MAGNETISM  . The See also:

• PRESENT

present See also:

• ARTICLE (from Lat. articulus, a joint)

article is a See also:

• DIGEST

digest, mainly from an experimental standpoint, of the leading facts and principles of magnetic See also:

• SCIENCE (Lat. scientia, from scire; to learn, know)

science . It is divided into the following sections: Terminology and Elementary Principles . Magnetic Measurements . Magnetization in Strong See also:

• FIELDS, JAMES THOMAS (1817-1881)

Fields . Magnetization in Weak Fields . Changes of Dimensions attending Magnetization . Effects of See also:

• MECHANICAL

Mechanical Stress on Magnetization . Effects of Temperature on Magnetism . Magnetic Properties of See also:

• ALLOYS (through the Fr. aloyer, from Lat. alligare, to combine)

Alloys and Compounds of See also:

• IRON [symbol Fe, atomic weight 55.85 (0=16)]

Iron . See also:

• MISCELLANEOUS

Miscellaneous Effects of Magnetization: Electric Conductivity—See also:

• HALL
• HALL (generally known as SCHWABISCH-HALL, tc distinguish it from the small town of Hall in Tirol and Bad-Hall, a health resort in Upper Austria)
• HALL (O.E. heall, a common Teutonic word, cf. Ger. Halle)
• HALL, BASIL (1788-1844)
• HALL, CARL CHRISTIAN (1812–1888)
• HALL, CHARLES FRANCIS (1821-1871)
• HALL, CHRISTOPHER NEWMAN (1816—19oz)
• HALL, EDWARD (c. 1498-1547)
• HALL, FITZEDWARD (1825-1901)
• HALL, ISAAC HOLLISTER (1837-1896)
• HALL, JAMES (1793–1868)
• HALL, JAMES (1811–1898)
• HALL, JOSEPH (1574-1656)
• HALL, MARSHALL (1790-1857)
• HALL, ROBERT (1764-1831)
• HALL, SAMUEL CARTER (5800-5889)
• HALL, SIR JAMES (1761-1832)
• HALL, WILLIAM EDWARD (1835-1894)

Hall Effect—Electro-Thermal Relations—Thermoelectric Quality—See also:

• ELASTICITY

Elasticity—Chemical and Voltaic Effects . II .

Feebly Susceptible Substances . 12 . Molecular Theory of Magnetism . 13 . See also:

• HISTORICAL

Historical and See also:

• CHRONOLOGICAL

Chronological Notes . Of these thirteen sections, the first contains a See also:

• SIMPLE

simple description of the more prominent phenomena, without mathematical symbols or numerical data . The second includes See also:

• DEFINITIONS

definitions of technical terms in See also:

• COMMON

common use, together with so much of the elementary theory as is necessary for understanding the experimental See also:

• WORK

work described in subsequent portions of the article; a number of formulae and results are given for purposes of reference, but the mathematical reasoning by which they are obtained is not generally detailed, authorities being cited whenever the demonstrations are not likely to be found in See also:

• ORDINARY (med. Lat. ordinarius, Fr. ordinaire)

ordinary textbooks . The subjects discussed in the remaining sections are sufficiently indicated by their respective headings . (See also See also:

• ELECTROMAGNETISM

ELECTROMAGNETISM, TERRESTRIAL MAGNETISM, MAGNETO-See also:

• OPTICS

OPTICS and See also:

• UNITS, DIMENSIONS OF
• UNITS, PHYSICAL

UNITS.) I . See also:

• GENERAL
• GENERAL (Lat. generalis, of or relating to a genus, kind or class)

GENERAL PHENOMENA Pieces of a certain highly esteemed iron ore, which consists mainly of the See also:

• OXIDE

oxide Fe3O4, are sometimes found to possess the See also:

• POWER [WILLIAM GRATTAN] TYRONE (1797-1841)

power of attracting small fragments of iron or See also:

• STEEL, FLORA ANNIE (1847– )

steel . Ore endowed with this curious See also:

• PROPERTY

property was well known to the See also:

• ANCIENT
• ANCIENT (also spelt ANTIENT; derived, through the Fr. ancien, old, from the late Lat. antianum, from ante, before)

ancient Greeks and See also:

• ROMANS
• ROMANS, EPISTLE TO THE

Romans, who, because it occurred plentifully in the See also:

• DISTRICT

district of See also:

• MAGNESIA

Magnesia near the See also:

• AEGEAN

Aegean See also:

• COAST (from Lat. costa, a rib, side)

coast, gave it the name of See also:

• MAGNES (c. 46o B.C.)

magnes, or the Magnesian See also:

• STONE
• STONE (0. Eng. shin; the word is common to Teutonic languages, cf. Ger. Stein, Du. steen, Dan. and Swed. sten; the root is also seen in Gr. aria, pebble)
• STONE, CHARLES POMEROY (1824-1887)
• STONE, EDWARD JAMES (1831-1897)
• STONE, FRANK (1800-1859)
• STONE, GEORGE (1708—1764)
• STONE, LUCY [BLACKWELL] (1818-1893)
• STONE, MARCUS (184o— )
• STONE, NICHOLAS (1586-1647)

stone . In See also:

• ENGLISH

English-speaking countries the ore is commonly known as See also:

• MAGNETITE

magnetite, and pieces which exhibit attraction as magnets; the cause to which the attractive property is attributed is called magnetism, a name also applied to the important See also:

• BRANCH (from the Fr. branche, late Lat. branca, an animal's paw)

branch of science which has been evolved from the study of phenomena associated with the magnet .

If a magnet is dipped into a See also:

• MASS (O.E. maesse; Fr. messe; Ger. Messe; Ital. messa; from eccl. Lat. missa)
• MASS, IN

mass of iron filings and with-See also:

• DRAWN

drawn, filings cling to certain parts of the stone in See also:

• MOSS

moss-like tufts, other parts remaining See also:

• BARE

bare . There are generally two regions where the tufts are thickest, and the attraction therefore greatest, and between them is a See also:

• ZONE (Gr. 'WV77, a girdle, from 'wvvLvay to gird)

zone in which no attraction is evidenced . The regions of greatest attraction have received the name of poles, and the See also:

• LINE

line joining them is called the See also:

• AXIS (Lat. for " axle ")

axis of the magnet; the space around a magnet in which magnetic effects are exhibited is called the See also:

• FIELD (a word common to many West German languages, cf. Ger. Feld, Dutch veld, possibly cognate with O.E. f olde, the earth, and ultimately with root of the Gr. irAaror, broad)
• FIELD, CYRUS WEST (1819-1892)
• FIELD, DAVID DUDLEY (18o5-1894)
• FIELD, EUGENE (1850-1895)
• FIELD, FREDERICK (18o1—1885)
• FIELD, HENRY MARTYN (1822-1907)
• FIELD, JOHN (1782—1837)
• FIELD, MARSHALL (183 1906)
• FIELD, NATHAN (1587—1633)
• FIELD, STEPHEN JOHNSON (1816-1899)
• FIELD, WILLIAM VENTRIS FIELD, BARON (1813-1907)

field of magnetic force, or the magnetic field . Up to the end of the 15th See also:

• CENTURY (from Lat. centuria, a division of a hundred men)

century only two magnetic phenomena of importance, besides that of attraction, had been observed . Upon one of these is based the principle of the mariner's See also:

• COMPASS (Fr. corn pas, ultimately from Lat. cum, with, and passus, step)

compass, which is said to have been known to the See also:

• CHINESE, JAPANESE AND

Chinese as See also:

• EARLY
• EARLY, JUBAL ANDERSON (1816-1894)

early as Iloo B.C., though it was not introduced into See also:

• EUROPE

Europe until more than 2000 years later; a magnet supported so that its axis is See also:

