Chapter XVI: Part 16

The logarithmic formulae for these concentration cells indicate that theoretically their electromotive force can be increased to any extent by diminishing without limit the concentration of the more dilute solution, log c1/c2 then becoming very great. This condition may be realized to some extent in a manner that throws light on the general theory of the voltaic cell. Let us consider the arrangement--silver | silver chloride with potassium chloride solution | potassium nitrate solution | silver nitrate solution | silver. Silver chloride is a very insoluble substance, and here the amount in solution is still further reduced by the presence of excess of chlorine ions of the potassium salt. Thus silver, at one end of the cell in contact with many silver ions of the silver nitrate solution, at the other end is in contact with a liquid in which the concentration of those ions is very small indeed. The result is that a high electromotive force is set up, which has been calculated as 0.52 volt, and observed as 0.51 volt. Again, Hittorf has shown that the effect of a cyanide round a copper electrode is to combine with the copper ions. The concentration of the simple copper ions is then so much diminished that the copper plate becomes an anode with regard to zinc. Thus the cell--copper | potassium cyanide solution | potassium sulphate solution--zinc sulphate solution | zinc--gives a current which carries copper into solution and deposits zinc. In a similar way silver could be made to act as anode with respect to cadmium.

It is now evident that the electromotive force of an ordinary chemical cell such as that of Daniell depends on the concentration of the solutions as well as on the nature of the metals. In ordinary cases possible changes in the concentrations only affect the electromotive force by a few parts in a hundred, but, by means such as those indicated above, it is possible to produce such immense differences in the concentrations that the electromotive force of the cell is not only changed appreciably but even reversed in direction. Once more we see that it is the total impending change in the available energy of the system which controls the electromotive force.

Any reversible cell can theoretically be employed as an accumulator, though, in practice, conditions of general convenience are more sought after than thermodynamic efficiency. The effective electromotive force of the common lead accumulator (q.v.) is less than that required to charge it. This drop in the electromotive force has led to the belief that the cell is not reversible. F. Dolezalek, however, has attributed the difference to mechanical hindrances, which prevent the equalization of acid concentration in the neighbourhood of the electrodes, rather than to any essentially irreversible chemical action. The fact that the Gibbs-Helmholtz equation is found to apply also indicates that the lead accumulator is approximately reversible in the thermodynamic sense of the term.

_Polarization and Contact Difference of Potential._--If we connect together in series a single Daniell's cell, a galvanometer, and two platinum electrodes dipping into acidulated water, no visible chemical decomposition ensues. At first a considerable current is indicated by the galvanometer; the deflexion soon diminishes, however, and finally becomes very small. If, instead of using a single Daniell's cell, we employ some source of electromotive force which can be varied as we please, and gradually raise its intensity, we shall find that, when it exceeds a certain value, about 1.7 volt, a permanent current of considerable strength flows through the solution, and, after the initial period, shows no signs of decrease. This current is accompanied by chemical decomposition. Now let us disconnect the platinum plates from the battery and join them directly with the galvanometer. A current will flow for a while in the reverse direction; the system of plates and acidulated water through which a current has been passed, acts as an accumulator, and will itself yield a current in return. These phenomena are explained by the existence of a reverse electromotive force at the surface of the platinum plates. Only when the applied electromotive force exceeds this reverse force of polarization, will a permanent steady current pass through the liquid, and visible chemical decomposition proceed. It seems that this reverse electromotive force of polarization is due to the deposit on the electrodes of minute quantities of the products of chemical decomposition. Differences between the two electrodes are thus set up, and, as we have seen above, an electromotive force will therefore exist between them. To pass a steady current in the direction opposite to this electromotive force of polarization, the applied electromotive force E must exceed that of polarization E', and the excess E - E' is the effective electromotive force of the circuit, the current being, in accordance with Ohm's law, proportional to the applied electromotive force and represented by (E - E')/R, where R is a constant called the resistance of the circuit.

When we use platinum electrodes in acidulated water, hydrogen and oxygen are evolved. The opposing force of polarization is about 1.7 volt, but, when the plates are disconnected and used as a source of current, the electromotive force they give is only about 1.07 volt. This irreversibility is due to the work required to evolve bubbles of gas at the surface of bright platinum plates. If the plates be covered with a deposit of platinum black, in which the gases are absorbed as fast as they are produced, the minimum decomposition point is 1.07 volt, and the process is reversible. If secondary effects are eliminated, the deposition of metals also is a reversible process; the decomposition voltage is equal to the electromotive force which the metal itself gives when going into solution. The phenomena of polarization are thus seen to be due to the changes of surface produced, and are correlated with the differences of potential which exist at any surface of separation between a metal and an electrolyte.

Many experiments have been made with a view of separating the two potential-differences which must exist in any cell made of two metals and a liquid, and of determining each one individually. If we regard the thermal effect at each junction as a measure of the potential-difference there, as the total thermal effect in the cell undoubtedly is of the sum of its potential-differences, in cases where the temperature coefficient is negligible, the heat evolved on solution of a metal should give the electrical potential-difference at its surface. Hence, if we assume that, in the Daniell's cell, the temperature coefficients are negligible at the individual contacts as well as in the cell as a whole, the sign of the potential-difference ought to be the same at the surface of the zinc as it is at the surface of the copper. Since zinc goes into solution and copper comes out, the electromotive force of the cell will be the difference between the two effects. On the other hand, it is commonly thought that the single potential-differences at the surface of metals and electrolytes have been determined by methods based on the use of the capillary electrometer and on others depending on what is called a dropping electrode, that is, mercury dropping rapidly into an electrolyte and forming a cell with the mercury at rest in the bottom of the vessel. By both these methods the single potential-differences found at the surfaces of the zinc and copper have opposite signs, and the effective electromotive force of a Daniell's cell is the sum of the two effects. Which of these conflicting views represents the truth still remains uncertain.

