Chapter XVII: Part 17

With respect to the variation of hysteresis loss in magnetic cycles having different maximum values for the flux density, Steinmetz found that the hysteresis loss (W), as measured by the area of the complete (B, H) cycle and expressed in ergs per centimetre-cube per cycle, varies proportionately to a constant called the _hysteretic constant_, and to the 1.6th power of the maximum flux density (B), or W = [eta]B^(1.6).

The hysteretic constants ([eta]) for various kinds of iron and steel are given in the table below:--

Metal. Hysteretic Constant.

Swedish wrought iron, well annealed .0010 to .0017
Annealed cast steel of good quality; small
percentage of carbon .0017 to .0029
Cast Siemens-Martin steel .0019 to .0028
Cast ingot-iron .0021 to .0026
Cast steel, with higher percentages of
carbon, or inferior qualities of wrought
iron .0031 to .0054

Steinmetz's law, though not strictly true for very low or very high maximum flux densities, is yet a convenient empirical rule for obtaining approximately the hysteresis loss at any one maximum flux density and knowing it at another, provided these values fall within a range varying say from 1 to 9000 C.G.S. units. (See MAGNETISM.)

The standard maximum flux density which is adopted in electro-technical work is 2500, hence in the construction of the cores of alternating-current electromagnets and transformers iron has to be employed having a known hysteretic constant at the standard flux density. It is generally expressed by stating the number of watts per lb. of metal which would be dissipated for a frequency of 100 cycles, and a maximum flux density (B max.) during the cycle of 2500. In the case of good iron or steel for transformer-core making, it should not exceed 1.25 watt per lb. per 100 cycles per 2500 B (maximum value).

It has been found that if the sheet iron employed for cores of alternating electromagnets or transformers is heated to a temperature somewhere in the neighbourhood of 200 deg. C. the hysteresis loss is very greatly increased. It was noticed in 1894 by G.W. Partridge that alternating-current transformers which had been in use some time had a very considerably augmented core loss when compared with their initial condition. O.T. Blathy and W.M. Mordey in 1895 showed that this augmentation in hysteresis loss in iron was due to heating. H.F. Parshall investigated the effect up to moderate temperatures, such as 140 deg. C., and an extensive series of experiments was made in 1898 by S.R. Roget (_Proc. Roy. Soc._, 1898, 63, p. 258, and 64, p. 150). Roget found that below 40 deg. C. a rise in temperature did not produce any augmentation in the hysteresis loss in iron, but if it is heated to between 40 deg. C. and 135 deg. C. the hysteresis loss increases continuously with time, and this increase is now called "ageing" of the iron. It proceeds more slowly as the temperature is higher. If heated to above 135 deg. C., the hysteresis loss soon attains a maximum, but then begins to decrease. Certain specimens heated to 160 deg. C. were found to have their hysteresis loss doubled in a few days. The effect seems to come to a maximum at about 180 deg. C. or 200 deg. C. Mere lapse of time does not remove the increase, but if the iron is reannealed the augmentation in hysteresis disappears. If the iron is heated to a higher temperature, say between 300 deg. C. and 700 deg. C., Roget found the initial rise of hysteresis happens more quickly, but that the metal soon settles down into a state in which the hysteresis loss has a small but still augmented constant value. The augmentation in value, however, becomes more nearly zero as the temperature approaches 700 deg. C. Brands of steel are now obtainable which do not age in this manner, but these _non-ageing_ varieties of steel have not generally such low initial hysteresis values as the "Swedish Iron," commonly considered best for the cores of transformers and alternating-current magnets.

The following conclusions have been reached in the matter:--(1) Iron and mild steel in the annealed state are more liable to change their hysteresis value by heating than when in the harder condition; (2) all changes are removed by re-annealing; (3) the changes thus produced by heating affect not only the amount of the hysteresis loss, but also the form of the lower part of the (B, H) curve.

_Forms of Electromagnet._--The form which an electromagnet must take will greatly depend upon the purposes for which it is to be used. A design or form of electromagnet which will be very suitable for some purposes will be useless for others. Supposing it is desired to make an electromagnet which shall be capable of undergoing very rapid changes of strength, it must have such a form that the coercivity of the material is overcome by a self-demagnetizing force. This can be achieved by making the magnet in the form of a short and stout bar rather than a long thin one. It has already been explained that the ends or poles of a polar magnet exert a demagnetizing power upon the mass of the metal in the interior of the bar. If then the electromagnet has the form of a long thin bar, the length of which is several hundred times its diameter, the poles are very far removed from the centre of the bar, and the demagnetizing action will be very feeble; such a long thin electromagnet, although made of very soft iron, retains a considerable amount of magnetism after the magnetizing force is withdrawn. On the other hand, a very thick bar very quickly demagnetizes itself, because no part of the metal is far removed from the action of the free poles. Hence when, as in many telegraphic instruments, a piece of soft iron, called an armature, has to be attracted to the poles of a horseshoe-shaped electromagnet, this armature should be prevented from quite touching the polar surfaces of the magnet. If a soft iron mass does quite touch the poles, then it completes the magnetic circuit and abolishes the free poles, and the magnet is to a very large extent deprived of its self-demagnetizing power. This is the explanation of the well-known fact that after exciting the electromagnet and then stopping the current, it still requires a good pull to detach the "keeper"; but when once the keeper has been detached, the magnetism is found to have nearly disappeared. An excellent form of electromagnet for the production of very powerful fields has been designed by H. du Bois (fig. 6).

