6 
 
 27-5 
 78-6 
 42-5 
 
 49, R, 
 51-2, 
 28, R 
 727, 
 43, P- 
 
 * Mean of six observers; A.R., Ampola and Rimatori, 1897; B., Berthelot ; C., Colson ; 
 Eykman, 1889; F -> Fischer; G., Griffiths (who used 0-0005 to 0*02 normal sugar solutions); '. 
 Lespieau, 1894; P., Paterno, 1889; Pe., Pettersson ; P.M., Paterno and Montemartini, 1894; P.\V 
 Pettersson and Widman ; R., Raoult ; T., Tolloczko, 1899. 
 
67 
 
 SOUND 
 
 VELOCITY OF SOUND 
 
 
 
 The velocity of sound (longitudinal waves) in a body, V = v E/p, E 
 
 being the 
 
 elasticity, and p the density. In gases and liquids E is the adiabatic volume 
 elasticity ; in isotropic solid rods or pipes E is Young's Modulus. For gases' 
 
 V = VyP/p, P being the pressure, and 7 the ratio of the 
 
 specific heat of the gas at 
 
 constant pressure to that at constant volume- For values of 7, see p. 58. 
 
 For moderate temperature variations, the velocity of 
 
 sound in gases is given by 
 
 V< = V (i + W) = V;, + 6i/ in cms. per sec. for dry air (a = '00367). 
 
 The velocity of sound decreases with decreasing intensity down to the normal 
 
 value. In gases in tubes the velocity increases with the diameter up to 
 
 a limiting 
 
 value for free space. The values below are for free space. Barton's " Sound " and 
 
 Poynting and Thomson's "Sound" may be consulted, [i foot = 30*48 cms.] 
 
 Substance. 
 
 Temp. 
 
 Velocity. 
 
 Observer. 
 
 Gases- 
 
 
 cms./sec. 
 
 
 
 
 Air (dry) .... 
 
 0C 
 
 (3-3145) x io 4 
 
 Calcd. (7 
 
 = 1-402) 
 
 55 .... 
 
 
 
 
 
 Violle, 1900 
 
 55 .... 
 
 
 
 3-3132 
 
 
 Stevens, 
 
 1900 
 
 55 .... 
 
 o 3*3129 , 
 
 
 Hebb, 1905 
 
 
 o 3-3192* , 
 
 
 Thiesen, 
 
 1908! 
 
 55 .... 
 
 - 45-6 3-056 
 
 
 Greely, 1890 
 
 , .... 
 
 -182-4 1-81? 
 
 
 Cook, 1906 
 
 , .... 
 
 100 
 
 3-865 , 
 
 
 Stevens, 
 
 1900 
 
 5 .... 
 
 500 
 
 5*53 
 
 
 5) 
 
 
 5 .... 
 
 1000 
 
 7*o 
 
 
 55 
 
 
 , (Krakatoa wave) 
 
 . 
 
 321 ,j 
 
 
 1883 
 
 
 , Sound-waves from 
 
 sparks 
 
 3-50-4-45 f 
 
 Topler, 1908 
 
 Hydrogen .... 
 
 
 
 12-86 
 
 
 Zoch, 1866 
 
 Oxygen . . 
 
 3-172 
 
 
 Dulong, 
 
 1829 
 
 
 184'7 
 
 I '7 77 
 
 
 Cook 19 
 
 -.6 
 
 Nitrous oxide, N 2 O 
 
 
 
 1 / Jl 5, 
 2'60 
 
 
 Wullner, 1878 
 
 Ammonia, NH :S . 
 
 
 
 4'l6 
 
 
 55 
 
 
 Carbon monoxide . 
 
 
 
 3*371 
 
 
 55 
 
 
 Carbon dioxide . 
 
 10-24 
 
 2 '573 
 
 
 Low, 1894 
 
 Coal-gas .... 
 
 
 
 4'9-5* '5 
 
 
 
 
 
 Sulphur dioxide . . 
 
 
 
 2-09 
 
 
 Masson, 
 
 1857 
 
 Water-vapour . . 
 
 
 
 
 
 5) 
 
 
 (satd.) 
 
 110 
 
 4* J 3 , 
 
 
 Treitz, 1903 
 
 Liquids 
 
 
 
 
 
 
 
 81 
 
 14-35 * 1C)4 
 
 
 Colladon & S 
 
 tnrm T8?7 
 
 
 4 
 
 13*99 
 
 
 Martini, 1888 
 
 
 
 25 
 
 I4/C7 
 
 
 
 
 (sea) Explosion 
 
 waves 18 
 
 *r j / ,, 
 
 f 
 
 Threlfall & Adair, 1889 
 
 Alcohol (abs.),C 2 H O 
 
 8-4 12-6 
 
 
 Martini, 
 
 1888 
 
 Ether, (C 2 H 5 ) 2 . 
 
 1 1-4 
 
 
 5) 
 
 
 Turpentine, C 10 H 16 . 
 
 3'5 137 
 
 
 
 
 * Free from CO 2 . t The range of speeds is given by varying 
 
 intensities. \ Reichsanstalt. 
 
 The values for metals are due to Wertheim, 1849 " Masson, 1857 ; and Gerossa, 1888. 
 
 Solid. Velocity Solid> Velocity 
 cms./sec. \ cms./sec. 
 
 Solid. 
 
 Velocity 
 cms./sec. 
 
 Aluminium. . 51*0 x io 4 Lead. ... 12*3 x io 4 
 
 Brass . . . 
 
 c. 36-5 x io 4 
 
 Cadmium . . 23*1 ,, Nickel . . . : 49-7 
 
 Deal (along 
 
 49-5 5, 
 
 Cobalt . . . 47-2 Platinum . . 26*8 
 
 grain) 
 
 
 Copper . . . 397 Silver . . . I 26-4 
 Gold .... 20'8 Tin . . . . j 24-9 
 
 Fir 
 Mahogany 
 
 42-53 
 41-46 
 
 Iron (wrought) 49-51,, Zinc . . . .36-8 ,, 
 
 Oak 
 
 40-44 
 
 (cast). . <r. 43 Glass (soda) .150-53,, 
 
 Pine 
 
 c - 33 
 
 Steel .... 47-52 (flint) . j c. 40 
 
 Indiarubber . 
 
 *5-7 
 
SOUND 
 
 68 
 
 VELOCITY (IN AIR) AND 
 PRESSURE 
 Koch (1907). 
 
 Press, 
 in 
 
 atmos. 
 
 1 
 
 25 
 
 50 
 
 100 
 
 150 
 
 200 
 
 Kelative Velocity 
 of Sound. 
 
 0C. -793C. 
 
 I '000 
 
 roo8 
 
 1-022 
 1-064 
 I-I32 
 1-220 
 
 8 4 2 
 
 8 3 I 
 
 830 
 
 885 
 
 1-047 
 
 1-239 
 
 SENSITIVENESS OF 
 EAR TO PITCH 
 
 Kayleigh (1907). 
 
 Fre- 
 quency. 
 
 512 
 
 256 
 
 128 
 
 85 
 
 Conden- 
 sation 
 : for same 
 ; audibility 
 
 i 
 1-6 
 
 3-2 
 6-4 
 
 ORGAN PIPES 
 
 End Correction. 
 
 For a pipe with a flange at the 
 open end, the antinode is situated 
 82 (radius of pipe) beyond end. 
 With no flange, the end-correction 
 is -57 (radius). (See Lamb's" Sound." 
 
 Wave-length. ^ l ^ 
 L = length of pipe. 
 
 Closed pipe . . 4L, -, etc. 
 
 2L 2L 
 
 Open pip? . . . 2L, ^ , etc. 
 
 TRANSVERSE VIBRATIONS OF RODS 
 
 L, length ; K, radius of gyration of cross- 
 section ; E, Young's Modulus ; p, density. 
 
 THE EAR 
 
 Both 
 ends 
 free 
 
 No. of 
 Nodes. 
 
 Distance of Nodes 
 from one end. 
 
 One 
 
 end 
 
 fixed 
 
 224 L ; 776L 
 
 I32L; '5L; '868L 
 
 o 94 L; '356L \ 
 
 644.L ; -906 L j 
 
 226L 
 
 I32L ; * 
 "094L; - 
 
 Frequency 
 
 K 
 
 276 
 5-40 
 
 6-27 
 
 17-5 
 34-4 
 
 Temp, correction of Frequency (n) of a Tuning-fork. 
 
 (M'Leod and Clarke, 1880, and Konig) 
 
 n t = (i -oooi i/) 
 
 Shortest time per- 
 ceivable by ear (Hill, 
 1908) 
 
 Amplitude of faintest 
 audible sound (Ray- 
 leigh, 1877) . . . 
 
 Ditto (Shaw, 1904) . 
 
 Pressure variation to 
 which normal ear can 
 respond (Abraham, 
 1907) . . . 
 
 Lower limit of audition 
 in vibns./sec. . . . 
 
 Upperlimit of audition 
 in vibns./sec. . . . 
 
 Extreme range of ear 
 
 Musically available . 
 
 The pressure exerted by Sound waves 
 
 has been measured directly up to '24 dyne/cm' 2 . 
 
 (Altberg, 1903) 
 
 Highest pitch in piano 
 Highest pitch in or- 
 chestra (piccolo d v ) . 
 Lowest pitch in 
 largest organs (64- 
 foot pipe) . . . . 
 
 007 sec. 
 
 10-4 x io- 8 cm 
 i'X io~ 8 cm 
 
 r.4 x io~ 7 mm 
 mercury. 
 
 About 30. 
 } 24,000 to 
 j 41,000. 
 c. 1 1 octaves. 
 
 3520 
 
 4752 
 
 8 
 
 FREQUENCY RATIOS OF MUSICAL SCALE 
 
 Natural scale . 
 
 C 
 
 Doh 
 
 D 
 Kay 
 
 i I 
 
 24 27 
 rooo 1-125 
 
 
 
 Me 
 
 4 
 30 
 
 F 
 
 Fah 
 
 32 
 i'333 
 
 
 
 Soh 
 
 A 
 
 Lah 
 
 B 
 Te 
 
 c 
 Doh 
 
 i 
 3 f 
 
 3* f 
 500 1-667 
 
 45 48 
 
 [-875 2-000 
 
 Equally tempered scale 1*000 ri22 1-260 1*335 1*498 1*682 r888 2-000 
 
 Standard forks (Konig) (\ c' d' e' 
 
 (marked c' =. 512 and so on)\! 256 288 320 
 
 a' 
 
 426-7 
 
 V- 
 
 480 
 
 c' 
 
 512 
 
 scales in vogue are Concert Pitch (c" = 546), Society of Arts (c" = 528), Tonic 
 Sol-fa (c" = 507), Philharmonic (c" = 540). (The "middle" c of the piano is c'.} 
 
69 
 
 VELOCITY OF LIGHT 
 
 VELOCITY OF LIGHT IN VACUO 
 
 Mean value in vacua = 2 9986 x 1O 10 cm./sec. = 186,326 miles/sec. For 
 values of r/, the ratio between the E.M. and E.S. units, see below. 
 
 cm./sec. 
 
 xio 10 
 
 3-07 
 
 2-998 
 
 3-I53 
 2-986 
 3-004 
 
 Method. 
 
 Eclipse of one of 
 I Jupiter's moons 
 Toothed wheel 
 Rotating mirror 
 Toothed wheel 
 
 Observer. 
 
 Romer, 1676 
 
 corrected 
 Fizeau, 1849 
 Foucault, 1862 
 Cornu, 1878 
 
 cm /sec 
 
 xio 10 
 
 2-999 
 
 3-014 
 
 2-9985 
 
 2-9986 
 
 2-9986 
 
 Method. 
 
 Observer. 
 
 Rotating mirror 
 Toothed wheel 
 Rotating mirror 
 
 Michelson, 1879 
 Young&Forbes,'8i 
 Michelson, 1882 
 
 jNewcomb, 1882 
 Toothed wheel Perrotin, 1900 
 
 VELOCITY OF LIGHT IN LIQUIDS 
 
 Liquid. 
 
 Vel. in vacuo 
 Vel. in liquid 
 
 Eefractive index 
 for Na D line. 
 
 Method. 
 
 Observer. 
 
 Water . . 
 CS 2 . . . 
 
 1758 
 
 1-333/20 
 1-627/20 
 
 Rotating mirror 
 
 Michelson, 1883 
 
 VELOCITY OF HERTZIAN WAVES 
 
 (See Blondlot and Gutton, Rep. Cong. Phys., Paris, 1900.) 
 
 cm./sec. 
 
 Observer. 
 
 cm./sec. 
 
 Observer. 
 
 cm./sec. 
 
 Observer. 
 
 
 
 i 
 
 
 
 XIO 10 
 
 
 X I0 10 
 
 
 X I0 10 
 
 
 2-989 
 
 Blondlot 
 
 3-003 
 
 Trowbridge 
 
 2-989 
 
 Saunders 
 
 2-991 
 
 McClean 
 
 
 and Duane 
 
 2991 
 
 Mean 
 
 
 RATIO OF ELECTROMAGNETIC TO ELECTROSTATIC UNIT OF CHARGE 
 
 This ratio 
 
 is a pure number, and is numerically equal to tj p.k, i.e> on 
 
 Maxwell's theory, to the velocity of electric disturbances, such as light and Hertzian 
 waves, through a medium whose magnetic permeability is /* and specific inductive 
 capacity k. (See pp. 7 and 84.) For the velocity of light, see above. 
 
 Most observers have used a "capacity method" of determining v. (See Gray, 
 "Absolute Measurements ; and Rosa, Bull. Bureau of Standards, 1907.) 
 
 x io lu 
 2-963 
 
 2-982 
 3-000 
 
 Observer. 
 
 J. J. Thomson, 
 
 1883 
 
 Rowland, 1889 
 Rosa, 1889 
 
 2-997 
 
 3-009 
 2-993 
 
 Observer. 
 
 Thomson and 
 
 Searle, 1890 
 Pellat, 1891 
 Abraham, 1892 
 
 xio 10 
 3'oor 
 
 2-997 
 2-997 
 
 Observer. 
 
 Hurmuzescu, '96 
 Perot and Fabry 
 Rosa & Dorsey, 
 1907 
 
PHOTOMETRY 
 
 70 
 
 PHOTOMETRIC STANDARDS 
 
 The Geneva Congress of 1896 proposed a set of units for measuring (i) luminous 
 intensity, (2) flux (the "lumen"), (3) illumination (the " lux "), (4) brightness, and 
 (5) quantity of light (see Electrician^ July 14, 1911). The British unit of intensity 
 is the " candle." The mean spherical candlepower of a light is the mean 
 of the intensities measured in all directions from the light. The mean horizontal 
 candlepower is the mean of all the intensities in a horizontal plane through the 
 lamp. 
 
 The British " candle " is a spermaceti candle, inch in diameter (6 to the Ib.) 
 which burns at the rate of 120 grains per hour. This is, however, found to be an 
 unsatisfactory standard, and in modern photometry the British unit is taken as being 
 one-tenth part of the light given out by the Harcourt 10 candlepower Pentane 
 lamp, burning at a pressure of 760 mms. mercury in an atmosphere containing 8 
 parts in 1000 by volume of water-vapour as measured by a ventilated hygrometer. 
 The candlepower of this lamp 
 
 = 10 + -066(8 - w) - -008(760 - H) 
 
 where iu is the number of parts in 1000 (by vol.) of water-vapour in air at a baro- 
 metric pressure of H mms. of mercury. 
 
 The United States " candle" prior to April i, 1909, was r6% greater than 
 the British. 
 
 The French unit is the Bougie decimale, which is the 2oth part of the light 
 given out by a sq. cm. of platinum at its solidifying point. This is a difficult unit to 
 reproduce, and the Carcel lamp burning colza oil is used in practice. The Carcel 
 unit is taken (with some uncertainty) as 4 % less than the Bougie decimale. 
 
 The German -unit is the light given out by the Hefner lamp (which burns 
 amyl acetate), burning at a pressure of 760 mms. mercury in an atmosphere contain- 
 ing 8-8 parts in 1000 (by vol.) of water-vapour as measured by a ventilated hygro- 
 meter. 
 
 The National Physical Laboratory, the Bureau of Standards of America, and the 
 Laboratoire Central d'Electricite' of Paris have come to an agreement which in- 
 volves the reduction of the old value of the American candle by i'6%. They agree 
 in future to employ as a common unit the proposed International candle = 
 i British Pentane candle = i American candle = i French Bougie decimale 
 10/9 German Hefner unit = '104 Carcel unit (see Paterson, Phil. Mag., 1909). 
 
 EFFICIENCIES OF VARIOUS LIGHTS 
 
 It has become customary to express efficiencies (or rather inefficiencies) in watts 
 per candle. The value of a luminous efficiency cannot be properly appreciated with- 
 out a knowledge of the distribution of the intensity. Estimates of the proportion 
 of light energy to the total energy vary widely. S. P. Thompson (" Manufacture of 
 Light ") quotes from i part in 7000 for a gas flame to i % for the most efficient lights. 
 
 The usual accepted " efficiencies " are given below in watts per mean spherical 
 candlepower. They must only be regarded as approximate (see Solomon, " Electric 
 Lamps," 1908). 
 
 Light. 
 
 Efficiency. 
 
 Light. 
 
 Efficiency. 
 
 Bat's-wing gas flame .... 
 
 c. 100 
 
 Tantalum lamps ...... 
 
 17-2-1 
 
 Paraffin lamps . ... 
 
 c. to 
 
 Tungsten (osram, etc.) lamps 
 
 I"* 
 
 \Velsbach mantle, etc. . . . 
 
 c. K 
 
 Open arc lamps .... 
 
 ri-i'4 
 
 
 c. 8 
 
 Enclosed arc lamps 
 
 2"\ 
 
 Carbon filament lamps .... 
 M etallized carbon filament lamps 
 Nernst lanrms . 
 
 3'5-4'S 
 2-8 
 
 2 I-2M 
 
 Yellow flame arc lamps . . . 
 Mercury vapour lamps . . . . 
 
 '4 
 
 *3-*4 
 
 In high-grade standard photometry the Luminer Brodhun photometer head is 
 usually employed. A unit of light may be maintained and reproduced with an 
 accuracy of the order of j 1 ^ %, by means of sets of properly seasoned glow lamps. 
 
 The candlepower of a carbon glow lamp varies as the 6th power (approx.) of the 
 voltage ; of a metallic filament lamp, as the 3'6th power. 
 
 A candle is visible at about a mile on a clear dark night. The energy in the 
 luminous raeliation from a standarel candle is about 5 x 10' ergs/sec. (Rayleigh, 
 " Collected Papers"), whence the energy falling on i sq. cm. at a distance of i metre 
 would be 4 ergs per sec. Angstrom (1902) gets values about double these. 
 
71 
 GASEOUS REFRACTIVE INDICES 
 
 GASEOUS REFRACTIVE INDICES AND DISPERSIONS 
 
 Dispersion. Cauchy's equation is /i i = A(i + B/A 2 ), where /* is the refractive 
 
 index for the wave-length A ; A and B are constants. B is the coefficient of dispersion. 
 
 The refraetivity Q*-i) = A, 
 
 when A = oo. The values of A and B are for 
 
 wave-lengths measured in cms. The refractive indices are mostly for 
 
 the sodium 
 
 D line (A = 5893 x io~ 8 cm.). The 
 
 values of p. are reduced to a standard density at 
 
 o and 760 mms. by assuming that 
 
 (/* - i)/p is a constant for each gas, 
 
 P being the 
 
 density. Cauchy's formula is in general inadequate over large dispersions. (See 
 
 Cuthbertson, Science Progress^ 1908 
 
 ; and Proc. &> Trans. Roy. Soc. for 1905 et seq.} 
 
 Or&s or 
 
 Refractive 
 
 Cauchy's 
 
 Constants. 
 
 Observer. 
 
 
 Index /j. for 
 
 
 
 Vapour. 
 
 Na D line. 
 
 A- 
 
 B. 
 
 Air ... 
 
 0002918 
 
 28*71 x io~ 5 
 
 5*67 x io~ n 
 
 Scheel (Reichsanstalt), 1907 
 
 Hydrogen , 
 
 0001384 
 
 13-58 
 
 7-52 
 
 3) 
 
 
 Helium . 
 
 0000350 
 
 3-48 
 
 2*3 
 
 Burton ; Cuthbertson & Metcalfe, 1 907 
 
 Neon 
 
 0000671 
 
 6-66 
 
 2*4 
 
 C. & M. Cuthbertson, 1909 
 
 Argon . . 
 
 "0002837 
 
 27*92 
 
 5-6 
 
 Burton, 1907 
 
 Krypton 
 
 0004273 
 
 41*89 
 
 6*97 
 
 C. & M. Cuthbertson; 1908 
 
 Xenon . . 
 
 000702 
 
 68*23 
 
 10-14 
 
 33 
 
 5? 
 
 Fluorine . 
 
 000195 
 
 
 
 
 
 Cuthbertson & Prideaux, 1906 
 
 Chlorine . 
 
 000768 
 
 
 
 
 
 Mascart, 1878 
 
 Bromine 
 
 001125 
 
 
 
 
 
 3) 33 
 
 
 Iodine . 
 
 00192 t 
 
 
 
 
 
 Hurion, 1877 
 
 Oxygen . 
 
 000272 
 
 26*63 
 
 5 '07 
 
 Rentschler, 1908 
 
 Sulphur . 
 
 001 III 
 
 104-6 
 
 21*2 
 
 Cuthbertson & Metcalfe, 1908 
 
 Selenium . 
 
 001565 
 
 
 
 
 
 33 
 
 33 
 
 Tellurium 
 
 002495 
 
 
 
 
 
 55 
 
 33 
 
 Nitrogen . 
 
 000297 
 
 29*06 
 
 77 
 
 Scheel (Reichsanstalt), 1907 
 
 Phosphorus 
 
 0012 I 2 
 
 116-2 
 
 i5'3 
 
 Cuthbertson & Metcalfe, 1908 
 
 Arsenic . 
 
 001552 
 
 
 
 
 
 )3 
 
 13 
 
 Zinc . 
 
 OO2O5O 
 
 
 
 
 
 33 
 
 3) 
 
 Cadmium . 
 
 '002675 
 
 
 
 
 
 3' 
 
 33 
 
 Mercury 
 
 000933 
 
 8 7 '8 
 
 22-65 
 
 33 
 
 M 
 
 
 Refractive 
 
 Observer. 
 
 
 Refractive 
 
 
 Gas or Vapour. 
 
 Index /j. for 
 
 Gas or Vapour. 
 
 Index ju for 
 
 Observer. 
 
 
 Na D line. 
 
 
 Na D line. 
 
 
 Water-vapour . . 
 
 1-000257 
 
 Mascart, '78 
 
 Tellurium tetra- 
 
 
 
 33 it ' ' 
 
 TOOO25O 
 
 Lorenz, '74 
 
 chloride . . . 
 
 1-002600 
 
 P. & M. 
 
 Ammonia . . . 
 
 F000377 
 
 Mascart, '78 
 
 Phosph. hydrogen 
 
 1-000786* 
 
 Dulong, '26 
 
 ,, ... 
 
 10003 73 
 
 Lorenz, '74 
 
 Phosphorus tri- 
 
 
 
 Nitrous oxide . . 
 
 1-000515 
 
 Mascart, 78 
 
 chloride . . . 
 
 1*001730 
 
 Mascart, '78 
 
 Nitric oxide . . 
 
 1*000297 
 
 33 
 
 J) 
 
 Methane, CH 4 . 
 
 1*000441 
 
 55 33 
 
 Hydrochloric acid 
 
 i '000444 
 
 jj 
 
 55 
 
 Pentane, C 5 H 12 . 
 
 1-001701 
 
 55 55 
 
 Hydrobromic acid 
 
 1*000570 
 
 33 
 
 33 
 
 Acetylene, C 2 H 2 . 
 
 1*000606 
 
 35 35 
 
 Hydriodic acid . 
 
 i '000906 
 
 Hurion, '77 
 
 Ethylene, C 2 H 4 . 
 
 1-000719 
 
 35 55 
 
 Carbon monoxide 
 
 1-000334 
 
 Mascart, '78 
 
 53 ... 
 
 1-000674 
 
 Prytz, '80 
 
 ,, dioxide . 
 
 1-0004498 
 
 Perreau, '96 
 
 Benzene, C 6 H Q 
 
 1*001812 
 
 Mascart, '78 
 
 bisulphide 
 
 1*001476 
 
 Mascart, '78 
 
 33 .... 
 
 1*001765 
 
 Prytz, '91 
 
 Sulph. hydrogen 
 
 roooo4i* 
 
 Dulong, '26 
 
 Methyl fluoride . 
 
 i '000449 
 
 Cuthbertson 
 
 35 
 
 1-000619 
 
 Mascart, '78 
 
 ,, chloride . 
 
 rooo865 
 
 Mascart, '78 
 
 Sulphur dioxide . 
 
 i '000660 
 
 Walker, '03 
 
 alcohol . 
 
 1-000552 
 
 Prytz, '80 
 
 trioxide . 
 
 1-000737 
 
 C.&M.,'o8 
 
 33 33 
 
 1*000619 
 
 Mascart, '78 
 
 hexafluoride 
 
 1*000783 
 
 33 
 
 Chloroform, CHC1 3 
 
 1*001455 
 
 15 55 
 
 Selenium 
 
 1*000895 
 
 33 
 
 Carbon tetra- 
 
 
 
 Tellurium ,, 
 
 1*000991 
 
 3 
 
 ' 
 
 chloride . . . 
 
 1*001768 
 
 55 35 
 
 * White light. f Violet light. ^i= I '00205 for red light. Iodine shows anomalous dispersion. 
 
 C. & M., Cuthbertson & Metcalfe; P. & M., Prideaux & Metcalfe. 
 
72 
 
 REFRACTIVE INDICES 
 
 REFRACTIVE INDICES 
 
 Refractive indices, /t, (against air) at 15 C. for various wave-lengths. 
 
 The temperature coefficient given below is the 
 
 change of refractive index 
 
 per i C. rise of temperature for the case of the sodium D 
 
 line. 
 
 The refractive indices are due chiefly to Gifford (Proc. Roy. Soc., 1902, 1904, 
 
 1910) ; Rubens and Paschen (for the infra-red) and Martens (1902). The two Jena 
 
 glasses are selected as typical. Other glasses are dealt with on p. 74. 
 
 Wave-length in 
 
 Calcspar, 18. 
 
 Jena glass. Flu- 
 
 nin+a 
 
 Quartz, 
 
 18. 
 
 
 A.IT. (10-* cm.). 
 
 ord. 
 
 ezt. 
 
 Crown* 
 
 flint. f 
 
 
 ord. 
 
 ezt. 
 
 X useo. ,. vin, water 
 silica. 'JJo' KC1 a t20 . 
 
 
 ray. 
 
 ray. 
 
 
 
 18 . 
 
 ray. 
 
 ray. 
 
 
 
 10 . 
 
 
 Infra-red. 
 
 r 
 
 r 
 
 r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I* 
 
 r 
 
 
 
 223,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 343 
 
 3712} 
 
 
 
 94,290 
 
 
 
 
 
 
 
 
 
 3161 
 
 
 
 
 
 
 
 
 4983 
 
 4587 
 
 
 
 42,OOO 
 
 
 
 
 
 
 
 
 
 4078 
 
 4569 
 
 
 
 
 
 
 5213 
 
 4720 
 
 
 
 21,72O 
 
 6210 
 
 4746 
 
 4946 
 
 6153 
 
 4230 
 
 5180 
 
 5261 
 
 
 
 5262 
 
 4750 
 
 
 
 12,560 
 
 6388 
 
 4782 
 
 5042 
 
 6268 
 
 4275 
 
 53 l6 
 
 5402 
 
 
 
 5297 
 
 4778 
 
 3210 
 
 Visible. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Li, (r) 6708 
 
 6537 
 
 4843 
 
 5140 
 
 6434 
 
 4323 
 
 5415 
 
 5505 
 
 4561 
 
 5400 
 
 4866 
 
 33o8 
 
 H, (C) 6563 
 
 6544 
 
 4846 
 
 5145 
 
 6444 
 
 4325 
 
 5419 
 
 5509 
 
 4564 
 
 5407 
 
 4872 
 
 
 Cd, (r} 6438 
 
 Na,(D)5893 
 
 6550 
 6584 
 
 .4847 
 4864 
 
 5149 
 5170 
 
 6453 
 6499 
 
 4327 
 4339 
 
 5423 
 5443 
 
 55M 
 
 5534 
 
 4568 
 
 4S85 
 
 5412 
 5443 
 
 4877 
 4904 
 
 33H 
 3330 
 
 Hg, (g) 5461 
 
 6616 
 
 4879 5191 
 
 6546 
 
 4350 
 
 5462 
 
 5553 
 
 4602 
 
 5475 
 
 4931 
 
 3345 
 
 Cd, (jr) 5086 
 
 6653 
 
 4895 5213 
 
 6598 
 
 4362 
 
 5482 
 
 5575 
 
 4619 
 
 559 
 
 4961 
 
 
 H, (F) 4861 
 
 6678 
 
 4907 5230 
 
 6637 
 
 437i 
 
 5497 
 
 5590 
 
 4632 
 
 5534 
 
 4983 
 
 337i 
 
 Cd, () 48OO 
 
 6686 
 
 4911 
 
 5235 
 
 6648 
 
 4369 
 
 5501 
 
 5594 
 
 4636 
 
 5541 
 
 4990 
 
 3374 
 
 Hg, ( V ) 4047 
 
 6813 
 
 4969 
 
 5318 
 
 6852 
 
 4415 
 
 5572 
 
 5667 
 
 4697 5665 
 
 5097 
 
 3428 
 
 Ultra-violet. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Sn 3O34 
 
 7196 
 
 5136 
 
 5552 
 
 
 
 4534 
 
 5770 
 
 5872 
 
 4860 
 
 6085 
 
 5440 
 
 358i 
 
 Cd 2144 
 
 8459 
 
 5600 
 
 
 
 
 4846 
 
 6305 
 
 6427 
 
 5339 
 
 7322 
 
 6618 4032 
 
 Al 1852 
 
 
 
 
 
 
 
 
 5099 
 
 6759 
 
 6901 
 
 5743 
 
 8933 
 
 8270 
 
 
 
 Temp, co- \ 
 
 efficient (D)J 
 
 + 0,5 
 
 + -<V4 
 
 -0,, 
 
 + 0.3 
 
 -o 4 i 
 
 -o 65 
 
 -0,6 
 
 -0,3 
 
 -o,4 
 
 -'0,4 
 
 -0,8 
 
 * Light barium crown. f Dense silicate flint. J /* 
 
 = 1*3692 for A = 225,000. 
 
 REFRACTIVE INDICES 
 
 
 Refractive indices /I D (against air) at 15 C. for sodium D line (\ = 5893 x io~ 8 
 
 cm.). 
 
 
 Substance. 
 
 io 
 
 Substance. 
 
 ,0 
 
 Substance. /* 
 
 Solids. 
 
 Alum (pot ish) . . 
 Cyanin 
 
 1-456 
 
 Alcohol, ethyl . . 
 amyl . . 
 
 362 
 
 Monobrom benzene 1*563 
 naphtha- 
 
 Diamond .... 
 Glass (see above 
 
 1-71 
 2-417 
 
 Benzene .... 
 Hromoform . . . 
 
 504 
 591 
 
 Nitrobenzene . . -1*553 
 Oil, cedar .... 1*516 
 
 and p. 74) 
 Ice 
 
 1-31 
 
 Canada balsam . 
 
 '53 
 f\t - 
 
 cloves . . . 1-532 
 
 Mica . . 1-56 to 
 
 r6o 
 
 176 
 
 Carb. bisulphide 
 tetrachloride 
 
 032 
 464 
 
 cinnamon . . '601 j 
 olive .... '46 
 
 Ruby 
 
 1-56 
 
 Chloroform . . . 
 
 "449 
 
 paraffin ... -44 
 
 
 Sugar 
 
 1-63 
 
 Ether, ethyl . . . 
 Ethylene dibromide 
 
 "354 
 540 
 
 Sulphuric acid . . -43 
 Turpentine . . . '47 
 
 Topaz . . 
 
 
 Liquids. 
 
 
 Glycerine .... 
 
 '47 
 
 Water (see above) . '333 
 
 Alcohol, methyl . 1*33 
 
 Methylene iodide . 
 
 744 
 
 
73 
 
 SILVERING SOLUTION 
 
 DISPERSIVE POWERS 
 
 The dispersive power () given below (jt c yu,.-)/0"n i), where jUc, MD, MF are 
 the refractive indices corresponding to the red (C) H line (6563^, the yellow Na (D) 
 line (5893), and the green-blue (F) hydrogen line (4862). 
 
 Substance. 
 
 Solids. 
 
 Calcite, ord. 
 
 ext.. . 
 Fluorite . . . 
 Glass (see p. 74) 
 
 0204 
 0125 
 0105 
 
 Substance. 
 
 Substance. 
 
 Quartz, ord. . . 
 
 0143 
 
 Liquids. 
 
 ext. . . . 
 Fused silica . . . 
 
 0146 
 0147 
 
 Carb. bisulphide . 
 Alcohol .... 
 
 Rock salt . . . 
 Sylvin 
 
 0233 
 0226 
 
 Turpentine . . . 
 Water 
 
 0545 
 
 0171 
 0206 
 0180 
 
 SILVERING SOLUTION 
 
 Due to the late Dr. Common. Other recipes will be found in Baly's " Spectroscopy " (Long- 
 mans) and Woollatt's " Laboratory Arts" (Longmans). 
 
 Make up 10 % solutions of (i) pure nitrate of silver, AgNO 3 ; (2) pure caustic 
 potash, KOH; (3) loaf sugar ; and (4) ammonia (90% water, 10 % ammonia of sp. gr. 
 880). To the sugar soln. add % of pure nitric acid and 10% of alcohol. The sugar 
 soln. is very much improved by keeping. Make up also a i% soln. of AgNO 3 . 
 Distilled water must be used for all the solns. 
 
 For silvering say a 12-in. mirror, take 400 c.c. of the AgNO 3 soln. and add strong 
 ammonia until the brown precipitate first formed is nearly dissolved, then use the 
 10 % ammonia until the soln. is just clear. Add 200 c.c. of the KOH soln. A brown 
 precipitate is again formed, which must be dissolved in ammonia exactly as before, 
 the ammonia being added until the liquid is just clear. Now add the i % soln. of 
 AgNO 3 until the liquid becomes a light brown colour about equal in density of 
 colour to sherry. This colour is important, and can only be properly obtained by 
 the use of the weak soln. Dilute the liquids to 1500 c.c. with distilled water. 
 
 The mirror should be thoroughly cleaned with acid and placed in a dish of 
 distilled water. 
 
 All being ready, add 200 c.c. of the sugar soln. to 500 c.c. of water ; add the mixture 
 to the silver-potash soln., mix thoroughly, and pour them into a clean empty dish. 
 Then lift the mirror out of its dish of distilled water and place it face downwards 
 in this soln., taking care to exclude all air-bubbles. 
 
 The liquid will turn light brown, dark brown, and finally black. In four or five 
 minutes, often sooner, a thin film of silver will commence to form on the mirror, 
 and this will thicken until in about 20 minutes the whole liquid has acquired a 
 yellowish-brown colour, with a thin film of metallic silver floating on the surface. 
 Half an hour is the usual time taken in silvering, but this is shortened by using 
 warmer liquids. About 18 C. is the best temperature. 
 
 Lift the mirror out, thoroughly wash with distilled water, and stand on its edge 
 for say 12 hours in an inclined position until it is dry. The slight yellowish " bloom " 
 can then be polished off by rubbing softly with a pad of chamois leather and cotton- 
 wool. The subsequent polishing is done with a little dry well-washed rouge on the 
 leather pad. The film should be opaque and brilliant, and with careful handling 
 will be very little changed with long use. 
 
 Porcelain, glass, or earthenware dishes should be used. 
 
 If a very thick film is required, two silvering baths can be used, the article being 
 left in the first bath for 15 minutes, then lifted out, rinsed with distilled water and at 
 once immersed in the second bath, which should be ready in another dish. The 
 film should not be allowed to dry during the operation of changing baths. 
 
 NOTE. The silver-potash solution will not keep beyond a couple of hours. Any excess 
 of this solution unused should have the silver precipitated at once with HC1. If the silver- 
 potash is kept, say for 10 or 12 hours, a black powder collects on the surface. This powder, 
 which is probably some form of fulminate of silver, is explosive, and may shatter the vessel. 
 
74 
 
 GLASS 
 
 GLASS 
 
 The raw materials for the manufacture of glass are (i) silica usually as sand 
 or felspar ; (2) salts of the alkali metals Na 2 SO 4 , Na,CO 3 , or K 2 CO 3 ; (3) salts of 
 bases other than alkalies red lead, limestone or chalk, BaCO 3 or BaSO 4 , MgCO 3 , 
 ZnO, MnO 2 , ALO 3 , As 2 O 3 , etc. In general, glasses rich in silica and lime are hard, 
 while glasses in which alkali, lead, or barium preponderate are soft. Hardness is, 
 of course, also largely dependent on annealing. Ordinary " soft " (i.e. easily fusible) 
 German glass is a soda-lime glass rather rich in alkali ; " hard " (refractory) glass 
 is a potash-lime glass rather rich in lime. Jena combustion tubing is a borosilicate 
 containing some magnesia. 
 
 Therinometry Glasses. Glasses which contain both soda and potash to any 
 extent give a large temporary zero depression (see p. 45). Data concerning Verre 
 dur (71% Si0 2 , 12% Na 2 0, % K 2 O, 14% CaO, 2% A1 2 O S and MgO), Jena 16'" 
 (67% SiO* 14% Na 2 0, 7% CaO, 12% ZnO, A1 2 O 3 and B 2 O 3 ), Jena 59'" (72% SiO 2 , 
 12% B 2 3 , 11% Na 2 0, 5% A1 2 3 ), Kew glass (44% SiO 2 , 34% PbO, 12% K 2 O, 
 2% Na 2 O, 2% CaO, MgO, etc.), will be found on p. 45. 
 
 Optical Glasses. In building up achromatic lens systems a knowledge of the 
 dispersive power () of each glass employed is essential. This is defined as the 
 ratio of the difference of the deviations (i.e. the dispersion) for any two colours to 
 the deviation of some mean intermediate colour. o> thus depends on the colours 
 selected ; for visual work they are usually the red (C) line of hydrogen (wave-length 
 AC' = 6563 X io~ 8 cm.), the yellow sodium (D) line (A D = 5893), and the green-blue 
 (F) hydrogen line (A F = 4862). If ^j /* D , MF are the corresponding refractive indices, 
 co = (fjL c /* F )/(/u D i) for the brightest part of the visible spectrum. 
 
 Flint glass a term which survives from times when ground flints were 
 extensively employed in making the best glass now always implies a dense glass 
 which contains lead and has a high refractive index and dispersive power. 
 
 Crown glass, originally designating only lime-silicate glasses, is now applied 
 generally to glasses having a low dispersive power. 
 
 Jena Optical Glasses. P^or ordinary flints and crowns and n are roughly 
 proportional, and this was true for all commercially available glasses prior to the 
 advances initiated in 1881 by Abbe* and Schott at Jena. They succeeded (e.g. by 
 the addition of barium) in producing glasses which do not obey any such propor- 
 tionality ; e.g. the very valuable barium crown glasses (below) combine the high 
 refractive index of a flint glass with the low dispersive power of a crown. Such 
 glasses have brought about the excellent achromatism and flatness of field which 
 now obtain in photographic lenses and large telescopic objectives. The intro- 
 duction of boron into a glass lengthens the blue end of the spectrum relatively to 
 the red ; the addition of phosphorus, fluorine, potassium, or sodium has the opposite 
 effect : such control over the dispersion has made the modern microscope possible. 
 
 Some typical examples of Jena glasses are subjoined. For a complete list, see 
 the catalogue of Schott and Genossen, Jena. The simple phosphate and borate 
 glasses have been withdrawn on account of their lack of durability. The borosilicate 
 crowns are among the most durable and chemically resistant of all glasses. The 
 U.V. glasses are markedly transparent to ultra-violet light as far as about A = 2880. 
 
 See p. 72, and Zschimmer's "History of the Jena Glass Works," Hovestadt's 
 "Jena Glass," and Rosenhain's "Glass Manufacture," 1908 (with bibliography). 
 
 (After Zschimmer, Zeit. Inst., 1908.) 
 
 Glass. 
 
 MD 
 
 (C,D;F) ' Dens. 
 
 Glass. 
 
 Mn 
 
 W(c,I),I-) 
 
 Dens 
 
 Crowns 
 
 
 grms. 
 
 ] ~^r 
 
 Flints (contd.} 
 
 
 
 grms. 
 c.c. 
 
 ( 
 
 1-4782 
 
 0152 1 2-23 
 
 U.V. flint 3492 . . 
 
 1-5329 
 
 0131 
 
 
 
 (Silicate) crown . < 
 
 1-5127 
 
 0175 
 
 Telescope (Sb) flint J 
 
 1-5286 
 
 0194 
 
 2-50 
 
 I 
 U.V. crown 3199 . 
 
 I-52I5 
 
 i*535 
 
 0168 2-50 
 0155 
 
 Borosilicate flint . | 
 
 I'5503 
 I'5753 
 
 0203 
 0218 
 
 2'8 1 
 2-90 
 
 Borosilicate crown < 
 
 1-4944 
 1-5141 
 
 0151 2-33 
 0156 2-47 
 
 
 1-5489 
 1-5825 
 
 Ol87 
 02l6 
 
 
 
 Barium crown . 
 
 1-5726 
 1-6120 
 
 0174 3-21 
 0180 
 
 Barium flint . . 
 
 1-5848 
 1-6235 
 
 Ol89 
 '0256 
 
 3-67 
 
 Heavy barium crown 
 
 r6 1 30 
 
 0178 3-60 
 
 
 1-6570 
 
 0276 
 
 3'95 
 
 Flints- 
 
 1 
 
 
 17174 
 
 0340 
 
 4-49 
 
 (Silicate) flint . 
 
 1-5794 | -0244 3-25 
 1-6138 -0271 3-58 
 
 
 17782 
 1-9044 
 
 0378 
 '6461 
 
 4-99 
 5-92 
 
 _ 
 
 1-6489 -0296 3-87 
 
 
 1-9625 
 
 0508 
 
 
 
75 
 
 SPECTROSCOPY 
 
 SPECTROSCOPY 
 
 It is now agreed that the use of the diffraction-grating in fundamental work must 
 be limited to interpolation between standard wave-lengths obtained by other means. 
 The accepted standard lines are three in the spectrum of cadmium. Their wave- 
 lengths (A.) obtained by interference methods, and measured (by direct comparison 
 with the standard metre at Paris) in dry air at 15 C. ( H -scale) O and 760 mrns. 
 mercury pressure, are given below in tenth-metres (= io~ 8 cm. = I Angstrom unit). 
 (See Michelson's "Light Waves and their Uses.") [/* = io~ 4 cm. ; /&/* = io~ 7 cm.] 
 
 Observer. 
 
 Michelson and Benoit, 1894 . . 
 Benoit, Fabry, and Perot, 1907 . 
 
 A Cd red. 
 
 A Cd green. A Cd blue. 
 
 6438-4700 
 6438-4702 
 
 5085-8218 
 
 4799-9085 
 
 The following values (all in tenth-metres) are of course only approximate : 
 
 Hertzian Waves. 
 
 io u 4 x io 7 
 
 Infra-red, j Red. Orange. Yellow. Green. Blue. Violet. Ultra-violet 
 
 ri X io (i 7700 6470 5880 55 4920 4550 3600 looo 
 
 STANDARD LINES IRON ARC SPECTRUM 
 
 Obtained by an interference method, and based on Benoit, Fabry, and Perot's 
 value for the wave-length of the red line of cadmium. The wave-lengths below are 
 given in tenth-metres (io~ 8 cm.), measured in dry air at 15 (H-scale) and 760 mms. 
 mercury. (Buisson and Fabry, Compt. Rend., 1907 and 1909.) 
 
 2 373737 
 2413-310 
 
 2435-I59* 
 
 2506-904 * 
 
 2528-516* 
 
 2562-541 
 
 2588-016 
 
 2628-296 
 
 2679-065 
 
 2714-419 
 
 2739-550 
 2778-225 
 2813-290 
 2851-800 
 2874-176 
 2912-157 
 
 2987-293 
 3030-152 
 
 3075725 
 3125-661 
 
 3 I 75'447 
 3225-790 
 3271-003 
 
 3323'739 
 3370-789 
 3399-337 
 3445-155 
 
 3513-820 
 
 355 6 " 8 79 
 3606-681 
 3640-391 
 3677-628 
 
 3724-379 
 3753-6I5 
 3805-346 
 3843-261 
 3865-526 
 3906-481 
 3935-8i8 
 
 3977-745 
 4021-872 
 4076-641 
 4118-552 
 4134-685 
 4147-677 
 4191-441 
 
 4 2 33 >6l 5 
 4282-407 
 
 4315-089 
 
 4375-935 
 4427-3H 
 4466-554 
 4494/572 
 4531-155 
 4547^54 
 4592-658 
 4602-944 
 
 4678-855 
 4707-287 
 
 4789-657 
 4823-521 f 
 
 4878-226 
 
 4903*324 
 4919-006 
 4966-104 
 5001-880 
 5012-072 
 5049-827 
 
 5083-343 
 5110-415 
 5127-364 
 5167-492 
 5192-362 
 5232-958 
 5266-568 
 5302-316 
 5324-196 
 
 5434-530 
 
 5497-52I 
 5506-783 
 5535-418 
 5569-632 
 5586-770 
 5615-658 
 5658-835 
 5709-396 
 5760-843! 
 
 5763-013 
 
 5805-211 J 
 
 5892-882 J 
 
 5952-739 
 6003-039 
 6027-059 
 6065-493 
 6137-700 
 6191-569 
 6230-732 
 6265*147 
 6318-029 
 
 6335-343 
 6393-612 
 6430-859 
 6494-994 
 
 * Si. 
 t Mn. 
 
 I Ni. 
 
 CHIEF ABSORPTION (FRAUNHOFER) LINES IN SOLAR SPECTRUM 
 
 Rowland's wave-lengths corrected approximately by the use of Fabry and Perot's 
 results, measured in tenth-metres (io~ 8 cm.) in air at 20 and 760 mms. Owing to 
 atmospheric absorption, the sun's spectrum extends only to about wave-length 3000. 
 
 Line. 
 
 3047-5 
 
 3057-3 
 
 3059-0 
 
 0/3440*6 
 
 1 3441-0 
 
 3524-5 
 
 N 3581-2 
 
 3608-8 
 
 36187 
 
 M 3719-9 
 
 3734-8 
 
 3737-1 
 
 Subst. 
 
 Fe 
 
 Ti-Fe 
 Fe 
 Fe 
 Fe 
 Ni 
 Fe 
 Fe 
 Fe. 
 Fe 
 Fe 
 Fe 
 
 Eel. 
 Intens. 
 
 20 
 20 
 20 
 
 20 
 
 15 
 
 20 
 
 30 
 
 20 
 20 
 
 40 
 40 
 30 
 
 Line. 
 
 L 3820-4 
 3825-8 
 3838-2 
 3859-8 
 
 K 3933*6 
 
 H 3968-4 
 
 4045-8 
 
 4063*6 
 
 H)4ior8 
 
 4226-7 
 
 G 437'9 
 
 Subst. 
 
 Fe-C 
 
 Fe 
 
 Mg~C 
 Fe-C 
 
 Ca 
 
 Al 
 
 Ca 
 
 Fe 
 
 Fe 
 
 H 
 
 Ca 
 
 Fe 
 
 Eel. 
 Intens. 
 
 25 
 
 20 
 
 25 
 
 20 
 1000 
 
 20 
 700 
 
 30 
 20 
 40 
 20 
 
 6 
 
 Line. 
 
 F 4861-37 
 
 ,51727 
 
 b\ 5178-22 
 E 5269*56 
 
 (035875-62)! 
 
 D 2 5889-97 
 
 C 6562-8 
 B 6867-3 
 A 7661* 
 Z8228* 
 
 Subst. 
 
 H 
 
 HO) 
 Mg 
 Mg 
 Fe 
 He 
 Na 
 Na 
 H() 
 t 
 
 Eel. 
 Intens. 
 
 20 
 30 
 
 20 
 
 30 
 20 
 40 
 
 6 
 
 Langley, 1900. 
 
 Oxygen in earth's atmos. 
 
 t Emission line in chromosphere alone. 
 Wood, 1911. 
 
76 
 
 EMISSION SPECTRA 
 
 EMI 
 
 For a fuller treatment 
 appendices, Kayser's " Hi 
 "Atlas of Emission Sped 
 Journal. The wave-lengtl 
 at 15 C. and 760 mms. T 
 The brightest lines are 
 violet region is indicated t 
 
 SSION SPECTRA OF SOLIDS 
 
 of wave-lengths see Watts' "Index of Spectra" and 
 indbuch der Spectroscopie," Hagenbach and Konen's 
 ra," 1905. For recent work consult the Astrophysical 
 is below are measured in tenth-metres (io~ s cm.) in air 
 he visible spectrum colours are indicated r, 0,7,^", ^, ?'. 
 emphasized and the approximate boundary of the ultra- 
 
 1US . 
 
 
 
 ALUMINIUM 
 
 (arc). 
 
 3083 
 3093 
 
 CADMIUM 
 
 (contd.) 
 4413 b 
 4678 b 
 4799-908 b 
 5058-822 .<r 
 5338 g 
 5379 g 
 6438-470 r 
 
 CALCIUM 
 (COIltd.) 
 
 6122 o 
 6162 o 
 6440 o 
 6463 o 
 6500 r 
 
 MAGNESIUM 
 
 (contd.) 
 
 3832 
 3838 
 5168 
 (^ 2 )5173- 
 5184^ 
 55297 
 
 RADIUM 
 
 (contd.) 
 4683 v 
 4826 b 
 5210^ 
 536o g 
 
 5655J 
 56857 
 
 6210 o 3 
 6216 o* 
 6228 3 
 6247 o* 
 6250 o* 
 6260 o 3 
 6269 3 
 6285 o 3 
 6329 3 
 63490 
 (6530 r 3 
 to 
 I6700r 3 
 6653 r 
 
 3 Bands. 
 
 SODIUM 
 (NaCl in flame). 
 Fabry and 
 Perot, 1902 ; 
 Rayleigh, '06. 
 
 (D.,)5889'9650 
 (DJ5895-9320 
 
 STRONTIUM 
 
 (SrCl 2 inflame). 
 
 Bandspectr'm 
 with lines at 
 
 4607-5 b 
 6387 o 
 
 3944 v 
 3962 v 
 4663 b 
 
 5<>57 g 
 56967 
 
 5723 y 
 
 COPPER 
 
 (arc in vacuo). 
 
 Fabry and 
 Perot, 1902. 
 
 3248 
 3274 
 
 MERCURY 
 
 (Mercury lamp). 
 Stiles, Astro. 
 Journ., 1909. 
 3126 
 
 3131 
 3650 
 
 CXESIUM 
 (CsCl in flame) 
 3611-8 
 3617 
 3877 
 3889 
 
 BARIUM 
 
 (Bad , in 
 flame). 
 Full of bands, 
 some diffuse, 
 and some 
 resolvable. 
 
 35oi 
 
 4023 v 
 4063 v 
 5105-543 g 
 5153-251 
 5218-202 g 
 5700 7 
 5782-0907 
 5782-159 7 
 
 1HALLIUM 
 (Tl or TiCL, in 
 flame)." 
 
 5350-7 g 
 
 TIN 
 
 (spark). 
 3009 
 3034 
 3175 
 3262 
 
 3283 
 3331 
 3596 
 3746 
 
 4046*8 v 
 4078*1 u 
 4358-343 v* 
 
 4916-4 bg 
 
 49597 g 
 5460-742 g* 
 5769-598 7 2 
 5790-659 7 2 
 
 6152 o 
 6232*0 o 
 
 2 Fabry and 
 Perot, 1902, 
 and Rayleigh, 
 1906. 
 
 POTASSIUM 
 (KC1 in flame). 
 3446 
 3447 
 
 4555 b 
 4593 b 
 
 56647 
 
 5845/ 
 6011 o 
 6213 o 
 6724 r 
 6974 r 
 
 3910 v 
 3994V 
 4131 v 
 4554 <* 
 4934 
 5536 gy 
 5778/ 
 5854J 
 6142 o 
 
 6497 r 
 
 BORON 
 
 (Boric acid in 
 flame). 
 
 Diffuse 
 maxima at 
 4500 b 
 4700 b 
 4900 b 
 5200 
 
 5450^ 
 58007 
 6000 o 
 
 INDIUM 
 
 (In(OH) 3 in 
 flame). 
 
 4102 v 
 4511 v 
 
 RUBIDIUM 
 
 iRbCl in flame). 
 
 3349 
 3351 
 3587 
 3592 
 
 CALCIUM 
 
 (CaCl 2 in 
 flame). 
 Bands pre- 
 dominate ; 
 line at 
 
 4227 
 
 (Flame arc). 
 3362 
 3644 
 
 IRON 
 
 (see p. 75). 
 
 4202 v 
 4216^ 
 56487 
 
 57247 
 6207 o 
 
 6298-7 
 
 4525 v 
 55637 
 55897 
 57997 
 
 6453 o 
 
 LITHIUM 
 
 (LiCl in flame) 
 
 4132 v 
 4602 b 
 6104 o 
 6707-846 r 1 
 
 1 Fabry and 
 Perot, 1902. 
 
 4044 v 
 4047 v 
 58027 
 7668 r 
 7702 r 
 
 SILVER 
 
 (arc in vacuo). 
 
 3281 
 3383 
 
 ZINC 
 (arc in vacuo), 
 
 3036 
 3072 
 
 3345 
 
 (K) 3934 v 
 (H) 3968 v 
 4227 v 
 
 4303 b 
 4426 b 
 
 4435* 
 4455 b 
 4586 
 4878 b 
 5270.?- 
 
 5350^ 
 55897 
 
 5595J 
 58587 
 
 MAGNESIUM 
 
 (arc). 
 3091 
 3093 
 3097 
 3330 
 3332 
 3337 
 3830 
 
 RADIUM 
 iRaBr, in 
 flame). 
 Range and 
 Precht, 1903. 
 3650 
 3815 
 
 4055 v 
 4212 v 
 4669 b 
 5209-081 *r 4 
 5465-489 g [ 
 5472 g 
 5623 g 
 4 Fabry and 
 Perot, 1902. 
 
 4680-138 d & 
 4722-164 b' 
 4810-535 b* 
 4912 b 
 4925 gb 
 6103 o 
 6362-345 <? 5 
 
 " Fabry and 
 Perot, 1902. 
 
 CADMIUM 
 
 (arc). 
 3261 
 3404 
 3466 
 3611 
 
 3982 v 
 
 4341 v 
 
77 
 EMISSION AND ABSORPTION SPECTRA 
 
 
 EMISSION SPECTRA OF GASES 
 
 
 The gases are all in vacuum tubes (2-4 mms. press.) ; only the brightest lines 
 
 
 are given. The visible spectrum colours are indicated r, o,y, g, b, v. 
 
 
 See the general remarks on last page. 
 
 
 ARGON, CARBON 
 
 HYDROGEN NEON (contd^ 
 
 NITROGEN 
 
 
 Red spectrum 
 (small current 
 density). 
 
 MONOXIDE or 
 DIOXIDE 
 
 (of common oc- 
 currence in 
 
 Elementary spec- 
 trum. 
 
 3750 
 
 5853 y 
 5882 o 
 5945<? 
 
 (contd.} 
 
 5804 v 
 5854 .r 
 
 coo6 n 
 
 
 4159 i> 
 4192 v 
 4198 -v 
 4201 v 
 
 many vacuum- 
 tube spectra). 
 Numerous 
 bands shaded 
 
 3771 
 3798 
 3836 
 3889 
 
 59760 
 6030 o 
 
 6075 
 
 6096 o 
 
 ^yuvj " 
 5959<> 
 
 6013 o 
 6069 o 
 With large cur- 
 
 
 4259 <* 
 4300 b 
 
 towards violet 
 edges at 
 
 3970 v 
 4102 (5) v 
 
 1 2Q O 
 
 6143 o 
 6164 o 
 
 rent densities, 
 N gives a line 
 
 
 4334^ 
 
 A T T h 
 
 3590 (CN) 
 
 4340 (7) b 
 
 6182 o 
 
 spectrum. 
 
 
 45 l l U 
 /1/7fiQ 7i 
 
 3884 (CN) 
 
 (F) 4861 (ft) gb 
 
 6217 o. 
 
 OXYGEN 
 
 
 tjf /UO 9 
 5452.?- 
 5607.T 
 59120 
 
 60310 
 
 6059 o 
 
 
 (C) 6563 (a) r 
 For very short 
 wave-lengths 
 
 (1030-1675) see 
 Lyman, Astro. 
 Journ., 1906. 
 
 6267 o 
 6305 o 
 6383 o 
 6402 o 
 6507 r 
 
 Elementary line 
 spectrum. 
 
 3919 
 3973 
 
 4123 v 
 4216 (CN)v 
 4393 b 
 4511 b 
 
 4735 (C) b 
 
 
 4070 if 
 
 
 
 4835 b 
 
 5'65(C) ff 
 
 Secondary spec- NITROGEN 
 trum Band spectrum 
 
 4072 v 
 
 
 
 5198 g 
 
 (see Watson, from positive 
 
 4076 "V 
 
 
 Blue spectrum 
 
 5610 y 
 6079 o 
 
 Prof. Roy. Soc., column. 
 1909). Man y bands 
 all made up of 
 
 4415 b 
 5208^ 
 Diffuse maxima 
 
 
 (large current 
 
 
 KRYPTON AND ~~ i;=. 
 
 at 
 
 
 density). 
 3583 
 
 HELIUM 
 
 Rayleigh, 1908. 
 
 XENON 
 
 Brit. Ass. Rep., 
 
 1905. 
 
 From 3000 to 
 4574 the edges 
 occur at inter- 
 
 5335- 
 5440 < 
 6110 o 
 
 
 4072 v 
 4104 v 
 " 4228 v 
 4331 b 
 4348 b 
 
 3188 
 
 NEON 
 
 Baly, Phil. 
 Trans., 1903. 
 Very rich in 
 red rays. 
 
 vals of about 60 
 A.U. 
 Other bands 
 have edges at 
 4648 b 
 
 6170 o 
 There are three 
 other oxygen 
 spectra: con- 
 tinuous, band, 
 and series 
 
 3889 v 
 4026 -v 
 4471-482 b 
 
 
 4426 b 
 
 47i3'i44 b 
 
 3448 
 
 46666 
 
 spectra. 
 
 
 4430 b 
 
 4921*930 / 
 
 3473 
 
 4723 b 
 
 
 
 443 r b 
 
 50 1 5 '680 
 
 3521 
 
 4813 b 
 
 RADIUM EMANA- 
 
 
 4610 < 
 
 (D 3 ) 5875-625 .r 
 
 3594 
 
 5340^- 
 
 TION 
 
 
 4806 ^ 
 
 6678*150 r 
 
 
 c6i4 y 
 
 Royds, Phil. 
 
 
 
 7065-200 r 
 
 5765 y 
 
 J VJ J. if. J 
 
 5755 y 
 
 Mag., 1909. 
 
 
 ABSORPTION SPECTRA 
 
 
 For wave-lengths of the Fraunhofer lines in the sun's spectrum, see p. 75. 
 
 
 Among the enormous literature on absorption spectra, reference may be made to 
 
 
 Kayser's " Handbuch der Spectroscopie," Baly's " Spectroscopy," Vogel's " Prak- 
 
 
 tische Spectralanalyse," the writings of Prof. Hartley, Jones and Anderson's 
 
 
 "Absorption Spectra of Solutions," 1909, Smiles' "Chemical Constitution and 
 
 
 Physical Properties," and the British Association Reports of 1901 et seq. 
 
 
 Convenient substances which show good absorption spectra are neodymium 
 
 
 and praseodymium salts and didymium glass (which yield some extremely narrow 
 
 
 absorption lines), iodine vapour, nitrogen peroxide, chlorine, chlorophyll, blood, and 
 
 
 potassium permanganate solution. 
 
78 
 
 OPTICAL ROTATIONS 
 
 OPTICAL ROTATIONS OF PU 
 
 A, = the rotation in degrees (for light 
 polarization by a liquid when 
 l t = the length of the column of liqu 
 Ip = the number of grams of active s 
 q = (100 p] = the percentage (by 
 p t = the density in grams per c.c. of 
 c t = pp t = the concentration express 
 c.cs. of solution at /. 
 
 [a], - the specific rotation (at /) = 
 
 A 
 
 For a pure liquid [a], = -^- . 
 
 For an active substance in solution [ 
 
 (/ + ?) = I0 - 
 The rotation depends on the wave-le 
 
 wave-length (A) diminishes (o oc - - appro 
 
 A 
 
 inactive solvent and with the concentratk 
 The rotation is called positive or 
 polarization appears to be rotated in an an 
 the liquid away from the source of light 
 The molecular rotation is the spec 
 weight, 
 [a]^ indicates that the specific rotatio 
 light. 
 (See Landolt's " Optical Rotations o 
 Application," and Schonrock in L.B.M.) 
 
 RE LIQUIDS AND SOLUTIONS 
 
 of some given wave-length) of the plane of 
 it the temperature / C. 
 d in decimetres (i.e. 10 cms.), 
 ubstance in 100 grams of solution. 
 weight) of inactive solvent in the solution, 
 the liquid or solution at /. 
 ed as grams of active substanre per 100 
 
 rotation per decimetre of sol. 
 
 grams of active 
 
 A A i( p 
 
 substance per c.c of sol. 
 \ icoA, looA, . 
 
 " i t l\p + ^j i,p ?t - &, '" j 
 
 ngth of the light used ; it increases as the 
 K.). a also varies with the nature of the 
 
 )n of the solution, 
 right-handed (clextro, d} if the plane of 
 ti-clockwise direction when looking through 
 The contrary rotation is called lasvo (/). 
 ific rotation multiplied by the molecular 
 
 n is measured at 20 C. using sodium (D) 
 f Organic Substances and their Practical 
 
 Optically Active Substance. 
 
 Solvent. 
 
 Conditions. 
 
 Specific Eotation [a], 
 
 Cane Sugar or Candy (</), 
 C 12 H 22 O U 
 (Landolt, 1888; Pellat, 
 1901) 
 
 water 
 
 c = 4 to 28 
 /= 14 to 30 C. 
 
 [ = + 66 * 6 7 - -0095^ 
 
 M? = [C (' - 37(/ 
 
 -20)} 
 
 Invert Sugar(/),* C 6 H 12 O G 
 = i mol. of dextrose + i 
 mol. of levulose 
 (Gubbe, 1885) 
 
 water 
 
 c = 9 to 35 
 / = 3 to 30 C. 
 
 [=-i97--o3&: 
 
 [I = Mi + '304C ~ 20) 
 + *ooi65(/ 2o) a 
 
 Dextrose (d glucose), 
 C C H 12 6 
 (Parcus and Tollens, 
 1890; Tollens, 1884) 
 
 water 
 
 c = 9*1 
 
 [ a ]^ = +io5'2 after 5-5 
 mins. (a modifica- 
 tion) 
 = +52 0> 5 after 6 hrs. 
 (j8 modification) 
 
 water 
 
 p = i to 18 
 
 [a= +52 '5 + -02 5 / 
 
 / - Glucose, C C H ]2 O 6 
 (Fischer, 1890) 
 
 water 
 
 j = 4 
 
 C ~ 10 
 
 [a]^ = 94'4 aftery mins. 
 = 5i'4 after 7 hrs. 
 
 Levulose (/) (fruit sugar), 
 C 6 H 12 6 
 (Parcus and Tollens, 
 1890; Ost, 1891) 
 
 water 
 
 [o]^ - - 104 after 6 mins. 
 = 92 after 33 mins. 
 
 water 
 
 p = 2 tO 31 
 
 [>= -9i 0< 9-'/ 
 
 * The molecular weight of cane-sugar is 342 ; which, after conversion to invert sugar, becomes 
 360. Hence the new concentration of the invert sugar solution is jjj >, where c is the number 
 of grams of cane-sugar in 100 c.cs. of the original solution. 
 
79 
 
 OPTICAL ROTATIONS 
 
 Optically Active Substance. 
 
 Solvent. 
 
 Conditions. 
 
 Specific Rotation [o] t 
 
 Galactose (d\ C G H 12 O 
 (Meissl, 1880) 
 
 water 
 
 p - 4 to 36 
 t= 10 to 30 C. 
 
 >1 D == +83'9 + 'o 
 
 78^ 
 
 Ordy. Tartaric acid (d\ 
 H 2 C 4 H 4 6 
 
 water 
 
 
 W:=+.5-o6--,3., 
 
 Potassium tartrate (W), 
 K 2 C 4 H 4 O e 
 (Thomsen, 1886) 
 
 water 
 
 c = 8 to 50 
 
 r J o = + 27-14 + -0992^- 
 
 Rochelle salt (,/), 
 KNaC 4 H 4 O 6 
 
 water 
 
 [= +2973 - -0078^ 
 
 / Turpentine, 
 
 (Gernez, 1864 ; 
 1877) 
 
 Landolt, 
 
 pure liquid 
 
 
 
 [E=-37 - 
 
 vapour 
 
 at 761 
 
 7 mms. 
 
 C]L= -35'5 for mean 
 yellow 
 
 alcohol 
 (p 2 o = 796) 
 
 q o to 90 
 
 [= -37 -'00482? 
 - -ooo 1 3? 2 
 
 benzene 
 
 q - o to 91 
 
 W= -37 -'0265? 
 
 paraffin oil 
 
 Within 
 
 wide limits [o] increases with the 
 percentage of paraffin. 
 
 Quinine sulphate (/), 
 
 C 20 H 24 N 2 2 .H 2 S0 4 
 (Oudemans, 1876) 
 
 water 
 
 c about r6 % of 
 alkaloid 
 (calculated) 
 
 Salt [oft = -214 
 Alkaloid [aft = -278 
 
 Nicotine (/), C 10 H 14 N 2 
 (Landolt, 1877 ; Hein, 
 1898) 
 
 pure 
 
 t= ioto3oC. 
 
 [.=-162 
 
 benzene 
 
 p 8 to 100 
 
 [=-i6 4 
 
 water 
 
 p = i to 16 
 
 [ = -77 
 
 Ethyl malate (/), 
 
 (C 2 H 5 ) 2 C 4 H 4 5 
 (Purdie & Williamson, '96 
 
 pure liquid 
 
 
 
 Wi= -io-3to-i2-4 
 
 Camphor (d), C 10 
 (Landolt, 187 
 bach, 1892) 
 
 H 16 
 
 alcohol 
 
 q = 45 to 91 
 
 [ ) =+54-4-'i35? 
 
 
 benzene 
 
 q = 47 to 90 
 
 [=+56-'i66^ 
 
 OPTICAL ROTATION AND 
 
 WAVE-LENGTH 
 
 
 Wave-length (\) 
 in 10 ' 8 cm. 
 
 Specific Rotation at 20 C. [a]* 
 
 QUARTZ AT 20 C. 
 
 Cane- 
 sugar or 
 Candy in 
 H 2 0. 
 
 Tartaric 
 Turpentine acid in 
 (pureliq.). H 2 
 
 (P = 41%). 
 
 Nicotine 
 (pure liq.) 
 
 Wave-length (A) 
 in 10~ 8 cm. 
 
 Rotation 
 for 1 mm. 
 thick- 
 ness. 
 
 H (C) 6563 (r} 
 Na (D) 5893 (o) 
 
 Tl 535i (g) 
 H (F) 4861 Qtf 
 
 52-9 
 66-5 
 8r8 
 100*3 
 
 -29'5 775 
 -37 8-86 
 '-45 9-65 
 - 54'5 9'37 
 
 -126 
 -162 
 -207-5 
 -253'5 
 
 Li 6708 (r) 
 H (C) 6563 (r) 
 Na(D) 5893 0) 
 
 Tl 535 1 (g) 
 H (F) 4861 (/) 
 H (5) 4102 (?) 
 
 i6'4 
 
 17-3 
 21-72* 
 26-53 
 
 327 
 
 * For quartz at temperature /, rotation = 2i72 {l + O'OOOI47(/ 20)} for D line. 
 
80 
 
 FARADAY EFFECT 
 
 MAGNETIC ROTATION OF POLARIZED LIGHT 
 
 This effect was discovered by Faraday in 1845. The rotation per cm. per unit 
 magnetic field Verdet's constant, r = /(H/), where a is the rotation in minutes 
 for the substance in a magnetic field of H gauss, and / is the length of light-path 
 parallel to the lines of force, r varies with the temperature and is roughly inversely 
 proportional to the square of the wave-length of the light used. Films of Fe, 
 Ni, and Co are exceptions to this rule. 
 
 If the light is travelling with the lines of force (i.e. from N. to S.), then the 
 direction of rotation is positive, if the plane of polarization is rotated clockwise, to 
 an observer looking in the direction in which the light is moving. If the light is 
 reflected back on its path, the rotation is increased. 
 
 The Molecular rotation r m - rM/d, where M is the molecular weight of the 
 substance, and d is its density. r m is an additive property in organic compounds 
 (Perkin, Journ. Chem. Soc., 1884). 
 
 The rotations below are for the sodium D line (A = 5893 X io~ 8 cm.). 
 
 (For Voigt's theory of magneto-rotation, see Schusters, " Optics," 1909. See also 
 Becquerel's papers in Compt. Rend., etc.) 
 
 Substance. 
 
 Water 
 
 Temp. 
 rfco/" 
 
 Carbon bisulphide 
 
 
 
 Quartz, _L axis . 
 