_Diffusion of Electrolytes and Contact Difference of Potential between Liquids._--An application of the theory of ionic velocity due to W. Nernst[7] and M. Planck[8] enables us to calculate the diffusion constant of dissolved electrolytes. According to the molecular theory, diffusion is due to the motion of the molecules of the dissolved substance through the liquid. When the dissolved molecules are uniformly distributed, the osmotic pressure will be the same everywhere throughout the solution, but, if the concentration vary from point to point, the pressure will vary also. There must, then, be a relation between the rate of change of the concentration and the osmotic pressure gradient, and thus we may consider the osmotic pressure gradient as a force driving the solute through a viscous medium. In the case of non-electrolytes and of all non-ionized molecules this analogy completely represents the facts, and the phenomena of diffusion can be deduced from it alone. But the ions of an electrolytic solution can move independently through the liquid, even when no current flows, as the consequences of Ohm's law indicate. The ions will therefore diffuse independently, and the faster ion will travel quicker into pure water in contact with a solution. The ions carry their charges with them, and, as a matter of fact, it is found that water in contact with a solution takes with respect to it a positive or negative potential, according as the positive or negative ion travels the faster. This process will go on until the simultaneous separation of electric charges produces an electrostatic force strong enough to prevent further separation of ions. We can therefore calculate the rate at which the salt as a whole will diffuse by examining the conditions for a steady transfer, in which the ions diffuse at an equal rate, the faster one being restrained and the slower one urged forward by the electric forces. In this manner the diffusion constant can be calculated in absolute units (HCl = 2.49, HNO3 = 2.27, NaCl = 1.12), the unit of time being the day. By experiments on diffusion this constant has been found by Scheffer, and the numbers observed agree with those calculated (HCl = 2.30, HNO3 = 2.22, NaCl = 1.11).

As we have seen above, when a solution is placed in contact with water the water will take a positive or negative potential with regard to the solution, according as the cation or anion has the greater specific velocity, and therefore the greater initial rate of diffusion. The difference of potential between two solutions of a substance at different concentrations can be calculated from the equations used to give the diffusion constants. The results give equations of the same logarithmic form as those obtained in a somewhat different manner in the theory of concentration cells described above, and have been verified by experiment.

The contact differences of potential at the interfaces of metals and electrolytes have been co-ordinated by Nernst with those at the surfaces of separation between different liquids. In contact with a solvent a metal is supposed to possess a definite solution pressure, analogous to the vapour pressure of a liquid. Metal goes into solution in the form of electrified ions. The liquid thus acquires a positive charge, and the metal a negative charge. The electric forces set up tend to prevent further separation, and finally a state of equilibrium is reached, when no more ions can go into solution unless an equivalent number are removed by voltaic action. On the analogy between this case and that of the interface between two solutions, Nernst has arrived at similar logarithmic expressions for the difference of potential, which becomes proportional to log (P1/P2) where P2 is taken to mean the osmotic pressure of the cations in the solution, and P1 the osmotic pressure of the cations in the substance of the metal itself. On these lines the equations of concentration cells, deduced above on less hypothetical grounds, may be regained.

_Theory of Electrons._--Our views of the nature of the ions of electrolytes have been extended by the application of the ideas of the relations between matter and electricity obtained by the study of electric conduction through gases. The interpretation of the phenomena of gaseous conduction was rendered possible by the knowledge previously acquired of conduction through liquids; the newer subject is now reaching a position whence it can repay its debt to the older.

Sir J.J. Thomson has shown (see CONDUCTION, ELECTRIC, S III.) that the negative ions in certain cases of gaseous conduction are much more mobile than the corresponding positive ions, and possess a mass of about the one-thousandth part of that of a hydrogen atom. These negative particles or corpuscles seem to be the ultimate units of negative electricity, and may be identified with the electrons required by the theories of H.A. Lorentz and Sir J. Larmor. A body containing an excess of these particles is negatively electrified, and is positively electrified if it has parted with some of its normal number. An electric current consists of a moving stream of electrons. In gases the electrons sometimes travel alone, but in liquids they are always attached to matter, and their motion involves the movement of chemical atoms or groups of atoms. An atom with an extra corpuscle is a univalent negative ion, an atom with one corpuscle detached is a univalent positive ion. In metals the electrons can slip from one atom to the next, since a current can pass without chemical action. When a current passes from an electrolyte to a metal, the electron must be detached from the atom it was accompanying and chemical action be manifested at the electrode.

BIBLIOGRAPHY.--Michael Faraday, _Experimental Researches in
Electricity_ (London, 1844 and 1855); W. Ostwald, _Lehrbuch der
allgemeinen Chemie_, 2te Aufl. (Leipzig, 1891); _Elektrochemie_
(Leipzig, 1896); W Nernst, _Theoretische Chemie_, 3te Aufl.
(Stuttgart, 1900; English translation, London, 1904); F. Kohlrausch
and L. Holborn, _Das Leitvermogen der Elektrolyte_ (Leipzig, 1898);
W.C.D. Whetham, _The Theory of Solution and Electrolysis_ (Cambridge,
1902); M. Le Blanc, _Elements of Electrochemistry_ (Eng. trans.,
London, 1896); S. Arrhenius, _Text-Book of Electrochemistry_ (Eng.
trans., London, 1902); H.C. Jones, _The Theory of Electrolytic
Dissociation_ (New York, 1900); N. Munroe Hopkins, _Experimental
Electrochemistry_ (London, 1905); Luphe, _Grundzuge der Elektrochemie_
(Berlin, 1896).

Some of the more important papers on the subject have been reprinted
for Harper's _Series of Scientific Memoirs in Electrolytic Conduction_
(1899) and the _Modern Theory of Solution_ (1899). Several journals
are published specially to deal with physical chemistry, of which
electrochemistry forms an important part. Among them may be mentioned
the _Zeitschrift fur physikalische Chemie_ (Leipzig); and the _Journal
of Physical Chemistry_ (Cornell University). In these periodicals will
be found new work on the subject and abstracts of papers which appear
in other physical and chemical publications. (W. C. D. W.)

