Chapter LXIII. repeats the promise of freedom to the English church

and of their rights and liberties to all.

Magna Carta is an elaboration of the accession charter of Henry I., and

is based upon the Articles of the Barons. It is, however, very much

longer than the former charter and somewhat longer than the Articles.

Moreover, it differs in several particulars from the Articles, these

differences being doubtless the outcome of deliberation and of

compromise. For instance, the provisions in Magna Carta concerning the

freedom of the church find no place in the Articles, while a comparison

between the two documents suggests that in other ways also influences

favourable to the church and the clergy were at work while the famous

charter was being framed. When one reflects how active and prominent

Langton and other prelates were at Runnimede the change is not

surprising. Another difference between the two documents concerns the

towns and the trading classes. Certain privileges granted to them in the

Articles are not found in Magna Carta, although, it must be noted, this

document bestows exceptionally favoured treatment on the citizens of

London. The conclusion is that the friends of the towns and the traders

were less in evidence at Runnimede than they were at the earlier

meetings of the barons, but that the neighbouring Londoners were strong

enough to secure a good price for their support.

Magna Carta throws much light on the condition of England in the early

13th century. By denouncing the evil deeds of John and the innovations

practised by him, it shows what these were and how they were hated; how

money had been raised, how forest areas had been extended, how minors

and widows had been cheated and oppressed. By declaring, as it does,

what were the laws and customs of a past age wherein justice prevailed,

it shows what was the ideal of good government formed by John's prelates

and barons. Magna Carta can hardly be said to have introduced any new

ideas. As Pollock and Maitland (_History of English Law_) say "on the

whole the charter contains little that is absolutely new. It is

restorative." But although mature study has established the truth of

this proposition it was not always so. Statesmen and commentators alike

professed to find in Magna Carta a number of political ideas which

belonged to a later age, and which had no place in the minds of its

framers. It was regarded as having conferred upon the nation nothing

less than the English constitution in its perfect and completed form.

Sir Edward Coke finds in Magna Carta a full and proper legal answer to

every exaction of the Stuart kings, and a remedy for every evil suffered

at the time. Sir William Blackstone is almost equally admiring. Edmund

Burke says "Magna Carta, if it did not give us originally the House of

Commons, gave us at least a House of Commons of weight and consequence."

Lord Chatham used words equally superlative. "Magna Carta, the Petition

of Rights and the Bill of Rights form that code, which I call the Bible

of the English Constitution." Modern historians, although less

rhetorical, speak in the highest terms of the importance of Magna Carta,

the view of most of them being summed up in the words of Dr Stubbs: "The

whole of the constitutional history of England is a commentary on this

charter."

Many regard Magna Carta as giving equal rights to all Englishmen. J. R.

Green says "The rights which the barons claimed for themselves they

claimed for the nation at large." As a matter of fact this statement is

only true with large limitations. The villains, who formed the majority

of the population, got very little from it; in fact the only clauses

which protect them do so because they are property--the property of

their lords--and therefore valuable. They get neither political nor

civil rights under Magna Carta. The traders, too, get little, while

preferential treatment is meted out to the clergy and the barons. Its

benefits are confined to freemen, and of the benefits the lion's share

fell to the larger landholders; the smaller landholders getting, it is

true, some crumbs from the table. It did not establish freedom from

arbitrary arrest, or the right of the representatives of the people to

control taxation, or trial by jury, or other conceptions of a later

generation.

The story of Magna Carta after the death of John is soon told. On the

12th of November 1216 the regent William Marshal, earl of Pembroke,

reissued the charter in the name of the young king Henry III. But

important alterations were made. War was being waged against Louis of

France, and the executive must not be hampered in the work of raising

money; moreover the personal equation had disappeared, the barons did

not need to protect themselves against John. Consequently the chapter

limiting the power of the crown to raise scutages and aids without the

consent of the council vanished, and with it the complementary one which

determined the method of calling a council. Other provisions, the object

of which had been to restrain John from demanding more money from

various classes of his subjects, were also deleted, and the same fate

befell such chapters as dealt with mere temporary matters. The most

important of these was Chapter LXI., which provided for the appointment

of 25 executors to compel John to observe the charter. The next year

peace was made at Lambeth (Sept. 11, 1217) between Henry III. and Louis

and another reissue of the charter was promised. This promise was

carried out, but two charters appeared, one being a revised issue of

Magna Carta proper, and the other a separate charter dealing with the

forests, all references to which were omitted from the more important

document. The date of this issue appears to have been the 6th of

November 1217. The issue of a separate forest charter at this time led

subsequently to some confusion. Roger of Wendover asserts that John

issued a separate charter of this kind when Magna Carta appeared. This

statement was believed by subsequent writers until the time of

Blackstone, who was the first to discover the mistake.

As issued in 1217 Magna Carta consists of 47 chapters only. It declares

that henceforward scutages shall be taken according to the precedents of

Henry II.'s reign. New provisions were introduced for the preservation

of the peace--unlawful castles were to be destroyed--while others were

directed towards making the administration of justice by the visiting

justices less burdensome. With regard to the land and the services due

therefrom a beginning was made of the policy which culminated in the

statutes of Mortmain and of Quia Emptores. The sheriffs were ordered to

publish the revised charter on the 22nd of February 1218. Then in

February 1225 Henry III. again issued the two charters with only two

slight alterations, and this is the final form taken by Magna Carta,

this text being the one referred to by Coke and the other early

commentators. Subsequently the charters were confirmed several times by

Henry III. and by Edward I., the most important occasion being their

confirmation by Edward at Ghent in November 1297. On this occasion some

supplementary articles were added to the charter; these were intended to

limit the taxing power of the crown.

There are at present in existence four copies of Magna Carta, sealed

with the great seal of King John, and several unsealed copies. Of the

four two are in the British Museum. Both came into the possession of

the Museum with the valuable collection of papers which had belonged

to Sir Robert Cotton, who had obtained possession of both. One was

found in Dover castle about 1630. This was damaged by fire in 1731;

the other is undamaged. The two other sealed copies belong to the

cathedrals of Lincoln and of Salisbury. Both were written evidently in

a less hurried fashion than those in the British Museum, and the one

at Lincoln was regarded as the most perfect by the commissioners who

were responsible for the appearance of the _Statutes of the Realm_

1810. The British Museum also contains the original parchment of the

Articles of the Barons. Magna Carta was first printed by Richard

Pynson in 1499. This, however, was not the original text, which was

neglected until the time of Blackstone, who printed the various issues

of the charter in his book _The Great Charter and the Charter of the

Forest_ (1759). The earliest commentator of note was Sir Edward Coke,

who published his _Second Institute_, which deals with Magna Carta, by

order of the Long Parliament in 1642. Modern commentators, who also

print the various texts of the charter, are Richard Thomson, _An

Historical Essay on the Magna Carta of King John_ (1829); C. Bémont,

in his _Chartes des libertés anglaises_ (1892); and W. Stubbs in his

_Select Charters_ (1895). A more recent book and one embodying the

results of the latest research is W. S. McKechnie, _Magna Carta_

(1905). The text of Magna Carta is also printed in the _Statutes of

the Realm_ (1810-1828), and in T. Rymer's _Foedera_ (1816-1869). In

addition to Blackstone, Coke and these later writers, the following

works may also be consulted: John Reeves, _History of English Law_

(1783-1784); L. O. Pike, _A Constitutional History of the House of

Lords_ (1894); W. Stubbs, _Constitutional History of England_ (1897);

Sir F. Pollock and F. W. Maitland, _The History of English Law_

(1895); W. S. Holdsworth, _A History of English Law_ (1903), and Kate

Norgate, _John Lackland_ (1902). (A. W. H.*)