 Jena (phosphate crown 
 glass\heaviest flint . . 
 FeCl 3 dens. = 1-693 . 
 1-023 
 
 2O 
 O 
 18 
 .20 
 20 
 20 
 18 
 18 
 15 
 15 
 
 Rotation r in 
 mins. of arc. 
 
 + -oi3ii,R.W 
 + -oi3i2,R.W 
 
 04200, Ra. 
 . -oi 368,* Bo. 
 | + "01664, Bo. 
 + -i 5 87,t Bo. 
 + 0161, D.B. 
 + 0888, D.B. 
 -2026, B. 
 
 + '0122, B. 
 
 Substance. 
 
 Ethyl alcohol 
 n. propyl alcohol 
 Amyl(iso) alcohol 
 Ethyl bromide . 
 
 chloride . 
 
 iodide . . 
 Formic acid . . 
 Acetic . . 
 Propionic acid . 
 Benzene . . . 
 
 Temp. 
 
 168 
 156 
 199 
 197 
 50 
 181 
 208 
 210 
 203 
 15 
 
 Rotation 
 
 relative 
 
 to Water. 
 
 8637, P. 
 9139, P. 
 9888, P. 
 
 1-395, P. 
 1-035, P. 
 2-251, P. 
 
 7990, P. 
 
 7976, P. 
 
 8369, P. 
 2-062, B. 
 
 * A = 6439. t A = 2194. B., Becquerel ; Bo., Borel, 1903 ; D.B., Du Bois, 1894 ; P., 
 Perkin ; Ra., Rayleigh, 1884 ; R.W., Rodger and Watson, 1896. 
 
 METALLIC REFLECTION OF LIGHT 
 
 (The percentage of normally incident light reflected from different surfaces.) 
 The column of figures (below) in the case of speculum metal (7 Cu, 3 Sn) 
 reads 30% (for A = 2510) ; 51%, 56%, 64%, 67%, 71%, 89%, 94% (for A = 140,000). 
 
 (See Hagen and Rubens in L.B.M.) 
 
 Wave-length A 
 in A.U. (10 * cm.). 
 
 Ultra- ( 2,510 
 I 3, 
 
 violet 
 
 Visible 
 
 3,570 
 4,200 
 5,500 
 7,000 
 
 Si 0,000 
 40,000 
 140,000 
 
 Cu. 
 
 26% 
 27 
 33 
 48 
 
 83 
 90 
 
 97 
 98 
 
 An. 
 
 39% 
 
 28 
 
 29 
 
 74 
 
 92 
 
 95 
 
 97 
 
 98 
 
 Ni. 
 
 38% 
 
 49 
 
 57 
 
 63 
 
 69 
 
 72 
 
 9i 
 
 97 
 
 Pt. 
 
 34% 
 43 
 
 L' 
 
 6 9 
 
 73 
 9i 
 96 
 
 34% 
 
 74 
 
 87 
 
 93 
 
 95 
 
 97 
 
 98 
 
 99 
 
 Steel. 
 
 33% 
 
 45 
 
 52 
 
 55 
 
 58 
 
 63 
 
 88 
 
 96 
 
 Magna- 
 lium.* 
 
 Glass mirror. 
 Ag back. Hg back 
 
 67% 
 Bi 
 
 83 
 83 
 83 
 84 
 89 
 92 
 
 86% f 
 
 88 
 
 90 
 
 73% t 
 
 7i 
 
 73 
 
 *6 9 Al, 3 iMg. 
 
 f A = 4500. 
 
 DIOPTER 
 
 In applied optics the " power " of a lens or mirror is expressed in diopters. The 
 number of diopters equals the reciprocal of the focal length expressed in metres. 
 
Si 
 
 RESISTIVITIES 
 
 ELECTRICAL RESISTIVITIES 
 
 Electrical specific resistances or resistivities in ohm-cms. Conductivities 
 
 (in reciprocal ohms) are the reciprocals of resistivities. For a table of reciprocals, 
 
 see p. 136. 
 
 
 
 METALS AND ALLOYS 
 
 The resistivity depends to 
 
 some extent on the state of the metal. In general, 
 
 cold drawing increases, while 
 
 annealing diminishes the resistance. The winding 
 
 of a wire into a coil increases its resistance. 
 
 For pure metals, the resistance is roughly proportional to the absolute tempera- 
 
 ture, and would apparently vanish not far from the absolute zero. This rule does 
 
 not hold even approximately for alloys. 
 
 For wire resistances, see p. 83 ; for temperature coefficients, next page. The 
 
 thermal conductivities of the 
 
 same samples of many of the substances below will 
 
 be found on p. 51. 
 
 
 Substance. 
 
 Temp. Sp. Be. 
 
 Observer. 
 
 Substance. 
 
 Temp. 
 
 Sp. Be. 
 
 Observer. 
 
 Metals- 
 
 C. 
 
 x 10-' 
 
 
 Metals (contd.} 
 
 C. 
 
 X lO" 6 
 
 
 Aluminium * 
 
 -160 
 
 081 
 
 \ Lees, 
 
 Platinum . . . 
 
 -203 
 
 2*4 
 
 D.&F., '96 
 
 u 
 
 18 
 
 2-94 
 
 ]P. T., '08 
 
 ,, ... 
 
 18 
 
 iro 
 
 \ J- & D., 
 
 . 
 
 18 
 
 3-21 
 
 1 J. & D., 
 
 . . 
 
 100 
 
 14*0 
 
 J 1900 
 
 
 
 1OO 413 
 
 / 1900 
 
 Potassium . . 
 
 O 
 
 6-64 
 
 B., '04 
 
 Antimony . . 
 
 15 i 40-5 
 
 Berget, '90 
 
 Rhodium . . . 
 
 18 
 
 6-0 
 
 
 Bismuth . . . 
 
 18 ji 19-0 
 
 \ J. & D., 
 
 Silver, 99-9 % . 
 
 -16O 
 
 0-56 \ Lees, 
 
 ... 
 
 100 ! 1 60-3 
 
 J 1900 
 
 ,, ... 
 
 18 
 
 I-66J 1908 
 
 Cadmium, drawn 
 
 -160 272 
 
 Lees, '08 
 
 ,, ... 
 
 18 
 
 1*63 
 
 1 J. & D., 
 
 ,, 
 
 18 
 
 7'54 
 
 \ J. & D, 
 
 ... 
 
 1OO 
 
 2-13 
 
 > 
 
 ) 1900 
 
 ^ 
 
 1OO 
 
 9-82 
 
 J 1900 
 
 Sodium . . . 
 
 O 
 
 474 
 
 B., 1904 
 
 Copper, drawn . 
 
 -160 
 
 0-49 
 
 Lees, '08 
 
 Strontium . . 
 
 2O 
 
 25 
 
 M., 1857 
 
 > 
 
 18 
 
 178 
 
 \ J- & D, 
 
 Tantalum 
 
 18 
 
 14*6 
 
 
 
 
 100 
 
 2-36 
 
 J 1900 
 
 Tellurium . . 
 
 20 
 
 21 
 
 M., 1858 
 
 ,, annealed 
 
 18 
 
 1-59 
 
 Mean 
 
 Thallium, pure . 
 
 O 
 
 I7'6 
 
 D.&F., '96 
 
 Calcium . . . 
 
 20 
 
 10-5 
 
 M.&C, '05 
 
 Thorium . . . 
 
 15 
 
 40-1 
 
 Bo., '09 
 
 Cobalt. . . . 
 
 20 
 
 971 
 
 R., 1901 
 
 Tin, drawn . . 
 
 -16O 
 
 3'5 
 
 Lees, '08 
 
 Gold .... 
 
 -183 
 
 0-68 
 
 D.&F., '96 
 
 .... 
 
 18 
 
 11-3 
 
 \ J- & D., 
 
 ,, .... 
 
 18 
 
 2-42 
 
 \ J. & D., 
 
 
 100 
 
 
 / 1900 
 
 ,, .... 
 
 1OO 
 
 3'i i 
 
 / 1900 
 
 Tungsten . . . 
 
 25 
 
 5*0 
 
 Fink, '10 
 
 Iridium . . . 
 
 18 
 
 5'3 
 
 
 
 Zinc, pure 
 
 -160 
 
 2'2 
 
 Lees, '08 
 
 Iron .... 
 
 18 
 
 9-15 
 
 Mean 
 
 ,, .... 
 
 18 
 
 6-1 
 
 \ J. & D., 
 
 /'i%\ . 
 
 18 
 
 I2'0 
 
 I J- & D-, 
 
 .... 
 
 100 
 
 7.9 
 
 / 1900 
 
 \c./ . . 
 
 100 
 
 16-8 
 
 / 1900 
 
 
 
 
 
 wrought . 
 
 -160 
 
 5'4 
 
 Lees, '08 
 
 Alloys- 
 
 
 
 
 ,, t 
 
 18 
 
 139 
 
 \ J. & D, 
 
 Brass .... 
 
 -160 
 
 4' i 
 
 \ Lees, 
 
 JJ 5) T 
 
 1OO 
 
 1 8-8 
 
 J 1900 
 
 t ... 
 
 17 
 
 6-6 
 
 ) 1908 
 
 steel /!%>. 
 
 18 
 
 19-9 
 
 1 J- & D, 
 
 ,, t -.. 
 
 18 
 
 6-9 
 
 Mean 
 
 , \CJ. 
 
 1OO 
 
 25-6 
 
 ; 1900 
 
 Constantan \ 
 
 18 
 
 49-0 |\ J. & D., 
 
 Lead, drawn 
 
 -160 
 
 7'43 
 
 Lees, '08 
 
 (Eureka) / 
 
 100 
 
 \t 
 49-1 !/ 1900 
 
 . . 
 
 18 
 
 20'8 
 
 I J- & D., 
 
 German silver || 
 
 18 
 
 16-40 Mean 
 
 V 
 
 1OO 
 
 277 
 
 J 1900 
 
 
 
 
 
 26-6 
 
 \ Lorenz. 
 
 Lithium . . 
 
 
 
 8-4 
 
 B., '04 
 
 v 
 
 1OO 
 
 27-6 / 1881 ' 
 
 Magnesium . . 
 
 O 
 
 4'35 
 
 D. & F. 
 
 Manganin ^[ . 
 
 -160 
 
 43'13\ Lees, 
 
 Mercury . . . 
 
 
 
 94-07 
 
 \ See 
 
 . . 
 
 18 
 
 44-50 / 1908 
 
 ,, ... 
 
 20 
 
 9576 
 
 ipp. 6, 82. 
 
 
 
 18 
 
 42-05 t J. & D., 
 
 Molybdenum 
 
 25 
 
 
 Fink, '10 
 
 )> * * 
 
 100 
 
 42'! i J 1900 
 
 Nickel . . . 
 
 -160 
 
 5*9 
 
 Lees, '08 
 
 Phosphor-bronzt 
 
 18 
 
 5-10 i Mean 
 
 /97%\ 
 
 18 
 
 11-8 
 
 \ I- & D-, 
 
 Platinoid || . . 
 
 -16O 
 
 32-5 } Lees, 
 
 . INiJ . 
 
 100 
 
 157 
 
 / 1900 
 
 
 
 18 
 
 34-4 / 1908 
 
 Osmium . . 
 
 20 
 
 9'5 
 
 Blair, '05 
 
 90 Pt, 10 Rh . 
 
 
 
 2 1- 1 D.&F., '96 
 
 Palladium . . 
 
 18 
 
 107 
 
 \ J *> 
 
 67 Pt, 33 Ag . 
 
 
 
 24-2 | 
 
 . 
 
 1OO 13-8 
 
 J 1900 
 
 
 
 
 * 99% Al. f 'i%C, 
 
 2 % Si, 'I % Mn. J 70 Cu, 30 Zn. 
 
 60 Cu, 40 Ni. || 62 Cu, 
 
 15 Ni, 22 Zn. f 84 Cu, 4 Ni, 12 Mn. 
 
 B., Bernini ; Bo., Bolton ; D. &f F., Dewar & Fleming ; J. & D., Jaeger and Diesselhorst ; 
 
 M., Matthiessen ; M. & C., Moissan & Chavanne ; R., Reichardt ; P. T., Phil. Trans. 
 
82 
 
 RESISTIVITIES 
 
 ELECTRICAL RESISTIVITIES (contd.) 
 
 NON-METALS AND INSULATORS 
 
 The resistivities are in ohm-cms, at room temperatures unless otherwise i 
 stated. The values for insulators naturally vary widely, and the figures below are ' 
 merely typical and are probably, in many cases, nothing more than the resistances 
 of the surfaces. For a discussion of some eltctrical insulators, see Kaye, Proc. Phy. 
 Soc. Lond., 1911. 
 
 Substance. 
 
 Sp. Ee. 
 
 Gas carbon 
 
 Graphite . . . 
 C. lamp filament 
 Selenium \ (1907) 
 Silicon . . . . 
 
 f -004 to 
 
 007 
 003 
 004 
 
 2 . I0 1C 
 06 
 
 Substance. 
 
 Sp. Be. 
 
 Sulphur, 70 . . 
 Ebonite . . . . | 
 Glass, soda-lime * 
 
 Jena, com-V 
 bustion * y 
 
 ,, conducting! 
 
 I0 1 
 I0 1 
 
 5 . io n 
 
 2. I0 1 
 
 10 s 
 
 Substance. 
 
 Guttapercha 
 Mica . . . 
 Paraffin wax 
 Porcelain, 50 
 Quartz . . , 
 Fused silica * 
 
 Sp. Re. 
 
 2 . I0 9 
 
 9 . io^ ; 
 
 2 . lo' ; 
 I '2. I0 14 
 >2.I0 14 
 
 National Physical Laboratory. 
 
 t Phillips. 
 
 % In dark. 
 
 Wick, 1908. 
 
 TEMPERATURE COEFFICIENTS OF RESISTANCE 
 
 To represent accurately over any considerable range the variation of electrical 
 resistance (R) with temperature (/) requires for almost all substances a parabolic 
 or cubic equation in /. But if the temperature interval is not large, a linear 
 equation R* = R (i + a/) may be employed ; and this gives a definition of the 
 mean temperature coefficient (a) over that temperature range. The table of resis- 
 tivities above will readily yield the associated values of o. The coefficients given 
 below are average ones. 
 
 Substance. 
 
 Metals- 
 Aluminium . . . 
 Bismuth . ' . . . 
 Cadmium . . . . 
 Copper* . . . . 
 
 Cobalt 
 
 Gold 
 
 Iron, pure . . . . 
 
 Steel 
 
 Lead 
 
 Mercury f . . . . 
 Nickel, electrolytic 
 
 commercial 
 Palladium . . . . 
 Platinum . 
 
 Molybdenum (1910) 
 
 Temp. 
 
 18 100 
 
 18 
 18-100 
 
 18 
 
 O 160 
 
 0-100 
 
 18 
 
 18 
 
 18 
 
 O 24 
 
 0-100 
 
 O 1OOO 
 
 18 1OO 
 
 -100-0 
 
 O-1OO 
 
 O-17O 
 
 x io~ 4 
 38 
 42 
 40 
 42*8 
 
 33 
 
 40 
 
 62 
 
 16-42 
 
 43 
 9-0 
 62 
 27 
 37 
 35 
 38 
 
 Substance. 
 
 Metals (contd.} 
 
 Silver 
 
 Tantalum .... 
 
 Tin 
 
 Tungsten (1910) 
 Zinc 
 
 Alloys- 
 Brass . . 
 
 Constantan (Eureka) . 
 
 German silver . 
 Manganin . . . . 
 Platinoid . . . . . 
 90 Pt, 10 Ir . . . . 
 90 Pt, 10 Rh . . . . 
 Platinum-silver (coils) 
 
 Temp. 
 
 100 
 
 o 100 
 
 O-1OO 
 17O 
 18 100 
 
 18 
 18 
 
 18 
 20 
 18 
 16 
 15 
 16 
 
 40 
 33 
 45 
 5i 
 37 
 
 lot 
 / - -4 to 
 
 +-lt 
 
 2-3-6 
 02-- 5 \ 
 
 2'5 
 
 15 
 
 17 
 
 2-4-3*3 
 
 * High conductivity annealed commercial. f R f = R (i + -o 3 88/ + 'Osi* 2 ) Smith 
 (N. P. L.), 1904. \ N. P. L. Most samples of manganin have a zero temp, coeff. at 
 from 30 C. to 40 C. 
 
83 
 
 WIRE RESISTANCES 
 
 STANDARD WIRE GAUGE 
 
 The sizes of wires are ordinarily expressed by an arbitrary series of numbers 
 There are, unfortunately, four or five independent systems of numbering, so that th 
 wire gauge used must be specified. The following are English Legal Standarc 
 wire gauge values. (See Foster's " Electrical Engineers' Pocket Book.") 
 
 Size. 
 
 < 
 
 8 
 
 10 
 12 
 14 
 16 
 18 
 
 Diameter. 
 
 Inch. 
 
 4-88 
 4-06 
 
 3'25 
 2-64 
 2-03 
 r6 3 
 
 T22 
 
 192 
 
 160 
 
 128 
 
 104 
 080 
 
 064 
 
 048 
 
 Size. 
 S.W.Q 
 
 20 
 22 
 24 
 26 
 28 
 30 
 32 
 
 Diameter. 
 
 Jffm. 
 
 914 
 
 711 
 '559 
 '457 
 376 
 
 315 
 
 274 
 
 Inch. 
 
 036 
 
 028 
 
 022 
 
 018 
 
 0148 
 
 0124 
 
 0108 
 
 Size. 
 
 SW.G 
 
 34 
 36 
 38 
 40 
 42 
 44 
 46 
 
 Diameter. 
 
 Mm. 
 
 234 
 193 
 152 
 
 '122 
 *I02 
 08 1 
 
 06 1 
 
 Inch. 
 
 0092 
 0076 
 0060 
 0048 
 0040 
 0032 
 0024 
 
 WIRE RESISTANCES 
 
 Average values in ohms per metre at 15 C. The safe currents for copper 
 (high conductivity annealed commercial) are calculated at the rate of about 270 
 amps./cm.' 2 for No. 12 wire, 430 amps./cm. 2 for No. 22 wire, and 500 amps /cm. 2 
 for smaller diameters (see the standards fixed by the Institution of Electrical 
 Engineers). To estimate the safe currents for manganin and platinoid coils allow 
 10 watts per coil. Eureka is practically identical with constantan. 
 
 The average temperature coefficient of resistance of copper is "00428 ; of 
 nickel, -0027 ; of manganin, -ooooi ; of German silver, -00044 ; of Eureka, -00002 ; 
 of platinoid, '00025 per degree Centigrade. The values for the alloys may vary 
 considerably. The composition of manganin is 8401, 4Ni, i2Mn; of German 
 silver, 6oCu, i5Ni, 25Zn ; of Eureka, c. 6oCu, 4oNi. Platinoid is said to be German 
 silver with a little tungsten. For specific resistances, see p. 81. 
 
 S.w.G 
 
 COPPER. 
 
 Ohms per ! Safe 
 metre, current. 
 
 MANGA 
 NIN. 
 
 Ohms 
 per 
 
 metre. 
 
 GERMAN 
 
 SILVER. 
 
 Ohms per 
 metre. 
 
 S.W.G. 
 
 COPPER. 
 
 Ohms 
 per 
 
 metre. 
 
 Safe 
 current 
 
 MANGA- 
 NIN. 
 
 GERMAN 
 SILVER. 
 
 Ohms 
 
 per 
 
 metre. 
 
 Ohms per 
 metre. 
 
 12 
 14 
 16 
 18 
 20 
 22 
 24 
 26 
 28 
 
 0032 
 0054 
 0083 
 0148 
 0260 
 
 0435 
 070 
 105 
 155 
 
 amps. 
 15-0 
 
 9-8 
 
 6-8 
 
 4-2 
 
 2-6 
 
 17 
 
 n 
 
 7 
 
 5 
 
 077 
 
 131 
 204 
 361 
 645 
 1-07 
 
 173 
 2-58 
 3-82 
 
 041 
 070 
 109 
 193 
 345 
 57 
 92 
 1-38 
 
 2 '02 
 
 30 
 32 
 34 
 36 
 38 
 4O 
 42 
 44 
 46 
 
 '222 
 
 293 
 404 
 590 
 950 
 
 1-48 
 
 2"IO 
 
 3-30 
 
 5-90 
 
 amp. 
 '4 
 '3 
 
 2 
 
 'IS 
 'I 
 
 06 
 05 
 03 
 02 
 
 5'45 
 
 7-18 
 9-90 
 
 H'5 
 23-2 
 
 53'4 
 817 
 
 2-90 
 
 3'83 
 
 5-27 
 
 774 
 12-4 
 19-4 
 
 27-8 
 43'5 
 77'4 
 
 EUREKA or CONSTANTAN. 
 
 .W.G. 
 
 12 
 14 
 16 
 18 
 
 Ohms 
 
 per 
 
 metre. 
 
 20 C. temp.- 
 
 rise caused 
 
 by 
 
 086 
 146 
 228 
 405 
 
 amps. 
 
 I2'2 
 
 8'2 
 
 4'9 
 2-7 
 
 S.W.G. 
 
 2O 
 22 
 24 
 26 
 
 Ohms 
 
 per 
 
 metre. 
 
 722 
 :-20 
 
 20 C. temp, 
 rise caused 
 
 by 
 
 amps. 
 
 7 
 '3 
 i 
 
 PLATINOID (Martino's). 
 
 S.W.G 
 
 Ohms 
 per 
 
 metre. 
 
 20 
 22 
 24 
 26 
 
 622 
 1-03 
 r6 7 
 
 2-50 
 
 S.W.G. 
 
 Ohms 
 
 per 
 
 metre. 
 
 28 
 3O 
 32 
 34 
 
 3-69 
 5-25 
 6-8 1 
 9'55 
 
 FUSES 
 
 The fusing currents are for wires mounted horizontally. 
 
 Fusing current. 
 
 lamp. 
 
 10 
 
 20 
 
 30 
 
 4O 
 
 5O 
 
 Tin . . 
 Copper . 
 
 S.W.G. 
 S.W.G. 
 
 37 
 47 
 
 28 
 
 24 
 38 
 
 21 
 
 33 
 
 18 
 28 
 
 16 
 
 25 
 
 23 
 
 13 
 
 22 
 
84 
 
 INDUCTIV1TIES 
 
 DIELECTRIC CONSTANTS 
 
 The inductivity, dielectric constant, or specific inductive 
 
 capacity k of a material may 
 
 be defined as 
 
 
 
 
 
 (i) The ratio of the capacity of a condenser with 
 
 the 
 
 material as 
 
 dielectric to its 
 
 capacity when the dielectric is a vacuum. 
 
 
 
 
 
 (2) The square of the ratio of the velocity of electromagnetic waves 
 
 in a vacuum to 
 
 their velocity in the material. This ratio is dependent on the wave-length, 
 
 \, of the 
 
 waves ; in most cases k increases with \. Unless otherwise stated, the inductivities 
 
 below are for very long waves (\ oo) and at room temperatures. 
 
 If A* is the refractive index, then on Maxwell's theory of light, k = /* 2 , provided the 
 
 frequency of the electrical oscillations is the same as 
 
 that of the light 
 
 vibrations. In 
 
 practice we cannot find k for vibrations as rapid as 
 
 those of the visible rays : the j 
 
 alternative is to obtain (by extrapolation) the refractive index for waves of very great 
 
 wave-length, e.g. by the use of Cauchy's formula, p. 71 
 
 When such data are 
 
 available 
 
 Maxwell's relation is found to hold fairly exactly in the 
 
 case of a number 
 
 of gases 
 
 and liquids, though there are many substances which provide marked exceptions. 
 
 In general, a rise of temperature diminishes the inductivity. The temperature 
 
 coefficient a between / and T is defined by T = k t { 
 
 _ a (T /)} 
 
 . In 
 
 the case 
 
 of water Palmer (1903) finds that o increases slightly with 
 
 the frequency of oscillation. 
 
 The Clausius-Mossotti r 
 
 . . k i 
 
 const. 
 
 (p being the density) 
 
 has been 
 
 elation + - 
 
 shown by Tangl (Ann. d. Phys., 1908) to hold from i to 100 
 
 atmos. in the 
 
 case of H 2 , N 2 , 
 
 and air. 
 
 
 (See Badeker in L.B.M.) 
 
 Substance. 
 
 k. 
 
 Substance. 
 
 k. 
 
 Substance. 
 
 k. 
 
 Solids- 
 
 
 
 
 
 
 
 
 Calcite .... 
 
 7'5-77 
 
 Bromine . . . 
 
 3' i 
 
 
 Oil, paraffin 
 
 . . 
 
 4-6-4-8 
 
 Ebonite .... 
 
 2-7-2*9 
 
 Carb. bisulphide . 
 
 2-62 
 
 
 Petroleum 
 
 . 
 
 2*O 2*2 
 
 Fluorite .... 
 
 6-8 
 
 tetrachloride 
 
 2-25/18 
 
 Toluene, o -ooi 
 
 2-3 
 
 Glass, crown . 
 
 5-7 
 
 Chloroform, 18 . 
 
 5-2 
 
 
 Turpentine 
 
 
 2*2-2-3 
 
 heavy crown 
 
 7-9 
 
 Ethyl acetate . . 6 
 
 
 Vaseline oil 
 
 
 I'9 
 
 flint . . . 
 
 7-10 
 
 chloride . . 10-9 
 
 
 Water, A. = oo . . 
 
 81 
 
 mirror . . 
 
 6-7 
 
 ether, a --005 4-37 
 
 
 \ = 3600 cms. 
 
 3-32* 
 
 Gypsum .... 
 
 6'3 
 
 Glycerine, \ = 200 39*1/1 
 
 .0 
 
 ) 
 
 ,, A. 1200 
 
 279* 
 
 Ice (-2) . . . 
 
 93*9 
 
 Nitrobenzene . . 
 
 34/17 
 
 o 
 
 a 17 = -0045 . 
 
 
 Indiarubber . . 
 
 2-1-2-3 
 
 Oil, castor . . . 
 
 4-6-4-8 
 
 Xylene, ;, o 
 
 = ' 3$ 
 
 2*4 
 
 Marble .... 
 
 8-3 
 
 olive . . . 
 
 3-1-3-2 
 
 
 
 
 Mica 
 
 57-7 
 
 
 
 
 
 
 
 Paper, dry . . . 
 
 2-2-5 
 
 
 
 
 Observer. 
 
 Paraffin wax . . 
 
 2-2-3 
 
 Substance. Temp. 
 
 
 k. 
 
 Pitch ..... 
 
 1-8 
 
 
 
 
 
 Porcelain . . . 
 
 44-6 8 
 
 
 
 76 cm. Hg. ; \ = oo 
 
 
 
 Quartz .... 
 
 4'5 
 
 Gases- 
 
 
 
 
 
 
 Resin i'8-2"6 
 
 Air 
 
 oC. 
 
 
 i * 000^86 
 
 Klemencic 188? 
 
 Rock salt ... 5-6 
 Selenium (16) . 6'i 
 
 
 20 
 
 
 
 i 000576 
 i 000264 
 
 Tangl, 1908 
 Boltzmann, 1875 
 
 Hydrogen . . . 
 
 Shellac .... 3-3-7 
 
 ,, ... 
 
 20 
 
 
 i '000273 
 
 Tangl 
 
 , 1908 
 
 Silica, fused . . 3'5~3'6 
 
 Helium .... 
 
 
 
 
 1*000074 
 
 Hockheim, 1908 
 
 Spermaceti ... c. 2'2 
 
 Nitrogen . . . 
 
 20 
 
 
 i '00058 1 
 
 Tangl 
 
 , 1008 
 
 Sulphur .... 1 3*6-4*3 
 
 Nitrous oxide,N 2 O o 
 
 
 1-00099 
 
 Klemencic, 1885 
 
 Sylvin .... 4-9 
 
 Carbon monoxide o 
 
 
 1-000695 
 
 
 
 Vaseline .... 
 
 2"2 
 
 dioxide . 
 
 
 
 
 1*000985 
 
 ( 
 
 
 
 
 bisulphide 
 
 15 
 
 
 i -0029 
 
 
 
 Liquids 
 
 
 Ethylene . . . 
 
 15 
 
 
 1-00146 
 
 
 
 Alcohol, methyl . 
 
 35'4/i3-4 
 
 Sulphur dioxide . 
 
 I4-7 
 
 
 1-00905 
 
 i 
 
 
 ethyl . . 
 
 26'8/i47 
 
 Ammonia . . . 
 
 20 
 
 
 1-00718 
 
 Badeker, 1901 
 
 amyl . . 
 
 16-0/20 
 
 Alcohol, methyl . 
 
 I 10 
 
 
 1-00600 
 
 i 
 
 } 
 
 Aniline, a = -004 . 
 
 7-30 
 
 ethyl 
 
 I 10 
 
 
 i -00647 
 
 
 5 j 
 
 Benzene, a = *o 3 7 . 
 
 2-29/18 
 
 Benzene . . . .no 
 
 
 i -00292 
 
 
 
 ?5 
 
 * Beaulard, 1908. 
 
85 
 
 IONIC DISSOCIATION 
 
 IONIC DISSOCIATION THEORY 
 
 On the Dissociation Theory (Arrhenius, 1887), the solute is dissociated into 
 electrically positive cathions and negative anions. For example, KC1 in water 
 exists as KC1, K + , Cl~ ; sulphuric acid as H 2 SO 4 , H + , H~ SO 4 ++ , HSO 4 + . Pro- 
 bably, in many cases, these ions are attached to molecules of solvent. The degree 
 of dissociation = (number of dissociated solute molecules)/(total number of 
 solute molecules), a is deduced from the osmotic pressure of the solution, and from 
 its electric conductivity at different dilutions. The osmotic pressure is determined 
 (i) directly, (2) from the raising of the boiling-point, and (3) from the depression of 
 the freezing-point of the solvent by the presence of the solute. The equivalent 
 conductivity (A) for different concentrations of any dilute solution is assumed to be 
 proportional to the number of ions present. A approaches asymptotically a limiting 
 conductivity (AOO ) for extreme dilutions, a state of things when, on this theory, the 
 solute is completely dissociated. A m /Aoo = a for the equivalent concentration ;//. 
 The cathion and anion with their charges +e and e (for monovalent ions) move 
 in unit electric field in opposite directions with speeds or mobilities // + and ^t_. 
 The electrolytic current also obeys Ohm's Law, so that X = (u + + u_}ne 
 (Kohlrausch, 1879), where X is the potential gradient in volts per cm., n the 
 number of -five or ive ions per c.c., K the conductivity of the solution in 
 ohm"- 1 cm.- 1 . This becomes u+ + u_ = 1-037 x io~ 5 A cm./sec., since K/H = A/N, 
 and N* = 96,740 coulombs per gm. equivalent of ions. 
 
 The mobility of electrolytic ions has been directly observed by Lodge (1886), 
 Whetham, Orme Masson, and D. B. Steele. The ratio u_j(u + + u_} = n is for the 
 negative ion, the migration ratio or transport number of Hittorf (1853-9). n can 
 be determined, when complex ions are absent, from the change of concentration at 
 the anode and cathode during electrolysis. The mobility of certain organic ions 
 is approximately inversely proportional to their linear dimension a (Laby and 
 Carse). The existence of this relation of Ohm's Law and of a relation between 
 the viscosity (77) of the solvent and the ionic mobilities (Kohlrausch, Hosking, and 
 Lyle) indicates that the motion of the ion through the solution may follow Stokes' 
 Law (v = F/^Tnjtf, where F is the driving force), with the numerical constant, 6ir, 
 possibly changed. 
 
 The dissociation theory postulates the conditions existing in very dilute solutions. 
 The role of the medium is rather neglected (Lowry, Science Progress, 1908). The 
 dissociation should be large for a solvent with a high dielectric constant, for then 
 the attraction between the cathion and anion is small (Thomson and Nernst). 
 This is generally true (Walden). 
 
 (Kohlrausch and Holborn, " Leitvermogen der Elektrolyten ; " Whetham's 
 " Theory of Solution.") 
 
 MIGRATION RATIOS 
 
 Hittorf's migration ratio or transport number of the anion, n u_/(t/ + + #_) ; m 
 equivalent concentration per litre ; / = temp, of observation. 
 
 Solute. /C. Cone, m 
 
 KC1 . 
 KBr . 
 
 KI . . 
 KNO 3 . 
 
 NaCl . 
 NaNO, 
 Lid 
 
 18 
 
 25 
 8 
 
 18 
 19 
 18 
 
 003 
 ( -03 to) 
 
 I'OI J 
 
 05 
 
 I 
 
 (03 to) 
 I '009) 
 
 05 
 
 -03 to\ 
 
 1 -008 / 
 
 Ratio n. Solute. 
 
 505, S.D 
 504, B. 
 505, Be. 
 '497, H. 
 604, B. 
 629, Be. 
 67 
 
 AgNO 
 NH 4 C1 20 
 T1C1 . 
 Cad, . 
 SrClo . 
 Bad, . 
 MgCl 2 
 ZnS0 4 
 
 CdBr 2 . 
 
 /C. Cone. m. Ratio . Solute. /C. Cone, m 
 
 17 
 
 20 
 
 22 
 
 21 
 18 
 
 21 
 
 18 
 
 '4t0'02 
 
 05 
 
 oi 
 
 005 
 
 oi 
 
 *OI 
 
 05 
 
 05 
 
 ('I2tO 
 
 \ -007 
 
 526, H. 
 507, Be. 
 516, Be. 
 562,S.D. 
 56, Be. 
 
 '55 
 615, Be. 
 
 64, H. 
 
 '57 
 
 CuS0 4 
 
 Hd . 
 
 HN0 3 . 
 H 2 SO 4 
 KOH . 
 NaOH. 
 NH 8 . 
 
 25 
 21 
 
 25 
 
 o8to) 
 
 '02 / 
 
 (os to) 
 
 I '02 / 
 
 25 
 
 05 
 
 i 
 
 04 
 
 05 
 
 oi 
 
 Ratio n. 
 
 625, M. 
 
 159, N.S. 
 
 17 
 
 17, Be. 
 74 
 
 8, Be. 
 56, Be. 
 376, L.N 
 
 B, Bogdan; Be., Bein ; H., Hittorf; L.N., Lob and Nernst; M., Metelka ; N.S., 
 Noyes and Sammet ; S.D., Steele and Denison. 
 
86 
 CONDUCTIVITY OF SOLUTIONS 
 
 ELECTRICAL CONDUCTIVITY OF SOLUTIONS 
 , a = specific electric conductivity (in ohms" 1 cm.- 1 ) of the solution at 18 C. 
 p mass of anhydrous solute per 100 gms. of solution, 
 ij = the number of gm. equivalents in i c.c of solution. Gm. equiv. per 
 
 litre = 100017. To find *? note that ic/A = t\. 
 
 V = volume in litres containing one gm. equivalent of solute = i/iooorj. 
 A = equivalent conductivity = */?, = the conductivity in reciprocal ohms of 
 i gm. equiv. in solution between electrodes I cm. apart. The chemical 
 equiv. of, for example, " i/2CaC! 2 " is 111/2. 
 
 Temp, coefficient = (dK/dt)/K lB . (See Kohlrausch and Holborn, " Das Leitver- 
 mogen der Elektrolyten " (Teubner), and Holborn, L.B.M.) K - Kohlrausch ; G = 
 Grotrian. 
 
 CONCENTRATED SOLUTIONS 
 
 K 
 
 A-- 
 
 1 KM (K.G.). 
 
 0690 
 
 99-9 
 
 5 
 
 io -1359, 
 15 '2020 9i '5 
 
 20 -2677 
 21 
 
 |'28lO 
 
 87-5 
 
 201 
 
 1 88 
 179 
 1 68 
 1 66 
 
 1 NaCl (K.G.). 
 
 5 -0672 76 
 
 10 !'I2II 66'2 
 
 15 -1642 57'8 
 20 'I957j49'9 
 25 -2135 42-0 
 26-4-2156 39-8 
 
 217 
 214 
 212 
 2l6 
 227 
 233 
 
 CaCl 2 (K.G.). 
 
 5 
 10 
 
 15 
 
 20 
 
 25 
 30 
 
 35 
 
 0643 
 1141 
 1505 
 1728 
 1781 
 1658 
 1366 
 
 68-6 213 
 58-3 i 206 
 
 49*2 I 202 
 40-6 200 
 32-1 204 
 
 23-9 216 
 
 16-^236 
 
 * CdCL. (G.). 
 
 0055 
 10 -0241 
 
 50-1 
 
 20'2 
 
 o 
 
 222 
 217 
 
 V 
 
 /C 
 
 0282 
 0137 
 
 .) (contd:)._ 
 o 
 
 252 
 
 353 
 
 6-5 
 i'49 
 
 1 AgN0 3 (K.). 
 
 0256 
 0476 
 0683 
 1565 
 
 "2. 10 1 
 
 o 
 
 83-4 218 
 
 74-3 217 
 67-9 215 
 
 45-0 1 205 
 
 31*1 
 
 1 (NH,) 2 S0 4 (K.). 
 
 5 i'0552 
 
 71-0 215 
 
 io 'loio 63*1 203 
 
 17791 527 193 
 2292) 43-1 (191 
 
 * CaS0 4 (K.). 
 
 2-5 -0109 
 
 5 -0189 
 
 10 1*0320 
 
 I7-5J-0458 
 
 287 
 23*1 
 17-4 
 
 o 
 
 213 
 
 216 
 
 218 
 
 236 
 
 * CdS0 4 (O.). 
 
 I -0042 429 
 
 5 -0146 29-0 
 
 25 -0430 13-8 
 
 36 -0421 8-25 
 
 o 
 
 210 
 
 206 
 
 223 
 255 
 
 = 
 
 1 HC1 (K.). 
 
 5 1-3948 28 ro 158 
 
 10 -6302219-1 156 
 
 20 7615126-2 154 
 
 30 -6620 69-8 152 
 
 1 HN0 3 (E.G.). 
 
 6-2-312 
 
 542 
 
 12-4 
 
 18-6-690 211 
 
 24*8 
 31 
 
 49*6 
 62 
 
 307 
 257 
 
 768 [169 
 782 133 
 
 634 
 496 
 
 61 
 
 36-4 
 
 IJ> 4 
 
 |l 4 2 
 137 
 137 
 
 |I39 
 
 157 
 157 
 
 H 2 S0 4 (K.). 
 
 208 
 '39 1 
 
 I 43 
 653 
 
 717 
 
 739 
 724 
 680 
 540 
 
 373 
 
 161 
 140 
 119 
 
 99 
 80 
 
 64 
 38 
 20-3 
 
 o 
 
 121 
 
 128 
 136 
 H5 
 
 170 
 I 7 8 
 193 
 213 
 
 A =- 
 
 n 
 
 70 
 80 
 
 216 9-4 
 i io 3-9 
 90 -107 3-22 
 
 loo -0157 
 
 1 XOH (K.). 
 
 o 
 256 
 
 349 
 320 
 
 031 
 
 
 
 
 o 
 
 4-2 
 
 1464 
 
 1 88 
 
 18 
 
 8-4 
 
 272 
 
 169 
 
 1 8 
 
 12-6 
 
 376 
 
 150 
 
 18 
 
 1 6-8 
 
 456 
 
 131 
 
 19 
 
 29-4 
 
 "543 
 
 81 
 
 22 
 
 42*0 
 
 421 
 
 39 
 
 28 
 
 1 NaOH (K.). 
 
 2-5 
 
 5 
 10 
 
 15 
 
 20 
 30 
 40 
 
 IO9 170 
 
 I 9 7 149 
 
 312 112 
 
 346 79 
 
 327 
 
 202 
 
 53 
 
 20 
 
 o 
 
 I 9 4 
 201 
 
 217 
 249 
 299 
 
 45 
 
 65 
 
 1 NH 3 (K.). 
 
 1-6 
 
 00025 
 00087 
 
 8 -00104 
 30-5-00019 
 
 It) 
 
 4-25 246 
 '93 238 
 23 ,262 
 
 012 
 
 STANDARD SOLUTIONS FO3 CALIBRATING CONDUCTIVITY VESSELS 
 
 *i 8 for the purest water in a vacuum = -04 x io~ 6 ohms" 1 cm." 1 (Kohlrausch 
 and Heydweiller) ; K ]8 for conductivity water in air is about io~ ohms" 1 cm.' 1 ; 
 KC1 i n = normal KC1 = 74*59 gm./litre at 18 C. ; NaCl sat. = saturated NaCl at 
 temp. /. of experiment. Unit ohm" 1 cm." 1 . (See Kohlrausch, Holborn, and 
 Diesselhorst.) 
 
 Solution. 
 
 NaCl, sat. . 
 KC1, i n . 
 I KC1, i/ io n 
 KC1, 1/50 n 
 KC1, 
 
 0C. 
 
 1345 
 
 06541 
 
 00715 
 
 00152 
 
 00078 
 
 8 
 
 1688 
 
 07954 
 
 00888 
 
 00190 
 
 00097 
 
 12 
 
 1872 
 
 08689 
 
 00979 
 
 -00209 
 
 00107 
 
 16 C 
 
 2063 
 09441 
 01072 
 00229 
 ooi 173 
 
 20 
 
 24 C 
 
 2260 
 
 10207 
 
 01167 
 
 00250 
 
 001278 
 
 2462 
 
 10984 
 
 01264 
 
 00271 
 
 001386 
 
87 
 CONDUCTIVITY OF SOLUTIONS 
 
 EQUIVALENT ELECTRIC CONDUCTIVITY A OF DILUTE AQUEOUS SOLUTIONS 
 
 Extrapolated numbers are indicated by ( ). A. for infinite dilution is given 
 under "6." Observers: inorganic solutes, Kohlrausch ; organic, Bredig, Zeit. 
 Phys. Chem., 1894. _____ 
 
 Solute 
 at 18 C. 
 
 KC1 . 
 KBr . 
 KI 
 
 KF . 
 KSCN 
 KNO 3 . 
 NaCl . 
 NaF . 
 NaNO., 
 L5C1 . 
 AgNO, 
 CsCl . 
 RbCl . 
 NH 4 C1 
 T1C1 
 
 Gm. equiv. per litre 1000??. 
 
 130-1 
 
 132-3 
 131*0 
 111-3 
 121-3 
 126-5 
 139-0 
 
 90-15 
 105-3 
 
 98-9 
 115-8 
 133*6 
 
 0001 -01 
 
 129-1 
 
 131-1 
 129-8 
 
 110-5 
 
 1 20' 2 
 
 125-5 
 
 108-1 
 
 89-3 
 104-5 
 
 98-1 
 115-0 
 132*3 
 132*3 
 129*2 
 
 122 
 124 
 123 
 104 
 114 
 
 118 
 
 102 
 83*5 
 
 99-2 
 
 108 
 125 
 125 
 
 122 
 120 
 
 102 
 
 105 
 
 1 06 
 
 83 
 
 957 
 89-2 
 80-9 
 60-0 
 74*o 
 70-7 
 
 77'5 
 
 101 
 
 Solute at 
 18 C. 
 
 CaCl 2 . 
 SrNOg . 
 BaCl. . 
 MgCl. . 
 ZnSO 4 . 
 CdN0 3 . 
 CuSO 4 . 
 
 Acids. 
 
 HC1 . . 
 HNO, . 
 J,- H 2 SO t . 
 I H 3 P0 4 . 
 
 Alkalies. 
 KOH 
 NaOH 
 NH, 
 
 Gm. equiv. per litre = 1000??. 
 
 0001 0002 
 
 115-2 
 1117 
 
 114*5 
 iiri 
 [ii7/-ooo5] 
 109-4 | 108-9 
 109-5 | 107-5 
 [ioo/-oo5] 
 
 109-9 
 120-7 
 
 001 
 
 (377) 
 
 (375) 
 
 361 
 
 (106) 
 
 (234) 
 
 107-9 
 119-9 
 
 002 
 
 376 
 374 
 35i 
 
 102 
 
 (233) 
 204-5 
 5 3/ -0002 387-0005 
 
 01 
 
 103 
 
 99 
 107 
 
 98*1 
 
 72-8 
 
 96 
 
 717 
 103 
 
 01 
 
 370 
 
 368 
 
 308 
 
 85 
 
 228 
 203-4 
 9-6 
 
 74*9 
 627 
 77*3 
 69-5 
 
 63-9 
 
 327 
 324 
 205 
 
 197 
 174 
 i'35 
 
 Solute at 25 C. 
 
 Na formate . . . 
 Na acetate .... 
 Na propionate . . 
 Na butyrate . . . 
 Na isobutyrate . . 
 Hydrochlorides of 
 
 -Methylamine . . 
 
 -Ethylamine . . 
 
 -Dimethylamine . 
 
 -Allylamine . . . 
 
 98-1 
 857 
 8ro 
 
 77*4 
 777 
 
 125-1 
 
 ii4*3 
 117-5 
 109-2 
 
 I00'4 
 87*5 
 
 83-5 
 79-9 
 
 80- 1 
 
 127-8 
 117*0 
 120-3 
 
 1117 
 
 Solute at 25 C. 
 
 Hydrochloride of 
 
 -Propylamine . 
 (CH 3 ) 4 PCl . . . 
 (C.H B ) 4 PC1 . . 
 (CH 3 ) 4 AsCl . . 
 
 Hydrochlorides of- 
 
 -Aniline . . . 
 -Methylaniline. 
 -o-Toluidine . 
 
 107-5 
 
 107-4 
 
 98-3 
 
 105 5 
 
 100-3 
 99*4 
 97*4 
 
 1 1 0*3 
 109-8 
 100-8 
 108-2 
 
 106 i 
 105-2 
 103-7 
 
 EQUIVALENT ELECTRIC CONDUCTIVITY OF NON-AQUEOUS SOLUTIONS 
 
 v = i/m = volume in litres in which i gm. equivalent is dissolved. (See Tower, 
 " Conductivity of Liquids," 1908.) 
 
 SD!- 
 vent. 
 
 NH, 
 
 HCN 
 
 S0 2 . 
 AsCl 3 
 
 Solute. 
 
 KBr 
 
 AgN0 3 
 
 KI 
 
 S(CH 3 U 
 KI 
 
 N(C a H B ) 4 I 
 N(C 2 H 5 ) 4 I 
 
 -38 
 
 -15 
 
 
 
 
 
 
 
 
 
 25 
 
 5740317-6 
 
 94; 1 88 
 
 3921298 
 
 512327 
 
 I024|lI2-5 
 
 512157-1 
 150, 63-2 
 
 12410,3297 
 
 192 no 
 
 1024 
 1024 
 
 308 
 332 
 
 2048J 134-5 
 1024 1677 
 750i 597 
 
 Solvent. 
 
 POC1 8 
 
 Formic 
 
 acid 
 
 Acetone 
 
 Solute. 
 
 N(C,H 8 ) 4 I 
 
 KC1 
 
 HC1 
 
 KI 
 
 LiCl 
 
 AgN0 8 
 
 tC. 
 
 25 
 
 25 
 25 
 18 
 18 
 18 
 
 750 38-5 
 256! 5 8 
 5'86j 32-8 
 
 H57I55 
 
 10 49-8 
 288 15-7 
 
 150044-3 
 51261 
 
 2315 163 
 13-8:99-5 
 576 17-6 
 
88 
 
 IONIC MOBILITIES 
 
 MOBILITIES OF IONS IN LIQUIDS 
 
 The mobility of the anion = z/_ = 1*037 x io~ 5 Mi. (n Hittorfs number.) 
 Example. For KC1, A& 130'!, n = '505, /. u- = 1-037 x io~ 5 x '505 x 
 
 130'! = 6'8 x Jo" 4 cm./sec. for Cl ions at 18. Observers, Kohlrausch and Bredig ; 
 
 :he latter's values have been multiplied by ri x io~ 5 to bring them to cm. /sec. 
 
 Unit io~ 5 cm./sec. * | Ca, etc. : the actual ionic velocity of the divalent ions is 
 
 half the value stated here ; these values, however, fit the various equations given. 
 
 Ion. // 18 
 
 H 
 
 Li 
 
 Na 
 
 K 
 
 Rb 
 
 Cs 
 
 330 
 34-6 
 
 67 
 
 70-5 
 
 70-5 
 
 Ion. u 18". 
 
 NH 4 
 Tl . 
 Ca*. 
 Sr*. 
 Ba*. 
 Mg* 
 
 66-3 
 68-4 
 537 
 53'6 
 
 57'5 
 477 
 
 Ion. n 18 . 
 
 Zn* 
 Cu* 
 
 Ag 
 
 Cd* 
 
 Pb* 
 
 48-4 
 49 
 56 
 49-2 
 
 63-5 
 
 OH . 180 
 
 Ion. 
 
 F . 
 Cl . 
 Br . 
 I. . 
 
 NO, 
 S0 4 * 
 
 18 
 
 48-3 
 
 67-8 
 
 70 
 
 68-8 
 
 64 
 
 Ion. 
 
 25. 
 
 HCOo . . 
 CH 3 C0 2 . 
 C 2 H,CO, . 
 n.C 3 H 7 CO, 
 Iso- 
 CH 3 H 3 N . 
 
 56-3 
 42-i 
 
 377 
 33;8 
 
 53'4 
 
 Ion. 
 
 C 2 H,H 3 N 
 (C.H.VP . 
 
 C 6 H,H 3 Nj 
 aniline } 
 C f) H 5 HN . 
 (CH 3 \As. 
 
 337 
 39'5 
 48-5 
 41-8 
 
 DIRECTLY OBSERVED MOBILITIES 
 
 Deduced from the observed movement of an ionic boundary. ;;/ = equivalent 
 concentration. Unit io~ 5 cm./sec. at i8C. (See Denison and Steel, Phil. 
 Trans., 1906.) 
 
 Ion. m 
 
 '5 
 
 55'3 
 
 Ion. m u 
 
 Na i 
 
 Ion. 
 Ba 
 
 5133 
 
 Ion. 
 
 Mg 
 
 "2 167 
 
 Ion. 
 
 Cl 
 
 Ion. m u 
 
 SO 4 -2 30-4 
 
 ELECTROMOTIVE FORCES AND RESISTANCES OF CELLS 
 
 The E.M.F.'s given are for cells on open circuit, and are only approximate ; in 
 the case of primary batteries they refer to freshly made up cells. The internal 
 resistances quoted are only typical ; they vary very widely in practice. With many 
 primary cells the E.M.F. drops and the internal resistance increases as the cell 
 ages. Nearly all modern dry cells are modified Leclanchd batteries. 
 
 (See Slingo and Brooker's " Electrical Engineering.") 
 
 Cell. 
 
 Bichromate . . . 
 
 Bunsen . . . . 
 
 Clark (see p. 8) . 
 
 Daniell . . . . 
 
 Grove . . . . 
 
 Leclanche' . . , 
 
 Secondary . . . 
 
 Tucker . . . . 
 Weston (see p. 8) 
 
 Description. 
 
 Zn and C in I vol. strong H 2 SO 4 and 
 
 20 vols. sat. K 2 Cr 2 O 7 sol. 
 Zn in i vol. H 2 SO 4 and 12 vols. H 2 O ; 
 
 C in strong HNO 3 
 
 Zn amalgam and Hg in sat. ZnSO 4 sol. 
 Zn in ZnSO 4 sol. or H 2 SO 4 (i to 12) ; 
 
 Cu in sat. CuSO 4 sol. 
 Like Bunsen with Pt instead of C 
 Zn and C in NH 4 C1, C, and MnO 2 
 Pb and PbO 2 (etc.) in H 2 SO 4 of density 
 
 T2 
 
 " Hygroscopic cell." Zn and C with 
 
 sat. CaCl 2 sol. 
 Cd amalgam and Hg in sat. CdSO 4 sol. 
 
 E.M.F. 
 
 Resistance 
 
 Volts. 
 C. TO 
 
 I-8-T9 
 
 1-433 
 ro7~ro8 
 
 i -8-i -9 
 c. 1-5 
 
 i '4 
 roi8 
 
 Ohms. 
 
 very low 
 
 c. 500 
 
 0-25-4 
 negligible 
 
 c. 500 
 
89 
 
 MAGNETISM 
 
 MAGNETIC INDUCTION 
 
 f$ = magnetic force ' 
 
 
 = intensity of magnetization 
 
 33, $?, and $ are in lines per cm. 2 , and are 
 
 = magnetic moment per cm. 3 
 
 1 vector quantities. 
 
 = pole strength per cm. 2 
 
 / Unit: 4ir lines start from unit magnetic 
 
 33 = magnetic induction, or flux density 
 
 pole. 
 
 n permeability = 23/J^. See p. 6. 
 
 
 H = susceptibility = /$ = (A* - 0/(4)- See P- 6 - 
 
 Coercivity, ^ B = o, is the demagnetizing force required to make 23 = o after saturation. 
 
 Coercive force is the demagnetizing force required to make 33 = o after some par- 
 
 ticular field strength. 
 
 
 Remanence, i8 H = , is the induction remaining when the magnetic force is removed 
 
 after saturation. 
 
 
 The work done, i.e. hysteresis loss, Q^, in 
 
 taking a cm. 3 of magnetic material through 
 
 a magnetic cycle between limits + H^ = /Pf^JE 
 
 = |7r/p^i3. Steinmetz's empirical formula 
 
 for the hysteresis loss is i?33' , where 17 is 
 
 a constant, and generally n i'6. The 
 
 magnetic properties of a material depend not only on its chemical composition, but on its 
 
 previous mechanical and heat treatment ; thus only general characteristics are indicated below. 
 
 Heusler alloys (discovered by Heusler in 1903) are composed of Cu, Mn, and Al. 
 
 They do not show the Kerr effect. 
 
 
 Good permanent magnet steel contains about '5 % W and '6% C, is free from Mn, Cu, 
 
 Ni, and Ti, and is hardened at 850 C. (Hannack, 1909). Cast iron, chilled from 1000 C.. 
 
 may also be used (Peirce and Campbell). 
 
 -- ; - -' . 
 
 References. Pure iron, Peirce, Ainer. Jour. Set., 27 and 28, 1909 ; Terry, Phy. Rev., 1909 ; 
 
 iron and manganese, Burgess and Aston, Phil f Mag., 1909 ; Heusler alloys, Stephenson, 
 Phy. Rev., 1910. (Ewing, "Magnetic Induction in Iron," and Kohlrausch, "Prakt. Phys.") 
 
 Permeability 
 Material 
 
 P" 
 
 Goer- Eema- 7t 
 
 Hyst. loss, 
 
 JILOibCllctlt 
 
 
 1 = 60,$ = 150 
 
 civity. nence. ' 
 
 
 
 
 
 
 ergs/cm. 3 
 
 Swedish wrought iron 2500 
 
 3710 2060 736 
 
 274 j 120 
 
 o'8 4,000 2OO 
 
 6,700 
 
 Annealed cast steel . 1450 
 
 3500 2100 747 
 
 280 | 123 
 
 0-97 7,100 151 
 
 11,700 
 
 Unannealed cast steel 490 
 
 970 1700 ; 680 
 
 270 i 122 
 
 2'o8 9,000 156 
 
 20,400 
 
 
 8 1 182 
 
 117 ' 65 
 
 1 1 '9 42^0 155 
 
 "j/t ion 
 
 Magnet ( Hardened . 
 
 68/15 { 78 
 
 193 ioo 
 
 52-6 11,700 234 
 
 211,000 
 
 steel \ Tungsten . 
 
 8o/lO | 119 
 
 204 105 
 
 27-5 9,880 5O5 
 
 Il6,000 
 
 
 
 Induction, 
 
 33, far 
 
 For $max. 
 
 T&i tori 8*1 
 
 7fe 
 
 
 
 
 S?max. 
 Winax. \ \ 
 
 [^ = 100. 
 
 Goer. Reman. Hyst.loss. 
 
 
 
 
 
 ergs/cm. 3 
 
 Mild steel** . . . 
 
 129 1 8 190 
 
 17,700 8350 
 
 0*6 10,300 
 
 4 QOO 
 
 Steel, 2-8 % Cr, -8 % C . . . 
 
 
 
 56 6,400 1 
 
 _- 
 
 5*5 %W, -6%C. . . 
 
 Hardened at 770 
 
 
 
 72 7,ooo| 
 
 280,000 
 
 77% W, 1-9 %C . . 
 
 800 i 
 
 
 
 85 4,700 J 
 
 . 
 
 4% Mo, 1-2% C . . 
 
 800 
 
 
 
 85 6,700 
 
 
 
 Ironf 
 
 50 17,100 j 
 
 17^0 
 
 2'2* C. 53 % Bmax. 
 
 
 
 Silicon iron, '6 % Si f . . . 
 
 50 i 16,000 
 
 1900 
 
 16* <;. 43% 
 
 4-5% Sif . . 
 
 50 ! 15,100 
 
 2500 
 
 i-2!*39% 
 
 
 
 Electrolytic iron (very pure) 
 
 210 21,250 
 
 
 
 1 8 10,000 
 
 
 
 '5 55 5} 
 
 Heated to 1 200 C.' 
 
 16,000 
 
 2-5 12,500 
 
 
 
 Hadfield's manganese steel || 
 
 _ 
 
 i -3-1-5 
 
 v. small 
 
 
 
 Nickel, annealed .... 
 
 100 5,137 
 
 296 
 
 8 3,570 
 
 
 
 Cobalt . . . 
 
 1 40 1 0,000 
 
 9,500 174 
 
 12 3,400 
 
 
 
 
 114 8,237 
 
 7,800 177 
 
 
 19,000 
 
 Heusler alloy 1" 
 
 92 2,735 
 
 
 ! 
 
 
 
 * H = io. t Otto, Deut. Phys. Ges. Berlin, 1910. J Bar magnet. 
 
 Burgess and Taylor, 1906. 
 
 || 12 % Mn, I % C. 
 
 H 24 Mn, 16 Al, 60 Cu. McClennan, 1907. ** Gumlich and Schmidt (Reichsanstalt), 1901. 
 
 
90 
 
 MAGNETISM 
 
 MAGNETIC SUSCEPTIBILITIES OF THE ELEMENTS, ETC. 
 
 The 
 
 susceptibility H = 5/|& = (/* i)/(4ir . H = o for a vacuum. 
 
 The susceptibility 
 
 depends very much on the purity of the material, especially upon the absence of iron. For- 
 
 pure elements H appears to be independent of &, except possibly in the case 
 
 of Mg, Sb, and 
 
 Ru. H 
 
 is a periodic property of the 
 
 atomic weight ; for example, P, As, Sb, and Bi are 
 
 comparatively strongly diamagnetic. 
 
 
 
 
 The 
 
 values 
 
 below are per cm. 3 at 
 
 1 8 C., except where some temperature is specified. 
 
 The gases are 
 
 at i atmosphere. [Honda (.///;/. d. Phys., 1910) used purest available 
 
 materials and corrected H for any traces of iron ; see also P. Curie, CEuvres, Paris, 1908.} 
 
 + means paramagnetic ; , diamagnetic. 
 
 Elem. 
 
 H 
 
 Obs. 
 
 Elem. 
 
 H Obs. 
 
 Elem. 
 
 H 
 
 
 Obs. 
 
 Solids 
 
 X 10-6 
 
 
 Solids 
 
 
 
 Solids 
 
 
 
 
 Al . 
 
 + '65 
 
 L., W., H 
 
 Uontd.} 
 
 X 10-6 
 
 
 (contd.) 
 
 X IO~ 6 
 
 
 Sb . 
 
 - "95 
 
 H. 
 
 P . . 
 
 - *9 
 
 H.,B,C,Q. 
 
 V . . 
 
 + rS 
 
 
 H. 
 
 As . 
 
 
 H. 
 
 Pt. . 
 
 -1- 1-32 
 
 
 Zn . . 
 
 
 
 K., L., H. 
 
 Bi . 
 
 r 4 
 
 B. C. D. E.W. 
 
 K. . 
 
 + '4 
 
 H. 
 
 Zr . . 
 
 - '45 
 
 
 H. 
 
 B . . 
 Cd . 
 
 - 7i 
 
 H. 
 H. 
 
 Rh . 
 Ru . 
 
 + ri 
 + 56 
 
 H., F. 
 H. 
 
 Liquids 
 
 
 
 r o 
 
 Cr . 
 Cu 
 
 Au . 
 
 + 37 
 -087 
 
 -'IS 
 -36 
 
 H. 
 H. 
 K., H. 
 B., C, H. 
 
 Se . 
 Si. . 
 Ag 
 
 Na . 
 
 -32 
 
 - '12 
 
 '2 
 
 H, C. 
 H. 
 H. 
 H. 
 
 H ! g ; ; 
 
 N liq. . 
 O liq. . 
 
 "41 
 - -19 
 
 + 28 
 + '3^4 
 
 'R-17 
 
 M \* 4 
 
 Q., M., H. 
 
 F., D. 
 F., 1). 
 Du B. 
 
 Ir . . 
 
 
 . H. 
 
 S . . 
 
 ~ '5 
 
 B.,C.,L.,K.,H. 
 
 HO i c 
 
 37 
 
 c 
 
 Fe . 
 
 See 
 
 p. 89. 
 
 Ta . 
 
 + ; 9 3 H. 
 
 '^-'j i 5 
 
 _ -77 
 
 
 O 
 
 Pb . 
 
 - '12 
 
 H., K., L. 
 
 Te . 
 
 
 E., C, H. 
 
 Gases 
 
 
 
 
 Mg . 
 
 + '55 
 
 H. 
 
 Tl. . 
 
 c- ~ *3 
 
 H. 
 
 Air, 1 6 
 
 + -032 
 
 Du B. 
 
 Mn . 
 
 + 10-6 
 
 H. 
 
 Th . 
 
 + r8 
 
 H. 
 
 A . . 
 
 'OIO 
 
 T. 
 
 Mo . 
 
 + '04 
 
 H. 
 
 Sn . 
 
 + -025 
 
 K., H. 
 
 He . . 
 
 - '002 
 
 T. 
 
 Nb . 
 
 + i'3 ? 
 
 H. 
 
 Ti. . 
 
 c. + 2 
 
 H. 
 
 H . . 
 
 - '008 
 
 Q. 
 
 Os . 
 
 + -04 
 
 H. 
 
 W . 
 
 + 33 
 
 H. 
 
 N . . 
 
 + '024 
 
 Du B. 
 
 Pd . 
 
 
 H.,K.,C.,F. 
 
 U . . 
 
 
 M., H. 
 
 . . 
 
 + '123 
 
 Du B., Q. ' 
 
 B., E. Becquerel 
 
 , 1855 ; C., Curie, 1895 ; 
 
 D., Dewar, 1892; Du B., Du Bois; E., 
 
 P'ttingshausenf 
 
 F., Finke ; F. D., Fleming and Dewar ; H., Honda ; K., Konigsberger, 
 
 1901 
 
 L., Lombard!, ' 
 
 1897 ; M., St 
 
 . Meyer ; Q., Quincke ; S. 
 
 , Scarpa, 1905 ; T., Tanzler, 1907 ; 
 
 W., Wills, 1898. 
 
 TEMPERATURE AND MAGNETIZATION 
 
 The 
 
 magnetic moment (M) of a 
 
 mngnet diminishes as the temperature (/) rises. 
 
 In M, = Mo(i 
 
 - a/), a varies widely, but is of the order -0003 to - oor. 
 
 The 
 
 permeability / 
 
 also depends on the temperature. There is a critical temperature above which A< is 
 very small ; in the case of iron it is one of the recalescence temperatures, and is the same 
 
 as for carbon steels containing up to '45 
 
 %ofC. 
 
 
 
 The 
 
 critical 
 
 temperature of a metal 
 
 is not perfectly definite, but depends to some extent 
 
 on whether the 
 
 metal is being heated or cooled. 
 
 
 
 i 
 
 
 
 
 
 Substance. 
 
 Grit. Temp. Observer. 
 
 Substance. 
 
 Crit. Temp. 
 
 Observer. 
 
 Iron . . . 
 
 69o-87o C. 
 
 Hopkinson 
 
 Nickel, 95% . 
 
 310 
 
 
 
 Hopkinson -i 
 
 ^.895 
 
 Roberts-Austen 
 
 ?> 
 
 300 
 
 
 Du Bois 
 
 855-867 
 
 Osmond 
 
 
 
 377 
 
 
 Weiss, 1907* 
 
 757 
 
 Weiss, 
 
 [907 
 
 Magnetite . . 
 
 582 
 
 
 ., ,, 
 
 
 
 
 Heusler alloys 
 
 c. 300 
 
 
 Gray, 1908 |j 
 
 Nickel steel (25 % Ni) ; O to 5O /* = 1-4 to 60 ; 5O to 580 M = 
 
 60 to 0-4. 
 
91 
 
 TERRESTRIAL MAGNETISM 
 
 STEINMETZ'S COEFFICIENT 
 
 Values of *n in Steinmetz's formula irt3^ x for the hysteresis loss in ergs per c.c. 
 per cycle. Bmax. is the maximum value of the induction. 
 
 Substance. 
 
 Silicon iron 
 
 Good transformer iron . . 
 Dynamo cast steel .... 
 High carbon steel, hardened 
 
 0007 
 ooi i 
 0026 
 025 
 
 Substance. 
 
 Grey cast iron 
 
 Nickel . . 
 Cobalt 
 
 013 
 012 to -038 
 
 012 
 
 TERRESTRIAL MAGNETIC CONSTANTS 
 
 Magnetic observatories no longer remain in large cities owing to electric tram 
 disturbances, and thus many of the places for which reliable data exist are not 
 generally known. The general locality of the station is indicated in many cases below. 
 
 Magnetic constants obtained in most physical laboratories are usually abnormal 
 owing to the proximity of iron in some form. 
 
 Much of the data below is derived from the Reports of Kew Observatory, and the 
 publications of the United States Coast and Geodetic Survey. 
 
 A W declination means that the N-seeking end of the magnetic needle points 
 west of true north ; a N inclination means that the same end of the needle points 
 downwards. 
 
 H and V are the horizontal and vertical components of the earth's magnetic field. 
 
 (See Chree, "Terrestrial Magnetism," Encyc. Brit., nth edit., 1911.) 
 
 Place. 
 
 North magnetic pole . . 
 South magnetic pole*. . 
 
 British Isles 
 
 Aberdeen (University) . 
 Eskdalemuir (Dumfries) 
 Falmouth (Cornwall). . 
 Greenwich . . . . . 
 
 Kew 
 
 Leeds (University) . . 
 St. Helier (Jersey). . . 
 Stonyhurst (Lanes.) . . 
 Valencia (S. W. Ireland) 
 
 Africa- 
 Cape Town 
 
 Helvan (Cairo). . . . 
 Mauritius . 
 
 America 
 
 Agincourt (Toronto) . . 
 Cheltenham (Washing- 
 ton) 
 
 Fairhaven (Mass.) . . 
 Goat Island (California) 
 Greenwich (New York) . 
 Rio de Janeiro . . . . 
 Santiago (Chili) . . . 
 Sitka (Alaska) . . . . 
 Waukegan (Chicago). . 
 
 Latitude. 
 
 70 5 N 
 7225 S 
 
 57 9N 
 55 19 N 
 
 50 9 N 
 
 51 28 N 
 51 28 N 
 534 8N 
 49 12 N 
 
 53 5i N 
 51 56 N 
 
 33 56 S 
 29 52 N 
 20 6 S 
 
 43 47 
 
 3 8 4 4 
 41 37 
 3749 
 
 41 o 
 
 22 55 
 3327 
 
 57 3 
 
 42 21 
 
 Longi- 
 tude. 
 
 Year. 
 
 96 45 W 
 54 E 
 
 2 7\V 
 
 3 i2W 
 5 5W 
 o o 
 
 o 19 W 
 I33W 
 2 5\V 
 
 2 28W 
 
 10 
 
 18 29E 
 31 21 E 
 5733E 
 
 79 i6W 
 
 76 50 W 
 70 54 W 
 
 122 22 W 
 
 7337W 
 43 iiW 
 70 42 W 
 
 135 20 W 
 
 87 51 W 
 
 [908 
 
 1909 
 1909 
 1909 
 1909 
 1909 
 1909 
 1907 
 1909 
 1909 
 
 1885 
 1908 
 1908 
 
 1906 
 
 1909 
 1908 
 1909 
 1908 
 
 1906 
 1906 
 
 1909 
 1908 
 
 Declina Inclina- 
 
 tion. 
 
 i634W 
 18 3oW 
 I748W 
 I5.48W 
 
 16 nW 
 18 2Wf 
 i627W 
 
 17 29 W 
 20 50 W 
 
 30 15 W 
 2 56W 
 9 i 4 W 
 
 545W 
 
 534W. 
 12 27 W 
 I753E 
 10 I4W 
 
 8 55 W 
 14 19 E 
 30 12 E 
 
 239W 
 
 tion. 
 
 o N 
 oS 
 
 70 39 N 
 6939 N 
 66 31 N 
 
 66 54 N 
 
 67 oN 
 6835 N 
 65.35N 
 
 68 43 N 
 68 15 N 
 
 56 oS 
 4039 N 
 5345 S 
 
 7436N 
 
 70 31 N 
 73 8N 
 62 1 1 N 
 72 13 N 
 I357S 
 
 3O 12 S 
 
 7437 N 
 7246N 
 
 H. 
 
 c.g.s. 
 O 
 O 
 
 163 
 
 1684 
 
 1880 
 
 1853 
 1851 
 
 176 
 
 1742 
 1788 
 
 199 
 
 3003 
 
 2342 
 
 1640 
 
 1988 
 1736 
 2525 
 1822 
 2477 
 
 1557 
 1830 
 
 c.g.s. 
 
 464 
 
 4519 
 
 4327 
 
 4343 
 
 4359 
 
 449 
 
 4472 
 4481 
 
 295 
 
 2579 
 
 3193 
 
 5950 
 
 5620 
 
 5724 
 4786 
 
 5680 
 0616 
 
 5659 
 
 * Mawson and David (with Shackleton), 1908. 
 
 t 1907- 
 
92 
 
 TERRESTRIAL MAGNETISM 
 
 TERRESTRIAL MAGNETIC CONSTANTS (could.) 
 
 Place. 
 
