Musi QuC 6/ )2V* (Rtmll Wafrmttg |f ifcOTg THE GIFT OF .-jQ.(y\y&W£) ±i d at any point of the surface, the ratio of the solid angle enclosed by a surface formed by moving a normal to the surface round the periphery of a small area containing the point, to the magnitude of the area. The dimensional formula is therefore — - §— or Lr' 2 , and the conversion factor is thus l~ % . surface 13. Momentum. — This is quantity of motion in the Newtonian sense, and is, at any instant, measured by the product of the mass-number and the velocity- number for the body. Thus the dimension formula is MV or MLT -1 , and the conversion factor mlt~ l - Example. — A mass of 10 pounds is moving with a velocity of 30 feet per sec- ond : what is its momentum when the centimetre, the gramme, and the second are fundamental units ? Here »z = 453-59> /= 3°-48, and t=i; .: m/t~ 1 = 453-59 X 3°-48 = 13825. The momentum is thus 13825 X 10 X 30 = 4 147 500. 14. Moment of Momentum. — The moment of momentum of a body with reference to a point is the product of its momentum-number and the number expressing the distance of its line of motion from the point. The dimensional formula is thus ML 2 ! 1-1 , and hence the conversion factor is mPf 1 . 15. Moment of Inertia. — The moment of inertia of a body round any axis is expressed by the formula Stfzr 2 , where m is the mass of any particle of the body INTRODUCTION. Xxi and r its distance from the axis. The dimension formula for the sum is clearly the same as for each element, and hence is ML 2 . The conversion factor is there- fore mP. 16. Angular Momentum. — The angular momentum of a body round any axis is the product of the numbers expressing the moment of inertia and the angular velocity of the body. The dimensional formula and the conversion fac- tor are therefore the same as for moment of momentum given above. 17. Force. — A force is measured by the rate of change of momentum it is capable of producing. The dimension formulae for force and " time rate of change of momentum " are therefore the same, and are expressed by the ratio of momentum-number to time-number or MLT -2 - The conversion factor is thus Note. — When mass is expressed in pounds, length in feet, and time in seconds, the unit force is called the poundal. When grammes, centimetres, and seconds are the corresponding units the unit of force is called the dyne. Example. Find the number of dynes in 25 poundals. Here m = 453-59. '= 3°-48, and/=i; .-. »z#- 2 = 453.59 X 3°-48 = 13825 nearly. The number of dynes is thus 13825 X 25 =345625 approximately. 18. Moment of a Couple, Torque, or Twisting Motive. — These are dif- ferent names for a quantity which can be expressed as the product of two numbers representing a force and a length. The dimension formula is therefore FL or ML 2 !" -2 , and the conversion factor is tnPt~\ 19. Intensity of a Stress. — The intensity of a stress is the ratio of the num- ber expressing the total stress to the number expressing the area over which the stress is distributed. The dimensional formula is thus FL -2 or MLr 1 !* -2 , and the conversion factor is mt^f*. 20. Intensity of Attraction, or " Force at a Point." — This is the force of attraction per unit mass on a body placed at the point, and the dimensional for- mula is therefore FM _1 or LT -2 , the same as acceleration. The conversion fac- tors for acceleration therefore apply. 21. Absolute Force of a Centre of Attraction, or " Strength of a Cen- tre." — This is the intensity of force at Unit distance from the centre, and is there- fore the force per unit mass at any point multiplied by the square of the distance from the centre. The dimensional formula thus becomes FL 2 M _1 or L'T -2 . The conversion factor is therefore /V -2 . 22. Modulus of Elasticity. — A modulus of elasticity is the ratio of stress intensity to percentage strain. The dimension of percentage strain is a length divided by a length, and is therefore unity. Hence, the dimensional formula of a modulus of elasticity is the same as that of stress intensity, or ML _1 T- 2 , and the conversion factor is thus also mt~ x t- 2 . XX11 INTRODUCTION. 23. Work and Energy. — When the point of application of a force, acting on a body, moves in the direction of the force, work is done by the force, and the amount is measured by the product of the force and displacement numbers. The dimensional formula is therefore FL or ML 2 !^ 2 . The work done by the force either produces a change in the velocity of the body or a change of shape or configuration of the body, or both. In the first case it produces a change of kinetic energy, in the second a change of potential energy. The dimension formulas of energy and work, representing quantities of the same kind, are identical, and the conversion factor for both is mlH~ 2 . 24. Resilience. — This is the work done per unit volume of a body in distort- ing it to the elastic limit or in producing rupture. The dimension formula is there- fore ML 2 T- 2 L- S 01 Mlr 1 T- 2 , and the conversion factor ml^r 2 . 25. Power, or Activity. — Power — or, as it is now very commonly called, ac- tivity — is defined as the time rate of doing work, or if W represent work and P power P = —r- . The dimensional formula is therefore WT -1 or ML 2 !" -8 , and the con- version factor mPf~*, or for problems in gravitation units more conveniently// -1 , where /stands for the force factor. Examples, (a) Find the number of gramme centimetres in one foot pound. Here the units of force are the attraction of the earth on the pound* and the gramme of matter, and the conversion factor is./?, where/ is 453-59 and /is 30.48. Hence the number is 453.59 X 30.48 = 13825. (b) Find the number of foot poundals in 1 000 000 centimetre dynes. Here m = i/453-59> l — 1/30-48, and t = 1 ; .: mPr* = i/453-59 X 3°-48 2 , and ioW 2 /- 2 = 107453.59 X 3°-48 2 = 2.373. (c) If gravity produces an acceleration of 32.2 feet per second per second, how many watts are required to make one horse-power ? One horse-power is 550 foot pounds per second, or 550 X 32.2 = 17710 foot poundals per second. One watt is io 7 ergs per second, that is, io 7 dyne centi- metres per second. The conversion factor is mPt~ s , where m = 453.59, /= 30.48, and t— 1, and the result has to be divided by io 7 , the number of dyne centime- tres per second in the watt. Hence, i77io^/ 2 /- 8 /io 7 = 17710 X 453-59 X 30.48710' = 746.3. (d) How many gramme centimetres per second correspond to 33000 foot pounds per minute ? The conversion factor suitable for this case \.s/lt~\ where/ is 453.59, / is 30.48, and / is 60. Hence, 33000 /r x = 33000 X 453-59 X 30.48/60= 7604000 nearly. * It is important to remember that in problems like that here given the term " pound " or " gramme " refers to force and not to mass. INTRODUCTION. HEAT UNITS. i. If heat be measured in dynamical units its dimensions are the same as those of energy, namely ML 2 T~~ a . The most common measurements, however, are made in thermal units, that is, in terms of the amount of heat required to raise the temperature of unit mass of water one degree of temperature at some stated temperature. This method of measurement involves the unit of mass and some unit of temperature, and hence if we denote temperature-numbers by © and their conversion factors by 6 the dimensional formula and conversion factor for quan- tity of heat will be M® and m6 respectively. The relative amount of heat com- pared with water as standard substance required to raise unit mass of different substances one degree in temperature is called their specific heat, and is a simple number. Unit volume is sometimes used instead of unit mass in the measurement of heat, the units being then called thermometric units. The dimensional formula is in that case changed by the substitution of volume for mass, and becomes L 8 ®, and hence the conversion factor is to be calculated from the formula l a B. For other physical quantities involving heat we have : — 2. Coefficient of Expansion. — The coefficient of expansion of a substance is equal to the ratio of the change of length per unit length (linear), or change of volume per unit volume (voluminal) to the change of temperature. These ratios are simple numbers, and the change of temperature is inversely as the mag- nitude of the unit of temperature. Hence the dimensional and conversion-factor formulas are ® _1 and &~\ 3. Conductivity, or Specific Conductance. — This is the quantity of heat transmitted per unit of time per unit of surface per unit of temperature gradient. The equation for conductivity is therefore, with H as quantity of heat, ®L*T L and the dimensional formula — — = :r =, which gives ml-^ior conversion factor. ®LT LT In thermometric units the formula becomes L Z T _1 , which properly represents diffusivity. In dynamical units H becomes MI/T -2 , and the formula changes to MLT -8 ® -1 . The conversion factors obtained from these are Pt~ x and mlffr" 1 respectively. Similarly for emission and absorption we have — 4. Emissivity and Immissivity. — These are the quantities of heat given off by or taken in by the body per unit of time per unit of surface per unit dif- ference of temperature between the surface and the surrounding medium. We thus get the equation EL 2 ®T = H = M®. The dimensional formula for E is therefore ML^T" 1 , and the conversion factor XXIV INTRODUCTION. mt 2 (-\ In thermometric units by substituting /* for m the factor becomes lt~\ and in dynamical units mt~ s &~-. 5. Thermal Capacity. — This is the product of the number for mass and the specific heat, and hence the dimensional formula and conversion factor are simply M and m. 6. Latent Heat. — Latent heat is the ratio of the number representing the quantity of heat required to change the state of a body to the number represent- ing the quantity of matter in the body. The dimensional formula is therefore M©/M or ®, and hence the conversion factor is simply the ratio of the tempera- ture units or 6. In dynamical units the factor is Pt~ 2 .* 7. Joule's Equivalent. — Joule's dynamical equivalent is connected with quantity of heat by the equation ML 2 T- 2 =JHor JM®. This gives for the dimensional formula of J the expression L 2 T~ 2 ®. The conver- sion factor is thus represented by Pir^O. When heat is measured in dynamical units J is a simple number. 8. Entropy. — The entropy of a body is directly proportional to the quantity of heat it contains and inversely proportional to its temperature. The dimen- sional formula is thus M®/® or M, and the conversion factor is m. When heat is measured in dynamical units the factor is mPt~ 2 0~\ Examples, (a) Find the relation between the British thermal unit, the calorie, and the therm. Neglecting the variation of the specific heat of water with temperature, or de- fining all the units for the same temperature of the standard substance, we have the following definitions. The British thermal unit is the quantity of heat required to raise the temperature of one pound of water i° F. The calorie is the quan- tity of heat required to raise the temperature of one kilogramme of water i° C. The therm is the quantity of heat required to raise the temperature of one gramme of water i°C. Hence : — (1) To find the number of calories in one British thermal unit, we have ^ = •45399 and0 = $; :. *«0=. 45399 X 5/9 = .25199. (2) To find the number of therms in one calorie, zrc=iooo and 6=1; .•. m6 = 1000. It follows at once that the number of therms in one British thermal unit is 1000 X- 25199 =251.99. (b) What is the relation between the foot grain second Fahrenheit-degree and the centimetre gramme second Centigrade-degree units of conductivity ? The number of the latter units in one of the former is given by the for- * It will be noticed that when is given the dimension formula L 2 T— 2 the formulae in thermal and dynamical units are always identical. The thermometric units practically suppress mass. INTRODUCTION. XXV mula mt-^t~W, where ^ = .064799, 71=30.48, and /= 1, and is therefore = .064 799/30.48 = 2.126 X io -8 - (c) Find the relation between the units stated in (6) for emissivity. In this case the conversion formula is ml~ a f\ where ml and t have the same value as before. Hence the number of the latter units in the former is 0.064799/30.48* = 6.975 X io -6 . (d) Find the number of centimetre gramme second units in the inch grain hour unit of emissivity. Here the formula is mt~*t~\ where m = 0.064 799> ^=2.54, an d ^ = 3600. Therefore the required number is 0.064 799/ 2 -54 2 X 3600 = 2.790 X io -6 . (e) If Joule's equivalent be 776 foot pounds per pound of water per degree Fahrenheit, what will be its value in gravitation units when the metre, the kilo- gramme, and the degree Centigrade are units ? Pr 2 6 The conversion factor in this case is ,._ 2 or 16, where /= .3048 and 6= 1.8 ; •'• 77 6 X -3048 X 1.8 = 425.7. (/) If Joule's equivalent be 24832 foot poundals when the degree Fahrenheit is unit of temperature, what will be its value when kilogramme metre second and degree-Centigrade units are used ? The conversion factor is Pf 2 9, where /= .3048, /= 1, and = 1.8 ; .-. 24832 X Pf*e = 24832 X .3048 2 X 1.8 = 4152-5- In gravitation units this would give 4152. 5/9.81 =423.3. ELECTRIC AND MAGNETIC UNITS. There are two systems of these units, the electrostatic and the electromagnetic systems, which differ from each other because of the different fundamental suppo- sitions on which they are based. In the electrostatic system the repulsive force between two quantities of static electricity is made the basis. This connects force, quantity of electricity, and length by the equation /= a ^p-, where / is force, a a quantity depending on the units employed and on the nature of the medium, q and q, quantities of electricity, and / the distance between q and q t . The magnitude of the force f for any particular values of q, q, and / depends on a property of the medium across which the force takes place called its inductive capacity. The in- ductive capacity of air has generally been assumed as unity, and the inductive capacity of other media expressed as a number representing the ratio of the induc- tive capacity of the medium to that of air. These numbers are known as the spe- cific inductive capacities of the media. According to the ordinary assumption, then, of air as the standard medium, we obtain unit quantity of electricity when in the above equation q = q t , and/, a, and / are each unity. A formal definition is given below. In the electromagnetic system the repulsion between two magnetic poles or XXVI INTRODUCTION. quantities of magnetism is taken as the basis. In this system the quantities force, quantity of magnetism, and length are connected by an equation of the form j- mm, where m and m t are in this case quantities of magnetism, and the other symbols have the same meaning as before. In this case it has been usual to assume the magnetic inductive capacity of air to be unity, and to express the magnetic induc- tive capacity of other media as a simple number representing the ratio of the in- ductive capacity of the medium to that of air. These numbers, by analogy with specific inductive capacity for electricity, might be called specific inductive capac- ities for magnetism. They are usually called permeabilities. ( Vide Thomson, " Papers on Electrostatics and Magnetism," p. 484.) In this case, also, like that for electricity, the unit quantity of magnetism is obtained by making m = m^, and f, a, and / each unity. In both these cases the intrinsic inductive capacity of the standard medium is suppressed, and hence also that of all other media. Whether this be done or not, direct experiment has to be resorted to for the determination of the absolute val- ues of the units and the relations of the units in the one system to those in the other. The character of this relation can be directly inferred from the dimen- sional formulas of the different quantities, but these can give no information as to the relative absolute values of the units in the two systems. Prof. Riicker has suggested (Phil. Mag. vol. 27) the advisability of at least indicating the exist- ence of the suppressed properties by putting symbols for them in the dimensional formulae. This has the advantage of showing how the magnitudes of the different units would be affected by a change in the standard medium, or by making the standard medium different for the two systems. In accordance with this idea, the symbols K and P have been introduced into the formulas given below to represent inductive capacity in the electrostatic and the electromagnetic systems respectively. In the conversion formulae k and p are the ordinary specific inductive capacities and permeabilities of the media when air is taken as the standard, or generally those with reference to the first medium taken as standard. The ordinary for- mulas may be obtained by putting K and P equal to unity. ELECTROSTATIC UNITS. 1. Quantity of Electricity. — The unit quantity of electricity is defined as that quantity which if concentrated at a point and placed at unit distance from an equal and similarly concentrated quantity repels it, or is repelled by it, with unit force. The medium or dielectric is usually taken as air, and the other units in ac- cordance with the centimetre gramme second system. In this case we have the force of repulsion proportional directly to the square of the quantity of electricity and inversely to the square of the distance between the quantities and to the inductive capacity. The dimensional formula is there- fore the same as that for [force X length 2 X inductive capacity]* or MiL'T^K 1 , and the conversion factor is wV 8 / -1 ^ 1 . INTRODUCTION. XXV11 2. Electric Surface Density and Electric Displacement. — The density of an electric distribution at any point on a surface is measured by the quantity per unit of area, and the electric displacement at any point in a dielectric is mea- sured by the quantity displaced per unit of area. These quantities have therefore the same dimensional formula, namely, the ratio of the formulae for quantity of electricity and for area or M'Lr'T^K*, and the conversion factor m i i~ i f 1 A i . 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 formulse for force and electric quantity, or MLT -2 — MiL-'T^K - * M»L»T- 1 K» _M1j ' which gives the conversion factor m i l~ i f x k~ i . 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 2 T- 2 _ M j L i T -i K -i which gives the conversion factor m^fit -1 ^. 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 =irT=i ==:LK ' 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 cap?c- ity of the substance to that of a standard substance, and hence the dimensional formula is K/K or 1.* 7. Electric Current. — Current is quantity flowing past a point per unit of time. The dimensional formula is thus the ratio of the formulae for electric quan- tity and for time, or MiL8 ™ = M>L*T-'K», and the conversion factor rfr* * 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 taken as inductive ca- pacity. Hence in that case the conversion factor must be taken as 1 on the electrostatic and as l-tp on the electromagnetic system. XXVU1 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 MiTJT-'K* _ electric quantity 2 M*L*T^K- J T ' area X potential gradient X time L L The conversion factor is t~ x 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- 1 and ttr\ 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 MVMK|__ Tr , K ., from which we get the conversion factor // -1 £ -1 . 11. Resistance. — This is the reciprocal of conductance, and therefore the dimensional formula and the conversion factor are respectively L _1 TK and l~*tk. EXAMPLES OF CONVERSION IN ELECTROSTATIC UNITS. (a) Pind the factor for converting quantity of electricity expressed in foot grain second units to the same expressed in c. g. s. units. By (1) the formula is «z*/ 3 / -1 £ l , in which in this case m = 0.0648, /= 30.48, t = 1, and k = 1 ; .". the factor is 0.0648* X 30.48 s = 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 m i I i t~ 1 i~ i , and in this case m = 0.001, /= 0.1, 2" = 1, and £=1; .'. the factor = o.ooi J X o.i } = 0.01. (c) 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 Ik, 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. 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 denned above by the substitution of magnetic for electric quantity may have their dimensional formulae derived from those of the corresponding quantity by substituting P for K. i. 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 2 X in- ductive capacity] or M*L S T _1 P J , and the conversion factor is mtyf 1 ^. 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 4 Lr l T~ 1 P i , which gives the conversion factor m i ?~ i r~ 1 p i . 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 MLT~ 2 = M i Lr } T- 1 p-* and the conversion factor ^z 1 / - */ - ^ - *. 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 ML 2 r 2 M J L S T -lpj which gives the conversion factor mftt~ x p~ ML'T-'P-*, 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 formula? for magnetic quantity and length, or M'UT^P 1 , and the con- version factor mH^f^. 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 M!^L i = M»L-*T- 1 P*. The conversion factor is therefore m i l~ i i~ 1 J> i . 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- 1 P* MiL-iT- 1 ?-* 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 2-KCJr. The dimen- sional formula is therefore the product of the formulae for magnetic field intensity and length, or MWT^P -1 , which gives the conversion factor m^Ptr^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 J L _s T _1 P _l and m i f~ i t~ 1 p~i. 11. Quantity of Electricity. — This is the product of the numbers for cur- rent and time. The dimensional formula is therefore M i L 1 T -1 P -i X T= M'L^P -4 and the conversion factor m i flp~ i . 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 ML 2 T- 2 = M»L 5 T- 2 P*, M*L*P-* and the conversion factor 0zV 8 / - ^> } . » 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 1 in the electromagnetic and l-*fi in the electrostatic systems. INTRODUCTION. xxx j 13. Electrostatic Capacity. — This is the ratio of the numbers for quantity of electricity and difference of potential. The dimensional formula is therefore M'UP-* 1YX ■'-' r T -IX2P-1 M^T-^P* - ' and the conversion factor / _1 /^ _1 . 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 M*TjT- 2 Pi _ M j L i T -i p -j — lji r - The conversion factor thus becomes ZT 1 /, 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 _1 TP _1 and l~ x tp- y . 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»L»P-* _ T _ a ™ t> _ T 2 ]VMJT- 2 P* — L TP ~- L L T The conversion factor is therefore t~ 2 tp~ x . 17. Specific Resistance. — This is the reciprocal of conductivity as defined in 15, and hence the dimensional formula and conversion factor are respectively UT- 1 ? and Pr~ l 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 formula? for electromotive force and time divided by that for current or M i L3T -2pj M. i UT- 1 ~p->' X T = LP. The conversion factor is therefore lp, and in the ordinary system is the same as that for length. 19. Coefficient of Mutual 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. XXX11 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 J L J T _1 P^ X LP = M^'T -1 ? 4 , and the conversion factor is m i flt~ 1 J> 1 . 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 i L i 'T~ i P i , and the conversion factor »zW~^ } . 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 MWT -1 ?*, and the conversion factor wVr 1 /. 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 MWr -2 ? 1 ® -1 , and the conversion factor m i l i t~*p i 6~ 1 . 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 „»?L = M»L-»P»8, MiUP-* ' and the conversion factor ni't^p^B. 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 0z } /-V _1 /-*, and in this case m = 0.0648, / = 30.48, t = 60, and/ = 1 ; .\ the factors = 0.0648* X 30.48 -5 X 6o _1 = 0.00076847. Similarly to convert from foot grain second units to c. g. s. units the factor is 0.0648 1 X 30.48""*= 0.046 108. (b) How many c. g. s. units of magnetic moment make one foot grain second unit of the same quantity ? By (5) the formula is mWr 1 ^, and the values for this problem are m = 0.0648, /= 30.48, / = 1, and/ = 1 ; .-. the number = 0.0648' X 30.48*= 1305.6. (c) If the intensity of magnetization of a steel bar be 700 in c. g. s. units what will it be in millimetre milligramme second units ? INTRODUCTION. XXxiii By (6) the formula is mW^pi, and in this case m = 1000,/= 10, t= 1, and /=i; ■"• the intensity = 700 X iooo J X io 1 = 70000. (d) Find the factor required to convert current strength from c. g. s. units to earth quadrant io -11 gramme and second units. By (9) the formula is w'Ar 1 /-*, and the values of these quantities are here m = io 11 , /= 10- 9 , t = 1, and/ = 1 ; .: the factor = 10H x io-S= 10. (e) Find the factor required to convert resistance expressed in c. g. s. units into the same expressed in earth-quadrant io-" grammes and second units. By (14) the formula is lt~ x p, and for this case /= io" 8 , t = 1, and p = 1 ; .". the factor = io~~ 9 (/) Find the factor required to convert electromotive force from earth-quadrant io -11 gramme and second units to c. g. s. units. By (12) the formula is m>Pt-*p\ and for this case m = io~ n , /= io 9 , t= 1, and/ = 1 ; .". the factor = io 8 . 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 denned 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 io 9 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 ampere, 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 ampere, 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 15° C, and prepared in the manner described in the accompanying specification.* " As a unit of quantity, the international coulomb, which is the quantity of elec- tricity transferred by a current of one international ampere 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.f " As a unit of work, the joule, which is equal to io 7 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 ampere in an international ohm. "As a unit of power, the watt, which is equal to 10' 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 ampere 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 1 5 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. Their report has not yet been received." 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. (a) Fundamental Units. Name of Unit. Symbol. Conversion Factor. Length. L / Mass. M m Time. T t Temperature. © 6 Electric Inductive Capacity. K k Magnetic Inductive Capacity. P P (b) Derived Units. I. Geometric and Dynamic Units. Name of Unit. Conversion Factor. Area. P Volume. P Angle. I Solid Angle. I Curvature. /- 1 Tortuosity. /-» Specific curvature of a surface. 1-* Angular velocity. l~ l Angular acceleration. ir 2 Linear velocity. it- 1 Linear acceleration. ir* Density. m?- 3 Moment of inertia. mP Intensity of attraction, or " force at a point." lt~ 2 Absolute force of a centre of attraction, or " strength ) of a centre." f Momentum. /T 1 m I f 1 Moment of momentum, or angular momentum. mPf 1 Force. mlr* Moment of a couple, or torque. m I 2 1~ 2 Intensity of stress. m I- 1 1~ 2 Modulus of elasticity. m l~ l t~ 2 Work and energy. m I 2 1~'' Resilience. m t- 1 r* Power or activity. mPlr* Smithsonian Tables. ■ 1 FUNDAMENTAL AND DERIVED UNITS. Table 1 . II. Heat Units. Name of Unit. Conversion Factor. Quantity of heat (thermal units). " " (thermometric units). " " (dynamical units). Coefficient of thermal expansion. Conductivity (thermal units). " (thermometric units), or diffusivity. " (dynamical units). Emissivity and imissivity (thermal units). " " ^thermometric units). " " (dynamical units). Thermal capacity. Latent heat (thermal units). " " (dynamical units). Joule's equivalent. Entropy (heat measured in thermal units). " ( " " dynamical units). mO P0 mPr 2 m I- 1 ir x i Pr l m i~ 2 t- 1 ir 1 m t~ 3 6- 1 m e Pr* Pr 2 6 m mPt^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 ) displacement. ) Intensity of electric field. Electric potential and e. m. f. Capacity of a condenser. Inductive capacity. Specific inductive capacity. Electric current. mi l~ s £-» mi l* r* & mi l* k~i mi l~i k~i I r 2 p k~ x m* /> r 1 ki m i i-i r 1 ki m i l-i r 1 k~i m* l h t"- k~i Ik k mi I* r 2 ki mi I s r x pi m i I-i t-^pi mi l~i t- X p-i m li 1r x p-i m i li t- x pi mi li tr 1 pi I p mi li pi mi l~*p-i m i li r*pi mi I s t~*pi I- 1 pp- 1 /-» pp- 1 I m i ii r x 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^k r 2 tp- 1 Specific resistance. tk- 1 i 2 f l P Conductance. i /- 1 k- 1 i- 1 tp- 1 Resistance. t*tk it-^P Coefficient of self induction and") coefficient of mutual induction, j I- 1 1 2 k~ x ip Electrokinetic momentum. m* /» tr* m i p f-ipi Electromotive force at a point. mi t* t- 1 £~» m i n t-ip\ Vector potential. wz 1 Z -1 k~~* m l /* t-^pi Thermoelectric height and specific | heat of electricity. \ Coefficient of Peltier effect. tn* fl f 1 k-i &- 1 m \ p t-ipi 0-1 «» t-*tk-+o tri> /-»/» 6 Smithsonian Tables. _ Table 2 EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS AND MEASURES.* (I) METRIC TO IMPERIAL. LINEAR MEASURE. I millimetre (mm.) ) (.001 m.) J : i centimetre (.01 m.) = 1 decimetre (.1 m.) = 1 metre (m.) 1 dekametre ) (10 m.) f 1 hectometre I (100 m.) ) 1 kilometre i (1,000 m.) J 1 myriametre | (10,000 m.) ) °°3937 »n. °-3937i " 3-93708 " (39-37079 " = 1 3.28089917 ft. ( 1-09363306 yds. = !o-93 6 33 " = 109.36331 " = 0.62138 mile. = 6.21382 miles. = 0.001 mm. SQUARE MEASURE. 1 sq. centimetre . . = 0.15501 sq. in. 1 sq. decimetre ) (100 sq. centm.) \ = r 5-5°°59 sq- m. 1 sq. metre or centi- I _ I 10.76430 sq. ft. are (100 sq. dcm.) j ) 1. 19603 sq. yd. 1 are (100 sq. m.) = 119.60333 sq. yds. I hectare (100 ares ) or 10,000 sq. m.) \ = 2 '47»S acres. CUBIC MEASURE. cub. centimetre ) (c.c.) (1,000 cubic > = 0.06103 CUD - m - millimetres) ) cub. decimetre ) (c.d.) (1,000 cubic £ = 61.02705 " " centimetres) CUB. METRE / , . orstere. .J = | 35-31658074 cub. ft. 1,000 (c.d IC5/ rRE ) d.)'i 1.30802151 cub. yd. MEASURE OF CAPACITY. 1 millilitre (ml.) (.001 ) , lit re ) I = 0.06103 CUD - ">• 1 centilitre (.01 litre) 1 decilitre (.1 litre) . . 1 litre (1,000 cub. centimetres or 1 cub. decimetre) 1 dekalitre (10 litres) . 1 hectolitre (100 " ) . 1 kilolitre (1,000 " ) =1 0.61027 " " 0.07043 gill. 0.17608 pint. = 1.76077 pints. 2.20097 gallons. 2.751 2 1 bushels. 3.43901 quarters. 1 microlitre . . . . = 0.001 ml. APOTHECARIES' MEASURE. 1 cubic centi- metre gramme w 1 cub. millimetre iti- ) ( 0.03 (i[ = \ 0.28 't) ) I is-43- 527 fluid ounce. 219 fluid drachm. ,235 grains weight. 6.01693 minim. AVOIRDUPOIS WEIGHT. 1 milligramme (mgr.) . : 1 centigramme (.01 gram.) : 1 decigramme (.1 " ) : I gramme -. 1 dekagramme (10 gram.) = 1 hectogramme (100 " ) = OOI543 grain. 0.15432 " r -543 2 4 grains. 15.43235 " 5.64383 drams. 3.52739 oz. ( 2.20462125 lb. I KILOGRAMME (l,000 " ) = ) 15432.34874 ( grains. 22.0462 1. lb. 1. 9684 1 cwt. 1 myriagramme(iokilog.) = 1 quintal (100 " ) = 1 millier or tonne I (1,000 kilog.) ) 0.98420591 ton. TROY WEIGHT. I GRAMME . 0.03215073 oz. Troy. 0.64301 pennyweight. i5-43 2 35 grains. APOTHECARIES' WEIGHT. ( 0.25721 drachm. . = } 0.77162 scruple. ( : 543235 grains. Note. — The Metre is the length, at the temperature of o° C, of the platinum-indium bar deposited with the Board of Trade. The present legal equivalent of the metre is 39*37079 inches, as above stated. If a brass metre is, however, compared, not at its legal temperature (o° C. or 32° F.), but at the temperature of 62 F., with a brass yard at the temperature also of 62 F., then the apparent equivalent of the metre would be nearly 39*382 inches. The Kilogramme is the weight in vacuo at o° C. of the platinum-iridium weight deposited with the Board of Trade. The Litre contains one kilogramme weight of distilled water at its maximum density (4° C), the barometer being at 760 millimetres. * Quoted from sheets issued in 1890 by the Standard Office of the British Board of Trade. Smithsonian Tables. Table 2. 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 0.0393707; 0.0787415! 0.1181123; O.I57483I* O.1968539. O.2362247* 0-2755955; O.31496631 0-3543371' ) 3.28090 i 6.56180 9.84270 ) 13.12360 , 16.40450 19.68540 22.96629 26.24719 29.52809 1.09363 2.18727 3.28090 4-37453 5.46817 6.56180 7-65543 8.74906 9.84270 O.62138 1.24276 I.86415 2.48553 3. 1 069 1 3.72829 4.34968 4.97106 5-59244 I 2 3 4 5 6 7 8 9 I.76077 3-52I54 5.28231 7.04308 8.80385 IO.56462 12.32539 14.08616 15.84693 2.20097 4.40193 6.60290 8.80386 II.00483 13.20580 1 5.40676 17.60773 19.80870 2.75121 5.50242 8.25362 II.00483 13.75604 16.50725 19.25846 22.00966 24.76087 3-43901 6.87802 10.31703 13.75604 17.19505 20.63406 24.07307 27.51208 30.95110 SQUARE MEASURE. WEIGHT (Avoirdupois). Square centimetres to square inches. Square metres to square feet. Square metres to square yards. Hectares to acres. Milli- grammes to grains. Kilogrammes to grains. Kilo- grammes to pounds. Quintals to hundred- weights. I 2 3 4 5 6 7 8 9 O.15501 0.31001 O.46502 O.62002 O.77503 0.93004 I.08504 I.24005 i-39 5°5 IO.7643O 21.52860 32.29290 43.05720 53.82150 64.58580 75.35010 86.11439 96.87869 1. 19603 2.39207 3.58810 4.78413 5.98017 7.17620 8.37223 9.56827 IO.7643O 2.471 14 4.94229 7-41343 9.88457 12-35572 14.82686 17.29800 19.76914 22.24029 I 3 4 5 6 7 8 9 O.O1543 0.03086 O.04630 O.06173 0.07716 O.09259 0.10803 O.12346 O.13889 I5432-34874 30864.69748 46297.O4622 6I729-39496 77161.7437O 92594.09244 108026.441 18 I23458.78992 I38891. 13866 2.20462 4.40924 6.61386 8.81849 II.02311 I3-22773 I5-43235 17.63697 19.84159 1. 96841 3.93682 5.90523 7.87364 9.84206 H.81047 13.77888 15.74729 17.71570 CUBIC MEASURE. ApOTHE- CARIRS' Measure. Avoirdupois (cont.) Trov Weight. Apothe- caries' Weight. 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. I 2 3 4 5 6 7 8 9 61.02705 122.05410 183.081 1 5 244.10821 3°5-'3526 366.16231 427.18936 488.21641 549.24346 35-3I658 70.63316 1 05.94974 141.26632 176.58290 211.89948 247.21607 282.53265 317.84923 I.30802 2.61604 3.92406 5.23209 6.5401 1 7.84813 9- ! 56i5 10.46417 11.77219 O.28219 O.56438 O.84657 1. 12877 1. 41096 I.69315 1-97534 2-25753 2.53972 I 2 3 4 5 6 7 8 9 O.9842I 1. 9684 1 2.95262 3.93682 4.92103 5.00524 6.88944 7.87365 8.85785 O.03215 O.06430 O.09645 O.12860 O.16075 O.19290 O.22506 O.25721 O.28936 O.643OI I.28603 I.92904 2.57206 3.21507 3.85809 4.501 10 5.I4412 5-787I3 O.77162 I-54323 2.31485 3.08647 3.85809 4.62970 5.40131 6.17294 6-94455 Smithsonian Tables. Table 2. EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS AND MEASURES. (3) IMPERIAL TO METRIC. LINEAR MEASURE. I inch . . . I foot (12 in.) I yard (3 ft.) 1 pole (5i yd.) . , 1 chain (22 yd. or ) 100 links) J 1 furlong (220 yd.) 1 mile (1,760 yd.) ={ ; = J 2 S-39954i 13 nuHi- metres. 0.30479449 metre. 0.91438348 " 5.02911 metres. 20.11644 " 201.16437 " ( 1.60931493 kilo- ) metres. SQUARE MEASURE. 1 square inch . . = < I sq. ft. (144 sq. in.) = < I SQ. YARD (9 sq. ft.) = i 1 perch (30J sq. yd.) = . 1 rood (40 perches) = I ACRE (4840 sq. yd.) = 1 sq. mile (640 acres) = < 6.45137 sq. cen- timetres. 9.28997 sq. deci- metres. 0.83609715 sq. , metres. 25.29194 sq. me- tres. 10.11678 ares. 0.40467 hectare. 258.98945312 hec- tares. CUBIC MEASURE. 1 cub. inch = 16.38617589 cub. centimetres. , , , „ , ( 0.02832 cub. metre, 1 cub. foot ( 1728 I N or J 28 3I s cub , cub. in.) ) ^ decimetres. 1 cub yard (27 1 = 0.76451342 cub. metre. APOTHECARIES' MEASURE. gallon (8 pints or ) _ 160 fluid ounces) ) fluid ounce, f 3 1 _ (8 drachms) J fluid drachm, f 3 I _ (60 minims) J : minim, rtl (0.91 146 1 _ grain weight) J 4.54346 litres. 28.39661 cubic centimetres. ( 3.54958 cubic j centimetres. j 0.05916 cubic j centimetres. Note. —The Apothecaries' gallon is of the same capacity as the Imperial gallon. MEASURE OF CAPACITY. 1 gill I pint (4 gills) . . I quart (2 pints) . I gallon (4 quarts 1 peck ( 2 galls.) . 1 bushel (8 galls.) 1 quarter (8 bushels = 1.41983 decilitres. = 0.56793 litre. = 1. 1 3 586 litres. = 4-54345797 " = 9.08692 = 3.63477 dekalitres. = 2.90781 hectolitres. AVOIRDUPOIS WEIGHT. 1 gram 1 dram -I' 64/79895036 milli- grammes. 1. 77 1 85 grammes. 1 ounce (16 dr.) . .= 28.34954 " 0-45359265 kilogr. 6.35030 " 12.70059 " j 50.80238 " ( 0.50802 quintal. ' 1.01604754 millier or tonne. 1 pound (16 oz. or 1 . 7,000 grains) J " 1 stone (141b.) . . = 1 quarter (28 lb.) . = 1 hundredweight ) (112 lb.) ) " 1 ton (20 cwt.) . = 1 TROY WEIGHT. t Troy ounce (480 ) = gra mmes. grams avoir.) J J JJ ° 1 pennyweight (24 i _ t « grains) ) '■'■'■' Note. — The Troy grain is of the same weight as the Avoirdupois grain. APOTHECARIES' WEIGHT. 1 ounce (8 drachms) = 31.10350 grammes. 1 drachm, 3 i (3 scru- 1 __ 3 .gg 7 g 4 « pies) 1 scruple, gi grains) (20 1 _ 1 1.29598 Note. — The Apothecaries' ounce is of the same weiEht as the Troy ounce. The Apothecaries grain is also of the same weight as the Avoirdupois grain. deP °Th| d Gl^ont"tl T lb d weight of distilled water at the temperature of 6*° Tahr., the barometer being a. 30 inches. The weight of a cubic inch of water is 252-28° grains. Smithsonian Tables. Table 2. EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS AND MEASURES. W IMPERIAL TO METRIC LINEAR MEASURE. MEASURE OF CAPACITY. Inches Feet Yards Miles Quarts Gallons Bushels Quarters to to to to to to to millimetres. metres. metres. metres. litres. litres. dekalitres. hectolitres. I 2S-399S4"3 O.30479 0.91438 I.60931 I 1-13586 4-54346 3-63477 2.90781 2 50.79908226 O.60959 1.82877 3.21863 2 2.27173 9.08692 7.26953 5-8I563 8.72344 3 76.19862340 O.9I438 2-743 '5 4.82794 1 340759 I3-63037 IO.90430 4 IOI.59816453 I.2I918 3-65753 6.43726 4 4-54346 18.17383 I4-539 7 II.63125 5 I26.99770566 I-52397 4.57192 8.04657 5 5.67932 22.71729 18.17383 I4-53907 6 I5 2 -39724679 I.82876 5.48630 9.65589 6 6.81519 27.26075 21.80860 17.44688 7 177.79678792 2-I3356 6.40068 1 1.26520 7 7-95 I0 5 9.08692 31.80421 25-44336 20.35469 8 203.I9632906 228.59587019 2-43835 7-3!5°7 12.87452 8 36.34766 29.07813 23.26250 9 2-743 r 5 8.22945 14.48383 9 10.22278 40.89112 32.71290 26.17032 SQUARE MEASURE. WEIGHT (Avoirdupois). Square inches Square feet Square yards to Acres to Grains to Ounces to Pounds to kilo- grammes Hundred- weights to . quintals. to square centimetres. to square decimetres. square metres. hectares. milligrammes. grammes. I 6-45 T 37 9.28997 O.83610 O.40467 I 64.79895036 28.34954 0-4535S O.50802 2 12.90273 18.57994 27.86990 I.67219 O.80934 2 129.59790072 56.69908 0.907 1 c 1.01605 3 19.35410 2.50829 I.21401 3 194.39685109 85.04862 1-3607* I.52407 4 25.80547 37-I5987 3-34439 I.61868 4 259.19580145 113.39816 i-8i437 2.03209 5 32.25683 46.44984 4.18049 2.02336 5 3 2 3-99475 l8 i 141.74770 2.26791: 2.54012 6 38.70820 55-7398I 5.01658 2.42803 6 388.79370218 170.09724 2-72I5« 3.04814 7 4515957 65.02978 5.85268 6.68878 2.83270 7 453-59265255 198.44679 3-1751; 3-556I7 8 51.61094 74-3>974 3-23737 8 518.39160291 226.79633 255.14587 3.62874 4.06419 9 58.06230 83.60971 7.52487 3.64204 9 583.19055327 4.0823; 4.57221 CUBIC MEASURE. Apothe- caries' Avoirdupois (cant.). Apothe- Measure. Weight. Cubic Cubic Fluid inches to cubic to cubic yards to cubic drachms to cubic Tons to milliers or Ounces to grammes. Penny- weights to Scruples to centimetres. metres. metres. metres. tonnes. grammes. grammes. I 16.38618 O.02832 0.76451 3-54958 I 1.01605 31.10350 I -S55 I 7 I.29598 2 3 2 -77235 0.05663 O.08495 I.52903 7.09915 2 2.03210 62.20699 3-"035 2.59196 3 49-I5853 2.29354 IO.64873 3 3.04814 93-3"049 466552 3.88794 4 65.54470 0.1 1326 3.05805 14.19831 4 4.06419 124.41398 6.22070 5. 1 8391 i 81.93088 0.14158 3.82257 17.74788 5 5.08024 155.51748 7-77587 6.47989 6 98.31706 O.16989 4.58708 21.29746 6 6.09629 186.62098 9-33105 777587 '/ "4-703 2 3 O.19821 5-35159 24.84704 7 7-"233 217.72447 10.88622 9.07185 IO.36783 1 1. 6638 1 8 131.08941 O.22652 O.25484 6.1 161 1 28.39661 8 8.12838 248.82797 12.44140 9 147.47558 6.88062 31.94619 9 9-14443 2 79-93 I 47 1 399657 8MITI HSONIAN Ta| 1LE 3. TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES (I) CUSTOMARY TO METRIC. Table 3. LINEAR. CAPACITY. Inches to millimetres. Feet to metres. Yards to metres. Miles to kilometres. Fluid drams to millimetres or cubic centimetres. Fluid ounces to millilitres. Quarts to litres. Gallons to litres. I 2 ■3 4 5 6 7 8 9 25.4001 50.8001 76.2002 IOI.6002 127.0003 152.4003 177.3004 203.2004 228.6005 O.304801 O.609601 ■ O.914402 1. 219202 I.524003 I.828804 2.133604 2.438405 2.743205 O.914402 I.828804 2.743205 3.657607 4.572009 5.48641 1 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 7 8 9 3-70 7-39 11.09 M-79 18.48 22.18 25.88 29.57 33-27 29.57 88.72 118.29 I47.87 177-44 207.02 266.16 O.94636 I.89272 2.83908 3-78543 4-73'79 5.67815 6.62451 7-57087 8.51723 3-78543 7.57087 n.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 9.290 18.581 27.871 37.161 46.452 55-742 65.032 74-3 2 3 83613 O.836 I.672 2.508 3-344 4.181 5-oi7 5-853 6.689 7-525 O.4047 O.8094 1. 2141 I.6187 2.0234 2.4281 2.8328 3-2375 3.6422 I 2 3 4 5 6 7 8 9 64.7989 129.5978 I94.3968 259.I957 323.9946 388.7935 453-5924 518.3914 28.3495 56.6991 85.0486 1 13.3981 141.7476 170.0972 198.4467 226.7962 255-!457 0-45359 0.90719 1.36078 1-81437 2.26796 2.72156 3-I75I5 3.62874 4.08233 31.10348 62.20696 93-3!044 124.41392 I55-5I740 186.62088 217.72437 248.82785 z 79-93'33 CUBIC. 1 Gunter's chain = 20.1168 metres. 1 sq. statute mile = 259.000 hectares. _ Cubic inches to cubic cen- timetres. Cubic feet to cubic metres. Cubic yards to cubic metres. Bushels to hectolitres. I 2 3 4 s 6 7 8 9 16.387 3 2 -774 49.161 65-549 81.936 98-323 1 14.7 10 131.097 147.484 O.02832 O.05663 O.08495 0.1 1 327 0. 141 58 O.1699O O.I9822 O.22654 O.25485 O.765 I.529 2.294 3.058 3-823 4.587 6.1 16 6.881 0.35239 O.70479 I.05718 I.40957 I.76196 2.1 1436 2.46675 2.81914 3-'7i54 15 1 fathom 1 nautical 1 foot 1 avoir, pc 132.35639 j mile = 1 und = jrains = 1.829 metres. 853.25 metres. 0.304801 metre. 453-5924277 gramme. 1. 000 kilogramme. The only authorized material standard of customary length is the Troughton scale belonging to the United States Office of Standard Weights and Measures, whose length at 59°.6z Fahr. conforms to the British standard. Ihe yard in use in the United States is therefore equal to the British yard. ,,,»«•• t. • „( <,«,.. nf .,n The only authorized material standard of customary weight is the Troy pound of the Mint. It is of brass '»' un- known density, and therefore not suitable for a standard of mass. It was derived from the British »*^«™™* pound of 1758 by direct comparison. The British Avoirdupois pound was also derived from the latter, and contains 7 ' 00 The a grain Troy is therefore the same as the grain Avoirdupois, and the pound Avoirdupois in use in the United States is equal to the British pound Avoirdupois. The British gallon = 4.54346 litres. Tta£5S'rffl!?™£S , Sito i ^» above and adopted by the U. S. Coast and Geodetic : Surve, ,™g yeare ago, is definld as that of a minute of arc of a great circle of a sphere whose surface equals that of the earth (Uarke s Spheroid of 1866). * Quoted from sheets issued by the United States Office of Standard Weights and Measures. Smithsonian Tables. Table 3. 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. Millilitres 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 39-3700 78.7400 118.1100 157.4800 196.8500 3.28083 6.56167 9.84250 I3-I 2 333 16.40417 I.093611 2.187222 3280833 4-374444 5.468056 O.62137 I.24274 1. 8641 1 2.48548 3.10685 I 2 3 4 5 O.27 O.54 O.81 I.08 1-35 0.338 O.676 I.014 1-353 1. 691 I.0567 2-1 134 3.1700 4.2267 5.2834 2.6417 5.2834 7.9251 10.5668 13.2085 2.8377 5-6755 8.5132 II.8510 14.1887 6 7 8 9 236.2200 275.5900 314.9600 354.33 00 19.68500 22.96583 26.24667 29.52750 6.561667 7.655278 8.748889 9.842500 3.72822 4-34959 4.97096 5-59233 6 7 8 9 I.62 I.89 2.l6 2-43 2.029 2.367 2.705 3-043 6.3401 7.3968 8-4535 9.5101 15.8502 18.4919 21.1336 23-7753 17.0265 19.8642 22.7019 25-5397 SQUARE. WEIGHT. Square centimetres to square inches. Square metres to square feet. Square metres to square yards. Hectares to acres. Milli- grammes to grains. Kilo- grammes to grains. Hecto- grammes to ounces avoirdupois. Kilo- grammes to pounds avoirdupois. I 2 3 4 5 0.1550 0.3100 0.4650 0.6200 0.7750 IO.764 21.528 32.292 43-055 53819 1. 196 3.588 4.784 5.980 2.471 4.942 7413 9.884 '2-355 I 2 3 4 5 O.01543 O.03086 0.04630 O.06173 O.07716 I543 2 -36 30864.71 46297.07 61729.43 77161.78 3-5274 7.0548 IO.5822 I4.IO96 17.6370 2.20462 4.40924 6.61387 8.81849 II.02311 6 7 8 9 0.9300 1.0850 1.2400 !-395° 64.583 75-347 86.111 96-875 7.176 8-372 9.568 10.764 14.826 17.297 19.768 22.239 6 7 8 9 O.09259 0.10803 0.12346 O.13889 92594.14 108026.49 123458.85 138891.21 21.1644 24.6918 28.2192 31.7466 '3-22773 1 54323 6 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 O.0610 0.1220 O.183I O.244I O.305I 61.023 122.047 183.070 244.094 305-"7 35-3I4 70.629 105.943 141.258 176.572 I.308 2.616 3-924 5-232 6.540 I 2 3 4 5 220.46 440.92 661.39 881.85 1 1 02.3 1 2204.6 4409.2 6613.9 8818.5 II023.I 32.1507 64.3015 96.4522 128.6030 160.7537 6 7 8 9 O.3661 O.4272 O.4882 O.5492 366.140 427.164 488.187 549.210 211.887 247.201 282.516 S^-S^o 7.848 9.156 IO.464 UN- 6 7 8 9 1322.77 1543-24 1763.70 1984.16 13227.7 I5432.4 17637.0 19841.6 192.9044 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-indium in the proportion of 9 parts of the former to 1 of the latter metal. From one of these a cer- tain number of kilogrammes were prepared, from the other a definite number of metre bars. These standards of weight and length were intercompared, without preference, and certain ones were selected as International prototype standards. The others were distributed by lot, in September, 188a, to the different governments, and are called National prototype standards. Those apportioned to the United States were received in 1890, and are kept in the Office of Standard Weights and Measures in Washington, D. C. The metric system was legalized in the United States in 1866. The International Standard Metre is derived from the Metre des Archives, and its length is defined by the dis- tance between two lines at 0° Centigrade, on a platinum-iridium bar deposited at the International Bureau of Weights and Measures. to _ The International Standard Kilogramme is a mass of platinum-iridium deposited at the same place, and its weight 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 maximum density, will counterpoise the standard kilogramme in a vacuum, the volume of such a quantity of water beine as nearly as has been ascertained, equal to a cubic decimetre. Smithsonian Tables. IO CONVERSION FACTORS. Tables 4,5. *. H J O h-1 O Ov I--VO *0 VD OM-i OCO OVOMDOO W N N ON "**■ tJ- into m m o 'fe'o O O S u xxxx o 55 •^NO QOrl CON O 5 Q QV CO "^"00 O O "") «*■ tj* tJ- \O0O n O "1 HH{j>rn« fab o iOtj- N hi "1 i- O OCO VO oo m com m i- covo OVQ »o O VO "i r^ w On coco "io »o u c t- 1 Tj-Tj-M M |M -i if I o o o o o 6 XXXX X ^ O N Q OH m o no o o VQVO O Q 1^. COOV O 5 co nw\o n on vo nHm to o h! 'trnn Ov ■■*• CO N N Hi 00 VO ON"-" 00 Ov w ror^-O O »o N co r-. N m N r> ->■}■ Ovto o o coco 6 In In * OWO t>. mOCOO co r-i covo vo n ro w ov hi ro co OV VD N hN n |m |-4l^-|ifHO I tlUo 6 X XXXX N H ovvO to r-. OO 0O co co -<"*■ o >-o oo ro^f r*-. Ov vo OvvO coco oo tJ-h Hiin bo o 1-1 Ov r-.vO ioO coco vooo lo N Tt" COh CO Qh * r^OO CO w VO to r^. Ov Ov ONN m N 1 "3 di-4-i-^-it/iivd UUo rt XXXX * H r*. n Tt-oo O lOCO ^N N hH w coco co toco 0M-» m hi VO 00 to N H 1>1M HO « *— n O »Ow O ih ^ H NM *^ wi-n« Ovn M 00 NN "t iO_ o o hvo o o\0 ►J r^. N M M N i looScd vd Lo U3 (4 r 6 e b < o . r^ t~ CI 03 IN II O O O O o rf & 6 XXX XX ovo O l ™ 1 OCO CO Tt-OO O ON ■^■vO O O ro m ov*" tnu-) ON-* tnoO Tj- H( M H N oo n ivco r*- VO ■«*■ COVO N & J N N VO OVN •<*■ "^ W ■** CO CO ■^ OV 00 ON o o r^.6 icoitolov « IS o ■b 'o b b M HI M HI & X .XXX CO 6 Tf o" *«*■ Ov ro 00 O "-fr cor--. N O -*-ovo CO O ■«*■ i^-vO NO OvO ■<*■ N ov vd « to to tv tnvO to N tcOOV N 00 O iNnN* bO hi _ , lONNN O OvO Tt-00 tvOO a Tt ooo O r-s vd |m|4i\oio t: Im rt o PS ■b tll'o & CO M HI M HI HI 6 X .XXXX o" w toco r^ £ vo >- O Ovm n h. vo toQ O*, hi m OWO ■ o M t> m q ro HH fC HI VO ION OOO r-. cor-- o vo Ov r*. cor*. tJ- tb ^00 ThvOVO m o O o "") ovco ov J u-iui rotoN ra '^^ISlSS a T f f t f is 'o 'o o o b a a* in c5 _,XXXXX " hH M00 W M no o*o,J iz; OONO hM) N00 OsyD >J 1 N iotJ-00 O^ roroN nn Smithsonian Tables. II Tables 6, 7. CONVERSION FACTORS. II £ bb o h1 00 O NO N o\-^- o ""> On (ON Tt-Q VO 00 ■* N .2 C E S J a a u u-, u~i -^- _ la's 2 ■fl XXXX O S5 n uro r-» CO "IhOO no -^- coco w\q oq vo ■<$- is n w l-l "INt CO "t O "3" ON "TOO 1^.-* >-0 0\0 row oo ■«i-\0 N r-s. J3 CJ .5 o =8 ■4 -<£ to in o o o o u . XXX .X 00 o o"^ "TO O **0 rococo « tJ-«0 N o «ro rs ■-■ a N ^- M no ►J O NO "T"-) On CO t(- ON no coOnO ■«*• « rf rs«r o o o "a J- M |-^-|io a T? o o o o U 6 2 XX XX oggH ^tN Jo O "fr rs o oo co •^- r^. *>^> h n ion o 00 no n o CO cOQ>ON "-) no O »o VOQ00 h\0 to o nn is «onn OS |ci|i>*b 1 y "2 U1 U XXXX oo" O t"1 r^ rs to o\ i-« nnts »o o-to % "r row >-t Hi WOO "IN no On "-)"-) -*■ o mo O'O n onoo N CO ""if) 0) u 3 o n u> » bUo u d XXXX Hvo nm\o N >ONO\ ^j-no n CO On ^ O oq rsO^Tj- Smithsonian Tables. VO N 'tN a "*"0 d o § O ^H is II n tj-co i^O hJ ioh n Ln w to tJ- eg "->nO .2 ~in d d c 10 3 s T o o XX 6 CO N N N H NO Is Tf-OQ ►h CO "TO *■ "T On o M O N ON © | NO COCO N u NCO CONO n CO00 ONOO £ On co "TOO rs co w r^ W ■3 js 00 NO o *■* M O I dico di"-I n rt ? V s W b b § 13 W H Cm ft) d X. X «O rt TtM H '3 £ p t> iOP. M ^ 00 O ON m i-i s I oq n O ^r- ■^- CO N NO jn. tJ- h ri o 1 ? 5^8, t> bb ""1 NO M Tj- D r^O toco"") Hi a Hi ro w no tI-co « co-^- IS co « (si i-3 J3 U u "o %% o '.3 9 u 6 53 X XXX s^SvP^ CO O " "T\0 NO "T bi ■* O vo On S 1 O « NO "Tts w NO M O •■*■ hJ is i-i N un o |41m|w|n o u TT VT 3 O O O O a U 6 XXXX oconS --h o O ONVO CO tfl C j .2 vd >on|n a a 6 A 1 'b'o'OID «-( hi CH M xxxx » "TO coosH Q CO ONOO S NHN O O ""> --tf- i-h o\"fvd VD CO 00 N bj] ro w O ■<*■ o "">vO loq co u ON 1 * Tt- W oo M M CO M d is rs n m '3 *b o°o o *_ o M M M M n XXX X 10 cd 6 O Q OH re O O O N s CO O O f) VO O O Tl- o g In m CO o w -tf- NO Tf- W g o 1 N 0 00 row H B o J Tf CT'^Tfr- Hi O VOCO o l H_ d i4ioom5 f "8 TT? o o o fe l H M W en o 15 XXX O ^ O "O w o ooo n O O N N N O "t O M O If « N N tt<0 '"<. CO miocO rs rs\D O ff oo o^n ^ w iotf o as g ovoco C\ boo |M|-j-lo6l^. §J3 ►J TTTT ^ o o o o o O n ■S~ xxxx 3 d H nOi'oi'i '^i *ON ""I O m co ■**• is n N \D Is tJ- q\-*- rocq oo ■^■'O dv 4 1 Smithsonian Tables. O « o I ro go. 2-3 £3 la 2 » 5 «S ■8* 13 II « qovo O On roo ;s C7 H> >0 -*r^ (U •^nn .2 a s 2 fc -S o £ a OOO XXX fc o -^- o t« o u w o\o ■«*■ N VO oo »n o o\ro o S 1 O t^ Tf -^J-co w w j . 00 VD « .rt COM |« fa a 3 T O o o o o • XX x fa » o ~H m O l-C M O M M OM3 VO ooo vo vo voco ff ro NVD con nn u-i w «w ro j m n*o S N |N(iO a P T3 p C Ah % 11 (H 1-1 W j3 X XX HH z O ^ Tj- lO O m w O Ms rs N N ff no o w tJ- tors J 00 H fO ■2 im-^-fvo a 9 TTT P4 boo M tH M O O fa 6 XXX ^■mo tJ-CO fO 1 Tables 10, 11. CONVERSION FACTORS. 1 hH O. II 8 bo 5 a ° 3 *5S (U _ |_! E J 2 A O r< "3 oo tS XX □ » "TOO 1 "' tots 0\rv. >ON M M t-( N N O Iv. trj M O fin 0) o P 6 X Ov N 5 r*» vo in ro CO M rv.00 o in |n a « T7 Pi 6 o o XX H„m row tnro TfcO tv. N m\o 8MITHS0NIAN TABLES. t-i II t5 (3 g 1 VO "tf- N m M t- O ""> mvovOoo w o u -^-Tj-fOhH CO J9 *o CO a E 5 XXXX s o v. o o oh tJ-Q O O vo o o o i- Tf-o 5 vovovo q coco" nvo m c\ "tvd m -1 ISA© «">-* on ^ i- Ontj- roo vooo "ICO Tf N w 05 hi -vo ■^- CO N w V 0\NO> W OnvO -*f «1 ■* -«00 W CO N HQOO n vo w w r^. -d- - v-i « O i^. in O O* (WIN O o a o 6 !Zi XX co cn O o Ovr-*. o o £8* 8£ W M vd CO 13 a o u * ro oo moo ro VOOO C\ VOO Ovr^m ►h On r^. ""> O |i-h|n|n If) t 7 ? cu ft b'o'o V 6 XXX VO tJ- OCO VO roco O VO f-i VOOO ■"*• H tJ-N bb o -1 ono w ro VO ioO ""> VO comvo O fOrOn CT, oo Nioro £ (M|lHtM|N. J5 ft (0 .■3 W rH i N c o o * fovo Tj- -^J-OO VD NO M\D M WVO _ CO ONi-. m N NfO in O m ro >-i o O CO voooo V 6 5 XX XX 00 ^,"00 "1 r^vo inxn rvvo i n On r^vo VD **) mQoo m On N NON N NN C\ a CU ft |N h|h O « rH co (3 'o 00 M M rH d X XX 5 p* VO O m*o m VO m On h MM fO •oOnn I Ooovo onoo S N»oONr> x *• m no n ft ta 00 o WW w XX X 1 o H 88?'S> <* 000 600 549 729 \o too\»o is Tables 14, 15. CONVERSION FACTORS. § g £ a I w tJ-N 'tO bb -*CQ CO O w 0^00 § o5 1-1 O Tf ON O »5 M M rC -^ d »o ■si fi — OO O S g XX x "s^ 0* ON."TCO H u «sj- u-»0 O m m "i *ooo r*. Q foq>o ^ W M W Th N ■* O tJ-OOCO Q \0 ^ CjjO O B . a a -*• a\ w 5 \Q 1-1 N O N|MJ10 1^1 B , T T 1 OOO O 31 0* XXX X uW OS "TOO ■"■ O s ^■100 O coon O --4-M W W ONOO VO VO lOON w w to wl W -* W O O moo i>*> a to - n m "frlw a. a rj* "2^ 2 2 2 xx_,xx 2 mo" om^ fe no 00 no com LTl O VO VO O O OO w w coco VO O W h- ro o\f)n r--0 -*■ On On <<*■ w coco 8 m I^OI^ CO » T T S£ ^> 6 XXX £ m'""' N O O u* m "T O m CO fOfO ON Tf M N OvhvovO ro-rj- xn"-» & VO "TON ON O m r^ -c w moo on on .J 1 ° tovo m m l^boimico tt ? r 0000 W II a a XXXX 6 H ONroO O O NCO00 §s ON O "">"T O t-^vOVO Tj-00 ■*■* m*"d- ci ci g g s g s e § ■a Pi M W Eh oo\o O on m Q TfVO ONO O M O I» M N^O NO \q -^ t> Q lOfOM N E-a o£ OOOO XXXX c"» d M O M O H £ 4o *tf-vo M N M O N ON O O •^- M \d « COVO O Q ON CO Q O vo m\o O ■^J-VO ONQ O J m \o r-*. O 1 . s ™ S'H VO •* t>- Q inI-^-no ii>. 7 T T T boo M — -H l-< as xxx_,x |tn £ M O N l "' O 3 O tJ-O ■^vo O O M W W O w ONQ O -tj- ci vd w ^,^8 8 to -1 O r^. "**- ^J- "tvo 000 ■^-00 N m 00 vo nw U) ro>-J ^n 11 OO ^3 O XX XX to d O N ^ M M O"- ww O W W HH O vO vD vo CO vo vo r^.-d- ww w m^ •* VD VO VO VO bb f) N VO VO ooonnn ►3 m v w nn w m"^ 1 '! 1— '* w |n rni^ §•1 OOO "o R w w w >-t d XXXX O" Tl-VO VO a O r^ r^. r^ w w mm r^. N N M m M vo on m m n m -t^i>o i3 00 w m m lcni-4- w|v6 §1 o3 f T T OOOO P*t3 sg XXXX "CO d S3 -3- "TO O •^J-CO COCO onm- m co VO w N « j 1 Smithsonian Tables. 16 CONVERSION FACTORS. Tables 16, 17. H s •J \O\O0Q » ??S,o a ►j O ^f r-^ r^oo ii 'fit! |Mll>lfO a II en T f CO O O O 5 XXX £ o o oH ro no VOVO O o o o >OiON COCO N C\0\0 Tt" _J inifl ij-j & COCO w |T>4C^ l4 JS § ceo §•3 T o f o T o *§ H M *-* o Ah 6 XX X o o "■> tn ro CO nn n O CO 00 » O VO m 0) Oq o "i o w -*o\ E E O m w 6J Tf 00 t 5^ Sna £ o 6 15 X XX oH>nN o mo a O N *0 o co r^. O roON M HI HI ococo ___ O VO «0 O h3 O ^f ON "S l-^-^-o g,OJ 1U o o fit HI M O 6 XX a fc H O "irs o O^O I Q N in oco r-*. o rooN Hi H M r^VO VO t-%vO 1-1 3; on m on ■**■ bb row ovo *h (3 o i-l voco -4--3-vo II £ ft E ™ T T* .2 ■go o o o o o o ,\0 O OOO NO\ I**. "T* i>, M ** ■*■ o i^.vo Tt- r^, row -4- .S 3 m O O w ^- O i^NiO *0 £i £ 0QVO -tn tJ- ■3-vo CO oo o -3- ftp. >-l CO O h, t^ w ro «6hm 6 .31 o o o l-> u HI HI HI ftft X XX a o vo -tf-co OplO O rOvQ O O vo o\no o o >OOCO O VQ s >o vq ^i o w 0\**\0\D U «s O COCO ON M ,")0\m rJ-O £ o bib vd Tt* ro oo n "*^ cT VO CO O O m \D h] P.JJ « TfO N iO 3 u 2 « ,13 to d| S5 r>- TfH -tH rt ft VO Tf ^ ONQO NO Tf roco O VD Tf hi mcO Ti" Tj" H ION m n" dv«-« ro hi O N O -fr 5 3 »0 M O "lO o hi 00 ^oroco EJi QOfl h h rON ►J !>s w h NO\N cu . VO ^NH ft ft M M H|H O rH J§ s O OOO H H M HI HI HI a> D ftft • X XXX • — , — ■ 53 Q H HI Tj-Hl»0 O 0\N Nh to O OCO CO N O C7\N m «t s O ONM fO vd -i- covd hI ON ON O ON TO ■^■vo loonlti ii S $ 00 vo rOM \D "1 O m ro rOLOON 1-1 p; 00 r^. q ro ft« ft 1- « I oi [ m ( m | «' | ri tN p-l r-t (M CM 1 s b 'o b 'o U H P, ft XXXXX 6 H r^co m n Tf & vo hi r^vO ON VO 00 rO lJ ">vO a vO hi hi ro ro a VO 00 N O M hh VO VO M M Smithsonian Tables. 17 Tables 18, 19. CONVERSION FACTORS. 3 3 ft a >4 CJ 3 8. •3 r cd u «g Pi CO NO ^N M rsoo Tf ON O OO «-■ CO vo _. O >-■ OO — coO O n ts m "4 l^icodlcvil'f 6 H 03 ^? T b'o 'o T o XX XX. O COCO fsco rt iv. in covo ts Tf Tf CO vO ts O isno ts m h vd m ri a "s P. 1-1 i-i o <•) *-> m cooo oo m o ro^- Tf « ro vo co Tf co o ^O t^. On *n ts to v^snN m c i d 4- i-l ro 6 •z, 'o t) o w o X XX X o oo ^o_i ro ON- ©NO" i-i ON Hm O N VO 00 vO O CO NN N O m covd ci vd Tj* jjl CUV ~ft c" J" 'is '- 1- HI p. a c Q5 ►J O CO — on ►-< hh Q CO 00 m CO OVOO M « on ci is n ts *> °. *? n n Oil- ci lei |ci 6 XX .XX CO O O" NO h- N ON VO O HN ON \D O 00 --f VO \Q O won vq q vj5 — to mvo o . v (0 « '§* Is i p. Gmn CnnO -Ttw d "M Tf" H O H II III o o o o o XX XXX tsco "co n^i vo rs >n cvm vfl N ri o i-i vo is m m ON , vq is vo Tf in ■4 m ci -4- *h a «i o w +3 ft D „ 1.S ft §■ j _ nn o n m o is ci w i- co onoo m OOftVO ON hh CO ts w i^inO ^ ts in on ci ts >H CO O |*H IN d ^ «« 7 ^ o o o o XX XX Q ■"' n O moO o m n^^i Q M ON — ON O CO Tf ON ^ O ifl^uiN vd -4- on « lo d 01 Q (U - P v C 10 o ON •-< O ON hH | ■*^MO rv OO I-" CO VO ON qnco h no\ v O N O N N N NN Tf ON IN ^li-lirod 6 T T? o o o o XXXX H no ^~>co o \0 o lo Lon o o h n o\ VO O ON^o Tf vq o iovo i-n - ^s ,,, ' n ON ts rooq CO P |i4 c4 VO ON ON ,_, 13 1 in «s c> q» O O o o o a> d xxxx_,x r^ on on m 1 ™ 1 vo in tf ION M ON LOCO N ^ > ^ Tf r-i vO N VO on is q "^" "^ OMON N IS ci m rs ts lo Is ON ON -* ts ON covO coco M VO rs CO—. ON M N CO ^»-0 N Q i- co ^- >- q o c o ^ |6to6i4- id 6 t/5 l~ 1- t T T T o boo o w c d xxx_,x i-i iooo rt ^00 4) ^ s VO O fs ON ^T ONVO rs vo io CO i-i ts Tf O cp ts rs cpq m ts N •"-•-* lo rs M O ts Is ON O^N bb o ^1 N vO covO vO 3 CO coo vO Lrv & 00 Tf ^* moo "*i vo 4" mvo m 1 IisJ4- coir^co t~ ■* i- 11 CO 1 Ml _rt O O o o o *o CO a d XX XXX COCO H O fs Tf i^N O ON ts 2 Cl is O CO ON N ts O Tf >- CO ts VO CO vO -f ci co 4- co tv. m m rj O is o O moo u"l COvO ON ON o ONQ vO ci - Tf ^ ►J ro u-i •- Tf i-. 3 n m i-i M i-i O K I CO CO ts| CO N n co rt »t- 1 (- o o o o o CO d X XXXX . m w N Cl Cl ts O ti f rs O co Tf o O O O co ci m v O - NO N J Q is COCO OOO ci vd on d on ei ■- o» os ^S OOO O o to XXX X s d O O VO CO ON £ H O VO ON Tf CO s o co Tf in in VO tsvo O O fs, q Tf 5 tr, m ci is ^ tC Smithsonian Tables. 18 CONVERSION FACTORS. Tables 20, 21. s a 1 I g r»-vo On « -* tno\o co 00 N mVD 00 co m- COvD ^O \D unw^D o o mrv.00 Tt- ■«3-|N dl« O XX X in. r*s ON m O r "' co*- m coo 00 w w in o i_ in hi CO»-0 CO w moo VO h O^O^O VO O ^ r- r^ >-. ONOOO *- o xr * COIN OIN l»- 03 £ 5 XX XX O'fl^ On" hi inOO ONN O O n^o^i r-. \0 >-i co Q\ co in ■<*■ O00 ON 4h fi N CO lO-tN M OO T CO ON CO ON NVO C\ W CO r-^oo vo o co co Cnco -tf- w rr ^ M m\O00 l>T|w M co co XXX XX n. hi r-* co -^-vo -* N O r-co co moo O H co vo N m co on mm Tj" CO COM oo r^ Tf cp o m o COCO COLOVH o no O N ^" CO i-t VO in ONCO hi VO N nn mini" XX XXX I N VO ^ ON ON W 4" H O M "~>00 ^t - - vo VO ONVO vO co comr*. OOnCO h. ON -tf- X X XX oh o i^- o m VO Oh. ONVO m O00 N ^" n •-*■ Tt- r^.00 M Tf O O !>. CO m N 1^. N ON N ION CO CO m LO00 m cot^ r-* on i-* O t- ON M ONO W ONtJ- O ^ CO TfVO CO CO ON Iv6l4ivdi4-im to -+■ « -r in b'olU XXXXX I ON ON CO "^ CO hi w r-- t^oo O >tON N O VO ■<** ON CO m rt coh. vq CO-^-VO N 00 Smithsonian Tables. I I I o ft. (A 4) §13 M 3 u-) m m hh On ^-00 ci vo ^J- O VO lo O CO M O M LO H. Q oo "fvo r^ m > "' CO — COCO M i VO ^ M VO CO i o OJ I- 1* o d Vor 2 w o XXXXX O "-o ". c c c d mm 2 2 xx_,xx NO m" « n CO ■*'* N CO CO CO N N CO M ^J- N W CO O CO O M CO M M ro c-i H« a C i i a I ! a C =1 o Ph o o hi o Tj- HI O 00 ON m in fOM s ir, M in co-* CO OOQ N ONIn m t-N.^^ m in co ion moo vo ^-w ^dico d i2S 'fc o "fe "o XX_,X X O O " lJ * 1 r^ O O O 00 M ON O O ■**■ COON O O m coco rO O « « co (OVO nN ^ t5 t fl o o in H OJ a G o o o fa to o co ON OnvO ON vO ^f* r--vo hi ro 00 COM CO OQ HI Tf HI ON ^t W N COCO m i-n. « i^ q oq N |N N|m|i>1 d "° 2°m 2 2 X xxxx O H N »oO O O \Q N^O O vo -rl- mro O VO N O CO m vo tJ* n n 1 o i ft o s bJG O t^vO vO 't m COCO h O "? VD "<*■ O CO ON O ON hi TfOCO moo ON Tf hi N -Tf ON CO m IcoHniMl^lrN d m m h t ": bbbt b XXXXX qq com m ^ COVO ON hi OO O CO hi CO i M COON N H 19 Tables 22, 23. CONVERSION FACTORS. S a I I i n S I a O N N f Q cow coco o On r^.\o lo o _ Oh O "lOO ONTf ^-ONO ■*f ■"* H< N o H •j) o i-5 1 O U NN-tO «^ II "0*0 lb *o c s — —, — >-H .2 XXX X E s 2 d m O «on Qr4 ONhh ioO O o VO ION *0 Q ONVOCO r-> O 5 q i>. fOON q ! ro N w m m O N N Tt* O tis o fO>i COCO O On r^.vo *-n o O h. o ^o o tn i-3 a | N N|hJ|lo JiO rH .« .a ci -i 1 | o o o o o £ • XXXX X o 1 •-• O ion" O 0\m mo O S4 QNO w n o HN m m h! VO CO CO vo vo Tf N ON 11 HI % CO M O Tf- Tf lovo "in -4- --, h-. g 1 WO On (Oro O^HQ rj- onon lo o lo lo lo ►J cp to w CO CO c 3 O roco i-^-di^o W CO 1 | P4 o o b b o o 6 XXX X fe O rt 'CO o O O *o o O Q Q CO coco Tt- o n to ro NO "* N N N « h NN CO O N CO CO <-* £, rococo fab N ONCO N N o ONQ 00 fOCO CO ,q h-4 ■"T w On lo uo lo q vq cq >o^ P 8 O N til b | -^-foo l toico ■* oo eo oo fill O O O O 8 = (2s o" _,XXXX Q rt OWiO O O 0Q0«O"l a O s O O w vo vo N 5 tt-m _ hi q »-h vq vo hh" lo j^ rn ro N N Tf- O O OO »^iOKN bfl I"-. in.vo O O o O O ON Tf ON ON J3 hh iO^o o o CNVO 00 ">"! §i - 1^14100 IPOloo 7 T T T T ■S 11 b o o o o ° a 6 xxxxx riNON"iri N a low io o O o CO H- r-, ONON NVOKN pi CN"^- rp n N i CO "^-vb roro Smithsonian Tables. E § I 01 O M W a o « ■* v. inroro bb o voco r^. W HH VOQ NiOO W mN -t E II rt l-I N |« u a .2 fc-ii a 11 .oo lo N M M aJ O o o a M M H< a XX X t5 ^ "OH co no co 00 O ON "IN CO On n CO * CO C\H oo ^co ►J n w xn^- On h. t^ Ic4 INICO « ■S u « w w b b o a Q f5 X XX co^ -^j-vo On CO i^N CO 00 ON CO N ON Cp ■<*• LO 00 h! 1>J 00 oo ■* cT O o^ ^*" f~^ NHN O N CO )-> M|COlN c obo w a _,xxx o ^ " OCO w O N !>. O tJ-ON O HI M *1 *> *> H H<0 20 Tables 24, 25. CONVERSION FACTORS. S "3 I s n ►J a II 00 II o i-l „£5 l^idirod c ■§ □ III s ■s 01 o fa XXX H IOV0VD r^ u-i- woo >. On On to M U-1LT) M Nnno OO c* g j-i «ONN VO CO CO 00 hh ^N N O vow w O on i , II u a> o l^diro |m m S CO jH ij i I T ooo o ) . N N b'o -o^ 6 XX XX O O wi^ Tf-O ONI*- i-i o »Owi « O •**■ co •4- m t^» rA. 01 g ►J CO O COON ON O >-H W vo o r^ i-*. -^O O M VO n w O r-«vo vo ooooo o *n t^. On ON R gj 2 'sITs J X XXX ^ toH ovooo o O u-l^t- tJ- O OM*-. l_, Q ^"l e* O ^fr" co ^- MNN 13 § M O -1 N N u-)_< O Oh n nrOO O O "^«JT0O CI w r-^. r-^ xt- -* co m m n w S 10 3 HflM^t ^glb^ a XXXX Ah o o fa o 2 H N N CO"1 O O h ON nno "i r-^ r^. r-N. -*■ N fi H M ON w m N tub N rococo O co covD o rococo OQ a w 1-1 hJ no o Tf w vo O O i-i is wiro^-* ii ' .§ to c .2 a U C* 1 •* Tfl c O O O O £ M M HI HI 1 E 6 XXXX a 2 a »ONN io 1 ^ \o mfrn UIOONN ON--- i-i CO N O O CO TJ-M w M t-- On On co Tj- -^ Th M o £ mvo VO ro >n n r^. r>Q On OnvO vo io i-l ■^•co CO CO m iNlodlM |iO II CI « rl LO (ft 13 b 'o 'o b IH >H M W d XXX X o & TtCOQO'^ ON OOO ON r^ co ro w o O r^. r*. ro fa 00 O M ON On O «j-)VO VO O rovo £ ■**■ o O w ih ►j w O fOON VO O ii On 0) iNlt^. 6\*h « i- in i i r 9 o o o £ 6 XX X no 1 ^ ono o 5 « o ■^■5 vo O H O lO I-I N O roco 4h w on CO Q i-i ON ON O ^OVD bfl o ►J VO O r-TO c ■^"O O « HI N v o no\ VO O H. ON *o tA.r^. n" « _E O OOO a HI HI HI M U X XXX h o o S3 fOH O ONO O O M o to •* ovo o )-! O^H H W O mco ^ M M ON N N Mw O O^n ro rOVO ON I O iriiONVD r-. t~^ O vo nr^ioro tn Ivd m nliro 1 C o T T o o o o P4 M HI HI HC o o fa XXXX d H N n o , ^- o O ^ON CO COCO t^. NNH N CO CO N CO I n ri nN Smithsonian Tables, 21 Tables 26, 27. CONVERSION FACTORS. s £ a O MO ! u bb vo o o ■v. c7 n m go s > a d XXX •-» GNO 00- N O s OO -^ Q M N M o n o in i-i o VO o o U) N "-h O O J n co o j w n o 1> h n N u 1) t- 3 a 1 o o o a, XX X , CO N O Q CO Tf Q -^--. o im N M n nn co co oo hi VO _ , ON ON u o w O coco .5 00 vovo V ico I-^-In s 3 [Q P< i T? o o o c 3 d xxx ■tfH \q \o O ■<+ ^ ^ fc -4" vo vo ■^- NOVO ON \Q VO N ONON NO <*^f nron ■-I QCO NN "-> n N o HOO0O »*-t N|pi d - ^ a Vo Ul 13 XX a 3 o 6 H O -. „ o n n CU Q G\OV "*?" *> *> = Smithsonian Tables. H N co to *v u h3 m con s II u 5 TfOO v£>0 -=r g o w NO ■* OlfniN c o c »• L- to 4) p 11 p. % b^ a . x_,xx Q fc « " N Q <~> VO O CO NO 3: o w T "TOO ""> « ON NVO H VO wiN hi f "TOO o Q rf N IT) J2 hj vovo io u N VO N a 1^-ltOfw M S a u V TTT a o o o T3 C d XXX 3 fc H covooo fS NCO N t^. N N COON O oq *noq M -^- M 22 Tables 28, 29. CONVERSION FACTORS. CO O ^-VO i tJ- M VO NO a £ I^-ND m O >>. tJ- tN Na too ■* ON° ~s Q U i-l s nw tj-io u IOIN w|co ii 3 3 u hi Im tf] a .2 ^r i "53 a o o o o a S 3 6 XXXX_, •^- -5 NO\ N M N ro co tI-co tJ- OQ "ION co vomo on » j= o "* o <* w o .5 J n^ooo ^* o lod 6 co N 'Jq 3 u I °o "b oj en d XXX a is lorooH h "1 O ON O ON Tt- o O CO 0"10 M. lo o O "") *o -4- »>•. c-i tJ-NO tN ^O * co "i b co "">-$■ ON00 M ION _ tj-n cnno 0"nn •g o i-3 .3 CO N h in Icil^r- ItJ-IN 3 ?r t? . w r^. o loco O CO COCO N &H co r^. -^- n w w ci vd* NiflNN NH H lO 00 -cf CO w to _ \D ^J" ON tN .cono O^M^3 ^ >ONH ON CO W CO "-O NMH Tf nM O O wl 0\NH h o twi 00 CO ON ON Ua o O "">0 o o*. lO N i-< M II rt £ tJ- r^io ■ , ^- n °s -» t- m -r _o O O O o "55 a re u XXXX o" t>- ON ^- •^■pJ Q ION N n NO >t COCO NO NN hqo d n row w m hCOO o # # CO^O O ON bO ON COO O VDh 0ft»0 ONWIO w ON K & t_] So rt 6 row O CO o cow |in •SB t -. h-] Tt- -^ ^^J- o . N w VO iolo tJ- *> O O io w ri. j>.io O- ON ON ON CO W HH O *. o Th O O w O Tt-n coco 4) >-) lo O O ON i-.no no t}- oi 6|w|io o.S « TT g'" ^o bo gH X XX »2, d H w ■«*■ ^- -d- '5? CO 00 co »o rt w 00 00 00 co o o -3- NO O O w *o-4- -^ CO Smithsonian Tables. 23 Tables 30, 31. CONVERSION FACTORS. 1 I Pi a 9 E-i 0\0 w n\D»o S oi o Ovoco O II h-1 OO ^N a wiVO I-- p .2 'i |CO|w|N u p ei "im CO C) HOOQ — i-l >-h w w w □ O OOOO N IN O w o « o ^t- coco ti ON -^- « o o^oco O w \ooo h J q m tj- 13 ri h n P O u (I ft % o"o •a XXX o d " no n o N lO"1 l-I M N © ■"^■^•IN, s nroM to fOr^N II o CO to^iQ _] - corn m 5 OnnO ti O CONO 2 o h-1 On mvO O w O "i C^ O ^J-VO |o eo [■*■!■*• Et3 « a, » TT jE o o o gi X^XX so J5 W d o H no co O CNOn H I.OOO 2.519 4-535 O Th\0 O CNNO U * Q tONO w Q O m O -^-NO 1° 1-1 1^.0 Q no o o VO o w o 6 VO O O £ •;. InIii In .SB g§ o b o c« o" XX X 5 a «oQrl O r^. O Q O O O t-i Q O VO O O N O Q r>. o o %> j VO o is |« K|H e^ O-o 1 | 88 o o o Sw d X XX "1H O Q o So HH o o VO o o "* MX* 00 00 00 N « M N N M o OVO VO VO O m|« *S a rts; o 8 O O 6 XX oooooo 00 CO CO vovOvO W N N Smithsonian Tables. s' Sv88 H o r^o o e a g 1 r^. o OO tj Tf O O MOO a bet; n n n ii ;= c 35 .2 c o ee e« c o ooo E J« . XXX 5 § is no O" vno O OOO -to O W M M NO O OvO O o* r^. O o f^O o O rro w o V 1-1 E H- O O E« O w |N « CI fc-Tj 1 « S O O — — ceo d X X V a CO OH O u no o »o o o o o o t°. 9 N o o Ov O Q t^. o 5 ►J $°8 8 i- o o BS [« l~|rO 6*3 «D O-o 7 T ? g g o bo UJ ° s« d X XX a COH o o m o o ""> o o o o o f 9 9 •" " OOOOOO ooo ti> W N N o O N N N ►3 00 00 00 0) Olxlro T T §1 b 'o feS d XX W H +■*■■*■ ioio»o wiwiui H M M t^. iC. r^. 26 Tables 36, 37. CONVERSION FACTORS. a II 01 a Is I' 3 v c is o o Hi <888 00 O Q ii o o a no o u vo q o ■ * h! CO o o o o o CO o o £8°8 VO o o |§ ■rt u o o rpO 8 -sfO Q o i-l OO O o ^8°8 a « o o s« t^l-l |.* Is T o o o XX X 4> % *0 H Q o o S no o " " " ■* o o N O O K 1J -iO O ►J M o o B-S N I •— i !»->> S'S OtJ c L 1 o o o a« 6 X XX g \o o o o o o ro o O >-i M l-l VOVOVO r^ r^ rs to o *•*■* i-l 00 00 oo IcoiTJ-bo S."S rt P 5 B M **< eo 'o T ob >■ M M M XXX W fe lOtOiO VO vo VO r*. r^r** Smithsonian Tables. 27 Table 38. HYPERBOLIC FUNCTIONS. Hyperbolic sines. Valnos ol — 0.0 o.i 0.2 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 "•3 1.4- 1.5 1.6 r-7 1.8 i-9 2.0 2.1 2.2 2 -3 2.4 2.5 2.6 2-7 2.8 2.9 3.0 3-i 3-2 3-3 34 3.5 3-6 37 3-8 3-9 4.0 4.1 4-2 4-3 4.4 4.5 4.6 47 4.8 4.9 0.0000 .1002 •20 J 3 .3045 .41 0.521 1 .6367 .7586 .8881 1.0265 1.1752 •3356 .5095 .6984 ■9043 2.1293 •37S6 .6456 .9422 3.2682 3.6269 4.0219 4-4571 4-9370 5.4662 6.0502 6.6947 7.4063 8.1919 9.0596 10.018 11.076 12.246 I3-538 14.965 16.543 18.285 20.211 22.339 24.691 27.290 30.1§2 33-33° 36.843 4O.719 45.OO3 49-737 54.969 60.751 67.141 0.0100 .1102 .2115 •3!5° .4216 0.5324 .6485 .7712 .9015 1.0409 1.1907 •35 2 4 .5276 .7182 .9259 2.1529 .4015 .6740 •9734 3-3025 3.6647 4.0635 4.5030 4.9876 5.5221 6.1118 6.7628 7.4814 8.2749 9.1512 10.119 11.188 12.369 I3-674 15.116 16.709 18.470 20.415 22.564 24.939 27.564 30.465. 33-67I 37-214 41.129 45-455 50-237 55.522 61.362 67.816 .1203 .2218 ■3255 •4325 0.5438 .6605 .7838 .9150 1.0554 1.2063 ■3693 .5460 738i •9477 2.1768 .4276 .7027 3.0049 •3372 3.7028 4.1056 4.5494 5-0387 5-5785 6.1741 6.8315 7-5572 8.3586 9-2437 10.221 1 1-301 12.494 13.812 15.268 16.S77 ^.655 20.620 22.791 25.190 27.842 30-772 34.009 37-588 41.542 45-912 50.742 56.080 61.979 68.498 0.0300 .1304 •2320 ■3360 ■4434 0-5552 •6725 .7966 .9286 1.0700 •3863 •5645 7583 .9697 2. 20018 .4540 7317 3-0367 .3722 3-7414 4.1480 4.5962 5.0903 5-6354 6.2369 6.9009 7-6338 8.4432 9-3371 10.324 11.415 12.620 I3-95I 15.422 17.047 18.843 20.828 23.020 25.444 28.122 31.081 34-351 37.966 41.960 46.374 51.252 56.643 62.601 69.186 0.0400 .1405 •2423 .3466 •4543 0.5666 .6846 .8094 •9423 1.0847 J-2379 4035 ■5831 .7786 .9919 2.2251 .4806 .7609 3.0689 4075 3-7803 4.1909 4.6434 5-1425 5.6929 6.3004 6.9709 7.7112 8.5287 94315 11.429 "•530 12.747 14.092 15-577 17.219 '9-033 21.037 23.252 25.700 28.404 31-393 34-697 38:347 42.382 46.840 51767 57-213 63.231 69.882 0.0500 .1506 .2526 •3572 •4653 0.5782 .6967 .8223 .9561 1.0995 1-2539 .4208 .6019 .7991 2.0143 2.2496 •5075 .7904 3-i°i3 •4432 3.8196 4.2342 4.6912 5-I95 1 5.7510 6-3645 7.0417 7.7894 8.6150 9.5268 "•534 12.647 12.876 14.234 15734 0.0600 .1607 .2629 .3678 .4764 0.5897 .7090 •8353 .9700 1.1 144 1.2700 .4382 .6209 .8198 2.0369 2-2743 •5346 .8202 3-1340 4792 3-8593 4.2779 47394 5-2483 5.8097 6.4293 7.1132 7.8683 8.7021 9.6231 0.0701 .1708 ■2733 •3785 4875 0.6014 7213 17.392 19.224 21.249 23.486 25.958 28.690 31-709 35-046 38.733 42.808 47-3" 52.288 57788 63.S66 70.584 1 1.640 12.764 13.006 14-377 I5-893 .9840 1.1294 1.2862 4558 .6400 .8406 2.0597 2.2993 .5620 •8503 3.1671 •5156 3-8993 4.3221 4.7880 5.3020 5. ' 17.567 19.418 21.463 23.722 26.219 28.979 32.028 35-398 39.122 43-238 47-787 52.813 58.369 64.508 71.293 6.4946 7-1854 7.9480 8.7902 9.7203 11.748 12.883 J3-I37 14.522 16.053 17-744 19.613 21.679 23.961 26.483 29.270 32-350 35-754 39-5I5 43-673 48.267 53-344 58-955 65.157 72.010 0.0801 .1810 .2837 .3892 .4986 0.6131 ■IP 6 .8615 .9981 1.1446 1.3025 •4735 ■6593 .8617 2.0827 2-3245 .5896 .8806 3.2005 •5523 3-9398 4.3666 4-8372 5-3562 5.9288 6.5607 7-2583 8.0285 8.8791 9.8185 11.856 12.003 13.269 14.668 16.214 17.923 19.81 1 21.897 24.202 26.749 0.0901 .1911 .2941 .4000 .5098 0.6248 .7461 .8748 .0122 1.1598 1-3190 .4914 .6788 .8829 2.1059 2.3499 .6175 .9112 3-2341 •5894 3.9806 4.41 17 4.8868 5.4109 5-9892 6.6274 7-33 J 9 8.1098 29.564 32-675 36.113 39-9I3 44.112 48752 53.880 59-548 65.812 72-734 9-9J77 11.966 12.124 '3403 14.816 16.378 18.103 20.010 22.117 24.445 27.018 29.862 33-004 36.476 40.314 44-555 49.242 54.422 60.147 66.473 73-465 • Tables 38-41 are quoted from " Des Ingenieurs Taschenbuch,'- herausgegeben vom Akademischea Verem (Hiitte). Smithsonian Tables. '««mnuHt(. 28 Table 39. HYPERBOLIC FUNCTIONS. Hyperbolic cosines. Values ol e '+ e " 2 X 1 2 3 4 5 6 7 8 9 0.0 1. 0000 1. 000 1 1.0002 1.0005 1.0008 1.0013 1.0018 1.0025 1.0032 1.0041 0.1 .0050 .0061 .0072 .0085 .0098 .0113 .0128 .0145 .0162 .0181 0.2 .0201 .0221 .0243 .0266 .0289 .0314 .0340 ■0367 •0395 ■0423 °-3 •°453 .0484 .0516 •0549 .0584 .0619 ■0655 .0692 •0731 .0770 0.4 .0811 .0852 •0895 ■0939 .0984 .1030 .1077 .1125 .1174 .1225 0.5 1. 1276 1. 1329 1-1383 1-1438 1. 1494 1.1551 1. 1609 1. 1669 1.1730 1. 