fyxntll mmvmitg | THE GIFT OF .1D.A ..vA...D .W^vJtc pibatg Azsm^z. 2.5. .IX.j.U Cornell University Library QC 61.S66 1910 3 1924 024 565 990 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924024565990 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLUME 58. NUMBER 1 SMITHSONIAN PHYSICAL TABLES FIFTH REVISED EDITION PREPARED BY F. E. FOWLE AID, SMITHSONIAN ASTROPHYSICAL OBSERVATORY (PUBLICATION 1944) CITY OF WASHINGTON PUBUSHED BY THE SMITHSONIAN INSTITUTION 1910 ^4 A.?.b(>']?2. ADVERTISEMENT. In connection with the system of meteorological observations established by the Smithsonian Institution about 1850, a series of meteorological tables was compiled by Dr. Arnold Guyot, at the request of Secretary Henry, and the first edition was published in 1852. Though primarily designed for meteorological observers reporting to the Smithsonian Institution, the tables were so widely used by physicists that it seemed desirable to recast the work entirely. It was decided to publish three sets of tables, each representative of the latest knowledge in its field, and independent of one another, but forming a homogeneous series. The first of the new series. Meteorological Tables, was published in 1893, the second, Geographical Tables, in 1894, and the third. Physical Tables, in 1896. In 1909 yet another volume was added, so that the series now comprises : Smithsonian Meteorological Tables, Smithsonian Geographical Tables, Smithsonian Physical Tables, and Smithsonian Mathematical Tables. The fourteen years which have elapsed since the publication of the first edition of the Physical Tables, prepared by Professor Thomas Gray, have brought such changes in the material upon which the tables must be based that it became necessary to prepare this almost wholly new set of tables for the present edition. Charles D. Walcott, Secretary, Smithsonian Institution, June, 1910. PREFACE. The present Smithsonian Physical Tables are the outcome of a radical revision of the set of tables compiled by Professor Thomas Gray in 1896. Recent data and many new tables have been added for which the references to the sources have been made more complete ; and several mathematical tables have been added, — some of them especially computed for this work. The inclusion of these mathematical tables seems warranted by the demand for them. In order to pre- serve a uniform change of argument and to facilitate comparison, many of the numbers given in some tables have been obtained by interpolation in the data actually given in the papers quoted. Our gratitude is expressed for many suggestions and for help in the improve- ment of the present edition : to the U. S. Bureau of Standards for the revision of the electrical, magnetic, and metrological tables and other suggestions ; to the U. S. Coast and Geodetic Survey for the revision of the magnetic and geodetic tables ; to the U. S. Geological Survey for various data ; to Mr. Van Orstrand for several of the mathematical tables ; to Mr. Wead for the data on the musical scales ; to Mr. Sosman for the new physical-chemistry data ; to Messrs. Abbot, Becker, Lanza, Rosa, and Wood ; to the U. S. Bureau of Forestry and to others. We are also under obligation to the authors and publishers of Landolt-Bornstein- Meyerhoffer's Physikalisch-chemische Tabellen (1905) and B. O. Peirce's Mathe- matical Tables for the use of certain tables. It is hardly possible that any series of tables involving so much transcribing, interpolation, and calculation should be entirely free from errors, and the Smith- sonian Institution will be grateful, not only for notice of whatever errors may be found, but also for suggestions as to other changes which may seem advisable for later editions. F. E. FowLE. ASTROPHYSICAL OBSERVATORY OF THE Smithsonian Institution, June, 1910 TABLE OF CONTENTS Introduction on units of measurement and conversion factors Units of measurement : general discussion .... Dimension formulae for dynamic units " " heat units of electric and magnetic units : general discussion formulae in electrostatic system .... " " electromagnetic system Practical units of electricity, legalization of . PAGE XV XV xvii xxiii XXV xxvi xxix xxxiii TABLB I. 4- S- 6. 7- 8. 9- lO. II. 12. 12a. 14. IS- Formulae for conversion factors : (a) Fundamental units ... 2 (l>) Derived units ... 2 I. Geometric and dynamic units 2 II. Heat units .... 3 III. Magnetic and electric units 3 Tables for converting U. S. weights and measures : (i) Customary to metric S (2) Metric to customary 6 Equivalents of metric and British imperial weights and measures : (i) Metric to imperial 7 (2) Multiples, metric to imperial 8 (3) Imperial to metric 9 (4) Multiples, imperial to metric 10 Volume of a glass vessel from weight of its volume of water or mercury 1 1 Elementary differential coefficients and integrals . . . .12 Reciprocals, squares, cubes and square roots of natural numbers . 13 Logarithms, 1000-2000 ......... 22 Logarithms 24 Antilogarithms 26 Antilogarithms, .9000-1.0000 28 Circular (trigonometric) functions, argument (° ,' .) . . . -3° «< " " argument (radians) . . -35 Factorials, n!, n^ I to 100 38 Values of ^~^ (hyperbolic sines), for values of x from o to 5 -39 2 Logarithms of (hyperbolic sines), for values of x from o to 5 . 40 Values of -''^ (hyperbolic cosines), for values of x from o to 5 .41 VI CONTENTS. l6. 17- i8. 19. 20. 21. 22. 23- 24. 25- 26. 27. 28. 29. 3°- 31- 32. 33- 34- 35- 36. 37- 38. 39- 40. 41. 42. 43- 44. 45- 46. 47- Logarithms of ''" (hyperbolic cosines) for values of x from o to 5 42 Values of e^ and L"-*T-iK*, and the conversion factor m^t-^r-^kK 3. Electric Force at a Point, or Intensity of Electric Field. — This is measured by the ratio of the magnitude of the force on a quantity of electricity at a point to the magnitude of the quantity of electricity. The dimensional formula is therefore the ratio of the formulae for force and electric quantity, or ^^"^^ = M*L-»T-iK-* M4L»T-'Ki which gives the conversion factor n^l-^1r^k~^. 4. Electric Potential and Electromotive Force. — Change of potential is proportional to the work done per unit of electricity in producing the change. The dimensional formula is therefore the ratio of the formulae for work and elec- tric quantity, or ML'T-" M*L*T-iK-* M*L'T-^K» ^ ^ ' which gives the conversion factor m^fit~^k~^. 5. Capacity of a Conductor. — The capacity of an insulated conductor is proportional to the ratio of the numbers representing the quantity of electricity in a charge and the potential of the charge. The dimensional formula is thus the ratio of the two formulae for electric quantity and potential, or M*L'T-iK» _ T XT M*L*T-^K-^ which gives Ik for conversion factor. When K is taken as unity, as in the ordinary units, the capacity of an insulated conductor is simply a length. 6. Specific Inductive Capacity. — This is the ratio of the inductive capac- ity of the substance to that of a standard substance, and hence the dimensional formula is K/K or i.* 7. Electric Current. — Current is quantity flowing past a point per unit of time. The dimensional formula is thus the ratio of the formula for electric quan- tity and for time, or. MipT- ^K* T and the conversion factor ni'l^tr^k^. ■ = MiVT-'K}, * According to the ordinary definition referred to air as standard medium, the specific inductive capacity of a substance is K, or is identical in dimensions with what is here talcen as inductive ca- pacity. Hence in that case the conversion factor must be taken as i on the electrostatic and as l-^fi on the electromagnetic system. XXviii INTRODUCTION, 8. Conductivity, or Specific * Conductance. — This, like the corresponding term for heat, is quantity per unit area per unit potential gradient per unit of time. The dimensional formula is therefore M^L'T-^K* _ rp-iT^ Qj electric quantity . M*L*T-^K-*™ ' area X potential gradient X time ^' L The conversion factor is f'^k. 9. Specific * Resistance. — This is the reciprocal of conductivity as above defined, and hence the dimensional formula and conversion factor are respec- tively TK-i and tk-^ 10. Conductance. — The conductance of any part of an electric circuit, not containing a source of electromotive force, is the ratio of the numbers represent- ing the current flowing through it and the difference of potential between its ends. The dimensional formula is thus the ratio of the formulae for current and poten- tial, or M»LiT-^K-i""^ ' from which we get the conversion factor If-^k. 1 1 . Resistance. — This is the reciprocal of conductance, and therefore the dimensional formula and the conversion factor are respectively I/""'TK~' and EXAMPLES OF CONVERSION IN ELECTROSTATIC UNITS. (a) I ind the factor for converting quantity of electricity expressed in foot grain second units to the same expressed in c. g. s. units. By (i) the formula is w'/'^"'^*, in which in this case m z=. 0.0648, /= 30.48, / = I, and k= 1; .'. the factor is 0.0648' X 30-48' = 4.2836. (6) Find the factor required to convert electric potential from millimetre milli- gramme second units to c. g. s. units. By (4) the formula is toV*/~'/5~*, and in this case m = o.ooi, /= 0.1, /= i, and >&= I ; .•. the factor = o.ooi* X o.i*::^ o.oi. (/) Find the factor required to convert from foot grain second and specific in- ductive capacity 6 units to c. g. s. units. By (5) the formula is li, and in this case /= 30.48 and k^:6 ; .'. the factor = 30.48 X 6=182.88. * The term "specific," as used here and in 9, refers conductance and resistance to that between the ends of a bar of unit section and unit length, and hence is different from the same term in specific heat, specific inductivity, capacity, etc., which refer to a standard substance. INTRODUCTION. xxix ELECTROMAGNETIC UNITS. As stated above, these units bear the same relation to unit quantity of magne- tism that the electric units do to quantity of electricity. Thus, when inductive capacity is suppressed, the dimensional formula for magnetic quantity on this sys- tem is the same as that for electric quantity on the electrostatic system. All quan- tities in this system which only differ from corresponding quantities defined above by the substitution of magnetic for electric quantity may have their dimensional formulae derived from those of the corresponding quantity by substituting P forK. 1. Magnetic Pole, or Quantity of Magnetism. — Two unit quantities of magnetism concentrated at points unit distance apart repel each other with unit force. The dimensional formula is thus the same as for [force X length" X in- ductive capacity] or M*L'T~"P*, and the conversion factor is w*/'^*/*. 2. Density of Surface Distribution of Magnetism. — This is measured by quantity of magnetism per unit area, and the dimension formula is therefore the ratio of the expressions for magnetic quantity and for area, or M*L"^T~'P*, which gives the conversion factor n^t^f^p^. 3. Magnetic Force at a Point, or Intensity of Magnetic Field. — The number for this is the ratio of the numbers representing the magnitudes of the force on a magnetic pole placed at the point and the magnitude of the magnetic pole. The dimensional formula is therefore the ratio of the expressions for force and magnetic quantity, or ^^'^'' = M^L-il^^P-* M*L9T-ipi ^' and the conversion factor «*/~*/~^~*. 4. Magnetic Potential. — The magnetic potential at a point is measured by the work which is required to bring unit quantity of positive magnetism from zero potential to the point. The dimensional formula is thus the ratio of the formula for work and magnetic quantity, or M*L«T-»P»~ ' which gives the conversion factor m^^t~^jri. 5. Magnetic Moment. — This is the product of the numbers for pole strength and length of a magnet. The dimensional formula is therefore the pro- duct of the formulas for magnetic quantity and length, or M*L'T~^P*, and the con- version factor m^l^f^p*. 6. Intensity of Magnetization. — The intensity of magnetization of any por- tion of a magnetized body is the ratio of the numbers representing the magni- XXX INTRODUCTION. tude of the magnetic moment of that portion and its volume. The dimensional formula is therefore the ratio of the formulae for magnetic moment and volume, or L' The conversion factor is therefore m^t^i~^JiK 7. Magnetic Permeability,* or Specific Magnetic Inductive Capacity. — This is the analogue in magnetism to specific inductive capacity in electricity. It is the ratio of the magnetic induction in the substance to the magnetic induc- tion in the field which produces the magnetization, and therefore its dimensional formula and conversion factor are unity. 8. Magnetic Susceptibility. — This is the ratio of the numbers which repre- sent the values of the intensity of magnetization produced and the intensity of the magnetic field producing it. The dimensional formula is therefore the ratio of the formulae for intensity of magnetization and magnetic field or M'L-*T-'pi M*L-*T-ip^ or P. The conversion factor is therefore /, and both the dimensional formula and con- version factor are unity in the ordinary system. 9. Current Strength. — A current of strength c flowing round a circle of radius r produces a magnetic field at the centre of intensity 2Trc/r. The dimen- sional formula is therefore the product of the formulae for magnetic field intensity and length, or M*L*T~^P~*, which gives the conversion factor mSH~^p-^. 10. Current Density, or Strength of Current at a Point. — This is the ratio of the numbers for current strength and area. The dimensional formula and the conversion factor are therefore M'L-'T^^P"* and m^l~^t~^p-^. 11. Quantity of Electricity. —This is the product of the numbers for cur- rent and time. The dimensional formula is therefore M*L*T~^P^ X T= M*L*P~* and the conversion factor m^fip'^. 12. Electric Potential, or Electromotive Force. — As in the electrostatic system, this is the ratio of the numbers for work and quantity of electricity. The dimensional formula is therefore r;^,!, , = MiL»T-'Pi, and the conversion factor m^'l^f^p^. • Permeability, as ordinarily taken with the standard medium as unity, has the same dimension formula and conversion factor as that which is here taken as magnetic inductive capacity. Hence for ordinary transformations the conversion factor should be taken as i in the electromagnetic and i'^fi in the electrostatic systems. INTRODUCTION. XXxi 13. Electrostatic Capacity. — This is the ratio of the numbers for quantity of electricity and difference of potential. The dimensional formula is therefore MiL»T-T* ' and the conversion factor /"V^-i. 14. Resistance of a Conductor. — The resistance of a conductor or elec- trode is the ratio of the numbers for difference of potential between its ends and the constant current it is capable of producing. The dimensional formula is therefore the ratio of those for potential and current or MiL'T-'Pt _ ^ MJL*T-ip-*~ The conversion factor thus becomes /i-'^f, and in the ordinary system resistance has the same conversion factor as velocity. 15. Conductance. — This is the reciprocal of resistance, and hence the dimen- sional formula and conversion factor are respectively L~'TP~i and l~^f/-\ 16. Conductivity, or Specific Conductance. — This is quantity of electric- ity transmitted per unit of area per unit of potential gradient per unit of time. The dimensional formula is therefore derived from those of the quantities men- tioned as follows : — M*Lip-» ^ L ^ = L-'TP-i. ,-1 The conversion factor is therefore Z^"/^' 17. Specific Resistance. — This is the reciprocal of conductivity as defined in 16, and hence the dimensional formula and conversion factor are respectively L'T-^P and Pr^J>. 18. Coefficient of Self-induction, or Inductance, or Electro-kinetic In- ertia. — These are for any circuit the electromotive force produced in it by unit rate of variation of the current through it. The dimensional formula is therefore the product of the formulae for electromotive force and time divided by that for current or MJLST-Jp! M5L»T-^P-i X T = LP. The conversion factor is therefore /p, and in the ordinary system is the same as that for length. 19. Coefficient of Mutaal Induction. — The mutual induction of two cir- cuits is the electromotive force produced in one per unit rate of variation of the current in the other. The dimensional formula and the conversion factor are therefore the same as those for self-induction. XXXil INTRODUCTION. 20. Electro-kinetic Momentum. — The number for this is the product of the numbers for current and for electro-kinetic inertia. The dimensional formula is therefore the product of the formulae for these quantities, or M*L'T~*P~* X LP = M*L'T-ip', and the conversion factor is m^flf^pK 21. Electromotive Force at a Point. — The number for this quantity is the ratio of the numbers for electric potential or electromotive force as given in 12, and for length. The dimensional formula is therefore M*L*T-'P*, and the conversion factor m^N~^p^, 22. Vector Potential. — This is time integral of electromotive force at a point, or the electro-kinetic momentum at a point. The dimensional formula may therefore be derived from 21 by multiplying by T, or from 20 by dividing by L. It is therefore M*L*T~^P*, and the conversion factor «?V*/~'/*. 23. Thermoelectric Height. — This is measured by the ratio of the num- bers for electromotive force and for temperature. The dimensional formula is therefore the ratio of the formulae for these two quantities, or M*L'T~^P'©~*, and the conversion factor m''^t~^p'd~^. 24. Specific Heat of Electricity. — This quantity is measured in the same way as 23, and hence has the same formulae. 25. Coefficient of Peltier Effect. — This is measured by the ratio of the numbers for quantity of heat and for quantity of electricity. The dimensional formula is therefore M*L4P-* ' and the conversion factor m^t^j'^O. EXAMPLES OF CONVERSION IN ELECTROMAGNETIC UNITS. (a) Find the factor required to convert intensity of magnetic field from foot grain minute units to c. g. s. units. By (3) the formula is w*^/-'/-*, and in this case m = 0.0648, /= 30.48, / = 60, and/ = I ; .-. the factors = 0.0648* X 30.48"* X 60-^= 0.00076847. Similarly to convert from foot grain second units to c. g. s. units the factor is 0.0648' X 30.48"- = 0.046 108. (i) How many c. g. s. units of magnetic moment make one foot grain second unit of the same quantity ? By (5) the formula is /«*/♦/-'/*, and the values for this problem are m = 0.0648, /= 30.48, /= I, and/ = 1 ; .-. the number = 0.0648* X 30.48'= 1305.6. (/-», and the values of these quantities are here m = 10", /= 10 °, /= I, and/ = I ; .-. the factor = loH x 10"!= 10. («) Find the factor required to convert resistance expressed in c. g. s. units into the same expressed in earth-quadrant ro-" grammes and second units. By (14) the formula is //"i/, and for this case /= lo"', /= i, and / = i ; .•. the factor = io""°. (/) Find the factor required to convert electromotive force from earth-quadrant io~" gramme and second units to c. g. s. units. By (12) the formula is wV'/-"/*, and for this case m = lo"", /= io«, /= i, and/ = I ; .•. the factor = 10'. PRACTICAL UNITS. In practical electrical measurements the units adopted are either multiples or submultiples of the units founded on the centimetre, the gramme, and the second as fundamental units, and air is taken as the standard medium, for which K and P are assumed unity. The following, quoted from the report to the Honorable the Secretary of State, under date of November 6th, 1893, by the delegates repre- senting the United States, gives the ordinary units with their names and values as defined by the International Congress at Chicago in 1893 : — " Resolved, That the several governments represented by the delegates of this International Congress of Electricians be, and they are hereby, recommended to formally adopt as legal units of electrical measure the following : As a unit of re- sistance, the international ohm, which is based upon the ohm equal to 10' units of resistance of the C. G. S. system of electro-magnetic units, and is represented by the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice 14.4521 grammes in mass, of a constant cross- sectional area and of the length of 106.3 centimetres. " As a unit of current, the international ampire, which is one tenth of the unit of current of the C. G. S. system of electro-magnetic units, and which is represented sufficiently well for practical use by the unvarying current which, when passed through a solution of nitrate of silver in water, and in accordance with accom^ panying specifications,* deposits silver at the rate of 0.001118 of a gramme per second. * " In the following specification the term ' silver voltameter ' means the arrangement of appara- tus by means of which an electric current is passed through a solution of nitrate of silver in water. The silver voltameter measures the total electrical quantity which has passed during the time of the experiment, and by noting this time the time average of the current, or, if the current has been kept constant, the current itself can be deduced. " In employing the silver voltameter to measure currents of about one ampere, the following arrangements should be adopted : — XXxiv INTRODUCTION. " As a unit of electromotive force, the international volt, which is the electro- motive force that, steadily applied to a conductor whose resistance is one interna- tional ohm, will produce a current of one international ampbre, and which is rep- resented sufficiently well for practical use by \%%% of the electromotive force between the poles or electrodes of the voltaic cell known as Clark's cell, at a tem- perature of is" C, and prepared in the manner described in the accompanying ^ speciiication.* " As a unit of quantity, the international coulomb, which is the quantity of elec- tricity transferred by a current of one international ampfere in one second. "As a unit of capacity, the international farad, which is the capacity of a con- denser charged to a potential of one international volt by one international cou- lomb of electricity.t " As a unit of work, the joule, which is equal to lo' units of work in the c. g. s, system, and which is represented sufficiently well for practical use by the energy expended in one second by an international ampfere in an international ohm. " As a unit of power, the watt, which is equal to lo' units of power in the c. g. s. system, and which is represented sufficiently well for practical use by the work done at the rate of one joule per second. " As the unit of induction, the henry, which is the induction in a circuit when the electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampbre per second. " The Chamber also voted that it was not wise to adopt or recommend a stand- ard of light at the present time." By an Act of Congress approved July 12th, 1894, the units recommended by the Chicago Congress were adopted in this country with only some unimportant verbal changes in the definitions. By an Order in Council of date August 23d, 1894, the British Board of Trade adopted the ohm, the ampere, and the volt, substantially as recommended by the Chicago Congress. The other units were not legalized in Great Britain. They are, however, in general use in that country and all over the world. " The kathode on which the silver is to be deposited should take the form of a platinum bowl not less than 10 centimetres in diameter and from 4 to 5 centimetres in depth. " The anode should be a plate of pure silver some 30 square centimetres in area and 2 or 3 millimetres in thickness. " This is supported horizontally in the liquid near the top of the solution by a platinum wire passed through holes in the plate at opposite corners. To prevent the disintegrated silver which is formed on the anode from falling on to the kathode, the anode should be wrapped round with pure filter paper, secured at the back with sealing wax. "The liquid should consist of a neutral solution of pure silver nitrate, containing about 15 parts by weight of the nitrate to 85 parts of water. " The resistance of the voltameter changes somewhat as the current passes. To prevent these changes having too great an effect on the current, some resistance besides that of the voltameter should be inserted in the circuit. The total metallic resistance of the circuit should not be less than 10 ohms." * A committee, consisting of Messrs. Helmholtz, Ayrton, and Carhart, was appointed to pre- pare specifications for the Clark's cell, but no report was made, on account of Helmholtz's death. t The one millionth part of the farad is more commonly used in practical measurements, and is called the microfarad. PHYSICAL TABLES Table 1 . FUNDAMENTAL AND DERIVED UNITS. To change a quantity from one system of units to another ; substitute in the correspond- ing conversion factor from the following table the ratio of the magnitudes of the old units to the new and multiply the old quantity by the resulting number. For example : to reduce velocity in miles per hour to feet per second, the conversion factor is It-^; l=t,zio/l, /=36oo/i, therefore the factor=528o/36oo=i.467. {a) Fundamental Units. Name of Unit. Symbol. Conversion Factor. Length. Mass. Time. Temperature. Electric Inductive Capacity. Magnetic Inductive Capacity. L M T K P / m t e k p {b) Derived Units. I. Geometric and Dynamic Units. Name of Unit. Conversion Factor. /« /» I I /-I /-I /-» /-» /-» //-I It-^ ml-" ml'' It-'' /»/-« mlt-"- ml^t-^ mlt-' mPt-'' ml-'-t-* ml-'-t-^ ml'^t-^ m /-> /-» ml^'t-" Area. Volume. Angle. Solid Angle. Curvature. Tortuosity. Specific curvature of a surface. Angular velocity. Angular acceleration. Linear velocity. Linear acceleration. Density. Moment of inertia. Intensity of attraction, or "force at a point." Absolute force of a centre of attraction, or " strength ) of a centre." r Momentum. Moment of momentum, or angular momentum. Force. Moment of a couple, or torque. Intensity of stress. Modulus of elasticity. Work and energy. Resilience. Power or activity. Smithsonian Tables. Table 1 . FUNDAMENTAL AND DERIVED UNITS. IL Heat Units. Name of Unit. Quantity of heat (thermal units). " " (thermometric units). " " (dynamical units). CoeflScient of thermal expansion. Conductivity (thermal units). " fthermometric units), or difEusivity. " (dynamical units). Thermal capacity. Latent heat (thermal units). " " (dynamical units). Joule's equivalent. Entropy (heat measured in thermal units). " ( " " " dynamical units). Conversion Factor. mB ml^t-^ m /-I t-'^ l^t~^ m I /-» e-i Pt-^6 m mi^t-^e III. Magnetic and Electric Units. Name of Unit, Conversion factor for electrostatic system. Conversion factor for electromag- netic system. Magnetic pole, or quantity of mag- netism. Density of surface distribution of magnetism. Intensity of magnetic field. Magnetic potential. Magnetic moment. Intensity of magnetisation. Magnetic permeability. Magnetic susceptibility and mag- netic inductive capacity. Quantity of electricity. Electric surface density and electric ) mi /' /5-» mi /' rV* } displacement. Intensity of electric field. Electric potential and e. m. f. Capacity of a condenser. Inductive capacity. Specific inductive capacity. Electric current. mi l-^ k-^ mi f-i t-^pi milit-^ki mi /> /-" ki mi /' k-* mi /J i-i mi l^ t-'^p-i mifir'-p-^ mi /5 rv* mirit-'pi I i-^ t" k-^ / mi /' t-"- ki milip-i mi /-* r' i» mi t-ip-i mi f-i rl k-i mi /i t-"- k-i Ik k miflt-^ki mi li t^pi mi /i /-V l-^ t'p-^ mi li r^p-i Smithsonian Tables. Table 1. FUNDAMENTAL AND DERIVED UNITS. III. Magnetic and Electric Units. Conversion factor Conversion factor Name of Unit. for electrostatic for electromag- system. netic system. Conductivity. r»/J i-" //-» Specific resistance. tk-^ l^t-^p Conductance. llr'k l--" //-I Resistance. t-uk-^ It-^P Coefficient of self induction and) coefficient of mutual induction. ) /-» /» /J-» ip Electrokinetic momentum. m^ I* Hr-i mi /3 rV* Electromotive force at a point. mi r» r^ /J-» mi /i t-^pi Vector potential. mif-ik-i mi /» tr-^pi Thermoelectric height and specific') heat of electricity. J Coefficient of Peltier effect. mi /i r» k-^ r-» mi /' rV* ^' mir''tJi-i$ mi i-ipi Smithsonian Tables. Table 2. TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES.* (1) CUSTOMARY TO METRIC. LINEAR. 1 CAPACITY. Inchei to milltnietres. Feet to metres. Yards to metres. Miles to kilometres. Fluid drams to millilitres or cubic centimetres. Fluid ounces to millilitres. Liquid quarts to litres. Gallons to litre.. I 2 3 4 s 6 9 25.4001 50.8001 76.2002 101.6002 127.0003 152.4003 177.8004 203.2004 228.6005 0.304801 0.609601 0.914402 1.219202 1.524003 1.828804 2.133604 2.438405 2.743205 O.Q14402 1.828804 2.743205 3.657607 4.572009 5.486411 6.400813 7-315215 8.229616 1-60935 3.21869 4.82804 6.43739 8.04674 9.65608 11. 26543 12.87478 14.48412 I 2 3 4 5 6 I 9 3-70 7-39 11.09 22.18 25.88 29-57 33-27 29.57 88.72 118.29 147-87 177-44 207.02 'A?6 0.94636 1.89272 2.83908 3-78543 4-73179 5.67815 6.62451 7-57087 8.51723 3-78543 7-57087 11.35630 15.14174 18.92717 22.71261 26.49804 30.28348 34.06891 SQUARE. WEIGHT. Square inches to square cen- timetres. Square feet to square decimetres. Square yards to square metres. Acres to hectares. Grains to milli- grammes. Avoirdu- pois ounces to grammes. Avoirdu- pois pounds to kilo- grammes. Troy ounces to grammes. I 2 3 4 ■5 6 7 8 9 6.452 12.903 19-355 25-807 32-258 38.710 45.161 51.613 58.065 18.581 27.871 37.161 46.452 55-742 65.032 74.323 83.613 0.836 1.672 2.508 3-345 4.181 S-OI7 7.525 0.4047 0.8094 I.2141 I.6187 2.0234 2.4281 2.8328 3-2375 3.6422 1 2 3 4 5 6 7 8 9 64.7989 129.5978 194.3968 259-1957 323-9946 388-7935 453-5924 518.3913 583-1903 28.3495 56.6991 S5.0486 113.3981 141.7476 170.0972 198.4467 226.7962 255.1457 0.45359 0.90718 1.36078 1. 8 1437 2.26796 2.72155 3-17515 3.62874 4.08233 31.10348 62.20696 93.31044 124.41392 155.51740 186.62088 217.72437 248.82785 279-93133 CUBIC. 1 Gunter's chain = 20.1168 I sq. statute mile = 259.000 1 fathom = 1.829 metres. hectares. metres. metres. metre. grammes. ogramme. I 2 3 4 S 6 7 8 9 Cubic inches to cubic cen- timetres. Cubic feet to cubic metres. Cubic yards^ to cubic metres. Bushels to hectolitres. 16.387 32-774 49.161 65-549 81.936 98-323 114-710 147.484 0.02832 0.05663 0.08495 O.II327 0.14159 0.16990 0.19822 0.22654 0.25485 0.765 1.529 2.294 3-058 3-823 4-587 6.1 16 6.881 0.35239 0.70479 1. 057 18 1.40957 1.76196 2.11436 2.46675 2.81914 3-I7154 IS 1 nautical r 1 foot 1 avoir, poi 432-35639 i nile = iS ind = i prains = iS3-25 0.304801 153-5924277 1. 000 kil According to an executive order dated April 15, 1893, the United Sutes yard is defined as 3600/3937 metre, and "" 'r^:^X'^n^^rL'i:l:i!?£\t^^n%u.tc,r..ry weight is the Troy pound of the Mn. I. is of bn>ss of un- known density, and therefore not suitable for a sUndard of mass. It was derived from the British standard Troy pound of 1758 by direct comparison. The British eallon = 4.5459*3 ' litres. The l^nSh^f th''e°'n^t?ral m?le g?ven above and adopted by the U. S. Coast and Geodetic Survey many years ago, is defined as that of a minute of arc of a great circle of a sphere whose surface equals that of the earth (Clarke's Sp£e- roid of 1866). • Quoted from sheets issued by the United States Bureau of Standard!. Smithsonian Tables. Table 2. TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES. (2) METRIC TO CUSTOMARY. ^ ^^^ _^^ LINEAR. CAPACITY. Metres to inches. Metres to feet. Metres to yards. Kilometres to miles. MiUilitres or cubic centi- metres to fluid drams. Centi- litres to fluid ounces. Litres to quarts. Deca- litres to gallons. Hecto- litres to bushels. I 2 3 4 5 6 9 39-3700 78.7400 118.1100 157.4800 196.8500 236.2200 275.5900 314.9600 3543300 3.28083 6.56167 9.84250 13-12333 16.40417 19.68500 22.96583 26.24667 29-52750 1. 09361 1 2.187222 3-280833 4-374444 5.468056 6.561667 7.655278 8.748889 9.842500 0.62137 1.24274 1.86411 2.48548 3.10685 3.72822 4-34959 4.97096 5-59233 I 2 3 4 5 6 7 8 9 0.27 0-54 0.81 1.08 1-35 1.62 1.89 2.16 2.43 0.676 1. 01 4 1. 691 2.029 2.367 2.70s 3-043 1.0567 2.1134 3-1700 4.2267 5-2834 6.3401 7.3968 8.4535 9.5101 2.6417 5-2834 iS:I^ 13.2085 15.8502 18.4919 21.1336 23-7753 2.8377 5-6755 8.5132 14.1887 17.0265 19.8642 22.7019 25-5397 SQUARE. WEIGHT. I 2 3 4 5 6 I 9 Scfuare centimetres to square inches. Square metres to square feet. Square metres to square yards. Hectares to acres. I 2 3 4 5 6 7 8 9 Milli- grammes to grains. Kilo- grammes to grains. Hecto. grammes to ounces avoirdupois. Kilo- grammes to pounds avoirdupois. 0.1550 0.3100 0.4650 0.6200 0.7750 0.9300 1.0850 1.2400 1-3950 10.764 21.528 32.292 43-055 53-819 64.583 75-347 86.111 96.875 1.196 2-392 4.784 5.980 7-176 8.372 9.568 10.764 2.471 4.942 7.413 9.884 12.355 14.826 19.768 22.239 0.01543 0.03086 0.04630 0.06173 0.07716 0.09259 0.10803 0.12346 0.13889 15432-36 30864.71 46297.07 61729.43 77161.78 92594.14 108026.49 123458.85 138891.21 3-5274 7-0548 10.5822 14.1096 17.6370 21.1644 24.6918 28.2192 31.7466 2.20462 4.40924 6.61387 8.81849 11.02311 13-22773 15-43236 17.63698 19.84160 CUBIC. WEIGHT. Cubic centimetres to cubic inches. Cubic decimetres to cubic inches. Cubic metres to cubic feet. Cubic metres to cubic yards. Quintals to pounds av. Milliers or onnes to pounds av. Kilogrammes to ounces Troy. I 2 3 4 S 6 7 8 9 0.0610 0.1220 0.1831 0.2441 0.3051 0.3661 0.4272 0.4882 0.5492 61.023 122.047 183.070 244.094 305-117 366.140 427.164 488.187 549.210 35-314 70.629 105.943 141-258 176.572 211.887 247.201 282.516 317.830 2;6i6 3-924 5232 6.540 7.848 9.156 10.464 11.771 I 2 3 4 5 6 9 220.46 440.92 661.39 881.85 1102.31 1322.77 1543-24 1763.70 1984.16 2204.6 4409.2 6613.9 8818.5 IIO23.I 13227.7 15432.4 17637.0 19841.6 32.1507 64.3015 96.4522 128.6030 160.7537 192.9045 225.0552 257.2059 289.3567 By the concurrent action of the principal governments of the world an International Bureau of Weights and Measures has been established near Pans. Under the direction of the International Committee, two ingots were cast of pure platinum-iridium m the proporlion of 9 parts of the former to i of the latter meial. From one of these a certain number of kilogrammes were prepared, from the other a definite number of metre bars. These standards ot weight and length were intercompared, without preference, and ceruin ones were selected as International proto- Upe standards. Ihe others were distributed by lot, in September, 1889, to the different governments, and are called J^ational prototvpe standards. Those apportioned to the United States were received in 1890, and are kept at the Bureau of Standards in Washington, D. C. v-. »- i The metric system was legalized in the United States in 1866. ,. . '^''^ International Standard Metre is derived from the Mitre des Archives, and its length is defined by the distance between two hnes at 0° Centigrade, on a platinum-iridium bar deposited at the International Bureau of Weights and Measures. The International Standard Kilogramme is a mass of platinum-iridium deposited at the same place, and its weieht in vacuo is the same as that of the Kilogramme des Archives. The litre is equal to a cubic decimetre, and it is measured by the quantity of distilled water which, at its maxi- mum density, will counterpoise the standard kilogramme in a vacuum, the volume of such a quantity of water beini as nearly as has been ascertained, equal to a cubic decimetre. "^'ufit Smithsonian Tables. Table 3. EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS AND MEASURES.* (1) METRIC TO IMPERIAL. LINEAR MEASURE. I millimetre (mm.) ) (.001 m.) ) I centimetre (.oi m.) I decimetre (.i m.) I METRE (m.) , I dekametre (10 m.) I Iiectometre | (lOO m.) I kilometre (i,ooo m.) j I myriametre (10,000 m.) I micron . , --! = O-03937 in- = 0.39370 " 3.93701 " 39.370113 " 3.280843 ft. 1. 09361425 yds. = 10.93614 " = 109.361425 " = 0.62137 mile. = 6.21372 miles. = o.ooi mm. SQUARE MEASURE. I sq. centimetre . . = I sq. decimetre I __ (100 sq. centm.) | I sq, metre or centi- 1 _ are (loosq. dcm.) J I ARE (100 sq. m.) = I hectare (100 ares I _ or 10,000 sq. m.) ( 0.1550 sq. m. 15.500 sq. in. ) 10.7639 sq. ft. ( 1.1960 Sq. yds. 1 19.60 -sq. yds. 2.47 1 1 acres. CUBIC MEASURE. 0.0610 cub. in. cub. centimetre (c.c.) (1,000 cubic millimetres) cub. decimetre (c.d.) (1,000 cubic centimetres) , CUB. METRE | _ , ^j 3,48 Cub. ft. Il^'ld.) r ■ ' '•3°79S4Cub.yds. bic [ = c[=6i .024 MEASURE OF CAPACITY. I millilitre (ml.) (.001 ) litre) j I centilitre (.01 litre) 1 decilitre (.1 litre) . I LITRE (1,000 cub. centimetres or i cub. decimetre) I dekalitre (to litres) 1 hectolitre (100 " ) 1 kilolitre (1,000 " ) = 0.0610 cub. in. 0.61024 " « 0.070 gill. 0.176 pint. 1.75980 pints. 2.200 gallons. 2.75 bushels. 3.437 quarters. =1 APOTHECARIES' MEASURE. 1 cubic centi- metre gramme w't I cub. millimetre nti-) v't)i 0.03520 fluid ounce. I 0.28157 fluid drachm. 1 5.43236 grains weight. 0.01693 minim. AVOIRDUPOIS WEIGHT. I milligramme (mgr.) . . I centigramme (.01 gram.) I decigramme (.1 " ) I GRAMME I dekagramme (10 gram.) I hectogramme (lOO " ) I KILOGRAMME (l,000 " ) I myriagramme (iokilog.)= I quintal (100 " )= 1 millier or tonne I (1,000 kilog.) J H 0.01543 gram. 0.15432 " 1.54324 grains. 15.43236 " 5.64383 drams. 3.52739 oz. 2.2046223 lbs. 15432-3564 grains. 22.04622 lbs. 1. 96841 cwt. 0.9842 ton. TROY WEIGHT. I GRAMME , = i 0.64301 pennyweight. (iS-4 ' 0.03215 oz. Troy. 3.64301 pennyv 5.43236 grains. APOTHECARIES' WEIGHT. I GRAMME ( O. ■] o.: (15- 0.25721 drachm. 77162 scruple. 43236 grains. Note -The Metre is tha length, at the temperature of 0= C, of the platinum-iridiun. bar deposited at the International Bureau of Weights and Measures at Sevres, near Pans, f ranee. The Dresent leeal eauivalent of the metre is 39-370' '3 mches, as above stated. at 760 millimetres. •In accordance with the schedule adopted under the Weights and Measures (metric system) Act, 1857- Smithsonian Tables. Table 3. EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS AND MEASURES. (2) METRIC TO IMPERIAL. LINEAR MEASURE. MEASURE OF CAPACITY. Millimetres to inches. Metres to feet. Metres to yards. Kilo- metres to miles. Litres to pints. Dekalitres to gallons. Hectolitres to bushels. Kilolitres to quarters. I 2 3 4 5 6 7 8 9 0.0393701 1 0.07874023 O.I 181 1034 0.1574804s 0.19685056 0.23622068 0.27559079 0.31496090 0.35433102 3.28084 6.56169 9-84253 13-12337 16.40421 19.68506 22.96590 26.24674 29.52758 I.09361 2.18723 3.28084 4-37446 5.46807 6.56169 7-65530 8.74891 9.84253 0.62137 1.24274 I.86412 3.72823 4-34960 4.97097 5-59235 I 2 3 4 5 6 7 8 9 1.75980 3.51961 5.27941 7.03921 8.79902 10.55882 12.31862 14.07842 15-83823 2.1997s 4.39951 6.59926 8.79902 10.99877 13.19852 15-39828 17-59803 19-79778 2.74969 5-49938 g.24908 10.99877 13.74846 16.49815 19-24785 21.99754 24-74723 3-43712 6.87423 10.3113s 13.74846 17.18558 20.62269 24.05981 27.49692 30-93404 SQUARE MEA SURE. WEIGHT (Avoirdupois). Square centimetres to square inches. Square metres to square feet. Square metres to square yards. Hectares to acres. Mim- grammes to grains. Kilogrammes to grains. Kilo- grammes to pounds. Quintals to hundred- weights. I 2 3 4 5 6 I 9 0.15500 0.31000 0.46500 0.62000 0.77500 0.93000 1.08500 1.24000 1.39501 10-76393 21.52786 32.29179 43-05572 53-81965 64-58357 75-34750 86.1 1 143 96.87536 I.I9599 2.39198 3-58798 4-78397 5.97996 7-17595 8.37194 9-56794 10.76393 2.471 1 4.9421 7-^i32 9.8842 12.3553 14.8263 17.2974 19.7685 22.2395 I 2 3 4 S 6 9 0.01543 0.03086 0.04630 0.06173 0.07716 0.09259 0.10803 0.12346 0.13889 15432.356 30864.713 46297.069 61729.426 77161.782 92594.138 108026.495 123458-851 138891.208 2.20462 4.40924 6.61387 8.81849 II.023H 13-22773 15-43236 17.63698 19.84160 3.93683 5-90524 7-87365 9.84206 11.81048 13.77889 15-74730 17-71572 CUBIC MEASURE. Apothe- caries' Measure. Avoirdupois Tbov Weight. ApOTHfi- CARIES' Weight. I 2 3 4 5 6 9 Cubic decimetres to cubic inches. Cubic metres to cubic feet. Cubic metres to cubic yards. Cub. cen- timetres to fluid drachms. Milliers or tonnes to tons. Grammes to ounces Troy. ,' Grammes to penny- weights. Grammes to scruples. 61.02390 122.04781 183.07171 244.09561 305.11952 366.14342 427.16732 488.19123 549-21513 35-31476 70.62952 105.94428 141.25904 176.57379 211.88855 247-20331 282.51807 317.83283 1-30795 2.61 591 3-92386 S.23182 6-53977 7.84772 9.15568 10.46363 11.77159 0.28157 0.56314 I.12627 1.40784 I.68941 1.97098 2.25255 2.53412 I 2 3 4 S 6 9 0.98421 1. 96841 2.95262 3-93683 4.92103 6.88944 7-87365 8.85786 0.03215 0.06430 0.09645 0.12860 0.16075 0.19290 0.22506 0.25721 0.28936 0.64301 1.28603 1.92904 2.57206 3.21507 3-85809 4.50110 5.14412 5-78713 0.77162 1-54324 2.31485 3-08647 3.85809 4.62971 5.40132 6.17294 6.94456 SniT HSONIAN Tab I.ES. HHMB Table 3. EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS AND MEASURES. (3) IMPERIAL TO METRIC. LINEAR MEASURE. .-{ I inch . . I foot (i2 in, I YARD (3 ft., 1 pole (ii yd.) . . I chain (22 yd. or } 100 links) ) I furlong (220 yd.) I mile (1,760 yd.) .== I 25.400 milli- metres. 0.30480 metre. = 0-914399 " = 5.0292 metres. = 20.1168 " = 201.168 •• __ J 1.6093 kilo- metres. SQUARE MEASURE. . , f 6.4516 sq. cen- I square inch . , = "^ timetres. . , . , ( 9.2903 sq. deci- I sq.ft. (144 sq. m.) = | ' metres. rsQ.VAKD(9sq.ft.)={°-Se,^'l- iperch(30isq.yd.) = {^5.293^sq.me- I rood (40 perches) = 10. 117 ares. I ACRE (4840 sq. yd.) = 0.40468 hectare, I sq. mile (640 acres) = jasg.oo hectares. CUBIC MEASURE. I cub. inch= 16.387 cub. centimetres. I cub. foot (17281 fo.o283i7cub me- cub. in.) ^— \ tre, or 28.317 I cub. decimetres. 0.76455 cub. metre. I CUB. YARD (27 ) cub. ft.) 5 APOTHECARIES' MEASURE. 4.5459631 litres, 128.4123 cubic centimetres. 3-5515 cubic centimetres. 0.05919 cubic centimetres. XoTB. — The Apothecaries' gallon is of the same capacity as the Imperial gallon. I gallon (8 pints or 1 160 fluid ounces) J I fluid ounce, f 3 (8 drachms) I fluid drachm, f 3 1 (60 minims) ) I minim, nj (0.91 146 1 grain weight) J -{ MEASURE OF CAPACITY. I gill ... . I pint (4 gills) . I quart (2 pints) I GALLON (4 quarts I peck (2 galls.) . I bushel (8 galls.) I quarter (8 bushels = 1.42 decilitres. = 0.568 litre. = 1.136 litres. = 4-5459631" ' = 9.092 " - 3-637 dekalitres. = 2.909 hectolitres. AVOIRDUPOIS WEIGHT. (64.8 milli- l grammes. I -772 grammes. 28.350 " 0.45359243 kilogr. 6.350 12.70 " / 50.80 t 0.5080 quintal. 1.0160 tonnes or 1016 kilo- grammes. I gram .... I dram .... I ounce (16 dr.) . I POUND (16 oz. or 7,000 grains) I stone (141b.) . I quarter (28 lb.) I hundredweight 1 (112 lb.) J 1 ton (20 cwt.) . i= A TROY WEIGHT. ''''g7ai^s"^v^o\¥1=3-°35 grammes. 1 pennyweight (24 1 ^,.,55, " Note. — The Troy grain is of the same weight as the Avoirdupois grain. APOTHECARIES' WEIGHT. I ounce (8 drachms) =31.1035 grammes. I drachm, si (3scru- 1 __ , Qse " pies) 1 2" Note. — The Apothecaries* ounce is of the same weight as the Troy ounce. The Apothecaries' grain is also of the same weight as the Avoirdupois grain. Note. —The Yard is the length at 62° Fahr., marked on a bronze bar deposited with the Board of Trade^ The Pound is the weight of a piece of platinum weighed in vacuo at the temperature of 0° C, and which is also deposited with the Board of Trade. , -,«•,,., The Gallon contains 10 lb. weight of distilled water at the temperature of 62° Fahr., the barometer being at 30 inches. Smithsonian Tables. lO Table 3. EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS AND MEASURES. (4) IMPERIAL TO METRIC. LINEAR MEASURE. MEASURE OF CAPACITY. Inches , to centimetres. Feet to metres. Yards to metres. Miles to kilo- metres. Quarts to litres. Gallons to litres. Bushels to dekalitres. Quarters to hectolitres. I 2 3 4 5 6 9 2.539998 5,079996 7.619993 I O.I 5999 1 12.699989 15.239987 17.779984 20.319982 22.859980 0.30480 0.60960 0.91440 1. 21920 1.52400 1.82880 2.13360 2.43840 2.74320 0.91440 1.82880 2.74320 3.65760 4.57200 5.48640 6.40080 7.31519 8.22959 1.60934 3.21869 4.82803 6.43737 8.04671 9.65606 11.26540 12.87474 14.4840S 1 2 3 4 5 6 7 8 9 1.13649 2.27298 3-40947 4-54596 5.68245 6.81894 7-95544 9.09193 10.22842 4-54596 9-09193 13-63789 18.18385 22.72982 27.27578 31.82174 36.36770 40.91367 3-63677 7-27354 10.91031 '^54708 18.18385 21.82062 25-45739 29.09416 32.73093 2.90942 5.81883 8.72825 11.63767 14-54708 17.45650 20.36591 23-27533 26.18475 SQUARE MEASURE. WEIGHT (Avoirdupois). Square inches to square centimetres. Square feet to square decimetres. Square yards to square metres. Acres to hectares. Grains to milli- grammes. Ounces to grammes. Pounds to kilo- grammes. Hundred- weights to quintals. I 2 3 4 S 6 9 6.45159 12.90318 19.35477 25.80636 32.25794 38.70953 45.16112 51.61271 58.06430 9.29029 18.58058 27.87086 37.16115 46.45144 55-74173 65.03201 74-32230 83.61259 0.83613 1.67225 2.50838 3-34450 4.18063 5.01676 5.85288 6.68901 7-52513 0.40468 0.80937 1.21405 I.61874 2.02342 2.4281 1 2.83279 3.23748 3.64216 1 2 3 4 5 6 9 64.79892 129.59784 194.39675 259.19567 323.99459 388.79351 453-59243 518.39135 583.19026 28.34953 56.69905 85.04858 113.39811 141.74763 170.09716 198.44669 226.79621 255-14574 0.45359 0.90718 1.36078 I.81437 2.26796 2.72155 3.62874 4.08233 0.50802 I.O1605 1.52407 2.03209 2.54012 3.04814 3.55616 4.06419 4.57221 CUBIC MEASURE. Apothe- caries' Measure. Avoirdupois Troy Weight. Apothe- caries' Weight. I 2 3 4 5 6 9 Cubic inches to cubic centimetres. Cubic feet to cubic metres. Cubic yards to cubic metres Fluid drachms to cubic centi- metres. Tons to milliers or tonnes. Ounces to grammes. Penny- weights to grammes. Scruples to grammes. 16.38702 32.77404 49.16106 65.54808 81.93511 98.32213 1 14.7091 5 131.09617 147.48319 0.02832 0.05663 0.08495 O.I 1327 O.14158 0.16990 0.19822 0.22653 0.25485 0.76455 I.52911 2.29366 3.05821 3.82276 4.58732 5-35187 6.1 1642 6.88098 3-55153 7-10307 10.65460 14.20613 17-75767 21.30920 24.86074 28.41227 31-96380 I 2 3 4 5 6 7 8 9 1.01605 2.03209 3.04814 4.06419 5.08024 6.09628 7-11233 8.12838 9.14442 31.10348 62.20696 93-31044 124.41392 155.51740 186.62088 217.72437 248.82785 279.93133 I-SS517 4.66552 6.22070 7.77587 9-33104 10.88622 12.44139 13-99657 1.29598 2.59196 3.88794 5.18391 6.47989 7.77587 9.07185 10.36783 11.66381 8mit HSONIAN TaI ILES. ^^^ Table 4, jj VOLUME OF A CLASS VESSEL FROM THE WEIGHT OF ITS EQUIVALENT VOLUME OF MERCURY OR WATER. ■,£1SZ1T^ T"^" '''/'^"^ S""""^^ °f ■"^^'^"^y' ''^'gl^'-d ^i* brass weights in air at 760 mm. pressure, then its volume in c. cm. at the same temperature, i, : V= PR = p^< at another temperature, h, : V= PR^ = Ppjd 1 1 + 7 (,i _ /) | / = the weight, reduced to vacuum, of the mass of mercury or water which, weighed with brass weights, equals i gramme ; d = the density of mercury or water at /° C, and 7 = 0.000 025, is the cubical expansion coefficient of glass. Temper ature WATER. MERCURY. t if. i?„ ti = 10°. Jf 1, ii = 2o°. X. JXi, /i = lo". /e,, ii = 20°. 0° I.OOII92 1.00144- J3S8 I.OOI693 0-0735499 0.0735683 0.0735867 I "33 1609 5633 5798 5982 2 1092 1068 1292 1342 5766 5914 6698 3 1243 1493 5900 6029 6213 4 1060 1210 1460 6033 6144 6328 S 1068 "93 1443 6167 6259 6443 6 1.001092 1.001192 1.OO1442 0.0736301 0.0736374 0.0736558 7 1131 1206 1456 6434 6490 6674 8 H84 1234 148s 6568 660s 6789 9 1252 1277 1527 6702 6720 6904 10 1333 1333 1584 6835 683s 7020 II 1.001428 1.001403 001653 0.0736969 0.0736951 0-0737135 12 1536 i486 1736 7103 7066 7250 13 1657 1582 1832 7236 7181 7365 14 1790 i6go 1940 7370 7297 7481 15 1935 1810 2060 75°4 7412 7596 16 1.002092 1.001942 1.002193 0-0737637 0.0737527 7642 0.07377" 17 2261 2086 2337 7771 7826 18 2441 2241 2491 7905 7757 7941 19 2633 2407 2658 8039 7872 8057 20 283s 2584 283s 8172 7988 8172 21 1.003048 1.002772 1.003023 0.0738306 0.0738103 0.0738288 22 3271 2970 3220 8440 8218 8403 23 3504 3178 3429 8573 8333 8518 24 3748 3396 3047 8707 8449 8633 25 4001 3624 387s 8841 8564 8748 26 1.004264 1.003862 1.004113 0.0738974 0.0738679 0.0738864 27 4537 4818 4110 4361 9108 8794 8979 28 4366 4616 9242 8910 9094 29 5110 4632 48S4 9376 9025 9210 30 5410 4908 SI 59 II 9510 9140 9325 Taken from Landoltf Bbrnstein, and MeyerbofEer's Pbysikalisch-Chemische Tabellen. Smithsonian Tables. 12 Table 5. DIFFERENTIAL COEFFICIENTS. INTEGRALS. DIFFERENTIAL COEFFICIENTS. INTEGRALS. «=*» loge* sin. X COS. X taii.x cot. a; sec. :v sin.—' X COS.—' X tan.—' X cot.—' X sec.—' X cosec.— ' X covers.—' x ax a^ log, a I X cos. X —sin. X sec.^ X —cosec' X sin, a; COS.' X COS.* fx"dx JaHx JeHx fix fdx X /cos. ax- dx sin.'* I I /sin. ax ■ dx /sec' ax • dx /cosec' ax • dx sin. X i+»' I ~ i+xi^ I I I \/{2 X—x') I A A cos.' X COS. * -d!« <2x sin.' a: dx V(o'-«') r dx Ja'+x' r dx J X\ *v/(»'-a') / " dx y v(2*— *') 1-2-3- -/o"/"+'(*+A-z)z"-3 9518 9523 9562 9566 957 I 9609 9614 9619 9657 9661 9660 9703 9708 9713 975° 9754 9759 9795 9800 9805 9841 9845 9850 9886 9890 9894 9930 9934 9939 9974 9978 9983 7459 7466 7474 7535 7543 755' 7612 7619 7627 7686 7694 7701 7760 7767 7774 7832 7839 7846 7903 7910 7917 7973 7980 7987 8041 8048 8055 8109 81 16 8122 8176 8182 8189 8241 8248 8254 8306 8312 8319 8370 8376 8382 8432 8439 8445 8494 8500 8506 8555 8561 8567 8615 8621 8627 8675 8681 8686 8733 8739 8745 8791 8797 8802 8848 8854 8859 8904 8910 8915 8960 8965 8971 9015 9020 9025 9069 9074 9079 9/22 9128 9133 9175 9180 9186 9227 9232 9238 9279 9284 9289 9330 9335 9340 ■9380 9385 9390 9430 9435 9440 9479 9484 9489 9528 9533 5538 9576 9581 9586 9624 9628 9633 9671 9675 9680 9717 9722 9727 9763 9768 9773 9809 9814 9818 9854 9859 9863 9899 9903 9908 9943 9948 9952 9987 9991" 9996 2 2 2 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 I I I I I I I I I I I I I Smithsonian Tables. 26 Table 9. ANTILOGARITHMS. 6 P.P. 12 3 4 5 lOOO 1023 1047 1072 1096 II22 1 148 "75 1202 1230 1259 1288 I3I8 '349 1380 1413 144.5 1479 1514 1549 1585 1622 i66o 1698 1738 1778 1820 1862 190S 1950 1995 2042 2089 2138 2188 2239 2291 2344 2399 2455 2512 2570 2630 2692 2754 2818 2884 2951 3020 3090 1002 1026 1050 1074 1099 1125 1151 1178 1205 1233 1262 1291 1321 '352 1384 1416 1449 1483 i5'7 1552 1589 1626 1663 1702 1742 1782 1824 1866 1910 1954 005 028 052 076 102 127 180 208 236 265 294 324 355 387 419 452 486 556 592 629 667 706 746 786 828 871 914 959 1007 1009 1030 1033 1054 1057 1079 I081 1 104 1 107 II30 1132 II56 "59 1 183 1 186 I2II 1213 1239 1242 2000 2004 2046 2051 2094 2099 2143 2148 2193 2198 2244 2249 2296 2301 2350 235s 2404 2410 2460 2466 2518 2523 2576 2582 2636 2642 2698 2704 2761 2767 2825 2831 2891 2897 2958 2965 3027 3034 3097 3105 1268 1297 1327 1358 1390 1422 1455 1489 1524 1560 1596 1633 1671 1710 1750 1791 1832 1875 1919 1963 2009 2056 2104 2' 53 2203 2254 2307 2360 2415 2472 2529 2588 2649 2710 2773 2838 2904 2972 3041 3112 1271 1300 1330 1361 >393 1426 1459 1493 1528 1563 1600 1637 1675 1714 1754 1795 1837 1879 1923 1968 012 03s 059 084 109 13s 161 189 216 245 274 3°3 334 365 396 429 462 496 531 567 603 641 679 718 758 799 841 884 928 972 2014 2018 2o5i 2065 2109 2II3 2158 ZI63 2208 2213 2259 2265 2312 2317 2366 2371 2421 2427 2477 2483 2535 2541 2594 2600 2655 2661 2716 2723 2780 2786 2844 2851 291 1 2917 2979 2985 3048 305s 3II9 3126 014 038 062 086 tI2 164 191 219 247 276 306 337 368 400 432 466 500 535 570 607 644 683 722 762 803 932 977 2023 2070 2118 2168 2218 2270 2323 2377 2432 2489 2547 2606 2667 2729 2793 2924 2992 3062 3133 1016 1040 1064 1089 1114 1 140 1 167 1 194 1222 1250 1279 1309 1340 137 1 1403 1435 1469 1503 1538 1574 1611 1648 1687 1726 1766 1807 1849 1892 1936 1982 2028 2075 2123 2173 2223 2275 2328 2382 2438 2495 2553 2612 2673 2735 2799 2864 2931 2999 3069 3141 1019 1042 1067 1091 1117 1143 1169 1 197 1225 1253 1282 1312 1343 1374 1406 1439 1472 1507 1542 1578 1614 1652 1690 1730 1770 1811 1854 1897 1941 1986 2032 2080 2128 2178 2228 2280 ^333 2388 2443 2500 2559 2618 2679 2742 2805 2871 2938 3006 3076 3148 102 1 1045 1069 1094 1119 1146 1172 1 199 1227 1256 1285 •315 1346 •377 1409 1442 1476 1510 1545 1581 1618 1656 1694 1734 1774 1816 1858 1901 1945 1 991 2037 2084 2133 2183 2234 2286 2339 2393 2449 2506 2564 2624 2685 2748 2812 2877 2944 3013 3083 3155 Smithsonian Tables. Table 9 (continued). ANTILOGARITHMS. 27 3 J 5 P.P. 12 3 4 5 .50 •SI .52 •S3 ■S4 .55 •S6 ■^, .58 ■S9 .60 .61 .62 .64 .65 .66 .67 .68 .69 .70 •71 .72 •73 •74 .75 .76 •77 .78 •79 .80 .81 .82 .84 .85 .86 .87 .88 .89 .90 .91 .92 •93 •94 .95 .96 •97 .98 •99 3162 3236 33" 3388 3467 3S48 3631 371S 3802 3890 3981 4074 4169 4266 436s 4467 4S7I 4677 4786 4898 5012 5129 5248 5370 S49S 5623 S754 5888 6026 6166 6310 6457 6607 6761 6918 7079 7244 7413 7586 7763 7943 8128 8318 8511 8710 8913 9120 9333 9S50 9772 3170 3177 3184 3243 32SI 32S8 3319 3327 3334 3396 3404 3412 3475 3483 3491 3S56 3565 3639 3648 3656 3724 3733 3741 3811 3819 3828 3S99 3908 3917 3990 3999 4009 4083 4093 4102 4178 4188 4198 4276 4285 4295 437S 4385 439S 4477 4487 4498 4581 4592 4603 4688 4699 4710 4797 480S 4819 4909 4920 4932 S023 S03S S°47 5140 5152 5164 5260 5272 5284 " 5395 5408 5521 5534 538: SSoi 5636 5649 5662 5768 5781 5794 5902 5916 5929 6039 6053 6067 6180 6194 6209 6324 6339 6353 6471 6486 0501 6622 6637 6653 6776 6792 6808 6934 6950 6966 7096 7112 7129 7261 7278 7295 7430 7447 7464 7603 7621 7638 7780 7798 7816 7962 7980 7998 8147 8166 8185 8337 8356 8375 8531 8551 8570 8730 8750 8770 8933 8954 8974 9141 9162 9183 9354 9376 9397 9572 9594 9D'o 9795 9817 9840 3192 3199 3206 3266 3273 3281 3342 3350 3357 3420 3428 3436 3499 3508 3516 3581 3589 3597 3664 3673 3681 3750 3758 3767 3837 3846 3855 3926 3936 3945 4018 4027 4036 4111 4121 4130 4207 4217 4227 4305 4315 4325 4406 4416 4426 4508 4519 4529 4613 4624 4634 4721 4732 4742 4831 4842 4853 4943 4955 49^6 5058 5070 5082 5176 5188 5200 5297 5309 5321 5420 5433 5445 5546 5559 5572 5675 5689 5702 5808 5821 5834 5943 5957 5970 6081 6095 6109 6223 6237 6252 6368 6383 6397 6516 6531 6546 6668 6683 6699 6823 6839 685s 6982 6998 7015 7145 7161 7178 73" 7328 7345 7482 7499 7516 7656 7674 7691 7834 7852 7870 8017 8035 8054 8204 8222 8241 8395 8414 8433 8590 8610 8630 8790 8810 8831 899s 9016 9036 9204 9226 9247 9419 9441 9462 9638 9661 9683 9863 9886 9908 3214 3221 3228 3289 3296 3304 3365 3373 3381 3443 345' 3459 3524 3532 3540 3606 3614 3622 3690 3698 3707 3776 3784 3793 3864 3873 3882 3954 3963 3972 4046 4055 4064 4140 4150 4159 4236 4246 4256 4335 4345 4355 4436 4446 4457 4539 4550 4560 4645 4656 4667 4753 4764 4775 4864 4875 4887 4977 4989 5000 5093 510S 5" 7 5212 5224 5236 5333 5346 5358 5458 5470 5483 5585 5598 5610 5715 5728 5741 5848 5861 5875 5984 5998 60 [2 6124 6138 6152 6266 6281 6295 6412 6427 6442 6561 6577 6592 6714 6730 6745 6871 6887 6902 7031 7047 7063 7194 72II 7228 7362 7379 7396 7534 7551 7568 7709 7727 7745 7889 7907 7925 8072 8091 8110 8260 8279 8299 8453 8472 8492 8650 8670 8690 8851 8872 8892 9057 9078 9099 9268 9290 9311 9484 9506 9528 9705 9727 9750 993" 9954 9977 z 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 \ 6 6 6 6 6 6 7 7 7 7 7 SMITHSONrAN TABLES. 28 Table 10. ANTILOGARITHMS. 1 2 3 4 5 6 7 8 9 10 .900 7943 7945 7947 7949 7951 7952 7954 7956 7958 7960 7962 .901 7962 7963 7965 7967 7969 7971 7973 7974 7976 7978 7980 .902 7980 7982 7984 798s 7989 7991 7993 7995 7997 7998 •903 .904 7998 8000 8002 8004 8006 8008 8009 8011 8013 8015 8017 8017 8019 8020 8022 8024 8026 8028 8030 8032 8033 8035 .905 803s 8037 8039 8041 8043 8045 8046 8048 8050 8052 8054 .906 8054 8056 8057 8059 8061 8063 ^°f5 f°^7 f°^ 8070 8072 .907 8072 8074 8076 8078 8080 8082 8084 8085 8087 8089 8091 .908 8091 8093 8095 8097 8098 8100 8102 8104 8106 8108 8110 .909 8110 8111 8113 811S 8117 8119 8121 8123 8125 8126 8128 .910 8128 8130 8132 8134 8136 8138 8140 8141 8143 8145 8147 .911 8147 8149 8.5. 8153 8155 8156 8158 8168 8162 8164 8166 .912 8166 8168 8170 8171 8173 817s 8177 8179 8181 8183 8185 .913 8185 8187 8188 8190 8192 8194 8196 8198 8200 8202 8204 .914 8204 8205 8207 8209 8211 8213 8215 8217 8219 8221 8222 .915 8222 8224 8226 8228 8230 8232 8234 8236 8238 ?'39 8241 .916 8241 8243 8245 8247 8249 8251 8253 8255 ?'57 8258 8260 .917 8260 8262 8264 8266 8268 8270 8272 8274 8276 8278 8279 .918 8279 8281 8283 8285 8287 8289 8291 8293 8295 8297 f^99 .919 8299 8300 8302 8304 8306 8308 8310 8312 8314 8316 8318 .920 8318 8320 8321 8323 8325 8327 8329 8331 8333 8335 ^^37 .921 8337 8339 8341 8343 8344 8346 8348 8350 8352 8354 8356 .922 8356 8358 8360 8362 8364 8366 8368 8370 8371 8373 8375 •923 837s 8377 8379 8381 8383 8385 8387 8389 8391 8393 8395 .924 839s 8397 8398 8400 8402 8404 8406 8408 8410 8412 8414 .925 8414 8416 8418 8420 8422 8424 8426 8428 8429 8431 8433 .926 8433 8435 8437 8439 8441 8443 8445 8447 8449 8451 8453 .927 8453 8455 8457 8459 8461 8463 8464 8466 8468 8470 8472 .928 8472 8474 8476 8478 8480 8482 8484 8486 8488 8490 8492 .929 8492 8494 8496 8498 8500 8502 8504 8506 8507 8509 8511 .930 8511 8513 851S 8517 8519 8521 8523 8525 8527 8529 8531 •931 8531 8533 8535 8537 8539 8541 8543 8545 8547 8549 8551 •932 8551 8553 8555 8557 8559 8561 8562 8564 8566 8568 8570 •933 8570 8572 8574 8576 8578 8580 8582 8584 8586 8588 8590 ■934 8590 8592 8594 8595 8598 8600 8602 8604 8606 8608 8610 .935 86io 8612 8614 8616 8618 8620 8622 8624 8626 8628 8630 •936 8630 8632 8634 8636 8638 8640 8642 8644 8646 8648 8650 ■937 8650 8652 8654 8656 8658 8660 8662 8664 8665 8668 8670 •938 8670 8672 8674 8676 8678 8680 8682 8684 8686 8688 8690 ■939 8690 8692 8694 8696 8698 8700 8702 8704 8706 8708 8710 .940 8710 8712 8714 8716 8718 8720 8722 8724 8726 8728 8730 .941 8730 8732 8734 8736 8738 8740 8742 8744 8746 8748 8750 .942 8750 8752 8754 8756 8758 8760 8762 8764 8766 8768 8770 ■943 8770 8772 8774 8776 8778 8780 8782 8784 8786 8788 8790 •944 8790 8792 8794 8796 8798 8800 8802 8804 8806 8808 8810 .945 88io 8813 8815 8817 8819 8821 8823 8825 8827 8829 8831 .946 8831 8833 883s 8837 8839 8841 8843 8845 8847 8849 8851 •947 !!5' 8853 8855 ^!S7 ^ll^ 8861 8863 8865 8867 8870 8872 .948 8872 8874 8876 8878 8880 8882 8884 8886 8888 8890 8892 •949 8892 8894 8896 8898 8900 8902 8904 8906 8908 8910 8913 Smithsonian Tables. Table 1 {cmtinued). 29 ANTILOGARITHMS. 1 2 3 4 5 6 7 8 9 10 .950 8913 891 5 8917 8919 8921 8923 8925 8927 8929 8931 8933 •951 8933 8935 ^937 8939 8941 8945 8947 8950 8952 8954 •952 8954 8956 8958 8960 8962 8964 8966 8968 8970 8972 8974 •953 8974 8976 8978 8980 8983 8985 8987 8989 8991 8993 899s •954 8995 8997 8999 9001 9003 9005 9007 9009 9012 9014 9016 .95S 9016 9018 9020 9022 9024 9026 9028 9030 9032 9034 9036 •956 9036 9039 9041 9043 9045 9047 9049 9051 9°53 9055 9057 •957 9057 ^Z 9061 9064 9066 9068 9070 9072 9074 9076 9078 •958 9078 9082 9084 9087 9089 9091 9°93 9095 9097 9099 •959 9099 9101 9i°3 9105 9108 9110 gii2 9114 9116 9118 9120 .960 9120 9122 9124 9126 9129 9131 9133 9135 9137 9139 9141 .961 9141 9143 9^45 9147 9150 9152 9154 9156 9158 9160 9162 .962 9162 9164 9166 9169 9171 9173 9175 9177 9179 9181 9183 •963 9183 9185 9188 9190 9192 9194 9196 9198 9200 9202 9204 .964 9204 9207 9209 9211 9213 9215 9217 9219 9221 9224 9226 .965 9226 9228 9230 9232 9234 9236 9238 9241 9243 924s 9247 .966 9247 9249 9251 9253 9256 9258 9260 9262 9264 9266 9268 •967 9268 9270 9273 9275 9277 9279 9281 9283 9285 9288 9290 .968 9290 9292 9294 9296 9298 9300 9303 9305 93°7 9309 93" •969 93" 9313 931S 93^8 9320 9322 9324 9326 9328 933° 9333 .970 9333 9335 9337 9339 9341 9343 9345 9348 935° 9352 9354 •971 9354 9356 9358 9361 9363 9365 9367 9369 9371 9373 9376 •972 9376 9378 9380 9382 9384 9386 9389 9391 9393 9395 9397 •973 9397 9399 9402 9404 9406 9408 9410 9412 9415 9417 9419 •974 9419 9421 9423 9425 9428 943° 9432 9434 9436 9438 9441 .975 9441 9443 9445 9447 9449 9451 9454 9456 9458 9460 9462 •976 9462 9465 9467 9469 9471 9473 9475 9478 9480 9482 9484 •977 9484 9486 9489 9491 9493 9495 9497 9499 9502 9504 9506 ■978 9506 9508 9510 9513 9515 9517 9519 9521 9524 9526 9528 •979 9528 9530 9532 9535 9537 9539 9541 9543 9546 9548 955° .980 955° 9552 9554 9557 9559 9561 9563 9565 9568 9570 9572 .gSi 9572 9574 9576 9579 9581 9583 9585 9587 959° 9592 ^^^i .982 9594 9596 9598 9601 9603 9605 9607 9609 9612 '^I'i QOIO .983 .984 9616 9618 9621 9623 9625 9627 9629 9632 9634 "^A ^f^ 9638 9641 9643 9645 9647 9649 9652 9654 9656 9658 9661 .985 9661 9663 9665 9667 9669 9672 9674 9676 9678 9681 9683 .986 9683 9685 9687 9689 9692 9694 9696 9698 9701 9703 9705 •987 9705 9707 971-0 9712 9714 9716 9719 9721 9723 9725 9727 .988 .989 9727 9750 9730 9752 9732 9754 9734 9757 9736 9759 9739 9761 9741 9763 %n 9745 9768 9748 9770 975° 9772 .990 .991 •992 •993 •994 9772 9795 9817 9840 9863 9775 9797 9820 9842 9865 9777 9799 9822 9845 9867 9779 9802 9824 9847 9870 9781 9804 9827 9849 9872 9784 9806 9829 9851 9874 9808 9831 9854 9876 9788 981 1 9833 9856 9879 9790 9813 9836 98^8 9793 9815 98^8 9883 9795 9817 % .995 9886 9888 9890 9892 9895 9897 9899 9901 9904 9906 9908 .996 •997 .998 •999 9908 9931 9954 9977 991 1 9933 9956 9979 9913 9936 9959 9915 9938 9984 9917 9940 9920 9943 9988 9922 9945 9991 9924 9947 997° 9993 9927 9949 9972 9995 9929 9952 9975 9998 993' 9954 9977 0000 Smithsonian Tables. 30 Table 11. CIRCULAR (TRIGONOMETRIC) FUNCTIONS. (Taken from B. O. Feirce's " Short Table o£ Integrals," Ginn & Co.) ii to " SINES. COSINES. TANGENTS. COTANGENTS. Nat. Log. Nat. Log. Nat. Log. Nat. Log. o.oooo qOoo' .0000 00 1. 0000 0.0000 .0000 CO » 00 90°oo' 1.5708 0.0029 10 .0029 7.4637 1. 0000 .0000 .0029 7.4637 343-77 2-5363 50 1.5679 0.0058 20 .0058 .7648 .0087 .9408 i.oooo .0000 .0058 .7648 171.89 .2352 40 1.5650 0.0087 30 1. 0000 .0000 .0087 .9409 I14-S9 .0591 30 1.5621 0.0116 40 .0116 8.0658 .9999 .0000 .0116 8.0658 85.940 68.750 1-9342 20 1.5592 0.0145 so .0145 .1627 .9999 .0000 .0145 .1627 •8373 10 1-5563 0.0175 i°oo' .0175 8.2419 .9998 9.9999 .0175 8.2419 57.290 1.7581 89°oo' 1-5533 0.0204 10 .0204 .3088 .9998 .9999 .0204 .3089 49.104 .6911 50 1.5504 0.0233 20 .0233 .3668 -9997 -9999 .0233 .3669 4?