MAGNA GRAECIA ([Greek: he megale Hellas]), the name given (first,

apparently, in the 6th century B.C.) to the group of Greek cities along

the coast of the "toe" of South Italy (or more strictly those only from

Tarentum to Locri, along the east coast), while the people were called

Italiotes ([Greek: Italiôtai]). The interior, which the Greeks never

subdued, continued to be in the hands of the Bruttii, the native

mountaineers, from whom the district was named in Roman times ([Greek:

Brettia] also in Greek writers). The Greek colonies were established

first as trading stations, which grew into independent cities. At an

early time a trade in copper was carried on between Greece and Temesa

(Homer, _Od._ i. 181).[1] The trade for a long time was chiefly in the

hands of the Euboeans; and Cyme (Cumae) in Campania was founded in the

8th century B.C., when the Euboean Cyme was still a great city. After

this the energy of Chalcis went onward to Sicily, and the states of the

Corinthian Gulf carried out the colonization of Italy, Rhegium having

been founded, it is true, by Chalcis, but after Messana (Zancle), and at

the request of the inhabitants of the latter. Sybaris (721) and Crotona

(703) were Achaean settlements; Locri Epizephyrii (about 710) was

settled by Ozolian Locrians, so that, had it not been for the Dorian

colony of Tarentum, the southern coast of Italy would have been entirely

occupied by a group of Achaean cities. Tarentum (whether or no founded

by pre-Dorian Greeks--its founders bore the unexplained name of

Partheniae) became a Laconian colony at some unknown date, whence a

legend grew up connecting the Partheniae with Sparta, and 707 B.C. was

assigned as its traditional date. Tarentum is remarkable as the only

foreign settlement made by the Spartans. It was industrial, depending

largely on the purple and pottery trade. Ionian Greeks fleeing from

foreign invasion founded Siris about 650 B.C., and, much later, Elea

(540).

The Italian colonies were planted among friendly, almost kindred, races,

and grew much more rapidly than the Sicilian Greek states, which had to

contend against the power of Carthage. After the Achaean cities had

combined to destroy the Ionic Siris, and had founded Metapontum as a

counterpoise to the Dorian Tarentum, there seems to have been little

strife among the Italiotes. An amphictyonic league, meeting in common

rites at the temple of Hera on the Lacinian promontory, fostered a

feeling of unity among them. The Pythagorean and Eleatic systems of

philosophy had their chief seat in Magna Graecia. Other departments of

literature do not seem to have been so much cultivated among them. The

poet Ibycus, though a native of Rhegium, led a very wandering life. They

sent competitors to the Olympic games (among them the famous Milo of

Croton); and the physicians of Croton early in the 6th century

(especially in the person of Democedes) were reputed the best in Greece;

but politically they appear to have generally kept themselves separate.

One ship of Croton, however, fought at Salamis, though it is not

recorded that Greece asked the Italiotes for help when it sent

ambassadors to Gelon of Syracuse. Mutual discord first sapped the

prosperity of Magna Graecia. In 510 Croton, having defeated the

Sybarites in a great battle, totally destroyed their city. Croton

maintained alone the leading position which had belonged jointly to the

Achaean cities (Diod. xiv. 103); but from that time Magna Graecia

steadily declined. In the war between Athens and Syracuse Magna Graecia

took comparatively little part; Locri was strongly anti-Athenian, but

Rhegium, though it was the headquarters of the Athenians in 427,

remained neutral in 415. Foreign enemies pressed heavily on it. The

Lucanians and Bruttians on the north captured one town after another.

Dionysius of Syracuse attacked them from the south; and after he

defeated the Crotoniate league and destroyed Caulonia (389 B.C.),

Tarentum remained the only powerful city. Henceforth the history of

Magna Graecia is only a record of the vicissitudes of Tarentum (q.v.).

Repeated expeditions from Sparta and Epirus tried in vain to prop up the

decaying Greek states against the Lucanians and Bruttians; and when in

282 the Romans appeared in the Tarentine Gulf the end was close at hand.

The aid which Pyrrhus brought did little good to the Tarentines, and his

final departure in 274 left them defenceless. During these constant wars

the Greek cities had been steadily decaying; and in the second Punic

war, when most of them seized the opportunity of revolting from Rome,

their very existence was in some cases annihilated. Malaria increased in

strength as the population diminished. We are told by Cicero (_De am._

4), _Magna Graecia nunc quidem deleta est_. Many of the cities

completely disappeared, and hardly any of them were of great importance

under the Roman empire; some, like Tarentum, maintained their existence

into modern times, and in these only (except at Locri) have

archaeological investigations of any importance been carried on; so that

there still remains a considerable field for investigation. (T. As.)

FOOTNOTE:

[1] This passage should perhaps be referred to the 8th century B.C.

It is the first mention of an Italian place in a literary record.

MAGNATE (Late Lat. _magnas_, a great man), a noble, a man in high

position, by birth, wealth or other qualities. The term is specifically

applied to the members of the Upper House in Hungary, the _Förendihaz_

or House of Magnates (see HUNGARY).

MAGNES (_c._ 460 B.C.), Athenian writer of the Old Comedy, a native of

the deme of Icaria in Attica. His death is alluded to by Aristophanes

(_Equites_, 518-523, which was brought out in 424 B.C.), who states that

in his old age Magnes had lost the popularity which he had formerly

enjoyed. The few titles of his plays that remain, such as the _Frogs_,

the _Birds_, the _Gall-flies_, indicate that he anticipated Aristophanes

in introducing grotesque costumes for the chorus.

See T. Kock, _Comicorum atticorum fragmenta_, i. (1880); G. H. Bode,

_Geschichte der hellenischen Dichtkunst_, iii. pt. 2 (1840).

MAGNESIA, in ancient geography the name of two cities in Asia Minor and

of a district in eastern Thessaly, lying between the Vale of Tempe and

the Pagasaean Gulf.

(1) MAGNESIA AD MAEANDRUM, a city of Ionia, situated on a small stream

flowing into the Maeander, 15 Roman miles from Miletus and rather less

from Ephesus. According to tradition, reinforced by the similarity of

names, it was founded by colonists from the Thessalian tribe of the

Magnetes, with whom were associated, according to Strabo, some Cretan

settlers (Magnesia retained a connexion with Crete, as inscriptions

found there attest). It was thus not properly an Ionic city, and for

this reason, apparently, was not included in the Ionian league, though

superior in wealth and prosperity to most of the members except Ephesus

and Miletus. It was destroyed by the Cimmerii in their irruption into

Asia Minor, but was soon after rebuilt, and gradually recovered its

former prosperity. It was one of the towns assigned by Artaxerxes to

Themistocles for support in his exile, and there the latter ended his

days. His statue stood in its market-place. Thibron, the Spartan,

persuaded the Magnesians to leave their indefensible and mutinous city

in 399 B.C. and build afresh at Leucophrys, an hour distant, noted for

its temple of Artemis Leucophryne, which, according to Strabo, surpassed

that at Ephesus in the beauty of its architecture, though inferior in

size and wealth. Its ruins were excavated by Dr K. Humann for the

Constantinople Museum in 1891-1893; but most of the frieze of the temple

of Artemis Leucophryne, representing an Amazon battle, had already been

carried off by Texier (1843) to the Louvre. It was an octostyle,

pseudo-dipteral temple of highly ornate Ionic order, built on older

foundations by Hermogenes of Alabanda at the end of the 3rd century B.C.