Various forms of electromagnets used in connexion with dynamo machines are considered in the article DYNAMO, and there is, therefore, no necessity to refer particularly to the numerous different shapes and types employed in electrotechnics.

BIBLIOGRAPHY.--For additional information on the above subject the
reader may be referred to the following works and original papers:--

H. du Bois, _The Magnetic Circuit in Theory and Practice_; S.P.
Thompson, _The Electromagnet_; J.A. Fleming, _Magnets and Electric
Currents_; J.A. Ewing, _Magnetic Induction in Iron and other Metals_;
J.A. Fleming, "The Ferromagnetic Properties of Iron and Steel,"
_Proceedings of Sheffield Society of Engineers and Metallurgists_
(Oct. 1897); J.A. Ewing, "The Magnetic Testing of Iron and Steel,"
_Proc. Inst. Civ. Eng._, 1896, 126, p. 185; H.F. Parshall, "The
Magnetic Data of Iron and Steel," _Proc. Inst. Civ. Eng._, 1896, 126,
p. 220; J.A. Ewing, "The Molecular Theory of Induced Magnetism,"
_Phil. Mag._, Sept. 1890; W.M. Mordey, "Slow Changes in the
Permeability of Iron," _Proc. Roy. Soc._ 57, p. 224; J.A. Ewing,
"Magnetism," James Forrest Lecture, _Proc. Inst. Civ. Eng._ 138; S.P.
Thompson, "Electromagnetic Mechanism," _Electrician_, 26, pp. 238,
269, 293; J.A. Ewing, "Experimental Researches in Magnetism," _Phil.
Trans._, 1885, part ii.; Ewing and Klassen, "Magnetic Qualities of
Iron," _Proc. Roy. Soc._, 1893. (J. A. F.)

FOOTNOTES:

[1] In the _Annals of Philosophy_ for November 1821 is a long article
entitled "Electromagnetism" by Oersted, in which he gives a detailed
account of his discovery. He had his thoughts turned to it as far
back as 1813, but not until the 20th of July 1820 had he actually
made his discovery. He seems to have been arranging a compass needle
to observe any deflections during a storm, and placed near it a
platinum wire through which a galvanic current was passed.

[2] See _Trans. Soc. Arts_, 1825, 43, p. 38, in which a figure of
Sturgeon's electromagnet is given as well as of other pieces of
apparatus for which the Society granted him a premium and a silver
medal.

[3] See S.P. Thompson, _The Electromagnet_ (London, 1891); J.A.
Fleming, _A Handbook for the Electrical Laboratory and Testing Room_,
vol. 2 (London, 1903); J.A. Ewing, _Magnetic Induction in Iron and
other Metals_ (London, 1903, 3rd ed.).

ELECTROMETALLURGY. The present article, as explained under ELECTROCHEMISTRY, treats only of those processes in which electricity is applied to the production of chemical reactions or molecular changes at furnace temperatures. In many of these the application of heat is necessary to bring the substances used into the liquid state for the purpose of electrolysis, aqueous solutions being unsuitable. Among the earliest experiments in this branch of the subject were those of Sir H. Davy, who in 1807 (_Phil. Trans._, 1808, p. 1), produced the alkali metals by passing an intense current of electricity from a platinum wire to a platinum dish, through a mass of fused caustic alkali. The action was started in the cold, the alkali being slightly moistened to render it a conductor; then, as the current passed, heat was produced and the alkali fused, the metal being deposited in the liquid condition. Later, A. Matthiessen (_Quarterly Journ. Chem. Soc._ viii. 30) obtained potassium by the electrolysis of a mixture of potassium and calcium chlorides fused over a lamp. There are here foreshadowed two types of electrolytic furnace-operations: (a) those in which external heating maintains the electrolyte in the fused condition, and (b) those in which a current-density is applied sufficiently high to develop the heat necessary to effect this object unaided. Much of the earlier electro-metallurgical work was done with furnaces of the (a) type, while nearly all the later developments have been with those of class (b). There is a third class of operations, exemplified by the manufacture of calcium carbide, in which electricity is employed solely as a heating agent; these are termed _electrothermal_, as distinguished from _electrolytic_. In certain electrothermal processes (e.g. calcium carbide production) the heat from the current is employed in raising mixtures of substances to the temperature at which a desired chemical reaction will take place between them, while in others (e.g. the production of graphite from coke or gas-carbon) the heat is applied solely to the production of molecular or physical changes. In ordinary electrolytic work only the continuous current may of course be used, but in electrothermal work an alternating current is equally available.

_Electric Furnaces._--Independently of the question of the application of external heating, the furnaces used in electrometallurgy may be broadly classified into (i.) arc furnaces, in which the intense heat of the electric arc is utilized, and (ii.) resistance and incandescence furnaces, in which the heat is generated by an electric current overcoming the resistance of an inferior conductor.

Arc furnaces.

Excepting such experimental arrangements as that of C.M. Despretz (_C.R._, 1849, 29) for use on a small scale in the laboratory, Pichou in France and J.H. Johnson in England appear, in 1853, to have introduced the earliest practical form of furnace. In these arrangements, which were similar if not identical, the furnace charge was crushed to a fine powder and passed through two or more electric arcs in succession. When used for ore smelting, the reduced metal and the accompanying slag were to be caught, after leaving the arc and while still liquid, in a hearth fired with ordinary fuel. Although this primitive furnace could be made to act, its efficiency was low, and the use of a separate fire was disadvantageous. In 1878 Sir William Siemens patented a form of furnace[1] which is the type of a very large number of those designed by later inventors.