-964 •6331 40 I-S475 0.0262 30 .0262 .4179 -9997 -9999 .0262 .4181 38.188 .5819 30 1.5446 0.0291 40 .0291 .4637 .9996 .9998 .0291 .4638 34-368 •5362 20 1.5417 0.0320 SO .0320 .5050 -9995 -9998 -0320 .5053 31.242 •4947 10 1.5388 0.0349 2°00' -0349 8.5428 •9994 9-9997 •0349 8.5431 28.636 1.4569 88°oo' I-S3S9 0.0378 10 ■0378 .5776 -9993 -9997 -0378 .5779 26.432 .4221 SO 1-5330 0.0407 20 .0407 .6097 .9992 .9996 .0407 .6101 24.542 •3899 40 1.5301 0.0436 30 .0436 .6397 -9990 -9996 .0437 .6401 22.904 •3599 30 1.5272 0.0465 0.0495 40 .0465 .6677 .9989 .9995 .0466 .6682 21.470 ■3318 20 1-5243 50 -0494 -6940 .9988 .9995 -0495 -694s 20.206 -3055 10 1.5213 0.0524 3°oo' .0523 8.7188 ■9986 9-9994 .0524 8.7194 19.081 1.2806 87°oo' 1.5184 0-0553 10 .0552 .7423 -9985 -9993 ■0553 -7429 18.075 .2571 SO i-S'SS 0.0582 20 -058 1 .7645 •9983 -9993 .0582 .7652 17.169 .2348 40 1.5126 0.061 1 30 .0610 .7857 .9981 .9992 .0612 .7865 16.350 -2135 30 1.5097 0.0640 40 .0640 .8059 .9980 .9991 .0641 .8067 15.605 -1933 20 1.5068 0.0669 SO .0669 .8251 .9978 .9990 .0670 .8261 14.924 •1739 10 1-5039 0.0698 4°oo' .0698 8.8436 .9976 9.9989 .0699 8.8446 14.301 1.1554 86000' 1.5010 0.0727 10 .0727 .8613 -9974 -9989 .0729 .8624 13-727 -1376 50 1.4981 0.0756 0.0785 20 .0756 .8783 .9971 .9988 .0758 .8795 .0787 .8960 13-197 .1205 40 1.4952 30 .0785 .8946 .9969 .9987 12.706 .1040 30 1.4923 0.0814 40 .0814 .9104 .9967 .9986 .0816 .9118 12.251 .0882 20 1.4893 0.0844 50 .0843 .9256 .9964 .9985 .0846 .9272 11.826 .0728 10 1.4864 0.0873 5°oo' -0872 8.9403 .9962 9.9983 .0875 8.9420 11.430 1.0580 85°oo' 1-4835 0.0902 10 •0901 .9545 -9959 -9982 -0904 -9563 11.059 -0437 SO 1.4806 0.0931 20 ■0929 .9682 •9957 -9981 .0934 .9701 10.712 .0299 40 1-4777 0.0960 30 -0958 .9816 -9954 -9980 .0963 .9836 10.385 .0164 30 1.4748 0.0989 40 ■0987 -9945 •9951 -9979 .0992 .9966 10.078 .0034 20 1.4719 0.1018 50 .1016 9.0070 .9948 .9977 .1022 9.0093 9.7882 0.9907 10 1.4690 0.1047 6°oo .1045 9.0192 -9945 9-9976 .1051 9.0216 9-5144 0.9784 84''oo' 1.4661 0.1076 10 .1074 .0311 .9942 .9975 .1080 .0336 9-2SS3 .9664 SO 1.4632 0.1 105 20 .1103 .0426 -9939 -9973 .1110 .0453 -9547 40 1.4603 0.1 134 30 .1132 .0539 .9936 .9972 .1139 .0567 §■7769 •9433 30 I -4574 0.H64 40 .1161 .0648 -9932 -9971 .1169 .0678 8-S55S .9322 20 1-4544 0.1 193 SO .1190 .0755 .9929 .9969 .1198 .0786 8.3450 .9214 10 i-4S'S 0.1222 7°oo' .1219 9.0859 -9925 9-9968 .1228 9.0891 8.1443 0.9109 83°oo' 1.4486 0.1251 10 .1248 .0961 .9922 .9966 -1257 -0995 7-9530 .9005 SO 1-4457 0.1280 20 .1276 .1060 .9918 .9964 .1287 .1096 7.7704 .8904 40 1.4428 0.1309 30 -■305 -"57 .9914 .9963 .1317 .1194 7-5958 .8806 30 '•4399 0.1338 40 .1334 .1252 .9911 .9961 .1346 .1291 7-4287 .8709 20 1-4370 0.1367 SO -1363 -1345 -9907 -9959 .1376 .1385 7.2687 .8615 10 1-4341 0.1396 8°oo' -1392 9-1436 .9903 9.9958 .1405 9.1478 7-1154 6.9682 0.8522 82°00' 1.4312 0.1425 10 .1421 .1525 .9899 .9956 -1435 -1569 .8431 50 1.4283 0.1454 0.1484 20 .1449 -1612 .9894 .9954 .1465 .1658 6.8269 .8342 40 1-4254 30 .1478 .1697 .9890 .9952 .1495 -1745 6.6912 ■8255 30 1.4224 0-1513 40 .1507 .1781 .9886 .9950 .1524 .1831 6.5606 .8169 20 1.4195 0.1542 50 .1536 .1863 .9881 .9948 .1554 .1915 6.4348 .8085 10 1.4166 0.1571 9°oo' .1564 9.1943 .9877 9.9946 .1584 9.1997 6-3138 0.8003 8i°oo' 1-4137 Nat. Log. Nat. Log. Nat. Log. Nat. Log. J. . COSINES. SINES. COTAN- GENTS. TANGENTS. Smithsonian Tables. Table 1 1 {continued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 31 ti SINES. COSINES. TANGENTS. ( ;OTANGENTS. l^ Nat. Log. Nat. Log. Nat. Log. Nat. Log. 0.1571 9°oo' .1564 9.1943 •9877 9-9946 .1584 9.1997 6.3138 0.8003 8l°00' I-4I37 0.1600 10 .1593 .2022 -9872 .9944 .1614 .2078 6.1970 .7922 SO 1.4108 0.1629 20 .1622 .2100 .9868 .9942 .1644 .2158 6.0844 -7842 40 1.4079 0.1658 30 .1650 .2176 •9863 -9940 .1673 -2236 5.9758 .7764 30 1.4050 0.1687 40 .1679 .2251 ■9858 .9938 -1703 -2313 5.8708 .7687 20 1.4021 0.1716 50 .1708 .2324 .9853 .9936 •1733 -2389 5.7694 .7611 10 1.3992 0.1745 IO°00' .1736 9.2397 .9848 9.9934 .1763 9.2463 5.6713 0.7537 80O00' 1-3963 0.1774 10 .1765 .2468 •9843 -9931 .9838 .9929 .1793 .2536 5.5764 .7464 50 1-3934 0.1804 20 .1794 .2538 .1823 .2609 5.4845 -7391 40 1.3904 0.1S33 30 .1822 .2606 -9833 -9927 .1853 .2680 .1883 .2750 5-3955 -7320 30 1-3875 0.1862 40 .1851 .2674 .1880 .2740 .9827 .9924 5.3093 .7250 20 1.3846 0.1891 50 .9822 .9922 .1914 .2819 5.2257 .7181 10 1.3817 0.1920 II°00' .1908 9.2806 .9816 9.9919 .1944 9.2887 5.1446 0.7113 79O00' 1-3788 0.1949 10 .1937 .2870 .9811 .9917 .1974 .2953 5.0658 .7047 SO 1-3759 0.1978 20 .1965 .2934 .9805 .9914 .2004 .3020 4.9894 .6980 40 1^3730 0.2007 30 .1994 .2997 -9799 -9912 -2035 .3085 4.9152 .6915 30 1.3701 0.2036 40 .2022 .3058 -9793 -9909 •2065 .3149 4.8430 .6851 4.7729 .6788 20 1.3672 0.2065 50 .2051 .3119 .9787 .9907 .2095 .3212 10 1^3643 0.2094 12°00' .2079 9.3179 .9781 9.9904 .2126 9.3275 4.7046 0.6725 78°oo' 1.3614 0.2123 10 .2108 .3238 •9775 -9901 .2156 .3336 4.6382 .6664 50 1^3584 0.2153 0.2182 20 .2136 .3296 .9769 .9899 •2186 .3397 4.5736 .6603 40 1-3555 30 ■2164 -3353 .9763 .9896 .2217 .3458 4.5107 .6542 30 1.3526 0.2211 40 •2193 -3410 ■9757 -9893 -2247 -35>7 4.4494 .6483 20 1-3497 0.2240 50 .2221 .3466 .9750 .9890 .2278 .3576 4.3897 .6424 10 1.3468 0.2269 13000' .2250 9.3521 ■9744 9-9887 -2309 9-3634 4.3315 0.6366 77000' 1-3439 0.2298 10 .2278 .3575 -9737 -9884 ■2339 -3691 4.2747 .6309 SO 1.3410 0.2327 20 .2306 .3629 ■9730 -9881 -2370 -3748 4.2193 .6252 40 1-3381 0.2356 30 .2334 .3682 .9724 .9878 .2401 .3804 4.1653 .6196 30 1-3352 0.2385 40 •2363 -3734 .9717 .9875 -2432 -3859 4.1 126 .6141 20 1-3323 0.2414 SO .2391 .3786 .9710 .9872 .2462 .3914 4.0611 .6086 10 1-3294 0.2443 14000' .2419 9.3837 -9703 9-9869 -2493 9-3968 4.0108 0.6032 76°oo' 1.3265 0-2473 10 .2447 .3887 .9696 .9866 .2524 .4021 3.9617 .5979 50 '■^l^r^ 0.2502 20 .2476 .3937 .9689 .9863 .2555 .4074 3.9136 .5926 40 1.3206 0.2531 30 .2504 .3986 .9681 .9859 .2586 .4127 3.8667 .5873 30 I-3I77 0.2560 40 .2532 .4035 .2560 .4083 .9674 .9856 .2617 .4178 3.8208 .5822 20 I.3I48 0.2589 50 .9667 .9853 .2648 .4230 3.7760 .5770 10 1-3119 0.2618 ISOOO* .2588 9.4130 .9659 9.9849 .2679 9.4281 3-7321 0.5719 75000' 1.3090 1.3061 0.2647 10 .2616 .4177 .9652 .9846 .2711 .4331 3.6891 .5669 50 0.2676 20 .2644 .4223 .9644 .9843 .2742 .4381 3.6470 .5619 40 1-3032 0.2705 30 .2672 .4269 .9636 .9839 -2773 -4430 3.6059 -5570 30 1-3003 0.2734 40 .2700 .4314 .9628 .9836 .2805 .4479 3-5656 -5521 20 1.2974 0.2763 50 .2728 .4359 .9621 .9832 .2836 .4527 3.5261 .5473 10 I -2945 0.2793 0.2822 16O0O' 10 .2756 9.4403 .2784 .4447 .9613 9.9828 .9605 .9825 .2867 9-4575 .2899 .4622 3.4874 0.542s 3-4495 -5378 74000' SO 1]2886 1.2857 1.2828 1.2799 0.2851 20 .2812 .4491 .9596 .9821 .2931 .4669 3.4124 .5331 40 0.2880 0.2909 0.2938 30 40 .2840 .4533 .2868 .4576 .9588 .9817 .9580 .9814 .2962 .4716 .2994 .4762 3-3759 -5284 3.3402 .5238 30 20 SO .2896 .4618 -9572 .9810 .3026 .4808 3.3052 .5192 10 1.2770 0.2967 0.2996 0.3025 0-3054 0.3083 0.3113 i7°oo' 10 20 30 40 5° .2924 9.4659 .2952 .4700 .2979 .4741 .3007 .4781 .3062 .4861 .9563 9.9806 -9555 -9802 .9546 .9798 -9537 -9794 .9528 -9790 .9520 .9786 -3057 9-4853 .3089 .4898 .3121 .4943 .3153 -4987 .3185 -5031 .3217 .5075 3.2709 0.5147 3.2371 .5102 3.2041 .5057 3.1716 .5013 3.1397 .4969 3.1084 .4925 73O00' SO 40 30 20 10 1-2741 1.2712 1.2683 1.2654 1.2625 1.2595 0.3142 i8°oo' .3090 9.4900 .9511 9.9782 .3249 9.5118 3.0777 0.4882 72°00' 1.2566 Nat. Log. Nat. Log. Nat. Log. Nat. Log. c/i COSINES SINES. COTAN- GENTS. TANGENTS i Smithsonian Tables. 32 Table 1 1 (conimued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. % SINES. COSINES. TANGENTS. COTANGENTS. Nat. Log. Nat. Log. Nat. Log. Nat. Log. 0.3142 i8°oo' .3090 9.4900 •95" 9-9782 .3249 9.51 18 3.0777 0.4882 72000' 1.2566 0.3I7I 10 •3118 .4939 .9502 .9778 .3281 .5161 3.047s .4839 50 1.2537 0.3200 20 -3145 -4977 .9492 .9774 .3314 .5203 3.0178 .4797 40 1.2508 0.3229 30 -3173 -5015 .9483 .9770 .3346 .5245 2.9887 .4755 30 1.2479 0.3258 40 .3201 .5052 •9474 ^9765 •3378 .5287 2.9600 .4713 20 1.2450 0.3287 50 .3228 .5090 •9465 .9761 .3411 .5329 2.9319 .4671 10 1. 2421 0.3316 I9''oo' .3256 9.5126 •9455 9-9757 •3443 9-5370 2.9042 0.4630 7i°oo' 1.2392 0-3345 10 .3283 .5163 .9446 .9752 .3476 .5411 2.8770 .4589 so '•2363 0-3374 20 •33' I ■5'99 -9436 -9748 •3508 .5451 2.8502 .4549 40 '•2334 0-3403 30 -3338 -5235 •9426 .9743 •3541 •549" 2.8239 ^4509 2.7980 .4469 30 1.2305 0.3432 40 -3365 -5270 •9417 ^9739 •3574 -5531 20 1.2275 0.3462 50 •3393 -5306 -9407 -9734 .3607 .5571 2.7725 .4429 10 1.2246 0.3491 2O°0O' •3420 9.5341 •9397 9-9730 .3640 9.561 1 2.7475 0.4389 7o°oo' ^■^^11 0.3520 10 -3448 -5375 .9387 .9725 .3673 .5650 .3706 .5689 2.7228 .4350 5° 1.2188 0-3549 20 ■3475 -5409 -9377 -9721 2.6985 .4311 40 1.2159 0-3578 30 .3502 .5443 .9367 .9716 •3739 -5727 2.6746 .4273 30 1-2130 0.3607 40 -3529 -5477 .9356 .9711 •3772 .5766 2.651 1 .4234 20 1.2101 0.3636 50 -3557 -5510 -9346 -9706 .3805 .5804 2.6279 .4196 10 1.2072 0.3665 2I°00' •3584 9-5543 -9336 9-9702 .3839 9.5842 2.6051 0.4158 69=00' 1.2043 0.3694 10 .3611 .5576 •9325 -9697 .3872 .5879 2.5826 .4121 50 1.2014 0-3723 20 .3638 .5609 •9315 -9692 .3906 .5917 2.5605 .4083 40 1. 1985 0-3752 0-3782 30 .3665 .5641 .9304 .9687 -3939 -5954 2.5386 .4046 30 1.1956 40 •3692 .5673 .9293 .9682 -3973 -5991 2.5172 .4009 20 1.1926 0.3811 50 -3719 -5704 .9283 .9677 .4006 .6028 2.4960 .3972 10 1.1897 0.3840 22°00' •3746 9-5736 .9272 9.9672 .4040 9.6064 2.4751 0.3936 68°oo' 1.1868 0.3869 10 -3773 -5767 .9261 .9667 .4074 .6100 2.4545 -3900 50 1.1839 0.3898 20 .3800 .5798 .9250 .9661 .4108 .6136 2.4342 .3864 40 1. 1810 0.3927 30 .3827 .5828 .9239 .9656 .4142 .6172 2.4142 .3828 30 1.1781 0.3956 40 .3854 -5859 .3881 .5889 .9228 .9651 .4176 .6208 2^3945 ^3792 20 1.1752 0.3985 50 .9216 .9646 .4210 .6243 2-3750 -3757 10 1.1723 0.4014 23°00' .3907 9.5919 .9205 9.9640 •4245 9^6279 2-3559 0.3721 67°oo' 1. 1694 0.4043 10 -3934 -5948 -9194 .9635 •4279 -6314 2-3369 -3686 5° 1. 1665 0.4072 20 .3961 .5978 .9182 .9629 .4314 .6348 2.3183 .3652 40 1.1636 0.4102 30 .3987 .6007 .9171 .9624 .4348 .6383 2.2998 .3617 30 1.1606 0.4131 40 .4014 .6036 .9159 .9618 .4383 .6417 2.2817 •3583 20 1-1577 0.4160 50 .4041 .6065 .9147 .9613 .4417 ^6452 2.2637 .3548 lo 1.1548 0.4189 24''00' .4067 9.6093 •913s 9-9607 .4452 9.6486 2.2460 0.3514 66°oo' 1.1519 0.4218 10 .4094 .612 [ .9124 .9602 .4487 .6520 2.2286 .3480 50 1.1490 0.4247 20 .4120 .6149 .9112 .9596 -4522 .6553 •4557 .6587 2.2113 .3447 40 1.1461 0.4276 30 .4147 -6177 •9100 .9590 2.1943 -3413 30 1.1432 0.4305 40 .4173 .6205 .9088 .9584 .4592 .6620 2.1775 -3380 20 1.1403 0.4334 50 .4200 .6232 •9075 ^9579 .4628 .6654 2.1609 -3346 10 1^1374 0.4363 25°00' .4226 9.6259 .9063 9.9573 .4663 9.6687 2.1445 0.3313 65°oo' 1^1345 0.4392 10 .4253 .6286 .9051 .9567 .4699 .6720 2.1283 ^3280 50 1.1316 0.4422 20 .4279 .6313 .9038 .9561 •4734 ^67 52 2. 1 1 23 .3248 40 1.1286 0.4451 30 -4305 -6340 .9026 .9555 .4770 .6785 2.0965 .3215 30 1.1257 0.4480 40 -433' -6366 •9013 ^9549 .4806 .6817 2.0809 •3183 20 1.1228 0.4509 50 .4358 .6392 .9001 .9543 .4841 .6850 2.0655 -3 '50 TO 1. 1199 0.4538 26''00' .4384 9.6418 .8988 9.9537 .4877 9.6882 2.0503 0.3118 64°oo' 1. 1170 0.4567 10 .4410 .6444 .8975 .9530 .4913 ^6914 2-0353 -3086 50 1.1141 0.4596 20 .4436 .6470 .8962 .9524 .4950 .6946 2.0204 .3054 40 1.1112 0.4625 30 .4462 .6495 .8949 .9518 .4986 .6977 2.0057 .3023 30 1.1083 0.4654 40 .4488 .6521 .8936 .9512 .5022 .7009 1.9912 .2991 20 1.1054 0.4683 50 .4514 .6546 •8923 ^9505 .5059 .7040 1.9768 .2960 10 1.1025 0.4712 27°00' .4540 9.6570 .8910 9.9499 •509s 9-7072 1.9626 0.2928 63=00' 1.0996 Nat. Log. Nat. Log. Nat. Log. . Nat. Log. Pes «2 COSINES. SINES. COTAN- GENTS. TANGENTS. Smithsonian Tables. Table 1 1 {coHtimitd). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 33 "1 SINES. COSINES. TANGENTS. COTANGENTS. Nat. Log. Nat. Log. Nat. Log. Nat. Log. 0.4712 27°00' •4540 9.6570 •^9'° 9.9499 •5095 9.7072 1.9626 0.2928 63»oo' 1.0996 0.4741 10 .4566 •6595 .8897 .9492 ■5'32 -7103 1.9486 .2897 £0 1.0966 0.4771 20 •4592 .6620 .8884 .9486 .5169 ■7134 1.9347 .2866 40 1-0937 0.4800 30 .4617 .6644 ili° •9479 .5206 -7165 1. 92 10 .2835 30 1.0908 0.4829 40 •4643 .6668 •8857 •9473 •5243 .7196 1.9074 .2804 20 1.0879 0.4858 SO .4669 .6692 •8843 .9466 .5280 .7226 1.8940 .2774 10 1.0850 0.4887 28°oo' .4695 9.6716 ■11-^ 9-9459 •53>7 9-7257 1.8807 0.2743 62000' 1.0821 0.4916 10 .4720 .6740 .8816 -9453 ■5354 •7287 1.8676 .2713 50 1.0792 0.4945 20 .4746 .6763 .8802 •9446 -5392 •7317 1.8546 .2683 40 1.0763 0.4974 30 •4772 •6787 .8788 •9439 •5430 •7348 I.84I8 .2652 30 1-0734 0.5003 40 •4797 .6810 .8774 •9432 •5467 •7378 I.829I .2622 20 1.0705 0.5032 50 .4823 •6833 .8760 .9425 ■5505 .7408 I.8I65 .2592 10 1.0676 0.5061 zg-oo' .4848 9.6856 .8746 9.9418 -5543 9^7438 1.8040 0.2562 eiooo- 1.0647 0.5091 10 .4874 .6878 .8732 •94" .5581 •7467 1-7917 -2533 50 I.06I7 0.5120 20 .4899 .6901 .8718 .9404 .5619 •7497 1.7796 .2503 40 1.0588 0.5149 30 .4924 •6923 .8704 •9397 .5658 .7526 1.7675 .2474 30 1-0559 0.5178 40 •4950 .6946 .8689 •9390 .5696 •7556 •7585 1.7556 .2444 20 1.0530 0.5207 50 -4975 .6968 .8675 •9383 ■5735 1.7437 .2415 10 1.0501 0.5236 30°oo' .5000 9.6990 .8660 9^9375 .9368 ■5774 9.7614 1.732 1 0.2386 60000' 1.0472 0.5265 10 .5025 .7012 .8646 •5812 •7644 1.7205 .2356 50 1.0443 0.5294 20 .5050 -7033 .8631 .9361 •5851 •7673 1.7090 .2327 40 1.0414 0-5323 30 •5075 -7055 .8616 ■9353 .5890 .7701 1.6977 ^2299 30 1.0385 0-5352 40 .5100 .7076 .8601 •9346 ■5930 •7730 1.6864 -2270 20 1-0356 0.5381 50 .5125 -7097 -8587 •9338 ■5969 •7759 1.6753 ^2241 10 1.0327 0.541 1 3i°oo' .5150 9.7 1 18 .8572 9-9331 .6009 9.7788 1.6643 0.2212 59000' 1.0297 0.5440 10 •5'7S -8557 •9323 ■^fo .7816 1.6534 .2184 50 1.0268 0.5469 20 .5200 .7160 .8542 -9315 .9308 .6088 •7845 1.6426 .2155 40 1.0239 0.5498 30 .5225 .7181 .8526 .6128 •7873 1.6319 .2127 30 1.0210 0.5527 40 •5250 .7201 .8511 .9300 .6168 .7902 1.62 1 2 .2098 20 1.0181 0-5556 50 -5275 .7222 .8496 .9292 .6208 •7930 1.6107 .2070 10 1.0152 0.5585 32°oo' .5299 9.7242 .8480 9.9284 .6249 9-7958 1.6003 0.2042 58=00' 1.0123 0.5614 10 -5324 .7262 .8465 .9276 .6289 .7986 1.5900 .2014 50 1.0094 0-5643 20 ■5348 .7282 .8450 .9268 ■6330 .8014 1.5798 .1986 40 .1.0065 0.5672 30 ■5373 -7302 -8434 .9260 •6371 .8042 1^5697 ^1958 30 1.0036 0.5701 40 ■5398 -7322 .8418 .9252 .6412 .8070 1-5597 -1930 20 1.0007 0.5730 50 .5422 -7342 .8403 -9244 •6453 .8097 1.5497 .1903 10 0.9977 0.5760 0.5789 33°oo' 10 •5446 •547' 9-7361 .7380 •8387 •8371 9.9236 .9228 •6494 .6536 9.8.25 1.5399 0.1875 1.5301 ,1847 S7°oo' 50 0.9948 0.9919 0.9861 0.9832 0.9803 0.5818 0.5847 0.5876 0.5905 20 30 40 50 -5495 •5519 -5544 -5568 .7400 -7419 •7438 •7457 •8355 .8339 -8323 .8307 .9219 .9211 -9203 .9194 .6661 •6703 .8180 .8208 •8235 •8263 1.5204 .1820 1.5108 .1792 1.5013 .1765 1.4919 .1737 40 30 20 10 0-5934 0.5963 0-5992 0.6021 0.6050 0.6080 34°oo' 10 20 30 40 50 •11 .5712 9.7476 -7494 •7513 •753' .8290 .8274 .8258 .8241 .8225 .8208 9.9186 .9177 .9169 .9160 .9151 .9142 •6745 .6787 -6830 .6873 .6916 ■6959 9.8290 •8317 •8344 •8371 .8398 .8425 1.4826 0.1710 1.4733 -1683 1.4641 .1656 1.4550 .1629 1.4460 .1602 1-4370 .1575 56°oo' SO 40 30 20 10 0.9774 0-9745 0.9716 0.9687 0.9657 0.9628 0.6109 0.6138 0.6167 0.6196 0.6225 0.6254 35000' 10 20 30 40 50 •5736 .5760 -5783 .5807 •5831 -5854 9.7586 .7622 .7640 -7657 •7675 .8192 .8 1 58 .8141 .8124 .8107 9-9134 .9125 .9116 .9107 .9098 .9089 .7002 .7046 .7089 •7133 •7177 .7221 9.8452 .8506 -8533 .8586 1.4281 0.1548 1.4193 .1521 1.4106 .1494 1.4019 .1467 1-3934 -1441 1.3848 .1414 S5O00' 50 40 30 20 10 0-9599 0.9570 0.9541 0.9512 0.9483 0.9454 0.6283 36000' .5878 9.7692 .8090 9.9080 .7265 9-8613 1-3764 0.^1387 54O00' 0.9425 Nat. Log. Nat. Log. Nat. Log. Nat. Log. COSINES. SINES. COTAN- GENTS. TANGENTS. . Smithsonian Tables. 34 Table 1 1 (cmtimud). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. ^1 SINES. COSINES. TANGENTS. COTANGENTS. Nat. Log. Nat. Log. Nat. Log. Nat. Log. 0.6283 se^oo' .5878 9.7692 -8090 9.9080 .7265 9.8613 '•3764 0.1387 S4°oo' 0.9425 0.9396 0.9367 o^9338 0.9308 0.6312 10 .5901 .7710 .8073 .9070 ■7310 ■^fli 1.3680 .1361 SO 0.6341 20 -5925 •7727 .8056 .9061 ■735S .8666 ••3597 •1334 40 0.6370 30 -5940 •7744 -8039 .9052 .7400 .8692 '•3514 .1308 30 0.6400 40 ■5972 .7761 .8021 .9042 ■7445 .8718 '•3432 .1282 20 0.6429 so •S99S .7778 .8004 ■9033 .7490 ■8745 '•335' .1255 10 0-9279 0.6458 37<'oo' .6018 9-7795 .7986 9-9023 ■7536 9.8771 1.3270 0.1229 S3°oo' 0.9250 0.6487 10 .6041 .7811 .7969 -9014 .7581 •1297 1.3190 •1203 SO 0.9221 0.6516 20 .6065 .7828 ■7951 .9004 .7627 .8824 1.3UI .1176 40 0.9192 0.6545 30 .6088 -7844 •7934 .8995 ■7673 •f?5? 1-3032 .1150 30 0.9163 0.6574 40 .6111 .7861 .7916 .8985 ■7720 .8876 1.2954 .1124 20 0.9134 0.6603 50 -6134 •7877 .7898 .8975 .7766 .8902 1.2876 .1098 10 0.9105 0.6632 38=00' -6157 9-7893 .7880 9.8965 .7813 9.8928 1.2799 0.1072 52°00' 0.9076 0.6661 10 .6180 .7910 .7862 .8955 .7860 .8954 1.2723 .1046 so 0.9047 0.6690 20 .6202 .7926 .7844 •8945 •7907 .8980 1.2647 .1020 40 0.9018 0.6720 30 .6225 .6248 .7941 .7826 ■8935 •7954 .9006 1.2572 .0994 30 0.8988 0.6749 40 ■7957 .7808 .8925 .8002 .9032 1.2497 .0968 20 0.8959 0.6778 50 .6271 ■7973 .7790 .8915 .8050 .9058 1.2423 .0942 10 0.8930 0.6807 39°oo' .6293 9.7989 ■7771 9.8905 .8098 9.9084 1.2349 0.0916 5i°oo' 0.8901 0.6836 10 -6316 .8004 •7753 .8895 .8146 .9110 1.2276 .0890 SO 0.8872 0.6865 20 -6338 .8020 ■7735 .8884 .8195 ■9135 1.2203 .0865 40 0.8843 0.6894 30 .6361 .8035 .7716 .8874 .8243 .9161 1.2131 .0839 30 0.8814 0.6923 40 •6383 .8050 .7698 .8864 .8292 .9187 1.2059 ■'^M 20 0.8785 0.6952 50 .6406 .8066 .7679 ■8853 •8342 .9212 1.1988 .0788 10 0.8756 0.6981 4o°oo' -6428 9.8081 .7660 9^8843 •8391 99238 1.1918 0.0762 So^oo' °-ll% 0.7010 10 .6450 .8096 .7642 .8832 .8441 .9264 1.1847 .0736 SO 0.8698 0.7039 20 .6472 .8111 -7623 .8821 .8491 .9289 1.1778 .0711 40 0.8668 0.7069 30 .6494 .8125 .7604 .8810 .8541 ■931 S 1. 1708 .0685 30 0.8639 0.7098 40 .6517 .8140 •7585 .8800 .8591 ■9341 1. 1640 .0659 20 0.8610 0.7:27 SO •6539 .8155 .7566 ■8789 .8642 .9366 1.1571 .0634 10 0.8581 0.7156 0.7185 4i°oo' .6561 9.8169 ■7547 9.8778 .8693 9.9392 1.1504 0.0608 49°oo' 0.8552 10 •6|83 .8184 .7528 .8767 .8744 •9417 1. 1436 .0583 SO 0.8523 0.7214 20 .8198 .7509 .8756 .8796 %t^ 1-1369 •0557 40 0.8494 0.7243 30 !6626 -8213 .7490 .8745 .8847 1-1303 •0532 30 0.8465 0.7272 40 .6648 .8227 ■7470 •8733 .8899 •9494 1. 1237 .0506 20 0.8436 0.7301 SO .6670 .8241 •7451 .8722 .8952 •9519 1.1171 .0481 10 0.8407 0.7330 42°0O' .6691 9.825s ■7431 9.87 1 1 .9004 99544 1.1106 0.0456 48°oo' 0.8378 0.73S9 10 •6713 .8269 .7412 .8699 -9057 .9570 1-1041 .0430 SO 0.8348 0.7389 20 •6734 -8283 •7392 .8688 -9110 •9595 1.0977 .0405 40 0.8319 0.7418 30 .6756 .8297 ■7373 .8676 .9163 .9621 1. 091 3 •0379 30 0.8290 0.7447 40 •6777 .8311 •7353 .8665 .9217 .9646 1.0850 1.0786 •0354 20 0.8261 0.7476 SO .6799 •8324 ■7333 .8653 .9271 .9671 .0329 10 0.8232 0.7505 43°oo' .6820 9-8338 ■7314 9.8641 ■9325 9.9697 1.0724 0.0303 47''oo' 0.8203 0-7534 10 .6841 ■8351 •7294 .8629 ■9380 .9722 1. 066 1 .0278 SO 0.8174 0.7563 20 .6862 ■8365 ■7274 .8618 ■9435 ■9747 1.0599 .0253 40 0.814s 0.7592 30 .6884 .8378 ■7254 .8606 .9490 .9772 '■0538 .0228 30 0.8116 0.7621 40 .6905 .8391 ■7234 ■8594 ■9545 ■9798 1.0477 .0202 20 0.8087 0.7650 50 .6926 .8405 .7214 .8582 .9601 .9823 1.0416 .0177 10 0.8058 0.7679 44='oo' .6947 9.8418 ■7193 9.8569 .9657 9.9848 '•035S 0.0152 46">oo' 0.8029 0.7709 10 .6967 .8431 ■7173 •8557 ■9713 .9874 1.0295 .0126 SO 0.7999 0.7738 20 .6988 .8444 ■7153 .8545 .9770 .9899 1.0235 .0101 40 0.7970 0.7767 30 -7009 .8457 ■7133 •8532 •9^f .9924 1.0176 .0076 30 0.7941 0-7796 40 -7030 .8469 .7112 .8520 .9884 ■9949 1.0117 .0051 20 0.7912 0.7825 SO -7050 .8482 .7092 .8507 ■9942 ■9975 1.0058 .0025 10 0.7883 0.7854 45°oo' .7071 9.8495 .7071 9.8495 1. 0000 0.0000 1.0000 0.0000 4S°oo' 0.7854 Nat. Log. Nat Log. Nat. Log. Nat. Log. COSINES. SINES. COTAN- GENTS. TANGENTS. Smithsonian Tables. Table 12. CIRCULAR (TRIGONOMETRIC) FUNCTIONS.* 35 CO § - SINES. COSINES. TANGENTS. COTANGENTS. 1 Nat Log. Nat Log. Nat. Log. Nat Log. 0.00 0.00000 — 00 1. 00000 0.00000 — 00 — 00 .00 00 00°00' .01 .01000 7-99999 0.99995 9-99998 O.OIOOO 8.00001 99-997 1.99999 0034 .02 .02000 8.30100 .99980 .99991 .02000 .30109 49-993 .69891 01 09 •03 .03000 •47706 -99955 .99980 .03001 •47725 33-323 •52275 01 43 02 18 .04 .03999: .60194 .99920 .99965 .04002 .60229 24.987 •39771 0.05 0.04998 8.69879 0-99875 9.99946 0.05004 8-69933 I9-983 1.30067 02°52' .06 •05996 ■77789 .99820 .99922 .06007 •77867 16.647 .22133 03 26 •07 .06994 ■84474 f^ •99894 .0701 1 •84581 14.262 .15419 04 01 .08 .07991 .90263 .99861 .08017 .90402 12.473 .09598 0435 .09 .08988 •95366 •99595 .99824 .09024 ■95542 11.081 .04458 0509 0.10 0.09983 8.99928 0.99500 9-99782 0.10033 9.00145 9.9666 0-99855 05044' .11 .10978 9.04052 ■99396 •99737 .11045 ■04315 9.0542 •95685 06 18 .12 .11971 .07814 .99281 •99687 .12058 .08127 8.2933 •io^?3 0653 ■13 .12963 .11272 .99156 .99632 •13074 .11640 7.6489 .88360 07 27 .14 •I39S4 .14471 .99022 •99573 .14092 .14898 7.0961 .85102 0801 0.15 0.14944 9.17446 0.98877 9.99510 0.15114 9-I7937 6.6166 0.82063 o8'>36' .16 •15932 .20227 -98723 •99442 .16138 .20785 6.1966 .79215 09 10 ■17 .1^18 .22836 -98558 •99369 .17166 .23466 5.8256 •76534 0944 .18 .17903 .25292 •98384 •99293 .18197 .26000 5^4954 .74000 10 19 .19 .18886 .27614 .98200 .99211 .19232 .28402 5-1997 •71598 10 53 0.20 0.19867 9.29813 0.98007 9.99126 0.20271 9.30688 4-9332 0.69312 11028' .21 .20846 .31902 .97803 .21314 .32867 4.6917 •67133 12 02 12 36 .22 .21823 .22798 •33891 .97590 .98940 .22362 •34951 4-4719. .65049 .23 •35789 ■97367 .98841 .23414 ■^M 4.2709 ■63052 13 II .24 .23770 •37603 ■97134 •98737 •24472, .38866 4.0864 , .61134 1345 0.25 a24740 9-39341 0.96891 9.98628 0.25534 9.40712 3-9163 0.59288 I4°i9' .26 .25708 .41007 .96639 •98515 .26602 .42491 3-7592 ■57509 14 54 1528 1603 1637 .27 .26673 .42607 ■96377 •98397 .27676 .44210 3-6133 •S5790 .28 .27630 •44147 .96106 .98275 .98148 •28755 •45872 3-4776 .54128 .29 ^595 45629 .95824 .29841 .47482 3-35" •52518 0.30 •31 •32 ■33 ■34 0.29552 .30506 •31457 .32404 •33349 9.47059 •48438 •49771 .51060 .52308 0-9S534 -95233 •94924 .94604 .94275 9.98016 -97879 -97737 .97591 .97440 0.30934 •32033 ■33>39 •34252 •35374 9^49043 •50559 .52034 ■53469 3-2327 3.1218 3.0176 ■ 2.9195 2.8270 0.50957 ■49441 .47966 •4653' •45132 17O11' 17 46 18 20 1854 1929 o^3S •36 fs •39 0.34290 .35227 .36162 ■37092 .38019 .58000 0-93937 -93590 •93^33 .92866 .92491 9.97284 •97123 &l .96610 0.36503 .37640 .38786 •39941 41 105 9-56233 •57565 .60142 .61390 2.6567 2.5782 2-5037 2.4328 0.43767 •42435 41132 .39858 .38610 20O03' 2038 21 12 21 46 22 21 0.40 .41 42 •43 ■44 0.38942 .40776 .41687 .42594 9.59042 .60055 .61041 .62000 •6293s 0.92106 .91712 .91309 .90897 .90475 9.96429 ■96243 .96051 ■95855 ■95653 0.42279 .43463 .44657 •45862 •47078 9.62613 .63812 .64989 .66145 .67282 2.3652 2.3008 2.2393 2.1804 2.I24I 0.37387 .36188 .35011 ■33855 .32718 22O55' 2329 2404 2438 25 13 ■47 .48 •49 0.43497 •44395 46178 .47063 9.63845 .64733 11 •?il57 .88699 .88233 9-95446 •95233 .95015 .94792 •94563 0.48306 •49545 •50797 .52061 •53339 9.68400 .69500 .70583 .71651 .72704 2.070Z 2.0184 1.9686 1.9208 1.8748 0.31600 .30500 .29417 .28349 .27296 25°47' 26 21 2656 27 30 28 04 50 0.47943 9.68072 0.87758 994329 0.54630 9-73743 I-830S 0.26257 28039' _ 8«.TH80N.«N TABLE3. ^ ^^^^^ ^^^ ^^^^ ^^ ^ ^ ^an Orstraud. 36 Table 1 2 {cotuinmj). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. < a < OS SINES. COSINES. TANGENTS. COTANGENTS. Nat. Loff. Nat. Log. Nat Log. Nat. Log. 0.50 0-47943 g.68072 0.87758 994329 0.54630 9^73743 '■*3°5 0.26257 28039' •51 .48818 .68858 .87274 .94089 •55936 ■74769 ■7878 .25231 29 13 ■52 .49688 .69625 .86782 •93843 ■57256 .75782 .7465 .24218 2948 •S3 ■50553 •7037 s .86281 ■93591 .58592 •76784 .7067 .23216 30 22 ■54 .51414 .71108 ■85771 •9Zii4 •59943 .77774 ■6683 .22226 3056 0-55 0.52269 9.71824 0.85252 9.93071 0.61311 9-78754 1.6310 0.21246 31^31' .56 ■S3"9 ■72525 .84726 .92801 .62695 •79723 ■5950 .20277 3205 •57 •53963 •73210 .84190 .92526 .64097 .80684 .5601 .19316 3240 .58 .54802 .73880 .83646 .92245 .65517 .81635 ■5263 .18365 33 H •59 •55636 •74536 .83094 •91957 .66956 .82579 •4935 .17421 3348 0.60 0.56464 9.75177 0.82534 9.91663 0.68414 9-835'4 1.4617 0.16486 34°23' .61 .57287 .75805 .81965 .81388 ■91363 .69892 •84443 ■4308 •'5557 34 57 .62 .58104 .76420 .91056 ■7 1 391 .85364 .4007 .14636 35 3" i^ .58914 .77022 .80803 ■90743 .72911 .86280 •3715 .13720 3606 .64 .59720 .77612 .80210 •90423 ■74454 .87189 •343» .12811 3640 0.65 0.60519 9.78189 0.79608 9.90096 0.76020 9.88093 'fit 0.1 1907 37''iS' .66 .61312 ■78754 .78999 .89762 .77610 .88992 .11008 37 49 ■^I .62099 .79308 .78382 .89422 .79225 .89886 .2622 .10114 3823 .68 .62879 .80382 •77757 .89074 .80866 ■90777 .2366 ■09223 3858 .69 .63654 •77125 .88719 •82534 .91663 .2116 ■08337 3932 0.70 0.64422 9.80903 0.76484 9-88357 .87988 0.84229 9.92546 1. 1872 0.07454 40<'o6' •71 ■65183 .81414 •75836 ■85953 ■93426 .1634 ■06574 40 41 .72 •^1?^^ .81914 .75181 .87611 •87707 ■94303 .1402 •05697 41 15 •73 .66687 .82404 •74517 .87226 .89492 .95178 .1174 .04822 41 50 •74 .67429 .82885 •73847 .86833 •9' 309 .96051 .0952 •03949 42 24 0.75 0.68164 9-83355 0.73169 9-86433 0.93160 9.96923 10734 0.03077 42=58' .76 .68892 .83817 .72484 .86024 ■95045 ■97793 .0521 .02207 43 33 •77 .69614 .84269 .71791 .85607 .96967 ■0313 •01338 44 07 .78 .70328 ■84713 .71091 •f5'82 .98926 9-9953' 1.0109 .00469 44 41 •79 •7103s .85147 ■70385 .84748 1.0092 0.00400 0.99084 9.99600 45 '6 0.80 0.7:736 9^85S73 0.69671 9.84305 1.0296 0.01268 0.97121 9.98732 4S''So' .81 .72429 ,85991 .68950 ■83853 .0505 .02138 ■95197 .97862 46 28 .82 ■73" 5 .86400 .68222 •83393 .0717 .03008 ■93309 .96992 46 59 •P ■73793 .86802 .67488 .82922 ■0934 .03879 ■9145s .96121 47 33 48 0§ .84 ■74464 .87195 .66746 .82443 .1156 •04752 ■8963s .95248 °-s^ 0.75128 9.87580 0.65998 9.81953 '■1383 0.05627 0.87848 9-94373 48=42' .86 ■75784 •1^558 .65244 .81454 .1616 .06504 .86091 .93496 49 16 .87 ■76433 .88328 .64483 .80944 ■■853 .07384 •84365 .92616 49 51 50 25 51 00 .88 ■77074 .88691 ■63715 .80424 .2097 .08266 .82g6§ .91734 .89 ■77707 .89046 .62941 .79894 .2346 •09153 .80998 .90847 0.90 o^78333 9.89394 0.62 1 61 9-79352 1.2602 0. 10043 o^7935S ■77738 9.89957 Si°34' 52 08 •91 .78950 ■8973s •61375 .78799 .2864 •10937 .89063 .92 i^5^ .90070 .60582 ■78234 ■3'33 .11835 .76146 .88165 5243 53 '7 •93 .80162 ■90397 •59783 .77658 ■3409 •12739 ■74578 .87261 ■94 .80756 .90717 .58979 .77070 .3692 .13648 ■73034 .86352 S3 51 °|l 0.81342 9-91031 0.58168 9.76469 1.3984 0.14563 0.7151 1 985437 54°26' .81919 •91339 •57352 .75228 .4284 .15484 .70010 .84516 >;? 00 •98 .82489 .83050 .83603 .91639 •56530 ■4592 .16412 .68531 .83588 ■91934 -55702 ■74587 .4910 ■17347 .67071 .82653 <;6 og •99 .92222 .54869 ■73933 ■5237 .18289 .65631 .81711 5643 » 1. 00 0.84147 ^._. 9.92504 0.54030 9.73264 '■5574 0.19240 0.64209 9.80760 S7°i8' Table 1 2 (cMtinmS). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 37 i.oo .OI .02 ■03 .04 .00 .07 .08 .09 1. 10 .11 .12 •13 .14 LIS .i5 •17 .18 .19 1.20 .21 .22 -23 .24 I.2S .26 •27 .28 .29 J.30 •31 •32 •33 •34 •36 •37 •38 ■39 1.40 .41 .42 ■43 •44 I.4S .46 47 .48 •49 1.50 SINES. Nat. l«g. 0,84147 9.92504 .84683 .92780 .85211 .93049 ■85730 •933' 3 .86240 .93571 0.86742 9.93823 .87236 .94069 .87720 .94310 .88196 .94545 .88663 ^94774 0.89121 9.94998 .89570 .95216 .90010 .95429 .90441 .95637 .90863 .95839 0.91276 .91680 .92075 .92461 .92837 0.93204 ■93562 .93910 .94249 .94578 0.94898 .95209 .95510 .95802 .96084 0.96356 .96618 .96872 .97115 ■97348 0.97572 .97786 •97991 .98185 •98370 0.98545 .98710 .98865 .99010 .99146 0.99271 ■99387 .99492 .99588 .99674 9.96036 .96228 .96414 .96596 .96772 9-96943 .97110 .97271 .97428 ■97579 9.97726 .97868 .98005 ■98137 .9S265 9.98388 .98506 .98620 ■98729 ■98833 9-98933 .99028 .99119 .99205 .99286 9^99363 .99436 .99504 .99568 .99627 9.99682 ■99733 .99779 .99821 .9985S COSINES. Nat. Log. 0.54030 .53186 •52337 .51482 .50622 9.73264 .72580 .71881 .71165 ■70434 0-49757 9.69686 .48887 .68920 .48012 .68135 •47133 -67332 .46249 .66510 0.45360 9.65667 .44466 .64803 .43568 .63917 .42666 .63008 .41759 .62075 0.40849 9.61 1 18 •39934 •60134 •39015 •59123 .38092 .58084 .37166 .57015 0.99749 9^9989i 0.36236 •35302 •34365 •33424 .32480 0-31532 •30582 .29628 .28672 .27712 0.26750 .25785 .24818 .23848 .22875 0.21901 .20924 •1994s .18964 .17981 0.16997 .16010 .15023 •14033 .13042 0.12050 .11057 .10063 .09067 .08071 9-55914 .54780 .53611 .52406 .51161 9.49875 .48546 •47170 •45745 .44267 9.42732 •4"37 .39476 •37744 •35937 9.34046 .32064 .29983 •27793 .25482 9.23036 .20440 .17674 .14716 .11536 9.08100 •04364 .00271 8.95747 .90692 TANGENTS. Nat. Log- 0.07074 8.84965 1.5574 0.19240 .5922 .20200 .6281 .21 169 .6652 .22148 .7036 .23137 •■7433 ■7844 .8270 .8712 .9171 1.9648 2.0143 .0660 ■"97 ■1759 2-2345 .2958 .3600 •4273 ■4979 2.5722 .6503 •7328 .8198 .9119 3.0096 .2236 •3413 •4672 3.6021 •7471 ■9033 4-0723 .2556 4-4552 •6734 -9131 S-1774 •4707 S-7979 6.1654 6.581 1 7-0555 7.6018 8.2381 8.9886 9.8874 10.983 12.350 0.24138 .25150 •26175 .27212 .28264 0.29331 •30413 .31512 .32628 •33763 0.34918 •36093 •37291 .38512 ■39757 0.41030 •42330 .43660 .45022 .46418 0.47850 •49322 •50835 .52392 •53998 0.55656 •57369 .59144 .60984 .62896 0.64887 .66964 .69135 .71411 .73804 0.76327 .78996 .81830 ■84853 .88092 0.91583 ■95369 .99508 1.04074 .09166 COTANGENTS. Nat. Log. 0.64209 9.80760 .62806 .79800 .61420 .78831 .60051 .77852 .58699 .76863 14.101 I.I 0.57362 .56040 •54734 •53441 .52162 0.50897 .49644 .48404 ■47175 ■45959 0.447 S3 43558 ■42373 .41199 .40034 0.38878 •3773' •36593 •35463 •3434' 0.33227 .32121 .31021 .29928 0.27762 .26687 .25619 •24556 •23498 0.22446 .21398 ■20354 ■'93'S ■18279 0.17248 .16220 •i5'95 •14173 ■i3'5S 0.12139 .11125 .10114 .09105 .08097 9.75862 .74850 ■73825 .72788 •71736 9.70669 •69587 .68488 ■67372 .66237 9.65082 .63907 .62709 .61488 .60243 9.58970 .57670 .56340 .54978 ■53582 9.52150 .50678 .49165 .47608 .46002 9-44344 .42631 .40856 .39016 -37104 9-35"3 •33036 .30865 .28589 .26196 9-23673 .21004 .18170 •i5'47 .11908 9.08417 .04631 .00492 8.95926 ■90834 O P 0.07091 8.85074 S7->i8' 57 52 5827 5901 59 35 60° 10' 60 44 61 18 61 53 62 27 63°02' 6336 64 10 6445 65 19 65°S3' 6628 67 02 6737 68 II 68°45' 6g 20 6954 70 28 7' 03 7i°37' 72 12 72 46 73 20 73 55 74°29' 7503 7538 76 12 7647 77=21' 77 55 78 30 7904 7938 8o°i3' 8047 81 22 81 56 82 30 83=05' 8339 84 13 8448 85 22 85°S7' Smithsonian Tables. 38 Tables 1 2 {.cmtinued) and 1 2a. CIRCULAR FUNCTIONS AND FACTORIALS. TABLE 12 (continued).— Vamiai (Tilgonomttilc) Fnncttons. •A S < SINES. COSINES. TANGENTS. COTANGENTS. M M Q Nat. Log. Nat. Log. Nat. Log. Nat. Log. 1.50 •SI •52 •S3 •S4 0.99749 .99815 •99871 .99917 •999S3 9.99891 .99920 .99944 •99964 .99979 0.07074 .06076 .05077 .04079 .03079 8.84965 •78361 •70565 .61050 •48843 14.IOI 16.428 19.670 24.498 32.461 1. 1 4926 .21559 •29379 •38914 .51136 .05084 .04082 .03081 8.85074 .78441 .70621 .61086 .48864 85°57' 8631 8705 87 40 88 14 '•SS •S6 :s^^ •S9 0-99978 0.99994 I -00000 0.99996 0.99982 9-99991 9-99997 0-00000 9.99998 9-99992 0.02079 .01080 .00080 -.00920 -.01920 8.31796 8.03327 6.90109 7.9639611 8.2833611 48.078 92.621 1255.8 108.65 52.067 1. 68195 1.96671 3.09891 2.03603 1.71656 0.02080 .01080 .00080 -.00920 -.01921 8.31805 8.03330 6.90109 7.9639711 8.2834411 88049' 8923 89 S7 9032 91 06 1.60 0-99957 9.99981 -0.02920 8.4653811 34-233 I -53444 -0.02921 8.46556n 9i°40' 90°= 1. 570 7963 radians. TABLE 12a.— Factorials. Logarithms of the products 1.2.3 "> " itoai i to 100. See Table 30 for log. X (« + 1), values of « between i and 2. ». log.(>..0 .. log.(n.') n^ log.(«.0 „. \os,.(n!) 1 0.000000 26 26.605619 51 66.190645 76 111.275425 2 0.301029 27 28.036982 52 67.906648 77 1 13.161916 3 0-778151 28 29.484140 S3 69-630924 78 115.054010 4 1. 3802 1 1 29 30.946538 S4 71-363318 79 116.951637 S 2.079181 30 32.423660 55 73.103680 80 118.854727 6 2-857332 31 33.915021 56 74.851868 81 120.763212 7 3^702430 32 35.420171 57 76-607743 82 122.677026 8 4.605520 33 36-938685 58 78.371171 83 124.596104 9 S-SS9763 34 38.470164 80.142023 84 128.449802 lO 6-559763 35 40.014232 bo 81.920174 85 11 7.601155 36 41-570535 61 83.705504 86 130-384301 12 8-680336 37 43-138736 62 85-497896 «7 132.323820 134-268303 13 9-794280 38 44.718520 63 87-297236 88 14 10.940408 .39 46.309585 64 89.103416 89 136.217693 IS 12.116499 40 47.911645 65 90.916330 90 I38^i7i935 16 13-320619 41 49-524428 66 92^735874 91 140.130977 17 14.551068 42 51-147678 % 94.561948 92 142.094765 18 15.806341 43 52.781146 68 96-394457 93 144063247 19 17.085094 44 54.424599 69 98-233306 100.078405 94 146.036375 20 18.386124 45 56.077811 70 95 148.014099 21 19.708343 46 57.740569 71 101.929663 96 149^996370 22 21-050766 '^^ 59.412667 72 103.786995 97 151.983142 23 22.412494 48 61.093908 73 105.650318 98 153-974368 24 23-792705 49 62.784104 74 107.519550 99 155.970003 25 25.190645 50 64.483074 75 109.394611 100 157.970003 Smithsonian Tables. Table 13. HYPERBOLIC FUNCTIONS.* Hjrperbollo sines. Values at «' — «"' , 39 as 1 2 3 4 5 6 7 8 9 0-0 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0701 0.0801 0.0901 O.I .1002 .1102 .i2o;5 .1304 .1405 .1506 .1607 .1708 .1810 .1911 0.2 .2013 .2115 .2218 .2320 .2423 •2526 -2629 ■2733 •2837 •2941 o-S ■3045 .4108 •3150 •3255 •3360 .3466 •3572 .3678 •3785 .4986 .4000 0.4 .4216 •4325 .4434 •4543 ■4653 .4764 .4875 .5098 0.S 0.5211 0.5324 0.5438 0.5552 0.5666 0.5782 0.5897 0.6014 0.6131 0.6248 0.6 .6367 .6485 .6605 •7838 .6725 .6846 .6967 .7090 •7213 •7336 •7461 0.7 ■If^ .7712 .7966 .8094 •8223 •8353 .8484 •8615 .8748 0.8 .8881 ■9015 ■9150 .9286 .9423 .956' .9700 .9840 .9981 .0122 0-9 1.0265 1.0409 1-0554 1.0700 1.0847 1-0995 1.1144 1.1294 1. 1446 1.1598 1.0 1.1752 1.1907 1.2063 1.2220 1-2379 '-2539 1.2700 1.2862 1.3025 1.3190 I.I •3356 •3524 •3693 •3863 -4035 .4208 •4382 •4558 •4735 ■49' 4 1.2 •5°95 .5276 .5460 .5645 •5831 .6019 .6209 .6400 •6593 .6788 1-3 .7182 •7381 •7583 •7786 •799' .8198 .8406 .8617 .8829 1.4 •9043 .9259 -9477 •9919 2.0143 2.0369 2.0597 2.0827 2.1059 1.5 2.1293 2.1529 2.1768 2.2008 2.2251 2.2496 2.2743 2.2993 2.3245 2.3499 1.6 •3756 .4015 .4276 .4540 .4806 •5075 •5346 .5620 !88o6 •6175 1-7 .6456 .6740 .7027 .73'7 .7609 .7904 .8202 .8503 .9112 1.8 .9422 •9734 3.0049 30367 3.0689 3-IOI3 3-'340 3.1671 3-2005 3-234' 1.9 3.2682 3-3025 •3372 •3722 •4075 •4432 .4792 •5156 ■5523 •5894 2.0 3-6269 3.6647 3.7028 3-7414 3-7803 3.8196 3-8593 3-8993 3-9398 3.9806 2.1 4.0219 4.0635 4.1056 4.1480 4.1909 4.2342 4.2779 4.3221 4.3666 4.4117 2.2 4.4571 4.5030 4-5494 4.5962 4-6434 4.6912 4-7394 4.7880 4.8372 4.8868 2-3 4-937° 4.9876 5-0387 5-0903 5-1425 5-195' 5-2483 5.3020 5-3562 5-4109 2.4 5.4662 5.5221 5-5785 5-6354 5-6929 5-75'o 5-8097 5.8689 5.9288 5.9892 2.5 6.0502 6.1 1 18 6.1741 6.2369 6.3004 6-3645 6.4293 6.4946 6.5607 6.6274 2.6 6.6947 6.7628 6.8315 6.9009 6.9709 7.0417 7.1132 7.1854 7.9480 2-^583 ?-33'§ 2.7 7.4063 7.4814 7-5572 7-6338 7.7112 7.7894 7-8683 8.0285 8.1098 2.8 8.1919 8.2749 8.3586 8.4432 8.5287 8.6150 8.7021 8.7902 8.8791 8.9689 2.9 9.0596 9-1512 9-2437 9-3371 9-43' 5 9.5268 9.6231 9.7203 9.8185 9-9177 3.0 10.018 10.119 10.221 10.324 11.429 ".534 11.640 11.748 11.856 11.966 3.1 1 1 .076 11.188 11.301 11,415 11.530 12.647 12.764 12.883 12.003 12.124 3.2 12.246 12.369 12.494 12-620 12.747 12.876 13.006 i3-'37 13-269 13-403 14.816 16.378 3-3 13-538 13-674 13.812 13-951 14.092 '4-234 '4-377 14.522 14.668 3-4 14.965 15.116 15.268 15.422 '5-577 '5-734 '5-893 16.053 16.214 3.5 16-543 16.709 16.877 17-047 17.219 17-392 17-567 '7.744 '7-923 18.103 3-6 18.285 18.470 18.655 18.843 '9-033 19.224 19.418 19.613 19.811 20.010 20.211 20.415 20.620 20.828 21.037 21.249 21.463 21.679 21.897 22.117 3-8 3-9 22.339 22.564 22.791 23.020 23.252 23.486 23.722 23.961 24.202 24.445 24.691 24.939 25.190 25.444 25.700 25-958 26.219 26.483 26.749 27.018 4.0 27.290 27.564 27.842 28.122 28.404 28.690 28-979 29.270 29-564 29.862 4.1 4.2 30.162 33-336 30.465 33-671 30.772 34-009 31.081 34-351 3'-393 34-697 3' -709 35.046 32.028 35-398 32.350 35-754 . 32-675 36-113 36.476 4.3 4.4 36.843 40.719 37-214 41.129 37-588 41-542 37.966 41.960 38-347 42-382 42.808 39.122 43-238 39-5' 5 43-673 39-9' 3 44.112 40.314 44.555 4.5 4.6 4.7 4.8 4-9 45.003 49-737 54-969 60.751 67.141 45-455 50-237 61.362 45.912 50.742 56.080 61.979 46-374 51.252 56.643 62.601 46.840 51.767 57-213 63.23' 47-3'' C2.288 57-7S8 63-866 47-787 52.813 64.508 48.267 53-344 58-955 65-' 57 53.880 59-548 65.812 49.242 54.422 60.147 66.473 73-465 67.816 68.498 69.186 69.882 70.584 7 '-293 72.010 72.734 * Tables 3S-41 are quoted from " Des Ingenieurs Taschenbuch," herausgegeben vom Akademischen Verein (Hutte). Smithsonian Tables. 40 Table 14. HYPERBOLIC FUNCTIONS. Oommon logailtlumi + 10 ol the hyporlioUc sines. 0.0 O.I 0.2 0-3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1-3 1.4 l.S 1.6 1-7 1.8 1.9 2.0 2.1 2.2 2-3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3-1 3-2 33 34 3.5 3-6 H 3-8 3-9 4.0 4.1 4.2 4-3 4.4 4.5 4.6 4-7 4.8 4.9 9.0007 3039 4836 9.6136 9.7169 8039 8800 9485 10.01 14 10.0701 1257 1788 2300 2797 10.3282 3758 4225 4687 5143 10.5595 6044 6491 6935 7377 10.7818 8257 8696 9134 9571 11.0008 0444 0880 1316 1751 11.2186 2621 3056 3491 3925 11.4360 4795 5229 5664 11.6532 6967 7401 7836 8270 i.0000 0423 3254 4983 6249 7262 8II9 8872 9550 0174 0758 I3II 1840 2351 2846 333° 3805 4272 4733 5640 6089 6535 6979 7421 7862 8301 8740 9178 9615 0051 0488 0923 1359 1794 2230 2665 3099 3534 3969 4403 4838 5273 5707 6141 6576 7010 7445 7879 8313 301 1 0802 3459 5125 6359 7354 8199 8942 9614 0234 0815 1365 1892 2401 2895 3378 3852 43'8 4778 5234 5685 6134 6580 7023 7465 7906 8345 8784 9221 9658 0095 0531 0967 1403 1838 2273 2708 3143 3578 4012 4447 4881 5316 6185 6619 7054 7488 7922 8357 4772 II 52 3656 5264 6468 7444 8277 9012 9678 0294 0871 1419 1944 2451 2944 3426 3899 4364 4824 5279 |739 6178 6624 7067 7509 7950 8389 8827 9265 9702 0139 0575 ion 1446 1881 2317 2752 3186 3621 4056 4490 4925 5359 6228 6663 7097 7966 8400 6022 1475 3844 5398 6574 7533 8354 9082 9742 0353 0927 1472 1995 2501 2993 3474 3946 441 1 4870 5324 5775 6223 6668 7112 7553 7994 8433 8871 9309 9746 0182 0618 1054 1490 1925 2360 2795 3665 4099 4534 4968 5403 5837 6272 6706 7141 7575 8009 8444 6992 1777 4025 5529 6678 7620 8431 9150 9805 0412 0982 1525 2046 2551 3°4i 3521 3992 4457 4915 5370 5820 6268 6713 7156 7597 8038 8477 8915 9353 9789 0226 0662 1098 2404 2839 3273 3708 4H3 4577 5012 5446 5881 6315 6750 7184 7618 8053 8487 7784 2060 4199 5656 6780 7707 8506 9218 0470 1038 1578 2098 2600 3090 3569 4039 4503 4961 5415 5865 6312 6757 7200 7642 8082 8521 8959 9396 9833 0270 0706 1141 "577 2012 2447 2882 3317 3752 4186 4621 505s 5490 5924 6359 6793 7227 7662 8096 8530 845s 4366 5781 6880 7791 8581 9286 993° 0529 1093 1631 2148 2650 3138 3616 4086 4549 5007 5460 5910 6802 7244 7686 8126 8564 9003 9440 9877 °3i3 0749 1185 1620 2056 2491 2925 3360 3795 4230 4664 S°99 \^ 6402 6836 7271 7705 8140 8574 9036 2576 4528 5902 6978 7875 8655 9353 9992 0586 1 148 1684 2199 2699 3186 3663 4132 4595 5052 5505 5955 6401 6846 7289 7730 8169 8608 9046 9484 9920 0357 0793 1228 1664 2099 2534 2969 3404 3838 4273 4708 5142 5577 6011 6446 6880 7314 7749 8183 8617 9548 2814 4685 6020 7074 7958 8728 2412 0053 0044 1203 1736 2250 2748 3234 37" 4179 4641 5098 555° 6446 6890 7333 7774 8213 8652 9090 9527 9964 0400 0836 1272 1707 2143 2578 3012 3447 3882 4317 4751 5ii6 5620 6055 6489 6923 7358 7792 8226 8661 Smithsonian Tables. Table 15. HYPERBOLIC FUNCTIONS HypeTboUo ooslnes. 41 Valnes 01 "' + ""' 0.0 0.1 0.2 0-3 0.4 O.S 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1-3 1.4 1.5 1.6 17 1.8 1.9 2.0 2.1 2.2 2-3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3-1 3-2 3-3 3-4 3.5 3-6 H 3-8 3-9 4.0 4.1 4.2 4-3 4.4 4.5 4.6 4-7 4.8 4-9 1. 0000 .0050 .0201 •04S3 .0811 1. 1276 .1855 .2552 •3374 •4331 I-S43I .6685 .8107 .9709 2.1509 2-3524 .8283 3-I07S ■4177 3.7622 4-1443 4.5679 S-°372 5-5569 6.1323 6.7690 7-4735 8.2527 9.1 146 10.068 II. 121 12.287 13-575 14.999 16-573 18.313 20.236 22.362 24.711 27.308 30.178 33-351 36-857 40-732 45.014 49-747 54-978 60.759 67.149 1. 0001 .0061 .0221 .0484 .0852 1.1329 .1919 .2628 -3464 4434 1-5549 .6820 •8258 .9880 .1700 2-3738 .6013 •8549 3-1371 .4506 3-7987 4.1847 4.6127 5.0868 5.6119 6.1931 6.8363 7-5479 8.3351 9.2056 10.168 12.233 12.410 13-7" 15.149 16-739 18.497 20.439 22.586 24-959 27.582 30.482 33-686 37-227 41. 141 45.466 50.247 55-531 61.370 67.823 1.0002 .0072 .0243 .0516 .0895 1-1383 .1984 .2706 -3555 ■4539 1.5669 .6956 .8412 2.0053 .1894 2-3955 .6255 .8818 3.1669 .4838 3-8355 4.2256 4.6580 5-1370 5.6674 6.2545 6.9043 7.6231 8.4182 9.2976 10.270 11-345 12-534 13.848 15.301 16.907 18.682 20.644 22.813 25.210 27.860 30.788 34.024 37.601 41-554 45-923 50.752 56.089 61.987 68.505 1.0005 .0085 .0266 -0549 -0939 1.1438 •2051 .2785 •3647 -4645 1.5790 •7093 .8568 2.0228 .2090 2.4174 -6499 .9090 3-1972 -5173 3.8727 4.2668 4-7037 5.1876 S-7235 6.3166 6.9729 7.6990 8.5022 93905 10.373 11.459 12.660 13-987 15-455 17.077 18.870 20.852 23.042 25.463 28.139 31-097 34-366 37-979 41.972 46.385 51.262 56.652 62.609 69-193 1.0008 .0098 .0289 .0584 .0984 1.1494 .2119 .2865 •3740 -4753 1-5913 -7233 .8725 2.0404 .2288 2-4395 .6746 •9364 3.2277 -5512 3-9103 4-3085 4.7499 5.2388 5.7801 6-3793 7.0423 7-7758 8.5871 9-4844 10.476 11.574 I2'.786 14.127 15.610 17.248 19.059 21.061 23-273 25.719 28.422 31-409 34-7" 38-360 42-393 46.851 51-777 57.221 63.239 69.889 1.0013 -01 1 3 .0314 .0619 .1030 '•'551 .2188 .2947 •3835 .4862 1.6038 •7374 2.0583 .2488 2.4619 .6995 .9642 3-2585 -5855 3-9483 4-3507 4.7966 5-2905 5-8373 6.4426 7.1123 7-8533 8.6728 95791 10.581 11.689 12.915 14.269 15.766 17.421 19.250 21.272 23-507 25-977 28.707 31-725 35.060 38-746 42.819 47-321 52.297 57-796 63-874 70.591 1.0018 .0128 •0340 .0655 .1077 1. 1609 .2258 •3030 •3932 •4973 .6164 •7517 •9045 2.0764 .2691 2.4845 .7247 .9922 3-2897 .6201 3-9867 4-3932 4-8437 5-3427 5-8951 6.5066 7.1831 7-9316 8.7594 9.6749 10.687 11.806 13044 14.412 15.924 17.596 19.444 21.486 23-743 26.238 28.996 32.044 35-412 39-135 43-250 47-797 52.823 58-377 64.516 71.300 1.0025 .0145 .0367 .0692 .1125 1. 1669 -2330 -3"4 .4029 .5085 1.6292 .7662 .9208 2.0947 .2896 2.5073 .7502 3.0206 .3212 -6551 4-0255 4.4362 4.8914 5-3954 5-9535 6.5712 7.2546 8.oio6 8.8469 9.7716 10.794 11.925 13-175 14.556 16.084 17.772 19-639 21.702 23.982 26.502 29.287 35.768 39-528 43.684 48.277 53-354 58.964 65.164 72.017 1 .0032 .0162 -0395 -0731 .1174 1.1730 .2402 -3199 .4128 .5199 1.6421 .7808 -9373 2.1132 -3103 2-5305 .7760 3.0492 -3530 .6904 4.0647 4-4797 4-9395 5.4487 6.0125 6.6365 7.3268 8.0905 8.9352 9.8693 10.902 12.044 13-307 14.702 16.245 17.951 19-836 21.919 24.222 26.768 29.581 32.691 36.127 39-925 44-123 48.762 53-890 59-556 65.819 72.741 1. 0041 .0181 .0423 -0770 .1225 1. 1792 .2476 .3286 .4229 -5314 1.6552 .7956 -9540 2.1320 -3312 2-5538 .8020 3.0782 ■3852 .7261 4.1043 4-5236 4-98 , 5.5026 6.0721 6.7024 7-3998 8.1712 9.0244 9.9680 U.OII 12.165 13-440 14.850 16.408 18.131 20.035 22.139 24.466 27.037 29.878 33019 36.490 40.326 44.566 49-252 54-43" 60.155 66.481 73-472 Smithsonian Tables. 42 Table 16. HYPERBOLIC FUNCTIONS. Common logailtlims at tlie bypeiboUc cosines. ac 1 2 3 4 5 6 7 8 9 0.0 0.0000 0000 0001 0002 0003 0005 0008 001 1 0014 0018 0078 O.I 0022 0026 0031 0037 0042 0049 0055 0062 0070 0.2 0086 0095 0104 01 14 0124 0134 0145 0156 0168 0180 0-3 0.4 0193 0205 0219 0232 0246 0261 0276 0291 0306 0322 0339 0355 0372 0390 0407 0426 0444 0463 0482 0502 0.5 0.0522 0542 0562 0583 0605 0626 0648 0670 0693 0716 0.6 0739 0762 0786 0810 0835 0859 0884 0910 0935 0961 0.7 0987 1013 1040 1067 1122 1149 1177 1206 1234 0.8 1263 1292 1321 135° 1380 1410 1440 1470 1501 1532 0.9 1563 1594 1625 1657 1689 1721 1753 1785 1818 1851 1.0 0.1884 1917 1950 1984 2018 2051 2086 2120 2154 2189 I.I 2223 2258 2293 2328 2364 2399 2435 2470 2506 2542 1.2 2578 2615 2651 2688 2724 2761 2798 283s 2872 ^999 1-3 2947 2984 3022 3059 3°97 313s 3173 3211 3249 ^f\ 1.4 3326 3365 3403 3442 3481 3520 3559 3598 3637 3676 1.5 0.37 IS 3754 3794 3833 3873 3913 3952 3992 4032 4072 1.6 41 1 2 4152 4192 4232 4273 4313 4353 4394 4434 "^iP 1.7 4515 4556 4597 4637 4678 4719 4760 4801 4842 4883 1.8 4924 4965 5006 5048 5089 5130 5172 5213 5254 5296 1.9 5337 5379 5421 5462 5504 5545 5587 5629 5671 5713 2.0 0.5754 5796 5838 5880 5922 5964 6006 6048 6090 6132 2.1 6175 6217 6259 6301 6343 6809 6428 6470 6512 6555 2.2 6597 6640 6682 6724 6767 6852 6894 6937 6979 2-3 7022 7064 7107 7150 7192 7235 7278 7320 7363 7406 2.4 7448 7491 7534 7577 7619 7662 7705 7748 7791 7833 2.5 0.7876 7919 7962 8005 8048 8091 8134 8176 8219 8262 2.6 8305 8348 IfA 8434 8477 8520 8563 8606 8649 8692 2.7 8735 8778 8864 8951 8994 9037 9080 9123 2.8 9166 9209 9252 9295 9338 P13 9425 9468 95" 9554 2.9 9597 9641 9684 9727 9770 9856 9900 9943 9986 3.0 1.0029 0073 0116 0159 0202 0245 0289 0332 0375 0418 3-1 0462 0505 0548 0591 0635. 0678 0721 0764 0808 0851 3-2 0894 0938 0981 1024 1067 mi IIS4 1 197 1 241 1284 3-3 1327 1804 1414 1457 1 501 1544 1587 1631 1674 1717 3-4 1761 1847 1891 1934 1977 2021 2064 2107 2151 3.5 1.2194 2237 2281 2324 2367 241 1 2454 2497 2541 2584 3-6 2628 2671 2714 2758 2801 2844 2888 2931 2974 3018 3-7 3061 3105 3148 3191 3235 3278 3322 3365 3408 3452 3886 3-8 3495 3538 3582 3625 3669 3712 3755 4189 3799 3842 3-9 3929 3972 4016 4059 4103 4146 4233 4278 4320 4.0 14363 4406 4450 4493 4537 4580 4623 4667 4710 fAi 4.1 4797 4840 4884 4927 4971 5014 5057 5101 5144 4.2 5231 5274 5318 5361 5405 ^if 5492 5535 5578 5622 4-3 5665 5709 m 5795 5839 5882 5920 5969 60I2 6056 4.4 6099 6143 6230 6273 6316 0360 6403 6447 6490 4.5 6968 6577 6620 6664 6707 6751 7185 6794 6837 6881 6924 4.6 701 1 7055 7098 7141 7228 7272 7315 7358 4-7 7402 7445 7489 7532 7576 7619 7662 7706 7749 7793 4.8 7836 7923 7966 8010 8053 8097 8140 8184 8227 4.9 8270 8314 8357 8401 8444 8487 8531 8574 8618 866i Smithsonian Tables. Table 1 7. EXPONENTIAL FUNCTIONS. 43 Values of e* and e-* intermediate to those here given may be found by adding or subtracting the values of the hyperbolic cosine and sine given in Tables 15 and 13. logii,(e«) e-' logio(e') 0.0 .1 .2 •3 •4 OS .6 •7 .8 1.0 •3 •4 1.5 .6 ■7 .8 •9 2.0 .1 .2 •3 ■4 2.5 .6 •7 3.0 .1 .2 ■3 •4 3.5 .6 •7 .8 •9 4.0 .1 .2 •3 •4 4.5 .6 ■7 .8 •9 5.0 •04343 .08686 .13029 ■17372 0.21715 .26058 .30401 •34744 .39087 0.43429 •47772 .52115 .56458 .60801 0.65144 .69487 •73830 •78173 .82516 0.86859 .91202 •95545 1. 04231 1.08574 .12917 .17260 .21602 •25945 1.30288 •34631 •38974 .47660 1.52003 .56346 .65032 •6937 s '•737I8 .78061 .82404 .86747 .91090 '•95433 •99775 2.041 18 .08461 .12804 2.17147 1. 0000 .1052 .2214 •3499 .49:8 1.6487 .8221 2.0138 .2255 .4596 2.7183 3.0042 .3201 .6693 4.0552 4.4817 •9530 5^4739 6.0496 6.6859 7^389i 8.1662 9.02 50 9.9742 11.023 12.182 13-464 14.880 16.445 18.174 20.086 22.198 24-533 27.113 29.964 33-"5 36-598 40.447 44.701 49.402 54-598 60.340 66.686 73.700 81.451 90.017 99-484 109.95 121.51 134^29 148.41 1. 000000 0.904837 .818731 .740818 .670320 0.606531 .548812 •496585 •449329 .406570 0.367879 .332871 .301194 .272532 .246597 0.223130 .201897 .182684 .165299 .149569 0-135335 .122456 .110803 .100259 .090718 0.082085 .074274 .067206 .060810 •055023 0.049787 .045049 .040762 .036883 •033373 0.030197 .027324 .024724 .022371 .020242 0.018316 .016573 .014996 .013569 .012277 0.011109 .010052 .009095 .008230 •007447 0.006738 5.0 .1 .2 •3 •4 5.5 .6 •7 .8 •9 6.0 .1 .2 •3 •4 6.5 .6 •7 7.0 .1 .2 •3 •4 7.5 .6 •7 .8 •9 8.0 .1 .2 •3 •4 8.5 .6 •7 9.0 .1 .2 •3 •4 9.5 .6 •7 .8 •9 10.0 2.17147 .21490 •25833 .30176 •34519 2.38862 •43205 •47548 .51891 .56234 2.60577 .64920 .69263 .73606 •77948 2.82291 .86634 .90977 •95320 .99663 3.04006 .08349 .12692 •17035 •21378 3.25721 .30064 •34407 •38750 •43093 3-47436 •51779 .56121 .60464 .64807 3.69150 •73493 .77836 .82179 .86522 3.90865 .95208 -99551 4-03894 .08237 4.12580 .16923 .21266 .25609 .29952 4.34294 148.41 164.02 181.27 200.34 221.41 244.69 270.43 298.87 330-30 365.04 403-43 445.86 492.75 544-57 601.85 665.14 735-10 812.41 897.85 992.27 1096.6 1212.0 1339-4 1480.3 1636.0 1808.0 1998.2 2208.3 2440.6 2697.3 3294-5 3641.0 4023.9 4447.1 4914.8 543'^7 6002.9 6634.2 7332.0 8103.1 8955-3 9897.1 10938. 12088. 1 3360. 14765^ 16318. 18034. 19930. 22026. 0.006738 .006097 •005517 .004992 .004517 0.004087 .003698 .003346 .003028 •002739 0.002479 .002243 .002029 .001836 .001662 o.ooi 503 .001360 .001231 .001114 .001008 0.000912 .000825 .000747 .000676 .000611 0.000553 .000500 .000453 .000410 .000371 0.000335 .000304 .000275 .000249 .000225 0.000203 .000184 .000167 .000151 .000136 0.000123 .0001 1 2 .000101 .000091 .000083 0.000075 .000068 .000061 .000055 .000050 0.000045 Taken from Glauber's ■Tables of geExg«^^^^^ volume also contains a ' Table of the l^escenams j-*f Newman. Trans. Cambridge Phil. Soc vol xiii. .883. ™5 Twelve or Fourteen Places of Decimals,' by F. W. 44 Table 18. EXPONENTIAL FUNCTIONS, LOG e: X log,o(^) X logio(^) 1 X logioM X logio(^) 1 0.0 .1 .2 ■3 •4 4-34294 ■38637 .42980 •47323 .51666 15.0 .1 .2 •3 ■4 6.51442 !6oi28 .64471 .68814 20.0 .1 .2 •3 •4 8.68589 .72932 •77275 .81618 .85961 25.0 .1 .2 •3 •4 10.85736 .90079 .94422 II.03108 ■I •9 4.56009 .60352 .64695 .69038 •73381 15^5 •9 6.73156 ■77499 .81842 .86185 .90528 20.5 •9 8.90304 .94647 .98990 9-03333 .07675 ■I •9 11-07451 .11794 .16137 .20480 .24823 II.O .1 .2 •3 •4 4-77724 .82067 .86410 •90753 .95096 16.0 .1 .2 •3 •4 6.94871 .99214 7^03557 .07900 .12243 21.0 .1 .2 •3 •4 9. 1 201 8 .16361 .20704 •25047 .29390 26.0 .1 .2 •3 •4 11.29166 •33509 •37852 .42194 •46537 11.5 •7 .8 •9 4-99439 5.03782 .08125 .12467 .16810 16.5 •9 7.16586 .20929 .25272 .29615 •33958 21.5 •9 9^33733 .38076 .42419 .46762 .51105 26.5 •7 .8 •9 11.50880 .55223 .59566 .63909 .68252 12.0 .1 .2 ■3 •4 5-2 "S3 .25496 •29839 .34182 •38525 17.0 .1 .2 ■3 ■4 7-38301 .42644 .46987 •S'329 -55672 22.0 .1 .2 •3 •4 9.55448 •59791 .64134 .68477 .72820 27.0 .1 .2 •3 •4 11-72595 ■76938 .81281 .85624 •89967 12.5 •9 5.42868 .472 u •51554 •55897 .60240 17-5 •7 .8 •9 7.60015 •64358 .68701 •73°44 •77387 22.5 •9 .85848 .90191 ■94534 27.5 •7 .8 •9 1 1. 943 10 .98653 12.02996 ■07339 .11682 13.0 .1 .2 •3 •4 5.64583 .68926 •73269 .77612 .81955 18.0 .1 .2 •3 ■4 7.81730 ■86073 .90416 ■94759 .99102 23.0 .1 .2 •3 •4 9-98877 10.03220 •07563 .11906 .16249 28.0 .1 .2 . ^3 •4 12.16025 .20367 .24710 •29053 •33396 •9 5.86298 .90640 •94983 S-99326 6.03669 18.5 l ■9 8.03445 .07788 .12131 .16474 .20817 23^S •7 .8 ■9 10.20592 ■24935 .29278 .33621 •37964 1 •9 12.37739 .42082 .46425 .50768 .55111 14.0 .1 .2 •3 •4 6.08012 ■12355 .21041 •25384 19.0 .1 .2 ■3 •4 8.25160 .29502 •33845 .38188 •42531 24.0 .1 .2 ■3 ■4 10.42307 .46650 •50993 •55336 •59679 29.0 .1 .2 •3 •4 12.59454 •63797 .68140 ■72483 .76826 14.5 •7 .8 ■9 6.29727 .34070 •38413 .42756 .47099 ■I ■9 8.46874 .51217 •55560 •59903 .64246 24.5 •7 .8 ■9 10.64021 .68364 •72707 •77050 •81393 29.5 •9 12.81169 .85512 •89855 .94198 .98541 15.0 6.51442 20.0 8.68589 25.0 10.85736 30.0 13.02883 Smithsonian Tables. Table 19. EXPONENTIAL FUNCTIONS. Value of e«' and e-^' anA tlieli logaxltluui. 45 The equation to the probability curve Isjf = e-'^t where jv may have any value, positive or negative, between zero and infiuity. X ^:r» log^j^ e-x' log e-J'' 0.1 I.OIOI 0.00434 0.99005 T.99566 2 1.0408 01737 96079 98263 3 1.0904 03909 91393 96091 4 I-I73S 06949 85214 93051 S 1.2840 10857 77880 89143 0.6 1-4333 0-15635 0.69768 T.84365 7 1.6323 21280 61263 78720 8 1.896s 27795 52729 72205 9 2.2479 35178 44486 64822 I.O 2.7183 43429 36788 56571 1.1 3-3S3S 0.52550 0.29820 1.47450 2 4.2207 62538 23693 37462 3 5-4195 73396 18452 26604 4 7-°993 85122 14086 14878 S 9.4877 97716 10540 02284 1.6 1.2936 X 10 1.11179 0.77306 X 1 0-1 2.88821 7 1.7993 2551 1 55576 " 74489 8 2-5534 " 407 1 1 39164 59289 9 3.6996 " 56780 27052 " 43220 2.0 5-4598 " 73718 18316 " 26282 2.1 8.2269 " I. 91 524 0.12155 " 2.08476 2 1.2647 X I02 2.10199 79070 X 10-2 3.89801 3 1-9834 " 29742 50418 K^l 4 s 3-1735 " 5.1802 " 50154 71434 31511 ;; 19304 49846 28566 2.6 8.6264 2.93583 0.11592 " „ 3.06417 7 1.4656X108 3.16601 68233 X 10-8 4.83400 8 2.5402 " 40487 39367 " 59513 9 4.4918 " 65242 22263 •' 34758 3-0 8.I03I " 90865 1 2341 " 09135 3.1 1.4913 X 10* 4-17357 0.67055 X 10-* 5.82643 55283 2 2.8001 44718 3ir3 ;; 18644 3 5-3638 " 72947 27053 5.97956 67989 4 1.0482 X 106 5.02044 95402 X I0-' 5 2.0898 320H 47851 " 3.6 4.2507 " 5.62846 0.23526 " 5.37154 9 4.0 8.8205 1.8673 X io« 4.0329 " 8.8861 " 94549 6.27121 60562 94871 "337 '' 53554 X 10-^ 24796 1 1 254 " _°545i 7.72879 39438 05129 4.1 2 3 4 S 1.9976 X 10' 4.5809 " 1.0718 X 108 ^•^601^ 8.0301 1 0.50062 X 10-' 21829 " 93393 X \°''' S.69951 9.96989 2-5583 " 6.2297 " 40796 79447 39088 " 16052 " 59204 20553 4.6 9 5-° 1.5476 X 10' 3.9228 " 1.0143 X 10" 2.6755 :: 7.200s 9.18967 59357 10.00615 42741 85736 0.64614 X lo"-* 98595 X lo-i" T0.81033 TT.99385 57259 14264 Smithsonian Tables. 46 Table 20. EXPONENTIAL FUNCTIONS. Values of e«' ana S * and tlieli logailtliinB, ST TT «■ ir X e*' loge** g— T* log e-^' 1 21933 0.34109 0.45594 T.65891 2 4.8105 .68219 .20788 _-3i78i 3 1. 0551 X 10 1.02328 .94780 X lo-i 2.97672 4 2.3141 -36438 .43214 " .63562 5 S-07S4 " -70547 .19703 " •29453 6 I.I 132 X io2 2.04656 0.89833 X 10-2 3-95344 7 2.4415 .38766 .40958 " .61234 8 S-3S49 " -72875 .18674 " .27125 9 1.1745 X 108 306985 .85144 X 10-8 4.93015 10 2.5760 " .41094 .38820 " .58906 11 5.6498 " 3-75204 0.17700 " 4.24796 12 1.2392 X 10* 4-09313 .80699 X 10-^ 5.90687 13 2.7168 .43422 -36794 -56578 H 5.9610 •77532 .16776 .22468 IS 1.3074 X io5 5.1 1 641 .76487 X 10-5 5.88359 16 2.8675 " 5-45751 0.34873 " 5.54249 17 6.2893 " .79860 .15900 " .20140 i8 1.3794 X 10' 6.13969 .72495 X io-« 7.86031 19 3.0254 " .48079 -33053 .51921 20 6.6356 " .82189 .15070 " .17812 Table 21. EXP( 3NENTIAL FUNCTIONS. Vif V* r Values ol e * ana e * "' and tbelr logaiithms. X log 6' 1 I-S576 °-'§^^^ 0.64203 1.80756 2 2.4260 .38488 .41221 .61512 3 3-7786 •57733 .26465 .42267 4 5-8853 .76977 .16992 .23023 S 9.1666 .96221 .10909 -03779 6 14.277 1.15465 0.070041 2-84535 z 22.238 •34709 .044968 .65291 8 34-636 -53953 -73198 .028871 .46047 9 53-948 .018536 .26802 10 84.027 .92442 .011901 •07558 11 130.87 2.1 1686 0.0076408 3.88314 12 203.85 .30930 .0049057 .69070 13 317-50 .50174 .0031496 .49826 14 494.52 .69418 .0020222 .30582 IS 770.24 .88663 .0012983 -II337 16 ;^ir5 3.07907 0.00083355 4.92093 i^ .27151 -00053517 .72849 2910.4 -46395 .00034360 •53605 19 4533-1 ■65639 .00022060 .34361 20 7060.5 .84883 .00014163 .15117 Smithsonian Tables. Tables 22 and 23. EXPONENTIAL FUNCTIONS AND LEAST SQUARES. 47 TABLB 22. —Exponential FnncUons. Value of e' and r^ and their logarithms. X «« log^ £-' X «• log«« /r-» 1/64 1/32 i/i6 i/io 1/9 1/8 1/7 1/6 1/4 1.0157 ■0317 .0645 .1052 •"75 '•1331 •1536 .1814 .2214 .2840 0.00679 •01357 .02714 •04343 .04825 0.05429 .06204 •07238 .08686 .10857 0.98450 .96923 •93941 .90484 .89484 0.88250 .86688 .84648 •81873 .77880 ■/3 1/2 3/4 1 5/4 3/2 7/4 2 9/4 5/2 1-3956 .6487 2.1170 •7183 3-4903 4.4817 5-7546 7-3891 9-4877 12.1825 0.14476 .21715 •32572 •43429 •54287 0.65144 .76002 .86859 .97716 1.08574 0.71653 .60653 •47237 •36788 .28650 0.22313 •17377 •13535 .10540 .08208 TABLE 23. —Least Sinaies. Values of P = ^ f'"' r<'^^' d(hx). This table gives the value of P, the probability of an observational error having a value posi- tive or negative equal to or less than x when h is the measure of precision, P = _£ /^** r"*'")" \-itJ o dfjix"). For values of the inverse function see the table on Diffusion. hx 0.0 .1 .2 •3 •4 0.5 .6 •7 .8 •9 1.0 .1 .2 •3 •4 1.5 .6 •7 .8 •9 2.0 .1 .2 •3 •4 2.5 .6 •7 .8 •9 3.0 01128 12362 23352 33891 43797 52924 ,61168 68467 74800 ,80188 ,84681 88353 ,91296 ,93606 95385 96728 97721 98441 98952 ,99309 99552 99715 822 99891 99935 99961 99978 99987 '99993 99996 99999 .02256 13476 24430 ■34913 44747 53790 ,61941 69143 80677 ,85084 ,88679 ■91553 93807 95538 I ,97804 98500 99338 ■99572 99728 99831 99897 99938 99963 99979 99993 99996 99999 •03384 14587 25502 ■35928 ,45689 54646 ■62705 ,69810 ■75952 ,81156 ,85478 88997 ,91805 94002 95686 ,96952 97884 ,98558 ■99035 99366 99591 99741 99839 99902 99941 99965 99980 99989 ■99994 ,99997 ,00000 04511 15695 26570 36936 46623 55494 63459 70468 76514 ,81627 85865 ■89308 92051 94191 95830 97059 962 98613 99074 99392 99609 ■99753 ,99846 99906 99944 99967 99994 99997 05637 16800 27633 37938 ■47548 56332 64203 71 1 16 77067 ,82089 ,86244 ,8961 2 ,92290 94376 95970 97162 98038 98667 991 1 1 99418 99626 99764 99854 ,99911 99947 99969 99990 ,99994 ■99997 06762 17901 28690 38933 48466 57162 ,64938 71754 77610 ,82542 ,86614 ,89910 ,92524 94556 ,96105 ,97263 no 98719 99147 99443 99642 99775 99861 ■99915 99950 99971 99983 99991 99995 99997 ,07886 ir 29742 39921 49375 57982 65663 ,72382 78144 ,82987 ,86977 ,90200 ■92751 .94731 96237 ,97360 ,98181 ,98769 ,99182 ,99466 ,99658 99785 ,99867 99920 ,99952 ,99972 ,99984 99991 ■99995 ■99997 8 09008 20094 ■30788 ,40901 50275 58792 ,66378 73001 78669 83423 87333 90484 92973 .94902 96365 ■97455 ,98249 ,98817 ,99216 99489 ■99673 99795 99874 99924 99955 99974 99985 ,99992 ■99995 ■99997 10128 21 1 84 31828 41874 51167 59594 67084 73610 79184 83851 ,87680 90761 93190 95067 96490 97546 98315 98864 .99248 ,99511 99805 ,99880 ,99928 •99957 99975 ,99986 99992 ,99996 99998 10 11246 22270 32863 42839 52050 ,60386 67780 74210 79691 ,84270 ,88021 .91031 93401 95229 9661 1 •97635 98379 ,98909 ,99279 99532 .99702 " 4 99931 99959 99976 99987 99992 99996 Taken from a paper by Dr. James Burgess ' on the Definite Integral ±-f^ ^« ■39649 401 18 .40586 0.8 .41052 .41517 .41979 .42440 .42899 ■43357 •43813 ■"it! .44719 .45169 0.9 .45618 .46064 .46509 .46952 •47393 •47832 48270 48605 •49139 •49570 1.0 .50000 .50428 ■50853 .51277 .51699 .52119 •52537 •51951 •53366 .53778 I.I .54188 •54595 .58558 .55001 .55404 .55806 .56205 .56602 .56998 •57391 .57782 1.2 .58171 .62671 ■59325 •59705 .60083 .60460 ■60833 .61205 •61575 1-3 .61942 .62308 .63032 m% ■63747 .64102 ■64554 .67856 .64804 :^^?: 1.4 .65498 .65841 .66182 .66521 ■67193 .67526 .68184 1.5 .68833 .69155 .69474 .69791 .70106 .70419 .70729 .71038 ■71344 .71648 1.6 ■71949 .72249 .72546 .72841 •73134 •73425 •73714 .74000 .74285 •74567 17 .74847 .75124 ■75400 ■75674 •75945 .78542 .76214 .76481 .76746 .77009 •77270 1.8 .77528 ■77785 ■78039 .78291 .78790 .79036 .79280 •79522 •V^^^l 1.9 .79999 .80235 .80469 .80700 .80930 .81158 •81383 .81607 .81828 .82048 2.0 .82266 .82481 .82695 .82907 .83 1 17 •83324 •83530 •83734 •83936 •84137 2.1 ■8433s ■84531 .84726 .84919 .85109 .85298 .85486 .85671 .85854 .86036 2.2 .86216 .86W .86570 .86745 .86917 .87088 ■lll^^ •f7+^5 .87591 •8775s 2-3 .87918 .88078 ■88237 ■88395 •89879 .88550 .88705 .88857 .89008 ■89157 .89304 2.4 .89450 .89595 •89738 .90019 .90157 .90293 .90428 .90562 .90694 2.5 .90825 .90954 .91082 .91208 •91332 ■91456 .91578 .91698 .91817 •9193s •93038 2.6 .92051 .92166 .92280 .92392 •92503 ■92613 .92721 .92828 •92934 2.7 ■93 141 ■93243 •93344 •93443 •93541 ■93638 •93734 .93828 •93922 .94014 2.8 .94105 .94195 .94284 •94371 .94458 •94543 •95338 .94627 .94711 •94793 •94874 2.9 •94954 ■95033 •95" I .95187 .95263 .95412 .95484 •95557 .95628 1 2 3 4 5 6 7 8 9 3 .95698 .96346 .96910 ■97397 .97817 .98176 .98482 •98743 .98962 .99147 4 .99302 ■99431 •99539 99627 .99700 .99760 .99808 .99848 •99879 .99905 S .99926 ■99943 .99956 .99966 •99974 .99980 ■99985 .99988 .99991 •99993 Table 25. LEAST SQUARES. Valnes ol tlie lactoi 0.6745-v/-^ . \ n— 1 This factor occurs in the equation e, = 0.6745-%/ —^ for the probable error of a single observation, and other yn—i similar equations. n = 1 2 3 4 5 6 7 8 9 00 0.6745 0.4769 0.3894 0.3372 .1803 0.3016 0.2754 0.2549 0.2385 10 0.2248 0.2133 .2029 .1947 .1871 .1742 .1686 .1636 .1590 20 •1547 .1508 .1472 .1438 .1406 •1377 •1349 •1323 .1298 .1275 30 !io8o .1231 .1211 .1192 .1174 .1157 .1140 .1124 .1109 .1094 40 .1066 •1053 .1041 .1029 .1017 .1005 .0994 .0984 .0974 50 0.0964 0.0954 0.0944 0.0935 0.0926 0.0918 0.0909 0.0901 0.0893 0.0886 60 .0878 .0871 .0864 •0857 .0850 .0789 •0843 •0837 .0830 .0824 .0818 70 .0812 .0806 .0800 .0795 .0784 .0778 •0773 .0768 .0763 80 ■0759 •0754 .0749 .0745 .0740 .0736 ■0731 .0727 •0723 .0719 90 •0715 .0711 .0707 .0703 .0699 .0696 .0692 .0688 .0685 .0681 Table 26. LEAST SQUARES. Valnn ol tba laotoi 0.6745-1 / ^ This factor occurs in the equation e„ = 0.6745-^-^^ for the probable error of the arithmetic r 49 n = 1 2 3 4 5 6 7 8 9 00 10 20 30 40 SO 0.07 1 1 .0346 0.0229 .0171 .0136 0.0643 .0329 0.0221 .0167 .0134 0.4769 .0587 .0314 0.0214 .0163 .0131 0-2754 .0540 .0300 0.0208 .0159 .0128 0.1947 .0500 .0287 0.0201 .0155 .0126 0.1508 .0465 .0275 0.0196 .0152 .0124 0.1 231 •0435 •0265 0.0190 .0148 .0122 0.1041 .0409 .0255 0^0185 •0145 .0119 0.0901 .0386 .0245 0.0180 .0142 .0117 0.0795 .0365 .0237 0.0175 .0139 .0115 Table 27. LEAST SQUARES. Values oi the iactor 0.8453-\/ , ^ . .. \ n(»»— 1) This factor occurs in the equation e, =■ 0.845377= for the probable error of a single observation. Vm(k — i) m. = 1 2 3 4 5 6 7 8 9 00 10 20 30 40 SO 0.0891 •0434 0.0287 .0214 .0171 0.0806 .0412 0.0277 .0209 .0167 0.5978 .0736 •0393 0.0268 .0204 .0164 0.3451 .0677 .0376 0.0260 .0199 .0161 0.2440 .0627 .0360 0.0252 .0194 .0158 0.1890 .0583 ■0345 0.0245 .0190 .0155 0.1543 .0546 •0332 0.0238 .0186 .0152 0.1304 •0513 .0319 0.0232 .0182 .0150 0.1 130 •0483 .0307 0.0225 .0178 .0147 0.0996 .0457 .0297 0.0220 .0174 .0145 Table 28. LEAST SQUARES. 1 Values of 0.84S3 rnVn— 1' This table gives the average error of the arithmetic mean when the pr n = 1 2 3 4 5 6 7 8 9 00 10 20 30 40 50 0.0282 .0097 0.0052 .0034 .0024 0.0243 .0090 0.0050 •0033 .0023 0.4227 .0212 .0084 0.0047 .0031 •0023 .0078 0.0045 .0030 .0022 0.1220 .0167 .0073 0.0043 .0029 .0022 0.084s .0151 .0069 0.0041 .0028 .0021 0.0630 .0136 .0065 0.0040 .0027 .0020 0.0493 .0124 .0061 0.0038 .0027 .0020 0.0399 .0114 .0058 0.0037 .0026 .0019 0.0332 .0105 .0055 0.0035 .0025 .0019 Smithsonian Tables. 50 Table 29. DIFFUSION. 2 pi r^ da. Inverse* values of v fc — '^~^j„ log X = log [2q) + \o%\/kt. t expressed in seconds. ^ log S + logv'^'- t expressed in days. = log 7 + log \/kt. " " years. J k = coefficient of diffusion, t c ^ initial concentration. V = concentration at distance x, time t. vie \ogiq iq log J < logy y 0.00 + 00 + 00 +00 + 00 00 00 .oi 0-56143 3.6428 3.02970 1070.78 4.31098 20463. .02 .51719 3.2900 2^98545 967.04 .26674 18481. ■03 .48699 3.0690 •95525 902.90 .23654 17240. .04 .46306 2.9044 ■93132 853^73 .21261 16316. 0.05 0.44276 2.7718 2.91 102 814.74 4.I923I i557i^ .06 .42486 2.6598 .89311 781-83 .17440 14942. -07 .40865 2.5624 .87691 753-20 .15820 I439^ 13908. .08 •39372 2.4758 .86198 727-75 ■14327 .09 ■yi9Ti 2-3977 .84804 704.76 •12933 13469. 0.10 0.36664 2.3262 2.83490 683.75 4.I1619 13067. .11 -35414 2.2602 .82240 664.36 .10369 12697. .12 .34218 2.1988 .81044 646.31 •09173 12352. •13 -33067 2.1413 •79893 629.40 .08022 12029. .14 -31954 2.0871 .78780 613-47 .06909 1 1724. 0.15 0.30874 2-0358 1.9S71 2.77699 598-40 4.05828 11436. .16 .29821 .76647 584.08 .04776 1 1 162. •'? .28793 1.9406 .75619 570.41 .03748 10901. .18 .27786 1. 8961 .74612 557-34 .02741 10652. .19 .26798 1-8534 .73624 544-80 •01753 10412. 0.20 0.25825 1.8124 2.72651 532.73 4.00780 10181. .21 .24866 1.7728 .71692 521.10 3.99821 9958.9 .22 .23919 1-7346 •70745 509.86 ■98874 9744-1 •23 .22983 1.6976 498.98 •97937 9536-2 .24 .22055 1.6617 .68880 488.43 .97010 9334-6 0.25 0.2 1 1 34 1.6268 2.67960 478.19 3.96089 91389 .26 .20220 1-5930 .67046 468.23 •95175 8948.5 •27 .19312 1.5600 .66137 458-53 .94266 8763.2 .28 .18407 1.5278 •65232 449.08 •93361 8582.5 .29 •1750S 1.4964 •64331 439-85 .92460 8406.2 0.30 0.16606 1.4657 2.63431 430.84 3.91560 82339 -31 .15708 1-4357 •62533 422.02 .90662 8065.4 ■32 .14810 1.4064 .61636 413-39 .89765 7900.4 -33 .13912 1-3776 .60738 404.93 .88867 7738-8 ■34 .13014 1-3494 .59840 396.64 .87969 7580-3 0.35 0.12114 1.3217 2.58939 388.50 3.87068 7424.8 -36 .II2tI 1.2945 •58037 380.51 .86166 7272.0 •32 .10305 1.2678 •57I3I 372.66 .85260 7122.0 •38 .09396 1.2415 .56222 364-93 •84351 6974.4 -39 .08482 I.2IS7 ■55308 357-34 ■83437 6829.2 0.40 0.07563 1.1902 2.54389 349.86 3.82518 6686.2 .41 .06639 1. 1652 •53464 342.49 •81593 6545-4 .42 .05708 1.1405 •52533 335-22 328.06 .80662 6406.6 •43 .04770 1.1161 •51595 •79724 6269.7 ■44 •03824 1.0920 •50650 320.99 •78779 6134.6 0.45 0.02870 1.0683 2.49696 314.02 3-77825 6001.3 .46 .01907 1.0449 •48733 307-13 .76862 5869-7 '\ .00934 '■°^oL .47760 300.33 •75889 5739-7 .48 9-9995' 0.99886 .46776 293.60 .74905 5611.2 -49 .98956 0.97624 .45782 286.96 -739" 5484.1 0.50 9.97949 0.95387 2.44775 280.38 3.72904 5358.4 • Kelvin, Mathematical and Physical Papers, vol. III. p. 428 ; Becker, Am. Jour, o£ Sci. vol. III. 1897, p. 280. t For direct values see table aj Taken from unpublished manuscript o£ C. E. Van Orstrand. Smithsonian Tables Table 29 (coHtmmd). 51 DIFFUSION. vie log 2? tq logi s logY V 0.50 9^97949 o^95387 2^44775 280.38 3.72904 5358.4 •SI .96929 •93174 •43755 273-87 .71884 5234^1 .52 .95896 .42722 267^43 .70851 5111.0 •S3 .94848 .88813 .41674 261.06 .69803 4989.1 •54 •93784 .86665 .40610 254^74 •68739 4868.4 0.S5 9.92704 0.84536 ^•39530 248.48 3-67659 4748.9 •S6 .91607 .82426 •38432 242.28 .66561 463o^3 4512.8 •S7 •8033s •37316 236.13 •65445 .58 •89354 .78260 .36180 230.04 .64309 4396-3 ■59 .88197 .76203 •35023 223.99 .63152 4280.7 0.60 9.87018 0.74161 2^33843 217.99 3-61973 4166.1 .61 .85815 •7213s •32640 212.03 .60770 4052.2 .62 .84587 .70124 .31412 206.12 •59541 3939^2 ■63 •83332 .68126 •30157 200.25 .58286 3827.0 .64 .82048 .66143 .28874 194.42 •57003 371S-6 0.65 9.80734 0.64172 2.27560 188.63 3^55689 3604.9 .66 •79388 .62213 .26214 182.87 •54343 3494-9 .67 .78008 .60266 •24833 I77^i5 .52962 3385-4 .68 .76590 •58331 .23416 171.46 !5oo88 3276.8 .69 •75133 .56407 •21959 165.80 3168.7 0.70 9^73634 0.54493 2.20459 160.17 3.48588 3061. 1 •71 .72089 .52588 .18915 154-58 .47044 2954-2 •72 •7049s .50694 .17321 149.01 .45450 2847.7 •73 .68849 .48808 •15675 143-47 .43804 2741.8 •74 .67146 .46931 .13972 137-95 .42101 2636.4 0.75 9.65381 0.45062 2.12207 132.46 3-40336 2531-4 .76 •63550 .43202 .10376 126.99 ■3(r°— r'') 3 ^iruir^dr 2'iTWar^ zirwabc 2irwa{r^—r''^) ^irwardr 2irwar^ 2wwabc zirwa{r^ — r^) ^rwardr Zwabc itWabe ^wabc Moment of Inertia lo. IS 8ira/a?-* IS i,irwabc(l>^-^c^) IS 8ira;(rS— r'S) IS Zmm*dr 3 rwai* ruiabc{b''+c') 2 irwa{t* — r**) ^nwar^dr 6 nwafe(3ir2-|_4a2) 6 6 i +4a2(r2— r«Z) ; Tnva{2r«-\-^a^)dr 8wabc{b^+c^) 3 zv>abc{&'^+c') 3 Zwabc{c'-\-2a'') 3 Square of Ra- dius of eola- tion (^. 2>f 5 s s 2(>-5__y/5) Sir^—r^) 2r» 3 2 4 - + - 4^3 £2 a2 4*^3 r2+r^ a2 4 "^3 2 ' 3 3 6 ^ a« 6 + 3 Smithsonian Tables, (Taken from Rankine.) Tables 35-36. BRITISH GAUGE NUMBERS AND SIZES OF WIRES. For Brown & Sharp American Gauge and Electrical Constants see Tables 40 and 41. TABLE 35. — BilUsli StanOard Wlie Qange. TABLB 36. — Blnnliigliam Wlie Gauge. 59 "I 7-0 6-0 5-0 4-0 3-0 2-0 o 1 2 3 4 S 6 7 8 9 10 11 12 13 14 IS 16 17 18 19 20 21 22 23 24 2S 26 27 28 29 30 31 32 33 34 35 36 3? 38 39 40 41 42 43 44 45 46 47 48 49 50 Section in Sq. Inches. 