The platform has been greatly overgrown since the excavation, but many

bases, capitals, and other architectural members are visible. In front

of the west façade stood a great altar. An immense _peribolus_ wall is

still standing (20 ft. high), but its Doric colonnade has vanished. The

railway runs right through the precinct, and much of Magnesia has gone

into its bridges and embankments. South and west of the temple are many

other remains of the Roman city, including a fairly perfect theatre

excavated by Hiller von Gärtringen, and the shell of a large gymnasium.

Part of the Agora was laid open to Humann, but his trenches have fallen

in. The site is so unhealthy that even the Circassians who settled there

twenty years ago have almost all died off or emigrated. Magnesia

continued under the kings of Pergamum to be one of the most flourishing

cities in this part of Asia; it resisted Mithradates in 87 B.C., and was

rewarded with civic freedom by Sulla; but it appears to have greatly

declined under the Roman empire, and its name disappears from history,

though on coins of the time of Gordian it still claimed to be the

seventh city of Asia.

See K. Haumann, _Magnesia am Maeander_ (1904).

(2) MAGNESIA AD SIPYLUM (mod. _Manisa_, q.v.), a city of Lydia about 40

m. N.E. of Smyrna on the river Hermus at the foot of Mt Sipylus. No

mention of the town is found till 190 B.C., when Antiochus the Great was

defeated under its walls by the Roman consul L. Scipio Asiaticus. It

became a city of importance under the Roman dominion and, though nearly

destroyed by an earthquake in the reign of Tiberius, was restored by

that emperor and flourished through the Roman empire. It was one of the

few towns in this part of Asia Minor which remained prosperous under the

Turkish rule. The most famous relic of antiquity is the "Niobe of

Sipylus" (_Suratlu Tash_) on the lowest slopes of the mountain about 4

m. east of the town. This is a colossal seated image cut in a niche of

the rock, of "Hittite" origin, and perhaps that called by Pausanias the

"very ancient statue of the Mother of the Gods," carved by Broteas, son

of Tantalus, and sung by Homer. Near it lie many remains of a primitive

city, and about half a mile east is the rock-seat conjecturally

identified with Pausanias' "Throne of Pelops." There are also hot

springs and a sacred grotto of Apollo. The whole site seems to be that

of the early "Tantalus" city. (D. G. H.)

MAGNESITE, a mineral consisting of magnesium carbonate, MgCO3, and

belonging to the calcite group of rhombohedral carbonates. It is rarely

found in crystals or crystalline masses, being usually compact or earthy

and intermixed with more or less hydrous magnesium silicate

(meerschaum). The compact material has the appearance of unglazed

porcelain, and the earthy that of chalk. In colour it is usually dead

white, sometimes yellowish. The hardness of the crystallized mineral is

4; sp. gr. 3.1. The name magnesite as originally applied by J. C.

Delamétherie in 1797 included several minerals containing magnesium, and

at the present day it is used by French writers for meerschaum. The

mineral has also been called baudisserite from the locality Baudissero

near Ivrea in Piedmont. Breunnerite is a ferriferous variety.

Magnesite is a product of alteration of magnesium silicates, and

occurs as veins and patches in serpentine, talc-schist or

dolomite-rock. It is extensively mined in the island of Euboea in the

Grecian Archipelago, near Salem in Madras, and in California, U.S.A.

It is principally used for the manufacture of highly refractory

fire-bricks for lining steel furnaces and electric furnaces; also for

making plaster, tiles and artificial stone; for the preparation of

magnesium salts (Epsom salts, &c.); for whitening; paper-pulp and

wool; and as a paint.

MAGNESIUM [symbol Mg, atomic weight 24.32 (O = 16)], a metallic chemical

element. The sulphate or "Epsom salts" (q.v.) was isolated in 1695 by N.

Grew, while in 1707 M. B. Valentin prepared _magnesia alba_ from the

mother liquors obtained in the manufacture of nitre. Magnesia was

confounded with lime until 1755, when J. Black showed that the two

substances were entirely different; and in 1808 Davy pointed out that it

was the oxide of a metal, which, however, he was not able to isolate.

Magnesium is found widely distributed in nature, chiefly in the forms of

silicate, carbonate and chloride, and occurring in the minerals olivine,

hornblende, talc, asbestos, meerschaum, augite, dolomite, magnesite,

carnallite, kieserite and kainite. The metal was prepared (in a state

approximating to purity) by A. A. B. Bussy (_Jour. de pharm._ 1829, 15,

p. 30; 1830, 16, p. 142), who fused the anhydrous chloride with

potassium; H. Sainte Claire Deville's process, which used to be employed

commercially, was essentially the same, except that sodium was

substituted for potassium (_Comptes rendus_, 1857, 44, p. 394), the

product being further purified by redistillation. It may also be

prepared by heating a mixture of carbon, oxide of iron and magnesite to

bright redness; and by heating a mixture of magnesium ferrocyanide and

sodium carbonate, the double cyanide formed being then decomposed by

heating it with metallic zinc. Electrolytic methods have entirely

superseded the older methods. The problem of magnesium reduction is in

many respects similar to that of aluminium extraction, but the lightness

of the metal as compared, bulk for bulk, with its fused salts, and the

readiness with which it burns when exposed to air at high temperatures,

render the problem somewhat more difficult.

Moissan found that the oxide resisted reduction by carbon in the

electric furnace, so that electrolysis of a fusible salt of the metal

must be resorted to. Bunsen, in 1852, electrolysed fused magnesium

chloride in a porcelain crucible. In later processes, carnallite (a

natural double chloride of magnesium and potassium) has commonly,

after careful dehydration, been substituted for the single chloride.

Graetzel's process, which was at one time employed, consisted in

electrolysing the chloride in a metal crucible heated externally, the

crucible itself forming the cathode, and the magnesium being deposited

upon its inner surface. W. Borchers also used an externally heated

metal vessel as the cathode; it is provided with a supporting collar

or flange a little below the top, so that the upper part of the vessel

is exposed to the cooling influence of the air, in order that a crust

of solidified salt may there be formed, and so prevent the creeping of

the electrolyte over the top. The carbon anode passes through the

cover of a porcelain cylinder, open at the bottom, and provided with a

side-tube at the top to remove the chlorine formed during

electrolysis. The operation is conducted at a dull red heat (about

760° C. or 1400° F.), the current density being about 0.64 amperes per

sq. in. of cathode surface, and the pressure about 7 volts. The

fusing-point of the metal is about 730° C. (1350° F.), and the

magnesium is therefore reduced in the form of melted globules which

gradually accumulate. At intervals the current is interrupted, the

cover removed, and the temperature of the vessel raised considerably

above the melting-point of magnesium. The metal is then removed from

the walls with the aid of an iron scraper, and the whole mass poured

into a sheet-iron tray, where it solidifies. The solidified chloride

is then broken up, the shots and fused masses of magnesium are picked

out, run together in a plumbago crucible without flux, and poured into

a suitable mould. Smaller pieces are thrown into a bath of melted

carnallite and pressed together with an iron rod, the bath being then

heated until the globules of metal float to the top, when they may be

removed in perforated iron ladles, through the holes in which the

fused chloride can drain away, but through which the melted magnesium

cannot pass by reason of its high surface tension. The globules are

then re-melted. F. Oettel (_Zeit. f. Elektrochem._, 1895, 2, p. 394)

recommends the electrolytic preparation from carnallite; the mineral

should be freed from water and sulphates.

