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and v, the velocity of propagation, is equal to /T. As the means of a number of experiments Blondlot found v to be 3.02X100 cm./sec., which, within the errors of experiment, is equal to 3X1010 cm./sec., the velocity of light. A second method used by Blondlot, and one which does not involve the calculation of the period, is as follows:-A and A' (fig. 10) are two equal Leyden jars coated inside and outside with tin-foil. The outer coatings form two separate rings a, a1; a', a'ı, and the inner coatings are connected with the poles of the induction coil by means of the metal pieces b, b'. The sharply pointed conductors p and p', the points of which are about mm. apart, are connected with the rings of the tin-foil a and a', and two long copper wires pca, p'c'a', 1029 cm. long, connect these points with the other rings a1, a'. The rings aa', aa, are connected by wet strings so as to charge up the jars. When a spark passes between b and b', a spark at once passes between pp', and this is followed by another spark when the waves travelling by the paths a cp, a'c'p' reach p and p'. The time between the passage of these sparks, which is the time taken by the waves to travel 1029 cm., was observed by means of a rotating mirror, and the velocity measured in 15 experiments varied between 2.92X1010 and 3.03X100 cm./sec., thus agreeing well with that deduced by the preceding method. Other determinations of the velocity of electromagnetic propagation have been made by Lodge and Glazebrook, and by Saunders. On Maxwell's electromagnetic theory the velocity of propagation of electromagnetic disturbances should equal the velocity of light, and also the ratio of the electromagnetic unit of electricity to the electrostatic unit. A large number of determinations of this ratio

C'

FIG. 10.

have been made:

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The mean of these determinations is 3.001 X 1010 cm./sec., while the mean of the last five determinations of the velocity of light in air is given by Himstedt as 3.002 X 1010 cm./sec. From these experiments we conclude that the velocity of propagation of an electromagnetic disturbance is equal to the velocity of light, and to the velocity required by Maxwell's theory.

In experimenting with electromagnetic waves it is in general more difficult to measure the period of the oscillations than their wave length. Rutherford used a method by which the period of the vibration can easily be determined; it is based upon the theory of the distribution of alternating currents in two circuits ACB, ADB in parallel. If A and B are respectively the maximum currents in the circuits ACB, ADB, then

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the other circuit ACB of a low metallic resistance bent to have considerable self-induction, the preceding equation becomes approximately p=S/L, so that when S and L are known is readily determined. (J. J. T.)

ELECTROCHEMISTRY. The present article deals with processes that involve the electrolysis of aqueous solutions, whilst those in which electricity is used in the manufacture of chemical products at furnace temperatures are treated under ELECTROMETALLURGY, although, strictly speaking, in some cases (e.g. calcium carbide and phosphorus manufacture) they are not truly metallurgical in character. For the theory and elemental laws of electro-deposition see ELECTROLYSIS; and for the construction and use of electric generators see DYNAMO and BATTERY: Electric. The importance of the subject may be gauged by the fact that all the aluminium, magnesium, sodium, potassium, calcium carbide, carborundum and artificial graphite, now placed on the market, is made by electrical processes, and that the use of such processes for the refining of copper and silver, and in the manufacture of phosphorus, potassium chlorate and bleach, already pressing very heavily on the older non-electrical systems, is every year extending. The convenience also with which the energy of waterfalls can be converted into electric energy has led to the introduction of chemical industries into countries and districts where, owing to the absence of coal, they were previously unknown. Norway and Switzerland have become important producers of chemicals, and pastoral districts such as those in which Niagara or Foyers are situated manufacturing centres. In this way the development of the electrochemical industry is in a marked degree altering the distribution of trade throughout the world.