0.500 .464 0.432 .400 •372 .348 •324 0.300 .276 .252 .232 .212 0.192 .176 .160 .144 .128 O.I 16 .104 .092 .080 .072 0.064 .056 .048 .040 .036 0.032 .028 .024 .022 .020 0.0180 .0164 .0148 .0136 .0124 O.OI16 .0108 .0100 .0092 .0084 0.0076 .0068 .0060 .0052 .0048 0.0044 .0040 .0036 .0032 .0028 0.0024 .0020 .0016 .0012 .0010 0.1963 .1691 0.1466 .1257 .1087 .0951 .0825 0.07069 •05983 Diameter in Centi- metres. .04227 •03530 0.02895 •02433 .020IO .01629 .01287 0.010568 .008495 .006648 ,005027 .004071 0.003217 .002463 .001810 .001257 .001018 0.0008042 .0006158 .0004524 .0003801 .0003142 0.0002 545 .0002112 .0001728 .0001453 .0001208 0.00010568 .00009161 .00007854 .00006648 .00005542 0.00004536 .00003632 .00002827 .00002124 .00001810 O.OOOOI52I .00001257 .00001018 .00000804 .00000616 0.00000452 .00000314 .00000201 .00000113 .00000079 Section in Sq. Cms. 1.2700 .1786 1.0973 .0160 0.9449 .8839 .8230 0.7620 .7010 .6401 •5893 •5385 0.4877 .4470 .4064 .3658 •3251 0.2946 .2642 •2337 .2032 .1829 0.16256 .14224 .12192 .10160 .09144 0.08128 .07112 .06096 .05588 .05080 0.04572 .04166 •03759 •03454 .03150 0.02946 .02743 .02540 .02337 .02134 0.01930 .01727 .01524 .01321 .01219 O.OII18 .01016 .00914 .00813 .00711 0.00610 .00508 .00406 .00305 .00254 1.267 .091 0.9456 .8107 .7012 .6136 •53^9 0.4560 •3858 .3218 .2727 .2277 0.18679 .15696 •12973 .10507 .08302 0.06818 .05480 .04289 •03243 .02627 0.020755 .015890 .011675 .008107 .006567 0.005189 003973 002922 ,002452 ,002027 0.00 1 64 1 7 .0013628 .0011099 .0009363 .0007791 0.0006818 .0005910 .0005067 .0004289 .0003575 0.0002927 .0002343 .0001824 .0001370 .0001167 0.0000982 .0000811 .0000656 .0000519 .0000397 0.0000292 .0000203 .0000129 .0000073 .0000051 „s .3 Sections in Diameter in Centi- metres. Section in n 11 Sq. Inches. Sq. Cms. »i '0 0000 0.454 0.16188 I.1532 1.0444 000 .425 .14186 •0795 .9152 00 .380 .11341 0.9652 ■73' 7 .340 .09079 .8636 •5858 1 0.300 0.07069 0.7620 0.4560 2 .284 .06335 .7214 .4087 3 .259 .05269 •6579 •3399 4 .238 .04449 .2870 5 .220 .03801 •5588 •2452 6 0.203 0.03237 0.5156 o.2o88i 7 .180 .02545 •4572 .16417 8 !i48 .02138 .4191 •13795 9 .01720 •3759 .11099 10 ■134 .01410 •3404 .09098 11 0.120 O.OII310 0.3048 0.07297 12 .109 .009331 .2769 .06160 13 .095 .007088 .2413 •04573 14 .083 .00541 1 .2108 •03491 15 .072 .004072 .1829 .02627 16 0.065 0.0033183 0.16510 0.021409 17 .058 .0026421 •14732 .017046 18 •049 .0018857 .12446 .012166 '9 .042 .0013854 .10668 .008938 20 •03s .0009621 .08890 .006207 21 0.032 0.0008042 0.08128 0.005189 22 .028 .0006158 .07 1 1 2 .003973 23 .025 .0004909 .06350 .003167 24 .022 .0003801 .05588 .002452 25 .020 .0003142 .05080 .002027 26 0.018 0.0002545 0.04572 0.0016417 27 .016 .000201 1 .04064 .0012972 28 .014 .0001539 •03556 .0009932 29 .013 .0001327 .03302 .0008563 30 .012 .0001181 .03048 .0007297 31 0.010 0.00007854 0.02540 0.0005067 32 .009 .00006362 .02286 .0004104 33 34 .008 .00005027 .02032 .0003243 .007 .00003848 .01778 .0002483 35 .005 .00001963 .01270 .0001267 36 0.004 0.00001257 o.oioi6 0.0000811 Smithsonian Tables. 6o Table 37. BRITISH UNITS. Gross seoUons and weights of wires. This table gives the cross section and weights in British units of copper, iron, and brass mres of the diameters given in the first column. For one tenth the diameter divide section and weiglits by loo. For ten times the diameter multiply by loo, and so on. u Area of cross section Copper — Density 8. go. Iron — Density 7.80. Brass— Density 8.56. is in Pounds Log. Feet per Pounds Log. Feet per Pounds Log. Feet per Sq. Mils. per Foot Pound. per Foot. Pound. per Foot. Pound. 10 78.54 .000303 4.48150 3300. .0002656 4.42420 3765- .0002915 4 46458 3^35- It 9S-°3 0367 .56429 2727- 03214 -50697 3112. 03527 54735 2836. 2383- 12 II3.IO 0436 .63986 2291. 0448? •58257 2615. 2228. 04197 62295 13 13273 0512 -70939 \ui .65208 04926 69246 2030. 14 153-94 0594 -77376 05206 .71646 1921. 05713 75684 1750. 15 176.71 .000682 4.83368 1467. .0005976 4-77637 1674. .0006558 4.81675 1525- 16 201.06 0776 .88974 1289. 06799 .83244 .88510 I471. 07461 .87282 1340. 17 226.98 0876 .94240 1 142. 07675 1303- 08423 .92548 1187. 18 25447 283-53 0982 .99205 1018. 08605 09588 -93475 .98171 I162. 09443 .•975I3 1059. 19 1094 3.03902 914. 1043. .0010522 3.02209 950. 20 314.16 .001212 3-08357 825.1 748.3 .001062 3.02626 941.4 .001166 3.06664 857^7 21 346.36 1336 .12594 II71 .06864 853.8 1285 .10902 778.0 22 380.13 1467 .16634 681.8 1286 .10904 777-8 141 1 .14942 708.9 23 415.48 1603 .20496 623.8 1405 .14766 711.7 1542 .18804 648.6 24 452-39 1746 .24192 572.9 1530 .18463 6537 1679 .22500 595^7 25 490.87 .001894 3-27738 528.0 .001660 3.22008 602.4 .001822 3.26046 549.0 26 530-93 2046 .31146 488.1 1795 ■2^693 557-0 1970 •29453 507^5 27 572-56 2209 -34423 452.6 1936 2082 516.5 2125 •3273' 470.6 28 ^^•^5 2376 -37583 420.9 .31852 480.3 2285 •35890 •38938 437-6 29 660.52 2549 .40630 392-4 2234 •34900 447^7 2451 408.0 30 706.86 .002727 3-43575 366.7 .002390 3-37845 418.4 .002623 3.41882 381.2 31 754-77 2912 .46424 343-4 2552 -40693 391.8 2801 •44731 357^0 32 804.25 3'03 .49181 322.2 2720 -43450 367^7 2985 .47488 335^1 33 855-30 3300 .51854 303-0 2892 .46123 345^8 3174 .50161 315-1 34 907.92 3503 •54446 285.4 3070 .48716 325^7 3369 •52754 296.8 35 36 962.11 .003712 3.56964 269.4 .003253 3-51233 307^4 .003570 3-55271 280.1 1017.88 3927 .59412 254.6 3442 -53691 290.5 3777 -57719 264.7 ^l 1075.21 4149 .61791 241.0 3636 .56061 275.0 3990 .60098 250.6 38 1134.11 4376 .64108 228.5 3844 .58476 260.2 4218 .62514 237.1 39 1194.59 4609 .66364 216.9 4040 -60633 247.6 4433 .64671 225.6 40 1256.64 .004849 3.68563 .70708 206.2 .004249 3-62833 235^3 .004664 3.66871 214.4 41 1320.25 5094 196.3 4465 .64977 224.0 4900 .69015 .71108 204.1 42 1385.44 5346 .72801 187.1 4685 .67070 213-5 5141 177.2 43 1452.20 5^23 .74845 178.5 49" .69114 203.6 5389 .73152 44 1520.53 5867 .76842 170.4 5142 .711H 194.5 5643 -75149 45 46 47 48 49 1590.43 1661.90 1734-94 1809.56 1885.74 .006137 6412 6694 6982 7276 3-78793 .80703 .82569 .84399 .86189 162.9 155-9 149.4 143.2 137-4 -005378 5620 5867 6119 6377 3-73063 .74972 .76840 .78669 .80459 185.9 177-9 170.5 .005902 6167 6438 3-77 loi .79010 .80878 .82706 .84497 169.4 162.1 142.9 50 51 1963.50 2042.82 ■°°mt 3-87945 .89664 132.0 126.9 .006640 6908 3.82214 •83934 150.6 144-8 .007287 7581 8187 8499 3.86252 .87972 .89659 •91313 •92937 137-2 131-9 126.9 122.1 117.7 52 53 54 2123.72 2206.18 2290.22 8194 8512 8837 •91352 .93005 .94630 122.0 "7-5 113-2 7181 7460 7744 .85621 -87275 .88899 139-2 1340 129.1 55 2375-83 .009167 3.96223 109.1 .00S034 3-90493 124-5 .008817 ^•9453i ii3^4 i Table 37 {contimud). BRITISH UNITS. boss saottons and vaigliti ol irirss. 6r Area of cross section in Sq. Mils. 55 56 59 60 61 62 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 ?3 84 85 86 87 90 91 92 93 94 95 96 9Z 98 99 100 Copper — Density 8.90. Pounds per Foot. 2375-83 2463.01 2551.76 2642.08 2733-97 2827.43 2922.47 3019.07 3117-25 3216.99 3318.31 3421.19 3525-65 3631.68 3739-28 3848.45 3959-19 4071.50 4185.39 4300.84 4417.86 4536.46 4656.63 4778.36 4901.67 5026.55 5153.00 5281.02 5410.61 5541-77 5674.50 5808.80 5944.68 6082.12 6221.14 6361.73 6503.88 6647.61 6792.91 6939.78 7088.22 7238.23 7389-81 7542.96 7697.69 7853-98 .009167 09504 09846 10195 10549 .01091 1 128 1165 1203 1241 .01280 1320 1360 1401 1443 .01485 1528 1615 1660 .01705 1751 1797 1844 1892 •01939 1988 2038 2088 2138 .02189 2241 2294 2347 2400 .02455 2509 2565 2621 2678 •0273s 2793 2851 2910 2970 .03030 Log. Feet per Pound. 3.96223 .97789 _-9932S 2.00837 .02320 2.03782 .05216 .06628 .08019 .09386 2.10732 .12061 •13367 •1465s .15924 2-17174 .18404 .19618 .20817 .22000 2.23165 •24317 •25453 .26574 .27681 2.28769 .29848 .30914 .31966 .33006 2.34034 •35050 .36054 •37047 .38028 5.38999 •39958 .40908 .41847 •42775 2.43694 .44604 .45504 •4639s ■47277 2.48150 Iron — Density 7.80. Pounds per Foot. I09.I 105.2 I0I.6 98.1 94.8 91.66 88.68 85.84 83.14 80.56 78.11 75^76 73-51 71-36 69.30 67-34 65.46 63.65 61.92 60.26 58.66 57-13 55-65 54-23 52.87 51.56 50.29 49.07 47.90 46.77 45-67 44.62 43.60 42.61 41.66 40.74 39-85 38-99 38- IS 37-35 36.56 3S-81 35-07 34-36 33-67 33-00 .008034 08329 08629 08934 09245 .00956 0988 1021 1054 io88 .01122 1157 1 192 1228 1264 .01302 1339 1377 I415 1454 •01494 «S34 1616 1658 .01700 1743 1786 1830 1874 .01919 1964 2010 2057 2104 .02151 2199 2248 2297 2347 •02397 2448 2499 2551 2603 .02656 Log. Feet per Pound. 3^90493 .92058 •93595 .95106 .96591 3.98050 _.99486 2.00898 .02288 •03656 2.05003 .06329 •07635 .08922 .10190 2.11451 .12672 .13887 .16267 2.17432 .18583 .19718 .20839 .21946 2.23038 .24117 .25183 .26236 .27276 2.28304 .29320 •30324 •31317 .32298 2.33269 .34228 •35178 .36116 •37046 2.37965 .38874 •39775 .40665 •41547 2.42420 Brass — Density 8. 56, Pounds per Foot. 124.5 120.1 1159 111.9 108.2 104.59 101.19 97 •gs 94.87 91.83 89.12 86.44 83.88 81.42 79.09 76.82 74.69 72.63 70.66 68.76 66.95 65.19 63.50 61.89 60.33 58.83 57-39 56.00 54.66 53-36 52.11 50.91 49-75 48.62 47-54 46.49 45-47 44-49 43-54 42-61 41.72 40.86 40.02 39.20 38.42 37.65 .008817 09140 09470 09805 10146 .01049 1085 1120 1157 1194 .01231 1270 1308 1348 1388 .01429 1469 1511 ISS3 1596 •01639 1684 1728 1773 1819 .01865 1912 i960 2008 2057 .02106 2156 2206 2257 2309 .02360 2414 2467 2521 2575 .02630 2686 2742 2799 2857 .02915 Log. Feet per Pound. 3-94531 .96096 •97633 _.99i44 2.00629 2.02088 .03524 •04936 .06326 .07694 2.09041 .10367 ■11673 .12960 .14228 2.15489 .16710 •17925 .19123 .20304 2.21460 .22621 •23756 .24877 •25974 2.27076 .28155 .29221 .30274 •31314 2.32342 •33358 -34362 -36336 2.37297 .38266 .39216 .40154 .41084 2.42003 .42912 .43812 •44703 •45585 2.46458 113-4 109.4 105.6 102.0 98.6 95-30 92.21 89.25 86.45 83-77 81.21 78.76 76-43 74.20 72.06 70.00 68.06 66.19 64.38 62.66 61.01 59-40 57-87 56^39 54-99 53-61 52.29 51-03 49.80 48.63 47-49 46-39 45-33 44-30 43-31 42-37 41-43 40.54 39-67 38-83 38.02 36-46 35-72 35-01 34-31 Smithsonian Tables. 62 Table 38. METRIC UNITS. GroM Mcttoni snA welghti of wires. This table gives the cross section and the weight in metric units of copper, iron, and brass wires of the diameteiri given in the first column. For one tenth the diameter divide sections and weights by loo. For ten tunes the diameter multiply by loo, and so on. ii « Copper — Density 8.90. Iron — Density 7.80. Brass — Density 8.56. | o n S^ II •S'S ° i S B 0) s i S ,i sj Et3 n £■5 B >.S Log. IsS iss Log. £ t. E 6^£ Log. a" < g m m i^s So sH 10 78.54 0.0699c 2.84448 14.306 11.823 0.06126 2.78718 16.324 0.0672' 2.82756 14.874 II 95-03 .08458 -92725 .07412 .86996 13.492 ■08135 .91034 12.293 12 113.10 .10065 1.00285 9.93s .08822 •94556 "-335 .09681 _-98s94 'tE 13 13273 .11813 .07236 8.465 •10353 1. 01 506 9.659 .11362 1.05544 H 153-94 .13701 ■13674 7.299 .12008 .07945 8.328 ■I3I77 .11983 7.589 15 176.71 0.1573 T.19665 6.358 5.588 0.1378 7.13936 7-255 0.1513 7.17974 6.611 i6 20 1. 06 .1789 .25272 .1568 .19542 .24808 6.376 .1721 •^35^° S.810 •7 226.98 .2020 •30538 4.951 .1770 5.648 ■1943 .28846 S^i47 i8 254-47 .2265 •35503 4.415 .1985 •29773 5.038 .2178 .338" •38507 4.591 19 283-53 •2523 .40199 3.963 .2212 .34469 4-522 .2427 4.120 20 314.16 0.2796 r.44654 3.577 0.2450 1.38925 4.081 0.2689 1.42963 3-719 21 346.36 •3083 .48892 .244 .2702 .43162 3-701 .2965 .47200 ■373 22 380.13 •3® •52932 2.956 .2965 •47203 •373 ■3254 .51241 ■073 23 415.48 .56794 .704 .3241 .51064 .086 ■3557 •55103 2.812 24 452.39 .4026. .60490 .484 •3529 .54761 2-834 •3872 .58799 .582 25 490.87 0.4369 T.64036 2.289 0.3829 r. 58306 2.612 0.4202 7.62344 2.380 , 26 53°-93 •4725 .67443 .116 .4141 .61713 .415 •4545 •65751 .200 27 572-56 .5096 .70721 1.962 .4466 .64992 •239 .4901 .69030 .040 28 615.75 .5480 .73880 .825 •4803 .68150 .082 .5271 .72188 1.897 29 660.52 .5879 .76928 .701 .5152 .71198 1.941 •5654 •75236 ■76^ 30 706.86 0.6291 r.79872 1.590 0.5514 7.74143 1.814 0.6051 7.78181 '■653 31 754.77 .6717 .82721 .489 •5887 .76991 .699 .6461 .81029 ■548 32 804.25 .7158 :ig .397 .6273 .79749 .594 .6884 •83787 33 855.30 .7612 •314 .6671 .82421 ■499 •7321 .86459 ■?66 34 907.92 .8081 •90744 .238 .7082 .85014 .412 •7772 .89052 .^7 35 36 962.11 0.856 T.93261 1.168 0.7504 i".87S3i 1-333 0.8236 7.91570 1.214 1017.88 .906 .95709 .98088 .104 •Z939 .89979 .260 •8713 .94017 .148 1^ 1075.21 .957 .045 0.988 i& .92359 .192 .9204 •96397 .087 1134.11 1.012 0.00504 .94775 .128 •9730 .98813 .028 39 1194.59 .063 .02661 .941 .9318 .96931 ■073 1.0230 0.00969 0.978 40 1256.64 I.I18 0.04861 0.8941 0.980 r.99131 1.0200 1.076 0.03169 0.9296 41 42 1320.25 1385.44 •175 ■233 .07005 .09098 .8511 .8uo ':Z 0.01275 .03368 0.9711 .9254 .130 .186 .05313 .07406 .8849 .8432 43 1452.20 .292 .11142 •7738 .133 .05412 .8828 ■243 .09450 .8044 44 1520.53 •353 •13139 •7389 .186 .07409 •8432 ■302 .11447 .7683 45 46 48 49 1590.43 1661.90 1734.94 1809.56 1885.74 141 5 ■479 •544 .611 .678 0.15091 .17000 .18868 .20696 .22487 . 0.7065 .6761 .6476 •5958 1.241 .296 .353 .411 .471 0.09361 .11270 •13138 :I6758 o.8o6i •7714 •7389 ■7085 .6799 1.361 ■423 •485 ■549 .614 0-13399 .15308 .17176 .19005 .20796 0^7345 .7029 .6456 .6195 50 51 52 S3 54 1963.50 2042.82 2123.72 2206.18 2290.22 1.748 .818 .890 2.038 0.24242 .25962 .27649 •29303 •30927 0.5722 .5500 .5291 •5093 .4906 1.532 •593 .657 .721 .786 0.18513 .20232 .21919 •23574 •25197 0.6530 .6276 .6037 .5811 •5598 1. 681 .888 .960 0.22551 •24371 •25957 .27612 •29235 0.5950 •5705 •SSoi •5295 •Sioi 55 2375-83 2.114 0.32521 0.4729 ^853 0.26791 0.5396 2.034 0.30829 0.4917 Bmithso NIAN Ta BLEB. Table 38 {.cmtmued). METRIC UNITS. 63 Gross sections and weights of wires. Copper — Density 8.90. C Q.** a"^ Log. Iron — Density 7.80. Log. Brass — Density 8.56. S >■£ ES.5 o S Log. S t E 55 56 S8 59 60 61 62 63 64 65 66 67 68 69 2375-83 2463.01 2551.76 2642.08 2733-97 2827.43 2922.47 3019.07 3"7-25 3216.99 33I8-3I 3421.19 3525-65 3631.68 3739-28 70 3848.45 71 3959-19 72 73 74 75 76 77 78 79 80 81 82 |3 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 4071.50 4185-39 4300.84 4417.86 4536.46 4656.63 4778.36 4901.67 5026.55 5153.00 5281.02 5410.61 554J-77 5674.50 5808.80 5944.68 6082.12 6221.14 6361.73 6503.88 6647.61 6792.91 6939-78 7088.22 7238-23 7389-81 7542.96 7697.69 7853-98 2.114 .192 .271 -351 •433 2.516 .601 .687 •774 •863 2-953 3-045 .138 ■232 .328 3.426 •524 .624 .725 .828 3-932 4-037 .144 ■253 .362 4-474 .586 .700 .815 •932 5-050 .170 .291 •413 •537 5.662 .788 .916 6.046 .176 6.309 •442 •577 •713 .851 6.990 0.32521 .34086 •35623 •37134 .38618 0.40078 .41514 .42926 .44316 .45684 0.47031 .49663 .50950 .52218 0-53479 .54700 •55915 •57113 .58294 0.59460 .6061 1 .61746 .62867 •63974 0.65066 .66145 .672 n .68264 •69304 0.70332 -71348 -72352 •73345 •74326 0.75297 .76256 .77206 .78144 •79074 0^79993 .80902 .81802 .82693 •83575 0.84448 .4729 .4562 •4403 •4253 .4112 •3974 •3845 •3722 .3604 •3493 •3386 .3284 •3187 •3094 .3005 .2919 .2838 •2759 .2685 .2612 •2543 .2477 .2413 •2351 .2292 .2235 .2180 .2128 •2077 .2027 .1980 •1934 .1890 .1847 .1806 .1766 .1728 .1690 .1654 .1619 •1585 •1552 .1520 .1490 .1460 •1431 i^853 .921 •990 2.061 .132 2.205 .280 •355 •431 .509 2.588 .669 •750 •833 .917 3^oo3 .088 .176 .265 •355 3-446 •538 .632 •727 .823 3.921 4.019 .119 .220 -323 4.426 -637 •744 .852 4.962 5^073 !298 •413 .646 .764 .884 6.004 6.126 0.26791 •28356 •29893 .31404 •32889 0.34349 •35784 •37196 •38587 •39954 0.41301 .42627 43933 45220 ,46488 0-47749 .48970 .50185 •51383 •52565 0-53731 .54881 .56017 •57137 .58244 0.59336 .60415 .61481 .62534 •63574 0.64602 .65618 .66622 .67615 .68596 0.69567 •70527 .71476 .72414 •73344 0.74263 •75173 •76073 .76964 .77846 0.78718 •5396 •5205 .5024 .4852 .4689 •4534 •4387 .4246 ■4113 •3985 .3864 •3747 •3636 •3530 •3429 •3330 •3238 •3149 •3063 .2981 .2902 .2826 •2753 .2683 .2615 ■^55° .2488 .2428 .2369 •2313 •2259 .2207 •2157 .2108 .2061 .2015 .1971 •'§o9 .1887 .1847 .1809 .1771 ■1735 .1670 .1665 2.034 .108 .184 .262 •340 2.420 .502 •584 .668 1760 2.840 .929 3.018 .109 .201 3.29s •389 .485 .682 3-782 .883 .986 4.090 ,177 4-303 411 •521 .631 -744 4-857 -972 5.089 .206 •325 5^446 •567 .690 ..815 •940 6.068 .196 .326 •457 ■589 .1632 6.723 0.30829 •32394 •3393" •35442 •36927 0.38387 •39823 •41235 .42625 .44092 0.45339 .46665 •47971 .49258 .50526 0.51787 .53008 •54223 .56603 0.57769 .58919 .60056 .61175 .62283 0.63375 •64454 .65519 .66572 .67612 0.68640 .69656 .70660 .71653 .72634 0.73605 •74565 •75514 •76452 •77382 0.78301 .79211 .80111 .81002 .81884 0.82756 .4917 •4743 •4578\ .4422 •4273 .4132 •3997 .3869 •3748 ■3623 •3521 •3415 •3313 .3217 •3124 •303s .2951 .2869 .2791 .2716 .2644 •2575 .2509 .2445 •2394 .2324 .2267 .2212 .2159 .2108 •2059 .2011 .1965 .1921 .1878 .1836 .1796 •1757 .1720 .1683 .1648 .1614 .1581 •1549 .1518 .1487 Smithsonian Tables. 64 Table 39. BRITISH AND METRIC UNITS. Cross sections and weights at wires. The cross section and the weight, in different units, of Aluminium wire of the diameters ^ven in the first column. For one tenth the diameter divide sections and weights by loo. For tea times the diameter multiply by lOO, and so on. 10 II 12 13 14 15 16 17 18 J9 20 31 22 23 24 25 26 27 28 29 30 31 32 33 Area of cross section.* Aluminium — Density 2,67. 35 36 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 S3 S4 55 78.54 9503 113.10 132.73 153-94 176.71 201.06 226.98 254.47 283-53 314.16 346-36 380.13 415.48 452-39 490.87 530-93 572.56 615.75 660.52 706.86 754-77 804.25 855-30 Pounds per Foot. .0000909 01 100 01309 01536 01782 .0002045 4.31079 34 907-92 962.11 1017.88 1075.21 1r34.11 "94-59 1256.64 1320.25 1385.44 1452.20 1520.53 1590-43 1661.90 1734-94 1809.56 1885.74 1963.50 2042.82 2123.72 2206.18 2290.22 2375-83 02327 02627 02946 03282 .0003636 04009 04400 04809 05237 .0005682 06147 06628 07127 07646 0008182 08737 09309 09900 10509 .001114 1 178 1245 1316 1383 .001455 1528 1604 1681 1760 ,001841 1924 2008 2095 2183 002273 2365 2458 2554 2651 Log. Feet per Pound. 5.95863 4.04139 .11699 .18650 .25088 .36685 .41952 .46917 .51613 4.56068 .60306 .64346 .68208 .71904 4-75450 .78867 .82135 -85393 .88341 4.91386 ■94134 .96893 ,-99565 3.03158 3-04675 .07123 .09502 .11918 .14075 3.16375 .18419 .20512 -22556 -24552 3.26504 .38413 .30281 .32110 -33901 3-35656 -37376 -39063 .40717 -43341 .002750 3.43934 IIOOO. 9091. 7638. 6509. 5612. 4889. 4297. 3876. 3395- 3047- 3750. 3494- 3373- 2079- 1910. 1760. 1627. 1509. 1403. 1308. 1332. "45- 1074. 1010. 953. 897.9 848.8 803-5 760.0 733-2 687.5 654-4 623.6 594-9 568.2 543-2 519.8 498.0 477-4 458.1 440.0 422.9 406.8 394-2 377-2 363-6 Ounces per Foot. .001455 01760 02095 03458 Log. 3.16374 .34551 .33111 .39062 03851 .45500 003373 03724 04304 04713 05351 .005818 06415 07040 07697 08378 .00909 0983 1060 1140 1223 .01309 1398 1489 1584 1681 .01782 1885 1991 2105 2212 .02327 2445 2566 2690 2816 -02946 3078 3213 3351 3492 03636 3783 3933 4086 4242 3-51491 -57097 .62364 -67329 .72025 3.76480 .80718 .84758 .88630 .92316 3.95862 .99269 2.02547 -05705 -08753 2.11698 .14546 'I7304 -19977 .22570 2.25087 -27535 .29914 -32339 .34487 3.36687 •38831 .40934 .42968 .44964 2.46916 .48825 .50693 •52533 -54313 2.56068 .57788 •59475 .61129 •63753 Feet per Ounce. .04400 2.64346 687.5 602.4 477-4 406.8 350.8 305.6 268.5 237-9 212.2 190.4 171.9 155-9 142.0 129.9 119.4 110.00 101.70 94-30 87.69 81.7s 76.39 71-54 66.89 63- '3 59-47 56.12 53-05 50.22 47-50 45.20 42.97 40.90 38.97 37.18 35-51 33-95 32-49 31.12 29.84 38.63 27-50 26.43 35.42 24-47 23-57 23.73 Grammes per Metre.* .03097 .03537 .03020 •03544 .04110 .04718 .05368 .06060 .06794 .07570 .08388 .09248 .10149 .11093 .12079 .1311 .1418 .1529 .1644 .1764 .1887 .2015 .2147 .2284 .2424 .2569 .2718 .2871 ■3035 .3190 •3355 •3525 •3699 .3877 .4060 .4246 •4437 -4632 .4832 .5035 -5243 -5454 -5670 -5891 .6115 -6343 Log. 2.32160 •40437 •47997 .54948 .61386 2.67377 .72984 .78250 .83215 .87911 2.92366 .96604 1.00644 .04506 .08202 r.11748 -15155 •18433 .21592 .24640 T.27584 -30433 ■33190 .35863 .38456 1.40973 .43421 .45800 .48216 -50373 1-52573 •54717 .56810 .58854 .60851 T.62803 .64713 .66580 .68408 .70199 r-7i954 •73674 •75361 .77015 .78639 1.80233 Metres per Gramme. 47.69 39-41 33-" 28.22 24-33 21.19 18.63 16.50 14.73 13.21 11.922 10.813 9-853 9.014 8.279 7-630 7.054 6.541 6.083 5.670 5.299 4.962 .657 •379 .125 .680 .483 •295 •»35 2.980 .837 •704 •579 •463 2-355 .254 •159 .070 1.986 1.907 .833 •764 .698 •63s 1.576 8«,THSO«.»« T.B*..'s°."'"""' ''"■ '" """"""""" °' ^" ■"^- ' '-"• ""'■''''"'"'■= "' ^ "■"'-'«• Table 39 (continued). BRITISH AND METRIC UNITS. 65 OroBft sactloni anA weights ol wlzai. Area of cross section.* Aluminium — Density 2.67. Founds _per Foot. Log. Feet per Pound. Ounces per Foot. Log. Feet per Ounce. Grammes per Metre.* Log. Metres „ per Gramme. 55 56 58 59 60 61 62 64 65 66 67 68 69 2375-83 2463.01 2551.76 2642.08 2733-97 2827.43 2922.47 3019.07 3"7-25 3216.99 3318.31 3421.19 3525-65 3631.68 3739-28 002750 3.43934 70 3848.45 71 72 73 74 75 76 77 78 79 80 81 82 ?3 84 85 86 87 88 89 3959-19 4071.50 4185.39 4300.84 4417.86 4536.46 4656.63 4778.36 4901.67 5026.55 5153-00 5281.02 5410.61 5541-77 5674.50 5808.80 5944.68 6082.12 6221.14 90 6361.7 9' 92 93 94 95 96 97 98 99 100 6503.8: 6647.61 6792.91 6939.78 7088.22 7238.23 7389.81 7542.96 7697.69 7853-98 2851 2954 3058 3165 •003273 3383 3495 3608 3724 .003841 3960 4081 4204 4328 .004456 4583 4713 4845 4978 .005114 5251 539° 5|3' 5674 .005818 5965 6113 6263 6415 .006568 6724 6881 7040 7201 .007364 7528 7695 7863 8033 .008205 8378 8554 8731 8910 .009091 .45500 ■47037 .48547 •50032 3-51492 .52928 •54340 •55730 .57098 3-58445 •59771 .61077 •62364 •63632 3-64893 •661 14 •67328 .68526 .69708 3.70874 .72025 .73160 .74281 •75387 3.76480 -77559 .78625 .79678 .80718 3.81746 .82762 .83766 .84758 -85740 3.86710 .87670 .88619 •89558 .90487 3.91407 .92316 .932:6 .94107 .94989 3.95862 363-6 350.8 338-6 327-0 316.0 305-S 295.6 286.2 277.1 268.5 260.3 252.5 245.0 237-9 231.0 224.4 218.2 212.2 206.4 200.9 195-S 190.4 185-^ 180.8 176.2 171.9 167.6 163.6 159-7 155-9 152-2 148.7 145-3 142.0 138-9 I3S-8 132-8 130.0 127.2 124.5 121.9 119.4 1 16.9 114.5 1 1 2.2 1 10.0 .04400 .04562 .04726 .04893 .05063 2.64346 .65912 •67449 .68959 .70444 .05236 2.71904 •05413 -73340 .05591 -05773 .05958 .06146 .06336 .06530 .06726 .06925 •07129 •07333 •07541 .07751 •07965 .08182 .08402 .08624 .08850 .09078 .09309 •09544 .09781 .10021 .10264 •1051 .1076 .HOI .1126 .1152 .1178 .1205 .1231 .1258 .1285 •1313 .1341 .1369 •1397 .1426 •1455 •74752 .76142 .77510 2.78857 .80183 .81489 •82777 •84044 5.85305 .86526 .87740 .88938 .90120 2.91286 -92437 ■93572 .94693 •95799 2.96892 •97971 _-99037 i.ooogo .01130 r.02158 •03174 .04178 .05170 .06152 T.07122 .08082 .09031 .09970 .10899 T.11819 .12728 .13628 .14519 .15401 T.16274 22.73 21.92 21.16 20.44 i9^7S 19.10 18.48 17.88 17^32 16.78 16.27 15.78 15-31 14.87 14-44 14-03 13.64 13.26 12.90 12-55 12.22 H.90 11.60 11.30 11.02 10.742 10-479 10.224 9-979 9-743 9-515 9.295 9.082 8.878 8.679 8.302 8.122 7-949 7-780 7-617 7-459 7-307 7.158 7.015 6.875 0.6343 .6576 .6813 .7054 .7300 0-7549 .7803 .8061 •1323 8589 0.8860 ■9135 -9413 -9697 -9984 1.028 .057 .087 .117 .148 1.180 .211 •243 .276 •309 1.342 •376 •410 •445 .480 1-515 ■55' ■r .624 .661 1.699 •737 •775 .814 •853 1.893 -933 ■973 2.014 .055 2.097 1.80233 .81798 •83335 .84846 .86331 T.87790 89226 ,90638 ,92028 •93396 1-576 .521 .468 .418 •370 '■325 .282 .241 .201 .164 1^94743 1. 1 29 ,96069 .095 •97375 •98662 •99930 o^oii9i .02412 .03627 .04825 .06006 0.07172 .08323 .09458 •10579 .11686 0.12778 •13857 -14923 .15976 .17016 0.18044 .19060 .20064 .21057 .22038 0.23009 .23968 .24918 .25856 .26786 0.27705 .28614 .29514 -30405 .31287 0.32160 0.4769 .062 •031 0.9730 .9460 .9199 .8949 ^708 0.8477 .8256 .8043 .783§ .7641 0.7451 .7268 .7092 .6922 ■6757 0.6600 .6448 .6300 .6158 .6020 0.5887 •5759 •5634 .5514 •5397 0.5284 -5174 .5068 .4965 .4865 « Columns 3-8, in thousandths of an inch; 9-". thousandths of a centimetre. Smithsonian Tables. 66 Table 40. SIZE, WEIGHT, AND ELECTRICAL Size, Weight, and Electrical ConBtants of pure hard drawn Copper Wire of different nuinben Size and Welglit Gauge Diameter in Square of Diameter Section in Pounds Log. Feet Number. Inches. (Cireular Inches). Sq. Inches. Foot per Found. OOOO 0.4600 0.21 16 0.1662 0.6412 T.807OI 1.560 000 .4096 .1678 .1318 •508s .70631 1.967 00 .3648 •I33I •1045 •4033 .60560 2.480 O •3249 •105s .0829 •3198 .50489 3-127 1 0.2893 0.08369 0.06573 0.2536 T.40419 3-943 2 .2576 .06637 •05263 .05213 .2011 ■30348 4.972 3 •2294 .04134 •1595 .20277 6.270 4 ■2043 .04174 .03278 .1265 .10206 7^905 S .1819 .03310 .02600 .1003 .00136 9.969 6 0.1620 0.02625 0.02062 0.07955 2.90065 15-85 7 ■1443 .02082 .01635 .06309 •79994 8 .1285 .01651 .01 297 .05003 •03968 .69924 19.99 9 .1144 .01309 .01038 .01028 •59853 .49782 25.20 10 .Z019 .00815 •03146 3178 11 0.09074 0.008234 0.006467 0.02495 2.397 1 1 40.08 12 .08081 .006530 .0051 Z9 •01979 .29641 50.54 13 .07196 .005178 .004067 .01569 .19570 63.72 H .06408 .004107 .003225 .002558 .01244 •09499 80.3s IS •05707 .003257 .00987 3^99429 101.32 16 0.05082 0.002583 .002048 0.002028 0.007827 3-89358 127.8 ; 'I .04526 .001609 .006207 .79287 161. 1 1 i8 .04030 .001624 .001276 .004922 .69217 203.2 1 «9 .03589 .001288 .OOIOIZ .003904 .59146 256.2 I 20 .03196 .001021 .000802 .003096 .49075 323^i i 21 0.02846 O.OO0810I 0.0006363 0.002455 3^39004 408.2 zz •02535 .0006424 .0005046 .001947 .28934 5 '3-6 1 23 .02257 .0005095 .0004001 .001544 .18863 647.7 24 .02010 .0004040 •0003173 .001224 .08792 876.7 25 .01790 .0003204 .0002517 .000971 4.98722 1029.9 26 0.01594 0.0002541 0.0001996 0.0007700 4.88651 .78580 1298. 1638. -27 28 .01419 .OOOZOI5 .0001598 .0001583 .0006107 .0001255 .0004843 .68510 2065. 2604. 29 .01126 .0001267 .0000995 .0003841 •58439 30 .01003 .0001005 .0000789 .0003046 •48368 3283- 31 0.008928 0.00007970 0.00006260 0.0002415 4.38297 4140. 5221. 32 .007950 .007080 .006304 .00006321 .00004964 .0001915 .28227 33 .00005013 .00003937 .0001519 .18156 .08085 5.98015 6583. 8301. 10468. 34 .00003975 .00003122 .0001205 35 .005614 .00003 1 5z .00002476 .0000955 36 0.005000 0.0000Z500 0.00001963 0.00007576 5^87944 •77873 .67802 13200. 16644. 20988. 26465. 33372. 11 •004453 .00001983 .00001557 .00006008 •003965 .00001372 .00001235 .00004765 .00003778 .00002996 39 40 SuiTUftOHIIAh •003531 •003145 T.Bi r. .00001247 X)oooo989 .00000979 .00000777 •57732 .47661 Table 40 (.emiinued). CONSTANTS OF' COPPER WIRE. according to the American Brown and Sliarp Gaoge. Common Measure. Temperature 32° F. Density 8.9a. Elaotrloal Constinti. 67 Resistance and Conductivity. Olims Foot. 0.00004629 .00005837 .00007361 .00009282 O.OOOH70 .0001476 .0001861 .0002347 .0002959 0.0003731 .0004705 .0005933 .0007482 .0009434 0.001190 .001500 .001892 .002385 .003008 0.003793 .004783 .006031 .007604 .009589 0.01209 .01525 .01923 .02424 •03057 0.03855 .04861 .06130 .07729 .09746 0.1229 .1550 .1954 .2464 .3107 0.3918 .4941 .6230 .7856 .9906 Log. 5.66551 .76622 .86693 .96764 4.06834 .16905 .26976 .37046 .47117 4.57188 •67259 ■77329 .87400 •9747 « 3-07541 .17612 .27683 •37753 .47824 .67966 .78036 .88107 .98178 2.08248 .18319 .28390 .38461 •48531 2.58602 .68673 •78743 .88814 .98885 1.08955 .19026 .29097 .39168 .49238 1.59309 .69380 •79450 .89521 .99592 Feet per Olim. Ohms per Pound. 21601. i7i3i^ i3586^ 10774. 8544. 6775- 5373^ 4261. 3379- 2680. 2125. 1685. 1337^ 1060. 840.6 666.6 528.7 419.2 332-5 263.7 209.1 165.8 131-5 104.3 82.70 65.59 52.01 41.25 32.71 25-94 20.57 16.31 12.94 10.26 8.137 6.452 5-117 4.058 3.218 2-552 2.024 1.605 1-273 1.009 0.00007219 .00011479 .00018253 ,00029023 0.0004615 .0007338 ,0011668 .0018552 .0029499 0.004690 .007458 .011859 .018857 .029984 0.04768 .07581 .12054 .19166 .30476 0.4846 .7705 1.2252 1.9481 3.0976 4.925 7-832 "2-453 19.801 31.484 50.06 79.60 126.57 201.26 320.01 508.8 809.1 1286.5 2045.6 3252.6 5172. 8224. 13076. 20792. 33060. Founds per Ohm. Gauge Number. 13852. 8712. 5479^ 3445- 2166.8 1362.8 857-0 . S39-0 339-0 213.22 134.08 84.32 53-03 33-35 20.973 13-191 8.296 5.218 3-281 2.0636 1.2979 0.8162 •5133 .3228 0.20305 .12768 .08030 .05051 .03176 0.019976 .012563 .007901 .004969 .003125 0.0019654 .0012359 .0007773 ,0004889 .0003074 0.0001934 .0001216 .0000765 .0000481 .0000303 0000 000 00 o 1 2 3 4 5 7 8 9 10 11 12 13 14 IS 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38 39 40 Smithsonian Tables. 68 Table 41 . SIZE, WEIGHT, AND ELECTRICAL Site. Weight, and Electrical Constants of pnie hard drawn Copper Wire of different numben Size and Weight. Square of Grammes Metres Gauge Diameter in Diameter Section in Il^e. Log. per Number. Centimetres. (Circular Sq. Cms. Gramme. Cms.). 0000 I.1684 1.3652 1.0722 954-3 2.97966 0.001048 ooo .0405 .0826 0.8503 756.8 .87896 .001322 oo 0.9266 .8251 0.8586 .6809 .6743 •53+8 600.1 475^9 •77825 •67754 .001666 .002101 1 0.7348 0.5400 0.4241 377^4 2.57684 0.002649 2 .6544 •5827 4282 •3363 299-3 •47613 •003341 3 •3396 .2667 ^11^ •37542 .004213 4 .5189 .2693 .2115 188.2 •27472 .005312 S .4621 .2136 .1677 1493 .17401 .006699 6 0.41 IS 0.16936 0.13302 118.39 93.88 2.07330 0.0084s J .3665 •I3431 .10549 1.97259 .01065 8 .3264 .10651 .08366 74-45 .87189 •01343 9 .2906 .08447 .06634 59-04 .77118 .01694 10 .2588 .06699 .05261 46.82 .67047 .02136 11 0.230s 0.05312 0.04172 37-13 1.56977 0.02693 12 ■2053 .04213 •03309 29-4S .46906 •03396 13 .1828 •03341 .02624 23-35 •3683s .04282 14 .1628 .02649 .02081 18.52 .26764 .05400 IS .1450 .02101 .01650 14.69 .16694 .06809 16 0.12908 0.016663 0.013087 11.648 1.06623 0.0859 •1083 17 •"495 .013214 .010378 9-237 "S 18 .10237 .010479 .008231 7-325 5.809 •136s 19 .09116 .08118 .008330 .006527 .76411 .1721 20 .006591 .005176 4.607 .66340 .2171 21 0.07229 0.005227 0.004105 iS 0.56270 0.2737 22 .06438 .004145 .003255 .46199 •3450 23 •05733 .003287 .002582 2.298 .36128 til 24 .05106 .002607 .002047 1.822 .26057 .15987 25 .04545 .002067 .001624 I -445 .6920 26 0.04049 0.0016394 0.0012876 ':^t 0.05916 0.873 27 .03606 .0013001 .0010211 1.95845 1. 100 28 .03211 .0010310 .0008098 .7207 •8S77S 1.388 29 .02859 .0008176 .0006422 •5715 •75704 1750 30 .02546 .0006484 .0005093 •4532 •65633 2.206 31 0.02268 0.0005142 0.0004039 0-3594 .2850 1.55562 2.782 32 .02019 .0004078 .0003203 •45492 3.508 33 .01798 .0003234 .0002540 .2261 •35421 4.424 34 .01601 .0002565 .0002014 -1793 •25350 5-578 35 .01426 .0002034 .0001597 .1422 .15280 7-034 36 0.01270 O.OOO1613 0.0001267 0.1 1 27 T.05209 8.87 H .01131 .0001 279 .0001005 .0894 2.95138 11.18 38 .01007 .0001014 .0000797 .0709 .85068 14.10 39 .00897 .0000804 .0000632 .0562 •74997 17.78 40 .00799 .0000638 .0000501 .0446 .64926 22.43 Smithsonian Tables. Table 41 (cotuimud). CONSTANTS OF COPPER WIRE. according to the American Brown and Sharp Gauge. Metric Measure. Temperature o° C. Density 8.9a. Electiloal Oonstaitts. 69 Resistance and Conductivity. Gauge Ohms Metres Ohms Grammes Metre. Log. Olim. per Gramme. Ohm. i!i umocr> 0.0001519 4.18150 6584. o.ooooooi 592 6283000. 0000 .0001915 .28221 5221. .0000002531 3951000. 2485000. 000 .0002415 .38191 4141. .0000004024 00 .0003045 .4S362 3284^ .0000006398 1563000. 0.0003840 4-58433 .68503 2604. O.OOOOOIOI7 982900. 1 .0004842 2065. 1638. .000001618 618200. 2 .0006106 •78574 .000002572 388800. 3 .0007699 .88645 1299. .000004090 244500. 153800. 4 .0009709 .98715 1030. .000006504 5 0.001224 3.08786 816.9 0.00001034 96700. 6 .001544 .18857 647.8 .00001644 60820. 7 .001947 .28928 51 3-7 .0000261 5 38250. 8 .002455 -38998 407.4 .00004157 24050. 9 .003095 .49069 323-1 .00006610 15130. 10 0.003903 3.59140 256-2 0.00010511 9514. 11 .004922 .69210 203-2 .00016712 5984^ 12 .006206 -79281 161. 1 .00026574 3763^ 13 .007826 •89352 127.8 .00042254 .00067187 ^3^Z' 14 .009868 .99423 101.3 1488. 13 0.01244 2-09493 80-37 0.0010683 IS 16 .01569 .19564 63-73 .0016987 17 18 .01979 •29635 50-54 .0027010 370.2 .02495 •39705 40-08 .0042948 232.8 19 .03146 .49776 31-79 .0068290 146.4 20 0.03967 2-59847 25-21 0.010859 92.09 21 .05002 .69917 19.99 .017266 57-92 36.42 22.91 11.88 22 .07954 .10030 •79988 .90059 1. 001 30 15-85 12-57 9-97 •027454 •043653 .069411 23 24 25 0.12647 T-I0200 7-907 0.11037 9.060 26 .15948 .20110 .20271 •30342 6.270 4-973 •17549 .27904 2^ •25358 .40412 3-943 •44369 2-254 29 .31976 .50483 3-127 •70550 1.417 30 0.4032 .5084 .6411 T.60554 2.480 1.967 1.560 I.I218 1-7837 2.8362 .3526 31 32 33 .8085 1.0194 .90766 0.00837 oigSi 4-5097 7-1708 .2217 , •1394 34 35 1.285s 1. 62 10 2.0440 2.5775 3.2501 0.10907 .20978 •31049 .41119 .51190 0.7779 .6169 •4f92 .3880 •3076 11-376 18.130 28.828 0-08790 .05516 .03469 .02182 .01372 36 f8 39 40 Smithsonian Tables. ;o Tables 42-43. WEIGHT OF SHEET METAL. TABLE 42.— WalglitotSlMetMataL (Metilo Meaanie.) This table gives the weight in giammet of a plate one metre square and of the thickness stated in the first column. Thickness in thou- Iron, Copper. Brass. Aluminum. Platinum. Gold. SUver. a cm. 1 78.0 89.0 85.6 26.7 215.0 193.0 105.0 2 156.0 178.0 171.2 ^^:l 430.0 386.0 210.0 3 234.0 267.0 256.8 6450 579-0 315-0 4 312.0 356.0 342-4 106.8 860.0 772.0 420.0 S 390-0 445-0 428.0 133-S 1075.0 965.0 525.0 6 468.0 534-0 513-6 160.2 1290.0 1158.0 630.0 7 546.0 623.0 599-2 186.9 1505.0 1351.0 735-0 8 624.0 712.0 684.8 213.6 1720.0 1544.0 840.0 9 702.0 801.0 770.4 240.3 1935-0 1737 -o 945.0 10 780.0 890.0 856.0 267.0 2150.0 1930.0 1050.0 TABLE 43. -Weight of Sheet HetaL (British Measnie.) Thickness Iron. Copper. Brass. Aluminum. Platinum. in MUs. Pounds per Pounds per Pounds per Pounds per Ounces per Founds per Ounces per Sq. B'oot. Sq. Foot. Sq. Foot. Sq. Foot. Sq. Foot. Sq. Foot. Sq. Foot. 1 .04058 .04630 .04454 .01389 .2222 .1119 1.790 2 .08116 .09260 .08908 .02778 •4445 .2237 3579 3 .12173 .13890 •13363 .04167 .6667 •3356 s-369 4 .16231 .18520 .17817 •05556 .8890 •4474 7.158 5 .20289 .23150 .22271 -06945 1.1112 -5593 8.948 6 •24347 .27780 .26725 -08334 '•3335 .6711 10.738 7 .28405 .32411 -3"79 .09723 1-5557 .7830 12.527 8 -32463 •37041 .40088 .11112 1.7780 .8948 14-317 9 .36520 .41671 .12501 2.0002 1.0067 16.106 10 .40578 .46301 .44542 .13890 2.2224 1.1185 17.896 Thick ness Gold. Silver. inM ib. Troy Ounces per Sq. Foot. Grains per Sq. Foot. Troy Ounces per Sq. Foot Grains per Sq. Foot. 1 1.4642 702.8 0.7967 382.4 2 2.9285 I4OC.7 2108.5 •-5933 764.8 ;• 4-3927 2.3900 1147.2 4 5-8570 2811.3 31867 1529.6 s 7.3212 35'4-2 39833 1912.0 6 8.7854 4217.0 4.7800 2294.4 7 10.2497 4919.8 5-5767 6-3734 2676.8 8 II-7139 5622.7 3059.2 9 13-1782 6325-5 7.1700 3441.6 10 14.6424 7028.3 7.9667 3824.0 Smithsonian TABLts. 71 Table 44. STRENGTH OF MATERIALS. The strength of most materiaU varies so that the following figures serve only as a rough indication of the strenitth of a particular sample. TABLE 44(a).-Uetali. Name of Metal. Tensile strength in pounds per sq. in. Aluminum wire 30000-40000 Brass wire 50000-150000 Bronze wire, phosphor, hard- drawn IIOOOO-I40OOO Bronze wire, silicon, hard- drawn 95000-1 I 5000 Bronze : Cu, 58.54 parts ; Zn, 38.70; Al, 0.21 J with 2.55 parts of the alloy, Sn, 29.03, wrought iron, 58.06, ferro- manganese, 12.91 60000-75000 Copper wire, hard-drawn 60000-70000 Gold wire 20000 Iron, cast 13000-33000 " wire, hard-drawn 80000-120000 " " annealed 50000-60000 Lead, cast or drawn 2600-3300 Palladium * 39000 Platinum * wire 50000 Silver * wire 42000 Steel 80000-330000 " wire, maximum 460000 " Specially treated nickel- steel, approx. com p. 0.40 C ; 3.25 Ni ; treatment secret 250000 " piano wire, 0.033 '"■ diam. 357000-390000 " piano wire, 0.051 in. diam. 325000-337000 Tin, cast or drawn 4000-5000 Zinc, cast 7000-13000 " drawn 22000-30000 According to Boys, quartz fibres have a tensile strength of between 116 loooand 167000 pounds per square inch. TABLE 44(li).-Stone».» Material. Size of test piece. ResisUnce to crushing in pds. per sq. in. Marble Tufa Brownstone Sandstone Granite Limestone 4 in. cubes 2 « it 4 in. cubes 4" « 4 « « 7600-20700 7700-11600 7300-23600 2400-29300 9700-34000 6000-25000 * Data furnished by the U. S. Geological Survey. TABLE 44(o).-Bllck.* Kind of Brick. Resistance to crushing in pds. per sq. in. Tested flatwise. Tested on edge. Soft burned Medium burned Hard burned VitriBed Sand-lime 1800-4000 4000-6000 6000-8500 8500-25000 1800-4000 1600-3000 3000-4500 4500-6500 6500-20000 Brick piers laid up in i part Portland cement, 3 of sand, have from 20 to 40 per cent the crushing strength of the brick. • Authority of Wertheim. * Data furnished by the U. S. Geological Survey. TABLE 44(1). — Ooncratas.* Coarse material. " Aggregate." Proportions by volume. Cement: sand: aggregate. Size of test piece. Resistance to crushing in pds. per sq. in. Sandstone Cinders Limestone Conglomerate Trap 5 : 14 to 1:1:5 3:6 "1:1:3 4:8 "1:2:4 6 : 12 " 1:2:4 2:9 "1:2:4 12 in. cube 12 " " 12 " " 12 " •< 12 " " 1550-3860 790-2050 1200-2840 1080-3830 820-2960 * Data furnished by the U. S. Geological Survey. Smithsonian Tables. 72 Table 45. STRENGTH OF MATERIALS. ATSiags Rasnlts ol Tlmtier Tasti. The test pieces were small and selected. Endwise compression tests of some of the first lot, made when green and containing over 40 per cent moisture, showed a diminishing in strength of 50 to 75 per cent. See also Table 46. A particular sample may vary greatly from these data, which can indicate only in a general way the relative values of a kind of timber. Note that the data below are from selected samples and therefore probably high. The upper lot are from the U. S. Forestry circular No. 15 ; the lower from the tests made for the loth U. S. Census. NAME OF SPECIES. TRANSVERSE TESTS. COMPRESSION. SHEAR- ING. Modulus of rupture. Ib./sq, in. Modulus of elasticity. Ibs./sq. in. II to grain. Ibs./sq. in. 1 to grain. Ibs./sq. in. Alon^ the grain. Ibs./sq. in. Long-leaf pine 12,600 2,070,000 8,000 1260 83s Cuban pine 13,600 2,370,000 8,700 1200 770 Short-leaf pine 10,100 1,680,000 6,500 1050 770 Loblolly pine 11,300 2,050,000 7,400 1150 800 White pine 7,900 1,390,000 5,400 700 400 Red pine 9,100 1,620,000 6,700 1000 1^ Spruce pine 10,000 1,640,000 7,300 1200 Bald cypress 7,900 1,290,000 6,000 800 500 White cedar 6,300 910,000 5,200 700 400 Douglass spruce 7,900 1,680,000 5,700 800 500 White oak 13,100 2,090,000 8,500 2200 1000 Overcup oak 11,300 1,620,000 7,300 1900 1000 Post oak 12,300 2,030,000 7,100 3000 IIOO Cow oak 11,500 1,610,000 7,400 1900 900 Red oak 11,400 1,970,000 7,200 2300 1100 Texan oak 13,100 1,860,000 8,100 2000 900 Yellow oak 10,800 1,740,000 7.300 7,800 1800 1100 Water oak 12,400 2,000,000 2000 1100 Willow oak 10,400 1,750,000 7,200 1600 900 Spanish oak 12,000 1,930,000 7,700 1800 900 Shagbark hickory 16,000 2,390,000 9,500 2700 1100 Mockernut hickory 15,200 2,320,000 IO,I0O 3100 IIOQ Water hickory 12,500 2,080,000 8,400 2400 1000 Bittemut hickory 15,000 2,280,000 9,600 2200 1000 Nutmeg hickory 12,500 1,940,000 8,800 2700 IIOO Pecan hickory 15.3°° 2,530,000 9,100 2800 1200 Pignut hickory 18,700 2,730,000 10,900 3200 1200 White elm 10,300 1,540,000 6,500 1200 800 Cedar elm 13.500 10,800 1,700,000 8,000 2100 1300 White ash 1,640,000 7,200 1900 IIOO Green ash 11,600 2,050,000 8,000 1700 1000 Sweet gum 9.S00 1,700,000 7,100 1400 800 Poplar 9,400 1,330,000 5,000 II20 Basswood 8,340 1,172,000 5,190 880 Ironwood 7.540 1,158,000 5.27 s 8,800 2000 Sugar maple 16,500 2,250,000 3600 White maple 14,640 1,800,000 6,850 4,580 2580 Box elder 7,580 873,000 Black walnut 11,900 1,560,000 8,000 2680 Sycamore 7,000 790,000 6,400 2700 Hemlock 9,480 1,138,000 5,400 1100 Red fir 13,270 1,870,000 7,780 1750 Tamarack 13.150 1,917,000 7,400 1480 Red cedar 11,800 938,000 6,300 2000 Cottonwood 10,440 1,450,000 5,000 1100 Beech 16,200 1,730,000 6,770 2840 Smithsonian Tables. Table 46. UNIT STRESSES FOR STRUCTURAL TIMBER EXPRESSED IN POUNDS PER SQUARE INCH. Recommended by the Committee on Wooden Bridges and Trestles, American Railway Engineering Association, 1909. n KIND OF TIMBER. BENDING. SHEARING. Extreme fibre stress. Modulus of elasticity. Parallel to grain. Lon^tudinal shear m beams. Average ultimate. Safe stress. Average. Average ultimate. Safe stress. Average ultimate. Safe stress. Douglass fir 6100 1200 1,510,000 690 170 270 IIO Long-leaf pine 6500 1300 1,610,000 720 180 300 120 Short-leaf pine 5600 1 100 1,480,000 710 170 316 130 White pine 4400 900 1,130,000 400 100 180 70 Spruce 4800 :ooo 1,310,000 600 150 170 70 Norway pine 4200 800 1,190,000 590 130 100 Tamarack 4600 900 1,220,000 670 170 260 lOO Western hemlock 5800 IIOO 1,480,000 630 160 270* 100 Redwood 5000 900 800,000 300 80 - - Bald cypress 4800 900 1,150,000 500 120 - - Red cedar 4200 800 860,000 - - - White oak 5700 IIOO 1,150,000 840 210 270 IIO KIND OF TIMBER. COMPRESSION. n Perpendicular to grain. Parallel to grain. lli Formulas for safe •3"." - a, stress in long columns over 15 Elastic Safe Average Safe "Ss diameters.t limit. stress. ultimate. stress. fe^" Douglass fir 630 310 3600 1200 900 I200(l-L/6o.D) 10 Long-leaf pine S20 260 3800 1300 980 i30o(i-L/6o.D) 10 Short-leaf pine 340 170 3400 IIOO 830 iioo(l-L/6o.D) 10 White pine 290 ISO 3000 1000 7 so iooo(i-L/6o.D) 10 Spruce 370 180 3200 IIOO 830 iioo(i-L/6o.D) - Norway pine 15° 2600* 800 600 8oo(i-L/6o.D) - Tamarack — 220 3200* 1000 7 so iooo(i-L/6o.D) — Western hemlock 440 220 35°o 1200 qoo i20o(i-L/6o.D) - Redwood 400 ISO 3300 900 680 9oo(i-L/6o.D) - Bald cypress 340 170 3900 IIOO 830 680 iioo(i-L/6o.D) - Red cedar 470 230 2800 900 90o(i-L/6o.D) - White oak 920 450 3500 1300 980 i30o(i-L/6o.D) 12 These unit stresses are for a green condition of the timber and are to be used without increasing the live- load stresses for impact. * Partially air-dry. t L=length in inches. D = least side m inches. Smithsonian Tables. 74 Tables 47-47a. ELASTIC MODULI. TABLE 47. — BlglOlty Hodnlns. K to the four consecutive faces of a cube a tangential stress is applied, opposite in direction on adjacent sides, the modulus of rigidity is obtained by dividing the numerical value of the tangential stress per unit area (kg. per sq. mm.) by the number representing the change of angles on the non-stressed faces, measured in radians. Substance. Aluminum " cast .... Brass t( " cast, 6oCu+ i2Sn Bismuth, slowly cooled . Bronze, cast, 88 Cu -|- I2 Sn Cadmium, cast .... Copper, cast 4i6 .00164 .0058 .00012 Smithsonian Tables. * Modulus of rigidity in toU dynes per sq. cm. Young's Modulus ■■ Table 48. ELASTIC MODULI. Toulk'i Uodnlns. Intensity of longitudinal stress (kg. per sq. mm.) _ Elongation per unit length 75 Substance. Temp. 11 Is Substance. Temp. °C. -rl 11 Aluminum .... 20 7200 I Nickel-Steel, 5^% ni. . _ 19900 13 93° 2075 2215 230 1590 1690 1730 1800 1890 1990 2090 2210 2340 260 1770 1870 1920 1985 2070 2166 2265 2375 2490 290 1950 2060 2100 2170 2260 2340 2440 2550 265s 320 213s 2240 2280 2360 2440 2525 2620 2725 2830 Relative values of pz ; pv at 0" C. and 1 atm. = i. 1 0° 10° 20° 30° 40° 60° foo 100° 137° xgtP »58° 50 0.105 0.114 0.680 0-775 0-750 0.984 1.096 1.206 1.380 _ _ 100 0.202 0.213 0.229 0.255 0-309 0.661 0.873 1.030 1.259 1-582 1-847 150 0.29s 0.309 0.326 0.346 0-377 0.485 0.681 0.878 1.159 1-530 1-8x8 300 0.559 0.578 0.599 0.623 0.649 0.710 0.790 0.890 1.108 1-493 1.820 500 0.S91 0.913 0.938 0.963 0.990 '•S54 1.124 1-201 1-362 1-678 - 1000 1.656 1.685 1.716 1-748 1.780 1.848 1. 92 1 1.999 Amagat, C. R. xii, iSgo; Ann chim. phys. (6) 29, 1893; 32, 1881. TABLE 69. — OompTessllilUty ol Oases. Gas. 02 H2 CO CO2 N2O Air NH3 p.v. {} atm.). pcvoii atm.). 1.00038 0.99974 1.00015 1.00026 1.00279 1.00327 1.00026 1.00632 I •».) p.v. dp t = a. — -00076 11-2° + .00052 10.7 — .00030 14.9 — .00052 13.8 — .00558 15.0 — .00654 11.0 — -00046 1 1.4 ~ " t = + 00094 00053 00056 ,0008 1 00668 00747 Density. O = 32, oOC. P z= 76"» 32- 2.015 ('6°) 28.005 28.000 44.268 44.285 Density- Very small pressure. 32- 2.0173 28.016 28.003 44.014 43996 Rayleigh, Zeitschr. Phys. Chem. 52, 1905. TABLE 60. — CompresslblUty of Air anl Oxygen between 18° and 22° 0. Pressures in metres of mercury, pv^ relative. Air O2 P pv 24.07 26968 34-90 26908 45.24 26791 26789 64.00 26778 72.16 26792 84.22 26840 101.47 27041 214.54 : 29585 » pv 24.07 26843 26614 - 55-50 26185 64.07 26050 25858 84.19 25745 101.06 25639 214.52 26536 ^28^75^ Smithsonian Tables. Amagat, C. R. 1879. Tables 61-62. 8l '*^KftT,'?i^PlI^^^'^ PRESSURE, TEMPERATURE AND VOLUME OF SULPHUR DIOXIDE AND AMMONIA.* TABLE 61.— SnlphuDloziaa. Original Toluiae looooo under one atmosphere of pressure and the temperature of the experi- ments as indicated at the top of the different columns. ^g Corresponding Volume for Ex- Pressure in Atmospheres for nts at Temperature — i< periments at Temperature — Volume. Experime 58°.o 99°.6 1830.2 SS^.o 99°-6 i83°.j 10 8.S60 9440 _ 12 6360 7800 - lOOOO _. 9.60 _ i8 4040 6420 S3IO 440s - 9000 8000 9.60 10.40 10.3s 11.8s : 20 - 4030 - 7000 "•SS 13.05 _ 24 28 _ 334S 2780 3180 6000 12.30 14.70 - 32 - 230s 2640 5000 13-15 16.70 - 36 - 1935 2260 4000 14.00 20.15 - 40 SO _ 1450 2040 1640 3500 14.40 23.00 - 60 - - 137s 3000 - 26.40 29.10 70 - - 1 130 2500 - 30.15 33-25 80 90 _ I 930 790 2000 - 35-20 40-95 100 - - 6§o 1500 — 39.60 55-20 120 - - 545 1000 - - 76.00 140 160 - - 430 325 SCO — - 117.20 TABLE 62.— Ammonia. Original volume looooo under one atmosphere of pressure and the temperature of the experiments as indicated at the top of the different columns. .2 . B. Corresponding Volume for Ex- periments at Temperature — Volume. Pressure in Atmospheres for Experiments 1 at Temperature — 1 46°.6 9,°.6 l83°.6 3C.°.2 46°.6 99°.6 1830.0 10 I2.S IS 20 2S 30 35 40 45 50 70 80 90 100 9500 7245 5880 _ 763s 6305 4645 3560 2875 2440 2080 1795 1490 1250 975 4875 383s 318s 2680 2345 203s 1775 1590 1450 1245 II2S 103s 950 lOOOO 9000 8000 7000 6000 5000 4000 3500 3000 2500 2000 1500 1000 8.8s 9.60 10.40 11.05 11.80 12.00 9-50 10.45 11.50 13.00 14-75 16.60 18-35 18.30 12.00 13.60 15-55 18.60 22.70 25-40 29.20 34-25 41.45 49.70 59-65 19.50 24.00 27.20 31-50 37-35 45-50 58.00 93.60 • From the experiments of Roth, " Wied. Ann." vol. 11, i88a Smithsonian Tables. 82 Table 63. COMPRESSIBILITY OF LIQUIDS. U Fiis the volume under pressure pi atmospheres at t°C, and fa is volume at pressure /a and the same temperature, then the compressibility coefficient may be defined at that temperature as ' /i—pa In absolute units (referred to megadynes) the coefficient is ''=A- 1.0137 Substuce. t. Pressures. ?.IO« Substance. t. Pressures. ^.I0< is Acetone 0.00 1-500 82 I Methyl alcohol 100. 8.68-37.3 221 3 M 0.00 500-1000 S9 tt ' II fl 18.10 8 120 2 ff 0.00 IOOO-1500 47 tt Nitric acid 20.3 1-32 338 II tt 99-S 8-94-36-5 276 3 Oils: Almond 17- 55 8 Benzole 5-9S 8 83 2 Olive 20.5 14.8 - 63 44 n 17.9 8 92 14 Paraffin - 63 6 tt '5-4 1-4 87 4 Petroleum 16.5 - 70 12 tl 78.8 1-4 126 Rock 19.4 - 75 8 Carbon bisulphide 0.00 1-500 66 I Rape-seed 20.3 - 60 " 41 «( 0.00 500-1000 S3 " Turpentin '9-7 - 79 ff II II 0.00 1000-1500 43 II Toluene 10. - 79 13 II II 49-2 1000-1500 5' " i< 100. - 150 44 Chloroform 0. - lOI 5 Xylene 10. - 74 " 11 20. _ 128 11 II 100. - 132 41 II 40, - 162 II Paraffins: CgHu 23- O-I •59 14 II 60. - 204 II CvHie II If 134 (4 II 100. 8-9 211 3 CsHis If ff 121 44 II 100. 19-34 206 C9H20 II ff "3 " Collodium 14.8 97 6 C10H22 If fl 105 44 Ethyl alcohol 28. 150-200 §6 7 C12H26 II If 92 H II II 28. 150-400 81 (( CuHjo II II 83 44 II II 65. 150-200 no tl Cl6H84 II II 75 44 II II 65. 150-400 100 tt Water 0. 1-25 525 I 11 II 100. 150-200 168 tl II 10. II 500 44 II II 100. 150-400 132 It II 20. If 491 " If It J85. 150-200 320 tt II 0. 25-50 5.6 (1 II II 185. 150-400 245 tt II 10. 11 492 44 II II 310. 150-200 4200 It II 20. fl 476 " M II 310. 150-400 «53o (( II 0. I-IOO 5" 44 II If 0. 1-50 96 I II 10. II tl tl If ff 20. 1-50 112 If II 20. II 44 II If 40. 1-50 'o^ " II 5°- " 449 44 If fl 0. 100-200 8s (( If 100. II 478 (1 li II 0. 300-400 ^ 41 ff 0. I 00-200 492 44 ff ff 20. 300-400 r 44 ff 10. " 461 44 ff ff 40. 300-400 87 44 If 20. " 442 14 ff ff 0. 500-600 64 44 ff 50. II 46S « If ff 0. 700-800 S6 41 fl 100. II 44 If ff 20. 700-800 62 14 If 0. 1-500 475 44 II ff 40. 700-800 65 <4 If 20.4 11^ 434 If ff fl 0. 900-1000 52 (1 ff 48.85 ■1 4* Ethyl chloride II. 8.5-34.2 138 3 If 0. 500-1000 4.6 U II II 15.2 8.7-37.2 153 44 If 0. lOOO-ICOO 358 It II fl 61.S 12.6-34.4 256 4( If 20.4 fl ■■ 338 tt -33S Alabaster : Gas carbon 1.88 119 Carbonate 2.69-2.78 168-173 Glass : Sulphate 2.26-2.32 141-145 Common 2.4-2.8 150-175 180-370 Alum, potash 1-75 109 Flint 2.9-5.9 Amber I.06-I.II 66-69 Glauber's salt . 1.4-1.5 87-93 Anthracite 1.4-1.8 87-112 Glue .... 1.27 80 Apatite . 3.16-3.22 197-201 Gneiss 2.4-3.2 150-200 Aragonite . 3-0 187 Granite 2.0-3.0 125-187 Arsenic S-7-572 356-358 Graphite . 1.9-2.3 1.2-1.8 120-140 Asbestos . 2.0-2.8 125-175 Gravel 94-112 Asphaltum i.i-i.S 69-94 Gray copper ore 4-4-5-4 275-335 180-185 Barite 4-5 281 Green stone 2.9-3.0 Basalt 2.4-3.1 150-193 Gum arabic 1.3-1.4 80-S5 Beeswax . 0.96-0.97 60-61 Gunpowder : Bole . 2.2-2.5 137-156 Loose 0.9 56 Bone . 1.7-2.0 106-125 Tamped . I-7S 109 Boracite . 2.9-3.0 181-187 Gypsum, burnt . 1.81 "3 Borax 1. 7-1. 8 106-I12 Hornblende 3-0 187 Borax glass 2.6 162 Ice ... . 0.88-0.91 55-57 Boron 2.45-2.69 153-168 Iodine 4.67 291 Brick 1.4-2.2 87-137 Ivory .... 1.83-1.92 1 14-120 Butter 0.86-0.87 53-54 Kaolin 2.2 '37 Calamine . 4.1-4.5 255-280 Lava: Calcspar . 2.6-2.8 162-175 Basaltic . 2.8-3.0 I7S-'8S 125-168 Carbon. Trachytic 2.0-2.7 See Graphite, etc. Lead acetate 2.4 150 Caoutchouc 0.92-0.99 57-62 Leather : Celestine . 3-9 243 Dry 0.86 54 Cement : Greased . 1.02 64 Pulverized loose . 1.15-1.7 72-105 Lime : Pressed . 1.8s 16S-187 Mortar . 1.65-1.78 103-1 I I Set 2.7-3.0 Slaked . I.3-I.4 81-87 Cetin 0.88-0.94 55-59 Lime .... 2-3-3-2 144-200 Chalk 1.9-2.8 I18-175 Limestone . 2.0-3.1 125-igo Charcoal : Litharge : Oak 0.57 35 Artificial 9-3-9-4 580-585 Pine 0.28-0.44 '7-5-27-5 Natural . 7.8-8.0 489-492 Chrome yellow 6.00 374 Magnesia . 3.2 200 Cinnabar . 8.12 507 Magnesite . 3-0 187 Clay . 1.8-2.6 122-162 Magnetite . 4-9-5-2 306-324 Clayslate . 2.8-2.9 175-180 Malachite . 3-7-4-1 231-256 Coal, soft . 1.2-1.5 75-94 Manganese : Cobaltite . 6.4-7-3 400-455 Red ore . 3-46 3-9-4-1 2.5-2.8 216 Cocoa butter Coke 0.89-0.91 1.0-1.7 56-57 62-105 Black ore Marble 243-256 157-177 100-156 116-144 Copal 1.04-1.14 65-71 Marl .... 1.6-2.5 1.85-2.3 Corundum Diamond . Anthracitic . Carbonado . Diorite Dolomite . 3-9-40 245-250 Masonry . 2.4-2.9 220-225 104 188-203 175-193 150-181 Meerschaum Melaphyre . Mica .... Mortar ."" . Mud .... .99-1.28 2.6 2.6-3.2 1.6 61.8-79.9 162 165-200 109 102 Earth, dry . Ebonite . Emery Epsom salts : Crystalline . Anhydrous . Feldspar . Flint . Fluor spar Gabronite . Gamboge . Galena 1.6-1.9 4.0 1. 7-1.8 2.6 2.53-2.58 100-120 72 250 IC6-112 162 1 58-161 Nitroglycerine . Ochre Opal .... Orpiment . Paper. Paraffin Peat .... 1.6 3-5 2.2 3-4-3-s 0-7-1.15 0.87-0.91 0.84 2?i 212-218 44-72 54-57 52 2.63 164 Phosphorus, white . 1.82 114 3.14-3-18 2.9-3.0 1.2 7-3-7-6 196-198 181-187 P 460-470 Pitch .... Porcelain . , Porphyry . Potash 1.07 2-3-2-5 2.6-2.9 2.26 67 143-156 162-181 141 SMiTHsonrAN Tables. * For elements, see Table 66. Tables 68 [coutinued) and 69. DENSITY OF VARIOUS SUBSTANCES. 89 TABLE 68 (coK/iVziuri/).— Density olVailons Solids. Grammes Pounds Grammes Pounds Substance. per cubic per cubic Substance. per cubic per cubic centimetre. foot. centimetre. foot. Pyrites 4-9-S-2 306-324 Snow, loose 0.125 7.8 Pyrolusite . 37-4-6 231-287 Soapstone, Steatite . 2.6-2.8 162-175 Pumice stone 0.37-0.9 23-56 Soda: Quartz 2.6s 165 Roasted . 2.5 156 Resin 1.07 67 Crystalline 1.45 90 Rock crystal 2.6 162 Spathic iron ore 3-7-3-9 231-243 Rock salt . 2.28-2.41 142-150 Starch 1-53 95 Sal ammoniac 1. 5-1.6 94-100 Stibnite 4.6-4.7 287-293 Saltpetre . 1.95-2.08 122-130 Strontianite 37 231 Sand: Syenite 2.1-3.0 130-190 Dry. 1.40-1.65 87-103 II9-128 Sugar .... 1. 61 100 Damp 1.90-2.05 Talc . . . . 2.7 168 Sandstone . 2.0-3.2 124-200 Tallow 0.91-0.97 570-605 Selenium . 4.2-4.8 262-300 Tellurium . 6.38-6.42 398-401 Serpentine . 2.43-2.66 152-166 Tile . . . . 1.4-2.3 87-143 Shale . 2.6 162 Tinstone . 6.4-7.0 399-437 Silicon 2.0-2.5 125-156 Topaz 3-S-3-6 219-223 Siliceous earth 2.66 166 Tourmaline 2.94-3.24 183-202 Slag, furnace 2.0-3.9 124-240 Trachyte . 2.7-2.8 168-175 Slate . 2.6-3.3 162-205 Trap . . . . 2.6-2.7 162-170 TABLE 89.— Density or Mass In Qrammes per Cublo Oentlmetre anlFonnds per Cnblo Footol Vulons Allays (Brasses and Bronzes). Grammes Pounds Alloy. per cubic per cubic centimetre. foot. Brasses : Yellow, 70CU -|- 3oZn, cast 8.44 527 " " " rolled . 8.56 534 " " " drawn 8.70 542 Red, goCu + loZn 8.60 536 White, 5oCu + joZn . 8.20 5'J Bronzes : goCu - - loSn .... 8.78 548 85CU - - i5Sn .... 8.89 555 8oCu - - 2oSn .... 8.74 545 7SCu ^ - 25Sn .... 8.83 "« German Silver: Chinese, 26.3CU + 36.6Zn + 36.8 Ni 8.30 518 " " Berlin (i) 52CU-I- 26Zn-- 22N1. 8.45 527 " " " (2) 59Cu4-3oZn-- iiNi. 8.34 520 " « " (3) 63CU + 3oZn - - 6Ni . 8.30 518 " " Nickelin 8.77 l!i^ Lead and Tin : 87.5Pb -|- i2.5Sn . 10.60 661 644 627 588 " " " 84Pb + i6Sn 10-33 " " " 77.8Pb--22.2Sn . 10.05 63.7Pb--36.3Sn . 9-43 873 8.24 10.56 ' 467 Pb-- 53-3Sn . 545 " " " 30.5Pb + 69.sSn .... Bismuth, Lead, and Tin : 53Bi 4- 4oPb -f- 7Cd . 5'4 659 605 480 1176 1145 Wood's Metal: 5oBi + 25Pb + i2.5Cd 4" i2.5Sn 9.70 Cadmium and Tin : gzCd-j- 68Sn . 18.84 18.36 Gold and Copper : 98AU -|- 2Cu . " " " 96AU -|- 4Cu . « « " 94AU -)- 6Cu . «7-95 « " " 92AU -i- 8Cu . 17.52 17.16 16.81 1093 " " " goAu -j- loCu . " " " 88Au -f- 12CU . 1049 « « " 86Au -1- 14CU . 2.80 21.62 21.62 21.87 22.38 1027 480 522 542 1348 1348 1364 1396 Aluminum and Copper : loAl 4- 9°^" " " " 5AI -f 95CU " " " 3AI -f 97CU Aluminum and Zinc : 91AI -f 9Zn Platinum and Iridium : 9oPt -|- loir . SsPt 4- I5lr . « " " 66.67 Pt 4- 33-33lr « " « 5Pt + 95lr Smithsonian Tables. go Table 70. DENSITY OF LIQUIDS. Density or miss in grammes per cubic centimetre and in pounds per cubic foot of various liqmds. Grammes per Founds per Temp. C. Liquid. cubic centimetre. cubic foot Acetone 0.792 49.4 0° Alcohol, ethyl . 0.791 49-4 " methyl 0.810 50-5 " proof spirit 0.916 57-2 Anilin .... I-03S 64.5 Benzene .... 0.899 56.1 Bromine .... 3-'87 ^ 199.0 Carbolic acid (crude) 0.950-0.965 59.2-&3.2 IS Carbon disulphlde . 1.293 80.6 15 18 Chloroform 1.480 923 Ether 0.736 45-9 Gasoline , 0.66-0.69 41.0-43.0 - Glycerine . Milk. 1.260 1.028-1.035 78.6 64.2-64.6 Naphtha (wood) 0.848-0.810 52.9-50.5 Naphtha (petroleum ethei ) 0.66s 41.S »S Oils : Amber . 0.800 49-9 »s Anise-seed 0.996 61.1 16 Camphor 0.910 56.8 "- Castor . 0.969 60.5 IS Cocoanut 0.925 ^l M Cotton seed . 0.926 Creosote . 1.040-1.100 64.9^.6 IS Lard 0.920 57.4 II Lavender 0.877 54.7 16 Lemon . 0.844 ^l-l 16 Linseed (boiled) 0.942 58.8 IS Mineral (lubricatlnj !) 0.900-0.925 56.2-57.7 20 Olive 0.918 S7-3 IS Palm 0.905 S6-S IS Pine 0.850-0.860 53-0-S4-0 IS Poppy . 0.924 S7-7 - Rapeseed (crude) 0.915 S7-I IS " (refined) 0.913 57.0 IS Resin 0-955 59-6 15 Train or Whale 0.918-0.925 S7.3-S7-7 M Turpentine 0.873 54.2 Valerian . 0.965 60.2 16 Petroleum 0.878 54.8 (light) . 0.795-0.805 49.6-50.2 IS Pyroligneous acid . 0.800 49.9 Sea water . 1.025 64.0 IS Soda lye . 1.210 75-S 17 Water 1. 000 62.4 4 Smithsonian Tables. Table 71 • DENSITY OF GASES. 91 The following table gives the density of the gases at 0° C, 76 cm. pressure, at sea-level and lati- tude 45° relative to air as unity and under the same conditions j also the weight of one litre in grammes and one cubic foot in pounds. Gas. Specific Gravity. Grammes per litre. Pounds pel* cubic foot. Reference. Air Acetylene Ammonia Argon Bromine Butane Carbon dioxide " monoxide Chlorine _ , ( from Coal gas I ^^ Cyanogen Ethane Fluorine Helium Hydrofluoric acid Hydrobromic acid Hydrochloric acid Hydrogen Hydrogen sulphide Krypton Methane Neon Nitrogen Nitric oxide, NO Nitrous oxide, N2O Oxygen Sulphur dioxide Steam at 100° Xenon 1. 000 0.92 0-597 1-379 5-524 2.01 1.5291 0.9672 2.491 0.320 0.740 1.806 I.07S 1.26 1.368 0.7126 2.71 J.2692 0.0696 1.1895 2.818 0.5576 0.674 0.9673 1.0387 1.5301 1-053 2.2639 0.469 4.422 1.2928 1. 1620 0.7621 1.782 7.1426 2.594 1.9652 1.2506 3.1666 0.414 0.957 2.3261 1. 3421 1.697 0.1787 0.894 3-6163 1.6283 0.09004 1-5230 3-654 0.7160 0.893 1.2542 1-3417 I 1.4292 2.861 1 0.581 5-717 .08071 .07254 .04758 .1112 •4459 .16194 .12269 .07807 .19769 .02583 •05973 .14522 .08379 .1059 .01 n6 .05581 .2258 .10165 .005621 .09508 .2281 .04470 .0558 .07829 .08376 .12291 .08922 .17862 -0363 ■3569 Rayleigh; Leduc. Berthelot, i860. Leduc, C. R. 125, 1897. Ramsey-Travers, Proc. R. Soc. 67, 1900. Jahn, 1882. Frankland, Ann. Ch. Fharm. 71. Rayleigh, Froc. R. Soc. 62, 1897. Leduc, C. R. 125, 1897. Gay-Lussac. Kolbe, Ann. Chem. Pharm. 65. Moissan, C. R. 109. Ramsey-Travers, Proc. R. Soc. 67, 1900. Thorpe- Hambley, J. Chem. Soc. 53. Lowig, Gmelin-Kraut, Org. Chem. Leduc, C. R. 125, 1897. Rayleigh, Proc. R. Soc. 53, 1893. Leduc, C. R. 125, 1897. Ramsey-Travers, Proc. R. Soc. 67, 1900. Thomson. Ramsey-Travers, Proc. R. Soc. 67, 1900. Rayleigh, Proc. R. Soc. 62, 1897. Leduc, C. R. 116, 1893. " C. R. 125, 1897. Rayleigh, Proc. R. Soc. 62, 1897. Leduc, C.R. 117, 1893. Ramsey-Travers, Proc. R. Soc. 67, 1900. Compiled partly from Landolt-Bornrtein-Meyerhoffer's Physikalisch-Chemische Tabellen. Smithsonian Tablcbi 92 Table 72/ DENSITY OF AQUEOUS SOLUTIONS.* The following table gives- the density of solutions of various salts in water. The numbers give the weight i grammes per cubic centunetre. For brevity the substance is indicated by formula only. Substance. Weight of the dissolved substance in loo parts by weight of the solution. 25 Authority. K2O . KOH NajO NaOH NHj. NH4CI KCl . NaCl. LiCl . CaCl2 CaCla + eHaO AlCls , MgCla MgCla+eHsO ZnCl2 CdCla . SrClj. , SrClj + eHaO BaCIz . . . BaCl2+2H20 CUCI2 NCI2. HgCla FeaCls PtCU. SnCl2+2H20 SnCU+sH20 LiBr . KBr . NaBr MgBr2 ZnBr2 CdBr2 CaBra BaBra SrBr2 KI . Lil . Nal . Znl2 . Cdlj . Mglj. Cals . Sris . Bala • NaClOs NaBrOa KNOb NaNOs AgNOa 1.047 1.040 I.073 1.058 0.978 1.015 1. 03 1 '■035 1.029 1.041 1.019 1035 1. 04 1 1.014 1.043 1.043 1.044 1.027 1.045 I -035 1.044 1.048 1. 04 1 1.041 1.046 1.032 1.029 I -033 1-035 1.038 1. 041 1.043 1. 04 1 1.042 1.043 1.043 1.036 1.036 1.038 1. 043 1.042 1. 04 1 1.042 1.043 1.043 1-035 1.039 1. 03 1 1.03 1 1.044 1.098 1.082 1.144 1. 114 0-9S9 1.030 1.065 1.072 1.057 1.086 1.040 1.072 1.085 1.032 1.089 1.087 1.092 i-°S3 1.094 1.075 1.091 1.098 1.092 1.086 1.097 1.067 1.058 1.070 1-073 1.078 1.085 1. 09 1 1.088 1.087 1.090 1.089 1.076 1.077 1.080 1.089 1.086 1.086 1.088 1.089 1.068 1.081 1.064 1.065 1.090 I-I53 1.027 1.218 1. 169 0.940 1.044 1.099 1. 110 1.085 1.132 1.061 i.iii 1.130 1.049 ••135 1.138 I-I43 1.082 1.147 1. 119 I-155 1.157 1.130 I-IS3 1.104 1.089 1.111 1.114 1-123 ■•135 1. 194 1-139 I.I37 1.142 1.140 1. 118 1.122 1.126 1.138 1.136 1-137 1.138 1.140 1.141 1.106 1.127 1.099 i.ioi 1.140 1.214 1.076 1.284 1.224 0.924 1.058 I-I35 1.150 1.116 1.181 1-083 1-153 1.177 1.067 1.184 1-193 1.198 i.iii 1.205 1.166 1.221 1.223 1.179 1.214 I-I43 1.122 1.154 1.157 1.172 1.189 1.202 1.197 1.192 1.199 1.198 1.164 1. 170 1.177 1.194 1.192 1.192 1.196 1.198 1.199 1.145 1.176 1-135 1.140 1.195 1.284 1.229 1-354 1.279 0.909 1.072 1.191 1.147 1.232 1.105 1.196 1.226 1.085 1.236 1.254 1.257 1.042 1.269 1.217 1.291 1.299 1-354 1-503 1-659 1.286 1.410 1.538 1.185 1-157 1.202 1.205 1.224 1.245 1.263 1.258 2.250 1.260 1.260 1.216 1.222 1.232 1-253 1.251 1.252 1.258 1.260 1.263 1.188 1.229 1.180 1.255 1.421 1.181 1.286 1.128 1.241 1.278 1.103 1.289 1-319 1.321 1.174 1-273 1.360 1.290 1.362 1.229 1193 1.252 1.254 1.279 1.308 1.328 1-324 1313 1-327 1.328 1.269 1.278 1.292 1.366 1-317 1-318 1-319 1-328 1-331 1-233 1.287 1.222 1-322 1-557 1.436 1-255 1.402 1.176 1.340 1.141 1.417 1.469 1.242 1.527 1-413 1.546 1-329 1.274 1.366 1.364 1.408 1-449 1-473 1.479 1.459 1.483 1.489 1-394 1.412 1.430 1.418 1.474 1-472 1-475 1.489 1-493 1.329 1-313 1.479 i.b»9 1-539 1.225 1.183 1-563 1-653 1-317 1-545 1.785 1.444 1-365 1.498 1-563 1.623 1.648 1.678 1.639 1.683 1-693 1.544 1-573 1.598 1.648 1.678 1.666 1.663 1.693 1.702 1.416 1-675 1.809 1.666 1.829 1.642 1.276 1.222 1-737 1.887 1.668 1.580 1.467 1-873 1-953 1-732 1-775 1.808 1-873 1-913 1.908 1-953 1.968 1.918 15- 15- 15- :i: IS- IS- IS- iS- 15- 18. IS- IS- 24- 19-5 19.S 15- IS- IS- 21. 17-S 17-S 20. 17-5 IS- IS- 19-5 I9-S 195 19.5 19.5 195 19.5 19-5 19.5 19.5 19-5 19.5 19.5 19.5 19-S 19-5 19.5 19.5 19.5 19s 15- 20.2 15- Schifif. Carius. Gerlach. Schia Gerlach. u Schiff. Kremers, Gerlach. It tt SchifE. Franz. MendelejeS. Hager. Precht Gerlach. Kremers. Gerlach. Schiff. Kohlrausch. * Compiled from two papers on the subject by Gerlach in the " Zeit. fur Anal. Chim.," vols. S and xj. Smithsonian Tables, Table 72 (enuiituid). DENSITY OF AQUEOUS SOLUTIONS. 93 Weight of the dissolved substance in loo parts by weight of the solution. u Substance. 1 Authority. 5 zo IS 20 n 30 40 50 60 NH4NO8 . . . 1.020 1. 041 1.063 1.085 1. 107 I.I3I 1. 178 1.229 1.282 17-5 Gerlach. ZnNOs .... 1.048 1.095 1. 146 1.201 1.263 1.325 1.178 1.456 1-597 - 17-5 Franz. ZnNOs+eHaO . - 1.054 - 1.113 - 1.250 1.329 - 14. Oudemans, Ca(N08)2 . . . Cu(N08)2 . . • 1-037 1-075 1. 118 1. 162 1. 211 1.260 1-367 1.482 1.604 17-5 Gerlach. 1.044 1.093 I-I43 1.203 1.263 1.328 1.471 - - 17-5 Franz. Sr(N08)2 . • • 1.039 1.083 1. 129 1.179 - - - - - 19.5 Kremers. Pb(NOa)2 . . . 1.043 1. 091 I-I43 1.199 1.262 1-332 - - - 17-5 Gerlach. Cd(N08)2 . . . Co(N08)2 . . . 1.052 1.097 1. 150 1.212 1.283 I-3SS 1.318 1-536 1-759 - 17-5 Franz. 1. 045 1.090 I-I37 1. 192 1.252 1-465 - - 17-5 " Ni(N08)2 . . • 1. 04s 1.090 I-I37 1.192 1.252 1.318 1.465 — — 17-5 " Fe2(N08)6 • • ■ 1.039 1.076 I.II7 1.160 1. 210 1.261 1-373 1.496 1-657 17-5 u Mg(N08)2+6H20 Mn(NOs)2+6HaO 1.018 1.038 1.060 1.082 1. 105 1. 129 1-179 1.232 — 21 Schiff. 1.025 1.052 1.079 i.ioS I.I38 1.169 1-235 1-307 1.386 8 Oudemans. KaCOs .... 1.044 1.092 1. 141 1.192 1.245 1.300 1.417 1-543 — . IS Gerlach. K2CO8+2H2O . 1-037 1.072 I. no 1.150 1. 191 1-233 1.320 1-415 I.5II 15- Na2C08loH20 . i.oig 1.038 1.057 1.084 1.077 1.098 1.118 - - - 15- Schiff. (NH4)2S04 . . te2(S04)8 . • . 1.027 1.055 1. 113 1.142 1. 170 1.226 1.287 - 't- 1.045 1.096 I.I 50 I.08I 1.207 1.270 1-336 1.238 — — is. Hager. Schiff. Gerlach. FeS04 + 7H20 . 1.025 1-053 I. Ill 1. 141 1-173 *- ~ 17.2 MgS04 . . . . 1. 05 1 1. 104 I.I6I 1.221 1.284 — — — ~ 15 MgSO + 7H2O . 1.025 1.050 1-075 I.IOI 1. 129 1.155 1.21S 1.278 - 15- u Na2So4+ioH20 1.019 1.039 1.059 i.o8i 1. 102 1.124 — — "" \l Schiff. Gerlach. Schiff. CUSO4+5H2O . 1. 031 1.064 1-134 I-I73 1.213 ■" 1-398 ~ MnS04 + 4H20 . I -03 1 1.064 1.099 '-'35 1.174 1.214 1-303 ~ 15- ZnS04+7H20 . 1.027 1.057 1.089 1. 122 1. 156 1. 191 1.269 1-351 1-443 20.5 Fe2(SO)8+K2S04 +24H2O. . . 1.026 1.045 1.066 i.o88 1.112 1.141 _ - - 17-S Franz. Cr2{SO)3+K2S04 + 24H2O . . 1.016 "033 I.05I 1-073 1.099 1.126 1.188 1.287 1-454 17-5 t( MgS04 + K2SO4 + 6H2O . . . 1.032 1.066 I.IOI 1.138 - - - - - 15- Schiff. (NH4)2S04 + u FeS04 + 6H20 1.028 1.058 1.090 1. 122 1.154 1. 191 ■■ •" ~ 19. it K2Cr04 . . . • 1-039 1.082 I.I27 1.174 1.225 1.279 1-397 ^ "* 19-5 K2Cr207 . . . 1-035 1.071 I.I08 1. 126 - - - - - 19.5 13 Kremers. Schiff. Fe(Cy)6K4 . • • 1.028 1.059 1.092 "" ~ li re(Cy)6K8 . . . 1.025 1.053 I.I45 1.179 ^ ~ Pb(C2H302)2 + 3H2O . . . . 1.031 1.064 1. 100 1-137 1.177 1.220 1-31 5 1.426 - 15- Gerlach. 2NaOH + AsjOs + 24H2O . . SOs 1.020 1.042 1.066 1.089 1. 114 1.140 1.194 - - 14. 15- 4- 15- 15- 15- Schiff. Brineau. Schiff. 5 10 '5 ao 30 40 60 80 100 1.040 1.084 I.I32 I.179 1.277 1-389 1-564 1.840 - SO2 • . N2O6 . ■ I.013 1-033 1.028 1.069 1.045 1. 104 1.063 1. 141 1. 217 1.294 1.422 1.506 - Kolb. Gerlach. C4H«0« . CeHgO, . 1. 02 1 I.018 I -047 1.038 1.070 1.058 1.096 1.079 1.150 r.123 1.207 1.170 1-273 - - Cane sugar 1. 01 9 1-039 1.060 1.082 1.129 1.178 1.289 ~ ~ 17-5 15- Kolb. HCl . . HBr . . 1.025 I-03S 1.050 1-073 1.075 1. 114 I.IOI I.I58 I.15I 1.257 1.376 - - - j 14- 13- 15- 17-5 17-5 15- 15- 15- Topsoe. HI . . H2SO4 . HsSiFU . P2O6 . . P2O5 + 3HS HNO. . C2H4O2 . o". 1-037 1.032 1.040 I -03s 1.027 t.028 1.007 1.077 1.069 1.082 1.077 1.057 1.056 1.014 i.n8 1. 106 1.127 1. 119 1.086 1.088 1. 02 1 1.165 1.145 1.174 1.167 1.119 1.02I 1. 27 1 1.223 1-273 1.271 I.I88 I.I84 1.041 1.400 1.307 1-38S 1.264 1.250 1.052 1.501 1.676 1.438 1-732 1.455 1.07 s 1.838 1.528 i-oSS Kolb. Stolba. Hager. Schiff. Kolb. Oudemans. Bmithsonian Tables. 94 Table 73. DENSITY OF WATER AT DIFFERENT TEMPERATURES BETWEEN O" AND 36°C. The temperatures are for the hydrogen thermometer. Temp. C. .0 .1 .H .3 .4 .6 .6 .7 .8 .9 0.999868 874 881 887 893 899 90s 911 916 922 I 2 927 968 932 971 936 974 941 977 945 980 P^ ut p7 961 989 965 991 3 992 994 99S 996 997, 99i. 999, 999 000 000 4 1.000000 000 000 999* 999* 998* 997* 996* 995* 993* 5 0.999 992 990 9^ 986 984 982 979 977 974 971 6 96s 962 958 954 95' 947 943 938 934 7 929 925 920 i'5 910 904 899 893 888 882 8 87S 870 864 851 844 837 830 823 816 9 8b8 801 793 78s 778 769 761 753 744 736 10 727 718 709 700 691 681 672 662 652 642 II 632 622 612 601 59' 580 569 558 547 536 12 525 513 502 490 478 466 454 442 429 '^F '3 •404 39' 379 366 353 339 326 312 299 285 J4 271 257 241 229 215 200 186 «7i 156 141 15 126 III 096 081 06s 050 034 0x8 002 986* i6 0.998 970 'vll 937 920 904 887 870 ?53 836 819 '7 801 766 749 731 '^ 695 677 6s9 640 i8 622 603 585 566 547 509 49° 471 451 19 432 412 392 372 352 332 312 292 271 251 20 230 210 189 168 147 126 los 083 062 040 21 019 997* 975* 953* 931* 909* 887* 864* 842* 819* 22 0.997 797 774 7SI 728 705 682 659 63s 612 S88 23 565 S4I 517 493 469 iU 421 396 372 ^*I 24 323 298 273 248 223 '73 H7 122 096 25 071 04S 019 994* 968* 941* 9rs» 889* 863* 836* 26 0.996810 783 756 730 703 676 648 621 594 567 27 539 5*2 484 456 428 400 372 344 316 288 28 259 23' 202 174 l*^ 116 087 % 029 000 29 0.995971 941 912 882 853 823 793 733 703 30 673 643 613 582 552 521 491 460 429 398 3' 367 336 ^8^. 