 Asia 
 
 Alibag (Bombay) . . . 
 Barrackpore (Calcutta) . 
 Hong Kong 
 
 Australasia 
 Christchurch (N.Z.) 
 Honolulu (Hawaii) 
 Melbourne . . . 
 Sydney .... 
 
 Europe- 
 Arctic | (Norway) . . 
 Regions \ (Spitzbergen). 
 
 Odessa 
 
 Pawlowsk (St. Peters- 
 burg) 
 
 Potsdam 
 
 Rude Skov (Copenhagen) 
 Uccle (Brussels) . . . 
 Val Joyeux (Paris) . . 
 
 , 
 Latitude. 
 
 Longi- 
 
 Year. 
 
 Declina- Inclina- 
 
 tion> 
 
 tion< 
 
 i8 39 N | 72 52 E 
 22 46 N ! 88 22 E 
 22 18 N 114 loE 
 
 43 32 S 
 21 19 N 
 37 50 S 
 33 52 S 
 
 6956 N 
 774i N 
 46 24 N 
 
 594i N 
 
 52 23 N 
 
 555i N 
 50 48 N 
 48 49 N 
 
 172 37 E 
 158 4\V 
 144 58 E 
 151 12 E 
 
 22 58 E 
 
 H5oE 
 3048 E 
 
 30 29 E 
 
 13 4 E 
 
 12 27 E 
 
 4 21 E 
 
 2 i E 
 
 1908 
 1907 
 1909 
 
 2E 
 
 10 E 
 
 2E 
 
 c.g.s. 
 23 22 N -3686 
 
 30 30 N -3729 
 
 31 I N -3709 
 
 1903 16 i8E 67 42 S 
 1909 i 9 26 E | 40 54 N 
 1901 
 1885 
 
 2266 
 2917 
 
 y t,\j j-j i f-^' j^ **?*/ 
 
 827E | 67 25 S -2331 
 
 93 oE 
 
 62 30 S 
 
 268 
 
 1903 043\V 76 21 N -1258 
 1903 1055 W| 80 8 N | -0942 
 1901 , 4 27W 162 18 N -2188 
 
 i 4 E 70 37 N 
 
 9 1 1 W 66 20 N 
 
 9 43 W 68 45 N 
 
 iyv, u 13 37 W 66 2 N 
 
 1909 14 33 W | 6444 N 
 
 1653 
 1883 
 
 1906 
 1973 
 
 C.g.S. 
 
 1592 
 
 2197 
 
 '2229 
 
 5526 
 
 2527 
 
 5602 
 
 515 
 
 5178 
 
 5417 
 4168 
 
 4696 
 
 4297 
 4476 
 4287 
 4179 
 
 SECULAR MAGNETIC CHANGES 
 
 At the present time (1911) we are going through a remarkable secular alteration. 
 For generations H had been steadily rising in Western Europe, but during the last ten 
 years a wave of depression has travelled across from the east. H has steadily fallen 
 at St. Petersburg since about 1900, at Potsdam since about 1905, at Greenwich and 
 Kew since 1907, while in 1909 H was still rising at Falmouth and Valencia. The 
 easterly motion of the declination needle has also increased notably since 1900. Thus 
 secular change data based on, say, the last five years will not serve to prospect the future. 
 
 Mean change per 
 annum at 
 
 Greenwich 
 Kew. . . 
 Stonyhurst 
 Falmouth . 
 Valencia 
 
 1908-1909. 
 
 Decln. 
 
 5 '9 
 6-1 
 7-0 
 6-3 
 5*4 
 
 c.g.s. 
 
 5 x 10" 
 
 - 9 
 -10 
 
 + 4 
 + 7 
 
 1904-1909. 
 
 Decln. 
 
 - 5'5 
 ~ 5'4 
 
 - 5 '9 
 -47 
 
 Incln. 
 
 07 
 ri 
 IT 
 i' 4 
 
 T2 
 
 H. 
 
 c.g.s. 
 
 4- i x 10' 
 
 + 2 
 
 + 6 
 + 9 
 + 7 
 
 c.g.s. 
 - 20 X 10" 
 
 -35 , 
 
 -25 
 
 -30 
 
 -25 
 
 SECULAR CHANGES AT LONDON (GREENWICH) 
 
 Year. 
 
 Decln. 
 
 1580 
 1660 
 1720 
 1815 
 
 ii 17 E 
 o o 
 13 oW 
 24 27 W* 
 
 Incln. 
 
 72 o N 
 
 73 15 N 
 
 74 40 N* 
 70 30 N 
 
 Year. 
 
 1851 
 1875 
 1907 
 1909 
 
 Decln. 
 
 Incln. 
 
 H. 
 
 22 25 W 68 47 N 
 
 19 21 W 67 42 N 
 
 16 o W I 66 56 N 
 
 15 48 W 66 54 N 
 
 c.g.s. 
 
 1729 
 
 1795 
 
 1853* 
 
 1853 
 
 * Maximum. 
 
93 
 
 SPARKING POTENTIALS 
 
 SPARKING POTENTIALS 
 
 The sparking voltages given below are those which will break down non-ionized 
 air at atmospheric pressure and room temperature. The electrodes are equal 
 smooth polished metal balls of various diameters. Russell (Phil. Mag., 1906) gives 
 the dielectric strength of air at atmospheric pressures as between 38,000 and 39,000 
 volts for either direct or alternating potentials. 
 
 (See J. J. Thomson, " Conduction of Electricity through Gases.") 
 
 
 Diameter of balls in cms. 
 
 
 Diameter of balls in cms. 
 
 Spark 
 
 
 Spark 
 
 
 gap- 
 
 
 
 
 
 gap. 
 
 
 
 
 
 
 05 
 
 10 
 
 20 
 
 50 
 
 
 05 
 
 10 
 
 20 
 
 50 
 
 cm. 
 
 volts. 
 
 volts. 
 
 volts. 
 
 volts. 
 
 cm. 
 
 volts. 
 
 volts. 
 
 volts. 
 
 volts. 
 
 
 X I0 3 
 
 X I0 3 
 
 X I0 3 
 
 X I0 3 
 
 
 X I0 3 
 
 X I0 3 
 
 X I0 3 
 
 X I0 3 
 
 01 
 
 4'8 
 
 4'8 
 
 47 
 
 
 
 09 
 
 19*6 
 
 2 5 -6 
 
 28-6 
 
 30T 
 
 02 
 
 8-4 
 
 8-4 
 
 8-1 
 
 
 
 10 
 
 20' 2 
 
 267 
 
 30'8 
 
 327 
 
 03 
 
 ii*3 
 
 ii*4 
 
 11-4 
 
 
 
 15 
 
 22 
 
 3r6 
 
 39 
 
 4 6 
 
 04 
 
 13-8 
 
 14-4 
 
 145 
 
 
 
 20 
 
 23 
 
 36 
 
 47 
 
 58 
 
 05 
 
 157 
 
 i7-3 
 
 17-5 
 
 1 8'4 
 
 30 
 
 24 
 
 42 
 
 57 
 
 77 
 
 06 
 
 17-2 
 
 19-9 
 
 20*4 
 
 21-6 
 
 40 
 
 25 
 
 45 
 
 64 
 
 92 
 
 07 
 
 183 
 
 22'0 
 
 23-2 
 
 24-6 
 
 50 
 
 26 
 
 47 
 
 69 
 
 105 
 
 08 
 
 19*0 
 
 24T 
 
 26'0 
 
 27-4 
 
 
 
 
 
 
 HOMOGENEOUS X-RAYS 
 
 Mass absorption coefficients, A/p, measured in Al foil. A is the absorption co- 
 efficient (see p. 107) of the predominant homogeneous component of the character- 
 istic X radiation from a metal ; p is the density of aluminium foil. (See Barkla & 
 Sadler, Phil. Mag., 1909; Kaye, Phil. Trans., 1908, Science Progress, 1908 ; Whid- 
 dington, Proc. Roy. Soc., 1911.) 
 
 Radiator. 
 
 Al 
 
 Cr 
 
 Fe 
 
 Ni 
 
 Co 
 
 Cu 
 
 Zn 
 
 As 
 
 Se 
 
 Ag 
 
 A/p 
 
 580 
 
 136 
 
 88-5 
 
 59-1 
 
 71-6 477 
 
 39'4 
 
 22-5 
 
 18-9 
 
 2'5 
 
 
 
 
 i 
 
 
 
 
 
 
 CATHODE DARK SPACE 
 
 The thickness (ft) of the Crookes dark space is given by d - (A//) + B/\//, where 
 p is the pressure, i the current density, and A and B are constants for each gas. 
 This equation is satisfied very exactly by the ordinary elementary gases, and a little 
 less so by the gases of the helium group. Unfortunately for the use of the dark 
 space as a pressure indicator, the current density term in the formula is almost as 
 large as the pressure term for pressures about i/io mm. 
 
 The values of A and B below are for large plane aluminium electrodes, d is 
 measured in cms., p in mms. of mercury. The unit of i is i/io milliampere per 
 sq. cm. of cathode, which is about the sort of current density that obtains with an 
 average coil discharge and a moderate-sized cathode. 
 
 (See Aston, Proc. Roy. Soc., 1907, 1911.) 
 
 Gas. 
 
 Hydrogen 
 
 Nitrogen 
 
 Air 
 
 Oxygen 
 
 A 
 
 B 
 
 26 
 43 
 
 068 
 40 
 
 065 
 42 
 
 057 
 50 
 
94 
 RECOMBINATION AND DIFFUSION 
 
 COEFFICIENTS OF RECOMBINATION a 
 
 a is given below in terms of iooo, where e is the numerical value of the ionic 
 charge : 47 x io~ 10 in electrostatic units. For air, a = 3320^ = 1-56 x io~ 10 cm. 3 sec~ 1 . 
 Room temp, and pressure. 
 
 Gas. 
 
 Air. 
 
 2 
 
 C0 2 
 
 3-42, T.; 3-38, Me.; 3-2, L.; 3-3, H.; 3-32 *,E. 3-38, T. | 3-5, T. 3-02, T ; 2-94, Me 
 
 E., Erikson, P.M., 1909; H., Hendren, P.R., 1905; L., Langevin, A.C.P., 1902; 
 Me., McClung, P.M., 1902; T., Townsend, P.T., 1899. * 17 C., 760 mm. Hg. 
 
 a IN AIR AND PRESSURE 
 
 Press, in atmos. 
 
 a (relative values), L. 
 
 5 
 
 12 
 
 1 
 
 27 
 
 26 
 
 L., Langevin. 
 H., Hendren. 
 
 Press, in cms. . 
 
 76 45 
 
 a (absolute values), H. . 
 
 3'3 2-65 
 
 25 
 
 2-07 
 
 15 
 
 175 
 
 10 
 
 3-5 2 
 
 '55 i'3i I i'* 
 
 1*15 roo 
 
 a IN AIR AND TEMPERATURE 
 
 Air at constant density. (E., Erikson ; P., Phillips, Electrician, 1909.) 
 
 Temp. C. . . . 
 o (in terms 1000e),E. 
 
 -179 -68 
 
 7'5 
 
 12 
 
 3*47 
 
 64 
 
 2-31 
 
 100 
 
 173 
 
 155 
 
 Temp. C. . . . |15 < 
 a (relative values), P . i 
 
 100 155 176 
 
 50 | -40 
 
 36 
 
 IONIC COEFFICIENTS OF DIFFUSION D 
 
 Rate of interdiffusion (in cm. 2 sec^ 1 ) of gaseous ions in dry air : D+ for positive, 
 D- for negative ions. (Townsend, Phil. Trans., 1899, 1900.) 
 
 locization 
 
 Rontgen Rays. 
 
 fi and 7 Rays. 
 
 Ultra-violet 
 light. 
 
 Point discharge. 
 
 D+ at 76 cm. 
 
 028 
 
 032 
 
 0247, '0216 
 
 D- at 76 cm. , 
 
 043 
 
 043 
 
 043 
 
 037, -032 
 
 GASES IONIZED BY RONTGEN RAYS 
 
 Air, CO 2 , and hydrogen at 15 C. and 760 mm. 
 
 Dry Gas. | D+ 
 
 Air 
 
 dried 
 
 by 
 
 2 CaCL 
 
 025 
 
 D- 
 
 028 -043 
 
 04 
 
 Dry Gas. 
 
 :o a 
 
 dried 
 
 by 
 CaCl 2 
 
 023 
 123 
 
 026 
 19 
 
 Moist Gas. D+ 
 
 D- 
 
 035 
 036 
 
 Moist Gas. 
 
 CO f sat - ) 
 H with 
 H2 (H 2 OJ 
 
 024 
 
 025 
 
 I28JT42 
 
 AIR IONIZED BY /S AND V RAYS 
 
 Press, p. in cms. 
 
 D+ at 15 C. 
 pD+ ,, 
 
 77-2 55 
 
 40 
 
 0317 -042-0578 
 45i 2-31' 2-31 
 
 30 20 
 
 078' '1 18 
 2-34 2-36 
 
 Press, p. in cms. 
 
 D- at 15 C. 
 
 77-2 
 
 0429 
 3*3 
 
 55 40 30 
 
 0542 
 
 0781-103 
 
 20 
 
 A.C.P. y Ann. de Chim. ct dc Phys. ; P.M., Phil. Mag. ; P.R., Physical Review ; 
 P. T., Phil. Trans. 
 
95 
 
 IONIC MOBILITIES 
 
 MOBILITIES OF IONS IN GASES 
 
 
 Velocities of ions are in cm. per sec. for unit field, or in cm. 2 
 
 sec." 1 volt x at 
 
 temp, and press, of room. K+ = mobility of positive ion, K_ of negative. 
 For moist air (i.e. saturated with H 2 O), K+ = 1*37, K- = 1-51. 
 
 For dry air (dried by CaCL>), K+ = 1-36, K- = 1-87. (Zeleny (air blast 
 
 method), Phil. Trans , 1900.) * Mean 
 
 = (K + +K_)/ 2 . 
 
 For mobilities of natural ions in air, see p. 105. 
 
 K+ K_ 
 
 lonization and Observer. 
 
 Try Gas. 
 
 TT i ** ! 
 
 lonization and 
 
 Dry Gas 
 
 76cm.Hg 
 
 76 cm. Hg 
 
 Observer. 
 
 Air ..1-32 
 
 I -80 
 
 Point disch., Chattock, 
 
 C0 2 . . . 
 
 0-76 0-8 1 X-rays, Zeleny, 1900. 
 
 
 
 P.M., 1899, 1901. 
 
 ,,.... 
 
 o-85 0-90 
 
 Langevin, '03. 
 
 i'54 
 
 178 
 
 X-rays, Wellisch, Phil. 
 
 ,,.... 
 
 0-81 0-85 ., 
 
 Wellisch, '09. 
 
 
 
 Trans., 1909. 
 
 HC1 . . . 
 
 1'27* 
 
 Rutherford. 
 
 . - 1-40 
 
 170 
 
 Langevin, 
 
 S0 2 . . . 
 
 0-44 0-41 
 
 Wellisch, '09. 
 
 
 
 A.C.P.,i 9 o 3 . 
 
 C1 2 . . . . 
 
 ro* 
 
 Rutherford. 
 
 j) i'39 
 
 I 7 8 
 
 Phillips,/ 3 ./^., 
 
 N 2 O . . . 
 
 0-82 0-90 
 
 Wellisch, '09. 
 
 
 
 1906. 
 
 NH 3 . . . 
 
 0-74 0-80 
 
 
 5, ' r36 
 
 I-8 7 
 
 Zeleny, Phil. 
 
 Me. acetate . 
 
 '33 0-36! 
 
 
 
 
 Trans., 1900. 
 
 Me. bromide 
 
 0-29 0-28 ,. 
 
 
 . . 1-401-78 
 
 Mean value. 
 
 Me. iodide . 
 
 0'2I O-22 
 
 
 H 2 . . 5'4 
 
 7'43 
 
 Point disch., Chattock. 
 
 Et. alcohol . 
 
 0-34 0'27j 
 
 
 . . 6-7 
 
 7'9 
 
 X-rays, Zeleny, 1900. 
 
 Et. acetate . 
 
 0-3I 0-28 ., 
 
 55 
 
 He . 5*09 
 
 6-31 
 
 Franck and 
 
 Et. aldehyde 
 
 0-3I 0-30 
 
 J 
 
 
 
 Pohl, V.D.P.G., '07. 
 
 Et. chloride . 
 
 '33 0-31 
 
 
 No . . r6* 
 
 
 
 X-rays, Rutherford, 
 
 Et. ether . . 
 
 0-29 0-31 
 
 
 
 
 P.M., 1897. 
 
 Et. formate . 
 
 0-30 0-31 
 
 55 
 
 O 2 . . i 1-36 
 
 i -80 
 
 Zeleny, 1900. 
 
 Et. iodide 
 
 0-17 0-16 
 
 55 
 
 J "3 
 
 1-85 
 
 Point disch., Chattock. 
 
 ecu - . - 
 
 0*30 0*31! 
 
 55 
 
 CO .In 
 
 1-14 
 
 X-rays, Wellisch, '09. 
 
 Pentane . . 
 
 0-36 0-35 
 
 5' 
 
 CO, . 0-83 
 
 0-92 
 
 Point disch., Chattock. 
 
 Acetone . . 
 
 0-31 0-29 
 
 >5 
 
 IONIC MOBILITY AND PRESSURE 
 
 
 Air ionized by Rontgen rays. (Langevin, A.C.P., 1903.) i 
 
 
 Press, cm. 
 
 7'5 
 
 20 415 76 143'5 1 Press, cm. 
 
 7-5 20 ; 4 
 
 1-5 76 142 
 
 
 
 1 
 
 
 
 K+ 
 
 14-8 
 
 5-45 2-61 1-40 075 1 K_ 
 
 21-9 7-35 . 
 
 3-31 1-7 0-9 
 
 IONIC MOBILITY AND TEMPERATURE 
 
 
 Air at 76 cm. press, ionized by Rontgen rays. (Phillips, P.R.S., 
 
 1906.) 
 
 Temp. C. 138" 126 110 100 75 60 12 
 
 -64 -179 
 
 K+ 2'oo 1-95 1-85 r8i 1-67 r6o 1-39 
 
 0-945 0-235 
 
 JL- 2'49 2-40 2-30 2'2I 2'12 2'CO 1*785 
 
 1-23 0-235 
 
 IONIC MOBILITIES IN LIQUIDS AND SOLIDS 
 
 
 Ionized by radium rays. (Bohm-Wendt and v. Schweidler, Phys. Zeit., 1909 ; 
 
 Bialobjeski, Coinpt. Rend., 1909.) 
 
 
 Substance. (K+ + K-) Substance. 
 
 (K+ + K_) 
 
 Petroleum ether . . . . ! 3-8 x io~ 4 Ozokerite at 100 . . . 
 
 5-1 x io~ 4 
 
 Vaseline 
 
 C-3 x IO" 6 
 
 80 . . . 
 
 35-0 x io- 4 
 
 
 A.C.P., Ann. ce Chim, et de Phys. ; P.M., Phil. Mag. ; P.X.S., Proc. Roy. 
 
 Soc.; V.D.P.G., 
 
 Verh. Deutsch. Phys. Gcsdl. 
 
 \ 
 
 
96 
 
 CONDENSATION 
 
 K 
 
 IONIC MOBILITIES AT HIGH TEMPS 
 
 in cm. sec.- 1 per volt cm.- 1 for coal-gas flames in most instances. The ionic 
 mobility is independent of the acid of the salt. Gold's and Wilson's values for K- 
 agree the best with existing theory, which makes K- = Xex/mit 17,000 at 
 1800 C. (Gold). X is the electric field per cm., \ is the mean free path, and u the 
 velocity of the corpuscle. 
 
 Salt. 
 
 Cs, Rb, K, Na, Li . . 
 1/20 normal KC1 . . 
 
 NaCl 
 
 1/256 normal K salt . 
 1/16 normal Na salt . 
 Concentrated sols, of 
 
 alkalies 
 
 Cs, Rb, K, Na, Li . . 
 Ba, Sr, Ca . . . . 
 K, Na 
 
 K 
 
 Na 
 
 Temp. 
 
 Flame,*:. 2000 C. 
 Flame 
 
 Flame, c. 2000 
 
 5J 
 
 Air at 1000 
 
 55 >J 
 
 Flame, c. 1800 
 
 Flame, c. 1800 
 Bunsen burner 
 Flame, c. 2000 
 
 62 
 260 
 340 
 
 80 
 
 7-2 
 
 K_ 
 
 C. 1000 
 
 1400 
 1800 
 1320 
 1280 
 
 - ) 
 
 8000 
 
 13,000 
 9600 
 1170 
 
 Observer. 
 
 H.A Wilson, P.T., 1899 
 Marx. Ann. der Phys. 
 
 1900 
 
 hys 
 
 1903 
 
 H.A. Wilson, P.T., 1 899 
 
 and P.M., 1906 
 Gold, P.R.S., 1907, ratio 
 
 of potential grad. to 
 
 current 
 Poten. grad., and gas 
 
 velocity 
 H. A. Wilson, P.R.S. 
 
 1909 
 Moreau, C./i'., 1909 
 
 CONDENSATION OF VAPOURS 
 
 Expansion = vjv^ where ^ is the volume of the gas before, and v. 2 the 
 volume after expansion. Snpersatnration of the vapour (at end of cooling by 
 expansion) necessary for condensation = S = (density of vapour when drops are 
 formed)/(density of saturated vapour at the same temp.). (See J. J. Thomson, 
 " Conduction of Electricity through Gases.") 
 
 CONDENSATION ON NATURAL IONS AND MOLECULES 
 
 Dust-free gas saturated with water-vapour. (C. T. R. Wilson, P. T., '97, '99, 'oo.) 
 
 Gas. 
 
 Air 
 2 
 
 N 2 
 
 Bain-like 
 
 Cloud-like 
 
 
 V pMMM 
 
 vjv l 
 
 8. 
 
 qfa 
 
 S. 
 
 1-252 
 
 1-257 
 1-262 
 
 4*2 
 4"3 
 
 4"4 
 
 1-38 
 1-38 
 1-38 
 
 7'9 
 
 7'9 
 7-9 
 
 Cas. 
 
 C0 2 
 
 C1 2 
 H 2 
 
 Rain-like 
 Condensation. 
 
 365 
 
 '3 
 
 4-2 
 3'4 
 
 Cloud-like 
 Condensation. 
 
 1-535 
 
 i-45 
 1-38 
 
 7'3 
 5'9 
 7'9 
 
 CONDENSATION IN AIR IONIZED BY RONTGEN AND RADIUM RAYS 
 (L., Laby, Phil. Trans., 1908; P., Przibram, Wien Per., 1906.) 
 
 Vapour and Observer. 
 
 Water (C. T. R. Wilson) 
 Water (C. T. R. Wilson) 
 
 Et. acetate, L 
 
 Me. butyrate, L. . . . 
 Me. iso-butyrate, L. . . 
 Propyl acetate, L. . . . 
 Et. propionate, L. . . . 
 Formic acid, L. . . . 
 
 Acetic acid, L 
 
 Propionic acid, L. . . . 
 
 Ion. 
 
 S. 
 
 4-15 
 5-8 
 
 8-9 
 5'3 
 
 1-25 
 1-31 
 
 1-48 i 
 i'33 
 i'35 
 1-31 5'o 
 1-41 7'8 
 178,25-1 
 i'44 9'3 
 i '34 9'4 
 
 Vapour and Observer. 
 
 n-Butyric acid, L. . 
 iso-Butyric acid, L. 
 iso-Valeric acid, L. 
 Methyl alcohol, P. 
 Ethyl alcohol, P. . 
 Propyl alcohol, P. . 
 iso-Butyl alcohol, P. 
 iso-Amyl alcohol, P. 
 j jj L. 
 
 Chloroform, P. . . 
 
 Ion. I v 2 /i\ S. 
 
 1-38 
 1-36 
 
 *22 
 25 
 17 
 
 18 
 
 2 
 22 
 
 18 
 
 15-0 
 
 'P 
 6-0 
 
 3-6 
 5'5 
 4'i 
 3-0 
 
 A.C.P., Ann. de Chim. et de Phys. ; C.R., Compt. Rend. ; P.M., Phil. Mag. ; P.A'.S., 
 Proc. Roy. Soc. ; P. T., Phil. Trans. 
 
97 
 
 IONIC CHARGE e 
 
 NE FOR ELECTROLYTIC IONS 
 
 NE is given both in electrostatic units (E.S-U.) and electromagnetic units (E.M.U.). 
 
 N is the number of molecules in a c.c. of gas at 76 cm. Hg (g = 980 '6) and 
 C, and E is the charge on the monovalent ion in electrolysis. 
 
 Antecedent data. i coulomb deposits 1-11827 mgm. Ag. At. wt. of Ag 
 107-88 ; of H, roo8. Density of H 2 = 8-987 x io~ 5 gm. per c.c. at o C. 
 
 Gas. 
 
 E.S.U. 
 
 H, at o C. 
 
 xio 10 
 1-29015 
 
 H 2 at 15 C. 1-2230 
 
 E.M.U. 
 
 0*4300 
 0-4077 
 
 Gas. 
 
 O 2 at o 
 2 at 15' 
 
 E.S.U. | E.M.U 
 
 x io lu 
 1-2924 
 1-2248 
 
 0-4308 
 0-4083 
 
 Gas. 
 
 E.S.U. E.M.U. 
 
 IdealUto c 
 
 x lo 1 
 1-2913 
 
 0-43044 
 
 gas (at 15) 1*2241 10-40803 
 
 Ne FOR GASEOUS IONS 
 
 N is the number of molecules per c.c. of air at room temp, and 76 cm. Hg ; e is 
 the ionic charge in E.S.U., e_ for negative and e+ for positive ions. 
 
 lonization. 
 
 X rays 
 Ra rays 
 
 Ne_ 
 
 1-23 x 
 1-24 x 
 
 Ne. 
 
 Observer. 
 
 2-41 x io 10 
 1-26 to 1-37 X 
 
 io 1 
 
 Townsend, P.R.S., 1908, 1909. 
 Haselfoot, P.R.S., 1909. 
 
 Ne CALCULATED 
 
 In E.S.U., N* = 3-04 x io 8 xK/D = 3-04 x io 8 x 1-40/0-028 = 1-52 x io 10 for 
 positive air ions at 76 cm. and room temp. For D and K, see pp. 94, 95- 
 
 Gas. 
 
 Ne+ 
 
 Ne- 
 
 Air 
 2 
 
 1-52. io 10 1-26. io 10 
 1-62. io 10 1-38. io 10 
 
 Gas. 
 
 Ne+ 
 
 Ne- 
 
 H 2 . 1-50. io 10 
 CO 2 . ! 1-07 . io 10 
 
 1-23 . io 1 
 ro2 . io 1 
 
 Mean- 
 
 Ne- 
 
 1*42. IO 10 I-22.I0 10 
 
 1-32. io 1 
 
 e 
 
 minations. 
 
 THE IONIC CHARGE e 
 4-7 x lO" 10 E.S.U. = 1'57 x 1O~ 20 E.M.TJ.,as a mean of the latest deter- 
 
 lonization. 
 
 Method. 
 
 Rontgen rays ; nega-") 
 
 tive ions. 
 Ultra - violet light on I 
 
 metal ; negative ions j 
 Rontgen rays ; nega- 
 tive ions. 
 
 Radium rays ; negative 
 ions. 
 
 Charged spray of elec- 
 trolytic O 2 . 
 
 aparticles(Ra,)assuming 
 charge = +2e. 
 
 Electrolytic ions. 
 
 Charged spray of elec- 
 trolytic O 2 . 
 
 a particles (Polonium) ; 
 charge ~ + 2^. 
 
 Electrolytic ions. 
 
 Radium rays ; negative 
 ions. 
 
 By measuring total charge on 
 a cloud and obtaining num- 
 ber of ions from size of drops 
 by Stokes' law. 
 
 Force (by Stokes' law) exerted 
 by an electric field on a singly 
 charged drop. 
 
 The observer's original method. 
 
 Total charge on a cloud. No. 
 
 of ions from weight of cloud 
 
 and size of drops, using 
 
 Stokes' law. 
 By counting a particles and 
 
 measuring their total charge. 
 By counting colloid particles. 
 By H. A. Wilson's method, 
 
 above. 
 By counting a particles, and 
 
 measuring their total charge. 
 From Brownian movements. 
 By H. A. Wilson's method, 
 
 above 
 
 einE.S.U.i 
 
 Observer. 
 
 6'5 
 6-8 
 
 3'i 
 3'4 
 3-0 
 
 4-65 
 
 rf 
 47 
 
 479 
 
 67 
 
 io~ 10 J. J. Thomson, 
 
 P.M., 1898. 
 J. J. Thomson, 
 
 P.M., 1899. 
 H. A. Wilson, 
 P.M., 1903. 
 
 Thomson, 
 Camb. 
 
 Phil.Soc., 1903. 
 Townsend, 
 Proc. Camb 
 Phil.Soc., 1897. 
 
 Rutherford & Gei- 
 
 4 
 
 Perrin, C.R., 1908. 
 Lattey, P.M., 
 
 1909. 
 Regener, Berl. 
 
 Ber., 1909. 
 Broglie, Le R., 
 Begeman. [1909. 
 
 C.R., Comples Rendus ; Le R., Le Radium ; P.M., Phil. Mag. ; P.R.S., Proc. Roy. Soc. 
 
98 
 
 e/m 
 
 NUMBER QF MOLECULES IN A GAS 
 
 N = the number of molecules in a gram molecule of gas (Perrin, Compt. Rend., 
 1908 ; Perrin and Dabrowski, C.R., 1909 by observations on colloidal particles). 
 The theoretical value is N = NE/e = 2-894 x io u /(47 x io~ 10 ) = 6-16 x io- 3 . 
 
 Method. 
 
 Gum mastic 
 
 Gamboge. 
 
 Method. 
 
 Gum mastic. Gamboge. 
 
 Counting by| 
 ultra micro- 
 scope . .] 
 
 N = 7 . io 2 
 
 3 N = 7-05 . io 23 
 
 Brownian 
 movements. 
 
 N = 7-3 . io 23 N = 7 . io 23 
 
 e/m FOR NEGATIVE ELECTRONS 
 
 efm in E.M.U. gm.- 1 . Velocities v in cm. sec." 1 . For some other values of 
 ejm see J. J. Thomson's "Conduction of Electricity through Gases." and Wolz, 
 Ad.P., 30, 274, 1909. The mean of Simon's, Becker's, Classen's, Kaufmann's, 
 Wolz's, Bucherer's, and Bestelmeyer's values ise/m = 1'772 x IO 7 E.M-U-gm.- 1 , 
 where m is the mass of the electron associated with very small velocities. P'or 
 the variation of e/m with velocity see p. 99. (See also Schuster, P.fi.S., 1890.) 
 
 e/m v Observer. 
 
 e/m v Observer. 
 
 CATHODE RAYS 
 
 LENARD RAYS 
 
 1*2 X IO 7 
 
 177 to r8,, 
 
 r86 
 r88 
 1*87 
 1*84 
 
 175 
 1-85 
 1774 
 1767 
 1771 
 
 2*4t03'2.I0 9 
 
 = e/tu } 
 57to7'5.io 9 
 3*8 to 13 
 
 ii'i ,,\ 
 = f/wfc / 
 
 1-9 . io 9 } 
 3-8 . io 9 
 = e/m J 
 
 . J. Thomson, 
 P.M., 1897 
 Kaufmann,^f .d.P., 
 1897, 1898 
 Simon, A.d.P., 
 1899 
 Seitz, A.d.P., 1902 
 Starke, V.D.P.G., 
 1903 
 Becker, A.d.P., 
 1905 
 
 Classen,/>.Z.,i9o8 
 
 0-68 . io 7 
 
 3'4toio7.io 9 
 
 Lenard, A.d.P., 
 1898 
 
 INCANDESCENT OXIDES, etc. 
 
 0-87 . io 7 
 
 0-56 
 
 i'5 
 
 o'ltoro.io 9 
 
 J. J. Thomson, 
 P.M., 1899 
 Owen, P.M., 1904 
 Wehnelt, A.d.P., 
 1904 
 
 SECONDARY CORPUSCULAR RAYS, 
 from X-rays incident on platinum 
 
 1773 -lo 7 
 
 - e/m (on 
 Lorentz's 
 theory) 
 
 Bestelmeyer, 
 A.d.P., 1907. 
 
 ft RAYS 
 
 O*I . IO 7 
 177 
 
 r66 
 r2 
 
 1763 
 > >* 
 
 1767 
 
 
 
 = *!**<> 
 
 - e/tn (on 
 Lorentz's 
 theory) 
 = e/m (on 
 Abraham's 
 theory) 
 = e/m 
 
 Becquerel, Rap 
 C.P., 1900 
 
 Kaufmann, Gott 
 Nachr., 1901 
 Kaufmann,/^./ 3 . 
 1906 
 
 Kaufmann,^4 .d.P. 
 1906 
 
 iBucherer,/^./ 3 . 
 / 1909 
 }Wolz,^.^./'.,i909 
 
 ULTRA VIOLET LIGHT ON METAL 
 
 076. io 7 
 ri . io 7 
 
 
 
 J. J. Thomson,' 
 P.M., 1899 
 Lenard, A. d.P , 
 1900 
 
 9'5to2o6.io 9 
 = .e/m 
 15 to 2 1 . io 9 
 
 ZEEMAN EFFECT 
 
 1775. io 7 
 
 
 Mean of 4 obser- 
 ver's values (see 
 below). 
 
 A. d.P., Ann. dtr Phys. ; P.M., Phil. Mag. ; P.R.S., Proc. Roy. Soc. ; P.Z., Phys. Zeit. ; 
 Rap. C.P., Rapports Congrh a Paris ; V.D.P.G., Verh. Deutschs. Phys. Gtsell. 
 
99 
 
 e/m 
 
 ELECTRONIC e/m FROM ZEEMAN EFFECT 
 
 For a spectrum line of wave-length A, which becomes a normal triplet with 
 a separation of 5\ in a magnetic field H (in gauss, i.e. E.M.U.), Lorentz has shown 
 '(A-H), where V is the velocity of light ; ejm is in E.M.U. gm.- 1 . 
 
 that elm 2n-V5A/(; 
 
 The values 179, 177, 1767, 
 
 with e/m^ above. 
 
 771, mean 1'775 . 10 7 E.M.U. gm.- 1 , agree well 
 
 Line. 
 
 e/m 
 
 Hg 5791, 5770 
 5461, 4358 . 
 
 Zn, Cd . . . 
 
 Cd 4678 
 Zn 4680 
 Cd 4678 
 Zn 4680 
 
 Xio 1 
 172 to 
 
 2-80 
 
 r6 
 1-59 
 
 171 
 179 
 
 Observer, 
 
 ( Blythswood & 
 Marchant, P.M.. 
 I 1900 [1900 
 ' Reese, As. Jl., 
 Kent, As. Jl., 
 
 1901 
 Farber, A.d.P., 
 
 1902 
 
 Stettenheimer, 
 A.d.P., 1907 
 
 Line. 
 
 e/m 
 
 Observer. 
 
 x io 7 
 
 Zn 4810 . .\! , /Cotton & Weiss, 
 
 4722,4680. ./i 2 !W|t c.A\, 1907 
 
 Lohmann, /'.Z., 
 
 He 
 
 Hg 5791 
 5770 
 
 177 
 
 5790,5770} 
 4916,4358; 
 
 * 9 ^ | Baeyer&Gehrcke, 
 j ^./>., 1909 
 
 |/Gmelin, A.d.P., 
 
 1771 
 
 1909 
 
 ELECTRONIC e/m AND VELOCITY 
 
 m is the electromagnetic mass of the negative electron for infinitely small 
 velocities, m the transverse mass for a velocity v ; v/V = 0, where V is the velocity 
 of light. (See Lorentz, LEclairage Electrique,}\\\y, 1905, and "The Theory of 
 Electrons," 1909.) On the theory of Abraham (Gott. Nachr., 1902), 
 
 transverse mass m 
 
 | Infinitely small. 01 
 
 roo 
 
 05 09 
 
 ri2 r8i 
 
 0-99 
 
 3-28 
 
 0-999 
 
 4-96 
 
 0-9999 
 
 6-68 
 
 999999 
 
 On the theory of Lorentz (Versl. Kon. Ac. Wet. Am., 1904) and the 
 relativity theory of Einstein (A.d.P., 1905), m = m (i 2 )~ 1/2 . This theory 
 has been confirmed by the experiments of Bucherer {A.d.P., 1909) and Wolz (tbid.\ 
 using rays from Ra with velocities from (9 to 21) x io 9 cm. per sec. Thus the 
 mass of the negative electron is wholly electromagnetic. 
 
 001 
 0-05 
 010 
 0-20 
 0-25 
 030 
 0-32 
 
 '045 
 ooi 
 005 
 
 'O2O 
 
 '033 
 048 
 '056 
 
 
 
 0-34 
 0-36 
 038 
 0-40 
 0-42 
 0-44 
 0-46 
 
 063 
 072 
 08 1 
 091 
 
 TO2 
 114 
 
 126 
 
 
 
 0-48 
 
 0-50 
 
 0-52 
 
 0-54 ! 
 
 0-56 
 
 0-58 
 
 0-60 
 
 1-140 
 
 i55 
 171 
 188 
 207 
 228 
 250 
 
 
 
 0-62 
 0-64 
 066 
 068 
 070 
 072 
 074 
 
 
 
 274 
 301 
 331 
 - 3 6 4 
 400 
 441 
 487 
 
 0-76 
 078 
 0-80 
 0-82 
 0-84 
 0-86 
 
 538 
 598 
 667 
 
 747 
 843 
 960 
 
 0-88 i 2-105 
 
 | #z/w 
 
 0'90 2-294 
 091 1 2-412 
 0-92 1 2-552 
 0-93 2-721 
 0'94 2-931 
 0-95 3-203 
 0-96 .3-571 
 
 
 
 0-97 
 098 
 099 
 0999 
 
 5-025 
 7-089 
 22-36 
 
 RH AND v: MAGNETIC DEFLECTION 
 
 When negative rays of velocity v are deflected by a uniform magnetic field H 
 (at right angles to their direction) into a circular path of radius R, then RH = 
 umfe = -z"K0) /(^/H))> where </>(0) = (i - 2 )~* on Lorentz's theory (see above), and 
 e/m Q = 1-772 x io 7 E.M.U. gm.- 1 . 
 
 v is in io 8 cm. sec." 1 ; RH in gauss cm. Example. If RH 1210 gauss 
 cm. 2 , then v = 174 x io 8 cm./sec. 
 
 RH 
 
 
 
 90 
 
 180 
 
 270 
 
 
 
 532 
 1270 
 
 6 
 
 33'9 
 572 
 1340 
 
 3490 | 3970 
 
 12 
 
 67-8 
 612 
 1410 
 4660 
 
 18 
 
 24 
 
 102 136 
 
 653! 695 
 1490 1570 
 5800 8330 
 
 30 36 42 
 
 170 
 739 
 
 204 
 
 784 
 
 1760 
 
 48 
 
 239 274 
 
 830 877 
 
 1860 1980 
 
 i 
 
 54 60 66 72 78 84 
 
 310 
 926 
 
 2IIO 
 
 346 382 419 
 
 977 1030 1090 
 2260 2420 2620 
 
 i 
 
 456 
 1150 
 2850 
 
 494 
 
 I2IC 
 3130 
 
 MJ.fi, Ann. der Phys.-, As. Jl. t Astrophy. Journ. ; C.R., Comft. Rend.; P.M., Phil. 
 Mag, ; P.Z. Phys. Zeit. 
 
IOO 
 
 a RAYS 
 
 RANGE AND VELOCITY OF a RAYS 
 
 Range in cms. in air at 76 cm. and / C. (see Bragg and Kleeman, Phil. Mag., 
 1905). Initial velocity (z/) in cms. /sec. (Rutherford, Phil. Mag., 1906, 1907). 
 Some of the velocities are calculated from the ranges of the a particles ; RaC, ThC, 
 and Polonium were observed. Energy of RaC o ray = mi/*/ 2 = %v 2 .2e.m/e a 
 = 2-o6 2 . io 18 */(5'07 . io 3 ) = 8-37 . io 14 ^ = 1-3 . io- 5 ergs = 3-1 . lo' 13 calories. Loss 
 of energy in air is proportional to path traversed : thus initial velocity of o 
 particle = (velocity of RaC a) x '347\fr+ 1-25 cm./sec., where r is the range of 
 particle. Also v I'o/jr 1 / 3 . io 9 cm./sec. (Geiger, P.R.S., 1910) 
 
 a Ray. 
 
 u . . 
 
 ux . 
 
 Io . . 
 Ra . . 
 RaEm 
 RaA . 
 RaC. . 
 RaF or 
 
 Eange. 
 
 roy? 
 2-8 
 
 4'23 
 
 /3'95 
 
 Initial Vel. Obs. 
 
 Polonium \3'95 
 
 cm./sec. 
 1-56 . IG 
 
 170 
 I 7 6 
 2'06 
 
 1-62 
 
 Mc.&R. 
 Hess. 
 
 B. 
 
 B. & K. 
 B. & K. 
 B. & K. 
 B. & K. 
 
 K. 
 K. & M. 
 
 L. 
 
 a Ray. 
 
 Rad.Ac 
 AcX . 
 Ac Em 
 AcB . 
 Th . . 
 Rad.Th 
 ThX . 
 ThEm 
 ThB . 
 ThC . 
 
 Range. 
 
 cms. 
 
 4-8 
 
 6-55 
 5-8 
 
 F5 
 
 3'5 
 3'9 
 57 
 5'5 
 5-0 
 8-6 
 
 Initial Vel 
 
 cm. /sec. 
 I 7 6 . I0 
 2'00 
 r90 
 
 r86 
 
 r6 3 ~ 
 
 1-89 
 
 1-86 
 
 179 
 
 2-25 
 
 Obs. 
 
 B., Boltwood, A.J.S., May, 1908; B. & K., Bragg & Kleeman, P.M., 1905 ; H., Hahn, 
 P.M., 1906; Hess, Wien. Her., 1907; K., Kleeman, P.M., 1906; K. & M., Kucera & 
 Masdk, P.Z., 1906 ; L., Levin, A.J.S., 1906 ; Me. & R., McCoy & Ross, f.A.C.S., 1907. 
 
 NUMBER OF a PARTICLES FROM Ra 
 
 Number of particles from Ra without its radioactive products = 3*4 . io 10 per 
 gm. per sec. Number of particles from Ra with its radioactive products 
 = 1*36 . io 11 per gm. per sec. (Rutherford and Geiger, Proc. Roy. Soc., 1908). 
 
 e/m FOR a RAYS 
 
 efm in E.M.U. per gm. 2 ejm for helium = 2NE/p = 478 . io 3 E.M.U./gm. Mean 
 for Ra, Pol, RaC = 4'82 . IO 3 E.M.U. gni" 1 . Since the a particle is a helium atom 
 with a charge of 2e, these values should be equal. * Final velocity of rays used. 
 
 Subst. 
 
 Ra . 
 Pol . 
 RaC. 
 
 Velocity.* 
 
 e/m 
 
 Observer. 
 
 cm./sec. E.M.U. 
 
 r 1816174. 10? 4-6. io 3 Mackenzie, 
 P.M., '05 
 
 1-41 
 1-57 
 
 1 4'8 
 ! 5*07 
 
 Huff (cor?); 
 
 Rutherford, 
 P.M,'o6 
 
 Subst. 
 
 RaA. 
 AcB . 
 ThC. 
 
 Velocity.' 
 
 cm./sec. 
 1*22 . IO 9 
 TO 
 I- 9 8 
 
 c\ni 
 
 E.M.U 
 
 5 -6 . io 3 
 
 47 
 5-6 
 
 io 3 'j 
 
 5? / 
 
 Observer. 
 
 Rutherford, 
 P.M., '06 
 
 Rutherford 
 & Hahn, 
 P.M., '06 
 
 STOPPING POWERS OF MATERIALS 
 
 If a layer of air of density p and thickness / decreases the range of an o particle 
 by the same amount as aluminium foil of density p (t and thickness /, then the 
 atomic stopping power, S, of Al relative to air is given by S = 27/p/i4'4/ u p a ) 
 = (number of atoms per cm. 2 in air layer)/(number of atoms per cm 2 in Al foil) 
 (Bragg and Kleeman, Phil. Mag., 1905 ; Bragg, Phil. Mag , 1906). 
 
 Metal. 
 
 (Air at 20 
 C., 76 cm.) 
 Al . . . 
 Cu . 
 
 100 
 
 '45 
 
 Metal. 
 
 S. 
 
 Sn 
 Pt 
 Fe 
 
 3-I7 
 3*37 
 4-16 
 2-26 
 
 Metal. 
 
 S. 
 
 Ni 
 Au 
 Pb 
 H 2 
 
 2 46 
 
 4'45 
 4-27 
 
 Gas. 
 
 2 . 
 N 2 O 
 C0 2 . 
 CS 2 . 
 
 1-055 
 
 1-46 
 
 1*47 
 2-18 
 
 Gas. 
 
 S. 
 
 ru 
 
 C 2 H 2 
 
 Ethylene 1*35 
 
 Benzene I 3*37 
 
 Methane! o'86 
 
 A.J.S., Amer. Jvtirn. Set.; J.A.C.S., Journ. Amer. Chtm. Soc.; P.M., Phil. Mag.; P.R.S., 
 Proc. Roy. Soc. ; P.Z., Phys. Zeil. 
 
101 
 
 RELATIVE IONiATIONS 
 
 NUMBER OF IONS MADE BY AN a PARTICLE 
 
 Total number of ion,s produced by the complete absorption of an a particle with 
 various initial velocities. Observer assumed e 4/65 x io- 10 E.S.U. (Geiger, Proc. 
 Roy. Soc., 1909). 
 
 
 Ra 
 
 RaEm. 
 
 RaA 
 
 RaC 
 
 BaF 
 
 Range in air at 20 C., 76 cm. . 
 
 3-5 cm. 
 
 4'33 
 
 4-83 
 
 7-06 
 
 3-86 
 
 Number of ions 
 
 I'<3 X IO 5 
 
 I"7/l X IO 5 
 
 i'&7 X io 5 
 
 2 "7 7 V TO 5 
 
 1*62 x io 5 
 
 
 
 i /q. A. iu 
 
 
 
 
 IONS PRODUCED AT DIFFERENT VELOCITIES BY AN a PARTICLE 
 
 Number of ions made per mm. of path in air by an a particle from RaC at 
 various distances from its source. Total number = 2*37 X io 5 (Geiger, see above). 
 
 Distance from RaC in cm. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 i 6 
 
 6'5 
 
 7 
 
 
 
 
 
 
 
 
 
 Ions per mm. of path in air at 12 C. and 76 cm. 
 
 2250 
 
 2300 
 
 2400 
 
 2800 
 
 3600 5500 
 
 7600 
 
 4000 
 
 TOTAL RELATIVE IONIZATION IN GASES BY a RAYS 
 
 l t total ionization (relative to air) produced by the complete absorption of 
 a particles in various gases. (B. Bragg, P.Af., 1907, used RaC rays ; B. and C., 
 Bragg and Cook, P.M , 1907 ; L., Laby, P.R.S., 1907, used U a rays ; R., Rutherford, 
 P.M., 1899, used U a rays.) 
 
 Gas. 
 
 I 
 
 Gas. 
 
 l t 
 
 Gas. 
 
 l t 
 
 Air . . 
 ! O a . . . . 
 
 100 
 
 1*09, B. ; ro6, R. 
 
 Methane 
 Acetylene 
 
 16, B. and C. 
 26, B ; 1-27, L. 
 
 Et. ether . . 
 
 /i'3i, B.; 
 11-29, L. 
 
 jN 2 . . . . 
 
 0-96, B. 
 
 Ethylene . . 
 
 28, B. 
 
 Et. iodide 
 
 1-28, B. 
 
 JN 2 . . . 
 
 1-05, B. ; 0-99, L. 
 
 Pentane . . 
 
 35, B.; 1-345, L. 
 
 Acetaldehyde 
 
 1-05, L. 
 
 ! NH 3 . . . 
 
 roi, R. ;o'9o, L 
 
 Me. alcohol . 
 
 22, B. 
 
 Chloroform . 
 
 1-29, B. 
 
 C0 2 . . . 
 
 ro8,B.;ro3,L. 
 
 Me. iodide . 
 
 i'33, B. 
 
 Carb. tetra- 
 
 
 Carbon bi- 
 
 
 Et. alcohol . 
 
 23, B. 
 
 chloride 
 
 1-31, B. 
 
 sulphide . 
 
 i'37, B. 
 
 Et. chloride . 
 
 30, B.; ri8, L 
 
 
 
 RELATIVE VOLUME IONIZATIONS FOR 0, y, AND X RAYS 
 
 Relative ionization = lr = ft\\p, where i is the amount of ionization per unit 
 volume for the gas at a press. ^, and I that for air af press. P, the other experi- 
 mental conditions being the same. In the experiments with 7 rays (column headed 7), 
 /8 rays would also be present. Observers : for ft and 7 rays, Kleeman, P.ft.S., 
 1907 ; X rays, C., Crowther, P.C.P.S., 1909 ; P.fi.S., 1909 ; Me., McClung,AJ/., 1904. 
 Ir for secondary 7 rays is much the same as for X rays (see Kleeman, P.R.S., 1909). 
 
 Gas. 
 
 Air. . . 
 
 H 2 . . . 
 
 2 . . . 
 
 NH 3 . . 
 
 N 2 . . 
 
 C0 2 . . . 
 
 C 2 N 2 . . 
 
 SO 2 . . . 
 
 CS 2 . . . 
 
 Pentane . 
 
 Benzene . 
 Me. acetate 
 
 7 HardX. Soft X. 
 
 1-00 1 00 1 00 
 o-i6'o-i6o-i8, C. 
 1-17 ri6 ri7,Mc 
 
 0*89 0-90 
 r6o 1-58 
 
 1-86 
 2-25 
 3-62 
 4'55 
 3'95 
 
 171 
 
 2-27 
 3*66 
 4'53 
 3'94 
 
 1-49, C. 
 479, Me, 
 
 3-90, C. 
 
 1-00 
 
 o-oi, C. 
 i'3, Me. 
 
 1-57, C. 
 iro, Me. 
 
 Gas. 
 
 Me. alcohol . 
 Me. bromide . 
 Me. iodide . 
 Chloroform . 
 CC1 4 . . . 
 Et. aldehyde 
 Et. bromide . 
 Et. chloride . 
 Et. ether . . 
 Et. iodide 
 Ni. carbonyl 
 Hg dimethyl- 
 
 7 Hard X. Soft X. 
 
 1-69 175 
 3733'Si 
 5-115-37 
 4'94|4-93 
 6-286-33 
 
 2-12 2T7 
 
 1*4 1 4-63 
 3-243-19 
 
 *'39 ! 4'29 
 5-90 6-47 
 
 - 5-98 
 
 125, C. 
 7i,C. 
 118 
 
 97, C. 
 
 71, C. 
 145, C. 
 
 67, C 
 
 72, C. 
 i8,C. 
 
 89, C. 
 425, C. 
 
 P.C.P.S., Proc. Camb. Phil. Soc. ; P.M., P,'n7. Mag. ; P.R.S., Proc. Roy. Soc. 
 
102 
 
 HEAT OF RADrOM 
 
 RELATIVE IONIZATION PER UNIT VOLUME BY OL RAYS 
 
 Relative ionization - (total ionization) x (stopping power), Metcalfe, P.Af., 1909. 
 
 Air . I'OO 
 
 H 2 . -233 
 
 He . 1 *2ii 
 Br 2 . 3'9 
 
 CO . 
 NO. 
 
 TOO 
 
 T28 
 
 HC1 . 
 Ethane 
 
 i '4 
 2-08 
 
 Propane 3*05 
 Butane . 4*02 
 
 Pentane 
 
 4-83 
 
 For calculated total ionization when Reutgen rays are completely absorbed 
 in various gases, see Crowther, Proc. Roy. Soc., 1909. 
 
 HEATING EFFECT OF RADIUM 
 
 In calories per sec. per gm. of metallic radium with its radioactive products. 
 E. von Schweidler and Hess, using 795 gm. Ra enclosed in i mm. glass + 5 mm. 
 Cu, obtained O328 calorie gm.- 1 sec. l = 118 cals. gm. 'hr.^ 1 The heating 
 effect of a radioactive substance is proportional to the ionization it produces (Duane, 
 Le Radium, 1909). The heat emission continues at temp, of liquid hydrogen 
 (Curie and Dewar, 1903), and is mainly due to the kinetic energy of the a rays 
 (Rutherford, " Radioactivity"). 
 
 Temp, and press, h ive no effect on heat emission (Schuster, Eve, and Adams, 
 Nature, 1907; Rutherford and Petavel, B.A. Rep., 1907 ; Schmidt, P.Z., 1908). 
 
 Heat. 
 
 Observer. 
 
 0278 Curie and Labjrde, C.R., 
 
 1903 
 0292 Runge and Precht., Berl. 
 
 Ber., 1903 
 0306 Rutherford and Barnes, 
 
 Nature, 1903 ; P.M., 1904 
 
 Heat. 
 
 25% 
 44% 
 
 Observer. 
 
 0325 
 0372 
 0328 
 
 Produced by Ra ) R.&B 
 
 RaC Ji 9 o4 
 
 Angstrom, P.Z., 1905 
 Precht, A.d.P., 1906 
 Schweidler and Hess, Wien. 
 Ber., 1908 
 
 HEAT EMISSION FROM RaEm, AND THORIUM 
 
 The 6 x io~ 4 c.c. of RaEm (with its products) in equilibrium with i gm. 
 Ra emit 75 of the "0328 calories emitted per sec. by the radium. Thus the 
 total quantity of heat given out by i c.c. of RaEm during its whole life = 
 75 * *0328/(A x 6 x jo" 4 ) = 1*9 x io 7 calories. 
 
 For old (mineral) thorium metal, the heat emitted is 5 x io~ !) calories per sec. 
 per gm. (Pegram and Webb, Phy. Rev., 1908). 
 
 RADIUM EMANATION 
 
 r is the period of decay (in days) to half initial activity. Taking r = 3-66 
 days, then the decay coefficient A = 2*19 x io- 6 sec.- 1 (see p. 107). 
 
 r in days. 
 
 Observer, etc. 
 
 r in days. 
 
 Observer, etc. 
 
 377 
 3-88 
 
 3-8 to 4-1 
 3-86 
 
 Rutherford and Soddy, P.M., 
 1903. 
 Bumstead and Wheeler, 
 A.J.S., 1904. 
 Debierne, C.R., 1909. 
 Sackur, Ber. C.G., 1905. 
 
 375 
 3-58 
 375 
 3-85 
 
 4*4 
 
 Riimelin, P.M., 1907. 
 For first 5 days. 
 During period 5 to 20 days. 
 20 to 40 days' old emanation. 
 One sample Rutherford and 
 Tuomikoski, P.M., 1909. 
 
 EQUILIBRIUM VOLUME OF RADIUM EMANATION 
 
 Final volume of radium emanation at o C. and 76 cm. Hg in equilibrium 
 with i gm. of metallic radium. Theoretical volume = (number of radium 
 atoms breaking up per sec.)/AN = 3'4 x io 10 /(2'75 x io 19 x 2*19 x io-) = 5-64 
 x io- 4 c.c. (Rutherford, " Kadioactivity "). The volume of the emanation changes 
 anomalously after it is first formed. 
 
 Observed vol. 
 
 Observer. 
 
 Observed vol. 
 
 Observer. 
 
 58 cub. mm. 
 601 
 
 Rutherford, P.M., 1908. 
 Gray & Ramsay, y.C.S.,\cp^. 
 
 58 cub. mm. 
 
 Debierne, C.R., 1909. 
 
 A.d.P., Ann. der Phys. ; A.J.S., Amer. Journ. Sci. ; B.A. Rep., Brit. Ass. Rep. ; C.R., 
 Compt. Rend.; J.C.S., Jonrn. Chem. Sci. ; P.M., Phil. Mag.; P.Z., Phys. Zeit. 
 
103 
 
 EMANATIONS 
 
 VAPOUR PRESSURE OF RADIUM EMANATION 
 
 Vapour pressure of liquid RaEm. in cm. Hg ; melting-point, 71 C. (R., Ruther- 
 ford, Nature, February, 1909 ; G. & R., Gray and Ramsay, J.C.S., June, 1909.) 
 
 Temp. C. . . . 
 Yap. press, cm. Hg 
 
 -127 C 
 
 R. 
 
 -101 C 
 
 -78 C 
 
 -65 = B.P. 
 
 76 
 
 Temp. C. 
 
 Vap. press, 
 cm. flg 
 
 r i-70-4 -62=B.P.!-60-6 -55-8 -38-5 - 
 
 ^- 
 
 & 
 
 R. 50 76 80 
 
 100 
 
 200 
 
 40O 
 
 -10-2+104-5crit.t. 
 
 500 
 
 4745 crit. press. 
 
 DIFFUSION OF EMANATIONS 
 
 D = coefficient of diffusion (in cm. 2 sec.- 1 ) of the emanation into the gas stated 
 at the pressure p cm. Hg and temp. / C. indicated. According to J. J. Thomson 
 {Nature, November 25, 1909) : " D would only vary slowly with atomic weight," 
 and not as the square root of the molecular weight of the emanation, as is assumed 
 in the table below. 
 
 Russ finds /D = const, for AcEm. and for ThEm. Bruhat gives /D/T 2 
 = const, for AcEm. between o and 20. (Molec. wgt. ThEm.)/(molec. wgt. 
 AcEm.) = 1-42 (Russ). Mol. wgt. of RaEm. = 218 (Gray & Ramsay, 1910). 
 
 Gas. 
 
 p. and 
 tC. 
 
 Molec. 
 wgt. 
 
 Obs. 
 
 Gas. 
 
 p. and 
 tC. 
 
 D. Mole . c 1 Obs, 
 wgt. 
 
 RADIUM EM. 
 
 ACTINIUM EM. 
 
 Air 
 
 CO 2 . . . 
 Biff, of Em. 
 into air com- 
 pared with 
 2 ,C0 2 ,S0 2 , 
 into air . . 
 Em. into 
 H 2 compared 
 with Hg vap 
 into H 9 . . 
 
 76? j -07 to '09 c. ioo iR.&B 
 
 76,10 -io ' ;C.&D 
 
 76, o -ioi 75 to ioo C. 
 
 
 250 
 
 -034 Em. 
 
 o/i'0376Em. 
 275 li-0407 Hg 
 
 Air 
 
 1 80 
 
 86 to 99 
 
 235 
 
 B.&W 
 
 M. 
 
 76-4 
 76 
 76) 
 to o c 
 
 9J 
 
 112 
 
 7*1 
 
 125 
 123 
 
 '10 
 
 70 
 
 70 
 
 THORIUM EM. 
 
 Em. into air, 
 com pared 
 with H 2 , O 2 , 
 
 ACTINIUM EM. 
 
 H 2 . . 
 H 2 . . 
 S0 2 . 
 Argon 
 C0 2 . 
 C0 2 . 
 
 76, i5 
 
 76, io 
 toi8 
 
 76, i5 
 
 412 
 
 '33 
 
 062 
 
 106 
 
 073 
 077 
 
 B. 
 R. 
 
 SO 2 
 into air 
 Air . 
 
 Argon 
 
 C0 2 , 
 
 09 
 
 c. c 
 
 103 
 
 
 966 
 
 
 to 
 
 
 103 
 
 
 103 
 
 084 
 
 
 *9o 
 
 76 
 8-2 
 to 
 
 76- 
 76 
 76 
 
 M. 
 
 Ruth 
 R. 
 
 B., Bruhat, Le Radium, 1909; B. & W,, Bumstead & Wheeler, A.J.S., 1903; C., 
 Chaumont, Le Radium, 1909; C. & D, Curie & Danne, C.R., 1903; D., Debierne, Le 
 Radium, 1907; M., Makower, P.M., 1905; P., Perkins, A.J.S. ; R., Russ, P.M., 1909, 
 Le Radium, 1909; Ruth., Rutherford, " Radioactivity " ; R. & B., Rutherford & Miss Brooks, 
 C.N., 1902. 
 
 A.J.S., Amer. Jaunt. Sci. ; C.N., Ghent. News ; C.R., Compt. Rend.; J.C.S., Journ. 
 Cktnt. Soe. ; P.M., Phil. Mag. 
 
104 
 
 Ra IN ROCKS 
 
 EQUILIBRIUM ACTIVITIES IN MINERALS 
 
 Relative activity of radioactive products in minerals. Boltwood (A.J.S., April, 
 1908) found U 2'22 times as active as the Ra alone in minerals (see McCoy and 
 Ross, A.J.S.). 
 
 
 TJ 
 
 lo 
 
 Ha 
 
 KaEm. 
 
 RaA 
 
 BaB 
 
 RaC 
 
 Ra7 
 
 Ac 
 
 Total. 
 
 
 
 
 
 
 
 
 
 
 
 
 Relative activity . . 
 
 i 
 
 "34 
 
 45 
 
 62 
 
 54 
 
 04? 
 
 91 
 
 46 
 
 28 
 
 4-64 
 
 3'4 X io ~ 7 gm. Ra is in equilibrium with i gm. U (Rutherford and Boltwood, 
 A.J.S., 1906). 7-3 x io fi gms. U equal inactivity i gm. of Ra + its products to RaC. 
 i.e. Ra just over 30 days old (corrected by Boltwood, A.J.S., 1908). 
 
 RADIUM AND THORIUM IN ROCKS 
 
 Rutherford and Soddy (P.M., May, 1903) and W. E. Wilson (Nature, July, 1903) j 
 suggested that the heat liberated by radioactive changes is one of the sources of j 
 the Earth's heat. Thus the distribution of radium and thorium in the Earth's crust ' 
 is of geophysical importance. Loss of heat from the Earth's surface = tempera- 
 ture gradient x thermal conductivity of crust x area of Earth's surface = (1/3200) 
 x '004 x 5- 1 X io 18 = 6 X io 12 calories per sec. Now, elementary radium in radio- 
 active equilibrium (i.e. whole U family) gives out 6 X io~ 2 cal./sec. gm. (Ruther- 
 ford^, and therefore ri x io 14 grms. of radium, or io 14 /io 27 = io~ 13 gm. per c.c., 
 throughout the Earth's volume would maintain it at a steady temperature. Thorium 
 contributes 5 x IQ- cal. /sec. gm. The total heating effect in calories per gram 
 of rock per hour is for the lava indicated below by *, 30 x io~ 10 ; and for the rock 
 
 indicated by t, 2*9 x io~ 10 ; for average igneous rock, 11 x io~ 10 . 
 (See Strutt, Proc. Roy. Soc., 1906-7 ; Joly, "Radioactivity and Geology," 1909.) 
 
 Rock, etc. 
 
 Obs. 
 
 Ra Th 
 
 gm. per gm. of rock. 
 
 
 St., 1906 
 E. M., 1907 
 
 i 11 
 11 11 
 11 11 
 J., 1909 
 
 F. F., 1909 
 J., 1909 
 other obs. 
 B., 1909 
 
 F. F., 1909 
 
 J., 1909 
 )) 
 
 j? 
 FL, 1910 
 f J., 1910 
 
 v 
 
 J) 
 11 
 V 
 
 x io- 12 
 
 17 
 
 ri 
 16 
 
 79 
 i to 4 
 
 '9 
 12-3 
 2-4 
 7-01 
 
 i'3 
 mean 
 
 { 1 
 
 77 
 3-4 to 4-9 
 
 7-6 
 8 
 mean of 7 
 27 samples 
 
 7-2 
 
 367 
 
 27 
 
 X 10 :> 
 
 2-3 
 
 i '3 
 
 5 
 igneous 
 sedimentary 
 
 1-9 
 
 *5 to T2 
 56 
 
 j6 
 <-o5 
 
 
 Sandstone 
 
 Clays 
 
 Devonian 
 
 Ordovician 
 
 Lavas ejected since 1631 * . . . 
 Lava Mount Erebus 
 
 126 igneous rocks . 
 
 82 
 
 Italian igneous rocks .... 
 
 Campbell and Auckland Islands,) 
 N.Z / 
 
 St. Gothard Tunnel 
 granite 
 
 schists and altered sedimentary^ 
 rocks / 
 
 
 Transandine Tunnel t 
 
 Calcareous and dolomitic European 
 rocks 
 
 Deep-sea deposits 
 
 Radiolarian ooze 2 
 
 Red clay 3 
 
 
 Extent : l 50, * 2*5, 3 5[ million square miles, f 1000 feet below the surface. Assum- 
 ing that the heat due to each member of the family is proportional to the ionization it produces. 
 || Preliminary result. B., Blanc., P.M. ; E.M., Eve and Mclntosh, P.M. ; F.F., Farr and 
 Florance, P.M. ; Fl., Fletcher; I., Joly, P.M. ; S., Strutt (above). A.J.S., Amer. Jonrn. 
 Sci. ; P. Af., Phil. Mag. 
 
105 
 
 ELECTRIC ARC 
 
 RADIUM IN SEA-WATER 
 
 In grams per gram of sea-water. Deduced from the observed amount of Ra 
 Em. 
 
 Amount. 
 
 Place. 
 
 2-3 x IQ 
 3-'6 
 
 '9 
 16 
 
 Mid. N.Atlantic 
 Atlantic 
 
 Observer. 
 
 Strutt, />./?..SVo 
 Eve, P.M., 1907 
 
 1909 
 Joly, P.M., 1908 
 
 Amount. 
 
 4 x i o~ 15 
 
 
 5 
 
 Place. 
 
 Nile 
 
 Mediterranean 
 Indian Ocean 
 
 Observer. 
 
 Joly, P. M. t 1 908 
 ! 99 
 
 RADIUM EMANATION IN ATMOSPHERE 
 
 RaEm. per cubic metre of air, expressed in terms of the number of grams of 
 radium with which it would be in equilibrium. The observers below absorbed the 
 emanation by charcoal. 
 
 RaEm. 
 
 Place. 
 
 Observer. 
 
 24-27 x io~ 12 Montreal Eve, P.M., 1907 
 
 60 1908 
 
 86-200 Chicago j Ashman, A.J.S.Jo 
 
 RaEm. 
 
 3 5-3 50 x i o- 1 
 Mean 105 
 
 Place. 
 
 \ Cam- ( 
 Jbridge\ 
 
 Observer. 
 
 Satterly, P.M., 
 1908 and 1910 
 
 MOBILITIES OF NATURAL IONS IN AIR 
 
 Mobility or speed K is in cm. 2 sec.- 1 volt" 1 at room temperature and 76 cm. (see 
 p. 95). The ions are named from their velocities : the small ions are assumed to 
 have the velocity of X-ray ions. (See Pollock, Science, 1909 ; Eve, Phil. Mag., 19, 
 1910 ; Lusby, Proc. Cainb. Phil. Soc., 1910.) 
 
 Ion. 
 
 Small . . . 
 Intermediate 
 
 Mean K 
 
 Observer. 
 
 K+ = n! 
 c. -oi Mean 
 
 Ion. 
 
 Large 
 Large 
 Large 
 
 Mean E. 
 
 0003 
 0003 * 
 0008 f 
 
 Observer. 
 
 Langevin,C.AVo$ 
 Pollock, 1908 
 
 * Humidity, 19 grms. H 2 O per cubic metre, f "5 'grm. H 2 O per cubic metre of air. 
 Pollock, Austl. Ass. Adv. Set., 1908. 
 
 ELECTRIC ARCS 
 
 Mrs. Ayrton's formula for carbon arcs, E = a + ftl -\ : , has been shown by 
 
 Guye and Ze'brikoff (Compt. Rend., 1907) to hold for short stable arcs between metals. 
 E is the voltage across the arc, i is the current in amperes, and / the length in mms. 
 of the arc in air at atmospheric pressure. Mrs. Ayrton's formula does not hold for 
 very long arcs, nor for cored carbons. For stability, an arc requires an external 
 
 resistance R which must be less than / , S A ~ ohms, where E,, is the 
 
 total available voltage ; or E,, must exceed + / + 2^R(y -f 5/). If R is too 
 small the arc hisses, in which case the current is independent of the voltage across 
 the terminals. The constants for carbon refer only to the particular sizes nnd quality 
 used by Mrs. Ayrton. 
 
 (See J. J. Thomson, " Conduction of Electricity through Gases.") 
 
 Metal. 
 
 C. 
 
 Fe 
 Ni 
 Co 
 Cu 
 
 38-88 
 1573 
 17*14 
 2071 
 21-38 
 
 2-074 
 2-52 
 
 3-89 
 2-05 
 
 3-03 
 
 11-66 
 
 9'44 
 o 
 
 2-07 
 10*69 
 
 10-54 
 15-02 
 17-48 
 
 IO'I2 
 I5-24 
 
 Metal. 
 
 Fd 
 Ag 
 Ft 
 An 
 
 21-64 
 14-19 
 24-29 
 20-82 
 
 370 
 
 4-80 
 4-62 
 
 o 
 
 11-36 
 o 
 
 12-17 
 
 2178 
 19-01 
 20-23 
 
 20-97 
 
 A.J.S., Amer. Journ. Sci. ; C.R '., Compt. Rend. ; P.M., Phil. Mag. ; P.K.S., Proc. Roy. Soc. 
 
106 
 
 ATOMIC CONSTANTS 
 
 ATOMIC AND RADIOACTIVITY CONSTANTS 
 
 References : J. J.Thomson's <; Conduction of Electricity through Gases," Ruther- 
 ford's "Radioactivity," H. A. Lorentz, Edairage Electrique, 4* I9C*5> "Theory 
 of Electrons," 1909, and Jeans' " Dynamical Theory of Gases." 
 
 Symbol. 
 
 Definition. 
 
 Value. 
 
 e. . 
 
 NE . 
 