Electrolytic Refining of Metals.-The principle usually followed in the electrolytic refining of metals is to cast the impure metal into plates, which are exposed as anodes in a suitable solvent, commonly a salt of the metal under treatment. On passing a current of electricity, of which the volume and pressure are adjusted to the conditions of the electrolyte and electrodes, the anode slowly dissolves, leaving the insoluble impurities in the form of a sponge, if the proportion be considerable, but otherwise as a mud or slime which becomes detached from the anode surface and must be prevented from coming into contact with the cathode. The metal to be refined passing into solution is concurrently deposited at the cathode. Soluble impurities which are more electro-negative than the metal under treatment must, if present, be removed by a preliminary process, and the voltage and other conditions must be so selected that none of the more electro-positive metals are co-deposited with the metal to be refined. From these and other considerations it is obvious that (1) the electrolyte must be such as will freely dissolve the metal to be refined; (2) the electrolyte must be able to dissolve the major portion of the anode, otherwise the mass of insoluble matter on the outer layer will prevent access of electrolyte to the core, which will thus escape refining; (3) the electrolyte should, if possible, be incapable of dissolving metals more electro-negative than that to be refined; (4) the proportion of soluble electro-positive impurities must not be excessive, or these substances will accumulate too rapidly in the solution and necessitate its frequent purification; (5) the current density must be so adjusted to the strength of the solution and to other conditions that no relatively electro-positive metal is deposited, and that the cathode deposit is physically suitable for subsequent treatment; (6) the current density should be as high as is consistent with the production of a pure and sound deposit, without undue expense of voltage, so that the operation may be rapid and the "turnover" large; (7) the electrolyte should be as good a conductor of electricity as possible, and should not, ordinarily, be altered chemically by exposure to air; and (8) the use of porous partitions should be avoided, as they increase the resistance and usually require frequent renewal. For details of the practical methods see GOLD; SILVER; COPPER and headings for other metals.

Electrolytic Manufacture of Chemical Products.-When an aqueous solution of the salt of an alkali metal is electrolysed, the

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metal reacts with the water, as is well known, forming caustic alkali, which dissolves in the solution, and hydrogen, which comes off as a gas. So early as 1851 a patent was taken out by Cooke for the production of caustic alkali without the use of a separate current, by immersing iron and copper plates on opposite sides of a porous (biscuit-ware) partition in a suitable cell, containing a solution of the salt to be electrolysed, at 21°-65° C. (70°-150° F.). The solution of the iron anode was intended to afford the necessary energy. In the same year another patent was granted to C. Watt for a similar process, involving the employment of an externally generated current. When an alkaline chloride, say sodium chloride, is electrolysed with one electrode immersed in a porous cell, while caustic soda is formed at the cathode, chlorine is deposited at the anode. If the latter be insoluble, the gas diffuses into the solution and, when this becomes saturated, escapes into the air. If, however, no porous division be used to prevent the intermingling by diffusion of the anode and cathode solutions, a complicated set of subsidiary reactions takes place. The chlorine reacts with the caustic soda, forming sodium hypochlorite, and this in turn, with an excess of chlorine and at higher temperatures, becomes for the most part converted into chlorate, whilst any simultaneous electrolysis of a hydroxide or water and a chloride (so that hydroxyl and chlorine are simultaneously liberated at the anode) also produces oxygen-chlorine compounds direct. At the same time, the diffusion of these compounds into contact with the cathode leads to a partial reduction to chloride, by the removal of combined oxygen by the instrumentality of the hydrogen there evolved. In proportion as the original chloride is thus reproduced, the efficiency of the process is of course diminished. It is obvious that, with suitable methods and apparatus, the electrolysis of alkaline chlorides may be made to yield chlorine, hypochlorites (bleaching liquors), chlorates or caustic alkali, but that great care must be exercised if any of these products is to be obtained pure and with economy. Many patents have been taken out in this branch of electrochemistry, but it is to be remarked that that granted to C. Watt traversed the whole of the ground. In his process a current was passed through a tank divided into two or three cells by porous partitions, hoods and tubes were arranged to carry off chlorine and hydrogen respectively, and the whole was heated to 120° F. by a steam jacket when caustic alkali was being made. Hypochlorites were made, at ordinary temperatures, and chlorates at higher temperatures, in a cell without a partition in which the cathode was placed horizontally immediately above the anode, to favour the mixing of the ascending chlorine with the descending caustic solution.

