PHYSICAL AND CHEMICAL CONSTANTS X RAYS. By G. W. C. KAYE, O.B.E., M.A., D.Sc. With 115 Plates and Diagrams and 28 Tables. 8vo. LONGMANS, GREEN & CO. LONDON, NEW YORK, BOMBAY, CALCUTTA AND MADRAS TABLES OF PHYSICAL AND CHEMICAL CONSTANTS AND SOME MATHEMATICAL FUNCTIONS BY G. W. C. KAYE O.B.E., M.A., D.SC. THE NATIONAL PHYSICAL LABORATORY AND T. H. LABY, M.A. PROFESSOR OF NATURAL PHILOSOPHY, THE UNIVERSITY OF MELBOURNB FOURTH EDITION LONGMANS, GREEN AND CO. 39 PATERNOSTER ROW, LONDON FOURTH AVENUE & 30TH STREET, NEW YORK BOMBAY, CALCUTTA, AND MADRAS 1921 All rights reserved PREFACE TO FOURTH EDITION t THE following alterations and additions have been made in this issue. Matter relating to the figure of the earth, the absolute determination of the acceleration of gravity, and more extended tables of the relative value of that constant have been added. The chemical data have been recalculated, using the international atomic weights. Some seven hundred additions and alterations in the physical constants of chemical compounds have been made. The published values of these constants have been critically examined, and what appear to be the more accurate values for the chemical compounds included in these pages, have been used. T. H. L. MELBOURNE, April, 1920. THROUGH the kind co-operation of Dr. Ezer Griffiths of the National Physical Laboratory, many of the heat tables have been revised and amplified. Among other additions and changes are tables of atomic numbers, spark-gap voltages, X-ray wave lengths and terrestrial magnetic constants. The effect has been slightly to increase the size of the book. G. W. C. K. LONDON, July, 1920. PREFACE TO SECOND EDITION WE regret that the difficulties of the times have not permitted the complete revision which we had contemplated. We have had to content ourselves with removing those mistakes of which, by the courtesy of many readers, we had become aware, and inserting a number of the more fundamental constants which contemporary research has yielded since 1911. A few tables have been thoroughly revised. G. W. C. K. T. H. L. September, 1916. . . 43492$ EXTRACT FROM PREFACE TO FIRST EDITION 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 rhumt 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 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. 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 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, may have eluded us. G. W. C. K. T. H. L. September, 1911. CONTENTS PAGES GENERAL PHYSICS, ASTRONOMY, ETC i 45 HEAT 46 70 SOUND 71 72 LIGHT 73 84 ELECTRICITY 8592 MAGNETISM 93 96 RAYS, RADIOACTIVITY AND GASEOUS IONIZATION 97_ II 6 CHEMISTRY 117 13 6 MATHEMATICAL TABLES ^^ INDEX 157161 ATOMIC WEIGHTS INTERNATIONAL ATOMIC WEIGHTS FOR 1920-21 (0 = 16) (See annual reports of the International Atomic Weight Committee (temporarily suspended in 1916) and of the Atomic Weight Committee of the American Chemical Society in the Journal of the Society, also F. W. Clarke, "A Re- calculation of the Atomic Weights," 1910) Element. Symbol. Atomic Weight. Element. Symbol. Atomic Weight. Aluminium Al 27*1 Neodymium Nd 144*3 Antimony Sb 120-2 l\| h rt rt . Ne 20*2 Argon .... A 39 ; 9 Nickel .... Ni 58-68 Arsenic As 74-96 Niobiumt . . . Nb 93' 1 Barium Ba 137-37 Niton (Ra. Em.) Nt 222*4 Beryllium* Be 9-1 Nitrogen * * N I4*008 Bismuth Bi 208 -o Osmium Os 190*9 Boron .... B 10*9 Oxygen .... 16*00 Bromine Br 79-92 Palladium Pd 106-7 Cadmium Cd 112*40 Phosphorus P 31*04 Caesium Cs 132-81 Platinum Pt 195-2 Calcium Ca 40-07 Potassium K 39*10 Carbon .... C 12-005 Praseodymium Pr 140-9 Cerium .... Co 140-25 Radium .... Ra 226-0 Chlorine - Cl 35-46 Rhodium Rh 102*9 Chromium Cr 52-0 Rubidium - Rb 85-45 Cobalt .... Co 58-97 Ruthenium Ru 101*7 Copper . . . Cu 63-57 Samarium Sa 150-4 Dysprosium Dy 162-5 Scandium * Sc 45' i Erbium .... Er 167-7 Selenium > So 79-2 Europium * * Eu 152-0 Silicon .... Si 28-3 Fluorine . . F 19*0 Silver .... Ag 107-88 Gadolinium - Gd I57-3 Sodium .... m *j Na 23*00 Gallium .... Ga 70-1 Strontium Sr 87-63 Germanium Ge 7 2 '5 Sulphur* * . . S 32-06 Gold Au 197-2 Tantalum * Ta 181-5 Helium .... He 4-00 Tellurium * Te 127*5 Holmium Ho 163-5 Terbium Tb 159-2 Hydrogen H i -008 Thallium . . Tl 204-0 Indium .... In 114-8 Thorium . Th 232-15 Iodine .... 1 126-92 Thulium . Tm 168-5 Iridium .... Ir 193-1 Tin 118*7 1 ro n Fe Titanium . . . Ti LU / 48-1 Krypton .... Kr 82-92 Tungsten . W 184*0 Lanthanum - La 139-0 Uranium > . u 238-2 Lead Pb 207-20 Vanadium . V 51*0 Lithium .... Li 6-94 Xenon .... Xe 130*2 Lutecium * Lu i75-o Ytterbium - . . Yb J 73'5 Magnesium Mg 24-32 Yttrium .... Y 8933 Manganese Mn 54'93 Zinc Mercury Hg 200'6 Zirconium Zr 90-6 Molybdenum Mo 96-0 * Beryllium or Glucinum (Gl). f Niobium or.Columbium (Cb). ATOMIC NUMBERS THE ELEMENTS IN THE ORDER OF ATOMIC NUMBERS | At Atomic | At Atomic JL No Weight (1920-1). First isolated by Date. 1 At No Weight (1920-1). First isolated by Date. H I rco8 Cavendish 1766 Ru 44 1017 Claus 1845 He 2 4*00 Ramsay & Cleve * 1895 Rh 45 I02'9 Wollaston 1803 Li 3 694 Arfvedson 1817 Pd 46 I06'7 Wollaston 1803 Be 4 9-1 Wohler and Bussy 1828 Ag 47 I07-88 P. B 5 10-9 Gay-Lussac &The'nard 1808 Cd 48 II2-40 Stromeyer 1817 C 6 12-005 P. In 49 II4-8 Reich and Richter 1863 N 7 14-08 Rutherford 1772 Sn 50 Il87 __ P. 8 1600 Priestley and Scheele 1774 Sb 5i 120*2 Basil Valentine 15 centy. F 9 19*0 Moissan 1886 Te 52 I27-5 v. Richenstein 1782 Ne 10 20-2 Ramsay and Travers 1898 I 53 126-92 Courtois 1811 Na ii 23'00 Davy 1807 Xe 54 I30-2 Ramsay and Travers 1898 Mg 12 2432 Liebig and Bussy 1830 Cs 55 I32-8I Bunsen and Kirchhoff 1861 Al 13 27-1 Wohler 1827 B a 56 I37-37 Davy 1808 Si H 28-3 Berzelius 1823 La 57 I39-0 Mosander 1839 P 15 31-04 Brand 1674 Ce 58 I40-25 Mosander '839 S 16 32*06 P. Pr 59 140-9 Auer von Welsbach 1885 Cl 17 35*46 Scheele 1774 Nd 00 I44-3 Auer von Welsbach 1885 A 18 39*9 Rayleigh & Ramsay 1894 Sa 62 I50-4 L. de Boisbaudran 1879 K 19 39-10 Davy 1807 Eu 63 I52'O Demargay 1901 Ca 20 40-07 Davy 1808 Gd 64 157-3 Marignac 1886 Sc 21 45'i Nilson and Cleve 1879 Tb 65 I59-2 Mosander 1843 Ti 22 48-1 Gregor 1789 Dy 66 162-5 U. & D. 1907 V 23 51-0 Berzelius 1831 Ho 67 163-5 L. de Boisbaudran 1886 Cr 24 52-0 Vauquelin 1797 Er 68 1677 Mosander 1843 Mn 25 54*93 Gahn 1774 Tm 69 168-5 Cleve 1879 Fe 26 55-84 _ P. Yb 70 I73-5 Marignac 1878 Co Ni 27 28 J J T^ 58-97 58-68 Brand Cronstedt 1735 1751 Lu Ta W 7i 73 74 175-0 181-5 184-0 Urbain Eckeberg Bros. d'Elhujar 1908 1802 1783 Cu 29 63'57 . Os 76 190-9 Smithson Tennant 1804 Zn 30 65*37 Ment. by B. Valentine 15 centy. Ir 77 193-1 Smithson Tennant 1804 Ga 31 70-1 L. de Boisbaudran 1875 Pt 78 195-2 . 16 centy. Ge 32 72-5 Winkler 1886 Au 79 197-2 P. As 33 74*96 Albertus Magnus 13 centy. Hg 80 200-6 Md. by Theophrastus 300 B.C. Se 34 79'2 Berzelius 1817 Ti 81 204-0 Crookes 1861 Br 35 79*92 Balard 1826 Pb 82 207-20 Mentd. by Pliny P. Kr 36 82-92 Ramsay and Travers 1898 Bi 83 208*0 Mtd. by B. Valentine 15 centy. Rb 37 85-45 Bunsen and Kirchhoff 1861 Po 84 M. & Mme. Curie 1898 Sr 38 87-63 Davy 1808 Nt 86 222 M. & Mme. Curie 1900 Y 39 89*33 Wohler 1828 Ra 88 226-0 Curies and Bdmont 1898 Zr 40 90*6 Berzelius 1825 Ac 89 Debierne 1898 1Mb* 4i 93*i Hatchett 1801 Th 90 232-I5 Berzelius 1828 Mo 42 96-0 Hjelm 1790 U 92 238-2 Peligot 1841 P., Prehistoric; * Lockyer (in sun), 1868 ; U. & D., Urbain & Demenitroux ; Be or Ge; NJ Nb or Cb. 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/ioo 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-indium bar of a nearly X-shaped section, called the International Prototype Metre. The alloy of 90 Ft, 10 Ir used (also for the International Kilogramme) 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- grammeshave 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 i/(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. 17). 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. 17). t 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. J 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 ; i.e. 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 = 86,164-0906 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 median plane of the bar, which is of i inch square section and 38 inches long. Its composition is 32 Cu, 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 been 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 Trav. et M6m. du Bur. Intl., tomes iv., 1885, and xii., 1902.) International Prototype. (Reciprocal.) '9H399 metre 1*093614 45359243 kilogramme 2*2046223 [NOTE. The yard is defined at 62 F., the metre at o C] Imperial Standard. I yard i pound 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. 24). and 760 mm. pressure (Prods Verbaux^ 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 1000*027 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/w^ 2 , where m is the mass of any particle of a body, and d its distance from the axis of reference. Uniti cm. 2 gm. (see p. 18). Angular Momentum : Moment of inertia multiplied by angular velocity round axis of reference. Uniti cm. 2 gm. sec.- 1 . Force : 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. Unit i 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. =^dyne cms. = g ergs. Energy : Measured by the work a body can do by reason of either (i) its motion Kinetic Energy (= mv z /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. Uniti dyne per cm. 2 i bar = io 6 dynes per cm. 2 = 750* mm. 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 = 7594 mm. mercury at o C. in London = 1*0132 x io 6 dynes per cm. 2 = 147 Ibs. per inch 2 = o - 94 ton per foot 2 , i millibar = icr 3 bar. * Correct to i part in 5000. Elasticity : Ratio of stress to resulting strain. Unit I dyne per cm. 2 , since the dimensions of a strain are zero. 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. 47) ; 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 t C. to (/ + i) C. The 20 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. 58, 59). 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, I-OI32 X K> X see p. 114). 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. 6 ELECTRICAL UNITS Current : Unit Unit quantity flowing uniformly past a point in unit time. Potential Difference and Electromotive Force: 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 on a 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. 88). 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. 93). Susceptibility: Unit intensity of magnetization per unit field (p. 93). 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 of prism of unit area and unit length. 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, be 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, Isee 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 at o C., H'452i 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 . . 100 Momentum . I I -i Strain . . . O Mass . . . 010 Moment of mo- Elasticity . . I 12 Time . . . 001 mentum . . 2 I -I Compressibility I -1 2 Angle . . . o o o Moment of in- Viscosity . . -I I -I Surface . . . 2 O ertia . . . 210 Diffusion . . 2 -I Volume . . . 300 Angular mo- Capillarity . . 12 Density . . . 3 i o mentum . . 2 -I Temperature . O O O Velocity . . . I I Force . . . I -2 Heat* . . . 2 I -2 Angular vel. . Acceleration . I I 0-2 Couple, Torque Work, Energy 2 2 2 -2 Thermal Con- ductivity * . 1 i-3 Angular accele- Power . . . 2 -3 Entropy* . . 2 1-2 ration . . . O 2 Pressure, Stress I 2 ELECTRICAL AND MAGNETIC UNITS z/, 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. 73). (See Riicker, Phil. Mag-,,22, 1889.) Unit. Dimensions. Eel at ions. Sym- bol. E.S. Unit. E.M. Unit. E.S.U. . L. M T ?> L. M. T. u E.M.U. rac ica m . E.M.U. E.S.U. Electrical Charge or quan- tity . . . . e f }-I 4 4 4 o-4 I/Z/ coulomb = IO" 1 = 3Xio 9 Resistance . R I I -I 10- I I V* ohm = I0 9 = 1 x jo"" 11 Current . . . i f 2" ~~ 2 2 44" i 4 I/V ampere = 10-1 = 3x10 Potential or E.M.F. . . . E i 1 I -1 I 4-2 v volt = I0 8 = 1/300 Electric field F ~\ 1 -I -I I 2 - -2 J V (volt/cm.) Conductivity . . K I I 2 I I I/V 2 " recipro- = io~ 9 = 9x10" cal ohm " Capacity . . C I O I -I 2 -I l/V* micro- = IO~" = 9X io 5 farad J Self and mutual} induction . / L;M i 2-1 I I * |henry \ cm. ^f "Ixi'o^o Dielectric con- stant f . . . k o O O I -2 2 -I I/7^ 2 Magnetic Pole strength , m i o - i f i- I i V Flux (total lines) N J J | li-i i ifv maxwell = I = 3xio 10 Force ; field strength . H i 4-2 4 4 ^ ~ i 4 llv gauss = I = 3Xio 10 Induction . . . B -f J o I f J ~ I 1 v gauss = I = x io~ 10 Intensity of mag- netization . . I -f 4 o -i ~4 4 ~ -I 4 V Permeability . /* 20 21 o 6 I V* * In dynamical units. t Specific inductive capacity. J io~ 6 farad. Example : To find the number () of ergs per sec. in a horse-power (33,000 ft.-lbs. per min.). Dimensions of power = L 2 MT~ 3 = LT" 1 fForce] ft. /min n = 33,000 ( - cm. \ sec . V Ib. weight 33,000 x 30- 48 t- X 4S3'6 x 981 / ' dyne ~~ 60 = 7*46 X io 9 ergs per sec. = 746 watts. ELECTRICAL UNITS S ABSOLUTE DETERMINATIONS OF ELECTRICAL UNITS See Baillehache, "Unite's Electriques," Paris, 1909, and the "Report of the London Conference" (p. 6). The appendix to this report (issued separately, gd.) 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 106'25 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). cm./0. Method. Observer. cm./0. Method. Observer. 106-28 I06*22 io6'32 Spinning disc > Mean result Rayleigh, 1882 Rayleigh and Mrs. Sedg- wick, 1883 Rowland, 1887 106-29 106-32 106-27 106-245 Induced dis- charge Spinning disc n Glazebrook, '88 V. Jones, 1894 Ayrton and V. Jones, 1897 Smith,N.P.L.,'i4 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 = '00111827 gm./cou- lomb. Compare the 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, 1907 1*11821 1*11829 Dynamometer Janet, Laporte, de la Gorce, 1909 Do., 1910 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 present 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 / E = Ea> - -oooo4o6(/ - 20) - 9-5 x icr\t 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 roi822 1-01834 Intl. ohm and current weigher Intl. ohm and intl. ampere Ayrton, Mather, and Smith, 1908 Dorsey, 1911 Jaeger and v. Steinwehr, 1909 The E.M.F. of the Clark cell = 1-433 volts at 15 C. It diminishes by about 1*2 parts in loco for i C. rise of temp. 9 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. (Eeciprocal.) British. Metric. (Keciprocal.) length Force I inch = 2-5400 cm.* '3937 t I poundal = 13,825 dynes 7-233 Xio~ 5 i yard = 9 1 44 metre* 1-0936 I pound wgt. = 4-45 x io 5 2-247 xio- 6 i mile = 1-6093 km. 6214 dynes Area Pressure i sq. inch = 6*45 1 6 sq. cm. I55of i Ib./sq. inch = 68,971 1-45 x io~ 5 Volume dynes/cm. 2 i cubic inch = 16-387 c.c. 0610 55 5J 70-31 01422 i cubic foot = 28-317 litre 03531 gm./cm. i pint = 5682 litre 17598 I ton/sq. inch = 1-545 x io 8 6-47 x io- 9 I gallon = 4-5460 litre t 220Oi dynes/cm. 2 Mass n i'575 6349 i grain = 0648 gram 15-432 k. gm./mm. 2 I oz. (avoir.) 28-350 grams 03527 Work I Ib. = 4536 k. gm. 2*2046 I ft. -pound = 1-356 joules 7373 i ton = Density ilb./cub.ft.= ioi6k. gm.|| 01602 039842 62*43 Power i horse-power = 746 k.watt. i '34 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% Stnd.) (Stand.' (I mm* io IYI ctrc i micron, fjL=io~ 6 2 Ibs. = i k. gram, vd. at > = \ yd. at ' _g 2 galls. = io litres, J ** "-* [ 62F.j ( 5 9-6F. O I ton = (} tonne .1 less 2% I Ib. = i Ib. I mil=io~ 3 inch (Xiooo -. gm.)) i gal. = I -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. jr 3-141592654 '49715 I Ib. (avoir.) = 7000 grains =454 grams 7r2 9*869604401 "99430 I oz. =437i =28*3 I/7T 318309886 1-50285 i oz. (troy) = I V-r. 1772453851 -24857 i oz. (apothe- 1 = 480 ,, =31-1 I radian 570-295 78 175812 caries)) 1 017453 radian 2*24188 i fl drachm 3 = 60 minims = 3*55 c.cs. e 2718281828 "43429 i fl. oz. $ = 8 fl. drachms- 28-41 log, io 2-302585 -36222 i pint = 20 fl. ozs. = 568 A 10% solution is i grain in io minims of solution 1 o convert , f '" 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. f Correct 4.0 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. MISCELLANEOUS DATA IO MISCELLANEOUS D AT A- continued. BRITISH COINAGE I nautical mile I admiralty mil I knot = i n i fathom = 6 fe i point = n\ NAUTICAL = 6082-66 feet Coin. Weight. Diameter. sovereign 8 grams less "15% 2'i8 cm. penny \ oz. (avoir.) 1*2 inch halfpenny \ ro farthing ^ -8 e = 6080 feet autical mile/hour et 10 Centigrade = 50 Panrenheit, whence the following is convenient for transforming room temperatures : 5(/ F. - 50) = 9 (/ C. - 10) British. C ontinental. Million. . . Billion . . . Trillion . . 10" I0 18 !o ia VOLUME OF A KILOGRAMME OF PURE WATER At 4C. and 760 mm. Values recalculated by BenoSt. (Trav. et Mem. Bur. Intl., 14, 1910.) (See p. 4.) Observer. c.cs. Observer. c.cs. Lefe"vre-Geneau and Fabbroni, 1799 . 1000-030 Schuckburgh and Kater, 1798 and 1821 999-525 Svanberg and Berzelius, 1825 . . . 999-710 Guillaums 1904 1000*029 . 1000*027 ChaoDuis 1007 de Lpinay, Benolt, and Buisson 1000-028 Kupffer, 1842 . . DENSITIES OF GASES Supplementary to p. 28. Densities in grams per litre sea-level, and lat. 45. at o C., 760 mm., Gas. gms./litre. Observer. Gas. gms./litn Observer. He . -1782 Ne . '9002 Kr . 3708 Xe . 5-851 Watson, J.C.S., 1910 Moore 1908 Ra, Em. 9727 CH 4 7168 Gray& Ramsay, P.R.S. 1910 Baume & Perrot, C.R., 1909 C.R., Compt. Rend.; J.C.S., Jwrn. 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 = ^ ^- ; m is a measure of the deviation of the gas from Boyle's law. Air, m = -'00191, Regnault. H,' 'm = T0772 } Chappuis, Rayleigh, Leduc, and Sacerdote. II GRAVITY GRAVITY, LONGITUDE AND LATITUDE ABSOLUTE VALUE OF THE ACCELERATION OF GRAVITY The first determinations of the absolute value of the acceleration of gravity were made with " simple " pendulums. Kater introduced the reversible pendulum. When the periods of this pendulum about both knife-edges, which are unsymmetrically placed in a straight line passing through the centre of mass of the pendulum, are equal then^=4ir 2 /// 2 cm./sec. 2 , where / sec. is the period about either knife-edge, and / cm. is the distance between the knife-edges. Bessel showed theoretically that the buoyant action of the air on the pendulum, and the inertia of the air carried by it could be eliminated by using a reversible pendulum symmetrical in external form about its middle point. The observed period of the pendulum is reduced to that for infinitely small arc, and to a standard temperature and air density. Other corrections are made for yield of support, for elastic lengthening and bending of pendulum, for the " radius " and slipping of the knife-edges. The weighted mean of the results contained in the following table is g - 98 1 '274 cm./sec. 2 at the Potsdam Geodetic Institute. This value is used by Borrass in a reduction of the relative determinations of g for 2736 stations in different parts of the world. No absolute standard determination of g has been made in England since Kater's time. References: Defforges, Observations du Pendule, Imprimerie Nationale, Paris 1894; Helmert, Theorie des Reversions pendels, Potsdam 1898 ; Kiihnen and Furtwangler, Bestimmung der absoluten Grosze der Schwerkraft, Berlin 1906. Observer. Station. Method. gfor Station * g for Potsdam Bessel 1826 . . . Konigsburg Simple pendulum using two lengths 981-449 981-246 of wire Pisati and Pucci . Rome, 1894 Do. do. 9 8o *343 274 Lorenzoni 1888 Padua Two .Bessel reversible pendulums 980-643! 263 Barraquer 1889 . Madrid Four Bessel reversible pendulums 979*977? 270 Defforges 1894. . Paris Obs. Four Bessel pendulums : I m. '5 m. 980-999 331 Rivesaltes '5m. '25 m. length, 5-2 kgm. 5*2 980-952! 282 kgm. 3*2 kgm. 2*3 kgm. v. Oppolzer 1904 . Vienna Obs. Two Bessel pend. of different mass 980-853! 273 Kiihnen and Furt- Pptsdam Five Bessel pendulums ; experi- 980-270 270 wangler 1906 . ments extended over period of six years * For difference between station and Potsdam see Kiihnen and Furtwangler. t Corrected by K. and F. for bending of pendulum. $ Corrected by Kiihnen and Furtwangler for bending of the pendulum, and yield of support. Geodetic Institute, Potsdam, 52 22'86' N. 13 4-06' E. altitude 87 m. RELATIVE VALUES OF GRAVITY. FIGURE OF THE EARTH Potsdam System. The publications of the International Geodetic Association use =981-274 cm./sec. 2 at Potsdam (see above) as the base for relative determinations of gravity. Gravity surveys initiated in 1818 by Kater and Sabine have been carried out in most of the European States, America, India, and Japan by observing the time of swing of invariable pendulums at the several stations in the area under survey, and at a base station where the value of g is well determined. In i88ov. Sterneck introduced the invariable half-second pendulum. Corrections to the period of the pendulum to infinitely small arc, for temperature, for buoyancy, and for the yield <5f the support are made. The square of the corrected period varies inversely as g. A large part of such observations was reduced by Helmert in 1896, and by Borrass for 2736 stations in 1909. (Relativen 12 GRAVITY RELATIVE VALUES OF GRAVITY. FIGURE OF THE EARTH (contd.) Messungen der Schwerkraft . . . Inter. Geod Ass. 1911). The base stations of this reduction are printed below in black type. The agreement of relative determinations of gravity is shown by three values for the difference between r at Potsdam and Paris Obs., viz. 330 cm./sec. 2 von Sterneck | -334 cm./sec. 2 Haid 1 -333 cm./sec. 2 Putnam Gravity at Sea. Hecker (1903) deduced g at sea from the boiling point of wate and the height of the barometer. Briggs (1916) and Duffield (1916) balanced the pressur of a constant mass of gas at o C. against a column of mercury, whose height was observed. The Figure of the Earth has been deduced from gravity observations. Each observed value of g is corrected to that value, g", which it would have at the ideal surface of the geoid, that is, it is corrected for terrain and altitude. We have ^"o" = g where tig = topographic correction (always positive) which corrects the observed value to what it would be if the terrain surrounding the station were horizontal. *ig = Stokes' correction for altitude, + 2 Jig lr, follows from Newton's Law o attraction at a point at an altitude ^, and is '0003086 cm./sec. 2 per metre. s a" = Bouguer's correction for elevated masses. This takes into account the attraction of the matter of density *f forming the elevation, and 15 where D is the mean density of the earth = 5*53 gm./cm 3 . Faye, assuming with Airy (1855) that elevated masses rest like the tops of icebergs on matter of low density, decreases Bouguer's correction. o"> the corrected value of jf, is compared with that calculated for assumed shapes of the geoid. Spheroid of Equilibrium. Clairaut, in 1743, assuming that the internal density of the earth varies so that layers of equal density are concentric coaxial spheroids of equilibrium, showed that the acceleration of gravity in latitude A at sea-level would be A = " { x + (5 m/2 - e) sin 2 A } where j^is gravity at the equator, m is the ratio of the centrifugal to the gravitational acceleration at the equator, that is '0034672, and* = ellipticity = (a-$)ja. Stokes showed I hat this relation is more general than Clairaut claimed. Adding small terms to the above relation and correcting for altitude H, Helmert (1901) obtains for gravity, 7H = 978*030 (i + '005302 sin 2 A '000007 sin 2 2A) '0003086!! = 980-616 2-5928 cos 2A + -0069 cos 2 2A 'ooo3o86H (H in metres) The value of the ellipticity used in these expressions is 1/298*3. The values of gravity given by Helmert's expression agree with the observed values. In the following table he latitude A, the longitude, altitude H in metres, the observed value of gravity g relative to Potsdam, namely, 981*274 cm./sec. 2 , g ", which is g corrected as stated above, y the value at sea-level calculated by Helmert's formula, and gj' 7o> the difference between the corrected observed value and the calculated value for an ellipsoid of revolution are given. When there is no observed value for a station is calculated and entered under observed but is marked*. The stations with values printed in heavier type are base stations. References : collected observed values of^: Helmert (1896), Borrass (1911) and others in the C. R. Association Ge'ode'sique International ; U.S. Geodetic Survey ; Trigonometrical Survey of India. Figure of the Earth: Clarke's " Geodesy," 1880 ; Helmert" Hohere Geodasie," "Die Grosse der Erde," 1906 ; Bourgeois andPerrier in 4 ' Recueil deConstantes Physiques," 1913 ; Poynting and Thomson, " Properties of Matter." 13 GRAVITY , - - - Place. Longitude. Latitude. X Alti- tude H metre. TJ. -5} ** S O o > *J "? *l W rii V s ! Observer. Pole o / ' 166 44 48 2 6 38 W 4 4 W 4 8 W 556 w i 54 W 235 w o 5 41 E 3 10 W 6 15 W 6 40 32 W 3 9 24 W 3 10 W 3 12 i8W 4 17 12 W 000 18 46 W i 33 15 W 2 57 37 w 20 II W o 10 23 W o 7S7 W 2 14 2\V i 36 53 W i 8 45 W i 15 39 W 4 8 24 W i 6 12 W 2 48 W o 5 50 E 2 28 10 W 26 40 E 31 17 14 E 18 29 E 30 40 E 28 7 E 57 33 9 E 76 37 W 71 3 48 W 87 36 71 7 48 W 84 25 18 W 76 29 o W 89 24 W 121 38 3 6 W 7334 W 73 57 30 W 7542 W 75 ii 42 W 105 2 W 74 39 30 W 7I 13 8 W 78 50 W 80 W 90 12 12 W 122 25 42 W 122 20 6 W 79 23 40 W 77 3 59 W 77 o 30 W 7255 8W O ' II 90 o o 000 77 50 48 S 57 8 58 N 52 25 N 53 i3 N 54 37 N 52 28 N 51 28 N 52 12 52 N 51 28 o N 53 20 35 N 53 23 13 N 55 57 24 N 55 58 3 N 55 18 4 8 N 55 52 31 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 35 N 50 22 12 N 50 48 3 N 56 20 N 53 23 2 N 53 50 40 N 29 o S 30 4 38 N 33 56 S 29 40 S 26 ii S 20 5 39 S 39 17 48 N 42 21 36 N 41 47 24 N 42 22 48 N 39 8 18 N 42 27 6 N 43 4 3 N 37 20 24 N 45 30 24 N 40 48 30 N 45 25 24 N 39 57 6 N 38 50 18 N 40 20 54 N 46 48 21 N o o 14 S o 3 i6S 38 38 6 N 37 47 30 N 47 36 36 N 43 39 36 N 38 56 32 N 38 53 12 N 41 19 22 N o 9 21 28 7 15 104 21 244 4 6 47 B! 51 10 14 28 39 55 58 65 43 5 114 33 ii 1753 55 30 22 182 14 245 247 270 1282 40 38 73 16 4293 64 70 2825 2 154 114 74 107 102 14 32 983-216* 978-030* 982-986 981-68* 981*279* 981-350* 981-471* 981-285* 981-197* 981-255* 981*197* 981-360* 981-360* 981-584 981-613 981-454* 981-563* 981-188 981-201 981-376* 981-350* 981*190* 981-195* 981-193* 981-359* 981-483* 981-309* 981-202* 981-148 981-136* 981-616* 981-370* 981-369* 979-244* 979-317* 979 '659 979-296* 978-482* 978-623* 980-097 980-396 980*283 980-398 980-004 980-300 980-365 979-660 980-652 980-267 980-607 980-196 978-954 980-178 980-758* 977-281 977-989 980-001 979-965 980*726 980-461* 980-097* 980-112 980-274* 982-988 981*605 617 198 203 157 979-661 980-103 401 3i9 401 -056 SS 2 "935 275 199 855 191 977'833 990 980*032 979-989 980741 '"5 982*984 981-584 5 86 198 197 099 979-640 980-104 '377 326 *379 089 386 442 932 238 654 162 062 197 977-030 047 980*045 979-971 980-852 067 + 4 + 21 + 31 O + 6 + 58 + 21 I + 2 4 + 22 - 33 - 34 + 3 + 37 + 37 -207 - 6 -197 - 57 - 13 + 18 in + 48 Bernacchi Gratzl Biot, Kater Putnam Burrard.Conyg- [ham Laurin Loesch, Preston Preston Putnam Defforges, P. Putnam P. ^894 Smith, '06 Mendenhall Smith, '99 Klotz, '02 Putnam Bourgeois Putnam Smith, Preston, [Mendenhall Putnam, 1900 Victoria Land .... British Isles- Aberdeen (Univ.) . . . Aberystwith .... Belfast Birmingham .... Cambridge (Obs.) . . Cardiff . Dublin (Trin. Coll. ) . . (R.C.S.) . . . Edinburgh (Old? Obs.) Leith Fort . Eskdalemuir (Obs.) . . Glasgow (Univ.) . . . Greenwich (Obs. ) . . AVo(Obs.) .... Leeds (Univ ) . . . . Liverpool (Univ.) . . London (N. P. L.) . . (Impl. Coll.) . (Univ. Coll.) . Manchester (Univ.) . . Newcastle (Armst. Coll.) Nottingham (Univ. C.) . Oxford (Radcliffe Obs.) . Portsmouth St. Andrews (Univ.) . . Sheffield (Univ. Obs.) . Stonyhurst (Obs. ) . . Africa Bloemfontein .... Cairo (Observatory) . . Cape Town (Obs.) . Durban Johannesburg (Univ. ) . Mauritius (Roy. Alf. O.) America- Baltimore (Univ.) . . Boston . .... Harvard, Cambridge Cincinnati . Ithica, Cornell . . . Mt. Hamilton .... Montreal (McGill Obs. ). New York (Columb. U.) Otta-wa Philadelphia .... Pikes Peak Princeton Quebec (Obs.) .... Quito (Obs.) .... Machala St. Louis San Francisco .... Seattle (Univ.) . . . Toronto Washington (B. of St.) . Washington (C. G. S.) . Yale, New Haven (O.) . * Calculated by Helmert's formula for the latitude and altitude stated ; where the altitude is not given, g is calculated for sea-level. GRAVITY 14 Place. Asia Bombay (Colaba) Dehra Dun . . . Calcutta .... Hong Kong (Obs.) ESS*. adras Sandakphu Tokyo (Phy. Ins.) . . . Australasia- Adelaide (Obs.) . . . Auckland Brisbane Melbourne (Obs.) . . (Univ.) . . Perth Sydney (Obs.) . . . . Wellington, N.Z. (Obs.) Europe- Basle Berlin (Reichsanstalt) . Christiania (Obs.) Copenhagen (Obs.) . . Geneva (Obs.) . . . . Leyden (Obs.) . . . . Moscow Paris (Obs.) . . . . ,, (Int. Bur. Sevres) Potsdam (Geod. Inst.) . Pulkowo Rome (Eng. Sch.) St. Petersburg (Phy. I. Vienna {Mil. Geo. Ins. Zurich . . . Longitude. 72 48 48 E 78 3 12 E 88 21 24 E [14 10 30 E 88 44 12 E 80 14 54 E 88 o 18 E :39 46 E 38 35 8 E 74 46 12 E 53 i 3 E 44 58 34 E 44 58 E IS 52 E 51 12 24 E 74 46 4 7 34 J 3 19 * 43 1234 6 9 4 29 37 39 2 20 2 13 3 4 30 19 12 29 30 18 16 21 833 48 E E 32 E 42 E 12 E 3E 48 E 12 E 10 E 6E 42 E 30 E 6E 30 E 12 E Latitude. 18 53 48 N 30 19 30 N 22 32 48 N 22 18 12 N 26 31 18 N 13 4 6N 27 6 6N 35 42 36 N 34 55 39 S 36 50 54 S 27 28 S 37 49 53 S 37 48 9 S 57 S 33 Si 42 S 41 17 4 S 47 33 52 31 59 54 55 4i 46 12 52 9 55 45 48 50 48 59 5222 59 46 54 59 56 48 12 47 22 36 N 42 N 12 N N 20 N 36 N ii N 53 S 54 N i8N N 30 N 42 N 42 N Alti- tude H metre 10 683 6 33 82 6 3586 18 43 3 40 26 43 14 43 127 277 30 28 14 405 147 59 70 87 7i 59 6 183 463 ,11 Is 978-633 979-065 978-816 978771 978-924 978-281 978-192 979-801 979-711* 979-962 979-148 979-987 979*979 979*473* 979-683 980*292 980-788 981-280* 981-927 981-559 980-599 981-280 981-562 980-943 980-941 981274 981-899 980-347 981-929 980860 980673 963 156 992 690 980-844 98I-933 562 980-682 981-281 592 980-956 981-294 914 897 770 978-635 978-571 979*210 978-817 777 '943 282 946 979-805 978-789 '773 060 294 101 979-791 888 129 '974 634 980-847 981-907 -562 980-724 981-257 980-962 981-277 896 80-336 981-909 980-906 831 til **** -136 + 28 + 4 -117 - 12 -155 + 14 + 75 + 27 + 18 Observer. Conyngham Elblein Hecker, '04 Conyngham Hecker Elblein Budik Mean 5 obser [vers 4- 57 Mean 5 obs. Wright + 26 + o - 42 + 24 + 24 6 + 17 + 18 + 23 - 9 - 61 Niethammer Schumann Messerschmitt Haid, 1900 Iweronow See above See above Borrass glione Achmatow v. Sterneck Messerschmitt ACCELERATION OF GRAVITY CALCULATED BY HELMERT'S FORMULA y = 980-616 2-5928 cos 2A -f- '0069 cos 2 2\. LAT. 90 7 = 983-216. The length (/) of the "seconds" pendulum (i.e. 2 sees, period). =/ir ? = -101321 g. I varies from 99-094 cms. at the equator to 99-620 cms. at the pole. Latitude. 2 6 9 10 11 12 13 14 fr 978-030 978-376 979'32i 980*616 981-914 982-867 032 422 400 706 992 911 036 481 '797 068* 952 044 S 6 3 142 990 055 646 '977 215 026* 069 634 730 o66 J 285 '058 086 693 815 155 '354 088 107 *754 902 244 -420 130 818 989 331 485 138 156 884 077^ 418 '547 159 186 952 166 5^4 606 176 218 022* 255 S88 190 253 094 345 672 718 291 168 '435 754 770 209 332 244 525 835 820 214 Calculated by Helmert's formula for the latitude and altitude stated : where the altitude is not given, g is calculated for tea-level. 15 THE EARTH SIZE AND SHAPE OF THE EARTH The spheroid of revolution which most nearly approximates to the earth, has the following dimensions : [i kilom. = '6214 mile.] Observer. Equatorial radius, a. Polar radius, b. EUipticity, (a-b}\a. Bessel, 1841 . . . Clarke, 1866 . . . 1880. . . Helmert, 1906* . U.S. Survey, 1906! 6,377,397 metres 8,206 8,249 8,200 8,388 j 6,356,079 metres 584 ,, 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. \ 3963'339 miles. || 3949-992 miles. MEAN DENSITY OF THE EARTH (See Poynting's " Mean Density of the Earth," 1893.) Observer. Common Balance Method. Poynting,. 1878 Richarz and Krigar-Menzel, 1898 Torsion Balance Method. Cavendish, 1798 Boys, Phil. Trans., 1895 . . Braun, 1896 Eotvos, 1896 Mean density of surface . . . Density. 5*493 5'45 5-527 5-527 5*534 2-65 SUN The mean equatorial ] solar parallax (Hinks, > = 8"-8o7 1909) J ( 1-494 x io n Whence mean distance)! metres from earth to sun \ ~ j 9-282 x io 7 I miles Mean time taken by] light to travel from > = 498-2 sees, sun to earth MOON Mean distance froml _ (60*27 * earth's earth to moon / ~~ { radius Mass of the moon) /(i/8i'53) x (Hinks, 1909) ;-\ earth's m Inclination of moon's) o/ // orbit to ecliptic ; * 43 mass Mean polar quad-) rant f Volume of earth Mass of earth Area of land Area of ocean Mean depth ofl ocean (Murray)/ Volume of ocean Mass of ocean = 10,002,100 metres* = i '083 x io 21 metres 3 * = 5'98xio 27 gramsf = 5*87 x io 21 tons = 1-45 X io 18 cm. 2 = 3-67 x io 18 cm. =3-85 x io 6 cm. = 1-41 x io 24 cm. 8 = 1-45 x io 24 grms. * Mean of Helmert and U.S. Survey, t Using Boys' and Braun's result for density. 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"- O 4 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). 16 SOLAR SYSTEM ELEMENTS OF THE SOLAR SYSTEM 8"*8o6 is taken as the equatorial horizontal solar parallax from the observations of the as'eroid 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 Stefdnik (1907). (See Newcomb's" Spherical Astronomy"and Ball's "Spherical Astronomy.") Name. Equatorial Semi-diameter. Angular.* Miles. Earth = Mass Earth = i Mean Density. Earth = i Water =i Gravity at Surf. Earth = i No. of Satellites.} Sun . . Mercury Venus . Earth . Mars . . Jupiter . Saturn , Uranus . Neptune 16 ri8 3-08 8-40 8-80 4*68 37'36 2475 34-28 36-56 432,890 1387 3783 3963'3 2108 43850 38170 15440 16470 109-2 350 '955 rooo 532 1 1 -06 9-63 3-90 4-15 329,390 '34 >-8i8 I'OOO 106 3i4'5o 94-07 14-40 1672 25 88 >'94 i -oo 071 25 12 24 23 27-61 28 5-527 3-90 '36 63 1*34 1-28 TOO 38 2'57 I -01 95 97 2(D) 8(7 D; i R) 4(R) i (R) Name. Inclina- tion of Equator to Orbit. Time of Axial Eolation. Semi-major Axis of Orbit. Sidereal Period. Earth = i. Millions of Miles. Mean j Julian Solar DaysJ Years. Sun . . Mercury . Venus . Earth . Mars . . Asteroids Jupiter . Saturn . Uranus . Neptune 23 27 24 52 26 49 27 ? d h m 25 9 7 23 4o (?) 823 56 4'09 24 37 22*74 9 $6~ 10 15 13? 3870986 7233315 I'OOOOOOO 1-523688 2-55 to 2-85 5-202803 9-538844 19*19098 30*07067 Bode's Law 4 = (0+4) 7 = (3 + 4) 10 = (6+4) 52 = (48 +4) 100 = (96+4) 196 = 092+4) 36*0 67-2 92-9 141-6 237 to 265 87-9693 224*7008 365*2564 686*9797 886*2 1782*8 2793*5 10759*20 30586*29 60187*65 24 62 i -oo r88 11*86 29*46 8374 164*78 Name. Ellipticity of Flanet. Mean Daily Motion in Orbit. Longitude of Perihelion. II Longitude of Ascending Node. Inclination of Orbit to Ecliptic. Eccentricity of Orbit.** Mercury. Venus . Earth . Mars. . Jupiter . Saturn . Uranus . Neptune 1/298*3 1/270 ? I//? i/9 i/95 ? 5 32-4 36 77 59 8-2 31 26-5 0-5 42*2 21*5 75 53 59 130 9 50 101 13 15 334 13 7 12 36 20 90 48 32 169 2 56 43 45 20 47 8 45 75 46 47 000 48 47 9 99 26 42 112 47 12 73 29 25 130 40 44 7 o 10 3 23 37 000 1 51 I 1 18 42 2 29 39 46 22 1 46 45 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. $ D means direct ; R, retrograde. The ellipticity = (a6)/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. 15). || 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(0 2 2 )/#, where a and b are the major and minor axes of the orbit. 17 THE STARS EQUATION OF TIME (+) means that the equation of time has to be added to the apparent solar time (/.specific volume corrections. The following table of values of the factor (/) is based on tables on pp. 2 1 and 24. Temp. (/) of weighing 10 C. 12 13 14 15 C 16 17 Value of / H 2 O . tor (/)\Hg . 00133 073683 i '00143 073697 1*00154 073710 ;-ooi66 073724 1-00179 1-00193 073737, '073750 1*00209 073764 1-00226 073777 Temp. (/) of weighing 18 19 C Value of JH 2 O . COlHg . 1*00244 1-00263 073790! -073804 20 21 C 22 23 1-00283 073817 1-00305 073831 1-00327 073844 24 25 C 1-00350 073857 1-00375 073871 1-00400 073884 The above gives the volume content V, of the vessel at the temperature of weighing, / C. At any other temperature, /', the volume V t , = V t {i + y(f - /)} = V t (F), where 7 is the coefficient of cubical expansion of the material of the vessel. Values of the factor (F) for glass vessels (y = -000025) ar e tabulated below. 2C. 8 -2C. I -4 C -6 C -8 r alue of factor (F) 1-00005 I'OOOIO 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 * 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. (Mendele"eff and Gutkowsky, 1877. See also Scheel and Heuse, Ann. d. Phys., 33, 1910.) Bore of tube. Height of meniscus in mms. 8 10 12 1*4 16 1*8 Eore of tube. Height of meniscus in mms. 8 1*0 1-2 1*4 1*6 1*8 mm. 4 5 6 7 8 83 '47 27 18 1*22 65 -S 20 56 40 29 mm. I- 9 8 78 "53 mm. 2*37 i -80 1*21 82 56 l'43 '97 65 1-13 77 9 10 11 12 13 21 "IS '10 07 04 mm. 28 *20 "H 10 07 '33 10 40 29 21 15 '12 46 '33 24 18 52 '37 27 19 14 BAROMETRY 20 REDUCTION OF BAROMETER READINGS TO 0C. Corrected height H Q = //|i - > ~ "M, where /f and / are the observed height and temperature of the barometer, ft = '00018 i 8 (Regnault), the coefficient of cubical expansion of mercury; a = '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 rums, to be subtracted. GLASS SCALE. Uncorrected height in nuns. 700 720 740 760 780 BRASS SCALE. Uncorrected height in nuns. 700 720 740 760 780 2C. 