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| committer | nfenwick <nfenwick@pglaf.org> | 2025-03-07 19:45:20 -0800 |
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diff --git a/43060-0.txt b/43060-0.txt new file mode 100644 index 0000000..96706ed --- /dev/null +++ b/43060-0.txt @@ -0,0 +1,20411 @@ +*** START OF THE PROJECT GUTENBERG EBOOK 43060 *** + +Transcriber's notes: + +(1) Numbers following letters (without space) like C2 were originally + printed in subscript. Letter subscripts are preceded by an + underscore, like C_n. + +(2) Characters following a carat (^) were printed in superscript. + +(3) Side-notes were relocated to function as titles of their respective + paragraphs. + +(4) Macrons and breves above letters and dots below letters were not + inserted. + +(5) [root] stands for the root symbol; [alpha], [beta], etc. for greek + letters. + +(6) The following typographical errors have been corrected: + + ARTICLE MADISON, JAMES: "On the 26th of December 1785 Jefferson's + Bill for establishing religious freedom in Virginia, which had been + introduced by Madison, was passed. In the Virginia House of + Delegates, as in the Continental Congress ..." 'Virginia' amended + from 'Viginia'. + + ARTICLE MADRAS: "... the college of agriculture at Coimbatore; the + teachers' college at Saidapet; the school of arts at Madras; and + the military orphanage at Ootacamund, in memory of Sir Henry + Lawrence." 'orphanage' amended from 'ophanage'. + + ARTICLE MAGNETISM: "... the ratio of magnetization to magnetizing + force remained sensibly constant at 6.4, which may therefore with + great probability be assumed to represent the initial value ..." + 'which' amended from 'wihch'. + + ARTICLE MAGNETISM: "From experiments of both classes it appears + that for a given field there is a certain value of the load for + which the magnetization is a maximum, the maximum occurring at a + smaller load the stronger the field." 'occurring' amended from + 'occuring'. + + ARTICLE MAGNETISM: "Recent researches have shown that other + important changes in its properties occur at the same critical + temperature." 'important' amended from 'imporant'. + + ARTICLE MAGNETISM: "Wills found that the susceptibility was + constant in fields ranging from 4200 to 15,000." 'susceptibility' + amended from 'suceptibility'. + + ARTICLE MAGNETISM, TERRESTRIAL: "As explained above, a would + represent the range in a year of no sun-spots, while 100 b would + represent the excess over this shown by the range in a year when + Wolf's sun-spot frequency is 100." "Wolf's" amended from + "Wolfer's". + + + + + ENCYCLOPAEDIA BRITANNICA + + A DICTIONARY OF ARTS, SCIENCES, LITERATURE + AND GENERAL INFORMATION + + ELEVENTH EDITION + + + VOLUME XVII, SLICE III + + McKinley, William to Magnetism, Terrestrial + + + + +ARTICLES IN THIS SLICE: + + + McKINLEY, WILLIAM MADISON (Wisconsin, U.S.A.) + McKINNEY (Texas, U.S.A.) MADOU, JEAN BAPTISTE + MACKINTOSH, SIR JAMES MADOZ, PASCUAL + MACKLIN, CHARLES MADRAS (Indian presidency) + MACK VON LEIBERICH, KARL MADRAS (Indian city) + McLANE, LOUIS MADRAZO Y KUNT, DON FEDERICO DE + MACLAREN, CHARLES MADRID (province of Spain) + MACLAREN, IAN MADRID (the capital of Spain) + MACLAURIN, COLIN MADRIGAL + M'LENNAN, JOHN FERGUSON MADURA (island) + MACLEOD, HENRY DUNNING MADURA (city) + MACLEOD, NORMAN MADVIG, JOHAN NICOLAI + MACLISE, DANIEL MAECENAS, GAIUS + MACLURE, WILLIAM MAECIANUS, LUCIUS VOLUSIUS + MacMAHON, MARIE EDMÉ MAURICE DE MAELDUIN, VOYAGE OF + McMASTER, JOHN BACH MAELIUS, SPURIUS + MACMILLAN MAELSTROM + MACMONNIES, FREDERICK WILLIAM MAENADS + MACNAGHTEN, SIR WILLIAM HAY MAENIUS, GAIUS + MacNALLY, LEONARD MAERLANT, JACOB VAN + MACNEE, SIR DANIEL MAES, NICOLAS + MACNEIL, HERMON ATKINS MAESTRO + McNEILE, HUGH MAETERLINCK, MAURICE + MACNEILL, HECTOR MAFEKING + MACOMB MAFFEI, FRANCESCO SCIPIONE + MACOMER MAFIA + MACON, NATHANIEL MAFRA + MÂCON (town of France) MAGADHA + MACON (Georgia, U.S.A.) MAGALDÁN + MACPHERSON, SIR DAVID LEWIS MAGALLANES + MACPHERSON, JAMES MAGAZINE + McPHERSON, JAMES BIRDSEYE MAGDALA + MACQUARIE MAGDEBURG + MACRAUCHENIA MAGEE, WILLIAM + MACREADY, WILLIAM CHARLES MAGEE, WILLIAM CONNOR + MACROBIUS, AMBROSIUS THEODOSIUS MAGELLAN, FERDINAND + MACROOM MAGELLANIC CLOUDS + MACUGNAGA MAGENTA + MacVEAGH, WAYNE MAGGIORE, LAGO + MADÁCH, IMRE MAGIC + MADAGASCAR MAGIC SQUARE + MADAN, MARTIN MAGINN, WILLIAM + MADDALONI MAGISTRATE + MADDEN, SIR FREDERIC MAGLIABECHI, ANTONIO DA MARCO + MADDER MAGLIANI, AGOSTINO + MADEC, RENÉ-MARIE MAGNA CARTA + MADEIRA MAGNA GRAECIA + MADELENIAN MAGNATE + MADELEY MAGNES + MADHAVA ACHARYA MAGNESIA + MADI MAGNESITE + MADISON, JAMES MAGNESIUM + MADISON (Indiana, U.S.A.) MAGNETISM + MADISON (New Jersey, U.S.A.) MAGNETISM, TERRESTRIAL + + + + +McKINLEY, WILLIAM (1843-1901), twenty-fifth president of the United +States, was born in Niles, Trumbull county, Ohio, on the 29th of January +1843. His ancestors on the paternal side were Scotch-Irish who lived at +Dervock, Co. Antrim, and spelled the family name "McKinlay." His +great-great-grandfather settled in York county, Pennsylvania, about +1743, and from Chester county, Pennsylvania, his great-grandfather, +David McKinley, who served as a private during the War of Independence, +moved to Ohio in 1814. David's son James had gone in 1809 to Columbiana +county, Ohio. His son William McKinley (b. 1807), like his father an +iron manufacturer, was married in 1829 to Nancy Campbell Allison, and to +them were born nine children, of whom William, the president, was the +seventh. In 1852 the family removed to Poland, Mahoning county, where +the younger William was placed at school. At seventeen he entered the +junior class of Allegheny College, at Meadville, Pennsylvania; but he +studied beyond his strength, and returned to Poland, where for a time he +taught in a neighbouring country school. When the Civil War broke out in +1861 he promptly enlisted as a private in the 23rd Ohio Volunteer +Infantry. He saw service in West Virginia, at South Mountain, where this +regiment lost heavily, and at Antietam, where he brought up hot coffee +and provisions to the fighting line; for this he was promoted second +lieutenant on the 24th of September 1862. McKinley was promoted first +lieutenant in February 1864, and for his services at Winchester was +promoted captain on the 25th of July 1864. He was on the staff of +General George Crook at the battles of Opequan, Fisher's Hill, and Cedar +Creek in the Shenandoah valley, and on the 14th of March 1865 was +brevetted major of volunteers for gallant and meritorious services. He +also served on the staff of General Rutherford B. Hayes, who spoke +highly of his soldierly qualities. He was mustered out with his regiment +on the 26th of July 1865. Four years of army life had changed him from a +pale and sickly lad into a man of superb figure and health. + +After the war McKinley returned to Poland, and bent all his energy upon +the study of law. He completed his preparatory reading at the Albany +(N.Y.) law school, and was admitted to the bar at Warren, Ohio, in March +1867. On the advice of an elder sister, who had been for several years a +teacher in Canton, Stark county, Ohio, he began his law practice in that +place, which was to be his permanent home. He identified himself +immediately with the Republican party, campaigned in the Democratic +county of Stark in favour of negro suffrage in 1867, and took part in +the campaign work on behalf of Grant's presidential candidature in 1868. +In the following year he was elected prosecuting attorney on the +Republican ticket; in 1871 he failed of re-election by 45 votes, and +again devoted himself to his profession, while not relaxing his interest +in politics. + +In 1875 he first became known as an able campaign speaker by his +speeches favouring the resumption of specie payments, and in behalf of +Rutherford B. Hayes, the Republican candidate for governor of Ohio. In +1876 he was elected by a majority of 3304 to the national House of +Representatives. Conditions both in Ohio and in Congress had placed him, +and were to keep him for twenty years, in an attitude of aggressive and +uncompromising partisanship. His Congressional district was naturally +Democratic, and its boundaries were changed two or three times by +Democratic legislatures for the purpose of so grouping Democratic +strongholds as to cause his defeat. But he overcame what had threatened +to be adverse majorities on all occasions from 1876 to 1890, with the +single exception of 1882, when, although he received a certificate of +election showing that he had been re-elected by a majority of 8, and +although he served nearly through the long session of 1883-1884, his +seat was contested and taken (May 28, 1884) by his Democratic opponent, +Jonathan H. Wallace. McKinley reflected the strong sentiment of his +manufacturing constituency in behalf of a high protective tariff, and he +soon became known in Congress (where he particularly attracted the +attention of James G. Blaine) as one of the most diligent students of +industrial policy and question affecting national taxation. In 1878 he +took part in the debates over the Wood Tariff Bill, proposing lower +import duties; and in the same year he voted for the Bland-Allison +Silver Bill. In December 1880 he was appointed a member of the Ways and +Means committee, succeeding General James A. Garfield, who had been +elected president in the preceding month, and to whose friendship, as to +that of Rutherford B. Hayes, McKinley owed much in his earlier years in +Congress. He was prominent in the debate which resulted in the defeat of +the Democratic Morrison Tariff Bill in 1884, and, as minority leader of +the Ways and Means committee, in the defeat of the Mills Bill for the +revision of the tariff in 1887-1888. In 1889 he became chairman of the +Ways and Means committee and Republican leader in the House of +Representatives, after having been defeated by Thomas B. Reed on the +third ballot in the Republican caucus for speaker of the House. On the +16th of April 1890 he introduced from the Ways and Means committee the +tariff measure known commonly as the McKinley Bill, which passed the +House on the 21st of May, passed the Senate (in an amended form, with a +reciprocity clause, which McKinley had not been able to get through the +House) on the 10th of September, was passed as amended, by the House, +and was approved by the president on the 1st of October 1890. The +McKinley Bill reduced revenues by its high and in many cases almost +prohibitive duties; it put sugar on the free list with a discriminating +duty of (1/10)th of one cent a pound on sugar imported from countries +giving a bounty for sugar exported, and it gave bounties to American +sugar growers; it attempted to protect many "infant" industries such as +the manufacture of tin-plate; under its provision for reciprocal trade +agreements (a favourite project of James G. Blaine, who opposed many of +the "protective" features of the Bill) reciprocity treaties were made +with Germany, France, Italy, and Belgium, which secured a market in +those countries for American pork. Abroad, where the Bill made +McKinley's name known everywhere, there was bitter opposition to it and +reprisals were threatened by several European states. In the United +States the McKinley Tariff Bill was one of the main causes of the +Democratic victory in the Congressional elections of 1890, in which +McKinley himself was defeated by an extraordinary Democratic gerrymander +of his Congressional district. In November 1891 he was elected governor +of Ohio with a plurality of more than 21,000 votes in a total of 795,000 +votes cast. He was governor of Ohio in 1892-1895, being re-elected in +1893. His administration was marked by no important events, except that +he had on several occasions in his second term to call out the militia +of the state to preserve order; but it may be considered important +because of the training it gave him in executive as distinguished from +legislative work. + +McKinley had been prominent in national politics even before the passage +of the tariff measure bearing his name. In 1888 in the National +Republican Convention in Chicago he was chairman of the committee on +resolutions (i.e. the platform committee) and was leader of the +delegation from Ohio, which had been instructed for John Sherman; after +James G. Blaine withdrew his name there was a movement, begun by +Republican congressmen, to nominate McKinley, who received 16 votes on +the seventh ballot, but passionately refused to be a candidate, +considering that his acquiescence would be a breach of faith toward +Sherman. In 1892 McKinley was the permanent president of the National +Republican Convention which met in Minneapolis and which renominated +Benjamin Harrison on the first ballot, on which James G. Blaine received +182(5/6) votes, and McKinley, in spite of his efforts to the contrary, +received 182 votes. In 1894 he made an extended campaign tour before the +Congressional elections, and spoke even in the South. In 1896 he seemed +for many reasons the most "available" candidate of his party for the +presidency: he had no personal enemies in the party; he had carried the +crucial state of Ohio by a large majority in 1893; his attitude on the +coinage question had never been so pronounced as to make him unpopular +either with the radical silver wing or with the conservative +"gold-standard" members of the party. The campaign for his nomination +was conducted with the greatest adroitness by his friend, Marcus A. +Hanna, and in the National Republican Convention held in St Louis in +June he was nominated for the presidency on the first ballot by 661½ out +of a total of 906 votes. The convention adopted a tariff plank drafted +by McKinley, and, of far greater immediate importance, a plank, which +declared that the Republican party was "opposed to the free coinage of +silver, except by international agreement with the leading commercial +nations of the world, which we pledge ourselves to promote, and until +such agreement can be obtained the existing gold standard must be +preserved." This "gold standard" plank drove out of the Republican party +the Silver Republicans of the West, headed by Senator Henry M. Teller of +Colorado. The Republican convention nominated for the vice-presidency +Garrett A. Hobart of New Jersey. The National Democratic Convention +declared for the immediate opening of the mints to the free and +unlimited coinage of silver at the ratio with gold of 16 to 1; and it +nominated for the presidency William Jennings Bryan of Nebraska, who +also received the nomination of the People's party and of the National +Silver party. There was a secession from the Democratic party of +conservatives who called themselves the National Democratic party, who +were commonly called Gold Democrats, and who nominated John M. Palmer +(1817-1900) of Illinois for president. In this re-alignment of parties +McKinley, who had expected to make the campaign on the issue of a high +protective tariff, was diverted to the defence of the gold standard as +the main issue. While his opponent travelled throughout the country +making speeches, McKinley remained in Canton, where he was visited by +and addressed many Republican delegations. The campaign was +enthusiastic: the Republican candidate was called the "advance agent of +prosperity"; "Bill McKinley and the McKinley Bill" became a campaign +cry; the panic of 1893 was charged to the repeal of the McKinley tariff +measure; and "business men" throughout the states were enlisted in the +cause of "sound money" to support McKinley, who was elected in November +by a popular vote of 7,106,779 to 6,502,925 for Bryan, and by an +electoral vote of 271 to 176. + +McKinley was inaugurated president of the United States on the 4th of +March 1897. The members of his cabinet were: secretary of state, John +Sherman (whose appointment created a vacancy in the Senate to which +Marcus A. Hanna was elected), who was succeeded in April 1898 by William +R. Day, who in turn was followed in September 1898 by John Hay; +secretary of the treasury, Lyman J. Gage, a Gold Democrat; secretary of +war, Russell A. Alger, who was succeeded in 1899 by Elihu Root; +secretary of the navy, John D. Long; attorney-general, Joseph McKenna, +succeeded in January 1898 by John William Griggs; postmaster-general, +James A. Gary, succeeded in April 1898 by Charles Emory Smith; secretary +of the interior, Cornelius N. Bliss, succeeded in February 1899 by Ethan +Allen Hitchcock; and secretary of agriculture, James Wilson. (For the +political history of McKinley's administration see UNITED STATES: +_History_). Immediately after his inauguration the president summoned +Congress to assemble in an extra session on the 15th of March. The +Democratic tariff in 1893 had been enacted as part of the general +revenue measure, which included an income-tax. The income-tax having +been declared unconstitutional by the Supreme Court, the measure had +failed to produce a sufficient revenue, and it had been necessary to +increase the public debt. McKinley's message to the new Congress dwelt +upon the necessity of an immediate revision of the tariff and revenue +system of the country, and the so-called Dingley Tariff Bill was +accordingly passed through both houses, and was approved by the +president on the 24th of July. + +The regular session of Congress which opened in December was occupied +chiefly with the situation in Cuba. President McKinley showed himself +singularly patient and self-controlled in the midst of the popular +excitement against Spain and the clamour for intervention by the United +States in behalf of the Cubans; but finally, on the 23rd of March, he +presented an ultimatum to the Spanish government, and on the 25th of +April, on his recommendation. Congress declared war upon Spain. During +the war itself he devoted himself with great energy to the mastery of +military details; but there was bitter criticism of the war department +resulting in the resignation of the secretary of war, Russell A. Alger +(q.v.). The signing of a peace protocol on the 12th of August was +followed by the signature at Paris on the 10th of December of articles +of peace between the United States and Spain. After a long discussion +the peace treaty was ratified by the United States Senate on the 6th of +February 1899; and in accordance with its terms Porto Rico, the +Philippine Archipelago, and Guam were transferred by Spain to the United +States, and Cuba came under American jurisdiction pending the +establishment there of an independent government. Two days before the +ratification of the peace treaty, a conflict took place between armed +Filipinos under the leadership of Emilio Aguinaldo and the American +forces that were in possession of Manila. The six months that had +elapsed between the signing of the peace protocol and the ratification +of the treaty had constituted a virtual interregnum, Spain's authority +having been practically destroyed in the Philippines and that of the +United States not having begun. In this period a formidable native +Filipino army had been organized and a provisional government created. +The warfare waged by these Filipinos against the United States, while +having for the most part a desultory and guerilla character, was of a +very protracted and troublesome nature. Sovereignty over the Filipinos +having been accepted by virtue of the ratification of the Paris treaty, +President McKinley was not at liberty to do otherwise than assert the +authority of the United States and use every endeavour to suppress the +insurrection. But there was bitter protest against this "imperialism," +both within the party by such men as Senators George F. Hoar and Eugene +Hale, and Thomas B. Reed and Carl Schurz, and, often for purely +political reasons, from the leaders of the Democratic party. In the +foreign relations of the United States, as directed by President +McKinley, the most significant change was the cordial understanding +established with the British government, to which much was contributed +by his secretary of state, John Hay, appointed to that portfolio when he +was ambassador to the court of St James, and which was due to some +extent to the friendliness of the British press and even more markedly +of the British navy in the Pacific during the Spanish War. Other +important foreign events during McKinley's administration were: the +annexation of the Hawaiian Islands (see HAWAII) in August 1898, and the +formation of the Territory of Hawaii in April 1900; the cessation in +1899 of the tripartite (German, British, and French) government of the +Samoan Islands, and the annexation by the United States of those of the +islands east of 171°, including the harbour of Pago-Pago; the +participation of American troops in the march of the allies on Pekin in +August 1900, and the part played by McKinley's secretary of state, John +Hay, in securing a guarantee of the integrity of the Chinese empire. In +1900 McKinley was unanimously renominated by the National Republican +Convention which met in Philadelphia on the 19th of June, and which +nominated Theodore Roosevelt, governor of New York, for the +vice-presidency. The Republican convention demanded the maintenance of +the gold standard, and pointed to the fulfilment of some of the most +important of the pledges given by the Republican party four years +earlier. The intervening period had been one of very exceptional +prosperity in the United States, foreign commerce having reached an +unprecedented volume, and agriculture and manufactures having made +greater advancement than in any previous period of the country's +history. The tendency towards the concentration of capital in great +industrial corporations had been active to an extent previously undreamt +of, with incidental consequences that had aroused much apprehension; and +the Democrats accused President McKinley and the Republican party of +having fostered the "trusts." But the campaign against McKinley and the +Republican party was not only "anti-trust" but "anti-imperialistic." +William Jennings Bryan, renominated by the Democratic party in July (and +in May by the Fusion People's party) on a free silver platform, declared +that imperialism was the "paramount issue" and made a second vigorous +campaign; and the opposition to McKinley's re-election, whether based on +opposition to his economic or to his foreign policy, was not entirely +outside of his own party. As the result of the polling in November, 292 +Republican presidential electors were chosen, and 155 Democratic +electors, elected in Colorado, Idaho, Montana, Nevada, and the Southern +states, represented the final strength of the Bryan and Stevenson +ticket. The Republican popular vote was 7,207,923, and the Democratic +6,358,133. Since 1872 no president had been re-elected for a second +consecutive term. + +In the term of Congress immediately following the presidential election +it was found possible to reduce materially the war taxes which had been +levied on the outbreak of the Spanish-American War. Arrangements were +perfected for the termination of the American military occupation of +Cuba and the inauguration of a Cuban Republic as a virtual protectorate +of the United States, the American government having arranged with the +Cuban constitutional convention for the retention of certain naval +stations on the Cuban coast. In the Philippines advanced steps had been +taken in the substitution of civil government for military occupation, +and a governor-general, Judge William H. Taft, had been appointed and +sent to Manila. Prosperity at home was great, and foreign relations were +free from complications. The problems which had devolved upon McKinley's +administration had been far advanced towards final settlement. He +retained without change the cabinet of his first administration. After +an arduous and anxious term, the president had reached a period that +promised to give him comparative repose and freedom from care. He had +secured, through the co-operation of Congress, the permanent +reorganization of the army and a very considerable development of the +navy. In these circumstances. President McKinley, accompanied by the +greater part of his cabinet, set forth in the early summer on a tour to +visit the Pacific coast, where he was to witness the launching of the +battleship "Ohio" at San Francisco. The route chosen was through the +Southern states, where many stops were made, and where the president +delivered brief addresses. The heartiness of the welcome accorded him +seemed to mark the disappearance of the last vestige of sectional +feeling that had survived the Civil War, in which McKinley had +participated as a young man. After his return he spent a month in a +visit at his old home in Canton, Ohio, and at the end of this visit, by +previous arrangement, he visited the city of Buffalo, New York, in order +to attend the Pan-American exposition and deliver a public address. This +address (Sept. 5, 1901) was a public utterance designed by McKinley to +affect American opinion and public policy, and apparently to show that +he had modified his views upon the tariff. It declared that henceforth +the progress of the nations must be through harmony and co-operation, in +view of the fast-changing conditions of communication and trade, and it +maintained that the time had come for wide-reaching modifications in the +tariff policy of the United States, the method preferred by McKinley +being that of commercial reciprocity arrangements with various nations. +On the following day, the 6th of September 1901, a great reception was +held for President McKinley in one of the public buildings of the +exposition, all sorts and conditions of men being welcome. Advantage of +this opportunity was taken by a young man of Polish parentage, by name +Leon Czolgosz, to shoot at the president with a revolver at close range. +One of the two bullets fired penetrated the abdomen. After the world had +been assured that the patient was doing well and would recover, he +collapsed and died on the 14th. The assassin, who, it was for a time +supposed, had been inflamed by the editorials and cartoons of the +demagogic opposition press, but who professed to hold the views of that +branch of anarchists who believe in the assassination of rulers and +persons exercising political authority, was promptly seized, and was +convicted and executed in October 1901. McKinley's conduct and +utterances in his last days revealed a loftiness of personal character +that everywhere elicited admiration and praise. Immediately after his +death Vice-President Roosevelt took the oath of office, announcing that +it would be his purpose to continue McKinley's policy, while also +retaining the cabinet and the principal officers of the government. +McKinley's funeral took place at Canton, Ohio, on the 19th of September, +the occasion being remarkable for the public manifestations of mourning, +not only in the United States, but in Great Britain and other countries; +in Canton a memorial tomb has been erected. + +Though he had not the personal magnetism of James G. Blaine, whom he +succeeded as a leader of the Republican party and whose views of +reciprocity he formally adopted in his last public address, McKinley had +great personal suavity and dignity, and was thoroughly well liked by his +party colleagues. As a politician he was always more the people's +representative than their leader, and that he "kept his ear to the +ground" was the source of much of his power and at the same time was his +greatest weakness: his address at Buffalo the day before his +assassination seems to voice his appreciation of the change in popular +sentiment regarding the tariff laws of the United States and is the more +remarkable as coming from the foremost champion for years of a form of +tariff legislation devised to stifle international competition. His +apparently inconsistent record on the coinage question becomes +consistent if considered in the same way, as the expression of the +gradually changing views of his constituency. And it may not be fanciful +to suggest that the obvious growth of McKinley in breadth and power +during his term as president was due to his being the representative of +a larger constituency, less local and less narrow-minded. He was an able +but far from brilliant campaign speaker. His greatest administrative +gift was a fine intuition in choosing men to serve him. McKinley's +private life was irreproachable; and very fine was his devotion to his +wife, Ida Saxton (d. 1907), whom he had married in Canton in 1871, who +was throughout his political career a confirmed invalid. He was from his +early manhood a prominent member of the Methodist Episcopal Church. + + His _Speeches and Addresses_ were printed in two volumes (New York, + 1893 and 1901). + + + + +McKINNEY, a city and the county-seat of Collin county, Texas, U.S.A., +about 30 m. N. by E. of Dallas. Pop. (1890), 2489; (1900), 4342 (917 +negroes); (1910) 4714. It is served by the Missouri, Kansas & Texas and +the Houston & Texas Central railways, and by the Dallas & Sherman +inter-urban (electric) line, the central power plant of which is +immediately north of the city. McKinney is in a fine farming region; +there are also manufactures. The municipal water supply is obtained from +artesian wells. The first settlement in Collin county was made about 10 +m. north of what is now McKinney in 1841. McKinney was named, as was the +county, in honour of Collin McKinney, a pioneer in the region and a +signer of the Declaration of the Independence of Texas. It was settled +in 1844, was laid out and became the county-seat in 1846, and was first +chartered as a city in 1874. + + + + +MACKINTOSH, SIR JAMES (1765-1832), Scottish publicist, was born at +Aldourie, 7 m. from Inverness, on the 24th of October 1765. He came of +old Highland families on both sides. He went in 1780 to college at +Aberdeen, where he made a friend of Robert Hall, afterwards the famous +preacher. In 1784 he proceeded for the study of medicine to Edinburgh, +where he participated to the full in the intellectual ferment, but did +not quite neglect his medical studies, and took his degree in 1787. + +In 1788 Mackintosh removed to London, then agitated by the trial of +Warren Hastings and the king's first lapse into insanity. He was much +more interested in these and other political events than in his +professional prospects; and his attention was specially directed to the +events and tendencies which caused or preceded the Revolution in France. +In 1789 he married his first wife, Catherine Stuart, whose brother +Daniel afterwards became editor of the _Morning Post_. His wife's +prudence was a corrective to his own unpractical temperament, and his +efforts in journalism became fairly profitable. Mackintosh was soon +absorbed in the question of the time; and in April 1791, after long +meditation, he published his _Vindiciae Gallicae_, a reply to Burke's +_Reflections on the French Revolution_. It was the only worthy answer to +Burke that appeared. It placed the author in the front rank of European +publicists, and won him the friendship of some of the most distinguished +men of the time, including Burke himself. The success of the _Vindiciae_ +finally decided him to give up the medical for the legal profession. He +was called to the bar in 1795, and gained a considerable reputation +there as well as a tolerable practice. In 1797 his wife died, and next +year he married Catherine Allen, sister-in-law of Josiah and John +Wedgwood, through whom he introduced Coleridge to the _Morning Post_. As +a lawyer his greatest public efforts were his lectures (1799) at +Lincoln's Inn on the law of nature and nations, of which the +introductory discourse was published, and his eloquent defence (1803) of +Jean Gabriel Peltier, a French refugee, tried at the instance of the +French government for a libel against the first consul. In 1803 he was +knighted, and received the post of recorder at Bombay. The spoilt child +of London society was not at home in India, and he was glad to return to +England, where he arrived in 1812. + +He courteously declined the offer of Perceval to resume political life +under the auspices of the dominant Tory party, though tempting prospects +of office in connexion with India were opened up. He entered parliament +in the Whig interest as member for Nairn. He sat for that county, and +afterwards for Knaresborough, till his death. In London society, and in +Paris during his occasional visits, he was a recognized favourite for +his genial wisdom and his great conversational power. On Mme de Stael's +visit to London he was the only Englishman capable of representing his +country in talk with her. His parliamentary career was marked by the +same wide and candid liberalism as his private life. He opposed the +reactionary measures of the Tory government, supported and afterwards +succeeded Romilly in his efforts for reforming the criminal code, and +took a leading part both in Catholic emancipation and in the Reform +Bill. But he was too little of a partisan, too widely sympathetic and +candid, as well as too elaborate, to be a telling speaker in parliament, +and was consequently surpassed by more practical men whose powers were +incomparably inferior. From 1818 to 1824 he was professor of law and +general politics in the East India Company's College at Haileybury. + +In the midst of the attractions of London society and of his +parliamentary avocations Mackintosh felt that the real work of his life +was being neglected. His great ambition was to write a history of +England. His studies both in English and foreign speculation led him to +cherish the design also of making some worthy contribution to +philosophy. It was not till 1828 that he set about the first task of his +literary ambition. This was the _Dissertation on the Progress of Ethical +Philosophy_, prefixed to the seventh edition of the _Encyclopaedia +Britannica_. The dissertation, written mostly in ill-health and in +snatches of time taken from his parliamentary engagements, was published +in 1831. It was severely attacked in 1835 by James Mill in his _Fragment +on Mackintosh_. About the same time he wrote for the _Cabinet +Cyclopaedia_ a "History of England from the Earliest Times to the Final +Establishment of the Reformation." His more elaborate _History of the +Revolution_, for which he had made great researches and collections, was +not published till after his death. Already a privy councillor, +Mackintosh was appointed commissioner for the affairs of India under the +Whig administration of 1830. He died on the 30th of May 1832. + +Mackintosh was undoubtedly one of the most cultured and catholic-minded +men of his time. His studies and sympathies embraced almost every human +interest, except pure science. But the width of his intellectual +sympathies, joined to a constitutional indecision and _vis inertiae_, +prevented him from doing more enduring work. _Vindiciae Gallicae_ was +the verdict of a philosophic Liberal on the development of the French +Revolution up to the spring of 1791, and though the excesses of the +revolutionists compelled him a few years after to express his entire +agreement with the opinions of Burke, its defence of the "rights of man" +is a valuable statement of the cultured Whig's point of view at the +time. The _History of the Revolution in England_, breaking off at the +point where William of Orange is preparing to intervene in the affairs +of England, is chiefly interesting because of Macaulay's admiring essay +on it and its author. + + A _Life_, by his son R. J. Mackintosh, was published in 1836. + + + + +MACKLIN, CHARLES (c. 1699-1797), Irish actor and playwright, whose +real name was McLaughlin, was born in Ireland, and had an adventurous +youth before coming to Bristol, where he made his first appearance on +the stage as Richmond in _Richard III_. He was at Lincoln's Inn Fields +about 1725, and by 1733 was at Drury Lane, where the quarrel between the +manager and the principal actors resulted in his getting better parts. +When the trouble was over and these were taken from him, he went to the +Haymarket, but he returned in 1734 to Drury Lane and acted there almost +continuously until 1748. Then for two seasons he and his wife (d. _c._ +1758), an excellent actress, were in Dublin under Sheridan, then back in +London at Covent Garden. He played a great number of characters, +principally in comedy, although Shylock was his greatest part, and Iago +and the Ghost in _Hamlet_ were in his repertory. At the end of 1753 +Macklin bade farewell to the stage to open a tavern, near the theatre, +where he personally supervised the serving of dinner. He also delivered +an evening lecture, followed by a debate, which was soon a hopeless +subject of ridicule. The tavern failed, and Macklin returned to the +stage, and played for a number of years in London and Dublin. His quick +temper got him into constant trouble. In a foolish quarrel over a wig in +1735 he killed a fellow actor in the green-room at Drury Lane, and he +was constantly at law over his various contracts and quarrels. The +bitterest of these arose on account of his appearing as Macbeth at +Covent Garden in 1772. The part was usually played there by William +Smith, and the public would not brook a change. A few nights later the +audience refused to hear Macklin as Shylock, and shouted their wish, in +response to the manager's question, to have him discharged. This was +done in order to quell the riot. His lawsuit, well conducted by himself, +against the leaders of the disturbance resulted in an award of £600 and +costs, but Macklin magnanimously elected instead that the defendants +should take £100 in tickets at three benefits--for himself, his daughter +and the management. He returned to Covent Garden, but his appearances +thereafter were less frequent, ending in 1789, when as Shylock, at his +benefit, he was only able to begin the play, apologize for his wandering +memory, and retire. He lived until the 11th of July 1797, and his last +years were provided for by a subscription edition of two of his best +plays, _The Man of the World_ and _Love in a Maze_. Macklin's daughter, +Mary Macklin (_c._ 1734-1781), was a well-known actress in her day. + + See Edward A. Parry, _Charles Macklin_ (1891). + + + + +MACK VON LEIBERICH, KARL, FREIHERR (1752-1828), Austrian soldier, was +born at Nenslingen, in Bavaria, on the 25th of August 1752. In 1770 he +joined an Austrian cavalry regiment, in which his uncle, Leiberich, was a +squadron commander, becoming an officer seven years later. During the +brief war of the Bavarian Succession he was selected for service on the +staff of Count Kinsky, under whom, and subsequently under the +commander-in-chief Field Marshal Count Lacy, he did excellent work. He +was promoted first lieutenant in 1778, and captain on the +quartermaster-general's staff in 1783. Count Lacy, then the foremost +soldier of the Austrian army, had the highest opinion of his young +assistant. In 1785 Mack married Katherine Gabrieul, and was ennobled +under the name of Mack von Leiberich. In the Turkish war he was employed +on the headquarter staff, becoming in 1788 major and personal +aide-de-camp to the emperor, and in 1789 lieutenant-colonel. He +distinguished himself greatly in the storming of Belgrade. Shortly after +this, disagreements between Mack and Loudon, now commander-in-chief, led +to the former's demanding a court-martial and leaving the front. He was, +however, given a colonelcy (1789) and the order of Maria Theresa, and in +1790 Loudon and Mack, having become reconciled, were again on the field +together. During these campaigns Mack received a severe injury to his +head, from which he never fully recovered. In 1793 he was made +quartermaster-general (chief of staff) to Prince Josias of Saxe-Coburg, +commanding in the Netherlands; and he enhanced his reputation by the +ensuing campaign. The young Archduke Charles, who won his own first +laurels in the action of the 1st of March 1793, wrote after the battle, +"Above all we have to thank Colonel Mack for these successes." Mack +distinguished himself again on the field of Neerwinden; and had a leading +part in the negotiations between Coburg and Dumouriez. He continued to +serve as quartermaster-general, and was now made titular chief +(_Inhaber_) of a cuirassier regiment. He received a wound at Famars, but +in 1794 was once more engaged, having at last been made a major-general. +But the failure of the allies, due though it was to political and +military factors and ideas, over which Mack had no control, was ascribed +to him, as their successes of March-April 1793 had been, and he fell into +disfavour in consequence. In 1797 he was promoted lieutenant field +marshal, and in the following year he accepted, at the personal request +of the emperor, the command of the Neapolitan army. But with the +unpromising material of his new command he could do nothing against the +French revolutionary troops, and before long, being in actual danger of +being murdered by his men, he took refuge in the French camp. He was +promised a free pass to his own country, but Napoleon ordered that he +should be sent to France as a prisoner of war. Two years later he escaped +from Paris in disguise. The allegation that he broke his parole is false. +He was not employed for some years, but in 1804, when the war party in +the Austrian court needed a general to oppose the peace policy of the +Archduke