The relation between the composition of the electrolyte and the various conditions of current-density, temperature and the like has been studied by F. Oettel (Zeitschrift f. Elektrochem., 1894, vol. i. PP. 354 and 474) in connexion with the production of hypochlorites and chlorates in tanks without diaphragms, by C. Häussermann and W. Naschold (Chemiker Zeitung, 1894, vol. xviii. p. 857) for their production in cells with porous diaphragms, and by F. Haber and S. Grinberg (Zeitschrift f. anorgan. Chem., 1898, vol. xvi. pp. 198, 329, 438) in connexion with the electrolysis of hydrochloric acid. Oettel, using a 20% solution of potassium chloride, obtained the best yield of hypochlorite with a high current-density, but as soon as 14% of bleaching chlorine (as hypochlorite) was present, the formation of chlorate commenced. The yield was at best very low as compared with that theoretically possible. The best yield of chlorate was obtained when from 1 to 4% of caustic potash was present. With high current-density, heating the solution tended to increase the proportion of chlorate to hypochlorite, but as the proportion of water decomposed is then higher, the amount of chlorine produced must be less and the total chlorine efficiency lower. He also traced a connexion between alkalinity, temperature and current-density, and showed that these conditions should be mutually adjusted. With a current-density of 130 to 140 amperes per sq. ft., at 3 volts, passing between platinum electrodes, he attained to a current-efficiency of 52%, and each (British) electrical horse-power hour was equivalent to a production of 1378.5 grains of potassium chlorate. In other words, each pound of chlorate would require an expenditure of nearly 5.1 e.h.p. hours. One of the earliest of the more modern processes was that of E. Hermite, which consisted in the production of bleach-liquors by the electrolysis (according to the 1st edition of the 1884 patent) of magnesium or calcium chloride between platinum anodes carried in wooden frames, and zinc cathodes. The solution, containing hypochlorites

and chlorates, was then applied to the bleaching of linen, paper-pulp or the like, the solution being used over and over again. Many modifications have been patented by Hermite, that of 1895 specifying the use of platinum gauze anodes, held in ebonite or other frames. Rotating zinc cathodes were used, with scrapers to prevent the accumulation of a layer of insoluble magnesium compounds, which would otherwise increase the electrical resistance beyond of electrolysed chlorides to the purification of starch by the oxidation reasonable limits. The same inventor has patented the application of less stable organic bodies, to the bleaching of oils, and to the purification of coal gas, spirit and other substances. His system for the disinfection of sewage and similar matter by the electrolysis of doned on the score of expense. chlorides, or of sea-water, has been tried, but for the most part abanReference may be made to papers written in the early days of the process by C. F. Čross and E. J. Bevan (Journ. Soc. Chem. Industry, 1887, vol. vi. p. 170, and 1888, vol. vii. P. 292), and to later papers by P. Schoop (Zeitschrift f. Elektrochem., 1895, vol. ii. pp. 68, 88, 107, 209, 289).

E. Kellner, who in 1886 patented the use of cathode (caustic soda) and anode (chlorine) liquors in the manufacture of cellulose from wood-fibre, and has since evolved many similar processes, has produced an apparatus that has been largely used. It consists of a either end forming the primary electrodes, and between them a stoneware tank with a thin sheet of platinum-iridium alloy at number of glass plates reaching nearly to the bottom, each having a platinum gauze sheet on either side; the two sheets belonging to each plate are in metallic connexion, but insulated from all the others, and form intermediary or bi-polar electrodes. A 10-12% solution of sodium chloride is caused to flow upwards through the apparatus and to overflow into troughs, by which it is conveyed (if necessary through a cooling apparatus) back to the circulating pump. Such a plant has been reported as giving o.229 gallon of a liquor containing 1% of available chlorine per kilowatt hour, or 0.171 gallon per e.h.p. hour. Kellner has also patented a “bleaching-block," as he terms it, consisting of a frame carrying parallel plates similar in principle to those last described. The block is immersed in the solution to be bleached, and may be lifted in or out as required. O. Knöfler and Gebauer have also a system of bi-polar electrodes, mounted in a frame in appearance resembling a filter-press.