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 24 48 73 '97 I*6 9 i '94 2-18 2-42 2-66 2-90 3'H 3-38 3-62 3'86 4*10 25 "49 75 99 1-25 1-49 174 1-99 2-24 2-49 273 2-98 323 3'47 372 3'97 4-21 26 'Si 77 I '02 1-28 179 2-05 2-30 2-56 2-81 26 '53 79 1-05 i'3i 1-58 1-84 2'10 2-36 2'62 2-89 3-32 3'57 3-83 4-08 4'33 27 i -08 i-35 1-62 1-89 2-16 2'43 2-69 2-96 3-23 3-5o 377 3*93 4-19 4'45 4'57 23 46 6 9 I-I4 i'37 r6o 1-82 2-05 2-28 2-51 3-64 3'87 24 "47 71 '94 1-17 1-41 1-64 1-88 2'34 2-58 2'8l 3'4 374 24 48 72 *97 '45 1*69 1-93 2-17 2-41 2-65 2-89 3-13 3-37 3-85 4-09 25 50 74 '99 1-24 1-49 173 1-98 2-23 2'47 272 2 - 97 3-21 25 '% I '02 1-27 I'53 178 2-03 2-29 2'54 279 3*05 3'30 3'55 37i 3*95 4-20 I 4-31 REDUCTION OF BAROMETER READINGS TO LAT. 45 AND SEA-LEVEL It is a convention to take u g 9 at lat. 45 and sea-level as the standard value for "gravity." The corrections below result from the variation of "/" with latitude and height above sea-level (see p. 11). The barometer correction for 'latitude = r^( c )> has to De subtracted from the temperature corrected barometer reading H Q for latitudes between o and 45 ; and added for latitudes from 45 to 90. Latitude 90 5 85 10 80 15 75 20 70 25 65 30 60 35 55 40 50 45 45 I'94 I-8 5 170 1-27 9 8 6 7 34* oo The correction of the barometer due to diminution of gravity with increasing height above sea-level amounts to about "24 mm. of mercury per 1000 metres above sea-level. The correction has to be subtracted from the observed reading. * London, '45. 21 WEIGHINGS: GAS VOLUMES REDUCTION OF WEIGHINGS TO VACUO The buoyancy correction = Mo-(i/A i//)) = M, where M is the apparent mass in grams of the body in air, / I'OIlS 770 1-0132 1-0145 1-0158 1-0171 1-0184 1-0197 I -021 1 i -0224 1-0237 I-0250 22 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. 28. 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. Element. Density. Element. Density. Element. Density. Aluminium . . . Antimony . . . Argon (liq.) . . . Arsenic .... Barium .... Beryllium . . . Bismuth .... 270 6-62 i-4/-i85 573 375 i'93 9-80 2-5 (?) 3-102/25 8*64 1-87 1-55/29 3;52 6-92 2-49/0 6-50 8-6 8'93 477 (?) rn/-i87 (?) 5'95 5*47 I9 /B.P. 07/B.P. 086/M.P Indium .... Iodine .... Iridium .... Iron (pure) . . . Krypton (liq.) . . Lanthanum . . . Lead 7'12 4'95 22-41 7-86 2-16 6-12 11-37 '534 174 7*39 IJ56/I5 I0'0 6-96 (?) 8-9 1275 79/-I96 22-5 I-27/-235 1 1-4 2'20 I-8 3 21'50 862 6-48 (?) 12-44 r532 I2'3 Samarium . . . Scandium . . . Selenium, amorph. cryst. . liq. . . Silicon .... Silver .... 7-8 9 4-8 4'5 4'27 ^.2-3 10-5 971 2-54 2-07 1-96 1-92 1-81 16-6 6-25 (?) 11*9 HI 7-29 3'54 18-8 187 L 7-1 4-15 Lithium .... Magnesium . . . Manganese . . . Mercury (see p. 24) Molybdenum . . Neodymium . . Neon (liq.) . . . Nickel .... Niobium .... Nitrogen (liq.) Osmium .... Oxygen (liq.) . . Palladium . . . Phosphorus, red . yellow Platinum . . . Potassium . . . Praseodymium Radium .... Rhodium . . . Rubidium . . . Ruthenium . . . Sodium .... Strontium . . . Sulphur, rhombic monoclinic amorphous liquid 113 Tantalum . . . Tellurium . . . Terbium .... Thallium . . . Thorium .... Tin Bromine .... Cadmium . . . Caesium .... Calcium .... Carbon- Diamond . . . Graphite . . . Cerium .... Chlorine (liq.) . . Chromium . . . Cobalt .... Copper .... Erbium .... Fluorine (liq.) . . Gadolinium . . . Gallium .... Germanium . . . Gold Titanium . . . Tungsten . . . Uranium . . . Vanadium . . . Xenon (liq.) . . Ytterbium . . . Yttrium .... Helium (liq.) . . Hydrogen (liq.) . Zirconium . . . 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. 25 et seq . ; of "chemical compounds," p. 117 ; of gases, p. 28 ; of other minerals, p. 134. Substance. Density. Substance. Density. Substance. Density. Metals & Alloys. Iron, cast . . . wrought . . wire . . . Steel 7-1-77 7-8-7-9 77 77-7'9 8-4-8-7 c. 8-4 8-7-8-9 8-96 17-72 Coins (English) silver? . . Constantan || t Duralumin . . German silver \ . Gunmetal . . . Magnalium ** . . Manganin ft Phosphor bronze \\ Platinoid . . . Pt( 9 o), Ir(io). . 10-31 8-88 279 ?5-?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 6--8 c. -4 7-'9 9-1-1 5 --6 ri-i'3 1-2-1-3 6-7 5-7 *4-'5 Brass (ordy.) * . . Brass weights . . Bronze (Cu, Sn) . Coins (English) bronze f. . goldt Ebony .... Lignum vitse . . Pitchpine ; walnut Red pine (deal) . White pine . . . * c. 66 Cu, 34 Zn. f 95 Cu, 4 Sn, I Zn. J 91^ Au, 8J Cu. 92$ Ag, 74 Cu. || 60 Cu, 40 Ni. 1 60 Cu, ,15 Ni, 25 Zn. ** c. 70 Al, 30 Mg. ft 84 Cu, 12 Mn, 4 Ni. JJ 92^ Cu, 7 Sn, \ P. Described as German silver with a little tungsten. 23 DENSITIES DENSITIES OF COMMON SUBSTANCES (.contd.} Substance. Density. Substance. Density. Substance. Density. Minerals, etc. Agate ; slate . Asbestos . . . board Carbon (see above) Charcoal .... Coal anthracite . Coke Gas carbon . . . Emery .... Granite .... Marble .... Masonry .... Pumice (natural) . Quartz .... Silica, fused transparent translucent . Sand (silver) . . Sandstone ; kaolin 2-5-27 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 2'2I 2 '07 2*63 2*2-2-3 Liquids. Glycerine . . Methylated spirit Milk .... Naphtha . . . Oil, castor . . linseed . . lubricating olive ; palm paraffin Petrol. . . . Sea-water . . Turpentine . . Vinegar . . . Miscellaneous. Amber . . . Bone .... Butter, lard . . Celluloid. . . Cork .... Ebonite . . . 1-26 83 c. 1-03 85 '97 "9 1 ~'93 90--92 9I--93 c. -8 68-72 i '01-1*05 87 I'02 VI 1-8-2-0 Gelatine . . . Glass, flint . . crown ; window Jena . . . Ice (Roth, 1908), o (Vincent,'o2),o Indiarubber (pure) Ivory Leather . . . . Paper Pitch . . . . . Porcelain . . . Resin Red fibre . . . . Snow (loose) . . Tar Wax, soft paraffin . hard white ; bees- sealing . . soft red . . T27 2'9-4'S 2*4-2-6 (see p. 78.) 9168 9160 9 1 --93 1-8-1-9 85-1 c. ri 2-2-2-4 c. ri rape oil, i'6/2o. 33 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 Moore, Phys. Rev., 1896. Substance. Temp. Relative Viscosity. Substance. Temp. Relative Viscosity. Ammonia 25 C. 1*02 Potassium chloride . 17 6C. 98 Ammonium chloride 17-6 98 Potassium iodide . . 17-6 91 Calcium chloride 20 Sodium hydrate . . 25 1*24 Hydrochloric acid . 25 1-07 Sulphuric acid . . . 25 1-09 VISCOSITIES OF SOLIDS Venice turpentine * at 17*3, 1300, c.g.s. Shoemaker's wax t at 8, 47 x IO 6 . C.g.S. Pitch t at 0, 5 1 x io"> ; at 15, 1-3 x io 10 . Soda glass t at 575, 1 1 x IO 12 . Glacier ice, % 12 X IO 13 . Golden Syrup (Lyle), 1400/12. * 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, 17, = "n (i + O, where o 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 273 + c expression i? = 170 Q , p ( e \* \ 2r( ) ' w ^ ere * is th absolute temperature, and C is Sutherland's constant. The formula only holds for temps, above the critical, and for pressures such that Boyle's law is approximately obeyed. Sutherland's relation is thus of the form (which lends itself to graphical treatment), = -C, where K is a constant. (See Fisher, Phys. Rev., 1907, 1909 et seq. ; O. E. Meyer's " Kinetic Theory of Gases." For a bibliography of gaseous viscosity, see Pedersen, Phys. Rev., 25, 1907.) The values below are for dry gases. Gas or Vapour. Temp. n- Observer. Gas or Vapour. Temp. n- Observer. xio-e XlO-'S Air . . . -21 C. 164 Breitenbach Nitrogen 0C. 1 66 v.Obermayer O 173 , (1901) (contd.} 11 171 (1876) O 171 Hogg, 1905 54 190 O 170 G.^ &G. 1908 Helium 189 Schultze, 'o i o 171 Fisher, 1909 15 197 15 181 .Markowski 185 270 99 99-6 221 (1904) Neon . . 15 312 Rankine, 'io Hydrogen 302 -21 299 82 Breitenbach (1901) Argon . . 15 2IO 221 Schultze, '01 86 5 184 322 ' 15 89 J J5 Krypton . 15 246 Rankine, 'ro 99 106 Xenon . . 15 222 302 139 55 55 Chlorine . 129 Graham, '46 Oxygen O 187 v. Obermayer 2O 147 15 195 (1876) Water(vap.) 90 Puluj* 1878 54 216 15 Q7 T 143 00269 dioxide . 240 158 00350 Helium .... 8c > 148 Nitrous oxide . . 313 172 00345 Neon 5^ 220 Ethylene . . 226 106 00350 Argon .... I7c 207 Chloroform (vap.) 454 159 Krypton. . . . 1 86 240 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. p I atmos. = roi32 x io 6 dynes/cm. 2 a molecular diameter in cms. = absolute temperature. ;;/ = mass of a single molecule (in R = gas constant. grams). b b of Van der Waals' equation (p. 36). G = square root of mean square mole- k = thermal conductivity of gas (p. 54). cular vel. (cm./sec. at o C.). c v specific heat at const, volume (p. 61). ft = mean molecular velocity (cm./sec.). i = viscosity of gas (p. 33). L = length of mean free path in cms. Assuming a Maxwcll-Boltzmann distribution of velocities G= V' .iV(Nw) = V "\i>lf = V 3R0 ft = 4G/Vo> = -9216 L = T?/( '3 1 pH) = 2'02r?/V% Collision frequency = fl/L = 5 x io 9 per sec. for O 2 35 MOLECULES SIZE, VELOCITY, AND FREE PATH OF MOLECULES (contd.) MOLECULAR SIZE The molecular diameter c ), and b = R0 C /(8A). Taking pressures in atmos., and the volume of the gas at o C. and i atmos. as i, R = pv\Q = 1/273. * n 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 e e = 273 + 31-1 = 304-1, whence b - 304'i/(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 Mtin. Bur. Intl., 1907). * Indicates calculated values. Substance. Hydrogen .... Oxygen. .... Nitrogen .... Air Helium Neon Argon . - . . . . Krypton .... Xenon Chlorine .... Bromine .... Water ..... Hydrochloric acid . Carbon monoxide . Carbon dioxide . . Carbon bisulphide . Ammonia, NH 3 . . Nitrous oxide, N 2 O Nitric oxide, NO . Nitrogen tetroxide,NO Sulphuretted hydrogen Sulphur dioxide . . Methane, CH 4 . . Acetylene, C 2 H a . Ethylene, C 2 H 4 . . Ethane, C 2 H 6 . . Ethylalcohol,C 2 H 6 OH Ether (C 2 H 6 ) 2 O . . Chloroform, CHC1 8 Aniline, C e H 5 NH 2 . Benzene, C 6 H 6 . . Critical Temp. C Press.p Vol. v, -234'5C -118 146 -140 -268 < 210 -II7-4 -62-5 147 I 4 6 302 365 52-3 I4ri 273 130 -93'5 171-2 - 100 -955 10 34 243 197 260 425-6 288-5 atmos. 20 50 33 39 2-3 52-9 54-3 57-2 93-5 131* 194-6 86 35'9 73 72-9 115-0 77'5 71-2 147* 887 78-9 50 61-6 517 50-2 627 35-8 54'9 52-3 47 '9 00264* 00426* 00517* Van der Waals' a. 00042 00273 00259 00468* '00257 00299* '00006 1 5 '00404* 00532" 0069* 00615" 00605 00386 0052* 00505* 0066 0090 00481* 00436 00347* 00413 00578* 00745* 00488* 0069* 00752* 00839* 0071 0158 0133 0183* 0161* 00259 00462 00818 01063 01434 01 18 00697 00275 00717 02316 00798 00710 00257 00756 00888 01316 00357 00880 00877 01060 02407 03496 0293 05282 03726 b. 00088 00142 00165 00156 000995 00135 00178 00230 00205 00202 OOI5O 00173 00168 OOI9I 00343 00161 00184 00116 00138 00193 00249 00162 00230 00251 0028 00377 00602 00445 00611 00537 Observer. Olszewski, '95 v.Wroblewski, '85 Olszewski, '84 Onnes, 1908 Ramsay and Travers, 1900 Knietch, '90 Nadejdine, '85 Battelli, '90 Dewar, 1884 v.Wroblewski, '83 Andrews, 1869 Battelli, 1890 Dewar, 1884 Villard, 1894 Olszewski, '85 Nadejdine, '85 Olszewski, '90 Sajotschewsky,'78 Dewar, 1884 Mackintosh, '07 Olszewski. '95 t'86 Ramsay & Young, Battelli, '92 Sajotschewsky,'78 Guye& Mallet, '02 Young, 1900 37 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 " Kinetic Theory of Gases.") Gases. ,.. D Gases. ,* D Gas (Winkelmann). iC. D into Air. C0 2 H 2 -H.O"' vJo 677, o. CO H 2 . 642, L. Formic acid . 131 088 513 Ho O 2 . 68 1, O. CO C 2 H 4 101, O. Acetic . . . O 106 071 404 H 2 ~ -CH 4 O 625, 0. Propionic acid 082 058 326 H 2 -CO . o 649, 0. CO 2 CO 131, O. Butyric acid . 053 037 201 H 2 C0 2 . 538, o. C0 2 CO o 141, L. Isobutyricacid 07 047 271 H 2 C 2 H 4 483, 0. CO 2 Air 142, L. Me. alcohol . o 132 088 500 H 2 N 2 O o '535, O. CO 2 CH 4 146, O. ; -16, L. Et. . 102 068 378 C0 2 -0 2 . 18, L. Propyl alcohol 080 058 315 O 2 N 2 . o 171,0. C0 2 N 2 o i, L.; -15,0. Butyl . o 068 048 272 2 -H 2 . 722, L. C0 2 -H 2 '55, L- w 99 126 088 504 H 2 C0 2 18 155, G. Air O 2 . 178, 0. Benzene . . 075 053 294 H 2 O Air 8 239, G. Air H 2 . 17 66, Sc. Me. acetate . 084 056 328 H 2 O Air 15 246, G. Et. formate . O 08 5 057 336 H 2 O 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 Et.iso-butyrate 055 040 224 G., Guglielmo, 1884; H., Houdaille, 1896; L., Loschmidt, 1870 j O., v. Obermayer, 1887 ; S., Stefan, 1879 ; Sc., Schulze, 1897. DETERMINATION OF ALTITUDES BY THE BAROMETER C(H, - H 2 ) Babinet's formula (Compt. Rend.) 1850) is, Altitude =. where barometer reading at lower station, H 2 at upper station. If altitudes are in metres, and barometric heights in mms., C = 32(500 + /j + / 2 ) where /j and t z are the corresponding station temperatures ( C.). In the table below the mean temperature, (/j -f / 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. The values are of course only approximate. Babinet's formula is not applicable to very great altitudes. Altitude 100 200 300 400 500 600 700 800 900 metres. 1000 mm. 760 674 mm. 751 666 mm. 742 658 mm. 733 650 mm. 724 6 4 2 mm. 7 I6 635 mm. 707 62 7 mm. 699 620 mm. 6 9 612 mm. 682 60 5 THICKNESS OF THIN METAL FOIL Approximate thickness of the thinnest beaten metal leaf at present commercially obtainable. Unit io~ 6 cm. Metal. . Al Cu Au Pt Ag Dutch metal. (Cigarette paper.) Thickness 20 34 8 25 21 70 2500 38 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. Tern] >erature variation. It follows from Eotvos' rule, that the surface tension T at temp. / is approximately proportional temp., the constant of proportionality being much to (/ /), where t is the critical the same for chemically similar substances. The surface tension at t c is zero. (For critical temps, see p. 36.) See Poynting and Thomson's " Properties of Matter." WATER (/ c = 365 C.) Surf. Tens. T at 15 C. Method. Observer. Temp. (/). T/T,, Temp. (/). *JT. dynes per cm. 72-8 (A) Vibrating jet Bohr., Phil. Trans., '09 0C. r030 60 C. 901 743 (A) Vibrating jet Pedersen,/*. Trans. ,'07 10 roio 70 876 74*2 (A) Capillary waves Kalahne, Ann. d. Phy., 15 1000 80 85 1 73'8 (A) Hanging drop Sentis, 1897 ['02 20 990 90 827 73'3 (A) Tension of film Hall, 1893 ['93 30 970 10O 80 74'3 (A) Capillary waves Rayleigh, Phil. Mag., 4O '947 120 75 73-3 (A) Capillary tube Volkmann, 1895 50 925 14O 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. INORGANIC. dynes cm. Cadmium CO 2 Molten 6Q1 Weight of drop Quincke Gold A 1O7OC. 612 Curvature of drop Heydweiller, '98 Lead CO, 335 471 Capillary waves Grunmach Mercury ( T, = T -'379/) ^^ ^^ 2 A 17-5 TV +) 547 Capillary tube Quincke Potassiuir c 0, 58 164. We acrht of dr on Sodium CO, 9O O ^ 520 x o _ _. ^. Sulphur (M.P. 115). . -*** -^r 2 A 16O j 59j Press, reqd.to bub- 1 Zickendraht, '06 ; ^ \ 25O b le airfrorr \. can. > and Qu nncke. (B.P.) A 445 44( tube thro' liquid) *C 7 '08 Liquid oxygen .... A -183 13*1 Capillary waves Grunmach, 1906 nitrogen . . . A -196 8-5 , 1906 nitrous oxide . . A -89'4 26-3 1904 Nickelcarbonyl,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? acid sol. (d= ri4) A 15 74'4 i) H 1907 Other solns. (see below) CARBON CP IMPOUNDS. Acetone, (CH 3 ) 2 CO . . V 16-8 23-3 Capillary tube J Ramsay and V 78-3 15-9 \ Shields, 1893 Acetic acid, CH S CO 2 H . V 20 23-5 , V 300 ri6 Alcohol methyl, CH 4 O V 20 23 , n V 20O 5-2 ,, , N ethyl,C 2 H 6 OH V 20 22'0 > (T, = To - -092/) . . V 150 9*5 propyl (n\ V 16*4 23-8 ,, H C,H,OH V 78-3 187 i Aniline, C 6 H 6 .NH 2 ' . . A 15 Vibrating jet Pedersen, 1907 Benzene, CH 6 . A 17-5 29-2 Capillary tube Volkmann 39 SURFACE TENSIONS Substance. Temp. (t). Surf. Tens. Method. Observer. CARBON COMPOUNDS. (contd.) 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 --iis/) . . Ethyl acetate, CH,C(XC 2 H 5 Formic acid, HCOOH . Olive oil (^/20 = -91) . Paraffin oil (d = '847) Propionic acid, C 3 H 6 O. 2 Pyridine, C 6 H 5 N . . . Toluene, C 6 H 5 . CH 3 . Turpentine, C 10 H 16 . . 15 C. 132 19-4 46-1 2O 25O 15 20 150 20 100 17 80 20 25 16-6 132 17-5 91 15 15 dynes cm. 267 164 33-6 29-4 257 i'93 27-2 16-5 2-9 23-6 14 37*5 30-8 32 26-4 26-6 ijj-5 367 26-5 28-8 273 Capillary tube ( Ram say and I Shields, 1893 Curvature of drop Capillary tube Vibrating jet Capillary tube Kaye, 1905 Jaeger, 1892 jRamsay and \ 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 . n T w is the surf. tens, of a sol. of n gram equivalents per litre, T that of water at same temp. Salt. NaCl . . KC1 . . . KNa 2 C0 3 ) |(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!. dynes/cm. 29-5 12*2 20'6 48-3 427* 399 399 Observer. 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. Angle. Observer. Liquid. Angle. Observer. Mercury . . Water . . . Water . . . Methyl alcohol Ethyl alcohol . Ether . . . Chloroform 5 2 4 o' * 8-Q y 1 6 o Quincke Wilberforce Magie, '88 Acetic acid Benzene Paraffin oil Turpentine 20 o 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 1 1. 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). 40 HYGROMETRY RELATIVE HUMIDITY AND DEW-POINT Relative humidity = r-rj . 100, where [p\ t is the actual pressure of water- vapour at temperature /, and is equal to (j*J p , the saturated vapour-pressure at the dew- point (dp} ; [/]J is the pressure of saturated vapour at /. For a table of saturated water-vapour pressures, see p. 42. (See " Smithsonian Meteorological Tables.") Percentage relative humidities for different dew-points and dew-point depressions are tabulated below. Dew-point Depression of dew-point = / (dp)*- (dp}. 0C. 1 92 93 94 94 94 2 "P" 87 88 89 89 3 4 5 6 7 8 53 57 60 62- 64 9 10 12 39 44 47 49 52 14 16 29 34 37 39 42 18 -15C. O + 10 20 30 IOO IOO IOO IOO IOO 79 81 82 83 84 73 75 77 78 80 67 70 72 74 75 62 65 68 70 71 58 61 64 66 68 49 53 56 58 61 46 5o 53 55 57 34 38 4i 44 46 26 30 33 35 38 WET AND DRY BULB HYGROMETER Apjohn (1835), August (1825), and others, by making various assumptions (some of doubtful legitimacy), have derived formulae of the type Kt - I>1 = AH(/ - O [i + B(/ - /)] where t is the temperature of the dry bulb, / that of the wet, [/] is the actual pressure of water- vapour in the air (at temperature /), [ is the saturated vapour pressure of water at the temperature (/) of the wet bulb, H is the barometric height, and A and B are constants. (See Love & Smeal, 1911.) 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 = '00068 for moving air, as in an Assmann ventilated psychrometer. A = '00075 in a Stevenson screen as used by Meteorological Office. A = '0008 in open air with slight wind. A = "00084 in open air with no wind. A = *ooi in a small closed room. Rizzo (1897) takes A = '00075 and B = *oo8, and the table below is derived by employing these values. [ can be got from the table of saturated vapour pressures on p. 42, and thus the desired vapour pressure [p~\ t can be determined. VALUES OF [ - [p] t (Rizzo) Barom. Difference of temperature of dry and wet bulb thermometers (/ f w }. Press. H. 1C. 2 3 4 5 6 7 8 9 10 mm. 770 760 750 73O 700 670 mm. '57 56 *55 '54 52 50 mm. 13 '12 'II 08 03 *99 mm. I'6 9 1-67 '65 r6o i'54 i -47 mm. 2-23 2' 20 2'17 2'12 2'03 1-94 mm. 2 7 8 274 271 2-63 2-52 2-42 mm. 3-30 3*25 3*2 1 3'i2 3-00 2-87 mm. 3-81 376 37i 3-61 3'46 3'32 mm. 4*32 4-27 4-21 4-10 3'93 376 mm. 4-87 475 4'69 4-56 4'37 4-19 mm. 5*31 5-24 5'17 5'03 4-82 4-62 11 C. 12 13 14 15 16 17 18 19 20 770 760 75O 730 700 670 578 571 5-63 5-48 5-26 5-03 6-26 6-18 6-09 5*93 5-69 5*44 672 6-63 6-54 6-37 6-1 1 5-84 7-17 7-08 6-98 679 6-52 6-24 7-62 7-52 7-42 7'22 6'93 6-63 8-06 7'95 784 7-63 7'32 7-01 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 41 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 DanielPs 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 /. For a table of saturated vapour pressures, see p. 42. (See " The Observers' Handbook," Meteorological Office.) Dry Bulb Temp. (t). 1 2 3 4 5 6 7 8 9 O + 10 20 3O 876 3'32 2'06 i*79 1*65 873 2*8 1 2 '02 177 1*64 8*55 2-54 1-99 5-63 8-26 2-39 i*95 1*74 1-62 7-82 2-31 1-92 172 r6i 7-28 2*26 1-89 170 1*60 6-62 2-21 I-8 7 1*69 577 2*17 1-58 4*92 2-13 1*83 1-67 1-57 4*04 2*10 1*81 1-66 1-56 CHEMICAL HYGROMETER The values below are grams of waiter vapour contained in a cubic metre (io 6 c.cs.) of saturated air at 760 mms. total pressure. Calculated from Regnault's observations. Temp. 1 2 3 4 5 6 7 8 9 0C. 10 2O 30 4-84 9*33 17-12 30-04 5-18 9'93 18-14 3170 5-54 10*57 19*22 33*45 5-92 11-25 20-35 35*27 6-33 1 1 '96 2i'54 37-18 676 1271 22-80 39-i8 7-22 13-50 24*11 4i'3 770 H'34 25*49 43*5 8-21 15*22 26-93 45*8 8-76 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 o~8% for water, ri % for alcohol and 1*7 % 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, Ann. Chim. Phys.. 30, 1850 Poyntmg and Thomson'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-gau^e glasses stand between 12 and 24 atmospheres.' Thickness Bore. of Wall. 1 mm. 2 3 4 5 6 7 atmos. 1 mm. 2 3 4 570 560 310 420 450 280 340 460 230 400 400 220 330 |? 150 240 320 190 220 230 280 42 VAPOUR PRESSURES VAPOUR PRESSURES Inter- and Extrapolation of Vapour Pressures. The Kirchhoff-Rankine- Dupr< formula, log p = A + B/0 4- C log 0, where p is the vapour pressure, the absolute temperature, and A, B, C are constants, is accurate and convenient (e.g. see p. 43). 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 and the other at fl 7 , have the same vapour pressure, the ratio 0/0', 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 (p} 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 ' P 1*%P 10 0'2 'Q04 '004 + 1*243 20 I7'5 1-243 2~ = ri 4 = 10g I2 ' 7 J '-*' P at I5 = I2 ' 7 ' actually it is 12*8. VAPOUR PRESSURE OF ICE In mms. of mercury at o C. ; g 980*62 cms. per sec.* ; hydrogen (const, vol.) scale of temps. (Scheel, and Reuse, Reichsanstalt Ann. d. Phys., 1909.) Temp. . . -50C. -40 -30 -20 -10 -5 -2 Vap. press. 030 mm. 096 288 78 4 1-963 3-022 3-885 4'579 (SATURATED) VAPOUR PRESSURE OF WATER g = 980*67 cms. per sec. 2 Thermodynamic the observations are due to Scheel In mms. of mercury at o C. scale of temp, (see p. 46). From 20 to o 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; -1,4'258. Temp. \ 2 3 4 5 6 7 8 9 0C. 4*579 4-924 5*290 5-681 6-097 6-541 7-011 7'5" 8-042 8-606 10 9-205 9-840 10-513 11-226 11-980 12-779 13-624 14*517 15-460 16-456 20 A I7*5J 18-62 19-79 2 1 -Q2 22-32 23-69 25-13 26-65 28-25 29-94 30 3171 33'57 35*53 37-59 39'75 42-02 44-40 46-90 49*51 52-26 2 4 6 8 10 12 14 16 18 40 55'i3 61-30 68-05 75-43 83-50 92-30 ioi'9 112-3 123*6 135-9 60 80 149-2 355-1 163-6 384'9 179-1 4167 I95-9 450-8 214-0 487-1 233-5 525-8 254-5 567-1 277-1 611-0 301-3 657-7 327-2 707-3 100 760-0 815-9 875-1 937-9 1004 1074-5 "49 1227 1310 1397 120 1489 1586 1687 1795 1907 2026 2150 2280 2416 2560 140 2709 2866 3030 3202 338i 3569 3764 3968 4181 4402 160 4633 4874 5 I2 4 5384 5655 5937 6229 6533 6848 7175 180 75H 7866 8230 8608 8999 9404 9823 10256 10705 11168 200 11647 12142 12653 (Battelli, 1892.) Temp. . . 220 C. 240 260 280 300 320 340 360 Vap. Press. 1 7,380 mm. 25,170 35,76o 50,600 67,620 88,340 113,830 141,870 Interpolate logs of vapour pressures as explained above. 43 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 9771 98' 1 1 98-49 98-88 99-25 99-63 ICO'OO 100-37 100-73 96-95 36 98-14 53 91 99-29 67 100-03 40 76 97-00 40 98-18 57 "95 99'33 70 100-07 97 '03 '44 83 98-22 61 99 99-37 74 loo- 1 1 47 84 87 98-26 65 99-03 *4i 78 100-15 87 52 9i 98-30 69 99-07 '44 81 100-18 '55 91 97-I5 56 95 72 99-10 48 85 100-22 58 '94 97-20 59 '99 98-38 76 99-14 52 89 100-26 62 98 97-24 63 98-03 42 80 99-i8 56 '93 100-29 66 lOI'OI 97-28 67 98-07 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 (A) From 270 to 450 log/ = 10-04087 - 3271-245/0 - 7020537 log at the boiling-point = 13*6 mm. per degree (Laby, Phil. Mag., Nov., 1908). Temp. 0C. 5 10 15 20 Vap. Press. mm. *OOOl6* 00026* 00043* 00069 '00109 Temp. 25 30 35 40 50 Vap. Press. mm. 00l68 00257 00387 00574 0122 Temp. 60 80 100 150 200 Vap. Press. 0246 0885 276 2-88 17-81 Temp. 250 300 356-7 400 450 Vap. Press. mm. 75^3 248-6 7 60 1566 3229 Temp. 500 600 700 800 880 Vap. Press. 8 22-3 50 102 162 * 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. 6 8 9 0C. 10 20 30 1273 24-08 44-0 78-4 13-65 25-59 46-7 14-6 27-19 49'5 28-9 52-5 16-62 307 557 17-7 32-6 59'o 18-84 34'6 62-5 20-04 36-8 66-2 21-31 39*o 70-1 22-66 41-4 74'i (Ramsay and Young, 1886.) Temp. 30 C. 40 50 60 70 80 100 120 140 160 Press. 78-1 mm. 133*4 219-8 350-2 541 812 1692 3220 5670 9370 Interpolate logs of vapour pressures as explained on p. 42. 44 VAPOUR PRESSURES VAPOUR PRESSURES OF ELEMENTS p vapour pressure in mms. of mercury at o C. lat. 45 and sea-level (g - 980-62) (*>. I mm. Hg = 1333*2 dynes per sq. cm.)- If followed by at., p is in atmospheres ; 6 = absolute temp. (A.) ; / = temp, in C. ; (s) solid ; (/) liquid. The thermometry is in many cases somewhat dubious. Interpolate logs of vapour pressures as explained on p. 42. , -121 C. 128-6 -129-6 -134-4 135-1 -136-2 -138'3 -139 1 > 50-6 at. 38-0 35-8 29-8 290 27-3 25-3 23-7 (Olszewski, 1895) ! 78'9 A. 86-9 97'9 107'3 155'6 = crit. temp. >110-5A. 1213 135-2 147'3 2105 = crit. temp. >148-9A. 163-9 182-9 199'6 287*8 = crit. temp. > 300 mm. 760 2000 4000 40,200 41,240 43,500 Krypton. MJJMH Xenon . (Ramsay & Travers) . . -16-6C. -120 5-0 8-2 169 234 40-5 51'9 58-7 > 20 mm. 30 50 100 150 200 400 600 760 (Ramsay & Young, 1886) . -80 C. 60 -40 33-6 20 10 20 30 ) 62*5 mm. 210 560 760 1*84 at. 3*66 4-95 6*62 8*75 (Knietsch, 1890) .... Iodine (Baxter, Hickey, & Holmes, 1907) . . . 0C. 15 30 55 85 117 137 160'9 185'3 > "03 mm. '131 "469 3-08 20 100 200 400 760 Hydrogen (Travers & Jaquerod, 1902) .... t-258-2C. -256-7 -255'7 -255'0 -254'3 -253-7 -253'2 -252 9 H. Scale ) loo mm. 200 300 400 500 600 700 | 760 Helium . T .... 9 1'2A. 4-3 1 Neon (Travers 10115 65 A.(*)20 4 (J)l He ) o'2 mm. 760 1 & Jaquerod, '02) [pi 2-4 mm. 12-8 /Scale (Onnes, 1911) .... See p. 43- 1 Ea. Emanation | | See p. in. Nitrogen (Baly, 1900 . . Fischer & Alt., 1902) . . ) 62 5 A. 67-8 724 77'3 80 83 86 89 91 ) 86mm. 200 400 760 1013 1386 1880 2465 2916 Oxygen (Jaquerod,Travers, & center, 1902) .... 979iA. 821 84-4 86'3 87*9 89'3 901 90'6 H. Scale 3 200 mm. 300 400 500 600 700 760 800 ; 165 C. 170 180 200 209 219 226 230 287'3 j 120 mm. 173 204 266 339 359 393 514 760 (Schrotter, 1848) . . . Sulphur (Ruff& Graff, '08 ; B., 1899; C., 1899) . . t 50 C. 100 147 211 400 444'5 St/5p = o-o 9 /mm. near 9 -0003 mm. '0089 '192 3-14 f. 372 760 B. P. (see p. 53). VAPOUR PRESSURES OF COMPOUNDS Hydrochloric acid . . . (F M 1845 ; Ansdell, 1880). -73-3C. -45-5 -233 -3'9 40 9'2 13*8 22-0 334 1-8 at. 6-3 12-8 23-1 29-8 33-9 377 457 5^8 Sulphuretted hydrogen (R.. 1862) . , . -25 C. -15 -5 10 30 50 60 70 4-93 at. 6-84 9-3 10-8 14-3 237 36-6 44-4 53-1 Sulphur dioxide .... (Regnault, 1862) . . . -30 C. -20 -10 10 20 30 40 50 39 at. -63 roo 1-53 2-26 3-24 4-52 6-15 8-19 Ammonia, NH, .... (Brill, 1906) ..... -80 C. -776 -70-4 -644 -60'8 -54'4 -462 -398 -330 35-2 mm. 44-1 - 74-9 116-0 157-6 239-5 403'5 568'2 761 Nitrous oxide, N,O . . . (Cailletet, '78; R., '62) . -80 C. -60 -40 -20 -10 10 20 40 1-9 at. 5-05 iro 23-1 28-9 36-1 44-8 55-3 83-4 Nitric oxide, NO ... (Olszewski, 1885) . . . -176'5C. -167 -138 -129 -119 -110 -105 -100-9 -97'5 024 at. '182 5-4 10-6 200 31-6 41-0 49-9 57*8 Nickel oarbonyl, NiCO 4 . (D. & Jones, 1903) . . . -9C. -7 -2 10 16 20 30 94-3 mm. 104-3 * 2 9'i '44*5 2I 5 28 3'5 3 2 9'5 462 Interpolate logs of vapour pressures as explained on p. 42. 45 VAPOUR PRESSURES VAPOUR PRESSURES OF COMPOUNDS (contd.) Interpolate logs of vapour pressures as explained on p. 42. Carbon dioxide . . . (Zeleny & Smith, 1906) . t -130C.(j)-100(j) -80 (s) -65 CO -56*4 J -65 (/) 40 (/) -20 (/) -10 (/) p 2-5 mm. 119 657 2100 3910 2508 7510 14,830 19,630 Carbon bisulphide . . . (Regnault, 1862) . . . t -20 C. -10 10 20 40 60 80 100 p 47-3 mm. 79-4 128 198 298 618 1164 2033 3325 Chloroform, CHC1 3 . . . (Regnault, 1862). . . . t 20 C. 30 40 50 60 70 80 90 100 p 160-5 mm. 248 369 535 755 1042 1408 1865 2429 Carbon tetrachloride, CC1 4 (R., 1862) t -20 C. -10 10 20 40 60 80 100 p 9-8 mm. 18-47 3 2 '9 56 9* 215 447 843 1467 Acetylene, C 2 H .... (Villard, 1895) .... t -90 C. (s) -85 (s) -81 -70 -50 -23*8 202 36'5 p -69 at. i-oo 1-25 2-22 5-3 13-2 26-05 4 2< 8 6r6(M.) Benzene, C 8 H 8 .... (Young, 1889) .... t -10 C. 10 20 40 60 80 100 120 E> 14-8 mm. 26-5 45-4 74-6 i8ri 389 754 1344 2238 Aniline, C 8 H 5 NH 2 . . . (Kahlbaum, 1898) . . . t 101-9C. M194 138-7 151-5 1611 168'7 1750 ISO'S 183-9 E> 50 mm. loo 200 300 400 500 600 700 760 Bromnaphthalene . . . C 10 H 7 Br (Ra. & Y., 1885) t 215 C. 220 230 240 250 260 270 275 2804 )i58'9mm. i8i'8 236-0 303*4 386-4 487-4 6o8'8 677^9 760 Me. alcohol, CK 3 OH . . (R.,'62;Ra.&Y.;Ri.,'86) t -10 C. 17 20 30 50 80 120 150 P 14-8 mm. 28-5 78-3 88-7 150 381-7 1238 4342 9361 n. propyl alcohol, t,C 3 H.OH (Ra. & Y. ; S. ; Ri., '86) . t 0C. 10 17 30 40 60 80 100 120 p 3-9 mm. 7-8 12-4 28-2 51-4 157 389 843 1668 Iso-butyl alcohol f . . . C 4 H 9 OH(Ri.,'86;S.,' 9 i) t 10 C. 17 20 40 60 80 100 108 120 p 4-1 mm. 6-8 8'l 30-3 94-2 245 569 760 1195 Iso-amyl alcohol t . . . C 5 H u OH(Ri.,'86;S.,'9i) t 17 C. 30 40 50 60 80 100 120 130 p 1-78 mm. 4-68 9-33 17-4 32-0 151 234 522 741 Formic acid,f CH 2 O 2 . . (S., 1891 ; K., 1898) . . t C. 10 17 20 30 40 70 80 101 D io-2 mm. 18*4 26*3 31*6 51*3 79-4 266 373 760 Acetic acid, tC 2 H 4 O a . . (Ra.&Y.;Ri.,'86;S.,'9i) : 17 C. 30 50 70 90 110 130 150 200 ) 9-8 mm. 20-6 56-2 133 288 582 1068 1847 5905 Propionic acid,f C 3 H a O 2 . (Ri., '86 ;S., '91; K., '98) . 15 C. 17 20 30 40 60 70 80 140 ) 1-7 mm. 2-0 2*45 4-9 9-1 28-2 46-1 74-5 760 Butyric acid,t C 4 H 8 O 2 . (Ra.&Y.,'86;S.' 9 i;K.'94) : 17 C. 20 30 50 70 90 110 130 150 > '52 mm.* '66* 1*4 5-2 i6'2 44-9 in 245 497 Iso-butyric acid,f C 4 H 8 O 2 (Ri.,'86;S.,' 9 i;K., '94) 17 C. 30 50 70 90 110 130 150 153*5 > -88 mm.* 1-9 8*2 25*1 67*6 162 347 684 760 Methyl fonnate f . CH0 2 CH 3 (Y. & T., '93) . : -20 C. -10 10 20 40 60 80 100 > 67-7 mm. 117-6 195 309 476 1029 1990 3497 5782 Methyl butyrate f . C 4 H 7 2 -CH 3 (Y.&T.,' 93 ) -10 C. 10 20 40 60 80 100 > 3-55 mm. 7-3 13-8 24-5 69-2 167-5 3 6 i 7oi Methyl isobutyrate t . . C 4 H 7 2 .CH 3 (Y.&T.,'9 3 ) -10 C. 10 20 40 60 80 100 120 6-22 mm. 12-15 22 '4 3$'9 104-7 244 505 956 1660 Ethyl acetate f .... C 2 H 3 2 .C 2 H 5 (Y.&T.,' 93 ) -20 C. -10 10 20 40 60 80 100 > 6-5 mm. 12-9 24-3 42-7 72-8 186 415 833 1515 Ethyl propionate f . . . C,H 8 2 .C 2 H 5 (Y.&T.,'93) -10 C. 10 20 40 60 80 100 120 > 4-05 mm. 8-3 15-5 27-7 77-9 188-0 403*6 785 1388 Propyl acetate t . . . . C 2 H 3 2 .C 3 H 7 (Y.&T.,'93) -10 C. 10 20 40 60 80 100 120 3-6 mm. 7-4 13-9 25-1 70-8 172 373 724 1288 Ethyl ether, (C 2 H 5 ) 2 O . (Young, 1910) .... -10 C. 10 20 40 60 80 100 193-811 112-3 184-9 290-8 439-8 921 1734 2974 4855 27,060 Interpolate logs of vapour pressure as explained on p. 42. * Extrapolated, t The vapour pressures here given have been graphically interpolated from the observers' values. B., Bodenstein; C., Callendar ; D., Dewar ; F., Faraday; K., Kahlbaum; M., Mackintosh; R., Regnault; Ra. and Y., Ramsay and Young ; Ri., Richardson ; S., Schmidt ; Y. and T., Young and Thomas. J Triple point. || Critical temp. 46 INTERNATIONAL TEMPERATURE SCALE THE INTERNATIONAL SCALE OF TEMPERATURE Immediately prior to the war an attempt was made to arrive at international agreement as to the adoption of a standard or fundamental temperature scale by the three national standardizing laboratories the National Physical Laboratory, the Bureau of Standards, Washington, and the Reichsanstalt. The outbreak of war prevented formal acceptance of the centigrade thermodynamic scale as the " international " scale of temperature. Lord Kelvin showed long ago the theoretical advantages of the thermodynamic (or absolute) scale, and that a perfect gas (i.e. one which obeys Boyle's law and suffers no temperature change when subjected to free expansion with no external work) would give a scale identical with the thermodynamic. The practical advantage of the thermodynamic scale is that the high temperature scale evaluated on the basis of the laws of radiation is consistent with that of the gas thermometer at lower temperatures. To promote the general use of the same temperature scale in both scientific and industrial circles, the following alternative methods have been agreed as a means of attaining a Practical Scale of temperature which approximates to the thermo- dynamic scale. A statement of the exact relationship between the two scales is deferred until a sufficient degree of concordance has been reached in the measure- ments. There is, however, every reason to believe that the Practical Scale over the range o C. to 100 C. agrees within the limits of experimental error with the hydrogen scale of the International Bureau (pp. 47, 57). (a). The Hydrogen Scale. In the interval between (o C.) and (100 C.) the Practical Scale is realized with the exactness required for work of the highest precision in the scale of the constant-volume hydrogen thermometer having for fixed points the temperature of pure ice melting under normal atmospheric pressure (o C.), and that of the vapour of distilled water in ebullition under normal atmospheric pressure (100 C.). (b). The Platinum-Resistance Thermometer Scale. In the interval between the freezing-point of mercury and the boiling-point of sulphur the Practical Scale is realized with sufficient exactness by the platinum-resistance thermometer standardized at the temperatures of melting ice (o C.), of the vapour of water boiling under normal atmospheric pressure (100 C.), and of the vapour of sulphur boiling under normal atmospheric pressure in a specified form of apparatus and under specified conditions. The temperature of the vapour under these conditions is to be taken as 444'5 C. The temperature / on the International Scale is deduced from the resistance of the platinum thermometer by the formula where t pt = 100 x (R-R )/(Rioo-Ro), and R, R & RIOO are the observed resist- ances of the thermometer at temperatures /, o & 100 respectively. The platinum of which the thermometer is made shall be of such a degree of purity that the value of 5 in this equation shall not be greater than 1*52, and RIOO/KO shall not be less than 1-386. The boiling-point of sulphur t s at pressure p millimetres is connected with that at standard pressure, 760 millimetres, by the formula /, = 444-5 +0-09080- 760) -o'oooo47(/- 76o) 2 (Cf. p. 53-) (c\. The Fixed Point Scale. The Practical Scale is also realized with sufficient exactness by the use of the following fixed points, in addition to the three fundamental points above specified : Temperature on the centigrade thermodynamic scale. Boiling point of Oxygen - 1 82 '9 5 + o-o 1258(^-760) -o-ocxx>o79(;>- 760)- Boiling point of Carbon Dioxide - 78'5 +o'oi 595(/ - 760) - o-ooooi i i(p - 76o) 2 Freezing point of Mercury ................. 38'88 Transformation point of Sodium Sulphate ............ 3 2 '38 Boiling point of Naphthalene .......... 2l7'9 e + o-o(|8(/ 760) Benzophenone (purest) ....... 3Q5'9 + o'o63(/-76o) Melting or freezing point of: Antimony . 630 Silver (in a reducing atmosphere) . 961 Gold . . . 1063 Copper (in a reducing atmosphere) . 1083 Fixed points of the second order are provided by the melting or freezing points of Tin 23i'8 4 Cadmium 32O'9 Zinc 4I9'4 Common Salt (pure) 801 47 GAS THERMOMETRY GAS THERMOMETRY The standard thermometric scale of the International Bureau 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 (= 1*3158 standard atmosphere). THERMODYNAMIC TEMPERATURE OF THE ICE-POINT Method. Air. CO, Computer. From Joule-Thomson effect Extrapolation to zero pressure (see p. 57) From Joule-Thomson effect 273-14 273-07 273-05 273-06 273-13 273-09 273-09 (273-17) 273-25 273-14 273-19 273-27 273-05 273-10 273-12 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 (i9o8).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. \ ( + ) 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. ft Mem. Bureau Intl. 1907. t Bull. Bureau of Standards. 1908. J See Dalton, Proc. Konink. Akad. Weten. Amsterdam^ April, 1909. tC. 240 200 150 100 50 10 20 30 40 50 60 Const. Pressure P = 1000 mm. + -26 + '1C + -04 + -02 -ooi -002 - -003 + -40 + -12 - -009 - -017 *O2I - -003 - '024 "OO3 -O22 Const. Volume P at = 1000 mm. + -06 + -033 -f 'oio + -005 '000 *ooo -ooi *OOI '001 -ooi + 03 -002 -004 -005 -006 - -007 - -006 70 80 90 100 200 300 400 450 600 800 1000 1200 Const. Pressure P = 1000 mm. '002 -001 + -oi4 + -034 + -07 (?) + '09 (?) -014 - 7 + -12 + -28 + -46 + -56 + 1-8 +2-3 Const. Volume P at = 1000 mm. -ooo -ooo + "004 + -on -02 (?) - "003 -002 + '04 + -19 + '3 + *5 + 7 -fi-o 48 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 corrections are given by the International Bureau ; those for the Jena glasses by Griitzmacher. 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 " Thermome'trie de Precision." Paris, 1889, and Chree's "Notes on Thermometry," Phil. Mag., 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. 78). Temp. -20 10 20 30 40 50 60 70 80 90 100 Kew Glass. oo '00 +005 + 01 +01 +01 +015 + 02 + 025 Verre Dor. '10 '10 - -09 - -07 - -05 _ o 3 Jena 16' -06 -09 'ii '12 'II *IO '08 -06 Jena 59'". f 59'" 'O2 -04 -04 -04 -03 -02 -oi '00 '00 Temp. 110 120 130 140 150 160 170 180 190 200 250 300 Verre Dur. +'0 4 + -06 + -07 + -07 + -06 + -03 o - -04 - -09 Jena 16"' +'03 + -05 + -07 + -09 + -io + TO + -08 + -06 + -02 - -04 ~ '63 -I-9I Jena 59" -- oo -02 -04 '08 * 13 '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. Verre Dur. Jena 16'". Jena 69'". Temp. Verre Dur. Jena 16'". Jena 59'". 10 C. 20 30 40 50 -oo8 017 027 037 048 005 on 017 024 03 1 0-005 009 014 017 60 C. 70 80 90 100 '060 071 084 097 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 16'" glass, with degree intervals about I mm. long. / is the indicated temperature, and taux 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. Inst., 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 - taua 70 C. 80 100 120 140 180 70 C. 80 100 120 140 180 24 '35 1*02 28 41 66 91 1-18 -07 22 39 56 89 1*21 I- 5 6 I' 9 8 29 48 68 1-09 1-52 1-97 2 '43 "17 38 *59 1-25 171 2-18 2-69 -27 78 1-04 1-58 2-15 270 3-26 'oi 08 25 30 52 *I2 28 '35 60 8 7 04 19 36 48 79 '5 '47 25 42 60 1-38 1-82 2-28 28 48 67 2-03 2 '49 1-98 2*55 3-I3 No. of degree divs. of exposed thread. 