Charles, Mack was made quartermaster-general of the army, with +instructions to prepare for a war with France. He did all that was +possible within the available time to reform the army, and on the opening +of the war of 1805 he was made quartermaster-general to the titular +commander-in-chief in Germany, the Archduke Ferdinand. He was the real +responsible commander of the army which opposed Napoleon in Bavaria, but +his position was ill-defined and his authority treated with slight +respect by the other general officers. For the events of the Ulm campaign +and an estimate of Mack's responsibility for the disaster, see NAPOLEONIC +CAMPAIGNS. After Austerlitz, Mack was tried by a court-martial, sitting +from February 1806 to June 1807, and sentenced to be deprived of his +rank, his regiment, and the order of Maria Theresa, and to be imprisoned +for two years. He was released in 1808, and in 1819, when the ultimate +victory of the allies had obliterated the memory of earlier disasters, he +was, at the request of Prince Schwarzenberg, reinstated in the army as +lieutenant field marshal and a member of the order of Maria Theresa. He +died on the 22nd of October 1828 at S. Pölten. + + See Schweigerd, _Oesterreichs Helden_ (Vienna, 1854); Würzbach, + _Biogr. Lexikon d. Kaiserthums Oesterr._ (Vienna, 1867); Ritter von + Rittersberg, _Biogr. d. ausgezeichneten Feldherren d. oest. Armee_ + (Prague, 1828); Raumer's _Hist. Taschenbuch_ (1873) contains Mack's + vindication. A short critical memoir will be found in _Streffleur_ for + January 1907. + + + + +McLANE, LOUIS (1786-1857), American political leader, was born in +Smyrna, Delaware, on the 28th of May 1786, son of Allan McLane +(1746-1829), a well-known Revolutionary soldier. He was admitted to the +bar in 1807. He entered politics as a Democrat, and served in the +Federal House of Representatives in 1817-1827 and in the Senate in +1827-1829. He was minister to England in 1829-1831, and secretary of the +treasury in Jackson's cabinet from 1831 (when in his annual report he +argued for the United States Bank) until May 1833, when he was +transferred to the state department. He retired from the cabinet in June +1834. He was president of the Baltimore & Ohio railway in 1837-1847, +minister to England in 1845-1846, and delegate to the Maryland +constitutional convention of 1850-1851. He died in Baltimore, Maryland, +on the 7th of October 1857. + +His son, ROBERT MILLIGAN MCLANE (1815-1898), graduated at West Point in +1837, resigned from the army in 1843, and practised law in Baltimore. He +was a Democratic representative in Congress in 1847-1851 and again in +1879-1883, governor of Maryland in 1884-1885, U.S. commissioner to China +in 1853-1854, and minister to Mexico in 1859-1860 and to France in +1885-1889. + + See R. M. McLane's _Reminiscences_, 1827-1897 (privately printed, + 1897). + + + + +MACLAREN, CHARLES (1782-1866), Scottish editor, was born at Ormiston, +Haddingtonshire, on the 7th of October 1782, the son of a farmer and +cattle-dealer. He was almost entirely self-educated, and when a young +man became a clerk in Edinburgh. In 1817, with others, he established +the _Scotsman_ newspaper in Edinburgh and at first acted as its editor. +Offered a post as clerk in the custom house, he resigned his editorial +position, resuming it in 1820, and resigning it again in 1845. In 1820 +Maclaren was made editor of the sixth edition of the _Encyclopaedia +Britannica_. From 1864-1866 he was president of the Geological Society +of Edinburgh, in which city he died on the 10th of September 1866. + + + + +MACLAREN, IAN, the pseudonym of JOHN WATSON (1850-1907), Scottish author +and divine. The son of John Watson, a civil servant, he was born at +Manningtree, Essex, on the 3rd of November 1850, and was educated at +Stirling and at Edinburgh University, afterwards studying theology at +New College, Edinburgh, and at Tübingen. In 1874 he entered the ministry +of the Free Church of Scotland and became assistant minister of Barclay +Church, Edinburgh. Subsequently he was minister at Logiealmond in +Perthshire and at Glasgow, and in 1880 he became minister of Sefton Park +Presbyterian church, Liverpool, from which he retired in 1905. In 1896 +he was Lyman Beecher lecturer at Yale University, and in 1900 he was +moderator of the synod of the English Presbyterian church. While +travelling in America he died at Mount Pleasant, Iowa, on the 6th of May +1907. Ian Maclaren's first sketches of rural Scottish life, _Beside the +Bonnie Briar Bush_ (1894), achieved extraordinary popularity and were +followed by other successful books, _The Days of Auld Lang Syne_ (1895), +_Kate Carnegie and those Ministers_ (1896) and _Afterwards and other +Stories_ (1898). Under his own name Watson published several volumes of +sermons, among them being _The Upper Room_ (1895); _The Mind of the +Master_ (1896) and _The Potter's Wheel_ (1897). + + See Sir W. Robertson Nicoll, _Ian Maclaren_ (1908). + + + + +MACLAURIN, COLIN (1698-1746), Scottish mathematician, was the son of a +clergyman, and born at Kilmodan, Argyllshire. In 1709 he entered the +university of Glasgow, where he exhibited a decided genius for +mathematics, more especially for geometry; it is said that before the +end of his sixteenth year he had discovered many of the theorems +afterwards published in his _Geometria organica_. In 1717 he was elected +professor of mathematics in Marischal College, Aberdeen, as the result +of a competitive examination. Two years later he was admitted F.R.S. and +made the acquaintance of Sir Isaac Newton. In 1719 he published his +_Geometria organica, sive descriptio linearum curvarum universalis_. In +it Maclaurin developed several theorems due to Newton, and introduced +the method of generating conics which bears his name, and showed that +many curves of the third and fourth degrees can be described by the +intersection of two movable angles. In 1721 he wrote a supplement to the +_Geometria organica_, which he afterwards published, with extensions, in +the _Philosophical Transactions_ for 1735. This paper is principally +based on the following general theorem, which is a remarkable extension +of Pascal's hexagram: "If a polygon move so that each of its sides +passes through a fixed point, and if all its summits except one describe +curves of the degrees _m_, _n_, _p_, &c., respectively, then the free +summit moves on a curve of the degree _2mnp_... which reduces to _mnp_ +... when the fixed points all lie on a right line." In 1722 Maclaurin +travelled as tutor and companion to the eldest son of Lord Polwarth, and +after a short stay in Paris resided for some time in Lorraine, where he +wrote an essay on the percussion of bodies, which obtained the prize of +the French Academy of Sciences for the year 1724. The following year he +was elected professor of mathematics in the university of Edinburgh on +the urgent recommendation of Newton. After the death of Newton, in 1728, +his nephew, John Conduitt, applied to Maclaurin for his assistance in +publishing an account of Newton's life and discoveries. This Maclaurin +gladly undertook, but the death of Conduitt put a stop to the project. + +In 1740 Maclaurin divided with Leonhard Euler and Daniel Bernoulli the +prize offered by the French Academy of Sciences for an essay on tides. +His _Treatise on Fluxions_ was published at Edinburgh in 1742, in two +volumes. In the preface he states that the work was undertaken in +consequence of the attack on the method of fluxions made by George +Berkeley in 1734. Maclaurin's object was to found the doctrine of +fluxions on geometrical demonstration, and thus to answer all objections +to its method as being founded on false reasoning and full of mystery. +The most valuable part of the work is that devoted to physical +applications, in which he embodied his essay on the tides. In this he +showed that a homogeneous fluid mass revolving uniformly round an axis +under the action of gravity ought to assume the form of an ellipsoid of +revolution. The importance of this investigation in connexion with the +theory of the tides, the figure of the earth, and other kindred +questions, has always caused it to be regarded as one of the great +problems of mathematical physics. Maclaurin was the first to introduce +into mechanics, in this discussion, the important conception of +_surfaces of level_; namely, surfaces at each of whose points the total +force acts in the normal direction. He also gave in his _Fluxions_, for +the first time, the correct theory for distinguishing between maxima and +minima in general, and pointed out the importance of the distinction in +the theory of the multiple points of curves. In 1745, when the rebels +were marching on Edinburgh, Maclaurin took a most prominent part in +preparing trenches and barricades for its defence. The anxiety, fatigue +and cold to which he was thus exposed, affecting a constitution +naturally weak, laid the foundation of the disease to which he +afterwards succumbed. As soon as the rebel army got possession of +Edinburgh Maclaurin fled to England, to avoid making submission to the +Pretender. He accepted the invitation of T. Herring, then archbishop of +York, with whom he remained until it was safe to return to Edinburgh. He +died of dropsy on the 14th of June 1746, at Edinburgh. Maclaurin was +married in 1733 to Anne, daughter of Walter Stewart, solicitor-general +for Scotland. His eldest son John, born in 1734, was distinguished as an +advocate, and appointed one of the judges of the Scottish court of +session, with the title of Lord Dreghorn. He inherited an attachment to +scientific discovery, and was one of the founders of the Royal Society +of Edinburgh, in 1782. + + After Maclaurin's death his account of Newton's philosophical + discoveries was published by Patrick Murdoch, and also his algebra in + 1748. As an appendix to the latter appeared his _De linearum + geometricarum proprietatibus generalibus tractatus_, a treatise of + remarkable elegance. Of the more immediate successors of Newton in + Great Britain Maclaurin is probably the only one who can be placed in + competition with the great mathematicians of the continent of Europe + at the time. (B. W.) + + + + +M'LENNAN, JOHN FERGUSON (1827-1881), Scottish ethnologist, was born at +Inverness on the 14th of October 1827. He studied at King's college, +Aberdeen, where he graduated with distinction in 1849, thence proceeding +to Cambridge, where he remained till 1855 without taking a degree. He +was called to the Scottish bar in 1857, and in 1871 was appointed +parliamentary draughtsman for Scotland. In 1865 he published _Primitive +Marriage_, in which, arguing from the prevalence of the symbolical form +of capture in the marriage ceremonies of primitive races, he developed +an intelligible picture of the growth of the marriage relation and of +systems of kinship (see FAMILY) according to natural laws. In 1866 he +wrote in the _Fortnightly Review_ (April and May) an essay on "Kinship +in Ancient Greece," in which he proposed to test by early Greek facts +the theory of the history of kinship set forth in _Primitive Marriage_; +and three years later appeared a series of essays on "Totemism" in the +same periodical for 1869-1870 (the germ of which had been contained in +the paper just named), which mark the second great step in his +systematic study of early society. A reprint of _Primitive Marriage_, +with "Kinship in Ancient Greece" and some other essays not previously +published, appeared in 1876, under the title of _Studies in Ancient +History_. The new essays in this volume were mostly critical, but one of +them, in which perhaps his guessing talent is seen at its best, "The +Divisions of the Irish Family," is an elaborate discussion of a problem +which has long puzzled both Celtic scholars and jurists; and in another, +"On the Classificatory System of Relationship," he propounded a new +explanation of a series of facts which, he thought, might throw light +upon the early history of society, at the same time putting to the test +of those facts the theories he had set forth in _Primitive Marriage_. +Papers on "The Levirate and Polyandry," following up the line of his +previous investigations (_Fortnightly Review_, 1877), were the last work +he was able to publish. He died of consumption on the 14th of June 1881 +at Hayes Common, Kent. + + Besides the works already cited, M'Lennan wrote a _Life of Thomas + Drummond_ (1867). The vast materials which he had accumulated on + kinship were edited by his widow and A. Platt, under the title + _Studies in Ancient History: Second Series_ (1896). + + + + +MACLEOD, HENRY DUNNING (1821-1902), Scottish economist, was born in +Edinburgh, and educated at Eton, Edinburgh University, and Trinity +College, Cambridge, where he graduated in 1843. He travelled in Europe, +and in 1849 was called to the English bar. He was employed in Scotland +on the work of poor-law reform, and devoted himself to the study of +economics. In 1856 he published his _Theory and Practice of Banking_, in +1858 _Elements of Political Economy_, and in 1859 _A Dictionary of +Political Economy_. In 1873 appeared his _Principles of Economist +Philosophy_, and other books on economics and banking were published +later. Between 1868 and 1870 he was employed by the government in +digesting and codifying the law of bills of exchange. He died on the +16th of July 1902. Macleod's principal contribution to the study of +economics consists in his work on the theory of credit, to which he was +the first to give due prominence. + + For a judicious discussion of the value of Macleod's writings, see an + article on "The Revolt against Orthodox Economics" in the _Quarterly + Review_ for October 1901 (No. 388). + + + + +MACLEOD, NORMAN (1812-1872), Scottish divine, son of Rev. Norman Macleod +(1783-1862), and grandson of Rev. Norman Macleod, minister of Morven, +Argyllshire, was born at Campbeltown on the 3rd of June 1812. In 1827 he +became a student at Glasgow University, and in 1831 went to Edinburgh to +study divinity under Dr Thomas Chalmers. On the 18th of March 1838 he +became parish minister at Loudoun, Ayrshire. At this time the troubles +in the Scottish Church were already gathering to a head (see FREE CHURCH +OF SCOTLAND). Macleod, although he had no love for lay patronage, and +wished the Church to be free to do its proper work, clung firmly to the +idea of a national Established Church, and therefore remained in the +Establishment when the disruption took place. He was one of those who +took a middle course in the non-intrusion controversy, holding that the +fitness of those who were presented to parishes should be judged by the +presbyteries--the principle of Lord Aberdeen's Bill. On the secession of +1843 he was offered many different parishes, and having finally settled +at Dalkeith, devoted himself to parish work and to questions affecting +the Church as a whole. He was largely instrumental in the work of +strengthening the Church. In 1847 he became one of the founders of the +Evangelical Alliance, and from 1849 edited the _Christian Instructor_ +(Edinburgh). In 1851 he was called to the Barony church, Glasgow, in +which city the rest of his days were passed. There the more liberal +theology rapidly made way among a people who judged it more by its +fruits than its arguments, and Macleod won many adherents by his +practical schemes for the social improvement of the people. He +instituted temperance refreshment rooms, a congregational penny savings +bank, and held services specially for the poor. In 1860 Macleod was +appointed editor of the new monthly magazine _Good Words_. Under his +control the magazine, which was mainly of a religious character, became +widely popular. His own literary work, nearly all of which originally +appeared in its pages--sermons, stories, travels, poems--was only a +by-product of a busy life. By far his best work was the spontaneous and +delightful _Reminiscences of a Highland Parish_ (1867). While _Good +Words_ made his name known, and helped the cause he had so deeply at +heart, his relations with the queen and the royal family strengthened +yet further his position in the country. Never since Principal Carstairs +had any Scottish clergyman been on such terms with his sovereign. In +1865 he risked an encounter with Scottish Sabbatarian ideas. The +presbytery of Glasgow issued a pastoral letter on the subject of Sunday +trains and other infringements of the Sabbath. Macleod protested +against the grounds on which its strictures were based. For a time, +owing partly to a misleading report of his statement, he became "the man +in all Scotland most profoundly distrusted." But four years later the +Church accorded him the highest honour in her power by choosing him as +moderator of her general assembly. In 1867, along with Dr Archibald +Watson, he was sent to India, to inquire into the state of the missions. +He undertook the journey in spite of failing health, and seems never to +have recovered from its effects. He returned resolved to devote the rest +of his days to rousing the Church to her duty in the sphere of foreign +missions, but his health was now broken, and his old energy flagged. He +died on the 16th of June 1872, and was buried at Campsie. He was one of +the greatest of Scottish religious leaders, a man of wide sympathy and +high ideals. His Glasgow church was named after him the "Macleod Parish +Church," and the "Macleod Missionary Institute" was erected by the +Barony church in Glasgow. Queen Victoria gave two memorial windows to +Crathie church as a testimony of her admiration for his work. + + See _Memoir of Norman Macleod_, by his brother, Donald Macleod (1876). + + + + +MACLISE, DANIEL (1806-1870), Irish painter, was born at Cork, the son of +a Highland soldier. His education was of the plainest kind, but he was +eager for culture, fond of reading, and anxious to become an artist. His +father, however, placed him, in 1820, in Newenham's Bank, where he +remained for two years, and then left to study in the Cork school of +art. In 1825 it happened that Sir Walter Scott was travelling in +Ireland, and young Maclise, having seen him in a bookseller's shop, made +a surreptitious sketch of the great man, which he afterwards +lithographed. It was exceedingly popular, and the artist became +celebrated enough to receive many commissions for portraits, which he +executed, in pencil, with very careful treatment of detail and +accessory. Various influential friends perceived the genius and promise +of the lad, and were anxious to furnish him with the means of studying +in the metropolis; but with rare independence he refused all aid, and by +careful economy saved a sufficient sum to enable him to leave for +London. There he made a lucky hit by a sketch of the younger Kean, +which, like his portrait of Scott, was lithographed and published. He +entered the Academy schools in 1828, and carried off the highest prizes +open to the students. In 1829 he exhibited for the first time in the +Royal Academy. Gradually he began to confine himself more exclusively to +subject and historical pictures, varied occasionally by portraits of +Campbell, Miss Landon, Dickens, and other of his literary friends. In +1833 he exhibited two pictures which greatly increased his reputation, +and in 1835 the "Chivalric Vow of the Ladies and the Peacock" procured +his election as associate of the Academy, of which he became full member +in 1840. The years that followed were occupied with a long series of +figure pictures, deriving their subjects from history and tradition and +from the works of Shakespeare, Goldsmith and Le Sage. He also designed +illustrations for several of Dickens's Christmas books and other works. +Between the years 1830 and 1836 he contributed to _Fraser's Magazine_, +under the pseudonym of Alfred Croquis, a remarkable series of portraits +of the literary and other celebrities of the time--character studies, +etched or lithographed in outline, and touched more or less with the +emphasis of the caricaturist, which were afterwards published as the +_Maclise Portrait Gallery_ (1871). In 1858 Maclise commenced one of the +two great monumental works of his life, the "Meeting of Wellington and +Blücher," on the walls of Westminster Palace. It was begun in fresco, a +process which proved unmanageable. The artist wished to resign the task; +but, encouraged by Prince Albert, he studied in Berlin the new method of +"water-glass" painting, and carried out the subject and its companion, +the "Death of Nelson," in that medium, completing the latter painting in +1864. The intense application which he gave to these great historic +works, and various circumstances connected with the commission, had a +serious effect on the artist's health. He began to shun the company in +which he formerly delighted; his old buoyancy of spirits was gone; and +when, in 1865, the presidentship of the Academy was offered to him he +declined the honour. He died of acute pneumonia on the 25th of April +1870. His works are distinguished by powerful intellectual and +imaginative qualities, but most of them are marred by harsh and dull +colouring, by metallic hardness of surface and texture, and by frequent +touches of the theatrical in the action and attitudes of the figures. +His fame rests most securely on his two greatest works at Westminster. + + A memoir of Maclise, by his friend W. J. O'Driscoll, was published in + 1871. + + + + +MACLURE, WILLIAM (1763-1840), American geologist, was born at Ayr in +Scotland in 1763. After a brief visit to New York in 1782 he began +active life as a partner in a London firm of American merchants. In 1796 +business affairs took him to Virginia, U.S.A., which he thereafter made +his home. In 1803 he visited France as one of the commissioners +appointed to settle the claims of American citizens on the French +government; and during the few years then spent in Europe he applied +himself with enthusiasm to the study of geology. On his return home in +1807 he commenced the self-imposed task of making a geological survey of +the United States. Almost every state in the Union was traversed and +mapped by him, the Alleghany Mountains being crossed and recrossed some +fifty times. The results of his unaided labours were submitted to the +American Philosophical Society in a memoir entitled _Observations on the +Geology of the United States explanatory of a Geological Map_, and +published in the Society's _Transactions_ (vol. iv. 1809, p. 91) +together with the first geological map of that country. This antedates +William Smith's geological map of England by six years. In 1817 Maclure +brought before the same society a revised edition of his map, and his +great geological memoir was issued separately, with some additional +matter, under the title _Observations on the Geology of the United +States of America_. Subsequent survey has corroborated the general +accuracy of Maclure's observations. In 1819 he visited Spain, and +attempted, unsuccessfully, to establish an agricultural college near the +city of Alicante. Returning to America in 1824, he settled for some +years at New Harmony, Indiana, and sought to develop his scheme of the +agricultural college. Failing health ultimately constrained him to +relinquish the attempt, and to seek (in 1827) a more congenial climate +in Mexico. There, at San Angel, he died on the 23rd of March 1840. + + See S. G. Morton, "Memoir of William Maclure," _Amer. Journ. Sci._, + vol. xlvii. (1844), p. 1. + + + + +MacMAHON, MARIE EDMÉ PATRICE MAURICE DE, duke of Magenta (1808-1893), +French marshal and president of the French republic, was born on the +13th of July 1808 at the château of Sully, near Autun. He was descended +from an Irish family which went into exile with James II. Educated at +the military school of St Cyr, in 1827 he entered the army, and soon saw +active service in the first French campaign in Algeria, where his +ability and bravery became conspicuous. Being recalled to France, he +gained renewed distinction in the expedition to Antwerp in 1832. He +became captain in 1833, and in that year returned to Algeria. He led +daring cavalry raids across plains infested with Bedouin, and especially +distinguished himself at the siege of Constantine in 1837. From then +until 1855 he was almost constantly in Algeria, and rose to the rank of +general of division. During the Crimean War MacMahon was given the +command of a division, and in September 1855 he successfully conducted +the assault upon the Malakoff works, which led to the fall of +Sebastopol. After his return to France honours were showered upon him, +and he was made a senator. Desiring a more active life, however, and +declining the highest command in France, he was once more sent out, at +his own request, to Algeria, where he completely defeated the Kabyles. +After his return to France he voted as a senator against the +unconstitutional law for general safety, which was brought forward in +consequence of Orsini's abortive attempt on the emperor's life. MacMahon +greatly distinguished himself in the Italian campaign of 1859. Partly +by good luck and partly by his boldness and sagacity in pushing forward +without orders at a critical moment at the battle of Magenta, he enabled +the French to secure the victory. For his brilliant services MacMahon +received his marshal's baton and was created duke of Magenta. In 1861 he +represented France at the coronation of William I. of Prussia, and in +1864 he was nominated governor-general of Algeria. MacMahon's action in +this capacity formed the least successful episode of his career. +Although he did institute some reforms in the colonies, complaints were +so numerous that twice in the early part of 1870 he sent in his +resignation to the emperor. When the ill-fated Ollivier cabinet was +formed the emperor abandoned his Algerian schemes and MacMahon was +recalled. + +War being declared between France and Prussia in July 1870, MacMahon was +appointed to the command of the Alsace army detachment (see +FRANCO-GERMAN WAR). On the 6th of August MacMahon fought the battle of +Wörth (q.v.). His courage was always conspicuous on the field, but the +two-to-one numerical superiority of the Germans triumphed. MacMahon was +compelled to fall back upon Saverne, and thence to Toul. Though he +suffered further losses in the course of his retreat, his movements were +so ably conducted that the emperor confided to him the supreme command +of the new levies which he was mustering at Châlons, and he was directed +to effect a junction with Bazaine. This operation he undertook against +his will. He had an army of 120,000 men, with 324 guns; but large +numbers of the troops were disorganized and demoralized. Early on the +1st of September the decisive battle of Sedan began. MacMahon was +dangerously wounded in the thigh, whereupon General Ducrot, and soon +afterwards General de Wimpffen, took command. MacMahon shared the +captivity of his comrades, and resided at Wiesbaden until the conclusion +of peace. + +In March 1871 MacMahon was appointed by Thiers commander-in-chief of the +army of Versailles; and in that capacity he suppressed the Communist +insurrection, and successfully conducted the second siege of Paris. In +the following December he was invited to become a candidate for Paris in +the elections to the National Assembly, but declined nomination. On the +resignation of Thiers as president of the Republic, on the 24th of May +1873, MacMahon was elected to the vacant office by an almost unanimous +vote, being supported by 390 members out of 392. The duc de Broglie was +empowered to form a Conservative administration, but the president also +took an early opportunity of showing that he intended to uphold the +sovereignty of the National Assembly. On the 5th of November 1873 +General Changarnier presented a motion in the Assembly to confirm +MacMahon's powers for a period of ten years, and to provide for a +commission of thirty to draw up a form of constitutional law. The +president consented, but in a message to the Assembly he declared in +favour of a confirmation of his own powers for seven years, and +expressed his determination to use all his influence in the maintenance +of Conservative principles. After prolonged debates the Septennate was +adopted on the 19th of November by 378 votes to 310. There was no _coup +d'état_ in favour of "Henri V.," as had been expected, and the president +resolved to abide by "existing institutions." One of his earliest acts +was to receive the finding of the court-martial upon his old comrade in +arms, Marshal Bazaine, whose death sentence he commuted to one of twenty +years' imprisonment in a fortress. Though MacMahon's life as president +of the Republic was of the simplest possible character, his term of +office was marked by many brilliant displays, while his wife was a +leader in all works of charity and benevolence. + +The president was very popular in the rural districts of France, through +which he made a successful tour shortly after the declaration of the +Septennate. But in Paris and other large cities his policy soon caused +great dissatisfaction, the Republican party especially being alienated +by press prosecutions and the attempted suppression of Republican ideas. +Matters were at a comparative deadlock in the National Assembly, until +the accession of some Orleanists to the Moderate Republican party in +1875 made it possible to pass various constitutional laws. In May 1877, +however, the constitutional crisis became once more acute. A peremptory +letter of censure from MacMahon to Jules Simon caused the latter to +resign with his colleagues. The duc de Broglie formed a ministry, but +Gambetta carried a resolution in the Chamber of Deputies in favour of +parliamentary government. The president declined to yield, and being +supported by the Senate, he dissolved the Chamber, by decree, on the +25th of June. The prosecution of Gambetta followed for a speech at +Lille, in which he had said "the marshal must, if the elections be +against him, _se soumettre ou se démettre_." In a manifesto respecting +the elections, the president referred to his successful government and +observed, "I cannot obey the injunctions of the demagogy; I can neither +become the instrument of Radicalism nor abandon the post in which the +constitution has placed me." His confidence in the result of the +elections was misplaced. Notwithstanding the great pressure put upon the +constituencies by the government, the elections in October resulted in +the return of 335 Republicans and only 198 anti-Republicans, the latter +including 30 MacMahonists, 89 Bonapartists, 41 Legitimists, and 38 +Orleanists. The president endeavoured to ignore the significance of the +elections, and continued his reactionary policy. As a last resort he +called to power an extra-parliamentary cabinet under General Rochebouet, +but the Republican majority refused to vote supplies, and after a brief +interval the president was compelled to yield, and to accept a new +Republican ministry under Dufaure. The prolonged crisis terminated on +the 14th of December 1877, and no further constitutional difficulties +arose in 1878. But as the senatorial elections, held early in 1879, gave +the Republicans an effective working majority in the Upper Chamber, they +now called for the removal of the most conspicuous anti-Republicans +among the generals and officials. The president refused to supersede +them, and declined to sanction the law brought in with this object. +Perceiving further resistance to be useless, however, MacMahon resigned +the presidency on the 30th of January 1879, and Jules Grévy was elected +as his successor. + +MacMahon now retired into private life. Relieved from the cares of +state, his simple and unostentatious mode of existence enabled him to +pass many years of dignified repose. He died at Paris on the 17th of +October 1893, in his eighty-sixth year. A fine, tall, soldierly man, of +a thoroughly Irish type, in private life MacMahon was universally +esteemed as generous and honourable; as a soldier he was brave and able, +without decided military genius; as a politician he was patriotic and +well-intentioned, but devoid of any real capacity for statecraft. + (G. B. S.) + + + + +McMASTER, JOHN BACH (1852- ), American historian, was born in Brooklyn, +New York, on the 29th of June 1852. He graduated from the college of the +City of New York in 1872, worked as a civil engineer in 1873-1877, was +instructor in civil engineering at Princeton University in 1877-1883, +and in 1883 became professor of American history in the university of +Pennsylvania. He is best known for his _History of the People of the +United States from the Revolution to the Civil War_ (1883 sqq.), a +valuable supplement to the more purely political writings of Schouler, +Von Holst and Henry Adams. + + + + +MACMILLAN, the name of a family of English publishers. The founders of +the firm were two Scotsmen, Daniel Macmillan (1813-1857) and his younger +brother Alexander (1818-1896). Daniel was a native of the Isle of Arran, +and Alexander was born in Irvine on the 3rd of October 1818. Daniel was +for some time assistant to the bookseller Johnson at Cambridge, but +entered the employ of Messrs Seeley in London in 1837; in 1843 he began +business in Aldersgate Street, and in the same year the two brothers +purchased the business of Newby in Cambridge. They did not confine +themselves to bookselling, but published educational works as early as +1844. In 1845 they became the proprietors of the more important business +of Stevenson, in Cambridge, the firm being styled Macmillan, Barclay & +Macmillan. In 1850 Barclay retired and the firm resumed the name of +Macmillan & Co. Daniel Macmillan died at Cambridge on the 27th of June +1857. In that year an impetus was given to the business by the +publication of Kingsley's _Two Years Ago_. A branch office was opened in +1858 in Henrietta Street, London, which led to a great extension of +trade. These premises were surrendered for larger ones in Bedford +Street, and in 1897 the buildings in St Martin's Street were opened. +Alexander Macmillan died in January 1896. By his great energy and +literary associations, and with the aid of his partners, there had been +built up in little over half a century one of the most important +publishing houses in the world. Besides the issue of many important +series of educational and scientific works, they published the works of +Kingsley, Huxley, Maurice, Tennyson, Lightfoot, Westcott, J. R. Green, +Lord Roberts, Lewis Carroll, and of many other well-known authors. In +1898 they took over the old-established publishing house of R. Bentley & +Son, and with it the works of Mrs Henry Wood, Miss Rhoda Broughton, _The +Ingoldsby Legends_, and also _Temple Bar_ and the _Argosy_. In 1893 the +firm was converted into a limited liability company, its chairman being +Frederick Macmillan (b. 1851), who was knighted in 1909. The American +firm of the Macmillan Company, of which he was also a director, is a +separate business. + + See Thomas Hughes, _Memoir of Daniel Macmillan_ (1882); _A + Bibliographical Catalogue of Macmillan & Co's Publications from 1843 + to 1889_ (1891), with portraits of the brothers Daniel and Alexander + after Lowes Dickinson and Hubert Herkomer; also articles in _Le Livre_ + (September 1886), _Publishers' Circular_ (January 14, 1893), the + _Bookman_ (May 1901), &c. + + + + +MACMONNIES, FREDERICK WILLIAM (1863- ) American sculptor and painter, +was born at Brooklyn, New York, on the 20th of September 1863. His +mother was a niece of Benjamin West. At the age of sixteen MacMonnies +was received as an apprentice in the studio of Augustus St Gaudens, the +sculptor, where he remained for five years. In 1884 he went to Paris and +thence to Munich, where he painted for some months. Returning to Paris +next year he became the most prominent pupil of Falguière. His "Diana" +brought him a mention at the Salon of 1889. Three life-sized figures of +angels for the church of St Paul, New York, were followed by his "Nathan +Hale," in the City Hall Park, New York, and a portrait of James S. T. +Stranahan, for Brooklyn. This last brought him a "second medal" in the +Salon of 1891, the first time an American sculptor had been so honoured. +In 1893 he was chosen to design and carry out the Columbian Fountain for +the Chicago World's Fair, which placed him instantly in the front rank. +His largest work is a decoration for the Memorial Arch to Soldiers and +Sailors, in Prospect Park, Brooklyn, consisting of three enormous groups +in bronze. In Prospect Park, Brooklyn, MacMonnies has also a large +"Horse Tamer," a work of much distinction. A "Winged Victory" at the +U.S. military academy at West Point, New York, is of importance; and his +"Bacchante," an extraordinary combination of realism and imagination, +rejected by the Boston Public Library, is now at the Metropolitan Museum +of Art, New York. He also became well known as a painter, mainly of +portraits. In 1888 he married Mary Fairchild, a figure painter of +distinction, but in 1909 they were divorced and she married Will H. Low. + + + + +MACNAGHTEN, SIR WILLIAM HAY, BART. (1793-1841), Anglo-Indian +diplomatist, was the second son of Sir Francis Macnaghten, Bart., judge +of the supreme courts of Madras and Calcutta. He was born in August +1793, and educated at Charterhouse. He went out to Madras as a cadet in +1809, but was appointed in 1816 to the Bengal Civil Service. He early +displayed a great talent for languages, and also published several +treatises on Hindu and Mahommedan law. His political career began in +1830 as secretary to Lord William Bentinck; and in 1837 he became one of +the most trusted advisers of the governor-general, Lord Auckland, with +whose policy of supporting Shah Shuja against Dost Mahommed, the +reigning amir of Kabul, Macnaghten was closely identified. As political +agent at Kabul he came into conflict with the military authorities and +subsequently with his subordinate Sir Alexander Burnes. Macnaghten +attempted to placate the Afghan chiefs with heavy subsidies, but when +the drain on the Indian exchequer became too great, and the allowances +were reduced, this policy led to an outbreak. Burnes was murdered on the +2nd of November 1841; and owing to the incapacity of the aged General +Elphinstone the British army in Kabul degenerated into a leaderless mob. +Macnaghten tried to save the situation by negotiating with the Afghan +chiefs and, independently of them, with Dost Mahommed's son, Akbar Khan, +by whom he was assassinated on the 23rd of December 1841; the disastrous +retreat from Kabul and the massacre of the British army in the Kurd +Kabul pass followed. These events threw doubt on Macnaghten's capacity +for dealing with the problems of Indian diplomacy, though his +fearlessness and integrity were unquestioned. He had been created a +baronet in 1840, and four months before his death was nominated to the +governorship of Bombay. + + + + +MacNALLY, LEONARD (1752-1820), Irish informer, was born in Dublin, the +son of a merchant. In 1776 he was called to the Irish, and in 1783 to +the English bar. He supported himself for some time in London by writing +plays and editing the _Public Ledger_. Returning to Dublin, he entered +upon a systematic course of informing against the members of the +revolutionary party, for whom his house had become the resort. He also +betrayed to the government prosecutors political clients whom he +defended eloquently in the courts. He made a fine defence for Robert +Emmet and cheered him in his last hours, although before appearing in +court he had sold, for £200, the contents of his brief to the lawyers +for the Crown. After living a professed Protestant all his life, he +received absolution on his deathbed from a Roman Catholic priest. He +died on the 13th of February 1820. + + + + +MACNEE, SIR DANIEL (1806-1882), Scottish portrait painter, was born at +Fintry in Stirlingshire. At the age of thirteen he was apprenticed, +along with Horatio Macculloch and Leitch the water-colour painter, to +John Knox, a landscapist of some repute. He afterwards worked for a year +as a lithographer, was employed by the Smiths of Cumnock to paint the +ornamental lids of their planewood snuff-boxes, and, having studied in +Edinburgh at the "Trustees' Academy," supporting himself meanwhile by +designing and colouring book illustrations for Lizars the engraver, he +established himself as an artist in Glasgow, where he became a +fashionable portrait painter. He was in 1829 admitted a member of the +Royal Scottish Academy; and on the death of Sir George Harvey in 1876 he +was elected president, and received the honour of knighthood. From this +period till his death, on the 18th of January 1882, he resided in +Edinburgh, where his genial social qualities and his inimitable powers +as a teller of humorous Scottish anecdote rendered him popular. + + + + +MACNEIL, HERMON ATKINS (1866- ), American sculptor, was born at Chelsea, +Massachusetts. He was an instructor in industrial art at Cornell +University in 1886-1889, and was then a pupil of Henri M. Chapu and +Falguière in Paris. Returning to America, he aided Philip Martiny in the +preparation of sketch models for the Columbian exposition, and in 1896 +he won the Rinehart scholarship, passing four years (1896-1900) in Rome. +In 1906 he became a National Academician. His first important work was +"The Moqui Runner," which was followed by "A Primitive Chant," and "The +Sun Vow," all figures of