Magnesium is a silvery white metal possessing a high lustre. It is

malleable and ductile. Sp. gr. 1.75. It preserves its lustre in dry air,

but in moist air it becomes tarnished by the formation of a film of

oxide. It melts at 632.7° C. (C. T. Heycock and F. H. Neville), and

boils at about 1100°C. Magnesium and its salts are diamagnetic. It burns

brilliantly when heated in air or oxygen, or even in carbon dioxide,

emitting a brilliant white light and leaving a residue of magnesia, MgO.

The light is rich in the violet and ultra-violet rays, and consequently

is employed in photography. The metal is also used in pyrotechny. It

also burns when heated in a current of steam, which it decomposes with

the liberation of hydrogen and the formation of magnesia. At high

temperatures it acts as a reducing agent, reducing silica to silicon,

boric acid to boron, &c. (H. Moissan, _Comptes rendus_, 1892, 114, p.

392). It combines directly with nitrogen, when heated in the gas, to

form the nitride Mg3N2 (see ARGON). It is rapidly dissolved by dilute

acids, with the evolution of hydrogen and the formation of magnesium

salts. It precipitates many metals from solutions of their salts.

_Magnesium Oxide_, magnesia, MgO, occurs native as the mineral

periclase, and is formed when magnesium burns in air; it may also be

prepared by the gentle ignition of the hydroxide or carbonate. It is a

non-volatile and almost infusible white powder, which slowly absorbs

moisture and carbon dioxide from air, and is readily soluble in dilute

acids. On account of its refractory nature, it is employed in the

manufacture of crucibles, furnace linings, &c. It is also used in

making hydraulic cements. A crystalline form was obtained by M.

Houdard (_Abst. J. C. S._, 1907, ii. p. 621) by fusing the oxide and

sulphide in the electric furnace. _Magnesium hydroxide_ Mg(OH)2,

occurs native as the minerals brucite and némalite, and is prepared by

precipitating solutions of magnesium salts by means of caustic soda or

potash. An artificial brucite was prepared by A. de Schulten (_Comptes

rendus_, 1885, 101, p. 72) by boiling magnesium chloride with caustic

potash and allowing the solution to cool. Magnesium hydroxide is a

white amorphous solid which is only slightly soluble in water; the

solubility is, however, greatly increased by ammonium salts. It

possesses an alkaline reaction and absorbs carbon dioxide. It is

employed in the manufacture of cements.

When magnesium is heated in fluorine or chlorine or in the vapour of

bromine or iodine there is a violent reaction, and the corresponding

halide compounds are formed. With the exception of the fluoride, these

substances are readily soluble in water and are deliquescent. The

fluoride is found native as sellaïte, and the bromide and iodide occur

in sea water and in many mineral springs. The most important of the

halide salts is the _chloride_ which, in the hydrated form, has the

formula MgCl2·6H2O. It may be prepared by dissolving the metal, its

oxide, hydroxide, or carbonate in dilute hydrochloric acid, or by

mixing concentrated solutions of magnesium sulphate and common salt,

and cooling the mixture rapidly, when the less soluble sodium

sulphate separates first. It is also formed as a by-product in the

manufacture of potassium chloride from carnallite. The hydrated salt

loses water on heating, and partially decomposes into hydrochloric

acid and magnesium oxychlorides. To obtain the anhydrous salt, the

double magnesium ammonium chloride, MgCl2·NH4Cl·6H2O, is prepared by

adding ammonium chloride to a solution of magnesium chloride. The

solution is evaporated, and the residue strongly heated, when water

and ammonium chloride are expelled, and anhydrous magnesium chloride

remains. Magnesium chloride readily forms double salts with the

alkaline chlorides. A strong solution of the chloride made into a

thick paste with calcined magnesia sets in a few hours to a hard,

stone-like mass, which contains an oxychloride of varying composition.

Magnesium oxychloride when heated to redness in a current of air

evolves a mixture of hydrochloric acid and chlorine and leaves a

residue of magnesia, a reaction which is employed in the

Weldon-Pechiney and Mond processes for the manufacture of chlorine.

_Magnesium Carbonate,_ MgCO3.--The normal salt is found native as the

mineral magnesite, and in combination with calcium carbonate as

dolomite, whilst hydromagnesite is a basic carbonate. It is not

possible to prepare the normal carbonate by precipitating magnesium

salts with sodium carbonate. C. Marignac has prepared it by the action

of calcium carbonate on magnesium chloride. A salt MgCO3·3H2O or

Mg(CO3H)(OH)·2H2O may be prepared from the carbonate by dissolving it

in water charged with carbon dioxide, and then reducing the pressure

(W. A. Davis, _Jour. Soc. Chem. Ind._ 1906, 25, p. 788). The carbonate

is not easily soluble in dilute acids, but is readily soluble in water

containing carbon dioxide. _Magnesia alba_, a white bulky precipitate

obtained by adding sodium carbonate to Epsom salts, is a mixture of

Mg(CO3H)(OH)·2H2O, Mg(CO3H)(OH) and Mg(OH)2. It is almost insoluble in

water, but readily dissolves in ammonium salts.

_Magnesium Phosphates._--By adding sodium phosphate to magnesium

sulphate and allowing the mixture to stand, hexagonal needles of

MgHPO4·7H2O are deposited. The _normal phosphate_, Mg3P2O8, is found

in some guanos, and as the mineral wagnerite. It may be prepared by

adding normal sodium phosphate to a magnesium salt and boiling the

precipitate with a solution of magnesium sulphate. It is a white

amorphous powder, readily soluble in acids. _Magnesium ammonium

phosphate_, MgNH4PO4·6H2O, is found as the mineral struvite and in

some guanos; it occurs also in urinary calculi and is formed in the

putrefaction of urine. It is prepared by adding sodium phosphate to

magnesium sulphate in the presence of ammonia and ammonium chloride.

When heated to 100° C., it loses five molecules of water of

crystallization, and at a higher temperature loses the remainder of

the water and also ammonia, leaving a residue of magnesium

pyrophosphate, Mg2P2O7. _Magnesium Nitrate_, Mg(NO3)2·6H2O, is a

colourless, deliquescent, crystalline solid obtained by dissolving

magnesium or its carbonate in nitric acid, and concentrating the

solution. The crystals melt at 90° C. _Magnesium Nitride_, Mg3N2, is

obtained as a greenish-yellow amorphous mass by passing a current of

nitrogen or ammonia over heated magnesium (F. Briegleb and A. Geuther,

_Ann._, 1862, 123, p. 228; see also W. Eidmann and L. Moeser, _Ber._,

1901, 34, p. 390). When heated in dry oxygen it becomes incandescent,

forming magnesia. Water decomposes it with liberation of ammonia and

formation of magnesium hydroxide. The chlorides of nickel, cobalt,

chromium, iron and mercury are converted into nitrides when heated

with it, whilst the chlorides of copper and platinum are reduced to

the metals (A. Smits, _Rec. Pays Bas_, 1896, 15, p. 135). _Magnesium

sulphide_, MgS, may be obtained, mixed with some unaltered metal and

some magnesia, as a hard brown mass by heating magnesia, in sulphur

vapour. It slowly decomposes in moist air. _Magnesium sulphate_,

MgSO4, occurs (with IH2O) as Kieserite. A hexahydrate is also known.

The salt may be obtained from Kieserite: formerly it was prepared by

treating magnesite or dolomite with sulphuric acid.

Grignard Reagent.

_Organic Compounds._--By heating magnesium filings with methyl and

ethyl iodides A. Cahours (_Ann. chim. phys._, 1860, 58, pp. 5, 19)

obtained magnesium methyl, Mg(CH3)2, and magnesium ethyl, Mg(C2H5)2,

as colourless, strongly smelling, mobile liquids, which are

spontaneously inflammable and are readily decomposed by water. The

compounds formed by the action of magnesium on alkyl iodides in the

cold have been largely used in synthetic organic chemistry since V.