10 20 30 40 60 80 100 120 49 ELECTRICAL THERMOMETRY Pt Temps. tpt. 20 40 60 80 100 120 140 160 180 t t / t t t t t t / -200 -i7i'5 19-76 -i53'2 39-64 -I34'7 59-64 -ii5- 9 79-76 IS' -77'84 1 20*4 -58-59 140-9 -39' 1 8 161-5 -i9-65 182-3 + 200 203-1 224-2 245'4 266-7 288-1 309-8 33I-5 353*4 375-5 397-8 400 420-2 442-8 465-5 488-5 511-6 534-9 558-4 52-I 606-0 630-1 600 654-4 679-0 703*7 728-7 754'o 779-4 805-2 831-2 857-4 884-0 800 910-8 937-9 965-3 993*0 1021 1050 1078 1107 H37 1167 1000 1197 1228 1259 1290 1323 1355 ~ -~~ PLATINUM THERMOMETRY TO REDUCE PT-SCALE TEMPS, (tpt) TO "PRACTICAL SCALE" TEMPS. (*) , Callendar's "difference formula" for the difference between the practical-scale temp. (/) (see p. 46) and the Pt-scale temp, (tpt) is given on p. 46. Pt-scale temps, result from assuming a linear relation R/* = R (i + atpi} between temp, and the electrical resistance (R) of Pt ; a is the mean coefficient for the range o to 100. The "difference formula" gives the correction yielded by the truer parabolic relation Rt R (i + a/ + /3/ 2 ). The difference-formula holds down to 40 C. The values given below for lower temps, are obtained by direct comparison with the gas thermometer. Pt thermometers should not be used above 1 100 C. See Ezer Griffiths' "Methods of Measuring Temperature" (Griffin). 8 = 1-50. CHANGE A* IN THE PRACTICAL-SCALE TEMP. (*) FOR A CHANGE OF +'01 IN S 8 for pure Pt varies between i -49 and i -50. Impure Pt has usually a high value of 5. t A; t A/ t A/ t A* / A/ -60 -40 -20 20 40 60 -oio P oo6 002 002 002 'OO2 80 100 120 140 160 180 200 -'002 002 006 oio 014 *O2O 250 300 350 400 450 500 550 c -038 060 088 *I2O I S 8 20 25 600 650 700 750 800 850 900 0-30 36 42 *49 'I 6 64 72 950 1000 1050 1100 o.g "9 I'D I'l HIGH TEMPERATURES (See Burgess and Le Chatelier's "High Temperature Measurements, 1912.") For the measurement of high temperatures (say above 1550 C., which is about the present upper experimental limit of the gas scale) the instruments in general use are thermo-junctions and optical or radiation pyrometers. Both involve extra- polation. Pt thermo-couples may be used up to 1400 C. At higher temperatures the total radiation or optical pyrometers afford the most reliable means. THERMO-ELECTRIC THERMOMETRY Temperature readings with thermo-couples are reduced by one of the formulae : (a) E = a + bt + cP, (V) E = mt n , or log E = n log / + m' , E being the e.m.f. generated, and t 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 neither formula will bear extrapolation to higher temps. The thermo-e.m.f.'s of these Pt couples gradually diminish with prolonged heating. The values of the constants below are only average values, and for accurate work a couple should always be calibrated. E IN MICRO VOLTS (1Q-6 VOLT) Couple. a b C n tn 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 -307* -550* 8-1* 14-8* icm 0017* *oo 1 6* -018^ rig I'lO 1-14 52 89 I '34 * These constants are not suitable for temperatures below 300. f Eureka, 60 Cu, 40 Ni. 50 THERMOMETRY THERMO-ELECTRIC THERMOMETRY (contd.) The following are the readings in io~s volt determined at the National Physical Laboratory for a Pt-Rh and a Pt-Ir couple, each having the cold junction at o C. The values only hold for the particular couples. Couple. Temp. 50 100 150 200 250 300 350 400 450 ;Pt and (90 Pt, 10 Rh) oc. 500 1000 377 880 23 423 935 5i 470 991 83 518 1048 119 567 1106 158 617 1165 199 668 1225 242 720 1286 286 773 1348 33i 826 Pt and (90 Pt, 10 Ir) 500 1000 o 737 1571 58 818 1657 125 899 1744 195 981 1831 268 1064 1919 343 1147 2007 420 1231 2096 498 1315 2185 577 1400 2275 657 1485 THERMO-E.M.F.-S AGAINST PLATINUM IN MICRO VOLTS (10-6 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. Metal. -190 + 100 Metal. -190 + 100 Metal. -190 + 100 Aluminium Antimony . Bismuth . Cadmium . Cobalt . . Copper. . Gold |. . Iron. . . + 390 + 12300 - 60 200 120 2900 + 380 +4/00 6500 + 900 -1520 + 740 + 730 + 1600 Lead. . Magne- sium . Mercury Nickel . Palla- dium . Silver . + 210 + 330 + 2220 + 790 I4O + 410 + 410 1640 - 560 + 710 Tantalum . Tin . . . Zinc . . . Brass . . . Constantan* German sil- verf. . . Manganin J + 200 I2O + 330 + 410 + 750 c.+ 400 -344 C. IOOO + 57o Eureka, 60 Cu, 40 Ni. t 60 Cu, 15 Ni, 25 Zn. \ 84 Cu, 4 Ni, 12 Mn. RADIATION AND OPTICAL THERMOMETRY Most radiation thermometers depend upon either (i) the Stefan-Boltzmann law, E = where E is the total energy (all wave-lengths) radiated per sec. by a black body at absolute temp. 6 to surroundings at absolute temp. , and a is a const, (ff 57 X io~ 12 watts per cm. 2 per i see p. 68) ; or (2) Wien's equation con- necting the temperature with the intensity of some particular wave-length of light emitted (p. 68). The Wien equation is, Intensity I = c^e~ c ^ Ke , where A is the wave-length, is the "black body" temp, on the absolute scale, c and c z 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 1550 C. Up to about 1400 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 AND COLOUR OF FIRE Appearance . Bed just visible. Dull Bed. Cherry Bed. Orange. White. Dazzling White. Temperature. c. 500 C. c. 700 c. 900 C. 1100 e. 1300 c. 1500 Temp, of positive crater of electric arc 3400 C. ; under pressure 3600 C. 51 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. 117 ; of fats and waxes, see p. 53. Element. Melting Observer. Boiling Point at Observer. Point. 760 mms. Aluminium . . 657 C. Holborn and Day, 1900 i8ooC Greenwood, 1909 Antimony . . Argon . . . 630 -188 > Ramsay and Travers, 1901 1440 -i 86 Greenwood, 1909 Arsenic . . . volatilizes ___ ( sublimes } __ \ 45 J 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 (?) J 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 . . 1520 Bureau of Standards 2200 Greenwood, 1909 Cobalt . . . 1480 Bureau of Standards Copper . . . / 1084 * I 1083 Holborn and Day, 1900 ) Day and Sosman, 1910 J 2310 Greenwood, 1909 Erbium . . . . Fluorine . . -223 Moissan and Dewar, 1903 -I8 7 Moissan & Dewar, 1903 Gallium . . . 30-2 L. de Boisbaudran, 1876 Germanium 960 Biltz, 1911 Gold .... r 1063 \ 1062 1 Holborn and Day, 1901 ) Day and Sosman, 1910 / 2530 (?) Helium . . . below 272 Onnes, 1911 -268'8 Onnes, 1911 Hydrogen . . -259 Travers, 1902 -2527 Travers, 1902 Indium . . . 155 Thiel, 1904 1000 (?) Iodine . . . Iridium . . . U3 2290 Lean & Whatmough, 1898 Mendenhall& Ingersoll,'o7 184-4 25 5 o(?) Drugmann & Ramsay, 'oo Iron .... 1530 Bureau of Standards 2450 Greenwood, 1909 Krypton . . . Lanthanum -169 810 Ramsay, 1903 Muthmann & Weiss, 1904 -151-7 Ramsay, 1903 Lead. . . . Lithium . . . Magnesium 327 1 86 633 Holborn and Day, 1900 Kahlbaum, 1900 Heycockand Neville, 1895 1525 >i4co 1 1 20 Greenwood, 1909 Ruff & Johannsen, 1906 Greenwood, 1909 Manganese Mercury . . Molybdenum . Neodymium . 1260 -38-80 2450 840 Bureau of Standards Chappuis, 1900 Pirani & Meyer, 1912 Muthmann & Weiss, 1904 1900 3567 3200 (?) Greenwood, 1909 Callendar, 1899 Neon .... -239 Dewar, 1901 Nickel . . . 1452 f 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. t Const, vol. N. thermometer. 52 MELTING AND BOILING POINTS MELTING AND BOILING POINTS OF THE ELEMENTS (contd.) Element. Melting Point. Observer. Boiling Point at Observer. 760 nuns. Osmium . . . 2700 C. Oxygen . . . -219 Dewar, 1911 -i82- 9 C. Travers, 1902 Palladium optical therm. 1549 Holborn & Henning, 1905 2540 ___ > 1545 Nernst&Wartenberg, 1906 const, vol. N. therm. . . 1549 Day and Sosman, 1910 __ calculated . . 1555 Hyde, 1917 Phosphorus . . 44* 1 760 Hulett, 1899 287 Schrotter, 1848 Platinum optical therm. 1753* Nernst&Wartenberg, 1906 2450 (?) > 1756* Holborn &Valentiner, 1907 1756* Waidner & Burgess, 1907 j> 1755 Day and Sosman, 1910 thermo-jn. 1752 )) j) Potassium . . Praseodymium 62-5 940 Holt and Sims, 1894 Muthmann and Weiss, 1 904 758 Ruff & Johannsen, 1905 Radium . . . 700 Curie and Debierne, 1910 Rhodium . . 1907 Mendenhall & Ingersoll, '07 2500 (?) Rubidium . . Ruthenium . . 38'5 1900 (?; Erdmann and K6 thner, 1 896 696 2520(?) Ruff & Johannsen, 1905 Samarium . . 135 Selenium . . 217 Saunders, 1900 690 Berthelot, 1902 Silicon . . . 1200 (?) 3500 (?) Silver. . . . / 962 f I 900 Holborn and Day, 1900 "1 Day and Sosman, 1910 J 1955 Greenwood, 1909 Sodium . . . 97*6 Ezer Griffiths, 1914 / 877 I 742 Ruff & Johannsen, 1905 Permann, 1889 Strontium . . 900 444-55 \ Eumorfopoulos, 1908 H5 (c.p. air) / (corrected, 1909) Sulphur . . . | rhombic I IJ 9 4447 (c.v. N) jchappuis & Harker,i902 I monoclinic 444'53 (c.p. N) \ Callendar, 1899 Tantalum . . / 2910 \ 2800 Burgess, 1907 Forsythe, 1911 Tellurium . . 450 Matthey, 1901 1390 Deville and Troost, 1880 Thallium . . 301 Kurnako w & Puschin, 1 90 1 I280(?) Wartenberg, 1907 Thorium . . 1690 Wartenberg, 1909 Tin .... 232 Hey cock & Neville, 1895 2270 Greenwood, 1909 Titanium . . 1800 Tungsten . . / 3270 1 3360 Langmuir, 1915 Forsythe, 1916 37oo (?) Vanadium . . 1720 Xenon . . . 140 Ramsay, 1903 -109 Ramsay, 1903 Zinc .... 418 Day and Sosman, 1910 918 Berthelot, 1902 Zirconium . . c. 2300 ~ ~ * Recomputed using Day and Sosman's figure (1549) for Pd. f In reducing atmosphere ; 995 in air. Alloys. Brass, M.P. 800-1000 C. ; Cast iron, M.P. c. noo C. ; Duralumin, M.P. 650 C. ; German Silver, M.P. 1000-1100 C. ; Nichrome, M.P. c. 1500 C. ; Phosphor Bronze, M.P. c. 1000 C. 53 BOILING POINTS EFFECT OF PRESSURE ON BOILING POINTS 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. = / 4.^(760 p)(t + 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. /// c Substance. S//5/ c Substance. 8//S/ c X lO" 6 XIO" 6 X IO" 6 Hydrogen . . 200 CC1 4 . . . . 23 123 Benzene . . 23*5 121 Oxygen . . . 77 146 Pentane, n . . 25-8 125 Toluene . . . 217 1 2O Carbon dioxide 55 Alcohol, methyl 29*6 100 Aniline . . . 19*6 112 Water . . . 27-2 99 ethyl . 30-3 94 Naphthalene . I7'l 119 Mercury . . i T 6 118 amyl . 25 98 Benzophenone I 5 '8 109 Sulphur* . . iro 114 Ether, ethyl . 26-9 121 Acetone. . . 26-4 "5 * tp - t JBO + -09io(/ - 760) - '0 4 49(/ - 760)% Mueller & Burgess, 1919. MELTING, FREEZING, AND BOILING POINTS OF FATS AND WAXES At 760 mm. pressure. t (See Lewkowitsch's treatise.) Substance. M.P. F.P. Substance. M.P. F.P. Substance. M.P. B.P. Butter . . . 28-33 20-23 Beeswax . . 61-64 60-63 Paraffin wax, C c. Lard . . . Tallow, beef . 36-40 40-45 27-30 27-35 Spermaceti . Stearin . . 42-49 71-6 42-47 70 Soft. . . Hard . . 38-52 52-56 350-390 390-430 mutton 44-45 36-41 Naphthalene 80-0 Olive oil . . c. 300 THERMAL CONDUCTIVITIES The thermal conductivity, k, is given below as the number of (g'ram) calories conducted per sq. cm. per sec. across a slab of the substance I cm. thick, having a temp.-gradient of i C. per cm., i.e. calorie cm." 1 sec." 1 temp.- 1 . To reduce to pound-calories per sq. inch per sec. across a slab I inch thick with a temp.-gradient of i C. per inch, the values below must be multiplied by 0-0056. (See Callendar, " Conduction of Heat," Encyc. Brit., and Winkelmann's " Handbuch der Physik." METALS AND ALLOYS k for most pure metals decreases with rise of temperature ; the reverse appears to be true for alloys. If K be the electrical conductivity and 9 the absolute temp., then &l(itQ) is very approximately a constant for pure metals. (See J. J. Thomson, "Corpuscular Theory of Matter.") The electrical conductivity of the same specimen of many of the substances below will be found on p. 85. 54 THERMAL CONDUCTIVITIES METALS AND ALLOYS (contd.) Substance. Temp. Cond. k. Observer. Substance. Temp. Cond. k. Observer. C. C. Metals- Nickel . -160 129 Lees. '08 Aluminium * -160 18 514 504 \_Lees, / P.T.,'6S ;; /97%\ \Ni/ 18 1OO 142 138 } J .&D., 1900 M . 18 480 U? &D, Palladium . . 18 168 j J .&D., 51 . 10O 492 r 1900 M . , 100 182 1900 Antimony . . . O 044 } Lorenz, Platinum . . . 18 166 \ J .&D., ,, ... 100 040 1881 ' f , ( 10O '173 f IQOO , Bismuth . . . -186 025 M., 1907 Silver, pure . . -160 998 | Lee's, J M . . . 18 0194 p &D, ~ . 18 "974 IQ08 ff * 1OO 0161 1900 ^ f 18 roo6 ) J . & D., Cadmium, pure -160 239 Lees, '08 ,, . 100 992 r IQOO . 18 222 U- &D., Tin, pure . . . -16O 192 Lees, '08 if . 1OO 216 / 1900 j) , . 18 155 \J .&D., v Copper, pure . -160 1-079 Lees, '08 . . 100 'H5 / IQOO . 18 918 1 J' &D., Tungsten . . . 18 "35 Coolidge ,, . 1OO Q08 / IQOO Zinc, pure . . -160 278 Lees, '08 Gold . . . . 18 700 \ J* & D., M . . . 18 265 u .&D., . . 100 703 / 1900 M . , . 10O 262 j 1900 Iron, pure . . 18 161 } J " &D., Alloys M . 1OO 151 1900 Al alloys. wrought t -160 18 152 144 Lee's, '08 I J- & D., A188 ,CUI2.{ 70 170 36 38 \ Griffiths, / 1920 " ,.t cast J 1OO 54 102 143 114 in / 1900 t Callendar /Al 797, Cu 6-6^ \Zn 0-9, Sn o'8 '/ 70 170 70 '39 41 "34 \ Griffiths, / 1920 \ Griffiths, 30 149 Hall \Cu 2- 7 . . ./ 17O '35 / 1920 steel (i%\ -160 113 Lees, Duralumin . . 18 31 tc 18 115 / 1908 Brass J. . , -16O 181 \ Lees, 5> 3J 18 loS i }J. & D., 17 260 / 1908 )' V 1OO 107 1900 Bronze, \ 15 099 \ Griffiths, Lead, pure . . -160 092 Lees, '08 Cu 89-4, Sn 9-6) 205 131 / 1920 t . 18 083 1 J. &D., Constantan \ 18 054 i] .&D., , . 100 082 I IQOO (Eureka) f / 10O 064 1900 Magnesium . . O to \ . / Lorenz, German Silver . O 070 \ Lorenz, i 100 |'37t 1 1881 u if 10O 089 / 1881 Mercury . . . O 0148 \ H . F. Manganin ** -16O 035 Lees, '08 . . . 50 0189 /Weber, '79 . 18 053 \] [. & D., . . 155 '0201 N , 1913 ^ . 10O 063 } 1900 ., 17 0197 R W., '02 Platinoid . . 18 060 Lees, '08 * 99% Al. t -i% C., -2% Si, -i% Mn. 1 2% C., 3% Si, 1% Mn. 3 5%C., i -4% Si, '5%Mn. || 70 Cu, 30 Zn. 1 60 Cu, 40 Ni. ** 84 Cu, 4 Ni, 12 Mn. A. , Angstrom ; J. & D., Jaeger & Diesselhorst ; M., Macchia: N., Nettleton; R. W., R. Weber ; P. 7'., Phil. Trans. GASES In the case of a gas the thermal conductivity k I '6037?^ where ?7 is the viscosity, and ment specific heat at constant volume, with this formula, that k for air, Stefan, and Kundt and Warburg have found, in agree- tiydrogen, etc., is constant between the pressures 76 cm. and ' 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 ID" 6 C. X I0~ 6 C. X I0~ 6 C. X I0~ 5 H, -150 117, E, Air 5 '40* CO 7 5'io, W. N 2 O 3-50, W. 2 7 5-63, W, C0 2 3-07, w. 1OO 5'o6, W. O 31*9! G. A O 99 O 3-27, Sc. NO 8 4'6o, W. M 100 36-9, G. CH 4 8 6-47! w. J9 100 5-06, Sc. Hg 203 1-85, Sc. He O 33*9, S. C 2 H 4 3-95, w. NH 3 O 4-58, w. N 2 7 CO O 4-99, W. 100 7-09, W. * 5*74/22, tJercus and Laby, 1919. E., Eckerlein, 1900; G., Graetz, 1885; S., Schwarze, 1903 ; Sc., Schleiermacher, 1889; W., Winkelmann, 1875. 55 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. Glass Crown ; window Flint . . . . Jena . . . . Soda .... Woods (dry) Mahogany . . Oak, teak . . . Pine, walnut Miscellaneous Asbestos paper . Bricks Diatoma- ceous, 100 500 Fireclay, 600 1000 Cardboard 2-5, L. 2, L. 5, L, 6 4, L. 45, 0. 3-o\L).H. 4-0 J & C. Substance. Cement . . Cotton . . Cotton wool . Cork, slab, o gran'ld. o Diatomace- 1 ous earth, o/ Earth's crustf Ebonite . . Felt . . . Flannel . . Gas carbon . Graphite . . Ice .... Marble, white 7 Mica * . Paper . . Paraffin wax Porcelain . X 1C 7, I '55, 04 ii, G. 10, G. 19, G. 4 42, L. 09 23, L. 10 12 i'8.' L. Substance. Quartz, || axis Quartz, j_ axis Rubber, Para Sand . . . Sawdust . . Silk . . . Slag wool, o Slate . . . Sulphur, 30. Substance. Water, x io~ 3 30, L. 1 6, L. 45, L. 13 12 22 L. 10, G. 47, L. 45, L. Temp. 17 20 4 236 11 25 Substance. Liquids- Alcohol, 25 Aniline, 12 Glycerine, 25 Paraffin oil, 1 7 Turpentine, 1 3 Vaseline, 25 X 10" 4'3, L. 4' i 6-8, L. 3'5 3 Cond. k. 00131 00143 00138 00152 00147 00136 Obs. R.W.'o3 M. &C. jH.F. /Weber \Lees, I 189! * Perp. to cleavage plane. f Average for igneous and sedimentary rocks ; see Brit. Ass. Reports. D. H. & C., Dougill, Hodsman and Cobb, 1915; G., Ezer Griffiths, 1916; L., Lees, 1892 & 1898; M. & C. Milner Chattock, 1898 ; R. W., R. Weber. 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 l t = / (i+o/) 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., a/id except when some temperature is specified, for a range round and about 20 C. Some substances expand irregularly, and extrapolation of a may therefore be dangerous. Interpolation of a from the constituent metals must be employed with caution in the case of alloys. (See Winkelmann's " Handbuch-der Physik," iii. 1906.) Element. Aluminium . Antimony Bismuth . . C. (diamond) (gas car- bon) (graphite) Cadmium . . Cobalt . . . Copper. . . 25-5 12 157 1*2 5'4 7'9 28-8 I2'3 167 Obs. V.'93 F. '69 V.' 93 F/6 9 F. '69 F. '69 M.'66 T.'99 V.' 9 3 Element. Gold . . . Iridium . . Iron (cast) . (wrought) Steel, io'5 to Lead . . . Magnesium . Nickel . . . Palladium . Platinum . X I0~ 6 'i'5 10-2 ir6 27-6 25-4 I2'8 117 8-9 Obs. V.' 9 3 B. '88 D. '02 H.D.'oo N.P.L. M.'66 V,' 9 3 T. '99 S. '03 B. '88 Element. Potassium Selenium, 40 Silver . . . Sodium . . Sulphur Thallium, 40 Tin . . . . Tungsten, 27 2027 Zinc, 25 8 to x io~ ( 83 36-8 1 8-8 75 c. 70 30-2 21-4 4'44 7*26 26-3 Obs. H. '82 F. '69 V.' 93 F. '69 M. '66 W.'i 7 W.-'i7 N.P.L. 56 COEFFICIENTS OF EXPANSION COEFFICIENTS OF LINEAR EXPANSION OF SOLIDS (contd^ Substance. a. Obs. Substance. a. Obs. Alloys Aluminium bronze . . . Brass (ordy.) c. 66 Cu, 34 Zn Bronze, 32 Cu, 2 Zn, 5 Sn Constantan (Eureka), 60 Cu, 40 Ni XKT 6 I7'0 18-9 177 17-0 22'6 1 8-4 18-1 24 13*0 19-5 1 2'0 0-9 6-0 97 12-5 16-8 87 15 25 i9'3 19 9'5 14 77 19 8-5 97 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. 3 68 Sc. Sc. Miscellaneous (contd.) Glass, flint, 45 SiO 2 , 8 K 2 0, 46 PbO Jena, 16'" (see p. 78) 59'" (see p. 78) Verre dur (see p. 78) Granite X IO" 6 7'8 7'8 57 r* 8'3 198 507 25-1 -5-6 3*5 4*4 7 c. no 2'8 3'i 3*4 2-5 ^3 7'S 137 '22 42 50 *54 12 10 f-3 c.s c.6o c. 40 '34 Sc. \ T.S.S. 1 ' 9 6 C.'o 7 Ru. '82 Vn. '02 B. '88 B. '88 N.P.L. S~o 3 H.G. '01 Bd. 'oo T. '02 B. '88 B. '88 S. '07 C.'o 3 S. '07 R. '10 VI. '68 VI. '68 VI. '68 VI. '68 VI. '68 Duralumin German silver, 60 Cu, 15 Ni,25Zn, 50 .... Gunmetal (Admiralty) . . Magnalium, 86 Al, 13 Mg Nickel steel, * 10 % Ni . . > 20 / Q . > 3O /o j, > 36 /o (Invarf) > 4 A) j > j 5o / o n o/ J 0< ~' /O * * Phosphor bronze, 97*6 Cu, 2 Sn, '2 P Gutta-percha Ice, - 10 to o . . . . Iceland spar, || axis . . . J_ axis . . . Marble, white Carrara, 15, 1-4 to black Masonry . 4 to Paraffin wax, o-4o . . Porcelain, Berlin .... 0-IOO Bayeux . . . ,, o . Portland stone .... Quartz (crystal), || axis . . J_ axis . . Silica (fused), -80 too . ot030. o to 100 o to 1000 Sandstone . . . . 7 to Slate ...... 6 to Platinum-iridium, 90 Pt, 10 Ir | 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 ... . 64 to Woods (i) along grain- Beech ; mahogany ; box . Fluor spar, CaF 2 .... Glass, soft, 68 SiO 2 , 14 NajO, 7 CaO hard, 64 SiO 2 , 20 K 2 O, ii CaO (2) across grain- Beech ; box Pine * See Guillaume's "Les Applications des Aciers au Nickel," 1904.- f Invar is obtainable in three qualities, with a range of coefficients of ('3 to -f- 2-5) X lo" 6 at ordinary temperatures. \ Used for international prototype metre (see p. 3). Used for Imperial Standard Yard (see p. 4). B. Benolt; Bd. Bedford; C. Chappuis ; D. Dittenberger ; Dl. Daniell; F. Fizeau ; G. Ezer Griffiths; H. Hagen ; H.D. Holbora and Day; H.G. Holborn and Griineiscn ; M. Matthiessen; N.P.L. National Physical Laboratory; Pf. Pfaflf; 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 ; W. Worthing. 57 COEFFICIENTS OF EXPANSION COEFFICIENTS OF CUBICAL EXPANSION OF GASES The volume coefficient, o, at constant pressure is defined by v t - VQ(I + a/) ; the pressure coefficient, , at constant volume is defined by p t =/o( I + #) where v t and p t are the volume and pressure respectively corresponding to /, the initial volume and pressure (VQ, / ) being measured at o C. The values of both a and depend on the initial pressure of the gas. If a gas obeys Boyle's law exactly, a = /3. Comparison of rarefied gas, H ? and absolute temperature scales. By graphically or otherwise extrapolating a and to zero pressure, they become equal (as we should expect, for rarefied gases should behave as ideal gases and obey Boyle's law), and we may write a = = 7. For example, Berthelot finds from Chappuis' data For H 2 , mean 7 N 2 , 7 00366207 .= 1/273*07 (see p. 47) 00366182 = 1/273-09 (see p. 47) 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 = 7 very nearly, and thus the constant-volume hydrogen scale of temperature may justifiably be taken as closely approximating to the thermodynamic scale (see also p. 46). (See Young's " Stoichiometry " ; and Berthelot and Chappuis, Trav. et Mtm. du Bur. Intl.* 1907.) Gas. Temp. Obs. Gas. I Temp. Obs. AT CONSTANT PRESSURE. AT CONSTANT VOLUME. Air H 2 . > > 2 . CO. C0 2 1 5) )J N 2 S0 2 c. 0-IOO O-IOO O-IOO O-IOO O-IOO O-IOO O-IOO 0-2O 0-40 O-IOO O-20 0-40 O-IOO O-2O 0-40 O-IOO O-IOO 0-50 100*1 76 100 76 76 100 139 200 atm. 1000 100 76 51-8 99-8 1377 76 76 76/15 76 0036728 3671 36600 3661 36609 367313 367750 434 218 486 3669 37128 37ioo 37073 37602 37536 374IQ 37972 37906 37703 37282 3719 3854 3903 C., 1903 R., 1847 C., 1903 R., 1847 R. M. C, 1903 C., 1903 A., 1890 A., 1890 A., 1890 R., 1847 C., 1903 Air J> H; R.M. R., 1847 P.D.,'o6 R.,i847 A., Amagat; C., Chappuis; J. P., Jac- querod & Perrot ; K. R., Kuenen & Randall ; M., Melander; M. N., Makower & Noble; O., Onnes ; P. D., Perman & Davies ; R., Regnault ; R. M., Richards & Marks ; T. J., Tr avers & Jacquerod. He CO ,, CO. ^o S0 2 0-IOO 0-1067 O-IOO O-IOO O-IOO O-IOO O-IOO O-IOO O-IOO O-IOO 0-1067 O-IOO O-IOO O-IOO O-IOO 0-1067 O-IOO 0-20 O-IOO 0-1067 cm. Hg. 58 1-32 I0'0 17-24 76 100*1 2OO 2OOO 23 52 70 100 109 53 79 100 66 18-23 52 70 IOO 99-8 24 76 76 0037666 37172 36630 36650 36744 3887 36643 36626 366255 366256 36627 36683 36718 367440 36738 36652 36627 36616 3668 3667 36648 36981 37335 37262 36756 3676 3845 M., 1892 R., 1847 C, 1903 R., 1847 J. P" T. J., '02 C., i"oo3 O., 1908 C., 1903 M.N.,'03 J.P. T.J.,'02 O., 1908 K. R, '96 R., p i8 47 C., 1903 J R. , 1847 R., 1847 58 COEFFICIENTS OF EXPANSION COEFFICIENTS OF CUBICAL EXPANSION OF LIQUIDS As with solids (see p. 55), if the temperature interval is not large, a linear equation 2/ t = VQ(I + at) may be employed to show the relation between the volume (v) of a liquid and its temperature (/). The mean coefficient (o) 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. TOater H scale. 17 to 4O o 3 i3oi9/(/) '0465769 + 'O 5 86797/ -077336/2 Chappuis, '97 (see p. 24 and below) 17 to 100 Dcn~itv i ('- 3-982). /+ 273. 350 -/ Thiesen, '03 466,700 *+6 7 365 -/ Mercury 24 to 299 00018179 + '09175^ + Oio35i/ 2 Regnault, '47 (see p. 24) to 100 00018169 '052847; + o 9 ii5/ 2 (Broch) Chappuis, '07 -lOtoSOO 000180555 + -o 7 i244/ + -o, 254/ 2 ( Callendar & \ Moss, 1911 (calcd.) to ISO 000181385 + 'O 8 977o/ + 'O 10 i83i8/ 2 Donaldson,' 1 2 Liquid. a Liquid. a Liquid. a Liquid. a X I0~ 6 X I0~ 6 X I0~ 5 X I0~ 5 Acetic acid . 107 Ether, ethyl . I6 3 Pentane . . 159 Water, 60-80 587 Alcohol, me. . 122 Ethyl bromide 137 Toluene . . 109 ethyl 110 Glycerine . . 53 Turpentine . 94 Solutions amyl 93 Mercury (see above) Xylol(m) . 101 CaCl 2 , 5 -8% . 25-0 Aniline . . 85 Methyl iodide 121 Water,5-io 5*3 4o-9% 45'8 Benzene . . 124 Oil, olive . . 70 10-20 15-0 Nad, 26% . 43'6 CS 2 ... 121 paraffin . 90 20-40 30-2 H 2 S0 4 , 100% 57 Chloroform . 126 ,,20-i99 no 40-60 45-8 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 i C. at some specified temperature. The 15 calorie is about i part in 1000 greater than the 20 calorie. (See p. 59.) See Griffith's "Thermal Measurement of Energy," 1901. Observer. Calorie. Ergs. Observer. Calorie. Ergs. Toule, 184.3 . N. scale 20 C. X I0 7 4-169 N. scale X IO T Rowland, 1878. . . . Griffiths, 1893 . . . . 20 20 4'lSo 4-I84 Crdmieu & Rispail, 1908 Reynolds & Moorby, 1897 Mean 4-185 4'i8j. Schuster and Gannon, 1894 20 4'i8l Barnes, 1909 (deduced) Mean 4-185 Callendar and Barnes, l8qq , 20 4' 1 80 59 SPECIFIC HEATS SPECIFIC HEAT OF WATER Callendar and Barnes (JPhil. Trans., 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*180 x io 7 ergs, being the mean of the results of Rowland (1879) and of Reynolds and Moorby (reduced), each of whom used a mechanical method of determining U 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., according to Callendar and Barnes. 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 ( = ^ of 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. Temp. Specific heat. Joules. -5C. 5 10 15 20 25 30 35 40 1-0158 1*0094 1*0054 i -0027 rooii 1-0000 9992 9987 9983 9982 4-246 4-219 4-202 4-191 4-184 4*180 4-177 4'i75 4' 1 73 4*173 45 C 50 55 60 65 70 75 80 85 90 9983 9987 999 2 'OOOO 0008 0016 0024 0033 0043 0053 4-173 4-175 4-177 4-180 4-183 4-187 4-190 4-194 4-198 4-202 95 C. 100 120 140 160 180 200 220 1*0063 1-0074 1*0121 I-OI76 I -0238 I-0308 1*0384 1-0467 4*206 4-2II 4-23I 4*254 4-280 4-309 4-341 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. Specific heat 0C. 0335 20 0333 0331 60 0329 80 0328 100 (-0327) 200 (032) SPECIFIC HEATS OF THE ELEMENTS For gases, see p. 61. (See Waterman, Phys. Rev., 1896.) Siab stance. Aluminium Antimony . . Arsenic, cryst. amorph Barium . . Beryllium . . Bismuth . . Boron, amor. Bromine, solid Temperature. Observer. Substance. -240 600 -186 to -79, 17 to 92 21 to 68 21 to 65 -185 to 20 to 100 -186 22 to 100 to 100 -78 to -20 0092 2096 282 '0462 0508 083 '076 068 425 0284 0304 307 084 Nernst, 1912 Griffiths, '14 Richards, '93 Behn, 1900 Gaede, 1902 B. & W., 1868 N. & B', 1906 N. & P., 1880 Giebe, 1903 W., 1896 M.&G., 1893 Regnault, '49 Bromide, liqd. Cadmium . . Caesium . . Calcium . , Carbon Gas carbon . Charcoal Graphite Temperature. Sp. heat. 13 to 45 -165 Oto26 -185 to 20 to 100 24 to 68 Oto24 to 224 -50 11 202 107 0491 0547! 048 157 149 204 165 238 114 160 297 Observer. Andrews, '48 Griffiths, '14 E. & G., 1900 N. & B., 1906 Be., 1906 B. &W., 1868 H.F.Weber, 3 75 SPECIFIC HEATS 6O 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 . -185 0023 Nernst, 1912 Phosphorus i> 11 173 H.F.Weber,'75 yellow -78 to 10 17 Regnault, 1849 > 206 273 M 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 Chromium. . -200 067 Adler, 1903 18 to 100 0324 M (i- 4 %Fe&Si) 104 1230 0461 Tilden, 1903 100 112 M 3 otassium . . -78 to 23 166 Schiiz, 1892 400 133 n Rhodium . . 10 to 97 058 Regnault, 1862 Cobalt . . . -182 to 15 082 Tilden, 1903 Ruthenium . to 100 061 Bunsen, 1870 15 to 100 103 ?> Selenium, cryst. 22 to 62 084 B. &W., 1868 15 to 630 123 H ,. amorph. 18 to 38 095 Copper . . . -250 0035 Nernst, 1912 Silicon, cryst. - 185 to 20 123 N. & B., 1906 0909 Griffiths, '14 57 183 H.F.Weber,'75 97-5 0952 M 232 203 9) Didymium . Gallium, solid to 100 12 to 23 046 079 H., 1876 B., 1878 Silver . . -238 0146 0556 Nernst, 1912 Griffiths, '14 liquid 12 to 119 080 9J 427 059 Tilden, 1903 Germanium . to 100 074 N. & P., 1887 Sodium . . . -150 2466 Griffiths, '14 Gold . . . -185 to 20 035 N. & B., 1906 2829 n 18 to 99 0303 Voigt, 1893 138 3189 M 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 0323 1 Tantalum . . -185 to 20 033 N. &B., 1906 Iron .... -133 0770 Griffiths, '14 58 036 v. Bolton, 1905 1045 '' Tellurium, cry s . 15 to 100 048 Fabre, 1887 97-6 1137 Thallium . . -192 to 20 0300 Schmitz, 1903 to 1100 153 Harker, 1905 20 to 100 0326 Lanthanum . to 100 045 H., 1876 Thorium . . to 100 028 Nilson, 1883 Lead . . . -250 0143 Griffiths, '14 Tin .... -186 to -79 0486 Behn, 1900 0302 0536 Griffiths, '14 300 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 to 100 113 N.&P., 1887 Magnesium . -186 to -79 '189 Behn, 1900 to 440 162 5> 18 to 99 246 Voigt, 1893 Tungsten . . -185 to 20 036 N.&B., 1906 225 28l Stiicker, 1905 20 to 100 034 Gin, 1908 Manganese . Mercury . . 14 to 97 See preced 122 ing p Regnault, 1862 age. Uranium . . 11 to 98 Oto98 062 028 Regnault, 1840 Bliimcke, 1885 Molybdenum. -185 to 20 15 to 91 072 N. & B., 1906 D. & G., 1901 Vanadium . . Zinc . : . . to 100 -233 115 0271 Mache, 1897 Nernst, 1912 Nickel . . . -186 to 18 086 Behn, 1898 0918 Griffiths, '14 18 to 100 'lOQ 300 104 Naccari, 1888 Osmium . . 19 to 98 S 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 & Bernoulli ; N. & P., Nilson & Pettersson ; W., Waterman. 61 SPECIFIC HEATS SPECIFIC HEATS OF GASES AND VAPOURS The values at const, pressure are, unless otherwise stated, all at atmospheric pressure. The specific heats given are calories per gram of gas per degree C. at the temp, stated. Gas. Temp. Sp. ht. Observer. Gas. Temp. Sp. ht. Observer. AT CONSTANT PRESSURE (^) Ammonia, NH 3 . . Nitrous oxide, N 2 O Nitric oxide, NO . N. peroxide, NO 2 . H,S. 23-100 26-103 13-172 27-67 20-206 86-190 34-115 27-118 101-223 108-220 25-111 179-249 520 213 232 1*625 245 160 591 404 299 144 458 '453 428 506 \Wiedemann, / 1876 Regnault, '62 B. & O., 1883 Regnault, '62 >5 55 Lussana, '94 55 55 )Wiedemann, J 1877 Regnault, '62 Regnault, '62 W., 1876 Regnault, '62 Air (dry) .... 55 55 .... 55 )5 .... 55 55 .... 55 55 .... 70 atmos. Argon ..... 20 C. 100 20-440 20-98 -102-17 -50 20-90 -200 20-440 20-800 -190 16-343 19-388 206-377 23-99 100 atmos. 100 100 2417 2430 2366 2372 2372 312 123 3:402- 3788 2350 '43 2419 2497 *347 115 055 034 242 2010 221 2670 4652 4878 Swann, 1909 55 55 H. & A., 1905 ) Witkowski, 1896 ) 5 55 D., 1897 Lussana, 1894 55 55 * H. & H.,'o7 Alt, 1904 H. & A., 1905 * ," " Alt, 1904 Strecker, 3 8i '82 )> >5 W., 1876 *H. &H M '07 Swann, 1909 Lussana, '94 *H. &H.,'o7 Brinkworth,'i5 CS 2 Methane, CH 4 . . Ethylene C 2 H 4 . . Benzene, C 6 H 6 . . Chloroform CHC1 3 . Me. alcohol CH 4 O. Et. alcohol C 2 H 6 O . ether (C 2 H 6 ) 2 0. Turpentine, C 10 H 16 Hydrogen . . . 30 atmos. Nitrogen .... (Kq.) . Oxygen .... ;:. (Hq.) : : Chlorine .... Bromine .... AT CONSTANT VOLUME (c v ) Air,t i atmos . . Hydrogen J . . . Carbon dioxide . Argon . ^.50 c. 55 0-2000 100 1715 2*402 1650 0746 175 340 Joly, 1891 55 55 I8 94 Pier, 1909 55 If Carbon monoxide . dioxide . . 55 > 3 Steam . Nitrogen || . . . Water vapour . . B. & O., Berthelot & Ogier; D., Dittenberger ; H. & A., Holborn & Austin (Reichsanstalt) ; W., Wiedemann. * H. & H., Holborn /Nitrogen (0-1400), cp = '2350 + 'ooooigt } Mean specific and Henning j C0 2 (0-1400), cp = '2010 + '0000742* - -o 7 i8/ I heats between (Reichsanstalt). ( Steam (100-1400), cp = '4669 - -ooooi68/ + 'tyw? J o and t C. t Air, c v - -1715 + -02788^ where pis the density (gm./c.c.). CO 2 , c v - '165 + '2125^ + -34/ 2 , p being density. 1 H, c v diminishes with increasing density and falling temp. H N, c v = '175 + -00016*, / being the temp. RATIO OF THE SPECIFIC HEATS FOR GASES AND VAPOURS 7 = the ratio of the specific heat at constant pressure to that at constant volume. 7 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 (Cle'ment and' Desormes, Lummer and Pringsheim's methods respectively), 7 can be deduced from/z/V = const, or tatf- * = const. (See Capstick, "Science Progress," 1895 ; and Moody, Phys. Rev., Ap., 1912.) Gas. Temp. 7 Observer. Gas. Temp. 7 Observer. Monatomic gases Helium .... Argon . . . 0C. 19 19 19 310 5-14 15 I-6 3 1-667 642 689 666 666 402 401 401 414 B. & G., 1907 Niemeyer, '02 Ramsay, 1912 > K.&W.,i876 L. & P., 1898 Stevens, 1905 Makower, '03 Hartmann,'o2 Air (dry) .... 55 .... 55 .... 55 .... 5, 200 \ ,., atmos. / Hydrogen . . . 55 ... Nitrogen .... Oxygen . ... Carbon monoxide . Nitric oxide, NO . 500 900 -79-3 -79-3 4r-iG 5-14 402 '402 '399 '39 405 828 '333 419 408 4i 400 401 '394 Koch, 1907 F., 1908 Kalahne, '03 Koch, 1907 >J 5 > 55 Hartmann,'o5 L. & P^_i^98 Cazin, re2 L. &P., 18^8 Leduc, 1898 Masson Krypton .... Xenon ..... Mercury vapour . Diatomic gases Air (dry) .... M >5 * 55 55 .... B. & G., Behn & Geiger ; F. Fiirstenau ; K. & W. Kundt & Warburg ; L. & P., Lummer & Pringsheim. 62 SPECIFIC HEATS RATIO OF THE SPECIFIC HEATS FOR GASES AND VAPOURS (eontd.) Gas. Temp. V Observer. Gas. Temp. 7 Observer. Triatoxnic gases Acetylene, C 2 H 2 . 1-26 M.& F., 1897 Ozone 100 (?) 4-11 500 20 150 1-29* 1-305 1-300 1-306 1-26 1-336 1-324 1*172 1*31 Jacobs, 1905 Makower, '03 L. &P., 1898 Hartmann, '05 F., 1908 Leduc, 1898 Natanson, '85 Ethylene Benzene, Chlorofor CHC1 3 CC1 4 . Me. alcol broi chic C 2 H 4 . . C 6 H 6 . . m, i 20 997 998 997 19-30 1-264 1-40 1-105 1*110 1*150 1-130 1-256 1-274 1-279 Capstick, '95 Pagliani, '96 Stevens, '02 Muller, 1883 Stephens, '02 Capstick, '95 Stevens, '02 Capstick, '93 Water vapour . . Carbon dioxide . . Ammonia, NH S Nitrous oxide, N a O Nitrogen jN 2 O 4 . . peroxide JNO 2 . . 10! . . . nide . . >ride . . H 2 S. 1-340 Capstick, '95 iodide . . . Et. alcohol . . . 53 1-286 Jaeger, 1889 CS, . Sulphur dioxide. | 16-34 500 1-26 1*2 Muller, 1883 F., 1908 bromide . . . chloride . . . 998 22-7 I-I35 1-188 1-187 Stevens, '02 Capstick, '93 Polyatomic gases ether .... 12-20 I -024 Low, 1894 Methane, CH 4 . . Ethane, C 2 H 6 . . I'22 Capstick, '93 r Daniel & Acetic acid . . . 99-7 136-5 1*112 I-I47 Stevens, '02 M Propane, C 3 H 8 . . I-I30 \ Pierron, '99 * Extrapolated ; F., Furstenau ; L. & P., Lummer & Pringsheim ; M. & F ., Maneuvrier and Fournier. SPECIFIC HEATS OF VARIOUS BODIES In most cases, the specific heats given must only be regarded as average values. Substance. Temp. Sp. ht. Substance. Temp. Sp. ht. Substance. Temp. Sp. ht. Alloys C Oil, linseed . . 20 44 I Ice (N & E) . -250 '0242 Brass, red . . 090 olive . . 7 '47 N . -160 273 yellow . Eureka . . . 18 088 098 paraffin 20-60 (-51 to I '54 "I -21 to -1 } "502 (Constantan) German silver . 0-100 095 rape . . sperm . . 20 20 "493 t Indiarubber 15-100 /*27 to I -48 Solder * ... 042 Sea-water ;*i Toluene . . . 17 18 '94 40 Marble, white . 18 (21 tO \ '22 Liquids- Turpentine . , 18 42 NaCl (N&E) -248 0099 Alcohol, amyl . 18 '55 , , 5 , -38 197 ethyl . "547 Miscel- i t . . 10 21 99 99 40 648 laneous KC1 (N & E) -250 0156 methyl 12 601 Asbestos . . 20-100 20 M -187 117 Aniline f . . . Benzene . 15 10 5H 340 Basalt . . 20-100 j"20tO 1 '24 Paraffin wax . 277 0-20 177 6 9 40 423 Ebonite . . . 20-100 33 Porcelain || 15-1000 255 Brine, j -20 69 Fluorspar, CaF 2 30 *2I Quartz, SiO 2 . 174 density =1*2 [ 71 Glass, crown . 10-50 16 . 350 279 (Marker) 15 72 flint . . 10-50 12 Sand . . * . 20-100 19 Ether, ethyl . 18 >6 Jena i6"'< 18 19 Silica (fused) ^ 15-200 '200 Glycerine . . 18-50 58 Jena 5Q"'i 18 19 > 15-800 248 Oil, castor . . 20 508: Granite . . . 20-100 r*i9 to \ -20 * S = -0422 + -000038/. Sn 54%, Pb 46%. Ezer Griffiths, 1914. t Griffiths, Phil. Mag., 1893. J Ezer Griffiths & Williams, 1918. N. & E. Nernst & Eucken, 1912. See p. 78. H Harker, 1905. ^ Greenwood, 1911. 63 LATENT HEATS 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. Lt. ht. Observer, etc. -6'5 C. O O O cals. 76'03 79*59 80-02 7977 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 15 C). VARIOUS SUBSTANCES Substance. Temp. Lt. ht. Substance. Temp. Lt. ht. Substance. Temp. Lt. ht. Elements- c. cals. . c. cals. Compounds C. cals. Aluminium . 657 77 Platinum . . 1750 27 NH, . . -75 108 Bismuth . . 269 13 Potassium 62 16 NaNO 8 . 63 Cadmium . . 321 14 Silver . . . 960 22 KN0 3 . . 339 47 Copper . . . Lead . . . 327 43 5 Sodium (G.) Sulphur . . 97-6 27-5 9 H 2 SO 4 . . Acetic acid 10-3 4 24 44 Mercury . . 3 Tin .... 232 Benzene . 5*4 30 Palladium 1550 36 Zinc. . . . 418 28 Glycerine . 13 42 Phosphorus . 44 5 Naphthalene 80 35 G., Ezer Griffiths, 1914. 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 latent heat of vaporisation vanishes at the critical temperature. Trouton'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 > 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. 59). 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 i84 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. Temp, range of ezpts. Latent heat L, at t C. Regnault, 1847 . 63-i 94 C. L t = 606-5 -695 / Griffiths, 1895 . 30 and 40 Lt = 598-0 - -605* Henning, Ann. d. Phys. t 1906, !3o-ioo (L t = 599-4 - *6o/, to -3 ' \or L t = 94*3 (365 - 0'? I * to -i % 1909 . . . ioo-i8o Lt = 538*97 *6428(/ 100) - "03834 :/-ioo) a Smith, Phys.\ Rev., 1907 ./ I4-40 L, = 597-2 '58o/ 64 LATENT HEATS LATENT HEAT OF STEAM (contd.) In terms of 15 calorie. Kegnault, 1847. Griffiths, 1895. Joly, 1895. Callendar, Dieterici, * 1905. Henning, 1906. Smith, 1911. Richards & Matthews, 1911. to - - 6o6f 598 1 595 1 596*0 1 599 1 __ 537 537*5 1 54o 540 538-9 11 539*4 540*5 538-0 * From sp. ht of steam experiments and total heat formula, t 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. 59). || Carlton-Sutton, 1917. 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. SnCl 4 . CC1 4 . Pent- ane (). Methyl Ethyl Propyl Ethyl ether. Methyl Ethyl Propyl Acetic acid. Temp. Ben- zene. Acetate. Alcohol. C. . cals. cals. cals. cals. 289-2 cals. 22O'9 cals. cals. 92-52 cals. cals. cals. cals. cals. 20 284*5 220-6 4 84-0-, 40 i $4*3! 277-8 2I8-7 82-83 87*02 60 80-07 269-4 2I3-4 4 98-59 80 46-00 75*33 259-0 206-4 I73-0 73*50 94*07 85-78 79-80 9i*5S 95^ 100 3176 44*15 69-94 246-0 197*1 164*0 68-42 88-39 82-15 76*33 92-32 91-41 120 30-54 42-08 64-48 232-0 184-2 153*0 62-24 8287 77-53 71-84 94*3* 86-58 140 2 9*12 39*92 56-58 216-1 I7I-I 142-4 55'93 76-83 72-24 67-66 91-8; 82-82 160 27-69 37*95 47-42 198-3 156-9 I29'0 46-07 69-96 65-91 62-80 89*6; 78*94 180 26-29 35*40 JC'OI I77-2 139*2 116-3 V* 7 6roo 59*87 57*23 87-71 74-62 200 2 4'57 32-61 24-68* I5I-8 II6-6 102 2 8} 50*56 52-71 5078 68-81 220 22-82 29-45 II2-5 88-2 8S '3 34'87 42-63 42-40 82-05 62-24 240 20-86 84*5t 40*3 2o*99 27-17 30-70 78-1* 54- 1 1 260 18-50 20-07 33*5 12-03!! 72-26 43*82 280 15-60 10-43 63-4* > 27*43 Crit. \ temp./ 3i8- 7 283 -i i97-2 240 243-! 