the North-American Indian. A "Fountain of +Liberty," for the St Louis exposition, and other Indian themes came +later; his "Agnese" and his "Beatrice," two fine busts of women, also +deserve mention. His principal work is the sculpture for a large +memorial arch, at Columbus, Ohio, in honour of President McKinley. In +1909 he won in competition a commission for a large soldiers' and +sailors' monument in Albany, New York. His wife, Carol Brooks MacNeil, +also a sculptor of distinction, was a pupil of F. W. MacMonnies. + + + + +McNEILE, HUGH (1795-1879), Anglican divine, younger son of Alexander +McNeile (or McNeill), was born at Ballycastle, Co. Antrim, on the 15th +of July 1795. He graduated at Trinity College, Dublin, in 1810. His +handsome presence, and his promise of exceptional gifts of oratory, led +a wealthy uncle, Major-General Daniel McNeill, to adopt him as his heir; +and he was destined for a parliamentary career. During a stay at +Florence, Hugh McNeile became temporarily intimate with Lord Byron and +Madame de Staël. On returning home, he determined to abandon the +prospect of political distinction for the clerical profession, and was +disinherited. In 1820 he was ordained, and after holding the curacy of +Stranorlar, Co. Donegal, for two years, was appointed to the living of +Albury, Surrey, by Henry Drummond. + +Edward Irving endeavoured, not without success at first, to draw McNeile +into agreement with his doctrine and aims. Irving's increasing +extravagance, however, soon alienated McNeile. His preaching now +attracted much attention; in London he frequently was heard by large +congregations. In 1834 he accepted the incumbency of St Jude's, +Liverpool, where for the next thirty years he wielded great political as +well as ecclesiastical influence. He repudiated the notion that a +clergyman should be debarred from politics, maintaining at a public +meeting that "God when He made the minister did not unmake the citizen." +In 1835 McNeile entered upon a long contest, in which he was eventually +successful, with the Liverpool corporation, which had been captured by +the Whigs, after the passing of the Municipal Reform Act. A proposal was +carried that the elementary schools under the control of the corporation +should be secularized by the introduction of what was known as the Irish +National System. The threatened withdrawal of the Bible as the basis of +denominational religious teaching was met by a fierce agitation led by +McNeile, who so successfully enlisted public support that before the new +system could be introduced every child was provided for in new Church of +England schools established by public subscriptions. At the same time he +conducted a campaign which gradually reduced the Whig element in the +council, till in 1841 it almost entirely disappeared. To his influence +was also attributed the defeat of the Liberal parliamentary candidates +in the general election of 1837, followed by a long period of +Conservative predominance in Liverpool politics. McNeile had the Irish +Protestant's horror of Romanism, which he constantly denounced in the +pulpit and on the platform; and Macaulay, speaking in the House of +Commons on the Maynooth endowment in April 1845, singled him out for +attack as the most powerful representative of uncompromising Protestant +opinion in the country. As the Tractarian movement in the Church of +England developed, he became one of its most zealous opponents and the +most conspicuous leader of the evangelical party. In 1840 he published a +volume of _Lectures on the Church of England_, and in 1846 (the year +after Newman's secession to Rome) _The Church and the Churches_, in +which he maintained with much dialectical skill the evangelical doctrine +of the "invisible Church" in opposition to the teaching of Newman and +Pusey. Hugh McNeile was in close sympathy with the philanthropic work as +well as the religious views of the 7th earl of Shaftesbury, who more +than once tried to persuade Lord Palmerston to raise him to the +episcopal bench. But although Palmerston usually followed the advice of +Shaftesbury in the appointment of bishops, he would not consent to the +elevation to the House of Lords of so powerful a political opponent as +McNeile, whom Lord John Russell had accused of frustrating for thirty +years the education policy of the Liberal party. In 1860 he was +appointed a canon of Chester; and in 1868 Disraeli appointed him dean of +Ripon. This preferment he resigned in 1875, and he lived in retirement +at Bournemouth till his death on the 28th of January 1879. McNeile +married, in 1822, Anne, daughter of William Magee, archbishop of Dublin, +and aunt of William Connor Magee, archbishop of York, by whom he had a +large family. + +Although a vehement controversialist, Hugh McNeile was a man of simple +and sincere piety of character. Sir Edward Russell, an opponent alike of +his religious and his political opinions, bears witness to the deep +spirituality of his teaching, and describes him as an absolutely unique +personality. "He made himself leader of the Liverpool people, and always +led with calm and majesty in the most excited times. His eloquence was +grave, flowing, emphatic--had a dignity in delivery, a perfection of +elocution, that only John Bright equalled in the latter half of the +19th century. Its fire was solemn force. McNeile's voice was probably +the finest organ ever heard in public oratory. His action was as +graceful as it was expressive. He ruled an audience." + + See J. A. Picton, _Memorials of Liverpool_, vol. i. (1873); Sir Edward + Russell, "The Religious Life of Liverpool," in the _Sunday Magazine_ + (June 1905); Charles Bullock, _Hugh McNeile and Reformation Truth_. + (R. J. M.) + + + + +MACNEILL, HECTOR (1746-1818), Scottish poet, was born near Roslin, +Midlothian, on the 22nd of October 1746, the son of an impoverished army +captain. He went to Bristol as a clerk at the age of fourteen, and soon +afterwards was despatched to the West Indies. From 1780 to 1786 he acted +as assistant secretary on board the flagships of Admiral Geary and Sir +Richard Bickerton (1727-1792). Most of his later life was spent in +Scotland, and it was in the house of a friend at Stirling that he wrote +most of his songs and his _Scotland's Skaith, or the History of Will and +Jean_ (1795), a narrative poem intended to show the deteriorating +influences of whisky and pothouse politics. A sequel, _The Waes of War_, +appeared next year. In 1800 he published _The Memoirs of Charles +Macpherson, Esq._, a novel understood to be a narrative of his own +hardships and adventures. A complete edition of the poems he wished to +own appeared in 1812. His songs "Mary of Castlecary," "Come under my +plaidy," "My boy Tammy," "O tell me how for to woo," "I lo'ed ne'er a +lassie but ane," "The plaid amang the hether," and "Jeanie's black e'e," +are notable for their sweetness and simplicity. He died at Edinburgh on +the 15th of March 1818. + + + + +MACOMB, a city and the county-seat of McDonough county, Illinois, +U.S.A., in the W. part of the state, about 60 m. S.W. of Peoria. Pop. +(1890), 4052; (1900), 5375 (232 foreign-born); (1910), 5774. Macomb is +served by the Chicago, Burlington & Quincy, and the Macomb & Western +Illinois railways. The city is the seat of the Western Illinois state +normal school (opened in 1902), and has a Carnegie library and a city +park. Clay is found in the vicinity, and there are manufactures of +pottery, bricks, &c. The city was founded in 1830 as the county-seat of +McDonough county, and was called Washington by the settlers, but the +charter of incorporation, also granted in 1830, gave it the present name +in honour of General Alexander Macomb. Macomb was first chartered as a +city in 1856. + + + + +MACOMER, a village of Sardinia in the province of Cagliari, from which +it is 95 m. N.N.W. by rail, and the same distance S.W. of Golfo degli +Aranci. Pop. (1901), 3488. It is situated 1890 ft. above sea-level on +the southern ascent to the central plateau (the Campeda) of this part of +Sardinia; and it is the junction of narrow-gauge lines branching from +the main line eastwards to Nuoro and westwards to Bosa. The old parish +church of S. Pantaleone has three Roman mile-stones in front of it, +belonging to the Roman high-road from Carales to Turris Libisonis. The +modern high-road follows the ancient. The district, especially the +Campeda, is well fitted for grazing and horse and cattle breeding, which +is carried on to a considerable extent. It is perhaps richer in +_nuraghi_ than any other part of Sardinia. + + + + +MACON, NATHANIEL (1758-1837), American political leader, was born at +Macon Manor, Warren county, North Carolina, on the 17th of December +1758. He studied at the college of New Jersey (now Princeton University) +from 1774 to 1776, when the institution was closed on account of the +outbreak of the War of Independence; served for a short time in a New +Jersey militia company; studied law at Bute Court-house, North Carolina, +in 1777-1780, at the same time managing his tobacco plantation; was a +member of a Warren county militia company in 1780-1782, and served in +the North Carolina Senate in 1781-1785. In 1786 he was elected to the +Continental Congress, but declined to serve. In 1791-1815 he was a +member of the national House of Representatives, and in 1815-1828 of the +United States Senate. Macon's point of view was always local rather than +national. He was essentially a North Carolinian first, and an American +afterwards; and throughout his career he was an aggressive advocate of +state sovereignty and an adherent of the doctrines of the "Old +Republicans." He at first opposed the adoption of the Federal +constitution of 1787, as a member of the faction led by Willie Jones +(1731-1801) of Halifax, North Carolina, but later withdrew his +opposition. In Congress he denounced Hamilton's financial policy, +opposed the Jay Treaty (1795) and the Alien and Sedition Acts, and +advocated a continuance of the French alliance of 1778. His party came +into power in 1801, and he was Speaker of the house from December 1801 +to October 1807. At first he was in accord with Jefferson's +administration; he approved the Louisiana Purchase, and as early as 1803 +advocated the purchase of Florida. For a number of years, however, he +was politically allied with John Randolph.[1] As speaker, in spite of +strong opposition, he kept Randolph at the head of the important +committee on Ways and Means from 1801 to 1806; and in 1805-1808, with +Randolph and Joseph H. Nicholson (1770-1817) of Maryland, he was a +leader of the group of about ten independents, called the "Quids," who +strongly criticized Jefferson and opposed the presidential candidature +of Madison. By 1809, however, Macon was again in accord with his party, +and during the next two years he was one of the most influential of its +leaders. In December 1809 he introduced resolutions which combined the +ideas of Peter Early (1773-1817) of Georgia, David R. Williams +(1776-1830) of South Carolina, and Samuel W. Dana (1757-1830) of +Connecticut with his own. The resolutions recommended the complete +exclusion of foreign war vessels from United States ports and the +suppression of illegal trade carried on by foreign merchants under the +American flag. The substance of these resolutions was embodied in the +"Macon Bill, No. 1," which passed the House but was defeated in the +Senate. On the 7th of April 1810 Macon reported from committee the +"Macon Bill, No. 2," which had been drawn by John Taylor (1770-1832) of +South Carolina, and was not actively supported by him. This measure +(amended) became law on the 1st of May, and provided for the repeal of +the Non-Intercourse Act of 1809, authorized the president, "in case +either Great Britain or France shall before the 3rd day of March next so +revoke or modify her edicts as that they shall cease to violate the +neutral commerce of the United States," to revive non-intercourse +against the other, and prohibited British and French vessels of war from +entering American waters. In 1812 Macon voted for the declaration of war +against Great Britain, and later was chairman of the Congressional +committee which made a report (July 1813) condemning Great Britain's +conduct of the war. He opposed the Bank Act of 1816, the "internal +improvements" policy of Calhoun (in the early part of his career) and +Clay, and the Missouri Compromise, his speech against the last being +especially able. In 1824 Macon received the electoral vote of Virginia +for the vice-presidency, and in 1826-1828 was president pro tempore of +the Senate. He was president of the North Carolina constitutional +convention in 1835, and was an elector on the Van Buren ticket in 1836. +He died at his home, Buck Springs, Warren county, North Carolina, on the +29th of June 1837. + + See William E. Dodd, _The Life of Nathaniel Macon_ (Raleigh, N.C., + 1903); E. M. Wilson, _The Congressional Career of Nathaniel Macon_ + (Chapel Hill, N.C., 1900). + + +FOOTNOTE: + + [1] Their names are associated in Randolph-Macon College, named in + their honour in 1830. + + + + +MÂCON, a town of east-central France, capital of the department of +Saône-et-Loire, 45 m. N. of Lyons on the Paris-Lyon railway. Pop. +(1906), 16,151. Mâcon is situated on the right bank of the Saône facing +the plain of the Bresse; a bridge of twelve arches connects it with the +suburb of St Laurent on the opposite bank. The most prominent building +is the modern Romanesque church of St Pierre, a large three-naved +basilica, with two fine spires. Of the old cathedral of St Vincent (12th +and 13th centuries), destroyed at the Revolution, nothing remains but +the Romanesque narthex, now used as a chapel, the façade and its two +flanking towers. The hôtel de ville contains a library, a theatre and +picture-gallery. Opposite to it stands a statue of the poet Alphonse +Lamartine, a native of the town. Mâcon is the seat of a prefecture, and +has tribunals of first instance and of commerce, and a chamber of +commerce. There are lycées and training colleges. Copper-founding is an +important industry; manufactures include casks, mats, rope and utensils +for the wine-trade. The town has a large trade in wine of the district, +known as Mâcon. It is a railway centre of considerable importance, being +the point at which the line from Paris to Marseilles is joined by that +from Mont Cenis and Geneva, as well as by a branch from Moulins. + +Mâcon (_Matisco_) was an important town of the Aedui, but under the +Romans it was supplanted by Autun and Lyons. It suffered a succession of +disasters at the hands of the Germans, Burgundians, Vandals, Huns, +Hungarians and even of the Carolingian kings. In the feudal period it +was an important countship which in 1228 was sold to the king of France, +but more than once afterwards passed into the possession of the dukes of +Burgundy, until the ownership of the French crown was established in the +time of Louis XI. In the 16th century Mâcon became a stronghold of the +Huguenots, but afterwards fell into the hands of the League, and did not +yield to Henry IV. until 1594. The bishopric, created by King +Childebert, was suppressed in 1790. + + + + +MACON, a city and the county-seat of Bibb county, Georgia, U.S.A., in +the central part of the state, on both sides of the Ocmulgee river (at +the head of navigation), about 90 m. S.S.E. of Atlanta. Pop. (1900), +23,272, of whom 11,550 were negroes; (1910 census) 40,665. Macon is, +next to Atlanta, the most important railway centre in the state, being +served by the Southern, the Central of Georgia, the Georgia, the Georgia +Southern & Florida, the Macon Dublin & Savannah, and the Macon & +Birmingham railways. It was formerly an important river port, especially +for the shipment of cotton, but lost this commercial advantage when +railway bridges made the river impassable. It is, however, partially +regaining the river trade in consequence of the compulsory substitution +of drawbridges for the stationary railway bridges. The city is the seat +of the Wesleyan female college (1836), which claims to be the first +college in the world chartered to grant academic degrees to women; +Mercer university (Baptist), which was established in 1833 as Mercer +Institute at Penfield, became a university in 1837, was removed to Macon +in 1871, and controls Hearn Academy (1839) at Cave Spring and Gibson +Mercer Academy (1903) at Bowman; the state academy for the blind (1852), +St Stanislaus' College (Jesuit), and Mt de Sales Academy (Roman +Catholic) for women. There are four orphan asylums for whites and two +for negroes, supported chiefly by the Protestant Episcopal and Methodist +Churches, and a public hospital. Immediately east of Macon are two large +Indian mounds, and there is a third mound 9 m. south of the city. +Situated in the heart of the "Cotton Belt," Macon has a large and +lucrative trade; it is one of the most important inland cotton markets +of the United States, its annual receipts averaging about 250,000 bales. +The city's factory products in 1905 were valued at $7,297,347 (33.8% +more than in 1900). In the vicinity are large beds of kaolin, 30 m. +wide, reaching nearly across the state, and frequently 35 to 70 ft. in +depth. Macon is near the fruit-growing region of Georgia, and large +quantities of peaches and of garden products are annually shipped from +the city. + +Macon (named in honour of Nathaniel Macon) was surveyed in 1823 by order +of the Georgia legislature for the county-seat of Bibb county, and +received its first charter in 1824. It soon became the centre of trade +for Middle Georgia; in 1833 a steamboat line to Darien was opened, and +in the following year 69,000 bales of cotton were shipped by this route. +During the Civil War the city was a centre for Confederate commissary +supplies and the seat of a Treasury depository. In July 1864 General +George Stoneman (1822-1894) with 500 men was captured near the city by +the Confederate general, Howell Cobb. Macon was finally occupied by +Federal troops under General James H. Wilson (b. 1837) on the 20th of +April 1865. In 1900-1910 the area of the city was increased by the +annexation of several suburbs. + + + + +MACPHERSON, SIR DAVID LEWIS (1818-1896), Canadian financier and +politician, was born at Castle Leathers, near Inverness, Scotland, on +the 12th of September 1818. In 1835 he emigrated to Canada, settling in +Montreal, where he built up a large fortune by "forwarding" merchandise. +In 1853 he removed to Toronto, and in the same year obtained the +contract for building a line of railway from Toronto to Sarnia, a +project from which sprang the Grand Trunk railway, in the construction +of which line he greatly increased his wealth. In 1864 he was elected to +the Canadian parliament as member of the Legislative Council for +Saugeen, and on the formation of the Dominion, in 1867, was nominated to +the Senate. In the following years he published a number of pamphlets on +economic subjects, of which the best-known is _Banking and Currency_ +(1869). In 1880 he was appointed Speaker of the Senate, and from October +1883 till 1885 was minister of the interior in the Conservative cabinet. +In 1884 he was knighted by Queen Victoria. He died on the 16th of August +1896. + + + + +MACPHERSON, JAMES (1736-1796), Scottish "translator" of the Ossianic +poems, was born at Ruthven in the parish of Kingussie, Inverness, on the +27th of October 1736. He was sent in 1753 to King's College, Aberdeen, +removing two years later to Marischal College. He also studied at +Edinburgh, but took no degree. He is said to have written over 4000 +lines of verse while a student, but though some of this was published, +notably _The Highlander_ (1758), he afterwards tried to suppress it. On +leaving college he taught in the school of his native place. At Moffat +he met John Home, the author of _Douglas_, for whom he recited some +Gaelic verses from memory. He also showed him MSS. of Gaelic poetry, +supposed to have been picked up in the Highlands, and, encouraged by +Home and others, he produced a number of pieces translated from the +Gaelic, which he was induced to publish at Edinburgh in 1760 as +_Fragments of Ancient Poetry collected in the Highlands of Scotland_. Dr +Hugh Blair, who was a firm believer in the authenticity of the poems, +got up a subscription to allow Macpherson to pursue his Gaelic +researches. In the autumn he set out to visit western Inverness, the +islands of Skye, North and South Uist and Benbecula. He obtained MSS. +which he translated with the assistance of Captain Morrison and the Rev. +A. Gallie. Later in the year he made an expedition to Mull, when he +obtained other MSS. In 1761 he announced the discovery of an epic on the +subject of Fingal, and in December he published _Fingal, an Ancient Epic +Poem in Six Books, together with Several Other Poems composed by Ossian, +the Son of Fingal, translated from the Gaelic Language_, written in the +musical measured prose of which he had made use in his earlier volume. +_Temora_ followed in 1763, and a collected edition, _The Works of +Ossian_, in 1765. + +The genuineness of these so-called translations from the works of a +3rd-century bard was immediately challenged in England, and Dr Johnson, +after some local investigation, asserted (_Journey to the Western +Islands of Scotland_, 1775) that Macpherson had only found fragments of +ancient poems and stories, which he had woven into a romance of his own +composition. Macpherson is said to have sent Johnson a challenge, to +which Johnson replied that he was not to be deterred from detecting what +he thought a cheat by the menaces of a ruffian. Macpherson never +produced his originals, which he refused to publish on the ground of the +expense. In 1764 he was made secretary to General Johnstone at +Pensacola, West Florida, and when he returned, two years later, to +England, after a quarrel with Johnstone, he was allowed to retain his +salary as a pension. He occupied himself with writing several historical +works, the most important of which was _Original Papers, containing the +Secret History of Great Britain from the Restoration to the Accession of +the House of Hanover; to which are prefixed Extracts from the Life of +James II., as written by himself_ (1775). He enjoyed a salary for +defending the policy of Lord North's government, and held the lucrative +post of London agent to Mahommed Ali, nabob of Arcot. He entered +parliament in 1780, and continued to sit until his death. In his later +years he bought an estate, to which he gave the name of Belville, in his +native county of Inverness, where he died on the 17th of February 1796. + +After Macpherson's death, Malcolm Laing, in an appendix to his _History +of Scotland_ (1800), propounded the extreme view that the so-called +Ossianic poems were altogether modern in origin, and that Macpherson's +authorities were practically non-existent. For a discussion of this +question see CELT: _Scottish Gaelic Literature_. Much of Macpherson's +matter is clearly his own, and he confounds the stories belonging to +different cycles. But apart from the doubtful morality of his +transactions he must still be regarded as one of the great Scottish +writers. The varied sources of his work and its worthlessness as a +transcript of actual Celtic poems do not alter the fact that he produced +a work of art which by its deep appreciation of natural beauty and the +melancholy tenderness of its treatment of the ancient legend did more +than any single work to bring about the romantic movement in European, +and especially in German, literature. It was speedily translated into +many European languages, and Herder and Goethe (in his earlier period) +were among its profound admirers. Cesarotti's Italian translation was +one of Napoleon's favourite books. + + AUTHORITIES.--For Macpherson's life, see _The Life and Letters of + James Macpherson ..._ (1894, new ed., 1906), by T. Bailey Saunders, + who has laboured to redeem his character from the suspicions generally + current with English readers. The antiquity of the Ossianic poems was + defended in the introduction by Archibald Clerk to his edition of the + _Poems of Ossian_ (1870). Materials for arriving at a decision by + comparison with undoubtedly genuine fragments of the Ossianic legend + are available in _The Book of the Dean of Lismore_, Gaelic verses, + collected by J. McGregor, dean of Lismore, in the early 16th century + (ed. T. McLauchlan, 1862); the _Leabhar na Feinne_ (1871) of F. J. + Campbell, who also discusses the subject in _Popular Tales of the + Western Highlands_, iv. (1893). See also L. C. Stern, "Die ossianische + Heldenlieder" in _Zeitschrift für vergleichende Litteratur-geschichte_ + (1895; Eng. trans. by J. L. Robertson in _Trans. Gael. Soc. of + Inverness_, xxii., 1897-1898); Sir J. Sinclair, _A Dissertation on the + Authenticity of the Poems of Ossian_ (1806); _Transactions of the + Ossianic Society_ (Dublin, 1854-1861); _Cours de littérature + celtique_, by Arbois de Jubainville, editor of the _Revue celtique_ + (1883, &c.); A. Nutt, _Ossian and the Ossianic Literature_ (1899), + with a valuable bibliographical appendix; J. S. Smart, _James + Macpherson: an Episode in Literature_ (1905). + + + + +McPHERSON, JAMES BIRDSEYE (1828-1864), American soldier, was born at +Sandusky, Ohio, on the 14th of November 1828. He entered West Point at +the age of twenty-one, and graduated (1853) at the head of his class, +which included Sheridan, Schofield and Hood. He was employed at the +military academy as instructor of practical military engineering (1853). +A year later he was sent to engineer duty at New York, and in 1857, +after constructing Fort Delaware, he was sent as superintending engineer +to San Francisco, becoming 1st lieutenant in 1858. He was promoted +captain during the first year of the Civil War, and towards the close of +1861 became lieutenant-colonel and aide-de-camp to General Halleck, who +in the spring of 1862 sent him to General Grant as chief engineer. He +remained with Grant during the Shiloh campaign, and acted as engineer +adviser to Halleck during the siege operations against Corinth in the +summer of 1862. In October he distinguished himself in command of an +infantry brigade at the battle of Corinth, and on the 8th of this month +was made major-general of volunteers and commander of a division. In the +second advance on Vicksburg (1863) McPherson commanded the XVII. corps, +fought at Port Gibson, Raymond and Jackson, and after the fall of +Vicksburg was strongly recommended by Grant for the rank of +brigadier-general in the regular army, to which he was promoted on the +1st of August 1863. He commanded at Vicksburg until the following +spring. He was about to go on leave of absence in order to be married in +Baltimore when he received his nomination to the command of the Army of +the Tennessee, Grant's and Sherman's old army, which was to take part +under Sherman's supreme command in the campaign against Atlanta (1864). +This nomination was made by Sherman and entirely approved by Grant, who +had the highest opinion of McPherson's military and personal qualities. +He was in command of his army at the actions of Resaca, Dallas, Kenesaw +Mountain and the battles about Atlanta. On the 22nd of July, when the +Confederates under his old classmate Hood made a sudden and violent +attack on the lines held by the Army of the Tennessee, McPherson rode +up, in the woods, to the enemy's firing line and was killed. He was one +of the most heroic figures of the American Civil War, and Grant is +reported to have said when he heard of McPherson's death, "The country +has lost one of its best soldiers, and I have lost my best friend." + + + + +MACQUARIE, a British island in the South Pacific Ocean, in 54° 49´ S. +and 159° 49´ E. It is about 20 m. long, and covered with a grassy +vegetation, with some trees or shrubs in the sheltered places which +afford food to a parrot of the genus _Cyanorhamphus_, allied to those of +the Auckland Islands. Although it has no settled population, Macquarie +is constantly visited by sailors in quest of the seals which abound in +its waters. + + + + +MACRAUCHENIA, a long-necked and long-limbed, three-toed South American +ungulate mammal, typifying the suborder _Litopterna_ (q.v.). + + + + +MACREADY, WILLIAM CHARLES (1793-1873), English actor, was born in London +on the 3rd of March 1793, and educated at Rugby. It was his intention to +go up to Oxford, but in 1809 the embarrassed affairs of his father, the +lessee of several provincial theatres, called him to share the +responsibilities of theatrical management. On the 7th of June 1810 he +made a successful first appearance as Romeo at Birmingham. Other +Shakespearian parts followed, but a serious rupture between father and +son resulted in the young man's departure for Bath in 1814. Here he +remained for two years, with occasional professional visits to other +provincial towns. On the 16th of September 1816, Macready made his first +London appearance at Covent Garden as Orestes in _The Distressed +Mother_, a translation of Racine's _Andromaque_ by Ambrose Philips. +Macready's choice of characters was at first confined chiefly to the +romantic drama. In 1818 he won a permanent success in Isaac Pocock's +(1782-1835) adaptation of Scott's _Rob Roy_. He showed his capacity for +the highest tragedy when he played Richard III. at Covent Garden on the +25th of October 1819. Transferring his services to Drury Lane, he +gradually rose in public favour, his most conspicuous success being in +the title-rôle of Sheridan Knowles's _William Tell_ (May 11, 1825). In +1826 he completed a successful engagement in America, and in 1828 his +performances met with a very flattering reception in Paris. On the 15th +of December 1830 he appeared at Drury Lane as Werner, one of his most +powerful impersonations. In 1833 he played in _Antony and Cleopatra_, in +Byron's _Sardanapalus_, and in _King Lear_. Already Macready had done +something to encourage the creation of a modern English drama, and after +entering on the management of Covent Garden in 1837 he introduced Robert +Browning's _Strafford_, and in the following year Bulwer's _Lady of +Lyons_ and _Richelieu_, the principal characters in which were among his +most effective parts. On the 10th of June 1838 he gave a memorable +performance of _Henry V._, for which Stanfield prepared sketches, and +the mounting was superintended by Bulwer, Dickens, Forster, Maclise, W. +J. Fox and other friends. The first production of Bulwer's _Money_ took +place under the artistic direction of Count d'Orsay on the 8th of +December 1840, Macready winning unmistakable success in the character of +Alfred Evelyn. Both in his management of Covent Garden, which he +resigned in 1839, and of Drury Lane, which he held from 1841 to 1843, he +found his designs for the elevation of the stage frustrated by the +absence of adequate public support. In 1843-1844 he made a prosperous +tour in the United States, but his last visit to that country, in 1849, +was marred by a riot at the Astor Opera House, New York, arising from +the jealousy of the actor Edwin Forrest, and resulting in the death of +seventeen persons, who were shot by the military called out to quell the +disturbance. Macready took leave of the stage in a farewell performance +of _Macbeth_ at Drury Lane on the 26th of February 1851. The remainder +of his life was spent in happy retirement, and he died at Cheltenham on +the 27th of April 1873. He had married, in 1823, Catherine Frances +Atkins (d. 1852). Of a numerous family of children only one son and one +daughter survived. In 1860 he married Cecile Louise Frederica Spencer +(1827-1908), by whom he had a son. + +Macready's performances always displayed fine artistic perceptions +developed to a high degree of perfection by very comprehensive culture, +and even his least successful personations had the interest resulting +from thorough intellectual study. He belonged to the school of Kean +rather than of Kemble; but, if his tastes were better disciplined and in +some respects more refined than those of Kean, his natural temperament +did not permit him to give proper effect to the great tragic parts of +Shakespeare, _King Lear_ perhaps excepted, which afforded scope for his +pathos and tenderness, the qualities in which he specially excelled. +With the exception of a voice of good compass and capable of very varied +expression, Macready had no especial physical gifts for acting, but the +defects of his face and figure cannot be said to have materially +affected his success. + + See _Macready's Reminiscences_, edited by Sir Frederick Pollock, 2 + vols. (1875); _William Charles Macready_, by William Archer (1890). + + + + +MACROBIUS, AMBROSIUS THEODOSIUS, Roman grammarian and philosopher, +flourished during the reigns of Honorius and Arcadius (395-423). He +himself states that he was not a Roman, but there is no certain evidence +whether he was of Greek or perhaps African descent. He is generally +supposed to have been praetorian praefect in Spain (399), proconsul of +Africa (410), and lord chamberlain (422). But the tenure of high office +at that date was limited to Christians, and there is no evidence in the +writings of Macrobius that he was a Christian. Hence the identification +is more than doubtful, unless it be assumed that his conversion to +Christianity was subsequent to the composition of his books. It is +possible, but by no means certain, that he was the Theodosius to whom +Avianus dedicates his fables. + +The most important of his works is the _Saturnalia_, containing an +account of the discussions held at the house of Vettius Praetextatus (c. +325-385) during the holiday of the Saturnalia. It was written by the +author for the benefit of his son Eustathius (or Eustachius), and +contains a great variety of curious historical, mythological, critical +and grammatical disquisitions. There is but little attempt to give any +dramatic character to the dialogue; in each book some one of the +personages takes the leading part, and the remarks of the others serve +only as occasions for calling forth fresh displays of erudition. The +first book is devoted to an inquiry as to the origin of the Saturnalia +and the festivals of Janus, which leads to a history and discussion of +the Roman calendar, and to an attempt to derive all forms of worship +from that of the sun. The second book begins with a collection of _bons +mots_, to which all present make their contributions, many of them being +ascribed to Cicero and Augustus; a discussion of various pleasures, +especially of the senses, then seems to have taken place, but almost the +whole of this is lost. The third, fourth, fifth and sixth books are +devoted to Virgil, dwelling respectively on his learning in religious +matters, his rhetorical skill, his debt to Homer (with a comparison of +the art of the two) and to other Greek writers, and the nature and +extent of his borrowings from the earlier Latin poets. The latter part +of the third book is taken up with a dissertation upon luxury and the +sumptuary laws intended to check it, which is probably a dislocated +portion of the second book. The seventh book consists largely of the +discussion of various physiological questions. The value of the work +consists solely in the facts and opinions quoted from earlier writers, +for it is purely a compilation, and has little in its literary form to +recommend it. The form of the _Saturnalia_ is copied from Plato's +_Symposium_ and Gellius's _Noctes atticae_; the chief authorities (whose +names, however, are not quoted) are Gellius, Seneca the philosopher, +Plutarch (_Quaestiones conviviales_), Athenaeus and the commentaries of +Servius (excluded by some) and others on Virgil. We have also two books +of a commentary on the _Somnium Scipionis_ narrated by Cicero in his _De +republica_. The nature of the dream, in which the elder Scipio appears +to his (adopted) grandson, and describes the life of the good after +death and the constitution of the universe from the Stoic point of view, +gives occasion for Macrobius to discourse upon many points of physics in +a series of essays interesting as showing the astronomical notions then +current. The moral elevation of the fragment of Cicero thus preserved to +us gave the work a popularity in the middle ages to which its own merits +have little claim. Of a third work, _De differentiis et societatibus +graeci latinique verbi_, we only possess an abstract by a certain +Johannes, identified with Johannes Scotus Erigena (9th century). + + See editions by L. von Jan (1848-1852, with bibliog. of previous + editions, and commentary) and F. Eyssenhardt (1893, Teubner text); on + the sources of the _Saturnalia_ see H. Linke (1880) and G. Wissowa + (1880). The grammatical treatise will be found in Jan's edition and H. + Keil's _Grammatici latini_, v.; see also G. F. Schömann, _Commentatio + macrobiana_ (1871). + + + + +MACROOM, a market town in the western part of county Cork, Ireland, on +the river Sullane, an affluent of the Lee, 24½ m. W. of Cork by the Cork +& Macroom railway, of which it is the terminus. Pop. (1901), 3016. +Besides a fine Roman Catholic church, a court house and barracks, +Macroom possesses a modernized castle, which is said to have been +founded by King John, though it is more probably attributable to Norman +invaders. It was besieged more than once in the 17th century, and is +said to have been the birthplace of Admiral Sir William Penn, whose more +famous son founded Pennsylvania. Here some rebels of 1798 were executed +and their heads exhibited on the spikes of the castle gate. Macroom has +trade in corn-milling, leather-work and dairy produce, and is a good +centre for salmon and trout fishing. It is governed by an urban district +council. + + + + +MACUGNAGA, a village of Piedmont, Italy, in the province of Novara, 20 +m. W.S.W. of Piedimulera, which is 7 m. S. of Domodossola by rail. Pop. +(1901), 798. It is situated 4047 ft. above sea-level, and is 10 m. N.E. +of the highest summit of Monte Rosa. It is frequented as a summer +resort. + + + + +MacVEAGH, WAYNE (1833- ), American lawyer and diplomatist, was born +near Phoenixville, Chester county, Pa., on the 19th of April 1833. He +graduated at Yale in 1853, was admitted to the bar in 1856, and was +district attorney of Chester county in 1859-1864. He held commands in +militia forces raised to meet threatened Confederate invasions of +Pennsylvania (1862-63). He became a leader in the Republican party, and +was a prominent opponent of his father-in-law, Simon Cameron, in the +fight within the party in 1871. MacVeagh was minister to Turkey in +1870-1871; was a member of the state constitutional convention of +1872-1873; was chairman of the "MacVeagh Commission," sent in 1877 by +President Hayes to Louisiana, which secured the settlement of the +contest between the two existing state governments and thus made +possible the withdrawal of Federal troops from the state; and was +attorney-general of the United States in 1881 under President Garfield, +but resigned immediately after Garfield's death. In 1892 he supported +Grover Cleveland, the Democratic nominee for the presidency, and from +1893 to 1897 was ambassador to Italy. He returned to the Republican +party in 1896. In 1903 he was chief counsel of the United States before +the Hague tribunal in the case regarding the claims of Germany, Great +Britain and Italy against the republic of Venezuela. + + + + +MADÁCH, IMRE (1829-1864), Hungarian dramatist, was born at +Alsó-Sztregova. He took part in the great revolution of 1848-49 and was +imprisoned; on his return to his small estate in the county of Nógrád, +he found that his family life had meanwhile been completely wrecked. +This only increased his natural tendency to melancholy, and he withdrew +from public life till 1861, devoting his time mainly to the composition +of his chief work, _Az ember tragoediája_ ("The Tragedy of Man"). John +Arany, then at the height of his fame as a poet, at once recognized the +great merits of that peculiar drama, and Madách enjoyed a short spell of +fame before his untimely death of heart-disease in 1864. In _The Tragedy +of Man_ Madách takes us from the hour when Adam and Eve were innocently +walking in the Garden of Eden to the times of the Pharaohs; then to the +Athens of Miltiades; to declining Rome; to the period of the crusades; +into the study of the astronomer Kepler; thence into the horrors of the +French Revolution; into greed-eaten and commerce-ridden modern London; +nay, into the ultra-Socialist state of the future, when all the former +ideals of man will by scientific formulae be shown up in their +hollowness; still further, the poet shows the future of ice-clad earth, +when man will be reduced to a degraded brute dragging on the misery of +his existence in a cave. In all these scenes, or rather anticipatory +dreams, Adam, Eve and the arch-fiend Lucifer are the chief and +constantly recurring _personae dramatis_. In the end, Adam, despairing +of his race, wants to commit suicide, when at the critical moment Eve +tells him that she is going to be a mother. Adam then prostrates himself +before God, who encourages him to hope and trust. The diction of the +drama is elevated and pure, and although not meant for the stage, it has +proved very effective at several public performances. + + Concerning Madách there is an ample literature, consisting mostly of + elaborate articles by Charles Szász (1862), Augustus