1792 0.6- ■1855 .1919 .1984 .2051 .2119 .2188 .2258 •2330 .2402 .2476 0.7 ■2552 .2628 .2706 .2785 .2865 •2947 •3030 •3"4 •3199 .3286 o.8 •3374 •3464 •3555 •3647 •3740 ■3835 ■3932 .4029 .4128 •4229 0.9 •4331 4434 •4539 •4645 ■4753 .4862 •4973 .5085 .5199 •53J4 1.0 I-543I 1-5549 1.5669 1.5790 I-59I3 1.6038 .6164 1.6292 1. 642 1 1.6552 1.1 .6685 .6820 .6956 •7093 ■7233 ■7374 •7517 .7662 .7808 •7956 1.2 .8107 .8258 .8412 .8568 .8725 .8884 .9045 .9208 •9373 .9540 J -3 •9709 .9880 2.0053 2.0228 2.0404 2.0583 2.0764 2.0947 2.1132 2.1320 1.4 2.1509 .1700 .1894 .2090 .2288 .2488 .2691 .2896 •3103 •3312 1.5 2.35 2 4 2.373 s 2-3955 2.4174 2-4395 2.4619 2.4845 2.5073 2-5305 2-5538 1.6 •5775 .6013 .6255 ■6499 .6746 •6995 .7247 •7502 .7760 .8020 1-7 .8283 .8549 .8818 .9090 •9364 .9642 .9922 3.0206 3.0492 3.0782 1.8 3- I0 75 3-J37I 3.1669 3.1972 3-2277 3-2585 3.2897 .3212 •3530 ■3852 *-9 ■4177 .4506 .4838 •5173 .5512 •5855 .6201 •655 1 .6904 .7261 2.0 3.7622 3-79 8 7 3-8355 3-8727 3-9'03 3-9483 3.9867 4.0255 4.0647 4.1043 2.1 4-1443 4.1847 4.2256 4.2668 4-3085 4-3507 4-3932 4.4362 4-4797 4.5236 4.9881 2.2 4.5679 4.6127 4.6580 4-7037 4.7499 4.7966 4-8437 4.8914 4-9395 2 -3 5.0372 5.0868 5-!37° 5.1876 5.2388 5-2905 5-3427 5-3954 5-4487 5-5026 2.4 5-5569 5.61 19 5.6674 5-7235 5.7801 5-8373 5-895 1 5-9535 6.0125 6.0721 2.5 6.1323 6.1931 6.2545 6.3166 6-3793 6.4426 6.5066 6.5712 6.6365 6.7024 2.6 6.7690 6.8363 6.9043 6.9729 7.0423 7-1123 7.1831 7.2546 7.3268 7-3998 2.7 7-4735 7-5479 7.6231 7.6990 7-7758 7-8533 7-9!3 6 7.0106 8.0905 8.1712 2.8 8.2527 8.3351 8.4182 8.5022 8.5871 8.6728 8-7594 8.8469 8-9352 9.0244 2.9 9.1 146 9.2056 9.2976 9-3905 9.4844 9-5791 9.6749 9.7716 9.8693 9.9680 3.0 10.068 10.168 10.270 10-373 10.476 10.581 10.687 10.794 10.902 II.OII 3- 1 11. 121 12.233 "•345 11.459 11.574 n.689 11.806 11.925 12.044 12.165 3-2 12.287 13.410 12.534 12.660 12.786 12.915 13.044 i3-'75 i3-3 7 13.440 3-3 3-4 13-575 14.711 13.848 I3-987 14.127 14.269 14.412 14.556 14.702 14.850 16.408 14.999 15.149 15.301 15-455 15.610 15.766 15.924 16.084 16.245 3.5 16.573 i6.739 16.907 17-077 17.248 17-421, 17.596 17.772 17.951 19.836 18.131 3-6 3-8 3-9 l8 -3i3 18.497 18.682 18.870 19.059 19.250 19.444 19.639 20.035 20.236 20.439 20.644 20.852 21.061 21.272 21.486 21.702 21.919 22.139 24.460 22.362 22.586 22.813 23.042 23-273 23.507 23-743 23.982 24.222 26.768 24.711 24.959 25.210 25.463 25.719 25-977 26.238 26.502 27-037 4.0 27.308 27.582 27.860 28.139 28.422 28.707 28.996 29.287 29.581 32.691 36.127 39-92S 44.123 29.878 4.1 4.2 4-3 4.4 30.178 33-35 1 36-857 40-732 30.482 33.686 37.227 41. 141 30.788 34.024 37.601 41-554 31.097 34-366 37-979 41.972 3M09 34-7" 38.360 42.393 31-725 35.060 38.746 42.819 32.044 35-412 39-J35 43-25° 32.365 35.768 39-528 43.684 33- OI 9 36.490 40.326 44.566 4.5 4.6 4-7 4.8 4-9 45.014 49-747 54-978 60.759 67.149 45.466 50.247 55-531 61.370 67.823 45-923 50-752 56.089 61.987 68.505 46.385 51.262 56.652 62.609 69-I93 46.851 5!-777 57.221 63-239 69.889 47-321 52.297 57-796 63-874 70.591 47-797 52.823 64.516 71.300 48.277 53-354 58.964 65.164 72.017 48.762 53.890 59-556 65.819 72.741 49.252 54-431 60.155 66.481 . 73-472 Smithsonian Tables. 29 Table 40. HYPERBOLIC FUNCTIONS. Common logarithms + 10 ol the hyperbolic sines. 0.0 o.i 0.2 °-3 0.4 0.5 0.6 0.7 o.S 0.9 1.0 1.1 1.2 i-3 1.4 1.5 1.6 1-7 1.8 1.9 2.0 2.1 2.2 2 -3 2.4 25 2.6 2.7 2.8 2.9 3.0 3-i 3-2 3-3 34 3.5 3-6 3 i 3-8 3-9 4.0 4.1 4-2 4-3 4.4 4.5 4.6 4-7 4.8 4.9 0007 3039 4836 9.6136 9.7169 8039 8800 9485 10.01 14 10.0701 1257 1788 2300 2797 10.3282 3758 4225 4687 5M3 io-5S95 6044 6491 6935 7377 10.7S18 8257 8696 9134 9571 11.0008 0444 0880 1316 i75i 11.2186 2621 3056 349 1 3925 11.4360 4795 5229 5664 6098 11.6532 6967 7401 7836 8270 0423 3254 4983 6249 7262 8119 8872 955° 0174 0758 1311 1840 2846 3330 3805 4272 47 J? 51$ 5640 6535 6979 7421 7862 8301 8740 9178 9615 0051 048S 0923 1359 !794 2230 2665 3°99 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 43i8 4778 5 2 34 5685 6134 6580 7023 7465 7906 §345 4772 1 1 52 3656 5264 9221 9658 0095 0531 0967 J 4°3 1838 2273 2708 3 r 43 3578 4012 4447 4881 53i6 575° 6185 6619 7054 7922 8357 7444 8277 9012 9678 0294 0871 1419 1944 2451 2944 3426 3899 4304 4824 5279 573° 6178 6624 7067 75°9 7950 8389 8827 9265 9702 0139 °575 ion 1446 2317 2752 3186 3621 4056 4490 4925 5359 5794 6228 6663 7097 753' 7966 8400 6022 1475 3844 5398 6574 7533 8354 9082 9742 °353 0927 1472 1995 2501 2993 3474 3946 441 1 4870 5324 5775 6223 6668 7112 7553 7994 &» 8871 9309 9746 0182 0618 1054 1490 1925 2360 2795 3230 3665 4099 4534 5403 5837 6272 6706 7141 7575 8009 8444 6992 1777 4025 5529 6678 7620 8431 9150 9805 0412 0982 1525 2046 2551 3041 3521 3992 4457 49*5 537o 5820 6268 6713 7156 7597 8477 8915 9353 9789 0226 0662 1098 1533 1968 2404 2839 3273 3708 4143 4577 5012 5446 5881 63 ! 5 6750 7184 7618 o°53 8487 7784 2060 4199 5656 6780 7707 8506 9218 0470 1038 1578 2098 2600 3090 3569 4039 45°3 4961 54i5 5865 6312 6757 7200 7642 8082 8521 8959 9396 9833 0270 0706 1141 1577 2012 2447 2882 33 J 7 3752 4186 4621 5055 5490 5924 6359 6793 7227 7662 8530 8455 4366 578i 6880 7791 8581 9286 993° 0529 ! °93 1631 2148 2650 3138 3616 4086 4549 5007 5460 5910 6357 6802 7244 76S6 8126 8564 9003 9440 9877 °3i3 0749 1185 1620 2056 2491 2925 336o 3795 4230 4664 5099 5533 5968 6402 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 773° 8169 8608 9046 9484 9920 °357 0793 1228 1664 2099 2534 2969 3404 3838 4273 4708 5142 5577 6011 6446 6S80 73'4 7749 8183 8617 Smithsonian Tables. 9548 2814 4685 6020 7074 7958 8728 9419 0053 0644 1203 1736 2250 2748 3234 37" 4179 4641 5098 555o 5999 6446 6890 7333 7774 8213 8652 9090 9527 9964 0400 0836 1272 1707 2143 2578 3012 3447 3882 4317 4751 51S6 5620 6°55 7358 7792 8226 8661 30 HYPERBOLIC FUNCTIONS. Common logarithms oi the hyperbolic cosines. Table 41 . 0.0 o.i 0.2 °-3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 '■3 1.4 1.5 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-i 3-2 3-3 34 3.5 3-6 37 3-8 3-9 4.0 4.1 4.2 4-3 4.4 4.5 4.6 47 4.8 4.9 0.0000 0022 0086 0193 0339 0.0522 0739 0987 1263 1563 0.1884 2223 2578 2947 3326 0-3715 4112 4SI5 4924 5337 0-5754 6175 6597 7022 7448 0.7876 8305 8735 9166 9597 1.0029 0462 0894 i3 2 7 1761 1. 2194 2628 3061 3495 3929 1-4363 4797 5231 5665 6099 1-6533 6968 7402 7836 8270 0000 0026 0095 0205 0355 0542 0762 1013 1292 '594 1917 2258 2615 2984 3365 3754 4152 4556 4965 5379 5796 6217 6640 7064 749i 7919 8348 8778 9209 9641 0073 0505 0938 1371 1804 2237 2671 3 io 5 353» 3972 4406 4840 5274 5709 6143 6577 701 1 7445 7880 83H OOOI 0031 0104 0219 0372 0562 0786 1040 1321 1625 1950 2293 2651 3022 3403 3794 4192 4597 5006 5421 5838 6259 6682 7107 7534 7962 8391 8821 9252 9684 0116 0548 0981 1414 1847 2281 2714 3148 3582 4016 445° 5318 5752 6186 6620 7°55 7489 7923 8357 0002 0037 0114 0232 0390 0583 0810 1067 !35° 1657 1984 2328 2688 3°59 3442 3833 4232 4637 5048 5462 5880 6301 6724 7150 7577 8005 8434 9295 9727 oi59 0591 1024 1457 1891 2324 2758 3^ 3625 4059 4927 5361 5795 6230 6664 7098 7532 7966 8401 0003 0042 0124 0246 0407 0605 0835 1094 1380 1689 2018 2364 2724 3097 348i 3873 4273 4678 5089 55°4 5922 Pi 3 6767 7192 7619 8477 8907 9338 9770 0202 0635 1067 1 501 1934 2367 2801 3235 3669 4103 4537 4971 5405 5839 6273 6707 7141 7576 8010 8444 0005 0049 0134 0261 0426 0626 0859 1122 1410 1721 2051 2 399 2761 3135 3520 3913 4313 4719 5545 5964 6386 6809 7235 7662 8091 8520 8951 9382 9813 0245 0678 mi 1544 1977 241 1 2844 3278 3712 4146 4580 5014 5448 5882 6316 675 1 7185 7619 8053 8487 0008 0055 0145 0276 0444 0648 1 149 1440 '753 2086 2 435 2798 3 J 73 3559 3952 4353 4760 5172 5587 6006 6428 6852 7278 7705 8134 8563 8994 9425 9856 0289 0721 1 154 1587 2021 2454 2888 33 22 3755 4189 4623 5°57 5492 5926 6360 6794 7228 7662 8097 8531 001 1 0062 0156 0291 0463 0670 0910 1177 1470 1785 2120 2470 2835 321 1 3598 399 2 4394 4801 5213 5629 6048 6470 6S94 7320 7748 8176 8606 9°37 9468 9900 0332 0764 1 197 1631 2064 2 497 2931 3365 3799 4233 4667 5101 5535 5969 6403 6837 7272 7706 8140 8574 n 0014 0070 0168 0306 0482 0693 °935 1206 1501 1818 2154 2506 2872 3 2 49 3637 4032 4434 4842 5254 5671 6090 6512 6937 7363 7791 8219 8649 9080 9511 9943 0375 0808 1 241 1674 2107 2541 2 974 3408 3842 4278 4710 5M4 5578 6012 6447 6881 7315 7749 8184 8618 0018 0078 0180 0322 0502 0716 0961 ' 2 34 *53 2 1851 2 542 2909 3288 3676 4072 4475 5296 5713 6132 6555 6979 7406 7833 8262 8692 9123 9554 0418 0851 1284 1717 2151 2584 3018 3452 3886 4320 4754 5188 5622 6056 6490 6924 7358 7793 8227 8661 Smithsonian Tables. 31 Table 42. EXPONENTIAL FUNCTIONS. Values of c and ol c-* and their logarithms. Values of e' and e~* for values of x intermediate to those here given may be found by adding or subtracting the values of the hyperbolic cosine and sine given in Tables 38-39. X ex log ex X ex log ex X e-x log«-jr 0.1 1. 1052 0-04343 5.1 164.03 2.21490 0.1 0.90484 I-95657 2 1.2214 08686 2 181.27 25833 2 81873 91314 3 1-3499 13029 3 200.34 30176 3 74082 86971 4 1.4918 17372 4 221.41 345'9 4 67032 82628 5 1.6487 21715 5 244.69 38862 5 60653 78285 0.6 1.8221 0.26058 5.6 270.43 2.43205 47548 0.6 0.54881 L73942 7 2.0138 30401 7 298.87 7 49659 69599 8 2.2255 34744 8 330-30 51891 8 44933 65256 9 2.4596 39087 9 365.04 56234 9 40657 60913 1.0 2.7183 43429 6.0 403-43 60577 1.0 36788 56570 1.1 3.0042 0.47772 6.1 445.86 2.64920 1.1 0.33287 I.52228 2 3-3 2 °i 5 f'J 2 492.75 69263 2 3°H9 47885 3 3-6693 56458 3 545-57 73606 3 27253 43542 4 4.0552 60801 4 601.85 77948 4 24660 39t99 5 4.4817 65144 5 665.14 82291 5 22313 34856 1.6 4-953° 0.69487 6.6 735-'o 2.86634 1.6 0.20190 '•30513 7 5-473? 73830 7 812.41 90977 7 18268 26170 8 6.0496 70173 8 897.85 95320 8 16530 21827 9 6.6859 82516 86859 9 992.27 99663 9 M957 17484 2.0 7-3 8 9! 7.0 1096.63 3.04006 2.0 13534 13141 2.1 8.1662 0.91202 7.1 1212.0 3-08349 2.1 0.12246 1.08798 2 9.0250 95545 2 1339-4 12692 2 11080 04455 3 9.9742 99888 3 1480.3 17035 3 10026 001 12 4 11.0232 1-04231 4 1636.0 21378 4 09073 2.95769 5 12.1825 08574 5 1808.0 25721 5 08208 91426 2.6 I3 '^ 3 1.12917 7.6 1998.2 3.30064 2.6 0.074274 2.87083 7 14.880 17260 7 2208.3 34407 7 067205 82740 8 16.445 21602 8 2440.6 38750 8 060810 78398 9 18.174 25945 9 2697.3 43093 9 055023 74055 3-o 20.0S6 30288 8.0 2981.0 47436 3-o 049787 69712 3.1 22.198 1-34631 8.1 3294-5 3-5'779 3.1 0.045049 2.65369 2 2 4-533 38974 2 3641.0 56121 2 040762 61026 3 27.113 43317 3 4023.9 60464 3 036883 56683 4 29.964 47660 4 4447.1 64807 4 °33373 5 2 340 S 33- lr 5 52003 5 4914.8 69150 5 030197 47997 3.6 7 8 36.598 40.447 1.56346 60689 8.6 7 543'-7 6002.9 3-73493 77836 3.6 7 0.027324 024724 2.43654 393" 44.701 65032 8 6634.2 82179 8 022371 34968 9 4.0 49.402 S4-598 69375 73718 9 9.0 733 2 - 8103.1 86522 90865 9 4.0 020242 018316 30625 26282 4.1 ! 2 3 60.340 66.686 73-700 81.451 1.78061 82404 86747 9.1 2 3 8955. 9897. 10938. 3.95208 99551 4.03894 4.1 2 0.016573 014996 013569 2.21939 17596 13253 08910 4 91090 4 12088. 08237 4 012277 5 90.017 95433 5 13360. 12580 5 011109 04567 4.6 7 8 9 5.0 99.48 109.95 121.51 134.29 148.41 '•99775 2.041 18 08461 12804 I7H7 9.6 7 8 9 1 0.0 14765. 16318. 18034. 19930. 22026. 4.16923 21266 25609 29952 34295 4.6 7 8 9 5-o 0.010052 009095 008230 007447 006738 2.00225 3.95882 91539 87196 82853 32 EXPONENTIAL FUNCTIONS. Value of <;'* and e-« 3 ana their logarltlims. Table 43. The equation to the probability curve is^ = e- * , where x may have any value, positive or negative, between zero and infinity. X «*• log ex* e-x* log «-•** 0.1 I.OIOI 0.00434 0.99005 T.99566 2 1.0408 oi737 96079 98263 3 1.0904 03909 91393 96091 4 i.!735 06949 85214 93051 S 1.2840 10857 77880 89143 0.6 1-4333 0.15635 21280 O.69768 I.84365 7 1.6323 61263 78720 8 1.8965 27795 35178 52729 72205 9 2.2479 44486 64822 1.6 2.7183 43429 36788 56571 1.1 3-3535 0.52550 O.29820 1-47450 2 4.2207 62538 23693 37462 3 5-4I95 73396 18452 26604 4 7-°993 85122 14086 14878 5 9.4877 97716 10540 02284 1.6 1.2936 X 10 1.11179 0.77306 X io -1 2.88821 7 1.7993 " 25511 55576 " 74489 8 2-5534 " 407 1 1 39164 " 59289 9 3.6996 " 56780 27052 " 43220 2.0 5-4598 " 737i8 18316 " 26282 2.1 8.2269 " 1. 91 524 0.12155 " 2.08476 2 1.2647 X io 2 2.10199 79070 X io -2 3.89801 3 4 S 1.9834 3-1735 " 5.1802 " 29742 50154 7H34 50418 3x51! « 19304 70258 49846 28566 2.6 8.6264 " 2.93583 0.1 1 592 " 3-06417 7 1.4656 X io 8 3.16601 68233 X io- 8 4.83400 8 2.5402 " 40487 39367 " 59513 9 4.4918 " 65242 22263 34758 3-° 8.1031 " 90865 1 2341 " 09135 3.1 1.4913 X io 4 4-J7357 0.67055 X io - * 5.82643 55283 2 2.8001 " 44718 35713 " 3 4 S 5.2960 " 1.0482 X io 6 2.0898 " 72947 5.02044 3201 1 18644 " e 95402 X io -6 47851 " 27053 5.97956 67989 3.6 4.2507 " 5.62846 0.23526 " &37I54 7 8 9 4.0 8.8205 " 1.8673 X io 8 4.0329 " 8.8861 " 94549 6.27121 60562 . 94871 "337 " 53554 X io-« 24796 11254 05451 7.72879 39438 05129 4.1 1.9976 X io 7 7.30049 0.50062 X io _T g.69951 2 ! 3 4 4.5809 " 1.0718 X io 8 66095 8.0301 1 21829 " 93303 X io" 8 33905 9.96989 2.5583 " 40796 39088 " 59204 5 6.2297 " 79447 16052 20553 4.6 7 8 1.5476 X io 9 3.9228 " 1. 01 43 X io 10 9.18967 59357 10.00615 0.64614 X io -9 25494 " 98595 X 10-1° 10.81033 40643 "•99385 9 2.6755 " 7.2005 42741 85736 37376 " 13888 " 57 2 59 14264 Smithsonian Tables. 33 Table 44. EXPONENTIAL FUNCTIONS. z — -* Values of 0* and £ * and their logarithms. X 7T log e^ e «* 7T log e~* 1 2-1933 0.34109 0.45594 1.65891 2 4.8105 .68219 .20788 .31781 3 1.0551 X 10 1.02328 .94780 X io -1 2.97672 4 2.3141 •36438 ■43214 •63562 5 5-0754 " ■70547 .19703 •29453 6 1.1132 X io 2 2.04656 0.89833 X icr* 3-95344 7 2.4415 " .38766 .40958 .61234 8 5-3549 " .72875 .18674 .27125 9 1. 1745 X io 8 3.06985 .85144 X io -8 4.93015 10 2.5760 " .41094 .38820 .58906 11 5.6498 " 3-75204 0.17700 " 4.24796 12 1.2392 X io 4 4-°93 '3 .80699 X io -4 5.90687 ! 3 2.716S .43422 ■3 6 794 " •56578 14 5.9610 " ■77532 .16776 .22468 IS 1.3074 X io 5 5.11641 .76487 X 10-6 5.88359 16 2.8675 5-4575 1 0-34873 5.54249 17 6.2893 .79860 .15900 " .20140 18 1.3794 X io 6 6.13969 .72495 X io -6 7.86031 i9 3.0254 .48079 •33053 " .51921 20 6.6356 .82189 .15070 " .17812 Table 45. EXPONENTIAL FUNCTIONS. Values ol 8 * * and 8 <■ * and their logarithms. X Vif e * log£" Vff , e~—' log e~ ~* 1 1.4429 0.19244 0.64203 T.80756 2 2.4260 .38488 .41221 .61512 3 3-7786 •57733 .26465 .42267 4 5-8853 ■76977 .16992 .23023 5 9.1666 .96221 .10909 •03779 6 14.277 1-15465 0.070041 2-84535 7 22.238 •34709 .044968 .65291 8 34-636 ■53953 .028871 .46047 9 53-948 -73 I 98 .018536 .26802 10 84.027 .92442 .011901 •07S58 11 130.87 2.1 1686 0.0076408 3.88314 12 203.S5 .30930 •0049057 .69070 '3 317-50 .50174 .0031496 .49826 H 494.52 .69418 .0020222 .30582 15 770.24 .88663 .0012983 ■"337 16 1199.7 3.07907 0.00083355 4.92093 '7 1868.5 ■27151 ■v^-ttW .72849 18 2910.4 •46395 •00034360 •53605 19 4533-1 .65639 .00022060 ■34361 20 7060.5 .84883 .00014163 .15117 Smithsonian Tables. 34 EXPONENTIAL FUNCTIONS. Value ol e" ana er* and tlielr logarithms. Table 46. 03 e* log e" e-« log e-» 1/64 1/16 i/:o i/9 1.0157 0.00679 0.98450 r.99321 ■0317 •OI357 .96923 .98643 .0645 .02714 •93941 .97286 .1052 •04343 .90484 ■95657 •»75 .04825 .89484 ■95175 ^ 8 !-i33i O.05429 0.88250 .86688 f-94571 ^ ■1536 .06204 ■9379 s 10 .1814 .07238 .84648 .92762 Vi .2214 .08686 .81873 ■9 J 3i4 J /4 .2840 .10857 .77880 .89143 i/3 1 '3956 O.14476 0.71653 r.85524 V 2 .6487 .21715 .60653 .78285 3/4 2.1170 •3 2 572 ■47237 .36788 .67428 1 •7183 .43429 •56571 5/ 4 34903 •54287 .28650 •45713 3/2 4.4817 0.65144 0.22313 1.34856 7/4 S-7546 .76002 -17377 .23998 z 7-3891 .86859 -I353S .13141 9/4 9.4877 .97716 .10540 .02284 : 5/2 12.1825 1.08574 .08208 2.91426 LEAST SQUARES. "Jix Table 47. 2 r htc Values of P = -^ I e-e*) 2 . v Vo . This table gives the values of the integrals between o and n/z of the function ( ,-ri««*«:„s*i±» j* f„, j-ft . , ues of the modulus corresoondintr to each ,W„»"r ?L\ '?'" A S 'T *> ^ £or different val .,»! * .1 j V — -'—"'•'-" " ""u n/aui me junction ( i — sm z 0s n 2 (M ues of the modulus corresponding to each degree of between o and 90. £ o° 1 2 3 4 5° 6 7 10° i 2 3 4 15° 6 7 20° 1 2 3 4 25° 6 7 30° 1 2 3 4 35° 6 7 40° 1 2 3 4 45° d 'O (1— sin 2 «sin 2 0)l I Number. 1.5708 5709 5713 5719 5727 1-5738 5751 5767 5785 5805 1.5828 5854 5882 5913 5946 1.5981 6020 6061 6105 6151 1.6200 6252 6307 6365 6426 1.6490 6557 6627 6701 6777 6941 7028 7119 7214 1.7312 7415 7522 7633 7748 1.7868 7992 8122 8256 8396 1.8541 Log. 0.196121 I96148 196259 196425 196646 O.I96949 197308 197749 197245 198794 O.198934 200139 200905 201752 202652 O.203604 204662 205773 206961 208199 O.209515 210907 212374 213916 2ISS32 O.217221 218982 220788 222742 224714 O.226806 228939 231 164 233478 235882 0-238347 240923 243584 246326 249149 O.252076 255079 258206 261406 264723 T (i— sin 2 0sm 2 $)V0 Number. I.5708 5707 5703 5697 5689 I.5678 5665 5649 5632 56U "•5589 5564 5537 5507 5476 1.5442 5405 5367 5326 5283 1.5238 5191 5141 5090 5037 1.4981 4924 4864 4803 4740 1-4675 4608 4539 4469 4397 1-4323 4248 4171 4092 4013 '•393' 3849 3 ^ s 3680 3594 Log. 0.268133 h-35 o6 0.196121 196093 '95983 195817 '95595 0.195291 194930 194487 194014 '93431 0.192818 192121 191367 190528 189659 0.188703 187662 186589 185429 184209 0.182928 181586 180155 178689 177161 0.175541 173885 172136 170350 168497 0.166578 164591 162534 160438 158272 0.156034 '53754 1 51400 148973 I4653 1 0.143982 141418 138776 136086 133347 0.130527 45° 6 7 50° 1 2 3 4 55° 6 7 60° 1 3 4 65° 6 7 70° 1 3 4 75° 6 7 80° 1 2 3 4 85° 6 7 90° Jo (>— si siii 2 Ssin 2 ef,)S af^ Number. 1.8541 901 1 9180 '•9356 9539 9729 9927 2.0133 2-0347 0571 0804 1047 1300 2-1565 1842 2132 2435 2754 3439 3809 4198 4610 2.5046 5507 5998 6521 7081 2.7681 8327 9026 9786 3.0617 3-1534 2553 3699 5004 6519 3-8317 4.0528 3387 7427 5-4349 Log. O.268133 271632 275265 279005 282849 O.286816 290902 295105 299442 303908 0.308500 313255 318147 323190 328380 0-333749 339 2 92 345021 350926 357058 0.363386 369939 376741 383779 39"i2 0.398738 406659 414940 423590 432665 0.4421S2 452201 462787 474056 485963 0.498779 5' 2591 527617 5441 18 562519 0-S8339I 607755 637360 677026 735192 mZHm^cfy Number. I.3506 34'8 3329 3238 3'47 I-3055 2963 2870 2776 2681 1.2587 2492 2397 2301 2206 1.2111 2015 1920 1826 1732 1. 1638 '545 '453 1362 1272 1.1184 1096 1011 0927 0844 [.0764 06S6 061 1 0538 0468 1. 0401 0338 0278 0223 0172 1.0127 00S6 0053 0026 0008 Log. 0.130527 127688 124798 121822 1 18827 0.115777 1 12705 109578 106395 '03'53 0.099922 096632 093317 089940 086573 O.083180 079724 076276 072838 069372 0.065878 062394 058919 055455 052001 O.048597 045166 041827 038501 035189 0.031974 028815 025756 022758 019864 0.017075 014436 01 1909 00957S 007406 0.005481 003719 002296 001 128 000347 Smithsonian Tables. 43 Table 57. BRITISH UNITS. Gross sections and weights of wires. This table gives the cross section and weights in British units of copper, iron, and brass wires of the diameters given in the first column. For one tenth the diameter divide section and weights by 100. For ten times the diameter multiply by ioo, and so on. .2 Area of cross section Copper — Density 8.90. Iron — Density 7.80. Brass — Density 8.56. Is in Pounds Log. Feet per Pounds Log. Feet per Pounds Log. Feet per n Sq. Mils. per Foot. Found. per Foot. Pound. per Foot. Pound. 10 78.54 .000303 4.48150 33°°- .0002656 4.42420 3765- .000291 5 4.46458 3431- ii 95-03 0367 .56429 2727. 03214 •50697 31 12. 03527 54735 2836. 12 113.10 0436 .63986 2291. 03825 04488 •58257 2615. 04197 62295 2383- 13 132-73 0512 •70939 1683. .65208 2220. 04926 69246 2030. 14 '53-94 0594 •77376 05206 .71646 1921. 05713 75684 1750. 15 176.71 .000682 4.83368 1467. .0005976 477637 1674. .OO06558 4.81675 I525- 16 201.06 0776 .88974 1289. 06799 .83244 1471. 07461 .87282 1340. 17 226.98 0876 .94240 1 1 42. 07675 .88510 !3°3- 08423 .92548 1 187. 18 254.47 0982 •99205 1018. 08605 09588 •93475 .98171 1 162. 09443 •975!3 1059. 19 283-53 1094 3.03902 914. 1043. .OOIO522 3.02209 950. 20 314.16 .001212 3-°8357 825.1 .OOI062 3.02626 941.4 .OOII66 3.06664 8577 21 346.36 1336 .12594 748.3 1171 .06864 853.8 1285 .10902 778.0 22 380-13 I467 .16634 681.8 1286 .10904 777-8 141 1 .14942 708.9 2 3 415.48 1603 .20496 623.8 1405 .14766 711.7 1542 .18804 648.6 24 452-39 I746 .24192 572-9 153° .18463 653-7 1679 .22500 5957 25 490.87 .OO1894 3-2773 8 528.0 .001660 3.22008 602.4 .001822 3.26046 549.0 26 530-93 2046 .31146 488.1 1795 •25415 557-° 1970 •29453 507-5 27 572-56 2209 •34423 452.6 '936 .28693 516.5 2125 ■32731 470.6 28 615-75 2376 ■37583 420.9 2082 .31852 480.3 2285 •3589° 437-6 29 660.52 2549 .40630 392-4 2234 .34900 447-7 2451 •38938 408.0 30 706.82 .OO2727 3-43575 366.7 .OO2390 3-37845 418.4 .002623 3.41882 381.2 3i 754-77 2912 .46424 343-4 2552 •40693 391.8 2801 •44731 357-° 32 804.25 3103 .49181 322.2 2720 4345° 3677 2985 .47488 335- 1 33 855-3° 33°° •51854 3°3-° 2892 .46123 345-8 3'74 .50161 3 r 5-i 34 907.92 35°3 •54446 285.4 3070 .48716 325-7 3369 •52754 296.8 35 962.11 .003712 3.56964 269.4 .003253 3-5 I2 33 3°74 .003570 3-5527I 280.1 36 1017.88 4927 .59412 254.6 3442 .53681 290.5 3777 •57719 264.7 3 l 1075.21 4149 .61791 241.0 3636 .56061 275.0 399° .60098 250.6 38 1 I34-J 1 4376 .64108 228.5 3 8 44 •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 206.2 .004249 3-62833 235-3 .004664 3.66871 214.4 41 1320.25 5094 .70708 196.3 4465 .64977 224.0 4900 .69015 204.1 42 1385.44 5346 .72801 187.1 4685 .67070 213-5 5 r 4i 7 1 108 194.5 43 1452.20 56°3 .74845 178.5 491 1 .69114 203.6 5389 •73152 185.6 44 '520-53 5867 .76842 170.4 5142 .71111 194.5 5643 •75149 177.2 45 1590.43 .006137 378793 162.9 .005378 373°63 185.9 .005902 3.77 101 169.4 46 1661.90 6412 ■80703 '55-9 5620 .74972 177.9 6167 .79010 1 62. 1 47 1734-94 6694 .82569 149.4 5867 .76840 i7°-5 6438 .80878 155-3 148.9 142.9 48 1809.56 6982 .84399 143.2 6119 78669 163.4 6715 .82706 49 1885.74 7276 .86289 1374 6377 .80459 156.8 6998 .84497 50 1963.50 .007576 7882 3-87945 132.0 .006640 3.82214 150.6 .007287 3.86252 .87972 137-2 I3I-9 126.9 122.1 Si 2042.82 .89664 126.9 6908 •83934 144.8 758i 52 2123.72 8194 •91352 122.0 7181 .85621 139.2 7881 .89659 .91313 S3 2206.18 8512 8837 •93005 117.5 7460 ■ll 27 $ i34-o 8187 54 2290.22 .94630 113.2 7744 .88899 1 29. 1 8499 •92937 117.7 55 237S-83 .009167 3.96223 109.1 .008034 3-90493 124.5 .008817 3-94531 "34 44 BRITISH UNITS. Cross sections anfi weights of wires. Table 57. .25 fl 55 56 s l 59 60 61 62 ?3 65 66 67 68 69 70 7i 72 73 74 75 76 77 78 79 80 81 82 S J 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Area of cross section in Sq. Mils. 2 375-83 2463.01 255I-76 2642.08 2733-97 2827.43 2922.47 3019.07 3II7-25 3216.99 33l8.3t 3421.19 3525-65 363I-6S 3739-28 3848.45 3959-19 4071.50 4185.39 4300.84 4417.86 4536.46 4656.63 4778 36 I 4901.67 5026.55 5I53-00 5281.02 5410.61 5541-77 5674.50 5808.80 5944-68 60S2.12 6221.14 6361-73 6503.88 6647.61 6792.91 6939.78 7088.22 7238.23 7389.81 7542.96 7697.69 7853.98 Copper — Density 8.90. Pounds per Foot. .009167 09504 09846 10,95 10549 Log. 3.96223 '.97789 -.■99325 2.00837 .02320 01091 2.03782 1 128 .05216 1165 1203 1241 .01280 1320 J 360 1401 1443 .01485 1528 1615 1660 01705 1751 1797 1844 1892 .0.1939 1988 2038 2088 2138 .02189 2241 2294 2347 2400 .02455 2509 2565 2621 2678 02735 2793 2851 2910 2970 .03030 .06628 .08019 .09386 2.10732 .12061 •13367 •14655 .15924 2-I7I74 .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 .45404 •46395 •47277 2.48150 Feet per Pound. 1 09. 1 IO5.2 I0I.6 98.I 94-8 91.66 88.68 85.84 83.14 80.56 78.11 7576 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 5I-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 38.15 37-35 36.56 35-Si 35-07 34-36 33-6y 33-oo Iron— Density 7.80. Pounds per Foot. .008034 08329 08629 08934 09245 .00956 1054 1088 .01122 "57 1 192 1228 1264 .01302 '339 1377 1415 1454 .01494 1534 1575 1616 1658 .01700 1743 1786 1830 1874 .01919 1964 2010 2057 2104 .02151 2199 2248 2297 2347 .02397 2448 2499 2551 2603 .02656 Log. 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 5.23038 .24117 .25183 .26236 .27276 1.28304 .29320 •30324 ■31317 .32298 5.33269 •34228 •35178 .36116 .37046 2.37965 .38874 •39775 .40665 •41547 2.42420 Feet per Pound. 124.5 1 20. 1 II5.9 1 1 1.9 108.2 IO4.59 IOI.I9 97-95 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 4975 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 Brass— Density 8.56. Pounds per Foot. Log. .008817 09140 09470 09805 IOI46 .01049 1085 1120 "57 H94 .01231 1270 1308 1348 1388 .01429 1469 1511 1553 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 3-9453' .96096 •97633 _-99'44 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 •3'3i4 2.32342 •33358 •34362 ■35355 ■36336 2.37297 .38266 .39216 .40154 .41084 2.42003 .42912 .43812 •44703 ■45585 2.46458 Feet per Pound. "3-4 109.4 105.6 102.0 98.6 95-30 92.21 89.25 S6.45 83-77 81.21 78.76 76.43 74.20 72.06 70.00 6£o6 66.19 64.38 62.66 61.01 59.40 57-87 56-39 54-99 53-6i 52.29 51-03 49.80 48.63 47-49 46.39 45-33 44-3° 43-31 42-37 41-43 40.54 39-67 38.83 38.02 36.46 3572 35-oi 34-3 1 Smithsonian Tables. 45 Table 58. METRIC UNITS. Cross sections and weights ol wires. This table gives the cross section and the weight in metric units of copper, iron, and brass wires of the diameters given in the first column. For one tenth the diameter divide sections and weights by 100. For ten times the diameter multiply by ioo, and so on. G-O eg = 3 » Copper — Density 8.90. Log. Iron — Density 7.80. E a «i O S Log. « E » 8.2 Brass — Density 8.56. 1 i c *- *■ Log. 10 11 12 13 14 15 16 17 18 19 20 21 22 2 3 24 25 26 27 28 29 30 3 1 3 2 33 34 35 36 37 38 39 40 4i 42 43 44 45 46 47 48 49 50 Si 52 53 54 78.54 95-°3 113.10 13273 153-94 176.71 201.06 226.98 254-47 2 83-53 314.16 346-36 380.1 415.4! 452-39 490.87 53°-93 572-56 6i5-75 660.52 706.86 75477 804.25 855-3° 907.92 962.11 1017.88 1075.21 1134.11 1194.59 1256.64 1320.25 1385.44 1452.20 '520.33 1 590-43 1661.90 '734-94 1809.56 1885.74 1963.50 2042.82 2123.72 2206.18 2290.22 0.06990 .08458 .10065 .11813 .13701 -i573 .1789 .2020 .2265 .2523 0.2796 •3083 ■3383 •3698 .4026 0.4369 ■4725 .5096 .5480 •5879 0.6291 .6717 .7158 .7612 .8081 0.856 .906 957 1.012 ■063 1.1 18 ■■75 •233 .292 •353 1-413 •479 •544 .611 .678 1.748 .818 .890 •964 2.038 2.84448 .-92725 1 .00285 .07236 •13674 r. 1 9665 .25272 •30538 •35503 55 2375.83 2.114 •52932 .56794 .60490 1.64036 ■67443 70721 73880 .76928 7.79872 .82721 •85478 .88151 •90744 r.93261 .95709 .98088 0.00504 .02661 0.04861 .07005 .09098 .11142 •'3139 0.1 5091 .17000 14.306 11.823 9-935 8.465 7.299 6.358 5-588 4.951 4.415 40199 3963 L44654 3-577 .244 2.956 ■704 .484 2.289 .116 1.962 .825 .701 1.590 .489 •397 •3M •238 1. 168 .104 .045 0.988 .941 0.8941 .8511 .8110 ■7738 •7389 0.7065 .6761 .6476 .6209 •5958 0.5722 •55oo •5291 •5093 .4906 .20696 .22487 0.24242 .25962 •27649 •29303 •30927 0.32521 0.4729 0.06126 .07412 .08822 ■!0353 .12008 0.1378 .1568 .1770 .1985 .2212 0.2450 .2702 2965 •3241 •3529 0.3829 .4141 .4466 •4803 .5152 0.5514 •5887 •6273 .6671 .7082 0.7504 7939 ■8387 .8866 .9318 0.980 1.030 .081 ■ r 33 .186 1. 241 .296 ■353 .411 .471 t-532 ■593 .657 721 786 ••853 2.78718 .86996 _-9455 6 1. 01 506 .07945 ^3936 .19542 .24808 •29773 .34469 T.38925 .43162 ■47203 .51064 .54761 1.58306 .61713 .64992 .68150 .71198 I74I43 76991 79749 .82421 .85014 7-87531 -89979 ■92359 •94775 .96931 1.99131 0.01275 •03368 .05412 .07409 0.09361 .11270 •13138 .14967 .16758 0.18513 .20232 .21919 ■23574 .25197 0.26791 16.324 13.492 "•335 9.659 8.328 7-255 6.376 5.648 5.038 4.522 4.081 3701 •373 .086 2.834 2.612 .415 •239 .082 1.941 1.814 •699 •594 •499 .412 1-333 .260 .192 .128 •073 1.0200 0.97 1 1 •9254 .8828 ■8432 0.8061 ■77H 7389 .7085 .6799 0.6530 .6276 •6037 •58" ■5598 0.3396 0.06723 •08135 .09681 .11362 •I3I77 0.1513 .1721 •1943 .2178 .2427 0.2689 .2965 •3254 •3557 •3872 0.4202 •4545 .4901 .5271 •5654 0.6051 .6461 7321 •7772 0.8236 •8713 .9204 ■9730 1.0230 1.076 .130 .186 ■243 .302 1-361 •423 .485 •549 .614 1 .68 1 •753 .960 i.034 Smithsonian Tables. 2.82756 .91034 _-98594 1.05544 .11983 1. 1 7974 .23580 .28846 •338i 1 ■38507 1.42963 .47200 .51241 •S5103 •58799 1.62344 .65751 .69030 .72188 •73236 r.78181 .81029 •83787 .86459 I-9I570 .94017 •96397 •98813 0.00969 0.03169 ■ 53'3 .07406 .09450 .11447 °- I 3399 •15308 .17176 .19005 .20796 0.22551 •24371 •25957 .27612 .29235 0.30829 14.874 12.293 8.801 7.589 6.61 1 5.810 5-!47 4.591 4.120 3719 •373 •073 2.812 .582 2.380 .200 .040 1.897 .769 1-653 .548 ■453 •366 .287 1. 214 .148 .087 .028 0.978 0.9296 .8849 .8432 .8044 7683 0-7343 7029 •6734 .6456 .6195 0.3930 ■5705 ■55oi .5293 .5101 0.4917 46 METRIC UNITS. Gross sections and weights of wires. Table 58. 55 56 57 58 59 60 61 62 64 65 66 67 68 69 70 7i 72 73 74 75 76 77 78 80 81 82 f 3 84 85 86 87 90 91 92 93 94 95 96 97 98 99 100 o o s'S 79 4901.67 2 37S-83 2463.01 255I-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 3848.45 3959-19 4071.50 4185.39 4300.84 4417.86 4536-46 4656.63 4778-36 Copper — Density 8.90. 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 2 8." 2.114 .192 .271 ■351 •433 2.516 .601 .687 •774 •863 2-953 3-045 .232 .328 3.426 •524 .624 •7 Z 5 .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 Log. 0.32521 .34086 ■35623 ■37134 .38618 0.40078 .41514 .42926 .44316 .45684 0.47031 •48357 ■49663 .50950 .52218 0-53479 .54700 •55915 ■57"3 .58294 0.59460 .6061 1 .61746 .62867 ■63974 0.65066 .66145 .67211 .68264 .69304 0.70332 •71348 •72352 •73345 •74326 0.75297 .76256 .77206 .78144 .79074 0.79993 .80902 .81802 •82693 •83575 s I « k p* 6.990 0.84448 I .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 •'43 1 Iron — Density 7.8a. B-E 1? a v O ft S '■853 .921 .990 2.061 .132 2.205 .280 •355 •431 .509 .669 ■75° •833 .917 3-003 .088 .176 .265 •355 3446 .538 .632 .727 .823 3.921 4.019 .119 .220 -323 4.426 •53i •637 •744 .852 4.962 5-073 .185 .298 •413 .646 .764 .884 6.004 6.126 Log. O.26791 •28356 .29893 ■3M04 .32889 0-34349 •35784 •37196 •38587 •39954 0.41301 .42627 43933 .45220 .46488 0.47749 .48970 .50185 •51383 •52565 o- 53731 .54881 .56017 •57137 .58244 0-5933 6 .6041 5 .61481 •62534 •63574 0.64602 .65618 .66622 .67615 .68596 0.69567 .70527 .71476 .72414 ■73344 0.74263 •75 ! 73 .76073 .76964 .77846 0.78718 aj S h >■ E 4! 0.2 •5396 •5205 .5024 •4852 4689 4534 •4387 .4246 41 13 •3985 .3864 •3747 •3636 ■353° •3429 •333° •3238 •3 J 49 •3063 .2902 .2826 ■2753 .2683 .2615 .2550 .2488 .2428 .2369 • 2 3!3 •2259 .2207 •2157 .2108 .2061 .2015 .1971 .1929 .1887 .1847 .1809 ■1771 •1735 .1670 .1665 .1632 Brass— Density 8.56. S .1 2S.S 2.034 .108 .184 .262 •340 2.420 .502 .584 .668 .760 2.840 .929 3.018 .109 .201 3-295 •389 485 <583 .682 3.782 4.090 .177 4-303 .411 .521 .631 •744 4.857 .972 5.089 .206 •325 Log. 0.30829 ■32394 ■3393 1 •35442 .36927 0.38387 .39823 41235 .42625 .44092 0-45339 .46665 47971 49258 .50526 0.51787 .53008 •54223 .55421 ■56603 0.57769 .58919 .60056 .61175 .62283 0-63375 .64454 .66572 .67612 0.68640 .69656 .70660 •71653 •72634 5446 0.73605 .567 •74565 .690 •755H .815 .76452 .77382 ■940 6.068 0.78301 .196 .79211 .326 .80111 •457 .81002 .589 .81884 6.723 0.82756 £ >■ E 41 & « .4917 4743 4578 .4422 4273 .4132 ■3997 •3869 •3748 •3623 ■3521 •3415 •3313 ■3217 .3124 •3035 .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. 47 Table 59. BRITISH AND METRIC UNITS. Cross sections and weights of wires. The cross section and the weight, in different units, of Aluminium wire of the diameters given in the first column. For one teuth the diameter divide sections and weights by ico. For ten times the diameter multiply by 100, and so on. Aluminium — Density 2.67. a Area of cross £=■"= section Pounds Feet Ounces Feet Grammes Metres .Is in per Log. per per Log. per per Log. per 10 Sq. Mils. Foot. Pound. Foot. Ounce. Metre.* Gramme. 78.54 .OOOO909 5.95862 I IOOO. .OOI455 3.16274 687.5 .02097 2.32160 47.69 II 95-03 OIIOO 4.04139 9091. OI760 .24551 602.4 •02537 40437 3941 12 II3.IO OI309 .11699 7638. 02095 .32111 4774 .03020 47997 33-" 13 I3 2 -73 OI536 .18650 6509. 02458 •39062 406.8 ■03544 •54948 28.22 14 153-94 01782 .25088 5612. 02851 .45500 350.8 .04110 .61386 24-33 15 176.71 .OOO2045 4.31079 4889. •OO3273 3-5I49I 305.6 .04718 2.67377 21.19 16 201.06 02327 .366S5 4297. 03724 •57097 26S.5 .05368 .72984 18.63 17 226.98 02627 41952 3876. 04204 .62364 237-9 .06060 .78250 16.50 18 254.47 02946 .46917 3395- 04713 .67329 212.2 .06794 .83215 14.72 19 283-53 03282 .51613 3047- 052SI .72025 190.4 .07570 .87911 13.21 20 314.16 .0003636 4.56068 2750. .005818 3.76480 171.9 .08388 2.92366 11.922 21 346.36 04009 .60306 2494. 06415 .80718 '55-9 .09248 .96604 10.813 22 380.13 04400 •64346 2273. 07040 •84758 142.0 .10149 1 .00644 9-853 23 41548 04809 .68208 2079. 07697 .88630 129.9 .11093 .04506 9.014 24 452-39 05237 .71904 1910. 08378 .92316 1 1 94 .12079 .08202 8.279 25 490.87 .OOO5682 4.75450 1760. .OO909 3.95862 110.00 .1311 T.i 1748 7.630 26 530-93 06147 .78S67 1627. 09S3 .99269 101.70 .1418 •15155 7.054 27 572.56 06628 .82135 1509. I060 2.02547 94-3° .1529 •18433 6.541 28 615.75 07127 .85293 1403. 1 140 ■05705 87.69 .1644 •21592 6.083 29 660.52 07646 ■88341 1308. 1223 •08753 81.75 .1764 .24640 5.670 30 706.86 .OO0S182 4.91286 1222. .01309 2.1 1698 76.39 .1887 1-27584 5- 2 99 3' 754-77 OS737 •94134 1 145. 1398 .14546 71-54 .2015 ■30433 4.962 3 2 804.25 09309 .96S92 1074. 1489 •17304 66.89 •2147 ■33 I 9° ■657 33 855-3° 09900 .99565 1010. 1584 •'9977 63-13 .2284 ■35863 •379 34 907.92 10509 3.02158 952. 1681 .22570 59-47 .2424 .38456 • I2 5 35 962. ii .001114 3.04675 897.9 OI782 2.25087 56.12 .2569 T.40973 3-893 3° 1017.8S 1 178 .07123 848.8 1885 •27535 53-°5 .2718 .43421 .680 37 38 1075.21 1245 .09502 803.5 1991 .29914 50.22 .2871 .45800 483 "34-n 1316 .11918 760.0 2105 •32329 47.50 •3035 .48216 •295 39 1194.59 '383 .14075 723.2 2212 •34487 45.20 .3190 ■50373 •*3S 40 1256.64 .001455 3.16275 687.5 .02327 2.36687 42.97 •3355 7-52573 2.980 41 1320.25 1528 .18419 654.4 2445 •38831 40.90 •3525 •54717 •837 42 I3 S 544 1604 .20512 623.6 2566 .40924 38-97 •3699 .56810 .704 43 1452.20 1681 .22556 594-9 269O .42968 37-i8 •3877 .58854 •579 4+ 1 520.53 1760 .24552 568.2 28l6 .44964 35-5" ■4060 .60851 463 45 46 159043 1661.90 .001841 3.26504 543-2 .02946 2.46916 33-95 .4246 1.62803 2.355 1924 .28413 519.8 3078 .48825 32-49 4437 .64712 •254 47 48 '734-94 1809.56 1885.74 2008 .302S1 498.0 3213 •50693 31.12 .4632 .66580 .159 2095 .32110 4774 335i .52522 29.84 4832 .68408 .070 49 2183 •33901 458.1 3492 •543 r 3 28.63 •5035 .70199 1.986 50 1963.50 .002273 3-35656 440.0 .03636 2.56068 27.50 •5243 1.71954 1.907 S 1 2042.82 2365 2458 2554 2651 •37376 422.9 3783 .57788 26.43 •5454 •73674 ■833 5 2 53 2123.72 2206.18 •39063 .40717 406.8 394-2 3933 4086 ■59475 .61129 25.42 24.47 .5670 .5891 •75361 .77015 .764 .698 54 2290.22 •42341 377-2 4242 •62753 23-57 .6115 .78639 •635 55 2375-83 .002750 3-43934 363-6 .04400 2.64346 22.73 •6343 7.80233 1.576 Smithsonian Tables * Diameters and sections in terms of thousandths of a centimetre. 48 BRITISH AND METRIC UNITS. Cross sections and weights of wires. Table 59. p 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 7i 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 Area of cross section in Sq. Mils. 90 91 92 93 94 95 96 97 98 99 2 375-83 2463.01 2551.76 2642.08 2 733-97 2827.43 2922.47 3019.07 3"7-25 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 5 1 53-oo 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 Aluminium — Density 2.67. Founds per Foot. 100 7853.98 .002750 2851 2954 3058 3165 .003273 3383 3495 3608 3724 .003841 3960 4081 4204 4328 ■004456 4583 4713 4845 4978 .005114 5251 5390 553i 5674 .005818 5965 61 13 6263 6415 .006568 6724 6881 7040 7201 .007364 7528 ■7695 7863 8033 .008205 8378 8554 873« 8910 .009091 Log. 3-43934 .45500 •47037 .48547 .50032 3.51492 .52928 •54340 •55730 •57098 3-58445 •59771 .61077 .62364 ■63632 3.64893 .66114 .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 .93216 .94107 .94989 3.95862 Feet per Pound. 363-6 350.8 338-6 327-0 316.O 305-5 295.6 286.2 277.1 268.5 260.3 252-5 245.O 237-9 231.O 224.4 218.2 212.2 206.4 2OO.9 195-5 I9O.4 185.5 180.8 I76.2 I7I-9 167.6 163.6 '59-7 '55-9 152.2 148.7 145-3 142.0 138.9 135-8 132.8 130.0 127.2 124.5 121.9 1 1 9.4 1 1 6.9 1 14.5 112.2 110.0 Ounces per Foot. .04400 .04562 .04726 •04893 .05063 .05236 ■05413 ■05591 •05773 •05958 .06146 .06336 .06530 .06726 .06925 .07129 ■07333 •07541 .07751 .07965 .08182 .08402 .08624 .08850 .09078 .09309 .09544 .09781 .10021 .IO264 .1051 .IO76 .1101 .1126 .II52 .II78 .1205 .1231 .1258 .I2§5 ■1313 •1341 •1369 •1397 .I426 ■'455 Log. 2.64346 .65912 •67449 .68959 .70444 2.71904 •73340 ■74752 .76142 ■77510 3.78857 .80183 .81489 .82777 .84044 2.85305 .86526 •87740 .90120 2.91286 ■92437 •93572 .94693 ■95799 2.96892 •97971 _-99°37 1 .00090 .01130 r.02158 ■03174 .04178 .05170 .06152 r.07122 .08082 .09031 .09970 .10899 r.11819 .12728 .13628 .14519 .15401 T.i 6274 Feet per Ounce 22.73 21.92 21.16 20.44 '9-75 19.10 18.48 17.88 I7-32 16.78 16.27 15.78 '5-3« 14.87 14.44 14.03 13.64 13.26 iz.90 12.55 12.22 11.90 11.60 n. 30 11.02 10.742 10.479 10.224 9-979 9-743 9-SI5 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 Grammes per Metre.* 0-6343 .6576 •6813 .7054 .7300 O.7549 •7803 .8061 •8323 8589 O.8860 ■9135 •9413 .9697 .9984 I.O28 .057 .087 .117 .148 1. 180 .211 •243 .276 •309 I.342 ■376 .410 •445 .480 '•5'5 •587 .624 .661 •737 ■775 .814 •853 1.893 •933 ■973 2.014 .055 2.097 Log. 1.80233 .81798 -§3335 ■86331 f.87790 .89226 .90638 .92028 ■93396 f-94743 ■97375 .98662 .99930 0.01191 .02412 .03627 .04825 .06006 0.07172 .08323 .09458 •'0579 .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 Metres per Gramme. "■576 .521 .468 .418 •370 1-325 .282 .241 .201 .164 1. 129 •095 .062 ■031 .002 O.973O .9460 .9199 ■8949 .8708 O.8477 .8256 •8043 .7838 .7641 0-745I .7268 .7092 .6922 •6757 0.6600 .6448 .63OO .6158 .6020 O.5887 •5759 •5634 •55H •5397 0.5284 •5 J 74 .5068 .4965 .4865 0.32160 0.4769 * Diameters and sections in terms of thousandths of a centimetre. Smithsonian Tables. 49 Table 60. BRITISH AND METRIC UNITS. Cross sections and weights of wires. The cross section and the weight, in different units, of Platinum wire of the diameters given in the first column. For one tenth the diameters divide sections and weights by ioo. For ten times the diameter multiply by 100, and so on. Platinun — Density 21.50. # a Area of cross es section Pounds Feet Ounces Feet Grammes Metres Ms in per Log. per per Log. per per Log. per a Sq. Mils. Foot. Pound. Foot. Ounce. Metre.* Gramme. 10 78.54 .0007321 4.86455 1366.O .01171 2.06867 85.38 O.1689 r.22753 5.922 i 95-°3 008858 ■94732 1 I 20.0 948.6 .01417 .15144 70.56 ■2043 .31030 4.894 12 II3.IO ,01054 3.02292 .01687 .22704 59.29 •2432 .38590 4-1 13 >3 I3 2 -73 01237 .09243 808.3 .01979 .29655 50-52 .2854 45541 3-504 14 153-94 01435 .15681 696.9 .02296 •36093 43-56 •33'° ■5!979 3.021 15 176.71 .001647 3.21672 607.I •02635 2.42084 37-95 0-3799 L57970 2.632 i6 20I.o6 01874 .27278 533-6 ■03005 .47790 33-27 •4323 •63576 2.31 1 '7 226.98 021 16 •32544 472.7 •03385 •5 2 956 29-54 .4880 .68843 2.049 18 254.47 02372 •37509 421.6 •03795 •57921 26.35 •5471 •73808 1.828 19 283-53 02643 .42206 378-4 .04228 .62618 23.65 .6096 .78504 1.640 20 314.16 .002928 3.46661 341-5 .04685 2.67073 21.34 0.6754 1-82959 1.481 21 346.36 03228 .50898 3°9-7 .05165 .71310 19.36 •7447 .87197 •343 22 380.I3 415.48 03543 03873 •54939 282.2 .05669 •75351 17.64 •8i73 ■91237 .224 23 .58801 258.2 .06196 •79213 16.14 ■8933 •95099 •9»795 .119 24 452-39 04217 .62497 237.2 ■06747 .82909 14.82 .9726 .028 25 490.87 .004575 3.66042 218.6 .07321 2.86454 13.66 1.055 0.02341 0.9475 26 530-93 04949 .69449 202.1 .07918 .89861 12.63 .142 •05748 .8760 27 572-56 05324 .72628 187.8 •08539 .93140 11. 71 .231 .09026 .8124 28 « S7S 05739 .75886 174.2 •09183 .96298 10.89 •324 .12184 •7553 29 660.52 06157 •78934 162.4 .09851 .99346 10.15 .420 .15232 .7042 30 706.86 .006589 3-81879 151.8 .1054 T.02291 9.486 1.520 0.18 1 77 0.6580 3 1 754-77 07035 •84727 142. 1 .1126 ■05139 8.884 .623 .21025 .6162 3 2 804.25 07496 .87485 '33-4 .1199 .07897 8.338 •729 •23783 •5783 33 855-30 07972 .90157 125.4 .1276 .10569 7.840 •839 .26456 •5438 34 907.92 08463 •92750 1 18.2 ■1354 .13162 7-385 .952 .29049 •5' 2 3 35 962.11 .008968 3.95268 in. 52 ■1435 .1518 T.i 5680 6.970 2.069 .031566 0.4834 3° 1017.88 09488 _-977i5 105.41 .18127 6.588 .188 .34014 4569 37 1075.21 10022 2.00095 99.78 .1604 .20507 6.236 .312 •36393 4326 38 1134.11 10595 .02511 94-38 .1695 .22923 5.899 •444 .38809 .4092 39 1194.59 I"34 .04668 89.81 .1782 .25080 5-613 .568 .40966 •3893 40 1256.64 .01171 2.06867 85.38 .1874 T.27279 5-336 2.702 0.43166 0.3701 4i 1320.25 1385.44 I23I .09011 81.26 .1969 .29423 5.079 •839 45309 •3523 42 I29I .11104 77-44 .2066 .31516 4.840 •979 .47403 •334« 43 1452.20 '354 .13148 73-88 .2166 •3356o 4.617 3.122 .49446 •3203 •3059 44 •520.53 1417 ■^HS 70.56 .2268 •35557 4.410 .269 •51443 45 46 ' 47 48 1590.43 1661.90 '734-94 1809.56 1885.74 .OI482 1549 1617 2.17097 .19006 .20874 67.46 64.56 61.84 .2372 .2478 •2587 i"-37509 .39418 .41286 4.216 4-035 3.865 3419 ■573 •730 0-53395 •55304 .57172 0.2924 ■2799 .2681 1687 .22703 59-29 .2699 •431 1 5 3705 .891 .59001 .2570 49 I758 •24494 56.89 .2812 .44906 3.556 4.054 .60792 .2467 50 1963.50 2042.82 .O183O 2.26249 54.64 .2928 T.46661 3.4I5 4.222 0.62547 0.2369 5 1 I904 .27969 52-52 •3047 .48381 3.282 •39 2 .64267 .2277 5 2 53 2123.72 2206.18 I979 2056 .29655 Wo 50-52 48.63 •3!67 .3290 .50067 .51722 3-157 3-°39 .566 •743 •65954 .67608 .2190 .2108 54 2290.22 2135 •32933 46.84 ■3415 •53345 2.928 •924 .69232 .2031 55 2375-83 .02214 2-34527 45.16 •3543 ^•54939 2.822 5.108 0.70825 0.1958 Smithsonian Tables. * Diameters and sections in terms of thousandths of a centimetre. 50 BRITISH AND METRIC UNITS. Cross sections and weights of wires. Table 60. E2 .22 a 55 56 % 58 59 60 6t 62 63 Area of cross section in Sq. Mils. 65 66 67 68 69 70 7i 72 73 74 75 76 77 78 79 2375-83 2463.01 2551.76 2642.08 2 733-97 2827.43 2922.47 3019.07 3H7-25 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 Platinum — Density 21.50. Founds per Foot. 80 5026.55 81 5153.OO 5281.02 54I0.6I 5541-77 85 86 87 88 89 90 9i 92 93 94 95 96 97 98 99 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 7697.69 100 7853-! .02214 2296 2378 2463 2548 .02635 2724 2814 2906 3999 •03093 3189 3286 3385 3485 .03588 3690 3795 3901 4009 .04118 4228 4340 4454 4569 .04685 4803 4922 5043 5165 .05289 54H S & 1 5669 5799 •05930 6062 6196 6469 .06607 6747 Log. 7031 7175 2-34527 ■36092 •37630 .39140 .40625 2.42085 •43521 •44933 ■46323 .47691 2.49037 •50363 •51670 •52956 .54224 2-55485 .56706 .57921 ■59"9 .60301 2.61467 .62617 ■63753 .64874 .65980 2.67073 68152 .69217 .70270 .71310 2.72338 •73354 •74358 •753SI •76333 2.77303 .78263 .79212 .80151 .81080 2.81999 .82909 .83809 .84700 .85582 Feet per Pound. 07321 2.86455 '3-66 45.16 43-56 42.04 40.61 39-24 37-94 36-71 35-54 34-42 33-35 32-33 31-36 30-43 29.54 28.69 27.87 27.10 26.35 25.63 24.95 24.28 23-65 23.04 22.45 21.89 21 -34 20.82 20.32 19-83 19.36 18.91 18.47 18.05 17.64 17.25 16.86 16.50 16.14 15-79 15.46 15.14 14.82 14.52 14.22 '3-94 Ounces per Foot. Log. 0-3543 •3673 .3806 ■3940 •4077 0.4217 •4358 .4502 •4649 Feet per Ounce. Grammes per I Metre.* O.4949 .5102 •5258 .5416 ■5577 o.574i •5904 .6072 .6242 .6414 0.6589 .6765 .6945 .7126 •73to 0.7496 •7685 •7876 .8069 .8265 0.8463 .8663 .8866 .9070 .9278 0.9487 •9699 .9914 1.0130 .0350 1.057 •079 .102 .125 .I48 I.17I 1 -54939 .56504 .58042 •59552 .61037 L62497 ■63933 iP 4S •66735 .68103 1.69449 •70775 .72082 •73368 .74636 175897 .77118 78333 79531 •80713 r.81879 .83029 ,84165 2.822 .722 .628 •538 •453 2.372 .294 .221 .151 .084 2.021 1.960 .902 .846 793 1.742 .694 •647 .602 •559 1.518 .478 440 .85286 .403 ■86392 .368 1 .87485 .88564 .89629 .90682 .91722 1.92750 .93766 ■94770 •95763 •96745 1-97715 .98675 .99624 0.00563 .01492 0.0241 1 .03321 .04221 .05112 .05994 0.06867 0.8538 1-334 .301 .270 •239 .210 I.182 .154 .128 .102 .078 I.O54I .0310 .0087 O.987I .9661 O.9460 .9264 .9074 .87II 5.108 ■295 .486 .680 .878 6.079 ■283 491 702 .917 7-'34 •356 .580 .808 8.O39 8.276 .512 754 •999 9.247 9.498 9-753 10.012 10.273 '0-539 10.81 11.08 u-35 11.63 n.gr 12.20 12.49 12.78 13.08 '3-37 13.68 13.98 14.29 14.60 14.92 15.24 15-56 15.89 16.22 16.55 16.89 Log. 0.70825 .72390 73928 ■75438 .76923 0.78383 .79819 .81231 .82621 .83989 0-85336 .86662 .87968 •89255 .90523 0.91784 .93004 .94219 •95417 .96599 0.97765 .98916 1.00051 .01172 .02278 '■03371 .04450 .05516 .06568 .07609 1.08637 .09652 .10657 .11649 .12631 1.13601 .14561 .15510 .16449 •17378 1. 18298 .19207 .20107 .20998 .21880 I.22753 Metres per Gramme. .1958 .1888 .1823 .1760 .1701 .1645 .1592 •1541 .1492 .1446 .1402 .1360 •'319 .1281 .1244 .1208 .1175 .1142 .1111 .1081 .10528 .10253 .09988 •09734 .09489 ■09253 .09026 .08807 .08596 ■ o8 393 .08197 .08007 .07807 .07647 ■07477 .07311 .07152 .06997 .06847 .06702 .06562 .06426 .06294 .06166 .06042 .05922 Smithsonian Tables. * Diameters and sections in terms of thousandths of a millimetre. Si Table 61. BRITISH AND METRIC UNITS. Cross sections and weights at wires. The cross section and the weight, in different nnits, of Gold wire of the diameters given in the first column. F S one tenth the diameters .divide sections and weights by ico. For ten times the diameter multiply by too. and so on. Area of Gold — Density 19.30. a Eg Q cross section in Sq. Mils. Troy Ounces per Foot. Log. Feet perJTroy Ounce. Grains per Foot. Log. Feet Grain. Grammes per Metre.* Log. Metres per Gramme. 10 78.54 .00958 3.98152 104-35 4.600 0.66276 .2174 O.1516 T.18065 6-597 ir 95°3 .01160 2.06429 86.24 5.566 •74553 ■1797 .1834 •26342 5-45 2 12 113. 10 .OI380 • r 3989 72.46 6.624 .82114 .1510 .2183 •33902 4.581 J 3 i3 2 -73 .01657 .21940 60.34 7-774 .89064 .1286 .2562 ■40853 3-904 3-366 14 •53-94 .01878 •27378 53-24 9.016 ■95503 .1109 .2971 .47291 15 176.71 .02156 2-33369 46.38 10.35 1.01493 .09662 O.341 1 T-53282 2.932 16 201.06 ■02453 •38976 40.76 11.78 .07100 .08492 .3880 .58888 ■577 17 226.98 .02770 .44242 36.11 13.29 .12366 .07522 .4381 .64154 .283 18 25447 •03105 .49207 32.21 14.90 •I733 1 .06710 .4911 .69119 .036 19 283-53 .03460 •53903 28.90 16.61 .22027 .06022 •5472 .738l6 1.827 20 314.16 •03833 2.58358 26.09 18.40 1.26482 ■05435 O.6063 T.78271 1.649 21 346-36 .04226 .62596 23.66 20.29 .30720 ■04939 .6685 .82509 .496 22 3 8o - : 3 .04638 .66636 21.56 22.26 •3476i .04492 •7337 ■86549 ■363 2 3 415.48 .04954 .69498 20.18 24-33 .38622 .04109 .8019 .9041 1 .248 24 452-39 .05520 •74194 18.12 26.50 .42319 •03774 ■8731 .94107 .145 25 490.87 .05990 2.77740 16.70 28.75 1.45865 .03478 0.9474 I.97652 1.0555 26 S3°-93 .06478 .81147 15.44 31.10 ■49271 .03216 1.0247 O.OIO59 0-9759 27 572-5 6 .06986 .84425 I4-3 1 33-53 •52549 .O2982 .1050 •04338 9050 28 6I5-75 •075 J 3 .87584 i3-3t 36.06 •557o8 .02773 .1884 .07496 .8415 29 660.52 .08060 .90632 12.41 38.69 •58756 .02585 .2748 .10544 •7844 30 706.86 .08625 2-93577 11.594 41.40 1.61701 .024T5 1.364 O.13489 0-733° 3 1 754-77 .09210 .96425 10.858 44.21 •64549 .02262 •457 •16337 .6912 32 804.25 .09813 .99182 10.190 47.10 .67306 .02123 •552 .19095 .6442 33 855-3o .10436 1.01855 9.582 50.09 .69979 .01996 .6 5I .21768 .6058 34 907.92 .11078 .04448 9.027 53-i8 .72572 .Ol88l •752 .24360 •5707 35 962.11 .1174 r.06965 8.518 56-35 1.75089 .OI775 1.857 O.26878 o-5385 36 1017.88 .1242 .09413 8.051 59.62 •77537 .01677 .965 ■29325 .5090 37 1075.21 .1312 .11792 7.622 62.97 •79917 .01588 2.070 .31605 .4830 38 "34-n •1387 .14208 7.210 66.58 •82332 .OI 502 .194 .34121 -4558 39 1194.59 .1458 .16365 6.861 69.97 .84489 .OI429 .306 .36278 •4337 40 1256.64 •1533 T.18565 6.521 73.60 1.86689 ■01359 2.425 O.38478 0,4123 4' 1320.25 .1611 .20709 6.207 77-33 .88833 .OI293 ■548 .40621 ■3924 42 i3 8 5-44 .1691 .22802 5-915 81.14 .90926 .OI232 .674 .42715 .44758 ■3740 43 1452.20 .1772 .24846 5-643 85.05 .92970 .OII76 .803 .3568 44 1520.53 .1855 •26843 5-390 89.06 .94967 .OII23 •935 ■46755 .3408 45 1590-43 ■1941 T.28795 5-153 93-15 1.96919 .OI0735 3.070 0.48707 0.3258 46 1661.90 .2028 .30704 4-931 97-34 .98828 .OIO273 .207 .50616 -3"8 47 1734-94 .2117 •32572 4.724 101.61 2.00696 .OO9842 •348 .52484 .2986 48 1809.56 .2208 .34400 4-529 105.99 .02525 .OO9435 .492 ■543'3 .2863 49 1885.74 •2301 .36191 4-346 110.45 •04315 .OO9054 ■639 .56104 .2748 50 1963.50 .2396 L37946 4.174 1 1 5.0 2.06070 .008696 3-79° 0.57859 0.2639 51 2042.82 •2493 .39666 4.012 119.6 .07790 .008358 •943 •59579 •2537 52 2123.72 .2591 •41353 3-859 124.4 .09477 .008039 4.099 .61265 .2440 53 2206.18 .2692 .43007 3-7I5 129.2 .11131 .007739 .258 .62920 •2349 i 54 2290.22 .2795 .44631 3-57» I34-I .12755 .007455 .420 •64543 .2262 55 2375-83 .2899 T.46225 3-449 139.2 2.14349 .OO7186 4.585 0.66137 0.2181 Smithsonian Tables. * Diameters and sections in terms of thousandths of a centimetre. 52 BRITISH AND METRIC UNITS. Cross sections and weights ol wires. Table 61 , P Area of cross section in Sq. Mils. Gold — Density 19.30. Troy Ounces per Foot. Log. Feet per Troy Ounce. Grains „ per Foot. Log. Feet per Grain. Grammes per Metre.* Log. Metres per Gramme. 55 2375.83 56 58 59 60 61 62 63 64 65 66 67 68 70 7i 72 73 74 75 76 77 78 79 80 81 82 P 84 85 86 87 88 89 90 91 92 93 94 95 96 9 l 98 99 100 2463.01 2551.76 2642.08 2733-97 2827.43 2922.47 3019.07 3 I1[ 7-2S 3216.99 3318.31 3421.19 3525-65 3631.68 3739-28 3848.45 3959- r 9 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 .3005 •3"4 .3224 •3336 •345° .3566 .3684 .3804 •3925 ■4175 .4302 •443 1 •4563 .4697 .4831 .4968 .5107 .5248 •5391 ■5535 .5682 •5831 .5981 •6i33 .6288 .6444 .6602 .6762 .6924 .7088 •7254 .7421 •7591 •7763 •7936 .8111 .8291 .8468 .8649 .8832 .9017 .9204 ■9393 •9583 1.46225 .47790 •49327 .50838 •52323 I-53782 .55218 .56630 .58020 .59388 .4049 1.60735 2 -47° 3-449 •327 .212 .102 2.998 2.899 .804 •715 .629 ■548 .62061 ■63367 .64654 .65922 1-67183 .68404 .69619 .70817 .71998 r.73164 •74315 •75450 .76571 .77678 T-78770 •79849 .80915 .81968 .83008 r. 84036 •85052 .86056 .87049 .88030 T.89001 .89960 .90910 .91858 .92778 1-93697 .94606 •95507 •96397 .97279 •395 ■3 2 4 •257 .192 2.129 .070 .013 1.958 •905 1.855 .807 .760 ■715 .672 1.630 •590 •552 -s^ ■479 1.444 .411 ■379 •347 •317 1.288 .260 .206 .181 1. 156 .132 .109 .086 .065 1. 981 52 1.043 139.2 H4-3 149-5 154-7 160.1 165.6 171. 2 176.8 182.6 188.4 194.4 200.4 206.5 212.7 219.0 225.5 231.9 238.4 245.1 251.9 258.8 265.7 272.7 279-9 287.1 294.4 301.8 3°9-3 316.9 324.6 332-4 340.2 348.2 356.2 364-4 372.6 380.9 389-3 397-9 406.5 415.2 423-9 432.8 441.8 450.9 460.0 2.14349 .15914 •I745 1 .18962 •20447 2.21906 •23342 •24754 .26144 .27512 2.28859 ■30185 ■3H9i .32778 •34046 2.35307 •36528 •37743 .38941 .40123 2.41288 •42439 •43574 .44695 .45801 2.46894 •47973 ■49039 .50092 .51132 2.52160 •53!76 .54180 •55*73 •56i54 2-57125 .58085 •59034 •59972 .60902 2.61821 •62731 .63631 .64521 .65403 2.66276 .007186 6932 6691 6462 6245 .006039 5842 5655 5477 5307 ■005145 4991 4843 4701 4566 .004435 43 12 4195 4079 3970 .003865 3764 3666 3573 3483 .003401 33*3 3233 3156 3081 .003009 2939 2872 2807 2744 .002684 2625 2568 2513 2460 .002409 2359 2310 2263 2218 .002174 4.585 4-754 4.925 5.099 5.277 5-457 5.640 5-827 6.0 1 6 6.209 6.404 6.603 6.805 7.010 7.217 7.429 7.641 7.858 8.078 8.301 8.526 8-755 8.987 9.222 9.460 9.701 9-945 10.192 10.442 10.696 10.95 11. 21 11.47 11.74 12.01 12.28 12.55 12.83 13.11 13-39 13.68 13-97 14.26 14.56 14.86 15.16 0.66137 .67702 .69240 .70750 •72235 0.73695 •75I3I •76543 •77933 •793 01 0.80647 ■8i973 .83280 .84566 •85835 0.87096 .88316 •8953' .90729 .91911 0.93077 .94227 ■95363 .96484 .97590 0.98683 .99762 1.00828 .01880 .02921 .04964 ■05969 .06961 •07943 1. 0891 3 .09873 .10822 .11761 .12690 1. 13609 .14519 .15419 .16310 .17192 1. 18065 .2181 .2104 .2031 .1961 .1895 •1833 ■1773 .1716 .1662 .1611 .1561 .1514 .1470 .1427 .1386 .1346 .1309 •1273 .1238 .1204 ■"73 .1142 .1113 .1084 .1057 .10308 .10055 .09812 .09577 •09349 .09131 .08919 .08716 .08519 .08328 .08145 .07967 .07794 .07628 .07466 .07310 .07158 .07011 .06869 .06731 .06597 Smithsonian Tables. ' Diameters and sections in terms of thousandths of a centimetre. 53 Table 62. BRITISH AND METRIC UNITS. Cross sections and weights of wires. The cross section and the weight, in different units, of Silver wire of the diameters given in the first column. For one tenth the diameters divide the section and weights by ioo. For ten times the diameter muliply by 100, and so on. Silvei — Density 10.50. • -A Area of _ cross " section Troy Feet Grains Feet Grammes Metres Is in Ounces Log. per Tro] per Log. per per Log. per a Sq. Mils. per Foot. Ounce. Foot. Grain. Metre.* Gramme. 10 78.54 .005214 3-7I7I5 191.79 2.503 0.39839 •3996 O.08247 2.91628 12.126 ii 95-°3 .006308 •79992 158.52 3.028 .48117 ■3302 ■09978 •99905 10.022 12 113.10 .007508 •87553 '33-19 3.604 •55677 •2775 .11876 I.07465 8.420 13 >3 2 -73 .008811 •94503 "3-49 4.229 .62627 .2364 •'3937 .14416 7-175 14 '53-94 .010219 2.00942 97.86 4.905 .69066 .2039 .16164 .20854 6.186 15 176.71 .01173 2.06932 85.24 5-63I O.75057 .1776 0.1855 T.26845 5-389 16 201.06 •01335 •12539 74.92 6.407 .80663 .1561 .2111 •32452 4-737 '7 226.98 .01507 .17805 66.37 7-233 .85929 •1383 •2383 •37718 4.196 18 254-47 283-53 .01689 .22770 59.20 8.109 .90894 •1233 .2672 •42683 3-743 19 .01882 .27466 53'3 9-034 •95590 .1107 •2977 •47379 3-359 20 314.16 .02086 2.31921 47-95 10.01 I.OOO46 .09990 0.3299 T.51834 3-03« 21 346.36 .02299 •36159 43-49 II.04 .04283 .09060 •3637 .56072 2.750 22 380.13 .02523 .02758 .40200 39-63 12. II ■08324 .08256 •399' .60112 •505 23 415.48 .44061 36.26 13.24 .12186 ■07553 ■4363 •63974 .292 24 452-39 ■03003 •47758 32-99 14.42 .15882 •06937 ■475° .67670 .105 25 490.87 .03259 2-5I303 30.69 15.64 1. 19427 .06425 0.5154 7.71216 1.940 26 530-93 •03525 .03801 .54710 28.37 16.92 .22834 .05911 ■5575 •74623 •794 27 572-56 •57988 26.31 18.24 .26113 .05481 .6012 .77901 •663 28 615.75 .04088 .61147 24.46 19.62 .29271 •05097 .6465 .81059 ■547 29 660.52 .04385 .64195 22.81 21.05 ■32319 .04751 •6935 .84108 .442 30 706.86 .04692 2.67140 21.31 22.52 I.35264 .04440 0.7422 r.87052 '•347 3i 754-77 .05010 .69988 19.96 24.05 .38112 O.4158 ■7925 .89900 .262 32 804.25 •05339 •72745 18.73 25-63 .40870 O.3902 •8445 .92658 .184 33 855-30 .05678 .75418 17.61 27.25 •43542 O.3669 .8981 •9533 1 •"3 34 907.92 .06027 .78011 16.59 28.93 ■46135 0-3457 •9533 .97924 .049 35 962.11 -06387 2.80528 15.66 30.66 I.48653 .03262 I.OIO 0.00441 0.9899 36 1017.88 •06757 .82976 14.80 32-43 .51100 .03083 .069 .02889 •9356 37 1075.21 .07138 •85356 14.01 34.26 •53480 .02919 .129 .05268 •8857 38 1134.11 .07546 .87772 I3-25 36.22 •55896 .58052 .02761 .194 .07684 .8378 39 1194.59 .07930 .89928 12.61 38.06 .02627 .254 .09841 •7973 40 1256.64 .08342 2.92128 11.99 40.04 I.60252 .02497 '•3'9 0.1 2041 0-7579 4i 1320.25 .08764 ■94272 11.41 42.07 .62396 •02377 .386 .14185 .16278 •7213 42 1385.44 .09197 .96365 10.87 44.15 .64489 .02265 •455 •6874 43 1452.20 .09640 .98409 10.37 46.27 •66533 .02161 •5 2 5 .18322 •6558 •6263 44 '520.53 .10094 I.O0406 9.91 48.45 .68530 .02064 •597 .20318 45 1590.43 .1056 r.02358 9.471 50.68 I.70482 •01973 1.670 0.22270 0.5988 ■573' .5489 •5263 .5050 46 1661.90 .1103 .04267 9.065 52.96 ■72391 .01888 •745 .24179 47 48 '734-94 1809.56 1885.74 .1152 .1201 .06135 .07964 8.683 8-32J 55.28 57-66 ■74259 .76088 .01809 ■01734 .822 .900 .26047 .27876 49 .1252 •09755 7.988 60.09 •77879 .01664 .980 .29667 50 1963.50 2042.82 •>303 ■1356 T.i 1 509 7.672 62.57 I.79634 .01598 2.062 0.31422 0.4850 .4662 S 1 .13229 7-374 65.09 •81354 •01536 .145 •33'42 5 2 53 2123.72 2206.18 .1410 .1465 .14916 .16570 7-093 6.828 67.67 70.30 .83040 .84695 .01478 .01422 .230 .316 •34829 ■36483 .4484 •43'7 .4158 54 2290.22 .1520 .18194 6.578 72.99 .86328 .01370 •405 .38107 1 55 2375-83-I577 T.19788 6.340 75-70 1.87912 .01321 2.495 0.39700 0.4009 Smithsonian Tables. * Diameters and sections in terms of thousandths of a centimetre. 54 BRITISH AND METRIC UNITS. Cross sections and weights of wires. Table 62. .a a ft Area of Sq. Mils. Silver — Density 10.50. Troy Ounces per Foot. Log. Feet per Troy Ounce. Grains per Foot. Log. Feet per Grain. Grammes per Metre.* Log. Metres per Gramme. 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 7i 72 73 74 75 76 77 78 79 80 81 82 2 3 84 85 86 87 88 89 90 9 1 92 93 94 95 96 9 l 98 99 100 237S-83 2463.01 2551.76 2642.08 2733-97 2827.43 2922.47 3019.07 3"7- 2 5 3216.99 33i8-3i 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 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 0.1577 •1635 .1694 •1754 .1815 0.1877 .1940 .2004 .2069 .2136 0.2203 .2271 .2340 .241 z .2482 0.2555 .2628 .2703 ■2778 .2855 0.2933 .3011 .3091 3i7 4901.67 .3254 0-3337 •3421 .3506 ■3592 •3 6 79 0.3767 .3856 •3946 .4038 .4130 0.4223 .4318 ■4413 .4509 .4607 0.4705 .4805 .4906 .5007 .5110 0.5214 1. 19788 •21353 .22890 .24401 .25886 1.27346 .28781 •3 OI 93 ■3>584 •3295 1 r.34298 .35624 •36930 .38217 •39485 1.40746 .41967 .43182 .44380 .45560 T.46728 .47878 .49014 •50134 .51241 I-52333 •53412 .54478 •55531 .56571 T-57599 .58615 .59619 .60612 •6i593 7.62564 .63524 •64473 .65411 .66341 T.67260 .68170 .69070 .69961 .70842 r.71715 6.340 .116 5-9°3 .701 .510 5.328 •155 4.990 •832 .683 4.540 ■403 •273 .148 .029 3-913 .805 .700 •599 .502 3.410 .321 •235 .152 •073 2.997 •923 .852 ■784 .718 2.655 •593 ■534 ■477 .421 2.368 .316 .266 .218 .171 2.125 .081 .038 1.997 •957 1. 91 8 75-70 78.48 81.31 84.19 87.12 90.09 93.12 96.20 99-33 102.51 105-7 109.0 1 1 2.3 1 1 5.7 119.1 122.7 126.2 129.7 133-4 i37-o 140.8 144.6 148.4 152-3 156.2 160.2 164.2 168.3 172.4 176.6 180.8 185.1 189.4 193.8 198.2 202.7 207.2 211.8 216.4 221. 1 225.9 230.6 235-5 240.4 245-3 250.3 1.87912 .89477 .91014 .92525 .94010 1-95470 .96906 .98318 .99708 2.01075 2.02422 .03748 .05054 .06341 .07609 2.08870 .10091 .11306 .12504 .13686 2.14852 .16002 .17138 .18258 •19365 2.20458 •21537 .22602 •23655 .24695 2.25723 •26739 •27743 .28736 .29717 2.30688 .31648 •32597 •33535 •34465 2.35384 .36294 •37194 .38085 .38967 2.39839 01 321 1274 1230 1 188 1 148 .01110 1074 1040 1007 0975 ■009457 09173 08903 08642 08393 .008153 07926 07708 07498 07297 .007104 06918 06739 06568 06402 .006243 06090 05942 05800 05663 .005531 05403 05279 05160 05045 •004933 04825 04721 04620 04522 .004428 04336 04247 04161 04077 .003996 2-495 •586 .679 •774 .871 2.969 3.069 .170 •273 •37» 3484 •592 .702 .813 .926 4.042 ■157 .275 •395 •516 4639 ■763 .889 5-oi7 .147 5.278 .411 •&* .681 .819 5-958 6.099 .242 ■386 •532 6.680 .829 .980 7-132 .287 7-443 .600 •759 .920 8.083 8.247 0.39700 .41266 .42803 ■443 1 4 •45798 0.47258 .48694 .50106 .51496 .52864 0.54211 ■55537 .56843 .58130 •59398 0.60659 .61880 .63094 .64293 .65474 0.66640. .67791 .68926 .70047 •7" 53 0.72246 •73325 •74391 •75444 .76484 0.77512 .78528 •79532 .80524 .81506 0.82476 .83436 .84385 •85324 .86254 0.87173 iz .89873 ■90755 0.91628 0.4009 .3867 •3732 .3605 •3484 0.3368 •3259 •3'55 •3055 .2961 0.2870 .2784 .2701 .2622 .2547 0.2474 .2406 •2339 .2275 .2214 0.2156 .2099 .2045 •1993 •1943 0.1895 .1848 .1803 .1760 .1719 0.1678 .1640 .1602 .1566 •1 53' 0.1497 .1464 •1433 .1402 .1372 0.1344 .1316 .1289 .1263 •1237 0.1213 * Diameters and sections in terms of thousandths of a centimetre. Smithsonian Tables. 55 Table 63. WEIGHT OF SHEET METAL. 4) .3 *a rt w c ^4 O ■5 S w u ■6 0) P la ooqqq o >-. — i-i n qqqqq d vo 6 *^> d \D r^-oo On o I o 2 qqqqq O\oo r-» tv.vo qqoqo od t-I "4- r^ d win - ) rj- ro CO Hi CO "1 1\ ON a o I s 8 3 -S qqqqq ri Tf->0 00 o qqqqq d ltj d »n d On O N ro*o _ - — _ C! •a o s % CO B .3 "S B M "TOO O fO N ON\D f">0 d\d no ts VOOO H ^NO KH (H N N N 2 M I is VO N 00 ■* O ^n\o fiod NO « CO Tf" O fOON -4- O ^O >- ONCO I s - »0 1 Ti- ll M fD"^- o q o o o ■^- rri ri i-4 d m N >i o On "TJ3 r-.oo oo d o q q o o o q o o o o oovd 4n d VO ^- M O 00 Thick- ness in thou- sandths of a cm. pI n n^-»o 10 t^00 ONO Smithsonian Tables. 56 Table 64. WEIGHT OF SHEET METAL. ■4 * Hi > GO P.O "So- ■tf-oq « vo o 00 >0 Tf 01 M "tf-OO N NO O •^-no ON i-I -4- nvoo 4oo N 0) CO CO CO 0) O -3 a 1 \o novo n C\ On onoooq i-v >-nco m on Oh N fOtO ON^ON o \o CO O NO 00 Nn iv.no isior^H on * O *- . 00 NVinN n inco >-3 -4- OOOmn h « n n O oq r-, in cp t^. On c^ ^hao •h i-H N N N « Onno ro O OJ +5 Co 0] o gjfc, §<* WONO N Tt-00 N 1^. m NO N ON u->N ^- ON COOO co i-5 ci t}- i>)i^- ■^■nonn ^ , lOON COCO N CO ■d-HNrf ooOHnt S I 3 a s O ON O\00 00 o\r-AO v~) ■*(■ h! co»nrs.od 00 rv. r*-NOVO COM m O ON N"inHco a) .* w O § =■ oni^-no Th co n co^r*. on i- co -^-vooo ivOO On O m NO r>.00 O m * ' ' ^ M s 3 "3 E 3 3 (n o 3* N "IN O N N Tj-VO ONhh N Tf-NQ 00 ii W ^-VOOO i-i >ONO N t1- CO^OOO O N M V) o •at, o <* ON0O f^VO *n oo r-^NO *n Tt- rONH »oa\ H CJ ^h "*^\Q O O O O O Tt- CON t-i O CON hh O ON CO tv. m IO00 OO ON m N CO O O w w h & w en Tt-oo rorsw ioOVOh n tj- on coco n Tt*oo rorsw O O i-i ih w lO ON "^-00 N N rv COCO Tt* nm\o O»o « CO co tj- , ^- P. o U 1- a o to O C . O Q O O O tOVO ON N *0 O NC0 "In rt- ON rooo PO O O »■* m M O M M M M CO >-< if t^O tv Tf" O NO CO MN NhVO « CO CO Tt- TT o 1— 1 c . 00\O Hh 0\ in m is, rooo O m n N (M " .01727 .0002983 .0002343 .2090 •3I9I7 4.784 38 .01524 .0002323 .0001824 .1623 .21045 6.160 39 .01321 .0001746 .0001370 .1219 .08616 8.201 40 .01219 .0001486 .0001167 .1039 .01663 9.625 41 O.OII18 0.0001249 0.0000982 0.0873 2.94105 "■45 42 .OIOl6 .0001032 .0000813 .0722 .85827 13.86 43 .00914 .0000836 .0000656 .0584 .76675 17.11 44 .00813 .0000661 .0000519 .0462 .66445 21.65 4S .007 1 1 .0000506 .0000397 •0354 .54847 28.28 46 0.00610 0.00003716 0.0000292 0.0260 2.41457 38.5 47 .00508 .00002581 .0000203 .0180 .25621 55-4 48 .00406 .00001652 .0000129 .0115 .06239 86.6 49 .00305 .00000929 .0000073 .0065 3.81251 154.0 50 .00254 .00000645 .0000051 .0045 .65415 221.8 Smithsonian Tables. 64 CONSTANTS OF COPPER WIRE. according to the British Standard Wire Gauge. Metric Measure. Temperature o° C. Density 8.90. Electrical Constants. Table 68. Resistance and Conductivity. Gauge Number. Ohms per Metre. Log. I Metres per Ohm. Ohms per Gramme. Grammes per Ohm. O.OOOI286 4.10907 7779- 0.000000 1 140 8770000. 7-0 .OOOI493 •17398 6699. .OOOOOO1537 6504000. 6-0 O.OOOI722 4.23605 5814. O.OOOOOO2046 4887000. 5-o .0002009 •30289 4979- .OOOOOO2784 3592000. 4-0 .0002322 •36593 4306. .OOOOOO3721 268700O. 3-o .0002653 .42376 3769- .OOOOOO4857 2059000. 2-0 .0003061 .48592 3266. .OOOOO06319 1 583000. O.OOO3571 4-55277 2801. O.OOOOO08798 I I 370OO. 1 .0004218 .62510 2371- .OOOOOI2275 814700. 2 .0005061 .70421 1976. .OOOOOI7671 565900. 3 .0005971 •77604 1675. .OOOOO24600 406500. 4 .OOO7151 ■85434 1398. .OOOOO35279 283500. 5 O.OO08718 4.94041 H47-I O.OOOO05244 190700. 6 .0010375 3-°' 599 9639 i .OOOOO9350 107000. 7 .OOI2554 .09877 796.6 .OOOOI0874 91960. 8 .0015499 .19029 645-2 .000016573 60340. 9 .0019615 .29259 509.8 .OOOO26547 37670. 10 0.002388 3-378io 418.7 O.OOO03936 25410. 11 .002978 •47295 335-8 .00006092 16420. 12 .003796 •57934 263.4 .00009945 .00017398 10060. "3 .005022 .70083 199.1 5748. 14 .006199 •79235 161.3 .00026518 377 1- 15 O.OO7846 3.89465 127.45 O.0004238 2359.6 16 .010248 2.01064 97.58 .0007246 1 380. 1 17 18 .013949 • '4453 71.69 .0013425 744-9 .020086 .30289 49-79 .0027837 359-2 19 .024798 ■39441 40.32 .0042428 235-7 20 O.03138 2.49671 31.86 0.005398 185.25 21 .04099 .61270 24-39 .011594 86.25 46.56 22 •05579 ■74659 17.92 .021479 2 3 .06640 .82217 15.06 .030421 32.87 24 .08034 .90495 12.45 •044539 22.45 2 5 O.09919 .11949 .14672 2.99647 1-07733 .16649 10.082 8.369 6.816 0.06782 .09851 ■14853 14-745 10.151 6.732 26 27 28 .17391 .24034 5-750 .20869 4.792 3-3i8 29 .20901 .32017 4.784 .30142 3° O.2388 •2755 •3214 •3797 •4555 0.5564 .6950 .8927 1. 1885 •3949 1.660 I.378 10 .44017 .50701 ■57944 .65846 1-74539 .84200 .95070 0.07501 •M453 0.2201 1 4.187 3.629 3.112 2.634 2.196 1-7973 •4388 .1202 0.8414 .7169 0.6024 0-3936 ■5238 .7126 •9947 I-43I3 2.136 3-333 7.019 9-747 I3-424 19.01 2.5407 1 .9091 1-4033 1-0053 0.6987 0.46816 .30003 •14247 .10260 ■07449 0.05260 31 32 33 34 35 36 37 38 39 40 41 2.009 2.480 3-I38 4.099 5-579 8.034 12.554 22.318 32.138 .30289 •39441 .49671 .61270 0.74659 .90495 1.09877 .34865 .50701 •4979 •4033 .3186 .2440 0.1792 .1245 ■0797 .0448 .0311 27.84 42.43 67.96 115.94 210.4 445-4 1087.4 3436-7 7126.3 .03592 •02357 .01471 .00863 0.004753 .002245 .000920 .000291 .000140 42 43 44 45 46 47 48 49 50 Smithsonian Tables. 65 Table 69. SIZE, WEIGHT, AND ELECTRICAL Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers Size and Weight. Gauge Diameter Square of Diameter Sections in Founds Log. Feet Number. in Inches. (Circular Inches). Sq. Inches. Foot. per Pound. 0000 0.454 O.2061 0.16188 O.6246 1.79561 1. 60I ■ 000 .425 .1806 .14186 •5474 .73828 I.827 00 .380 .1440 .H341 •4376 .64107 2.285 . : o •340 .1156 .09079 •3503 .54446 2-855 i i 1 0.300 0.09000 O.07069 O.2727 7-43574 .38814 3.666 2 .284 .08065 •06335 .2444 4.091 ; 3 .259 .06708 .05269 •2033 .30810 4.919 4 .238 .05664 .04449 .1717 ■23465 5.826 ; 5 .220 .04840 .03801 .1467 .16634 6.818 6 0.203 O.O4I 2 1 O.03237 0.12488 r.09649 8.008 7 .180 .O324O •02545 .02138 .09818 2.99204 IO.185 8 .165 .02723 .08250 .91647 12.121 9 .148 .02190 .01720 .06638 .82202 15.065 10 •134 .OI796 .01410 .05441 •73571 18-379 11 0.120 O.OI44OO O.OII310 O.04364 2.63986 22.91 12 .109 .OIl88l .009331 .03600 ■55635 27-77 '3 .095 .OO9O25 .007088 •02735 .02088 •43695 36.56 ! : H .083 .006889 .005411 •31965 47.90 ! s .072 .OO5184 .004072 .01571 .19616 63.65 16 0.06? .058 O.OO4225 0.0033183 0.012803 2.10733 78.10 17 .OO3364 .0026421 .010194 .00835 98.10 18 .049 .OO24OI .0018857 .007276 3.86189 1 37-44 '9 .042 .OOI764 .0013854 •005346 .72800 187.06 20 •035 .OOI225 .0009621 .003712 .56963 269.40 21 0.032 O.OOIO24 0.0008042 0.003103 3.49180 3 Z2 -3 22 .028 .OOO784 .00061 58 .002376 ■37581 420.9 23 .025 .OO0625 .0004909 .001894 •27738 528.0 24 .022 .OOO484 .0003801 .001467 .16634 681.8 25 .020 .000400 .0003142 .001212 .08356 824.9 26 0.018 O.OOO324 O.OOO2545 0.0009818 4.99204 1018. 27 28 .016 .OOO256 .0002011 .0007758 .88974 1289. .014 .OOOI96 .0001539 .0005940 ■77375 1684. 29 .013 .OOOI69 .0001327 .0005121 ■70939 r 953- 3° .012 .OOOI44 .0001131 .0004364 .63986 2292. 31 0.010 0.000100 O.OOOO7854 0.00030304 4.48150 33°o. 32 .009 .000081 .00006362 .00024546 .38998 4074. 33 .008 .000064 .00005027 .00019395 .28768 5156. 34 .007 .000049 .00003848 .00014849 .17169 6734. 35 .005 .000025 .OOOO1963 .00007576 5-87944 13200. 36 0.004 0.000016 O.OOOOI257 0.00004849 5.68562 20620. 66 Table 69. CONSTANTS OF COPPER WIRE. according to the Birmingham Wire Gauge. British Measure. Temperature o° C. Density 8.90. Electrical Constants. Ohms per Foot. Resistance and Conductivity. Log. Feet per Ohm. Ohms per Pound. Pounds per Ohm. Gauge Number. O.OOOO4752 .00005423 .OOO06784 .00008474 O.OOOI088 .0001214 .OOOI460 .OOOI729 .0002024 O.OOO2377 .0003023 .0003598 .0004472 .0005455 O.OO06802 .0008245 .OOI0854 .0014219 .0018896 O.OO2318 .002980 .004080 •°°5553 .007996 0.009566 .012494 .015709 .020239 .024489 0.02887 .03826 .05796 .06802 0.09796 .12095 .15306 .19991 .39182 0.61222 5.67692 •73425 .83146 .92807 4.03679 .08439 .16443 .23788 .30618 4.37604 .55606 .65051 .73682 4.83267 .91618 3-°3558 .15287 .27636 3.36520 •47417 .61064 •74453 .90289 I-9 8 °73 2.0967 1 •I95I5 .30618 •38897 2.46048 .58279 .69877 •763H .83266 2.99103 1.08254 .18485 .30083 ■59309 T.78691 21040. 18440. 14740. 1 1800. 9188. 8234. 6848. 5783- 4941. 4207. 3308. 2779. 2236. 1833- 1470.2 1212.9 921.3 703-3 529.2 43 I -3 335-6 245- 1 180.1 125.1 104.54 80.04 63.66 49.41 40.83 34-64 26.13 20.01 17.25 14.70 10.209 8.269 6-533 5.002 2.552 1.663 0.0000761 .0000991 .0001 550 .0002419 0.0003991 .0004969 .0007183 .0010074 .0013799 0.001903 .003079 .004361 .006737 .010025 0.01559 .02290 .03969 .06811 .12028 0.1811 .2923 .5607 1.0388 2.1541 3-083 5-259 8.275 13-799 20.203 29.41 49-32 84.14 113.18 155-88 323-2 492.7 789.2 1346.3 5i7i-9 12627. 13140- 10090. 6451. 4i34- 2505.8 2012.5 1392.2 992.6 724.7 525.26 324.76 229.30 148.43 99-75 64.148 43.670 25-195 14.682 • 8.3:4 5-5225 3.421 1 I-7835 0.9627 •4643 0.32439 .19015 .12085 .07246 .04950 0.034006 .020275 .011885 .008835 .006415 0.0030936 .0020290 .0012671 .0007420 .0001933 0.00007920 0000 000 00 o 1 2 3 4 5 6 7 8 9 10 11 12 '3 H '5 16 17 18 '9 20 21 22 23 24 25 26 27 28 29 3° 31 32 33 34 35 36 Smithsonian Tables. 67 Table 70. SIZE, WEIGHT, AND ELECTRICAL Size, Weight, and Electrical Constants of pure hard drawn Copper Wire of different numbers Size and Weight Square of Grsmraes Metres Gauge Diameter in Diameter Section in Log. Number. Centimetres. (Circular Cms.). Sq. Cms. per Metre. per Gramme. OOOO I-I53 2 I.3298 I.0444 929.5 2.96826 O.OOIO76 OOO .0795 •1653 .9152 814.6 .91093 .001228 00 0.9652 O.9316 •73'7 651.2 .81372 .001536 O .8636 .7458 •5858 521-3 .71711 .001918 1 0.7620 O.5806 0.4560 405-9 2.60839 O.OO2464 2 .7214 .5216 .4087 3 6 3-7 .56079 .002749 3 .6579 .4328 •3399 302.5 .48075 .003306 4 .6045 ■3655 .2870 255.4 .40730 .003915 S .5588 •3 IZ 3 .2452 218.3 •33899 .004581 6 0.5156 0.2659 0.20881 185.84 2.26914 0.005381 7 .4572 .2090 .16417 146.11 .16469 .006844 8 .4191 .1756 •13795 122.78 .08912 .008145 9 •3759 ■1413 .11099 98.78 I.99467 .010124 IO ■3404 .1158 .09098 80.98 .90836 .012349 11 0.3048 0.09290 0.07297 64.94 I.81251 O.01540 12 .2769 .07665 .06160 54-83 .73900 .01824 '3 •2413 .05823 •04573 40.70 .60960 .02457 H .2108 •04445 .03491 3t- 7 •4923 1 .03219 15 .1829 •03345 .02627 23-43 •36981 .04268 16 0.16510 0.027258 0.021409 19.054 I.27998 0.05248 17 •H732 .021703 .017046 15-171 .18101 .06592 18 .12446 .015490 .012166 10.828 ■03454 ■09235 19 .10668 .011381 .008938 7-955 O.90065 .12571 20 .08890 .007903 .006207 5-524 •74229 .18103 21 0.08128 0.006606 0.005189 4.618 O.66445 O.2165 22 .07112 .005058 •003973 3-536 •54847 .2828 z 3 .06350 .004032 .003167 2.820 •45003 ■3547 24 .05588 ■003123 .002452 2.183 •33899 .4581 25 .05080 .002581 .002027 1.804 .25621 ■5544 26 0.04572 0.0020903 0.0016418 1. 461 1 O.16469 0.6S44 27 .04064 .0016516 .0012972 ■ I 545 .06239 .8662 28 •03556 .0012645 .0009932 0.8839 T.94641 I - I 3 I 3 29 .03302 .0010903 .0008563 .7621 .88204 .3122 3° .03048 .0009290 .0007297 .6494 .81251 ■5399 31 0.02540 0.0006452 0.0005067 0.4510 I-654I5 2.217 32 .02286 .0005226 .0004104 ■3653 .56263 2.738 33 .02032 .0004129 .0003243 .2886 •46033 3-465 34 .01778 .0003161 .0002483 .2210 •34435 4-525 35 .01270 .0001613 .0001267 .1127 .05209 8.870 36 0.01016 0.0001032 0.000081 1 0.0722 5.85827 13.861 Smithsonian Tables. 68 Table 70. CONSTANTS OF COPPER WIRE. according to the Birmingham Wire Gauge. Metric Measure. Temperature o° C. Density 8.90. Electrical Constants. Resistance and Conductivity. Gauge Number. Ohms Metres Ohms Grammes per Metre. Log. per per per Ohm. Gramme. Ohm. O.OOOI559 4.19290 6414. O.OOOOOO1677 5962000. 0000 .0001779 .25024 5620. .OOOOOO2184 4578000. 000 .0002226 •34745 4493- .OOOOOO3418 2926000. 00 .OOO2780 .44406 3597- .OOOOOO5333 18750OO. O.OOO3571 4-55 z 77 2800. O.OOOOO08798 1 1 37000. 1 .0003985 .60038 2510. .OOOOOIO955 912800. 2 .0004791 .68041 2087. .OOOOO15837 631400. 3 .0005674 •75386 1763- .0000022210 450200. 4 .0006640 .82217 1506. .OOOOO30420 328700. 5 O.OO07799 4.89202 1282.2 O.OOOOO4196 238300. 6 .0009257 ■99647 1080.3 .000006789 147300. 7 .0011804 3.07205 847.2 .OOOO09615 104000. 8 .0014672 .16649 681.6 .OOOOI4853 67330. 9 .0017898 .25280 558-7 .OOOO22103 45240. 10 O.OO2232 3-34865 448.1 O.OOOO3437 2910O. 11 .002643 .42216 378.3 .OOOO4822 20740. 12 .003561 -55 I 57 280.8 .OOO08749 »43°- 13 .004665 .66886 214.4 .00015016 6660. 