• FREE

free to turn in a See also:

• HORIZONTAL

horizontal See also:

• PLANE

plane will come to See also:

• REST (O. Eng. rest, reste, bed, cognate with other Teutonic forms, e.g. Ger. Rast, Riiste, rest, and probably Gothic Rasta, league, i.e. resting or stopping place)

rest with its poles pointing approximately See also:

• NORTH
• NORTH, BARONS
• NORTH, MARIANNE (1830—1890)
• NORTH, ROGER (1653-1734)
• NORTH, SIR THOMAS (1535?-16o1?)

north and See also:

• SOUTH
• SOUTH, ROBERT (1634–1716)

south . The other phenomenon is mentioned by See also:

• GREEK
• GREEK, ETRUSCAN AND

Greek and See also:

• ROMAN

Roman writers of the 1st century: a piece of iron, when brought into contact with a magnet, or even held near one, itself becomes " inductively " magnetized, and acquires the power of lifting iron . If the iron is soft and fairly pure, it loses its attractive property when removed from the neighbourhood of the magnet; if it is hard, some of the induced magnetism is permanently retained, and the piece becomes an artificial magnet . Steel is much more retentive of magnetism than any ordinary iron, and some See also:

• FORM (Lat. forma)

form of steel is now always used for making artificial magnets . Magnetism may be imparted to a See also:

• BAR
• BAR (0. Fr. barre, Late Lat. barra, origin unknown)
• BAR, CONFEDERATION OF
• BAR, FRANCOIS DE (1538-1606)
• BAR, THE

bar of hardened steel by stroking it several times from end to II I . 2 . 3 . 4 .

5 . 6 . 7 . 8 . 9 . to . end, always in the same direction, with one of the poles of a magnet . Until 182o all the artificial magnets in See also:

• PRACTICAL

practical use derived their virtue, directly or indirectly, from the natural magnets found in the See also:

• EARTH
• EARTH (a word common to Teutonic languages, cf. Ger. Erde, Dutch aarde, Swed. and Dan. jord; outside Teutonic it appears only in the Gr. 'pq'e, on the ground; it has been connected by some etymologists with the Aryan root ar-, to plough, which is seen in
• EARTH, FIGURE OF
• EARTH, FIGURE OF THE

earth: it is now recognized that the source of all magnetism, not excepting that of the magnetic ore itself, is See also:

• ELECTRICITY

electricity, and it is usual to have See also:

• DIRECT

direct recourse to electricity for producing magnetization, without the intermediary of the magnetic ore . A See also:

• WIRE (A.S. wir, a wire; cf. Swed. vire, to twist, M.H.G. wiere, a gold ornament, Lat. viriae, armlets, ultimately from the root wi, to twist, bind)

wire carrying an electric current is surrounded by a magnetic field, and if the wire is See also:

• BENT
• BENT (E1. BENI)
• BENT, JAMES THEODORE (1852–1897)

bent into the form of an elongated coil or See also:

• SPIRAL

spiral, a field having certain very useful qualities is generated in the interior . A bar of soft iron introduced into the coil is at once magnetized, the magnetism, however, disappearing almost completely as soon as the current ceases to flow . Such a See also:

• COMBINATION (Lat. combinare, to combine)

combination constitutes an electromagnet, a valuable See also:

• DEVICE

device by means of which a magnet can be instantly made and unmade at will . With suitable arrangements of iron and coil and a sufficiently strong current, the intensity of the temporary magnetization may be very high, and electromagnets capable of lifting weights of several tons are in daily use in See also:

• ENGINEERING

engineering See also:

• WORKS

works (see ELECTROMAGNETISM) .

If the bar inserted into the coil is of hardened steel instead of iron, the magnetism will be less intense, but a larger proportion of it will be retained after the current has been cut off . Steel magnets of See also:

• GREAT

great strength and of any convenient form may be prepared either in this manner or by treatment with an electromagnet; hence the natural magnet, or lodestone as it is commonly called, is no longer of any See also:

• INTEREST

interest except as a scientific curiosity . Some of the See also:

• PRINCIPAL

principal phenomena of magnetism may be demonstrated with very little apparatus; much may be done with a small bar-magnet, a See also:

• POCKET

pocket compass and a few ounces of iron filings . Steel articles, such as See also:

• KNITTING (from O.E. cnyttan, to knit; cf. Ger. Knutten; the root is seen in " knot ")

knitting or sewing needles and pieces of See also:

• FLAT (a modification of O. Eng. flet, an obsolete word of Teutonic origin, meaning the ground beneath the feet)

flat See also:

• SPRING (from " to spring," " to leap or jump up," " burst out," O. Eng., springau, a common Teut. word, cf. Ger. springer, possibly allied to Gr. QnrFpxecOac, to move rapidly)

spring, may be readily magnetized by stroking there with the bar-magnet; after having produced magnetism in any number of other bodies, the magnet will have lost nothing of its own virtue . The compass See also:

• NEEDLE (O. Eng. ncedl; the word appears in various forms in Teutonic languages, Ger. Nadel, Dutch naal, the root being ne-, to sew, cf. Ger. nahen, and probably Lat. nere, to spin, Gr. vi)ats, spinning)

needle is a little steel magnet balanced upon a See also:

• PIVOT (Fr. pivot; probably connected with Ital. pivolo, peg, pin, diminutive of piva, pipa, pipe)

pivot; one end of the needle, which always bears a distinguishing See also:

• MARK
• MARK, CARL (1858– )
• MARK, GOSPEL OF ST
• MARK, ST

mark, points approximately, but not in general exactly, to the north,' the See also:

• VERTICAL (from Lat. vertex, highest point)

vertical plane through the direction of the needle being termed the magnetic See also:

• MERIDIAN
• MERIDIAN (from the Lat. meridianus, pertaining to the south or mid-day)

meridian . The bar-magnet, if suspended horizontally in a See also:

• PAPER
• PAPER (Fr. papier, from Lat. papyrus)

paper See also:

• STIRRUP (O. Eng. slirap, stigrap, M. Eng. stirop,styrope,&c.,i.e. a mounting or climbing-rope; O. Eng. stigan, to mount, climb, and rap, rope, cf. Du. stijbeugel, literally mounting bow or loop, Ger. Steigbugel)

stirrup by a See also:

• THREAD (0. Eng. praed, literally, that which is twisted, prawan, to twist, to throw, cf. " throwster," a silk-winder, Ger. drehen, to twist, turn, Du. draad, Ger. Draht, thread, wire)

thread of unspun See also:

• SILK

silk, will also come to rest in the magnetic meridian with its marked end pointing northwards . The north-seeking end of a magnet is in English-speaking countries called the north See also:

• POLE (FAMILY)
• POLE, REGINALD (1500-1558)
• POLE, RICHARD DE LA (d. 1525)
• POLE, WILLIAM (1814—1900)

pole and the other end the south pole; in See also:

• FRANCE
• FRANCE, ANATOLE (1844– )

France the names are interchanged . If one pole of the bar-magnet is brought near the compass, it will attract the opposite pole of the compass-needle; and the magnetic See also:

• ACTION

action will not be sensibly affected by the interposition between the bar and the compass of any substance whatever except iron or other magnetizable See also:

• METAL
• METAL (through Fr. from Lat. metallum, mine, quarry, adapted from Gr. µATaXAov, in the same sense, probably connected with ,ueraAAdv, to search after, explore, µeTa, after, aAAos, other)

metal . The poles of a piece of magnetized steel may be at once distinguished if the two ends are successively presented to the compass; that end which attracts the south pole of the compass needle (and is therefore north) may be marked for easy See also:

• IDENTIFICATION (Lat. idem, the same)

identification . Similar magnetic poles are not merely indifferent to each other, but exhibit actual repulsion . This can be more easily shown if the compass is replaced by a magnetized knitting needle, supported horizontally by a thread . The north pole of the bar-magnet will repel the north pole of the suspended needle, and there will likewise be repulsion between the two south poles .