Grignard (_Comptes rendus_, 1900 et seq.) observed that magnesium and

alkyl or aryl halides combined together in presence of anhydrous ether

at ordinary temperatures (with the appearance of brisk boiling) to

form compounds of the type RMgX(R = an alkyl or aryl group and X =

halogen). These compounds are insoluble in ether, are non-inflammable

and exceedingly reactive. A. V. Baeyer (_Ber._, 1902, 35, p. 1201)

regards them as oxonium salts containing tetravalent oxygen

(C2H5)2:O:(MgR) (X), whilst W. Tschelinzeff (_Ber._, 1906, 39, p. 773)

considers that they contain two molecules of ether. In preparing the

Grignard reagent the commencement of the reaction is accelerated by a

trace of iodine. W. Tschelinzeff (_Ber._, 1904, 37, p. 4534) showed

that the ether may be replaced by benzene containing a small quantity

of ether or anisole, or a few drops of a tertiary amine. With

unsaturated alkyl halides the products are only slightly soluble in

ether, and two molecules of the alkyl compound are brought into the

reaction. They are very unstable, and do not react in the normal

manner. (V. Grignard and L. Tissier, _Comptes rendus_, 1901, 132, p.

558).

The products formed by the action of the Grignard reagent with the

various types of organic compounds are usually thrown out of solution

in the form of crystalline precipitates or as thick oils, and are then

decomposed by ice-cold dilute sulphuric or acetic acids, the magnesium

being removed as a basic halide salt.

_Applications._--For the formation of primary and secondary alcohols

see ALDEHYDES and KETONES. Formaldehyde behaves abnormally with

magnesium benzyl bromide (M. Tiffeneau, _Comptes rendus_, 1903, 137,

p. 573). forming ortho-tolylcarbinol, CH3·C6H4·CH2OH, and not

benzylcarbinol, C6H5CH2·CH2OH (cf. the reaction of formaldehyde on

phenols: O. Manasse, _Ber._ 1894, 27, p. 2904). Acid esters yield

carbinols, many of which are unstable and readily pass over into

unsaturated compounds, especially when warmed with acetic anhydride:

R·CO2R´(R´´)2·R·:C·OMgX -> (R´´)2R·:C·OH.

Formic ester yields a secondary alcohol under similar conditions. Acid

chlorides behave in an analogous manner to esters (Grignard and

Tissier, _Comptes rendus_, 1901, 132, p. 683). Nitriles yield ketones

(the nitrogen being eliminated as ammonia), the best yields being

given by the aromatic nitriles (E. Blaise, ibid., 1901, 133, p. 1217):

R·CN -> RR´:C:NMgI -> R·CO·R´. Acid amides also react to form ketones

(C. Béis, ibid., 1903, 137, 575):

R·CONH2 -> RR´:C(OMgX)·NHMgX + R´H -> R·CO·R´;

the yield increases with the complexity of the organic residue of the

acid amide. On passing a current of dry carbon dioxide over the

reagent, the gas is absorbed and the resulting compound, when

decomposed by dilute acids, yields an organic acid, and similarly with

carbon oxysulphide a thio-acid is obtained:

RMgX -> R·CO2MgX -> R·CO2H; COS -> CS(OMgX)·R -> R·CSOH.

A. Klages (_Ber._, 1902, 35, pp. 2633 et seq.) has shown that if one

uses an excess of magnesium and of an alkyl halide with a ketone, an

ethylene derivative is formed. The reaction appears to be perfectly

general unless the ketone contains two ortho-substituent groups.

Organo-metallic compounds can also be prepared, for example

SnBr4 + 4MgBrC6H5 = 4MgBr2 + Sn(C6H5)4.

For a summary see A. McKenzie, _B. A. Rep._ 1907.

_Detection._--The magnesium salts may be detected by the white

precipitate formed by adding sodium phosphate (in the presence of

ammonia and ammonium chloride) to their solutions. The same reaction

is made use of in the quantitative determination of magnesium, the

white precipitate of magnesium ammonium phosphate being converted by

ignition into magnesium pyrophosphate and weighed as such. The atomic

weight of magnesium has been determined by many observers. J.

Berzelius (_Ann. chim. phys._, 1820, 14, p. 375), by converting the

oxide into the sulphate, obtained the value 12.62 for the equivalent.

R. F. Marchand and T. Scheerer (_Jour. prakt. Chem._, 1850, 50, p.

358), by ignition of the carbonate, obtained the value 24.00 for the

atomic weight, whilst C. Marignac, by converting the oxide into the

sulphate, obtained the value 24.37. T. W. Richards and H. G. Parker

(_Zeit. anorg. Chem._, 1897, 13, p. 81) have obtained the value 24.365

(O = 16).

_Medicine._--These salts of magnesium may be regarded as the typical

_saline purgatives_. Their aperient action is dependent upon the minimum

of irritation of the bowel, and is exercised by their abstraction from

the blood of water, which passes into the bowel to act as a diluent of

the salt. The stronger the solution administered, the greater is the

quantity of water that passes into the bowel, a fact to be borne in mind

when the salt is administered for the purpose of draining superfluous

fluid from the system, as in dropsy. The oxide and carbonate of

magnesium are also invaluable as antidotes, since they form insoluble

compounds with oxalic acid and salts of mercury, arsenic, and copper.

The result is to prevent the local corrosive action of the poison and to

prevent absorption of the metals. As alkaloids are insoluble in alkaline

solutions, the oxide and carbonate--especially the former--may be given

in alkaloidal poisoning. The compounds of magnesium are not absorbed

into the blood in any appreciable quantity, and therefore exert no

remote actions upon other functions. This is fortunate, as the result of

injecting a solution of a magnesium salt into a vein is rapid poisoning.

Hence it is of the utmost importance to avoid the use of salts of this

metal whenever it is necessary--as in diabetic coma--to increase the

alkalinity of the blood rapidly. The usual doses of the oxide and

carbonate of magnesium are from half a drachm to a drachm.

MAGNETISM. The present article is a digest, mainly from an experimental

standpoint, of the leading facts and principles of magnetic science. It

is divided into the following sections:

1. General Phenomena.

2. Terminology and Elementary Principles.

3. Magnetic Measurements.

4. Magnetization in Strong Fields.

5. Magnetization in Weak Fields.

6. Changes of Dimensions attending Magnetization.

7. Effects of Mechanical Stress on Magnetization.

8. Effects of Temperature on Magnetism.

9. Magnetic Properties of Alloys and Compounds of Iron.

10. Miscellaneous Effects of Magnetization:--Electric

Conductivity--Hall Effect--Electro-Thermal Relations--Thermo-electric

Quality--Elasticity--Chemical and Voltaic Effects.

11. Feebly Susceptible Substances.

12. Molecular Theory of Magnetism.

13. Historical and Chronological Notes.

Of these thirteen sections, the first contains a simple description of

the more prominent phenomena, without mathematical symbols or numerical

data. The second includes definitions of technical terms in common use,

together with so much of the elementary theory as is necessary for

understanding the experimental 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 ordinary textbooks. The

subjects discussed in the remaining sections are sufficiently indicated

by their respective headings. (See also ELECTROMAGNETISM, TERRESTRIAL

MAGNETISM, MAGNETO-OPTICS and UNITS.)