2630-7 I93'8 233*7 250' i 27 6, 3 2i-6 288-5 * At 190. t At 230. J At 190. At 230. || At 249, U At 275 C. Substance. Temp. Lt. ht. Substance. Temp. Lt. ht. Substance. Temp. Lt. ht. C. cals. C. cals. C. cals. Mercury . . 358 68 Liquid N 2 O . -20 6 7 Chloroform . 61 58 Sulphur . ^62 M NH S . 341 Et. bromide . 38 60 Phosphorus . Liquid H 2 . . 287 130 123 n CO 2 22 57 32 propionate 100 iodide . . 71 79 47 O, > . -188 58 it S0 2 . 10 96 formate 50 98 N 2 . . 50 CS 2 . 4 6 85 Am. alcohol . 131 120 air . . c. 50 Me. formate . 32*5 Aniline ... 104 Cl. . 22 67 M iodide . . 42 46 Toluene . . in 8 4 Bromine . . 58 46 Chloroform . 67 Turpentine. . 159 70 Iodine . 174 24 65 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. Phys., 1878; T.B., mean of both these observers' values. For organic compounds, see p. 67. INORGANIC COMPOUNDS Compound. Mol. H.F. in calories. Compound. Mol. H.F. in calories. Compound. Mol. H.F. in calories. Non-Metals XIO 3 X I0 3 XIO 3 HClgas . . 22-0, T. CO 2 from j O7"2 "R T 1 NH 4 Cl.Aq . 72-4 HCl.Aq . . HBr gas . . 39'3, T. 8-4, T. amorph. C / CO 2 from | y/ j, " A r\ /i i "R (NH 4 ) 2 S0 4 . (NH 4 ) 2 S0 4 .Aq 283, T.B. 280-6 HBr.Aq . . 28-6, T. diamond / 94 3, - 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 . . HF . . + 13-2, T.B. -t-38'5 SiO 2 Aq; crys. As 2 O 3 . . [Si 1 80, B. 155, T. Ba(OH) 2 . . BaCl 2 . . . 217, T. 197, T. H 2 01iq. . . 68-4, T. As 2 O 5 . . . 219, T. BaCl 2 Aq . . . . 69-0, B. CC1 4 from 1 6 B Bi 2 3 . . . 20 gas . . 58-1, B. diamond / 70, i. BiCI 3 . . . 91, T. H 2 2 .Aq. . H 2 S from 1 47*o 2'7 T SbCl 3 solid . SbCl 6 liq. . 91-4, T. 105, T. Cd(OH) 2 . .| 66, T. rhombic S. ./ */ * CS 2 from j CdCl 2 . ? . 93, T. NH 3 . . . 12 diamond &> -19, B. CdSO 4 . . . 222, T. AsH 3 . . . SbH 3 . . . SiH 4 . . . -367 -87, B. 25 rhombic S. .J C 2 N 2 gas \ from diam. ./ -74, B. CdSO 4 .8/3H 2 O] on sol. in Aq J CdSO 4 .Aq . + 2-66,T. 2327, T. SO 2 from | H 2 SO 4 liq. . 193 T. Cs 2 O. . . . 100 rhombic S. ./ 70 H 2 S0 4 .Aq ] CaO . . . .} SO 3 liq. from \ from rhombic > 210, T. Moissan.f J 45 rhombic S. ./ 103 S J Ca(OH) 2 , . 22Q N 2 ... NO .... -19 -21-6, T. HN0 3 liq. . HN0 3 .Aq . 41-6, B. 49 CaC 2 . . .. CaCl 2 . . . -7-25 170, T. N 2 3 . . . N 02/22 . . -21-4, B. -17, B. HCN. gas | from diam. / -30-5 CaCl 2 .Aq. . CaSO. . . . 187-4, T. 3i8, T. N 2 6 liq '. ' P 2 O 5 solid . -7'6,B. 3'6, T. 369 HCN liq. . H 3 P0 4 Hq. . -24-8 302 CaC0 3 . . . Ca(N0 3 ) 2 . . CoO .... 270, T. 202, B. 64 P 2 6 .Aq. . CO from \ amorph. C. ./ 405 29, T. Metals A1 2 O S . . . AlClg . . . 380, B. 161 CoCl, . .- . QoS0 4 .7H 2 Co(N0 3 ) r 6H 2 76-5, T. 234, T. 119, T. CO from ) diamond .( 26-1, B. Al 2 (S0 4 ) 3 .Aq NH 4 C1 . . 880 76-3, T.B. CuO. . . . CuCl 2 ... 37-2, T. 5 r6 66 HEATS OF FORMATION INORGANIC COMPOUNDS (amid.} Compound. Mol. H.F. in calories. Compound. Mol. H.F. in calories. Compound. Mol. H.F. in calories. Metals (contd^} X IO 3 X IO 3 X IO 3 CuSO 4 . . . 183, T. MgCl, . . 151, T. AgCl . . . 29-2, T.B. CuSO 4 .Aq . CuS0 4 .5H 2 \ on sol. in Aq ./ 198-8, T. -275 MgS0 4 . . . MgS0 4 .Aq . MnO . . . 302, T. 322 91 Na 2 O . . . NaHO . . . NaHO.Aq . 102 112 to 100 3, T.B. 2, T.B. AuBr 8 . . 8-8, T. MnCl 2 . . 112 NaCl . 97 8, T.B. AuCL 23, T. HgoO . 24,'Q T. NaNO 3 . in T R FeO . . . .j 64-6 **f>J ** HgO . \ *+ 7} 2I'I Na,S0 4 . \ 328-3, T.B. Fe 2 3 /4oo . .! 196 Hg 2 S0 4 . 175 Na 2 C0 3 , 272 , T.B. Le Chatelier .J HgCl . . 31-3 SrO . . . 130, T.B. FeSO 4 .7H 2 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, . . 74'5, T. SrCl, . Aq 196 T. PbO . . . . 50-3, T. NiSO 4 .Aq . 229, T. 1*1,0. . 42 '2,T. Pb0 2 . . . . 62-4 PtCl 4 . . 59'4 T1C1 . . . 48-6, T. PbCl 2 . . . 83, T. K 2 O . . . 97 T1 2 SO 4 . . 221 > PbSO 4 . . , 216, T. KHO . 104, B.T. SnO . . . . 70 Pb(N0 3 ), . . 105-5 KHO.Aq 117, B.T. SnCl 2 . Si, T. Pb(N0 3 ) 2 .Aq 97-9 KC1 . . . 106, B.T. SnCl 4 . . 128 Li 2 O . . . 140 KCl.Aq . . ior6, T. ZnO . . . 85-4, T. LiOH . . , in KN0 3 . . 119, B.T. ZnCl 2 . 97 3, T.B. LiCl . . . . 94, T. K 2 S0 4 . . 344, T.B. Zn(N0 3 ), .Aq 132 LiCLAq . 102-4 Ag 2 . . 5'9, T. ZnSO 4 . 230-3, T.B. Li 2 SO 4 . . LiN0 3 . . 334, T. 112, T. AgN0 3 . 7>B. ZnSO 4 .Aq . ZnSO 4 .7H 2 O j 248-7 . . 287, T.B. MgO. . . 143, B. AgN0 3 .Aq . 233, 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 4- 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 HP HN0 3 HCN H 2 S0 4 Wco. 1H 3 P0 4 1 Oxalic. X IO 3 XIO 3 XIO 3 X IO 3 X IO 3 X IO 3 XIO 3 X IO 3 iNaOH . I374,T.; i6- 3 ,T. I37,T.; 2-8 15-64, T. io- 1, T. ; 14-8, T. I3'8,T. 137, B. 13*5, B. 10-2, B. 2NaOH . - 3i'38t, T. 20-2 , T. 27-1* T. 28- 3 ,T. iLiOH . 13-85, T. 16-4 t 2-93 15-64, T. iKOH . 137, T. ; 16-1 13-8, T. 2-8, T. 1 57, T.B. _ T5 IO I xi I3'8,B. 13-6, B. iNH 4 OH. 15-2 12-3, T. 1-3, B. 14-3, T.B. 8-4, T. ; I3'5, B. 127 12-4, B.' 5*3, B. . 4Ca(OH) a 14-0, B. 18-4 1 13-9, B. 3'2 15-6, T. 9-8, f B/ iSr(OH) 2 . 13-8, T. 17*8 1 I3*9> B. 3-15 I5'4, T. io-4,tT.B. |Ba(OH) a 16-1 14-1, T.; 3-15 18-4, B.T. iro,fT.B. I3-9, B. iMg(OH). 13-8, B. 15-2 I3'8,T. I'S i5'3, B.T. 8'95,t B. }Cu(OH) 2 7'5, T. lO'I 7-6 9-2 ~~ ~ ~ * 3NaOH gives 34-0 X io 8 , T. f Base in solid state. J iH,SO 4 IH.CO,. 67 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. 65. 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. 1 6 gms. of methane, CH 4 , give out 212,000 gram calories of heat when burnt at constant pressnre, to water and CO 2 at 18 C. (T., Thomsen, " Thermochemistry ; " B., Berthelot.) Compound. H.C. H.F. Compound. H.C. u. X IO 3 X IO 3 X IO 3 X IO 3 Methane, CH 4 . . .{ 212, T.I 213, B./ 217 Me. acetate, C 3 H 6 O 2 . Carb. bisulphide, CS 2 . 399, T. 265, T. 967 ~ 2O Ethane, C 2 H 6 . . . .{ 370, T.j 372, B./ 28-6 Methylamine, CH 6 N . Dimethylamine, C 2 H 7 N 258, T. 420, T. 9' 5 127 Propane, C 3 H 8 . . . Acetylene, C 2 H 2 . . .| 529, T. 3io, T.j 3H / -47-8 Aniline, C 6 H 7 N . . . Pyridine, C 5 H 6 N. . . Sugar, Ci 2 H 22 On. . 838, T. 675, T. 1364 17-4 19*4 Ethylene, C 2 H 4 . . . 333, T. -27 Illuminating gas pen 5600 to Benzene, C 6 H 6 . . . 799, T. -12-5 cub. metre . . . ./ 6500 Naphthalene, Ci H 8 . 1239 Coal (anthracite) . . 7-6 to 3er gm. Toluene, C 7 H 8 . . . 956, T. -3*5 8-4 Me. alcohol, CH 4 O . . 182, T. Coal (brown) .... 47 , Me. chloride, CH 3 C1 177 T O'vA C k e 6-0 Chloroform, CHC1 3 . . 1 //, x - IO7 T. 2-l'T Paraffin oil 9-8 " " Et. alcohol,' C 2 H 6 O . . L\J/ , J. . 340, T. +*~4- 1 Wood (3'9 toj " " Et. ether, C 4 H 10 O . . 660, T. 70 \4'4 / Et. chloride, C 2 H 6 C1 . 334, T. 30-7 Albumens Acetic aldehyde, C 2 H 4 O _O_ *T d.8'7 ?-86 Formic acid, CH 2 O 2 60*4 T *r / QC'Q Flesh j vw 5-66 " " Acetic acid, C 2 H 4 O 2 . wy ^J.j A , 225, T. V3 V I05-3 White of egg .... j w 5-67 Propionic acid, C 3 H 6 O 2 387, T. I09-4 Yolk of egg .... 8-12 ., Me. formate, C 2 H 4 O 2 . 241, T. 8 9 -4 Haemoglobin .... 5'9 ), 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, 30O H 2 O), 17,300 calories per 36-5 grams of HC1 are set free ; diluting 2NaCl, H 2 O( = 20) to (2NaCl, 100H 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 HN0 3 H 2 80 4 NaHO NH 3 * 2NaCl 2NaN0 3 Ka 2 S0 4 ZnCL Zn(N0 3 ), n = n = n = 3 n = 20 n = 12 n = 50 n = 5 n = 10 H 2 5-37 11-36 H 2 5 v io s If 6 - 6 H 2 5 38 H 2 O 5 7 Xio" 2-I 3 2'Q H 2 O 3 Xio* 1-26 38S H 2 O 100 200 Xio' -1-06 -1-31 H 2 O 50 100 -2-26 -3-29 H 2 100 200 Xxo* -66 5 I-I3 H 2 O 10 20 Xio* 1-85 ris H 2 15 20 x - 5 14-96 10 7-32 49 16-7 5-8 21 400 -1-41 200 -3-86 400 -1-38 50 50 50 17-1 20 7-46 199 17-1 25 V26 9-5 02 400 -4;I9 800 -1-48 100 6-8 1 100 300 17-3 320 7-49 1600 17-9 200 2*94 110 00 1 "" ~~ 400 8-02 200 * Heat developed on diluting NH,.H 2 O to NH 3 .2ooH a O (Berthelot). SOLAR CONSTANT 68 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 Ste/an's law, E = 730 cm. deg.), we have (to i % at least) EX = fiA""^*""** * Ray leigtts formula (See Preston's "Heat," 3rd edit.; Kayser's " Spectroscopie," II.; Lorentz's " Theory of Electrons," 1910.) WIEN'S DISPLACEMENT LAW A W = const. = A. (See above.) A is measured in cms. STEFAN'S LAW Total radiation from a full radiator = 5-89 572 Kurlbaum, 1912 Shakespeare, 1911 Keene, 1912 Coblentz, 1917 A. d. P., Ann. der Phys.; B. B., Berlin Ber.; C. R., Compt. Rend. ^ AND r 2 The determination of the constant c^ in Planck's equation has received considerable attention on account of its importance in optical pyrometry. A knowledge of ^ is not, how- ever, necessary for such work. c \ '353 erg.-cm. 2 sec." 1 . C 2 is given below in micron-degrees, i.e. lo" 4 cm. degrees. Observer. 14,350 micron-degrees H,300 14,350 Holborn and Valentiner, 1912 Warburg, 1916 Coblentz, 1917 THE UNIVERSAL CONSTANT h Planck's radiation law (above) may also be written where c is the velocity of light, R is the gas constant (p. 5), and h is Planck's universal constant. Planck's constant on the quantum theory is the constant of proportionality connecting the energy of a quantum with the frequency of vibration (*), i.e. the energy of a quantum = hv. h is intimately related with the several radiation constants, and may be determined by use of either of the following relations h = . . 1000 7-0 , ,, (Krakatoa wave; 1883 Sound-waves from sparks 3-50-4-45 ,t Topler, 1908 Hydrogen . ... 12-86 Zoch, 1866 VI72 Dulong, 1820 - 184-7 y\*/ m tt 1*737 Cook, 1906 Nitrous oxide, N 2 O * / j/ 2-60 Wullner, 1878 Ammonia, NH 3 . . 4'l6 Carbon monoxide . 3'37 r , ), Carbon dioxide . . 10-24 2-573 ,, Low, 1894 Coal-gas . . 4'9-5'iS Sulphur dioxide . . 2-09 Masson, 1857 Water-vapour . . 4'o M (satd.) no 4-I3 Treitz, 1903 Liquids Water 81 I4."jr x IO 4 Collad on & Sturm, 1827 4 * 'r J J ** I VQQ Martini, 1888 25 waves 18 J 77 , 14^7 I7-3-20-I t Threlfall & Adair, 1889 (sea) Explosion Alcohol (abs ),C 2 H 6 8-4 12-6 Martini, 1888 Ether, (C 2 H 6 ) 2 . 1 1-4 tt Turpentine, C 10 H 16 . 3-5 137 H * Free from CO,, t The range of speeds is given by varying intensities. J Reichsanstalt. The values for metals are due to Wertheim, 184$ ; Masson, 1857 ; and Gerossa, 1888. Solid. Velocity golid Velocity Solid. Velocity cms./sec. cms./sec. 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 Cobalt . . . 47*2 Platinum . . 26-8 , grain) Copper . . . 39-7 , Silver . . . 26-4 , Fir 42-53 ,, Gold .... 20-8 , Tin .... 24-9 , . Mahogany 41-46 Iron (wrought) 49-51, Zinc - 36-8 , Oak 40-44 (cast). . c. 43 , Glass (soda) . 50-53, Pine c- 33 Steel .... 47-52, (flint) . c. 40 Indiarubber . '5-7 SOUND 72 VELOCITY (IN AIR) AND PRESSURE Koch (1907). Press, in atmos. 1 25 50 100 150 200 Belative Velocity of Sound. 0C. -79-3C. I -000 1-008 I'022 I-064 ri32 1*220 842 831 830 885 1-047 1-239 SENSITIVENESS OF EAR TO PITCH Bayleigh (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 = length of pipe. Closed pipe Open pipe . , 4L 4L 4^> V' V> 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. One end fixed Distance of Nodes from one end. 224 L ; 776L I32L; '5L; '868L / -094L ; '356L \ V-644L; -906L/ 226L I32L ; -5L Frequency i 276 5-40 i 6-27 17-5 34'4 Temp, correction of Frequency (n) of a Tuning-fork. (M'Leod and Clarke, 1880, and Konig) n t = n (i 'ooon/) 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. . . . Upper limit of audition in vibns./sec. . . . Extreme range of ear Musically available . 007 sec. io~ 8 cm io~ 8 cm io- 7 mm mercury. About 30. I 24,000 to I 41,000. c. ii octaves. c-7 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") . Lowest pitch in largest organs (64- foot pipe) . . . . 3520 4752 8 FREQUENCY RATIOS OF MUSICAL SCALE C Doh D Eay E Me F Fah G Soh A Lah B Te c Doh Natural scale . . . I V I if i i J I I I 2 24 27 30 32 36 40 45 48 i "ooo 1-125 1*250 1*333 i'5oo 1*667 1*875 2'ooo Equally tempered scale rooo 1-122 1-260 1-335 1-498 1-682 1-888 2*000 Standard forks (Konig) ( (marked ^-512 and so on)\ c' d' e' f g' a' V c" 256 288 320 341*3 384 426*7 480 512 The French Standard, " Diapason Normal " of 1859 (which adopts a fork having c" = 522 at 20 C.) is coming into general adoption for organs and pianos in England, the Continent, and America, as the result of a makers' conference in 1899. Other scales in vogue are Concert Pitch (c" = 546), Society of Arts (c" = 528), Tonic Sol-fa (c'' = 507), Philharmonic (o" = 540). (The "middle" c of the piano is c'.) 73 VELOCITY OF LIGHT VELOCITY OF LIGHT IN VACUO lean value in vacua = 2*9986 x 1O 10 cm./sec. = 186,326 miles/sec. For values of v t the ratio between the E.M. and E.S. units, see below. ./sec. XIO 10 3-07 2-998 3*153 2-986 3-004 Method. Eclipse of one of '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. Rotating mirror Toothed wheel Rotating mirror Toothed wheel Observer. Michelson, 1879 Young&Forbes,'8i Michelson, 1882 Newcomb, 1882 Perrotin, 1900 VELOCITY OF LIGHT IN LIQUIDS Liquid. Vel. in vacuo Vol. in liquid' Refractive index for Na D line. Method. Observer. Abater . CS 2 . . 1-330 1758 1-333/20 1-627/20 Rotating mirror Michelson, 1883 VELOCITY OF HERTZIAN WAVES (See Blondlot and Gutton, Rep. Conf. Phys.> Paris, 1900.) cm./sec. Observer. cm./sec. Observer. cm./sec. Observer. XIO 10 2-989 2-991 Blondlot McClean x io 10 3-003 Trowbridge and Duane XIO 10 2-989 2991 Saunders Mean RATIO OF ELECTROMAGNETIC TO ELECTROSTATIC UNIT OF CHARGE This ratio tl v n is a pure number, and is numerically equal to VA^> ** 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 88.) 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.) Observer. Observer. Observer. 2-963 2-982 3 'ooo J. J. Thomson, 1883 Rowland, 1889 Rosa, 1889 XIO 10 2-997 3'009 2-993 Thomson and Searle, 1890 Pellat, 1891 Abraham, 1892 x io 10 3-001 2-997 2-997 Hurmuzescu, '96 Perot and Fabr) Rosa & Dorsey 1907 74 PHOTOMETRY 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 w 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 1*6% 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'Electricitd 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-wincr eras flame c. 100 Tantalum lamps I '7 2*1 c. qo Tungsten (osram, etc.) lamps . 1*3 ^^elsbach mantle etc C 1 1 Open arc lamps .... . 1*1 1*4. High-pressure eras . . . c. 8 2"* Carbon filament lamps .... Metallized carbon filament lamps Nernst lamps 3*5-4-5 2-8 2 'I 2 '4. Yellow flame arc lamps . . . Mercury vapour lamps .... 4 '3-'4 In high-grade standard photometry the Lummer Brodhun photometer head is usually employed. A unit of light may be maintained and reproduced with an accuracy of the order of ^ %, 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 radiation from a standard candle is about 5 X io 5 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. 75 GASEOUS REFRACTIVE INDICES GASEOUS REFRACTIVE INDICES AND DISPERSIONS Dispersion. Cauchy's equation is /* 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 refract! vity (/* i) = A, when x = 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/* are reduced to a standard density at o and 760 mms. by assuming that (A* i)/p is a constant for each gas, p being the density. Caucby's formula is in general inadequate over large dispersions. (See Cuthbertson, Science Progress, 1908 ; and Proc. &> Trans. Roy. Soc. for 1905 et seq.) fin Q AT Refractive Cauchy's Constants. VTcis or Index /j. for Observer. Vapour. Na D line. A. B. Air ... i '00029 1 8 2871 x lo" 6 5-67x10"" Scheel (Reichsanstalt), 1907 Hydrogen . i 'ooo 1 384 13-58 7'52 n Helium . . 1-0000350 3-48 2*3 Burton; Cuthbertson & Metcalfe, 1907 Neon . . 1-0000671 6-66 2'4 C. & M. Cuthbertson, 1909 Argon . . i '0002837 27-92 5'6 Burton, 1907 Krypton 1-0004273 41-89 6'97 C. & M. Cuthbertson, 1908 Xenon . . i -000702 68-23 10-14 >j M Fluorine . 1-000195 Cuthbertson Prideaux, 1906 Chlorine . 1-000768 Mascart, 1878 Bromine . 1-001125 > Iodine . . 1-00192 1 Hurion, 1877 Oxygen . . 1-000272 26-63 5'7 Rentschler, 1908 Sulphur . . rooiiii 104-6 21-2 Cuthbertson & Metcalfe, 1908 Selenium . 1-001565 >> Tellurium 1-002495 )) 55 Nitrogen . i '000297 29-06 77 Scheel (Reichsanstalt), 1907 Phosphorus 1-001212 116-2 15*3 Cuthbertson & Metcalfe, 1908 Arsenic . . 1-001552 Zinc . . . 1-002050 Cadmium . 1-002675 V Mercury . 1-000933 87-8 22-65 ' Eefractive Refractive Gas or Vapour. Index for Observer. Gas or Vapour. Index /tf or Observer. Na D line. Na D line. Water-vapour . . i '000257 Mascart, '78 Tellurium tetra- j> * 1-000250 Lorenz, '74 chloride . . . 1-002600 P. &M. Ammonia . . . 1-000377 Mascart, '78 Phosph. hydrogen 1-000786* Dulong, '26 ... 1-000373 Lorenz, '74 Phosphorus tri- Nitrous oxide ., . i -0005 1 5 Mascart, '78 chloride . . . 1*001730 Mascart, '78 Nitric oxide . . i '000297 > Methane, CH 4 . 1-000441 j> Hydrochloric acid i '000444 )) V Pentane, C 5 H 12 . 1-001701 5? Hydrobromic acid 1*000570 55 ?> Acetylene, C 2 H 2 .'000606 )) 55 Hydriodic acid . 1*000906 Hurion, '77 Ethylene, C 2 H 4 . 1-000719 55 55 Carbon monoxide 1-000334 Mascart, '78 ,, ... 1-000674 Prytz, '80 dioxide . 1-0004498 Perreau, '96 Benzene, C 6 H 6 . 1*001812 Mascart, '78 bisulphide 1-001476 Mascart, '78 .... 1-001765 Prytz, '91 Sulph. hydrogen 1*000641* Dulong, '26 Methyl fluoride . I -000449 Cuthbertson 1*000619 Mascart, '78 chloride . 1*000865 Mascart, '78 Sulphur dioxide . i -000660 Walker, '03 alcohol . 1*000552 Prytz, } 8o trioxide . 1-000737 C. & M., '08 5J )) 1*000619 Mascart, '78 hexafluoride 1-000783 ti Chloroform, CHC1 3 1*001455 J5 Selenium 1-000895 M Carbon tetra- Tellurium 1-000991 > chloride . . . 1*001768 n 55 * White light, f Violet light, p. 1*00205 for red light. Iodine shows anomalous dispersion. C. & M., Cuthbertson & Metcalfe ; P. & M., Prideaux & Metcalfe. 76 REFRACTIVE INDICES REFRACTIVE INDICES Refractive indices, ju, (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 GifTord (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. 78. Calcspar, 18. Jena glass. Flu- Quartz, 18. Syl- Wave-length in Fu^ed AOCK vin, TIT 4- A.U. (10- 8 cm.). ord. ext. Crown* flint.f CaF 2 . 1 BO ord. ext. silica. salt, 18. KC1 at 20. ray. ray. 18 . ray. ray. ' Infra-red. -I* r r I* r 223,000 __ 3403 3712$ 94,290 3161 4983 4587 42,OOO 4078 4569 5213 4720 21,72O 6210 4746 4946 6153 4230 5180 5261 5262 4750 12,56O 6388 4782 5042 6268 4275 5316 5402 5297 4778 3210 Visible. Li, (r) 6708 H, (C) 6563 Cd, (r) 6438 Na,(D)5893 6537 6544 6550 6584 4843 4846 4847 4864 5140 5145 5149 5170 6434 6444 6453 6499 4323 4325 4327 4339 5415 5419 5423 5443 5505 5509 ,5514 5534 4561 4564 4568 4585 5400 5407 5412 5443 4866 4872 4877 4904 3308 3311 33H 3330 Cd,'0f) 5086 H, (F) 4861 6616 6653 6678 4879 4895 4907 5191 5213 5230 6546 6598 6637 4350 4362 4371 5462 5482 5497 5553 5575 5590 4602 4619 4632 5475 5509 5534 4931 4961 4983 3345 3300 3371 Cd, () 48OO Hg,(*)4047 6686 6813 4911 4969 5235 5318 6648 6852 4369 4415 5501 5572 5667 4636 4697 554i 5665 4990 5097 3374 3428 Ultra-violet. Sn 3034 Cd 2144 7196 8459 5136 5600 5552 4534 4846 5770 6305 5872 6427 4869 5339 6085 7322 5440 6618 4032 Al 1852 5099 6759 6901 5743 8933 8270 Temp, co- \ efficient (D)l + '0 S5 + '0 4 I4 -0*1 + -o 5 3 -o,. -o 65 -o B 6 -0.3 -0.4 -0,4 -o 4 8 * Light barium crown. t Dense silicate flint. J /* = 1*3692 for A. = 225,000. REFRACTIVE INDICES Refractive indices MD (against air) at 15 C. for sodium D line (\ = 5893 x lo- 8 cm.). Substance. MO Substance. r Substance. MD Solids. Alum (potash) . . Alcohol, ethyl . . amyl . . 1-362 1-41 Monobrom benzene naphtha- I'563 Cyanin T*3 lene I -660 Diamond .... Glass (see above 171 2^17 Benzene .... Bromoform . . . 1-504 1-591 Nitrobenzene . . Oil, cedar .... 1-553 1-516 and p. 78) T"5 T Canada balsam . i'53 cloves . . . 1-532 Ice 1-60 1-76 Carb. bisulphide . tetrachloride 1-632 1-464 cinnamon . . olive .... r6oi 1-46 Mica . . 1*56 to "Riibv r^6 Chloroform . . . 1-449 paraffin . . . 1-44 / Sucrar . Ether, ethyl . . . i'354 Sulphuric acid . . 1*43 Topaz . . . Ethylene dibromide 1-540 Turpentine . . . i"47 Liquids. Glycerine .... 1-47 Water (see above) . i'333 Alcohol, methyl i'33 Methylene iodide . 1744 77 SILVERING SOLUTION DISPERSIVE POWERS The dispersive power () given below = Qu c jU F )/(,u D i), where juc> /*D, 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. Quartz, ord. ext. Fused silica Rock salt Sylvin. . 0143 0146 0147 0233 0226 Substance. Liquids. Carb. bisulphide Alcohol . . . Turpentine . . Water. ,..-.' 0545 0171 0206 0180 SILVERING SOLUTION Due to the late Dr. Common. Other recipes will be found in Baly's " Spectroscopy mans) and Woollatt's " Laboratory Arts" (Longmans). (Long- 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 5 % 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. 78 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^SO,, Na^COg, or K 2 CO 3 ; (3) salts of bases other than alkalies red lead, limestone or chalk, BaCO 8 or BaSO 4 , MgCO 3 , ZnO, MnO 2 , A1 2 O 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. Thermometry Glasses. Glasses which contain both soda and potash to any extent give a large temporary zero depression (see p. 48). Data concerning Verre dur (71% Si0 2 , 12% Na 2 0, % K 2 O, 14% CaO, 2% A1 2 O 3 and MgO), Jena 16'" (67% SiO* 14% Na 2 0, 7% CaO, 12% ZnO, A1 2 O 3 and B 2 O 8 ), Jena 59'" (72% SiO 2 , 12% B 2 8 , 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. 48. 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. &> thus depends on the colours selected ; for visual work they are usually the red (C) line of hydrogen (wave-length AC = 6563 x lo" 8 cm.), the yellow sodium (D) line (A D = 5893), and the green-blue (F) hydrogen line (\ P = 4862). If /UGJ MD, J"F are the corresponding refractive indices, = (MC MF)/^ 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. For 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 Abb 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. 76, and Zschimmer's " History of the Jena Glass Works," Hovestadt's "Jena Glass," and Rosenhain's " Glass Manufacture " (with bibliography). (After Zschimmer, Zeit. Inst., 1908.) Glass. /*D (C,D,F) Dens. Glass. Mo "(C.D.F) Dens. Crowns grms. C.C. Flints (contd.} grms. c.c. f r4782 '0152 2-23 U.V. flint 3492 . . I-5329 0131 (Silicate) crown . { r5I27 0175 Telescope (Sb) flint 1-5286 0194 2*50 ( U.V. crown 3199 . r52l5 I'5035 0168 0155 2-50 Borosilicate flint . | I-5503 i'5753 0203 02l8 2'Sl 2-00 Borosilicate crown / 1-4944 I-5I4I -OI5I 0156 2-33 2 '47 1-5489 1-5825 Ol87 02l6 - 1 " n ~ Barium crown . | I-5726 1-6120 0174 Ol80 3-21 Barium flint . . 1-5848 1*6235 0189 0256 3^7 Heavy barium crown 1-6130 0178 3-60 1-6570 0276 3-95 Flints ( : 1-7174 0340 4'49 (Silicate) flint . | i'5794 1-6138 0244 0271 3-25 .Vtf 1-7782 1-9044 0378 046l 4*99 5-92 1 i -6489 '0296 3-87 1-9625 0508 79 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 mms. 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. ; nn 10 T cm.] Observer. \ Cd red. A Cd green. A. Cd blue. Michelson and Benoit, 1894 .... Benoit, Fabry, and Perot, 1907 . . . 6438-4700 6438-4702 5085-8218 4799-9085 The following values (all in tenth-metres) are of course only approximate : Hertzian Waves. Infra-red. Bed. Orange. Yellow. | Green. Blue. Violet. Ultra-violet. io u - 4 X IO T 3-1 Xio 8 7700 6470 5880 5500 4920 4550 3600 600 11 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.) 2373-737 2987-293 3'724'379 4352-74I 4878-226 5405*78o 5952-739 2413-310 3030-152 3753-6I5 4375*935 4903*324 5434*530 6003-039 2435-159* 3075725 3805-346 4427-3I4 4919-006 5455-6i6 6027-059 2506-904 * 3125-661 3843-261 4466-554 4966-104 5497*521 6065-493 2528-516* 3175-447 3865-526 4494*572 5001-880 5506-783 6137-700 2562-541 3225-790 3906-481 453i*i55 5012-072 5535*4i8 6191-569 2588-016 3271-003 3935*8i8 4547*854 5049-827 5569-632 6230-732 2628-296 3323*739 3977745 4592-658 5083-343 5586-770 6265-147 2679-065 3370-789 4021-872 4602-944 5110-415 5615-658 6318-029 2714-419 3399*337' 4076-641 4647-437 5127-364 5658-835 6335*343 2739-550 3445*155 4118-552 4678-855 5167-492 5709-396 6393-612 2778-225 3485-344 41.34-685 4707-287 5192-362 5760-843$ 6430-859 2813-290 3513-820 4147-677 4736*785 5232-958 5763-013 6494-994 2851-800 3556*879 4191-441 4754-046 f 5266-568 5805-211 1 2874-176 3686-681 4233*615 4789-657 5302-316 5857-76o J * Si. 2912-157 3640-391 4282-407 4823-521 f 5324-196 5892-882 J t Mn. 2941-347 3677-628 4315-089 4859*756 537i'498 5934-683 % 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. Subst. Bel. Intens. Line. Subst. Bel. Intens. Line. Subst. Bel. Intens. 3047*5 Fe 20 L 3820-4 Fe-C 25 (H y )434o'4 H 20 3057*3 Ti-Fe 20 3825*8 Fe 20 F 4861-37 HW 30 3059-0 Fe 20 3838*2 Mg-C 25 &s 5*72*7 Mg 20 0/3440*6 \344i *o Fe Fe 20 15 3859-8 K 3933*6 Fe-C Ca 20 1000 d l 5178-22 E 5269-56 Mg Fe 3 l 3524'5 Ni 20 . 3961-5 Al 20 (D 35 8 7 5*62)t He N 3581-2 Fe 30 H 3968-4 Ca 700 D 2 5889-97 Na 30 3608-8 Fe 2O 4045-8 Fe 30 D! 5895'93 Na 20 36187 Fe 20 4063*6 Fe 2O C 6562-8 H() 40 M 37 19*9 3734*8 Fe Fe 40 40 (H)4ior8 4226-7 H Ca 40 20 B 6867*3 A 7661 * | 6 3737*1 Fe 30 G 4307-9 Fe 6 .Z8228* Langley, 1900. Oxygen in earth's atraos. f Emission line in chromosphere alone. Wood, 1911. || X and 7 rays 8-4 to 0*07* 80 EMISSION SPECTRA EMIS For a fuller treatment appendices, Kayser's " Hai "Atlas of Emission Spectr Journal. The wave-length at 1 5 C. and 760 mms. Ti The brightest lines are e violet region is indicated th JSION SPECTRA OF SOLIDS of wave-lengths see Watts' "Index of Spectra" and idbuch der Spectroscopie," Hagenbach and Konen's a," 1905. For recent work consult the Astropky steal 5 below are measured in tenth-metres (io~ 8 cm.) in air le visible spectrum colours are indicated r, o t y^g t , v. mphasized and the approximate boundary of the ultra- us . ALUMINIUM (arc). 3083 3093 CADMIUM (contd.) 4413 * 4678 b 4799-908 b 5085-822 5338 g 5379 g 6438-470 r CALCIUM (contd.) 6122 o 6162 o 6440 o 64630 6500 r MAGNESIUM (contd.) 3832 3838 5168 g PJ5178? 5184 5529 y RADIUM (contd.) 4683 v 4826 b 5210 536o g 56557 5685 y 6210 o 3 6216 o* 6228 o* 6247 o 3 6250 o 3 6260 o* 6269 o* 62850 s 6329 3 63490 (6530 r 3 to 16700 r* 6653 r 3 Bands. SODIUM NaCl in flame). Fabry and Perot, 1902 ; Rayleigh, '06. D 2 )5889'9650 DJ5895-9320 3944 * 3962 v 4663 b ^l g 5696.7 5723^ COPPER arc in vacuo). Fabry and Perot, 1902. 3248 3274 MERCURY Mercury lamp). Stiles, Astro. Journ., 1909. 3126 3i3i 3650 STRONTIUM 8rCl 2 inflame). Bandspectr'm with lines at 4607-5 b 6387 o CAESIUM CsCl in flame). 3611-8 3617 3877 3889 BARIUM (Bad, in flame). Full of bands, some diffuse, and some resolvable. 3501 4023 v 4063 v 5105-543 g 5153-251 g 5218-202 g 5700 y 5782-090 .y 5782-159 y THALLIUM (Tl or T1C1 2 in flame). 5350-7 4555 4593 b 56647 5845 .r 6011 o 6213 o 6724 r 6974 r 4046*8 v 4078-1 v 4358-343 v* 4916-4 bg 49597 g 5460-742 g* 5769-598 7 2 5790-659 y* 6152 o 6232*0 o 2 Fabry and Perot, 1902, and Rayleigh 1906. TIN (spark). 3009 3034 3175 3262 3283 3331 3596 3746 3910 v 3994 v 4131 v 4554* 4934 5536 gy 5778 y 5854J 6142 o 6497 r INDIUM (In(OH) s in flame). 4102 v 4511 v RUBIDIUM (EbCl in flame) 3349 3351 3587 3592 CALCIUM (CaCL, in flame). Bands pre- dominate ; line at 4227 (Flame arc). 3362 3644 IRON (see p. 79)-, BORON (Boric acid in flame). Diffuse maxima at 4500 4700 b 4900 b 5200 g 5450^ 5800 .y 6000 o 4202 v 4216s/ 5648 .r 57247 6207 o 6298-7 4525 v 5563 y 55897 57997 64530 POTASSIUM (KC1 in flame). 3446 3447 LITHIUM (LiCl in flame). 4132 v 4602 If 6104 o 6707-846 r 1 1 Fabry and Perot, 1902. 4044 v 4047 v 58027 7668r 7702 r SILVER (arc in vacno) 3281 3383 ZINC (arc in vacuo). 3036 3072 3345 (K) 3934 v (H) 3968 v 422JV \ 43 2 { ./ 4426 b 4435* * 4455 b 4586* 4878 b 5270 g- K 5595S 58587 MAGNESIUM (arc). . 3091 3093 3097 3330 3332 3337 3830 RADIUM (KaBr 2 in flame). Runge and Precht, 1903 3650 3815 4055 v 4212 v 4669 b 5209-081^* 5465-489 g* 5472 g 5623 g 4 Fabry and Perot, 1902. 4680-138 b b 4722-164 ^ 6 4810-535 6 4912 b 4925 gb 6103 o 6362-345 6 5 Fabry and Perot, 1902. CADMIUM (arc). 3261 3404 3466 3611 3982 V 4341 v Si 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, Bed spectrum (small current density). 4159 v 4192 v 4198 -u 4201 v 4259 b 4300 b 4334 b 4511 b 4703 b 5452 g 5607 y 5912 o 6059 o Blue spectrum (large current density). 3583 CARBON MONOXIDE or DIOXIDE (of common oc- currence in many vacuum- tube spectra). Numerous bands shaded towards violet edges at 3590 (CN) 3884 (CN) HYDROGEN Elementary spec- trum. 3750 3771 3798 3836 3889 NEON (contd.} 5853 y 5882 o 5945* 5976 o 6030 o 6075 o 6096 o 6129 o 6143 o 6164 o 6182 o 6217 o 6267 o 6305 o 6383 o 6402 o 6507 r NITROGEN (contd.} 5804 y 5854/ 5906* 5959* 6013 o 6069 o With large cur- rent densities, N gives a line spectrum. 3970 v 4102(5) v 4340 (7) b (F) 4861 (18) gb (C) 6563 (a) r For very short wave-lengths (1030-1675) see Lyman, Astro. Journ., 1906. Secondary spec- trum (see Watson, Proc. Roy. Soc., 1909). OXYGEN Elementary line spectrum. 3919 3973 4123 v 4216 (CN) -v 4393 b 4511 b 4735 (C) b 4835 b 5i6 5 (C) g 5198 g 5610 y 6079 o NITROGEN Band spectrum from positive column. Many bands all made up of fine lines. From 3000 to 4574 the edges occur at inter- vals of about 60 A.U. Other bands have edges at 4648 b 4666 b 4723 b 4813 <* 5340 - 5614 y 5755.X 4070 v 4072 v 4076 V 4415 b 5208^ Diffuse maxima at 5335^ 5440.T 6110 o 6170 o There are three other oxygen spectra: con- tinuous, band, and series spectra. KRYPTON AND XENON Brit. Ass. Rep., 1905. HELIUM Rayleigh, 1908. 3188 4072 v 4104 v 4228 v 433 1 b 4348 4426 4430 443i b 4610 4806 NEON Baly, Phil. Trans., 1903. Very rich in red rays. 3448 3473 3521 3594 3889 v 4026 z/ 4471-482 b 4713-144 b 4921-930^ 50 1 5 '680 (D 3 ) 5875-625 y 6678-150 r 7065-200 r RADIUM EMANA- TION Royds, Phil. Mag., 1909. 5765 y ABSORPTION SPECTRA For wave-lengths of the Fraunhofer lines in the sun's spectrum, see p. 79- 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. OPTICAL ROTATIONS 82 OPTICAL ROTATK A, = the rotation in deg polarization by a l t = the length of the c !p = the number of gra q = (ioo -/) = the p p t = the density in grai c t = pp t = the concenti c.cs. of solutic M< ~ the specific rota DNS OF PI rees (for ligh liquid when olumn of liqi ms of active srcentage (ty ns per c.c. oi ation expres >n at /. bion (at /) i >.' in solution n the wave-] (o oc ^ apprc e concentrati positive or tated in an ai >urce of ligh L is the spe >ecific rotati( Rotations c JRE LIQUIDS AND SOLUTIONS it of some given wave-length) of the plane of at the temperature * C. lid in decimetres (t.e. 10 cms.), substance in ioo grams of solution. r weight) of inactive solvent in the solution. " the liquid or solution at /. sed as grams of active substance per ioo rotation per decimetre of sol. For a pure liquid [a], = : For an active substance (P + ?) = ico- The rotation depends o wave-length (A) diminishes inactive solvent and with th The rotation is called polarization appears to be ro the liquid away from the s( The molecular rotation weight, [a]^ indicates that the s] light. (See Landolt's " Optical Application.") grams of active substance per c.c. of sol. r a i t - A 'l( * p \ IooA < IooA ' s ; nf lx.). a also varies with the nature of the on of the solution, right-handed (dextro, d) if the plane of iti-clockwise direction when looking through :. The contrary rotation is called Isevo (/). cific rotation multiplied by the molecular MI is measured at 20 C. using sodium (D) )f Organic Substances and their Practical Optically Active Substance. Solvent. Conditions. Specific dotation [a]. Cane Sugar or Candy (d\ C 12 H2 2 O n (Landolt, 1888; Pellat, 1901) water c - 4 to 28 /= 14 to 30 C. MM = + 66 ' 6 7 - '0095 c [1 D = [ (I - 'ooo 37 (t -20)} Invert Sugar(/),* C 6 H 12 O 6 water c = 9 to 35 / = 3 to 30 C. [ = - 197 - '036^ mol. of levulose (Gubbe, 1885) [> D =[ + '304(/2o) 4- -oo 1 65 (/-2o) 2 Dextrose (d glucose), C 6 H 12 6 (Parcus and Tollens, 1890; Tollens, 1884) water 20 = 796) q = o to 90 [= -37 -'00482? - -ooo 1 3^ 2 benzene q = o to 91 = -37 -'0265^ paraffin oil Within wide limits [a] increases percentage of paraffin. with the Quinine sulphate (/), C 20 H 24 N 2 O 2 .H 2 SO 4 (Oudemans, 1876) water c about r6 % of alkaloid (calculated) Salt [= -214 Alkaloid [aJ 7 = -278 Nicotine (/), C 10 H 14 N 2 (Landolt, 1877 ; Hein, 1898) pure /= 10 t03oC. [=-i62 benzene p = 8 to 100 [=-i6 4 water p i to 16 [=-77 Ethyl malate (/), (C 2 H 6 ) 2 C 4 H 4 6 (Purdie & Williamson, '96) pure liquid ^=--3,-,,, Camphor (^), C 10 Hi 6 O (Landolt, 1877 ; Rim- bach, 1892) alcohol q = 45 to 91 [= +54'4-'i35^ benzene q = 47 to 90 [] 2 D o=+56-'i66^ OPTICAL ROTATION AND WAVE-LENGTH Wave-length (\) in 10 ~ 8 cm. Specific Rotation at 20 C. 3 QUARTZ AT 20 C. Cane- sugar or Candy in H 2 0. rurpentine (pureliq.). Tartario acid in H 2 (P = 41%). Nicotine (pure liq.). Wave-length (x) in 10-" cm. Rotation for 1 mm. thick- ness. H (C)6 5 6 3 (r) Na (D) 5893 (o) TI 5351 Cr) H (F) 4861 Qr) 52-9 66-5 8r8 ioo'3 -2 9 '5 -37 -45 -54'5 775 8-86 9-65 9'37 -126 -162 -207*5 -253'? Li 6708 (r) H (C) 6563 (r) Na(D) 5893 0) SmSIIffi 'H (S) 4102 (b) i6'4 I7'3 2172* 26-53 327 47H8 * For quartz at temperature /, rotation = 2i72 {i + O'oooi47(/ - 20)} for D line. 84 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 IQ-* cm.). (For Voigt's theory of magneto-rotation, see Schusters, " Optics," 1909. See also Becquerel's papers in Compt. Rend., etc.) Substance. Temp. Kotation r in mins. of arc. Substance. Temp. Kotation relative to Water. Water OC. 20 Carbon bisulphide . J O + -oi3ii,R.W +-oi3i2,R.W Quartz, JL axis Jena (phosphate crown ;lass\heaviest flint . . r eCl s dens. = 1*693 . 1*023 .18 .20 20 2O 18 18 15 15 + 04200, Ra. +01 368,* Bo + 01664, Bo. + 1587,1 Bo. + 0161, D.B. + 0888, D.B. -2026, B. +0122, B. Ethyl alcohol . n. propyl alcohol Amyl(iso) alcohol Ethyl bromide . chloride . iodide . . Formic acid . . Acetic . . Propionic acid . Benzene . . . 168 156 199 19-7 5O 181 208 210 203 15 8637, P. 9139, P. 9888, P. T395, P. 1-035, P. 2-251, P 7990, P 7976, P 8369, P 2-062, B * \ = 6439. t *.= 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). Wave-length A in A.U. (10- 8 cm.). Ultra- violet Visible 2,510 3,570 4,200 5,500 7,000 ! 1 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 E 6 9 73 9i 96 Ag. 34% 74 87 93 95 97 98 99 Steel. 33% 45 52 55 58 63 88 96 Magna- lium.* Ag back. Hg back 67% 81 83 83 83 84 89 92 Glass mirror. 90 73% t 7i 73 f A = 4500. Mg 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. 85 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. 144. 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. 87 ; for temperature coefficients, next page. The thermal conductivities of the same samples of many of the substances below will be found on p. 54. Substance. Temp. Sp. Ee. Observer. Substance. Temp. Sp. Be. Observer. Metals- Aluminium * Antimony Bismuth . . Cadmium, drawn u Copper, drawn . annealed Calcium . . . Cobalt. . . . Gold . Iridium Iron wrought > > steel fi%\ n M VC./ Lead, drawn Lithium . . Magnesium . Mercury . . Molybdenum Nickel . . /97%\ \Ni./ Osmium . . Palladium 160 18 18 100 15 18 100 160 18 100 160 18 100 18 20 2O 183 18 100 18 18 18 100 160 18 100 18 1OO 160 18 1OO O O O 2O 25 160 18 100 20 18 100 x icr 6 0-8 1 2*94 3*2 1 4-13 40-5 119*0 160*3 272 7'54 9-82 0-49 178 2-36 1-59 10-5 971 0-68 2-42 3'i 5'3 9-15 I2'0 16-8 5*4 13-9 1 8-8 19-9 25-6 7'43 20'8 277 8-4 4'35 94-07 9576 4T 5*9 u-8 157 9'5 107 13-8 \ Lees, f />. T., '08 I J- & D, I 1900 Berget, '90 [ J. & D, I 1900 Lees, '08 I J. & D., I 1900 Lees, '08 I J. & D., I 1900 Mean M.&C.,'os R., 1901 D.&F., '96 \ J. & D., / 1900 Mean J. & D, 1900 Lees, ; o8 J. & D, 1900 J. & D, 1900 Lees, '08 J. & D, 1900 B., '04 D.&F. \ See J pp. 6, 82. Fink, J io Lees, '08 J. & D., 1900 Blair, '05 . J- & D, 1900 Metals (c Platinum . Potassium . Rhodium . . Silver, 99-9 % Sodium . . Strontium Tantalum Tellurium Thallium, pure Thorium . . Tin, drawn . Tungsten . Zinc, pure Alloys Brass . . Constantan \ (Eureka) / German silver || Manganin *f . . Phosphor-bronze Platinoid || . 90 Pt, 10 Rh 67 Pt, 33 Ag 203 18 100 O 18 160 18 18 100 O 20 18 2O O 15 160 18 100 25 160 18 1OO 160 17 18 18 100 18 O 1OO 160 18 18 10O 18 160 18 O O X IO" 6 2-4 iro 14*0 6-64 6-0 0-56 r66 r6 3 2-13 474 14-6 21 17-6 40-1 3*5 5-0 2'2 6-1 7'9 6-6 6-9 49-0 49-1 16-40 26*6 27-6 43*13 44-50 42-05 42-11 5-10 32'5 34'4 2TI D.&F., '96 I J- & D, I 1900 B., '04 \ Lees, / 1908 I J. & D., [ 1900 B., 1904 M., 1857 M., 1858 D.&F., '96 Bo., '09 Lees, '08 I J. & D, I 1900 Fink, '10 Lees, '08 \ J. & D., I 1900 Lees, 1908 Mean J- & D., 1900 Mean Lorenz, 1881 Lees, 1908 J. & D., 1900 Mean Lees, 1908 D.&F., '96 * 99 % Al. f -i% C, v % Si, -i % Mn. I 70 Cu, 30 Zn. 60 Cu, 40 Ni. || 62 Cu, 15 Ni, 22 Zn. ^ 84 Cu, 4 Ni, 12 Mn. B., Bernini ; Bo., Bolton ; D. & F., Dewar & Fleming ; J. & D., Jaeger and Diesselhorst ; M., Matthiessen ; M. & C., Moissan & Chavanne ; R., Reichardt ; P. T., Phil. Trans. 86 RESISTIVITIES ELECTRICAL RESISTIVITIES (contd.) NON-METALS AND INSULATORS The resistivities are in ohm-cms, at room temperatures unless otherwise 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 electrical insulators, see Kaye, Proc. Phy. Soc. Lend., 1911. Substance. Sp. Be. Substance. Sp. Be. Substance. Sp. Be. Gas carbon . . ( '004 to 1 '007 Sulphur, 70 . . Ebonite .... 4.io 16 2 . IO 16 Guttapercha . . Mica 2. IO 9 9. io 16 Graphite . . . 003 Glass, soda-lime * 5 . io 11 Paraffin wax . . 3 . io 18 C. lamp filament Selenium J (1907) Silicon . . . . 004 2.I0 16 06 Jena, com-1 bustion* j conducting! >2 . IO 14 5.10* Porcelain, 50. . Quartz .... Fused silica* . . 2 . iq 15 I'2. IO* 14 ^^2 IO * National Physical Laboratory. t Phillips. \ In dark. Wick, 1908. TEMPERATURE COEFFICIENTS 9F 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 t = R (i + /) 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 a. The coefficients given below are average ones. Substance. Temp. a Substance. Temp. a Metals Aluminium ... 