Greguss (1872), + B. Alexander (1871), M. Palágyi (1890), and others. + + + + +MADAGASCAR, an island in the Indian Ocean, and after New Guinea and +Borneo the largest island in the world, about 260 m. distant, at the +nearest point, from the S.E. coast of Africa, from which it is separated +by the Mozambique Channel. Since 1896 Madagascar has been a French +colony. It is 995 m. in length from N. to S., and about 250 m. in +average breadth, although near the centre it is nearly 360 m. across; +its area is about 228,000 sq. m., or not quite four times the extent of +England and Wales. It lies mainly between 44° and 50° E. Its +northernmost point, Cape Ambro, in 12° S., inclines 16° to the E. from +the longitude of Cape St Mary, the southernmost point, in 25° 35´ S., so +that the main axis of the island runs from N.N.E. to S.S.W. In its broad +structure Madagascar consists of an elevated mountainous region, from +3000 to 5000 ft. in altitude, occupying from two-fifths to a half of the +centre and the eastern side of the island, around which are extensive +plains at a much less elevation above the sea, and most developed on the +western and north-west sides. But this lower region is broken up by +masses of hills, with several elevated plateaus, especially in the +south-west and south. + + _Physical Features._--Madagascar has a very regular and compact form, + with few indentations considering its great extent of shore-line. In + general outline it has a strong resemblance to the impression of a + human foot--the left side. Along two-thirds of its eastern side the + coast is almost a straight line, without any inlet, Tamatàve, the + chief port on this side of the island, being only protected by coral + reefs. North of this line, however, is Antongil Bay, a deep and wide + inlet running northwards for about 50 m.; farther north is Port + Louquez, and at almost the extreme point of the island is Diégo-Suarez + Bay, one of the finest harbours in the world. But the north-western + side of Madagascar is broken up by a number of inlets, some of them + land-locked and of considerable size. South of Cape St Andrew, the + north-west angle of the island, the coast-line is unbroken until the + estuary of the river Onilàhy, or St Augustine's Bay, is reached. + Rounding the southern end of the island, there is no other inlet save + the small bay north of Fort Dauphin, at the southern end of the + straight line of coast already mentioned. + + The islands around Madagascar are few and unimportant. The largest are + Ste Marie, near the eastern coast, a narrow island about 35 m. long, + and Nossi-bé (q.v.), larger and more compact in form, opposite + Ampàsindàva Bay on the N.W. coast. Except the Minnow group, north of + Nossi-bé, the rest are merely rocky islets, chiefly of coral. + + The shores of the greater portion of the southern half of the island + are low and flat, but in the northern half the coast is often bold and + precipitous, the high land occasionally approaching the sea. On the + eastern side the plains vary from 10 to 50 m. in breadth, but on the + western side they exceed in some localities 100 m. From these + coast-plains the ground rises by successive ranges of hills to the + high interior land. This elevated region is broken in all directions + by mountains, from which the crystalline rocks show most frequently as + huge bosses, and in certain regions present very varied and + picturesque outlines, resembling Titanic castles, cathedrals, domes, + pyramids and spires. The highest mountain mass is centrally situated + as regards the length of the island, but more to the eastern side. + This is the ancient extinct volcano Ankàratra, three of the highest + points varying in elevation from 7284 to 8635 ft. above the sea, and + from 4000 to 5000 ft. above the general level of the surrounding + country. The loftiest of these is named Tsi-àfa-jàvona, i.e. "That + which the mists cannot climb." It had been supposed that Ankàratra was + the highest point in the island, but in 1903 it was found that Ambòro, + in the northern province of Antankàrana, is about 9490 ft. in + altitude. Besides these highest points there are a considerable number + of mountains in the central provinces of Imèrina and Bétsiléo and the + intervening and surrounding districts; and in the Bàra country the + Isàlo range has been compared to the "Church Buttes" and other + striking features of the scenery of Utah. One of the finest of the + Madagascar mountains is an isolated mass near the northern point of + the island called Ambòhitra. This is 4460 ft. high, and rising from + land little above the sea-level, is well seen far out to sea. + + In the elevated region of Madagascar are many fertile plains and + valleys, the former being the dried-up beds of ancient lakes. Among + these are Bètsimitàtatra in Imèrina, and Tsiènimparìhy in Bétsiléo, + supplying a large proportion of the rice required for the capitals of + these two provinces. Still more spacious valleys are the Antsihànaka + country and the Ankày district, between the two eastern lines of + forest. The extensive coast plains on the western side of the island + are chiefly in Ibòina (N.W.) and in Ménabé (S. of the Tsìribìhina + River); those on the east are widest in the Taifàsy country (S.E.). + The water-parting for six-sevenths of the whole length of the island + is much nearer the eastern than the western side, averaging from 80 to + 90 m. from the sea. There are no arid districts, except in the extreme + south-west and towards the southern point of the island. The general + surface of the interior highland consists of bare rolling moor-like + country, with a great amount of red clay-like soil, while the valleys + have a rich humus of bluish-black alluvium. + + The chief rivers flow to the west and north-west sides of the island. + The eastern streams are all less in size, except the Mangòro, which + flows parallel with the coast. Few of them therefore are of much + service for navigation, except for the light-draught native canoes; + and all of them are more or less closed at their outlets by sand-bars. + Beginning at the south-eastern point and going northwards, the + principal rivers are the Mànanàra, Mànampàtrana, Màtitànana, + Mànanjàry, Mangòro, with its great affluent Onivé, Vòhitra, Màningòry, + and the Antànambàlana at the head of Antongil Bay. On the N.W. coast, + going southwards, are the Sofià and Màhajàmba, falling into Màhajàmba + Bay, the Bétsiboka with the Ikòpa--the great drains of the northern + central provinces, forming unitedly the second largest river of the + island and falling into Bèmbatòka Bay--the Màhavàry, Mànambòlo, + Tsìribìhina or Onimàinty, the third largest river, with its + tributaries the Kìtsàmby, Màhajìlo and Manìa, the Mòrondàva, Mangòky, + probably the largest river in the country, with its important + tributaries the Matsìatra, Mànantànana and Rànomàitso, the Fiherènana + and Onilàhy. On the south coast are four considerable streams, the + largest of which is the Mènaràndra. Of the western rivers the + Bètsibòka can be ascended by small steamers for about 100 m., and the + Tsìribìhina is also navigable for a considerable distance. The former + is about 300 m. long; the latter somewhat less, but by its affluents + spreads over a greater extent of country, as also does the Mangòky. + The rivers are all crossed frequently by rocky bars, which often form + grand waterfalls. The eastern rivers cut their way through the + ramparts of the high land by magnificent gorges amidst dense forest, + and descend by a succession of rapids and cataracts. The Màtitànana, + whose falls were first seen by the writer in 1876, descends at one + plunge some 400 ft.; and on the Vòhitra River, whose valley is + followed by the railway, there are also many fine waterfalls. + + On the eastern side of Madagascar the contest between the fresh water + of the rivers and the sea has caused the formation of a chain of + lagoons for nearly 300 m. In many places these look like a river + following the coast-line, but frequently they spread out into + extensive sheets of water. By cutting about 30 m. of canal to connect + them, a continuous waterway could be formed for 270 m. along the + coast. This has already been done for about 55 m. between Ivòndrona + and Andòvorànto, a service of small steamers forming part of the + communication between the coast and the capital. Besides these + lagoons, there are few lakes of any size in Madagascar, although there + were some very extensive lakes in a recent geological epoch. Of the + largest of these, the Alàotra Lake in the Antsihànaka plain is the + relic; it is about 25 m. long. Next comes Kinkòny, near Maròambitsy + Bay (N.W. coast), about 16 m. long, and then Itàsy, in western + Imèrina, about half as large. There is also a salt lake, + Tsimànampetsòtsa (S.W. coast), about as large as Alàotra. + + There is now no active volcano in Madagascar, but a large number of + extinct cones are found, some apparently of very recent formation. + Some miles south of Diégo-Suarez is a huge volcanic mountain, + Ambòhitra, with scores of subsidiary cones on its slopes and around + its base. About 40 m. south-west of Antanànarìvo there is a still + larger extinct volcano, Ankàratra, with an extensive lava field + surrounding it; while near Lake Itàsy are some 200 volcanic cones. + Another group of extinct volcanoes is in the Vàkinankàratra district, + S.W. of Ankàratra. Many others exist in other parts of the island (see + § _Geology_). Slight shocks of earthquake are felt every year, and hot + springs occur at many places. Several of these are sulphurous and + medicinal, and have been found efficacious in skin diseases and in + internal complaints. + + _Geology._--Madagascar may be divided into two very distinct + geological regions, viz. (I.) the Archean Region, which extends over + the central and eastern portions of the island and occupies about + two-thirds of its whole area, and is composed of crystalline schists; + and (II.) the Western Region, of sedimentary rocks, including the + remaining third of the island, in the centre of which, however, is an + isolated patch of Archean rocks, near Cape St Andrew. There are also + found in both regions numerous masses of igneous rocks, both plutonic + and volcanic, in some places of considerable extent, which pierce + through and overflow the earlier formations. + + [Illustration: Map of Madagascar.] + + I. _The Archean Region._[1]--This region, nearly coincident with the + mountainous upper portion of the island, is chiefly composed of the + following crystalline rocks: gneiss, which is the most common of them + all, quartzite and quartz-schist, with occasional beds of crystalline + limestone and mica-schist, although this latter rock is very rare. The + gneiss is mostly grey, but occasionally pinkish, its essential + constituents (felspar and quartz) being almost always associated with + dark mica (biotite) and hornblende in variable quantity. The rock is + therefore a hornblende-granitite-gneiss. Granite--more frequently + granitite--occurs in several places, as well as pyroxene-granulite, + serpentine, argillate, &c.; and gold is found widely disseminated, as + well as other metals, but these latter, as far as at present known, + except iron, are not abundant. The general strike of the rocks is the + same as that of the trend of the island itself (N.N.E. to S.S.W.), + but in its western portion the strike is frequently from N.N.W. to + S.S.E. In both cases the strike of the rocks is coincident with the + direction of several large valleys, which mark huge faults in the + crystalline rocks. Almost the whole of this region is covered by a red + soil, often of great thickness, which resembles and is often described + as "clay," but is really decomposed rock, chiefly gneiss, reddened + with oxidized magnetite. + + II. _The Sedimentary Region._--The sedimentary rocks extend + continuously along the western side of Madagascar, following the + coast-line; in the north these series of strata are only from 20 to 30 + m. across, but farther south they reach a breadth of nearly 100 m., + while opposite the Bétsiléo province they extend nearly half across + the island. A narrow band, of Cretaceous age, occurs also on the east + coast, for about 120 m., between Vàtomàndry and Mànanjàry. The + following formations are represented:-- + + 1. _Primary._ It is thought that certain beds of slaty rocks, which + have been recognized at different places, may belong to some of the + Primary strata. Some siliceous schists of the Permian age were + discovered in 1908 in the valley of the Sàkamèira, south of the + Onilàhy, or Augustine river. (S.W. coast). These contain reptilian + remains, and also clear imprints of leaves of the _Glossopteris + indica_, as well as other indications of an ancient vegetation. In the + same region conglomerates have been found containing enormous blocks, + apparently brought by glacial action, and said to be identical in + character with those described as existing in the Transvaal. True coal + has also been obtained in the same district, the deposits varying from + a third to half a metre in thickness. + + 2. _Secondary._ The lowest members of these rest directly upon the + central mass of crystalline rocks, and consist of sandstones, + conglomerates and shales, which have been supposed by some to belong + to the Trias, without, however, the discovery of any fossil necessary + to confirm this supposition, except some silicified trunks of trees. + These beds are most probably lower members of the Jurassic series. + Westward of and above these strata, the Middle and Upper Jurassic + formations are found (Lias, Lower Oolite, Oxfordian, &c.), with + well-marked and numerous fossils (_Ammonites_, _Nerinaea_, _Natica_, + _Astarte_, _Rhynchonella_, _Echinodermata_, &c.); then the Cretaceous + rocks, both these and the Jurassic series being largely developed, the + Cretaceous fossils including _Nautilus_, _Belemnites_, _Ostrea_, + _Gryphaea_, &c., and some very large Ammonites (_Pachydiscus_). The + Secondary strata show generally a very slight dip westwards and are + consequently almost horizontal. They do not seem to have been greatly + disturbed, although faults occur here and there. + + 3. _Tertiary._ A small strip of coast of Eocene age is known near + Tullear (S.W. coast), and rocks of the same period occur in Nòssi-bé, + at Màhajamba Bay, and at Diégo-Suarez, with Nummulites and other + foraminifera. Near the latter locality, beds of Oligocene age have + been noticed, consisting of coarse limestones. + + 4. _Quaternary and Recent._ A narrow band of these deposits extends + along the west coast, from north of Cape St Andrew nearly to the + extreme southern point of the island. But the most noticeable of these + are those in the ancient bed of the Alàotra Lake, which formerly + extended far southwards along the valley of the Mangòro; also those in + the marshes of Antsìrabè and of Ifànja, in the Ikòpa valley (the great + rice plain west of the capital), and also in the plain of + Tsiénimpàrìhy in Bétsiléo, and especially the recent deposits of + Ampàsambazìmba, north-west of Lake Itàsy, discovered in 1902. These + beds, rich in subfossil remains, have yielded important additions to + our knowledge of the extinct fauna of the island. (See § + _Palaeontology_.) + + _Igneous Rocks._ (1) _Plutonic rocks._--The ancient or plutonic + igneous rocks (including granite, syenite, diorite, gabbro, porphyry, + porphyrite, norite and retinite) appear at various points of the two + previously described regions. In the Archean region the gneiss is very + often found passing into granite, but certain granitic masses have a + sufficiently distinct character. In the midst of the sedimentary + region are two well-recognized masses of plutonic rocks, belonging to + the syenites, sometimes quartziferous in structure. (2) _Volcanic + rocks._--Recent volcanic eruptive rocks (including rhyolite, trachyte, + phonolite, andesite and basalt) have been examined at a number of + points throughout both the geological regions of the island. In the + Archean region these are very noticeable near Lake Itàsy, in the + _massif_ of Ankàratra (an ancient volcano) and in Vàkinankàratra (at + Bètàfo, Antsìrabé, &c.); while there are numerous outflows of + doleritic rocks, probably from faults, along the eastern side of the + island and almost parallel with the coast line. In the sedimentary + region volcanic rocks are very numerous; the most extensive of these + is a tract of country, more than 80 m. long, on the west coast, where + the basalt has overflowed the Cretaceous strata. It must be remembered + that the geology of Madagascar is still only known in its broad + features.[2] + + _Minerals and Metals._--The country has considerable mineral wealth. + Gold is found almost all over the region of crystalline rocks, except + in and around the Antsihànaka province, the richest auriferous + districts being a band of country parallel with the east coast and + spreading at its southern end into the interior; and another tract, + whose centre is about 100 m. N. of the capital (see § _Industries_, + &c.). Silver has been detected in certain galenas, and also platinum; + copper has been found in various localities, as well as zinc, lead, + nickel, antimony and manganese, but none of these metals has yet been + discovered in sufficient quantities for profitable working. Iron, on + the contrary, especially magnetite, is found abundantly and has for + long been worked by the Malagasy with the simple appliances brought by + their ancestors from their original home in the Far East. The + principal seats of the native industry are on the edge of the upper + forest, where charcoal is easily procured. The following precious + stones are reported: corundum (rubies and sapphires), beryl, topaz, + zircon, garnet, amazon-stone, tourmaline, often in large crystals, and + variously coloured quartz, also often found in crystals of great size. + Bitumen and petroleum have been found; graphite is plentiful, and + sulphur, salt, saltpetre and lime are also procured. On the north-west + coast thin beds of lignite occur, and coal has been found in the + valley of the Sàkamèira. + + _Palaeontology._--Researches in various parts of the island have + revealed the existence, in a subfossil state, of the bones of numerous + birds of the family _Struthidae_. These have been arranged in twelve + species, belonging to two genera, _Aepyornis_ and _Mullerornis_, which + varied in size from that of a bustard to birds much exceeding an + ostrich, and rivalling the recently extinct moa of New Zealand, the + largest species being about 10 ft. in height. One species of these + great wingless birds laid an egg which is the largest known, being 12½ + in. by 9½ in. Associated with these remains there have been found + those of many other birds, including a hawk, a duck, a darter, a + spoonbill, a heron, a rail and a wild-goose, some of these being much + larger than any now inhabiting Madagascar. In the same beds the + remains of two, if not three, species of hippopotamus have been found, + about two-thirds the size of the living South African species; also + the bones and carapace, &c., of gigantic tortoises, and the bones of a + crocodile, now extinct on the coast and rivers, but still living in + the two chief lakes; also the remains of a river-hog, of a species of + swine, and of a slender-legged form of zebu-ox. Near the south-west + coast the skull of a large lemuroid animal was discovered in 1893, + much longer than that of any living lemur, the animal being probably + three times the size of any previously known Madagascar lemuroid. + Later still, in 1899 and subsequently, the bones of two other + creatures of the same suborder have been discovered, one of them + indicating an animal much larger than a man. Many of these birds and + animals were probably contemporaneous with the earliest human + inhabitants of Madagascar. The remains of two species of Edentata have + been found, as well as those of several species of small Rodents, also + of a Carnivore (_Cryptoprocta_), a larger variety of the species still + living in the island. + + In the deposits of a much more remote era than those already spoken + of--the Jurassic--the bones of some enormous terrestrial lizards have + been brought to light, belonging to Sauropodous Dinosaurs of the + genera _Bothriospondylus_ and _Titanosaurus_, and to a Theropod of the + genus _Megalosaurus_. In the beds of the Lower Oolite portions of the + skull of a reptile resembling the gavial of the Ganges had been + previously discovered, from which a new genus called _Steneosaurus_ + has been founded. Since the French occupation (1895) considerable + additions have been made to our knowledge of the fossil fauna of + Madagascar from researches made both on the west and south-west coast + (at Bèlo and Ambòlisatrana) and in the interior (at Antsìrabè), + especially in the rich deposits near Tsàrazàza (Ampàsambazimba), to + the north-west of Lake Itàsy. From these various localities the + subfossil remains of thirteen or fourteen extinct species of lemuroid + animals (including the gigantic species already mentioned) have been + obtained, and have been classified under five new genera: viz. + _Megaladapis_ (3 sp.), _Palaeopropithecus_ (3 sp.), _Archaeolemur_ (2 + sp.), _Bradylemur_ (1 sp.) and _Hadropithecus_ (1 sp.), together with + three new species of lemur. Of these, the _Archaeolemurs_ seem to have + combined the characteristics of lemuroid animals with those of the + monkeys, while _Hadropithecus_ is pronounced to be the nearest known + link with them. A list of all the fossils of the island known in 1895, + but omitting the vertebrates above mentioned, included 140 + species,[3] belonging to the Mollusca, Foraminifera, Echinodermata, + Actinozoa and Plantae; but the researches of French geologists made + the total number of Madagascar fossils known in 1907 to be not fewer + than 280 species. + + _Climate._--In the high interior the climate resembles that of the + temperate zones, although six-sevenths of the island are within the + tropics; there is no intense heat, and it is quite cold, occasionally + touching freezing point, during the nights of the cool season. These + parts of the country are tolerably healthy for Europeans. But the + coasts are much hotter, especially on the western side, as is also the + interior west of the highland region; and from the large amount of + marsh and lagoon on the coasts, malarial fever is common and + frequently fatal, both to Europeans and to natives from the interior. + Epidemics of influenza and fever have been very prevalent of late + years in the central provinces. The seasons are two--the hot and rainy + season from November to April, and the cool and dry season during the + rest of the year; this remark applies chiefly to the interior, for + rain falls throughout the year on the eastern coast, which is exposed + to the vapour-laden south-east trade winds. The rainfall diminishes as + one goes westward and especially south-westward, there being very + little rain in the south-west corner of the island. No snow is known, + even on the loftiest mountains, but thin ice is occasionally seen; and + hail-showers, often very destructive, are frequent in the rainy + season. Terrific thunderstorms are also common at that period; + waterspouts are sometimes seen; and as the Indian Ocean cyclone region + touches the eastern coast, hurricanes occur every few years, at rare + intervals ascending into the interior highland. The yearly rainfall of + the Imèrina province (Antanànarìvo) averages about 54½ in.; accurate + statistics as to that of other parts of the island are not available; + but on the east coast it appears to be about double that of the + interior; in the south-east considerably more than that amount; while + at Mòrondàva (west coast) it is given as about 21 in. annually, and at + Tullear (south-west coast) as only 10 in. At Tamatàve (east coast) the + mean annual temperature is given as 76.5°, while at the capital it is + about 66°; the temperature of Antanànarìvo resembles that of Naples or + Palermo.[4] The following table gives the mean of two different sets + of government returns of mean rainfall: Antanànarìvo, 1369 mm.; + Tamatàve, E. coast, 1863 mm.; Fàrafangàna, S.E. coast, 2803 mm.; + Diégo-Suarez, N. end of island, 1196 mm.; Mòrondàva, W. coast, 543 + mm.; Tullear, S.W. coast, 273 mm.; Màrovoày, W. interior, 1413 mm. + + _Fauna._--The fauna of Madagascar, while deficient in most of the + characteristic tropical forms of life, is one of great interest to the + naturalist from its remote affinities, much of its animal life having + Asiatic rather than African relationships. The central portions of the + island, from their generally bare and treeless character, are poor in + living creatures; but the lower country, and especially the forests + and coast plains, are fairly well stocked. But it is noticeable that + many species have a very limited range. Although a continental island, + it possesses no large quadrupeds--none of the larger carnivorous, + ungulate, proboscoid or quadrumanous animals; but it is the + headquarters of the _Lemuroidea_, no fewer than thirty-nine species of + which are found in its forests and wooded plains. Some of these + creatures are highly specialized, while the curious aye-aye (_Chiromys + madagascariensis_), an allied form, is one of the most remarkable + animals known, forming a genus and family by itself. Its whole + structure is strangely modified to enable it to procure the + wood-boring larvae which form its food. Other peculiar animals are + twenty-three species of the _Centetidae_, a family of the Insectivora + almost confined to Madagascar; while of the _Carnivora_ there are + several small creatures belonging to the civets (_Viverridae_). The + largest of these ferocious animals, also forming a genus and family by + itself, is the _Cryptoprocta ferox_; it is a plantigrade animal, 3 ft. + long, but very like an enormous weasel, and attacks other animals with + the greatest ferocity. The island contains twenty-five species of + bats, mostly of African, but some of Indian, affinities. African + humped cattle were introduced several hundred years ago and now exist + in large herds all over the country. The fat-tailed sheep, goats and + swine have also been naturalized, as well as all kinds of domestic + poultry. + + The avi-fauna is much richer than the mammalian, and, although wanting + the largest birds as well as the most brilliantly coloured, comprises + two hundred and sixty species, half of which are endemic. Many of the + birds are remarkable not so much for their shape or colouring as for + their distant relationships; many belong to peculiar genera, and some + are so isolated that new families have had to be formed for their + reception. There is a large variety of perching birds, including + several species of brilliant plumage--sun-birds, kingfishers, rollers + and flycatchers, &c.; kites, hawks and owls are numerous, and the + lakes and marshes abound with water-fowl and herons, ibises, &c. + + The island is free from deadly serpents, but contains two or three + small species of boa; crocodiles abound in the rivers and lakes; and + numerous species of lizard, chameleon and tree-frog inhabit the woods. + Madagascar may be considered as one of the headquarters of the + _Chamaeleonidae_, for of the fifty known species no fewer than + twenty-five have already been described from the island. Many of these + are of curious form, with remarkable developments of the plates of the + head and projecting horns and spines. There are several peculiar + tortoises, but the gigantic species are now found alive only on the + little island of Aldabra, to the north. The insect life comprises many + brilliantly-coloured beetles, butterflies (about eight hundred species + of which are known), moths, locusts, spiders and flies, and also + noxious spiders, with scorpions and centipedes. The river fishes + belong chiefly to the family _Chromididae_; many of them are of + brilliant and bizarre appearance, with strongly contrasted colours in + bands and spots. Those found in the coast waters do not differ + materially from the widely spread Indian Ocean species. + + As a whole, the Madagascar fauna is marked by a strong individuality, + which would appear to be the result of long isolation from the other + zoological "regions." The Asiatic and Malayan affinities of many of + its animals, as well as the physical conditions of the bed of the + Indian Ocean, make it highly probable that Madagascar, while once + forming part of Africa, is the chief relic of a considerable + archipelago formerly connecting that continent with Asia, its other + portions being shown by groups of small islands, and by coral atolls + and shoals, which are gradually disappearing beneath the waves. These + questions have been fully treated by Dr A. R. Wallace in his + _Geographical Distribution of Animals_ (vol. i. ch. ix., 1876) and + _Island Life_, ch. xix. (1880). + + _Flora._--The flora of Madagascar is one of great interest. One of its + most prominent features is the belt of forest round a large part of + the island at no great distance from the sea, and generally following + the coast-line. This forest is densest on the east side, and for about + 120 m. forms a double line, the lower one being much the broader and + averaging 30 m. across, but attaining a breadth of 60 or 70 m. on the + north-east, near Antongil Bay. The vegetation on the western side of + the island is much less dense, often appearing as scattered clumps of + trees on savannah-like plains rather than continuous forest; while in + the south-west, where the rainfall is very scanty, the vegetation is + largely of fleshy-leaved and spiny plants--aloes and cacti (the latter + introduced), with several species of Euphorbia, as well as numerous + lianas, one of which (_Intisy_) yields india-rubber. It is estimated + that there are about 30,000 sq. m. of forest-covered country in + Madagascar, or about one-eighth of its whole surface. The vegetation + of the forests, the abundant epiphytes, the tree-mosses, the filmy + ferns and the viviparous character of many of the ferns, show clearly + how abundant the rainfall is in the eastern forest region. This + contains a large variety of hard-wooded and valuable timber trees, + including species of _Weinmannia_ (_Lalòna_[5]), _Elaeocarpus_ + (_Voànana_), _Dalbergia_ (_Vòambòana_), _Nuxia_ (_Vàlanìrana_), + _Podocarpus_, a pine, the sole species in the island (_Hètatra_), + _Tambourissa_ (_Ambòra_), _Neobaronia_ (_Hàrahàra_), _Ocotea_ + (_Varòngy_) and probably ebony, _Diospyros_ sp., &c. The following + trees are characteristic of Madagascar vegetation, some of them being + endemic, and others very prominent features in the landscape: the + traveller's-tree (_Urania speciosa_), with its graceful crown of + plantain-like leaves growing like an enormous fan at the top of a tall + trunk, and affording a supply of pure cool water, every part of the + tree being of some service in building; the Raphia (rofia) palm + (_Sagus ruffia_); the tall fir-like _Casuarina equisetifolia_ or + beefwood tree, very prominent on the eastern coast, as well as several + species of screw-pine (_Pandanus_); the Madagascar spice (_Ravintsara + madagascariensis_), a large forest tree, with fragrant fruit, leaves + and bark; a beautiful-leaved species of _Calophyllum_; and the Tangèna + (_Tanghinia veneniflua_), formerly employed as a poison ordeal. On the + lagoons and lower reaches of the rivers the Vìha (_Typhonodorum + lindleyanum_), an arum endemic to Madagascar, grows in great profusion + to a height of 12 or 13 ft. and has a white spathe more than a foot in + length; and on the western coast dense thickets of mangrove line the + creeks and rivers. In the interior rivers is found the curious and + beautiful lace-leaf plant (_Ouvirandra fenestralis_), with an edible + tuberous root. On the western side of the island the baobab, the + tamarind, the ròtra (_Eugenia_ sp.), the rofia palm, and several + species of fan-palm (_Hyphaene_) and of _Ficus_ are prominent; and the + mango (introduced) grows to a large tree. In the generally bare + interior highlands, large trees, species of _Ficus_ (_Amòntana_, + _Aviàvy_, _Nònoka_, _Adàbo_, &c.), often mark the position of the old + towns; and some of these, as Ambòhimànga, Vòhilèna, &c., are + surrounded by remnants of the original forest, which formerly covered + large portions of the interior. The most prominent tree in the central + province is now the Cape-lilac (_Melia azederach_) introduced about + 1825; and since the French conquest several species of eucalyptus have + been planted in vast numbers by the road sides. These have given quite + a new aspect to the vegetation, while bright colour is imparted by + species of _Bougainvillea_ and _Poinsettia_. In the eastern forests + palms, bamboos, lianas and tree-ferns, as well as species of + _Dracaena_, are found. + + Although flowers growing on the ground or on shrubs are not + conspicuous for number or beauty, there are many fine flowering trees, + such as _Poinciana regia_, presenting a mass of scarlet flowers; + _Colvillia racemosa_, with yellow flowers; _Astrapaea Wallichii_, + striking attention from its abundant flowers; and species of + _Cryptostegia_, a purple-flowered creeper, and _Strongylodon_, another + creeper with cream-coloured blossoms. Among attractive plants are + species of _Hibiscus, Euphorbia, Buddleia, Ixora, Kitchingia, + Clematis_, &c. On the east coast two orchids, species of _Angraecum_, + with large white waxy flowers, one with an extraordinarily long spur + or nectary, attract the attention of every traveller during June and + July by their abundance and beauty. Some 320 species o£ fern have been + collected, and there are large numbers of spiny and prickly plants, as + well as numerous grasses, reeds and rushes, many of them of great + service in the native manufactures of mats, hats, baskets, &c. + + The Rev R. Baron divides the flora into three distinctly marked + "regions," which run in a longitudinal direction, following + approximately the longer axis of the island, and are termed + respectively eastern, western and central. The central includes the + elevated highland of the interior, while the eastern and western + include the forest belts and most of the wooded country and coast + plains. Of the 4100 known plants--of which about three-fourths are + endemic--composing the Madagascar flora, there are 3492 Dicotyledons, + 248 Monocotyledons and 360 Acotyledons. Of these, the orders most + largely represented (together with their species) are: Leguminosae, + 346; Filices, 318; Compositae, 281; Euphorbiaceae, 228; Orchideae, + 170; Cyperaceae, 160; Rubiaceae, 147; Acanthaceae, 131; Gramineae, + 130. The number of endemic genera now known is 148. Of the 3178 + species of plants whose localities have been determined, 35% are + peculiar to the eastern region, 27.5% to the central, and 22% to the + western. One natural order, Chlaenaceae, is strictly confined to + Madagascar. "A small proportion of the species are Asian, but not + African; and the flora of the mountains corresponds closely with that + of the great ranges of the tropical zone of Africa." "The general plan + of the flora follows thoroughly the same lines as that of the tropical + regions of the Old World." + + Among the food-giving plants are rice--the staff of life to the + majority of the Malagasy--in many varieties, maize, millet, manioc, + yams, sweet-potatoes, arrowroot, which is largely used by the western + tribes--as well as numerous vegetables, many of them of foreign + introduction. The fruits--the majority of which are introduced--are + the banana, peach, loquat, pineapple, mango, melon, grape, quince, + plum, apple, mulberry, orange, lemon, citron, guava, Chinese-guava, + Cape-gooseberry, fig, raspberry, tomato, &c. Several spices are grown, + including ginger, capsicum, &c.; sugar-cane, coffee, indigo, vanilla, + tobacco, cotton, hemp, gourds, dye-woods, gums, mulberry and other + trees and plants for silk-culture, are also among the vegetable + productions; gum-copal was formerly, and india-rubber is still, an + important article of export. + +_Provinces and Towns._--The island may be divided into districts or +provinces, which in the main indicate tribal divisions. Of these tribal +territories the following may be distinguished, taking them in three +main divisions, from north to south: (1) _Eastern_: Antankàrana, +occupying the northern peninsula; the country of the Bétsimisàraka, who +inhabit a long extent of the coast plains, about 500 m. in length; +parallel with this for about a third of it, and between the two lines of +forest, is the Bézànozàno country. South again are the districts of the +Taimbahòaka, the Taimòro, the Taifàsy and the Taisàka; and at the +south-eastern corner are the Tanòsy. (2) _Central_: the districts of +Tsimihèty and the Sihànaka; Imèrina, the Hòva province; the Bétsiléo; +the Tanàla or foresters; the Bàra; and the emigrant Tanòsy. (3) +_Western_: the people from almost the northern to the southern +extremities of the island are known as Sàkalàva, but consist of a number +of distinct tribes--the Tibòina, the Màilaka, the Taménabé, and the +Fiherènana, &c. South of these last are the Màhafàly, with the Tandròy +at the extreme south. There are no distinctly marked boundaries between +any of these tribal territories; and west of Imèrina and Bétsiléo there +is a considerable extent of country with hardly any population, a kind +of "no-man's-land." There are numerous subdivisions of most of the +tribes. + +The capital, Antanànarìvo (pop. 69,000), in the highlands of Imèrina, +and Tamatàve (pop. 4600), on the east coast and the chief seaport, are +separately described. Majunga (properly Mojangà, pop. 5300) on the +north-west coast, just north of 16° S., and Diégo-Suarez, are important +ports for foreign trade, the latter being also a fortified naval and +military station. Other ports and towns are Màhanòro, Mànanjàry (S.E. +coast, pop. 4500), Tullear (S.W. coast), and Fianàrantsòa (pop. 6200), +the chief town of the Bétsiléo. There are very few places besides these +with as many as 2000 people. + +_Inhabitants._--The population is somewhat under two and three-quarter +millions,[6] including some 10,000 or 11,000 Europeans, and a smaller +number of Indian, Arab, and other Asiatics, mostly small traders found +in the seaports, the Chinese being found in every town of any size. The +island, it will be seen, is very sparsely inhabited; the most densely +peopled province is that of Imèrina with (1905) 388,000 inhabitants. The +natives, collectively known as Malagasy, are divided into a considerable +number of tribes, each having its distinct customs. Although +geographically an African island, the majority of its inhabitants are +derived, the lighter portion of them from the Malayo-Polynesian stock, +and the darker races from the Melanesian. This is inferred from their +similarity to the peoples of the Indian and Pacific archipelagoes in +their physical appearance, mental habits, customs, and, above all, in +their language. Their traditions also point in the same direction. There +is, however, an undoubted African mixture in the western and some other +tribes. There is also an Arab element both on the north-west and +south-east coasts; and it appears that most of the families of the +ruling classes in all parts of the island are descended from Arabs, who +married native women. It is believed that there are traces of an +aboriginal people (the Vazimba), who occupied portions of the interior +before the advent of the present inhabitants, and these appear to have +been a somewhat dwarfish race, and lighter-coloured than the Malagasy +generally. The Hòva became the dominant tribe from the beginning of the +19th century; they appear to be the latest immigrants, and are the +lightest in colour; and they are also the most intelligent and civilized +of all the peoples inhabiting the island. + +The most striking proof of the virtual unity of the inhabitants of +Madagascar is that substantially but one language is spoken over the +whole country. The Malay affinities of Malagasy were noted in the 16th +century; indeed, the second and fifth books published upon the country +(in 1603 and 1613) were comparative vocabularies of these two languages. +Later investigations have confirmed the conclusions thus early arrived +at; and Van der Tuuk, Marre de Marin and W. E. Cousins have shown +conclusively the close relationships between the language of the +Malagasy and those of the Malayo-Polynesian regions; similar connexions +exist, especially in grammatical construction, between the Malagasy and +Melanesian languages. The Malagasy had never invented for themselves a +written character, and had consequently no manuscripts, inscriptions or +books, until their language was reduced to writing, and its orthography +settled by English missionaries. Their speech nevertheless is very full +in many of its verbal and other forms, while it also exhibits some +curious deficiencies. It is very soft and musical, full of vowels and +liquids, and free from all harsh gutturals. Native oratory abounds in +figures, metaphors and parables; and a large number of folk-tales, songs +and legends, together with the very numerous proverbs, give ample +evidence of the mental ability