Other Electrochemical Processes.—It is obvious that electrolytic iodine and bromine, and oxygen compounds of these elements, may be produced by methods similar to those applied to chlorides (see ALKALI MANUFACTURE and CHLORATES), and Kellner and others have patented processes with this end in view. Hydrogen and oxygen may also be produced electrolytically as gases, and their respective reducing and oxidizing powers at the moment of deposition on the electrode are frequently used in the laboratory, and to some extent industrially, chiefly in the field of organic chemistry. Similarly, the formation of organic halogen products may be effected by electrolytic chlorine, as, for example, in the production of chloral by the gradual introduction of alcohol into an anode cell in which the electrolyte is a strong solution of potassium chloride. Again, anode reactions, such as are observed in the electrolysis of the fatty acids, may be utilized, as, for example, when the radical CH3CO2-deposited at the anode in the electrolysis of acetic acid-is dissociated, two of the groups react to give one molecule of ethane, CH, and two of carbon dioxide. This, which has long been recognized as a class-reaction, is obviously capable of endless variation. Many electrolytic methods have been proposed for the purification of sugar; in some of them soluble anodes are used for a few minutes in weak alkaline solutions, so that the caustic alkali from the cathode reaction may precipitate chemically the hydroxide of the anode metal dissolved in the liquid, the precipitate carrying with it mechanically some of the impurities present, and thus clarifying the solution. In others the current is applied for a longer time to the original sugar-solution with insoluble (e.g. carbon) anodes. F. Peters has found that with these methods the best results are obtained when ozone is employed in addition to electrolytic oxygen. Use has been made of electrolysis in tanning operations, the current being passed through the tan-liquors containing the hides. The current, by endosmosis, favours the passage of the solution into the hide-substance, and at the same time appears to assist the chemical combinations there occurring; hence a great reduction in the time required for the completion of the process. Many patents have been taken out in this direction, one of the best known being that of Groth, experimented upon by S. Rideal and A. P. Trotter (Journ. Soc. Chem. Indust., 1891, vol. x. p. 425),

When properly performed the effect is painless and instantaneous death. The mechanism of life, circulation and respiration cease with the first contact. Consciousness is blotted out instantly, and the prolonged application of the current ensures permanent derangement of the vital functions beyond recovery. Occasionally the drying of the sponges through undue generation of heat causes desquamation or superficial blistering of the skin at the site of the electrodes. Post-mortem discoloration, or Post-mortem lividity, often appears during the first contact. The pupils of the eyes dilate instantly and remain dilated after death.