Such experiments as these demonstrate the fundamental See also:

• LAW
• LAW (0. Eng. lagu, M. Eng. lawe; from an old Teutonic root lag, " lie," what lies fixed or evenly; cf. Lat. lex, Fr. loi)
• LAW, JOHN (1671—1729)
• LAW, WILLIAM (1686-1761)

law that like poles repel each other; unlike poles attract . It follows that between two neighbouring magnets, the poles of which are regarded as centres of force, there must always be four forces in action . Denoting the two pairs of magnetic poles by N, S and N', S', there is attraction between N and S', and between S and N'; repulsion between N and N', and between S and S' . Hence it is not very easy to determine experimentally the law of magnetic force between poles . The 'In See also:

• LONDON

London in 1910 the needle pointed about 16° W. of the See also:

• GEOGRAPHICAL

geographical north . (See TERRESTRIAL MAGNETISM.)difficulty was overcome by C . A . See also:

• COULOMB, CHARLES AUGUSTIN (1736-1806)

Coulomb, who by using very See also:

• LONG, GEORGE (1800-1879)
• LONG, JOHN DAVIS (1838– )

long and thin magnets, so arranged that the action of their distant poles was negligible, succeeded in establishing the law, which has since been confirmed by more accurate methods, that the force of attraction or repulsion exerted between two magnetic poles varies inversely as the square of the distance between them . Since the poles of different magnets differ in strength, it is important to agree upon a definite unit or See also:

• STANDARD
• STANDARD, BATTLE OF THE

standard of reference in terms of which the strength of a pole may be numerically specified . According to the recognized See also:

• CONVENTION (Lat. conventio, an assembly or agreement, from convenire, to come together)
• CONVENTION, THE NATIONAL

convention, the unit pole is that which acts upon an equal pole at unit distance with unit force: a north pole is reckoned as See also:

• POSITIVE (or PORTABLE) ORGAN

positive (+) and a south pole as negative (—) . Other conditions remaining unchanged, the force between two poles is proportional to the product of their strengths; it is repulsive or attractive according as the signs of the poles are like or unlike . If a wire of soft iron is substituted for the suspended magnetic needle, either pole of the bar-magnet will attract either end of the wire indifferently .

The wire will in fact become temporarily magnetized by See also:

• INDUCTION (from Lat. inducere, to lead into; cf. Gr. ilrayu yli)

induction, that end of it which is nearest to the pole of the magnet acquiring opposite See also:

• POLARITY (Lat. polaris, poles, pole)

polarity, and behaving as if it were the pole of a permanent magnet . Even a permanent magnet is susceptible of induction, its polarity becoming thereby strengthened, weakened, or possibly reversed . If one pole of a strong magnet is presented to the like pole of a weaker one, there will be repulsion so long as the two are separated by a certain minimum distance . At shorter distances the magnetism induced in the weaker magnet will be stronger than its permanent magnetism, and there will be attraction; two magnets with their like poles in actual contact will always cling together unless the like poles are of exactly equal strength . Induction is an effect of the field of force associated with a magnet . Magnetic force has not merely the property of acting upon magnetic poles, it has the additional property of producing a phenomenon known as magnetic induction, or magnetic See also:

• FLUX (Lat. fluxus, a flowing; this being also the meaning of the English term in medicine, &c.)

flux, a See also:

• PHYSICAL

physical See also:

• CONDITION (Lat. condicio, from condicere, to agree upon, arrange; not connected with conditio, from condere, conditum, to put together)

condition which is of the nature of a flow continuously circulating through the magnet and the space outside it . Inside the magnet the course of the flow is from the south pole to the north pole; thence it diverges through the surrounding space, and again converging, re-enters the magnet at the south pole . When the magnetic induction flows through a piece of iron or other magnetizable substance placed near the magnet, a south pole is See also:

• DEVELOPED

developed where the flux enters and a north pole where it leaves the substance . Outside the magnet the direction of the magnetic induction is generally the same as that of the magnetic force . A See also:

• MAP
• MAP (or MAPES), WALTER (d. c. 1208/9)

map indicating the direction of the force in different parts of the field due to a magnet may be constructed in a very simple manner . A See also:

• SHEET

sheet of cardboard is placed above the magnet, and some iron filings are sifted thinly and evenly over the See also:

• SURFACE

surface: if the cardboard is gently tapped, the filings will arrange themselves in a See also:

• SERIES (a Latin word from serere, to join)

series of curves, as shown in fig . 1 .

This experiment suggested to See also:

• FARADAY, MICHAEL (1791-1867)

Faraday the conception of " lines of force," of which the curves formed by the filings afford a rough indication; Faraday's lines are however not confined to the plane of the cardboard, but occur in the whole of the space around the magnet . A line of force may be defined as an imaginary line so drawn that its direction at every point of its course coincides with the direction of FIG . 1 . the magnetic force at that point . Through any point in the field one such line can be drawn, but not more than one, for the force obviously cannot have more than one direction; the lines therefore never intersect . A line of force is regarded as proceeding from the north pole towards the south pole of the magnet, its direction being that in which an isolated north pole would be urged along it . A south pole would be urged oppositely to the conventional " direction " of the line; hence it follows that a very small magnetic needle, if placed in the field, would tend to set itself along or tangentially to the line of force passing through its centre, as may be approximately verified if the compass be placed among the filings on the cardboard . In the See also:

• INTERNAL

internal field of a long coil of wire carrying an electric current, the lines of force are, except near the ends, parallel to the axis of the coil, and it is chiefly for this See also:

• REASON (Lat. ratio, through French raison)

reason that the field due to a coil is particularly well adapted for inductively magnetizing iron and steel . The older operation of magnetizing a steel bar by See also:

• DRAWING

drawing a magnetic pole along it merely consists in exposing successive portions of the bar to the action of the strong field near the pole . Faraday's lines not only show the direction of the magnetic force, but also serve to indicate its magnitude or strength in different parts of the field . Where the lines are crowded together, as in the neighbourhood of the poles, the force is greater (or the field is stronger) than where they are more widely separated; hence the strength of a field at any point can be accurately specified by reference to the concentration of the lines . The lines presented to the See also:

• EYE
• EYE (O. Eng. edge, Ger. Auge; derived from an Indo-European root also seen in Lat. oc-ulus, the organ of vision (q.v.)

eye by the scattered filings are too vague and See also:

• ILL

ill-defined to give a satisfactory indication of the field-strength (see Faraday, Experimental Researches, § 3237) though they show its direction clearly enough .