18-100 X I0~* ^8 Metals (contd) O-100 X IO~ 4 4 Bismuth 18 A.2 Tantalum . ... O-1OO 2-2 18-100 AD Tin ... O-100 4C Copper * 18 42'8 Tungsten (1910) O-17O Cobalt : O-160 -J-3 Zinc . . .... 18-10O 77 Gold O-100 AO Iron pure ..... 18 62 Alloys Steel *. . 18 164 18 lot Lead 18 A/l ( '4. to Mercury f . . . 24 *tJ Q'O Constantan (Eureka) . 18 1 +'Tt Nickel, electrolytic commercial Palladium ... 0-10O 0-1000 18-1OO 62 27 27 German silver . . . Manganin .... Platinoid 18 20 18 2-3-6 02-'5 t 2*5 - 10O-O ae 90 Pt, io Ir . . . 16 15 O-1OO P 90 Pt, io Rh . . . . 15 17 Molybdenum (1910) . O-17O Platinum-silver (coils) 16 2'4-3'3 * High conductivity annealed commercial. t R = R (i + 'O 3 88/ + 'Oji/ 5 ) Smith (N. P. L.), 1904. % N. P. L. Most samples of manganin have a zero temp, coeff. at from 30 C. to 40 C. 87 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 the wire gauge used must be specified. The following are English Legal Standard wire gauge values. (See Foster's " Electrical Engineers' Pocket Book.") Size. S.W.G. 6 8 1O 12 14 16 18 Diameter. Mm. 4-88 4'06 3-25 2-64 2-03 1-63 T22 Inch. 192 160 128 104 080 064 048 Size. S.W.G 20 22 24 26 28 30 32 Diameter. Mm. 914 711 '559 457 376 315 274 Inch. 036 028 022 018 0148 0124 01 08 Size. S.W.G 34 36 38 4O 42 44 46 Diameter. Mm. 234 193 152 122 102 08 1 061 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. Larger current densities than these are allowed in the revised "Wiring Rules" of the Institution of Electrical Engineers. 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 P er degree Centigrade. The values for the alloys may vary considerably. The composition of manganin is 84Cu, 4Ni, i2Mn; of German silver, 6oCu, i5Ni, 2$Zn ; of Eureka, c. 6oCu, 4oNi. Platinoid is said to be German silver with a little tungsten. For specific resistances, see p. 85. S.W.G. COPPER. MANGA NIN. Ohms per metre. Safe current, Ohms per metre. GERMAN SILVER. Ohms per metre. S. /V.G. COPPER. Ohms per metre. Safe current MANGA NIN. Ohms per metre. GERMAN SILVER. Ohms per metre. 12 14 16 18 2O 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 I'l 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 40 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 'O2 5'45 jrii 9-90 H'5 23-2 36-3 53*4 817 145-5 2-90 3-83 5-27 774 12-4 19-4 27-8 43*5 77'4 EUREKA or CONSTANTAN. S.W.G. Ohms per metre. 20 C. temp.- rise caused S.W.G. Ohms per metre. 20 C. temp.- rise caused by PLATINOID (Martino's). S.W.G. Ohms per metre. S.W.G. Ohms per metre. 12 14 16 18 086 146 228 405 amps. I2'2 8'2 4'9 27 20 22 24 26 722 I'2O i '93 2-89 amps. I'5 7 '3 20 22 24 26 622 1-03 r6 7 2-50 28 3O 32 34 6-8 1 FUSES The fusing currents are for wires mounted horizontally. Fusing current. lamp. 5 10 2O 30 40 50 Tin . . Copper . S.W.G. S.W.G. 37 47 28 41 24 38 21 33 18 28 16 25 14 23 13 22 88 INDUCTIVITIES 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, A, 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 M is the refractive index, then on Maxwell's theory of light, k jt 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 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. 75. 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 o between / and T is defined by T = k t { i o(T /)}. In the case of water Palmer (1903) finds that a increases slightly with the frequency of oscillation. The Clansins-Mossotti r< ... k i a 1 o vi n Yi . const, (p being the density) has been p(k + 2) shown by Tangl (Ann. d. Phys., 1908) to hold from i to 100 atmos. in the case of H 2 , N 2 , and air. Substance. k. Substance. k. Substance. k. Solids- Calcite .... 7*5-77 Bromine . . . 3-1 Oil, paraffin . 4*6-4*8 Ebonite .... 2-7-2-9 Carb. bisulphide . 2-62 Petroleum . . 2-0-2*2 Fluorite .... 6-8 tetrachloride 2-25/18 Toluene, a = *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 . . 1*9 flint . . . 7-10 chloride . . 10-9 Water, \ = oo . . 81 mirror . . 6-7 ether, a = -005 4*37 \ = 3600 cms. 3-32* Gypsum .... Ice (-2) . . . 6-3 93*9 Glycerine, \ = 200 Nitrobenzene . . 39-1/15 34/17 A=I200 a 17 = -0045 . 279* Indiarubber . . 2-1-2-3 Oil, castor . . . 4-6-4-8 Xylene, ;, a = -o 3 5 2*4 Marble .... 8-3 olive . . . 3-1-3-2 Mica 57-7 Paper, dry . . . 2-2-5 k. Observer. Paraffin wax . . 2-2-3 Substance. Temp. Pitch 1-8 Porcelain . . . 4-4-68 76 cm. Hg. ; A = oo Quartz .... 4'5 Gases- 1-8-2-6 Air oC. 1*000586 Klem anrir iKSC Rock salt . . . 5-6 20 1-000576 Tangl, 1908 Selenium (16) . 6-1 Hydrogen . . . i -000264 Boltzmann, 1875 Shellac .... 3-37 ... 20 i -000273 Tangl, 1908 Silica, fused . . 3'5~3'6 Helium .... O i '000074 Hockheim, 1908 Spermaceti . . . C. 2'2 Nitrogen . . . 20 1-000581 Tangl, 1908 Sulphur .... 3*6-4'3 Nitrous oxide,N 2 O O 1-00099 Klemencic, 1885 Sylvin .... 4*9 Carbon monoxide 1-000695 i > j Vaseline. . . . 2'2 dioxide . 1-000985 > i bisulphide 15 i '0029 , , , Liquids Ethylene . . . 15 1-00146 j i > Alcohol, methyl . 35'4/i3-4 Sulphur dioxide . I4-7 1*00905 ethyl. . 26-8/i47 Ammonia . . . 20 1*00718 Badeker, 1901 amyl . . 16-0/20 Alcohol, methyl . 110 1-00600 4 Aniline, a = "004 . 7-30 ethyl . no 1-00647 H Benzene, a = -o 3 7 . 2-29/18 Benzene .... 1 10 i -00292 n m * Beaulard, 1908. 89 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 a = (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 (AQO ) for extreme dilutions, a state of things when, on this theory, the solute is completely dissociated. A^/AQQ = a for the equivalent concentration m. 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 u + and //_. The electrolytic current also obeys Ohm's Law, so that X/c = (u + + _)* (Kohlrausch, 1879), where X is the potential gradient in volts per cm., n the number of +ive 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~s A cm./sec., since K/n. = 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 #_/(#+ + #_)==# 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 (?]) 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/6ir7ia, where F is the driving force), with the numerical constant, 6w, possibly changed. The dissociation theory postulates the conditions existing in very dilute solutions. The rdle 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 Elektroly ten ; " Whetham's " Theory of Solution.") MIGRATION RATIOS HittorPs migration ratio or transport number of the anion, n #_/(#+ + *O '> m equivalent concentration per litre ; / = temp, of observation. Solute. /C. Cone. m. Batio n. Solute. /C. Cone. m. Batio . Solute. /C. Cone, m. Batio n. KC1 . KBr . KI . . 18 25 003 (03 to) Voi / 05 505, S.D. 504, B. 505, Be. AgNO s NH 4 C1 T1C1 . CaCl a . 17 20 22 *4tO'O2 05 '01 005 526, H. 507, Be. 516, Be. 562, S.D. CuSO 4 . HC1 . . 18 10 f'o8 to\ 1 *02 / /'OS to) I '02 / 625, M. 159, N.S. KN0 3 . 8 I 497, H. SrCl 2 . 21 oi 56, Be. HNO 3 . . 18 25 17 NaCl . 18 r-03 to) \ '009 / 604, B. BaCl 2 . MgCl 2 18 21 oi 05 '55 615, Be. H 2 S0 4 . KOH . . 11 05 I 17, Be. 74 NaNO 3 19 05 629, Be. ZnSO 4 05 64, H. NaOH. . 25 04 8, Be. LiCl . 18 r-03 toi \-oo8/ 67 CdBr 2 . 18 {12 to} 1-007 / '57 NH 3 . . AgC 2 H 3 ? 21 25 05 oi 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. 90 CONDUCTIVITY OF SOLUTIONS ELECTRICAL CONDUCTIVITY OF SOLUTIONS it l8 = pacific electric conductivity (in ohms" 1 cm." 1 ) of the solution at 18 C. p mass of anhydrous solute per 100 gms. of solution. i? = the number of gm. equivalents in I c.c. of solution. Gm. equiv. per litre = loooij. To find -n note that *c/A = 77. v volume in litres containing one gm. equivalent of solute = 1/100017. 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 = ( where 17 is a constant, and generally n = 1-6. 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, Amer. Jonr. Set., 27 and 28, 1909 ; Terry, Phy. Rev., IOOQ ; iron and manganese, Burgess and Aston, Phil. Mag.. 1909 ; Heusler alloys, Stephenson, Phy. Rev., 1910. (Ewing, "Magnetic Induction in Iron," and Kohlrausch, "Prakt. Phys.") "Material Permeability /A. Coer- Bema- Hyst. loss, iXLl* t Cl Icii* ft~* B| = l 8 = fc = a >P? = 60 1^ = 150 civity. nence. ergs/cm.* Swedish wrought iron 2500 37 ^0 2060 736 274 120 0-8 4,000 200 6,700 Annealed cast steel . 1450 35oo 2100 747 280 123 0-97 7,100 151 11,700 Unannealed cast steel 490 970 1700 680 270 122 2-08 9,000 156 2O,40O ____ _.__ KT 182 117 6c I I'Q A. 2^O 155 1 A *2fV*l Magnet ( Hardened . 68/15 78 * * / 193 100 1 L 7 *f:^ J w 11,700 234 211,000 steel \ Tungsten . 8o/10 119 204 105 27^ 9,880 505 Il6,OOO Material. -. Induction, 3$, for For ma . max. p? = 100. /nuuc. Goer. Beman. Hyst.loss. ergs/cm. 3 Mild steel**. . . 120 18 A W IQO 17,700 S^o 0-6 10,^00 4..QOO Steel, 2-8 % Cr, -8 % C *7 i^w / J / * x ^5O vyv ^ 6,400 J i^.,v^W 5'5%W,-6%C , . . Hardened at 770 72 7,000 f 28o,OOO 77 %W, 1-9 %C . . ,, 800 85 4,7oo | 4% Mo, 1-2% C . ,J 800 85 6,700 Iron f CO I7,IOO 17:0 2'2* c. 53% g __ Silicon iron, -6 % Si f J 5 l6,000 * / 2 1900 ** JJ /O ,j 4-5% Sif , 5< ) 15,100 2500 I 1 '2* c- 39% Electrolytic iron (very pure) 2IO 21,250 18 10,000 ' ^%n Heated to 1 200 C. 16,000 2'5 12,500 Hadfield's manganese steel |] 1-3-1-5 v. small Nickel, annealed . 100 5J37 296 8 3,570 Cobalt I4C T IO ooo Q ?OO 174. 12 3,4 oo . ,96% ... . i^.*" 114 8,237 7^800 * / T" 177 I9,OOO Heusler alloy *|f . . 97. y-51- / J J ' * H = 10. t Otto, Dent. Phys. Ges. Berlin^ 1910. J Bar magnet. Burgess and Taylor , 1906. 1! 12 ? ; Mn, i % C. TI 24 Mn, 16 Al, 60 Cu. McClennan, 1907. ** Gumlich and Schmidt (Reichsanstalt), 1901. 94 MAGNETISM MAGNETIC SUSCEPTIBILITIES OF THE ELEMENTS, ETC. The susceptibility H = /$! = (/* i)/(4 7r ) 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 grm. at 18 C., except where some temperature is specified. The gases are per cm. 3 at I atmos. [Honda (Ann. d. Phys.^ 1910) used purest available materials and corrected H for any traces of iron ; see also P. Curie, CEuvres, Paris, ioo8.1 + means paramagnetic ; , diamagnetic. Elem. H Obs. Elem. H Obs. Elem. H Obs. Solids X 10-6 Solids Solids Al . + '65 L.,W, H. (contd.} X IO- 6 (contd.) X 10 -6 Sb . -'95 H. P . . -9 H,B.,C.,Q. V . . + i't H. As . -'31 H. Pt. . + 1-32 Zn . . 'i: K., L., H. Bi . B. C. D. E.W. K. . + *4 H. Zr . . - *45 H. B . . Cd . -71 '17 H. H. Rh . Ru . + ri + 56 H.,F. H. Liquids C/-V Cr . Cu . Au . I . . Ir. . Fe . + 37 - -087 -15 -36 See H. H. K., H. B., C, H. H. p. 89. Se . Si. . Ag Na . S . . Ta . 1 j -32 '12 '2 -*5 + '93 H.,C. H. H. H. I3.,C.,L., Is.., H. H. Br . . Hg. . N liq. . liq. . H 2 0,i 5 H 2 0,i5 - -41 + 28 + 324 -837 -77 ., Q. Q., M, H. F., D. F, D. Du B. S. Pb . '12 H., K., L. Te . - -32 E., C, H. Gases Mg . + '55 H. Tl. . * - '3 H. Air, 16 + "032 DuB. Mn . + 10-6? H. Th . + r8 H. A . . *OIO T. Mo . + '04 H. Sn . + 025 K., H. He . . '002 T. Nb . + 1-3? H. Ti. . c. + 2 H. H . . -008 Q. Os . + '04 H. W . + '33 H. N . . + "024 DuB. Pd . + 5-8 H,K,C.,F. U. . M., H. O . . + 123 Du B., Q. B., E. Becquerel, 1855; C., Curie, 1895 ;'D., Dewar, 1892; Du B., Du Bois ; E. , Ettingshausen ; 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 magnet diminishes as the temperature (/) rises. In M/ = M (i o/), o varies widely, but is of the order '0003 to 'ooi. The permeability /* also depends on the temperature. There is a critical temperature above which M 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 % of C. The critical temperature of a metal is not perfectly definite, but depends to some extent on whether the metal is being heated or cooled. Substance. Grit. Temp. Observer. Substance. Grit. Temp. Observer. Iron .... 6 9 o-8 7 o C. Hopkinson Nickel, 95% . 310 Hopkinson .... c. 895 Roberts-Austen 377 Weiss, 1907 ! ! 855-867 Osmond Magnetite. . 582 757 Weiss, 1907 Heusler alloys c. 300 Gray, 1908 Cobalt . . . 1075 Stifler, 1911 Stalloy . . . 760 Hadfield Nickel steel (25 % Ni ; O to 5O jt = 1-4 to 60 ; 5O to 58O /i = 60 to 0-4- 95 TERRESTRIAL MAGNETISM STEINMETZ'S COEFFICIENT Values of i? in Steinmetz's formula ^^ x for the hysteresis loss in ergs per c.c. per cycle. Bmax. is the maximum value of the induction. Substance. Substance. Silicon iron (Stalloy) . ood transformer iron . . Dynamo cast steel .... High carbon steel, hardened 0007 ooi i 0026 025 Grey cast iron Nickel . . Cobalt , . 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 ediJ., 1911 ; and " Studies in Terrestrial Magnetism " (Macmillan). 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 (Maryland) Fairhaven (Mass.) . . Goat Island (California) Greenwich (New York) . Rio de Janeiro . . . . Santiago (Chili) . . . Sitka (Alaska) . . . . Waukegan (Chicago) . . llongil Latitude. (Longitude 70 5N 72258 57 9 N 55 19 N 50 9 N 51 28 N 51 28 N 5348N 49 12 N 53 5i N 51 56 N 33 56 S 2952N 20 6 S 4347N 3844N 41 37 N 37 49 N 41 o N 22558 3327S 57 3N 42 21 N 9645 154 2 7\V 3 12 W 5 5\V o o o igW I33W 2 5\V 228W 10 15 W 18 29 E 31 21 E 5733E 79 i6W 76 50 W 70 54\v 122 22W 7337W 43 ii W 70 42 W 135 20W 8 75 iW Year. 1908 1909 1915 1912 1919 1918 1909 1907 1919 1915 1885 1913 1916 1916 1915 1908 1909 1908 1906 1906 1916 1908 Declina- tion. 20 34 W 36 W 24 W i8W 50 W 2Wf 59 W 4 W 30 15 W 2 17 W 948W 6 33 W 6 4\V I227W I753E 10 8 55 W 14 igE 3024E 2 39 W Inclina- tion. 90 o N 90 o S 7039N 6937N 6627N 6654N 6658N 68 3 5N 6535N 6843N 68 8 N 56 oS 4048N 5255S 74 44 N 7047N 73 8N 62 ii N 72 13 N I357S 30 12 S 7426N 7246N c.g.s. O O 'I6 3 1679 I880 1845 1843 176 1729 1787 I 99 3003 2320 '1599 1941 '1736 '2525 1822 2477 1559 '1830 c.g.s. 464 4517 4312 4325 4336 *449 4438 4452 295 2592 3069 5854 5569 5724 4786 5680 O6l6 5592 5898 Mawson and David (with Shackleton), 1908. f 1907 96 TERRESTRIAL MAGNETISM TERRESTRIAL MAGNETIC CONSTANTS (eontd.) Place. Asia Alibag (Bombay) . . Barrackpore (Calcutta) Hong Kong .... Australasia Christchurch (N.Z.) . Honolulu (Hawaii) . Melbourne .... Sydney Europe Arctic ( (Norway) . Regions \ (Spitzbergen). Odessa Pawlowsk (Petro- grad) Potsdam Rude Skov (Copenhagen) Uccle (Brussels) . . Val Joyeux (Paris) Latitude. I839N 2246N 22 18 N 4332S 21 19 N 37 50 S 3352S 6956N 7741 N 4624N 594iN 5223 N 555iN 5048N 4849 N Longi- tude. 72 52 E 8822E 114 loE 172 37 E 158 4W 144 58 E 151 I2E 22 58 E 14 50 E 3048 E 30 29 E 13 4 E 12 27 E 4 21 E 2 I E Year. 1915 1914 1916 1914 1916 1916 1885 1903 1903 1901 1906 1914 1916 1911 1916 Declina- tion. 041 E o 32 E o 14 E 1645 E 944E 8 E 043W 10 55 W 427W 828W 8 35 W I3HW I33IW Inclina- tion. 24 21 N 3059 N 30 52 N 68008 3929N 67498 62308 7621 N 80 8 N 62 18 N 7Q37N 662oN 68 53 N 66 oN 64 40 N c.gs- 3687 '3740 2241 2897 2300 268 1258 0942 2i88 1653 1880 1723 1903 1970 V. 1669 2246 2221 '5547 2386 5640 515 5178 5417 4168 4696 4289 4460 4273 4162 SECULAR MAGNETIC CHANGES At the present period we are going through a remarkable secul&r alteration. For generations H had been steadily rising in Western Europe, but during the last few- years a wave of depression has travelled across from the east. H has steadily fallen at Petrograd 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 1908-1909. Decln. H. 1904-1909. Decln. Incln. V. Greenwich Kew. . . Stonyhurst Falmouth . Valencia . 5'9 6- 1 7-0 6-3 5*4 c.g.s. - 5 x 10" - 9 -10 + 4 + 7 5'4 5'9 47 5-0 -07 - IT ri - 1-4 1*2 c.g.s + I X 10 + 2 + 6 + 9 + 7 -5 c.g.s. 20 X 10" -35 -25 -30 -25 SECULAR CHANGES AT LONDON (GREENWICH) Year. 1580 1660 1720 1815 Decln. II 17 E o o 13 oW 24 27 W* Incln. 72 o N 73 15 5. 74 40 N* 70 30 N Year. 1851 1875 1907 1919 Decln. o / 22 25 W 19 21 W 16 o W 14 18 W Incln. 68 47 N 67 42 N 66 56 N 66 54 N c.g.s. 1729 1795 1853* 1845 Maximum. 97 SPARKING POTENTIALS SPARKING POTENTIALS The work of Peek and others has shown that a spark gap between spherical electrodes of equal size is a convenient means of measuring high voltages. The spark between points is now generally discredited for high voltages on account of its inconsistent dependency on atmospheric humidity and frequency of discharge. By reason of its time-lag, its readings may be 300 or 400 per cent, in error, in the case of high frequency steep impulses. On the other hand, frequency and wave shape have no appreciable effect in the case of the sphere gap, and the effects of variation in the atmospheric con- ditions are well known, and can be readily corrected for. The size of the spheres is important. A good rule is not to use a gap bigger than the diameter of either of the balls, though some latitude may be permitted in this direction. The main point is to avoid the break-down discharge being pre- ceded by brush-discharge or corona, otherwise a pulsating discharge will, in general, give gap readings much too high. With the above precaution, a sphere gap is capable of measuring (peak) voltages from say, 10,000 volts to 500,000 to an accuracy of about 2 per cent. The table below is based on Dr. A. Russell's formula, and incorporates the latest results of the American Institute of Electrical Engineers (1918). It includes also for convenience a column of figures for a needle point gap (No. oo new sewing needles), which furnish a rough notion of the voltages for an instrument which is still much used. The A.I.E.E. recommend that for voltages above 70,000 (and preferably above 40,000) a sphere gap should always be employed. The gap should not be exposed to any extraneous ionizing influence, such as an arc or an adjacent spark, nor should the gap be enclosed. The first spark is the one for which the reading should be taken. SPARK-GAP VOLTAGES AT 760mm. PRESSURE AND 25 C. Where any gap is being used outside its recommended limits, the figures are shown in brackets. The blank spaces indicate that the gap is no longer suitable. The gaps are given to 3 significant figures for interpolation purposes. TABLE A. DIAMETER OF SPHERES. Kilo Volts (peak). Needle Points. 2-5 cms. 5 cms. 10 cms. 36 cms. 50 cms. j i cms. inches. cms. cms. cms. cms. cms. gap- gap. gap. gap. gap. gap. gap. 5 (0-42) (0-I 7 ) (0-13) (0-15) (O'lS)- (0-16) (0-I 7 ) 1O (o-8 5 ) (0-33) 0-27 0-29 0-30 0-32 o'33 15 I-30 0-5I 0-42 0'44 0-46 0-48 o'5o 20 175 0'69 0-58 0-60 0-62 0-64 0*67 25 2'20 O-S/ 076 077 078 0-8 1 0-84 3O 2*69 I -06 0-95 0-94 0'95 0-98 oi 35 3'20 1-26 1-17 1*12 1*12 rij 18 4O 3*i 1-50 1-41 1-30 I-2 9 1-32 *35 45 4*49 177 r68 I'SO I -47 1-49 52 50 6O 5*20 6-81 2-68 2*00 2'82 171 2'17 1-65 2*02 r66 2'01 69 2*04 70 8'8i 3 '47 (4*05) 2-68 2-42 2'37 ' 2-39 8O (in) (4-36) 3-26 2-84 274 275 9O (i3'3) (5*23) 3*94 3*28 3'II 3'io 10O d5'5) . (6-10) 477 375 3 '49 3'46 no (177) (6-96) 579 4-25 3'88 3-83 12O (19-8; (7'8i) (7-07) 478 4-28 4-20 130 (contd.} (22-0) (8-65) ~ 5'35 4-69 4*57 98 SPARKING POTENTIALS TABLE A. (contd.) DIAMETEE OF SPHERES. Kilo Volts (peak). Needle Points. 25 cms. 5 cms. 10 cms. 25 cms. 50 cms. cms. inches. cms. cms. cms. cms. cms. g a P- gap- gap- gap. gap- gap- gap- 140 (24-1) (9'48) 5 '97 5'10 4*94 ISO (26-1) (10-3) 6-64 5-52 5'32 16O (28-1) (II'I) 7'37 5'95 570 17O (30-1) (II'9) 8-16 6-39 6 '09 180 (32-0) (12-6) 9'03 6-84 6-48 19O (33'9) (13-3) I0'0 7-30 6-88 2OO (357) (14-6) in 776 7-28 210 (37'6) (14-8) (12-3) 8'24 7-68 220 (39'5) (15-5) (137) 873 8-09 230 (4^4) (16-3) (15-3) 9-24 8-50 240 (43'3) (17-0) 976 8-92 250 (45 *2) (17-8) ' 10-3 9'34 AIR-DENSITY CORRECTION TO SPARKING POTENTIALS Applicable only to sphere gaps. The following table gives the relative air density under different conditions. The figures are relative to dry air at 25 C. and 760 mm. pressure : TABLE B. Temp. Press. 720mm. Press. 740mm. Press. 760mm. Press. 780mm. C. 1-04 I -06 1-09 ri2 10 I '00 I '02 1-05 ro8 20 0-96, 0'99 I'02 1-04 30 o - 93 0*96 0-98 I'OI Within the limits of the above table, the correction factor for a sphere gap agrees substantially with the relative air density. Thus for a given length of spark gap, the tabulated kilovoltage in Table A must be multiplied by the appropriate cor- rection factor in Table B. Alternatively, to calculate the gap which will just be sparked over by some specified voltage, the voltage must first be divided by the appropriate correction factor before Table A is used. It will be seen that under normal conditions the correction is small or negligible. X-RAY SPECTRA For an account of X-ray Spectroscopy, see W. H. and W. L. Bragg's ' X Rays and Crystal Structure" (Bell), Kaye's "X Rays" (Longmans), and the various papers of Siegbahn and his co-workers in the Phil. Mag. , 1916, and onwards. Also Duane and others in the Phy. Rev. for 1916 and onwards. 99 X-RAY SPECTRA LATTICE CONSTANTS OF CRYSTALS In a crystal the atoms are regularly disposed in a network of intercrossing planes, each series of planes being parallel and equi-distant. The lattice constant of a crystal is the distance separating the main atomic planes parallel to some specified crystal face. Crystal. Lattice Constant. Observer. Rock Salt, NaCl Calcite (cleavage face) CaCO 3 .... Potassium ferrocyanide K 4 Fe(CN) 6 '3H 2 O Gypsum CaSO 4 '2H 2 O x icr 8 cm. 2*8140 3 '0290 8-408 7-621 W.L. Bragg, P.K.S., 1913 Siegbahn, P.M., 1919 CHARACTERISTIC X-RAY SPECTRA Up to now about 16 lines have been found to be associated with the charac- teristic X-ray spectrum of each element. Three series of lines are known at present the K, L, and M, of which the K has the highest frequency. A J series has also been claimed to exist, but the evidence needs confirmation. The K series contains at least 4 lines, a 2 , aj, /3 and 7, of which the 7 line has the highest frequency. The L series contains probably 3 groups of lines, each group similar to the K series. The values of the wave lengths of the principal lines are given below in Angstrom units. It should be noted that all the values rest on W. L. Bragg's estimate of the lattice constant of rock salt (see above). K SERIES. At. No. Element. Observer. X io~ cm. II 12 13 H \l 17 19 20 21 22 23 24 25 26 2? 28 29 30 32 39 40 4i 42 44 45 Na' Mg Al Si P S Cl K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ge Y Zr Nb Mo Ru Rh cm. 11-95 9-92 8-36 7'i3 6-17 5-36 47187 37339 X I0~ cm. 9-48 7-99 6-76 5-81 5-02 xio- 8 cm. Siegbahn & Stenstrom, P.Z., July,'i6 2-746 2-502 2-097 1-437 1-261 0*6164 3-0253 2742 2-498 2-2852 2-093 1-9324 17852 1-6547 i'5374 i '433 1-257 0-833 0-790 0-746 0-717 0-635 0'6l2I 3-4474 3-0879 27745 2-509 2-281 2-0814 1-902 17540 1*6176 13895 1-294 1-131 0-5453 2-492 I-8Q2 ri2i 0-5342 Siegbahn, P.M., June, '19 Siegbahn & Stenstrom, P.Z., July, '16 Siegbahn, P.M., June, '19 Siegbahn & Stenstrom, P.Z., Feb., '16 Siegbahn, P.M., June, '19 Siegbahn & Stenstrom, P.Z., Feb., '16 Moseley (corrected), P.M., April, '14 Duane & Hu, P.R., 1919 X-RAY SPECTRA 100 K SERIES (contd.) At. No. Element. 0, a, ft ft Observer. XIO' 8 xio- X I0~ 8 X I0~ 8 cm. cm. cm. cm. 46 Pd 0-589 0*583 0-516 Bragg 47 48 Ag Cd 0-562 o-557 o-537 o*495 o-475 ~ Siegbahn, V.D.P.G., 1916 49 In 0-506 0-454 50 Sn 0-486 0-432 H 51 Sb 0-469 0*416 52 Te 0*456 0*404 N 53 I o-437 0*388 M 56 Ba 0-388 o*344 74 W 0-2135 0-2089 0-1844 0-1794 Siegbahn, P.M., Nov., 1919 92 U 0-15 O'lO ~~ " L SERIES. At. No. Ele- ment. *, 4 ft * Observer. XIO~ 8 XIO~ 8 XIO" 8 X IO~ 8 X IO" 8 cm. cm. cm. cm. cm. 30 Zn 12-35 Friman, P.M., Nov., '16 33 As 9-701 9*449 5 , 35 Br 8-391 8-141 37 Rb 7*335 7-091 n 38 Sr 6-879 6-639 39 Y 6-464 6*227 40 Zr 6-083 5*851 5386 4 1 Nb 5731 5724 5*493 5-3I7 w 42 Mo 5-410 5-403 5T75 44 Ru 4-853 4-845 4-630 f> 45 Rh 4-596 - 46 Pd 4*374 4-363 4-142 3*93 3720 }) 47 Ag 4-156 4-146 3-698 3-5I5 48 Cd 3'959 3*949 3733 3-5I4 3*33i 49 In 3774 3766 3-550 3-335 3-160 J) 50 Sn 3*604 3-594 3*172 2-999 51 Sb 3*443 3-434 3-222 3 -02 1 2-849 52 Te 3-299 3*290 3*074 2-881 2712 53 I 3*155 3-146 2*934 2750 2-583 55 Cs 2-899 2-891 2-684 2-514 2*350 56 Ba 2786 2776 2-569 2-407 2-245 57 La 2-674 2-665 2-461 2-307 2-146 58 Ce 2-573 2-563 2-359 2'2I2 2*052 59 Pr 2-472 2-462 2-259 2' 1 2O 1-958 60 Nd 2*379 2-369 2-167 2*036 1-875 62 Sa 2-210 2*200 2*000 1-884 1725 63 Eu 2-I3I 2*121 918 1-810 1-662 J? 64 Gd 2*054 2-043 844 i'744 i'597 65 Tb 1*983 1*973 775 1-682 M 66 Dy 1*916 1-907 709 1-622 1-470 67 Ho 1-854 1-843 646 1-568 1-415 68 Er 1794 1783 586 1-514 1-367 fl 70 Yb I-68I 1*670 '474 1-414 1*267 7i Lu 1-629 1-619 1-421 1-368 1*224 i IO! X-RAY SPECTRA L SERIES (contd.) At. Ele- /_ a. ^ ^ 7i Observer. No. iment. **2 **i 1 /i XIO~ 8 X I0~ 8 XIO~ 8 X IO~ 8 + I0~ 8 cm. cm. cm. cm. cm. 73 Ta 1-528 518 -323 280 1-135 Siegbahn & Friman, P.M., July, '16 74 W 76 Os 1-4845 1-398 '4735 388 2792 194 2419 167 1-0955 I -02 1 Siegbahn, P.M., Nov., '19 Siegbahn & Friman, P.M., July, '16 77 Ir 1-360 "350 154 133 0-989 78 Pt 1-323 313 120 101 0-958 ii 79 Au 1-283 271 080 065 O-922 80 Hg 1-251 240 049 042 0-896 81 Tl 1-215 205 012 006 0-864 JJ 82 Pb 1-186 175 0-983 0-983 0-842 83 Bi 1-153 144 0-950 0-954 0'8lO 84 Po 109 0-920 88 Ra oio . 90 Th 0-969 0-957 0766 0797 0-654 92 U 0-922 0-911 0-720 0756 0-615 " M SERIES At. No. Element. a i 7 5 Observer. xio- 8 X I0~ 8 X I0~ 8 Xio- 8 cm. cm. cm. cm. 79 Au 5-838 5-623 (5348 \5-284 5-146) 5-102 / Siegbahn, V.D.P.G., 1916 81 Tl 5*479 5*256 4-826 82 Pb 5-303 5-095 4-9I (?) 4-695 83 Bi 5-117 4-903 (4-561 4-532) 4-456) 90 Th 4*139 3-94I (3-812) i.3'678/ ,/* M 92 U 3-905 3715 3-480 {33J i P.M., Phil. Mag.; P.R.S., Proc. Roy. Soc. ; P.Z., Phy. Zeit.; V.D.P.G., Verh. Deutsch. Phys. Gesell. CATHODE DARK SPACE The thickness (d} of the Crookes dark space is given by d (AI6) + B/V*, where p is the pressure, * 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 * 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 and Watson, Proc. Roy. Soc., 1911.) Gas. Hydrogen Nitrogen Air Oxygen A B 26 -068 065 -057 43 *4o 42 -50 IO2 RECOMBINATION AND DIFFUSION COEFFICIENTS OF RECOMBINATION a a is given below in terms of loop*, 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. 3-42, T.; 3-38, Me.; 3-2, L.; 3-3, H.; 3-32 *,E. -38, T. CO, 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. 2 12 26 18 L., Langevin. H., Hendren. Press, in cms. . 76 45 25 15 10 3-5 a (absolute values), H. . 3*3 2*65 2*07 175 1-55 1-31 1-25 1-15 r a IN AIR AND TEMPERATURE Air at constant density. (E., Erikson ; P., Phillips, Electrician, 1909.) Temp. C. . . . a(intermslOOOe),E. -179 7'5 -68 5-64 12 3*47 64 2-31 100 173 155 1-38 Temp. C. . . . a (relative values), P, 15 i 100 50 155176 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.) lonization Rontgen Rays.l ft and y Rays. Ultra-violet light. Point discharge. D+ at 76 cm. 028 032 0247, '02 1 6 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. iDry Gas. D- 028 -043 025 -04 Dry Gas. dried by CaCl 2 023 123 D- 026 19 Moist Gas. sat. D- 036 Moist Gas. C0 2 f H, sat. \ with [H 2 024 128 D- 025 142 AIR IONIZED BY j3 AND Y RAYS Press, p. in cms. 77-2 55 40 30 20 Press, p. in cms. 77-2 55 40 30 20 D+ at IP C. 0317 2'45 042 2-31 0578 2-31 078 2'34 118 2-36 D- at!5C. pD- 0429 -0542 3*3 078 3-12 103 A.C.P., Ann. de Chim. tt dc Phys. ; P.M., Phil. Mag.; P.R., Physical Review ; P. T., Phil. Trans. 103 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 l 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 2 ), 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. 113. 3ry Gas. X- 76cm.Hg lonization and Observer. Dry Gas. 76 cm. Hg X+ X- lonization and Observer. Air H 2 . He N 2 . 2 . cd' co 2 1-32 1*54 1*40 i'39 1-36 5-4 67 1-36 1-80 178 170 178 1-87 1-401*78 7*43 7*9 5-096-31 1-6* -80 ,1-85 ri 0-83 0*92 14 X Point disch., Chattock, P.M., 1899, 1901. X-rays, Wellisch, Phil. Trans., 1909. Langevin, A.C.P.,i903. Phillips,/>./e.6-., 1906. Zeleny, Phil. Trans., 1900. Mean value. Point disch., Chattock. X-rays, Zeleny, 1900. Franck and Pohl, V.D.P.G., '07. X-rays, Rutherford, P.M., 1897. Zeleny, 1900. Point disch., Chattock. -rays, Wellisch, '09. Point disch., Chattock. C0 2 HC1 . . . S0 2 . . . C1 2 . . . . N 2 O . . . NH 8 . . . Me. acetate . Me. bromide Me. iodide . Et. alcohol . Et. acetate . Et. aldehyde Et. chloride . Et. ether . . Et. formate . Et. iodide . C.C1 4 . . . Pentane . . Acetone . 076 0-86 0-81 1*27* 0-44 ro* 0-82 074 0-33 0-29 0-21 o*34 0-31 0-31 o*33 0*29 0-30 0-17 0-30 0-36 0-31 0-8 1 0-90 0-85 0-41 0-90 0-80 0-36 0-28 O'22 0'27 0-28 0-30 0-3I 0- 3 I 0- 3 I 0-16 0-31 o'35 O-29 X- rays, Zeleny, 1900. Langevin, '03. Wellisch, '09. Rutherford. Wellisch, '09. Rutherford. Wellisch, '09. ; IONIC MOBILITY AND PRESSURE Air ionized by Rontgen rays. (Langevin, A.C.P., 1903.) Press, cm. 7*5 14-8 20 5*45 41-5 2-61 76 i '40 143*5 I Press, cm. 075 K_ 7*5 21-9 20 7'35 41*5 76 7 142 0-9 IONIC MOBILITY AND TEMPERATURE Air at 76 cm. press, ionized by Rontgen rays. (Phillips, P.R.S., 1906.) Temp. C. K. 138 C 2'OO 126 C 1-95 110 r8 5 100 r8i 75 C 1-67 60 i '60 12 t'39 -64 -179 C 0-945 0-235 2-49 2-40 2-30 2'2I 2*12 2-00 1785 0-235 IONIC MOBILITIES IN LIQUIDS AND SOLIDS Ionized by radium rays. (Bohm-Wendt and v. Schweidler, Phys. Zeit., 1909 ; Bialobjeski, Compt. Rend., 1909.) Substance. Substance. (X+ + X-) Petroleum ether . Vaseline 3-8 x i o-* 5*3 x I O H> Ozokerite at 100 80 5-1 x io~ 4 35-0 x lo- 4 A.C.P., Ann. de Chim. et de Pkys. , P.M., Phil. Mag. ; P.R.S., Proc. Roy. Soc. ; V.D.P.G. Verh. Deutsch. Phvs. Gesell. 104 CONDENSATION IONIC MOBILITIES AT HIGH TEMPS K 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- = Xe\/mu = 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. Temp. K+ K_ Observer. Cs, Rb, K, Na, Li . . 1/20 normal KC1 . . NaCl Flame, c. 2000 C. Flame 62 260 ^4.0 C. 1000 1400 \ 1800 J H. A. Wilson,/'. T., 1899 Marx. Ann. der Phys.^ IQOO 1/256 normal K salt . 1/16 normal Na salt . Concentrated sols, of alkalies Flame, c. 2000 si 80 1320 1280 Moreau,^ 'ourn.de Phys., 1903 Cs, Rb, K, Na, Li . . Ba, Sr, Ca .... K, Na Air at 1000 >j i> Flame c 1800 7-2 3'8 *} 8000 \ H. A. Wilson, P. T., 1 899 and P.M., 1906 Gold P R S. 1907 ratio K Flame c 1800 I "^ OOO of potential grad. to current Poten grad.. and gas K 2 CO, . Bunsen burner i < 5,\_*^w i 0600 velocity H A. Wilson, P.R.S., Na Flame c. 2000 1 1 70 1909 Moreau, C JR , 1909 CONDENSATION OF VAPOURS Expansion = vjv^ where v l is the volume of the gas before, and z> 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, J oo.) Gas. Rain-like Condensation. Cloud-like Condensation. Gas. Bain-like Condensation. Cloud-like Condensation. 8 /i S. 4/i S. A 8. "A S. Air . . 2 . . N 2 . . 1-252 1-257 1-262 4-2 4*3 4-4 1-38 1-38 1-38 7'9 7'9 7*9 C0 2 . . C1 2 . . H 2 . . 1-365 i'3 4-2 3'4 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 Ber., 1906.) Vapour and Observer. Ion. */! 8. Vapour and Observer. Ion. v 2 / Vl S. Water (C. T. R. Wilson) T25 4*15 n-Butyric acid, L. . . . ? 38 15-0 Water (C. T. R. Wilson) + T3I 5-8 iso-Butyric acid, L. . . ? 36 1 3'3 Et. acetate, L + I- 4 8 8-9 iso- Valeric acid, L. . . ? 22 6-0 Me. butyrate, L. . . . + i'33 5*3 Methyl alcohol, P. . . + 25 3'i Me. iso-butyrate, L. . . ? i'35 5-2 Ethyl alcohol, P. ... + 17 2-3 Propyl acetate, L. . . . + i'3i 5-0 Propyl alcohol, P. ... ? 18 3-0 Et. propionate, L. . . . p 1-41 7'8 iso-Butyl alcohol, P. . . ? 2 3-6 Formic acid, L. . . . ? 1-78 25-1 iso-Amyl alcohol, J'. . . + 22 5'5 Acetic acid, L + 1-44 9'3 T *' " + 18 4' I Propionic acid, L. . . . ? i'34 9'4 Chloroform, P + '54 3-0 A.C.P., Ann. de Chtm. et de Phys. ; C.R., Compt. Rend. ; P.M., Phil. Mag.; P.R.S., Proc. Roy. Soc. ; P. T. t Phil. Trans. 105 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. H 2 at o C. H 2 ati5C E.S.U. Xio 10 1-29015 1-2230 E.M.U. 0-4300 0-4077 Gas. O 2 at o 2 ati 5 < E.S.U. E.M.U. XIO 10 1-2924 1-2248 0-4308 0-4083 Gas. E.S.U. E.M.U. IdeaH at o gas | at 15 XIO 10 1-2913 1-2241 0-43044 0-40803 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. Ne- Ne+ Observer. X rays Ra rays 1-23 x 10 1-24 x lo 1 10 2*41 x io 10 1-26 to 1-37 x io 10 Townsend, P.R.S., 1908, 1909. Haselfoot, P.R.S., 1909. Ne CALCULATED In E.S.U., Ntf = 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. 102, 103. Gas. Ne+ Gas. Ne+ Ne+ Ne- Air 2 1-52. io 10 1-62 . io 10 1-26. io 10 1-38. io 10 H 2 . C0 2 . 1-50. io 10 1-07 . io 10 1-23 . io 10 1-02 . IO 10 -32. io THE IONIC CHARGE e e = 4-77 x IO- 10 E.S.U. = 1'59 x IO- 20 E.M.U., as a mean of the latest determinations. See Millikan, P.M., July, 1917. lonization. Rontgen rays ; nega-^j tive ions. Ultra - violet light on metal ; negative ions J Rontgen rays ; nega- tive ions. Radium rays ; negative ions. Charged spray of elec- trolytic O 2 . o particles (Ra.)assuming charge = +2e. Electrolytic ions. Charged spray of elec- trolytic O 2 . a particles (Polonium) ; ' charge =: + ie. Electrolytic ions. Radium rays ; negative Method. e in E.S.U. 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 6-5 . io 6-8 3T * 3*4 -10 4' i ,, 47 479 4*67 " 4774,, Observer. f. J. Thomson, P.M., 1898. [. J. Thomson, .M^ 1899. H. A. Wilson, P.M., 1903. J. J. Thomson, Proc. Camb. Phil.Soc., 1903. Townsend, Proc. Camb Phil.Soc^ 1897. Rutherford & Gei- Perrin, C.R., 1908. Lattey, P.M., 1909. Regener, Berl. Ber., 1909. Broglie, Le R., Begeman. [1909. Millikan, P.M.J\ C.R., Comptes Rendus ; Le R., Le Radium ; P.M., Phil. Mag. ; ., Proc. Roy. Soc. 106 em NUMBER OF 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/* = 2*894 * io 14 /(477 * io~ 10 ) = 6'o6 x lo 23 . Method. Gum mastic. Gamboge. Method. Gam mastic. Gamboge. Counting byj ultra micro-) N = 7 . lo 23 N = 7-05 . io 23 scope . .J Brownianj N = 23 N = ^ movements/ e/m FOR NEGATIVE ELECTRONS ejm in E.M.U. gm.- 1 . Velocities v in cm. sec.- 1 . For some other values of e/m 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 Q is the mass of the electron associated with very small velocities. For the variation of e/m with velocity see p. 107. (See also Schuster, P.R.S., 1890.) e/m v Observer. e/m v Observer. CATHODE RAYS LENARD RAYS I "2 X IO 7 I77tor8,, r86 r88 1-87 1-84 175 1-85 1*774 1767 1771 2*4t03'2.I0 9 = ejm^ } 57to7'5.io 9 3-8 to 13 "'I ,,} = e/m Q j 1-9 . io 9 ) 3-8. ioM = e/m Q } J. J. Thomson, P.M., 1897 Kaufmann,/? . */./'., 1897, 1898 Simon, Ad. P., 1899 Seitz, A.d.P., 1902 Starke, V.D.P.G., 1903 Becker, A.d.P., 1905* Classen^.Z.jigoS 0-68 . io 7 3*4toio7.io 9 Lenard, A.d.P. y 1898 INCANDESCENT OXIDES, etc. 0-87 . io 7 0-56 I'S o-itoro.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 Io7 = e/m (on Lorentz's theory) B e s t e 1 m e yer, A.d.P., 1907. ft RAYS O'l . IO 7 177 M r66 1-82 1763 i 1767 11 pi Becquerel, Rap. C.P., 1900 Kaufmann, Gbtt. Nachr.) 1901 Kaufmann,^4 ^/./ ) ., 1906 Kaufmann,^ .d.P., 1906 ^Bucherer,/!.^./'., / 1909 JWolz,^^.P.,ioo9 e/ftiQ ULTRA VIOLET LIQHT ON METAL Lorentz's theory) = e/m (on Abraham's theory) = e/m 9 < 5to2o*6.io 9 = e/w Q 151021 .10? 076 . io 7 ri . io 7 J. J. Thomson, P.M., 1899 Lenard, A.d.P., 1900 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.X.S., Prof. Roy. Soc. ; P.Z., Phys. Zcit.; Rap. C.P., Rapports Congris a Paris ; V.D.P.G., Verh. Deutschs. Phys. Gesell. 107 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 that e/m = 27rV8\/(\ 2 H), where V is the velocity of light ; e]m is in E.M.U. gm.- 1 . The values 179, 177, 1767, 1771, mean 1'775 . 10 r E.M.U. gm.- 1 , agree well with e/m above. Line. e/m Observer. Line. e/m Observer. Hg579i! 546i, 435* Zn, Cd . Cd 4678 Zn 4680 Cd 4678 Zn 4680 770 xio 7 172 to 2-80 r6 1-59 171 179 ( Blythswood & j Marchant, P.M.. [ 1900 [1900 Reese, As. Jl., Kent, As. $7, 1901 Farber, A.d.P., 1902 Stettenheimer, A.d.P., 1907 Zn 4810 . .\ 4722,4680. .) He .... Hg 5791 . . 5770 5790,5770 xio 7 2X 1767 177 1-93 2*06 r8i 1771 /Cotton Weiss, C.R., 1907 Lohmann, P.Z., 1908 Baeyer&Gehrcke, 1909 Ad.P., 1909 ELECTRONIC e/m AND VELOCITY 0*p is the electromagnetic mass of the negative electron for infinitely small velocities, m the transverse mass for a velocity v ; v/V = 0, where V is the velocity of light. (See Lorentz, D Eclair age Electrique, July, 1905, and " The Theory of Electrons," 1909.) On the theory of Abraham (Gott. Nachr., 1902), transverse mass m = tnf 1 .log 1 t-| - A/40 2 Infinitely small. 01 0-5 09 099 0-999 0-9999 999999 i -co 1-015 ri2 1*81 3-28 4-96 6-68 lO'I On the theory of Lorentz (Versl. Kon. Ac. Wet. Am., 1904) and the relativity theory of Einstein (A.d.P., 1905), m = m (i 2 )~ 1/2 . This theory has been confirmed by the experiments of Bucherer (A.d.P., 1909) and Wolz (ibid.\ using rays from Ra with velocities from (9 to 21) x io 9 cm. per sec. Thus the mass of the negative electron is wholly electromagnetic. 001 0-05 0-10 0-20 0-25 0-30 0-32 I'OOI 1*005 ro2o 1*033 1*048 1*056 0-34 0-36 038 0-40 0-42 0-44 0-46 1-063 072 081 091 102 114 126 0-48 0-50 0-52 0-54 0-56 0-58 0-60 140 155 171 188 207 228 250 0-62 0-64 066 068 0-70 0-72| 0741 1-274 1-301 400 441 487 0-76 078 0-80 0-82 0-84 0-86 0-88 1-667 1747 1-843 1-960 2-105 0-90 091 0-92 0-93 0-94 0*95 0-96 2-294 2-412 2*552 2721 2-931 3-203 3-57I 0-97 0-98 099 0-999 4*113 5-025 7-089 22-36 RH AND v: MAGNETIC DEFLECTION When negative rays of velocity v are deflected by a uniform magnetic field H (at right angles to their direction) into a circular path of radius R, then RH = vm/e = V$OB) /((0) = - 2 )~* on Lorentz's theory (see above), and efm Q = 1772 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 o 532 1270 3490 6 33-9 572 1340 3970 12 18 24 30 36 42 48 54 60 66 72 78 84 67-8 612 1410 4660 102 653 1490 5800 695 1570 8330 170 739 1660 204 784 1760 239 830 1860 274 877 1980 310 926 2110 346 977 382 1030 2260 2420 419 1090 456 1150 2620 2850 494 1210 3130 A.d.P. t Ann. der Phys. , As. ?/., Astrophy. Journ. ; C.R., Compt. Rend. ; P.M., Phil. Mag. ; P.Z. Phys. Zeit. 108 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 o particles ; RaC, ThC, and Polonium were observed. Energy of RaC a ray = mv^j^ %v*.2e.tn/e a = 2-o6 a . io 18 */(5'07 . io 3 ) = 8-37 . io 14 * = 1-3 . io- 6 ergs = 3-1 . io~ 13 calories. Loss of energy in air is proportional to path traversed : thus initial velocity of a particle = (velocity of RaC o) x '347 Jr + 1*25 cm./sec., where r is the range of particle. Also V = ro77r 1 / 3 . io 9 cm./sec. (Geiger, P.R.S., 1910.) a Bay. Eange. Initial Vel. Obs. a Bay. Kange. Initial Vel. Obs U . . . ux . . Io . . . Ra. . . RaEm . RaA . . RaC. . . RaF or . Polonium 3-4 1-07? 