 Ionic charge, half charge on an particle 
 
 Total charge carried in electrolysis 
 
 atoms in \ c.c. of gas 
 For ideal gas at o and 76 cm. 
 
 by the 
 
 oxygen 
 hydrogen 
 
 (gm. molecule) of 
 
 47. i o- 10 E.S.U.; 1-57. io- 
 
 HE. M. U.; 1-57. io-* 
 
 |_coulombs 
 1-2913 . io 10 E.S.U. cm.- 3 
 
 4304 E.M.U. cm." 3 
 1-292 . io 10 E.S.U. cm." 3 
 
 4308 E.M U. cmr* 
 1-290 . io 10 E.S.U. cm.~ 3 
 
 4300 E.M.U. cm." 3 
 
 2-894 . io 1 
 
 9*647 io 
 2-75 . io 19 cm. 
 
 E.S.U, cmr 3 
 E.M.U. cm." 3 
 
 -3 
 
 Total charge carried by 
 
 hydrogen ions 
 Number of molecules per c.c. of a gas at 
 
 o C. and 76 cm. = NE/* = 1-29 . io 20 /47 
 Number of molecules in i gm. molecule of gas |6'i6. io 23 gm.- 1 
 Ratio of charge to electromagnetic mass for 5*31 . io 17 E.S.U. gin." 1 ; 
 
 the negative electron at small velocities 177 . io 7 E.M.U. gm.- 1 
 
 The same ratio for the hydrogen ion in elec- 9,647 E.M.U. gm.- 1 ; 96,470 
 
 trolysis(= the Faraday) = io7'88/-ooi 1 1827 | coulombs gm.- 1 
 The same ratio for the a particle 4*8 . io 3 E.M.U. gm.- 1 
 
 Calculated for helium = 2NE/p = 2 x -43. io- 6 /j 4-78 . io 3 E.M.U. gm.- 1 
 
 (2 x 8-987) 
 
 gm. 
 
 1-64. io~ 24 gm. 
 
 6-56. 
 
 1835 
 
 " 24 
 
 gm. 
 
 a . 
 
 Electromagnetic mass of negative elec- 8-8 . io~ 28 
 
 tron for small velocities = */(*//) 
 Mass of hydrogen atom = p/2N 
 Mass of o particle, i.e. of helium atom 
 Number of electrons equal in mass to hydrogen 
 
 atom = (*H*)/(woE) 
 
 Energy of a gas molecule at 3 C. = o =3//2N 
 For i gm. of oxygen, R = pv/6 = 1-0132 
 
 . io 6 /(273'09 . 1*429. io- 3 ). Press, in dynes/ 
 
 cm. 2 ; volume in c.c. (see p. 5) 
 For i gm. molecule of an ideal gas, R= ! -08207 litre atm./gm. 
 
 22-412/273-09. Press, in atmos. = 76 cm. 
 
 Hg(#- = 980-6) ; vol. in litres (D. Berthelot, 
 
 Trav. et Mm. Bur. Intl.] 
 The radius of a negative electron = 2/3 
 
 2 '02 . io~ 16 ergs/degree 
 (2-5963 . io 6 cm. 2 /sec. 2 
 12-5963 . io 6 ergs/gm. 
 
 The diameter of a hydrogen molecule 
 (Sutherland (after Jeans), Phil. Mag., 1910) I 
 
 1-85 . io- 13 cm. 
 
 2-17. io~ 8 cm. (see p. 33) 
 
 Heat given out by i gm. of metallic radium with its 
 
 products 
 Number of o particles emitted by i gm. radium 
 
 without products 
 
 Initial velocity of particle from RaC 
 Initial energy of particle from RaC = ;## 2 /2 = v^e 
 
 I (2?/;;/a) = 2-o6 2 . io 18 x 1-57 . io- 20 /( 2 x 5*07 . io 3 ) 
 Total number of ions produced in air by an o ray 
 
 (RaC) 
 Volume of helium at o and 76 cm. produced by 
 
 i gm. radium 
 Calculated volume = 4 x number of o rays emitted/N 
 
 = 4.3-4. io-/275 
 Number of ' & particles emitted per sec. by the RaC 
 
 in equilibrium with i gm. Ra (Makower, Phil. Mag., 
 
 1909) 
 
 0328 cal./sec. ; 1 18 cal./hr. 
 3-4 . io 10 gm." 1 sec.- 1 
 
 2*06 . io 9 cm./sec. 
 
 1*3 . io~ 5 ergs ; 3-1 . io" 13 cal. 
 
 2-37 . io 5 
 
 5-17. io- 9 c.c./(sec. gm.), or 
 
 163 mm. 3 /(yr. gm). 
 4-94 . io- c.c./(sec. gm.) ; 
 
 156 mm 3 / (yr. gm). 
 5 . io' gm.~ l sec." 1 
 
107 
 
 RADIOACTIVITY 
 
 CONSTANTS OF RADIOACTIVE SUBSTANCES 
 
 The table below is based on one compiled 
 
 by Blanc, Bloch., Danne, Godlewski, 
 
 Hahn, Kolowrat, Le Vin, S. Meyer, Moulin, H. W. Schmidt, Schweidler, and 
 
 Szilard (Le Radium, Jan., 1909, Jan., 1910, and Jan., 1911). 
 
 Atomic weights : O = 16, U = 238-5, Ra = 226-4, Th = 232-4. 
 
 Rate of decay : If I is the radioactivity of a substance at a time /, then 
 
 I = lo*-**, where 1 is the initial activity when / = o. A is given below in sec.- 1 . 
 If r is the period in which the activity decreases to half its initial value (i.e. I/I = |), 
 
 then A = '693 1 5 /r sec.- 1 , r is given below 
 
 in sees. (s.J, mins. (m.), hrs. (h.), 
 
 days (d.), or years (y.). 
 
 
 Coefficients of absorption A are given in cm.- 1 for rays in Al foil and for 
 
 7 rays in lead foil. If J is the intensity of the rays incident on foil of thickness 
 
 d cm., and J is the intensity of the emergent rays, then J = J <? ^ A . 
 
 (See Rutherford's " Radioactivity," 2nd ed., 
 
 Camb. Univ. Press, 1905.) 
 
 
 . 
 
 
 Absorptn. Coef. in cm.- 1 . 
 
 Substance. 
 
 A in sec.--. =-*** 
 
 Rays 
 emitted. 
 
 Bays. 
 
 7 Bays. 
 
 
 
 
 A A i 
 
 Apb 
 
 jj 
 
 4-3 . io- 18 6. lo 9 y. 
 sevl. y. 
 
 a 
 
 
 
 Ead.U .... 
 
 U.X 
 
 37. io- 7 
 
 21*5 d. 
 
 0,7 
 
 14-4 and 510 
 
 72 
 
 Io 
 
 2. io- 12 
 
 c. io 4 y. 
 
 a 
 
 __ 
 
 _ 
 
 Ra 
 
 I'l . I0- u 
 
 2000 y. 
 
 a, 
 
 312 
 
 
 
 RaEm. 
 
 2 - o8 . IO~ 
 
 -j-gi; d 
 
 a 
 
 
 
 RaA .... 
 
 3'85 io- 
 
 O J u> 
 
 3 m. 
 
 a 
 
 
 
 
 
 RaB 
 
 4' 11 IO 
 
 26*7 ni 
 
 ft 
 
 1 1 to 800 
 
 
 RaC t . . 
 
 JO lu 
 
 5 '93- io- 
 
 I9'S m. 
 
 a 
 
 i ^ LW oyvj 
 
 13 to 53 
 
 '46 to -57 
 
 
 RaC, . . 
 
 
 
 1-2-5 m. 
 
 0,7 
 
 
 RaD~ 
 
 r8. io- 
 
 12 y. 
 
 ray less 
 
 
 
 RaE! . . . 
 
 i"i io~ 6'2 d. 
 
 
 
 
 RaE 2 . . . 
 
 1*7 . io~ 4*8 d. 
 
 j * 
 
 ft AA 
 
 
 RaF (Polonium) . 
 
 5-73.10- 140 d. 
 
 
 tt 
 
 
 
 Ac 
 
 
 ? 
 
 ray less 
 
 
 
 Rad.Ac .... 
 
 4-1 . io- 7 19-5 d. 
 
 a, |8 
 
 170 
 
 
 
 AcX 
 
 7"6 . io- lo-n d. 
 
 a 
 
 
 
 
 AcEm. . 
 
 r8 . io 
 
 7'Q S 
 
 ct 
 
 
 
 i AcA . . . 
 
 3-20. io- 
 
 o y = 
 36'! m. 
 
 
 
 
 
 
 
 AcB 
 
 5'37 io- 
 
 2-115 m. 
 
 a 
 
 
 
 AcC . 
 
 2*26 . io- 5-10 m. 
 
 0,7 29 
 
 2'0 to 3'6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Th 
 
 7 IO 
 
 t'IO 10 V 
 
 a 
 
 
 
 
 MesoThl . . . 
 
 1 xv -' 
 4-0 . io- 
 
 J 1<J f 
 
 S'S y- 
 
 rayless 
 
 
 
 MesoTh 2 ... 
 
 3-1 . io- 
 
 6-2 h. 
 
 0, 7 20-2 to 38-5 
 
 '5 
 
 Rad.Th .... 
 
 1-09 . io- 
 
 737 d. 
 
 a 
 
 
 ThX .... 
 
 2" 1 7 IQ 
 
 3 "71 d. 
 
 a 
 
 
 
 ThEm. . . 
 
 1-31 . io- 
 
 / * * 
 
 53 s. 
 
 a 
 
 
 
 
 
 ThA . . . 
 
 i'8i . io 
 
 10*6 h. 
 
 ft 1 i>in 
 
 
 
 ThB . . . . 
 
 2'10. 10- 
 
 55 m - 
 
 a 
 
 T^ 
 
 
 
 ThC . . . 
 
 
 some sees. 
 
 a 
 
 
 
 
 
 | TnD 
 
 37. io- 3 
 
 3-1 m. 
 
 0,7 
 
 157 
 
 46 to -57 
 
 
 
 
 
 
 
 
108 
 
 RADIOACTIVITY 
 
 PROPERTIES OF RADIOACTIVE SUBSTANCES 
 
 Compiled by authors mentioned above (Le Radium, 1911). 
 
 But stance. 
 
 Properties. 
 
 Substance. 
 
 Properties. 
 
 u. 
 
 Sol. in excess of am. carb. 
 
 
 Carried down by PbCO 3 , ! 
 
 
 Nitrate soluble in ether and 
 
 
 and by SnCl 2 with Hg and 
 
 
 acetone. 
 
 
 Te. RaD, E,, E 2 , and F 
 
 Bad. IT . 
 
 Carried down by BaSO 4 
 and ferric hydrate. Soluble 
 
 
 can be separated by electro- 
 lysis. 
 
 
 in HC1. 
 
 
 
 U.X . , 
 
 Less volatile than U. Volatile 
 
 Ac - 
 
 Produces helium. Precipi- 
 
 
 in electric arc. Insoluble in 
 
 
 tated by oxalic acid in acid 
 
 
 excess of am. carb. Soluble 
 
 
 solutions. Oxalate insoluble ; 
 
 
 in water and ether. Carried 
 
 
 in HF ; accompanies 
 
 
 down by barium sulphate, 
 
 
 thorium and rare earths. 
 
 
 by moist ferric hydrate, and 
 
 Bad.Ac . 
 
 Slightly volatile at high temps. 
 
 
 by animal charcoal. 
 
 
 Insoluble in NH 4 OH. 
 
 
 
 
 Separated from Ac by elec- i 
 
 lo. . . 
 
 Soluble in excess of am. 
 
 
 trolysis, by fractional pre- 
 
 
 oxalate. Carried down by 
 
 
 cipitation, by ammonia, and 
 
 
 H 2 O 2 in presence of U salts. 
 
 
 by animal charcoal. 
 
 Ba . . 
 
 Characteristic spectrum. 
 
 AcX . . 
 
 Deposited by electrolysis in 
 
 
 Spontaneously luminous. 
 
 
 alkaline solution. Not 
 
 
 Analogous to Ba. RaCl 2 and 
 
 
 precipitated by NH 4 OH. 
 
 
 RaBr 2 are less soluble than 
 
 AC Em. 
 
 Behaves as inert gas. Coef. 
 
 
 BaCl 2 and BaBr 2 . 
 
 
 of diffusion in air o'li. 
 
 BaEm. . 
 
 One of group of inert gases. 
 
 
 Condenses at - 120 C. 
 
 
 Characteristic spectrum. 
 Coef. of diffusion in air = 
 
 AcA . . 
 
 Volatile below 400 C. 
 Soluble in NH 4 OH and ! 
 
 
 o'i (see p. 103). Mol. wt. 
 
 
 strong acids. 
 
 
 = 218. 
 
 
 
 BaA . . 
 
 Behaves as a solid. Deposited 
 
 AcB . . 
 
 Volatile below 700 C. Soluble 
 
 
 on cathode in an electric 
 
 
 in NH 4 OH and strong 
 
 
 field. Volatile at 800-900 C. 
 
 
 acids. Deposited by electro- 
 
 
 Soluble in strong acids. 
 
 
 lysis of active deposit on 
 
 BaB . . 
 
 Like RaA. Volatile at 600- 
 
 
 the cathode in HC1. 
 
 
 700 C. Precipitated by 
 
 
 
 BaC . . 
 
 BaSCH. 
 Physically like RaA. Vola- 
 tile at 800-1300 C. Chemi- 
 cally, like RaB. Deposited 
 on Cu and Ni. Carried 
 
 Th . . 
 
 Volatile in electric arc. 
 Colourless salts not spon- 
 taneously phosphorescent. ' 
 Salts pptd. by NH 4 OH and 
 oxalic acid. 
 
 BaD . . 
 
 down with precipitated 
 copper. Perhaps a mixture 
 of 2 or 3 products. 
 Volatile below 1000 C. 
 Soluble in strong acids. 
 Reactions analogous to 
 
 Bad.Th . 
 ThX . . 
 
 Carried down by hydrates, 
 precipitated by NH 4 OH. 
 Soluble in NH 4 OH. Carried 
 down by iron. Deposited 
 by electrolysis in alkaline j 
 soln. 
 
 BaE, . 
 
 those of Pb. 
 Volatile at red heat. Soluble 
 
 ThEm. . 
 
 Inert gas. Condenses just 
 above 120 C. Coeffi- 
 
 
 in cold acetic acid. Reac- 
 
 
 cient of diffusion in air 
 
 
 tions analogous to those of 
 
 
 = 'IO. 
 
 BaE 2 . . 
 
 Pb. 
 Not volatile at red heat. Re- 
 
 ThA . . 
 
 Volatile under 630 C. Soluble 
 in strong acids. 
 
 
 actions analogous to those 
 
 ThB . . 
 
 Volatile below 730 C Like 
 
 BaF(Pol.) 
 
 of bismuth. 
 Volatile towards 1000 C. 
 Deposited from its solutions 
 
 
 ThA. Deposited on Ni. 
 Separated from ThA by 
 electrolysis. 
 
 
 on Bi, Cu, Sb, Ag, Pt. 
 
 ThC . . 
 
 Like ThB. 
 
109 
 
 PHYSICAL CONSTANTS 
 
 PHYSICAL CONSTANTS OF CHEMICAL COMPOUNDS 
 
 For properties of the elements, see : density, p. 20 ; melting and boiling points, 
 p. 48 ; solubility in water, p. 124. Metallo-organic compounds are given under 
 " Organic Compounds," p. 118. 
 
 Formulae. Hydra ted forms (which are often crystalline) are indicated thus : 
 CaI 2 (and + 6H 2 O) ; the properties given are for the anhydrous substance. 
 
 Formula (Molecular) Weights are calculated with atomic weights for 1911. 
 
 Densities. When no temp, is given, grams per c.c. at 15 may be assumed. 
 When preceded by " A" the density is relative to that of air (-001293 gram per c.c. at 
 o and 760 mms.). To convert this into a density relative to O 2 = 16, multiply by H'47- 
 For those gaseous densities known with accuracy, see p. 26. Other densities on pp. 20-26. 
 
 Melting and Boiling Points are for anhydrous substances at 760 mms. mercury 
 unless some other conditions are specified. T = temp, of transition or pseudo- 
 " melting " point of hydrated substance. For fats and waxes, see p. 50. 
 
 Solubilities are given as grams of substance in 100 grams of water at the temp, 
 stated. " p n indicates grams per 100 grams of solution. "V" means volumes of 
 substance at o and 760 mms. per 100 volumes of water at the temp, stated. u Soluble " 
 infers solubility in either hot or cold water ; " insoluble " indicates solubility in neither. 
 (See also pp. 124, 125.) 
 
 For more complete tables, see Van Nostrand's "Chemical Annual" and Bieder- 
 mann's " Chemiker-Kalender " for current year; Dammer's " Handbuch der Anor- 
 ganischen Chemie;' 3 Beilstein's "Handbuch der Organischen Chemie;" Watts' 
 " Dictionary of Chemistry ; " and F. W. Clarke's " Specific Gravities." 
 
 INORGANIC COMPOUNDS 
 
 Formula, formula (molecular) weight, density, melting and boiling points, and 
 solubility in water. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16). 
 
 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, 
 
 Boiling 
 Point, 
 
 Solubility 
 in Water. 
 
 Aluminium 
 
 
 at./temp. 
 
 at./nims* 
 
 at ./mms. 
 
 at./temp. 
 
 bromide, Al 2 Br 6 (and + I2H 2 O) 
 
 5337 
 
 / 2-54; \ 
 
 \A. 18-62) 
 
 93 
 
 263 /747 
 
 soluble 
 
 chloride, A1 2 C1 6 (and + 1 2H 2 O) 
 
 267-0 
 
 A. 9-34/400 
 
 19071910 
 
 1827752 
 
 4 I / I 5 C W 
 
 iodide, A1 2 I 6 (and + 1 2H 2 O) . 
 
 8157 
 
 I A. 27} 
 
 185 
 
 3 60 
 
 soluble 
 
 nitrate, A1(NO 3 ) 3 .9H 2 O . . 
 
 375'3 
 
 
 T = 73 
 
 dec. 134 
 
 v. soluble 
 
 oxide, A1 2 O 3 . ... 
 
 IO2'2 
 
 3.7 A 
 
 
 
 ITlCr^l V\1o 
 
 phosphate, A1PO 4 .... 
 sulphate, A1 2 (SO 4 ) 3 . i8H 2 O . 
 
 I22-I 
 
 666-7 
 
 / 4 
 1-62 
 
 wh. heat 
 infusible 
 decomp. 
 
 
 
 insoluble 
 36/20 
 
 Potassium alum, 
 
 
 
 
 
 
 A1 2 (S0 4 ) 3 K 2 S0 4 .24H 2 
 Ammonium- 
 
 949-1 
 
 1757/20 
 
 8 4 '5 
 
 |2 3 H 2 
 \ at 190 
 
 96/15 
 357/ioo 
 
 ammonia, NH 3 
 
 
 /(liq.) -623/o\ 
 
 7 C 
 
 , 
 
 seep. 124. 
 
 
 j 
 
 I A. -5896 J 
 
 75 
 
 Jo b 
 
 
 acetate, NH 4 C 2 H 3 O 2 . . . 
 
 77-07 
 
 
 89 
 
 
 
 148/4 
 
 arsenate, (NH 4 ) 3 AsO 4 . 3H 2 O. 
 
 247-1 
 
 
 
 
 
 
 soluble 
 
 bromide, NH 4 Br 
 
 Q7'Q6 
 
 i 2-33/15 \ 
 
 S VI 1)1 1 111 CS 
 
 
 (66/10 
 
 
 y/ v w 
 
 ] A.i-64/440 / 
 
 
 
 \i 28/100 
 
 carbonate, (NH 4 ) 2 CO 3 . H 2 O 
 
 114-1 
 
 
 dec. 85 
 
 
 
 /W 
 
 chloride, NH 4 C1 
 
 cvco 
 
 ( i*52/i7\ 
 
 der ^Co 
 
 
 /35/I5 J 
 
 
 jj j 
 
 \ A. -89 / 
 
 vlCl- Oj 
 
 
 \seep.i25 
 
 chloroplatinate, (NH 4 ) 2 PtCl 6 . 
 
 444-0 
 
 3-06 
 
 decomp. 
 
 
 
 67/20 
 
 chromate, (NH 4 ) 2 CrO 4 . . . 
 
 152-2 
 
 1-88/11 
 
 decomp. 
 
 
 
 decomp. 
 
 iodide, NH 4 I 
 
 
 2*5 
 
 sublimes 
 
 
 
 v. soluble 
 
 molybdate,(NH 4 ) 2 MoO 4 . . 
 
 196-1 
 
 2-4 - 2-9 
 
 decomp. 
 
 
 
 decomp. 
 
 nitrate, NH 4 NO 3 .... 
 
 80-05 
 
 172/15 
 
 152 
 
 dec. 210 
 
 200/18 
 
 dec. or decomp. = decomposes ; v. = very ; wh. = white. 
 
MO 
 
 PHYSICAL CONSTANTS 
 
 INORGANIC COMPOUNDS (con /</.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (P = 16). 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, 
 C. 
 
 Boiling 
 Point, 
 C. 
 
 Solubility 
 in Water. 
 
 Ammonium (contd.} 
 nitrite, NH 4 NO 2 
 
 64-05 
 142'! 
 
 228-2 
 
 I93 1 
 132-2 
 76-12 
 
 360-0 
 226-6 
 
 297-5 
 123-2 
 
 501-0 
 
 288-4 
 
 34'4 
 320-4 
 
 332*3 
 
 336-6 
 400-7 
 
 3H7 
 181-3 
 132-0 
 170-0 
 
 77-98 
 328-8 
 
 4557 
 709-6 
 
 I97-9 
 229-9 
 
 333'2 
 i97'4 
 244'3 
 I39-4 
 39i'2 
 261-4 
 
 I53-4 
 169-4 
 
 233-4 
 
 168-9 
 80-02 
 177-2 
 
 at./temp. 
 17 
 
 r 5 
 
 1-77/20 
 1-31/13 
 
 4-15/23 
 |3-o6/26) 
 \ A. 8-1 f 
 
 2-35/20 
 
 A. 4-3/1 5 
 U-8 5 /26 
 \ A. 17-6 
 5-2-57 
 4-07 
 3-8 
 
 2-6 
 
 4-65 
 4-12/0 
 
 /37/I5 \ 
 \ A. 10-91) 
 2-2/0 ; A. 6-3 
 2-7 ; A. 4-57 
 A. -415 
 A. 2-7 
 
 4-4/13 
 
 3'93 
 3-6-4-1 
 
 3-9-4-2 
 
 3-85/24 
 4'3 
 3-1/24 
 
 4-2/0 
 
 4-92 
 
 3-24/23 
 
 47 - 5'5 
 4-96 
 
 *r 
 
 17/10 
 
 at./mms. 
 
 decomp. 
 decomp. 
 
 140 
 159 
 
 93 
 73-2 
 
 -6 
 -91-5 
 167 \ 
 subl. ii4/ 
 red heat 
 O/8oo 
 0/300 
 
 H 2 O/ioo 
 
 fusible 
 fusible 
 
 31 
 
 - 18 
 -8-5 
 - 80 
 - H3 
 
 146 
 
 70 
 subl. 218 
 red heat 
 
 anhy. 880 
 
 795 
 anhy. 960 
 volatile 
 740 
 
 575 
 Ba0 2 /45o 
 BaO/45o 
 infusible 
 
 601 
 c. 600 
 dec. r. ht. 
 
 at./mms. 
 
 dec. 280 
 dec. 170 
 
 280 
 223 
 
 i02/68 
 - 18 
 
 401 
 1550 
 
 0^/800 
 
 decomp. 
 volatilizes 
 
 221 
 
 I30-2 
 63 
 
 - 53 
 - 54-8 
 
 (394-414 
 \ V.D.i6-i 
 
 V.D. 13-8 
 decomp. 
 
 2H 2 O/ioo 
 dec. 1450 
 2H 2 0/n 3 
 1400 
 
 2H 2 O/ioo 
 
 at./temp. 
 
 soluble 
 
 4/15 
 58/0 
 
 03/15 
 76/20 
 162/20 
 
 decomp. 
 /8i6/i5 
 I =0/72* 
 decomp. 
 
 20 V. 
 
 decomp. 
 
 002/15 
 insoluble 
 insoluble 
 
 J5/9 
 { 36/100 
 insoluble 
 insoluble 
 
 decomp. 
 
 decomp. 
 decomp. 
 soluble 
 slgtly sol. 
 
 30/100 
 
 decomp. 
 1-7/16 
 
 245/12 
 
 103/15 
 0022/18 
 see p. 125. 
 decomp. 
 170/0 
 5/0 
 1-5/0 
 insoluble 
 0,23/18 
 
 soluble 
 v. soluble 
 44/30 
 
 oxalate, (NH 4 ) 2 C 2 O 4 . H 2 O . 
 persulphate, (NH 4 ) 2 S 2 O 8 . . 
 phosphomolybdate, 
 (NH 4 ) 3 P0 4 .i2Mo0 3 .3H 2 
 sulphate, (NH 4 ) 2 SO 4 . . . 
 sulphocyanate, N H 4 C N S . . 
 Antimony 
 bromide SbBrq . 
 
 chloride, tri-, SbCl 3 .... 
 
 ,, penta-, SbCl 5 . . 
 hydride SbH 3 . ... 
 
 iodide, tri-, SbI 3 
 
 oxide, tri-, Sb 2 O 3 .... 
 tetr-, Sb 2 O 4 .... 
 pent-, Sb 2 5 .... 
 
 potassium tartrate, 
 K(SbO)C 4 -H 4 O a .jH a O 
 
 sulphide, tri-, Sb 2 S 3 . . . 
 penta-, Sb 2 S 5 . . . 
 Arsenic 
 
 chloride, AsCl 3 . . . 
 
 fluoride, tri-, AsF 3 .... 
 penta-, AsF 6 . . . 
 hydride, AsH 3 
 
 iodide, di-, AsI 2 . . . . . 
 
 
 pent-, AsI 6 .... 
 oxide, tri-, As 2 O 3 . . . 
 
 pent-, As 2 O 6 .... 
 Barium- 
 bromide, BaBr 2 . 2 H 2 O . . 
 carbonate, BaCO 3 .... 
 chloride, BaCl 2 .2H 2 O. . . 
 hydride, BaH 2 ... 
 
 iodide, BaI 2 
 
 nitrate, Ba(NO 3 ) 2 .... 
 oxide, BaO. . . . 
 
 per-, BaO 2 .... 
 sulphate, BaSO 4 .... 
 
 Beryllium- 
 bromide, BeBr 2 
 
 chloride, BeCl 2 . 
 
 sulphate, BeSO 4 . 4H 2 O . . 
 
 anhy. = anhydrous ; dec. or decomp. = decomposes ; r. ht. = red heat ; subl. = sublimes ; 
 v. = very ; V.D. = vapour density ; oo = soluble in all proportions. 
 
Ill 
 
 PHYSICAL CONSTANTS 
 
 INORGANIC COMPOUNDS (contd.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16). 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, 
 C. 
 
 Boiling 
 Point, 
 C. 
 
 Solubility 
 in Water. 
 
 Bismuth 
 
 44776 
 3I4-38 
 
 484-11 
 464-0 
 
 5I2'2I 
 
 II7-38 
 
 68-0 
 70-0 
 
 62-0 
 
 272-24 
 183-32 
 308-48 
 128-4 
 208-47 
 769-54 
 
 325-62 
 168-27 
 133-82 
 149-82 
 194-82 
 
 199-93 
 100-09 
 uro 
 219-1 
 42-11 
 74-11 
 293-1 
 236-17 
 56-09 
 310-3 
 136-16 
 
 i53'84 
 68-00 
 28-00 
 44-00 
 44-07 
 76-14 
 
 246-63 
 328-5 
 172-25 
 
 712-84 
 86-92 
 
 at./temp. 
 
 5-6 
 
 ( f 6/U ) 
 I A. 11-35 / 
 
 2-8 
 8-8 - 9 
 7-7-8 
 
 1-35/0; A.4/i7 
 A. 2-3 
 1-83/4 
 
 1-43/15 
 
 4-7-4-9/H 
 3-6/15 
 2-4 
 6-9-8-1 
 
 47/15 
 3-05 
 
 3-97/20 
 27 
 4-02 
 3-69/28 
 
 3-3/20 
 2-7-2-9 
 
 2-3/20 
 1-65 
 17 
 2-08 
 4- 9 /20 
 1-82 
 3-08 
 3'2 
 2-96 
 
 r582/2I 
 
 A.^6 7 
 liq. 772/20 f 
 1-6-1-83 
 1-292/0 
 
 3-88/1 5'5 
 6-9-7 
 6-74 
 
 3-22 
 
 /liq. 3-87 \ 
 
 \ A. 3-007) 
 
 at./mms. 
 200-2I5 
 
 22 7 
 
 74 
 820-860 
 decomp. 
 
 -"1^7 
 577 
 
 184-186 
 
 571 
 ,590 
 59-5 
 infusible 
 
 1000 
 
 < red heat 
 631 
 decomp. 
 red heat 
 414 
 
 760 
 dec. 825 
 780 
 29 
 
 740 
 561 
 infusible 
 
 - 2 3 '8 
 
 -207 
 -65 
 
 -IIO 
 
 v. fusible 
 
 8H 2 O/63o 
 explosive 
 
 at./mms. 
 
 453 
 429 
 5H 2 0/8o 
 
 I8'2 
 101 
 
 H 2 O/ioo 
 
 806-812 
 c. 900 
 132 
 
 dec. 610 
 sublimes 
 
 decomp. 
 c. 8op 
 
 J 4 H 2 0/ 3 o, 
 }6H 2 O/2oo 
 
 c. 710 
 dec. 132 
 
 767 
 7/76i 
 -190 
 -78-2 
 
 46*2 
 -19 
 
 at./temp. 
 
 decomp. 
 decomp. 
 
 decomp. 
 insoluble 
 insoluble 
 
 decomp. 
 decomp. 
 16/102 
 
 4/i 8 
 
 48-9/1 8^. 
 140/20 
 ^127/18 
 insoluble 
 
 59/23 
 see p. 125. 
 
 v. soluble 
 174/10 
 decomp. 
 soluble 
 15/10 
 
 125/0 
 0018 cold 
 63/10 
 96/0 
 decomp. 
 see p. 125. 
 192/0 
 54-8/18 
 13/0 
 oo3--oo8 1 
 i 8/0 
 
 insoluble 
 
 * 
 
 see p. 124. 
 see p. 124. 
 
 2/0 
 
 soluble 
 insoluble 
 insoluble 
 
 16-5/0 
 
 200V/0 
 
 chloride, tri-, BiCl 3 . . . 
 
 ! nitrate, Bi (NO 3 ) 3 . 5 H 2 O . 
 oxide BiTOo 
 
 sulphide Bi 2 S 3 
 
 Boron 
 
 chloride BC1 3 
 
 fluoride BFo . . 
 
 i oxide BiOo 
 
 Borax. See Sodium borate. 
 Boric acid, H 3 BO 3 . . . . 
 Cadmium 
 
 chloride CdCl 2 
 
 nitrate, Cd(NO 3 ) 2 4H 2 O . . 
 oxide CdO 
 
 sulphate, anhy. CdSO 4 . . 
 hydr. 3CdSO 4 .8H 2 O 
 Caesium 
 carbonate, Cs 2 CO 3 .... 
 chloride CsCl . . 
 
 hydride CsH 
 
 hydroxide, CsOH .... 
 nitrate CsNO 3 
 
 Calcium 
 
 carbonate, CaCO 3 .... 
 chloride, anhy. CaCl 2 . . . 
 hydr. CaCl 2 . 6H 2 O. 
 hydride CaH 9 
 
 hydroxide, Ca( k OH) 2 . . . 
 iodide, CaI 2 (and + 6H 2 O) . 
 nitrate, Ca(NO 3 ) 2 4H 2 O . . 
 oxide CaO * 
 
 phosphate, Ca 3 (P0 4 ) 2 . . . 
 sulphate CaSO 4 
 
 Carbon 
 
 chloride, tetra-, CC1 4 . . . 
 oxide, sub- (1906), C 3 O 2 . . 
 mon-, CO .... 
 di- COo 
 
 sulphide, mono- CS . . . 
 bi-, CS 2 .... 
 Cerium 
 chloride (cerous), CeCl 3 . 
 oxide (cerous), Ce 2 O 3 . . . 
 (eerie), CeO 2 . . . 
 sulphate (cerous), 
 Ce 2 (S0 4 ) 3 8H 2 
 Chlorine- 
 oxide, mon-, C1 2 O .... 
 
 * Forms malonic acid. t Behn, Ann. d. Phys., 1900. anhy. = anhydrous ; 
 dec. or decomp. = decomposes j hydr. hydrated ; liq. = liquid ; v. = very. 
 
112 
 
 PHYSICAL CONSTANTS 
 
 INORGANIC COMPONDS (contd.) 
 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16) 
 
 Density, 
 gms./o.c. 
 
 Melting 
 Point, 
 
 Boiling 
 Point, 
 
 Solubility 
 in Water. 
 
 Chlorine (contd?) 
 
 
 at./temp. 
 
 at./mms. 
 
 at./mms. 
 
 at./temp. 
 
 oxide, di-, C1O 2 .... 
 
 67-46 
 
 1-5 ; A. 2-3 
 
 -76 
 
 9-97731 j 2oV/ 4 
 
 Chromium 
 
 
 
 1 
 
 chloride (chromous), CrCl 2 
 
 122-92 
 
 . 2 '75/H 
 
 
 
 
 
 v. soluble 
 
 (chromic), CrCl 3 
 
 158-38 
 
 \ A. 1 1/1200 j 
 
 
 
 c. 1300 
 
 slgtlysol. 
 
 oxide, Cr 2 O s 
 
 152-0 
 
 5-04 white heat 
 
 
 
 insoluble 
 
 tri-, CrO 3 . . . . 
 
 lOO'O 
 
 274 190 
 
 decomp. 
 
 62'I/O(^) 
 
 sulphate, Cr 2 (SO 4 ) 3 i5H 2 O 
 
 662-65 
 
 1-867/17 
 
 i5H 2 O/ioo 
 
 
 
 120/20 
 
 Cobalt 
 
 
 
 
 
 
 cobaltous chloride, 
 
 
 
 
 
 
 CoCl 2 (and + 6H 2 O) 
 
 129-9 
 
 2-94 
 
 subl. c. 87 
 
 
 
 29-5/0 
 
 hydrate, Co(OH) 2 
 
 93-02 
 
 3*6/15 
 
 
 
 
 
 insoluble 
 
 oxide, CoO . . 
 
 74-98 
 
 57 
 
 dec. 100 
 
 
 
 insoluble 
 
 sulphate, 
 
 
 
 
 
 CoSO 4 .7H 2 O 
 
 281-2 i -9 1 8/1 5 g6-8 
 
 
 
 26/3 
 
 cobaltic chloride, CoCl 3 . 
 
 165-35 
 
 2*94 sublimes 
 
 
 
 soluble 
 
 oxide, Co 2 O 3 . . . 
 
 165-95 
 
 5' 1 
 
 dec. r. ht. 
 
 
 
 insoluble 
 
 sulphate, Co 2 (S0 4 ) 3 
 
 406-15 
 
 
 
 
 
 
 
 soluble 
 
 Columbium. See Niobium. 
 
 
 
 
 
 
 Copper- 
 
 
 
 
 
 
 cuprous chloride, Cu 2 Cl 2 . . 
 
 198-06 
 
 /37 1 
 \ A. 6-6/1 600; 
 
 410 
 
 C. 1000 
 
 insoluble 
 
 oxide, Cu 2 O . . . 
 
 I43*H 
 
 5 -8-6' i red heat 
 
 
 
 insoluble 
 
 cupric chloride, CuCl 2 . . . 
 
 
 3*5 
 
 498 
 
 decomp. 
 
 75/17 
 
 nitrate, Cu(NO 3 ) 2 3H 2 O 
 
 241-64 
 
 2-17 
 
 114-5 
 
 (\ 70 
 i dec. r. ht. 
 
 }6o/2 5 (/>) 
 
 oxide, CuO .... 
 
 79*57 
 
 6-30 
 
 
 
 
 
 insoluble 
 
 sulphate, CuSO 4 5H a O 
 
 249-65 
 
 2-28/15 
 
 |4H 2 0/iooj 
 
 dec. r. ht. 
 
 seep. 125. 
 
 Cyanogen, C 2 N 2 
 
 52*02 
 
 niq.-866/i 7 > 
 1 A. i -806 } 
 
 -35 
 
 - 20-7 
 
 4'5 V/20 
 
 
 Erbium- 
 
 
 
 
 
 
 oxide Kr 2 O 3 
 
 382-8 
 
 8-6 
 
 infusible 
 
 
 
 insoluble 
 
 sulphate, Er 2 (SO 4 ) 3 8H 2 O. . 
 Gadolinium 
 
 j \j ** \j 
 
 767-14 
 
 
 dec. 950 
 
 
 
 23/20 
 
 sulphate, Gd 2 (S0 4 ) 3 . . . 
 
 602-81 
 
 4-14/15 
 
 
 
 
 
 2-3/34 
 
 Gallium- 
 
 
 
 
 
 
 chloride, tri-, GaCl, . . . 
 
 176-28 
 
 A. 12-2/240 
 
 75*5 
 
 220 
 
 decomp. 
 
 Germanium 
 
 
 
 
 
 
 chloride, tetra-, GeCl 4 . . . 
 
 2i4'34 
 
 1-89/18 
 
 
 
 86 
 
 decomp. 
 
 / r\ 
 
 oxide di- GeO 2 
 
 
 d*7O/l8 
 
 
 
 . 
 
 4/20 
 
 Glucinum. See Beryllium. 
 
 
 4 / y/ * 
 
 
 
 
 Gold 
 
 
 
 
 
 
 
 2Q V 5 
 
 
 
 288* 
 
 dec. 1 80 
 
 68 
 
 Hydrazine, NH 2 .NH 2 . . . 
 
 O^J J 
 
 32-05 
 
 1-01/15 
 
 
 113 
 
 v. soluble 
 
 hydroxide, 
 
 
 
 
 
 
 N 2 H 4 .H 2 O 
 
 50-07 
 
 1-030/21 
 
 < 40 
 
 119 
 
 v. soluble 
 
 Hydrobromic acid, HBr . . 
 
 80-93 
 
 I 1 ! 8 ) -86 
 \ A. 279/ 
 
 -687 
 
 [221/0 
 ,I30/I00 
 
 Hydrochloric acid, HC1 . . 
 
 36-47 
 
 929/0 f -112-5 
 
 -83'i/755 
 
 seep. 124. 
 
 Hydrocyanic acid, HCN . 
 
 27-02 
 
 697/18 -13*8 
 
 26-1 
 
 00 
 
 * Under chlorine at 1520 mms. f Rupert, 1909. dec. or decomp. = decomposes ; 
 
 liq. = liquid ; r. ht. = red heat ; subl. = sublimes ; v. = very ; oo = soluble in all proportions. 
 
113 
 
 PHYSICAL CONSTANTS 
 
 INORGANIC COMPOUNDS (contd.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16). 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, 
 C. 
 
 Boiling 
 Point, 
 C. 
 
 Solubility 
 in Water. 
 
 Hydrofluoric acid, HF . . . 
 
 Hydriodic acid, HI . . . . 
 
 Hydrogen 
 
 peroxide H On . . 
 
 20-01 
 
 127-93 
 
 34*02 
 81-22 
 
 34-08 
 129-52 
 33'03 
 
 233*3 
 '75*93 
 
 i95'85 
 126-8 
 7i*85 
 
 278-03 
 
 392-15 
 
 23i*55 
 162-23 
 404-02 
 159*7 
 
 399-91 
 
 379*2 
 267-1 
 277-8 
 460-94 
 223-1 
 685-3 
 239-1 
 303-2 
 
 73*88 
 42-40 
 68-95 
 29-88 
 133*8 
 
 IIO'O 
 
 84*32 
 203-34 
 256-44 
 40-32 
 
 335*2 
 246-5 
 
 at. /temp. 
 
 /988/1 5) 
 \ A. -691; 
 
 A. 4-38 
 
 1-458/0 
 A. 2-805 
 /liq. '9 \ 
 \ A. I-I78J 
 
 A. 4*39 
 
 1-227/14 
 
 3-11 
 
 4*63/0 
 
 j i -494/0) 
 i A. 6-5 / 
 
 2-99/18 
 
 1-88 
 
 1-81 
 
 5-5*4 
 / 2-8/11 \ 
 \ A. 11-2/320; 
 1-683/20 
 5*2-5*3 
 
 3*i/i8 
 
 2'5 
 6'4 
 5*8 
 6-12 
 
 *9'3 , 
 9-09/15 
 8-91-9-5 
 6-23 
 
 2'I I 
 
 2-2-07 
 2-3-2-4 
 2-10/15 
 
 2-4/15 
 2-21/15 
 
 3*o 
 1-56/17 
 1-46 
 
 3*2-3*7 
 1-64/15 
 1-678/16 
 
 at./mms. 
 
 - 9 2- 3 
 
 -51*3 
 
 -? 
 
 -64 
 
 -86 
 
 -48 
 33 
 
 ioi/i6atm. 
 iH 2 0/i 7 o 
 
 -197 
 64 
 
 301 
 47*2 
 
 3H 2 0/ 75 
 
 447 
 373 
 red heat 
 dc.5oo-53o 
 decomp. 
 937 
 
 618-710 
 491-600 
 c. 258 
 
 857 
 818-853 
 
 dec. 350 
 2H 2 O/ioo 
 90 
 
 >2000 
 
 5 H 2 0/i 5 o 
 
 at./mms. 
 
 I9*4 
 
 -36 7 /752 
 
 8o2/ 47 
 
 -42 
 
 -61-6 | 
 
 o 
 7o/6o 
 
 dec. 25 
 
 io27/764 
 volatilizes 
 
 6H 2 0/ioo 
 
 28o-285 
 decomp. 
 
 280 
 
 c. 900 
 861-954 
 
 dec. w. ht. 
 
 decomp. 
 H3 
 
 at./temp. 
 
 111/35 
 
 (42,500 
 \ V/io 
 
 v. soluble 
 33iV/i 3 
 3 o 5 V/i5 
 seep. 124. 
 soluble 
 soluble 
 
 soluble 
 75/16 p. 
 
 50/19 
 insoluble 
 
 20-8/10 
 
 fi8/o 
 
 I 78/75 
 insoluble 
 
 537/100 
 
 v. soluble 
 insoluble 
 
 v. slgt. sol. 
 
 46/15 
 decomp. 
 
 *7/o 
 04/0 
 
 002/20 
 
 insoluble 
 insoluble 
 004/18 
 
 seep.i25. 
 
 72/0 
 35/o 
 5/0 
 04 
 26/0 
 
 or 
 54/20 
 42/18^. 
 ooi 
 
 '02 
 
 27/0 
 
 selenide H^Se . . 
 
 sulphide H 2 S 
 
 telluride, H 2 Te 
 
 Hydroxylamine, NH 2 OH . . 
 Iodine 
 
 lodic acid, HIO 3 .... 
 Iron 
 
 carbonyl, Fe(CO) 5 .... 
 
 ferrous chloride, FeCl 2 . . 
 oxide, FeO .... 
 ,, sulphate, 
 FeSO 4 .;H 2 O 
 amm.sulphate,FeSO 4 . 
 
 (NH 4 ) 2 S0 4 6H 2 
 oxide (magnetic), Fe 3 O 4 . . 
 ferric chloride, FeCl 3 . . . 
 
 nitrate, Fe(NO 3 ) 3 9H 2 O 
 ,, oxide, Fe 2 O 3 .... 
 sulphate, 
 Fe 2 (S0 4 ) 3 (and + 9 H 2 0) 
 Lead- 
 acetate, Pb(C 2 H 3 O 2 ) 2 . 3H 2 O 
 ! carbonate, PbCO, .... 
 i chloride, PbCl 2 .'.... 
 
 iodide, PbI 2 
 
 oxide, mon- (litharge), PbO . 
 ,, red lead, Pb 3 O 4 . . . 
 per- (brown), PbO 2 
 sulphate, PbSO 4 . 
 
 Lithium- 
 carbonate, Li. 2 CO 3 .... 
 chloride, LiCl 
 nitrate LiNO 3 
 
 oxide, Li,O ... 
 
 phosphate, Li 3 PO 4 . H 2 O . . 
 sulphate, Li 2 SO 4 
 
 Magnesium 
 carbonate, MgCO s .... 
 chloride, MgCl 2 . 6H 2 O . . 
 1 nitrate, Mg(NO 3 ) 2 6H 2 O . . 
 i oxide, MgO 
 
 phosphate, Mg 3 (PO 4 ) 2 . 4H 2 O 
 sulphate, MgSO 4 . 7 H 2 O . . 
 
 atm. = atmospheres ; dc., dec., or decomp. = decomposes ; liq. = liquid ; slgt. = slightly ; 
 v. = very ; w. ht. = white heat. 
 
114 
 
 PHYSICAL CONSTANTS 
 
 INORGANIC COMPOUNDS (confd.) 
 
 
 - 
 
 For general heading, see p. 109. 
 
 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16) 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, 
 
 Boiling 
 Point, 
 
 Solubility 
 in Water. 
 
 Manganese- 
 
 
 at. /temp. 
 
 at./mms. 
 
 at./mms. 
 
 at. /temp. 
 
 carbonate, MnCO 3 .... 
 
 1 14*93 
 
 3-1-37 
 
 decomp. 
 
 
 
 v. slgt. sol. 
 
 chloride, MnCl 2 . 4H 2 O . . 
 
 197-9 
 
 1-91 
 
 87-6 
 
 
 
 107/10 
 
 nitrate, Mn(NO 3 ) 2 .6H 2 O . 
 oxide, -ous, MnO .... 
 
 287-05 
 70-93 
 
 1-82 
 
 87-5 
 white heat 
 
 dec. i29'4 
 
 54-5/I I/. 
 
 insoluble 
 
 -ic, MnX) 3 .... 
 
 157-86 
 
 4-3-4*8 
 
 
 
 
 
 insoluble 
 
 tetr-, Mn 3 O 4 .... 
 
 22879 
 
 4-7-4-9 
 
 
 
 
 
 1 insoluble 
 
 di-, Mn0 2 .... 
 sulphate,* MnSO 4 4H 2 O . . 
 
 86-93 
 223-06 
 
 47-5-0 
 2*1 
 
 dec. 390 
 
 i8and3o1 
 
 
 
 insoluble 
 111/54 
 
 Mercury 
 
 
 
 
 
 
 mercurous chloride, HgCl . 
 
 235-46 
 
 (6-48 and 7-2 } 
 { A. 8-21 / 
 
 400-500 
 
 sublimes 
 
 0002/18 
 
 nitrate, 
 
 
 
 
 
 
 HgNO 3 .2H 2 O 
 
 298-04 
 
 4-78 
 
 decomp. 
 
 
 
 v. soluble 
 
 sulphate, Hg 2 SO 4 
 
 496-07 
 
 7-56 
 
 melts, dec. 
 
 decomp. 
 
 2 cold 
 
 mercuric bromide, HgBr 2 . 
 
 359-84 
 
 57 
 
 244 
 
 subl. c. 322 i 1/9 
 
 chloride, HgCl 2 . 
 
 270-92 
 
 /5'3-5'5\ 
 I A. 9-8 f 
 
 287 
 
 303-307 
 
 \seep.i25- 
 
 iodide, red, HgI 2 . 
 
 453-84 
 
 (6-2-6-3 I 
 t A. i 5 -6/ 
 
 241-257 
 
 349 
 
 003/17 
 
 yellow, Hgl 2 
 
 453-84 
 
 / 5-9-6- 1 } 
 t A. 15-6; 
 
 241 
 
 349 
 
 insoluble 
 
 ., oxide, HgO . . . 
 
 2 1 6'0 
 
 11-14 
 
 dec. r. ht. 
 
 
 
 I -005/25 
 
 sulphate, HgSO 4 . 
 
 296-07 
 
 6-47 
 
 dec. r. ht. 
 
 
 
 decomp. 
 
 Molybdenum- 
 
 
 
 
 
 
 chloride MoCl 5 ... 
 
 273-3 
 128-0 
 
 A. 9-5/350 
 6-4/10 
 
 194 
 
 268 
 
 decomp. 
 insoluble 
 
 oxide, di- MoO 2 . . . 
 
 tri-, MoO 3 .... 
 
 144-0 
 
 TV 
 
 4-4/21 
 
 759 
 
 sublimes 
 
 2 cold 
 
 Nickel 
 
 
 
 
 
 
 carbonyl, Ni(CO) 4 .... 
 
 170-7 
 
 1-318/17 
 
 -25 
 
 43 
 
 insoluble 
 
 chloride NiCl 2 . 
 
 I2Q'6 
 
 
 sublimes 
 
 
 35/o(/) 
 
 nitrate, Ni(NO 3 ) 2 .6H 2 O . 
 
 i ^.y \j 
 290-8 
 
 2-06/14 
 
 567 
 
 136-7 
 
 
 sulphate, NiSO 4 .7H 2 O . . 
 
 280-86 
 
 1-98 
 
 98-100 
 
 
 
 31-5/9 
 
 Niobium 
 
 
 
 
 
 
 chloride, penta-, NbCl 5 . . 
 
 270-8 
 
 /4'4-4'5 \ 
 \ A. 9-6/360; 
 
 194 
 
 240-5 
 
 decomp. 
 
 Nitrogen- 
 
 
 
 
 
 
 nitric acid, HNO 3 .... 
 
 63-02 
 
 i-53/i5 
 
 -41-3 
 
 dec. 86 
 
 oo 
 
 nitrous oxide, N 2 O .... 
 
 44-02 
 
 | A. 1-614 ) 
 
 102 
 
 -8 9 - 4 /74i 
 
 /74V/i5 
 \seep.i24. 
 
 nitric NO .... 
 
 30-01 
 
 ( -0013 j 
 \ A. 1-039 / 
 
 -l6 7 
 
 -153 
 
 \seep.i24. 
 
 nitrogen trioxide, N 2 O 3 . . 
 
 76-02 
 
 I-447/-2 
 
 -III 
 
 decomp. 
 
 : soluble 
 
 peroxide, NO 2 or 
 
 
 
 
 
 
 N 2 4 
 
 46-OI 
 
 1-49/0 
 
 IOT 
 
 26 
 
 soluble 
 
 pentoxide, N 2 O g . 
 oxychloride, NOCI. 
 
 I08'02 
 65^7 
 
 1-64/18 
 
 30 
 -60 
 
 dec. 45-50 
 -5*6/7*1 
 
 soluble 
 decomp. 
 
 Osminm 
 
 
 
 
 
 
 oxide, tetr-, OsO 4 .... 
 
 25^9 
 
 A. 8-89 
 
 20 
 
 100 
 
 soluble 
 
 Ozone, O 3 
 
 48-00 
 
 (-00214 \ 
 1 A. 1-659; 
 
 dec. 270 
 
 -119 
 
 v. slgt. sol. 
 
 
 Palladium 
 
 
 V, J 77 
 
 
 
 
 chloride, PdCl 2 .2H 2 O . . 
 
 2I3-65 
 
 
 
 dec. r. ht. 
 
 
 
 soluble 
 
 * The ordinary salt ; also six other hydrates. t Stable between temps, given. 
 
 t Also anhy. and 6II 2 O. Density, p. 26. dec. or decomp. = decomposes ; 
 
 r. ht. = red heat ; slgt. = slightly j subl. = sublimes ; v. = very ; oo = soluble in all proportions. 
 
115 
 
 PHYSICAL CONSTANTS 
 
 INORGANIC COMPOUNDS (coxtd.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula j Densit 
 (0 W =f6). */.. 
 
 Melting 
 Point. 
 C. 
 
 Boiling 
 Point, 
 C. 
 
 Solubility 
 in Water. 
 
 Perchloric acid, HC1O 4 . . . 
 Fhosph or us 
 
 bromide, tri-, PBr 3 .... 
 
 chloride, tri-, PC1 3 .... 
 
 penta-, PC1 6 . . . 
 fluoride, tri-, PF 3 .... 
 oxide, tri-, P 4 O 6 
 tetr-, P 2 4 .... 
 pent-, P 2 O 5 .... 
 Phosphine PH 3 . . . 
 
 ioo'47 
 
 270-8 
 
 I373 
 208-3 
 88-04 
 
 220-2 
 I26-I 
 I42T 
 34-06 
 
 66-11 
 
 70-53 
 
 337'o 
 
 II9'02 
 
 138-2 
 
 122-56 
 
 74-56 
 294-2 
 65-11 
 329-21 
 
 422-36 
 
 56*11 
 214-02 
 
 166-1 
 
 lorn 
 158-03 
 174-27 
 136-18 
 97-18 
 
 386-24 
 
 230-9 
 120-9 
 266-97 
 
 229-32 
 lira 
 
 12922 
 
 145-22 
 
 170-14 
 104-3 
 
 at. /temp. 
 1-76/22 
 
 J2-Q2/0 \ 
 
 i 1 A. 9-706; 
 / r6 1 2/0 \ 
 | \ A. 4-875! 
 A. 3-6/296 
 A. 3-02 
 1-94/25 
 
 2-54/23 
 2-39 
 A. 1-185 
 1-007-1-016 
 
 2-76/20 
 2-29 
 2-34/17 
 1-99/15 
 2-69/4 
 1-52/16 
 1-82/17 
 
 1-85/17 
 2-04 
 3-97/18 
 ( 3-04/24 } 
 \A. 5-5/i32oj 
 2-1/4 
 
 2-70/10 
 
 2-66/20 
 2-24* ; 2-61 1 
 1-91 
 
 2'2 
 
 3-6i 
 
 2-91/17 
 
 3-95/I5 
 3-oi/i 5 - 7 
 2-95/15 
 
 11-520 } 
 \ A. 5-94) 
 A. 3-57 
 
 at./mms. 
 
 -35 
 -4i'5 
 
 112 
 148 
 
 -160 
 22-5 
 
 >IOO 
 
 subl. r. ht. 
 -133 
 
 <-IO 
 
 26 
 decomp. 
 
 750 
 c. 880 
 370 
 ^770 
 400 
 red heat 
 decomp. 
 
 3 H 2 0/6o-8o 
 red heat 
 560 
 
 614-723 
 
 ^345 
 dec. 240 
 1070 
 
 200 
 
 161 
 
 728 
 
 837 
 710 
 
 sub. c. 260 
 decomp. 
 58 
 
 -89 
 
 -102 
 
 at./mms. 
 I 9 /II 
 
 175 
 7 6 
 162 
 
 -95 
 173 
 c. 1 80 
 
 -85 
 
 57/735 
 sublimes 
 
 subl. w. ht. 
 dec. 8 10 
 dec. 400 
 subl. w. ht. 
 decomp. 
 red heat 
 
 subl. w. ht. 
 
 decomp. 
 
 sublimes 
 decomp. 
 
 dec. 740 
 
 dec. c. 145 
 260 
 
 57-5 
 -107 
 
 at./temp. 
 
 soluble 
 decomp. 
 
 55 
 
 
 soluble 
 
 v. soluble 
 slgtly sol. 
 insoluble 
 decomp. 
 
 v. soluble 
 
 seep. 125. 
 89/0 
 
 3/o 
 seep. 125. 
 5/0 
 122/103 
 
 33/4 
 
 28/12 
 seep. 125. 
 
 8/20 
 
 / 127/0 
 \seep.i25 
 eep 125. 
 
 6-4/15 
 9-2/10 
 36/0 
 217/20 
 
 soluble 
 
 v. soluble 
 
 84/10 
 43/io 
 
 decomp. 
 v. soluble 
 
 55 
 5 
 
 decomp. 
 
 5> 
 
 liquid, P 2 H 4 . . 
 Phosphonium chloride, PH 4 C1 
 Platinum 
 chloride, tetra-, PtCl 4 . . . 
 Potassium- 
 
 carbonate, K 2 CO 3 .... 
 chlorate KC1O 3 
 
 chloride KC1. . 
 
 chromate, bi-, K 2 Cr 2 O 7 . . 
 cyanide KCN 
 
 ferricyanide, K,Fe(CN) 6 . . 
 ferrocyanide, 
 K 4 Fe(CN) 6 .3H a O 
 hydroxide, KOH .... 
 iodate, KIO 3 
 
 
 nitrate, KNO S 
 
 permanganate, KMnO 4 . . 
 sulphate, K 2 SO 4 ..... 
 
 acid, KHS0 4 . . 
 sulphocyanate, KCNS . . 
 Radium 
 
 Rubidium 
 
 carbonate, Rb 2 CO 3 .... 
 chloride, RbCl 
 
 sulphate, Rb 2 SO 4 .... 
 Selenium- 
 
 oxide, SeO 2 
 
 Selenious acid, H 2 SeO 3 . . 
 Selenic acid, H 2 SeO 4 . . . 
 Silicon- 
 chloride, tetra-, SiCl 4 . . . 
 fluoride, SiF 4 
 
 
 * Monoclinic. f Rhombic, 
 amorph. = amorphous J cryst. = crystalline ; dec. or decomp. = decomposes ; r. ht. = red 
 heat ; sub. or subl. = sublimes ; v. = very ; w. ht. = white heat. 
 
116 
 
 PHYSICAL CONSTANTS 
 
 INORGANIC COMPOUNDS (contd.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16) 
 
 Density, 
 gms./c.c. 
 
 Melting Boiling 
 Point, Point, 
 C. C. 
 
 Solubility 
 in Water. 
 
 j 
 
 Silicon (contd.} 
 oxide (silica), amorph, SiO a 
 ., cryst., SiO 2 
 Silico chloroform, SiHCl 3 
 
 Silver- 
 bromide, AgBr 
 
 chloride, AgCl 
 iodide Agl 
 
 135-69 
 
 187-8 
 
 H3-34 
 234-8 
 169-89 
 311-83 
 
 382-16 
 102-92 
 106*0 
 84-01 
 58-46 
 40-01 
 149-92 
 85-01 
 78-00 
 
 358-2 
 142-07 
 
 322-23 
 252-18 
 
 248*22 
 
 247-5 
 147-6 
 
 158-5 
 
 2ir6 
 103-6 
 119-6 
 1837 
 
 64-07 
 
 80-07 
 
 iydroge 
 98-09 
 
 198-42 
 159*5 
 I75-5 
 
 at./temp. 
 2-2/16 ( 
 
 2-66 ] 
 
 I 1 ' 6 * i 
 1 A. 4-6J 
 
 m 6-47/25 
 
 5-67/25 5 
 435/19 
 54 
 
 169/17 
 2-4-2-5 
 
 2'2 
 2-17/20 
 2-13 
 3-65/18 
 
 2-27/20 
 
 2-8 
 
 1-52/16 
 
 2-67/20 
 
 I -492/20 
 
 1-56 
 1-73/17 
 
 4-2/24 
 
 3-6 
 3-05 
 
 3/17 
 3-6 
 546 
 37-4 
 
 n sulphide. 
 1-834/18 
 
 5-9/0 
 5-07/15 
 
 at./mms. at./mms. 
 
 indefinite 
 i 500- i 600 i 
 
 4 1*3 34 
 
 427 dec. 700 
 
 c. 540 
 218 dec. r. ht. 
 654-676 decomp. 
 
 red heat i 
 
 733-765 j 
 849 decomp. 
 
 C0 2 /2 7 
 
 80 1* w. heat 
 1 100 w. heat 
 603-695 
 
 c- 313 
 decomp. 
 
 38 i 3H 2 OA.i6o 
 884 
 
 7H 2 O/i5o decomp. 
 32-48 dec. 220 
 
 498-630 
 dec. 1 1 60 dec. r. ht. 
 ., f. Q,., (4H 2 O/6o \ 
 796-854 ,{6 H |o/ioo f 
 dec. 645 
 3000 
 decomp. 
 dec. w. ht. 
 
 10-5 dec. 40 
 
 175 327 
 dull r. ht. : < 700 
 decomp. 
 
 at./temp. 
 C. "OOI 
 
 insoluble 
 decomp. 
 
 : -0,8/20 
 
 6 3/2I 
 
 see p. 125. 
 
 77/17 
 
 soluble 
 77/o 
 see p. 125. 
 8/10 
 see p. 125. 
 
 63-5/I5 
 178/20 
 
 73/o 
 sol. ; dec. 
 
 3-9/10 
 see p. 125. 
 
 5 25/i 2 5 7 
 
 60/10 
 
 93/10 
 001/24 
 
 ts/io 
 
 35/o 
 decomp. 
 011/18 
 
 decomp. 
 
 CO 
 
 decomp. 
 insoluble 
 j> 
 
 nitrate, AgNO 3 
 
 sulphate, Ag 2 SO 4 .... 
 Sodium 
 borate (borax), 
 Na 2 B 4 O 7 . ioH a O 
 bromide NaBr 
 
 carbonate, Na 2 CO 3 .... 
 bi-, NaHCO 3 . . 
 i chloride NaCl . . 
 
 hydroxide, NaOH .... 
 ' iodide Nal 
 
 nitrate, NaNO 3 
 
 
 phosphate, di-, 
 Na 2 HPO 4 .i2H 2 O 
 sulphate, anhy., Na 2 SO 4 . . 
 hydr., 
 
 Na 2 SO 4 .ioH 2 O 
 
 sulphite, Na 2 SO 3 . 7H 2 O . . 
 thiosulphate (hypo'), 
 Na 2 S 2 3 .5H 2 
 Strontium 
 
 carbonate, SrCO 3 .... 
 chloride, SrCl 2 (and + 6H 2 O) 
 
 nitrate, Sr(NO 3 ) a .... 
 oxide, SrO 
 
 per-, SrO 2 .... 
 sulphate, SrSO 4 
 
 Sulphur- 
 dioxide, SO 2 .... 
 
 trioxide, SO 3 
 
 Sulphuretted hydrogen. See 
 Sulphuric acid, H 2 SO 4 . . 
 Tellurium 
 chloride, TeCl a 
 
 oxide, di-, TeO 2 
 
 tri-, TeO 3 .... 
 
 * Practically same for ordinary table salt as for pure salt (Harker). 
 anhy. = anhydrous ; dec. or decomp. = decomposes ; hydr. = hydrated ; r. ht. = red heat ; 
 w. ht. = white heat ; oo = soluble in all proportions. 
 
117 
 
 PHYSICAL CONSTANTS 
 
 INORGANIC COMPOUNDS (contii.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16) 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, 
 C. 
 
 Boiling 
 Point, 
 C. 
 
 Solubility 
 in Water. 
 
 Thallium- 
 carbonate, T1 2 CO S .... 
 
 chloride, tri-, T1C1, . . . 
 oxide (thallous), TJ 2 O . . . 
 sulphate, T1 2 SO 4 .... 
 Thorium 
 nitrate, Th(NO 3 ) 4 . I2H 2 O . 
 oxide ThO 2 
 
 468*0 
 310-38 
 424-0 
 504-07 
 
 696-2 
 264-0 
 
 189*92 
 260-84 
 
 135-0 
 151-0 
 
 189-94 
 80- 1 
 
 396-76 
 232-0 
 
 270-5 
 
 843-5 
 286-5 
 557-0 
 34i'42 
 
 502-62 
 
 192-9 
 182-1 
 
 125-37 
 136-29 
 
 287-55 
 97-44 
 
 122*6 
 
 at./temp. 
 7'I 
 
 6-77 
 9-87/15 
 
 (2-27/20) 
 
 I A. 9-2 f 
 6-3 
 6-6-6-9 
 
 r 176/0 \ 
 
 \ A. 6-836; 
 
 37-4-2 
 
 A. I3-3/350 
 
 7-2 
 
 10-9 
 7'3 
 5'i 
 
 8-4-9-2 
 
 2-81 
 
 ji-86 ) 
 \ A. 6-69) 
 3-5/20 
 
 4*4 
 2-91/25 
 ri-96 \ 
 
 \ 3-4 anhy./ 
 4*0 
 
 5-1-57 
 
 at./mms. 
 2 7 2 
 
 25 
 300 
 632 
 
 infusible 
 
 249 
 -33 
 dec. r. ht. 
 1130 
 
 -25 
 c. 1500 
 
 275 
 red heat 
 
 oxidises 
 decomp. 
 decomp. 
 
 fusible 
 59'5 
 
 -18 
 658 
 
 dec. 300 
 262 ? 
 
 6H 2 O/ioo 
 1050 
 
 infusible 
 
 at./mms. 
 
 decomp. 
 
 5) 
 
 decomp. 
 
 620 
 114-1 
 
 136 
 
 347 
 
 decomp. 
 118 
 
 154 
 
 730 
 ftH.OatH 
 [red heat./l 
 
 at./temp. 
 4/15 
 
 v. soluble 
 v. soluble 
 
 47/15 
 
 v. soluble 
 insoluble 
 
 270/15 
 soluble 
 insoluble 
 j> 
 
 decomp. 
 insoluble 
 
 
 
 
 
 ?> 
 320/18 
 
 200 
 
 soluble 
 0-8/20 
 
 0-001/15 
 33o/io 
 42/o 
 80-8/100 
 insoluble 
 
 
 
 Tin- 
 chloride (stannous), SnCl 2 . 
 
 (stannic), SnCl 4 . 
 
 oxide (stannous), SnO . . 
 (stannic), SnO 2 . . . 
 Titanium 
 
 chloride, tetra-, TiCl 4 . . . 
 oxide di- TiO? 
 
 Tungsten- 
 chloride, hexa-, WC1 6 . . . 
 oxide tri- WO 3 
 
 Uranium 
 
 oxide di- UO.> 
 
 (green), U 3 O 8 . . . 
 (yellow), U0 3 . . . 
 (black), U 2 5 . . . 
 Uranyl chloride, UO 2 C1 2 . . 
 nitrate, 
 UO 2 (NO 3 ) 2 .6H 2 O 
 Vanadium 
 
 chloride, tetra-, VC1 4 . . . 
 
 oxide, pent-, V 2 O 6 .... 
 Zinc 
 carbonate, ZnCO 3 .... 
 chloride ZnClo 
 
 sulphate, ZnSO 4 . 7H 2 O . . 
 
 sulphide ZnS . 
 
 Zirconium 
 
 
 anhy. = anhydrous ; dec. or decomp. = decomposes ; r. ht. = red heat ; v. = very. 
 FREEZING MIXTURES 
 
 Parts by weight. 
 
 Temp. Parts by weight. Temp. 
 
 i of NH 4 NO 3 , i of water . . 
 8 of Na 2 SO 4 , 5 of water . . 
 
 I5C. 2 of snov 
 - 17 NaCl 
 3 of snov 
 
 / or crushed ice, I ofl 
 
 - 1 8 
 
 -48 
 
 v, 4 of cryst. CaCl 2 . ! 
 
IIS 
 
 PHYSICAL CONSTANTS 
 
 ORGANIC COMPOUNDS 
 
 Formula (Molecular) Weight, Density, Melting and Boiling Points. 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16). 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, c C. 
 
 Boiling 
 Point, C. 
 
 Acetaldehyde, CH 3 .CHO .... 
 Acetic acid, CH 3 .COOH .... 
 Aceto-acetic ether, CH 3 CO . CH 2 CO 2 
 . C 2 H 5 
 
 44*03 
 60*03 
 
 1 30' i 
 58-05 
 
 26'02 
 
 72-03 
 240-I 
 58-05 
 76-46 
 99-08 
 I30T 
 
 88-10 
 
 88-10 
 88-10 
 
 88-10 
 93-07 
 1 08- 1 
 178-1 
 165-3 
 132-1 
 106-1 
 78-05 
 
 I22'0 
 I82T 
 I40-5 
 1 08 I 
 67-18 
 295-1 
 I54-I 
 I57-0 
 74-08 
 74-08 
 
 88-10 
 92-53 
 130-1 
 88-06 
 88-06 
 138-0 
 212-3 
 152-1 
 
 200-1 
 
 116-1 
 
 76-14 
 
 60-07 
 I53'8 
 
 at. /temp. 
 
 788/16 C. 
 
 .1-05/20 
 1-028/20 
 
 797/15 
 
 f46/-7\ 
 I A. -91) 
 1-062/16 
 
 858/15 
 
 937/19 
 1-017/10 
 879/20 
 812/20 
 
 825/0 
 
 825/0 
 
 814/15 
 1-023/15 
 99/25 
 1-15 
 
 1-52/15 
 1-55/4 
 1-05/15 
 879/20 
 
 T20/2I 
 1-098/50 
 1-212/20 
 1-043/20 
 
 2-3/18 
 I'OI 
 1-49/20 
 8l/20 
 8l 9 /22 
 812/20 
 887/20 
 
 77/20 
 96/19 
 950/20 
 
 1-23/19 
 992/10 
 1-19 
 929/20 
 
 1-292/0 
 2-104 
 1-582/21 
 
 at./mms. 
 -120 
 
 16-7 
 
 <-8o 
 -95 
 -81-5/895* 
 
 10 
 
 290 
 liquid 
 liquid 
 liquid 
 liquid 
 liquid 
 
 liquid 
 liquid 
 
 -12 
 
 -8 
 -37-8 
 216 
 liquid 
 decomp. 
 -i3'5 
 5'4 
 121-4 
 48 
 
 liquid 
 
 210 
 
 -31-1 
 liquid 
 
 5 2 
 liquid 
 
 -8 
 -79 
 
 200 
 
 234 
 176-4 
 178 
 8 
 
 no 
 ~3o 
 
 at./mms. 
 20'8 
 
 1 18-5, Y. 
 
 181 
 56-5 
 -85 
 140 
 430 
 96-7 
 46 
 
 I5i 
 148 
 
 137 
 
 129 
 II8-5/753 
 
 102-5 
 183-9 
 155 
 351 
 86 
 decomp. 
 179-5 
 80-2 Y. 
 249-2 
 306 
 198/749 
 206-5 
 187 
 107 
 sublimes 
 156, Y. 
 