In the best-known form a plumbago crucible was used with a hole cut in
the bottom to receive a carbon rod, which was ground in so as to make
a tight joint. This rod was connected with the positive pole of the
dynamo or electric generator. The crucible was fitted with a cover in
which were two holes; one at the side to serve at once as sight-hole
and charging door, the other in the centre to allow a second carbon
rod to pass freely (without touching) into the interior. This rod was
connected with the negative pole of the generator, and was suspended
from one arm of a balance-beam, while from the other end of the beam
was suspended a vertical hollow iron cylinder, which could be moved
into or out of a wire coil or solenoid joined as a shunt across the
two carbon rods of the furnace. The solenoid was above the iron
cylinder, the supporting rod of which passed through it as a core.
When the furnace with this well-known regulating device was to be
used, say, for the melting of metals or other conductors of
electricity, the fragments of metal were placed in the crucible and
the positive electrode was brought near them. Immediately the current
passed through the solenoid it caused the iron cylinder to rise, and,
by means of its supporting rod, forced the end of the balance beam
upwards, so depressing the other end that the negative carbon rod was
forced downwards into contact with the metal in the crucible. This
action completed the furnace-circuit, and current passed freely from
the positive carbon through the fragments of metal to the negative
carbon, thereby reducing the current through the shunt. At once the
attractive force of the solenoid on the iron cylinder was
automatically reduced, and the falling of the latter caused the
negative carbon to rise, starting an arc between it and the metal in
the crucible. A counterpoise was placed on the solenoid end of the
balance beam to act against the attraction of the solenoid, the
position of the counterpoise determining the length of the arc in the
crucible. Any change in the resistance of the arc, either by
lengthening, due to the sinking of the charge in the crucible, or by
the burning of the carbon, affected the proportion of current flowing
in the two shunt circuits, and so altered the position of the iron
cylinder in the solenoid that the length of arc was, within limits,
automatically regulated. Were it not for the use of some such device
the arc would be liable to constant fluctuation and to frequent
extinction. The crucible was surrounded with a bad conductor of heat
to minimize loss by radiation. The positive carbon was in some cases
replaced by a water-cooled metal tube, or ferrule, closed, of course,
at the end inserted in the crucible. Several modifications were
proposed, in one of which, intended for the heating of non-conducting
substances, the electrodes were passed horizontally through
perforations in the upper part of the crucible walls, and the charge
in the lower part of the crucible was heated by radiation.

The furnace used by Henri Moissan in his experiments on reactions at high temperatures, on the fusion and volatilization of refractory materials, and on the formation of carbides, silicides and borides of various metals, consisted, in its simplest form, of two superposed blocks of lime or of limestone with a central cavity cut in the lower block, and with a corresponding but much shallower inverted cavity in the upper block, which thus formed the lid of the furnace. Horizontal channels were cut on opposite walls, through which the carbon poles or electrodes were passed into the upper part of the cavity. Such a furnace, to take a current of 4 H.P. (say, of 60 amperes and 50 volts), measured externally about 6 by 6 by 7 in., and the electrodes were about 0.4 in. in diameter, while for a current of 100 H.P. (say, of 746 amperes and 100 volts) it measured about 14 by 12 by 14 in., and the electrodes were about 1.5 in. in diameter. In the latter case the crucible, which was placed in the cavity immediately beneath the arc, was about 3 in. in diameter (internally), and about 3-1/2 in. in height. The fact that energy is being used at so high a rate as 100 H.P. on so small a charge of material sufficiently indicates that the furnace is only used for experimental work, or for the fusion of metals which, like tungsten or chromium, can only be melted at temperatures attainable by electrical means. Moissan succeeded in fusing about 3/4 lb. of either of these metals in 5 or 6 minutes in a furnace similar to that last described. He also arranged an experimental tube-furnace by passing a carbon tube horizontally beneath the arc in the cavity of the lime blocks. When prolonged heating is required at very high temperatures it is found necessary to line the furnace-cavity with alternate layers of magnesia and carbon, taking care that the lamina next to the lime is of magnesia; if this were not done the lime in contact with the carbon crucible would form calcium carbide and would slag down, but magnesia does not yield a carbide in this way. Chaplet has patented a muffle or tube furnace, similar in principle, for use on a larger scale, with a number of electrodes placed above and below the muffle-tube. The arc furnaces now widely used in the manufacture of calcium carbide on a large scale are chiefly developments of the Siemens furnace. But whereas, from its construction, the Siemens furnace was intermittent in operation, necessitating stoppage of the current while the contents of the crucible were poured out, many of the newer forms are specially designed either to minimize the time required in effecting the withdrawal of one charge and the introduction of the next, or to ensure absolute continuity of action, raw material being constantly charged in at the top and the finished substance and by-products (slag, &c.) withdrawn either continuously or at intervals, as sufficient quantity shall have accumulated. In the King furnace, for example, the crucible, or lowest part of the furnace, is made detachable, so that when full it may be removed and an empty crucible substituted. In the United States a revolving furnace is used which is quite continuous in action.

Incandescence furnaces.