2-8 7-06 /3'95 13-95 cm./sec. 1-56 . io 9 170 I 7 6 2'06 1-62 MC.&R. Hess. B. B. & K. B. & K. B. & K. B. & K. K. K. &M. L. Rad.Ac AcX . AcEm AcB . Th. . Rad.Th ThX . ThEm ThB . ThC . 6-5 5-8 5'5 3'5 3'9 57 5'5 5-0 8-6 cm. /sec. 176 . io 9 2'00 1*90 1-63 1-89 r86 179 2-25 B., Boltwood, A.J.S., May, 1908; B. & K., Bragg & Kleeman, P.M., 1905 ; H., Hahn, P.M., 1906; Hess, Wien. Ber., 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 a particles from Ra without its radioactive products = 3*4 . io 10 per gm. per sec. Number of a 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 e/m in E.M.U. per gm. 2 efm for helium = 2NE/p = 478 . lo 3 E.M.U./gm. Mean for Ra, Pol, RaC = 4*82 . IO 3 E.M.U. gin" 1 . Since the o particle is a helium atom with a charge of 2e, these values should be equal. * Final velocity of rays used. Subst. Velocity.' e\m Observer. Subst. Velocity.' ejtn Observer. Ra . Pol . RaC. cm./sec. ri8 to 174.10 1-41 . io 9 E.M.U. 4-6 . io 3 5-07 Mackenzie, P.M., '05 Huff (cor?); RaA AcB ThC cm./sec. 1*22 . IO 9 TO I- 9 8 E.M.U. 5-6. io 3 s* r, Rutherford, P.M., '06 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 a particle by the same amount as aluminium foil of density p a and thickness /, then the atomic stopping power, S, of Al relative to air is given by S = 27/^/1 4'4/"apa) = (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. Metal. Metal. Gas. Gas. S. (Air at 20' C., 76 cm.) Al . . Cu . 1-00 2'43 Q Sn Pt Fe 3-17 3'37 4*16 2-26 Ni Au Pb H 2 2-46 4'45 4-27 2'43 2 . N 2 O CO 2 . CS 2 . 1-055 1-46 i '47 2-18 C 2 H 2 Ethylene Benzene Methane I'll i'35 3*37 0-86 A.J.S., Amer. Journ. Sci.; J.A.C.S., Jorirn. Amtr. Chtm. Soc.; P.M., Phil. Mag.; P.R.S., Proc. Roy. Soc. ; P.Z., Phys. Zcti. 109 RELATIVE IONIZATIONS NUMBER OF IONS MADE BY AN a PARTICLE Total number of ions produced by the complete absorption of an a particle with various initial velocities. Observer assumed e 4*65 x io-*>E.S.U. (Geiger, Proc. Roy. Soc., 1909). Ba EaEm. EaA RaC BaF Bange in air at 20 C., 76 cm. . 3'5 cm. 4-83 7-06 3-86 Number of ions 1-53 X io s 174x10* 1-87x10* 2-37 x io 5 1*62 X 10* IONS PRODUCED AT DIFFERENT VELOCITIES BY AN a PARTICLE t 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. Ions per mm. of path in air at 12 C. and 76 cm. 2250 2300 2400 2800 3600 5500 6'5 7600 4000 TOTAL RELATIVE IONIZATION IN GASES BY a RAYS I t = total ionization (relative to air) produced by the complete absorption of o particles in various gases. (B. Bragg, P.M., 1907, used RaC o 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. Gas. Gas. Air . . O a . . . N 2 . . . N 2 O . . NH S . . C0 2 . . Carbon bi sulphide 1-00 ro9,B. ; ro6, R 0-96, B. 1-05, B. ; 0-99, L i -oi, R.;o'9o, L ro8,B. ; 1-03, L i'7 B. Methane Acetylene Ethylene . Pentane . Me. alcohol Me. iodide Et. alcohol Et. chloride i 6, B. and C. 26, B. ; 1-27, L. 28, B. 35, B.; 1-345, 22, B. 33, B. 23, B. 30, B.; ri8, L. Et. ether . . Et. iodide Acetaldehyde Chloroform . Carb. tetra- chloride . '1*31, B.; .1-29, L. 1-28, B. 1-05, L. 1-29, B. 1-31, B. RELATIVE VOLUME IONIZATIONS FOR /?, y, AND X RAYS Relative ionization = Ir = *P/IA where i is the amount of ionization per unit volume for the gas at a press./, and I that for air at press. P, the other experi- mental conditions being the same. In the experiments with 7 rays (column headed 7), j3 rays would also be present. Observers : for and 7 rays, Kleeman, P.R.S., 1907 ; X rays, C., Crowther, P.C.P.S., 1909 ; P.R.S., 1909 ; Me., Me Clung, P.M., 1904. I r 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 O . . C0 2 . . . C 2 N a . . SO 2 . . . CS 2 . . . Pentane . Benzene . Me. acetate 1-001-00100 o-i6o'i6o-i8, C. 1-17 ri6 ri7,Mc, i -60 1-86 2-25 3-62 4'55 3'95 0-89 o'9o i'55 Hard X. i'49, C. 1-5 171 2-27 479>Mc, 3-66 4*53 3'94 3-90, c. Soft X. 1-00 o-o i, C. i'3, Me. 1-57, C. iro, Me. 4*95, C. Gas. Me. alcohol . Me. bromide. Me. iodide . Chloroform . CC1 4 . . -. Et. aldehyde Et. bromide . Et. chloride . Et. ether . . Et. iodide Ni. carbonyl Hg dimethyl- 1-69 373 5-1 1 '75 3'8 1 5'37 4'94 4'93 6-28 6-33 2'12 2-17 3-243-19 4'39 4-29 5-90 6-47 5*98 Hard X. 7I.C. 118 Soft X. 71, C. 145, C. 72, C. 18, C. 89, C. 425, C. P.C.P.S., Proc. Camb. Phil. Soc. ; P.M., Phil. Mag. ; P.R.S., Proc. Roy. Soc. 110 HEAT OF RADIUM RELATIVE IONIZATION PER UNIT VOLUME BY a RAYS Relative ionization = (total ionization) x (stopping power), Metcalfe, P.M., 1909. Air H 2 1-00 He 233 I Br 2 211 3*9 CO. NO. TOO 1-28 HC1 . Ethane i '4 I Propane 2-08 I Butane . 3'05 IPentane 4-02 4-83 For calculated total ionization when Bontgen rays are completely absorbed in various gases, see Crowther, Proc. Roy. Soc., 1 909. 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." 1 =^ 118 cals. gm^hr." 1 The heating effect of a radioactive substance is proportional to the ionization it produces (Duarie, 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, have no effect on heat emission (Schuster, Eve, and Adams, Nature, 1907 ; Rutherford and Petavel, B.A. Rep., 1907 ; Schmidt, P.Z., 1908). Heat. 0278 0292 0306 Observer. Curie and Laborde, C.R., 1903 Runge and Precht., Berl. Ber., 1903 Rutherford and Barnes Nature, 1903 ; P.M., 1904 Heat. 0372 0328 Observer. Produced by Ra 1R.&B Em + RaB[/W. RaC jioo4 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 x -0328/(A x 6 x io- 4 ) = 1-9 x io 7 calories. For old (mineral) thorium metal, the heat emitted is 5 x io~ 9 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. 115). 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 l /(275 x io 19 x 2-19 x io- 6 ) = 5-64 x io- 4 c.c. (Rutherford, " Radioactivity"). The volume of the emanation changes anomalously after it is first formed. Observed vol. Observer. Observed vol. Observer. 58 cub. mm. 60 1 Rutherford, P.M., 1908 Gray & Ramsay, 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., Ccmpt. Rend. ; J.C.S., Journ. Chcm. Set. ; P.M., Phil. Mag. ; P.Z., Phys. Zeit. Ill 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 R. -127 C -101 C -78 -65 = B.P. 76 Temp. C. Vap. press.l em. Hg J -70 -4 ! -62 =B.P 76 -60-6 80 -55-8 100 -38'5 200 400 -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. t 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 I = const, for AcEm. between o and 20. (Molec. wgt. ThEm.)/(moleC. wgt. AcEm.) = 1*42 (Russ). Mol. wgt. of RaEm. = 222 (Gray & Ramsay, 1910). Gas. p. and tC. D. Molec. wgt. Obs. Gas. p. and tC. D. Molec. wgt Obs. RADIUM EM. ACTINIUM EM. (contd.~) Air C0 2 . . . Diff. of Em. into air com- pared with 2 ,C0 2 ,S0 2 , into air . . Em. into H 2 compared with Hg vap. into H 2 . 76? 76, io 76,0 275 07 to '09 10 101 034 Em. 037 Hg 0407 Hg C. 100 75 to 100 1 80 to 99 235 R.&B C.&D C. B.&W M. Air i '4 76-4 76 76 to *9 '112 7-81 125 123 10 70 70 THORIUM EM. ACTINIUM EM. H 2 . . H 2 . . S0 2 . Argon C0 2 . CO., 76, 15 76, 10 toi8 76, 15 412 '33 062 106 073 077 B. R. B. Em. into air, compared with H 2 , O 2 , S0 2 , C0 2 , into air . . Air . . Argon 76 8-2 I to 76- 1 j 76 76 09 103 966 to 103 103 084 -.90 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 j 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. Journ. Set.; C.N., Chem. News ; C.R., Compt. Rend.; J.C.S., Journ. Chem. Soc. ; P.M., Phil. Mag. 112 Ra IN ROCKS EQUILIBRIUM ACTIVITIES IN MINERALS Relative activity of radioactive products in minerals. Bolt wood (A.J.S., April, 1908) found U 2*22 times as active as the Ra alne in minerals (see McCoy and Ross, A.J.S.). Product U lo Ea RaEm. RaA BaB BaC BaF 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 6 gms. U equal in activity 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) suggested that the heat liberated by radioactive changes is one of the sources of 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 u 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 io"- 8 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 f, 2*9 X io~ 10 ; for average igneous rock, 1 1 x io~ 10 . (See Strutt, Proc. Roy. Soc., 1906-7 ; Joly, "Radioactivity and Geology," 1909.) Bock, etc. Obs. Ba Th gm. per gm. of rock. St., 1906 E. M" 1907 11 11 11 11 11 ]., 1009 F. F., 1909 J., 1909 other obs. B., 1909 F. F., 1909 J- *909 Fl.,"i9io ( J., 1910 * > 11 ' 11 X io- 17 PJ 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 I0~ 6 2-3 i '3 5 igneous sedimentary 1-9 *5 to I'2 ~ 5 16 <'05 Sandstone Clays Ordovician ... Lavas ejected since 1631 * . . . LJIVJI Mount F rebus - - i*>6 igneous rocks 64 Italian igneous rocks Campbell and Auckland lslands,\ N.Z / St. Gothard Tunnel granite schists and altered sedimentary \ Simplon Tunnel II Calcareous and dolomitic European rocks ......... Deep-sea deposits Red clay 8 Extent : l 50, * 2*5, 3 51 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. R Preliminary result. B., Blanc., P.M. ; E.M., Eve and Mclntosh, P.M. ; F.F., Farr and Florance, P.M. ; Fl. f Fletcher; J., Joly, P.M. ; S., Strutt (above). A.J.S., Amer. Journ. Sci.; P.M., Phil. Mag. 113 ELECTRIC ARC RADIUM IN SEA-WATER In grams per gram of sea-water. Deduced from the observed amount of Ra Em. Amount. Place. Observer. Amount. Place. Observer. 2-3 xio- 15 16 Mid. N. Atlantic Atlantic Eve, P.M., 1907 Jo'iy, P.M., 1908 4 x io~ 15 H 5 Nile Mediterranean Indian Ocean ' ^1909 ?' D M 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. RaEm. Place. Observer. 24-27 x io~ 12 60 86-200 Montreal Chicago Eve, P.M., 1907 1908 Ashman,^4.y.v$Vo8 35-350 xio- 12 Mean 105 \ Cam- / /bridge! 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. Camb. Phil. Soc., 1910.) Ion. Mean K Observer. Ion. Mean K. Observer. Small . . . Intermediate c. -oi Langevin, '03 Mean Large . . Large . . Large . . 0003 0003 * 0008 f Langevin, C. A 1 ., '05 Pollock, 1908 J * Humidity, 19 grms. H Z O per cubic metre, t '5 grm. H 2 O per cubic metre of air. Pollock, Austl. Ass. Adv. Sri., 1908. ELECTRIC ARCS Mrs. Ayrton's formula for carbon arcs, E = a + + - : , has been shown by Guye and Zdbrikoff (Contpt. Rend., 1907) to hold for short stable arcs between metals. E is the voltage across the arc, * 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 -, ohms, where E, is the total available voltage ; or E x must exceed a + / + 2*/R(y + 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 and quality used by Mrs. Ayrton. (See J. J. Thomson, " Conduction of Electricity through Gases;") Metal. a I 7 i Metal. a | 7 5 C. . 38-88 2-074 n-66 10-54 Pd . . . 21-64 370 O 2178 Fe . Ni . 1573 I7-I4 2-52 9*44 15-02 17-48 Pt ' " ' I4-I9 24-29 3^4 4'8o 11-36 19*01 20-23 Co . Cu . 2071 21-38 2-05 3-03 2-07 10*69 IO'I2 I5-24 An . . . 20-82 4-62 12-17 20-97 A. J.S. , Amer. Journ. Sci. ; C.R., Compt. Rend. ; P.M., Phil. Mag. ; P.R.S. , Proc. Roy. Soc. ATOMIC CONSTANTS 114 ATOMIC AND RADIOACTIVITY CONSTANTS References : J. J. Thomson's " Conduction of Electricity through Gases," Ruther- ford's " Radioactivity," H.A. Lorentz, Eclairage Electrique, 44, 1905, "Theory of Electrons," 1909, Jeans' " Dynamical Theory of Gases," and Millikan, P.M., 1917. Symbol. Definition. Value. e. . NE . II e/m 2e/m He m a E a. Ionic charge, half charge on an particle Total charge carried in electrolysis by the atoms in c.c. of gas For ideal gas at o and 76 cm. oxygen hydrogen Total charge carried by i (gm. molecule) of hydrogen ions Number of molecules per c.c. of a gas at o C. and 76 cm. NE/ = 2 x -43 . iQ- 6 / (2 x 8-987) Electromagnetic mass of negative elec- tron for small velocities = */() oxide, CuO .... 79'57 6*30-6-43 II48 insoluble sulphate, CuSO 4 5H 2 O 249*71 2-28/15 /4H 2 O/ioo) \5H0 2 /2 4 o| dec. r. ht. see p.i3 3 . 5203 /liq. -866/17! I A. 52-32 J -39 -22 4*5V/2o Erbium "}8v4 8*6 infusible . insoluble sulphate, Er 2 (SO 4 ) 3 . . . 76771 3*i8 dec. 950 23/20 Gadolinium sulphate, Gd 2 (S0 4 ) 3 . . 602*78 4*14/15 2*3/34 Gallium chloride, tri-, GaCl 3 . . . 176*48 A. 353/240 75*5 220 decomp. Germanium chloride, tetra-, GeCl 4 . . 214*34 1*89/18 86 decomp. oxide, di-, GeO 2 .... 104*5 4-70/18 4/20 Glucinum. See Beryllium. Gold -Q-.-g __ 288* dec. 1 80 68 Hydrazine, NH,.NH t . . 32-05 1-01/15 1*4 v. soluble hydroxide, NH 4 . H,O 50-07 1*030/21 <-40 119 v. soluble Hydrobromic acid, HBr . . 80-93 { A. 80*77 ) -86 -668 /22I/0 (130/100 Hydrochloric acid, HC1 . . 36-47 929/0 f -112 84-1 see p. 1 32. Hydrocyanic acid, HCN . . 27-02 697/18 -i3'8 26-1 00 * Under chlorine at 1520 mms. f Rupert, 1909. dec. or decomp. = decomposes; Moissan, 170-172; oo = soluble in all proportions. 121 PHYSICAL CONSTANTS INORGANIC COMPOUNDS (contd.) For general heading, see p. 117. 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 2O'OI I27'93 34*02 81-22 34-08 I29-52 33 '03 233*3 i75'93 195-86 126-8 71-84 278*01 392-14 231-52 162*22 404-01 159-68 399-86 379-32 267-20 278-12 461-04 223-20 685-6 239-2 303-26 73-88 42-40 68-95 29-88 133-88 109-94 84-32 203-34 256-44 40-32 335'i 246*49 at /temp. /'988/1 5) \A. 20-04) /2799/-357\ 1 A. 126-8 / 1-458/0 A. 8 1*20 (liq. -9 \ \A. 34'ioj A. 127*1 1-227/14 3-11 4-63/0 |r4664/i8 } \ A. 188-2 / 2-99/J8 1-8988/14-4 1-865/15 5-5'4 ( 2-804/10-8 \ ^A.324-2/320 / 1-683/20 S'2-5'3 3-097/18 2-5 6-43 5-873/15 6-12 9'37> 8-74 9-09/15 8-91-9-5 6-23 2*1 1 2-2*07 2-3-2-4 2-10/15 2- 4 /I5 2-21/15 3^4 I-56/I 7 1-464 3'2-3-7 1-64/15 1-678/16 at. /mms. - 92-3 -50-6 _o -6 4 -83-8 - 4 8 33 4H a O/i 7 o -19-7 1419 64 1538 301 47-2 3H 2 0/75 447 375 877 dc.5oo-53o decomp. 937 618-710 614 c. 258 subl. 1000 857 818-853 dec. 350 2H 2 O/ioo 90 c. 2800 5H 2 0/i5o at./mms. I 9 -4 -35-6 8o-2/47 ' -42 -59-4 { 7 o ? /6o dec. 25 io2'7/764 volatilizes 6H a O/ioo 28o-285 decomp. 280 c. 900 861-954 dec. w. ht. decomp. 5H 2 0/3 3 o at./temp. 111/35 ("42,500 \ V/io v. soluble 33iV/i 3 3os"V/i5 seep. 132. soluble soluble soluble 75/i6 p. 50/19 insoluble 20-8/10 (i 8/0 \ 78/75 insoluble 537/ioo v. soluble insoluble v. slgt. sol. '46/15 decomp. 7/0 04/0 -002/20 insoluble insoluble 004/18 seep. 133. 72/o 35/o 5/o 04 26/0 oi 54/20 42/18% ooi 02 27/0 fpllnride H A Te . Hydroxylamine, NH 2 OH . . Iodine lodic acid, HIO 3 .... Iron carbonyl, Fe(CO) 5 .... ferrous chloride, FeQ 2 . . oxide, FeO .... sulphate, FeS0 4 .7H 2 amm.sulphate,FeSO 4 (NH 4 ) 2 SO 4 6H a O 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 a (S0 4 ) 3 (and + 9 H 2 0) Lead- acetate, Pb(C 2 H 3 O 2 ) a . 3H 2 carbonate, PbCO 3 .... chloride, PbCl 2 iodide, Pbl 2 oxide, mon- (litharge), PbO . red lead, Pb 3 O 4 . . . per- (brown), PbO 2 . sulphate, PbSO 4 Lithium- carbonate, Li 2 C0 3 . . . . nitrate, LiNO 3 phosphate, Li 3 PO 4 . H a O . . Magnesium- carbonate, MgCO 3 .... chloride, MgCl 2 .6H 2 O . . nitrate, Mg(NO 3 ) 2 6H 2 O . . oxide, MgO phosphate, Mg 3 (PO 4 ) 2 . 4H 2 O sulphate, MgSO 4 . 7H 2 O. . atm. = atmospheres ; dc., dec., or decomp. = decomposes ; liq. = liquid ; slgt. = slightly ; v. = very ; w. ht. = white heat. 122 PHYSICAL CONSTANTS INORGANIC COMPOUNDS (contd.) For general heading, see p. 117. Substance and Formula. Formula weight (0 = 16). Density, gms./c.c. Melting Point, C. Boiling Point, C. Solubility in Water. Manganese at./temp. at./mms. at./mms. at./temp. carbonate, MnCOs .... 114*93 S'I-3'7 decomp. v. slgt. sol. chloride, MnCl.4H 2 O . . I97-9 I-9I T. 87-6 M.P. 650 107/10 nitrate, Mn(NO 3 ),.6H 2 O . 287-05 1-82 T. 25-8 54-5/1 iA oxide, -ous, MnO .... 70-93 5'I 1500 insoluble ,^ -ic, Mn,O 8 .... 157-86 4-3-4-8 O, 1080 insoluble tetr-, Mn,O 4 .... 228-79 47-4*9 ' .'. insoluble cli-. MnO .... 86-93 4-7-5 'o 4 0, 535 insoluble sulphate,* MnSO 4 4H,O . . 223-05 2-1 1 8 and 30 t M.P. 700 111/54 Mercury mercurous chloride, HgCl . 236-06 /6"48and 7-2 ( I A. 237 7 I sublimes 382-5 0002/18 nitrate, HgNO.2H 2 O 298*64 4-78 decomp. v. soluble sulphate, Hg 2 SO 4 497-26 -7-06/25 melts. decomp. 2 cold mercuric bromide, HgBr- . 360-44 574 235 subl. c. 322 i/ 9 chloride, HgClg . 271-52 /S-3-5'5 \ I A. 283! 287 303-307 /5'4/2o(,) (see p. 1 33. iodide, red, Hgl, . 454-44 (6-2-6-3 1 \ A.452J 241-257 349 003/17 yellow, Hgl, 454-44 5'9-6-x 241 349 insoluble oxide, HgO . . . 216-6 11-14 dec. r. ht. 005/25 sulphate, HgSO 4 . 296-66 6-47 dec. r. ht. decomp. Molybdenum chloride MoClg 27 VI A. 27 '(/'{JO IQ4 268 decomp. */ J J I28-O * / Ji jj v 6-4/10 * VT- insoluble tri-, MoO f .... I44-0 \J -+j 1 V 4-696/26 759 sublimes *2 cold Nickel carbonyl, Ni(CO) 4 .... I70-7 1-318/17 ~ 2 5 43 insoluble chloride NiCl, . . I2O/6 2-56 sublimes r izlo( 6} nitrate, Ni(NO,),.6HO. . 290-8 2-06/14 56-7 J3l^ J \r'/ 4 8- 5 /i8A sulphate, NiSO 4 . 7 H a O:t 280-85 1-98 98-100 6H a O/io3 3I-5/9 Niobium chloride, penta-, NbCl 5 . . 270-4 14-4-4-5 \ \ A. 278/360; 194 240-5 decomp. Nitrogen nitric acid, HNO 8 . . . . 63-02 1-53/15 -41-3 86 CO nitrous oxide, N,O . . . . 44-02 /i*226/-8 9 -4\ \ A. 44-28 || / -102 -89-8 /74V/I 5 (seep.132. nitric NO .... 30-01 A. 30*011 -160-9 -153 K-iV/15 \seep.i32. nitrogen trioxide, NfO, . . 76-02 i*447/-2 -102 42*7/757 soluble peroxide, NO 2 to N,0 4 46-01 1*49/0 - 10-8 21-64 soluble pentoxide, N a O B . 1 08 -02 1-64/18 30 dec. 45-50 soluble oxychloride, NOC1. 65-47 i -367; -8 '6 -60 -S'0 /75" decomp. Osmium oxide, tetr-, OsO 4 . . . . 254-9 A. 257-3 20 100 soluble Ozone, Os 48*00 /'002I4 \ \ A. 48-03 / dec. 270 -119 v. slgt. sol. Palladium chloride, PdCl 8 . 2 H,O . . 2I3-65 501 soluble * The ordinary salt ; also six other hydrates. t Stable between temps, given. J Also anhy. and 6H 2 O. Density, p. 28. || -698/23-7 ; r. ht. = red heat j slgt. = slightly ; subl. = sublimes ; v. = very ; oo = soluble in all proportions. 123 PHYSICAL CONSTANTS INORGANIC COMPOUNDS (contd.} For general heading, see p. 117. Substance and Formula. Formula weight = 16) Density, gms./c,c. Melting Point, C. Boiling Point, C. Solubility in Water. Perchloric acid, HC1O 4 . . Phosphorus- bromide, tri-, PBr 3 .... chloride, tri-, PC1 3 .... penta-, PCI, . . . fluoride, tri-, PF 3 .... oxide, tri-, P 4 O 6 .... tetr-, P 2 O 4 .... pent-, P 2 O 5 . . . . Phosphine PH 3 ico-47 270-8 I37'42 208-34 88-04 220-2 I26-I I42-I 34-06 66-n 70'53 337-04 119-02 138-2 122-56 74-56 294-2 65-11 329-23 422-38 56-11 214-02 166-02 lorn 158-03 174-26 136-17 97-18 385-84 230:9 120*9 at. /temp. 1-76/22 2-92/0 A. 281 i 612/0 A. 141 A. 104-2/296 A. 87-4 liq. 1-94/28 2-54/23 2-39 A. 34-31 i -007- ro 1 6 2-76/20 2-29 2-34/17 1-99/15 2-69/4 1-52/16 1-8109/17 I-8533/I7 2-04 3-97/I8 / 3-04/24 \ \ A. 159/1320) 2-1/4 270/10 2-66/20 2'24* ; 2'6l f 1-91 27 9 8/25 3-6II/20 2- 9 I/I7 3-95/15 3-9I/I5-7 2- 9 5/I5 1*520 A. 172 A. 103-4 at./mms, 35 -41-5 -112 148 -1 60 22-5 >IOO 800 -133 <-IO 26 decomp. 733 909 5 357 790 400 red heat decomp. . / 3 H a O/6ol \ -80 / 360-4 560 678 337 dec. 240 1066-5 200 173-8 728 837 726 39~o decomp. 58 -89 -77 at./mms. I 9 /II 175 76 . 162 -95 173 c. 1 80 subl. r. ht. -85 57/735 ' sublimes subl. w. ht. dec. 810 dec. 400 subl. w. ht. dec. 500 red heat subl. \v. ht. 1420 dec. 400 sublimes decomp. dec. 740 dec. c. 145 sub. c. 260 260 57-5 -657181 at./temp. soluble decomp. M soluble 51 v. soluble slgtly sol. insoluble decomp. v. soluble seep. 133. 89/0 3/o seep. 133. 5/o 122/103 33/4 28/12 seep. 133. 8/20 / 127/0 \seep.i33- seep. 133. 6-4/15 9-2/10 36/0 217/20 soluble v. soluble 84/10 43/io decomp. v. soluble 51 >) decomp. liquid, P 2 H 4 . . Phosphonium chloride, PH 4 C1 Platinum chloride, tetra-, PtCl 4 . . . Potassium carbonate, K 2 CO 3 .... chlorate KC1O 3 chromate, bi-, K 2 Cr 2 O 7 . cyanide K.CN . ferricyanide, K 3 Fe(CN) 6 . . ferrocyanide, K 4 Fe(CN) 6 . 3 H 2 hydroxide, KOH .... iodate, KIO 3 nitrate KNO 3 permanganate, KMnO 4 . . sulphate, K^SO 4 .... acid, KHSO 4 . . sulphocyanate, KCNS . . Radium Rubidium carbonate, Rb 2 CO 3 . . . chloride, RbCl sulphate, Rb 2 SO 4 .* . . . Selenium 266-96 229-32 IIT2 I29-22 I45-22 I70-I4 104-3 oxide, SeO 2 .... Selenious acid, H 2 SeO 3 . . Selenic acid, H 2 SeO 4 . . Silicon chloride, tetra-, SiCl^ . . . fluoride, SiF 4 * Monoclinic. t Rhombic. * Moissan, 1905. amorph. = amorphous ; cryst. = crystalline ; dec. or decomp. = decomposes ; r. Jit. = red heat ; sub. or subl. = sublimes; v. -=very ; w. ht. = white heat. PHYSICAL CONSTANTS 124 INORGANIC COMPOUNDS (contd.) For general heading, see p. 117. Substance and Formula. Formula weight (0 = 16). Density, gms./o.c. Melting Point, C. Boiling Point, C. Solubility in Water. Silicon (contd.) oxide (silica), amorph, SiO 2 ,, quartz, SiO 8 . Silico chloroform, SiHCl 3 . Silver- 60-3 60-3 135-69 187-8 H3'34 234-8 169-89 311-82 38176 102-92 106-0 84-01 58-46 40*01 149-92 85-01 78-00 358-2 142-06 322-22 252-17 248-20 247-46 147-64 158-55 211-65 103-63 119-63 183-69 64*06 80-06 ftydroge 98-076 198-42 I59"5 175'S at./temp. 2-2/16 2-6495/20 1-65 A. 133-2 6-47/25 {A.i65 5 /i735 } 5-67/25 4'35/i9 5'4 1-694/17 3'i 2-4-2-5 2-2 2-17/20 2-13 3-65/18 2-27/20 2-80 1-52/16 2-67/20 1-492/20 1-594/15 1-73/17 4-2/24 3-6 3-05 3/17 4-45-4-6 546 37-4 fi'434/ol \A. 65-541 /I-923/20 ) IA. 80-19 / n sulphide. 1-834/18 A. I99-5 5-9/0 5-07/15 at./mms. indefinite 1780 -1-3 398 436 c. 540 218 660 red heat 765 852 C0 2 /2 7 801* 3i8 650 c. 3I3 decomp. 38 883-2 T. 3 2-383 7H 2 0/i 5 o 32-48 498-630 830 { dec. 645 3000 decomp. 1605 -76 16-79 10-5 175 dull r. ht. decomp. at./mms. sT dec. 700 dec. r. ht. decomp. decomp. w. heat w. heat 3H 2 0/r.i6o 7H 2 0/i 5 o{ decomp. dec. 220 C0 2 /i 3 4o 4H 2 0/6ol 6H 2 O/ioo.l -10-8 44-88 dec. 40 327 * > 700 at./temp. C. '001 insoluble decomp. 6 8/20 *0 3 I5/20 o 6 3/2i seep. 133. 77/17 52-3/100 77/0 seep. 133. 8/10 seep 133- 63-5/I5 178/20 73/o sol. ; dec. 9-3/20 seep. 133. 5/o 50-6/32-7 25/15 60/10 93/io 001/24 f 48/10 \seep.i33- 55/io 35/o decomp. 011/18 f 4730 V. 15; P- (132. decomp. CO decomp. 0007 insoluble chloride AgCl nitrate AgNO 3 .... sulphate, Ag 2 SO 4 .... Sodium borate (borax), Na 2 B 4 O 7 . ioH 2 carbonate, Na 2 CO 3 . . . bi-,NaHC0 3 . . chloride, NaCl .... hydroxide, NaOH .... iodide Nal nitrate NaNO .... peroxide, Na 2 O 2 .... phosphate, di-, Na 2 HPO 4 .i2H 2 O sulphate, anhy., Na 2 SO 4 . . Na 2 SO 4 .ioH 2 O sulphite, Na 2 SO 3 . 7H 2 O . thiosulphate (hypo'), Na a S 2 O s .5H 2 Strontium carbonate, SrCO 3 .... chloride, SrCl 2 (and + 6H 2 O) nitrate, Sr(NO 3 ) 2 .... oxide, SrO per-, Sr0 2 .... sulphate, SrSO 4 .... Sulphur dioxide, S0 trioxide, SO S a form . . . Sulphuretted hydrogen. See Sulphuric acid, H 2 bO 4 . . Tellurium chloride, TeClj oxide, di-, TeOj. . . . tri-, TeO s .... * 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. 125 PHYSICAL CONSTANTS INORGANIC COMPOUNDS (contd.) For general heading, see p. 117. 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 3 chloride, tri-, T1C1 3 . . * . mono-, T1C1 . . oxide (thallous), T1 2 O . . sulphate, T1 2 SO 4 .... 468-0 310-38 239-46 424-0 504-06 at. /temp. 7'i 7-02 6- 7 7 at /mms. 272 25 426 >87Q 632 at./mms. decomp. 7c8-7i9 decomp. at. /temp. 4/15 v soluble 2/0 v. soluble 47/15 Thorium nitrate, Th(NO 3 ) 4 . I2H 2 O ox ; de ThO 2 696-38 264-15 9-87/I5 ~~~ v. soluble insoluble Tin- chloride (stannous), SnCl 2 (stannic), SnCl 4 . oxide (stannous), SnO . . 189-62 260-54 1347 S f 1 J 2-279/0 A. 266 6'3 249 -33 dec. r. ht. 620 114-1 270/15 soluble insoluble (stannic), SnO a . . 1507 6>6^6'9 113 ii Titanium- chloride, tetra-, TiCl 4 . . oxide, di-, TiO 2 .... 189-94 80- 1 1-76/0 A. 198 37-4-2 1560 136-4 decomp. insoluble Tungsten- chloride, hexa-, WC1 6 . . 39676 A. 379/350 275 347 5) oxide, tri-, WO 3 .... 232-0 7-2 red heat ) Uranium oxide, di-, UO 2 . . . . 270*2 10-9 2176 5> (green), U 3 O 8 . . 842-6 7*3 decomp. J5 (yellow), U0 3 . . 286-2 5-1 decomp. ,. (black), U 2 5 . . Uranyl chloride, UO 2 C1 2 . 55^4 34i'J2 8-4-9-2 fusible decomp. 320/I8 nitrate, UO 2 (NO 3 ) 2 .6H 2 O 502-32 2-81 T. 59-5 200 Vanadium chloride, tetra-, VC1 4 . . 192-84 1-86 A. 1937 -18 154 soluble oxide, pent-, V 2 O 5 . . . 182-0 3-357/18 658 0-8/20 Zinc- carbonate, ZnCO 3 . . . 125-37 4'4 C0 2 , 300 0-001/15 chloride, ZnCl 2 .... 136-29 2-91/25 262 730 33o/ro sulphate, ZnSO 4 . 7H t O . 287-54J 1-966 3'623/i5anhy. J6H 2 O/ioo / 7 H 2 Oam (red heat./ ( 42/0 80-8/100 sulphide, ZnS Q7M3 4-'O IOSO subl. 1 1 80 insoluble Zirconium 7/ TO ^T * J I22'6 C'I-C'7 c. 2500 __ j j / J> 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 . . 15 C. 2 of snow or .crushed ice, I of\ __ T oo 8ofNa 2 SO 4 5 of water -17 NaCl / ~ lo CO j and ether 78*35 3 of snow, 4 of cryst. CaCh . -48 i l^\J PHYSICAL CONSTANTS 126 ORGANIC COMPOUNDS Formula (Molecular) Weight, Density, Melting and Boiling Points. For general heading", see p. 117. Substance and Formula. Formula weight (0 = 16). Density, gms./c.c. Melting Point, C. Boiling Point, C. Acetaldehyde, CH 8 . CHO . . Acetic acid, CH 3 . COO H . . 44-04 60-04 130-11 58-06 26-03 72-05 240-13 58-06 76-52 9913 130-15 88-12 88-12 88-12 88-12 93-10 108-1 178-15 165-29 132-1 106-08 78-08 122-08 182-15 140-54 108-10 67-20 295-15 154-19 157-0 58-10 74-10 74-10 88-12 92-55 130-18 88-07 88-07 138-03 212-18 152-19 200-18 116-13 76-13 60-07 I53-85 at./tmp. 788/i6C. 1-05/20 1-028/20 7900/15 / -46/-7 \ \ A. 26-34 / 1-062/16 8525/20 937/I9 1-017/10 879/20 812/20 825/0 825/0 814/15 1-023/15 9925/25 1-15 1-52/15 1-55/4 1-05/15 87843/20 1-26/21 1-098/50 'I-2I2/20 I -043/20 2-3/^8 i-oi 1-4948/20 6o/o j 813/20 819/22 812/20 887/20 77/20 96/19 950/20 1-23/19 992/10 1-19 9220/20 1-292/0 2*104 1-5936/20 at./mms. -123-6 I6'7 <-8o -95 -8i'5/S95* 10 290 liquid -136-4 liquid liquid liquid liquid liquid -12 -6-4 -37-2 216 liquid decomp. -I3'5 5'4 121-4 48 i liquid 210 -30-6 -135 -79-9 52 liquid -3'I2 -79 200 234 I76-4 200 2 8 -112, H. -22-95 at./mms. 20-8 1 18-5, Y. 181 56-5 -83-6 140 430 96-7 46 151 148 137-8 129 118-5/753 102*5 183-9 154 360 86 decomp. 179-5 80-2, Y. 249-2 305-9 197 206*5 187 107 sublimes 156, Y. "3 II7-5 99-8 H3 78 141 162-3 154 sublimes 205-3 distin. CO 2 207-5 46-2 -47 767, Y. Aceto-acetic ether, CH 3 CO . CH 2 CO 2 . C 2 H K Acetone, CII 3 COCH 3 Acetylene, C 2 H 2 Acrylic acid, CH 2 : CHCO 2 H . Alizarine, C,H 4 (CO) 2 C 8 H 2 ^OH) 2 . . Allyl alcohol, CH 2 : CH . CH 2 OH . . chloride, CH 2 : CHCH a Cl . . . thiocyanate, CH 2 : CHCH 2 CNS Amyl acetate, C 5 Hn . CH 3 CO 2 . . . alcohol (n.), CH 8 (CH 2 ) S CH 2 OH (act.),CH 8 C 2 H 5 CHCH 2 - OH (sec.),C 3 H 7 CH(OH)CH 3 (tert.),(CH 3 ) 2 C(OH)C,H 6 Aniline, C 6 H 6 . 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 ) 3 . . . Asparagine(l.)C 2 H 3 NH 2 CO a H.CONH 2 Benzaldehyde, CH 6 CHO Benzene, C e H 6 Benzoic acid, C 6 H 6 . COOH .... Benzophenone, (C 6 H 5 ) 2 CO .... Benzoyl chloride, C C H 5 COC1 . . . Benzyl alcohol, C 6 H 5 CH 2 OH . . . Beryllium ethyl, Be(C 2 H s) 2 .... Bismuth triethyl, Bi(C 2 H 6 ) 3 .... Borneol Ci.), C 10 H 17 OH Bromo benzene, t^HsBr ... Butane (n.),*CH 3 . CH 2 . CH 2 . CH, . Butyl alcohol (n.),CH 3 (CH 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 4 H 9 ) 2 O Butyric acid (n.), CH 8 (CH 2 ) t COOH . (iso),(CH 8 ) 2 CHCOOH . Cacodylic acid, (CH 3 ) 2 AsO . OH . . Caffeine, C 8 H 10 N 4 O 8 . H 2 O .... Camphor, C 10 Hi6O Camphoric acid (d.), C 8 H 14 (COOH) a . Caproic acid, CH,(CH) 4 COOH . . Carbolic acid. See Phenol. Carbon bisulphide, CS a oxysulphide COS .... tetrachloride, CC1 4 .... * Mackintosh, 1907; decomp. = decomposes ; 1. = Isevo-rotatory (see p. 82). Y., Young, Journ. de Phys. t Jan., 1909. H. = Henning. 127 PHYSICAL CONSTANTS ORGANIC COMPOUNDS (contd.) For general heading, see p. 117. Substance and Formula. Formula weight (0=16). Density, gms./c.c. Melting Point, C. Boiling Point, C. Cellulose (CgHjoOs) Xlfo'Il 94'49 112-53 165-41 H939 228-19 154-19 148-11 132'!! 2IO'II I2I'I4 I27-I9 I08-I 43-02 52-03 I34-I6 324-22 86-07 128-95 73-12 .149-18 86-11 45-08 178-11 168-08 154-14 169-16 92-52 122*10 30-06 74'IQ 88-07 I30-II 46-06 45-08 150-13 I08-97 II6T3 64-51 55-07 74-06 I56-0 , 116*13 62-I2 91-06 at./temp. 1*27 1 61 I-39/75, 1-1062/20 1-90 1-49887/15 9275/16 1-247 1-05/24 1-542/18 953/22 849/25 1052/15 1-14/0 /liq. -866/17) \A. 52-3 J 852/25 1-04 9734/22 1-522/15 706/20 94/18 8231/12-4 686/-6 1-341/15 1-546/17 1-16 1-159 ' 1-203/0 i'45/i7 liq.*446/oA,3o 7135/20 9005/20 1-028/20 79360/15 699/8 1-05/16 1-45/15 879/20 92 1/0 A. 64-22 794/7 9226/20 1-944/14 890/0* 839/20 1-116/15 at./mms. 67 -45-5 H Ife 250 2 133 ~7'5 153 -2'5 .3. liquid -35 -73'5 -4 -40 -38-1 liquid 48 91. 70-5 54 126 -177-5 - 123-3 H -83-4 <-8o -114-9 -85 -3 2 '7* -116 -93'3 140-85 -103 -80-5 1 10-9 22 112 at./mms. 1 86 132, Y. 97-5 61-2 448/76o 176 300 I29/20 decomp. 1 80 170 190*1 dec. -207 175 877 190 55'5 216 ioi'5 7*2 280 302-8/770 255 302 116 330 -84-1 34-6, Y. 77-1 181 78-3, Y. 187 2IT2 38-4 120'6 12-5 97 54-3, Y. 72-3 IIO'I . 36-2 87 Chlor acetic acid, CClH 2 .COOH . . hen/pne CH K C1 . Chloral hydrate, CCi 3 . CH(OH) 2 . . Chloroform CHCU Cineol, eucalyptol, C 10 H 18 O .... Cinnamic acid, C 6 H 5 CH : CHCOOH aldehyde, C 6 H 5 CH : CHCHO Citric acid, (CO 2 HCH 2 ) 2 C(OH)CO 2 H 4. H 2 O Collidine, aCH 3 .C 5 H 3 N.C 8 H B . . Coniine (d.), r: 2, C 5 H 10 N . C 3 H 7 . . Cresol (o) CH 3 C 6 H 4 OH Cyanic acid, HCNO . . '. . . . . Cvano"en CoN 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 arnine, (C 2 H 5 ) 2 NH .... aniline, (C 2 H 5 )NC 8 H 6 . . . ketone, C 2 H 6 COC 2 H 5 . . . Dimethyl amine, (CHs^sHN . . . . tartrate, (CH 3 ) 2 C 4 H 4 O 6 . . Dinitrobenzene (m.), C 6 H 4 (NO 2 ) 2 . . Dipheny), C 6 H 6 . C 6 H- Diphenylamme, (C 6 H 5 ) 2 HN . . . Epichlorhvdrine, C 3 H 5 C1O .... Erythrite, (CH 2 OH . CHOH) 2 . . . Ethane, CH, . CH 3 Ether, C 2 H 6 OC 2 H 5 Ethyl acetate, CH 3 CO 2 . C 2 H 5 . . . aceto-acetate, CH 3 COCH 2 CO 2 . C 2 H 5 . . alcohol, C 2 H 6 OH ... benzoate, C 6 H 6 CO 2 . C 2 H 5 . . bromide C,H 5 . 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 H 5 I isobutyrate (CH 3 ),CHCOOC 2 H 5 mercaptan, C 2 H 5 SH .... nitrate, C 2 H-NO 3 dec. or decomp. = decomposes. Y., Young, Journ. de PAys., Jan., 1909. H., Henning. * Other form 40. PHYSICAL CONSTANTS 128 ORGANIC COMPOUNDS (contd.) For general heading, see p. 117. Substance and Formula. Formula weight (0=16) Density, gms./c.c. Melting Point, C. Boiling Point, C. Ethyl propionate, C 2 H fi CO 2 CoH 5 . . salicylate, C 6 H 4 (HO)CO 2 . C 2 H 5 sulphide, (C 2 H 5 ) 2 S . . 102'H I66-I3 90-l6 206-I5 I30*I5 . 28-04 187-88 9890 44'04 98-96 154-19 164-15 9607 46*02 30-02 180-13 116-05 96-06 180-13 198-14 132-09 92-08 75-07 62-06 7604 58-03 92-04 loo* 1 6 86-14 86-14 27-02 262-18 117-11 39377 147-09 130-15 88-12 58-10 74-10 73'i2 88-08 72-12 I02'II 60-08 at./temp. 8901/20 I-I38/I5 837/20 I "206/20 876/20 f-565/- 102-5 I A. 28-32 2-1838/18 1-28/0 897/0 1-186/12 927/20 1-0620/25 1-024/20 1-218/20 8i5/-2oA.48 1-55/0 ' 1-625 1-159/20 1-54-1-57 1-26/20 1-161 1-125/25 1-14/20 syrup 6836/20 6595/20 6617/20 697/18 i'35 4-08/17 8708/20 81/20 800/18 736/I5 9516/20 / -6393/0 \ 1 -6196/20 / 917/0 789/20 at. /mms. -74-25 i '3 -99'5 } -169 9*97 -35'3 liquid -96-7 2 liquid 20 8-35 95 286 -36-5 170 146 97*5 17 c. 234 -11-2 78 I 5 -97-1 -94-3 liquid -14 390-2 52 119 201 -134 -145 - 108-4 -79 -158-5 -85-8 at./mms. 990 231-5 92-6 280 144-5 I02'7 I3r6 837 I3-5/746 59'9 176 247-5 85-2, Y. 100-5 21 161 303 290 197-4 decomp. 50-5 with steam 98-4, Y. 69, Y. 58-1, Y. 26-1 subl. 156 253-4 subl. &dec. sublimes 140 131 I0'2 I08'4 68 I55'5 27'9 90-93 82-8 ., 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 2 C1 oxide, <(CH 2 ),O .... Ethylidene chloride, CH 3 . CHC1 2 . . Eugenol, C 6 H 3 . (OH) . OCH 8 . C 3 H 5 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 . CO H Oalactose (d.), CHO[CHOH] 4 CH 2 OH Glucose (d.), CHO[CHOH] 4 CH 2 OH + H 2 O . . . . Glutaric acid, COOH(CH 2 ) 3 COOH . Glycerine, OHCH . CHOH . CH 2 OH Glycocoll, glycine, CH,NH 2 COOH . Glycol, CH.OH . CH 2 OH .... Glycollic acid, CH 2 OH . COOH . . Glyoxal, CHO . CHO . . , Glyoxalic acid, CHO . COOJtf + 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, L(CH 3 ) 2 CH] 2 . Hydrocyanic acid, HCN Indigo, C 6 H 4 <0 > C : C< 0>C 6 - H 4 Indol, C 6 H 4 NHCH : CH Isatine, C.H 4 < C J>COH .... Isoamyl acetate, CH S . COOC 5 H n . . alcohol, (CH 8 ) 2 CH(CH 2 ) 2 OH Isobutane, (CH 3 ) 2 CHCH, .... Isobutyl alcohol, (CH 3 ) 2 CH . CH 2 OH amine, (CH 3 ) 2 CHCH 2 NH 2 , Isobutyric acid, (Crt 3 ) 2 CH . COOH . Isopentant, (CH,) 2 CHCH 2 CH 3 . . Isopropyl acetate, CH 3 COOCH(CH 3 ) g alcohol, (CH 3 ) 2 HC(OH) . d., dextro-rotatory (see p. 82) ; dec. or decomp. = decomposes ; subl. = sublimes ; Y., Young, Journ. de Phys., Jan., 1909. 129 PHYSICAL CONSTANTS ORGANIC COMPOUNDS (contd.) For general heading, see p. 117. Substance and Formula. Formula weight (0 = 16). Density, gms./c.c. Melting Point, C. Boiling Point, C. Isopropyl amine, (CH 3 ) 2 CHNH S . . cyanide, (CH 3 ) a CHCN . . 59-08 69-09 129-1 102 II 90-06 II6-05 I34-07 I04'05 360-25 230-66 I20-I4 16*04 32'04 74-06 31-06 104-09 50-47 46-06 60-08 60'04 I4I-95 102*11 48-IO 77*04 61*04 48-09 88-08 I52-I 62-II I73'86 360-25 303'26 128-11 I44-II I43-I2 I62-I8 I23-08 75-06 6I-04 II4-I8 282-38 256-34 I32*I3 70*11 102-16 72-12 at. /temp. 690/18 1-098/20 9 3I/20 I-248/I5 1-59 1-60/20 1-54/17 3-07 869/10 liq. '4 1 6/- 1 64 7958/I5 93^7/16 r-6oo/-iii \A. 32-4 ; 94/0 9207 1 8 A. 50- 1 A. 46 8 725/0 9745/20 2*2X5/15 8890/20 1-217/15 991/15 9151/20 1-182/15 845/21 2*493 1-525/20 1-32 1-152/15 1-224/4 1-01/20 I-I9868/25 I-056 I'I44/I5 7062/15 89I/I2 846/7-6 '994/20 751/20 917/0 6263/20 at./mms. liquid liquid 24-6 -5 -30 130 130-1 132 liquid -54'4 -184 -94-9 IOT2 gas -91-5 -138-5 -9975 -66-1 -130-5 liquid -26-5 gas -75 -8-3 -83*2 203 dec. 243-4 80 95 5o dec. 250 5-8 to 8-7 194-196 liquid -56-6 14 62-6 10-5 c. 15 200 at./mms. 33 107-108 240 176-3 83/1 mm. decomp. decomp. 96 164*5 164 64-7, Y. 57-1 -6*7/756 65 -24-1 -23-6 10-8 3r9, Y. 42-3 92-3 5-8/752 65 explodes 12 -14 797 224 ^.38 98-5 decomp. decomp. 217-96 c. 279 300 246-7/745 210-85 114*4 101*7 125 -8, Y. 286/100 278/100 124 50*6 178 36-2, Y. Isovaleric acid, (CH 3 ) 2 CHCH 2 COOH Lactic acid (i.), CH 3 CHOH . COOH . Lactose. See Milk sugar. Maleic acid, (COOH. CH:), . . . .Malic acid (i.), COOH . CHOH . CH,- COOH ... Malonic acid, COOH . CH, . COOH . Maltose, C ia H 22 On + H 2 O . . . . Mercury methyl, (CH 3)2 Hg .... Mesitylene, 1:3:5, C 6 H,(CH 3 ) 3 . . Methane CH 4 . Methyl alcohol, CH 3 OH acetate, CH 3 COO : CH S . . borate, (CH 3 ) 3 B0 3 .... chloride, CH 3 C1 ether, (CH 3 ) 2 O ethyl ether, CH 3 . O . C 2 H 5 . formate, HCOO . CH 3 . . . isobutyrate,(CH 3 ) 2 CHCOOCH 3 mercaptan, CH 3 . SH . . . nitrate, CH 3 . NO 3 .... nitrite CH 3 . NO 2 . . phosphine, CH 3 H 2 P .... propionate, C 2 H 5 COO . CH, . salicylate, C 6 H 4 (OH)COOCH 3 sulphide, (CH 3 ) 2 S . . . . . Methylene bromide, CH 2 Br 2 .... Milk sugar, C lt H M O n + H 2 O . . . Morphine, C 17 H 19 NO 3 + H 2 O . . . Naphthalene, C 6 H 4 : C 4 H 4 .... Naphth.l (a), C 10 H 7 OH .... Nap'ithyl amine (a), C 10 H 7 H 2 N . . Nicotine (1.), C 10 Hi 4 N 2 Nitro benzene, C a H 5 \O a ...... ,, ethane, C a H 6 \'O 2 methane, CH 3 NO 2 Octane (n.), CH 3 (CH 2 ) 8 CH 3 .... Oleic acid. CH 3 (CH 2 ) 7 CH:CH(CH a ) 7 - . COOH . . .* Palmitic acid, CH 3 (CH 2 ) 14 COOH . . Paraldehyde, (CH 3 . HCO) 3 .... Penta methylene, (CH 2 ) 6 . ... v D diamine (cadaverine), NH,(CH 2 ) 5 NH 2 Pentane (n.), CH 3 (CH 2 ) 3 CH, . . . dec. or decomp. = decomposes ; 1., laevo-rotatory (see p. 82) ; Y., Young, Journ. de Phys. t Jan., 1909. PHYSICAL CONSTANTS 130 ORGANIC COMPOUNDS (contd) For general heading, see p. 117. Substance and Formula. Formula weight = 16). Density, gms./c.c. Melting Point, C. Boiling Point, C. Phenetol C a H 5 OC 2 H 6 . . . 122-12 94'OS I36-I 103-09 108-1 162-11 166-09 148-07 93-10 22908 44-08 74-06 I02TI 60'08 78-53 88-08 I7O-0 42*06 120 14 79-08 I26-08 67-07 129-II 324*3I 872-8I 1 68 08 282-22 305-28 183-15 13808 52-05 284-38 891-16 118-07 342-24 209-18 228-22 168-08 150-07 150-07 166-09 154-19 at. /temp. 963/25 1-06/33 1-23 I-008/I7 I 098/20 1-59 1-53/4' 93322 1-767/19 '535 9870/20 8884/20 804/20 891/18 9058/20 1745/20 A.43'36 8748/20 985/15 1-46/40 967/21 1-094/20 1-69/7 177 1-48/4 843/80 924/65 1-564/15 , I-5877/I8 1-67 176/7 P. 176 at./mms. -34 427 76-5 -17 I9-35 218 anhy. 180-200 128 liquid 122-5 -187-8 -I9'3 -92-5 -127 101-4 gas -57-4 -42 .133 liquid -22-6 anhy. 174-9 205, dry 205 188-9 220 dec. 158/760 27 69-3 71-1-5 185 189 chars 125 142 anhy. 170 170 sublimes 70 at./mms. 171 l8l-5 265 100 243-5 sublimes 284 . 129 explodes -44-1 140 ioi'6 97-2 46-5 80-9, Y. 102 -50-2 169-8 II5-4 293 131 241 sublimes 291/100 235 300 dec. Phenol CeH 6 OH . . ... Phenyl acetic acid, C 6 H 6 CH 2 COOH . cyanide, CeHsCN hydrazine, C 6 H 5 HN . NH 2 . Phloroglucin, 1:3: 5,CH 3 (OH) 8 2H 2 O Phthalic acid, o. C 6 H 4 (COOH) 2 . . anhydride, C 6 H 4 <(CO) 2 >O Picoline (a), CH 3 . C 6 H 4 N .... Picric acid, i : 2: 4: 6, C 6 H 2 OH(NO 2 ) 3 Pinene. See Turpentine. Propane, CH 3 . CH 2 .CH 8 .... 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 3 CH 2 CH 2 C1 . formate, H . COO . C 3 H 7 . . iodide, CH 3 . CH 2 . CH 2 I . . Propylene, CH 8 .CH: CH 2 . . . . Pseudo-cumene, i: 2: 4, C 6 H 3 (CH 8 ) 8 . Pyridine, C 5 H B N Pyrogallol ( ic acid, or " pyro "), i: 2: 3, C.H 8 (OH) 8 Pyrrol, (CH) 4 >NH Quinoline, C.H 4 < C ** ; g> . . . Quinine, C 20 Hj 4 N 2 O 2 ... . . sulphate, (C 20 H 24 N 2 O 2 ) 2 .- H 2 SO 4 + ;H 2 O .... Bacemic acid, (COOH . CH(OH)),- + H 2 O Rochelle salt (d.), KNaC 4 H 4 O 6 .4H 2 O Rosaniline (p.), (C 6 H 4 NH 2 ) 8 COH . . Saccharin, CH 4 < COSO 2 > NH . . Salicylic acid, OH . C.H 4 . COOH . Sodium ethyl NaC 2 H 5 . . . . Stearic acid, CH 3 (CH 2 ) 16 COOH . . . Stearine, (C, a H.Oo) CoH* Succinic acid, COOH(CH 2 ) 2 COOH . Sugar, cane- Ci S H 22 Oii Sulphanilic acid (p.), NH 2 .C 6 H 4 .SO 3 H . 2H 2 O Sulphonal, (CH 8 ) 2 C(SO 2 C 2 H 6 ) 2 . . . Tartaric acid (i- or meso), COOH- [CHOH]. 