FOOTNOTES:

[1] See Hittorf, _Pogg. Ann._ cvi. 517 (1859).

[2] _Grundriss der Elektrochemie_ (1895), p. 292; see also F. Kaufler
and C. Herzog, _Ber._, 1909, 42, p. 3858.

[3] _Brit. Ass. Rep._, 1906, Section A, Presidential Address.

[4] See _Theory of Solution_, by W.C.D. Whetham (1902), p. 328.

[5] W. Ostwald, _Zeits. physikal. Chemie_, 1892, vol. IX. p. 579; T.
Ewan, _Phil. Mag._ (5), 1892, vol. xxxiii. p. 317; G.D. Liveing,
_Cambridge Phil. Trans._, 1900, vol. xviii. p. 298.

[6] See W.B. Hardy, _Journal of Physiology_, 1899, vol. xxiv. p. 288;
and W.C.D. Whetham, _Phil. Mag._, November 1899.

[7] _Zeits. physikal. Chem._ 2, p. 613.

[8] _Wied. Ann._, 1890, 40, p. 561.

ELECTROMAGNETISM, that branch of physical science which is concerned with the interconnexion of electricity and magnetism, and with the production of magnetism by means of electric currents by devices called electromagnets.

_History._--The foundation was laid by the observation first made by Hans Christian Oersted (1777-1851), professor of natural philosophy in Copenhagen, who discovered in 1820 that a wire uniting the poles or terminal plates of a voltaic pile has the property of affecting a magnetic needle[1] (see ELECTRICITY). Oersted carefully ascertained that the nature of the wire itself did not influence the result but saw that it was due to the electric conflict, as he called it, round the wire; or in modern language, to the magnetic force or magnetic flux round the conductor. If a straight wire through which an electric current is flowing is placed above and parallel to a magnetic compass needle, it is found that if the current is flowing in the conductor in a direction from south to north, the north pole of the needle under the conductor deviates to the left hand, whereas if the conductor is placed under the needle, the north pole deviates to the right hand; if the conductor is doubled back over the needle, the effects of the two sides of the loop are added together and the deflection is increased. These results are summed up in the mnemonic rule: _Imagine yourself swimming in the conductor with the current, that is, moving in the direction of the positive electricity, with your face towards the magnetic needle; the north pole will then deviate to your left hand._ The deflection of the magnetic needle can therefore reveal the existence of an electric current in a neighbouring circuit, and this fact was soon utilized in the construction of instruments called galvanometers (q.v.).

Immediately after Oersted's discovery was announced, D.F.J. Arago and A.M. Ampere began investigations on the subject of electromagnetism. On the 18th of September 1820, Ampere read a paper before the Academy of Sciences in Paris, in which he announced that the voltaic pile itself affected a magnetic needle as did the uniting wire, and he showed that the effects in both cases were consistent with the theory that electric current was a circulation round a circuit, and equivalent in magnetic effect to a very short magnet with axis placed at right angles to the plane of the circuit. He then propounded his brilliant hypothesis that the magnetization of iron was due to molecular electric currents. This suggested to Arago that wire wound into a helix carrying electric current should magnetize a steel needle placed in the interior. In the _Ann. Chim._ (1820, 15, p. 94), Arago published a paper entitled "Experiences relatives a l'aimantation du fer et de l'acier par l'action du courant voltaique," announcing that the wire conveying the current, even though of copper, could magnetize steel needles placed across it, and if plunged into iron filings it attracted them. About the same time Sir Humphry Davy sent a communication to Dr W.H. Wollaston, read at the Royal Society on the 16th of November 1820 (reproduced in the _Annals of Philosophy_ for August 1821, p. 81), "On the Magnetic Phenomena produced by Electricity," in which he announced his independent discovery of the same fact. With a large battery of 100 pairs of plates at the Royal Institution, he found in October 1820 that the uniting wire became strongly magnetic and that iron filings clung to it; also that steel needles placed across the wire were permanently magnetized. He placed a sheet of glass over the wire and sprinkling iron filings on it saw that they arranged themselves in straight lines at right angles to the wire. He then proved that Leyden jar discharges could produce the same effects. Ampere and Arago then seem to have experimented together and magnetized a steel needle wrapped in paper which was enclosed in a helical wire conveying a current. All these facts were rendered intelligible when it was seen that a wire when conveying an electric current becomes surrounded by a magnetic field. If the wire is a long straight one, the lines of magnetic force are circular and concentric with centres on the wire axis, and if the wire is bent into a circle the lines of magnetic force are endless loops surrounding and linked with the electric circuit. Since a magnetic pole tends to move along a line of magnetic force it was obvious that it should revolve round a wire conveying a current. To exhibit this fact involved, however, much ingenuity. It was first accomplished by Faraday in October 1821 (_Exper. Res._ ii. p. 127). Since the action is reciprocal a current free to move tends to revolve round a magnetic pole. The fact is most easily shown by a small piece of apparatus made as follows: In a glass cylinder (see fig. 1) like a lamp chimney are fitted two corks. Through the bottom one is passed the north end of a bar magnet which projects up above a little mercury lying in the cork. Through the top cork is passed one end of a wire from a battery, and a piece of wire in the cylinder is flexibly connected to it, the lower end of this last piece just touching the mercury. When a current is passed in at the top wire and out at the lower end of the bar magnet, the loose wire revolves round the magnet pole. All text-books on physics contain in their chapters on electromagnetism full accounts of various forms of this experiment.