The class of furnaces heated by electrically incandescent materials has been divided by Borchers into two groups: (1) those in which the substance is heated by contact with a substance offering a high resistance to the current passing through it, and (2) those in which the substance to be heated itself affords the resistance to the passage of the current whereby electric energy is converted into heat. Practically the first of these furnaces was that of Despretz, in which the mixture to be heated was placed in a carbon tube rendered incandescent by the passage of a current through its substance from end to end. In 1880 W. Borchers introduced his resistance-furnace, which, in one sense, is the converse of the Despretz apparatus. A thin carbon pencil, forming a bridge between two stout carbon rods, is set in the midst of the mixture to be heated. On passing a current through the carbon the small rod is heated to incandescence, and imparts heat to the surrounding mass. On a larger scale several pencils are used to make the connexions between carbon blocks which form the end walls of the furnace, while the side walls are of fire-brick laid upon one another without mortar. Many of the furnaces now in constant use depend mainly on this principle, a core of granular carbon fragments stamped together in the direct line between the electrodes, as in Acheson's carborundum furnace, being substituted for the carbon pencils. In other cases carbon fragments are mixed throughout the charge, as in E.H. and A.H. Cowles's zinc-smelting retort. In practice, in these furnaces, it is possible for small local arcs to be temporarily set up by the shifting of the charge, and these would contribute to the heating of the mass. In the remaining class of furnace, in which the electrical resistance of the charge itself is utilized, are the continuous-current furnaces, such as are used for the smelting of aluminium, and those alternating-current furnaces, (e.g. for the production of calcium carbide) in which a portion of the charge is first actually fused, and then maintained in the molten condition by the current passing through it, while the reaction between further portions of the charge is proceeding.

Uses and advantages.

For ordinary metallurgical work the electric furnace, requiring as it does (excepting where waterfalls or other cheap sources of power are available) the intervention of the boiler and steam-engine, or of the gas or oil engine, with a consequent loss of energy, has not usually proved so economical as an ordinary direct fired furnace. But in some cases in which the current is used for electrolysis and for the production of extremely high temperatures, for which the calorific intensity of ordinary fuel is insufficient, the electric furnace is employed with advantage. The temperature of the electric furnace, whether of the arc or incandescence type, is practically limited to that at which the least easily vaporized material available for electrodes is converted into vapour. This material is carbon, and as its vaporizing point is (estimated at) over 3500 deg. C., and less than 4000 deg. C., the temperature of the electric furnace cannot rise much above 3500 deg. C. (6330 deg. F.); but H. Moissan showed that at this temperature the most stable of mineral combinations are dissociated, and the most refractory elements are converted into vapour, only certain borides, silicides and metallic carbides having been found to resist the action of the heat. It is not necessary that all electric furnaces shall be run at these high temperatures; obviously, those of the incandescence or resistance type may be worked at any convenient temperature below the maximum. The electric furnace has several advantages as compared with some of the ordinary types of furnace, arising from the fact that the heat is generated from within the mass of material operated upon, and (unlike the blast-furnace, which presents the same advantage) without a large volume of gaseous products of combustion and atmospheric nitrogen being passed through it. In ordinary reverberatory and other heating furnaces the burning fuel is without the mass, so that the vessel containing the charge, and other parts of the plant, are raised to a higher temperature than would otherwise be necessary, in order to compensate for losses by radiation, convection and conduction. This advantage is especially observed in some cases in which the charge of the furnace is liable to attack the containing vessel at high temperatures, as it is often possible to maintain the outer walls of the electric furnace relatively cool, and even to keep them lined with a protecting crust of unfused charge. Again, the construction of electric furnaces may often be exceedingly crude and simple; in the carborundum furnace, for example, the outer walls are of loosely piled bricks, and in one type of furnace the charge is simply heaped on the ground around the carbon resistance used for heating, without containing-walls of any kind. There is, however, one (not insuperable) drawback in the use of the electric furnace for the smelting of pure metals. Ordinarily carbon is used as the electrode material, but when carbon comes in contact at high temperatures with any metal that is capable of forming a carbide a certain amount of combination between them is inevitable, and the carbon thus introduced impairs the mechanical properties of the ultimate metallic product. Aluminium, iron, platinum and many other metals may thus take up so much carbon as to become brittle and unforgeable. It is for this reason that Siemens, Borchers and others substituted a hollow water-cooled metal block for the carbon cathode upon which the melted metal rests while in the furnace. Liquid metal coming in contact with such a surface forms a crust of solidified metal over it, and this crust thickens up to a certain point, namely, until the heat from within the furnace just overbalances that lost by conduction through the solidified crust and the cathode material to the flowing water. In such an arrangement, after the first instant, the melted metal in the furnace does not come in contact with the cathode material.

Aluminium alloys.