 II7-5 
 99-8 
 
 113 
 
 78 
 141 
 162-3 
 
 155 
 
 sublimes 
 
 205-3 
 decamp. 
 205 
 
 46-2 
 gas 
 76-7, Y. 
 
 Acetone, CH. CO CH 3 
 
 Acetylene C 2 H 2 . 
 
 Acrylic acid, CH 2 : CHCO 2 H . . . 
 Alizarine, C 6 H 4 (CO) 2 C 6 H 2 (OH) 2 . . 
 Allyl alcohol, CH 2 : CH . CH 2 OH . 
 chloride, CH 2 : CHCH 2 C1 . . 
 thiocyanate, CH 2 : CHCH 2 CNS 
 Amyl acetate, C 6 H n . CH 3 CO 2 . . . 
 alcohol (n.), CH 3 (CH 2 ) 3 CH 2 OH 
 (act.),CH 3 C 2 H 6 CHCH 2 - 
 OH .... 
 
 (sec.),C 3 H 7 CH(OH)CH 3 
 (tert.), (CH 3 ) 2 C(OH> 
 C 2 H 5 
 
 Aniline, C 6 H 5 . NH 2 
 
 Anisol C 6 H 5 OCH 3 
 
 Anthracene, C 6 H 4 : C 2 H 2 C 6 H 4 . . . 
 Antimony trimethyl, Sb(CH 3 ) 8 . . . 
 Asparagine(l.)C 2 H 3 NH 2 CO 2 H.CONH 2 
 Benzaldehyde, C 6 H 5 CHO .... 
 
 Benzoic acid, C 6 H 5 . COOH . . . 
 Benzophenone, (C 6 Hj) 2 CO , . . . 
 Benzoyl chloride, C 6 H 5 COC1 . . . 
 Benzyl alcohol, C 6 H 5 CH 2 OH . . . 
 Beryllium ethyl, Be(C 2 H,) 2 . . . . 
 Bismuth triethyl, B5(C 2 H 5 ) 3 .... 
 Borneol (\.\ C 10 H 17 OH 
 
 Bromo benzene C R HBr 
 
 Butyl alcohol (n.),CH 3 (CH 2 ) 2 CH 2 . OH 
 (sec.),CH 3 CHOH.C 2 H 6 
 carbinol(tert.),(CH 3 ) 3 C.CH 2 OH 
 chloride, CH 3 (CH 2 ) 3 C1 . . . 
 ether (C.Ho'hO 
 
 Butyric acid (n.), CH 3 (CH 2 ) 2 COOH . 
 (iso), (CH 3 ) 2 CHCOOH. 
 Cacodylic acid, (CH 3 ) 2 AsO . OH . . 
 Caffeine, C 8 H 10 N 4 O 2 . H 2 O .... 
 Camphor, C 10 H 16 O 
 
 Camphoric acid (d.), C 8 H 14 (COOH) 2 . 
 Caproic acid, CH 3 (CH 2 ) 4 COOH . . 
 Carbolic acid. See Phenol. 
 Carbon bisulphide, CS 2 
 
 oxysulphide, COS .... 
 tetrachloride, CC1 4 .... 
 
 * Mackintosh, 1907; decomp. = decomposes; 1., = loevo-rotatory (see p. 78). Y., Young, 
 Journ. de Phys., Jan., 1909. 
 
119 
 
 PHYSICAL CONSTANTS 
 
 ORGANIC COMPOUNDS (contd.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16). 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, C. 
 
 Boiling 
 Point, C. 
 
 Cellulose, (C 6 H 10 6 ), 
 Chlor acetic acid, CC1H 2 . COOH . . 
 benzene C 6 HrCl 
 
 162-1 
 94-48 
 112-5 
 165-4 
 119-4 
 228-1 
 
 at./temp. 
 I-525 
 
 1-39/75 
 rii8/io 
 
 1 9 
 
 1-526/0 
 
 92 
 1-247 
 
 1-05/24 
 
 i 54 
 953/22 
 849/25 
 1-005 
 1-14/0 
 /liq. -866/1 7 i 
 \A. i -806 / 
 852/25 
 1-04 
 
 973 
 1-522/15 
 706/20 
 94/18 
 83/0 
 686/-6 
 34i/i5 
 '37 
 16 
 159 
 203/0 
 
 45/17 
 cliq.'446/o\ 
 I A. 1-036 / 
 718/17 
 9 o 3 /i8-5 
 
 1-028/20 
 
 79^7/15 
 699/8 
 1-05/16 
 
 1-45/15 
 898/18 
 (-921/0 j 
 
 \A. 2-2I9J 
 
 794/7 
 938/0 
 1-944/14 
 890/0 
 839/20 
 1-116/15 
 
 at./mms. 
 
 6 3 
 -40 
 
 -57 
 -70 
 250 
 - i 
 133 
 
 -7'5 
 153 
 
 -2-5 
 
 .3. 
 liquid 
 
 -35 
 liquid 
 
 -4 
 -40 
 liquid 
 
 liquid 
 48 
 9i 
 
 7o-5 
 54 
 
 112 
 -I7r4 
 
 -117 
 -83-8 
 
 <-8o 
 -112-3 
 
 ~ 85 , 
 111 116 
 
 -116 
 
 liquid 
 -103 
 
 liquid 
 
 22 
 112 
 
 at./mms. 
 
 1 86 
 132, Y. 
 
 97'5 
 61-2 
 sublimes 
 176 
 300 
 
 decomp. 
 1 80 
 170 
 191 
 dec. o 
 
 -20-7 
 175 
 
 877 
 190 
 
 55'5 
 213-5 
 
 103 
 8 to 9 
 280 
 297 
 
 255 
 310 
 116 
 330 
 
 -85-4/749 
 
 34A Y. 
 
 77-1 
 
 181 
 78-3, Y. 
 187 
 
 2IT2 
 
 38-4 
 120 
 
 I2'5 
 
 97 
 54-3, Y. 
 
 72-3 
 
 IIO'I 
 
 36-2 
 87 
 
 Chloral hydrate, CCJ 3 . CH(OH) 2 . . 
 Chloroform CHC1 3 . 
 
 
 Cineol C 10 Hi 8 O 
 
 154-2 
 148-1 
 
 132-1 
 192*1 
 
 121 I 
 I27-2 
 
 108-1 
 43-02 
 
 52-02 
 
 134-12 
 
 324-2 
 86-05 
 128-9 
 
 73'I3 
 149-2 
 86-08 
 
 457 
 178-1 
 168-1 
 154-1 
 169-1 
 92-49 
 
 I22'I 
 30-05 
 
 74'OS 
 88-06 
 
 I30-I 
 46-05 
 45-07 
 I50T 
 108-96 
 
 116-1 
 64-50 
 
 55-05 
 74-05 
 156-0 
 116-1 
 62-11 
 91-08 
 
 Cinnamic acid, C 6 H 5 CH : CHCOOH 
 aldehyde, C 6 H 5 CH : CH- 
 CHO 
 
 Citric acid, (CO 2 HCH 2 ) 2 C(OH)CO 2 H 
 + H 2 O 
 
 Collidine, a CH 3 . C 5 H 3 N . C 2 H 5 . . 
 Coniine (d.), i : 2, C 5 H 10 N . C 3 H 7 . 
 Cresol (o ) CH^C-H OH . . 
 
 Cyanic acid HCNO .... 
 
 
 Cymene (p.), CH 3 . C 6 H 4 . C 3 H 7 . . 
 
 Diacetyl, CH 3 CO . COCH 3 .... 
 Dichlor acetic acid, CHC1 2 . COOH . 
 Diethyl amine, (C 2 H 5 ) 2 NH . . . . 
 aniline, (C 2 H 5 )NC 6 H 5 . . . 
 ketone, C 2 H 5 COC 2 H 5 . . . 
 Dimethyl amine, (CH 3 ) 2 HN . . . 
 tartrate, (CH 3 ) 2 C 4 H 4 O 6 . . 
 Dinitrobenzene (m.), C G H 4 (NO 2 ) 2 . . 
 Diphenyl C H 5 C Hr 
 
 Uiphenylamine, (C G H 5 ) 2 HN . . . 
 Epichlorhydrine, C 3 H 5 C1O .... 
 | Erythrite, (CH 2 OH . CHOH -) 2 
 
 Ethane CH H CH 3 ... 
 
 Ether, C 2 H r OC 2 Hr 
 
 Ethyl acetate, CH 3 CO 2 .C,H r , . . . 
 aceto-acetate, CH 3 COCH.>CO 2 
 . C 2 H 5 
 
 alcohol, C 2 H OH 
 
 ,, amine, C 9 H 6 H 2 N .... 
 
 benzoate, C 6 H 5 CO 2 . C 2 H 5 . . 
 bromide, C 2 H 6 . Br .... 
 butyrate, C 3 H 7 . COOC 2 H 5 . . 
 
 ., chloride C 2 H 5 C1 . . . 
 
 ., cyanide, C 2 H 5 . CN .... 
 formate, HCOOC 2 H 5 .... 
 ,, iodide, C 2 HrI 
 
 isobutyrate(CH 3 ),CHCOOC 2 H 5 
 mercaptan, C 2 H 6 SH .... 
 nitrate, C 2 H F NO 3 .... 
 
 
 dec. or decomp. = decomposes. Y., Young, jfourn. de Phys., Jan., 1909. 
 
I2O 
 
 PHYSICAL CONSTANTS 
 
 ORGANIC COMPOUNDS (conti.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16). 
 
 Density, 
 gms./c.c. 
 
 at./temp. 
 896/16 
 I-I84/20 
 837/20 
 1-206/20 
 876/20 
 
 diq. -6 1 \ 
 \A. -9784/ 
 2-19/11 
 1-28/0 
 897/0 
 1-186/12 
 927/20 
 1-0779/0 
 i -024/20 
 
 1-22/20 
 
 /8 is/ -20 I 
 \A. 1-6 / 
 
 i-5S/o 
 1-625 
 1-159/20 
 
 1-54-1-57 
 
 1-26/20 
 ri6i 
 
 1-125/25 
 
 syrup 
 
 688/15 
 658/21 
 668/17 
 697/18 
 
 i'35 
 
 2-25/25 
 
 876/15 
 81/20 
 
 800/18 
 
 736/I5 
 949/20 
 628/14 
 917 
 789/20 
 
 Melting 
 Point, C. 
 
 Boiling 
 Point, C. 
 
 at /m ins. 
 
 99'o 
 231-5 
 92-6 
 280 
 I44-5 
 - 102 7 
 131-6 
 
 837 
 13-5/746 
 
 59'9 
 176 
 247-5 
 85-2. Y. 
 1008 
 
 -21 
 
 161 
 
 299 
 290 
 
 197-4 
 decomp. 
 dec. 160 
 with steam 
 
 98-4, Y. 
 69, Y. 
 58-1, Y. 
 261 
 
 subl. 156 ! 
 
 245 
 subl. & dec. 
 
 sublimes ; 
 
 140 
 1297 
 1 16'3 
 108-4 
 68 
 i55'5 
 27-9 
 90-93 
 82-8 
 
 Ethyl propionate, C 2 H 6 CO 2 C 2 H 5 . . 
 salicylate, C 6 H 4 (HO)CO 2 .C 2 H 6 
 sulohide (CoHe)oS 
 
 I02'I 
 
 1 66- 1 
 90-15 
 206- 1 
 1 30' i 
 
 28-03 
 187-9 
 98-93 
 44-03 
 98-93 
 154-1 
 164-1 
 96-04 
 46-02 
 
 30-02 
 
 1 80- 1 
 1 1 6-0 
 96-03 
 1 80- 1 
 198-1 
 132-1 
 92-06 
 75-08 
 62*05 
 76-03 
 58-02 
 92-03 
 
 TOO* I 
 
 86-12 
 86-12 
 27-05 
 
 262 2 
 II7-I 
 
 393-8 
 147-1 
 
 130-1 
 
 88-10 
 58-08 
 74-08 
 
 73-I3 
 88-06 
 72*10 
 
 102*1 
 00-06 
 
 at./mms. 
 
 liquid 
 
 - 169 
 
 9*5 
 -40 
 liquid 
 liquid 
 
 liquid 
 40 
 8-6 
 
 95 
 286 
 liquid 
 163 
 146 
 91 
 17 
 c. 234 
 -17-4 
 78 
 
 liquid 
 liquid 
 -14 
 
 52 
 119 
 
 201 
 -134 
 
 liquid 
 
 -79 
 
 liquid 
 
 tartrate (d.), C 4 H 4 O 6 (C 2 H 5 ) 2 . 
 valeriate, C 4 H 9 CO 2 C 2 H 5 . . . 
 
 Ethylene CH 2 : CH 2 
 
 bromide, di-, CH 2 Br . CH 2 Br 
 chloride, di-, CH 2 C1 . CH.,C1 
 oxide, <(CH,,) 2 .... 
 j Ethylidene chloride, CH 3 .CHC1 2 . . 
 Eucalyptol C 10 Hi 8 O .... 
 
 Eugenol, C 6 H 3 . (OH) . OCH 3 . C 3 H 5 
 Fluor benzene C 5 H 5 F 
 
 Formic acid H COOH 
 
 Formaldehyde, H . COH . . . . 
 
 Fructose (d.), CH 2 OH[CHOH] 3 CO- 
 CH 2 OH 
 
 Fumaric acid, (COOH . CH :) 2 . . 
 Furfural C 4 H 3 O COH 
 
 Galactose (d.), CHO[CHOH] 4 CH 2 OH 
 Glucose (d.), CHO(HCOH) 4 CH 2 OH . 
 Glutaric acid, COOH(CH 2 ) 3 COOH . 
 Glycerine, OHCH 2 .CHOH.CH 2 OH 
 Glycocoll, CH 2 NH 2 COOH .... 
 Glycol, CH 2 OH . CH,OH .... 
 Glycollic acid, CH 2 OH . COOH . . 
 Glyoxal, CHO .CHO . . 
 
 Glyoxalic acid, CHO. COOH + H 2 O . 
 Grape sugar. See Glucose. 
 Heptane (n.),CH 3 (CH 2 ) 5 CH 3 . . . 
 Hexane (n.), CH 3 (CH 2 ) 4 CH 3 . . . 
 di-isopropyl, [(CH 3 ) 2 CH] 2 . 
 Hydrocyanic acid, HCN 
 
 Indigo, C.H 4 <>C:C<^>C fl - 
 H 4 .... 
 
 Indol, C 6 H 4 NHCH : CH .... 
 ! lodoform, CHI 3 . 
 
 Isatine, C 6 H 4 <C>COH .... 
 
 Isoamyl acetate, CH 3 . COOC 6 H n . 
 alcohol,(CH 3 ) 2 CH(CH 2 ) 2 OH 
 Isobutane, (CH 3 ) 2 CHCH 3 .... 
 Isobutyl alcohol, (CH 3 ) 2 CH . CH 2 OH 
 amine,(CH 3 ) 2 CHCH 2 NH 2 . 
 Isobutyric acid, (CH 3 ) 2 CH . COOH . 
 Isopentane, (CH 3 ) 2 CHCH 2 CH 3 . . 
 Isopropyl acetate,CH,COOCH(CH<,) 2 
 alcohol, (CH 3 ) 2 HC(OH) ' . 
 
 cl., dextro-rotatory (see p. 78) ; dec. or decomp = decomposes ; subl. = sublimes ; Y., Young, 
 Journ. de Fkys., Jan., 1909. 
 
121 
 
 PHYSICAL CONSTANTS 
 
 ORGANIC COMPOUNDS (contd.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0= 16). 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, C 
 
 Boiling 
 Point, C. 
 
 Isopropyl amine, (CH 3 ) 2 CHNH 2 . . 
 cyanide, (CH 3 ) 2 CHCN. . 
 Isoquinoline, C 6 H 4 C 3 H 3 N .... 
 Isovaleric acid, (CH 3 ) 2 CHCH 2 COOH 
 Lactic acid (i.), CH 3 CHOH . COOH 
 Lactose. See Milk sugar. 
 Maleic acid, (COOH. CH:) 2 . . . 
 Malic acid (i.), COOH.CHOH .CH 2 - 
 .COOH 
 
 59-11 
 69-07 
 129-1 
 
 I02'I 
 90-05 
 
 1 1 6-0 
 134-0 
 
 lO-j-'O 
 
 360-2 
 230-0 
 
 1 20' I 
 
 16*03 
 32-03 
 74-05 
 
 3I-08 
 104-1 
 5048 
 46-05 
 
 60-06 
 60-03 
 142-0 
 
 I02'I 
 
 48-09 
 77-03 
 6l-03 
 48-04 
 88-06 
 I52T 
 62-I2 
 
 173*9 
 
 360-2 
 
 303'2 
 128-1 
 144-1 
 I43' 1 
 162*2 
 123-1 
 75'oS 
 61-07 
 114-1 
 
 282-3 
 256-3 
 132-1 
 70-08 
 
 I02'2 
 
 at./temp. 
 690/18 
 
 I-098/20 
 931/20 
 
 1-248/15 
 
 1-59 
 
 1-60/20 
 1-54/17 
 
 3'07 
 869/10 
 liq. '4 1 6/- 1 64 
 796/I5 
 941/14 
 (699/-ui 
 I A i -08 } 
 94/0 
 ( -920/1 8 \ 
 \A 1-73 / 
 A 1-62 
 725/0 
 986/11 
 2-285/15 
 912/0 
 
 1-217/15 
 991/15 
 
 937/0 
 1-182/15 
 845/21 
 
 2*493 
 525/20 
 
 152/15 
 
 224/4 
 
 01/20 
 
 I87/I4 
 056 
 
 1-144/15 
 719/0 
 
 '891/12 
 846/7-6 
 '994/20 
 
 751/20 
 
 9I7/0 
 
 at./mms. 
 
 liquid 
 liquid 
 24-6 
 -51 
 
 100 
 
 130-1 
 132 
 
 liquid 
 
 -184 
 -94-9 
 
 IOT2 
 
 gas 
 
 gas 
 liquid 
 
 liquid 
 gas 
 
 -30 
 liquid 
 
 203 dec. 
 
 80 
 95 
 5o 
 dec. 250 
 3-6 
 194-196 
 liquid 
 liquid 
 
 U 
 62-6 
 10-5 
 
 at./mms. 
 
 3i'5/743 
 107-108 
 240 
 176-3 
 83/1 mm. 
 
 decomp. 
 decomp. 
 
 f 
 164-5 
 
 164 
 64-7, Y. 
 57-1 
 
 -6-7/756 
 
 65 
 -24-1 
 
 -23-6 
 10-8 
 3i'9,Y. 
 
 42-3 
 92-3 
 
 A 5>8/ ? 5 , 2 
 
 65 explodes 
 
 12 
 
 -14 
 797 
 224 
 c. 3 8 
 98-5 
 decomp. 
 decomp. 
 
 2l8'I 
 
 c. 279 
 300 
 2467/745 
 209-4/745 
 114-4 
 101-7 
 125-8, Y. 
 
 286/100 
 278/100 
 124 
 50*6 
 
 178 
 
 Malonic acid, COOH . CH, . COOH . 
 Maltose, C 12 H 22 O U + H 2 O .... 
 Mercury methyl, (CH 3 ) 2 Hg . . 
 Mesitylene, 1:3:5, C 6 H 3 (CH 3 ) 3 . . 
 Methane, CH 4 ... 
 
 Methyl alcohol, CH,OH . 
 
 acetate, CH S COO.CH S . . . 
 ,, amine, CH 3 H 2 N . . . 
 
 borate, (CH 3 ) 3 BO 3 .... 
 chloride, CH 3 C1 . . . 
 
 ether, (CH 3 ) 2 O . . . 
 
 ethyl ether, CH 3 .O.C 2 H 5 . . 
 formate, HCOO. CH 3 . . . 
 iodide, CH.J .... 
 
 isobutyrate,(CH 3 ) 2 CHCOOCH 3 
 mercaptan, CH 3 . SH . . . 
 nitrate, CH 3 . NO 3 .... 
 nitrite, CH 3 .NO 2 
 
 phosphine, CH S H 2 P .... 
 propionate, C 2 H 5 COO . CH 3 . 
 salicylate, C 6 H 4 (OH)COOCH 3 
 sulphide, (CH 3 ) 2 S 
 
 Methylene bromide, CH 2 Br 2 . . . 
 Milk sugar, C 12 H 22 O n + H 2 O . . . 
 Morphine, C 17 H 19 NO 3 + H 2 O . . . 
 Naphthalene, C 6 H 4 : C 4 H 4 . . . 
 Naphthol (a), C 10 H 7 OH .... 
 
 Naphthyl amine (a), C 10 H 7 H 2 N . 
 Nicotine (l.),C 10 H 14 N 9 . 
 
 Nitro benzene, C 6 H 5 NO 9 . 
 
 ethane, C 2 H 5 NO 2 
 methane, CH 3 NO 2 .... 
 
 Octane (n.), CH 3 (CH 2 ) 6 CH 3 . . . . 
 Oleic acid, CH 3 (CH 2 ) 7 CH :CH(CH 2 ) 7 - 
 
 Palmitic acid, CH 3 (CH 2 ) 14 COOH . 
 Paraldehyde, (CH 3 . HCO) 3 . . . 
 Penta methylene, (CH 2 ). .' 
 
 5> )j diamine(cadaverine), 
 NH 2 (CH 2 ) 5 NH, ..... 
 
 
 dec. or decomp. = decomposes ; 1., Izevo-rotatory (see p. 78) ; Y., Young, Journ. de Phys., 
 Jan., 1909. 
 
122 
 
 PHYSICAL CONSTANTS 
 
 ORGANIC COMPOUNDS (ccntd.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 
 (0 = 16). 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, C. 
 
 Boiling 
 Point, C. 
 
 Pentane (n.), CH 3 (CH 2 ) 3 CH 3 . . . 
 Phenetol C 6 H 5 OC 2 H 5 
 
 72-10 
 
 I22'08 
 94-05 
 1 36' I 
 I03T 
 
 108-1 
 162-1 
 1 66- 1 
 148-0 
 
 93-07 
 229-1 
 44-07 
 74-05 
 
 102*0 
 60-06 
 78-5I 
 88-06 
 I70-0 
 42-05 
 1 20' I 
 79-08 
 
 I26-I 
 67-08 
 
 I29T 
 3243 
 8727 
 
 168-1 
 
 305-2 
 183-1 
 138-0 
 52-04 
 
 284-3 
 890-9 
 1 1 8-0 
 
 342-2 
 
 209-2 
 228-2 
 
 1 68- 1 
 150-0 
 
 150-0 
 1 66-0 
 154-1 
 
 at. /temp. 
 
 634/I5 
 963/25 
 1-06/33 
 1-23 
 roo8/I7 
 1-1/23 
 
 T'59 
 
 1-53/4 
 933/22 
 1-813 
 
 995/20 
 891/18 
 804/20 
 891/18 
 909/17 
 1745/20 
 A. 1-498 
 879/20 
 985/15 
 
 1-46/40 
 967/21 
 
 i '094/20 
 
 1-69/7 
 
 1-48/4 
 
 843/80 
 924/65 
 
 F588/ao 
 
 1-67 
 176/7 P. 
 176 
 
 at./mms. 
 
 liquid 
 
 -34 
 427 
 
 76-5 
 -17 
 23 
 218 anhy. 
 i 80-200 
 128 
 liquid 
 122-5 
 -195 
 
 22 
 
 liquid 
 
 gas 
 liquid 
 
 133 
 liquid 
 
 19-5 
 1749 
 205, dry 
 205 
 
 220 dec. 
 158 
 
 69-3 
 185 
 
 chars 
 125 
 
 142 anhy. 
 170 
 i/o 
 70 
 
 at./mms. 
 
 36'2, Y. 
 171 
 181-5 
 265 
 190 
 
 233 
 sublimes 
 
 284 
 129 
 explodes 
 
 -(38-39) 
 140 
 ior6 
 97-2 
 46-5 
 80-9, Y. 
 
 102 
 -50-2 
 169-8 
 
 117 
 
 293 
 131 
 
 241 
 
 sublimes 
 291/100 
 
 235 
 1 60 
 
 300 dec. 
 sublimes 
 
 Phenol C 6 H 5 .OH 
 
 Phenyl acetic acid, C 6 H 6 CH 2 COOH. 
 cyanide, CtLCN . 
 
 hydrazine, C 6 H 5 H N . N H 2 . 
 Phloroglucin, i : 3 :j, C 6 H 3 (OH) 3 2H 2 O 
 Phthalic acid, o. C 6 H/COOH) 2 . . 
 anhydride, C 6 H 4 <(CO) 2 >O 
 Picoline(a), CH 3 .C 5 H 4 N. . . . .' 
 Picric acid, 1:2:4:6, C 6 H 2 OH(NO 2 ) 3 . 
 Propane, CH 3 .CH 2 .CH 3 .... 
 Propionic acid, CH 3 .CH 2 .COOH . 
 Propyl acetate (n.), CH 3 COO . C 3 H 7 . 
 alcohol (n.), CH 3 CH 2 CH 2 .OH 
 chloride (n.), CH S CH 2 CH 2 C1 . 
 formate, H . COO . C 3 H r . . 
 iodide, CH 3 .CH 2 .CH 2 I . . 
 Propylene, CH 3 .CH:CH 2 .... 
 Pseudo-cumene, 1:2:4, C 6 H 3 (CH 3 ) 3 
 Pyridine, CH 5 N . 
 
 Pyrogallol ( ic acid, or "pyro"), 
 1:2:3, C,Ho(OH) q . 
 
 Pyrrol, (CH; 4 >NH 
 
 Quinoline, i C 6 H 4 < C 1 J I ; c C ^ 1 > 
 Quinine, C2oH 24 N 2 O 2 
 sulphate, (C 20 H 24 N 2 O 2 ) 2 .- 
 H 2 SO 4 4- ;H 2 O .... 
 Bacemic acid, (COOH . CH(OH)) 2 - 
 + H 2 O 
 
 Rochelle salt (d .), KNaC 4 H 4 O G . . . 
 Rosaniline (p.), (C 6 H 4 NH 2 ) 3 COH . . 
 Saccharin, C 6 H 4 < COSO 2 > NH . 
 Salicylic acid, OH . C C H 4 . COOH. . 
 Sodium ethyl, NaC 2 Hr. . . 
 
 Stearic acid, CH 3 (CH 2 ) 16 COOH . . 
 Stearine,(C 18 H 35 2 ) 3 C 3 H 6 . . , . 
 Succinic acid, COOH(CH 2 ) 2 COOH . 
 Sugar, cane-, C^H^On 
 
 Sulphanilic acid (p.), NH 2 .C 6 H 4 .SO S H 
 . 2H 2 O. ... 
 
 Sulphonal,(CH 3 ) 2 CCS0 2 C 2 H 5 ) 2 . . . 
 Tartaric acid (i. or meso), COOH- 
 [CHOH] 2 COOH.H 2 O 
 
 (d.), COOH(CHOH) 2 - 
 COOH 
 (1.), COOH(CHOH) 2 - 
 COOH 
 Terephthalic acid (p.), C 6 H 4 (COOH) 2 
 Terpenol, C, H 18 O .... 
 
 
 anhy. = anhydrous ; d. = dextro-rotatory (see p. 78) ; P., Perkin ; dec. = decomposes ; 
 1., Izevo-rotatory (see p. 78); Y., Young. | 
 
 
123 
 
 PHYSICAL CONSTANTS 
 
 ORGANIC COMPOUNDS (contd.) 
 For general heading, see p. 109. 
 
 Substance and Formula. 
 
 Formula 
 weight 
 (0 = 16). 
 
 Density, 
 gms./c.c. 
 
 Melting 
 Point, C. 
 
 Boiling 
 Point, C. 
 
 Terpineol CioH 17 HO 
 
 154-1 
 343'S 
 180-2 
 59-09 
 76*12 
 
 150-1 
 179-1 
 92-06 
 107*1 
 107-1 
 163-4 
 
 IOT2 
 I62-I 
 
 Il8'I 
 59-08 
 120-0 
 253-1 
 
 74'08 
 76-07 
 
 2I3-I 
 I36-I 
 60' 1 1 
 I02'I 
 1 06' I 
 1 06' I 
 
 106-1 
 
 123-5 
 95-42 
 
 at./temp. 
 936/20 
 
 I-42 
 
 -994/0 
 I-3U 
 
 866/20 
 999/20 
 ro46/- 
 1-63/61 
 
 735/15 
 1-15/17 
 812/15 
 673/0 
 
 2-30/18 
 786/20 
 >i 
 
 865/15 
 1-32 
 943/20 
 
 756/I4 
 878/0 
 862/20 
 1-182/18 
 1-386/10 
 
 at./mms. 
 
 35 
 53 
 330 
 -12-5 
 1 80 
 
 50 
 
 -97 
 liquid 
 
 45 
 52-3 
 liquid 
 
 liquid 
 liquid 
 
 25 
 liquid 
 
 121*2 
 
 132 
 
 -58-5 
 -28 
 
 -54 
 
 -^ 
 
 -40 
 
 at. /nuns. 
 
 218 
 
 decomp. 
 200 dec. 
 
 232 
 78 
 in 
 197 
 198 
 195 
 -89 
 (Ho/736 
 \ dec. 
 127/744 
 3'5 
 
 <IOO 
 
 no 
 82-9 
 41 
 
 decomp. 
 
 159 
 decomp. 
 186-4 
 142 
 139-8 
 138 
 118 
 46 
 
 Tetrabromethylene, CBr 2 . CBr 2 . . 
 Theobromine C-HoN^Oi 
 
 Thiocyanic acid HCNS .... 
 
 Thiourea, NH 2 .CS.NH 2 .... 
 Thymol, 3:2:1, (CH 3 ) 2 : CH . C 6 H 3 - 
 (CHo)OH . 
 
 Tin tetramethyl, Sn(CH 3 ) 4 .... 
 Toluene, C 6 H 5 .CH S 
 
 Toluidine (o.), CH 3 C f H 4 .NH 2 . . . 
 (p.), CH 3 C 6 H 4 NH 2 . . . 
 Trichloracetic acid, CC1 S . COOH . 
 Tritthyl amine, (C 2 H 5 ) 3 N .... 
 
 arsine, (C 2 H 5 ) 3 As .... 
 
 phosphine, (C 2 H 5 ) 3 P . . . 
 Trimethyl amine, (CH 3 ) 3 N .... 
 arsine, (CH 3 ) 3 As . . . . 
 bismuth, (CH 3 ) a Bi . . . 
 carbinol, (CH S ) 3 C . OH . 
 phosphine, (CH 3 ) 3 P. . . 
 Trinitro benzene (s.), 1:3:5, C 6 H 3 - 
 (NO 2 ) 3 
 
 Turpentine (pinene), C 10 H 16 . . . . 
 Urea, NH 2 . CO. NH 2 
 
 Valeric acid (n.),CH 3 (CH 2 ) 3 . COOH 
 ! Xylene (o.), C,H 4 (CHA, .' 
 
 ,, (m), 
 
 (p), 
 
 Zinc ethyl, Zn(C 2 H 5 ) 2 
 
 methyl, Zn(CH 3 ) 2 
 
 dec. or decomp. = decomposes. 
 
 ELECTROCHEMICAL EQUIVALENTS 
 
 Faraday's laws of electrolysis are expressed by m = izt, where ;;/ is the mass in 
 grammes of an ion liberated in / sees, by a current of i amperes ; ss is the electro- 
 chemical equivalent of the ion, i.e. the mass liberated by I ampere in I second. 
 The exactness of Faraday's laws is obscured in many cases by secondary 
 chemical reactions, and the values of the different electrochemical equivalents are 
 practically always derived by calculation from that of silver, which has been 
 accurately determined (see p. 8). Electrochemical equivalents are proportional 
 to chemical equivalents. 
 ~, . , atomic weight of element 
 
 Element. Chemical eq 
 Silver 107-88; 
 
 alency of element for electrolyte used 
 uivalent. z. 
 'i . . . o'ooiu83 gm. sec." 1 amp." 1 
 2 ... 0-003294 
 i ... 0-11968 (seep. 106) 
 
 
 Hydrogen. . . . rob8/ 
 
 
124 
 
 SOLUBILITIES 
 
 SOLUBILITIES OF GASES IN WATER 
 
 AIR IN WATER 
 
 1000 c.cs. of water saturated with air at a pressure of 760 mms. contain the 
 following volumes of dissolved oxygen, etc., in c.cs. at o and 760 mms. 
 
 Temperature of Water. 
 
 0C. 5 C 
 
 10 
 
 15 C 
 
 20 25 30 
 
 Oxygen 
 
 Nitrogen, argon, etc 
 
 Sum of above 
 
 % of oxygen in dissolved air (by vol.) 
 
 c.cs. 
 
 10*19 8-9 
 
 19-0 , 16-8 
 
 29-2 25.7 
 
 34*9% 347 
 
 7'9 
 15-0 
 
 22'8 
 34'5 
 
 7'0 
 I3-5 
 
 20-5 
 
 34-2 
 
 6'4 
 12-3 
 187 
 
 5-8 5'3 
 1 1*3 10-4 
 I7'i | 157 
 
 GASES IN WATER 
 
 S indicates the number of c.cs. of gas measured at o and 760 mms. which dis- 
 solve in i c.c. of water at the temperature stated, and when the pressure of the gas 
 plus that of the water-vapour is 760 mms. 
 
 A indicates the same, except that the gas itself is at the uniform pressure of 760 
 mms. when in equilibrium with the water. (For other values, see p. 109.) 
 
 Gas. 
 
 Ammonia, A 
 
 Argon, A 
 
 Carbon dioxide, A . . 
 Carbon monoxide, A . . 
 
 Chlorine, S 
 
 Helium, A . . . . . 
 Hydrogen, A . . . . 
 Hydrochloric acid, S . . 
 
 Nitrogen, A 
 
 Nitrous oxide, A . . . 
 Nitric oxide, A . . . . 
 
 Oxygen, A 
 
 Sulphuretted hydrogen, A 
 Sulphur dioxide, S 
 
 oc. 
 
 c cs. 
 
 1300 
 058 
 
 035 
 
 0150 
 0215 
 
 506 
 
 0239 
 
 1-05/5 
 
 074 
 049 
 
 4-68 
 
 79-8 
 
 10 
 
 910 
 
 045 
 1-194 
 
 028 
 3-09 
 
 0144 
 
 0198 
 
 474 
 
 0196 
 
 88 
 
 057 
 
 038 
 
 56-6 
 
 15 C 
 
 20 
 
 802 j 710 
 
 040 | -037 
 
 1-019 -878 
 
 025 | -023 
 
 2*63 i 2'26 
 
 0139 -0138 
 
 0190 '0184 
 
 458 
 0179 
 
 74 
 051 
 
 '034 
 
 47'3 
 
 442 
 
 0164 
 
 63 
 
 047 
 031 
 2-67 
 
 39*4 
 
 30 C 
 
 595/28 c 
 030 
 66 
 
 020 
 
 177 
 0138 
 
 411 
 0138 
 
 040 
 026 
 
 27-2 
 
 40 
 
 50 
 
 60 
 
 027 
 
 "53 
 oi 8 
 1-41 
 0139 
 
 '44 
 oi 6 
 
 I '20 
 
 0140 
 
 386 362 
 
 oi 1 8 -0106 
 
 035 
 023 
 
 031 
 
 021 
 
 18-8 
 
 36 
 015 
 ro 
 
 339 
 
 oioo 
 
 029 
 019 
 
 , 
 
 Ne, -0147/20 ; Kr, '0670 - -0788/20 ; Xe, -1109/20 - Antropoff, 1910 
 
 MUTUAL SOLUBILITIES OF LIQUIDS 
 
 The data for the uppermost layer of the two solutions in equilibrium are given 
 in the first line in each case. The pressure in some cases exceeds one atmosphere. 
 Numbers are grams per 100 grams of solution. (Fi om data in Seidell's " Solubilities.") 
 
 Liquids. 
 
 (Water in ether ; ethereal layer . . . . 
 \Ether in water ; aqueous layer . . . . 
 
 | Aniline(C 6 H 6 N H 2 ) in water ; aqueous layer 
 \Anilineinwater; aniline layer . . . . 
 
 (Phenol (C 6 H 6 OH) in water ; aqueous layer 
 \Phenol in water ; phenol layer . . . . 
 
 (Triethylamine in water ; amine layer . . 
 \Triethylamine[N(C 2 H 5 ) 3 ]in aqueous layer 
 
 (CS 2 in methyl alcohol ; alcoholic layer . 
 \CS 2 in CH,OH ; carbon bisulphide layer 
 
 0C. 
 
 ro 
 12 
 
 r 
 
 ri 
 
 87 
 
 75 
 75 
 
 51-91 at 72 
 
 20 
 
 6-5 
 3*2 
 
 95-5 
 
 8-3 
 72 
 
 5 ! 
 97 |9 
 
 40 
 
 W |50 
 
 1-517 
 4-54'i 
 3'5- 
 95 
 
 9-6 
 67 
 
 96 
 
 60 
 
 rS 
 37 
 
 70 80 
 
 2-02-2 
 
 - .4-5 
 93 
 
 100 
 
 6 
 92 
 crit. 
 
 3'6 2'9 2'2j 
 
 80-51 at crit. temp. 
 
125 
 
 SOLUBILITIES 
 
 1 
 
 
 
 
 
 
 
 
 SOLUBILITIES OF 
 
 SOLIDS IN WATER 
 
 s = number of grams of anhydrous substance 
 
 which when dissolved in 100 grams 
 
 of water make a saturated solution at the temperature stated. 
 
 p = no. of grams of anhydrous substance per 100 grams of saturated solution. 
 The formula given is that of the solid phase which is in equilibrium with the 
 
 solution. (See Seidell's "Solubilities," New York, 1907, where the most complete 
 
 and accurate data will be found for solubilities.) For other 
 
 solutions 
 
 , see p. 109. 
 
 Substance. 
 
 
 oc. 
 
 10 
 
 15 
 
 20 
 
 40 
 
 60 
 
 80 
 
 100 
 
 Am. chloride, NH 4 C1 
 
 s 29*4 
 
 33*3 
 
 35*2 
 
 37-2 
 
 45* 
 
 8 
 
 55*2 
 
 
 65-6 
 
 77'3 
 
 Barium chloride, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 BaCl 2 .2H 2 
 
 
 s 31-6 
 
 33'3 
 
 
 34*4 
 
 357 
 
 407 
 
 46-4 
 
 
 52-4 
 
 58-8 
 
 Barium hydrate, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ba(OH) 2 .8H 2 O . 
 
 s 1-67 
 
 2-48 
 
 
 3' 2 3 
 
 
 3*89 
 
 8- 
 
 22 
 
 20*9 
 
 
 101-4 
 
 
 
 Bromine (liquid\ Br. 
 
 S 4*22 
 
 3'4 
 
 
 3' 2 5 
 
 
 3'20 
 
 
 
 
 
 
 
 
 
 
 Cadmium sulphate, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CdS0 4 .8/ 3 H 2 . 
 
 s 76-5 
 
 76*0 
 
 76-3 
 
 76-6 
 
 78- 
 
 5 
 
 837 
 
 
 697* 
 
 6077* 
 
 Ca. hydrate, Ca(OH) 2 
 
 s -185 
 
 176 
 
 
 170 
 
 
 165 
 
 
 
 141 
 
 116 
 
 094 -077 
 
 Copper sulphate, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CuSO 4 .5H 2 O. . 
 
 s 
 
 H'3 
 
 17-4 
 
 
 18-8 
 
 207 
 
 28- 
 
 5 
 
 40*0 
 
 
 55' 
 
 ! 75'o 
 
 Li. carbonate, Li 2 CO H 
 
 s 
 
 
 i'43 
 
 
 1-38 
 
 
 i'33 
 
 r 
 
 17 
 
 I '01 
 
 850; 720 
 
 Merc.chloride,HgCl 2 
 
 p 3-50 
 
 4-50 
 
 
 5-00 
 
 5-40 
 
 9-30 
 
 I4'o 
 
 
 23*1 
 
 38-0 
 
 Potass, chloride 
 
 , KC1 
 
 s 27-6 
 
 31-0 
 
 
 32-4 
 
 34'o 
 
 40*0 
 
 45'5 
 
 
 51-1 
 
 567 
 
 Potass, bromide 
 
 ,KBr 
 
 
 53'5 
 
 59'5 
 
 62-5 
 
 65-2 
 
 75' 
 
 5 
 
 85-5 
 
 
 95'o 
 
 104 
 
 Potassium iodide, KI 
 
 s 127-5 
 
 136 140 144 
 
 160 
 
 
 176 
 
 
 192 
 
 (208 
 
 Potassium hydrate, 
 
 
 
 
 
 
 
 
 
 
 
 KOH.2H 2 O 
 
 
 s 97-0 
 
 103 107 112 
 
 138 
 
 
 
 
 
 
 i78 
 
 Potass.nitrate,KNO 3 
 
 s 13*3 
 
 20'9 
 
 
 25-8 
 
 32 
 
 64 
 
 
 I 10 
 
 
 169 
 
 246 
 
 Silv. nitrate, AgNO 3 
 
 S 122 
 
 170 
 
 196 
 
 222 
 
 376 
 
 
 525 
 
 
 669 
 
 952 
 
 Sodium carbonate, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Na 2 CO 3 .ioH 2 O . 
 Sod. chloride, NaCl 
 
 S 
 
 s 
 
 7-0 
 357 
 
 125 
 
 35'8 
 
 16-4 
 35'9 
 
 2 
 
 3 
 
 5-o 
 
 46-1 II 
 36-6 
 
 46*0 
 
 37 
 
 
 45-8 
 38 
 
 45*5 
 39' 
 
 Sodium sulphate, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Na 2 SO 4 .ioH 
 
 2 . 
 
 s 
 
 5-0 
 
 9-0 
 
 
 I3-4 
 
 19-4 
 
 49 1 
 
 45 1 
 
 
 44 1 
 
 42 1 
 
 Strontium chloride, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 SrCl 2 .6H 2 O 
 
 . 
 
 s 
 
 43 
 
 48 
 
 
 5 
 
 53 
 
 65 
 
 
 82 
 
 
 9i t 
 
 101 | 
 
 Succinic acid, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 (CH 2 ) 2 (COOH) 2 . 
 
 s 
 
 2-80 
 
 4-50 
 
 
 57 
 
 6-9 
 
 16-2 
 
 35-8 
 
 
 70-8 
 
 125 
 
 Sugar (Cane), 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 C 12 H 22 O n . 
 
 
 s 
 
 79 
 
 190 197 
 
 204 
 
 238 
 
 
 287 
 
 
 362 
 
 487 
 
 * Solid phase becomes CclSO 4 . H 2 O at 74. 
 
 t Becomes Na 2 SO, at 32'38. 
 
 \ Becomes SrCl 2 . 2H,O at 70. 
 
 Becomes KOH .3H 2 O at 32 
 
 '5 and KOH . H 2 O 
 
 at 50. 
 
 || Becomes Na 2 Co 3 . H 2 O at 35. 
 
 
 COMPOSITION OF DRY ATMOSPHERIC AIR 
 
 (Ramsay, Proc. Roy. Soc., 1908 
 
 ; G. Claude, Compt. Rend., 
 
 1909.) 
 
 
 
 N 2 
 
 2 
 
 A 
 
 C0 2 
 
 Kr 
 
 Xe 
 
 Ne 
 
 He 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 By weight . 
 
 75'5 
 
 23-2 
 
 1*3 
 
 046 to '4 
 
 028 
 
 005 
 
 o 3 86 
 
 0,56 
 
 By volume . 
 
 78-05 
 
 21'0* 
 
 '95 
 
 03 to -3 
 
 
 
 
 0,123 
 
 
 * 20*91 according to Kreusler. 
 
126 
 
 MINERALS 
 
 MOHS' SCALE OF MINERAL HARDNESS 
 
 The numbers are not quantitative, but merely indicate the sequence of hardness. 
 
 Hardness. Mineral. 
 
 Hardness. Mineral. Hardness. 
 
 Mineral. 
 
 1. Talc 
 
 5 Apatite 9 
 
 Corundum 
 
 2 Rock salt 
 
 6 Felspar 10 
 
 Diamond 
 
 3 Calcspar 
 
 7 Quartz c 2 '5 
 
 Finger-nail 
 
 4 Fluor spar 
 
 8 Topaz Ct 6 . 5 
 
 Penknife 
 
 COMPOSITION, DENSITY, AND HARDNESS OF SOME MINERALS 
 
 See Dana's "System of Mineralogy" and Appendices, 1892, 1899, and 1909. 
 
 Radioactive minerals are indicated thus * ; see Szilard, Le Radium, August, 1909. 
 
 Name and Formula. 
 
 Density. 
 
 Hard- 
 ness. 
 
 Name and Formula. 
 
 Density. 
 
 Hard- 
 ness. 
 
 Albite, Na 2 Al 2 Si 6 Oi 6 . . 
 
 C.2'6 
 
 6-7 
 
 Mica (common, Musco- 
 
 2-7-3-1 
 
 2-2-5 
 
 Amber (fossil resin) . . 
 
 ro8 
 
 2-2-5 
 
 vite), 
 
 
 
 Anhydrite, CaSO 4 . . 
 
 2-8-2-9 
 
 3-3*5 
 
 K 2 O.3Al 2 3 .6SiO 2 .2H 2 
 
 
 
 Anorthite, Ca 2 Al 4 Si 4 O 16 . 
 
 c. 2-7 
 
 6-7 
 
 Mica (Biotite, Magnesia 
 
 2-7-3-1 
 
 2-5-3 
 
 Apatite, 
 
 2-9-3-2 
 
 5 
 
 mica) 
 
 
 
 Ca5(Cl,F,OH)(P0 4 ) 8 
 
 
 
 Monazite,* (CeLaDi)PO 4 
 
 5 
 
 5-2 
 
 Aragonite, CaCO 3 . . . 
 
 2-93 
 
 3'5-4 
 
 (i-i6%Th) 
 
 
 
 Augite, 
 
 3*2-3'5 
 
 5-6 
 
 Nepheline, 
 
 2-5-2-6 
 
 5-5-6 
 
 Mg,Fe,Ca,Al silicate 
 
 
 
 Na 6 K 6 Al 8 Si 9 36 
 
 
 
 Barytes, Heavy spar, 
 
 4'5 
 
 3-3-5 
 
 Olivine, Mg 2 Fe 2 SiO 4 . . 
 
 3-3-3-5 
 
 6-7 
 
 BaSO 4 
 
 
 
 Orthoclase, K 2 Al 2 Si 6 O I6 . 
 
 2*4-2-6 
 
 6 
 
 Beryl, Be 3 Al 2 Si 6 O 18 . . 
 
 2-6-2-7 
 
 7-8 
 
 Pitchblende,* U 3 O 8 with ( 
 
 6-4 
 
 
 Broggerite,* a pitch- 
 
 (56-68% 
 
 (2-8% 
 
 oxides of Pb, and Ca, 
 
 (mas- 
 
 
 blende which contains 
 
 U) 
 
 Th) 
 
 Fe,Bi,Mn,Mg,Cu,Si,A 
 
 sive) 
 
 5-5 
 
 thorium 
 
 
 
 Al, etc. (25-80% U; 
 
 9-7 
 
 
 Calcite, Calcspar, Iceland 
 
 2-6-27 
 
 c- 3 
 
 1-6 %Th) I 
 
 (cryst.) 
 
 
 spar, CaCO 3 
 
 
 
 Pyrites (iron), FeS 2 . . 
 
 4-8-5-1 
 
 6-6-5 
 
 Carnallite, 
 
 r6 
 
 i 
 
 (copper), CuFeS 2 
 
 4*1-4-3 
 
 3-5-4 
 
 KCl.MgCl 2 6H 2 O 
 
 
 
 Pyrolusite, MnO 2 . . . 
 
 4-8-5 
 
 2-5-5 
 
 Carnotite,* 
 
 (c. 55% 
 
 (yel- 
 
 Quartz, SiO 2 .... 
 
 2-5-2-8 
 
 7 
 
 K. 2 0(U 2 5 ) 2 V 2 5 . 3 H 2 
 
 U) 
 
 low) 
 
 Rock salt, NaCl . . . 
 
 2*1-2-2 
 
 2-2-5 
 
 Celestine, SrSO 4 . . 
 
 VQ 
 
 J--I-C 
 
 Rutile TiO 2 .... 
 
 J.*2 4."} 
 
 6-6-; 
 
 Cerussite, PbCO 3 ... . 
 
 3 s 
 
 6-4 
 
 j j j 
 3-3-5 
 
 Selenite cryst. gypsum 
 
 4^ 4 J 
 
 u u 5 
 
 Chalcolite,* 
 
 3-4-3-6 
 
 2-2-5 
 
 Serpentine, H 4 Mg 3 Si 2 O 9 
 
 f.2'6 
 
 3-4 
 
 Cu(U0 2 )(P0 4 ) 2 .8H 2 0; 
 Cle'veite * pitchblende 
 
 (48% U) 
 (c. 60% 
 
 (c. 4% 
 
 Spinel, MgOAl 2 O 3 . . 
 Svlvine, KC1 .... 
 
 3-5-3-6 
 I-Q-2 
 
 8 
 
 2 
 
 which contains Th & Y 
 
 U) 
 
 Th) 
 
 Talc, H 2 Mg 3 Si 4 12 . . 
 
 2-5-2-8 
 
 I 
 
 Corundum, A1 2 O 3 . . . 
 
 3-9-4-2 
 
 9 
 
 Thorianite,* Th, U ox- 
 
 8-9-7 
 
 7 
 
 Dolomite, CaMgC 2 O 6 . 
 
 2-8-2-9 
 
 3'5-4 
 
 ides, etc. ; (4-10% U ; 
 
 
 (black 
 
 Felspar, Al 2 K 2 Si 6 16 . . 
 
 2-4-2-6 
 
 6 
 
 c. 60% Th) contains He 
 
 
 cubes) 
 
 Flint ; agate, SiO 2 . . 
 
 2'6 
 
 c.6 
 
 Thorite* ThSiO 4 (1-9% 
 
 4-6 
 
 (tetra- 
 
 fluorspar, Fluorite, CaF 2 
 
 3-3'3 
 
 4 
 
 U ; 40-60% Th) 
 
 
 gonal) 
 
 Galena, PbS .... 
 
 7-4-7-6 
 
 2-3 
 
 Tourmaline, hydrated si- 
 
 2-9-3-3 
 
 7-7-5 
 
 Gummite,* Pb,Ca,U, silic 
 
 ate(5o 
 
 65% U) 
 
 licate and borate of Al, 
 
 
 
 Gypsum, CaSO 4 2H 2 O . 
 
 2-3 
 
 1-5-2 
 
 Na with Li or Fe or Mg 
 
 
 
 Haematite, Fe 2 O 3 . . . 
 
 4-5-5-3 
 
 5-5-6-5 
 
 Trogerite,* 
 
 (53% 
 
 (ye!- 
 
 Hornblende, 
 
 2-9-3'4 
 
 5-6 
 
 (U0 2 ) 8 As 2 O 8 i2H 2 O 
 
 U) 
 
 low) 
 
 Ca,Mg,Fe, Na,Al, silicate 
 
 
 
 Uraninite * crystalline 
 
 (Black 
 
 octahe- 
 
 Kainite,MgSO 4 KCl3H 2 O 
 
 2'I 
 
 
 
 pitchblende (q.v.} 
 
 
 dra) 
 
 Kaolin, H 4 Al 2 Si 2 O 9 . 
 
 2'5 
 
 i 
 
 Uranite lime,* 
 
 3-3-2 
 
 2-2-5 
 
 Kieserite, MgSO 4 H 2 O 
 
 2-55 
 
 3 
 
 CaO(U0 2 ) 2 (P0 4 ) 2 8H 2 
 
 
 
 1 Lepidolite (Lithia mica) 
 
 2-8-3 
 
 2-5-4 
 
 (50% U) 
 
 
 
 i (F,OH) 2 (Li,K,Na) 2 Al 2 - 
 
 
 
 Willemite, Zn 2 SiO 4 . . 
 
 4 
 
 5 
 
 Si 3 9 
 
 
 
 Wolfram, (Fe,Mn)WO 4 . 
 
 7-1-7-9 
 
 5-5-5 i 
 
 Limestone, CaCO 3 
 
 2-5-2-8 
 
 
 
 Wollastonite, CaSiO 3 . 
 
 2-7-2-9 
 
 4-5-5 
 
 Magnesite, MgCO 3 . 
 
 ^3 
 
 3'5-4-5 
 
 Zeunerite,* Cu,U arse- 
 
 (f. 50% 
 
 (tetra- 
 
 Magnetite, Fe 3 O 4 . . 
 
 4-9-5-2 
 
 5-5-6-5 
 
 nate 
 
 U) 
 
 gonal) 
 
 Meerschaum, 
 
 c. 26 
 
 2-2-5 
 
 Zircon,* ZrSiO 4 . . . 
 
 47 
 
 7'5 
 
 2MgO.3SiO 2 .2H 2 O 
 
 
 
 Zincblende, ZnS . . 
 
 3-9-4-2 3-5-4 
 
127 
 
 GRAVIMETRIC FACTORS 
 
 FACTORS FOR GRAVIMETRIC ANALYSIS 
 
 Calculated with atomic weights for 1911 (p. i). 
 Example. i gram A1 2 O 3 is chemically equivalent to "5303 gram Al, or 
 i gram Al is equivalent to 17*5303 A1 2 O 3 . A table of reciprocals is given on p. 136. 
 (See Van Nostrand's " Chemical Annual," London.) 
 
 ' 1 part by weight of 
 
 is equivalent 
 (by weight) to 
 
 1 part by weight of 
 
 is equivalent 
 (by weight) to 
 
 Aluminium. 
 
 A1 2 O 3 . ... 
 
 5303 Al 
 3-350 A1 2 (SO 4 ) 3 
 
 1-216 NH 3 
 1-288 NH 4 
 3-819 NH 4 C1 
 2-058 NH 4 OH 
 
 1-1997 Sb.,O 3 
 1-3328 Sb 2 5 
 1-1109 Sb 2 O 5 
 7897 Sb 
 9474 Sb 2 O 3 
 1-0526 Sb 2 O 3 
 
 7575 As 
 1-1617 As 2 O 5 
 6521 As 
 3938 As 
 5i99As 2 O 3 
 6040 As 2 O 5 
 4827 As 
 6373 As 2 O 3 
 7403 As 2 O 5 
 
 6960 Ba 
 7771 BaO 
 5885 Ba 
 6570 BaO 
 7255 Ba0 2 
 
 3626 Be 
 
 1-1154 Bi 2 O 3 
 8966 Bi 
 8017 Bi 
 8942 Bi 2 O 3 
 
 3H3 B 
 2-7297 Na 3 B 4 O 7 . 
 ioH 2 O 
 
 4256 Br 
 8754 Cd 
 
 i -060 Cs 2 O 
 3945 Cs 
 4184 Cs 2 O 
 
 1-399 Ca 
 4005 Ca 
 5604 CaO 
 2-275 CaCO 3 
 
 Calcium (contd.) 
 Ca 3 (P0 4 ) 2 . . . 
 Mg 2 P 2 7 . . . . 
 
 PA 
 Carbon. 
 
 CO, 
 
 5422 CaO 
 1-3935 Ca 3 (P0 4 ) 2 
 2-1844 Ca 3 (P0 4 ) 2 
 
 4-4860 BaCO 3 
 2-2748 CaCO 3 
 
 2474 Cl 
 6066 Cl 
 
 6846 Cr 
 1-3154 CrO 3 
 
 1-2713 CoO 
 7343 Co 
 9336 CoO 
 1306 Co 
 1661 CoO 
 1416 Co 
 
 1-2517 CuO 
 4866 F 
 
 1-5395 AuCl 3 
 1119 H 
 5405 I 
 
 1-2865 FeO 
 1-4297 Fe 2 O 3 
 7-0218 FeSO 4 . 
 (NH 4 ) 2 S0 4 .6H 2 O 
 7773 Fe 
 I'll 13 Fe 2 O 3 
 1-4508 FeCO 3 
 9666 Fe 3 O 4 
 1-6330 FeO 
 2-6330 FeCO 3 
 
 1-0773 pb 
 6831 Pb 
 7358 PbO 
 7887 PbO 3 
 7536 Pb 3 4 
 
 1879 Li 
 4044 Li 2 O 
 179/Li 
 3868 Li 2 O 
 
 Ammonium. 
 
 N . . 
 
 
 
 
 NH S .... 
 
 Chlorine. 
 
 AgCl 
 
 Antimony, 
 Sb 
 
 NaCl 
 
 
 Chromium. 
 
 Cr Oo 
 
 Sb O> 
 
 Sb 2 O 4 . . . 
 
 
 j) 
 
 Cobalt. 
 Co 
 
 Arsenic. 
 
 As.,(X , 
 
 Co.,O< . 
 
 
 
 Co(N0 2 ) 3 .(KN0 2 ) 3 
 
 (CoS0 4 ) 2 .(K 2 S0 4 ) 3 
 Copper. 
 Cu . . ... 
 
 As 2 O 5 
 
 MgNH 4 AsO 4 4H 2 O 
 > 
 
 Mg 2 As 2 7 . . . 
 ,, ... 
 ,, ... 
 Barium. 
 BaCO 3 .... 
 ,, .... 
 BaSO 4 
 
 Fluorine. 
 
 CaF 
 
 Glucinum. See 
 Beryllium. 
 Gold. 
 Au 
 
 Hydrogen. 
 H 2 
 Iodine. 
 Agl 
 
 
 
 Beryllium. 
 
 ReO 
 
 Bismuth. 
 
 Bi 
 
 Iron. 
 Fe 
 
 Bi O, 
 
 ) 
 
 BiOCl 
 
 
 FeO 
 
 Boron. 
 
 B O 
 
 
 Fe 9 O, . 
 
 Bromine 
 
 Ap-Br 
 
 
 CO, 
 
 
 Cadmium. 
 
 CdO . . . 
 
 Lead. 
 
 Pb 
 
 Caesium. 
 Cs 
 
 PbSO 4 . . 
 
 Cs 2 PtCl 6 .... 
 
 Calcium. 
 Ca 
 
 
 
 Lithium. 
 
 Li 2 CO 3 .... 
 
 Li s pp 4 : .' : ; 
 
 5> .... 
 
 CaCO 3 .... 
 
 5) .... 
 
 CO 2 . . 
 
 
128 
 
 GRAVIMETRIC FACTORS 
 
 FACTORS FOR GRAVIMETRIC ANALYSIS (conti.) 
 
 1 part by weight of 
 
 is equivalent 
 (by weight) to 
 
 1 part by weight of &$$& 
 
 Magnesium. 
 
 M^O 
 
 6032 Mg 
 2184 Mg 
 3621 MgO 
 
 rui3 Mn 2 O 3 
 7203 Mn 
 9307 MnO 
 1-0350 Mn 2 O 3 
 1-1399 MnO 2 
 
 1-1603 HgS 
 8963 Hg 2 
 9308 HgO 
 
 1-2727 NiO 
 3-8551 N 2 5 
 
 4362 P 
 2787 P 
 8534 P0 4 
 6378 P 2 O 5 
 
 4015 Pt 
 
 6933 Ptci 4 
 
 5202 KC1 
 6338. KBr 
 7071 KI 
 4863 KCN 
 5244 K 
 3285 K 
 1-2316 K 2 CO 3 
 8395 K 2 
 5403 K 2 O 
 
 Potassium (contd.) 
 KoSO 4 
 
 1-1604 KNO 3 
 1609 K 
 
 2953 Rb 
 4693 Si 
 
 7526 Ag 
 *5744 Ag 
 '4595 Ag 
 
 4078 NaCl 
 3691 Na 2 
 3238 Na 
 4364 Na 2 O 
 1-5740 NaNO 3 
 
 7019 SrO 
 5641 SrO 
 
 1460 H 2 S 
 
 1374 s 
 
 2744 SO 2 
 3429 S0 3 
 4115 S0 4 
 
 7881 Sn 
 
 8482 U 
 9620 UO 2 
 8817 U 
 
 1-2448 ZnO 
 8033 Zn 
 
 Mg 2 P 2 7 .... 
 .... 
 Manganese. 
 MnO 
 
 K 2 PtCl 6 .... 
 Rubidium. 
 Rb 2 PtCl c . . . 
 Silicon. 
 
 SiO 
 
 Mn 3 O 4 
 
 j 
 
 Silver. 
 
 Ao-Pl 
 
 
 
 Mercury. 
 Hg 
 
 Agl 
 Sodium. 
 AgCl 
 NaHCO 3 . . . 
 Na 2 SO 4 .... 
 .... 
 N.O. 
 
 HffS 
 
 
 Nickel. 
 
 Ni ... 
 
 Nitrogen. 
 N 
 
 Strontium. 
 SrC0 3 .... 
 SrS0 4 .... 
 Sulphur. 
 BaSO 4 .... 
 
 Phosphorus. 
 
 P,0 6 
 Mg 2 P 2 7 .... 
 ) .... 
 .... 
 Platinum. 
 K 2 PtCl 6 .... 
 
 Potassium. 
 AgCl ..... 
 
 AcrRr 
 
 
 
 
 Tin. 
 SnO 2 
 
 Agl 
 
 AcrCN 
 
 Uranium. 
 U.O. 
 
 rt.g^.l> 
 KC1 
 KBr 
 
 ^ 3 w 8 
 
 UO 2 
 
 KOH 
 
 
 K SO. 
 
 Zinc. 
 Zn 
 
 ZnO 
 
 A *-2 ovy 4 ' 
 
 SOME BOILING-POINT MIXTURES 
 
 Boiling-points under 760 mms. of mercury. Percentage compositions by weight. 
 A large number of minimum boiling-point mixtures are known. 
 
 (Sidney Young, " Fractional Distillation," 1903.) 
 
 Maximum 
 
 boiling- 
 point 
 mixtures. 
 
 Mixture. 
 
 Water I Nitric acid 
 
 I Hydrochloric acid 
 
 Formic acid 
 
 Me. ether Hydrochloric acid 
 
 Boiling Points 
 
 iooC. 
 
 100 
 100 
 
 -23-6 
 
 I %ofA 
 
 Mixt inmixt. 
 
 86 i25 c 
 
 8o I 1 10 
 
 100-8 I 107 
 
 c. - 80 - 2 
 
 32% 
 80 
 
 23 
 61 
 
 Ob- 
 server. 
 
 Roscoe 
 
 Friedel 
 
 minimum 
 boiling- 
 point 
 mixtures. 
 
 Water 
 Pyridine 
 Benzene 
 Me.alcohol 
 
 Ethyl alcohol 
 Water 
 
 Methyl alcohol 
 Acetone 
 
 100 
 
 117 
 80-2 
 647 
 
 78-3 
 
 100 
 
 647 
 56-5 
 
 78-1 
 92-5 
 58-3 
 
 55*9 
 
 4-4 Y.&F. 
 59 G.&C, 
 
 60 
 
 Y. & F. 
 Pettit 
 
 G. & C., Goldschmidt and Constan ; Y. & F., Young and Fortey. 
 
129 
 
 THE EXPONENTIAL O~ x 
 
 e 271828. To derive e* use reciprocals on p. 136. e~ ' 6g315 = '5. 
 
 (Based on Newman, Trans. Camb. Phil. Soc., 13, 1883.) 
 
 For values of x from -0000 to '0999. 
 
 Subtract Differences. 
 
 X 
 
 
 
 001 
 
 002 
 
 003 
 
 004 
 
 005 
 
 006 
 
 007 
 
 008 j'009 
 
 0001 234 
 
 5 
 
 6789 
 
 oo 
 
 rooo 
 
 9990 
 
 9980 
 
 9970 
 
 9960 
 
 995o 
 
 9940 
 
 9930 -9920 -9910 
 
 1234 
 
 5 
 
 6789 
 
 01 
 
 9900 
 
 9891 
 
 9881 
 
 9871 
 
 9861 
 
 9851 
 
 9841 
 
 9831 -9822 
 
 98l2 
 
 1 2 3 4 
 
 S 
 
 6789 
 
 02 
 
 9802 
 
 9792 
 
 9782 
 
 '9773 
 
 9763 
 
 '97 S3 
 
 '9743 
 
 97341-9724 
 
 9714 
 
 1234 
 
 5 
 
 6789 
 
 i '03 
 
 9704 
 
 9695 
 
 9685 
 
 9675 
 
 9666 
 
 9656 
 
 9646 
 
 96371-9627 
 
 9618 
 
 1 2 3 4 
 
 5 
 
 6789 
 
 ! '04 
 
 9608 
 
 9598 
 
 95*9 
 
 '9579 
 
 9570 
 
 9560 
 
 955o 
 
 954i|'953i 
 
 9522 
 
 1 2 3 4 
 
 5 
 
 6789 
 
 05 
 
 9512 
 
 9502 
 
 '9493 
 
 9484 
 
 '9474 
 
 9465 
 
 "9455 
 
 9446 
 
 '9436 
 
 9427 
 
 1 2 3 4 
 
 5 
 
 6789 
 
 06 
 
 9418 
 
 9408 
 
 '9399 
 
 9389 
 
 9380 
 
 937i 
 
 9361 
 
 9352 
 
 9343 '9333 
 
 1234 
 
 S 
 
 6789 
 
 07 
 
 9324 
 
 '93 IS 
 
 9305 
 
 9296 
 
 9287 
 
 9277 
 
 9268 
 
 '92 59 
 
 9250 
 
 9240 
 
 1 2 3 4 
 
 S 
 
 6788 
 
 08 
 
 9231 
 
 9222 
 
 9213 
 
 9204 
 
 9194 
 
 9185 
 
 9176 
 
 9167 
 
 91^8-9148 
 
 1234 
 
 S 
 
 6778 
 
 09 
 
 9139 
 
 9130 
 
 9121 
 
 9112 
 
 9103 
 
 9094 
 
 9085 
 
 9076 
 
 9066 -9057 
 
 1234 
 
 5 
 
 6678 
 
 For values of x from '100 to 2 '999. 
 
 Subtract Differences. 
 
 X 
 
 
 
 m 
 
 02 
 
 03 
 
 04 
 
 05 
 
 06 -07 
 
 08 
 
 09 
 
 001 234 
 
 5 
 
 6789 
 
 1 
 
 9048 
 
 8958 
 
 8869 -8781 
 
 8694 
 
 8607 
 
 85211-8437 
 
 8353 
 
 8270 
 
 9 17 26 34 
 
 43 
 
 52 60 69 77 
 
 2 
 
 8187 
 
 8106 
 
 8025 7945 
 
 7866 
 
 7788 
 
 771 1 17634 
 
 7558 
 
 7483 
 
 8 16 23 31 
 
 39 
 
 47 55 62 70 
 
 3 
 
 7408 
 
 7334 
 
 7261 7189 
 
 7118 
 
 7047 
 
 6977 '6907 
 
 68^9 
 
 6771 
 
 7 14 21 28 
 
 35 
 
 42 49 56 63 
 
 4 
 
 6703 
 
 6637 
 
 6570-6505 
 
 6440 
 
 6376 
 
 6313 -62501-6188 
 
 6126 
 
 6 13 19 26 
 
 32 
 
 38 45 5i 57 
 
 5 
 
 6065 
 
 6005 
 
 5945'5886 
 
 5827 
 
 5769 
 
 5712 -5655 '5599 
 
 '5543 
 
 6 12 17 23 
 
 29 
 
 35 40 46 52 
 
 6 
 
 5488 
 
 '5434 
 
 "5379 '5326 
 
 5273 
 
 5220 
 
 5169 -51171-5066 
 
 5016 
 
 5 10 16 21 
 
 26 
 
 31 37 42 47 | 
 
 7 
 
 4966 
 
 4916 
 
 4868 -4819 
 
 477i 
 
 4724 
 
 4677 
 
 '4630 
 
 4584 
 
 4538 
 
 5 9 H 19 
 
 24 
 
 28 33 38 43 
 
 8 
 9 
 
 '4493 
 4066 
 
 '4449 
 4025 
 
 4404^4360 
 3985 -3946 
 
 43i7 
 3906 
 
 "4274 
 3867 
 
 4232 
 3829 
 
 4190 -4148 
 '3791 "3753 
 
 4107 
 3716 
 
 4 9 13 17 
 4 8 12 15 
 
 21 
 19 
 
 26 30 34 38 
 23 27 31 35 
 
 I'O 
 
 3679 
 
 3642 
 
 3606-3570 
 
 '3535 
 
 '3499 
 
 3465 
 
 3430 
 
 3396 
 
 3362 
 
 4 7 ii 14 
 
 18 
 
 21 25 28 32 1 
 
 1-1 
 
 3329 
 
 ^296 
 
 3263-3230 
 
 3198 
 
 3166 
 
 3135 
 
 3104-3073 
 
 3042 
 
 3 6 9 13 
 
 16 
 
 19 22 25 29 
 
 1-2 
 
 3012 
 
 2982 
 
 2952 
 
 292^ 
 
 2894 
 
 286s 
 
 2837 
 
 2808-2780 
 
 2753 
 
 3 6 9 ii 
 
 14 
 
 17 20 23 26 
 
 1-3 
 
 272=; 
 
 2698 
 
 "2671 
 
 26 4 s 
 
 2618 
 
 2592 
 
 2567 
 
 2541 
 
 2516 
 
 2491 
 
 3 5 8 10 
 
 13 
 
 16 18 21 23 j 
 
 1'4 
 
 2466 
 
 2441 
 
 2417 
 
 2393 
 
 2369 
 
 2346 
 
 2322 
 
 2299 
 
 2276 -2254 
 
 2579 
 
 12 
 
 14 16 19 21 
 
 1-5 
 
 2231 
 
 2209 
 
 2187 
 
 2165 
 
 2144 
 
 '2122 
 
 2101-2080 
 
 2o6oj-2039 
 
 2468 
 
 II 
 
 13 15 17 19 
 
 1-6 
 
 2019 
 
 1999 
 
 1979 
 
 1959 
 
 1940 
 
 T92O 
 
 1901 
 
 1882 
 
 1864 
 
 1845 
 
 2468 
 
 10 
 
 12 I 3 I 5 17 
 
 1-7 
 
 1827 
 
 1809 
 
 1791 
 
 1773 
 
 '1755 
 
 1738 
 
 1720 
 
 1703 
 
 1686 
 
 1670 
 
 2357 
 
 9 
 
 10 12 14 16 
 
 1*8 
 
 1653 
 
 1637 
 
 1620 
 
 1604 
 
 1588 
 
 1572 
 
 1557 
 
 1541 
 
 1526 
 
 1511 
 
 2356 
 
 8 
 
 9 ii 13 H 
 
 1-9 
 
 1496 
 
 1481 
 
 '1466 
 
 -1451 
 
 H37 
 
 1423 
 
 1409 
 
 1395 
 
 1381 
 
 1367 
 
 1346 
 
 7 
 
 9 10 ii 13 
 
 2-0 
 
 1353 
 
 1340 
 
 1327-1313 
 
 1300 
 
 1287 
 
 1275 "1262 
 
 1249 
 
 1237 
 
 1 3 4 5 
 
 6 
 
 8 9 10 12 
 
 2-1 
 
 1225 
 
 1212 
 
 1200-1188 
 
 1177 
 
 1165 
 
 1153 '1142 
 
 1130 
 
 1119 
 
 2 4 5 
 
 6 
 
 7 8 9 ii 
 
 2*2 
 
 1108 
 
 1097 
 
 1086 '1075 
 
 1065 
 
 1054 
 
 1044-1033 
 
 1023 
 
 1013 
 
 234 
 
 5 
 
 6789 
 
 I 2'3 
 
 1003 
 
 0993 
 
 0983 '09 7 3 
 
 0963 
 
 09 54 
 
 0944 
 
 093 S 
 
 0926 
 
 0916 
 
 234 
 
 5 
 
 6789 
 
 2'4 
 
 0907 
 
 0898 
 
 0889-0880 
 
 0872 
 
 0863 
 
 0854 
 
 0846 
 
 0837 
 
 0829 
 
 233 
 
 4 
 
 5678 
 
 2-5 
 
 0821 
 
 0813 
 
 o8o5;o797 
 
 0789 
 
 0781 
 
 0773 '0765 
 
 0758 
 
 0750 
 
 223 
 
 4 
 
 5567 
 
 2'6 
 
 0743 
 
 0735 
 
 0728 -0721 
 
 0714 
 
 0707 
 
 0699 -0693 -0686 
 
 0679 
 
 i 2 3 
 
 4 
 
 4566 
 
 | 2'7 
 
 0672 
 
 0665 '0659 '0652 
 
 0646 
 
 06^9 
 
 063 3! '06271 0620 
 
 0614 
 
 i 2 3 
 
 3 
 
 4456 
 
 \ 2'8 
 
 0608 
 
 0602 
 
 0596 '0590 
 
 os8 4 
 
 0578 
 
 0573 '0567 
 
 0561 
 
 0556 
 
 122 
 
 3 
 
 3455 
 
 2'9 
 
 0550 
 
 0545 
 
 0539-0534 
 
 0529 
 
 0523 
 
 0518-0513 
 
 0508 
 
 0503 
 
 122 
 
 3 
 
 3445 
 
 For values of x from 3*0 to 8*9. 
 