In 1825 another important step forward was taken when William Sturgeon (1783-1850) of London produced the electromagnet. It consisted of a horseshoe-shaped bar of soft iron, coated with varnish, on which was wrapped a spiral coil of bare copper wire, the turns not touching each other. When a voltaic current was passed through the wire the iron became a powerful magnet, but on severing the connexion with the battery, the soft iron lost immediately nearly all its magnetism.[2]

At that date Ohm had not announced his law of the electric circuit, and it was a matter of some surprise to investigators to find that Sturgeon's electromagnet could not be operated at a distance through a long circuit of wire with such good results as when close to the battery. Peter Barlow, in January 1825, published in the _Edinburgh Philosophical Journal_, a description of such an experiment made with a view of applying Sturgeon's electromagnet to telegraphy, with results which were unfavourable. Sturgeon's experiments, however, stimulated Joseph Henry (q.v.) in the United States, and in 1831 he gave a description of a method of winding electromagnets which at once put a new face upon matters (_Silliman's Journal_, 1831, 19, p. 400). Instead of insulating the iron core, he wrapped the copper wire round with silk and wound in numerous turns and many layers upon the iron horseshoe in such fashion that the current went round the iron always in the same direction. He then found that such an electromagnet wound with a long fine wire, if worked with a battery consisting of a large number of cells in series, could be operated at a considerable distance, and he thus produced what were called at that time _intensity electromagnets_, and which subsequently rendered the electric telegraph a possibility. In fact, Henry established in 1831, in Albany, U.S.A., an electromagnetic telegraph, and in 1835 at Princeton even used an earth return, thereby anticipating the discovery (1838) of C.A. Steinheil (1801-1870) of Munich.

Inventors were then incited to construct powerful electromagnets as tested by the weight they could carry from their armatures. Joseph Henry made a magnet for Yale College, U.S.A., which lifted 3000 lb. (_Silliman's Journal_, 1831, 20, p. 201), and one for Princeton which lifted 3000 with a very small battery. Amongst others J.P. Joule, ever memorable for his investigations on the mechanical equivalent of heat, gave much attention about 1838-1840 to the construction of electromagnets and succeeded in devising some forms remarkable for their lifting power. One form was constructed by cutting a thick soft iron tube longitudinally into two equal parts. Insulated copper wire was then wound longitudinally over one of both parts (see fig. 2) and a current sent through the wire. In another form two iron disks with teeth at right angles to the disk had insulated wire wound zigzag between the teeth; when a current was sent through the wire, the teeth were so magnetized that they were alternately N. and S. poles. If two such similar disks were placed with teeth of opposite polarity in contact, a very large force was required to detach them, and with a magnet and armature weighing in all 11.575 lb. Joule found that a weight of 2718 was supported. Joule's papers on this subject will be found in his _Collected Papers_ published by the Physical Society of London, and in _Sturgeon's Annals of Electricity_, 1838-1841, vols. 2-6.

_The Magnetic Circuit._--The phenomena presented by the electromagnet
are interpreted by the aid of the notion of the magnetic circuit. Let
us consider a thin circular sectioned ring of iron wire wound over
with a solenoid or spiral of insulated copper wire through which a
current of electricity can be passed. If the solenoid or wire windings
existed alone, a current having a strength A amperes passed through it
would create in the interior of the solenoid a magnetic force H,
numerically equal to 4[pi]/10 multiplied by the number of windings N
on the solenoid, and by the current in amperes A, and divided by the
mean length of the solenoid l, or H = 4[pi]AN/10l. The product AN is
called the "ampere-turns" on the solenoid. The product Hl of the
magnetic force H and the length l of the magnetic circuit is called
the "magnetomotive force" in the magnetic circuit, and from the above
formula it is seen that the magnetomotive force denoted by (M.M.F.) is
equal to 4[pi]/10 (= 1.25 nearly) times the ampere-turns (A.N.) on the
exciting coil or solenoid. Otherwise (A.N.) = 0.8(M.M.F.). The
magnetomotive force is regarded as creating an effect called magnetic
flux (Z) in the magnetic circuit, just as electromotive force E.M.F.
produces electric current (A) in the electric circuit, and as by Ohm's
law (see ELECTROKINETICS) the current varies as the E.M.F. and
inversely as a quality of the electric circuit called its
"resistance," so in the magnetic circuit the magnetic flux varies as
the magnetomotive force and inversely as a quality of the magnetic
circuit called its "reluctance." The great difference between the
electric circuit and the magnetic circuit lies in the fact that
whereas the electric resistance of a solid or liquid conductor is
independent of the current and affected only by the temperature, the
magnetic reluctance varies with the magnetic flux and cannot be
defined except by means of a curve which shows its value for different
flux densities. The quotient of the total magnetic flux, Z, in a
circuit by the cross section, S, of the circuit is called the mean
"flux density," and the reluctance of a magnetic circuit one
centimetre long and one square centimetre in cross section is called
the "reluctivity" of the material. The relation between reluctivity
[rho] = 1/[mu] magnetic force H, and flux density B, is defined by the
equation H = [rho]B, from which we have Hl = Z([rho]l/S) = M.M.F.
acting on the circuit. Again, since the ampere-turns (AN) on the
circuit are equal to 0.8 times the M.M.F., we have finally AN/l =
0.8(Z/[mu]S). This equation tells us the exciting force reckoned in
ampere-turns, AN, which must be put on the ring core to create a total
magnetic flux Z in it, the ring core having a mean perimeter l and
cross section S and reluctivity [rho] = 1/[mu] corresponding to a flux
density Z/S. Hence before we can make use of the equation for
practical purposes we need to possess a curve for the particular
material showing us the value of the reluctivity corresponding to
various values of the possible flux density. The reciprocal of [rho]
is usually called the "permeability" of the material and denoted by
[mu]. Curves showing the relation of 1/[rho] and ZS or [mu] and B, are
called "permeability curves." For air and all other non-magnetic
matter the permeability has the same value, taken arbitrarily as
unity. On the other hand, for iron, nickel and cobalt the permeability
may in some cases reach a value of 2000 or 2500 for a value of B =
5000 in C.G.S. measure (see UNITS, PHYSICAL). The process of taking
these curves consists in sending a current of known strength through a
solenoid of known number of turns wound on a circular iron ring of
known dimensions, and observing the time-integral of the secondary
current produced in a secondary circuit of known turns and resistance
R wound over the iron core N times. The secondary electromotive force
is by Faraday's law (see ELECTROKINETICS) equal to the time rate of
change of the total flux, or E = NdZ/dt. But by Ohm's law E = Rdq/dt,
where q is the quantity of electricity set flowing in the secondary
circuit by a change dZ in the co-linked total flux. Hence if 2Q
represents this total quantity of electricity set flowing in the
secondary circuit by suddenly reversing the direction of the magnetic
flux Z in the iron core we must have

RQ = NZ or Z = RQ/N.