273 242 211 179 148 116 084 32 052 020 956* 924* 892* 859* 827* 794* 762* 33 0.994729 696 663 630 597 564 531 498 464 431 34 398 364 330 296 263 229 195 161 126 092 35 058 023 989 954 920 88s 850 815 780 745 Ifw e put D't for the density of water containing air and Di for the densit; of water free from air, we get the following, due to Marek : t= 0123456789 10 io'(Df -D't)=25 27 29 31 32 33 33 34 34 33 32 t= 11 12 13 14 15 16 17 18 19 20—32 io'(Df -D't)=3i 29 27 25 22 19 i6 12 8 4 negligible From the obsenrations oi Thiesen, Scheel, and Siesselhont, Win. Abh. Fhys-Techn. Reich*. 3, 68 i 1900. Smithsonian Tables. Table 74. 95 VOLUME IN CUBIC CENTIMETRES AT VARIOUS TEMPERA- TURES OF A CUBIC CENTIMETRE OF WATER AT THE TEMPERATURE OF MAXIMUM DENSITY. The water in this case is supposed to be free from air. by the hydrogen thermometer. The temperatures are Temp.C. .0 .4 .6 I 2 3 4 S 6 I 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 29 30 31 32 33 34 35 i.ooo 132 073 032 008 000 008 032 071 124 192 273 368 476 596 729 874 i.ooi 031 200 380 571 773 98; 1.002 208 441 685 938 1.003 2°i 473 1.004046 346 65s 972 1.005 299 634 978 126 069 029 006 000 010 03s 075 130 199 282 487 609 743 757 890 048 218 399 591 794 007* 465 710 964 227 52' 783 07 s 376 686 005* 332 668 013* 119 064 026 005 000 012 039 080 137 207 291 388 499 622 905 064 23s 417 610 81S 029* 254 489 735 990 254 ?29 812 105 407 717 037* 36s 702 047* "3 059 023 004 001 014 042 085 143 215 300 399 5" 63s 772 920 081 253 436 630 051* 277 760 016* 281 841 135 437 749 070* 399 736 082* 107 055 020 003 001 016 046 090 149 223 309 409 522 648 786 936 098 271 650 857 073' sp 7§5 °5i 018 002 002 018 050 096 156 231 319 420 534 661 800 951 114 289 474 671 878 096* 324 562 810 042* 068* 094* 308 870 165 468 781 102* 432 771 118* 336 613 899 194 499 812 135" 465 805 153' 095 047 016 001 003 021 054 lOI 163 239 328 431 675 815 967 131 307 493 691 118* 347 586 835 089 043 013 001 004 023 058 107 170 247 338 442 688 830 844 363 641 928 225 530 844 167* 499 839 188* 983 148 325 513 711 921 140* 370 611 861 121* 390 669 957 255 561 §76 200* 533 874 084 039 on 000 005 026 062 112 177 256 348 453 571 702 999 165 343 532 732 942 163* 394 886 147* 418 698 987 28s 592 908 566 908 223* 259* 079 035 009 000 007 029 066 118 184 264 464 584 859 015* 361 55« 752 964 186* 418 660 912 174* 445 726 016* 3"5 623 940 266* 600 943 294* W the ob«rvation, o£ ThUsen. Scheel, and Di«s.lho«.. Wis.. Abh. Phys.-Techn. Rdch.. 3, 00 I 1900. Smithsonian Tables. 96 Table 75. DENSITY AND VOLUME OF WATER. The mass of one cubic centimetre at 4° C. is taken as unity. Temp. C. Density. Volume. Temp. C. Density. Volume. —10° O.9981S 1.00X86 +350 0.99406 1.00598 =^ 157 36 371 633 869 131 37 336 669 —7 892 108 38 299 706 -6 912 088 39 262 743 —5 0.99930 1.00070 40 0.99224 1.00782 —4 945 958 055 41 186 821 —3 042 42 147 861 — 2 970 031 43 107 901 — I 979 021 44 066 943 +0 0.99987 I.OOOI3 45 0.99025 1.0098s I 993 007 46 0.98982 1.01028 2 997 003 47 §45 072 3 999 001 48. 896 116 4 I.OOOOO I.OOOOO 49 852 162 5 0.99999 I.OOOOI 50 0.98807 1.01207 6 997 003 51 762 254 7 9^^ 007 52 11^ 301 8 012 S3 669 349 9 981 019 54 621 398 10 0-99973 1.00027 55 0.98573 1.01448 II 963 037 60 324 70s 12 952 048 • 6s 059 979 13 940 060 70 0.97781 1.02270 14 927 073 75 489 576 15 0.99913 1.00087 80 0.97183 1.02899 16 103 85 0.96865 1-03237 17 880 120 90 534 590 18 862 138 95 192 959 19 843 157 100 0.95838 i^04343 20 0.99823 I.OOI77 110 0.9510 1.051S 21 802 198 120 •9434 1.0601 22 780 221 130 ■9352 1.0693 23 7S6 'i^ 140 .9264 1.0794 24 732 268 150 •9173 1.0902 25 0.99707 1.00294 160 0.907 s 1.1019 26 681 320 170 •8973 1.1145 27 654 347 180 .8866 1. 1279 28 626 375 190 .8750 1.1429 29 597 405 200 .8628 1.1590 30 0.99567 1.00435 210 0.850 1. 177 31 537 466 220 .837 1.19s 32 50s 497 230 .823 1.215 33 473 530 240 .809 1.236 34 440 563 250 •794 1.259 * From — 10° to o° the values are due to means from Pierre, Weidner, and Rosetti : Irom o°to 35O, to Thiesen, Scheel, and Diesselhorst ; 31° to 100°, to Thiesen i 110° to 250°, to means from the works of Ramsey, Young, Waterston, and Him. Smithsonian Tables. Table 76. DENSITY OF MERCURY. 97 Density or mass in grammes per cubic centimetre, and tiie volume in cubic centimetres of one gramme of mercury. Tlie density at o° is taken as 13.59545,* and the volume at temperature t is Vj=V,(i+.oooi8i792/ + i7SXio-i2^2+35u6Xio-i6^).t Mass in Volume of Mass in Volume o£ Temp. C. grammes per X gramme in Temp. C. grammes per I gramme in cu. cm. cu. cms. cu. cm. cu. cms. —10° 13.6202 0.073420? 30° 13-5217 0.0739552 —9 6177 4338 31 ^1 9686 —8 6152 4472 32 9820 —7 6128 4606 33 5144 9953 —6 6103 4739 34 5119 40087 —5 13.6078 0.0734873 35 13-5095 0.0740221 —4 6053 5006 36 5070 °^li —3 6029 5140 37 5046 0488 — 2 6004 5273 38 5021 0622 — I 5979 5407 39 4997 0756 13-5955 0.0735540 40 13-4973 0.0740891 I 5930 5674 50 4729 2229 2 5808 60 4486 3569 3 5881 5941 70 4244 4910 4 5856 6075 80 4003 6252 5 '3-5832 0.0736209 90 13.3762 0.0747594 6 5807 6342 100 3522 8939 7 5782 6476 no 3283 50285 8 5758 6610 120 3044 1633 9 5733 6744 130 2805. 2982 10 13-5708 0.0736877 140 13.2567 °-°"li^ II 5684 701 1 150 2330 12 5659 7145 160 2093 7044 13 14 5634 5610 7278 7412 180 ,856 1620 8402 9764 15 13-5585 0.0737546 190 13-1384 0.0761 1 28 16 5561 200 1 148 ^i? 17 5536 7813 210 °i'3 3865 iS 55'2 220 0670 il?i 19 5487 8081 230 0443 20 13.5462 0.0738215 240 13.0209 0.0767996 9381 70769 2161 3558 21 22 23 24 5438 5413 5389' 5364 8348 . 8482 8616 8750 250 270 280 12.9975 9741 9507 9273 25 26 27 28 29 13-5340 5315 5266 5242 0.0738883 9017 9iqi 9285 9419 290 300 310 320 330 8572 8339 8105 0.0774958 7774 9189 80609 30 13.5217 0.0739552 340 360 12.7872 7638 7405 0.0782033 3464 4900 * Thiesen und Scheel, ThStigkeitsbericht der Phys. Reichsanstalt. 1897-1898. t Broch, /. e. Smithsonian Tables. 98 Table 77. SPECIFIC GRAVITY OF AQUEOUS ETHYL ALCOHOL. (a) The numbers here tabulated are the specific gravities at 60° F., in terms of water at ?'«,^f"' *™P°^; ture, of water containing the percentages by weight of alcohol of speafic gravity .7938, with reference to me same temperatures.* tit 1 2 3 4 6 6 7 8 Specific gravity at I5°.s5 C. in terms of water at the same temperature. 10 20 30 40 50 60 1° 80 90 1. 0000 .9841 .9716 .9578 •9396 0.9184 .8956 .8721 .8483 .8228 ■9703 .9560 •9376 .9160 .8932 .8696 .8459 .8199 .9965 •9815 .9691 •9544 •9356 .8672 .8434 .8172 .9678 .9528 •9335 l886 .8408 .8145 •9930 .9789 .9665 .9511 •9314 18863 .8625 .8382 .8118 .9914 •9778 .9652 •9490 .9292 !8840 .8603 •8357 .8089 .9898 .9766 .9638 .9470 .9270 fstl .8581 .9884 •9753 •9623 •9452 .9249 .9025 ■8793 •8557 ■8305 •8031 .9869 .9741 .9609 •9434 .9228 .9001 .8769 •8533 .8279 .8001 •985s .9728 •9593 .9416 ,9206 .8979 .8745 .8508 .8254 .7969 Cb) The following are the values adopted by the " Kaiserlichen Normal-Aichungs Kommission." They are based on Mendelejefi's fonnula,t and are for alcohol of specific gravity .79425. at 15 C, in terms of water at 15° C. i temperatures measured by the hydrogen thermometer. a oS 1 2 3 4 5 6 7 8 • Specific gravity at 15° C. in terms of water at the same temperature. 10 20 30 40 50 60 11 90 1.00000 •98393 .97164 •95770 •93973 0.91865 89604 87265 84852 82304 .99812 .98262 .97040 .95608 •93773 .91644 •89373 .87028 .84606 .82036 •99630 •98135 .96913 •95443 •93570 .91421 .89141 .86789 •84358 •81763 ■99454 .98010 .96783 ■95273 •93365 .91197 .88909 ■86550 .84108 .81488 •99284 .97888 .96650 .95099 •93157 .86310 •83857 .81207 .99120 •97768 •96513 .94920 .92947 .90746 .88443 .86070 .83604 .80923 .98963 .97648 •96373 •94738 •92734 •§2519 .88208 .85828 .98812 .97528 .96228 •94552 •92519 .90292 .87974 .85586 .83091 •80339 .98667 •97408 .96080 •94363 •92303 11 .80040 .98528 •97287 •95927 .94169 .92085 .89834 .87502 .85098 .82569 •79735 (0) The inste speci following values have the same authority as the last ; the percentage of alcohol being given by volume id of by^ weight, and the temperature 15°. 56 C. on the mercury in Thuringian glass thermometer ; the ic gravity 01 the absolute alcohol being .79391. III PI 1 2 3 4 6 6 7 8 9 Specific gravity at i5°.56 C. in terms of water at same temperature. 10 20 30 40 50 60 1° 80 90 1. 00000 .98657 .97608 .96541 .95185 0.93445 •91358 .89010 .86395 .83400 .99847 •98543 •97507 ,96421 .95029 .93250 •91134 .88762 .86116 ■83065 •98432 .97406 .96298 .94868 .93052 18851 1 •85833 .82721 •99555 .98324 •97304 .96172 .94704 .92850 •85547 .82365 •99415 .98218 .97201 •96043 •94536 .92646 ■85256 .81997 •99279 .98114 •97097 .95910 ■94364 .92439 .90214 •87740 .84961 .81616 .99147 .98011 .96991 .94188 .92229 .89978 •87477 .84660 .81217 .90019 ■X •95632 .94008 .92015 .89740 .87211 .80800 .97808 .96772 •95487 .93824 .91799 •89499 •86943 .84044 .80359 .98774 ■97708 .96658 •95338 •93636 •^9256 .86670 .83726 .79891 • Fownes, " Phil. Trans. Roy. Soc." 1847. t " Pogg. Ann." vol. 138, 1869. Smithsonian Tables. Table 78. DENSITY OF AQUEOUS METHYL ALCOHOL.* 99 Dennties of aqueous methyl alcohol at o" and i5.;6 C, water at 4° C. being taken as looooo. The numbers in the columns iz and j are the coefficients in the ei{uation pi — - -" »j« — •-*— -. :- .v. j — ■ This equation may be taken to hold between o" and 20^^ columns a and i are the coefficients in the equation M = p|>— ai — U' whire u is the density at temperature t. _. . . . . .... •■ - :oO d. . Quoted from the results of Dit.mar & Fawsitt, " Trans. Roy. So.. Edin." vol. „. SMiTHaoNtAN Tables. lOO Table 79.~ VARIATION OF THE DENSITY OF ALCOHOL WITH TEMPERATURE. (a) The density of alcohol at t° in terms of water at 4° is given* by the following equation : ^^0.80025 — 0.0008340/ — 00000029/*. From this formula the following table has been calculateA U 0. 1 Density or Mass in grammes per cubic centimetre. 1 2 3 4 6 6 7 8 9 10 20 30 .80625 •79788 •78945 •78097 .80541 .78012 •80457 .79620 •78775 .77927 .80374 .77841 .80290 •77756 .80207 •79367 .78522 •77671 .80123 .79283 •78437 •77585 .80039 .79198 •78352 .77500 •79956 .79114 .78267 •77414 .79872 •77329 (b) Variations with temperature of the density of water containing different percentages of alcohol. Water at 4° C. is taken as unity.t Percent- age of alcohol by weight. Density at temp. C. Percent- age of alcohol by weight. Density at temp. C. o" 10° 20° 30° 0° 10° 20° 30= 5 10 IS 20 25 30 3S 40 4S 50 0.99988 •9913s •98493 •9799S .97566 0.971 1 5 .96540 •95784 •94939 •93977 0.92940 0.99975 ■^"^ .97816 •97263 0.96672 •95998 •95174 •9425s •93254 0.92182 0.99831 .98945 .98195 ■96877 0.96185 •95403 .94514 •935' I .92493 0.91400 °» •97892 .97142 .96413 0.95628 •94751 •93813 .92787 .91710 0.90577 50 65 70 75 80 85 90 9S 100 0.92940 .91848 .90742 •89595 .88420 0^87245 ^847^9 .83482 .82119 0.80625 0.92182 .91074 •87613 0.86427 .85215 •83967 ». 82665 .81291 0.79788 0.91400 •90275 .89129 186781 0.85580 .84366 .83115 .81801 •80433 0.78945 0.90577 .89456 .88304 .87125 .85925 0.84719 •83483 .82232 .80918 •79553 0.78096 * Mendelejefif, "Pogg. Ann." vol. 138. t Quoted from Landolt and Bomstein, " Phys. Chem. Tab." p. 359. Smithsonian Tables. Table 80i VELOCITY OF SOUND IN SOLIDS. lOl The numbers given in this table refer to the velocity of sound along a bar of the substance, and hence depend on the Young's Modulus of elasticity of the material. The elastic constants of most of the materials given in this table ^ vary through a somewhat wide range, and hence the numbers can only be talcen as rough approximations to the velocity which may be obtained in any particular case. When temperatures are not marked, between io° and 20° is to be understood. Velocity in Velocity in _> Substance, Temp. C. metres per second. feet per Authority. ^second. Metals: Aluminum 5104 ' • 16740 Masson. Brass - 3500 '11480 Various. Cadmium . - 2307 757*5 Masson. Cobalt - 4724 '15500 ** Copper 20 3560 "1167Q Wertheim.;" ' 100 3290 •1080b ti (( 200 2950 • 969(0 " Gold (soft)' 20 1743 57 1> ti " (hard) - 2100 • 689O Various. ; Iron and soft ste el '. - 5000 16410 " Iron . 20 5130 16820 Wertheim. (t 100 53°o 17390 I( tt 200 4720 15480 , « " cast steel 20 4990 16360 U 14 It 4( 200 4790 15710 it Lead . 20 1227 " 4026 tt Magnesium _ 4602 15100 Melde. ' Nickel - 4973 16320 Masson, Palladium - 315° 10340 Various. Platinum 20 2690 8815 Wertheim. 100 2570 8437 E. S., the table gives the 24 notes to the octave required in the simplest enharmonic organ; the notes fall into pairs that difier by a comma, 0.2a E. S. The line "mean tone" is based on Dom Bedos' rule for tuning the organ (1746). The tables have been checked by the data in Ellis' HelmholU's " Sensations of Tone." 6 4 : 5 E G B 30 36 45 „ 30 32 36 40 4S 48 By transferring t) to the left and using the 6 D 54 TABLE 82. Note. -Interval. Ratios. Xogarithms, Number of Vibrations per second. Beats for 0.1 E. S. Tern- , pered. Just. Tem- pered. Just. Tem- pered. Just. Just. Just, Just. Tem- pered. d' e' f a' b' c" E. S. I 2 3 4 I 9 10 II 12 E. S. 0. 2.04 3.86 4.98 7.02 8.84 10.88 12.00 1. 00 I.I25 1.25 J^33 1.50 1.67 1.875 2.00 1. 00000 1.05926 1. 12246 I.I892I 1.25992 i^33484 1.41421 1.49831 1.58740 1.68179 1. 78 1 80 1.88775 2.00000 0.0000 .05115 .09691 .12494 .17609 .22185 .27300 •30103 0.00000 .02509 .05017 .07526 .10034 •I2S43 .15051 .17560 .20069 .22577 .25086 •27594 •30103 2S6 288 320 34I-3 384 426.7 480 512 264 297 330 352 396 258^7 291.0 323^4 344-9 388 431-1 485.0 S»7^3 258.7 274.0 290.3 307.6 325-9 365.8 387-5 410.6 43S-0 460.9 488.3 S'7-3 1.50 1.68 1.89 2.00 2.25 2.52 2-83 3-00 TABLE 83- Key of C D E F G A B C 7«s 6" S" 4" 3" 2 » i# il» 2bs 3" 4" 7" CS F# B ,E A D G C F Bl> El. Al» V\> & 0.00 0.00 0.00 0.00 -.22 -.22 -.22 I.I4 0.92 1.14 ■0.92 1. 14 -0.92 0.92 0.70 0.92 0.70 0.92 0.90 0.90 0.90 0.90 2.04 1.82 2.04 2.04 2.04 1.82 1.82 1.82 3-18 2.96 2.96 2-74 2.96 2.74 2.96 2-74 2.94 2.94 2.94 2.94 2.72 2.72 4.68 3.86 4.08 3.86 4.08 3-85 4.08 3.86 3-86 3-86 3-84 5.00 4-78 5.00 4.78 4.98 4.98 4.98, 4.98 4.76 4.76 4.76 6.12 5.90 6.12 IT. 5.90 6.12 5.90 5.90 5,68 5.90 5.90 5.88 5.88 5.88 7.02 7.02 7.02 7.02 6.80 6.80 6.80 3.16 7-94 8.16 7-94 7-94 7-72 7-94 7-72 7-94 7.72 7.92 7.92 7.92 7.92 7.70 9.06 8.84 9.06 8.84 9.06 9.06 8.84 8.84 8.84 9.,8 9.76 9-98 9-?6 9-98 9.75 9.96 9.96. 9.96 9.96 9-74 9-74 9-74 1 1. 10 10.88 II. 10 10.88 II. 10 ia.88 II. 10 10.88 10.88 10.88 10.88 10.86 10.86 12.02 11.80 12.00 12.00 12.00 12.00 11.78 11.78 11.78 Harmonic Series Cycle of fifths Cycle of fourths Mean tone Equal 7 step 8 0.0 0-0 0.0 0.0 0.0 til) 1. 14 0.90 0.76 9 2.04 2.04 1.80 1-93 1.7 1 U) 3.18 2.94 3-iJ 3-43 10 3-86 4.08 Hi (4^0) 5.22 4.98 5-03 S.14 s'sr 6.12 5.88 5-79 12 7.02 7.02 6.78 6.97 6.86 (7'^) S.16 7.92 7.72 13 8.41 9.06 8.82 8.90 8.57 9.69 10.20 9.96 10.07 10.29 10.88 II. 10 10.86 10.83 16 ' 12.00 12.24 11. 76 12.00 12.00 ■""" Smithsonian Tables. I04 Table 84. ACCELERATION OF GRAVITY. For SM Lavel and DUterent Latltndes. This table has been calculated from the formiUa £-^=rui [i —.002662 co5 2fl,* where 4> is the latitude. Lati- tude ^. 9 in cms. per Log. in inches per Log. in feet per Log. sec. per sec. sec. per sec. sec. per sec. 0° 977.989 2-99°334 385^034 2.585498 32.0862 1.506318 ■5 8.029 0352 .050 5517 •0875 Pit 10 ■'f 0404 .096 5570 .0916 6388 15 0490 •173 5655 .0977 . 6474 20 .600 0605 •275 577 1 .1062 6590 25 978.922 2.990748 385.402 2.585914 32.1168 1.506732 30 9.295 0913 ■548 6079 .1290 6898 31 •374 0949 .580 6114 .1316 6933 32 •456 0985 .612 ^'5° •1343 6969 33 •538 1021 .644 6187 •1370 7005 34 979.622 2.991059 385-677 2.586224 32.1398 1.507043 35 .707 1096 •7" 6262 .1425 7080 36 "35 •745 6300 .1454 7119 37 .880 "73 •779 6339 .1490 7167 38 .968 1212 •813 6377 .1511 7196 39 980.057 2.991251 385.849 2.586417 32.1540 1.507236 40 .147 1 291 .884 6457 .1570 7275 41 •237 1331 .919 6496 .1607 7325 42 ■327 1372 •955 6537 .1630 7356 43 .418 141 1 .990 6577 .1659 7395 44 980.509 2.991452 386.026 2.586617 32.1688 1.507436 45 .§00 1492 .062 6657 .1719 7470 46 .691 1532 .098 6698 .1748 7516 47 .782 '573 •134 M .1778 7557 48 •873 1613 .170 6778 .1808 7597 49 980.963 2.991653 386.205 2.586818 32.1838 1.507637 5° 1053 1693 .241 6858 .1867 7677 SI ■143 1732 .276 6898 .1896 7716 52 .231 1772 •3" 6937 .1924 7756 53 •318 1810 •345 6975 ••954 7794 54 981.407 2.991849 386.380 2.587014 32.1983 '•507833 55 •493 •578 1887 .414 7053 .2011 7871 56 1925 •447 7090 •2039 7909 57 .662 1962 .480 7127 .2067 7946 58 •744 1998 •513 7164 .2094 7983 59 981.825 2.992034 386.545 2.587200 32.2121 1.508018 60 .905 2070 .576 7235 •2147 8054 65 2.278 2234 •723 7400 .2276 8229 70 .600 2377 •849 7542 •2375 8361 75 .861 2492 .952 7657 .2460 8476 80 983^053 2.992577 387.028 2.587742 32.2523 1.508561 85 .171 2629 .074 7794 .2562 8613 90 .210 2646 .090 7812 •2575 8631 * The constant .002662 is based on Harkness* data (Solar Parallax and Related Constants, Washington, 1891). The acceleration of gravity for any latitude 4> and elevation above sea level A is very nearly expressea by the equation ^0=^46 (1— .002662 cos 2^) \j—^(^~^]* where Ji is the earth's radius, S the density of the surface strata, and A the mean density of the earth. When fi^o v/e get the itormula for elevation in air. For ordinary elevations on land — - is nearly }, which gives for the correction at latitude 45° for elevated portions of the earth's surface £■«■— ™980'6X-^=i22s.7s— cm. per sec. per sec. =386.o62X ^=482.562— in. per sec. per sec 4^ i? «='32.i7i9X 140.3x49 — feet per sec. per sec This gives per 100 feet elevation a correction of .00588 cm. per sec. per sec. .00232 in. per sec. per sec. .000193 £set per sec. per sec. Smithsonian Tables. Sdiininutioa. 105 Table 85. GRAVITY. '" show rt,'? ^^Srl?^?L°i * number of the more recent gravity ieteminations are b«ught together. They serve to show the degree of accuracy which mav be assumed for thB n„mV,.,-= in T,KU ,,, ^„ ».5.„i „.„;..y:. ' iT..!? '^i^^',hX XZ, t "("'"""""ne more recent gravity Heterminatons are brought tot- .„,„ „ show the degree of accuracy which majr be assumed for the numbers in Table 1.2. In general, gravit^is a Me ,n the calculated value tor stations far inland and slightly higher on the coast line. lower than 1 Place. Singapore Georgetown, Ascension . Green Mountain, Ascension Loanda, Angola . . . Caroline Islands . . . Bridgetown, Barbadoes Jamestown, St. Helena Longwood, " Pakaoao, Sandwich Islands Lahaina, " " Haiki, " " Honolulu, " " St. Georges, Bermuda Sidney, Australia . . Cape Town .... Tokio, Japan .... Auckland, New Zealand Mount Hamilton, Cal. (Lick Obs, San Francisco, Cal. Washington; D. C* Denver, Colo. . . . York, Pa Ebensburgh, Pa. . . Allegheny, Pa. . . Hoboken, N. J. . . Salt Lake City, Utah Chicago, 111. . . . Pampaluna, Spain . Montreal, Canada . Geneva, Switzerland Berne, " Zurich, " Paris, France .... Kew, England . . . Berlin, Germany . . . Port Simpson, B. C. . Burroughs Bay, Alaska Wrangell, " Sitka, " St. Paul's Island, " Juneau, " Pyramid Harbor, " Yakutat Bay, " Latitude. N. +, S. -. 1" 17' -7 56. -7 57 -8 49 -10 00 13 04 -IS 55 -15 57 20 43 20 52 20 56 21 18 32 23 -33 52 -33 56 35 41 -36 52 37 20 37 20 37 47 37 47 38 S3 39 54 39 58 40 27 40 28 40 44 40 46 41 49 42 49 45 31 46 12 46 12 46 57 47 23 48 50 51 28 52 30 54 34 5§ 59 56 28 57 03 57 07 58 18 59 1° 59 32 Elevation in metres. ;i8 'lO i33 3001 ■ 3 "7 3 2 43 II 6 43 1282 1282 114 114 10 1645 122 348 II 1288 i6S 450 100 405 405 572 466 67 7 '1 12 S 5 4 Gravity, 55^ Observed. 978.08' 9?8.25 9^8.to' 978.15 978-37 978.18 978.67 978.28 978.86 978.91 978-97 979-77 979.68' 979.62 979-9S, 979.68 979.66 979.68 979.96 980.02 980.11 979.68 980.12 980.08 980.09 980.27 979.82 980.34 980.34 980.73 980.58 980.60 980.61 980.67 980.96 981.20 981.26 981.46 981.51 981.60 981.69 981.67 981-74 981.82 981.83 Reduced to .sea level. 978.08 978.25 978.23 978.16 978.37 978.18 978-67 978.59 978.85 978.86 978.93 978.97 979-77 979.69 979.62 979-95 979.69 979.91 979.92 979.98 980.04 980.11 979.98 980.14 980.20 980.15 980.27 980.05 980.37 980.42 980.75 980.64 980.66 980.69 980.74 980.97 981.20 981.27 981.46 981.51 981.60 981.69 981.67 981.74 981.82 981.83 Refer- ence. 4 4 4 4 t 4 4 4 1 Smith : " United States Coast and Geodetic Survey \P°'ll°'jf„^,f'll-''!^^ 2 Preston : " United States Coast and Geodetic Survey Report for 1890, App. 12. 3 Preston : Ibid. 1888, App. 14. 4 Mendenhall : Ibid. 1891, App. 15. 1; Defforges : " Comptes Rendus," vol. 118, p. 231. ? C^ibrfa,; L^d t:;-!^^; .^b^^^ef Cni^fd^^S.ances de la Commission Perma- 8 Pi^ = ^l}?^rc"frG^I° Sort \IX^^%. As.,.A,,. ,7." 9 Messerschmidt: Same reference as 7. • T. . , ™ln.. >re derived by comparative experiment! with invariable pendulums, the value for W J°nyot"£" a;",t"\r lor theTaUe'ree Appendix s oi^the Coast and Geodetic Survey Report for t,o.. Smithsonian Tables. io6 Table 86. SUMMARY OF RESULTS OF THE VALUE OF GRAVITY (g) AT STATIONS •'in the united STATES AND ALASKA.* Station. Latitude. Longitude. Elevation. observed. o t n Q t n Metres. cm./sec.' Calais, Me 45 II II 67 i6 54 38 980.630 Boston, Mass. 42 21 33 42 22 48 71 03 5° 22 980.39s Cambridge, Mass. 1; % '^ 14 980.397 Worcester, Mass. 42 16 29 170 980.323 New York, N. Y. . 40 48 27 73 57 43 f 980.266 Princeton, N. J. . 40 20 57 74 39 28 64 ■ 980.177 Philadelphia, Pa. 39 57 06 75 " 40 16 980.19s Ithaca, N. Y. . 42 27 04 76 29 00 247 980.299 Baltimore, Md. . 39 «7 50 76 37 30 30 980.096 Washington, C. & G. S. . 38 53 13 77 00 32 14 980.IH Washington, Smithsonian . 38 53 2° •77 01 32 10 980.113 CharlottesvUle, Va. . 38 02 01 78 30 16 166 979'937 \ Deer Park, Md. , , 39 25 02 79 19 5° 770 979-934 Charleston, S. C. , 32 47 14 79 56 03 6 979-545 Cleveland, Ohio . , 41 30 22 81 36 38 210 980.240 Key West, Fla. . , 24 33 33 33 44 58 81 48 25 84 23 18 I 978.969 Atlanta, Ga. , 324 979-523 Cincinnati, Ohio , 39 08 20 84 25 20 245 980.003 Terre Haute, Ind. , 39 28 42 87 23 49 151 182 980.071 Chicago, III. . 41 47 25 87 36 03 980.277 Madison, Wis. (Univ. of Wis.) 43 °4 35 89 24 00 270 980.364 New Orleans, La. , 29 56 58 90 04 14 2 979-323 St. Louis, Mo. . , 38 38 03 90 12 13 '^9 980.000 Little Rock, Ark. ^ 34 44 57 92 16 24 979.720 Kansas City, Mo. . 39 oq 50 29 18 12 94 35 21 278 979.989 Galveston, Tex. . , 94 47 29 3 979.271 Austin, Texas (University) 30 17 II 97 44 14 189 979.282 Austin, Texas (Capitol) 30 16 30 97 44 16 170 979.287 Ellsworth, Kan. . 38 43 43 98 13 32 469 979-925 Laredo, Tex. 27 30 29 99 3' 12 129 979.081 Wallace, Kan. . 38 54 44 loi 35 26 1005 ■ 979-754 Colorado Springs, Co! 38 50 44 104 49 02 1 841 979.489 Denver, Col. 39 40 30 104 56 55 1638 979.608 Pike's Peak, Col. 38 50 20 105 02 02 4293 978.953 Gunnison, Col. . 38 32 33 106 56 02 2340 979-341 Grand Junction, Col. 39 04 09 108 33 56 1398 979.632 Green River, Utah 38 59 23 no 09 56 1243 979-635 Grand Canyon, Wyo. 44 43 16 no 29 44 2386 979.898 Norris Geyser Basin, Wyo. 44 44 09 no 42 02 2276 ■ 979-949 Lower Geyser Basin, Wyo. 44 33 21 no 48 08 2200 979-931 Pleasant Valley Jet., Utah . 39 50 47 III 00 46 2191 979-5" Salt Lake City, Utah . 40 46 04 in 53 46 1322 979.802 Ft. Egbert, Eagle, Alaska .... 64 47 22 141 iz 24 174 982.182 * All the values in this table depend on relative determination of gravity and an adopted value for gravity at Wash- ington (Coast and Geodetic Survey Office) of 980.111. This adopted value was the result of the determination in igoo of the relative value of gravity at Potsdam and at Washington. See footuote on previous page. Smithsonian Tables. Tables 87-88. LENGTH OF THE SECONDS PENDULUM. TABLE 87.-LB]igtli ot Seoonds Fenaulnm at Sea LeTal fox DUteiant LatltnAm.* 107 Lati- tttde. Length in centi- metres. Log. Length in inchea- Log. Lati- tude. Length in centi- metres- Log. '-S'^es!"' Log. s 10 IS 2Q 25 30 35 40 45 99-0910 .0950 .1079 .1265 .1529 99-1855 •2234 .2651 .3096 •3555 1.996034 6052 6104 6190 6306 1.996448 6614 6796 6991 7192 39-0121 •0137 .0184 .0261 .0365 39-0493 .0642 .0806 .0982 .1163 1.591200 1217 ■^270 1356 1471 I.591614 1779 1962 2157 2357 50 65 70 75 80 85 90 99.4014 99-5845 -6040 .6160 .6200 1-997393 7587 7770 7935 8077 1.998192 8277 8329 8347 39-1344 .1520 .1683 •1832 .i960 39.2065 .2141 .2188 .2204 1-592558 2753 2935 3100 3242 1-593358 3442 3494 3512 * Calculated from force of gravity table by the formula /=^/ir>. For each loo feet of elevation subtract ojooosqS centimetres, or 0-000235 inches, or .0000196 feet. TABLE 88. — Lsngtli ol the Seoonds Pendnlum.* Date of determi- nation. Number of obser- vation stations. Range of latitude included by the stations. Length of pendulum in metres for. latitude^. ■Correspond- ing length of,pendulum for lat. 45° Refer- ence. 1799 IS 1816 31 1821 8 1825 25 1827 41 1829 s 1830 49 1833 1869 51 1876 73 1884 123 From +67°05' " +74° S3' " +38°4o' " +79° 50' " +79° 50' " 0° o' " +79° 51' " +79° 50' " +79° SO' " +79° SO' to— 33056' " — 5I°2I' " — 6o°45' " -12° 59' " -Si°3S' •• +67=04' " — 5i°3S' " — Si°3S' •• —62° 56' " — 62=56' 0.990631-I-, 0.990743+' o.9go88o-f-. 0.990977+, 0.991026+. 0-990555+. 0.991017-^-, 0.990941-j-, 0.9909704- 0.9910114-. 0.990918+, ,005637 sin' i() .005466 sin' ^ .005340 sin'^ .00514251:1'^ .00507 2 sin '^ ,005679 sin'^ ,005087 sin' If) ,005142 sin'^ .oosiSssin'^ ,005105 sin'^ ,005262 sin' ^ Combining the above results 0.990910+ .oo5290sin'^ 0-993450 0.993976 0-993550 0-993548 0.993562 0-993395 0.993560 0.993512 0-993S54t 0-993563 0-993549 0-993555 I 2 3 4 I 7 8 9 10 II 1 Laplace ; "Traite de Mecanique Celeste," T. 2, livre 3, chap. 5, sect. 42. 2 Mathieu: "Sur les experiences du pendule;" in " Connaissance des Temps 1S16. •J Bkj't^^t'A'rago : " Recueil d'Observations g^odesiques, etc." Paris, 1821, p. 575- 4 Sabine: "An Account of Experiments to determine the Figure of the Earth, etc., by Sir Edward Sabine." London, 1825, p. 352. . , , •. 1 r^„^.= . f,u« „,, c Saigey: " Comparaison des Observations du pendule idiverees latitudes ; faites par MM. BiotfKater, Sabine, de Freycinet, et Duperry;" m "Bulletm des Sciences Mathe- matinues etc. " T. I. DP. •?l-4^. and 171-184. Pans, 1827. . „ _ ^-- 6 Pont'ecoulant : "Theorie analvtique du Systfeme du monde,' Paris, 1829, T. 2, p. 466. 7 Airy : " Figure of the Earth ; '*^ in " Encyc. Met." 2d Div. vol. 3, p. 230- „ 8 Poisson: ''Traite de Mecanique," T. i, p. 377 i "Connaissance des Temps. 1834. DD 12-Tl : and Puissant : " Traite de g^od^sie," T. 2, p. 464. ., ,, « „u,.„ „ ,Bfi„ 9 Unfe^dinger : " Das Pendel als geodatisches Instrument j " m Grunert's "Archiv," 1869, ^' i^J^Fischer : " Die Gestalt der Erde und die Pendelmessungen j " in " Ast Nach." 1876, "^ii^Helmert: "Die mathematischen und physikalischen Theoiieen der hbheren Geo- da^ie, von Dr. F. R. Helmert," IL TheU. Leipzig, 1884, p. 241. 12 Harkness. t OdSd fSm afogarithmic expression given by Unferdinger. Smithsonian Tables. i08 Table 89. MISCELLANEOUS DATA WITH REGARD TO THE EARTH AND PLANETSJ Length of the seconds pendulum at sea level =/=39.oi 2540+0.208268 sin= inches. =3.251045+0.017356 sin'' feet. =0.9909910+0.005290 sin' ^ metres. Acceleration produced by gravity per second per second mean solar time . . . =^=32.o86528+o.i7i293sin''0feet. =977.9886+5.2210 sin' (j> centimetres. Equatorial radius =0=6378206 metres ; 3963.225 miles. Polar semi-diameter =^=6356584 metres ; 3949.790 miles. Reciprocal of flattening= ; =295.0 a — a'—f Square of eccentricity =^= — -j— =0.006768658 6378388±i8 metres ; 9 3963-339 mUes. 5J_ 6356909 metres ; ? 3949-992 miles. ' ». 297.o±o.s ^ O.cio67237±o.ooooi20. Cp5o J Difference between geographical and geocentric latitude= 0—0'= 688.2242" sin 2 0—1. 1482" sin 4 0+0.0026" sin 60. Mean density of the Earth^5.5247±o.ooi3 (Burgess Phys. Rev. 1902), Continental surface density of the Earth=2.67 1 tT,.i._g5._ Mean density outer ten miles of earth's crust^2.40 J Moments of inertia of the Earth; the principal moments being taken as A,B, and C, and C the greater: C-A , I — 7;— =0.0032652 1 = — -p ; C -^ ■' 306.259 C—./4 =0.001064767 £a*; ^=5=0.325029^0"; C =0.326094 .£«'; where E is the mass of the Earth and a its equatorial semidiameter. Length of sidereal year=365.2563578 mean solar days; ^365 days 6 hours 9 minutes 9.314 seconds. Length of tropical year=365.242l99870— 0.0000062124^— ^ mean solar days; 100 ^ =365 days 5 hours 48 minutes ^46.069—0.53675^^^-^ ) seconds. Length of sidereal month =27.321661162—0.00000026240 — days; =27 days 7 hours 43 minutes ^^11.524-0.022671-^^-^ J seconds. Length of sjmodical month =29.530588435—0.00000030696^^ — ^days; =29 days 1 2 hours 44 minutes ( 2.841 -0.026522 ^^^i^j seconds. Length of sidereal day = 86164.09965 mean solar seconds. N. B.— The factor containing t in the above equations (the epoch at which the values of the quantities are required) may in all ordinary cases be neglected. • Mosdy from Harkness, " Solar Parallax and Allied Constants." Smithsonian Tables. Table 89 (cotuinued^ 109 MISCELLANEOUS DATA WITH REGARD TO THE EARTH AND PLANETS. Masses of the Planets. Reciprocals of the masses of the planets relative to the sun and the mass of the moon relative to the Eaith. Mercury = 6000000 Venus = 408000 Earth » = 329390 Mars = 3093500 Jupiter = 1047-35 Saturn = 3501.6 Uranus = 22869 Neptune = 19700 Moon = 81.4s Mean distance from earth to sun = 92900000 miles = 149500000 kilometres. Eccentricity of the earth's orbit = « = 0.01675104 — 0.0000004180 (t — 1900) — 0.000000126 I ^ 1 • Solar parallax = 8.7997" J^ 0.003 (Weinberg, A. N. 165, 1904) j 8.807 i 0.0027 (Hinks, Eros, 7) ; 8.799 (Samson, Jupiter satellites; Harvard observations). Lunar parallax = 3422.68". Mean distance from earth to moon = 60.2669 terrestrial radii ; = 238854 miles ; = 384393 kilometres. Lunar inequality of the earth = Z = 6.454". Parallactic inequality of the moon = C = 124.80"- ft — i8oo\ Mean motion of moon's node in 365.25 days = ;.. = — 19° 21' 19.6191" + 0.14136" \—[^^ J Eccentricity and inclination of the moon's orbit = e^=^ 0.05490807. Delaunay's 7 = sin J /= 0.044886793. /= 5° 08' 43-3546". Constant of nutation = 9.2'. Constant of aberration = 20.4962 J; 0.006 (Weinberg, 1. c.).t Time taken by light to traverse the mean radius of the earth's orbit = 498.82 -t 6.1 seconds (Weinberg) ; = 498.64 (Samson). Velocity of light = 186330 miles per second (Weinberg) j = 299870 J^ 0.03 kilometres per second. General precession = 50.2564" + 0.000222 (t — 1900). Obliquity of the ecliptic = 23° 27' 8.26" — 0.4684 (t— 1900). Gravitation constant = 666.07 X lo"" cm'/gr. sec^i 0.16 X io-i». • Earth + moon, 1 Recent work oJ DooHttle's and others indicates a value not less than 20.5.. Smithsonian Tables. ixo Table 90. TERRESTRIAL MAGNETISM. Secular Obange of Deollnatlon. Changes m the magnetic declination between 1810, the date of the earliest available observa- tions, and 1910, for one or mo're places in each state and territory. State. Station. 1810 1820 1830 1840 X850 i860 1870 1880 1890 1900 1910 Ala. Montgomery 5.6E S.8E S.8E S.6E s-aE S.oE 4.sE 3.9E 3.2E 2.8E 2.9E Alas. Sitka _ _ - - - 28.7E 29.0E 29.3E 29.sE 29.7E 30.2E Kodiak _ _ _ - - 26.1E 2S.6E 2S.1E 24.7 E 24.4E 24.1E Unalaska _ _ _ - - 204E 20.1E 19.6E 19.0E 18.3E 17.sE St. Michael - - - - - - — 24.7E 23.1E 22.1E 214E Ariz. Holbrook _ _ _ _ I3.6E 13.7E 13.8E 13.7E 134E 13. sE 13.9E Prescott - _ - - I3.3E 13.sE 13.7E 13.6E 13 -SE 13.7E 14.3E Ark. LitUe Rork 8.6E 8.8E g.oE 9.0E 8.8E 8.6E 8.2E 7.6E 7.0E 6.6E. 6.9E Cal. Los Angeles 12.1E 12.6E 13.2E 13.6E 14.0E 14.2E 14.4E 14.6E 14.6E 14.9E iS-SE San Jose iS-oE IS-SE 16.0E 164E 16.8E 17.1E I7-3E 17-SE 17.sE 17 .8E iS.sE Cal. Redding IS.6E 16.1E 16.6E 17.0E 174E 17 .8E 18.1E 18.2E 18.3E 18.6E 19.3E Colo. Pueblo - - - 13 .8E 13.8E 13.8E 13 .5 E i3.oE X2.9E I3.3E GlenwoodSp. - - - - 16.1E I6.2E 16.3E l6.lE 1S.7E IS.6E 16.1E Conn. Hartford S.iW S.6W 6.rW 6.8W 7.SW 8.2W 8.7W 9.4W 9.8W 10.4W ii.oW Del. Dover I.6W 1.9W 2.3W 2.8W 3AVi 4.0W 4.7W S.3W S.9W 6.4W 7.0W D. C. Washington o.sE 0.3E 0.0 o.sW i.oW I.7W 2.4W 3.0W 3.6W 4.2W 4.7W Fla. Jacksonville S.iE S.iE 4.9E 4.6E 4.2E 3.7E 3.1E 2.4E 1.8E 1.3E 1.2E Pensacola 7.7E 7.8E 7.7E 7.5E 7.2E 6.8E 6.2E S.6E S.oE 4-5E 4.4E Tampa 6.4E 6.2E S.9E S.sE 5.0E 4-SE 3.9E 3.3E 2.8E 2.3E 2.0E Ga. Macon 5-9E S-PE S.7E S.4E S.oE 4.SE 3.9E 3.2E 2.6E 2.1E 2.0E Haw. Honolulu _ „ _ _ 9.4E 9.4E 9.SE 9.8E lO.iE 10.4E ro.6E Idaho Pocatello _ - - - 17. 4E I7.7E 17 .8E 17. 9E 17 .7 E 17. BE 1S.4E Boise - - - - 18.0E 18.4E I8.6E 18.7E 18.6E 18.8E 194E 111. Bloomington 6.3E 6.sE 6.6E 6.SE 6.3E S.9E S.4E 4.7E 4.1E 3-6E 3.4E Ind. Indianapolis S.oE S.iE S.oE 4.7E 4.4E 3.8E 3.2E 2.6E 2.0E I.4E i.iE la. Des Moines _ 10.2E 10.4E lO.sE 10.4E 10.2E 9.7E 9.1E 8.4E 7.9E 8.1E Kans. Emimria - - - - 11.6E ii.sE I1.2E 10.7E lO.iE 9.8E lO.iE Ness City - - - - 124E I2.4E I2.2E 11.9E 11.4E ii.iE 11.4E Ky. Lexington 4.SE 4.sE 4.4E 4.1E 3-6E 3.1E 2.sE 1.9E 1.2E 0.7E O.sE Princeton 6.8E 7.0E 7.0E 6.8E 6.sE 6.1E S.6E S.oE 4-3E 3.8E 3-7E La. Alexandria 8.4E 8.7E 8.8E 8.8E 8.7E 8.4E S.oE 7.4E 6.9E 6.6E 6.SE Me. Eastport 13.6W 14.4W IS.2W 16.0W 17. oW 17.7W 18.2W 18.6W 18.7W 19.0W 19.4W Portland 9.0W 9.6W 10.3W ii.oW H.6W 12.3W I2.8W 13.4W 13.9W 14.4W 14.8W Md. Baltimore 0.9W i.iW 1.4W 1.9W 2.4W 3.1W 3-8W 4.4W S.oW S-6W 6.1W Mass. Boston 7.3W 7.8W 8.4W 9.1W 9.8W lO.sW I I.oW ii.sw 12.0W 12.6W 13.1W Mass. Pittsfield S.7W 6.1W 6.7W 7.4W 8.lW 8.7W 9-3W lO.oW 10.4W 11.0W II.SW Mich. Marquette - 6.7 E 6.7 E 6.sE 6.0E S.4E 4.6E 3-8E 3-oE 2.3E 2.0E Lansing - 4.2E 4.1E 3.8E 3.3E 2.8E 2.1E 1.3E O.sE o.oE 0.4E Minn. Northome - 10.4E 10.7E 10.8E 10.7E 10.4E lO.oE 9-3E 8.6E S.oE 8.1E Mankato ' 11.3E I1.6E 11.7E 11.6E 11.3E 10.9E 10.4E 9-SE 9.0E 9.1E * Tables have been compiled from United States Magnetic Tables and Magnetic Charts for igoji published by the Coast and Geodetic Survey in 1908* Smithsonian Tables. Table 90 [cmtimud). TERRESTRIAL MAGNETISM (eotUinuti). Secnlat Obanse at DeoUnatlou {contitmeil). Ill State. Station. iSio 1820 1830 1840 i8so i860 1870 1880 1890 190a [910 o o> Misa. Jackson 8.2E 84E 8.5E 8.4E 8.2E 7.9E 7.SE 6.9E 5.4E 6.0E 5.2E Mo. Sedalia - I o.oE I 0.2E I 0.2E I o.iE 9.8E 9.4E 8.7E B.oE 7.6E 7-9E Mont. Forayth - - - I 8.2E I 8.5E 18.6E li 8.6E 18.4E I17.9E |i7.8£ li 8.3E Helena — - - 18.9E I19.3E I19.6E |i9.8E |i9.6E I19.4E lig.sE Ijo.oE 11 Nebr. Hastings - 11.6E 12.0E |i2aE I12.1E |i2.oE |ir.7E 11.2E lO.sE 10.2E lo.sE 1 Nebr. Alliance _ _ _ — ■ S.4E 1 S.4E 1 S-sE' 14.8E 14.3E 14.2E 14.5E 1 Nev. Elko - — - — 7.3E 17.6E 17.7E I17.7E I17.6E I17.8E |i 8.3E Hawthorne - — - - 6.3E 16.6E 6.9E 17.0E 17.0E 17.3E 17.8E N.H. Hanover 7.1W 7.SW 8.2W 8.9W 9.8W lO.sW [i.iW 11.6W 12.0W i2.sW 13.0W N.J. Trenton 2.8W 3.1W 3.SW 4.1W 4.7W S.4W 6.0W 6.7W 7.2W 7.8W 84W N. M. Santa Rosa _ — _ _ [2.7E [2.8E i2.7E' 12.5E 12. lE 12.0E 12.4E 1 Laguna - - -• - 13. 4E 13.6B 13.6E 3.4E 13.0E 1 3.0E I3,5E N. y. Albany S.6W S.8W 6.3W 6.9W 7.6W 8.4W 9.1W 9.8W 0.2W O.SW 11.4W 1 Elmira 2.2W 2.4W 2.8W 3.3W 4.0W 4-8W S.4W 6.3W 7.0W 7.6W 8.1W N.C. Newbein 1.7E I.6E 1.3E 0.8E 0.3E 0.3W 1.0W 1.6W 2.2W 2.8W 3.3W N. C. Salisbury 3.9E 3.8E 3.6E 3.2E 2.7E 2.1E 1.5E 0.8E 0.2E 0.4W 0.7W N. Dak. Jamestown - - - - 14.sE 14.3E 14.0E 13-SE 12.7E 12.4E [2.8E Dickinson - - - - 17 .6E 17. 6E 17 .4E r7.oE 16.4E 16.2E I6.6E Ohio Columbus 3.4E 3.4E 3.2E 2.9E 2.4E 1.8E I.2E' 0.6E 0.0 0.7W i.iW Okla. Okmulgee - - — 10.2E lo.iE 9.8E 9.4E 8.8E 8.SE 8.9E Okla. Enid _ _ - - 11.2E ii.iE I0.9E lO.sE 9.9E 9.7E lO.iE Oreg. Sumpter _ - - - 19.3E 19.7E 20.0E 20.2E 20.2E 20.4E 21.0E Detroit 16.7E 17.4E 18.0E 18.6E 19.2E 19.7E 20.lE' 20.4E 20.5E 20.8E 21.5E Pa. Philadelphia 2.2W 2.4W 2.8W 3.4W 4.1W 4.8W s.sw 6.3W 6.8W 7.4W 8.0W Altoona o.sW 0.6W 0.9W 1.3W 1.8W 2.4W 3.1W 3.8W 4.SW S-iW S.6W P.R. R.I. S. C. San Juan Newport 6-6W 7.1W 7.7W 8.4W 9.1W 9.8W 10.3W 10.8W I1.3W I.OW 1I.9W 2.0W 12.4W Columbia 44E 4-3E 4.1E 3.7E 3.2E 2.7E 2.1E 1.4E 0.8E 0.2E o.iW S.D. Huron Rapid City _ _ 13. lE 13.1E 12.9E i2j6E 12.1E 114E II. lE 11.4E - - - - 16.4E 16.4E 16.3E 1S.8E IS-3E iS.iE IS.4E Tenn. Tex. Chattanooga Huntington Houston San Antonio Pecos S.3E S-3E 7.4E 8.9E S.iE 7.4E g.zE 9.6E 10.8E 4.8E 7.3E 9.3E 9.8E II.0E 4.4E 7.0E 9.3E 9.9E ii.iE 3.9E 6.6E 9.2E 9.8E ii.iE 3.3E 6.1E 8.9E 9.6E ii.oE 2.6E S-sE 8.sE 9-3E 10.8E 2.0E 4.9E 7.9E 8.9E 10.4E I.SE 4.4E 7.7E 8.7E 10.3E 1.3E 4.3E 8.1E 9.1E 10.7E II.3E 11.3E 11.2E 10.9E 10.4E 10.3E 10.7E Tex. Floydada __ I6.4E 16.6E 16.7E i6.sE 16.3E i6.sE 17. oE Utah Vt. Va. Salt Lake Rutland Richmond Lynchburg 6.8W 0.8E 1.9E 7.2W 0.6E 1.8E 7.8W 0.3W 1.6E 8.sW o.iW 1.2E 0.2W 0.6W 0.8E 10.0W 1.2W 0.2E 10.6W 1.8W o.sW It.2W 2.SW , I.2W 11.6W 3-lW I.8W 12.1W 3.7W 2.4W 12.7W 4.2W 2.8W Wilson creek Seattle Charleston 21. 3E 21.6E 21.9E 2I.9E 22.1E 22.4E 22.9E Wash. W. Va. 19.1E 2.3E 19.7E 2,2E 8.6E 20.3E 2.0E 8.7E 20.8E 1.6E 8.6E 21.3E i.iE 8.3E 21.8E o.sE 7.8E 22.1E 0.2W 7.2E 22.3E O.9W 6.4E 22.6E 1.5W S.6E 23.0E 2.1W S.oE 23.sE 2.6W 4.9E Wis. Madison 15.8E 16.0E 16.0E IS.8E IS-4E 1S.3E IS-7E Wyo. Douglas Green River - — *" 16.8E 17. oE 17. oE 16.9E 16.6E 16.6E 17. oE Smithsonian Tables. 112 Tables 91-92. TERRESTRIAL MAGNETISM Iconlimui). TABLE 91. — Dip 01 InoUsatlon. This table gives for the epoch January i, 1905, the values of the magnetic dip, I, corresponding to the longitudes west of Greenwich in the heading and the north latitudes in the first column. 6s» 70° 75° 80° 8s° 90° 95° 100° 105° 110° IIS° 120° 125° 19 _ - 48.8 49.1 47- S 46.3 44.8 44.2 43-9 - - - - 21 - - 51.0 Si.i 50.0 49-3 48.2 47.0 ^s-s - - — ~ 23 - - 53-7 S3-0 52-4 S1.8 50.7 49.6 48.8 48.2 — — ~ 25 - - S6.3 56.0 55-0 54-5 ,S3-z 524 51-5 50.6 49.8 48-3 — 27 - - 58.9 58.1 57.6 Sb.8 55-6 54-7 53-9 S3-' 52.6 51.0 " 29 _ 60.7 61.0 60.2 59.8 S8.q S8.2 S7.2 56.2 Sl-S 54.8 53-7 - 3" _ 63.0 6^.1 62.6 62.0 61.3 60.6 S9.6 S8.7 ''''■7 56-7 56.0 - 33 - 65.0 65.0 64.6 64.0 63. S 62.7 62.0 61.0 59-8 58.9 58.1 - 35 _ 67.0 66.9 66. s 66.0 6S.6 64.9 63.7 b2.7 62.3 61.0 60.2 - 37 - 68.6 68.9 68.6 68.2 67.7 66.9 66.2 65.1 64.6 62.9 62.2 — 39 _ 70-3 70.6 70.4 70.2 6q.7 68.8 68.1 67.2 66.1 6 15.0 64.0 62.8 41 _ 71.8 72.2 72.2 71.9 71.4 70.8 69.8 68.9 67.8 66.8 65.6 04-7 43 _ 73-5 73-9 74.1 73-8 73-3 72.6 71.6 70.7 69.6 68.6 67.S 66.3 45 74-4 7S.6 7';-5 7';4 7S.0 74-3 73-t' 72.4 71-5 rd b9.2 68.1 47 75-7 76.2 76.9 76.8 76.9 76.8 76.0 75.2 74.2 73-0 70.8 69.9 49 76.8 78.1 78.2 78.3 78.7 78.1 77-5 76.8 75-8 74-S 73-5 72-3 71.4 TABLE 92. — Seonlar Change of Dip. Values of magnetic dip for places designated by the north latitudes and longitudes west of Greenwich in the first two columns for January 1st of the years in the heading. The degrees are given in the third column and minutes in the succeeding columns. Lati- tude. Longi- tude, I8SS i860 1865 1870 1875 1880 188s 1890 189s 1900 190S igio / / / / / / / / r 1 / 25 80 S'>+ 49 49 48 46 43 40 35 u 39 48 60 77 25 IIO 49-- 08 20 30 39 46 S5 61 76 86 96 106 3° 83 60-f 66 70 74 73 67 57 51 63 78 06 ,30 100 .■>7t 44 49 67 70 t>5 60 61 68 77 90 105 30 "S 54-1- S3 62 69 71 70 72 75 79 85 91 96 lOI 3S 80 66+ 57 58 57 54 45 35 26 21 20 22 30 38 35 90 65+ 65 .59 5' 44 37 32 2b 25 25 27 36 48 3S 10^ b2+ - - - 32 30 24 24 24 28 34 42 5° 3S 120 bo+ 03 Ob 08 08 07 06 08 II 13 14 12 08 40 75 714- 82 82 78 73 • 65 55 43 33 27 24 24 24 40 90 70+ .30 31 34 37 ,36 32 29 26 2S 26 30 36 40 105 07-- - 5f .53 51 51 S» 52 56 60 65 40 120 b4-- - 48 4b 44 i'^ 44 44 44 45 45 48 48 45 65 74-- 116 no lOI 92 80 68 57 46 35 28 20 45 75 75+ 103 99 95 90 «5 73 62 53 43 38 36 34 45 90 74-f 81 81 81 79 77 75 68 63 61 59 60 60 45 loS 72-- - - - - - 22 20 20 21 22 24 27 45 122.5 68-- 35 .34 .37 40 40 .39 37 34 ,30 26 24 20 49 92 78-- 26 2S 24 22 20 20 15 12 II 09 06 04 49 120 72+ 26 24 22 22 19 20 19 19 19 18 16 Smithsonian Tables, Tables 93-94. TERRESTRIAL MAGNETISM icontimud). TABLE 93.— HoUzontal Inteiulty. 113 This table gives for the epoch January i, 1905, the horizontal intensity, H, expressed in C. G. S. units, corresponding to the longitudes in the heading and the latitudes in the first column. 6s° J0° 75° 80° 85° 90° 9S° 100° 105° 110° IIS° 120° 125° •9 - - •307 •314 ■319 •322 .328 •332 •331 " ~ •JOl •309 •314 •310 .320 •324 •324 ^i — — •293 •303 •305 •309 .312 •3'5 •317 .320 ■'i) — — .284 .292 •295 •299 ■304 ■307 .308 •309 .312 •304 V ^ ~ .274 .280 .286 .289 .296 .298 .300 ■303 .306 .298 29 - .237 .262 .269 .276 .281 .286 .289 .292 •294 .297 .291 31 — .246 .251 .2,,5 .263 .269 .274 .277 .282 .284 .28, .282 33 - •233 ■239 •24 s .251 .2S7 .262 .266 .270 ■273 ■274 .274 3S - .220 .225 .232 .240 .242 .248 •2 S3 .2,6 ■259 .262 .26s 37 — .208 .209 .218 .222 .226 .232 .238 .245 .246 .252 .251 39 - .197 .198 .203 .206 .212 .217 .224 .229 •237 .240 .242 •245 41 - .184 .185 .186 .192 .196 .202 .207 .216 .223 .228 .240 .236 43 - .170 .170 .169 •175 .178 .187 .194 .201 .210 •215 .222 .226 45 .i6i ■157 ■'.SS .iSb ■157 .162 .169 .177 .190 .192 .208 .215 47 ■HS .144 .140 .142 .142 .150 .152 .161 .170 .180 .188 .196 .201 49 •131 .129 .125 .126 .124 .129 .i3« .146 ■153 .165 •'75 .182 .187 TABLE 94. — Secnlar Cbange ol Horizontal Intensity. Values of horizontal intensity in C. G. S. units for places designated by the latitude and longi- tude in the first two columns for January i of the years in the heading. ■5 . 80 no 83 100 "5 80 90 105 t20 75 go 105 120 65 75 90 105 122.5 92 120 18SS •3°99 .3229 .2803 .3040 .2384 .1880 •i5°4 .1483 .2175 .1332 .1841 i860 .3086 .3218 .2795 .3026 •2379 .1883 .2086 .1514 •1485 •1635 .2170 .1330 .1841 i86s •3073 .3204 .2788 .2961 .3011 ■2374 .1891 .2082 •'525 .1488 ■1633 .2162 .1328 .1840 1870 •3057 .3189 .2780 .2942 .2996 .2369 .2462 .2720 .1902 .2079 .2272 .2429 •1537 ■1495 .1631 .1920 •2153 •1324 .1839 187s .3042 •3170 .2772 •2924 .2979 .2367 .2462 .2620 .2707 .1911 .2076 .2266 .2420 •1553 .1506 .1628 .1919 .2145 .1321 .1836 1880 .3025 ■3155 .2763 .2907 .2964 ■2363 .2461 .2608 .2695 .1919 .2075 .2261 .2412 .1567 .1516 .1626 .1918 ■2135 • i3'9 .1831 i88s .3008 •3143 .2752 .2891 .2952 ■2359 .2458 .2599 .2683 .1925 .2074 .2257 .2406 •1578 ■1527 .1624 .1916 .2127 .1318 .1826 1890 .2990 ■3130 .2740 .2877 .2940 •2352 •2455 .2590 .2672 .1930 .2072 •2253 ■2399 .1589 ■1538 .1623 •1913 .2121 .1318 .1821 189s .2970 •3"7 •2725 .2865 .2929 •2347 .2447 .2663 •1931 .2068 .2248 ■2392 .1600 .1546 .1624 .1910 .2117 .1321 .1819 .2949 .3104 .2706 .2850 .2920 •2337 •2437 •2573 .2656 .1928 .2060 .2240 .2386 .1608 .1550 .1623 .1906 .2115 .1324 .1820 190S .2920 .3090 .2680 .2830 .2910 .2320 .2430 .2560 .2650 .1920 .2050 .2230 .2380 .1610 .1550 .1620 .1900 .2115 .1330 .1820 1910 .2890 •3075 .2644 .2804 .2296 •2399 .2544 .2644 .1909 .2036 .2217 •2379 .1610 •1554 .1616 .1892 .2115 •133s .1824 Smithsonian Tables. 114 Tables 95-96. TERRESTRIAL MAGNETISM Icontimitd). TABLE 96. — Total Intsnalty. This table gives for the epoch January i, 1905, the values of total intensity, F, expressed in C. G. S. units corresponding to the longitudes in the heading and the latitudes in the first column. 6s° 70° 75° 80° 85° 90° 95° 100° 105° 110° 115° 120° 125" 19 ,466 .480 •472 .466 .462 •463 •459 _ _ _ ^ 21 - - .47« .492 .489 •485 .480 •475 .471 - — — — 23 - - •495 .504 .500 .SCO •493 .486 .481 .480 — — *" 25 - - .512 ,522 .514 • SIS •507 •503 •495 .487 •483 457 — 27 - - •530 •53° .534 .528 .524 .51b .509 •505 •504 •474 ^ 29 _ •52s .540 .541 ■ W •544 ■543 •534 •525 •519 •515 .492 - 31 - •542 •SSb .Sbo .S60 •55ii •547 •543 •531 •519 •5°4 - 33 - '55" .566 •571 •572 • S76 •571 .5b7 •557 •543 •530 .518 - 3S - .^b^ •574 .582 .590 .586 •584 •571 .558 •557 •540 ■M — 37 - ■570 .5«i •598 •598 .59b •591 .590 .582 •573 •553 — 39 _ .■;84 • ^6 .60c .608 .611 .600 .600 •S9I .585 .368 t ■536 41 - .-i«9 .605 .608 .618 .614 .614 .600 .600 • 590 • W •55* 43 - •599 .6n .617 .627 .619 .62, .614 .608 .602 •589 .580 .562 45 •S99 •599 .623 .6r8 .623 .623 .626 .624 .627 .628 .60s •590 .Sbb .S7b 47 .587 .604 .622 .626 •6S7 .628 .630 .624 .616 .602 •59t> ;f5 49 •574 .626 .611 .621 .633 .626 .638 •^39 .624 .bi7 .616 ■599 TABLE 96.— SeGslar Change ol Total Intensity. Values of total intensity in C. G. S. units for places designated by the latitudes and longitudes in the first two columns for January i of the years in the heading. (Computed from Tables 92 and 94.) Lati- tude. Longi- tude. 1855 i860 1865 1870 1875 1880 1885 1890 189s 1900 190S 1910 25 80 •5Si6 •5493 •5467 •5434 .S400 •5364 ■5322 .5290 .5264 ■5247 •S222 .5206 25 no •4935 •4938 ■4933 •4925 .4908 .4902 .4891 •4883 .487b •4873 .4868 .4860 30 83 .5800 •5796 •5790 •5777 •5757 •5720 .5668 .5625 .5600 ■5590 •5581 •5559 .30 100 - - •5583 •5570 •5544 ■5499 •.S456 •5432 • 5427 .5421 .5416 •5405 30 "5 •5285 .5280 •5269 .5247 •5215 .5194 •5'79 •5167 .5160 •5158 .5151 .5140 35 80 .6089 .6080 .6063 .6038 •5996 .5946 .5900 •5863 .5874 .5830 .5818 •5789 35 90 - - - •5991 •5964 ■5942 .5912 .5901 .5882 .5865 .58^8 .5582 •5852 35 los - - - - .5674 .5629 .5610 .5590 .5588 •5585 •5572 35 120 - - - .5462 •5433 .5406 .5388 •5374 •5361 •5350 •5332 •5309 40 75 .6206 .6216 6220 .6227 .6212 .6182 .6136 .6098 .6070 .6045 .6019 •5985 40 90 - .6254 •6258 .6264 .6250 .6226 .6208 .6187 .6170 .6151 .6141 •6135 40 105 - - - .6048 .6019 ■5997 •5986 •5976 •5967 •5963 •5953 •5940 40 120 - - ,- .3691 .5670 .56,1 •5637 .5620 .5608 •5593 •5590 •5591 45 bS .6188 .6186 .6167 .6132 .6134 .6107 .6077 .6048 .6019 .6005 •5987 •5962 .6235 45 75 •6454 .6431 .6413 .6404 .6412 ■6363 .6327 .6306 .6266 .6247 •6233 45 90 - .6463 •6457 •6434 .6408 .6386 •6330 .6291 .6382 .6264 .6259 .6244 45 105 - - - - - .6332 .6314 •6303 .5804 .6299 .6392 .6284 .6275 45 122.5 •595" •5938 •5930 •5918 .5896 .5864 •5834 ■5776 .^8 •5754 .6447 •5992 •5745 49 49 92 120 .bb43 .6624 .61 00 .6604 .6085 .6566 .6071 :^? ■^i .6472 .6017 •6445 •5995 .6450 .5986 Smithsonian Tables. Table 97. AGONIC LINE. "S The line of no declination appears to be still mov- ing westward in the United States, but the line of no annual change is only a short distance to the west of it, so that it is probable that the extreme westerly position will soon be reached. Longitudes of the agonic line for the years ^ Lat. N. iSoo 1S50 1875 1S90 igoj o o 25 - - - m 76.1 3° - - - 79-7 35 _ 76.7 79.0 79-9 81.7 6 75.2 77-3 79-7 80.5 82.8 7 76.3 77-7 80.6 82.2 P. 8 76.7 78.3 81.3 82.6 9 76.9 78.7 81.6 82.2 83.6 40 77.0 79-3 81.6 82.7 84.0 I 77-9 80.4 81.8 82.8 84.6 2 79.1 81.0 82.6 83-7 84.8 3 79-4 81.2 83.1 84-3 85.0 4 79.8 - 833 84.9 85.5 45 ^ ^ 83.6 85.2 86.0 6 - - 84.2 84.8 86.4 7 - - 8S.1 85-4 864 8 _ - 86.0 85.9 86.S 9 •" — 86.S 86.3 87.2 Smithsonian Tables. Il6 Table 98. PRESSURE OF COLUMNS OF MERCURY AND WATER. British and metric measures. Correct at o" C. for mercury and at 4° C for water. Metric Measure. British Measure. Cms. of Hg. Pressure in grammes per sq. cm. Pressure in pounds per sq. inch. Inches of Hg. Pressure in grammes per sq. cm. Pressure in pounds per sq. inch. 1 2 3 4 5 6 7 8 9 10 13-5956 27.1912 40.7868 54.3824 67.9780 81.5736 95.1692 108.7648 122.3604 135.9560 0.193376 0.386752 0.580128 0.773504 0.966880 1. 160256 1.353632 1.547008 1.740384 1.933760 1 2 3 4 S 6 7 8 9 10 34-533 69.066 103.598 138.131 172.664 207.197 241-730 276.262 310.795 345-328 0.491174 0.982348 1.473522 1.964696 2.455870 2.947044 3.438218 3929392 4.420566 4.911740 Cms. of HjO. Pressure in grammes per sq. cm. Pressure in pounds per sq. inch. Inches of HjO. Pressure in grammes per sq. cm. Pressure in pounds per sq. inch. 1 2 3 4 5 6 7 8 9 10 * I 2 3 4 5 6 7 8 9 10 0.0142234 0.0284468 0.0426702 0.0568936 0.07 HI 70 0.0853404 0.0995638 0.1137872 O.I280I06 0.1422340 1 2 3 4 S 6 7 8 9 10 2.54 5.08 7.62 10.16 12.70 15-24 17.78 20.32 22.86 25.40 0.036127 0.07225s 0.108382 0.144510 0.180637 0.216764 0.252892 0.289019 0.325147 0.361274 Smithsonian Tables. Table 99. jl^ REDUCTION OF BAROMETRIC HEIGHT TO STANDARD TEMPERATURE.^ Corrections for brass scale and English measure. Corrections for brass scale and metric measure. Corrections for glass scale and metric measure. Height of barometer in inches. a in inches for temp. F. Height of barometer in mm. in mm. for temp. C. Height of barometer in mm. a in mm. for temp. C. 15.0 16.0 0.00135 400 0.0651 50 0.0086 .00145 410 .0668 100 .0172 .0258 •0345 .0431 .0517 17.0 18.0 18.5 .00154 .00158 .00163 .00167 420 430 440 450 .0684 .0700 .0716 .0732 150 200 250 300 19.0 .00172 460 .0749 350 .0603 19.5 .00176 470 .0765 20.0 O.OO181 480 490 .0781 .0797 400 450 0.0689 •0775 20.5 .00185 500 .086? 21.0 .00190 soo 0.0813 520 .0898 21.5 .00194 510 .0830 540 •0934 22.0 .00199 520 .0846 560 .0971 22.5 .00203 53° .0862 580 .1007 23.0 .00200 540 .0878 23-S .00212 550 .0894 600 0.1034 560 .0911 610 .1051 24.0 0.00217 570 .0927 620 .1068 24.5 .00221 580 ■0943 630 .1085 25.0 .00226 590 .0959 640 .1103 25-S .00231 6ro .1120 26.0 .00236 600 0.0975 660 •"37 26.5 .00240 610 .0992 27.0 .00245 620 .1008 670 0.1 1 54 27.S .00249 630 .:o24 680 .1172 640 .1040 690 .1189 28.0 0.00254 650 .1056 700 .1206 28.S .00258 660 .1073 710 .1223 29.0 .00263 670 .1089 720 .1240 29.2 .00265 680 .1105 730 .1258 29.4 .00267 690 .1121 29.6 .00268 740 0.127s 29.8 .00270 700 0.1 137 750 .1292 30.0 .00272 710 .1154 760 .1309 720 .1170 770 ■1327 30.2 0.00274 730 .1186 780 •1344 304 .00276 740 .1202 790 .1361 30.6 .00277 750 .1218 800 •1378 30.8 .00279 760 •123s 31.0 .00281 770 .1251 850 0.1464 31.2 .00283 780 .1267 900 •1551 314 .00285 79° .1283 950 .1639 31-6 .00287 800 .1299 1000 .1723 I *The height of the barometer is affected by the relative thermal expansion of the mercury and ' the glass, in the case of instruments graduated on the glass tube, and by the relative expansion of the mercury and the metallic inclosing case, usually or brass, in the case of instruments graduated on the brass case. This relative expansion is practically proportional to the first power of the tem- perature The above tables of values of the coefficient or relative expansion will be found to give correction for temperature. The standard temperature is o° C. for the metric system and 28°.5 F. for the English system. The English barometer is correct for the temperature of melting ice at a temperature of approximately 28°.5 F., because of the fact that the brass scale is graduated so as to be standard at 62° F., while mercury has the standard density at 32° F. Example.— A barometer having a brass scale gave //= 765 mm. at 25° C. ; required, the cor- responding reading at 0° C. Here the value of a is the mean of .1235 and .1251, or .1243 ; .• .a(_l'—t) = .I243X25 = 3-"- Hence/ro = 765 — 3.ii = 76i-89- ^. ^ , . .= .= ... ,j NB— Although a is here given to three and sometimes to four significant figures, it is seldom worth" while to use more than the nearest two-figure number. In fact, all barometers have not the same values for a, and when great accuracy is wanted the proper coefficients have to be deter- mined by experiment. Smithsonian Tables. Ilg Table 100. CORRECTION OF BAROMETER TO STANDARD CRAVITY. Height Observed height of barometer in millimetres. level in metres. 400 450 500 550 600 650 700 750 Sao 100 .014 .015 .016 200 .028 .030 .032 300 Conection in mMime- .041 .044 .047 400 700 tres for elevation above ■^ .059 .063 .078 sea level in first column .064 •073 and height of barometer in top line* .077 .090 .082 .096 .102 800 .103 .109 .117 900 1000 1100 .108 .118 .118 .130 .141 .123 •137 .ISO •'3' .146 1200 .129 .142 .154 .164 1300 .140 •153 .166 .178 1400 .151 .i6| .179 .191 1500 1600 .147 •157 .162 .172 .191 .204 .205 1700 .167 .183 .200 .217 1800 •'Z7 .194 .212 .230 1.245 15000 1900 .187 .204 .224 .242 1.203 14500 2000 2100 .176 .185 .196 .206 :iu •235 •247 •255 1.340 1.292 1. 162 1. 120 14000 13500 2200 .194 .216 •237 .259 1.244 1.088 13000 2300 .203 .226 .248 .271 1-345 1. 196 1.046 12500 2400 .212 •236 •259 .283 1. 291 1.149 1.004 12000 2500 2600 .195 .203 .220 .24s .255 .270 •295 1-315 1.237 1. 184 I.IOI 1-053 .962 .920 11500 1 1000 2700 •211 .265 1.255 1. 130 1.005 .879 10500 2800 .219 .247 .275 1. 196. 1.076 •957 .837 lOOOO 2900 .227 .256 .285 .918 1.136 1.022 Tel •813 •795 9500 3000 3100 •23s ■243 .265 .274 .283 .294 1.076 1.016 .969 •915 •753 9000 8500 3200 .251 •853 •957 .861 .765 8000 3300 If .292 1.077 .787 .897 .807 7500 3400 .201 1.005 .721 •837 •753 7000 3500 3600 ■'^l •309 ■'^ ■%l •777 .718 .700 6500 6000 3700 3800 .291 .790 .724 •658 5500 .299 •779 .718 .658 .598 5000 3900 •307 .701 .646 •592 4500 4000 •314 •623 ■545 •574 •503 .526 .461 4000 3500 ■503 •467 •389 •431 •395 Corrections in hnndredths of an inch for elevation above 3000 .419 •359 sea level in last column and 2500 •3S9 •335 •3" .287 height of barometer in bottom 2000 .269 .251 •233 .215 line. 1500 .192 •179 .167 •'55 1000 .096 .090 .084 .078 500 33 30 aS 26 '24 22 20 ig x6 14 Height above sea level in Observed height oi baromet er in inches. feet. Smithsonian Tables. Table 1 01 . REDUCTION OF BAROMETER TO STANDARD GRAVITY.* Haanctlon to LaUtnde 46°. — Bnglljli stals. ^' ^' f mS !=,'l'"j' °°o ° "*!=*''? ""-"'ion » to be subtracted. From latitude 90° to 46° the correction is to be added. 119 Height of the barometer in inches. Latitude. ^ 19 30 21 22 23 »4 25 26 27 28 29 30 0° 90° Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. 0.051 0.053 0.056 0.059 0.061 0.064 0.067 0.069 0.072 0.074 0.077 0.080 5 6 85 84 82 81 0.050 0.052 0.055 0.058 0.060 0.063 0.066 0.068 0.071 0.073 •073 0.076 .076 0.079 .078 •077 •077 .076 .049 .052 •055 •057 .060 .062 .065 .068 .070 I .049 .052 .054 .057 .059 .062 .065 .067 .070 .072 •075 .074 .049 .051 .054 .056 .059 .061 .064 .067 .069 .072 9 .048 .051 •053 .056 .058 .061 .063 .066 .068 .071 -073 10 80 0.048 0.050 0.053 0.05s 0.058 0.060 0.063 0.065 0.068 0.070 0.073 0.075 21 li •047 ■049 .052 .054 ■057 •059 .062 .064 .067 .069 .072 -074 12 78 .046 •049 .051 ■054 .056 .058 .061 .063 .066 .068 .071 •073 .072 13 77 76 .045 .048 .050 •053 •05s .057 .060 .062 .065 .067 .069 14 .045 ■047 .049 .052 ■054 .056 .059 .06! .063 .066 .068 .071 15 16 75 0.044 0.046 0.048 0.051 0.053 0.055 0.058 0.060 0.062 0.065 0.067 0.069 74 ■043 •045 .047 .050 .052 •054 .056 .059 .061 •063 .065 .068 17 73 .042 .044 .046 .049 .051 •053 .055 .057 .060 .062 .064 .066 18 72 .041 ■043 •045 .047 .050 .052 .054 .056 .058 .060 .062 .065 19 71 .040 .042 .044 .046 .048 .050 .052 ■055 •057 .059 .061 .063 20 70 0.039 0.041 0.043 0.045 0.047 0.049 0.051 0.053 0.055 0.057 0.059 0.061 21 69 •038 .040 .042 .044 ■045 .047 .049 .051 ■053 •055 -957 •059 22 68 .036 .038 .040 .042 .044 .046 .048 .050 .052 •054 .056 .057 23 ^^ •03s •037 ■039 .041 •043 .044 .046 .048 .050 .052 •054 •055 24 66 •034 .036 •037 ■039 .041 •043 .045 .046 .048 .050 .052 •053 25 65 0-033 0.034 0.036 0.038 0.039 0.041 0.043 0.044 0.046 0.048 0.050 0.051 26 64 ■031 •033 •034 .036 .038 ■039 .041 •043 ■044 .046 .048 •049 27 P ■030 .031 •033 •034 .036 .038 •039 .041 .042 .044 .045 -047 28 62 .028 .030 .031 •033 ■034 ■036 ■037 -039 .040 .042 -043 -045 29 61 .027 .028 .030 .031 .032 •034 •035 ■037 .038 •039 .041 .042 30 60 0.025 0.027 0.028 0.029 0.031 0.032 0-033 0.035 0.036 0.037 0.039 0.040 31 59 .024 .025 .026 .027 .029 .030 .031 .032 •034 -035 .036 •037 32 58 .022 .023 .025 .026 .027 .028 .029 .030 .032 ■033 -034 •035 33 57 .021 .022 .023 .024 .025 .026 .027 .028 .029 .030 .031 .032 34 S6 .019 .020 .021 .022 .023 .024 .025 .026 .027 .028 .029 .030 35 55 0.017 0.018 0.019 0.020 0.021 0.022 0.023 0.024 0.025 0.025 0.026 0.027 36 54 .016 .016 .017 .018 .019 .020 .021 .021 .022 .023 .024 .025 37 53 .014 .015 •015 .016 .017 .0l8 .018 .019 .020 .021 .021 .022 38 52 .012 .013 .014 .014 .015 .015 .016 .017 .017 .018 .019 .019 39 51 .011 .Oil .012 .012 .013 .013 .014 .014 .015 .015 .016 .017 40 50 0.009 o.oog O.OIO O.OIO 0.0 1 1 O.OII 0.012 0.012 0.012 0.013 0.013 0.014 41 49 .007 .007 .008 .008 .009 .009 .009 .010 .010 .010 .011 .011 42 48 .005 .006 .006 .006 .006 .007 .007 .007 .008 .008 .008 .008 43 47 .004 .004 .004 .004 .004 .004 .005 .005 .005 .005 .005 .006 44 46 .002 .002 .002 .002 .002 .002 .002 .002 .003 .003 .003 ■003 * " Smithsonian Meteorological Tables," p. 58. Smithsonian Tables. 120 Table 102. REDUCTION OF BAROMETER TO STANDARD GRAVITY. RsduoUon to Latltnde 46°. — Hetiio Scale. KB— From latitude o° to 44° the correction is to be subtracted. From latitude 90° to 46° the correction is to be added. Latitude. Height of the barometer in millimetres. 520 560 600 620 640 660 680 700 720 740 760 780 mm. mm. mm. mm. mm. mm. mm. mm. mm. nim> mm. mm. 0° 90° 1.38 1.49 1.60 1.6s 1.70 1.76 I.81 1.86 1.92 1.97 2.02 2.08 5 85 1.36 1.47 ■•57 1.63 1.68 ■•73 I.81 1.84 1.89 1.94 1.99 2.04 6 84 '•35 1.46 ■ •56 1.6I 1.67 1.72 1.78 1.82 1.87 ■•93 1.98 2.03 7 83 1.34 1.45 '•55 1.60 1.6s 1.70 ■•77 1.81 1.86 1.91 1.96 2.01 8 82 1.33 '•43 1.54 1-59 1.64 1.69 1.76 ■■79 1.84 1.89 1.94 2.00 9 81 1.32 1.42 1.52 '•57 1.62 1.67 ■•74 ■■77 1.82 1.87 1.92 ■•97 10 80 1.30 1.40 1.50 '■55 1.60 1.6s 1.70 ■•75 1.80 1.85 1.90 ■•95 II 79 1.28 1.38 1.48 '•53 1.58 1.63 1.68 ■•73 1.78 1.83 1.88 ■■93 12 78 1.26 1.36 1.46 1.51 1.56 1.60 1.65 1.70 ■•75 1.80 1.85 1.90 13 77 1.24 1-34 1.44 1.48 ■•53 1.58 1.63 1.67 1.72 1.77 1.82 1.87 ■ ■83 H 76 1.22 1.32 1.41 1.46 1.50 ■•55 1.60 1.65 1.69 1.74 ■•79 15 75 1.20 1.29 1.38 1.43 1.48 1.52 ■•57 1.61 1.66 1.71 ■•75 1.80 16 74 1. 17 1.26 ■•35 1.40 ■■44 1.49 ■•54 1.58 1.63 1.67 1.72 1.76 17 73 1.15 1.24 1.32 1-37 1.41 1. 45 1.50 ■•54 1.59 1.63 1.68 1.72 18 72 1.12 1. 21 1.29 ■•34 ■ .38 1.42 1.46 ■•51 ■•55 1.59 1.64 1.68 19 71 1.09 1. 17 1.26 1.30 ■•34 1.38 ■•43 1.47 1.51 ■•55 1.59 1.64 20 70 1.06 1. 14 1.22 1.26 ■■31 ■•35 ■•39 ■ •43 ■•47 '■^l ■•55 ■■59 21 69 1.03 I. II 1. 19 1.23 1.27 ■•31 ■•35 1.38 ..42 1.46 1.50 1.54 22 68 1. 00 1.07 1.15 1. 19 1.23 1.26 1.30 ■■34 1.38 1.42 1.46 ■•49 23 67 0.96 1.04 I. II 1. 15 1. 18 1.22 1.26 1.29 ■•33 ■•37 1.41 1.44 24 66 •93 1. 00 1.07 1. 10 1.14 1.18 1.21 1.25 1.28 1.32 ■•35 ■•39 25 65 0.89 0.96 1.03 0.98 1.06 1. 10 i!o8 1.16 1.20 1.23 1.27 1.30 ■•33 26 64 •85 .92 1.02 1.05 I. II LIS 1. 18 1. 21 I.2S 1.28 27 63 .8? .88 •94 0.97 1. 00 1.03 1.06 1. 10 ■■13 1. 16 1. 19 1.22 28 62 •77 •83 .89 .92 0-95 0.98 I.OI 1.04 1.07 1. 10 ■•■3 1. 16 29 61 •73 •79 •85 .87 .90 •93 0.96 0.99 1.02 1.04 1.07 1. 10 30 60 0.69 0.75 0.80 0.83 0.85 0.88 0.91 0.94 0.96 0.98 I.OI 1.04 31 59 .65 .70 •75 •77 .80 .82 •85 •f7 ■i° .92 0.9s 0.97 32 58 .61 •65 .70 •72 •75 •77 •79 .82 .84 .86 .89 .91 33 57 .56 .61 .65 .67 .69 •71 •74 .76 .78 .80 .82 .84 34 56 •52 ■56 .60 .62 .64 .66 .68 .70 •72 •74 .76 .78 35 55 0.47 0.51 0.5s 0.56 0.58 0.60 0.62 0.64 0.66 0.67 0.69 0.71 36 54 ■43 .46 •49 •51 •53 •54 •56 •58 •59 .61 •63 .64 37 53 •38 .41 •44 •45 •47 .48 .50 •5^ •53 •54 .56 •57 38 52 •33 •36 •39 .40 .41 •43 .44 •45 .46 .48 •49 •5° 39 5S .29 •31 •33 •34 •35 •37 •38 •39 .40 .41 •42 •43 40 50 0.24 0.26 0.28 0.29 0.30 0.3^ 0.31 0.32 o^33 0^34 0.35 0.36 41 49 .19 .21 .22 •23 ■^i .24 •25 .26 •27 •27 .28 .29 42 48 .14 .16 •17 •17 .18 .18 .19 •19 .20 .21 .21 .22 43 47 .10 .10 .11 .12 .12 .12 •■3 •■3 •■3 •14 .14 .14 44 46 •05 •05 .06 .06 .06 .06 .06 .07 .07 .07 .07 .07 * " Smithsonian Meteorological Tables," p. 59. Smithsonian Tables. Table 103. 121 CORRECTION OF THE BAROMETER FOR CAPILLARITY. I. Metric Measure. Diameter of tube in mm. Height of Meniscus in Millimetres. 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Correction to be added in millimetres. 4 0.83 1.22 I.S4 1.98 2-37 S •47 0.65 0.86 1.19 1-45 1.80 _ _ 6 ■% •*l .56 0.78 0.98 1.21 '■43 _ 8 .18 .28 .40 •S3 .67 0.82 0.97 1-13 ^ .20 .29 •3f .46 .56 •65 0.77 9 — •15 .21 .28 •33 .40 .46 .52 II - - •15 .10 .20 .14 ■2 .29 .21 ■33 .24 •37 •27 ~ "- .07 .10 ■13 •15 .18 .19 13 ~ .04 .07 .10 .12 •13 .14 2. British Measure. Diameter Height of Meniscus in Inches. of tube in inches. .01 .02 .03 .04 .OS .06 .07 .08 Correction to be added in hundredths of an inch. •IS 2.36 4.70 6.86 923 11.56 _ _ _ .20 1. 10 2.20 3.28 4-54 5-94 7.85 - - •25 0.55 1.20 1.92 2.76 3.68 4.72 5.88 - •30 •36 0.79 1.26 1.77 2.30 2.88 3-48 4.20 •35 •51 0.82 '•js 1.49 1.85 2.24 2.6s .40 - .40 .61 0.81 1.02 1.22 1.42 1.62 •45 - - •32 •51 0.68 0.83 0.96 1. 15 .50 - - .20 •35 •47 .56 .64 0.71 •5S .08 .20 ■31 .40 •47 .52 * The first table is from Kohlrausch (Experimental Physics), and is based on the experiments of Mendelejeff and Gutkowsld (Jour, de Phys. Chem. Geo. Petersburg, 1877, or Wied. Beib. 1867). The second table has been calcu- lated from the same data by conversion into inches and graphic interpolation. A number of tables, mostly based on theoretical formulie and the capillary constants of mercury in glass tubes in air and vacuum, were given in the fourth edition of Guyot's Tables, and may be there referred to. They are not repeated here, as the above is probably more accurate, and historical matter is excluded for convenience in the use of the book. Smithsonian Tables. 122 Table 104^ AERODYNAMICS. The pressure on a plane surface normal to the wind is for ordinary wind velocities expressed by />= kwav^ where /f is a constant depending on the units employed, w the mass of unit volume of the air, a the area of the surface and v the velocity of the wind.* Engineers generally use the table of values of P given by Smeaton in 1759. This table was calculated from the formula /> ^. 00492 »^ and gives the pressure in pounds per square foot when v is expressed in miles per hour. The corresponding formula when v is expressed in feet per second is /'=. 00228 Z'2. Later determinations do not agree well together, but give on the average somewhat lower values for the coefficient The value of w depends, of course, on the temperature and the baro- metric pressure. Langleji's experiments give kw = . 00166 at ordinary barometric pressure and 10° C. temperature. For planes inclined at an angle o less than 90° to the direction of the wind the pressure may be expressed as /"a = ^o^90- Table 104, founded on the experiments of Langley, gives the value of Fa for different values of o. The word aspect, in the headings, is used by him to define the position of the plane relative to the direction of motion. The numerical value of the aspect is the ratio of the linear dimension transverse to the direction of motion to the linear dimension, a vertical plane through which is parallel to the direction of motion. TABLE 104.— Values si Fa In Egnatlan Pa=I'aF9o- Plane 30 in. X 4.8 in. Aspect 6 (nearly). Plane 12 in. X 12 in. Aspect I, Plane 6 in. X 24 in. Aspect i. a Pa K J-^ a Pa 0° 0.00 0° 0.00 0° 0.00 5 10 0.28 0.44 s 10 0.15 0.30 5 10 0.07 0.17 15 20 0.62 15 20 0.44 0.57 15 20 0.29 0-43 2S 0.66 25 0.69 25 0.58 3° 35 40 45 0.69 0.72 0.74 0.76 30 35 40 45 0.78 0.84 0.88 0.91 30 0.71 50 0.78 50 - - • The following pressures in pounds per square inch show roughly the influence of the shape and size of the re^t* ing surface {Dines results). The wind velocity was 20.9 miles per hour. The flat plates were g in. thick. Square, sides 4 in. Circle, same area . . . Rectangle, 16 in, by 1 Sijuare, 12 in. sides . . Circle, same area . . . Rectangle, 24 in. by 6. , Square, sides 16 in. . . Plate, 6 in. diam. 45 thick Ditto, curved side to wind Sphere, 6 in. diam. . . Smithsonian Tables. 1. 51 Plate, 6 in. diam. 90*^ cone at back 1.49 1. 51 Same, cone in front 0.98 170 •' sharp 30° cone at back ..,..,.. 1.54 1.57 " cone in front 0.60 155 5 in. Robinson cup on 8} in. of i in. rod .... 1.68 J .59 Same, with back to wind , . , , , 0.73 1.52 9 in. cup on 6J in. of | in. rod 1.75 1.45 Same, with back to wind 0.60 o.g2 2.\ in. cup on 9I in. of \ in. rod 2.60 0.67 Same, with back to wind 1,04 Table 1 05. 123 AERODYNAMICS. soSlfof^"'*' °^ '^^ "^f^ ^''" '" "^"^'"^ '°4 L^^sley states the following condition for the soaring of an aeroplane 76.2 centimetres long and .2.2 centimetres broad, weighing 500 grammes. Wizolri H-^T °"'."1"^^^ ^°°' '"" area, weighing ,.i pounds. It is supposed to soar in a norizontal direction, with aspect 6. TABLE 105. -Data lor the Soaring ot PlaneB 70.2 X 12.2 cms. weighing 600 Cliainmes, Aepeot 8. Inclination to the hori- zontal a. Soaring speed v. Work expended per minute (actWty> Weight of planes of like form, capable of soaring at speed v with the ex- penditure of one horse power. Metres per sec. Feet per sec. Kilogramme metres. Foot pounds. Kilogrammes. Founds. 2° 5 10 IS 30 45 20.0 15.2 12.4 II.2 10.6 II.2 66 SO 41 37 35 37 24 86 336 174 297 474 126^ 2434 950 55-S 26.5 'it 209 122 29 IS In general, if />= weight Soaring speed v=K 4 ^ — ^ ^ V i/icosa Activity per unit of weight = v tan a The following data for curved surfaces are due to Wellner (Zeits. fiir Luftschifffahrt, x., Oct. 1893)- Let the surface be so curved that its intersection with a vertical plane parallel to the line of motion is a parabola whose height is about ^ the subtending chord, and let the surface be bounded by an elliptic outline symmetrical with the line of motion. Also, let the angle of incli- nation of the chord of the surface be a, and the angle between the direction of resultant air pressure and the normal to the direction of motion be ;8. Then /3 < o, and the soaring speed is ^=v^ -, while the activity per unit of weight =2/ tan ^. ] k J^a cos j3 The following series of values were obtained from experiments on moving trains and in the wind. Angle of inclination 0= —3" 0° +3" 6» 9° 12" Inclination factor Fa = 0.20 0.50 0.75 0.90 i.oo 1.05 tan/8= 0.0 1 0.02 0.03 0.04 o.io 0.17 Thus a curved surface shows finite soaring speeds when the angle of inclination a is zero or even slightly negative. Above a = 12° curved surfaces rapidly lose any advantage they may have for small inclinations. Smithsonian Tables. 