 Subtract Differences. 
 
 x 
 
 
 
 1 
 
 2 
 
 3 *4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 3 
 
 4 
 
 0498 
 oi8s 
 
 0450 
 0166 
 
 0408 
 0150 
 
 0368 -0334 
 0136 '0123 
 
 0302 
 
 01 1 1 
 
 0273 -0247 
 
 'OIOI '0091 
 
 -Q224 -Q2O2 
 0082-0074 
 
 Mean differences no longer 
 
 5 
 
 0067 
 
 0061 
 
 0055 
 
 0050 -0045 
 
 0041 
 
 0037 1-0033 
 
 '0030 -OO27 
 
 sufficiently accurate. 
 
 6 
 
 0025 
 
 0022 
 
 0020 
 
 0018 -0017 
 
 0015 
 
 OOI4-OOI2 
 
 001 1 
 
 ooio 
 
 
 7 
 
 0009 
 
 0008 
 
 OOO7 
 
 0007 -0006 
 
 0006 
 
 0005 -0005 
 
 0004 -0004 
 
 
 8 
 
 0003 
 
 0003 '03 
 
 0002 '0002 
 
 'OOO2 
 
 OOO2 'OOO3 
 
 OOO2 -OOOI 
 
 
FOUR-FIGURE 
 
 130 
 LOGARITHMS 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789; 
 
 1ft / 
 
 0000 
 
 0043 
 
 0086 
 
 0128 
 
 0170 
 
 
 
 
 
 
 4 9 13 17 
 
 21 
 
 25 30 34 38 ! 
 
 10 ( 
 
 
 
 
 
 
 O2I2 
 
 0253 
 
 0294 0334 
 
 374 
 
 4 8 12 16 
 
 2O 
 
 24 28 32 36 ; 
 
 11 / 
 
 0414 
 
 0453 
 
 0492 
 
 053 * 
 
 0569 
 
 
 
 
 
 4 8 12 15 
 
 19 
 
 23 27 31 35 
 
 11 I 
 
 
 
 
 
 0607 
 
 0645 
 
 0682 0719 
 
 0755 
 
 4 7 ii '5 
 
 18 
 
 22 26 30 33 
 
 19 / 
 
 0792 
 
 0828 0864 
 
 0899 
 
 0934 
 
 0969 
 
 
 
 
 4 7 ii 14 
 
 18 
 
 21 25 28 32 
 
 12 \ 
 
 
 
 
 
 
 
 1004 
 
 1038 1072 
 
 1106 
 
 3 7 10 14 
 
 17 
 
 20 2 4 27 31 
 
 <Q f 
 
 H39 
 
 H73 
 
 1206 
 
 1239 
 
 1271 
 
 
 
 
 
 3 7 10 13 
 
 16 
 
 2O 23 26 30 
 
 13 ( 
 
 
 
 
 
 1303 
 
 1335 
 
 1367,1399 
 
 1430 
 
 3 6 9 13 
 
 16 
 
 19 22 25 28 
 
 4A / 
 
 1461 
 
 1492 1523 1553 
 
 
 
 
 
 
 3 6 9 12 
 
 15 
 
 18 21 24 27 
 
 14 ( 
 
 
 
 1584 
 
 1614 
 
 1644 
 
 1673 1703 
 
 1732 
 
 3 6 9 12 
 
 15 
 
 18 21 24 27 
 
 IK/ 
 
 1761 
 
 1790 1818 
 
 1847 
 
 1875 
 
 1903 
 
 
 
 
 3 6 9 ii 
 
 H 
 
 17 2O 23 26 
 
 15 | 
 
 
 
 
 
 
 I93 1 
 
 1959 1987 
 
 2014 
 
 3 6 8 ii 
 
 H 
 
 17 19 22 25 
 
 <R I 
 
 2041 
 
 2068 2095 
 
 2122 
 
 2148 
 
 
 
 
 
 3 5 8 ii 
 
 13 
 
 16 19 21 24 ! 
 
 ID < 
 
 
 
 
 2175 
 
 2201 
 
 2227 2253 
 
 2279 
 
 3 5 8 10 
 
 i3 
 
 16 18 21 23 
 
 17 J 
 
 2304 
 
 2330 2355 2380 
 
 2405 
 
 2430 
 
 
 
 
 3 5 8 10 
 
 J 3 
 
 15 18 20 23 
 
 1 
 
 
 
 
 
 2455 
 
 2480 2504 
 
 2529 
 
 2 5 7 10 
 
 12 
 
 15 17 2O 22 
 
 j r> I 
 
 2 553 
 
 2577 2 6oi 
 
 2625 
 
 2648 
 
 
 
 
 
 
 2 5 7 10 
 
 12 
 
 14 17 19 21 ' 
 
 18 | 
 
 
 
 
 
 2672 
 
 26 9 5 
 
 2718 2742 
 
 2765 
 
 2579 
 
 12 
 
 14 16 19 21 
 
 4 t~\ \ 
 
 2788 
 
 2810 2833 2856 
 
 2878 
 
 
 
 
 
 
 2579 
 
 I I 
 
 14 16 18 20 
 
 19 
 
 
 
 
 2900 
 
 2923 
 
 2945 
 
 2967 
 
 2989 
 
 2479 
 
 I I 
 
 13 15 18 20 
 
 BO 
 
 3010 
 
 3032 3054 3075 
 
 3096 
 
 38 
 
 3139 
 
 3160 
 
 3181 
 
 3201 
 
 2468 
 
 II 
 
 13 15 17 19 
 
 21 
 
 3222 
 
 3243 3263 3284 
 
 3304 
 
 3324 
 
 3345 
 
 3365 
 
 3385 
 
 3404 
 
 2468 
 
 10 
 
 12 14 16 18 
 
 22 
 
 3424 
 
 3444 3464 3483 
 
 3502 
 
 3522 
 
 354i 
 
 356o 3579 
 
 3598 
 
 2468 
 
 IO 
 
 12 14 15.17 
 
 23 
 
 24 
 
 3617 
 3802 
 
 3636 3655 3 6 74 
 3820 3838 3856 
 
 3692 
 3874 
 
 37" 
 
 3892 
 
 3729 
 399 
 
 3747 j 3766 3784 
 3927 3945 3962 
 
 2467 
 2457 
 
 9 
 9 
 
 II 13 15 17 
 
 ii 12 14 16 
 
 25 
 
 3979 
 
 3997 
 
 4014 4031 
 
 4048 
 
 4065 
 
 4082 
 
 4099 4116 
 
 4133 
 
 2357 
 
 9 
 
 10 12 14 15 
 
 26 
 
 415 
 
 4166 
 
 4183 4200 
 
 4216 
 
 4232 
 
 4249 
 
 4265 4281 
 
 4298 
 
 2357 
 
 8 
 
 10 ii 13 15 
 
 27 
 
 43H 
 
 4330 
 
 4346 4362 
 
 4378 
 
 4393 
 
 4409 
 
 4425 4440 
 
 445 6 
 
 2356 
 
 8 
 
 9 ii *3 H 
 
 28 
 29 
 
 4472 
 4624 
 
 4487 
 4639 
 
 4502 
 4654 
 
 4518 
 4669 
 
 4533 
 4683 
 
 4548 
 4698 
 
 4564 
 4713 
 
 4579 4594 
 4728 4742 
 
 4609 
 '4757 
 
 2356 
 1346 
 
 8 
 
 7 
 
 9 ii 12 14 
 9 10 12 13 
 
 30 
 
 477i 
 
 4786 
 
 4800 4814 
 
 4829 
 
 4843 
 
 4857 
 
 4871 
 
 4886 
 
 4900 
 
 I34 6 
 
 7 
 
 9 10 ii 13 
 
 31 
 
 4914 
 
 4928 
 
 4942 
 
 4955 
 
 4969 
 
 4983 
 
 4997 
 
 5011 
 
 5024 
 
 5 38 
 
 1346 
 
 7 
 
 8 10 II 12 
 
 32 
 
 5051 
 
 5065 
 
 5079 
 
 5092 
 
 5105 
 
 5"9 
 
 5132 
 
 5M5 
 
 S 1 S9 
 
 5172 
 
 1 3 4 5 
 
 7 
 
 8 9 ii 12 
 
 33 
 
 5185 
 
 5198 
 
 5211 
 
 5224 
 
 5237 
 
 5250 
 
 5263 
 
 5276 
 
 5289 
 
 i5302 
 
 1345 
 
 6 
 
 8 9 10 12 
 
 34 
 
 53'S 
 
 5328 
 
 5340 
 
 5353 
 
 5366 
 
 5378 
 
 5391 
 
 5403 
 
 54i6 
 
 ,5428 
 
 1345 
 
 6 
 
 8 9 10 ii 
 
 35 
 
 544i 
 
 5453 
 
 5465 
 
 5478 
 
 5490 
 
 55 2 
 
 55H 
 
 5527 
 
 5539 
 
 555i 
 
 1245 
 
 6 
 
 7 9 10 ii 
 
 36 
 
 5563 
 
 5575 
 
 5587 
 
 5599 
 
 5611 
 
 5623 
 
 5 6 35 
 
 5 6 47 
 
 5658 
 
 5670 
 
 1245 
 
 6 
 
 7 8 10 ii 
 
 37 
 38 
 
 5682 
 5798 
 
 5694 
 5809 
 
 5705 
 5821 
 
 5717 
 5832 
 
 5729 
 5843 
 
 5740 
 5855 
 
 5752 
 5866 
 
 57 6 3 
 5877 
 
 5775 
 5888 
 
 5786 
 5899 
 
 1235 
 1235 
 
 6 
 6 
 
 7 8 9 10 
 7 8 9 10 
 
 39 
 
 59" 
 
 5922 
 
 5933 
 
 5944 5955 
 
 5966 
 
 5977 
 
 5988 
 
 5999 
 
 6010 
 
 1234 
 
 ( 
 
 7 8 9 10 
 
 40 
 
 6021 
 
 6031 
 
 6042 
 
 6053 6064 
 
 6075 
 
 6085 6098 
 
 6107 
 
 6117 
 
 1234 
 
 5 
 
 6 8 9 10 
 
 41 
 
 6128 
 
 6138 
 
 6149 
 
 6160 
 
 6170 
 
 6180 
 
 6191 
 
 6201 
 
 6212 
 
 6222 
 
 1234 
 
 1 
 
 6789 
 
 1 42 
 
 6232 
 
 6243 
 
 6253 
 
 6263 6274 
 
 6284 
 
 6294 
 
 6304 
 
 63M 
 
 6325 
 
 12^4 
 
 j 
 
 6789 
 
 43 
 
 6335 
 
 6345 
 
 6355 
 
 6365 6375 
 
 6385 
 
 6395 
 
 6405 
 
 6415 
 
 6425 
 
 1234 
 
 r 
 
 6789 
 
 44 
 
 6435 
 
 6444 
 
 6454 
 
 6464 6474 
 
 6484 
 
 6493 
 
 6503 
 
 6 5i3 
 
 6522 
 
 1234 
 
 i 
 
 6789 
 
 45 
 
 6532 
 
 6542 
 
 655i 
 
 6561 6571 
 
 6580 
 
 6590 
 
 6599 
 
 6609 
 
 6618 
 
 1234 
 
 5 
 
 6789 
 
 46 
 
 6628 
 
 6637 
 
 6646 
 
 6656 6665 
 
 6675 
 
 6684 
 
 6693 
 
 6702 
 
 6712 
 
 1234 
 
 c 
 
 6778 
 
 47 
 
 6721 
 
 6730 
 
 6 739 
 
 6749 6758 
 
 6767 
 
 6776 
 
 6785 
 
 6794 
 
 6803 
 
 1234 
 
 t 
 
 5678, 
 
 48 
 
 6812 
 
 6821 
 
 6830 
 
 6839 6848 
 
 6857 
 
 6866 
 
 6875 6884 
 
 6893 
 
 1234 
 
 ^ 
 
 56 7 8 
 
 49 
 
 6902 
 
 6911 
 
 6920 
 
 6928 
 
 6937 
 
 6946 
 
 6955 
 
 6964 
 
 6972 
 
 6981 
 
 1234 
 
 i 
 
 5678 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
131 
 
 FOUR-FIGURE LOGARITHMS 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
 50 
 
 6990 
 
 6998 
 
 7007 
 
 7016 
 
 7024 
 
 7033 
 
 7042 7050 7059 
 
 7067 
 
 1233 
 
 4 
 
 5678 
 
 51 
 
 7076 
 
 7084 
 
 7093 
 
 7101 
 
 7110 
 
 7118 
 
 7126 7135:7143 
 
 7152 
 
 1233 
 
 4 
 
 5678 
 
 52 
 
 7160 
 
 7168 7177 
 
 7185 
 
 7i93 
 
 7202 
 
 72101 7218 7226 
 
 7235 
 
 1223 
 
 4 
 
 5 6 77 
 
 53 
 
 7243 
 
 7251 7259 
 
 7267 
 
 7275 
 
 7284 
 
 729217300 7308 
 
 7316 
 
 1223 
 
 4 
 
 5667 
 
 54 
 
 7324 
 
 7332 7340 
 
 7348 
 
 7356 
 
 7364 
 
 7372 
 
 7380 7388 
 
 7396 
 
 1223 
 
 4 
 
 5667 
 
 55 
 
 7404 
 
 7412 7419 
 
 7427 i 7435 
 
 7443 
 
 745i 
 
 7459 7466 
 
 7474 
 
 1223 
 
 4 
 
 5567 
 
 56 
 57 
 
 7482 
 7559 
 
 7490 7497 7505 7513 
 75 66 17574 758217589 
 
 75 2 o 
 7597 
 
 7528 
 7604 
 
 7536 ! 7543 
 7612 7619 
 
 755i 
 7627 
 
 1223 
 1223 
 
 4 
 4 
 
 5567 
 5567 
 
 58 
 
 7634 
 
 7642 7649 ; 7657 1 7664 
 
 7672 
 
 7679 
 
 7686 7694 
 
 7701 
 
 1123 
 
 4 
 
 45 6 7 
 
 59 
 
 7709 
 
 77i6;.7723 773 1 
 
 7738 
 
 7745 
 
 7752 
 
 7760 
 
 7767 
 
 7774 
 
 1123 
 
 4 
 
 4567 
 
 6O 
 
 7782 
 
 7789 
 
 7796 
 
 7803 
 
 7810 
 
 7818 
 
 7825 
 
 7832 
 
 7839 
 
 7846 
 
 1123 
 
 4 
 
 4566 
 
 61 
 
 7853 
 
 7860 
 
 7868 
 
 7875 
 
 7882 
 
 7889 
 
 7896 
 
 7903 
 
 7910 
 
 7917 
 
 1123 
 
 4 
 
 4566 
 
 62 
 
 7924 
 
 793i 
 
 7938 7945 
 
 795 2 
 
 7959 
 
 7966 
 
 7973 798o 
 
 7987 
 
 1123 
 
 3 
 
 4566 
 
 63 
 
 7993 
 
 8000 
 
 8007 8014 
 
 8021 
 
 8028 
 
 8035 
 
 8041 
 
 8048 
 
 8055 
 
 1123 
 
 3 
 
 4556 
 
 64 
 
 8062 
 
 8069 
 
 8075 8082 
 
 8089 
 
 8096 
 
 8102 8109 
 
 8116 
 
 8122 
 
 1123 
 
 3 
 
 4556 
 
 65 
 
 8129 
 
 8136 
 
 8142 8149 
 
 8156 
 
 8162 
 
 8169 8176 8182 
 
 8189 
 
 1123 
 
 3 
 
 4556 
 
 66 
 
 8i95 
 
 8202 
 
 820918215 
 
 8222 
 
 8228 
 
 8235 8241 
 
 8248 
 
 8254 
 
 1123 
 
 3 
 
 4 5 5 6 
 
 67 
 
 8261 
 
 8267 
 
 8274 8280 
 
 8287 
 
 8293 
 
 8299 8306 
 
 8312 
 
 8319 
 
 1123 
 
 3 
 
 4556 
 
 68 
 
 8325 
 
 8331 8338 8344 
 
 8351 
 
 8357 
 
 8363 
 
 8370 
 
 8376 
 
 8382 
 
 1123 
 
 3 
 
 4 4 5 6 
 
 69 
 
 8388 
 
 8395 
 
 8401 8407 
 
 8414 
 
 8420 
 
 8426 
 
 8432 
 
 8439 
 
 8445 
 
 I I 2 2 
 
 3 
 
 4456 
 
 70 
 
 8451 
 
 8457 
 
 8463 | 8470 
 
 8476 
 
 8482 
 
 8488 
 
 8494 
 
 8500 
 
 8506 
 
 I I 2 2 
 
 3 
 
 4456 
 
 71 
 
 8513 
 
 8519 
 
 8525 8531 
 
 8537 
 
 8543 
 
 8549 
 
 8555 
 
 8561 
 
 8567 
 
 I I 2 2 
 
 3 
 
 4455 
 
 72 
 
 8573 
 
 8579 
 
 8585 8591 
 
 8597 
 
 8603 
 
 8609 
 
 8615 
 
 8621 
 
 8627 
 
 I I 2 2 
 
 3 
 
 4455 
 
 73 
 
 8633 
 
 8639 
 
 8645 8651 
 
 8657 
 
 8663 
 
 8669 
 
 8675 
 
 868158686 
 
 I I 2 2 
 
 3 
 
 4455 
 
 74 
 
 8692 
 
 8698 
 
 8704 8710 
 
 8716 
 
 8722 
 
 8727 
 
 8733 
 
 8739 8745 
 
 I I 2 2 
 
 3 
 
 4455 
 
 75 
 
 8751 
 
 8756 
 
 8762 1 8768 
 
 8774 
 
 8779 
 
 8785 
 
 8791 
 
 8797 
 
 8802 
 
 I I 2 2 
 
 3 
 
 3455 
 
 76 
 
 8808 
 
 8814 
 
 8820 8825 
 
 8831 
 
 8837 
 
 8842 
 
 8848 
 
 8854 
 
 8859 
 
 I I 2 2 
 
 3 
 
 3455 
 
 77 
 
 8865 
 
 8871 
 
 8876 8882 
 
 8887 
 
 8893 
 
 8899 8904 
 
 8910 
 
 8915 
 
 I I 2 2 
 
 3 
 
 3445 
 
 78 
 
 8921 
 
 8927 
 
 8932 8938 
 
 8943 
 
 8949 
 
 8954 8960 
 
 8965 
 
 8971 
 
 I I 2 2 
 
 3 
 
 3445 
 
 79 
 
 8976 
 
 8982 
 
 8987 
 
 8993 
 
 8998 
 
 9004 
 
 9009 
 
 9015 
 
 9020 
 
 9025 
 
 I I 2 2 
 
 3 
 
 3445 
 
 80 
 
 9031 
 
 9036 
 
 9042 
 
 9047 
 
 9053 
 
 9058 
 
 9063 
 
 9069 
 
 9074 
 
 9079 
 
 I I 2 2 
 
 3 
 
 3445 
 
 81 
 
 9085 
 
 9090 
 
 9096 
 
 9101 
 
 9106 
 
 9112 
 
 9117 
 
 9122 
 
 9128 
 
 9133 
 
 I I 2 2 
 
 3 
 
 3445 
 
 82 
 
 9138 
 
 9H3 
 
 9149 
 
 9154 
 
 9i59 
 
 9165 
 
 917019175 
 
 9180 
 
 9186 
 
 I I 2 2 
 
 3 
 
 3445 
 
 83 
 
 9191 
 
 9196(9201 
 
 9206 
 
 9212 
 
 9217 
 
 9222 9227 
 
 9232 
 
 9238 
 
 I I 2 2 
 
 3 
 
 3445 
 
 84 
 
 9243 
 
 9248 9253 
 
 9258 
 
 9263 
 
 9269 
 
 9274 
 
 9279 
 
 9284 
 
 9289 
 
 I I 2 2 
 
 3 
 
 3445 
 
 85 
 
 9294 
 
 9299 
 
 9304 
 
 9309 
 
 93i5 
 
 9320 
 
 9325 
 
 9330 
 
 9335 
 
 9340 
 
 I I 2 2 
 
 3 
 
 3445 
 
 86 
 
 9345 
 
 935o 
 
 9355 
 
 9360 
 
 9365 
 
 9370 
 
 9375 938o 
 
 9385 
 
 9390 
 
 I I 2 2 
 
 3 
 
 3445 
 
 87 
 88 
 
 9395 
 9445 
 
 9400 9405 
 945 9455 
 
 9410 
 9460 
 
 94i5 
 9465 
 
 9420 
 9469 
 
 9425 9430 
 9474 9479 
 
 9435 
 
 9484 
 
 9440 
 9489 
 
 O I I 2 
 I I 2 
 
 2 
 2 
 
 3344 
 3344 
 
 89 
 
 9494 
 
 9499 
 
 954 
 
 959 
 
 95'3 
 
 9518 
 
 9523 i 9528 
 
 9533 
 
 9538 
 
 O I I 2 
 
 2 
 
 3344 
 
 9O 
 
 9542 
 
 9547 
 
 9552 
 
 9557 
 
 9562 
 
 9566 
 
 957i 9576 
 
 958i 
 
 9586 
 
 O I I 2 
 
 2 
 
 3344 
 
 91 
 
 9590 
 
 9595 
 
 9600 
 
 9605 
 
 9609 
 
 9614 
 
 9619 9624 
 
 9628 
 
 9633 
 
 O I I 2 
 
 2 
 
 3344 
 
 92 
 
 9638 
 
 9643 9647 
 
 9652 
 
 9657 
 
 9661 
 
 9666:9671 
 
 9675 
 
 9680 
 
 I I 2 
 
 2 
 
 3344 
 
 93 
 
 9685 
 
 9689 1 9694 
 
 9699 
 
 9703 
 
 9708 
 
 9713 
 
 9717 
 
 9722 
 
 9727 
 
 I I 2 
 
 2 
 
 3344 
 
 ! 94 
 
 9731 
 
 9736 
 
 974i 
 
 9745 
 
 975 
 
 9754 
 
 9759 
 
 9763 
 
 9768 
 
 9773 
 
 I I 2 
 
 2 
 
 3344 
 
 95 
 
 9777 
 
 9782 
 
 9786 
 
 9791 
 
 9795 
 
 9800 
 
 9805 
 
 9809 
 
 9814 
 
 9818 
 
 O I I 2 
 
 2 
 
 3344 
 
 96 
 
 9823 
 
 9827 
 
 9832 
 
 9836 
 
 9841 
 
 9845 
 
 9850 
 
 9854 
 
 9859 
 
 9863 
 
 O I I 2 
 
 2 
 
 3344 
 
 97 
 
 9868 
 
 9872 
 
 9877 
 
 9881 
 
 9886 
 
 9890 
 
 9894 9899 
 
 9903 
 
 9908 
 
 I I 2 
 
 2 
 
 3344 
 
 98 
 
 9912 
 
 9917 
 
 9921 
 
 9926 
 
 9930 
 
 9934 
 
 9939 9943 
 
 9948 
 
 9952 
 
 O I I 2 
 
 2 
 
 3344 
 
 99 
 
 9956 
 
 9961 
 
 9965 
 
 9969 
 
 9974 
 
 9978 
 
 9983 9987 
 
 9991 
 
 9996 
 
 O I I 2 
 
 2 
 
 3334 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
132 
 
 ANTILOGARITHMS 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
 00 
 
 1000 
 
 IOO2 
 
 1005 
 
 1007 
 
 1009 
 
 1012 
 
 1014 
 
 1016 
 
 1019 
 
 1021 
 
 0011 
 
 i 
 
 1222 
 
 01 
 
 1023 1 IO26 i 1028 j 1030 
 
 I0 33 
 
 I0 35 
 
 1038 1040 1042 1045 
 
 O O I I 
 
 
 1222 
 
 02 
 
 1047 1050 1052 j 1054 
 
 1057 
 
 1059 
 
 1062 1064 1067 1069 
 
 O O I I 
 
 
 1222 
 
 03 
 
 1072 1074 1 1076 1 1079 
 
 1081 
 
 1084 
 
 1086 1089 1091 109/1 
 
 I I 
 
 
 1222 
 
 04 
 
 1096 
 
 1099 
 
 I IO2 i 1 104 
 
 1107 
 
 1109 
 
 III2 III4 III7 III9 
 
 O I I I 
 
 
 2222 
 
 05 
 
 1122 
 
 U25 
 
 1127 
 
 1130 
 
 1132 
 
 "35 
 
 1138 1140 1143 1146 
 
 I I I 
 
 
 2222 
 
 06 
 07 
 
 1148 II5I 
 1175 1178 
 
 "53 
 1180 
 
 1156 
 1183 
 
 1186 
 
 1161 
 1189 
 
 1164 
 II9I 
 
 1167 
 "94 
 
 1169 
 
 "97 
 
 1172 
 
 "99 
 
 O I I I 
 I I I 
 
 
 2222 
 2222 
 
 08 
 
 1 2O2 1 2O5 
 
 1208 
 
 1211 1213 
 
 1216 
 
 1219 I222J 1225 1227 
 
 O I I I 
 
 
 222 
 
 09 
 
 1230 
 
 1233 
 
 1236 
 
 1239 
 
 1242 
 
 1245 
 
 1247 
 
 1250 
 
 1253 1256 
 
 O I I I 
 
 
 222 
 
 10 
 
 1259 
 
 1262 
 
 1265 
 
 1268 
 
 1271 
 
 1274 
 
 1276 
 
 1279 
 
 1282 1285 
 
 O I I I 
 
 i 
 
 222 
 
 11 
 
 1288 
 
 1291 
 
 1294 
 
 1297 
 
 1300 
 
 1303 
 
 1306 
 
 1309 1312 1315 
 
 I I I 
 
 2 
 
 222 
 
 12 
 
 I3l8 
 
 1321 
 
 *3 2 4 
 
 1327 
 
 1330 
 
 1334 
 
 ^37 
 
 '340 1343 > !346 
 
 O I I I 
 
 2 
 
 222 
 
 13 
 
 1349 
 
 1352 
 
 1355 
 
 1358 1361 
 
 
 1368 
 
 I37i 1374 1377 
 
 I I I 
 
 2 
 
 22 3 
 
 14 
 
 I 3 80 
 
 1384 
 
 1387 
 
 1390 1393 
 
 1396 
 
 I4OO 
 
 H3 
 
 1406 1409 
 
 I I I 
 
 2 
 
 
 15 
 
 HI3 
 
 I4l6 
 
 1419 
 
 I 4 22 
 
 1426 
 
 1429 
 
 H32 
 
 H35 
 
 1439 
 
 1442 
 
 I I I 
 
 2 
 
 223 i 
 
 16 
 17 
 
 H45 
 H79 
 
 1449 
 1483 
 
 MS 2 
 1486 
 
 1485 
 
 H93 
 
 1462 
 1496 
 
 1466 
 1500 
 
 1469 
 
 1472 1476 
 1507 1510 
 
 I I I 
 O I I I 
 
 2 
 
 2 
 
 2233 
 2233 
 
 18 
 
 I5H 1517 
 
 1521 
 
 1524 
 
 1528 
 
 1531 
 
 J 535 
 
 1538 
 
 1542 1545 
 
 I I I 
 
 2 
 
 2233, 
 
 19 
 
 1549 
 
 1552 
 
 1556 
 
 I 5 60 
 
 1563 
 
 i5 6 7 
 
 1570 
 
 1574 
 
 1578 1581 
 
 I I I 
 
 2 
 
 2333 
 
 20 
 
 1585 
 
 1589 
 
 1592 
 
 1596 
 
 1600 
 
 1603 
 
 1607 
 
 1611 
 
 1614 1618 
 
 O I I I 
 
 2 
 
 2333 
 
 21 
 
 1622 
 
 1626 
 
 1629 
 
 1633 
 
 1637 
 
 1641 
 
 1644 
 
 1648 1652 1656 
 
 O I I 2 
 
 2 
 
 2 3 3 3 
 
 22 
 
 1660 
 
 I66 3 
 
 1667 
 
 1671 
 
 1^75 
 
 1679 
 
 1683 
 
 1687 
 
 1690 1694 
 
 O I I 2 
 
 2 
 
 2333' 
 
 23 
 
 1698 
 
 1702 
 
 1706 
 
 1710 
 
 1714 
 
 1718 
 
 1722 
 
 1726 
 
 1730 1734 
 
 I I 2 
 
 2 
 
 2334 
 
 24 
 
 1738 
 
 I 74 2 
 
 1746 
 
 1750 
 
 1754 
 
 1758 
 
 1762 
 
 1766 
 
 1770 1774 
 
 O I I 2 
 
 2 
 
 
 25 
 
 1778 
 
 1782 
 
 1786 
 
 1791 
 
 J795 
 
 1799 
 
 1803 
 
 1807 
 
 1811 1816 
 
 I I 2 
 
 2 
 
 2334 
 
 26 
 
 1820 
 
 1824 
 
 1828 
 
 1832 
 
 *837 
 
 1841 
 
 1845 
 
 1849 
 
 1854 1858 
 
 I I 2 
 
 2 
 
 3 3 3 4 ^ 
 
 27 
 
 1862 
 
 1866 
 
 1871 
 
 1875 
 
 1879 
 
 1884 
 
 1888 
 
 1892 1897 
 
 1901 
 
 O I I 2 
 
 2 
 
 3314 
 
 28 
 
 1905 
 
 1910 
 
 1914 
 
 1919 
 
 1923 
 
 1928 
 
 1932 1936 1941 1945 
 
 I I 2 
 
 2 
 
 3344 
 
 29 
 
 1950 
 
 1954 
 
 1959 
 
 1963 
 
 1968 
 
 1972 
 
 1977 
 
 1982 : 1986 1991 
 
 I I 2 
 
 2 
 
 3344 
 
 30 
 
 1995 
 
 2OOO 
 
 2004 
 
 2OO9 
 
 2014 
 
 2018 
 
 2023 
 
 2028 2032 
 
 2037 
 
 I I 2 
 
 2 
 
 3344 
 
 31 
 
 2042 
 
 2046 
 
 2051 
 
 2056 
 
 2061 
 
 2065 
 
 2070 
 
 2075 2080 
 
 2084 
 
 I I 2 
 
 2 
 
 3344 
 
 32 
 
 2089 
 
 2094 
 
 2099 
 
 2104 
 
 2109 
 
 2113 
 
 2118 
 
 2123 2128 
 
 2133 
 
 O I I 2 
 
 2 
 
 3 3 4 4 : 
 
 33 
 
 2138 
 
 2H3 
 
 2148 
 
 2153 
 
 2158 
 
 2163 
 
 2168 
 
 217312178 
 
 2183 
 
 I I 2 
 
 2 
 
 3 3 4 4 
 
 34 
 
 2188 
 
 2193 
 
 2198 
 
 2203 
 
 2208 
 
 2213 
 
 2218 
 
 2223 2228 
 
 2234 
 
 I I 2 2 
 
 3 
 
 3445: 
 
 35 
 
 2239 
 
 2244 
 
 2249 
 
 2254 
 
 2259 
 
 2265 
 
 2270 
 
 2275 
 
 2280 2286 
 
 I I 2 2 
 
 3 
 
 3445 
 
 36 
 
 2291 
 
 2296 
 
 2301 
 
 2307 
 
 2312 
 
 2317 
 
 2323 
 
 2328 
 
 2333 2339 
 
 I I 2 2 
 
 3 
 
 3445 
 
 37 
 
 2344 
 
 2350 
 
 2355 
 
 2360 
 
 2366 
 
 2371 
 
 2377 238212388 2393 
 
 I I 2 2 
 
 3 
 
 3445 
 
 38 
 39 
 
 2399 
 2455 
 
 2404 
 2460 
 
 2410 
 2466 
 
 2415 
 2472 
 
 2421 
 
 2477 
 
 2427 
 2483 
 
 2432 2438 
 2489 2495 
 
 2443 
 2500 
 
 2449 
 2506 
 
 I I 2 2 
 I I 2 2 
 
 3 
 3 
 
 3445 
 3455 
 
 40 
 
 2512 
 
 2518 
 
 2523 
 
 2529 
 
 2535 
 
 2541 
 
 2547 
 
 2553 
 
 2559 
 
 2564 
 
 I I 2 2 
 
 3 
 
 4455 
 
 41 
 
 2570 
 
 2576 
 
 2582 
 
 2588 
 
 2594 
 
 2600 
 
 2606 2612 
 
 2618 
 
 2624 
 
 I I 2 2 
 
 3 
 
 4455! 
 
 42 
 
 2630 
 
 2636 
 
 2642 
 
 2649 
 
 2655 
 
 2661 
 
 2667 2673 
 
 2679 
 
 2685 
 
 I I 2 2 
 
 3 
 
 4 4 5 6 
 
 43 
 
 2692 
 
 2698 
 
 2704 
 
 2710 
 
 2716 
 
 2723 
 
 2729 2735 
 
 2742 
 
 2748 
 
 II2 3 
 
 3 
 
 4 4 5 6 ! 
 
 44 
 
 2754 
 
 2761 
 
 2767 
 
 2773 
 
 2780 
 
 2786 
 
 2793 
 
 2799 
 
 2805 
 
 2812 
 
 II2 3 
 
 3 
 
 4 4 5 6 | 
 
 45 
 
 2818 
 
 2825 
 
 2831 
 
 2838 
 
 2844 
 
 2851 
 
 2858 
 
 2864 
 
 2871 
 
 2877 
 
 1123 
 
 3 
 
 4556 
 
 46 
 
 2884 
 
 2891 
 
 2897 
 
 2904 
 
 2911 
 
 2917 
 
 2924 2931 
 
 2938 
 
 2944 
 
 1123 
 
 3 
 
 4556 
 
 47 
 
 295112958 
 
 2965 
 
 2972 
 
 2979 
 
 2985 
 
 2992 
 
 2999 
 
 3006 
 
 3013 
 
 fI2 3 
 
 3 
 
 4 5 5 6 
 
 48 
 
 3020 ! 3027 
 
 3034 
 
 3041 
 
 3048 
 
 3055 
 
 3062 3069 
 
 3076 3083 
 
 1123 
 
 4 
 
 4566 
 
 49 
 
 3090 
 
 3097 
 
 3105 
 
 3 II2 
 
 3119 
 
 3126 
 
 3133 
 
 3i4i 
 
 3148 
 
 3 '55 
 
 II2 3 
 
 4 
 
 4566 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
133 
 
 ANTILOGARITHMS 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 50 
 
 3162 
 
 3170 
 
 3i77 
 
 3184 
 
 3192 
 
 3i99 
 
 3206 
 
 3214 
 
 3221 
 
 3228 
 
 1123 
 
 4 
 
 4 5 6 7 
 
 51 
 
 3236 
 
 3 2 43 
 
 3251 
 
 3258 
 
 3266 
 
 3273 
 
 3281 
 
 3289 
 
 3296 
 
 3304 
 
 1223 
 
 i 
 
 5567 
 
 '52 
 
 33i 
 
 33i9 
 
 3327 
 
 3334 
 
 3342 
 
 335 
 
 3357 
 
 3365 
 
 3373 
 
 338 
 
 122; 
 
 ^. 
 
 5 5 6 7 
 
 53 
 
 3388 
 
 3396 
 
 3404 
 
 3412 
 
 3420 
 
 3428 
 
 3436 
 
 3443 
 
 345i 
 
 3459 
 
 I 2 2 ] 
 
 4 
 
 5667 
 
 54 
 
 346 
 
 3475 3483 
 
 3491 
 
 3499 
 
 35o8 
 
 35i6 
 
 35 2 4 
 
 3532 
 
 3540 
 
 122; 
 
 ^ 
 
 5667 
 
 55 
 
 3548 
 
 3556 
 
 3565 
 
 3573 
 
 358 
 
 3589 
 
 3597 
 
 3606 
 
 3614 
 
 3622 
 
 1223 
 
 i 
 
 5677 
 
 56 
 
 363 
 
 3639 
 
 3648 
 
 3656 
 
 3664 
 
 3673 
 
 3681 
 
 3690 
 
 3698 3707 
 
 I 2 3 
 
 4 
 
 5678 
 
 57 
 
 3715 
 
 3724 
 
 3733 
 
 374i 
 
 3750 
 
 3758 
 
 3767 
 
 3776 
 
 3784 3793 
 
 1233 
 
 4 
 
 56 7 8 
 
 58 
 
 3802 
 
 3811 
 
 3819 
 
 3828 
 
 3837 
 
 3846 
 
 3855 
 
 3864 
 
 3873 ! 3882 
 
 1234 
 
 4 
 
 5678 
 
 59 
 
 3890 
 
 3899 
 
 3908 
 
 3917 3926 
 
 3936 
 
 3945 
 
 3954 
 
 3963 3972 
 
 1234 
 
 i 
 
 5678 
 
 60 
 
 398 
 
 3990 
 
 3999 
 
 4009 4018 
 
 4027 
 
 4036 
 
 4046 
 
 4055 
 
 4064 
 
 1234 
 
 5 
 
 6678 
 
 61 
 
 4074 
 
 4083 
 
 4093 
 
 4102 4111 
 
 412 
 
 4130 
 
 4140 
 
 4150 
 
 4159 
 
 1234 
 
 5 
 
 6789 
 
 62 
 
 4169 
 
 4178 
 
 4188 
 
 4198 
 
 4207 
 
 4217 
 
 4227 
 
 4236 
 
 4246 
 
 4256 
 
 1234 
 
 i 
 
 6789 
 
 63 
 64 
 
 4266 
 4365 
 
 4276 i 4285 
 4375 4385 
 
 4295 430 
 4395 4406 
 
 4315 
 4416 
 
 4325 
 4426 
 
 4335 
 4436 
 
 4345 
 4446 
 
 4355 
 4457 
 
 1234 
 1234 
 
 i 
 
 6789 
 6789 
 
 65 
 
 4467 
 
 4477 
 
 4487 
 
 4498 4508 
 
 4519 
 
 4529 4539 455 
 
 4560 
 
 1234 
 
 i 
 
 6789 
 
 66 
 
 457i 
 
 458r 
 
 4592 
 
 4603 4613 
 
 4624 
 
 4634 
 
 4645 4656 4667 
 
 1234 
 
 i 
 
 6 7 9 10 
 
 67 
 
 4 6 77 
 
 4688 
 
 4699 4710 
 
 4721 
 
 4732 
 
 4742 
 
 4753 4764 4775 
 
 1234 
 
 i 
 
 7 8 9 10 
 
 68 
 
 4786 
 
 4797 
 
 4808 
 
 4819 
 
 4831 
 
 4842 
 
 4853 
 
 4864 4875 4887 
 
 1234 
 
 ( 
 
 7 8 9 10 
 
 69 
 
 4898 
 
 4909 
 
 4920 
 
 4932 
 
 4943 
 
 4955 
 
 4966 
 
 4977 4989 5000 
 
 I 2 3 
 
 6 
 
 .7 8 9 10 
 
 70 
 
 5012 
 
 5023 5035 
 
 5047 
 
 5058 
 
 50/0 
 
 5082 
 
 5093 5105 5"7 
 
 1245 
 
 6 
 
 7 8 9 ii 
 
 71 
 
 5129 
 
 5 HO 
 
 5152 
 
 5164 
 
 5176 
 
 5188 
 
 5200 
 
 S2I2 
 
 5224 
 
 5236 
 
 1245 
 
 6 
 
 7 8 10 ii 
 
 72 
 
 5248 
 
 5260 
 
 5272 
 
 5284 
 
 5297 
 
 5309 
 
 532i 
 
 5333 5346 5358 
 
 1245 
 
 6 
 
 7 9 10 ii 
 
 73 
 
 5370 
 
 5383 
 
 5395 
 
 5408 
 
 5420 
 
 5433 
 
 5445 
 
 545815470 5483 
 
 1345 
 
 6 
 
 8 9 10 i[ 
 
 74 
 
 5495 
 
 5508 
 
 552i 
 
 5534 
 
 5546 
 
 5559 
 
 5572 
 
 5585 
 
 5598|56io 
 
 1345 
 
 6 
 
 8 9 10 12 
 
 75 
 
 5623 
 
 5636 ' 5649 
 
 5662 
 
 5675 
 
 5689 
 
 5/02 
 
 5715 
 
 572815741 
 
 1345 
 
 7 
 
 8 9 10 12 
 
 76 
 
 5754 
 
 5768 
 
 578i 
 
 5794 58o8 
 
 5821 
 
 5834 
 
 5848 5861 5875 
 
 1345 
 
 7 
 
 8 9 ii 12 
 
 77 
 
 5888 
 
 5902 
 
 59i6 
 
 5929 ! 5943 
 
 5957 
 
 5970 
 
 5984 5998! 6012 
 
 1345 
 
 7 
 
 8 IO II 12 
 
 78 
 
 6026 
 
 6039 
 
 6053 
 
 6067 6081 
 
 6095 
 
 6109 
 
 6124 
 
 6138 6152 
 
 1346 
 
 7 
 
 8 10 ii 13 
 
 79 
 
 6166 
 
 6180 
 
 6194 
 
 6209 
 
 6223 
 
 6237 
 
 6252 
 
 6266:6281 
 
 6295 
 
 1346 
 
 7 
 
 9 10 ii 13 
 
 80 
 
 6310 
 
 6324 
 
 6339 
 
 63^3 
 
 6368 
 
 6383 
 
 6397 6412 
 
 6427 6442 
 
 1346 
 
 7 
 
 9 10 12 13 
 
 81 
 
 6 457 
 
 6471 
 
 6486 
 
 6501 
 
 6516 
 
 6531 
 
 6546 6561 
 
 6577 6592 
 
 2356 
 
 8 
 
 9 ii 12 14 
 
 82 
 83 
 
 6607 
 6761 
 
 6622 
 6776 
 
 6637 
 6792 
 
 665316668 
 6808 6823 
 
 6683 
 6839 
 
 6699 6714 
 6855 6871 
 
 6730 
 6887 
 
 6745 
 6902 
 
 2356 
 2356 
 
 8 
 8 
 
 9 ii 12 14 
 9 ii 13 14 
 
 84 
 
 6918 
 
 6 934 
 
 6950 
 
 6966 
 
 6982 
 
 6998 
 
 7015 
 
 7031 
 
 7047 
 
 7063 
 
 2356 
 
 8 
 
 10 ii 13 15 
 
 85 
 
 7079 
 
 7096 
 
 7112 
 
 7129 
 
 7H5 
 
 7161 
 
 7178 
 
 7194 
 
 7211 
 
 7228 
 
 2357 
 
 8 
 
 10 12 13 15 
 
 86 
 
 7244 
 
 7261 
 
 7278 7295 
 
 73'i 
 
 7328 
 
 734S 
 
 7362 
 
 7379 
 
 7396 
 
 2357 
 
 8 
 
 10 12 13 15 
 
 87 
 
 74i3 
 
 7430 
 
 7447 
 
 7464 
 
 7482 
 
 7499 
 
 7516 
 
 7534 
 
 7551 
 
 7568 
 
 2357 
 
 9 
 
 10 12 14 16 
 
 88 
 
 7586 
 
 7603: 
 
 7621 
 
 7638 
 
 7656 
 
 7674 
 
 7691 
 
 7709 
 
 7727 
 
 7745 
 
 2457 
 
 9 
 
 ii 12 14 16 
 
 89 
 
 7762 
 
 7780 1 
 
 7798 
 
 7816 
 
 7834 
 
 7852 
 
 7870 7889 
 
 7907 
 
 7925 
 
 2457 
 
 9 
 
 ii 13 14 16 
 
 90 
 
 7943 
 
 7962! 
 
 798o 
 
 7998 
 
 8017 
 
 8035 
 
 8054 
 
 8072 
 
 8091 8110 
 
 2467 
 
 9 
 
 II 13 15 17 
 
 91 
 92 
 93 
 
 8128 
 8318 
 8511 
 
 8147 
 ^337 
 8531 
 
 8166 8185 
 8356:8375! 
 855i 8570 
 
 8204 
 
 8395 
 8590 
 
 8222 
 8414 
 16 10 
 
 8241 
 
 8433 
 8630! 
 
 8260 8279 8299 
 8453 8472,8492 
 8650 8670^690 
 
 2468 
 2468 
 2468 
 
 9 
 10 
 10 
 
 II 13 15 17 
 
 12 14 15 17 
 
 12 14 16 18 
 
 94 
 
 8710 
 
 8730 
 
 8750 8770 
 
 8790 
 
 8810 
 
 8831 8851 8872 
 
 8892 
 
 2468 
 
 
 
 12 14 16 18 
 
 95 
 
 8913 
 
 8933 
 
 8954 8974 
 
 8995 
 
 9016 
 
 9036 
 
 9057 
 
 9078 
 
 9099 
 
 2468 
 
 
 
 12 15 17 19 
 
 96 
 
 9120 
 
 9141 
 
 9162 9183 
 
 9204 
 
 9226 
 
 9247 
 
 9268 
 
 9290 
 
 93ii 
 
 2468 
 
 I 
 
 13 15 17 19 
 
 97 
 
 9333 
 
 9354 
 
 9376 9397 
 
 9419 
 
 9441 
 
 9462 
 
 9484 
 
 9506 
 
 9528 
 
 2479 
 
 I 
 
 I 3 15 17 20 
 
 98 
 
 9550 
 
 9572 
 
 9594 9616 
 
 9638 
 
 9661 
 
 9683 
 
 9705 
 
 9727 9750 
 
 2479 
 
 I 
 
 13 16 18 20 
 
 99 
 
 9772 
 
 9795 
 
 9817 9840 
 
 9863 
 
 9886 
 
 908 
 
 9931 
 
 9954 9977 
 
 2579 
 
 I 
 
 4 16 18 20 
 
 
 
 
 1 
 
 2 ! 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
134 
 
 FIVE-FIGURE LOGARITHMS 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
 to/ 
 
 00000 
 
 00432 
 
 00860 
 
 01284 
 
 01703 
 
 
 
 
 
 
 43 85 127 170 
 
 212 
 
 2 55 297 340 382 
 
 10{ 
 
 
 
 
 
 
 02119 
 
 02531 02938 
 
 03342 
 
 03743 
 
 41 81 121 162 
 
 202 
 
 243 283 323 364 
 
 1 
 
 04139 
 
 04532 
 
 049220530805690 
 
 
 1 
 
 
 
 39 77 116 155 
 
 193 
 
 232 270 309 348 
 
 I 
 
 
 
 
 
 
 06070 
 
 0644606819 
 
 07188 
 
 07555 
 
 37 74 in 148 
 
 185 
 
 222 259 296 33J 
 
 I 
 
 07918 
 
 08279 
 
 0863608991 
 
 09342 
 
 
 
 
 
 
 36 71 106 142 
 
 I 77 
 
 213 248 284 319 
 
 I 
 
 
 
 
 
 09691 
 
 10037 
 
 10380 
 
 10721 
 
 11059 
 
 34 68 102 136 
 
 170 
 
 205 239 273 307 
 
 ( 
 
 "394 
 
 11727 
 
 12057' 12385 
 
 12710 
 
 
 
 
 
 
 33 66 98 131 
 
 l6 4 
 
 197 230 262 295 
 
 i 
 
 
 
 
 
 13033 
 
 ^3354 
 
 13672 
 
 13988 
 
 14301 
 
 32 63 95 126 
 
 I 5 8 
 
 190 221 253 284 
 
 K 
 
 14613 
 
 14922 
 
 15229 
 
 15534 
 
 15836 
 
 16137 
 
 16435 
 
 16732 
 
 17026 
 
 I73I9 
 
 31 61 91 122 
 30 59 88 118 
 
 152 
 
 147 
 
 183 213 244 274 
 177 206 236 265 
 
 I 
 
 17609 
 
 17898 
 
 18184 
 
 18469 
 
 18752 
 
 
 
 
 
 
 2 9 57 85 114 
 
 142 
 
 171 199 228 256 
 
 \ 
 
 
 
 
 
 
 19033 
 
 19312 
 
 19590 
 
 19866 
 
 20140 
 
 28 55 83 i 10 
 
 138 
 
 166 193 221 248 
 
 f 
 
 20412 
 
 20683 
 
 20951 
 
 21219 
 
 21484 
 
 
 
 
 
 
 27 53 80 107 
 
 134 
 
 160 187 214 241 
 
 I 
 
 
 
 
 
 
 21748 
 
 2201 1 
 
 22272 
 
 22531 
 
 22789 
 
 26 52 78 104 
 
 130 
 
 156 182 208 23; 
 
 17/ 
 
 23045 
 
 23300 
 
 23553 23805 
 
 24055 
 
 
 
 
 
 
 25 50 76 101 
 
 126 
 
 151 176 2OI 227 
 
 I/I 
 
 
 
 
 
 24304 
 
 24551 
 
 24797 
 
 25042 
 
 25285 
 
 24 49 73 98 
 
 122 
 
 147 171 196 220 
 
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 26007:26245 
 
 26482 
 
 
 
 
 
 
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 119 
 
 143 167 190 214 
 
 ( 
 
 
 
 
 
 
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 27184 
 
 27416 
 
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 2 3 46 70 93 
 
 116 
 
 139 l62 185 2OC 
 
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 28556 
 
 28780 
 
 
 
 
 
 
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 113 
 
 135 158 181 203 
 
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 29226 
 
 2,9447 29667 
 
 29885 
 
 22 44 66 88 
 
 no 
 
 132 154 176 19* 
 
 20 
 
 30103 
 
 30320 30535 30750 
 
 30963 
 
 3H75 
 
 3<387 
 
 3159731806 
 
 32015 
 
 21 42 64 85 
 
 1 06 
 
 127 148 170 igi 
 
 21 
 
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 32222 
 34242 
 
 32428 32634132838 
 34439:3463534830 
 36361:36549136736 
 
 33041 
 35025 
 36922 
 
 33244 
 35218 
 37107 
 
 33445 
 37291 
 
 33646 33846 
 
 3560335793 
 3747537658 
 
 34044 
 35984 
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 20 40 61 81 
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 18 37 S 6 74 
 
 IOI 
 
 97 
 92 
 
 121 141 162 182 
 
 116 135 155 174 
 in 130 148 166 
 
 24 
 
 38021 
 
 382023838238561 
 
 38739 
 
 38917 
 
 39094 
 
 3927039445 
 
 39620 
 
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 89 
 
 106 124 142 160 
 
 25 
 
 39794 
 
 39967 40140 40312 40483 
 
 40654 
 
 40824 
 
 4099341162 
 
 41330 
 
 17 34 51 68 
 
 85 
 
 102 119 136 153 
 
 26 
 
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 41664418304199642160 
 
 42325 
 
 42488 
 
 4265142813 
 
 42975 
 
 J 6 33 49 66 
 
 82 
 
 98 115 131 148 
 
 27 
 
 43136 
 
 43297 43457 436i6J43775 
 
 43933 
 
 44091 44248444041441560 
 
 16 32 47 63 
 
 79 
 
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 28 
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 44871 
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 4502545179 
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 15 30 46 61 
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 76 
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 91 107 122 137 
 
 88 103 118 133 
 
 30 
 
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 47857 
 
 48001 
 
 48144 
 
 48287 
 
 48430 
 
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 7i 
 
 85 ico 114 128 
 
 31 
 32 
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 49554 
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 49831 
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 49969 50106 
 
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 52892 
 
 50379 
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 69 
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 53529 
 
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 13 25 38 5 
 
 63 
 
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 54777 
 
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 55388 
 
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 12 24 37 49 
 
 61 
 
 73 86 98 110 
 
 36 
 
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 12 24 36 48 
 
 60 
 
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 57287 
 
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 12 23 35 46 
 
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 580925820658320 
 592185932959439 
 
 58433 
 
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 58883,58995 
 5998860097 
 
 ii 23 34 45 
 n 22 33 44 
 
 56 
 
 55 
 
 68 79 90 102 
 
 66 77 88 99 
 
 40 
 
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 603146042360531 
 
 60638 
 
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 6085360959 
 
 6106661172 
 
 n 21 32 43 
 
 54 
 
 64 75 86 97 
 
 41 
 
 42 
 
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 61384 
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 61700 
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 61805 
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 6190962014 
 62941 63043 
 63949 64048 
 
 6211862221 
 6314463246 
 64147 64246 
 
 10 21 31 42 
 10 20 31 41 
 
 10 20 30 40 
 
 52 
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 63 73 84 94 
 61 72 82 92 
 60 70 80 90 
 
 44 
 
 64345 
 
 64444 
 
 64542 64640 
 
 64738 
 
 64836 
 
 6493365031 
 
 6512865225 
 
 10 20 29 39 
 
 49 
 
 59 68 78 88 
 
 45 
 
 65321 
 
 65418 
 
 6551465610 
 
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 10 19 29 38 
 
 48 
 
 57 67 76 86 
 
 46 
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 66652 
 67578 
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 68574 
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 66839 66932 
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 69548 69636 
 
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 9 19 28 37 
 9 18 27 37 
 9 18 27 36 
 9 18 26 35 
 
 47 
 46 
 
 45 
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 56 65 75 84 
 55 64 73 82 
 54 63 72 81 
 53 61 70 79 
 
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 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
135 
 
 FIVE-FIGURE LOGARITHMS 
 
 1 
 
 50 
 
 51 
 52 
 53 
 54 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 43 
 
 42 
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 4i 
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 70757 
 71600 
 72428 
 73239 
 
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 7168471767 
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 70157 
 
 71012 
 71850 
 72673 
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 70243 
 
 71096 
 71933 
 72754 
 7356o 
 
 70329 
 
 71181 
 72016 
 72835 
 73640 
 
 7041570501 
 
 7126571349 
 7209972181 
 7291672997 
 7371973799 
 
 70586 
 
 7H33 
 72263 
 73078 
 73878 
 
 70672 
 
 715*7 
 
 72346 
 73159 
 73957 
 
 9 17 26 34 
 
 8 17 25 34 
 
 8 17 25 33 
 8 16 24 32 
 8 16 24 32 
 
 52 60 69 77 
 
 51 59 67 76 
 
 50 58 6b 74 
 49 57 65 73 
 48 56 64 72 
 
 55 
 
 74036 
 
 7411574194 
 
 74273 
 
 7435i 
 
 74429 
 
 7457 
 
 74586 
 
 7466374741 
 
 8 16 23 31 
 
 39 
 
 47 55 63 70 
 
 56 
 57 
 58 
 59 
 
 74819 
 75587 
 76343 
 77085 
 
 7489674974 
 7566475740 
 7641876492 
 77^977232 
 
 75051 
 
 7 I 8 1 5 
 76567 
 
 77305 
 
 75128 
 
 75891 
 76641 
 
 77379 
 
 75205 
 75967 
 76716 
 
 77452 
 
 75282 
 76042 
 76790 
 
 77525 
 
 75358 
 76118 
 76864 
 
 77597 
 
 75435 
 76193 
 76938 
 77670 
 
 755" 
 76268 
 77012 
 77743 
 
 8 15 23 31 
 8 15 23 30 
 7 15 22 30 
 7 IS 22 29 
 
 39 
 
 38 
 37 
 
 37 
 
 46 54 62 69 
 45 53 60 68 
 44 52 59 67 
 44 51 58 66 
 
 60 
 
 778i5 
 
 77887 
 
 77960 
 
 78032 
 
 78104 
 
 78176 
 
 78247 
 
 78319 
 
 78390 
 
 78462 
 
 7 14 22 29 
 
 36 
 
 43 5o 58 65 
 
 61 
 62 
 63 
 64 
 
 78533 
 79239 
 79934 
 80618 
 
 78604 
 
 79309 
 80003 
 
 80686 
 
 78675 
 79379 
 80072 
 
 80754 
 
 78746 
 79449 
 80140 
 80821 
 
 78817 
 795 J 8 
 80209 
 80889 
 
 78888 
 79588 
 80277 
 80956 
 
 78958 
 79657 
 80346 
 81023 
 
 79029 
 
 79727 
 80414 
 81090 
 
 79099 
 
 80482 
 81158 
 
 79169 
 79865 
 80550 
 81224 
 
 7 14 21 28 
 7 14 21 28 
 7 14 21 27 
 7 13 20 27 
 
 36 
 
 35 
 34 
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 43 5 57 64 
 42 49 56 63 
 41 48 55 62 
 40 47 54 61 
 
 65 
 
 81291 
 
 81358 
 
 81425 
 
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 81558 
 
 81624 
 
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 81823 
 
 81889 
 
 7 13 20 27 
 
 33 
 
 40 46 53 60 
 
 66 
 67 
 68 
 69 
 
 8i954 
 
 82607 
 83251 
 
 83885 
 
 82020 
 82672 
 
 83315 
 83948 
 
 82086 
 82737 
 83378 
 84011 
 
 82151 
 82802 
 83442 
 84073 
 
 82217 
 82866 
 83506 
 84136 
 
 82282 
 82930 
 
 83569 
 84198 
 
 82347 
 82995 
 83632 
 84261 
 
 82413 
 
 83059 
 83696 
 
 84323 
 
 82478 
 83123 
 
 83759 
 84386 
 
 82543 
 83187 
 83822 
 84448 
 
 7 13 20 26 
 6 13 19 26 
 6 13 19 25 
 6 12 19 25 
 
 33 
 32 
 32 
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 39 46 52 59 
 39 45 5i 58 
 38 44 5i 57 
 37 44 5o 56 
 
 70 
 
 84510 
 
 84572 
 
 84634 
 
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 84819 
 
 84880 
 
 84942 
 
 85003 
 
 85065 
 
 6 12 18 25 
 
 3i 
 
 37 43 49 55 
 
 71 
 72 
 73 
 74 
 
 85126 
 
 85733 
 86332 
 86923 
 
 85187 
 85794 
 86392 
 86982 
 
 85248 
 
 85854 
 86451 
 87040 
 
 85309 
 85914 
 86510 
 87099 
 
 85370 
 85974 
 86570 
 87157 
 
 8543i 
 86034 
 86629 
 87216 
 
 8549i 
 86094 
 86688 
 87274 
 
 85552 
 86153 
 86747 
 87332 
 
 85612 
 86213 
 86806 
 87390 
 
 85673 
 86273 
 86864 
 87448 
 
 6 12 18 24 
 6 12 18 24 
 6 12 18 24 
 6 12 17 23 
 
 3i 
 
 30 
 
 30 
 29 
 
 37 43 49 55 
 36 42 48 54 
 
 35 4i 47 53 
 35 4i 47 52 
 
 75 
 
 87506 
 
 87564 
 
 87622 
 
 87679 
 
 87737 
 
 87795 
 
 87852 
 
 87910 
 
 87967 
 
 88024 
 
 6 12 17 23 
 
 29 
 
 35 40 46 52 
 
 76 
 77 
 78 
 79 
 
 88081 
 88649 
 89209 
 89763 
 
 8813888195 
 88705188762 
 8926589321 
 8981889873 
 
 88252 
 sssis 
 89376 
 89927 
 
 88309 
 88874 
 89432 
 89982 
 
 88366 
 88930 
 89487 
 90037 
 
 88423 
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 89542 
 90091 
 
 88480 
 89042 
 
 89597 
 90146 
 
 88536 
 89098 
 
 89653 
 90200 
 
 88593 
 89154 
 89708 
 
 90255 
 
 6 ii 17 23 
 
 6 II 17 22 
 6 II 17 22 
 6 11 17 22 
 
 29 
 28 
 28 
 28 
 
 34 40 46 51 
 34 39 45 50 
 33 39 44 50 
 33 39 44 50 
 
 80 
 
 90309 
 
 90363 
 
 90417 
 
 90472 
 
 90526 
 
 90580 
 
 90633 
 
 90687 
 
 90741 
 
 90795 
 
 5 ii 16 22 
 
 27 
 
 32 38 43 49 
 
 81 
 1 82 
 83 
 84 
 
 90848 
 91381 
 91908 
 92428 
 
 90902 
 
 91434 
 91960 
 92480 
 
 90956 
 91487 
 92012 
 92531 
 
 91009 
 91540 
 92064 
 
 92583 
 
 91062 
 
 91593 
 92117 
 92634 
 
 91116 
 91645 
 92169 
 92686 
 
 91169 
 91698 
 92221 
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 91222 
 9i75i 
 92273 
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 91275 
 91803 
 92324 
 92840 
 
 91328 
 
 91855 
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 5 ii 16 21 
 5 ii 16 21 
 5 10 16 21 
 5 10 15 21 
 
 27 
 26 
 26 
 26 
 
 32 37 43 48 
 32 37 42 47 
 31 36 42 47 
 31 36 41 46 
 
 85 
 
 92942 
 
 92993 
 
 93044 
 
 93095 
 
 93146 
 
 93197 
 
 93247 
 
 93298 
 
 93349 
 
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 5 10 15 20 
 
 26 
 
 31 36 41 46 
 
 86 
 87 
 88 
 89 
 
 9345 
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 94002 
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 93551 
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 93601 
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 9365 
 94i5i 
 94645 
 95134 
 
 93702 
 94201 
 
 94694 
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 93752 
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 94743 
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 93802 
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 94792 
 95279 
 
 93852 
 94349 
 94841 
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 93902 
 
 94399 
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 95376 
 
 5 10 15 20 
 5 10 15 20 
 5 10 15 20 
 5 1 *5 '9 
 
 25 
 25 
 25 
 24 
 
 30 35 40 45 
 30 35 40 45 j 
 29 34 39 44 | 
 29 34 39 44 
 
 9O 
 
 95424 
 
 95472 
 
 95521 
 
 95569 
 
 956i7 
 
 95665 
 
 95713 
 
 9576i 
 
 95809 
 
 95856 
 
 5 10 14 19 
 
 24 
 
 29 34 38 43 
 
 91 
 92 
 93 
 94 
 
 95904 
 96379 
 96848 
 
 97313 
 
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 95999 
 96473 
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 96047 
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 9745 i 
 
 96095 
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 96142 
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 96190 
 96661 
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 96237 96284 
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 9717497220 
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 96332 
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 97267 
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 5 9 H 19 
 5 9 H 19 
 5 9 H 19 
 5 9 J 4 18 
 
 24 
 24 
 23 
 23 
 
 28 33 38 43 
 28 33 38 42 
 28 33 37 42 
 28 32 37 42 
 
 95 
 
 97772 
 
 97818 
 
 97864 
 
 97909 
 
 97955 
 
 98000 
 
 9804698091 
 
 98i37 
 
 98182 
 
 5 9 H 18 
 
 23 
 
 27 32 36 4 
 
 96 
 97 
 98 
 99 
 
 98227 
 
 98677 
 99123 
 
 99564 
 
 98272 
 98722 
 99167 
 99607 
 
 98318 
 98767 
 99211 
 99651 
 
 98363 
 98811 
 
 99255 
 99695 
 
 98408 
 98856 
 99300 
 99739 
 
 98453 
 98900 
 
 99344 
 99782 
 
 98498 
 
 98945 
 99388 
 99826 
 
 98543 
 98989 
 
 99432 
 99870 
 
 98588 
 99034 
 99476 
 99913 
 
 98632 
 99078 
 99520 
 99957 
 
 5 9 H 18 
 4 9 13 18 
 4 9 13 18 
 4 9 13 17 
 
 23 
 
 22 
 22 
 22 
 
 27 32 36 41 
 27 3 1 36 40| 
 26 31 35 40 
 26 31 35 39 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
136 
 
 RECIPROCALS 
 
 
 
 
 
 
 
 
 
 
 Subtract Differences. 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 234 
 
 5 
 
 6789 
 
 10 
 
 000 
 
 901 
 
 2804 
 
 ?79 
 
 9615 
 
 524 
 
 434 
 
 9346 
 
 9259 
 
 9174 
 
 18 27 36 
 
 45 
 
 55 64 73 82 
 
 11 
 
 12 
 
 9091 
 
 333 
 
 9009 8929 885018772 
 264 8197 8130' 8065 
 
 696 
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 621 8547 
 937 7874 
 
 8475 
 78i3| 
 
 8403 
 7752 
 
 15 23 30 
 6 13 19 26 
 
 8 
 
 >2 
 
 45 53 61 68 
 38 45 5i 58 
 
 13 
 
 692 
 
 634 7576 7519 
 
 7463 
 
 407 
 
 353 7299 
 
 7246 7194 
 
 II l6 22 
 
 27 
 
 33 38 44 49 
 
 14 
 
 H3 
 
 092 7042 
 
 &993 
 
 6944 
 
 897 
 
 849 6803 
 
 6757 
 
 6711 
 
 10 14 19 
 
 24 
 
 29 33 38 43 
 
 15 
 
 667 
 
 623 6579 
 
 &536 
 
 6494 
 
 452 
 
 410 6369 
 
 6329 
 
 6289 
 
 4 8 13 17 
 
 21 
 
 25 29 33 38 
 
 16 
 
 250 
 
 211 
 
 6i73!6i35 
 
 6098 
 
 061 
 
 6024 
 
 5988 5952 
 
 5917 
 
 4 7 ii 15 
 
 1 8 
 
 22 26 29 33 
 
 17 
 
 882 
 
 848 
 
 5814:5780 
 
 747 
 
 714 
 
 682 
 
 5650 5618 
 
 5587 
 
 , 6 10 13 
 
 16 
 
 20 23 26 29 
 
 18 
 
 556 
 
 525 
 
 5495 
 
 5464 
 
 5435 
 
 405 
 
 376 
 
 5348 53i9 
 
 5291 
 
 i 6 9 12 
 
 15 
 
 17 2O 23 26 
 
 19 
 
 263 
 
 2 3 6 
 
 5208 
 
 5181 
 
 555 
 
 126 
 
 102 
 
 5076 
 
 5051 
 
 5025 
 
 3 5 8 ii 
 
 13 
 
 16 18 21 24 
 
 20 
 
 000 
 
 975 
 
 4950 
 
 4926 
 
 .902 
 
 878 
 
 854 
 
 4831 
 
 4808 
 
 4785 
 
 2 5 7 10 
 
 12 
 
 14 17 19 21 
 
 21 
 
 762 
 
 4739 
 
 4717 
 
 4695 
 
 4673 
 
 6 5 I 
 
 4630 
 
 4608 
 
 4587 
 
 4566 
 
 2479 
 
 II 
 
 13 15 17 19 
 
 22 
 
 545 
 
 4525 
 
 4505 
 
 4484 
 
 4464 
 
 4444 
 
 4425 
 
 4405 4386 
 
 4367 
 
 2468 
 
 10 
 
 12 14 16 18 
 
 23 
 
 348 
 
 4329 
 
 4310 4292 
 
 4274 
 
 4255 
 
 4237 
 
 4219 4202 
 
 4184 
 
 2457 
 
 9 
 
 ii 13 14 16 
 
 24 
 
 4167 
 
 4149 
 
 4132 4115 
 
 4098 
 
 4082 
 
 4065 
 
 4049 
 
 4032 
 
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 2357 
 
 8 
 
 10 12 13 15 
 
 25 
 
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 3984 
 
 3968 3953 
 
 3937 
 
 922 
 
 39 06 
 
 3891 
 
 3876 
 
 3861 
 
 2356 
 
 8 
 
 9 ii 12 14 
 
 26 
 
 3846 
 
 3831 
 
 3817 3802 
 
 3788 
 
 3774 
 
 3759 
 
 3745 
 
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 3717 
 
 1346 
 
 7 
 
 8 10 ii 13 
 
 27 
 
 3704 
 
 3690 
 
 3676 3663 
 
 3 6 5 
 
 3636 
 
 3623 
 
 3610 
 
 3597 
 
 3584 
 
 1345 
 
 7 
 
 8 9 ii 12 
 
 28 
 
 3571 
 
 3559 
 
 3546 
 
 3534 
 
 352i 
 
 3509 
 
 3497 
 
 3484 
 
 3472 
 
 3460 
 
 1245 
 
 
 
 7 9 10 ii 
 
 29 
 
 3448 
 
 343 6 
 
 3425 
 
 3413 
 
 340i 
 
 3390 
 
 3378 
 
 3367 
 
 3356 
 
 3344 
 
 1235 
 
 6 
 
 7 8 9 10 
 
 3O 
 
 3333 
 
 3322 
 
 33" 
 
 3300 
 
 3289 
 
 3279 
 
 3268 
 
 3257 
 
 3247 
 
 3236 
 
 1234 
 
 5 
 
 6 7 9 10 
 
 31 
 
 3226 
 
 3215 
 
 3205 3^95 
 
 3185 
 
 3!75 
 
 3165 
 
 3155 
 
 3H5 
 
 3135 
 
 1234 
 
 5 
 
 6789 
 
 32 
 
 3!25 
 
 3"5 
 
 3106 3096 
 
 3086 
 
 3077 
 
 3067 
 
 3058 3049 
 
 3040 
 
 1234 
 
 t^ 
 
 6789 
 
 33 
 
 3030 
 
 3021 
 
 3012 3003 
 
 2994 
 
 2985 
 
 2976 
 
 2967 
 
 2959 
 
 2950 
 
 1234 
 
 A 
 
 5678 
 
 34 
 
 2941 
 
 2933 
 
 2924 2915 
 
 2907 
 
 2899 
 
 2890 
 
 2882 
 
 2874 
 
 2865 
 
 1233 
 
 4 
 
 5678 
 
 35 
 
 285 
 
 2849 
 
 2841 2833 
 
 2825 
 
 2817 
 
 2809 
 
 2801 
 
 2793 
 
 2786 
 
 1223 
 
 4 
 
 5667 
 
 36 
 
 2778 
 
 2770 
 
 2762 2755 
 
 2747 
 
 2740 
 
 2732 
 
 2725 
 
 2717 
 
 2710 
 
 1223 
 
 4 
 
 5567 
 
 37 
 
 270 
 
 2695 
 
 2688 
 
 2681 
 
 2674 
 
 2667 
 
 2660 
 
 2653 
 
 2646 
 
 2639 
 
 1123 
 
 4 
 
 4566 
 
 38 
 
 263 
 
 2625 
 
 2618 
 
 2611 
 
 260, 
 
 259 
 
 2591 
 
 2584 
 
 2577 
 
 2571 
 
 1123 
 
 ^ 
 
 4556 
 
 39 
 
 256 
 
 2558 
 
 255 1 
 
 2545 
 
 2538 
 
 253 
 
 2525 
 
 2519 
 
 2513 
 
 2506 
 
 1123 
 
 j 
 
 4456 
 
 40 
 
 2500 
 
 2494 
 
 2488 
 
 2481 
 
 2475 
 
 2469 
 
 2463 
 
 2457 
 
 2451 
 
 2445 
 
 I I 2 2 
 
 3 
 
 4455 
 
 41 
 
 243 
 
 2433 
 
 2427 
 
 2421 
 
 241 
 
 2410 
 
 2404 
 
 2398 
 
 2392 
 
 2387 
 
 I I 2 2 
 
 3 
 
 3455 
 
 42 
 
 238 
 
 2375 
 
 2370 
 
 236* 
 
 2358 
 
 235 
 
 2347 
 
 2342 
 
 2336 
 
 233 
 
 I I 2 2 
 
 I 
 
 3445 
 
 43 
 
 232 
 
 2320 
 
 2315 2309 
 
 2304 
 
 229 
 
 2294 
 
 2288 
 
 2283 
 
 2278 
 
 I I 2 2 
 
 I 
 
 3445 
 
 44 
 
 227 
 
 2268 
 
 2262 
 
 2257 
 
 225 
 
 224 
 
 2242 
 
 2237 
 
 2232 
 
 222 
 
 I I 2 2 
 
 3 
 
 3445 
 
 45 
 
 222 
 
 2217 
 
 2212 
 
 2208 
 
 220 
 
 219 
 
 2193 
 
 2188 
 
 2183 
 
 2179 
 
 I I 2 
 
 2 
 
 3344 
 
 46 
 
 217 
 
 2169 
 
 2165 
 
 2160 
 
 215 
 
 215 
 
 2146 
 
 2141 
 
 2137 
 
 2132 
 
 I I 2 
 
 2 
 
 3344 
 
 47 
 
 212 
 
 2123 
 
 2119 
 
 2114 
 
 2110 
 
 210 
 
 2101 
 
 2096 
 
 2092 
 
 2088 
 
 I I 2 
 
 2 
 
 3344 
 
 48 
 49 
 
 208 
 2O4 
 
 2079 
 2037 
 
 2075 
 2033 
 
 2070 
 2028 
 
 2O66 
 202 
 
 206 
 202 
 
 2058 
 20l6 
 
 205312049 
 2012' 2008 
 
 204 
 2004 
 
 I I 2 
 I I 2 
 
 \ 
 
 3334 
 2334 
 
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 2000 
 
 1996 
 
 1992 
 
 1988 
 
 I 9 8 4 
 
 I 9 8 
 
 1976 
 
 1972 
 
 1969 
 
 196 
 
 I I 2 
 
 2 
 
 2334 
 
 51 
 
 I 9 6 
 
 1957 
 
 1953 
 
 1949 
 
 194 
 
 194 
 
 1938 
 
 1934 
 
 I93i 
 
 I 9 2 
 
 I I 2 
 
 2 
 
 2333 
 
 52 
 53 
 
 192 
 
 188 
 
 1919 
 1883 
 
 1916 
 I880 
 
 1912 
 
 1876 
 
 190 
 
 I8 7 
 
 190 
 
 1 86 
 
 1901 
 1866 
 
 1898 1894 
 1862^1859 
 
 I8 9 
 
 I8 55 
 
 I I 
 I I 
 
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 2333 
 2233 
 
 54 
 
 185 
 
 1848 
 
 1845 
 
 1842 
 
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 183 
 
 I8 3 2 
 
 1828 1825 
 
 182 
 
 I I 
 
 ~ 
 
 2233 
 
 
 
 
 
 
 
 
 
 
 
 
 1234 
 
 5 
 
 6789 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 
 
 
 
 
 
 Subtract Differences. 
 