The measurement of the total quantity of electricity Q can be made by
means of a ballistic galvanometer (q.v.), and the resistance R of the
secondary circuit includes that of the coil wound on the iron core and
the galvanometer as well. In this manner the value of the total flux Z
and therefore of Z/S = B or the flux density, can be found for a given
magnetizing force H, and this last quantity is determined when we know
the magnetizing current in the solenoid and its turns and dimensions.
The curve which delineates the relation of H and B is called the
magnetization curve for the material in question. For examples of
these curves see MAGNETISM.

The fundamental law of the non-homogeneous magnetic circuit traversed
by one and the same total magnetic flux Z is that the sum of all the
magnetomotive forces acting in the circuit is numerically equal to the
product of the factor 0.8, the total flux in the circuit, and the sum
of all the reluctances of the various parts of the circuit. If then
the circuit consists of materials of different permeability and it is
desired to know the ampere-turns required to produce a given total of
flux round the circuit, we have to calculate from the magnetization
curves of the material of each part the necessary magnetomotive forces
and add these forces together. The practical application of this
principle to the predetermination of the field windings of dynamo
magnets was first made by Drs J. and E. Hopkinson (_Phil. Trans._,
1886, 177, p. 331).

We may illustrate the principles of this predetermination by a simple
example. Suppose a ring of iron has a mean diameter of 10 cms. and a
cross section of 2 sq. cms., and a transverse cut on air gap made in
it 1 mm. wide. Let us inquire the ampere-turns to be put upon the ring
to create in it a total flux of 24,000 C.G.S. units. The total length
of the iron part of the circuit is (10[pi] - 0.1) cms., and its
section is 2 sq. cms., and the flux density in it is to be 12,000.
From Table II. below we see that the permeability of pure iron
corresponding to a flux density of 12,000 is 2760. Hence the
reluctance of the iron circuits is equal to

10[pi] - 0.1 220
------------ = ----- C.G.S. units.
2760 X 2 38640

The length of the air gap is 0.1 cm., its section 2 sq. cms., and its
permeability is unity. Hence the reluctance of the air gap is

0.1 1
----- = -- C.G.S. unit.
1 X 2 20

Accordingly the magnetomotive force in ampere-turns required to
produce the required flux is equal to

/ 1 220 \
0.8(24,000) ( -- + ----- ) = 1070 nearly.
\20 38640/

It follows that the part of the magnetomotive force required to
overcome the reluctance of the narrow air gap is about nine times that
required for the iron alone.

In the above example we have for simplicity assumed that the flux in
passing across the air gap does not spread out at all. In dealing with
electromagnet design in dynamo construction we have, however, to take
into consideration the spreading as well as the leakage of flux across
the circuit (see DYNAMO). It will be seen, therefore, that in order
that we may predict the effect of a certain kind of iron or steel when
used as the core of an electromagnet, we must be provided with tables
or curves showing the reluctivity or permeability corresponding to
various flux densities or--which comes to the same thing--with (B, H)
curves for the sample.

_Iron and Steel for Electromagnetic Machinery._--In connexion with the technical application of electromagnets such as those used in the field magnets of dynamos (q.v.), the testing of different kinds of iron and steel for magnetic permeability has therefore become very important. Various instruments called permeameters and hysteresis meters have been designed for this purpose, but much of the work has been done by means of a ballistic galvanometer and test ring as above described. The "hysteresis" of an iron or steel is that quality of it in virtue of which energy is dissipated as heat when the magnetization is reversed or carried through a cycle (see MAGNETISM), and it is generally measured either in ergs per cubic centimetre of metal per cycle of magnetization, or in watts per lb. per 50 or 100 cycles per second at or corresponding to a certain maximum flux density, say 2500 or 600 C.G.S. units. For the details of various forms of permeameter and hysteresis meter technical books must be consulted.[3]

An immense number of observations have been carried out on the magnetic permeability of different kinds of iron and steel, and in the following tables are given some typical results, mostly from experiments made by J.A. Ewing (see _Proc. Inst. C.E._, 1896, 126, p. 185) in which the ballistic method was employed to determine the flux density corresponding to various magnetizing forces acting upon samples of iron and steel in the form of rings.

The figures under heading I. are values given in a paper by A.W.S.
Pocklington and F. Lydall (_Proc. Roy. Soc_., 1892-1893, 52, pp. 164
and 228) as the results of a magnetic test of an exceptionally pure
iron supplied for the purpose of experiment by Colonel Dyer, of the
Elswick Works. The substances other than iron in this sample were
stated to be: carbon, _trace_; silicon, _trace_; phosphorus, _none_;
sulphur, 0.013%; manganese, 0.1%. The other five specimens, II. to
VI., are samples of commercial iron or steel. No. II. is a sample of
Low Moor bar iron forged into a ring, annealed and turned. No. III. is
a steel forging furnished by Mr R. Jenkins as a sample of forged
ingot-metal for dynamo magnets. No. IV. is a steel casting for dynamo
magnets, unforged, made by Messrs Edgar Allen & Company by a special
pneumatic process under the patents of Mr A. Tropenas. No. V. is also
an unforged steel casting for dynamo magnets, made by Messrs Samuel
Osborne & Company by the Siemens process. No. VI. is also an unforged
steel casting for dynamo magnets, made by Messrs Fried. Krupp, of
Essen.

TABLE I.--_Magnetic Flux Density corresponding to various Magnetizing
Forces in the case of certain Samples of Iron and Steel_ (_Ewing_).