124 Table 106. FRICTION. The following table of coefficients of friction y and its reciprocal i If, together with the angle of friction or angle of repose ^, is quoted from Rankine's "Applied Mechanics." It was compiled by Rankine from the results of General Morin and other authorities, and is sufficient for all ordinary purposes. Material. / Vf « Wood on wood, dry .25-.S0 4.00-2.00 14.0-26.5 " " " soapy .20 5.00 11.5 Metals on oak, dry .50-.60 2.00-1.67 26.5-31.0 " " " wet .24-26 4.17-3.85 i3^5-i4^S " " soapy .20 5.00 11.5 " elm, dry .20-.25 5.00-4.00 11.5-14.0 Hemp on oak, dry ■IZ 1.89 28.0 " " " wet •33 3.00 18.5 Leather on oak .27-.38 3.70-2.86 15.0-19.5 " metals, dry .56 1.79 29.5 " " " wet •36 2.78 20.0 greasy ■23 4-3S 13.0 oily ■15 6.67 ^-s Metals on metals, dry . .15-20 6.67-5.00 8.5-11.5 " " " wet . •3 3-33 16.5 Smooth surfaces, occasionally greased . .07-.08 I4-3-I2-SO 4.0-4.5 " " continually greased . •OS 20.00 3-0 " " best results .... .03-.036 33.3-27.6 1.75-2.0 Steel on agate, dry * .20 5.00 1 1.5 " " " oiled* .107 9-35 6.1 Iron on stone .30-70 3-33-' -43 16.7-35.0 Wood on stone About .40 2.50 22.0 Masonry and brick work, dry ... . .60-.70 1.67-1-43 33.0-35.0 '• " " damp mortar •74 '•35 36-5 " on dry clay •51 1.96 27.0 " " moist clay •33 3.00 18.25 Earth on earth .25-1.00 4.00-1.00 14.0-45.0 " " " dry sand, clay, and mixed earth . •38-75 2^63-i^33 21.0-37.0 damp clay 1. 00 1. 00 45.0 " " " wet clay •31 3-23 17.0 " " " shingle and gravel .8i-i.li 1.23-0.9 39.0-48.0 * Quoted from a paper by Jenkin and Ewing, " Phil. Trans. R. S." vol. 167. In this paper it is shown that in cases where " static friction " exceeds " kinetic friction " there is a gradual increase of the coefficient of frictioD as the speed is reduced towards zero. Smithsonian Tables. Table 107. VISCOSITY. 125 The coefBcient of viscosity is the tangential force per unit area of one face of a plate of the fluid which is required to keep up unit distortion between the faces. Viscosity is thus measured '."J""?* °^ ^^^ temporary rigidity which it gives to the fluid. Solids may be included in this definition when only that part of the rigidity which is due to varying distortion is considered. One of the most satisfactory methods of measuring the viscosity of fluids is by the observation of the rate of flow of the fluid through a capillary tube, the length of which is great in comparison with its diameter. Poiseuille * gave the following formula for calculating the viscosity coefiicient in this case : fi = —^^, where h is the pressure height, r the radius of the tube, j the density of the fluid, z< the quantity flowing per unit time, and / the length of the capillary part of the tube. The liquid is supposed to flow from an upper to a lower reservoir joined by the tube, hence k and / are different. The product hs is the pressure under which the flow takes place. Hagen- bach t pointed out that this formula is in error if the velocity of flow is sensible, and suggested a correction which was used in the calculation of his results. The amount to be subtracted from k, according to Hagenbach, is 1— , where g is the acceleration due to gravity. Gartenmeister % points out an error in this to which his attention had been called by Finkener, and states that the quantity to be subtracted from h should be simply — ; and this formula is used in the reduction of his observations. Gartenmeister's formula is the most accurate, but all of them nearly agree if the tube be long enough to make the rate of flow very small. None of the formulae take into account irregularities in the distortion of the fluid near the ends of the tube, but this is probably negligible in all cases here quoted from, although it probably renders the results obtained by the " viscosimeter " commonly used for testing oils useless for our purpose. The term " specific viscosity " is sometimes used in the headings of the tables ; it means the ratio of the viscosity of the fluid under consideration to the viscosity of water at a specified tem- perature. The friction of a fluid is proportional to the size of the rubbing surface, to ^, where v is the velocity of motion in a direction perpendicular to the rubbing surface, and to a constant known as the viscosity. Variation ol Viscosity ol Water, with Temperature. Dynes pei sg. cm. Temp. C. Poiseville. 1846. Sprang. 1875. Slotte. 1883. Thorpe-Rogers. i894-§ Specific viscosity. Temp. C. It 65 70 11 85 90 95 100 Slotte. 1883. Thorpe-Rogers. 1894. Specific Viscosity. 0° S 10 IS 20 25 30 35 40 45 SO O.OI716 .01515 .01309 .01146 .01008 .00897 .00803 .00721 .00653 .00595 0.01778 .01510 .01301 .01135 .01003 .00896 .00802 .00723 .00657 .00602 •OOSS3 0.01808 .01524 .01314 .01144 .01008 .00896 .00803 .00724 .00657 .00602 •00553 0.01778 .01510 .01303 .01134 .01002 .00891 .00798 .00720 .00654 .00597 .00548 1. 000 •849 .564 .501 •449 0.00510 .00472 .00438 .00408 .00382 .00358 •00337 .00318 .00301 .00285 0.00506 .00468 .00436 .00406 .00380 •00356 •0033s .00316 .00299 .00283 .285 .263 [228 .214 .200 .188 .178 .i68 .159 ' Mim. Serv. ]^tr." 1846. * " Comptes rendus," vol. 15, 1842 ; t " Pogg. Ann." vol. 109, i860. t " Zeitschr. Phys. Chem." vol. 6, 1890. „ „ « o , § Thorpe and Rogers, « PhUo.. Trans." i8sA, .894; " !•««• Ro^ Soc" SS> ■894- Smithsonian Tables. 126 Tables 108-110. VISCOSITY. TABLE 108.-Solntlon of Alcoliol In Water.* Coefficients of viscosity, in C. G. S. units, for solution of alcohol in water. Temp. C. PercenUge by weight of alcohol in the mixture. 8.31 16.60 34-58 43-99 53-36 75.75 87.45 99-7» 0° 5 10 '5 20 25 30 35 40 45 50 1^ 0.0181 .0152 .0131 .0114 .0101 0.0090 .0081 .0073 .0067 .0061 0.0056 .0052 .0048 0.0287 ■0234 .0195 .0165 .0142 0.0123 .0108 .0096 .0086 .0077 0.0070 .0063 .0058 0.0453 .0230 .0193 0.0163 .0141 .0122 .0108 .0095 0.0085 .0076 .0069 0.0732 .0558 •0435 ■0347 .0283 0.0234 .0196 .0167 .0143 .0125 0.0109 0.0707 .0552 .0438 ■im 0.0241 .0204 .0174 .0150 ■0131 0.0115 .0102 .0091 0.0632 .0502 ■0405 •0332 .0276 0.0232 .0198 .0171 .0149 .0130 0.0115 .0102 .0092 0.0407 •0344 .0292 .0250 .0215 0.0187 .0163 .0144 .0127 •01 1 3 0.0102 .0091 .0083 .0256 .0223 .0195 .0172 0.0152 ■0135 .0120 .0107 .0097 0.0088 .0086 •0073 0.0180 .0163 .0148 .0134 .0122 O.OIIO .0100 .0092 .0084 .0077 0.0070 .0065 .0060 The following tables (152-153) contain the results of 3 number of experiments in the viscosity of mineral oils derived from petroleum residues and used for lubricating puTpose3.t TABLE 109. — Ulontl 01Is.t a IS °c. u ft °c. Sp. viscosity. Water at 20<'C. = t. 20° C. 50° C. 100° C. •931 .921 .906 243 216 189 274 246 208 - 11.30 7-31 3^45 2.9 2-5 15 .921 .917 163 132 190 168 - 27.80 2.8 2.6 .878 •855 170 151 108 42 207 182 148 45 8.65 4^77 2-94 1.65 1.86 1.48 1-7 1-3 i 165 139 90 202 270 224 7-60 2.50 3-6o 1.50 1-3 TABLE 110. -Oils. &■ :5c bo Ifr lot oa. |a |a a °c. °c. ?V5 Cylinder oil . . •917 227 274 191 Machine oil . . .914 213 260 102 Wagon oil . . ■914 148 182 80 .911 IS7 187 70 Naphtha residue .910 134 162 55 Oleo-naphtha . .910 219 257 121 .904 201 242 66 a 184 222 26 Oleonid . . . best 18s 217 28 quality .881 188 224 20 Olive oil . . . .916 22 Whale oil . . •S79 _ _ (( (( •875 ~ — ^ t 1 he different groups m this able are from different residuesf viscosity. Smithsonian Tables. Table 111. 127 VISCOSITY. This table ^ves some miscellanecmB data as to the viscosity of liquids, mostly referring to oils and paraffins. The viscosities are in C. G. S. units. Liquid. G.% Coefficient of viscosity. Temp. Cent. ° Authority. Ammonia 0.0160 0.0149 II.9 14.5 Foiseuille. II Anisol 0.0m 20.0 Gartenmeister. Glycerine <4 It 42.20 25.18 13.87 8.30 4.94 2.8 8.1 14-3 20.3 26.5 Schottner. 11 11 11 II Glycerine and water . ' "... <( ** . . . 94.46 80.31 64.0s 49-79 7437 1.02 1 0.222 0.092 8.S 11 II II Glycol 0.0219 0.0 Arrhenios. Mercury* II . . • . . If , . . . . II . . • • • II • . . f • II ... 0.0184 0.0170 0.0157 0.0122 0.0102 0.0093 —20 0.0 20.0 lOO.O 200.0 300.0 Koch. tt (f (( tt U Meta-cresol 0.1878 20.0 Gartenmeister, Olive oU 0.9890 IS.0 Brodmann. Paraffins: Decane Dodecane . Heptane . Hexadecane Hexane Nonane 0.0077 0.0126 0.004s 0.0359 0.0033 0.0062 22.3 23-3 24.0 22.2 237 22.3 BartolU & Stracciati. ti tt tt tt tt (( u tt Octane Pentane Pentadecane Tetradecane Tridecane . Undecane . 0.0053 0.0026 0.0281 0.0213 0.01 SS 0009s 22.2 21.0 22.0 21.9 23-3 22.7 tl It tt tl ti it tt tt tt tl tt « Petroleum (Caucasian) Rape oil II 11 II II , . . • • II II 0.0190 25.^ 0.96 17.S 0.0 1 0.0 20.0 30.0 Petroff. 0. E. Meyer. It tt tt , ,_ ™o66/4- 00000021P- .00000000025'' (vide Koch, Wied. Ann. vol. i^ * Calculated from the formula ji=. 017 — oooooor-t-ooooooj. p. r). . Smithsonian Tables. 128 Table 112. VISCOSITY. This table gives the viscosity of a number of liquids together with their temperature variation. The hea£ngs are temperatures in Centigrade degrees, and the numbers under them the coeffi- cients of viscosity in C. G. S. units.* Liquid. Temperature Centigrade. 30" Acetates: Methyl Ethyl Propyl AUyl Amyl Acids : Formic Acetic Propionic t( Butyric Valeric Salicylic Alcohol : Methyl Ethyl Propyl Butyric Allyl Isopropyl Isobutyl Amyl (op..inac.) Aldehyde Aniline Benzole Bromides : Ethyl Propyl Allyl Ethylene Carbon bisulphide Carbon dioxide (llq.) Chlorides : Propyl Allyl Ethylene Chloroform Ether Ethylbenzole Ethylsulphide Iodides : Methyl Ethyl Propyl Allyl Metaxylol Nitrobenzene Paraffines : Fentane Hexane Heptane Octane Isopentane Isohexane Isoheptane Propyl aldehyde Toluene .00813 .01770 .03882 .05185 .02144 .04564 .08038 .08532 .00267 .00902 .00478 .00645 .00619 •02435 .00429 .00099 .00436 .00402 .01128 .00700 .00874 .00559 .00594 .00719 .00938 .00930 .00802 .00283 .00396 .00519 .00703 .00273 .00371 .00477 .00768 .0046 .0051 .0066 .0068 .0106 .02262 .0150 .0125 .0139 .0196 .0271 .0320 .00686 .01449 .02917 .03872 .01703 •03245 ■05547 .06000 .00244 .00759 .00432 .00575 .00552 .02035 .00396 .00085 .00390 .00358 .00961 .00626 .0026 .00758 .00496 .00536 .00645 .00827 .00819 .00698 .00256 •00355 .00460 .0061 2 .00246 .00332 .00423 .0047 .00668 .0041 .0044 .0059 .0061 .0089 .01804 .0126 .0107 .oii8 •01 63 .0220 .0271 .00591 .01192 .02255 .02947 .01361 .02369 .03906 .04341 .00222 .0440 .00649 .00392 .00517 .00496 .01716 .00367 .00071 •00352 .00322 .00833 .00564 .0023 .00666 .00444 .00487 .00583 ■00737 .00726 .00615 .0203 .00232 .00320 .00410 .00538 .00223 .00300 ,00379 ,0041 ,00586 .0036 .0040 .0052 .0054 •0077 .01465 .0109 .0092 .0101 .0136 .0183 .0222 .00515 .00990 .01778 .02266 .01165 .01755 .02863 .03206 .0319 .00562 •00357 .00467 .00449 .01470 .00342 .00319 .00292 .00730 .00511 .0021 .00592 .00401 .00446 .00530 .00662 .00652 .00547 .0170 .00212 .00290 .00369 .00478 .00204 .00272 .00342 .0036 .00520 .0032 .0035 .0044 .0049 .0065 .01224 .0094 .0081 .0091 .0118 •0155 .0181 .00450 .00828 .01403 .01780 .00911 .01329 .02121 .02414 .0241 .00492 .00425 .00410 .01280 .00319 .00291 .00646 .00466 .00529 .00363 .00409 .00484 .00598 .00588 .00491 .0144 ,00264 ■00334 ,00428 ,00247 ,00309 ,00466 .0030 .0032 .0039 .0044 .0058 .01025 .0082 .0073 .0080 .0102 .0127 .0150 .00396 .00698 .01 1 28 .01409 .00760 .01026 .01609 .01849 .0189 .00437 .00388 .00374 .01124 .00576 .00390 .00477 •00331 .00444 .00544 •00534 .00444 .0124 .00241 .00303 .00386 .00226 .00282 .00420 .00504 .00757 .00926 .00548 .00642 •00973 .01147 .00351 .00328 .00316 .00895 ,00470 ,00394 ,00279 .00378 00456 00448 00369 00221 .00253 .00318 .00235 .00348 .00526 .00633 .00407 .00631 .0075? •00733 .00330 ,00237 .00387 .00381 00313 ,00214 00266 ,00292 1 Pribram-Handl, Wien. Ber. 78, 1878, 80, 1879, 84, 1881. 2 Gartenmeister, Zeitschr. Phys. Chem. 6, i8go. 3 Rellstab, Diss. Bonn, 1868. 4Tliorpe-Roger, Philos. Tians. 185 A, 1894, 189 A, 1897; Proc. Roy. Soc. 55, 1894, 60, 1896; Jour. ,„S:r='"; Soc. 7,, ,897; Chem. News, 75, 1897. 5 Wijkander, Wied. Beibl. 3, 1879. 6 Warburg-Babo, Wied. Ann. 17, 1882. * Calculated from the specific viscosities given in Landolt & Bomstein's Phys. Chem. Tab. For inorganic adds, see Solutions. Smithsonian Tables. Tabuc 1 1 3. VISCOSITY OF SOLUTIONS. 129 ^'?oS„s\rSttfn^l?er 'lLlS°/c^s?^^^^^^^ ?■>■» "="-«= <" temperature on the viscosity of pe^tures in ti^e case oi eaci. solutioT tsSt^r ^p'eSiiXoTi^^^^^^^^ SaJt. Percentage by weight of salt in solution. Density. (« t »» i C < M i Authority. BaCla 7.60 15.40 24-34 - 77-9 86.4 100.7 10 44-0 56.0 66.2 30 35-2 39-6 47-7 5° (1 - - Sprung. Ba(NOs)2 2.98 5-24 1.027 1. 05 1 62.0 68.1 15 51-1 54-2 25 42-4 44-1 35 34-8 36-9 45 Wagner. CaCla 15-17 31.60 39-75 44.09 - 1 10.9 272.5 670.0 lO (( « 71-3 177.0 379-0 593-1 30 tt tt ti . 50-3 124.0 245-5 363-2 50 ~ ~ Sprung. (( tt ti Ca(N08)2 17-55 30.10 40.13 1.171 1.274 1.386 93-8 144.1 242.6 tt 74-6 112.7 217.1 tt 60.0 90.7 156-5 35 49-9 75-1 1 28. 1 45 a Wagner. (( ti CdCla 11.09 16.30 24.79 1. 109 1. 181 1.320 104.0 te 60.5 80.4 25 (( 49-1 35 it 40.7 47.2 53-6 1? ti tt a tt Cd(N08)2 7-8i 15.71 22.36 1.074 I-159 I.241 61.9 85.1 tt S0.1 S8.7 69.0 ti 41-1 48.8 57-3 35 34-0 41-3 47-5 45 it ti tt tt CdSOi 14.66 22.01 1.068 1.159 1.268 78.9 96.2 120.8 \5 61.8 72.4 91.8 ^.5 ^1? 73-5 3? tt 6o.i tt It tt tt C0CI2 22.27 1.081 1. 161 1.264 83.0 111.6 i6i.6 \5 tt 65.1 85.1 126.6 25 a 53-6 73-7 101.6 35 it it 44.9 85-6 15 It it tt C0(N08)2 (( 8.28 15.96 24-53 1-073 I.144 1.229 74-7 87.0 II 0.4 tt 57-9 69.2 88.0 25 tt 48.7 55-4 71-5 35 39-8 44-9 59-1 45 tt tt It It C0S04 7.24 14.16 21.17 1.086 I-159 1.240 86.7 117.8 193.6 \5 it 68.7 146,2 25 S5-0 76.0 1 13.0 35 45-1 61.7 89-9 45 (( (( :: (I CuCl2 it 12.01 21-35 I.104 I.215 87-2 121.5 IS 67.8 95-8 'J 55-1 77-0 35 45-6 6,1-2 45 ti 11 tt tt 33-03 1-331 178.4 tt 137-2 ti 107.6 " 87.1 ** it CU(N03)2 18.99 26.68 46.71 I.177 1.264 1-536 97-3 126.2 382.9 15 tt 76.0 98.8 283.8 25 n 61.5 80.9 215-3 35 It 172.2 45 It ti CUS04 tt 6-79 12-57 17.49 1.055 I.I15 1. 163 79.6 98.2 124.5 15 tt ti 61.8 lit 25 49-8 59-7 75-9 35 41.4 52.0 61.8 45 a tt tt tt HCl ti 8.14 16.12 23.04 1-037 1.084 I.II4 80.0 91.8 IS 79-9 25 48-3 56-4 65-9 35 40.1 48.1 56-4 15 tt It It it HgCla ft 0.23 3-55 1.023 1-033 76.75 10 58.S 59-2 20 46.8 46.6 3f 38-3 .38.3 40 tt 11 ti Smithsonian Tables. 130 Table 113 (cnimued). — Sola1imtj ol Inorganic Salts In Water; Variation wltli tlie Temperatnre. The numbers give the number of grammes of the anhydrous salt soluble in looo grammes of water at the given temperatures. Temperature Cendgtade. 0° 10° 20° 30° 40" so" 60° yfl" 80° 54-57 202.00 261.20 334-55 120.20 158-85 207.35 267.85 342.75 123.67 163.25 212.80 274.65 351.10 127.22 167.70 218.40 281.60 359-65 130.86 172.30 224.15 288.70 368.40 134-59 176.95 230.00 295-95 377-30 250 260 270 386.35 487-35 608.75 395-60 498-55 622.10 405-05 509.90 635-70 414.65 521.50 649.50 424.45 533-35 663-55 434-45 ^77-^5 444.65 557.60 692.40 455.00 570.05 707-15 465.60 582.70 722.15 476.35 595-60 737-45 (g) Mercury. 270° 280 290 123.92 157-35 198.04 126.97 161.07 202.53 130.08 164.86 207.10 137.26 211.76 136-50 172.67 216.50 139.81 176.79 221.33 143.18 180.88 226.25 146.61 185.05 231.25 150.12 189.30 236-34 153-70 193-63 241-53 300 310 320 330 340 246.81 304-93 373-67 454.41 548.64 252.18 381.18 463.20 558-87 257.65 317-78 388.81 472.12 569.25 263.21 324-37 396.56 481.19 579-78 268.87 331-08 404-43 490.40 590.48 274-63 337-89 412.44 499-74 601.33 280.48 344.81 420.58 509.22 612.34 286.43 35'|5 428.83 518.85 623-51 292.49 359.00 437-22 528.63 634.85 298.66 366.28 445-75 646.36 350 360 658.03 784-31 669.86 681.86 694.04 706.40 718.94 731-65 744-54 757-61 770.87 6MITH50NIAN TABLES. Table 134. 149 VAPOR PRESSURE OF SOLUTIONS OF SALTS IN WATER.* The first column ^ves the chemical formula of the salt. The headings of the other columns give the number of gramme-molecules of the salt in a litre of water. The numbers in these columns give the lowering of the vapor pressure produced by the salt at the temperature of boiling water under 76 centimetres barometric pressure. Substance. 0.6 1.0 2.0 3.0 4.0 6.0 6.0 8.0 10.0 Al!!(S04)8 . . . 12.8 36.5 AlCls .... 22.5 61.0 179.0 318.0 Ba(SOs)2 • 6.6 15.4 34-4 Ba(OH)2 . 12.3 22.5 39'0 Ba(N08)2 - 13-5 27.0 Ba(C10s)2 • 15.8 33'3 70.5 108.2 BaCl2 .... 16.4 367 77.6 BaBra .... 16.8 38.8 91.4 150.0 204.7 Ca(S0B)2 . • • 9.9 23.0 56.0 106.0 Ca(N08)2 . . . 16.4 34-8 74.6 139-3 161.7 205.4 CaCIj .... 17.0 39-8 95-3 166.6 241-5 ^If^ CaBrj. 177 44.2 105.8 191.0 283-3 368.5 CdSOi 4.1 8.9 18.1 Cdia .... 7.6 14-8 33-5 527 CdBra. 8.6 17.8 36-7 557 80.0 CdCl2. 9.6 18.8 367 S7.0 77-3 99-0 Cd(N08)2 • Cd(C103)2 . 1 5-9 36.1 78.0 122.2 17-5 C0SO4 S-S 10.7 22.9 45-5 C0CI2. 15.0 34-8 83.0 136.0 186.4 C0(N03)2 . . . 17-3 39-2 89.0 152.0 218.7 282.0 332-° FeS04 5.8 10.7 24.0 42.4 H3BO3 6.0 12.3 ^5-' 38.0 51.0 H3PO4 6.6 14.0 28.6 45.2 62.0 81.5 103.0 146.9 189.5 H8ASO4 . 7-3 15.0 30.2 46.4 64.9 H2SO4 12.9 26.5 62.8 104.0 148.0 198.4 247.0 343-2 KH2PO4 . 10.2 19.5 33-3 47.8 60.5 73-1 85.2 148.0 KNO3. 10.3 21. 1 40.1 57.6 74-5 88.2 102.1 126.3 KClOs 10.6 21.6 42.8 62.1 80.0 KBrOs 10.9 22.4 45.0 KHSO4 . 10.9 21.9 43-3 65-3 85-5 107.8 129.2 170.0 198.8 KNO2 II. I 22.8 67.0 90.0 110.5 i3°-7 167.0 KCIO4 II. 5 22.3 KCl .... 12.2 24.4 48.8 74.1 100.9 128.5 152.2 KHCO2 • 11.6 23-6 59.0 77.6 104.2 132.0 160.0 210.0 255.0 KI . . . . 12.5 25-3 52.2 82.6 II 2.2 141.5 171.8 225.5 278.5 K2C2O4 . 13-9 28.3 59-8 94.2 131.0 226.4 K2WO4 139 33-0 It, 123.8 175-4 258.5 K2CO8 14.4 31.0 105.5 152.0 2og.o 350.0 387.8 KOH .... 15.0 29.5 64.0 99.2 140.0 181.8 223.0 309-5 K2Cr04 . LiNOs 16.2 12.2 29.5 25.9 60.0 557 88.9 122.2 IS5-I 188.0 253-4 309.2 LiCl . . . • 1 2. 1 25.5 57-1 95.0 132-5 'Ik^ 219.5 311-5 ?Il LiBr . . . ■ 12.2 26.2 60.0 97.0 140.0 186.3 241.5 341-5 438.0 Li2S04 133 28.1 56.8 89.0 LiHS04 . Lil • • • • 12.8 13.6 27.0 28.6 57-0 647 93-0 105.2 130.0 154-5 168.0 206.0 264.0 357-0 445.0 Li2SiFl6 . 15.4 340 70.0 78.1 106.0 LiOH. 15.9 37-4 UiCiOi . 16.4 32.6 74.0 120.0 171.0 # r"«rnT-i;iofl frnm a table b » Tamma an, " M^ n. Ac. St . Petersb " 3S. No . 9, 1887. See als Refera e, " Zeit. f. Phys." ch. 2, 42j '886. Smithsonian Tables. 150 Table i 3* (contmueJ). VAPOR PRESSURE OF SOLUTIONS OF SALTS IN WATER. Substance. 0.6 1.0 2.0 3.0 4.0 6.0 6.0 8.0 10.0 MgSOi . . . lei 12.0 24.5 47-5 MgCla. . . . 39-0 100.5 183.3 277.0 377-0 Mg(N03)2 . . . 17.6 42.0 lOI.O 174.8 MgBrj 17.9 44-0 115.8 205.3 298.5 MgH2(S04)2 . . 18.3 46.0 1 1 6.0 MnSOi 6.0 10.5 21.0 MnCla. 15.0 34-0 76.0 122.3 167.0 209.0 NaH2P04 . 10.5 20.0 36s Si-7 66.8 82.0 96.5 126.7 157.1 NaHSOi . 10.9 22.1 47-3 u-°. 100.2 1 26. 1 148.5 189.7 231-4 NaNOs 10.6 22.5 46.2 90-3 111.5 131-7 167.8 198.8 NaCIOs . 10.5 23.0 48.4 73-5 98.5 123-3 I47-S 196.5 223-5 53 154 155 156 158 '59 160 161 162 164 165 166 167 168 169 170 171 172 '73 174 175 176 177 178 179 180 i8i 182 '?3 184 185 186 187 188 189 190 191 192 193 194 195 1 96 197 3581.2 3678.4 3777-7 3879-2 3982.8 4088.6 4196.6 4306.9 4419-5 4534-4 4651.6 4771.3 4893-4 50'7-9 5145-0 5274-5 5406.7 5541-4 5678.8 5818.9 5961.7 6107.2 6406.6 6560.6 6717.4 6877.2 7040.0 7205.7 7374-5 7546.4 7721.4 7899-5 8080.8 8265.4 8453-2 8644.4 g* u a 9036.7 9238.0 9442.7 9650.9 9862.7 0078.0 10297.0 10519.6 10746.0 10975.0 198 1 1209.8 199 1 1447.5 4868.9 5001.1 5'36-' 5275-0 5414.8 5558-6 5705-5 5855-5 6008.5 6164.7 6324.2 6486.8 6652.8 6822.2 6994.9 7171-1 7350-7 7533-9 7720.7 791 I.I 8105.2 8303-1 8504-7 8710.2 89'9-5 9132.8 9350-0 9571-3 9796.6 10026.1 10259.7 10497.7 10739.9 10986.4 11237-3 1 1490.0 "752-5 12016.9 12285.9 12559.6 •H-S 5 t> 69.26 71.14 73-06 75.02 77-03 79-07 81.22 83.29 85-47 87.69 89.96 92.27 94.63 97.04 99-50 102.01 104.56 107.18 109.84 112.53 .1^ il Si'" ,?° 115.29 1 18.11 120.98 123.90 126.87 129.91 133.00 136-15 '39-35 142.62 '45-93 149.32 152.77 156-32 159.84 141.0 144.8 148-7 152.7 156.8 161.0 165.2 169.6 174.0 178-5 183.1 187.9 192.7 197.6 202.6 207.7 212.9 218.2 223.6 229.1 234-1 240.4 246.3 252.2 258-3 264.5 270.8 277.2 283.7 290.3 297-1 304.0 311.0 318.1 325-4 ■■•5 163-47 332-3 12837.9 13121.0 13408.9 3701.7 13999-4 14302.7 14609.8 14921.2 15240.4 15563-5 167.17 170.94 174.76 178.65 182.61 186.63 190.72 194.88 199-13 203.43 207.81 212.25 216.77 221.37 4.712 .840 .971 S.104 .240 5.380 .522 .667 .815 .966 6.120 .278 ■439 .603 •770 6.940 7.114 .291 .472 .656 7.844 8.036 .231 -430 .632 8.839 9-049 .263 .481 •703 9-929 10.150 -394 -633 B 876 363.2 340-3 348.0 355-8 363-7 371-8 380.0 388.3 396.8 405-4 414.1 423-' 432-1 441-3 450.7 11.123 -374 .630 .885 12.155 12.425 12.699 12.977 3.261 '3-549 13.842 14-139 14.441 14.749 15.062 302.0 303-8 305-6 307-4 309.2 3110 312.8 314-6 316.4 318.2 320.0 321.8 323-6 325-4 327-2 3290 330-8 332-6 334-4 336-2 338-0 339-8 341-6 343-4 345-2 347-0 348.8 350-6 352-4 354-2 356.0 357-8 359-6 361.4 365-0 366.8 368.6 370-4 372.2 374-0 375-8 377-6 379-4 381.2 383-0 384,8 386.6 388.4 390-2 Smithsonian Tables. 154 Tables 1 37 (amtaae 3555-079 Fe 9 3059.212s Fe 20 3440.762s 1 Q 3441.155s i Fe 20 3558.672s Fe 8 3067.369s Fe 8 Fe 15 3565-5353 Fe IZ 3073-091 3078.769s Ti,- 6Nd.' 3442.118 Mn 3566.522 Ni 10 Ti.- 8d? 3444.020s Fe 8N 3570-2733 Fe 20 3088.145s Ti 7d? 3446.406 Ni )\ 3572-014 Ni 6 3134.23OS Ni, Fe 8 3449-583 Co 6d? 3572.712 Se, - 6 3188.656 - Fe 6d? 3453039 Ni 6d? 3578.832 Cr 10 3236.703s Ti 7N 3458.601 Ni 8 3581.349s Fe 30 3239.170 Ti 3461.801 Ni 8 3584.800 Fe 6 3242.125 Ti,- 8 3462.950 Co 6 3585-105 Fe 6 3243.189 -, Ni 6 3466.01 5s Fe 6 3585-479 Fe 7 3247.688s Cu 10 347 5- 594s Fe 10 3585-859 Fe 6 3256.021 Fe.' 6 3476.849s Fe 8 3587-130 Fe 8 3267.834s V 6 3483.923 Ni 6d? 35^7-370 Co 7 3271.129 Fe 6 3485.493 FeCo 6 3588.084 Ni 6 3271.791 Ti, Fe 6d? 3490.733s Fe 10 N 3593-636 3594-784 Cr § 3274.096s Cu 10 3493-"4 Ni 10 N Fe 6 3277.482 Co-Fe 7d? 3497.982s Fe 8 3597-854 Ni 8 3286.898 3295.951s 3302.SIOS 3315-807 331 8. 1 60s 3320.391 3336.820 3349-597 3361-327 3365-908 3366.3 n 3369-713 Fe 7N 3500.996s Ni 6d? 3605.479s Cr 7 Fe, Mn Na 6 6 3510.466 3512.785 Ni Co 8 6 3606.838s 3609.008s Fe Fe 6 • 20 Ni 7d? 3513.965s Fe 7 3612.882 Ni 6 d? Ti 6 3515.206 Ni 12 3617.934s Fe 6 Ni Mg Ti Ti Ni Ti, Ni Fe, Ni 7 8N 6 6d? .6 3519-904 3521.410S 3524-677 3526.183 3526.988 3529.964 3533-156 N Fe Ni Fe Co Fe-Co Fe 7 8 20 6 6 6 6 3618.919s 3619-539 3621.612s 3622.147s 3631.605s 3640.535s 3642.820 Fe Ni Fe Fe Fe Cr-Fe Ti 20 8 6 6 7 '"S!rdiffrrence''s'"TFal?yX"son-arc.iron)-(Ro«land-sol^^^^ lines were plotted, a smooth carve drawn, and the following values obtained : Wave-length 3000. 3100. s^oo- 33°o. 3400. 35°o. 36«.. 37"^ Correction -.106 -.us -■■24 - -m --mS --154 --'SS •>40 H. A. Rowland, " A preliminary table of solar-spectrum wave-lengths," AstrophyMcal Journal, 1-6, .895-1897. Smithsonian Tables. 1 72 Table 1 52 (amtinuedi. STANDARD SOLAR WAVE-LENGTHS. ROWLAND'S VALUES. Wave-length. SubsUDCe. Inten- sity. Wave-length. Substance. Inten- sity. Wave-length. Substance. Inten- sity. 3647.988s Fe 12 3826.027s Fe 20 4045-9755 Fe 30 3651.247 Fe,- 6 3827.980 Fe 80 4055.701S Mn 6 3651.614 Fe 7 3829. 50IS Mg 10 4057.668 - 7 3676-457 Fe, Cr 6 3831-837 Ni 6 4063.7595 Fe 20 3680.069s Fe 9 3832.450s Mg 15 4068.137 Fe-Mn 6 3684.2S8S Fe 7d? 3834.364 Fe 10 4071.908s Fe IS 3685-339 Ti lod? 3838.43SS Mg-C 1 4077.885s Sr 8 3686.141 Ti-Fe 6 3840.580s Fe-C 4102.000HS H, In 40N 3687.61OS Fe 6 3841.195 Fe-Mn 10 4121.477s Cr-Co 6d? 3689.614 Fe 6 3845.606 C-Co 8d? 4128.251 Ce-V,- 6d 3701-234 Fe 8 3850.118 Fe-Cr 10 4132-235 Fe-Co 10 3705.708s Fe 9 3856.524s Fe 8 4137-156 4140.089 Fe 6 3706.175 Ca, Mn 6d? 3857.805 Cr-C 6d.? Fe 6 3709.389s Fe 8 3858.442 Ni 7 4144.038 Fe 15 3716.59IS Fe 7 3860.055s Fe-C 20 4167.438 - 8 3720.084s Fe 40 3865.674 Fe-C 7 4187.204 Fe 6 3722.692s Ni 10 3872-639 Fe 6 4191.595 4Z02.198S Fe 6 3724.526 Fe 6 3878.152 Fe-C 8 Fe 8 3732-5455 Co-Fe 6 3878.720 Fe 7Nd.' 4226.904sg Ca 20 d? 3733-469S Fe- yd} 3886.434s Fe IS 4233-772 Fe 6 3735.014s Fe 40 3887.196 Fe 7 4236.112 Fe 8 3737.281S Fe 30 3894.211 - 8d 4250.287s Fe 8 3738.466 - 6 3895-803 Fe 7 4250.945s Fe 8 3743-508 Fe-Ti 6 3899.850 Fe 8 4254.505s Cr 8 3745.717s Fe 8 3903.090 Cr, Fe, Mo 10 4260.640s Fe 10 3746.058s Fe 6 3904.023 - 8d 4271.934s Fe IS 3748.408s Fe 10 3905.660s Si 12 4274.958s 4308.081SG Cr 7d? 3749-63IS Fe 20 3906.628 Fe 10 Fe 6 3753-732 Fe-Ti 6d.' 3920.410 Fe 10 4325-939S Fe 8 3758-375S Fe 15 3923-054 Fe I2d? 4340.634H7 H 20N 3759-447 Ti I2d? 3928.075s Fe 8 4376.107s Fe 6 3760.196 Fe 5 3930.450 Fe 8 4383.720s Fe IS 3761.464 Ti 7 3933-523 ,^ - 8N 4404.927s Fe 10 3763-94SS Fe 10 3933.82CSK 3934-108 Ca 1000 4415.293s Fe 8 3765.689 Fe 6 Co, V-Cr 8N 4442.510 Fe 6 3767-341S Fe 8 3944.160S Al ■S 4447.892s Fe 6 3775-717 Ni 7 3956.819 Fe 6 4494.738s Fe 6 3783-674S Ni 6 3957- 1 77s Fe-Ca 7d? 4528.798 Fe 8 3788.046s Fe 9 3961.674s Al 20 4534.139 Ti-Co 6 3795- 147s 3798.655s Fe 8 3968.350 -,Zr 6N 4549.808 Ti-Co 6d? Fe 6 3968.62 5sH Ca 700 4554.211S Ba 8 3799.693s Fe 7 3968.886 - 6N 4572.1 s6s Ti- 6 3805.486s Fe 6 3969.413 Fe 10 4603.126 Fe 6 3806.865 Mn-Fe 8d? 3974-904 Co-Fe 6d? 4629.521S Ti-Co 6 3807-293 Ni 6 3977.891S Fe 6 4679.027s Fe 6 3807.681 V-Fe 6 3986.903s - 6 4703.177s Mg 10 3814.698 - 8 4005.408 Fe 7 4714.599s Ni 6 3815.987s Fe 15 4030.918s Mn lOd.? 4736.963 Fe 6 3820.586SL Fe-C 25 4033.224s Mn 8d? 4754.225s Mn 7 3824.591 Fe ^ 4034.644s Mn 6d 4783.613s Mn 6 Corrections to reduce Rowland's wave-lengths to Fabry and Buisson's system (the accepted standard 1008) Tem- perature 15° C, pressure 760 mm. '■ Wave-length 360a 370a 380a 3900. 4000. Correction — .155 — .140 — .141 — .144 — .148 - Smithsonian Tables. 4100. 4200. 4300. 4400. 4500. -.«S* — .156 — .161 — .167 — .172 . 4600. 4700. 4800. -.176 —.179 —.179. Table 1 62 (continued). STANDARD SOLAR WAVE-LENGTHS. ROWLAND'S VALUES. 173 Wave-length. 4861.527SF 4890.948s 4891.683 4919-1743 4920.685 49S7'78ss 5050.008s Si67.497sb4 5171.778s 5i72.856sb2 5i83.79isbi 5233.122s 5266.738s 5269.723SE 5283.802s S324-373S 5328.236 5340.121 5341-213 5367.669s 5370.166s 5383.578s S397-344S 5405.989s 5424.290s 5429.911 5447- 130S 5528.641s 5569.848 SS73-07S 5586.991 S588.985S 5615.877s 5688.436s 5711.313s 5763.21SS 5857.674s 5862.582s 5890.186SD2 5896.155 Di 5901.682s 5914.430s 5919.860s 5930.406s Substance. H Fe Fe Fe Fe Fe Fe Mg Fe Mg Mg Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Mg Fe^ Fe Fe Ca Fe Na Mg Fe Ca Fe Na Na A(wv) -, A(wv) A(wv) Fe Inten- sity. 'I 8 6 10 8 6 IS 6 20 30 7 6 8d.? 6 7 8d? 6 7 6 6 6 7d? 6 6 6d? 6d.? 8 6 6 \ 6 6 6 6 8 6 30 20 6 6 7 6 Wave-length. 5948.7653 5985.040s 6003.239s 6008.785s 6013.715s 6016.86IS 6022.0l6s 6024. 28IS 6065.709s 6102.392s 6102.937s 6108.334s 6122.434s 6136.829s 6137.915 6141.938s 6155-350 61 62.390s 6169.249s 6169.778s 6170.730 6191-3938 6191.779s 6200.527s 6213.644s 6219.494s 6230.943s 6246.535s 6252.773s 6256.572s 63or.7i8 6318.239 6335-554 6337048 6358.898 6393.820s 6400.217s 6411.865s 6421. 570s 6439-2938 6450.033s 6494.004s 6495.213 6546.479s Substance. Si Fe Fe Fe Mn Mn Mn Fe Fe Fe Ca Ni Ca Fe Fe Fe,Ba Ca Ca Ca Fe-Ni Ni Fe Fe Fe Fe V-Fe Fe -Fe Ni-Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Ca Ca Ca Fe Ti-Fe Inten- sity. 6 6 6 6 6 6 6 7 7 6 i 7 7 7 15 6 7 6 6 I 6 7 6 I 6 7 6 7 8 7 7 8 6 6 Wave-length. 6563.045SC 6s93.i6is 6867.457SB 6868.336 I 6868.478 J* 6869.142s 6869.353s 6870.U6I 6870.249 j' 6871. 180S 6871.532s 6872.486s 6873.080s 6874-0378 6874.8993 6875.830s 6876.958s 6877.882s 6879.288s 6880.172s 6884.076s 6886.000s 6886.990s 6889.192s 6890.151S 6892.618s 6893.5603 6896.289s 6897.208s 6900.199s 6901.117s 6904.3623 6905.2713 6908.783s 6909.676s 6913.4483 6914.337s 6918.370S 6919.250S 6923-5538 6924.427s 7191-755 7206.692 Sub- stance. H Fe A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A{0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A(0) A,- - A Inten- sity, 40 6 6d? 6 6 7 6 8 10 II 12 12 13 13 13 12 12 6 10 II 12 13 14 14 15 14 15 14 15 14 14 13 13 II II 9 9 9 9 6N 6 Corrections to reduce Rowland's wave-lengths to Fabry and Buisson's system (the accepted standard, 1908) ; tem- .peiature 15° C, pressure 760 mm. : Wave-length 4800. 4900. 5000, 5100. 5200. 5300. Correction — .179 — ,176 — ,173 — .170 — .t66 — .17a 5400. 5500. 5600. 5700. 5800. -.212 — .217 —.218 — .213 — .209 Wave-length 5800. 5900. 6000. 6100. 6200. 6300. 6400. 6500. 6tioo. Correction — .209 — .209 — .213 ^.214 — ,213 — .aio — .209 — ,210. SMrTHSONIAN TABLES. 6700. 6800. 174 Table 153. STANDARD WAVE-LENGTHS. KAYSER'S IRON (ARC) LINES. r= easily reversible. Wave- Inten- Correc- Wave- Inten- Correc- Wave- Inten- Correc- Wave- Inten- Correc- length. sity. tion.* length. sity. tion.* length. sity. tion.* length. sity. tion.* 2327.468 3 2518.198 8r 2742.506 lor 2973-254 8r 31-384 3 22.950 20r 44-163 8r 73-366 sr 32.869 3 23-754 4r 44-624 4r 81.565 7r 38-073 I 27.525 I or 45-177 sr 83.690 lor 43-567 48.196 3 29.223 8r 46.580 4r 87.410 4 —.117 2 33-9" 4 47.080 sr 90.511 4 48.380 2 35-699 6r 50.238 I or 94-554 I or 54.969 2 37-263 4r 55-834 sr 2999.630 8r 59-187 3 41.064 8r 56.412 4r 3001.068 lor 60.079 2 44.016 4r |7-£3 4r 07.262 2 60.373 2 46.072 I or 61.883 sr 07.409 2r 64.904 2 49.708 8r 62.125 sr 08.254 8r 66.678 2 56.404 2 68.621 5r Sr 09.690 4r 68.670 2 56-963 2 72.205 16.043 3 70.588 2 62.619 S —.078 78.327 6r — .102 16.305 3 73-813 ar — .076 67.001 4 78.946 2 17-747 Sr 75-273 3 75-445 3 81.936 3 20.619 4r 80.840 4 78.012 3 88.207 I or 20.764 lor 82.114 7r 84.623 5r 91.989 3 21.194 lor 84-473 3 85.964 3 2797.877 2 25.960 8r 88.711 2 88.102 5r —.086 2804.622 sr 31-332 4 91-563 2 98.456 5r 07.088 5r 31-753 4r 95.709 Sr 99-483 5r 13-391 8r —.101 37-505 I or 2399.322 Sr 2599-663 V 17.612 3 41-753 3 2404.519 3 2606.920 3'- 23-382 5r 41.860 3 04.969 Sr 07-155 sr 25.660 6r 47-719 lor 06.742 5'" 11.963 5' 25.803 4r 51.179 i 10.601 5'' 13-914 4r 32.543 8r 57562 II. 152 4r 17.706 4r 35-562 4r 59.202 I or 13-393 4r -.083 18.108 2r 38.231 3r 67.363 8r 24.231 3 23.627 sr 43-742 3r 68.286 3 31.126 2 25.754 28.383 5"- 44.083 or 75.850 6r —.125 35-234 (Si) -.075 sr -.087 51.910 sr — .110 So.iio 2 39-834 4r 31-139 sr 59-007 3 83-853 sr 40.201 4r 35-899 3r 63-973 3 91.687 3 42.658 4r 44.085 3r 67.679 3 95-013 2 47.808 4r 47.649 3 69.418 sr 3095-384 2 53-568 2 51.800 2 74.284 sr —.108 3100.057 4r 57.686 Sr 56.232 3 77-414 3 00.418 4r 62.279 4r 66.897 3r 83.840 3 00.778 4r 62.740 lor 73-315 2 90.000 3r 12.183 2 65.244 5'' 79.148 8r —.083 94.617 3 16.747 3 68.974 4r 80.544 3 2899.531 3 25.770 3 -.109 72-436 4r 89.302 or 2901.496 3 32.627 sr 72.976 lor 90.153 2 07.630 3 40.503 3" 74.906 4r 92.710 2 12.273 8r —.1x6 44.096 3" 78.657 C 2699.193 3 18.144 3 51.460 3u 79.872 lor 2706.672 4r 23.409 s 57-157 4 83.361 2or 08.663 2 25-479 60.764 3 83.618 3r 14-503 s —.084 29.119 or 65.129 3 84.280 or 18.530 4r 37-030 lor 71-473 3 88.232 I or 19.121 lor 41.462 8r —•"5 75-556 78.122 7 —.109 89.844 8r 20.997 lor 44-519 3 5 90-737 lor 23.671 8r 47.996 9r 80.339 7 91.249 I or 25.024 4r 48.557 4 85.015 88.947 3 93-33' 7r 33-978 8r 54-061 9r S 2496.625 4r 35-566 8r 57-484 9r 91.778 2501.228 8r 37-407 I or 65-379 7r 92.921 8 07.991 4r 39639 8r —.089 67.019 I or 93-423 8 2510.927 8r 2742.349 sr 2970.227 lor 3199.63S 7 Taken from Kayser's Handbuch der Spectroscopie. * For reducing to Fabry and Buisson's system of wave-lengths see Table 149 (the accepted standard, 1908)} tempera- ture 15° C, pressure 760 mm. Smithsonian Tables. Table 1 53 (continued). STANDARD WAVE-LENGTHS. KAYSER'S IRON (ARC) LINES. r = easily reversible. 175 Wave- length. 3200-593 05.SIS »°-953 14.158 19.701 19-935 22.187 25-905 31.091 34-745 39-564 44.308 48-333 51-357 57-724 62.413 65.746 71.129 80.386 84.720 86.884 3292.721 3306.106 06.479 14.868 17.251 28.992 37-793 42.034 48.056 66.917 67.675 78.814 80.242 84.113 89.882 94.721 3397- "7 3402.392 06.578 06.938 13-275 24-430 27-263 40.762 41.138 44.025 45-301 50.484 58.454 60.067 66.006 71-413 71-497 75.600 76.850 83.159 3485.490 Inten- sity. 7 8 5 10 5 5 lor I or 8 8 8 5 5 5 3 2 8 5 5 3 7 5 7 7 5 2 S 4 3 4 4 3 5 51 4 4 2 3 3 4 2 4 5 5r 4 9'- 8r 71- 5 4 3 4 5r 3 3 6r 6r 3 3 Correc- tion.* —.115 — .126 —.146 — .146 Wave- length. 3490.721 3497-989 3506.650 08.627 08.663 •3-974 21.415 26.196 26.822 29.960 40.287 58-672 65-535 70-257 81.348 85-478 87-137 94.767 3599-781 3605.619 06.836 12.242 17-934 18.918 22.158 30.506 31.617 32-195 40.541 47-997 50.429 51.615 55-625 69-674 76.461 80.062 83.205 87.609 3695.202 3702.180 05.714 09-395 20.083 22.710 27.769 33-470 35-016 37-278 43-5 'O 45.710 48.409 49-634 58.3S1 63.940 67-339 76.606 78.670 3788.031 Inten- sity. 6r 5r 3 2 2 5'- 5r V 4 3 2 8r 7r 4r 4r 4u 2 4 4 2 5 I 5 5 7r 3 5 3 5 5 3 41- 3 4r 3 2 4r 5>- I or 6r 5'- 5'- 9r 8r 6r 7r 7'- 8r 8r 8r 7r 3 2 5 Correc- tion.* —.154 —•155 —.150 Wave- length. 3790.242 95-149 3798-658 3801.822 06.847 13.202 15.987 20.573 24.591 26.028 27.967 34-370 40.586 41.194 50-114 56.515 60.054 65.670 72.640 78.166 78.722 86.426 87-193 95.801 3899-853 3903.097 06.624 09.980 13-784 20.404 28.073 41.032 45.269 48.927 56.610 56.823 66.219 69.411 77-892 84.112 86.330 96.147 3998-2 4007.429 17-303 22.029 30.670 32.796 44.776 45-978 55.706 62.605 '& 71.901 79.999 84.666 96.135 4098.346 Inten- sity. Correc- tion.* 8r 6r 6r 3" 9r 6r 8r 7r 8r 7r 8r 8r 6r lor 6ru 4r 6r 4 6r 5r Sr Ir 6 3 i 5r 4 2 4 3 5 I 6 4 4 3 3 3 2 5 3 2 2 lor 3 5 I or —.144 —•143 —.147 —.157 Wave- length. 4107.646 14.608 18.709 37-156 44-033 54.662 71.069 75-799 81.918 87.221 91.611 4199-256 4202.195 10.521 19523 22.387 27.606 33-771 36-118 45-423 47.604 50.299 50.948 60.656 71-333 71-933 82.567 85.614 91.631 94.290 4299.420 4308.072 09.542 '5-255 25.941 37-219 46739 52.910 58.689 67-759 69.954 76.104 83-724 4391-137 4404.929 15.301 27.490 30.801 42.522 47-907 54-572 61.838 66.737 69.566 76.207 84.420 89.929 4494-755 Inten- sity. Correc- tion.* 6 lou 4 4 5 I 8 6 8 5 5 I 7 9 7 lor 7 4 i 6r 7r 4 6 3 5 3 5 I 8r 4 8 8 6 I 6 4 I 6 6 S 4 6 —.157 — .170 — .146 — .160 -.166 — .169 — .176 -.183 -183 Taken from Kayser's Handbuch der Spectroscopie. * For reducing to Fabry and Buisson's system of vave-Iengths see Table 149 (the accepted standard, 1908) ; tern, perature 15° C, pressure 760 mm. Smithsonian Tables. 176 Table 154. WAVE-LENGTHS OF FRAUNHOFER LINES. For convenience of reference the values of the wave-lengths corresponding to the Fraunhofer lines usually designated by the letters in the column headed " index letters," are here tabulated separately. The values are in ten millionths of a millimetre, on the supposition that the D line value is 5896.155. The table is for the most part taken from Rowland's table of standard wave- lengths. Index Letter. Line due to — Wave-length in centimetres X lo". Index Letter. Line due to— Wave-length in centimetres X lo^. A 1: 7621.28* 7594.06* G JFe ^Ca 4308.081 4307.907 a - 7164.725 g Ca 4226.904 B 6870.182 1 horHj H 4102.000 CorH„ H 6563.045 H Ca 3968.625 a 6278.303 t K Ca 3933-825 Di Na 5896.15s L Fe 3820.586 D2 Na 5890.186 M Fe 3727-778 Ds He 5875-985 N Fe 3581-349 El TFe 5270.558 Fe 344I-ISS ^Ca 5270.438 P Fe 3361-327 Es Fe 5269.723 Q Fe 3286.898 bi Mg 5183-791 ■D (Ca 3181.387 bj Mg 5172.856 ix ica 3179-453 bs f Fe (Fe 5169.220 5169.069 l\ , Fe Fe 3100.787 3100.430 b4 (Fe 5167.678 32 J Fe 3100.046 (Mg 5167.497 s Fe 3047-725 ForHp H 4861.527 T Fe 3020.76 d Fe 4383-721 t Fe 2994-53 G' or H^ H 4340.634 U Fe 2947.99 f Fe 4325-939 * The two lines here given for A are stated by Rowland to be : the firsti a line " beginning at the head of A, out- side edge ; " the second, a " single line beginning at the tail of A." t The principal line in the head of B. t Chief line in the a group. See Table 152, Row]and*s Solar Ware-lengths (foot of page) for correction lo reduce these values to Fabry-Buisson .system of wave-lengths. Smithsonian Tables. Table 1 55. 177 PHOTOMETRIC STANDARDS • < No primary photometric standard has been generally adopted by the various governments. In Germany the Hefner lamp is most used j in England the Pentane lamp and sperm candles are used ; in France the Carcel lamp is preferred; in America the Fentane and Hefner lamps are used to some extent, but candles are more largely employed in gas photonjetry. For the photometry of electric lamps, and generally in accurate photometric work, electric lamps, standardized at a national standardizing institution, are commonly employed. The " International candle " is the name recently employed to designate the value of the candle as maintained by cooperative effort between the national laboratories of England, France, and America; and the value of various photometric units in terms of this international candle is given in the following table (taken from Circular No. 15 of the Bureau of Standards). I International Candle = i Pentane Candle. I International Candle :^ i Bougie Decimale. I International Candle = i American Candle. I International Candle = i.n Hefner Unit. 1 International" Candle = 0.104 Carcel Unit. Therefore i Hefner Unit = 0.90 International Candle. The values of the flame standards most commonly used are as follows : 1. Standard Pentane Lamp, burning pentane 10.0 candles. 2. Standard Hefner Lamp, burning amyl acetate 0.9 candles. 3. Standard Carcel Lamp, burning colza oil 9.6 candles. 4. Standard English Sperm Candle, approximately .... 1.0 candles. Slight differences in candle power are found in different lamps, even when made as accurately as possible to the same specifications. Hence these so-called primary standards should be them- selves standardized. Smithsonian Tables. 1 78 Tables 1 56-1 58. SENSITIVENESS OF THE EYE TO RADIATION. (Compiled from Nutting, Bulletin of the Bureau of Standards.) Radiation is easily visible to most eyes from 0.330/1 in the violet to 0.770/1 in the red. At low intensities approaching threshold values (red vision) the maximum of spectral sensibility lies in the green at about 0.510/a for 90% of all persons. At higher intensities with the establish- ment of cone vision the maximum shifts towards the yellow at least as far as o.36o;u. TABLi: 156. - Variation of tlie Sensltlvensss ol tlie Eye wltli the Wave-lengtli at Low Intensities (near ThieslioM Values). KSnlg. A .410 •430 ■450 .470 .490 .510 •530 ■550 .570 •590 .610 Mean sensitiveness 0.02 0.06 0.23 0.49 0.81 1. 00 0.81 0.49 0.22 0.077 0.026 TABLE 1S7. — Variation ol Sensitiveness to Radiation of Greater Intensities. The sensibility is approximately proportional to the intensity over a wide range. The ratio of optical- to radiation-intensity increases more rapidly for the red than for the blue or green (Purkinje phenomenon). The intensity is given for the spectrum at 0.535^1 (green). Intensity (nietre.cand]es) = .oo(»4 .00225 .0360 •S7S 2.30 q.22 36.9 147.6 590.4 Ratio to preceding step = . ' -■ 938 16 16 4 4 4 4 4 Wave-length, A. Se isitivenes fi. 0.430/i .081 ■093 .127 .128 .114 .1.4 - - - .450 ■33 •30 .29 ■3i •23 ■•75 .16 - - .470 •63 •59 •54 •s« .51 .29 .26 .23 - .490 .96 {.89) (76) (■«9) (•S3) .50 •45 •38 •35 .505 1. 00 1. 00 1. 00 1. 00 ■99 (■7b) .66 .61 •54 .520 .88 .86 .86 •94 •99 (•S^) .8, .8s M •S3S .61 .62 ■b^ .72 •?' (■98) .98 •99 .98 ■5SS .26 •30 •34 .41 .62 •«4 •93 •97 .98 •S7S .074 .102 .122 .168 (■39) (•63) (.76) (•«2) (.84) ■^ ]oo8 •034 .054 .091 .27 •49 .61 .68 .69 .60s .012 .024 .056 •173 •35 (•45) •54 •55 .625 .004 .004 .oti .027 .098 .20 •27 •35 •35 .650 .000 .000 .003 .007 .025 .060 .08 s .122 •133 .670 .000 .000 .001 .002 .007 .017 .025 .030 .030 X, maximum sensitiveness •503 .504 .504 .508 •513 •530 •541 •543 •544 TABLE 168. —Sensibility to Small Differences In Intensity measured as a Fraction of tlie Wliole. The sensibility to small differences in inten- sity is independent of the intensity (Fech- ner's law). About 0.016 for moderate intensities. Greater for extreme values. It is independent of wave-length, extremes excepted (Konig's law). Sensibility to slight differences in wave- length has two pronounced maxima (one in the yellow, one in the green) and two slight maxima (extreme blue, extreme red). The visual sensation as a function of the time approaches a constant value with the lapse of time. With blue light there seems to be a pronounced maximum at 0.07 sec, with red a slight one at 0.12 sec- onds, with green the sensation rises stead- ily to its final value. For lower intensi- ties these max. occur later. An intensity of 300 metre-candles is about that on a hotizontal plane on a cloudy day. A = .670 .605 •575 ■505 .470 •430 White [Qinm.c = 0.060 0.0056 0.0029 0.00017 0.00012 0.00012 0.00072 I 51: '. Konig's data, measures fro mone r ormal 1 Person only. 1,000,000 _ » .036 300,000 - .042 - - - .027 100,000 .024 .032 - - - .019 50,000 .021 .025 .026 - - .017 30,000 .016 .018 .020 .019 — ■. .017 10,000 .016 .016 .oi8 .018 . .oig 5,000 .018 .016 .017 .016 -. .018 2,000 .016 .018 .018 .017 .018 _ .018 1,000 .017 .020 .018 .018 .017 .018 .018 500 .020 .02 1 .oi8 .019 .018 .021 .019 200 .022 •022 .022 .022 .021 .024 .022 100 .02g .028 .027 .024 .022 .025 .030 50 .038 .0,8 •032 .025 ■02s .027 /)32 10 .obs .061 .058 .036' .037 .040 .048 5 .og2 .103 .089 ■049 .046 .049 .059 X •258 .212 .170 .080 .088 ■074 .123 05 .376 .276 .21 .091 .096 .097 .188 0.10 - - .40 ."33 ..38 ■137 •377 0.05 - - - .183 ..8, ■154 •484 O.OI .271 .289 .249 0.005 ■ 32s .300 ■3" Smithsonian Tables. Tables 159-162. SOLAR ENERGY. 179 TT,o t 11 I^^E/BS. -Solar Energy and Its AbsorpUon by the Earth's Atmosphere. and aDnrov^,r.t»v— ff^ vu j°^^ * ™^^^ °* ^''■' "*' « = "">'y when the sun is in the zenith, wherft^^un f^^^^ atmosphere, . is the amount transmitted 0.30 •32 •34 •38 .40 .46 .60 .70 .80 1. 00 1.50 2.00 Transmission coefficient, a. Wash- ington, (•360) •542 •653 .704 .762 .838 .867 .901 •923 .909 Mount Wilson. (■48s) (.562) .626 .676 •713 .746 .816 .850 .884 •937 .968 •977* .969* 687 745 788 .821 .879 ,902 ,942 966 981 991 956 925 gN •505 .800 .829 .862 .894 .909 •930 .950 •932 Intensity o£ Solar Energy. Mt Whit- ney, 95 50 '95 120 305 210 420 313 501 394 S8o 476 730 642 b8s 618 590 556 454 439 342 •\^S iqo 188 82 78 30 28 Mount Wilson. 46 no 284 357 433 596 582 522 425 327 184 80* 29* 22 62 120 192 255 3^3 486 495 461 399 312 178 78* 28* 05 19 47 88 129 180 1.2 6.2 18 40 66 100 323 215 2S8 360 281 IT. 307 260 '^7 156 7S* 71* 26* 25* Washington, 180 314 477 482 450 380 297 171 76 27 65 171 3" 340 343 319 257 154 70 25 23 92 203 239 261 267 223 139 64 23 8 50 133 169 199 224 193 '6^ 20 I.I 15 I 116 157 145 102 51 17 * These may be too high because of the usual increased humidity towards noon at Mount Wilson, TABLE 160. — Solar Constant Solar constant (amount of energy falling at normal incidence on one square centimetre per min- ute on body at earth's mean distance) ^ 1.92 small calories. Mount Wilson and Mount Whitney observations. Computed effective temperature of the sun : Goldhammer's method (Ann. der Phys. (4) 25, 905, 1908), 6200° Absolute ; from form of black body curves, 6000 to 7000° ; from A, max, = 2930, 6370°; from Total Radiation, J = 76,8X10-", 5830°, TABLE 161, — Dlstilbntlon of Brightness (RaAlatlon) over the Solar Disk, (These observations extend over only a small portion of a sun-spot cycle.) Wave-length. 0.323 0.386 1^ 0.433 0.456 0.481 0.501 "•534 0,604 1^ 0.670 0.699 0.866 1.03 1 1.225 '•655 2.097 fo.oo 144 ,S38 4S6 515 ^V 489 463 399 .333 .307 174 in 77-6 .39-5 14.0 n 0.40 128 312 423 48b 4«3 463 440 382 320 295 169 108 75-7 38-9 13.8 ■•3 0.55 120 289 39S 455 4.5'' 437 417 365 308 284 163 i05^5 73-8 38.2 1,3-6 (? 0.65 112 267 368 428 430 414 .396 348 295 273 159 103 72.2 .37-6 I.3-4 c " 0.75 99 240 ^^^ .390 394 380 366 326 281 2,8 152 99 69.8 .36,7 '■^•J 0.825 86 214 296 351 S.'iS 347 337 .304 262 243 ■'^S 94-5 b7.i 35-7 12.8 i 0.875 76 188 266 3>7 324 323 312 284 247 229 138 90.5 64.7 34^7 I2^5 b 0.92 64 163 233 277 290 286 281 2S9 227 212 .130 86 bi.b 33-6 12.2 [0.9s 49 141 205 242 255 254 254 237 210 195 122 81 S8.7 323 11.7 TABLE 162. — RelatlTe SlstrlhnUon In Normal Spectnun ol Son and Sky-Ught at Honnt Wilson, Zenith distance about 50°, »i c 1^ jIA (i )* c D b F 1 Place in Spectrum 0,422 0.457 0.491 0.566 0.614 0.660 Intensity Sunlight 186 232 227 211 191 166 Intensity Sky-light 1 194 906 701 395 231 174 Ratio at Mount Wilson 642 425 309 187 121 105 25 35 60 77 Ratio computed by Rayleigh - - - - 25 40 63 80 Ratio observed by Rayleigh 25 41 71 90 n.r;v«1 from vol II and unpublished daU of the Astrophysical Observatory of the Smithsonian Institution, Abbot uenvca i^^ Yoitit, Astrophysical Journal, 29, 1909, and Schwartichild and Villiger, same Journal, 13, 19A, Smithsonian Tables. l80 Tables 163-165. INDEX OF REFRACTION FOR GLASS. TASLE 163. — aiassei Mads T17 Schott asA Osn, Jena. The following constants are for glasses made by Schott and Gen, Jena : «ai «o. «d. «f> «o> are the indices of refraction in air for A=o.^(&2|l, C=o.6563/i», D=o.5893, F=o.486i, G'=o.434i. z/=(«B — !)/(«!■ — Ko). Ultra-violet indices: Simon, Wied. Ann. 53, 1894. Infra-red: Rubens, Wied. Ann. 45, 1892. Table is revised from Landolt, Bomstein and Meyerhoffer, Kayser, Hand- buch der Spectroscopie, and Schott and Gen's list No. 751, 1909. See also Hovestadt's "Jena Glass." Catalogue Type = 0546 O381 O184 O102 O165 S57 Designation = Zinc-Crown. Hi|;her Dis- persion Crown. Light Silicate Flint. Heavy Silicate FUnt. Heavy Silicate Flint. Heaviest Sili- cate Flint. Melting Numbers 1092 1151 451 469 500 .63 V = 60.7 S..8 41. 1 33-7 27.6 32.3 r cd 0.27631^1 '•56759 _ _ « « f. Cd .2837 1.56373 - - — — - tp Cd .2980 I-SS723 1.57093 1.65397 - - - S Cd .3403 1.54369 1.55263 1.63320 ..71968 1.85487 - s Cd .3610 1.53897 1.54664 1.61388 ..70535 1.83363 • i" H 4340(1 1.53788 1-53313 '•5935S ..67561 ..78800 1-94493 H .4861 1.52399 1.53715 1.58515 .-66367 .-77091 ..91890 s- Na .5893 1.51698 1.53003 1.57524 .-64985 l-75>30 ..88995 H .6563 1.51446 1.51713 1.57119 1-64440 1.74368 1-87893 ^ K .7682 1.51143 ..51368 ..56669 ..63830 1.73530 ..86702 .J .8oo(t 1.5103 1.5131 .■5659 .■6373 .-7339 ..8650 i.aoo 1.5048 1.5069 .•5585 1.6277 1.721S ..8481 1.600 1.5008 1.5024 1-5535 1. 6217 ..7151 ..8396 V 3.000 1.4967 >.4973 1-S487 ..617. 1.7104 1.83 16 3.400 1-5440 1.6131 1.8286 Percentage composition of the above gla sses : 0546, Si02,6s.4i K2O, 15.0; Na20, 5.0; BaO, 9.6; ZnO, 2.0; Mn208, O.I ; As^Oa, 0.4 ; 1 1 BjOg, 2.5. O381, SiOz, 68.7; PbO 13.3; NaaO, 15.7; ZnO, 2.0; MnOa, o.i ; AS2O5, 0.2 184, SiOa, 53.7 ; PbO 36.0; K2O, i 5.3; NajO, I. oj MnzOs, 0.06; AS2OS, 0. 3- O102, SiOa, 40.0; PbO, 52.6; K2O, ( ).5 ; NazO, 0. 5; Mn20a, 0.09; AS2O5, 0. 3- O165, SiOi, 29.26; PbC ), 67.5; K2O, 3.0; Mn20s, 0.04; AS2O8, 0.2. SS7. SiOj, 21.9; PbO, 78.0 J AS2O6 0.1. TABLE 164. — Jena Glasses. No. and Type of Jena Glass. ttn for D Specific Weight. O 225 Light phosphate crown O 802 Boro-silicate crown . UVsiM Ultra-violet crown O 227 Barium-silicate crown O 1 14 Soft-silicate crown . O 608 High-dispersion crown UV 3248 Ultra-violet flint . O381 High-dispersion crown O 602 Baryt light flint . . S 389 Borate flint . . . O 726 Extra light flint . . O 154 Ordinary light flint . O184 " ^' " . O 748 Baryt flint .... O 102 Heavy flint ... O41 " " . . . . Oi6s " " . . . . S 386 Heavy flint .... S 57 Heaviest flint ... 1-5159 1.4967 1.5035 1.5399 1.5151 1.5149 1.5333 1.5263 1.5676 1.5686 1-5398 1-5710 J.5900 .-623s t.6489 1.7174 ..7541 1.9170 1.9626 .00737 0765 0781 0909 0910 °943 0964 1026 1073 1102 1142 1327 1438 1599 1919 2434 3743 4289 4882 70.0 64-9 64.4 59-4 56.6 54-6 55-4 5'-3 53-0 51-6 47-3 43-0 41.1 39-1 33-8 »9-5 27.5 21.4 '9-7 .00485 0504 0514 0582 0577 0595 o6it 0644 0675 0712 0711 0819 0882 9965 1152 1439 1607 2451 2767 .00515 0534 0546 0639 0642 0666 0680 0727 0759 077s 081Q 0943 1022 1143 .372 '749 1974 3109 3547 .00407 0423 0432 0514 0521 0543 0553 0596 0618 0629 0669 0791 0861 0965 1180 1521 1730 2808 3252 2.58 2.38 2.41 2-73 »-55 2.60 3.75 3.70 3-12 3.83 3.87 3.16 3.38 3-67 3-87 4-49 4-78 6.01 6.33 TABLE 166. — Obinge 0! InUoes ot Retraction fer lo In Units ot tlie FUtli Deoimal Flaos. No. and Designation. Mean Temp. C D F C — A» .00 n S 57 Heavy silicate flint . . . 154 Light silicate flint . . . 327 Baryt flint light .... 225 Light phosphate crown . 58.8° 58.4 S8.3 58. 1 t.304 0.235 —0.008 — 0.203 1.447 0.261 0.014 — 0.190 3.090 0-334 0.080 —0.168 3.810 0.407 0.137 — 0.143 0.0166 0.0078 0.0079 0.0049 Smithsonian Tables. Pulfrich, Wied. Ann. 45, p. 609, 189a. Table 166. INDEX OF REFRACTION. InOlcei ot Rebaotton lor tlie vuloiu Alnms.* l8l E U Index of refraction for the Fraunhofer lines. Aluminium Alums. ^AlCSOjjj+izHjO.t Na NHslCHa) K Rb Cs NH4 Tl 1.667 1.568 I-73S 1.852 1.961 1.631 2.329 17-28 7-17 14-15 7-21 15-25 15-20 10-23 1.43492 ■45013 .45226 ■45232 •45437 .45509 .49226 1-43563 .45062 ■45303 •45328 •45517 •45599 •49317 '•43653 •45177 •45398 •45417 .45618 •45693 •49443 1.43884 .45410 •45645 .45660 .45856 •45939 .49748 1.44185 .45691 •45934 •45955 .46141 .46234 .50128 1.44231 •45749 .45996 ■45999 .46203 .46288 .50209 1. 4441 2 •45941 .46181 .46192 .46386 .46481 •S0463 1.44804 •46363 .46609 .46618 .46821 ■46923 .51076 Indium Alums. jein(S0,)2+i2Hj0.t Rb Cs 2.065 2.241 2.01 1 3-13 17-22 17-21 1.45942 .46091 .46193 1.46024 .46170 .46259 1. 461 26 .46283 .46352 1.46381 .46522 .46636 1.46694 .46842 •46953 1.46751 •46897 .47015 1.4695s .47105 ■47234 1.47402 ■47562 •4775° Gallium Alums. jeGaCSOilj+ijHjO.f Cs K Rb NH4 Tl 2.113 1.895 1.962 1^777 2.477 17-22 19-25 1 3-' 5 15-21 18-20 1.46047 .46118 .46152 .46390 .50112 1.46146 •46195 .46238 .46485 .50228 1.46243 .46296 •46332 •46575 •50349 1.46495 .46528 ■46579 .46835 .50665 1.46785 .46842 .46890 .47146 .51057 1.46841 .46904 •46930 .47204 •51131 1.47034 •47093 .47126 .47412 •51387 1.47481 .47548 .47581 .47864 .52007 Chrome Alums. ifCr(S04)2+i2H20.t Cs K Rb Tl 2.043 1.817 1.946 1.719 2.386 6-12 6-17 12-17 7-18 9-25 1.47627 .47642 .47660 .47911 .51692 '•47732 •47738 •47756 .48014 .51798 1.47836 •47865 .47868 .48125 •51923 1. 48 1 00 •48137 .48151 .48418 .52280 1.48434 •48459 .48486 •48744 .52704 1. 48491 •48513 .48522 .48794 .52787 1.48723 •48753 •48775 .49040 •53082 1.49280 •49309 •49323 ■49594 ■53808 Iron Alums. ^Fe(S04)j+i2H20.t K Rb Cs NH4 Tl 1.806 1.916 2.061 '■7I3 2.385 7-1 1 7-20 20-24 7-20 15-17 1.47639 .47700 .47825 •47927 .51674 1.47706 ■47770 .47921 .48029 .51790 '•47837 •47894 .48042 .48150 •51943 1.48169 .48234 .48378 .48482 •52365 1.48580 .48654 •48797 .48921 •52859 1.48670 .48712 .48867 •48993 .52946 1.48939 .49003 .49136 .49286 •53284 [.49605 .49700 .49838 .49980 ■54" 2 * According to the experiments of Soret (Arch. d. Sc. Phys. Nat. Geneve, 1884, i8i t R stands for the different bases given in the first column. Smithsonian Tables. St and Comptes Rendus, 1885)* 1 82 Table 167. INDEX OF REFRACTION. Index ol Retraction of Hetals and Metallic Oxldai. (a) Experiments of Kundt* by transniission of %ht through metallic prisms of small angle. Index of refraction for Red. WUte. Blue. Silver _ 0.27 _ Gold 0.38 0.58 1.00 Copper 0.45 0.65 0.9s Platinum . 1.76 1.64 1.44 Iron 1.81 1-73 I.5Z Nickel . 2.17 2.01 1.85 Bismuth . 2.61 2.26 2.13 Gold and gold oxide 1.04 - I.2S 11 (t 11 0.89 0.99 1-33 It U (( 4- - Z.03 - Bismuth oxide . - 1.91 - Iron oxide 1.78 2.1 1 2.36 Nickel oxide , 2.18 2.23 2-39 Copper oxide . , 2.63 2.84 3.18 Platinum and platinum oxide . 3-31 329 2.90 4.99 4.82 4.40 (W Experiments of Du Bois and Rubens by transmission of light through prisms of small angle. The experiments were similar to those of Kundt, and were made with the same spectrometer. Somewhat greater accuracy is claimed for these results on account of some improvements intro- duced, mainly by Prof. Kundt, into the method of experiment. There still remains, however. a somewhat large chance of error. Name of metal. Index of refraction for light of the following color and wave-length. Red (Lia). "Red." Yellow (D). Blue (F). Violet (G). X=:67.i A = 64-4 A = 58.9 A =48.5 A = 43-1* Nickel . 2.04 1-93 1.84 I.71 1.54 Iron 3.12 3.06 2.72 2-43 2.05 Cobalt . 3.22 3.10 2.76 2.39 2.10 (C) Experiments of Dmde. The following table gives the results of some of Drude's experiments. § The index of refrac- tion is derived m this case from the constants of elliptic polarization by reflection, and are for sodiimi light. Metal. Index of refraction. Metal. Index of refraction. Aluminium 1.44 Mercury 1-73 Antimony 3-04 Nickel . 1.79 Bismuth 1.90 Platinum 2.06 Cadmium 113 Silver O.181 Copper . 0.641 Steel 2.41 Gold . 0.366 Tin, solid 1.48 Iron 2.36 " fluid 2.10 Lead 2.01 Zinc 2.12 Magnesium . _ 0-37 • " Wied. Ann." vol. 34, and " Phil. Mag." (5) vol. j6. X Wave-lengths A are in millionths of a centimetre. Smithsonian Tables. t Nearly pure oxide. § " Wied. Ann." vol. 39. Tables 168-170. INDEX OF REFRACTION. TABLE 168. —Index ol RetraoUon ol Bock Salt In Air. 183 Ki^). ff. Obser- ver. Mm). «. Obser- ver. Ki^). Obser- ver. 0.185409 1.89348 M 0.88396 1.5340H L 5.8932 I.516014 p .204470 1.76964 .972298 1-532532 U 11 1-515553 - II .291368 1.61325 " .98220 1-53243S P 6.4825 1.513628 > .358702 1-57932 ** 1.036758 1.531762 L « ■" 1.513467 L II .441587 1.55962 1.1786 1.530372 P 7.0718 1.511062 ' .486149 1-55338 " 1-530374 L 7.661 1 1.508318 1.553406 L \W 1.52821 1 U 7-9558 1.506804 • .58902 1-553399 P 1.527440 P 8.8398 1.502035 1.544340 L " 1.527441 L 10.0184 1.494722 ' .58932 1-544313 P 2.073516 \-m (( 11.7864 I.481816 ,656304 1.540672 P 2-35728 P 12.9650 1.471720 ' " 1.540702 L 1-525849 L 14.1436 1.460547 .706548 1538633 P 2.9466 1-524534 P 14-7330 1.454404 .766529 1.536712 P 3-5359 1-523173 (( 15.3223 1.447494 ' .76824 1.53666 M 4.1252 1.521648 P 15.9116 1.441032 i?576 1-536138 P (( 1.521625 L 20.57 1-3735 4N .88396 1.5340U P 5.0092 1.518978 P 22.3 1.340 ( -a^+. Ml ,+ ■ Mi Ml Mi M« where 0^=2.330165 ^1^0.01278685 Ai2=o.oi485oo .^2=0.005343924 A2''=o.025474i4 b^=ti.(&oi:if ^=0.0009285837 .^3=12059.95 A ^0.000000286086 A3''=36oo. (P) TABLE 16a.— Oliange ol Index of Rebactlon for 1° In Units of tbe 5tli Deolmal Place. 0.202/1 +3-134 Mi 0.441/1 —3-425 Mi Cline —3-749 PI 0.760/1 ~3-73 L .210 + 1.570 U .508 —3-517 " D " —3-739 " 1.368 —3.88 L .224 —0.187 " .643 —3-636 It F " -3648 1.88 -3-8 S L .298 —2.727 u G' " -3-585 4-3 —3.82 L L Annals of the Astrophysical Observatory of the Smithsonian Institution, Vol. I, igoo. M Martens, Ann. d. Phys. 6, 1901, 8, 1902. Mi Micheli, Ann. d. Phys. 7, 1902. P Paschen, Wied. Ann. 26, 1908. PI Pulfrich, Wied. Ann. 45, 1892. RN Rubens and Nichols, Wied. Ann. 60, 1897. TABLE 170.— Index of Refraction of SllTlne (Fotasslnm Chloride) in Air. Ki^). Obser- ver, Kl^)- Obser- ver. A(m). Obser- ver. 0.185409 .200090 .21946 •257317 .281640 .308227 .358702 •394415 .467832 .508606 ■58932 .67082 .78576 .88398 .98220 -82710 ,71870 ,6474s 58125 55836 54136 52IJ5 51219 50044 49620 490443 ,48669 483282 481422 480084 M P M P P 1.1786 1.7680 2.35728 2.9466 ti 3-5359 a 4.7146 5-3039 It 5.8932 1.478311 1.47824 1.475890 1.47589 1-474751 1-473834 ^ -47394 1-473049 1.47304 1.471122 1.47129 1.470013 1.47001 1.468804 1.46880 P W P w p w p w p w p w p w 8.2505 it 8.8398 10.0184 ti 11.786 it 12.965 14.144 15.912 17.680 20.60 22.5 1.462726 .46276 .460858 .46092 .45672 ■45673 .44919 .44941 .44346 ■44385 ■43722 .42617 ■41403 .3882 •369 p w p w p w p w p w p RN :2=a2-f Ml i+- Mi 02 = 2.174967 Ml =0.008344206 Ai2=:o.oii9o82 ^1/2=0.00698382 W Weller, see Paschen's article, Smithsonian Tables. -/fA^— /5A*or=^2-f A2''=o.o2555So ^=0.000513495 Ml ,+ Mi i+- Mi X2— a,i2'^a2— Aa^^As"— A" i2= 3.866619 ■^3= 5569^7 IS /i=o.ooooooi67587 A3''=3292.47 (P) Other references as under Table 169, above. i84 Tables 171-174. INDEX OF REFRACTION. TABLE 171. — laAez ol Rabaotlon of Flnorits In All. AW ff Obser- ver AW n Obser- ver AW » Obser- ver, 0.1856 1.50940 S 1-4733 1.42641 P 4.1252 1.4085s P .19881 1.49629 1-5715 1.42596 4.4199 ••40559 .21441 1.48462 U 1.6206 1.42582 4.7146 1.40238 .22645 1.47762 1.7680 1.42507 tt 5.0092 1.39898 •25713 1.46476 1-9153 1-42437 " 5-3036 HI 1.39529 •32525 1.44987 tt 1.9644 I.42413 1. 39142 '^'^fk^ 1.44697 2.0626 ••42359 1-38719 1.44214 «< 2.1608 1.42308 6.4825 7.0718 I.37819 •48607 1-43713 P 2.2100 1.42288 ** I.3680S •58930 1-43393 P 2-3573 I.42199 tt 7.6612 1.35680 .65618 1-43257 s 2-5537 1.42088 " 8.2505 1-34444 1.43200 (I 2.6519 1.42016 (1 8.8398 1-33079 41 .71836 1-43157 2.7502 I.4197I 9.4291 1.31612 .76040 1.43101 (( 2.9466 I.41826 H 51.2 3-47 RA .8840 1.42982 p 3-'430 I.41707 " 6i.i 2.66 I.I786 1.42787 (( 3-2413 I.41612 « 2.63 S 1-3756 1.42690 '• 3-8306 I-4I379 " 1-4733 1. 42641 1. 41 120 References under Table «73- «a==a2 + M, X2 — Xi" where a' = 2.03882 .A/i = 0.0062183 Al2 = 0.007706 «=: 0.0031999 -e\^—/\*or = lfi+ f Mi r+: Mi \^ — \fi ' \^ — )ir- 0.000002916 i1/8==5ii4-65 2 = 6.09651 Af2=i 0.0061386 V= 0.00884 A,2== 1260.56 Xi, = 0.0940/1 Ar=35-5/' (P) TABLE 172. — Ohanga ol InAez ol Rebaotton tor 1°0 In Units of the Btli Decimal Plaos. C line, — 1.220 J D, — 1.206; F, — 1.170; G, — 1.142. (PI) TABLE 173. —Index ol RetraoUon of loelanA Spai (CaOOa) In All. AW "o •h Obser- ver. AW «. a. Obser- ver. AW «0 «• Obser- ver, 0.198 _ 1.5780 M 0.508 i!6628 1.4896 M 0.991 1.6438 1.4802 c .200 1.9028 1-5765 •533 1.4884 II 1.229 1-6393 1.4787 tt .208 1-8673 1.5664 .589 1.6584 1.4864 " 1-307 '-6379 ••4783 It .226 I.8I30 1.5492 - -643 1.6550 1.4849 " \:^l 1.6346 1-4774 u .298 1.7230 1.5I5I C .656 1.6544 1.4846 II I-63I3 it ■340 1.7003 1.5056 M .670 1-6537 1.4843 II 1-749 1.4764 €t .361 1.6932 1.5022 C .760 1.6500 1.4826 - 1.849 1.6280 tt .410 1.6802 1.4964 - .768 1.6497 1.4826 M 1.908 - I-47S7 tt 434 1.675s 1.6678 1-4943 M .801 1.6487 1.4822 C 2.172 I.62IO tt .486 1.4907 (( .905 1.6458 1.4810 2.324 " 1-4739 tt C Carvallo, J. de Phys. (3), 9, i9c». M Martens, Ann. der Phys. (4) 6, 1901, 8, 1903. P Paschen, Wied. Ann. 561 1895. PI Pulfrich, Wied. Ann 45, 1892. RA Rubens-Aschkinass, Wied. Ann. 67, 1899, S Starke, Wied. Ann. 60, 1S97. TABLE 174.— Index of Refraction of Nltroso-dlmetliyl-anlUiie. (Wood.) A « A n \ « A « A n 0.497 2.140 0.525 '•945 0,584 1.815 1.796 0.636 1.647 0-713 I.718 .500 2.114 •536 1.909 .602 .647 1-758 •730 ••7I3 .506 2.074 .546 1.879 .611 1.783 1.778 .659 1.750 •749 1.709 .508 2.025 •557 1.857 .620 .669 1-743 •763 1.697 .516 1.98s •569 1.834 .627 1.769 .696 1-723 Nitroso-dimethyl-aDiline has enormous dispersion in yellow and green, metallic absorption in riolet. See Wood, Fbil. Mag. 1903. Smithsonian Tables, -- - Table 1 75. INDEX OF REFRACTION. Index ol Relraotton ol Quartz (SlOi). i8s Wave- length. Index Ordinary Ray. Index Extraordinary Ray. Tempera- ture C. Wave- length. Index Ordinary 1 Ray. Index Extraordinary Ray. Tempera- ,ture ° C. o.i8s 1.67582 1.68999 iS 0.656 .686 1. 54189 1.55091 18 .193 .65997 ■67343 (( .54099 .198 .65090 .66397 i( .760 •53917 .54811 .206 .64038 .65300 If 1. 160 .5329 - .214 .63041 .64264 (1 .969 .5216 - .219 .62494 .63698 (( 2.327 ■5156 - .231 •61399 .62560 .84 •5039 - •257 .59622 .60712 3.18 .4944 — .274 ■58752 .59811 " .63 ■4799 Rubens. - •340 .56748 .57738 (( .96 .4679 - •396 .55815 .56771 4.20 .4569 - .410 ■55650 .56600 5.0 .417 - .486 .54968 .55896 6.45 .274 — 0.598 1.54424 '■55334 7.0 1. 167 Except Rubens' values, ■ Smithsonian Tables. -means from various authorities. 1 86 Table 176. INDEX OF REFRACTION. Vailans Monoiefrlneait or 0ptlcall7 Introplo Solids. Substance. Index of Refraction. Authority. Agate (light color) Ammonium chloride Arsenite Barium nitrate . Bell metal Blende Boric acid Borax (vitrified) Camphor . . Diamond (colorless) Diamond (brown) Ebonite Fuchsin Garnet (different varieties) Gum arable Hanyne .... Helvine .... Obsidian .... Opal Pitch Potassium bromide . " chlorstannate . " iodide Phosphorus Resins : Aloes . Canada balsam , Colophony . Copal . Mastic . Peru balsam Selenium, vitreous ( bromide Silver < chloride . ( iodide . Sodalite I ^}'^^ ;.. • , • j clear hke water Sodium chlorate Spinel .... Strontium nitrate D red I to De Senarmont. Grailich. DesCloiseauz. Fock. Beer. Ramsay. Bedson and Carleton Williams. Kohlrauscb. Mulheims. DesCloiseaux. Schrauf, Ayrton & Perry. Means. Various. Jamin. WoUaston. Tschichatscheff. Levy & Lecroiz. Various. Wollaston. Topsoe and Christiansen. Gladstone & Dale. Jamin. Wollaston. Jamin. it Wollaston. Baden Powell. Wood. Wernicke. Feusner. Dussaud. DesCloiseaux. Fock. Smithsonian Tables. Tables 1 77, 1 78. INDEX OF REFRACTION. TABLE 177.— Uniaxial Crystals. 187 Line of Index of refraction. Substance. spec- Authority, trum. Ordinary ray. Extraordi- nary ray. Alunite (alum stone) . Ammonium arseniate . Anatase Apatite Benzil .... D red D D D '-573 1-577 2-5354 IS 1.592 4.524 2-4959 1-6345 1-6784 Levy & Lacroix. De Senarmont. Schrauf. DesCloiseaux. Beryl .... Brucite 1.589 to 1.570 1.560 1-582 to 1-566 1-581 } Various. Kohlrausch. Calomel red 1.96 2.60 De Senarmont. Cinnabar red 2.854 3199 DesCloiseaux. Corundum (ruby, sapphire, etc.) redj 1-767 to 1.769 1-759 r.762 } " Dioptase green 1.667 1-723 u Emerald (pure) . green 1.584 1-578 •' Ice at — 8° C. . D 1.309 1313 Meyer. Idocrase M 1.719 to 1.722 1.717 to 1.720 DesCloiseaux. Ivory .... D 1-539 1-541 Kohlrausch. Magnesite . D 1-717 1-515 MaUard. Potassium arseniate . red 1-564 1515 DesCloiseaux. H (( red 1-493 1. 501 De Sernamont. Silver (red ore) . red 3-084 2.881 Fizeau. Sodium arseniate D 1-459 1-467 Baker. " nitrate . D 1-587 1-336 Schrauf. " phosphate D 1-446 2-452 Dufet. Strychnine sulphate . D 1.614 1-519 Martin. Tin stone D 1-997 2.093 Grubenman. Tourmaline (colorless) D 1-637 1.619 Heusser. " (different colors) D 1 1-633 to 1.650 I. 61 6 to 1.625 i Jerofejew. Zircon (hyacinth) red 1.92 1-97 De Senarmont. D 1.924 1.968 Sanger. TABLK 178. -Biaxial Crystals. Substance. Line of spec- trum. Index of refraction. Authority. Minimum. Interme- diate- Maximum. Anglesite Anhydrite . Antipyrin Aragonite . Axinite Barite .... Borax .... Copper sulphate . Gypsum Mica (muscovite) . Olivine .... Orthoclase . Potassium bichromate . " nitrate " sulphate Sugar (cane) Sulphur (rhombic) Topaz (Brazilian) Topaz (different kinds) Zinc sulphate D D D D red D D D D D D D D D D D D D Si 1.8771 1-5693 1.5101 1-5301 1.6720 1.636 1.4467 1.5140 1.5208 1.5601 1.661 1.5190 1.7202 13346 1-4932 '•5397 I -9505 1-6294 1.630 to 1.613 1-4568 1.8823 1.6816 1-6779 1-637 1-4694 1.5368 1.5228 1-5936 1-678 1-5237 1.7380 1.5056 1.4946 1.5667 1.631 to I.6I6 I.480I 1.8936 1.6130 1.6858 1.6859 I.6810 1.648 1.4724 1-5977 1-697 1.5260 1-8197 1-5064 1.4980 1-5716 2.2405 1-6375 1-637 to 1.623 1.4836 Arzruni. Miilheims. Glazebrook. Rudberg. DesCloiseaux. Various. Dufet. Kohlrausch. Miilheims. Pulfrich. DesCloiseaux. Dufet. Schrauf. Topsoe & Christiansen. Calderon. Schrauf. Miilheims. > Various. Topsoe & Christiansen. Smithsonian Tables. i88 Table 1 79. INDEX OF REFRACTION. Indices of RsfracUon relative to Air for Solutloiis ol Salts and Aoldi. Density. Temp. C. Indices of refraction for spectrum lines. Substance. Authority. O P H, H (a) Solutions in Water. 1 Ammonium chloride 1.067 270.05 1-37703 1-37936 1-38473 _ 1-39336 Willigen. It tt .025 29-75 .34850 -35050 -35515 - -36243 Calcium chloride 25.65 .44000 •44279 -44938 - .46001 u tt .215 22.9 -3941 1 .39652 .40206 - .41078 tt tt ■143 25.8 •37152 -37369 -37876 - .38666 (( Hjrdrochloric acid . I.166 20.75 I.40817 I.41109 1.41774 - 1. 428 1 6 it Nitric acid .... •359 18.75 •39893 .40181 •40857 - .41961 " Potash (caustic) . . .416 Il.O .40052 .34087 .40281 .40808 - 41637 Fraunhofer. Potassium chloride . normal solution -34278 -34719 1.35049 Bender. (( tt double normal .34982 -35179 -35645 ■35994 - " tt u triple normal -35831 .36029 .36512 .36890 - " Soda (caustic) . . 1-376 21.6 I.41071 141334 1.41936 _ 1.42872 Willigen. Sodium chloride . . .189 18.07 •37562 ■37789 .3S322 1.38746 - Schutt. tt tt .log 18.07 -3575' -35959 .36442 .36S23 - ** tt tt •03s 18.07 .34000 •34191 .34628 •34969 - Sodium nitrate . . '•358 .81 1 22.8 1.38283 1-38535 1-39134 _ 1. 401 21 Willigen. Sulphuric acid . . 18.3 -43444 .43669 .44168 - ■44883 tt tt •632 18.3 .42227 .42466 -42967 - .43694 (( tt tt .221 18.3 -36793 -37009 .37468 - .T«iS8 (( It tt .028 18.3 -33663 .33862 •34285 - •34938 tt Zinc chloride . . . '•359 26.6 1-39977 1.40222 1.40797 - 1.41738 tt .209 26.4 .37292 -37515 .38026 "■ .38845 tt (1)) Solutions in Ethyl Alcohol. Ethyl alcohol . . . 0.789 25^5 I -35791 I-3597I 1-36395 _ 1.37094 Willigen. •932 27.6 -35372 -35556 -35986 - .36662 ft Fuchsin (nearly sat- urated) .... - 16.0 .3918 •,398 .361 - -3759 Kundt. Cyanin (saturated) . "" 1 6.0 -3831 •3705 .3821 (( Note. — Cyanin in chloroform also acts anomalously ; for example, Sieben gives for a 4.5 per cent, solution «^= 1.4593, a»b= 14695- Mi'Cgreen) = 1.4514, fia (blue) = 1.4554. For a 9.9 per cent, solution he gives /tx= 1.4902. iiij'(green) = 1.4497, /to (blue) = 1.4597. (0) Solutions of Potassium Permanganate in Water.