14 .006185 ■79' 35 161.7 .OOO26396 3789- 15 O.O07607 3.881 19 131.46 O.OOO3992 2504.9 16 .009553 .98016 104.68 .0006297 1588.O 17 18 .OI3385 2.12662 74-71 .OOI2362 808.9 .018219 .26052 54-89 .0022902 436.6 19 .026235 .41888 38.12 .0047489 210.6 20 O.03138 2.49671 31.86 O.O06796 147.14 86.25 54.82 32.87 21 .04099 .61270 24-39 .011594 22 .05142 •7i"3 19.45 .018243 23 .06640 .82217 15.06 .030421 24 •08034 .90495 12.45 •044539 22.45 2 5 O.09919 .12583 2.99647 1.09877 10.08 7-947 O.06789 .10874 14-731 9.196 26 27 28 29 30 .16397 .19016 .22138 .21476 •279!3 •34865 6.099 5- 2 59 4-5 r 7 .18550 •24951 ■34367 5-391 4.008 2.910 O.3214 •3968 .5022 ' - 6 S59 1.2855 1-50701 •59853 .70083 .81682 0.10907 3.112 2.520 1. 991 1.525 0.778 O.7126 I.0862 17398 2.9861 1 1 .4020 1.4032 0.9206 •5748 ■3349 .0877 31 32 33 34 35 2.0086 0.30289 0.498 27.8370 0.0359 36 Smithsonian Tables. 69 Table 71 . STRENGTH OF MATERIALS.* (a) METALS. Name of metal. Aluminium wire Brass wire, hard drawn . Bronze, phosphor, hard drawn " silicon " " . Copper wire, hard drawn Gold t wire .... Iron,{ cast .... " wire, hard drawn . " " annealed Lead, cast or drawn Palladium t .... Platinum t wire Silver t wire .... Steel, mild, hard drawn . " hard " " . Tin, cast or drawn . Zinc, cast .... " drawn .... Tensile strength in pounds per sq. in. 3OOOO-40OOO 5OOOO-I 50OOO 1 1 OOOO- 1 4OOOO 950OO-1 1 5000 6000O-7OOOO 380OO-4IOOO I3OOO-290OO 80OOO-I 20000 50OOO-60OOO 2600O-33OOO 39OOO 50OOO 4200O IOOOOO-200000 1 50000-33000 4OOO-50OO 7OOO-I3O0O 22000-30000 (i) STONES AND BRICKS. Name of substance. Resistance to crush- ing in pounds per sq. in. Basalt Brick, soft " hard " vitrified Granite . Limestone Marble . Sandstone Slate 18000-27000 300-1500 1500-5000 9000-26000 17000-26000 4000-9000 9000-22000 4500-8000 1 1 000-30000 (c) TIMBER. Name of wood. Tensile strength in pounds per sq. in. Resistance to crushing in pounds per sq. in. Ash . Beech Birch Chestnut . Elm . Hackberry Hickory . Maple Mulberry . Oak, burr . " red . " water " white Poplar Walnut . 11000-21000 11000-18000 1 2000-1 8000 10000-13000 12000-18000 10000-16000 1 5000-25000 8000-12000 8000-14000 1 5000-20000 13000-18000 1 2000-1 6000 20000-25000 10000-1 5000 8000-14000 6000-9000 9000-10000 5000-7000 4000-6000 6000-10000 7000-12000 6000-8000 7000-10000 5000-7000 4000-6000 6000-9000 5000-8000 4000-8000 * The strength of most materials is so variable that very little is gained by simple tabulation of the results which have been obtained. A few approximate results are given for materials of common occurrence, mainly to indicate the limits between which the strength of fairly good specimens may lie. Some tables are also given indicating the rela- tion of strength to composition in the case of alloys. It has not been thought worth while to state these results in other than the ordinary inch pound units. t On the authority of Wertheim. t The crushing strength of cast iron is from 5.5 to 6.5 times the tensile strength. Notes. — According to Boys, quartz fibres have a tensile strength of between 116000 and 167000 pounds per square Leather belting of single thickness bears from 400 to 1600 pounds per inch of its breadth. Smithsonian Tables. jq PHYSICAL 'ROPERTIES OF STEEL * Table 72. Percentages of S8 2 3 ■3 O •1 = Q..I. 1) O U © Pi § «H Sn s. P. Si. C. Mn. Cu. Co. Ni. Sb. to' go h'o u R « > S.s eft 1= u I a 3 .004 .014 .084 .145 .257 .020 .002 .008 .010 216 379 246 9-5 106 3°-9 .009 '.id .009 .020 .023 .021 .016 2S2 434 260 12.3 129 32.6 .on .109 .042 •051 .028 .028 .044 276 481 234 17.4 119 27.5 .027 .24V .216 .036 .072 .027 .048 .070 322 529 243 24.7 117 24.9 .014 .029 ■"37 .161 .121 .001 trace trace 317 534 277 18.4 151 32.0 trace •°39 .084 •234 .000 .014 .036 .057 •"5 260 605 250 TS-fi no 20.8 .008 •034 •°73 .316 .064 .008 .016 .023 419 649 263 37-9 130 22.3 .056 "3 .007 •139 •105 •364 .076 .107 478 687 261 46.3 no rS.i .004 .024 .087 •447 .072 .005 .018 .023 461 7S ,5 785 271 46.0 124 18.6 .058 .128 .013 .254 ■341 .278 .045 .065 487 293 55-o 9i '5-5 .066 .099 .016 .326 •525 .306 •°54 .078 549 793 255 S8.0 38 5-6 .002 .022 .123 ■595 .124 .001 .007 .006 480 828 267 42.7 '5 1 21.0 .008 .062 .071 •447 ■493 .007 .040 .065 484 859 284 38.2 174 22.7 .041 .125 .028 •355 .404 ■253 .049 .102 543 880 2S4 55-9 49 6.7 .062 .136 .018 •39° .584 •344 •°73 .110 505 953 259 73-7 44 5-6 .002 .020 .096 .652 .061 .030 .007 .018 5io 955 269 50.2 112 13-7 .002 .026 .164 •935 .099 .004 .018 .016 557 957 278 6S.3 123 16.6 •°43 .104 .074 •75^ ■4D5 •346 .052 .120 652 1010 237 94-6 14 i-7 .028 .065 .028 .690 •459 .022 .000 .000 516 1022 285 55-6 37 4.6 .003 .031 .204 .929 .129 .007 .013 .010 590 1050 284 62.1 148 16.0 .038 .092 .070 •387 .625 .210 .050 .US 631 1112 279 83.2 135 r 3-7 .001 . OI s .150 .971 .074 .003 .003 .ois 555 668 1171 262 6s.6 99 9-9 .000 .019 .192 1. 105 .226 .001 .002 .004 1254 272 82.7 93 9.0 .014 .063 ■043 .681 .625 .038 .000 .000 614 1288 260 82.2 108 9.9 Steel containing Chromium. trace .020 .116 .461 .027 trace .000 .612 Cr. 370 810 275 28.3 44.8 no iS-6 .001 .019 •130 •454 .023 .000 .000 .921 Cr. 495 915 287 157 19.1 trace .007 .154 ■639 .050 .008 trace 1.044 Cr. Soo 967 281 S6.1 2S 3-5 — — — .600 — — — 2.200 Cr. 675 1030 — 19.9 1. 100 4.000 Cr. 1770 1778 ~~" ^~ 7-5 Steel containing Tungsten. _ _„ .oq 1.99 ■19 7.81 per cent tungsten . 1464 _ 0.0 — •oq 2.06 2.66 6.73 " " 760 — — 0.0 Same after heatin g to dull red and quenching in oil 940 — — 0.0 - | - .21 | 1.20 1 .35 1 6.45 per cent tungsten . 1900 " o-75 Steel containing Manganese. .06 .08 •37 .72 9.8 j another test .... — 1065 1 190 — — — 22.0 28.9 * The samples here given are arranged in the order of ultimate strength. The table illustrates the great com- plexity of the problem of determining the effect of any given substance on the physical properties. It will Denoticed that the specimens containing moderately large amounts of copper are low in ductility, — that high carbon or high sum of carbon and manganese generally gives high strength. The first specimen seems to indicate a weakening effect of silicon when a moderate amount of carbon is present. It has to be remembered that no table of this kind proves much unless nearly the same amount of work has been spent on the different specimens in the process of manufacture. Most of the lines give averages of a number of tests of similar steels. The table has been largely compiled from the Report of the Board on Testing Iron and Steel, Washington, 1881, and from results quoted in Howe's " Metallurgy of Steel " t The strengths and elasticity data here given refer to bar or plate of moderate thickness, and are in pounds per square inch. Mild steel wire generally ranges in strength between 100000 and 200000 pounds per square inch, with an elongation of from 8 to 4 per cent. Thoroughly annealed wire does not differ greatly in strength from the data fiven in the table unless it has been subjected to special treatment for the purpose of producing high density and ne-grained structure. Drawing or stretching and subsequent rest tend to increase the Young's Modulus. Smithsonian Tables. 71 Table 73. ELASTICITY AND STRENGTH OF IRON.* Area of cross sec- tion of the bar in percentage of the area of the cross section of the pile. Relative values of ultimate strength. Relative values of the stress at the yield point. The variation of the yield point is not regular, and seems to have been much affected by the temperature of rolling. I 2 3 4 5 7 IO IS 125 112 106 104 103 IOI IOO 98 194 170 144 140 130 114 IOO 92 Table 74. APPROXIMATE VARIATION OF THE STRENCTH OF BAR IRON, WITH VARIATION OF SECTION.! Diameter Strength per sq. Total strength of Diameter Strength per sq. Total strength in inches. in. in pounds. bar. in inches. in. in pounds. of bar. 2.2 59OOO 224000 I.I 543 00 52000 2.1 585OO 203OOO 1.0 54000 42000 2.0 580OO 182OOO 0.9 53700 34000 J 1.9 57600 1630OO 0.8 S33 00 27000 1.8 57IOO I450OO 0.7 53000 2OO0O i-7 567OO I29OOO 0.6 52700 14900 1.6 563OO I I 3OOO 0.5 52400 10300 i-5 55900 99000 0.4 52100 6600 1.4 55500 85000 °-3 51900 3700 i-3 55IOO 73000 0.2 51600 1600 1.2 547OO 62000 0.1 51300 400 1 * This table was computed from the results published in the Report of the U. S. Board on Testing Iron and Steel, Washington, j88i, and shows approximately by the relative effect of different amounts of reduction of section from the pile to the rolled bar. A reduction of the pile to 10 per cent of its original volume is taken as giving a strength of 100, and the others are expressed in the same units. t The strength of bar iron may be taken as ranging from 15 per cent above to 15 per cent below the numbers here given, which represent the average of a large number of tests taken from various sources. Notes. — The stress at the yield point averages about 60 per cent of the ultimate strength, and generally lies be- tween 50 and 70 per cent. The variation depends largely on the temperature of rolling if the iron be otherwise fairly pure. According to the experiments of the U. S. Board for Testing Iron and Steel, above referred to, a bar of iron which has been subject to tensile stress up to its limit of strength gains from 10 to 20 per cent in strength if allowed to rest free from stress for eight days or more before breaking. The effect of stretching and subsequent rest in raising the elastic limit and tensile strength was discovered by Wohler, and has been investigated by Bauschinger, who shows that the modulus of elasticity is also raised after rest. The strengthening effect of stretching with rest, or continuous very slowly increased loading, has been rediscovered by a number of experimenters. Smithsonian Tables. 72 Tables 75-77. EFFECT OF RELATIVE COMPOSITION ON THE STRENGTH OF ALLOYS OF COPPER, TIN, AND ZINC* TABLE 75. — Copper-Tin Alloys. (Bronzes.) TABLE 76. — Copper-Zinc Alloys. (Brasses. 4> an . 2S b a v a. ss ft. *3 "S fi-S ■S 11 ■od Ti'o is a ij a a K — e ■i S a, u 0. Founds per square inch. IOO OO 28000 14000 42000 8. 44 95 5 31000 17000 46000 10. 4i go 10 29000 21000 54000 4- 31 85 15 33OOO 260OO 74000 1.6 24 80 20 32000 28000 1240OO 0.5 14 75 25 18000 180OO 1500OO 0.0 8 70 30 6500 65OO 1430OO 0.0 2 65 35 2800 2800 75000 0.0 4 W" . J3 Mja JJ M p v V u *3 pi Founds per square inch. IOO 27000 14000 41000 7 95 5 28000 12000 28000 12 90 10 300OO 10000 29000 l8 2 s 15 32000 9000 33000 25 80 20 34000 8000 39000 33 j 75 25 37000 9000 46000 3 ! 70 3° 41000 1 0000 54000 38 b;5 35 46000 13000 63000 33 60 40 49000 17000 74000 19 55 45 44000 20000 90000 10 1 So 50 30000 24000 1 16000 4 45 55 14000 14000 126000 TABLE 77. — Copper-Zinc-Tln Alloys.? Percentage of Tensile strength in pounds Percentage o Tensile strength in pounds Copper. Zinc. Tin. per sq. in. Copper. Zinc. Tin. per sq. in. 45 5° 5 15000 '25 5 45000 5° 45 5 50000 20 10 44000 5° 40 10 150OO 70 ■ '5 15 37000 43 2 650OO 10 20 30000 40 5 62000 I 5 25 24000 55 ■* 35 10 32500 20 5 45000 3° 15 150OO 75 15 10 45000 (V 3 60OOO 10 15 43OOO 60 35 5 5250O . 5 20 41000 ' 3° 10 40000 \ J $ 5 45000 20 20 1 0000 80 1 I0 10 45000 [3° 5 50000 ' 5 15 47500 65 25 20 10 15 42000 30OOO 85 10 5 10 435 00 46500 15 20 180OO 90 5 5 42000 . IO 25 12000 * These tables were compiled from the results published by the U. S. Board on Testing of Metals. The numbers refer to unwrought castings, and are subject to large variations for individual specimens. t The crushing strengths here given correspond to 10 per cent compression for those cases where the total com- pression exceeds that amount. t For crushing strength, 10 per cent compression was taken as standard. S This table covers the range of triple combinations of these three metals which contain alloys of useful strength and moderate ductility. The weaker cases here given, and those lying outside the range here taken, are generally weak and brittle. The absolute strength may of course be varied by -the method of fusing and casting and certainly can be greatly increased by working. The object of the table is to show relative values, and to give an ,dea of the strength of sound castings of these alloys. Smithsonian Tables. 73 Table 78. ELASTIC MODULI. Rigidity Modulus* ■ Substance. Modulus of Rigidity. Authority. Pounds per Grammes per square inch square centi- -^ 10°. metre -f- 10 6 . Metals : — Aluminium 3.4-4.8 2 4I-33S Thomsont-Katzenelsohn. Brass and Bronze wire 4.6-5.8 320-410 Various. Copper, drawn . 5.6-6.7 393-473 Thomson.t U tl 5.0 35 2 Katzenelsohn. German silver 6.2 7-i 43 z 496 Gray. Gold, pure . 5-6 395 Katzenelsohn. u «< 4.0 281 Thomson.t Iron, soft 9.6 671 Wertheim. " drawn 10-14 700-800 Various. Platinum 8.9 94 622 663 Thomson.t Pisati. Silver . 3-6 3-8 270 256 265 Thomson.t Pisati. Baumeister. Steel, cast 10.6 746 Wertheim. tl u 11.8 829 Pisati. Tin . 2.2 J 54 Kiewiet. Zinc . 5-i 360 Thomson.t u 54 382 Kiewiet. Glass 3-3 3-9 235 273 Wertheim. Kowalski. Stone : — Clay rock n 177 Granite 128 Gray Marble 17 119 • & Slate . 3- 2 229 Milne. Tuff . 2.7 189 Wood . .1-.17 7-12 Gray. * The modulus of rigidity as used in this table may be shortly defined by the olio wing equation : — Mc dulus of igidity - Intens ty of tangential st ress. Distortion in radians. To interpret the equation imagine a cube of the material, to four consecutive faces of which a tangential stress of uniform intensity is applied, the direction of the stress being opposite on adjacent faces. The modulus of rigidity is the number obtained by dividing the numerical value of the tangential stress per unit of area by the number repre- senting the change of the angles on the nonstressed faces of the cube measured in radians, t Lord Kelvin. Smithsonian Tables. 74 Table 79. ELASTIC MODULI. Young's Modulus.* Substance. Young's Modulus. Authority. Pounds per Grammes per square inch square centi- -i- IO S . metre -7- xo°. Metals : — Brass and bronze, cast .... 8.6-10 600-700 Various. Brass, drawn 14-17 IO0O-I 200 (t Copper, drawn 16-18 H 50-1250 « " annealed . IS IO52 Wertheim. German silver, drawn . 17-20 I 209-I 400 Various. Gold, drawn 12-14 813-980 u " annealed 18 558 Wertheim. Iron, cast 8-i7t 550-1200 Various. " wrought 24-30 17OO-2IOO (1 Iron wire n it (t tt *' Lead, cast or drawn . 2.2-2.9 I56-2OO <( Palladium, soft 14 979 Wertheim. " hard . 17 1176 « Platinum, drawn . 23-26 1600-1700 Various. " soft 22 1552 Wertheim. Silver, drawn 10- 10.7 700-750 Various. Steel . 23~3°t 1600-2100 " " hard drawn . To 30 1 900-2 1 00 Various. Tin 417 Wertheim. Zinc 12-14 870-960 Various. Bone .... . abt 2 -3 160 - Carbon 2.2-3.6 iS I -2SS Beetz. Glass .... 8.6-1 1.4 600-800 Various. Ice .... 7-10 500-700 Stone : — Clay rock 4-7 329 Granite 5-9 416 Gray Marble . Slate . H 9.8 400 686 • & Milne. Tuff . 2.7 189 Whalebone Wood . abt 0.85 1.0-2.2 60 70-154 Various. * The Young's Modulus of elasticity is used in connection with elongated bars or wires of elastic material. It is the ratio of the number representing the longitudinal stress per unit of area of transverse section to the number rep- resenting the elongation per unit of length produced by the stress, or : — . ., j . _ Intensity of l ongitudinal stress . Youngs Modulus E i ongation per u mt length. In the case of an isotropic substance the Young's Modulus is related to the elasticity of form (or rigidity modulus) and the elasticity of volume (or bulk modulus) in the manner indicated in the following equation . - ^e^^-t^ the bounding surface of a body (solid, liquid or gas) to the number expressing the change of volume, per unit volume, Pr °t d The modulusrcas. iron varies greatly, not only for different specimens, but in the same specimen for different intensities of stress. It is diminished for tension stress by permanent elongation. t See also Table 72. 6MITHSONIAN TABLES. 75 Tables 80, 81. ELASTIC MODULI. TABLE 80. —Variation of the Rigidity ol Metals with Temperature.* The modulus of rigidity at temperature t is given by the equation «, = » (i -f at + PP +- yfi). Metal. no a y Authority. Brass 320 X io 6 — .OOO455 — .002158 — .OOOOOI36 — K. &L. k 265 X 10 6 — .00000048 — .0000000032 Pisati. Copper 397 X io 6 ■ — .OO2716 -)- .OOOOOO23 — .0000000047 it 390 X io 6 — .000572 — .OOOOOO28 — K. & L. Iron 694 X io 6 — .OOO483 — .OO0OOOI2 — It « 81 1 X io 6 — .OOO206 — .OOOOOOI9 + .000000001 1 Pisati. Platinum 663 X io 6 — .OOOIII — .OOOOOO50 -f .0000000008 «* Silver 257 X io 6 — .000387 — .OOOOOO38 — .000000001 1 Steel 829 X io 5 — .000187 — .OOOOOO59 + .0000000009 TABLE 81. — Ratio p ol Transverse Contraction to Longitudinal Extension under Tensile Stress (Folsson's Ratio). Name of substance. Range of the value of p. Mean of each Final Authority. range. Brass .... , . O.469 ] Everett. " O.340-O.50O O.420 Baumeister. (( — — O.387 Kirchhoff. it — — O.325 ' 0-357 Mallock. u — — °-3 T 5 Wertheim. tt — — O.226 Littmann. Copper . — — O.348 / o-33 2 ) 0-340 Mallock. O.224-O.441 Thomson. Iron — — 0.310 1 Everett. a tt O.250-O.420 O.214-O.268 °- 2 S3 I 0.304 f 0.243 J O.277 Mallock. Baumeister. Littmann. Lead — — °-37S °-375 Mallock. Steel, hard O.293-0.295 O.275-0.328 O.266-O.303 0.294 1 0.294 > 0.296 ) 0.295 Kirchhoff. Okatow. Schneebeli. " soft — — 0.304 i Okatow. <( u — — 0.306 1 Schneebeli. u tt — — 0-253 [ Mallock. tt tt — — o-333 J Goetz & Kurz. Zinc O.180-0.230 0.205 0.205 Mallock. Ebonite . — — — 0.389 " Ivory — — about 0.500 <( Pararnn . — — — 0.500 a Cork — — — 0.000 it Caoutchouc (for small extensions) M (i (* O.370-O.640 0.505 ) 0.500 ) 0.502 ( Rbntgen. | Amagat. Jelly 0.500 0.500 Maurer. Katzenelsohn gives the following values, together with the per centage variation 6 between o° and ioo° C. Substance. p S 15.7 3-9 34 2.5 3-7 5-5 12.2 * According to the experiments of Kohlrausch and Loomis (Pogg. Ann. vol. 141), and of Pisati (N. Cim. (3) vols. 4, 5). Smithsonian Tables. 7 6 Table 82. ELASTICITY OF CRYSTALS.* ^^^■V^&^^&^SJT"**" P™?*^. ™t from the crystal. These bars « /3 V, a, ft yi a „ d TVv, represent «f^WJ f - d the . COTr «pondmg Elastic Moduli deduced. The symbols dimensions oAheprSrJ , with Terence to thiS" T'" 65 « £ he lengt , h ' the greater and the less transverse compression, and Tis the modulus for term inalSSv "nfl*? P*^ E iS the modulus for extension ° r r lermm a' rigidity. I he moduli are in grammes per square centimetre. Barite. ioi°_ E — 16.13^+ 18.51^*+ I o. 4 2 7 4 + 2( 3 8.79 J 3V+ 13.217V + 8.88a 2 2 ) io 10 tj 69.520* + 1 17.660* +'i 16.467* + 2(20.i6j3V + 85.297V 4- 127.35^^) Beryl (Emerald). 10™ ■g- = 4-32S sin 4 ^ + 4.619 cos*0 + 13.328 sin 2 cos 2 ^ where fa fa are the angles which the length, breadth, and thickness of the specimen make with the principal axis of the crystal. Tji- = 1 5.00 — 3.675 cos 4 2 — 17-536 COS 2 COS 2 0i Fluor spar. 10W — = 13.05 - 6.26 (a 4 + 0* + y) 10 10 -ijr- = 58.04 — 50.08 (0 2 7 2 + 7 2 o 2 + o 2 2 ) Pyrites. io 10 — = 5.08 — 2.24 (a 4 + 0* + -y 4 ) io 10 ijr-= 18.60— 17.95 (0V+ 7 2 « 2 + a 2 2 ) Rock salt. io 10 -g- = 33-48 - 9.66 (a* + 4 + -y 4 ) io 10 -^ = 1 54.58 — 77.28 (jBV + 7 2 « 2 +a 2 /3 2 ) Sylvine. i E i° = 75-i-48.2(o 4 +i8 4 + 7 4 ) io 10 -^- = 306.0 — 192.8 (0 V + 7 2 <* 2 + a 2 2 ) Topaz. io 10 -g- = 4.341 o 4 + 346o0 4 + 3-77 IT 4 + 2 (3-8790 V + 28. 567V + 2. 39 a 2 2 ) io 10 -^- = i4-88o 4 + 16-54/8* + 16.457 4 + 3O-890V + 40.897V + 43-5ia 2 2 Quartz. io 10 -g- = 12.734 (1 — 7 2 ) 2 + 16.693 (1 -7 2 )7 2 + 9-7057 4 -8-46007 (3<» 2 -<8 2 ) io 10 -^- = 19.665 + 9.o6o7 2 2 + 22.g847 2 7i 2 — 16.920 [( 7 + p yi ) ( 3 «ai — 00,) — 272 )] * These formulae are taken from Voigt's papers (Wied. Ann. vols. 31, 34, and 35). Smithsonian Tables. 77 Table 83. ELASTICITY OF CRYSTALS. Some particular values of the Elastic Moduli are here given. Under E are given moduli for extension or compression in the directions indicated by the subscripts and explained in the notes, and under T the moduli for torsional rigidities round the axes similarly indicated. (a) Regular System.* Substance. E„ Authority. Fluor spar Pyrites . . Rock salt . Sylvine . . Sodium chloride Potash alum . Chrome alum Iron alum . . 1473 X 10° 3530 X io 6 416 X io 6 403 X io 6 401 X io 6 372 X io 6 405 X io 6 181 X io 6 161 X io 6 186 X io 6 1008 X io 6 2530 X io 6 346 X io 6 339 X io 6 209 X io 6 196 X io 6 319 X io 6 199 X io 6 177 X io 6 910 X io 6 2310 X io 6 311 X io 6 345 X 10° 1075 X io 6 129 X io 6 655 X io 6 Voigt.t Koch.J a Voigt. Koch. Beckenkamp.l (b) Rhombic System.| Substance. Barite Topaz E, 620 X io 6 2304 X io 6 540 X io 6 2890 X io 6 959 X io 6 2652 X io 6 376 X io 6 2670 X io 6 702 X 10" 2893 X io 6 E, 740 X 10° 3180 X io 6 Authority. Voigt. Substance. Barite Topaz Ti 2 — 1*2 1 283 X io 6 1336 X io 6 Ti a — T 3 293 X io 6 1353 X io 6 To 9 — To 121 X IO 6 1104X IO 6 Authority. Voigt. In the Monoclinic System, Coromilas (Zeit. fur Kryst. vol. 1) gives G sum ( E„„ = 887 X io 6 at 21.9 to the principal axis. (E min = 313X10° at 75.4 Mica \ '^™* i = 22I 3 X 10° in the principal axis. I E^ia = 1554 X io 6 at 45 to the principal axis. In the Hexagonal System, Voigt gives measurements on a beryl crystal (emerald). The subscripts indicate inclination in degrees o£ the axis of stress to the principal axis of the crystal. £0 = 2165X10°, £45=1796X10°, E 90 = 23i2 X io 6 , To = 667X10°, P90 = 883X10°. The smallest cross dimension of the prism experimented on (see Table 82), was in the principal axis for this last case. In the Rhomeohedric System, Voigt has measured quartz. The subscripts have the same meaning as in the hexagonal system. E =iO3oXio 6 , E_ « = 1305X10°, E +45 = 8soXio°, E90 = 785 X 10°, T = 508X10°, T 90 = 348X10°. Baumgarten IT gives for calcspar E =5oiXio°, E_ 46 = 44i X 10°, E +45 = 772 X 10°, E 8 o = 79oXio°. * In this system the subscript a indicates that compression or extension takes place along the crystalline axis, and distortion round the axis. The subscripts b and c correspond to directions equally inclined to two and normal to the third and equally inclined to all three axes respectively. t Voigt, " Wied. Ann." vol. 31, 34-35. X Koch, "Wied. Ann." vol. 18. § Beckenkamp, "Zeit. fur Kryst." vol. 10. II The subscripts r, 2, 3 indicate that the three principal axes are the axes of stress ; 4, 5, 6 that the axes of stress are in the three principal planes at angles of 45 to the corresponding axes. IT Baumgarten, " Pogg. Ann." vol. 152. Smithsonian Tables. 78 Tables 34-87. COMPRESSIBILITY OF CASES.* Th dep£t"r S e Mb^S?" w ^ £*£*%/& £ ° r ?*«?' P ressure * ™* temperatures, and hence show the arbitrary. The tejperatura are in cTmfg'ade degreed u * "'^^ ° r in atm ° s P heres - th * «*»» ««* TABLE 84. -Nitrogen. Pressure in Relative values of /» at — metres of mercury. i7°-7 30°. 1 5°°-4 75°-5 IOO°.I £ 2745 287 5 3080 3330 3575 60 2740 2875 3100 336o 3610 100 2790 2930 3170 344 5 3 6 95 140 2890 3040 327S 3S5° 3820 180 30I5 31.S0 339° 367S 3950 220 3'40 328.S 353° 3820 4090 260 3290 344° 3t>8s 397 5 4240 300 345° 3600 3840 4I3 4400 320 3S2S 3°75 3915 4210 4475 TABLI 85.- Hydrogen. Pressure in metres of Relative values of pv at — mercury. 170.7 400.4 60° 4 8i°.i IOO . 1 30 2830 3°45 3235 3430 3610 60 2885 3110 3295 35°° 3680 IOO 2985 3200 3400 3620 3780 140 3080 330° 35°° 3710 3880 180 3i«5 3420 3620 3«3° 4010 220 3290 3520 372S 3930 4110 260 3400 3&25 3«3° 4040 4220 300 35°° 373° 3935 4140 4325 320 355° 37So 399° 4200 4385 TABLE 88. — Methano. Pressure in metres of Relative values of pv at — mercury. i 4 °.7 2 9 °-5 40°.6 60° 1 79°.8 IOO . 1 3° 2580 2745 2880 3100 _ . 60 2400 2590 2735 2995 3230 3460 IOO 2275 2480 2640 2935 3180 3435 140 2260 2480 2655 2940 3190 3460 180 2360 2560 2730 3015 3260 3525 1 220 25IO 2690 284O 3125 3360 3625 TABLE 87. — Ethylene. Pressure in metres of Relative values of pv at — mercury. i6°. 3 2o°3 30°. I 4o°.o 5o°.o 6o°.o 7 o°.o 79°-9 8 9 °-9 IOO°.0 3° 1950 2055 2220 24IO 2580 1875 2715 2865 2970 3090 3225 60 8lO 900 1 190 !535 2100 2310 2500 2680 2860 90 1065 III5 1 195 1325 1510 I7IO 1930 2160 2375 2565 120 1325 1370 1440 1540 1660 I780 1950 21 1 5 2305 2470 150 1590 1625 169O 1785 1880 1990 2125 2250 2390 2540 180 1855 1890 1945 2035 2130 2225 2450 2450 2565 2700 210 2IIO 2145 2200 2285 2375 247O 2680 2680 2790 2910 240 2360 2395 2450 2540 2625 272O 29IO 2910 3015 3125 270 2j5lO 2640 27IO 2790 2875 2965 315° 3*5° 3380 3240 3345 300 2860 2890 2960 3040 3125 3215 3380 3470 356o 320 3°35 3065 3 I2 5 3200 3285 3375 3545 3545 3625 3710 * Tables 84-89 are from the experiments of Amagatj "Ann. de chim. et de phys.," 1881, or " Wied. Bieb.," 1881, p. 418. Smithsonian Tables. 79 Tables 88-90. COMPRESSIBILITY OF CASES. TABLE 88. — Carton Dioxide. Relative values o pv at — Pressure in mercury. l8°.2 35°-i 4O .2 5o°.o 6o°.o 7 o°.o 8o°.o 90°.o ioo°.o 3° liquid 2360 2460 2590 2730 2870 2995 3120 3225 50 - 1725 1900 2145 z 33° 2525 2685 284S 2980 80 625 750 8 P I20O 1650 1975 2225 2440 263s no 825 93° 980 1090 1275 I550 1845 2105 2325 140 1020 1 1 20 "75 1250 1360 I5ZS 1715 1950 2160 170 1210 1310 1360 1430 1520 1645 1780 1975 2135 200 1405 1500 1550 1615 1705 l8lO 1930 2075 2215 230 1590 1690 173° 1800 1890 1990 2090 22IO 2340 260 1770 1870 1920 1985 2070 2166 2265 2375 2490 290 1950 2060 2100 2170 2260 2340 2440 2550 265s 320 2135 2240 2280 2360 244O 252S 2620 2725 2830 TABLE 89. — Carbon Dioxide.* Pressure in atmospheres. Value of the ratio ^vfp\v y at — 50° 100° 200° 250 O.725 1.440 2.850 1.0037 1.0075 1. 1045 1. 002 1 1.0048 1.0087 1.0009 1.0025 1 .0040 I.O0O3 I.O0I5 1.0020 TABLE 90. — Air, Oxygen, and Carton Monoxide at Temperature Between 18° and 22°.t The pressure p x is in metres of mercury ; the product $v is simply relative. Air. Oxygen. Carbon monoxide. P jto > pv P fi> 2407 26968 24.07 26843 24.06 27147 34-9° 26908 34-89 26614 34-91 27102 45.24 26791 - - 45-25 27007 55-3° 26789 55-5° 26185 55-52 27025 64.00 26778 64.07 26050 64.00 27060 72.16 26792 72.15 25858 72.17 27071 84.22 26840 84.19 25745 84.21 27158 101.47 27041 101.46 25639 101.48 24420 i33- 8 9 27608 133-88 25671 '33-90 28092 177.60 28540 177.58 25891 177.61 29217 214.54 29585 214.52 26536 214.54 30467 250.18 3°572 — - 250.18 31722 304.04 32488 3°3-03 28756 304.05 33919 * Similar experiments made on air showed the ratio Pvlf-jpi to be practically constant. t Amagat, " Compte Rendu," 1879. Smithsonian Tables. 80 Tables 91 , 92. RE b£ r,ON BE TWEEN PRESSURE, TEMPERATURE AND VOLUME OF SULPHUR DIOXIDE AND AMMONIA.* TABLE 91. — Sulphur Dioxide. Original volume iooooo under one atmosphere of pressure and the temperature of the experi- ments as indicated at the top of the different columns. c II Corresponding Volume for Ex- periments at Temperature — Volume. Pressure in Atmospheres for Experiments at Temperature — 58°.o 99°-6 i8 3 °2 58°.o a 9 °6 l8 3 °2 10 12 14 16 18 20 24 28 32 36 40 to 70 80 90 100 120 140 160 8560 6360 4040 9440 7800 6420 53IO 4405 4030 3345 2780 2305 1935 1450 3180 2640 2260 2040 1640 »375 1 130 93° 790 680 545 43° 325 1 0000 9000 80OO 7000 60OO 50OO 4000 3500 3000 2500 2000 I50O 1000 500 9.60 IO.40 11.55 12.30 I3-I5 14.00 14.40 9.60 IO-35 II.85 I3-°5 14.70 16.70 20.15 23.OO 26.40 30-I5 35.20 39.60 29.IO 33-25 40.95 55.20 76.OO 117.20 TABLE 92. —Ammonia. Original volume iooooo under one atmosphere of pressure and the temperature of the experiments as indicated at the top of the different columns. c Corresponding Volume for Ex- Pressure in Atmosph eres for Experiments V 1. b periments at Temperature — Volume. at Temperature — 1/1 S 4 6°.6 99°-6 i8 3 °-6 3o°.2 46° 6 99°-6 i8 3 c .o IO 950O _ _ I OOOO 8.85 9-50 - 12.5 7 oP 7035 - 9000 9.60 IO.45 - '5 20 5880 63 S 4645 4875 8000 IO.40 II.50 12.00 13.60 - 2 5 - 3560 3S35 7000 II.05 13.00 ~* 3° - 2875 3J§5 6000 II. 80 14-75 15-55 35 - 2440 2680 5000 12.00 16.60 18.60 19.50 40 - 2080 2345 4000 _ i8-35 22.70 24.00 45 5° _ 1795 1490 2035 1775 3500 - 18.30 25.40 27.20 55 - I250 1590 30OO - — 29.20 3I-50 60 - 975 145° 2500 - - 34-25 37-35 70 - — 1245 2O0O _ _ 41.45 45-5° 80 90 100 - - 1125 1035 950 1500 IOOO - - 49.70 59-65 58.00 93.60 * From the experiments of Roth, " Wied. Ann." vol. n, Smithsonian Tables. 81 Table 93. COMPRESSIBILITY AND BULK MODULI OF LIQUIDS. c , d w Calculated values of .2o S 8*3 S °"« s" bulk modulus in — Liquid. Temp. C. Compre per unit ume per Pressur range o; sure in mosphe Authority. Grammes per sq. cm. Pounds per sq. iu. Acetone . . . . 14 110 8-7-35-4 Amagat .* . . . 94 X io 6 1.34 Xio 5 Benzene . . . . 16 90 8.12-37.2 tt 115 " I.64 " (t 1 5-4 87.I 1-4 Pagliani & Palazzo 119 " I.69 " a 50. 1 III 1-4 tt 93 " I.32 " Carbon bisulphide 78 — Colladon & Sturm '33 " I.89 " it tt IS 62.6 — Quincke . . . . 165 " 2.35 " <( « 15.6 87.2 8-35 Amagat 119 " I.69 " (( a 100 174 8-35 " 59 " I.84 " Chloroform . . . 8.5 62.5 1.267 Grassi . 165 " 2.35 " a 9.2 62.6 4.247 it 165 " 2-35 " it 12 64.8 1.309 tt 159 " 2.26 " Ether . . '3 168 8-30 Amagat 61 " 0.87 " it a 99 99 555 523 8.6-13.5 8.6-36.5 tt 18.6 " 19.8 " 0.26 " 0.28 " a 63 300 8.57-22.29 it 34-4 " 0.49 " (i 63 293 8-57-34-33 if 35-3 " 0.50 " " . . 25.4 190 8.46-34.22 tt 54-4 " 0.77 " Ethyl alcohol 10 94-5 1-2 Colladon & Sturm 109 " 1.55 " It ft 12 73-3 1-456 Tait . 140 " 2.00 " tl tl 14 101 8.5-37.12 Amagat 102 " 1.45 " tt tt 28 86 150-200 Barus 120 " 1.71 " tl It 28 81 1 50-400 tt 127 " 1.81 " tt tt tt It 65 65 no 100 1 50-200 150-400 tt 94 " 103 " i-34 " 1.47 " It tt 100 168 150-200 tt 61 " 0.87 " tt a tt it 100 132 320 150-400 150-200 tt 78 " 32 " 1. 1; " 0.46 " tl tt 185 274 1 50-300 tt 38 " 0.54 " tl It 185 245 1 50-400 " 42 " 0.60 " It It 310 4200 1 50-200 tt 2.5 " 0.036 " tl tl it it 310 310 2200 1530 150-300 150-400 tt tt 4-7" 6.7 " 0.067 " 0.095 " Ethyl chloride 12.8 156 8-53-13-9 Amagat 66.3 " 0.94 " tt tt 12.8 151 8-53-36-45 ti 68.5 " 0.97 " tt tt 61.5 256 I2-65-34-36 tf 40-3 " 0.57 " tt it 99 510 12.79-19.63 tt 20.3 " 0.29 " it tt 99 495 12.79-34.47 tt 20.9 " 0.30 " Glycerine 20.53 25.1 — Quincke 411. 2 " 5-85 " Mercury - . 3-38 1-30 Colladon St Sturm 3058.0 " 43-5 " " 3-92 — Amagat 2629.0 " 37-4 " Methyl alcohol !3-5 90.4 1. 01 2 Grassi . 1 14.5 " 1.63 " tt tt r 3-5 91.1 „ 7 ' 5I 3 tt 113.1 " 1. 61 " it it 100 221 8.68-37.32 Amagat 046.3 " 0.66 " Nitric acid . 20.3 338-5 '-32 Colladon Si. Sturm 030.2 " °-43 " Oils : Almond 17 55-19 Quincke 187.7 " 7 tt 2.67 Olive . 20.5 14.84 63-32 — tt 163.0 " 2.32 " Paraffine 62.69 — De Metz 164.5 " 148.3 " 2-34 " 2.11 " Petroleum . 16.5 69.58 — Martini Rock . . . 19.4 74-58 — Quincke 138.4 " 1.97 " Rape seed . 20.3 59.61 — " ! 74-3 " 2.48 " Turpentine . 19.7 79.14 — tt 130.7 " 1.86 " Sulphur dioxide . 302.5 1-16 Colladon & Sturm °34-4 " 0.49 " Toluene .... 10 79 — De Heen .... 130.7 " 1.86 " Xylene .... 10 73-8 140.0 " 1.99 " Smithsonian Tables. 82 Table 93. COMPRESSIBILITY AND BULK MODULI OF LIQUIDS. §■3! . " cumpueo. irom uarn - Constants of Nature," and L t When the temperature is not given, ordinary atmospheric temperature is to be understood. Smithsonian Tables. 86 Table 97. DENSITY OR MASS IN GRAMMES PER CUBIC CENTIMETRE AND POUNDS PER CUBIC FOOT OF THE METALS. Metal. Physical state. Grammes per cubic centi- metre. Pounds per cubic foot. E Authority. Sodium .... O.97-O.99 605-618 <( Solid . . . 0.9519 59-4 97-6 1 Vincentini and ) Omodei. « Liquid . . . O.9287 58.O 97.6 it At boiling pt. O.7414 46-3 Ramsay. Strontium . — 2.50-2.58 1 56-161 Matthieson. Thallium — II.8-II.9 736-742 Tin . . Cast. . . . 7.290 455 Matthieson. " Wrought . . 7.300 455 (I Crystallized . 6.97-7.18 435-448 a Solid . . . 7-1835 454 226 ) Vincentini and j Omodei. a Liquid . . . 6.988 43 6 226 Titanium t — 5.3OO J 4 l Thorium J — 9.4-IO. I 587-630 Tungsten — 19.120 "93 Roscoe. Uranium — 18.33-18.65 1143-1163 Zinc . . Cast . . . 7.04-7.16 439-447 u Wrought . . 7.190 449 ti Liquid . . . 6.480 404 Roberts & Wrightson. Zirconium — 4.140 258 Froost. Table 9£ . MASS IN GRAMMES PER CUBIC CENTIMETRE AND IN POUNDS PER CUBIC FOOT OF DIFFERENT KINDS OF WOOD. The wood is supposed to be seasoned and of average dryness. Wood. Alder . Apple . Ash . - Basswood. See Linden Beech . . Blue gum Birch . . Box . . Bullet tree Butternut Cedar . Cherry Cork . Ebony . Elm . - Fir or Pine, American White " Larch . . « Pitch . • » Red . • « Scotch . " Spruce . " Yellow • Grammes per cubic centimetre. O.42-O.68 O.66-O.84 O.65-O.85 O.70-O.90 0.84 O.5I-O.77 0.95-1. 1 6 1.05 0.38 0.49-0.57 0.70-0.90 0.22-0.26 1.11-1.33 0.54-0.00 o.35-°-5° 0.50-0.56 0.83-0.85 0.48-0.70 0.43- - 53 0.48-0.70 0.37-0.60 Pounds per cubic foot. 26-42 41-52 40-53 43-56 5 2 32-48 59-72 65 24 3°-35 43-56 14-16 69-83 34-37 22-31 3'-35 5 2 -53 3o-44 27-33 3°-44 23-37 Grammes per cubic centimetre. Greenheart Hazel . . Hickory . Iron-bark Laburnum Lancewood Lignum vitse Linden or Lime-tree Locust .... Mahogany, Honduras " Spanish Maple . . Oak . . Pear-tree . Plum-tree Poplar Satinwood Sycamore Teak, Indian '• African Walnut . . Water gum . Willow . . 0.93-1.04 0.60-0.80 0.60-0.93 1.03 0.92 0.68-1.00 I-I7-I-33 0.32-0.59 0.67-0.71 0.56 0.85 0.62-0.75 0.60-0.90 0.61-0.73 0.66-0.78 0-35-0-5 0.95 0.40-0.60 0.66-0.88 0.98 0.64-0.70 1.00 0.40-0.60 Pounds per cubic foot. 58-65 37-49 37-58 64 42-62 73-83 20-37 42-44 35 53 39-47 37-56 38-45 41-49 22-31 59 24-37 41-55 61 40-43 62 24-37 • t SnlyTtS^ I The lower va^ue for thorium represents mrpure material. Smithsonian Tables. °7 Table 99. DENSITY OF LIQUIDS. Density or mass in grammes per cubic centimetres and in pounds per cubic foot of various liquids. Liquid. Grammes per cubic centimetre. Pounds per cubic foot. Temp. C. Acetone Alcohol, ethyl " methyl . " proof spirit . Anilin Benzene Bromine ... Carbolic acid (crude) . Carbon disulphide Chloroform ... Ether Glycerine . . . . Mercury ... Naphtha (wood) . Naphtha (petroleum ether) . Oils: Amber Anise-seed . Camphor . Castor Cocoanut . Cotton seed Creosot Lard . . . . Lavender . Lemon Linseed (boiled) Mineral (lubricating) . Olive . . . . Palm . . . . Pine . . . . Poppy Rapeseed (crude) " (refined) Resin Train or Whale . Turpentine Valerian . Petroleum . . . . (light) . . . Pyrol igneous acid Sea water . . . . Soda lye ... . Water 0.792 0.791 0.810 0.916 i-°35 0.899 3-i8 7 0.950-0.965 1.293 1.480 0.736 1.260 13-59° 0.848-0.810 0.665 0.800 0.996 0.910 0.969 0.925 0.926 1.040-1.100 0.920 0.877 0.844 0.942 0.900-0.925 0.918 0.905 0.850-0.860 0.924 0.915 0.913 0.955 0.918-0.925 0.873 0.965 0.878 0.795-0.805 0.800 1.025 1.210 1. 000 49.4 49.4 5°-5 57-2 64.5 56.x 199.0 59.2-60.2 80.6 9 2 -3 45-9 78.6 836.0 52.9-50.5 41.5 49.9 61.1 56.8 60.5 57-7 60.2 64.9-68.6 57-4 54-7 52.7 58.8 56-2-57-7 57-3 56.5 53.0-54.0 57-7 57-i 57.0 59.6 57-3-57-7 54.2 60.2 54-8 49.6-50.2 49.9 64.0 62.4 o u o o o o o o 15 15 18 o o o o 15 15 16 15 15 16 15 \l 16 15 20 15 15 15 r 5 15 15 ;i 16 o 15 o r 5 17 4 Smithsonian Tables. 88 Table 1 0O DENSITY OF CASES. The following table gives the specific gravity of gases at o° C. and 76 centimetres pressure relative to air at o° and 76 centimetres pressure, together with their mass in grammes per cubic centimetre and in pounds per cubic foot. Gas. Sp. gr. Grammes per cubic centimetre. Pounds per cubic foot. Air 1. 000 O.OOI293 O.0807I Ammonia 0.597 O.OOO770 O.O4807 j Carbon dioxide 1.529 O.OOI974 O.I2323 Carbon monoxide O.967 0.001234 O.07704 Chlorine 2.422 O.OO3133 O.19559 ( from Coal gas < I to O.340 O.450 O.OOO42I O.OO0558 O.02628 O.03483 Cyanogen I.806 O.OO2330 O.14546 Hydrofluoric acid .... 2.370 O.OO2937 0-I833S Hydrochloric acid . . I.250 O.OO1616 0.10088 Hydrogen O.0696 O.OOOO90 0.00562 Hydrogen sulphide .... I.IC-t O.OOI476 O.09214 Marsh gas 0-559 O.OOO727 O.04538 Nitrogen 0.972 O.OOI257 O.07847 Nitric oxide, NO .... 1.039 O.OOI343 O.08384 Nitrous oxide, N2O .... i-5 2 7 O.OO1970 O.12298 Oxygen 1. 105 O.OOI430 O.08927 Sulphur dioxide .... 2.247 O.OO2785 O.17386 :j Steam at ioo° C 0.469 O.OO0581 O.03627 Smithsonian Tables. 89 Table 101 . DENSITY OF AQUEOUS SOLUTIONS.* The following table gives the density of solutions of various salts in water. The numbers give the weight in grammes per cubic centimetre. For brevity the substance is indicated by formula only. Weight of the dissolved substance in ioo parts by weight of the solution. u Substance. p. E H Authority. 5 10 "5 20 25 30 4° 5° 60 K 2 .... I.047 1.098 '•'53 1.214 1.284 1-354 i-5°3 1.659 1.809 IS- Schiff. KOH . I.040 1.082 I.O27 1.076 1.229 1.286 1.410 1-538 1.666 '5- " Na 2 . . . 1-073 1. 144 I.218 1.284 1-354 1. 42 1 '•557 1.6S9 1.829 'S- NaOH . . . 1.058 1.114 H69 1.224 1.279 l S 3 l 1.436 '■539 1.642 '5- " NH 3 .... 0.978 0.949 O.94O 0.924 0.909 0.896 — — ~ 16. Carius. NH4CI . . . 1. 01 5 1.030 I.O44 1.058 1.072 - - - - iS- Gerlach. KC1 . . . . 1-031 1.065 I.099 i-i35 - - - - — 'S- NaCl. . . . i-°35 1.072 1. 110 1. 150 1.191 - — — — 15- LiCl .... 1.029 1.057 I.085 1. 116 1.147 1.181 1.255 - - 'S- CaCl 2 . . . 1. 04 1 1.086 1. 132 1. 181 1.232 1.286 1.402 - *~ '5- CaCl 2 + 6H 2 1.019 1.040 1. 06 1 1.083 1. 105 1.128 1. 176 1.225 1.276 18. Schiff. A1C1 8 . . . 1-035 1.072 I. Ill I-I53 1. 196 1. 241 1.340 - - IS- Gerlach. MgCl 2 . . . 1. 041 1.085 1-13° 1. 177 1.226 1.278 - - - IS- MgCl 2 +6H 2 1.014 1.032 I.O49 1.067 1.085 1-103 1.141 1.183 1.222 24. Schiff. Z11CI2 . • • 1.043 1.089 i-i35 1.184 1.236 1.289 1.417 i-5 6 3 1-737 19.5 Kremers. CdCl 2 . . . 1.043 1.087 1-138 '■193 1.254 I-3I9 1.469 1-653 1.887 19.5 a SrCl 2 . . . . 1.044 1.092 I-I43 1.19S 1.257 1-321 - - - iS- Gerlach. SrCl 2 + 6H 2 1.027 1-053 1.0S2 1. in 1.042 1. 174 1.242 i-3*7 - 'S- " BaCl 2 . . 1.045 1.094 1.147 1.205 1.269 — - - IS- " BaCl 2 +2H 2 1-035 1-075 1.1 19 1.166 1.217 1-273 — — - 21. Schiff. CuCl 2 . . . 1.044 1. 091 1.155 1.221 1. 291 1.360 i-5 2 7 - - 17-5 Franz. NC1 2 . . • • 1.048 1.098 I-I57 1.223 1.299 - - - - 17-5 HgCl 2 . . . 1.041 1.092 - - - - - 20. Mendelejeff. Fe 2 Cl 6 . • • 1.041 1.086 1-13° 1.179 1.232 1.290 1-413 1-545 1.668 17-5 Hager. PtCU. . . . 1.046 1.097 I-I53 1. 214 1.285 1.362 1.546 I-7S5 - — Precht. SnCl 2 +2H 2 1.032 1.067 1. 104 I-I43 1.185 1.229 1.329 1.444 1.5S0 iS- Gerlach. SnCl 4 +sH 2 1.029 1.058 1.089 1. 122 1.1 57 1193 1.274 1-365 1.467 iS- " LiBr .... J-033 1.070 1. in 1. 154 1.202 1.252 1.366 1.498 - 19-5 Kremers. KBr .... 1-035 1-073 1. 114 1.1 57 1.205 1.254 1.364 - - 19.5 « NaBr . . . 1.038 1.078 1-123 1. 172 1.224 1.279 1.408 '•563 i9-5 n MgBr 2 . . . 1.041 1.085 i-i35 1.189 1.245 1.308 1.449 1.623 - 19-5 " ZnBr 2 . . . 1.043 1. 091 i-i94 1.202 1.263 1.328 1-473 1.648 ••873 19.5 (( CdBr 2 . . . 1. 041 1.088 i-i39 1. 197 1.258 1-324 1.479 1678 - 19.5 « CaBr 2 . . . 1.042 1.087 i-i37 1. 192 2.250 "■3'3 1.459 1-639 - i9-5 U BaBr 2 . . . 1.043 1.090 1. 142 1. 199 1.260 1-327 1.4S3 1.683 - 19.5 (( SrBr 2 . . . 1.043 1.089 1. 140 1.198 1.260 1.328 1.489 1.693 1-953 19.5 (f KI . . . . 1.036 1.076 1.118 1. 164 1.216 1.269 1-394 1.544 i-73 2 19-5 (1 Lil . . . . 1.036 1.077 1. 122 1. 170 1.222 1.278 1.412 '•573 1-775 19-5 f( Nal . . 1.038 1.0S0 1. 1 26 1.177 1.232 1.292 1.430 1.598 1.808 19.5 (( Znl 2 . . . 1.043 1.0S9 1.138 I-I94 1-253 1.366 1.418 1.648 1-873 19-5 " Cdl 2 .... 1.042 1.086 1. 136 1. 192 1. 251 I-3I7 1.474 1.67S - i9-5 (( Mgl 2 . . . . 1.041 1.086 i-i37 1. 192 1.252 1-318 1.472 1.666 1-913 19-5 (( Cal 2 . . . . 1.042 1.088 1-138 1. 196 1.258 i-3'9 1-475 1.663 1.908 19-5 It Srl a . . . . 1.043 1.089 1. 140 1.19S 1.260 1.328 1.489 1.693 '■953 19.5 u Bal 2 .... 1.043 1.089 1. 141 1. 199 1.263 1 -331 1-493 1.702 1.968 19.5 (( NaClOs . . . 1-035 1.068 1. 106 i-M5 1.18S 1-233 1.329 _ _ 19-5 ct NaBrOs . . . 1.039 1.081 1. 127 1. 176 1.229 1.287 - 19-5 t* KNOs . . . 1-031 1.064 1.099 i-i35 - - - - - IS- Gerlach. NaNOs . . . 1-031 1.065 I.IOI 1. 140 1. 180 1.222 r -3 T 3 1.416 - 20.2 Schiff. AgNOs . . . 1.044 1.090 1. 140 1.195 1-255 1.322 1.479 1.675 1.918 15- Kohlrausch. * Compiled from two papers on the subject by Gerlach in the " Zeit. fur Anal. Chim.," vols. 8 and 27. Smithsonian Tables. 90 DENSITY OF AQUEOUS SOLUTIONS. Table 101 . Weight of the dissolved substance in 100 parts by weight of the solution. Substance. d a H Authority. 5 10 '5 20 25 30 40 50 60 NH 4 NO a . . . 1.020 1.041 I.063 1.085 1. 107 1.131 1. 178 1.229 1.282 17-5 Gerlach. ZnNO s .... I.048 1.095 1. 146 1. 201 1.263 1-325 1. 178 1.456 1-597 - "7-5 Franz. Z11NO8+6H2O . - 1.054 - 1-113 - 1.250 1.329 - 14. Oudemans. Ca(NO s ) 2 . . . 1-037 1-075 1.118 1. 162 1. 211 1.260 1-367 1.482 1.604 17-5 Gerlach. Cu(N0 8 ) 2 . . • I.044 1.093 I-H3 1.203 I.263 1.328 1.47 1 - - 17-5 Franz. Sr(NO s ) 2 • • • I.039 1.083 1. 129 1. 179 - - - - - 19.5 Kremers. Pb(N0 3 )2 • ■ • Cd(NO s ) 2 • • • Co(N0 8 ) 2 . . . I.043 1.091 I-I43 1. 199 I.262 1-332 - - - 17-5 Gerlach. I.052 1.097 1.150 1. 212 I.283 1-355 1-536 t-759 - 17-5 Franz. 1. 045 1.090 I-I37 1. 192 I.252 1.318 1.465 - — 17-5 " Ni(NO B ) 2 ■ • • I.045 1.090 I-I37 1. 192 I.252 1.318 1.465 — !7-5 Fe 2 (N0 8 )« • • ■ I.039 1.076 1.117 1. 160 1. 2IO 1. 261 1-373 1.496 '•657 17-5 Schiff. Mg(N0 8 )2+6H 2 Mn(N0 8 ) 2 +6H 2 I.018 1.038 1.060 1.082 1. 105 1. 129 1. 179 1.232 - 21 I.025 1.052 1.079 1. 108 I.I38 1. 169 1-235 1-307 1.386 8 Oudemans. Gerlach. K 2 C0 8 .... I.044 1.092 1.141 1. 192 1-245 1.300 1.417 1-543 — 15 K 2 CO s +2H 2 . I.037 1.072 1. no 1.150 1. 191 1-233 1.320 1-415 1.511 r 5- Na 2 C0 3 ioH 2 . 1.019 1.038 1.057 1.077 1.098 i.ii8 - - - 'S- Schiff. Hager. ! Schiff. Gerlach. (NH 4 ) 2 S0 4 . . I.027 1.055 1.084 1-113 1. 142 1. 170 1.226 1.287 — 19. 18. Fe 2 (S0 4 )8 • • • I.045 1.096 1.1 50 1.207 1.270 I-336 1.489 — ~- FeS0 4 + 7H20 . I.025 1-053 1. 08 1 1. in 1. 141 i-i73 1.238 — "" 17.2 15 MgS0 4 .... I.051 1. 104 1. 161 1. 221 1.284 — MgSO+7H 2 . I.025 1.050 1.075 I.IOI 1. 129 1.1 55 1.215 1.278 - iS- u Na 2 So 4 + ioH 2 I.019 1.039 1.059 1. 081 1. 102 1. 124 — ~ iS- 18. Schiff. Gerlach. Schiff. CuS0 4 +sH 2 . 1-031 1.064 i.oy8 I-I34 I-I73 1-213 1-398 MnS0 4 + 4H 2 . 1-031 1.064 1.099 I-I3S 1. 174 1. 214 i-3°3 '5- ZnS0 4 +7H 2 . I.O27 1.057 1.089 1. 122 1.1 56 1.191 1.269 J-35 1 1-443 20.5 Fe 2 (SO) 8 +K 2 S0 4 +24H2O . . . 1.026 1.045 1.066 1.088 1.112 1. 141 - - - 17-5 Franz. Cr 2 (SO) 8 +K 2 S0 4 + 24H2O . . I.016 1-033 1.051 1-073 1.099 1. 126 1. 188 1.287 1.454 17-5 " MgSOi + K 2 S0 4 1.138 iS- Schiff. + 6H2O . . . I.032 1.066 I.IOI - (NH 4 ) 2 S0 4 + FeS0 4 + 6H 2 I.028 1.058 1.090 1. 122 1-154 1. 191 - - 19. 19-5 19.5 iS- 13 it it K 2 Cr0 4 . . . • K 2 Cr 2 7 . . • I039 I -°35 1.082 1.07 1 1. 127 1. 108 1.174 1. 126 1.225 1.279 1-397 - - Kremers. Schiff. Fe(Cy) 6 K 4 . . . Fe(Cy) 8 K 3 . • • I.028 i-o59 1.092 ~ I.025 1-053 1- 145 1. 179 ~ Pb(C 2 H 3 2 ) 2 + 3 H 2 . . . • 1-031 1.064 1. 100 I.I37 1.177 1.220 i-3 : 5 1.426 - iS- Gerlach. zNaOH + As 2 6 14. iS- 4- iS- iS- 15- Schiff. + 24H2O . • 1.020 1.042 1.066 1.089 1. 114 1. 140 1. 194 Brineau. Schiff. Kolb. Gerlach. 5 10 "5 20 30 40 60 80 ICO S0 8 • • so 2 . • N2O5 • • I.040 I.0I3 1-033 1.084 1.028 1.069 1. 132 I.045 2.IO4 1. 179 1.063 1. 141 1.096 1.079 1.277 1. 217 I-389 1.294 1.564 1.422 1.840 1.506 _ C 4 H 6 Oe • C 6 H 8 7 • 1.021 1.018 1.047 1.038 I.070 I.058 1. 150 1-123 1.207 1. 170 1-273 Cane sugar HC1 . . HBr . . 1.019 1.025 io-35 1.039 1.050 1-073 I.060 1-075 1. 114 1.082 I.IOI 1. 1 58 1. 129 1. 151 1.257 1. 178 1.200 1.376 1.289 - - 17-5 iS- 14. 13- iS- 17-5 17-5 iS- iS- iS- Kolb. Topsbe. it HI . . H2SO4 • H 2 SiFI 6 • P 2 6 • • P2O5 + 3 H S HNO. . C 2 H 4 2 • O'. 1-037 1.032 1.040 1-035 1.027 1.028 1.007 1.077 1.069 1.082 1.077 1.057 1.056 1.014 1.118 1. 106 1. 127 1. 119 1.086 1.088 1.02 1 1.16c 1.145 1.174 1. 167 1. nc I. IIC I.02J 1. 271 1.223 1-273 1. 271 1. 188 1. 184 1. 041 1.400 1.307 '•383 1.264 1.25c 1.052 1. 501 1.676 i-43* !-37: I.06S i-73 2 1-459 1.075 I.838 1.528 1-055 Kolb. Stolba. Hager. Schiff. Kolb. Oudemans. Smithsonian Tables. 9 1 Table 102. DENSITY OF WATER AT DIFFERENT TEMPERATURES BETWEEN 0° AND 32° C* The following table gives the relative density of water containing air in solution, — the maximum density of water free from air being taken as unity. The correction required to reduce to densities of water free from air are given at the foot of the tabie. For all ordinary purposes the correction may be neglected. The temperatures are for the hydrogen thermometer. Temp. C. .3 .4 .5 .6 .7 .9 — + i 2 3 4 5 6 7 10 ii 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 0.9998742 0.9998742 9287 9671 9897 9968 0.9999886 9656 9278 8 7S 8 8095 0.9997295 6360 5292 4096 2772 °-999 I 3 2 5 897S7 8071 6270 4357 -998233S 0205 77972 5639 3207 0.9970681 68061 5353 2 558 59679 0.9956720 3682 8678 8804 9332 9701 991 1 9966 9870 9625 9232 8697 8021 7208 6259 5178 3969 2633 1 174 7594 7896 6084 4160 4126 8613 9987 7744 5400 2959 0423 7794 5°77 2274 9387 6419 3374 9376 9729 9923 9964 9852 9592 9185 8636 7946 7119 6157 5063 3841 2493 9429 7720 5897 396i 121Z 9767 75 r 4 5160 2709 0164 75 2 7 4801 1989 9094 6118 3066 8547 8922 9419 9755 9934 9959 9833 9558 9'37 8 £ 3 7869 7029 6053 4947 3712 2351 0867 9264 7543 57o8 3762 1707 9545 7283 4920 2459 9904 7258 4523 1703 8800 5816 2756 8478 8979 9460 9780 9944 9953 9812 9522 9087 8509 7791 6937 5949 4829 358i 2208 0712 9097 7365 55i8 356i 1496 9325 7°5' 4678 2208 9644 8336 4245 1416 8505 55H 2446 9035 9499 9803 9952 9946 9790 9485 9035 8443 7712 6844 5842 4710 3450 2064 0556 8929 7185 5328 3359 1283 9102 6818 4435 1956 9382 6718 3966 1129 8209 5210 2135 9536 9825 9958 9933 9766 9446 8982 8376 7631 6750 5735 4590 3317 1919 0399 8760 7004 5136 3157 1070 6584 4191 1762 9120 6447 3686 0840 8913 4906 1823 8263 9140 9572 9846 9963 9927 9740 9407 8928 7549 6654 5626 4468 3182 1772 0240 8589 6823 4943 2 953 °855 8653 6340 3947 1448 8S57 6175 3405 7616 4601 1511 9191 9607 9864 9966 9915 9714 9365 8873 8238 7466 6558 55'6 4345 3°47 1624 0080 8418 6640 4749 2748 0640 8427 61 14 37oi "93 S592 5901 3 I2 4 0261 73i8 4296 1198 Sin 9240 9640 9881 9968 9901 9685 9322 8815 8167 738i 6459 5405 4221 2910 1475 9919 8245 6456 4553 2542 0423 8200 5877 3455 °937 SW 5628 2841 9971 7019 39?9 If we put D', for the density of water containing air and D, for the density of water free from air, we get the following corrections on the above table to reduce to pure water : — t= io'(D,-D',) = 25 t= 11 iof(D«-D',)= 31 1 27 2 29 12 13 29 27 3 3i 14 25 4 32 15 22 5 33 16 19 6 33 17 16 7 34 18 12 8 34 19 8 9 33 10 32 20 — 32 4 negligible. * This table is given by Marek in " Wied. Ann.," vol. 44, p. 17a, 1S91. Smithsonian Tables. 92 Table 103. VOLUME IN CUBIC CENTIMETRES AT VARIOUS TEMPERATURES OF A mum C densSy' TRE ° F WATER AT THE temper ature OF MAX,- The water in this case is supposed to be free from air. The temperatures are by the hydrogen thermometer. Temp. C. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 0° 1.000127 120 114 108 102 096 091 086 080 075 I 070 066 . 061 057 052 048 044 040 °37 °33 2 030 027 024 021 019 017 014 012 010 009 3 007 006 004 003 002 002 001 001 000 000 4 000 000 001 001 001 002 003 004 005 007 S 6 1.000008 010 012 014 016 018 020 023 026 029 032 °35 038 041 045 049 °53 057 061 065 7 8 069 074 079 084 089 094 099 l°5 no 116 122 128 134 141 147 '54 160 167 174 181 9 189 196 204 211 219 227 235 244 252 260 10 1.000269 278 287 296 3°5 3H 324 334 343 353 ii 363 373 383 394 405 415 426 437 448 459 12 47i 482 494 5°5 517 529 54i 553 681 566 578 ! ! 3 59i 603 616 629 642 655 668 695 838 709 14 722 736 7,50 765 779 794 809 823 853 15 1.000868 884 899 914 93° 945 961 977 993 009 16 1025 042 058 °75 091 108 125 142 r 59 177 17 194 211 229 247 265 283 3 ™ 319 338 356 ! 18 37 A 393 412 431 450 469 488 507 5 2 7 546 19 566 585 605- 625 645 666 686 707 727 748 20 1.001768 789 810 ?3I 852 874 §25 916 238 960 21 981 003 025 047 069 092 114 137 159 T82 22 2 20 j 438 682 228 2 il 274 297 320 343 367 39i 414 23 462 486 510 534 559 5 8 3 607 632 657 24 707 732 757 782 807 833 858 884 910 25 1.002935 961 987 014 040 665 692 "9 145 172 26 3199 226 253 280 3°7 335 362 389 417 445 27 472 500 812 55 6 584 612 641 669 697 726 28 7S4 783 841 870 899 928 957 987 016 29 4045 075 105 134 164 194 224 529 254 284 315 30 1.004345 375 406 436 467 498 560 izi 199, 59i 622 3' 3 2 653 971 684 003 716 035 748 558 780 1 01 811 '33 843 156 4 907 231 239 264 33 5297 330 363 396 43° 463 497 53° 870 564 597 l 34 631 665 699 733 767 801 83S. 904 939 35 1.005973 60S 042 677 in 145 18T 217 252 2S7 * The table is quoted from Landolt and Bernstein's " Physikalische Chemie Tabellen," and depends on experi- ments by Thiesen, Scheel, and Marek. Smithsonian Tables. 93 Table 104. 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.998145 I.OO1858 25° O.99712 I.00289 — 9 8427 1575 26 687 3H -8 868 S i3!7 27 660 341 — 7 891 1 1089 28 633 368 — 6 9118 0883 29 605 396 — 5 O.999298 1.000702 30 0.99577 I.00425 — 4 9455 0545 3i 547 4 55 486 — 3 9590 0410 32 S l 7 — 2 9703 0297 33 485 518 — I 9797 0203 34 452 551 0.999871 1.000129 35 O.99418 1.00586 1 9928 0072 36 383 621 2 9969 0031 3 l 347 657 3 9991 0009 38 310 694 4 1. 000000 0000 39 273 73 2 5 0.999990 I.OOOOIO 40 0-99235 1.00770 6 9970 0030 41 197 809 7 9933 0067 42 I5 £ 849 8 9886 0114 43 118 889 9 9824 0176 44 078 929 10 0.999747 1.000253 45 0.99037 1. 0097 1 11 9655 0345 46 8996 "I014 12 9549 0451 47 954 057 13 943° 0570 48 910 101 14 9299 0701 49 865 148 15 0.999160 1. 000841 50 0.98820 i.o#i95 16 9002 0999 55 582 1439 *7 8841 1160 60 338 1691 18 8654 1348 65 074 1964 '9 8460 1542 70 7794 ^256 20 0.998259 1.001744 75 0.97498 '■% 21 8047 1957 80 194 22 7826 2177 85 6879 ■J22I 23 7601 2405 90 556 3567 24 73 6 7 2641 95 219 393 1 25 0.997120 1.002888 100 0.95865 1.0J312 Smithsonian Tables. * Rossetti, "Berl. Ber." 1867. 94 Table 105. DENSITY OF MERCURY. D ™£ it 4° r , cuT Trap's oS b ; s c s^' Md ?. e ml rt in c , ubic cemimetres ° f »• «™« Temp. C. Mass in grammes per cub. cm. Volume of 1 gramme in cub. cms. Temp. C. Mass in grammes per cub. cm. Volume of z gramme in cub. cms. — 10° — 9 — 8 — 7 — 6 13.6203 6178 6153 6129 6104 °-°734i95 4329 4463 4596 473° 30° 3i 32 33 34 13.5218 5194 5169 5M5 5120 0-0739544 9678 9812 9945 40079 — 5 — 4 13.6079 6055 6030 0.0734864 4997 35 36 13.5096 5071 0.0740213 0346 _ 3 5131 37 5°47 0480 — 2 6oo S 5265 38 5022 0614 — I 5981 5398 39 4998 0748 I3-5956 °-°735532 40 J 3-4974 0.0740882 I 5931 5666 50 473 1 2221 2 5907 5800 60 4488 35 6t 3 5882 5933 70 4246 4901 4 5857 6067 80 4005 6243 5 6 l3 -gs 0.0736201 90 100 I3-3764 3524 0.0747586 8931 7 5783 6468 no 3284 50276 8 5759 6602 120 3045 1624 9 5734 6736 130 2807 2974 10 I3-5709 0.0736869 140 13.2569 O-0754325 ii 5685 7003 150 2331 5679 12 5660 7137 160 2094 7035 13 5635 7270 170 1858 8394 14 5611 7404 180 1621 9755 15 13.5586 0-0737538 190 13-1385 0.0761 1 20 16 5562 7672 200 1150 2486 17 5537 7805 210 0915 3854 18 55!3 5488 7939 220 0680 5230 19 8073 230 0445 6607 20 I3-5463 0.0738207 240 13.0210 0.0767988 21 5439 8340 250 12.9976 9372 22 5414 8474 260 9742 70760 23 539° 8608 270 9508 1252 24 5365 8742 280 9274 3549 25 I3-534I 0.0738875 290 12.9041 0.0774950 26 53i6 9009 300 8807 6355 27 5292 9143 310 8573 7765 28 5267 9277 320 8340 9180 29 5243 941 1 33° 8107 80600 30 13.5218 0.0739544 340 12.7873 0.0782025 350 7640 3455 1 360 7406 ^ * Marek, " Trav. et Mem. du Bur. Int. des Poids et M<5s." 2, 1883. t Broch, 1. b. Smithsonian Tables. 95 Table 106. SPECIFIC CRAVITY OF AQUEOUS ETHYL ALCOHOL. (a) The numbers here tabulated are the specific eravities at 6o° F., in terms of water at the same tempera- ture, of water containing the percentages by weight of alcohol of specific gravity .7938, with reference to the same temperatures.* ui C ri > C4 O.Q 1 2 3 4 6 6 7 8 9 Specific gravity at is°.s6 C. in terms of water at the same temperature. I. OOOO .9981 .9965 •9947 •993° .9914 .9898 .9884 .9869 •9855 10 .9841 .9828 .9815 .9802 •9789 .9778 .9766 •9753 .9741 .9728 20 .9716 ■9703 .9691 .9678 .9665 •9652 .9638 .9623 .9609 •9593 3° ■9578 .9560 •9544 .9528 •95" .9490 •9470 .9452 •9434 .9416 40 ■939° •9376 ■9356 •9335 •93 : 4 .9292 .9270 .9249 .9228 ,9206 50 O.9184 .9160 •9135 .8908 •9"3 .9090 .9069 •9047 .9025 .9001 .8979 6o .8956 .8932 .8886 .8863 .8840 .8816 •8793 •8769 •8745 70 .8721 .8696 .8672 .8649 .8625 .8603 .8581 •8557 ■8533 .8508 8o .8483 .8459 •8434 .8408 .8382 ■8357 •8331 .8305 .8279 .8254 go .8228 .8199 .8172 .8145 .8118 .8089 .8061 •8031 .8001 •7969 (b) The following are the values adopted by the " Kaiserlichen Normal-Aichungs Kommission." They are basec . on Mendelejeff s formula,! and are for alcohol of specific gravity .79425, at 15 C, in terms of water at is 3 C. ; temperatures measured by the hydrogen thermometer. ttJ o o 1 2 3 4 5 6 7 8 9 Specific gravity at 15 C. in terms of water at the same temperature. I. OOOOO .99812 .99630 .99454 .99284 .99120 .98963 .98812 .98667 .98528 10 •98393 .98262 •98135 .98010 .97888 •97768 .97648 •97528 .97408 •97287 20 .97164 .97040 .96913 .96783 .96650 ■96513 ■96373 .96228 .96080 ■95927 30 •95770 .9560S •95443 ■95 2 73 •95099 .94920 •94738 ■94552 •94363 .94169 40 •93973 ■93773 •93570 ■93365 •93157 .92947 •92734 .92519 •92303 .92088 50 0.91865 .91644 .91421 .91197 ■90972 .90746 .90519 .90292 .90063 •89834 60 89604 ■89373 .89141 .88909 .88676 .88443 .88208 .87974 •87738 .87502 70 87265 .87028 .86789 .86550 .86310 .86070 .85828 .85586 .85342 .82832 .85098 80 84852 .84606 •84358 .84108 ■838S7 .83604 •83349 .83091 .82569 90 82304 .82036 .81763 .81488 .81207 .80923 .80634 •80339 .80040 •79735 (C) The 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 fie gravity of the absolute alcohol being .79391. inste speci no £ c-g = i- rt •* Ph 0,£> 1 2 3 4 6 6 7 8 9 Specific gravity at i5°.56 C. in terms of water at same temperature. 1. 00000 .99847 .99699 •99555 .99415 .98218 •99279 .99147 .90019 .98895 .97808 •9 8 774 10 ■98657 •98543 .98432 ■98324 .98114 .98011 .97909 ■97708 20 .97608 •97507 .97406 •97304 .97201 •97097 .96991 .96883 .96772 .96658 30 .96541 .96421 .96298 .96172 .96043 •95910 •95773 .95632 .95487 •9533 8 40 ■95185 .95029 .94868 .94704 ■94536 •94364 .9418S .94008 .93824 •93636 50 0-93445 •91358 •93 2 5° .93052 •92850 .92646 .92439 .92229 .92015 .91799 .91580 60 ■9"34 .90907 .90678 ■90447 .90214 .89978 .89740 •89499 .89256 70 .89010 .88762 .88511 .88257 .88000 .87740 ■87477 .87211 .86943 .86670 80 •86395 .86116 •85833 •85547 .85256 .84961 .84660 -84355 .80800 .84044 .83726 90 .83400 .83065 .82721 ■82 3 bs .81997 .81616 .81217 .80359 .79891 Smithsonian Tables. * Fownes, " Phil. Trans. Roy. Soc." 1847. t "Pogg. Ann." vol. 138, 1869. 96 DENSITY OF AQUEOUS METHYL ALCOHOL.* Table 107. Densities of aqueous methyl alcohol at o° and 15.56 C, water at 4 C. being taken as 100000. The numbers in the columns a and b are the coefficients in the equation pt = po — at — bP where pt is the density at temperature t. This equation may be taken to hold between o° and 20 C. Percent- age of CH 4 0. Density at o°C. Density at i S "-56 C. Percent- age of CHjO. Density at o°C. Density at i5°.56 C. I 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 1 3 2 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 99987 99806 99631 99462 99299 99142 98990 98843 98701 98S63 ■ 98429 98299 98171 98048 97926 97806 97689 97 573 97459 97346 97233 97120 97007 96894 96780 96665 96549 96430 96310 96187 99907 99729 99554 99382 99214 99048 98726 98569 98414 98262 98m 97962 97814 97668 97523 97379 97235 97093 96950 96808 96666 96524 96381 96238 96093 95949 95802 95655 95506 — 6.0 — S-4 -4.8 — 3-9 — 3-o — 2.2 — 1.2 — 0.2 + 0.9 2.1 3-3 4.8 6.2 7.8 9-5 11.0 12.5 14-5 16.2 18.3 20.0 22.2 24-3 26.4 29.0 31-3 33-8 36.0 38.8 41.1 Equation pt = Po — ai 96057 95921 95783 95643 95500 95354 95204 95051 94895 94734 94571 94400 94239 94076 939" 93744 93575 93403 93229 93052 95367 9521 1 95053 9473 2 94567 94399 94228 94055 93877 93697 935 10 93335 93155 92975 92793 92610 92424 92237 92047 44-36 45.66 46-93 48.17 49-39 50.58 5'-75 52.89 54.01 55.10 56.16 57.20 58.22 59.20 60.17 61.10 62.01 62.90 63.76 64.60 0.705 ■694 .681 .670 .659 0.648 •634 .621 .609 •596 0.581 •569 -55| ■536 .519 0.500 .480 .461 .440 .420 0.398 •373 •35° .321 .291 0.261 .230 .191 .106 a % S H 50 5 1 52 53 54 55 56 5 Z 58 59 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 % 98 99 100 92873 92691 92507 92320 92130 91938 91742 9*544 9*343 9" 39 60 90917 61 90706 62 90492 63 90276 64 90056 65 89835 66 8961 1 67 89384 68 89154 69 88922 70 88687 71 88470 72 88237 73 88003 74 87767 75 87530 76 87290 77 87049 78 86806 79 86561 86314 86066 85816 85564 85310 8505; 84798 84539 84278 84015 83751 83485 83218 82677 82404 82129 81853 81576 81295 81015 91855 91 661 9*465 91267 91066 90863 90657 90450 90239 90026 89580 89358 89133 88676 88443 88208 87970 87714 87487 87262 87021 86779 86535 86290 86042 85793 85542 85290 85035 84779 84521 84262 84001 83738 83473 83207 82938 82668 82396 82123 81849 81572 81293 8jau 80731 80164 79872 79589 65.41 66.19 66.95 67.68 68.39 69.07 69.72 70-35 70.96 71-54 71.96 72-37 72.91 73-45 73-98 74-51 75-o5 75-57 76.10 76.62 77-H 77.66 78.18 78.69 79.20 79-71 80.22 80.72 81.23 81-73 82.22 82.72 83.21 83.70 84.19 84.67 85.16 85.64 86.12 86.59 87.07 87.54 88.01 88.48 88.94 .86 90.32 90.78 91.23 91.68 * Quoted from the results of Dittmar & Fawsitt, " Trans. Roy. Soc. Edin." vol. 3 3- Smithsonian Tables. _ Table 108. VARIATION OF THE DENSITY OF ALCOHOL WITH TEMPERATURE. (a) The density of alcohol at P in terms of water at 4 is given* by the following equation : d t = 0.80025 — 0.0008340^ — 00000029* 2 . From this formula the following table has been calculated. O s V H Density or Mass in grammes per cubic centimetre. 1 2 3 4 6 6 7 8 9 .80625 ■79788 .80541 .80457 .80374 .80290 .80207 .80123 .80039 .79956 .79872 10 .79704 .79620 •79535 ■7945 1 •79367 .79283 .79198 .79114 .79029 20 ■78945 .78860 •78775 .78691 .78606 .78522 ■78437 •78352 .78267 .78182 3° .78097 .78012 •779 2 7 .77841 .77756 .77671 •77585 .77500 ■77414 •77329 (b) Variations with temperature of the density of water containing different percentages of alcohol at 4^ C. is taken as unity, t Water Percent- Density at temp. C. . Percent- Density at temp. C. alcohol by weight. o° IO° 20° 3°° alcohol by weight. o° IO° 20° 3°° O.99988 O.99975 O.99831 0.99579 50 0.92940 0.92182 O.9I4OO O.90577 5 •99135 ■991 13 •98945 .98680 55 .91848 .91074 .90275 .89456 10 .98493 .98409 •98195 .97892 60 .90742 .89944 .89129 .88304 is •97995 .97816 ■97527 .97142 65 •89595 .88790 .97961 .87125 20 .97566 .97263 .96877 ■96413 70 .88420 •87613 .8678I .85925 25 O.971 1 5 O.96672 O.96185 0.95628 75 O.87245 0.86427 O.85580 0.84719 3° .96540 .95998 •95403 •947 5 1 80 .86035 .85215 .84366 •83483 35 •95784 •95 r 74 .94514 ■938i3 85 .84789 •83967 ■83»5 .82232 40 •94939 •94255 ■935" .92787 90 .83482 .82665 .8l80I .80918 45 •93977 •93 2 54 .92493 .91710 95 .82119 .81291 •80433 •79553 50 0.92940 0.92182 0.91400 0.90577 100 O.80625 0.79788 O.78945 0.78096 * Mendelejeff, " Pogg. Ann." vol. 138. t Quoted from Landolt and Bbmstein, " Phys. Chem. Tab." p. 223. Smithsonian Tables. 98 Table 109. VELOCITY OF SOUND IN AIR. Rowland has discussed (Proc. Am. Acad. vol. 15, p. 144) the principal determination of the velocity of sound in atmospheric air. The following table, together with the footnotes and references, are quoted from his paper. Some later determinations -will be found in Table in, on the velocity of sound in gases. K 3 .a .2 T3 t 1 >» "5 O go a It ■3 locity approxi- tely reduced to C. and dry air (mean)." 11 II £ !>S >B I>E° H u 172.56 T. 332.9m. _ 332.6m. 2 - 333-7 " - 332-7 2 1149.2ft. 1131.5 ft. 333-o c 329.6" :( 330-9 2 340.89 m. 33J-36 - 330-8 4 — 33 2 -96 — 332-5 3 340.37 333-62 332.82"* :| 7 339- 2 7 332.62 331.91" — 332.27/ - 332-0 1 336-5° 332.20" - 33»-» 1 338-oi 33 2 - J i 332-37 ~ 4 - - 330-7I — 10 1738 1811 1821 1822 1822 1823 824-5 1839 1844 1868* France . . Diisseldorf India. ■I France Austria . . Holland j Port Bowen Alps . . . France . . 40 120 70 30 88 22 shots 14 " 51 34 149 5°-7^5 C 83°-95 F- 79°-9 F- i 5 °. 9 C. 9°. 4 C. n°.6 C. n°.oC. e -38° F. to +33° F 5°-5 to 9 C. 8°.i7 C. 2° to 20° C. General mean deduced by Rowland, 331-75. Correcting for the normal carbonic acid in the atmosphere, this becomes 331.78 metres per second in pure dry air at 0° C. References. 1 French Academy : " Mem. de l'Acad. des Sci." 1738, p. 128. 2 Benzenburg: Gibberts's " Annalen," vol. 42, p. 1. 3 Goldingham : " Phil. Trans." 1823, p. 96. 4 Bureau of Longitude : " Ann. de Chim." 1822, vol. 20, p. 210 ; also, " ffiuvres d'Arago, ' " Mem. Sci." ii. 1. 5 Stampfer und Von Myrbach : " Pogg. Ann." vol. 5, p. 496. 6 Moll and Van Beek : " Phil. Trans." 1824, p. 424- 7 Parry and Foster : " Journal of the Third Voyage," 1824-5, App. p. 86 ; " Phil. Trans." 1828, p. 97- 8 Savant : " Ann. de Chim." ser. 2, vol. 71, p. 20. Recalculated. 9 Bravais and Martins : " Ann. de Chim." ser. 3, vol. 13, p. 5- 10 Regnault : " Rel. des Exp." iii. p. 533. a I believe that I calculated these reduced numbers on the supposition that the air was rather more than half saturated with moisture. b Reduced to 0° C. by empirical formula. d Mo"? andean Beek found 332.049 at 0° C. for dry air. They used the coefficient .00375 to reduce. I take the numbers as recalculated by Schroder van derKolk. „_.„_.,,. Tau error of 0.21° C. was made in the original. See Schroder van der Kolk, Phil. Mag. 1865. J Corrected for wind by Galbraith. g Recalculated from Savart's results. * This is given as :86 4 in Rowland's table. The original paper is in " Mem. de 1'Institut," vol. „, .868. Smithsonian Tables. 99 Table 110. VELOCITY OF SOUND IN SOLIDS. The numbers riven in this table refer to the velocity of sound along a bar of the substance, and hence depend on the yS?lfS "of "elasticity of the material. ^The elastic constants of most of the materials given in this table ^throuin a somewhat wide range, and hence the numbers can only be taken as rough approximations to the vSity wSch ma™be obtained in fny particular case. When temperatures are not marked, between 10° and zo° is to be understood. Substance. Temp. C. Velocity in metres per Velocity in feet per Authority. o second. second. Metals: Aluminium . 5104 16740 Masson. Brass - 3500 1 1 480 Various. Cadmium - 2307 757° Masson. Cobalt . — 4724 I5S00 " Copper . 20 IOO 3560 3290 1 1 670 I0800 Wertheim. it tt 200 2950 9690 tt Gold (soft) . 20 1743 5717 " a IOO 1720 5640 " » 20O I73S 5691 it Gold (hard) '. '. - 2IOO 6890 Various. Iron and soft steel — 5000 16410 " Iron 20 S^o 16820 Wertheim. it IOO 53°° 1739° " tt 200 4720 I5480 (c " cast steel 20 499° 16360 « tt tt tt IOO 4920 161 50 ' tt tt tt 200 479° IS7I0 ' Magnesium . - 4602 I51OO Melde. , Nickel . - 4973 IO320 Masson. Palladium — 3^° I0340 Various. Platinum 20 2690 8815 Wertheim. " IOO 2570 8437 " « 200 2460 8079 " Silver . 20 2610 8553 tt " IOO 2640 8658 tt u 200 2480 8127 tt Tin - 2500 8200 Various. Zinc - 37°° I2140 " ' Various: Brick . - 3652 1 1980 Chladni. Clay rock . - 3480 1 1420 Gray & Milne. Granite - 395° I2960 tt Marble - 3810 I250O " Slate . - 4510 14800 tt Tuff . - 2850 935° tt <-.i ( fro Glass . . < m - to 5000 6000 16410 19690 Various. tt Ivory . - 3°i3 9886 Ciccone & Campanile. Vulcanized rubber S 5° 54 177 Exner. (black) 31 102 tt " " (red) 69 226 tt « tt tt 70 34 III tt Woods : Ash, along the fibre 4670 1 5310 Wertheim. " across the rings - 1390 457° « " along the rings - 1260 4140 a Beech, along the fibre - 334° 10960 tt " across the rings - 1840 6030 it " along the rings - 1415 4640 tt Elm, along the fibre - 4120. 1351° tt " across the rings - 1420 4665 tt " along the rings - 1013 33 2 4 tt Fir, along the fibre . 4640 15220 tt Maple " — 4110 1347° tt Oak " - 385° 12620 tt Pine - 33 2 ° 10900 tt Poplar " ■ - 4280 14050 tt Sycamore " 4460 14640 " Smithsonian Tables. IOO Table 111, VELOCITY OF SOUND IN LIQUIDS AND CASES. Substance. Temp. C. Velocity in Velocity in metres per second. feet per second. Authority. Liquids: Alcohol .... 8.4 1264 4148 Martini. Ether 23 1 160 3806 Wertheim. Oil of turpentine Water (Lake Geneva) 24 9 1159 1212 x 435 3803 3977 4708 Colladon & Sturm. {from Seme river) " M (( K IS 1437 4714 Wertheim. " « tt (( 30 1528 5513 u Water .... ft 60 3-9 1724 !399 5657 4591 it Martini. I( 13-7 '437 4714 " Gases: Air tt 25.2 1457 333 4780 1092 Dulong. • 33J-6 T087 Wertheim. s • 333 1092 Masson. 33°-7 1085 Le Roux. 332-1 1089 Schneebeli. a 332-5 33!-9 1091 1089 Kayser. Wullner. tt . 33'-7 33 1 - 2 . 1088 1086 Blaikley. Violle & Vautier. « * — 10.9 — 25.7 326.1, 3i7-i 1070 1040 Greely. " • -37-8 3°9-7 1016 " if — 45-6 305.6 33 2 -4 1002 1091 it Stone. Ammonia 4i5 1 361 Masson. Carbon monoxide 337-1 1 106 Wullner. " " 337-4 1 107 Dulong. " dioxide . 261.6 858 i< Carbon disulphide 189 606 Masson. Chlorine 206.4 677 Martini. " 205.3 674 Strecker. Ethylene 314 1030 Dulong. Hydrogen . 1269.5 4165 K tt 1286.4 4221 Zoch. Illuminating gas 490.4 1609 a Methane 422 138S Masson. Nitric oxide 3 2 S 1066 (c Nitrous oxide 261.8 859 Dulong. Oxygen 3I7-2 1041 a Vapors : Alcohol 230.6 756 Masson. Ether 179.2 588 tt Water 401 1315 " (( 96 410 '345 tt Smithsonian Tables. IOI Table 112. _.,.,-«» FORCE OF CRAVITY FOR SEA LEVEL AND DIFFERENT LATITUDES. This table has been calculated from the formula *$=*■„ [i-. 002662 cos 2« * where * is the latitude. Lati- a in cms. per Log. g in inches per Log. 9 in feet per Log. tude <£. sec. per sec. sec. per sec. sec. per sec. 0° 977.989 2-990334 385-°34 2.585498 32.0862 1. 506318 6336 5 8.029 0352 .050 5517 ■0875 10 .147 0404 .096 5570 .0916 6388 15 •339 0490 •173 5655 •0977 6474 20 .600 0605 .275 5771 .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 61 14 .1316 6933 32 .456 0985 .612 £'5° •1343 6969 33 •538 1021 .644 6187 .1370 7005 34 979.622 2.991059 3 8 5- 6 77 2.586224 32.1398 I.507043 35 .707 IO96 .711 6262 .1425 7080 36 •793 "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 1291 .884 6457 .1570 7275 41 •237 1331 .919 6496 .1607 7325 42 •3 2 7 1372 •955 6537 .1630 7356 43 .418 1411 .990 6577 .1659 7395 44 980.509 2.991452 386.026 2.586617 32.1688 1.507436 45 .600 1492 .062 6657 .1719 7476 4§ .691 IS3 2 .098 6698 .1748 7516 47 .782 1573 ■i34 6738 .1778 7557 48 •873 1613 .170 6778 .1808 7597 49 980.963 2.991653 386.205 2.586818 32.1838 1.507637 50 I -°53 1693 .241 6858 .1867 7677 51 •143 I73 2 .276 6898 .1896 7716 5 2 .231 1772 ■3 11 6937 .1924 7756 53 .318 1810 •345 6975 .1954 7794 54 981.407 2.991849 386.380 2.587014 32.1983 1-507833 55 ■493 1887 .414 7053 .2011 7871 56 .578 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 2.278 2070 .576 7235 •2147 8054 65 2234 •723 7400 .2276 8229 70 .600 2377 .849 7542 •2375 8 J 6 l 75 .861 2492 •952 7657 .2460 8476 80 983-°53 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 data given by Harkness (Solar Parallax and Related Constants, Washington, 1891). The force of gravity for any latitude <£ and elevation above sea level k is very nearly expressed by the equation g$=ea(i — .002662 cos 2*) [x— ^(1 — ^)]> where R is the earth's radius, S the density of the surface strata, and A the mean density of the earth. When 8 = we get the formula for elevation in air. For ordinary elevations on land -- is nearly J, which gives for the correction at latitude 45° for elevated portions of the earth's surface 180.6 X-£~ =z 1225.75 — in dynes. 4R R = 386.062 xii: 4R 82.562 — in inch pound units. R = 32.1719 X-— = 40.2149— inpoundals. 4-A. R This gives per xoo feet elevation a correction of .00588 dynes . ) , .00232 inch pound units > diminution* .000193 poundals ) Smithsonian Tablcc. 102 GRAVITY. Table 1 1 3. In p^^iT^cy^ h °^Z^Z^I t et % m ' mti T^ e broU ^t together. They serve to lower than the emulated value for 5^gA^ a ^ 1 ^T^l^;.-^^ I ,P.P°"'. «Wi. a li«£ Place. Singapore Georgetown, Ascension . Green Mountain, Ascension Loan da, 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. -. I u 17' -7 56 -7 57 -8 49 — 10 00 13 04 -"5 55 — '5 57 20 43 20 52 20 56 21 18 3 2 23 — 33 52 — 33 56 35 4i — 36 52 37 20 37 20 37 47 37 47 38 53 39 54 39 58 40 27 40 28 40 44 40 46 41 49 42 49 45 3i 46 12 46 12 46 57 47 23 48 50 51 28 52 3° 54 34 55 59 56 28 57 03 57 07 58 18 59 10 59 32 Elevation in metres. 14 5 686 46 2 18 10 533 3001 3 117 3 2 43 n 6 i 3 1282 1282 114 114 10 1645 122 6s l 348 11 1288 •165 450 100 4°5 4°5 572 466 67 7 49 6 Gravity in dynes. Observed. 978.07 978.24 978.08 978.14 978.36 978.16 978.66 978.52 978.27 978.85 978.90 978.96 979-75 979.67 979.61 979-94 979.67 979.64 979.68 979-95 980.02 980.10 979.68 980.12 980.08 980.09 980.26 979.82 980.34 980.34 980.73 980.58 980.60 980.61 980.67 980.96 981.20 981.26 981.45 981.49 98i-59 981.68 981.66 9 8l -73 981.81 981.82 Reduced to sea level. 978.07 978.24 978.21 978.I5 978.36 978.16 978.66 978.58 978.84 978.85 978.92 978.96 979-75 979-68 979.61 979-94 979.68 979.89 979.92 979-97 980.04 980.10 97998 980.14 980.20 980.15 980.26 980.05 980.37 980.42 980.75 980.64 980.66 980.69 980.74 980.97 981.20 981.27 981.45 981.49 981.59 981.68 981.66 98i-73 981.81 981.82 Refer- ence. 2 3 3 3 3 2 1 2 1 1 4 5 4 5 4 5 6 6 6 4 5 5 7 4 4 4 t 4 4 4 1 Smith : " United States Coast and Geodetic Survey Report for 1884," App. 14. 2 Preston : " United States Coast and Geodetic Survey Report for i860," App. 12. 3 Preston : Ibid. 1888, App. 14. 4 Mendenhall : Ibid. 1891, App. 15. 5 Defforges : " Comptes Rendus," vol. 118, p. 231. 6 Pierce : " U. S. C. and G. S. Rep. 1883," App. 19. 7 Cebrian and Los Arcos : " Comptes Rendus des Seances de la Commission Perma- nente de l'Association Geodesique International," 1893. 8 Pierce: " U. S. C. and G. S. Report 1876, App. 15, and 1881, App. 17." 9 Messerschmidt : Same reference as 7. * In all the values given under references 1-4 gravity at Washington has been taken at 980.100, and the others derived from that by comparative experiments with invariable pendulums. Smithsonian Tables. 103 Table 114. SUMMARY OF RESULTS OF THE VALUE OF GRAVITY to) AT STATIONS IN THE UNITED STATES, OCCUPIED BY THE U. S. COAST AND GEODETIC SURVEY DURINC THE YEAR 1894.* Station. Latitude. Longitude. Elevation. g observed. Atlantic Coast. 1 II / // Metres. Dynes. Boston, Mass 42 21 33 71 03 5° 22 980.382 Cambridge, Mass. 42 22 48 71 07 45 14 980.384 Princeton, N. J. 40 20 57 74 39 28 64 980.164 Philadelphia, Pa. 39 57 06 75 " 4° 16 980.182 Washington, C. & G. S. 38 S3 >3 77 00 32 14 980.098 Washington, Smithsonian . 38 S3 20 77 01 3 Z 10 980. ioot Appalachian Elevation. Ithaca, N. Y. . 42 27 04 76 29 00 247 980.286 Charlottesville, Va. . 38 02 01 78 30 16 166 979.924 Deer Park, Md. 39 2 5 ° 2 79 19 5° 770 979.921 Central Plains. Cleveland, Ohio 41 30 22 81 36 38 210 980.227 Cincinnati, Ohio 39 08 20 84 25 20 245 979.990 Terre Haute, Ind. 39 28 42 87 23 49 151 980.058 Chicago, 111. 41 47 25 87 3° °3 182 980.264 St. Louis, Mo. . 38 38 03 90 12 13 I5 2 979.987 Kansas City, Mo. 39 °5 5° 94 35 2i 278 979.976 Ellsworth, Kan. . 38 43 43 98 13 32 469 979.912 Wallace, Kan. . 38 54 44 101 35 26 IO05 979-741 Colorado Springs, Col. 38 5° 44 104 49 02 1841 979.476 Denver, Col. 39 40 36 104 56 55 1638 979-595 Rocky Mountains. Pike's Peak, Col. 38 5° zo 105 02 02 4293 978.940 Gunnison, Col. . 38 3 Z 33 106 56 02 2340 979.328 Grand Junction, Col. 39 04 09 108 33 56 1398 979.619 Green River, Utah . 38 59 23 no 09 56 1243 979.622 Grand Canyon, Wyo. 44 43 16 no 29 44 2386 979.885 Norris Geyser Basin, Wyo. 44 44 °9 no 42 02 2276 979-936 Lower Geyser Basin, Wyo. 44 33 21 no 48 08 2200 979.918 Pleasant Valley, Jet., Utah 39 5° 47 m 00 46 2I9I 979.498 Salt Lake City, Utah 40 46 04 in 53 46 1322 979.789 Table 115. LENGTH OF SECONDS PENDULUM AT SEA LEVEL FOR DIFFERENT LATITUDES.! e - H3 .5 & .5 ■ U TJ •s£ q , ■S3- rt %i if £ gc % Mo s s bb (J ►J 8 a ti -j 1-1 .005340 sin 2 if .005142 sin 2 $ .005072 sin 2 (f .005679 sin 2 (( .005087 sin 2 (( .005142 sin 2 ^l .005185 sin 2 ^ .005105 sin 2 (I .005262 sin 2 (j 0.993450 0.993976 0-99355° 0-993548 0.993562 0-993395 0.993560 0.993512 o-993554t 0-993S63 0-993549 i 2 3 4 5 6 7 8 9 10 11 0.990910 + -005290 sin 2 tp 0-993555 I2 In iS , from the series of observations used by Dr. Fischer, Dr. G. W. Hill 18 found /= 0.9927148 metre + 0.0050890 p -4 (sin 2 — \) -j- 0.0000979 p -4 cos 2 cos (2m' +29 04') — 0.0001355 p~ 5 (sin 3 — f sin )(j> -j- 0.0001489 p-° (sin 4 — f sin 2 *+ „„ + 0.0007386 p- 8 (sin 8 — f sin — ^) cos 2 cos (2<»' 4- 262 17') -4- 0.0003126 p -0 sin cos 8 cos (30)' + 148 20') + 0.0000584 p- 6 cos 4 * cos (A«>' + 248° 19') , where 6 is the geocentric latitude, «' the geographical longitude, and p a factor, varying with the latitude, such that the radius of the earth at latitude is ap where a is the equa- torial radius of the earth. 1 Laplace : " Traite" de Mecanique Celeste," T. 2, livre 3, chap. 5, sect. 42. 2 Mathieu: " Sur les experiences dupendule;" in " Connaissance des Temps 1816, A 3 d Bret P i^gol 3 " R^cu 3 e 3 ild'Observations geodesiques etc.]' Paris 182,, p 575- 4 Sabine : " An Account of Experiments to determine the Figure of the Earth, etc., by ^^siTgey - ctipara^onles Options du pendule a diverses latitudes ; faites par MM.Bl?t, y Kater?srbine,de Freycinet, et Duperr^j » in " Bulletin des Sciences Mathe- m f PonSlInT": *%&$^-£^*^« Pans ,1829, T. 2, p. 466. l^o^T^^^^ PP- 32-33; and Puissant: "Traits de g^odesie," T. 2 p. 464- rnln „ t > s "Archiv" 9 Unferdinger : " Das Pendel als geodatisches Instrument ; in Grunert s Archiv, l8 io" Fisher : « Die Gestalt der Erde und die Pendelmessungen ; » in " Ast. Nach." 1876, CO ii 8 Helmert: "Die mathematischen und physikalischen Theorieen der hoheren Geo- dasie, von Dr. F. R. Helmert," II. Theil. Leipzig, 1884, p. 241. \\ HmSronomical paper prepared for the use of the "American Ephemeris and Nautical Almanac," vol. 3, p. 339- Se Tcalc«lated fr rXarithmic expression given by Unferdinger. Smithsonian Tables. 105 Table 1 1 7. MISCELLANEOUS DATA WITH RECARD TO THE EARTH AND PLANETS. Length of the seconds pendulum at sea . l eve l =/ = 39.012540 + 0.208268 sin 2 inches. = 3.251045 + 0.017356 sin 2 (f> feet. = 0.9909910 + 0.005290 sin 2