+------------+-----------------------------------------------------+
|Magnetizing | |
| Force | |
| H (C.G.S. | Magnetic Flux Density B (C.G.S. Units). |
| Units). | |
+------------+--------+--------+--------+--------+--------+--------+
| | I. | II. | III. | IV. | V. | VI. |
+------------+--------+--------+--------+--------+--------+--------+
| 5 | 12,700 | 10,900 | 12,300 | 4,700 | 9,600 | 10,900 |
| 10 | 14,980 | 13,120 | 14,920 | 12,250 | 13,050 | 13,320 |
| 15 | 15,800 | 14,010 | 15,800 | 14,000 | 14,600 | 14,350 |
| 20 | 16,300 | 14,580 | 16,280 | 15,050 | 15,310 | 14,950 |
| 30 | 16,950 | 15,280 | 16,810 | 16,200 | 16,000 | 15,660 |
| 40 | 17,350 | 15,760 | 17,190 | 16,800 | 16,510 | 16,150 |
| 50 | .. | 16,060 | 17,500 | 17,140 | 16,900 | 16,480 |
| 60 | .. | 16,340 | 17,750 | 17,450 | 17,180 | 16,780 |
| 70 | .. | 16,580 | 17,970 | 17,750 | 17,400 | 17,000 |
| 80 | .. | 16,800 | 18,180 | 18,040 | 17,620 | 17,200 |
| 90 | .. | 17,000 | 18,390 | 18,230 | 17,830 | 17,400 |
| 100 | .. | 17,200 | 18,600 | 18,420 | 18,030 | 17,600 |
+------------+--------+--------+--------+--------+--------+--------+

It will be seen from the figures and the description of the materials
that the steel forgings and castings have a remarkably high
permeability under small magnetizing force.

Table II. shows the magnetic qualities of some of these materials as found by Ewing when tested with small magnetizing forces.

TABLE II.--_Magnetic Permeability of Samples of Iron and Steel under
Weak Magnetizing Forces._

+-----------------+-------------+----------------+---------------+
| Magnetic Flux | I. | III. | VI. |
| Density B | Pure Iron. | Steel Forging. | Steel Casting.|
| (C.G.S. Units). | | | |
+-----------------+-------------+----------------+---------------+
| | H [mu] | H [mu] | H [mu] |
| 2,000 | 0.90 2220 | 1.38 1450 | 1.18 1690 |
| 4,000 | 1.40 2850 | 1.91 2090 | 1.66 2410 |
| 6,000 | 1.85 3240 | 2.38 2520 | 2.15 2790 |
| 8,000 | 2.30 3480 | 2.92 2740 | 2.83 2830 |
| 10,000 | 3.10 3220 | 3.62 2760 | 4.05 2470 |
| 12,000 | 4.40 2760 | 4.80 2500 | 6.65 1810 |
+-----------------+-------------+----------------+---------------+

The numbers I., III. and VI. in the above table refer to the samples mentioned in connexion with Table I.

It is a remarkable fact that certain varieties of low carbon steel (commonly called mild steel) have a higher permeability than even annealed Swedish wrought iron under large magnetizing forces. The term _steel_, however, here used has reference rather to the mode of production than the final chemical nature of the material. In some of the mild-steel castings used for dynamo electromagnets it appears that the total foreign matter, including carbon, manganese and silicon, is not more than 0.3% of the whole, the material being 99.7% pure iron. This valuable magnetic property of steel capable of being cast is, however, of great utility in modern dynamo building, as it enables field magnets of very high permeability to be constructed, which can be fashioned into shape by casting instead of being built up as formerly out of masses of forged wrought iron. The curves in fig. 3 illustrate the manner in which the flux density or, as it is usually called, the magnetization curve of this mild cast steel crosses that of Swedish wrought iron, and enables us to obtain a higher flux density corresponding to a given magnetizing force with the steel than with the iron.

From the same paper by Ewing we extract a number of results relating to permeability tests of thin sheet iron and sheet steel, such as is used in the construction of dynamo armatures and transformer cores.

No. VII. is a specimen of good transformer-plate, 0.301 millimetre
thick, rolled from Swedish iron by Messrs Sankey of Bilston. No. VIII.
is a specimen of specially thin transformer-plate rolled from scrap
iron. No. IX. is a specimen of transformer-plate rolled from
ingot-steel. No. X. is a specimen of the wire which was used by J.
Swinburne to form the core of his "hedgehog" transformers. Its
diameter was 0.602 millimetre. All these samples were tested in the
form of rings by the ballistic method, the rings of sheet-metal being
stamped or turned in the flat. The wire ring No. X. was coiled and
annealed after coiling.

TABLE III.--_Permeability Tests of Transformer Plate and Wire_.

+---------+--------------+--------------+--------------+--------------+
|Magnetic | VII. | VIII. | IX. | X. |
| Flux | Transformer- | Transformer- | Transformer- | Transformer- |
|Density B| plate of | plate of | plate of | wire. |
| (C.G.S. | Swedish Iron.| Scrap Iron. | of Steel. | |
| Units). | | | | |
+---------+--------------+--------------+--------------+--------------+
| | H [mu] | H [mu] | H [mu] | H [mu] |
| 1,000 | 0.81 1230 | 1.08 920 | 0.60 1470 | 1.71 590 |
| 2,000 | 1.05 1900 | 1.46 1370 | 0.90 2230 | 2.10 950 |
| 3,000 | 1.26 2320 | 1.77 1690 | 1.04 2880 | 2.30 1300 |
| 4,000 | 1.54 2600 | 2.10 1900 | 1.19 3360 | 2.50 1600 |
| 5,000 | 1.82 2750 | 2.53 1980 | 1.38 3620 | 2.70 1850 |
| 6,000 | 2.14 2800 | 3.04 1970 | 1.59 3770 | 2.92 2070 |
| 7,000 | 2.54 2760 | 3.62 1930 | 1.89 3700 | 3.16 2210 |
| 8,000 | 3.09 2590 | 4.37 1830 | 2.25 3600 | 3.43 2330 |
| 9,000 | 3.77 2390 | 5.3 1700 | 2.72 3310 | 3.77 2390 |
| 10,000 | 4.6 2170 | 6.5 1540 | 3.33 3000 | 4.17 2400 |
| 11,000 | 5.7 1930 | 7.9 1390 | 4.15 2650 | 4.70 2340 |
| 12,000 | 7.0 1710 | 9.8 1220 | 5.40 2220 | 5.45 2200 |
| 13,000 | 8.5 1530 | 11.9 1190 | 7.1 1830 | 6.5 2000 |
| 14,000 | 11.0 1270 | 15.0 930 | 10.0 1400 | 8.4 1670 |
| 15,000 | 15.1 990 | 19.5 770 | .. .. | 11.9 1260 |
| 16,000 | 21.4 750 | 27.5 580 | .. .. | 21.0 760 |
+---------+--------------+--------------+--------------+--------------+