* Wave- length Spec- trum Index for Index for Index for Index for Wave- length Spec- Index for Index for Index for Index for X IO«. line. I % sol. 2% sol. 3 % sol. 4 % sol. Xio". line. I % sol. 2 % sol. 3 % sol. 4 % sol. 68.7 B I..3.328 1.3342 _ 1-3382 SI.6 _ 1-3368 1-3385 _ 65.6 C •3335 •3348 1-3365 -3391 50.0 - •3374 •3383 1-3386 1.3404 61.7 - •3343 •3365 •3381 .3410 48.6 F •3377 .3408 594 — ■3354 •3373 -3393 .3426 48.0 - -3381 -3395 •3398 •3413 r.^ D •3353 •3372 - -3426 46.4 - •3397 .3402 -3414 •3423 •^^fi •3387 .3412 -3445 44.7 - •3407 •3421 -3426 •3439 S5-3 — ■3366 •3395 •3417 •3438 43-4 - •3417 - - •3452 52.7 E •3363 - - - 42-3 - •3431 -3442 •3457 .3468 52.2 •3362 •3377 •3388 Smithsonian Tables. ' According to Christiansen. Table 180. INDEX OF REFRACTION. Indloai of HetraoUon ot Unniia relaUvo to Air, 189 Index of refraction for spectrum lines. Substance. Temp. Authority. c. D P =y H Acetone .... Almond oU . . . Analin * 10° 1.3626 •47 SS 1.3646 .4782 1.3694 .4847 i^3732 - Korten. Olds. Aniseed oil . . . 20 21.4 ■S993 ■5410 •5863 ■5475 .6041 .5647 .6204 — Weegmann. Willigen. ' ' 15.1 .5508 •SS72 •5743 - 1.6084 Baden Powell. Benzene t ■ . . . 10 1.4983 1.5029 1.5148 _ I-S35S Gladstone. Bitter almond oil . Bromnaphtalin . . 21.5 20 20 •4934 •5391 .6495 •4979 .6582 •5095 •S77S .7041 ■5304 . ^7289 it Landolt. Walter. Carbon disulphide J 1.6336 i^6433 1.6688 1.6920 1-7175 Ketteler. t* n 20 .6182 .6276 .6523 .6748 .6994 1 1 •V.M r It n It "1 E 3 Js 1 1 n 1 iii5 1 X) § hi "O .251 _ _ 67.0 35-8 29.9 37.8 _ 32-9 25.9 3|-i 38.8 - 341 - - 70.6 37-1 37-7 42.7 - 35-0 24-3 38.8 34-0 - 21.2 •3°5 - - 72.2 37-2 41.7 44.2 - 37-2 25-3 39-8 31.8 — 9.1 .3>6 — — — - — — - — — — — 4.2 u - - 75-S 39-3 - 45.2 - 40.3 24.9 414 28.6 - 14.6 •338 - - - fl - - - - - - ss-s Ws - - 81.2 43-3 51.0 - 45-0 ^l-^ 43-4 27.9 - Z4-5 ■- •- 83-9 44-3 53' 49.6 " 47.8 28.6 45-4 27.1 " 814 .420 _ _ 83.3 47.2 56.4 56.6 Si-9 32-7 SI.8 29-3 _ 86.6 450 85.7 72.8 834 49.2 60.0 Pi 48.8 54.4 37-0 ^f^ 33- • - 90.5 .500 86.6 70.9 833 49-3 63.2 60.8 53-3 S4.8 43-7 58.4 47.0 - 91-3 •55° 88.2 71.2 82.7 48.3 64.0 62.6 59-5 83s 54-9 47-7 61. 1 74.0 - 92.7 .000 88.1 69.9 83.0 47-S 643 64.9 55-4 71.8 64.2 84.4 - 92.6 .650 89.1 V^.l 82.7 51-5 65.4 66.6 89.0 56.4 80.0 66.5 88.9 - 94-7 .700 89.6 833 54-9 66.8 68.8 90.7 57.6 83.1 69.0 92-3 " 95-4 .800 _ _ 84.3 63.1 69.6 _ 58.0 88.6 70-3 94-9 _ 96.8 I.O - - 84.1 69.8 70.5 72.0 - 63.1 90.1 72.9 - - 97.0 i-S - - 85.1 79-1 75.0 78.6 - 70.8 93-8 77-7 97-3 - 98.2 2.0 - - 86.7 82.3 80.4 83.S - 76.7 95-5 80.6 96.g 91.0 97.8 3-0 - - 87.4 85.4 86.2 88.7 - 83.0 97-1 88.8 93-7 98.1 4.0 - - 88.7 87.1 88.5 91.1 - 87.8 97.3 91-5 96.9 95-7 98.5 5.0 - - 89.0 87.3 89.1 94-4 - 89.0 97-9 93-5 97 -o 95-9 98.1 7.0 - - 90.0 88.6 90.1 94-3 - 92.9 98.3 95-5 98.3 97.0 98.S 9.0 - - 90.6 90-3 92.2 95.6 - 92.9 98.4 95-4 98.0 ^li 9fi 1 1.0 - - 90.7 90.2 92.9 95-9 - 94.0 98.4 95.6 98.3 96.6 98.8 14.0 92.2 90-3 93-6 97.2 96.0 97-9 964 97-9 98.3 Based upon the work of Hagen and Rubens, Ann. der Phys. (i) 352, 1900; (8) 1, 1902; (ii) 873, 1903 Taken partly from Landolt-Bbmstein-MeyerboSer's Physikalisch-chemische Tabellen. Further references : Conroy, Proc. Roy. Soc. 35, 26, 1883. De la Provastaye and P. Desains, Ann. Chim. Phys, (3) 30, 276, 18^0. Langley, Phil. Mag. (5) 27, 10, 1889. Mach and Schumann, Wien. Ber. xo8, 135, 1899. Smithsonian Tables* Nichols, Wied. Ann, 60, 401, 1897, Nutting, Phys. Rev. 13, 193, 1901. Paschen, Ann. der Phys. 4, 304, 1901. Rayleigh, Proc. Roy. Soc. 41, 274, 18S6.. Rubens, Wied. Ann. 37, 249, 1SS9. Trowbridge, Wied. Ann. 65, 595, 1898. Tables 186-188. TRANSMISSIBILITY FOR RADIATION OF JENA GLASSES. 193 TABLE 186. Coefficients, a, in the formula 7, = I^\ wliere /o is tiie Intensity before, and /t after, transmission through the thiclcness t, expressed in centimetres. Deduced from observations by Miiller, Vogel, and Rubens as quoted in Hovestadt's Jena Glass (English translation). Type of Glass. Coefficient of tiansmissioD, a. 1 A = •375*' 390 M .400/1 •434(1 •436(1 .4551* ■477(1 .503(1 .580(1 .677(1 340, Ord. light flint .388 .4S6 .614 .S6-? .680 •814 .880 .880 .878 •939 O102, H'vy silicate flint .025 •463 .502 .S66 .663 .700 .782 .828 •794 93, Ord. " " - - - .714 .807 .899 .871 •903 •943 O203, " « crown 598, (Crown) •.SS.T •.■i83 .695 .667 .806 .822 .860 .872 .872 •903 •797 .770 •77" .776 .818 .860. x= 0.7 Jl 0.9s ii 1.1(1 1.4 c 1.7 ji 2.0 (1 ».3(i J-Sd a.7(i 2.9(1 3.i(i S 204, Borate crown I.O .qo •SS •17 .21 .12 .02 s .02 .04 .03 S 179, Med. phosp. cr. - .82 .61 •17 •17 .018 .08 .25 •OS 1 143, Dense, bor. sil. cr. - - •74 .61 •SO •V, .18 •034 .06 .021 1092, Crown ,91 .b7 .61 .90 .91 .41 .14 •0.33 .006 .07 ■043 O1151, " .82 - .qi .qo .82 ■SS •V, .10 :o^.^ .04 .010 O451, Light flint 1.0 - •91 .82 .61 •4S •17 .002 .019 469, Heavy " 1.0 - .82 - .91 .82 .82 ■74 •33 .017 .010 500, " " 1.0 - 1.0 — 1.0 — 1.0 .90 •4S % .019 S 163, « " 1.0 ~ .82 "" •9t " .91 •SS .062 TABLE 187. Note : With the following data, t must be expressed in millimetres ; 1. e. the figures as given give the transmissions for thickness of i mm. No. and Type of Glass. Wave-length in (i. 1 Visible Spectrum. Ultra-violet Spectrum. 1 .644(1 •578(1 .546(1 .509(1 .480(1 .436(1 .405(1 ■384 c ■361(1 .340(1 ■J32(i •309(1 .280 (1 F381S Dark neutral .3S ■35 •37 •35 •34 •30 •IS .06 F4S12 Red filter .94 •o.S F 2745 Copper ruby •75 ■39 •47 •f 45 •43 •43 F4313 Dark yellow .98 •97 •93 •^3 .09 F4351 Yellow .q8 •97 .9b •93 •44 •15 .18 .06 F 4937 Bright yellow 1.0 1.0 i.o •99 •74 .40 .31 .28 .22 .14 F4930 Green filter •17 •SO .04 .b2 •44 •36 F3873 Blue filter - .18 •50 •73 .Oy •59 .10 F36S4 Cobalt glass, transparent for outer red _ _ _ •IS •44 •85 1.0 1.0 1.0 1.0 1.0 .81 .18 F 3653 Blue, ultraviolet F 3728 Didymium, str'g bands - - - .11 .bs 1.0 1.0 1.0 1.0 1.0 •99 •72 •99 .96 •95 ■96 •99 •99 •89 .89 •77 •54 ' TABLE 188. — TianamlsglblUty ol Jona Pltra-vlolot Glasses No. and Type of Glass. Thickness. 0.397 (1 0.383 (1 0.361 (1 0.346 (1 0.32s (1 0.309(1 0.280(1 UV 3199 Ultra-violet 11 << UV3248 " 1 mm. 2 mm. I dm. 1 mm. 2 mm. I dm. 1.00 0.99 0.95 1. 00 0.98 0.96 1. 00 0.99 0.95 1. 00 0.98 0.87 1. 00 0.89 1. 00 0.98 0.79 1. 00 0.97 0.70 1. 00 0.92 0-45 1. 00 0.90 0.36 0.98 0.78 0.08 0.95 0.57 0.91 0.38 0.56 0.35 Smithsonian Tables. 194 Table 189. TRANSMISSIBILITY FOR RADIATION. TiansmlsslblUty ol tlit Vailoni Snbstanoei ot TaUes 166 to 176. Alum : Ordinary alum (crystal) absorbs the infra-red. Metallic reflection at g-o^/t and 30 to 40;*. Rock-salt : Rubens and Trowbridge (Wied. Ann. 65, 1898) give the following transparencies for a I cm. thick plate in % : \ 9 10 12 13 14 IS 16 17 18 19 20.7 23-7M % 99-S 99-5 99-3 97.6 931 84.6 66.1 S1.6 27.5 9.6 0.6 0. Pfluger (Phys. Zt. 5. 1904) gives the following for the ultra-violet, same thickness : z8o/i/«, 95.5% j 231,86%; 210,77%; 186,70%. Metallic reflection at o.iio;i, 0.156, 51.2, and 87/1. Sylvine : Transparency of a i cm. thick plate (Trowbridge, Wied. Ann. 60, 1897). X 9 10 II 12 13 14 IS 16 17 18 19 20.7 237A' % 100. 98.8 99.0 99-S 99-5 97.S 9S4 93-6 92. 86. 76. S8. IS- Metallic reflection at 0.114^ o.i6i, 61. i, 100. Fluorite : Very transparent for the ultra-violet nearly to o.\\i. Rubens and Trowbridge give the following for a i cm. plate (Wied. Ann. 60, 1897) : 8/. 84.4 S4-3 16.4 II i.o I2/U Metallic reflection at 24/1, 31.6, 40^ Iceland Spar: Merritt (Wied. Ann. 55, 1895) gives the following values of * in the formula i = i.e-" (d in cm.) : For the ordinary ray : X 1.02 I.4S 1.72 2.07 2.11 2.30 2.44 2- S3 2.60 2.65 2-74M k 0.0 0.0 0.03 0-13 0.74 1.92 3-00 1.92 1.21 1.74 2.36 X 2.83 2.90 2.95 3-04 3-30 3-47 3.62 3.80 398 4-35 4.52 4.83M k 1.32 0.70 1.80 4-71 22.7 19.4 9.6 18.6 00 6.6 14-3 6.1 For the extraordinary ray : X 2.49 2.87 3-00 3-28 338 3-S9 3-76 3-90 4.02 4.41 4.67M k 0.14 0.08 0.43 1.32 0.89 1-79 2.04 1.17 0.89 1.07 2.40 X 4-91 S-04 S-34 S-SOM k I.2S 213 4-41 12.8 Quartz : Very transparent to the ultra-violet ; Pfliiger gets the following transmission values for a plate i cm. thick : at 0.222/j, 94.2% ; 0.214, 92 ; 0.203, 83.6 ; o. 186, 67.2%. Merritt (Wied. Ann. 55, 1895) gives the foUowing values for k (see formula under Iceland Snarl • For the ordinary ray : i""i- X 2.72 2.83 2.95 3-07 3-17 3-38 3-67 3-82 3-96 4.12 4-SOM k 0.20 0.47 0.57 0.31 0.20 0.1S 1.26 1.61 2.04 3-41 7-30 For the ext raordin iry ray 2.74 2.89 3.00 0-33 3.08 0.26 3.26 3-43 0.51 3-S2 0.76 3-S9 3-64 1.83 3-74 1.62 391 4.19 3-3S 4-36M 8.0 ^"par'^ent a^i^^"""'* "''*''"*' '°^'^''' reflection at 8.50^ 9.02, 20.75-24.4^, then trans- The above are taken from Kajrser'a " Handbuch der Spectroscopic," vol. iii. Smithsonian Tables. Tables 190-191. TRANSMISSIBILITY FOR RADIATION. 195 TABLE ISO. — Color Soieeni. *J|'?_f°Uowing light-filters are quoted from Landolt's " Das optische Drehungsvermogen, etc." 1898. Although only the potassium salt does not keep well it is perhaps safer to use freshly prepared solutions. J r r Color, Thick- ness, mm. Water solutions of Grammes of _ substance in 100 c.cm. Optical cen- tre of band. Transmission. Red Yellow II II Green 11 Bright ( blue i Dark ( blue \ 20 20 20 15 15 20 20 20 20 20 20 Crystal-violet, 5BO Potassium monochromate Nickel-sulphate, NiS04.7aq. Potassium monochromate Potassium permanganate Copper chloride, CuCl2.2aq. Potassium monochromate Double-green, SF Copper-sulphate, CuS04.5aq. Crystal-violet, 5BO Copper sulphate, CuSOi-Saq. 0.005 10. 3°- 10. 0.025 60. 10. 0.02 15- O.OOJ IS- 0.6659 0.5919 0-533° 0.4885 0.4482 j begins about 0.718/1. j ends sharp at 0.639/1. 0.614-0.574/1, 0.540-0.505/1 ( 0.526-0.494 and I 0.494-0.458/1 0.478-0.410/1 TABLE 191. — OoIOT Scieens. The following list is condensed from Wood's Physical Optics, 2nd edition ; Methyl violet, 4R- (Berlin Anilin Fabrik) very dilute, and nitroso-dimethyl-aniline transmits 0.365/1. Methyl violet -f- chinin-sulphate (separate solutions), the violet solution made strong enough to blot out 0.4359/1, transmits 0.4047 and 0.4048, also faintly 0.3984. Cobalt glass -j- aesculin solution transmits 0.4359/1. Guinea green B extra (Berlin) -f- chinin sulphate transmits 0.4916/1. Neptune green (Bayer, Elberfeld) + chrysoidine. Dilute the latter enough to just transmit 0.5790 and 0.5461 ; then add the Neptune green until the yellow lines disappear. Chrysoidine -j- eosine transmits 0.5790/1. The former should be dilute and the cosine added until the green line disappears. Silver chemically deposited on a quartz plate is practically opaque except to the ultra-violet region 0.3160-0.3260 where 90% of the energy pa.sses through. The film should be of such thickness that a window backed by a brilliantly lighted sky is barely visible. In the following those marked with a * are transparent to a more or less degree to the ultra-violet : • Cobalt chloride: solution in water, — absorbs 0.50-.53/1; addition of CaCla widens the band to 0.47-.50. It is exceedingly transparent to the ultra-violet down to 0.20. If dissolved in methyl alcohol + water, absorbs 0.50-. 53 and everything below 0.35. In methyl alcohol alone 0.485- 0.S55 and below 0.40/1. . , , , 1 « Copper chloride : in ethyl alcohol absorbs above 0.585 and below 0.535 ; in alcohol + 50% water, above 0.595 ^'^^ below 0.37/1. . , , r ^1. v ..• Neodymium salts are useful combined with other media, sharpening the edges of the absorption bands. In solution with bichromate of potash, transmits 0.535-.565 and above 0.60/1, the bands very sharp (a useful screen for photographing with a visually corrected objective). Praesodymium salts : three strong bands at 0.482, .468, .444. In strong solutions they fuse into a sharp band at 0.435-.485/1. Absorption below 0.34. Picric acid absorbs 0.36-.42/1, depending on the concentration. Potassium chromate absorbs 0.40-.35, 0.30-.24, transmits 0.23/1. • Potassium permanganate : absorbs 0.555-. 50, transmits all the ultra-violet. Chromium chloride : absorbs above 0.57, between 0.50 and .39, and below 0.33/1. These hmits vary with the concentration. _ , ,^ • , ,. Aesculin : absorbs below 0.363/1, very useful for removing the ultra-violet. • Nitroso-dimethyl-anUine : very dilute aqueous solution absorbs 0.49-.37 and transmits all the Ve"ry'^dens°e'cobalt glass -|- dense ruby glass or a strong potassium bichromate solution cuts off evervthing below 0.70 and transmits freely the red. . . .. ■ r j Iodine : saturated solution in CSj is opaque to the visible and transparent to the infra-red. Smithsonian Tables. 196 Table 1 92. TRANSMISSIBILITY FOR RADIATION. Color Soiaens. Jsna Glasses. Kind of Glass. Maker*s No, Copper-ruby Gold-ruby . Uranium . Nickel . . . Chromium (I Green copper , Chromium . . Copperchromium Green-filter . Copper . . . Blue-violet . Cobalt Nickel Violet Gray. 2728 459^° 454° 455"" 440" 414" 433'" 431m 432"' 436"' 437" 438"" 2742 447"" 424- 450" 452" 444" 445" Color. Deep red Red . . Bright yellow . . . \ Bright yellow, fluo- ) resces. Bright yellow-brown Yellow-green . Greenish-yellow Green. . . . Yellow-green . Grass-green Dark green . . U it Blue, as CuSOi Blue, as cobalt glass Blue . . . Dark violet , iGray, no recog- 1 nizable color ( Region Transmitted. Thick- ness, mm. Only red to o.6/t I Red, yellow ; in thin layers also j blue and violet. I Red, yellow, green to Eb ; in 1 ] thin layer also blue ) I Red, yellow, green (weakened), ) I blue (very weakened) ) Yellowish-green Red, green ; from o.65-.50fi . . . Green, yellow, some red and blue . Yellowish-green, some red . . . Green Green (in thin sheets some blue) . Green Green, blue, violet Blue, violet ( Blue, violet, blue-green (weak- J ( ened), no red J Blue, violet, extreme red . . . . Violet (G-H), extreme red . . . Violet (G-H), some weakened . . All parts o£ the spectrum weakened 1-7 16. II. 10. 5- 2-3 2.5 5- 5- S-12 5- 2-5 0.1-8 0.1-3 See " Uber FarbglSser fiir wissenschaftliche und technische Zwecke," by Zsigmondy, Z. fUr In- strumentenkunde, 21, igoi (from which the above table is taken), and " Uber Jenenser Licht- filter," by Grebe, same volume. (The following notes are quoted from Everett's translation of the above in the English edition of Hovestadt's " Jena Glass.") Division of the spectrum into complementary colors : 1st by 2728 (deep red) and 2742 (blue, like copper sulphate). 2nd by 454"' (bright yellow) and 447'" (blue, like cobalt glass). 3rd by 433'" (greenish-yellow) and 424"' (blue). Thicknesses necessary in above : 2728, 1.6-1.7 mm.; 2742,5; 454™, 16; 447™, I.5-2.O; 433"°, 2.5-3.5; 424™, 3 mm. Three-fold division into red, green and blue (with violet) : 2728, 1.7 mm. ; 414'", 10 mm.; 447'", 1.5 mm., or by 2728, 1.7 mm. ; 436"', 2.6 mm.; 447 , 1.8 mm. Grebe found the three following glasses specially suited for the additive methods of three-color projection : 2745, red; 438"', green; 447"°, blue violet ; corresponding closely to Young's three elementary color sensations. Most of the Jena glasses can be supplied to order, but the absorption bands vary somewhat in different meltings. See also " Atlas of Absorption Spectra," Uhler and Wood, Carnegie Institution Publications, 1907. Smithsonian Tables. Tables 193, 104. ROTATION OF PLANE OF POLARIZED LIGHT. 197 TABLE 103.— Taitailo AolA; Oamphoi; Santonin; Sontonic AclA; Oane Sngar. * *r,!!=?""P'°^?''°*'!I!? f'™° showing the effect of wave-length on the roUtion of the plane of polarization. The Mif,!>= " SIf '°'r-t""'=^'i?>,°' S?u^ Heciraetre of the solution. The examples are quoted from Landolt & Born- Biem s i-Hys. l,hem. Tab." The followmg symbols are used : — / = number grammes of the active substance in too grammes of the solution. c — solvent '* *' " '* 9 — " active «( .1 cubic centimetre " Right-handed rotation is marked -f-, left-handed—. Line of Wave-length Tartaric acid,* CuHeOj, Camphor,* CioHmO, Santonin.t CibHioOb, dissolved in cnforoiorm. according to Angstrom in dissolved in water. dissolved in alcohol. spectrum. f — SO togs. J := 50 to 95, temp. =r 22.9*^ C. ?= 75 1096.5, temp. = 20° C temp. = 24° C. B 68.67 — 140°.! + 0.2085 ? C 65.62 + 2°.748 4- 0.09446 jT 38°. 549 — 0.0852 ? — 149.3 +0-1555? — 202.7 +0.3086? D 58-92 -f 1.950 -f 0.13030? 51.945-0.0964? E 52.69 + 0.153 + 0.17514? 74-331— 0-1343? — 285.6 -- 0.5820? bi 51-83 - - - - — 302.38- -0.6557? ba 51.72 — 0.832 + 0.19147? 79-348-0.1451? F 48.61 — 3.598 -f 0.23977? 99.601 — 0.1912? -365-55 + 0-8284? — 534-98+1-5240? e 43-83 — 9-657 -f 0.31437? 149.696 — 0.2346? Santonin.t CisHisOa, * dissolved in alcohol. 1858. 1 1 t Nariri, " R. Ace. de 1 Lmcei," (3) n, 1882. 1 t Stefan, " Sitzb. d. Wien. Akad." 52, 1865. 11 TABLE 184. — Sodlnm OUorate; Qnartz. Sodium chlorate (Guye, C. R. 108, 1889). Spec- trum line. B C D E F G G H L M N P Q R T Cdl7 Cdis Wave- length. 71.769 67.889 65-073 59-085 53-233 48.9IZ 45-532 42-834 40.714 38.412 37-352 35-8i8 33-931 32-341 30.645 29.918 28.270 25.038 Temp. C. i5°.o 17.4 20.6 18.3 16.0 11.9 lO.I 14.5 '3-3 14.0 10.7 12.9 I2.I 1 1.9 12.8 12.2 II.6 Rotation per mm. 2°.o68 2.318 2-599 3.104 3.841 4.587 5-331 6.005 6.754 7.654 8.100 8.861 9.801 10.787 11.921 12.424 13.426 14-965 Quartz (Soret & Sarasin, Arch, de Gen. i88z, or C. R. 95, 1882).* Spec- trum line. A a B C Di Da E F G h H K L M Wave- length. 76.04 71.836 68,671 65.621 58-951 58.891 52.691 48.607 43-072 41.012 39.681 39-333 38.196 37-262 Rotation per mm. i2°.668 14-304 15.746 17.318 21.684 ZI.727 27-543 32-773 42.604 47-481 51-193 52-155 1-625 Spec- trum line. Cd» N Cdio O Cdn P Q, Cdi2 R Cdi7 Cdi8 CdjB Cd24 Cdjs Cdae Wave- length. 36.090 35.818 34-655 34-406 34-015 33.600 32.858 32.470 31-798 27-467 25-713 23.125 22.645 21-935 21.431 Rotation per mm. 63°628 64-459 69-454 70-587 72.448 74-571 78-579 80.459 84-972 121.052 143.266 190.426 201.824 220.731 235.972 * The paper is quoted from the Fraunhofer lines. Angstrom'! Smithsonian Tables. a naner by Ketteler in " Wied. Ann." vol. 21, p. 444-^ The wave-lengths are for ivaSsfor'u.e ultra violet sun, and Comu's values for the cadmium hues. 198 Table 195. NEWTON'S RINGS. Newton's Table ol Oolon. The following table gives the thickness in millionths of an inch, according to Newton, of a plate of air, water, and glass corresponding to the different colors in successive rings commonly called colors of the first, second, third, etc., orders. c Color for re- Color for transmitted Thickness in millionths of an inch for — 1 Color for re- flected Ught. Color for trans- mitted light. Thickness in millionths of an inch for — light. i 1 5 < 1 I. II. III. Very black Black . . Beginning of black . Blue . . White . . Yellow. . Orange Red. . . Violet . . Indigo . . Blue . . Green . . Yellow. . Orange Bright red Scarlet . . Purple . . Indigo . . Blue . . Green . . White . . Yellowish red . . Black. . Violet . Blue . . White . Yellow . Red . . Violet . Blue . . Green Yellow . Red . . o-S I.O 2.0 2.4 5.2 7.1 8.0 9.0 II.2 12.8 14.0 16.3 17.2 18.2 19.7 21.0 21. 1 23.2 25.2 0.4 0-7S 1-5 1.8 3-9 5-3 6.0 6.7 u 10.5 "■3 12.2 13.0 '37 14.7 17.6 0.2 0.9 1-3 i-S 4.6 4.2 5.8 7.2 8.4 9.0 97 10.4 1 1-3 1 1.8 12.7 13-5 14.2 IV. V. VI. VII. Yellow. . Red. . . Bluish red Bluish green . Green . . Yellowish green . Red. . . Greenish blue . . Red. . . Greenish blue . . Red. . . Greenish blue . . Reddish white Bluish green Red . Bluish green Red . 27.1 29.0 32.0 24.0 35-3 36.0 40.3 46.0 S2-S 587 65.0 72.0 71.0 20.3 21.7 24.0 25-5 26.5 27.0 30.2 34-5 394 46 48.7 S3-2 577 '2-5 18.7 20.7 22.0 22.7 23.2 26.0 397 34-0 38.0 42.0 45.8 494 The above table has been several times revised both as to the colors and the numerical values. Professors Reinold and Rucker, in their investigations on the measurement of the thickness of soap films, found it necessary to make new determinations. They give a shorter series of colors, as they found difficulty in distinguishing slight differences of shade, but divide each color into ten parts and tabulate the variation of thickness in terms of the tenth of a color band. The position in the band at which the thickness is given and the order of color are indicated by numerical subscripts. For example : Ri 5 indicates the red of the first order and the fifth tenth from the edge furthest from the red edge of the spectrum. The thicknesses are in millionths of a centimetre. 1 Color. Posi- tion. Thick- ness. 1 Color. Posi- tion. Thick- ness. 1 Color. Posi- tion. Thick- ness. I. II. III. Red* . Violet . Blue. . Green . Yellow* Orange * Red . . Purple . Blue. . Blue* . Green . Yellow* R16 V26 B25 G2 6 Y26 O2S R2 6 P36 Bs B35 Gs B Y35 .8.4 30-S 35-3 40.9 454 49.1 52.2 SS-9 65.6 71.0 IV. V. Red* . Bluish red*. Green . Yellow ' green * Red* . Green . Green*. Red . . Red* . R36 BR8 6 G4 YG45 R46 G5 G5 c R50 Rb 6 76.5 81.S 84.1 893 96.4 105.2 III.9 1 18.8 126.0 I33-S VI VII VIII. Green . Green* Red . . Red* . Green . Green*. Red . . Red* . Green . Red . . Ge G6 6 Reo Re 6 G7 G76 R70 R7 6 Gs Rs 141.0 147.9 154.8 162.7 170.5 178.7 186.9 193.6 200.4 2H.5 *1 ~hc » QSmo 9 nth. ^" — — Smithsonian Tables. Table 196. 199 CONDUCTIVITY -FOR HEAT. The coefficient k is the quantity of heat in small calories which is transmitted per second through a plate one centimetre thick per square centimetre of its surface when the difference of tempera- ture between the two faces of the plate is one degree Centigrade. The coefficient k is found to vary with the absolute temperature of the plate, and is expressed approximated' by the equation i5i=^o (i + o/). In the table k, is the value of kt for 0° C, t the temperature Centigrade, and a a constant. Substance. Substance. k. Aluminum . . l Antimony , . \ Bismuth . . . ^ Brass (yellow) . < « (red) . .| Cadmium . . Constantin 6oCu+4oNi .1 Copper . . . < German silver . \ Iron . . . . < " (wrought)* \ Lead . . . .| Mercury . . . j Magnesium . . Manganin 84Cu-f4Ni+( i2Mn Nickel . . Palladium Platinum . Steel (hard) " (soft) . Silver . . . Tin ... . Wood's alloy Zinc . • • ■\ ■I o 100 o 100 o 100 o 100 o 100 o 100 18 100 o 100 o 100 o 100 o 100 o 100 o 5° O-IOO 18 100 18 18 18 100 o o 100 18 0-3435 I ■3619 S ■0442 I •0396 ) .0177 I .0164 i .Z041 I .2540 s .2460 I .2827 ] .2200 i .2045 ) .5402 .6405 .7189) .7226 ) .0700 I .0887 i .1665 1 .1627 i .2070 ) .1567 s .0764 ) .0148 1 .0189 ) .3760 .5186 .6310 .1420 .1683 .1664 •1733 .0620 .1110 1.0960 0.1528 1 •1423 ) ■0319 .2653 .0005356 —.001041 —.000735 .002445 .001492 — .000705 .000051 .002670 — .000228 — .000861 — .000687 1 Lorenz. 4 H. F. Weber. 2 J -f. Dt. 5 Kohlrausch. 3 J. Forbes. 6 H. L. & D.t 7 Hjeltstrom. Carborundum Slate .... Soil dry . . . " wet . . Diatomic earth Fire-brick . Granite . . Lime . . . Magnesia . Marbles, lime- f rom to from to from to from to stone, cal cite, com- pact dolo- mite . . Micaceous flagstone : along cleavage . . across cleavage Paraffine. . . . < Pasteboard .... Plaster of Paris . . " " " powder Quartz Sand (white dry) . . Sandstone and ' hard grit (dry) . . Sawdust Serpentine (Corn- wall red) .... Slate : along cleav- ( from age . . I to across cleav- i from age . . I to Snow, compact layers Strawboard . . . Vulcanite . . . . Vulcanized ( from rubber (soft) ( to Wax (bees) . . . . Wood, fir : parallel to axis . . perpendicular to o 100 ,00050 ,0036 .00033 ,0010 .00013 .00028 .00510 .00550 .00029 .00016 ,00045 .00470 .00560 .00632 00441 .00014 .0002; ,00161 00045 ,00070 .0026 ,00036 .00093 .00545 .00565 ,00441 ,00550 I g 00650 j ,00315 ,00360 ,00051 .00033 .00087 00034 00054 ,00009 .00030 .00009 8 G. Forbes. 9 R. Weber. 10 Stefan. 11 Lees-Chorlton. 12 Hutton-BIard. A repetition of Forbes's experiment, by Mitchell, under the direction of Tait, shows the conductivity to with rise of temperature. (Trans. R. S. E. ™- 33^ Lebour, and Dunn (British Association Committee), t Jaeger and Diesseinorsi. + Smithsonian Tables. increase 200 Tables 197-200. CONDUCTIVITY FOR HEAT. TABLE 197.— Vaiiona SnbBtaiioeB. TABLE 198. -Water and Salt Solatlons. Substance. t it Au- thor- ity. Asbestos paper . Blotting paper . , Carbon .... Portland cement . Cork Cotton wool . . Cotton pressed . Chalk Ebonite .... Felt Flannel (dry) . . Glass jfr. : : Horn Haircloth . . . Ice .... Leather, cow-hide " chamois . Linen Silk Caen stone (build-l ing limestone) ) Calc's sandstone 1 (freestone) . } 49 .00043 .00015 .000405 .00071 .000717 .000043 .000033 .002000 .000370 .000087 .00012 .0011 1 .0023 ( .000087 .000042 .00223 .00568 .00042 .00015 .00021 .000095 ■00433 .00211 2 2 1 G. Forbes. 4 Neumann. 2 H., L., & D.* S Lees-Chorlton. Au- Substance. Density. .^1 thor- ity. Water . . _ _ .002 I (( — .00120 2 u - 9-15 .00136 2 It - 4 .00129 3 - ■■^2 .00157 4 18 .00124 5 Solutions in water. i.i6o 4-4 .00118 2 CUSO4 . . KCl . 1.026 13 .00116 4 NaCl . ^^Wc 10-18 .00267 6 H2SO4 1.054 20.5 .00126 S I( 1. 100 20.5 .00128 S <( 1. 180 21 .00130 ■S ZnSO* 1.134 4-5 .00118 2 K 1. 136 4-S .00115 2 I Bottom! ey. 4 Graetz. 2 H. F. Weber. 5 Chree. 3 Wachsmuth. 6 Winkelmann. TABLE 199.- - Organic Lit lids. Substance. Xiooo a < Acetic acid . . . Alcohols : amyl . ethyl . methyl Benzole .... Carbon disulphide Chloroform . . . Ether Glycerine . . . Oils : olive . . . castor . . petroleum . turpentine . Vaseline .... 9-1 S 9-15 9-15 9-15 S 9-15 9-15 9-15 9-iS 13 13 .472 .328 ■423 •495 •333 f^ •39S .425 •355 •325 •44 0.12 0.01 1 0.0067 2 3 3 2 2 4 1 H. F. Weber. 3 Wachsmuth. 2 Graetz. 4 Lees. TABLE 200. — OaiSB. Substance. t k, Xioooo a < Air Argon .... Ammonia . . . Carbon monoxide " dioxide . Ethylene . . . Helium. . . . Hydrogen . . . Methane . . . Nitrogen . . . Nitrous oxide . Oxygen .... 7-8 7-8 7i 7-8 .568 •389 •458 •499 •307 •395 3^39 3-27 .647 .524 .00190 .00260 .00548 ■00445 .00318 .00175 .00446 I 2 1 Winkelmann. 2 Schwarze. Smithsonian Tables, * Herschel, Lebour, and Dunn (British Association Committee). Table 201 . 201 HEAT OF COMBUSTION. Heat of combustion of some common organic compounds. Products of combustion, COj or SOj and water, whicli is assumed to be in a state of vapor. Substance. Small calories per gramme of substance. Authority. Acetylene . 1 1923 Thomsen. Alcohols: Amyl 8958 Favre and Silbermann. Ethyl 7183 C. Smithsonian Tablcs. Table 207. MELTING-POINTS OF THE CHEMICAL ELEMENTS. 209 The metals in heavier type are often used as standards. The melting-points are reduced as far as possible to a common temperature scale which is the one used by the United States Bureau of Standards in certifying pyrometers. This scale is de- fined in terms of Wien's law with C taken as 14000, and on which the melting-point of platinum is 1755° C (Nemst and Wartenburg, 1731; Waidner and Burgess, 1753 j Holborn and Valentiner, 1770; see C. R. 148, p. 1177, 1909). Above iioo" C, the temperatures are expressed to the nearest 5° C. Temperatures above the platinum point may be uncertain by over 50° C. Element. Melting- point. L Remarks. Element. Melting- point. Remarks. Aluminum 658 ± I Most samples Manganese 1225 Adjusted. give 657 or less Mercury Molybdenum — 39 (Burgess). > 2000 Probably. Antimony 630^1 "Kahlbaum"pu. Neodymium 840 (Muthmann-Weiss.) rity. Neon — 252 Argon — 188 Ramsay-Travers. Nickel 1450 Adjusted (Day-Sos- Arsenic >Sb, 2000 1 ( <25ooS Weintraub. Oxygen — 230? unpublished.) Bromine —7-3 Palladium '545 i IS (Waidner-Burgess, Cadmixun 321 Range : 320.7- 32' -7 Nernst-Warten- burg.) Caesium 26 Range : 26.37- Phosphorus 44.2 2S-3 Platinum 1755 ±20 See Note. Calcium 80s Adjusted. Potassium 62.S Chlorine — 102 (Olszewski.) Prassodymium 940 (Muthmann-Weiss.) Carbon {> 3500) Sublimes. Rhodium 1910 (Mendenhall-Inger- Cerium 623 (Muthmann- soU.) Weiss.) Rubidium 38-5, Chromium 1505 Adjusted. Ruthenium 1900? Cobalt 1490 Day-Sosman. Samarium 1300-1400 (Muthmann-Weiss.) Copper 1083 i 3 Mean, Holborn- Silicon 1420 Adjusted. Day, Day- Silver 961 ± I Ad usted. Clement. Sodium 97 Erbium Strontium Between Ca and Ba? Fluorine — 223 (Moissan - De- war.) Sulphur 113.3-119-5 Various forms. See Landolt-Bornstein. Gallium 30.1 Tantalum 2800 Adjusted from Waid- Germanium i7002250 1 <230o Adjusted. Titanium Tungsten ? 2950 Above 2000? Mean, Waidner-Bur- Iron 15*0 Adjusted. gess and Warten- Krypton T .anthanum -,69 Sio (Ramsay.) (Muthmann- Uranium Near Mo burg. Moissan. Weiss.) Vanadium 1750 Vogel-Tammann. Lead 327^0.5 Xenon -140 Ramsay. Lithium 186 (Kahlbaum.) Zinc 41940.S Magnesium 651 (Grube) in clay crucibles, 635. Zirconium >Si Troost. Smithsonian Tables. 2IO Table 208. BOILING-POINTS OF THE CHEMICAL ELEMENTS. Element. Range. Boiling- point. Observer; Remarks. Aluminum o 1800. Greenwood, Ch. News, 100, 1909. Antimony - 1440. II II II II II Argon - — 186.I Ramsay-Travers, Z. Phys. Ch. 38, 1901. Arsenic 449-450 - Gray, sublimes, Conechy. " >36o. Black, sublimes, Engel, C. R. 96, 1883. II 280-310 - Yellow, sublimes. Barium - - Boils in vacuo, Guntz, 1903. Bismuth I420-I43S 1430. Barus, 1894; Greenwood, 1. c. Boron Volatilizes without melting in electric arc. Bromine 59-63 61.1 Thorpe, 1880 ; van der Plaats, 1886. Caesium 670. Ruff-Johannsen. Carbon - 3600. Computed, Violle, C. R. 120, 1895. II - - Volatilizes without melting in electric oven, Moisson. Cadmium 760-782 770. CUorine - —33-6 Regnault, 1863. Chromium - 2200. Greenwood, Ch. News, 100, 1909. Copper 2 100-2310 2310. 1. c. Fluorine .- -187. Moisson-Dewar, C. R. 136, 1903. Helium - -267. Computed, Tracers, Ch. News, 86, 1902. Hydrogen —252.5-252.8 — 252.6 Mean. Iodine — >200. Iron - 2450. Greenwood, 1. c. Krypton - —1 51.7 Ramsay, Ch. News, 87, 1903. Lead — 1525. Greenwood, 1. c. Lithium - 1400. Ruff-Johannsen, Ch. Ber. 38, 1905. Magnesium - 1 1 20. Greenwood, 1. c. Manganese - 1900. II II Mercury - 357- Crafts; Regnault Nitrogen -I95.7-I94.4 Mean. Oxygen —182.5-182.9 —182.7 II Ozone - —119. Troost, C. R. 126, 1898. Phosphorus 287-290 288. Potassium 667-757 712. Perman ; Ruff-Johannsen. Rubidium 696. Ruff-Johannsen. Selenium 664-694 690. Silver - 1955- Greenwood, 1. c. Sodium 742-757 750. Perman ; Ruff-Johannsen. Sulphur 444-7-445 444-7 Mean. Tellurium 1390. Deville-Troost, C. R. 91, i88o. Thallium 1600-1800 1700. Tin 2270. Greenwood, 1. c. Xenon - — 109.1 Ramsay, Z. Phys. Ch. 44, 1903. Zinc 916-942 930- Smithsonian Tables. Table 209. MELTING-POINTS OF VARIOUS INORGANIC COMPOUNDS.* 211 Substance. Chemical Formula. Melting-point. Min. Max. Particular or Average Value. Date of Publication. Aluminum chloride " nitrate . Ammonia .... Ammonium nitrate . " sulphate " phosphite Antimonietted hydrogen Antiniony trichloride " pentachloride Arsenic trichloride . Arsenietted hydrogen Barium chlorate . . " nitrate . . " perchlorate Bismuth trichloride Boric acid .... " anhydride . . Borax (sodium borate) Cadmium chloride . " nitrate . Calcium chloride . U tl " nitrate . . fi it Carbon tetrachloride " trichloride . " monoxide . " dioxide . . " disulphide . Chloric acid . . . Chlorine dioxide Chrome alum . . . " nitrate . . Cobalt sulphate . . Cupric chloride . . Cuprous "... " nitrate . . Hydrobromic acid . Hydrochloric " Hydrofluoric " . Hydroiodic " Hydrogen peroxide " phosphide " sulphide . Iron chloride . . . " nitrate . . . " sulphate. . . Lead chloride . . " metaphosphate Magnesium chloride (' nitrate . '• sulphate Manganese chloride " nitrate . " sulphate Mercuric chloride . AlCls Al(N08)a + 9H20 NHs (NHiNOg (NH4)aS04 NH4H2POS SbHs SbCls SbCls AsCls AsHa Ba(C108)2 Ba(N08)2 Ba(C104)2 Bids HaBOs B2O8 NajBiOj CdCl2 Cd(N03)2 + 4H20 CaCl2 CaCl2 + 6H20 Ca(N08)2 Ca(N08)2 + 4H20 CCI4 C2CI6 CO CO2 CS2 HCIO4+H2O CIO2 KCr(S04)a+i2H20 Cr2(N08)6 + 18H2O C0SO4 CuCl2 CU2CI2 Cu(N08)2 + 3H20 HBr HCl HFl HI H2O2 PHs H2S FeCla Fe(N08)8 + 9H20 FeSOi + yHzO PbCla Pb(P08)2 MgCl2 Mg(N08)2 + 6H20 MgS04 + sH20 MnCl2 +4H2O Mn(N08)2 + 6H20 MnS04 + SH2O HgCl2 145- 72. 225. 184. 719. 499. 182. -199. -56.5 96. 49-S 301. 447- 287. 166. 73-2 230. 186. 878. 590. 806. 187. —207. — S7-S Si-3 307- 580. 190. 72.8 150. 140. 123- — 9I-S 72.8 —6. —18. — "3-S 414. 593- 505. ^27.5 i85. 577. 561. S4I. S9-S 762. 29.6 S6i. 44. —24.7 184.5 203. ~57- —1 12.8 —76. 89. 37- 97- 293- 434- 9 114.S 2 —86.7 3 — 111.3 17 -92.3 6 51-3 17 — 2. 18 — I32-S 6 -85.6 3 303- - 47.2 2 64. 16 506. - 800. 9 708. 9 90. 2 87.5 16 19 25.S 2 54- 16 290. - 1 Friedel & Crafts. 2 Ordway. 3 Faraday. 4 Marchand, 5 Amat. 6 Olszewski. 7 Kammerer. 8 Baskerville, a Camelley. 13 Wroblewski & 10 Camelley & O'Shea. Olszewski. 13 Regnault 14 Holbom&Wien. 11 Muir. IS Roscoe. 1888 1859 1875 1837 1887 1886 1875 1903 1884 1S78 1878 1884 1876 1878 1878 1878 1878 1859 1878 1863 1845 1903 I86I 1845 1884 1859 1884 1878 1878 1859 1845 1900 1886 1900 1886 1845 1859 1884 1878 1878 1859 1884 1859 1884 16 Tilden. >7 Ladenburg. 18 Staedel. 19 Clarke, " Const, of Kat.' •For more extensive tables on this subject, see Camelley's "Melting and BoUing-point Tablet,'' or Landolt and BSmstein's " Phys. Chem. Tab." Smithsonian Tables. 212 Table 209 (ctmUmuJ). MELTING-POINTS OF VARIOUS INORGANIC COMPOUNDS. Chemical Formula. Melting-point. 9 Date of Publication, Substance. Min. Mai. Particular or Probable Value. < Nickel carbonyl .... NiCOi _ _ -25. I 1890 " nitrate . . . Ni(NOj)2 + 6H2O - - 56.7 2 1859 *' sulphate . . NiSOi + tHjO 98. 100. 99. 3 Nitric acid .... HNOa — —47- 4 Isjt " anhydride . . N2O6 - - 30. 1 1872 " oxide * . . . NO 150. - -167. 6 1885 " peroxide . . . N2O4 — 9- — 12. — 10.6 - - Nitrous anhydride . . NjOs - —82. 7 1889 " oxide . . . N2O - - —102.3 8 1893 Phosphoric acid (ortho) . H8PO4 38.6 41.7 40-3 - Phosphorous acid . , . HsPOg 70.1 74- 7^-o - - Phosphorus trichloride PCls 1 1 1.8 10 1883 " oxychloride . POCls - - — i-S II 187 1 " disulphide . . PsSs 296. 298. 297. 12 1879 " pentasulphide P2S6 274- 276. 290. 13 1879 " sesquisulphide " trisulphide P4S8 PaSa 142. 167. H 1864 Potassium carbonate . . K2COS 834- 897. 840. - - " chlorate . , KClOs 334- 372- 360. - - " perchlorate . KCIO4 610. 15 1880 " chloride . . KCl 740. 804. 779- - " nitrate . . KNOs 327- 3S3- 340 - - " acid phosphate KH2PO1 96. 3 1884 " acid sulphate . KHSO4 — - 200. 16 1840 Silver chloride .... AgCl 450. 460. 455- - - " nitrate . . . AgNO, 198. 224. 214. - - " nitrogenietted AgNs 250. 17 1890 " perchlorate . AgC104 - - 486. 18 1884 " phosphate . . Ag8P04 - - 849. IS 1878 " metaphosphate AgPOa - - IS 1878 " sulphate . . Ag2S04 654. 676. 665. - Sodium chloride . . NaCl 772. 820. 795- - - " hydroxide . NaOH - 66. 19 1884 " nitrate . . NaNOa 308. 330. 315- - " chlorate . . NaClOa 248. 302. 275- - - " perchlorate . NaC104 - 482. 18 1884 " carbonate . NaaCOs 814. 920. 852. - - 41 <• _ ^ Na2C08 + 10H2O - 34- 3 1884 " phosphate . Na2HP04 + 4H2O 35- 36.4 35-4 - " metaphosphate . NaPOs 617. 15 1878 " pyrophosphate . Na4P207 888. 970. 938- - " phosphite . . . (H2NaPOa)2 + SH2O - - 42. 20 1888 " sulphate . NasSOi 861. 865. 863, IS 1878 " " . . Na2S04 + 10H2O - 34- 3 1884 " hyposulphite Na2S208 + 5H2O 45- 48.1 47- - Sulphur dioxide . . SO2 73- 79. 76. - - Sulphuric acid . . H2SO4 10.1 10.6 104 21 1884 " "... 12H2SO4 + H2O - - —0.5 22 i8S3 It It H2SO4 + H2O 7-5 8.5 8. - " (pyro) ." H2S2O, 35- 22 1853 Sulphur trioxide . . SOs 14.8 IS- 14.9 S 1876-1886 Tin, stannic chloride SnCl4 - —33- 23 1889 " stannous " SnCl2 - - 250. 24 - Zinc chloride . . . ZnCl2 - - 262. 25 187s 11 H ZnClj + 3H2O - - 6-5 26 1904 " nitrate . . . Zn(N08)2 + 6H2O - - 364 3 1884 " sulphate . . . ZnSOi + 7H2O - - 50. 3 1884 1 Mond, Laager 5 R. Weber, 10 Wroblewskia 13 V.& C. Meyer. 18 Carnell ey & 22 W arign IC. & Quincke. 6 Olszewski. Olsiewski. 14 Lem cine. O'Sh :a. y B 14 Clark esson. X Ordway. 7 Birhaus. 11 Genther&Mi- 15 Can elley. 19 Cripps. e,"Cc nst. of Nat." 3 Tilden. 8 Ramsay. cbaelis. i5 Mils clierlich. 20 Amat. 25 B raun. 1 4 Berthelot. q Wills, 12 Ramme. 17 Curt ius, 21 Mende] ejeS. 26 M ylius. Smithsonian Tables. * Under pressure 138 mm. mercury, Table 210. BOILING-POINTS OF INORGANIC COMPOUNDS.* 213 Substance. Chemical Formula. Boiling-poiut. 3 Date of PublicatioD. Min. Max Particular or Aver- ageValues < Air t . •* - - - — 192.2 I '!^4 Aluminum chloride J . AlCIa z " — 191.4 207.5 134- 2 3 4 5 2 1884 1888 " nitrate . Ammonia . . . . Antimonietted hydrogen . Al{NOa)8+9H20 NHs SbHa — "■ 1859 1886 Antimony pentachloride § . " trichloride Bismuth trichloride . SbCls SbClj BiCls 102. 216. 427. S61. 103. 223-5 447- 954- 220. 6 1889 Cadmium chloride . CdCla 1880 " nitrate Cd(N08)2+4H20 _ 132. 4 1859 1859 1863-1880 Calcium nitrate . Ca(N08)3+4H20 _ 132. 4 Carbon dioxide . CO2 —78.2 —80. — 79-1 " disulphide . CSj 46. 474 46.1 _ " monoxide . CO 190. — '93- — IQI.? 2, 1 1884 Chromic oxychloride Cr02Cl2 115.9 111 7 J 117. Chromium nitrate Cr2(N03)e+i8H20 125.5 4 1859 Copper nitrate . Cu(N08)2+3H20 - - 170. ll^ Cuprous chloride CuaCli) 954- 1032. 993- g Hydrobromic acid || . HBr _ -gg.i 9 1900 Hydrochloric acid || . HCl - _ —83.1 9 1900 Hydrofluoric acid || . HF - - -36-7 9 1900 Hydroiodic acid HI - - 127. 10 1870 Iron nitrate Fe{N08)8+9H20 - - 125. 4 1859 Magnesium nitrate . Mg(N08)2+6H20 - - 143- 4 1859 Manganese chloride . MnCl2+4H20 - - 106. II " nitrate . Mn(NOs)2+6H20 - - 129.5 4 1859 Mercuric chloride HgCl2 302. 307. 304- Nickel nitrate . Ni(N08)2+6H20 'It' 4 1859 Nitric acid HNOg - - 12 1830 " anhydride N2OB 45- SO. - 13 1849 " oxide NO — 153- 2 1885 Nitrous anhydride . N2O8 — 10. 3-5 - oxide . . N2O -87.9 89.8 88.8 - - Phosphorus trichloride PCls 73-8 76. 75- - - " sesquisulphide P4S8 380. 14 1883 " trisulphide P2S8 - - 490. 14 1886 " pentasulphide P2S6 518. 530. 522. - - " trioxide . P20a - 173- IS 1890 Silicon chloride SiCU 56.S 59- 58- - Sulphuric acid . 12H2SO4+H2O - 338. 16 1853 Sulphur trioxide SOa 46. 47- 46.3 - " dioxide SO2 —8. — lo-s —9.6 — — " chloride S2CI2 138. 144. 139- - - Tin, stannous chloride SnCl2 606. 628. 617. - - " stannic " . SnCli - - "3-9 17 1876 Zinc chloride ZnCla 676. 730- 703- - - " nitrate Zn(N08)2+6H20 — 131- 4 1859 I Wroblewski. 7 Pictet. [3 Deville. 2 Olszewski. 8 Camelley and Carl eton-Wil iams. 4 Isambert. i 3 Friedel and Crafts. 9 Ladenburg and Kr iigel. r5 Thorpe anc i Tutton. 4 Ordway. 10 Topsoe. 6 Marignac. 5 Regnault. II Clarke, "Const, of Nature." 7 Thorpe. 6 Anschiitz and Evans. 12 Mitscherlich. * For a more complete table, see Landolt-BBrnstein-Meyerhoffer's Physikalisch-chemische Tabellen. t Pressure 76 cm. t Pressure a.64 atmos. $ Pressure 68 mm. Pressure 75.5 cm. Smithsonian Tables. 214 Tables 211-213. MELTING-POINTS. TABLE 211.— UelUng-polnt ol Hlztuns. Metals. Melting-points, C. 1 Percentage of metal in second colunm. o% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Pb. Sn. 326 290 270 250 230 215 200 180 190 210 232 I Bi. 322 290 — — 179 145 126 168 205 — 268 7 Te. 322 710 790 88a 917 760 600 480 410 42s 446 8 Ag. 328 460 S4S 590 620 650 70s 775 840 90s 959 Na. — 360 420 400 370 330 290 250 200 130 96 13 Cu. 326 930 953 953 953 953 953 975 lOIO 1045 IO81 2 Sb. 326 2S0 275 330 395 440 490 S25 560 600 632 16 Al. Sb. 650 750 840 92s 945 950 970 1000 1040 lOIO 632 17 Cu. 650 630 600 560 540 S8o 610 75S 930 loss 1084 18 Au. 6SS 67,'i 740 80a 855 915 970 1025 1055 675 1062 10 Ag. 650 62,? 6IS 600 590 580 575 S70 6so 750 954 17 Zn. 654 640 620 600 580 560 530 510 475 42s 419 II Fe. 654 b^a 630 1 125 I170 1200 13SO I4S0 1520 1570 1600 3 Sn. 650 64s 635 62s 620 605 S90 S70 S60 540 232 17 Sb. Bi. 632 610 590 S7S 555 540 520 470 405 330 268 i6 Ag. 630 S9S 570 545 520 500 505 S4S 680 850 959 9 Sn. 622 600 S70 525 48a 430 395 350 310 255 232 19 Zn. 632 SSS Sio 540 570 565 540 S2S 510 470 419 17 Ni. Sn. I4SS 1380 1290 1200 1235 1290 1305 1230 1060 800 232 17 Na. Bi. 96 42s S20 590 64s 690 720 730 71S 570 268 13 Cd. 96 1 25 185 24s 28s 32s 330 340 360 390 322 13 Cd. Ag. 322 420 520 610 700 760 805 8so 80s 940 954 17 Tl. 321 300 28s 270 262 2S8 245 230 210 235 302 14 Zn. 322 280 270 295 313 327 340 355 370 390 419 Au. Cu. 1063 940 910 92s 943 968 993 1018 104a 1060 1083 ^8- 1064 1062 I06I 1058 1054 1049 1039 I02S 1006 q82 963 5 Pt. I07S II2S 1 190 1250 1320 1380 I4S5 1530 1610 168S I77S E.Na. 62 17.5 — 10 — 3-S 5 II 26 41 S8 77 97.5 IS Hg. — - — — — 90 no 135 162 265 13 Tl. 62.S 133 165 188 205 215 220 240 280 305 301 14 Cu. Ni. 1080 1 180 1240 1290 Z320 1335 1380 1410 1430 1440 I4SS 17 Ag. 1082 I03S 990 945 910 870 830 788 814 87^ 960 Sn. 1084 lOOS 89a 755 725 680 630 580 530 440 232 12 Zn. 1084 loss 1000 945 890 870 840 78s 700 570 419 6 Ag. Zn. 9S9 850 755 70s 690 660 630 610 570 SOS 419 Sn. 959 870 7SO 630 550 495 450 420 375 300 232 Na. Hg. 96.S 90 80 70 60 45 22 55 95 2IS 13 1 Roberts-Austen, Engineering, 63, 223, 1897. 2 " '*( Rap. Cong. Phys. Paris, 1900. " " Engineering, 59, 744, 1895. " " Proc. Roy. Soc. 67, 105, 1900. " " Chem. News, 87, 2, 1903. " " _ Engineering, 12/2, 221, 1897. pp. Diss., Konigsberg, 1901. 8 Fay and Gilson, Trans. Am. Inst. Min. Eng. Nov. 1901. 9 Heycock and Neville, Phil. Trans. 189A, 1897. o " " " ■' " 194A, 201, 1900. 3 4 5 6 7 Kapp, Diss., II Heycock and Neville, J. Chem. Soc. 71, 1897. '2 " " " Phil. Trans. 202A, i, 1903. 13 Kumakow, Z. Anorg. Chem. 23, 439, 1900. ' '* •'. "• ,'. ',' 30, 86, 1902. ^1 " " 30, 109. 1902. 16 Roland-Gossehn, Bui. Soc. d'Encour. (5) i, 1896. 17 Gautier, " " •* (e\ j « 18 Le Chatelier, (4) {o, 573; 1895. 19 Reinders, Z. Anorg. Chem. 25, 113, 1896. 20 Erhard and Schertel, Jahrb. Berg -u. Hiittenw. Sachsen. 1879, 17. TABLE 212. — AU07 ol Leal, Tin, an! Blsmntli. Percent. || Lead .... Tin Bismuth . . . 32.0 15.5 52.S 25.8 19.8 54-4 25.0 15.0 60.0 43.0 14.0 43.0 33.3 33.3 33,3 10.7 23.1 66.2 50.0 33.0 17.0 35-8 52.1 12.1 20.0 60.0 20.0 70.9 9.1 20.0 Solidification at 96° 101° 125° 128° 145° 148° 161° 181° 182° 234° Charpy, Soc. d'Encours, Paris, 1901. TABLE 213. — Low Melttng-polnt AII07. Percent. || Cadmium . . Tin ... . Lead .... Bismuth . . . 10.8 14.2 24.9 SO.I 10.2 14.8 14.3 7.0 2S.I 26.0 50.4 52.2 13. 1 13.8 243 48.8 6.2 9.4 34-4 50.0 7.1 39.7 53.2 6.7 43.4 49.9 Solidification at 65.5° 67.5° 68.5° 68.5° 76.5° 89.5° 95° Drewitz, Diss. Rostock, 1902. All compiled from Landolt-Bomstein-Meyerhoffer's PhysikaUsch-chemische Tabellen. Smithsonian Tables. Table 214. 21 5 DENSITIES, MELTING-POINTS, AND BOILING-POINTS OF SOME ORGANIC COMPOUNDS. N.B. — The data in this table refer only to normal compounds. Substance. Formula Temp. °C. Den- sity. Melting- point Boiling-point. Authority. (a) Paraffin Series = C„Hj„+3,. Methane* . . . CH4 —164. 0-415 _ -165. Olszewski, Young. Ethanet . . C2HJ .446 —171.4 — 93^ Ladenburg, " Propane . CaHs •536 —45- Young, Hainlen. Butane . . C4H10 .60 - I. Butlerow, Young. Pentane . CsHia .647 - 36.3 Thorpe, Young. Hexane . CaHii 17- .663 - 69. Schorlemmer. Heptane . C7H1S .701 - 98.4 Thorpe, Young. Octane . CsHia .719 — i2S^5 II « Nonane . C9H20 •733 —s^- 150. Krafft. Decane . C10H22 -74S — 3'- 173^ (1 Undecane C11H24 -26. 195^ It Dodecane C12H26 .765 — 12. 214. (1 Tridecane CiaH28 .771 -6. 234- it Tetradecane C14H80 4- -775 5. 252. tt Pentadecane C16H82 10. -776 10. 270. it Hexadecane C16H84 18. •775 18. 287. tt Heptadecane C17H86 22. •777 22. 303^ tt Octadecane CisHss 28. •777 28. 3i7^ It Nonadecane C19H40 32- -777 32- 330^ ft Eicosane . , C20H42 37- .778 37- I2I.§ tt Heneicosane C21H44 40. .778 40. I29.§ tt Docosane . C22H46 44- .778 44. i36-5§ tt Tricosane . C23H48 48. -779 48. I42^5§ 243-t tt Tetracosane C24H50 51- .779 51- tt Heptacosane C27H66 60. .780 60. I72^§ tt Pentriacontane . C8lH64 68. .781 68. i99-§ tt Dicetyl .... C82H66 70. .781 70. 205.1 tt Penta-tria-contane C86H72 75- .782 75- 33i^t tt (b) Olefines or the Ethylen e Series : C„P i«- Ethylene . . . C2H4 _ 0.610 -169. —103. Wroblewski or Olszewski. Propylene CsHe - - — 50.2 Ladenburg, Kriigel. Butylene . C4H8 —13-5 •63s - I. Sieben. Amylone C5H10 - 36. Wagner or Saytzeff. Hexylene C6H12 .76 - 69. Wreden or Znatowicz. Heptylene C7H14 19.S •703 - 96.-99. Morgan or Schorlemmer. Octylene . C8H16 17- .722 - 122.-123. Moslinger. Nonylene Decylene C9H18 C10H20 20. .767 _ 140.-142. Beilstein, " Org. Chem." II II 11 Undecylene C11H22 20. •773 - 196.-197. " Dodecylene C12H24 —31- •795 —31- 212.-214. II II •• Tridecylene C18H26 IS- •774 - 233^ Bemthsen. Tetradecylene Cl4H28 — 12. .794 — 12. 127.J Krafft. Pentadecylene Hexadecylene CibHso C16H82 4. .814 .792 4. 247. i55^t Bernthsen. Krafft, Mendelejeff, etc. Octadecylene CisHse 18. .791 18. i79^t Krafft. Eicosylene . C20H40 .871 - 390.-400. Beilstein, " Org. Chem." Cerotene . C27H64 - 58. - Bemthsen. Melene . . CsoHeo 62. * Liauid at— ii.° C. and i8o atmospheres' pressure (Cailletet). t " " + 4-° " " 46 '^ t Boiling-point under 15 mm. pressure. J In vacuo. eMITHSONIAN TABLES. 2l6 Table 214 (««/;«»«rf). DENSITIES, MELTING-POINTS, AND BOILING-POINTS OF SOME ORGANIC COMPOUNDS. Substance. Chemical formula. Temp. C. Specific gravity. Melting- point. Boiling- point. Authority. (c) Acetylene Series: C„H^_. [ Acetylene C2H2 - _ —81. -85. Villard. AUylene CsHi - - - Ethylacetylene . . . CiHe - — " •f 18. Bruylants, Kutsche- roff, and others. Propylacetylene . . . C.Hs - - - 48.-50. Bruylants, Taworski. Butylacetylene . . . CeHio - - - 68.-70. Taworski. Oenanthylidene . . . C7H12 - - - IOO.-IOI. Beilstein, and oth- Caprylidene .... CsHu 0. 0.771 .. I33--I34- ers. Behal. Undecylidene . . . . C11H20 - - 2 1 0.-2 1 5. Bruylants. Dodecylidene . . . C12H22 — 9- .810 — 9- io5.« KrafEt. Tetradecylidene . . . C14H26 + 6.S .806 + 6.5 134.* 11 Hexadecylidene . . . CieHso 20. .804 20. 160.* K Octadecylidene . . . CisHsi 30- .802 30. 184.* M (d) Monatomic ale ohols:C„H,„+,OH. | Methyl alcohol . . . CH3OH 0. 0.812 _ 66. Ethyl alcohol .... CaHjOH 0. .806 — i3o.t 78. Propyl alcohol . . . C8H,OH 0. .817 - 97- From Zander, "Lieb. Butyl alcohol .... C4H9OH 0. •823 - 117. Ann." vol. 224, p. 85, Amyl alcohol .... CsHiiOH 0. .829 - 138^ and Krafft, "Ber.'^' Hexyl alcohol . . . CsHisOH 0. •833 - 157- vol. 16, 1714, Heptyl alcohol . . . CtHisOH 0. .836 - .76. " 19, 2221, Oc^l alcohol .... C8H17OH 0. •839 - '95- " 23, 2360, Nonyl alcohol . . . C9H19OH 0. .842 — S- 213. and also Wroblew- Decyl alcohol . . . C10H21OH -I-7- •839 + 7. 231. ski and Olszewski, Dodecyl alcohol . . . C12H25OH 24. .831 24. 143-* " Monatshefte," Tetradecyl alcohol . . C14H29OH 38- .824 38. 167.* vol. 4, p. 338. Hexadecyl alcohol . . CieHssOH 50. .818 50. 190.* Octadecyl alcohol . . CisHstOH 59- .813 59- 2II,» (e) Alcoholic e thers : C„H,.+,0. Dimethyl ether . . . C2H6O - - - — 23.6 Erlenmeyer, Kreich- baumer. Regnault, Olszewski. Diethyl ether .... C4H10O 4- 0.731 — 117 + 34.6 Dipropyl ether . . . CeHiiO 0. •763 - 90.7 Zander and others. Di-iso-propyl ether . . CeHiiO 0. •743 - 69. u Di-n-butyl ether . . . CsHisO 0. .784 — 141. Lieben, Rossi, and others. Di-sec-butyl ether . . CsHisO 21. .756 - 121. Kessel. Di-iso-butyl " . . CgHjsO IS- .762 - 122. Reboul. Di-iso-amyl " . . C10H22O 0. •799 - I7O.-175. 203.-208. Wurtz. Di-sec-hexyl " . . C12H26O - - Erlenmeyer and Wanklyn. Moslinger. Di-norm-octyl " . . C10H84O '7- .805 - 280.-282. (f) Ethyl eth« rs : C„H,„+,0. j Ethyl-methyl ether . . CsHsO 0. 0.725 - It. Wurtz, Williamson. " propyl " . . C6H12O 20. 0-739 - 63.-64. Chancel, Bruhl. " iso-propyl ether . CsHiaO 0. •745 - 54- Markownikow. " norm-butyl ether CsHhO 0. .769 - 92. Lieben, Rossi. " iso-butyl ether . CeHiiO - ■ui - 78.-80. Wurtz. " iso-amyl ether C7H16O 18. - 112. Williamson and others. " norm-hexyl ether CgHiaO - - - 134.-137- Lieben, Janeczek. " norm-heptyl ether C9H20O 16. .790 - 165. Cross. " norm-octyl ether C10H22O 17- ■794 — 182.-184. Moslinger. * Boiling-point under 15 mm. pressure. t Liquid at — ii.° C. and 180 atmospheres* pressure (Cailletet), Smithsonian Tables. 217 Tabl^ 21 5. LOWERING OF FREEZING-POINTS BY SALTS IN SOLUTION. Vramm^l' J°'T" Hv,^"^" ''i* number of gramme-molecules (anhydrous) dissolved in looo W nSnf • IV the second contams the molecular lowering of the freezing-point ; the freez- Sfm^w 1 ^^^^^j;! ^^J' P'°duct of these two columns. After the chemical formila is given the molecular weight, then a reference number. Pb(N03)2,33i.o: I, J. 0.000363 .001204 .002805 .005570 •01737 •5015 Ba(NO,,).,26i.s: 0.000383 .001259 .002681 .005422 .008352 Cd(NO,)3, 236.5: 0.00298 .00689 .01997 .04873 AbNOs, 167.0: 4, 0.1506 .5001 .8645 1-749 3.856 0.0560 .1401 ■3490 KN03, IOI.9 0.0100 .0200 .0500 .100 .200 .250 .500 •75° 1. 000 NaNOj, 85.09 : O.OIOO .0250 .0500 .2000 .500 •5015 1. 000 1.0030 NHiNOs, 80.11 O.OIOO .0250 6,7. 5-S° S-30 S-I7 +97 -ll 4.69 2.99 5-28 S-23 S-I3 5.04 5.18 S-iS ' 3-32' 2.96 2.87 2.27 1.8s 1.64 3.82 3-58 3-28 3-5 3-5 3-41 3-3' 3-19 3-08 2.94 2.81 2.66 J46 3-44 3-345 3-24 3-30 3-15 3-03 6,8. 3-6° 3-5° 0.0500 .1000 .2000 .500 1. 000 UNO,, 60.07: 9- 0.0398 .1671 .4728 I.0164 AIs(SO,)s, 343.4 : 0.0131 .0261 •0543 .1086 .217 CdSO,, 208.5 : i> 0.000704 .002685 .01151 .03120 •1473 .4129 •7501 1-253 KjSO,, 174-4: 3. 5 0.00200 .00398 .00865 .0200 .0500 .1000 .200 ■454 CuSOj, 159.7 : 0.000286 .000843 .002279 .006670 .01463 .1051 .2074 -4043 3-47' 3-42 3-32 3.26 3-14 3-4° 3-35 3-35 3-49 O. 5-6° 4-9 4-5 4-03 3-83 3-35' 3-05 2.69 2.42 2.13 1.80 1.76 1.86 , 6, 10, 12. 5-4° S-3 4.9 4.76 4.60 4-32 4.07 3-87 , II. 3-3° 3-15 3-03 2-79 2.59 2.28 1.95 1.84 1.76 MgSO,, 1S0.4 : I, 4, 11. 0.000675 3-29 .002381 3-10 .01263 2.72 .0580 2.65 .2104 2.23 0.4978 .8112 1-5233 BaCIo, 208.3 : 0.00200 .00498 .0100 .0200 .04805 .100 .200 .500 .586 •750 CdCIj, 183.3: 0.00299 .00690 .0200 .0541 .0818 .214 .429 .858 1.072 CuClj, 134.5: 0.0350 -1337 -3380 .7149 C0CI2, 129.9 '■ 0.0276 .1094 .2369 -4399 -538 CaClj, iii.o: O.OIOO .05028 .1006 .5077 .946 2.432 3-469 3.829 0.0478 •153 •331 .612 .998 2.02' 2.01 2.28 3i6, 13. 5-5° 5.2 5.0 4-95 4.80 4.69 4.66 4.82 5-03 5.21 3>I4- 4.8 4.64 4.11 3-93 3-39 3-03 2-71 2-75 9- 4.9° 4.81 4.92 S-32 '■ 5-0- 4-9 5-03 S-30 5-5 5. 13-16. H° 4-85 4-79 5-33 tl 11.5 14.4 5-2 4.91 S-15 5-47 6-34 MgCli, 95.26 : 6, O.OIOO .0500 .1500 .3000 .6099 KCl, 74.60: 9, 17- 0.02910 •05845 .112 ■3139 .476 I.OOO 1.989 3.269 NaCl, 58.50 : 3, 20, 0.00399 .01000 .0221 .04949 .1081 •2325 •4293 .700 NH4CI, 53-52 : 6, O.OIOO .0200 .0350 .1000 .2000 .4000 .7000 LiCl, 42.48: 9, 15, 0.00992 .0455 .09952 .2474 .5012 •7939 BaBrj, 297.3 O.I 00 .150 .200 .500 AlBrj, 267.0 0.0078 •0559 .1971 •4355 14. ; 9. 14. i< 4.98 4-96 5-186 S-69 ■19. 3-54° 3-46 3-43 3-41 3-37 3.286 3-25 3-25 I, 12, 16. 367 3-55 3-5i 3-48 3-42 3-37 3-43 ■'3.6° 356 3-50 3-43, 3-396 3-393 3-41 3-7° 3-5 3-53 3-50 3.61 3-71 5-1° 4-9 5.00 S-18 1-4° 1.2 1.07 1.07 1 Hausrath, Ann. Phys. 9, 1902. 2 Leblanc-Noves, Z. Phys. Ch. 6, 1890. 3 Jones, Z. Phys. Ch. 11, 1893- 4 Raoult, Z. Ph^. Ch. 2, 1888. 5 Arrhenius, Z. Phys. Ch. 2, 1888. 6 Loomis, Wied. Ann. 57, 1S96. 7 Jones, Am. Chem. J. 27, 1902. S Jones-Caldwell, Am. Chem. J. 5, 1901. 9 Biltz, Z. Phys. Ch. 40, ,1902. 10 Jones-Mackay, Am. Chem. J. 19, '89I: Compiled from Landolt-Bomstem SMITHSONrAN TABLES. 11 Kahlenberg, J. Phys. Ch. 5, 1901. 12 Abegg, Z. Phys. Ch. 20, 1896. 13 Jones-Getman, Am. Ch. J. 27, igo2. 14 Jones-Chambers, Am. Ch. J. 23, 1900, 15 Loomis, Wied. Ann. 60, 1897. x6 Roozeboom, Z. Phys. Ch. 4, 1889. 17 Raoult, Z. Phys. Ch. 27, 1898. 18 Roloff, Z. Phys. Ch. 18, 1895. 19 Kistiakowsky, Z. Phys. Ch. 6, 1890. 20 Loomis, Wied. Ann. 51, 1894. ■MeyerhoSer's Physikalisch-chemische Tabellen. 21 8 Table 215 («»/m«^. LOWERING OF FREEZING-POINTS BY SALTS IN SOLUTION (coniimtdi. R ^ «i S" »«■ g. mol. ^1 g. mol. 3.£ g. mol. 3'2 •si g. mol. icxK) g. HjO 1000 g. H2O 1000 g. HjO 1000 g. H2O Sj S3 ShJ S,j CdBr2, 272.3 : 3. I 4- KOH, 56.16: 1,1 5' '3; „ Na^SiOs, 122.5 : i K r. 0.472 2.20° 0.00324 5.1° 0.00352 3^6o° 0.01052 HI •944 ^■2 .00718 4.6 .00770 3^59 •05239 .1048 5.86 1.620 2.60 .03627 3^84 .02002 3-44 ^i! (COOH)2,go.oa: 4.15- .0719 3-39 .05006 3-43 .2099 4.66 0.01002 3-3° .1122 3^i8 .1001 342 •5233 3^99 .02005 3-I9 .220 2.96 .2003 3^424 HCl, 36.46 : .05019 3-03 .440 2.76 -230 3^S° 1-3. 6, 13 l8, 22. .1006 2.83 .800 2.59 .465 3^57 0.00305 3-^° .2022 2.64 CuBfj, 223.5 : 9^ CH3OH, 32.03 : 24, IS- .00695 3.66 3^6 .366 2.56 0.0242 S-i° O.OIOO 1.8° .0100 .648 2-3 .0817 .2255 5^27 .0301 .2018 1.82 1.811 .01703 .0500 3-59 3-5? 3^56 C,Hs(OH)„ 92.06 0.0200 \':ii^ .6003 5.89 1.046 1.86 .1025 .1008 1.86 CaBr^, 200.0: 14. 0.0871 K 341 6.200 1.88 1.944 .2000 .3000 .464 .516 1.003 1.032 1.500 3^57 3.612 3.68 3-79 3^95 4.10 4.42 •2031 •535 1.8s 1.91 .1742 S.18 CjHjOH, 46.04: 2.40 1.98 •3484 .5226 MgBr,, 184.28: I 5.64 •• I, 13, 17 0.000402 .004993 .0100 1.67° 1.67 1.81 5.24 (C2Hb)2O,74^08: O.OIOO 2.13 n.6o 0.0517 .103 .207 •517 S.16 5.26 .02892 .0705 .1292 .2024 1.707 1.8s 1.829 1.832 2.000 2.1 1 5 3.000 3°53 4^97 4.52 6.03 4.90 .0201 .1011 .2038 Dextrose, 180.1 : 1.67 1.72 1.702 KBr, iig.x : 9, 21. ■5252 1.834 4.065 5^67 0.0198 1.84" 0.0305 3.61° i.o8gi 1.826 4-657 6.19 .0470 1.85 .1850 3-49 1.760 1.83 HNO„ 63.05 : 3, 1 3i JS- .1326 1.87 .6801 3-3? 3-78 3.901 1.92 0.02004 3-55° .4076 1.894 .250 7.91 2.02 .05015 3-50 1.102 1.921 .500 3-30 II. II 2.12 .0510 J7I Levulose, 180.1 : »4. 25- Cdl,, 366.1 : 3, 5, 12. 18.76 1.81 .1004 348 0.0201 1.87° 0.00210 .00626 4-5° 0.0173 1.80 .1059 3-53 .2050 1.871 4.0 .0778 1.79 .2015 3-45 •554 2.01 .02062 .04857 3-S2 KjC03, 138.30:6. .250 3-50 1.384 2.32 2.70 O.OIOO S^i° .500 3.62 2.77 3-04 .1360 2^35 .0200 4-93 1. 000 3.80 CHO, 342.2 : I, 24 ,26. !888 2.13 .0500 4.71 2.000 4.17 0.000332 1.90° 2.23 .100 4^54 3.000 4.64 .001410 1.87 2.51 .200 4^39 HjPOj, 66.0: 29. .009978 1.86 KI, 166.0: 9,1. Na^CO,, 106.10: 6. 1 0.1260 2.90° .0201 1.88 0.0651 .2782 .6030 3^5° O.OIOO S^'° .2542 2-75 •1305 1.88 3-5° 3-42 .0200 .0500 4-93 4.64 .5171 1.07 1 2.59 2.45 H2SO,, 98.08 : 13, 20, 31-33- 1.003 3^37 .1000 4.42 HPO, 820: 4,5. 0.00461 4.8° Srij, 341.3: 22. .2000 4.17 0.0745 3.0" .0100 4^49 0.054 S-^° NaoSOj, 126.2 : 28 .1241 2.8 .0200 4^32 .108 5.2 0.1044 4.51° .2482 2.6 .0461 4.10 .216 5-35 ■3397 3-74 1.00 2-39 .100 3f •327 S^S2 .7080 3^38 H3PO.,98.o:6, 22. .200 igs NaOH, 40.06 : 15 NajHPOi, 142.1: 22, 29. O.OIOO 2.8° .400 0.02002 3-45° O.OIOO! 5-2° .0200 2.68 1.000 4.19 .05005 3-45 .02003 .05008 4.84 .0500 2.49 1.500 4.96 .lOOI 341 4.60 .1000 2.36 2.000 s-65 .2000 3-407 .1002 4^34 .2000 2.25 2.500 6.S3 1-20 See^ 21 Sherril 22 Chambers-Frazer, Am.'Ch.' JT 23, 23 Noyes-Whitney, Z. Phys. Ch. 15, page 217. 11, Z. Phys. Ch. 43, 1903. 1900. .894. 24 Loomis, Z. Phys. Ch. 32, 1900. 25 Abegg, Z. Phys. Ch. ij, 1894. 25 Nernst-Abegg, Z. Phys. Ch. 15, 1894. Smithsonian Tables. 27 Pictet-Altschul, Z. Phys. Ch. 16, 1895. 28 Earth, Z. Phys. Ch. 9, 1892. 29 Petersen, Z. Phys. Ch. 11, 1893. 30 Roth, Z. Phys. Ch. 43, 1903. 31 Wildermann, Z. Phys. Ch. 15, 1894. 32 Jones-Carroll, Am. Ch. J. 28, 1902. 33 Jones-Murray, Am. Ch. J. 30, 1903. Table 216. 2IQ RISE OF BOILING-POINT PRODUCED BY SALTS DISSOLVED IN WATER.* ^"boiltL^oh" by'theTmount smtTfn .1'^' ?" ''"?''L'''i?S ''■="''™* '" loogrammes of ,.ater, will raise the centiletres. '^ headings of the different columns. Ae pressure is supposed to be ,6 Salt. 1°C. 2° 30 40 6° 7° 10° 16° 20° 25° BaClj + zHaO . CaCl2 Ca(N08)2 + 2H2O . ICOH 6.0 12.0 31-1 47-3 16.5 39-5 18.0 63-5 (71-6 gives 4= .5 rise of temp.) "•5 25-S 21.0 S3S ^'5 32.0 lOI.O 41-5 152.5 55-5 240.0 6g.o 331-5 84-5 443-5 KC2H3O2 . 4-7 6.0 9-3 12.0 17.4 24.5 20.S 31-0 26.4 44.0 r,i 47-0 98.0 57-5 134.0 67.3 171.5 KCl . . . . K2CO3 . . . KCIOa . . . KI . . . KNOs 9.2 16.7 23-4 29.9 36.2 48.4 (57-4 gives a rise of 8°.i;) 1 1 ii-S 13-2 22.5 27.8 32.0 44.6 r. 47-5 60.5 78.5 103.5 127.5 152-5 15.0 15.2 30.0 31-0 45.0 47-S 60.0 64.5 74.0 82.0 99-5 120.5 i88'.5 185.0 338.5 (220 gives i8°.5) KaCiHiOs + iHaO . 18.0 36.0 54.0 72.0 90.0 126.5 182.0 284.0 KNaC4H406 KNaC4H406 + 4H20 LiCl + 2H2O '. '. 17-3 25.0 34-S S3-S 84.0 68.1 1 18.0 84.8 157.0 1 1 9.0 266.0 171.0 554-0 272.5 5510.0 390.0 510.0 il 7.0 13.0 1 0.0 19.5 12.S 26.0 15.0 32.0 20.0 44-0 26.0 62.0 35-0 92.0 42.5 123.0 50.0 160.5 MgCla + eHaO . n.o 22.0 33-0 44.0 55-0 77.0 1 1 0.0 170.0 241.0 334-5 MgS04 + 7H20 41-5 87.S 138.0 196.0 262.0 NaOH 4-3 8.0 "■3 143 17.0 22.4 30.0 41.0 51.0 60.1 NaCl .... 6.6 12.4 17.2 21.5 25-5 (40.7 ; jives 8° 8 rise) NaNOg 9.0 18.5 28.0 38.0 48.0 68.0 99-5 156.0 222.0 NaC2H302 + 3H2O . 14.9 30.0 46.1 62.5 79-7 118.1 194.0 480.0 6250.0 NajSaOs . 14.0 27.0 39-0 59.0 »5-3 77.0 104.0 152.0 214-5 311.0 NaaHPOi . 17.2 34-4 Si-4 68.4 NaaCiHiOe + 2H2O . 21.4 44.4 68.2 93-9 121.3 183.0 (237-; gives 8°.4 rise) || Na2S208 + 5H2O . 23.8 50.0 78.6 108. 1 139-3 216.0 400.0 1765.0 NaaCOs + 10H2O . 34-1 86.7 177.6 369.4 1052.9 NasBiO, + 10H2O . 39- 93-2 254.2 898.5 (5555-5 gives 4°. 5 rise) NH4CI 6.5 12.8 19.0 24.7 29.7 39-6 56.2 88.5 NH4NO3 . 1 0.0 20.0 30.0 41.0 52.0 74.0 108.0 172.0 248.0 337-0 NH4SO4 . 15.4 30.1 44.2 58.0 71.8 99-1 (115.3 gives ^ 108.2) SrC!2 + 6H2O . 20.0 40.0 60.0 81.0 103.0 150.0 234.0 524.0 Sr(N03)2 . . . 24.0 45.0 63.6 81.4 97-6 C4H6O6 . . . 17.0 34-4 52.0 70.0 87.0 123-0 177.0 272.0 374-0 484.0 C2H2O4 + 2H2O 19.0 40.0 62.0 86.0 1 1 2.0 169.0 262.0 540.0 1316.0 50000.0 CeHgOr + H2O 29.0 58.0 87.0 1 1 6.0 145.0 208.0 320.0 553-0 952.0 Salt. 40° 60° 80° 100° 120° 140° 160° 180° 200° 240° CaCl2 . 137- 5 222.0 314.0 KOH . 92. 5 I2I.7 152.6 185.0 219.8 263.1 312. 5 375- 444. t 623.0 NaOH 93- 5 150-8 230.0 345-0 526.3 800.0 1333- 3 2353. 6452. D NH4NO3 . 682.( 3 1370.0 2400.0 4099.0 8547-0 00 CiHeOs 980.C 3 3774-0 ( infinity gives 170) * Compiled from a paper by Gerlach, " Zeit. f. Anal. Chem." vol. 26. Smithsonian Tables. 220 Table 217. FREEZING mixtures: Column I gives the name of the principal refrigerating substance* j4 the proportion of that substance, B the propor- tion of a second substance named in the column, C the proportion of a third substance, D the temperature of the substances before mixture, E the temperature of the mixture, ^the lowering of temperature, G the temjierature when all snow is melted, when snow is used, and H the amount of heat absorbed in heat units (small calories when A is grammes). Temperatures are in Centigrade degrees. Substance. A B C D £ jr G H NaCaHsOa (cryst.) 85 HjO-ioo _ 10.7 — 47 18.4 ^ _ NH4CI . 30 (( (( - 13-3 — S-i - ~ NaNOs . 75 (( u - 13.2 -1:1 18.5 - ~ NaaSaOj (cryst.) . no tt tt - 10.7 18.7 - - KI. 140 it U - 10.8 — 11.7 22.5 - — CaCl2 (cryst.) 250 u tt - 10.8 —12.4 23.2 - - NHiNO, . 60 tt tt - 13.6 -13.6 27.2 - _ (NH4)2S04 . . 25 " so NH4NOS-2S 26.0 - - NHiCl . 25 tt tt It tt - - 22.0 - - CaCla . 25 it tt tt tt - - 20.0 - _ KNOs . 25 (( i( NH4CI-2S - - 20.0 - - NasSOi 25 " " tt tt - - 19.0 - - NaNOs. 25 (( tt It tt - - 17.0 - - KjSOi . to Snow 100 - — I —1.9 0.9 - NaaCOa (cryst.) . 20 (1 i( - — I — 2.0 I.O - - KNO, . . . 13 (( it - — I —2.85 1.8s - - CaCls . 30 ft tt - — I — 10.9 9-9 - - NH4CI . 25 ti (( - — I —15-4 14.4 - - NH4NO3 45 (( tt - — I — 16.75 15-75 - - NaNOs . 50 it tt - — I —17-75 16.75 - - NaCl . 33 It tt - — I —21.3 20.3 - - I '• 1-097 - — I — 37-0 36.0 -37-0 0.0 I " 1.26 - — I — 36.0 3S-0 — 30.2 17.0 H2SO4+H2O I " 1.38 - — I — 35-° 34-0 — 25.0 27.0 {66.i%H2S04) I t ** 2.52 " 432 - — I — 30.0 — 25.0 29.0 24.0 — 12.4 — 7.0 133-0 273.0 I " ?-92 — — I — 20.0 19.0 -3-1 553-0 I " 13.08 - — I — 16.0 15.0 — 2.1 967.0 I " 0.35 - - 0.0 52-1 I " .49 — - - — 19.7 49-5 I " .61 — — — — 39-0 40-3 CaCIa + 6H20 I I " .81 _ _ : — 54-9t — 40-3 30.0 46.8 I 1 " 1-23 " 2.46 : : _ -21.5 — 9.0 88.5 192.3 I " 4.92 — - - — 4.0 392-3 Alcohol at 4° 77 " 73 CO2 solid ~ —30.0 — 72.0 ~ - Chloroform . - u u - _ —77.0 _ _ _ Ether . - tl tt _ _ — 77.0 _ ^ — Liquid SO2 . - tt tt - - —82.0 - _ _ H20-.7S - 20 5.0 - - 33-0 " -94 — 20 — 4-0 — — 21.0 tt tt - 10 — 4.0 - - 34-0 Snow " _ 5 — 4.0 — 4.0 _ ~ 40.5 122.2 NH4NOS . H20-I.20 - 10 — 14.0 _ _ 17.9 129.5 Snow " - — 14.0 - _ H20-I.3I - 10 -17-St - _ 10.6 Snow " - -I7-St - _ 131-9 H20-3.6I - 10 — 8.0 _ _ 0.4 Snow " ■ — 8.0 — — 327-0 * Compiled from the results of OuIIetet and Colardeau, Hammerl, Hanamann, Moritz, Pfanndler, Rudorf, and Zollinger. ' t Lowest temperature obtained. Smithsonian Tables. Table 218. 221 CRITICAL TEMPERATURES, PRESSURES, VOLUMES, AND [DENSITIES OF GASES.* * = Critical temperature. P = Pressure in atmospheres. ^= Volume referred to air at o" and 76 centimetres pressure. '^ = density m grammes per cubic centimetre. Substance. Air . Alcohol (CzHeO) " (CH4O) Ammonia . Argon Benzol Bromine Carbon dioxide . " monoxide " disulphide Chloroform Chlorine Ether Ethane Ethylene Helium Hydrogen Krypton Methane chloride sulphide Neon . Nitric oxide (NO) Nitrogen . " monoxide Oxygen Sulphur dioxide Water (N2O) — 140.0 243.6 237-9 23995 130.0 — 121.0 288.5 302.2 30.92 — 141.1 2777 260.0 141.0 146.0 197.0 194.4 3S-0 9.2 13-0 <— 264.0 —234-5 51.25 52.3 1 00.0 —62.5 —81.8 —99-5 <— 205.0 —93-5 — 146.0 35-4 — nS.o 155-4 358-1 364-3 39-0 62.76 78.5 115.0 50.6 47-9 77 35-9 78.1 54-9 83-9 35-77 35-61 45.2 58.0 20.0 86.0 86.0 88.7 54-3 54-9 50.0 71.2 35-0 75-0 50.0 78.9 194.6 0.00713 0.0098 1 0.00605 0.0066 o.oi 584 0.01344 0.00569 0.0048 0.00587 0.001874 0.00386 0.288 1-5 0.305 1.18 0.208 0.262 0.61 0.44 0.41 0.6044 0.49 0.429 Observer, Olszewski. Ramsay-Young. Mean of ten. Young. Dewar. Olszewski. Young. Nadejdine. Andrews. Wroblewski. Hannay. Sajotschewsky. Dewar. Knietsch. Battelli. Young. Dewar. Van der Waals. Cailletet. Dewar. Dewar. Ansdell. Dewar. Olszewski. Ramsey-Travers. Olszewski. Dewar. Ramsey-Travers. Olszewski. It Dewar, Cailletet. Wroblewski. Sajotschewsky, Cailletet. Nadejdine. Batelli. Andrews, Trans. Roy. Soc. 166, 1876. Ansdell, Chem. News, 41, 1880. Batelli, Mem. Torino (2), 41, 1890. Cailletet, C. R. 85, 1877 ; C. R. 94, 1882. Dewar, Phil. Mag. 18, 1884 j Ch. News, 84, igoi. Hannay, Pr. Roy. Soc. 32, 1882. Knietsch, Lieb. Ann. 259, 1890. Nadejdine, Beibl. 9, 1885. Olszewski, C. R. 98, 1884 ; 99, 1884 j 100, 1885 ; Beibl. 14, 1890; Z. Phys. Ch. 16, 1893. Ramsay- Young, Tr. Roy. Soc. 177, 1886. Sajotschewsky, Beibl. 3, 1879. Van der Waals, Beibl. 4, 1880. Wroblewski, Wied. Ann. 20, 1883 j Stz. Wien. Ak. 91, 1885. Young, Phil. Mag. 1900. * Abridged for the most part from Landolt and Bonutein's " Fhys..Chem. Tab." Smithsonian Tables. 222 Table 219. COEFFICIENTS OF THERMAL EXPANSION. OoefUclents ol Linear Ezianslon ol tlie Gbemloal Elements. In the heading of the columns 7" is the temperature or range of temperature; C is the coefficient of linear expansion ; Ai is the authority for C; Mis the mean coefficient of expansion between o° and 100° C. ; a and $ are the coefficients in the equation /( = /o (i + «' + P'^)i where /o is the length at 0° C. and /,the length at ^ C. ; A2 is the authority for o, j8, and m. Substance. T CXio« At ATX 10* a X lo» pXio« Ai Aluminum .... 40 0.2313 0.2220 - - z "..... 600 •3' 5° ** . . — 191 to +16 •183s - •23536 .00707 S Antimony : Parallel to cryst. axi.s . 40 .1692 Perp. to axis 40 .0882 Mean 40 .1152 .1056 .0923 .0132 6 Arsenic 40 ■0559 Bismuth : Parallel to axis . 40 .1621 Perp. to axis 40 .1208 Mean 40 .1346 .1316 .1167 .0149 6 Cadmium .... 40 .3069 •3159 .2693 .0466 6 Carbon : Diamond .... 40 .0118 Gas carbon .... 40 .0540 Graphite .... 40 .0786 Anthracite .... 40 .2078 Cobalt 40 .1236 Copper 40 .1678 .1666 .J481 .0185 6 « — 191 to +16 .1409 - .16070 .00403 5 Gold '.'.'.'.'. 40 ■1443 .1470 •1358 .0112 6 Indium 40 .4170 Iron : Soft 40 .1210 Cast 40 — 191 to +16 .1061 .0850 Wrought ! ! '. . — 18 to 100 .1140 .11705 .005254 .008336 8 Steel 40 .1322 - ■09173 8 " annealed 40 .1095 .1089 .1038 .0052 9 Lead 40 .2924 .2709 .0273 .0074 6 Magnesium . . . . 40 .2694 Nickel 40 .1279 - .13460 •00331 s 8 « — 191 to +16 .1012 Osmium 40 .0657 Palladium . . . . 40 .1176 - .11670 .002187 8 Phosphorus , . . . 0-40 1.2530 0.0899 Platinum 40 - .08868 .001324 8 Potassium . . . . 0-50 .8300 .0850 Rhodium . . . . 40 Ruthenium . . , . 40 .0960 Selenium 40 .3680 .6604 - - 12 Silicon 40 .0763 Silver 40 .1921 - .18270 .004793 8 u — 191 to +16 .1704 Sulphur : Cryst. mean . . . . 40 .6413 1.180 - - 12 Tellurium . . , . 40 •1675 •3687 - - 12 Thallium . . . . 40 .3021 Tin 40 .2234 .2296 •2033 .0263 6 Zinc 40 .2918 .2976 .2741 .0234 6 I Fizeau. 4 h enning. 7 Andrews. 10 Fisati and De 2 Calvert, Johnson 5 T ittenberger. 8 Holbom-Day. Franchis. and Lowe. 6 ^ latthiessen. 9 Benoit. II Hagen. 3 Chatelier. 12 Spring. The above table has been partly compiled from the results published by Fizeau, " Comptes Rendus," vol. 68, and Matthiessen, " Proc. Roy. Soc," vol. 15, The Holbom-Day data are for temperatures from 20° to looo" C. The Dittenberger, 0° to 600° C. Smithsonian Tables, Table 220. COEFFICIENTS OF THERMAL EXPANSION. OoeUiolents of Llneai Ezpanilon loi Hlscellaneons Substances. 223 The coe£&cient of cubical expansion may be taken as three times the linear coefficient. T is the temperature or range of temperature, C the coefficient of expansioDi and A the authority. Substance. T^C. CXio« A. II Substance. roc. CXio* A. Brass : Platinum-silver : Cast . O-IOO 0.1875 I lPt-|-2Ag 0-100 0.1523 4 Wire . ^^ 0.1930 I Porcelain 20-790 0.0413 19 — ... u 1783-193 2 " Bayeux . 1000-1400 0-0553 20 7i.5Cu+27.7Zn+ Quartz : o.3Sn+o.sPb 40 0.1859 3 Parallel to axis . 0-80 0.0797 6 7lCu-f-29Zn O-IOO 0.1906 / (( (1 i( — i90to-|-i6 0.1070 21 Bronze : Perpend." " '. 0-80 0.1337 6 SCu+iSn . I6.6-IOO 0.1844 5 Quartz glass . — i90to-)-i6 —.0026 13 « « 16.6-350 0.21 16 1 Rock salt 40 0.4040 3 tl u 16.6-957 0-1737 5 Speculum metal O-IOO 0.1933 I 86.3Cu+9.7Sn+ ' Topaz: 4Zn 40 0.1782 3 Parallel to lesser 97.6CU+ 2.2Sn+ (hard { soft 0-80 0.1713 t 0.1708 t horizontal axis Parallel to greater It 0.0832 8 0.2P horizontal axis <( 0.0836 8 Caoutchouc . _ .657-.686 2 Parallel to verti- 99.8 •37335 It Carbon monoxide . 