1. GENERAL PHENOMENA

Pieces of a certain highly esteemed iron ore, which consists mainly of

the oxide Fe3O4, are sometimes found to possess the power of attracting

small fragments of iron or steel. Ore endowed with this curious property

was well known to the ancient Greeks and Romans, who, because it

occurred plentifully in the district of Magnesia near the Aegean coast,

gave it the name of _magnes_, or the _Magnesian stone_. In

English-speaking countries the ore is commonly known as _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 branch of science which has been evolved from

the study of phenomena associated with the magnet.

If a magnet is dipped into a mass of iron filings and withdrawn, filings

cling to certain parts of the stone in moss-like tufts, other parts

remaining bare. There are generally two regions where the tufts are

thickest, and the attraction therefore greatest, and between them is a

zone in which no attraction is evidenced. The regions of greatest

attraction have received the name of _poles_, and the line joining them

is called the _axis_ of the magnet; the space around a magnet in which

magnetic effects are exhibited is called the _field of magnetic force_,

or the _magnetic field_.

Up to the end of the 15th 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 compass, which is said to

have been known to the Chinese as early as 1100 B.C., though it was not

introduced into Europe until more than 2000 years later; a magnet

supported so that its axis is free to turn in a horizontal plane will

come to rest with its poles pointing approximately north and south. The

other phenomenon is mentioned by Greek and 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 form of steel is

now always used for making artificial magnets. Magnetism may be imparted

to a bar of hardened steel by stroking it several times from end to

end, always in the same direction, with one of the poles of a magnet.

Until 1820 all the artificial magnets in practical use derived their

virtue, directly or indirectly, from the natural magnets found in the

earth: it is now recognized that the source of all magnetism, not

excepting that of the magnetic ore itself, is electricity, and it is

usual to have direct recourse to electricity for producing

magnetization, without the intermediary of the magnetic ore. A wire

carrying an electric current is surrounded by a magnetic field, and if

the wire is bent into the form of an elongated coil or 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 combination constitutes an

_electromagnet_, a valuable 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 engineering 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 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 interest except as a scientific curiosity.

Some of the principal phenomena of magnetism may be demonstrated with

very little apparatus; much may be done with a small bar-magnet, a

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

knitting or sewing needles and pieces of flat spring, may be readily

magnetized by stroking them 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 needle is a little steel magnet

balanced upon a pivot; one end of the needle, which always bears a

distinguishing mark, points approximately, but not in general exactly,

to the north,[1] the vertical plane through the direction of the needle

being termed the _magnetic meridian_. The bar-magnet, if suspended

horizontally in a paper stirrup by a thread of unspun 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 pole_ and the other end the _south pole_; in

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 action will not be sensibly affected by

the interposition between the bar and the compass of any substance

whatever except iron or other magnetizable 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 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

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

difficulty was overcome by C. A. Coulomb, who by using very 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 standard of reference in terms of which the strength of a pole

may be numerically specified. According to the recognized convention,

the unit pole is that which acts upon an equal pole at unit distance

with unit force: a north pole is reckoned as 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.

[Illustration: FIG. 1.]

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

induction, that end of it which is nearest to the pole of the magnet

acquiring opposite 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 flux_, a physical 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 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 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 sheet of cardboard is placed above the magnet, and some iron

filings are sifted thinly and evenly over the surface: if the cardboard

is gently tapped, the filings will arrange themselves in a series of

curves, as shown in fig. 1. This experiment suggested to 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 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 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 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 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 eye by the scattered filings are

too vague and 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. Lay the compass upon the

cardboard, and observe the rate at which its needle vibrates after being

displaced from its position of 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 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 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 body such as

iron is ultimately due. This was pointed out by W. Thomson (afterwards

Lord 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 part of the field which happens to

be 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 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 settle with its axis in a

horizontal position, but would come to rest with its north-seeking pole

either higher or 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 angle which the

magnetic axis makes with the plane of the horizon is called the

_inclination_ or _dip._ Along an irregular line encircling the earth in

the neighbourhood of the geographical 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 area in the

Arctic Circle (about 97° W. long., 70° N. 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 Antarctic Circle (148° E.

long., 74° 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. 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 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 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 Greenwich in 1910 was about

67°. It is by the horizontal component of the earth's 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 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 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 evidence of magnetization; if, however, the wire is twisted,

poles will be developed at the two ends, for reasons which will be

explained later. A wire or 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 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 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 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 process of magnetization

consists in turning 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 cork and floated upon 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 balance before and after magnetization, no change whatever in

its 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. Nickel and cobalt are also strongly

magnetic, and in 1903 the interesting discovery was made by F. Heusler

that an alloy consisting of copper, aluminium and 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 gap. The

maximum magnetic susceptibility of iron is half a million times greater

than that of liquid oxygen, one of the strongest paramagnetic substances

known. 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 influence of magnetism. On the other hand, the

magnetic properties of a substance are affected by such causes as

mechanical stress and changes of temperature. An account of some of

these effects will be found in another section.[2]

2. TERMINOLOGY AND ELEMENTARY PRINCIPLES

In what follows the C.G.S. electromagnetic 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 symbol is to be attended

to, it is usual to employ for the symbol either a block letter, as H,

I, B, or a German capital, as [H], [F], [B].[3]

_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 m1 and m2 are the strengths of two poles, d the distance

between them expressed in centimetres, and f the force in dynes,

[f] = m1m2/d² (1).

The force is one of attraction or repulsion, according as the sign of

the product m1m2 is negative or positive. The poles at the ends of an

infinitely thin uniform magnet, or _magnetic filament_, would 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 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 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 attention to the fact that it is

a vector quantity, by the block letter H, or the German character [H].

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.[4] 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 radius r through which current

is passing is

H = 2[pi]i/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 wound coil

containing n turns of wire and having a length of l centimetres is

(except near the ends)

H = 4[pi]in/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 2[pi]r, and the field inside

the coil may be expressed as

H = 2ni/r. (5)

The uniformity of the field is not in this 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 be large in

relation to that of the convolutions, or the ring should have the form

of a short 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 [M], 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 l 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 _intensity of magnetization_,

or, more shortly, the _magnetization_ of a uniformly magnetized body

is defined as the magnetic moment per unit of volume, and is denoted

by I, I, or [I]. 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 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 an angle [epsilon] with the normal, the

normal component of the magnetization, I cos [epsilon], is called the

_surface density_ of the magnetism, and is generally denoted by

[sigma].

_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-ordinate axes and n the line along which the force

is directed, then

[delta]V [delta]V [delta]V/ [delta]V

- -------- = F, - -------- = X, - --------- = Y, - -------- = Z. (6)

[delta]n [delta]x [delta]y [delta]z

Surfaces for which the potential is 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 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 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 [theta] and [theta]´ with the axis, it is easily shown

that the equation to a line of force is

cos [theta] - cos [theta]´ = constant. (9)

[Illustration: FIG. 2.]

[Illustration: FIG. 3.]

At the point where a line of force intersects the perpendicular

bisector of the axis r = r´ = r0, say, and cos [theta] - cos [theta]´

obviously = l/r0, l being the distance between the poles; l/r0 is

therefore the value of the constant in (9) 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 [theta]/r², (10)

where [theta] 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

[delta]V M

X = - -------- = --- (3 cos² [theta] - 1),

[delta]x r³

[delta]V M

Y = - -------- = --- (3 sin [theta] cos [theta]). (11)

[delta]y r³

If F_r is the force along r and F_t that along t at right angles to r,

M

F_r = X cos [theta] + Y sin [theta] = --- 2 cos [theta], (12)

r³

M

F_t = -X sin [theta] + Y cos [theta] = --- sin [theta], (13)

r³

For the resultant force at P,

M

F = [root](F_r² + F_t²) = --- [root](3 cos² [theta] + 1). (14)

r³

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, [theta] = 0; therefore cos [theta] = 1,

and the point D coincides with C; the magnitude of the force is, from

(14),

F_x = 2M/r³, (15)

its direction being along the axis OX. For a point in the line OY

bisecting the magnet perpendicularly, [theta] = [pi]/2 therefore cos

[theta] = 0, and the point D is at an infinite distance. The magnitude

of the force is in this case

F_y = M/r³, (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.