and imaginative powers of the Malagasy. + + Native society in Imèrina among the Hòva was formerly divided into + three great classes: the Andrìana, or nobles; the Hòva, freemen or + commoners; and the Andèvo, or slaves; but these last became free by a + proclamation issued in 1896. The Andrìana are, strictly speaking, + royal clans, being descendants of petty kings who were conquered or + otherwise lost their authority through the increasing power of the + ancestors of the reigning family. Their descendants retained certain + honours in virtue of their royal origin, such as special terms of + salutation, the use of the smaller scarlet umbrella (the larger one + was the mark of royal rank), the right to build a particular kind of + tomb, &c.; they also enjoyed exemption from certain government + service, and from some punishments for crime. The Hòva[7] or commoners + form the mass of the population of Imèrina. They are composed of a + large number of tribes, who usually intermarry strictly among + themselves, as indeed do families, so that property and land may be + kept together. The third great division was the slave population, + which since 1896 has become merged in the mass of the people. The + Mozambiques or African slaves, who had been brought from the African + coast by Arab dhows, were in 1877 formally set free by an agreement + with the British government. + + Royalty and chieftainship in Madagascar had many peculiar customs. It + had a semi-sacred character; the chief was, in heathen tribes, while + living, the high priest for his people, and after death, was + worshipped as a god; in its modern development among the Hòva + sovereigns it gathered round it much state and ceremony. There were + many curious examples of the taboo with regard to actions connected + with royalty, and also in the words used which relate to Malagasy + sovereigns and their surroundings. These were particularly seen in + everything having to do with the burial of a monarch. While the + foregoing description of native society applied chiefly to the people + of the central province of Imèrina, it is applicable, with local + modifications, to most of the Malagasy tribes. But on the island + becoming a French colony, in 1896, royalty was formally abolished; and + little regard is paid to native rank by French officials. + + The chief employment of the Malagasy is agriculture. In the + cultivation of rice they show very great ingenuity, the _kètsa_ + grounds, where the rice is sown before transplanting, being formed + either on the margins of the streams or in the hollows of the hills in + a series of terraces, to which water is often conducted from a + considerable distance. In this agricultural engineering no people + surpass the Bétsiléo. No plough is used, all work being done by a + long-handled spade; and oxen are only employed to tread out the soft + mud preparatory to transplanting. The rice is threshed by being beaten + in bundles on stones set upright on the threshing-floor; and when + beaten out the grain is stored by the Hòva in rice-pits dug in the + hard red soil, but by the coast tribes in small timber houses raised + on posts. In preparing the rice for use it is pounded in a wooden + mortar to remove the husk, this work being almost always done by the + women. The manioc root is also largely consumed, together with several + other roots and vegetables; but little animal foods (save fish and + freshwater _Crustacea_) is taken by the mass of the people except at + festival times. Rice is used less by the western tribes than by those + of the central and eastern provinces, and the former people are more + nomadic in their habits than are the others. Large herds of fine + humped cattle are found almost all over the island. + + The central and eastern peoples have considerable manual dexterity. + The women spin and weave, and with the rudest appliances manufacture a + variety of strong and durable cloths of silk, cotton and hemp, and of + ròfia palm, aloe and banana fibre, of elegant patterns, and often with + much taste in colour. They also make from straw and papyrus peel + strong and beautiful mats and baskets in great variety, some of much + fineness and delicacy, and also hats resembling those of Panama. The + people of the south and south-east make large use of soft rush matting + for covering, and they also prepare a rough cloth of bark. Their + non-employment of skins for clothing is a marked distinction between + the Malagasy and the South African races, and their use of vegetable + fibres an equally strong link between them and the Polynesian peoples. + The men wear a loincloth or _salàka_, the women a _kitàmby_ or apron + folded round the body from waist to heel, to which a jacket or dress + is usually added; both sexes use over these the _làmba_, a large + square of cloth folded round the body something like the Roman toga, + and which is the characteristic native dress. The Malagasy are skilful + in metal-working; with a few rude-looking tools they manufacture + silver chains of great fineness, and filagree ornaments both of gold + and silver. Their iron-work is of excellent quality, and in copper and + brass they can produce copies of anything made by Europeans. They + display considerable inventive power, and they are exceedingly quick + to adopt new ideas from Europeans. + + There is a considerable variety in the houses of the different + Malagasy tribes. The majority of Hòva houses were formerly built of + layers of the hard red soil of the country, with high-pitched roofs + thatched with grass or rush; while the chiefs and wealthy people had + houses of framed timber, with massive upright planking, and lofty + roofs covered with shingles or tiles. But the introduction of + sun-dried and burnt bricks, and of roofing tiles in the central + provinces has led to the general use of these materials in the + building of houses, large numbers of which are made in two storeys and + in European fashion. The forest and coast tribes make their dwellings + chiefly of wood framing filled in with the leaf-stalks of the + traveller's tree, with the leaves themselves forming the roof + covering. The houses of the Bétsiléo and Sàkalàva are very small and + dirty, but those of the coast peoples are more cleanly and roomy. + Among the Hòva and Bétsiléo the old villages were always built for + security on the summits of lofty hills, around which were dug several + deep fosses, one within the other. In other districts the villages and + homesteads are enclosed within formidable defences of prickly-pear or + thorny mimosa. + + Apart from the modern influence of religious teaching, the people are + very immoral and untruthful, disregardful of human life and suffering, + and cruel in war. Until lately polygamy has been common among all the + Malagasy tribes, and divorce effected in an absurdly easy fashion. At + the same time the position of woman is much higher in Madagascar than + in most heathen countries; and, the fact that for nearly seventy years + there were (with a few months' exception) only female sovereigns, + helped to give women considerable influence in native society. The + southern and western peoples still practise infanticide as regards + children born on several unlucky days in each month. This was formerly + the general practice all over the island. The old laws among the Hòva + were very barbarous in their punishments, and death in various cruel + forms was inflicted for very trifling offences. Drunkenness is very + prevalent in many parts of the island; and it can hardly be said of + many of the Malagasy that they are very industrious. But they are + courageous and loyal to their chiefs and tribe, and for short periods + are capable of much strenuous exertion. They are affectionate and firm + in their friendships, kind to their children and their aged and infirm + relatives, very respectful to old age, most courteous and polite and + very hospitable to strangers. Slavery had a patriarchal and family + character, and was seldom exercised in a cruel or oppressive way. + + The Malagasy have never had any organized religious system or forms of + worship; there are no temples, images or stated seasons of devotion, + nor is there a priesthood, properly so-called. Yet they have never + been without some distinct recognition of a supreme being, whom they + call _Andriamànitra_, "The Fragrant One," and _Zànahàry_, "The + Creator"--words which are recognized all over the island. They have + also retained many ancient sayings, proverbial in their style, which + enforce many of the truths of natural religion as to the attributes of + God. With all this, however, there has long existed a kind of + idolatry, which in its origin is simply fetishism--the belief in + charms--as having power to procure various benefits and protect from + certain evils. Among the Hòva in modern times four or five of these + charms had acquired special sanctity and were each honoured as a kind + of national deity, being called "god," and brought out on all public + occasions. Together with this idolatry there is also a firm belief in + the power of witchcraft and sorcery, in divination, in lucky and + unlucky days and times, in ancestor worship, especially that of the + sovereign's predecessors, and in several curious ordeals for the + detection of crime. The chief of these was the celebrated tangèna + poison ordeal, in which there was implicit belief, and by which, until + its prohibition by an article in the Anglo-Malagasy treaty of 1865, + thousands of persons perished every year. Sacrifices of fowls and + sheep are made at many places at sacred stones and altars, both in + thanksgiving at times of harvest, &c., and as propitiatory offerings. + Blood and fat are used to anoint many of these stones, as well as the + tombs of ancestors, and especially those of the Vazimba. In some of + the southern districts it is said that human sacrifices were + occasionally offered. The chief festival among the Hòva, and almost + confined to them, was that of the New Year, at which time a kind of + sacrificial killing of oxen took place, and a ceremonial bathing, from + which the festival took its name of Fàndròana (the Bath). This + festival is now merged in the French national fête of the 14th of + July. Another great festival was at circumcision times. This rite was + observed by royal command at intervals of a few years; these were + occasions of great rejoicing, but also of much drunkenness and + licentiousness. Since 1868 circumcision has been observed by each + family at any time convenient to itself. It is practised by all the + Malagasy tribes. Funerals were also times of much feasting, and at the + death of people of rank and wealth numbers of bullocks were and are + still killed. Although there was no proper priesthood, the + idol-keepers, the diviners, the day-declarers and some others formed a + class of people closely connected with heathen customs and interested + in their continued observance. + +_Industries and Commerce._--The rearing of cattle and the dressing of +hides, the collection of rubber and bee culture are important +industries. The chief food crops grown have been indicated (see +_Flora_), and the gold-mining is separately noticed below. Other +industries undertaken or developed by Europeans are silk and cotton +weaving and raphia-fibre preparation, and ostrich farming. Sugar, rice, +soap and other factories have been established. In 1904 the exportation +of straw and other fibre hats began; these resemble those of Panama and +promise to become an important item. Tanning bark, coffee and guano are +also recent exports. + +Since 1862, when the country was thrown open to foreign trade, the +growth of over-sea commerce has been comparatively slow. In the early +days cattle were the chief export. About 1870 india-rubber began to be +exported in considerable quantities, and cattle, rubber and hides +continue staple products. Other important exports are raphia fibre and +beeswax. Since 1900 gold has become a leading export, the value of the +gold sent out of the country in the five years 1901-1906 being +£1,384,493. The imports consist chiefly of tissues (mostly cotton +goods), breadstuffs and rice, liquors, metal-ware and coal. Better means +of internal transport and increased production in the island have +greatly reduced the import of rice, which came mostly from Saigon. + +Before the occupation of Madagascar by France the duty on imports and +exports was 10% _ad valorem_, and the foreign trade was very largely in +the hands of British and American merchants. In July 1897 the French +tariff was applied and increased rates levied on foreign goods, notably +cottons. This practically killed the American trade and reduced the +British trade to a very small proportion. In 1897 the British imports +were valued at £179,000; the next year, with the new tariff in force, +they had dropped to £42,000. The only export duties are: cattle 2s. per +head and rubber 2d. per lb. + +In 1880-1885 the entire foreign trade of Madagascar, imports and +exports, was estimated to be about £1,000,000; in 1900-1906 the volume +of trade had increased to a little over £2,500,000 a year. But while +from 1900 onwards imports had a tendency to decrease (they were +£1,841,310 in 1901 and £1,247,936 in 1905), exports steadily increased, +owing to the working of gold-mines. The total value of the exports rose +from £359,019 in 1901 to £822,470 in 1906.[1] About 90% of the trade is +with France or other French colonies. The remaining trade is nearly all +British and German. + +Banking business is in the hands of French companies. The legal currency +is the French 5-franc piece and the smaller French coins. There was no +native coinage, the French 5-franc piece or dollar being the standard, +and all sums under that amount were obtained by cutting up those coins +into all shapes and sizes, which were weighed with small weights and +scales into halves, quarters, eighths, twelfths and twenty-fourths of a +dollar, and even reckoned down to the seven hundred and twentieth +fraction of the same amount. + + _Gold-mining._--Gold-mining has been carried on regularly since 1897, + and by 1900 the value of the ore extracted exceeded £100,000. Reports + of rich discoveries attracted considerable attention in South Africa + and Europe during 1904-1906, but experts, sent from the Transvaal, + came to the conclusion that Madagascar would not become one of the + rich goldfields of the world. The chief mining districts have been + already indicated (see under _Geology_). Rich finds were reported from + the north of the island during 1907, in which year the export of gold + was £320,000. The mines afford a lucrative occupation for some + thousands of persons, and many of the claim-holders are British. + Decrees of 1902 and 1905 regulate the conditions under which mining is + carried on. By decree of the 23rd of May 1907, the radius of the + circle within which claims may be pegged is 2 kilometres (1¼ m.), and + a tax of 5% is levied on the value of the gold extracted. + + _Communications._--There is regular steamship communication between + the chief ports and Marseilles, Zanzibar and India (via Mauritius and + Ceylon); and a submarine cable to Mozambique places the island in + telegraphic connexion with the rest of the world. The French have + built carriage roads from the interior to the principal ports as well + as to connect the principal towns. On these roads large use is made of + bullock wagons, as well as carts drawn by men, and women also. + Tamatàve and Antanànarìvo are joined by coast canals and lakes and by + a railway service. Where other means are not available, goods are + carried by canoes, or on the shoulders of bearers along the native + footpaths. + + There is a well-organized postal service, and all the towns of note + are linked by a telegraph system, which has a length of over 4000 + miles. + +_Government, Revenue, &c._--The colony is not represented in the French +Chambers, nor has it self-government. At the head of the administration +is a governor-general, who is assisted by a nominated council of +administration which includes unofficial members. This council must be +consulted on matters affecting the budget. In several towns there are +_chambres consultatives_, composed of local merchants and planters. The +island is divided into _circles_, placed under military officers, and +_provinces_, presided over by a civilian. As far as possible in local +affairs, each of the native races is granted autonomy, the dominion of +the Hòva over the other tribes being abolished. Each province has its +native governor and minor officials, the governor being generally +selected by popular vote. Each village has an organization (the _Fòkon' +òlona_) resembling that of a commune; at its head is a chief or +_mpiadidy_, who serves for three years. + + +-----------------+---------+----------+----------+ + | Exports: | 1901 | 1906 | Increase.| + +-----------------+---------+----------+----------+ + | Rubber | £26,679 | £301,518 | £274,839 | + | Hides and skins | 31,548 | 250,339 | 218,791 | + | Gold | 131,987 | 270,613 | 138,626 | + +-----------------+---------+----------+----------+ + + For Europeans and in suits between Europeans and natives the French + judicial code is applicable; suits between natives are tried by native + tribunals (established 1898) presided over by a European assisted by + two native assessors. These tribunals judge according to native law + and usages, except when such customs (e.g. polygamy and slavery) have + been expressly abolished. Arbitration councils are available + everywhere for the settlement of disputes between native workmen and + their employers. The native laws respecting land tenure have been + improved by the adoption of a method of registration based on the + Torrens system. + + Revenue is derived from land, house and capitation taxes, from + customs, posts and telegraphs, ferries, licences and other indirect + imposts. The excess of expenditure over revenue is made good by + subventions from France. A considerable portion of the revenue is + expended on public works. Revenue and expenditure in 1905 were each + just beneath £1,000,000. This is exclusive of the sums spent by France + in the island on the army, and for the naval base at Diégo-Suarez. + There is a public debt amounting (1907) to £4,055,600. As stated in + the French senate (February 1909), everything is taxed in the island; + and no sooner has any enterprise become fairly successful than it is + so heavily taxed as to be no longer worth carrying on, and certain + crops have therefore been destroyed by the colonists who had planted + them. This has been the case with tobacco, sugar, rum, and also in + butter-making, cattle-breeding and other things. Notwithstanding this + taxation, from 1895 to 1908 £12,000,000 was required for Madagascar + from the home government, and the demand is constantly increasing. + +_History._--From the earliest accounts given of the people of Madagascar +by European travellers, as well as from what may be inferred from their +present condition, they seem for many centuries to have been divided +into a number of tribes, often separated from one another by a wide +extent of uninhabited country. Each of these was under its own chief, +and was often at war with its neighbours. No one tribe seems to have +gained any great ascendancy over the rest until about the middle of the +17th century, when a small but warlike people called Sàkalàva, in the +south-west of Madagascar, advanced northward, conquered all the +inhabitants of the western half of the island, as well as some northern +and central tribes, and eventually founded two kingdoms which retained +their supremacy until the close of the 18th century. About that time, +the Hòva in the central province of Imèrina began to assert their own +position under two warlike and energetic chieftains, Andrianimpòina and +his son Radàma; they threw off the Sàkalàva authority, and after several +wars obtained a nominal allegiance from them; they also conquered the +surrounding tribes, and so made themselves virtual kings of Madagascar. +From that time until 1895 Hòva authority was retained over a large part +of the central and eastern provinces, but it was only nominal over much +of the western side of the island, while in the south-west the people +were quite independent and governed by their own chiefs. + + + Arab Intercourse and Influence. + +While European intercourse with Madagascar is comparatively recent, the +connexion of the Arabs with the island dates from a very remote epoch; +and in very early times settlements were formed both on the north-west +and south-east coasts. In the latter locality there are still traces of +their influence in the knowledge of Arabic possessed by a few of the +people. But in these provinces they have become merged in the general +mass of the people. It is different, however, in the north-west and west +of the island. Here are several large Arab colonies, occupying the ports +of Anòrontsànga, Mòjangà, Màrovoày and Mòrondàva, and retaining their +distinct nationality. There is also in these districts a Hindu element +in the population, for intercourse has also been maintained for some +centuries between India and northern Madagascar, and in some towns the +Banyan Indian element is as prominent as the Arab element. In the early +times of their intercourse with Madagascar, the Arabs had a very +powerful influence upon the Malagasy. This is seen in the number of +words derived from the Arabic in the native language. Among these are +the names of the months and the days of the week, those used in +astrology and divination, some forms of salutation, words for dress and +bedding, money, musical instruments, books and writings, together with a +number of miscellaneous terms. + + + European Intercourse. + +The island is mentioned by several of the early Arabic writers and +geographers, but medieval maps show curious ignorance of its size and +position. Marco Polo has a chapter upon it, and terms it "Madeigascar," +but his accounts are confused with those of the mainland of Africa. The +first European voyager who saw Madagascar was a Portuguese named Diogo +Diaz, captain of one of the ships of a fleet commanded by Pedro Cabral +and bound for India. Separated from his companions by a storm near the +Cape, he sighted the eastern coast of the island on the 10th of August +1500. That day being the feast of St Lawrence, Madagascar was named the +"Isle of St Lawrence," and retained that name on all maps and charts for +a hundred years. The Portuguese gave names to most of the capes, but +made no persistent attempts at colonization. After them the Dutch +endeavoured, but with little success, to form colonies; and in the time +of Charles I. proposals were made to form an English "plantation," but +these were never carried into effect, although for a short time there +was a settlement formed on the south-west coast. In the latter part of +the 17th and during most of the 18th century the French attempted to +establish military positions on the east coast. For some time they held +the extreme south-east point of the island at Fort Dauphin; but several +of their commandants were so incapable and tyrannical that they were +frequently involved in war with the people, and more than once their +stations were destroyed and the French were massacred. Early in the 19th +century all their positions on the mainland were relinquished, and they +retained nothing but the island of Ste Marie on the east coast. In 1811 +Tamatàve had been occupied by British troops, and the Treaty of Paris of +1814 recognized as British the "French settlements in Madagascar," but +as a matter of fact France had then no settlements on the mainland. The +then governor of Mauritius, Sir Robert Farquhar, endeavoured to +prosecute British claims and obtained a cession of Diégo-Suarez Bay. +These claims were not backed up by the home government, and a little +later the policy was adopted by Great Britain of supporting the Hòva +authority. + + + Radàma I. + + Introduction of Christianity. + +The political history of Madagascar as a whole may be said to date from +the reign of Radàma I. (1810-1828). He was a man much in advance of his +age--shrewd, enterprising, and undeterred by difficulty--a kind of Peter +the Great of his time. He saw that it was necessary for his people to be +educated and civilized if the country was to progress; and making a +treaty with the governor of Mauritius to abolish the export of slaves, +he received every year in compensation a subsidy of arms, ammunition, +and uniforms, as well as English training for his troops. He was thus +enabled to establish his authority over a large portion of the island. +For some years a British agent, Mr Hastie, resided at Radàma's court, +and exercised a powerful influence over the king, doing much for the +material advance of the country. At the same period (1820) Christian +teaching was commenced in the capital by the London Missionary Society, +and by its missionaries the language was reduced to a systematic written +form, and the art of printing introduced; books were prepared, the +Scriptures were translated, numerous schools were formed, and several +Christian congregations were gathered together. The knowledge of many of +the useful arts was also imparted, and many valuable natural productions +were discovered. The power of superstition was greatly broken, a result +partly due to the keen good sense of the king, but chiefly to the spread +of knowledge and religious teaching. + + + Rànavàlona I. + +The bright prospects thus opening up were clouded by the death of Radàma +at the age of thirty-six, and the seizure of the royal authority by one +of his wives, the Princess Rànavàlona. She looked with much suspicion +upon the ideas then gaining power among many of her people, and +determined to strike a decisive blow at the new teaching. In 1835 the +profession of the Christian religion was declared illegal; all worship +was to cease, and all religious books were ordered to be given up. By +the middle of 1836 all the English missionaries were obliged to leave +the island, and for twenty-five years the most strenuous efforts were +made by the queen and her government to suppress all opposition to her +commands. This, however, only served to show in a very remarkable manner +the courage and faith of the Christian Malagasy, of whom about two +hundred suffered death in various cruel forms, while many hundreds were +punished more or less severely by fine, degradation, imprisonment and +slavery. During the queen's reign the political condition of the country +was deplorable; there were frequent rebellions, many of the distant +provinces were desolated by barbarous wars; and for some years all +Europeans were excluded, and foreign commerce almost ceased. This last +circumstance was partly owing to an ill-managed attack upon Tamatàve in +1846 by a combined British and French force, made to redress the wrongs +inflicted upon the foreign traders of that port. But for the leaven of +Christianity and education which had been introduced into the country it +would have reverted to a state of barbarism. + + + Radàma II. + +This reign of terror was brought to a close in 1861 by the death of the +queen and the accession of her son Radàma II. The island was reopened to +European trade, and missionary efforts were recommenced. A determined +attempt was made by some Frenchmen to gain for their country an +overwhelming influence by means of a treaty which they induced the king +to sign. But this act, as well as the vices and insane follies into +which he was led by worthless foreign and native favourites, soon +brought his reign and his life to an end. He was put to death in his +palace (1863) and his wife was placed on the throne. The new sovereign +and her government refused to ratify the agreement which had been +illegally obtained, choosing rather to pay a million francs as +compensation to the French company. During the five years' reign of +Queen Rasohérina, quiet and steady advances were made in civilization +and education, and treaties were concluded with the British, French and +American governments. + + + Rànavàlona II. + +At the death of Rasohérina in 1868, she was succeeded by her cousin, +Rànavàlona II. One of the first acts of the new queen was the public +recognition of Christianity; and very soon afterwards she and her +husband, the prime minister, were baptized, and the erection of a chapel +royal was commenced in the palace yard. These acts were followed in the +succeeding year by the burning of the royal idols, and immediately +afterwards by the destruction of the idols throughout the central +provinces, the people generally putting themselves under Christian +instruction. From that time education and enlightenment made great +progress, chiefly through the labours of missionaries of various +societies. + + + Native Government. + +The native Malagasy government, though theoretically despotic, was +limited in various ways. Radàma I. and Rànavàlona I. were much more +absolute sovereigns than those before or after them, but even they were +largely restrained by public opinion. New laws were announced at large +assemblies of the people, whose consent was asked, and always given +through the headmen of the different divisions of native society; this +custom was no doubt a survival from a time when the popular assent was +not a merely formal act. The large disciplined army formed by Radàma I. +aided much in changing what was formerly a somewhat limited monarchy +into an absolute one. The Hòva queen's authority was maintained over the +central and eastern portions of Madagascar, and at almost all the ports, +by governors appointed by the queen, and supported by small garrisons of +Hòva troops. At the same time the chiefs of the various tribes were left +in possession of a good deal of their former honours and influence. +Rànavàlona II., her predecessor and her successor were successively +married to the prime minister, Ràinilaiàrivòny, a man of great ability +and sagacity, who, by his position as husband and chief adviser of the +sovereign, became virtual ruler of the country. Chiefly owing to his +influence, many measures tending to improve the administration were +introduced. The Hòva army was estimated at from 30,000 to 40,000 men, +several English non-commissioned officers and, latterly, others of +higher rank being engaged to train them in European methods. Revenue was +derived from customs duties, firstfruits, fines and confiscation of +offenders' property, and a money offering called _hàsina_, presented on +a great variety of occasions both to the sovereign in person and to her +representatives; and these were supplemented by "benevolences" (in the +medieval sense of the word) levied upon the people for occasional state +necessities. The government also claimed the unpaid service of all +classes of the community for every kind of public work. + + + Foreign Relations. + +The Hòva government aspired to have Madagascar recognized as an +independent civilized state, and consuls appointed by the British, +French and American governments were accredited to the Malagasy +sovereign, the queen having a consul in England, and a consular agent at +Mauritius. The treaty with Great Britain, concluded in 1865, gave the +consuls of that nation jurisdiction over the British subjects in the +island. At this period, on the initiative of the 4th earl of Clarendon, +then foreign secretary, an understanding was come to between the British +and French governments by which it was agreed that each power should +respect the independence of Madagascar; and the future of the country +appeared to be bound up in the gradual consolidation of the central Hòva +authority over the whole island. While this prospect would have +satisfied the British interests in the island, it was otherwise with the +French. The tradition of their former settlements in and influence over +the island was strong; in 1840 they had taken under their protection the +Sàkalàva ruler of the small island of Nossi-bé, off the north-west +coast, and in virtue of that act claimed a vague protectorate over the +adjacent shores of the mainland. A treaty, concluded in 1868, while +establishing French consular jurisdiction in Madagascar, recognized +Rànavàlona II. as queen of Madagascar, and under the Second Empire +attempts to establish French political influence were discouraged, and +even as late as 1872 the subsidy enjoyed by the Jesuit missionaries was +withdrawn. In 1878 the French consul, Laborde, died, and a dispute arose +as to the disposal of his property. This dispute was the occasion of +further intervention on the part of the French, for the Paris government +supported the claims of Laborde's heirs, and revived their claim to a +protectorate over the Sàkalàva of the north-west coast, as based on +their agreement with them in 1840, ceding Nossi-bé to France. A policy +of colonial expansion generally, and in Africa in particular at this +time, was manifest in France, as in other European countries, and the +French claims on the Hòva were pressed with vigour. + + + Franco-Malagasy War of 1883-85. + + French Protectorate, 1885-1894. + + French Invasion and Conquest, 1895. + +Towards the middle of 1882 the relations between the native government +and that of France became much strained, and to settle, if possible, +these causes of dispute, two Hòva officers of high rank were sent to +France as ambassadors, but as they were not authorized to concede any +territory, their visit accomplished very little. Treaties had been +concluded with Great Britain, Germany and America, giving improved +facilities for trade with Madagascar, but before the return of the +envoys matters had come to a crisis in the island. In May 1883 an +ultimatum was sent to the Malagasy queen, requiring immediate compliance +with the demands of France; and as these were refused by the Hòva +government, Tamatàve was bombarded by a French squadron and then +occupied by the marines. The war continued in a desultory fashion for +many months; but no serious attempt was made to invade the interior; and +in 1885 terms of peace were agreed to. By a treaty signed on the 17th of +December it was agreed that the foreign relations of Madagascar should +be directed by France; that a resident should live at the capital, with +a small guard of French soldiers; and that the Bay of Diégo-Suarez, +together with surrounding territory, should be ceded to France. The word +"protectorate" was carefully excluded from the treaty, although +doubtless the French envoys intended that this should be its practical +issue. It was at the same time agreed that there should be no foreign +interference with the internal government of the country, and that the +queen should retain her former position, with all its honours and +dignity. It should be here noticed that the queen, Rànavàlona II., died +just at the beginning of the war, on the 13th of July 1883, and was +succeeded by her niece, Princess Razàfindrahèty, under the title of +Rànavàlona III., who maintained the same policy as her predecessor, and +was much beloved by her people and respected by all. Several French +residents successively represented France at Antanànarìvo; but these +found themselves unable to obtain that influence which the home +authorities thought they had a right to demand. Although the British +government, in return for concessions in Zanzibar, had consented, in +1890, to recognize a French protectorate over Madagascar, the Malagasy +prime minister, Ràinilaiàrivòny, was not disposed to give any advantage +to France and continued to arm and train, by the help of British +officers, a large body of native soldiers. This state of tension and +irritation could not last, and at length, towards the close of 1894, the +French government sent an ultimatum to the Malagasy sovereign, demanding +such powers as would have made French authority supreme in the island. +These demands were refused by the native government, and other +conditions were offered; but the French envoy, together with the +resident's escort, left the capital, as also did the French traders and +others, including the large Jesuit mission. As soon as these had left +the island, the chief ports were occupied by French troops, and an +expeditionary force under General Duchesne was afterwards landed on the +north-west coast at Mòjangà--commonly, but incorrectly, written +Majunga--with the object of breaking the Hòva authority. Owing to the +necessity of making a road for the passage of artillery and military +stores, many months were spent on the march into the interior, and there +was considerable loss of life by fever and other disease among the +invading troops. But no effectual resistance was made by the Malagasy, +and at length, on the 30th of September 1895, the French forces appeared +on the heights north and east of Antanànarìvo, bombarded the city, which +surrendered in the afternoon, and on the evening of the same day the +French entered the capital. + + + Rebellion of 1896, and Gradual Subjection of the Malagasy. + +The result was that the protectorate of France was re-established in the +central provinces, but the queen was allowed to retain her position. +Early in 1896, however, a serious rebellion broke out in several parts +of Imèrina. This movement was not only anti-French and anti-foreign, but +also distinctly anti-Christian. The French troops gradually broke up the +power of the rebellion in the central provinces, but as there appeared +to be considerable unrest in many other parts of the island, General +Gallieni, an officer with a reputation for vigour and ability in the +Sudan and Tongking campaigns, was sent out to relieve the then +resident-general. + + + Administration of General Gallieni. + +General Gallieni had a difficult task in establishing the authority of +France throughout the island among numbers of tribes who had never +submitted to any control from others. Among the first steps he took were +to put the country under martial law, to abolish royalty and all +semblance of Hòva government, and to declare Madagascar to be henceforth +a colony of France. Queen Rànavàlona III. was exiled to Réunion, and +subsequently to Algeria. Meanwhile carriage roads were commenced to +connect all the chief centres, and the military posts were gradually +extended so as to consolidate French rule over all the outlying tribes. +French residents and numerous other officials were placed at every +important town, and various projects were started for the civilization +of the Malagasy in accordance with French ideas. At the close of 1899, +General Gallieni was able to report that only portions of the west and +south-west remained to be brought into submission. Not long afterwards +the authority of France was recognized throughout the island. General +Gallieni, whose firm and vigorous administration, and desire to treat +the Malagasy justly and kindly, made him liked by the people, retired in +1905, and was succeeded in that office by M. Victor Augagneur, late +mayor of Lyons. Since the French occupation the Malagasy have conformed +pretty readily to the new order of things, although many of the most +intelligent Hòva deeply regret that their country did not retain its +independence. Justice is administered, on the whole, with fairness and +impartiality; but the taxation seems too heavy for the means of the +people, indeed it is affirmed by trustworthy natives that the well-to-do +classes are being gradually drained of their property. To an outsider it +also appears that the staff of officials is very largely in excess of +any real needs of administration; several monopolies, which interfere +with the habits of the people, tend to produce discontent; and the +taking of their land and houses for public works, roads, &c., while but +a mere fraction of their real value is allowed as compensation, does not +help to increase their acquiescence in foreign control. But the most +serious cause for dislike to government action was the interference by +the governor-general, in 1907, with their religious customs, by the +suppression of hundreds of their congregational schools, and the closing +of numbers of their churches. In July 1910 M. Augagneur was replaced as +governor-general by N. Picquié, a prominent official of the Colonial +Department, who had previously served with acceptance as deputy +governor-general of French Indo-China, and who had a reputation for tact +and impartiality. + + _Christian Missions and Education._--As already noticed, the Malagasy + owe to missionaries of the London Missionary Society their first + school system and their first literature, in 1820 and subsequent + years;[8] and for fifteen years all educational work was carried on by + them, some 10,000 to 12,000 children having been instructed in their + schools. On the reopening of the country to Europeans in 1862, the + L.M.S. mission was resumed and was carried on with vigour for several + years, stations being formed in several parts of Imèrina, in the + Bétsiléo and Antsihànaka provinces, and at the ports of Tamatàve, + Majunga and Fàrafangàna (south-east coast). In 1890 the number of + their churches was 1220; adherents, 248,000; and scholars, 68,000; so + that for long the greater part of the educational work was in their + hands, carried on not only in primary schools, but also in high + schools and colleges. In 1863 the Church of England began work in the + island through the Society for the Propagation of the Gospel and the + Church Missionary Society. After some time, however, the latter + society withdrew, leaving the field to the S.P.G. A bishop is + stationed in the capital, with a theological college in its + neighbourhood, but the chief work of the Anglican mission is on the + east coast. In 1866 the Norwegian Lutheran Society began work in + Madagascar, and was joined in 1888 by an American Lutheran Society. + With a representative church at the capital, the chief work of these + missions is in the Vàkinankàratra district (south-west of Imèrina), in + the Bétsiléo province, and on the south-east and south-west coasts; in + these places they have a large number of converts and (until lately) + schools. In 1867 a mission was begun by the Society of Friends, who + gave great attention to education and literary work, and afterwards + took up as their field of labour the western and south-western parts + of Imèrina, where they have a large and well-organized mission. + Immediately after the island became a French possession the French + Protestant Churches began (in 1896) to take part in the evangelizing + of their new colony, and about half the area for long occupied by the + London Missionary Society was transferred to the Paris Society. The + bulk of the Malagasy Christians are Protestants, probably + three-fourths or four-fifths of those professing Christianity. A Roman + Catholic (Jesuit) mission was begun in 1861, and a large force of + priests with a bishop and lay brethren and sisters engaged in + education, have been at work in the island since then, except during + the two Franco-Malagasy wars.