_Electrothermal Processes._--In these processes the electric current is used solely to generate heat, either to induce chemical reactions between admixed substances, or to produce a physical (allotropic) modification of a given substance. Borchers predicted that, at the high temperatures available with the electric furnace, every oxide would prove to be reducible by the action of carbon, and this prediction has in most instances been justified. Alumina and lime, for example, which cannot be reduced at ordinary furnace temperatures, readily give up their oxygen to carbon in the electric furnace, and then combine with an excess of carbon to form metallic carbides. In 1885 the brothers Cowles patented a process for the electrothermal reduction of oxidized ores by exposure to an intense current of electricity when admixed with carbon in a retort. Later in that year they patented a process for the reduction of aluminium by carbon, and in 1886 an electric furnace with sliding carbon rods passed through the end walls to the centre of a rectangular furnace. The impossibility of working with just sufficient carbon to reduce the alumina, without using any excess which would be free to form at least so much carbide as would suffice, when diffused through the metal, to render it brittle, practically restricts the use of such processes to the production of aluminium alloys. Aluminium bronze (aluminium and copper) and ferro-aluminium (aluminium and iron) have been made in this way; the latter is the more satisfactory product, because a certain proportion of carbon is expected in an alloy of this character, as in ferromanganese and cast iron, and its presence is not objectionable. The furnace is built of fire-brick, and may measure (internally) 5 ft. in length by 1 ft. 8 in. in width, and 3 ft. in height. Into each end wall is built a short iron tube sloping downwards towards the centre, and through this is passed a bundle of five 3-in. carbon rods, bound together at the outer end by being cast into a head of cast iron for use with iron alloys, or of cast copper for aluminium bronze. This head slides freely in the cast iron tubes, and is connected by a copper rod with one of the terminals of the dynamo supplying the current. The carbons can thus, by the application of suitable mechanism, be withdrawn from or plunged into the furnace at will. In starting the furnace, the bottom is prepared by ramming it with charcoal-powder that has been soaked in milk of lime and dried, so that each particle is coated with a film of lime, which serves to reduce the loss of current by conduction through the lining when the furnace becomes hot. A sheet iron case is then placed within the furnace, and the space between it and the walls rammed with limed charcoal; the interior is filled with fragments of the iron or copper to be alloyed, mixed with alumina and coarse charcoal, broken pieces of carbon being placed in position to connect the electrodes. The iron case is then removed, the whole is covered with charcoal, and a cast iron cover with a central flue is placed above all. The current, either continuous or alternating, is then started, and continued for about 1 to 1-1/2 hours, until the operation is complete, the carbon rods being gradually withdrawn as the action proceeds. In such a furnace a continuous current, for example, of 3000 amperes, at 50 to 60 volts, may be used at first, increasing to 5000 amperes in about half an hour. The reduction is not due to electrolysis, but to the action of carbon on alumina, a part of the carbon in the charge being consumed and evolved as carbon monoxide gas, which burns at the orifice in the cover so long as reduction is taking place. The reduced aluminium alloys itself immediately with the fused globules of metal in its midst, and as the charge becomes reduced the globules of alloy unite until, in the end, they are run out of the tap-hole after the current has been diverted to another furnace. It was found in practice (in 1889) that the expenditure of energy per pound of reduced aluminium was about 23 H.P.-hours, a number considerably in excess of that required at the present time for the production of pure aluminium by the electrolytic process described in the article ALUMINIUM. Calcium carbide, graphite (q.v.), phosphorus (q.v.) and carborundum (q.v.) are now extensively manufactured by the operations outlined above.

_Electrolytic Processes._--The isolation of the metals sodium and potassium by Sir Humphry Davy in 1807 by the electrolysis of the fused hydroxides was one of the earliest applications of the electric current to the extraction of metals. This pioneering work showed little development until about the middle of the 19th century. In 1852 magnesium was isolated electrolytically by R. Bunsen, and this process subsequently received much attention at the hands of Moissan and Borchers. Two years later Bunsen and H.E. Sainte Claire Deville working independently obtained aluminium (q.v.) by the electrolysis of the fused double sodium aluminium chloride. Since that date other processes have been devised and the electrolytic processes have entirely replaced the older methods of reduction with sodium. Methods have also been discovered for the electrolytic manufacture of calcium (q.v.), which have had the effect of converting a laboratory curiosity into a product of commercial importance. Barium and strontium have also been produced by electro-metallurgical methods, but the processes have only a laboratory interest at present. Lead, zinc and other metals have also been reduced in this manner.

For further information the following books, in addition to those
mentioned at the end of the article ELECTROCHEMISTRY, may be
consulted: Borchers, _Handbuch der Elektrochemie_; _Electric Furnaces_
(Eng. trans. by H.G. Solomon, 1908); Moissan, _The Electric Furnace_
(1904); J. Escard, _Fours electriques_ (1905); _Les Industries
electrochimiques_ (1907). (W. G. M.)

FOOTNOTE:

[1] Cf. Siemens's account of the use of this furnace for experimental
purposes in _British Association Report_ for 1882.

ELECTROMETER, an instrument for measuring difference of potential, which operates by means of electrostatic force and gives the measurement either in arbitrary or in absolute units (see UNITS, PHYSICAL). In the last case the instrument is called an absolute electrometer. Lord Kelvin has classified electrometers into (1) Repulsion, (2) Attracted disk, and (3) Symmetrical electrometers (see W. Thomson, _Brit. Assoc. Report_, 1867, or _Reprinted Papers on Electrostatics and Magnetization_, p. 261).

_Repulsion Electrometers._--The simplest form of repulsion electrometer is W. Henley's pith ball electrometer (_Phil. Trans._, 1772, 63, p. 359) in which the repulsion of a straw ending in a pith ball from a fixed stem is indicated on a graduated arc (see ELECTROSCOPE). A double pith ball repulsion electrometer was employed by T. Cavallo in 1777.

It may be pointed out that such an arrangement is not merely an
arbitrary electrometer, but may become an absolute electrometer within
certain rough limits. Let two spherical pith balls of radius r and
weight W, covered with gold-leaf so as to be conducting, be suspended
by parallel silk threads of length l so as just to touch each other.
If then the balls are both charged to a potential V they will repel
each other, and the threads will stand out at an angle 2[theta], which
can be observed on a protractor. Since the electrical repulsion of the
balls is equal to C^2V^24l^2 sin^2[theta] dynes, where C = r is the
capacity of either ball, and this force is balanced by the restoring
force due to their weight, Wg dynes, where g is the acceleration of
gravity, it is easy to show that we have

2l sin [theta] [root](Wg tan [theta])
V = -------------------------------------
r

as an expression for their common potential V, provided that the balls
are small and their distance sufficiently great not sensibly to
disturb the uniformity of electric charge upon them. Observation of
[theta] with measurement of the value of l and r reckoned in
centimetres and W in grammes gives us the potential difference of the
balls in absolute C.G.S. or electrostatic units. The gold-leaf
electroscope invented by Abraham Bennet (see ELECTROSCOPE) can in like
manner, by the addition of a scale to observe the divergence of the
gold-leaves, be made a repulsion electrometer.