It is however easy to demonstrate by means of the compass that the force is much greater in some parts of the field than in others . See also:

• LAY

Lay the compass upon the cardboard, and observe the See also:

• RATE

rate at which its needle vibrates after being displaced from its position of See also:

• EQUILIBRIUM (from the Lat. aequus, equal, and libra, a balance)

equilibrium; this will vary greatly in different regions . When the compass is far from the magnet, the vibrations will be comparatively slow; when it is near a pole, they will be exceedingly rapid, the frequency of the vibrations varying as the square See also:

• ROOT (late O.E. rot, adopted from Scand., cf. Norw. and Swed. rot, Dan. rod; the true O.E. word was wyrt, plant, represented in Ger. Wurz or Wurzel; the ultimate root is the same in both words, and is seen in Lat. radix)
• ROOT, ELIHU (1845– )

root of the magnetic force at the spot . In a refined form this method is often employed for measuring the intensity of a magnetic field at a given See also:

• PLACE (through Fr. from Lat. platea, street; Gr. IrAar6s, wide)

place, just as the intensity of gravity at different parts of the earth is deduced from observations of the rate at which a pendulum of known length vibrates . It is to the non-uniformity of the field surrounding a magnet that the apparent attraction between a magnet and a magnetizable See also:

• BODY

body such as iron is ultimately due . This was pointed out by W . See also:

• THOMSON, JAMES (1822-1892)
• THOMSON, JAMES (1834-1882)
• THOMSON, JAMES (r700-1748)
• THOMSON, JOHN (1778-184o)
• THOMSON, JOSEPH (1858-1895)
• THOMSON, SIR CHARLES WYVILLE (1830-1882)
• THOMSON, THOMAS (1773-1852)
• THOMSON, WILLIAM (1819-189o)

Thomson (afterwards See also:

• LORD
• LORD (O. Eng. hldford, i.e. hldfweard, the warder or keeper of bread, hlIf, loaf; the word is not represented in any other Teutonic language)
• LORD, JOHN (1810-1894)

Lord See also:

• KELVIN, WILLIAM THOMSON, BARON (1824-1907)

Kelvin) in 1847, as the result of a mathematical investigation undertaken to explain Faraday's experimental observations . If the inductively magnetized body lies in a See also:

• PART

part of the field which happens to be See also:

• UNIFORM

uniform there will be no resulting force tending to move the body, and it will not be " attracted." If however there is a small variation of the force in the space occupied by the body, it can be shown that the body will be urged, not necessarily towards a magnetic pole, but towards places of stronger magnetic force . It will not in general move along a line of force, as would an isolated pole, but will follow the direction in which the magnetic force increases most rapidly, and in so doing it may See also:

• CROSS

cross the lines of force obliquely or even at right angles . If a magnetized needle were supported so that it could move freely-about its centre of gravity it would not generally See also:

• SETTLE
• SETTLE, ELKANAH (1648–1724)

settle with its axis in a horizontal position, but would come to rest with its north-seeking pole either higher or See also:

• LOWER

lower than its centre . For the practical observation of this phenomenon it is usual to employ a needle which can turn freely in the plane of the magnetic meridian upon a horizontal axis passing through the centre of gravity of the needle . The See also:

• ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

angle which the magnetic axis makes with the plane of the See also:

• HORIZON (Gr. 6pfTwv, dividing)

horizon is called the inclination or See also:

• DIP (Old Eng. dyppan, connected with the common Teutonic root seen in " deep ")

dip .

Along an irregular line encircling the earth in the neighbourhood of the geographical See also:

• EQUATOR (Late Lat. aequator, from aequare, to make equal)

equator the needle takes up a horizontal position, and the dip is zero . At places north of this line, which is called the magnetic equator, the north end of the needle points downwards, the inclination generally becoming greater with increased distance from the equator . Within a certain small See also:

• AREA

area in the See also:

• ARCTIC (Gr. "ApKroc, the Bear, the northern constellation of Ursa Major)

Arctic Circle (about 970 W. long., 7o° N. See also:

• LAT

lat.) the north pole of the needle points vertically downwards,the dip being 90° . South of the magnetic equator the south end of the needle is always inclined downwards, and there is a spot within the See also:

• ANTARCTIC
• ANTARCTIC (Gr. &vri, opposite, and apKTos, the Bear, the northern constellation of Ursa Major)

Antarctic Circle (148° E. long., 740 S. lat.) where the needle again stands vertically, but with its north end directed upwards . All these observations may be accounted for by the fact first recognized by W . See also:

• GILBERT
• GILBERT (KINGSMILL) ISLANDS
• GILBERT (or GYLBERDE), WILLIAM (1544-1603)
• GILBERT, ALFRED (1854– )
• GILBERT, ANN (1821-1904)
• GILBERT, GROVE KARL (1843– )
• GILBERT, J
• GILBERT, JOHN (1810-1889)
• GILBERT, MARIE DOLORES ELIZA ROSANNA [" LOLA MONTEZ "] (1818-1861)
• GILBERT, NICOLAS JOSEPH LAURENT (1751–1780)
• GILBERT, SIR HUMPHREY (c. 1539-1583)
• GILBERT, SIR JOSEPH HENRY (1817-1901)
• GILBERT, SIR WILLIAM SCHWENK (1836– )

Gilbert in 1600, that the earth itself is a great magnet, having its poles at the two places where the dipping needle is vertical . To be consistent with the terminology adopted in See also:

• BRITAIN (Gr. Hperavuml vi7vot, Bperravia; Lat. Britannia, rarely Britannia)

Britain, it is necessary to regard the pole which is geographically north as being the south pole of the terrestrial magnet, and that which is geographically south as the north pole; in practice however the names assigned to the terrestrial magnetic poles correspond with their geographical situations . Within a limited space, such as that contained in a See also:

• ROOM

room, the field due to the earth's magnetism is sensibly uniform, the lines of force being parallel straight lines inclined to the horizon at the angle of dip, which at See also:

• GREENWICH

Greenwich in 1910 was about 67° . It is by the horizontal component of the earth's See also:

• TOTAL

total force that the compass-needle is directed . The magnets hitherto considered have been assumed to have each two poles, the one north and the other south . It is possible that there may be more than two . If, for example, a knitting needle is stroked with the south pole of a magnet, the strokes being directed from the See also:

• MIDDLE

middle of the needle towards the two extremities alternately, the needle will acquire a north pole at each end and a south pole in the middle .

By suitably modifying the manipulation a further number of consequent poles, as they are called, may be developed . It is also possible that a magnet may have no poles at all . Let a magnetic pole be drawn several times around a uniform steel See also:

• RING (O.E. hring; a word common to Teutonic languages; and probably cognate with the Lat. circus, Gr. KtpKOS or KpLKOS, Skt'. chakra, wheel, circle, cf. also " harangue "); in art, a band of circular shape of varying sizes, made of any material and used f

ring, so that every part of the ring may be successively subjected to the magnetic force . If the operation has been skilfully performed the ring will have no poles and will not attract iron filings . Yet it will be magnetized; for if it is cut through and the cut ends are drawn apart, each end will be found to exhibit polarity . Again, a steel wire through which an electric current has been passed will be magnetized, but so long as it is free from stress it will give no See also:

• EVIDENCE (Lat. evidentia, evideri, to appear clearly)

evidence of magnetization; if, however, the wire is See also:

• TWISTED

twisted, poles will be developed at the . two ends, for reasons which will be explained later . A wire or See also:

• ROD (O.E. rodd, probably related to Norw. rudda, stick, rodda, stake)
• ROD, EDOUARD (1857-1910)

rod in this condition is said to be circularly magnetized; it may be regarded as consisting of an indefinite number of elementary ring-magnets, having their axes coincident with the axis of the wire and their planes at right angles to it . But no magnet can have a single pole; if there is one, there must also be at least a second, of the opposite sign and of exactly equal strength . Let a magnetized knitting needle, having north and south poles at the two ends respectively, be broken in the middle; each See also:

• HALF

half will be found to possess a north and a south pole, the appropriate supplementary poles appearing at the broken ends . One of the fragments may again be broken, and again two bipolar magnets will be produced; and the operation may be repeated, at least in See also:

• IMAGINATION

imagination, till we arrive at molecular magnitudes and can go no farther . This experiment proves that the condition of magnetization is not confined to those parts where polar phenomena are exhibited, but exists throughout the whole body of the magnet; it also suggests the See also:

• IDEA (Gr. Ibia, connected with i&eiv, to see; cf. Lat. species from specere, to look at)

idea of molecular magnetism, upon which the accepted theory of magnetization is based . According to this theory the molecules of any magnetizable substance are little permanent magnets the axes of which are, under ordinary conditions, disposed in all possible directions indifferently .