137 
 
 RECIPROCALS 
 
 
 
 
 4" 
 
 
 
 
 
 
 Subtract Differences. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 d 
 
 
 
 
 
 
 
 
 1234 
 
 5 
 
 6789 
 
 55 
 
 i8i8 
 
 1815 
 
 1812 
 
 1808 
 
 1805 
 
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 1799 
 
 1795 
 
 1792 
 
 1789 
 
 O I I I 
 
 2 
 
 2233 
 
 56 
 57 
 
 1786 
 1754 
 
 1783 
 
 1779 
 
 1748 
 
 1776 
 1745 
 
 1773 
 1742 
 
 1770 
 1739 
 
 1767 
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 1764 
 1733 
 
 1761 
 1730 
 
 1757 
 
 1727 
 
 I I I 
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 2233 
 
 2223 
 
 58 
 59 
 
 1724 
 1695 
 
 1721 1718 
 1692 1689 
 
 1715 1712 
 
 1686 1684 
 
 1709 
 
 1681 
 
 1706 
 1678 
 
 1704 
 1675 
 
 1701 
 1672 
 
 1698 
 1669 
 
 I I I 
 Oil I 
 
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 2223 
 
 2223 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 1667 
 
 1664 1661 
 
 1658 
 
 1656 
 
 1653 
 
 1650 
 
 1647 
 
 1645 
 
 1642 
 
 O I I I 
 
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 61 
 
 1639 
 
 1637 
 
 1634 
 
 1631 
 
 1629 
 
 1626 
 
 1623 
 
 1621 
 
 1618 
 
 1616 
 
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 62 
 
 1613 
 
 1610 
 
 1608 1605 
 
 1603 
 
 1600 
 
 1597 
 
 1595 
 
 1592 
 
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 63 
 
 1587 
 
 1585 1582 1580 
 
 1577 
 
 1575 
 
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 64 
 
 1563 
 
 1560 
 
 1558 
 
 1555 
 
 1553 
 
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 1548 
 
 1546 
 
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 1222 
 
 65 
 
 1538 
 
 1536 
 
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 1529 
 
 1527 
 
 1524 
 
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 1520 
 
 1517 
 
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 66 
 
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 1504 
 
 1502 
 
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 67 
 
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 1481 
 
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 1475 
 
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 68 
 
 1471 
 
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 1464 1462 
 
 1460 
 
 1458 
 
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 1443 
 
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 70 
 
 1429 
 
 1427 
 
 1425 
 
 1422 
 
 1420 
 
 1418 
 
 1416 
 
 1414 
 
 1412 
 
 1410 
 
 O O I I 
 
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 I I 2 2 
 
 71 
 
 1408 
 
 1406 
 
 1404 
 
 1403 
 
 1401 
 
 1399 
 
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 1395 
 
 I393 
 
 i39i 
 
 I I 
 
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 I I 2 2 
 
 72 
 
 1389 
 
 1387 1385 
 
 1383 
 
 1381 
 
 1379 
 
 1377 
 
 1376 
 
 1374 
 
 1372 
 
 I I 
 
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 73 
 
 74 
 
 1370 
 
 1368 
 1350 
 
 1366 
 1348 
 
 1364 1362 
 1346 1344 
 
 1361 
 1342 
 
 1359 
 1340 
 
 1357 
 1339 
 
 1355 
 1337 
 
 1353 
 
 1335 
 
 O O I I 
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 75 
 
 T 1 ? f 
 
 
 
 8 
 
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 76 
 
 1 oo: 
 
 1316 
 
 1314 
 
 1312 
 
 1311 1309 
 
 J 3 2 5 
 
 J 3 2 3 
 
 1321 
 1304 
 
 1302 
 
 1300 
 
 O O I I 
 
 I 
 
 I I I 2 
 
 77 
 
 1299 
 
 1297 1295 
 
 1294 1292 
 
 1290 
 
 1289 
 
 1287 
 
 1285 
 
 1284 
 
 O O O I 
 
 I 
 
 I I I I 
 
 78 
 
 1282 
 
 1280 1279 1277 
 
 1276 
 
 1274 
 
 1272 
 
 1271 
 
 1269 
 
 1267 
 
 O O O I 
 
 I 
 
 I I I I 
 
 79 
 
 1266 
 
 1264 1263 
 
 1261 
 
 1259 
 
 1258 
 
 1256 
 
 1255 
 
 1253 
 
 1252 
 
 0001 
 
 I 
 
 I I I I 
 
 8O 
 
 1250 
 
 1248 
 
 1247 
 
 1245 
 
 1244 
 
 1242 
 
 1241 
 
 1239 
 
 1238 
 
 1236 
 
 0001 
 
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 III I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 1235 
 
 1233 
 
 1232 
 
 1230 
 
 1229 
 
 1227 
 
 1225 
 
 1224 
 
 1222 
 
 1221 
 
 O O O I 
 
 I 
 
 I I I I 
 
 82 
 
 1220 
 
 1218 
 
 I2l7jI2l5;l2l4 
 
 1212 
 
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 1209 
 
 1208 
 
 1206 
 
 0001 
 
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 83 
 
 1205 
 
 1203 
 
 1202 1200 1199 
 
 1198 
 
 1196 
 
 "95 
 
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 1192 
 
 0001 
 
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 84 
 
 1190 
 
 1189 
 
 1188 
 
 1186 
 
 1185 
 
 1183 
 
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 1181 
 
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 85 
 
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 "75 
 
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 1172 
 
 1171 
 
 1170 
 
 1168 
 
 1167 
 
 1166 
 
 1164 
 
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 I I I I 
 
 86 
 
 1163 
 
 1161 
 
 1160 
 
 "59 
 
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 1156 
 
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 1152 
 
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 0001 
 
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 I I I I 
 
 87 
 
 "49 
 
 1148 
 
 "47 
 
 "45 
 
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 1142 1140 
 
 "39 
 
 1138 
 
 0001 
 
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 88 
 
 1136 
 
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 "33 
 
 1131 
 
 1130 
 
 1129 1127 
 
 1126 
 
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 89 
 
 1124 
 
 1122 
 
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 1 120 
 
 1119 
 
 1117 
 
 1116 
 
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 1114 
 
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 90 
 
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 1107 
 
 1106 
 
 1105 
 
 1104 
 
 1103 
 
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 0001 
 
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 91 
 
 1099 
 
 1098 
 
 1096 1095 
 
 1094 
 
 1093 
 
 1092 
 
 1091 
 
 1089 
 
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 92 
 
 1087 
 
 1086 
 
 1085 1083 
 
 1082 
 
 1081 
 
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 93 
 
 1075 
 
 1074 
 
 1073 1072 1071 
 
 1070 
 
 1068 1067 
 
 1066 
 
 1065 
 
 0000 
 
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 I I I I 
 
 94 
 
 1064 
 
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 1062 
 
 1060 
 
 1059 
 
 1058 
 
 1057 
 
 1056 
 
 1055 
 
 1054 
 
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 1 
 
 I I I I 
 
 95 
 
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 1052 
 
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 1049 
 
 1048 
 
 1047 
 
 1046 
 
 1045 
 
 1044 
 
 1043 
 
 0000 
 
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 I I I I 
 
 96 
 
 1042 
 
 IO4I 
 
 1040 
 
 1038 
 
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 1036 
 
 1035 
 
 1034 
 
 1033 
 
 1032 
 
 0000 
 
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 I I I I 
 
 97 
 
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 1030 
 
 IO29 
 
 1028 
 
 1027 
 
 1026 
 
 1025 
 
 1024 
 
 1022 
 
 1021 
 
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 I I I I 
 
 98 
 
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 1019 
 
 1018 
 
 1017 
 
 1016 
 
 1015 
 
 1014 
 
 1013 
 
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 I I I I 
 
 99 
 
 1010 
 
 1OO9 
 
 1008 
 
 1007 
 
 1006 
 
 1005 
 
 1004 
 
 1003 
 
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 3 
 
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 7 
 
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 5 
 
 6789 
 
 
 
 A 
 
 
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 T 1 
 
 
 
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 Subtract Differences. 
 
138 
 
 SQUARES 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 2468 
 
 5 
 
 6789 
 
 1-0 
 
 I'OOO 
 
 I'020 
 
 1-040 
 
 ro6i 
 
 1-082 
 
 1-103 
 
 1-124 
 
 I-H5 
 
 i 166 
 
 n88 
 
 10 
 
 13 15 17 19 
 
 1-1 
 
 1-2 
 1-3 
 1-4 
 
 l'2\0 
 I-440 
 
 I<6 
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 1*232 
 1-464 
 1716 
 1-988 
 
 1*254 
 1-488 
 1-742 
 
 2'0l6 
 
 1-277 
 1-513 
 1-769 
 2-045 
 
 1-300 
 i-538 
 1-796 
 2-074 
 
 1-323 
 1-563 
 1-823 
 2-103 
 
 1-346 
 1-588 
 1-850 
 2-132 
 
 1-369 
 1-613 
 1-877 
 2-161 
 
 1-392 
 1-638 
 1-904 
 2*190 
 
 1-416 
 1-664 
 1-932 
 
 2'22O 
 
 2579 
 2 5 7 10 
 3 5 8 ii 
 3 6 9 12 
 
 ii 
 
 12 
 
 13 
 H 
 
 14 16 18 21 
 
 15 17 20 22 
 l6 19 22 24 
 17 20 23 26 
 
 1-5 
 
 2-250 
 
 2-280 
 
 2-310 
 
 2341 
 
 2-372 
 
 2-403 
 
 2-434 
 
 2-4652-496 
 
 2-528 
 
 3 6 9 12 
 
 15 
 
 19 22 25 28 
 
 1-6 
 1-7 
 1-8 
 1-9 
 
 2-560 
 2-890 
 3-240 
 
 3-610 
 
 2'592 
 2-924 
 3-276 
 3-648 
 
 2-624 
 
 2-958 
 3-312 
 
 J686 
 
 2-657 
 2-993 
 3-349 
 3-725 
 
 2-690 
 3-028 
 3-386 
 3-764 
 
 2723 
 3-063 
 
 3-423 
 3-803 
 
 2-756 
 3-098 
 3-460 
 
 3-842 
 
 2-7892-822 
 3-1333-168 
 
 3-4973-534 
 3-881 3-920 
 
 2-856 
 3-204 
 3-572 
 3-960 
 
 3 7 10 13 
 3 7 10 14 
 
 4 7 ii 15 
 4 8 12 16 
 
 16 
 
 17 
 
 18 
 
 19 
 
 2O 23 26 30 
 21 24 28 31 
 
 22 26 30 33 
 23 27 31 35 
 
 2-0 
 
 4-000 
 
 4-040 
 
 4-080 
 
 4-121 
 
 4-162 
 
 4*203 
 
 4-244 
 
 4-285 
 
 4-326 
 
 4-368 
 
 4 8 12 16 
 
 20 
 
 25 2 9 33 37 
 
 2-1 
 2'2 
 2'3 
 2'4 
 
 4-410 
 4-840 
 5-290 
 5-760 
 
 4*452 
 4-884 
 S'SS^ 
 5-808 
 
 4-494 
 4-928 
 5-382 
 5-856 
 
 4-537 
 4*973 
 5-429 
 5-905 
 
 4'58o 
 5*018 
 5H76 
 5-954 
 
 4-623 
 5-063 
 
 5-523 
 6-003 
 
 4-666 
 5-108 
 5-570 
 6-052 
 
 4-7094-752 
 5-1535-198 
 5-6175-664 
 
 6-101 6-150 
 
 4-796 
 
 5- 2 44 
 5712 
 
 6-200 
 
 4 9 13 17 
 4 9 13 18 
 
 5 9 H 19 
 5 10 15 20 
 
 21 
 
 22 
 23 
 2 4 
 
 26 30 34 39 
 27 31 36 40 
 28 33 38 42 
 29 34 39 44 
 
 2-5 
 
 6-250 
 
 6-300 
 
 6-350 
 
 6-401 
 
 6-452 
 
 6-503 
 
 6-554 
 
 6-605 
 
 6-656 
 
 6-708 
 
 5 10 15 20 
 
 25 
 
 31 36 41 46 
 
 2'6 
 2'7 
 2'8 
 2'9 
 
 6760 
 7-290 
 7-840 
 8-410 
 
 6-812 
 7*344 
 7-896 
 8-468 
 
 6-864 
 7-398 
 7-952 
 8-526 
 
 6-917 
 
 7-453 
 8-009 
 
 8-585 
 
 6-970 
 7-508 
 8-066 
 8-644 
 
 7-023 
 
 7-563 
 8-123 
 8-703 
 
 7076 
 7-618 
 8- 1 80 
 8-762 
 
 7-1297*182 
 7-6737-728 
 8-2378-294 
 8-821 8'88o 
 
 7-236 
 7-784 
 8-352 
 
 8-940 
 
 5 ii 16 21 
 5 ii 16 22 
 6 ii 17 23 
 
 6 12 18 24 
 
 26 
 27 
 28 
 29 
 
 32 37 42 48 
 
 33 38 44 49 
 34 40 46 51 
 
 35 4i 47 53 
 
 3-0 
 
 9-000 
 
 9-060 
 
 9-120 
 
 9-181 
 
 9-242 
 
 9-303 
 
 9-364 
 
 9-425 
 
 9-486 
 
 9-548 
 
 6 12 18 24 
 
 30 
 
 37 43 49 55 
 
 3-1 { 
 
 3'2 
 3'3 
 3'4 
 
 9*610 
 
 10-24 
 10-89 
 11-56 
 
 9-672 
 
 10*30 
 10-96 
 II-63 
 
 9734 
 10-37 
 
 11-02 
 
 11-70 
 
 9-797 
 
 10-43 
 11-09 
 11-76 
 
 9-860 
 
 10-50 
 ii'i6 
 11-83 
 
 9923 
 10-56 
 
 U'22 
 11*90 
 
 9-986 
 
 10*63 
 11-29 
 
 11-97 
 
 10-05 '10*11 
 
 10*69 I0 "7 6 
 11-3611-42 
 12-0412-11 
 
 10-18 
 10-82 
 11-49 
 12-18 
 
 6 13 19 25 
 1123 
 1123 
 
 I I 2 
 1123 
 
 3 1 
 3 
 
 3 
 3 
 3 
 
 38 44 50 57 
 4556 
 4556 
 4556 
 4566 
 
 3-5 
 
 12-25 
 
 I2-32 
 
 12-39 
 
 12-46 
 
 12-53 
 
 1 2 '60 
 
 12-67 
 
 12-74 
 
 12-82 
 
 12-89 
 
 1123 
 
 4 
 
 4566 
 
 3'6 
 3'7 
 3'8 
 3'9 
 
 12-96 
 13-69 
 14-44 
 15-21 
 
 I3-03 
 13-76 
 
 I4-5 2 
 15-29 
 
 13-10 
 13-84 
 14-59 
 15-37 
 
 13-18 
 13-91 
 14-67 
 I5H4 
 
 13-25 
 13*99 
 I4-75 
 15-52 
 
 I3-32 
 14-06 
 14-82 
 I5-60 
 
 13-40 
 14-14 
 14-90 
 15-68 
 
 13-47 
 
 L 4 '2I 
 14-98 
 15-76 
 
 13-54 
 14-29 
 
 15-05 
 15-84 
 
 13-62 
 14-36 
 
 15-13 
 15-92 
 
 I I 2 j 
 I 2 2 
 122 
 I 2 2 
 
 4 
 
 4 
 4 
 4 
 
 4567 
 4567 
 5567 
 5667 
 
 4-0 
 
 16-00 
 
 16-08 
 
 16-16 
 
 16-24 
 
 16-32 
 
 16-40 
 
 16-48 
 
 I6-56 
 
 16-65 
 
 16-73 
 
 I 2 2 
 
 4 
 
 566 7 
 
 4*1 
 4'2 
 4'3 
 
 4'4 
 
 16-81 
 17-64 
 18-49 
 19-36 
 
 16-89 
 17-72 
 18-58 
 19-45 
 
 16-97 
 17-81 
 18-66 
 19-54 
 
 17-06 
 17-89 
 
 18-75 
 19*62 
 
 17-14 
 
 17-98 
 18-84 
 19-71 
 
 I7-22 
 
 18-06 
 18-92 
 19-80 
 
 17-31 
 18-15 
 19-01 
 19-89 
 
 I7-39 
 18-23 
 I9TO 
 I 9 - 9 8 
 
 17-47 
 18-32 
 19-18 
 20-07 
 
 17-56 
 18*40 
 19-27 
 
 20'l6 
 
 1223 
 1233 
 1233 
 1234 
 
 4 
 4 
 4 
 4 
 
 5677 
 5678 
 5678 
 5678 
 
 4-5 
 
 20*25 
 
 20-34 
 
 20-43 
 
 26-52 
 
 20' 6 1 
 
 20-70 
 
 20-79 
 
 20-88 
 
 20-98 
 
 21-07 
 
 1234 
 
 5 
 
 5678 
 
 4-6 
 4-7 
 4'8 
 4'9 
 
 2I'l6 
 
 22-09 
 
 23-04 
 
 24-01 
 
 21-25 
 22-18 
 23-14 
 24-11 
 
 21-34 
 22-28 
 23-23 
 24-21 
 
 21-44 
 
 22-37 
 
 23-33 
 24-30 
 
 21-53 
 22-47 
 
 23-43 
 24-40 
 
 21-62 
 22-56 
 23-52 
 24-50 
 
 21-72 
 
 22-66 
 
 2362 
 
 24 60 
 
 21-81 
 
 22-75 
 23-72 
 
 24-70 
 
 21-90 
 22*85 
 23-81 
 24-80 
 
 22'OO 
 22-94 
 23-91 
 24-90 
 
 1234 
 1234 
 1234 
 I2 34 
 
 5 
 5 
 
 5 
 5 
 
 6778 
 6789 
 6789 
 6789 
 
 5-0 
 
 25-00 
 
 25-10 
 
 25-20 
 
 25-30 
 
 25-40 
 
 25-50 
 
 25-60 
 
 25-70 
 
 25-81 
 
 25-91 
 
 1234 
 
 5 
 
 6789 
 
 5-1 
 5-2 
 5-3 
 5'4 
 
 26-01 
 
 27-04 
 28-09 
 29-16 
 
 26*11 
 27-14 
 28-20 
 29-27 
 
 26-21 
 27-25 
 28*30 
 29-38 
 
 26-32 
 
 27-35 
 28-41 
 
 29-48 
 
 26-42 
 
 27-46 
 28-52 
 
 29-59 
 
 26-52 
 27-56 
 28-62 
 29-70 
 
 26-63 
 
 27-67 
 28-73 
 29-81 
 
 26-73 
 
 27-77 
 28-84 
 29-92 
 
 26-83 
 27-88 
 28-94 
 30-03 
 
 26-94 
 27- 9 8 
 29-05 
 30-I 4 
 
 1234 
 1234 
 1234 
 1234 
 
 5 
 5 
 5 
 5 
 
 5 
 
 6789 
 6789 
 6 7 9 10 
 7 8 9 10 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 6789 
 
139 
 
 SQUARES 
 
 5-5 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234. 
 
 5 
 
 6789 
 
 30-25 
 
 30-36 
 
 30*47 
 
 30*58 
 
 30-69 
 
 30-80 
 
 30-91 
 
 31-02 
 
 3i*i4 
 
 31-25 
 
 1234 
 
 6 
 
 7 8 9 10 
 
 5'6 
 5-7 
 5'8 
 5'9 
 
 3i'3 6 
 3^49 
 33^4 
 34'8i 
 
 31-47 
 32-60 
 
 33-76 
 34-93 
 
 3I-58 
 32-72 
 33*87 
 35'05 
 
 31-7031*81 
 32-8332-95 
 
 33*9934-" 
 35-1635*28 
 
 31-92 
 33-06 
 34-22 
 35-40 
 
 32-04 
 33'i8 
 34*34 
 35*52 
 
 32*15 
 
 33 29 
 34'46 
 35*64 
 
 32-26 
 33*4i 
 34*57 
 35*76 
 
 32*38 
 33*52 
 34*69 
 
 35*88 
 
 1235 
 1235 
 1245 
 1245 
 
 6 
 
 6 
 6 
 6 
 
 7 8 9 10 
 78 9 10 
 7-8 9 ii 
 7 8 10 ii 
 
 6-0 
 
 36 -oo 
 
 36-12 
 
 36-24 
 
 36-36 
 
 36*48 
 
 36-60 
 
 36*72 
 
 36-84 
 
 36*97 
 
 37*09 
 
 1245 
 
 6 
 
 7 8 10 ii 
 
 6-1 
 6'2 
 6'3 
 6'4 
 
 37-21 
 
 38-44 
 39-69 
 40-96 
 
 37*33 
 38-56 
 39-82 
 41-09 
 
 37*45 
 38-69 
 
 39 "94 
 41-22 
 
 37*58 
 38-81 
 40-07 
 4i*34 
 
 37-70 
 38-94 
 40*20 
 
 4i*47 
 
 37-82 
 39-06 
 40-32 
 41-60 
 
 37*95 
 39* I 9 
 40-45 
 4i*73 
 
 38-07 
 
 39*3! 
 40-58 
 41-86 
 
 38-19 
 39*44 
 40-70 
 41-99 
 
 38-32 
 39*56 
 40-83 
 42-12 
 
 1245 
 1345 
 1345 
 1345 
 
 6 
 6 
 6 
 6 
 
 7 9 10 ii 
 8 9 10 ii 
 8 9 10 ii 
 8 9 10 12 
 
 6-5 
 
 42-25 
 
 42-38 
 
 42*51 
 
 42-64 
 
 42-77 
 
 42-90 
 
 43*03 
 
 43-16 
 
 43*30 
 
 43*43 
 
 1345 
 
 7 
 
 8 9 10 12 
 
 6'6 
 6'7 
 6'8 
 6'9 
 
 43'56 
 
 44-89 
 46-24 
 47-61 
 
 43*69 
 45-02 
 46-38 
 
 47*75 
 
 43*82 
 45* 16 
 46-51 
 47-89 
 
 43*96 
 45' 2 9 
 46*65 
 48-02 
 
 44-09 
 45*43 
 46-79 
 48-16 
 
 44-22 
 
 45-56 
 46-92 
 48-30 
 
 44*36 
 45*70 
 47-06 
 48-44 
 
 44*49 
 45*83 
 47-20 
 
 48-58 
 
 44-62 
 45*97 
 47*33 
 48-72 
 
 44-76 
 46-10 
 
 47*47 
 48-86 
 
 1345 
 1345 
 1345 
 1346 
 
 7 
 
 7 
 7 
 7 
 
 8 9 ii 12 
 8 9 ii 12 
 
 8 IO II 12 
 
 8 10 ii 13 
 
 7'0 
 
 49-00 
 
 49-14 
 
 49-28 
 
 49H2 
 
 49*56 
 
 49-70 
 
 49*84 
 
 49-98 
 
 50*13 
 
 50-27 
 
 134-6 
 
 7 
 
 8 10 ii 13 
 
 7'1 
 7'2 
 7'3 
 7'4 
 
 5'4i 
 51-84 
 53-29 
 54-76 
 
 50*55 
 5i*98 
 53'44 
 54'9 I 
 
 50-69 
 52-13 
 53-58 
 55-o6 
 
 50-84 
 
 52-27 
 
 53-73 
 55-20 
 
 5o*98 
 52*42 
 53*88 
 55*35 
 
 51-12 
 5 2 -56 
 54*02 
 55*50 
 
 51-27 
 52-71 
 54-17 
 55-65 
 
 5J-4I 
 
 52-85 
 54*32 
 55-80 
 
 5I-55 
 53*00 
 54*46 
 55-95 
 
 5i 70 
 53*14 
 54*6i 
 56*10 
 
 1346 
 1346 
 1346 
 1346 
 
 7 
 7 
 7 
 7 
 
 9 10 ii 13 
 9 10 12 13 
 9 10 12 13 
 9 10 12 13 
 
 7-5 
 
 56-25 
 
 56-40 
 
 56-55 
 
 56-70 
 
 56-85 
 
 57*oo 
 
 57-I5 
 
 57-30 
 
 57-46 
 
 57*6i 
 
 2356 
 
 8 
 
 9 ii 12 14 
 
 7'6 
 
 7*7 
 7'8 
 7'9 
 
 57-76 
 59-29 
 60-84 
 62-41 
 
 57-9! 
 59*44 
 61-00 
 62-57 
 
 58-06 
 59-60 
 61*15 
 62-73 
 
 58-22 
 
 59*75 
 61-31 
 62-88 
 
 58*37 
 59-91 
 
 6i-47 
 63*04 
 
 58*52 
 60 "06 
 61*62 
 63-20 
 
 58-68 
 
 6O"22 
 61-78 
 63*36 
 
 58-83 
 60-37 
 61-94 
 63-52 
 
 58*98 
 60*53 
 62*09 
 63*68 
 
 59*H 
 60-68 
 62-25 
 63*84 
 
 2356 
 2356 
 2356 
 2356 
 
 8 
 8 
 8 
 8 
 
 9 ii 12 14 
 9 ii 12 14 
 
 9 ii 13 H 
 10 ii 13 14 
 
 8-0 
 
 64-00 
 
 64-16 
 
 64-32 
 
 64-48 
 
 64-64 
 
 64-80 
 
 6 4 * 9 6 
 
 65-12 
 
 65-29 
 
 65*45 
 
 2356 
 
 8 
 
 10 ii 13 14 
 
 8-1 
 8'2 
 8'3 
 8'4 
 
 65-61 
 
 67-24 
 68-89 
 70-56 
 
 65'77 
 67-40 
 69-06 
 7073 
 
 65-93 
 67-57 
 69*22 
 70-90 
 
 66-10 
 67*73 
 69-39 
 71-06 
 
 66*26 
 67-90 
 69-56 
 71-23 
 
 66-42 
 68-06 
 69*72 
 71*40 
 
 66*59 
 68*23 
 69*89 
 7i*57 
 
 66-75 
 68-39 
 70*06 
 
 71-74 
 
 66-91 
 68-56 
 70-22 
 71-91 
 
 67*08 
 68-72 
 
 72*39 
 72-08 
 
 2357 
 2357 
 2357 
 
 2357 
 
 8 
 8 
 8 
 8 
 
 10 n 13 15 
 
 10 12 13 15 
 10 12 13 15 
 10 12 14 15 
 
 8'5 
 
 72-25 
 
 72*42 
 
 72-59 
 
 72-76 
 
 7293 
 
 73-10 
 
 73*27 
 
 73*44 
 
 73*62 
 
 73*79 
 
 2357 
 
 9 
 
 10 12 14 15 
 
 8*6 
 8'7 
 8'8 
 8-9 
 
 73-96 
 75-69 
 77-44 
 79-21 
 
 74*13 
 75*86 
 77-62 
 
 79*39 
 
 74-30 
 76-04 
 
 7779 
 79-57 
 
 74*48 
 76*21 
 
 77*97 
 79-74 
 
 74*65 
 76-39 
 78-15 
 79*92 
 
 75*82 
 76-56 
 78*32 
 80* 10 
 
 75*00 
 76-74 
 78*50 
 80-28 
 
 75-17 
 76*91 
 
 78-68 
 80*46 
 
 75*34 
 77*09 
 78-85 
 80-64 
 
 75*52 
 77*26 
 
 79*03 
 80*82 
 
 2357 
 2457 
 2457 
 2457 
 
 9 
 9 
 9 
 9 
 
 10 12 14 16 
 n 12 14 16 
 ii 12 14 16 
 ii 13 14 16 
 
 9-0 
 
 8 1 -oo 
 
 81-18 
 
 81*36 
 
 8r54 
 
 81-72 
 
 81-90 
 
 82-08 
 
 82-26 
 
 82-45 
 
 82-63 
 
 2457 
 
 9 
 
 ii 13 14 16 
 
 9-1 
 9'2 
 9'3 
 9'4 
 
 82-81 
 84-64 
 86-49 
 88-36 
 
 82-99 
 84-82 
 86-68 
 88-55 
 
 83-17 
 85-01 
 86-86 
 88-74 
 
 83-36 
 85-19 
 87*05 
 88-92 
 
 83*54 
 85*38 
 87*24 
 89-11 
 
 83*72 
 85-56 
 87-42 
 89-30 
 
 83-91 
 
 85*75 
 87-61 
 
 89*49 
 
 84*09 
 
 85-93 
 87*80 
 89-68 
 
 84*27 
 86-12 
 
 87*98 
 89*87 
 
 84*46 
 86-30 
 88-17 
 90-06 
 
 2457 
 2467 
 2467 
 2468 
 
 9 
 
 9 
 9 
 9 
 
 ii 13 15 16 
 ii 13 15 17 
 ii 13 15 17 
 ii 13 15 17 
 
 9-5 
 
 90-25 
 
 90-44 
 
 90-63 
 
 90-82 
 
 91*01 
 
 91-20 
 
 9i*39 
 
 91-58 
 
 91-78 
 
 91-97 
 
 2468 
 
 10 
 
 ii 13 15 17 
 
 9'6 
 9-7 
 9'8 
 9'9 
 
 92*16 
 94-09 
 96-04 
 98-01 
 
 92*35 
 94-28 
 96-24 
 98-21 
 
 92-54 
 94-48 
 
 96-43 
 98*41 
 
 92*74 
 94-67 
 
 96*63 
 98-60 
 
 92*93 
 94*87 
 96-83 
 98-80 
 
 93-12 
 
 95-06 
 97-02 
 99-00 
 
 93*32 
 95-26 
 97-22 
 99-20 
 
 93*5i 
 
 95*45 
 97-42 
 99-40 
 
 93-70 
 
 95'65 
 97-61 
 99-60 
 
 93*90 
 95*84 
 97*81 
 99-80 
 
 9 
 
 2468 
 2468 
 2468 
 2468 
 
 10 
 IO 
 IO 
 
 10 
 
 12 14 15 17 
 
 12 14 16 18 
 
 12 14 16 18 
 12 14 16 18 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 1234 
 
 5 
 
 6789 
 
140 
 
 NATURAL SINES 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 1' 2' 3' 4' 5' 
 
 
 
 oooo 
 
 0017 
 
 '0035 
 
 0052 
 
 0070 
 
 0087 
 
 0105 
 
 0122 
 
 0140 
 
 015 
 
 3 6 9 12 15 
 
 1 
 
 0175 
 
 0192 
 
 0209 
 
 0227 
 
 0244 
 
 0262 
 
 0279 
 
 0297 
 
 0314 
 
 033 
 
 3 6 9 12 15 j 
 
 2 
 
 0349 
 
 0366 
 
 0384 
 
 0401 
 
 0419 
 
 0436 
 
 0454 0471 
 
 0488 
 
 0506 
 
 3 6 9 12 15 
 
 3 
 
 '0523 
 
 0541 
 
 55 8 
 
 0576 
 
 0593 
 
 0610 
 
 0628 0645 
 
 0663 
 
 0680 
 
 3 6 9 12 15 ; 
 
 4 
 
 0698 
 
 0715 
 
 0732 
 
 0750 
 
 0767 
 
 0785 
 
 0802 
 
 0819 
 
 0837 
 
 0854 
 
 3 6 9 12 14 | 
 
 5 
 
 0872 
 
 0889 
 
 0906 
 
 0924 
 
 0941 
 
 0958 
 
 0976 
 
 0993 
 
 ion 
 
 1028 
 
 3 6 9 12 14 
 
 6 
 
 1045 
 
 1063 
 
 1080 
 
 1097 
 
 1115 
 
 1132 
 
 1149 
 
 Il67 
 
 1184 
 
 120 
 
 3 6 9 12 14 ; 
 
 7 
 
 1219 
 
 1236 
 
 1253 
 
 1271 
 
 1288 
 
 1305 
 
 1323 
 
 1340 
 
 1357 
 
 *374 
 
 3 6 9 12 14 
 
 8 
 
 1392 
 
 1409 
 
 1426 
 
 1444 
 
 1461 
 
 1478 
 
 U95 
 
 !5i3 
 
 1530 
 
 ^547 
 
 3 6 9 12 14 
 
 9 
 
 1564 
 
 1582 
 
 1599 
 
 1616 
 
 1633 
 
 1650 
 
 1668 
 
 1685 
 
 1702 
 
 1719 
 
 3 6 9 ii 14 
 
 10 
 
 1736 
 
 1754 
 
 1771 
 
 1788 
 
 1805 
 
 1822 
 
 1840 
 
 1857 
 
 1874 
 
 189 
 
 3 6 9 ii 14 
 
 11 
 
 1908 
 
 1925 
 
 1942 
 
 1959 
 
 1977 
 
 1994 
 
 2OII 
 
 2028 
 
 2045 
 
 2062 
 
 3 6 9 ii 14 ; 
 
 12 
 
 2079 
 
 2096 
 
 2113 
 
 2130 
 
 2147 
 
 2164 
 
 2181 
 
 2198 
 
 2215 
 
 2233 
 
 3 6 9 ii 14 
 
 13 
 
 2250 
 
 2267 
 
 2284 
 
 2300 
 
 2317 
 
 2334 
 
 2351 
 
 2368 
 
 2385 
 
 2402 
 
 3 6 8 ii 14 
 
 14 
 
 2419 
 
 2436 
 
 2453 
 
 2470 
 
 2487 
 
 2504 
 
 2521 
 
 2538 
 
 2554 
 
 257i 
 
 3 6 8 ii 14 
 
 15 
 
 2588 
 
 2605 
 
 2622 
 
 2639 
 
 2656 
 
 2672 
 
 2689 
 
 2706 
 
 2723 
 
 2740 
 
 3 6 8 ii 14 
 
 16 
 
 2756 
 
 2773 
 
 2790 
 
 2807 
 
 2823 
 
 2840 
 
 2857 
 
 2874 
 
 2890 
 
 2907 
 
 3 6 8 ii 14 
 
 17 
 
 2924 
 
 2940 
 
 2957 
 
 2 974 
 
 2990 
 
 3007 
 
 3024 
 
 3040 
 
 3057 
 
 3074 
 
 3 6 8 ii 14 
 
 18 
 
 3090 
 
 3107 
 
 3123 
 
 3 MO 
 
 3156 
 
 3i73 
 
 3I 9 
 
 3206 
 
 3223 
 
 3239 
 
 3 6 8 ii 14 
 
 19 
 
 3256 
 
 3272 
 
 3289 
 
 3305 
 
 3322 
 
 3338 
 
 3355 
 
 337i 
 
 3387 
 
 3404 
 
 3 5 8 ii 14 
 
 2O 
 
 3420 
 
 3437 
 
 3453 
 
 3469 
 
 3486 
 
 35 2 
 
 35i8 
 
 3535 
 
 355i 
 
 3567 
 
 3 5 8 ii 14 
 
 21 
 
 3584 
 
 3600 
 
 3616 
 
 3633 
 
 3649 
 
 3665 
 
 3681 
 
 3 6 97 
 
 37H 
 
 3730 
 
 3 5 8 ii 14 
 
 22 
 
 3746 
 
 3762 
 
 3778 
 
 3795 
 
 3811 
 
 3827 
 
 3843 
 
 3859 
 
 3875 3891 
 
 3 5 8 ii 13 
 
 23 
 
 3907 
 
 3923 
 
 3939 
 
 3955 
 
 397i 
 
 3987 
 
 4003 
 
 4019 
 
 4035 
 
 4051 
 
 3 5 8 ii 13 
 
 24 
 
 4067 
 
 4083 
 
 4099 
 
 4"5 
 
 4131 
 
 4H7 
 
 4163 
 
 4i79 
 
 4i95 
 
 4210 
 
 3 5 8 ii 13 
 
 25 
 
 4226 
 
 4242 
 
 4258 
 
 4274 
 
 4289 
 
 4305 
 
 432i 
 
 4337 
 
 4352 
 
 4368 
 
 3 5 8 ii 13 
 
 26 
 
 4384 
 
 4399 
 
 4415 
 
 443i 
 
 4446 
 
 4462 
 
 4478 
 
 4493 
 
 4509 
 
 4524 
 
 3 5 8 10 13 
 
 27 
 
 4540 
 
 4555 
 
 457i 
 
 4586 
 
 4602 
 
 4617 
 
 4633 
 
 4648 
 
 4664 
 
 4679 
 
 3 5 8 10 13 
 
 28 
 
 4695 
 
 4710 
 
 4726 
 
 474i 
 
 4756 
 
 4772 
 
 4787 
 
 4802 
 
 4818 
 
 4833 
 
 3 5 8 10 13 i 
 
 29 
 
 4848 
 
 4863 
 
 4879 
 
 4894 
 
 4909 
 
 4924 
 
 4939 
 
 4955 
 
 4970 
 
 4985. 
 
 3 5 8 10 13 
 
 30 
 
 5000 
 
 5015 
 
 5030 
 
 5045 
 
 5060 
 
 5075 
 
 5090 
 
 5105 
 
 5120 
 
 5135 
 
 3 5 8 10 13 
 
 31 
 
 5150 
 
 5165 
 
 5180 
 
 5195 
 
 5210 
 
 5225 
 
 5240 
 
 5255 
 
 5 2 7o 
 
 5284 
 
 2 5 7 10 12 
 
 32 
 
 5299 
 
 53H 
 
 5329 
 
 5344 
 
 5358 
 
 5373 
 
 5388 
 
 5402 
 
 54i7 
 
 5432 
 
 2 5 7 10 12 
 
 33 
 34 
 
 5446 
 5592 
 
 546i 
 5606 
 
 5476 
 5621 
 
 5490 
 5635 
 
 5505 
 5650 
 
 5519 
 5664 
 
 5534 
 5678 
 
 5548 
 5 6 93 
 
 5563 
 5707 
 
 5577 
 572i 
 
 2 5 7 10 12 
 
 2 5 7 10 12 
 
 35 
 
 5736 
 
 575 
 
 5764 
 
 5779 
 
 5793 
 
 5807 
 
 5821 
 
 5835 
 
 5850 
 
 5864 
 
 2 5 7 9 12 
 
 36 
 
 5878 
 
 5892 
 
 5906 
 
 5920 
 
 593* 
 
 5948 
 
 5962 
 
 5976 
 
 5990 
 
 6004 
 
 2 5 7 9 12 
 
 37 
 
 6018 
 
 6032 
 
 6046 
 
 6060 
 
 6074 
 
 6088 
 
 6101 
 
 6115 
 
 6129 
 
 6143 
 
 2 5 791^ 
 
 38 
 
 6157 
 
 6170 
 
 6184 
 
 6198 
 
 6211 
 
 6225 
 
 6239 
 
 6252 
 
 6266 
 
 6280 
 
 2 5 7 9 ii 
 
 39 
 
 6293 
 
 6307 
 
 6320 
 
 6334 
 
 6 347 
 
 6361 
 
 6 374 
 
 6388 
 
 6401 
 
 6414 
 
 2 4 7 9 ii 
 
 40 
 
 6428 
 
 6441 
 
 6455 
 
 6468 
 
 6481 
 
 6494 
 
 6508 
 
 6521 
 
 6534 
 
 6 547 
 
 2 4 7 9 ii 
 
 41 
 
 6561 
 
 6574 
 
 6587 
 
 6600 
 
 6613 
 
 6626 
 
 6639 
 
 6652 
 
 6665 
 
 6678 
 
 2 4 7 9 ii 
 
 42 
 43 
 44 
 
 6691 
 
 6820 
 6947 
 
 6704 
 6833 
 6959 
 
 6717 
 6845 
 6972 
 
 6730 
 6858 
 6984 
 
 6743 
 6871 
 6997 
 
 6756 
 6884 
 7009 
 
 6769 
 6896 
 7022 
 
 6782 
 6909 
 7034 
 
 6794 
 6921 
 7046 
 
 6807 
 6934 
 7059 
 
 2 4 6 9 n 
 2 4 6 8 ii 
 2 4 6 8 10 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 64' 
 
 ' 2' 3' 4.' 5' 
 
141 
 
 NATURAL SINES 
 
 45 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 1' 2' 3' 4' 5' 
 
 7071 
 
 7083 
 
 7096 
 
 7108 
 
 7120 
 
 7i33 
 
 7H5 
 
 7i57 
 
 7169 
 
 7181 
 
 2 4 6 8 10 
 
 46 
 47 
 48 
 49 
 
 7193 
 7314 
 
 743 i 
 7547 
 
 7206 
 7325 
 7443 
 7559 
 
 7218 
 7337 
 7455 
 7570 
 
 7230 
 
 7349 
 7466 
 758i 
 
 7242 
 736i 
 7478 
 7593 
 
 7254 
 7373 
 7490 
 7604 
 
 7266 
 7385 
 75oi 
 7615 
 
 7278 
 7396 
 75i3 
 7627 
 
 7290 
 
 7408 
 7524 
 7638 
 
 7302 
 7420 
 7536 
 7649 
 
 2 4 6 8 10 
 2 4 6 8 10 
 2 4 6 8 10 
 24689 
 
 50 
 
 7660 
 
 7672 
 
 7683 
 
 7694 
 
 7705 
 
 7716 
 
 7727 
 
 7738 
 
 7749 
 
 7760 
 
 24679 
 
 51 
 52 
 53 
 54 
 
 7771 
 7880 
 7986 
 8090 
 
 7782 
 7891 
 
 7997 
 8100 
 
 7793 
 7902 
 8007 
 8111 
 
 7804 
 7912 
 8018 
 8121 
 
 7815 
 7923 
 8028 
 8131 
 
 7826 
 7934 
 8039 
 8141 
 
 7837 
 7944 
 8049 
 8151 
 
 7848 
 
 7955 
 8059 
 8161 
 
 7859 
 7965 
 8070 
 8171 
 
 7869 
 7976 
 8080 
 8181 
 
 24579 
 24579 
 23579 
 23578 
 
 55 
 
 8192 
 
 8202 
 
 8211 
 
 8221 
 
 8231 
 
 8241 
 
 8251 
 
 8261 
 
 8271 
 
 8281 
 
 23578 
 
 56 
 57 
 58 
 59 
 
 8290 
 
 8387 
 8480 
 
 8572 
 
 8300 
 8396 
 8490 
 8581 
 
 8310 
 8406 
 
 8499 
 8590 
 
 8320 
 
 8415 
 8508 
 
 8599 
 
 8329 
 
 8425 
 8517 
 8607 
 
 8339 
 8434 
 8526 
 8616 
 
 8348 
 8443 
 8536 
 8625 
 
 8358 
 8453 
 
 3S 
 
 8368 
 8462 
 8554 
 8643 
 
 8377 
 8471 
 8563 
 8652 
 
 23568 
 23568 
 23568 
 13467 
 
 60 
 
 8660 
 
 8669 
 
 8678 
 
 8686 
 
 8695 
 
 8704 
 
 8712 
 
 8721 
 
 8729 
 
 8738 
 
 13467 
 
 61 
 62 
 63 
 64 
 
 8746 
 8829 
 8910 
 8988 
 
 8755 
 8838 
 8918 
 8996 
 
 8763 
 8846 
 8926 
 9003 
 
 8771 
 8854 
 8934 
 9011 
 
 8780 
 8862 
 8942 
 9018 
 
 8788 
 8870 
 8949 
 9026 
 
 8796 
 8878 
 8957 
 9033 
 
 8805 
 
 8886 
 8965 
 9041 
 
 8813 
 8894 
 8973 
 9048 
 
 8821 
 8902 
 8980 
 9056 
 
 13467 
 
 1 3 4 5 7 
 13456 
 13456 
 
 65 
 
 9063 
 
 9070 
 
 9078 
 
 9085 
 
 9092 
 
 9100 
 
 9107 
 
 9114 
 
 9121 
 
 9128 
 
 12456 
 
 66 
 67 
 68 
 69 
 
 9135 
 9205 
 9272 
 9336 
 
 9H3 
 9212 
 9278 
 9342 
 
 9i5 
 9219 
 
 9285 
 9348 
 
 9157 
 9225 
 9291 
 9354 
 
 9164 
 
 9232 
 9298 
 9361 
 
 9171 
 
 9239 
 9304 
 9367 
 
 9178 
 9245 
 93" 
 9373 
 
 9184 
 9252 
 9317 
 9379 
 
 9191 
 
 9259 
 9323 
 9385 
 
 9198 
 9265 
 9330 
 939i 
 
 12356 
 12346 
 12345 
 1 2 3 4 5 
 
 70 
 
 9397 
 
 9403 
 
 9409 
 
 9415 
 
 942i 
 
 9426 
 
 9432 
 
 9438 
 
 9444 
 
 9449 
 
 12345 
 
 71 
 72 
 73 
 74 
 
 9455 
 95" 
 95 6 3 
 9613 
 
 9461 
 
 95 l6 
 9568 
 9617 
 
 9466 
 952i 
 9573 
 9622 
 
 9472 
 9527 
 9578 
 9627 
 
 9478 
 9532 
 9583 
 9632 
 
 9483 
 9537 
 9588 
 9636 
 
 9489 
 9542 
 
 9593 
 9641 
 
 9494 
 9548 
 
 9 I 9 ! 
 9646 
 
 9500 
 
 9553 
 9603 
 9650 
 
 955 
 9558 
 9608 
 
 9655 
 
 12345 
 12334 
 12234 
 12234 
 
 75 
 
 9 6 59 
 
 9664 
 
 9668 
 
 9673 
 
 9677 
 
 9681 
 
 9686 
 
 9690 
 
 9694 
 
 9699 
 
 11234 
 
 76 
 77 
 78 
 79 
 
 9703 
 9744 
 978i 
 9816 
 
 9707 
 9748 
 9785 
 9820 
 
 9711 
 
 975i 
 9789 
 
 9823 
 
 9715 
 9755 
 9792 
 9826 
 
 9720 
 
 9759 
 9796 
 9829 
 
 9724 
 9763 
 9799 
 9833 
 
 9728 
 9767 
 9803 
 9836 
 
 9732 
 9770 
 9806 
 9839 
 
 973 6 
 9774 
 9810 
 9842 
 
 9740 
 9778 
 9813 
 9845 
 
 11233 
 11233 
 11223 
 11223 
 
 80 
 
 9848 
 
 9851 
 
 9854 
 
 9857 
 
 9860 
 
 9863 
 
 9866 
 
 9869 
 
 9871 
 
 9874 
 
 I I 2 2 
 
 81 
 82 
 83 
 84 
 
 9877 
 9903 
 9925 
 9945 
 
 9880 
 
 9905 
 9928 
 
 9947 
 
 9882 
 9907 
 9930 
 9949 
 
 9885 
 9910 
 9932 
 
 995 i 
 
 9888 
 9912 
 9934 
 995 2 
 
 9890 
 9914 
 993 6 
 9954 
 
 9893 
 9917 
 
 9938 
 9956 
 
 9895 
 9919 
 9940 
 9957 
 
 9898 
 992i 
 9942 
 
 9959 
 
 9900 
 9923 
 9943 
 9960 
 
 I I 2 2 
 O I I 2 2 
 I I I 2 
 I I I I 
 
 85 
 
 9962 
 
 9963 
 
 9965 
 
 9966 
 
 9968 
 
 9969 
 
 9971 
 
 9972 
 
 9973 
 
 9974 
 
 I I I 
 
 86 
 87 
 88 
 89 
 
 9976 
 9986 
 9994 
 9998 
 
 9977 
 9987 
 
 9995 
 9999 
 
 9978 
 9988 
 9995 
 9999 
 
 9979 
 9989 
 9996 
 9999 
 
 18' 
 
 9980 
 9990 
 9996 
 9999 
 
 998i 
 9990 
 9997 
 
 I'OOO 
 
 9982 
 9991 
 9997 
 
 OCX) 
 
 9983 
 9992 
 9997 
 
 I '000 
 
 9984 
 9993 
 9998 
 
 I 'OCX) 
 
 9985 
 9993 
 9998 
 
 I'OOO 
 
 O O I I I 
 I I 
 O O O O O 
 O O O O O 
 
 
 0' 
 
 6' 
 
 12' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 1' 2' 3' 4' 5' 
 
142 
 
 NATURAL COSINES 
 
 
 
 
 
 
 
 
 
 
 
 
 Subtract 
 
 
 V 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 Differences. 
 
 
 
 
 
 
 
 
 
 
 
 
 1' 2' 3' 4' 5' 
 
 
 
 I'OOO 
 
 rooo 
 
 I '000 
 
 I 'OCX) 
 
 rooo 
 
 I'OOO 
 
 9999 
 
 9999 
 
 '9999 
 
 9999 
 
 o o o o o 
 
 1 
 
 9998 
 
 9998 
 
 9998 
 
 9997 
 
 9997 
 
 9997 
 
 9996 
 
 9996 
 
 9995 
 
 9995 
 
 o o o o o 
 
 2 
 
 9994 
 
 9993 
 
 9993 
 
 9992 
 
 9991 
 
 9990 
 
 9990 
 
 9989 
 
 9988 
 
 9987 
 
 000 I I 1 
 
 3 
 
 9986 
 
 9985 
 
 9984 
 
 9983 
 
 9982 
 
 9981 
 
 9980 
 
 9979 
 
 9978 
 
 9977 
 
 O O I I I 
 
 4 
 
 9976 
 
 9974 
 
 9973 
 
 9972 
 
 9971 
 
 9969 
 
 9968 
 
 9966 
 
 9965 
 
 9963 
 
 O O I I I 
 
 5 
 
 9962 
 
 9960 
 
 9959 
 
 9957 
 
 9956 
 
 9954 
 
 9952 
 
 9951 
 
 9949 
 
 9947 
 
 O I I I I 
 
 6 
 
 9945 
 
 9943 
 
 9942 
 
 9940 
 
 9938 
 
 9936 
 
 9934 
 
 9932 
 
 9930 
 
 9928 
 
 O I I I 2 
 
 7 
 
 9925 
 
 9923 
 
 9921 
 
 9919 
 
 9917 
 
 9914 
 
 9912 
 
 9910 
 
 9907 
 
 9905 
 
 I I 2 2 
 
 8 
 
 9903 
 
 9900 
 
 9898 
 
 9895 
 
 9893 
 
 9890 
 
 9888 
 
 9885 
 
 9882 
 
 9880 
 
 I I 2 2 
 
 9 
 
 9877 
 
 9874 
 
 9871 
 
 9869 
 
 9866 
 
 9863 
 
 9860 
 
 9857 
 
 9854 
 
 9851 
 
 O I I 2 2 
 
 10 
 
 9848 
 
 9845 
 
 9842 
 
 9839 
 
 9836 
 
 9833 
 
 9829 
 
 9826 
 
 9823 
 
 9820 
 
 II223 
 
 11 
 
 9816 
 
 98i3 
 
 9810 
 
 9806 
 
 9803 
 
 9799 
 
 9796 
 
 9792 
 
 9789 
 
 9785 
 
 I I 223 
 
 12 
 
 9781 
 
 9778 
 
 9774 
 
 9770 
 
 9767 
 
 9763 
 
 9759 
 
 9755 
 
 975i 
 
 9748 
 
 i i 2 3 3 i 
 
 13 
 
 9744 
 
 9740 
 
 9736 
 
 9732 
 
 9728 
 
 9724 
 
 9720 
 
 9715 
 
 9711 
 
 9707 
 
 11233 
 
 14 
 
 9703 
 
 9699 
 
 9694 
 
 9690 
 
 9686 
 
 9681 
 
 9677 
 
 9673 
 
 9668 
 
 9664 
 
 11234 
 
 15 
 
 9659 
 
 9655 
 
 9650 
 
 9646 
 
 9641 
 
 9636 
 
 9632 
 
 9627 
 
 9622 
 
 9617 
 
 12234 
 
 16 
 
 9613 
 
 9608 
 
 9603 
 
 9598 
 
 9593 
 
 9588 
 
 9583 
 
 9578 
 
 9573 
 
 9568 
 
 12234 
 
 17 
 
 9563 
 
 9558 
 
 9553 
 
 9548 
 
 9542 
 
 9537 
 
 9532 
 
 9527 
 
 9521 
 
 95i6 
 
 12334 
 
 18 
 
 "95" 
 
 9505 
 
 9500 
 
 9494 
 
 9489 
 
 9483 
 
 9478 
 
 9472 
 
 9466 
 
 9461 
 
 12345 
 
 19 
 
 '9455 
 
 9449 
 
 9*44 
 
 9438 
 
 9432 
 
 9426 
 
 9421 
 
 9415 
 
 9409 
 
 9403 
 
 12345 
 
 20 
 
 '9397 
 
 9391 
 
 9385 
 
 9379 
 
 9373 
 
 93^7 
 
 9361 
 
 9354 
 
 9348 
 
 9342 
 
 12345 
 
 21 
 
 9336 
 
 9330 
 
 9323 
 
 9317 
 
 93ii 
 
 9304 
 
 9298 
 
 9291 
 
 9285 
 
 9278 
 
 12345 
 
 22 
 
 9272 
 
 9265 
 
 9259 
 
 9252 
 
 9245 
 
 9239 
 
 9232 
 
 9225 
 
 9219 
 
 9212 
 
 12346 
 
 23 
 
 9205 
 
 9198 
 
 9191 
 
 9184 
 
 9178 
 
 9171 
 
 9164 
 
 9157 
 
 9150 
 
 9H3 
 
 12356 
 
 24 
 
 9135 
 
 9128 
 
 9121 
 
 9114 
 
 9107 
 
 9100 
 
 9092 
 
 9085 
 
 9078 
 
 9070 
 
 12456 
 
 25 
 
 9063 
 
 9056 
 
 9048 
 
 9041 
 
 9033 
 
 9026 
 
 9018 
 
 9011 
 
 9003 
 
 8996 
 
 1 3 4 5 6 
 
 26 
 
 8988 
 
 8980 
 
 8973 
 
 8965 
 
 8957 
 
 8949 
 
 8942 
 
 8934 
 
 8926 
 
 8918 
 
 13456 
 
 27 
 
 8910 
 
 8902 
 
 8894 
 
 8886 
 
 8878 
 
 8870 
 
 8862 
 
 8854 
 
 8846 
 
 8838 
 
 13457 
 
 28 
 
 8829 
 
 8821 
 
 8813 
 
 8805 
 
 8796 
 
 8788 
 
 8780 
 
 8771 
 
 8763 
 
 8755 
 
 13467 
 
 29 
 
 8746 
 
 8738 
 
 8729 
 
 8721 
 
 8712 
 
 8704 
 
 8695 
 
 8686 
 
 8678 
 
 8669 
 
 13467 
 
 30 
 
 8660 
 
 8652 
 
 8643 
 
 8634 
 
 8625 
 
 8616 
 
 8607 
 
 8599 
 
 8590 
 
 8581 
 
 13467 
 
 31 
 
 32 
 
 8572 
 8480 
 
 8563 
 8471 
 
 8554 
 8462 
 
 8545 
 8453 
 
 8536 
 8443 
 
 8526 
 8434 
 
 8517 
 8425 
 
 8508 
 84'5 
 
 8499 
 8406 
 
 8490 
 8396 
 
 23568 
 23568 
 
 33 
 34 
 
 8387 
 8290 
 
 8377 
 8281 
 
 8368 
 8271 
 
 8358 
 8261 
 
 8348 
 8251 
 
 8339 
 8241 
 
 8329 
 8231 
 
 8320 
 8221 
 
 8310 
 8211 
 
 8300 
 8202 
 
 23568 
 23578 
 
 35 
 
 8192 
 
 8181 
 
 8171 
 
 8161 
 
 8151 
 
 8141 
 
 8131 
 
 8121 
 
 Sin 
 
 8100 
 
 23578 
 
 36 
 
 8090 
 
 8080 
 
 8070 
 
 8059 
 
 8049 
 
 8039 
 
 8028 
 
 8018 
 
 8007 
 
 7997 
 
 23579 
 
 37 
 
 7986 
 
 7976 
 
 7965 
 
 7955 
 
 7944 
 
 7934 
 
 7923 
 
 7912 
 
 7902 
 
 7891 
 
 24579 
 
 38 
 
 7880 
 
 7869 
 
 7859 
 
 7848 
 
 7837 
 
 7826 
 
 78i5 
 
 7804 
 
 7793 
 
 7782 
 
 24579 
 
 39 
 
 7771 
 
 7760 
 
 7749 
 
 7738 
 
 7727 
 
 7716 
 
 7705 
 
 7694 
 
 7683 
 
 7672 
 
 24679 
 
 40 
 
 7660 
 
 7649 
 
 7638 
 
 7627 
 
 7615 
 
 7604 
 
 7593 
 
 7581 
 
 7570 
 
 7559 
 
 24689 
 
 41 
 
 7547 
 
 7536 
 
 75 2 4 
 
 75U 
 
 7501 
 
 7490 
 
 7478 
 
 7466 
 
 7455 
 
 7443 
 
 2 4 6 8 10 
 
 42 
 
 743' 
 
 7420 
 
 74 oS 
 
 7396 
 
 7385 
 
 7373 
 
 736i 
 
 7349 
 
 7337 
 
 7325 
 
 2 4 6 8 10 
 
 43 
 
 73H 
 
 7302 
 
 7290 
 
 7278 
 
 7266 
 
 7254 
 
 7242 
 
 7230 
 
 7218 
 
 7206 
 
 2 4 6 8 10 
 
 44 
 
 7193 
 
 7181 
 
 7169 
 
 7157 
 
 7M5 
 
 7133 
 
 7120 
 
 7108 
 
 7096 
 
 7083 
 
 2 4 6 8 10 
 
 
 
 
 
 
 
 
 
 
 
 
 1' 2 3' 4' 5' 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 Subtract 
 
 
 
 
 
 
 
 
 
 
 
 
 Differences. 
 
143 
 
 NATURAL COSINES 
 
 
 
 
 
 
 
 
 
 
 
 Subtract 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 Differences. 
 
 
 
 
 
 
 
 
 
 
 
 
 1' 2' 3' 4' 5' 
 
 45 
 
 7071 
 
 7059 
 
 7046 
 
 7034 
 
 7022 
 
 7009 
 
 6997 
 
 6984 
 
 6972 
 
 6959 
 
 2 4 6 8 10 
 
 46 
 
 6947 
 
 6934 
 
 6921 
 
 6909 
 
 6896 
 
 6884 
 
 6871 
 
 6858 
 
 6845 
 
 6833 
 
 2 46 8 n 
 
 47 
 
 6820 
 
 6807 
 
 6794 
 
 6782 
 
 6769 
 
 6756 
 
 6743 
 
 6730 
 
 6717 
 
 6704 
 
 2 4 6 9 ii 
 
 48 
 
 6691 
 
 6678 
 
 6665 
 
 6652 
 
 6639 
 
 6626 
 
 6613 
 
 6600 
 
 6587 
 
 6574 
 
 2 4 7 9 ii 
 
 49 
 
 6561 
 
 6547 
 
 6534 
 
 6521 
 
 6508 
 
 6494 
 
 6481 
 
 6468 
 
 6455 
 
 6441 
 
 2 4 7 9 ii 
 
 50 
 
 6428 
 
 6414 
 
 6401 
 
 6388 
 
 6374 
 
 6361 
 
 6347 
 
 6 334 
 
 6320 
 
 6307 
 
 2 4 7 9 ii 
 
 51 
 
 6293 
 
 6280 
 
 6266 
 
 6252 
 
 6239 
 
 6225 
 
 6211 
 
 6198 
 
 6184 
 
 6170 
 
 2 5 7 9 ii 
 
 52 
 
 6157 
 
 6143 
 
 6129 
 
 6115 
 
 6101 
 
 6088 
 
 6074 
 
 6060 
 
 6046 
 
 6032 
 
 2 5 7 9 12 
 
 53 
 
 6018 
 
 6004 
 
 5990 
 
 5976 
 
 5962 
 
 5948 
 
 5934 
 
 5920 
 
 5906 
 
 5892 
 
 2 5 7 9 12 
 
 54 
 
 5878 
 
 5864 
 
 5850 
 
 5835 
 
 5821 
 
 5807 
 
 5793 
 
 5779 
 
 5764 
 
 575o 
 
 2 5 7 9 12 
 
 55 
 
 5736 
 
 572i 
 
 5707 
 
 5693 
 
 5678 
 
 5664 
 
 5650 
 
 5635 
 
 5621 
 
 5606 
 
 2 5 7 10 12 
 
 56 
 
 559 2 
 
 5577 
 
 5563 
 
 5548 
 
 5534 
 
 55i9 
 
 5505 
 
 5490 
 
 5476 
 
 546i 
 
 2 5 7 10 12 
 
 57 
 
 5446 
 
 5432 
 
 54i7 
 
 5402 
 
 5388 
 
 5373 
 
 5358 
 
 5344 
 
 5329 
 
 53H 
 
 2 5 7 10 12 
 
 58 
 
 5 2 99 
 
 5284 
 
 5270 
 
 5255 
 
 5240 
 
 5225 
 
 5210 
 
 5195 
 
 5180 
 
 5165 
 
 2 5 7 10 12 
 
 59 
 
 5150 
 
 5135 
 
 5120 
 
 5io5 
 
 5090 
 
 5075 
 
 5060 
 
 5045 
 
 5030 
 
 5015 
 
 3 5 8 10 13 
 
 60 
 
 5000 
 
 4985 
 
 4970 
 
 4955 
 
 4939 
 
 4924 
 
 4909 
 
 4894 
 
 4879 
 
 4863 
 
 3 5 8 10 13 
 
 61 
 
 4848 
 
 4833 
 
 4818 
 
 4802 
 
 4787 
 
 4772 
 
 4756 
 
 474i 
 
 4726 
 
 4710 
 
 3 5 8 10 13 
 
 62 
 
 4695 
 
 4679 
 
 4664 
 
 4648 
 
 4633 
 
 4617 
 
 4602 
 
 4586 
 
 457i 
 
 4555 
 
 3 5 8 10 13 
 
 63 
 
 '4540 
 
 4524 
 
 459 
 
 4493 
 
 4478 
 
 4462 
 
 4446 
 
 443i 
 
 44i5 
 
 4399 
 
 3 5 8 10 13 
 
 64 
 
 4384 
 
 4368 
 
 4352 
 
 4337 
 
 432i 
 
 4305 
 
 4289 
 
 4274 
 
 4258 
 
 4242 
 
 3 5 8 ii 13 
 
 65 
 
 4226 
 
 4210 
 
 4195 
 
 4179 
 
 4163 
 
 4H7 
 
 4131 
 
 4H5 
 
 4099 
 
 4083 
 
 3 5 8 ii 13 
 
 66 
 
 4067 
 
 4051 
 
 4035 
 
 4019 
 
 4003 
 
 3987 
 
 3971 
 
 3955 
 
 3939 
 
 3923 
 
 3 5 8 ii 14 
 
 67 
 
 3907 
 
 3891 
 
 3875 
 
 3859 
 
 3843 
 
 3827 
 
 3811 
 
 3795 
 
 3778 
 
 3762 
 
 3 5 8 n 14 
 
 68 
 
 3746 
 
 3730 
 
 37H 
 
 3 6 97 
 
 3681 
 
 3665 
 
 3649 
 
 3633 
 
 3616 
 
 3600 
 
 3 5 8 u 14 
 
 69 
 
 3584 
 
 3567 
 
 355i 
 
 3535 
 
 35i8 
 
 3502 
 
 3486 
 
 3469 
 
 3453 
 
 3437 
 
 3 5 8 n 14 
 
 70 
 
 3420 
 
 3404 
 
 3387 
 
 3371 
 
 3355 
 
 3338 
 
 3322 
 
 3305 
 
 3289 
 
 3272 
 
 3 5 8 u 14 
 
 71 
 
 3256 
 
 3239 
 
 3223 
 
 3206 
 
 3190 
 
 3173 
 
 3156 
 
 3HO 
 
 3123 
 
 307 
 
 3 6 8 u 14 
 
 72 
 
 3090 
 
 374 
 
 3057 
 
 3040 
 
 3024 
 
 3007 
 
 2990 
 
 2974 
 
 2957 
 
 2940 
 
 3 6 8 n 14 
 
 73 
 
 2924 
 
 2907 
 
 2890 
 
 2874 
 
 2857 
 
 2840 
 
 2823 
 
 2807 
 
 2790 
 
 2773 
 
 3 6 8 n 14 
 
 74 
 
 2756 
 
 2740 
 
 2723 
 
 2706 
 
 2689 
 
 2672 
 
 2656 
 
 2639 
 
 2622 
 
 2605 
 
 3 6 8 ii 14 
 
 75 
 
 2588 
 
 257i 
 
 2554 
 
 2538 
 
 2521 
 
 2504 
 
 2487 
 
 2470 
 
 2453 
 
 2436 
 
 3 6 8 n 14 
 
 76 
 
 2419 
 
 2402 
 
 2385 
 
 2368 
 
 2351 
 
 2334 
 
 2317 
 
 2300 
 
 2284 
 
 2267 
 
 3 6 8 ii 14 
 
 77 
 
 2250 
 
 2233 
 
 2215 
 
 2198 
 
 2181 
 
 2164 
 
 2*47 
 
 2130 
 
 2113 
 
 2096 
 
 3 6 9 u 14 
 
 78 
 
 2079 
 
 2062 
 
 2045 
 
 2028 
 
 201 1 
 
 1994 
 
 1977 
 
 1959 
 
 1942 
 
 1925 
 
 3 6 9 n 14 
 
 79 
 
 1908 
 
 1891 
 
 1874 
 
 1857 
 
 1840 
 
 1822 
 
 1805 
 
 1788 
 
 1771 
 
 1754 
 
 5 6 9 n 14 
 
 80 
 
 1736 
 
 1719 
 
 1702 
 
 1685 
 
 1668 
 
 1650 
 
 1633 
 
 1616 
 
 1599 
 
 1582 
 
 3 6 9 ii M 
 
 81 
 
 1564 
 
 1547 
 
 1530 
 
 1513 
 
 M95 
 
 1478 
 
 1461 
 
 1444 
 
 1426 
 
 1409 
 
 3 6 9 12 14 
 
 82 
 
 1392 
 
 1374 
 
 1357 
 
 1340 
 
 1323 
 
 1305 
 
 1288 
 
 1271 
 
 1253 
 
 1236 
 
 3 6 9 12 14 
 
 83 
 
 1219 
 
 I2OI 
 
 1184 
 
 1167 
 
 1149 
 
 1132 
 
 "i5 
 
 1097 
 
 1080 
 
 1063 
 
 3 6 9 12 14 
 
 84 
 
 1045 
 
 1028 
 
 ion 
 
 0993 
 
 0976 
 
 0958 
 
 0941 
 
 0924 
 
 0906 
 
 0889 
 
 3 6 9 12 14 
 
 85 
 
 0872 
 
 0854 
 
 0837 
 
 0819 
 
 0802 
 
 0785 
 
 0767 
 
 0750 
 
 0732 
 
 0715 
 
 3 6 9 12 14 
 
 86 
 
 0698 
 
 0680 
 
 0663 
 
 0645 
 
 0628 
 
 0610 
 
 0593 
 
 0576 
 
 0558 
 
 0541 
 
 3 6 9 12 15 
 
 87 
 
 0523 
 
 0506 
 
 0488 
 
 0471 
 
 0454 
 
 0436 
 
 0419 
 
 0401 
 
 0384 
 
 0366 
 
 3 6 9 12 15 
 
 88 
 
 0349 
 
 0332 
 
 03 H 
 
 0297 
 
 0279 
 
 0262 
 
 0244 
 
 0227 
 
 0209 
 
 0192 
 
 3 6 9 12 15 
 
 89 
 
 0175 
 
 0157 
 
 0140 
 
 OI22 
 
 0105 
 
 0087 
 
 0070 
 
 0052 
 
 0035 
 
 0017 
 
 3 6 9 12 15 
 
 
 
 
 
 
 
 
 or* ' 
 
 
 
 
 1' 2' 3' 4' 5' 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36 
 
 42' 
 
 48' 
 
 54' 
 
 Subtract 
 
 
 
 
 
 
 
 
 
 
 
 
 Differences . 
 