_Attracted Disk Electrometers._--A form of attracted disk absolute electrometer was devised by A. Volta. It consisted of a plane conducting plate forming one pan of a balance which was suspended over another insulated plate which could be electrified. The attraction between the two plates was balanced by a weight put in the opposite pan. A similar electric balance was subsequently devised by Sir W. Snow-Harris,[1] one of whose instruments is shown in fig. 1. C is an insulated disk over which is suspended another disk attached to the arm of a balance. A weight is put in the opposite scale pan and a measured charge of electricity is given to the disk C just sufficient to tip over the balance. Snow-Harris found that this charge varied as the square root of the weight in the opposite pan, thus showing that the attraction between the disks at given distance apart varies as the square of their difference of potential.

The most important improvements in connexion with electrometers are due, however, to Lord Kelvin, who introduced the guard plate and used gravity or the torsion of a wire as a means for evaluating the electrical forces.

His portable electrometer is shown in fig. 2. H H (see fig. 3) is a
plane disk of metal called the guard plate, fixed to the inner coating
of a small Leyden jar (see fig. 2). At F a square hole is cut out of H
H, and into this fits loosely without touching, like a trap door, a
square piece of aluminium foil having a projecting tail, which carries
at its end a stirrup L, crossed by a fine hair (see fig. 3). The
square piece of aluminium is pivoted round a horizontal stretched
wire. If then another horizontal disk G is placed over the disk H H
and a difference of potential made between G and H H, the movable
aluminium trap door F will be attracted by the fixed plate G. Matters
are so arranged by giving a torsion to the wire carrying the aluminium
disk F that for a certain potential difference between the plates H
and G, the movable part F comes into a definite sighted position,
which is observed by means of a small lens. The plate G (see fig. 2)
is moved up and down, parallel to itself, by means of a screw. In
using the instrument the conductor, whose potential is to be tested,
is connected to the plate G. Let this potential be denoted by V, and
let v be the potential of the guard plate and the aluminium flap. This
last potential is maintained constant by guard plate and flap being
part of the interior coating of a charged Leyden jar. Since the
distribution of electricity may be considered to be constant over the
surface S of the attracted disk, the mechanical force f on it is given
by the expression,[2]

S(V - v)^2
f = ----------,
8[pi]d^2

where d is the distance between the two plates. If this distance is
varied until the attracted disk comes into a definite sighted position
as seen by observing the end of the index through the lens, then since
the force f is constant, being due to the torque applied by the wire
for a definite angle of twist, it follows that the difference of
potential of the two plates varies as their distance. If then two
experiments are made, first with the upper plate connected to earth,
and secondly, connected to the object being tested, we get an
expression for the potential V of this conductor in the form

V = A(d' - d),

where d and d' are the distances of the fixed and movable plates from
one another in the two cases, and A is some constant. We thus find V
in terms of the constant and the difference of the two screw readings.

Lord Kelvin's absolute electrometer (fig. 4) involves the same
principle. There is a certain fixed guard disk B having a hole in it
which is loosely occupied by an aluminium trap door plate, shielded by
D and suspended on springs, so that its surface is parallel with that
of the guard plate. Parallel to this is a second movable plate A, the
distances between the two being measurable by means of a screw. The
movable plate can be drawn down into a definite sighted position when
a difference of potential is made between the two plates. This
sighted position is such that the surface of the trap door plate is
level with that of the guard plate, and is determined by observations
made with the lenses H and L. The movable plate can be thus depressed
by placing on it a certain standard weight W grammes.

Suppose it is required to measure the difference of potentials V and
V' of two conductors. First one and then the other conductor is
connected with the electrode of the lower or movable plate, which is
moved by the screw until the index attached to the attracted disk
shows it to be in the sighted position. Let the screw readings in the
two cases be d and d'. If W is the weight required to depress the
attracted disk into the same sighted position when the plates are
unelectrified and g is the acceleration of gravity, then the
difference of potentials of the conductors tested is expressed by the
formula
_______
/8[pi]gW
V - V' = (d - d') / -------,
\/ S

where S denotes the area of the attracted disk.

The difference of potentials is thus determined in terms of a weight,
an area and a distance, in absolute C.G.S. measure or electrostatic
units.

_Symmetrical Electrometers_ include the dry pile electrometer and Kelvin's quadrant electrometer. The principle underlying these instruments is that we can measure differences of potential by means of the motion of an electrified body in a symmetrical field of electric force. In the dry pile electrometer a single gold-leaf is hung up between two plates which are connected to the opposite terminals of a dry pile so that a certain constant difference of potential exists between these plates. The original inventor of this instrument was T.G.B. Behrens (_Gilb. Ann._, 1806, 23), but it generally bears the name of J.G.F. von Bohnenberger, who slightly modified its form. G.T. Fechner introduced the important improvement of using only one pile, which he removed from the immediate neighbourhood of the suspended leaf. W.G. Hankel still further improved the dry pile electrometer by giving a slow motion movement to the two plates, and substituted a galvanic battery with a large number of cells for the dry pile, and also employed a divided scale to measure the movements of the gold-leaf (_Pogg. Ann._, 1858, 103). If the gold-leaf is unelectrified, it is not acted upon by the two plates placed at equal distances on either side of it, but if its potential is raised or lowered it is attracted by one disk and repelled by the other, and the displacement becomes a measure of its potential.