2 COOH . H 2 O (d.), COOH(CHOH) 2 - COOH GO, COOH(CHOH) 2 - COOH Terephthalic acid (p.), C 8 H 4 (COOH) 2 . anhy. = anhydrous ; d. = dextro-rotatory (see p. 82) ; P., Perkin ; dec. = decomposes; 1., Isevo-rotatory (see p. 82) ; Y., Young. 131 PHYSICAL CONSTANTS ORGANIC COMPOUNDS (contd.) For general heading, see p. 117. Substance and Formula. Formula weight (0 = 16). Density, gms./c.o. Melting Point, C. Boiling Point, C. at /temp. at./mms. at./mms. Terpineol, a, Ci H l7 HO .... 154-19 936/20 35 218 - Tetrabromethylene, CBr 2 .CBr, . . 343'69 53 100/15 Theobromine, C 7 H 8 N 4 O 2 .... 180*14 330 subl. Thiocyanic acid, (HCNS) 3 .... 5908 -12-5 200 dec. Thiophene (CH) 4 S 84-11 I*06I/I5 _ 84 Thiourea, NH,.CS.NH 2 . . . . 76-12 1-42 1 80 Thymol, 4:1:3, (CH 3 ) 2 : CH . C 6 H 3 - (CH 3 )OH 150*16 *994/0 50 232 Tin tetramethyl, Sn(CH 3 ) 4 .... Toluene C H 5 CH 3 .... 178*82 Q2*IO I O I*3I4/0 866/20 94*5 78 III Toluidine (o.), CH 3 C 6 H 4 . NH 2 . . 7^ 107*12 '999/20 a-2I,-l5*5 1997 (p.), CH 3 C 6 H 4 NH a . . . 107*12 i *O46/ 45 200*3 Trichloracetic acid, CC1 8 .COOH . Triethyl amine, (C 2 H 5 ) 3 N .... 163-48 iori6 1-63/61 725/15 52-3 liquid 195 89 arsine, (C,H fi ) 3 As .... 162-11 1-15/17 liquid (140/736 t dec. phosphine, (C 2 H 5 ) 3 P . . . 118-19 '812/15 liquid 127/744 Trimethyl amine, (CH 8 ) 3 N .... 59-10 673/0 3*5 arsine, (CH.),As. . . . 120*05 i liquid 41 Trinitro benzene (s.), 1:3: 5, C 6 H 3 - (NOA, 213*08 1-688 121*2 decomp. Turpentine (pinene), C 10 H 16 . . . 136-18 865/15 159 Urea NH 2 CO.NH 2 60-06 1*32 T-J2 decomp. Valeric acid(n.),CH s (CH 2 ) 3 . COOH '943/20 -58*5 186-4 Xylene (o.), C 6 H 4 (CH 3 ) 2 .... 106*12 8811/20 -28 142-6 (m), ,, .... 106*12 8658/20 -54 139*8 (P), .... 106*12 8611/20 15 138 Zinc ethyl Zn(C 2 H 5 \ I2VA7 1-182/18 -28 118 * O ^/ i '386/10 46 * O 1 *r v dec. or decomp. = decomposes. ELECTROCHEMICAL EQUIVALENTS Faraday's laws of electrolysis are expressed by m izt, where m is the mass in grammes of an ion liberated in t sees, by a current of t amperes ; z 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. Chemical equivalent = V. atomic weight of element ilency of element for electrolyte used Element. Chemical equivalent. ' z. Copper . 6v>7/2 . fvnooi^oe Hydrogen i*oo8/ -J 7 J I ... 0-00001045 > > ( see P* TI 4) 132 SOLUBILITIES SOLUBILITIES OF GASES IN WATER AIR IN WATER looo 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. Winkler 1904. Temperature of Water. 0C. 10 15 20 25 30 Oxygen Nitrogen, argon, etc Sum of above % of oxygen in dissolved air (by vol.) c.cs. 10*19 19-0 29-2 34'9% 8-9 16-8 25.7 347 7*9 15-0 22-8 34'5 7-0 13*5 20-5 12-3 187 5-8 33-8 5'3 157 33-6 GASES IN WATER S indicates the number of ccs. 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 water. (For other values, see p. 117) See Constantes Physiques, 1913. Gas. 0C. 10 15 C 20 30 40 50 60 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 . . 1300 058 1713 035 0150 0215 506 0239 1-05/5 074 049 4-68 79-8 910 045 1-194 028 3-09 0144 0198 474 0196 88 057 038 3-52 56-6 802 040 I '019 025 2-63 0139 0190 458 0179 74 051 "034 47'3 710 037 878 023 2-26 0138 0184 442 0164 63 047 031 2-67 39"4 595/28 030 66 020 177 0138 411 0138 040 026 27-2 027 '53 018 1-41 0139 386 01 1 8 035 023 18-8 44 oi 6 1*20 0140 362 0106 031 021 36 015 ro 359 'OIOO 029 019 Ne, -0147/20 ; Kr, '073/20 ; Xe, 'II 09/20 -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. (From data in Seidell's" Solubilities.") Liquids. f Water in ether ; ethereal layer .... \Ether in water ; aqueous layer . . . . /Aniline(C 6 H 5 NH 2 )in water ; aqueous layer \Aniline in water ; aniline layer .... {Phenol (C 6 H a OH) in water; aqueous layer \Phenol in water ; phenol layer . . . . f Triethylamine in water ; amine layer . . \Triethylamine [N(C,H a ) 5 ] in aqueous layer /CS 2 in methyl alcohol ; alcoholic layer . lCS 2 in CH,OH ; carbon bisulphide layer 0C. ro 12 . 10 ri 87 7'5 75 5I 'o\ at 5I-9/I8 - i8-6 20 30 40 50i60 70 1*2 6-5 3*2 95'5 8-3 72 72 14-2 51 97 1-7 4'54-i 3*5 95 9-612 2-2 2-0 33*4 33*4 00 6 92 4*5 93 at crit. temp. 68'3 3-62-9 80-51 at 'crit temp. 80-5; 133 SOLUBILITIES 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, 1916, where the most complete and accurate data will be found for solubilities.) For other solutions ? see p. 117. Substance. oc. 10 15 20 40 60 80 100 Am. chloride, NH.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 I0i"4 __ Bromine (liquid], Br. s 4-22 3'4 3-25 3*20 Cadmium sulphate, CdSO 4 .8/3H 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 .sH 8 O. . s 14*3 17-4 1 8-8 20-7 28-5 40*0 55' 75*0 Li. carbonate, Li 2 CO 3 s i'43 1-38 *'33 1-17 I'OI 850 720 Merc. chloride, HgCl 2 p 3-50 4-50 5-00 5-40 9-30 14-0 23-1 38-0 Potass, chloride, KC1 s 27-6 31*0 34'o 40*0 45'5 51-1 567 Potass, bromide, KBr 53'5 59'5 62-5 65-2 75*5 85-5 95-0 104 Potassium iodide, KI s 127-5 136 140 144 160 176 192 208 Potassium hydrate, KOH.2H 2 O . . s 97*o 103 107 112 138 178 Potass.nitrate,KNO 3 s 13*3 20-9 25-8 32 64 no 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 Sodium sulphate, s s 7'0 357 12-5 35-8 16-4 35'9 36-0 46-1 36-6. 46*0 37 45*8 38 45*5 39 -o Na 2 SO 4 .ioH 2 O . Strontium chloride, s 5-0 9-0 I3'4 I9-4 49 1 45 t 44 1 42 1 SrCl 2 .6H 2 O . . s 43 48 5 , 53 65 82 91 1 101 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 179 190 197 204 238 287 362 487 * Solid phase becomes CdSO 4 . H 2 O at 74. f Becomes Na 2 SO 4 at 32'38. J 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 C0 3 .H 2 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 By weight . 75-5 23-2 By volume . 78x55 21*0 1*3 '95 046 to '4 03 to -3 028 -005 o 3 86 -o<56 o 2 i23 *o 3 4o Leduc, 1917, weight % Kr 14 x io-s, Xe 3X io-, Ne 8-4 xio- 4 , He 7Xio- B , H 7x10-6. 134 MINERALS MOMS' 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 Felspar 10 Diamond 3 Calcspar 7 Quartz c 2*5 4 Fluor spar 8 Topaz ^6*5 Finger-nail 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- J ness. Albite, Na 2 Al 3 Si 6 O 16 . . C. 2'6 6-7 Mica (common, Musco- 27-3-1 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 O 3 .6SiO 2 .2H 2 O Anorthite, Ca a Al 4 Si 4 O 16 . f.2'7 6-7 Mica (Biotite, Magnesia 2-7-3-1 2-5-3 Apatite, 2-9-3-2 5 mica) Ca.(Cl,F,OH)(P0 4 ), Monazite,* (CeLaDi)PO 4 5 5-2 Aragonite, CaCO 3 . . . 2-93 3-5-4 (1-16% Th) Augite, 3-2-3-5 5-* Nepheline, 2-5-2-6 5-5-6 Mg,Fe,Ca,Al silicate Na a 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 BaS0 4 Orthoclase, K2Al 2 Si 6 O ]8 . 2-4-2-6 6 Beryl, Be 3 Al 3 Si 6 O 18 . . 2-6-2-7 7-8 Pitchblende,* U S 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,SM sive) 5*5 thorium Al, etc. (25-80 % U ; 97 Calcite, Calcspar, Iceland 2-6-27 ft 3 1-6 %Th) I (cryst.) , spar, CaCO 8 Carnallite, r6 I Pyrites (iron), FeS 2 . . (copper), CuFeS 3 4-8-5-1 4*1-4*3 6-6-5 3-5-4 KCl.MgCl a .6H 2 O Pyrolusite, MnO a .. . 4-8-5 2-5*5 Carnotite,* (c- 55% (yel- Quartz, SiO 2 .... 2-5-2-8 7 K 2 0(U 2 O c ) a V 2 8 . 3 H 2 U) low) Rock salt, NaCl . . . 2*1-2-2 2-2-5 Celestine, SrSO 4 . ... VQ 3_-5'C Rutile TiO 2 . . x2-4.-7 6-6-5 Cerussite, PbCO s . . . i-4 J J J 3-3-5 Selenite cryst. gypsum r *" *T J u j Chalcolite,* 3-4-3-6 2-2'5 Serpentine, H > Mg 2 As 2 7 . . . > ... j) . Barium. BaCO 3 .... * .... RoQn Fluorine. CaF 3 Glucinum. See Beryllium. Gold. Au Hydrogen. H 2 Beryllium. BeO Iodine. Acrl Bismuth. Bi Iron. Fe BioO, BiOCl j) ...... FeO ? FeoOo Boron. BoO, . Bromine. AgBr co a Cadmium. CdO Lead. Pb Caesium. Cs PbSO 4 . . , . Cs 2 PtCl, .... . Calcium. Ca Lithium. Li 2 CO, ..... Li s po 4 ! * ! ! ... CaCO, .... ... CO 2 136 GRAVIMETRIC FACTORS FACTORS FOR GRAVIMETRIC ANALYSIS (contd.) 1 part by weight of is equivalent (by weight) to 1 part by weight of is equivalent (by weight) to Magnesium. MgO . . . Mg 2 P 2 7 . . > Manganese. MnO . . . Mn 8 O 4 . . . Mercury. Hg . . HgS . Nickel. Ni . . . . Nitrogen. N . . . . Phosphorus. P 2 6 . . . Mg 2 P 2 7 . . Platinum. K 2 PtCl 8 . )> Potassium. AgCl . . AgBr . . Agl . . AgCN . . KC1 . . KBr . . KOH . . 6032 2184 3621 1*1113 7203 9307 1-0350 1-1399 1-1598 8966 9310 Mg Mg MgO Mn 2 O 3 Mn MnO Mn 2 O 3 MnO 2 HgS Hg,0 HgO Potassium (contd.} KoSO 4 .... 1-2727 NiO 3-8555 N 2 5 Rubidium. Rb 2 PtCl a Silicon. SiO 2 .. Silver. AgCl .. AgBr .. Agl .. Sodium. AgCl .. NaHCO 8 Na 2 S0 4 . K 2 SO 4 4362 2787 I 53 * 6378 4015 6933 5202 6338 7071 4863 5244 3285 1-2316 8395 5406 P P P0 4 Pt PtCl 4 KC1 KBr KI KCN K K K 2 C0 3 K 2 O K 2 O N 2 fl . . Strontium. SrC0 3 . SrS0 4 . Sulphur. BaSO 4 . Tin. SnO 2 . Uranium. U 8 8 . UO 2 Zinc. Zn . ZnO 1-1604 KNO 3 1609 K 2953 Rb 4693 Si 7526 Ag 5744 Ag '4595 Ag 4078 NaCl 3690 Na 2 O 3238 Na 4364 Na 2 O 1^5740 NaNO 3 7019 SrO" 5641 SrO 1460 H 2 S 1374 S 2744 S0 2 3429 SO 3 4115 S0 4 7876 Sn 8481 U 9620 UO a 8816 U 1-2448 ZnO 8033 Zn SOME BOILING-POINT MIXTURES Bojling-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.) Mixture. B. Boiling Points. Mixt. %ofA in mixt, Ob- server. Maximum boiling- point mixtures. Water Me. ether Nitric acid Hydrochloric acid Formic acid Hydrochloric acid 100 C. 100 100 -23-6 86 joo-8 -8o no 107 - 2 23 61 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 59 60 Y.&F, G.&C, Y.&F, Pettit G. & C., Goldschmidt and Constan ; Y. & F., Young and Fortey. 137 THE EXPONENTIAL O~* e 271828. To derive e x use reciprocals on p. 136. e~ ' 693IS = '5. (Based on Newman, Trans. Camb. Phil. Soc., 13, 1883.) For values of x from -0000 to -0999. Subtract Differences. X 001 002 003 004 005 006 007 008 009 oooi 234 6 6789 00 rooo 9990 9980 9970 9960 9950 9940 9930 9920 9910 1234 5 6789 01 9900 9891 9881 9871 9861 9851 9841 9831 9822 9812 234 5 6789 02 '9802 9792 9782 "9773 9763 *9753 '9743 '9734 9724 97H 234 5 6789 03 9704 1 9695 9685 9675 9666 9656 9646 9637 9627 9618 234 5 6789 04 9608 9598 9589 '9579 957o 9560 9550 954i 953i 9522 234 5 6789 O5 9512 9502 "9493 9484 '9474 9465 '9455 9446 9436 9427 234 5 6789 06 9418 9408 9399 9389 9380 937i 9361 9352 '9343 '9333 234 5 6789 07 9324 9315 9305 9296 9287 9277 9268 9259 -9250 9240 234 5' 6788 08 9231 9222 9213 9204 9194 9185 9176 9167 '9158 9148 234 5 6 7. 7 8 09 9139 9130 9121 9112 9103 9094 9085 9076-9066 9057 234 5 6678 For values of x from -100 to 2-999. Subtract Differences. x 01 02 03 04 05 06 07 08 09 001 234 5 6789 1 9048 8958 8869 8781 8694 '8607 8521 8437 8353 8270 9 17 26 34 43 52 60 69 77 2 8187 8106-8025 7945 7866 7788 7711 7634 7558 7483 8 16 23 31 39 47 55 62 70 3 7408 7334 7261 7189 7118 7047 697^ 69071-6839 6771 7 14 21 28 35 42 49 56 63 4 6703 6637 6570 -6505 6440 6376 6313 6250 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 "5U7 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 '4493 '4449 4404 -4360 43i7 4274 4232 4190 4148 4107 4 9 13 17 21 26 3 34 38 9 4066 4025 3985 3946 3906 3867 3829 3791 '3753 3716 4 8 12 15 19 23 27 31 35 1-0 3679 3642 3606 3570 '3535 "3499 3465 3430 3396 3362 4 7 ii 14 18 21 25 28 32 1-1 3329 3296 3263 3230 3198 3166 3135 3104 3073 3042 3 6 9 13 16 19 22 25 29 1-2 3012 2982 2952 2923 2894 2865 2837 2808 2780 2753 3 6 9 ii H 17 20 23 26 1-3 1-4 2725 2466 2698 2441 2671 2417 2645 2393 2618 2369 2592 2346 2567 2322 2541 2299 2516 2276 2491 2254 3 5 8 10 2579 13 12 16 18 21 23 14 16 19 21 1-5 2231 2209 2187 2165 2144 2122 '2IOI 2080 2060 2039 2468 II 13 15 17 19 1-6 2019 1999 1979 1959 1940 T92O 1901 1882 1864 1845 2468 IO 12 13 15 17 1*7 1827 1809 1791 1773 '1755 1738 I72O 1703 1686 1670 2357 9 10 12 14 16 1-8 1653 1637 1620 1604 1588 1572 1557 i54i 1526 IS" 2356 8 9 ii 13 14 1-9 1496 1481 1466 1451 1437 1423 1409 1395 1381 1367 1346 7 9 10 ii 13 2-0 1353 1340 1327 I3I3 1300 1287 1275 1262 1249 1237 i 345 6 8 9 10 12 2-1 1225 '1212 1200 1188 1177 Il6 5 "53 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 2-3 1003 0993 0983 '0973 0963 'OQS4 0944 *935 0926 0916 234 5 6789 2'4 0907 0898 0889 0880 0872 0863 0854 0846 0837 0829 233 4 5678 2-5 0821 0813 0805 0797 0789 0781 0773 0765 0758 0750 223 4 5567 2'6 0743 '735 0728 0721 0714 0707 0699 0693 0686 0679 i 2 3 4 4566 2-7 0672 0665 0659 0652 0646 0639 0633 0627 0620 0614 i 2 3 3 4456 2*8 0608 0602 0596 0590 0584 0578 0573 0567 0561 0556 122 3 3455 2'9 0550 0545 0539 0534 0529 0523 0518 05131-0508 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 0183 0450 0166 0408 0150 0368 0136 0334 0123 0302 01 1 1 0273 QIOI 0247 0091 0224 0082 'O2O2 0074 Mean differences no longer 5 0067 0061 oo55 0050 0045 0041 0037 -0033 0030 OO27 sufficiently accurate. 6 0025 'OO2 2 OO20 0018 0017 0015 OOI4 'OOI2 QOII 'OOIO 7 0009 0008 '0007 0007 0006 0006 0005 0005 0004 0004 8 0003 0003 0003 OOO2 'OOO2 0002 OOO2 OOO2 'OOO2 oooi 138 FOUR-FIGURE LOGARITHMS 1 2 3 4 5 6 7 8 9 1234 5 6789 1 fl / 0000 0043 0086 0128 0170 4 9 13 17 21 25 30 34 38 1 0212 0253 0294 0334 0374 4 8 12 16 20 24 28 32 36 11 / 0414 0453 0492 0531 0569 4 8 12 15 19 23 27 31* 35 11 1 0607 0645 0682 0719 0755 4 7 ii 15 18 22 26 30 33 12 1 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 24 27 31 / 1139 H73 1206 1239 1271 3 7 10 13 16 20 23 26 30 I 1303 1335 1367 1399 1430 3 6 9 13 16 19 22 25 28 f 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 IE/ 1761 1790 1818 1847 1875 1903 3 6 9 ii 14 17 20 23 26 I '93 1 1959 1987 2014 3 6 8 ii 14 17 19 22 25 16 / 2041 2068 2095 2122 2148 3 5 8 ii 13 16 19 21 24 2175 2201 2227 2253 2279 3 5 8 10 13 16 18 21 23 17 / 2304 2330 2355 2380 2405 2430 3 5 8 10 13 15 18 20 23 i 2455 2480 2504 2529 2 5 7 10 12 15 IJ 2O 22 40 J 2553 2577 2601 2625 2648 2 5 7 10 12 14 17 19 21 18 j 2672 2695 2718 2742 2765 2579 12 14 16 19 21 i 2788 2810 2833 2856 2878 2579 II 14 16 18 20 19 j 2900 2923 2945 2967 2989 2479 II 13 15 18 20 20 3010 3032 3054 3075 3096 3Il8 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 3541 3579 3598 2468 IO 12 14 15 17 23 24 3617 3802 3636 3820 3655 3838 3674 3856 3692 3874 37" 3892 3729 399 3747 3927 3766 3945 3784 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 42OO 4216 4232 4249 4265 4281 4298 2 3* 5 7 8 10 ii 13 15 27 43H 4330 4346 4362 4378 4393 4409 4425 4440 445 6 2356 8 9 ii 13 14 28 29 4472 4624 4487 4639 4502 4654 4518 4669 4533 4683 4548 4698 4564 4713 4579 4728 4594 4742 4609 4757 2356 1346 8 7 9 ii 12 14 9 10 12 13 3O 477i 4786 4800 4814 4829 4843 4857 4871 4886 4900 1346 7 9 10 ii 13 31 49H 4928 4942 4955 4969 4983 4997 5011 5024 5038 3 4 6 7 8 IO II 12 32 5051 5065 5079 5092 5J05 5"9 5132 5M5 5*59 5172 3 4 5 7 8 9 ii 12 33 5185 5211 5224 5237 5250 5263 5276 5289 5302 345 6 8 9 10 12 34 5315 5328 5340 5353 5366 5378 5403 5428 345 6 8 9 10 ii 35 5441 5453 5465 5478 5490 552 55H 5527 5539 5551 245 6 7 9 10 ii 36 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 245 6 7 8 10 ii 37 5682 5 6 94 5705 5717 5729 5740 5752 57 6 3 5775 5786 235 6 7 8 9 10 38 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 235 6 7 8 9 10 39 59ii 5922 5933 5944 5955 5966 5977 5988 5999 6010 234 5 7 8 9 10 40 6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 2 3. 4 5 6 8 9 10 41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 234 5 6789 42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 234 5 6789 43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 234 5 6789 44 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 234 5 6789 45 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 234 5 6789 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 234 5 6778 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 234 5 5678 48 6812 6821 6830 6848 6866 6884 6893 234 4 5678 49 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 234 4 5678 1 2 3 4 5 6 7 8 9 1284 5 6789 139 FOUR-FIGURE LOGARITHMS 1 2 3 4 5 6 7 8 9 1234 5 6789 5O 6990 6998 7007 7016 7024 7033 042 7050 7059 7067 1233 4 5678 51 7076 7084 7093 7101 7110 7118 7126 7135 7H3 7152 1233 4 5678 52 7160 7168 7177 7185 7i93 7202 7210 7218 7226 7235 1223 4 5677 53 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 1223 4 5667 54 7324 7332 7340 7348 7356 73 6 4 7372 7380 7388 7396 1223 4 5667 55 7404 7412 74i9 7427 7435 7443 745i 7459 7466 7474 1223 4 5567 56 7482 7490 7497 7505 7513 7520 7528 7536 7543 755i 1223 4 5567 57 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 1223 4 5567 58 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 1123 4 4567 59 7709 7716 7723 773i 7738 7745 7752 7760 7767 7774 1123 4 4567 60 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 63 7924 7993 793i 8000 7938 8007 7945 8014 7952 8021 llll 7966 8035 7973 8041 7980 8048 7987 8055 1123 1123 3 3 4566 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 112 3 4556 66 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 112 3 4 5 5 6 67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 112 3 4 5 5 6 68 8325 8331 833* 8344 8351 8357 8363 8370 8376 8382 112 3 4 4 5 6 69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 I I 2 3 4456 70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 I I 2 2 3 4456 71 72 8513 8573 8519 8579 8525 8585 8531 8591 8537 8597 8543 8603 8549 8609 8555 8615 8561 8621 8567 8627 I I 2 2 I I 2 2 3 3 4455 4455 73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 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 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 897i I I 2 2 3 3445 79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 I I 2 2 3 3445 8O 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 9159 9165 9170 9175 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 9315 9320 9325 9330 9335 9340 I I 2 2 3 3445 86 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 I I 2 2 3 3445 87 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 01 2 2 3344 88 9445 945 9455 9460 9465 9469 9474 9479 9484 9489 01 2 2 3344 89 9494 9499 9504 959 9513 95i8 9523 9528 9533 9538 01 2 2 3344 90 9542 9547 9552 9557 9562 9566 9571 9576 958i 9586 01 2 2 3344 91 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 01 2 2 3344 92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 01 2 2 3344 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 01 2 2 3344 94 973 9736 974i 9745 975 9754 9759 9763 9768 9773 01 2 2 3344 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 01 2 2 3344 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 01 2 2 3344 97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 01 2 2 3344 98 9912 9917 992i 9926 9930 9934 9939 9943 9948 9952 01 2 2 3344 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 01 2 2 3334 1 2 3 4 5 6 1 7 8 9 1234 5 6789 140 ANTILOGARITHMS 3. 7 i f 00 1000 1002 1005 1007 1009 1012 1014 1016 1019 1021 O O I I I 1222 01 1023 1026 1028 1030 1033 1035 1038 1040 1042 1045 O O I I I 1222 02 1047 IO5O 1052 1054 1057 '059 1062 1064 1067 1069 I I I 1222 03 1072 1074 1076 1079 1081 1084 1086 1089 1091 1094 O O I I I 1222 04 1096 1099 IIO2 1104 1107 1109 I 112 1114 1117 III9 O I I I I 2222 05 1122 H25 1127 1130 1132 "35 1138 1140 "43 II 4 6 I I I I 2222 06 1148 II5I "53 1156 "59 1161 1164 1167 1169 1172 I I I I 2222 07 "75 1178 1180 1183 1186 1189 II9I "94 "97 "99 O I I I I 2222 08 1202 1205 1208 1211 1213 1216 1219 1222 1225 1227 I I I I 2223 09 1230 '233 1236 1239 1242 1245 1247 I25O 1253 1256 O I I I I 2223 10 1259 1262 1265 1268 1271 1274 1276 1279 1282 1285 O I I I I 2223 11 1288 1291 1294 1297 1300 1303 1306 1309 1312 1315 I I I 2 2223 12 1318 1321 1324 1327 1330 1334 1337 1340 1343 1346 O I I I 2 2223 13 14 1349 1380 1352 1384 1355 1387 1358 1390 1361 1393 1365 1396 I 3 68 1400 1371 1374 1406 1377 1409 I I I I I I 2 2 2233 2233 15 1413 I4l6 1419 I 4 22 1426 1429 1432 1435 1439 1442 I I I 2 2233 16 1445 1449 M5 2 1455 H59 1462 1466 1469 1472 1476 I I I 2 2233 17 1479 1483 1486 1489 1493 1496 I5OO I53 1507 1510 I I I 2 2233 18 1517 1521 1524 1528 1535 1538 1542 1545 I I I 2 22 33 19 1549 1552 1556 1560 1563 1567 1570 1574 1578 1581 O I I I 2 2333 2O 1585 1589 1592 1596 1600 1603 1607 1611 1614 1618 I I I 2 2333 21 1622 1626 1629 1633 I 6 37 1641 1644 1648 1652 1656 I I 2 2 2333 22 1660 I66 3 1667 1671 1675 1679 1683 1687 1690 1694 O I I 2 2 2333 23 1698 1702 1706 I7IO 1714 1718 1722 1726 1730 1734 I I 2 2 2334 24 1738 1742 1746 175 1754 1758 1762 1766 1770 1774 O I I 2 2 2334 25 1778 1782 1786 1791 1795 1799 1803 1807 1811 1816 I I 2 2 2334 26 1820 1824 1828 1832 1837 1841 1845 1849 1854 1858 I I 2 2 3334 27 1862 1866 1871 1875 1879 1884 1888 1892 1897 1901 I I 2 2 3334 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 2000 2004 2009 2014 2018 2023 2028 2032 2037 I I 2 2 3344 31 2042 2046 2051 2056 2061 2065 2070 2075 2080 2084 O I I 2 2 3344 32 2089 2094 2099 2104 2109 2113 2118 2123 2128 2133 I I 2 2 3344 33 2138 2143 2148 2153 2158 2163 2168 2173 2178 2183 O I I 2 2 3344 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 2382 2388 2393 I I 2 2 3 3445 38 2399 2404 2410 2415 2421 2427 2432 2438 244 1 2449 I I 2 2 3 3445 39 2455 2460 2466 2472 2477 2483 2489 2495 2500 2506 I I 2 2 3 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 1123 3 4456 44 2754 2761 2767 2773 2780 2786 2793 2799 2805 2812 1123 3 4456 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 2951 2958 2965 2972 2979 2985 2992 2999 3006 3013 1123 3 4556 48 3020 3027 3034 3041 3048 3055 3062 3069 3076 3083 1123 4 4566 49 3090 3097 3105 3"2 3"9 3126 3133 3MI 3148 3 ! 55 1123 4 4566 1 2 3 4 5 6 7 8 9 1234 5 6789 141 ANTILOGARITHMS 1 2 3 4 5 6 7 8 9 1234 5 6789 50 3162 3170 3*77 3184 3192 3*99 3206 3214 3221 3228 1123 4 4 5 6 7 51 3236 3 2 43 3251 3258 3266 3273 3281 3289 3296 334 1223 4 5567 52 33ii 33i9 3327 3334 3342 3150 3357 33 6 5 3373 338i 1223 4 556 7 53 3388 3396 3404 3412 3420 3428 3436 3443 345i 3459 1223 4 5667 54 3467 3475 3483 3491 3499 35o8 35i6 3524 3532 3540 1223 4 5667 55 3548 3556 3565 3573 358i 3589 3597 3606 3614 3622 1223 4 5677 56 3631 3639 3648 3656 .1664 3 6 73 3681 3690 3698 3707 1233 4 5678 57 37i5 3724 3733 374i 3750 3758 3767 3776 3784 3793 1233 4 5678 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 5 5678 60 398i 3990 3999 4009 4018 4027 4036 4046 4055 4064 1234 5 6678 61 4074 4083 4093 4102 4111 4121 4130 4140 4150 4159 1234 5 6789 62 4169 4178 4188 4198 4207 4217 4227 4236 4246 4256 1234 5 6789 63 4266 4276 4285 4295 430 5 43 J 5 4325 4335 4345 4355 1234 5 6789 64 4365 4375 4385 4395 4406 4416 4426 443 6 4446 4457 1234 5 6789 65 4467 4477 4487 4498 4508 4519 4529 4539 4550 4560 1234 5 6789 66 457i 458i 4592 4603 4613 4624 4634 4645 4656 4667 1234 5 6 7 9 10 67 4677 4688 4699 4710 4721 4732 4742 4753 4764 4775 1234 5 7 8 9 10 68 4786 4797 4808 4819 4831 4842 4853 4864 4875 4887 1234 6 7 8 9 10 69 4898 4909 4920 4932 4943 4955 4966 4977 4989 5000 1235 6 7 8 9 10 70 5012 5023 5035 5047 5058 5070 5082 5093 5105 5"7 1245 6 7 8 9 ii 71 5129 5140 5152 5164 5176 5188 5200 5212 5224 5236 1245 6 7 8 10 ii 72 5248 5260 5272 5284 5297 5309 532i 5333 5346 5358 1245 6 7 9 10 n 73 5370 5383 5395 5408 5420 5433 5445 5458 5470 5483 1345 6 8 9 10 ii 74 5495 5508 552i 5534 5546 5559 5572 5585 5598 5610 1345 6 8 9 10 12 75 5623 5636 5649 5662 5675 5689 5702 5715 5728 5741 1345 7 8 9 10 12 76 5754 5768 578i 5794 5808 5821 5834 5848 5861 1 5875 1345 7 8 9 ii 12 77 5888 5902 59i6 5929 5943 5957 5970 5984 5998 6012 1345 7 8 10 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 6353 6368 6383 6397 6412 6427 6442 1346 7 9 10 12 13 81 6457 6471 6486 6501 6516 653i 6546 6561 6577 6592 2356 8 9 ii 12 14 82 6607 6622 6637 6653 6668 6683 6699 6714 6730 6745 235 6 8 9 ii 12 14 83 6761 6776 6792 6808 6823 6839 6855 6871 6887 6902 235 6 8 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" 7328 7345 7362 7379 7396 2357 8 10 12 13 15 87 74i3 7430 7447 7464 7482 7499 75i6 7534 755i 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 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 8128 8147 8166 8185 8204 8222 8241 8260 8279 8299 2468 9 II 13 15 17 92 8318 337 8356 8375 8395 8414 8433 8453 8472 8492 2468 10 12 14 15 17 93 8511 8531 8551 8570 8590 8610 8630 8650 8670 8690 2468 10 12 14 16 18 94 8710 8730 8750 8770 8790 8810 8831 8851 8872 8892 2468 10 12 14 16 18 95 8913 8933 8954 8974 8995 9016 9036 9057 9078 9099 2468 10 12 IS 17 19 96 9120 9141 9162 9183 9204 9226 9247 9268 9290 93 11 2468 II 13 15 17 19 97 9333 9354 9376 9397 9419 9441 9462 9484 9506 9528 2479 II 13 IS 17 20 98 9550 9572 9594 9616 9638 9661 9683 9705 9727 9750 2479 II 13 16 18 20 99 9772 9795 9817 9840 9863 9886 9908 993i 9954 9977 2579 II 14 16 18 20 1 2 3 4 5 6 7 8 9 1234 5 . 6789 142 FIVE-FIGURE LOGARITHMS 1 2 3 4 5 6 7 8 9 1234 5 6789 ooooo 00432 00860 01284 01703 43 85 127 170 212 255 297 340 382 1OJ 02119 02531 02938 03342 03743 41 81 121 162 2O 2 243 283 323 364 { 04139 04532 04922 05308 05690 06070 06446 06819 07188 07555 39 77 "6 155 37 74 in 148 *93 I8 5 232 270 309 348 222 259 296 333 , 07918 08279 08636 08991 09342 36 71 106 142 177 213 248 284 319 12| 09691 10037 10380 10721 11059 34 68 102 136 170 205 239 273 307 , 11394 11727 12057 12385 12710 33 66 98 131 I6 4 197 230 262 295 13| 13033 13354 13672 13988 14301 32 63 95 126 I 5 8 190 221 253 284 , 14613 14922 15229 15534 15836 31 61 91 122 *52 183 2I 3 244 274 14| 16137 * 6 435 16732 17026 *73*9 30 59 88 118 *47 177 206 236 265 . 17609 17898 18184 18469 18752 29 57 85 114 142 171 199 228 256 15| *933 19312 19590 19866 20140 28 55 83 i 10 *38 166 193 221 248 / 20412 20683 20951 21219 21484 27 53 80 107 *34 160 187 214 241 16| 21748 220 1 1 22272 22531 22789 26 52 78 104 130 156 182 208 233 , 23045 23300 23553 23805 24055 2 5 50 76 101 126 151 176 201 227 17| 243 4 2455* 24797 25042 25285 24 49 73 98 122 147 171 196 220 , 25527 25768 26007 26245 26482 24 48 71 95 119 143 167 190 214 18| 26717 26951 27184 27416 27646 2 3 46 70 93 116 139 162 185 209 / 27875 28103 28330 28556 28780 23 45 68 90 "3 135 158 181 203 19| 29003 29226 29447 29667 29885 22 44 66 88 1 10 132 154 176 198 20 30103 30320 30535 30750 30963 3"75 3*387 3*597 31806 32015 21 42 64 85 106 127 148 170 191 21 32222 32428 32634 32838 3304* 33244 33445 33646 33846 34044 20 40 61 81 101 121 141 162 182 22 34242 34439 34635134830 35025 354*i 35603 35793 35984 *9 39 58 77 97 116 135 155 174 23 24 36173 38021 36361 38202 36549 38382 36736 38561 36922 38739 37107 389*7 37291 39094 37475 39270 37658 39445 37840 39620 18 37 56 74 *8 35 53 7* 92 89 in 130 148 166 106 124 142 160 25 39794 39967 40140 40312 40483 40654 40824 40993 41162 41330 *7 34 5* 68 85 102 119 136 153 26 4H97 41664 41830 41996 42160 42325 42488 42651 42813 42975 16 33 49 66 82 98 115 131 148 27 28 43 '3' 44716 43297 44871 43457 45025 43616 45*79 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53 61 70 79 1 2 3 4 5 6 7 8 9 1234 5 6789 143 FIVE-FIGURE LOGARITHMS 1 2 3 4 5 6 7 8 9 1234 5 6789 50 69897 6998470070 70157 70243 70329 70415 70501 70586 70672 9 17 26 34 43 52 60 69 77 51 70757 70842 70927 71012 71096 71181 71265 71349 71433 7i5i7 8 17 25 34 42 51 59 67 76 52 71600 7168471767 71850 71933 72016 72099 72181 72263 72346 8 17 25 33 4i 50 58 66 74 53 72428 72509 72591 72673 72754 72835 72916 72997 73078 73159 8 16 24 32 4i 49 57 65 73 54 73239 73320 73400 7348o 7356o 73640 73719 73799 73878 73957 8 16 24 32 40 48 56 64 72 55 74036 74"5 74194 74273 74351 74429 74507 74586 74663 74741 8 16 23 31 39 47 55 63 70 56 74819 74896 74974 75051 75128 75205 75282 75358 75435 755" 8 15 23 31 39 46 54 62 69 57 75587 75664 75740 758i5 75891 75967 76042 76118 76193 76268 8 15 23 30 38 45 53 60 68 58 76343 76418 76492 76567 76641 76716 76790 76864 76938 77012 7 15 22 30 37 44 52 59 67 59 77085 77159 77232 77305 77379 77452 77525 77597 77670 77743 7 15 22 2 9 37 44 5i 58 66 6O 77815 77887 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91855 5 ii 16 21 26 32 37 42 47 83 91908 91960 92012 92064 92117 92169 92221 92273 92324 92376 5 10 16 21 26 31 36 42 47 84 92428 92480 92531 92583 92634 92686 92737 92788 92840 92891 5 10 15 21 26 31 36 41 46 85 92942 92993 93044 93095 93H6 93197 93247 93298 93349 93399 5 10 15 20 26 31 36 41 46 86 9345 935oo 93551 936oi 93651 93702 93752 93802 93852 93902 5 10 15 20 25 30 35 40 45 87 93952 94002 94052 94101 94i5i 94201 94250 943oo 94349 94399 10 15 20 25 30 35 40 45 88 94448 94498 94547 94596 94645 94694 94743 94792 94841 94890 10 15 20 25 29 34 39 44 89 94939 94988 95036 95085 95134 95182 95231 95279 95328 95376 5 I0 *5 1 9 24 29 34 39 44 90 95424 95472 95521 95569 956i7 95665 95713 9576i 95809 95856 5 10 14 19 24 29 34 38 43 91 92 93 95904 96379 96848 9595 2 96426 96895 95999 96473 96942 96047 96520 96988 96095 96567 97035 96142 96614 97081 96190 96661 97128 96237 96708 97174 96284 96755 97220 96332 96802 97267 5 9 14 19 5 9 14 19 5 9 14 1 9 24 24 23 28 33 38 43 28 33 38 42 28 33 37 42 94 97313 97359 97405 97451 97497 97543 97589 97635 97681 97727 5 9 14 18 23 28 32 37 42 95 97772 97818 97864 97909 97955 98000 98046 98091 98137 98182 5 9 14 18 23 27 32 36 41 96 97 98227 98677 98272 98722 98318 98767 98363 98811 98408 98856 98453 98900 98498 98945 98543 98989 98588 99034 98632 99078 5 9 14 18 4 9 13 18 23 22 27 32 36 4i 27 31 36 40 98 99 99123 99564 99167 99607 99211 99651 99255 99695 99300 99739 99344 99782 99388 99826 99432 99870 99476 99913 99520 99957 4 9 13 18 4 9 13 17 22 22 26 31 35 40 26 31 35 39 1 2 3 4 5 6 7 8 9 1284 5 6789 144 RECIPROCALS o 1 2 3 4 5 6 7 g g Subtract Differences. <7 1234 5| 6 7 8 9 10 IOOO 9901 9804 9709 9615 9524 9434 9346 9259 9174 r^~ 11 9091 9009 8929 8850 8772 8696 8621 8547 8475 8403 Mean differences 12 8333 8264 8197 8130 8065 8000 7937 7874 7813 775 2 not sufficiently 13 7692 7634 7576 75i9 7463 7407 7353 729917246 7194 accurate. 14 7143 7092 7042 6993 6944 6897 6849 6803 6757 6711 15 6667 6623 6579 6536 6494 6452 6410 6369 6329 6289 4 8 13 17 21 25 29 33 38 16 6250 6211 6i73 6i35 6098 6061 6024 5988 5952 5917 4 7 " 15 18 22 26 29 33 17 5882 5848 5814 578o 5747 57H 5682 565015618 5587 3 6 10 13 16 20 23 26 29 18 5556 5525 5495 5464 5435 5405 5376 5348 53i9 5291 3 6 9 12 15 17 20 23 26 19 5263 5236 5208 5181 5155 5126 5102 5076 5051 5025 3 5 8 ii 13 16 18 21 24 20 5000 4975 49^0 4926 4902 4878 4854 4831 4808 4785 2 5 7 10 12 14 17 19 21 21 4762 4739 4717 4695 4673 4651 4630 4608 4587 4566 2479 II 13 15 17 19 22 4545 4525 4505 4484 4464 4444 4425 4405 4386 4367 2468 10 12 14 16 18 23 4348 4329 43io 4292 4274 4255 4237 4219 4202 4184 2457 9 ii 13 14 16 24 4167 4149 4132 4H5 4098 4082 4065 4049 4032 4016 2357 8 10 12 13 15 25 4000 3984 3968 3953 3937 3922 3906 3891 3876 3861 2356 8 9 ii 12 14 26 3846 3831 3817 3802 3788 3774 3759 3745 373i 3717 1346 *t / 8 10 ii 13 27 3704 3690 3676 3663 3650 3636 3623 3610 3597 3584 1345 7 8 9 ii 12 28 357i 3559 3546 3534 352i 3509 3497 3484 3472 3460 1245 6 7 9 10 ii 29 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2268 2262 2257 2252 2247 2242 2237 2232 2227 I I 2 2 3 5445 45 2222 2217 22ia 2208 2203 2198 2193 2188 2183 2179 I I 2 2 3344 46 2174 2169 2165 2160 2155 2151 2146 2141 2137 2132 I I 2 2 3344 47 2128 2123 2119 2114 2110 2105 2101 2096 2092 2088 I I 2 2 3344 48 2083 2079 2075 2070 2066 2062 2058 2053 2049 2045 O I I 2 2 3334 49 2O4I 2037 2033 2028 2024 2020 20l6 2OI2 2008 2004 I I 2 2 2334 50 2000 1996 1992 1988 1984 1980 1976 1972 1969 1965 I I 2 2 2334 51 I96l 1957 1953 1949 1946 1942 1938 1934 '93* 1927 I I 2 2 2333' 52 1923 1919 1916 1912 1908 1905 1901 I8 9 8 1894 1890 I I I 2 2333 53 1887 1883 1880 1876 1873 1869 1866 1862 1859 1855 I I I 2 2233 54 1852 1848 1845 1842 1838 1835 1832 1828 1825 1821 I I I 2 2233 1234 5 6789 4 7 J. . _. 1 7 Subtract Differences. 145 RECIPROCALS Subtract Differences. 1 2 3 4 5 234 > 6789 55 8x8 815 1812 808 805 802 799 1795 792 789 ill 2233 56 786 783 1779 776 773 770 767 1764 761 757 i i i 2233 57 754 75 * 1748 745 742 739 736 1733 73 727 ill 2223 58 724 721 1718 712 709 706 1704 701 698 I I i 2223 59 695 692 1689 686 684 681 678 1675 672 669 III 2223 60 667 664 1661 658 656 653 650 1647 645 642 I I i 2223 61 639 637 1634 631 629 626 623 1621 618 616 X I I 2222 62 613 610 1608 605 603 600 597 1595 592 590 I I I 2222 63 587 585 1582 580 577 575 572 1570 567 565 O O I I 1222 64 563 560 1558 555 553 550 548 1546 543 54i I I 1222 65 538 536 1534 53i 529 527 524 1522 520 517 I I 1222 66 5*5 5*3 15" 508 506 504 502 1499 497 495 I I 1222 67 493 49 1488 486 484 481 479 1477 475 473 I I 1222 68 1471 468 466 464 462 460 458 453 I I 1222 69 1449 1447 445 443 441 439 437 1435 433 43i I I I I 2 2 70 1429 1427 H25 422 420 418 416 1414 412 410 I I I I 2 2 71 1408 1406 1404 403 401 399 397 1395 393 391 I I i I I 2 2 72 1389 1387 1385 383 38i 379 377 1376 374 372 I I i I I 2 2 73 1370 1368 1366 364 362 359 1357 355 353 I I i I I 2 2 74 1350 1348 1346 344 342 340 1339 337 335 O I I 1 I I I 2 75 7fi 1333 1332 1330 1328 326 325 323 1321 1319 *jr\r\ I 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IOO; 100 100 O O XIII o 1 2 3 4 5 6 7 8 9 123 5 6789 Subtract Differences. SQUARES 146 1 2 3 4 5 6 7 8 9 1234 5 6789 l-O I -000 I"O2O 040 ro6i 082 1-103 1-124 ri45 1-166 1*188 2468 10 13 15 17 19 1-1 1-2 1-4 I-2IO l;6gS 1*464 I7I6 1-988 254 488 742 2-016 1-277 1-513 1-769 2-045 300 538 796 2-074 1-323 1-563 1-823 2*103 i-346 1-588 1-850 2-132 1*369 1-613 1-877 2'l6l 1-392 1-638 1-904 2-190 1-416 1-664 1-932 2*220 2579 2 5 7 10 3 5 8 ii 3 6 9 12 ii 12 13 14 14 16 18 21 15 17 20 22 l6 19 22 24 17 20 23 26 1-5 2-250 2-280 2-310 2-341 2-372 2-403 2*434 2-465 2-496 2*528 3 6 9 12 s 19 22 25 28 1-6 1-7 1-8 1-9 3*240 3-610 2-592 2-924 3^76 3-6 4 8 2-624 2-958 3*312 3-686 2*657 2'993 3*349 2-690 3-028 3-386 3-764 2-723 3-063 3-423 3-803 2756 3-098 3-460 3*842 2-789 3*133 3*497 3-881 2-822 3-168 3*534 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 20 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 29 33 37 2-1 2-2 2-3 2-4 4-410 4-840 5-290 [-884 4-494 4*928 4*537 4*973 ;*oi8 T476 4*623 5*063 5-523 6-003 4-666 5-108 5-570 6-052 4-709 5-153 5-6i7 6-101 4*752 5-198 5-664 6-150 4*796 5-244 5-7I2 6-200 4 9 13 17 4 9 13 18 5 9 J 4 19 5 10 13 20 21 22 23 26 30 34 39 27 31 36 40 28 33 38 42 2 9 34 39 44 57 6o 5-808 5*856 5*905 5-954 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 6-760 7-290 7-840 8*410 6-812 7*344 7-896 8-468 6-864 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 7-076 7-618 8- 1 80 8-762 7*1297*182 8-237:8-294 8-8218-880 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 41 47 53 3-0 9-000 9-060 9*120 9*181 9-242 9*303 9-364 9H25 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 11-63 9734 10-37 11*02 11*70 9-797 10-43 11*09 11-76 9*860 10-50 11-16 11-83 10-56 H'22 11*90 9*986 10*63 II*2C 11-97 10*05 10-69 11*36 12-04 IO-II 10-76 11-42 12-11 10-18 10-82 11-49 12-18 6 13 19 25 1123 1123 1123 1123 31 3 3 3 3 38 44 50 57 4556 4556 4556 4566 3-5 12-25 12-32 I2-39 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 13-03 1376 H-52 15-29 I 3 *IO I3*84 14*59 15*37 13-18 13-91 14-67 15*44 13*99 I4-75 15-52 ll'll I 4 -82 15-60 I3*40 I4-I4 I4-90 15-68 I3-47 14-21 14-98 15-76 I3-54 14-29 15-05 15-84 13-62 14-36 15-92 1123 1223 1223 122^ 4 4 4 4 4567 4567 5567 5667 4-0 16-00 1 6- 08 16-16 16*24 16-32 l6*40 16-48 16-56 16-65 16-73 1223 4 5667 4-1 4-2 4-3 4-4 16-81 17-64 18-49 16-89 17*72 18-58 19-45 16-97 17-81 18-66 19-54 17-06 17-89 1875 19-62 17*14 17-98 18-84 19*71 17*22 18-06 18-92 19-80 I8-I5 I9-OI 19-89 I7-39 I8-23 I9-IO 19-98 17*47 18-32 I9'ic 20*07 17*56 18-40 19*27 20* 1 6 1223 1233 1233 1234 4 4 4 4 5677 5678 5678 5678 4-5 20-25 20-34 20*43 20*52 20'6l 20-70 20-79 20-88 20*98 21*07 1234 5 5678 4-6 4-7 4-8 4*9 21*16 22-09 23-04 24-01 21*25 22'li 23-14 24-II 21*34 22*28 23-23 24-21 21*44- 22-37 2333 24-30 21-53 22*47 23-43 24*40 21-62 22-56 23-52 24-50 21*72 22-66 23-62 24-60 21-81 22*75 23-72 24-70 21-90 22-85 23*81 24-80 22"OO 22-94 23-9I 24-90 1234 1234 1234 e 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' 1 1 27-I4 28-20 29-27 26*2 27*25 28-30 29-38 26*32 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*0-: 26*94 27*98 29-05 1234 1234 1234 1234 c 6789 6789 6 7 9 10 7 8 9 10 1 2 3 4 6 6 7 8 9 1234 5 6789 147 SQUARES 1 2 3 4 5 6 7 8 9 234 5 6789 5-5 0-25 0-36 jo-47 0-58 0-69 0-80 0-91 I'02 1-14 1-25 234 6 7 8 9 10 5*6 5*7 5'8 5'9 1-36 3 2 '49 33-64 34-81 1-47 2-60 3-76 4*93 Ji-58 52-72 33-87 35-05 1-70 2-83 3'99 5-16 1-81 2-95 4-1 1 5-28 1-92 3-06 4-22 5-40 2-04 3-18 4'34 5-52 2-15 3-29 4-46 5-64 2-26 3-4i 4-57 5-76 2-38 3-52 2 3 5 235 245 245 6 6 6 6 7 8 9 10 7 8 9 10 7 8 9 ii 7 8 10 ii 6-0 36-00 6-12 36-24 6-36 6-48 6-60 6-72 6-84 36-97 7-09 245 6 7 8 10 ii 6*1 6'2 6'3 6'4 37-21 38*44 39-69 40-96 7*33 8-56 ,1-09 37'45 38-69 39'94 H'22 7-58 8-81 0-07 41-34 7-70 8-94 0-20 I'47 7-82 39-06 40-32 41-60 37-95 39-I9 .0-45 41-73 8'07 9-31 0-58 1-86 38-I9 39'44 40-70 41-99 38-32 39-56 40-83 .2-12 245 345 345 i 3 4 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 42-5I 42-64 277 42-90 43-03 43-16 43-30 43*43 i 3 4 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 %% 48-02 44-09 ,6' 7 c 48-16 44-22 45-56 46-92 48-30 44-36 4570 47-06 48-44 4-49 .7-20 48-58 44-62 45-97 47-33 48-72 44*76 46*10 47*47 48-86 i 3 4 i 3 4 i 3 4 i 3 4 ; 8 9 ii 12 8 9 ii 12 8 10 II 12 8 10 ii 13 7-0 49-00 49-14 49-28 49*42 49-56 49-70 49-84 49-98 50*13 50-27 1346 7 8 10 ii 13 7-1 7'2 7'3 7'4 50-41 51*84 53- 2 9 54-76 50-55 51-98 53'44 54*9! 