§ I.-a. FORMULÆ OF THE ABSOLUTE UNITS. * 1. Fundamental Units. Centimetre for Length. Gramme for Mass. Second for Time. 5. Electro-Static System of Units. Quantity of Electricity Strength of Electric Current * See "Units and Physical Constants, "-Everett † length between poles. v=3x 1010 centimetres per second approximatively, and is the ratio of the Electro-magnetic to the Electro-static Unit of Quantity. PRACTICAL ELECTRICAL UNITS OF MEASUREMENT. 303 b. PRACTICAL ELECTRICAL UNITS OF MEASUREMENT (British Association and International Congress of Electricians, Paris, 1881.) 1. For electrical measurements the fundamental units, the centimetre (for length), the gramme (for mass), and the second (for time), forming the C.G.S. system, are adopted. 2. Resistance = (R).—The Ohm is equal to 109 C.G.S.* units of resistance. It is equal to the resistance of a column of pure mercury 1.0624 metres long, of a square millimetre section, at the temperature of zero Centigrade. The Megohm = one million ohms. The Siemens Mercury Unit (length 1 metre, section 1 sq. mm. at 0° C.) = 0.94125 ohms. The above are according to Lord Rayleigh's latest determinations, as given in his letter to the Paris International Conference du Electric Units, Oct. 1882. One mercury unit = 0·95412 of the B.A. unit, and one B.A. unit = 0·98651 of the true ohm. 3. Electro-motive Force = (E).—The Volt is equal to 108 C.G.S.* units of electro-motive force, or about 8 per cent. less than the E.M.F. of a standard Daniell's cell. Electro-motive force is equivalent to the difference of potential between two points. 4. Current(C).—The Ampere is equal to 10-1 C.G.S.* units of current. It is the current produced by a volt through an ohm. Ohm's Law...Current= Electro-motive force or C= = E R 5. Quantity =(Q).—The Coulomb is equal to 10-1 C.G.S.* units of quantity. It is the quantity of electricity given by an ampère in a second. 6. Capacity=(K).—The Farad is equal to 10-9 C.G.S.* units of capacity. It is the capacity defined by the condition that a coulomb charges it to the potential of a volt. A microfarad = (mfd.) = 10-15 C.G.S.* units of capacity, or onemillionth of a Farad. = † 7. Power (P).-The Watt is equal to 107 C.G.S.* units of power. It is the power conveyed by a current of an ampere through a conductor whose ends differ in potential by a volt; or, in other words, the rate of doing work when an ampere passes through an ohm, and it is equal to 107 ergs, or a Joule per second (16 of a Ex C horse-power nearly)... Ex C = Watts, and = horse-power. 746 8. Heat or Work = (W).—The Joule is equal to 107 C.G.S.* units of work or ergs. It is the work done, or heat generated by a Watt *Electro-magnetic system. Two units proposed by Dr. Siemens at British Association, 1882, and likely to be adopted in practice. in a second-i.e., the work done, or heat generated in a second by an ampère flowing through the resistance of an ohm, or the heat generated by a coulomb running down through a difference of potential of 1 volt. It is therefore the amount of heat equivalent to 107 ergs. Assuming Joule's equivalent = 42,000,000, it is the heat necessary to raise 238 gramme of water 1° C., or approximately Dog of the arbitrary unit now in use of 1 lb. of water raised 1° C. c. MECHANICAL UNITS. 1. Acceleration is the rate of change of velocity, and may be either positive or negative. 2. Gravity. The acceleration of a body falling freely under the action of gravity in vacuo is denoted by (g). The value of (g) in C.G.S. units at any part of the earth's surface is approximately 981 (at Greenwich = 981∙17); or 32.2 foot second units. = 3. Force. The C.G.S. unit of force is called the dyne. It is the force which, acting upon a gramme for a second, generates a velocity of a centimetre per second. 4. Work. The C.G.S. unit of work is called the erg. It is the amount of work done by a dyne working through a distance of one centimetre. 5. Energy. The C.G.S. unit of energy is also called the erg; work done being equal to the energy expended. 6. Work expressed in Gravitation Measure: One gramme centimetre = (g) ergs = 981 ergs. = 1·356 × 107 ergs = 13.56 million ergs. 7. The Unit Rate of Working is one erg per second. Watt's “Horse-power” = 33,000 foot-pounds per minute = 550 foot-pounds per second = 7.46 × 109 ergs per second = 7,460 million ergs per second. The equivalent electrical energy of a Ex C horse-power = 746 (where E = electro-motive force in volts and C = current in ampères). The French "force de cheval"=75 kilogramme-metres per second = 7.36 x 109 ergs per second = 7,360 million ergs per second. d. HEAT UNITS. 