[9] Since the French conquest, the north + of the island has been occupied by a mission of priests of the Saint + Esprit, and the southern portion by the Lazarist mission, each with a + bishop at its head. The following table gives the statistics of the + various Protestant missions at the close of 1906:-- + + +-------------------+------------+--------+---------+--------+--------+ + | Mission |Missionaries|Churches|Adherents| Members|Scholars| + +-------------------+------------+--------+---------+--------+--------+ + | Lond. Miss. Soc. | 25 | 630 | 120,000 | 32,000 | 27,000 | + | Soc. Prop. Gospel.| 15 | 121 | 13,000 | 4,094 | 7,655 | + | Norweg. Luth. | 60 | 892 | 84,000 | 71,500 | 38,000 | + | Am. Luth. | 14 | ? | ? | ? | ? | + | Soc. of Friends. | 27 | 178 | 15,000 | 2,540 | 7,122 | + | French Prot. Miss.| 29 | 491 | 110,660 | 10,500 | 18,200 | + +-------------------+------------+--------+---------+--------+--------+ + + Since 1897 high schools, and medical and technical schools, and a few + primary schools, have been formed by the French government; and all + other schools have been placed under regulations issued by an + educational department, the scholars being required to learn the + French language; but until the end of 1906 the bulk of the educational + work was carried on by the various missions. At that date the + anti-clerical movement in France began to affect Madagascar. In all + the missions the churches had, in the vast majority of cases, been + used as school-houses, but in November 1906 it was strictly forbidden + to use churches for educational purposes after two months from that + date; and the effect of the decree, with other provisions, was to + close hundreds of schools, probably three-fourths of the whole number. + + For many years (1862-1896), all medical aid to the sick, the formation + of hospitals and dispensaries, the training of native doctors, + midwives and nurses, and the production of medical literature was + entirely due to the Protestant missionaries, viz. the London + Missionary Society, the Friends and the Norwegians. Numbers of young + men received a full course of medical and surgical training, and were + awarded diplomas after passing strict examinations. This work is now + mostly in charge of a government department, and mission medical work + is much restricted; but for thirty-five years the Malagasy owed all + such help to the benevolence of European Christians. Besides care for + the sick in ordinary diseases, asylums for lepers were for many years + carried on; two by the London Missionary Society, one, a large one, + with 800 or 900 inmates, by the Norwegian Society, and another by the + Roman Catholic mission. This last, with one of those of the L.M.S., is + now taken over by the government. + + AUTHORITIES.--As regards the scientific aspects of the country, almost + everything of value in previous books and papers is included in the + magnificent work (1882 et seq.), in 28 4to vols., by Alfred + Grandidier, entitled _Histoire naturelle, physique, et politique de + Madagascar_. Many of the volumes consist of coloured lithograph plates + illustrating the natural history of the country, as well as atlases of + maps from the earliest period. + + _General_: Étienne de Flacourt, _Histoire de la grande isle + Madagascar_ (Paris, 1658); _Madagascar, or Robert Drury's Journal + during Fifteen Years' Captivity on that Island_ (London, 1729; new + ed., 1890); _Voyages et mémoires de Maurice Auguste, comte de + Benyowski_ (Paris, 1791); Froberville, _Histoire de Madagascar_ (Isle + de France, 1809); Ellis, _History of Madagascar_ (London, 1838); + Guillain, _Documents sur ... la partie occidentale de Madagascar_ + (Paris, 1845); Macé Descartes, _Histoire et géographie de Madagascar_ + (Paris, 1846); Ellis, _Three Visits to Madagascar_ (London, 1859); J. + Sibree, _Madagascar and its People_ (London, 1870); _Tantara ny + Andrìana eto Madagascar: Histoire des rois d'Imérina d'après les + manuscrits malgaches_ (Antanànarìvo, 1875); Mullens, _Twelve Months in + Madagascar_ (London, 1875); Blanchard, _L'Île de Madagascar_ (Paris, + 1875); Dahle, _Madagaskar og dets Beboere_ (Christiania, 1876-1878); + Sibree and Baron (eds.), _The Antanànarìvo Annual_, Nos. i-xxiv. + (1875-1900, pp. 3115); _Notes, reconnaissances, et explorations, revue + mensuelle_ (Antanànarìvo, 5 vols., 1897-1899, pp. 3041); Sibree, _A + Madagascar Bibliography_ (Antanànarìvo, 1885); Vaissière, _Histoire de + Madagascar_ (Paris, 1884), _Vingt ans à Madagascar_ (Paris, 1885); + Oliver, _Madagascar: an Historical and Descriptive Account_ (2 vols., + London, 1886); Cousins, _Madagascar of To-day_ (London, 1895); + _Bulletin du comité de Madagascar_ (monthly) (Paris, 1895, et seq.); + Sibree, _Madagascar before the Conquest_ (London, 1896); Catat, + _Voyage à Madagascar_ (Paris, 1895); _Annuaire de Madagascar_ + (Antanànarìvo, 1898, et seq.); J. S. Gallieni; _Rapport d'ensemble sur + la situation générale de Madagascar_ (2 vols., Paris, 1899); _Revue de + Madagascar, mensuelle, illustrée_ (1895, et seq.); _Guide de + l'immigrant à Madagascar_ (3 vols., with atlas, Paris, 1899); + _Collection des anciens ouvrages relatifs à Madagascar, par les soins + du comité de Madagascar_ (a collection and translation of all works + relating to the island from 1500 to 1800, in 10 vols.), (Paris, 1899 + et seq.); _Bulletin trimestriel de l'académie de Malgache_ (quarterly) + (Antanànarìvo, 1902 et seq.); G, Grandidier et autres, _Madagascar au + début du xx^e siècle_ (Paris, 1902); G. Grandidier, _Bibliographie de + Madagascar_ (2 vols., Paris, 1905 and 1907). + + _Political_: Sibree, "What are 'French Claims' on Madagascar?" + _Madagascar Tracts_ (1882); Oliver, _True Story of the French Dispute + in Madagascar_ (London, 1885); Shaw, _Madagascar and France_ (London, + 1885); Saillens, _Nos droits sur Madagascar_ (Paris, 1885); K. Blind + "The Fictitious French Claim to Madagascar," _Contemp. Rev._ (1894); + Martineau, _Étude de politique contemporaine. Madagascar_ (Paris, + 1894); Rentier, _Les droits de la France sur Madagascar_ (1895); + Corlay, _Notre campagne à Madagascar_ (Paris, 1896); Knight, + _Madagascar in War-time_ (London, 1896); Carol, _Chez les Hovas_ + (Paris, 1898); Gallieni, _Neuf ans à Madagascar_ (Paris, 1908). + + _Philology_: Houtman, _Spraak ende woord boek in de Maleische ende + Madagaskarsche talen_ (Amsterdam, 1603); _Voyage de C. van Heemskerk; + vocabulaire de la langue parlée dans l'Île Saint-Laurent_ (Amsterdam, + 1603) Megiser, _Beschreibung der Mechtigen und Weitberhümbten Insul + Madagascar_, with dictionary and dialogues (Altenburg, 1609); Arthus, + _Colloquia latino-maleyica et madagascarica_ (Frankfort, 1613); + Challand, _Vocabulaire français-malgache et malgache-français_ (Île de + France, 1773); Froberville, _Dictionnaire français-madécasse_ (3 + vols., Île de France, 1809); Freeman and Johns, _Dictionary of the + Malagasy Language (Eng.-Mal. and Mal.-Eng.)_, (Antanànarìvo, 1835); + Dalmond, _Vocabulaire et grammaire pour les langues malgaches, + Sàkalàva et Bétsimisàra_ (Bourbon, 1842); R. C. Missionaries' + _Dictionnaire français-malgache_ (Réunion, 1853); and _Dictionnaire + malgache-français_ (Réunion, 1855); Van der Tunk, "Outlines of a + Grammar of the Malagasy Language," _Jour. Roy. Asiat. Soc._ (1860); + Ailloud, _Grammaire malgache-hòva_ (Antanànarìvo, 1872); W. E. + Cousins, _Concise Introduction to the Study of the Malagasy Language + as spoken in Imèrina_ (Antanànarìvo, 1873); Marre de Marin, _Grammaire + malgache_ (Paris, 1876); id., _Essai sur le malgache, ou Étude + comparée des langues javanaise, malgache, et malayse_ (Paris, 1876); + id., _Le Jardin des racines océaniennes_ (Paris, 1876); Dahle, + _Specimens of Malagasy Folk-lore_ (Antanànarìvo, 1877); and W. E. + Cousins, "The Malagasy Language," in _Trans. Phil. Soc._ (1878). + Besides these there are several valuable papers by Dahle in the yearly + numbers of The _Antanànarìvo Annual_ (_ante_) (1876-1877); Richardson, + _A New Malagasy-English Dictionary_ (Antanànarìvo, 1885); Cousins and + Barrett, _Malagasy Proverbs_ (Antanànarìvo, 1885); Caussèque, + _Grammaire malgache_ (Antanànarìvo, 1886); Abinal et Malzac, + _Dictionnaire malgache-français_ (Antanànarìvo, 1889); Brandstetter, + "Die Beziehungen des Malagasy zum Malaiischen," _Malaio-polynesische + Forschungen_, pt. 2 (Lucerne, 1893). + + _Missions and Religious History:_ Freeman and Johns, _Narrative of the + Persecutions of the Christians in Madagascar_ (London, 1840); Prout, + _Madagascar, its Missions and its Martyrs_ (London, 1863); Ellis, + _Madagascar Revisited_ (London, 1867); id., _The Martyr Church_ + (London, 1869); "Religion in Madagascar," _Ch. Quar. Rev._ (1878); + Briggs, _The Madagascar Mission_ (L.M.S. 1879); id., _Ten Years' + Review of Mission Work in Madagascar_ (L.M.S. 1870-1880, 1881); + Johnson, _Review of Work of the Friends' Foreign Mission Association + in Madagascar_, 1867-1880 (Antanànarìvo, 1880); Vaissière, _Histoire + de Madagascar, ses habitants et ses missionaires_ (Paris, 1884); _The + Church in Madagascar_ (_S.P.G._, _15 years' progress_, 1874-1889, + 1889); _La Liberté religieuse à Madagascar_ (Paris, 1897); Matthews, + _Thirty Years in Madagascar_ (London, 1904); Sibree, _The L.M.S. + Mission in Madagascar_ (L.M.S. Mission Hand Books, London, 1907); id., + "Christian Missions in Madagascar and French Colonial Policy," _The + East and the West_ (Jan. 1909); and General Gallieni's "Neuf ans à + Madagascar", _Journal of the African Society_ (April 1909). + (J. Si.*) + + +FOOTNOTES: + + [1] In the apparent absence of any Cambrian formation above them, + there is little doubt that these rocks are Archean, although this + cannot be absolutely proved. + + [2] For most of the information here given on the geology the writer + is indebted to Captain Mouneyres, chef de services des mines, and the + Rev. R. Baron, F.G.S., F.L.S. + + [3] See "On a Collection of Fossils from Madagascar," by R. B. + Newton, _Quart. Journ. Geol. Soc._ (Feb. 1895). + + [4] The following are figures of mean temperature, kindly supplied by + the Rev. E. Colin, S. J., director of the observatory: Diégo-Suarez, + N., 79°; Fàrafangàna, S.E. coast, 75°; Màrovoày, W. intr., 81°; + Mòrondàva, W. coast, 77°; Tullear, S.W. coast, 78°. + + [5] The words in parentheses are the native Malagasy names. + + [6] The census taken in 1905 gives 2,664,000 as the total population, + but it is probably a little over that amount, as some localities are + still imperfectly known. + + [7] This is a special and restricted use of the word, Hòva in its + widest sense being a tribal name, including all ranks of people in + Imèrina. + + [8] It is true that 200 years earlier than this, persistent efforts + were made for nineteen years (1600-1619) by Portuguese Roman Catholic + missionaries to propagate their faith among the south-east coast + tribes. But although much zeal and self-denial were shown by these + men, their efforts were abortive, and the mission was at length + abandoned, leaving no fruit of their labours in a single church or + convert. Half a dozen small books of devotion are all that remain to + show their presence in Madagascar. + + [9] The work of the "Frères chrétiens" was, however, almost broken up + by the anti-clerical policy of the French government. + + + + +MADAN, MARTIN (1726-1790), English writer, was educated at Westminster +School, and at Christ Church, Oxford, where he graduated in 1746. In +1748 he was called to the bar, and for some time lived a very gay life, +until he was persuaded to change his ways on hearing a sermon by John +Wesley. He took holy orders, and was appointed chaplain to the Lock +Hospital, London. He was closely connected with the Calvinistic +Methodist movement supported by the countess of Huntingdon, and from +time to time acted as an itinerant preacher. He was a first cousin of +William Cowper, with whom he had some correspondence on religious +matters. In 1767 much adverse comment was aroused by his support of his +friend Thomas Haweis in a controversy arising out of the latter's +possession of the living of Aldwinkle, Northamptonshire (see _Monthly +Review_, xxxvii. 382, 390, 465). In 1780 Madan raised more serious storm +of opposition by the publication of his _Thelyphthora, or A Treatise on +Female Ruin_, in which he advocated polygamy as the remedy for the evils +he deplored. The author was no doubt sincere in his arguments, which he +based chiefly on scriptural authority; but his book called forth many +angry replies. Nineteen attacks on it are catalogued by Falconer Madan +in _Dict. Nat. Biog._ Madan resigned his chaplainship and retired to +Epsom, where he produced, among other works, _A New and Literal +Translation of Juvenal and Persius_ (1789). He died on the 2nd of May +1790. + + + + +MADDALONI, a town of Campania, Italy, in the province of Caserta, about +3½ m. S.E. of Caserta, with stations on the railways from Caserta to +Benevento and from Caserta to Avellino, 200 ft. above sea-level. Pop. +(1901), 19,778 (town); 21,270 (commune). It is prettily situated at the +base of one of the Tifata hills, the towers of its medieval castle and +the church of San Michele crowning the heights above. The fine old +palace of the Caraffa family, once dukes of Maddaloni, the old college +now named after Giordano Bruno, and the institute for the sons of +soldiers are the chief points of interest. About 2½ m. east of Valle di +Maddaloni, the Ponte della Valle, an aqueduct built by the orders of +Charles III. of Naples and his son to convey the water of the Tiburno to +Caserta (19 m.), is carried across the valley between Monte Longano and +Monte Gargano by a threefold series of noble arches rising to a height +of 210 ft. The work was designed by Lodovico Vanvitelli, and +constructed between 1753 and 1759. + + + + +MADDEN, SIR FREDERIC (1801-1873), English palaeographer, the son of an +officer of Irish extraction, was born at Portsmouth on the 16th of +February 1801. From his earliest years he displayed a strong bent to +linguistic and antiquarian studies. In 1826 he was engaged by the +British Museum to assist in the preparation of the classified catalogue +of printed books then contemplated, and in 1828 he became assistant +keeper of manuscripts. In 1833 he was knighted, and in 1837 succeeded +Josiah Forshall as keeper of manuscripts. He was not entirely successful +in this office, partly owing to want of harmony with his colleagues; he +retired in 1866. He edited for the Roxburghe Club _Havelok the Dane_ +(1828), discovered by himself among the Laudian MSS. in the Bodleian, +_William and the Werwolf_ (1832) and the old English versions of the +_Gesta Romanorum_ (1838). In 1839 he edited the ancient metrical +romances of _Syr Gawayne_ for the Bannatyne Club, and in 1847 Layamon's +_Brut_, with a prose translation, for the Society of Antiquaries. In +1850 the magnificent edition, in parallel columns, of what are known as +the "Wycliffite" versions of the Bible, from the original MSS., upon +which he and his coadjutor, Forshall, had been engaged for twenty years, +was published by the university of Oxford. In 1866-1869 he edited the +_Historia Minor_ of Matthew Paris for the Rolls Series. In 1833 he wrote +the text of Henry Shaw's _Illuminated Ornaments of the Middle Ages_; and +in 1850 edited the English translation of Silvestre's _Paléographie +universelle_. He died on the 8th of March 1873, bequeathing his journals +and other private papers to the Bodleian Library, where they were to +remain unopened until 1920. + + Madden was perhaps the first palaeographer of his day. He was an acute + as well as a laborious antiquary, but his ignorance of German + prevented his ranking high as a philologist, although he paid much + attention to the early dialectical forms of French and English. His + minor contributions to antiquarian research were exceedingly numerous: + the best known, perhaps, was his dissertation on the orthography of + Shakespeare's name, which, mainly on the strength of the Florio + autograph, he contended should be "Shakspere." + + + + +MADDER, or DYERS' MADDER, the root of _Rubia tinctorum_ and perhaps also +of _R. peregrina_, both European, _R. cordifolia_, a native of the hilly +districts of India and of north-east Asia and Java, supplying the Indian +madder or _manjit_. _Rubia_ is a genus of about thirty-five species of +the tribe _Galieae_ of the order Rubiaceae, and much resembles the +familiar _Galiums_, e.g. lady's bedstraw (_G. verum_) and the cleavers +(_G. aparine_) of English hedges, having similarly whorled leaves, but +the parts of the flowers are in fives and not fours, while the fruit is +somewhat fleshy. The only British species is _R. peregrina_, which is +found in Wales, the south and west of England, and in east and south +Ireland. The use of madder appears to have been known from the earliest +times, as cloth dyed with it has been found on the Egyptian mummies. It +was the [Greek: ereuthedanon] used for dyeing the cloaks of the Libyan +women in the days of Herodotus (Herod. iv. 189). It is the [Greek: +eruthrodanon] of Dioscorides, who speaks of its cultivation in Caria +(iii. 160), and of Hippocrates (_De morb. mul._ i.), and the _Rubia_ of +Pliny (xix. 17). _R. tinctorum_, a native of western Europe, &c., has +been extensively cultivated in south Europe, France, where it is called +_garance_, and Holland, and to a small extent in the United States. +Large quantities have been imported into England from Smyrna, Trieste, +Leghorn, &c. The cultivation, however, decreased after alizarin, the red +colouring principle of madder, was made artificially. Madder was +employed medicinally by the ancients and in the middle ages. Gerard, in +1597, speaks of it as having been cultivated in many gardens in his day, +and describes its supposed many virtues (_Herball_, p. 960); but any +pharmacological or therapeutic action which madder may possess is +unrecognizable. Its most remarkable physiological effect is that of +colouring red the bones of animals fed upon it, as also the claws and +beaks of birds. This appears to be due to the chemical affinity of +phosphate of lime for the colouring matter (Pereira, _Mat. med._, vol. +ii. pt. 2, p. 52). This property has been of much use in enabling +physiologists to ascertain the manner in which bones develop, and the +functions of the various types of cells found in growing bone. _R. +chilensis_ has been used for dyeing red from time immemorial. The +chay-root, which furnishes a red dye in Coromandel and other parts of +India, is the root-bark of _Oldenlandia umbellata_, a low-growing plant +of the same family as madder. + + + + +MADEC, RENÉ-MARIE (1736-1784)--called Medoc in Anglo-Indian +writings--French adventurer in India, was born at Quimper in Brittany on +the 7th of February 1736, of poor parents. He went out to India and +served under Dupleix and Lally, but being taken prisoner by the British +he enlisted in the Bengal army. Deserting with some of his companions +shortly before the battle of Buxar (1764), he became military instructor +to various native princes, organizing successively the forces of +Shuja-ud-Dowlah, nawab of Oudh, and of the Jats and Rohillas. He took +service under the emperor Shah Alam in 1772, and when that prince was +defeated at Delhi by the Mahrattas, Madec rejoined his own countrymen in +Pondicherry, where he took an active part in the defence of the town +(1778). After the capitulation of Pondicherry he returned to France with +a considerable fortune, and died there in 1784. At one time he formed a +scheme for a French alliance with the Mogul emperor against the British, +but the project came to nothing. + + See Émile Barbé, _Le Nabab René Madec_ (1894). + + + + +MADEIRA, or THE MADEIRAS, a group of islands in the North Atlantic +Ocean, which belong to Portugal, and consist of two inhabited islands +named Madeira and Porto Santo and two groups of uninhabited rocks named +the Desertas and Selvagens. Pop. (1900), 150,574; area, 314 sq. m. +Funchal, the capital of the archipelago, is on the south coast of +Madeira Island, in 32° 37´ 45´´ N. and 16° 54´ W. It is about 360 m. +from the coast of Africa, 535 from Lisbon, 1215 from Plymouth, 240 from +Teneriffe, and 480 from Santa Maria, the nearest of the Azores. + +_Madeira_ (pop. 1900, 148,263), the largest island of the group, has a +length of 30 m., an extreme breadth of 12 m., and a coast-line of 80 or +90 m. Its longer axis lies east and west, in which direction it is +traversed by a mountain chain, the backbone of the island, having a mean +altitude of 4000 ft., up to which many deep ravines penetrate from both +coasts and render travel by land very difficult. Pico Ruivo, the highest +summit, stands in the centre of the island, and has a height of 6056 +ft., while some of the adjacent summits are very little lower. The depth +and narrowness of the ravines, the loftiness of the rugged peaks, often +covered with snow, that tower above them, the bold precipices of the +coast, and the proximity of the sea, afford many scenes of picturesque +beauty or striking grandeur. The greater part of the interior is +uninhabited, though cultivated, for the towns, villages and scattered +huts are usually built either at the mouths of ravines or upon the lower +slopes that extend from the mountains to the coast. The ridges between +the ravines usually terminate in lofty headlands, one of which, called +Cabo Girão, has the height of 1920 ft., and much of the seaboard is +bound by precipices of dark basalt. The north coast, having been more +exposed to the erosion of the sea, is more precipitous than the south, +and presents everywhere a wilder aspect. On the south there is left very +little of the indigenous forest which once clothed the whole island and +gave it the name it bears (from the Portuguese _madeira_, Lat. +_materia_, wood), but on the north some of the valleys still contain +native trees of fine growth. A long, narrow and comparatively low rocky +promontory forms the eastern extremity of the island; and here is a +tract of calcareous sand, known as the Fossil Bed, containing land +shells and numerous bodies resembling the roots of trees, probably +produced by infiltration. + +_Porto Santo_ is about 25 m. N.E. of Madeira. Pop. (1900), 2311. It has +a length of 6(1/3) m. and a width of 3 m. The capital is Porto Santo, +called locally the _villa_ or town. The island is very unproductive, +water being scarce and wood wholly absent. Around the little town there +is a considerable tract of pretty level ground covered by calcareous +sand containing fossil land-shells. At each end of the island are hills, +of which Pico do Facho, the highest, reaches the altitude of 1663 ft. +Barley, but little else, is grown here, the limited requirements of the +inhabitants being supplied from Funchal. + +_The Desertas_ lie about 11 m. S.E. of Madeira, and consist of three +islands, Ilheo Chão, Bugio and Deserta Grande, together with Sail Rock +off the north end of Ilheo Chão. They present lofty precipices to the +sea on all sides. Rabbits and goats abound on them. The archil weed +grows on the rocks, and is gathered for exportation. The largest islet +(Deserta Grande) is 6½ m. long, and attains the height of 1610 ft. These +rocks are conspicuous objects in the sea-views from Funchal. + +[Illustration: Map of Madeira Islands.] + +The _Selvagens_ or _Salvages_ are a group of three islands, 156 m. from +Madeira, and between Madeira and the Canary Islands. The largest island +is the Great Piton, 3 m. long, and 1 m. broad. The inclusion of the +Selvagens in the Madeira Archipelago is due to political rather than to +geographical reasons. + + _Geology._--All the islands of the group are of volcanic origin. They + are the summits of very lofty mountains which have their bases in an + abyssal ocean. The greater part of what is now visible in Madeira is + of subaerial formation, consisting of basaltic and trachytic lavas, + beds of tuff and other ejectamenta, the result of a long and + complicated series of eruptions from innumerable vents. Besides this + building up by the emission of matter from craters and clefts, a + certain amount of upheaval in mass has taken place, for at a spot + about 1200 ft. above the sea in the northern valley of São Vicente, + and again at about the same height in Porto Santo, there have been + found fragments of limestone accompanied by tuffs containing marine + shells and echinoderms of the Miocene Tertiary epoch. We have here + proof that during or since that epoch portions at least of these + islands have been bodily uplifted more than 1000 ft. The fossils are + sufficiently well preserved to admit of their genera, and in many + instances even their species, being made out. + + There were pauses of considerable duration whilst the island of + Madeira was being increased in height. The leaf bed and the + accompanying carbonaceous matter, frequently termed lignite, although + it displays no trace of structure, which lie under 1200 ft. of lavas + in the valley of São Jorge, afford proof that there had been + sufficient time for the growth of a vegetation of high order, many of + the leaf impressions belonging to species of trees and shrubs which + still exist on the island. Moreover, great alterations and + dislocations had taken place in the rocks of various localities before + other lavas and tuffs had been thrown upon them. + + There are no data for determining when volcanic action began in this + locality, but looking at the enormous depth of the surrounding sea it + is clear that a vast period of time must have elapsed to allow of a + great mountain reaching the surface and then rising several thousand + feet. Again, considering the comparatively feeble agents for effecting + the work of denudation (neither glaciers nor thick accumulations of + alpine snow being found here), and then the enormous erosion that has + actually taken place, the inference is inevitable that a very great + lapse of time was required to excavate the deep and wide ravines that + everywhere intersect the island. Nor is anything known as to the + period of the cessation of volcanic action. At the present day there + are no live craters or smoking crevices, as at the Canaries and Cape + Verdes, nor any hot springs, as at the Azores. + + In one of the northern ravines of Madeira by Porto da Cruz some masses + of a coarsely crystalline Essexite are exposed to view; this rock is + evidently the deep-seated representative of the Trachydoleritic and + Nepheline basalt lavas. Fragments of a sodalite-syenite have also been + found at Soca in the same neighbourhood. + + In the eastern part of the island several small crater rings are to be + seen; their rims are formed of spheroidal basalt, while within the + craters themselves masses of bauxite are found accompanied by + evidences of fumerolic action. + + In the sections afforded by the ravines, which strike north and south + from the central ridge of Madeira to the sea, the nucleus of the + island is seen to consist of a confused mass of more or less + stratified rock, upon which rest beds of tuff, scoriae and lava, in + the shape of basalt, trap and trachyte, the whole traversed by dykes. + These beds are thinnest near the central axis; as they approach the + coast they become thicker and less intersected by dykes. + + In various parts are elevated tracts of comparatively level ground. + These are supposed to have been formed by the meeting of numerous + streams of lava flowing from cones and points of eruption in close + proximity, various ejectamenta assisting at the same time to fill up + inequalities. Deep down in some of the lateral ravines may be seen + ancient cones of eruption which have been overwhelmed by streams of + melted matter issuing from the central region, and afterwards exposed + to view by the same causes that excavated the ravines. These ravines + may be regarded as having been formed at first by subterranean + movements, both gradual and violent, which dislocated the rocks and + cut clefts through which streams flowed to the sea. In course of time + the waters, periodically swollen by melted snows and the copious rains + of winter, would cut deeper and deeper into the heart of the + mountains, and would undermine the lateral cliffs, until the valleys + became as large as we now find them. Even the Curral, which from its + rounded shape and its position in the centre of the island has been + usually deemed the ruins of a crater, is thought to be nothing more + than a valley scooped out in the way described. The rarity of + crateriform cavities in Madeira is very remarkable. There exists, + however, to the east of Funchal, on a tract 2000 ft. high, the Lagoa, + a small but perfect crater, 500 ft. in diameter, and with a depth of + 150 ft.; and there is another, which is a double one, in the district + known as Fanal, in the north-west of Madeira, nearly 5000 ft. above + the sea. The basalt, of which much of the outer part of the island is + composed, is of a dark colour and a tough texture, with small + disseminated crystals of olivine and augite. It is sometimes full of + vesicular cavities, formed by the expansion of imprisoned gases. A + rudely columnar structure is very often seen in the basalt, but there + is nothing so perfect as the columns of Staffa or the Giant's + Causeway. The trachytic rocks are small in quantity compared with + those of the basaltic class. The tufa is soft and friable, and + generally of a yellow colour; but where it has been overflowed by a + hot stream of lava it has assumed a red colour. Black ashes and + fragments of pumice are sometimes found in the tufaceous strata. + + There are no metallic ores, nor has any sulphur been found; but a + little iron pyrites and specular iron are occasionally met with. The + basalt yields an excellent building-stone, various qualities of which + are quarried near Camara de Lobos, five or six miles west of Funchal. + + In Porto Santo the trachytic rocks bear a much greater proportion to + the basaltic than in Madeira. An adjacent islet is formed of tuffs and + calcareous rock, indicating a submarine origin, upon which supramarine + lavas have been poured. The older series contains corals and shells + (also of the Miocene Tertiary epoch), with water-worn pebbles, + cemented together by carbonate of lime, the whole appearing to have + been a coral reef near an ancient beach. The calcareous rock is taken + in large quantities to Funchal, to be burnt into lime for building + purposes. + + _Climate._--Observations taken at Funchal Observatory (80 ft. above + sea-level) in the last twenty years of the 19th century showed that + the mean annual temperature is about 65° F. The mean minimum for the + coldest part of the year (October to May inclusive) does not fall + below 55°, and the average daily variation of temperature in the same + period does not exceed 10°. Madeira thus has a remarkably mild + climate, though it lies only 10° north of the Tropic of Cancer. This + mildness is due to the surrounding ocean, from which the atmosphere + obtains a large supply of watery vapour. The mean humidity of the air + is about 75 (saturation = 100). The prevalent winds are from the north + or from a few points east or west of north, but these winds are much + mitigated on the south coast by the central range of mountains. The + west wind usually brings rain. That from the east is a dry wind. A hot + and dry wind, the leste of the natives, occasionally blows from the + east-south-east, the direction of the Sahara, and causes the hill + region to be hotter than below; but even on the coast the thermometer + under its influence sometimes indicates 93°. The _leste_ is often + accompanied by sandstorms. As the thermometer has never been known to + fall as low as 46° at Funchal, frost and snow are there wholly + unknown; but snow falls on the mountains once or twice during the + winter, very seldom, however, below the altitude of 2000 ft. + Thunderstorms are rare, and scarcely ever violent. + + Madeira has long had a high reputation as a sanatory resort for + persons suffering from diseases of the chest. Notwithstanding the + ever-increasing competition of other winter resorts, a considerable + number of invalids, especially English and German, winter at Funchal. + + _Fauna._--No species of land mammal is indigenous to the Madeiras. + Some of the early voyagers indeed speak of wild goats and swine, but + these animals must have escaped from confinement. The rabbit, black + rat, brown rat and mouse have been introduced. The first comers + encountered seals, and this amphibious mammal (_Monachus albiventer_) + still lingers at the Desertas. Amongst the thirty species of birds + which breed in these islands are the kestrel, buzzard and barn owl, + the blackbird, robin, wagtail, goldfinch, ring sparrow, linnet, two + swifts, three pigeons, the quail, red-legged partridge, woodcock, + tern, herring gull, two petrels and three puffins. Only one species is + endemic, and that is a wren (_Regulus madeirensis_), but five other + species are known elsewhere only at the Canaries. These are the green + canary (_Fringilla butyracea_, the parent of the domesticated yellow + variety), a chaffinch (_Fringilla tintillon_), a swift (_Cypselus + unicolor_), a wood pigeon (_Columba trocaz_) and a petrel + (_Thalassidroma Bulwerii_). There is also a local variety of the + blackcap, distinguishable from the common kind by the extension in the + male of the cap to the shoulder. About seventy other species have been + seen from time to time in Madeira, chiefly stragglers from the African + coast, many of them coming with the _leste_ wind. + + The only land reptile is a small lizard (_Lacerta dugesii_), which is + abundant and is very destructive to the grape crop. The loggerhead + turtle (_Caouana caretta_, Gray) is frequently captured, and is cooked + for the table, but the soup is much inferior to that made from the + green turtle of the West Indies. A single variety of frog (_Rana + esculenta_) has been introduced; there are no other batrachians. + + About 250 species of marine fishes taken at Madeira have been + scientifically determined, the largest families being _Scombridae_ + with 35 species, the sharks with 24, the _Sparidae_ with 15, the rays + with 14, the _Labridae_ with 13, the _Gadidae_ with 12, the eels with + 12, the _Percidae_ with 11, and the _Carangidae_ with 10. Many kinds, + such as the mackerel, horse mackerel, groper, mullet, braise, &c.., + are caught in abundance, and afford a cheap article of diet to the + people. Several species of tunny are taken plentifully in spring and + summer, one of them sometimes attaining the weight of 300 lb. The only + freshwater fish is the common eel, which is found in one or two of the + streams. + + According to T. V. Wollaston (_Testacea atlantica_, 1878), there have + been found 158 species of mollusca on the land, 6 inhabiting fresh + water, and 7 littoral species, making a total of 171. A large majority + of the land shells are considered to be peculiar. Many of the species + are variable in form or colour, and some have an extraordinary number + of varieties. Of the land mollusca 91 species are assigned to the + genus _Helix_, 31 to the genus _Pupa_, and 15 to the genus _Achatina_ + (or _Lovea_). About 43 species are found both living and fossil in + superficial deposits of calcareous sand in Madeira or Porto Santo. + These deposits were assigned by Lyell to the Newer Pliocene period. + Some 12 or 13 species have not been hitherto discovered alive. More + than 100 species of _Polyzoa_ (_Bryozoa_) have been collected, among + them are some highly interesting forms. + + The only order of insects which has been thoroughly examined is that + of the _Coleoptera_. By the persevering researches of T. V. Wollaston + the astonishing number of 695 species of beetles has been brought to + light at the Madeiras. The proportion of endemic kinds is very large, + and it is remarkable that 200 of them are either wingless or their + wings are so poorly developed that they cannot fly, while 23 of the + endemic genera have all their species in this condition. With regard + to the _Lepidoptera_, 11 or 12 species of butterflies have been seen, + all of which belong to European genera. Some of the species are + geographical varieties of well-known types. Upward of 100 moths have + been collected, the majority of them being of a European stamp, but + probably a fourth of the total number are peculiar to the Madeiran + group. Thirty-seven species of _Neuroptera_ have been observed in + Madeira, 12 of them being so far as is known peculiar. + + The bristle-footed worms of the coast have been studied by Professor + P. Langerhans, who has met with about 200 species, of which a large + number were new to science. There are no modern coral reefs, but + several species of stony and flexible corals have been collected, + though none are of commercial value. There is, however, a white stony + coral allied to the red coral of the Mediterranean which would be + valuable as an article of trade if it could be obtained in sufficient + quantity. Specimens of a rare and handsome red Paragorgia are in the + British Museum and Liverpool Museum. + + _Flora._--The vegetation is strongly impressed with a south-European + character. Many of the plants in the lower region undoubtedly were + introduced and naturalized after the Portuguese colonization. A large + number of the remainder are found at the Canaries and the Azores, or + in one of these groups, but nowhere else. Lastly, there are about a + hundred plants which are peculiarly Madeiran, either as distinct + species or as strongly marked varieties. The flowering plants found + truly wild belong to about 363 genera and 717 species,--the + monocotyledons numbering 70 genera and 128 species, the dicotyledons + 293 genera and 589 species. The three largest orders are the + _Compositae_, _Leguminosae_ and _Graminaceae_. Forty-one species of + ferns grow in Madeira, three of which are endemic species and six + others belong to the peculiar flora of the North Atlantic islands. + About 100 species of moss have been collected, and 47 species of + _Hepaticae_. A connexion between the flora of Madeira and that of the + West Indies and tropical America has been inferred from the presence + in the former of six ferns found nowhere in Europe or North Africa, + but existing on the islands of the east coast of America or on the + Isthmus of Panama. A further relationship to that continent is to be + traced by the presence in Madeira of the beautiful ericaceous tree + _Clethra arborea_, belonging to a genus which is otherwise wholly + American, and of a _Persea_, a tree laurel, also an American genus. + The dragon tree (_Dracaena Draco_) is almost extinct. Amongst the + trees most worthy of note are four of the laurel order belonging to + separate genera, an _Ardisia_, _Pittosporum_, _Sideroxylon_, + _Notelaea_, _Rhamnus_ and _Myrica_,--a strange mixture of genera to be + found on a small Atlantic island. Two heaths of arborescent growth and + a whortleberry cover large tracts on the mountains. In some parts + there is a belt of the Spanish chestnut about the height of 1500 ft. + There is no indigenous pine tree as at the Canaries; but large tracts + on the hills have been planted with _Pinus pinaster_, from which the + fuel of the inhabitants is mainly derived. A European juniper (_J. + Oxycedrus_), growing to the height of 40 or 50 ft., was formerly + abundant, but has been almost exterminated, as its scented wood is + prized by the cabinet-maker. Several of the native trees and shrubs + now grow only in situations which are nearly inaccessible, and some of + the indigenous plants are of the greatest rarity. But some plants of + foreign origin have spread in a remarkable manner. Among these is