76. •3669 3 " o°-ioo'= 99.8 .37262 (« Nitrous oxide 76. ■3719 (1 " o°-ioo= 1 00.0 .37248 5 Sulphur dioxide , 76. ■3903 4( Carbon monoxide 76. •36667 3 II (1 98. •3980 « Helium . 56.7 •366s ■3328 4 ro°-ii9° 76. .4187 10 Hydrogen i6°-i32' .0077 6 Water- o°-i4i° 76. .4189 li " I5°-I32' .025 •3623 o''-i62<' 76. .4071 (1 i2''-i8s= •47 ■3656 II vapor 0°-200° 76. ■3938 (( (( •93 .37002 I lo°-247° 76. ■3799 (( U II. 2 .36548 " it 76.4 .36504 it " ' o°-ioo' ' lOO.O .36626 2 Thomson has given, Encyc. BriL " Heat," Nitrogen I3°-I32' ' .06 .3021 6 the following for the calculation of the ex- :: 9°-i33' ■53 .3290 " pansion, E, between 0° and 100° C. Expansion " 0°-20° 100.2 •36754 2 is to be taken as the change of volume under " qO-IOO" ' 100.2 •36744 .36682 .4161 .3984 :36683 " constant pressure : Oxygen Ii''-i32'' Q°-I32'' I 10-132° II 76. .007 .25 .51 1.9 18.5 I it Hydrogen, E = .3662(1 — .00049^/1/), Air, .£ = .3662(1 — .0026 Vfv), Oxygen, £ = .3662(1 — .0032 V /v). 8 Nitrogen, £^.3662(1 — .0031 V/v), II tt COj £ = .3662(1 — .0164 V/v). II 75.9 "36681 tt V/v is the ratio of the actual density of the Nitrous oxide . 76 •3676 3 gas at 0° C to what it would have at 0° C and Sulpli'r dioxide SO 2 76. •3845 u 1 Atm. pressure. I Meleander, Wie d. Beibl. 14, i 890; Wi ed. 5 Chappuis, Arch. sc. phys. (3), 18, 1892. Ann. 47, 1892 6 Baly-Ramsay, Phil. Mag. (5), 38, 1894. 2 Chappuis, Trav Mem. Bur. I ntem. V J\a. 7 Andrews, Proc. Roy. Soc. 24, 1876. Meas. 13, 190 3- 8 Meleander, Acta Soc. Fenn. 19, 1891. 3 Regnault, Ann. chim. phys. (3 )S. '842 9 Amagat, C. R. 11 1, 1890. 4 Keunen-Randal 1, Proc. R. So c. 59, 18 96. 10 Hirn, Theorie mec. chaleur, 1862. Smithsonian Tables. Tables 224-226. MECHANICAL EQUIVALENT OF HEAT. TABLE 224. — Snnunuy. Taken from J. S. Ames, L'^quivalent m^canique de la chaleur, Rapports present^s mternational du physique, Paris, 1900. 227 au congr&s Name. Joule . Rowland Reynolds-Morby . Griffiths Schuster-Gannon Callendar-Barnes Method. Mechanical Mechanical Mechanical Electrical E2t . R Scale. Latimer-Clark = i. 4342V at 15° C. International Ohm i Latimer-Clark := 1.4340V. at 15° } C, Elec. Cham. Equiv. Silver > ^o.ooiii8g ) Electrical Eit. I Latimer-Clark = 1.4342V. at 15° C. Result. 4-173 4- 19s 4.187 4.181 4.176 4.1832 4.198 4.192 4.187 4.190S 4.179 Temp. °C. 16.S 10. «S- 20, 25- Mean- calory. 15- 20. 25. 19.1 40. TABLE 225. — Reduced to aramme-Galory at 20° 0. (Nitrogen thermometer). Joule . 4.169 X 10' ergs • 4.169 X 10' ergs. Rowland 4.181 " " 4.181 " " Griffiths 4.192 " " 4.184 " " Schuster-Gannon . 4.189 " « 4.181 " " Callendar-Bames . 4.186 « " 4.178 •' " * Admitting an error of i part per rooo in the electrical scale. The mean of the last four then gives 1 smaU (20<=> 0.) oaloiy = 4.181 X lo? ergs. TABLE 226. — Oonverslon Factors for Units of Worlc. Joules Watts per sec. Volt-amp. per sec. Small 20" Calories. Ei-gs. Kilo- gramme- metres. Foot-poundals. Foot-pounds. I joule = I watt per second I small 20° cal- ory = I erg = I kilog.-metre ^= I foot-poundal = I foot-pound = I 4.181 I0-' g .04214 .042i4g 0.2392 I 0.2392 X 10-' 0.2392g .01008 .oiooSg lo' 4.181 X 10' I gXio' 421400. 42i400g I E 4. 181 g 10-' g I .a^^■n g .04214 23-73 99.22 23-73 X 10-' 23-73g I g 23-73 E 99-22 g 23:13 X 10-' 23-73 g I Smithsqnian Tables. 228 Table 227. SPECIFIC HEAT OF THE CHEMICAL ELEMENTS. Element. Range • of Temperature, °C. Specific heat. •Si S i2S Element. Range * of Temperature, S;>eci£c Aluminum —250 0.1428 1 Iodine 9-98 0.0541 25 " .2089 " Iridium . —186- +18 .0282 26 " 100 .2226 It " 18-100 ■0323 " u 250 .2382 " Iron, cast t 20-100 .1189 'I tl 500 •2739 ti " wrought . 15-100 '"9^ 28 tl 16-100 .2122 43 4( tl 1000-1200 tt Antimony IS .0489 2 " " 500 .176 tt (( 100 .0503 " " hard-drawn 0-18 .0986 29 (( 200 .0520 " tt 14 11 20-100 .1146 tt Arsenic, gray . 0-100 .0822 3 U —185- +20 .0958 4 black . O-IOO .0861 Lanthanum 0-100 .0448 «5 Barium —185- +20 .068 4 Lead 15 .0299 2 Bismuth —186 .0284 " ■ > 100 .0311 " K •0301 6 (( 300 ■0338 tt (1 75 .0309 •' " 'fluid '. to 310 .0356 3° It 20-100 .0302 7 " *' . " 360 .0410 (t " fluid . 280-380 •0363 8 tt 18-100 .03096 43 Boron O-IOO •3°7 9 tt 16-256 .03191 tt Bromine, solid . —78 — 20 .0843 10 Lithium . — 100 •5997 31 fluid . '3-45 .107 11 11 •795' ti Cadmium . 21 .0551 2 tt 50 tt ** 100 .0570 tl tt 100 1.0407 tt n 200 .0594 " tt 190 1-3745 tt " 300 .0617 " Magnesium —185- +20 0.222 4 Caesium 0-26 .0482 12 «i 60 •2492 7 Calcium —185—1-20 ■»57 4 tt 325 •323s 41 (( 0-181 .170 >3 tt 625 •4352 tt Carbon, graphite —50 ■ 114 14 t( 20-100 .2492 tt K (( +11 .160 Manganese 60 .1211 it l( (( 977 •467 ti «i 325 •1783 tl " diamonc -50 .0635 tt 20-100 .1211 '* 11 (( +11 •"3 tt a — 100 .0979 31 (( u 98s •459 tt it .1072 II Cerium O-IOO .0448 15 " 100 •1143 II Chlorine, liquid 0-24 .2262 16 Mercury . — 185-+20 .032 4 Chromium — 200 .0666 17 tl •03346 32 it .1039 tt (( 85 .0328 it it 100 .1121 tt tt 100 .03284 2 tt 600 .1872 tt tt 250 .03212 II tl —185- +20 .086 4 Molybdenum . —185- +20 .062 4 Cobalt 500 .1452 18 (( 60 .0647 7 it 1000 .204 (( " 475 .0750 II H — T82-+I5 .0822 19 (( 20-100 .0647 i« it 15-100 .1030 Nickel '. '. —185- +20 .092 4 Copper 17 .0924 2 tl 100 .1128 18 ti too .0942 (( tt 300 .1403 it ft 15-238 .09510 43 tt 500 .1299 tt " 900 .1259 20 tt 1000 .1608 tt u —181- +13 .0868 21 tt 18-100 .109 26 « 23-100 .0940 tt Osmium . 19-98 .0311 10 Gallium, liquid . to 113 .080 22 Palladium . — 186— fi8 .0528 26 solid . 12-23 .079 22 (1 O-IOO .0592 24 Germanium 0-100 •0737 23 tl 0-1265 .0714 It Gold . —185- +20 •033^ 4 Phosphorus, red 0-51 .1829 33 " . O-IOO .0316 24 " yellow 13-36 .202 II Indium O-IOO .0570 13 tl ' tt —186- -1-20 .178 4 See opposite page for References. * Where one temperature alone is given, the " tme " specific heat is given ; otherwise, the " mean " specific heat t See Appendix. Tables 334-335. Smithsonian Tables. Tables 227 (c902! Phys. Rev. 15, r902; 16, 1903. (H thermometer.) Rowland's as revised by Pemet. (H thermometer.) Bames-Regnault's as revised by Peabody ; Steam Tables. The mercury data from 0° C to 80, Bames-Cooke (H thermometer) ; from 90° to 140, mean of Winklemann, Nac- cari and MUthaler (air thermometer) ; above 140°, mean of Naccari and Milthaler. Smithsonian Tables. 230 Tables 229-230. TABLE 22a.-SpeoUlo Heat ol Vulona SoUda.* SoUd. Alloys : Bell metal Brass, red " yellow 80 Cu-f-20 Sn 88.7 Cu+11.3 Al German silver Lipowitz alloy: 24.97 Pb + '0.13 Cd + 50.66 Bi -I-14.24 Sn . . . . ft (( Rose's alloy : 27.5 Pb+48.9 Bi+23.6 Sn Wood's alloy: 25.85 Pb + 6.99 Cd + 52.43 Bi + 14-73 Sn " " (fluid) Miscellaneous alloys : 17.5 Sb+29.9 Bi4-i8.7 Zn+33.9 Sn . . . 37.1 Sb4-62.9 Pb 39.9 Pb-l-60.1 Bi " (fluid) 637 Pb+36.3 Sn 46.7 Pb+53.3 Sn 63.8 Bi+36.2 Sn 46.9 Bi+53.1 Sn Gas coal Glass, normal thermometer 16™ " French hard thermometer .... " crown " flint Ice it India rubber (Para) Paraffin It " fluid .' . Vulcanite Temperature 15-98 o o 14-98 20-100 o-ioo 5-50 100-150 —77-20 20-89 5-50 100-150 20-99 10-98 16-99 144-358 12-99 10-99 20-99 20-99 20-1040 19-100 10-50 10-50 -188- —252 —78 188 —18 78 ?-ioo — 20--+3 — 19- +20 0-20 35-40 60-63 20-100 Specific Heat. 0.0858 .08991 .08831 .0862 .10432 .09464 •034s .0426 .0356 .0552 •0352 .0426 •°S657 .03880 .03165 ■03500 .04073 .04507 .04001 .04504 •3145 .1988 .1869 .161 .117 .146 .285 •463 .481 .3768 ■5251 •6939 .622 .712 •3312 Authority.t R L U R Ln T M. tl S (C M R (( P (t R W z H M G-T RW B AM TABLE 230. — SpedUo Beat ol Vartons LlqnUs.* Liquid. Temper- ature °C. Specific Heat. Author- ity. Liquid. Temper- ature °C. Specific Heat. Author- ity.t Alcohol, ethyl . — 20 o-S°53 R Nitrobenzole 28 0.362 A •■W« " Napthalene, CioHg 80-85 .396 B 40 .648 tl 90-95 .409 (( methyl . 5-10 •590 Oils : castor . •434 W 15-20 .601 " citron . 5-4 •438 HW Anilin .... 15 ■<,H G olive . 6.6 .471 U 30 .520 sesame - .387 w 5° ■529 turpentine . .411 R Benzole, CeHs. 10 •340 H-D Petroleum 21-58 .511 Pa 40 .423 (t Toluol, CeHg 10 •364 H-D 6S .482 " (« 6S .490 (( Diphenylamine, C12H11N 53 ■464 B (( 8S •534 (1 •* ... 65 .482 a CaClo, sp. err. 1.14 . — 'S .764 DMG Ethyl ether .529 R «t '^ *? « ■775 (( Glycerine 15-5° .S76 E (( If (( -1-20 .787 it Nitrobenzole . 14 •350 A " 1.20. 20 •69s tt • These specific heat tables are compiled partly from more extended tables in Landolt-Bornstein-Meyerhoffer's Tables, t For references see Table 230, page 231. Smithsonian Tables. Tables 230 (c(mtimied)-23i . TABLE 830 — SpeGlllo Heat of Vuloiu UvMb. 23t Liquid, Tempera- ture °C. CaCl2, sp. gr. 1.20 " <• <> " 1.26 CuSo4+5oHsO " +200 " " +400 " ZnS04+50 HaO " 4- 200 " o +20 — 20 o +20 12-15 12-14 13-17 20-52 20-52 Specific Heat. 0.712 ,725 651 663 .676 •951 842 ,952 Author- ity. DMG <( t( tt tt Pa U l( Ma Liquid. Tempera- Specific ture°C. Heat. KOH+joHjO. " -l-ioo " . NaOH + 5oHaO " 4- 100 " • NaCl-fioHaO . " 4-200 " . Sea water, sp.gr. 1.0043 " " " 1-0235 " 1.0463 18 18 18 18 18 18 17-5 17-5 17-5 0.876 •975 •942 •983 791 978 ,980 •938 •903 Autlur- ity. TH A, Abbot. AM, A. M. Mayer. B, Batelli. D, Bewar. E, Emo. G, Griffiths. G-T, Gee and Terry. DMG, Dickinson, Mueller, and George. T, Tomlison. H-D, de Heen and Deruyts. S, Schiiz. HM, H. Meyer. Th, Thomsen. L, Lorenz. P, Person. W, Waohsmuth. Ln, Luginen. Pa, Pagliani. Wn, Winkelmann. M, Mazotto. R, Regnault Z, Zouloff. Ma, Marignac. RW, R. W. Weber. TABLE 231. — SpeaUlo Heat ol Minerals and Rooks. Substance. Andalusite . Anhydrite, CaS04 Apatite . Asbestos Augite . Barite, BaSO* Beryl . Borax, Naj2B407 fiKed Calcspar, CaCOj . Casiderite, SnOs . Corundum Cryolite, AlaFle.eNaF Fluorite, CaFa Galena, PbS . Garnet . Hematite, FeaOs . Hornblende . Hypersthene . Labradorite Magnetite Malachite.CuaCOi-HaO Mica (Mg) . " (K) . . Oligoclase Orthoclase . Pyrites, copper Pyrolusite, MnOa . Quartz, SiOa Tempera- ture o C. O-IOO O-IOO 15-99 20-98 20-98 10-98 15-99 16-98 0-50 O-IOO 0-300 16-98 9-98 16-99 15-99 O-IOO 16-100 15-99 20-98 20-98 20-98 18-45 15-99 20-98 20-98 20-98 15-99 15-99 17-48 12-100 o 35° 400-1 200 Specific Heat. Refer- ence. 0.1684 ■1753 •1903 ••95 •1931 .1128 .1979 .2382 .1877 .2005 .2204 •0933 .1976 .2522 .2154 .0466 .1758 .1645 .1952 .1914 .1949 .156 •1763 .2061 .2080 .2048 .1877 .1291 .159 .188 •1737 .2786 •3°S Substance, Rock-salt Serpentine Siderite Spinel . Talc . Topaz . Wollastonite Zinc blende, ZnS Zircon . Rocks : Ba,salt, fine, black Dolomite . Gneiss Granite Kaolin Lava, Aetna K It " Kilauea Limestone . Marble Quartz sand Sandstone . Tempera- ture ° C. 16-98 9-98 15-47 20-98 O-IOO 19-51 O-IOO 21-51 20-470 470-750 750-880 880-1190 20-98 17-99 17-213 12-100 20-98 23-100 31-776 25-100 15-100 O-IOO 20-98 Specific Heat. Refer- ence. 0.219 .2586 •1934 .194 .2092 .2097 .178 .1146 .132 .1996 .199 ■243 .626 •323 .222 .196 ,214 .192 .224 .201 .259 .197 .216 .21 .191 .22 6 2 4 6 3 I 6 I 6 6 9 9 9 9 3 10 10 7 3 II II II 12 1 Lindner. 2 Oeberg. 3 Ulrich. 4 Regnault. 5 Tilden. 6 Kopp. 7 Joiy- 11 Bartoli. 12 Morano. 8 Pionchon. 9 Roberts- Austen, Riicker. 10 R. Weber. Compiled from LandoIt-Bornsteiu-MeyerhofEer's Physiltalisch-chemische TabeUen. Smithsonian Tables. 232 Table 232. SPECIFIC HEATS OF GASES AND VAPORS. Mean Substance. Range of Temp. "C. Sp.Ht Constant Pressure. • Authority. Range of Temp.°C Ratio of Specific Heats. Cp/C. Authority. Acetone, CaHeO . 26-110 0.3468 Wiedemann. " " . . 27-179 0.3740 (1 « (( 129-233 0.4125 Regnault. Air . . ! .' -30- + 10 0-2377 II 5-14 1.402s Lummer and It O-IOO 0-2374 •* Pringsheim, MeyerhoSer's Physikalisch-chemische TabeUen. Smithsonian Tables. 234 Tables 237, 238. AIR AND MERCURY THERMOMETERS. TABLE 337. tAm-tiv (All — W".) OC. 0° lO 2» 3° 4° 5° 6° 7° go 9° o .000 — .006 —.012 —.017 — .022 — .027 -.032 —037 — .041 —045 lO —.049 -°M — 057 — .061 -.065 — .068 —.071 —.074 —077 —.080 20 -.083 —.089 —.091 —•093 -.09s — 097 —.099 — .101 —.102 30 —.103 — .104 —.105 -.106 — .107 —.108 — .109 — .110 — .110 — .110 40 — .110 — .110 — .Ill — .Ill — .110 — .110 — .110 —.109 —.109 — .108 SO —.107 —.107 —.106 —.105 — .104 — .103 — .102 — .101 — .100 -.098 60 -.096 —.095 — 093 —.092 —.090 —.088 —.086 —.084 —.082 —.080 70 —.078 — .076 —•074 —.072 — .070 -.067 -.ob5 —.062 —.060 —.057 80 —.054 —.052 —.049 —.047 —.044 — .041 — 039 —036 —034 —031 90 —.028 — .025 —023 — .020 —.017 —.014 — .011 —.009 —.006 —003 100 .000 r.003 +.006 +.008 ^ -.oil +.014 ■+-.017 +.019 --.022 +.025 no - -.028 -.030 - --033 --•03s - -.038 +.041 +.043 --.046 - -.048 - -•oso 120 -•OSS r.OSS - --057 --.060 - -.062 +.064 +.066 --.068 - -.070 --.072 130 -.074 -.076 --.078 --.080 - -.081 +.083 +.084 --.086 --.087 --.089 140 -.oqo -.091 --.092 --.093 - -.094 +•095 +.096 --.096 --•097 --•097 150 -.098 -.098 --.098 --.099 - -.099 +.099 +.098 --.098 + °ff - -.097 160 - -.097 - -.oq6 --.095 --.094 - -•093 +.092 +.090 --.089 --.088 --.086 170 -.084 - -.082 --.080 - -.078 -.076 -[-•073 +.071 --.068 -.06S --.062 180 - -.0S9 - -.OSS --.052 - -.048 -.045 +.041 -f-037 +•033 -(-.028 +•023 190 H I-.019 H h.014 +.009 +.004 — .001 —.007 —.013 — .019 —.025 —031 200 —.038 —•045 —.051 —.058 —.066 —.073 —.080 —.088 — .096 — !r98 210 -:^ — .122 —.130 —139 —.148 — .158 —.168 —.177 -.187 220 — .219 —230 -.241 —.252 — .264 —.275 -.287 —300 —312 2^0 —■325 -g — •35' —36s —378 —392 —.407 —.421 —436 —450 240 -.466 —•497 —•513 —.529 —.546 -.562 —579 —597 -.614 2 SO —632 — .650 —.668 -.687 -.706 —.725 —745 -.765 —978 —785 —.805 260 -.82s —1.048 —.846 —.867 -.889 —.911 —•933 —955 — I.OOI — 1.025 270 — 1.072 — 1.096 — 1. 121 — 1. 146 — 1.171 —1.196 — 1.222 —1.248 —1.274 280 — 1-301 —1.328 — '•356 — 1.384 — I.4I2 —1.440 —1.469 -1.498 —1.528 —1.841 -1.558 —1.874 290 —1.588 — i.6i8 —1.649 — 1.680 — I.7II —I •743 —1.776 —1 .808 300 —1.908 =»= TABLE 238. tm— ttf (All-68m.) OC.

eter .eros. TABLE 244. -Stem OoneoUon lor a so-caUed Normal Thermometer ol Jena fllass (0°-100° 0). Divided into tenth degrees ; degree length about 4 mm. Correction to be added to the Reading t. n t-tf 30° 35° 40° 4B° 60° 56° 60° 66° 70° 75° 80° 86° 10 20 30 40 50 60 ^0 90 100 0.04 0.12 0.21 0.28 0.36 0.4S 0.04 0.12 0.22 0.29 0.38 0.48 0.05 0.13 0.23 0.31 0.40 0.51 0.05 0.14 0.24 0-33 0.42 0-S3 0.05 O.IS 0.25 0.3s 0.44 0.5s 0.06 0.16 0.2 s 0.37 0.46 o!66 0.06 0.17 0.27 0.39 0.48 0.60 0.69 0.76 0.07 0.18 0.29 0.41 0.50 0.63 0.71 0.81 0.92 0.08 0.19 0.31 0.43 075 0.87 0.99 1. 10 0.09 0.20 0-33 0.45 0.69 o.8r 0-93 1.06 1.18 O.IO 0.22 0.48 o.6i 0.73 0.87 1. 00 1.26 O.IO 0.23 0-37 0.51 0.65 0.78 0.92 1.06 1.20 1.34 Smithsonian Tables. 238 Tables 245-247. RADIATION CONSTANTS. TABLE 24S.— BadlaUon Foimnla and Oonitanta for Ferfeot BadlBtor. The radiation per sq. cm. from a " black body " (exclusive of convection losses) at the temper- ature T° (absolute, C) to one at /° is equal to /= lnt«l7 Gold Spao«(— 273° 0). Computed from the Stefan-Boltzmann formula (Ekholm, Met. Z 1902). fiC / fiC / e>c / fiC / fic / ^C J —273 — 120 60 — 10 528 + 12 728 +34 980 -fs6 \zcp. — 220 I — 110 7« —8 544 -14 748 --36 1006 -S8 1324 210 2 — 100 99 —6 561 -16 769 -38 1032 -60 1356 — 200 ^ —90 124 —4 S7« -18 7QI --40 1059 --70 1530 — 190 -«0 \l^ — 2 595 -20 -42 1086 --80 1713 — 180 8 —70 613 -22 836 --44 1114 -90 1916 —170 12 —60 227 --2 631 --24 l^f -4b 1 142 + 100 Z134 —160 18 —50 273 --4 -26 -4« 1171 +200 SS19 —150 Zl) —40 324 --6 668 -28 906 —50 1 201 -l-iooo 290X108 —140 3S —3° 3SS -8 688 -^30 930 -52 1231 -I-2000 294X10* —130 4b — 20 452 +10 708 +32 955 -f54 1261 -(-5000 852X106 TABLE 247.— Valnos of J^ lor Vaiions Temperatnrts Oenttgrade. Ekholm, Met. Z. 1902, used Cl ^ 8346 X 10 and C^ = X4349t ^^^ ^^"^ the unit of time the day. For 10°, the values for J;^ have been multiplied by 10, for the other temperatures by 100. \ TiriooPC 30OC 15° C oOC -30° C -80° C A looOC 30OC .50 c 6OC -30" C — 80OC 2 I 18 5" 2961 2281 2175 1491 623 3 80 "•l 18 7 I 19 443 2626 1954 •363 594 4 469 508 272 1.38 27 I 20 38b 2329 2034 17 S4 1242 561 \ 1047 1777 1085 628 172 8 21 337 2068 I8I6 IS74 1 1 29 527 1526 3464 2296 I4S4 493 39 22 295 1840 1622 1413 1026 494 7 1768 49 S4 3481 3^i 931 105 23 1639 1448 1270 931 460 8 1810 43 S2 1372 203 24 228 1462 1298 1141 846 428 9 1724 6382 4834 3646 1730 316 25 202 1307 1165 1028 768 10 1573 638b 4979 3781 1971 42b 26 179 1 170 1047 926 698 369 II '39° 6127 4833 3798 2098 520 28 142 947 850 7S7 579 317 12 1225 .S7IZ 4b33 3b7b 2114 592 ,30 114 771 696 623 482 272 13 1063 5222 4300 3467 2090 640 40 44 .3" 285 259 209 "4 918 4713 .3930 321 S 2004 666 SO 20 146 ns 124 102 15 792 4220 3S55 2944 1889 673 60 10 77 72 66 IS 38 16 683 37.S9 3198 2b74 1760 663 80 4 27 25 24 20 14 17 39° 3340 2862 2417 1626 649 100 2 12 II 10 9 7 Smithsonian Tables, Tables 248, 249. COOLING BY RADIATION AND CONVECTION. 239 TABLE 248. -At OrStaary Pieisnrei. Accordiog to McFarlane* the rate of loss of heat by a sphere p aced in the centre of a spherical enclosure which has a blackened surface, and is kept at a constant temperature of about 140 C, can be expressed by the equations e = .oooijS + 3.06 X 10-0/ — J. 6 X io-*/», when the surface of the sphere is blackened, or « = .000168 + 1.98 X io-«< — 1.7 X 10-tfl, when the surface is that of polished copper. In these equa- tions, t is the amount of heat lost in c. g. s. units, that is, the quantity of heat, small calories, radiated per second per square centimetre of surface of the sphere, per degree differ- ence of temperature t, and t is the difference of temperature between the sphere and the enclosure. The medium through which the heat passed was moist air. The following table gives the results. Differ- ence of tempera- ture t Value of e. Ratio. Polished surface. Blackened surface. S 10 20 25 30 35 40 4S 50 55 60 .000178 .000186 .000193 .000201 .000207 .000212 .000217 .000220 .000223 .000225 .000226 .000226 .000252 .000266 .000279 .000289 .000298 .00(3306 .000313 .000319 .000323 .000326 .000328 .000328 .707 .699 .692 .695 .694 •693 •693 ■693 .690 .690 .690 .690 TABLE 249. — At SUIsrent Fiessnies, Experiments made by J. P. Nicol in Tail's Labo- ratory show the effect of pressure of the en- closed air on the rate of loss of heat. In this case the air was dry and the enclosure kept at about 80C. Polished surface. Blackened surface. t et t et Pressure 76 cms. of Mercury. 638 .00987 61.2 .01746 57-1 .00862 50.2 .01360 50-5 .00736 41.6 .01078 44.8 .00628 34-4 .00860 40.5 .00562 27^3 .00640 34-2 .00438 20.5 •00455 29.6 .00378 23-3 .00278 - - 18.6 .00210 "" — Pressure 10.2 cms. of Mercury. 67.8 .00492 62.S .01298 61.I •00433 .00383 57-5 .01158 55 53^2 .01048 497 .00340 47^5 .00898 44.9 .00302 43'0 .00791 40.8 .00268 28.5 .00490 Pressure i cm . OF Mercury. 65 .00388 62.5 .01182 60 •00355 .00286 57-5 .01074 50 54.2 .01003 40 .00219 41.7 .00726 30 .00157 37-5 .00639 235 .001 24 34^0 .00569 - 27.5 .00446 24.2 .00391 Smithsonian Tables. * " Proc. Roy. Soc." 1872. t " Eroc Roy. Soc." Edinb. 1869. See also Compan, Annal. de chi. et phys. 26, p. S'^- 240 Tables 250, 251 . COOLING BY RADIATION AND CONVECTION. TABLE 260. — Cooling ol PlaUnnm Wire Is Coppsr Envelope. Bottomley gives for the radiation of a bright platinum wire to a copper envelope when the space between is at the highest vacuum attainable the following numbers : — t = 408° C, */ ^ 378.8 X 10—*, temperature of enclosure i6° C. t=S°S°C,et=ji6.iXjo-^, " " 17° C It was found at this degree of exhaustion that considerable relative change of the vacuum produced very small change of the radiating power. The curve of relation between degree of vacuum and radiation becomes asymp- totic for high exhaustions. The following table illustrates the variation of radiation with pressure of air is enclosure. Temp, of enclosure 16° C, <=4o8'' C Temp, of enclosure 17° C, ^ ^ 505° C. Pressure in mm. et Pressure in mm. et 740. 8137.0 X 10-* 0.094 1688.0 X 10-* 440. 7971.0 " •053 1255.0 " 140. 7873.0 " -034 1 1 26.0 " 42. 7S9I-0 " .013 920.4 " 831.4 " 4- 6036.0 " 2683.0 " .0046 0.444 .00052 767.4 " .070 1045.0 « .00019 JA^A " •034 727-3 " Lowest reached 1 but not measured ) 726.1 « .012 539-2 " .0051 436-4 " .00007 378.8 " TABLE 261. — Ellect ot Piessnro on Lou ol Heat at SlBeient Temperatures. The temperature of the enclosure was about 15° C. The numbers give the total radiation in therms per square cen. timetre per second. Pressure in mm. Temp, of wire in C°. Z0.0 0.2s 0.02s 0.1 M. 100° 0.14 0.1 1 0.05 O.OI 0.005 200 •31 .24 .11 .02 .0055 300 .50 •38 .i8 .04 .0105 400 -75 ■P •25 .07 .025 500 - •^ •33 •13 .055 600 - .85 •45 •23 •13 700 — — — •37 .24 800 - - - •56 .40 900 " " .61 Note. — An interesting example (because of its practical importance in electric light- ing) of the effect of difference of surface condition on the radiation of heat is given on the authority of Mr. Evans and himself in Bottomley's paper. The energy required to keep up a certain degree of incandescence in a lamp when the filament is dull black and when it is "flashed " with coating of hard bright carbon, was found to be as follows : — Dull black filament, 57.9 watts. Bright « " 39.8 watts. ^ Smithsonian T ABLES. Table 252. PROPERTIES OF STEAM. Matrio Heaanie, 241 °r™teVl|lfor rt™St\rL'dk^^^^ t^Perature in degrees Centigrade, together with other data for steam nes according as the gramme or thllSogl'a'mmeTtlkVo asThlSof maT""""" °' ^ "' '" ""™= " "^^ * Where A is the reciprocal of the mechanical equivalent of the thermal unit. t —. H — [h + Apv) ^ internal-work pressure Where v is taken in litres the pressure is given per square V mechanical equivalent of heat t t. ■ decimetre, and where v is taken in cubic metres the pressure is given per square metre, — the mechanical equivalent being that of the therm and the kilogramme-degree or calorie respectively. Smithsonian Tables, 242 Table 253. PROPERTIES OF STEAM. BiltlBli Measure. The quantities jriven in the different columns of this table are sufSciently explained by the headings. The abbrevia- tion B. T. U. stands for British thermal units. With the exception of column 3, which was calculated for tllis table, the data are taken from a table given by Dwelshauvers-Deiy (Tians. Am, Sue. Mech. £ng. vol. xi.). h .B ti-o t) bS Ill gag SI'S m cri •ss S|, if dii it m •III I.S lb .sg..s lis 1 144 0.068 102.0 334-23 0.0030 70.1 980.6 62.34 1043. 1113.0 2 288 .136 126.3 173-23 117.98 .0058 .0085 94.4 961.4 64.62 1026. 1120.4 3 432 .204 I4I.6 109.9 949.2 66.58 1011. 1127.0 4 576 .272 i53^i 89.80 .0111 121.4 940.2 67.06 1007. 1128.6 5 720 •340 162.3 72.50 •0137 1 30^7 932.8 67.89 1001. I131.4 6 864 0.408 170.1 61.10 0.0163 138.6 926.7 68.58 995.2 "33-8 7 1008 .476 176.9 53.00 .0189 145.4 921.3 69.18 990-5 "35-9 8 II52 •544 182.9 46.60 .0214 151.5 916.5 69.71 986.2 "37-7 9 1296 .612 188.3 41.82 .0239 156.9 912.2 70.18 982.4 "39-4 10 1440 .680 193.2 37.80 .0264 161.9 908.3 70.61 979-0 1140.9 11 1584 0.748 197.8 34.61 0.0289 166.5 904.8 70.99 975-8 1142.3 12 1728 .816 202.0 31.90 .0314 170.7 901.5 71-34 972-8 "43-5 13 1872 .884 205.9 29.58 -0338 174-7 898.4 71.68 970.0 1144.7 14 2016 •952 209.5 27.59 .0362 178.4 895.4 72.00 967.4 1145.9 15 2160 1.020 213.0 25.87 -0387 181.9 892.7 72.29 965.0 1146.9 16 2304 1.088 216.3 24-33 22.98 0.0411 185.2 188.4 890.1 72-57 72.82 962.7 1147.9 'I 2448 .156 219.4 -0435 887.6 960.4 1148.9 18 2592 .224 222.4 21.78 .0459 191.4 ^^S-3 73-07 958-3 1149-8 19 2736 2880 .292 225.2 20.70 .0483 194-3 ?f3-' 73-30 956-3 1 1 50.6 20 .360 227.9 19.72 .0507 197.0 880.9 73-53 954-4 1151.4 21 3024 1.429 230.5 18.84 0.0531 199.7 878.8 73-74 952-6 1152.2 22 3168 •497 233-0 18.03 .0554 202.2 876.8 73-94 950-8 1153.0 23 3312 •565 235-4 17-30 .0578 204.7 874.9 74-13 949-1 "53-7 24 3456 •633 237-7 16.62 .0602 207.0 873-1 74-32 947-4 1154.4 2S 3600 .701 240.0 15-99 .0625 209.3 871-3 74-51 945-8 "5S-I 26 mi 1.769 242.2 'Si? 0.0649 211.5 869.6 74.69 944-3 1155.8 ^l 3888 •837 244^3 14.88 .0672 213-7 867.9 74-85 942.8 1156.4 28 4032 .905 246.3 14.38 .0695 215.7 866.3 75.01 941-3 1157.1 29 4176 •973 248.3 13-91 .0619 217.8 864.7 75-17 939-9 "57-7 30 4320 2.041 250.2 13.48 .0742 219.7 863.2 75-33 938-5 1158.3 31 4464 2.109 252.1 '3-?7 0.0765 221.6 861.7 75-47 937-2 1158.8 32 4608 .177 2539 12.68 .0788 223-5 860.3 75.61 935-9 "59-4 33 H^l •245 255-7 12.32 .0811 225-3 858.9 75-76 934-6 1159.9 34 4896 •3J3 257-5 11.98 .0858 227.1 857-5 75-89 933-4 1160.5 35 5040 .381 259.2 11.66 228.8 856.1 76.02 932-1 1161.0 36 5184 2.449 260.8 11.36 0.0881 230.5 854.8 76.16 931.0 1161.5 3^ 5328 •5^7 262.5 11.07 .0903 232.2 853-5 76.28 929.8 1162.0 38 547? •|8S 264.0 10.79 .0926 233-8 852-3 76.40 928.7 1162.5 39 5616 •653 265.6 10.53 .0949 235-4 851.0 76.52 927.6 1162.9 40 5760 .722 267.1 10.29 .0972 236-9 849.8 76.63 926.5 1163.4 41 ^i 2.789 268.6 10.05 0.0995 .1018 238-S 848.7 7!-75 76.86 925-4 1163.9 42 6048 ■857 270.1 9-83 239-9 847.5 924.4 1164.3 43 6192 ■925 271.5 9.61 .1040 241.4 846.4 76.97 923-3 1164.7 44 i^^ •993 272.9 9.41 .1063 242.9 845.2 77-07 922-3 H65.2 4S 6480 3.001 274-3 9.21 .1086 244-3 844.1 77-18 921.3 1165.6 46 6624 3.129 275.6 fo^ 0.1108 245-6 843.1 77-29 920.4 1166.0 '^l 6768 .197 277.0 8.84 .1131 247.0 842.0 77-39 919.4 1166.4 48 6912 .265 278.3 8.67 •"53 248.3 841.0 77-49 77-58 918.5 1166.8 49 7056 •333 279.6 8.50 .1176 249-7 840.0 9'7-S 1167.2 Smithson IAN TaBL ES. Table 253 {.cmtinutd). PROPERTIES OF STEAM. Biltlib Mmiuis. 243 .5 Zu £ S 3 .Sfe« £ 3 a. PM o. s& So I II sg.a ^1 §1 S B,.H •a SEP n g "b..E ■a za m lis ■s s3 ■ as • IS "& H§-S SO SI 52 53 S4 55 56 57 58 59 60 61 62 64 65 66 67 68 69 70 71 72 73 74 75 76 78 79 80 81 82 ?3 84 85 86 87 88 89 90 91 92 93 94 95 96 9Z 98 99 7200 7344 7488 7632 7776 7920 8064 8208 |351 8496 8640 8784 8928 9072 9216 9360 9504 9648 9792 9936 10080 10224 10368 10512 10656 10800 10944 1 1088 1 1 232 1 1376 11520 1 1 664 11808 1 1952 12096 12240 1 1 384 12528 12672 12816 12960 13104 13248 13392 13536 13680 13824 13968 141 1 2 14256 3.401 .469 •|37 .605 •673 3-741 .801 .878 .946 4.014 4.082 .150 .218 .286 •354 4.422 .490 .626 .694 4.762 .830 .898 .966 5-034 5.102 .170 .238 .306 •374 5.442 .510 ■^A •714 5-782 .850 .918 .986 6.054 6.122 .190 .258 •327 •396 6.463 •531 .667 •735 280.8 282.1 283-3 284.5 285.7 286.9 288.1 289.2 290.3 291.4 292.5 293-6 294-7 295.7 296.7 297.8 298.8 299.8 300.1 301.8 302.7 303-7 304.6 305-5 306.5 307-4 308.3 309-2 310.1 310.9 311.8 312.7 313-S 314-4 315-2 316.0 316.8 317.6 318.4 3"9-2 320.0 320.8 321.6 322.4 323-1 323-9 324-6 325-4 326.1 326.8 8.34 8.19 8.04 7-90 7.76 763 7-50 7.38 7.26 7.14 703 6.92 6.82 6.72 6.62 6.52 6.43 6-34 6.25 6.17' 6.09 6.00 5-§3 5.8s 5.78 5.70 563 5-57 5.50 5-43 5-37 5-31 5-25 5-19 s-n 5.07 5.02 4.96 4.91 4.86 4.81 4-76 4.71 4.66 4.62 4-57 4-53 4.48 4-44 4.40 0.1198 .1221 .1243 .1266 .1288 0.1310 •1333 •1355 ■1377 .1400 0.1422 .1444 ,1466 .1488 .1511 0^1 533 •1555 •1577 •1599 .1621 0.1643 .1665 .1687 .1709 •1731 0.1753 ■1775 .1818 .1840 0.1862 .1884 .1906 .1928 .1949 0.I97I •1993 .2015 .2036 .2058 0.2080 .2102 .2123 .2145 .2166 0.2188 .2209 .2231 .2252 .2274 251.0 252.2 253-5 254-7 256.0 257-1 258.3 259-5 260.7 261.8 262.9 264.0 265.1 266.1 267.2 268.3 269.3 270.4 271.4 272.4 273-4 274-3 275-3 276.3 277.2 278.2 279.1 280.0 280.9 281.8 282.7 283.6 284.5 285.3 286.2 287.0 287.9 288.7 289.5 290.4 291.2 292.0 292.8 293.6 294-3 295.1 295-9 296.7 297.4 298.2 839.0 838.0 837.0 836.0 835-1 834.2 8332 832-3 831-5 830.6 829.7 828.9 828.0 827.2 826.4 825.6 824.8 824.0 823.2 822.4 •821.6 820.9 820.1 819.4 818.7 817.9 817.2 816.5 815.8 815.1 8M.4 813.8 813-0 812.4 811.7 811. 1 810.4 809.8 809.2 808.5 807.9 807-3 806.7 806.1 805.5 804.9 804.3 803.7 803.1 802.5 77.67 77.76 77-85 77-94 78.03 78.12 78.21 78.29 78.37 78.45 78-53 78.61 78.68 78.76 78.83 78.90 78-97 79.04 79.11 79.18 79.25 7932 79-39 79.46 79-53 79-59 79.65 79.71 79-77 79-83 79.89 79-95 80.01 80.07 80.13 80.19 80.25 80.30 80.3s 80.40 80.45 80.50 80.56 80.61 80.66 80.71 80.76 80.81 80.86 80.91 916.6 915-7 914.9 914.0 91 3- 1 912.3 911.5 910.6 909.8 909.0 go8.2 907-5 9067 905.9 905.2 904.5 903-7 903.1 902.3 901.6 900.9 900.2 899-5 898.8 898.1 897-5 896.9 896.2 895.6 895.0 894-3 8937 893.1 892.5 891.9 891.3 890.7 890.1 889.5 888.9 888.4 887.8 887.2 886.7 886.1 885.6 885.0 884.5 884.0 883.4 1 167.6 1168.0 1168.3 1168.7 1169.1 1 169.4 1169.8 1170.1 1170.5 1170.8 1171.2 1171.5 1171.8 1172.1 1172.4 1 172.8 "73-1 "73-4 "73-7 1174.0 "74-3 1174.6 1174.9 "75-1 1175.4 "75-7 1176.0 1176.2 1176.5 1 1 76.8 1177.0 "77-3 1177.6 1177.8 1178.0 1178.3 1178.6 1178.9 1179.0 "79-3 1179.; 1179.8 1 180.0 1180.3 1180.5 1180.7 1180.9 1181.2 1181.4 1181.6 Smithsonian Tables. 244 Table 253 icmimueJ). PROPERTIES OF STEAM. Biltlsli Heasnie. ♦j-O c'O •s »• s « i ^ a s<= £§ Is -§ S.S . Hi 11 ill -ES it ^ s y ■3 =-3 ii ill ternal lal at per poi steam in T. U. eternal la at per poi steam in T-U. >tal laten at per po steam in T. U. ial &i.S Crt E^-S >a3 ^sa ansa i.c'Sai w.S'Sed H-S-Sm £SS,S 100 14400 6.803 327.6 4-356 0-2295 298.9 802.0 80.95 882.9 II8I.8 lOI 14544 .871 328-3 -316 •2317 299.7 801.4 81.00 882.4 1 182.1 102 14688 -939 329.0 .276 ■2338 300.4 800.8 81.05 881.9 II82.3 103 14832 7.007 3297 •237 .2360 301.1 800.3 81.10 881.4 1182.5 104 14976 -075 330-4 .199 •2381 301-9 799-7 81.14 880.8 1 182.7 105 I5I20 7-143 33I-I 4.161 0.2403 302.6 799.2 81.18 880.3 1182.9 106 15264 .211 331-8 .125 .088 ■2424 303-3 798.6 81.23 879.8 1183.1 107 15408 •279 332-5 .2446 304.0 798-1 81.27 879-3 1183.4 108 15552 -347 333-2 -053 .2467 304-7 797-5 81.31 878-8 1183.6 109 15696 -415 333-8 -018 .2489 305^4 797.0 81-36 878-3 1183.8 110 15840 7-483 334-5 3984 0.2510 306.1 796-5 81.41 877-9 1 184.0 III 15984 •551 335-2 ■950 •2531 306.8 795-9 81.45 877-4 1184.2 112 I6I28 •5o9 335-8 ■?i7 •2553 307-5 795-4 81.50 876.9 1184.4 "3 16272 .687 336-5 -885 -2574 308-2 794-9 81.54 876.4 1184.6 114 I64I6 •757 337-2 •853 .2596 308-8 794-4 8158 875-9 1184.8 115 16560 7.823 337-8 3.821 0.2617 309-5 793-8 81.62 875-5 1185.0 n6 16704 .891 338-5 .790 •2638 310-2 793-3 81.66 875.0 1185.2 117 16848 •959 339-1 .760 .2660 310.8 792-8 81.70 874-S 1185.4 118 16992 8.027 339-7 •730 .2681 3"-S 792-3 81-74 874-1 1185.6 119 1 71 36 .095 340-4 .700 .2702 312-1 791.8 81-78 873.6 1185.7 120 17280 8.163 341.0 3-671 0.2724 312.8 79i^3 790-8 81.82 873.2 1185.9 121 17424 .231 341-6 •643 -2745 313-4 81.86 872.7 1186.1 122 17568 .299 342-2 .615 .2766 314-1 790-3 81.90 872.2 II86.3 123 '77" •367 342-8 -587 -2787 3'4-7 789.9 81.94 871.8 1186.5 124 17856 •435 3435 -560 -2809 315-3 789-4 81.98 871.4 1186.7 125 18000 8.503 344-1 3-534 0.2830 316-0 788.9 82.02 870.9 H86.9 126 18144 •571 344-7 .507 .2851 316-6 788.4 82.06 870.5 1187.1 "I 18288 •639 345-3 .481 .2872 317-2 787-9 82.09 870.0 1187.2 128 18432 .708 345-9 -456 .2893 317-8 787-5 82.13 869.6 1187.4 129 18576 -776 346-5 •431 .2915 318-4 787-0 82.17 869.2 II87.6 130 18720 8.844 347-1 3.406 0.2936 319.0 786.5 82.21 868.7 1187.8 131 18864 .912 347-6 .382 •2957 319-7 786.1 82.25 868.3 867.9 1188.0 132 19008 .980 348.2 ■358 .2978 320.3 785.6 82.28 1188.1 133 19152 9.048 348.8 ■334 •2999 320.9 785-1 82.32 867.5 1188.3 134 19296 .116 349-4 -310 •3021 321.5 784-7 82-35 86^.5 1188.5 135 19440 9.184 349-9 3.287 0.3042 322.1 784.2 82.38 866.6 1188.7 1188.8 136 19584 .252 350-5 .265 ■3063 322.6 783.8 82.42 866.2 '^l 19728 .320 35I-I -424 .3084 323-2 783-3 82-45 865.8 1189.0 1 189.2 138 19872 .388 351-6 -220 •3105 3238 782.9 82.49 865.4 •39 20016 -456 352-2 -199 -3126 324-4 782.4 82.52 865.0 1189.4 140 20160 9.524 352-8 3-177 0.3147 3250 782.0 82.56 864.6 1189.5 1189.7 1189.9 1190.0 1190.2 141 20304 •592 353-3 .156 -3168 325-5 781.6 82.59 864.2 142 20448 -660 353-9 •135 .3190 326-1 781.1 82.63 863.8 143 20592 .728 354-4 .115 -3211 326-7 780.7 82.66 863.4 144 20736 .796 355-0 -094 •3232 327-2 780.3 82.69 863.0 145 146 20880 9.864 355-5 3-074 0-3253 327-8 779-8 82.72 862.6 II90.4 1190.5 1190.7 1190.9 1191.0 21024 2u68 21312 21456 ■932 ^^^•2 .054 •3274 328-4 779-4 82.75 862.2 147 148 149 10.000 -068 -136 356-6 357-1 357-6 •035 .016 -997 •3295 •3316 •3337 328.9 329-5 330-0 779.0 778-6 778.1 82.79 82.82 82.86 861.8 861.4 861.0 Smithsonian Tables. Table 253 {continued), PROPERTIES OF STEAM. BilUsli Maainie. 245 Smithsonian Tables. 246 Table 253 {cmimud). PROPERTIES OF STEAM. BrlUsIi Haasnie. ^ s-§ t% •g i!§ III Hi III hi III ^1 Internal late heat per pou of steam in B. T. U. External late heat per pou of steam in B. T. U. Total latent heat per pou of steam m B. T. U. as . Hg-a 200 28800 13.605 381.6 2-273 0-4399 354-9 759.2 84.23 843-4 1 198.3 201 28944 13-673 382.0 .262 .4420 355-3 355-8 356.2 758.9 84.26 843-1 1 198.4 202 29088 13-742 3^'i .252 .4441 758-5 ^4.28 842.8 1 198.6 203 29232 13.810 382.8 .241 .4461 758.2 84.30 842.5 1 198.7 204 29376 13-878 383-2 .231 .4482 356-6 757-9 84-33 842.2 1 198.8 205 29520 13.946 383-7 2.221 0.4503 357-1 757-5 84-35 841.9 1199.0 206 29664 14.014 384.1 .211 •4523 357-5 757-2 84-37 841.6 1199.1 207 29808 14.082 384-5 .201 •4544 357-9 756.9 84.40 841.3 1199.2 208 29952 14.150 3849 .191 •4564 Lti 756.6 84.42 841.0 "99-3 209 30096 14.218 385-3 .181 .4585 756.2 84.44 840.7 1199.4 210 30240 14.386 385-7 2.I7I 0.4605 359-2 755-9 84.46 840.4 1199.6 2H 30384 14.454 386.1 .162 .4626 359-6 755-6 84.48 840.1 1199.7 212 30528 14.522 386.5 .152 .4646 360.0 755-3 84-51 839-8 1199.8 213 30672 14.590 386.9 -143 .4666 360.4 755-0 8453 839-S 1199.9 214 30816 14.658 387-3 •134 .4687 360.9 754-7 84-55 839-2 1 200. 1 215 30960 14.726 3i^-7 2.124 0.4707 361-3 754-3 84-57 838.9 1200.2 216 31 104 14-794 388.1 .115 .4727 361-7 754.0 84.60 838.6 1200.3 217 31248 14.862 3|i-5 .106 .4748 362.1 753-7 84.62 838.3 1200.4 218 31392 14.930 388.9 .097 .4768 362.5 753-4 84.64 838.0 1200.5 219 31536 14.998 389-3 .088 .4788 362.9 753-1 84.66 837-7 1200.7 Smithsonian Tables. Table 254. 247 RATIO OF THE ELECTROSTATIC TO THE ELECTROMAGNETIC UNIT OF ELECTRICITY = F. Date. Cm. per sec. Mean. Detemiined by Reference. 1856 3.iiXioi» R. Kohlrausch and l868 2.75-2.92 X I0«> 2.84 W. Weber. Maxwell. Pogg. Ann. 99 ; 1856. Phil. Trans. ; 1868. 1869 1874 2.71-2.88 2.8l Thomson and King. B. A. Report j 1869. 2.86-3.00 2.90 McKichan. Phil. Mae. 47 ; 1874. 1879 2.950-3.018 2.981 Rowland. PhU. Mag. 28; 1889. 1879 1880 — 2.96 Ayrton and Perry. Phil. Mag. 7 ; 1879. — 2.967 Hockin. B. A. Report ; 1879. — 2-955 Shida. Phil. Mag. 10; 1880. 1881 2.98-3.00 Stoletow. Jour, de Phys. ; 1881. 1882 - 2.87 Exner. Wien. Ber. ; 1882. 1883 — 2.963 J. J. Thomson. Phil. Trans. ; 1883. 1884 3.001-3.029 3.019 Klemencic. Wien. Ber. 83, 89, 93; 1881-6. " 3.016-3.031 1886 - 3-015 CoUey. Wied. Ann. 28 ; 1886. 1886-S 2.999-3.009 3.003-3.008 3.005-3.015 3.009 Himstedt. Wied. Ann. 29,33, 35 ) 1887-8. 1888 2.92 Thomson, Ayrton and Perry. Electr. Rev. 23 ; 1888-9. 1889 2.995-3-010 3.000 Rosa. Phil. Mag. 28; 1889. 1890 — 2.996 J. J. Thomson and Searle. Phil. Trans. ; i8go. 1891 - 3.009 Pellat. Jour, de Phys. 10 ; 1891. 1892 2.990-2.995 2.991 Abraham. Ann. Chim. et Phys. 27; 1829. 'f9^ 3.001 Hurmuzescu. Ann. Chim. et Phys. 10 ; 1897. '^98 - 2-9973 Perot and Fabry. Ann. Chim. et Phys. 13 ; i8g8. 1898 - 3.026 Webster. Phys. Rev. 6; 1898. 1899 ~ 3.009 Lodge and Glaze- brook. Cam. Phil. Soc. 18 ; 1899. 1904-7 2.99706-2.99741 2.9971 Rosa and Dorsey. Bull. Bur. Standards 3 ; 1907. The last of the above determinations is the result of an extended series of measurements upon various forms of condensers, and is believed to be correct within i /:oo per cent. This, however, assumes that the International Ohm is 10' c.g.s. units. The value of Kis therefore subject to one-half the error of the International Ohm, Smithsonian Tables. 248 Tables 255, 256. DIELECTRIC STRENGTH. TABLE 266. — SteaAy Potential Dllf eienoe In Volts letnlied to pioAnco a Spaik In Air with Ball Bloctrodes. Spark length. cm. /f = o. Points. cm. cm. ;t=i cm. ^ = 2cm. if = 3 cm. Plates. 0.02 _ _ 1560 153° 0.04 - - 2460 2430 2340 0.06 - - 3300 3240 3060 0.08 - - 4050 3990 3810 O.I 3720 5010 4740 4560 4560 4500 43S0 0.2 4680 8610 8490 8490 8370 7770 759° 0-3 53'° 1 1 140 1 1460 II 340 III90 10560 10650 0.4 S970 14040 14310 14340 14250 13140 13560 0.5 6840 15990 16950 17220 16650 16470 16320 0.6 I7I30 19740 20070 20070 19380 19110 0.8 8070 18960 23790 24780 25830 26220 24960 I.O 8670 20670 26190 27810 29850 32760 30840 I 5 9960 22770 29970 37260 2.0 10140 ^^57° 33060 45480 30 11250 28380 4.0 12210 29580 S-o 13050 Based on the results of Bailie, Bichat-Blondot, Freyburg, Liebig, Matiarlane, Orgler, Paschen, Quincke, de la Rue, Wolff. For spark lengths from i to 200 wave-lengths of sodium Ught, see Earhart, Phys. Rev. 15, p. 163; Hobbs, Phil. Mag. 10, p. 607, 1905. TABLE 266. — Altexnatljig Gnirent Potentlala required to produoe a Spark in Air with varloiu Ball Elec- trodes. The potentials given are the maxima of the alternating waves used. Frequency, 33 cycles per second. SfKirk length. cm. 0.08 .10 •IS .20 •2S 0.30 •3S .40 •45 .50 0.6 >1 .8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 R=\ cm. 3770 4400 599° 7510 9045 10480 11980 13360 14770 16140 18700 21-350 23820 26190 28380 32400 35850 38750 40900 42950 /e=i.92 4.380 5940 7440 8970 10400 11890 13300 14700 16070 18730 21380 24070 26640 29170 34100 38850 43400 4330 5830 7340 8850 10270 11670 13100 14400 15890 18550 21 140 23740 26400 28950 33790 38850 43570 48300 je = 7.s 4290 5790 7250 8710 10130 11570 12930 14290 15640 18300 20980 23490 26130 28770 33660 38580 43250 47900 52400 /?=! 4245 5800 7320 8760 10180 11610 12980 14330 15690 18350 20990 23540 261 10 28680 33640 38620 43520 R = xi 4230 5780 7330 8760 10150 11590 12970 14320 15690 18400 21000 23550 26090 28610 33620 38580 Smithsonian Tables. Based upon the results of Kawalski, Phil. Mag. i8, 1909. Tables 257, 258. 249 DIELECTRIC STRENGTH. TABLE 257. — Potential Necessary to proance a Spark In Air between more widely Separate! Electrodes. 0-3 0-5 0.7 1.0 1.2 i-S 2.0 2-5 3-° 3-5 4.0 4-5 S-o S-5 is§ Steady potentials. Ball electrodes. Cup electrodes. R=l cm. R«2.5Cin 29200 40000 48500 56500 I7610 30240 33800 37930 42320 45000 46710 49100 50310 17620 23050 31390 36810 44310 56000 65180 71200 75300 78600 81540 83800 Projection. 4.5 mm. 1.5 mm. 31400 56500 80400 IOI70O 1 1 280 17420 22950 31260 36700 44510 56530 68720 81 140 92400 103800 1 14600 126500 135700 6.0 7.0 8.0 1 0.0 12.0 14.0 15.0 16.0 20.0 25.0 30.0 35-0 .t ■sg s a a 61000 67000 73000 82600 92000 lOIOOO I I 9000 140600 165700 190900 Steady potentials. Ball electrodes. R=2.5Cm, 52000 52400 74300 86830 90200 91930 93300 94400 94700 lOIOOO This table for longer spark lengths contains the results o£ Voege, Ann. der Phys. 14, 1904. using alternating current and "duU po>t" eSodes, and the results with steady potential found in the recent very careful work of C. Mul- ler, Ann. d. Phys. 29, 1909. (■iiJ. ]/ atm.> V The specially constructed elec- trodes lot the columns headed " cup electrodes " had the form of a projecting; knob 5 cm. in diame- ter and havmg a height of 4.5 mm. and 1.5 mm. respectively, attached to the plane face of the electrodes. These electrodes give a very satis- factory linear relation between the spark lengths and the voltage throughout the range studied. TABLE 2B8.-Bfleot ol tie Pressure ol the Oas on the Dielectric Strength. Voltages are given for different spark lengths /. Pressure, cm. Hg. 2 4 6 10 IS 25 35 45 11 75 ;=o.o4 mo 1375 1640 1820 2040 22SS /=o.o6 483 582 771 1060 1420 1820 2150 2420 2720 303s /=o.o8 1^7 690 933 1280 1725 2220 2660 3025 3400 380s 1=0.10 795 1090 1490 2040 2615 3120 3610 4060 4565 /=0.20 744 1015 1290 1840 2460 3500 4505 5475 637 s 7245 8200 7=0 30 939 1350 1740 2450 3300 4800 6270 7650 8950 10210 11570 7=0.40 mo 1645 2140 3015 4080 6000 7870 9620 11290 12950 14650 7=0.50 1266 1915 2505 3580 4850 7120 9340 1 1420 13455 15470 17450 — — ^ , .rs , 0^ See this paper for work on Other gases (or Landolt-BBmslein- InfelaTatcSSlerseTwifnrint^IXs.^ Smithsonian Tables. 250 Tables 259, 260. DIELECTRIC STRENGTH. TABLE 269. — DlelecMo Stiengtii ol Hateilals. Potential necessary for puncture expressed in kilovolts per centimetre thickness of the dielectric. Substance. Kilovolts per cm. Substance. 3^ Substance. KilovolU per cm. Ebonite . . . . 300-1100 Oils : Thickness. Papers : Empire cloth . . 80-300 Castor 0.2 mm. 190 Beeswaxed . . 770 " paper . . 450 1.0 " 130 Blotting . . . ISO Fibre 20 Cottonseed 70 Manilla . . . 25 Fuller board . . 200-300 Lard 0.2 " 140 Paraffined . . 500 Glass 300-1500 1.0 " 40 Varnished . . 100-350 Granite (fused) 90 Linseed, raw 0.2 " i8s Paraffine : Guttapercha . . . 80-200 1.0 " 90 Melted . . . 75 . Impregnated jute . 20 boiled 0.2 " Melt point. Leatheroid . . . 30-60 " " 1.0 " 80 Solid 43° 350 Linen, varnished . 100-200 Lubricating SO 47° 400 Liquid air ... 40-90 Neatsfoot 0.2 " 200 52° 230 Mica : Thickness 1.0 " go 70° 450 Madras o.i mm. 1600 Olive 0.2 " 170 Presspaper . . . 4S-7S " i.o " 300 1.0 " 7S Rubber .... 160-500 Bengal o.i " 2200 Paraffin 0.2 " 21S Vaseline. . . . 90-130 " 1.0 " 700 1.0 " 160 Thickness. Canada 0.1 " 1500 Sperm, mineral 0.2 " i8o Xylol 0.2 mm. 140 1.0 " 500 " " 1.0 " 8S " 1.0 " 80 South America . 1500 " natural 0.2 " IPS Micanite . . . 4000 " " 1.0 " Turpentine 0.2 " 1.0 " 160 no TABLE 260. — Potentials In Volts to Frolnce a Spaik In Kerosene. Electrodes Balls of Diam. d. Spark length. inin> 0.5 cm. 1 cm. 3 cm. 3 cm. O.I 3800 3400 2750 2200 .2 7500 6450 4800 3500 ■3 10250 9450 7450 4600 .4 11750 10750 9100 5600 .5 13050 12400 IIOOO 6900 .6 14000 13550 12250 8250 .8 15500 15100 13850 10450 1.0 16750 16400 15250 12350 Determinations of the dielectric strength of the same substance by different observers do not agree well. For a dis- cussion of the sources of error see Mo^icki, Electrotechn. Z. 25, 1904. For more detailed information on the dependence of the sparking distance in oils as a functioD of the nature of the electrodes, see Edmondson, Phys. Review 6, 1898. Smithsonian Tables. Table 261 . 25 1 ABSOLUTE MEASUREMENTS OF CURRENT AND OF THE ELECTROMO- TIVE FORCE OF STANDARD CELLS. Date. 1884 1890 1896 1898 1899 1903 1904 1906 1907 1907 1908 1908 1908 Observer. F. and W. Kohlrausch | Rayleigh & Sidgwick . | Potier and Pellat . . i Kahle Patterson and Guthe . ] Carhart and Guthe . . Pellat and Leduc . . -j Van Dijk and Kunst . •! Guthe Ayrton, Mather and Smith Smith and Lowry . . Janet, Laporte and J Jouaust 1 Pellat GuUlet Method. Tangent galvanometer . Filter paper voltameter Current balance . . . Filter paper voltameter Current balance . . . Filter paper voltameter Current balance . . . Electrodynamometer . Silver oxide voltameter Electrodytiamometer . Current balance . . . Leduc voltameter , . Tangent galvanometer . Filter paper voltameter Electrodynamometer . Current balance . . . Filter paper voltameter Filter paper voltameter Current balance . . . Current balance . . . Current balance . . . Electromotive Force of Clark Cell at 15°. volts. I -4345 }- 1.4328 '•4333 [- 14330 1-4323 \'- Weston Cell at 20°. volts. 1. 0186 I.0185 I.01819 I.0187 I.0184 I.0182 Electrochemical Equivalent found with Voltameter of Rayleigh Form, mg. 1.1183 I.H79 1.1192 1.1182 ••"95 1.1182 1.11827 1.1182 Porous Cup Form. I.II92 I.I 177 The most probable value o£ the Weston cell at 20° is 1.0182 volts, assuming the International ohm to be 10' c. g. s. units and the volt to be 10' c. g. s. units. The corresponding value o£ the Clark cell, as prepared at present, at 15°, is 1.4324 volts. The legal values of the Weston cell, however, are different in different countries, as follows : United States (Bureau of Standards) 1.019125* v. at 20° Germany (Physikalisch-Technische Reichsanstalt) 1.0186 volts at 20° England (National Physical Laboratory) 1.0184 volts at 20° The value of the Weston standard cell, used in the United States, is based upon the value adopted by the Chicago Electrical Congress (1893) for the Clark cell. The value used by Ger- many was adopted in 1896, and is based on Kahle's work at the Reichsanstalt. The value used in England was adopted January i, 1909, and is based on the recommendation of the London Electrical Conference of 1908. It is expected that a new value will soon be agreed upon by the International Committee on Electrical Units and Standards, which will be adopted generally in all countries. ,.„ , ., ,ti 1 • l The value of the electrochemical equivalent of silver is different when filter paper (Rayleigh form) silk, or other textile is used to separate the anode from the cathode from what it is when a porous cup is employed. The value found is also affected by the addition of silver oxide to the silver nitrate solution. The legal value in all countries is 1. 1 18 mg. of silver per coulomb, and this is nearly the value found when using a porous cup voltameter, and the best determinations of the current that have been made by absolute current balances. Some corrections have been made to the figures given in the above table for the excess due to filter paper, but such corrections are very uncertain, * Based on i.oi^ at 25° C. Smithsonian Tablcs. 252 Table 262. COMPOSITION AND ELECTROMOTIVE FORCE OF VOLTAIC CELLS. The electromotive forees given in this table approximately represent what may be expected from a cell in good work- ing order, but with the exception of the standard cells all of them are subject to considerable variation. (a) Double Fluid Cells. Name of cell. Negative pole. Solution. Positive pole. Solution. fc.2 Bunsen . Chromate . Daniell* Grove Marie Davy Partz . Amalgamated zinc ( I part H2SO4 to I ( 12 parts H2O . ) 12 parts K2Cr207 to 25 parts of H2SO4 and 100 parts H2O . . ( I part H2SO4 to I I 12 parts H2O . ) ( I part H2SO4 to 1 ( 4 parts H2O . ) ( I part H2SO4 to I j 12 parts H2O.) Carbon ( 5% solution of I i ZnS04 + 6H20f ( I part NaCl to I i 4 parts H2O . ) ( I part H2SO4 to I ( 12 parts H2O . j Solution of ZnSOi ( H2SO4 solution, ) ( density 1.136 . J !H2S04 solution, 1 density 1.136 . ) {H2SO4 solution, 1 density 1.06 . j Copper Platinum Fuming H2NO8 HNOs, density 1.38 ( I part H2SO4 to ) ( 12 parts H2O . ) (12 parts K2Cr207 I I to loo parts H2O J Saturated solution ) CUSO4+SH2O ( (Sal I of {H2SO4 solution, ) density 1.14 . ) ( H2SO4 solution, ) ( density 1.06 . ) NaCl solution . . I I part H2SO4 to I ( 12 parts H2O ) Solution of MgS04 Carbon Fuming HNOs • • HNOs, density 1.33 Concentrated HNOs HNOs, density 1.33 HNOs, density 1.19 " density 1.33 ( Paste of protosul- ) < phate of mercury > ( and water . . . ) Solution of K2Cr207 1.94 1.86 2.00 2.03 1.06 1.09 1.08 1.05 1-93 1.66 1-93 1.79 1.71 1.66 1. 61 1.88 1.50 2.06 i\In\'eSTbo°u^th:1^^re^'ecfrS"'f!r4^^^^^^ Lockwood celU are modifications of the Daniell. aud hence have about the same electromotive' foice' Gmithsohian Tables. Table 262 {pmiintied). 253 COMPOSITION AND ELECTROMOTIVE FORCE OF VOLTAIC CELLS. Name of cell. Negative pole. Solution. Positive pole. (b) Single Fluid Cells. I..eclanche . . . Chaperon . . . Edison-Lelande . Chloride of silver Law Dry cell (Gassner) Poggendorfi . . J. Regnanlt . . Volta couple . Amal.zinc Zinc . . Amal.zinc Zinc . i Solution of sal-ammo- 1 ! niac j i Solution of caustic ] [ potash I 23 % solution of sal- [ ammoniac .... 15 % ript.ZnO, ipt-NHiCl, I 3 pts. plaster of paris, 2 pts. ZnCl2,and water [ to make a paste . . i Solution of chromate \ of potash .... ' 12 parts KaCraOv + 25 parts H2SO4 -f- 100 parts H2O . . : I part H2SO4 + 12 parts H2O + ' I part CaSOi . . H2O ..... . Carbon. Depolari- zer : manganese peroxide with powdered carbon ( Copper. DepolaT' 1 izer : CuO . I Silver. Depolari. 1 zer : silver chl'ride Carbon . . Cadmium Copper . (c) Standard Cells. Weston normal Clark standard ICadmi'ml I am'lgam) ( Zinc I I am'lgam $ Saturated solution of CdS04 Saturated solution of ZnSO* Mercury. Depolarizer: paste of Hg2S04 and CdS04 . . . . Mercury. Depolarizer: paste of Hg2S04 and ZnS04 . , . . E. M. F. in volts. 1.46 0.98 0.70 1.02 '■37 »-3 1.08 2.01 0-34 0.98 1.0191 at 20° C 1-434* at is°C (d) Secondary Cells. Lead accumulator Regnier (1) . . . (2). . . Main . Edison Lead Copper . Amal. zinc Amal. zinc Iron . . [ H2SO4 solution of I I density i.i . . . ) CuS04-f H2SO4 . . ZnS04 solution . . . H2SO4 density ab't I.I KOH 20 % solution . PbOo " inH2S04 u A nickel oxide 2.2t ( 1.68 to } 0.85, av- ( erage 1.3. 2.36 2.50 ' I.I, mean of full ' discharge. - * E. M. F. hitherto used at Bureau of Standards. See p. 251. The temperature formula is £(= £2.-0.0000406 (t—zo) — 0.00000095 (t— 20)2 -f- o.oooooooi (t— 2o)s. The value given is that adopted by the Chicago International Electrical Congress in 1893. The temperature formula is £,= £,,, - 0.00119 (t— 15) — 0.000007 (t- JS)^- t F. Streintz gives the following value of the temperature variation — at different stages of charge : E. M. F. i.g22j 1.9828 2.0031 2.0084 2.0105 2.0779 a. 2070 dE/dtXio» 140 228 335 285 255 130 73 Dolezalek gives the following relation between E. M. F. and acid concentration : Per cent H2SO4 64.5 52.2 35-3 a'-4 S-a Smithsonian Tables. E.M.F., qOC 2.37 "5 »-'o *-°° '-^S 254 Table 263; CONTACT DIFFERENCE OF SolUs wltli Lltnlds and Temperature of substances 1 u . ^ i 1 a H (3 ( .01 .269 f .28s) f-.ios Distilled water .... ] to to .148 .171 ] '° ( •177 f to C-i? .100 ^345) { +-156 Alum solution : saturated at i6°.5 C —.127 -653 —139 .246 -.225 -536 Copper sulphate solution : .103 _ _ sp. gr. 1.087 at 160.6 C. Copper sulphate solution : .070 _ _ — _ _ saturated at 15° C. . . Sea salt solution: sp. gr. i.i8 at 20°.s C. . . . - —475 —.60s - —.856 —334 —565 Sal-ammoniac solution : saturated at 1 50.S C. . -396 -.652 —.189 .059 -364 -637 Zinc sulphate solution: sp. _ _ _ -238 gr. 1. 125 at i6°.9 C. . . Zinc sulphate solution : _ —430 saturated at I5°.3 C. . One part distilled water + 3 parts saturated zinc > - - - - — —444 sulphate solution • • • . 1 Strong sulphuric acid ii distilled water : I to 20 by weight . . - - - - - - —344 I to 10 by volume . . 1 about > ■ I— 03Sf - - _ - - - I to S by weight . . . <■ 01 ) - — — — ~" ~ 5 to I by weight . . . (•55/ - - —.120 - —.25 - ( -72 1.3 ) Concentrated sulphuric aci i J to [ (•85) 1.113 ~ { to ( 1-252 to ■ 1.6 ) ■■ ^ Concentrated nitric acid . - - .672 - - Mercurous sulphate paste - - - - - - - Distilled water containing _ —.241 trace of sulphuric acid * Everett's " Units and Physical ConstanU: " Table of Smithsonian Tables. Table 263 {cmUmudi. 2S5 POTENTIAL IN VOLTS. LUnlds wltli LlauldB In All.* during experiment about i6° C. ■5 u s 1 n il 1? 1: Is 1! p.- Is. no, 1+ 1 ■3 bO Distilled water Alum solution : saturated 1 ati6°.5C ( Copper sulphate solution : ) sp. gr. 1.087 at i6°.6 C. j Copper sulphate solution : 1 saturated at 15° C. . . ) Sea salt solution : sp. gr. 1 1.18 at 20°.s C. . . . i Sal-ammoniac solution : ) saturated at is°.5 C. . Zinc sulphate solution : sp. gr. 1.125 at i6°.9 C. Zinc sulphate solution : saturated at is°.3C. . One part distilled water + 3 parts saturated zinc , sulphate solution . . Strong sulphuric acid in distilled water : 1 to 20 by weight . . . I to 10 by volume . . . I to 5 by weight . . . . 5 to 1 by weight . . . . Concentrated sulphuric acid Concentrated nitric acid . Mercurous sulphate paste . Distilled water containing trace of sulphuric acid . .100 —.284 -.358 .429 .848 .231 —.014 —435 —348 —.016 •47S —•043 — .200 1.298 1.456 —•043 -.095 — .102 1.269 .090 .164 •095 1.699 .102 .078 Ayrton and Perry's results, prepared by Ayrton. Smithsonian Tables. 256 Table 264. CONTACT DIFFERENCE OF POTENTIAL IN VOLTS. SoUds wltli SoUds In All.* The following results are the " Volta differences of potential," as measured by an electrometer. They represent the difference of the potentials of the air near each of two metals placed m con- tact. This should not be confused with the junction electromotive force at the junction of two metals in metallic contact, which has a definite value, proportional to the coefficient of Peltier effect The Volta difference of potential has been found to vary with the condition of the me- taUic surfaces and with the nature of the surrounding gas. No great relUnce, therefore, can be placed on the tabulated values. . v 00 /- The temperature of the substances during the experiment was about i»° C. Zinc Carbon. Copper. Iron. Lead. Platinum. Tin. Zinc. amal- gam. Brass. Carbon . . . •370 .485 .858 •"3 •79S 1.096! I.208t 4I4t Copper . . . —370 .146 ■542 -.238 .456 .750 .894 .087 Iron .... — 485t -.146 .401 1 —•369 ■3i3t .6oot ■744t — .064 Lead . . . —.858 -.542 — .401 —.771 —.099 .210 •3S7t —.472 Platinum . . — ii3t .238 •369 .771 .690 .981 I.I25t .287 Tin ... . — 795t -.458 -•313 .099 — .690 .281 463 —•372 Zinc .... — i.096t —750 — .600 —.216 -.981 .281 .144 —.679 " amalgam — I.208t —.894 —•744 — osrt — I.I25t —463 —.144 —.822 Brass . . . —.414 -.087 .064 .472 -.287 •372 .679 .822 The numbers not marked were obtained by direct experiment, those marked with a dag- ger by calculation, on the assumption that in a compound circuit of metals, all at the same temperature, there is no electromotive force. The numbers in the same vertical column are the differences of potential in volts between the substance named at the top of the column and the substance named on the same line in the first column, when the two substances aire in contact. The metals used were those ordinarily obtained in commerce. * Everett^s " Units and Physical Constants." The table is from Ayrton and Perry's experiments, and was pre- pared by Ayrton. Smithsonian Tables. Table 265. 2S7 DIFFERENCE OF POTENTIAL BETWEEN METALS IN SOLUTIONS OF SALTS. The following numbers are given by G. Magnanini* for the difference of potential in hundredths of a volt between zinc in a normal solution of sulphuric acid and the metals named at the head of the different columns when placed in the solution named in the iirst column. The solutions were contained in a U-tubCt and the sign of the differ- ence of potential is such that the current will flow from the more positive to the less positive through the ex- ternal circuit. Strength of the solution in gramme molecules per litre. Zinct Cadmium.t Lead. Tin. Copper. Silver. No. of molecules. 0-S I.O I.O 0.5 I.O I.O I.O 0.5 0.5 o-S 0.5 0.25 0.167 I.O 1.0 O-S 0.125 I.O 0.2 0.167 I.O I.O I.O I.O I.O 0.5 -II 1.0 o-S 0.5 Salt. Difference of potential in cendvolts. H2SO4 NaOH KOH NaaS04 NaaSsOa KNOg NaNOg KaCr04 KsCtsOt K2SO4 (NH4)2S04 K4FeC6N6 K6Fe2(CN)2 KCNS NaNOg SrNOg Ba(NOg)2 KNOg KClOa KBrOs NH4CI KF NaCl KBr KCl Na) " (above 3400) 0.76 11.94 ).0O39 0.0506 —2.63 —1-34 —2.80 —17.15 21.8 83-57 3-04 0.0424 >.oo94 — 0.OI0I 0.0482 0.0000 0.0094 0.0506 — 0.2384 0.0506 0.68 —6.0 — 22.6 — 26.4 —17.0 12.95 13-56 97.0 89.0 65.0 45-0 —3-48 22. —1.52 — o.io -3-8 — 1.2 — 16.2 —17-5 0.00 — 2.03 0.413 22.8 0.56 14.47 12.7 39-9 —4-75 —2-45 —3-30 —14.74 — 12.10 — 9.10 0.00 —1-75 3-30 15-50 24-33 195 -236. —62 -143 [-277] 356 236 [-431] T M B T B M B T B M T M M B T M B Smithsonian Tables> Tables 266 lc 10.84 " 0.1380 1.646 65.21 2-359 0.065 Smithsonian Tables. 263 Table 271. SPECIFIC RESISTANCE OF METALS. The specific resistance is here given as the resistance, in microhms, per centimetre of a bar one square centimetre in cross section. Substance. Physical state. Specific resistance. Temp. C. Authority. Aluminum . . 2.6-3.0 354-4S-8 Antimony . . - Various. II tt tt Solid Liquid 182.8 129.2 •Melting-point 11 De la Rive. II Arsenic . , . "• 1377 860 tt 333 Matthiessen and Bismuth . . it Electrolytic soft hard 108.0 108.7 Vogt. VanAubel. Boron . , . Commercial Pulverized and com- 110-268 Various. Cadmium . . 4t pressed :8 X loM 6.2-7.0 - Moissan. Various. Solid 16.S 318 Vassura. Gold. '. * '. Calcium . . Cobalt . . . Liquid 37-9 3'8 tt - 2.04-2.09 9.1 1.55-1.63 16.8 Various. Matthiessen. tt Copper . . . Annealed Various. (( Hard-drawn 1.6I-I.6S Iron .... Commercial 9.7-12.0 tt « Electrolytic 11.2 Ordinary Kohlrausch. II M 105.5 114.8 Red heat Yellow heat .... tt 118.3 Iron magnetic heat it Steel. . . , Cast 19.1 Ord. temp. it tt 11 85.8 Red heat tt ft II 104.4 Yellow heat It U II "3-9 Nearly white heat «■ tt Tempered glass hard 45-7 (I + .00161^) / Barus and Strouhal. tt " light yellow 28.9 (i -f- .00244^) / ti tt tt " yellow 26.3 (1 + .002804 / •i it tt blue 20.5 (1 -f .00330/) / tt tt tt " light blue 18.4 (i + .00360O / tt tt H soft 15.9 (1 + .00423/) / tt 41 Iron .... Cast, hard 97.8 It tt (( " soft 744 « tl Indium . . . - 8.38 Erhard. Lead. . . . - 18.4-1916 Various, Lithium . . . - 8.8 20 Matthiessen. Magnesium , - 4.1-5.0 Various. Nickel . , . - 10.7-12.4 (( Palladium . . - 1 0.6-1 3.6 tt Platinum . . - 9.0-15.5 tt Potassium . . _ 25.1 Matthiessen. it Fluid 50.4 100 (( Silver . '. '. _ 1.5-1.7 Various. :Strontium ■ - 25-'3 20 Matthiessen. Tellurium , , _ 2.17 X 106 19.6 ft tt - SS-oS 294 Vincentini and Omodei. Tin ... . _ 9.53-11.4 Various. At , , , . _ 9-53 Vassura. tt Solid 20.96 226.S ti tt Liquid 44-56 226.5 tt Zinc .* .' .' '. _ 5.56-6.04 tt Solid 18.16 Melting-point De la Rive, u Liquid 36.00 II tt Smithsonian Tables. 264 Table 272. RESISTANCE OF METALS AND The electrical resistance of some pure metals and of some alloys have been determined by Bewar and Fleming and increases as the temperature is lowered. The resistance seems to approach zero for the pure metals, but not for temperature tried. The following table gives the results of Dewar and Fleming.* When the temperature is raised above o° C. the coefficient decreases for the pure metals, as is shown by the experi- experiments to be approximately true, namely, that the resistance of any pure metal is proportional to its absolute is greater the lower the temperature, because the total resistance is smaller. This rule, however, does not even zero Centigrade, as is shown in the tables of resistance of alloys. (Cf. Table 263.) Temperature = -80° Metal or alloy. Specific resistance in c g. s. units. Aluminium, pure hard-drawn wire . Copper, pure electrolytic and annealed Gold, soft wire .... Iron, pure soft wire Nickel, pure (prepared by Mond's process from compound of nickel and carbon monoxide) Platinum, annealed Silver, pure wire Tin, pure wire German silver, commercial wire Palladium-silver, 20 Pd + 80 Ag Phosphor-bronze, commercial wire Platinoid, Martino's platinoid with i to 2% I tungsten ' Platinum-iridium, 80 Pt + 20 Ir Platinum-rhodium, 90 Pt + 10 Rh . Platinum-silver, 66.7 Ag + 33.3 Pt . Carbon, from Edison-Swan incandescent ) lamp J Carbon, from Edison-Swan incandescent ) lamp ^ Carbon, adamantine, from Woodhouse and Rawson incandescent lamp 474S 1920 2665 i3970t 19300 10907 2139 13867 35720 15410 9071 44590 31848 18417 27404 3834X108 6168 Xio» 3505 1457 2081 9521 13494 8752 1647 10473 34707 14984 43823 29902 14586 26915 4046X 10' 39o8xio« 6300X10' 3161 1349 1948 8613 12266 8221 1559 957S 34524 14961 8479 43601 29374 '3755 26818 4092 Xio* 39SSXio» 6363X10= 1400 7470 6133 1138 6681 33664 14482 8054 43022 27504 10778 26311 4189X108 4054X108 6495X108 * " Phil. Mag." vol. 34, 1892. t This is given by Dewar and Fleming as .3777 for gS".*, which appears from the other measurements too high. Bmithsonian Tables. Table 272 {continued). ALLOYS AT LOW TEMPERATURES. 265 by Cailletet and Eouty at very low temperatures. The results show that the coefficient of change with temperature the alloys. The resistance of carbon was found by Dewar and Fleming to increase continuously to the lowest ments or Miiller, Benoit, and others. Probably the simplest rule is that suggested by Clausius, and shown by these temperature. This gives the actual change of resistance per degree, a constant ; and hence the percentage of change approximately hold for alloys, some of which have a negative temperature coefficient at temperatures not far from Temperature = Metal or alloy. — 182° — 197° Specific resistance in c. g. s. units. Mean value of temperature co- efficient between — 100° and + 100° C* Aluminum, pure hard-drawn wire . Copper, pure electrolytic and aimealed Gold, soft wire .... Iron, pure soft wire Nickel, pure (prepared by Mond's process ) from compound of nickel and carbon > monoxide) } Platinum, annealed Silver, pure wire Tin, pure wire . German silver, commercial wire Palladium-sUver, 20 Pd + 80 Ag Phosphor-bronze, commercial wire Platinoid, Martino's platinoid with i to 2% ) tungsten ) Platinum-iridium, 80 Pt + 20 Ir Platinum-rhodium, 90 Pt + 10 Rh . Platinum-silver, 66.7 Ag + 33.3 Pt . Carbon, from Edison-Swan incandescent ) lamp ) Carbon, from Edison-Swan incandescent) lamp ' Carbon, adamantine, from Woodhouse and I Rawson incandescent lamp ) 1928 894 757 272 1207 604 4010 1067 61 10 529s 962 5671 33280 14256 7883 4238s 26712 9834 26108 4218 Xio» 4079X108 6533X10= 1900 2821 472 25S3 32512 13797 7371 4US4 24440 7134 25S37 4321 Xio» 4i8oXio» 178 608 2290 .00446 431 37S S78 538 341 377 428 03s 039 070 025 087 312 024 031 029 * This is o in the equation i? = iTo (» + '»0. as Smithsonian Tables. calculated from the equation a — moRa 266 Table 273. CONDUCTIVITY OF THREE-METAL AND MISCELLANEOUS ALLOYS. Conductivity in mhos or ohms per cm. culie ^CfnC, (i-ra<+««). Metals and alloys. Composition Ijy weiglit. io« aXio« iXio» Gold-copper-silver « = — .000045, " = .00721. Silver '' »>= — .000112, " = .00538. Copper" « = — .000386, «=.ooos5. * From the experimenta of Matthiessen and Vogt, " PhU. Trans. R. S." v. 154. t Hard-drawn. Smithsonian Tables. 268 Table 274 (cmtimu^. CONDUCTING POWER OF ALLOYS. Group 3. Alloys. Weight % Volume % of first named. £0 lo« oX lo* «X io» Variation per 100° C Observed. Calculated. Gold-copper t Gold-silver t . " " t . " « * _ Gold-copper t " t Platinum-silver t " t it » = Z»^ [i — o(^— 9) -f- i8(/— 8)2]. The temperature coefficients are due to Badeker. Gas. - P Range of temp. ° C. Ammonia . . Sulphur dioxide Water vapor . 5.45X10-* 6.19 X Ior« I.4XIO-* 2.59 X io-» 1.86 X10-' 10 — no — no MS The dielectric constant of air at atmospheric pressure but with varying tem- perature may also be calculated from the fact that Z> — I is approximately pro- portional to the density. Smithsonian Tables. 28o Tables 288, 289. DIELECTRIC CONSTANTS {.cmtinutJ). TABLB 28B.— Obanse ol tlia DlalecUo Oonstant of Oasn wltli tba Fraunn, Gu. Air Carbon dioxide . . II II Nitrous oxide, N2O Temper- ature,° C. 19 IS IS Pressure atmos. 20 40 60 80 100 20 40 60 80 100 120 140 160 180 10 20 40 10 20 40 Dielectric constant. I.OI08 I.0218 1.0330 1-0439 1.054B I.OIOI 1. 0196 1.0294 1.0387 1.0482 1.0579 1.0674 1.0760 I. 0845 1.008 1.020 1.060 I.OIO 1.025 1.070 Authority. Tangl, 1907. Occhialini, 1905. Linde, 1895. II II » II TABLE 289.— Sleleotrlo Oonstants of Utnlds. A wave-length greater than loooo centimetres is denoted by 00 . Keferences oa page 281. Substance. Temp. Wave- length, cm. Dielectric constant. Substance. Temp. Wave- length, cm. Dielectric constant. Alcohol : Alcohol : Amyl . . frozen 00 2.4 I Methyl . . -50 00 4S-3 I " — 100 *' 30.1 I 3S-0 I (( —SO II 23.0 I (1 +20 II 31.2 I 17.4 I 17 7S 33-2 2 +20 " 16.0 1 Propyl — 120 00 46.2 I (( 18 200 10.8 2 —60 ** 33-7 I " 18 73 4-7 2 u " 24.8 I Ethyl frozen 00 2.7 I tt +20 II 22.2 I «4 — 120 54-6 1 f( IS 7S 12.3 2 i< -80 II 44-3 I Acetone . -80 00 33-8 S «( —40 " 35-3 I tt II 26.6 i " I " IS 1200 21.85 +20 25.8 1 It 17 73 20.7 7 fl 17 200 24.4 2 Acetic acid 18 00 9-7 8 " 7S 23.0 2 " " IS 1200 10.3 6 S3 20.6 3 17 200 7.07 2 . Substance. Nitrobenzol Octane . Oils: Almond Castor . Colza . Cottonseed Lemon . Linseed Neatsfoot Olive . Peanut . Petroleum Petroleum ether Rape seed Sesame Sperm , Turpentine Vaseline Phenol , Toluol . Meta-xylol Water . . . for temp, coeff. see Table. Temp. "C. (frozen) — 10 —5 o +IS 3° 18 17 17 20 II 20 "4 21 13 20 1 1.4 20 16 134 20 20 48 -83 + 16 19 18 17 18 17 17 17 Wave- lengtU cm. 73 73 73 00 73 200 74 38 Diel. const. 9.9 42.0 41.0 37.8 3^-45 34-0 1.949 2.83 4.67 3" 3.10 2.25 3-35 3.02 3-" 303 2.13 1.92 2.85 3.02 3-17 2.23 2.17 9.68 2.51 2-33 2.376 2-37 81.07 80.6 81.7 83.6 II 2 16 18 19 20 21 22 21 20 23 21 24 20 21 25 2 5 4t 2 II 2 II 2 1 Abegg-Seitz, 1899. 2 Drude, 1896. 3 Marx, 1898. 4 Lampa, 1896. 5 Abegg, 1897. 6 Thwing, 1894. 7 Drude, 1898. 8 Francke, 1893. 9 Lowe, 1898. 10 Landolt-Jahn, ^892. 11 Turner, 1900. 12 Schlundt. 13 Tangl, 1903. 14 Coolidge, 1899. 15 V. Lang, 1896. 16 Nemst, 1894. 17 Calvert, 1900. 18 Hasenohrl, 1896. 19 Arons-Rubens, 1892. 20 Hopkinson, 1881. 21 Salvioni, 1S88. 22 Tomaszewski, 1888. 23 Heinke, 1896. 24 Marx. 25 Fuchs. Smithsonian Tables. 282 Tables 290-291. DIELECTRIC CONSTANTS OF LIQUIDS (.centimuiO- TABLE 290.— Tnnpentiire OostUoients el tha Foimnla : D0=Di[l—a.{t—0)-\-0{t—ef\. Substance. Amyl acetate . . Aniline .... Benzol .... Carbon bisulphide Chloroform . Ethyl ether . Methyl alcohol Oils: Almond Castor . Olive . Paraffine Toluol . Water Meta-xylol 0.0024 0.00351 0.00106 0.000966 0.00092Z 0.00410 0.00459 0.0057 0.00163 0.01067 0.00364 0.000738 0.000921 0.000977 0.004474 0.004583 0.00436 0.000817 P 0.0000087 0.00000060 0.000015 0.000026 0.0000072 0.00000046 0.0000117 Temp, range, ° C. 10-40 20-181 22-181 0-13 20-l8l 5-20 0-76 4-25 20-181 Authority. Lowe. Ratz. Hasenobrl. Ratz. Tangl. Ratz. Drude. Hasenbhrl. Heinke, 1896. Hasenohrl. Ratz. Tangl. Heerwagen. Drude. Coolldge. Tangl. (See Table 387 for the signification of the letters.) TABLE 291.