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37, p. 723). These experiments showed that over moderate ranges | values as the "Swedish Iron," commonly considered best for of induction, such as may be expected in electro-technical work, the hysteresis loss per cycle per cubic centimetre was practically the same when the iron was tested in an alternating field with a❘ periodicity of 100, the field remaining constant in direction, and when the iron was tested in a rotating field giving the same maximum flux density.

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 16th power of the maximum flux density (B), or W=ŋ B1·.

The hysteretic constants (n) for various kinds of iron and steel are given in the table below:

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Swedish wrought iron, well annealed. Annealed cast steel of good quality; small percentage of carbon

Cast Siemens-Martin steel
Cast ingot-iron

Cast steel, with higher percentages of carbon, or inferior qualities of wrought

iron.

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.0010 to 0017

0017 to 0029. 0019 to 0028 .0021 to 0026

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° 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. Bláthy 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° 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° C. a rise in temperature did not produce any augmentation in the hysteresis loss in iron, but if it is heated to between 40° C. and 135° 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° C., the hysteresis loss soon attains a maximum, but then begins to decrease. Certain specimens heated to 160° C. were found to have their hysteresis loss doubled in a few days. The effect seems to come to a maximum at about 180° C. or 200° 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° C. and 700° 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° 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

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

་་་་་1011

FIG. 6. Du Bois's Electromagnet.

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

papers:

The

dynamo machines are considered in the article DYNAMO, and there | metal and the accompanying slag were to be caught, after leaving is, therefore, no necessity to refer particularly to the numerous the arc and while still liquid, in a hearth fired with ordinary different shapes and types employed in electrotechnics. fuel. Although this primitive furnace could be made to act, its BIBLIOGRAPHY.-For additional information on the above subject efficiency was low, and the use of a separate fire was disadvanthe reader may be referred to the following works and original tageous. In 1878 Sir William Siemens patented a form of furnace1 which is the type of a very large number of those designed by H. du Bois, The Magnetic Circuit in Theory and Practice; S. P. Thompson, The Electromagnet; J. A. Fleming, Magnets and Electric later inventors. Currents; J. A. Ewing, Magnetic Induction in Iron and other Metals; In the best-known form a plumbago crucible was used with a J. A. Fleming, "The Ferromagnetic Properties of Iron and Steel," hole cut in the bottom to receive a carbon rod, which was ground Proceedings of Sheffield Society of Engineers and Metallurgists (Oct. in so as to make a tight joint. This rod was connected with the 1897); J. A. Ewing, "The Magnetic Testing of Iron and Steel," positive pole of the dynamo or electric generator. The crucible Proc. Inst. Civ. Eng., 1896, 126, p. 185; H. F Parshall, was fitted with a cover in which were two holes; one at the side to Magnetic Data of Iron and Steel," Proc. Inst. Civ. Eng., 1896, serve at once as sight-hole and charging door, the other in the 126, p. 220; J. A. Ewing, "The Molecular Theory of Induced centre to allow a second carbon rod to pass freely (without touching) Magnetism," Phil. Mag., Sept. 1890; W. M. Mordey, "Slow Changes into the interior. This rod was connected with the negative pole of in the Permeability of Iron," Proc. Roy. Soc. 57, p. 224; J. A. the generator, and was suspended from one arm of a balance-beam, Ewing, Magnetism," James Forrest Lecture, Proc. Inst. Civ. Eng. while from the other end of the beam was suspended a vertical hollow 138; S. P. Thompson, Electromagnetic Mechanism," Electrician, iron cylinder, which could be moved into or out of a wire coil or 26, pp. 238, 269, 293; J. A. Ewing, "Experimental Researches in solenoid joined as a shunt across the two carbon rods of the furnace. Magnetism," Phil. Trans., 1885, part ii.; Ewing and Klassen, The solenoid was above the iron cylinder, the supporting rod of which Magnetic Qualities of Iron," Proc. Roy. Soc., 1893. (J. A. F.) passed through it as a core. When the furnace with this well-known ELECTROMETALLURGY. The present article, as explained regulating device was to be used, say, for the melting of metals or other conductors of electricity, the fragments of metal were placed under ELECTROCHEMISTRY, treats only of those processes in in the crucible and the positive electrode was brought near them. which electricity is applied to the production of chemical re- Immediately the current passed through the solenoid it caused the actions or molecular changes at furnace temperatures. In iron cylinder to rise, and, by means of its supporting rod, forced the many of these the application of heat is necessary to bring end of the balance beam upwards, so depressing the other end that the negative carbon rod was forced downwards into contact with the the substances used into the liquid state for the purpose of metal in the crucible. This action completed the furnace-circuit, electrolysis, aqueous solutions being unsuitable. Among the and current passed freely from the positive carbon through the earliest experiments in this branch of the subject were fragments of metal to the negative carbon, thereby reducing the those of Sir H. Davy, who in 1807 (Phil. Trans., 1808, current through the shunt. At once the attractive force of the solenoid on the iron cylinder was automatically reduced, and the p. 1), produced the alkali metals by passing an intense cur- falling of the latter caused the negative carbon to rise, starting an rent of electricity from a platinum wire to a platinum dish, arc between it and the metal in the crucible. A counterpoise was through a mass of fused caustic alkali. The action was started placed on the solenoid end of the balance beam to act against the attraction of the solenoid, the position of the counterpoise determinin the cold, the alkali being slightly moistened to render ing the length of the arc in the crucible. Any change in the resist conductor; then, as the current passed, heat was produced ance of the arc, either by lengthening, due to the sinking of the charge and the alkali fused, the metal being deposited in the liquid in the crucible, or by the burning of the carbon, affected the procondition. Later, A. Matthiessen (Quarterly Journ. Chem. Soc. portion of current flowing in the two shunt circuits, and so altered viii. 30) obtained potassium by the electrolysis of a mixture the position of the iron cylinder in the solenoid that the length of arc was, within limits, automatically regulated. Were it not for the of potassium and calcium chlorides fused over a lamp. There use of some such device the arc would be liable to constant fluctuation are here foreshadowed two types of electrolytic furnace-opera- and to frequent extinction. The crucible was surrounded with a tions: (a) those in which external heating maintains the bad conductor of heat to minimize loss by radiation. The positive electrolyte in the fused condition, and (b) those in which a current-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 density is applied sufficiently high to develop the heat necessary modifications were proposed, in one of which, intended for the heating to effect this object unaided. Much of the earlier electrometal-of non-conducting substances, the electrodes were passed horizontally lurgical work was done with furnaces of the (a) type, while through perforations in the upper part of the crucible walls, and the nearly all the later developments have been with those of class charge in the lower part of the crucible was heated by radiation. (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.