8. Heat (H).—The unit of heat is the amount of heat required to raise one gramme of water from 0° to 1° Cent. 9. The mechanical equivalent of heat (see Proceedings Royal Society, vol. xxvii., p. 38, by Joule) 772-55 foot-pounds at the sea level of Greenwich for each degree Fah. in a pound of water = 4.1624 × 107 ergs per gramme degree Cent., say 42 million ergs, generally represented by letter (J). X 10. The Heat Generated in time T (seconds) by a current C C2 RT ECT through a wire of resistance R is J (gramme degrees), where J=4.2 x 107, and C, R, and E are expressed either in absolute electro-magnetic or electro-static units. For practical use when C is amperes, R ohms, E volts, and T seconds, the heat generated in time T-C2 RT × 0·2405, or ECT×0-2405 gramme degrees. e. LIGHT UNITS. 1. The English unit of light is the light given out by one sperm candle burning 120 grains per hour; (six candles weighing one pound). 2. Mr. Vernon Harcourt's standard flame equals the average of one English standard candle. It consists of an air-gas flame, 2 inches in height, rising from an opening inch diameter. Mixture of air and pentane: 576 volumes of air to one of liquid pentane at 60° Fah., or if both are in form of gas 20 of air to 7 of pentane. 3. The French unit of light is the light given out by one Carcel burner, and equals 9-3 English standard candles. § II.-ELECTRO-CHEMICAL EQUIVALENTS. 1. *Quantitative Laws of Electrolysis.-I. The amount of chemical action is equal at all points of a circuit. II. The quantity of an ion liberated at an electrode in a given time, is proportional to the strength of the current in ampères. III. The quantity of an ion liberated at an electrode in one second, is equal to the strength of the current multiplied by the "electro-chemical equivalent" of the ion. z= the electro-chemical equivalent (see Table I. col. 5). w= the weight in grammes of the ion (or element) liberated; then w=CTz=Q z. The above rules, as may be inferred from law (I.), apply not only to the decomposition in a depositing bath, or outside the battery, but also to that taking place inside the charging battery itself. * See "Magnetism and Electricity," Art. 211, Sylvanus P. Thompson. X 2. Polarization.-Whenever an electrolyte is decomposed by a current of electricity, the resolved ions have a tendency to reunite, thus setting up an opposing electro-motive force to the decomposing current. This tendency to reunite is commonly termed "chemical affinity." The electro-motive force of the decomposing current must therefore be greater than that due to the chemical affinity of the resolved ions. For example, when water is decomposed by a current of electricity into its constituent ions, oxygen and hydrogen, the opposing electromotive force due to the chemical affinity of these two gases is about 1.5 volts; therefore no battery can decompose water unless it has an electro-motive force at least greater than 1.5 volts. 3. Electrolysis.—If Q = the quantity of electricity passed through an electrolyte in C.G.S. units, E the opposing electro-motive force in C.G.S. units, = Z the electro-chemical equivalent of the ion deposited per H = heat of combination in gramme degrees of the ion in JJoule's equivalent = (42 x 10o), Then the amount of work done = EQ = QZHJ = Joule's. E = =ZHJ.* Or, the electro-motive force of any chemical reaction is equal to the product of the electro-chemical equivalent of the separated ion into the heat of combination expressed in fundamental units or ergs.† The principle and action of SECONDARY BATTERIES depend upon the above laws and rules. One ampere decomposes 0000945 gramme of water per second, liberating 0000105 gramme of hydrogen, and 0000840 gramme of oxygen. The amount in grammes of any other ion liberated from an electrolyte in one second by a current of one ampère is given by the electro-chemical equivalent of the ion. The electro-chemical equivalent of any element is found by multiplying its chemical atomic weight equivalent (or ight) by the equivalent for hydrogen, valency viz., 0000105 (see Table I. col. 5). *To express E in volts, divide by 10o. +For example:-In decomposing water we can calculate the opposing E. M. F. that will be set up by the hydrogen tending to unite with the oxygen. By formula E ZHJ (see Table I. for Z, and Table II. for H and J), ... E=000105 × 34000 × 42 × 10o·000105 × 1·43 × 1012 = 1·5 × 10° = C.G.S. units of E.M.F... E = 108 1.5 volts. In the same way we may calculate the opposing E.M.F. set up in charging any secondary battery, or effecting any particular electrolysis. |