— DlslNtilo Constants ol LitnUled Oases. A wave-length greater than loooo centimetres is designated by 00. Substance. Temp. Dial. constant. •q •< Sabstance* Temp, OC. Dial constant. f Air — 191 00 1432 I Nitroxis oxide ti 14 75 7S 1.47-1.50 21-23 2 N2O —88 00 1.938 1.630 R Ammonia . , . —34 3 — S II s (1 H 130 16.2 4 + S *' 1-578 Carbon dioxide . —5 00 I.6O8 S +!■; (I 1.520 ti 41 U (( 1.588 Oxygen . . . —182 It 1-491 p " " + 10 it 1-540 (( Watts % Transformer Capactty). (d) Thomson-Houston 1500 Watts Transformer. M B M Bl M B M Bl M 20 I B a B Ma M I B a B Ma o.6;2 ss: 7760 3.24 " 3-45 " 3280 3080 80 2.76 6S9 " 6590 I.2I « 2390 160 200 3-3f 4.20 408 " 456 " 9100 10200 3.92 2710 2430 100 1-4'; 714 " 7140 1.40 " 2070 240 ,5-04 495 " IIOOO 2190 280 5.88 524 " 11690 5-35 " 1990 120 4.14 748 " 7490 1.60 " 181O 320 360 6.72 7-56 5S0 ;; 573 " 12270 12780 5.82 " 1820 1690 140 4.83 777 " 7770 1.80 " 161O 400 440 8.40 9.24 591 ;; 504 " I3I80 13470 6.78 " 7.28 « 1570 1460 288 Tables 298-300. MAGNETIC PROPERTIES OF IRON. TABLE 298.— Uagnstlo Fropeittes ot lion and Steel. Electro, lytic Iron. Good Cast Steel. Poor Cast Steel Steel. Cast Iron. Electrical Sheets. Ordinary. Silicon Steel. Chemical composi- tion in per cent C Si Mn P S 0.024 0.004 0.008 0.008 O.OOI 0.044 0.004 0.40 0.044 0.027 0.56 0.18 0.29 0.076 0.035 0.99 O.IO 0.40 0.04 0.07 3-' I 3-27 0.56 0.06 0.036 0-33° 0.260 0.040 0.068 0.036 3-9° 0.090 0.009 0.006 Coercive force . . . ■ t 2.83 [0.36] I.51 [0.37] 7-1 (44-3) 16.7 (S2-4) 1 1.4 [4.6] [1-30] [0.77] Residual B . . . . | 1 1400 [10800] 10600 [1 1000] 10500 (10500) 13000 (7500) 5100 IS3SO] [9400] [9850] Maximum permeability 1850 [14400] [» 700 (170) 37S (no) 240 [600] [3270] [6130] B for H=iso ... 1 19200 [18900] 18800 [19100] 17400 (15400) 16700 (11700) 10400 [iiooo] [18200] '[I7SS0] 4irl for saturation 21620 [21630] 21420 [21420] 20600 (20200) 19800 (18000) 16400 [16800] [20500] [19260] £. Gumlich, Zs. fiir Electrochemie, 15, p. 599 i i9^- BracktU indicate annealing at 800® C in Tacnum. Parentheses indicate hardening by quenching from cberiT-red. TABLE 299. ~ Oast Iron in Intensa Fields. Soft Cast Iron. 1 Hard Cast Iron. || H B I (t H B I C 114 9950 782 62.8 142 7860 614 55-4 172 10800 846 254 9700 752 38.2 433 13900 1070 32.1 10850 836 30.6 744 15750 1200 21.2 13050 983 19.1 1234 17300 1280 14.0 915 14050 1044 15.4 1820 18170 1300 10.0 1570 15900 1138 10.1 12700 31100 1465 2-5 2020 16800 1 146 8-3 13550 13800 32100 \%l 2.4 10900 26540 1235 2.4 32500 2.4 13200 28600 1226 2.2 15100 33650 1472 2.2 14800 30200 1226 2.0 B. O. Peirce, Proc. Am. Acad. 44, 1909. TAILS 300. — Oonectloiis lor Blng Specimens. In the case of ring specimens, the average magnetizing force is not the value at the mean radius, the ratio of the two being given in the table. The flux density consequently is not uniform, and the measured hysteresis is less than it would be for a uniform distribution. This ratio is also given for the case of constant permeability, the values being applicable for magnetizations in the neigh- borhood of the maximum permeability. For higher magnetizations the flux density is more uni- form, for lower it is less, and the correction greater. Ratio of Radial Width to Diameter of Ring. Ratio of Average H to H at Mean Radius. Ratio of Hysteresis for Uniform 1 Distribution to Actual Hysteresis. 1 Rectangular Cross-section. Circular Cross-section. Rectangular Cross-section. Circular Cross-section. •i' •il 'A i/io I/I9 1.0986 1-0397 I.0216 1.0137 1.0094 1.0069 1.0052 10033 1.0009 1.0718 1.0294 1.0162 1.0102 1.0070 1.0052 1.0040 1.0025 1.0007 1. 112 1.045 1.024 1.015 l.OIO 1.008 1.006 1.003 I.OOl 1.084 1033 1.018 l.OIl 1.008 1.006 1.004 1.002 I.OOl M. G. Lloyd, Bull. Bur. Standards, ;, p. 4)5 ; 1908. Smithsonian Table*. Tables 301, 302. 289 DEMAGNETIZING FACTORS FOR RODS. TABLE 301. /r=true intensity o,. magnetizing field, ZT' = intensity of applied field, /= in- tensity of magnetization, H^= H' — NI. Shuddemagen says: The demagnetizing factor is not a constant, falling for highest values of /to about 1/7 the value when unsaturated; for values of B [==H-\-«,ii I^ less than loooo, N is approximately constant; using a solenoid wound on an insulating tube, or a tube of split brass, the reversal method gives values for iV which are considerably lower than those given by the step-by-step method ; if the solenoid is wound on a thick brass tube, the two methods prac- tically agree. Ratio of Length to Diameter. Values o£ A^X io<. ll Ellipsoid. Cylinder. UniEorm Magneti- zation. Magneto- metric Metliod (Mann). Ballistic Step Metliod. Dubois. Shuddemagen for Range of Practical Constancy. Diameter. 0.158 cm. 0.317s cm. I. Ill cm. 1.905 cm. S 10 701 s 2549 630 6800 2550 2160 i960 15 1350 280 1400 I205 - - 1075 20 848 160 898 775 - - 671 30 432 70 460 393 388 350 343 40 266 39 274 238 234 212 209 t 181 25 182 162 160 145 149 132 18 131 118 116 106 106 z lOI 80 'l8 ?i 69 88 66 63 90 ICO 6s 7.8 63 SS 5" 54 6.3 51.8 45 46 41 41 150 200 56 2.8 25.1 20 23 21 16 I-S7 IS-2 II 12.5 II 300 7-5 0.70 7-S 5-2 2.8 400 4-5 0-39 C R. Mann, Physical Review, 3, p. 3S9i 1896. ?;£"l.thuSagen"-^™"c.Tm'. S. Arts and Sd. «. P- -Ss, .907 (Bibliography). TABLE 302. Shuddemagen also gives the following, where ^is determined by the step method Ratio of Length to Diameter. Values of KXio'. Diameter 0.3175 cm. Diameter I.I to 2.0 cm. IS 20 25 3° 40 '^ 80 100 150 32-2 18.6 12.7 9.2s Ik 1.83 85.2 36.6 16.6 II.6 8.45 3.26 1.67 290 Table 303. COMPOSITION AND MAGNETIC This table and Table 289 below are taken from a paper by Dr. Hopkinson • on the magnetic properties of iron and steeL which is suted in the paper to have been 240. The maximum magnetization is not tabulated ; but as stated in the by 4ir. " Coercive force " is the magnetizing force required to reduce the magnetization to zero. The '• demag- previous magnetization in the opposite direction to the " maximum induction " stated in the table. The " energy which, however, was only found to agree roughly with the results of experiment. No. of Test. Temper. Chemical analysb. Description of specimen. Total Carbon. Manga- nese. Sulphur. Silicon. Phos- phorus. Other substances. I Wrought iron . Annealed _ - - - - - 2 Malleable cast iron . (( - ~ — ~ ~ — 3 Gray cast iron . — — — — — — ~ 4 Bessemer steel . - 0.045 0.200 0.030 None. 0.040 — Whitworth mild steel Annealed 0.090 0.153 0.016 (( 0.042 — g u tt It 0.320 0.438 0.017 0.042 0-035 - it (* ( OU-hard- ( ened t( tt tt tt tt _ 7 8 " " Annealed 0.890 0.165 0.005 0.081 0.019 - Oil-hard- ened ii ,( ( ampere turns for demagnetization . . . . ) Gray cast iron " " " containing | % aluminium " " " " i% " . . ( A square rod 6 sq. cms. section and 6.5 cms. long, } from the Tilly Foster mines, Brewsters, Putnam ( County, New York, staged to be a very pure sample Soft wire {Annealed wire, calculated by Steinmetz from Ewing's experiments Hardened, also from Ewing's experiments ( Rod containing about 2 % of iron, also calculated ( from Ewing's experiments by Steinmetz ' Consisted of thin needle-like chips obtained by milling grooves about 8 mm. wide across a pile of thin sheets clamped together. About 30 % by vol- ume of the specimen was iron, ist experiment, continuous cyclic variation of m. m. f. 180 cycles per second 2d experiment, 114 cycles per second 3d " 79-91 cycles per second . Value of .00227 .00326 .00548 .00458 .00286 .00425 .00349 .00848 .00457 .00318 .02792 .07476 .02670 .01899 .06130 .02700 .011445 .01300 .01365 •01459 .02348 .0122 .0156 .0385 •0457 .0396 •0373 * " Trans. Am. Inst. Elect. Eng." January and September, 1892. t See T. Gray, " Proc. Roy. Soc." vol. Ivi. Smithsonian Tables. 296 Table 318. ENERGY LOSSES IN TRANSFORMER STEELS. Determined by the wattmeter method. Loss per cycle per cc^AB'-^-bnBv, where 5 = flux density in gausses and « = frequency in cycles per second, x shows the variation of hysteresis with B between 5000 and loooo gausses, and^ the same for eddy currents. Ergs per Gramme per Cycle. Watts per Pound at 60 Cy- Thick- cles and loooo Gausses. loooo Gausses. 5000 Gausses. Q IB, DesiguatioD. ness. cm* X y a Hyste. resis. Total. Hyste- 4|. Hyste- ^3 resis. r^^ resis. tai a^i Unannealed A 0.0399 1599 186 562 46 1-5' 2.02 0.00490 0.41 4-35 4.76 B .0326 I156 134 384 36 1-59 1.89 .00358 0.44 3-14 3-58 C .0422 1032 242 356 70 1.51 1-79 .00319 0.47 2.81 3.28 D .0381 1009 184 353 48 1.52 1.94 .00312 0.44 2.74 3-i8 Annealed E .0476 735 236 246 58 1.58 2.02 .00227 0.36 2.00 2.36 F .0280 666 100 220 27 1.60 1.88 .00206 0.44 1.81 2.25 G .0394 563 210 13^-5 54 1.54 1.96 .00174 0.47 1-53 2.00 H« .0307 412 146 39 1.58 1.90 .00127 0.54 1. 12 1.66 L .0318 341 202 iii.S 55 1.02 1.88 .00105 0.70 0-93 1.63 .0282 394 124 130 32 1.61 1.90 .00122 0.54 1.07 1. 61 L .0346 381 184 125 116 50 1. 61 1.88 .00118 0-535 I -035 0.96 1-57 B ■0338 354 200 57 i.6i 1.81 .00110 0.61 1-57 M •033s 372 178 127 46 1-55 1-95 .00115 0-55 I.OI 1.56 N .0340 321 210 105 56 1.62 1.90 .00099 0.63 0.87 1.50 P •0437 334 184 107 50 1.64 1.88 .00103 0.34 0.91 1.25 Silicon steels g^ .0361 isi 54 98 15 1.63 - .00094 0.14 0.825 0.965 R ■031S 42 93 II 1.64 - .00089 0.15 0.78 0-93 S .0452 278 72 90 18 \% - .00086 0.12 S^^ 0.875 T •0338 250 60 78 18 - .00077 0.18 0.86 U .0346 270 42 86 12 1.66 - .00084 0.12 0-735 0.855 V» .0310 251-5 47 79 13 1.68 - .00078 0.17 0.685 0.855 w« .0305 197 13 62.3 12.4 1.67 - .00061 0.16 0-535 0.695 X .0430 200 65 64.2 16.6 1.65 ^ .00062 0.12 0.545 0.665 • German. t English. t In order to make a fair comparison, the eddy_ current loss has been computed for a thickness of 0.0357 cm. (Gage No. 29), assuming the loss proportional to the thickness. Lloyd and Fisher, Bull. Bur. Standards, 5, p. 453 ; 1909. Smithsonian Tables. Table 31 9. 297 NIACNETO-OPTIC ROTATION. Faraday discovered that, when a piece of heavy glass is placed in magnetic field and a beam of plane polarized light passed through it in a direction parallel to the lines of magnetic force, the plane of polarization of the beam is rotated. This was subsequently found to be the case with a large number of substances, but the amount of the rotation was found to depend on the kind of matter and its physical condition, and on the strength of the magnetic field and the wave-length of the polarized light. Verdet's experiments agree fairly well with the formula— where ^ is a constant depending on the substance used, / the length of the path through the substance, H the intensity of the component of the magnetic field in the direction of the path of the beam, r the index of refraction, and K the wave-length of the light in air. If H be dif- ferent, at different parts of the path, lH\s to be taken as the integral of the variation of mag- netic potential between the two ends of the medium. Calling this difference of potential v, we may write 9 = Av, where A is constant for the same substance, kept under the same physical conditions, when the one kind of light is used. The constant A has been called " Verdet's con- stant," * and a number of values of it are given in Tables 303-310. For variation with tempera- ture the following formula is given by Bichat : — R=^ Ra (I — 0.00104/ — 0.000014;^, which has been used'to reduce some of the results given in the table to the temperature corre- sponding to a given measured density. For change of wave-length the following approximate formula, given by Verdet and Becquerel, may be used : — where y. is index of refraction and A. wave-length of h'ght. A large number of measurements of what has been called molecular rotation have been made, particularly for organic substances. These numbers are not given in the table, but numbers proportional to molecular rotation may be derived from Verdet's constant by multiplying in the ratio of the molecular weight to the density. The densities and chemical formulae are given in the table. In the case of solutions, it has been usual to assume that the total rotation is simply the algebraic sum of the rotations which would be given by the solvent and dissolved substance, or substances, separately ; and hence that determinations of the rotary power of the solvent medium and of the solution enable the rotary power of the dissolved substance to be calculated. Experiments by Quincke and others do not support this view, as very different results are obtained from different degrees of saturation and from different solvent media. No results thus calculated have been given in the table, but the qualitative result, as to the sign of the rotation produced by a salt, may be inferred from the table. For example, if a solution of a salt in water gives Verdet's constant less than 0.0130 at 20° C, Verdet's constant for the salt is negative. The table has been for the most part compiled from the experiments of Verdet,t H. Becque- rel,t Quincke, § Koepsel,|| Arons,T Kundt,** Jahn,tt Schbnrock,tt Gordon, §§ Rayleigh and Sidgewick,|||| Perkin.TIT Bichat.*** As a basis for calculation, Verdet's constant for carbon disulphide and the sodium line D has been taken as 0.0420 and for water as 0.0130 at 20° C. * The constancy of this quantity has been verified through a wide range of yaiiation of magnetic field by H. T. G. Du Bois (Wied. Ann. vol. 35). t " Ann. de Chim. et de Phys." [3] vol. 52. X "Ann. de Chim. et de Phys." [5] vol. 12 i " C. R." vols. 90 and 100. 5 " Wied. Ann." vol. 24. II " Wied. Ann." vol. 26. IT "Wied. Ann." vol. 24. ** " Wied. Ann." vols. 23 and 27. tt "Wied. Ann." vol. 43. XX " Zeits. fiir Phys. Chem." vol. 11. §§ " Proc. Roy. Soc" 1883. nil " Phil. Trans. R. S." 1885. lilt "Jour. Chem. Soc." vols. 8 and 12. *** " Jour, de Phys." vols. 8 and 9. Smithsonian Tables. 298 Table 320. MACNETO-OPTrc ROTATION. Solids. Substance. Chemical formula. Density or grammes per c. c. Kind of light Verdet's consunt in minutes. Temp. C. Authority. Amber - - D 0.0095 18-20° Quincke. Blende ZnS - (I 0.2234 IS BecquereL Diamond C - (( 0.0127 (( « Fluor spar .... CaFlj - U 0.0087 (( i( Glass : Crown - - it 0.0203 II u Faraday A . . . . - 5.458 ft 0.0782 18-20 Quincke. B . . . . - 4.284 ft 0.0649 11 (( Flint - - » 0.0420 ft (( it - - tf 0.0325 IS Becquerel. U - - tf 0.0416 " tt " dense .... - - tf 0.0576 it ti u u - - ft 0.0647 tt tt Plate - - ft 0.0406 18-20 Quincke. Lead borate .... PbBaO* - " 0.0600 IS Becquerel. Quartz (perpendicular to axis) - - ft 0.0172 18-20 Quincke. Rock salt .... NaCl " 00355 IS Becquerel. Selenium Se - B 0.4625 " it Sodium borate NajBiOT - D 0.0170 ft (t Spinel (colored by chrome) - - K 0.0209 it ft Sylvine . . , . . KCl - l( 0.0283 (f tt Ziqueline (suboxide of copper) CU2O - B 0.5908 (( u Smithsonian Tables. Table 321 . 299 MACNETO-OPTIC ROTATION. Uiinldi. Density Kind of light. Verdet's Chemical formula. in grammes constant in Temp. C. Authority. per c. c. minutes. Acetone CsHoO 0.7947 D O.OII3 20 Jahn. It U 0-7957 tt 0.0115 15 Parkin. i( It 0.7947 tt 0.01 1 4 16 Schonrock. Acids : (see also solutions in water) Acetic C2H4O2 1.0561 tt 0.0105 21 Perkin. Butyric . C4H8O2 0.9663 tt 0.0116 IS '* Formic . CHjOa 1.2273 tt 0.0105 15 " Hydrochloric tt HCl 1.2072 tt tt 0.0224 0.0206 IS 15 It Becquerel. Hydrobromic HBr 1.7859 tt 0.0343 IS Perkin. Hydroiodic . Nitric . HI 1-9473 " 0.0513 IS jj HNO3 1.5190 " 0.0070 13 " (fuming) . Propionic (( tt 0.0080 IS Becquerel. CsHeOa 0.9975 tt O.OIIO IS Perkin. Sulphuric H2SO4 tt 0.0I2I 15 Becquerel. Sulphurous . Valeric . H2SOS C5H10O2 0.9438 tt 0.0153 O.OI2I IS IS Perkin. Alcohols : Amyl . CsHiiOH If 0.8107 tt It 0.01 31 0.0128 15 20 Becquerel. Jahn. Butyl . " . . • C4H9OH l( 0.8021 tt a 0.0124 0.0124 20 IS Becquerel. Ethyl '. C2H6OH 0.7929 0.7900 tt tt 0.0107 0.0112 18-20 20 Quincke. Jahn. (f U 0.7944 tt O.OII4 IS Perkin. (( tt 0-7943 tt O.OII3 16 Schonrock. Methyl '. CHsOH 0.7915 0.7920 tt tt 0.0094 0.0093 18-20 20 Quincke. Jahn. 11 u 0.0106 IS Becquerel. ' .. 0.7966 u 0.0096 IS Perkin. u •• 0.7903 tt 0.0096 21.9 Schonrock. Octyl . Propyl . CsHitOH CsH,OH tt 0.8296 0.8050 0.8082 tt tt 0.0134 o.oi 20 0.0120 15 „ 20.8 15.0 Perkin. Schonrock. Perkin. (, tt tt 0.0II8 IS Becquerel. tt 0.8042 tt 0.0120 20 Jahn. Benzene . CeH, tt 0.8786 tt 0.0297 0.0268 20 15 Jahn. Becquerel. it ^ tt ^ ^ " 0.8718 u 0.0301 26.9 Schonrock. Bromides : Bromoform . Ethyl . Ethylene CHBra C2H6Br C2H4Br2 2.9021 1.4486 2.1871 2.1780 tt tt tt tt 0.0317 0.0183 0.0268 0.0269 IS IS IS 20 Perkin. tt tt Jahn. Methyl . Methylene . Octyl . Propyl . Carbon disulphide 11 '< CHaBr CH2Br2 CsHnBr CsHTBr CS2 tt 1-7331 2.4971 1.1170 1.3600 1.2644 tt It tl tt tt 0.0205 0.0276 0.0164 0.0180 0.0441 0.0434 IS IS IS 18-20 Perkin. (( Quincke. ( Becquerel, \ 1885. tt tt 0.0433 Gordon. u " tt tt 0.0420 18 Rayleigh. It << tt tl 0.0420 18 Koepsel. It - It 0.0439 Arons. Smithsonian Tables. 300 Table 321 {cmiinutd). MACNETO-OPTIC ROTATION. UtnUs. Density Kind Verdet's Substance. Chemical formula. in grammes of light. constant in Temp. C Authority. perc. c. minutes. Chlorides : Amyl CHCl 0.8740 D 0.0140 20 Jahn. Arsenic .... As - u 0.0422 15 Becquerel. Carbon .... C - tt 0.0170 15 II " bichloride ecu - it 0.0321 15 II Chloroform CHCla 1.4823 (I 0.0164 20 Jahn. " .... (( 1.4990 f( 0.0166 15 Perkin. Ethyl C2H5CI 0.9169 " 0.0138 6 « Ethylene .... CsHiClj 1.2589 (( 0.0166 15 (( tt ** 1.2561 tt 0.0164 20 Jahn. Methyl ! ! '. ! CHjCl - u 0.0170 IS Becquerel. Methylene .... CH2CI2 I-336I (( 0.0162 15 Perkin. Octyl CbHitCI 0.8778 tt O.OI41 15 a Phosphorus protochloride . PCIa - tt 0.0275 IS Becquerel. Propyl .... CsHjCl 0.8922 tt 0.0135 IS Perkin. Silicon .... SiCU - tt 0.0275 IS Becquerel. Sulphur bichloride S2CI2 - tt 0-0393 15 It Tin bichloride . SnCU — tt O.OI51 15 u Zinc bichloride . ZnClj - '• 0.0437 15 tt Iodides : Ethyl C2H5I 1.9417 " 0.0296 IS Perkin. Methyl .... CHsI 2.2832 *( 0.0336 IS li Octyl CsHi,! 1-3395 1.7658 11 0.0213 15 u Propyl CsHjI II 0.0271 15 tt Nitrates : Ethyl CjHsO.NOs I.I 149 II 0.0091 15 tt Ethylene (nltroglycol) C2H4(N08)2 1.4948 II 0.0088 15 tt Methyl .... CHsO.NOa 1-2157 II 0.0078 15 " Propyl .... C8H7O.NO2 1.0622 II 0.0 1 00 15 tt Trinitrin (nitroglycerine) . C8H6(N08)8 1.5996 II 0.0090 15 tt Nitro ethane C2H6NO2 1.0552 II 0.0095 IS It Nitro methane . CH8NO2 1-1432 It 0.0084 15 tt Nitro propane CsHsNOs I.OIOO " 0.0102 15 tt Paraffins : Decane .... C10H22 0.7218 II 0.0128 23.1 Schonrock. Heptane .... C7H16 0.6880 ** 0.0125 15 Perkin. Hexane .... CeHii 0.6580 II 0.0122 22.1 Schonrock. " .... 0.6743 II 0.0125 0.0128 15 Perkin. Octane .... CsHis 0.701 1 II 23.1 Schonrock. Pentane .... CeHu 0.6196 II 0.0II9 21. 1 II (( (1 0.6332 II 0.01 18 15 Perkin. Phosphorus (melted) P It 0.1316 33 Becquerel, Sulphur (melted) . S - II 0.0803 114 II Toluene .... C7H, 0.8581 II 0.0269 28.4 Schonrock. a *' - II 0.0243 IS Becquerel. Water H2O 0.9992 II 0.0130 15 " ** . .... " 0.9983 II 0.0I3I 18-20 Quincke. tt (( 0.9983 " 0.0132 20 Jahn. Xylene ..... CsHio II 0.0221 IS Becquerel. i< 0.8746 a 0.0263 27 Schonrock. Smithsonian Tables. Table 322. MACNETO-OPTIC ROTATION. Solnttons ol AclOs and Salts In Water. 301 Substance. Chemical formula. Density, grammes per c. c. Kind of light. Verdet's constant n minutes. Temp. Authority. Acetone CsHjO 0.9715 D 0.0129 20° Jahn. Acids : Hydrobromic HBr 1.7859 11 0.0343 IS Perkin, It (( 1. 61 04 II 0.0304 a 11 (( I-377S 11 0.0244 tt tt 11 it 1.2039 II 0.0194 ti tt 11 (t 1.1163 " 0.0168 a it Hydrochloric HCl 1.2072 11 0.0225 n ti 11 (( 1.1856 II 0.0219 tl it 11 " I-I573 11 0.0204 " it 11 it 1. 1279 11 0.0193 a it 11 it 1.0762 II 0.0168 " (( II 1-0323 1. 01 58 11 II 0.0150 0.0140 20 tl Jahn. Hydriodic . HI 1-9473 11 0.0513 it Perkin. II (( 1.9057 11 0.0499 •1 (( 1.8229 II 0.0468 " it 11 (( 1.7007 II 0.0421 (t " II (( I-449S II 0.0323 * * 11 11 it tl 1.2966 1. 1760 II 0.0258 0.0205 " it Nitric . HNOs 1.5190 II 0.00 10 tt 11 " 1.3560 11 0.0105 " Sulphuric + 3H2 Ammonia 3 H2SO4 NHs 0.8918 II II 0.0121 0.0153 tt IS Becquerel. Perkin. Bromides : Ammonium . NHiBr 1.2805 11 0.0226 " tt 1. 1 576 11 0.0186 ** Barium BaBr2 1-5399 II 0.0215 20 * Jahn. 11 " 1.2855 •' 0.0176 Cadmium 11 ^ CdBrg u 1. 3291 1. 1608 II 11 0.0192 0.0162 (( ti Calcium 11 , CaBra 1. 2491 I-I337 11 0.0189 0.0164 it it it Potassium . KBr ti 1. 1424 1.0876 11 0.0163 0.01 51 it it Sodium 11 Strontium . II ^ NaBr SrBr2 1-1351 1.0824 I. 2901 1.1416 11 11 II II 0.0165 0.0152 0.0186 0.01 59 it u tt it tt Carbonate of potassium " " sodium K2CO3 NajCOs 1. 1906 1. 1006 11 It 0.0140 0.0140 20 tt tt a it II 11 " ti 1.0564 11 0.0137 Chlorides : Ammonium (sal i Barium 11 immc miac) NH4CI BaCla 1.0718 1.2897 1-1338 II II II 0.0178 0.0168 0.0149 IS 20 Verdet. Jahn. 41 Cadmium 11 CdCla it 1-3179 1.2755 11 If 0.0185 0.0179 it (( 11 11 it 1.1732 1-1531 11 11 0.0160 0.0157 tt it Calcium 11 , CaCla • ti i.i;o4 1.0832 1. 1049 1.5158 1.2789 II II 11 0.0165 0.0152 0.0157 0.0221 0.0186 It 16 tt Schonrock. If , Copper CuCl2 II II 11 'i|S Becquerel. " ! 11 1-1330 11 0.0156 __ Smithsonian Tables. 302 Table 322 icmtinutd). MACNETO-OPTIC ROTATION. Solutions ol Aolds and Salts In Watei. Substance. Chemical formula. Density, grammes per c. c. Kind of light. Verdet's constant in minutes. Temp. C. Authority. Chlorides : Iron . . . . FeCla I -4331 D 0.0025 \f Becquerel. ** . ** I.2I4I ** 0.0099 " (( *' I.I093 1.0548 " 0.0118 " K " " u 0.0124 " " " (ferri :) FejCle 1-6933 tt — 0.2026 ti l( ** ti I-53I5 tt — 0.1140 " H ti tt it tt \fd°. ft — 0.0348 — 0.0015 ti If It tt it ti 1.0864 tt 0.0081 " II ti ti 1.0445 " 0.0113 II II ** " 1.0232 tt 0.0122 Optlo Rotation. Oasoi. Substance. Pressure. Temp. Verdefs constant in minutes. Authority. Atmospheric air Carbon dioxide Carbon disulphide Ethylene Nitrogen Nitrous oxide . Oxygen . Sulphur dioxide u u Atmospheric 74 cms. Atmospheric a u u a 246 cms. Ordinary 70° C. Ordinary « u (( t< 20° C. 6.83 X 10-8 13.00 " 23.49 " 34-48 " 6.92 " 16.90 " 6.28 " 3'-39 :: 38.40 " BecquereL Bichat. Becquerel. tt (t (( Bichat. Du Bois discusses Kundt's results and gives additional experiments on nickel and cobalt. He shows that in the case of substances like iron, nickel, and cobalt which have a variable mag- netic susceptibility the expression in Verdet's equation, which is constant for substances of con- stant susceptibility, requires to be divided by the susceptibility to obtain a constant. For this expression he proposes the name " Kundt's constant." These experiments of Kundt and Du Bois show that it is not the difference of magnetic potential between the two ends of the medium, but the product of the length of the medium and the induction per unit area, which controls the amount of rotation of the beam. TABLE 326.— Verdet's and Eimdt's Constants. The following short table is f]uoted from Du Bois' paper. The quantities are stated in c. e. s. measure, circular measure (radians) being used in the expression of " Verdet's constant " and ** Kundt^ constant." Name of substance. Magnetic susceptibility. Verdet's constant. Wave-length of light in cms. Kundt's constant. Number. Authority. Cobalt . Nickel . Iron Oxygen : i atmo. . Sulphur dioxide Water . Nitric acid Alcohol . Ether. . Arsenic chloride Carbon disulphide . Faraday's glass -f 0.0126X10-* — 0.0751 " -0.0694 " -0.0633 " — 0.0566 " — 0.0541 " -0.0876 " — 0.0716 " — 0.0982 " 0.000179 X IO-* 0.302 " 0.377 0.356 « 0.330 ; 0-315 1.222 « 1.222 1-738 Becquerel. (( Arons Becquerel. De la Rive. (1 Becquerel. Rayleigh. Becquerel. 6.44 X I0-* 6.56 ■' 5.89 ;; tt tt tt tt tt tt 3-99 2.63 0.014 — 4.00 =S =?s —14.9 — I7.I —17.7 Smithsonian Tables. Tables 327, 328. TABLE 327.-BUgiiatto BnioepttUUty of LlanMi uA Oasas. 305 ^^^^ u»i.u«!i. V eraet 9 and Kundt's constants are in radians for the sodium line D. _^^ Substance. Verdet's constant. Faraday's value Becquerel's value *Xio» Wahner's value *Xio» Water 377 X io-« — 0.69 —0.63 -0.536 Alcohol, CjHeO . 3-30 " -0.57 -0.49 -0.388 Ether, C4H10O . 3-iS " -0-54 - —0.360 Carbon disulphide 12.22 " — 0.7a —0.84 -0.46s Oxygen at i atmosphere . o.oor79 " 0.13 0.12 . Air at i atmosphere . 0.00194 " 0.024 0.025 - Quincke at jo° C. Du Bois at 15° C. Density. *Xio« Density. *Xlo9 Kundt's constant.. Water 0.9983 —0.815 0.9992 -0.837 —4.50 Alcohol, CaHeO . . . 0.7929 -0.660 0.7963 -0.694 -47S Ether, C4H10O . 0.7152 —0.607 0.7250 — 0.642 —4.91 Carbon disulphide 1.2644 —0.724 1.2692 —0.816 -14.97 Oxygen at i atmosphere - - 0.00135 0.1 17 0.016 Air at i atmosphere . - - 0.00123 0.024 0.081 TABLS 328.— Valnei of Kerr's Oonstontt Da Bois has shown that the rotation of the major axis of vibration of radiations normally reflected from a maenet is _i — 1 — ;__ti.. — iial to the normal component of magnetization multiplied in' — ' — * ^ " "- '' > constant for the magnetized substance fonning the magnet. algebraically equal to the normal component of magnetization multiplied into a constant IC. He calls this con- stant, A", Kerr's coi Color of light. Spectrum line. Wave- length in cms. Xio« Kerr's constant in minutes per c. g. s. unit of magnetization. Cobalt. Nickel. Iron. Magnetite. Red . . . Red . . . Yellow - Green . Blue . Violet . Li a D i F G 67.7 62.0 58.9 SI7 48.6 431 — 0.0208 —0.0198 —0.0193 — 0.0179 —0.0180 — 0.0182 —0.0173 — 0.0160 — 0.0154 — 0.0159 — 0.0163 —0.0175 —0.0154 — 0.0138 — 0.0130 —O.OIII — 0.OI0I — 0.0089 +0.0096 +0.0120 +0.0133 +0.0072 +0.0026 * " Wied. Ann." vol. 3Si p. i^S- Smithsonian Tables. t H. E. J. G. Du Bois, " Phil. Mag." vol. 19. 306 Tables 329-331 . RESISTANCE OF METALS. TABLE 329. — VarUtlon of Reslstanoe ol Blamntli, with Tempentiue, In a TTonsTene Hagnetlo FlaU. Proportional Values of Resistance. H -193° -I3S° — 100° -37° 0° +18° +60° +100° +183° o 2000 4000 6ooo 8000 lOOOO I200O 14000 16000 iSooo 20000 25000 30000 35000 0.40 1.16 2.32 4.00 5-90 8.60 10.8 12.9 15-2 17.S 19.8 25.5 30.7 35-5 0.60 0.87 1.35 2.06 2.88 3.80 4-76 S.82 6.9s 8.1S 9-50 Vd 30.3S 0.70 0.86 1.20 1. 6a 2.00 2.43 2.93 3.50 4.II 4.76 S.40 7.30 9-8 12.2 0.88 0.96 1. 10 1.29 I. SO 1.72 ITe 2.38 2.60 2.81 3.50 4.20 4-95 1. 00 1.08 I.lS 1.30 1-43 1.57 1.71 1.87 2.02 2.18 2.33 2.73 3.17 3.62 1.08 I.ll 1.21 1.32 1.42 1.54 1.67 1.80 2.20 2.52 2.86 3.2s 1.25 1.26 1.31 1.39 1.46 1.54 1.62 1.70 1-79 1.88 1.97 2.22 2.46 2.69 142 1.43 Z.46 1.51 1.57 1.62 1.67 1.73 1.80 1.87 1.95 2.10 2.28 24s 1.79 1.80 1.82 I.8S 1.87 1.89 1.92 1.94 1.96 1.99 2.03 2.09 2.17 2.25 TABLE 330. — Inoiaaso ol Reslstanoe ol Nickel dna to a TransTarse MagneUo FlaU, axpressed as % ol Reslstasca at 0° anaH=0. H — 190° -75° 0° +18° +100° +182° +0 1000 +0.20 +0.23 +0.07 +0.07 +0.96 +0.04 2000 +0.17 +0.16 +0.03 +0.03 +0.72 —0.07 3000 0.00 —0.0s -0.34 —0.36 -0.14 —0.60 4000 -0.17 -o.is —0.60 -0.72 —0.70 -1.15 6000 —0.19 —0.20 —0.70 —0.83 — 1.02 -I. S3 8000 —0.19 -0.23 —0.76 — 0.90 -I.IS -1.66 lOOOO —0.18 -0.27 —0.82 -0.95 -1.23 -1.76 12000 T-0.I8 —0.30 —0.87 — 1. 00 -1.30 — 1.85 14000 —0.18 -0.32 —0.91 —1.04 -1.37 -1.95 16000 -0.17 -0.35 -0.94 —1.09 -1-44 -2.05 18000 -0.17 —0.38 —0.98 -I.I3 -1-51 -2.15 20000 -0.16 —0.41 -1.03 -1. 17 -1.59 -2.25 25000 -0.14 -0.49 — 1. 12 -1.29 -1.76 -2.50 30000 — 0.12 -0.56 -1.22 —1.40 -1. 95 -2.73 35000 — O.IO —0.63 -1.32 -I. so -2.13 -2.98 F. C. Blake, Ann. der Physik, 28, p. 449; 1909. TABLE 331. — Oliasga ot Raslstanoa ol Vailona Katals in a Tiansvana Uagnatlo Flald. Room TampaTatnra. Metal. Field Strength In Gausses. Per cent Increase. Authority. Nickel loooo -1.2 Wmiams, Phil. Mag. 9. 1905. * " -1.4 Barlow, Pr. Roy. Soc. 71, 1903. ** 6000 — I.O Dagostino. Atti Ac. Lbic. 17, 1908. ** lOOOO -1.4 Grummach, Ann. der Phys. 22, 1906. Cobalt " -0.53 " Cadmium ■ -0.03 •• Zinc •• - -O.OI •t Copper •■ - -0.004 •• Silver •• - -0.004 •• Gold •■ - -0.003 *■ Tin ** •• Palladium •' - -O.OOI •• Platinum •* - -o.ooos •• Lead " - -0.0004 •• Tantalum *• - -0.0003 '* Magnesium Manganin 6000 +o.ot +0.01 Dagostino, (. c. Tellurium ? +0.02 to 0.34 +0.02 to 0.16 Goldhammer, Wled Ann. 31, 1887. Antimony ? Different specimens show very Grummach, (. c. diverse results, usually an in- Barlow, I. c. crease in weak fields, a decrease in strong. Williams, I. e. Nickel steel Alloys behave similarly to Iron. Williams, r. e. Smithsonian Tables. 307 Tables 332, 333. TASLE 332.-Traii»verBe Oalvanomagnetlo and ThermomagneUo EHects. andthf prima°v'c™Th!.''t "'""I' *!"■ '?"'S?-^'''= ^f^ "^""S ^"^'^^^ avvay from the observer, ^ ^-diijenceof potential produced; r=difference of temperature produced; /-primary '^"*°*: ^x =P"'nary temperature gradient, ^= breadth, and Z) = thickness, of specimen: ^=mtensity of field. C. G. S. units. pcumen, Hall effect (Galvanomagnetic difference of Potential), E = R— Ettingshausen effect ( " " « Temperature), T=P^ Nemst effect (Thermomagnetic Leduc effect ( " dt " Potential), .ff = e.a5^ " Temperature), T=SHB^ dt Substance. Values o£ R. P X 108. Q X io«. SXi^. Tellurium Antimony ... Steel +400 to 800 + 0.9 " 0.22 4- .012 " 0.033 +.010 " 0.026 +.007 " O.OII +.0016 " 0.0046 +.00055 +.00040 +.00009 —.00003 — .0002 — .00052 —.00054 — .00057 to .00071 — .0009 —.00093 .0007 to .0012 .0008 " .0015 — .0023 — .00094 to .0035 — .00036 " .0037 .0045 " .024 —.017 — up to 16. +200 +2 — 0.07 — 0.06 +0.01 +0.04 to 0.19 , +5- +3 to 40 —360000 +9000 to 18000 —700 " 1700 +1600 " 7000 — 1000 " 1500 +1800 " 2240 —54 " 240 up to — 5.0 -5.0 (?) -4.0 (?) —90 to 270 +50 to 130 —46 " 430 +2000 " 9000 + 100 — up to 132000 +400 +200 +69 +39 +13 +13 +5 — 2 —18 —3 —41 —45 — 200 Hensler alloy .....'. Iron Cobalt Zinc Cadmium Iridium Lead Tin Platinum Copper German silver Gold Constantino Manganese Palladium Silver Sodium Magnesium Aluminum Nickel Carbon Bismuth TABLE 333. —Variation ol Hall Constant with tlie Temporatuie, Bismuth.^ Antimony.3 H — 182O -,0° -«3° +".S° +100° H —186° -79° +21.5° +58° 1000 2000 3000 4000 5000 6000 62.2 S5-0 497 45.8 42.6 40.1 28.0 25.0 22.9 21.5 20.2 18.9 17.0 16.0 15.1 14-3 13.6 12.9 13.3 12.7 12.1 11.5 II.O 10.6 7.28 7.17 7.06 ni 6.72 1750 6160 0.263 0.252 0.245 0.249 0.243 02.35 0.217 0.21 1 0.209 0.203 Bismuth.' H +■4.5° +<04° 125° 189° 212° 239° 259° 269° 270° 890 S.28 2-57 2.12 1.42 1.24 I.II 0.97 0.83 0.77* 1 Barlow, Ann. der Phys. 12, 1903. ' Everdingen, Comm. Phys. Lab. Leiden, 58. » Traubenberg, Ann. der Phys. 17, 1905. .... * Melting-point. „ , ,_ Both tables taken from Jahn, Jahrbuch der Radioactlvitit und Electronik, 5, p. 166; 1908, who has collected data Of all observera and gives extensive bibliography. Smithsonian Tables. APPENDIX I. Tables 334, 335. THE SPECIFIC HEAT OF IRON AT HIGH TEM- PERATURES. Analysis of iron — (o.oi C, .02 Si, .03 S, .04 P, trace Mn). TABLE 334. —Mean SpeolUo Heat Iwtwegn 0° and T° Oenttgiade, S?. T sj T sj 200° 0.1 17s 700° 1487 250 .1204 750 1537 300 •"33 800 1 597 35° .1257 850 1647 400 .1282 900 1644 450 .1311 950 1612 Soo •1338 I0CX3 ISS7 55° .1361 1050 1512 600 .1396 IIOO 1534 650 .1440 TABLE 336. — Total Heat between 0° and 1° Genttgrade, Qo- qS QJ Pionchon's value recalculated. Barker's value. 200 23-S 23-S 300 36.8 37 -o 400 51.6 51-3 500 66.0 66.9 600 83.2 83.8 700 102.2 1 04. 1 800 125.0 127.8 900 146.7 148.0 1000 166.0 1S5-7 IIOO " 168.8 T. A. Harker, Proc. Physical Society, London, 19, p. 703 \ '905- Pionchon's data, based on experiments made many years ago, should be regarded only as corroborative of the more recent and careEul experi- ments of Harker. Smithsonian Tables. APPENDIX II. DEFINITIONS OF UNITS. AMPErF* TTn^T ?' ?^^ ?^ '*°'"S work; unit, the watt. unk of cu^"nt of1he?'^'^"'"^ ^he international ampere, "which is one tenth of the suffidMtlv well fnr t. ?■ ^- ^^K "" 2^ electro-magnetic units, and which is represented TsoE or^ IrpL^nf T*' • '^ ^y ^^^ unvarying current which, when passed through tions" r^^, nn™ -^ ^'^r' "? Z""}^"' """^ '" accordance with accompanying specific- second." ^ '^'^' «^^P°^'ts ^»ver at the rate of o.ooi 1 18 of a gramme per The ampere = I coulomb per second = i volt through i ohm; Amperes =volts/ohms= watts/ volts = (watts /ohms)*. ^ Amperes X volts = amperes ' Xohms = watts. iS™gfRE''"Ll:r/rt"u^r^': = '°~" '"^^^^^ English normal = 14.7 pounds per sq. in. =29.929 in. =760.18 mm. Hg. m" F. B Jr Tn r r ^ ^^v""? " °^ "^- °° ^- =^9-922 in. = 4.70 lbs. per s|. in. n/^fr^^ ""'* °' pressure = I dyne per sq. cm. gOUGIE DECIMALE. Photometric standard; see page 177. BKl 1 IbH THERMAL UNIT. Heat required to raise one pound of water at its temper- r-iT?^Sv c ^^'i"""?^ density, 1° F.=252 gramme-calories. CALUKY. bmall calory = gramme-calory = therm = quantity of heat required to raise one gramme of water at its maximum density, one degree Centigrade. Large calory =kilogramme-calory = 1000 small calories = one kilogramme of water raised one degree Centigrade at the temperature of maximum density. For conversion factors see page 227. CANDLE. Photometric standard, see page 177. CARAT. The diamond carat =3.168 grains =0.2053 grammes. The gold carat: pure gold is 24 carats; a carat is 1/24 part. CARCEL. Photometric standard; see page 177. CIRCULAR AREA. The square of the diameter = 1. 2733 Xtrue area. True area =0.785398 Xcircular area. COULOMB. Unit of quantity. The international coulomb is the quantity of electricity transferred by a current of one international ampere in one second. Coulombs = (volts- seconds) /ohms = amperes X seconds. CUBIT = 18 inches. DAY. Mean solar day = i440 minutes = 86400 seconds = 1.0027379 sidereal day. • Sidereal day = 86164.10 mean solar seconds. DIGIT. 3/4 inch; 1/12 the diameter of the sun or moon. DYNE. C. G. S. unit of force = that force which acting for one second on one gramme pro- duces a velocity of one centimetre per second. = weight in grammes divided by the acceleration of gravity in cm. per sec. ENERGY. 5eeErg. ERG. C. G. S. unit of work and energy = one dyne acting through one centimetre. For conversion factors see page 227. FARAD. Unit of electrical capacity. The international farad is the capacity of a con- denser charged to a potential of one international volt by one international coulomb of electricity. The one-millionth part of a farad (microfarad) is more commonly used. Farads = coulombs/ volts. FOOT-POUND. The work which will raise one pound one foot high. For conversion factors see page 227. FOOT-POUNDALS. The English unit of work = foot-pounds /g. For conversion factors see page 227. g. The acceleration produced by gravity. GAUSS. A unit of intensity of magnetic field = 10' C. G. S. units. GRAMME. See page 6. 3IO APPENDIX. GRAMME-CENTIMETRE. The gravitation unit of work=g. ergs. For further conversion factors see page 227. HEAT UNIT. See Calory. .... HEAT OF THE ELECTRIC CURRENT generated in a metalhc circuit without self- induction is proportional to the quantity of electricity which has passed in coulombs multiplied by the fall of potential in volts, or is equal to (coulombsXvolts)/4.i8i in small calories. The heat in small or gramme-calories per second = (amperes''Xohms)/4.l8i=volts V (ohms X 4.181) = (volts X am peres)/4.l8i = watts/4.181. HEAT. Absolute zero of heat = -273° Centigrade, -459.4° Fahrenheit, -^18.4° Reaumur. HEFNER UNIT. Photometric standard; see page 177. HENRY. Unit of induction. It is "the induction in a circuit when the electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampere per second." HORSE-POWER. The practical unit of power =33,000 pounds raised one foot "per min- ute. JOULE. Unit of work = 10' ergs. Joules = (volts^ Xseconds) /ohms = watts X seconds = amperes' Xohms X sec. For conversion factors see page 227. JOULE'S EQUIVALENT. The mechanical equivalent of heat = 4.181X10' ergs. See page 227. KILODYNE. 1000 dynes. About i gramme. LITRE. See page 6. MEGABAR. Unit of pressure =0.987 atmospheres. MEGADYNE. One million dynes. About one kilogramme. METRE. See p^e 6. METRE CANDLE. The intensity lumination due to standard candle distant one metre. METRET. An exponential subdivision of the metre. The ordinal number before the word metre denotes the power of ten serving as the divisor; e. g., a tenth-metret = io-"' = l/io'" metre. The first metret is the decimetre, the second, the centimetre, etc. MHO. The unit of electrical conductivity. It is the reciprocal of the ohm. MICRO. A prefix indicating the millionth part. MICROFARAD. One millionth of a farad, the ordinary measure of electrostatic capacity. MICRON, (m) =one millionth of a metre. MIL. One thousandth of an inch. MILE. See pages 5, 6. MILE, NAUTICAL or GEOGRAPHICAL = 6080.204 feet. MILLI-. A prefix denoting the thousandth part. MONTH. The anomalistic month = time of revolution of the moon from one perigee to another =27.55460 days. The nodical month = draconitic month = time of revolution from a node to the same node again =27.21222 days. The sidereal month = the time of revolution referred to the stars=27.32i66 days (mean value), but varies by about three hours on account of the eccentricity of the orbit and "perturbations." The synodic month = the revolution from one new moon to another =29.5306 days (mean value) = the ordinary month. It varies by about 13 hours. OHM. Unit of electrical resistance. The international ohm is based upon the ohm equal to 10' units of resistance of the C. G. S. system of electromagnetic units, and "is repre- sented by the resistance offered to an unvarying electric current by a column of mer- cury, at the temperature of melting ice, 14.4521 grammes in mass, of a constant cross section and of the length of 106.3 centimetres." International ohm = 1.01367 B. A. ohms = 1.06292 Siemens' ohms. B. A. ohm =0.98651 international ohms. Siemens' ohm = 0.94080 international ohms. See page 261. PENTANE CANDLE. Photometric standard. See page 177. PI =ir = ratio of the circumference of a circle to the diameter =3.14159265359. POUNDAL. The British unit of force. The force which will in one second impart a veloc- ity of one foot per second to a mass of one pound. RADIAN = i8o°/t = 57-29578° = 57° 17' 45"=2o6625". SECOHM. A unit of self-induction = i second X I ohm. THERM =small calory = quantity of heat required to warm one gramme of water at its temperature of maximum density one degree Centigrade. THERMAL UNIT, BRITISH = the quantity of heat required to warm one pound of water at its temperature of maximum density one degree Fahrenheit = 252 gramme-calories. VOLT. The unit of electromotive force (E. M. F.). The international volt is "the electromotive force that, steadily applied to a conductor whose resistance is one inter- national ohm, will produce a current of one international ampere, and which is repre- sented sufficiently Well for practical use by 1000/1434 of the electromotive force be- APPENDIX. 311 ' tween the poles or electrodes of the voltaic cell known as Clark's cell, at a temperature of 15° C and prepared in the manner described in the accompanying specification." 5ee pages xxxiv and 251. VOLT-AMPERE. Equivalent to Watt. WATT. The unit of electrical power = 10' units of power in the C. G. S. system. It is re- presented sufficiently well for practical use by the work done at the rate of one Joule per second. Watts = volts Xamperes = amperes'' Xohms =volts'/ohms. For conversion factors see page 227. Watts Xseconds = Joules. WEBER. A name formerly given to the coulomb. YEAR. See page 108. Anomalistic year =365 days, 6 hours, 13 minutes, 48 seconds. Sidereal " =365 " 6 " 9 " 9.314 seconds. Ordinary " =365 " 5 " 48 " 46+ Tropical . " same as the ordinary year. INDEX. For the definitions of units, see Appendix. Aberration constant . ''*°^- Absorption of gases by liquids' .' t^? AbsorpUonofUghtiatmosplierlc: .'.'.'.'. lig color screens ..." I ! 19s Jena glasses 193 Acceleration of gravrtf""'.^^' • • •, • j'* Aerodynamic date: soaring data . • ■ '"4 J°7 Agonic Une . . .™d pressures . . ! ! ! i.. Air: density .....'.' til Air thermometer, comparisons 31^ Air: transmissibiUty of. for radiation '.'.'.'. l^g Alcohol: density p8_JJj vapor pressure 146 viscosity ^25 Alloys: densities .' ! ! ! 89 electrical conductivity of . '. '. * '266-268 resistance of .... 262-268 , . low temp. . . . 264 meltmg-points 214 specific heats 230 thermal conductivity 199 thermoelectric powers 258-259 Alternating currents, resistance of wires for . . 269 Aluminum wire, weights of 64 Alums: indices of refraction 181 Antilogarithms 26-28 Aqueous solutions : boiling-points 219 densities 92 alcohols 98 alcohol, temperature var'n 100 diffusion of 136 electrolytic conductivities 272-278 Aqueous vapor: vapor pressure, low temp . . .151 0° to 100° C . 152 100° to 230° C . 153 pressure of, in atmosphere . . 155 (saturated) weight of . . . .154 Astronomical data 108-X09 Atmosphere, aqueous vapor in 155 transmissibility for radiation . . . 179 Atomic weights 270 Barometer: boiling temperature of water for va- rious heights 168-169 . 121 . 119 . 120 . 118 . 117 . 167 . 252 . 84 . 59 . 306 . 238 . 2X0 . 213 . 215 , 219 . 168 . 60 . 62 . 71 . 59 7-10 correction for capillarity latitude, inch metric sea level . . temperature . heights, determination of, by Batteries: composition, electromotive forces Beaume scale: conversion to densities . Birmingham wire gauge Bismuth, resistance of, in magnetic field " Black-body " radiation Boiling-points: chemical elements . . inorganic compounds organic compounds . . Boiling-point, raising of, by salts in solution of water and barometric pressure Brass wire, weights of, common measure metric measure Brick, crushing strength of .... British wire gauge British weights and measures .... Cadmium line, wave-length red . . Candle power, standard . . . . Capacity, specific inductive: crystals liquids liquid gases , 170 , 177 . 284 i 279 . 280 2Sa Catacily, stecific inductive: solids .... 283 Capillarity, correction to barometer for , . 121 hquids 142-143 hquids near solidifying point . . . 143 salt solutions in water 142 thicimess of soap films 143 Carcel unit ! 177 Cells, voltaic: composition, E, M. F. ! 252-253 double-fiuid .253 secondary 253 single-fluid 252 standard 251, 253 storage 253 Chemical, electro-, equivalents 270 _. . , , equivalent of silver . . ! ! 251 Chemical elements: atomic weights 270 boiling-points 210 compressibility 76 conductivity, thermal , , , X99 densities 85, 91 electro-chemical equivalents 270 hardness 76 melting-points 209 resistance, electrical . 262-263 specific heats 228 thermal conductivities . . 199 „. . , expansion, linear . 222 Circular functions; argument (°') 30 (radians) .... 35 Coals, heat of combustion of 202 Cobalt, magnetic properties of 293 Color screens 195-196 Combination, heat of 204 Combustion, heat of: coals 202 explosives 203 fuels (liquid) 202 peats 202 Compressibility: chemical elements .... 76 gases 79-61 liquids 82 solids 83 Concretes: resistance to crushing 7r Conductivity, electrical: see Resistance. alloys 266-268 alternating currents, effect of . 269 magnetic field, effect of . . . 306 electrolytic 272-278 equivalent , . , 275-278 ionic (separate ions) . . 278 specific molecular . . . 273 limiting values 274 temp'ture coef. 274 glass and porc'l'n, temp'ture coef. 285 Conductivity, thermal: gases 200 liquids 200 salt solutions .... 200 solids X99 water 200 Contact differences of potential .... 254-256 Convection, cooling by 239-240 Conversion : Beaume to specific gravities ... 84 factors for work units 227 Cooling by radiation, perfect radiator .... 238 and convection . . 239-240 Cosines, hyperbolic natural 41 logarithmic 42 Critical data for gases 221 Crushing, resistance to: bricks 71 concretes 71 stones 71 timber, wood .... 73 Cubical thermal expansion: gases 226 liquids . . . . . 225 solids 224 314 INDEX. Crystals: dielectric constant 384 elasticity 77-78 expansion, cubical thermal .... 224 transmissibility for radiation . . . .194 Current, absolute, measures 251 Cyclic magnetization, energy losses in . , 294-296 Declination, secular change of magnetic . . .110 Demagnetizing factors for rods 289 Density : air : values of h/^6o z6o alcohol : aqueous ethyl 98 methyl 98 temperature variation . . .100 alloys 89 aqueous alcohol 98 salt, acid, basic solutions , . 92 chemical elements 85, 91 earth zo8 gases 91 liquids 90 mercury 97 metals 85 organic compounds 215 water 95-96 woods 87 Dew points 156 Dielectric constant: (specific inductive capacity) calibration, standards for . 283 gases, atm. pressure . . 279 pressure coef. . . 279 temperature coef. . 280 liquids 280 temperature coef. . 282 solids 283 Dielectric strength: air: alternating potential . 248 steady potential . . . 248 kerosene 250 large spark-gaps . . . 249 pressure effect . . . 249 various materials . .250 Difference of potential: c^ls: double fluid 253 secondary 253 single fluid 252 standard 251,253 storage 253 contact: liquids-liquids in air . 254 metals in salt solutions 257 salts with liquids . . 354 solids-solids in air . . 256 thermo-electric 258 platinum couples 259 Differential formulx 12 Diffusion : aqueous solutions, water 136 gases and vapors : coefficients . . . 138 metals into metals 138 vapors 137 Diffusion integral 50 Dip, magnetic 113 secular change iz2 Dynamical equivalent of thermal unit .... 227 e, value of la e*. <~*, and their logarithms 43. 47 log. ^, X from 10 to 30 44 e* > «~* , and their logarithms 45 0* , ^**, and their logarithms 46 € ', ^ ~ ' '. and their logarithms .... 46 — - — , and their logarithms 4i» 43 e'-e-^ —r~ 39,40 Earth : densities loS miscellaneous data 108 Elasticity: crystals 77. 78 moduli of rigidity 74 modulus. Young's 75 Electrical conductivity: alloys .... 266-268 alternating current, effect of 269 magnetic field, effect of . . 306 Electrical resistance: see Conductivity. metals and alloys, low temp. 264 ohm, various determinations 261 specific : metallic wires . . 363 metals 263 temperature effect, glass . 385 Electricity, specific heat of 258 Electric units, dimensional formulae zxvi Electrochemical equivalents 370, 272 silver 251 Electrolytic conductivity: 373-278 dilute solutions 273 equivalent s . . . . 375-378 ionic 278 specific molecular .... 273 limiting values 274 temp. coef. . 274 Electromagnetic system of units xzix Electromagnetic/^ectrostatic units = v ... 247 Electromotive force: cells: double fluid . . . 253 secondary .... 353 single fluid .... 353 standard . . . 351, 253 storage 253 liquids-liquids in air . . 254 metals in salt solutions . . 257 salts with liquids .... 254 solids-solids in air ... 256 thermo-electric . . . .258 (platinum) . 259 Elements: atomic weights 270 boiling-points 210 compressibility 76 conductivity, thermal 199 densities 85, 91 electrochemical equivalents .... 270 hardness 76 melting-points 209 resistance, electrical 263 specific heats 228 spectra (prominent lines) .... 170 thermal conductivities igg expansion, linear .... 333 cubical, gases . . 226 Elliptic integrals 57 Emission of periect radiator 338 Equivalent, electro-chemical: elements . , . 270 ionic 373 silver 251 Equivalent, mechanical, of heat 227 Energy, data relating to solar 179 Ethyl alcohol, specific gravity of aqueous ... 98 Ettinghausen effect 307 Expansion, thermal: cubical, crystals .... 324 gases 226 liquids .... 335 solids 224 linear, elements .... 323 various 223 perfect gas 163 Explosives, composition, etc 203 Exponential functions: «". «"*, their logs. . . 43, 47 log. e*. * =: 10 to 30 . . 44 «*'. «"**# their logs ... 45 ^-.e-^-- •■ . . . 46 *"*, ^~* ■, their logs. 46 ■ , their logs. . . 41, 43 —^ . . 39.40 diffusion integral ... 50 hyperbolic sines • . . 39 cosines . , 41 logs. hyperboUc sines , 40 cosines . 43 probability integral . 47, 48 Eye, sensitiveness of. to radiation 178 Fabry-Buisson, standard arc Fe wave-lengths , 170 Factorials, « 1 38 Fechner's law . . _ 178 Field: earth's magnetic field, components of 110-115 magnetic, behavior of met^s in . . 386-296 resistance of metals in 306 rotation of plane of polarization 297-304 thermo-, galvanometric effects . . 307 Films, thin: thickness, colors, tension of . 142, 143 Fluorite: index of refraction 184 Formulae, conversion: dynamic units .... 2 dectric " 3 fundamental 2 geometric 2 INDEX. 315 Pormula, conversion: heat 3 magnetic 3 _. see Introduction. ^raunhofer lines, wave-lengths of 176 Freezing mixtures 220 greezing-points. lowering of, by salts in solution 217 friction, coeflficients of . . 12! Fuels, heats of combustion of * 202 Functions: circular arguments (° ') . . . ! \ 30 (radians) . ". '. 35 exponential 39-47 gamma ' S2 '?8 hyperbolic .' .' ' %(>-a2 Fundamental units .... t Fusion, latent heat of .' ! ! ! 208 Galvauometric effects of magnetic field . . .307 Gamma function 52 38 Gases; absorption of, by liquids ..'.', 140 141 atomic weights 270 compressibility of I 70-81 conductivity, thermal ' . 200 critical data for 221 densities ! 91 dielectric constants 279, 280 diffusion 138 expansion of perfect ] 162 expansion, thermal 226 heat, conductivity for 200 indices of refraction 190 magnetic susceptibility 305 magneto-optic rotation 304 refractive indices of 190 sound, velocity of , in 102 solubility of 140, 141 specific heats ?32 thermal conductivity 200 thermal expansion 226 viscosity of 134 volume of perfect (1+0.00376O . . 162-166 Gas thermometry 233-233 Gauges, wire: Birmingham 59 British standard 59 Brown and Sharp 66 Geodetic data zoS Geometric units, conversion factors for . . . 2 Glass: indices of refraction 180 transmissibility of Jena 193 various . . . 195-196 dectric resistance, temp, variation . . 285 Glass vessels, volumes of 11 Gravity, force of 104-106 correction to barometer 1 1 8 Gyration, radii of 5B Hall effect 307 Hardness 76 Harmonics, zonal 54 Heat: combination, heat of 204 combustion: coals 202 explosives 203 fuels liquid 202 peats 202 conductivity for: gases 200 liquids 200 salt solutions .... 200 solids 199 water 200 latent heat of fusion 208 vaporization .... 206, 241 mechanical equivalent of 227 specific: elements 228 gases 232 liquids 230 mercury 229 minerals 231 rocks 231 solids 230 vapors 232 water 229 " Heat, specific," of electricity 258 Hefner photometric unit i77 Heights determinations of by barometer . . . 167 Horizontal intensity of earth's field . . . .114 secular change 114 Humidity, relative is8 Humidity term, 0.378* IS9 Hydrogen thermometer 233 Hyperbolic cosines, natural 41 logarithmic 42 Hyperbolic sines, natural 39 logarithmic 40 Hysteresis: soft iron cable transformer .... 294 wire 294 steel, transformer ...... 296 various substances 295 Iceland spar, refractive index of 184 Inclination (dip) of magnetic needle . . . .112 secular change of 112 Index of refraction: alums 181 crystals 187 fluorite 184 gases and vapors .... 190 glass x8o Iceland spar 184 liquids 189 metals, metallic oxides . .182 monorefringent solids . . 186 nitroso-dimethyl-aniline . 184 quartz 185 rock-salt 183 salt solutions 188 silvlne 186 solids, isotropic . . . . 1S6 Inductance, table for computing mutual . . . 56 Inductive capacity, specific: calibration st'ds . 283 gases, atm. pressure 279 pressure coef. 279 temp. coef. . 280 liquids 280 temp. coef. . 282 solids 283 Inertia, table of moments of 58 Inorganic compounds: boiling-points .... 213 melting-points . , . 21X Integral, diffusion 50 elliptic 57 gamma function 52 probability 4Si 47-48 Integrals, elementary 12 Intensity, horizontal, of earth's field .... 113 secular variation Z13 total, of earth's field 114 secular variation 114 Ionization of water 278 Ions: equivalent conductivity of 27S Iron: hysteresis in soft 294 magnetic properties of, weak fields . . . 294 saturated . . , 293 permeabilities 286-292 specific heat at high temperatures . . . 308 standard arc lines, Fabry-Buisson . . . 170 Kayser 174 Joule's (mechanical) equivalent of heat , , . 227 Kayser's standard iron arc spectrum .... 174 Kerosene, dielectric strength 250 Kerr's constant 30S Kundt's constant 304 definition of 304 Latent heat of fusion 208 vaporization 206, 241 Latitude correction to barometer .... 119-120 Least squares 47~4 9 Legal electrical units xxxiv Leduc thermomagnetic effect 307 Light: indices of refraction 181-190 reflection of; function of "rt" .... 191 metals 192 sensitiveness of eye to 178 transmissibility to, of substances . 193-196 polarized: rotation of plane by solutions 197 rotation, magneto • . . 297-304 wave-lengths: cadmium st'd line . . . 170 elements, brighter lines . 170 Fraunhofer, lines . . . 176 st'd iron arc, Fabry . , 170 Kayser . .174 solar, Rowland . . Z7i velocity of . . • ■ • ■ ■ • • • ^°S> Linear thermal expansion coef. of elements , . 223 various . . . 223 Liquids: absorption of gases by 141 capillarity of ^42-i43 compressibility of 82-83 conductivity, thermal 200 densities 8s, 90. 95-90 dielectric constants 280-282 dielectric strength 250 diffusion, aqueous solutions .... 130 expansion, thermal 225 3i6 INDEX. Liquids : fuels, heat of combustion 202 magnetic susceptibility 305 magneto-optic rotation 304 potential differences with liQUids , . 254 metals . . 357 salts . . . 254 specific heats 230 surface tensions 142-143 thermal conductivity 200 expansion 225 vapor pressures 144-153 velocity of sound X02 viscosity 127-128 Logarithms 24 1000-2000 22 anti- 26 .gooo-i.oooo 28 Lowering of freezing-points by salts 2x7 Maclaurin's theorem 12 M£Lgnetic field: bismuth, resistance In ... , 306 Ettingshausen effect .... 307 galvanomagnetic effects . . . 307 Hall effect 307 Leduc effect 307 Nemst effect 307 nickel, resistance in , . . . 306 optical rotation .... 297-304 resistance of metals in ... 306 thermo-magnetic effects . , . 307 Magnetic properties: of cobalt at 100° C . . . 293 iron: hysteresis . 294-296 permeability 286-288. 292-293 saturated . . . 293 weak fields . . 294 magnetite 293 nickel at 100° C . . . 293 Magnetic susceptibility, liquids, gases .... 305 Magnetic units, conversion formulae .... 3 Magnetism, terrestrial: agonic line 115 declination no dip 112 horizontal intensity . .113 inclination 112 intensity, horizontal . .113 total. . . . 114 Magneto-optic rotation 297-304 Masses of the earth and planets 109 alloys 89 elements, liquid and solid 85 solids 88 woods 87 Materials, strength of: bricks 71 concrete 71 metals 71 stones 71 timber 72-73 woods 72-73 Mechanical equivalent of heat 227 Melting-points: chemical elements 209 inorganic compounds . . . .211 mixtures (alloys) 214 (low melting-points) . 214 organic compounds .... 215 Mercury: density of 97 electric resistance of ... . 263-263 pressure of columns of 116 specific heat 229 vapor pressure 148 Metals : diffusion of, into metals 138 indices of refraction 182 potential differences with solids . , . 256 solutions . . 257 reflection of light by 192 refracti ve indices 182 resistance, electrical 263-263 specific 263 sheet, weight of 70 Metallic oxides, refractive indices ..... 182 Methyl alcohol, density of aqueous 98 Metric weights and measures: British equiv . 7-10 U. S. equivalents s-6 Minerals, specific heats of 231 Mixtures, freezing 220 Moduli of elasticity: rigidity , . 74 Young's 75 Molecular conductivities: equivalent . . 275-278 specific . . . 371-274 Moments of inertia 58 Musical scales Z03 Mutual inductance, table for computing ... 56 Nemst thermo-magnetic difference of potential . 307 Neutral points, thermo-electric . . , . 358-259 Newton's rings and scale of colors 198 Nickel: Kerr's constants for 305 magnetic properties of, at 100° C . . . 293 resistance in magnetic field .... 306 Nitmso-dimethyl-aniline, refractive index . . 184 Ohm, various determinations of 261 legal value 261 Oils, viscosity of 126 Organic compounds, boiling-points 315 densities 215 melting-points .... 21Z Parallax: solar; lunar 109 Peltier effect 258, 260 Pendulum, length of seconds 107 Perfect gas, expansion of 162 volume of 162 Permeabilities, magnetic . . . 286-288, 292-293 Photometric standards 177 Pi, TT, value of 12 Planck's radiation formula 338 Plane, data for the soaring of a 123 Planets, miscellaneous data 109 Poisson's ratio 76 Polarized light: by reflection 191 rotation by magnetic field 297-304 solutions .... 197 Potential difference: cells: double fluid .... 253 secondary .... 353 single fluid .... 252 standard. . . 251*253 storage 353 contact: liquid-liquid . . 354 iiquid-salt . . . 354 metal-liquid . , 357 solid-solid . . . 356 sparking: air . . . 248-249 kerosene . . . 250 various . . . 350 thermoelectric . . . 358-259 Precession 109 Pressure: barometric measures .... 117-121 barometric and boiling water . . 168-169 heights 167 mercury columns, due to xi6 water columns, " " xi6 wind X22 Pressure, vapor: alcohol, ethyl and methyl . . 146 aqueous : low temperature . . 151 0° to 100° C . . . 152 100° to 230° C . . 153 in atmosphere . . 155 mercury 148 salt solutions X49 various 144-148 Probability tables 47-48 Purkinje's phenomenon , X78 Quartz fibres, strength of 71 refractive index of 185 Radiation: black-body 338 constants of 23S cooling by, and convection . . 339-240 eye, sensitiveness of, to 178 Planck's formula 238 sensitiveness of the eye to . . , ,178 "solar constant" of X79 Stefan's formula 238 transmissibility of atmosphere to . X79 Radii of gyration 58 Refraction, indices of: alums iSx crystals 187 fiuorite X84 gases and vapors . . . 190 glass 180 Iceland spar 184 liquids 189 metals, metallic oxides . X82 monorefringent solids . 186 nitroso-dimethyl-aniline . 184 quartz x85 rock-salt X83 salt solutions . . . .188 silvine 183 solids, isotropic . , . 186 Reflection of light: by metals 192 termsof "n" and "<" . 191 Relative humidity 158 INDEX. 317 Resistance: sue oJso Conductivity. alloys, low temperature .... 364 alternating current, effect of . , . 269 electrolytic, see Conductivity, glass and porcelain 285 legal unit of . ... magnetic field, of bismulii hi . metals in . niclcel in . . metals at low temperatures . ohm, various determinations of specific: metala 261 306 306 306 264 261 . 253 wires 262 temperature variation . . 262-266, 285 wire (copper) table, common units . 66 d:»!j-. j , . metric units . . 68 Rigidity, modulus of 74 „. . , temperature variation '. '. 74 Rmg correction (magnetization) 288 Rock-salt, indices of refraction 183 Rods, demagnetizing factors for 289 Rotation of polarized light: by solutions . . .197 Rotation, magneto-optic: formulae 297 gases 304 Kerr's constant . , 305 liquids 299 solids 298 solutions . . . 301-303 Verdet's constant 297-304 Rowland 3 standard wave-lengths 171 Salts, lowering of freezing-point by 217 raising '* boiling- " " 219 Saturation, magnetic, for steel 293 Scales, musical 103 Screens, color 19S-196 Seconds pendulum 107 Secondary batteries 253 Sections of wires 59-66 Shearing tests of timber 72-73 Sheet metal, weights of 70 Silver, electro-chemical equivalent . . . 251, 270 Silvine, indices of refraction 183 Sines, natural and logarithmic, circular . , 30-38 hyperbolic . 39-40 Sky-light, comparison with sunlight 179 Soaring of planes, data for 123 Solar constant of radiation 179 energy, data of 179 wave-lengths, Rowland's 171 SoUds: compressibility 76, S3 densities S5-89 dielectric constant 283 electrical resistance 261-269 hardness 76 indices of refraction 183-187 magneto-optic rotation by 298 thermal conductivity 199 expansion 222-224 Solutions: boiling-point, raising by salts in . . 219 boiling-points of aqueous . . . .219 conductivity, thermal 200 electrolytic . . 272-278 densities of aqueous 92-93 diffusion of aqueous 136 freezing-points, lowering by salt . .217 of aqueous .... 217 indices of refraction 188 magneto-optic rotation of . . 301-303 potential (contact) differences . 254-257 specific heats 230-231 surface tensions 142 viscosities _ 129-133 Sound, velocity of, in solids * ■ • loi liquids and gases . . . 102 Sparking potentials 248-250 Specific gravity, see Density. heat of air 232 elements 228 gases 232 iron at high temperatures . . 308 liquids 230 mercury 229 minerals and rocks 23 x solids 23a vapors 232 water 229 " Specific heat of electricity " 258 Specific toductive capacity: gases . . . 279-280 liquids . . . 280-282 solids 283 Specific molecular conductivities .... 373-274 Specific resistance 262-263 viscosity: gases and vapors . . . 134-135 liquids and oils . . . 126-128 „ ^ . solutions 129-133 spectra: elements, brighter lines 170 iron, Fabry-Buisson 170 Kayser 174 solar, Fraunhofer lines 176 Rowland's measures . . . .171 Squares, least, tables 47-49 Standard cells 251-253 wave-lengths: Fabry-Buisson . . . 170 Kayser 174 o» J . ,. . Rowland 171 standards, photometric 177 Steam tables: metric units 241 common " 242 .Steel: magnetic properties: hysteresis 291, 294-296 - , „ , permeabilities 286-294 atefan-Boltzmann radiation formula .... 23S Stone: strength of 71 thermal conductivity 199 Storage batteries 253 Strength of materials: bricks 71 concrete 71 metals 71 stones 71 timber, woods . . . 72-73 Sun: constant of radiation 179 disk; distribution of intensity .... 179 light; ratio to sky-light 179 parallax 109 radiation 179 spectrum 171, 179 temperature 179 Surface tension 142-143 Susceptibility, magnetic, liquids and gases . . 305 Sylvine, refractive indices 183 Taylor's series X3 Temperature, critical, for gases 321 resistances for low 264 sun's 179 Tensile strengths 71-73 Tension, surface 142-143 vapor, see 'Vapor pressure. Terrestrial magnetism: agonic line 115 declination, secular change no dip 112 secular change . . .112 horizontal intensity . . . 113 secular change 113 inclination 1x2 secular change .112 total intensity X14 secular change 114 Thermal conductivities: gases 200 liquids 200 salt solutions .... 200 solids X99 water 200 Thermal expansion: cubical: crystals . . . .224 gases .... 226 liquids .... 325 solids .... 224 linear: elements .... 222 various .... 223 Thermal unit, dynamical equivalent .... 227 Thermo-electricity 258-260 Peltier effect .... 258, 260 Thermo-magnetic effects 307 Thermometer: air-i6, 0" to 300° C 234 59, 100° to 200" C . . . . 234 high-temperature-S9 . . . 235 hydrogen-i6, 0° to 100" C . . . 233 16, 59, -5° to -35° C . 233 59, 0° to 100° C . . .333 various 335 Thermometer stem correction 236-237 Thomson thermo-electric effect 258 Timber, strength of 72-73 Time, sidereal, solar 108 Transformer-iron, permeability of . . . 286-287 steels, energy losses in . . . 294, 296 ■ ■ X79 194 193 30 35 United States weights and measures, conversion to metric units S-O Transmissibility to radiation: atmospheric crystals . . Trigonometric functions: arguments {'") • • (radians) 3i8 INDEX. Units of measurement: definitions, see Appendix. conversion factors .... 3-3 discussion, see Introduction. photometric X77 ratio of electro-magnetic to static . . . 247 V, ratio of electro-magnetic to -static units . . 247 Vapor, aqueous; vapor pressure, low temp. . . 151 o°-ioo° C . ,153 ioo''-230'' C . 153 pressure of, in atmospliere . , iss relative humidity 158 (saturated) weight of . . . .154 Vaporization, latent heat of 206 for steam . . 241, 242 Vapors: densities 91 diffusion of I37i 138 indices of refraction 190 pressures: alcohol, ethyl, methyl . . . 146 aQueous: low temp. . . . 151 o^-ioo" C . . , 152 I00**-230'' C . . .153 mercury 148 Bait solutions 149 various 144-148 specific heats 232 viscosity, specific 134 Velocity of light 109 sound; in gases and liquids , . . 102 solids loi Verdet's constants: Verdet and Kundt's . . . 304 gases' 304, 305 liquids 299. 305 solids 298 solutions, alcoholic .... 303 aqueous .... 301 hydrochloric . . 303 Viscosity: alcohol in water 126 gases 135 liquids X27 vapors 135 water: temperature variation . . .125 specific: gases 134 oils 126 solutions 129-133 vapors 134 water: temp, var 12s Voltaic cells: composition, £. M. F. . . 352-253 double-fluid 253 secondary 253 single-fluid 252 standard 251, 253 storage 253 Volts, legal (international) laadv, 251 Volumes: critical, for gases 33 x Volumes: gases, perfect 163 glass vessels, determinations of . . . 11 Water: boiling-points for various pressures: common measures 168 metric measures . 169 densities, temperature variation . . 95i 96 ionization of 278 solutions in: boiling-points .... 219 densities 92 diffusion 136 electrolytic conduction 372-278 solutions of alcohol, densities . . . 98-100 thermal conductivity 200 vapor pressure: low temperatures . . 151 o" to 100° C .... 152 too" to 230° C . . . 153 vapor, pressure of, in atmosphere . > I55 (saturated) weights of ... . 154 viscosity: absolute, temp. var. . . . 12s specific, temp, var 125 Wave-lengths: cadmium red line 170 elements, brighter lines . . . 170 Fabry-Buisson iron arc lines . . 170 Fraunhofer lines , 176 iron lines, Fabry-Buisson . . . 170 Kayser 174 Kayser's iron arc lines .... 174 Rowland's solar lines . . . .171 solar lines (Rowland) . . . .171 Weights and measures: British to metric . . 9-10 metric to British . . . 7-8 metric to U. S. . . . 6 U. S. to metric ... S Weights of bodies 58 Weights of sheet metal 70 wire: copper, iron, brass: common units 60 metric units . 62 aluminum, common and metric . . 64 copper wire, electrical constants common units 66 metric units . 68 Wind pressures 122 Wire gauges: Birmingham < 59 British standard 59 Brown and Sharp 66 Wire, weights of: brass, copper, iron , , . 60, 62 aluminum 64 copper 66, 68 Woods: densities of 87 strength of 72-73 Young's modulus of elasticity 75 Zonal harmonica 54 CAMBRIDGE • MASSACHUSETTS