who employed copper anodes, 4 sq. ft. in area, with current- switch-board controlling the current are located in the executiondensities of 0.375 to 1 (ranging in some cases to 7.5) ampere per room; the dynamo-room is communicated with by electric sq. ft., the best results being obtained with the smaller current- signals. Before each execution the entire apparatus is thoroughly densities. Electrochemical processes are often indirectly used, tested. When everything is in readiness the criminal is brought as for example in the Villon process (Elec. Rev., New York, in and seats himself in the death-chair. His head, chest, arms 1899, vol. xxxv. p. 375) applied in Russia to the manufacture of and legs are secured by broad straps; one electrode thoroughly alcohol, by a series of chemical reactions starting from the pro- moistened with salt-solution is affixed to the head, and another to duction of acetylene by the action of water upon calcium carbide. the calf of one leg, both electrodes being moulded so as to secure The production of ozone in small quantities during electrolysis, good contact. The application of the current is usually as and by the so-called silent discharge, has long been known, and follows: the contact is made with a high voltage (1700-1800 the Siemens induction tube has been developed for use industri- volts) for 5 to 7 seconds, reduced to 200 volts until a half-minute ally. The Siemens and Halske ozonizer, in form somewhat has elapsed; raised to high voltage for 3 to 5 seconds, again reresembling the old laboratory instrument, is largely used in duced to low voltage for 3 to 5 seconds, again reduced to a low Germany; working with an alternating current transformed voltage until one minute has elapsed, when it is again raised to up to 6500 volts, it has been found to give 280 grains or more the high voltage for a few seconds and the contact broken. The of ozone per e. h. p. hour. E. Andreoli (whose first British ammeter usually shows that from 7 to 10 amperes pass through ozone patent was No. 17,426 of 1891) uses flat aluminium plates the criminal's body. A second or even a third brief contact is and points, and working with an alternating current of 3000 sometimes made, partly as a precautionary measure, but rather volts is said to have obtained 1440 grains per e.h.p. hour. the more completely to abolish reflexes in the dead body. CalYarnold's process, using corrugated glass plates coated on one culations have shown that by this method of execution from 7 to side with gold or other metal leaf, is stated to have yielded as 10 h. p. of energy are liberated in the criminal's body. The much as 2700 grains per e.h.p. hour. The ozone so prepared time consumed by the strapping-in process is usually about 45 has numerous uses, as, for example, in bleaching oils, waxes, seconds, and the first contact is made about 70 seconds after the fabrics, &c., sterilizing drinking-water, maturing wines, cleansing criminal has entered the death-chamber. foul beer-casks, oxidizing oil, and in the manufacture of vanillin. For further information the following books, among others, may be consulted:-Haber, Grundriss der technischen Elektrochemie (München, 1898); Borchers and M'Millan, Electric Smelling and Refining (London, 1904); E. D. Peters, Principles of Copper Smelting (New York, 1907); F. Peters, Angewandte Elektrochemie, vols. ii. and iii. (Leipzig, 1900); Gore, The Art of Electrolytic Separation of Metals (London, 1890); Blount, Practical Electro-Chemistry (London, 1906); G. Langbein, Vollständiges Handbuch der galvanischen Metall-Niederschläge (Leipzig, 1903), Eng. trans. by W. T. Brannt (1909); A. Watt, Electro-Plating and Electro-Refining of Metals (London, 1902); W. H. Wahl, Practical Guide to the Gold and Silver Electroplater, &c. (Philadelphia, 1883); Wilson, Stereotyping and Electrotyping (London); Lunge, Sulphuric Acid and Alkali, vol. iii. (London, 1909). Also papers in various technical periodicals. The industrial aspect is treated in a Gartside Report, Some ElectroChemical Centres (Manchester, 1908), by J. N. Pring. (W. G. M.) ELECTROCUTION (an anomalous derivative from "electro-registered within fifteen minutes in many cases. After the removal execution "; syn. "electrothanasia "), the popular name, invented in America, for the infliction of the death penalty on criminals (see CAPITAL PUNISHMENT) by passing through the body of the condemned a sufficient current of electricity to cause death. The method was first adopted by the state of New York, a law making this method obligatory having been passed and approved by the governor on the 4th of June 1888. The law provides that there shall be present, in addition to the warden, two physicians, twelve reputable citizens of full age, seven deputy sheriffs, and such ministers, priests or clergymen, not exceeding two, as the criminal may request. A post-mortem examination of the body of the convict is required, and the body, unless claimed by relatives, is interred in the prison cemetery with a sufficient quantity of quicklime to consume it. The law became effective in New York on the 1st of January 1889. The first criminal to be executed by electricity was William Kemmler, on the 6th of August 1890, at Auburn prison. The validity of the New York law had previously been attacked in regard to 'this case (Re Kemmler, 1889; 136 U.S. 436), as providing cruel and unusual punishment " and therefore being contrary to the Constitution; but it was sustained in the state courts and finally in the Federal courts. By 1906 about one hundred and fifteen murderers had been successfully executed by electricity in New York state in Sing Sing, Auburn and Dannemora prisons. The method has also been adopted by the states of Ohio (1896), Massachusetts (1898), New Jersey (1906), Virginia (1908) and North Carolina (1910).

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The apparatus consists of a stationary engine, an alternating dynamo capable of generating a current at a pressure of 2000 volts, a "death-chair" with adjustable head-rest, binding straps and adjustable electrodes devised by E. F. Davis, the state electrician of New York. The voltmeter, ammeter and

The post-mortem examination of "electrocuted" criminals reveals a number of interesting phenomena. The temperature of the body rises promptly after death to a very high point. At the site of the leg electrode a temperature of over 128° F. was

of the brain the temperature recorded in the spinal canal was
often over 120° F. The development of this high temperature is
to be regarded as resulting from the active metabolism of tissues
not (somatically) dead within a body where all vital mechanisms
have been abolished, there being no circulation to carry off the
generated heat. The heart, at first flaccid when exposed soon
after death, gradually contracts and assumes a tetanized con-
dition; it empties itself of all blood and takes the form of a heart
in systole. The lungs are usually devoid of blood and weigh
only 7 or 8 ounces (avoird.) each. The blood is profoundly
altered biochemically; it is of a very dark colour and it rarely
coagulates.
(E. A. S.*)

ELECTROKINETICS, that part of electrical science which is concerned with the properties of electric currents.