' = 688.2242" sin 2 — 1. 1482" sin 4 + 0.0026" sin 6 =. 00228 v 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. Langley's t experiments give kw = .00166 at ordinary barometric pressure and 10° C. temperature. For planes inclined at an angle a less than 90 to the direction of the wind the pressure may be expressed as P a = FaPsa- Table 118, founded on the experiments of Langley, gives the value of F a for different values of a. 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 118.— Values of T a In Equation P„=F a Poo Plane 30 in. X 4.8 in. Aspect 6 (nearly). Plane 12 in. X 12 in. Aspect 1. Plane 6 in. X 24 in. Aspect \. a K a K a Fa. 0° 5 10 15 20 25 3° 35 40 45 50 0.00 0.28 0.44 0.55 0.62 0.66 0.69 0.72 0.74 0.76 0.78 0° 5 10 15 20 25 3° 35 40 45 50 0.00 0.15 0.30 0.44 0.57 0.69 0.78 0.84 0.88 0.91 0° 5 10 '5 20 25 3° O.OO O.O7 O.I7 O.29 o-43 0.58 0.71 * The pressure on a spherical surface is approximately 0,36 that on a plane circular surface of the same diameter as the sphere ; on a cylindrical surface with axis normal to the wind, about 0.5 that on a rectangular surface of length equal to the length, and breadth equal to the diameter of the cylinder. t The data here given on Professor Langley's authority were communicated by him to the author. Smithsonian Tables. IO8 Table 119. AERODYNAMICS. On the basis of the results given in Table 118 Langley states the following condition for the soaring of an aeroplane 76.2 centimetres long and 12.2 centimetres broad, weighing 500 grammes, -that is, a plane one square foot in area, weighing 1.1 pounds. It is supposed to soar in a horizontal direction, with aspect 6. TABLE 119. -Data ior the Soaring of Planes 76.2X12.2 cms. weighing 600 Grammes, Aspect 6. Inclination to the hori- zontal a. Soaring speed v. Work expended per minute (activity). 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° s 10 is 3° 45 20.0 15.2 I2.4 II. 2 IO.6 II. 2 66 S° 41 37 35 37 24 41 65 86 336 174 474 623 1268 2434 95.0 55-5 34-8 26.5 i-j.o 5.8 209 122 77 58 29 IS In general, if p weight Soaring speed v= II £.- ; F a cos a 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 ^j 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 o, and the angle between the direction of resultant air pressure and the normal to the direction of motion be 0. Then /3 < o, and the soaring speed is -Vfc -, while the activity per unit of weight =z'tan0. i -Fa cos The following series of values were obtained from experiments on moving trains and in the wind. Angle of inclination a = -3 °° +3° 6 ° 9° " Inclination factor F a = 0.20 0.50 0.75 °-9° i°° l -°S tan/3= 0.01 0.02 0.03 0.04 0.10 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. IO9 Tables 120, 121. TERRESTRIAL MACNETISM. TABLE 120. — Total Intensity of the Terrestrial Magnetic Field. This table gives in the top line the total intensity of the terrestrial magnetic field for the longitudes given in the first column and the latitudes given in the body of the table. Under the headings 13, 13.5, and 13.75 '""« ? re s0 ™ 6 - times several entries for one longitude. This indicates that these lines of total force cut the same longitude line more than once. The isodynamic lines are peculiarly curved and looped north of Lake Ontario. The values are for the epoch January 1, 1885, and the intensities are in British and C G. S. units. Longi- tude. 10.5 or II. or 11. 5 or 12.0 or 12.5 or 13.0 or .5994 13.5° .6225 13.75 ° r °34° .4841 .5072 ■5302 ■5533 ■5704 O 67 - - - - - 44-5 45-5 - - - - - - 68 - - - — - 43-i 48.2 - - - - — 70 - - - - - 4i-9 - - - - - - - 72 — — — - — 40.6 — - — — - - — 75 - - - - - 3 6 7 - - — - - — - 76 _ _ _ _ - 3 6 4 - 44-7 - - - - - 77 - - - - - 36.0 - 43- 6 454 - - - - 78 - 22.6 24-5 - - 34-1 - 43-3 45.2 - - - - 80 - 22.8 24-5 27.9 31.2 35-' - 43-9 44.6 - - - - 81 22.8 24.5 27.I 3I.2 35-5 — 41.4 41.9 44-3 45.8 — — 82 - 22.8 24.6 26.4 31-3 35-5 - 41.2 42.1 43-6 45.8 - - 83 22.7 24.8 26.6 31.2 35-2 - 41.0 46.2 - - - - 85 19.6 22.2 25.0 27.9 30.8 34-4 - 40.8 47.6 - - 45-5 46.1 86 I9.8 22-3 - 28.3 30.6 35-3 - 41. 1 48.0 - - 45.2 474 87 20.O 22.5 — 28.6 3°4 35-5 — 41.9 48.4 ~ — 43-2 47-7 90 20.1 22.5 - 29.9 3'-9 36.6 - 41.6 49.1 - - 43-2 48.2 92 20.1 22.3 - 29-3 33-3 37-4 - 41.7 50.2 - - 44-7 4S.2 95 20.0 22.3 - 28.3 33-i 37-2 - 41.2 - - - 43-7 - 100 20.0 22.8 — 30.0 34-i 39-o — 41-4 — — — 42.7 — 105 21.7 244 - 33' 36.1 39-8 - 43° - - - 44.8 - 110 23.2 26.9 3'-2 34-4 37-7 41.6 - 45-2 - - - 47.0 - "5 - 29.I 31.8 36.2 40.1 44-5 - - - - - - - 120 - 3°-7 34-7 37-8 42-3 46.4 - - - - - - - 124 39° 44.2 TABLE 121. —Secular Variation ol the Total Intensity. Values in British units of total intensity of terrestrial magnetic force at stations given in the first column and epochs January 1 of the years given in the lop line. Station. 1840 1845 1850 1865 1860 1865 1870 1876 1880 1885 Cambridge . . 13.48 13-33 13.21 13.22 13-37 '345 '3-49 '3-39 I3- J 4 12.79 New Haven . 1347 13.40 I3-25 13.11 13.20 J 3-33 1341 1341 13.29 '3-°5 New York 13 56 13-5* 13-39 !3-27 I3-32 '3-36 I3-36 ^t '3- : 9 12.99 Sandy Hook . 1370 '3-59 13-3° !3-'7 !3- 2 3 •3-35 13.40 13-39 13-3° '3-!3 Albany . . I3.6S '3-65 1372 13.80 13-87 •3-93 I3-92 13.82 13.61 13-27 Philadelphia . 1352 1344 1345 1338 1347 '3-51 13-55 n-s8 13-57 '3-49 J 3- 2 5 Baltimore . . '3-5° J345 '3-37 13-44 13.46 13.48 13.48 I3-38 13.22 Washington . '343 I3-3 5 !3-3i 13-34 '3-39 '342 1342 I3-38 13.29 13.20 Toronto . . 14.03 13-93 '3-95 r 3-9i 13.82 13.82 13-77 1378 13-78 '376 Cleveland I3-85 13-78 I3-76 12.75 I3-78 1383 13.84 13.81 1374 13.61 Detroit . . . I3-85 13.80 1 37 1 13.68 1372 1375 1376 I3-78 1373 13.62 * Tables 120-125 have been compiled from a very full discussion of the magnetic dip and intensity for the United States and adjacent countries, given in Appendix 6 of the Report of the United States Coast and Geodetic Survey for 1885. Later Reports of the survey have been consulted, particularly in connection with the extrapolation of the values of horizontal intensity to 1890 and 1895, but most of the data are taken from Mr. Schott's Appendix to the 1885 Report. Smithsonian Tables. 110 TERRESTRIAL MAGNETISM. Tables 122, 123. TABLE 122. -Values ol the Magnetic Dip. and latitude 3 o u the dip was 59° on January i "arSwI a y th = table - T °"s, for longitude q 3 the dtvision line in Stable IL i^^^Lii^^^^^SS^^S^S!^. *'° r >»*£»• ■»>& Dip. Longitudes west of Greenwich. ■ 1 66° 70 75° 80° 85° 90° 95° I0O° 105 IIO° 115° 120° 1 24 o 44 o o o 17.9 O 18.4 19.1 19.6 O 45 6 - - - - - 18.7 19.2 19.8 20.3 _ — 19.2 I9.8 20.6 21. 1 _ . 7 8 9 "~ — — 20.0 20.5 21.2 2 1. '8 _ - - 17.9 18.7 - - 20.5 21.2 21.2 21.9 2I.9 22.6 22.5 23.2 2 3-3 24.0 - - 50 I — - - ~ 21.4 22.1 22.7 2.3- 1 24.1 24.7 _ _ 22.2 22.8 23.6 2 4-3 24.8 2 5-5 _ _ _ 2 23.0 2 37 24.4 25.I 25.6 26.3 27.4 _ _ 3 ~ 2 3-3 2 3-9 24-5 25.2 2« 26.5 27.1 28.2 _ ,_ 4 55 6 7 8 - - 24.0 24.7 2 5-5 2 5-3 26.1 26.O 26.8 26.7 27.5 27.2 28.1 28.1 29.0 29.9 - - 24.8 28.9 - - 24.7 2 5 .b 26.4 2b '3 26.9 27.7 27.5 28.3 28.1 28.9 28.9 29.7 30.6 30.6 - - 27.1 29.7 3'-4 — 27-3 27.9 28.5 29.I 29.8 3°-5 31.4 3 2 -3 - _ 9 ~ 28.0 20.7 29.4 30.0 3O.6 3i-5 324 33-3 34-4 - 60 i 2 - - - 28.6 29.9 30.6 29.6 3°-3 3J-3 30.2 30.9 30.8 31-5 3 2 4 3 2 -4 33-3 34-3 33-4 34- 2 35-2 34-3 35-3 36-3 .36.2 37-i : 3'7 3 2 -5 3'-9 33-3 3 — ~ ~~ 31.0 32.0 3 2 7 33-t> 34-2 35- 2 36.2 37-i 38.1 39-° 4 ~ — 3 2 7 33-2 33- 6 34-5 3S- 2 36.1 37- 2 3B-I 39-0 40-3 65 6 - - - 33-5 34-o 34-6 35-5 36.2 37-i 38.2 39-2 4°-3 4i-S — — — 34-3 35-° 35-8 3&-5 .37-2 38.1 39-2 40-3 4i-S 4 2 -5 7 — - 35-' 35-3 35-9 3b.b 37- 2 38.2 39-i 40.2 41.4 42.5 43-6 8 — — 35-o 36.0 3 b.b 3 l' s 38.2 39-2 40.0 41.2 42.4 43-6 447 9 ~~ — 37-o 37-5 37-6 3«-5 39- 2 40.0 41.2 42.2 43-5 44.b 457 70 - - 38.0 38.5 39-o 39-6 40.4 41.0 42.1 43-3 44- S 4S-6 46.9 I — — 39-i 39-5 39-8 40.7 41. 1 41.8 43- 2 44-3 4S7 47.2 47-9 2 — — 40.4 40-3 40.9 41.6 42.1 43-i 44-3 4S-S 47-i 48.6 49.2 3 - 4'7 41.2 41.9 42.2 42.7 43-4 44.4 4S-S 46.9 48.b 50.0 - 4 43-5- 43-' 42.9 43-i 43-4 43-9 44-5 45.6 46.7 4«-3 497 - - 75 44-9 44- S 44-3 44.0 445 45.0 457 46.7 48.0 49- 1 Si.o - - 6 45-7 45-9 45- S 45-4 45-5 46.1 47.1 48.2 49-5 .S°7 - - 7 47-3 47-6 46.7 46.9 47.0 47-4 4»-3 49.4 50.6 - - - - 8 - - - 48.2 48.0 48.8 49-7 5°-7 51.8 - - - - 9 — — — 49-3 49-3 - 51-° 5i-9 - - - 80 " — — 50.4 5°-4 - - - - - - " TABLE 123. — Secular Variation of the Magnetic Sip. Values of magnetic dip at stations given in the first column, and epochs, January i, of the years given in the top line. Station. 1840 1845 1850 1866 1860 1865 1870 1876 1880 1885 Cambridge . 74-25 74.29 74-35 74-40 74.42 74-38 74.26 74.02 73-65 73.12 New Haven 73-47 73-51 73-56 73-6i 73-64 73.62 73-54 73-30 73-" 72.72 New York . 72-75 72-73 72.75 72.78 72.80 72.78 72.71 72.56 72.31 7'-93 Sandy flook 72.63 72.61 72.63 72.66 72.68 72.66 72.59 72.44 72.19 71.81 Albany . . 74-75 74.80 74.88 74.96 75.02 75.02 74-95 74-77 74.46 73-99 Philadelphia 71.99 72.02 72.08 7 2 -i5 72.20 72.21 72.16 72.02 71.77 71.48 71-38 71.16 Baltimore . 71-74 71.66 71.66 71.69 71-74 71-77 71.76 71.67 Washington 71-39 71-39 7i-3» 7I-36 7I-32 71.25 71.15 71.00 70.80 7°-& 74.88 72.78 Toronto . . 75.28 7S- 2 5 75-3 2 75-39 754' 75-35 75- 2 7 75.20 75-°3 Cleveland . 73.22 73-'9 73-21 73-24 73.28 73- 2 9 73- 2 7 73- l8 73-03 Detroit . . 73.61 73-6i 73-63 73.66 73.68 73-69 73-67 73.60 73-47 73.28 Smithsonian Tables. Ill Tables 124, 125. TERRESTRIAL MAGNETISM. TABLE 124. — Horizontal Intensity. This table gives, for the epoch January i, 1885, the horizontal intensity, H, corresponding to the longitudes in the top line and tin: latitudes in the body of the table. At epoch 1K85 the force was increasing for positions above the ; division line, and was decreasing for positions below the division line. H in British units. Longitudes west of Greenwich. H inC.G.S. units. 65° 7°° 75° 80° 85° 90 95° 100° 105° IIO° "5° I20° 124° 2.50 2-75 3.00 3 25 3-5° 3.75 4.00 4.25 4.50 475 5.00 5- 2 5 5.50 6.00 6.25 6.50 6.75 7.00 7-25 O 48 3 45-5 43-2 O 47-3 45.6 43-8 42.2 40.7 O 46.6 45-5 43-6 42.5 41.2 39-6 38.1 36.6 35-i 48.5 47.2 45-8 44.0 42.6 41.5 40.2 38.7 37-4 35-8 34-6 33° 31.0 28.8 49 8 4I8 47.6 46.1 44.6 43-2 42.1 40.4 39-2 37-6 36.2 49.8 48.5 46.7 45.I 43-6 42.4 41.0 39-7 38-4 O 49.I 47.6 45-8 44.6 43-4 41.8 40.4 50. 1 48-S 47.2 45.8 44.6 43-° 41.6 47-3 45-7 44.2 42.8 48.4 46.8 4S-4 O 49.4 O 48.7 47.0 45.2 43-6 41.9 39-6 377 35-6 33-6 49.6 47.6 457 44.2 42.6 39-8 37-4 .1153 .1268 •1383 .149S .1614 .1729 .1844 ■1959 •2075 .2190 .2305 .2422 •2536 .2651 .2766 .2881 ■2997 .3112 .3228 •3343 477 46-3 44.6 42.8 41.1 39-2 37-2 35-2 33-i 3li 28.6 43^ 42.0 40-3 37-7 367 34-8 32-3 28.4 26.1 24.0 21.2 39- 1 37-8 35-9 34-5 3 2 7 31.0 29.8 27.7 22.8 19.9 39-9 38.5 37-o 35-3 33-6 316 29.9 28.0 23.0 20.3 41.0 39-3 38.0 36-3 34-7 3'-9 28.2 23.2 20.5 36-9 35-4 33-8 32.1 30-3 28.1 27-3 22.5 '9-5 33-8 32.2 30.6 29.2 27-3 22.1 27.4 25.8 23.6 20.8 24.1 18.2 TABLE 125. — Secular Variation ol the Horizontal Intensity. Values of the horizontal intensity, H, in British units, for stations given in first column and epochs given in top line The values for 1890 and 1895 have been extrapolated from the values up to 1885. The epochs are for January 1 of the different years given. Station. 1840 1845 1850 1855 1860 1865 1870 1875 1880 1885 1890 1895 Cambridge . . 3.66 3.61 3-56 3-55 3- 19 3.62 3.66 3.68 3-7° 371 3-73 3.74 New Haven . . 3-83 3.80 375 3-70 372 3-70 3.80 3.83 3.86 3.87 3.87 3.86 New York . . 4.02 4.01 3-97 3-93 3-94 3-9S 3-97 3-99 4.01 403 4.05 4.07 Sandy Hook . 4.09 4.06 3-99 3-92 3-94 3-98 4.01 4.04 4.07 4.10 4-13 3-67 4.16 Albany . . . 3.60 3-58 3-58 3-58 3-58 3.60 3-6i 3-63 3-64 3-66 3-69 Philadelphia 4.18 4-15 4.14 4-i3 4-1.3 4.14 4.16 4.19 4.22 4-23 4.24 4.24 Baltimore . . Washington Toronto . . . 4-2i 4.28 3-56 4-23 4.26 4.21 4.25 4.20 4.26 4.21 4.29 4.21 4-31 4.22 4-33 4.24 4-35 4-25 4-37 4.27 4-39 4.28 4.41 4-3° 4.42 3-54 S-bi 3-5i 3-48 3-4° 3- SO 4-5 2 3. S 6 3-5« 4.60 4.61 Cleveland . . 4.00 3-98 3-97 3-9t> 3-9° 3-97 3-98 3-99 4.01 4-°3 4.05 4.07 j Detroit . . . 3-91 3-89 3.86 3-85 l s k 3-86 3-87 3-89 3-90 3-92 3-93 3-94 San Diego , . 6.12 6.19 6.22 6.25 6.26 | 6.24 6.20 6.T5 6.10 6.07 6.04 6.03 577 Santa Barbara . 5.87 5-93 5-94 5-95 5-96 5-95 5-94 5-92 S-88 c.84 5.80 Monterey . . 5<>3 57' 575 577 57° 57 S 5-72 5.69 S.66 5-6S 5-64 5-63 San Francisco . 5-49 5-54 5-5° 5-57 5-59 5-59 5-58 5-54 5-5i 5-49 5-47 5-45 Fort Vancouver 4.44 4.51 4-55 4.56 4.58 4.58 4-57 4.56 4-54 4-53 4-52 4.52 Smithsonian Tables. 112 TERRESTRIAL MAGNETISM. Table 1 2q, Secular Variation of Declination In the Form ol a Function of the Time for a Nnmher of Stations Station. Latitude. West longitude. The magnetic declination (Z>) expressed as a function of time. {a) Eastern Series of Stations. St. Johns, N. F. . Quebec, Canada . Charlottetown, P. E. I. Montreal, Canada Bangor, Me. Halifax, N. S. . Albany, N. Y. . Cambridge, Mass. New Haven, Conn. New York, N. Y. Harrisburg, Pa. . Philadelphia, Pa. Washington, D. C. Cape Henry, Va. Charleston, S. C. 47 344 46 48.4 46 14.0 45 30-5 44 82.2 44 39-6 42392 42 22.9 41 18.5 40 42.7 40 15.9 39 56-9 38 53-3 36 55-6 32 46-6 52 4i-9 71 14.5 63 27.0 73 34-6 6846.9 63 35-3 73 45.8 71 07.7 72 55-7 74 00.4 70 52.6 75 °9-o 77 00.6 76 00.4 70 55.8 21.94 + 14.66 + + 15-95 + 11.88 + + 13.86 + 16.18 + 8.17 + 9-54 + + 7.78 + 7.04 + + 2-93 + 5-36 + + 2-73 + + 2.42 4- -1.82 4- 3-03 0.61 7.78 4.17 0.36 3-55 4-53 3.02 2.69 0.18 3-" 2.77 0.14 2.98 3-i7 0.19 2.57 0.14 2.25 2.75 sin (1.05 m + 63.4)* sin (1.4 ?« 4- 4-6) sin (4.0 m 4- °-3) sin (1.2 m 4- 49.8) sin (1.5 in — 18.5) sin (4.9 m 4" '9-o) sin (1.30 m + 8.6) sin (1.00 m + 46.1)* sin (1.44 m — 8.3) sin (1.30 m + 7.0) sin (3.20 m 4- 44.0) sin (1.40 m — 22.1) sin (1.30 m — 18.1) sin (6.30 m 4- 64.0) sin (1.50 m-j- 0.2) sin (1.50 m — 26.1) sin (4.00 m 4- 14-6) sin (1.45 m — 21.6) sin (12.00 m + 27) sin (1.47 m — 30.6) sin (1.40 m — 12. 1)* Paris, France St. George's Town, Bermuda Rio de Janeiro, Brazil 48 50.2 32 23.0 -22 54.8 t 2 20.2 64 42.0 43 °9-5 6.479+ 16.002 sin (0.765 m + 118.77) 4- [0.85 — 0.35 sin (0.69 «)] sin [(4.04 + 0.0054 n + .000035 k 2 )«] % 6.95 + 0.0145 '" 4" 0.00056m 2 * 2.19 + 9.91 sin (0.80 m — 10.4)* (i) Central Series of Stations. York Factory, B. N. A. Fort Albany, B. N. A. Sault Ste Marie, Mich. Toronto, Canada Chicago, 111. Cleveland, Ohio Denver, Colo. Athens, Ohio Cincinnati, Ohio St. Louis, Mo. . New Orleans, La. Key West, Fla. . Kingston, Port Royal, Jamaica 56 59-9 52 22.0 46 29.9 43 394 41 50.0 41 30.4 39 45-3 39 '9- 39 o8 4 38 38.0 29 52.2 24 33-5 17 55-9 92 26.0 82 38.0 84 20.1 79 23-5 87 36.8 81 41.5 104 59.5 82 02.0 84 25.3 90 12.2 90 03.9 81 48.5 76 50.6 7-34 15.78 1.54 3.60 3-77 0.47 ■15-30 ■ i-5' ■ 2.59 5.91 ■ 5.20 ' +3 1 3.81 +16.03 sin + 6.95 sin -j- 2.70 sin 4- 2.82 sin -j- 0.09 sin -j- 0.08 sin -j- 2.48 sin -j- 2.39 sin 4- 0.011 m 4- 2.63 sin + 2.43 sin -j- 3.00 sin 4- 2.98 sin + 2.86 sin + 2.39 sin (1. 10 m — 97.9) (1.20 m — 99.6)* 1.45 m — 58.5) 1.40 m — 44.7) 9.30 m + 136) (19.00 m + 247) (1.45 m — 62.5) (1.30 m — 14.8) + 0.0005 '" 2 (1.40 m — 24.7) (1.42 m — 37.9) (1.40 m — ji-0 (1.40 m — 69.8) (1.30 m — 23.9) (1.10 m — 10.6) (b) Stations on the Pacific Coast, etc. City of Mexico, Mex. Cerros Island, Lower Cal., Mex San Francisco, Cal. . Vancouver, Wash. Sitka, Alaska Port Etches, Alaska . Petropavlovsk, Siberia 19 26.0 28 04.0 37 47-5 45 37-5 57 02.9 60 20.7 53 OI -° 99 1 1.6 115 12.0 122 27.3 122 39.7 135 '9-7 146 37.6 h58 43.0 — 5.34 + 3-28 sin ( 1. 00 m— 87.9)* — 7.40 + 4.61 sin (1.05 m — 107.0) — 13.94 + 2.65 sin (1.05 m — 135.5) — 17.93 + 3 12 sin ('-35 m ~ I 34- 1 ) — 25.79 + 3-3° sin ( l -3° m — : °4- 2 ,) — 23.71 + 7-89 sin (1.35 m— 80.9) — 3.35+2.97 sin (1.30m + 12.2) wave « "=-t — 1700. - 1700 Smithsonian Tables "3 Table 127. TERRESTRIAL MAGNETISM. Secular Variation ol the Declination. — Eastern Stations.* Station. St. Johns, N. F. . Quebec, Canada ■ Charlottetown, P. E. I. . . . Montreal, Canada Eastport, Me. . . Bangor, Me. . . Halifax, N. S. . . Burlington, Vt. . Hanover, N. H. . Portland, Me. . . Rutland, Vt. . . Portsmouth, N. H. Chesterfield, N. H. Newburyport, Mass Williamstown, Mass Albany, N. Y. . Salem, Mass. . . Oxford, N. Y. . . Cambridge, Mass. Boston, Mass. . . Provincetown, Mass Providence, R. I. . Hartford, Conn. . New Haven, Conn Nantucket, Mass. Cold Spring Harbor, N. Y New York, N. Y. Bethlehem, Pa. . Huntingdon, Pa. . New Brunswick, N.J Jamesburg, N. J. . Harrisburg, Pa. . Hatboro, Pa. . . Philadelphia, Pa. Chambersburg, Pa. Baltimore, Md. . Washington, D. C. Cape Henlopen, Del Williamsburg, Va. Cape Henry, Va. . New Berne, N. C. Milledgeville, Ga. Charleston, S. C. Savannah, Ga. Paris, France . . St. George's Town, B. I Rio de Janeiro, Bra- zil 1800 23-5 I2.I 8.0 13.2 10.9 1 5-9 7-3 6-3 74 7-3 5-7 6-3 3-° 7-1 6.9 7.2 6.5 5.2 4-7 6.S 4-7 2.6 1.0 2-5 3-i 0.0 1.8 2.1 -o-3 0.6 0.2 0.8 -1.9 -5.0 -4-5 22.6 —5-4 1810 25.0 I2.I 7-8 I4.O 1 1.4 l6. 7 7.2 6.0 8.9 6.2 7-7 6.0 7.6 5-9 5-4 6.6 3-i 7-5 7-3 7-7 6.5 5-2 4-7 7.2 4.9 4-5 a 2.9 3-' °-3 2.0 2.2 -0.5 0.7 0.2 0.9 -°-3 0.2 —1.9 5-3 —4.4 —4-7 22.3 1820 26.5 12.3 7-9 14.8 12.1 17.4 6.5 9-5 £s 8.1 6.4 8.x 6-3 5-8 7.2 3-4 8.0 7.8 8.2 6.7 5-5 5.0 7-7 4.6 2 -3 0.9 3-4 0.8 2-5 2.4 -°-3 0.9 0.4 1.1 -0.2 0.2 —1.6 -5-6 —4.0 —4-7 21.9 1830 —4-5 28.0 12.9 1840 12.8 18.2 8.1 7.2 10.1 6.9 87 7.0 8.6 6.8 6.3 7-9 n 8.4 8.9 7-3 5.8 5.6 5.0 2-5 1.1 4.0 3-8 1.4 3-o 2.9 0.2 1.2 0.7 i-5 0.0 o-5 -1.2 -5.6 _3-6 21.8 6.9 —3.4 —2.2 29.0 13-8 19.3 20.7 8.4 9.4 15.6 16.4 13.6 18.9 8.9 7-9 10.8 7.6 9-5 7-7 9-3 7-4 7.0 8.7 4-5 9-3 9.0 9.6 8.2 6.2 5-9 9.0 6.1 5.6 2.9 1-5 4-7 4-3 2.2 3-7 3-4 0.7 1-7 1.1 2.0 0.4 0.8 — 5-5 —3-0 —4.2 21.8 6.9 -0.9 1850 29.9 14.9 21.9 10.7 17.1 14.4 19.4 9-7 8.8 1 1.6 8.5 10.3 8.| 10.0 8.1 1860 10.2 9.2 6.8 6.6 9.6 6.7 6-3 3-5 2.1 5-3 4-9 2.9 4-3 4.1 1.4 2.3 1.8 2.6 0.9 i-3 -0.2 -5-3 —2.4 -3-8 20.9 6.9 0.4 35-o 16.0 22.8 12.0 17.8 15.2 19.9 10.3 9.8 12.3 9.4 11. 1 9.4 10.7 8.8 7-7 9.6 1 0.0 9.7 10.3 8-5 10.6 10.6 1870 1880 10.9 9.8 7-4 7-3 10.1 6.9 4.2 2.7 6.0 5.6 3-7 S-o 4-7 2.0 2.9 2-5 2.4 \i 0.5 -5.0 —i-7 —3-3 19.1 7-i i.8 30.8 16.9 234 T 3 15.9 20.3 II.O 10.8 13.0 10.4 1 1.9 10.3 11.4 9.6 9.2 ii-5 6.6 11. 2 10.9 11.5 10.2 8.0 8.1 10.6 7-9 74 5-° 3-5 6.6 6-3 44 5-7 54 27 3-5 2.9 4.1 2.1 2.4 1.1 —4-5 1.1 —2-7 17-5 7-5 3-i 30.8 17.4 237 13.8 18.7 16.5 20.6 11.9 11.7 13.6 "•3 12.7 11. 2 12.0 10.3 9-9 12.3 74 1 1.6 11.5 12.0 10.8 8.6 8.8 II.O 1890 8.4 4.2 7-1 7.0 S-o 6.7 6.2 34 4.2 37 4.9 2.7 2.9 17 —4.0 —0.4 — 2.1 16.6 3°-5 I7-S 237 14.4 18.9 16.9 20.7 12.8 I2 -5 14. 1 12.3 '3-3 12.0 12.5 10.9 10.5 13.0 8.0 11.9 11.9 12.4 11.6 9.2 95 "■3 8-9 8-5 6.7 4-9 7-5 7.6 5-5 7.6 7-o 4.2 4-7 5.6 3-3 3-5 2-3 -34 0.1 —1.4 15.1 7.9 8.4 4.5 5-8 «„! J ^ \^t?Z, f? lar X 3 " 3 '!?","! the declination since the year 1800 for a series of stations in the Eastern States and accent countries. Compiled from a paper by Mr. Schott, forming App. 7, Report of the United States Coast and Geodetic Survey for 1888. The minus sign indicates eastern declination. uuiirai.MMe» Smithsonian Tables. 114 Table 128. TERRESTRIAL MAGNETISM. Sooular Variation of tie Leollnatlon. - Central Stations.' Station. 1800 1810 1820 1830 1840 1860 1860 1870 1880 1880 1900 York Factory, Brit. N. A. . . . . Fort Albany, Brit. O.I —2-5 —4-7 -6-5 -7-8 —8.5 —8.6 —8.2 —7.2 -5.6 -3-6 Duluth, Minn. . . Superior City, Wis. Sault Ste. Marie, (« I2.I 10.9 IO.C 9-3 8.9 -9.8 8.8 — 10.0 9.1 — IO.I 9.6 — IO.I 10.3 —9.9 1 1.4 -9-5 -0.5 — O.9 — I.I —1.6 — 1.0 —0.8 -o-3 0.2 0.8 i-S 2.2 Pierrepont Manor, N. Y. . . . ! Toronto, Canada . Grand Haven.Mich. Milwaukee, Wis. . Buffalo, N. Y. . . 0.2 0.2 2.6 — 5-° 0.4 3-c 0.8 -5-2 0.8 3-7 i-3 —5.2 i-3 1.6 —4.9 —7-4 2.0 54 2.2 —4.4 -6.9 2.8 6-3 2.7 —37 —6.2 3-7 7.2 3-6 —2.7 —5-4 4-5 8.0 4.1 — i-S —4-5 5-3 8.8 4.8 6.0 Detroit, Mich. . . Vpsilanti, Mich. . Erie, Pa Chicago, 111. . . . Michigan City, Ind. —3-2 — °-5 —3-1 —4.1 —O.5 —2.9 -3-6 —0.4 —6.2 —2-5 —3-o — O.I -6-3 -5.6 — 2.1 — 2.2 0.4 —6.2 — 5-4 —1.6 -1.4 — 6.0 —S-o — 1.0 —0.6 1.6 —4.6 —0.4 0.2 2-3 —5-1 —4.0 0.1 0.9 3 i —4.6 —3-5 0.6 i-5 3-6 —4.0 —2.9 0.9 1.9 4.2 —3-3 —2-3 Cleveland, Ohio . Omaha, Neb. . . Beaver, Penn. . . Pittsburg, Pa. . . Denver, Colo. . . —1.9 — 1.1 —1-7 -12.5 —J-3 — »-5 — 12.6 —i-3 — 1.1 — 12.6 — 1.1 —0.6 — 12.4 —0.8 0.2 — 0.1 — 12.0 —o-3 0.7 0.4 —"•5 0.2 i-3 -1 5. 1 0.9 — 10.9 0.9 1.9 —14.9 1.4 — 10.2 '•5 2.5 —14.5 1.9 —9-5 2.2 3-i — 14.1 2' 3 -8-7 2.8 3-5 Marietta, Ohio . . Athens, Ohio . . Cincinnati, Ohio . St. Louis, Mo. . . Nashville, Tenn. . —4.1 —4.9 —2.9 —4.1 -5.0 —2.8 —3-9 — 5-° -6.7 —2.7 -3-6 -4.8 —8.9 — 6.9 —2.3 —3-i —4-5 —8.6 -6.9 — 2.6 —4.1 —8.2 -6.7 —i-3 — 2.0 -3-6 —7-7 -6-3 — 0.6 —1.4 —3-o —7-i -5.8 0.1 —0.7 —2.4 -6.4 -5- 1 0.8 — 0.1 —1.8 - 5 .6 —4.4 1.4 0.4 —i-3 —4.9 -3-6 Florence, Ala. . . Mobile, Ala. . . . Pensacola, Fla. . . New Orleans, La. . San Antonio, Texas -5.8 —6.8 —7-i —6-3 —7.2 -7.6 zk 6 —6.7 —8.0 —9.8 -6.5 —7.0 -7.6 —8.1 — IO.I — 6.4 —7-i —7-4 —8.2 —10.3 —6.1 —7.0 —7-i —8.0 — 10.2 —6.7 —6.6 —7-7 — IO.I zk 3 —6.4 —6.0 —7.2 —9-7 -4.8 -5-8 —5-3 —6.6 —9-3 —4-3 z% ~ 3 i —4.6 -3-8 IS Key West, Fla. . Havana, Cuba . . Kingston, Port Royal, Jamaica . —7.0 —6.0 -S.8 -6.9 —6.6 — S-S —6-3 —6.0 -5-8 —4-7 — 5-5 —5-3 —4-1 -4.8 -4.8 -3.8 —4.2 —4.2 —3-3 ~ 3 i —3-6 —2.9 —3-° —3-o —2-5 —2.4 —2.5 — 2.1 Barbadoes, Car. I si. Panama, New Gra- nada .... —3-4 —7-9 — 3-o -7.8 —2-5 -7.6 — 2.0 —7-3 —i-5 —7.0 —0.9 -6.7 —0.4 -6-3 0.1 — 5-9 0.5 -5-5 0.9 —5.0 1.2 -46 1 * This table gives the secular variation of the declination since the year 1S00 for a series of stations in the Central States and adjacent countries. The minus sign indicates eastern declination. Reference same as Table 127. Smithsonian Tables. "5 Table 129. TERRESTRIAL MACNETISM. Secular Variation of tie Declination. — Western Stations.* Station. 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 o O - O O O Acapulco, Mex 7.6 8.i 8.5 8.7 8.9 8.9 8.7 8.5 8.1 7.6 7-i Vera Cruz, Mex 8.6 9.0 9-3 9-3 9.2 8.9 8.4 7.8 7.0 6.2 5-3 City of Mexico, Mex. . . 7-5 7-9 8.2 8.5 8.6 8.6 8-5 8.4 8.1 7.8 74 San Bias, Mex 7-i 7.8 8.4 8.9 9-3 94 94 9-3 9.0 8.5 7-9 Cape San Lucas, Mex. . . 6.2 6.9 7.6 8-3 8.8 9.2 9-5 9.6 9.6 94 9.0 Magdalena Bay, L. Cal. . 6.6 74 8.2 8.9 9-5 1 0.0 10.3 10.5 10.5 10.3 10.0 Ceros Island, Mex. . . . 9.0 9.8 10.5 11.0 11.5 11.8 12.0 12.0 1 1.9 1 1.6 11.2 El Paso, Mex - 12.3 12.5 12.4 12.3 1 1.9 1 1.4 San Diego, Cal 10.3 10.8 1 1.4 1 1.9 '2-3 12.7 13.0 13.2 '3-3 133 132 Santa Barbara, Cal. . . . 1 1.6 12.3 12.9 134 •3-9 14-3 14.6 14.8 14.8 14.8 14.6 Monterey, Cal 12.3 12.9 13.4 !3-9 14.4 14.9 '5-3 16.6 15.9 16.0 16.1 San Francisco, Cal. . . . 13.6 14. 1 14.5 15.0 15.4 i 5 .8 16. 1 16.3 16.5 16.6 16.6 Cape Mendocino .... 15.1 15.6 16.0 16.5 16.9 17.2 17.4 17.6 17.7 17.7 17.6 Salt Lake City, Utah . . — - 16.0 16.4 16.6 16.6 16.3 '57 Vancouver, Wash. . . . 16.8 J 7-S 18.2 18.9 19.6 20.2 20.6 20.9 21.0 21.0 20.8 Walla Walla, Wash. . . _ _ _ _ _ 20.4 20.8 21.0 21.1 21.0 20.8 Cape Disappointment, Wash 177 18.2 18.7 19.2 19.8 20.3 20.8 21.2 21.6 21.8 21.9 Seattle, Duwanish Bay, Wash — — — — — 21.3 21.8 22.1 22.3 22.2 22.1 Port Townsend, Wash. 18.1 18.8 19.6 20.3 20.9 21.4 21.7 21.8 21.8 21.5 21. 1 Nee-ah Bay, Wash. . . . 18.3 18.9 19.6 20.3 21.0 21.6 22.1 22.5 22.7 22.7 22.6 Nootka, Vancouver Island 19.6 20.1 20.7 21.3 22.0 22.5 23.0 2 3-5 23.8 2 3-9 24.0 Captain's and Iliuliuk Har- bors, Unilaska Island . 19-3 19.6 19.7 19.8 19.7 19.7 19.5 *9-3 18.9 18.6 18.2 Sitka, Alaska 26.4 27.1 27.8 28.3 28.7 29.0 29.1 29.0 28.8 28.4 27.9 St. Paul, Kadiak Island . 2 S-5 26.4 27.0 27-3 27.4 27.1 26.6 25.9 25.0 2 3-9 22.7 Port Mulgrave, Yakutat Bay, Alaska 27.8 29.2 30-4 31.2 31-7 3i-8 3i4 3°7 29.7 28.4 26.8 Port Etches, Alaska . . . 27.8 29-3 3°4 31.2 31.6 3'-5 31.0 30.1 28.8 27-3 2 5-5 Port Clarence, Alaska . . - 26.6 27.0 26.9 26.4 25.6 24.4 22.9 21.2 19.5 Chamisso Island, Kotze- bue Sound - - 3I- 1 3'-3 3 1 - 1 3°-5 29.6 28.3 26.8 25.2 23-5 Petropavlovsk, Kamchatka, Siberia 5-7 5.2 4-7 4-i 34" 2.7 2.1 J-S 1.0 0.7 0.5 * This table gives the secular variation of the declination since the year 1800 for a series of stations in the Western States and adjacent countries. The declinations are all east of north. Reference same as Table 127. Smithsonian Tables. Il6 Table 130. TERRESTRIAL MAGNETISM. Agonic Lines.* The line of no declination is moving westward in the United States, and east declination is decreasing west of, while west declination is increasing east of the agonic line. Longitudes of the agonic line for the years — 1800 1850 1876 1890 o 25 - - 75-5 3° - - - 78.6 35 - 76.7 79.O 79-9 6 75-z 77-3 79-7 80.5 7 76-3 77-7 80.6 82.2 8 76.7 78-3 81.3 82.6 9 76.9 78.7 81.6 82.2 40 77.0 79-3 81.6 82.7 1 77-9 80.4 81.8 82.8 2 79.1 81.0 82.6 837 3 794 81.2 83.1 84-3 4 79.8 - 83-3 84.9 45 _ 83.6 85.2 6 _ - 84.2 84.8 7 _ - 85.1 85.4 8 _ - 86.0 85.9 9 - — 86.5 86.3 ! * Reference same as Table 127. Smithsonian Tables. 117 Table 131 . TERRESTRIAL MAGNETISM. Date of Maximum East Declination.* This table gives the date of maximum east declination for a number of stations, beginning at the northeast of the United States and ex- tending down the Atlantic coast to New York and west to the Pacific. Station. Date. Halifax,! N. S. 1714 Eastport, Me. 1753 Bangor, Me. . 1774 Portland, Me. 1779 Boston, Mass. 1780 New Haven, Conn 1800 New York, N. Y. 1784 Jamesburg, N. J. 1802 Philadelphia, Pa. 1802 Pittsburg, Pa. 1808 Cincinnati, Ohio 1814 Florence, Ala. 1821 St. Louis, Mo. 1822 Nashville, Tenn. 1834 Chicago, 111. . 1831 Denver, Colo. ■839 Salt Lake, Utah 1873 Vancouver, Wash. 1883 Cape Mendocino, Cal. 1886 San Francisco, Cal. 1893 * Reference same as Table 127. t The opposite phase of maximum west declination is now located at Halifax. Smithsonian Tables. 118 Table 132. 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 I3-S956 27.1912 40.7868 54.3824 67.9780 81.5736 95.1692 I08.7648 122.3604 135.9560 0-I93376 O.386752 O.580I28 °-7735°4 0.966880 1. 160256 1-353632 1.547008 1.740384 i-93376o 1 2 3 4 5 6 7 8 9 10 34-533 69.066 103.598 138-131 172.664 207.197 241.730 276.262 3 IO -795 345-328 O.491 174 O.982348 I.473522 I.964696 2.455870 2.947044 3.438218 3-929392 4.420566 4.91 1740 Cms. of H„0. Pressure in grammes per sq. cm. Pressure in pounds per sq. inch. Inches of H 2 0. Pressure in grammes per sq. cm. Pressure in pounds per sq. inch. 1 2 3 4 S 6 7 8 9 10 I 2 3 4 5 6 7 8 9 10 O.OI42234 O.O284468 O.O4267O2 O.O568936 0.07 1 1 170 O.0853404 O.O995658 0.1 137872 0.1 280106 O.I42234O 1 2 3 4 5 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 O.036227 O.072255 O.I08382 O.144510 O.180637 O.216764 O.252892 O.289019 0.325147 O.361274 Smithsonian Tables. 119 Table 1 33. REDUCTION OF BAROMETRIC HEIGHT TO STANDARD TEMPERATURE.' Corrections for brass scale and Corrections for brass scale and Corrections for glass scale and English measure. metric measure. metric measure. Height of a Height of a Height of w barometer in in inches for barometer in in mm. for barometer in in mm. for inches. temp. F. mm. temp. C. mm. temp. C. 150 O.OOI35 400 O.0651 50 O.O086 1 6.0 .OOI45 410 .0668 100 .0172 17.0 .00154 420 .0684 150 .0258 I7 / 5 .OOI58 43° .0700 200 ■034S 18.0 .OOI63 440 .0716 250 .0431 18.5 .00167 450 .0732 300 .0517 19.0 .OOI72 460 .0749 35° .0603 19.5 .OOI76 470 .0765 480 .0781 400 O.0689 20 O.O0l8l 490 .0797 450 •0775 20.5 .OO185 500 .0861 21.0 .00190 500 O.0813 520 .0898 21.5 .OOI94 510 .0830 540 •0934 22.0 .OOI99 520 .0846 560 .0971 22.5 .00203 53° .0862 580 .1007 23.0 .0020S 54° .0878 23-5 .002I2 55° .0894 600 0.1034 560 .09H 610 .1051 24.0 O.OO217 570 .0927 620 .1068 24.5 .0022I 580 ■0943 630 .1085 25.0 .OO226 590 .0959 v 640 ■n°3 25-5 .OO23I 650 .1120 26.0 .OO236 600 O.0975 660 •"37 26.5 .OO240 610 .0992 27.0 .OO245 620 .1008 670 0.1154 27-5 .00249 630 .1024 680 .1172 640 .1040 690 .1189 28.0 O.OO254 650 .1056 700 .1206 28.5 .OO258 660 •I°73 710 .1223 29.0 .O0263 670 .1089 720 .1240 29.2 .OO265 680 .1105 73° .1258 29.4 .OO267 690 .1121 29.6 .00268 740 0.1275 29.8 .OO270 700 O.I I37 75° .1292 30.0 .OO272 710 .1154 760 .1309 720 .II70 770 • T 3 2 7 30.2 O.OO274 73° .1186 780 •1344 3°-4 .00276 740 .1202 790 .1361 30.6 .00277 750 .1218 800 •1378 30.8 .OO279 760 •1235 31.0 .OO281 770 .125: 850 0.1464 31.2 .00283 780 .I267 900 .1551 3M .00285 790 .1283 950 .1639 31.6 .OO287 800 .I299 1000 ■1723 _ * 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 of brass, in the case of instruments graduated on the brass case. This relative expansion is practically proportional to the first power of the temperature. The above tables of values of the coefficient of relative expansion will be found to give corrections almost identical with those given in the International Meteorological Tables. The numbers tabulated under a are the values of a in the equation Ht = Hi! — a (t' — t) where Ht is the height at the standard temperature, HI the observed height at the tem- perature t>, and at the 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 corresponding reading at 0° C. Here the value of a is the mean of .1235 and .1251, or .1243 ; .'• o U' — t) =.1243 X 25 =3.11. Hence Hq— 765 — 3.11 = 761.89. N. B. — Although o 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 determined by experiment. Smithsonian Tables. I20 Table 134. CORRECTION OF BAROMETER TO STANDARD GRAVITY. Height above sea level in metres. IOO 200 300 400 SOO 600 700 800 900 1000 I IOO 1200 I3OO 1400 1500 1600 1700 i8co 1920 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 33°° 34°° 35°° 3600 3700 3800 39°° 4000 .192 .096 Observed height of barometer in millimetres. 195 2 °3 211 219 227 2 35 2 43 251 259 267 27 J 283 291 299 3°7 3'4 .176 -i8 S .194 .203 .212 .220 .229 .238 .247 .256 .265 .274 .283 .292 .201 •3°9 •359 .269 ■'79 .090 .147 .167 •177 .187 .196 .206 .216 .226 .236 •245 .255 .265 .275 .285 .294 5i3 429 345 261 177 0S4 •779 .701 .623 •545 .467 •389 •3" •233 ■155 .078 Correction in millime- tres for elevation above sea level in first column and height of barometer in top line. 108 118 129 140 162 172 183 194 204 215 226 237 248 259 270 1.077 1.005 •934 .862 •79° .718 .646 •574 •5°3 •43' •359 .287 .215 .118 .130 .142 •153 .165 .176 .188 .200 .212 .224 •235 •247 .259 .271 .283 •295 9»4 .918 3 7»7 721 6 S 5 789 724 658 592 526 461 395 650 .064 .077 .090 •i°3 .115 .128 .141 .154 .166 .179 .191 .204 .217 .230 .242 ■255 .014 .028 .041 .055 .068 .082 .096 .109 .123 •137 .150 .164 .178 .191 •205 1-345 1.291 1-237 1.184 1.130 1.076 1.022 .969 •915 .86: .807 ■753 .700 .015 .030 .044 .059 •°73 .088 .102 .117 .146 34° 292 244 196 149 101 °53 005 957 909 861 813 765 .016 .032 .047 .063 .078 315 255 196 13° 076 .016 2 57 897 837 777 718 .658 598 Corrections in hundredths of an inch for elevation above sea level in last column and height of barometer in bottom line. 245 203 162 120 088 O46 .OO4 .962 920 879 ■837 795 753 30 28 26 24 22 20 Observed height of barometer in inches. 15000 I4500 14000 13500 13000 12500 12000 1 1 500 1 1000 10500 1 0000 95°° 9000 8500 8000 75°° 7000 6500 6000 55°° 5000 45°° 4000 3500 3000 2500 2000 1500 1000 500 Height above sea level in feet. Smithsonian Tables. 121 Table 135. REDUCTION OF BAROMETER TO STANDARD GRAVITY.* Redaction to Latitude 45°. — English Scale. N . B. From latitude o° 44 the correction is to be subtracted. From latitude go° to 46 the correction is to be added. Height of the barometer in inches. Latitude. 19 20 21 22 23 24 25 26 27 28 29 30 Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. Inch. 0° 90° O.051 O.053 O.O56 O.059 O.061 O.064 O.067 O.069 O.O72 O.074 O.077 O.080 5 85 O.050 O.052 O.055 O.058 O.060 O.063 O.066 0.068 O.071 O.073 O.O76 O.O79 6 84 .049 .052 •055 •057 .060 .062 .065 .068 .070 •073 .076 .078 7 83 .049 .052 .054 .057 .059 .062 .065 .067 .070 .072 .075 .077 8 82 .049 .051 .054 .056 .059 .061 .064 .067 .069 .072 ■074 .077 9 81 .048 .051 •053 .056 .058 .061 .063 .066 .068 .071 ■073 .076 10 80 O.048 O.050 O.053 O.055 O.058 O.060 O.063 O.065 0.068 O.070 O.O73 O.O75 ii 79 .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 13 77 .045 .048 .050 •053 .055 .057 .060 .062 .065 .067 .069 .072 14 76 .045 •047 .049 .052 .054 .056 .059 .061 .063 .066 .068 .071 15 75 O.O44 O.O46 O.O48 O.051 O.053 O.O55 O.O58 O.060 O.062 O.065 O.067 O.069 16 74 •°43 ■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 7' .040 .042 .044 .046 .048 .050 .052 •055 .057 .059 .061 .063 20 70 O.O39 0.041 O.043 O.045 O.047 O.O49 O.O51 0-053 O.O55 O.057 O.059 O.061 . 21 69 .038 .040 .042 .044 ■045 ■047 •049 .051 ■053 .055 •057 .059 22 68 .036 .038 .040 .042 •044 .046 .048 .050 .052 .054 .056 •057 23 67 •035 •037 •°39 .041 •043 .044 .046 .048 .050 .052 •054 ■055 24 66 •°34 .036 •037 •039 .041 •043 .045 .046 .048 .050 .052 •053 25 65 0-033 O.O34 O.O36 O.O38 O.039 0.041 O.O43 0.044 O.O46 O.O48 O.050 O.051 26 64 031 •033 ■034 •036 .038 •039 .041 •043 •044 .046 .048 .049 27 63 .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 O.O27 O.O28 O.029 O.03I O.032 0-033 0.035 O.O36 O.037 O.O39 0.040 3i 59 .024 .025 .026 .027 .029 .030 .031 .032 •034 •°35 .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 56 .OI9 .020 .021 .022 .023 .024 .025 .026 .027 .028 .029 •030 35 55 O.OI7 0.018 O.OI9 0.020 0.02I 0.022 O.O23 0.024 O.O25 0.025 O.O26 O.O27 36 54 .016 .016 .OI7 .018 .019 .020 .021 .021 .022 .023 .024 .025 37 53 .014 .015 .015 .016 .017 .018 .018 .019 .020 .021 .021 .022 38 52 .012 .013 .014 .014 .015 .015 .016 .017 .OI7 .018 .019 .OI9 39 5i .Oil .Oil .012 .OI2 •013 .013 .014 .014 .015 .015 .Ol6 .OI7 40 50 O.OO9 O.OO9 O.OIO O.OIO 0.0 1 1 O.OII 0.012 0.012 0.012 0.013 O.OI3 O.OI4 41 49 .007 .007 .008 .008 .009 .009 .009 .010 .OIO .010 .Oil .Oil 42 48 •.005 .O06 .006 .006 .006 .007 .007 .007 .008 .008 .008 .008 43 47 .OO4 .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 Tables. * " Smithsonian Meteorological Tables," p. 58. 122 Table 136. REDUCTION OF BAROMETER TO STANDARD GRAVITY.* Reduction to Latitude 45°. —Metric Scale. N. B. — From latitude o° to 44° the correction is to be subtracted. Drom latitude 90 to 46° the correction is to be added. Height of the barometer in millimetres. Lat tude. 520 560 600 620 640 660 680 700 720 740 760 780 0° 90° mm. 1.38 mm. I.49 mm. 1.60 mm. i.6 S mm. I.70 mm. I.76 mm. I.81 mm. 1.86 mm. I.92 mm. I.97 mm. 2.02 mm. 2.08 5 6 85 84 8 J 82 81 1.36 '•35 I.47 I.46 1.56 1.63 1. 61 1.68 I.67 1-73 I.72 I.81 I.78 1.84 1.82 I.89 I.87 I.94 '■93 I.99 I.98 I.96 2.04 2.03 2.01 7 8 '•34 1-45 '■55 1.60 I.65 I.70 I.77 1.81 1.86 1.91 r -33 i-43 i-54 1.59 I.64 L69 I.76 1.79 1.84 1.89 I.94 2.00 ■ 9 1.32 1.42 1.52 '•57 I.62 I.67 I.74 i-77 1.82 1.87 I.92 I.97 ! io 80 1.30 1.40 1.50 '•55 I.60 I.65 I.70 '•75 1.80 1.85 I.90 1.88 i-95 i-93 1.90 II 79 78 1.28 1.38 1.48 !-53 1.58 I.63 1.68 i-73 1.78 1.83 12 1.26 1.36 1.46 i-5» I.56 I.60 1.65 1.70 1-75 1.80 1.85 T 3 77 76 1.24 i-34 1.44 1.48 '■53 I.58 1.63 1.67 1.72 1.77 1.82 1.87 H 1.22 1.32 1.41 1.46 1.50 r -55 1.60 1.65 1.69 1.74 1.79 1.83 15 16 75 1.20 1.29 1.38 1-43 1.48 1.52 i-57 1.61 1.66 1.71 1.75 1.80 74 1. 17 1.26 '•35 1.40 1.44 1.49 i-54 1.58 1.63 1.67 1.72 1.76 17 73 1. 15 1.24 1.32 i-37 1.41 1.45 1.50 i-54 '•59 1.63 1.68 1.72 18 72 1. 12 1. 21 1.29 1-34 1.38 1.42 1.46 i-5i '•55 1.59 1.64 1.68 19 7i 1.09 1.17 1.26 1.30 i-34 1.38 i-43 1.47 I-5" r -55 i-59 1.64 20 70 1.06 1.14 1.22 1.26 1-3' '•35 i-39 1 43 1.47 i-5i i-55 1.59 21 69 1.03 1. 11 1. 19 1.23 1.27 1.31 i-35 1.38 1.42 1.46 1.50 1.54 22 68 1. 00 1.07 i-i5 1. 19 1.23 1.18 1.26 1.30 i-34 1.38 1.42 1.46 1.49 23 67 0.96 1.04 1. 11 '•is 1.22 1.26 1.29 i-33 i-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 i-35 i-39 25 65 0.89 0.96 1.03 0.98 1.06 1. 10 1. 13 I.I6 1.20 1.23 1.27 1.30 1.33 26 64 ■ 8 J ■11 1.02 1.05 1.08 I. II i-i5 1. 18 1.21 '■ 2 5 1.28 27 6 J .81 .88 •94 0.97 1.00 1.03 I.06 1. 10 *- l 3 1. 16 1. 19 1.22 28 62 •77 ■83 .89 .92 o-95 0.98 I.OI 1.04 1.07 1. 10 '•'3 1.16 29 61 ■73 ■79 •85 .87 .90 •93 O.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 O.9I 0.94 0.96 0.98 I.OI 1.04 3i 59 •f 5 .70 •75 ■77 .80 .82 •85 .87 .90 .92 °-95 0.97 32 58 .61 .65 .70 .72 •75 •77 •79 .82 .84 .86 .89 .91 33 5 l •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 o-55 0.56 0.58 0.60 0.62 0.64 0.66 0.67 0.69 0.71 36 54 •43 .46 ■49 ■5i •53 •54 ■56 .58 •59 .61 •63 .64 3 l 53 •38 .41 •44 •45 •47 .48 .50 •5i •53 •54 •56 ■57 38 52 •33 •36 •39 .40 .41 •43 •44 •45 .46 .48 •49 •5° j 39 5i .29 ■31 •33 ■34 ■35 •37 •38 ■39 .40 .41 .42 ■43 40 50 0.24 0.26 0.28 0.29 0.30 0.31 0.31 0.32 o-33 °-34 0.35 0.36 4i 49 .19 .21 .22 •23 .24 .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 • r 3 • r 3 •13 .14 .14 .14 44 46 •05 •05 .06 .06 .06 .06 .06 .07 .07 .07 .07 .07 Smithsonian Tables. " Smithsonian Meteorological Tables," p. 59. 123 Table 137. CORRECTION OF THE BAROMETER FOR CAPILLARITY.* i. Metric Measure. Diameter Height of Meniscus in Millimetres. of tube 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 id mm. Correction to be added in millimetres. 4 0.83 1.22 1.54 1.98 2-37 _ _ _ 5 •47 0.65 0.86 1.19 1.45 1.80 - - 6 .27 .41 •56 0.78 0.98 1. 21 '•43 - 7 .18 .28 .40 •53 .67 0.82 0.97 '•13 8 - .20 .29 • 3 f .46 .56 •65 0.77 9 - •15 .21 .28 •33 .40 .46 •52 10 - - •15 .20 :U .29 •33 •37 ii — — .10 .14 .21 .24 •27 12 - - .07 .10 •13 ■15 .18 .19 13 .04 .07 .10 .12 •13 .14 2. British Measure. Diameter Height of Meniscus in Inches. of tube .01 .02 .03 .04 .05 .06 .07 .08 in inches. Correction to be added in hundredths of an inch. •IS 2.36 4.70 6.86 9-23 11.56 _ _ _ .20 I. IO 2.20 3.28 4-54 5-94 7.85 - - •25 O.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 - •5i 0.82 *i s 1.49 1.85 2.24 2.65 .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 •55 .08 .20 •3i .40 •47 •52 * The first table is from Kohlrausch (Experimental Physics), and is based on the experiments of Mendelejeff and Gutkowski (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 formulas 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. 124 Table 138. ABSORPTION OF CASES BY LIQUIDS.* Absorption Coefficients, a,, for Gases in Water. Temperature Centigrade. t Carbon dioxide. C0 S Carbon monoxide. CO Hydrogen. H Nitrogen. Nitric oxide. NO Nitrous oxide. N 2 Oxygen. I.797 O.0354 0.021 10 O.02399 O.0738 1-305 O.04925 5 I.450 •0315 .02022 .02134 .0646 I.095 •04335 10 I.185 .0282 .01944 .01918 •0571 O.920 .03852 '5 1.002 .0254 .01875 .01742 •0515 0.778 •03456 20 O.OOI .0232 .01809 .01599 .0471 O.670 •03137 25 O.772 .0214 .OI745 .01481 .0432 - .02874 30 - .0200 .O169O .01370 - - .02646 40 O.506 .0177 .01644 .01195 - - .02316 50 - .0161 .Ol6o8 .01074 - - .02080 100 O.244 - .01600 .01011 — — .01690 Temperature Centigrade. * Air. Ammonia. NH, Chlorine. CI Ethylene. C 2 H 4 Methane. CH« Hydrogen sulphide. H 3 S Sulphur dioxide. S0 2 O O.02471 1 174.6 3 '2 3 S 0.2563 O.05473 4-371 79-79 5 .02179 971-5 2.808 ■2153 .04889 3-965 67.48 10 ■OI953 840.2 2.585 ■1837 .04367 3.586 56.65 47.28 '5 .01795 756.0 683-1 2.388 .1615 •O3903 3- 2 33 20 .01704 2.156 .1488 .03499 2.905 39-37 25 " 610.8 I.950 " .02542 2.604 3 2 -79 Absorption Coefficients, a t , for Gases in Alcohol, C s H B OH. Centigrade. t Carbon dioxide. C0 3 Ethylene. C 3 H 4 Methane. CH 4 Hydrogen. H Nitrogen. N Nitric oxide. NO Nitrous oxide. N„0 Hydrogen sulphide. H 2 S Sulphur dioxide. S0„ 4-3 2 9 3.091 3-595 O.5226 O.0692 O.1263 O.3161 4 i 9 ° 17.89 328.6 5 3-3 2 3 .5086 .0685 .1241 .2998 3-838 14.78 251.7 10 3-5'4 3.086 •4953 .4828 .0679 .1228 .2861 3-525 11.99 IOO.3 15 3'99 2.882 .0673 .1214 .2748 3-215 9-54 144-5 20 2.946 2.713 .4710 .0667 .1204 .2659 3015 7.41 "4-5 99-8 25 2.756 2.578 .4598 .0662 .1196 -2595 2.819 5.62 • This table contains the volumes of different gases, supposed measured at o° C. and 76 centimetres' pressure, which unit volume of the liquid named will absorb at atmospheric pressure and the temperature stated in the first column. The numbers tabulated are commonly called the absorption coefficients for the gases in water, or in alcohol, at the temperature t and under one atmosphere of pressure. The table has been compiled from data published by Bohr & Bock, Bunsen, Carius, Dittmar, Hamberg, Henrick, Pagliano & Emo, Raoult, Schonfeld, Setschenow, and Winkler. The numbers are in many cases averages from several of these authorities. Note. — The effect of increase of pressure is generally to increase the absorption coefficient. The following is approximately the magnitude of the effect in the case of ammonia in alcohol at a temperature of 23° C. : {P = 45 cms. 50 cms. 55 cms. 60 cms. 65 cms. 053 = 69 74 79 84 88 According to Setschenow the effect of varying the pressure from 45 to 85 centimetres in the case of carbonic acid in water is very small. Smithsonian Tables. 125 Table 139. VAPOR PRESSURES. The vapor pressures here tabulated have been taken, with one exception, from Regnault's results, pressure of Pictet's fluid is given on his own authority. The vapor Tem- pera- Acetone. Benzol. Carbon bisul- Carbon tetra- Chloro- form. Ethyl alcohol. Ethyl ether. Ethyl bromide. Methyl alcohol. Turpen- tine. ture Cent. C s H 6 CsH 8 phide. CS a chloride. CClj CHClj C a H 6 CiH 10 O CjH 5 Br CH,0 CioH 8 —25° _ _ _ _ _ _ 4.41 .41 _ 20 - :! f 7 l .98 - •33 6.89 5.92 •63 - —is - 6.16 1-35 - •I 1 8-93 7.81 •93 - — IO - 1.29 7-94 248 - .65 II.47 IO.15 i-35 - — S — 1.83 10.13 - .91 14.61 13.06 1.92 — - 2-53 12.79 3-29 - 1.27 18.44 16.56 2.68 .21 s - 3-42 16.00 4-3 2 - 1.76 23.09 20.72 3-69 - 10 - 4-S 2 19.85 5.60 - 2.42 28.68 2574 5.01 .29 IS - 5.89 24.41 7.17 - 3-30 35-36 31.69 6.71 - 20 17.96 7.56 29.80 9.10 16.05 445 43.28 38.70 8.87 44 25 22.63 9-59 36.11 II-43 20.02 5-94 52.59 46.91 11.60 - 3° 28.IO 12.02 43-46 14.23 24-75 7.85 63.48 56.45 15.00 .69 35 34-52 14-93 51-97 17-55 30-35 10.29 76.12 67.49 19.20 - 40 42.01 18.36 61.75 21.48 36-93 13-37 90.70 80.19 24-35 1.08 45 50-75 22.41 72.95 26.08 44.60 17.22 107.42 9473 30.61 — 50 62.29 27.14 85-7I 3 r -44 53-50 21-99 126.48 1 1 1.28 38-17 1.70 55 72.59 32.64 100.16 37-63 63-77 27.86 148.II 130.03 47-22 - 6o 86.05 39.01 116.45 44-74 75-54 35.02 172.50 199.89 I5I-I9 57-99 2.65 65 IOI.43 46-34 134-75 52-87 88.97 43-69 174-95 7o-73 - 70 118.94 54-74 IS5-2I 62.11 104.21 54.11 230.49 201.51 85.71 4.06 75 138.76 64.32 177.99 72.57 121.42 66.55 264.54 231.07 103.21 _ 80 161. 10 Z 5 - 1 ? 203.25 84-33 140.76 81.29 302.28 263.86 123.85 6.13 8S 186.18 87.46 231-17 97-51 162.41 98.64 343-95 300.06 147.09 - 90 214.17 101.27 261.91 112.23 186.52 "8.93 389-83 339-89 174.17 9.06 95 245.28 116.75 296.63 128.69 213.28 142-51 440.18 383-55 205.17 - 100 27973 134.01 332-5' 146.71 242.85 16975 495-33 43 1 - 2 3 240.51 13.11 i°5 3'7-7o 153.18 37272 166.72 275.40 201.04 555.62 483.12 280.63 - no 359-40 174.14 416.41 188.74 3"-io 236.76 621.46 539-40 325-96 18.60 "5 405.00 197.82 46374 212.91 350.10 277-34 693-33 600.24 376.98 120 454.69 223.54 514.88 239-37 392-57 323-I7 771.92 665.80 434.18 25.70 125 508.62 251.71 569.97 268.24 438.66 374-69 - 736.22 498.05 1 130 566.97 282.43 629.16 299.69 488.51 432-3° - 811.65 569-I3 34-90 135 629.87 3I5-85 692.59 333-86 542.25 496.42 - 892.19 647-93 140 697.44 352-07 760.40 370.90 600.02 567.46 - 977.96 733-71 46.40 H5 - 391.21 832.69 411.00 661.92 645.80 - 830.89 - 150 433-37 909.59 454-31 728.06 73I-84 _ _ 936-I3 60.50 l P - 478.65 - 501.02 798-53 825.92 - - 68.60 160 - 527.14 - 2 5I - 3 J 873.42 - - - - 77-5° 165 568.30 - 605.38 952-78 - - - _ 170 634.07 663.44 ~ *■* """ Smithsonian Tables. 126 VAPOR PRESSURES. Table 139. Tem- pera- ture, Centi- grade. Ammonia. NH 3 Carbon dioxide. C0 2 Ethyl chloride. C 2 H 5 C1 Ethyl iodide. C 2 H C I Methyl chloride. CH„C1 Methylic ether. C 2 H„0 Nitrous oxide. N 2 Pictet's fluid. 64CS0 -f- 46C0 8 Weight per cent. Sulphur dioxide. S0 2 Hydrogen sulphide. H 2 S —30° 86.61 - 11.02 - 57.90 57-65 - 58.52 28.75 - —25 20 —is — 10 — s IIO.43 139.21 I73-65 214.46 264.42 1300.70 1514.24 1758.25 2034.02 2344-I3 14.50 18.75 23.96 30.21 37-67 - 71.78 88.32 I07.92 130.96 157.87 71.61 88.20 107.77 130.66 '57-25 1569.49 1758.66 1968.43 2200.80 2457.92 67.64 74.48 89.68 IOI.84 121.60 37-38 47-95 60.79 76.25 94.69 374-93 443-85 5I9-65 608.46 706.60 s IO 15 20 318.33 383-03 457.40 543-34 638.78 2690.66 3075-38 3499.86 3964.69 4471.66 46.52 56.93 61. n 83.26 99.62 4.19 5-41 6.92 8.76 11.00 189.IO 225.11 266.38 3I3-4I 366.69 187.90 222.90 262.90 307.98 358.60 2742.IO 3055.86 3401.91 3783-I7 4202.79 139.08 167.20 193.80 226.48 258.40 116.51 142.11 171.95 206.49 246.20 820.63 949.08 1089.63 1244.79 I4I5-I5 25 30 35 40 45 747.70 870.10 1007.02 "59-53 1328.73 5020.73 5611.90 6244.73 6918.44 7631.46 1 18.42 139.90 164.32 191.96 223.07 13.69 16.91 20.71 25.17 30-38 426.74 494.05 569.II 415.10 477.80 4664.14 5170.85 6335-98 297.92 338.20 383.80 434-72 478.80 291.60 343-18 401.48 467.02 540-35 1601.24 1803.53 2002.43 2258.25 2495-43 50 55 60 65 70 1515-83 1721.98 1948.21 2196.51 2467.55 - 257-94 266.84 340.05 387-85 440.50 36.40 43-32 51.22 - - - 521.36 622.00 712.50 812.38 922.14 2781.48 3069.07 3374-02 3696.15 4035-32 75 80 85 90 95 2763.00 3084.31 3433-09 3810.92 4219.57 - 498.27 561.41 630.16 7°4-75 785-39 - - - - - - - 100 4660.82 - 872.28 - - - - - - - Smithsonian Tables. 127 Tables 140-142. CAPILLARITY. -SURFACE TENSION OF LIQUIDS.* TABLE 140.— Water and Alcohol In Contact with Air. Temp. Surface tension in dynes per centimetre. Temp. C. Surface tension in dynes per centimetre. Temp. Surface tension in dynes per cen- timetre. Water. Ethyl alcohol. Water. Ethyl alcohol. Water. o° 5 10 15 20 25 30 35 75.6 74-9 74.2 73-5 72.8 72-1 71.4 70.7 23-5 23.I 22.6 22.2 21.7 2I.3 20.8 20.4 40° 45 50 65 70 75 70.0 69-3 68.6 67.8 67.I 66.4 65.7 65.O 20.0 '9-5 19. 1 18.6 18.2 .7.8 '7-3 16.9 8o° 85 90 95 100 643 63.6 62.9 62.2 61.5 TABLE 141. — Miscellaneous Liquids In Contact with All. Surface Liquid. Temp. tension in dynes per cen- timetre. Authority. ! Aceton . . . . 14.0 25.6 Average of various. Acetic acid . . . 17.0 30.2 ti Amyl alcohol . . 15.0 24.8 u Benzene . . . . 15.0 28.8 " Butyric acid . . 15.0 28.7 " Carbon disulphide 20.0 3°-5 Quincke. Chloroform . . . 20.0 28.3 Average of various. Ether 20.0 18.4 " Glycerine . . . 17.0 63.14 Hall. Hexane . . . . 0.0 21.2 Schiff. 11 68.0 14.2 «( Mercury . . . 20.0 470.0 Average of various. Methyl alcohol 15.0 24.7 " Olive oil ... . 20.0 34-7 «« Petroleum . . . 20.0 25.9 Magie. Propyl alcohol . . 5-8 23.9 Schiff. « i( 97-i 18.0 a Toluol . . . . 15.0 29.1 «* (i 109.8 18.9 tt Turpentine . . . 21.0 28.5 Average of various. TABLE 142. — Solutions ol Salts in Water.t Salt in solution. BaCl 2 CaCl 2 U HC1 it a KCl It a MgCl* ft tt NaCl U ti NH4CI SrCl 2 it it K 2 CO s it tt Na 2 CO s it KNO s it NaNOs ti CuS0 4 tt H 2 S0 4 it it K 2 S0 4 it MgS0 4 it Mn 2 S0 4 tt ZnS0 4 Density. I.2820 I.0497 i-35" 1-2773 1.1190 1.0887 1.0242 1. 1699 1. ion 1.0463 '•2338 1. 1694 1.0362 ii93 2 1. 1074 1.0360 1.0758 '■0535 1. 028 1 1.3114 1. 1204 1.0567 '•3575 1. 1576 1 .0400 1. 1329 1.0605 1.0283 1.1 263 1.0466 1.3022 1.1311 1. 1775 1.0276 1.8278 1-4453 1.2636 1.0744 1.0360 1.2744 1.0680 1.1119 1.0329 1-3981 1.2830 1-1039 Temp. C.° Tension in dynes per cm. 15-16 8l.8 15-16 77-5 19 95.0 19 90.2 20 73-6 20 74-5 20 75-3 15-16 82.8 I5-I6 80.1 15-16 78.2 I5-16 90.1 15-lb 8c,2 I5-16 78.0 20 85.8 20 80.5 20 77.6 16 84.3 16 81.7 16 78.8 I5-16 8 S .6 I5-16 79-4 15-16 77.8 15-16 90.9 I5-I6 81.8 15-16 77-5 I4-I5 79-3 77-8 14-15 I4-I5 77.2 14 78.9 14 77.6 12 83.S 12 80.0 I5-l6 78.6 I5-I6 77.0 15 63.0? '5 79-7 "i 79-7 15-16 78.0 15-16 77-4 1 5-16 83.2 15-lb 77.8 15-16 79.1 15-16 77-3 15-16 83 3 15-16 80.7 15-16 77.8 *i. Th 't S i ete J'S inati . 0n ° f ,he capillary constants of liquids has been the subject of many careful experiments, but the S?l^l.^fc n ^ Xpe Tr ,CT f' an t eVeno£ lh =^™= observer when the methodof measurement £ changed! do not agree well together The values here quoted can only be taken as approximations to the actual values for the hqmds in a state.of purity in contact with pure air In the case of water the values given by Lord Rayleiph from e Xrf „ e ,T tl n rKSfSi5 ¥%■ I 89 "' "? by Ha " f ™ m v dir cct measurement of the tension of a flat fffinf PhS. Mag 1893) have been preferred, and the temperature correction has been taken as o. 141 dyne per degree centigrade. The J^S^^^S^^^^ ° f HaU ab0TC refmd » a " d < h * Spa&- h on^e effect of ^£^2^ t ^^S^t^^ b ^^L aetm £01 ' hem0St *"* "-ge values derived t From Volkmann (Wied. Ann. vol. 17, p. 353). Smithsonian Tables. 128 TENSION OF LIQUIDS. TABLE 143. — Surface Tension of Liquids.* Tables 143-145. Liquid. Water . Mercury Bisulphide of carbon Chloroform . Ethyl alcohol Olive oil Turpentine . Petroleum Hydrochloric acid Hyposulphite of soda solution Specific gravity. 13-543 1.2687 1.4878 0.7906 0.9136 0.8867 9-7977 1. 10 1. 1248 Surface tension in dynes per cen- timetre of liquid in contact with — Air. 75.0 5*3-° , 3 °'5 (31-8 (24.1 34-6 28.8 29.7 (729) 69.9 Water. Mercury. 0.0 392.O 41.7 26.8 18.6 "-S (28.9) (392) (387) (415) 3°4 317 241 271 (392) 429 TABLE 144. — Surface Tension of Liquids at Solidifying Point, t Tempera- Surface Tempera- Surface tension in dynes per tension in dynes per Cent.° centimetre. Cent.° centimetre. Platinum 2O0O 1691 Antimony 43 2 249 Gold . 1200 1003 Borax . IOCO 216 Zinc 360 877 Carbonate of soda 1000 2*0 Tin 230 599 Chloride of sodium n6 Mercury —40 588 Water . 8 7 . 9 t Lead 33° 457 Selenium 217 71.8 Silver . 1000 427 Sulphur III 42.1 Bismuth 265 1390 Phosphorus . 43 42.0 Potassium 58 37i Wax . 68 34-i ' Sodium 90 258 TABLE 145. — Tension of Soap Films. Elaborate measurements of the thickness of soap films have been made by Reinold and Rucker.H They find that a film of oleate of soda solution containing 1 of soap to 70 of water, and having 3 per cent of KNOs added to increase electrical conductivity, breaks at a thickness varying between 7.2 and 14.5 micro-millimetres, the average being 12. 1 micro- millimetres. The film becomes black and apparently of nearly uniform thickness round the point where fracture begins. Outside the black patch there is the usual display of colors, and the thickness at these parts may be estimated from the colors of thin plates and ihe refractive index of the solution (vide Newton's rings, Table 146). When the percentage of KNO3 is diminished, the thickness of the black patch increases. For example, KNO3 =3 1 0.5 0.0 Thickness = 12.4 13.5 14.5 22.1 micro-mm. A similar variation was found in the other soaps. It was also found that diminishing the proportion of soap in the solution, there being no KNO3 dissolved, increased the thickness of the film. I part soap to 30 of water gave thickness 21.6 micro-mm. 1 part soap to 40 of water gave thickness 22.1 micro-mm. 1 part soap to 60 of water gave thickness 27.7 micro-mm. I part soap to 80 of water gave thickness 29.3 micro-mm. * This table of tensions at the surface separating the liquid named in the first co'unin and air, -water or mercury as stated at the head of the last three columns, is from Quincke's experiments (Pogg. Ann. vol. 130. and Phil. Mag. 1871I The numbers given are the equivalent in degrees per centimetre of those obtained by Worthington from Ouincke's results (Phil. Mag. vol. 20, 1885) with the exception of those in brackets, wliich were not corrected by Worthington ; they are probably somewhat too high, for the reason stated by Worthington. The temperature was about 20° C. n t It win be observed "that the value here' given on the authority of Quincke is much higher than his subsequent measurements, as quoted above, give. || " Proc. Roy. Soc." 1877, and " Phil. Trans. Roy. Soc' 1881, 1883, and 1891. Note — Onincke points out that substances may be divided Into groups in each of which the ratio of the surface tension to the density is nearly constant. Thus, if this ratio for mercury be taken as unit, the ratio for the bromides and iodides s about a half : that of the nitrates, chlorides, sugars, and fats, as well as the metals, lead bismuth, and tntimony about iV that of water, the carbonates, sulphates, and probably phosphates, and the metals platinum, gold, silver, cadmium, tin, and copper, 2 ; that of zinc, iron, and palladium, 3 i and that of sodium, 6. Smithsonian Tables. 129 Table 146. NEWTON'S RINGS. Newton's Table of Colors. 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. ii. in. Color for re- flected light. Very black Black . . Beginning of black Blue . White . Yellow . Orange Red. . Violet . Indigo . Blue . Green . Yellow . Orange Bright red Scarlet . Purple . Indigo . Blue . Green . Color for transmitted light. White Yellowish red . . Black . . Violet . Blue . . White . Yellow . Red . . Violet . Blue . . Green Yellow Red . Thickness in millionths of an inch for — < IS o-.S 0.4 I.O 0.75 2.0 '•5 2. 4 1.8 5- 2 3-9 7-i 8.0 6.0 9.0 6.7 1 1.2 12.8 9.6 14.0 10.5 iS-i "•3 16.3 12.2 17.2 13.0 18.2 '37 19.7 14.7 21.0 21. 1 '57 17.6 23.2 25.2 17-5 18.6 0.2 0.9 1-3 i-5 4.6 4.2 5.8 7.2 8.4 9.0 97 10.4 "■3 n.8 12.7 r 3-5 14.2 1 5. 1 16.2 IV. VI. VII. Color for re- flected light. Yellow . . Red . . . Bluish red Bluish green . Green . . Yellowish green . Red. . . Greenish blue . Red. . Greenish blue . Red. . Greenish blue . Reddish white Color for trans- mitted light. Bluish green Red . Bluish green Red . Thickness in millionths of an inch for — »• < 27.1 29.0 32.0 20.3 21.7 24.0 24.0 35-3 25-5 26.5 36.0 27.0 40-3 30.2 46.0 52.5 34-5 39-4 587 65.0 46 48.7 72.0 53-2 71.0 577 I Z-5 18.7 20.7 22.0 22.7 23.2 26.0 397 34-o 38.0 42.0 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. II. III. Colo Red* . Violet . Blue . . Green . Yellow * Orange * Red . . Purple . Blue . . Blue* . Green . Yellow* Posi- tion. Kit v 26 G2 5 Y 26 o 26 I<2 5 P 36 B3 B8 5 Gs 5 Ys 5 Thick- ness. 28.4 3°-5 35-3 40.9 45-4 49.1 52.2 55-9 577 60.3 65.6 71.0 IV. V. Color. Red* . Bluish red*. Green . it Yellow green * Red* . Green . Green*. Red . . Red* . Posi- tion. Rs 5 BRs 5 G4 G4 5 YG 45 R*6 G6 G5 5 R50 R6 6 Thick- ness. 76.5 8l. S 84.I 89-3 96.4 105.2 IU.9 1 18.8 126.0 '33-5 VI. VII. VIII. Color. Green . Green* Red . . Red* . Green . Green*. Red . . Red* . Green . Red . . Posi- tion. G6 G6 5 Re Re s G 7 G7 5 R7 K75 Gs ^8 Thick- ness. 141.O 147-9 I S4 .8 162.7 170-5 178.7 186.9 193.6 20O.4 211. 5 * The colors marked are the same as the corresponding colors in Newton's table. Smithsonian Tables. I30 CONTRACTION PRODUCED BY SOLUTION.* Table 147. Across the top of the heading are given the formulas of the salt dissolved, its molecular weight (M. W. ), and the den* sity of the salt, with the authority for that density. Grammes of the salt in 100 of water. Observed volume. Calculated volume. Per cent of contraction. Grammes of the salt in 100 of water. Observed volume. Calculated volume. Per cent of contraction. K 2 0. NaOH. M. W. = 47.02. Density = 2.656 (Karsten). M. W.= 39.95. Density = 2.i3o(Filhol). (Hager.) (Schiff.) 4.702 99.88 IOI.77 1.86 3-995 994 101.88 2-43 9.404 99.92 103-55 4.20 7.990 994 103-75 4.19 14.106 IOO.18 105.32 4.88 II.985 99.6 105.63 5-7i 18.808 IOO.60 107.09 6.06 1 5.980 100.2 107.50 6.79 23.510 IOI.20 108.86 7.04 19-975 100.8 109.38 7.84 28.212 I02.00 IIO.64 7.81 23.970 101.7 III. 26 8.59 32.914 102.90 1 1 2.41 8.46 27.965 102.7 II 3- I 3 9.22 37.616 103.90 1 14.18 9.01 31.960 103.8 115.01 9-75 42.318 104.96 115.96 9.80 35-955 105.0 116.88 10.17 47.020 IOO.IO "7-73 9.88 39-95° 106.2 118.76 10.58 7°-53° II2.20 126.59 n-37 59-925 1 1 34 128.14 11.50 79-934 114.88 130.14 "•73 79.900 119.850 159.800 121. 2 138.6 156.6 I37-52 156.28 175.04 11.87 11.31 10.54 9.80 199.750 174.8 193.80 M A KOH. V. = 56. Density = 2.044 (Filhol). 239.970 193.6 212.56 8.92 NH 8 . - (Schiff.) 5.6 I0I.2 102.74 1.50 II. 2 16.8 22.4 102.6 I04.O 105.4 105.48 108.22 110.26 2-73 3-90 5.01 M.W.= : 17. Density = 0.616 (Andreef). (Carius.) 28.0 33-6 106.8 108.4 113.70 116.44 6.07 6.91 39-2 44.8 IIO.O 119.18 7.70 i-7 I02.5 102.76 0.25 in.6 121.92 8.46 3-4 105.0 105.52 108.28 0.49 50.4 113.2 124.66 9.19 H 107.4 0.81 56.0 84.0 1 1 5.0 127.40 9.72 6.8 109.8 1 1 1 .04 1. 12 124.2 141. 10 11.98 8.5 1 1 2.2 113.80 1.41 112.0 134.6 154.80 i3- 5 10.2 1 1 4.6 116.56 1.68 168.0 157.6 181.8 182.20 '3- 5° 11.9 I I7.O 119.32 1.95 224.0 209.60 13.26 ,3.6 1 19.4 122.08 2.20 15-3 I2I.8 124.2 135-8 1 24.84 127.60 141.40 2.44 266 25-5 3-96 Na.O. 34-o 147-3 155.20 5.09 M. W. = 30.97. Density = 2.8o5 (Karsten). 51.0 169.7 182.80 7-17 (Hager.) 3-°97 99.OI IOI.IO 2.07 3.86 6.194 98.26. 102.21 NH 4 C1. 9.291 12.388 15485 18.582 21.679 24.776 27-873 30.970 46.455 52.649 97.76 97-45 97.29 97-23 97-32 97-55 97.84 98.20 100.94 102.30 103.31 104.42 106.63 107.73 108.83 109.94 1 1 1.04 116.56 118.77 6.67 7.80 8.81 M. W.= 53.38. Density=t.52(Schroeder). (Gerlach.) 9.66 10.37 11.00 11.56 13.40 1387 H 3 l 10.676 16.014 21.352 26.690 IO3.7 107.5 in. 5 "5-3 1 19.2 103.51 107.02 110.54 114.05 117.56 0.18 0-45 0.87 1. 10 1.40 * The table was comp Smithsonian Tables. 131 Table 1 47. CONTRACTION PRODUCED BY SOLUTION. Grammes of the salt in ioo of water. Observed volume. Calculated volume. Per cent of _ contraction. Grammes of the salt in 100 of water. Observed volume. Calculated volume. Per cent of contraction. KC1. M. W. — 74.41. Density = 1.945 (Clarke). BaCl 2 . M.W. = 207.54. Density=3.75 (Schroeder). (Gerlach.) (Gerlach.) 7.441 14.882 22.323 102.8 105.8 108.9 103.83 107.65 1 1 1.48 O.99 1.72 2.31 10.377 20.754 3I-I3I I0I.6 102.9 104.9 102.77 105.53 108.30 1. 14 2.50 3-'4 NaCl. M. W. = 58.36. Density = 2.150 (Clarke). KI. M. W. = 166.57. Density = 3.o 7 (Clarke). (Gerlach.) (Kremers. ) 16.657 33-3'4 49-971 66.628 83.285 104.5 109.3 114.2 119.1 124.0 105-39 IIO.77 1 16.18 121.57 126.97 0.85 1-34 1.70 2.20 2-34 5.836 II.672 17.508 23-344 29.180 IOI.7 I°3-7 IO5.8 I07.9 IIO.I 102.71 I05-43 108.14 1 10.86 113.58 O.99 I.64 2.16 2.67 3.06 LiCl. M. W. = 42. Density =1.980 (Gerlach). KC10 S . M. W. = 122.29. Density = 2.331 (Clarke). (Kremers.) (Gerlach.) 6.II4 IO2.3 102.62 0.314 4.2 8.4 12.6 16.8 21.0 42.0 1 01 .9 IO3.8 IO5.8 107.8 1 1 0.O 120.7 102.14 104.28 106.42 108.56 110.70 121.40 O.24 O.46 O.58 O.70 O.63 O.58 KNO3. M. W. = 100.93. Density= 2.092 (Clarke). (Gerlach.) | 5.046 IO.O93 20.186 IOI.90 104.84 108.40 IO2.41 104.83 109.65 0.50 0.79 1. 14 CaCl 2 . M. W. = 110.64. Densiiy = 2.216 (Schroeder). (Gerlach.) NaN0 3 . M. W. = 84.88. Density= 2.244 (Clarke). 5-532 II.064 16.596 22.128 27.660 33-192 66.384 IOI.2 102.2 I03-5 IO4.8 106.3 I08.O 1 18.6 102.50 104.99 107.49 109.99 112.48 114.98 1 29.96 I.26 2.66 3-7i 4.72 5.50 6.07 8.74 (Kremers.) 8.488 16.976 42.440 84.880 102.9 1 06. 1 1 16.2 '34-3 103.78 107.56 1 1 8.91 137.82 0.85 1.36 2.28 2-55 SrCU. M. W. = 157.94. Densitv= 3.05 (Schroeder). NH,N0 3 . M. W. 1=79.90. Density = 1.74 (Schroeder). (Gerlach.) (Gerlach.) 7.895 15-79° 23-685 31.580 39-475 IOI.4 IO2.5 IO4.O IO5.5 I07.2 102.59 105.17 107.76 110.34 112.93 1. 16 2-55 3-43 4-39 5.07 7.990 15.980 39-95° 79.900 IO4.6 I09.3 124.4 149.8 104.59 109.18 122.96 I45-9 2 0.076 0.106 1.170 2.660 Smithsonian Tables. 132 CONTRACTION PRODUCED BY SOLUTION. Table 147. Grammes of the salt in too of water. Observed volume. Calculated volume. Per cent of contraction. Grammes of the salt in 100 of water. Observed volume. Calculated volume. Per cent of contraction. CatfJOsV M. W. = 163.68. Density = 2.36 (Clarke). NaaCOs- M. W. = 105.83. Density 2.476 (Clarke and Schroeder). (Gerlach.) (Gerlach.) 1-637 3-274 4.910 6.547 8.184 16.368 32-736 49.104 65-472 81.840 100.45 IOO.90 IOI.35 IOI.85 102.30 104.70 109.90 "5-55 121.50 127-65 IOO.69 101.39 102.08 102.77 10347 106.94 113.87 1 20.8 1 127.74 134.68 O.24 O.48 O.72 O.90 113 2.09 3-49 4-35 4.89 5.22 5.292 10.582 15-875 100.00 IOO.44 IOI.06 102.14 104.27 106.41 2.09 3-68 5-03 K 2 S0 4 . M. W. = 173.90. Density 2.647 (Clarke). (Gerlach.) Ba(NO s ) 2 . M. W. = 260.58. Density = 3.23 (Clarke). 8.695 IOI.94 103.29 1.30 (NH 4 ) 2 S0 4 . M. W. = 131.84. Density 1.762 (Clarke). (Gerlach.) 2.606 5.212 7.817 IOO.5 IOI.O 101.5 100.81 101.61 102.42 0.30 0.60 0.90 (Schiff.) 6.592 13.184 19.776 26.369 65.920 98.880 102.92 105.96 IO9.20 112.60 135.20 154.50 10374 107.48 112.26 114.97 I37-42 156.13 0.792 1.418 1. 82 1 2.060 1.615 1.044 Sr(N0 3 ) 2 . M. W. =210.98. Density = 2.93 (Clarke). (Gerlach.) FeS0 4 . M. W. = 151.72. Density 2.gg (Clarke). 2.II0 4-220 6.329 8-439 IO.549 21.098 42.196 63.294 IOO.48 IOO.95 IOI.4O 101.95 IO2.45 IO4.95 IIO.20 116.15 IOO.72 101.44 102.16 102.88 103.60 107.20 114.40 121.60 0.24 0.48 0.74 0.90 1. 11 2.10 3-67 4.48 # 7.586 15.172 22.758 3°-344 IOO.52 101.30 102.40 103.70 102.54 105.07 107.61 IIO.15 1.97 3-59 4.84 5-85 Pb(N0 8 ) 2 . M. W. — 165.09. Density = 4.41 (Clarke). MgSO,. M. W. = 197.6. Density 2.65 (Clarke). (Gerlach.) 16.509 33-OI8 82.545 IO2.4 105. 1 1 14.O 103.74 107.49 118.72 1.29 2.22 3-97 # 5.988 II.976 17.964 23-952 IOO.13 IOO.40 IOI.26 I02.IO 102 26 I04.52 106.78 IO9.O4 2.08 3-94 5.16 6.36 KX0 8 . M. W. = 137.93. Density 2.29 (Clarke and Schroeder). Na 2 S0 4 . M. W. =141.80. Density= 2.656 (Clarke). (Gerlach.) 6.897 13-793 20.689 27.586 68.965 96-55I IOO.96 102.22 103.78 105.44 118.20 128.10 I03.OT 100.02 109.08 112.05 130.12 142.16 1.99 3-59 4.82 5.90 9.16 9.89 (Gerlach. ) 7.09 14.18 IOO.96 102.26 IO2.67 IO5.34 1.67 2.92 Smithsonian Tables. : Authority not given. 133 Table 147. CONTRACTION PRODUCED BY SOLUTION. Grammes of the salt in ico of water. Observed volume. Calculated volume. Per cent of contraction. Grammes of the salt in 100 of water. Observed volume. Calculated volume. Per cent of contraction. ZnSO,. M. W. — 160.72. Density 3.49 (Clarke). KCgHgOj. M. W. = 97.90. Density = r.472 (Gerlach). * (Gerlach.) 8.036 16.072 24.108 32-I44 40.180 IOO.06 IOO.44 IOI.08 101.90 102.86 102.30 104.61 106.91 109.21 III. 51 2.19 3-98 5-45 6.69 7.76 979 19.58 48.95 97.90 I05.2 1 10.5 127-3 156.4 106.65 113-3° I33-26 166.51 I.36 2.47 4-47 6.07 K2C4H4O8. M. W. = 225.72. Density 1.98 (Gerlach). A1 2 K 2 (S0 4 )4- M. W. = 1 28.99. Density = 2.228 (Clarke). (Gerlach.) (Gerlach.) 6.450 IOO.58 102.90 2.25 22.572 45.144 67.716 90.288 112.860 '35-43 2 1 58.004 108.8 118.3 128.2 138.7 149.2 1 59-7 170.6 1 1 1.39 122.79 134.18 145.58 156.97 168.36 179.76 2-33 3.66 4.46 4-73 4-95 5-'5 5.10 NaCjHsOs. M. W. = 81.85. Density = 1.476 (Gerlach). (Gerlach.) 8.185 16.360 104.1 108.3 105.55 1 1 1.09 i-37 2.51 PMCjHjO.V M. W. = 162.06. Density 3.251 (Schroeder). Na 2 C,H 4 0,. M. W. = 193.62. Density 1.83 (Gerlach). (Gerlach.) (Gerlach.) 16.206 32.412 81.030 104.7 109.5 124.6 104.98 109.96 124.91 0.27 0.42 0.25 19.362 38-724 106.6 H4.2 IIO.57 121. 15 3-59 5-74 Table 148. CONTRACTION DUE TO DILUTION OF A SOLUTION.! The first column gives the name of the salt dissolved, the second the amount of the salt required to produce saturation and the third the contraction produced by mixing with an equal volume of water. Parts of an- Parts of an- Water with equal volume hydrate salt Contraction Water with equal volume hydrate salt Contraction of saturated solution of dissolved by when mixed. of saturated solution of dissolved by when mixed. following salts. 100 parts of H s O at io° C. Per cent. following salts. 100 parts of H 2 at io° C. Per cent. KC1 . 3'-97 °-3 2 5 NH4NOS . 185.OO 0.772 K 2 S0 4 IO.IO O.082 CaCl 2 . 63-30 1135 KNO3 . 20.77 O.144 BaCl 2 . 33-3° 0-235 K 2 CO a 88.72 2.682 MgS0 4 3°-5° O.677 NaCl . 35-75 8.04 O.490 Z11SO4 . 48.36 O.835 Na 2 S0 4 0.107 FeS0 4 . 19.90 O.327 NaN0 3 84.30 °-975 A1 2 K 2 (S0 4 )4 - 4.99 O.033 Na 2 CO s 16.66 0.206 C11SO4. 20.92 O.218 NH4CI 36.60 0.273 Pb(NO s ) 2 . 48.30 O.228 (NH4) 2 S04 . 1.302 Smithsonian Tables. * Authority not given. t R. Broom, " Proc. Roy. Soc. Edin." vol. 13, p. 172. 134 Table 149. FRICTION. The following table of coefficients of friction / and its reciprocal . //, together with the angle of friction or angle of repose * ,s quoted from Rankine's "Applied Mechanics." It was compiled by Rankine from the results of General Monn and other authorities, and is sufficient for all ordinary purposes. Material. f 1// * Wood on wood, dry .25-.50 4.0c— 2.00 14.0-26.5 " " " soapy Metals on oak, dry .20 .50-.60 5.00 2.00-1.67 26.5-31.0 " " " wet .24-.26 4-I7-3-8S '3-5-I4-S " " " soapy " elm, dry Hemp on oak, dry " " wet Leather on oak " metals, dry .20 5.00 11.5 .20-.25 •S3 • 33 „ ,27-. 3 8 .56 5.00-4.00, 1.89 3.00 3.70-2.86 1.79 1 1. 5-14.0 28.0 18.5 15.0-19.5 29.5 " " " wet •36 2.78 20.0 ' greasy ■ 2 3 4-35 13.0 " " " oily • J S 6.67 8.5 Metals on metals, dry . .15-.20 6.67-5.00 8.5-1 1.5 " " " wet . •3 3-33 16.5 Smooth surfaces, occasionally greased . .07-.08 14.3-12.50 4.0-4.5 " " continually greased . .05 20.00 3-o " " best results .... .03-.036 33.3-27.6 1.75-2.0 Steel on agate, dry * .20 5.00 11. 5 " " " oiled* .107 9-35 6.1 Iron on stone •30-70 3-33-1-43 16.7-35.0 Wood on stone About .40 2.50 22.0 Masonry and brick work, dry .... .60-.70 i-67-i-43 33.0-35.0 " '• " " damp mortar ■74 i-35 36-5 " on dry clay •Si 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 2-63-1-33 21.0-37.0 " " " damp clay 1. 00 1. 00 45.0 " " " wet clay •31 3-23 17.0 " " " shingle and gravel .81-1.11 1.23-0.9 39.0-48.0 * Quoted from a paper by Jenlcin and Ewing, " Phil. Tratis. 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 friction as the speed is reduced towards zero. Smithsonian Tables. 135 Table 150. VISCOSITY. The coefficient 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 in terms of the 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 whkh is great in compari- son with its diameter. Poiseuille * gave the following formula for calculating the viscosity coef- ficient in this case : /i= . , , where h is the pressure height, r the radius of the tube, 8 the density of the fluid, v 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 h and / are different. The product hs is the pressure under which the flow takes place. Hagenbach t pointed out that this formula is in error if the velocity of flow is sensible, and sug- gested a correction which was used in the calculation of his results. The amount to be sub- tracted from A, according to Hagenbach, is ~= — , where g is the acceleration due to gravity. \lz-g Gartenmeister % points out an error in this to which his attention had been called by Finkener, and states that the quanti ty to be subtracted from h should be simply — ; and this formula is g 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 formulas 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 temperature. TABLE 150. — Specific Viscosity of Water at different Temperatures relative to Water at 0° C. Authorities Absolute Temp. inC°. Mean value. value in C. G. S. Poiseuille. Gral am. Rellstab. Sprung. Wagner. Slotte. units. ioo.o 100.0 IOO.O IOO.O IOO.O IOO.O IOO.O IOO.O O.OI78§ 5 85.2 84.4 84.8 85-3 84.9 - - 84.9 O.OI51 10 73-5 73° 72.9 73-5 73- 2 - - 73-3 0.0131 '5 643 63-5 637 63.0 63-9 639 - 637 O.OI 13 20 56.7 56.0 56.O 55-5 56.2 56.2 56.4 56.2 0.0100 25 - 49-5 50-5 48.7 5°-5 5°-3 49.9 0.0089 3° 45.2 44-7 45.0 45.0 45.2 44.6 45.2 45.0 0.0080 35 - 40.2 41. 1 40.0 40.8 40.3 - 40.5 0.0072 40 - 36.8 37-o 37-= 37-o 3 6 7 36-9 36-9 0.0066 45 — 33-9 33-9 34-5 34-o 34-5 - 34-2 0.0061 50 30.8 3i-i 3'-' 31.2 3'-3 31-7 - 31.2 0.0056 * " Comptes rendus, 1 ' vol. 15, 1842. " M^m. Serv. Etr.'' 1846. t " Pogg. Ann." vol. iog, i860. X " Zeits. fiir Phys. Chim. ,: vol. 6, 1890. 5 The value 0.0178 is taken from a paper by Crookes (Phil. Trans. R. S. L. 1886), where the coefficient is given as (1=0.0177931/', where P-' = 1 + .0336793 7"+ .0002209936 7" 2 , where T is the temperature of the water in degrees Centigrade. The numbers in the table were calculated not from the formula but from the numbers in the column headed " mean value." Smithsonian Tables. 136 Tables 151-153. VISCOSITY. TABLE 151. — Solution ol Alcohol In Water.* Coefficients of viscosity, in C. G. S. units, for solution of alcohol in water. Temp. Percentage by weight of alcohol in the mixture. 8.21 16.60 34-58 43-99 53-36 75-75 87-45 99.72 0° 0.0l8l O.0287 O.O453 0.0732 O.0707 O.0632 O.O407 O.O294 0.0180 5 .0152 .0234 •0351 .0558 ■0552 .0502 •0344 .0256 ■01 63 .0131 ■OI95 .0281 •0435 .0438 .0405 .0292 .0223 .0148 '5 .0114 .0165 .0230 •°347 ■0353 •0332 .0250 .0195 .0134 .0101 .0142 •°I93 .O283 .0286 .0276 .0215 ■ .0172 .0122 25 0.0090 O.OI23 .OIOS a.0163 O.O234 O.O24I O.O232 O.O187 O.OI52 0.01.10 30 .0081 .0141 , .OI96 .0204 .0198 .0163 • OI 35 .0100 35 .0073 .0096 .0122 .OI67 .0174 .OI7I .0144 .0120 .0092 40 .0067 .0086 .0108 .OI43 .0150 .0149 .0127 .0107 .0084 4S .0061 .0077 .OO95 .0125 .0131 .OI3O .01 1 3 .0097 .0077 50 0.0056 O.O070 O.O085 0.0109 0.0II5 O.OII5 0.0102 0.0088 0.0070 55 .0052 .0063 .OO76 .OO96 .0102 .0102 .O09I .0086 .0065 60 .0048 .0058 .OO69 .0086 .OO9I .0092 .0083 .0073 .0060 The following tables (152-153) contain the results of a number of experiments in the viscosity of mineral oils derived from petroleum residues and used for lubricating purposes.! TABLE 152. — Mineral Oils.t TABLE 153. — Mineral Oils. >1 "Jo c a be □ . J; no °c. '2 S - ° °c. Sp. viscosity. Water at 20°C = 1. 