The See also:

• PROCESS

process of magnetization consists in turning See also:

• ROUND (O. Fr. rond, Lat. rotundus, the Fr. is the source also of Du. rond; Ger., Swed., Dan. and Nor. rond)

round the molecules by the application of magnetic force, so that their north poles may all point more or less approximately in the direction of the force; thus the body as a whole becomes a magnet which is merely the resultant of an immense number of molecular magnets . In every magnet the strength of the south pole is exactly equal to that of the north pole, the action of the same magnetic force upon the two poles being equal and oppositely directed . This may be shown by means of the uniform field of force due to the earth's magnetism . A magnet attached to a See also:

• CORK
• CORK (perhaps through Sp. corcha from Lat. cortex, bark, but possibly connected with quercus, oak)
• CORK, RICHARD BOYLE

cork and floated upon See also:

• WATER

water will set itself with its axis in the magnetic meridian, but it will be drawn neither northward nor southward; the forces acting upon the two poles have therefore no horizontal resultant . And again if a piece of steel is weighed in a delicate See also:

• BALANCE (derived through the Fr. from the Late Lat. bilantia, an apparatus for weighing, from bi, two, and lanx, a dish or scale)

balance before and after magnetization, no See also:

• CHANGE (derived through the Fr. from the Late Lat. cambium, cambiare, to barter; the ultimate derivation is probably from the root which appears in the Gr. «a urmu', to bend)

change whatever in its See also:

• WEIGHT

weight can be detected; there is consequently no upward or downward resultant force due to magnetization; the contrary parallel forces acting upon the poles of the magnet are equal, constituting a couple, which may tend to turn the body, but not to propel it . Iron and its alloys, including the various kinds of steel, though exhibiting magnetic phenomena in a pre-eminent degree, are not the only substances capable of magnetization . See also:

• NICKEL
• NICKEL (symbol Ni, atomic weight 58.68 (0=16))

Nickel and See also:

• COBALT (symbol Co, atomic weight 59)

cobalt are also strongly magnetic, and in 1903 the interesting See also:

• DISCOVERY

discovery was made by F . Heusler that an alloy consisting of See also:

• COPPER (symbol Cu, atomic weight 63.1, H=1, or 63.6, O = 16)

copper, See also:

• ALUMINIUM (symbol Al; atomic weight 27.0)

aluminium and See also:

• MANGANESE (symbol Mn; atomic weight, 54.93 (0=16)], a metallic chemical element. Its dioxide (pyrolusite)

manganese (Heusler's alloy), possesses magnetic qualities comparable with those of iron . Practically the metals iron, nickel and cobalt, and some of their alloys and compounds constitute a class by themselves and are called ferromagnetic substances . But it was discovered by Faraday in 1845 that all substances, including even gases, are either attracted or repelled by a sufficiently powerful magnetic pole . Those substances which are attracted, or rather which tend, like iron, to move from weaker to stronger parts of the magnetic field, are termed paramagnetic; those which are repelled, or tend to move from stronger to weaker parts of the field, are termed diamagnetic . Between the ferromagnetics and the paramagnetics there is an enormous See also:

• GAP

gap .

The maximum magnetic susceptibility of iron is half a million times greater than that of liquid See also:

• OXYGEN (symbol 0, atomic weight 16)

oxygen, one of the strongest paramagnetic substances known . See also:

• BISMUTH

Bismuth, the strongest of the diamagnetics, has a negative susceptibility which is numerically 20 times less than that of liquid oxygen . Many of the physical properties of a metal are affected by magnetization . The dimensions of a piece of iron, for example, its elasticity, its thermo-electric power and its electric conductivity are all changed under the See also:

• INFLUENCE (Late Lat. influentia, from influere, to flow in)

influence of magnetism . On the other See also:

• HAND
• HAND (a word common to Teutonic languages; cf. Ger. Hand, Goth. handus)
• HAND, FERDINAND GOTTHELF (1786-185r)

hand, the magnetic properties of a substance are affected by such causes as mechanical stress and changes of temperature . An See also:

• ACCOUNT
• ACCOUNT (through O. Fr. acont, Late Lat. comptum, cornputare, to calculate)

account of some of these effects will be found in another See also:

• SECTION
• SECTION (Lat. sectio, cutting, secare, to cut)

section.' 2 . TERMINOLOGY AND ELEMENTARY PRINCIPLES In what follows the C.G.S. electromagnetic See also:

• SYSTEM

system of units will be generally adopted, and, unless otherwise stated, magnetic substances will be assumed to be isotropic, or to have the same physical properties in all directions . Vectors.—Physical quantities such as magnetic force, magnetic induction and magnetization, which have direction as well as magnitude, are termed vectors; they are compounded and resolved in the same manner as mechanical force, which is itself a vector . When the direction of any vector quantity denoted by a See also:

• SYMBOL (Gr. o-uµ(3oXov, a sign)

symbol is to be attended to, it is usual to employ for the symbol either a See also:

• BLOCK
• BLOCK (from the Fr. bloc, and possibly connected with an Old Ger. Block, obstruction, cf. " baulk ")
• BLOCK, MAURICE (1816–19or)

block See also:

• LETTER (through Fr. lettre from Lat. littera or litera, letter of the alphabet; the origin of the Latin word is obscure; it has probably no connexion with the root of linere, to smear, i.e. with wax, for an inscription with a stilus)

letter, as H, I, B, or a See also:

• GERMAN
• GERMAN, DUTCH AND SCANDINAVIAN

German See also:

• CAPITAL (i.e. capital stock or fund)
• CAPITAL (Lat. caput, head)

capital, as t,, 2 Magnetic Poles and Magnetic Axis.—A unit magnetic pole is that which acts on an equal pole at a distance of one centimetre with a force of one dyne . A pole which points north is reckoned positive, one which points south negative . The action between any two magnetic poles is mutual . If ml and m2 are the strengths of two poles, d the distance between them expressed in centimetres, and f the force in dynes, i For the relations between magnetism and See also:

• LIGHT

light see MAGNETO-OPTICS .

2 Clerk See also:

• MAXWELL
• MAXWELL, JAMES CLERK (1831–1879)

Maxwell employed German capitals to denote vector quantities . J . A . See also:

• FLEMING, PAUL (1609-1640)
• FLEMING, RICHARD (d. 1431)
• FLEMING, SIR SANDFORD (1827- )
• FLEMING, SIR THOMAS (1S44-1613)

Fleming first recommended the use of blockletters as being more convenient both to printers and readers.terminate outside the magnet or inside, have a resultant, equal to the sum of the forces and parallel to their direction, acting at a certain point N . The point N, which is the centre of the parallel forces, is called the north or positive pole of the magnet . Similarly, the forces acting in the opposite direction on the negative poles of the filaments have a resultant at another point S, which is called the south or negative pole . The opposite and parallel forces acting on the poles are always equal, a fact which is sometimes expressed by the statement that the total magnetism of a magnet is zero . The line joining the two poles is called the axis of the magnet . Magnetic Field.—Any space at every point of which there is a finite magnetic force is called a field of magnetic force, or a magnetic field . The strength or intensity of a magnetic field at any point is measured by the force in dynes which a unit pole will experience when placed at that point, the direction of the field being the direction in which a positive pole is urged . The field-strength at any point is also called the magnetic force at that point; it is denoted by H, or, when it is desired to draw See also:

• ATTENTION (from Lat. ad-tendo, await, expect; the condition of being " stretched " or " tense ")

attention to the fact that it is a vector quantity, by the block letter H, or the German See also:

• CHARACTER (Gr. xapareri7p, from xap&crew, to scratch)

character S~ . Magnetic force is sometimes, and perhaps more suitably, termed magnetic intensity; it corresponds to the intensity of gravity g in the theory of heavy bodies (see Maxwell, Electricity and Magnetism, § 12 and § 68, footnote) .