Classification of Electric Currents.-Electric currents are classified into (a) conduction currents, (b) convection currents, (c) displacement or dielectric currents. In the case of conduction currents electricity flows or moves through a stationary material body called the conductor. In convection currents electricity is carried from place to place with and on moving material bodies or particles. In dielectric currents there is no continued movement of electricity, but merely a limited displacement through or in the mass of an insulator or dielectric. The path in which an electric current exists is called an electric circuit, and may consist wholly of a conducting body, or partly of a conductor and insulator or dielectric, or wholly of a dielectric. In cases in which the three classes of currents are present together the true current is the sum of each separately. In the case of conduction currents the circuit consists of a conductor immersed in a non-conductor, and may take the form of a thin wire or cylinder, a sheet, surface or solid. Electric conduction currents may take place in space of one, two or three dimensions, but for

the most part the circuits we have to consider consist of thin | position of simple sine currents differing in maximum value and cylindrical wires or tubes of conducting material surrounded in phase. with an insulator; hence the case which generally presents itself is that of electric flow in space of one dimension. Self-closed electric currents taking place in a sheet of conductor are called "eddy currents."

Although in ordinary language the current is said to flow in the conductor, yet according to modern views the real pathway of the energy transmitted is the surrounding dielectric, and the so-called conductor or wire merely guides the transmission of energy in a certain direction. The presence of an electric current is recognized by three qualities or powers: (1) by the production of a magnetic field, (2) in the case of conduction currents, by the production of heat in the conductor, and (3) if the conductor is an electrolyte and the current unidirectional, by the occurrence of chemical decomposition in it. An electric current may also be regarded as the result of a movement of electricity across each section of the circuit, and is then measured by the quantity conveyed per unit of time. Hence if dq is the quantity of electricity which flows across any section of the conductor in the element of time dt, the current i=dq/dt.

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Electric currents may be also classified as constant or variable and as unidirectional or "direct," that is flowing always in the same direction, or "alternating," that is reversing their direction at regular intervals. In the last case the variation of current may follow any particular law. It is called a " periodic current if the cycle of current values is repeated during a certain time called the periodic time, during which the current reaches a certain maximum value, first in one direction and then in the opposite, and in the intervals between has a zero value at certain instants. The frequency of the periodic current is the number of periods or cycles in one second, and alternating currents are described as low frequency or high frequency, in the latter case having some thousands of periods per second. A periodic current may be represented either by a wave diagram, or by a polar diagram. In the first case we take a straight line to represent the uniform flow of time, and at small equidistant intervals set up perpendiculars above or below the time axis, representing to scale the current at that instant in one direction or the other; the extremities of these ordinates then define a wavy curve which is called the wave form of the current (fig. 1). It is obvious that this curve can only be a single valued curve. In one particular and important case the form of the current curve is a simple harmonic curve or simple sine curve. If T represents the periodic time in which the cycle of current values takes

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place, whilst n is the frequency or number of periods per second and p stands for 2πn, and i is the value of the current at any instant t, and I its maximum value, then in this case we have i=I sin pt. Such a current is called a " sine current " or simple

periodic current.

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Definitions of Unit Electric Current.—In electrokinetic investigations we are most commonly limited to the cases of unidirectional continuous and constant currents (C.C. or D.C.), or of simple periodic currents, or alternating currents of sine form (A.C.). A continuous electric current is measured either by the magnetic effect it produces at some point outside its circuit, or by the amount of electrochemical decomposition it can perform in a given time on a selected standard electrolyte. Limiting our consideration to the case of linear currents or currents flowing in thin cylindrical wires, a definition may be given in the first place of the unit electric current in the centimetre, gramme, second (C.G.S.) of electromagnetic measurement (see UNITS, PHYSICAL). H. C. Oersted discovered in 1820 that a straight wire conveying an electric current is surrounded by a magnetic field the lines of which are self-closed lines embracing the electric circuit (see ELECTRICITY and ELECTROMAGNETISM). The unit current in the electromagnetic system of measurement is defined as the current which, flowing in a thin wire bent into the form of a circle of one centimetre in radius, creates a magnetic field having a strength of 27 units at the centre of the circle, and therefore would exert a mechanical force of 27 dynes on a unit magnetic pole placed at that point (see MAGNETISM). Since the length of the circumference of the circle of unit radius is 2 units, this is equivalent to stating that the unit current on the electromagnetic C.G.S. system is a current such that unit length acts on unit magnetic pole with a unit force at a unit of distance. Another definition, called the electrostatic unit of current, is as follows: Let any conductor be charged with electricity and discharged through a thin wire at such a rate that one electrostatic unit of quantity (see ELECTROSTATICS) flows past any section of the wire in one unit of time. The electromagnetic unit of current defined as above is 3X1010 times larger than the electrostatic unit.