A vast improvement in this instrument was made by the invention of the quadrant electrometer by Lord Kelvin, which is the most sensitive form of electrometer yet devised. In this instrument (see fig. 5) a flat paddle-shaped needle of aluminium foil U is supported by a bifilar suspension consisting of two cocoon fibres. This needle is suspended in the interior of a glass vessel partly coated with tin-foil on the outside and inside, forming therefore a Leyden jar (see fig. 6). In the bottom of the vessel is placed some sulphuric acid, and a platinum wire attached to the suspended needle dips into this acid. By giving a charge to this Leyden jar the needle can thus be maintained at a certain constant high potential. The needle is enclosed by a sort of flat box divided into four insulated quadrants A, B, C, D (fig. 5), whence the name. The opposite quadrants are connected together by thin platinum wires. These quadrants are insulated from the needle and from the case, and the two pairs are connected to two electrodes. When the instrument is to be used to determine the potential difference between two conductors, they are connected to the two opposite pairs of quadrants. The needle in its normal position is symmetrically placed with regard to the quadrants, and carries a mirror by means of which its displacement can be observed in the usual manner by reflecting the ray of light from it. If the two quadrants are at different potentials, the needle moves from one quadrant towards the other, and the image of a spot of light on the scale is therefore displaced. Lord Kelvin provided the instrument with two necessary adjuncts, viz. a replenisher or rotating electrophorus (q.v.), by means of which the charge of the Leyden jar which forms the enclosing vessel can be increased or diminished, and also a small aluminium balance plate or gauge, which is in principle the same as the attracted disk portable electrometer by means of which the potential of the inner coating of the Leyden jar is preserved at a known value.

According to the mathematical theory of the instrument,[3] if V and V'
are the potentials of the quadrants and v is the potential of the
needle, then the torque acting upon the needle to cause rotation is
given by the expression,

C(V - V') {v - 1/2(V + V')},

where C is some constant. If v is very large compared with the mean
value of the potentials of the two quadrants, as it usually is, then
the above expression indicates that the couple varies as the
difference of the potentials between the quadrants.

Dr J. Hopkinson found, however, before 1885, that the above formula
does not agree with observed facts (_Proc. Phys. Soc. Lond._, 1885, 7,
p. 7). The formula indicates that the sensibility of the instrument
should increase with the charge of the Leyden jar or needle, whereas
Hopkinson found that as the potential of the needle was increased by
working the replenisher of the jar, the deflection due to three volts
difference between the quadrants first increased and then diminished.
He found that when the potential of the needle exceeded a certain
value, of about 200 volts, for the particular instrument he was using
(made by White of Glasgow), the above formula did not hold good. W.E.
Ayrton, J. Perry and W.E. Sumpner, who in 1886 had noticed the same
fact as Hopkinson, investigated the matter in 1891 (_Proc. Roy. Soc._,
1891, 50, p. 52; _Phil. Trans._, 1891, 182, p. 519). Hopkinson had
been inclined to attribute the anomaly to an increase in the tension
of the bifilar threads, owing to a downward pull on the needle, but
they showed that this theory would not account for the discrepancy.
They found from observations that the particular quadrant electrometer
they used might be made to follow one or other of three distinct laws.
If the quadrants were near together there were certain limits between
which the potential of the needle might vary without producing more
than a small change in the deflection corresponding with the fixed
potential difference of the quadrants. For example, when the quadrants
were about 2.5 mm. apart and the suspended fibres near together at the
top, the deflection produced by a P.D. of 1.45 volts between the
quadrants only varied about 11% when the potential of the needle
varied from 896 to 3586 volts. When the fibres were far apart at the
top a similar flatness was obtained in the curve with the quadrants
about 1 mm. apart. In this case the deflection of the needle was
practically quite constant when its potential varied from 2152 to 3227
volts. When the quadrants were about 3.9 mm. apart, the deflection for
a given P.D. between the quadrants was almost directly proportional to
the potential of the needle. In other words, the electrometer nearly
obeyed the theoretical law. Lastly, when the quadrants were 4 mm. or
more apart, the deflection increased much more rapidly than the
potential, so that a maximum sensibility bordering on instability was
obtained. Finally, these observers traced the variation to the fact
that the wire supporting the aluminium needle as well as the wire
which connects the needle with the sulphuric acid in the Leyden jar in
the White pattern of Leyden jar is enclosed in a metallic guard tube
to screen the wire from external action. In order that the needle may
project outside the guard tube, openings are made in its two sides;
hence the moment the needle is deflected each half of it becomes
unsymmetrically placed relatively to the two metallic pieces which
join the upper and lower half of the guard tube. Guided by these
experiments, Ayrton, Perry and Sumpner constructed an improved
unifilar quadrant electrometer which was not only more sensitive than
the White pattern, but fulfilled the theoretical law of working. The
bifilar suspension was abandoned, and instead a new form of adjustable
magnetic control was adopted. All the working parts of the instrument
were supported on the base, so that on removing a glass shade which
serves as a Leyden jar they can be got at and adjusted in position.
The conclusion to which the above observers came was that any quadrant
electrometer made in any manner does not necessarily obey a law of
deflection making the deflections proportional to the potential
difference of the quadrants, but that an electrometer can be
constructed which does fulfil the above law.