A line of force is a line drawn through a magnetic field in the, direction of the force at each point through which it passes . A uniform magnetic field is one in which H has everywhere the same value and the same direction, the lines of force being, therefore, straight and parallel . A magnetic field is generally due either to a conductor carrying an electric current or to the poles of a magnet . The magnetic field due to a long straight wire in which a current of electricity is flowing is at every point at right angles to the plane passing through it and through the wire; its strength at any point distant r centimetres from the wire is H = 2i/r, (2) i being the current in C.G.S. units.' The lines of force are evidently circles concentric with the wire and at right angles to it; their direction is related to that of the current in the same manner as the rotation of a corkscrew is related to its thrust . The field at the centre of a circular conductor of See also:

• RADIUS

radius r through which current is passing is H =tai/r, (3) the direction of the force being along the axis and related to the direction of the current as the thrust of a corkscrew to its rotation . The field strength in the interior of a long uniformly See also:

• WOUND (O. Eng. wund,connected with a Teutonic verb, meaning to strive, fight, suffer, seen in O. Eng. winnan, whence Eng. " win ")

wound coil containing n turns of wire and having a length of 1 centimetres is (except near the ends) H =4ain/l . (4) In the middle portion of the coil the strength of the field is very nearly uniform, but towards the end it diminishes, and at the ends is reduced to one-half . The direction of the force is parallel to the axis of the coil, and related to the direction of the current as the thrust of a corkscrew to its rotation . If the coil has the form of a ring of mean radius r, the length will be See also:

• EAR (common Teut.; O.E. are, Ger. Ohr, Du. oor, akin to Lat. auris, Gr. ovs)

ear, and the field inside the coil may be expressed as H = 2ni/r . (5) The uniformity of the field is not in this See also:

• CASE
• CASE, JOHN (d. 1600)

case disturbed by the influence of ends, but its strength at any point varies inversely as the distance from the axis of the ring . When therefore sensible uniformity is desired, the radius of the ring should he large in relation to that of the convolutions, or the ring should have the form of a See also:

• SHORT, FRANCIS JOB (1857– )

short See also:

• CYLINDER (Gr. KvAwSpos, from KvXivaety, to roll)

cylinder with thin walls . The strongest magnetic fields employed for experimental purposes are obtained by the use of electromagnets .

For many experiments the field due to the earth's magnetism is sufficient; this is practically quite uniform throughout considerable spaces, but its total intensity is less than half a unit . Magnetic Moment and Magnetization.—The moment, M, M or X171, of a uniformly and longitudinally magnetized bar-magnet is the product of its length into the strength of one of its poles; it is the moment of the couple acting on the magnet when placed in a field of unit intensity with its axis perpendicular to the direction of the field . If 1 is the length of the magnet, M = ml . The action of a magnet at a distance which is great compared with the length of the magnet depends solely upon its moment; so also does the action which the magnet experiences when placed in a uniform field . The moment of a small magnet may be resolved like a force . The in-tensity of magnetization, or, more shortly, the magnetization of a uniformly magnetized body is defined as the magnetic moment per unit of See also:

• VOLUME

volume, and is denoted by I, 1, or j . Hence I=M/v=ml/v=m/a, v being the volume and a the sectional area . If the magnet is not uniform, the magnetization at any point is the ratio of the moment of an See also:

• ELEMENT (Lat. elementum)

element of volume at that point to the volume itself, or I = m.ds/dv. where ds is the length of the element . The direction of the magnetization is that of the magnetic axis of the element ;'in isotropic substances it coincides with the direction of the magnetic force at the point . If the direction of the magnetization at the surface of a magnet makes 3 The C.G.S. unit of current =10 amperes . f =See also:

• MIME

mime/d' (I) . The force is one of attraction or repulsion, according as the sign of the product mime is negative or positive .

The poles at the ends of an infinitely thin uniform magnet, or magnetic filament, would See also:

• ACT (Lat. actus, actum)

act as definite centres of force . An actual magnet may generally be regarded as a bundle of magnetic filaments, and those portions of the surface of the magnet where the filaments terminate, and so-called " free magnetism " appears, may be conveniently called poles or polar regions . A more precise See also:

• DEFINITION (Lat. definitio, from de-finire, to set limits to, describe)

definition is the following: When the magnet is placed in a uniform field, the parallel forces acting on the positive poles of the constituent filaments, whether the filaments an angle a with the normal, the normal component of the magnetization, I See also:

• COS
• COS, or STANKO (Ital. Stanchio, Turk. Islan-keui, by corruption from Etc rav KW)

cos e, is called the surface See also:

• DENSITY (Lat. densus, thick)

density of the magnetism, and is generally denoted by a . Potential and Magnetic Force.—The magnetic potential at any point in a magnetic field is the work which would be done against the magnetic forces in bringing a unit pole to that point from the boundary of the field . The line through the given point along which the potential decreases most rapidly is the direction of the resultant magnetic force, and the rate of decrease of-the potential in any direction is equal to the component of the force in that direction . If V denote the potential, F the resultant force, X, Y, Z, its components parallel to the co-See also:

• ORDINATE

ordinate axes and n the line along which the force is directed, then —SV=F —lV=X —SV_ Y bV=Z an ax ' sy az Surfaces for which the potential is See also:

• CONSTANT, BENJAMIN (1845-1902)

constant are called equipotential surfaces . The resultant magnetic force at every point of such a surface is in the direction of the normal (n) to the surface; every line of force therefore cuts the equipotential surfaces at right angles . The potential due to a single pole of strength m at the distance r from the pole is V =m/r, (7) the equipotential surfaces being See also:

• SPHERES, MUSIC OF THE

spheres of which the pole is the centre and the lines of force radii . The potential due to a thin magnet at a point whose distance from the two poles respectively is r and r' is V =m(l/r =l/r') . (8) When V is constant, this See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

equation represents an equipotential surface . The equipotential surfaces are two series of ovoids surrounding the two poles respectively, and separated by a plane at zero potential passing perpendicularly through the middle of the axis . If r and r' make angles B and 0' with the axis, it is easily shown that the equation to a line of force is cos 8—cos 0' =constant .

(q) At the point where a line of force intersects the perpendicular bisector of the axis r=r' =ro, say, and cos 8—cos 8' obviously=l/re, I being the distance between the poles; l/ro is therefore the value of the constant in (g) for the line in question . Fig . 2 shows the lines of force and the plane sections of the equipotential surfaces for a thin magnet with poles concentrated at its ends . The potential due to a small magnet of moment M, at a point whose distance from the centre of the magnet is r, is V=M cos 02, (1o) where 8 is the angle between r and the axis of the magnet . Denoting the force at P (see fig . 3) by F, and its components parallel to the co-ordinate axes by X and Y, we have SV M 2 X=—ax= —(3 cos' 0 Sy Y = — =—(3 See also:

• SIN
• SIN (O. Eng. syn: a common Teutonic word, cf. Dutch zonde, Ger. Siinde)

sin 8 cos B . — If Fr is the force along r and F, that along t at right angles to r, Fr=X cos0+Y sing=M z cos 8, (12) F,=—X sing+Y cos0=M sin B . For the resultant force at P, F=' Fr2+F,2=M,13cos28+t . The direction of F is given by the following construction : Trisect OP at C, so that OC=OP/3; draw CD at right angles to OP, to cut the axis produced in D; then DP will be the direction of the force at P . For a point in the axis OX, 8=o; therefore cos a=1, and the point D coincides with C; the magnitude of the force is, from (14), F==2M/r3, (15) its direction being along the axis OX . For a point in the line OYbisecting the magnet perpendicularly, 0 =ir/2 therefore cos 8 =0, and the point D is at an See also:

• INFINITE (from Lat. in, not, finis, end or limit; cf. findere, to deave)

infinite distance . The magnitude of the force is in this case Fy (16) and its direction is parallel to the axis of the magnet .