50*69 52*13 53-58 55-o6 50-84 52-2 53'73 55-20 50-98 52-42 53-88 55'35 51-12 52-56 54-02 55-50 51-27 52-7 54-i 55*6 51*4 52-85 54-32 55-8o 5i'55 53*00 54-46 55-95 5^70 53-J4 54'6 56-10 1346 1346 1346 1346 9 10 ii 13 9 10 12 13 9 10 12 13 9 10 12 13 7'5 56-25 56-40 56-55 5670 56-85 57*00 57-i 57-30 57-46 57-6 2356 9 ii 12 14 7'6 7'7 7'8 7*9 57-76 59- 2 9 60-84 62-4 57*9 59*44 6i'oo 62-57 58-06 59-6o 62-7 58-2 59*7 61-3 62-8 58-37 59-9 61-47 63-04 f52 60-06 61-62 63-20 58-6 60-2 61-7 63-3 58-8 60-3 61-9 63-5 58-9 60-5 62-09 63-6 59*H 60-68 62-2 63-84 2356 235 235 2 3 5 9 ii 12 14 9 ii 12 u 9 ii 13 14 10 ii 13 14 8'0 64-00 64-16 64-3 64-4 64-6^ 64-80 64-9 65-1 65-2 65*4 2 3 5 10 ii 13 14 8-1 8'2 8-3 8'4 65-6 67-24 68-89 70-5 6577 67-40 69-06 7073 65-9 67-5 69-2 70-9 66-1 677 69-3 71-0 66-26 67-90 69-5 71*2 66-4 68-06 69-7 71-4 66-5 68-2 69-8 7i-5 66-75 68-39 70-06 71-74 66-9 68-5 70-2 71-9 67-0 68-7 72-39 72*0 235 2 3 5 235 2 3 5 10 n 13 15 IO 12 13 If 10 12 13 15 IO 12 14 If 8-5 72-2 72-42 72-5 727 72-9 73'i 73*2 73*44 73-6 73-7 235 10 12 14 15 8*6 8-7 8'8 8'9 73-9 75'6 77-44 79-2 74*13 75-86 77-62 79-39 74-3 76-0 77'7 79-5 7f4 76-2 77'9 797 74*6 76-3 78-1 79'9 75-8 76-5 78-3 80- 1 75'oc 76-7 78-5 80-2 75*17 76-91 78-68 80-46 75*3 77*o 78-8 80-6 75*5 77*2 79*o 80-8 2 3 5 245 2 4 5 245 10 12 14 I II 12 14 l6 II 12 14 16 ii 13 14 16 9-0 8ro 81-18 81-3 81-5 817 81-9 82-0 82-26 82-4 82-6 2 4 5 ii 13 14 16 9-1 9'2 9'3 9'4 82-8 84-6 86-4 88-3 82-99 84-82 86-68 88-55 83-I7 85*01 86-86 88-74 8 3 -3 85-1 87-0 88-9 8 3 -5 f 5 ' 3 87-2 89-1 837 85-5 87-4 89-3 83-9 85-7 87-6 89-4 84-05 85-93 87 -8c 89-68 84-2 86-1 87-9 89*83 84-4 86-3 88-1 90*0 245 246 246 246 ii 13 15 16 ii 13 15 17 ii 13 15 17 ii 13 IS 17 9-5 90-2 90-44 90-63 90-8 91-0 91-2 9i-3 91-58 91*7* >9i'9 246 i ii 13 15 17 9'6 9-7 9*8 9'9 92-1 94-0 96-0 98-0 92'35 94'2* 96-24 98-21 92-54 94'4* 96-43 98-41 ^927 ,94-6 ,96-6 9 8-6c 92-9 94-8 96-8 98-8 93-i 95' 97-o 99-0 93-3 95 '2 97-2 99"2 93-5I 95*45 97-42 99'4C 937C 95-65 97-61 99 -6c >93'9 95-8 97-8 >99'8 246 2 4 6 246 2 4 6 i i i i 12 14 15 17 12 14 16 ii 12 14 l6 it 12 14 16 i 1 2 3 4 5 6 7 8 9 128 5 6789 148 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 0157 3 6 9 12 15 1 2 3 4 0175 0349 0523 0698 0192 0366 0541 0715 0209 0384 0558 0732 0227 0401 0576 0750 0244 0419 0593 0767 0262 0436 0610 0785 0279 0454 0628 0802 0297 0471 0645 0819 0314 0488 0663 0837 0332 0506 0680 0854 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 3 6 9 12 14 5 0872 0889 0906 0924 0941 0958 0976 0993 10 1 1 1028 3 6 9 12 14 6 7 8 9 1045 1219 1392 1564 1063 1236 1409 1582 1080 1253 1426 1599 1097 1271 1444 1616 i"5 1288 1461 1633 1132 1305 1478 1650 "49 1323 1495 1668 Il67 1340 1513 1685 1184 1357 1530 1702 1 201 1374 1547 1719 3 6 9 12 14 3 6 9 12 14 3 6 9 12 14 3 6 9 ii 14 10 1736 1754 1771 1788 1805 1822 1840 1857 1874 1891 3 6 9 ii 14 11 12 13 14 1908 2079 2250 2419 1925 2096 2267 2436 1942 2113 2284 2453 1959 2130 2300 2470 1977 2147 2317 2487 1994 2164 2334 2504 2OII 2181 2351 2521 2028 2198 2368 2538 2045 2215 2385 2554 2062 2233 2402 2571 3 6 9 ii H 3 6 9 n 14 3 6 8 ii 14 3 6 8 ii 14 15 2588 2605 2622 2639 2656 2672 2689 2706 2723 2740 3 6 8 ii 14 16 17 18 19 2756 2924 3090 3256 2773 2940 3107 3272 2790 2957 3123 3289 2807 2974 3 J 40 3305 2823 2990 3156 3322 2840 3007 3i73 3338 2857 3024 3190 3355 2874 3040 3206 3371 2890 3057 3223 3387 2907 3074 3239 3404 3 6 8 ii 14 3 6 8 ii 14 3 6 8 ii 14 3 5 8 n 14 20 3420 3437 3453 3469 3486 3502 35i8 3535 355' 3567 3 5 8 ii 14 21 22 23 24 3584 3746 3907 4067 3600 3762 3923 4083 3616 3778 3939 4099 3633 3795 3955 4"5 3649 3811 397i 4131 3665 3827 3987 4H7 3681 3843 4003 4163 3697 3859 4019 4179 37M 3875 4035 4195 3730 3891 4051 4210 3 5 8 ii 14 3 5 8 ii 13 3 5 8 n 13 3 5 8 n 13 25 4226 4242 4258 4274 4289 4305 432i 4337 4352 4368 3 5 8 ii 13 26 27 28 29 4384 4540 4695 4848 4399 4555 4710 4863 4415 4571 4726 4879 4431 4586 474i 4894 4446 4602 4756 4909 4462 4617 4772 4924 4478 4633 4787 4939 4493 4648 4802 4955 4509 4664 4818 4970 4524 4679 4833 4985 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 30 5000 BO'S 5030 5045 5060 5075 5090 5105 5120 5135 3 5 8 10 13 31 32 33 34 5150 5299 5446 5592 5^5 53H S46i 5606 5180 53 2 9 5476 5621 5195 5344 5490 5635 5210 5358 5505 5650 5225 5373 5519 5664 5240 5388 5534 5678 5255 5402 5548 5693 5270 54J7 5563 5707 5284 5432 5577 5721 2 5 7 10 12 2 5 7 10 12 2 5 7 10 12 2 5 7 10 12 35 5736 5750 5764 5779 5793 5807 5821 5835 5850 5864 2 5 7 9 12 36 37 38 39 til 6157 6293 5892 6032 6170 6307 59o6 6046 6184 6320 5920 6060 6198 6334 5934 6074 6211 6347 5948 6088 6225 6361 5962 6101 6239 6374 5976 6115 6252 6388 5990 6129 6266 6401 6004 6143 6280 6414 2 5 7 9 12 2 5 7 9 12 2 5 7 9 ii 2 4 7 9 ii 40 6428 6441 6455 6468 6481 6494 6508 6521 6534 6547 2 4 7 9 ii 41 42 43 44 6561 6820 6947 6574 6704 6833 6959 6587 6717 6845 6972 6600 6730 6858 6984 6613 Sjf 6997 6626 6756 6884 7009 6639 6769 6896 7022 6652 6782 6909 7034 6665 6794 6921 7046 6678 6807 6934 7059 2479" 2 46 9 ii 2 4 6 8 ii 2 4 6 8 10 0' 6' 12' 18' 24' 30' 36' 42' 48' 64' 1' 8' 3' 4' 5' 149 NATURAL SINES 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' 1' 2' 8' 4' 5' 45 7071 7083 7096 7108 7120 7133 7H5 7157 7169 7181 2 4 6 8 10 46 47 48 49 7193 "73H 7431 7547 7206 7325 7443 7559 7218 7337 7455 7570 7230 7349 7466 758i 7242 7361 7478 7593 7254 7373 7490 7604 7266 7385 75oi 7615 7278 7396 7513 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 61 52 53 54 7771 7880 7986 8090 7782 7891 7997 8100 7793 7902 8007 Sin 7804 7912 8018 8121 78i5 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 8545 8634 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 llii 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 1 3 4 6 7 13457 13456 13456 65 9063 9070 9078 9085 9092 9100 9107 9114 9121 9128 12456 66 67 68 69 9135 9205 9272 9336 9143 9212 9278 9342 9150 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 9391 12356 12346 12345 12345 70 '9397 9403 9409 9415 9421 9426 9432 9438 9444 9449 12345 71 72 73 74 '9455 "95" 9563 9613 9461 9516 9568 9617 9466 952i 9573 9622 9472 9527 9578 9627 9478 9532 9583 9632 9483 9537 9 ^ 9636 9489 9542 9593 9641 9494 9548 9598 9646 9500 9553 9603 9650 9505 9558 9608 9655 12345 12334 12234 12234 75 9659 9 66 4 9668 9673 9677 9681 9686 9690 9694 9699 11234 76 77 78 79 9703 9744 9781 9816 9707 9748 9785 9820 9711 9751 9789 9823 9715 9755 9792 9826 9720 9759 9796 9829 9724 9763 9799 9833 9728 9767 9803 9836 9732 9770 9806 9839 9736 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 * 9888 9912 9934 9952 9890 9914 9936 9954 9893 9917 9938 9956 9895 9919 9940 9957 9898 9921 9942 9959 9900 9923 9943 9960 O I I 2 2 I I 2 2 O I I I 2 I I I I 85 9962 9963 9965 9966 9968 9969 9971 0972 9973 9974 O I I I 86 87 88 89 9976 9986 9994 9998 9977 9987 9995 9999 9978 9988 9995 9999 9979 9989 9996 9999 9980 9990 9996 9999 9981 9990 9997 I '000 9982 9991 9997 I '000 9983 9992 9997 I'OOO 9984 9993 9998 I'OOO 9985 9993 9998 I'OOO I I I O O O I I 00000 00000 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' 1' V V 4' 5' ISO NATURAL COSINES Subtract 0' 6' 12* 18' 24' 30' 36' 42* 48' 54' Differences. 1' 2' 3' 4' 5' I '000 rooo rooo I '000 I '000 I '000 '9999 9999 9999 9999 00000 1 9998 9998 9998 9997 9997 9997 9996 9996 9995 9995 o o o o o 2 '9994 9993 9993 9992 9931 9990 9990 9989 9988 9987 I I 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 I I I 5 9962 9960 9959 9957 995.6 9954 9952 995 i 9949 9947 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 I I 2 2 10 9848 9845 9842 9839 9836 9833 9829 9826 9823 9820 II223 11 9816 9813 9810 9806 9803 9799 9796 9792 9789 9785 II223 12 9781 9778 9774 9770 9767 9763 9759 9755 9748 II233 13 '9744 9740 9736 9732 9728 9724 9720 97" 9707 II233 14 9703 9699 9694 9690 9686 9681 9677 9673 9668 9664 II234 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 9516 12334 18 "95" 9505 9500 9494 9489 9483 9478 9472 9466 9461 12345 19 '9455 9449 9444 9438 9432 9426 9421 9415 9409 9403 12345 20 '9397 9391 9385 9379 9373 9367 936i 9354 9348 9342 12345 21 9336 9330 9323 9317 93" 9304 9298 9291 9285 9278 12345 22 9272 9265 9259 9252 9245 9239 9232 9225 9219 9212 12346 23 9205 9198 9191 9184 9 r 78 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 13456 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 3O 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 8415 8499 8406 8490 8396 23568 23568 33 8387 8377 8368 8348 8339 8329 8320 8310 8300 23568 34 8290 8281 8271 8261 8251 8241 8231 8221 8211 8202 23578 35 8192 8181 8171 8161 8151 8141 8131 8121 8111 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 7815 7804 7793 7782 24579 | 39 7771 7760 7749 7738 7727 7716 7705 7694 7683 7672 24679 40 7660 7649 7638 7627 76i5 7604 7593 7581 7570 7559 24689 41 7547 7536 7524 7513 75oi 7490 7478 7466 7455 7443 2 4 6 8 10. 42 7431 7420 740* 7396 7385 7373 736i 7349 7337 7325 2 4 6 8 10 43 7302 7290 7278 7266 7254 7242 7230 7218 7206 2 4 6 8 10 44 7193 7181 7169 7157 7H5 7133 7120 7108 7096 7083 2 4 6 8 10 A >/ r- A t 1' 2' 3' 4' 5' 0' 6' 12' 18' 24' 30' 36' 42' 48 54 Subtract Differences. 151 NATURAL COSINES Subtract 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' Differences. w 1' 2' 3' 4' 5' 45 7071 7059 7046 7034 7022 7009 6997 6984 6972 6959 2 4 6 8 10 46 47 6947 6820 6934 6807 6921 6794 6909 6782 6896 6769 6884 6756 6871 6743 6858 6730 6845 6717 6833 6704 2 4 6 8 ii 2 4 6 9 ii 48 49 6691 6561 6678 6547 6665 6534 6652 6521 6639 6508 6626 6494 6613 6481 6600 6468 6587 6455 6574 6441 2 4 7 9 ii 2 4 7 9 ii 50 6428 6414 6401 6388 6374 6361 6347 6334 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 5750 2 5 7 9 12 55 5736 5721 5707 5693 5678 5664 5650 5635 5621 5606 2 5 7 10 12 56 5592 5577 5563 5548 5534 5519 5505 5490 5476 5461 2 5 7 10 12 57 5446 5432 5417 5402 5388 5373 5358 5344 5329 53H 2 5 7 10 12 58 5299 5284 5270 5255 5240 5225 5210 5 T 95 5180 5165 2 5 7 10 12 59 5150 5135 5120 5io5 5090 5075 5060 5045 5030 5oi5 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 4509 4493 4478 4462 4446 443i 44i5 4399 3 5 8 10 13 64 4384 4368 4352 4337 4321 4305 4289 4274 4258 4242 3 5 8 ii 13 65 4226 4210 4195 4179 4163 4M7 4131 4"5 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 ii 14 68 3746 3730 37H 3697 3681 3665 3649 3633 3616 3600 3 5 8 ii 14 69 3584 3567 355i 3535 35i8 3502 3486 3469 3453 3437 3 5 8 ii 14 70 3420 3404 3387 3371 3355 3338 3322 3305 3289 3272 3 5 8 ii 14 71 3256 3239 3223 3206 3190 3173 3156 3HO 3123 3107 3 6 8 ii 14 72 3090 374 3057 3040 3024 3007 2990 2974 2957 2940 3 6 8 ii 14 73 2924 2907 2890 2874 2857 2840 2823 2807 2790 2773 3 6 8 ii 14 74 2756 2740 2723 2706 2689 2672 2656 2639 2622 2605 3 6 8 ii 14 75 2588 2571 2554 2538 2521 2504 2487 2470 2453 2436 3 6 8 ii 14 76 2419 2402 2385 2368 2351 2334 2317 2300 2284 2267 3 6 8 ii 14 77 2250 2233 2215 2198 2181 2164 2147 2130 2113 2096 3 6 9 ii 14 78 2079 2062 2045 2028 2OII 1994 1977 1959 1942 i9 2 5 3 6 9 ii H 79 1908 1891 1874 1857 1840 1822 1805 1788 1771 1754 3 6 9 ii H 80 1736 1719 1702 1685 1668 1650 1633 1616 1599 1582 3 6 9 ii 14 81 1564 1547 1530 1513 1495 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 IOII 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 0314 0297 0279 0262 0244 0227 0209 0192 3 6 9 12 15 89 0175 0157 0140 0122 0105 0087 0070 0052 0035 0017 3 6 9 12 15 Of 61 4 O' 4 O' O A 9 O/"V Or* ' A f">' A rtt A 9 1' 2' 3' 4' 5' 12 18 24 30 36 42 48 54 Subtract Differences. 152 NATURAL TANGENTS 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' ' 2' 8' 4' 6' oooo 0017 0035 0052 0070 0087 0105 0122 0140 oi57 3 6 9 12 15 1 2 3 4 0175 0349 0524 0699 0192 0367 0542 0717 0209 0384 0559 0734 0227 0402 0577 0752 0244 0419 0594 0769 0262 0437 0612 0787 0279 0454 0629 0805 0297 0472 0647 0822 0314 0489 0664 0840 0332 0507 0682 0857 3 6 9 12 15 1 6 9 12 15 3 6 9 12 15 3 6 9 12 15 5 0875 0892 0910 0928 0945 0963 0981 0998 1016 1033 3 6 9 12 15 6 7 8 9 1051 1228 1405 1584 1069 1246 1423 1602 1086 1263 1441 1620 1104 1281 1459 1638 1122 1299 H77 1655 "39 I3i7 1495 1673 "57 1334 1512 1691 "75 1352 1530 1709 1192 1370 1548 1727 I2IO 1388 1566 1745 369 12 15 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 10 1763 1781 1799 1817 1835 1853 1871 1890 1908 1926 3 6 9 12 15 11 12 13 14 1944 2126 2309 2493 1962 2144 2327 2512 1980 2162 2345 2530 1998 2180 2364 2549 2016 2199 2382 2568 2035 2217 2401 2586 2053 2235 2419 2605 2071 2254 2438 2623 2089 2272 2456 2642 2107 229O 2475 2661 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 3 6 9 12 16 15 2679 2698 2717 2736 2754 2773 2792 2811 2830 2849 3 6 9 13 16 16 17 18 19 2867 3057 3249 3443 2886 3076 3269 3463 2905 3288 3482 2924 3H5 3307 3502 2943 3^34 3327 3522 2962 3153 3346 3541 2981 3172 3365 356i 3000 3191 3385 358i 3019 3211 3404 3600 3038 3230 3424 3620 3 6 9 13 16 3 6 10 13 16 3 6 10 13 16 3 7 10 13 16 20 3640 3659 3679 3699 3719 3739 3759 3779 3799 3819 3 7 10 13 17 21 22 23 24 3839 4040 4245 4452 3859 4061 4265 4473 3879 4081 4286 4494 3899 4101 4307 4515 3919 4122 43 2 7 4536 3939 4142 4348 4557 3959 4163 4369 4578 3979 4183 4390 4599 4000 4204 44" 4621 4O2O 4224 4431 4642 3 7 10 13 17 3 7 10 14 17 3 7 10 14 17 4 7 ii 14 18 25 4663 4684 4706 4727 4748 4770 4791 4813 4834 4856 4 7 ii 14 18 26 27 28 29 4877 5095 5317 '5543 4899 5"7 5340 5566 4921 5139 5362 5589 4942 5161 5384 5612 4964 5184 5407 5635 4986 5206 5430 5658 5008 5228 5452 5681 5029 5250 5475 574 5051 5272 5498 5727 5073 5295 5520 5750 4 7 " 15 l8 4 7 " 15 l8 4 8 ii 15 19 4 8 12 15 19 30 '5774 5797 5820 5844 5867 5890 59H 5938 5961 5985 4 8 12 16 20 31 32 33 34 6009 6249 6494 6745 6032 6273 6519 6771 6056 6297 6544 6796 6080 6322 6569 6822 6104 6346 6.S94 6847 6128 6171 6619 6873 6152 6395 6644 6899 6176 6420 6669 6924 6200 6445 6694 6950 622t 6469 6720 6976 4 8 12 16 20 4 8 12 16 20 4 8 13 17 21 4 9 13 17 21 35 7002 7028 7054 7080 7107 7133 7159 7186 7212 7239 4 9 13 18 22 36 37 38 i 39 7265 7536 7813 8098 7292 7563 7841 8127 7319 7590 8156 7346 7618 7898 8185 7373 7646 7926 8214 7400 7673 7954 8243 7427 7701 7983 8273 7454 7729 8012 8302 7481 7757 8040 8332 7S 08 7785 8069 8361 5 9 H 18 23 5 9 *4 18 23 5 9 H 19 24 5 10 15 20 24 40 8391 8421 8451 8481 8511 8541 8571 8601 8632 8662 5 10 15 20 25 41 42 43 44 8693 900^ 9325 9657 8724 9036 9358 9691 %% 9391 9725 8785 9099 9424 9759 8816 9*31 9457 9793 8847 9163 9490 9827 8878 9!95 9523 9861 8910 922$ 9556 9896 8941 9260 9590 9930 8972 9293 9623 9965 5 10 16 21 26 5 ii 16 21 27 6 II 17 22 2 ( t> 6 ii 17 23 29 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' 1' 2' 3' 4' 5' 153 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 O2 1 2 0247 0283 0319 6 12 18 24 30 46 47 48 49 1-0355 1-0724 1*1106 1-1504 0392 0761 "45 1544 0428 0799 1184 1585 0464 0837 1224 1626 0501 0875 1263 1667 0538 0913 1303 1708 0575 0951 1343 1750 0612 0990 1383 1792 0649 1028 1423 1833 0686 1067 1463 1875 6 12 18 25 31 6 13 19 25 32 7 13 20 27 33 7 14 21 28 34 50 1-1918 1960 2002 2045 2088 2131 2174 2218 2261 2305 7 14 22 29 36 51 52 53 54 i'2349 1-2799 1-3270 1-3764 2393 2846 33'9 38i4 2437 2892 3367 3865 2482 2938 34i6 3916 2527 2985 3465 3968 2572 3032 35M 4 or 9 2617 3079 3564 4071 2662 3127 3 6 i3 4124 2708 3'75 3663 4176 2753 3222 37i3 4229 8 15 23 30 38 8 16 24 31 39 8 16 2q 33 41 9 17 26 34 43 55 1-4281 4335 43 88 4442 4496 4550 4605 4659 4715 4770 9 18 27 36 45 56 57 58 59 i -4826 i '5399 1-6003 1-6643 4882 5458 6066 6709 4938 5517 6128 6775 4994 5577 6191 6842 5051 5637 6255 6909 5108 5697 6319 6977 5166 5757 6383 7045 5224 5818 6447 7"3 5282 5880 6512 7182 5340 594i 6577 7251 10 19 29 38 48 10 20 30 40 50 ii 21 32 43 53 ii 23 34 45 57 60 17321 7391 7461 7532 7603 7675 7747 7820 7893 7966 12 24 36 48 60 61 62 63 64 1-8040 1-8807 1-9626 2-0503 8115 8887 9711 0594 8190 8967 9797 0686 8265 9047 9883 0778 8341 9128 9970 0872 8418 9210 2-0057 0965 7495 9292 2-0145 1060 8572 9375 2-0233 "55 8650 9458 2-0323 1251 8728 9542 2-0413 1348 13 26 38 51 64 14 27 41 55 68 15 29 44 58 73 16 31 47 63 79 65 2'i445 1543 1642 1742 1842 1943 2045 2148 2251 2355 17 34 51 68 85 66 67 68 69 2-2460 2-3559 2-4751 2*6051 2566 3673 4876 6187 2673 3789 5002 6325 2781 3906 5i 2 9 6464 2889 4023 5257 6605 2998 4142 5386 6746 3109 4262 ilg 3220 4383 5649 7034 3332 454 5782 7179 3445 4627 59i6 7326 18 37 55 73 92 20 40 60 79 99 22 43 65 87 108 24 48 71 95 119 70 2-7475 7625 7776 7929 8083 8239 8397 8556 8716 8878 26 52 78 105 131 71 72 73 74 2-9042 3'0777 3-2709 3H874 9208 0961 2914 5105 9375 1146 3122 5339 9544 1334 3332 5576 97H i5 2 4 3544 5816 9887 1716 3759 6059 3-0061 1910 3977 6305 3-0237 2106 4i97 6554 3*04i5 2305 4420 6806 3-0595 2506 4646 7062 29 58 87 116 145 32 64 96 129 161 36 72 108 144 180 41 81 122 163 204 75 76 77 78 79 3'732i 4-0108 4-3315 4-7046 5-1446 7583 0408 3662 7453 1929 7848 0713 4015 7867 2422 8118 IO22 4374 8288 2924 8391 1335 4737 8716 3435 8667 1653 5107 9152 3955 8947 1976 5483 9594 4486 9232 2303 5864 5*0045 5026 9520 2635 6252 5-0504 5578 9812 2972 6646 5-0970 6140 46 93 139 186 232 8O 5-6713 7297 7894 8502 9124 9758 6*0405 6-1066 6-1742 6-2432 81 82 83 84 6-3138 7-H54 8-1443 9 % 5H 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 9-05/9 10-78 9395 9158 9-2052 10-99 7-0264 8-0285 9*3572 11-20 VTean differences no longer suffi- ciently accurate. 85 "'43 11-66 11-91 I2"l6 12-43 12-71 13-00 13*30 13-62 I3-95 86 87 88 89 14-30 19-08 28-64 57 '29 14-67 19-74 30-14 63-66 15-06 20-45 31-82 71-62 I5-46 21-20 33- 6 9 81-85 15-89 22*02 35-8o 95'49 16-35 22 90 38-I9 II4-6 16-83 23-86 40-92 143-2 17*34 24-90 44-07 191 o 17-89 26-03 4774 286-5 18-46 27-27 52-08 573*0 0' 6' 12', 18' 24' 30' 36' 42' 48' 54' L 2 RADIANS 154 O 1 2 3 4 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 0' 6' 12' 18' 24' 30' 36' oooo I -0017 -0035 -0052 -0070 I -0087 I -0105 0175 I 0192 0209 0227 0244 1 0262 I 0279 0349 1 03 6 7 0384 0401 0419 0436 0454 0524 1 0541 0559 0576 0593 06 1 1 I 0628 0698 1 0716 0733 0750 0768 1 0785 0803 0873 I 0890 0908 0925 0942 I 0960 I 0977 1047! 1065 1082 1 100 1117 I 1134 1 1152 1222 I 1239 1257 1274 1292 I 1309 I 1326 1396 I I4H 1431 H49 H66 I 1484 I 1501 1571 I 1588 1606 1623 1641 I6S8| 1676 1745 1763 1780 1798 I8IS 1833 I8SO 1920 I 1937 1955 1972 1990 I 2007 2025 2094| 2112 2129 2147 2164! 2l82| 2199 2269 2286 2304 2321 2339 2356 2374 2443 I 2461 2478 2496 2513 2531 2548 26l8 I 2635 2653 2670 2688 I 2705 I 2723 2793 I 2810 2827 2845 2862 I 2880 I 2897 2967 I 2985 3002 3019 3037 3054 3072 3H2 3159 3176 3194 32" 3229 3246 3334 3351 3368 3386 3403 3421 349i 3526 3543 3578 3595 3665 3683 3700 3718 3735 3752 3770 3840! 3857 3875 3892 3910! 3927 I 3944 4014 I 4032 4049 4067 4084 I 4102 I 4119 4189 1 4206 4224 4241 4259 4276 4294 4363 I 438i 4398 44i6 4433 I 445 1 I 4468 4538 1 4555 4573 4590 4608 4625 1 4643 4712 4730 4747 4765 4782 4800 4817 4887 I 4904 49 2 2 4939 4957 I 4974 | 499.2 5061 5079 5096 5114 5131 5149 5236 1 5253 5271 5288 5306 5323) 534 5411 5428 5445 5463 548o 5498 5585 5603 5620 5637 5655 5672 5 6 9 ( 5760 5777 5794 5812 5829 5847 5864 *5934 I 5952 59 6 9 5986 6004 I 6021 I 603 6109 I 6126 6144 6161 6178 I 6196 I 621 6283 I 6301 6318 6336 6353 I 6370 I 638 6458 6475 6493 6510 6528 6545 656 6632 6650 6667 6685 6702 6720 673 6807 I 6824 6842 6859 6877 I 6894 I 691 6981 1 6999 7016 7034 7051 I 7069 I 708 7156! 7173 7191 7208 7226! 7243! 726 7330 7348 7365 7383 7400 7418 743 7505 1 7522 7540 7557 7575 7592 761 7679 7697 7714. 7732 7749 7767 778 6' 12' 18' 24' 30' 36 42' 122 0297 0471 0646 0820 0995 1169 1344 1518 1693 1868 2042 2217 2391 2566 2740 2915 3089 3264 3438 3 6l 3 3787 3962 4136 43" 4485 4660 483.' 5009 5184 5358 553; 570' 588: 6051 623 640 658 675 692 710 727 745 762 780 42 48' 140 3H 0489 0663 0838 1012 Il87 1361 1536 1710 1885 2059 2234 2409 2583 2758 2932 3107 3281 3456 3630 3805 3979 4154 4328 453 4677 4852 5027 5201 5376 555' 572 589* 6074 624: 642 659 677 694 712 729 747 764 54' 1' 2' 3' 4' 5' 015713 6 9 12 15 0332 I 3 6 9 12 15 0506 I 3 6 9 12 15 0681 I 3 6 9 12 15 0855 13 6 9 12 15 1030 I 3 6 9 12 15 1204! 3 6 9 12 15 1379 I 3 6 9 12 15 1553 3 6 1728 3 1902 3 9 12 15 6 9 12 15 6 9 12 15 2077 I 3 6 9 12 15 2251 I 3 6 9 12 15 2426! 3 6 9 12 15 2601 13 6 9 12 15 2775 | 3 6 9 12 15 2950 I 3 6 9 12 15 3124 3 6 9 12 15 3299 3 6 9 12 15 3473 3 6 9 12 15 3648 3 6 9 12 15 3822 3997 4171 4346 3 6 3 6 9 12 15 9 I2 15 3 6 9 12 15 3 6 9 12 15 4520 3 6 9 12 15 4695 4869 5044 5 2I 9 9 12 15 9 12 15 9 12 15 9 12 15 5393 \3 6 9 12 15 5568(3 6 9 12 15 5742 3 6 9 12 15 5917 3 6 9 12 15 6091 I 3 6 9 12 15 6266 I 3 6 9 12 15 6440 6615 6789 6964 3 6 3 6 3 I 3 6 9 12 15 9 12 15 9 12 15 9 12 15 7138 3 6 9 12 15 7313 7487 7662 7837 9 12 15 9 I2 15 9 12 15 9 I2 15 48' 54' 1' 2' 3' 4' 5' 155 RADIANS 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' 1' 2' 3' 4' 5' 45 7854 7871 7889 7906 7924 7941 *7959 7976 *7994 8011 3 6 9 12 15 46 8029 8046 8063 8081 8098 8116 8i33 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 12 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 9303 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 99 T 3 993i 3 6 9 12 15 57 9948 9966 9983 i-oooi 1-0018 1-0036 1-0053 1-0071 roo88 roio5 3 6 9 12 15 58 1-0123 0140 0158 oi75 0193 0210 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 IIOO 1118 II3S "53 3 6 9 12 '15 64 1-1170 1188 1205 1222 1240 1257 1275 1292 1310 1327 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 , 5 g 9 1606 1624 1641 l6 59 1676 3 6 9 12 i' 67 1-1694 1711 1729 1746 1764 I78l 1798 1816 1851 3 6 9 12 15 68 i -1868 1886 1903 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 3 6 9 12 15 71 1-2392 2409 2427 2444 2462 2479 2497 25H 2531 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 3H2 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 78 79 1*3439 1-3614 I-3788 3456 3631 3806 3474 3648 3823 3491 3666 3840 3509 3683 3858 3526 3701 3875 3544 37i8 3893 3736 3910 3579 3753 3928 3596 3771 3945 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 80 i*3963 3980 3998 4015 4032 4050 4067 4085 4102 4120 3 6 9 12 15 81 oo i*4i37 4155 4172 4190 4207 4224 4242 4259 4277 4294 3 6 9 12 15 82 83 84 1-4312 1-4486 1-4661 4329 4504 4678 4347 4521 4696 4364 4539 4713 4382 4556 4399 4573 4748 4416 4591 4765 4434 4608 4783 445 i 4626 4800 4469 4643 4818 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 85 i*4835 4853 4870 4888 4905 4923 4940 4957 4975 4992 3 6 9 12 15 86 87 88 89 1-5010 1-5184 1*5359 i*5533 5027 5202 5376 5045 5219 5394 5568 5062 5237 54H 5586 5080 5254 5429 5603 5097 5272 5446 5621 5289 5464 5638 5132 5307 548i 5656 5H9 5324 5499 5673 5167 534i 5691 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' 157 INDEX PAGE 15 .107 46,57 47, 57 81 in 112 133 21 ABERRATION, constant of Abraham, electronic theory of Absolute temperature scale . . ,, zero of temperature . . Absorption, coefficients, and 7 rays Absorption spectra . . Actinium emanation, diffusion of . Activities, equilibrium (minerals) . Air, composition of ... , (damp) ,, , (dry) density of ... 27, 28 , (saturated) water in . . 41 A loys, composition of 22, 29, 54, 56, 85, 93 a ays, e/m of ..... 108 , gaseous ionization by . . 109, 1 10 , number of . . . . 108, 114 , number of ions from . . 109, 1 14 , range and velocity of . . 108,114 108 13 , determination of, by barometer Ampere, determinations of ,, , international . Angles of contact .... , stopping powers Altitudes above sea-level Angstrom unit Antilogarithms ..... 140 Apothecaries' units . 9 Arcs, electric . . . 50, 113 Aries, first point of . . , . 3 Astronomy ... . I5~ I 7 Atmosphere, composition of . . 133 , RaEm. in . . 113 " Atmosphere," value of 5 Atomic constants . . . . .114 numbers ..... 2 ,, weights, international . . I, 2 BABINET'S altitude formula ... 37 Bar, value of ..... 5 Barometer, capillarity corrections . . 19 ,, , determination of altitudes by . 37 ,, , reduction to lat. 45 . . 20 ,, , reduction to o C. . . 20 ,, , reduction to sea-level . . 20 Baume's hydrometer .... 23 rays, absorption coefficients of . .115 , e/m of . 106 ,, , ionization by . . 109 ,, , number of . .114 ,, , velocity of . .106 Black body radiation . . 50 Board of Trade unit (electric energy) . 5 Bode's Law ...... 16 Boiling points, effect of pressure on . 53 , elements ... 51 ,, ,, , inorganic compounds 117-134 ,, , mixtures, maximum . 136 , ,, , minimum . . 136 Boiling points, 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 PAGE 126-131 43 53 10 . 18 10, 22 9 4 4 21 23 . 41 CADMIUM cell, determinations of . . 8 Calories, values of . . . 5, 58, 59 Candle, standard ..... 74 , energy from .... 74 ,, , visibility of . .74 Capacity, specific inductive ... 88 Capillarity corrections (mercury columns) 19 Carcel light unit ..... 74 Cathode rays, e/m of , velocity of Cauchy's dispersion formula . Cells, e.m.f.'s of . ,, , resistances of ... Centigrade and Fahrenheit degrees . Centimetre, definition of C.G.S. units . . Charge on the ion Clark cell, e.m.f. and temp. coef. of Clausius-Mossotti relation Coefficients of expansion, gases ,. , liquids . , solids Coercive force .... Coercivity ..... Coins (British), composition of ,, ,, , density of ,, ,, , dimensions of ,, ,, , weight of Combustion, heats of . Composition of air ... ,, of alloys . of minerals Compressibility . Condensation of vapours Conductivities, electrical 106 . 106 ! 8,92 . 92 10 3 3 105, 114 . 8 57 58 55 93 93 22 22 10 10 . . . 6 7 133 22, 29, 54, 56, 85, 93 . 134 29-31 . 104 . . .85 (solutions) 90 53 9,4 ,, , thermal . Conversion factors Cosines, natural . . . . .150 Critical data. . . . . 36, 64 ,, temperature (magnetization) . 94 Crookes dark space .... 101 Cryoscopic constant .... 70 Crystals, lattice constants of . . 99 INDEX 158 PAGE DARK space . . . . 101 Dates of isolation of elements . . 2 Day, definition of . . . . . 3 Declination, magnetic .... 95 Densities, acids ..... 25 air (dry) ... 27, 28 (damp) .... 23 alcohol (ethyl) ... 24 alkalies .... 26 aqueous solutions ... 27 calcium chloride ... 26 common substances . . 22 elements .... 22 gases . . . . 28, i o inorganic compounds . 117-125 Jena glasses .... 78 mercury .... 24 minerals . . . .134 organic compounds . 126-131 steam ..... 28 water ..... 24 water vapour. ... 28 Density determination corrections . . 23 Depression of freezing point (solutions) . 70 Depression of ice point of mercury thermo- meters 48 Dew point ...... 40 " Diapason Normal " . . .72 Dielectric constants .... 88 Diffusion of Ac, Ra, Th emanations . in of gases 37 ,, of ions (gaseous) . . .102 Dilution, heats of 67 Dimensions of units ... 7 Diopter, the 84 Discoverers of elements . . .2 Dispersions, optical . . . 75 Dispersive powers . . . 77, 78 Dissociation, ionic . .89 Distances of stars . . . . 17 Drachm, value of 9 c (exponential), value of ... 9 *, the ionic charge . . . 105,114 EAR 72 Ear, sensitiveness of - . . . . 72 Earth, density of, etc. . . . .15 , elements of .... 15 , size and shape of . . . 15 Ecliptic, obliquity of . . . 15 Efficiencies, luminous . . . .74 Einstein, relativity theory of . . . 107 Elasticities 29 Electrical conductivities ... 85 (solutions) . 90, 91 units, determinations of . . 8 Electric arcs . . . . .113 Electrochemical equivalents . . .131 Electrolysis, laws of . . .131 Electromotive forces of cells ... 92 Electronic e/m . . . . .106 e/m, change of, with velocity . 107 ,, , from Zeeman effect . 107 Electrons (negative), magnetic deflection of 107 ,, , velocity of .106 e/m of a rays ..... 108 ,, electrons .... 106, 107 ,, helium ..... 114 hydrogen ion . . . .114 Emergent-column, thermometer correction 48 Emission spectra ..... 80 Energy of full radiation .... 68 Equation of time . . . . 17 Equilibrium activities (minerals) . .112 Equivalents, electrochemical . . . 131 Expansion coefficients, sases ... 57 , liquids . . 58 ,. , solids ... 55 Exponential er* 137 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 . US 10 84 I3i 53 50 104 9 37 65 79 125 70 68 87 63 GALLON, definition of . . . 4, 9 7 rays, absorption coefficients of 1 1 5 ,, , ionization by .... 109 Gas constant . . . . 5 I: 4 Gaseous volumes, reduction of . .21 Gas thermometers, thermodynamic correc- tions to ..... 46, 47 Gas thermometry . . . 46, 47 Gauge, standard wire . . . 87 Gauss, the ... 7 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 Gravity, values of .... h, (Planck's constant) .... HARDNESS, of minerals , scale of (Mobs') . Half-periods, radioactive substances Heat conductivities .... Heat from radium . . . 108, RaEm rocks thorium . Heat, mechanical equivalent ot . . Heats, latent Heats of combustion .... dilution ,, formation ... 65 ,, neutralization .... Heats, specific, elements ,, , gases .... , mercury . . , . 10 78 41 9 3 135 20 II 68 134 J 34 54 114 1 08 112 108 <;8 67 59 61 59 159 INDEX PAGE Heats, specific, miscellaneous . 62 , water .... 59 Hefner light unit ..... 74 Heights above sea-level ... 13 Helium from radium . . . .114 Helmert's formula (gravity) . . 12, 14 Henry, the ...... 7 Hertzian waves, velocity of . . 73 Heusler alloys .... * 93 Humidity, relative Hydrometers .... Hygrometer, chemical . , wet and dry bulb Hygrometry .... Hyperbolic logs, conversion factor . Hysteresis, magnetic . . . 40 23 41 40 40 9 93 ICE-point, thermodynamic temperature of 47, 57 95 . 88 . 88 . 18 . 46 105, 114 Inclination, magnetic . Inductive capacity, specific . Inductivity .... Inertia, moments of International temperature scale Ionic charge dissociation . ,, mobilities (gaseous) I0 3 (gaseous) at high tempera- tures . (liquids) (solids) . lonization by a, , 7, and X rays . Ions gaseous (diffusion ol) . . ,, ,, 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 ..... Lattice-constants of crystals . 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 MAGNETIC constants, terrestrial . _ deflection of electrons . Magnetic induction . 92, 104 103 . 103 109, 1 10 . 102 ., 102 . 78 . 78 78 . 76 48,78 58 47 42 10 69 13,95 99 . 106 . 84 . 82 . 84 74 73 17 . 4, 10 . 142 . 138 13,95 . 107 74 95 . 107 93 FAC.B 84 9 136 88 Magnetic rotations of polarized light Maihematical constants Maximum boiling-point mixtures . Maxwell's relation Maxwell, the . . . . . 7 Mechanical equivalent of heat . . 58 Melting points, elements and alloys . 51 ,, , fats and waxes . . 53 ,, ,, , inorganic compounds . 117 ,, ,, , organic compounds . 126 Mercury thermometers, depression of zero of 48 , reduction to gas scale of . .48 ,, , stem exposure cor- rection . . 48 thermometry .... 48 Metal leaf, thickness of . . . .37 Metallic reflection of light ... 84 Metre, definition of . . 3 Metric units ..... 3 Meyer's viscosity equation . . 33, 34 Micron p. (and P.(JL) .... 9 Migration ratios ..... 89 Mil, value of 9 Millibar, value of . . . . 5, 2 9 Minerals, activities in . . . .112 ,, , composition of . . .134 ,, , density of . p , . . 134 ,, , hardness of . . . 134 ,, , radioactive . . .112, 134 ,, , scale of hardness (Mohs') . 134 Minim, value of . . . . .9 Minimum boiling-point mixtures . . 136 Miscellaneous data . . . 9, !O Mobilities of ions flames . . . 104 gaseous . . .103 gaseous at high tem- peratures . . 104 liquids . . 9 2 , i3 natural . . 1 13 solids . . .103 Mohs' scale of hardness . . 134 Molecules, free path of . . . .34 ,, , number of, in gas . 105, 106, 114 , size of 34 ,, , velocity of . . . 34 Moments of inertia . . . .18 Moon, elements of . . . J 5 Mossotti, Clausius-, relation ... 88 Motions of stars . . . . .17 Musical scales ..... 7 2 NAUTICAL mile 10 Negative electrons, e/m of . . 106,114 ,, ,, , mass of . . .114 ,, ,, , radius of . . .114 , velocity of . . 106 Neutralization, heats of . . . .66 Normal diapason ..... 7 2 OHM, determinations of . ,, , international .. Optical rotations, quartz . .liquids . Optical thermometry . . Organ pipes, end correction of ,, , wave lengths from Ounce, values of . . . 5 6 83 82 7 2 72 9 INDEX I6O PAGE PARALLAX, equatorial solar . . .15 , stars 17 Permeability ..... 93 Photometry ...... 74 Physical constants, inorganic compounds 117-125 ,, ,, , organic compounds 126-131 T, value of . . . . . .9 Planck's radiation formula . . 50, 68 universal constant (A) . . 68 Planets 16 Platinum thermometers, reduction to gas scale 46,49 Platinum thermometry . . . 46, 49 Poisson's ratio ..... 29 Polarized light, magnetic rotation of . 84 Polonium . . . . . 115, 116 Pound, definition of . . .4 Precession, constant of . . . 15 Pressure coefficient of expansion . . 57 ofPV . . . 10 Pressure, critical 36 Pressure, vapour. See Vapour pressure 43, in Pressure, effect of, on boiling points . 53 Psychrometry ..... 40 PV, pressure coefficient of . .10 Pyrometers ..... 49, 50, 68 RADIANS 9, 154 Radiation, full . 50, 68 Radiation thermometers ... 50 Radioactive decay constants . . 115 ,, minerals . . . . 112 ,, substances, constants of . 115 ,, ,, , properties of . 116 Radioactivity constants . . 114, 115 Radium emanation, decay of . . . 1 10 , density of . .10 , diffusion of . .Ill , equilibrium, volume of 1 10 , heat from . 1 10 , in atmosphere . 1 13 , molecular weight of . 1 1 1 ,, , vapour pressure of . 1 1 1 Radium, heat from . . . no , in rocks. . . 112 , helium from . . -.114 ,, , in rocks . . . . .112 ,, , in sea water .... 113 Ramsay and Young's vapour pressure law 42 Range of a rays ..... 108 Rankine, vapour pressure formula of . 42 Ratio of E.M. to E.S. unit . . 73 Rayleigh's radiation formula . . 68 Reciprocals . . . . 144 Recombination of ions (gaseous) . 102 Reflection of light (metallic) . . 84 Refractive indices, gases , Jena glasses 76, ,, , miscellaneous Relativity theory of Einstein . Resistance, specific temperature coefficient Resistances of cells v ,, of wires . Resistivities .... Rigidity, modulus of , temperature coefficient of Rocks, Ra, Th, in of 76 108 85 86 92 87 86 29 30 112 PAGE 109 82 Rontgen rays, ionization by . . ,, ,, , wave lengths of Rotations (magnetic) of polarized light (optical) SAFE currents for wires ... 87 Satellites of planets . . . .16 Saturated air, water in . . . .41 Scale of hardness (Mohs') . . . 134 Scales, musical ..... 72 Screws, pitch of, etc. . . . .18 Sea-water, radium in . . .113 Second, definition of . . .3 Secular magnetic changes ... 96 Sensitiveness of ear to pitch ... 72 Sikes' hydrometer .... 23 Silvering solution . . . 77 Sines, natural ..... 148 Size of drops . . . . . 39 Solar constant ..... 69 ,, parallax, equatorial . . 15 spectrum ..... 79 ,, system ..... 16 Solubilities aqueous, gases . . .132 ,, ,, , inorganic compounds 117-125 ,, , solids . ,, of liquids (mutual) Sound, velocity of ... Sparking potentials Specific heats, elements , gases, constant pressure ,, , constant volume ,, , ratio of . , mercury . , miscellaneous . , water Specific inductive capacity . . Specific resistances Specific volume .... Spectra, absorption ,, , emission (gases) (s 133 132 7 1 97 59 61 61 61 59 62 59 88 85 24 81 81 80 79 146 4 4, 9 3 9 79 4^ 17 87 , (solids) , X-ray .... Spectroscopy .... Squares ..... Standards, British , British and metric equivalents ,, , metric .... Standard conductivity solutions spectrum lines temperatures . times .... wire gauge Stars, distances of . . . 17 ,, , motions of . . . . 17 ,, , parallaxes of . . . 17 Stefan- Boltzmann law ... 50, 68 Steinmetz' hysteresis formula ... 94 Stem exposure corrections of mercury ther- mometers .... Stopping powers (a rays) Strengths, bursting (glass tubing) ,, , tensile (liquids) (solids) Sun, elements of . ,, , temperature of 108 4 1 41 3 , 16 69, 70 , --- r _-_ ----- -- . Q Surface tensions ..... 3 5 Susceptibility . . . . 93> 94 161 PAGE 33. 34 Sutherland's viscosity equation TANGENTS, natural . . . .IS 2 Temperature coefficient, conductivity (solns.) 90 dielectric constant 88 magnetization . 94 refractive index . 76 resistance . 86, 87 rigidity . . 30 surface tension . 38 tuning fork . 72 viscosity (gaseous) 34 Weston cell . 8 Young's modulus 30 Temperature of fire, by appearance . 50 of sun . . . 69, 7 Temperatures, critical .... 36 ,, , standard . . .46 Tenacities 30 Tensile strengths, liquids . . -41 ,, , solids ... 30 Tension, surface 38 Terrestrial magnetic constants . . 95 Thermal conductivities . . . .53 Thermochemistry ..... 65 Thermo-couples .... 49, 50 Thermodynamic correction to gas thermo- meters . . 46, 47 scale . . .46, 47, 57 ,, temperature of ice-point 47 Thermo-junctions .... 49, 50 Thermometry, gas .... 47 ,, , mercury .... 48 , optical .... 50 ,, , platinum . . 46, 49 , radiation . . 50, 68 , thermoelectric ... 49 Thickness of liquid films 39 ,, metal leaf . . .37 Thorium emanation, diffusion of . .Hi Thorium, heat from . . . . HO ,, , in rocks . . . 112 Time, equation of . . . .17 Times, standard 17 Tonne, value of ..... 9 Transport numbers .... 89 Transverse vibrations of rods ... 72 Trouton's Rule ..... 63 Troy units 9 Tubing (glass), bursting strengths of . 41 Tuning fork, temperature coefficient of . 72 Twaddell's hydrometer .... 23 UNITS , British , derived ..... , dimensions of . , electrical, determinations of , electrical, practical definitions of , light , metric , United States Universal constant (A) " V " ratio of electrical units Van der Waals* 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 . Vibrations of rods . * Viscosities gases . INDEX PACK P 63 42 43 44 44 42 43 in 42 104 108 73 73 ,3 . 72 (temperature coefficients of) 34 liquids .... 32 solids 33 solutions aqueous . . 33 vapours 33 Volt, international .... 6 Volume calibration . . .19 coefficient of expansion . . 57 critical . . . . .36 ,, elasticity ..... 29 Volumes (gaseous) reduction to o C. and 760 mm 21 WATER vapour, density of . ^ ,, ,, , in saturated air Watt, the . Waxes, melting points of Weighings, reduction to vacuo Weights and measures, British Weston cell, determinations of Wet and dry bulb hygrometer Whitworth screws Wien's displacement law . radiation formula 28 41 5,6 53 21 8 40 18 68 50,68 Wire gauge, standard .... 87 Wire resistances . . . .87 , temperature coefficient of 87 X RAYS, ionization by . , wave lengths of YARD, definition of . . . 4, 9 Years, various ..... 3 Young's modulus 29 , temperature coefficient of 30 Young's, Ramsay and, vapour pressure formula. , , . . . 42 ZEEMAN effect, e/m from 106, 107 THE END PRINTED IN GREAT BRITAIN BY WILLIAM CLOWES AND SONS, LIMITED, BECCLES. THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. MAR 14 1935 1AP 15 1935 M4ft 1y 1A 1 ** JS3i ? 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