Some typical flux-density curves of iron and steel as used in dynamo and transformer building are given in fig. 4.

The numbers in Table III. well illustrate the fact that the permeability, [mu] = B/H has a maximum value corresponding to a certain flux density. The tables are also explanatory of the fact that mild steel has gradually replaced iron in the manufacture of dynamo electromagnets and transformer-cores.

Broadly speaking, the materials which are now employed in the manufacture of the cores of electromagnets for technical purposes of various kinds may be said to fall into three classes, namely, forgings, castings and stampings. In some cases the iron or steel core which is to be magnetized is simply a mass of iron hammered or pressed into shape by hydraulic pressure; in other cases it has to be fused and cast; and for certain other purposes it must be rolled first into thin sheets, which are subsequently stamped out into the required forms.

For particular purposes it is necessary to obtain the highest possible magnetic permeability corresponding to a high, or the highest attainable flux density. This is generally the case in the electromagnets which are employed as the field magnets in dynamo machines. It may generally be said that whilst the best wrought iron, such as annealed Low Moor or Swedish iron, is more permeable for low flux densities than steel castings, the cast steel may surpass the wrought metal for high flux density. For most electro-technical purposes the best magnetic results are given by the employment of forged ingot-iron. This material is probably the most permeable throughout the whole scale of attainable flux densities. It is slightly superior to wrought iron, and it only becomes inferior to the highest class of cast steel when the flux density is pressed above 18,000 C.G.S. units (see fig. 5). For flux densities above 13,000 the forged ingot-iron has now practically replaced for electric engineering purposes the Low Moor or Swedish iron. Owing to the method of its production, it might in truth be called a soft steel with a very small percentage of combined carbon. The best description of this material is conveyed by the German term "Flusseisen," but its nearest British equivalent is "ingot-iron." Chemically speaking, the material is for all practical purposes very nearly pure iron. The same may be said of the cast steels now much employed for the production of dynamo magnet cores. The cast steel which is in demand for this purpose has a slightly lower permeability than the ingot-iron for low flux densities, but for flux densities above 16,000 the required result may be more cheaply obtained with a steel casting than with a forging. When high tensile strength is required in addition to considerable magnetic permeability, it has been found advantageous to employ a steel containing 5% of nickel. The rolled sheet iron and sheet steel which is in request for the construction of magnet cores, especially those in which the exciting current is an alternating current, are, generally speaking, produced from Swedish iron. Owing to the mechanical treatment necessary to reduce the material to a thin sheet, the permeability at low flux densities is rather higher than, although at high flux densities it is inferior to, the same iron and steel when tested in bulk. For most purposes, however, where a laminated iron magnet core is required, the flux density is not pressed up above 6000 units, and it is then more important to secure small hysteresis loss than high permeability. The magnetic permeability of cast iron is much inferior to that of wrought or ingot-iron, or the mild steels taken at the same flux densities.

The following Table IV. gives the flux density and permeability of a typical cast iron taken by J.A. Fleming by the ballistic method:--

TABLE IV.--_Magnetic Permeability and Magnetization Curve of Cast
Iron._

+------+------+-----++-------+------+-----++--------+--------+-----+
| H | B | [mu]|| H | B | [mu]|| H | B | [mu]|
| .19 | 27 | 139 || 8.84 | 4030 | 456 || 44.65 | 8,071 | 181 |
| .41 | 62 | 150 || 10.60 | 4491 | 424 || 56.57 | 8,548 | 151 |
| 1.11 | 206 | 176 || 12.33 | 4884 | 396 || 71.98 | 9,097 | 126 |
| 2.53 | 768 | 303 || 13.95 | 5276 | 378 || 88.99 | 9,600 | 108 |
| 3.41 | 1251 | 367 || 15.61 | 5504 | 353 || 106.35 | 10,066 | 95 |
| 4.45 | 1898 | 427 || 18.21 | 5829 | 320 || 120.60 | 10,375 | 86 |
| 5.67 | 2589 | 456 || 26.37 | 6814 | 258 || 140.37 | 10,725 | 76 |
| 7.16 | 3350 | 468 || 36.54 | 7580 | 207 || 152.73 | 10,985 | 72 |
+------+------+-----++-------+------+-----++--------+--------+-----+

The metal of which the tests are given in Table IV. contained 2% of silicon, 2.85% of total carbon, and 0.5% of manganese. It will be seen that a magnetizing force of about 5 C.G.S. units is sufficient to impart to a wrought-iron ring a flux density of 18,000 C.G.S. units, but the same force hardly produces more than one-tenth of this flux density in cast iron.

The testing of sheet iron and steel for magnetic hysteresis loss has developed into an important factory process, giving as it does a means of ascertaining the suitability of the metal for use in the manufacture of transformers and cores of alternating-current electromagnets.

In Table V. are given the results of hysteresis tests by Ewing on samples of commercial sheet iron and steel. The numbers VII., VIII., IX. and X. refer to the same samples as those for which permeability results are given in Table III.