Although the above useful formulae, (10) to (15), are true only for an infinitely small magnet, they may be practically applied whenever the distance r is considerable compared with the length of the magnet . Couples and Forces between Magnets.—If a small magnet of moment M is placed in the sensibly uniform field H due to a distant magnet, the couple tending to turn the small magnet upon an axis at right angles to the magnet and to the force is MH sin B, (17) where 0 is the angle between the axis of the magnet and the direction of the force . In fig . 4 S'N' is a small magnet of moment M', and SN a distant fixed magnet of moment M ; the axes of SN and S'N' make angles of 8 and s/s respectively with the line through their middle points . It can be deduced from (17), (12) and (13) that the couple on S'N' due to SN, and tending to increase ¢, is MM' (sin 0 cos 4—2 sin ¢ cos 8)/r3 . (18) This vanishes if sin 0 cos 41=2 sin 4' cos 0, i.e. if tan q, =1 tan 0, S'N' being then along a line of force, a result which explains the construction given above for finding the direction of the force F in (14) . If the axis of SN produced passes through the centre of S'N', 8=0, and the couple becomes 2MM'sin¢/r3, (19) tending to diminish 4, ; this is called the " end on " position . If the centre of S'N' is on the perpendicular bisector of SN, 0=Via, and the couple will be MM'cos ¢/r3, (20) tending to increase ¢; this is the " See also:

• BROADSIDE

broadside on " position . These two positions are sometimes called the first and second (or A and B) principal positions of See also:

• GAUSS, KARL FRIEDRICH (1777-1855)

Gauss . The components X, Y, parallel and perpendicular to r, of the force between the two magnets SN and S'N' are X=3MM'(sin 8 sin 41—2 cos 8 cos 0)/r4, (21) Y=3MM'(sin 8 cos ¢+sin q, cos 0)/r4 . (22) It will be seen that, whereas the couple varies inversely as the See also:

• CUBE (Gr. K46os, a cube)

cube of the distance, the force varies inversely as the See also:

• FOURTH

fourth power . Distributions of Magnetism.—A magnet may be regarded as consisting of an infinite number of elementary magnets, each having a pair of poles and a definite magnetic moment .

If a series of such elements, all equally and longitudinally magnetized, were placed end to end with their unlike poles in contact, the See also:

• EXTERNAL

external action of the filament thus formed would be reduced to that of the two extreme poles . The same would be the case if the magnetization of the filament varied inversely as the area of its cross-section a in different parts . Such a filament is called a simple magnetic solenoid, and the product aI is called the strength of the solenoid . A magnet which consists entirely of such solenoids, having their ends either upon the surface or closed upon themselves, is called a solenoidal magnet, and the magnetism is said to be distributed solenoidally; there is no free magnetism in its interior . If the constituent solenoids are parallel and of equal strength, the magnet is also uniformly magnetized . A thin sheet of magnetic See also:

• MATTER

matter magnetized normally to its surface in such a manner that the magnetization at any place is inversely proportional to the thickness h of the sheet at that place is called a magnetic See also:

• SHELL
• SHELL (O. Eng. scell, scyll, cf. Du. sceel, shell, Goth. skalja, tile; the word means originally a thin flake,. cf. Swed. skalja, to peel off; it is allied to " scale " and " skill," from a root meaning to cleave, divide, separate)

shell; the constant product hI is the strength of the shell and is generally denoted by 4, or O . The potential at any point due to a magnetic shell is the product of its strength into the solid angle co subtended by its edge at the given point, or V =4,w . For a given strength, therefore, the potential depends solely upon the boundary of the shell, and the potential outside a closed shell is everywhere zero . A magnet which can be divided into simple magnetic shells, either closed or having their edges on the surface of the magnet, is called a lamellar magnet, and the magnetism is said to be distributed lamellarly . A magnet consisting of a series of plane shells of equal strength arranged at right angles to the direction of magnetization will be uniformly magnetized . It can be shown that uniform magnetization is possible only when the form of the body is ellipsoidal . (Maxwell, Electricity and Magnetism, II., § 437) .

The cases of greatest practical importance are those of a See also:

• SPHERE (Gr. vclsa?pa, a ball or globe)

sphere (which is an See also:

• ELLIPSOID

ellipsoid with three equal axes) and an ovoid or prolate ellipsoid of revolution . The potential due to a uniformly magnetized sphere of radius a for an external point at a distance r from the centre is V = bra3l cos 0/See also:

• R2(rt-s2)

r2, (23) B being the inclination of r to the magnetic axis . Since }ira'l is the moment of the sphere (= volume X magnetization), it appears from (10) that the magnetized sphere produces the same external effect as a very small magnet of equal moment placed at its centre and magnetized in the same direction; the resultant force therefore is the same as in (14) . The force in the interior is uniform, opposite (6) (13) (14) s to the direction of magnetization, and equal to 1irI . When it is desired to have a uniform magnet with definitely situated poles, it it usual to employ one having the form of an ovoid, or elongated ellipsoid of revolution, instead of a rectangular or cylindrical bar . If the magnetization is parallel to the See also:

• MAJOR
• MAJOR (Lat. for " greater ")
• MAJOR (or MAIR), JOHN (1470-1550)

major axis, and the lengths of the major and See also:

• MINOR
• MINOR (Lat. for smaller, lesser)
• MINOR, ROBERT CRANNELL (1839-1904)

minor axes are 2a and 2c, the poles are situated at a distance equal to la from the centre, and the magnet will behave externally like a simple solenoid of length la . The internal force F is opposite to the direction of the magnetization,' and equal to NI, where N is a coefficient depending only on the ratio of the axes . The moment = tirac2I = — tirac2FN . The See also:

• DISTRIBUTION (Lat. distribuere, to deal out)

distribution of magnetism and the position of the poles in magnets of other shapes, such as cylindrical or rectangular bars, cannot be specified by any general statement, though approximate determinations may be obtained experimentally in individual cases.' According to F . W . G . Kohlrausch2 the distance between the poles of a cylindrical magnet the length of which is from to to 3o times the See also:

• DIAMETER (from the Cr. &a, through, µErpov, measure)

diameter, is sensibly equal to five-sixths of the length of the bar .