In the selection of a practical unit of current it was considered that the electromagnetic unit was too large for most purposes, whilst the electrostatic unit was too small; hence a practical unit of current called i ampere was selected, intended originally to be 1/10 of the absolute electromagnetic C.G.S. unit of current as above defined. The practical unit of current, called the international ampere, is, however, legally defined at the present time as the continuous unidirectional current which when flowing through a neutral solution of silver nitrate deposits in one second on the cathode or negative pole o·001118 of a gramme of silver. There is reason to believe that the international unit is smaller by about one part in a thousand, or perhaps by one part in 800, than the theoretical ampere defined as 1/10 part of the absolute electromagnetic unit. A periodic or alternating current is said to have a value of 1 ampere if when passed through a fine wire it produces in the same time the same heat as a unidirectional continuous current of 1 ampere as above electrochemically defined. In the case of a simple periodic alternating current having a simple sine wave form, the maximum value is equal to that of the equiheating continuous current multiplied by 2. This equiheating continuous current is called the effective or root-mean-square (R.M.S.) value of the alternating one.

Resistance. A current flows in a circuit in virtue of an electro

motive force (E.M.F.), and the numerical relation between the current and E.M.F. is determined by three qualities of the circuit called respectively, its resistance (R), inductance (L), and In a polar diagram (fig. 2) a number of radial lines are drawn from a point at small equiangular intervals, and on these lines capacity (C). If we limit our consideration to the case of continuous unidirectional conduction currents, then the relation are set off lengths proportional to the current value of a periodic between current and E.M.F. is defined by Ohm's law, which states current at corresponding intervals during one complete period that the numerical value of the current is obtained as the quotient represented by four right angles. The extremities of these of the electromotive force by a certain constant of the circuit radii delineate a polar curve. The polar form of a simple sine called its resistance, which is a function of the geometrical form current is obviously a circle drawn through the origin. As a of the circuit, of its nature, i.e. material, and of its temperature, consequence of Fourier's theorem it follows that any periodic but is independent of the electromotive force or current. The curve having any wave form can be imitated by the super-resistance (R) is measured in units called ohms and the electro

1 See J. A. Fleming, The Alternate Current Transformer, vol. i. motive force in volts (V); hence for a continuous current the value of the current in amperes (A) is obtained as the quotient

p. 519.

manner, if we take a point in a line at right angles to the plane of the circle through its centre and at a distance d, the magnetic force along this line is expressed by 2πr2I/(r2+d2). Another important case is that of an infinitely long straight current. By summing up the magnetic force due to each element at any point P outside the continuous straight current I, and at a distance d from it, we can show that it is equal to 21/d or is inversely proportional to the distance of the point from the wire. In the above formula the current I is measured in absolute electromagnetic units. If we reckon the current in amperes A, then I=A/10.

of the electromotive force acting in the circuit reckoned in volts | elements are at the same distance from the centre. In the same by the resistance in ohms, or A=V/R. Ohm established his law by a course of reasoning which was similar to that on which J. B. J. Fourier based his investigations on the uniform motion of heat in a conductor. As a matter of fact, however, Ohm's law merely states the direct proportionality of steady current to steady electromotive force in a circuit, and asserts that this ratio is governed by the numerical value of a quality of the conductor, called its resistance, which is independent of the current, provided that a correction is made for the change of temperature produced by the current. Our belief, however, in its universality and accuracy rests upon the close agreement between deductions made from it and observational results, and although it is not derivable from any more fundamental principle, it is yet one of the most certainly ascertained laws of electrokinetics.

Ohm's law not only applies to the circuit as a whole but to any part of it, and provided the part selected does not contain a source of electromotive force it may be expressed as follows:The difference of potential (P.D.) between any two points of a circuit including a resistance R, but not including any source of electromotive force, is proportional to the product of the resistance and the current i in the element, provided the conductor remains at the same temperature and the current is constant and unidirectional. If the current is varying we have, however, to take into account the electromotive force (E.M.F.) produced by this variation, and the product Ri is then equal to the difference between the observed P.D. and induced E.M.F.