TABLE V.--_Hysteresis Loss in Transformer-iron._

+-------+------------------------------+-------------------------------+
| | Ergs per Cubic Centimetre | Watts per lb. at a Frequency |
| | per Cycle. | of 100. |
|Maximum+-------+-------+-------+------+-------+-------+-------+-------+
| Flux | VII. | VIII. | IX. | X. | | | | |
|Density|Swedish| Forged| Ingot-| Soft | | | | |
| B. | Iron. |Scrap- | steel.| Iron | VII. | VIII. | IX. | X. |
| | | iron. | | Wire.| | | | |
+-------+-------+-------+-------+------+-------+-------+-------+-------+
| 2000 | 240 | 400 | 215 | 600 | 0.141 | 0.236 | 0.127 | 0.356 |
| 3000 | 520 | 790 | 430 | 1150 | 0.306 | 0.465 | 0.253 | 0.630 |
| 4000 | 830 | 1220 | 700 | 1780 | 0.490 | 0.720 | 0.410 | 1.050 |
| 5000 | 1190 | 1710 | 1000 | 2640 | 0.700 | 1.010 | 0.590 | 1.550 |
| 6000 | 1600 | 2260 | 1350 | 3360 | 0.940 | 1.330 | 0.790 | 1.980 |
| 7000 | 2020 | 2940 | 1730 | 4300 | 1.200 | 1.730 | 1.020 | 2.530 |
| 8000 | 2510 | 3710 | 2150 | 5300 | 1.480 | 2.180 | 1.270 | 3.120 |
| 9000 | 3050 | 4560 | 2620 | 6380 | 1.800 | 2.680 | 1.540 | 3.750 |
+-------+-------+-------+-------+------+-------+-------+-------+-------+

In Table VI. are given the results of a magnetic test of some exceedingly good transformer-sheet rolled from Swedish iron.

TABLE VI.--_Hysteresis Loss in Strip of Transformer-plate rolled
Swedish Iron._

+------------+---------------------------+--------------------+
|Maximum Flux| Ergs per Cubic Centimetre | Watts per lb. at a |
|Density B. | per Cycle. | Frequency of 100. |
+------------+---------------------------+--------------------+
| 2000 | 220 | 0.129 |
| 3000 | 410 | 0.242 |
| 4000 | 640 | 0.376 |
| 5000 | 910 | 0.535 |
| 6000 | 1200 | 0.710 |
| 7000 | 1520 | 0.890 |
| 8000 | 1900 | 1.120 |
| 9000 | 2310 | 1.360 |
+------------+---------------------------+--------------------+

In Table VII. are given some values obtained by Fleming for the hysteresis loss in the sample of cast iron, the permeability test of which is recorded in Table IV.

TABLE VII.--_Observations on the Magnetic Hysteresis of Cast Iron._

+------+---------+-----------------------------------+
| | | Hysteresis Loss. |
| | +-------------+---------------------+
| Loop.| B (max.)| Ergs per cc.| Watts per lb. per. |
| | | per Cycle. | 100 Cycles per sec. |
+------+---------+-------------+---------------------+
| I. | 1475 | 466 | .300 |
| II. | 2545 | 1,288 | .829 |
| III. | 3865 | 2,997 | 1.934 |
| IV. | 5972 | 7,397 | 4.765 |
| V. | 8930 | 13,423 | 8.658 |
+------+---------+-------------+---------------------+

For most practical purposes the constructor of electromagnetic machinery requires his iron or steel to have some one of the following characteristics. If for dynamo or magnet making, it should have the highest possible permeability at a flux density corresponding to practically maximum magnetization. If for transformer or alternating-current magnet building, it should have the smallest possible hysteresis loss at a maximum flux density of 2500 C.G.S. units during the cycle. If required for permanent magnet making, it should have the highest possible coercivity combined with a high retentivity. Manufacturers of iron and steel are now able to meet these demands in a very remarkable manner by the commercial production of material of a quality which at one time would have been considered a scientific curiosity.

It is usual to specify iron and steel for the first purpose by naming the minimum permeability it should possess corresponding to a flux density of 18,000 C.G.S. units; for the second, by stating the hysteresis loss in watts per lb. per 100 cycles per second, corresponding to a maximum flux density of 2500 C.G.S. units during the cycle; and for the third, by mentioning the coercive force required to reduce to zero magnetization a sample of the metal in the form of a long bar magnetized to a stated magnetization. In the cyclical reversal of magnetization of iron we have two modes to consider. In the first case, which is that of the core of the alternating transformer, the magnetic force passes through a cycle of values, the iron remaining stationary, and the direction of the magnetic force being always the same. In the other case, that of the dynamo armature core, the direction of the magnetic force in the iron is constantly changing, and at the same time undergoing a change in magnitude.

It has been shown by F.G. Baily (_Proc. Roy. Soc._, 1896) that if a mass of laminated iron is rotating in a magnetic field which remains constant in direction and magnitude in any one experiment, the hysteresis loss rises to a maximum as the magnitude of the flux density in the iron is increased and then falls away again to nearly zero value. These observations have been confirmed by other observers. The question has been much debated whether the values of the hysteresis loss obtained by these two different methods are identical for magnetic cycles in which the flux density reaches the same maximum value. This question is also connected with another one, namely, whether the hysteresis loss per cycle is or is not a function of the speed with which the cycle is traversed. Early experiments by C.P. Steinmetz and others seemed to show that there was a difference between slow-speed and high-speed hysteresis cycles, but later experiments by J. Hopkinson and by A. Tanakadate, though not absolutely exhaustive, tend to prove that up to 400 cycles per second the hysteresis loss per cycle is practically unchanged.

Experiments made in 1896 by R. Beattie and R.C. Clinker on magnetic hysteresis in rotating fields were partly directed to determine whether the hysteresis loss at moderate flux densities, such as are employed in transformer work, was the same as that found by measurements made with alternating-current fields on the same iron and steel specimens (see _The Electrician_, 1896, 37, p. 723). These experiments showed that over moderate ranges 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.