20° C. 5°° C. 100° c. •931 .921 .906 243 216 189 274 246 208 - 11.30 7-31 3-45 2.9 2.5 i-5 .921 .917 163 132 190 168 - 27.80 2.8 2.6 .904 .891 .878 •855 170 108 42 207 182 148 45 8.65 4-77 2.94 1.65 2.65 1.86 1.48 i-7 i-3 .905 .894 .866 165 139 90 202 270 224 7.60 2.50 3.10 3.60 1.50 i-5 i-3 >. M ]B c EJii Oil. *5J a !'" b ° ■a ':-> b CO a °c. °c. J2o " Cylinder oil . . .917 227 274 iqi Machine oil . . .914 213 260 102 Wagon oil . . .914 148 182 80 .QII M7 187 70 Naphtha residue .910 134 162 55 Oleo-naphtha . .910 219 257 121 ■904 201 242 66 tt tt ■894 184 222 26 Oleonid . . . .884 i»5 217 28 " best quality .881 188 224 20 Olive oil . . . .916 _ _ 22 Whale oil . . .879 - - 9 « « .875 8 * This table was calculated from the table of fluidities given by Noack (Wied. Ann. vol. 27, p. 217), and shows a maximum for a solution containing about 40 per cent of alcohol. A similar result was obtained for solutions of acetic t Table 152 is from a paper by Engler in Dingler's " Polv. Jour." vol. 268, p. 76, and Table 153 is from a paper by Lamansky in the same journal, vol. 248, p. 29. The very mixed composition of these oils renders the viscosity a very uncertain quantity, neither the density nor the flashing point being a good guide to viscosity. t The different groups in this table are from different residues. Smithsonian Tables. ■> 137 TABLE 154. VISCOSITY. This table gives some miscellaneous 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 O.O160 O.OI49 II.9 14.5 Poiseuille. Anisol O.OI II 20.0 Gartenmeister. Glycerine it tt 42.20 25.18 13.87 8.30 4-94 2.8 8.1 143 20.3 26.5 Schottner. tt u Glycerine and water . <• it a it u tt 94.46 80.31 64.05 49-79 7-437 1.02 1 0.222 0.092 f" 5 8.5 tt it tt Glycol 0.0219 0.0 Arrhenius. Mercury* u it it a 0.0184 0.0170 0.0157 0.0122 0.0102 0.0093 — 20 0.0 20.0 1 00.0 200.0 300.0 Koch. <( it tt tt 1 Meta-cresol 0.1878 20.0 Gartenmeister. Olive oil 3.2653 1 0.0 Reynolds. Paraffins : Decane Dodecane . Heptane Hexadecane Hexane Nonane 0.0077 0.0126 0.0045 0.0359 0.0033 0.0062 22,3 2 3-3 24.0 23-7 22.3 Bartolli & Stracciati. tt 41 " it tt u tt tt tt it Octane Pentane Pentadecane Tetradecane Tridecane . Undecane . 0.0053 0.0026 0.0281 0.0213 0.0155 00095 22.2 21 22.0 21.9 23-3 22.7 tt tt tt tt tt it it tt tt tt tt tt Petroleum (Caucasian) 0.0190 17-5 Petroff. Rape oil tt tt 2 5'2 3-85 1.63 0.96 0.0 1 0.0 20.0 30.0 O. E. Meyer. tt tt tt | * Calculated from the formula ^=.017 — .00006M+ 00000021^ — .00000000025/= (vide Koch, Wied. Ann. vol. 14. p. 0- t Given as = 3.2653 «-■ hum 1 , where T is temperature in Centigrade degrees. Smithsonian Tables. 138 Table 1 55. VISCOSITY. This table gives the viscosity of a number of liquids together with their temperature variation. The headings are temperatures in Centigrade degrees, and the numbers under them the coefficients of viscosity in C. G. S. units.* Liquid. Temperatures Centigrade. Authority. Acetone .... Acetates : Allyl Amyl . Ethyl . Methyl . Propyl . Acids : t Acetic Butyric . Formic . Propionic it Salicylic Valeric Alcohols : Allyl . Amyl Butyl Ethyl Isobutyl Isopropyl Methyl . Propyl . Aldehyde .... Aniline Benzene .... Benzoates : Ethyl . Methyl Bromides : Allyl . Ethyl . Ethylene Carbon disulphide Carbon dioxide (liquid) Chlorides: Allyl . Ethylene Chloroform . . . Ether Ethyl sulphide . . Iodides : Allyl . . Ethyl . . Metaxylol. . . . Nitro benzene . . " butane . • " ethane. . . " propane . . " toluene . • Propyl aldehyde . Toluene .... .0043 .0068 .0106 .0051 .0046 .0066 .0150 .0196 .0231 .0125 .0139 .0320 .0271 .0206 .0651 .0424 .0150 .0580 •0338 .0073 .0293 .0037 .0073 .0265 .0231 .0061 .0043 .0008 .0039 .0064 .0026 .0048 .0080 .0064 .0075 .0119 .0080 .0099 .0047 .0068 .0039 .0061 .0089 .0044 .0041 .0059 .0126 .0163 .0184 .0107 .0118 .0271 .0220 .0163 .0470 .0324 .0122 .0411 .0248 .0062 .0227 .0037 .0440 .0064 .0217 .0196 .0053 .0037 .0169 .0036 .0007 .0036 .0083 .0057 .0023 .0043 .0072 .0057 .0066 .0203 .0103 .0071 .0087 •0233 .0041 .0059 .0036 .0054 .0077 .0040 .0036 .0052 .0109 .0136 .0149 .0092 .0101 .0222 .0183 .0128 •0344 .0247 .0102 .0301 .0185 .0054 .0179 .0319 .0055 .0174 .0160 .0048 .0035 .0149 .0035 .0005 •0033 .0072 .0052 .0021 .0039 .0065 .0052 .0058 .0170 .0089 .0064 .0077 .0190 .0036 .0052 .0032 .0049 .0065 .0035 .0032 .0044 .0094 .0118 .0125 .0081 .0091 .0181 •01 SS .0103 .0255 .0190 .0085 .0223 .0140 .0047 .0142 .0241 .0048 .0146 .0134 .0045 .0034 .0063 .0046 •°°35 .0059 .0048 .0052 .0144 .0078 .0057 .0068 .0159 •0033 .0047 .0028 .0044 .0058 .0032 .0030 .0039 .0082 .0102 .0104 .0073 .0080 .0150 .0127 .0083 .0196 .0150 .0072 .0170 .0108 .0041 .0115 .0189 .0043 .0124 .0115 .0041 .0056 .0043 .0032 .0053 .0044 .0047 .0124 .0069 .0052 .0061 .0136 .0042 Pribram & Handl. Gartenmeister. it Rellstab. Pribram & Handl. Rellstab. u Pribram & Handl. » << u tt Gartenmeister. Rellstab. Wijkander. Rellstab. it Pribram & Handl. Wijkander. Warburg & Babo. Pribram & Handl. - Calculated from the specific viscosities given in Landolt & Boernstein's " Phys. Chem. Tab." P . *8 9 et «,, on the assumption that the coefficient for water at o° C. is .0.78. t For inorganic acids, see Solutions. Smithsonian Tables. 139 Table 156. VISCOSITY OF SOLUTIONS. This table is intended to show the effect of change of concentration and change of temperature on the viscosity of solmions of salts in water. The specific viscosity X 100 is given for two or more densities and fa.r several tem- peratures in the case of each solution, /i stands for specific conductivity, and / for temperature Centigrade. Salt. Percentage by weight of salt in soiution. Density. H- t f t f t H- t Authority. BaCl 2 it 7.60 15.40 24-34 - 77-9 86.4 100.7 10 44.0 56.0 66.2 3? It 35-2 39-6 47-7 50 it it - : Sprung. it Ba(N0 3 ) 2 (f 2.98 5.24 1.027 1.051 62.0 68.1 15 51.1 54.2 25 42.4 44.1 35 34-8 36-9 45 Wagner. 11 CaCl2 it ft tt 15.17 31.60 3975 44.09 - 1 10.9 272.5 670.0 10 7i-3 177.0 379-o 593-1 30 ft ff 11 50-3 124.0 245-5 363-2 50 - - Sprung. !( 11 If Ca(N0 3 ) 2 tt it '7-55 30.10 40.13 1.171 1.274 1.386 93-8 144. 1 242.6 15 74.6 1 1 2.7 217.1 25 (( (( 60.0 90.7 156.5 35 (1 49.9 75-i 128.1 45 11 Wagner. CdCl 2 1 1.09 16.30 24.79 1. 109 1.181 1.320 77-5 88.9 104.0 15 11 60.5 70.5 80.4 25 11 it 49-i 35 11 40.7 47.2 53-6 45 it Cd(NO s ) 2 (( ff 7.81 15.71 22.36 1.074 1-159 1.241 61.9 71.8 85.1 15 (1 If 50.1 58.7 69.0 25 41. 1 48.8 57-3 35 11 34-0 4i-3 47-5 45 11 tt CdS0 4 11 u 7.14 14.66 22.01 1.068 1-159 1.268 78.9 96.2 120.8 15 (1 61.8 72.4 91.8 25 49.9 58.1 73-5 35 41-3 48.8 60.1 45 tt tt tt tt u C0C1 2 11 ft 7-97 14-86 22.27 1. 08 1 1.161 1.264 83.0 1 1 1.6 161.6 15 65.1 85.1 126.6 25 ft 11 53-6 73-7 1 01 .6 35 44.9 58.8 g 5 .6 45 a u Co(N0 8 ) 2 11 8.28 15.96 24-53 1-073 1.144 1.229 74-7 87.0 1 10.4 15 It tt 57-9 69.2 88.0 25 11 487 55-4 7i-5 35 39-8 44-9 59.1 45 ff tt u u C0SO4 It it 7.24 14.16 21.17 1.086 1. 159 1.240 86.7 1 17.8 193.6 15 a 68.7 95-5 146.2 25 11 55-o 76.0 1 13.0 35 45.1 61.7 89.9 45 ti tt CUCI2 (1 II 12.01 21-35 33-°3 1. 104 1.215 i-33i 87.2 121. 5 178.4 15 ff 67.8 95-8 137-2 25 55-i 77.0 107.6 35 (1 45.6 63.2 87.1 45 If tt tt tt Cu(NO s ) 2 11 tt 18.99 26.68 46.71 1.177 1.264 1-536 97-3 126.2 382.9 15 76.0 98.8 283.8 25 (( 11 61.5 80.9 2153 35 tt Si-3 68.6 172.2 45 1( It tt tt if C11SO4 11 11 6.79 12.57 17.49 1.055 1.115 1-163 79.6 98.2 124.5 15 it tt 61.8 74.0 96.8 25 ti 49.8 59-7 75-9 35 ff 11 41.4 52.0 61.8 45 it 11 11 HC1 11 (( 8.14 16.12 23.04 1-037 1.084 1.114 71.0 80.0 91.8 15 it 57-9 66.5 79-9 25 tt 48.3 56.4 65.9 35 40.1 48.1 56.4 45 11 tt tt HgCl 2 0.23 3-55 1.023 1-033 76.75 10 58.5 59-2 20 It 46.8 46.6 3° 38-3 38.3 40 11 tt tt Smithsonian Tables. I40 VISCOSITY OF SOLUTIONS. Table 156 Salt. Percentage by weight of salt in solution. Density. »* 1 * t m / H t Authority. HNO s a 8-37 12.20 28.31 I.067 1. 116 1. 178 66.4 69.5 80.3 '5 ti 54-8 57-3 65-5 25 it 45-4 47-9 54-9 35 tt (( 37-6 40-7 46.2 45 (I it Wagner. H 2 S0 4 ii tt 7.87 2343 I.065 1. 130 1.200 77-8 95-i 122.7 r 5 It ti 61.0 75-o 95-5 25 it It 50.0 60.5 77-5 35 (1 tt 41.7 49.8 64-3 45 ii ti a t( KC1 10.23 22.21 - 70.0 70.0 10 46.1 48.6 30 36-4 5p _ - Sprung. KBr tt I4.O2 23.16 34-64 - 67.6 66.2 66.6 10 tt 44.8 44-7 47-0 30 tt 32.1 33-2 35-7 50 it - - a ti KI tt tt tt 8.42 17.01 33-°3 45.98 S4-oo - . 69-5 65-3 61.8 63.0 68.8 10 (( tt tt 44.0 42.9 42.9 45.2 48.5 3p it (( it 3i-3 31-4 32-4 35-3 37-6 50 tt it ti tt - - u tt tt KClOs ii 5.69 - 7i-7 10 (( 44-7 45.0 30 it 3i-5 314 50 it _ - ti ti KNO s 6.32 12.19 17.60 _ 70.8 68.7 68.8 10 a 44.6 44.8 46.0 30 It 3i-8 32-3 33-4 50 ti ti - - ti K 2 S0 4 ti 5-'7 9-77 - 77-4 81.0 10 48.6 52.0 30 34-3 36-9 50 ii - - (t K 2 Cr0 4 it "•93 19.61 24.26 32-78 i- 2 33 75.8 85-3 97.8 109.5 TO it tt it 62.5 68.7 74-5 88.9 30 tt it tt 41.0 47-9 62.6 4p - - a Slotte. Sprung. ■ 4.71 6.97 1.032 1.049 72.6 73-i 10 55-9 56-4 20 45-3 45-5 30 (f 37-5 37-7 40 Slotte. LiCl it 7.76 1391 26.93 : 96.1 121. 3 229.4 10 tt a 59-7 75-9 1 42. 1 3° it 41.2 52.6 98.0 50 tt — - Sprung. a ti ! Mg(N0 8 ) 2 (C 18.62 34-19 39-77 1. 102 1.200 I.43O 99.8 2 i3-3 3'7-° 15 81.3 164.4 250.0 25 a tt 66.5 132.4 191.4 35 ii 56.2 109.9 158-1 45 ii Wagner. u tt MgS0 4 ii ti 4.98 9.50 19.32 _ 96.2 130.9 302.2 10 59.0 77-7 166.4 3° 40.9 53-° 106.0 50 tt - ~ Sprung. n ■ MgCr0 4 12.31 21.86 27.71 I.089 1. 164 I.2I7 111.3 1 67. 1 232.2 10 84.8 I2 5-3 172.6 20 674 99.0 133-9 30 tt 55.0 79-4 106.6 40 it Slotte. ! u tt MnC1 2 ti 8.01 iS-65 3°-33 40.13 I.O96 H96 1-337 1-453 92.8 130-9 256-3 537-3 15 71. i 104.2 193-2 393-4 25 tt 84.0 155.0 300.4 35 U it 48.1 68.7 123.7 246.5 45 Wagner. ; tt Smithsonian Tables. 141 Table 156. VISCOSITY OF SOLUTIONS. Percentage Salt. by weight of salt in solution. Density. p t !>■ 1 H- t c t Authority. Mn(NO a ) 2 18.31 1. 148 96.O 15 76.4 25 64.5 35 55-6 45 Wagner. " 29.60 I-323 167.5 ff 126.0 it IO4.6 88.6 ff tt " 49-31 I.506 396.8 " 30I.I " 221.0 (( 188.8 ft it MnS0 4 11.45 1. 147 129.4 15 98.6 25 78.3 35 63-4 45 tt " 1S.80 1.251 228.6 " 172.2 it I37-I 107.4 n tt tt 22.08 I.306 661.8 " 474-3 It 347-9 " 266.8 " tt NaCl 7-95 - 82.4 10 52.0 30 3i-8 50 - - Sprung. it I4-3 1 - 94-8 (( 60.1 a 30-9 ti - - a ci 23.22 — 128.3 79-4 tt 47-4 " — — it NaBr f 7 l - l^ 10 48.7 30 34-4 50 - — " " 18.58 - 82.6 (( 53-5 a 38.2 - tt (( 27.27 — 95-9 (( 61.7 tt 43-8 (( - ti Nal 8.83 - 73 i 10 46.0 3° 32-4 5° - - u " 17.15 — 73-8 H 47-4 n 33-7 tt — — tt it 35-69 - 86.0 " 55-7 a 40.6 it - tt " 55-47 - 157-2 it 96.4 tt 66.9 (i - - 11 NaClOs 11.50 - 78.7 10 50.0 3° 35-3 50 - - tt ft 20.59 - 88.9 tt 56.8 it 40.4 (( - - a 33-54 — 121.0 ti 75-7 it 53-o ft - tt NaNOs 7.25 - 75.6 10 47-9 3° 33-8 5° - - u (( 12-35 - 81.2 it 51.0 36.1 tt - — it ft 18.20 - 87.0 a 55-9 (( 39-3 tt - it it 3'-55 - 121. 2 it 76.2 it 53-4 (( - it ! Na 2 S0 4 4.98 - 96.2 10 59.0 30 40.9 50 - - tt " 9.50 - 130.9 " 77-7 " 53-° tt - - it " 14.03 — 187.9 a 107.4 (C 71. 1 ct — — tt ft 19.32 - 302.2 if 166.4 " 106.0 tt - - tt Na 2 Cr0 4 5-76 I.058 85.8 10 66.6 20 53-4 30 43-8 40 Slotte. tf 10.62 1. 112 i°3-3 " 79-3 tt 63-5 a 5 2 -3 tt tt 14.81 1. 164 127.5 a 97.1 77-3 it 63.0 " tt NH4CI 3.67 - 7i-5 TO 45.0 30 3i-9 50 - _ Sprung. ft 8.67 - 69.1 " 45-3 t« 32.6 " - - " tt 15.68 - 67-3 it 46.2 " 34-o it - - tf tt 23-37 - 67.4 " 47-7 it 36.1 " - - u NH 4 Br 15-97 - 65.2 10 43-2 3° 3i-5 5° _ _ tt " 25-33 36.88 - 62.6 " 43-3 it 32.2 ft - - it " — 62.4 « 44.6 it 34-3 tt - - tt NH4NO3 5-97 - 69.6 10 44-3 3° 31.6 5° _ _ » " 12.19 - 66.8 K 44-3 (( 3'-9 tt - - a « 27.08 - 67.0 << 47-7 a 349 tt - - it (( 37-22 — 7i-7 (i 51.2 tt 38.8 tt — _ tt ff 49-83 - 81.1 u 63-3 tt 48.9 " - - tt (NH 4 ) 2 S0 4 8.10 - 107.9 10 52-3 30 37-o 50 _ _ « " 15.94 - 120.2 u 60.4 « 43-2 (< - - a " 25-51 148.4 «( 74-8 54.1 <( " tt Smithsonian Tables. I42 VISCOSITY OF SOLUTIONS. Table 156. Salt. (NH 4 ) 2 Cr0 4 ti tt (NH 4 )2Cr 2 07 (( (« NiCl 2 it tt Ni(N0 3 ) 2 U NiS0 4 11 (( Pb(NO s ) 2 « Sr(N0 8 )i, ti it ZnCl 2 a Zn(N0 3 ) 2 tt It ZnS0 4 Percentage by weight of salt in solution. 10.52 1975 28.04 6.85 13.00 19-93 11.45 22.69 30.40 16.49 30.01 40.95 10.62 18.19 25-35 17-93 32.22 10.29 21.19 32.61 15-33 23-49 3378 15-95 3°- 2 3 44.50 7.12 16.64 23.09 Density. I.063 1. 120 I-I73 1.039 1.078 1. 126 1. 109 1.226 1-337 1.136 1.278 1.388 1.092 1. 198 i-3H 1.179 1.362 1.088 1. 124 1.307 1. 146 1.229 1-343 1.115 1.229 1-437 1. 106 "95 1.281 79-3 88.2 72-5 72.6 77.6 90.4 140.2 229.5 90.7 J35-6 222.6 94.6 154.9 298.5 74.0 91.8 69-3 87-3 116.9 93-6 111.5 151.7 80.7 104.7 167.9 97.1 156.0 232.8 15 15 15 15 15 15 IS 15 62.4 70.0 80.7 56-3 57-2 58.8 70.0 109.7 171.8 70.1 105.9 169.7 73-5 1 19.9 224.9 59.1 72.5 56.0 69.2 93-3 72.7 86.6 117.9 64-3 85.7 130.6 79-3 1 18.6 177-4 25 25 25 25 25 25 25 25 57-8 60.8 45-8 46.8 48.7 g 7 .8 139.2 574 128.2 60.1 99-5 173.0 48.5 59.6 45-9 57.8 76.7 57.8 69.8 90.0 52.6 69.5 105.4 62.7 94-2 135-2 3° 3° U 35 tt 35 35 it il 35 35 ti ft 35 (( i( 35 (( (( 35 42.4 48.4 56-4 38.0 39-i 40.9 48.2 72.7 111.9 70.7 152.4 49.8 75-7 152.4 40.3 50.6 39' 48.1 62.3 48.2 72.6 43-8 57-7 87.9 S'-S 73-5 108. 1 40 40 45 45 45 45 45 45 45 45 Authority. Slotte. Wagner. Smithsonian Tables. 143 Table 157. SPECIFIC VISCOSITY. Dissolved salt. Normal solution. i normal. i normal. J normal. Authority. >, >, >, E-l >, c H v u c 'y c V (J c u ° e a. w a a Acids : Cl 2 08 . . HC1 . . . 1.0562 I. OI2 1.0283 I.003 1.0143 I. OOO 1 .0074 O.999 Reyher. 1.0177 I.067 1.0092 I.034 1.0045 1. 01 7 1.0025 I.009 " HClOs . . 1.0485 I.O52 1.0244 I.025 1. 01 26 1.014 1.0064 I.OO6 « HN0 8 . . 1 -°33 2 1.027 1. 01 68 I.OII 1.0086 1.005 1.0044 I.003 " H 2 S0 4 . . 1.0303 I.O9O 1.0154 I.O43 1.0074 1.022 1.0035 I.OO8 Wagner. Aluminium sulphate Barium chloride . . 1.0550 1.0884 I.406 I-I23 1.0278 1. 0441 1. 178 1-057 1.0138 1.0226 1.082 1.026 1.0068 1.0114 I.O38 I.OI3 « " nitrate . . — — 1.0518 I.O44 1.0259 1. 02 1 1. 0130 I.OOO tt Calcium chloride 1.0446 1. 156 1. 02 18 I.O76 1.0105 1.036 1.0050 I.0I7 a " nitrate 1.0596 1. 117 1.0300 1-OS3 1.0151 1.022 1.0076 I.OO8 a Cadmium chloride . 1.0779 I-I34 1.0394 I.063 1.0197 1. 03 1 1.0098 1.020 tt " nitrate 1.0954 I.I6S 1.0479 I.O74 1 .0249 1.038 1.0119 I.0I8 t* " sulphate . i-°973 I.348 1.0487 1. 157 1.0244 1.078 1.0120 1-033 " Cobalt chloride . . 1.057 1 1.204 1.0286 I.097 1.0144 1.048 1.0058 1.023 tt " nitrate . . 1.0728 1. 166 1.0369 I.O75 1.0184 1.032 1.0094 1.018 tt " sulphate . . 1.0756 2-354 1-0383 I. l6o 1-0193 1.077 I.OIIO 1.040 11 Copper chloride . . 1.0624 1.205 1-0313 I.09S 1.0158 1.047 1.0077 1.027 tt " nitrate . . 1-0755 i-'79 1.0372 I.080 1.0185 1.040 1.0092 1.018 " " sulphate 1.0790 1-358 1 .0402 1. 160 1.0205 1.080 1.0103 1.038 u Lead nitrate . . . 1.13S0 I.IOI 0.0699 I.O42 1. 0351 1.017 1-0175 1.007 tt Lithium chloride 1.0243 1. 142 1.0129 I.066 1 .0062 1-031 1.0030 1. 01 2 u " sulphate 1 -04S3 1.290 1.0234 I-I37 1.0115 1.065 1.0057 1.032 tt Magnesium chloride i-'375 1. 231 1.0188 I.O94 1. 009 1 1.044 1.0043 1. 021 tt " nitrate . 1.0512 1.171 1.0259 1.082 1. 01 30 1.040 i.oc66 1.020 tt " sulphate 1.0584 1-367 1.0297 1. 164 1.0152 1.078 1.0076 1.032 tt Manganese chloride 1.0513 1.209 1.0259 I.O98 1.0125 1.048 1.0063 1.023 tt " nitrate . 1.0690 1.1S3 1-0349 I.087 1.0174 1.043 1.0093 1.023 a " sulphate 1.0728 i-3 6 4 1.0365 1. 169 1.0179 1.076 1.0087 1-037 " Nickel chloride . . 1.0591 1.205 1.0308 I.O97 1.0144 1.044 1.0067 1.021 « " nitrate . '■°755 1.1S0 1. 038 1 I.084 1.0192 1.042 1 .0096 1.019 tt " sulphate . . 1 -0773 1. 361 1-0391 I. l6l 1.0198 1.075 1. 001 7 1.032 « Potassium chloride . 1.0466 0.9S7 1.0235 O.987 1.0117 0.990 1.0059 0-993 it " chromate r -°935 I-H3 1.0475 T -o53 1. 0241 1.022 1. 01 2 1 1.012 K " nitrate . 1.0605 °-975 1-0305 0.982 1.0161 0.987 1.0075 0.992 tt sulphate 1.0664 1. 105 1-0338 1.049 1.0170 1. 02 1 1.0084 1.008 (( Sodium chloride . . 1.0401 1.097 1.0208 1.047 1.0107 1.024 1.0056 1-013 Reyher. " bromide . . 1.0786 1.064 1.0396 1.030 1.0190 1.015 1. 0100 1.008 « " chlorate 1.07 10 1.090 i-°359 1.042 1.0180 1.022 1.0092 1.012 » " nitrate . . I-0554 1.065 1.0281 1.026 1.0141 1. 01 2 1. 007 1 1.007 a Silver nitrate . . . 1.1386 1.05S 1.0692 1.020 1.0348 1.006 1.0173 1.000 Wagner. Strontium chloride . 1 .0676 1.141 1-0336 1.067 1.0171 1.034 1.0084 1.014 (( " nitrate . 1.0S22 1. ii S 1. 0419 1.049 1.0208 1.024 1.0104 r\ou i( Zinc chloride 1.0509 1. 189 1.0302 1.096 1.0152 i-o53 1.0077 1.024 » " nitrate 1-0753 1. 164 1.0404 1.0S6 1.0191 1.039 1 .0096 1. 019 » " sulphate . . . 1.0792 I-367 1.0402 I-I73 1.0198 1.082 1.0094 1.036 u * In the case of solutions of salts it has been found {vide Arrhennins, Zeits. fur Phvs. Chem. vol. i, p. 28O that the specific viscosity can in many cases be nearly expressed by the equation M = ^», where ft, is the specific viscosity for a normal solution referred to the solvent at the same temperature, and n the number of gramme molecules in the solution under consideration. The same rule may of course be applied to solutions stated in percentages instead of gramme molecules. The table here given has been compiled from the results of Reyher (Zeits. fur Phys. Chem. vol 2, p. 749) and of Wagner (Zeits. fur Phys. Chem. vol. 5, p. 31) and illustrates this rule. The numbers are all for 2s C. Smithsonian Tables. I44 Table 158. VISCOSITY OF CASES AND VAPORS. The values of ji given in the table are 10° times the coefficients of viscosity in C. G. S. units. Substance. Temp. °C. *<• Authority. Substance. Temp. °C. f Authority. Acetone .... 18.0 78 Puluj. Carbon dioxide . 12.8 1 00.0 147 208 Schumann. Air 0.0 172 Thomlinson. 0.0 168 Obermeyer. Carbon monoxide 0.0 163 Obermeyer. 16.7 183 Puluj. Chlorine . . . 0.0 129 Graham. Alcohol : Methyl . 66.8 J3S Stendel. tt 20.0 H7 it Ethyl . 78.4 142 <( Normal Chloroform . . 17.4 103 Puluj. propyl 974 142 « Ether .... 16.0 73 » Isopropyl 82.8 162 " Normal Ethyl iodide . . 73-3 216 Stendel. butyl 116.9 143 " Methyl "... 44.0 232 a Isobutyl 108.4 144 " Tertiary Mercury . . . 270.0 489 Koch* butyl 82.9 160 tt tt 300.0 330-° 536 582 (( Ammonia . . . 0.0 96 Graham. tt 360.0 627 tt tt 20.0 108 it tt 390.0 671 (t Benzene . . . 19.0 79 Schumann. Water .... 0.0 90 Puluj. « 1 00.0 118 tt " .... 16.7 97 " u 100.0 132 L. Meyer & Carbon disulphide 16.9 99 Puluj. Schumann. * The values here given were calculated from Koch's table (Wied. Ann. vol. 19, p. 869) by the formula H = 489 [1 + 746 (t — 270)]. Smithsonian Tables. 145 Table 159. COEFFICIENT OF VISCOSITY OF CASES. The following are a few of the formulae that have been given for the calculation of the coefficient of viscosity of £ for different temperatures. Gas. Value of fj.. Authority. Air it it Ho (I + .002751 / — .00000034/ 2 ) .000172 (1 + 00273/) .0001683 ( x + -00274/) Holman. O. E. Meyer. Obermeyer. Carbon dioxide . . U t( jio (i + .003725 / — .00000264 / 2 + .OOOOOOOO417 / 8 ) .0001414 (1 + .00348/) Holman. Obermeyer. Carbon monoxide . .0001630 (1 + -00269/) .0000966 (1 + .00350/) Ethylene chloride . .0000935 (1 + .00381 /) Hydrogen .... .0000822 (1 + .00249/) Nitrogen .... .0001635 (1 + .00269/) Nitrous oxide (N 2 0) .0001408 (1 + .00345 /) .0001873 (1 + .00283/) Smithsonian Tables. I46 Table 1 60. DIFFUSION OF LIQUIDS AND SOLUTIONS OF SALTS INTO WATER. The coefficient o£ diffusion as tabulated below is the constant which multiplied by the rate of change of concentration in any direction gives the rate of flow in that direction in C. G. S. units. Suppose two liquids diffusing into each other, and let p_ be the quantity of one of them per unit volume at a point A , and p' the quantity per unit volume at an adjacent point B, and x the distance from A to B. Then if x is small the rate of flow from A towards B is equal to k (p — p')/x, where k is the coefficient of diffusion. Similarly for solutions of salts diffusing into the sol- vent medium, p and p' being taken as the quantities of the salt per unit volume. The results indicate that h depends on the absolute density of the solution. Under c will be found the concentration in percentage of *' normal solu- tion " of the salt; under n the number of grammes of water per gramme of salt or of acid or other liquid. Substance. c n 7c X 10' Temp. C. Authority. Ammonia _ 16.0 123 4-5 Scheffer.* <( - 85.0 123 4-5 (( Ammonium chloride . 2 3 — J 35 1 0.0 Schumeister.f <( <( 61.0 152 J 7-5 Scheffer Barium chloride . - 46.0 76 8.0 « Calcium chloride - 13.0 83 9.0 u (( 1C - 297.0 74 9.0 tt u tt — 384.0 79 9.0 " tt tt 10 79 1 0.0 Schumeister. Cobalt chloride . 10 - S3 10.0 ft Copper " 10 - 5° 10.0 «( Copper sulphate 10 — 24 1 0.0 " Hydrochloric acid - S o 267 0.0 Scheffer. U It — 9.8 215 0.0 " U (i - 14.1 i9S 0.0 " ft tt - 27.1 176 0.0 " tt tt - 129.5 161 0.0 tt tt tt - 7- 2 3°9 1 1.0 " it tt - 27.6 245 II.O " tt tt - 69.4 234 1 1.0 " it it - 108.4 213 II.O " Lead nitrate - 136.0 76 12.0 " tt tt _ 514.0 82 12.0 Lithium chloride 14 81 1 0.0 Schumeister. " bromide 20 — 93 10.0 a tt 38 — 100 1 0.0 " iodide . 17 93 1 0.0 " ( Magnesium sulphate 10 45.0 32 32 10.0 5- 5 Scheffer. u >• - 184.0 37 5-5 " •• tt - 30.0 31 1 0.0 tt tt - 248.0 39 10.0 Potassium chloride - 32.0 106 7.0 u tt tt 107.0 7.0 tt tt 10 127 10.0 Schumeister. it " 3° - 147 10.0 " bromide 10 - I3 1 10.0 (i tt tt 3° - 144 10.0 it " iodide 10 - 130 10.0 it tt 3° — H5 1 0.0 it tt 90 - 168 10.0 tt " nitrate " sulphate Sodium chloride tt tt 15 13 10 3° - § 3 87 106 10.0 1 0.0 1 0.0 10.0 ti tt tt " bromide 3° 99 10.0 tt " iodide . 15 - 93 1 0.0 tt tt tt 3° - 100 1 0.0 ti " nitrate . " carbonate " sulphate 10 13 10 2.9 7-3 69 76 225 234 1 0.0 10.0 10.0 9.0 9.0 Scheffer. Nitric acid . _ (( _ 3S-o 206 9.0 " " _ 426.0 200 9.0 Sulphuric acid . u tt - 18.8 125.0 124 "5 8.0 8.5 ti tt tt _ 686.0 132 9.0 " " _ 0.5 150 13.0 u it « - 35-° 144 13.0 * " Chem. Ber." vol. 15, p. 788. t "Wiei 1. Akad. Ber " VOl. 78, 2 Abth. p. 957- Smithsonian Tables. T/17 Table 161. DIFFUSION OF GASES AND VAPORS. Coefficients of diffusion of vapors in C. G. S. units. The coefficients are for the temperatures given in the table and a pressure of 76 centimetres of mercury.* Vapor. Temp. C. kt for vapor diffusing into ht for vapor diffusing into Tct for vapor diffusing into hydrogen. air. carbon dioxide. Acids : Formic .... O.O o-S r 3i O.I315 O.0879 u 65.4 07873 O.2035 01343 " .... 84.9 0.8830 O.2244 O.1519 Acetic .... O.O 0.4040 O.IOOI O.0713 " .... 65.5 0.62 1 1 O.1578 O.IO48 a 98.5 0.7481 O.I965 O.1321 Isovaleric .... O.O 0.21 18 0-0555 0-0375 98.O °-3934 O.IO3I O.0696 Alcohols : Methyl .... O.O 0.5001 O.I325 O.0880 i* 25.6 0.6015 O.1620 O.IO46 n 49.6 0.6738 O.1809 0.1234 Ethyl . . . . O.O 0.3806 O.O994 O.0693 O.0898 . 40.4 0.5030 O.1372 . 66.9 0.5430 O.I475 0.1026 Propyl .... O.O 0-3I53 O.0803 O.0577 " .... 66.9 0.4832 O.I237 O.090I " .... 83-5 0-5434 0-I379 O.0976 Butyl .... O.O 0.2716 O.0681 O.0476 it 99.O 0.5045 O.I265 O.0884 Amyl .... O.O 0.2351 O.0589 0.0422 " .... 99.I 0.4362 O.IO94 0.0784 Hexyl .... 0.0 0.1998 O.O499 O.0351 99° 0.3712 O.0927 O.0651 Benzene 0.0 0.2940 O.075I 0.0527 " ...... 19.9 0.3409 O.0877 0.0609 45.0 0.3993 O.IOII O.0715 Carbon disulphide .... 0.0 0.3690 O.0883 0.0629 it (C 19.9 0.4255 O.IOI5 0.0726 ti it 32-8 0.4626 0.1 120 O.0789 Esters : Methyl acetate . 0.0 o-3357 0.0852 O.057 i t( n 20.3 0.3928 0.1013 O.0679 Ethyl "'.'.'. 0.0 0-2373 0.0630 O.0450 "... 46.1 0.3729 0.0970 O.0666 Methyl butyrate . 0.0 0.2422 0.0640 O.0438 it a 92.1 0.4308 0.1 139 O.0809 Ethyl "'.'.'. 0.0 0.2238 0-0573 0.0406 it ti 96.5 0.41 12 0.1064 O.0756 " valerate . 0.0 0.2050 0.0505 O.0366 97.6 0.3784 0.0932 O.0676 Ether 0.0 0.2960 0.0775 O.0552 19.9 0.3410 0.0893 O.0636 Water 0.0 0.6870 0.1980 O.I310 . . . . . 49-5 1. 0000 0.2827 O.IOII 92.4 1.1 794 0-345 1 0.2384 * Taken from Winkelmanirs papers (Wied. Ann. vols. 22, 23, and 26). The coefficients for o° were calculated by Winkelmann on the assumption that the rate of diffusion is proportional to the absolute temperature. According to the investigations of Loschmidt and of Obermeyer the coefficient of diffusion of a gas, or vapor, at o° C. and a pressure of 76 centimetres of mercury may be calculated from the observed coefficient at another temperature and pressure by the formula k^ = k T \-^j T-, where T is temperature absolute and /> the pressure of the gas. The exponent « is found to be about 1.75 for the permanent gases and about 2 for condensible gases. The following are examples: Air — C0 2 , »=i.o68; C0 S — N 2 0, n — i.oi; C0 2 — H, »=i. 74 2; CO — O, «= 1.785 ; H — O, «="-75S; O — N, n= 1.792. Winkelmann's results, as given in the above table, seem to give about 2 for vapors diffusing into air, hydrogen or carbon dioxide. Smithsonian Tables. I48 Table 162. COEFFICIENTS OF DIFFUSION FOR VARIOUS CASES AND VAPORS.* Gas or vapor diffusing. Gas or vapor diffused into. Temp. Coefficient of diffusion. Authority. Air Carbon dioxide . 0-1343 Obermayer. a Oxygen 0.1775 a Carbon dioxide . Air O 0.1423 Loschmidt. it u k 0.1360 Waitz. (( it Carbon monoxide 0.1405 0.1314 Loschmidt. Obermayer. a a Ethylene 0.1006 if a (( Hydrogen 0-5437 ' a « Methane O 0.1465 " (i « Nitrous oxide 0.0983 Loschmidt. tt <« Oxygen 0.1802 " Carbon disulphide Air 0.0995 Stefan. Carbon monoxide Carbon dioxide 01314 Obermayer. (c a Ethylene o 0.1164 " « Hydrogen 0.6422 Loschmidt. Oxygen it o 0.1802 0.1872 Obermayer. i Ether Air . '. o 0.0827 Stefan. it Hydrogen 0.3054 " Hydrogen . Air Carbon dioxide o 0.6340 0.5384 Obermayer. ( " monoxide o 0.6488 " « Ethane . 0-4593 0.4863 i Ethylene t Methane o 0.6254 i Nitrous oxide o 0-5347 < Oxygen o 0.6788 Nitrogen Oxygen 0.1787 <{ Oxygen n a Carbon dioxide Hydrogen . Nitrogen o 0-1357 0.7217 0.1710 Loschmidt. Obermayer. Sulphur dioxide Water Hydrogen Air 8 0.4828 0.2390 Loschmidt. Guglielmo. it n Hydrogen 18 18 0.2475 0.8710 * Compiled for the most part from a similar table in Landolt & Boernstein's " Phys. Chem. Tab.' Smithsonian Tables. 149 Table 163. OSMOSE. The following table given by H. de Vries* illustrates an apparent relation between the isotonic coefficient t of solu- tions and the corresponding lowering of the freezing-point and the vapor pressure. The freezing-points are taken on the authority of Raoult, and the vapor pressures on the authority of Tammann. t Isotonic Molecular lowering of the freezing point X 100. Molecular lowering of Substance. Formula. coefficient X 100. the vapor pressure X 1000. Glycerine .... CsHgOg 178 171 _ Cane sugar . C12H22011 188 185 - Tartaric acid C 4 H 6 6 202 19s 188 1 Magnesium sulphate MgSO* I96 192 156 Potassium nitrate KN0 3 3OO 308 267 Sodium nitrate . NaNOs 3OO 337 296 Potassium chloride KC1 287 336 3 r 3 Sodium chloride . NaCl 3°5 35 1 33° Ammonium chloride NH4CI 3OO 348 313 Potassium acetate KC 2 H 3 2 3OO 345 33 1 Potassium oxalate K 2 C 2 4 393 45° 37 2 Potassium sulphate K 2 S0 4 39 2 39° 35i Magnesium chloride MgCl 2 433 488 5'3 Calcium chloride CaCl 2 463 466 5i7 Table 1 64. OSMOTIC PRESSURE. The following numbers give the result of Pfef£er's§ measurement of the magnitude of the osmotic pressure for a one per cent sugar solution. The result was found to agree with that of an equal molecular solution of hydrogen. The value for the hydrogen solution is given in the third column of the table. Temperature C. Osmotic pressure in atmospheres. 0.649 ( J ~T" .00367 £) 6.8 O.664 O.665 13-7 O.69I 0.68 1 14.2 O.671 0.682 i5-5 O.684 0.686 22.0 O.72I 0.701 32.0 O.716 0.725 36.0 O.746 °-735 * "Zeits. fiir Phys. Chem." vol. 2, p. 427. t The isotonic coefficient is the relative value of the molecular attraction of the different salts for water or the relative value of the osmotic pressures for normal solutions. In the above table the coefficient for KN0 3 was taken as 3 arbitrarily and the others compared with it. The concentrations of different salts which give equal osmotic pres- sures are called by Tammann and others isosmotic concentrations; they are sometimes called isotonic concentrations. The reciprocals of the numbers of molecules in the isotonic concentrations are called by De Vries the isotonic coeffi- cients. t See also Tammann, "Wied. Ann." vol. 34, p. 315. § Winkelmann's " Handbuch der Physik," vol. 1, p. 632. Smithsonian Tables. 150 Table 165. PRESSURE OF AQUEOUS VAPOR, ACCORDING TO RECNAULT. The last four columns were calculated from the data given in the second column and the density of mercury. & 0) D- S e 6 o P. £ 01 h s *• 4) L» 1- V S E Oj O II IS 2 u & w u a ■8 J P O 1* 3 22 U ii • •A V P. 11 re & 6 o> § u d E 01 u u |E §"8 u . 01 a> ": 0> n E = U O. in • •B-8 3 .E 43 • s i aj u I s Jo o5 £ O) 0, P. = 1 II 1 § H ft O ft 0. ft H H ft O s, H. ft H i o 4.60 6.254 O.0890 0.181 0.0061 32.0 40 54.91 74-653 1. 061 2.162 0.072 104.0 I 4-94 6.716 .0955 .194 .0065 33-8 41 57-9' 78.678 1. 121 2.280 .076 105.8 2 5-3° 7.206 .1025 .209 .0070 35-6 42 61.01 82.947 1. 2l6 2.404 .080 107.6 3 5-69 7-73 6 .1100 .224 .0075 37-4 43 64-35 87.488 I.244 2-533 .085 109.4 ; 4 6.10 8.291 .1180 .240 .0080 39-2 44 67.79 92.165 I-3I2 2.669 .089 in. 2 5 6-53 8.878 0.1263 0.257 0.0086 41.0 45 71-39 97-059 I.38I 2.811 0.094 1 1 3.0 6 7.00 9-517 •1354 .276 .0092 42.8 46 75.16 102.184 I.454 2.959 ■099 1 1 4.8 7 7-49 10.183 .1452 •295 .0099 44.6 47 79.09 107.528 '■53° 3-"4 .104 1 1 6.6 8 8.02 10.904 •i5S' .316 .0107 46.4 48 83.20 113.115 1.609 3.276 .109 1 1 8.4 9 8-57 11.651 .1657 •338 .0114 48.2 49 87.50 118.962 1.692 3-444 •"5 120.2 10 9.17 12.467 o-i773 0.361 0.012 50.0 50 91.98 125.05 1.78 3.62 0.121 122.0 ii 9-79 I3-3 10 .1893 .386 .013 51.8 5' 96.66 131.42 1.87 3.81 .127 123.8 12 10.46 14.207 .2023 .412 .014 53-6 5 2 101.54 138.04 1.96 4.00 •134 125.6 13 11. 16 i5- r 73 .2158 •439 .015 55-4 53 106.64 144.98 2.06 4.20 .140 127.4 14 1 1. 91 16.192 •2303 .469 .016 57-2 54 1 11.95 1 52.20 2.17 4.41 .147 129.2 15 12.70 17.266 0.2456 0.500 0.017 59° 55 117.48 159.72 2.27 4-63 0.155 131-0 16 13-54 18.408 .2618 •533 .018 60.8 56 123.24 167.55 2-39 4.85 .163 132.8 17 14.42 19.605 ■2789 .568 .019 62.6 S l 129.25 175.72 2.50 5-09 .170 134.6 18 r S-3 6 20.883 .2970 .605 .020 64.4 58 I35-5I 184.23 2.62 5-33 .178 136.4 '9 16-35 22.229 .3162 .644 .022 66.2 59 142.02 193.08 2-75 5-59 .187 138.2 20 17-39 23-643 0-3363 0.685 0.023 68.0 60 148.79 202.29 2.88 5-86 0.196 140.0 21 18.50 25.152 •3577 .3802 .728 .024 69.8 61 155.84 211.87 3.01 6.14 .205 141.8 22 19.66 26.729 •774 .026 71.6 62 163.17 221.84 3.16 6.42 .215 143.6 23 20.89 28.401 .4040 .822 .028 73-4 63 170.79 232.20 3-3° 6.72 .225 H5-4 24 22.18 3°-!55 .4289 •873 .029 75.2 64 178.71 242.97 3-46 7.04 •235 147.2 25 23.55 32.018 0-4554 •4»33 0.927 0.031 77.0 65 186.95 254.17 3.62 7-36 0.246 149.0 150.8 152.6 26 24.99 33-975 .984 ■°33 78.8 66 195.50 265.79 378 7.70 .257 27 26.51 36.042 .5126 1.044 ■034 80.6 67 204.38 277.87 3-95 8.05 .267 .281 28 28.10 38.204 •5434 .106 ■037 82.4 68 213.60 290.40 4-i3 8.41 154.4 156.2 29 29.78 40.488 ■5759 .172 •039 84.2 69 223.17 303-41 4-3 2 8-79 •494 30 3'-55 33-41 35-36 37-41 39-57 42.894 0.6101 1.242 0.042 86.0 70 233- 9 316.90 4.51 9.18 0.306 158.0 159.8 1 61. 6 163.4 165.2 31 32 33 34 45423 48.074 50.861' 53-798 .6461 .6838 •7 2 34 •7655 •3'5 •392 •473 •558 .044 .047 .049 .052 87.8 89.6 91.4 93-2 71 72 73 74 243-39 254.07 265.15 276.62 33°-9° 345-42 360.49 376.08 4.71 4.91 5.12 5-35 9.58 10.00 10.44 10.89 .320 •334 •349 •364 35 36 3 Z 38 39 41.83 44.20 46.69 49-3° 52.04 56.870 60.091 63.478 67.026 70.752 0.810 •855 •903 •954 1.007 1.647 .740 .838 .941 2.049 0.055 ■°i .061 .065 .068 95-o 96.8 98.6 100.4 102.2 75 76 77 78 79 288.52 300.84 313.60 326.81 340.49 392.26 409.01 426.36 444.32 462.92 5.82 6.06 6.32 6.58 11.36 11.84 12.35 12.87 13.40 0.380 •39 6 .414 ■43° •448 167.0 168.8 170.6 172.4 174.2 Smithsonian Tables. ISI Table 165. PRESSURE OF AQUEOUS VAPOR, ACCORDING TO RECNAULT. a o o a § k •• £ V £■3 M k* ■ fti: us v aj 11 in V a 10 . c E t 3E c aj O a E h s S E in — £ - tn V 41 II E S 0* u at a e a s IB V V. V it £ « a E H d. &. Si A H H P< A. (6 Ph H 80 354- 6 4 482.15 6.85 13.96 O.446 I76.O 120 1491.28 2027.48 28.85 29.78 58.71 1.962 248.0 81 369.29 502.07 7.14 14.54 .486 177.8 121 I539-25 2092.70 60.61 2.025 249.8 82 384.44 522.67 7-44 15.14 .506 179.6 122 1588.47 2159.62 3°-73 62.54 .091 251.6 83 400.10 543-96 7-74 15-75 .526 181.4 123 1638.96 2228.26 3I.7O 64-53 ■157 2534 84 416.30 565-99 8.05 16.39 .548 183.2 124 1690.76 2298.69 32.7O 66.56 .225 255.2 85 433-°4 588.74 8-37 17.05 O.57O 185.O 125 1743.88 2370.91 33-72 68.66 2.295 257.0 86 45°- 34 612.26 8.71 1773 ■593 186.8 126 1798-35 2444.96 34-78 70.80 .366 25S.8 87 468.22 636.57 9.05 18.43 .616 188.6 127 1854.20 2520.89 35.86 73.00 •430 260.6 88 486.69 661.68 9.41 19.16 .640 180.4 128 1911.47 2598.76 36-97 75-25 •515 262.4 89 5°S-76 687.61 9.78 19.91 .665 192.2 129 1970.15 2678.54 38.11 77-57 .592 264.2 90 5 2 5-45 714-38 10.16 20.69 0.691 194.O 130 2030.28 2760.29 39.26 79-93 2.671 266.0 9' 54578 740-31 10.56 21.49 .719 '95-8 I 3 I 2091.94 2844.12 40.47 82.36 •753 267.8 92 566.76 770-54 10.95 22.31 •746 197.6 ■3 2 2l55- 3 2929.89 41.68 84.84 .836 269.6 93 588.41 799.98 11.38 23-17 ■774 199.4 133 2219.69 3017.80 42-93 87-39 .921 271.4 94 610.74 830.34 1 1 .Si 24.04 .804 201.2 134 2285.92 3107.85 44.21 89.99 3.008 273.2 95 63378 861.66 12.26 24.95 0.834 203.0 135 2353-73 3200.04 45.52 92.67 3-097 275.0 96 657-54 893-97 12.71 25.89 .865 204.8 136 2423.16 329443 46.87 95-39 .188 276.8 97 682.03 927.26 I3-I9 26.85 •897 206.6 '37 2494-23 3391.06 48.24 98.19 .282 278.6 98 707.2S 961.59 13.68 27-85 •931 208.4 '38 2567.00 3489-99 49.65 101.06 •378 280.4 99 733-3 1 996.9S 14.18 28.87 •965 210.2 r 39 2641.44 3591.29 51.06 103.99 ■476 282.2 100 760.00 1033.26 14.70 29.92 1. 000 212.0 140 2717.63 3694.78 52-55 106.99 3-576 284.0 101 787-59 1070.78 I5-23 31.01 .036 213.8 141 2795-57 3800.75 54.07 110.06 .678 285.8 102 8r6.oi 1 109.41 1579 32-13 .074 215.6 142 2875.30 3909.14 55.60 113.20 783 287.6 103 845.28 1149.21 16.35 33-28 .112 217.4 M3 2956.86 4020.03 57.16 1 16.41 .890 289,4 104 875.41 H90.17 16.94 34-46 .152 219.2 144 3040.26 413342 58.79 1 19.69 4.000 291.2 105 906.41 1232.32 '7-53 35-69 i-i93 221.0 145 3125.55 4249-37 60.44 123.05 4«3 2930 106 938-3I 1275.69 18.15 36-94 •235 222.8 146 3212.74 4367.91 62.13 126.48 .227 294.8 107 971.14 1320.32 18.78 38-23 .278 224.6 147 3301.87 4489.09 63.86 129.99 •344 296.6 108 1004.91 1366.24 19.44 39-56 • 3 ™ 226.4 148 3392-98 4612.96 65.62 I33-58 ■464 298.4 109 1039.65 1413-47 20.11 40-93 .368 228.2 149 3486.09 4739-55 67.41 I37-25 •587 300.2 110 1075-37 1462.03 20.80 42-34 1.415 230.0 150 358i-2 4868.9 69.26 141.0 4.712 302.0 in 1 1 12.09 1 51 1.97 21.51 43-78 •463 231.8 151 3678.4 5001. 1 71.14 144.8 .840 303-8 112 1149.83 1563.26 22.24 4 ^o 5 -513 233-6 152 3777-7 5136.1 73.06 148.7 .971 305.6 "3 1188.61 1615.99 22.99 46.80 •564 2 354 '53 3879.2 5275-0 75.02 152.7 5.104 3074 114 1228.47 1670.18 23.76 48.37 .616 237-2 ■54 3982.8 5414.8 77-03 156.8 .240 309.2 115 1 269.41 1725.84 =4-55 49.98 1.670 2390 155 4088.6 5558.6 79.07 1 61.0 5.380 311.0 116 i3"-47 1783.02 2 5-37 5'-63 .726 240.8 156 4196.6 5705-5 81.22 165.2 .522 312.8 117 1354.66 1841.74 26.20 53-34 .7S2 242.6 157 4306.9 5855-5 83.29 169.6 .667 314.6 118 1399.02 1902.05 27.06 55.08 .84I 244.4 158 44I9-5 6008.5 85.47 174.0 .815 316.4 119 1444-55 '963-95 2 7-94 56.87 .9OI 246.2 '59 4534-4 6164.7 87.69 178.5 .966 318.2 Smithsonian Tables. IS2 Table 165. PRESSURE OF AQUEOUS VAPOR, ACCORDING TO RECNAULT. a U o d E u H k u at SB SB'S p. in u . v V p. j: "> £ aj a E-s IS O k. p. w . ■g-s 3 C Pi .§£■ "3 - 1 E Pi IS Pi 1 d E WEIGHT IN CRAMMES OF THE AQUEOUS VAPOR CONTAINED IN A WEI CUBIC METRE OF SATURATED AIR. Temp. °C. -20 -10 +0 10 20 30 0.0 1.078 2.363 4.835 4-835 9-330 17. no 30.039 1.0 2.0 992 2.192 4-5'3 5.176 9-935 18.143 31.704 0.913 2.032 4.211 5-538 10.574 19.222 33-449 3.0 0.839 1.882 3.926 5.922 II.249 20.355 35-275 4.0 0.770 1.742 3-659 6.330 1 1. 961 21.546 37- l8 7 5.0 O.706 1.611 3407 6.761 12.712 22.796 39- l8 7 6.0 0.647 1.489 7.219 13-505 24.109 41.279 7.0 0-593 1-375 2.949 7-703 14-339 25.487 43465 80 0.542 1.269 2.741 8.215 15.218 26.933 45-75 1 9.0 0.496 1. 170 2.546 8.757 16.144 28.450 48.138 Smithsonian Tables. * See " Smithsonian Meteorological Tables," pp. 132-133- iS5 Table 169. PRESSURE OF AQUEOUS VAPOR AT LOW TEMPERATURE.* Pressures are given in inches and millimetres of mercury, temperatures in degrees Fahrenheit and degrees Centigrade* (a) Pressures in inches of mercury ; temperatures in degrees Fahrenheit. Temp. F. o°.o 1°0 2°.0 3°0 4°0 5°.0 6°.0 7°.0 8°.0 9°.0 —50° 0.002 1 0.0019 0.0018 0.0017 0.0016 0.0015 0.0013 0.0013 O.OOI2 O.OOII —40 .0039 .0037 .0035 ■0033 .0031 .0029 .0027 .0026 .0024 .0022 —3° .0069 .0065 .0061 .0057 .0054 .0051 .0048 .0046 .0044 .0041 — 20 .0126 .0119 .0112 .0106 .0100 .0094 .0089 .0083 .0078 .0074 — 10 .0222 .0210 .0199 .0188 .0178 .0168 .0159 .0150 .0141 •0133 —0 0.0383 O.O263 0.0244 0.0225 0.0307 0.0291 0.0275 0.0260 O.0247 0.0234 +0 •0383 .0403 .0423 .0444 .0467 .0491 •0515 .0542 .0570 .0600 10 .0631 .0665 .0699 ■0735 .0772 .0810 .0850 .0891 ■0933 •0979 20 .1026 .IO77 .1130 .1185 .1242 .1302 •1365 .1430 .1497 .1568 3° .1641 .1718 ■1798 (V) Pressures n millimetres of mercury ; temperatures in degrees Fahrenheit Temp. F. o°.o 1°0 2°.0 3°.0 4°.0 B°.0 6°0 7°0 8°0 9°0 —50° 0053 O.049 0.046 0.043 0.040 0.037 0.034 0.032 0.030 0.028 —40 .100 .094 .089 .084 .079 .074 .069 .065 .061 .057 —3° .176 .165 •155 .146 .138 .130 ■123 .117 .III .105 — 20 •319 .301 .2S4 .268 •253 ■ 2 39 .225 .212 .199 .187 — 10 .564 ■534 .505 .478 .452 .427 •403 ■384 •358 •338 —0° 0.972 0.922 0.873 0.826 0.781 0.738 0.698 O.661 0.627 o-595 +0 .972 1.023 1.075 1. 129 1. 186 1.246 1.309 1-376 1.447 '•523 10 1.603 1.688 1.776 1.867 1. 961 2.058 2.158 2.262 2-371 2.486 20 2.607 2-735 2.869 3.009 3-155 3-3°7 3.466 3-63 1 3-803 3-982 3° 4.169 4-3 6 4 4.568 ( c) Pressur es in inches of mercury ; temperatures in degrees Centigrade. Temp. C. o°.o 1°0 2°.0 3°.0 4°0 s°.o 6°0 7°0 8°.0 9°.0 —0° 0.1798 0.1655 0.1524 0-1395 0.1290 0.1185 0.1091 0.0998 0.0916 0.0S42 — 10 .0772 .0706 .0645 .0588 ■0537 .0491 .0449 .0411 •0375 .0138 .0341 — 20 .0307 .027S .0252 .0229 .0208 .0188 .0171 ■ OI 53 .0124 —3° .0112 .0101 .0091 .00S2 .0073 .0065 .0059 .0053 .0048 .0044 —40 .0040 .0036 .0032 .0029 .0025 .0022 .0020 .0017 .0015 .0013 (u) Pressures in millimetres of mercury ; temperatures in degrees Centigrade Temp. C. o°.o 1°.0 2°.0 3°.0 4°.0 5°0 6°.0 7°.0 8°0 9°0 —0° 4.568 4.208 3-875 3-565 3- 2 77 3.009 2.767 2 -534' 2.327 2.138 — 10 1. 96 1 1.794 I-637 1-493 1-363 1.246 1.140 1.044 0.952 0.864 — 20 0.781 0.706 O.641 0.583 0.528 0.478 0.432 0.389 0.350 °-3 : 5 —3° 0.284 0.256 O.231 0.207 0.185 0.165 0.148 ai 33 0.121 O.IIO —40 0.1 00 0.090 O.081 0.072 0.064 0.057 0.050 0.044 0.039 0.034 * Marvin's results (Ann. Rept. U. S. Chief Signal Officer, 1891, App. 10). Smithsonian Tables. IS6 Table 170, PRESSURE OF AQUEOUS VAPOR IN THE ATMOSPHERE. This table gives the vapor pressure corresponding to various values of the difference t — U between the readings of dry and wet bulb thermometers and the temperature t x of the wet bulb thermometer. The differences t — ty are given by two-degree steps in the top line, and t x by degrees in the first column. Temperatures in Centigrade degrees and Regnault's vapor pressures in millimetres 01 mercury are used throughout the table. The table was calculated for barometric pressure B equal to 76 centimetres, and a correction is given for each centimetre at the top of the columns.* *1 = 2 4 6 8 10 12 14 16 18 20 f- & r. 1 Correctic ns for B per centi- .013 .026 .040 .053 .066 •"79 .092 .106 .119 .132 *S° metre. r Q%» —10 I.96 O.96 O.IOO —9 2.14 1. 14 0.14 O.I 00 —8 —7 2-33 2-53 '•33 i-53 o-33 o-53 Example. O.IOO O.IOO —6 2.76 1.76 0.76 t — h= 7- J O.IOO —5 *!= IO.O 3.01 2.01 1. 00 ■5=74-5 O.IOO —4 3.28 2.28 1.27 0.27 Tabular number=6. 12 — 6 X .ioi = 5.51 O.IOO —3 3-57 2.57 1.56 O.56 Correction for 5=1.5 X. 048 .. = -°7 O.IOO — 2 3-88 2.88 1.87 0.87 Hence we get^ . . . = 5.58 O.IOO — i 4.22 3.22 2.21 1. 21 0.21 O.IOO 4.60 3.60 2.59 i-59 O.59 O.IOO 1 4.94 3-93 2.92 1.92 O.92 1 O.IOO 2 5-3° 4.29 3- 2 9 2.28 I.28 O.27 O.IOO 3 5.69 4.68 3.68 2.67 1.66 0.66 O.IOI 4 6.10 5-°9 4.09 3.08 2.07 I.06 O.05 O.IOI 5 6-53 5-5 2 4-5i 3-5° 2.49 I.48 O.48 O.IOI 6 7.00 5-99 4.98 3-97 2.96 i-95 O.94 O.IOI 7 7-49 6.48 5-47 4-45 3-44 2.43 I.42 0.41 O.IOI 8 8.02 7.01 5-99 4.98 3-97 2.96 I.94 0.93 O.IOI 9 8-57 7-56 6.54 5-53 4.51 3-5° 2.49 I.48 0.46 O.IOI 10 9.17 8.16 7.14 6.12 5.11 4.09 3.08 2.07 1.06 0.05 O.IOI 11 9-79 8.77 7.76 6.74 5-73 4.71 3-69 2.68 1.66 0.64 0.102 12 10.46 9-44 8.43 7.41 6-39 5-37 4-3 6 3-34 2.32 1.30 0.28 0.102 14 11. 16 10.14 9.12 8.10 7.09 6.07 5-°5 4-03 3.01 1.99 0.97 0.102 11.91 10.89 9.87 8.85 7-83 6.81 5-79 4-77 3-7i 2.69 1.67 0.102 15 12.70 11.68 10.66 9.64 8.62 7.60 6.58 5-56 4-54 3-5 2 2.50 0.102 16 13-54 14.42 12.52 11.50 10.47 9-45 8.43 l 4 l 6-39 5-37 4-35 3-33 0.102 17 13.40 12.37 "•35 io-33 9-3 1 8.28 7.26 6.24 5.22 6.15 4.20 0.102 18 x 5-3 6 •4-34 I3-3 1 12.29 11.26 10.24 9.21 8.19 7-!7 8.15 5-!3 6.1 1 0.102 l 9 i6-35 '5-33 14.30 13.27 12.25 11.22 10.20 9.17 7-13 0.102 ; 20 21 17-39 18.50 16.37 17-47 15-34 16.45 M-3 1 15.42 13.28 14-39 12.26 13-36 11.23 12.33 10.21 11-31 9.18 10.28 8.15 9.25 7.12 8.22 0.103 0.103 22 23 24 19.66 20.89 22.18 18.63 19.86 21.15 17.60 18.83 20.12 16.57 17.80 19.09 15-54 16.77 18.05 H-5 1 15-74 17.02 13.48 14.71 15-99 12.46 13.68 14.96 n-43 12.66 13-94 10.40 11.63 12.91 9-37 10.60 11.88 0.103 0.103 0.103 ! 25 26 27 28 29 23-55 24.99 26.51 28.10 29.78 22.52 23.96 25.48 27.07 28.75 21.49 22.92 24.44 26.03 27.71 20.45 21.89 23.40 24.99 26.67 19-43 20.86 22.37 23.96 25-63 i8-39 19.82 21.34 22.92 24.59 17-36 18.79 20.30 21.89 23-56 16.33 17.76 19.27 20.85 22.52 15-3° 1673 18.24 19.82 21.49 14.27 15.70 17.21 18.79 20.46 13.24 14.67 16.18 17.76 19-43 0.103 0.103 0.103 0.103 0.103 j 30 3i 32 33 34 35 36 37, 38 39 31-55 33-41 35-36 37-41 39-57 3°-5' 32-37 34-32 36-37 38-53 29.47 31-33 33-2» 35-33 37-48 28.43 30.29 3 2 -24 34-29 36.44 27.40 29.25 31.21 33-25 35-40 26.36 28.22 30-17 32.22 34-36 25.32 27.18 29.13 31.18 33-32 24.29 26.14 28.09 30-14 32.28 23.25 25.10 27.05 29.10 31.24 22.22 24.07 26.01 28.06 30.20 21.18 23.03 2497 27.02 29.16 0.104 0.104 0.104 0.104 0.104 41.83 44.20 46.69 49-3° 52.04 40.79 43.16 45-65 48.26 51.00 39-74 42.11 44.60 47.21 49-95 38.70 41.07 43-56 46.17 48.91 37.66 40.03 42.52 45 'o? 47.86 36.62 38-99 41.48 44.08 46.82 35-68 37-95 40.44 43-°4 45-77 34-64 36.90 39-39 41.99 44-73 33- 6 ° 35.86 38-35 40.95 43.78 32.56 34.82 37-3 1 39-91 42.74 31-52 33-78 36.27 38.87 41.69 0.104 0.104 0.104 0.104 0.105 * The table -..-kdjgd I ro-nthe formula ^-0.00066^) < 1+ a»»5« V«* [^^ :d, and i57 * The table was caLcumicu nv*« *..-_-- U - f^M£fS5 f/tt^ctn is to be added, and W hen B is greater than 7 6 it is ,0 be subtracted. Smithsonian Tables. Table 171 DEW- The first column of this table gives the temperatures of the ^-^\^°^^t^^ e t^^ aKe^ui^^^ «1 t — i 2 = l 2 3 4 6 6 7 8 87/85 = Dew-points corresponding to the difference of temperature given in the above line and the wet-bulb thermometer reading given in first column. .04 .11 .22 •49 — 10 — 13.2 — 17.9 — 9 12.0 16.0 — 22.0 — 8 10.7 14-3 I9.4 — 7 9-5 12.7 I7.I — 24.0 — 6 8-3 11.2 I4.9 20.3 ST/SB = •03 .06 .11 .18 ■31 ■43 — 5 — 7- 1 — 9-7 — I2.9 — 17-5 — 24.5 — 4 6.0 8-3 II. I 14.8 20.1 — 3 4.8 6.9 9.4 12.6 16.8 — 23-4 2 3-6 5-5 7.8 10.5 13-9 18.9 I 2.5 4.2 6.2 8.5 11.5 15.4 — 21.0 87785 = .02 .04 .07 .10 .14 .19 .26 •38 — 1-3 — 2.9 -4.8 — 6.8 — 9-3 — 12.3 — 16.5 — 22.9 i o-3 i-7 3-5 5-3 7.6 10.2 13-5 18.3 2 + 0.6 0.7 2.2 3-9 6.1 8.3 II. I 14.7 3 i-7 + 0.2 1.0 2.6 4.6 6.4 8.9 11.9 4 2.8 1-4 0.0 i-3 3-i 4-7 6.9 94 87785 = .02 •03 •05 .07 .09 .11 •14 .18 5 3-8 2.6 + 1.2 — 0.1 — 1.6 — 3-2 — 5.0 — 7-1 6 4-9 3-7 2.5 + 1.1 0.2 17 3-3 5- 2 7 6.0 4-9 ' 3-7 2.4 + 1.1 o-3 1.8 3 'f 8 7.0 6.0 4.9 3-7 2-5 + 1.1 °-3 1.8 9 8.1 7-i 6.1 5-° 3-9 2.6 + 1.2 0.1 87/85 = .01 .02 •03 •°5 .06 .08 .10 .12 10 9.1 8.3 7-3 6-3 %' 2 4.1 2.8 + i-5 ii 10.2 9-3 8.4 7-5 6.5 %■% 4-3 3 1 12 11.2 10.4 9.6 8.7 7.8 6.8 5.8 47 13 12-3 11.5 10.7 9-9 9.1 8.2 7.2 6.2 14 '3-3 12.6 11.9 11. 1 10.3 9.05 8.6 7.6 87785 = .01 .02 •03 .04 .05 .06 .07 .08 15 14.4 13-7 13.0 12.3 11.5 10.8 9-9 9.1 16 15.4 14.8 14. 1 13-5 12.7 12.0 "•3 10.5 i7 16.4 15.8 15-2 14.6 13-9 '3-3 12.6 1 1.8 18 17-5 16.9 16.3 15-7 iS-i 14-5 13.8 J3- 1 19 18.5 18.0 17.4 16.9 16.3 1 57 15.1 14.4 87785 = .005 .01 ■015 .02 .027 •°33 .04 •°5 20 19.5 19.0 18.5 18.0 17.4 16.9 16.3 157 21 20.5 20.1 19.6 19.1 18.6 18.1 17-5 17.0 22 21.6 21. 1 20.7 20.2 19.7 19.2 18.7 18.2 2 3 22.6 22.2 21.7 21.3 20.8 20.4 19.9 19.4 24 23.6 23.2 22.8 22.4 22.0 21-5 21. 1 20.6 87/85 = •005 .01 .015 .02 ■025 ■03 ■035 a" 4 25 24.6 24.2 23-9 23-5 23.1 22.7 22.2 21.8 j 26 25.6 25-3 24.9 24-5 24.2 23.8 234 23.0 27 26.7 26.3 26.0 25.6 25-3 24.9 24-5 24.1 28 27.7 27-3 27.0 26.7 26.4 26.0 257 25-3 29 28.7 28.4 28.1 27.8 27.4 27.1 26.8 26.4 57785 = .003 .006 .01 .013 .017 .01 g .022 .026 30 29.7 29.4 29.1 28.8 28.5 28.2 27.9 27.6 31 30-7 3°-5 30.2 29.9 29.6 293 29.0 28.7 32 3 J -7 3i-5 31.2 3°-9 3°7 3°4 30.1 29.8 33 32.8 32-5 32.2 32.0 317 3i-5 31.2 3°-9 34 33-8 33-5 33-3 33-° 32.8 3 2 -5 32-3 32.0 87785 = .003 .005 .008 .010 .013 .016 .019 .021 35 34-8 34-5 3+3 34-1 33-8 33-6 334 33-i 36 35-f 35-5 35-3 35- 1 34-9 34-6 344 34-2 : 3 Z 36.8 36.6 3 6 4 36.2 36.0 357 3 $-$ 35-3 38 37 A 37-6 37-4 37-2 37-0 36.8 36.6 364 39 38.8 38.6 384 38.2 38.0 37-9 37-6 37-S Smithsonian Tables. i S 8 POINTS. Table 171. between the dry and the wet bulb, when the dew-point has the values given at corresponding points in the body of from 76 centimetres the corresponding numbers in the lines marked ST/ SB are to be multiplied by the difference, or above 76. See examples. t — «i = 9 10 11 12 13 14 15 Dew-points corresponding to the difference of temperature given in the above line and the wet-bulb thermometer reading given in first column. ST/SB = 1 2 3 4 ST/SB = 5 6 7 8 ST/SB = 10 13 14 st/sb= 15 16 17 18 19 5T/5B-- 20 23 24 ST/SB = 25 26 27 28 29 57/85 = 30 3i 32 33 34 ST/SB- 35 36 3 Z 38 39 •45 — 20.0 15.8 12.4 ■23 — 19.8 7-4 5-3 3-3 1.6 .14 0.0 + 1.8 3-5 5-i 6.7 .09 8.2 9.6 11.0 12.4 138 .06 16.4 17.6 18.9 20.1 •045 21.4 22.6 237 24.9 26.1 ■031 27.2 28.4 29.5 3°7 31.8 .024 3 2 -9 34-° 36.2 37-3 I I I EXAMPLES. .67 — 22.2 16.8 .29 -131 10. 1 7.6 5.2 3-2 •17 — 1-3 + 0.3 2.2 5.6 .11 7.2 8.7 10.2 11.7 I3- 1 .07 14-5 1 5.8 17.1 18.4 19.6 05 20.9 22.1 23-4 24.5 25.7 ■035 26.9 28.1 29.2 3°4 3i-5 .027 32.6 33-7 34-9 35-9 37- 1 (1) Given B= 72, t^= 10, t — 1\—5- Then tabular number for t, = 10 and t — ^ = 5 is 5.2 Also 76 — 72 = 4 and S /'/ SB = .06. .'. Correction = 0.06 X4= . . . .24 Hence the dew-point is 5.44 (2) Given £ = 71.5, ^=7,*— 4=8. Then, as above, tabulated number = . . 3.4 ST/SB= li + - l *=.is Correction = 0.15 X4-5 = Dew-point = .67 4.07 ■37 — 17-7 134 10.1 74 5-i .20 — 3-o 1.0 + 0.8 2.7 4-5 .12 6.2 7.8 94 10.9 12.4 .08 13-8 16.5 " 17-9 19.2 .06 20.4 21.7 22.9 24.2 25.4 .041 26.6 27.8 28.9 30.1 31.2 029 324 33-5 34-6 *H 36.8 44 -18.1 13-5 10. 1 7.2 .22 — 47 2.6 0.6 + i-3 3-3 .14 I-.8 8-5 10.1 1 1.6 .09 14.5 15.9 17-3 18.7 .06 20.0 21.3 22.5 23.8 25.0 .047 26.2 27.4 28.6 29.8 3°-9 .032 32.1 33-3 344 ■54 -18.3 13-5 9.9 •25 — 6.8 4-3 2.1 0.1 + 1-9 .16 5.8 7-5 9.2 10.8 .10 12.4 13-9 15-3 16.8 18.1 .07 19.5 20.8 22.1 234 24.6 •053 25.9 27.1 28.3 29.5 3°7 ■037 31.8 33-° 34-2 35-3 364 .66 -18.3 I3- 1 .29 -9.4 6-3 1.6 + 0.5 .18 2.7 47 8-3 10.0 .II 1 1.6 13.2 14.7 16.2 17.6 .08 19.0 20.3 21.7 23.0 24.2 .06 25-5 26.8 28.0 29.2 3°4 .037 31.6 32.8 33-9 36.2 •72 — 17.2 ■36 — 12.5 8.8 57 3-i 0.9 .20 + i-3 3-5 5-5 74 9.1 • 13 10.8 12.5 14.0 157 17.0 .09 18.5 19.9 21.2 22.6 23-9 .07 25.2 26.4 27.7 28.9 30.1 .04 3i4 3 2 -5 337 34-8 36.0 Smithsonian Tables. 1 59 Table 1 72. VALUES OF 0,378c* This table gives the humidity term 0.378*, which occurs in the equation S=zS -r —&o * — for the calcu- 760 7"° lation of the density of the dry air in a sample containing aqueous vapor at pressure e ; 60 is the density at normal barometric pressure, £ the observed barometric pressure, and h the pressure corrected for humidity. For values of -— - see Table 174. Temperatures are in degrees Centigrade, and pressures in millimetres of mercury. Vapor Dew- Vapor Dew Vapor point. pressure. e 0.378 e. point. pressure. e 0.378 e. point. pressure. e 0.378 e. — 30° O.38 0.14 4-57 '•Z 3 30° 3I-5I 11.91 — 29 .42 .16 1 4.91 1.86 3i 33-37 I2.6l — 28 .46 •17 2 5-27 1.99 32 35-32 13-35 — 27 •5° .19 3 5.66 2.14 33 37-37 14-13 — 26 •55 .21 4 6.07 2.29 34 39-52 14.94 — 25 0.61 O.23 5 6.51 2.46 35 41.78 15-79 — 24 .66 .25 6 6.97 2.63 36 44.16 16.69 — 2 3 ■73 .28 7 7-47 2.82 37 46.65 17-63 — 22 •Z 9 •30 8 7-99 3.02 38 49.26 18.62 — 21 .87 •33 9 8-55 3-23 39 52.00 19.66 — 20 0.94 0.36 10 9.14 3-45 40 54.87 20.74 — 19 1.03 •39 11 9-77 3-69 41 57-87 21.86 — 18 .12 .42 12 10.43 3-94 42 61.02 23.06 — 17 .22 .46 13 11. 14 4.21 43 64.31 243 1 — 16 ■32 •5° 14 11.88 4.49 44 67.76 25.61 — 15 1.44 o-54 15 12.67 4-79 45 7I-36 26.97 — 14 .56 •59 16 '3-51 5-" 46 75-13 28.40 — r 3 .69 .64 17 14.40 5-44 47 79.07 29.89 — 12 .84 .70 18 15-33 5-79 48 83.19 31-45 — 11 •99 •75 19 16.32 6.17 49 87.49 33-°7 — 10 2.15 0.81 20 I7-36 6.56 50 91.98 34-77 — 9 •33 .88 21 18.47 6.98 51 96.66 36-54 — 8 •51 •95 22 19-63 7.42 52 101.55 38-39 — 7 .72 1.03 2 3 20.86 7.89 53 106.65 40.31 — 6 •93 .11 24 22.15 8-37 54 1 11.97 42.32 — 5 3-i6 1.19 25 23-52 8.89 55 117.52 44.42 — 4 .41 .29 26 24.96 9-43 56 123.29 46.60 — 3 .67 •39 27 26.47 10.01 57 129.31 48.88 — 2 •95 •49 28 28.07 10.61 58 I35-58 51.25 — 1 4.25 .61 29 29.74 11.24 59 142.10 53-71 * This table is quoted from ' Smithsonian Tables. Smithsonian Meteorological Tables," p. 225. 160 Table 173. RELATIVE HUMIDITY.* This table gives the humidity of the air, for temperature t and dew-point d in Centigrade degrees, expressed in percentages of the saturation value for the temperature t. Qegree5 ' ex P ress «l Depression of the dew-point. t—d Dew-point () This part gives the values of 1 + .00367/ for values of t between— go° and -J- 1990° C. by io° steps. These two parts serve to give any intermediate value to one tenth of a degree by a sim- ple computation as follows : — In the {&) table find the number corresponding to the nearest lower temperature, and to this number add the decimal part of the number in the (a) table which corresponds to the difference between the nearest temperature in the (/•■) table and the actual temperature. For example, let the temperature be 6&z°.2 : We have for 680 in table (£) the number .... 3.49560 And for 2.2 in table (a) the decimal .00807 Hence the number for 682.2 is 3-50367 (0) This pan gives the logarithms of 1 -f- .00367 1 for values of t between — 49 and -+- 399 C. by degrees. (d) This part gives the logarithms of 1 -f- .00367 1 for values of t between 400° and 1990 C. by io° steps. (a) Values of 1-f- .00367 1 for Values of t between 0° and 10° C. by Tenths of a Degree, * 0.0 0.1 02 0.3 0.4 1. 00000 1.00037 1.00073 I.OOIIO 1. 00147 I .00367 .00404 .00440 .00477 .00514 .00881 2 .00734 .00771 .00807 .00844 3 .OIIOI .01138 .01174 .OI2II .01248 4 .01468 .01505 .01541 .01578 .01615 5 1-01835 1.01872 1.01908 I.OI945 1. 01982 6 .02202 .02239 .02275 .02312 .02349 7 .02569 .02606 .02642 .02679 .02716 8 .02936 .02973 .03009 .03046 •03083 9 •03303 •0334° ■03376 -03413 .03450 * 0.5 0.6 0.7 0.8 0.9 1. 00184 I.0022O 1.00257 I.00294 1.00330 1 .00550 .00587 .00624 .00661 .00697 2 .00918 .00954 .00991 .01028 .01064 3 .01284 .01321 •OI3S8 •01395 .01431 4 .01652 .01688 .01725 .01762 .01798 5 I.02018 1.02055 I.02092 1. 02 1 29 1.02165 6 .02386 .02422 .02459 .O2496 •02532 7 .02752 .02789 .02826 .02863 .02899 8 .03120 ■03156 •03193 .O329O .03266 9 .03486 ■03S23 •03560 •03597 •03033 Smithsonian Tables. 164 Table 1 76. VOLUME OF PERFECT CASES. (b) Values of 1 + .00367 1 for Valnes oJ * between —90° and + 1990° 0. by 10° Steps. t 00 10 20 30 40 —000 -1-000 100 200 300 400 500 600 700 800 900 1000 1 100 1200 1300 1400 1500 1600 1700 1800 1900 2000 I. ooooo 1. ooooo 1.36700 1.73400 2.IOIOO 2.46800 2.83500 3.20200 3.56900 3.93600 4.30300 4.67000 5.03700 5.40400 5.77100 6.13800 6.50500 6.87200 7.23900 7.60600 7.97300 8.34000 0.96330 1.93670 1.40370 1.77070 2.13770 2.50470 2.87170 3.23870 3.60570 3.97270 4-33970 4.70670 5-07370 5.44070 5.80770 6.17470 6.54170 6.90870 7.27570 7.64270 8.00970 8.37670 O.92660 I.07340 1.44040 1.80740 2.17440 2.54140 2.90840 3.27540 3.64240 4.00940 4.37640 4-74340 5. 1 1 040 5-47740 5.84440 6.21140 6.57840 6.94540 7.31240 7.67940 8.04640 8.41340 O.88990 I.IIOIO 1. 447 10 1. 84410 2.21110 2.57810 2.94510 3.31210 3.67910 4.04610 4.41310 4.78010 5.14710 5.51410 5.88110 6.24810 6.61510 6.98210 7.34910 7.71610 8.08310 8.45010 0.85320 1. 14680 1. 51380 1.88080 2.24780 2.61480 2.98180 3.34880 3.71580 4.08280 4.44980 4.81680 5.18380 5.55080 5.91780 6.28480 6.65180 7.01880 7-38580 7.75280 8.11980 8.48680 * 50 60 70 80 90 —000 +000 100 200 300 400 500 600 700 800 900 1000 1 100 1200 1300 1400 1500 1600 1700 1800 1900 2000 0.81650 1. 18350 1.55050 1.91750 2.28450 2.65150 3.01850 3-38550 3-75250 4.1 1950 4.48650 4.85350 5.22050 5-58750 5-95450 6.32150 6.68850 7-05550 7.42250 7.78950 8.15650 8.52350 0.77980 I.22020 1.58720 I.95420 2.32120 2.68820 3.05520 3.42220 3.78920 4.15620 4-52320 4.89020 5.25720 5.62420 5.99120 6.35820 6.72520 7.09220 7.45920 7.82620 8.19320 8.56020 0.74310 I.25690 1.62390 1.99090 2.55790 2.72490 3.09190 3.45890 3.82590 4.19290 4.55990 4.92690 5-29390 5.66090 6.02790 6.39490 6.76190 7.12890 7.49590 7.86290 8.22990 8.59690 0.70640 1.29360 1.66060 2.02760 2.39460 2.76160 3.12860 3-49560 3.86260 4.22960 4.59660 4.96360 5.33060 5.69760 6.06460 6.43160 6.79860 7.16560 7.53260 7.89960 8.26660 8.63360 0.66970 I-33030 1.69730 2.06430 2.43130 2.79830 3-I6530 3-53230 3-89930 4.26630 4-63330 5.00030 5-36730 5-73430 6.10130 6.46830 6.83530 7.20230 7.56930 7-93630 8.30330 8.67030 Smithsonian Tables. 165 Table 176. VOLUME OF (c) Logarithms of 1 + .00367 ( for Values t 1 2 3 4 Mean diff. per degree. — 40 1.931051 1.929179 T.927299 T.925410 r-923513 1884 — 3° •949341 .947546 ■945744 ■943934 .942117 1805 — 20 .966892 .965169 ■963438 .961701 •959957 J 733 — IO .983762 .982104 .980440 .978769 .977092 1667 — 0.000000 .998403 .996801 .995192 ■993577 1605 + 0.000000 0.001591 0.003176 0.004755 0.006329 1582 10 ■015653 .017188 .018717 .020241 .021760 1526 20 .030762 •032244 ■033721 ■°3Sm .036661 1474 3° .045362 .046796 .048224 .049648 .051068 1426 40 .059488 .060875 .062259 .063637 .065012 1381 50 0.073168 0.074513 0.075853 0.077190 0.078522 1335 6o .086431 •087735 .089036 .090332 .091624 1299 70 .099301 .100567 .101829 .103088 .104344 1259 8o .111800 .113030 .114257 .115481 .116701 1226 9° .123950 .125146 •126339 .127529 .128716 1191 100 0.135768 0.136933 .248408 0.138094 0.139252 0.140408 1158 no .147274 •H9539 .150667 •i5 r 793 1 1 29 120 .158483 .159588 .160691 .161790 .162887 IIOI 130 .169410 .170488 •171563 .172635 ■173705 1074 140 .180068 .181120 .182169 .183216 .184260 1048 150 0.190472 0.191498 0.192523 0-193545 0.194564 1023 160 .200632 .201635 .202635 .212518 .203634 .204630 1000 170 .210559 .211540 .213494 .214468 976 180 .220265 .221224 .222180 •223135 .224087 956 190 .229959 .230697 •231633 .232567 •233499 935 200 0.239049 0.239967 0.240884 0.241798 0.242710 916 210 .248145 •249044 .249942 .250837 • 2 5 I 73 I 897 220 • 2 57054 •257935 .266648 .258814 .259692 .260567 878 230 .265784 .267510 .268370 •276877 .269228 861 240 •274343 .275189 .276034 .277719 844 250 0.282735 0.283566 0.284395 0.285222 0.286048 828 260 .290969 .291784 .292597 .293409 .294219 798 270 .299049 .299849 .300648 .301445 .302240 280 .306982 .307768 .308552 ■309334 .310115 784 290 •3 r 4773 ■315544 ■3 I 63H •3 1 7083 .317850 769 300 0.322426 0.323184 0.323941 0.324696 0.325450 756 3™ •329947 .330692 ■331435 ■33 2 i78 .332919 743 320 ■337339 .338072 .338803 •339533 .340262 730 33° .344608 •345329 .345048 .346766 .347482 719 34° •351758 .352466 ■353'74 •353880 •354585 707 350 0.358791 0.359488 0.360184 0.360879 0-361573 696 360 ■365713 •366399 .367084 .367768 .368451 684 37° 380 •372525 •373201 •373875 •374549 .375221 674 •379233 .379898 .380562 .381225 .381887 664 654 39° •385439 .386494 .387148 .387801 •388453 Smithsonian Tables. 166 PERFECT CASES. ol * between —49° and +399° 0. by Degrees. Table 1 76. e Mean difE. per degree. — 40 — 3° — 20 — 10 — O + 10 zo 30 40 50 60 70 So 90 100 no 120 130 140 150 160 170 180 1 go 200 210 220 230 240 250 260 270 2S0 290 300 310 320 33° 340 350 360 37° 380 39° 1.921608 .940292 .958205 .975409 .991957 0.007897 .023273 .038123 .052482 .066382 0.079847 .092914 •I0559S .117917 .I2Q O.I41559 .152915 .163981 .174772 .185301 O.I95581 .205624 • 2I 5439 .225038 .234429 0.243621 .252623 .261441 .270085 .278559 0.286872 .295028 ■303034 .310895 .318616 0.326203 ■333659 .340989 .348198 ■355289 0.362266 ■3 6 9i3 2 •375892 .382548 .389104 1.919695 .938460 •956447 •973719 ■99033° 0.009459 .024781 .039581 •053893 .067748 0.081174 .094198 .106843 .119130 .131079 0.142708 .1 54034 .164072 .175836 .186340 0.196596 .206615 .216409 .225986 •235357 0.244529 •253512 .262313 .270940 .279398 0.287694 ■295835 .303827 •3 Il6 73 ■3!938i 0.326954 •334397 •3417 1 5 .348912 •355991 0.362957 .369813 .376562 .383208 •389754 i-9 r 7773 .936619 .954681 .972022 .988697 0.011016 .026284 .041034 .055298 .069109 0.082495 .095516 .108088 .120340 .132256 0.143854 •I55I5I .166161 .176898 •187377 0.197608 .207605 ■217376 .226932 .236283 0.245436 .254400 .263184 .271793 .280234 0.288515 .296860 .304618 ■3 I2 45° .320144 0.327704 •335'35 •342441 .349624 •356693 0.363648 ■370493 •377232 •390403 i-9!5 8 43 ■934771 .952909 •970319 .987058 0.012567 .027782 .042481 .056699 .070466 0.08381 1 .096715 .109329 .121547 ■133430 0.144997 .156264 .167246 •J7795 8 .188411 0.198619 .208592 .218341 .227876 .237207 0.246341 .255287 .264052 .272644 .281070 0.289326 •297445 .305407 .313226 .320906 0.328453 ■335871 ••343 l6 4 •350337 •357394 0.364337 ■37 1 171 .377900 •384525 .391052 1.913904 .932915 .951129 .985413 0.014113 .029274 .043924 .058096 .071819 0.085123 .098031 . 1 10566 .122750 .134601 0.1 461 37 ■157375 .168330 .179014 .189443 0.199626 •209577 .219904 .228819 .238129 0.247244 .256172 .264919 •273494 .281903 0.290153 .298248 .306196 .314000 .321667 0.329201 .336606 .343887 .351048 •358093 0.365025 .371849 .378567 •385'83 .391699 1926 1845 177 1 1699 1636 1554 1500 1450 1402 1359 1315 1 281 1243 1210 "75 1144 1087 1060 1035 966 946 925 870 853 S36 820 805 79° 776 763 75° 737 7-4 713 701 6go 678 66S 658 648 Smithsonian Tables. 167 Table 1 76. VOLUME OF PERFECT CASES. (fl) Logarithms of 1-f .00367* ior Values ol t between 400° anfl 1990° 0. by 10° Steps. t 00 10 20 30 40 400 °-39 2 345 0.398756 O.405073 0.41 1300 0417439 500 6oo 700 800 900 0452553 .505421 •552547 •595°55 •633771 0.458139 •5 I0 37i .556990 .599086 .637460 O.463654 .515264 .561388 .603079 .641117 0.469100 .520103 ■565742 .607037 .644744 0474479 .524889 .570052 .610958 .648341 1000 1100 1200 1300 1400 0.669317 .702172 •73 2 7i5 .761251 .788027 0.672717 •7053 2 5 ■735655 .764004 .790616 O.676090 ■708455 •738575 .766740 .793190 O.679437 •71 1 563 •741745 •769459 •795748 O.682759 .714648 •744356 .772160 .798292 1500 1600 1700 1800 1900 0.813247 .837083 .859679 .881156 .901622 0.81 5691 •839396 .861875 .883247 .90361 6 O.818120 .841697 .864060 .885327 .905602 0.820536 .843986 .866234 •887398 .907578 O.822939 .846263 .868398 .889459 •909545 t 60 60 70 80 90 400 0.423492 O.429462 0435351 O.441 161 0.446894 500 600 700 800 900 0.479791 .529623 •5743 21 .614845 .651908 O.48504O •534305 •578548 .618696 •655446 O.490225 •538938 .552734 .622515 •658955 0495350 •543522 .586880 .626299 .662437 0.500415 •548058 .590987 .630051 .665890 1000 1 100 1200 1300 1400 0.686055 .717712 .747218 •774845 .800820 O.689327 •720755 .750061 •7775*4 •803334 O.692574 .723776 .752886 .780166 .805834 O.695797 .726776 .755692 .782802 .808319 O.698996 .729756 .758480 .785422 .810790 1500 1600 1700 1800 1900 0.825329 .848828 .870550 .891510 .911504 0.827705 .850781 .872692 •893551 •9^454 0.830069 .853023 .874824 •895583 •915395 0.832420 •855253 •876945 .897605 .917327 O.834758 .857471 .879056 .899618 .91925! Smithsonian Tables. 168 Table 177. DETERMINATION OF HEIGHTS BY THE BAROMETER. Formula of Babinet : Z = C ^2J B aj B- £ + B' C (in feet) = 52494 |i + ° "*" 4 | English measures. L goo J C (in metres) =: 16000 1 + - ■ ■■ — I metric measures. L_ 1000 J In which Z — difference of height of two stations in feet or metres. barometric readings at the lower and upper stations respectively, corrected for all sources of instrumental error. to, t — air temperatures at the lower and upper stations respectively. Values of C. English Measures. Metric Measures. i«o+*)- c LogC i(h + t). c LogC Fahr. Feet. Cent. Metres. 10° 49928 4.69834 —10° 15360 4.18639 IS 5°5" •70339 —8 —6 15488 1 5616 .19000 •19357 20 5 I0 94 4.70837 —4 15744 .19712 25 51677 •71330 — 2 15872 .20063 30 52261 4.71818 16000 4.204I 2 35 52844 .72300 + 2 4 16128 16256 16384 .20758 .21101 40 53428 4.72777 6 .21442 45 5401 1 .73248 8 16512 .21780 50 54595 4-737I5 10 16640 4.22II5 55 55178 •74177 12 14 16768 16896 .22448 .22778 60 5576i 474633 16 17024 .23106 65 56344 .75085 18 17152 .23431 70 56927 4-75532 20 17280 4-23754 75 575" ■75975 22 24 17408 17536 •24075 ! ■24393 80 58094 4.76413 26 17664 .24709 85 58677 •76847 28 17792 .25022 90 59260 4.77276 30 17920 4-25334 95 59844 •77702 32 34 18048 18176 ■25643 •2595° 100 60427 478123 36 18304 •26255 Smithsonian Tables. I69 Table 178. BAROMETRIC Barometric pressures corresponding to different This table is useful when a boiling-point apparatus is used (a) British Measure. Temp. F. .7 .9 185° 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 17.05 17.42 17.81 18.20 18.59 19.00 19.41 19.82 20.25 20.68 21.13 21.58 22.03 22.50 22.97 2 3-45 23-94 24.44 24.95 25.46 25.99 26.52 27.07 27.62 28.18 28.75 2 9-33 29.92 17.08 17.46 17-84 18.24 18.63 19.04 19.45 19.87 20.29 20.73 21.17 21.62 22.08 22.54 23.02 23.50 2 3-99 24.49 25.00 25.52 26.04 26.58 27.12 27.67 28.24 28.81 29-39 29.98 17.12 17.50 17.88 18.27 18.67 19.08 19.49 19.91 20.34 20.77 21.22 21.67 22.12 22.59 23.07 23-55 24.04 24.54 25.05 25-57 26.10 26.63 27.18 27-73 28.29 28.87 29.45 30.04 17.16 17-54 17.92 18.31 18.71 19.12 19-53 19.95 20.38 20.82 21.26 21.71 22.17 22.64 23.11 23.60 24.09 24.59 25.10 25.62 26.15 26.68 27.23 27-79 28.35 28.92 29.51 30.10 17.20 17.58 17.96 18.35 18.75 19.16 19-57 19.99 20.42 20.86 21.30 21.76 22.69 23.16 23-65 24.14 24.64 25.15 25.67 26.20 26.74 27.29 27.84 28.41 28.98 29-57 30.16 17-23 17.61 18.00 18.39 18.79 19.20 19.61 20.04 20.47 20.90 21-35 21.80 22.26 22.73 23.21 23.70 24.19 24.69 25.21 25-73 26.25 26.79 27-34 27.90 28.46 29.04 29.62 30.22 17.27 17.65 18.04 18.43 18.83 19.24 19.66 20.08 20.51 20.95 21.39 21.85 22.31 22.78 23.26 23-75 24.24 24.74 25.26 25.78 26.31 26.85 27.40 27.95 28.52 29.10 29.68 30.28 I7-3 1 17.69 18.08 18.47 18.87 19.28 19.70 20.12 20.55 20.99 21.44 21.89 22.36 22.83 23.31 23.80 24.29 24.80 25-31 25-83 26.36 26.90 27-45 28.01 28.58 29.16 29.74 3°-34 17-35 17-73 18.12 18.51 18.91 '9- 32 19-74 20.17 20.60 21.04 21.48 21.94 22.40 23-36 23-85 24-34 24.85 25-36 25.88 26.42 26.96 27.51 28.07 28.64 29.21 29.80 30.40 '7-39 17-77 18.16 18.55 18.95 19.36 19.78 20.21 20.64 21.08 21-53 21-99 22.45 22.92 23.40 23.89 24-39 24.90 25.41 25.94 26.47 27.01 27.56 28.12 28.69 29.27 29.86 30.46 Smithsonian Tables. I70 PRESSURES. temperatures of the boiling-point of water. in place of the barometer for the determination of heights. (t>) Metric Measure.* Table 1 78. Temp. C. .0 .1 .2 ■3 .4 .6 .6 .7 .8 .9 80° 354-6 356-1 357-5 359-0 360.4 361.9 363-3 364.8 366.3 367.8 8i 3 6 9-3 370.8 372-3 373-8 375-3 376.8 378-3 379-8 38I.3 382.9 82 3 8 44 385-9 387-5 389.0 390.6 392.2 393-7 395-3 396-9 398-5 83 400.1 401.7 403-3 404.9 406.5 408.1 409.7 41 1-3 413.0 414.6 84 416.3 417.9 419.6 421.2 422.9 424.6 426.2 427.9 429.6 43'-3 85 433-0 434-7 436-4 438.1 439-9 441.6 443-3 445-1 446.8 448.6 86 45°-3 452.1 453-8 455-6 4574 459.2 461.0 462.8 464.6 466.4 87 468.2 470.0 471.8 473-7 475-5 477-3 479.2 481.0 482.9 484.8 88 486.6 488.5 490.4 49 2 -3 494.2 496.1 498.0 499.9 501.8 503.8 89 505-7 507.6 509.6 5«-5 5I3-5 5'5-5 5'74 519.4 521.4 5234 90 5 2 54 527.4 529.4 5314 533-4 535-5 537-5 539-6 541.6 543-7 91 545-7 547.8 549-9 55 r -9 554.0 556.1 558.2 560.3 562.4 564.6 92 566.7 568.8 571.0 573-1 575-3 5774 579-6 581.8 584.0 586.1 93 588.3 590-5 592-7 595-o 597-2 599-4 601.6 603.9 606.I 608.4 94 610.7 612.9 615.2 617.5 619.8 622.1 624.4 626.7 629.0 631.4 95 633-7 636.0 638.4 640.7 643.1 645-5 647-9 650.2 652.6 655.0 96 6574 659.9 662.3 664.7 667.1 669.6 672.0 674.5 677.0 679.4 97 681.9 684.4 686.9 689.4 691.9 694.5 697.0 699.5 702.1 704.6 98 707.2 709.7 712.3 714.9 717-5 720.1 722.7 725-3 727.9 730-5 99 733- 2 735-8 738-5 74J-2 743-8 746.5 749.2 751-9 754-6 757-3 xoo 760.0 762.7 765-5 768.2 770.9 773-7 776.5 779.2 782.0 784.8 * Pressures in millimetres of mercu ry. Smithsonian Tables 171 Table 1 79. STANDARD WAVE-LENGTHS. This table is an abridgment of the table published by Rowland (Phil. Mag. [5] vol. 36, pp. 49-75). The first column gives the number of the line reckoned from the beginning of Rowland's table, and thus indicates the number of lines of the table that have been omitted. The second column gives the chemical symbol of the element repre- sented by the line of the spectrum. The third column indicates approximately the relative intensity of the lines recorded and also their appearance ; X stands for reversed, d for double, ? for doubtful or difficult. The fourth column gives the relative "weights" to be attached to the values of the wave-lengths as standards. The last column gives the values of the wave-lengths in Angstrom's units, i. c, in ten millionths of a millimetre in ordinary air at about 20 C. and 760 millimetres pressure. When two or more elements are on the same line of the table it indicates that they have apparently coincident lines in the spectrum for that wave-length. When two or more lines are bracketed it means that the first one has a line coinciding with one side of the corresponding line in the solar spectrum and so on in order. Lines marked A (») and /f(n») denote lines due to absorption by the oxygen or water vapor in the earth's atmosphere. The letters placed in front of some of the numbers in the first column are the symbols of well-known lines in the spectrum. The footnotes are from Rowland's paper. No. of line. Element. Inten- sity and appear- ance. Weight. Wave- length (arc spectrum). No. of line. Element. Inten- sity and appear- ance. Weight. Wave- length (arc spectrum). I Sr 2 I 2152.912 "5 Fe 10 J? 4 2937.020 4 Si 3 2 2210.939 117 Fe iR 4 2954.058 7 Si 2 2 2218.146 121 Fe 8R 12 2967.016 9 Al 4 2 2269.161 124 Fe 12R 15 2973-358 2983.689 11 Ca 20 R 3 2275.602 126 Fe 10 j? *5 14 Ba 20 R 1 2335- 26 7 129 Fe 8R 18 2994.547 16 Fe - 2 2348.385 131 Ca 10R 3 2997-43° 19 Al 7 3 2373-213 i35 Fe 8R 15 3001.070 22 Fe 2388.710 136 Ca i S R 3 3006.978 24 Ca 25 j? 5 2398.667 141 Fe 6R 15 3008.255 151 Fe 25* 18 3020.759 29 Si 8 15 2435.247 163 Fe 20* 13 3047.720 31 Si Si 3 10 2443.460 169 Fe 10 R '5 3059.200 33 3 10 2452.219 (Sun spectrum.) 37* 46 C Bo 10 20 15 20 2478.661 2497.821 136 3 - 3005.160 51 Si 15 7 2516.210 144 4 - 3012.557 55 Si 9 10 2524.206 ls i 5 7 3024.475 59 1 Hg 50 R 2 2536.648 158 5 7 3°35-850 6 3 Al 10 5 2568.085 164 Zd 5 3050.212 68 Ma - 2 2593.810 171 Co 3 5 3061.930 *73 Si 5 7 2631.392 177 Fe? 4 6 3078.148 1 77 Fe - 3 2720.989 187 ? 2 9 3094-739 78 Ca 5 1 2721.762 i97 VaJ 5 9 3121.275 82 Fe - 3 2742.485 201 - 3 5 3140.869 85 Fe - 3 2756.427 203 Mn 1 5 3167.290 99 Mg 20 .ff 12 2795.632 207 Cr? 4 5 3188.164 102 Mg 20 .ff 10 2802.805 209 Ti 4 5 32OO.032 106 Fe 4 7 2832.545 211 Ti 3 6 3218.390 in Mg 100 .ff 15 2852.239 215 Ti 4 3 3224.368 112 Si 15 12 2881.695 222 Cu 9 5 3247.680 • Seen is to be the c nly single carbon line not belonging to a banc . in the arc ipectrum It was determined to belong to carbon by the spark spectrum. t This line appears as a sharp reversal, with no shading, in the s; lectra of all £ ubstance s tried tl at contained I any trace > E a continuo us spectrum in the region. X The e is a faint 1 ne visible on the violet side. Smithsonian Tables. 172 STANDARD WAVE-LENGTHS. Table 1 79. Wave- length (sun spectrum). No. of Line. Element. Inten sity and appear- ance. Weight, Wave- length (sun spectrum). 3267.839 3302.501 3318.163 3356.222 3389.887 3406.955 3455-3^4 3478.OOI 3500.721 3518.487 3540.266 3564.680 35 8l -344 3583483 3597-192 3609.015 3612.217 3618.924 3623-332 3631.619 3647-995 3667-397 3683.202 3707.186 3720.086 3732-542 3789-633 3758-379 378I-33 3804-153 3820.567 3826.024 3843.406 3860.048 3883-472 3897-599 3924.669 3933-8°9 3944-159 3950.101 3960.429 3968.620 3981.914 409t 410 4i7 420 422 424 428 431 434 436 439 ,?445 448 456 G462 /465 467 7 2 7389.696 737t Ca 7 14 5857.672 997 II A(o) 4 7594.059 A 74°§ He - - 5875.982 998 A(o) 10 5 7621.277 A 743 Na '5 20 5890.182 1004 A(o) 14 3 7660.778 A 745 Na 10 20 5896.154 IOIO ? 4 1 7714.686 * Compo lent about .088 apart on the p lotographic p] ate. It is an exceedingly difficult ( ouble. t Lines u sed by Pierce in the letermin ition of absolu te wave-lengt hs. X There i 3 a nickel line near to the red. § This va .ue of the wave-lengt 1 is the 1 esult of three series of mea surements \v ith a gn ting of 20,000 lines to the inch If Beginn and is accurate to pe ng at the head of A , haps .02 outside < dge. Smithsonian Tables. 174 Table 180. 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 mil- lionths of a millimetre on the supposition that the D line value is 5896.156. The table is for the most part taken from Rowland's table of standard wave-lengths, but when no corresponding wave-length is there given, the number given by Kayser and Runge has been taken. These latter are to two places of decimals. Index letter. Line due to — Wave-length in centimetres X io 8 . Index letter. Line due to — Wave-length in centimetres X io 8 . A (O (0 7621.277* 7594.059* G' or H y H Fe 4340.66 § 4308.071 a - 7184.781 G ■ - 4308.034 B 6870. l86t Ca 4307.904 C or H„ H 6563.054 g Ca 4226.892 a O 6278.289$ h or Hj H 4101.87 Di Na 5896.154 H Ca 3968.620 r»2 Na 5890.182 K Ca 3933- 8 °9 D 8 He 5875.982 L Fe 3820.567 Fe S270-533 M Fe 3727-763 E, - 5 2 70.49S N Fe 35 8l -344 ,Ca 5270.448 O Fe 344I-I35 E 2 Fe 5269.722 P Fe 33 6l -3° bi Mg 5183.792 Q Fe 3286.87 b 2 Mg Fe 5172.871 5169.218 Rll (Ca (Ca 3181.40 3 r 7945 bs < - 5169.161 vir Fe 3M4-58 (?) .Fe Fe 5169.066 5167.686 Si s 2 Fe Fe 3100.779 3100.415 b* - 5167.572 .Fe 3100.064 Mg 5167.501 s Fe 3047.720 ( F or Up H 4861.496 T Fe 3020.759 | d Fe 43 8 3-72I t Fe 2994.542 f Fe 4325.940 U Fe 2947-993 * The two lines here given for A are stated by Rowland to be : the first, a line " beginning at the head of A, out- side edge J " the second, a " single line beginning at the tail of A." t The principal line in the head of B. % Chief line in the a group. I Co 1 ™ giv"*,' whth^wing for the different value of the standard D line, corresponds to about 3.80.3. IT Cornu gives 3144.7, which would correspond to about 3i45-»- Smithsonian Tables. 175 Table 181. DETERMINATIONS OF THE VELOCITY OF LIGHT, BY DIFFERENT OBSERVERS.* Date of determi- nation. No. of experi- ments made. Method. Interval worked across in kilometres. Velocity in kilometres per second. Velocity in miles per second. Refer- ence. Wtof obser- vation as esti- mated by Hark- ness. 1849 1862 1872 1874 1879 1880 1880 to ■ 1882 1882 80 658 546 IOO 12 I48 39 65 23 Toothed wheel Revolving mirror Toothed wheel If « Revolving mirror Toothed wheel Revolving mirror (i a u u (( t. 8.633 0.02 IO.3IO 22.9I O.6054 5 5-13^3 1 1 5.5510 ( 5-1019 7.4424 7.4424 0.6246 315324 298574 =t 204 298500^995 300400 ^ 300 299910 ±51 301384^263 299709 299776 299860 299853±60 195935 185527^127 185481^618 186662^186 186357 ±31-7 187273 ± '64 186232 186274 186326 186322^37 I 2 3 4 5 6 7 7 7 8 I I 2 3 1 6 3 Mean from all weighted measurements . . Mean from those having weights > 1 . . . 299835 ±'54 299893 ± 2 3 186310^95-6 186347 ± 14.3 9 9 - 1 Fizeau, " Comptes Rendus," 1849. 2 Foucault, " Recueil des travaux scientifiques," Paris, 1878. 3 Cornu, " Jour, de l'Ecole Polytechnique," Paris, 1874. 4 Comu, " Annales de PObservatoire de Paris," Memoires, tome 13, p. A. 298, 1876. 5 Michelson, " Proc. A. A. A. S." 1878. 6 Young and G. Forbes, " Phil. Trans." 1882. 