the + common cactus or prickly pear (_Opuntia Tuna_), which in many spots on + the coast is sufficiently abundant to give a character to the + landscape. As to _Algae_, the coast is too rocky and the sea too + unquiet for a luxuriant marine vegetation, consequently the species + are few and poor. + +_Inhabitants._--The inhabitants are of Portuguese descent, with probably +some intermixture of Moorish and negro blood amongst the lower classes. +The dress of the peasantry, without being picturesque, is peculiar. Both +men and women in the outlying country districts wear the _carapuça_, a +small cap made of blue cloth in shape something like a funnel, with the +pipe standing upwards. The men have trousers of linen, drawn tight, and +terminating at the knees; a coarse shirt enveloping the upper part of +their person, covered by a short jacket, completes their attire, with +the exception of a pair of rough yellow boots. The women's outer +garments consist of a gaudily coloured gown, made from island material, +with a small cape of coarse scarlet or blue woollen cloth. The +population tends to increase rapidly. In 1900 it amounted to 150,574, +including 890 foreigners, of whom the majority were British. The number +of females exceeds that of males by about 6000, partly because many of +the able-bodied males emigrate to Brazil or the United States. The +density of population (479.5 per sq. m.) is very great for a district +containing no large town and chiefly dependent on agriculture and +viticulture. + +_Agriculture._--A large portion of the land was formerly entailed in the +families of the landlords (_morgados_), but entails have been abolished +by the legislature, and the land is now absolutely free. The deficiency +of water is a great obstacle to the proper cultivation of the land, and +the rocky nature or steep inclination of the upper parts of the islands +is an effectual bar to all tillage. An incredible amount of labour has +been expended upon the soil, partly in the erection of walls intended to +prevent its being washed away by the rains, and to build up the plots of +ground in the form of terraces. Watercourses have been constructed for +purposes of irrigation, without which at regular intervals the island +would not produce a hundredth part of its present yield. These +watercourses originate high up in the ravines, are built of masonry or +driven through the rock, and wind about for miles until they reach the +cultivated land. Some of them are brought by tunnels from the north side +of the island through the central crest of hill. Each occupier takes his +turn at the running stream for so many hours in the day or night at a +time notified to him beforehand. In this climate flowing water has a +saleable value as well as land, which is useless without irrigation. + + The agricultural implements employed are of the rudest kind, and the + system of cultivation is extremely primitive. Very few of the + occupiers own the land they cultivate; but they almost invariably own + the walls, cottages and trees standing thereon, the land alone + belonging to the landlord. The tenant can sell his share of the + property without the consent of the landlord, and if he does not so + dispose of it that share passes to his heirs. In this way the tenant + practically enjoys fixity of tenure, for the landlord is seldom in a + position to pay the price at which the tenant's share is valued. Money + rents are rare, the métayer system regulating almost universally the + relations between landlord and tenant; that is, the tenant pays to the + owner a certain portion of the produce, usually one half or one third. + The holdings are as a rule rarely larger than one man can cultivate + with a little occasional assistance. There are few meadows and + pastures, the cattle being stall-fed when not feeding on the + mountains. Horses are never employed for draught, all labour of that + kind being done by oxen. + + + Wine. + + The two staple productions of the soil are wine and sugar. The vine + was introduced from Cyprus or Crete soon after the discovery of the + island by the Portuguese (1420), but it was not actively cultivated + until the early part of the 16th century. The vines, after having been + totally destroyed by the oidium disease, which made its first + appearance in the island in 1852, were replanted, and in a few years + wine was again made. The phylloxera also made its way to the island, + and every vineyard in Madeira was more or less affected by it. The + wine usually termed Madeira is made from a mixture of black and white + grapes, which are also made separately into wines called Tinta and + Verdelho, after the names of the grapes. Other high-class wines, known + as Bual, Sercial and Malmsey, are made from varieties of grapes + bearing the same names. (See also WINE.) + + + Sugar. + + The sugar cane is said to have been brought from Sicily about 1452, + and in course of time its produce became the sole staple of the + island. The cultivation languished, however, as the more abundant + produce of tropical countries came into the European market, and sugar + had long ceased to be made when the destruction of the vines compelled + the peasants to turn their attention to other things. Its cultivation + was resumed and sugar machinery imported. A considerable quantity of + spirit is made by the distillation of the juice or of the molasses + left after extracting the sugar, and this is consumed on the island. + The cane does not flourish here as luxuriantly as within the tropics; + but in localities below 1000 ft., where there is a good supply of + water, it pays the cultivator well. + + The grain produced on the island (principally wheat, barley and Indian + corn) is not sufficient for the consumption of the people. The common + potato, sweet potato and gourds of various kinds are extensively + grown, as well as the _Colocasia esculenta_, the _kalo_ of the Pacific + islanders, the root of which yields an insipid food. Most of the + common table vegetables of Europe are plentiful. Besides apples, pears + and peaches, all of poor quality, oranges, lemons, guavas, mangoes, + loquats, custard-apples, figs, bananas and pineapples are produced, + the last two forming articles of export. The date palm is occasionally + grown, but its fruit is scarcely edible. On the hills large quantities + of the Spanish chestnut afford an item in the food of the common + people. A little tobacco is grown, and is made into cigars of inferior + quality. + + The total foreign trade of Madeira was valued at £628,000 in 1900. The + principal exports are wine, sugar, embroidery, vegetables, fruits and + wicker goods. Coal is imported for the ships calling at Funchal, which + is the headquarters of Madeiran commerce and industry. Spirits, beer, + olive oil, soap, butter, linen and woollen goods, straw hats and + leather, are manufactured for home consumption, and there are + important fisheries. + +_Chief Towns and Communications._--Funchal (pop. 20,850) is described in +a separate article. The other chief towns are Camara de Lobos (7150), +Machico (6128), Santa Cruz (5876), Ponta do Sol (5665), São Vicente +(4896), Calheta (3475), Sant' Anna (3011) and Porto Santo (2311). Each +of these is the capital of a commune (_concelho_), to which it gives its +name. Madeira is connected by regular lines of steamships with Great +Britain, Germany, Portugal, Cape Colony, Brazil and the United States. +There is no railway in the archipelago, and partly owing to the +irregularities of the surface of the roads, of which there are some 580 +m., are bad, except in the neighbourhood of Funchal. Wheel carriages are +rare, and all heavy goods are transported either on the backs of mules +or upon rude wooden sledges drawn by bullocks. When horses are not +employed, locomotion is effected either by means of hammocks or by +bullock cars. The hammock (_rêde_) is a piece of stout canvas gathered +up and secured at each end to a long pole carried by a couple of +bearers. In place of cabs, curtained cars on sledges, made to hold four +persons, and drawn by a pair of bullocks, are employed. They are +convenient, but the rate of progress is very slow. + +_Administration._--The archipelago is officially styled the district of +Funchal; it returns members to the Portuguese Cortes, and is regarded as +an integral part of the kingdom. The district is subdivided into the +eight communes already enumerated, and is administered in accordance +with the same laws that regulate local government on the mainland (see +PORTUGAL). Funchal is a Roman Catholic bishopric in the archiepiscopal +province of Lisbon. Education is compulsory in name only, for less than +2% of the population could read when the census of 1900 was taken. An +infantry regiment and a battery of garrison artillery are permanently +stationed in Madeira. + +_History._--It has been conjectured, but on insufficient evidence, that +the Phoenicians discovered Madeira at a very early period. Pliny +mentions certain Purple or Mauretanian Islands, the position of which +with reference to the Fortunate Islands or Canaries might seem to +indicate the Madeiras. There is a romantic story, to the effect that two +lovers, Robert Machim, à Machin, or Macham, and Anna d'Arfet, fleeing +from England to France (c. 1370) were driven out of their course by a +violent storm and cast on the coast of Madeira at the place subsequently +named Machico, in memory of one of them. Both perished here, but some of +their crew escaped to the Barbary coast, and were made slaves. Among +them was the pilot Pedro Morales of Seville, who is said to have been +ransomed and to have communicated his knowledge of Madeira to João +Gonçalvez Zarco (or Zargo). How far this story is true cannot now be +ascertained. It is, however, certain that Zarco first sighted Porto +Santo in 1418, having been driven thither by a storm while he was +exploring the coast of West Africa. Madeira itself was discovered in +1420. It is probable that the whole archipelago had been explored at an +earlier date by Genoese adventurers, and had been forgotten; for an +Italian map dated 1351 (the Laurentian portolano) shows the Madeiras +quite clearly, and there is some reason to believe that they were known +to the Genoese before 1339. When Zarco visited Madeira in 1420 the +islands were uninhabited, but Prince Henry the Navigator at once began +their colonization, aided by the knights of the Order of Christ. +Sanctioned by the pope and by two charters which the king of Portugal +granted in 1430 and 1433, the work proceeded apace; much land was +deforested and brought into cultivation, and the Madeiran sugar trade +soon became important. For the sixty years 1580-1640 Madeira, with +Portugal itself, was united with Spain. Slavery was abolished in Madeira +in 1775, by order of Pombal. In 1801 British troops, commanded by +General Beresford, occupied the island for a few months, and it was +again under the British flag from 1807 to 1814. It shared in the civil +disturbances brought about by the accession of Dom Miguel (see PORTUGAL: +_History_), but after 1833 its history is a record of peaceful +commercial development. + + See A. S. Brown, _Madeira, the Canary Islands and the Azores_ (1903), + a comprehensive study of the three archipelagoes. _The Land of the + Wine_, by A. J. D. Biddle (Philadelphia, 1901) is generally valuable, + but its history cannot be trusted. See also P. Langerhaus, _Handbuch + für Madeira_ (1884) and Vahl, _Madeira's Vegetation_ (Copenhagen, + 1904). + + + + +MADELENIAN, a term derived from La Madeleine, a cave in the Vézère, +about midway between Moustier and Les Eyzies, France, and given by the +French anthropologist Gabriel de Mortillet to the third stage of his +system of cave-chronology, synchronous with the fourth or most recent +division of the Quaternary Age. The Madelenian epoch was a long one, +represented by numerous stations, whose contents show progress in the +arts and general culture. It was characterized by a cold and dry +climate, the existence of man in association with the reindeer, and the +extinction of the mammoth. The use of bone and ivory for various +implements, already begun in the preceding Solutrian epoch, was much +increased, and the period is essentially a Bone age. The bone +instruments are very varied: spear-points, harpoon-heads, borers, hooks +and needles. Most remarkable is the evidence La Madeleine affords of +prehistoric art. Numbers of bones, reindeer antlers and animals' teeth +were found, with rude pictures, carved or etched on them, of seals, +fishes, reindeer, mammoths and other creatures. The best of these are a +mammoth engraved on a fragment of its own ivory; a dagger of reindeer +antler, with handle in form of a reindeer; a cave-bear cut on a flat +piece of schist; a seal on a bear's tooth; a fish well drawn on a +reindeer antler; and a complete picture, also on reindeer antler, +showing horses, an aurochs, trees, and a snake biting a man's leg. The +man is naked, and this and the snake suggest a warm climate, in spite +of the presence of the reindeer. The fauna of the Madelenian epoch +seems, indeed, to have included tigers and other tropical species side +by side with reindeer, blue foxes, Arctic hares and other polar +creatures. Madelenian man appears to have been of low stature, +dolichocephalic, with low retreating forehead and prominent brow ridges. +Besides La Madeleine the chief stations of the epoch are Les Eyzies, +Laugerie Basse, and Gorge d'Enfer in Dordogne; Grotte du Placard in +Charente and others in south-west France. + + See G. de Mortillet, _Le Préhistorique_ (1900); Edouard Lartet and + Henry Christy, _Reliquiae Aquitanicae_ (1865-1875); Edouard Dupont, + _Le Temps préhistorique en Belgique_ (1872); Lord Avebury, + _Prehistoric Times_ (1900). + + + + +MADELEY, a market town in the municipal borough of Wenlock, and the +Wellington (Mid) parliamentary division of Shropshire, England, 159 m. +N.W. from London, with stations on the London & North Western (Madeley +Market) and Great Western railways (Madeley Court). Pop. of civil parish +(1901), 8442. There are large ironworks, ironstone and coal are mined, +and potter's clay is raised. The church of St Michael (1796) replaced a +Norman building. The living was held from 1760 to 1783 by John William +Fletcher or de la Flechêre, a close friend of the Wesleys. The parish +includes a portion of Coalbrookdale (q.v.), and the towns of Ironbridge +and Coalport. IRONBRIDGE, a town picturesquely situated on the steep +left bank of the Severn, adjoins Madeley on the south-west. It takes its +name from the iron bridge of one span crossing the river, erected in +1779. This bridge is a remarkable work considering its date; it was +probably the first erected, at any rate on so large a scale, and +attracted great attention. It is the work of Abraham Darby, the third of +the name, one of the famous family of iron-workers in Coalbrookdale. +Here are brick and tile works and lime-kilns. There is a station +(Ironbridge and Broseley) on the Great Western railway, across the +river. COALPORT lies also on the Severn, S. of Madeley and 2 m. S.E. of +Ironbridge, with a station on the Great Western railway. It has large +china works, founded at the close of the 18th century, which +subsequently incorporated those of Caughley, across the Severn, and of +Nantgarw in Glamorganshire. + + + + +MADHAVA ACHARYA (_fl._ c. 1380), Hindu statesman and philosopher, lived +at the court of Vijayanagar (the modern Humpi in the district of +Bellary), the vigorous Southern Hindu kingdom that so long withstood +Mahommedan influence and aggression. His younger brother Sayana (d. +1387) was associated with him in the administration and was a famous +commentator on the _Rigveda_. Sayana's commentaries were influenced by +and dedicated to Madhava, who is best known as the author of the +_Sarvadarsana Samgraha_ (_Compendium of Speculations_). With remarkable +mental detachment he places himself in the position of an adherent of +sixteen distinct systems. Madhava also wrote a commentary on the Mimamsa +Sutras. He died as abbot of the monastery of Sringeri. + + + + +MADI (A-MADI), a negro race of the Nile valley, occupying both banks of +the Bahr-el-Jebel immediately north of Albert Nyanza. Tradition makes +them immigrants from the north-west. They are remarkable for the +consideration shown to their women, who choose their own husbands, are +never ill-treated or hard-worked, and take part in tribal deliberations. +The Madi build sepulchral monuments of an elaborate type, two huge +narrow stones sloping towards each other with two smaller slabs covering +the opening between them. They have been much harried by the Azandeh and +Abarambo. They were visited by W. Junker in 1882-1883, and described by +him in _Petermann's Mittheilungen_ for May 1883. + + + + +MADISON, JAMES (1751-1836), fourth president of the United States, was +born at Port Conway, in King George county, Virginia, on the 16th of +March 1751. His first ancestor in America may possibly have been Captain +Isaac Maddyson, a colonist of 1623 mentioned by John Smith as an +excellent Indian fighter. His father, also named James Madison, was the +owner of large estates in Orange county, Virginia. In 1769 the son +entered the college of New Jersey (now Princeton University), where, in +the same year, he founded the well-known literary club, "The American +Whig Society." He graduated in 1771, but remained for another year at +Princeton studying, apparently for the ministry, under the direction of +John Witherspoon (1722-1794). In 1772 he returned to Virginia, where he +pursued his reading and studies, especially theology and Hebrew, and +acted as a tutor to the younger children of the family. In 1775 he +became chairman of the committee of public safety for Orange county, and +wrote its response to Patrick Henry's call for the arming of a colonial +militia, and in the spring of 1776 he was chosen a delegate to the new +Virginia convention, where he was on the committee which drafted the +constitution for the state, and proposed an amendment (not adopted) +which declared that "all men are equally entitled to the full and free +exercise" of religion, and was more radical than the similar one offered +by George Mason. In 1777, largely, it seems, because he refused to treat +the electors with rum and punch, after the custom of the time, he was +not re-elected, but in November of the same year he was chosen a member +of the privy council or council of state, in which he acted as +interpreter for a few months, as secretary prepared papers for the +governor, and in general took a prominent part from the 14th of January +1778 until the end of 1779, when he was elected a delegate to the +Continental Congress. + +He was in Congress during the final stages of the War of Independence, +and in 1780 drafted instructions to Jay, then representing the United +States at Madrid, that in negotiations with Spain he should insist upon +the free navigation of the Mississippi and upon the principle that the +United States succeeded to British rights affirmed by the treaty of +Paris of 1763. When the confederation was almost in a state of collapse +because of the failure of the states to respond to requisitions of +Congress for supplies for the federal treasury, Madison was among the +first to advocate the granting of additional powers to Congress, and +urged that congress should forbid the states to issue more paper money. +In 1781 he favoured an amendment of the Articles of Confederation giving +Congress power to enforce its requisitions, and in 1783, in spite of the +open opposition of the Virginia legislature, which considered the +Virginian delegates wholly subject to its instructions, he advocated +that the states should grant to Congress for twenty-five years authority +to levy an import duty, and suggested a scheme to provide for the +interest on the debt not raised by the import duty--apportioning it +among the states on the basis of population, counting three-fifths of +the slaves, a ratio suggested by Madison himself. Accompanying this plan +was an address to the states drawn up by Madison, and one of the ablest +of his state papers. In the same year, with Oliver Ellsworth of +Connecticut, Nathaniel Gorham of Massachusetts. Gunning Bedford of +Delaware, and John Rutledge of South Carolina, he was a member of the +committee which reported on the Virginia proposal as to the terms of +cession to the Confederation of the "back lands," or unoccupied Western +territory, held by several of the states; the report was a skilful +compromise made by Madison, which secured the approval of the rather +exigent Virginia legislature. + +In November 1783 Madison's term in Congress expired, and he returned to +Virginia and took up the study of the law. In the following year he was +elected to the House of Delegates. As a member of its committee on +religion, he opposed the giving of special privileges to the Episcopal +(or any other) church, and contended against a general assessment for +the support of the churches of the state. His petition of remonstrance +against the proposed assessment, drawn up at the suggestion of George +Nicholas (c. 1755-1799), was widely circulated and procured its defeat. +On the 26th of December 1785 Jefferson's Bill for establishing religious +freedom in Virginia, which had been introduced by Madison, was passed. +In the Virginia House of Delegates, as in the Continental Congress, he +opposed the further issue of paper money; and he tried to induce the +legislature to repeal the law confiscating British debts, but he did not +lose sight of the interests of the Confederacy. The boundary between +Virginia and Maryland, according to the Baltimore grant, was the south +shore of the Potomac, a line to which Virginia had agreed on condition +of free navigation of the river and the Chesapeake Bay. Virginia now +feared that too much had been given up, and desired joint regulation of +the navigation and commerce of the river by Maryland and Virginia. On +Madison's proposal commissioners from the two states met at Alexandria +(q.v.) and at Mount Vernon in March 1785. The Maryland legislature +approved the Mount Vernon agreement and proposed to invite Pennsylvania +and Delaware to join in the arrangement. Madison, seeing an opportunity +for more general concert in regard to commerce and trade (and possibly +for the increase of the power of Congress), proposed that all the states +should be invited to send commissioners to consider commercial +questions, and a resolution to that effect was adopted (on Jan. 21, +1786) by the Virginia legislature. This led to the Annapolis convention +of 1786, and that in turn led to the Philadelphia convention of 1787. In +April 1787 Madison had written a paper, _The Vices of the Political +System of the United States_, and from his study of confederacies, +ancient and modern, later summed up in numbers 17, 18, and 19 of _The +Federalist_, he had concluded that no confederacy could long endure if +it acted upon states only and not directly upon individuals. As the time +for the convention of 1787 approached he drew up an outline of a new +system of government, the basis of the "Virginia plan" presented in the +convention by Edmund Jennings Randolph. Madison's scheme, as expressed +in a letter to Washington dated the 16th of April 1787, was that +individual sovereignty of states was irreconcilable with aggregate +sovereignty, but that the "consolidation of the whole into one simple +republic would be as inexpedient as it is unattainable." He considered +as a practical middle ground changing the basis of representation in +Congress from states to population; giving the national government +"positive and complete authority in all cases which require uniformity"; +giving it a negative on all state laws, a power which might best be +vested in the Senate, a comparatively permanent body; electing the lower +house, and the more numerous, for a short term; providing for a national +executive, for extending the national supremacy over the judiciary and +the militia, for a council to revise all laws, and for an express +statement of the right of coercion; and finally, obtaining the +ratification of a new constitutional instrument from the people, and not +merely from the legislatures. The "Virginia plan" was the basis of the +convention's deliberations which resulted in the constitution favourably +voted on by the convention on the 17th of September 1787. Among the +features of the plan which were not embodied in the constitution were +the following: proportionate representation in the Senate and the +election of its members by the lower house "out of a proper number of +persons nominated by the individual legislatures"; the vesting in the +national Congress of power to negative state acts; and the establishment +of a council of revision (the executive and a convenient number of +national judges) with veto power over all laws passed by the national +Congress. Madison, always an opponent of slavery, disapproved of the +compromise (in Art. I. § 9 and Art. V.) postponing to 1808 (or later) +the prohibition of the importation of slaves. He took a leading part in +the debates of the convention, of which he kept full and careful notes, +afterwards published by order of Congress (3 vols., Washington, 1843). +Many minute and wise provisions are due to him, and he spoke before the +convention more frequently than any delegate except James Wilson and +Gouverneur Morris. In spite of the opposition to the constitution of the +Virginia leaders George Mason and E. J. Randolph, Madison induced the +state's delegation to stand by the constitution in the convention. His +influence largely shaped the form of the final draft of the +constitution, but the labour was not finished with this draft; that the +constitution was accepted by the people was due in an eminent degree to +the efforts of Madison, who, to place the new constitution before the +public in its true light, and to meet the objections brought against it, +joined Alexander Hamilton (q.v.) and John Jay in writing _The +Federalist_, a series of eighty-five papers, out of which twenty +certainly, and nine others probably, were written by him. In the +Virginia convention for ratifying the constitution (June 1788), when +eight states had ratified and it seemed that Virginia's vote would be +needed to make the necessary nine (New Hampshire's favourable vote was +cast only shortly before that of Virginia), and it appeared that New +York would vote against the constitution if Virginia did not ratify it, +Madison was called upon to defend that instrument again, and he appeared +at his best against its opponents, Patrick Henry, George Mason, James +Monroe, Benjamin Harrison, William Grayson and John Tyler. He answered +their objections in detail, calmly and with an intellectual power and +earnestness that carried the convention. The result was a victory +against an originally adverse public opinion and against the eloquence +of the opponents of the constitution, for Madison and for his +lieutenants, Edmund Pendleton, John Marshall, George Nicholas, Harry +Innes and Henry Lee. At the same time Madison's labours in behalf of the +constitution alienated from him valuable political support in Virginia. +He was defeated by Richard Henry Lee and William Grayson in his +candidacy for the United States Senate, but in his own district he was +chosen a representative to Congress, defeating James Monroe, who seems +to have had the powerful support of Patrick Henry. + +Madison took his seat in the House of Representatives in April 1789, and +assumed a leading part in the legislation necessary to the organization +of the new government. He drafted a Tariff Bill giving certain notable +advantages to nations with which the United States had commercial +treaties, hoping to force Great Britain into a similar treaty; but his +policy of discrimination against England was rejected by Congress. It +was his belief that such a system of retaliation would remove the +possibility of war arising from commercial quarrels. He introduced +resolutions calling for the establishment of three executive +departments, foreign affairs, treasury and war, the head of each +removable by the president. Most important of all, he proposed nine +amendments to the constitution, embodying suggestions made by a number +of the ratifying states, especially those made by Virginia at the +instance of George Mason; and the essential principles of Madison's +proposed amendments were included in a Bill of Rights, adopted by the +states in the form of ten amendments. The absence of a Bill of Rights +from the constitution as first adopted had been the point on which the +opposition had made common cause, and the adoption of this now greatly +weakened the same opposition. Although a staunch friend of the +constitution, Madison believed, however, that the instrument should be +interpreted conservatively and not be made the means of introducing +radical innovations. The tide of strict construction was setting in +strongly in his state, and he was borne along with the flood. It is very +probable that Jefferson's influence over Madison, which was greater than +Hamilton's, contributed to this result. Madison now opposed Hamilton's +measures for the funding of the debt, the assumption of state debts, and +the establishment of a National Bank, and on other questions he sided +more and more with the opposition, gradually assuming its leadership in +the House of Representatives and labouring to confine the powers of the +national government within the narrowest possible limits; his most +important argument against Hamilton's Bank was that the constitution did +not provide for it explicitly, and could not properly be construed into +permitting its creation. Madison, Jefferson and Randolph were consulted +by Washington, and they advised him not to sign the bill providing for +the Bank, but Hamilton's counter-argument was successful. On the same +constitutional grounds Madison objected to the carrying out of the +recommendations in Hamilton's famous report on manufactures (Dec. 5, +1791), which favoured a protective tariff. In the presidential campaign +of 1792 Madison seems to have lent his influence to the determined +efforts of the Jeffersonians to defeat John Adams by electing George +Clinton vice-president. In 1793-1796 he strongly criticized the +administration for maintaining a neutral position between Great Britain +and France, writing for the public press five papers (signed +"Helvidius"), attacking the "monarchical prerogative of the executive" +as exercised in the proclamation of neutrality in 1793 and denying the +president's right to recognize foreign states. He found in Washington's +attitude--as in Hamilton's failure to pay an instalment of the moneys +due France--an "Anglified complexion," in direct opposition to the +popular sympathy with France and French Republicanism. In 1794 he tried +again his commercial weapons, introducing in the House of +Representatives resolutions based on Jefferson's report on commerce, +advising retaliation against Great Britain and discrimination in +commercial and navigation laws in favour of France; and he declared that +the friends of Jay's treaty were "a British party systematically aiming +at an exclusive connexion with the British government," and in 1796 +strenuously but unsuccessfully opposed the appropriation of money to +carry this treaty into effect. Still thinking that foreign nations could +be coerced through their commercial interests, he scouted as visionary +the idea that Great Britain would go to war on a refusal to carry Jay's +treaty into effect, thinking it inconceivable that Great Britain "would +wantonly make war" upon a country which was the best market she had in +the world for her manufactures, and one with which her export trade was +so much larger than her import. + +In 1797 Madison retired from Congress, but not to a life of inactivity. +In 1798 he joined Jefferson in opposing the Alien and Sedition Laws, and +Madison himself wrote the resolutions of the Virginia legislature +declaring that it viewed "the powers of the Federal government as +resulting from the compact to which the states are parties, as limited +by the plain sense and intention of the instrument constituting that +compact; as no further valid than they are authorized by the grants +enumerated in that compact; and that, in case of a deliberate, palpable +and dangerous exercise of other powers, not granted by the said compact, +the states, who are parties thereto, have the right and are in duty +bound to interpose for arresting the progress of the evil, and for +maintaining within their respective limits, the authorities, rights and +liberties appertaining to them." The Virginia resolutions and the +Kentucky resolutions (the latter having been drafted by Jefferson) were +met by dissenting resolutions from the New England states, from New +York, and from Delaware. In answer to these, Madison, who had become a +member of the Virginia legislature in the autumn of 1799, wrote for the +committee to which they were referred a report elaborating and +sustaining in every point the phraseology of the Virginia +resolutions.[1] + +Upon the accession of the Republican party to power in 1801, Madison +became secretary of state in Jefferson's cabinet, a position for which +he was well fitted both because he possessed to a remarkable degree the +gifts of careful thinking and discreet and able speaking, and of large +constructive ability; and because he was well versed in constitutional +and international law and practised a fairness in discussion essential +to a diplomat. During the eight years that he held the portfolio of +state, he had continually to defend the neutral rights of the United +States against the encroachments of European belligerents; in 1806 he +published _An Examination of the British Doctrine which subjects to +Capture a Neutral Trade not open in Time of Peace_, a careful +argument--with a minute examination of authorities on international +law--against the rule of war of 1756 extended by Great Britain in 1793 +and 1803. + +During Jefferson's presidency and whilst Madison was secretary of state, +by the purchase of Louisiana, Madison's campaign begun in 1780 for the +free navigation of the Mississippi was brought to a successful close. +The candidate in 1808 of the Republican party, although bitterly opposed +in the party by John Randolph and George Clinton, Madison was elected +president, defeating C. C. Pinckney, the Federalist candidate, by 122 +votes to 47. Madison had no false hopes of placating the Federalist +opposition, but as the preceding administration was one with which he +was in harmony, his position was different from that of Jefferson in +1801, and he had less occasion for removing Federalists from office. +Jefferson's peace policy--or, more correctly, Madison's peace policy--of +commercial restrictions to coerce Great Britain and France he continued +to follow until 1812, when he was forced to change these futile +commercial weapons for a policy of war, which was very popular with the +extreme French wing of his party. There is a charge, which has never +been proved or disproved, that Madison's real desire was for peace, but +that in order to secure the renomination he yielded to that wing of his +party which was resolved on war with Great Britain. The only certain +fact is that Madison, whatever were his personal feelings in this +matter, acted according to the wishes of a majority of the Republicans; +but whether in doing so he was influenced by the desire of another +nomination is largely a matter of conjecture. Madison was renominated on +the 18th of May 1812, issued his war message on the 1st of June, and in +the November elections he was re-elected, defeating De Witt Clinton by +128 votes to 89. His administration during the war was pitiably weak. +His cabinet in great part had been dictated to him in 1809 by a +senatorial clique, and it was hopelessly discordant; for two years he +was to all intents and purposes his own secretary of state, Robert Smith +being a mere figure-head of whom he gladly got rid in 1811, giving +Monroe the vacant place. Madison himself had attempted alternately to +prevent war by his "commercial weapons" and to prepare the country for +war, but he had met with no success, because of the tricky diplomacy of +Great Britain and of France, and because of the general distrust of him +coupled with the particular opposition to the war of the prosperous New +England Federalists, who suggested with the utmost seriousness that his +resignation should be demanded. In brief, Madison was too much the mere +scholar to prove a strong leader in such a crisis. The supreme disgrace +of the administration was the capture and partial destruction in August +1814 of the city of Washington--this was due, however, to incompetence +of the military and not to any lack of prudence on the cabinet's part. +In general, Congress was more blamable than either the president or his +official family, or the army officers. With the declaration of peace the +president again gained a momentary popularity much like that he had won +in 1809 by his apparent willingness at that time to fight France. + +Retiring from the presidency in 1817, Madison returned to his home, +Montpelier (in Orange county, Virginia), which he left in no official +capacity save in 1829, when he was a delegate to the state +constitutional convention and served on several of its committees. +Montpelier, like Jefferson's Monticello and Monroe's Oak-Hill, was an +expensive bit of "gentleman farming," which with his generous Virginia +hospitality nearly ruined its owner financially. Madison's home was +peculiarly a centre for literary travellers in his last years; when he +was eighty-three he was visited by Harriet Martineau, who reported her +conversations with him in her _Retrospect of Western Travel_ (1838). He +took a great interest in education--his library was left to the +university of Virginia, where it was burned in 1895--in emancipation, +and in agricultural questions, to the very last. He died at Montpelier +on the 28th of June 1836. Madison married, in 1794, Dorothy Payne Todd +(1772-1849), widow of John Todd, a Philadelphia lawyer. She had great +social charm, and upon Madison's entering Jefferson's cabinet became +"first lady" in Washington society. Her plump beauty was often +remarked--notably by Washington Irving--in contrast to her husband's +delicate and feeble figure and wizened face--for even in his prime +Madison was, as Henry Adams says, "a small man, quiet, somewhat precise +in manner, pleasant, fond of conversation, with a certain mixture of +ease and dignity in his address." Her son, spoiled by his mother and his +step-father, became a wild young fellow, and added his debts to the +heavy burden of Montpelier upon Madison. + + Madison's portrait was painted by Gilbert Stuart and by Charles + Willson Peale; Giuseppe Ceracchi made a marble bust of him in 1792 and + John H. J. Browere another in 1827, now in possession of the Virginia + Historical Society at Richmond. Though commonly dignified and a little + stiff he seems to have had a strong sense of humour and he was fond of + telling a good story. Henry Clay, contrasting him with Jefferson, said + that Jefferson had more genius, Madison more judgment and common + sense; that Jefferson was a visionary and a theorist; Madison cool, + dispassionate, practical, and safe.[2] The broadest and most accurate + scholar among the "founders and fathers," he was particularly an + expert in constitutional history and theory. In the great causes for + which Madison fought in his earlier years--religious freedom and + separation of church and state, the free navigation of the + Mississippi, and the adoption of the constitution--he met with + success. His greatest and truest fame is as the "father of the + constitution." The "commercial weapons" with which he wished to + prevent armed conflict proved less useful in his day than they have + since been in international disputes. + + AUTHORITIES.