We may otherwise define the resistance of a circuit by saying that it is that physical quality of it in virtue of which energy is dissipated as heat in the circuit when a current flows through it. The power communicated to any electric circuit when a current i is created in it by a continuous unidirectional electromotive force E is equal to Ei, and the energy dissipated as heat in that circuit by the conductor in a small interval of time dt is measured by Ei dt. Since by Ohm's law E-Ri, where R is the resistance of the circuit, it follows that the energy dissipated as heat per unit of time in any circuit is numerically represented by Ri2, and therefore the resistance is measured by the heat produced per unit of current, provided the current is unvarying.

Inductance. As soon as we turn our attention, however, to alternating or periodic currents we find ourselves compelled to take into account another quality of the circuit, called its" inductance." This may be defined as that quality in virtue of which energy is stored up in connexion with the circuit in a magnetic form. It can be experimentally shown that a current cannot be created instantaneously in a circuit by any finite electromotive force, and that when once created it cannot be annihilated instantaneously. The circuit possesses a quality analogous to the inertia of matter. If a current i is flowing in a circuit at any moment, the energy stored up in connexion with the circuit is measured by Li2, where L, the inductance of the circuit, is related to the current in the same manner as the quantity called the mass of a body is related to its velocity in the expression for the ordinary kinetic energy, viz. Mo2. The rate at which this conserved energy varies with the current is called the "electrokinetic momentum" of this circuit (Li). Physically interpreted this quantity signifies the number of lines of magnetic flux due to the current itself which are self-linked with its own circuit. Magnetic Force and Electric Currents. In the case of every circuit conveying a current there is a certain magnetic force (see MAGNETISM) at external points which can in some instances be calculated. Laplace proved that the magnetic force due to an element of length dS of a circuit conveying a current I at a point P at a distance r from the element is expressed by IdS sin 0/r2, where is the angle between the direction of the current element and that drawn between the element and the point. This force is in a direction perpendicular to the radius vector and to the plane containing it and the element of current. Hence the determination of the magnetic force due to any circuit is reduced to a summation of the effects due to all the elements of length. For instance, the magnetic force at the centre of a circular circuit of radius r carrying a steady current I is 27I/r, since all

It is possible to make use of this last formula, coupled with an experimental fact, to prove that the magnetic force due to an element of current varies inversely as the square of the distance. If a flat circular disk is suspended so as to be free to rotate round a straight current which passes through its centre, and two bar magnets are placed on it with their axes in line with the current, it is found that the disk has no tendency to rotate round the current. This proves that the force on each magnetic pole is inversely as its distance from the current. But it can be shown that this law of action of the whole infinitely long straight current is a mathematical consequence of the fact that each element of the current exerts a magnetic force which varies inversely as the square of the distance. If the current flows N times round the circuit instead of once, we have to insert NA/10 in place of I in all the above formulae. The quantity NA is called the ampere-turns" on the circuit, and it is seen that the magnetic field at any point outside a circuit is proportional to the ampereturns on it and to a function of its geometrical form and the distance of the point.

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There is therefore a distribution of magnetic force in the field of every current-carrying conductor which can be delineated by lines of magnetic force and rendered visible to the eye by iron filings (see MAGNETISM). If a copper wire is passed vertically through a hole in a card on which iron filings are sprinkled, and a strong electric current is sent through the circuit, the filings arrange themselves in concentric circular lines making visible the paths of the lines of magnetic force (fig. 3). In the same manner, by passing a circular wire through a card and sending a strong current through the wire we can employ iron filings to delineate for us the form of the lines of magnetic force (fig. 4).

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The work done in carrying a unit magnetic pole once round a circuit conveying a current is called the line integral of magnetic force" along that path. If, for instance, we carry a unit pole in a filamentary current I, the line integral is 4πI. circular path of radius once round an infinitely long straight It is easy to prove that this is a general law, and that if we have any currents flowing in a conductor the line integral of magnetic force taken once round a path linked with the current circuit is 4 times the total current endless solenoid. If a copper wire insulated or covered with cotton flowing through the circuit. Let us apply this to the case of an or silk is twisted round a thin rod so as to make a close spiral, this

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