7 Newcomb, "Astronomical Papers of the American Ephemeris," vol. 2, pp. 194, 201, and 202. 8 Michelson, " Astronomical Papers of the American Ephemeris," vol. 2, p. 244. 9 Harkness. Table 182. PHOTOMETRIC STANDARDS.t Name of standard. Violle units. Carcels. Star candles. German candles. English candles. Hefner- Alteneck lamps. Violle units { . . . . Carcels Star candles .... German candles English candles Hefner-Alteneck lamps . I. OOO O.481 O.062 0.061 0.054 0.053 2.08 I.oo O.130 O.I27 O.II2 O.II4 16.I 775 1.00 0.984 0.870 0.853 16.4 7.89 I.02 1.00 0.886 0.869 18.5 8.91 I.15 1.13 1.00 0.98 18.9 9.08 I.I7 1. 15 I.02 1.00 * Quoted from Harkness, " Solar Parallax," p. 33. t This table, founded on Violle's experiments, is quoted from Paterson's translation of Palaz' '* Industrial Pho- tometry,'' p. 173. t The Violle unit is sometimes called the absolute standard of white light. It is the quantity of light emitted normally by one square centimetre of the surface of melted platinum at the temperature of solidification. Smithsonian Tables. 176 Table 183. SOLAR ENERGY AND ITS ABSORPTION BY THE EARTH ATMOSPHERE. This table gives sdme of the results of Langley's researches on the atmospheric absorption of solar energy.* The first column gives the wave-length K, in microns, of the spectrum line, while the second and third columns give the corresponding absorption, according to an arbitrary scale, for high and low solar attitudes. The fourth column, E, gives the relative values of the energy for the different wave-lengths which would be observed were there no terrestrial atmosphere. A «i "2 E °"-375 112 27 M .400 235 63 •45° 424 140 1031 .500 57o 225 1203 .600 621 3" 1083 .700 S53 324 849 .800 372 246 519 .900 238 167 316 1. 000 23S 167 3°9 Table 184. THE SOLAR CONSTANT. The " solar constant " is the amount of heat per unit of area of normally exposed surface which, at the earth's mean distance, would be received from the sun's radiation if there were no terrestrial atmosphere. The following table is taken from Langley's researches on the energy of solar radiation.f The first column gives the wave-length in microns. The second and third columns give relatively on an arbitrary scale an upper and a lower limit to the possible value of spectrum energy. Spectrum Spectrum Spectrum Spectrum Wave- S energy energy Wave- energy energy length. (upper (lower length. (upper (lower limit). limit). limit). limit). °*-SZ° 203.9 I22.5 I*\ooO 105.0 78.2 102.3 •375 196.6 1 1 0.O 1.200 61.3 .400 242.2 139- 1 I.40O 65.I 52.2 .450 783.2 105.5 I.600 48.O 45.O .500 852.9 374-1 I.800 39-2 36-4 .600 514-7 333-0 2.0O0 29.1 27.I .700 3 T 7-7 25S-4 2.200 19.4 J 7-5 .800 173-9 167-3 2.400 7.0 6.8 The areas of the energy curves are respectively The solar constants deduced from these areas are 149,060 and 95,933 3.505 and 2.630 Langley concludes that "in view of the large limit of error we can adopt three calories as the most probable value of the solar constant," or that " at the earth's mean distance, in the absence of its absorbing atmosphere, the solar rays would raise one gramme of water three degrees per minute, for each normally exposed square centimetre of its surface." * "Am. Jour, of Sci." vols, xxv., xxvii., and xxxii. t "Professional Papers of U. S. Signal Service," No. 15, 1884. Smithsonian Tables. Table 185. INDEX OF REFRACTION FOR CLASS. The table gives the indices of refraction for the Fraunhofer lines indicated in the first column. The kind of glass, the density, and, where known, the corresponding temperature of the glass are indicated at the top of the different columns. When the temperature is not given, average atmospheric temperature may be assumed. (a) Fraunhofer's Determinations. (Ber. Munch. Akad. Bd. 5.) Flint glass. Crown glass. Density = 3-723 i8*. 7S 3-5>2 2.756 2-535 2-535 Temp. C. = — — i7°-5 — B I.62775 I.60204 1-55477 I.52583 I.5243I C .62965 .60380 •55593 ■52685 •5253° D .63504 .60849 •55908 •52959 •52798 E .64202 •61453 •56315 •53301 ■S3'37 F .64826 .62004 .56674 ■53605 •53434 G .66029 .63077 •57354 .54166 •539?i H .67106 •64037 •57947 •54657 .54468 (b) Baille's Determinations. (Quoted from the Ann. du Bur. des Long. 193, p. 620.) Flint glass. Density ™ 2.98 23 <5 .2 3-22 3-M 3-44 3-54 3-63 3.68 4.08 5.00 Temp. C. = l8°. + 22°.0 i9°-5 23 .2 i3°-7 24°.o I2°-4 22°. 5 B I.5609 I-5659 1.5766 I.5966 I.6045 I.613I 1.6237 1.677 1 i. 7 801 C .5624 •5675 ■5783 .5982 .6062 .6149 ■6255 .6795 •7831 D .566O •5715 .5822 .6027 .6109 .6198 •6304 .6858 .7920 bi •5715 ■5776 .5887 .6098 .6183 •6275 •6384 ■6959 .8062 F •5748 •5813 •5924 .6141 .6225 •6321 .6429 .7019 .8149 G .5828 .5902 .6018 .6246 •6335 .6428 •6435 •6549 .7171 .8368 H .5898 •5979 .6098 •6338 •6534 .6647 .7306 •8567 Crown glass. (Bailie, ibid.) Density = 2.49 2.50 i 7 s .8 2-55 2.80 3.00 Temp. C. = 23°-5 i8°.4 2I°.2 2I°.9 B 1.5126 I.5244 I.5226 '■5I57 1-5554 C ■5134 •5254 •5237 .5166 ■5568 D .5160 .5280 •5265 .5192 .5604 bi .5198 .5320 ■5307 •5234 .5658 F .5222 •5343 •5332 .5256 .5690 G •5278 •5397 •5392 •53'3 •5769 H ■5323 •5443 •5442 .5360 .5836 00 Hopkinson's Determinations. (Proc. Roy. Soc. vol. 26.) Hard crown. Soft crown. Titani- silicic crown. Flint glass. Density = 2.486 2.550 2-553 2.866 3.206 3-659 3.889 4.422 A I-5"755 I.508956 - I-534067 - - I-639H3 1-696531 B •5 I 3625 .514568 .510916 I-539I55 .536450 I.568558 1.615701 .642874 .701060 C .511904 •540255 •537673 .57OOII .617484 .644866 .703478 D .517114 •5H59I •543249 .541011 .574015 .622414 .650388 .710201 E •520331 .518010 •547088 .545306 •579223 .628895 •657653 .719114 bi .520967 .518686 •547852 .546166 .580271 .630204 .659122 .720924 F •523139 .520996 .550471 .549121 .583886 •634748 .664226 .727237 (G) •527994 .526207 .556386 .556830 •555863 .592190 •645267 .676111 •742063 G •528353 •526595 •556372 .592824 .646068 .677019 .743204 h .530902 •529359 •559999 .560010 ■S9733 2 .651840 .683577 .751464 Hj .532792 .531416 .562392 .562760 .600727 .656219 .688569 •757785 N. B. — D is the more refrangible of the pair of sodium lines ; (G) is the hydrogen line near G. Smithsonian Tables. I 7 8 INDEX OF REFRACTION FOR GLASS. Table 185. (d) Mascart's Determinations. (Ann. Chim. Phys 1S68.) (e) Langley's Determinations. (Silliman's Jour- nal, 27, 1884.) Density^ Temp. = A B c D E b* F G H L M N O P Q Flint glass. Fraun- hofer line. B C D bi F 30°.o I.60927 .61268 .61443 .61929 .62569 .62706 .63148 .64269 .65268 .65817 .662 II .66921 ■67733 3-239 26°.o I.57829 .58U4 .58261 .58671 •59197 •59304 •59673 .60589 .61390 .62012 .62138 .62707 ■63341 •63754 .64174 Crown glass. 2-S78 28 u .o 1. 52814 .53011 ■53"3 •53386 ■53735 .53801 ■54037 •54607 ■55°93 •55349 ■55531 •55853 .56198 .56419 .56646 Flint glass. Wave length in mm. X io°. 2030 1918 1870 1810 1580 1540 1360 1270 1 130 940 910 890 850 815 760.1 = A 656.2 = C 588.9 = D X 516.7 = b 4 486.1 =F 396.8 = Hi 344.0=0 Index of refraction. I-55I5 .5520 •5535 •5544 •557; •5576 .5604 .5616 •5636 .5668 •5674 .5678 ■5687 ■5697 •57M •5757 .5798 .5862 •5899 .6070 .6266 (I) Effect of Temperature. (Vogel, Wied. Ann. vol. 25.) „, 4- nt = a. (t - 1') 4- /3 (r - t'f, where nt is the absolute index of refraction for the temperature t, and o and /3 are constants. For tem- peratures ranging from 12 to 260° Vogel obtains the Following values of o and for the Fraunhofer lines given at the tops of the columns. White Flint i«.io B = |j8.I0«t= i O.I0 8 = l/3.ioi°= H* 96 107 190 101 123 106 190 147 Ha 224 97 362 221 H„ 3 2 7 93 575 221 (g) Effect of Temperatore. (MiUler, Publ. d. Astrophys. Obs. zu Potsdam, 1885.) Flint glass. Density = 3.855. emp. C. = — 1 Temp. C to 24° I.643776 + .00000474 1 •645745 + .00000486 / .651 193 + .00000495* •659632 -(- -00000710 1 .664936 + .00000653 1 .676720 + .00000783 1 .684144 -j- .00000861 1 Density = 3 -218. Temp. C. = — 3° to 21 . 1-574359 .575828 ■579856 .586000 .598205 .603398 .OOOOO324 / .OOOO0333 t .OOOOO323 t .OOOOO443 t .OOOO0439 t .OOOOO560 t .OOOOO636 1 Crown glass. Density = 2.522. Temp. C.=— 5° to 23 . 1.512588 — ■513558 — .516149 + .520004 + .522349 + .527360 + .520376 + .OOOOOO43 t .OOOOOO33 t .OOOOOO17 t .OOOOOO54 t .OOOOOO48 t .OOOOO082 t .OOOOOI43 t ~T B -The above examples on the effect of temperature give % Jta of the order of magnitude of that effect', but are only applicable to the particular specimens experimented on. Table 186. INDEX OF REFRACTION. Indices ol Refraction for the various Alums.* R a a O u H Index of refraction for the Fraunhofer lines. a B c D E b F a Aluminium Alums. J?Al(S0 4 ) 2 4-i2H 2 0.t Na NH 3 (CH 3 ) K Rb Cs NH 4 Te I.667 1.568 1-735 I.852 1. 961 1. 631 2.329 17-28 7-17 14-15 7-21 15-25 15-20 IO-23 1.43492 ■45 OI 3 .45226 .45232 ■45437 .45509 .49226 '•43563 .45062 •453°3 .45328 •45517 ■45599 •49317 I-43653 •45'77 •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 .44412 .45941 .46181 .46192 .46386 .46481 .50463 1.44804 46363 .46609 .46618 .46821 .46923 .51076 Indium Alums. /?In(S0 4 ) 2 +i2H 2 0.t Rb Cs NH 4 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. 4638 1 .46522 .46636 1.46694 .46842 46953 1.46751 .46897 .47015 1.46955 .47105 47234 1.49402 47562 4775° Gallium Alums. tfGa(S0 4 ) 2T -i2H 2 0.t Cs K Rb NH 4 Te 2.113 I.895 I.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 •5°349 1.46495 .46528 •46579 46835 .50665 1.46785 .46842 .46890 .47146 .51057 1. 46841 .46904 .46930 47204 •5"3i 1.47034 47093 .47126 .47412 •51387 1.47481 .47548 .47581 .47864 •52007 Chrome Alums. jeCrfSOJs+^HjO.t Cs K Rb NH 4 Te 2.043 1.817 1.946 i-7i9 2.386 6-12 6-17 12-17 7-18 9-25 1.47627 .47642 .47660 •479" .51692 I-4773 2 ■47738 ■47756 .48014 .51798 1.47836 .47865 .47868 .48125 •5!923 1. 48 1 00 48137 .48151 .48418 .52280 1.48434 48459 .48486 .48744 .52704 1.48491 48513 .48522 ■48794 .52787 I.48723 •48753 48775 .49040 ■53082 1.49280 .49309 49323 ■49594 •53808 Iron Alums. i?Fe(S0 4 ) 2 +i2H 2 0.t K Rb Cs NH 4 Te 1.806 1.916 2.061 r-7'3 2.385 7-1 1 7-20 20-24 7-20 15-17 1.47639 .47700 .47825 .47927 •5 l6 74 1.47706 ■47770 .47921 .48029 .51790 147837 47894 .48042 .48150 ■S!943 1.48169 48234 .48378 .48482 •52365 1.48580 .48654 .48797 .48921 .52859 1.48670 .48712 .48867 48993 .52946 I.48939 .49003 .49136 .49286 •53284 1.49605 .49700 .49838 .49980 .54112 * According to the experiments of Soret (Arch. d. Sc. Phys. Nat. Geneve, 1884, 1888, and Comptes Rendus, 18S5). t R stands for the different bases given in the first column. Smithsonian Tables. I8O Table 1 87. INDEX OF REFRACTION. Index ot Retraction ol Metals and Metallic Oxides. (a) Experiments of Kundt* by transmission of light through metallic prisms of small angle. Name of substance. Index of refraction for Red. White. Blue. Silver .... O.27 Gold O.38 O.58 1. 00 Copper Platinum . Iron 0-45 I.76 1.81 O.65 I.64 I.73 O.95 I.44 )f 5 Nickel 2.17 2.01 Bismuth . 2.6l 2.26 2.13 Gold and gold oxide 1.04 _ 1.25 0.89 O.99 J-33 — 2.O3 Bismuth oxide . _ 1. 91 _ Iron oxide I.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 3- 2 9 2.90 4-99 4.82 4.40 (b) 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 (Li a ). "Red." Yellow (D). Blue (F). Violet (G). A = 67.1 A = 64.4 A =58.9 A =48.6 A = 43.it Nickel . * . 2.04 i-93 I.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 Drude. The following table gives the results of some of Drude's experiments.! The index of refrac- tion is derived in this case from the constants of elliptic polarization by reflection, and are for sodium light. Metal. Index of refraction. Metal. Index of refraction. Aluminium I.44 Mercury- 1-73 Antimony 3-°4 Nickel . I.79 2.06 Bismuth 1.90 Platinum Cadmium 113 Silver . 0.181 Copper . Gold 0.641 Steel 2.41 0.366 Tin, solid I.48 Iron 2.36 " fluid 2.IO Lead 2.01 Zinc 2.12 Magnesium . o.37 * "Wied. Ann." vol. 34, and "Phil. Mag." (5) vol. 26. t Wave-lengths A are in millionth! of a centimetre. t Nearly pure oxide. § " Wied. Ann." vol. 39. Smithsonian Tables. I8l Tables 188, 189. INDEX OF REFRACTION. TABLE 188. —Index ol Refraction of Sock Salt Determined by Langley. Temp. 24 C. Determined by Rubens and Snow. Determined by other authorities. Line of spec- trum. Wave- length in cms. XioH. Index of refraction. Line of spec- trum. Wave- ,„ length In in cms. X io°. ' dex of ifrac- ion. Line of spec- trum. Index of refraction. Authority. M 37- 2 7 I.57486 H v 434 1 5607 H tt I.54046 ) L 38.20 .57207 F 48.5 553i H0 •5S3I9 > Haagen at 20 C. H 2 $8 .56920 D 58-9 5441 Hy .56056 ) H, •56833 C 65.6 5404 G 43-°3 •56133 75-5 5370 Ha I.54095 ) Bedson and F 48.61 ■553 2 3 79-o 5.358 H0 •55384 > Carleton Williams bi 51.67 .54991 83-1 5347 Hy .52515 ) at 15 C. bi 5183 ■54975 87.6 5337 Di 57.89 .54418 92-3 5329 B I.53884 D 2 58-95 .54414 97.8 5321 C .54016 C 65.62 68.67 •54051 I0 3-5 53n D •54381 • Miilheims. B •53919 1 10.7 5305 E .54866 A 76.01 •5367 1 18.6 5299 F .55280 _ far 94- ■5328 127.7 5293 4> "3- •5305 138.4 5286 A I-53663 V 139- -52f7 151.! 5280 B < •53918 a 132. .5268 166.0 527 5 .53902 184.5 207.6 5270 5264 C j .54050 .54032 •544l8 Stefan at 17 and Determined by Baden Powell. 237.2 5257 D \ 22 C. The up- 277.1 5247 .54400 per values are at 17 and the 302.2 5239 E \ .54901 B - 1-5403 332-0 5230 .54882 C ■5415 369.0 5217 F \ •55324 D .5448 415.0 5208 •55304 E - ■5498 474-5 5197 G | .56129 F •5541 554-0 5184 .56108 G - .5622 644.7 5163 H j ■56823 H .5691 830.7 5138 .56806 1 J TABLE 189. — Index of Refraction of Sylvlne (Potassium Chloride). Determined by Rubens and Snow. Determined by other authorities. Wave-length in cms. X io 6 . Index of refraction. Wave- length in cms. X io 6 . Index of refraction. Line of spec- trum. Index of refraction. Authority. 434 (Hy) 48.6 (F) 58.9 (D) 65.6 (C) 80.2 84.5 89-3 944 100.3 107.0 1 14.5 123.4 1337 I.5048 .4981 .4900 .4868 I.4829 .4819 .4809 .4807 1-4795 •4789 .4781 .4776 I.477 1 145.8 160.3 I78.I 2OO.5 229.I 267.3 320.9 356-1 400.I 457-7 534-5 641.2 802.2 I.4766 .4761 4755 4749 1.4742 473 z .4722 4717 1.4712 .4708 .4701 •4693 1.4681 A B C D E F G H B C D E F G D D I-48377 .48597 •48713 .49031 49455 .49830 ■50542 .51061 4754 .4767 .4825 4877 4903 •5005 .4904 4930 - Stefan at 20 C. - Grailich. Tschermak. Groth. Smithsonian Tables. 182 Table 1 go. INDEX OF REFRACTION. Index ol Refraction ol Fluor-Spar. Determined by Rubens and Snow. Wave-length in cms. Xio«. Index of refraction. 434(H V ) M393 48.5(F) •4372 58-9(D) •434° 65.6(C) •4325 80.7 •4307 85.0 •43°3 89.6 .4299 95.0 .4294 100.9 .4290 107.6 .4286 115.2 .4281 124.0 .4277 J 34-5 .4272 146.6 .4267 161.3 .4260 179.2 .4250 201.9 .4240 230-3 .4224 268.9 •4205 322.5 •4174 4°3-S .4117 462.0 .4080 538.0 .4030 646.0 .3960 807.0 .3780 Determined by Sarasin. Line of spectrum. A a B c D F h H Cd Zn Al Wave- length in cms. X io°. Index of refraction. 76.040 1.431010 71.836 •43IS75 68.671 ■431997 65.618 ■432571 58.920 •433937 48.607 •437051 41.012 .441215 39-68i .442137 36.090 •445356 34-655 .446970 34-oi5 •447754 32-525 .449871 27.467 •459576 25713 .464760 23.125 .475166 22.645 .477622 21-935 .481515 21.441 .484631 20.988 .487655 20.610 .490406 20.243 •493256 19.881 .496291 19.310 .502054 18.560 .509404 Determined by the authorities quoted. Line of spectrum. B c D E F B D F G H Red Yellow Na Index of refraction. M339 1.43003 •43153 .43200 .43250 •43384 •43551 .43696 1.43200 •4339° •43709 .43982 .44204 '•433 •435 1.4324* J •4342t ! Authority. Fizeau. Mulheims. Stefan. DesCloi- seaux. Kohl- rausch. Smithsonian Tables. * Gray at 23° C. t Black at 19° C. 183 Table 191 . INDEX OF REFRACTION. Various Monoielrlngent or Optically Isotropic Solids, Substance. Line of Spectrum. 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 arabic Hanyne Helvine Obsidian Opal .... Pitch .... Potassium bromide . " chlorstannate " iodide Phosphorus Resins : Aloes . Canada balsam Colophony . Copal . Mastic . Peru balsam Selenium, vitreous f bromide Silver ) chloride . ( iodide . Sodalite {cle U a e riike water' Sodium chlorate Spinel . Strontium nitrate Smithsonian Tables. red D D D D Li Na Tl C D F C D F D red green II D f A B C G H D red D D D 1-5374 1.6422 '•755 1.5716 1.0052 2.34165 2.36923 2.40069 1.46245 1.46303 1.47024 1.51222 1.51484 1.52068 '•53 2 \ 1.5462 2.414 ) 2.428 J 2.46062 ) 2.46986 [ 2.47902 ) 1.6 1.81 1.90 '•3' 1.54 ( 1.74 to 1 '-9° 1.480 1.514 1. 4961 '■739 ( 1.482 to i ] 1.486 ) ( 1.406 1 1 1.450 ) '•53i '•5593 i 1.6574 1.6666 I 2.1442 1.619 1.528 1.548 1.528 '■535 '•593 2.653 2.730 2.86 2.98 2 -533 2.061 2.182 1.4827 '■4833 1-515° 1.5667 De Senarmont. Grailich. DesCloiseaux. Fock. Beer. Ramsay. Bedson and Carleton Williams. Kohlrausch. Mulheims. DesCloiseaux. Schrauf. Ayrton & Perry. Wernicke. Various. Jamin. Wollaston. Tschichatscheff. Levy & Lecroix. Various. Wollaston. Topsoe and Christiansen. Gladstone & Dale. Jamin. Wollaston. Jamin. Wollaston. Baden Powell. Sirks. Wernicke. Feusner. Dussaud. DesCloiseaux. Fock. 184 Table 192. INDEX OF REFRACTION. Index of Refraction of Iceland Spar. The determinations of Carvallo, Mascart, and Sarasin cover a considerable range of wave-length, and are here given. Many other determinations have been made, but they differ very Tittle from those quoted. Line of spectrum. Wave- length in cms. X io 6 . Index of refraction for — Ordinary ray. Extraordi- nary ray. Line of spectrum. Wave- length in cms. X io B . Index of refraction for— Ordinary ray. Extraordi- nary ray. Authority: Carvallo. Authority : Sarasin. A B 215 198 177 154 122 108 76.04 68.67 1.6279 ■6350 .6361 .6403 .6424 .65006 •65293 Authority: Sarasin. A 76.04 a 71.84 B 68.67 Cdi 64-37 D 58.92 Cd 2 53-77 Cd 3 5336 Cd* 50.84 F 48.61 Cd 5 47-99 Cd 8 46.76 Cd 7 44.14 h 41.01 H 39.68 Cd 9 36.09 Cdio 34-65 Cdn 34.01 1.65000 .65156 .65285 .65501 ■65839 .66234 .66274 .66525 .66783 .67023 .67417 .68036 .68319 •69325 .69842 .70079 1-4753 .4766 •4779 •44799 .48275 .48406 1. 48261 •48336 •48391 .48481 .48644 .48815 ■48843 •48953 49079 .491 1 2 .49185 •49367 •49636 ■49774 .50228 •5°45 2 •5°559 B C D E b 4 F G H L M N O P Q R S T Cdi2 32-53 1.70740 1.50857 Cd 17 27.46 .74151 .52276 Cd 18 25.71 .76050 •53019 Cd23 23.12 .80248 •54559 Cd24 22.64 .81300 .54920 Cd 2 5 21.93 .83090 •55514 Cd 2 e 21.43 .84580 •55993 Authority : Mascart. 1-65013 .65162 .65296 .65446 .65846 .66354 .66446 .66793 .67620 .68330 .68706 .68966 .69441 •69955 .70276 .70613 •7"55 .71580 •71939 I.48285 .48409 ■48474 .48654 .49084 .49470 •49777 .49941 •50054 .50256 .50486 .50628 .50780 .51028 Smithsonian Tables. 185 Table 1 93. INDEX OF REFRACTION. Index of Refraction of Quartz. Index for — Index for — Line or wave- length in cms. Line of X 10°. Ordinary Extraordinary spectrum. Ordinary Extraordinary ray. ray. ray. ray. Authority : Sarasir Quincke (right-handed quartz). B c 1-53958 .54087 I.54780 ■54933 Cdi I.54227 1.55124 D E •54335 .54649 •55 r 99 .55508 D .54419 •55335 F .54868 •55758 Cd 2 Cd s Cdi •54655 •54675 .54825 ■55573 •55595 G .55241 •56193 •55749 Cd 5 Cd 6 .55014 •55 I °4 ■55943 .56038 Quincke (left-handed quartz). Cd 7 •553i8 .56270 Cd 9 Cdio Cdn Cd 12 Cd 17 .56348 .56617 .56744 .57094 •58750 •57319 ■57599 ■57741 .58097 .59812 B C D E F I.54022 .54092 •543'8 •54575 .54845 1.54880 •54945 •55245 •55533 .55801 Cd 18 Cd 28 .59624 .61 402 .61816 .60713 .62561 .62992 •63705 .64268 ■64813 .65308 .65852 .66410 G .55246 .56163 Cd 25 Cd 26 Zn 2 7 .62502 .63040 .63569 Authority: Mascart. Zn 2 8 Zn 2 9 AI30 .64041 .64566 .65070 A a B C D E 1.53902 54018 1.54812 .54919 Aim. AI32 .65990 .67500 .67410 .68910 .54099 .54188 ■54423 .54718 •5477° .55002 •55095 •55338 •55636 •55694 b 4 F .54966 •55897 Authority : Rubens G H L M •55429 .55816 .56019 .56150 •56372 •56770 •56974 .57121 434(H V ) I.5538 N .56400 •5738i 48.5(F) •5499 _ O .56668 •57659 59.0(G) .5442 _ P .56842 .57822 65.6(C) .5419 _ Q — •57998 83-9 •5376 - R — •58273 90.4 97-9 •5364 ■5353 - 106.7 •5342 - Authority: Vai 1 der Willigen (left-handed quartz). 117.4 -53 2 5 — I3°S •S3 r ° _ 146.8 .5287 - A I-539H 1.54806 167.9 •5257 - B •54097 •54998 1957 .5216 - C •54185 •55085 234.8 .5160 - D .54419 •55329 E F •54715 .54966 •55633 •55855 G •55422 •56365 H .55811 ■56769 Smithsonian Tables. * For wave-lengths, see Tables 190 and 192. 186 INDEX OF REFRACTION. Tables 194, 195. Line of spec- trum. Index of refraction. " 1 Substance. Authority. Ordinary ray. Extraordi- nary ray. Alunite (alum stone) . Ammonium arseniate . D red '•573 1.592 Levy & Lacroix. Anatase r -577 4.524 De Senarmont. Apatite D 2 -5354 2.4959 Schrauf. Benzil . D D 1.6390 1.6588 1.589 to 1.570 1-6345 1.6784 DesCloiseaux. Beryl . Brucite D J 1.582 to 1.566 \ Various. Calomel D 1.560 1-581 Kohlrausch. red 1.96 2.60 ■ De Senarmont. red 2.854 3- r 99 DesCloiseaux. Corundum (ruby, sapp] lire, etc. red j green green 1767 to 1-759 * : u Dioptase Emerald (pure) . Ice at — 8° C. . 1.769 1.667 1.584 1.762 1-723 1.578 D 1.309 '■3'3 Meyer. Idocrase Ivory .... Magnesite . Potassium arseniate . <* « D red 1.719 to 1.722 '•539 I-7I7 1.564 1.717 to 1.720 i-54i I-5I5 I-5I5 } DesCloiseaux. Kohlrausch. Mallard. DesCloiseaux. Silver (red ore) . Sodium arseniate red red D '■493 3.084 1.459 1. 501 2.881 1.467 De Sernamont. Fizeau. Baker. " phosphate Strychnine sulphate . Tin stone . Tourmaline (colorless) D D D D D 1.587 1.446 1.614 J-997 1-637 J -336 2.452 1.519 2.093 1.619 Schrauf. Dufet. Martin. Grubenman. Heusser. " (different C( )lors) D i 1.633 t° 1.650 1.92 1.616 to 1.625 1.97 | Jerofejew. De Senarmont. Zircon (hyacinth) red D 1.924 1.968 Sanger. TABLE 195. —Biaxial Crystals. Line of Index of refraction. Authority. tnim. Minimum. Interme- diate. Maximum Anglesite D I-877I 1.8823 1.8936 Arzruni. Anhydrite . D I-S693 1.5752 1.6130 Miilheims. Antipyrin D 1.5101 1.6812 1.6858 Glazebrook. Aragonite D I.5301 1.6816 1.6859 Rudberg. Axinite . red I.6720 1.6779 1.6810 DesCloiseaux. Barite . D I.636 1-637 1.648 Various. Borax . D 14467 1.4694 1.4724 Dufet. Copper sulphate . D I.5140 1-5368 1-5433 Kohlrausch. Gypsum D I.5208 1.5228 1.5298 Miilheims. Mica (muscovite) . D 1. 5601 1-5936 '•5977 Pulfrich. Olivine . D I.661 1.678 1.697 DesCloiseaux. Orthoclase . D I.5190 i-5 2 37 1.5260 " Potassium bichromate . D I.7202 1.7380 1. 8197 Dufet. " nitrate D 13346 1.5056 1.5064 Schrauf. ! " sulphate D i'493 2 1.4946 1.4980 Topsoe & Christiansen. Sugar (cane) D r '5397 1.5667 1. 5716 Catderon. Sulphur (rhombic) D i-95°5 2.0383 2.2405 Schrauf. Topaz (Brazilian) D 1.6294 1.6308 I-6375 Miilheims. Topaz (different kinds) D l 1.630 to 1 .613 1. 63 1 to 1.616 1.637 to 1.623 > Various. Zinc sulphate D 1.4568 1.4801 1.4836 Topsoe & Christiansen. Smithsonian Tables. 187 Table 1 96. INDEX OF REFRACTION. Indices ol Refraction relative to All loi Solutions of Salts and Acids. Density. Temp. C. Indices of refraction for spectrum lines: Substance. Authority. C D P *y H (a) Solutions in Water. Ammonium chloride I.067 27°-°5 I-37703 I-37936 I-38473 _ I-39336 Willigen. it a .025 29.75 .34850 •35050 •355*5 - •36243 " Calcium chloride •398 25-65 .44000 •44279 .44938 - .46001 " U (( .215 22.9 •394" .39652 .40206 - .41078 tt tt •143 25.8 •37I5 2 •37369 •37876 - .38666 Hydrochloric acid . I.166 20.75 1. 408 1 7 1.41109 1.41774 - 1. 428 1 6 " •359 18.75 •39893 .40181 .40857 - .41961 " Potash (caustic) . . .416 II.O .40052 ■34087 .40281 .40808 - •41637 Fraunhofer. Potassium chloride . normal solution .34278 •34719 1.35049 - Bender. it it double normal .34982 •35*79 ■35645 •35994 - H it triple normal •35831 .36029 .36512 .36890 - - Soda (caustic) . . I-37D 21.6 1.41071 I-4I334 1.41936 - 1.42872 Willigen. Sodium chloride . . .189 18.07 •37562 •37789 •3S322 1.38746 - Schutt. it a .109 18.07 •3575 1 ■35959 .36442 .36823 - a it •°35 18.07 .34000 •34I9I .34628 .34969 — Sodium nitrate . . 1.358 22.8 1.38283 I-38535 I-39I34 - 1.401 21 Willigen. Sulphuric acid . . .811 18.3 •43444 .43669 .44168 - .44883 a it .632 18.3 .42227 .42466 .42967 - .43694 " " .221 18.3 ■36793 •37009 .37468 - ■38158 " u tt .028 18.3 •33663 .33862 .34285 - •34938 Zinc chloride . . . '■359 26.6 1-39977 1.40222 1.40797 - '■41738 a tt tt .209 26.4 .37292 •37515 .38026 " •38845 (b) Solutions in Ethyl Alcohol. Ethyl alcohol . . . 0.789 25-5 I-3579I J-3597I I-36395 _ 1-37094 Willigen. " " •932 27.6 ■35372 ■35556 .35986 - .36662 Fuchsin (nearly sat- urated) .... - 16.0 ■39i8 •398 .361 - •3759 Kundt. Cyanin (saturated) . - 16.0 •383" •3705 — •3821 u Note. — Cyanin in chlor oform also acts anomalously ; for example, Sieben gives for a 4.5 per cent, solut ion ha= 1-4593. /»*= 1-4695- Mgreen) = 1.4514. ha (blue) = 1.4554. For a 9.9 per cent. >olution tie gives /i A = 1.4902, p r (green) = 1.4497, /io(blue) = 1.4597. (« ) Solutio ns of Potassium Permanganate in Water.* Wave- length Spec- Index Index Index Index Wave- length Spec- Index Index Index Index trum for for for for for for for for X io«. Hue. 1 % sol. 2 % sol. 3 % sol. 4 % sol. Xio«. line. 1 % sol. 2 % sol. 3 % sol. 4 % sol. 68.7 B 1.3328 1-3342 _ I-3382 S T.6 _ 1-3368 '■3385 _ 65.6 C •3335 •3348 I-3365 •3391 50.0 - •3374 •3383 1-3386 I.3404 61.7 - •3343 •3365 •338l .3410 48.6 F ■3377 .3408 59-4 - •3354 •3373 ■3393 •3426 48.0 - •338i •3395 •3398 •3413 5?'§ D •3353 ■3372 - ■3426 46.4 - •3397 •3402 •3414 •3423 56.8 - •3362 •3387 ■3412 •3445 •3438 44-7 - •3407 •3421 •3426 ■3439 55-3 - •3366 •3395 •3417 43-4 - •3417 - - •3452 52.7 E •3363 - - - 42-3 - •343 1 •3442 •3457 •3468 52.2 •3362 ■3377 ■3388 Smithsonian Tables. * According to Christiansen. 188 Table 197. INDEX OF REFRACTION. Indices ol Refraction ol Liquids relative to All. Index of refraction for spectrum lines. >ll 1 r\ Qfcl Tl tf*l* Temp. Authority. okiuo ut Ul#C* C. D P H v E Acetone .... 10° 1.3626 1.3646 1.3694 1 -373 2 Korten. Almond oil . . . o •47SS .4782 .4847 - Olds. Analin* .... 20 •S993 .5863 .6041 .6204 - Weegmann. Aniseed oil . . . 21.4 •54io •5475 .5647 - - Willigen. '5-i .5508 ■5572 •5743 - I.6084 Baden Powell. Benzene t .... IO 1.4983 1.5029 1.5148 - 1-5355 Gladstone. .... 2Z.5 •4934 ■4979 .5095 - •53°4 u Bitter almond oil . 20 •S39I .5623 •S77S Landolt. Bromnaphtalin . . 20 •6495 .6582 .6819 .7041 .7289 Walter. Carbon disulphide J 1.6336 1-6433 1.6688 1.6920 I-7I75 Ketteler. « u 20 .6182 .6276 ■ 6 5 2 3 .6748 .6994 " tt u IO .6250 •6344 .6592 .7078 Gladstone. " It it 19 .6189 .6284 ■£ 3 5 2 .6389 - .7010 Dufet. Cassia oil ... . IO .6007 .6104 - •7039 .6985 Baden Powell. <( *t 22.5 •593° .6026 .6314 - a tt Chinolin .... 20 1.6094 1.6171 1. 6361 1.6497 _ Gladstone. Chloroform . . . 10 .4466 .4490 •45SS .4661 Gladstone & Dale. n 3° - •4397 - .4561 » u " ... 20 ■4437 .4462 l6so8 - - Lorenz." Cinnamon oil . . 23-5 .6077 .6188 - - Willigen. Ether 15 1-3554 1.3566 1.3606 - 1-3683 Gladstone & Dale. " IS •3573 •3594 .3641 - •3713 Kundt. Ethyl alcohol . . •3 6 77 •369S ■3739 •3773 - Korten. tt a 10 •3 6 3 6 •3654 .3698 •3732 *■ " " " . . 20 •3596 .3614 •3657 •3683 .3690 — " a it IS •3621 •3638 - •3751 Gladstone & Dale. Glycerine .... 20 1.4706 _ 1.4784 1.4828 - Landolt. Methyl alcohol . . IS •3308 1.3326 ■33 62 - •3421 Baden Powell. Olive oil ... . ■4738 •4763 .4825 - — Olds. Rock oil ... . . •434S •4573 .4644 — — Turpentine oil . . 10.6 I-47I5 1.4744 1.4817 1-4939 Fraunhofer. " " 20.7 .4692 .4721 ■4793 •4913 Willigen. Toluene .... 20 •49" •4955 .5070 ■S170 — Bruhl. Water§ .... 16 •33i8 •3336 ■3377 •3409 — Dufet. it 16 ■33i8 ■3337 •3378 •3442 Walter. * Weegmann gives |» fl r= 1.59668— .000518*. Knops gives p r = 1.61500—. 000561!. t Weegmann gives ^=1.51474 — -000665*. Knops gives ^=1.51399 — 000644*. t Wullner gives ^ dissolved in water. g = 50 to 95, temp. = 24 C. Camphor,* C, H 1() O, dissolved in alcohol. } = 50 to 95, temp. = 22.9 C. Santonin,! C 1G H 18 3 , dissolved in chloroform. t— 75 to 96.5, temp. = 20 C. B C D E bi b 2 F e 68.67 65.62 58.92 52.69 5I-83 51.72 48.61 43-83 + 2°748+ 0.09446? + I.950 + 0.13030? + 0.153 + O.17514? — O.832 + 0.19147? — 3-598 + O.23977 ? — 9-657 + 0.31437? 38 - 549 — 0.0852? 51.945 — 0.0964? 74-33 1 — 0-I343? 79-348 — 0.1451 ? 99.601 — 0.1912? 149.696 — 0.2346 ? — I40°.I +0.2085? — 149-3 +0.1555? — 202.7 +0.3086? — 285.6 + 0.5820 ? — 302.38 + 0.6557 ? — 365-55 + 0-8284? — 534.98+1.5240? Santonin.t C«H la 3 , , dissolved in alcohol. c=z 1.782. temp. = 20 C. Santonin,! C 1B H 18 08, San tonic acid,! dissolved in chloroform. c = 27.192. temp. = 20 C. Cane sugar, + C^H^On, dissolved in water. p = 10 to 30. dissolved in alcohol. c =4.046. temp. = 20° C. dissolved in chloroform c =3.1-30. 5. temp. = 2o d C. B C D E bi b 2 F e G g 68.67 65.62 58.92 52.69 5I-83 5 J -72 48.61 43-83 43-°7 42.26 — I IO.4 — 1 18.8 — 161.O 222.6 — 237.I 261.7 — 380.O 442° 5°4 693 991 1053 1323 201 1 2381 484° 549 754 1088 1 148 1444 2201 2610 -49° — 57 — 74 — 105 — 112 — 137 — 197 — 230 47°-56 52.70 60.41 84.56 87.88 101.18 131.96 * Arndtsen, " Ann. Chim. Phys." (3) 54, 1858. t Narini, " R. Ace. dei Lincei," (3) 13, 1882. t Stefan, " Sitzb. d. Wien. Akad." 52, 1865. ROTATION OF PLANE OF POLARIZED LIGHT. Table 200. Sodium chlorate (Guye, C. R. 108, 1889). Quartz (Soret & Sarasin, Arch. de Gen. 1882, or C. R . 95, 1882).* Spec- trum line. Wave- length. Temp. C. Rotation per mm. Spec- trum line. Wave- length. Rotation per mm. Spec- trum line. Wave- length. Rotation per mm. a 71.769 i5°.o 2°.o68 A 76.04 i2°.66S Cd» 36.090 630.268 64.459 B 67.889 17.4 2.318 a 71.836 14.304 N 35-818 C 65-073 20.6 2-599 B 68.671 15.746 Cd w 34-655 69.454 70.587 D 59.085 18.3 3.104 O 34.406 E 53-233 16.0 3.841 C 65621 58.951 17.318 F 48.912 11.9 4.587 L>2 21.684 Cd u 34-015 72.448 G 45-532 42.834 IO.I 5-33' Di 58.891 21.727 P 33.600 74-571 G 14-5 6.005 ^ 32.858 78-579 H 40.714 '3-3 6.754 E 52.691 27-543 Cdi2 32.470 80.459 L 38.412 14.0 7.654 F 48.607 32-773 M 37-352 35-544 33-931 32-34I 10.7 8.100 G 43.072 42.604 R 3!-798 84.972 N 12.9 8.86i Cdn 27.467 121.052 P 12.1 9.801 h 41.012 47.481 Cd 18 25-7I3 143.266 Q 1 1.9 10.787 H 39-68i 5 I - I 93 Cd28 23.125 190.426 R T 30.645 29.918 28.270 I3 i 12.8 11.921 1 2.424 K 39-333 52-I55 Cd24 22.645 201.824 Cd 17 12.2 13.426 L 38.196 58.894 Cd 2 6 21-935 220.731 Cdis 25.038 11.6 14.965 M 27.262 Cd26 21.431 235-972 * The paper is quoted from a paper by Ketteler in " Wied. Ann." vol. »., p. 444- The wave -lengths are for the Fraunnofer lines, Angstrom's values for the ultra violet sun, and Cornu's values for the cadmium lines. Smithsonian Tables. .„ j Table 201. LOWERING OF FREEZING-POINT BY SOLUTION OF SALTS. Under P is the number of grammes of the substance dissolved in 100 cubic centimetres of water. Under C is the amount of lowering of the freezing-point. The data have been obtained by interpolation from the results pub- lished by the authorities quoted. Substance and P C° Substance and P C° Substance and P C° observer. observer. observer. AgNO s 5 °-93 Z11SO4 1 0.10 MgCl 2 °-5 0.26 F. M. Raoult.* 10 1.71 F. M. Raoult* 2 0.23 S. Arrhenius.t 1.0 o-53 IS 2.38 3 0.36 i-5 0.81 20 2.97 4 0.49 2.0 no 25 3-53 5 061 2.5 '•39 3° 4.00 10 1.23 3-o 1.69 35 4-43 '5 1.8s 3-5 2.00 40 4.80 20 2.50 4.0 2.32 45 5-15 25 3i9 4-5 2.65 2.98 5° 5-45 3° 3-94 5.0 55 575 5-5 3-32 60 6.00 CuS0 4 1 0.15 6.0 3-67 65 6.26 F. M. Raoult.* 2 0.29 3 0.40 BaCl 2 0.5 0.1 19 Ca(N0 3 ) 2 1 0.28 4 e.51 Harry C. Jones.§ 1.0 0.234 F. M. Raoult* 2 0.56 0.84 5 0.62 i-5 0.344 3 6 0.72 2.0 0.450 4 1. 12 7 0.82 5 1.40 8 0.92 SrCl 2 0.5 0.17 10 2.78 9 1.02 S. Arrhenius.t 1.0 o-34 15 4.26 10 1. 12 i-5 0.50 20 6.00 2.0 0.65 CdSOi 1 0.09 2-5 0.80 Cd(N0 8 )i! 0.5 0.112 F. M. Raoult* 2 0.19 30 0.95 Harry C. Jones.§ 1.0 0.217 3 4 0.28 0.38 3-5 4.0 1. 12 1.29 Na 2 S0 4 1 0.28 5 0.48 , 4-5 1.44 F. M. Raoult* 2 0.56 10 1. 00 5.0 1.60 3 0.84 15 1.54 5-5 1.76 4 1. 12 20 2.U 6.0 '•93 5 1.40 25 2.77 3° 3-5' CuCl 2 +2H 2 0.5 0.15 K 2 S0 4 °-5 0.14 35 4.4O S. Arrhenius.t 1.0 0.30 S. Arrhenius. 1.0 0.27 i-5 0.44 i-5 o-39 NaCl 0.5 O.32 2.0 0.58 2.0 0.51 S. Arrhenius.t 1.0 0.62 2-5 0.72 2-5 0.63 i-5 O.92 3-o 0.86 3-° 0.74 2.0 1.22 3-5 1.00 3-5 0.85 2-5 I.52 4.0 1.14 4.0 0.96 3-o I.S2 4-5 1.29 4-5 1.07 5.0 M3 5-° 1.17 KC1 o-S O.234 5-5 i-S7 5-5 1.27 Harry C. Jones.J 1.0 O.464 6.0 1.71 6.0 i-37 i-5 O.693 6.5 1.85 6-5 1.47 2.0 O.915 2.0 2.00 7.0 1-57 2-5 H36 l S 1.67 3-o "•359 CdCl 2 0.5 0.120 8.0 i-77 Harry C. Jones. § 1.0 0.227 MgS0 4 1 0.18 LiCl S. Arrhenius.t o-5 1.0 0.45 0.89 CaCl 2 i-5 0.322 F. M. Raoult * 2 °-35 0.52 '•5 2.0 i-34 1.78 0.5 0.23 3 S. Arrhenius.t 1.0 0.45 0.68 4 0.70 2-5 2.23 i-5 5 0.89 2.0 0.91 10 1.77 NH4CI 0.5 0.326 2.5 1.14 15 2.78 Harry C. Jones.} 1.0 0.644 3° i-37 20 3.68 i-5 0.957 3-5 4.0 1.61 1.85 Smithsonian Tables. * In " Zeits. fur Physik. Chem." vol. 2, p. 489, 1888. t Ibid. vol. 2, p. 491, 1888. % Ibid. vol. 11, p. no, 1893. § Ibid. vol. n t p. 529, 1893. 192 Table 201. LOWERING OF FREEZING-POINT BY SOLUTION OF SALTS. Substance and P c° Substance and P C° Substance and P C° observer. observer. observer. ZnCl 2 °-5 0.185 Alcohol, C 2 H 6 0.1 0.044 H 2 SO s 0.5 O.I5 Harry C. Jones.* 1.0 0.348 Harry C. Jones.} 0.2 o-3 O.087 0.129 S. Arrhenius.t 1.0 i-5 O.3O 0-45 CdBr 2 °-5 0.080 0.4 O.170 2.0 O.60 Harry C. Jones.* I.O 0.142 o-S 0.212 2.5 O.75 i-5 0.195 1.0 O.402 3-° O.9O 2.0 0.248 3-5 I.05 2-5 0.300 4.0 1.20 3-° o-3S 2 4-5 i-35 Acetic acid, 0.1 0.034 5-o 1.50 Cdl 2 i 0.06 C 2 H40 2 0.2 0.067 I s 1.65 S. Arrhenius.t 2 0.12 Harry C. Jones.} °-3 0.099 6.0 1.80 3 0.19 0.4 0.131 6.5 i-95 4 0.25 0.5 0.162 7.0 2.10 S 0.32 1.0 °'3i3 10 0.03 H 2 S0 4 0.1 0.044 15 0.92 Harry C. Jones.} 0.2 0.088 20 1.22 0-3 0.131 2 5 1.52 P(OH), 0.5 0.18 0.4 0.172 S. Arrhenius.t 1.0 o-3S 0.5 0.212 NaOH 0.1 0.092 i-5 0.50 1.0 0.402 Harry C. Jones.} 0.2 °-3 0.4 °-5 0.178 0.260 2.0 0.65 H 8 P0 4 0.5 0.14 °-337 0.410 S. Arrhenius.t 1.0 i-5 0.27 0.38 HIOs 0.5 0.09 2.0 0.49 KOH 0.1 0.064 S. Arrhenius.t 1.0 0.18 2.5 0.60 Harry C. Jones.} 0.2 o-3 0.126 0.189 i-5 2.0 0.27 o-3S 3-° 3-5 0.70 0.80 0.4 0.252 2.5 0.44 4.0 0.90 0.5 0.6 0.312 3° 0.52 0.370 0.430 3-5 0.61 Cane sugar. 0.5 0.030 0.7 4.0 4-5 0.69 0.78 F. M. Raoult.§ 1.0 2.0 0.060 0.1 18 0.176 0.234 0.292 0.587 I NH 4 OH Harry C. Jones.} 0.05 0.10 0.15 0.028 0.056 0.084 5.0 0.86 3-° 4.0 5.0 10.0 0.20 0.25 0.1 0.2 o-3 0.4 0.1 13 0.143 HC1 0.1 0.099 15.0 0.881 Na 2 C0 8 Harry C. Jones.} 0.048 0.096 0.143 0.188 Harry C. Jones.} 0.2 o-3 0.4 0.5 0.198 0.296 o-395 o-493 20.0 25.0 30.0 350 40.0 1. 174 1.465 1.752 2.048 2-333 0.5 1.0 0.228 0.417 HNOs 0.1 0.061 Glycerine.|| S. Arrhenius.t 1.0 2.0 0.22 0.42 0.64 0.87 K 2 COs O.I 0.039 Harry C. Jones.] 0.2 0.118 0.175 0.232 0.281 o-33» 0.390 3-o 4.0 5-° 6.0 8.0 10.0 12.0 Harry C. Jones.} 0.2 °-3 0.4 0.5 1.0 0.078 0.1 16 0.152 0.187 0-343 °-3 0.4 0.6 0.7 1. 11 1-34 1.83 2.32 2.83 * In " Zeits. fur Physik. Chem." vol. n, p. 5»9. '883. t Ibid. vol. 2, p. 49'i l888 - t Ibid. vol. 12, p. 623, 1893. f J^SS-fil&i^-^G, according to Fabian, "Ding. Poly. Joum.-vol. ,55, P- 345- irage or .3 per gramme. This gives an average "of .3 per gramme Smithsonian Tables. 193 Table 202. VAPOR PRESSURE OF SOLUTIONS OF SALTS IN WATER.* The first column gives 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. 0.5 1.0 2.0 3.0 4.0 6.0 6.0 8.0 10.0 A1 2 (S0 4 ) 3 . . - 12.8 36-5 AICI3 .... 22.5 61.0 179.0 318.O Ba(SO s ) 2 • 6.6 15.4 344 Ba(OH) 2 . 12.3 22.5 39-o Ba(N0 3 ) 2 • ' • i3S 27.0 Ba(C10 3 ) 2 . 15.8 33-3 70.5 108.2 BaCl 2 .... 16.4 3 6 -7 77.6 BaBr 2 .... 16.8 38.8 91.4 150.0 204.7 Ca(S0 3 ) 2 . 9-9 23.0 56.0 106.0 Ca(NO s ) 2 . 16.4 34-8 74.6 139-3 161.7 205.4 CaCl 2 .... 17.0 39-8 95-3 166.6 241.5 3'9-5 CaBr 2 .... 17.7 44.2 135.8 191.0 283-3 368.5 CdS0 4 4.1 8.9 18.1 Cdl 2 .... 7.6 14.8 33-5 52.7 CdBr 2 . 8.6 17.8 367 557 80.0 CdCl 2 . 9.6 18.8 367 57-0 77-3 99.O Cd(N0 3 ) 2 . Cd(C10 3 ) 2 • 15.9 36.1 78.0 122.2 '7-5 CoS0 4 5-5 10.7 22.9 45-5 CoCl 2 .... 15.0 34-8 83.0 136.0 186.4 Co(NO s ) 2 . 17-3 39- 2 89.0 152.0 218.7 282.0 33 2 - FeS0 4 5-8 10.7 24.0 42.4 H3BO3 6.0 12.3 25.1 38.0 51.0 H3PO4 6.6 14.0 28.6 45.2 62.0 81.5 103.0 146.9 189.5 H 3 As0 4 7-3 15.0 30.2 46.4 64.9 H 2 S0 4 12.9 26.5 62.8 104.0 148.0 198.4 247.0 343-2 KH 2 P0 4 . 10.2 19.5 33-3 47.8 60.5 73- 1 85.2 KN0 3 . 10.3 21. 1 40.1 57-6 74-5 88.2 102.1 126.3 148.0 KCIO3 10.6 21.6 42.8 62.1 80.0 KBrOs 10.9 22.4 45.0 KHS0 4 . 10.9 21.9 43-3 65-3 85.5 107.8 129.2 170.0 KN0 2 KC10 4 11. 1 "■5 22.8 22.3 44.8 67.0 90.0 1 10.5 i3 -7 167.0 198.8 KC1 .... 12.2 24.4 48.8 74.1 100.9 128.5 152.2 KHC0 2 1 1.6 23.6 59.0 77.6 104.2 132.0 160.0 210.0 255.0 KI . . . . K 2 C20 4 12.5 13-9 25-3 28.3 52.2 59.8 82.6 94.2 112.2 131.0 Hi-5 171.8 225-5 278.5 K 2 WOi r 3-9 33-° 75.0 68.3 64.0 123.8 175-4 226.4 K 2 CO s KOH .... 14.4 15.0 31.0 29.5 i°5-5 99.2 152.0 140.0 209.0 181.8 258.5 223.0 350.0 309-5 387.8 K 2 Cr0 4 . 16.2 29.5 60.0 L1NO3 LiCl .... LiBr .... Li 2 S0 4 12.2 25.9 557 88.9 122.2 155.1 188.0 2534 309.2 12.1 12.2 13-3 26.2 28.1 57-i 60.0 56.8 95.0 97.0 89.0 '32-5 140.0 '75-5 186.3 219.5 241.5 3"-5 34'-5 393-5 438.0 LiHS0 4 . 12.8 27.0 57.0 93-o 130.0 168.0 Lil .... Li 2 SiFI 6 . 13.6 15.4 28.6 34-0 64.7 70.0 105.2 106.0 154-5 206.0 264.0 357-0 445-0 LiOH .... IS- 9 37-4 78.1 Li 2 Cr0 4 16.4 32.6 74.0 120.0 171.0 Phy^'Th^V™^ taMe b/ Tammann ' " M6m - Ac - St - P««sb.» 35, No. 9, 1887. See also Referate, "Zeit. f. Smithsonian Tables. 194 Table 202. VAPOR PRESSURE OF SOLUTIONS OF SALTS IN WATER. Substance. 0.5 1.0 2.0 3.0 4.0 5.0 6.0 8.0 10.0 MgS0 4 MgCl 2 . . . . Mg(NO s ) 2 . . . MgBr 2 MgH 2 (S0 4 )2 . . 6-5 16.8 17.6 17-9 18.3 12.0 39-0 42.0 44.O 46.O 24-5 100.5 IOI.O 115.8 1 1 6.0 47-5 183.3 174.8 205-3 277.0 298.5 377-0 MnS0 4 MnCl 2 . NaH 2 P0 4 . NaHS0 4 6.0 15.0 10.5 IO.5 34-o 20.0 21.0 76.0 36.5 122.3 5i-7 167.0 66.8 209.0 82.0 96.5 126.7 157.1 NaNO s ! ! ! IO.9 10.6 22.1 22.5 46.2 75.0 68.1 100.2 90-3 1 26. 1 m.5 148.5 1317 189.7 167.8 2314 198.8 NaCIOs . (NaPO s ) 6 . . 10.5 11.6 23.0 48.4 73-5 98-5 123-3 147-5 196.5 223-5 NaOH NaN0 2 1 1.8 n.6 12.1 22.8 48.2 77-3 107.5 1391 172.5 243-3 314.0 NaHP0 4 ! '. 24.4 2 3-5 50.0 43-o 7S-o 60.0 98.2 78.7 122.5 99.8 146.5 1 22. 1 189.0 226.2 NaHC0 2 . NaS0 4 NaCl .... NaBrOs NaBr .... 12.9 12.6 12.3 I2.I 12.6 24.1 25.0 25.2 25.0 25.9 48.2 48.9 52.1 54.1 57.0 77-6 74.2 80.0 81.3 89.2 102.2 III.O 108.8 124.2 127.8 143.0 136.0 159-5 152.0 176.5 '97-5 198.0 268.0 239-4 Nal . Na4P 2 7 . I2.I I3.2 25.6 22.0 60.2 99-5 I36-7 177-5 221.0 301.5 370.0 Na 2 CO s 14-3 27-3 53-5 80.2 III.O Na 2 C 2 C- 4 . 14.5 30.0 6 5 i 105.8 146.0 Na 2 W0 4 . 14.8 33-6 71.6 1 1 5.7 162.6 Na 3 P0 4 . 16.5 30.0 5 2 -5 (NaPOg) 3 . 17.1 365 NH 4 NO a . (NH 4 ) 2 SiFl 6 12.8 11.5 22.0 25.0 42.1 44-5 62.7 82.9 103.8 1 21.0 152.2 180.0 NH 4 C1 12.0 23-7 45-1 69-3 94-2 1 18.5 138.2 179.0 213.8 NH 4 HS0 4 . 11.5 22.0 46.8 71.0 94-5 118. 139.0 181.2 218.0 (NH 4 ) 2 S0 4 . 1 1.0 24.0 46.5 48.8 69.5 93-o 1 17.0 141.8 NH 4 Br 1 1.9 23-9 74.1 99-4 121. 5 '45-5 190.2 228.5 NH 4 I .... NiS0 4 12.9 5.0 25.1 10.2 49.8 21.5 78.5 104.5 J 32-3 156.0 200.0 243-5 i NiCl 2 .... 16.1 37-o 86.7 147.0 212.8 i Ni(N0 8 ) 2 . 16.1 37-3 9'-3 156.2 2 35-o Pb(N0 8 ) 2 . 12.3 23-5 45.0 63.0 Sr(S0 8 ) 2 . Sr(NO s )2 ■ 7.2 20.3 47.0 15.8 31.0 64.0 97-4 I3I-4 SrCl 2 .... 16.8 38.8 91.4 156.8 223.3 281.5 SrBr 2 .... 17.8 42.0 IOI.I 179.0 267.0 ZnS0 4 4.9 10.4 21.5 42.1 66.2 ZnCl 2 .... 9.2 18.7 46.2 75.0 107.0 '53-o 195.0 Zn(N0 8 ) 2 • 16.6 39-o ' 93-5 157-5 223.8 Smithsonian Tables. I9S Table 203. RISE OF BOILING-POINT PRODUCED BY SALTS DISSOLVED IN WATER.* This table gives the number of grammes of the salt which, when dissolved in 100 igrammes of water, will raise the boiling-point by the amount stated in the headings of the different columns. The pressure is supposed to be 76 centimetres. Salt. 1°C. 2° 3° 40 6° 7° 10° 15° 20° 25' BaCl 2 + 2H 2 . 15.0 3I-I 47-3 63-5 (71.6 gives 4 C .5 rise of temp.) CaCl2 6.0 II. 5 16.5 21.0 25.0 32.0 41.5 55-5 69.0 84-5 Ca(N0 8 ) 2 + 2H2O . 12.0 25.5 39-5 53-5 68.5 98.7 I52-5 240.0 331-5 443-5 KOH 4-7 9-3 13.6 18.0 17.4 20.5 26.4 34-5 47.0 57-5 67-3 KC2H8O2 . 6.0 12.0 24.5 31.0 44.0 63-5 98.0 134.0 I7I-5 KC1 .... 9.2 16.7 23-4 29.9 36.2 48.4 (57-4 gives a rise of 8°. 5) K2CO3 11.5 22.5 27.8 32.0 40.0 47-5 60.5 78.5 1035 127.5 I S 2 -5 KCI0 8 13.2 44.6 62.2 | KI . 15.0 30.0 45.0 60.0 74.0 99-5 134- 185.0 (220 gives i8°.5) KNOs 15.2 31.0 47-5 64.5 82.0 120.5 188.5 338.5 K2C 4 H 4 6 + }H20 . 18.0 36.0 54-° 72.0 90.0 126.5 182.0 284.0 KNaC 4 H 4 O e . 17-3 34-5 51-3 68.1 84.8 1 19.0 171.0 272.5 390.0 510.0 KNaC 4 H 4 6 + 4H2O 25.0 53-5 84.0 1 18.0 157.0 266.0 554.0 55'o-o LiCl .... 3-5 7.0 1 0.0 12.5 15.0 18.5 26.0 35-o 42.5 50.0 L1CI+2H2O . 6.5 13.0 '9-5 26.0 32.0 44.0 62.0 92.0 123.0 160.5 MgCl 2 + 6H 2 . 11.0 22.0 33-o 44.0 55-o 77.0 1 1 0.0 170.0 241.0 334-5 MgS0 4 + 7H 2 41.5 87.5 138.0 196.0 262.0 NaOH 4-3 8.0 "•3 14-3 17.0 22.4 30.0 41.0 51.0 60.1 NaCl .... 6.6 12.4 17.2 21.5 25-5 33-5 (40.7 jives 8° .8 rise) NaNO a 9.0 18.5 28.0 38.0 48.0 68.0 99-5 156.0 222.0 NaC 2 H 8 02 + 3H2O . 14.9 30.0 46.1 62.5 79-7 118.1 194.0 484.0 6250.0 Na 2 S 2 8 . 14.0 27.0 39-° 49-5 59.0 76.0 104.0 147.0 214.5 302.0 Na 2 HP0 4 . 17.2 34-4 51-4 68.4 85-3 Na 2 C 4 H 4 6 + 2H2O . 21.4 44.4 68.2 93-9 121.3 183.0 ( 2 37-; gives 8°4 rise) Na 2 S 2 O s + 5H2O . 23.8 50.0 78.6 1 08. 1 139-3 216.0 400.0 1765.0 Na 2 CO s + 10H2O . 34-i 86.7 177.6 3694 1052.9 Na 2 B 4 7 + ioH 2 . 39- 93- 2 254.2 898-5 (5555-5 gives 4°. 5 rise) NH 4 C1 6.5 12.8 19.0 24.7 29.7 39-6 56.2 1 88.5 NH4NO3 . 1 0.0 20.0 30.0 41.0 52.0 74.0 108.0 1 172.0 248.0 337- NH 4 S0 4 . 1 5-4 30.1 44.2 58.0 71.8 99.1 (115.3 gives 108.2) SrCl 2 + 6H 2 . 20.0 40.0 60.0 81.0 103.0 150.0 234.0 524.0 Sr(NO s ) 2 24.0 45.0 63.6 81.4 97.6 C 4 H 8 Og 17.0 34-4 52.0 70.0 87.0 123.0 177.0 273.0 374-0 484.0 C 2 H 2 4 + 2H z O 19.0 40.0 62.0 86.0 1 1 2.0 169.0 262.0 536.0 1316.0 50000.0 C 6 H 8 0, + H 2 29.0 58.0 87.0 n 6.0 145.0 208.0 320.0 553-0 952.0 Salt. 40° 60° 80° 100° 120° 140° 160 c 180° 200° 240° CaCl 2 . '37-5 222.0 314.0 KOH . 92.5 121.7 152.6 185.0 219.8 263.1 312. 5 375-° 444-4 623.0 NaOH J 3 ' 5 150.8 230.0 345-0 526.3 800.0 J 333- 2353.0 6452.0 - NH 4 NO s • 682.0 1370.0 2400.0 4099.0 8547-0 00 C 4 H 8 Oe 980.0 3774-0 infinity gives 170) 1 1 * Compiled from a paper by Gerlach, " Zeit. £. Anal. Chem." vol. 26. Smithsonian Tables. I96 Table 204. CONDUCTIVITY FOR HEAT. Metals ana Allays. The coefficient k is the quantity of heat in therms which is transmitted per second through a plate one centimetre thick per square centimetre of its surface when the difference of temperature 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 ex- pressed approximately by the equation k t = k (i + at). In the table k is the value of kt for o° G, t the tempera- ture Centigrade, and a a constant. Substance. Aluminium . Antimony . . Bismuth . . Brass (yellow) " (red) . Cadmium . . Copper . . German silver Iron . . . " (wrought) * \ Lead Mercury . Magnesium Steel (hard) " (soft) Silver . . Tin . . . I Wood's alloy Zinc .... o ioo o IOO o too o IOO o IOO o IOO o o IOO o IOO o IOO o IOO O IOO O 5° 0-100 O-IOO o o IOO 0-3435 \ •3 6l 9 S .0442 ) .0396 ( .0177 \ .0164 .2041 .2540 .2460 I .2827 J .2200 I .2045 J 1.0405 ) .7189 \ .7226 .0700 ) .0887 j .1665 / .1627 j .2070 i .1567 \ .0836 / .0764 s .0148 1 .0189 j .0201 .3760 .0620 .mo .0960 .1528 1 •1423 s •0319 1 ■3°3° ) •°°5357 — .001041 — .000735 — .002445 — .001492 — .000705 .000039 .000051 .002670 — .000228 — .000861 .001267 .000000 ■ .000687 Substance. from to Clay slate, (Devonshire) . Granite . . . < . Slate : along cleav- ( from age . . .( to across cleav- j from age . . . j to Marbles, in- cluding lime- stone, cal- cite, and compact do- lomite . . „ Micaceous flagstone : along cleavage . across cleavage . Sand (white dry) . Sandstone and ' hard grit (dry) .... Serpentine (Cornwall red) . . Snow in compact . layers Plaster of Paris . . Pasteboard . . . . Strawboard . . . . Paraffin . . . . < from to Sawdust Vulcanite . . . . Vulcanized] from rubber (soft) ( to Wood, Fir : parallel to axis . . perpendicular to axis Wax (bees) . . . . o 100 .00272 .00510 .00550 .00550 .00650 .00315 .00360 .00470 .00560 00632 00441 00093 00545 00565 .00441 .00051 .0013 .00045 .00033 .00014 .00023 .00168 .00012 .00087 .00034 .00054 .0003 .00009 .00009 1 Lorenz. 2 Berget. 3 J. Forbes. 4 H. F. Weber. Authorities. 5 Kohlrausch. 6 H.L.&D.t 7 Hjeltstrom. 8 G. Forbes. 9 R. Weber. 10 Stefan. > A repetition of Forbes's experiments by Mitchell, under the direction of Tail, shows the conductivity to increase with rise of temperature. (Trans. R. S. E. vol. 33, 1887.) t Herschel, Lebour, and Dunn (British Association Committee). Smithsonian Tables. 197 Tables 205-208. CONDUCTIVITY FOR HEAT. TABLE 205. — Various Substances. TABLE 206. —Water and Salt Solutions. Substance. t fc« Au- thor- ity. 49 .000405 .000162 .000717 .000043 .000033 .002000 .000370 .000087 .000035 .0005 ) .0023 j .000087 .000042 .00223 .00568 •00433 .00211 I I I I I 2 2 I I 3 1 1 1 4 2 2 Cement . . Cotton wool . Cotton pressed Chalk . . . Ebonite . . Felt .... Flannel . . Glass |^; Haircloth . . Caen stone (builc ing limestone) Calcareous sand- stone (£reeston( i 1-1 •f 0) Authorities. i G. Forbes. 3 Various. 2 H., L., & D.* 4 Neumann. Au- Substance. Density. t fc« thor- ity. Water . . _ _ .002 I - .00120 2 - 9-1 S .00136 2 - 4 .00129 3 - 3 ? .001 57 4 18 .00124 s Solutions in water. 1. 160 4.4 .00118 2 C11SO4 . . KC1 . I.026 *3 .00116 4 NaCl . 33*% 10-18 .00267 6 H 2 S0 4 1.054 20.5 .00126 5 " 1. 100 20.5 .00128 5 " 1.180 21 .00130 5 ZnS0 4 I-I34 4-5 .00118 2 1.136 4-5 .00115 2 Authorities. 1 Bottomley. 4 Graetz. 2 H. F. Weber. 5 Chree. 3 Wachsmuth. 6 Winkelmann. TABLE 207. — Organic Liquids. Substance. t X 1000 a T 3 < Acetic acid . . . Alcohols : amyl . ethyl . methyl Carbon disulphide Chloroform . . . Ether Glycerine . . . Oils : olive . . . castor . . petroleum . turpentine . 9-15 9-15 9-iS 9-i 5 9-15 9-15 9-i5 9-i 5 13 13 .472 .328 •423 •495 ■ 3 &? .288 •303 ■637 •395 .425 •355 •325 0.12 .011 .0067 2 3 3 2 2 Authorities. 1 H. F. Weber. 2 Graetz. 3 Wachsmuth. TABLE 208. — Oases. Substance. t ft! X iooo a •c 3 1 1 1 1 1 1 1 1 1 1 Air Ammonia . . . Carbon monoxide " dioxide . Ethylene . . . Hydrogen . . . Methane. . . . Nitrogen . . . Nitrous oxide . . Oxygen .... 7-8 7-8 7-8 7-8 .568 •458 •499 •307 •395 •327 .647 .524 •350 •563 .00190 .00548 .00445 •00175 .00446 Authority. 1 Winkelmann. Smithsonian Tables. * Herschel, Lebour, and Dunn (British Association Committee). I98 Table 209. FREEZING MIXTURES.* ^tfr£%P%^*^'&^'*>^**' Proportion o£ that substance, ^thepropo, the substances before mixtnr. i? fh.^.i? c0 ' ul ™. C the proportion of a third substance, D the temperature of ture when ali snotTs nXd'when snow fs usTand PZV™' f WTO* JJT*"- G the '""W A is grammes). Temperatures are to Ceitigrade degrfes "' ^ abS ° rbed in1leat U " itS (therras " hen Substance. A B C D E F G H NaC 2 H s O a (cryst.) NH4CI . . ; NaNOs . 85 3° 75 no 140 250 60 2 5 2 5 2 5 25 2 5 2 5 10 H2O-IOO « u It It _ 10.7 ! 3-3 — 4-7 — 5-i 18.4 - - Na 2 S0 2 (cryst.) . KI . . . . CaCl 2 (cryst.) NH 4 NO s . (NH 4 ) 2 S0 4 . NH4CI . CaCl 2 . KNOa • Na 2 S04 NaNOa . K2SO4 . tl It H tt it ll It (( " 50 « (( tt (« tt (t It (t Snow 100 NH4NOS-25 « ft tt tt NH4CI-25 « (t it ,t 13.2 10.7 10.8 10.8 13.6 =8 — 11.7 — 12.4 -136 —1.9 — 2.0 —2.85 — 10.9 -15.4 —16.75 —17.75 —21.3 18.5 18.7 22.5 23.2 27.2 26.O 22.0 20.0 20.0 I9.O I7.O O.9 1.0 I.85 9-9 14.4 15-75 16.75 20.3 - - Na 2 CO a (cryst.) . KNOs . . . CaCl 2 . NH4CI . NH 4 NOs NaNOa - NaCl . 20 13 3° 2 5 45 5° 33 U it it tt (t tl tt (t tl it a tt tt tt ~ — 1 - - " i-°97 ~ — 1 — 37-0 36.0 — 37-0 0.0 " 1.26 " 138 ~ — 1 — 36.0 35-° — 30.2 17.0 H 2 S04+H 2 ~ — 1 — 35-° 34-o — 25.0 27.0 (66.1 % H 2 S0 4 ) ' " 2 -5 2 ~ — 1 — 30.0 29.0 — 12.4 133-0 " 4-3 2 — — 1 — 25.0 24.0 — 7.0 273.0 " 7-9 2 " 13.08 - 1 — 20.0 — 16.0 19.0 15.0 — 3-i — 2.1 553-o 967.0 " 0.35 - - - 0.0 52.1 " -49 " .61 - - _ — 19.7 — 39-0 49-5 40-3 CaCl 2 + 6H 2 - " .70 " .81 ~ — - — 54-9t 3 ?'° _ — — — 40-3 46.8 " 1.23 — — — — 21-5 88.5 " 2.46 ~ - - — 9.0 192.3 Alcohol at 4° j " 4-9 2 ~ - - — 4.0 39 2 -3 77 " 73 C0 2 solid I — 30.0 — 72.0 — — Chloroform . - a a _ — 77.0 _ _ Ether . - tt u _ — 77.0 _ _ _ Liquid S0 2 . - ft tl - _ — 82.0 _ 1 H20-.75 - 20 5-o - - 33-o 1 " -94 - 20 — 40. — 21.0 1 It tl - 10 — 4.0 - - 34-o 1 1 Snow " _ 5 — 4.0 — 4.0 : — 40.5 122.2 NH 4 NOs . 1 H2O-1.20 - 10 — 14.0 - 17.9 1 Snow " - — 14.0 - - 129.5 1 H 2 0-i. 3 i — 10 -i7-5t - — io.o 1 Snow " - — 17-5+ - - I 3 I -9 1 H 2 0- 3 .6i - 10 -8.0 - - 0.4 1 '• 1 Snow " — 8.0 " 1 327.0 * Compiled from the results of Cailletet and Colardeau, Hammerl, Hanamann, Moritz, Pfanndler, Rudorf, and Tollinger. t Lowest temperature obtained. Smithsonian Tables. 199 Table 210. CRITICAL TEMPERATURES, PRESSURES, VOLUMES, AND OF CASES.* = Critical temperature. p-=. Pressure in atmospheres. = Volume referred to air at o° and 76 centimetres pressure. d— Density in grammes per cubic centimetre. DENSITIES Substance. e p •P d Observer. Air — 140.0 39° Olszewski. Alcohol (C 2 H 6 0) . 243.6 62.76 0.00713 0.288 Ramsay and Young. (( <( 2337 — — Jouk (lowest value recorded). " (CH 4 0) . 239-95 78.5 Ramsay and Young. Ammonia .... 130.0 1 1 5.0 _ _ Dewar. Argon — 121.0 50.6 - i-5 Olszewski. Benzene 288.5 47-9 0.00981 0-355 Young. Carbon dioxide 30.92 77 0.0066 _ Andrews. " monoxide . — 141. 1 35-9 - Wroblewski. " disulphide . 277.7 78.1 - Dewar. Chloroform .... 260.0 54-9 - Sajotschewski. Chlorine .... 141.0 83-9 _ Dewar. « 148.0 - - Ladenburg. Ether 19.7 35-77 0.01 584 0.208 Battelli. « 194.4 35-6i 0.01344 0.246 Ramsay and Young. Ethylene .... 9.2 58.0 — — Van der Waals. tt 13.0 - 0.00569 0.21 Cailletet. Hydrogen .... — 220.0 20.0 _ _ Olszewski. " chloride 51.25 86.0 - Ansdell. it » 5 2 -3 86.0 - 0.61 Dewar. " sulphide 1 00.0 88.7 - - Olszewski. Methane .... —81.8 54-9 - - tt «( —99-5 50.0 - - Dewar. Nitric oxide (NO) . —93-5 71.2 - - Olszewski. Nitrogen .... — 146.0 35-° - 0.44 " " .... — 146.0 33-° — — Wroblewski. " monoxide (N 2 0) . 354-o 75.0 - - Dewar. Oxygen —1 18.0 50.0 _ 0.6044 Wroblewski. Sulphur dioxide 155-4 78.9 - - Sajotschewski. It tt I57-Q — — — Clark. Water 358-1 - 0.001874 0.429 Nadejdine. tt 370.0 !95-5 Dewar. * Abridged for the most part from Landolt and Boernstein's " Phys. Chem. Tab. " Notb. — Guldberg shows (Zeit r fur Phys. Chem. vol. 5, p. 375) that for a large number of organic substances the ratio of the absolute boiling to the absolute critical temperature, although not constant, lies between 0.58 and 0.7, the majority being between .65 and .7. Methane, ethane, and ammonia gave approximately 0.58. H 2 S gave .566, and CS 2 , N 2 0, and O gave about .59. Smithsonian Tables. 200 Table 211. HEAT OF COMBUSTION. Heat of combustion of some common organic compounds. Products of combustion, C0 2 or S0 2 and water, which is assumed to be in a state of vapor. Substance. Therms per gramme of substance. Authority. Acetylene . 1 1923 Thomsen. Alcohols : Amyl 8 95 8 Favre and Silbermann. Ethyl 7183 tt « u Methyl S3°7 a if « Benzene 9977 Stohmann, Kleber, and Langbein. Coals : Bituminous 7400-8500 Various. Anthracite 7800 Average of various. Lignite . 6900 « « •> Coke . 7000 M 11 it Carbon disulphide 3 2 44 Berthelot. i Dynamite, 75% . 1290 Roux and Sarran. Gas : Coal gas . 5800-1 1000 Mahler. Illuminating 5200-5500 Various. Methane . 13063 Favre and Silbermann. Naphthalene 9618-9793 Various. Gunpowder 720-750 « Oils: Lard 9200-9400 " Olive 9328-9442 Stohmann. Petroleum, Am . crude 1 1 094 Mahler. " " refined ii°4S " " Russian . 10800 ft Woods : Beech with 12.9 % H 2 C ) 4168 Gottlieb. Birch " 11.83 " 4207 it Oak " 133 3990 it Pine " 12.17 " 4422 H Smithsonian Tables. 201 Table 212. HEAT OF Heat of combination of elements and compounds expressed in units, such that when unit mass of the substance is units, which will be raised in temperature Substance. Combined with oxygen forms — Heat units. Combined with chlorine forms — Heat units. Combined with sulphur forms — Heat units. Calcium .... CaO 3284 CaCl 2 4255 CaS 23O0 I Carbon — Diamond co 2 7859 - - - 2 « ft CO 2141 - _ — - 3 " — Graphite co 2 7796 - - - - 3 Chlorine . C1 2 — 254 — — — — 1 Copper Cu 2 321 CuCl 520 - - 1 u CuO 585 CC1 2 819 CuS 158 1 ti " 593 - - 4 Hydrogen* H 2 34IS4 HC1 22OO0 H 2 S 2250 3 " 11 34800 - - - - 5 " " 34417 - — — — 6 Iron . FeO 1353 FeCl 2 1464 FeSH 2 428 3 tt - FeCl 8 1714 - — 3 Iodine i 2 o 6 177 - - - 1 Lead PbO 243 PbCl 2 400 PbS 98 1 Magnesium MgO 6077 MgCl 2 6291 MgS 3'9' 1 Manganese MnOH 2 1721 MnCl 2 2042 MnSH 2 2 841 1 Mercury . Hg 2 105 HgCl 206 - - 1 II HgO 153 HgCl 2 3'° HgS 84 1 Nitrogen* N 2 — 654 - - 1 it NO — 1541 — — — — 1 a NO s — '43 - - _ _ 1 Phosphorus (red) p 2 o 6 5272 - - - - 1 " (yellow) « 5747 - - - - 7 if it It 5964 - - — - i Potassium K 2 1745 KC1 2705 K 2 S 1312 8 Silver Ag 2 27 AgCl 271 Ag 2 S 24 1 Sodium Na 2 3293 NaCl 4243 Na 2 S 1900 8 Sulphur . so 2 2241 - - - - 1 ii " 2165 - - - _ 2 Tin . SnO 573 SnCl 2 690 - - 4 ii - - SnCU 1089 — - 7 Zinc . ZnO 1185 — — _ _ 4 ii it 13H ZnCl 2 1495 - - 1 Combined Heat units. Combined Combined it Substance. with S0 4 to form — with N0 3 to form — ■ Heat units. with C0 3 to form — Heat units. J2 . Calcium .... CaS0 4 7997 Ca(N0 3 ) 2 5080 CaCOs 6730 Copper CuS0 4 2887 Cu(NO s ) 2 I3°4 - Hydrogen H 2 S0 4 96450 HNOs 41500 - _ Iron . FeS0 4 4208 Fe(NO s ) 2 2134 - _ Lead PbS0 4 1047 Pb(N0 3 ) 2 512 PbCOs 814 Magnesium MgS0 4 12596 _ _ _ Mercury . - - _ _ _ _ Potassium K 2 S0 4 44i6 KNO3 3061 K 2 CO s 3583 Silver Ag 2 S0 4 776 AgNOs 266 Ag 2 CO s 56l Sodium Na2S0 4 7119 NaNOs 4834 NasCOs 5841 Zinc ZnS0 4 3538 ~ ' - A UTHORI riES. i Thomsen. 3 Favre and Silberma Jin. 5 1 less. 7 ' \ndrews. 2 Berthelot. 4 Joule. 6 J Average of s even di: lerent. 8 ' Woods. Smithsonian Tables. * Combustion at constant pressure. 202 Table 212. COMBINATION. STfol" c °™M?e with oxygen or the negative radical, the numbers indicate the rrom o u to i° C. by the addition of that heat. amount of water, in the same Substance. In dilute solutions. Forms — Heat units. Forms — Heat units. Forms — Heat units. <•- Calcium . Carbon — Diamond . CaOH 2 3734 CaCl 2 H 2 4690 CaS + H 2 2457 1 2 " —Graphite . _ : — ~ — - 3 3 Chlorine . _ _ Copper - - - - - - 1 1 Hydrogen - - "* - - - 4 3 5 Iron . FeO + H 2 1220* FeCl 2 + H 2 1785 - 6 3 " . — — FeCl 8 2280 _ _ 3 1 Iodine _ _ _ _ _ Lead . - - PbCl 2 368 _ _ 1 Magnesium Mg0 2 H 2 9050 MgCl 2 7779 MgS 4784 1 Manganese — — MnCl 2 2327 — 1 Mercury . - - - _ _ 1 «( - - HgCl 2 299 - - 1 Nitrogen - - - - - 1 « - - - - - - 1 Phosphorus (red) _ _ _ _ : : 1 1 " (yellow) . U ft - - - - - - 7 I Potassium . K 2 2 1 10* KC1 2592 K 2 S 1451 8 Silver — — — _ 1 Sodium Na 2 337S NaCl 4190 Na 2 S 2260 8 Sulphur - - - - 1 u — _ _ _ _ _ 2 Tin . - - SnCl 2 691 _ - 7 « - - S11CI4 1344 - - 7 Zinc . — - — — - 4 ti — "~ ZnCl 2 1735 - — 1 Substance. In dilute solutions. 1* Forms — Heat units. Forms — Heat units. Forms — Heat units. Calcium . _ _ Ca(NO s ) 2 SI7S _ _ Copper CuSC-4 3150 Cu(NO„) 2 I310 - - Hydrogen H 2 S0 4 10530 H 2 NO s 2455° - Iron . FeSC-4 4210 Fe(NO s ) 3 2134 — — Lead . - - Pb(N0 8 ) 2 475 - - Magnesium MgSOi 13420 Mg(N0 8 ) 2 8595 - - Mercury . - - Hg(N0 8 ) 2 IP - - Potassium . k 2 scm 4324 KNO s 2860 — - Silver Ag 2 S0 4 7S3 AgN0 3 216 - Sodium Na 2 SO* 7160 NaNOa 4620 NajsCOa 5995 Zinc . ZnSOi 3820 Zn(NOa) 2 2035 AUTH< DEITIES. i Thomsen. 3 Favre and Silbi ;rmann. 5 Hess. 7 A ndrews. 2 Berthelot. 4 Joule. 6 Average of seven c ifferent. 8 ¥ foods. Smithsonian Tables. * Thomsen. 203 Table 213. LATENT HEAT OF VAPORIZATION. The temperature of vaporization in degrees Centigrade is indicated by T ; the latent heat in calories per kilogramme or in therms per gramme by H ; the total heat from o° C. in the same units by H'. The pressure is that due to the vapor at the temperature T. Substance. Formula. T H H' Authority. Acetic acid .... C2H4O2 118 84.9 - Ogier. Alcohol : Amyl C 6 Hi 2 131 I20 - Schall. Ethyl . C 2 H 6 _ 209 _ Favre and Silbermann. it tc 78.1 205 255 Wirtz. it " 236 236 Regnault. " ... it 5° - 264 u it " 100 - 267 " It tt 150 - 285 tt Methyl . CH4O 64.5 2.67 3°7 Wirtz. it it 289 289 Ramsay and Young. "... " 5° — 274 ti 1 tt 1 K it 100 - 246 it t tt ti it 150 - 206 a t it ti a 200 — 152 u 1 tt tt 238-S - 44-2 U it ti Ammonia .... NH 3 7.8 294.2 - Regnault. ** 11 291.3 — tt " .... a 16 297-4 - a a a 17 296-5 - u Benzene .... CeH 6 80.1 92.9 127.9 Wirtz. Bromine .... Ba 88 45-6 - Andrews. Carbon dioxide, solid . co 2 _ _ I38-7 Favre. liquid . " —25 72.23 Cailletet and Mathias. ** " . " 57-4» — tt a a " it J2-3S 44-97 - Mathias. u " 22.04 31.8 — " it U U " 29.85 14.4 - « it it it it 30.82 3-72 - ti " disulphide cs 2 46.1 83.8 94.8 Wirtz. " " ** 90 90 Regnault. 100 — 100.5 (< ti 140 - 102.4 it Chloroform .... CHCls 60.9 58-5 78.8 Wirtz. Ether C4H10O 34-5 88.4 107 « " 34-9 90.5 - Andrews. tt 94 94 Regnault. 5° — 115.1 tt 120 - 140 tt Iodine I - 2.95 - Favre and Silbermann. Sulphur dioxide . so 2 91.2 _ Cailletet and Mathias. ... ** 3° 80.5 — « n tt " 65 68.4 - tt » tt Turpentine .... C10H10 159-3 74.04 - Brix. Water H 2 100 535-9 _ Andrews. 100 637 Regnault Smithsonian Tables. 204 LATENT HEAT OF VAPORIZATION.* Table 213. Substance, formula, and temperature. Acetone, C 8 H 6 0, -3° to 147 . Benzene, CeHe, 7° to 215° Carbon dioxide, co 2 , — 25° to 31° Carbon disulphide, CS2, — 6° to 143°. Carbon tetrachloride, CCI4, 8° to 163° Chloroform, CHC1 8 , — 5 to 159°. Nitrous oxide, N 2 0, — 20° tO 36 . Sulphur dioxide, S0 2 , o° to 60°. I — total heat from fluid at o° to vapor at r°. r= latent heat at <°. I— 140.5 + 0.36644 1 — 0.000516 fl l = !39-9 + 0.23356 1 + 0.00055358 fl r — '39-9 — 0.27287 1 + 0.0001571 fl 7= 109.0 + 0.24429 t — 0.0001315 fl r*= 1 18.485 (31 — t) — 0.4707 (31 — fl) 7 = 90.0 + 0.14601 1- l = 8 9-5 + 0.16993/- r = 89.5 — 0.06530 1- 7 = 52.0 + 0.14625 1- 7 = 51.9 4- 0.17867 t- r=5i.9 — 0.01931 1- 7=67.0 + 0.1375/ 7=67.0 + 0.14716/- r = &J.O — 0.08519;- -O.OOO412/ 2 - 0.0010161 fl + 0.000003424 fl • 0.0010976 fl + 0.000003424 fl • 0.000172 Z 2 - 0.0009599 ** + 0.000003733 fl ■ 0.0010505 fl + 0.000003733 fl ■ 0.0000437 fl ■ 0.0001444 fl t*= 131.75 (36.4 — 7) —0.928 (36.4 — t) 2 r = 91.87 — 0.3842 1 — 0.000340 fl Authority. Regnault. Winkelmann. Regnault. Cailletet and Mathias. Regnault. Winkelmann. Regnault. Winkelmann. Regnault. Winkelmann. Cailletet and Mathias. Mathias. * Quoted from Landolt and Boernstein's " Phys. Chem. Tab." p. 350. Smithsonian Tables. 205 Table 214. LATENT HEAT OF FUSION. This table contains the latent heat of fusion of a number of solid substances. It has been compiled principally from Landolt and Boernstein's tables. C indicates the composition, T the temperature Centigrade, and H the latent heat. Substance. H Authority. Alloys : 3 o.sPb + 6o.5Sn . 36-9Pb + 6i-3Sn . 63.7Pb-i-36.3Sn . 77-8Pb -)- 22.2S11 . Britannia metal, 9Sn -f- 1 Pb Rose's alloy, 24Pb + 27-3Sn + 48-7Bi Wood's aUoy{;S.8Pb+H7Snj Bromine . Bismuth Benzene Cadmium . Calcium chloride Iron, Gray cast White " Slag . Iodine Ice " (from sea-water) Lead . Mercury Naphthalene Palladium . Phosphorus Potassium nitrate Phenol Paraffin Silver Sodium nitrate . Sodium phosphate Spermaceti Sulphur Wax (bees) Zinc . PbSn 4 PbSn 8 PbSn Pb 2 Sn Br Bi CeHe Cd CaCl 2 -|-6H 2 I H 2 H.O + 3-S3S1 of solids Pb Hg C10H8 Pd P KN0 8 C 6 H 6 Ag NaNOs ( Na 2 HPCX, ) \ +I2H 2 Q \ Zn 183 179 177-5 176.5 236 98.8 75-5 — 7-3 2 266.8 5-3 320.7 28.5 o o -8.7 325_ 79-87 (1500)? 40.05 333-5 25-37 52.40 999 305.8 36.1 43-9 "5 61.8 415-3 17 11.6 9-54 28.0* 6.85 8.40 16.2 12.64 13.66 40.7 2 3 33 5° 11.71 79.24 80.02 54.0 5-86 2.82 35.62 36-3 4-97 48.9 24-93 35-io 21.07 64.87 66.8 36.98 9-37 42.3 28.13 Spring. Ledebur. Mazzotto. Regnault Person. Fischer. Person. « Gruner. Favre and Silbermann Regnault. Bunsen. Petterson. Rudberg. Person. Pickering. Violle. Petterson. Person. Petterson. Batelli. Person. Batelli. Person. Smithsonian Tables. * Total heat from o° C. 206 MELTING-POINT OF CHEMICAL ELEMENTS. Table21 5. ^reSlJs'olSd bf dM,r™» m ^ al elemeil £.? re ™ m ? n y "ses somewhat uncertain, owing to the very different one observatton dhWd ™ ^ST* T, h ' S ,' able gives the ex ? reme vailles rec ° rded ««P' in * few <*»« where tafaifflK?» d tf£ d , protabfe average vdue" 8 " '° ""^ US """^ ^^ im P r ° babk - *"• «*»» Substance. Aluminium Antimony Arsenic . , Barium . Beryllium Bismuth . , Boron, amorph, Bromine . , Casmine . . Caesium . , Chlorine, liquid Chromium . Cobalt . . Copper . . Gallium . . Germanium Gold . . . Indium . . Iodine . . Iridium . . Iron (pure) . " (white pig) " (gray pig) Steel . . . . " (cast) . . Lanthanum . . Lead . . . . Range. Mil Max. Mean. C.° C.° C.° 600. 850. 625. 425. 450. 435. bet. Sb and Ag above that of cast iron below that of silver 266.8 I 269.2 I 268.1 melts in elect, arc —7-2 —7-3 —7-27 315- 32i- 3i8- 26.5 - - — 102. above that of platinum 1500. 1800. 1650. 1050. 1330. 1 100. 30.15 900. 1035. 1250. 1080. 176. 107. 115. 112. 1950. I S 00 - 2225. 1500. 1800. 1635. 1050. 1 100. 1075. 1 100. 2275. 1200. 1300. 1400. 1360. , - - 1375- between Sb and Ag 3 22 - I 335- I 326. 9 10 11 12 Substance. Lithium . Magnesium Manganese Mercury . Molybdenum Nickel . Osmium . Nitrogen Palladium Phosphorus Platinum Potassium Rhodium Rubidium Ruthenium Silenium . Silicon Silver . . Sodium . Strontium Sulphur . Tellurium Thallium Tin . . Tungsten Zinc . . Range. Min. Max. 750. -38.5c 800. -39-44 Mean. C.° 180. 775- 1900 ■39-°4 above white heat 1500. 2500. —208. 1600. 44-25 1900. 60. 2000. 38-5 1800. 217. bet. cast iron and steel 916. I 1040. I 950. 95-6 1—97-61 97.6 red heat in. 120. 115.1 452. 525. 470. 288. 290. 289. 226.5 2 35- 2 3°- above that of manganese 400. 433. 415. 1450. 1600. —203. 1350- 44.2 1775- 55- — 214. 1950. 44.4 2200. 63- - - 13 13 14 15 16 16 17 7 18 19 1 Mallet. 2 Frey. 8 Debray. 4 Despretz. 6 Setterberg, 1882, 6 Olszewski, 1884. 7 Deville, 1856. 8 Lecoq de Bois- baudran, 1876. » Winkler, 1886. n> Winkler, 1867. 11 Ledebur, 1881. 12 Hildebrand and Norton, 1875. 18 Bunsen. 14 Carnelley, 1879. 15 Buchholz. M Wohler. 16 Pictet, 1879. 17 Hittorf, 1851. 18 Matthieson, 1855. BOILING-POINT OF CHEMICAL ELEMENTS. Table 216. The column headed " Range " gives the extremes of the records found. Where the results are from one observer the authority is quoted with date of publication. Range. Mean. t Substance. Range. Mean. I Substance. H Min. Max. S Min. Max. Si O Aluminium . . abov e white heat 1 Nitrogen . . . _ - —194.4 8 Antimony . . 1470. 1700. 1535- Oxygen . . . —181. —184. -183- Arsenic . . . 449. 450. - 2 Ozone. . . . - - — 106. 9 Bismuth . . . 1090. 1700. 1413- Phosphorus 287.3 290. 288. Bromine . . . S9- 2 7 63.05 62.08 Potassium . . 667. l 2 > 695. Cadmium . . 720. 860. 779- Selenium . . 664. 683. 675. Chlorine . . . - - —33-6 3 Sodium . . . 742. 907. 825. Iodine . . . over 200 4 Sulphur . . . 447- 448.4 448.I Lead . . . bet. 1 4^0° and 1600 s Thallium . . . 1600. 1800. 1700. Magnesium . . - - 1 100. 6 Tin .... bet. 1450 and 1600 Mercury . . . — — 357- 7 Zinc .... 891. I 1040. 958. 1 Deville, 1854. ~ Regnault, 1863. B Ca rnelle' f, 1879. ' Regnault, 1862. 9 Olszewski, 1887. 2 Conechy. » Stas, 1865. » Di tte, 18' 71. 8 Olszewski, 1884. Smithsonian Tables. 207 Table 217. MELTING-POINTS OF VARIOUS INORCANIC COMPOUNDS.* Substance. Chemical formula. Melting-points. ■c 3 Date of publication. Min. Max. Particular or average values. . 16.6-350 0.21 16 5 Topaz : " " 16.6-957 0-'737 5 Parallel to lesser 86.3Cu+97Sn+ horizontal axis tt 0.0832 8 4Z11 40 0.1782 3 Parallel to greater 97.6Cu+2.2Sn+ horizontal axis tt 0.0836 8 0.2P, hard 0-80 0.17 13 6 Parallel to verti- " " " " soft (( 0.1708 6 cal axis " 0.0472 8 Caoutchouc . 16.7-25.3 .657-.686 0.770 2 7 Tourmaline : Parallel to longi- Ebonite . 2 S-3-35-4 0.842 7 tudinal axis ft 0.0937 8 Fluor spar : CaF2 . O-IOO 0.1950 8 Parallel to hori- German silver . " 0.1836 8 zontal axis tt 0.0773 8 Gold-platinum : Type metal 16.6-254 0.1952 5 • 2Au+lPt (( 0.1523 4 Vulcanite 0-18 0.6360 18 Gold-copper : Wedgwood ware O-IOO 0.0890 5 2Au+iCu tt 0.1552 4 Wood: Glass : Parallel to fibre : Tube . " 0.0833 1 Ash . tt 0.0951 19 "... tt 0.0828 9 Beech 2-34 0.0257 20 Plate . " 0.0891 10 Chestnut . (i 0.0649 20 Crown (mean) tt 0.0897 10 Elm . tt 0.0565 20 tt 50-60 0.0954 0.0788 11 Mahogany u 0.0361 20 Flint . tt 11 Maple tt 0.0638 20 Jena thermometer Oak . a 0.0492 20 (normal) O-IOO 0.081 12 Pine . » 0.0541 20 " " 59 111 (< 0.058 12 Walnut . tt 0.0658 20 Gutta percha . 20 1.983 !3 Across the fibre : Ice .... -20 tO -I o-375 14 Beech » 0.614 20 Iceland spar : Chestnut . " 0.325 20 Parallel to axis . O-80 0.2631 6 Elm . » 0-443 20 Perpendicular to Mahogany " 0.404 20 axis it 0.0544 6 Maple " 0.484 20 Lead-tin (solder) Oak . a 0.544 20 2Pb+iSn O-IOO 0.2508 1 Pine . it 0.341 20 Paraffin . 0-16 1.0662 15 Walnut . " 0.484 20 a 16-38 i-3 30 15 Wax: White . 10-26 2.300 21 "... 38-49 4.7707 15 a 26-31 3.120 21 Platinum-iridium it 31-43 4.860 21 ioPt+iIr 40 0.0884 3 it 43-57 15.227 21 Autj WRITIES. I Smeaton. 6 Benoit. II Pulfrich. 16 Braun. 21 Kopp. 2 Various. 7 Kohlrausch. 12 Schott. i7Devillean 1 Troost. 3 Fizeau. 8 Pfaff. 13 Russner. 18 Mayer. 4 Matthieson. 9 Deluc. 14 Brunner. 19 Glatzel. 5 Daniell. 10 Lavoisier and - Laplace. 1 5 Rodwell. 20 Villari. Smithsonian Tables. 215 Table 223. COEFFICIENTS OF THERMAL EXPANSION. Coefficients of Cubical Expansion of some Crystalline and other Solids. - T= temperature or range of temperature, C= coefficient of cubical expansion, A = authority. Substance. T CX 10* A Antimony . . . . O-IOO 0.3167 Matthieson. Beryl O-IOO 0.0105 Pfaff. Bismuth . . . . - 0.4000 Kopp. Diamond . 40 0.0354 Fizeau. Emerald . 40 0.0168 " Fluor spar .... 14-47 0.6235 Kopp. Garnet .... O-IOO 0.2543 Pfaff. Glass, white tube O-IOO 0.2648 Regnault. " green tube O-IOO 0.2299 «( " Swedish tube . O-IOO 0.2363 " " hard French tube . O-IOO 0.2142 (( " crystal tube O-IOO 0.2I0I " " common tube . 0-1 0.2579 " " Jena O-IOO °- 2 533 Reichsanstalt. Ice — 20 to 1 1. 1250 Brunner. Iceland spar 50-60 0.1447 Pulfrich. Idocrase .... O-IOO 0.2700 Pfaff. Iron O-IOO °-355° Dulong and Petit. it 0-300 0.4410 <( « u Magnetite, FesO^ O-IOO 0.2862 Pfaff. Manganic oxide, M112O3 . O-IOO 0.522 Playfair and Joule. Orthoclase (adularia) O-IOO 0.1794 Pfaff. Porcelain . O-IOO 0.1080 Deville and Troost. Quartz 50-60 °-353° Pulfrich. Rock salt . 50-60 1.2120 u Spinel ruby 40 0.1787 Fizeau. Sulphur, rhombic O-IOO 2-2373 Kopp. Topaz O-IOO 0.2137 Pfaff. Tourmaline O-IOO 0.2181 tt Zincite, ZnO 40 0.0279 Fizeau. Zircon O-IOO 0.2835 Pfaff. * For more complete tables of cubical expansion, (Smithsonian Collections), published in 1876. see Clarke's " Constants of Nature," Smithsonian Tables. 2l6 Table 224. COEFFICIENTS OF THERMAL EXPANSION. Ooofflctents of Cubical Expansion ol Lin.ulas. ™ ta *S'p?Lt If 5 t n u S n d° f r s e ffl nSi °r rivfT *"** a " d soluti <™ ° f -»»■ When not otherwise stated for range T Tn degrees C , and 1 he authoritv or r 'TTfT ""% C ' h |= mean ?° effici 40.9 % " Carbon disulphide . 500 atmos. pressure 3000 " " Chloroform . . . Ether Glycerine .... Hydrochloric acid : HC1 + 6.2SH 2 . HCI + 5oH 2 . Mercury .... Olive oil .... Potassium chloride : K.C1, 2.5 % solution . KC1, 24.3 % " Potassium nitrate : KN0 8 , 5.3 % sol'n KN0 8 , 21.9% " Phenol, C 6 H 6 . . . Petroleum Sp. gr. 0.8467 . . . Sodium chloride : NaCl, 1.6 % solution . Sodium sulphate : Na 2 S04, 24 % sol'n . Sodium nitrate : NaN0 3> 36.2 % sol'n . Sulphuric acid : H 2 S0 4 H 2 S0 4 + SoH 2 . Turpentine .... Water i6°-I07° c-54 -IS to +80 0-80 o-39 18-39 0-40 0-40 -38 to +70 11-81 —7 to +60 18-25 17-24 -34 to +60 0-50 0-50 0-63 -1510+38 0-30 0-30 24-299 C X 1000 .866 .524 .940 .581 36-157 7-38 24-120 10-40 20-78 0-30 0-30 -9 to +106 0-200 .992 •1433 .1616 •1433 !n68 .0506 .0510 .1468 •1399 .2150 ■°S34 .0489 •0933 .0742 .0572 .0477 ■0539 .0577 .0899 .1039 .1067 .0611 .0627 .0489 .0799 .1051 ■ Xi 1.0630 1.3240 0.8900 1.0414 0.7450 0.2928 1. 1856 1.1763 1.0382 0.0788 0.4238 1-1398 1.1071 1.5132 0.4853 0.4460 0.0625 0.1818 0.6821 0.8340 0.8994 0.0213 0-3599 0.5408 0-5758 0.2835 0.9003 — .0658 /3X 10° 0.1264 3.8090 0-6573 O.7836 I.850 I7.9OO I.5649 1-2775 1.7114 4.2742 0.8571 1.3706 4.6647 2.3592 0.4895 0.430 8.710 0.000175 1.1405 0.1073 1.396 10.462 2.516 1.075 0.864 5.160 1-959 8.507 yX io» I.0876 O.8798 1. 1846 1.7 168 O.730 II.87 0.91 1 1 O.8065 O.5447 1.9122 1-7433 4.0051 0.003512 -•539 0.4446 -6.769 1 Amagat. 2 Barrett. 3 Zander. 4 Pierre. 5 Kopp. 6 Recknagel. Authorities. 7 Decker. 10 Broch. 8 Emo. 11 Spring. 9 Marignac. 12 Nicol. 13 Pinette. 14 Frankenheim. 15 Scheel. Smithsonian Tables. 217 Table 225. COEFFICIENTS OF THERMAL EXPANSION. constant pressure. Coefficients of Expansion of Oases. The numbers obtained by direct experiment on the change of volume at constant pressure, Ep, are separated in the table from those obtained from the change of pressure at constant volume, £»• The two parts of the table are headed " Coefficient at constant pressure '" and " Coefficient at constant volume," respectively. Ordinary changes of atmospheric pressure produce very little change in the coefficient, of expansion, and hence entries in the pressure column of i atm. have been made for all pressures near to 76 centimetres of mercury. The other numbers in the pressure columns are centimetres of mercury at o° C. and approx. 45 latitude, unless otherwise marked. Thomson has given {vide Encyc. Brit. art. "Heat") the following equations for the calculation of the expan- sion, E, between o° and 100° C. of the gases named. Expansion is to be understood as change of volume under £=.3662(1 — .00049 — ) £ — .3662(1 + .0026 ?J>) £• = .3662(1 + .0032 ^) v VqI £ = .3662(1+ .0031 V -*\ £=.3662(1 + .0x64 —°) V v J where V / v o is the ratio of the actual density of the gas at o° C. to the density it would have at o° C. and one atmosphere of pressure. The same experiments (Thomson & Joule, Trans. Roy. Soc. i860), — which, together with Regnault's data, led to these equations, — give for the absolute temperature of melting ice 2.731 times the temperature interval between the melting-point of ice and the boiling-point of water under normal atmospheric pressure. Hydrogen . . Common air . Oxygen . . . Nitrogen . . Carbon dioxide Coefficient at constant volume. Coefficient at constant pressure.! Substance. Pressure. X 100 O h < Substance. Pressure. Xioo. O < Air ... 0.6 •3765 Air ... 76. 0.3671 3 « 1.6 •3703 tt 2 57- 0.3695 3 it 7.6 .3665 Hydrogen . 76. 0.36613 3 " 10.0 •3 66 3 M 254. 0.36616 3 tt 26.0 .3660 Carbon dioxide 76. 0.3710 3 " 37-6 .3662 1 (i 252. 0.3845 3 t* 75.0 76-83 •3665 * " o°-64° 17. 1 atm. 0.5136 6 1 u .3670 2* 1 " 64°-ioo° 17.1 " 0.4747 6 » 11-15 .3648 3 t " o c -7.5° 24.81 " 0.7000 6 ti 17-24 ■3651 3 1 " o°-64 c 24.81 " 0.6204 6 « 37-Si .3658 3 1 " 64°-ioo° 24.81 " °-5435 6 tt 76 .3665 3 t " o - 7 . 5 ° 34-49 " 1.0970 6 tt 200 .3690 3 t " o°-64° 34-49 " 0.8450 6 tt 2000 .3887 3 " " o°-ioo° 34-49 " 0.6574 6 tt 1 0000 .4100 3 Carbon monoxide 76. 0.3669 3 n 76 .3669 3* Nitrous oxide . 76. 0-37I9 3 tt 76 .3671 4 Sulphur dioxide 76. °-39°3 3 tt 1 atm. .3670 5* (C ti 98. 0.3980 3 Carbon dioxide 1 " .3706 5 Water vapor, o°-H9° 1 atm. 0.4187 7 U It 1 " ■%£ 1 " " o°-i4i° 1 " 0.4189 7 t tt 76-104 .3686 3 " " 0°-l62° 1 " 0.4071 7 it ti 174-234 ■3752 3 " " 0°-200° 1 " -3938 7 tt a 793 .4252 3 " o°-247° 1 " o-3799 7 " " o c -64° . 10.4 atm. ■4754 6 '■ " 64°-ioo° 16.4 " .4607 6 ; « « o°-64°. 25.87 " .5728 6 Authorities. " " 64°-ioo° 25.87 " .5406 6 " " o°-64° . 33-53 " •6973 6 1 Melander. 5 Jolly. " " 64°-ioo° 33-53 " ■ 6 334 6 2 Magnus. 6 Andrews. Carbon monoxide 1 .3667 3 3 Regnault. 7 Him. Hydrogen . 1 " .3669 3 4 Rowland. tt 1 .3656 5 Nitrogen 1 .3668 3 Nitrous oxide a tt 1 " 1 " .3676 •3707 3 5 Oxygen 1 " •3 6 74 5 Sulphur dioxide, SO2 . 1 " ■3845 5 * Corrected by Mendelejeff to 45 latitude and absolute expansion of mercury. Rowland gets almost the same correction on Regnault, using Wiiliner's value of the expansion of mercury. t The series of results at different pressures are given because of their interest. The absolute values are a little too low. (See preceding. 