144 
 
 NATURAL TANGENTS 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 1' 2' 3' 4' 5' 
 
 
 
 'OOOO 
 
 0017 
 
 0035 
 
 0052 
 
 0070 
 
 0087 
 
 0105 
 
 0122 
 
 0140 
 
 0157 
 
 3 6 9 12 15 
 
 1 
 
 0175 
 
 0192 
 
 0209 
 
 0227 
 
 0244 
 
 0262 
 
 0279 
 
 0297 
 
 0314 
 
 0332 
 
 3 6 9 12 15 
 
 2 
 
 0349 
 
 0367 
 
 0384 
 
 0402 
 
 0419 
 
 0437 
 
 0454 
 
 0472 
 
 0489 
 
 0507 
 
 3 6 9 12 15 
 
 3 
 
 0524 
 
 0542 
 
 0559 
 
 0577 
 
 0594 
 
 0612 
 
 0629 
 
 0647 
 
 0664 
 
 0682 
 
 3 6 9 12 15 
 
 4 
 
 0699 
 
 0717 
 
 0734 
 
 0752 
 
 0769 
 
 0787 
 
 0805 
 
 0822 
 
 0840 
 
 0857 
 
 3 6 9 12 15 
 
 5 
 
 0875 
 
 0892 
 
 0910 
 
 0928 
 
 0945 
 
 0963 
 
 0981 
 
 0998 
 
 1016 
 
 1033 
 
 3 6 9 12 15 
 
 6 
 
 1051 
 
 1069 
 
 1086 
 
 1104 
 
 1 122 
 
 "39 
 
 H57 
 
 U75 
 
 1192 
 
 1210 
 
 3 6 9 12 15 
 
 7 
 
 1228 
 
 1246 
 
 1263 
 
 1281 
 
 1299 
 
 1317 
 
 1334 
 
 1352 
 
 1370 
 
 I 3 88 
 
 3 6 9 12 15 
 
 8 
 
 1405 
 
 1423 
 
 1441 
 
 1459 
 
 1477 
 
 M95 
 
 1512 
 
 1530 
 
 1548 
 
 1566 
 
 3 6 9 12 15 
 
 9 
 
 1584 
 
 1602 
 
 1620 
 
 1638 
 
 1655 
 
 1673 
 
 1691 
 
 1709 
 
 1727 
 
 1745 
 
 3 6 9 12 15 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10 
 
 1763 
 
 1781 
 
 1799 
 
 1817 
 
 1835 
 
 1853 
 
 1871 
 
 1890 
 
 1908 
 
 1926 
 
 3 6 9 12 15 
 
 11 
 
 1944 
 
 1962 
 
 1980 
 
 1998 
 
 20l6 
 
 2035 
 
 2053 
 
 2071 
 
 2089 
 
 2IO7 
 
 3 6 9 12 15 
 
 12 
 
 2126 
 
 2144 
 
 2162 
 
 2180 
 
 2199 
 
 2217 
 
 2235 
 
 2254 
 
 2272 
 
 2290 
 
 3 6 9 12 15 
 
 13 
 
 2309 
 
 2327 
 
 2345 
 
 2364 
 
 2382 
 
 2401 
 
 2419 
 
 2438 
 
 2456 
 
 2475 
 
 3 6 9 12 15 
 
 14 
 
 2493 
 
 2512 
 
 2530 
 
 2549 
 
 2568 
 
 2586 
 
 2605 
 
 2623 
 
 2642 
 
 2661 
 
 3 6 9 12 16 
 
 15 
 
 2679 
 
 2698 
 
 2717 
 
 2736 
 
 2754 
 
 2773 
 
 2792 
 
 2811 
 
 2830 
 
 2849 
 
 3 6 9 13 16 
 
 16 
 
 2867 
 
 2886 
 
 2905 
 
 2924 
 
 2943 
 
 2962 
 
 2981 
 
 3000 
 
 3019 
 
 3038 
 
 3 6 9 13 16 
 
 17 
 
 3057 
 
 3076 
 
 3096 
 
 3U5 
 
 3'34 
 
 3153 
 
 3172 
 
 3191 
 
 3211 
 
 3230 
 
 3 6 10 13 16 
 
 18 
 
 3249 
 
 3269 
 
 3288 
 
 3307 
 
 3327 
 
 3346 
 
 3365 
 
 3385 
 
 3404 
 
 3424 
 
 3 6 10 13 16 
 
 19 
 
 3443 
 
 3463 
 
 3482 
 
 3502 
 
 3522 
 
 3541 
 
 35 61 
 
 358i 
 
 3600 
 
 3620 
 
 3 7 10 13 16 
 
 20 
 
 3640 
 
 3659 
 
 3679 
 
 3699 
 
 3719 
 
 3739 
 
 3759 
 
 3779 
 
 3799 
 
 3819 
 
 3 7 10 13 17 
 
 21 
 
 3839 
 
 3859 
 
 3879 
 
 3899 
 
 3919 
 
 3939 
 
 3959 
 
 3979 
 
 4000 
 
 4020 
 
 3 7 10 13 17 
 
 22 
 
 4040 
 
 4061 
 
 4081 
 
 4101 
 
 4122 
 
 4142 
 
 4163 
 
 4183 
 
 4204 
 
 4224 
 
 3 7 10 14 17 
 
 23 
 
 4245 
 
 4265 
 
 4286 
 
 4307 
 
 4327 
 
 4348 
 
 4369 
 
 4390 
 
 4411 
 
 4431 
 
 3 7 10 14 17 
 
 24 
 
 4452 
 
 4473 
 
 4494 
 
 45i5 
 
 4536 
 
 4557 
 
 4578 
 
 4599 
 
 4621 
 
 4642 
 
 4 7 ii 14 18 
 
 25 
 
 4663 
 
 4684 
 
 4706 
 
 4727 
 
 4748 
 
 4770 
 
 479 i 
 
 4813 
 
 4834 
 
 4856 
 
 4 7 ii 14 18 
 
 26 
 
 4877 
 
 4899 
 
 4921 
 
 4942 
 
 4964 
 
 4986 
 
 5008 
 
 5029 
 
 5051 
 
 5073 
 
 4 7 ii 15 18 
 
 27 
 
 5095 
 
 5"7 
 
 5139 
 
 5161 
 
 5^4 
 
 5206 
 
 5228 
 
 5250 
 
 5272 
 
 5295 
 
 4 7 ii 15 18 
 
 28 
 29 
 
 5317 
 
 '5543 
 
 5340 
 5566 
 
 5362 
 5589 
 
 5384 
 5612 
 
 5407 
 5635' 
 
 5430 
 5658 
 
 5452 
 5681 
 
 5475 
 5704 
 
 5498 
 
 5727 
 
 5520 
 5750 
 
 4 8 ii 15 19 
 4 8 12 15 19 
 
 30 
 
 "5774 
 
 5797 
 
 5820 
 
 5844 
 
 586 7 
 
 5890 
 
 59H 
 
 5938 
 
 596i 
 
 5985 
 
 4 8 12 16 20 
 
 31 
 
 6009 
 
 6032 
 
 6056 
 
 6080 
 
 6l04 
 
 6128 
 
 6152 
 
 6176 
 
 6200 
 
 6224 
 
 4 8 12 16 20 
 
 32 
 
 6249 
 
 6273 
 
 6297 
 
 6322 
 
 6346 
 
 6371 
 
 6395 
 
 6420 
 
 6445 
 
 6469 
 
 4 8 12 16 20 
 
 33 
 
 6494 
 
 6519 
 
 6 544 
 
 6569 
 
 6$94 
 
 6619 
 
 6644 
 
 6669 
 
 6694 
 
 6720 
 
 4 8 13 17 21 
 
 34 
 
 6745 
 
 6771 
 
 6796 
 
 6822 
 
 6847 
 
 6873 
 
 6899 
 
 6924 
 
 6950 
 
 6976 
 
 4 9 13 17 21 
 
 35 
 
 7002 
 
 7028 
 
 7054 
 
 7080 
 
 7107 
 
 7133 
 
 7159 
 
 7186 
 
 7212 
 
 7239 
 
 4 9 13 18 22 
 
 36 
 
 7265 
 
 7292 
 
 7319 
 
 7346 
 
 7373 
 
 7400 
 
 7427 
 
 7454 
 
 7481 
 
 7508 
 
 5 9 14 18 23 
 
 37 
 
 7536 
 
 7563 
 
 7590 
 
 7618 
 
 7646 
 
 7673 
 
 7701 
 
 7729 
 
 7757 
 
 7785 
 
 5 9 H '8 23 
 
 38 
 
 7813 
 
 7841 
 
 7869 
 
 7898 
 
 7926 
 
 7954 
 
 7983 
 
 8012 
 
 8040 
 
 8069 
 
 5 9 14 19 24 
 
 39 
 
 8098 
 
 8127 
 
 8156 
 
 8185 
 
 8214 
 
 8243 
 
 8273 
 
 8302 
 
 8332 
 
 8361 
 
 5 10 15 20 24 
 
 40 
 
 8391 
 
 8421 
 
 8451 
 
 8481 
 
 8511 
 
 8541 
 
 8571 
 
 8601 
 
 8632 
 
 8662 
 
 5 10 15 20 25 
 
 41 
 
 8693 
 
 8724 
 
 8754 
 
 8785 
 
 8816 
 
 8847 
 
 8878 
 
 8910 
 
 8941 
 
 8972 
 
 5 10 16 21 26 
 
 42 
 
 9004 
 
 9036 
 
 9067 
 
 9099 
 
 9UI 
 
 9163 
 
 9*95 
 
 9228 
 
 9260 
 
 9293 
 
 5 ii 16 21 27 
 
 43 
 
 9325 
 
 9358 
 
 939i 
 
 9424 
 
 9457 
 
 9490 
 
 9523 
 
 9556 
 
 9590 
 
 9623 
 
 6 II 17 22 28 
 
 44 
 
 9657 
 
 9691 
 
 9725 
 
 9759 
 
 9793 
 
 9827 
 
 9861 
 
 9896 
 
 9930 
 
 9965 
 
 6 ii 17 23 29 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 1' 2' 3' 4' 5' 
 
145 
 
 NATURAL TANGENTS 
 
 
 0' 
 
 6' 
 
 12'! 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 1' 2' 3' 4' 5' 
 
 45 
 
 I '0000 
 
 0035 
 
 0070 
 
 -0105 
 
 0141 
 
 0176 
 
 Q2I2 
 
 0247 
 
 0283 
 
 0319 
 
 6 12 18 24 30 
 
 46 
 
 1-0355 
 
 0392 
 
 0428 
 
 0464 
 
 0501 
 
 0538 
 
 0575 
 
 0612 
 
 0649 
 
 0686 
 
 6 12 18 25 31 
 
 47 
 
 I -0724 
 
 0761 
 
 0799 
 
 0837 
 
 0875 
 
 0913 
 
 095 I 
 
 0990 
 
 1028 
 
 1067 
 
 6 13 19 25 32 
 
 48 
 
 i 1 106 
 
 H45 
 
 1184 
 
 1224 
 
 1263 
 
 1303 
 
 1343 
 
 1383 
 
 1423 
 
 1463 
 
 7 13 20 27 33 
 
 49 
 
 1-1504 
 
 1544 
 
 1585 
 
 1626 
 
 1667 
 
 1708 
 
 175 
 
 1792 
 
 1833 
 
 1875 
 
 7 14 21 28 34 
 
 50 
 
 I-I9I8 
 
 1960 
 
 2OO2 
 
 2045 
 
 2088 
 
 2131 
 
 2174 
 
 2218 
 
 2261 
 
 2305 
 
 7 14 22 29 36 
 
 51 
 
 I '2349 
 
 2393 
 
 2437 
 
 2482 
 
 2527 
 
 2572 
 
 2617 
 
 2662 
 
 2708 
 
 2753 
 
 8 15 23 30 38 
 
 52 
 
 1-2799 
 
 2846 
 
 2892 
 
 2938 2985 
 
 3032 
 
 3079 
 
 3127 
 
 3i75 
 
 3222 
 
 8 16 24 31 39 
 
 53 
 
 1-3270 
 
 33i9 
 
 3367 
 
 3416 3465 
 
 35H 
 
 3564 
 
 3613 
 
 3663 
 
 37i3 
 
 8 16 25 33 41 
 
 54 
 
 1-3764 
 
 3814 
 
 3865 
 
 3916 
 
 3968 
 
 4019 
 
 4071 
 
 4124 
 
 4176 
 
 4229 
 
 9 17 26 34 43 
 
 55 
 
 1-4281 
 
 4335 
 
 4388 
 
 4442 
 
 4496 
 
 4550 
 
 4605 
 
 4659 
 
 47i5 
 
 4770 
 
 9 18 27 36 45 
 
 56 
 
 i -4826 
 
 4882 
 
 4938 
 
 4994 
 
 5051 
 
 5108 
 
 5166 
 
 5224 
 
 5282 
 
 5340 
 
 10 19 29 38 48 
 
 57 
 
 1-5399 
 
 5458 
 
 55!7 
 
 5577 
 
 5637 
 
 5697 
 
 5757 
 
 5818 
 
 5880 
 
 594i 
 
 10 20 30 40 50 
 
 58 
 
 i -6003 
 
 6066 
 
 6128 
 
 6191 
 
 6255 
 
 6319 
 
 6383 
 
 6447 
 
 6512 
 
 6577 
 
 ii 21 32 43 53 
 
 59 
 
 i '6643 
 
 6709 
 
 6775 
 
 6842 
 
 6909 
 
 6977 
 
 7045 
 
 7"3 
 
 7182 
 
 7251 
 
 ii 23 34 45 57 
 
 60 
 
 17321 
 
 739i 
 
 746i 
 
 7532 
 
 7603 
 
 7675 
 
 7747 
 
 7820 
 
 7893 
 
 7966 
 
 12 24 36 48 60 
 
 61 
 
 i '8040 
 
 8115 
 
 8190 
 
 8265 
 
 8341 
 
 8418 
 
 7495 
 
 8572 
 
 8650 
 
 8728 
 
 13 26 3 8 51 6 4 
 
 62 
 
 1-8807 
 
 8887 
 
 8967 
 
 9047 
 
 9128 
 
 9210 
 
 9292 
 
 9375 
 
 9458 
 
 9542 
 
 14 27 41 55 68 
 
 63 
 
 1*9626 
 
 9711 
 
 9797 
 
 9883 
 
 9970 
 
 2-0057 
 
 2-0145 
 
 2-0233 
 
 2-0323 
 
 2*0413 
 
 15 29 44 58 73 
 
 64 
 
 2-0503 
 
 0594 
 
 0686 
 
 0778 
 
 0872 
 
 0965 
 
 1060 
 
 "55 
 
 1251 
 
 1348 
 
 16 31 47 63 79 
 
 65 
 
 2*1445 
 
 1543 
 
 1642 
 
 1742 
 
 1842 
 
 J943 
 
 2045 
 
 2148 
 
 2251 
 
 2355 
 
 17 34 51 68 85 
 
 66 
 
 2-2460 
 
 2566 
 
 2673 
 
 2781 
 
 2889 
 
 2998 
 
 3109 
 
 3220 
 
 3332 
 
 3445 
 
 18 37 55 73 92 
 
 67 
 
 2'3559 
 
 3673 
 
 3789 
 
 3906 
 
 4023 
 
 4142 
 
 4262 
 
 4383 
 
 4504 
 
 4627 
 
 20 40 60 79 99 
 
 68 
 
 2-475I 
 
 4876 
 
 5002 
 
 5129 
 
 5257 
 
 5386 
 
 5517 
 
 5649 
 
 5782 
 
 59i6 
 
 22 43 65 87 108 
 
 69 
 
 2*6051 
 
 6187 
 
 6325 
 
 6464 
 
 6605 
 
 6746 
 
 6889 
 
 7034 
 
 7179 
 
 7326 
 
 24 48 71 95 "9 
 
 70 
 
 2-7475 
 
 7625 
 
 7776 
 
 7929 
 
 8083 
 
 8239 
 
 8397 
 
 8556 
 
 8716 
 
 8878 
 
 26 52 78 105 131 
 
 71 
 
 2-9042 
 
 9208 
 
 9375 
 
 9544 
 
 97H 
 
 9887 
 
 i'oo6i 
 
 3-0237 
 
 3-0415 
 
 3'0595 
 
 2 9 58 87 116 145 
 
 72 
 
 3-0777 
 
 0961 
 
 1146 
 
 1334 
 
 1524 
 
 1716 
 
 1910 
 
 2106 
 
 2305 
 
 2506 
 
 32 64 96 129 161 
 
 73 
 
 3-2709 
 
 2914 
 
 3122 
 
 3332 3^44 
 
 3759 
 
 3977 
 
 4197 
 
 4420 
 
 4646 
 
 36 72 108 144 180 
 
 74 
 
 3H874 
 
 5io5 
 
 5339 
 
 5576 
 
 5816 
 
 6059 
 
 6305 
 
 6554 
 
 6806 
 
 7062 
 
 |.i 81 122 163 204 
 
 75 
 
 37321 
 
 7583 
 
 7848 
 
 8118 
 
 8391 
 
 8667 
 
 8947 
 
 9232 
 
 9520 
 
 9812 
 
 46 93 139 186 232 
 
 76 
 77 
 
 4-0108 
 4-3315 
 
 0408 
 3662 
 
 0713 
 4015 
 
 1022 
 
 4374 
 
 1335 
 4737 
 
 1653 
 5 I0 7 
 
 1976 
 5483 
 
 2303 
 5864 
 
 2635 
 6252 
 
 2972 
 6646 
 
 
 78 
 
 4-7046 
 
 7453 
 
 7867 
 
 8288 
 
 8716 
 
 9152 
 
 9594 
 
 5'Q045 
 
 5-0504 
 
 5'097o 
 
 
 79 
 
 5-I446 
 
 1929 
 
 2422 
 
 2924 
 
 3435 
 
 3955 
 
 4486 
 
 5026 
 
 5578 
 
 6140 
 
 
 80 
 
 5'67i3 
 
 7297 
 
 7894 
 
 8502 
 
 9124 
 
 9758 
 
 6-0405 
 
 6-1066 
 
 6-1742 
 
 6-2432 
 
 
 81 
 
 82 
 83 
 
 ! 84 
 
 6-3138 
 7-ii54 
 
 8'i443 
 9*5*4 
 
 3859 
 2066 
 2636 
 9-677 
 
 4596 
 3002 
 3863 
 9-845 
 
 5350 
 3962 
 5126 
 
 IO'O2 
 
 6122 
 
 4947 
 6427 
 10 20 
 
 6912 
 5958 
 7769 
 10-39 
 
 7720 
 6996 
 9152 
 10-58 
 
 8548 
 8062 
 
 9-0579 
 10-78 
 
 9395 
 9158 
 9-2052 
 10-99 
 
 7-0264 
 8-0285 
 93572 
 
 11-20 
 
 Mean differences 
 no longer suffi- 
 ciently accurate. 
 
 85 
 
 n-43 
 
 n-66 
 
 11-91 
 
 I2'l6 
 
 12-43 
 
 12-71 
 
 13-00 
 
 13-30 
 
 13-62 
 
 i3'95 
 
 
 86 
 
 14-30 
 
 14-67 
 
 15-06 
 
 15-46 
 
 15-89 
 
 16-35 
 
 16-83 
 
 17*34 
 
 17-89 
 
 18-46 
 
 
 87 
 
 19-08 
 
 I9-74 
 
 20-45 
 
 21-20 
 
 22-02 
 
 22-90 
 
 23-86 
 
 24-90 
 
 26-03 
 
 27-27 
 
 
 88 
 
 28-64 
 
 30-14 
 
 31-82 
 
 33-69 
 
 35-80 
 
 38-19 
 
 40-92 
 
 44-07 
 
 47'74 
 
 52-08 
 
 
 89 
 
 57'29 
 
 63-66 
 
 71-62 
 
 81-85 
 
 95'49 
 
 114-6 
 
 143-2 
 
 1910 
 
 286-5 
 
 573'Q 
 
 
 
 0' 
 
 6' 
 
 12', 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 
146 
 
 RADIANS 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 008 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 1' 2' 3' 4' 5' 
 
 
 
 oooo 
 
 0017 
 
 0035 
 
 0052 
 
 0070 
 
 0105 
 
 0122 
 
 0140 
 
 0157 
 
 3 6 9 12 15 
 
 1 
 
 2 
 3 
 
 4 
 
 0175 
 0349 
 0524 
 
 0698 
 
 0192 
 0367 
 
 0541 
 0716 
 
 0209 
 0384 
 0559 
 0733 
 
 0227 
 0401 
 0576 
 0750 
 
 0244 
 04 1< 
 
 593 
 0768 
 
 0262 
 0436 
 06 1 
 0785 
 
 0279 
 
 0454 
 0628 
 0803 
 
 0297 
 0471 
 0646 
 0820 
 
 03H 
 0489 
 0663 
 0838 
 
 0332 
 0506 
 0681 
 0855 
 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 
 5 
 
 0873 
 
 0890 
 
 0908 
 
 0925 
 
 0942 
 
 0960 
 
 0977 
 
 0935 
 
 1012 
 
 1030 
 
 3 6 9 12 15 
 
 6 
 7 
 8 
 9 
 
 '1047 
 
 '1222 
 I 39 6 
 1571 
 
 1065 
 1239 
 1414 
 1588 
 
 io3 2 
 1257 
 1431 
 1606 
 
 IIOO 
 
 1274 
 1449 
 1623 
 
 1117 
 1292 
 1466 
 1641 
 
 "34 
 1309 
 
 1484 
 1658 
 
 1152 
 1326 
 1501 
 1676 
 
 1169 
 
 I3H 
 I5l8 
 1693 
 
 Il87 
 1361 
 1536 
 1710 
 
 1204 
 1379 
 J 553 
 1728 
 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 
 1O 
 
 1745 
 
 1763 
 
 1780 
 
 1798 
 
 1815 
 
 1833 
 
 1850 
 
 1868 
 
 1885 
 
 1902 
 
 3 6 9 12 15 
 
 11 
 12 
 13 
 14 
 
 1920 
 2094 
 2269 
 2443 
 
 '937 
 
 2112 
 2286 
 2\6l 
 
 J 955 
 2129 
 2304 
 
 2478 
 
 1972 
 2147 
 2321 
 2496 
 
 1990 
 2164 
 2 339 
 2513 
 
 2007 
 2182 
 2356 
 2531 
 
 2025 
 2199 
 
 2 374 
 2548 
 
 2042 
 22I 7 
 
 2391 
 2566 
 
 2059 
 2234 
 2409 
 2583 
 
 2077 
 2251 
 2426 
 2601 
 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 
 15 
 
 26l8 
 
 2635 
 
 2653 
 
 2670 
 
 2688 
 
 2705 
 
 2723 
 
 2740 
 
 2758 
 
 2775 
 
 3 6 9 12 15 
 
 16 
 17 
 18 
 19 
 
 2793 
 2967 
 
 '3H2 
 3316 
 
 28lO 
 2985 
 3159 
 
 3334 
 
 2827 
 3002 
 3176 
 335i 
 
 2845 
 3019 
 3194 
 3368 
 
 2862 
 
 3037 
 3211 
 
 3386 
 
 2880 
 
 3054 
 3229 
 
 3403 
 
 2897 
 3072 
 3246 
 3421 
 
 2915 
 3089 
 3264 
 3438 
 
 2932 
 3107 
 3281 
 3156 
 
 2950 
 3124 
 3299 
 3473 
 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 
 20 
 
 3491 
 
 35o8 
 
 3526 
 
 3543 
 
 356o 
 
 3578 
 
 3595 
 
 3 6 I3 
 
 3630 
 
 3648 
 
 3 6 9 12 15 
 
 21 
 22 
 23 
 24 
 
 3665 
 3840 
 4014 
 4189 
 
 3683 
 
 3857 
 4032 
 4206 
 
 3700 
 
 3875 
 4049 
 4224 
 
 37i8 
 3892 
 4067 
 4241 
 
 3735 
 3910 
 4084 
 4259 
 
 3752 
 3927 
 4102 
 4276 
 
 37/0 
 
 3944 
 4119 
 4294 
 
 3787 
 3962 
 4136 
 
 43" 
 
 3805 
 
 3979 
 4154 
 4328 
 
 3822 
 
 3997 
 4171 
 
 4346 
 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 
 25 
 
 4363 
 
 438i 
 
 4398 
 
 4416 
 
 4433 
 
 4*5i 
 
 4468 
 
 4485 
 
 4503 
 
 4520 
 
 3 6 9 12 15 
 
 26 
 27 
 28 
 29 
 
 4538 
 4712 
 4887 
 5061 
 
 4555 
 4730 
 4904 
 5079 
 
 4573 
 4747 
 4922 
 5096 
 
 4590 
 4765 
 4939 
 5"4 
 
 4608 
 4782 
 4957 
 5i3i 
 
 4625 
 4800 
 4974 
 5M9 
 
 4643 
 4817 
 4992 
 5166 
 
 4660 
 
 4835 
 5009 
 5i8| 
 
 4677 
 4852 
 5027 
 5201 
 
 4695 
 4869 
 
 5044 
 5219 
 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 
 30 
 
 5236 
 
 5253 
 
 5271 
 
 5288 
 
 53o6 
 
 5323 
 
 5341 
 
 5358 
 
 5376 
 
 5393 
 
 3 6 9 12 15 
 
 31 
 32 
 33 
 34 
 
 54" 
 
 5585 
 .5760 
 
 5934 
 
 5428 
 5603 
 5777 
 5952 
 
 5445 
 5620 
 
 5794 
 5969 
 
 5463 
 5637 
 5812 
 5986 
 
 548o 
 
 5655 
 5829 
 6004 
 
 5498 
 5672 
 
 5847 
 6021 
 
 551.5 
 5690 
 5864 
 6039 
 
 5533 
 5707 
 5882 
 6056 
 
 5550 
 5725 
 5*>99 
 6074 
 
 5568 
 
 5742 
 5917 
 6091 
 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 
 35 
 
 6109 
 
 6126 
 
 6144 
 
 6161 
 
 6178 
 
 6196 
 
 6213 
 
 6231 
 
 6248 
 
 6266 
 
 3 6 9 12 15 
 
 36 
 37 
 38 
 39 
 
 6283 
 6458 
 6632 
 6807 
 
 6301 
 
 6475 
 6650 
 6824 
 
 6318 
 
 6493 
 6667 
 6842 
 
 6336 
 6510 
 6685 
 6859 
 
 6353 
 652* 
 6702 
 6877 
 
 6370 
 
 6545 
 6720 
 6894 
 
 6388 
 6562 
 
 6737 
 6912 
 
 6405 
 6580 
 
 6754 
 6929 
 
 6423 
 
 6597 
 6772 
 6946 
 
 6440 
 6615 
 6789 
 6964 
 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 
 40 
 
 6981 
 
 6999 
 
 7016 
 
 7034 
 
 7051 
 
 7069 
 
 7086 
 
 7103 
 
 7121 
 
 7138 
 
 3 6 9 12 15 
 
 41 
 42 
 43 
 44 
 
 7156 
 7330 
 7505 
 7679 
 
 7173 
 7348 
 7522 
 7697 
 
 7191 
 
 7365 
 7540 
 77H 
 
 7208 
 7383 
 7557 
 7732 
 
 7226 
 7400 
 7575 
 7749 
 
 7243 
 7418 
 75f 
 7767 
 
 7261 
 
 7435 
 7610 
 
 7784 
 
 7278 
 
 7453 
 7627 
 7802 
 
 7295 
 7470 
 
 7645 
 7819 
 
 7313 
 
 7487 
 7662 
 
 7837 
 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 3 6 9 12 15 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 1' 2' 3' 4' 5' 
 
147 
 
 RADIANS 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 1' 2 3' 4' 5' 
 
 45 
 
 7854 
 
 78711-7889 
 
 7906 
 
 7924 
 
 7941 
 
 '7959 
 
 7976 
 
 '7994 
 
 8on 
 
 3 6 9 12 15 
 
 46 
 
 8o29 
 
 8046 8063 
 
 8081 
 
 8098 
 
 8116 
 
 8133 
 
 8151 
 
 8168 
 
 8186 
 
 3 6 9 12 15 
 
 47 
 
 8203 
 
 8221 8238 
 
 8255 
 
 8273 
 
 8290 
 
 8308 8325 
 
 8343 
 
 8360 
 
 3 6 9 12 15 
 
 48 
 
 8378 
 
 8395 8412 
 
 8430 
 
 8447 
 
 8465 
 
 8482 8500 
 
 8517 
 
 8535 
 
 3 6 9 !2 15 
 
 49 
 
 8552 
 
 8570 
 
 8587 
 
 8604 
 
 8622 
 
 8639 
 
 8657 
 
 8674 
 
 8692 
 
 8709 
 
 3 6 9 12 15 
 
 5O 
 
 8727 
 
 8744 
 
 8762 
 
 8779 
 
 8796 
 
 8814 
 
 8831 
 
 8849 
 
 8866 
 
 8884 
 
 3 6 9 12 15 
 
 51 
 
 8901 
 
 8919 
 
 8936 
 
 8954 
 
 8971 
 
 8988 
 
 9006 
 
 9023 
 
 9041 
 
 9058 
 
 3 6 9 12 15 
 
 52 
 
 9076 
 
 9093 
 
 9111 
 
 9128 
 
 9146 
 
 9163 
 
 9180 
 
 9198 
 
 9215 
 
 9233 
 
 3 6 9 12 15 
 
 | 53 
 
 9250 
 
 9268 
 
 9285 
 
 93^3 
 
 9320 
 
 9338 
 
 9355 
 
 9372 
 
 9390 
 
 9407 
 
 3 6 9 12 15 
 
 54 
 
 9425 
 
 9442 
 
 9460 
 
 9477 
 
 9495 
 
 9512 
 
 9529 
 
 9547 
 
 9564 
 
 9582 
 
 3 6 9 12 15 
 
 55 
 
 '9599 
 
 9617 
 
 9634 
 
 9652 
 
 9669 
 
 9687 
 
 9704 
 
 9721 
 
 9739 
 
 9756 
 
 3 6 9 12 15 
 
 56 
 
 '9774 
 
 9791 
 
 9809 
 
 9826 
 
 9844 
 
 9861 
 
 9879 
 
 9896 
 
 9913 
 
 993i 
 
 3 6 9 12 15 
 
 57 
 
 9948 
 
 9966 
 
 9983 
 
 roooi 
 
 1-0018 
 
 1-0036 
 
 1-0053 
 
 1-0071 i -0088 
 
 1-0105 
 
 3 6 9 12 15 
 
 58 
 
 i -0123 
 
 0140 
 
 0158 
 
 0175 
 
 0193 
 
 O2IO 
 
 0228 
 
 0245 
 
 0263 
 
 0280 
 
 3 6 9 12 15 
 
 59 
 
 1-0297 
 
 0315 
 
 0332 
 
 0350 
 
 0367 
 
 0385 
 
 0402 
 
 0420 
 
 0437 
 
 0455 
 
 3 6 9 12 15 
 
 60 
 
 1-0472 
 
 0489 
 
 0507 
 
 0524 
 
 0542 
 
 0559 
 
 0577 
 
 0594 
 
 0612 
 
 0629 
 
 3 6 9 12 15 
 
 61 
 
 1-0647 
 
 0664 
 
 0681 
 
 0699 
 
 0716 
 
 0734 
 
 0751 
 
 0769 
 
 0786 
 
 0804 
 
 3 6 9 12 15 
 
 62 
 
 1-0821 
 
 0838 
 
 0856 
 
 0873 
 
 0891 
 
 0908 
 
 0926 
 
 0943 
 
 0961 
 
 0978 
 
 3 6 9 12 15 | 
 
 63 
 
 1-0996 
 
 1013 
 
 1030 
 
 1048 
 
 1065 
 
 1083 
 
 noo 
 
 1118 
 
 H35 
 
 "53 
 
 3 6 9 12 15 | 
 
 64- 
 
 1-1170 
 
 1188 
 
 1205 
 
 1222 
 
 1240 
 
 1257 
 
 1275 
 
 1292 
 
 1310 
 
 
 3 6 9 12 15 
 
 65 
 
 I-I345 
 
 1362 
 
 1380 
 
 1397 
 
 1414 
 
 H32 
 
 1449 
 
 1467 
 
 1484 
 
 1502 
 
 3 6 9 12 15 
 
 66 
 
 1-1519 
 
 1537 
 
 1554 
 
 1572 
 
 1589 
 
 1606 
 
 1624 
 
 1641 
 
 1659 
 
 1676 
 
 3 6 9 12 15 
 
 67 
 
 1-1694 
 
 1711 
 
 1729 1746 
 
 1764 
 
 I78l 
 
 1798 
 
 1816 
 
 1833 
 
 1851 
 
 3 6 9 12 15 
 
 68 
 
 1-1868 
 
 1886 
 
 190^ 
 
 1921 
 
 1938 
 
 1956 
 
 1973 
 
 1990 
 
 2008 
 
 2025 
 
 3 6 9 12 15 
 
 69 
 
 1-2043 
 
 2060 2078 
 
 2095 
 
 2113 
 
 2130 
 
 2147 
 
 2165 
 
 2182 
 
 2200 
 
 3 6 9 12 15 
 
 70 
 
 1-2217 
 
 2235 
 
 2252 
 
 227O 
 
 2287 
 
 2305 
 
 2322 
 
 2339 
 
 2357 
 
 2374 
 
 36 9 12 15 
 
 71 
 
 1-2392 
 
 2409 
 
 2427 
 
 2444 
 
 2462 
 
 2479 
 
 2497 
 
 25H 
 
 253 1 
 
 2549 
 
 3 6 9 12 15 
 
 72 
 
 1*2566 
 
 2584 
 
 2601 
 
 2619 
 
 2636 
 
 2654 
 
 2671 
 
 2689 
 
 2706 
 
 2723 
 
 3 6 9 12 15 
 
 73 
 
 1-2741 
 
 2758 
 
 2776 
 
 2793 
 
 2811 
 
 2828 
 
 2846 
 
 2863 
 
 2881 
 
 2898 
 
 3 6 9 12 15 
 
 74 
 
 1-2915 
 
 2933 
 
 2950 
 
 2968 
 
 2985. 
 
 3003 
 
 3020 
 
 3038 
 
 3055 
 
 3073 
 
 3 6 9 12 15 
 
 75 
 
 1-3090 
 
 3107 
 
 3125 
 
 3142 
 
 3160 
 
 3177 
 
 3195 
 
 3212 
 
 3230 
 
 3247 
 
 3 6 9 12 15 
 
 76 
 
 1-3265 
 
 3282 
 
 3299 
 
 3317 
 
 3334 
 
 3352 
 
 3369 
 
 3387 
 
 3404 
 
 3422 
 
 3 6 9 12 15 
 
 77 
 
 J "3439 
 
 3456 
 
 3474 
 
 3491 
 
 3509 
 
 3526 
 
 3544 
 
 35 61 
 
 3579 
 
 3596 
 
 3 6 9 12 15 
 
 78 
 
 1-3614 
 
 3631 
 
 3648 
 
 3 666 
 
 3683 
 
 3701 
 
 37i8 
 
 3736 
 
 3753 
 
 3771 
 
 3 6 9 12 15 
 
 79 
 
 1-3788 
 
 3806 
 
 3823 
 
 3840 
 
 3858 
 
 3875 
 
 3893 
 
 3910 
 
 3928 
 
 3945 
 
 3 6 9 12 15 
 
 80 
 
 I-3963 
 
 398o 
 
 3998 
 
 4015 
 
 4032 
 
 4050 
 
 4067 
 
 4085 
 
 4102 
 
 4120 
 
 3 6 9 12 15 
 
 81 
 
 I'4I37 
 
 4155 
 
 4172 
 
 4190 
 
 4207 
 
 4224 
 
 4242 
 
 4259 
 
 4277 
 
 4294 
 
 3 6 9 12 15 
 
 82 
 
 1-4312 
 
 4329 
 
 4347 
 
 4364 
 
 4382 
 
 4399 
 
 4416 
 
 4434 
 
 445 i 
 
 4469 
 
 3 6 9 12 15 
 
 83 
 
 i -4486 
 
 4504 
 
 4521 
 
 4539 1 4556 
 
 4573 
 
 4591 
 
 4608 
 
 4626 
 
 4643 
 
 3 6 9 12 15 
 
 84 
 
 1-4661 
 
 4678 
 
 4696 
 
 4713 
 
 4731 
 
 4748 
 
 4765 
 
 4783 
 
 4800 
 
 4818 
 
 3 6 9 12 15 
 
 85 
 
 1 "4835 
 
 4853 
 
 4870 
 
 4888 
 
 4905 
 
 4923 
 
 4940 
 
 4957 
 
 4975 
 
 4992 
 
 3 6 9 12 15 
 
 86 
 
 1-5010 
 
 5027 
 
 5045 
 
 5062 
 
 5080 
 
 5097 
 
 5"5 
 
 5132 
 
 5H9 
 
 5167 
 
 3 6 9 12 15 
 
 87 
 
 1-5184 
 
 5202 
 
 5219 
 
 5237 
 
 5254 
 
 5272 
 
 5289 
 
 5307 
 
 5324 
 
 534i 
 
 3 6 9 12 15 
 
 88 
 
 !"5359 
 
 5376 
 
 5394 
 
 54" 5429 
 
 5446 
 
 5464 
 
 548i 
 
 5499 
 
 55*6 
 
 3 6 9 12 15 
 
 89 
 
 1-5533 
 
 
 5568 
 
 5586 
 
 5603 
 
 5621 
 
 5638 
 
 5656 
 
 5673 
 
 5691 
 
 3 6 9 12 15 
 
 
 0' 
 
 6' 
 
 12' 
 
 18' 
 
 24' 
 
 30' 
 
 36' 
 
 42' 
 
 48' 
 
 54' 
 
 1' 2' 3' 4' 5' 
 
149 
 
 INDEX 
 
 ABERRATION, constant of 
 Abraham, electronic theory of . 
 Absolute temperature scale 
 
 ,, zero of temperature . 
 Absorption coefficients, ft and 7 rays 
 
 , X rays . 
 
 Absorption spectra . 
 Actinium emanation, diffusion of 
 Activities, equilibrium (minerals) 
 Air, composition of 
 , (damp) ,,... 
 ,, , (dry) density of 
 ,, , (saturated) water in !;w;, : ' .. 
 Alloys, composition of 
 a rays, e/m of 
 
 gaseous ionization by 
 number of . 
 
 PAGJC 
 
 13 
 
 . 99 
 44, 54 
 44, 54 
 
 . 107 
 
 93 
 
 77 
 . 103 
 . 104 
 
 . 125 
 
 21 
 25, 26 
 
 39 
 20, 27, 51,53, 81, 89 
 
 . 100 
 101, 102 
 IOO, 1 06 
 
 number of ions from . . 101, 106 
 range and velocity of . . 100, 106 
 stopping powers .... 100 
 Altitudes above sea-level . . 1 1 
 
 , determination of, by barometer . 35 
 Ampere, determinations of . .8 
 
 ,, , international .... 6 
 Angles of contact . . . . -37 
 Angstrom unit . . . -9 
 
 Antilogarithms . . . . -132 
 Apothecaries' units ..... 9 
 Arcs, electric . . . -105 
 
 Aries, first point of .... 3 
 
 Astronomy ..... I 3~'S 
 Atmosphere, composition of . . .125 
 ,, , Ra Em. in . . . . 105 
 "Atmosphere," value of . , . 5 
 
 Atomic constants . . . . .106 
 Atomic weights, international . . . I, 2 
 
 BABINET'S altitude formula . . 35 
 
 Barometer, capillarity corrections . 17 
 
 ,, , determination of altitudes by . 35 
 
 ,, , reduction to lat. 45 . .18 
 
 ,, , reduction to o C. . . .18 
 
 ,, , reduction to sea-level . .18 
 
 Baume's hydrometer . . . .21 
 
 j8 rays, absorption coefficients of . .107 
 
 ,, , e/m of 98 
 
 ,, , ionization by .... 101 
 
 ,, , number of . . . . . 106 
 
 ,, , velocity of . . . . .98 
 
 Black body radiation . . . -47 
 
 Board of Trade unit (electric energy) . 5 
 
 Bode's Law 14 
 
 Boiling points, effect of pressure on . 50 
 
 ,, ,, , elements . . . .48 
 
 Boiling points, inorganic compounds 
 
 , mixtures, maximum . 
 
 , ,, , minimum . 
 
 , organic compounds . 
 
 , water 
 
 , wax 
 
 Boyle's Law, deviation from 
 British Association screws 
 British coinage . 
 British thermal unit 
 British units . 
 
 British weights and measures . 
 Buoyancy correction of weighings 
 
 ,, ,, of densities 
 
 Bursting strengths of glass tubing 
 
 I'ACiE 
 
 I09-II7 
 
 . 128 
 
 . 128 
 
 II8-I23 
 
 . 41 
 
 50 
 10 
 
 . 16 
 
 10, 20 
 
 q 
 4 
 
 4 
 . 19 
 
 . 21 
 
 39 
 
 CADMIUM cell, determinations of . . 8 
 
 Calories, values of . . . . 5, 55, 56 
 
 Candle, standard . . . . 70 
 
 ,, , energy from . . . .70 
 
 ,, , visibility of . . . 70 
 
 Capacity, specific inductive . . -84 
 
 Capillarity corrections (mercury columns) . 17 
 
 Carcel light unit . . . . 70 
 
 Cathode rays, e/m of . . .98 
 
 , velocity of ... 98 
 
 Cauchy's dispersion formula . . .71 
 
 Cells, e.m.f.'s of . . . . S, 88 
 
 ,, , resistances of .... 88 
 
 Centigrade and Fahrenheit degrees . . 10 
 
 Centimetre, definition of . . . .3 
 
 C.G.S. units 3 
 
 Charge on the ion .... 97, 106 
 Clark cell, e.m.f. and temp. coef. of . .8 
 Clausius-Mossotti relation . . .84 
 Coefficients of expansion, gases . . 54 
 ,, "'.! liquids . . 55 
 
 ,, , solids 
 
 Coercive force .... 
 Coercivity ..... 
 Coins (British), composition of 
 ,, ,, , density of 
 
 .,, ,. , dimensions of . 
 
 ,, ,, , weight of 
 
 Combustion, heats of ... 
 Composition of air . 
 
 of alloys 20, 27, 51, 53, 
 ,, of minerals . 
 
 Compressibility .... 
 Condensation of vapours . 
 Conductivities, electrical . 
 
 Conductivities, thermal 
 
 (solutions) 
 
 . 89 
 
 . 20 
 2O 
 
 . 10 
 . 10 
 
 . 64 
 . 125 
 
 Si, 89 
 . 126 
 27-29 
 . 96 
 . Si 
 . 86 
 51 
 
 Conversion factors . . . . 9, 4 
 
INDEX 
 
 Cosines, natural .... 
 Critical data ..... 
 ,, temperature (magnetization) . 
 Crookes dark space 
 Cryoscopic constant 
 
 150 
 
 PAGE 
 . 142 
 
 34, 6 1 
 . 90 
 
 25, 
 
 2 5 
 . 24 
 . 20 
 . 20 
 
 26, 10 
 I09-II7 
 
 74 
 
 DARK space .... -93 
 
 Dates of isolation of elements ... 2 
 Day, definition of . . . . .3 
 Declination, magnetic . . . . 91 
 Densities, acids . . . . -23 
 , air (dry) 
 ,, , ,, (damp) 
 ,, , alcohol (ethyl) 
 , alkalies . 
 
 , aqueous solutions . 
 , calcium chloride 
 , common substances 
 , elements 
 , gases . 
 
 , inorganic compounds 
 , Jena glasses . 
 
 , mercury . . . . .22 
 , minerals . . . .126 
 
 , organic compounds . 118-123 
 
 ,, , steam . . . . .26 
 ,, , water \ . . . . .22 
 ,, , water vapour . . . .26 
 Density determination corrections . .21 
 Depression of freezing point . . .66 
 Depression of ice point of mercury thermo- 
 meters ... -45 
 Dew point . . . . . -38 
 " Diapason Normal" . . . .68 
 Dielectric constants . . 84 
 Dielectric strength of air ... 93 
 Diffusion of Ac, Ra, Th emanations . . 103 
 
 ofgases 35 
 
 ,, of ions (gaseous) . . 94 
 Dilution, heats of . . . . ^64 
 Dimensions of units .... 7 
 
 Diopter, the 80 
 
 Discoverers of elements .... 2 
 Dispersions, optical . . . 71 
 
 Dispersive powers . . . 73> 74 
 
 Dissociation, ionic . . -85 
 
 Distances of stars . . . . 15 
 
 Distances on earth's surface . . .12 
 Drachm, value of . . . . 9 
 
 (exponential), value of . 
 e, the ionic charge . 
 Ear . . . . : 
 Ear, sensitiveness of . . 
 Earth, density of, etc. 
 ,, , elements of . 
 ,, , size and shape of . 
 Ecliptic, obliquity of 
 Efficiencies, luminous 
 Einstein, relativity theory of . 
 Elasticities .... 
 Electrical conductivities . 
 
 ,, ,, (solutions) 
 
 ,, units, determinations of 
 Electric arcs .... 
 Electrochemical equivalents 
 Electrolysis, laws of 
 Electromotive forces of cells 
 Electronic e/m 
 
 97 
 
 9 
 
 1 06 
 68 
 . 68 
 
 13 
 
 13 
 
 '3 
 
 13 
 . 70 
 . 99 
 . 27 
 . 81 
 
 86,87 
 . 8 
 . 105 
 . 123 
 . 82 
 . 88 
 . 98 
 
 Electric e/m, change of, with velocity 
 , from Zeeman effect . 
 
 Electrons (negative), magnetic deflection of 
 
 ,, ,, , velocity of 
 
 j e/m of a rays ..... 
 
 electrons .... 98 
 
 ,, helium ..... 
 
 ,, hydrogen ion .... 
 Emergent- column, thermometer correction . 
 Emission spectra ..... 
 Energy of full radiation .... 
 Equation of time . 
 Equilibrium activities (minerals) 
 Equivalents, electrochemical . 
 Expansion coefficients, gases . 
 
 > ,, , liquids . 
 
 ,, ,, , solids . 
 
 Exponential e~ x ..... 
 
 Factors, gravimetric . 
 Fahrenheit and Centigrade degrees . 
 Faraday effect ..... 
 
 Faraday's laws of electrolysis . 
 
 Fats, melting points of . 
 
 Fire, temperature of .... 
 
 Flames, ionic mobilities in 
 
 Fluid ounce ...... 
 
 Foil (metal), thickness of ... 
 Formation, heats of .... 
 
 Fraunhofer lines ..... 
 
 Freezing mixtures . 
 
 Freezing point, depression of . 
 
 Full radiation 
 
 Fuses ....... 
 
 Fusion, latent heats of 
 
 GALLON, definition of . 
 
 y rays, absorption coefficients of 
 
 ,, , ionization by .... 
 
 Gas constant 5, 
 
 Gaseous volumes, reduction of . 
 
 Gas thermometers, thermodynamic correc- 
 tions to ...... 
 
 Gas thermometry ..... 
 
 Gauge, standard wire .... 
 
 Gauss, the ...... 
 
 Geographical mile ..... 
 
 Glaisher's factors ..... 
 
 Glass 
 
 , Jena .... 
 
 Glass tubing, bursting strengths of . 
 
 Grain ....... 
 
 Gramme, definition of 
 
 Gravimetric factors .... 
 
 Gravitation, constant of . 
 
 Gravity correction of barometer 
 
 99 
 99 
 99 
 98 
 100 
 
 ^, 99 
 106 
 106 
 45 
 76 
 65 
 
 *5 
 
 104 
 123 
 
 54 
 55 
 52 
 129 
 
 127 
 
 10 
 80 
 82 
 5o 
 47 
 96 
 9 
 35 
 62 
 
 75 
 117 
 66 
 65 
 83 
 60 
 
 4.9 
 107 
 101 
 106 
 19 
 
 44 
 44 
 83 
 7 
 10 
 
 39 
 74 
 74 
 39 
 9 
 3 
 127 
 
 13 
 ll 
 
 Gravity, values of . . . . . 1 1 
 
 HARDNESS, of minerals . 
 
 ,, , scale of (Mohs') . 
 Half-periods, radioactive substances 
 Heat conductivities 
 Heat from radium . . . 
 
 Ra Em. 
 
 ,, rocks . 
 
 ,, ,, thorium 
 Heat, mechanical equivalent of 
 Heats, latent .... 
 Heats of combustion 
 
 102, 
 
 126 
 126 
 107 
 
 102 
 104 
 102 
 
 II 
 
 6 4 
 
151 
 
 INDEX 
 
 Heats of dilution 
 ,, formation 
 , , neutralization 
 
 Heats, specific elements 
 
 gases 
 mercury 
 
 PAGE 
 
 . 64 
 62,64 
 . 64 
 
 * 
 56 
 
 59 
 56 
 70 
 ii 
 106 
 
 4 
 
 21 
 
 39 
 
 Heats, specific _, . 
 
 miscellaneous . 
 
 water 
 Hefner light unit 
 Heights above sea-level . 
 Helium from radium 
 Henry, the .... 
 Hertzian waves, velocity of 
 Heusler alloys 
 Humidity, relative . 
 Hydrometers 
 Hygrometer, chemical 
 
 ,, , wet and dry bulb 
 Hygrometry .... 
 Hyperbolic logs, conversion factor 
 Hysteresis, magnetic 
 
 lCE-point, thermodynamic temperature of 
 
 44, 54 
 Inclination, magnetic . . . .91 
 
 Inductive capacity, specific . . .84 
 Inductivity . . . . . .84 
 
 Inertia, moments of . . . .16 
 
 Ionic charge ..... 97, 106 
 
 ,, dissociation . . . . . 85 
 
 ,, mobilities (gaseous) . 95, 105 
 
 ,, ,, (gaseous) at high tempera- 
 
 tures . . . 
 (liquids) . 
 
 ,, a (solids) . 
 lonization by a, ft, y, and X rays 
 Ions gaseous (diffusion of) 
 ,, ,, recombination of . 
 
 JENA glasses, density of . 
 
 ,, ,, , dispersive power of 
 
 ,, ,, .optical . 
 
 ,, ,, , refractive index of 
 
 ,, ,, , thermometric 
 Joule, the ..... 
 Joule's equivalent .... 
 Joule -Thomson effect 
 
 KIRCHHOFF, vapour pressure formula 
 Knot, the ..... 
 
 LANGLEY and Abbot's solar work . 
 Latent heat of fusion 
 
 ,, ,, of vaporisation 
 Latitudes ..... 
 Lenard rays ..... 
 Light, magnetic rotation of 
 
 ,, , optical rotation of 
 
 , reflection of . 
 
 ,, , units of .... 
 
 ,, , velocity of . 
 
 Light-year ..... 
 Litre, definition of ... 
 
 Logarithms, five-figure . 
 ,, , four-figure . 
 Longitudes . . . 
 Lorentz, electronic theory of . 
 Luminous efficiencies 
 
 96 
 88,95 
 
 95 
 
 101, 102 
 
 . 94 
 
 94 
 
 74 
 
 74 
 
 74 
 
 . 72 
 
 45, 74 
 
 5 
 
 55 
 . 44 
 
 . 40 
 . 10 
 
 . 60 
 u, 91 
 
 . 78 
 
 . 80 
 
 . 70 
 
 . 69 
 
 15 
 4,10 
 
 '34 
 . 130 
 u, 91 
 
 . 99 
 . 70 
 
 MAGNETIC constants, terrestrial . .91 
 ,, deflection of electrons . . 99 
 Magnetic induction . . . .89 
 
 Magnetic rotations of polarized light . 80 
 
 Mathematical constants .... 9 
 Maximum boiling-point mixtures . .128 
 Maxwell's relation . . . .84 
 
 Maxwell, the ..... y 
 
 Mechanical equivalent of heat . . -55 
 Megabar, value of . . . . 5> 27 
 
 Melting points, elements . . . 4$ 
 
 ,, ., , fats and waxes . . 50 
 
 ,, MI inorganic compounds . 109 
 
 ,, ,, , organic compounds . .118- 
 
 Mercury thermometers, depression of zero of 45, 
 
 ,, ,, , reduction to gas 
 
 scale of . . 45, 
 
 ,, ,, , stem exposure cor- 
 
 rection . . 45. 
 
 ,, thermometry . . . -45 
 Metal leaf, thickness of . . . -35 
 Metallic reflection of light . . .80- 
 Metre, definition of . . . 3 
 
 Metric units ...... 
 
 Meyer's viscosity equation . . 3 
 Micron fj. (and /t/t) .... 
 
 Migration Ratios ..... 
 
 Mil, value of . 
 
 Minerals, activities in .... 
 
 ,, , composition of ... 
 
 ,, , density of .... 
 
 ,, , hardness of . . 
 
 ,, , radioactive . . . 104 
 
 ,, , scale of hardness (Mohs') . 
 Minim, value of ..... 
 Minimum boiling-point mixtures 
 Miscellaneous data 
 Mobilities of ions, flames 
 
 3 
 3* 
 
 9 
 85 
 
 9 
 
 104 
 126 
 126 
 126 
 126 
 126 
 
 9 
 128 
 9, 10 
 96 
 95 
 
 ,, ,, , liquids 
 
 ,, ,, , natural 
 
 ,, , , , solids . 
 
 Mohs' scale of hardness . 
 Molecules, free path of . 
 ,, , number of, in gas 
 ,, , size of . 
 ,, , velocity of 
 Moments of inertia 
 Moon, elements of . 
 Mossotti, Clausius-, relation 
 Motions of stars 
 Musical scales 
 
 Nautical mile 
 
 Negative electrons, e/m of 
 ,, ,, , mass of 
 
 ,, ,, , radius of 
 
 ,, ,, , velocity of 
 
 Neutralization, heats of . 
 
 Normal diapason . 
 
 OHM, determinations of . 
 
 ,, , international 
 Optical rotations, quartz 
 
 ,, ,, , liquids 
 
 Optical thermometry 
 Organ pipes, end correction of 
 
 gaseous 
 
 gaseous at high tempera- 
 tures . . .96 
 . 88, 95 
 . 10$ 
 
 9> 
 . 126 
 . 32 
 
 97, 98, 106 
 
 32 
 
 n 
 
 II 
 
 . 10 
 98, 106 
 . 106 
 . 106 
 . 98 
 63. 
 . 68 
 
 . 8- 
 6 
 
152 
 
 INDEX 
 
 Organ pipes, wave lengths from 
 Ounce, values of . 
 
 CAiiK 
 
 68 
 
 PARALLAX, equatorial solar . . .13 
 ,, , stars . . . . 15 
 
 Permeability 89 
 
 Photometry . . . . . .70 
 
 Physical constants, inorganic compounds 
 
 109-117 
 
 ,, ,, , organic compounds 118-123 
 
 ir, value of . . . . . .9 
 
 Planck's radiation formula . . .65 
 
 Planets 14 
 
 Platinum thermometers, reduction to gas 
 
 scale .46 
 
 Platinum thermometry . . . .46 
 Poisson's ratio . . . . 27 
 
 Polarized light, magnetic rotation of . 80 
 Polonium ..... 107, 108 
 Pound, definition of .... 4 
 Precession, constant of . . . 13 
 
 Pressure coefficient of expansion . . 54 
 ofPV ... 10 
 Pressure, critical . . . . -34 
 Pressure, vapour. See Vapour pressure 40, 103 
 Pressure, effect of, on boiling points . 50 
 
 PV, pressure coefficient of . . .10 
 Pyrometers ..... 46, 47 
 
 RADIANS 9, 146 
 
 Radiation, full ..... 65 
 
 Radiation thermometers . . . 47 
 
 Radioactive decay constants . . .107 
 
 ,, minerals . . . .104 
 
 ,, substances, constants of .107 
 
 ,, ,, properties of . 108 
 
 Radioactivity constants . . . 106, 107 
 Radium emanation, decay of . . . 102 
 , density of. . .10 
 , diffusion of . -103 
 , equilibrium, volume of 102 
 , heat from . . .102 
 , in atmosphere . .105 
 , molecular weight of . 103 
 , vapour pressure of . 103 
 Radium, heat from . . . .102 
 
 , in rocks . . .104 
 ,, , helium from . . . .106 
 
 ,, , in rocks ..... 104 
 
 , in sea water . . . .105 
 
 Ramsay and Young's vapour pressure law . 40 
 Range of a rays ..... 100 
 
 Rankine, vapour pressure formula of . 40 
 
 Ratio of E.M. to E.S. unit . . .69 
 Rayleigh's radiation formula . . -65 
 Reciprocals . . . . . .136 
 
 Recombination of ions (gaseous) . . 94 
 
 Reflection of light (metallic) . . .80 
 
 Refractive indices, gases . . . 71 
 
 , Jena glasses . 72, 74 
 
 ,, , miscellaneous . . 72 
 
 Relativity theory of Einstein . . -99 
 
 Resistance, specific . . . .81 
 
 ,, , temperature coefficient of . 82 
 Resistances of cells . . . .88 
 
 ,, of wires . . . -83 
 
 Resistivities 82 
 
 Rigidity, modulus of . . .27 
 
 ,, , temperature coefficient of . .28 
 
 Rocks, Ra, Th, in .... 104 
 
 Rontgen rays, homogeneous . . -93 
 
 ,, ,, , ionization by ... 101 
 
 Rotations (magnetic) of polarized light . 80 
 
 ,, (optical) of liquids . . -78 
 
 ,i ,, of quartz . . -79 
 
 SAFE currents for wires . . . .83 
 
 Satellites of planets . . . -14 
 
 Saturated air, water in . . -39 
 
 Scale of hardness (Mohs') . . . 126 
 
 Scales, musical . . . . .68 
 
 Screws, pitch of, etc. . . . .16 
 
 Sea- water, radium in . . .105 
 
 Second, definition of . . .3 
 
 Secular magnetic changes . . . 92 
 
 Sensitiveness of ear to pitch . . .68 
 
 Sikes' hydrometer . . . . .21 
 
 Silvering solution . . . . . 73 
 
 Sines, natural . . . . .140 
 
 Size of drops . . . . -37 
 
 Solar constant . . . . -65 
 
 ,, parallax, equatorial . . -13 
 
 ,, spectrum . . . . -75 
 
 system 14 
 
 Solubilities aqueous, gases . . .124 
 ,, ,, , inorganic compounds 
 
 109-117 
 
 ,, , solids . . .125 
 
 ,, of liquids (mutual) . . . 124 
 
 Sound, velocity of . . . . .67 
 
 Sparking potentials . . . -93 
 
 Specific heats, elements . . . 56 
 
 , gases, constant pressure . 58 
 
 , constant volume . 5 8 
 
 ,, , ratio of . . .58 
 
 , mercury . . . .56 
 
 , miscellaneous . . -59 
 
 , water . . . -56 
 
 Specific inductive capacity . . .84 
 
 Specific resistances . . . . .81 
 
 Specific volume . . . . .22 
 
 Spectra, absorption . . . -77 
 
 ,, , emission (gases) . . -77 
 
 ,, , ,, (solids) . . .76 
 Spectroscopy ...... 75 
 
 Squares 138 
 
 Standards, British . 4 
 
 , British and metric equivalents 4, 9 
 
 ,, , metric 3 
 
 Standard conductivity solutions . . 86 
 
 ,, spectrum lines . . . -75 
 
 ,, temperatures . . . .50 
 
 ,, times ..... 15 
 
 ,, wire gauge . . . -83 
 
 Stars, distances of ... 
 
 , motions of . 
 
 ,, , parallaxes of ... 
 
 Stefan-Boltzmann law 
 
 Steinmetz' hysteresis formula . 
 
 Stem exposure corrections of mercury th< 
 
 mometers ..... 
 Stopping powers (a rays) 
 Strengths, bursting glass tubing 
 ,, , tensile (liquids) 
 (solids) 
 Sun, elements of 
 
 ,, , temperature of ... 
 Surface tensions .... 
 
 47, 
 
 15 
 *5 
 
 6 5 
 
 90 
 
 45 
 
 100 
 
 39 
 39 
 28 
 
 , M 
 
 6 1 
 36 
 
153 
 
 Susceptibility 
 
 Sutherland's viscosity equation 
 
 PAGE 
 
 89,90 
 
 TANGENTS, natural .... 144 
 
 Temperature coefficient, conductivity (solns.) 86 
 
 ,, ,, , dielectric constant 84 
 
 ,, ,, , magnetization . 90 
 
 ,, ., , refractive index . 72 
 
 ,, ,, , resistance . 82, 83 
 
 ,, ,, , rigidity . . 28 
 
 ,, ,, , surface tension 36 
 
 ,, ,, , tuning fork . 68 
 
 ,, ,, , viscosity (gaseous) 32 
 
 , Westoncell. . 8 
 
 ,, ,, , Young's modulus . 28 
 
 Temperature of fire, by appearance . . 47 
 
 , , of sun . . . -65 
 
 Temperatures, critical . . . -34 
 
 ,, , standard . . . 50 
 
 Tenacities 28 
 
 Tensile strengths, liquids . . -39 
 
 , solids . . . .28 
 Tension, surface . . . . 36 
 
 Terrestrial magnetic constants . . . 91 
 Thermal conductivities . . . 51 
 
 Thermochemistry . . . . .62 
 Thermo-couples .... 46, 47 
 Thermodynamic correction to gas thermo- 
 meters . . -44 
 scale . . 44, 54 
 
 ,, temperature of ice-point . 44 
 
 Thermo-junctions .... 46, 47 
 Thermometry, gas . . . . . 44 
 mercury . . . -45 
 optical . . . -47 
 platinum . . . .46 
 radiation . . . -47 
 thermoelectric . . 46, 47 
 Thickness of liquid films . . -37 
 
 ,, metal leaf . . . -35 
 Thorium emanation, diffusion of . . 103 
 Thorium, heat from , . . . IO2 
 ,, , in rocks .... 104 
 
 Time, equation of . . . . 15 
 
 Times, standard . . . . 15 
 
 Tonne, value of . . . -9 
 
 Transport numbers . . . .85 
 
 Transverse vibrations of rods . . .68 
 Trouton's Rule . . . . .60 
 Troy units . . . . . 9 
 
 Tubing (glass), bursting strengths of . 39 
 
 Tuning fork, temperature coefficient of . 68 
 Twaddell's hydrometer . . . .21 
 
 UNITS 3 
 
 , British .... -4 
 
 , derived ..... 4 
 
 , dimensions of .... 7 
 , electrical, determinations of . .8 
 , electrical, practical definitions of . 6 
 
 , light 70 
 
 , metric ...... 3 
 
 , United States . . -9 
 
 "V," ratio of electrical units . 
 Van der Waal's equation 
 Vaporisation, latent heats of . 
 Vapour pressures . 
 
 alcohol, ethyl 
 compounds . 
 elements 
 ice 
 
 mercury 
 Vapour pressures, Ra Em. 
 ,, , water . 
 
 Vapours, condensation of 
 Velocity of a rays . 
 
 Hertzian waves 
 ions. See Mobilities 
 light (in liquids) 
 ,, (in vacuo) 
 negative electrons . 
 sound . 
 
 and pressure . 
 Verdet s constant . 
 Vibrat ons of rods . . 
 Viscosities gases . 
 
 INDEX 
 
 PAGE 
 
 . 69 
 
 40 
 41 
 42 
 42 
 40 
 41 
 103 
 
 4 ? 
 96 
 
 100 
 
 69 
 
 69 
 
 ? 9 
 67 
 
 68 
 80 
 68 
 31 
 
 (temperature coefficients of) 32 
 liquids . . . . 30 
 
 solids . . . . -31 
 solutions aqueous . . . 31 
 vapours . . . .31 
 
 Volt international ..... 6 
 Volume calibration . . . . -17 
 ,, coefficient of expansion . . 54 
 ,, critical . . . . -34 
 ,, elasticity . . . . -27 
 Volumes (gaseous) reduction to o C. and 
 
 760 mm. ...... 19 
 
 WATER vapour, density of . .26 
 
 ,, ,, , in saturated air . . 39 
 
 Watt, the ...... 5, 6 
 
 Waxes, melting points of ... 50 
 Weighings, reduction to vacuo . 19 
 
 Weights and measures, British . . 4 
 
 Weston cell, determinations of 8 
 
 Wet and dry bulb hygrometer . . .38 
 Whitworth screws . 
 
 . 65 
 47, 65 
 
 Wire gauge, standard . . . -83 
 Wire resistances . . . . -83 
 
 ,, ,, , temperature coefficient of 83 
 
 Wien's displacement law 
 radiation formula . 
 
 X RAYS, homogeneous . . . -93 
 ionization by . . . . IOI 
 
 YARD, definition of . . . 4> 9 
 Years, various ..... 3 
 Young's modulus . . . . -27 
 ,, ,, , temperature coefficient of 28 
 
 Young's, Ramsay and, vapour pressure 
 
 formula 
 
 Zeeman effect, e/m from 
 
 40 
 98,99 
 
 THE END 
 
 PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, LONDON AND BECCLES. 
 
O"' 
 
YD 24252 
 
 THE UNIVERSITY OF CALIFORNIA LIBRARY