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 1ft/ 25527 25768 26007:26245 26482 24 48 71 95 119 143 167 190 214 ( 26717 26951 27184 27416 27646 2 3 46 70 93 116 139 l62 185 2OC j 27875 28103 28330 28556 28780 23 45 68 90 113 135 158 181 203 I 29003 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 ! 22 23 32222 34242 32428 32634132838 34439:3463534830 36361:36549136736 33041 35025 36922 33244 35218 37107 33445 37291 33646 33846 3560335793 3747537658 34044 35984 37840 20 40 61 81 '9 39 58 77 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 18 35 53 7i 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 4H97 41664418304199642160 42325 42488 4265142813 42975 J 6 33 49 66 82 98 115 131 148 27 43136 43297 43457 436i6J43775 43933 44091 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58433 5955C 58546 59660 5865958771 5977059879 58883,58995 5998860097 ii 23 34 45 n 22 33 44 56 55 68 79 90 102 66 77 88 99 40 60206 603146042360531 60638 60745 6085360959 6106661172 n 21 32 43 54 64 75 86 97 41 42 i 43 61278 62325 63347 61384 62428 63448 6149061595 62531^62634 63548:63649 61700 62737 63749 61805 62839 63849 6190962014 62941 63043 63949 64048 6211862221 6314463246 64147 64246 10 21 31 42 10 20 31 41 10 20 30 40 52 5 1 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 65706 65801 65896 65992 6608766181 10 19 29 38 48 57 67 76 86 46 ! 47 48 49 66276 67210 68124 69020 663706646466558 6730267394^7486 6821568305:68395 691086919769285 66652 67578 68485 69373 66745 67669 68574 69461 66839 66932 6776167852 6866468753 69548 69636 6702567117 6791368034 6884268931 6972369810 9 19 28 37 9 18 27 37 9 18 27 36 9 18 26 35 47 46 45 44 56 65 75 84 55 64 73 82 54 63 72 81 53 61 70 79 i 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 4i 4i 40 6789 69897 70757 71600 72428 73239 6998470070 7084270927 7168471767 7250972591 7332073400 70157 71012 71850 72673 7348o 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 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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 ooo 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 \oi6 2357 8 10 12 13 15 25 ooo 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 373 1 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 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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 5O 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 \ 2333 2233 54 185 1848 1845 1842 I8 3 183 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 r8o2 1799 1795 1792 1789 O I I I 2 2233 56 57 1786 1754 1783 1779 1748 1776 1745 1773 1742 1770 1739 1767 I73 6 1764 1733 1761 1730 1757 1727 I I I I I I 2 2 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 I 2223 2223 60 1667 1664 1661 1658 1656 1653 1650 1647 1645 1642 O I I I I 2223 61 1639 1637 1634 1631 1629 1626 1623 1621 1618 1616 O I I I I 2222 62 1613 1610 1608 1605 1603 1600 1597 1595 1592 1590 O I I I I 2222 63 1587 1585 1582 1580 1577 1575 1572 1570 I I I 1222 64 1563 1560 1558 1555 1553 1550 1548 1546 '543 *54i O O I I I 1222 65 1538 1536 1534 i53i 1529 1527 1524 1522 1520 1517 I I I 1222 66 I5i5 1513 IS" 1508 1506 1504 1502 1499 M97 M95 I I 1 1222 67 M9: 1490 1488 1486^1484 1481 M79 1477 1475 1473 I I I 1222 68 1471 1468^1466 1464 1462 1460 1458 1456 1453 1451 O O I I I 1222 69 1449 1447 1 445 1443 1441 1439 M37 1435 1433 H3I I I I I I 2 2 70 1429 1427 1425 1422 1420 1418 1416 1414 1412 1410 O O I I I I I 2 2 71 1408 1406 1404 1403 1401 1399 I397 1395 I393 i39i I I I I I 2 2 72 1389 1387 1385 1383 1381 1379 1377 1376 1374 1372 I I I I I 2 2 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 I I I I I I 2 2 I I I 2 75 T 1 ? f 8 T '? / > C 1 O'} i TOOT g 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 I III I ! 81 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 I2II 1209 1208 1206 0001 I III I 83 1205 1203 1202 1200 1199 1198 1196 "95 "93 1192 0001 I I I I I 84 1190 1189 1188 1186 1185 1183 Il82 1181 "79 II 7 8 O O O I I I III 85 II 7 6 "75 "74 1172 1171 1170 1168 1167 1166 1164 0001 I I I I I 86 1163 1161 1160 "59 "57 1156 "55 "53 1152 II5I 0001 I I I I I 87 "49 1148 "47 "45 "44 "43 1142 1140 "39 1138 0001 I I I I I 88 1136 "35 "34 "33 1131 1130 1129 1127 1126 "25 O O O I I I I I I 89 1124 1122 II2I 1 120 1119 1117 1116 riI 5 1114 III2 0001 I I I I I 90 mi IIIO I.I09 1107 1106 1105 1104 1103 IIOI IIOO 0001 I I I I I 91 1099 1098 1096 1095 1094 1093 1092 1091 1089 1088 o o o o ! I I I I 92 1087 1086 1085 1083 1082 1081 loSo 1 1079 1078 1076 0000 I I I I I 93 1075 1074 1073 1072 1071 1070 1068 1067 1066 1065 0000 I I I I I 94 1064 I06 3 1062 1060 1059 1058 1057 1056 1055 1054 o o o o 1 I I I I 95 I0 53 1052 IO5O 1049 1048 1047 1046 1045 1044 1043 0000 I I I I I 96 1042 IO4I 1040 1038 '037 1036 1035 1034 1033 1032 0000 I I I I I 97 1031 1030 IO29 1028 1027 1026 1025 1024 1022 1021 o o o o I I I I I 98 IO2O 1019 1018 1017 1016 1015 1014 1013 IOI2 IOII o o o o [ I I I I 99 1010 1OO9 1008 1007 1006 1005 1004 1003 IOO2 1001 o o o o o I I I I o \ 2 3 4 7 e g 1 1 2 3 4 5 6789 A o T 1 i o 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 I-960 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