[Illustration: FIG. 4.]

_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 [theta], (17)

where [theta] 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 [theta] and [phi] 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 [phi], is

MM´(sin [theta] cos [phi] - 2 sin [phi] cos [theta])/r³. (18)

This vanishes if sin [theta] cos [phi] = 2 sin [phi] cos [theta],

i.e. if tan [phi] = ½ tan [theta], 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´, [theta] = 0, and the

couple becomes

2MM´ sin [phi]/r³, (19)

tending to diminish [phi]; this is called the "end on" position. If

the centre of S´N´ is on the perpendicular bisector of SN, [theta] =

½[pi], and the couple will be

MM´ cos [phi]/r³, (20)

tending to increase [phi]; this is the "broadside on" position. These

two positions are sometimes called the first and second (or A and B)

principal positions of 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 [theta] sin [phi] - 2 cos [theta] cos [phi])/r^4, (21)

Y = 3MM´(sin [theta] cos [phi] + sin [phi] cos [theta])/r^4. (22)

It will be seen that, whereas the couple varies inversely as the cube

of the distance, the force varies inversely as the 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 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 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

shell_; the constant product hI is the _strength_ of the shell and is

generally denoted by [Phi] or [phi]. The potential at any point due to

a magnetic shell is the product of its strength into the solid angle

[omega] subtended by its edge at the given point, or V = [Phi][omega].

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 sphere (which is an 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 = (4/3)[pi] a³I cos [theta]/r², (23)

[theta] being the inclination of r to the magnetic axis. Since

(4/3)[pi]a³I is the moment of the sphere (= volume × 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 to the direction of magnetization, and equal to

(4/3)[pi]I. 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 major axis, and the lengths of the major and minor axes are 2a and

2c, the poles are situated at a distance equal to (2/3)a from the

centre, and the magnet will behave externally like a simple solenoid

of length (4/3)a. 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 = (4/3)[pi] ac²I =

-(4/3)[pi] ac²FN.

The 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.[5] According to F.

W. G. Kohlrausch[6] the distance between the poles of a cylindrical

magnet the length of which is from 10 to 30 times the 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.[7] 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 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 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 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 1 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

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 crevasse cut in the body, the walls of the

crevasse being 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

[B]) is briefly called the _induction_, or, especially by electrical

engineers, the _flux-density_. The direction of magnetic induction may

be indicated by _lines of induction_; a line of induction is always a

closed curve, though it may possibly extend to and return from

infinity. Lines of induction drawn through every point in the contour

of a small surface form a re-entrant 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

special meaning has been assigned to the term "lines of induction."

Suppose 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 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 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 factor of proportionality

will be 1-4[pi], so that

I = (B - H)/4[pi], (24)

or

B = H + 4[pi] I. (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 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 absence of the magnetized metal. The

intensity (at any point) of the field due to the magnetization may be

denoted by H_i, that of the external field by H0, 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_.

_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 µ. The ratio I/H is called the _susceptibility_ of

the magnetized substance, and is denoted by [kappa]. Hence

B = µH and I = [kappa]H. (26)

Also

B H + 4[pi]I

µ = --- = ---------- = 1 + 4[pi][kappa], (27)

H H

and

µ - 1

[kappa] = ----- (28)

4[pi]

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 1 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 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 [kappa] expresses the numerical relation

of the magnetization to the magnetizing force. From the equation

[kappa] = (µ - 1)/4[pi], it follows that the magnetic susceptibility

of a vacuum (where µ = l) is 0, that of a diamagnetic substance (where

µ < l) has a negative value, while the susceptibility of paramagnetic

and ferromagnetic substances (for which µ > 1) is positive. No

substance has yet been discovered having a negative susceptibility

sufficiently great to render the permeability (= 1 + 4[pi][kappa])

negative.

_Magnetic 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 good

and bad conductors. Just as the lines of flow of an electric current

all pass in closed curves through the 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-motive

force, to the electromotive force in the circuit. The principal points

of difference are that (1) the magnetic permeability, unlike the

electric conductivity, which is 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 relating

to the distribution of magnetic induction may be solved by methods

similar to those employed for the solution of analogous problems in

electricity. For the elementary theory of the magnetic circuit see

ELECTRO-MAGNETISM.

_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. Ewing (_Phil. Trans._ clxxvi. 524) has given the name of

_hysteresis_ (Gr. [Greek: hystereô], to lag behind). Thus it happens

that there is no definite relation between the magnetization of a

piece of metal which has been previously magnetized and the strength

of the field in which it is placed. Much depends upon its antecedent

magnetic condition, and indeed upon its whole magnetic history. A

well-known example of hysteresis is presented by the case of permanent

magnets. If a bar of hard steel is placed in a strong magnetic field,

a certain intensity of magnetization is induced in the bar; but when

the strength of the field is afterwards reduced to zero, the

magnetization does not entirely disappear. That portion which is

permanently retained, and which may amount to considerably more than

one-half, is called the _residual magnetization_. The ratio of the

residual magnetization to its previous maximum value measures the

_retentiveness_, or _retentivity_, of the metal.[8] Steel, which is

well suited for the construction of permanent magnets, is said to

possess great "coercive force." To this term, which had long been used

in a loose and indefinite manner, J. Hopkinson supplied a precise

meaning (_Phil. Trans._ clxxvi. 460). The _coercive force_, or

_coercivity_, of a material is that reversed magnetic force which,

while it is acting, just suffices to reduce the residual induction to

nothing after the material has been temporarily submitted to any great

magnetizing force. A metal which has great retentiveness may at the

same time have small coercive force, and it is the latter quality

which is of chief importance in permanent magnets.

_Demagnetizing Force._--It has already been mentioned that when a

ferromagnetic body is placed in a magnetic field, the resultant

magnetic force H, at a point within the body, is compounded of the

force H0, due to the external field, and of another force, H_i,

arising from the induced magnetization of the body. Since H_i

generally tends to oppose the external force, thus making H less than

H0, it may be called the _demagnetizing force_. Except in the few

special cases when a uniform external field produces uniform

magnetization, the value of the demagnetizing force cannot be

calculated, and an exact determination of the actual magnetic force

within the body is therefore impossible. An important instance in

which the calculation can be made is that of an elongated _ellipsoid

of revolution_ placed in a uniform field H0, with its axis of

revolution parallel to the lines of force. The magnetization at any

point inside the ellipsoid will then be

[kappa]H0

I = ------------ (29)

1 + [kappa]N

where

/ 1 \ / 1 1 + e \

N = 4[pi]( --- - 1 ) ( --- log ----- ),

\ e2 / \ 2e 1 - e /

e being the eccentricity (see Maxwell's _Treatise_, § 438). Since I =

[kappa]H, we have

[kappa]H + [kappa]NI = [kappa]H0, (30)

or

H = H0 - NI,

NI being the demagnetizing force H_i. N may be called, after H. du

Bois (_Magnetic Circuit_, p. 33), the _demagnetizing factor_, and the

ratio of the length of the ellipsoid 2c to its equatorial diameter 2a

(= c/a), the _dimensional ratio_, denoted by the symbol [m].