'footnote.) Smithsonian Tables. 218 Table 226. DYNAMICAL EQUIVALENT OF THE THERMAL UNIT. Rowland in his paper quoted in Table 227 has given an elaborate discussion of Joule's determinations and the cor- rections required to reduce them to temperatures as measured by the air thermometer. The following table con- tains the results obtained, together with the corresponding results obtained in Rowland's own experiments. The variation for change of temperature in Rowland's result is due to the variation with temperature of the specific heat of water. Date. 1847 1850 1850 1850 1850 1850 1867 1878 1878 1878 1878 1878 Method of experiment. Friction of water mercury « 1* u Electric heating . Friction of water 11 11 11 it ii 11 Temp. of water C.° IS 14 9 9 9 9 18.6 14.7 12.7 15-5 14.5 17-3 Joule's value. 781.5 772.7 772.8 775-4 776.0 773-9 772.7 774.6 773- 1 767.0 774.0 Joule's value reduced to air thermometer and latitude of Baltimore. Eng. units. 787.0 778.0 779.2 781.4 782.2 780.2 776.1 778-5 776.4 770.5 777.0 Met. units. 442.8 426.8 427-5 428.7 429.I 428.O 428.O 425.8 427.I 426.O 422.7 426.3 Row- land's value. 427.4 427.7 428.8 428.8 428.8 428.8 426.7 427.6 428.O 427-3 427.5 426.9 J-R- + 15-4 —0.9 —i-3 — 0.1 +0.3 —0.8 +i-3 —1.8 —0.9 —i-3 -4.8 —0.6 U > « rttj o 10 2 2 I 1 3 2 3 5 1 1 From the above values and weights Rowland concludes as the most probable value from Joule's experiments, at the temperature 14.6 C. and the latitude of Baltimore, 426.75, and from his own experiments 427.52. The mean of these results is 427.13 in metric units, or 778.6 in British units. Correct- ing back for latitude, and to mercury thermometer, this gives about 774.5 for the latitude of Manchester, instead of 772, as has been commonly used. An elaborate determination recently made by Griffith and referred to in Table 227 gives a value about one tenth of one per cent higher than Rowland's. Probably when a mer- cury thermometer is involved in the measurements we may take 776 as the nearest whole number in foot-pounds and British thermal units for the latitude of Manchester, and 777 for that of Baltimore. The corresponding values in the metric system will be 425.8 and 426.3, or in round numbers 426 for both latitudes. The following quantities should be added to the equivalent of Baltimore to give the equivalent at the latitude named : — Latitude .... 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° Kilogramme-metres 0.89 0.82 0.63 0.34 0.08 —0.41 —0.77 —1.06 —1.26 —1.33 Foot-pounds . . . 1.62 1.50 1.15 0.62 0.15 —0.75 — 1.41 —1.93 —2.30 —2.43 Smithsonian Tables. 219 Table 227. MECHANICAL EQUIVALENT OF HEAT. The following historical table of the principal experimental determinations of the mechanical equivalent of the unit : of heat has been, with the exception of the few determinations bearing dates later than 1879, 'aken from Rowland* The different determinations are divided into four groups, according to the method used. Calculations based on the constants of gases and vapors as determined by others are not included in this table. Method. Observer. Date. Result. Compression of air . Joule 1 1845 443-8 Expansion " " Joule x 1845 437-8 Experiments on steam engine . Hirn 2 1857 413.0 (t a << (t Hirn 2 1860-1 420-432 443-6 Expansion and contraction of metals Edlund 8 1865 j 430.1 428.3 437-8 428.1 (1 (( it u « Haga* 1881 1 Measurement of the specific volume 0; Perot 6 1886 424-3 Boring of cannon .... Rumf ord • 1798 940 ft.-lbs. Friction of water in tubes Joule 7 1843 424.6 " " " " calorimeter Joule 1 1845 488.3 »( << if « (1 Joule B 1847 428.9 it (( tt tt it Joule 9 1850 4239 " " mercury in " Joule 9 1850 424.7 " " plates of iron Joule 9 1850 425.2 " " metals .... Hirn 2 1857 371-6 " " " in mercury calorimeter Favre 10 ifSf 413-2 tt it U Hirn 2 18 Jl 400-450 Boring " " .... Hirn 2 1858 425.0 Water in balance afrottement . Flow of liquids under strong pressure Hirn 2 1860-1 432.0 Hirn 2 1860-1 432.0 Crushing of lead .... Hirn 2 1860-1 425.0 Friction of metals .... Puluj u 1876 426.6 Friction of water in calorimeter Joule 12 1878 423-9 « (< <( tt it Rowland ls 1879 426.3 " " metals .... Sahulka « 1890 427.5 Heating by magneto-electric currents Joule 7 1843 460.0 Heat generated in a disc between the 435-2 poles of a magnet .... Violle i 6 1870 • 434-9 435-8 Flow of mercury under pressure Bartoli 16 1880 437-4 428.4 Heat developed in wire of known abso - ( Quintus Icilius, 17 j also Weber } 1857 lute resistance .... 399-7 Heat developed in wire of known abso - ( Lenz ) Weber } 1859 { 396-4 lute resistance .... 478.2 Heat developed in wire of known abso lute resistance .... Joule 1S 1867 429.5 Heat developed in wire of known abso lute resistance .... H.F.Weber 19 1877 428.15 Heat developed in wire of known abso 1885 j lute resistance .... Webster 20 414.0 ergs per gramme degree. Heat developed in wire of known abso lute resistance .... Dieterici a 1888 424.36 Re FERENCES. See pposite page. Smithsonian Tables. * " Proc Am. Acad. Arts and Sci." vol. 15. 220 Table 227. MECHANICAL EQUIVALENT OF HEAT. Method. Observer. Date. Result. Diminishing the heat contained in a battery when the current produces work Diminishing the heat contained in a battery when the current produces work Heat due to electrical current, electro-chemical equivalent of water = .009379, absolute resist- ance, electro-motive force of Daniell cell, heat developed by action of zinc on sulphate of copper Heat developed in Daniell cell .... Electromotive force of Daniell cell Combination of electrical heating and mechan- ical action by stirring water .... Joule 7 Favre 22 Weber, Boscha, Favre, and Silbermann j Joule ( Boscha 28 Griffiths M 1843 1858 1857 1859 1893 499.0 443-0 432.1 4I9-S 428.0 References. 1 Joule, " Phil. Mag." (3) vol. 26. 2 Him, " Theorie Mec. de la Chaleur," ser. 1, 3me ed. 3 Edlund, " Pogg. Ann." vol. 114. 4 Haga, " Wied. Ann." vol. 15. 5 Perot, " Compt. Rend." vol. 102. 6 Rumford, " Phil. Trans. Roy. Soc." 1798 ; Favre, " Compt. Rend." if 7 Joule, " Phil. Mag." (3) vol. 23. 8 Joule, " " " " 27- 9 Joule, " " " " 3 1 - 10 Favre, " Compt. Rend." 1858 ; " Phil. Mag." (4) vol. 15. 11 Puluj, " Pogg. Ann." vol. 157. 12 Joule, " Proc. Roy. Soc." vol. 27. 13 Rowland, " Proc. Am. Acad. Arts & Sci." vols. 15 & 16. 14 Sahulka, " Wied. Ann." vol. 41. 15 Violle, "Ann. de Chim." (4) vol. 22. 16 Bartoli, " Mem. Ace. Lincei," (3) vol. 8. 17 Quintus Icilius, " Pogg. Ann." vol. 101. 18 Joule, " Rep. Com. on Elec. Stand.," " B. A. Proc." 1867. 19 H. F. Weber, " Phil. Mag." (5) vol. 5. 20 Webster, " Proc. Am. Acad. Arts & Sci." vol. 20. 21 Dieterici, " Wied. Ann." vol. 33. 22 Favre, " Compt. Rend." vol. 47. 23 Boscha, " Pogg. Ann." vol. 108. 24 Griffiths, " Phil. Trans. Roy. Soc." 1893. Smithsonian Tables. 221 Tables 228, 229. SPECIFIC HEAT. Specific Heat at Water. The specific heat of water is a matter of considerable importance in many physical measure- ments, and it has been the subject of a number of experimental investigations, which unfortu- nately have led to very discordant results. Regnault's measurements, published in 1847,* show an increase of specific heat with rise of temperature. His results are approximately expressed by the equation c = I + .0004 1 -f- 0000009 1 2 , which makes the specific heat nearly constant within the atmospheric range. A different equa- tion was found from Regnault's results by Boscha, who thought the temperatures required cor- rection to the air-thermometer. Regnault, however, pointed out that the results had already been corrected. Jamin and Amaury t found, for a range from 9° to 76° C, the equation c = 1 + .0011 / + .0000012 f 3 , which nearly all the evidence available shows to be very much too rapid a change. Wullner gives, for some experiments of Miinchhausen,} the equation c=\ 4- .00030102 1 in vol. 1, changed to c= 1 -f- .000425? in vol. 10, for a range of temperature from 17 to 64°. In 1879, experiments are recorded by Stamo,§ by Henrichsen,|| and by Baumgarten, || all of them giving large variation with temper- ature. In 1879, Rowland inferred from his experiments on the mechanical equivalent of heat that the specific heat of water really passes through a minimum at about 30° and he attempted to verify this by direct experiment. The results obtained by direct experiments were not by any means so satisfactory as those obtained from the friction experiment; but they also indicated that the specific heat passed through a minimum, — but, in this case, at about 20° C. Further, direct experiments were made in 1883, in Rowland's laboratory, by Liebig, using the same calorimetric apparatus ; and these experiments also show a minimum at about 20 C.1T Since the publica- tion of Rowland's paper a number of new determinations have been made. Gerosa gave, in 188 1, a series of equations which show a maximum at 4°.4, then a minimum a little above 5° and afterwards a rise to 24 ! Neesen ** found a minimum near 30°, but got rather less variation than Rowland. Rapp,tt taking the mean specific heat between o° and ioo° as unity, gives the equa- tion c= 1.039925 — .007068/+ .00021255 fi — .000001 584 fl, which gives a minimum between 20 and 30 and a maximum about 70° Voltenjf gives an equation which is even more extraordinary with regard to coefficients than the last, namely, c = \ — .0014625512 / + .0000237981 fl — .00000010716 r 3 , which puts the minimum between 40° and 50° and gives a maximum at 100 ; which maximum is, however, less than unity. Dieterici, in his paper on the mechanical equivalent of heat, dis- cusses this subject ; but his own results being in close agreement with Rowland's, his table prac- tically only extends Rowland's results through a greater range of temperature, assuming straight- line variation to the two sides of the minimum. Bartoli and Stracciati §§ found a minimum at about 30° ; while Johanson in the same year gives a minimum at about 4° and then a rise about 1 2 times as rapid as that of Regnault. Griffiths || || finds the equation and _ _. u u t* 27-280 0.650 ) Ogier _ _ Nitrous oxide 16-207 0.2262 Regnault _ tt tt 26-103 0.2126 Wiedemann _ _ H (C 27-206 0.2241 it - - mean 0.2214 - 1. 29 1 Wiillner .1715 Sulphur dioxide (SO2) . 16-202 0.1544 Regnault 1.26 ( Cazin ) \ Miiller ) 0.1225 Water 128-217 0.4805 <( _ tt 100-125 0.3787 Macfarlane Gray _ mean 0.4296 1 1.300 Various 0-3305 Smithsonian Tables. 224 Tables 231 , 232. VAPOR PRESSURE. TABLE 231. — Vapor Pressure of Ethyl Alcohol.* u & e H 0° 1° 2° 3° 4° 5° 6° 7° 8° 8° Vapor pressure in millimetres of mercury at o° C. 0° IO 20 3° 40 5° 6o 70 12.24 23-78 44.OO 78.06 I33-70 220.00 350-30 541.20 13.18 25-3I 46.66 82.50 140.75 230.80 366.40 564.35 I4-I5 27.94 49-47 87.17 148.10 242.50 383-10 588.35 15.16 28.67 52.44 92.07 155.80 253.80 400.40 613.20 16.21 30.50 55-56 97.21 163.80 265.90 418.35 638.95 I7-3 1 3 z -44 58.86 102.60 172.20 278.60 437.00 665.55 18.46 34-49 62.33 108.24 181.00 291.85 456-35 693.10 19.68 36.67 65-97 H4-I5 190.10 305-65 476.45 721.55 20.98 38-97 69.80 120.35 199.65 3 1 9-9S 497-25 751.00 22.34 41.40 73-83 126.86 209.60 518.85 781.45 From the fori nula logj t> = a + icf + c& Ramsay and Young obtain the following numbers.t t 0° 10° 20° 30° 40° 60° 60° 70° 80° 90° Vapor pressure in millimetres of mercury at o° C. 0° ioo 200 12.24 1692.3 22182. 23-73 2359.8 26825. 43-97 3223.0 32196. 78.II 38389- 133-42 5686.6 455I9- 219.82 7368.7 350.21 9409.9 540.91 H858. 811.81 14764. 1 186.5 18185. TABLE 232. — Vapor Pressure of Methyl Alcohol.} u d S V 0° 1° 2° 3° 4° 5° 6° 7° 8° 9° Va por pressui e in millimetres of mercury at o >C. 0° 10 20 30 40 50 60 29.97 53-8 94.0 158.9 259.4 409.4 624.3 31.6 57.0 99.2 167. 1 271.9 427.7 650.0 33-6 60.3 104.7 1757 285.0 446.6 676.5 35-6 63.8 1 10.4 184.7 466.3 703.8 37-8 67.5 1 16.5 194.1 312.6 486.6 732.0 40.2 71.4 122.7 203.9 327-3 507-7 761. 1 42.6 75-5 129.3 214.1 342.5 529.5 791.1 45.2 79.8 136.2 224.7 358-3 552.0 022.0 47-9 84-3 143-4 235.8 374-7 575-3 50.8 89.0 151-0 247.4 391-7 599-4 * This table lias been compiled from results published by Ramsay and Voung (Jour. Chem. Soc. vol. 47, and Phil. Trans. Roy. Soc, 1886). t In this formula (1 = 5.0720301 ; Iog*=2.64o6i3i; log c — 0.6050854 ; log = 0.003377538; logP— 1.99682424 (c is negative). t Taken'from a paper by Dittmar and Fawsitt (Trans. Roy. Soc. Edin. vol. 33). Smithsonian Tables. 225 Table 233. VAPOR PRESSURE.* Carbon Bisulphide, CMorobenzene, Bromobenzene, and Aniline. Temp. 0° 1° 2° 3° 40 6° 6° 7= 8° 9° (a) Carbon Disulphide. 0° 127.90 I33-85 140.05 146.45 153.10 160.00 167.15 174.60 182.25 190.20 IO 198.45 207.00 215.80 224.95 234.40 244.15 254-25 264.65 275.40 286.55 20 298.05 309.90 322.10 334-70 347-70 361.10 374-95 389.20 403.90 419.00 3° 434.60 450.65 467.15 484.15 501.65 5I9-65 538-I5 s5 rj 576.75 596.85 40 617.50 638.70 660.50 682.90 705.90 729.50 753-75 778.60 804.10 830.25 (b) Chlorobenzene. 20° 8.65 9.14 9.66 10.21 10.79 11.40 12.04 12.71 13-42 14.17 3° 14-95 15-77 16.63 17-53 18.47 19.45 20.48 21.56 22.69 23-87 40 25.10 26.38 27.72 29.12 30.58 32.10 33-69 35-35 37.08 38.88 50 40.75 42.69 44.72 46.84 49-05 5'-35 53-74 83.02 56.22 58.79 61.45 6o 64.20 67.06 70.03 73-" 76.30 79.60 86.56 90.22 94.00 70 97.90 101.95 106.10 1 10.41 114.85 119.45 124.20 129.10 I34-I5 139.40 8o 144.80 150.30 156.05 161.95 168.00 174.25 181.70 187.30 194.10 201.15 9° 208.35 215.80 223.45 231-30 239-35 247.70 256.20 265.00 274.00 283.25 100 292.75 302.50 312.50 322.80 333-35 344-15 355-25 366.65 378.30 390-25 no 402.55 415.10 558-7° 427.95 441.15 454.65 468.50 482.65 497.20 512.05 527.25 120 542.80 575-°5 591.70 608.75 626.15 643-95 662.15 680.75 699.65 I TO 718.95 738-65 758.80 — — " "~ *~ ~ ~ (o) Bromobenzene. 40° - - - - - 12.40 13.06 1375 14.47 15.22 50 16.00 16.82 17.68 18.58 19.52 20.50 21.52 22.59 2371 24.88 6o 26.10 27.36 28.68 30.06 3i-5o 33-oo 34 "5o 36.18 37.86 39.60 70 41.40 43.28 45.24 47.28 49.40 51.60 53.88 56-25 58.71 61.26 8o 63.90 66.64 69.48 7242 75.46 78.60 81.84 85.20 88.68 92.28 9° 96.00 99.84 103.80 107.88 112.08 116.40 120.86 125.46 130.20 135.08 100 140.10 145.26 I50-57 1 56.03 161.64 167.40 173-32 179.41 185.67 192.10 no 198.70 205.48 212.44 219.58 226.90 234.40 242.10 250.00 258.10 266.40 120 274.90 283.65 292.60 301-75 3l ol S 320.80 330-70 340.80 3 ^o- IS 361.80 '3° 372-65 383-75 395- I0 406.70 418.60 430-75 443-20 455.90 468.90 482.20 140 495.80 509.70 523.90 538.40 553-20 568.35 583-85 599-65 615.75 632.25 150 649.05 666.25 683.80 701.65 7I9-95 738-55 757-55 776.95 796.70 816.90 (d) Aniline. 80° 18.80 19.78 20.79 21.83 22.90 24.00 25.14 26.32 27-54 28.80 90 30.10 3 r -44 32-83 34-27 35-76 37-30 38.90 40.56 42.28 44.06 100 45.90 47.80 49.78 5I-84 53-98 56.20 58.50 60.88 63-34 65.88 no 68.50 71.22 74.04 76.96 79.98 83.10 86.32 89.66 93.12 96.70 120 100.40 104.22 108.17 112.25 116.46 120.80 125.28 129.91 134.69 139.62 130 144.70 149.94 155-34 160.90 166.62 172.50 178.56 184.80 191.22 197.82 140 204.60 211.58 218.76 226.14 233-72 241.50 249.50 257.72 266.16 274.82 150 283.70 292.80 302.15 3"75 321.60 33 ! -70 342.05 352-65 363-50- 374.60 160 386.00 397-65 409.60 421.80 434-3° 447.10 460.20 473.60 487.25 501.25 170 515.60 530.20 545-2° 560.45 576.10 592-05 608.35 625.05 642.05 659.45 180 677-I5 695.30 7I3-75 73 2 -65 751.90 771.50 * These tables of vapor pressures are quoted from results published by Ramsay and Young (Jour. Chem. Soc. vol. 47). The tables are intended to give a series suitable for hot-jacket purposes. Smithsonian Tables. 226 VAPOR PRESSURE Table 23_, Methyl Salicylate, Bromonaphthaline, and Mercury. Temp. C. 0° 1° 2° 3° 4° 6° 6° 7° 8° 8° (e) Methyl Salicylate. 70° 80 90 2.40 4.60 7.80 2.58 4.87 8.20 2.77 2.97 5-44 9.60 3-18 5-74 9.52 3-4° 6.05 9-95 3.62 6-37 10.44 3-85 6.70 10.95 4.09 7.05 11.48 4-34 7.42 12.03 100 no 120 130 140 12.60 19.80 30.25 45-30 66-55 13.20 20.68 3I-52 47.12 69.08 13.82 21.60 32.84 49.01 71.69 14.47 22.55 34.21 50.96 74-38 15-15 23-53 35-63 52-97 77-15 I5-85 24.55 37.10 55-°S 80.00 16.58 25.61 38.67 57.20 82.94 17-34 26.71 40.40 59-43 85-97 18.13 27.85 41.84 6i-73 89.09 18.95 29.03 43-54 64.10 92.30 150 160 170 180 190 95.60 134-25 184.70 2 49-35 330-85 99.00 138.72 190.48 256.70 340.05 102.50 143-31 196.41 264.20 349-45 106.10 148.03 202.49 271.90 359-°5 109.80 152.88 208.72 279.75 368.85 113.60 1 57.85 215.10 287.80 378.90 "7-51 162.95 221.65 296.00 389-.1 5 121.53 168.19 228.30 304.48 399.60 125.66 I73-56 235-15 3!3-°5 410.30 1 29.90 179.06 242.15 321.85 421.20 200 210 220 43 2 -35 557-5° 710.10 443-75 571-45 727.05 455-35 585-7° 744-35 467.25 600.25 761.90 479-35 6! 5.05 779- 8 5 491.70 630.15 798.10 5°4-35 645-55 661.25 53°-4° 677.25 543.80 693.60 (f) Bromonaphthaline. 110° 120 130 140 3.60 8.50 i3-!5 3-74 5-7° §.89 13-72 3-89 5-96 9.29 T 4-3> 4-°5 6.23 9.71 14.92 4.22 6.51 10.15 15-55 4.40 6.80 10.60 16.20 4-59 7.10 11.07 16.87 4-79 7.42 11.56 17.56 5.00 7.76 12.07 18.28 5.22 8.12 12.60 19.03 150 160 170 180 190 19.80 28.85 40.75 56.45 77-15 20.59 29.90 42.12 58.27 79-54 21.41 30.98 43-53 60.14 81.99 22.25 32.09 44-99 62.04 84.51 23.11 33-23 46.50 64.06 87.10 24.00 34-4° 48.05 66.10 89.75 24.92 35-6o 49.64 68.19 92.47 25.86 36-83 51.28 7°-34 95.26 26.83 38.10 52.96 72-55 98.12 27-83 39-41 54.68 74.82 101.05 200 210 220 230 240 104.05 138.40 181.75 235-95 3°3-35 107.12 142.30 186.65 242.05 310.90 110.27 146.29 191.65 248.30 318.65 "3-5° i5°-38 196.75 254.65 326.50 116.81 154-57 202.00 261.20 334-55 120.20 158.85 207.35 267.85 342-75 123.67 163.25 212.80 274.65 351.10 127.22 167.70 218.40 281.60 359-65 130.86 172.30 224.15 288.70 368.40 134-59 176.95 230.00 295-95 377-3° 250 26b 270 386.35 487-35 608.75 395.60 498.55 622.10 405.05 509.90 635-7° 414.65 521.50 649.50 424.45 533-35 663-55 434-45 545-35 677-85 444.65 557.60 692.40 455-°° 570.05 707.15 465.60 582.70 722.15 476-35 595.60 737-45 (g) Mercury. 270° 280 290 123.92 157-35 198.04 126.97 161.07 202.53 130.08 164.86 207.10 133.26 168.73 211.76 136.50 172.67 216.50 139.81 176.79 221.33 143.18 180.88 226.25 146.61 185.05 231.25 150.12 189.30 236-34 153-7° 193-63 241-53 300 310 320 33° 340 246.81 3°4-93 373-67 454.41 548.64 252.18 3»-30 381.18 463.20 558-87 257-65 317.78 388.81 472.12 569.25 263.21 3 2 4-37 396.56 481.19 579-78 268.87 331.08 404.43 490.40 590.48 274.63 337-89 412.44 499.74 601.33 280.48 344.81 420.58 509.22 612.34 286.43 35I-85 428.83 518.85 623.51 292.49 359.00 437.22 528.63 634.85 298.66 366.28 445-75 538.56 646.36 350 658.03 669.86 681.86 694.04 706.40 718.94 73I-65 744-54 757.61 770.87 360 784-3 1 Smithsonian Tables. 227 Table 234. AIR AND MERCURY THERMOMETERS. Rowland has shown (Proc. Am. Acad. Sci. vol. 15) that, when o° and ioo° are chosen for fixed points, the relation between the readings of the air and the mercury in glass thermometers can be very nearly expressed by an equation of the form /= T— at {too — t)(b — t), where t is the reading of the air thermometer and T that of the mercury one, a and b being constants. The smaller a is, the more nearly will the thermometers agree at all points, and there will be absolute agreement for tz=o or 100 or b. Regnault found that a mercury thermometer of ordinary glass gave too high a reading between o° and ioo°, and too low a reading between ioo° and about 245 . As to some other thermometers experimented on by Regnault, little is recorded of their performance between o° and ioo°, but all of them gave too high readings above ioo°, indicating that below ioo° the mercury thermometer probably reads too low. Regnault states this to be the case for a thermometer of Choisy le R01 crystal glass, and puts the maximum error at from one tenth to two tenths of a degree. Regnault "s comparisons of the air and mercury thermometers and a Comparison by Recknagel of a mercury thermometer of common glass with the air thermometer are compared with the above formula by Rowland, The tables are interesting as showing approximately the error to be expected in the use of a mercury thermom- eter and the magnitude of the constants a and b for different glasses. They are given in the following Table. Regnault's results above ioo° C. compared with the formula £= T—at{ioo — t)\b — /), give for the constants a and b the following values : Cristal de Choisy le Roi . - 7-j,) = . 00543(100- T m ) r„ + ,. 4a X io-»( I00 »- T n ») T„- 1.323 X «o-« (ico»- r«,») T m 1000 (r 00 ,- 7» = .0359 (-oo- 7" m ) r„-o.2 34 Xio-«(ioo»- TV) r„- . 5 i X ,(ioo>- T m ")T„ N— nitrogen; H= hydrogen ; C0 2 = carbon dioxide ; m = mercury. TABLE 23B. — Hydrogen Thermometer compared with others. This table gives the correction which added to the thermometer reading gives the temperature by the hydrogen thermometer. Tempera- Chap] ius's experiments.t Marek's experiments, i: ture by Hard M ercury in glass. hydrogen thermom- eter. French glass mercury ther- mometer. Nitrogen thermome- ter. Carbon dioxide thermome- Hard French Thuringian glass. French glass. crystal glass. normal glass. 1830-40. 1888. — 20 +O.I72 +0.014 +O.071 — 10 +O.073 +0.007 +O.032 O.OOO 0.000 O.OOO 0.000 O.OOO 0.000 0.000 0.000 10 — °'°5 2 — O.006 — O.025 — O.044 — O.060 —O.056 —O.086 — 0.072 20 —0.085 — 0.0 10 —O.043 —O.073 — O.I 00 — 0.091 —O.149 — 0.125 3° — 0.102 0.01 1 —O.054 — O.091 — O.125 — 0.109 — O.I91 —0.159 40 — 0.107 — O.OII —0.059 — O.098 —O.134 — O.I 1 1 —O.213 —0.178 SO —0.103 — 0.009 —O.059 — O.096 —0.132 —0.103 — O.216 — 0.180 60 — 0.090 — 0.005 —O.053 —O.086 — 0.1 18 —0.086 0.201 —0.168 70 — 0.072 — 0.00 1 — O.044 — O.070 — O.096 — 0.064 0.I7I —0.143 80 — 0.050 +0.002 —O.O30 —0.050 —O.068 — 0.041 O.I27 — 0.106 90 — 0.026 +0.003 —0.016 — O.026 —O.035 — 0.018 O.069 — 0.058 IOO 0.000 0.000 0.000 0.000 O.OOO 0.000 0.000 0.000 TABLE 236. — Air Thermometer compared with others. This table gives the correction which added to the thermometer reading gives the temperature by the air thermometer. Temperature by air thermome- ter. Mercury in Thuringian glass thermometer (Grommach §). Mercury in Jena glass thermome- ter (Wiebe and Bbttcher II). Temperature by air thermome- ter. Mercury in Jena glass thermome- ter (Wiebe and Bultcher 11). Temperature by air thermome- ter. Baudin alcohol thermometer (."White If). — 20 +O.03 +°-I S3 130 — 0.07 — 0.000 — 10 +O.02 +O.067 140 O.O9 — S —O.144 O O.OO O.OOO 150 O.IO — 10 —0.382 10 —O.03 — O.049 160 — O.IO —is — O.704 20 O.II —O.083 170 —0.08 20 — I. IOO 3° — 0.12 —O.103 180 — 0.06 —25 —1-563 40 —0.08 O.IIO 190 — 0.02 —30 — 2.082 5° - — 0.107 200 +0.04 —35 —2.648 54 — 04 - 210 +0.1 1 —40 — 3- 2 53 60 - — 0.096 220 +0.21 —45 —3.887 70 _ — 0.078 230 +O.32 —50 — 4-541 I 3 80 —0.06 - 24O +O.46 ~P — 5.206 _ —0.054 25O +O.63 —60 —5.872 82 — 0.04 - 2§0 +0.82 -65 —6-53' 90 100 _ — 0.028 270 + 1.05 —70 —7-174 0.000 280 + i-3° —80 -8-371 no _ —0.03 29O +1.58 —90 —9-392 —10.163 120 — — 0.05 300 +1.91 — 100 * These two tables are taken with some slight alteration from Landolt and Boemstein's " Phys. Chem. Tab." t P Chappius, "Trav. et Mem. du Bur. internat. des Poids et M 385- 231 Table 241 • CORRECTION FOR TEMPERATURE OF MERCURY IN THERMOMETER STEM.* r=*-o.oooo 795 n «'-*), in Fahrenheit degrees; r=*-o.ooo.43 * ("-*), ™ Centigrade degrees. Where T= corrected temperature, 1= observed temperature, t<- mean temperature of glass stem and mercury column, n — the length of mercury in the stem in scale degrees. (a) Correction for Fahrenheit Thermometer = value of 0.0000795 « (/'-/). 71 t'—t 10° 20° 30° 40° 60° 60° 70° 80° 90° 100° 10° O.OI 0.02 0.02 O.03 O.04 0.05 0.06 0.06 0.07 0.08 20 0.02 O.O3 O.O5 0.06 0.08 0.10 O.II 0.13 0.14 0.16 3° 0.02 O.OS O.O7 O.IO 0.12 0.14 0.17 0.19 0.21 0.24 40 0.03 O.Ob O.IO 0.13 0.l6 O.19 0.22 0.25 0.29 0.32 5° 0.04 O.08 0.12 O.IO O.20 O.24 0.28 0.32 0.36 0.40 60 0.05 O.IO O.I4 0.19 O.24 0.29 o-33 0.38 0-43 0.48 7° 0.06 O.II 0.17 0.22 0.28 0.33 039 0.4s 0.50 0.56 80 0.06 0.13 O.I9 0.25 O.32 O.38 0.45 0.51 o-S7 0.64 90 0.07 0.14 0.2I 0.29 O.36 o-43 0.50 0.57 0.64 0.72 100 0.08 0.16 O.24 0.32 O.4O 0.48 0.56 0.64 0.72 0.79 110 0.09 0.17 0.26 0.35 0.38 O.44 0.52 0.61 0.70 0.79 0.87 120 O.IO 0.19 O.29 O.48 0.57 0.67 0.76 0.86 °-95 130 O.IO 0.21 O.3I 0.41 O.52 0.62 0.72 0.83 o-93 1.03 (b) Corr BCTJON FOR CENTIGF = value of 0.000143 adb Thermometer n(fi-fy n v—t 10° 20° 30° 40° 60° 60 70° 80° 10° O.OI 0.03 < 3.04 0.06 0.07 0.0 9 0.10 0.11 20 0.03 0.06 ( 3.09 O.II 0.14 O.I 7 0.20 0.23 3° 0.04 0.09 ( 3-13 0.17 0.21 0.2 6 0.30 0-34 40 0.06 O.II < 3.17 0.23 0.29 o-3 4 0.40 0.46 5° 0.07 0.14 < 3.21 0.29 0.36 0.4 3 0.50 o-S7 60 0.09 0.17 ( 3.26 0-34 o-43 a-l 1 0.60 0.69 70 O.IO 0.20 3.30 0.40 0.50 0.6 3.70 0.80 80 O.II 0.23 3-34 0.46 0.57 o.fc 9 D.80 0.92 90 0.13 0.26 *39 0.51 0.64 0.7 7 3.90 1.03 100 0.14 0.29 3-43 o-S7 0.72 0.8 b 1 .00 1.14 N. B.— When t' — /is negative the correction becomes ac ditive. Smithsonian Tables. * " Smithsonian Meteorological Tables," p. 12. 232 Table 241. CORRECTION FOR TEMPERATURE OF MERCURY IN THERMOMETER STEM. (C) CORRBCTION TO BE ADDED to Thermometer Reading.* t — V 70° 80° 90° 100° 120° 140° 160° 180° 200° 220° 10° 0.02 0.03 0.05 0.07 o.n 0.17 0.21 0.27 °-33 0.38 10° 20 0.13 O.15 0.18 0.22 0.29 0.38 O.46 0-53 0.61 0.67 20 3° O.24 0.28 o-33 °-39 0.48 O.59 0.82 O.7O O.78 0.88 0.97 30 40 °-35 0.41 0.48 0.56 0.68 O.94 1.04 1.16 1.28 40 50 0.47 0.53 0.62 0.72 0.88 I.03 I.I7 i-3i 1.44 1.59 50 60 o-57 0.66 0.77 0.89 1.09 1.25 I.42 1.58 1.86 1.74 1.90 60 70 0.69 0.79 0.92 1.06 1.30 I.47 I.67 2.04 2.23 70 80 0.80 0.91 1. os I.2I 1.52 1.71 I.94 2.15 2-33 2.55 80 90 0.91 1.04 1.19 I.38 i-73 1.96 2.20 2.42 2.64 2.89 90 100 1.02 1.18 i-35 i. Sb 1.97 2.18 2.45 2.70 2.94 3-23 IOO no - - 1.78 2.19 2-43 2.70 2.98 3.26 3-57 no 120 - - - 1.98 2-43 2.69 2.95 3.26 3-5« 3-92 120 130 _ _ _ 2.68 2.94 3.2O 3-r* 3-89 4.28 130 140 - - - - 2.92 3.22 347 3.86 4.22 4.64 140 150 - - - - - - 3-74 4-i5 4.56 5.01 150 160 - - - - - - 4.00 4.46 4.90 5-39 160 170 _ _ _ _ _ - 4.27 4.76 5-24 5-77 170 180 _ - - - - - 4-54 5.07 5-59 0.1 s 180 190 - - - - - - - 5-3" 5-95 6.54 190 200 - - - - - - - 5.70 6.30 6.94 200 210 _ _ _ _ - - - 6.68 7-35 210 220 — 7.04 7-75 220 * This table is quoted from Rimbach's results, " Zeit. fur Instrumentenkunde," vol. 10, p. 153. The numbers represent the correction made by direct experiment for thermometers of Jena glass graduated from o° to 360° C, the degrees being from 1 to 1.6 mm. long. The first column gives the length of the mercury in the part of the stem which is exposed in the air, and the headings under t — V give the difference between the observed temperature and that of the air. Smithsonian Tables. 233 Tables 242, 243. EMISSIVITY. TABLE 242. — Emisstvity at Ordinary Pressures. According to McFarlane* the rate of loss of heat by a sphere placed in the centre of a spherical enclosure which has a blackened surface, and is kept at a constant temperature of about 14 C, can be expressed by the equations e = .000238 + 3.06 X io-°* — 2.6 X 10- 8 * 2 , when the surface of the sphere is blackened, or e ~ .000168 + x.98 X io-o* — 1.7 X io-8j?2, when the surface is that of polished copper. In these equa- tions e is the emissivity in c. g. s. units, that is, the quantity of heat, in therms, radiated per second per square centimetre of surface of the sphere, per degree difference of tempera- ture 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. 5 10 r 5 20 25 30 35 40 45 5° 55 60 .000178 .000186 .OOOI93 .000201 .000207 .000212 .000217 .000220 .OOO223 .000225 .000226 .000226 .000252 .000266 .000279 .000289 .000298 .000306 .000313 .OOO319 .000323 .OOO326 .000328 .000328 .707 .699 .692 .695 .694 •693 •693 •693 .690 .690 .690 .690 TABLE 243. — Emissivity at Different Pres- sures. 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 8° C. Polished surface. Blackened surface. ] t et t et Pressure 76 cms. op Mercury. 63.8 .00987 61.2 .01746 57-i .00862 50.2 .01360 50.5 44.8 .00736 41.6 .01078 .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 62.5 .01298 61. 1 •00433 57-5 .01158 55 •00383 53-2 .01048 497 •00340 47-5 .00898 44.9 .00302 43-o .00791 40.8 .00268 28.5 .00490 Pressure i cm of Mercury. 6 J .00388 62.5 .01182 60 ■00355 .00286 57-5 .01074 5° 54.2 .01003 40 .00219 41.7 .00726 3° .00157 37-5 .00639 23-5 .00124 34-o .00569 - - 27.5 .00446 24.2 .00391 Smithsonian Tables. * " Proc. Roy. Soc." 1872. t " P.roc. Roy. Soc." Edinb. 234 Tables 244, 245. EMISSIVITY. TABLE 244. — Constants ol EmissIvKy. Dulong and Petit s law gives for the amount of heat radiated in a given time thf equation H=Asa 9 (a'—i) where A is a constant depending on the units employed and on the nature of the surface s the onhe'^rdosurandfthed iff* by *??"* ^ ? 4 t0 be 1M W> ' the -LZe^mperittt ot tne enclosure, and t the difference of temperature between the hot surface and the enclosure The following values of A are taken from the experiments of W. Hopkins Ae results beine reduced to centimetre second units, and the thermos unit of heat "° pKmS ' me resuIts bem S Glass A = .00001327 Dry chalk .4 ==.00001195 Dry new red-sandstone A = .00001162 Sandstone (building) . A = .00001232 Polished limestone . . ^==.00001263 Unpolished limestone (same block) . . . A == .0001777 Stefan's law is expressed by the equation H=) __ internal-work pressure where * is taken in litres the pressure is given per square gfi oflhftterm and the kilogramme -degree or calorie respecuve.y. Smithsonian Tables. 237 Table 249. PROPERTIES OF STEAM. British Measure. The quantities given in the different columns of this table are sufficiently 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 this table, the data are taken from a table given by DweJshauvers-Dery (Trans. Am. Sue. Mech. Eng. vol. xi.). P 3 5 •973 2.041 2.109 .177 •245 " 3 o 3 .381 2.449 .585 ■653 .722 2.789 .857 ■925 •993 3.061 3.129 .197 .265 •333 102.0 126.3 141.6 r 53-i 162.3 170.1 176.9 182.9 188.3 193.2 197.8 202.0 205.9 209.5 213.0 216.3 219.4 222.4 225.2 227.9 2 3°-5 233-o 235-4 237-7 240.0 242.2 244-3 246.3 248.3 250.2 252.1 253-9 255-7 257-5 259.2 260.8 262.5 264.0 265.6 267.1 268.6 270.1 271.5 272.9 274-3 275.6 277.0 278.3 279.6 334-23 1 73- 2 3 117.98 89.80 72.50 61.10 53.00 46.60 41.82 37.80 34.61 31.90 29.58 27.59 25.87 24-33 22.98 21.78 20.70 19.72 18.84 18.03 '7-3° 16.62 15.99 15.42 14.88 14.38 J3-9 1 13.48 13-07 12.68 12.32 11.98 11.66 11.36 11.07 10.79 J o-53 10.29 10.05 9-83 9.61 9.41 9.21 9.02 8.84 8.67 8.50 0.0030 .0058 .0085 .0111 •0137 0.0163 .0189 .0214 .0239 .0264 0.0289 .0314 -0338 .0362 .0387 0.0411 •°435 •0459 .0483 .0507 0.0531 •°554 .0578 .0602 .0625 0.0649 .0672 .0695 .0619 •0742 0.0765 .0788 .0811 •°^5 .0858 0.0881 .0903 .0926 .0949 .0972 0.0995 .1018 .1040 .1063 .1086 0.1108 .1131 •"53 .1176 70.1 94-4 109.9 121.4 i3°7 138.6 145.4 I5I-5 156.9 161.9 166.5 170.7 174-7 178.4 181.9 185.2 188.4 191-4 194-3 197.0 199.7 202.2 204.7 207.0 209.3 211.5 2137 2157 217.8 219.7 221.6 223.5 225.3 227.1 228.8 230.5 232.2 233-8 235-4 236.9 238-5 239-9 241.4 242.9 244-3 245.6 247.0 248.3 249.7 980.6 961.4 949.2 940.2 932.8 926.7 921.3 916.5 912.2 908.3 904.8 901.5 898.4 895.4 892.7 890.1 887.6 ff" 883.1 880.9 878.8 876.8 874.9 873-1 871-3 869.6 867.9 866.3 864.7 863.2 861.7 860.3 858.9 |57-S 856.1 854.8 853-5 852.3 851-0 848.7 847.5 846.4 845.2 844.1 843.1 842.0 841.0 840.0 62.34 64.62 66.58 67.06 67.89 68.58 69.18 69.71 70.18 70.61 70.99 71-34 71.68 72.00 72.29 72-57 72.82 73-°7 73-3o 73-53 73-74 73-94 74-13 74-3 2 74-51 74.69 74-85 75-oi 75-17 75-33 75-47 75-6i 75-76 75.89 76.02 76.16 76.28 76.40 76.52 76.63 7675 76.86 76.97 77-07 77.18 77.29 77-39 77-49 77-58 1043. 1026. ion. 1007. 1001. 995.2 990.5 986.2 982.4 979.0 975-8 972.8 970.0 967.4 965.0 962.7 960.4 958-3 956-3 954-4 952.6 950.8 949.1 947-4 945-8 944-3 942.8 941-3 939-9 938-5 937-2 935-9 934-6 933-4 932.1 931.0 929.8 928.7 927.6 926.5 925.4 924.4 9233 922.3 921-3 920.4 919.4 918.5 9I7-5 i"3-o 1 1 20.4 1 127.0 1 1 28.6 1131.4 "33-8 "35-9 "377 "39-4 1 140.9 1142.3 "43-5 1 144.7 1 145.9 1 146.9 1 147.9 1 148.9 1 1 49.8 1150.6 1151.4 1 1 52.2 1 1 53.0 "53-7 1 1 54.4 1155.1 1 1 55.8 1 1 56.4 1157.1 " 577 1 158.3 1 1 58.8 1 1 59.4 1 1 59.9 1 160.5 1161.0 1161.5 1 162.0 1 162.5 1162.9 1 163.4 1163.9 1 164.3 1 164.7 1165.2 1 165.6 1 166.0 1 1 66.4 1 166.8 1167.2 Smithsonian Tables. 238 Table 249. PROPERTIES OF STEAM. British Measure. Smithsonian Tables. 239 Table 249. PROPERTIES OF STEAM. British Measure. j5 ^ a 3 s J" 3 T3 is! a mj3 C u ~ .5 £ rt 01 «-~ n a c eg a coo -S u o c Ee, p. *» &-o — CU" ~- 0,-. _ V ft— rtj^ w u as HI 4) O.O - «t! in £ ri P 3 3 Is- t B I'S.a g-° £$4 Mo a ■sip ternal at per steam T. U. External heat per of steam B. T. U. Hal lat at per steam T. U. *** (Sag - Jr 2 o* Pi rt H-S >as fe- 3 O E> u ft MM HfloB E-i^-SB Ei 8,5 100 14400 6.803 327.6 4356 0.2295 298.9 802.0 80.95 882.9 1181.8 IOI 14544 .871 328-3 .316 ■2317 299.7 801.4 81.00 882.4 H82.I 102 14688 •939 329.0 .276 •2338 3004 800.8 81.05 881.9 1182.3 I03 14832 7.007 3297 •237 .2360 301.1 800.3 81.10 881.4 1182.5 104 14976 .075 33°-4 .199 .2381 301.9 799-7 81.14 880.8 1 182.7 105 15120 7-143 33i-i 4.161 0.2403 302.6 799.2 81.18 880.3 1 182.9 106 15264 .211 331-8 !o88 •2424 303-3 798.6 81.23 879.8 1 183.I 107 15408 .279 332-5 .2446 304.0 798.1 81.27 879-3 1 183.4 108 IS552 •347 333-2 •053 .2467 3°4-7 797-5 81.31 878.8 1183.6 109 15696 .415 333-8 .018 .2489 305-4 797.0 81.36 878.3 H83.8 110 15840 7483 334-5 3-984 0.2510 306.1 796-5 8141 877.9 1 184.O in 15984 ■551 335-2 .950 ■2531 306.8 795-9 81.45 8774 1 184.2 112 16128 .619 335-8 .917 •2553 307-5 7954 81.50 876.9 1 184.4 "3 16272 .687 336-5 .885 •2574 3 °io 794-9 81.54 876.4 1 184.6 114 16416 •757 337-2 •853 .2596 308.8 7944 8158 875.9 1184.8 115 16560 7823 337-8 3.821 0.2617 309-5 793-8 81.62 875-5 1 185.O 116 16704 .891 338-5 .790 .2638 310.2 793-3 81.66 875.0 1 185.2 117 16848 •959 339-1 .760 .2660 310.8 792.8 81.70 874-5 1 185.4 118 16992 8.027 339-7 ■73° .2681 3"-5 792-3 81.74 874.1 1185.6 119 1 7136 .095 340-4 .700 .2702 312.1 791.8 81.78 873.6 1 185.7 120 17280 8.163 341.0 3- 6 7i 0.2724 312.8 79J-3 81.82 873.2 1185.9 121 17424 .231 341.6 •643 •2745 3134 790.8 81.86 872.7 1 186. 1 122 17568 .299 342.2 .615 .2766 3i4-i 790-3 81.90 872.2 1 186.3 123 17712 •3°7 342.8 •5f7 •2787 3 r 4-7 789.9 81.94 871.8 1 186.5 124 17856 •435 343-5 .560 .2809 3I5-3 789-4 81.98 8714 1 186.7 125 18000 8.503 344-1 3-534 0.2830 316.0 788.9 82.02 870.9 1 186.9 126 18144 •57i 344-7 •5°7 .2851 316.6 7884 82.06 870.5 1 187.I 127 18288 •639 345-3 .481 .2872 3*7-2 787.9 82.09 870.0 1 187.2 128 18432 .708 345-9 456 •2893 317-8 787-5 82.13 869.6 1187.4 129 18576 .776 346-5 •43' .2915 318.4 787.0 •82.17 869.2 1 187.6 130 18720 8.844 347-1 3.406 0.2936 319.0 786.5 82.21 868.7 1 187.8 '3' 18864 .912 347-6 .382 ■2957 3*9-7 786.1 82.25 82.28 868.3 867.9 1188.0 132 19008 .980 348.2 •358 .2978 320.3 785.6 II88.I '33 191 52 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 82.35 867.0 1188.5 135 19440 9.184 349-9 3-287 0.3042 322.1 784.2 82.38 866.6 1 188.7 136 19584 .252 35°-5 .265 •3063 322.6 783.8 82.42 866.2 1 188.8 137 19728 19872 20016 ' 3 £ 35i-i •424 .3084 323-2 783.3 82.45 865.8 1 189.O 138 .388 351-6 .220 •3'°5 323-8 782.9 82.49 865.4 1 189.2 139 456 352-2 .199 .3126 324-4 7824 82.52 865.0 1 189.4 140 20160 9.524 352-8 3-177 °-3'47 325-0 782.0 82.56 864.6 1 189.5 1 189.7 1189.9 1 1 90.O 1 190.2 141 20304 •|^ 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 •"5 ■321 1 326.7 780.7 82.66 863.4 144 20736 .796 355-° .094 •3232 327.2 780.3 82.69 863.0 145 20880 9.864 355-5 3-°74 o-3253 327.8 779.8 82.72 862.6 1 190.4 H90.5 II 90.7 1 190.9 1191.0 146 21024 •93 2 356.0 ■054 •3274 328.4 779-4 82.75 862.2 147 21168 10.000 356.6 •035 ■3295 328.9 779.0 82.79 861.8 148 21312 21456 .068 357-1 .016 •33i6 3295 778.6 82.82 861.4 149 .136 357-6 •997 •3337 330-o 778.1 82.86 861.0 Smithsonian Tables. 24O Table 249. PROPERTIES OF STEAM. British Measure. .3. aj o oi B-.S 111 150 'Si 152 153 154 155 156 I5 Z 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 .sss gl a 9* a 3 (Sal Ph « 21600 21744 21888 22032 22176 2232O 22464 22608 22752 22896 2304O 23184 23328 23472 23616 23760 23904 24048 24192 2433° 24480 24624 24768 24912 25056 25200 25344 25488 25632 25776 25920 26064 26208 26352 26496 26640 26784 26928 27072 27216 27360 27504 27648 27792 27936 28080 28224 28368 28512 28656 eh 10.204 .272 •340 .408 .476 10.544 .612 .680 ■748 .816 10.884 •9S2 11.020 .088 ■157 11.225 •293 .361 .429 •497 11.565 •633 .701 .769 •837 11.905 •973 12.041 .109 .177 12.245 >3 o 3 .381 •449 •S'7 12.585 •653 ■ 7 f r ■789 .857 12.925 ■993 13.061 .129 .197 I3- 26 S •333 .401 .469 •537 1 if 358.2 358-7 359-2 359-7 360.2 360.7 361.3 362.3 362.8 363-3 363-8 364.3 364.8 365-3 3 ^ 7 366.2 366.7 367.2 367-7 368.2 368.6 3 ^i 369.6 370.0 370-5 371.0 371-4 37J-9 372-4 372.8 373-3 373-7 374-2 374-6 375-' 375-5 376.0 376-4 376.8 377-3 377-7 378.2 378.6 379-° 3794 379-9 380.3 380.7 381-1 MO £ te 3 o !> u ft 2.978 .960 .941 •923 .906 .871 •854 •837 .820 2.803 .787 .771 ■755 •739 2.724 .708 .693 .678 .663 2.649 •634 .620 .606 .592 2.578 ■564 •55° •537 5 2 4 2.510 497 485 472 459 447 434 422 410 398 386 374 362 35i 339 328 3i7 306 295 .284 2 a °i . v 1- W acq 0-3358 •3379 .3400 •342i •3442 0.3462 •3483 ■3504 ■35 2 5 •3546 0-3567 •3588 .3609 ■3630 .3650 0.3671 •3692 .3713 •3734 •3754 0-3775 ■3796 ■3817 .3838 .3858 0.3879 .3900 •392i •3942 .3962 0.3983 .4004 .4025 .4046 .4066 0.4087 .4108 .4129 .4150 .4170 0.4191 .4212 4233 .4254 4275 0.4296 .4316 ■4337 4358 4379 «T3 a a 4) 3 Sft-S a "is e°-s. a ^—~ HH.fi OH 33°-6 33i-i 33'-6 332-2 332-7 333-2 333-8 334-3 334-8 335-3 335-9 336-4 336-9 3374 337-9 338.4 338.9 339-4 339-9 340-4 340-9 341-4 341-9 3424 342-9 343-4 343-9 344-3 344-8 345-3 345-8 346-3 346-7 347-2 347-7 348.1 348.6 349- 1 349-5 350.0 350-4 350-9 35 I "3 351-8 352.2 352-7 353-1 353-6 354-0 354-4 S 3 ri o a 1s§s K 8 ™ . 777-7 777-3 776.9 776.5 776.1 775-7 775-3 774-9 774-5 774-1 773-7 773-3 772.9 772.5 772.1 771-7 771-3 771.0 770.6 770.2 769.8 769.4 769.1 768.7 768.3 767.9 767.6 767.2 766.8 766.5 766.1 765-8 7654 765.0 764.7 764-3 764.0 763.6 763-3 762.9 762.6 762.2 ^i 761.6 761.2 760.9 760.5 760.2 759-9 759-5 82.89 82.92 82.95 82.98 83.01 83.04 83-07 83.10 8313 83.16 83-19 83.22 83-25 83.28 83-31 83-34 83-37 83-39 83.42 83-45 83.48 83-51 83-54 83-56 83-59 83.62 83.64 83.67 83.70 83-73 8.3-75 83-77 83.80 83-83 83.86 83.88 83.90 83.92 83-95 83-97 83-99 84.02 84.04 84.06 84.08 84.10 84.13 84.16 84.19 84.21 IfcfjD 860.6 860.2 859-9 859-5 859.I 858.7 858.3 858.0 857.6 857.2 856.9 856.5 856.I 855.8 855.4 855.I 854.7 854-3 854.0 853.6 853-3 852.Q 852.6 852.2 851.9 851.6 851.2 850.9 850.5 850.2 849.9 849-5 849.2 848.9 848.5 847-9 847.5 847.2 846.9 846.6 846.3 845-9 845-6 845-3 845.O 844.7 844-4 844.O 843-7 u E ftaj . ts»t> •a -0 • 1191.2 1191.3 1191.5 1191.7 1191.8 1 192.O 1192.1 1192.3 1 192.4 1 192.6 1 192.7 1 192.9 1 193.0 1 193.2 "93-3 "93-5 1 193.6 1 193.8 1 193-9 1194.1 1 194.2 1 1 94.4 1194.5 1 194.7 1 194.8 1 194.9 1195.1 1 195.2 "954 "95-5 1 195.6 1 195.8 1 195.9 1 196. 1 1 196.2 1 196.3 1 196.0 1 196.7 1 196.9 1 197.0 1197-1 "97-3 1 197.4 1 197.5 1 197.7 1 197.8 1197.9 1198.1 1 198.2 Smithsonian Tables. 241 Table 249. PROPERTIES OF STEAM. British Measure. c [in U 0. _ *" s .s S a b a at 3 3 8,8 S 3 rt a -a a *. 3 c f c at per I steam U. p ft a l-s's >Off Ph P.U V B.,2 W 5 (4 K 3 fc3 Cm !§■§ f> 0.0 *• ° en £38. Ea Su C l>u- ' M^a oh £ o. w v +. Ski 8 " . H 0,5 200 28800 13605 381.6 2.273 0.4399 354-9 759.2 84.23 843-4 1 198.3 201 28944 i3- 6 73 382.0 .262 .4420 355-3 355-8 758-9 84.26 843.I 1 198.4 202 29088 13-742 382.4 .252 .4441 758-5 84.28 842.8 1 198.6 203 29232 13.810 382.8 .241 .4461 356.2 758.2 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 13946 383-7 2.221 0.4503 357-1 757-5 84-35 841.9 1 1 99.O 206 29664 14.014 384.1 .211 •4523 357-5 757-2 84-37 841.6 1 199. 1 207 29808 14.082 384-5 .201 •4544 357-9 756-9 84.40 841.3 1 199.2 208 29952 14.150 3849 .191 .4564 35f-3 756.6 84.42 84I.O "99-3 209 30096 14.218 385-3 .l8l •4585 358.8 756.2 84.44 84O.7 1 199.4 210 30240 14.386 3|S-7 2.I7I 0.4605 359-2 755? 84.46 840.4 1 1 99.6 211 3 384 14.454 386.1 .162 .4620 359-6 755-6 84.48 84O.I 1 199.7 212 30528 14.522 386.5 .152 .4646 360.0 755-3 84.51 839.8 1 1 99.8 213 30672 14.590 386.9 •143 .4666 360.4 755-0 84.53 839-5 1 199.9 214 30816 14.658 387-3 •134 .4687 360.9 754-7 84-55 839.2 1200.1 215 30960 14.726 3 oZ 7 2.124 0.4707 36i-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 14.862 388.5 .106 .4748 362.1 753-7 84.62 838.3 1200.4 218 3 r 39 2 M-93° 388.9 .097 •4768 362-5 753-4 84.64 838.O 1200.5 219 3IS36 14.998 389-3 .088 .4788 362.9 753-t 84.66 8377 1200.7 Smithsonian Tables. 242 Table 250. RATIO OF THE ELECTROSTATIC TO THE ELECTROMACNETIC UNIT OF ELECTRICITY (») IN RELATION TO THE VELOCITY OF LICHT. Ratio of electrical units. Reference. Date of determina- tion. V in cms. per sec* Determined by — Publication. Year. 1856 3.107 X io 10 Weber & Kohlrausch . Pogg. Ann. . 1856 1868 2.842 X low Maxwell Phil. Trans. . 1868 i 1869 2.808 X IO 10 W. Thomson & K ng . B. A. Report . 1869 1872 2.896 X IO 10 McKichan . Phil. Trans. . 1872 1879 2.96b X ioi' Ayrton & Perry . Jour. Soc. Tel. Eng. 1879 l8 7 9 2.968 X 10 10 Hocken B. A. Report . 1879 1880 2.953 X io 10 Shida . Phil. Mag. 1880 1881 2.99 XloMf Stoletow Soc. de Phys. . 1881 1881 3.019 X io 10 Klemencic . Wien. Ber. 1884 1882 2.923 X io 10 Exner . Wien. Ber. 1882 1883 2.963 X io 1 " J. J. Thomson Phil. Trans. . 1883 1888 3.009 X io 1 " Himstedt Wied. Ann. 35 1888 1889 2.981 X io 10 Rowland Phil. Mag. 1889 1889 3.000 X io 10 Rosa " " . . 1889 1889 3.004 X io 10 W. Thomson Phil. Mag. 1889 1890 2.995 X io w J. J. Thomson & Searle Phil. Trans. . 1890 * The results in this column correspond to a value of the B. A. ohm = .98664 X io° cms. per sec. If we neglect the first four determinations, and also that of Exner and Shida, because of their large deviation from the mean, the remaining determinations give a mean value of 2.9889 -f- .0137, a value which practically agrees with the best deter- minations of the velocity of light. (Cf. Table 181.) t Given as between 2.98 X io 10 and 3.00 X io 10 . Smithsonian Tables. 243 Table 251. DIELECTRIC STRENGTH. Dillerence ol Electric Potential required to produce a Spark In Air. (a) Medium, Air. Electrode Terminals, Flat Plates. Difference of potential in volts required to produce a spark according to — Spark length in centimetres. W. Thomson. 1 De la Rue. 2 MacFarlane. 8 Bailie.* Freyberg. 6 O.O I 790 500 - - - O.02 1340 970 - — — O.04 1840 1900 - — — O.07 2940 3170 - — - 0.10 40IO 4330 3507 4401 4344 0.14 5300 5740 - - — 0.20 7620 57 T S 7818 7653 7539 O.30 - 10400 10603 1067 1 O.40 - - 9879 I343I 13665 O.50 - - 11925 16341 16293 0.6b - - 13956 19146 19059 O.80 - - 18006 25458 24465 I. OO - - 22044 31647 28800 1 " Reprint of Papers on Elect, and Mag." p. 252. * " Proa R. Soc." vol. 36, p. 151. » " Phil. Mag." vol. 10, 1880. * " Ann. de Chim. etde Phys." vol. 25, 1882. c " Wied. Ann." vol. 38, 1889. (b) Medium, Air. Electrode Terminals, Balls of Diameter d in Centimetres. Experiments of Freyberg. Spark length in d = (points). d = 0.50 d — 1.0 d = 2.0 d zz 4.0 d = 6.0 centimetres. O.I 3720 505O 4660 4560 - 4530 0.2 4700 860O 9500 8700 8400 7900 0-3 5300 IIIOO 1 1 700 11600 1 1200 10500 12800 0.4 6000 13500 I4000 I4400 14200 0.6 6900 16600 19300 19500 20IOO 19200 0.8 8100 184OO 23200 24600 25800 26000 1.0 8600 I95OO 25800 29000 29900 31600 2.0 IOIOO 24600 35400 - - - 50 13100 307OO — — - - From the above table it appears, as remarked by Freyberg, that for each length of spark there is a par- ticular size of ball which requires the greatest difference of potential to produce the spark. (0) Comparison of Results of Determinations, the Terminals being Balls. Spark length in cms. Difference of potential required to produce a spark in air according to — Bailie. Bichat and Blondlot. 1 Paschen. Freyberg. Paschen. Freyberg. Quincke. 2 Bailie. Freyberg. Balls 1 centimetre diameter. Balls 2 cms. diameter. Balls 6 cms. diam. .1 459° 4200 4860 4660 4830 4560 4440 4440 4530 7860 .2 8040 813O 8430 9500 8340 8700 7920 7680 •3 11190 I0860 1 1670 H670 1 1670 "550 III90 10830 10470 •4 13650 I4I3O 14830 13980 14820 14400 14010 ^OO 12750 •S 1 6410 l6800 17760 16800 18030 17040 16920 16530 16410 .6 19560 1935° 20460 19260 20820 19470 19980 19560 19200 ■7 21690 2IO30 22640 20970 23670 22530 24630 22590 22620 22590 .8 23280 2319O 24780 23220 - 25770 26400 26010 •9 24030 24540 2580O - 251 IO - 27240 - 29220 28770 1.0 24930 ~ 25770 ~ 29040 - 33870 31620 » " Electricien," Aug. 1886. * "Wied. Ann." vol. 19, 1K3. 8miths< )NI« N Tables 244 Tables 252, 253. DIELECTRIC STRENGTH. TABLE 262.-EHeot of Pressure ol the Gas on the Lleleotrlo Strength* Length of spark is indicated by I in centimetres. The pressure is in centimetres of mercury at o° C. Pressure. 15 20 2 5 3° 35 40 45 5° 6o 65 70 75 Hydrogen. 510 729 945 logs 1242 1584 1866 2169 2475 2748 3051 3339 3606 2834 4107 4476 473 1 4914 /=^o-4 606 1017 1323 1572 1806 2376 2937 3444 3957 4407 4863 5334 5829 0294 6747 7197 7629 8031 fco.6 1437 1839 2I?2 2463 333° 4020 4668 5331 5997 6681 7347 7971 8583 9222 9867 10476 1 1040 Air. 819 1 140 M5S 1740 2004 2664 3294 3816 4347 4845 5349 m 671 1 7134 8016 8487 /— 0.4 1725 2229 2721 3186 4212 5205 6108 7020 7980 8853 9639 10431 1 1 259 12084 12885 13710 14523 /=o.6 1536 2289 3012 3684 4272 5736 7074 8346 9570 I0797 12009 13224 I4361 15441 16548 17688 18804 I9896 Carbon dioxide. /l=0.2 1125 1431 "755 2070 2355 2991 3705 4248 4707 5163 5772 6222 6489 6789 7197 7605 8001 1446 1971 2484 2913 3288 4227 5235 6120 6921 7737 8543 9303 10038 10650 "397 12114 1 281 6 13506 /=o.6 1650 2373 3105 38l3 4278 680I 8004 9H7 IO293 "397 12483 13557 1 4610 15702 16740 17727 18705 Paschen deduces from the above, and also shows by separate experiments, that if the product of the pressure of the gas and the length of spark be kept constant the difference of potential required to produce the spark also remains constant. In the following short table / is length of spark, P pressure, and V difference of potential, the unit being the same as above. The table illustrates the potential difference required to produce a spark for different values of the product l.P. IP. V for Air. V for CO. fforH V for Air. VlarCOi 0.2 0.4 0.6 1.0 2.0 4.0 456 567 660 846 I427 1884 669 837 996 I326 2019 3216 873 mo 1281 1599 2271 3468 6.0 1 0.0 20.0 30.0 45.0 2481 3507 5835 8004 11013 4251 6162 10392 13448 4443 6198 IOOII 13527 18705 TABLE 253. — Dielectric Strength (or Difference of Potential per Centimetre of Spark Length) of Different Substances, In Kilo Volts, t Substance. ■u "a ■3s 3" Substance. ■32 0" Substance. 5" Air (thickness 5 mm.) Carbon dioxide " . . Coal gas " • • Hydrogen " ■ • Oxygen " • • 23.8 22.7 15.I 22.2 22.3 Beeswaxed paper . Paraffined paper Paraffin (solid) . . 540. 360. 130. Kerosene oil . . . Oil of turpentine . Olive oil .... Paraffin oil . . . Paraffin (melted) . 5°- 94. 82. 87. 56. Smithsonian Tables. * Paschen. t MacFarlane and Pierce, " Phys. Rev." vol. i, p. 165, 1893. 245 Table 254. COMPOSITION AND ELECTROMOTIVE FORCE OF BATTERY CELLS. The electromotive forces 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 Batteries. Name of cell. Negative pole. Solution. Positive pole. Solution. W.S Eunsen ■ Chromate . Daniell* Amalgamated zinc Grove Marie Davy Partz . ( i part H 2 S0 4 to I j 12 parts H 2 . ) fi2partsK 2 Cr207' to 25 parts of H2SO4 and 100 parts H2O . . ( 1 part H 2 S0 4 to 1 ( 12 parts H 2 . J ( I part H2SO4 to I ( 4 parts H a O . J ( 1 part H2SO4 to I I 12 parts H 2 . ) ( 5% solution of I 1 ZnS04 + 6H 2 0f ( 1 part NaCl to 1 ( 4 parts H 2 . ) ( 1 part H2SO4 to ) ( 12 parts H 2 . J Solution of ZnSC>4 ( H2SO4 solution, ) ( density 1.136 . J 2SO4 s density Carbon Copper Platinum Fuming HjNOg HNOa, density 1.38 ( 1 part H2SO4 to 1 ( 12 parts H 2 . J (12 parts K2Cr 2 7 1 ( to 100 parts H 2 ) ( Saturated solution ) \ of CuS0 4 +sH 2 J H2SO4 solution, ) 1.136 • f I ( density {H 2 S04 solution, ) density 1.14 . ) ( H2SO4 solution, ) ( density 1.06 . ) NaCl solution . . ( 1 part H 2 S0 4 to 1 ( 12 parts H 2 ) Solution of MgSC>4 H2SO4 solution, I 1.06 .J Carbon Fuming HNO s . . HNOs, density 1.33 Concentrated HNO B HNO3, density 1.33 HNO s , density 1.19 u u " density 1.33 ( Paste of protosul- ) < phate of mercury > ( and water . . . ) Solution of K 2 Cr 2 7 1.94 1.86 2.00 2.03 1.06 1.09 1.08 1.05 '•93 1.66 '•93 1.79 171 1.66 1. 61 1.88 1.50 2.06 * The Minotto or Sawdust, the Meidi n? er the Callaud, and the Lockwood cells are modifications of the Daniell, and hence have about the same electromotive force. *»«mBu, Smithsonian Tables. 246 Table 254. COMPOSITION AND ELECTROMOTIVE FORCE OF BATTERY CELLS. Name of cell. Negative pole. Solution. Positive pole. (b) Single Fluid Batteries. E. M. F. in volts. Leclanche . . . Chaperon . . . Edison-Lelande . Chloride of silver Law Dry cell (Gassner) Poggendorff . . J. Regnault. . . Volta couple . . Amal. zinc Zinc Amal. zinc Zinc ( Solution of sal-ammo- i ( niac I ( Solution of caustic potash [ 23 % solution of sal- | ammoniac . . . 15 % ript.ZnO,ipt.NH 4 Cl, I 3 pts. plaster of paris, I 2pts.ZnCl 2 ,andwater [ to make a paste . . i Solution of chromate ! of potash . . . . [ 12 parts K 2 Cr 2 07 -+- 25 parts H2SO4 -j- 100 parts H 2 <3 . . : 1 part H 2 S0 4 + ; 12 parts H 2 -f- 1 part CaSOi . . H 2 i Carbon surround- ed by powdered carbon and perox- ide of manganese Copper and CuO ( Silver surrounded 1 ( by silver chloride j Carbon .... Cadmium . . . Copper .... 1.46 0.98 0.70 1.02 i-37 i-3 1.08 2.01 o-34 0.98 (c) Standard Cells. Kelvin, Gravity, ) Daniell . . . J Clark standard Bailie & Ferry Gouy ... Amal. zinc ZnSC>4 solution, den- 1 sity 1.40 . . . . J Mercurous sulphate in | paste with saturated I solution of neutral [ ZnS0 4 J >' Zinc chloride, density I : 1-157 J Oxide of mercury in a J 10 % sol. of ZnSC-4 > (paste) ) Electrolytic cop- per in CuSO^ sol. density 1.10 . . Mercury. . . . ' Lead surrounded by powdered ' PbCl 2 . . . . Mercury . ', 1.072 [1 [ — .00016 ! e-15)] 1 1-434 [1 I — .00077 ! e-15)] 0.50 tem- perature coeffic't about .00011 I-387 [1 — .0002 C-12)] Lodge's standard cell and Fleming's standard cell are, like the Kelvin cell above, modifications of the Dan- iell zinc-zinc sulphate, copper-copper sulphate cell. (d) Secondary Cells. Faure-Sellon- (Volckmar) Regnier (1) . " (2) • Main . . . Lead Copper . Amal. zinc Amal. zinc ( H 2 S0 4 solution of 1 ( density 1.1 . . . ) CuSC-4 -H H 2 S0 4 • - ZnS0 4 solution . . . H 2 S0 4 density ab't 1.1 Pb0 2 in H 2 S04 2.2* ; 1.68 to [ 0.85, av- erage 1.3. 2.36 2.50 * F. Streintz gives the following value of the temperature variation ^ at different degrees of charge : — E. M. F. dE/dtX 10° E. M. F. dE/MXio* E. M. F. dEfdtXio" 1.9223 1.9S28 140 228 z.0031 2.0084 2.0105 335 28s 255 2.0779 2.2070 130 73 Smithsonian Tables. 247 Table 255. THERMOELECTRIC POWER. The thermoelectric power of a circuit of two metals at mean temperature / is the electromotive force in the circuit for one degree difference of temperature between the junctions. It is expressed by dE / ' di = A + Bt t when dE / dt = o, t = — A / B, and this the neutral point or temperature at which the thermoelectric power vanishes. The ratio of the specific heat of electricity to the absolute value of the temperature t is expressed by — B for any one metal when the other metal is lead. The thermoelectric power of different couples may be inferred from the table, as it is the difference of the tabulated values with respect to lead, which is here taken as zero. The table has been compiled from the results of Becquerel, Matthieson, and Tait. In reducing the results the electromotive forces of the Grove's and the Daniell cells have been taken as 1.95 and 1.07 volts respectively. Thermoelectric power Neutral Substance. A B X io-> at mean temp, of junctions (microvolts). point A Author- ity. 20° C. 50° c. B Aluminium .... O.76 — °-39 0.68 0.56 J 95 T Antimony, comm'l pressed wire - —6.0 - M " axial — — — 22.6 — — tt " equatorial - - — 26.4 - - tt " ordinary . - - — 17.0 - - B Argentan . II.94 5.06 12.95 14.47 —236 T tt — — — 12.7 — B Arsenic — '3-56 _ M Bismuth, comm'l pressed wire . - - 97.0 _ _ u ! " pure " " . - 89.0 - - it " crystal, axial - - 65.0 - - u ! " equatorial - - 45.0 - - " 1 " commercial — — 39-9 _ B Cadmium . —2.63 —4.24 -3-48 —4-75 —62 T " fused . — — — — 2.45 _ B Cobalt - _ 22. _ M Copper —1-34 —O.94 —1.52 — 1.81 —M3 T " commercial — 0.10 _ M " galvanoplasti C - - -3-8 _ a Gold . - - — 1.2 _ _ " "... —2.80 — 1 .01 —3° —3-30 —277 T Iron . —17.15 4.82 — 16.2 —14.74 356 It " pianoforte wire — — — '7-5 M " commercial - - — 12.10 - B " — — — — 9.10 — " Lead . — 0.00 0.00 0.00 _ „ Magnesium — 2.22 0.94 —2.03 —1.75 236 T Mercury - - 0.413 M Nickel '. '. (— 18 to I75 c ) 21.8 5.06 22.8 3-30 15-5° 2 4-33 —438 B tl T " (25o°-3oo°) 83-57 —23.84 — tt " (above 340 ) 3-°4 5.06 _ _ _ It Palladium . 6.18 3-55 6.9 7.96 —174 a Phosphorus (red) _ : — 29.9 6.9 B M Platinum . - _ — 0.9 _ U (hardened) — 2-S7 0.74 — 2.42 — 2.20 347 T " (malleable) 0.60 1.09 8.82 1.15 —55 tt " wire .... " another specimen _ _ - —0.94 2.14 B Platinum-iridium alloys : 8 5 %Pt + i 5 %Ir . . —7.90 — 0.62 —8.03 — 8.21 — 1274 T 90 % Pt + 10 % Ir —5.90 '•33 —S-63 —5- 2 3 444 (( 95%Pt+ S%Ir -6.15 —0.55 —6.26 — 6.42 — 1 1 18 « Selenium . —807. M Silver — 2.12 —1.47 —2.41 —2.86 — 144 T " (pure hard) - —3.00 _ M " wire - - —2.18 _ B Steel .... Tellurium . — 11.27 3-25 — 10.62 — 502. —9.65 347 T M Tin (commercial) - - _ —429-3 — °-33 __ B (I - — — 0.1 — M Zinc '. '. " pure pressed 043 —2^8 o-33 0.16 78 T —2.32 —2.79 —3-7 —3-51 -98 tt M B ~ Ed. Becquerel, " Ann. de Chim. t de Phys." [4] vol. 8. MzzMa tthieson, " P< >gg > . Ann." v ming Jenkii ol. 103, T = Tait, " Trans. R. S. E." vol. 27, reduced by 1 Vlascart. r educed by Fl Smithsonian Tables, 248 Table 256. THERMOELECTRIC POWER OF ALLOYS. The thermoelectric powers of a number o£ alloys are given in this table, the authority being Ed. Becquerel. They are relative to lead, and {or a mean temperature of 50° C. In reducing the results from copper as a reference metal, the thermoelectric power of lead to copper was taken as — 1.9. Substance. Thermo- electric power in microvolts. Substance. Relative quantity. Thermo- electric power in microvolts. Antimony Cadmium Antimony Cadmium Zinc . Antimony Cadmium Bismuth Antimony Zinc . Antimony Zinc . Bismuth Antimony Cadmium Lead . Zinc . Antimony Cadmium Zinc . Tin . Antimony Zinc . Tin . Antimony Cadmium Zinc . Antimony Tellurium 227 146 m 95 8.1 76 46 43 35 Antimony . Bismuth Antimony . Iron . Antimony . Magnesium Antimony . Lead . Bismuth Bismuth Antimony . Bismuth Antimony . Bismuth Antimony . Bismuth Antimony . Bismuth Antimony . Bismuth Tin . Bismuth Selenium . Bismuth Zinc . Bismuth Arsenic Bismuth Bismuth sulphide 'A A A SI :} A A "A ■:t A -A "A "A A 2.5 1.4 —0.4 -43-8 —334 -51.4 —63.2 —68.2 —66.9 6.0 —24.5 —31-1 — 46.0 68.1 Table 257. NEUTRAL POINTS WITH LEAD.* Substance. Temp. C. Substance. Temp. C. Bismuth . —580° Zinc . . . -95° Nickel —424 Cadmium . —59 Gold . . — 276 Platinum . -56 Argentan -238 Tin . . • 75 Cobalt . —228 Rhodium . 132 Palladium —172 Ruthenium 136 Antimony -156 Aluminium 212 Silver . . —144 Magnesium 239 Copper . —132 Iron . . . 356 Table 258. SPECIFIC HEATS OF ELECTRICITY.t The numbers are the coefficients B in the equation 4E. = A + Bl, and have to be multiplied by the absolute temperature T to give the specific heat of electricity. (See also Table 255.) Metal. Sp.ht. of el Alumin- ium . . Antimony Argentan Bismuth . Cadmium Cobalt Copper Gold . Iron . Iridium Lead . .00039 .02221 -.00507 -.01073 .00425 -.01141 .00094 .00101 -.00481 .00000 .00000 Metal. Sp. ht. of el. Magnesium Nickel : To 175 C. 25o°-3io° Above 340 c Platinum (soft) Palladium . Rhodium Rubidium , Silver . . Tin . . Zinc ■ ■ — .00094 — .00507 .00219 — .00351 — .00109 —■°°355 —.00113 — .00206 .00055 .00235 t Slculatedlro'm Stable given by Tait by assuming the electromotive force of a Grove's cell = ,. 95 volts. Smithsonian Tables. Table 259. THERMOELECTRIC POWER OF METALS AND SOLUTIONS.* Thermoelectric power of circuits, the two parts of which are.either a metal and a solution of a salt ;°* *at m^l I »r two solutions of salts. The concentration of the solution was such that in 1000 parts of the solution there was one half gramme equivalent of the crystallized salt. The circuit is indicated symbolically ; for example, Cu and CuS0 4 indicates that the circuit was partly copper and partly a solution of copper sulphate. Substances forming circuit. trie power in Insoluble salts mixed with a solution of microvolts. the corresponding zinc or cadmium salts for the purpose of acting as a conductor. Cu and CUSO4 . 754 The other part of the circuit was the metal Zn and ZnSC>4 760 of the insoluble salts. The results are com- Cu and CuAc (acetate Pb and PbAc . ) 660 176 plex and of doubtful value. Zn and ZnAc Cd and CdAc . Zn and ZnC^ Cd and CdCl 2 . 693 562 562 Substances forming circuit. Thermoelectric power in microvolts. Zn and ZnBr2 Zn and Znl2 632 602 Cd and Cdl2 594 Ag and AgCl in ZnCl2 143 Ag and AgCl in CdCk 310 CuSC>4 and ZnSC>4 40 Ag and AgBr in ZnBr 2 3 2 7 CuAc and ZnAc . 8 Ag and AgBr in CdBr2 461 ZnAc and CdAc . Ag and Agl in Znl 2 . 414 CuAc and CdAc. Ag and Agl in Cdl2 . unsuccessful PbAc and ZnAc . 73 Hg and Hg 2 Cl2 in ZnCl2 680 PbAc and CdAc . 54 Hg and Hg 2 Cl 2 in CdCl 2 673 PbAc and CuAc . '33 Hg and Hg2Br2 in ZnBr 2 650 ZnCl2 and CdCl2 9 Hg and Hg 2 Br 2 in CdBr 2 815 ZnBr2 and CdBr2 15 Hg and Hg 2 l2 in Znl 3 . 948 Znl2 and Cdl2 82 Hg and Hg 2 l2 in Cdl 2 891 Tables 260, 261. PELTIER EFFECT. TABLE 260. — Jahn's Experiments. t TABLE 261. — Lo Ronx's Experiments.}: Current flows from copper to metal mentioned. Table gives therms per ampere per hour, and current flows Table gives therms per ampere per hour. from copper to substance named. Metals. Therms. Cadmium . Iron .... Nickel .... Platinum — O.616 —3-6I3 4.362 O.320 Silver .... Zinc .... —O.413 ^..585 CdtoCdS0 4 Cu to CuSC>4 Ag to AgNOs Zn to ZnS0 4 4.29 —1.4 7-53 —2.14 Metals. Therms. Antimony (Becquerel's) § " (commercial) 13.02 4.8 Bismuth (pure) (Becquerel's) || 19.1 2 S .8 Cadmium German silver O.46 2.47 iron .... Zinc .... 2-5 o-39 * Gockel, " Wied. Ann." vol. 24, p. 634. t " Wied. Ann." vol. 34, p. 767. t " Ann. de Chim. et de Phys." (4) vol. 10, p. 201. § Becquerel's antimony is S06 parts Sb +406 parts Zn + 121 parts Bi. II Becquerel's bismuth is 10 parts Bi + 1 part Sb. Smithsonian Tables. 2SO Table 262. CONDUCTIVITY OF THREE-METAL AND MISCELLANEOUS ALLOYS. Conductivity Ct~ C„ (i -f- at+ifi). Metals and alloys. Gold-copper-silver «« <» it « <• ■< Nickel-copper-zinc Brass .... " hard drawn " annealed . German silver Aluminium bronze . Phosphor bronze . Silicium bronze . . , Manganese-copper . , Nickel-manganese-copper Nickelin . Patent nickel Rheotan Copper-manganese-iron Manganin Composition by weight. 58.3 Au + 2 6.sCu+ 15.2 Ag 66.5 Au+ 15.4 Cu+18.1 Ag 74 Au + 78.3 Cu+ 14.3 Ag ( 12.84 ■ Ni + 30.59 Cu + ) I 0.57 Zn by volume ... J Various 70.2 Cu + 29.8 Zn . . . ! Various 60.16 Cu-f- 25.37 Zn + .03 Ni-f .30 Fe with trace cobalt and manganese . v ariou: ( 6o.i6( ] 14-03 ; ( of cob 3oMn + 70 Cu . . . 3 Ni + 24 Mn + 73 Cu 18.46 Ni + 61.63 Cu + 19.67 Zn -j- 0-24 Fe + 0.19 Co + 0.18 Mn . . . 25.1 Ni 4- 7441 Cu + 0.42 Fe -f- 0.23 Zn + 0.13 Mn + trace of cobalt ' 53.28 Cu + 25.31 Ni + 1 16.89 Zn + 4.46 Fe + 0.37 Mn 91 Cu + 7.1 Mn 4- 1.9 Fe . 70.6 Cu 4- 23.2 Mn + 6.2 Fe 69.7 Cu -j- 29.9 Ni 4- 36 Fe . 84CU+ i2Mn + 4Ni C„ 7.58 6.83 28.06 4.92 12.2-15.6 12.16 I43S 3-5 3-33 7-5-8-5 10-20 41 1. 00 2.10 3.01 2.92 1.90 4.98 1.30 2.60 2-33 tXio" 574 529 1830 444 1-2 X io 8 360 5-7 X io 2 40 —3° 300 190 410 120 22 120 25 14 4 3 1 — 1 — 2 —4 924 93 7280 5i Temp. C 10-20 20-30 3°-35 35-40 40-45 45-50 IPS 1 Matthieson. 2 Various. 8 W. Siemens. 4 Feusner and Lindeck. 6 Van der Ven. 8 Blood. 7 Feusner. 8 Lindeck. Smithsonian Tables. 2SI Table 263. CONDUCTING POWER OF ALLOYS. This able shows the conducting power of alloys and the variation of the conducting power with temperature.* The values of C„ were obtained from the original results by assuming silvers ^ mhos. The conductivity is taken as Ct = C„ (i — at + pP), and the range of temperature was 'froino° "_*£>_",, c ; The table is arranged in three groups to show (i) that certain metals when melted together produce a solution which has a conductivity equal to the mean of the conductivities of the components, (2) the behavior of those metals alloyed with others, and (3) the behavior of the other metals alloyed together. „,-,i MrA from ,„. It is pointed out that, with a few exceptions, the percentage variation between o° and ioo° can be calculated irom the formula P — P c l j t where / is the observed and V the calculated conducting power of the mixture at roo° C, and P e is the calculated mean variation of the metals mixed. Alloys. Weight % Volume % of first named. Co 10 1 aXio" *Xio» Variation per ioo° C. Observed. Calculated. Group Sn 6 Pb Sn 4 Cd SnZn PbSn ZnCd 2 SnCd4 CdPb 6 77.04 83.96 82.41 83.10 78.06 77.71 64.13 5341 24.76 26.06 23.05 23.50 7-37 10.57 7 - 57 , 9.18 10.56 6.40 16.16 13.67 5.78 3890 4080 3880 3780 3780 3850 3500 8670 30.18 1 1870 28.89 8720 30.12 8420 29.41 8000 29.86 9410 29.08 7270 27.74 29.67 30-03 30.16 29.10 29.67 30.25 27.60 Group 2. Lead-silver (Pb 2 oAg) Lead-silver (PbAg) Lead-silver (PbAg 2 ) Tin-gold (Sni 2 Au) " " (Sn 6 Au) Tin-copper t. t. t. t. t. t. Tin-silver . Zinc-copper t U u + n tt + " " t " " t 95.05 48.97 3 2 44 77-94 59-54 92.24 80.58 12.49 10.30 9.67 4.96 1.15 91.30 53-85 36.70 25.00 i6-53 8.89 4.06 94.64 46.90 30.64 90.32 79-54 93-57 83.60 14.91 12-35 11.61 6.02 1.41 96.52 75-51 42.06 29.45 23.61 10.88 5-°3 5.60 8.03 13.8b 5.20 3-03 7-59 8.05 6.41 7.64 12.44 39-41 7.81 8.65 13-75 I3-70 13-44 29.61 38.09 3630 i960 1990 3080 2920 3680 3330 547 666 691 995 2670 3820 3770 1370 1270 1880 2040 2470 7960 3100 2600 6640 6300 8130 6840 294 1 185 3°4 705 5070 8190 8550 1340 1240 1800 3030 4100 28.24 i6-53 I7-3 6 24.20 22.90 28.71 26.24 5.18 5.48 6.60 9.25 21.74 30.00 29.18 12.40 1 1.49 12.80 17.41 20.61 19.96 7-73 10.42 14.83 5-95 19.76 14-57 3-99 4.46 5.22 7-83 20-53 23-31 II.89 11.29 I0.05 I2.3O 1742 20.62 Note. — Barus, in the " Am. Jour, of Sci." vol. 36, has pointed out that the temperature variation of platinum alloys containing less than 10% of the other metal can be nearly expressed by an equation y — — — tttj where y is the temperature coefficient and x the specific resistance, m and n being constants. If a be the temperature coefficient at o° C- and s the corresponding specific resistance, s(a-\-m) = n. For platinum alloys Barus's experiments gave m = — .000194 and » = .0378. For steel m ~ — .000303 and « = .0620. Matthieson's experiments reduced by Barus gave for Gold alloys m = — .000045, n ~ .00721. Silver m= — .000112, « = . 00538. Copper il m = — .000386, « — .00055. * From the experiments of Matthieson and Vogt, " Phil. Trans. R. S.' t Hard-drawn. v. 154. Smithsonian Tables. 252 CONDUCTING POWER OF ALLOYS. Table 263. Group 3. Alloys. Weight % Volume' of first named. C bX I09 Variation per ioo° C. Observed. Calculated. Gold-copper t Gold-silver t " " t « " * " " t ft ff * Gold-copper t Platinum-silver t " t " t Palladium-silver t Copper-silver Iron-gold t ■ « B « t • u ft + Iron-copper t Phosphorus-copper t Arsenic-copper t ■ " " t • tt « { * Annealed. Smithsonian Tables. 99-23 9°-S5 87.93 87.95 64.80 64.80 31-33 31-33 34-83 1.52 33-33 9.81 S-oo 25.00 98.08 94.40 76.74 42.75 7.14 I-3 1 13-59 9.80 4.76 0.40 2.50 o-95 5.40 2.80 trace 98.36 81.66 79-86 79.86 52.08 52.08 19.86 19.86 19.17 0.71 19.65 5°5 2.51 23.28 98-35 95-17 77.64 46.67 8.25 i-53 27-93 21.18 10.96 0.46 35-42 10.16 13.46 13.61 9.48 9.51 13.69 13-73 12.94 53.02 4.22 11.38 19.96 5-38 56.49 51-93 44.06 47-29 50.65 50.30 1.26 1.46 24.51 4.62 14.91 3-97 8.12 38-52 2650 749 1090 1 140 673 721 885 908 864 3320 33° 774 1240 324 345° 3250 3°3° 2870 2750 4120 349° 2970 487 1550 476 1320 736 2640 46. 793 1160 246 495 641 57° 7300 208 656 1 150 154 7990 6940 6070 5280 4360 8740 7010 1220 103 2090 145 1640 446 4830 21.87 7.41 10.09 10.21 6.49 6.71 8.23 8.44 8.07 25.90 3.10 7.08 n.29 3-4° 26.50 25-57 24.29 22.75 23.17 26.51 27.92 '7-55 3-84 13-44 t Hard-drawn. 23.22 7-53 9-65 6.58 6.42 8.62 8.31 8.18 25.86 3.21 7-25 11.88 4.21 27.30 25.41 21.92 24.00 25-57 29.77 14.70 11.20 13.40 14.03 253 Table 264. SPECIFIC RESISTANCE OF METALLIC WIRES. This table is modified from the table compiled by Jenkin from Matthieson's results by taking the resistance of silver, gold, and copper from the observed metre gramme value and assuming the densities found by Matthieson, namely, 10.468, 19.265, and 8.95. Substance. ♦ ffl V cj to . %s.s »s« B «■- Kg • S°E — B « ft « E.S e a A rf a & » ° S "g£ g O £ M rt « a C U M ■a °3 •s £.» "o rj u °o§g o«*« a a «- M 4>.i:.-c °oJ& istsg a£j 5 5 5 = a "■& ■j.b 3 pits O so So" So ■ ■SfeE c ° aJa a « V o-SS Silver annealed . 1.460 -f- IO 6 0.01859 •1523 8.781 .2184 0-377 " hard drawn 1.585 " 0.02019 .1659 9538 ■2379 - Copper annealed 1.584 " 0.02017 .1421 9.529 .2037 0.388 " hard drawn 1.619 " 0.02062 .1449 9.741 .2078 - Gold annealed . 2.088 " 0.02659 .4025 12.56 •5771 0.365 " hard drawn 2.125 " 0.02706 .4094 12.78 .5870 - Aluminium annealed 2.906 " 0.03699 .0747 17.48 .1071 - Zinc pressed 5.613 " 0.07146 .4012 33-76 •5753 0.365 Platinum annealed 9.035 " 0.1 1 50 1-934 54-35 2.772 - Iron " 9.693 " 0.1234 ■7S5I 58-3I 1.083 - Nickel " 12.43 " 0.1583 1.057 74-78 I-5I5 - Tin pressed 13.18 " 0.1678 .9608 79.29 1-377 0.365 Lead " 19.14 " 0.2437 2.227 115.1 3-193 0.387 Antimony pressed 35-42 " 0.4510 2-379 213.1 3.410 0.389 Bismuth " 130.9 " 1.667 12.86 787-5 18.43 0-354 Mercury " 94.07 " 1.198 12.79 565.9 18.34 0.072 Platinum-silver, 2 part 1 part Pt, by weight sAgJ I 24-33 " 0.3098 2.919 146.4- 4.186 0.031 German silver . 20.89 " 0.2660 1.825 125.7 2.617 0.044 Gold-silver, 2 parts A.u, ) 1 part Ag, by weigh > 10.84 " t .) 0.1380 1.646 65.21 2-359 0.065 Smithsonian Tables. 254 SPECIFIC RESISTANCE OF METALS. Table 265. The specific resistance is here siven as the -Utance^^ns, per centre of a bar one sauare centimetre in Substance. Physical state. Specific resistance. Temp. C. Authority. Aluminium Antimony . <* tt Solid Liquid 2 -9-4-5 35-4-45-8 182.8 129.2 O Melting-point Various. De la Rive. Arsenic - 137-7 33-3 860 it Matthieson and Bismuth . « Electrolytic soft hard 108.0 108.7 110-268 Vogt. Van Aubel. Boron . . Commercial Pulverized and com- Various. Cadmium . pressed 8 X ioi° 6.2-7.0 i6. S 37-9 - Moissan. « Gold . ! Solid Liquid 3 'f 3'8 Various. Vassura. Calcium 2.04-2.09 Various. Cobalt . . 1.58-2.20 16.8 Matthieson. Copper . . Iron Commercial Various. tt Electrolytic 9.7-12.0 11. 2 105-5 Ordinary Red heat Kohlrausch. tt a 1 14.8 1 18.3 Yellow heat Iron magnetic 11 Steel. . . Cast l 9 'l heat Ord. temp. it u • - ■ " 85.8 Red heat n « it 104.4 "3-9 Yellow heat Nearly white heat / n "... Tempered glass hard 45-7 (1 + -00161/) Barus and Strouhal. "... " light yellow 28.9 (1 + .00244*) / « tt "... " yellow " blue 26.3 (1 -j- .00280/) t tt it "... 20.5 (1 + -00330/) t 11 u 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 1 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 1 lamp J Carbon, adamantine, from Woodhouse and ) Rawson incandescent lamp ) — 80° Specific resistance in c. g. s. units. 4745 1920 2665 139701 19300 10907 2139 13867 35720 15410 9071 4459° 31848 18417 27404 3834x10 s 6168X10 8 3505 H57 2081 9521 13494 8752 1647 10473 34707 14984 43823 29902 14586 26915 4046X io 8 3908 XioS 6300X10 8 3161 1349 1948 8613 12266 8221 1559 9575 345 2 4 1 4961 8479 43601 29374 13755 26818 4092X10' 3955X10' 6363X10' 1400 7470 6i33 1 138 6681 33664 14482 8054 43022 27504 10778 2631 1 4189X10' 4054 x10 s 6495x10 s * " Phil. Mag." vol. 34, 1892. t This is given by Dewar and Fleming as 13777 for 96°.4, which appears from the other measurements too high. Smithsonian Tables. 256 Table 266. ALLOYS AT LOW TEMPERATURES. by Cailletet and Bouty 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 — ioo° and + ico° C* 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 1 to 2% \ tungsten ) Platinum-iridium, 80 Pt + 20 Ir Platinum-rhodium, 90 Pt + 10 R Q • 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 757 1207 4010 61 10 S29S 962 5671 33280 14256 7883 4238S 26712 9834 26108 4218X10 8 4079 X 1 o 8 6533 x10 s 894 272 604 1067 1900 2821 47 2 2553 32512 13797 7371 41454 24440 7134 25537 4321 Xio 8 4180X10 8 178 608 2290 .00446 43i 375 578 538 34i 377 428 035 039 070 025 087 312 024 031 029 i ?ioo — K — 10 * This is a in the equation R = X„ (i + «*)> « calculated from the equation a _ ^^ Smithsonian Tables. 257 Table 267. EFFECT OF ELONGATION ON THE SPECIFIC RESISTANCE OF SOFT METALLIC WIRES.* Substance. Increase of specific resistance for i % of elongation — Permanent elongation. Elastic elongation. German silver .... From .50 % to .60 % " .70 " " .80 " " .50 " " .55 " From 2.5 % to 7.7 % " 4.6 " " 4.8 " " 0.7 " « 1.0 " Table 268. EFFECT OF ALTERNATING THE CURRENT ON ELECTRIC RESISTANCE. This table gives the percentage increase of the ordinary resistance of conductors of different diameters when the current passing through them alternates with the periods stated in the last column. f Diameter in — Area n — Percentage increase of ordinary resistance. Number of complete periods per second. Millimetres. Inches. Sq. mm. Sq. in. IO •3937 78.54 .122 Less than -^ 1 '5 •59°5 176.7 .274 2.5 20 .7874 314.16 .487 8 25 .9842 490.8 .760 17-5 • 80 40 1-575 1256 I.95 68 IOO 3-937 7854 12.17 3.8 times 1000 39-39 785400 1217 35 times 9 •3543 63.62 .098 Less than jjj- 134 .5280 I4I-3 .218 2.5 18 .7086 254.4 •394 8 • 100 22.4 .8826 394 .611 17-5 7-75 ■3013 47.2 .071 Less than ^j 1 1. 61 •4570 106 .164 2.5 15-5 .6102 189 .292 8 • 133 19.36 .7622 294 •456 17-5 Smithsonian Tables. * T. Gray, " Trans. Roy. Soc. Edin." 1880. t W. M. Mordey, " Inst. El. Eng. London," 1889. 258 Tables 269, 270. CONDUCTIVITY OF ELECTROLYTIC SOLUTIONS. This subject has occupied the attention of a considerable number of eminent workers in molecular physics, and a few results are here tabulated. It has seemed better to confine the examples to the work of one experimenter, and the tables are quoted from a paper by F. Kohl- rausch * who has been one of the most reliable and successful workers in this field. The study of electrolytic conductivity, especially in the case of very dilute solutions, has fur- nished material for generalizations, which may to some extent help in the formation of a sound theory of the mechanism of such conduction. If the solutions are made such that per unit volume of the solvent medium there are contained amounts of the salt proportional to its electro- chemical equivalent, some simple relations become apparent. The solutions used by Kohlrausch were therefore made by taking numbers of grammes of the pure salts proportional to their elec- trochemical equivalent, and using a litre of water as the standard quantity of the solvent. Tak- ing the electrochemical equivalent number as the chemical equivalent or atomic weight divided by the valence, and using this number of grammes to the litre of water, we get what is called the normal or gramme molecule per litre solution. In the table, m is used to represent the number of gramme molecules to the litre of water in the solution for which the conductivities are tabulated. The conductivities were obtained by measuring the resistance of a cell filled with the solution by means of a Wheatstone bridge alternating current and telephone arrangement. The results are for 18° C, and relative to mercury at o° C, the cell having been standardized by filling with mercury and measuring the resistance. They are supposed to be accurate to within one per cent of the true value. The tabular numbers were obtained from the measurements in the following manner : — Let -ff" 18 = conductivity of the solution at i8° C. relative to mercury at o° C. ^T B = conductivity of the solvent water at 18° C. relative to mercury at o° C. Then jf 18 — K^ a = & la = conductivity of the electrolyte in the solution measured. - 11 - = ii. = conductivity of the electrolyte in the solution per molecule, or the " specific molecular conductivity." TABLE 269. —Value of fr 18 for a few Electrolytes. This short table illustrates the apparent law that the conductivity in very dilute solutions is proportional to the amount of salt dissolved. 