a

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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 in. in height. The fact that energy is being used at so high a rate as too 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 Ib of either of these metals in 5 or 6 minutes in a furnace similar to that last described. He also arranged an experimental tubefurnace by passing a carbon tube horizontally beneath the arc 1 Cf. Siemens's account of the use of this furnace for experimental purposes in British Association Report for 1882.

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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° C., and less than 4000° C., the temperature of the electric furnace cannot rise much above 3500° C. (6330° 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

descence 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 blastfurnace, 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 watercooled 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.

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 manufarture of calcium carbide on a large scale are chiefly develop-run at these high temperatures; obviously, those of the incanments 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. 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 Incan. with a substance offering a high resistance to the descence furnaces. 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. 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 Uses and and steam-engine, or of the gas or oil engine, with a advigLages. 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

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

Alumin

lum

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)
alloys. and ferro-aluminium (aluminium and iron) have
been made in this way; the latter is the more satis-
factory 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 hours, until the operation is
complete, the carbon rods being gradually withdrawn as the
action proceeds. In such a furnace a continuous current, fore
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 electrometallurgical 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 électriques (1905); Les Industries électrochimiques (1907). (W. G. M.)

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 suspended by parallel silk threads of length / so as just to touch each and weight W, covered with gold-leaf so as to be conducting, be 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 20, which can be observed on a protractor. Since the electrical repulsion of either ball, and this force is balanced by the restoring force due of the balls is equal to CV 4/2 sin 20 dynes, where C=r is the capacity to their weight, Wg dynes, where g is the acceleration of gravity, it is casy to show that we have

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as an expression for their common potential V, provided that the balls are small and their distance sufficiently great not sensibly to with measurement of the value of I and reckoned in centimetres disturb the uniformity of electric charge upon them. Observation of 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
electrified. The attraction between the two plates was balanced
was suspended over another insulated plate which could be
by a weight put in
the opposite pan.
A similar electric
balance was subse-

[graphic]

quently devised by
SirW.Snow-Harris,'
one of whose instru-
ments is shown in
fig. 1. C is an in-
sulated disk over
which is suspended
another disk at-

tached 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
just sufficient to
FIG. 1.-Snow-Harris's Disk Electrometer.
tipover the balance.
of the weight in the opposite pan, thus showing that the
Snow-Harris found that this charge varied as the square root

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.

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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 sig ed 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 ƒ on it is given by the expression,'

S(V-v)2, f= 8d

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. FIG. 4.-Kelvin's Ab- There is a certain fixed guard disk B solute Electrometer. 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

1 See Maxwell, Treatise on Electricity and Magnetism (2nd ed.), i 308.

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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 bed 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

[graphic]

V-V' = (d-d')√√8gW,

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 electro static units.

FIG. 5.

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 paddleshaped 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

[graphic]
[graphic]

meter.

needle dips into this acid. FIG. 6.-Kelvin's Quadrant ElectroBy 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

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