The importance of this investigation resides in the fact that an
electrometer of the above pattern can be used as a wattmeter (q.v.),
provided that the deflection of the needle is proportional to the
potential difference of the quadrants. This use of the instrument was
proposed simultaneously in 1881 by Professors Ayrton and G.F.
Fitzgerald and M.A. Potier. Suppose we have an inductive and a
non-inductive circuit in series, which is traversed by a periodic
current, and that we desire to know the power being absorbed to the
inductive circuit. Let v1, v2, v3 be the instantaneous potentials of
the two ends and middle of the circuit; let a quadrant electrometer be
connected first with the quadrants to the two ends of the inductive
circuit and the needle to the far end of the non-inductive circuit,
and then secondly with the needle connected to one of the quadrants
(see fig. 5). Assuming the electrometer to obey the above-mentioned
theoretical law, the first reading is proportional to

/ v1 + v2\
v1 - v2 ( v3 - ------- )
\ 2 /

and the second to

/ v1 + v2\
v1 - v2 ( v2 - ------- ).
\ 2 /

The difference of the readings is then proportional to

(v1 - v2)(v2 - v3).

But this last expression is proportional to the instantaneous power
taken up in the inductive circuit, and hence the difference of the two
readings of the electrometer is proportional to the mean power taken
up in the circuit (_Phil. Mag._, 1891, 32, p. 206). Ayrton and Perry
and also P.R. Blondlot and P. Curie afterwards suggested that a single
electrometer could be constructed with two pairs of quadrants and a
duplicate needle on one stem, so as to make two readings
simultaneously and produce a deflection proportional at once to the
power being taken up in the inductive circuit.

Quadrant electrometers have also been designed especially for measuring extremely small potential differences. An instrument of this kind has been constructed by Dr. F. Dolezalek (fig. 7). The needle and quadrants are of small size, and the electrostatic capacity is correspondingly small. The quadrants are mounted on pillars of amber which afford a very high insulation. The needle, a piece of paddle-shaped paper thinly coated with silver foil, is suspended by a quartz fibre, its extreme lightness making it possible to use a very feeble controlling force without rendering the period of oscillation unduly great. The resistance offered by the air to a needle of such light construction suffices to render the motion nearly dead-beat. Throughout a wide range the deflections are proportional to the potential difference producing them. The needle is charged to a potential of 50 to 200 volts by means of a dry pile or voltaic battery, or from a lighting circuit. To facilitate the communication of the charge to the needle, the quartz fibre and its attachments are rendered conductive by a thin film of solution of hygroscopic salt such as calcium chloride. The lightness of the needle enables the instrument to be moved without fear of damaging the suspension. The upper end of the quartz fibre is rotated by a torsion head, and a metal cover serves to screen the instrument from stray electrostatic fields. With a quartz fibre 0.009 mm. thick and 60 mm. long, the needle being charged to 110 volts, the period and swing of the needle was 18 seconds. With the scale at a distance of two metres, a deflection of 130 mm. was produced by an electromotive force of 0.1 volt. By using a quartz fibre of about half the above diameter the sensitiveness was much increased. An instrument of this form is valuable in measuring small alternating currents by the fall of potential produced down a known resistance. In the same way it may be employed to measure high potentials by measuring the fall of potential down a fraction of a known non-inductive resistance. In this last case, however, the capacity of the electrometer used must be small, otherwise an error is introduced.[4]

See, in addition to references already given, A. Gray, _Absolute
Measurements in Electricity and Magnetism_ (London, 1888), vol. i. p.
254; A. Winkelmann, _Handbuch der Physik_ (Breslau, 1905), pp. 58-70,
which contains a large number of references to original papers on
electrometers. (J. A. F.)

FOOTNOTES:

[1] It is probable that an experiment of this kind had been made as
far back as 1746 by Daniel Gralath, of Danzig, who has some claims to
have suggested the word "electrometer" in connexion with it. See Park
Benjamin, _The Intellectual Rise in Electricity_ (London, 1895), p.
542.

[2] See Maxwell, _Treatise on Electricity and Magnetism_ (2nd ed.),
i. 308.

[3] See Maxwell, _Electricity and Magnetism_ (2nd ed., Oxford, 1881),
vol. i. p. 311.

[4] See J.A. Fleming, _Handbook for the Electrical Laboratory and
Testing Room_, vol. i. p. 448 (London, 1901).

ELECTRON, the name suggested by Dr G. Johnstone Stoney in 1891 for the natural unit of electricity to which he had drawn attention in 1874, and subsequently applied to the ultra-atomic particles carrying negative charges of electricity, of which Professor Sir J.J. Thomson proved in 1897 that the cathode rays consisted. The electrons, which Thomson at first called corpuscles, are point charges of negative electricity, their inertia showing them to have a mass equal to about 1/2000 that of the hydrogen atom. They are apparently derivable from all kinds of matter, and are believed to be components at any rate of the chemical atom. The electronic theory of the chemical atom supposes, in fact, that atoms are congeries of electrons in rapid orbital motion. The size of the electron is to that of an atom roughly in the ratio of a pin's head to the dome of St Paul's cathedral. The electron is always associated with the unit charge of negative electricity, and it has been suggested that its inertia is wholly electrical. For further details see the articles on ELECTRICITY; MAGNETISM; MATTER; RADIOACTIVITY; CONDUCTION, ELECTRIC; _The Electron Theory_, E. Fournier d'Albe (London, 1907); and the original papers of Dr G. Johnstone Stoney, _Proc. Brit. Ass._ (Belfast, August 1874), "On the Physical Units of Nature," and _Trans. Royal Dublin Society_ (1891), 4, p. 583.