1 m KC1 NaCl AgN0 3 K.C2H3O2 KjSOj MgS0 4 0.000001 0.00002 0.00006 O.OOOI 1.216 2.434 7.272 12.09 1.024 2.056 6.162 10.29 I.080 2.146 6.462 IO.78 1.886 5.610 9-34 1.275 2-532 7.524 12.49 1.056 2.104 6.216 10.34 TABLE 270. —Electro-Chemical Equivalents and Normal Solutions. The following table of the electro-chemical equivalent numbers and the densities of approximately normal solutions of the salts quoted in Table 271 may be convenient. They represent grammes per cubic centimetre of the solution at the temperature given. Salt dissolved. Grammes per litre. m Temp. C. Density. Salt dissolved. Grammes per litre. m Temp. C. Density. KC1 . . . 74-59 1.0 i&6 1-0457 4K 2 so 4 . 87.16 I.O 18.9 I.0658 NH4CI 53-55 I.0009 1.0152 iNaaSOi . 71.09 I.OOO3 18.6 I.0602 NaCl . 58.50 I.O 18.4 1.0391 JLi 2 S04 . 55.09 1.0007 18.6 I.0445 LiCl . 42.48 1.0 18.4 1.0227 JMgS0 4 . 60.17 1 .0023 18.6 1-0573 JBaCla 104.0 I.O 18.6 1.0888 |ZnS0 4 . 80.58 I.O 18.2 1.0794 |ZnCl 2 KI. . 68.0 1 .012 15.0 1.0592 fCuSO* . 79-9 I.OOI 1.0776 165.9 I.O 18.6 1.1183 iK 2 C0 3 . 69.17 1.0006 10.3 1.0576 KNOg 101.17 I.O 18.6 1. 0601 iNasCOs . 53°4 I.O 17.9 1-0517 NaN0 8 85.08 I.O 18.7 1.0542 KOH . . 56.27 1.0025 18.8 1.0477 AgNOs 169.9 I.O - HC1 . . 36-51 1. 004 1 18.6 1.0161 4Ba(N0 8 ) 2 • KCIO3 • • 65.28 0.5 - - HNOa . . 63-13 1.0014 18.6 1.0318 61.29 0.5 "g-3 1.0367 £H 2 S0 4 . 49.06 1.0006 18.9 1.0300 KC 2 H s 2 . 98.18 1.0005 18.6 1.0467 Smithsonian Tables. * " Wied. Ann." vol. 26, pp. 161-226. 259 Table 271. SPECIFIC MOLECULAR CONDUCTIVITY fi : MERCURY=tO , 1 Salt dissolved. «— 10 5 3 1 o-S o.x .os .03 .01 £K 2 S0 4 . __ _ 672 736 897 959 1098 KC1 - - 827 919 958 1047 1083 1 107 "47 KI. . . . - 770 900 968 997 1069 1 102 1123 1161 NH4CI . - 752 825 907 948 1035 1078 IIOI 1 142 KNO3 . - 572 752 839 983 1037 1067 1 122 £BaCl 2 . _ _ 487 658 725 861 904 939 1006 KClOs • - — - - 799 927 (9 J 6 ) 1006 i°53 JBaaNaOs - - - - 5 3o 755 828 (870) l St |CuS0 4 . — — 150 241 288 424 479 537 675 AgNOs . - 351 448 635 728 886 936 (966) 1017 PnS0 4 . - 82 146 249 302 43i 500 556 685 4MgS0 4 . • . - 82 'Si 270 33° 474 532 587 7I | £Na 2 S0 4 - - 475 559 734 784 ,828 906 fZnCl 2 . 60 180 280 5 r 4 601 768 817 851 915 NaCl - 398 528 695 757 865 897 (920) 962 NaNOs ■ _ _ 43° 617 694 817 ! 55 877 907 KC 2 H 8 2 3° 240 381 594 671 784 820 841 879 £Na 2 C0 8 - 254 427 510 682 751 799 899 £H 2 S0 4 . . . 660 1270 1560 1820 1899 2084 2343 2515 2855 C 2 H 4 . °-5 2.6 5-2 12 19 43 62 79 132 HC1 600 1420 2010 2780 3017 3244 3330 3369 3416 HNOg . 610 1470 2070 2770 2991 3225 3289 3328 3395 £H 3 P0 4 . . . KOH . 148 423 160 990 170 i3'4 200 1718 250 1841 43° 1986 540 2045 620 2078 790 2124 NH 8 0.5 2.4 3-3 8.4 12 3i 43 5° 92 Salt dissolved. .006 .002 .001 .0006 .0002 .OOOI .OOO06 .00002 .OOOOI iK 2 S0 4 . . . 1 130 1181 1207 1220 1 241 1249 1254 1266 1275 KC1 1 162 1185 "93 1 199 1209 1209 1212 1217 1216 KI . 1 176 1197 1203 1209 1214 1216 1216 1216 1207 NH 4 C1 . 1157 1 180 1 190 1 197 1204 1209 1215 1209 1205 KNOj . 1 140 "73 1 180 1190 1 199 1207 1220 1198 1215 PaCl 2 . 1031 1074 1092 1 102 1118 H26 "33 "44 1142 KClOs . 1068 1091 IIOI 1 109 1 1 19 1122 1126 "35 1141 iBa 2 N 2 O e 982 1033 1054 1066 1084 1096 1 100 1114 1114 |CuS0 4 . 740 873 950 987 1039 1062 1074 1084 1086 AgNOg ■ i°33 1057 1068 1069 1077 1078 1077 1073 1080 £ZnS0 4 . 744 861 919 953 IOOI 1023 1032 1047 1060 JMgS0 4 . • • 773 881 935 967 1015 1034 1036 1052 1056 £Na 2 S0 4 . . 933 980 998 1009 1026 1034 1038 1056 1054 £ZnCl 2 . 939 979 994 1004 1020 1029 1031 1035 1036 NaCl 976 998 1008 1014 1018 1029 1027 1028 1024 NaNOs • 921 942 952 956 966 975 970 972 975 KC 2 H 8 2 891 913 919 923 933 934 935 943 939, |Na 2 CO g 956 IOIO 1037 1046 988 874 790 7'5 697* £H 2 S0 4 . . . 3001 3240 33i6 3342 3280 31 18 2927 2077 1413* C 2 H 4 . 170 283 380 470 796 995 "33 1328 1304* HC1 3438 3455 3448 3455 3440 3340 3 r 70 2968 2057 1254* HNO3 . 3 i 2 l 3427 3408 3285 3088 2863 1904 "44* £H 8 P0 4 . . . 858 945 968 977 920 1689 746 497 402» KOH . 2141 2140 2110 2074 1892 1474 845 747* NH 8 . . . 116 190 260 33° 500 610 690 700 560* Smithsonian Tables. * Acids and alkaline salts show peculiar irregularities. 260 Table 272. LIMITING VALUES OF /*. This table shows limiting values of » = I .,„« for infinite dilution for neutral salts, calculated from Table 2 7 ,. Salt. F- Salt. /» Salt. /» Salt. c iK 2 S0 4 . KCl. . . KI . . . NH4CI. . KNOs • • 1280 1220 1220 1210 1210 iBaCl 2 . *KC10 8 . iBaN 2 O e . iCuS0 4 . AgNOs • iZnS0 4 . 1150 1150 1 120 1 100 1090 1080 iMgS0 4 . 4Na 2 S0 4 . iZnCl . . NaCl . . NaNOs • K2C2H8O2 1080 1060 1040 1030 980 940 iH 2 S0 4 . HCl . . HN0 8 . • 3-H8PO4 . KOH . . iNa 2 C0 8 . 3700 35°° 35°° 1100 2200 1400 If the quantities in Table 271 be represented by curves, it appears that the values of the specific molecular conductivities tend toward a limiting value as the solution is made more and more dilute. Although these values are of the same order of magnitude, thev are not equal, but depend on the nature of both the ions forming the electrolyte. When the numbers in Table 272 are multiplied by Hittorf's constant, or o.ooon, quan- tities ranging between 0.14 and 0.10 are obtained which represent the velocities in milli- metres per second of the ions when the electromotive force gradient is one volt per millimetre. ' Specific molecular conductivities in general become less as the concentration is in- creased, which may be due to mutual interference. The decrease is not the same for different salts, but becomes much more rapid in salts of high valence. Salts having acid or alkaline reactions show marked differences. They have small specific molecular conductivity in very dilute solutions, but as the concentration is in- creased the conductivity rises, reaches a maximum and again falls off. Kohlrausch does not believe that this can be explained by impurities. HsPO* in dilute solution seems to approach a monobasic acid, while H 2 S04 shows two maxima, and like H 8 P04 approaches in very weak solution to a monobasic acid. Kohlrausch concludes that the law of independent migration of the ions in media like water is sustained. 1 ^ Table 273. TEMPERATURE COEFFICIENT. The temperature coefficient in general diminishes with dilution, and for very dilute solutions appears to approach a Dmmon value. The following table gives the temperature coefficient for solutions containing 0.01 gramme mole- ale of the salt. Salt. Temp. Coeff. Salt. Temp. Coeff. Salt. Temp. Coeff. Salt. Temp. Coeff. KCl . . . NH4CI . . NaCl . . LiCl. . . PaCl 2 . • |ZnCl 2 . . iMgCl 2 . O.022I 0.O226 O.O238 O.O232 O.O234 O.0239 O.O24I KI . . . KNOs • ■ NaNOs. • AgNOs. • Pa(N0 8 ) 2 KCIOa • • KC 2 Hs0 2 . O.O2I9 0.02l6 0.0226 0.0221 0.0224 0.0219 O.O229 iK 2 S0 4 . |Na 2 S04 . iIJ2S04 . iMgS0 4 . iZnSOs . iCuSOi . O.0223 O.0240 O.0242 O.0236 O.0234 O.0229 iK 2 CO s . . iNa 2 CO s . . O.O249 O.O265 KOH . . . HCl . . . HNOs . . . £H 2 S04 . . O.OI94 0.01 59 O.Ol62 O.OI25 *H 2 S04 1 for m = .001 j O.OI59 Smithsonian Tables. 26l Table 274. VARIOUS DETERMINATIONS OF THE VALUE OF THE OHM, ETC.* Observer. Date. Method. Value of B. A. U. in ohms. Value of ioo cms. of Hg in B. A.U. Value of ohm in cms. of Hg. Lord Rayleigh . Lord Rayleigh . Mascart .... Rowland . . . Kohlrausch . . Glazebrook . . Wuilleumeier . . Duncan & Wilkes Jones Strecker . . Hutchinson Salvioni . . Salvioni . . H. F. Weber H. F. Weber Roti . . . Heinstedt . Dorn . . . Wild . . . Lorenz . . 1882 1883 1884 1887 1887 1882 to 18 1890 1890 Rotating coil . Lorenz method . Induced current Mean of several methods . . Damping of mag. nets. . . . Induced currents 1890 884 885 889 883 885 Lorenz method . Lorenz method . Mean . . . An absolute de- termination of re- sistance was not made. The value .98656 has been used. Mean . . . Induced current Rotating coil . Mean effect of in duced current .98651 .98677 .98611 .98644 .98660 .98665 .98686 .98634 ■98653 Damping of mag- net .... Damping of mag net .... Lorenz method . (.95412) •95374 •95349 •95338 •95352 •95355 ■95341 •95334 •95352 ■95332 •95354 106.31 106.27 106.33 106.32 106.32 106.29 106.31 106.34 106.31 106-31 106.32 106.30 106.33 106.30 •9S3S4 106.31 Absolute measure- ments compared with German silver wire coils issued by Siemens or Strecker. 106.16 105.89 105.98 106.24 106.03 105-93 The Board of Trade committee recommended for adoption the values .9866 and 106.3. The specific resistance of mercury in ohms is thus -9407 X io -4 . Also 1 Siemens unit = -9407 ohm. = -9535 B. A.U- 1 ohm . . . = 1.01358 B. A. TJ. The following values have been found for the mass of silver deposited from a solution of silver nitrate in one second by a current of one ampere : — Mascart, " J. de Physique," iii. 1884 Rayleigh, " Phil. Trans." ii. 1884 . Kohlrausch, "Wied. Ann." xxvii. 1886 . T. Gray, " Phil. Mag." xxii. 1886 . Portier et Pellat, "J. de Physique," ix. 1890 . .001 1 1 56 . .0011179 . .0011183 about t .ooi 1 18 . .0011192 The following values have been found for the electromotive force of a Clark cell at 15 C. They have been reduced from those given in the original papers on the supposition that 1 B. A. U. = .9866 ohm, and that the mass of silver deposited per second per ampere is .ooi 1 18 gramme. Rayleigh, " Trans." ii. 1884 1-4345 volt. Carhart 1-4340 " Kohle, " Zeitschrift fur Instrumentenkunde," 1892 . . . 1.4341 " Glazebrook and Skinner, " Proc. R. S." Ii. 1892 . . . 1.4342 " * Abstract from the Report of the British Association Committee on Practical Standards for Electrical Measure- ment, " Proc. Brit. Assoc." 1892. t i .0000002 T. G. Smithsonian Tables. 262 Table 275. SPECIFIC INDUCTIVE CAPACITY OF CASES. With the exception of the results given by Avion and Perry, for which no temperature record has been found, the values are for o° C. and 760 mm. pressure. Gas. Sp. ind. cap. Authority. Vacuum =z 1. Air = 1. Air ... 1. 0000 Ayrton and Perry. 1. 0000 KlemenciC. - - - - - - —■444 sulphate solution . . . ) Strong sulphuric acid in distilled water : 1 to 20 by weight . . . - - - - - - —•344 I to 10 by volume . . . 1 about 1 I — -°35 < - - - - - 1 to 5 by weight .... - - - - - - 5 to 1 by weight .... i to l (30) (•55) - — .120 - —•25 - ( -7 2 '•3 ) Concentrated sulphuric acid ] to \ (•8S) 1.113 - /o ' r - 2 5 2 to 3 1.6 ) - - Concentrated nitric acid _ _ .672 Mercurous sulphate paste . - _ _ _ _ Distilled water containing I trace of sulphuric acid J — .241 * Everett's " Units and Physical Constants: " Table of Smithsonian Tables. 266 Table 278. POTENTIAL IN VOLTS. liWUfls with Liquids In Air.* during experiment about i6° C. ■a 8 rt a &. E.S m V % » 5 in fl M O -M E 3 P O h U to "S M 0." ■3*0 SiS as 8% Is, « -a 1 . 5 0. •2U p m ^^ w ;n. u ■*-• rt « ^3 II ■03 v in ».E ■•a n Is c + 3 « 1 "S s> 1 in Mercury Distilled water Alum solution : saturated ) at i6°.5 C ( Copper sulphate solution : \ sp. gr. 1.087 at i6°.6 C. J Copper sulphate solution : I saturated at 15° C. . . j Sea salt solution : sp. gr. I 1. 18 at 20°s C. . . . j Sal-ammoniac solution : 1 saturated at I5°5 C. . j Zinc sulphate solution : i sp. gr. 1. 125 at i6°-9 C. J Zinc sulphate solution : 1 saturated at i5°-3 C. . J One part distilled water -f- ) 3 parts saturated zinc > sulphate solution . . ) Strong sulphuric acid in distilled water : 1 to 20 by weight . . . 1 to 10 by volume . . . 1 to 5 by weight .... 5 to 1 by weight .... Concentrated sulphuric acid Concentrated nitric acid Mercurous sulphate paste . Distilled water containing 1 trace of sulphuric acid . ) .100 —.284 —358 .429 .848 .231 — .014 —435 -•348 — .016 •475 —•043 — .200 1.298 I.456 —•043 —.095 — .102 1.269 .090 .164 .095 1.699 .102 .078 Ayrton and Perry's results, prepared by Ayrton. Smithsonian Tables. 267 Table 279. CONTACT DIFFERENCE OF POTENTIAL IN VOLTS. Solids with Solids In All.* Temperature of substances during the experiment about i8° C. Carbon. Copper. Iron. Lead. Platinum. Tin. Zinc. Zinc amal- gam. Brass. Carbon . . . ■370 .485 .858 •"3 •795 1.096! I.208t •4i4t Copper . . . —•370 .146 .542 —.238 .456 ■75° •894 .087 Iron .... — 4 8 5 t — .146 .401 1 —•369 •3' 3t .6oot •744t — .064 Lead . . . —.858 —•542 — .401 O —•771 —.099 .210 •357t —.472 Platinum . . — "3t .238 ■369 •771 .690 .981 I.I25t .287 Tin ... . — 795t -.458 —•313 .099 — .690 .281 •463 — 372 Zinc .... — 1.096! —•75° — .600 — .216 —.981 .281 .144 —.679 " amalgam — I.208t -.894 —•744 — -357t — I.I25f —■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 are 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. 268 Table 280. 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 first column. The solutions were contained in a U-tube, 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 fitre. Zinct Cadmium.! Lead. Tin. Copper. Silver. tto. of molecules. Salt. Difference of potential in centivolts. i °-5 H 2 S0 4 0.0 36.6 51-3 Si-3 100.7 121.3 1.0 NaOH —32.1 19-5 31.8 0.2 80.2 95.8 1.0 KOH —42.5 15-5 32.0 — 1.2 77.0 104.0 °-5 Na 2 S0 4 1.4 35-6 S0.8 51.4 101.3 120.9 1.0 Na 2 S 2 O s — S-9 24.1 45-3 4S-7 38-8 64.8 1.0 KNO3 ii.8j 3i-9 42.6 3" 81.2 1057 1.0 NaN0 8 11.5 32-3 51.0 40.9 95-7 1 14.8 o-s K 2 Cr0 4 23-9t 42.8 41.2 40.9 94.6 I2I.0 °-5 K 2 Cr 2 7 72.8 61.1 78.4 68.1 123.6 I32.4 o-s K 2 S0 4 1.8 34-7 51.0 40.9 95-7 1 14.8 0.5 (NH 4 ) 2 S0 4 -0.5 37-i S3-2 57-6* 101.5 I25.7 87.8 0.25 K 4 FeC 6 N 6 —6.1 §3-6 50.7 41.2 — t 0.167 K 6 Fe 2 (CN)i! 4 I.0§ 80.8 81.2 130.9 1 10.7 I24.9 1.0 KCNS — 1.2 32-5 52.8 52.7 52.5 72-5 1.0 NaNOs 4-5 35-2 50.2 49.0 103.6 IO4.6 ? 0.5 SrNOs 14.8 38-3 50.6 48.7 103.0 "9-3 0.125 Ba(NO s ) 2 21.9 39-3 S'-7 52.8 109.6 121. 5 1.0 KNO3 -t 35-6 47 -S 49.9 104.8 1 1 5.0 0.2 KClOs iS-ioJ 39-9 53-8 57-7 105-3 120.9 120.8 0.167 KBrOs 13-20J 40.7 5 r -3 So-9 111.3 1.0 NH4CI 2.9 3 2 -4 S'-3 50.9 81.2 61.3 101.7 61.5 1.0 KF 2.8 22.5 41.1 50.8 1.0 NaCl — 3 r -9 51.2 50-3 80.9 101.3 82.4 107.6 1.0 1.0 KBr KC1 2-3 3J-7 32.1 47-2 Si.6 52-S 52-6 73-6 81.6 -II 1.0 o-S o-S Na 2 SO s NaOBr —8.2 18.4 28.7 41.6 41.0 73- 1 31.0 70.6 1 68.7 89.9 103.7 99-7 C 4 H 6 6 C 4 H 6 O b C 4 H 4 KNa0 6 5-5 4.1 —7-9 39-7 4i-3 31-5 61.3 61.6 Si-5 S4-4§ 57-6 42-47 104.6 110.9 100.8 123.4 125-7 1 19.7 Smithsonian Tables. * "Rend, della R. Ace. di Roma," 1890. f Amalgamated. t Not constant. § After some time. _ || A quantity of bromine was used corresponding to NaOtl — 1. 269 Table 281. VARIATION OF ELECTRICAL RESISTANCE OF CLASS AND PORCELAIN WITH TEMPERATURE. The following table gives the values of a, 6, and c in the equation log R = a + U + cf, where R is the specific resistance expressed in ohms, that is, the resistance in ohms per centimetre of a rod one square centimetre in cross section.* No. Kind of glass. Density. a i c Range of temp. Centigrade. I Test-tube glass .... - 13.86 —•044 .000065 0°-250° 2 it U It 2.458 14.24 —.055 .0001 37-131 3 Bohemian glass .... 2-43 l6.2I —■043 .0000394 60-174 4 Lime glass (Japanese manufacture) . 2-55 I3-H —.031 — .000021 IO-85 5 tt it it It 2-499 14.002 — .025 — .00006 3S-9S 6 Soda-lime glass (French flask) 2-533 14.58 —.049 .000075 45-120 7 Potash-soda lime glass 2.58 16.34 —.0425 .0000364 66-193 8 Arsenic enamel flint glass 3-°7 18.17 —.055 .000088 ioS-^S 9 Flint glass (Thomson's electrometer jar) 3-'7z 18.021 —.036 — .0000091 100-200 10 Porcelain (white evaporating dish) . - 15.65 — .042 .00005 68-290 Composition of some of THE ABOVE SPECIMENS OF GLASS. Number of specimen = 3 4 5 7 8 9 Silica 61.3 57.2 70.05 7 5.65 54.2 55.18 Potash 22.9 21. 1 1.44 7.92 10.5 13-28 Soda Lime, etc. Lime, etc. 14-32 S.92 7.0 - Lead oxide .... by diff. by diff. 2.70 - 23-9 31.OI Lime 15.8 16.7 io-33 . 5.48 o-3 °-3S Magnesia .... - - - 5.36 0.2 0.06 Arsenic oxide - - - - 3-5 - Alumina, iron oxide, etc. - - 1.45 3.70 0.4 0.67 Smithsonian Tables. * T. Gray, " Phil. Mag." 1880, and " Proc. Roy. Soc." 1882. 270 Table 282. RELATION BETWEEN THERMAL AND ELECTRICAL CONDUCTIVITIES. That there is a close relation between the thermal and the electrical conductivities of metal was shown experimen- tally by Wiedemann and Franz in 1853, and had been referred '? „ b 5 r . Forbes, with whom a difficulty arose with regard to the direction of the variation with temperature. The ex- periments of Tait and his stu- dents have shown that this difficulty was largely, if not entirely, due to experimental error. The same relation has been shown to hold for alloys by Chandler Roberts and by Neumann. Tins relation was a. Values in Arbitrary Units at 15 C. Substance. h* *15 I™ Lead . . 7-93 4.569 8.823 1.74 Tin . . . 14.46 1.64 Zinc . . . 2 5-45 14.83 1.72 Copper . . 41.52 24.04 '■73 Iron, No. 1 14.18 6.803 2.08 " 2 9.64 4.060 2-37 " " 3 I37S 6.565 2.09 denied by H, F. Weber, and has been again experimentally investigated and apparently established by the experiments of Kirchhoff and Hansemann, of L. Lorenz, of F. Kohl- rauschj and of Berget. _ Putting /= thermal conduc- tivity, and k = electrical con- ductivity, Kirchhoff and Hansemann find the values in Table a. This table shows iron to deviate considerably from the other metals in the relationship of the two con- ductivities ; but this may possi- bly be explained by its mag- netic properties. at 0° and'^o 3 ^' 3 h ^ZfT ,he - ra ' i0 l/ k $ r the different mela,s ' **«& lron > is near, y «>»**"* f<" ™lues at o ana no U, but that the ratio is generally greater for poorly conducting substances. He shows that the rati ° *I^" f ""*7 remaills nearl y constant for all metals examined, with the exception of iron, and has an aver- age value, as shown by Table b, of about 1.37. He concludes that l/k= constant X T, where T is the abso- lute temperature. »i. I . n ' his * abl e the values of / and k are given in c. g. s. units, and the metals are arranged in the order of their heat conductivities. The same specimens were used for both the thermal and the electrical experiments. Ta. Values in C. G. S. Units. Substances. Copper Magnesium Aluminium 0.7198 0.3760 0-3435 Brass, red . Cadmium . 0.2460 0.2200 Brass, yellow Iron . 0.2041 0.1665 Tin . 0.1528 Lead . 0.0836 German silver . 0.0700 Antimony . Bismuth . 0.0442 0.0177 '10 0.7226 0.3760 0.3619 0.2827 0.2045 0.2540 0.1627 0.1423 0.0764 0.0887 0.0396 0.0164 A„Xi 45-74 24.47 22.46 15-75 14.41 12.62 io-37, 9-346 5.141 3.766 2.199 0.929 *ioo X io 5 33-82 17.50 I7-3 1 I3-3I 10.18 11.00 6.628 6.524 3.602 3-632 1.522 0-633 1574 1537 1529 1562 1527 1617 1605 1635 1627 1858 201 1 1900 1-358 1.398 i-3 6 7 1.360 I-3I5 1.428 1-530 1-334 1.304 i-3H 1.294 1.372 C. Berget's Experiments.! The same specimens were used for both experiments. It will be seen that the ratio is nearly constant, but not exactly so. Substance. k X 10-= Substance. AXio-s Copper . Zinc . . Brass . Iron . . 1.0405 0.303 0.2625 0.1587 65.13 18.00 15-47 9.41 1.6 1-7 i-7 1-7 Tin . . . Lead . . Antimony Mercury . 0.151 0.0810 0.042 0.0201 8-33 5.06 2.47 1.06 1.8 1.6 i-7 1.8 d. Kohlrausch's Results. An interesting confirmation of the relationship of the two conductivities has been furnished by F. Kohl- rausch, who has shown that tempering steel causes equal proportional changes in the thermal and electrical conductivities of the metal, thus leaving the ratio l/k unchanged by the process.* Tempered steel Soft steel /= 0.062; ^ = 3-3! //* = 0.019 " = o.m; " = 5-5; " =0.020 In the consideration of this subject it must be borne in mind that closely accurate values of thermal conduc- tivity are very difficult to obtain, and hence fairly large variations are to be expected. * " Wied. Ann." vol. 13, p. S98. t " Compt. Rend." vol. 110, p. 76. Smithsonian Tables. t lis in c. g. s. units and i in terms of mercury. 271 Table 283. ELECTROCHEMICAL EQUIVALENTS. With the exception of the values in heavy type for copper and silver, the numbers in this table have been calculated from the atomic weights and valence, on the basis of the value given for silver which was adopted by the Inter- national Congress of Electricians at Chicago in 1894. Many of the substances have not been separated electri- cally, and in these cases the numbers are purely theoretical. Relative Relative combining Electrochemical Substance. atomic \vt. Valence. weights ; oxygen equivalent in grammes Oxygen = 16. = 8. per coulomb X 1000. Aluminium .... 27.II 3 9.04 O.09358 Antimony 120.43 3 °r 5 40.11 or 25.09 0.4155 or 0.2492 Arsenic 75.09 3 °r 5 25.03 or 15.02 0.2593 or 0.1555 Barium ..... '37-43 2 63-7I 0.7119 Bismuth 20S.11 3 or 5 69.37 or 41.62 0.7218 or 0.4333 Boron 10.95 3 3-65 0.03783 Bromine 79-95 1 79-95 0.8283 Cadmium 111.93 2 55.96 0.5798 Caesium 132.89 1 132.89 1.3767 Calcium 40.08 2 20.04 0.2076 Carbon 12.01 4 3-o 0.03108 Cerium 140.2 2 70.1 0.7262 Chlorine Chromium .... 35-45 52.14 1 3 or 6 3S4 5 17.38 or 8.69 0-3673 0.1 80 1 or 0.0901 Cobalt 58-93 2 or 3 29.46 or 19.64 0.3052 or 0.2034 Columbium .... 94.0 5 18.8 0.1948 Copper Erbium Fluorine Gadolinium .... 63.6 166.3 19.03 1 56. 1 1 or 2 2 I 63.6 or 31.8 83-I5 19.03 0.6589 or 0.3290 0.8614 0.1971 Gallium Germanium .... 69.0 72-3 9.08 197.24 3 23.0 0.2383 Glucinum Gold 2 3 4-54 65.75 0.04703 0.6812 Hydrogen .... 1.008 1 1.008 0.0104 Indium Iodine Iridium Iron Lanthanum .... "3-7 126.85 193.12 56.02 138.6 3 1 4 2 or 3 2 37-9 126.85 48.28 28.01 or 18.67 69-3 0.3926 1.3142 0.5002 0.2902 or .1934 0.7179 Lead Lithium Magnesium .... Manganese .... Mercury 206.92 7-03 24.29 54-99 200.0 2 1 2 2 or 4 1 or 2 103.46 7-03 12.15 2 7-5°r 13-75 200.0 or 100.0 1-0717 0.07283 0.1259 0.2849 or 0.1424 2.0720 or 1.0360 Molybdenum .... Neodidymium .... 95.98 140.5 6 16.0 0.1658 Nickel Nitrogen Osmium 58.69 14.04 190.99 2 or 3 3 °r 5 6 29.35 or 19.57 4.68 or 2.81 3I-83 0.2996 or 0.1997 0.04849 or 0.02909 0.3297 Oxygen Palladium Phosphorus Platinum . . . Potassium 16.0 106.36 31.02 194.89 39-n 2 2 or 5 3 or 5 2 or 4 1 8.0 53.18 or 21.27 10.34 or 6.20 97-44 or 48.72 39-" 0.08288 0.5310 or 0.2124 0.1 174 or 0.07043 1.0095 °r 0.5048 0.4052 * The atomic weights are from a paper by F. W. Clarke. " Journ. Am. Chem. Soc." vol. 18, p. 213, 1896. 8mithsonian Tales. 272 ELECTROCHEMICAL EQUIVALENTS. Table 283. Relative Relative combining Electrochemical Substance. atomic wt. Valence. weights ; oxygen equivalent in prammes Oxygen = 16. = 8. per coulomb X 1000. Praseodidymium 143-5 _ _ Rhodium 103.01 3 34-34 0-3558 Rubidium 8543 I 8 5-43 O.8851 Ruthenium .... 101.68 4 25.42 O.2633 Samarium 150.0 - Scandium 44.0 _ _ - Selenium 79.0 2 39-5 O.4092 Silicon 28.4 4 7-i O.07356 Silver 107.92 1 107.92 I.I180 Sodium 23.05 1 23-°5 O.2387 Strontium 87.61 2 43-8 0.4538 Sulphur 32.07 2 16.03 O.1661 Tantalum 182.6 5 36.52 O.3783 Tellurium 127.0? 2 63-5 O.6578 Terbium 160.0 - - "" Thallium 204.15 1 204.15 2.OI47 Thorium 232.63 2 1 1 6.31 I.2049 Thulium 170.7 — — — Tin 119.05 2 or 4 59.52 or 29.76 0.6166 or 0.3083 Titanium 48.15 4 12.04 0.1247 Tungsten Uranium 184.84 6 3 °'o 7 0.3177 239-59 2 or 3 1 19.8 or 79.86 1.2410 or 0.8273 0.1778 or 0.1065 Vanadium .... 5I-38 3 or 5 17.13 or 10.28 Ytterbium .... 173.2 — — ~ Yttrium 88.95 2 44-47 0.4603 Zinc 65.41 2 3 2 -7 0.3385 1 Zirconium 1 90.6 4 22.65 0.2346 Smithsonian Tables. 273 Tables 284, 285. PERMEABILITY OF IRON. TABLE 284. — Permeability of Iron Rings and Wlie. This table gives, for a few specimens of iron, the magnetic induction B, and permeability p., corresponding to the magneto-motive forces H recorded in the first column. The first specimen is taken from a paper by Rowland,* anf refers to a welded and annealed ring of " Burden's Best " wrought iron. The ring was 6.77 cms. in mean diameter, and the bar had a cross sectional area of 0.916 sq. cms. Specimens 2-4 are taken irom a paper Dy Bosanauet.t and also refers to soft iron rings. The mean diameters were 21.5, 22.1, and 22.725 cms., ana me thickness of the bars 2.535, i-*95. ana -7544 cms. respectively. These experiments were intended to illustrate the effect of thickness of bar on the induction. Specimen 5 is from Ewmg's book,t and refers to one ot his own experiments on a soft iron wire .077 cms. diameter and 30.5 cms. long. H Specimen 1 2 3 4 5 high e re- bility rawn 5- B H 3 c B H- B !>■ B f ratively ing fore permea a thin c ecimen 0.2 80 400 126 630 6S 32 5 8.S 425 22 110 1 s Ifi.s O.5 33° 660 377 754 224 448 214 428 74 148 I.O 1450 1450 1449 1449 840 840 885 88c 246 246 2'x E-3 2.0 4840 2420 4564 2282 3533 1766 2417 1208 95O 475 E -1 59 8884 1777 I2430 2486 1 0.0 12970 1297 13023 1302 12540 1254 1 1 388 "39 15020 1502 5 o~-S ° 20.0 14740 737 14911 746 14710 735 13273 664 I5790 709 « v a'" 50.0 16390 V8 16217 3 2 4 16062 321 13890 278 - - Is vah quii whe wir 1 00.0 17148 171 17900 179 14837 148 TABLE 285. — Permeability of Transformer Iron.§ This table contains the results of some experiments on transformers of the Westinghouse and Thomson- Houston types. Referring to the headings of the different columns, Mis the total magneto-motive force applied to the iron; M '/ 1 the magneto-motive force per centimetre length of the iron circuit ; B the total induction through the mag- netizing coil ; B / a the induction per square centimetre of the mean section of the iron core ; M/B the magnetic reluctance of the iron circuit ; Bl/Ma the permeability of the iron, a being taken as the mean cross section of the iron circuit as it exists in the transformer, which is thus slightly greater than the actual cross section of the iron. (a) Westinghouse Nc . 8 Transformers (about 2500 Watts Capacity). First specimen. Second specimen. M I B M Bl B M Bl a B Ma a B Ma 20 O.597 218 X10 8 1406 0.917 X 10- 4 2360 16 X IO* IO32 I.25 XlO- 4 1730 40 I-I94 587 " 3790 O.681 " 3120 49 " 3H° O.82 " 2640 60 1. 791 878 " 5660 O.683 " 3180 82 " 5290 O.73 " 2970 80 2.338 1091 " 7040 o-734 " 2960 104 " 6710 O.77 " 2820 100 2.985 1219 " 7860 0.819 " 2640 118 " 7610 O.85 " 2560 120 >5S 2 1330 " 8580 0.903 " 24IO 124 " 8000 O.97 " 2250 I40 4-179 1405 " 9060 0.994 " 2l86 131 " 8450 I.07 " 2036 l6o 4.776 1475 " 9510 1.090 " 2O0O 135 " 8710 1. 18 " 1830 l8o 5-373 1532 " 9880 1. 180 " 1850 140 " 9030 I.29 " 1690 200 5.970 1 581 " 10200 1.270 " 1720 142 " 9160 1.41 " I540 220 6.567 1618 " I043O 1.360 " I590 144 " 9290 i-53 " 1410 26b 7.761 1692 " I09IO 1.540 " 14IO Smithsonian Tables. * " Phil. Mag. M 4th series, vol. xlv. p. 151. + Ibid. 5th series, vol. xix. p. 73. X " Magnetic Induction in Iron and Other Metals.' 1 § T. Gray, from special experiments. 274 Table 285. PERMEABILITY OF TRANSFORMER IRON. (b) Westinghouse No. 6 Transformers (about 1800 Watts Capacity). M First specimen. Second specimen. M T B B M Bl B M Bl a B Ma a B Ma 20 0.62 I47XI0 3 I320 I.36XIO-4 2140 215X10 8 1940 O.93X10- 4 3H° 40 1.23 442 " 3980 0.91 ' 3260 615 " 5540 O.64 " 4490 60 1.6,5 697 " 6280 0.86 ■ 3390 826 " 7440 O.72 " 4030 80 2.46 862 " 7770 0.93 • 3 T 40 986 " 8880 O.81 " 3590 100 3-oo 949 " 8550 1.05 ' 2770 1050 " 9460 O.95 " 3060 1 20 37" 1010 " 9106 1. 19 ' 2450 1 100 " 9910 I.09 " 2670 140 4-3' 1060 " 9550 9820 i-33 ' 2210 1140 " 10300 I.23 " 2430 160 4-93 1090 " 1.47 ' 1990 1170 " 10500 I.37 " 2180 180 5-55 1 1 20 " IOIOO 1.61 ' 1830 1680 1 190 " 10700 I.5I " 1970 200 6.16 1150 " 10400 1.74 " — — — (C) Westin (about ghouse no. " 1200 Watts ^ Transformer Capacity). (d) Thomson-Houston 1500 Watts Transformer. M B M Bl M B M Bl M I B a B Ma M I B a B Ma 20 O.69 147 XIO 8 1470 I.36X10- 4 2140 20 40 O.42 O.84 70X10 8 142 " 1560 3160 2.86XIO- 4 2.8l " 373° 3780 40 I.38 406 4066 O.98 " 2940 60 80 I.26 1.68 214 " 265 " 4770 5910 2.8l " 3.02 " 3790 3520 60 2.07 573 M 573° I.05 " 2770 100 120 2.10 2.52 309 " 348 " 6890 7760 3.24 " 3-45 " 3280 3080 80 2.76 659 6590 1. 21 " 2390 l6o 200 3-36 4.20 408 " 456 " 9100 10200 3.92 " 4-39 " 27IO 2430 100 345 714 it 7140 I.40 " 207O 24O 280 5.04 S .88 495 " 524 « 1 1000 1 169O 4.87 " 5-35 " 219O 1990 120 4.14 748 a 7490 I.60 " l8lO 32O ^6o 6.72 7-56 550 " 573 " I2270 12780 5.82 " 6.29 " 6.78 " 1820 1690 140 4.8^ 777 " 7770 I.80 " l6lO 400 8.40 591 " 1 3 180 1570 440 9.24 5°4 " 13470 7.28 " 1460 27s Table 286. 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 stated in the paper to have been 240. The maximum magnetization is not tabulated ; but as stated in the by 47r. " 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. Description of Chemical analysis. of Temper. Test 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 . - O.O45 O.200 0.030 None. O.04O _ 5 Whitworth mild steel Annealed O.O90 O.153 0.016 <( O.O42 _ 6 u <( " O.32O O.438 0.017 0.042 O.035 - 7 U tt ( Oil-hard- ( ened ti tt u . ~ 8 11 tl Annealed O.890 O.165 0.005 0.081 0.019 _ 9 tt tl ( Oil-hard- j ened «t (( it — 10 Hadfield's manganese ) steel j ' - I.O05 12.360 0.038 0.204 O.070 _ 11 Manganese steel As forged O.674 4-73° 0.023 0.608 O.O78 _ 12 u a Annealed it ti ti <( it _ '3 " . . ( Oil-hard- 1 ened " " tt <( ii - 14 ti it As forged 1.298 8.740 0.024 0.094 O.O72 _ IS « <( Annealed (« a u a tt 16 it a ( Oil-hard- ( ened tt « u - tt _ 17 Silicon steel As forged 0.685 O.694 « 3-438 O.123 _ 18 (( K Annealed a " m u it 19 tt it ( Oil-hard- | ened tl tt tt a tt _ 20 Chrome steel As forged 0.532 0-393 0.020 0.220 O.041 0.621 Cr. 21 " " Annealed *' « n tt « 22 tt K ( Oil-hard- | ened tt It tt tt « it 23 24 « tt a tt As forged Annealed 0.687 0.028 (( tt it 0.134 (4 O-O43 ti I-I95 Cr. 25 tt a ( Oil-hard- j ened tt " tt tt tt 385 6818 3161 5108 5554 77 51.20 13.67 12.24 12.24 70.69 17-03 20.40 197660 39789 41072 36383 Smithsonian Tables. 277 Table 287. PERMEABILITY OF SOME OF THE SPECIMENS IN TABLE 286. This table gives the induction and the permeability for different values of the magnetizing force of s f "« of the speci- mens in Table 286. The specimen numbers refer to the same table. The numbers in tins table have ^beenl £ ken from the curves given by Dr. Hopkinson, and may therefore be slightly in error; they are the mean values tor rising and falling magnetizations. Magnetiz- ing force. H Specimen 1 (iron). Specimen 8 (annealed steel). Specimen 9 (same as 8 tempered). Specimen 3 (cast iron). B f B »* B H- B C I 2 3 5 10 20 3° 40 S° 70 100 150 200 200 10050 12550 H55° 15200 15800 16000 16360 16800 17400 17950 IOO 2010 1255 727 507 395 320 234 168 116 90 1525 9000 1 1 500 I2650 I33OO 13800 14350 I490O I57OO l6l00 300 900 575 422 332 276 205 149 80 750 1650 5875 9875 1 1600 12000 I34OO 145OO I580O l6lOO 165 294 329 290 240 191 145 105 80 265 700 1625 30OO 50OO 60OO 6500 7IO0 7350 7900 8500 9500 IOI90 265 35° 542 60O 500 3O0 217 177 149 63 51 Tables 288-292 give the results of some experiments by Du Bois,* on the magnetic properties of iron, nickel, and cobalt under strong magnetizing forces. The experiments were made on ovoids of the metals 18 centimetres long and 0.6 centimetres diameter. The specimens were as follows: (1) Soft Swedish iron carefully annealed and having a density 7.82. (2) Hard English cast steel yellow tempered at 230° C. ; density 7.78. (3) Hard drawn best nickel containing 99 % Ni with some Si0 2 and traces of Fe and Cu ; density 8.82. (4) Cast cobalt giving the following composition on analysis: Co = 93.1, Ni=5-8, Fe = o.8, Cu = o.2, Si = o.i, and C = o.3 ; The speci- men was very brittle and broke in the lathe, and hence contained a surfaced joint held together by clamps during the experiment. Referring to the columns, H, B, and n have the same meaning as in the other tables, S is the magnetic moment per gramme, and / the magnetic moment per cubic centimetre. _ H and .? are taken from the curves published by Du Bois ; the others have been calculated using the densities given. Table 288. MACNETIC PROPERTIES OF SOFT IRON AT 0° AND 100° C. Soft iron at c °C. Soft iron at ioc °c. H s / B V- H S I B f IOO 180.0 1408 17790 177.9 IOO 180.0 1402 17720 177.2 200 194.5 1 521 19310 20830 96.5 200 194.O 1511 I9190 96.O 40O 208.0 1627 52.I 400 207.O 1613 20660 51.6 700 215-5 1685 21870 31.2 700 213.4 1663 21590 29.8 IOOO 218.0 1705 22420 22.4 IOOO 215.O 1674 22040 2I.O I20O 218.5 1709 22670 18.9 1200 215-5 1679 22300 18.6 Tables 289. MACNETIC PROPERTIES OF STEEL AT 0° AND 100° C. Steel at o° C. Steel at 100° C. H s / B V- H s / B M IOO 200 400 700 IOOO 1200 375ot 165.0 18 1.0 193.0 199.5 203.5 205.0 212.0 1283 1408 1500 1552 1583 1595 1650 16240 17900 19250 20210 209OO 21240 24470 162.4 89.5 48.1 28.9 20.9 17.7 6.5 IOO 200 400 70O IOOO 1500 3OOO 5OOO 165.0 180.0 191.0 197.0 199.0 203.0 205.5 208.0 1278 '395 1480 1527 1543 1573 1593 1612 1 61 70 17730 19000 19890 20380 21270 23020 25260 161.7 88.6 47-5 28.4 20.4 14.2 7-7 5 1 * "Phil. Mag." 5 series, vol. xxbc. t The results in this and the other tables for forces above 1200 were not obtained from the ovoids above referred to, but from a small piece of the metal provided with a polished mirror surface and placed, with its polished face nor- mal to the lines of force, between the poles of a powerful electromagnet. The induction was then inferred from the rotation of the plane of a polarized ray of red light reflected normally from the surface. (See Kerr's " Constants/' p. 292.) 278 Tables 290-296. NIACNETIC PROPERTIES OF METALS. TABLE 290. - Cobalt at 100= 0. TABLB 291 . _ Nlc]£el at 100 o . | H S / B ^ 200 106 848 I0850 54.2 300 116 928 1 1 960 39-9 SOO 127 1016 I3260 26.5 700 W 1048 13870 19.8 IOOO 134 1076 14520 14.5 1500 13* 1 104 IS380 10.3 2500 143 1 144 16870 6.7 4000 H5 1 164 18630 47 6000 147 1176 20780 3-5 9000 149 1 192 23980 2.6 Ato° C. this specimen gave the fol- lowing results : 7900 1 54 | 1232 | 23380 | 3.0 H £• I B V- 100 35.0 3°9 3980 39-8 200 43-o 380 4966 24.8 300 46.0 406 5399 18.0 500 50.0 441 6043 12.1 700 5i-5 454 6409 9.1 IOOO 53-° 468 6875 6.9 1500 56.0 494 7707 5-i 2500 58.4 515 8973 3-6 4000 59-o 520 10540 2.6 6000 59.2 522 1 2561 2.1 9000 59-4 524 15585 18606 i-7 12000 59-6 526 1-5 Ato°C . this specimen gave the fol- lowing results : 12300 67.5 595 1 19782 1.6 TABLE 292. —Magnetite. The following results are given by Du Bois * for a specimen of magnetite. H / | B V- 500 IOOO 2000 I2000 325 345 35° 35° 8361 9041 10084 20084 16.7 9.0 5.0 i-7 Professor Ewing has investigated the effects of very intense fields on the induction in iron and other metals.t The results show that the intensity of magnetization does not increase much in iron after the field has reached an in- tensity of 1000 c. g. s. units, the increase of induction above this being almost the same as if the iron were not there, that is to say, dBj dH is practically unity. For hard steels, and particularly manganese steels, much higher forces are required to produce saturation. Hadfield's manganese steel seems to have nearly constant susceptibility up to a magnetizing force of 10,000. The following tables, taken from Ewing's papers, illustrate the effects of strong fields on iron and steel. The results for nickel and cobalt do not differ greatly from those given above. TABLE 293. - Lowmooi Wrought Iron. H / B A* 3080 1680 24130 7-8.3 6450 1740 283OO 4-39 10450 I730 32250 3-°9 13600 1720 35200 2.59 16390 1630 1680 36810 2.25 18760 399OO 2.13 18980 1730 4°73° 2.15 TABLE 294. -Victor's Tool Steel. H / B V- 6210 IS30 25480 4.IO 9970 1570 29650 2.97 I2I20 1550 31620 2.6o I4660 1580 34550 35820 2.36 15530 1610 2.31 TABLE 295. - Hadfield's Manganese Steel. H / B V- 1930 55 2620 1.36 2380 84 3430 1.44 3350 84 4400 I-3 1 5920 in 7310 1.24 662O 187 8970 i-35 7890 191 10290 1.30 8390 203 1 1 690 i-39 98IO 39° 14790 1.51 TABLE 296. —Saturation Values for Steels of Different Kinds. Bessemer steel containing about 0.4 per cent carbon . . . Siemens-Marten steel containing about 0.5 per cent carbon Crucible steel for making chisels, containing about 0.6 per cent carbon • ■ • Finer quality of 3 containing about 0.8 per cent carbon . . Crucible steel containing 1 per cent carbon Whitworth's fluid-compressed steel 17600 18000 19470 18330 19620 18700 1770 1660 1480 1580 1440 1590 39880 38860 38010 38190 37690 38710 2.27 2.16 i-9S 2.08 1.92 2.07 * " Phil. Mag." 5 series, vol. xxbt. t "Phil. Trans. Roy. Soc." 1885 and 18 279 Table 297. MACNETIC PROPERTIES OF IRON IN VERY WEAK FIELDS. The effect of very small magnetizing forces has been studied by C. Baur* and by Lord Rayleigh.t The following short table is taken from Baur's paper, and is taken by him to indicate that the susceptibility is finite for zero values of H and for a finite range increases in simple proportion to H. He gives the formula £— 15 -f- 100 H, or 7~ 15 H -\- 100 H 2 . The experiments were made on an annealed ring of round bar 1.013 cms. radius, the ring having a radius of 9.432 cms. Lord Rayleigh's results for an iron wire not annealed give £ = 6.4 + 5.1 #", or / = 6.4 .ff + 5.1 H 2 . The forces were reduced as low as 0.00004 c. g- s., the relation of k 10 H remaining constant. First experiment. Second experiment. H * / H k .01 580 .03081 .07083 .I 3 .8S .230II .38422 16.46 17.65 23.OO 28.90 39.81 58.56 2.63 547 !6-33 38i5 91.56 224.87 .0130 .0847 .0946 .1864 .2903 •3397 15.50 18.38 20.49 25.07 32.40 35.20 Tables 298, 299. DISSIPATION OF ENERGY IN CYCLIC MAGNETIZATION OF MACNETIC SUBSTANCES. When a piece of iron or other magnetic metal is made to pass through a closed cycle of magnetization dissipation of energy results. Let us suppose the iron to pass from zero magneti- zation to strong magnetization in one direction and then gradually back through zero to strong magnetization in the other direction and thence back to zero, and this operation to be repeated several times. The iron will be found to assume the same magnetization when the same magne- tizing force is reached from the same direction of change, but not when it is reached from the other direction. This has been long known, and is particularly well illustrated in the permanency of hard steel magnets. That this fact involves a dissipation of energy which can be calculated from the open loop formed by the curves giving the relation of magnetization to magnetizing force was pointed out by Warburg t m 1881, reference being made to experiments of Thomson, S where such curves are illustrated for magnetism, and to E. Cohn, || where similar curves are given for thermo- electricity The results of a number of experiments and calculations of the energy dissipated are given by W arburg. The subject was investigated about the same time by Ewing, who pub- lished results somewhat later, t Extensive investigations have since been made by a number of investigators. ' »u««.i TABLE 298.- Soft Iron Wire. (From Ewing's 1885 paper.) Horse- Total Dissipation power induction of energy wasted per per sq. cm. in ergs per ton at 100 B cu. cm. cycles per sec. 2000 420 O.74 3000 800 1. 41 4000 1230 2.l8 5000 1700 3.OI 6000 2200 3-89 700O 2760 4.88 8000 345° 6.10 9000 4200 7-43 I OOOO 5000 8.84 1 1 000 5820 10.30 12000 6720 11.89 I3OOO 7650 r 3-53 14000 8650 r 5-3° I5OOO 967O 17.10 * " Wied. Ann." vol. xi. + " Wied. Ann." vol. xiii. p. 141. II " Wied. Ann.'* vol. 6. #» Smithsonian Tables. TABLE 299. — Cable Transformers. This table gives the results obtained by Alexander Siemens with one of Siemens' cable transformers. The transformer core consisted of 900 soft iron wires 1 mm. diameter and 6 metres long.** The dissipation of energy in watts is for 100 complete cycles per second. Mean maxi- mum induc- tion density in core. B Total ob- served dis- sipation of energy in the core in watts per 112 lbs. Calculated eddy^ current loss in watts per 112 lbs. Hysteresis loss of energy in watts per rt2 lbs. Hysteresis loss of energy in ergs per cu. cm. per cycle. IOOO 20O0 30O0 4000 50OO 60OO 43-2 96.2 158.0 231.2 3°9-5 390.1 4 16 36 64 IOO 144 39-2 80.2 122.0 167.2 209.5 246.1 602 1231 1874 2566 3 2I 7 3779 , 'Phil. Mag." vol. xxiii. § " Phil. Trans. Roy. Soc." vol. 17s. . t> t . VU >roc -, Roy ;, S ,. oc - l882 ' aDd " Tn ">s- Roy. Soc" 1885. Proc. Inst, of Elect. Eng." Lond., 1892. 280 Table 300. DISSIPATION OF ENERGY IN THE CYCLIC MAGNETIZATION OF VARIOUS SUBSTANCES. C. P. Steinmetz concludes from his experiments* that the dissipation of energy due to hysteresis in magnetic metals can be expressed by the formula e = aB x -\ where e is the energy dissipated and a a constant. He also concludes that the dissipation is the same for the same range of induction, no matter what the absolute value of the terminal inductions may be. His experiments show this to be nearly true when the induction does not exceed ^ 15000 c. g. s. units per sq. cm. It is possible that, if metallic induction only be taken, this may be true up to saturation ; but it is not likely to be found to hold for total inductions much above the satura- tion value of the metal. The law of variation of dissipation with induction range in the cycle, stated in the above formula, is also subject to verification.! Values of Constant a. The following table gives the values of the constant a as found by Steinmetz for a number of different specimens. The data are taken from his second paper. Nximber of specimen. Kind of material. Description of specimen. Value of I 2 3 4 S 6 7 8 9 10 11 12 13 14 ;* 17 18 19 20 22 23 24 25 26 Iron Steel Cast iron « « Magnetite Nickel is ti Cobalt Iron filings Norway iron • Wrought bar Commercial ferrotype plate Annealed " Thin tin plate Medium thickness tin plate Soft galvanized wire Annealed cast steel Soft annealed cast steel Very soft annealed cast steel Same as 8 tempered in cold water .... Tool steel glass hard tempered in water " " tempered in oil " " annealed ' Same as 13, 14, and 15, after having been subjected ) \ to an alternating m. m. f. of from 4000 to 6000 > I ampere turns for demagnetization , . . . ; Gray cast iron " " " containing J % aluminium « " " i% ■ • f A square rod 6 sq. cms. section and 6.5 cms. long, from the Tilly Foster mines, Brewsters, Putnam J County, New York, stated to be a very pure sample Soft wire • j Annealed wire, calculated by Steinmetz from I Ewing's experiments . ■ Hardened, also from Ewing's experiments ( Rod containing about 2 % of iron, also calculated ) j from Ewing's experiments by Steinmetz . . J 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. 1st experiment, continuous cyclic variation of m. m. I f. 180 cycles per second S 2d experiment, 114 cycles per second tA " 79-91 cycles per second . Smithsonian Tables. * " Trans. Am. Inst. Elect. Eng." January and September, 1892. t See T. Gray, " Proc. Roy. Soc." vol. lvi. 281 .00227 .00326 .00548 .00458 .00286 .00425 .00349 .00848 .00457 .00318 .02792 .07476 .02670 .01899 .06130 .02700 .01445 .01300 .01365 .01459 .02348 .0156 .0385 •0457 .0396 ■°373 Table 301. DISSIPATION OF ENERGY IN THE CYCLIC MAGNETIZATION OF TRANS- FORMER CORES.* This table gives, for the most part, results obtained for transformer cores. The electromagnet core formed a closed iron circuit of about 320 sq. cms. section and was made up of sheets of Bessemer steel about 1-20 inch thick. The No. 20 transformer had a core of soft steel sheets about 7-1000 inch thick insulated from each other by sheets of thin paper. The cores of the other transformers were formed of soft steel sheets 15-1000 inch thick insulated from each other by their oxidized surfaces only. The following are the particulars of the data given in the different columns: — Column 1. Description of specimen. t *' 2. The total energy, in joules per cycle, required to produce the magnetic induction given in column B " 3. The energy, in joules per cycle, returned to the circuit on reversal of the magnetizing force. * ( *. The energy dissipated, in joules per cycle, or the difference of columns 2 and 3. , 6, and 7. The quantities in columns 2, 3, and 4 reduced to ergs per cubic centimetre of the core. " B. The maximum induction in c g. s. units per sq. cm. 1 2 3 4 6 6 7 B 6-5 0.9 5.6 IOIO 140 867 2660 24.4 2.6 21.8 3800 406 3400 6700 66.8 10.4 56.4 10400 1620 8800 11600 81.4 l H 66.0 12700 2400 10300 12700 Electromagnet. . . . - 96.6 126.2 21.8 38.2 74.8 88.0 15100 19700 3400 5960 1 1700 13700 14100 I520O 153-0 57.6 95-4 23900 8990 14900 15900 . 178.4 79.2 99.2 27800 12400 15500 16600 221.2 1 1 6.8 104.4 34500 18300 16300 16800 17240 275.6 168.0 107.6 42900 26200 1742O ''I 1 0.30 1. 01 1435 328 1 107 2330 4980 4.65 1. 10 3-55 51 10 I2IO 3900 Westinghouse No 20 8.25 1.62 6.63 9060 I780 7280 6620 transformer . . . . 10.36 1.89 8.47 1 1 350 2070 9280 7720 12.20 2.98 9.22 13440 3280 10160 8250 ■ 18.20 5-15 13-05 19980 5660 14320 9690 0-45 0.055 0.400 875 I05 770 3480 Westinghouse No. 8 0.80 1.66 2.42 0.102 O.IOI 1.460 2.010 1544 I96 1348 5140 transformer, specimen 1 0.199 0.406 3200 4650 380 780 2820 3870 7570 9250 . 3-54 0.795 2.750 6820 1530 5290 I0940 c 0-399 0.046 0-353 768 88 680 3060 Westinghouse No. 8 0.820 0.085 o-735 1574 164 1410 4830 transformer, specimen 2 1 1713 0.183 i-53o 3300 352 2948 7570 I 2.663 o-343 2.320 5120 660 4460 9270 f 0.488 0.062 0.426 1360 172 1 188 4640 Westinghouse No. 6 J 0.814 0.096 0.718 2260 266 1994 6760 transformer, specimen 1 1 1.430 0.205 1.225 3980 570 34IO 9370 I 2.000 0-330 1.670 556o 918 4642 IO950 • 0.722 0.100 0.622 2000 278 1722 7290 Westinghouse No. 6 1.048 0.164 0.884 2920 456 2464 9000 transformer, specimen 2 " 1-379 0.222 I-I57 3830 616 3 2I 4 9990 • I-73 1 O.328 1.403 4810 912 3898 II2I0 Westinghouse No. 4 transformer . . . . o-355 0-549 0.783 O.O44 0.074 O.I26 0.31 1 0.475 0.657 1210 1880 2690 152 255 433 1058 1625 2257 4540 5920 7140 0.970 0.175 0.795 3340 603 2737 780O Thomson-Houston 1500 watt transformer . . 0.413 0.681 1.207 O.IO5 O.189 O.389 0.308 0.492 0.818 1930 3190 5660 49o 880 1830 1440 2310 3830 615O 825O IIIIO 1.797 0.710 1.087 8420 3320 5100 13290 * T. Gray, from special experiments ; see Table 285 for other properties. Smithsonian Tables. 282 Table 302. DISSIPATION OF ENERGY DUE TO MAGNETIC HYSTERESIS IN IRON.* The first column gives the maximum magnetic induction B per square centimetre in c. g. s. units. The other col- umns give the dissipation of energy in ergs per cycle per cubic centimetre for the iron specified in the foot-note. B 1 2 3 4 5 6 7 2000 40O 420 53° 600 7S0 93° 1 100 3000 780 800 1050 1150 '35° 1700 2150 4000 I20O 1260 1670 1780 2030 2600 33°° SOOO 1680 1770 2440 2640 2810 3800 4700 60OO 2200 2370 3!70 3360 3700 5200 6200 7OOO 2800 3!5° 4020 4300 4650 6600 7800 8000 . 343° 3940 5020 5300 5770 8400 9500 9O0O 4l60 4800 6100 6380 6970 IOIOO 1 1400 I OOOO 4920 573° 7200 7520 8340 1 1 800 13400 IIOOO 5800 6800 8410 8750 9880 13600 15600 12000 67OO 8000 975° 10070 "55° 15400 - I3OOO 762O 9200 1 1 200 1 1460 13260 17300 - I40OO 8620 10500 12780 13100 1 5180 - — ISOOO 973° 1 21 50 14600 14900 17300 1 1 The iron for which data are given in columns 1 to 7 is described as follows : ■ 1. Very soft iron wire (taken from a former paper). 2a. Sheet iron 1.95 millimetres thick ^ ) a i most a ]ike. 2b. Thin sheet iron 0.367 millimetres thick ) 3 Iron wire 0.975 millimetres diameter. I Iron wire of hedgehog transformer 0.602 millimetres diameter. 5. Thin sheet iron 0.47 millimetres thick. 6. Fine iron wire 0.2475 millimetres diameter. 7. Fine iron wire 0.34 millimetres diameter. » Ewing and Klassen, " Phil. Trans. Roy. Soc." vol. cl«xiv. A, p. .015. 283 Table 303. MAGNETO-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 — B = clH(r-Xp) r l \ dK/K*' where c 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 A the wave-length of the light in air. If H be dif- ferent, at different parts of the path, IH is 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 B = 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 = j? (1 — 0.00104? — O.OOOOI4* 2 ), 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 : — » 1 _ /» 1 1 V-i)V where fi is index of refraction and A wave-length of light. 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 formula: 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 Becaue relt Quincke § KoepseU AronsJ Kundt** Jahn.tt Schonrock.tf Gordon, §§ Rayleigh and Sidgewick.HH Perkin.lT Bichat.*** J ° 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. J. G T Du Bou't w7ed°. £ Ann. vole's') 7 *"* ^ "^ ^"^ * "^ range ° £ Tariation of ma S neti «= fi ^ by H. E. t "Ann. de Chim. et de Phys." [3] vol. 52. I » Ar" n :, de . Chi , m " ? de Fh ^" fc] vol. 12 ; " C. R.» vols. 90 and 10a § 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. tt " Zeits. fur Phys. Chem." vol. n. §§ " Proc. Roy. Soc." 1883. III! "Phil. Trans. R. S." 1883. Till " Jour. Chem. Soc." vols. 8 and 12. *** "Jour, de Phys." vols. 8 and 9. Smithsonian Tables. 284 Table 303. MACNETO-OPTIC ROTATION. Solids, Substance. Chemical formula. Density or grammes per c. c. Kind of light. Verdet's constant . * n minutes. lemp. C. Authority. Amber - - D O.OO95 l8-20° Quincke. Blende ZnS - tt 0.2234 15 Becquerel. Diamond C - (t O.OI27 it u Fluor spar .... CaFlj! - tt O.O087 ti tt Glass : Crown - - it O.0203 it » Faraday A . . . . - 5458 tt O.0782 l8-20 Quincke. " B . . . . - 4.284 ti O.0649 » « Flint - tt O.0420 tt tt u - it O.0325 15 Becquerel. « ... - - U O.0416 " tt " dense .... - - it O.0576 " u U It ... - - " O.0647 « u Plate - - tt O.0406 18-20 Quincke. Lead borate . PbB 2 4 - tt O.060O 15 Becquerel. Quartz (perpendicular to axis) - - ti O.O172 18-20 Quincke. Rock salt . . . • NaCl - it 0-0355 15 Becquerel. Selenium Se - B 0.4625 ti « Sodium borate Na 2 B 4 7 - D 0.0170 it tt Spinel (colored by chrome) . Sylvine KC1 - tt tt 0.0209 0.0283 tt tt tt Ziqueline (suboxide of copper) Cu 2 B 0.5908 Smithsonian Tables. 285 v\ Table 304. MAGNETO-OPTIC ROTATION. Liquids. Substance. Chemical formula. Density in grammes per c. c. Kind of light. Verdet*s constant in minutes. Temp. C. Authority. C 8 H e O 0-7947 D 0.0113 20 Jahn. « it 0-7957 tt 0.0115 IS Perkin. tt " O.7947 tt 0.0114 16 Schonrock. Acids : (see also solutions in water) Acetic C2H4O2 1.0561 " O.OI05 21 Perkin. Butyric . C4H8O2 0.9663 tt 0.0116 IS " Formic . CH 2 2 1.2273 " 0.0105 IS " Hydrochloric it HC1 a 1.2072 i( O.0224 O.0206 15 IS Becquerel. Hydrobromic HBr 1.7859 " 0-0343 is Perkin. Hydroiodic . HI 1-9473 O.0513 IS Nitric . HNOs 1.5190 " O.OOJO 13 " (fumin g) it tt 0.0080 IS Becquerel. Propionic C8H6O2 0.9975 n O.OIIO is Perkin. Sulphuric H 2 S0 4 - tt O.OI2I 15 Becquerel. Sulphurous H 2 SO s — 11 O.OI53 15 " Valeric . C6H10O2 0.9438 tt O.OI2I IS Perkin. Alcohols : Amyl . CtHuOH - tt O.OI 31 15 Becquerel. " ti 0.8107 tt O.OI28 20 Jahn. Butyl . C 4 H 9 OH 0.8021 tt O.OI24 20 tt it " - it O.OI24 15 Becquerel. Ethyl '. C 2 H 5 OH 0.7929 u 0.0107 18-20 Quincke. tt 41 0.7900 " O.OI 12 20 Jahn. it ti 0.7944 (< 0.01 14 15 Perkin. it it 0-7943 tt 0.01 13 16 Schonrock. Methyl . CH 3 OH o.79!5 tt O.OO94 18-20 Quincke. a it 0.7920 tt tt O.O093 O.OI06 20 IS Jahn. Becquerel. tt tt tt 0.7966 0.7903 a O.OO96 O.OO96 IS 21.9 Perkin. Schonrock. Octyl . C 8 Hi 7 OH 0.8296 tt O.OI34 is Perkin. Propyl . C s H,OH 0.8050 0.8082 tt 0.0120 20.8 Schonrock. » it tt . 0.0120 15.0 Perkin. u tt - it 0.01 18 iS Becquerel. tt a 0.8042 " O.OI20 20 Jahn. Benzene . CgHe 0.8786 it O.O297 20 Jahn. " it - tt O.O268 IS Becquerel. " ti 0.8718 tt O.O3OI 26.9 Schonrock. Bromides : Bromoform CHBr 3 2.9021 tt O.O317 IS Perkin. Ethyl . C 2 H 6 Br 1.4486 tt O.O183 IS tt Ethylene C2H4Br2 2.1871 a O.O268 IS n " n 2.1780 tt O.O269 20 Jahn. Methyl . CH 8 Br 1 -733 1 a O.O205 Perkin. Methylene CH 2 Br 2 2-4971 tt O.O276 15 " Octyl . CgHi7Br 1.1170 tt O.O164 15 n Propyl . C 3 H 7 Br 1.3600 " O.OlSo 15 tt Carbon disulphide CS 2 1.2644 it O.O441 18-20 Quincke. " " - it O.O434 ( Becquerel, 1 1885. it ti tt tt 0.0433 Gordon. a a tt - " O.O420 18 Rayleigh. tt it " - (( O.O42O 18 Koepsel. a ti tt t( O.O439 Arons. J Smithsonian Tables. 286 Table 304. MACNETO-OPTIC ROTATION Liquids. Substance. Chemical formula. Density in grammes Kind of light. Verdet's constant in Temp C. Authority. per c. c. minutes. Chlorides : Amyl ... Arsenic CHCl As c O.8740 D O.O140 20 Jahn. Carbon — " O.0422 15 Becquerel. " bichloride . ] CCI4 ~ O.OI70 '5 ' a Chloroform CHC1 S tt I.4823 tt 0.0321 O.0164 15 20 a Jahn. Ethyl ..'..] Ethylene . . '. C 2 H 5 C1 C2H4CI2 1.4990 0.9169 I.2589 tt O.0166 O.OI38 O.0166 15 6 15 Perkin. Methyl ! . '. '. CH S C1 CH2CI2 C 8 Hi 7 Cl PC1 S C 8 H 7 C1 SiCL, S2CJ2 S11CI4 ZnCl 2 1. 2561 tt O.0164 20 Jahn. Methylene . Octyl ; Phosphorus protochloride . Propyl .... Silicon .... !-336i 0.8778 0.8922 it tt O.OI70 O.0162 O.OI41 O.0275 O.OI35 !5 '5 15 IS '5 Becquerel. Perkin. Becquerel. Perkin. Sulphur bichloride (t O.0275 15 Becquerel. Tin bichloride . Zinc bichloride . - O.0393 0.0151 15 15 « Iodides : -0437 IS Ethyl Methyl Octyl ....'. C 2 H 5 I CH 3 I C8H17I 1.9417 2.2832 1-3395 u 0.0296 0.0336 0.0213 0.0271 'S •5 15 IS Perkin. Propyl Nitrates : C8H7I 1.7658 tt a Ethyl C 2 H 5 O.N0 2 1.1149 li 0.0091 15 •s IS IS IS is is IS (i Ethylene (nitroglycol) C 2 H 4 (N0 8 ) 2 1.4948 a 0.0088 tt Methyl .... CH3O.NO2 1-2157 « 0.0078 {( Propyl .... C 8 H 7 O.N0 2 1.0622 " 0.0 1 00 tt Trinitrin (nitroglycerine) . C 3 H s (N0 8 ) 8 1.5996 « 0.0090 0.0095 0.0084 tt Nitro ethane C 2 H 6 N0 2 1.0552 " tt Nitro methane . CH 8 N0 2 1-1432 tt tt Nitro propane C 8 H 6 N0 2 I.OIOO it 0.0102 te Paraffins : Decane .... .C10H22 0.7218 0.0128 23.1 Schonrock. Heptane .... C7Hl 6 0.6880 " 0.0125 15 Perkin. Hexane .... C 8 Hi4 0.6580 0.0122 22.1 Schonrock. " 0.6743 " 0.0125 15 Perkin. Octane .... C 8 Hig 0.701 1 it 0.0128 23.1 Schonrock. Pentane .... C5H12 0.6196 " 0.0119 21. 1 tt " .... 11 0.6332 " 0.0118 15 Perkin. Phosphorus (melted) P " 0.1316 33 Becquerel. Sulphur (melted) . S - (( 0.0803 114 <( Toluene .... C7H1J 0.8581 " 0.0269 28.4 Schonrock. .... li - " 0.0243 IS Becquerel. Water H 2 0.9992 It 0.0130 15 tt « " 0.9983 tt 0.0131 1 8-20 Quincke. tt a 0.9983 tt 0.0132 20 Jahn. Xylene ..... C 8 Hio tt 0.0221 15 Becquerel. P ° f the Co1 " Temp. C.= 0° 10° 18° 30° 50° 80° Field. Resistance. OOO 1. 000 1. 000 1. 000 1.000 1. 000 1. 000 1000 I.018 1.019 1.018 1.017 1.014 1.007 2000 1.045 1.050 1.045 1. 041 1.034 1-015 3000 I.088 1.094 1.084 1.074 1.055 1.085 1.032 40O0 I-I35 1-185 "53 1. 131 1.118 1.050 5000 1.214 1-183 1. 156 1.113 1.074 6000 1.240 1-273 1.242 1.202 1. 148 1. 100 7000 1.304 1.340 1.295 1.258 1. 190 1. 127 8000 1-365 1.406 1-358 1.308 1.223 1-154 1.182 9000 1.423 1.467 1.417 1-355 1.266 10000 1.480 1-535 1.480 1.409 i-3°3 1.203 I5O00 1-743 1.875 1.785 1.665 1.505 1-343 2O0OO - 2.507 2.087 1.927 1-713 1.490 25OOO - 2.846 2-393 2.193 1 -931 1.804 3OOOO - - 2.704 - - - 35000 - - 3-031 - - - 40000 3-369 TABLE 313. —Resistance One Ohm for Zero Field and Temperature Zero Cen- tigrade. This table gives the resistance in different magnetic fields and at different temperatures of a wire, the resistance of which is one ohm at o° C, when the magnetic field is zero. The current is supposed to be steady and to flow across the field. Temp. C= 0° 10° 18° 30° 60° 80° Field. Resistance. OOOO 1000 2000 3OOO 4000 5000 OOOO 7000 80OO 9OOO I OOOO 15000 20000 25OOO 1. 000 1.018 1.045 I.088 I.I35 I.185 I.240 I.304 I-365 I-423 1.480 1-743 1.037 1.057 1.089 1-134 1.198 1.260 1323 1.392 1.458 1-523 1.592 1.946 2.295 2.645 1.072 1. 091 1.118 1. 162 I.2I0 I.265 I.327 I-385 1-453 I.5J5 I-583 1.907 2.243 2.560 1.115 1. 129 I.156 1.198 I.246 I.290 1 -341 1.404 1.460 1.509 1.860 2.148 2.445 1.200 1.217 1.241 I.266 I.302 1-335 1-379 1.428 1.465 1.520 1.562 1.805 2.055 2.320 1-332 I-34I 1-352 1-375 1-397 1.428 1.464 1.500 1-536 1-573 1.610 1.784 1.980 2.157 • Calculated from the results of J. B. Henderson's experiments, " Phil. Mag." vol. 38, p. 488. Smithsonian Tables. 293 Table 314. SPECIFIC HEATS OF VARIOUS SOLIDS AND LIQUIDS.* Solids. Substance. Temperature in degrees C. Specific heat. Authority. Alloys : Bell metal Brass, red " yellow . 80 Cu + 20 Sn 88.7 Cu + 11.3AI German silver Lipowitz alloy : 24.97 Pb -f- IaI 3 Cd -f- 50. + 14.24 Sn ditto Rose's alloy : 27.5 Pb + 48.9 Bi + 23-6 Sn ditto Wood's alloy : 25.85 Pb + 6.99 Cd + 52.43 1473 Sn ditto (fluid) Miscellaneous alloys : 17.5 Sb + 29.9 Bi + 18.7 Zn + 33.9 Sn 37.1 Sb + 62.9 Pb 39.9 Pb + 60.1 Bi ditto (fluid) . 63.7 Pb + 36.3 Sn 46.7 Pb + 53.3 Sn 63.8 Bi + 36.2 Sn 46.9 Bi + 53. t Sn CdSn 2 Basalt Calcspar Diamond Gas coal Glass, crown " flint " mirror Gneiss Granite Graphite 66 Bi Bi + 15-98 o o 14-98 20-100 O-IOO 5-5° 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 — 77-20 20-100 16-48 — 5°-5 10.7 140.0 206.0 606.7 985 20-1040 10-50 10-50 10-50 — 19-20 17-213 O-IOO —50-3 io.8 138-5 201.6 641.9 977.0 16-1040 A M = A. M. Mayer. G & T = Gee & Terry. H W = H. F. Weber. L = Lorenz. P = Person. R W = R. Weber. References. B = Batelli. D = Dewar. H & D = De Heen & Deruyts. J&B = Joly&Bartoli. Ln = Luginin. M = Mazotto. Pa = Pagliani. Pn = Pionchon. T = H. Tomlinson. Th = Thomsen. 0.0858 .08991 .08831 .0862 .10432 .09464 •0345 .0426 .0356 .0552 .0352 .0426 •05657 .03880 •03165 .03500 .04073 .04507 .04001 .04504 •05537 .20-.24 .206 .0635 .1128 .2218 •2733 .4408 .4589 •3!45 .161 .117 .186 .1726 •2143 .19-.20 .1138 .1604 .2542 .2966 .4450 .4670 .310 R L « R Ln T M S M R a p it R K H W HM RW J&B H W D E = Emo. HM=H. Meyer. K = Kopp. Ma = Marignac. R = Regnault. W = Wachsmuth. * Condensed from more extensive tables given in Landolt and Bomstein's '* Phys. Chem. Tab.' ! Smithsonian Tables. 294 Table 314. SPECIFIC HEATS OF VARIOUS SOLIDS AND LIQUIDS. Substance. Gypsum . Ice « India rubber (Para) Marble, white . " gray . Paraffin u (( M " fluid '. Quartz <* « Sulphur, cryst. . Vulcanite . Temperature in degrees C. 16-46 —78-O —30-0 — 2I-I ?-IOO 16-98 23-98 —20-3 I9-2O O-20 35-40 60-63 O 35° 400-1200 17-45 20-100 Specific heat. O.259 .4627 •5°5 ■5 OI 7 .481 .2158 .2099 .3768 •5251 ■6939 .622 .712 .2786 •3°5 .163 •33 12 Authority. K R P (( G&T R « R W B Pn K AM Liquids. Alcohol, ethyl methyl Benzene Ethyl ether Glycerine Oils, castor " citron " olive " sesame " turpentine Petroleum CuS0 4 + 5oH 2 " + 200 H 2 " -j- 400 H2O ZnS0 4 + 50 H 2 " -f- 200 H 2 KOH + 3° H2O " + 200 H 2 NaOH + 5° H 20 " + 100 H 2 NaCl +ioH 2 " -j- z0 ° h 2 o Sea water : density 1.0043 . ■ ■ « <■ " 1.0235 (about normal) " 1.0463 — 20 o 40 5-10 15-10 10 40 o 15-50 5-4 6.6 o 21-58 12-15 12-14 13-17 20-52 20-52 18 18 18 18 18 18 17-5 17-5 17-5 0-5053 ■5475 .6479 .5901 .6009 •3402 •4233 .5290 .576 •434 ■438 .471 ■387,. .4106 .951 •975 .842 .952 .876 •975 .942 ■983 .791 .978 .980 ■938 •903 References. A M = A. M.Mayer. B = Batelli. D = Dew f- £ & T = Gee & Terry. H & D = De Heen & Deruyts. HW = H.F.Weber. J & B = Joly & Bartoh I-Lorenz. Ln = Luginin. M = Mazotto. P- Person p a = Pa#liani. Pn = Pionchon. RW=R Weber. T = H. Tomlinson. Th = Thomsen. H&D U R E W H W W R Pa Ma « Th E = Emo. H M = H. Meyer. K = Kopp. Ma = Marignac. R = Regnault. W = Wachsmuth. Smithsonian Tables. 295 Table 315. SPECIFIC HEAT OF METALS.* Metal. Temperature in Specific heat. ■c Metal. Temperature in Specific •f degrees C. "3 degrees C. heat. •S 2I resistance, electric . . . .' 23 stress 19, 22 temperatures 25 tension, film or surface 20 298 INDEX. Conversion (continued). time, intervals of H velocities 1 5 volumes I2 work 20, 21 Critical temperature of gases 200 Crystals, cubic expansion of 216 elastic constants of 78 formulae for elasticity of 77 refractive indices of 187 Cubic expansion, gases 218 liquids 217 solids 216 Cyclic magnetization, dissipation of energy in : 280-283 Declination, magnetic 1 13-1 18 Densities, of air, values of .4/760 162 alcohol 96-98 alloys and other solids 85 aqueous solutions 9° gases 89 liquids 88 mercury 95 metals 86 organic compounds 212 water 92-94 woods 87 Density, conversion factors for 23 Dew-points, table for calculating 158 Diamonds, unit of weight for 13 Dielectric strength 244, 245 Diffusion of gases and vapors 149 liquids and solutions 147 Dilution of solution, contraction due to .... 134 Dimension formulae (see also Units) xvii Dip, magnetic in Dynamic units, dimension formulae of xvii formulae for conversion of 2 Dynamical equivalent of thermal unit 219 Earth, miscellaneous data concerning 106 Elasticity, moduli of 74-78 Electric conductivity of alloys 251, 252 of metals 255 relation to thermal 271 constants of wires 58-68, 254 displacement 25 potential, conversion factors for 27 resistance, conversion factors for 23 resistance, effect of elongation on 258 units, conversion factors for 3 units, dimension formulae xxv Electrochemical equivalents and atomic weights 272 of solutions 259 Electrolytes, conductivities of 259 Electrolytic deposition, conversion factors for . 24 Electromagnetic system of units xxix Electromotive force of battery cells. . . .246, 247 Electrostatic system of units xxvi Electrostatic unit of electricity, ratio of, to electromagnetic 243 Elliptic integrals 43 Elongation, effect on resistance of wires 258 Emissivity 234, 235 Energy, conversion factors for 20, 21 Equivalent, electrochemical 272 electrochemical of solutions 259 mechanical, of heat 220 Expansion, thermal 214, 218 Factors, conversion 1 1-27 formulae for conversion 2, 3 Film-tension, conversion factors for 20, 22 constants for 128, 129 Fluor spar, refractive index of 183 Formulae for conversion factors, dynamic units 2 electric and magnetic units 3 fundamental units 2 geometric units z heat units 3 Formulae, dimension (see also Units), .xvii-xxix Force, conversion factors for 17 Force de cheval, definition of 19 Fraunhofer lines, wave-lengths of 175 Freezing mixtures 199 Freezing-point, lowering of, by salts 192 Friction, coefficients of 135 Functions, hyperbolic 2 ^~~35 gamma 38 Fundamental units 2 Fusion, latent heat of 206 Gamma functions 38 Gases, absorption by liquids 125 compressibility of 79-81 critical temperatures of 200 density and specific gravity of 89 expansion of 218 magnetic susceptibility of 292 magneto-optic rotation in 291 refractive indices of 190 specific heat of 224 thermal conductivity of 198 viscosity of 145, 146 volume of perfect (values of 1 -j- .00367 /) 164-168 Gauges, wire 58-68 Geometric units, conversion formulae for 2 Glass, electric resistance of 270 indices of refraction for 178, 179 Gravity, force of 102-104 Harmonics, zonal 40 Heat, conversion factors for quantities of. . . .24 latent heat of fusion 206 latent heat of vaporization 204 mechanical equivalent of 220 units, conversion factors for 24 dimension formulae for xxiii formulas for conversion factors of 3 Heats of combustion and combination. . 201, 202 Heights, determination by barometer 169 Humidity, relative 161 Hydrogen thermometer 233 Hyperbolic cosines 29-31 Hyperbolic functions 28-35 Hyperbolic sines 2 ^ _ 3° Hysteresis, magnetic 280-283 Iceland spar, refractive index of 185 Indices of refraction for alums 180 crystals 187 fluor spar 185 gases and vapors 190 glass 178, 179 Iceland spar 185 liquids, various 189 metals and metallic oxides 181 monorefringent solids ..., 184 INDEX. 299 Indices of refraction for alums (continued). quartz ...186 rock salt _ T 3 2 solutions of salts .... 1^8 T , s ylvine ...".!i82 Inductance, mutual 42 Integrals, elliptic ..'.'.'....'.'.' I3 Intensity, horizontal, of earth's magnetic field 112 total, of earth's magnetic field no Iron, elasticity and strength of 72 hysteresis in 280-283 magnetic properties of 274-283, 292 ""Isotonic coefficients . .150 Jewels, unit of weight for 13 Joule's equivalent 220 Kerr's constant, definition and table of 292 Kilogramme, definition of xvi Kundt's constants 291 definition of 291 Latent heat 204, 206 Least squares, various tables for 35, 37 Legalization of practical electric units xxxiv Length, conversion factors for n Light, velocity of 176-243 rotation of plane of polarized 191 Linear expansion of chemical elements 214 of various substances 215 Liquids, absorption of gases by 125 compressibility and bulk moduli of 82 density of 88 magneto-optic rotation in 286, 287 magnetic susceptibility 292 refractive indices of 189 specific heat of 295 thermal conductivity of 197, 198 thermal expansion of 217 Lowering of freezing-point by salts 192 Magnetic field, effect of, in resistance of bis- muth 293 moment, conversion factors for 27 permeability 274-280 properties of cobalt, manganese steel, magnetite and nickel 279 properties of iron and steel 276 saturation values for steel 279 susceptibility of liquids and gases 292 units, conversion formulas for 3 dimension formulae for xxv Magnetism, conversion factors for surface density 2 ° terrestrial .110-1 IH Magnetization, conversion factors for inten- sity of • 26 Magnetite, Kerr's constant for 292 magnetic properties of 279 Magneto-optic rotation, general reference to tables of ■ 28 5- 2 9i Masses, conversion factors for 13 Materials, strength of 7°~73 Measurement, units of ..... - -™ Mechanical equivalent of heat. 220 Melting-points of chemical elements 207 of inorganic compounds zoo Melting-points (continued). of mixtures and alloys 211 of organic compounds 212 Mercury, density of 86 electric resistance of 255, 256 index of refraction 181 specific heat of 225 strength of . '. 70 Metals, density of 86 electric resistance of 254-258 specific heat of 296 thermal conductivity of 197 Metals and metallic oxides, indices of refrac- tion for 181 Metre, definition of xvi Metric weights and measures — equivalents in British 5 equivalents in United States 10 Mixtures, freezing 199 Moduli of elasticity 74-78 Molecular conductivities 261, 262 Moments of inertia, conversion factors for. . . 13 Moment of momentum, conversion factor for 16 Momentum, conversion factors for 13 Mutual inductance, table for calculating 42 Neutral-points, thermoelectric 249 Newton's rings and scale of colors 130 Nickel, Kerr's constants for 292 magnetic properties of 279 Ohm, various determinations of 262 Osmose and osmotic pressure 150 Pearls, unit of weight for 13 Peltier effect 250 Pendulum, length of seconds 104, 105 Permeability, magnetic 274-280 Photometric standards 176 Planets, miscellaneous data concerning 106 Poisson's ratio 76 Polarized light, rotation of the plane of 191 Potential, contact difference of 268 difference of, between metals in solu- tions 269 electric, conversion factors for 27 Pound, definition of xvi Power, conversion factors for 19, 21 Practical electrical units xxxiii Pressure, barometric, for different boiling- points of water 170, 171 critical, of gases 200 effect on radiation 236 of aqueous vapor 1 51-1 54 at low temperatures 156 in the atmosphere 1 57 of mercury column 119 osmotic 15° of vapors 126, 225-227 of wind 108 Probability, table for calculating 36 Quartz, fibres, strength of 7° refractive index of 186 Radiation, effect of pressure on 236 Relative humidity 161 3°° INDEX. Resistance (see also Conductivity), electric. of alloys 251-253, 256, 257 of electrolytes 259 of glass and porcelain 270 of metals and metallic wires 254-257 of wires, effect of elongation on 258 Rigidity, modulus defined 74 of metals . . , 74 variation of, with temperature 7° Rotation, magneto-optic 284-291 Saturation values, magnetic, for steel 279 Seconds pendulum, length of 104, 105 Secondary batteries 247 Sections of wires 44~54> 58-68 Sheet metal, weight of 56, 57 Soaring of planes, data for 109 Solar constant '77 Solar spectrum, wave-length in 172 Solids, compressibility and bulk moduli of . . .83 density of 85 magneto-optic rotation in 284 Solution, contraction produced by 131-134 Solutions, aqueous, boiling-points of 196 density of 90 magneto-optic rotation in 288-290 refractive indices for 188 specific heat of 224 Sound, velocity of, in air 99 in gases and liquids 101 in solids 100 Specific electrical resistance, conversion fac- tors for 23, 254-256 Specific gravity (see also Density). of aqueous ethyl alcohol 96 methyl alcohol 97 of gases 89 Specific heat of air 223 of gases and vapors 224 of metals 296 of solids and liquids 294, 295 of water 223 of water, formulae for 222 Specific inductive capacity 263-265 viscosity, aqueous solutions 144 oils 137 water 136 Spectra, wave-lengths in arc and solar 172 Standard cells 247 wave-lengths of light 172 Standards, photometric 176 Steel, physical properties of 71 Steam, properties of saturated 237 Steinmetz, constants for hysteresis of 281 Stone, strength of 70 thermal conductivity of 197 dielectric 244 Strength of materials 70-73 Stress, conversion factors for 19, 22 Surface-tension, constants of 128, 129 conversion factors for 20, 22 Sylvine, refractive index of 182 Temperature, conversion factors for 25 critical, of gases 200 Terrestrial magnetism, agonic lines 117 declination, data for maximum east at various stations 118 dip and its secular variation for differ- ent latitudes and longitudes in Terrestrial magnetism {continued). horizontal intensity and its secular varia- tion for different latitudes and longi- tudes 112 secular variation of declination . . . . 1 13-1 16 Thermal conductivities i97i Ic £ relation to electrical 271 expansion, coefficients of 214-218 units, dynamic equivalent of 219 Thermoelectricity 248-250 Thermometer 228-233 air 228, 231 correction of, for mercury in stem 232 hydrogen 231 mercury in glass 229 zero change due to heating 229 zero, change of, with time 230 Timber, strength of 7°, Time, unit of, defined xvii Times, conversion factors for . ... 14 Transformers, permeability of iron in 274, 275, 280, 282 Units of measurement xv dimension formulae for dynamic xviii electric and magnetic xxv electromagnetic xxix electrostatic xxvi fundamental 2 heat xxiii practical, legalization of electric xxxiii ratio of electrostatic to electromagnetic 243 United States weights and measures in metric 9 Vapor, density of aqueous 155 diffusion of 149 pressure of 126, 225-227 pressure of aqueous 1 51-154 values of 0.3781? 160 pressure of, for aqueous solutions 194 refractive indices for 190 specific heats of 224 Vaporization, latent heat of 204 Velocity, angular and linear, conversion fac- tors for 15 of light 176, 243 of sound 99, 101 Verdet's constants for alcoholic solution of salts 290 aqueous solutions of salts 287 gases 291 hydrochloric acid solutions of salts 290 liquids and solids 285-287 and Kundt's constants 292 Viscosity, coefficient, definition of 136 coefficient of, for aqueous alcohol 137 for gases 146 for liquids 138 temperature effect on, for liquids 139 specific, for oils 137 for water 136 Volumes, conversion factors for 12 critical, of gases 200 Water, boiling-point for various barometric pressures 170, 171 density of 92-94 specific heat of 222, 223 INDEX. 301 Water (continued). thermal conductivity of 198 viscosity of 136 Wave-lengths of Fraunhof er lines 175 standard for arc and solar spectrum. ... 172 Weights and measures — British Imperial to Metric 7, 8 Metric to British Imperial 5, 6 Metric to United States 10 United States to Metric 9 Weights of sheet metal 56, 57 Weights of wires 44-54 Wind, pressure of I0 8 Wire, gauges ^~as Woods, densities of °° Work, conversion factors for 20, 21 Yard, definition of xvl Young's moduli 75 modulus, definition of 75 Zonal harmonics 4°