Since e = [root](1 - a²/c²) = [root](1 - 1/[m]²),

the above expression for N may be written

4[pi] / [m] [m] + [root]([m]² - 1) \

N = -------- ( ------------------ log ---------------------- - 1 )

[m]² - 1 \ 2 [root]([m]² - 1) [m] - [root]([m]² - 1) /

_ _

4[pi] | [m] / \ |

= -------- | ---------------- log ( [m] + [root]([m]² - 1) ) - 1 |,

[m]² - 1 |_ [root]([m]² - 1) \ / _|

from which the value of N for a given dimensional ratio can be

calculated. When the ellipsoid is so much elongated that 1 is

negligible in relation to [m]², the expression approximates to the

simpler form

4[pi]

N = ----- (log 2[m] - 1). (31)

[m]²

In the case of a _sphere_, e = O and N = (4/3)[pi]; therefore from

(29)

[kappa]H0 3[kappa]

I = [kappa]H = -------------------- = ---------------- H0, (32)

1 + (4/3)[pi][kappa] 3 + 4[pi][kappa]

Whence

3 3

H = ---------------- H0 = ----- H0, (33)

3 + 4[pi][kappa] µ + 2

and

3µ

B = µH = ----- H0. (34)

µ + 2

Equations (33) and (34) show that when, as is generally the case with

ferromagnetic substances, the value of µ is considerable, the

resultant magnetic force is only a small fraction of the external

force, while the numerical value of the induction is approximately

three times that of the external force, and nearly independent of the

permeability. The demagnetizing force inside a _cylindrical rod_

placed longitudinally in a uniform field H0 is not uniform, being

greatest at the ends and least in the middle part. Denoting its mean

value by [H]_i, and that of the demagnetizing factor by [N], we have

H = H0 - [H]_i = H0 - [N]I. (35)

Du Bois has shown that when the dimensional ratio [m] (=

length/diameter) exceeds 100, [N][m]² = constant = 45, and hence for

long thin rods

[N] = 45/[m]². (36)

From an analysis of a number of experiments made with rods of

different dimensions H. du Bois has deduced the corresponding mean

demagnetizing factors. These, together with values of [m]²[N] for

cylindrical rods, and of N and [m]²N for ellipsoids of revolution, are

given in the following useful table (_loc. cit._ p. 41):--

_Demagnetizing Factors._

+------+--------------------+-------------------+

| | Cylinder. | Ellipsoid. |

| [m]. +----------+---------+----------+--------+

| | [N]. | [m]²[N].| N. | [m]²N. |

+------+----------+---------+----------+--------+

| 0 | 12.5664 | 0 | 12.5664 | 0 |

| 0.5 | -- | -- | 6.5864 | -- |

| 1 | -- | -- | 4.1888 | -- |

| 5 | -- | -- | 0.7015 | -- |

| 10 | 0.2160 | 21.6 | 0.2549 | 25.5 |

| 15 | 0.1206 | 27.1 | 0.1350 | 30.5 |

| 20 | 0.0775 | 31.0 | 0.0848 | 34.0 |

| 25 | 0.0533 | 33.4 | 0.0579 | 36.2 |

| 30 | 0.0393 | 35.4 | 0.0432 | 38.8 |

| 40 | 0.0238 | 38.7 | 0.0266 | 42.5 |

| 50 | 0.0162 | 40.5 | 0.0181 | 45.3 |

| 60 | 0.0118 | 42.4 | 0.0132 | 47.5 |

| 70 | 0.0089 | 43.7 | 0.0101 | 49.5 |

| 80 | 0.0069 | 44.4 | 0.0080 | 51.2 |

| 90 | 0.0055 | 44.8 | 0.0065 | 52.5 |

| 100 | 0.0045 | 45.0 | 0.0054 | 54.0 |

| 150 | 0.0020 | 45.0 | 0.0026 | 58.3 |

| 200 | 0.0011 | 45.0 | 0.0016 | 64.0 |

| 300 | 0.00050 | 45.0 | 0.00075 | 67.5 |

| 400 | 0.00028 | 45.0 | 0.00045 | 72.0 |

| 500 | 0.00018 | 45.0 | 0.00030 | 75.0 |

| 1000 | 0.00005 | 45.0 | 0.00008 | 80.0 |

+------+--------------------+-------------------+

In the middle part of a rod which has a length of 400 or 500 diameters

the effect of the ends is insensible; but for many experiments the

condition of endlessness may be best secured by giving the metal the

shape of a ring of uniform section, the magnetic field being produced

by an electric current through a coil of wire evenly wound round the

ring. In such cases H_i = 0 and H = H0.

The residual magnetization I_r retained by a bar of ferromagnetic

metal after it has been removed from the influence of an external

field produces a demagnetizing force [N]I_r, which is greater the

smaller the dimensional ratio. Hence the difficulty of imparting any

considerable permanent magnetization to a short thick bar not

possessed of great coercive force. The magnetization retained by a

long thin rod, even when its coercive force is small, is sometimes

little less than that which was produced by the direct action of the

field.

_Demagnetization by Reversals._--In the course of an experiment it is

often desired to eliminate the effects of previous magnetization, and,

as far as possible, wipe out the magnetic history of a specimen. In

order to attain this result it was formerly the practice to raise the

metal to a bright red heat, and allow it to cool while carefully

guarded from magnetic influence. This operation, besides being very

troublesome, was open to the objection that it was almost sure to

produce a material but uncertain change in the physical constitution

of the metal, so that, in fact, the results of experiments made before

and after the treatment were not comparable. Ewing introduced the

method (_Phil. Trans._ clxxvi. 539) of demagnetizing a specimen by

subjecting it to a succession of magnetic forces which alternated in

direction and gradually diminished in strength from a high value to

zero. By means of a simple arrangement, which will be described

farther on, this process can be carried out in a few seconds, and the

metal can be brought as often as desired to a definite condition,

which, if not quite identical with the virgin state, at least closely

approximates to it.

_Forces acting on a Small Body in the Magnetic Field._--If a small

magnet of length ds and pole-strength m is brought into a magnetic

field such that the values of the magnetic potential at the negative

and positive poles respectively are V1 and V2, the work done upon the

magnet, and therefore its potential energy, will be

W = m(V2 - V1) = m dV,

which may be written

dV dV

W = m ds -- = M -- = -MH0 = -vIH0,

ds ds

where M is the moment of the magnet, v the volume, I the

magnetization, and H0 the magnetic force along _ds_. The small magnet

may be a sphere rigidly magnetized in the direction of H0; if this is

replaced by an isotropic sphere inductively magnetized by the field,

then, for a displacement so small that the magnetization of the sphere

may be regarded as unchanged, we shall have

[kappa]

dW = -vI dH0 = -v -------------------- H0 dH0;

1 + (4/3)[pi][kappa]

whence

v [kappa]

W = - --- -------------------- H^2_0. (37)

2 1 + (4/3)[pi][kappa]

The mechanical force acting on the sphere in the direction of

displacement x is

dW [kappa] dH^2_0

F = - -- = v -------------------- ------. (38)

dx 1 + (4/3)[pi][kappa] dx

If H0 is constant, the force will be zero; if H0 is variable, the

sphere will tend to move in the direction in which H0 varies most

rapidly. The coefficient [kappa]/(1 + (4/3)[pi][kappa]) is positive

for ferromagnetic and paramagnetic substances, which will therefore

tend to move from weaker to stronger parts of the field; for all known

diamagnetic substances it is negative, and these will tend to move

from stronger to weaker parts. For small bodies other than spheres the

coefficient will be different, but its sign will always be negative

for diamagnetic substances and positive for others;[9] hence the

forces acting on any small body will be in the same directions as in

the case of a sphere.[10]