This statement, however, is only approximately correct, the distance between the poles depending upon the intensity of the magnetization.' In general, the greater the ratio of length to section, the more nearly will the poles approach the end of the bar, and the more nearly uniform will be the magnetization . For most practical purpose a knowledge of the exact position of the poles is of no importance; the magnetic moment, and therefore the mean magnetization, can always be determined with accuracy . Magnetic Induction or Magnetic Flux.—When magnetic force acts on any See also:

• MEDIUM

medium, whether magnetic, diamagnetic or neutral, it produces within it a phenomenon of the nature of a flux or flow called magnetic induction (Maxwell, loc. cit., § 428) . Magnetic induction, like other fluxes such as See also:

• ELECTRICAL
• ELECTRICAL (or ELECTROSTATIC) MACHINE

electrical, thermal or fluid currents, is defined with reference to an area ; it satisfies the same conditions of continuity as the electric current does, and in isotropic See also:

• MEDIA

media it depends on the magnetic force just as the electric current depends on the electromotive force . The magnitude of the flux produced by a given magnetic force differs in different media . In a uniform magnetic field of unit intensity formed in empty space the induction or magnetic flux across an area of I square centimetre normal to the direction of the field is arbitrarily taken as the unit of induction . Hence if the induction per square centimetre at any point is denoted by B, then in empty space B is numerically equal to H ; moreover in isotropic media both have the same direction, and for these reasons it is often said that in empty space (and practically in See also:

• AIR (from an Indo-European root meaning " breathe," " blow ")
• AIR, or ASBEN

air and other non-magnetic substances) B and H are identical . Inside a magnetized body, B is the force that would be exerted on a unit pole if placed in a narrow See also:

• CREVASSE

crevasse cut in the body, the walls of the crevasse bein perpendicular to the direction of the magnetization (Maxwell, § 399, 604); and its numerical value, being partly due to the free magnetism on the walls, is generally very different from that of H . In the case of a straight uniformly magnetized bar the direction of the magnetic force due to the poles of the magnet is from the north to the south pole outside the magnet, and from the south to the north inside . The magnetic flux per square centimetre at any point (B, B, or $) is briefly called the induction, or, especially by electrical See also:

• ENGINEERS, MILITARY

engineers, the flux-density . The direction of magnetic induction may be indicated by lines of induction; a line of induction is always a closed See also:

• CURVE (Lat. curvus, bent)

curve, though it may possibly extend to and return from infinity . Lines of induction drawn through every point in the See also:

• CONTOUR

contour of a small surface form a re-entrant See also:

• TUBE (Lat. tuba)

tube bounded by lines of induction; such a tube is called a tube of induction .

The cross-section of a tube of induction may vary in different parts, but the total induction across any section is everywhere the same . A See also:

• SPECIAL

special meaning has been assigned to the See also:

• TERM

term " lines of induction." Sup-pose the whole space in which induction exists to be divided up into unit tubes, such that the surface integral of the induction over any cross-section of a tube is equal to unity, and along the axis of each tube let a line of induction be drawn . These axial lines constitute the system of lines of induction which are so often referred to in the See also:

• SPECIFICATION (from Med. Lat. specificatio, specificare, to enumerate or mention in detail)

specification of a field . Where the induction is high the lines will be crowded together; where it is weak they will be widely separated, the number per square centimetre See also:

• CROSSING

crossing a normal surface at any point being always equal to the numerical value of B . The induction may therefore be specified as B lines per square centimetre . The direction of the induction is also of course indicated by the direction of the lines, which thus serve to map out space in a convenient manner . Lines of induction are frequently but inaccurately spoken of as lines of force . When induction or magnetic flux takes place in a ferromagnetic metal, the metal becomes magnetized, but the magnetization at any point is proportional not to B, but to B—H . The See also:

• FACTOR (from Lat. facere, to make or do)

factor of proportionality will be I-4r, so that ' The principal theoretical investigations are summarized in Mascart and See also:

• JOUBERT, BARTHELEMY CATHERINE (1769–1799)
• JOUBERT, JOSEPH (1754–1824)
• JOUBERT, PETRUS JACOBUS (1834–1900)

Joubert's Electricity and Magnetism, i . 391—398 and ii . 646-657 . The case of a long iron bar has been experimentally studied with great care by C .

G . See also:

• LAMB (a word common to Teutonic languages; cf. Ger. Lamm)
• LAMB, CHARLES (1775–1834)

Lamb, Proc . Phys . See also:

• SOC

Soc., 1899, 16, 509 . 2 Wied . See also:

• ANN

Ann., 1884, 22, 411 . 2 See C . G . Lamb, loc. cit. p . 518.I = (B —H)/4ir, (24) or B = H +471 . (25) Unless the path of the induction is entirely inside the metal, free magnetic poles are developed at those parts of the metal where induction enters and leaves, the polarity being south at the entry and north at the exit of the flux . These free poles produce a magnetic field which is superposed upon that arising from other See also:

• SOURCES

sources .

The resultant magnetic field, therefore, is compounded of two fields, the one being due to the poles, and the other to the external causes which would be operative in the See also:

• ABSENCE (Lat. absentia)

absence of the magnetized metal . The intensity (at any point) of the field due to the magnetization may be denoted by Hi, that of the external field by Ho, and that of the resultant field by H . In certain cases, as, for instance, in an iron ring wrapped uniformly round with a coil of wire through which a current is passing, the induction is entirely within the metal ; there are, consequently, no free poles, and the ring, though magnetized, constitutes a poleless magnet . Magnetization is usually regarded as the direct effect of the resultant magnetic force, which is therefore often termed the magnetizing force . See also:

• PERMEABILITY, MAGNETIC

Permeability and Susceptibility.—The ratio B/H is called the permeability of the medium in which the induction is taking place, and is denoted by A . The ratio I/H is called the susceptibility of the magnetized substance, and is denoted by K . Hence B =µH and I =xH . (26) Also B H +47r1 =H= H —I+41rx, (27) and x 4I (28) Since in empty space B has been assumed to be numerically equal to H, it follows that the permeability of a vacuum is equal to 1 . The permeability of most material substances differs very slightly from unity, being a little greater than i in paramagnetic and a little less in diamagnetic substances . In the case of the ferromagnetic metals and some of their alloys and compounds, the permeability has generally a much higher value . Moreover, it is not constant, being an apparently arbitrary See also:

• FUNCTION

function of H or of B; in the same specimen its value may, under different conditions, vary from less than 2 to upwards of 5000 . The magnetic susceptibility K expresses the numerical relation of the magnetization to the magnetizing force .

From the equation x = — I)/47r, it follows that the magnetic susceptibility of a vacuum (where µ =I) is o, that of a diamagnetic substance (where /2 < 1) has a negative value, while the susceptibility of paramagnetic and ferromagnetic substances (for which µ>I) is positive . No substance has yet been discovered having a negative susceptibility sufficiently great to render the permeability (= I +4xK) negative . Magnetic See also:

• CIRCUIT (Lat. circuitus, from circum, round, and ire, to go)

Circuit.—The circulation of magnetic induction or flux through magnetic and non-magnetic substances, such as iron and air, is in many respects analogous to that of an electric current through See also:

• GOOD, JOHN MASON (1764-1827)

good and See also:

• BAD, BCD

bad conductors . Just as the lines of flow of an electric current all pass in closed curves through the See also:

• BATTERY (Fr. batterie, from battles, to beat)

battery or other generator, so do all the lines of induction pass in closed curves through the magnet or magnetizing coil . The total magnetic induction or flux corresponds to the current of electricity (practically measured in amperes) ; the induction or flux density B to the density of the current (number of amperes to the square centimetre of section); the magnetic permeability to the specific electric conductivity; and the line integral of the magnetic force, sometimes called the magneto. See also:

• MOTIVE (from Lat. movere, to move)

motive force, to the electro-motive force in the circuit . The principal points of difference are that (I) the magnetic permeability, unlike the electric conductivity, which is See also:

• INDEPENDENT

independent of the strength of the current, is not in general constant; (2) there is no perfect insulator for magnetic induction, which will pass more or less freely through all known substances . Nevertheless, many important problems See also:

• RELATING

relating to the distribution of magnetic induction may be solved by methods similar to those employed for the See also:

• SOLUTION (from Lat. solvere, to loosen, dissolve)

solution of analogous problems in electricity . For the elementary theory of the magnetic circuit see ELECTRO-MAGNETISM . See also:

• HYSTERESIS (Gr. IQTEprIo-es, from vvrkp€iv, to lag behind)

Hysteresis, Coercive Force, Retentiveness.—It is found that when a piece of ferromagnetic metal, such as iron, is subjected to a magnetic field of changing intensity, the changes which take place in the induced magnetization of the iron exhibit a tendency to lag behind those which occur in the intensity of the field—a phenomenon to which J . A .