--Madison's personality is perplexingly vague; the + biographies of him are little more than histories of the period, and + the best history of the later period in which he was before the + public, Henry Adams's _History of the United States from 1801 to 1817_ + (1889-1890), gives the clearest sketch and best criticism of him. The + lives of Madison are: J. Q. Adams's (Boston, 1850); W. C. Rives's + (Boston, 1859-1869, 3 vols.), covering the period previous to 1797; S. + H. Gay's (Boston, 1884) in the "American Statesmen Series"; and + Gaillard Hunt's (New York, 1902). Madison's _Writings_ (7 vols., New + York, 1900-1906) were edited by Hunt, who also edited _The Journal of + the Debates in the Convention which framed the Constitution of the + United States, as Recorded by James Madison_ (2 vols., New York, + 1908). See also Mrs Madison's _Memoirs and Letters_ (Boston, 1887) and + Maud Wilder Goodwin, _Dolly Madison_ (New York, 1897). + + +FOOTNOTES: + + [1] Thirty years later Madison's arguments for the Virginia + resolutions and the resolutions themselves were freely used by + Calhoun and his followers in support of his doctrine of + nullification. But Madison insisted that the Resolutions of 1798 did + not involve the principles of nullification. Nearly all his + arguments, especially where he attempts to interpret Jefferson's + writings on the point, notably the Kentucky resolutions, are rather + strained and specious, but it does seem that the Virginia resolutions + were based on a different idea from Calhoun's doctrine of + nullification. Madison's theory was that the legislature of Virginia, + being one of the bodies which had chosen delegates to the + constitutional convention, was legally capable of considering the + question of the constitutionality of laws passed by the Federal + government, and that the state of Virginia might invite other states + to join her, but could not singly, as Calhoun argued, declare any law + of the Federal legislature null and void. (It is to be noted the + words "null and void" were in Madison's first draft of the Virginia + resolutions, but that they were omitted by the Virginia legislature.) + It is notable, besides, that Madison had always feared that the + national congress would assume too great power, that he had approved + of Supreme Court checks on the national legislature, and of veto + power by a council of revision. + + [2] Clay's opinion is given in a report written by Mrs Samuel H. + Smith of a conversation in 1829 between Clay and her husband, a + prominent politician. + + + + +MADISON, a city and the county-seat of Jefferson county, Indiana, +U.S.A., on the N. bank of the Ohio river, about 90 m. below Cincinnati, +and 44 m. above Louisville, Kentucky. Pop. (1870), 10,709; (1890), 8936; +(1900), 7835 (554 foreign-born and 570 negroes); (1910), 6934. Madison +is served by the Pittsburg, Cincinnati, Chicago & St Louis railroad and +by river steamboats. The city is picturesquely situated on bluffs above +the river and has two public parks. In Madison are a King's Daughters' +Hospital, a children's home, and the Drusilla home for old ladies, and +immediately north of the city are the buildings of the Indiana +South-eastern Insane Hospital. Madison is a trading centre of the +surrounding farming region, whose principal products are burley tobacco, +grain and fruits (peaches, apples, pears, plums and small fruits). The +municipality owns and operates the waterworks. Madison was settled about +the beginning of the 19th century; was incorporated as a town in 1824, +and was first chartered as a city in 1836. + + + + +MADISON, a borough of Morris county, New Jersey, U.S.A., 27 m. (by rail) +W. of New York City and 4 m. S.E. of Morristown. Pop. (1890), 2469; +(1900), 3754, of whom 975 were foreign-born and 300 were negroes; +(1905), 4115; (1910), 4658. It is served by the Morris & Essex division +of the Delaware, Lackawanna & Western railroad. The borough is +attractively situated among the hills of Northern New Jersey, is +primarily a residential suburb of New York and Newark, and contains many +fine residences. There are a public library and a beautiful public park, +both given to the borough by Daniel Willis James (1832-1907), a +prominent metal manufacturer; the library is closely allied with the +public schools. Madison is the seat of the well-known Drew theological +seminary (Methodist Episcopal; founded in 1866 and opened in 1867), +named in honour of Daniel Drew (1788-1879), who, having acquired great +wealth from steamboat and railway enterprises, especially from trading +in railway stocks, presented the large and beautiful grounds and most of +the buildings. The seminary's course covers three years; no fee is +charged. In connexion with the seminary the Drew settlement in New York +City--officially the department of applied Christianity--has for its +object the "practical study of present-day problems in city evangelism, +church organization, and work among the poor." In 1907-1908 the seminary +had 9 instructors, 175 students, and a library of more than 100,000 +volumes, especially rich in works dealing with the history of Methodism +and in Greek New Testament manuscripts. About 2 m. N.W. of Madison is +Convent Station, the seat of a convent of the Sisters of Charity, who +here conduct the college of St Elizabeth, for girls, founded in 1859; +also conducted by the Sisters of Charity is St Joseph's preparatory +school for boys, founded in 1862. The cultivation of roses and +chrysanthemums is practically the only industry of Madison. Madison owns +and operates its waterworks and electric-lighting plant. Before 1844 +when it took its present name (in honour of President Madison), Madison +was called Bottle Hill; it is one of the older places of the state, and +its first church (Presbyterian) was built about 1748. The borough was +incorporated in 1889. + + + + +MADISON, the capital of Wisconsin, U.S.A., and the county-seat of Dane +County, situated between Lakes Mendota and Monona in the south central +part of the state, about 82 m. W. of Milwaukee and about 131 m. N.W. of +Chicago. Pop. (1890), 13,426; (1900) 19,164, of whom 3362 were +foreign-born and 69 were negroes; (1910 census) 25,531. Madison is +served by the Chicago & North-Western, the Chicago, Milwaukee & St Paul, +and the Illinois Central railways (being the northern terminus of the +last), and by interurban electric lines, connecting with Janesville, +Beloit and Chicago. It has a picturesque situation in what is known as +"the Four-Lakes region"; this region takes its name from a chain of +lakes, Kegonsa, Waubesa, Monona and Mendota, which, lying in the order +named and connected with one another by the Yahara or Catfish River, +form the head-waters of Rock river flowing southward through Illinois +into the Mississippi. The city occupies a hilly isthmus about a mile +wide between Lakes Mendota and Monona, bodies of water of great +clearness and beauty, with bottoms of white sand and granite. + +The state capitol is in a wooded park at the summit of a hill 85 ft. +high in the centre of the city. From this park the streets and avenues +radiate in all directions. The capitol, built in 1860-1867 (with an +addition in 1883) on the site of the original capitol building +(1837-1838), was partially destroyed by fire in 1904, and in 1909-1910 +was replaced by a larger edifice. The principal business portion of the +city is built about the capitol park and the university. Among the +public buildings on or near the park are the federal building, housing +the post office and the United States courts, the city hall, the Dane +county court-house, the public library, the Fuller opera-house, the +county gaol, and the high school. Running directly west from the capitol +is State Street, at the western end of which lie the grounds of the +university of Wisconsin (q.v.), occupying a hilly wooded tract of 300 +acres, and extending for a mile along the south shore of Lake Mendota. +University Hill, on which the main building of the university stands, is +125 ft. above the lake; at its foot stands the magnificent library +building of the State Historical Society. In it, in addition to the +interesting and valuable historical museum and art gallery, are the +Society's library of more than 350,000 books and pamphlets, the +university library of 150,000 volumes, and the library of the Wisconsin +academy of arts and sciences, 5000 volumes. Other libraries in the city +include the state law library (45,000 volumes) in the capitol, the +Madison public library (22,500 volumes), and the Woodman astronomical +library (7500 volumes). The Madison public library houses also the state +library school maintained by the Wisconsin library commission. Connected +with the university is the Washburn observatory. On the margin of the +city lies the extensive experimental farm of the state college of +agriculture. In addition to the state university, Madison is the seat of +several Roman Catholic and Lutheran parochial schools, two business +schools, and the Wisconsin academy, a non-sectarian preparatory school +of high grade. On the banks of Lake Monona are the beautiful grounds of +the Monona Lake assembly, a summer assembly on the Chautauqua model. +Near the city is one of the five fish-hatcheries maintained by the +state; it is largely devoted to the propagation of trout and other small +fish. North of the city, occupying a tract of 500 acres, on Lake +Mendota, are the buildings and grounds of the state hospital for the +insane, opened in 1860. + +The city's streets are broad and heavily shaded with a profusion of elm, +oak and maple trees. There are many fine stone residences dating from +the middle of the 19th century. There are several parks of great beauty, +and along the shores of Lake Mendota there is a broad boulevarded drive +of 12 m. The municipality owns its waterworks, the water being obtained +from eleven artesian wells, and being chemically similar to that of +Waukesha Springs. The city and surrounding region are a summer resort, +the lakes affording opportunities for fishing and for yachting and +boating. + +Madison is an important jobbing centre for central and south-western +Wisconsin; it has an extensive trade in farm, garden and dairy products, +poultry and tobacco; and there are various manufactures. In 1905 the +value of the total factory product was $3,291,143, an increase of 22.4% +over that in 1900. + +At the time of the settlement by the whites the aboriginal inhabitants +of the Four-Lakes region were the Winnebago. Prehistoric earthworks are +to be seen in the neighbourhood, several animal-shaped mounds upon the +shores of Lakes Mendota, Monona and Waubesa being among the best +examples. A regular trading post is known to have been established on +Lake Mendota as early as 1820. The title to the Indian lands was +acquired by the United States by treaty in 1825. Colonel Ebenezer +Brigham established himself at Blue Mounds, in the western part of Dane +county, in 1827. In 1832 the "Four-Lakes" country was in the theatre of +hostilities during the Black Hawk War; Colonel Henry Dodge held a +conference with Winnebago chiefs on Lake Mendota, and there were several +skirmishes in the neighbourhood between his troops and the followers of +Black Hawk, one of which took place on the site of Madison. After Black +Hawk's defeat on the Bad Axe he fled to the Wisconsin river Dalles, near +the present Kilbourn, where he was betrayed by the Winnebago. In 1836 +Stevens T. Mason, governor of Michigan, and James Duane Doty, then U.S. +district judge, who had visited the region as early as 1829, recorded a +tract of land, including most of the present site of Madison. Here they +surveyed a "paper" city which they named in honour of James Madison. On +the 3rd of December 1836 the territorial legislature in session at +Belmont, after a protracted and acrimonious debate, determined, largely +through Doty's influence, to make Madison the permanent capital. The +construction of houses began in the early spring of 1837. The first +constitutional convention met here in 1846, the second in 1847. Madison +was chartered as a city in 1856. In 1862 a large number of Confederate +prisoners were confined in Camp Randall, at Madison, and many of them +died in hospital. + + See D. S. Durrie, _History of Madison, Wisconsin_ (Madison, 1874); + Lyman C. Draper, _Madison the Capital of Wisconsin_ (Madison, 1857); + J. D. Butler, "The Four Lakes Country" in _Wisconsin Historical + Society Collections_, vol. 10 (1888), and R. G. Thwaites, "Madison" in + _Historic Towns of the Western States_ (New York, 1900), and his + "Story of Madison" in _The University of Wisconsin_ (Madison, 1900). + + + + +MADOU, JEAN BAPTISTE (1796-1877), Belgian painter and lithographer, was +born at Brussels on the 3rd of February 1796. He studied at the Brussels +Academy of Fine Arts and was a pupil of François. While draughtsman to +the topographical military division at Courtrai, he received a +commission for lithographic work from a Brussels publisher. It was about +1820 that he began his artistic career. Between 1825 and 1827 he +contributed to _Les Vues pittoresques de la Belgique, to a Life of +Napoleon_, and to works on the costumes of the Netherlands, and later +made a great reputation by his work in _La Physionomie de la société en +Europe depuis 1400 jusqu' à nos jours_ (1836) and _Les Scènes de la vie +des peintres_. It was not until about 1840 that he began to paint in +oils, and the success of his early efforts in this medium resulted in a +long series of pictures representing scenes of village and city life, +including "The Fiddler," "The Jewel Merchant," "The Police Court," "The +Drunkard," "The Ill-regulated Household," and "The Village Politicians." +Among his numerous works mention may also be made of "The Feast at the +Château" (1851), "The Unwelcome Guests" (1852, Brussels Gallery), +generally regarded as his masterpiece, "The Rat Hunt" (acquired by +Leopold II., king of the Belgians), "The Arquebusier" (1860), and "The +Stirrup Cup." At the age of sixty-eight he decorated a hall in his house +with a series of large paintings representing scenes from La Fontaine's +fables, and ten years later made for King Leopold a series of decorative +paintings for the château of Ciergnon. Madou died at Brussels on the +31st of March 1877. + + For a list of his paintings see the annual report of the Academy of + Belgium for 1879. (F. K.*) + + + + +MADOZ, PASCUAL (1806-1870), Spanish statistician, was born at Pampeluna +on the 7th of May 1806. In early life he was settled in Barcelona, as a +writer and journalist. He joined the Progresista party formed during the +first Carlist war, 1833-40. He saw some service against the Carlists; +was elected deputy to the Cortes of 1836; took part for Espartero, and +then against him; was imprisoned in 1843; went into exile and returned; +was governor of Barcelona in 1854, and minister of finance in 1855; had +a large share in secularizing the Church lands; and after the revolution +of 1868 was governor of Madrid. He had, however, no great influence as a +leader and soon went abroad, dying at Genoa in 1870. Madoz was +distinguished from most of the politicians of his generation by the fact +that in middle life he compiled what is still a book of value--a +geographical, statistical and historical dictionary of Spain and its +possessions oversea, _Diccionario geográfico, estadístico y historico de +España, y sus posesiones de Ultramar_ (Madrid, 1848-1850). + + + + +MADRAS, a presidency of British India--officially styled Fort St +George--occupying, with its dependencies, the entire south of the Indian +peninsula. The north boundary is extremely irregular. On the extreme +N.E. is the Bengal province of Orissa; then the wild highlands of the +Central Provinces; next the dominions of the nizam of Hyderabad; and +lastly, on the N.W., the Bombay districts of Dharwar and North Kanara. +Geographically Mysore and Coorg lie within the bounds of Madras, and +politically it includes the Laccadive Islands, off the Malabar coast, in +the Indian Ocean. Its total area, including native states, is 151,695 +sq. m., and its population in 1901 was 42,397,522, showing an increase +of 7.7% in the decade. The seat of government is at Madras city (q.v.). + + _Physical Aspect._--The Madras presidency may be roughly divided into + three tracts: (1) the long and broad east coast, (2) the shorter and + narrower west coast, and (3) the high interior table-land. These + divisions are determined by the great mountain ranges of the Eastern + and Western Ghats (q.v.). Between these two ranges lies the central + table-land, with an elevation of 1000 to 3000 ft., which includes the + whole of Mysore, and extends over about half a dozen districts of + Madras. The Anaimudi mountain (8837 ft.) in Travancore is the highest + in southern India. The Nilgiri hills, which join the Ghats, culminate + in Dodabetta (8760 ft.). There are besides many outlying spurs and + tangled masses of hills, of which the Shevaroys, Anamalais and Palnis + are the most important. The Godavari, Kistna and Cauvery rivers, each + having a large tributary system, all rise in the Western Ghats, and + run across the peninsula in a south-east direction into the Bay of + Bengal. In the upper parts of their course they drain rather than + water the country through which they flow, and are comparatively + valueless either for navigation or irrigation; but before reaching the + sea they spread over alluvial deltas. Smaller rivers of the same + character are the Pennar and South Pennar or Ponniar, Palar, Vaigai, + Vellar and Tambraparni. The principal lake is that of Pulicat on the + east coast, which is 37 m. long from north to south, and forms an + important means of communication between Madras city and the northern + districts. On the west coast are a remarkable series of backwaters or + lagoons, fringing the seaboard of Kanara, Malabar and Travancore. The + largest is the backwater of Cochin, which extends 120 m. from north to + south. + + _Geology._--By far the greater part of Madras is occupied by granitic + and gneissic rocks of very ancient date. Among them are the + "charnockites," a series of associated eruptive rocks characterized by + the presence of rhombic pyroxenes. In Bellary and Anantapur districts, + as well as in Mysore and Hyderabad, several long narrow strips of a + later formation, known as the Dharwar system, are folded or faulted + into the gneissic floor. They run from N.N.W. to S.S.E., and consist + of conglomerates, lavas and schists. All the quartz reefs which + contain gold in paying quantities are found within these Dharwar + bands, those of the Kolar goldfield in Mysore being the most + important. The gneissic and Dharwar rocks are overlaid unconformably + by the sandstones, limestones, shales, &c., of the Cuddapah and + Kurnool series. It is in the sandstones and shales of the Kurnool + group that most of the diamonds of southern India are found; but as + these rocks are of sedimentary origin, it is probable that the + diamonds were originally derived from some still unknown source. A + strip of Gondwana beds follows approximately the course of the + Godavari. In Hyderabad it includes the important Singareni coalfield, + but in the Presidency no good coal seams have yet been found. Upper + Gondwana beds also occur in small patches at several other places near + the east coast. Marine cretaceous deposits are found in three detached + areas, near Trichinopoly, Viruddhachalam and Pondicherry. Some of the + coastal sandstones may be of late Tertiary age, but Tertiary fossils + have not been found except in a few small patches on the west coast, + the most southerly being near Quilon in Travancore. + + _Climate._--The climate varies in accordance with the height of the + mountain chain on the western coast. Where this chain is lofty, as + between Malabar and Coimbatore, the rainclouds are intercepted and + give a rainfall of 150 in. on the side of the sea, and only 20 in. on + the landward side. Where the range is lower, the rainclouds pass over + the hills and carry their moisture to the interior districts. The + Nilgiri hills enjoy the climate of the temperate zone, with a moderate + rainfall. The Malabar coast has a rainfall of 150 in., and the clouds + on the Western Ghats sometimes obscure the sun for months at a time. + Along the eastern coasts and central table-lands the rainfall is low + and the heat excessive. At Madras city the average rainfall is 50 in., + but this is considerably above the mean of the east coast. + + _Minerals._--The mineral wealth of the province is undeveloped. Iron + of excellent quality has been smelted by native smiths in many + localities from time immemorial; but attempts to work the beds after + European methods have proved unsuccessful. Carboniferous sandstone + extends across the Godavari valley as far as Ellore, but the coal has + been found to be of inferior quality. Among other minerals may be + mentioned manganese in Vizagapatam, and mica in Nellore. Garnets are + abundant in the sandstone of the Northern Circars, and diamonds of + moderate value are found in the same region. Stone and gravel quarries + are very numerous. + + _Forests._--The forest department of Madras was first organized in + 1856, and it is estimated that forests cover a total area of more than + 19,600 sq. m., the whole of which is under conservancy rules. An area + of about 1500 sq. m. is strictly conserved. In the remaining forests, + after supplying local wants, timber is either sold direct by the + department or licences are granted to wood-cutters. The more valuable + timber trees comprise teak, ebony, rosewood, sandal-wood and redwood. + The trees artificially reared are teak, sandal-wood, _Casuarina_ and + eucalyptus. The finest teak plantation is near Beypur in Malabar. At + Mudumalli there are plantations of both teak and sandal-wood; and the + eucalyptus or Australian gum-tree grows on the Nilgiris in magnificent + clumps. + + _Fauna._--The wild animals include the elephant, bison, sambur and + ibex of the Western Ghats and the Nilgiris. Bison are found also in + the hill tracts of the Northern Circars. In Travancore state the black + leopard is not uncommon. The elephant is protected by law from + indiscriminate destruction. The cattle are small, but in Nellore and + along the Mysore frontier a superior breed is carefully kept up by the + wealthier farmers. The best buffaloes are imported from the Bombay + district of Dharwar. + +_Population._--The population in 1901 was divided into Hindus +(37,026,471), Mahommedans (2,732,931), and Christians (1,934,480). The +Hindus may be subdivided into Sivaites, Vishnuvites and Lingayats. The +Sivaites are most numerous in the extreme south and on the west coast, +while the Vishnuvites are chiefly found in the northern districts. The +Lingayats, a sect of Sivaite puritans, derive their name from their +practice of carrying about on their persons the _linga_ or emblem of +Siva. The Brahmans follow various pursuits, and some of them are recent +immigrants, who came south in the train of the Mahratta armies. A +peculiar caste of Brahmans, called Nambudri, is found in Malabar. The +most numerous of the hill tribes are the Kondhs and Savaras, two cognate +races who inhabit the mountainous tracts of the Eastern Ghats, attached +to several of the large estates of Ganjam and Vizagapatam. On the +Nilgiris the best known aboriginal tribe is the Todas (q.v.). The +Mahommedans are subdivided into Labbai, Moplah, Arab, Sheikh, Sayad, +Pathan and Mogul. The Labbais are the descendants of Hindu converts, and +are traders by hereditary occupation, although many now employ +themselves as sailors and fishermen. The Moplahs are the descendants of +Malayalam converts to Islam--the head of the tribe, the raja of +Cannanore, being descended from a fisher family in Malabar. They are a +hard-working, frugal people, but quite uneducated and fanatical, and +under the influence of religious excitement have often disturbed the +public peace. Christians are more numerous in Madras than in any other +part of India. In Travancore and Cochin states the native Christians +constitute as much as one-fourth of the population. The Roman Catholics, +whose number throughout southern India is estimated at upwards of +650,000, owe their establishment to St Francis Xavier and the famous +Jesuit mission of Madura; they are partly under the authority of the +archbishop of Goa, and partly under twelve Jesuit vicariates. Protestant +missions date from the beginning of the 18th century. The Danes were the +pioneers; but their work was taken up by the Society for Promoting +Christian Knowledge, under whom laboured the great Lutherans of the 18th +century--Schultz, Sartorius, Fabricius and Schwartz. The Church +Missionary Society entered the field in 1814; and subsequently an +American mission joined in the work. + +_Languages._--Broadly speaking, the entire population of Madras belongs +to the five linguistic offshoots of the great Dravidian stock, dominant +throughout southern India. At an early period, before the dawn of +history, these races appear to have accepted some form of the +Brahmanical or Buddhist faiths. Many storms of conquest have since swept +over the land, and colonies of Mogul and Mahratta origin are to be found +here and there. But the evidence of language proves that the ethnical +character of the population has remained stable under all these +influences, and that the Madras Hindu, Mahommedan, Jain and Christian +are of the same stock. Of the five Dravidian languages in British +territory Telugu is spoken by over 14,000,000 persons; Tamil by over +15,000,000 persons; Kanarese by over 1,500,000 persons; Malayalam by +nearly 3,000,000 persons; and Tulu by about 500,000 persons. Oriya is +the native tongue in the extreme north of Ganjam, bordering on Orissa; +and various sub-dialects of Dravidian origin are used by the hill tribes +of the Eastern Ghats, of whom the Kondhs may be taken as the type. + + _Agriculture._--Over the greater part of the area of Madras artificial + irrigation is impossible, and cultivation is dependent upon the local + rainfall, which rarely exceeds 40 in. a year, and is liable to fall + irregularly. The Malabar coast is the only part where the rainfall + brought by the south-west monsoon may be trusted both for its amount + and regularity. Other districts, such as Bellary, are also dependent + upon this monsoon; but in their case the rainclouds have spent + themselves in passing over the Western Ghats, and cultivation becomes + a matter of hazard. Over the greater part of the presidency the rainy + season is caused by the south-east monsoon, which breaks about the end + of September. The deltas of the Godavari, Kistna and Cauvery rivers + are the only spots on the east coast which artificial irrigation is + able to save from the risk of occasional scarcity. The principal food + staples are rice, cholam, cambu, ragi and varagu (four kinds of + millet). The most common oil-seed is gingelly (sesamum). Garden crops + comprise tobacco, sugar-cane, chillies, betel-leaf and plantains. + Sugar is chiefly derived from the sap of palms. The fruit trees are + coco-nut, areca-nut, palmyra palm, jack, tamarind and mango. Special + crops include cotton, indigo, coffee, tea, cinchona. The best cotton + is grown in Tinnevelly. The principal coffee tract stretches along the + slopes of the Western Ghats from the north of Mysore almost down to + Cape Comorin. The larger portion of this area lies within Mysore, + Coorg and Travancore states, but the Wynaad and the Nilgiri hills are + within Madras. The first coffee plantation was opened in the Wynaad in + 1840. Many of the early clearings proved unprofitable, and the + enterprise made little progress till about 1855. Coffee, which is much + cultivated on the Nilgiris, covers about 100 sq. m., though the area + fluctuates. The tea plant was also introduced into the Nilgiri hills + about 1840, but was not taken up as a commercial speculation till + 1865, and is still unimportant. The cinchona plant was successfully + introduced into the Nilgiri hills by the government in 1860, and there + are now a few plantations belonging to private owners. + + The greater part of the soil in Madras is held by the cultivators + direct from the government under the tenure known as _ryotwari_. + Besides these lands in the hands of the government, there are also + proprietary or _zamindari_ estates in all parts of the country. These + estates are either the remains of ancient principalities, which the + holder cannot sell or encumber beyond his own life interest, or they + are creations of British rule and subject to the usual Hindu custom of + partition. The total area of the _zamindari_ estates is about 26 + million acres, more than one-fourth of the whole presidency. The + _peshkash_ or tribute payable to government in perpetuity amounts to + about £330,000 a year. _Ináms_, revenue-free or quit-rent grants of + lands made for religious endowments or for services rendered to the + state, occupy an aggregate area of nearly 8 million acres. + + _Manufactures._--Madras possesses few staple manufactures. The chief + industries of the presidency are cotton-ginning, coffee-curing, + fish-curing, indigo-pressing, oil-pressing, printing, rice-curing, + rope-making, sugar-refining, tanning, tile and brick-making, and + tobacco-curing. Up to the close of the 18th century cotton goods + constituted the main article of export. Masulipatam, where the first + English factory on the Coromandel coast was established in 1620, + enjoyed a special reputation for its chintzes, which were valued for + the freshness and permanency of their dyes. There is still a small + demand for these articles in Burma, the Straits and the Persian Gulf; + but Manchester goods have nearly beaten the Indian exporter out of the + field. Native looms, however, still hold their own in the local + market, in face of strenuous opposition. After weaving, working in + metals appears to be the most widespread native industry. Among local + specialities which have attracted European curiosity may be mentioned + the jewelry of Trichinopoly, ornaments of ivory and horn worked at + Vizagapatam, and sandal-wood carving in Kanara. + + _Commerce and Trade._--The continuous seaboard of the Madras + presidency, without any natural harbours of the first rank, has tended + to create a widely diffused trade. Madras city conducts nearly + one-half of the total sea-borne commerce; next comes Malabar, + containing the western railway terminus near Calicut; then Godavari, + with its cluster of ports along the fringe of the delta; Tinnevelly, + with the harbour at Tuticorin, which has opened large dealings with + Ceylon and Burma; Tanjore, South Kanara, Ganjam and Vizagapatam. As + compared with the other provinces, the trade of Madras is broadly + marked by the larger proportion assigned to coasting trade with other + Indian ports and with Ceylon. The chief staples of the export trade + are hides and skins, coffee and raw cotton. + + _Railways and Irrigation._--The presidency is well supplied with + railways, which naturally have their centre in Madras city, the chief + seaport. The broad-gauge line of the Madras & Southern Mahratta + railway connects with Bombay and Bangalore, and also crosses the + peninsula to Calicut on the western coast. The South Indian + (narrow-gauge) serves the extreme south, with its terminus at + Tuticorin, and branches to Tinnevelly, Negapatam, Erade, Pondicherry + and Nellore. The narrow-gauge line of the Madras & Southern Mahratta + railway traverses the Deccan districts; and the East Coast line + (broad-gauge), through the Northern Circars, has brought Madras into + direct communication with Calcutta. The Madras system of irrigation + has been most successful in the case of the three great eastern + rivers, the Godavari, Kistna and Cauvery. Each of these is intercepted + by an _anicut_ or dam at the head of its delta, from which canals + diverge on each side for navigation as well as irrigation. The scheme + for diverting the waters of the Tungabhadra (a tributary of the + Kistna) over the thirsty uplands of Kurnool proved a failure. The bold + project of leading the Periyar river through a tunnel across the + watershed of the Travancore hills on to the plain of Madura has been + more successful. + +_Administration._--The Madras presidency is administered by a governor +and a council, consisting of two members of the civil service, which +number may be increased to four. There is also a board of revenue of +three members. The number of districts is 24, each under the charge of a +collector, with sub-collectors and assistants. The districts are not +grouped into divisions or commissionerships, as in other provinces. For +legislative purposes the council of the governor is augmented by +additional members, numbering 45 in all, of whom not more than 17 may be +nominated officials, while 19 are elected by various representative +constituencies. Members of the legislative council enjoy the right of +interpellation, of proposing resolutions on matters of public interest, +and of discussing the annual financial statement. The principle of local +devolution is carried somewhat further in Madras than in other +provinces. At the bottom are union _panchayats_ or village committees, +whose chief duty is to attend to sanitation. Above them come _taluk_ or +subdivisional boards. At the head of all are district boards, a portion +of whose members are elected by the _taluk_ boards. + +_Education._--The chief educational institutions are the Madras +University, the Presidency College, Madras Christian College, and +Pachayyappa's College at Madras; the government arts colleges at +Combaconum and Rajahmundry; the law college, medical college and +engineering college at Madras; the college of agriculture at Coimbatore; +the teachers' college at Saidapet; the school of arts at Madras; and the +military orphanage at Ootacamund, in memory of Sir Henry Lawrence. In +1907, the total number of pupils at all institutions was 1,007,118, of +whom 164,706 were females, and 132,857 were learning English. + +_History._--Until the British conquest the whole of southern India had +never acknowledged a single ruler. The difficult nature of the hill +passes and the warlike character of the highland tribes forbade the +growth of great empires, such as succeeded one another on the plains of +Hindustan. The Tamil country in the extreme south is traditionally +divided between the three kingdoms of Pandya, Chola and Chera. The west +coast supplied the nucleus of a monarchy which afterwards extended over +the highlands of Mysore, and took its name from the Carnatic. On the +north-east the kings of Kalinga at one time ruled over the entire line +of seaboard from the Kistna to the Ganges. Hindu legend has preserved +marvellous stories of these early dynasties, but our only authentic +evidence consists in their inscriptions on stone and brass, and their +noble architecture (see India). The Mahommedan invader first established +himself in the south in the beginning of the 14th century. Ala-ud-din, +the second monarch of the Khilji dynasty at Delhi, and his general Malik +Kafur conquered the Deccan, and overthrew the kingdoms of Karnataka and +Telingana, which were then the most powerful in southern India. But +after the withdrawal of the Mussulman armies the native monarchy of +Vijayanagar arose out of the ruins. This dynasty gradually extended its +dominions from sea to sea, and reached a pitch of prosperity before +unknown. At last, in 1565, it was overwhelmed by a combination of the +four Mahommedan principalities of the Deccan. At the close of the reign +of Aurangzeb, although that emperor nominally extended his sovereignty +as far as Cape Comorin, in reality South India had again fallen under a +number of rulers who owned no regular allegiance. The nizam of the +Deccan, himself an independent sovereign, represented the distant court +of Delhi. The most powerful of his feudatories was the nawab of the +Carnatic, with his capital at Arcot. In Tanjore, a descendant of Sivaji +ruled; and on the central table-land a Hindu chieftain was gradually +establishing his authority and founding the state of Mysore, destined +soon to pass to a Mahommedan usurper. + +Vasco da Gama cast anchor off Calicut on the 20th of May 1498, and for a +century the Portuguese retained in their control the commerce of India. +The Dutch began to establish themselves on the ruin of the Portuguese at +the beginning of the 17th century, and were quickly followed by the +English, who established themselves at Calicut and Cranganore in 1616. +Tellicherry became the principal English emporium on the west coast of +Madras. The Portuguese eventually retired to Goa, and the Dutch to the +Spice Islands. The first English settlement on the east coast was in +1611, at Masulipatam, even then celebrated for its fabrics. Farther +south a fort, the nucleus of Madras city, was erected in 1640. +Pondicherry was purchased by the French in 1762. For many years the +English and French traders lived peacefully side by side, and with no +ambition for territorial aggrandisement. The war of the Austrian +succession in Europe lit the first flame of hostility on the Coromandel +coast. In 1746 Madras was forced to surrender to La Bourdonnais, and +Fort St David remained the only English possession in southern India. By +the peace of Aix-la-Chapelle Madras was restored to the English; but +from this time the rivalry of the two nations was keen, and found its +opportunities in the disputed successions which always fill a large +place in Oriental politics. English influence was generally able to +secure the favour of the rulers of the Carnatic and Tanjore, while the +French succeeded in placing their own nominee on the throne at +Hyderabad. At last Dupleix rose to be the temporary arbiter of the fate +of southern India, but he was overthrown by Clive, whose defence of +Arcot in 1751 forms the turning point in Indian history. In 1760 the +crowning victory of Wandewash was won by Colonel (afterwards Sir Eyre) +Coote, over Lally, and in the following year, despite help from Mysore, +Pondicherry was captured. + +Though the English had no longer any European rival, they had yet to +deal with Mahommedan fanaticism and the warlike population of the +highlands of Mysore. The dynasty founded by Hyder Ali, and terminating +in his son Tippoo Sultan, proved itself in four several wars, which +terminated only in 1799, the most formidable antagonist which the +English had ever encountered (see HYDER ALI and INDIA). Since the +beginning of the 19th century Madras has known no regular war, but +occasional disturbances have called for measures of repression. The +_pálegárs_ or local chieftains long clung to their independence after +their country was ceded to the British. On the west coast, the feudal +aristocracy of the Nairs, and the religious fanaticism of the Moplahs, +have more than once led to rebellion and bloodshed. In the extreme +north, the wild tribes occupying the hills of Ganjam and Vizagapatam +have only lately learned the habit of subordination. In 1836 the +_zamíndarí_ of Gumsur in this remote tract was attached by government +for the rebellious conduct of its chief. An inquiry then instituted +revealed the wide prevalence among the tribe of Kondhs of human +sacrifice, under the name of _meriah_. The practice has since been +suppressed by a special agency. In 1879 the country round Rampa on the +northern frontier was the scene of riots sufficiently serious to lead to +the necessity of calling out troops. The same necessity arose three +years later, when the Hindus and Mahommedans of Salem came into +collision over a question of religious ceremonial. A more serious +disturbance was that known as the "Anti-Shanar riots" of 1899. The +Maravans of Tinnevelly and parts of Madura, resenting the pretensions of +the Shanans, a toddy-drawing caste, to a higher social and religious +status, organized attacks on Shanan villages. The town of Sivakasi was +looted and burnt by five thousand Maravans. Quiet was restored by the +military, and a punitive police force was stationed in the disturbed +area. + +The different territories comprising the Madras presidency were acquired +by the British at various dates. In 1763 the tract encircling Madras +city, then known as the Jagir now Chingleput district, was ceded by the +nawab of Arcot. In 1765 the Northern Circars, out of which the French +had recently been driven, were granted to the Company by the Mogul +emperor, but at the price of an annual tribute of £90,000 to the nizam +of Hyderabad. Full rights of dominion were not acquired till 1823, when +the tribute was commuted for a lump payment. In 1792 Tippoo was +compelled to cede the Baramahal (now part of Salem district), Malabar +and Dindigul subdivision of Madura. In 1799, on the reconstruction of +Mysore state after Tippoo's death, Coimbatore and Kanara were +appropriated as the British share; and in the same year the Mahratta +raja of Tanjore resigned the administration of his territory, though his +descendant retained titular rank till 1855. In 1800 Bellary and Cuddapah +were made over by the nizam of Hyderabad to defray the expense of an +increased subsidiary force. In the following year the dominions of the +nawab of the Carnatic, extending along the east coast almost +continuously from Nellore to Tinnevelly, were resigned into the hands of +the British by a puppet who had been put upon the throne for the +purpose. The last titular nawab of the Carnatic died in 1855; but his +representative still bears the title of prince of Arcot, and is +recognized as the first native nobleman in Madras. In 1839 the nawab of +Kurnool was deposed for misgovernment and suspicion of treason, and his +territories annexed. + + See _Madras Manual of Administration_, 3 vols. (Madras, 1885 and + 1893); S. Ayyangar, _Forty Years' Progress in Madras_ (Madras, 1893); + J. P. Rees, _Madras_ (Society of Arts, 1901); _Madras Provincial + Gazetteer_ (2 vols., Calcutta, 1908). + + + + +MADRAS, the capital of Madras presidency, and the chief seaport on the +eastern coast of India, is situated in 13° 4´ N. and 80° 17´ E. The +city, with its suburbs, extends nine miles along the sea and nearly +four miles inland, intersected by the little river Cooum. Area, 27 sq. +m.; pop. (1901), 509,346, showing an increase of 12.6% in the decade. +Madras is the third city in India. + +Although at first sight the city presents a disappointing appearance, +and possesses not a single handsome street, it has several buildings of +architectural pretensions, and many spots of historical interest. It is +spread over a very wide area, and many parts of it are almost rural in +character. Seen from the roadstead, the fort, a row of merchants' +offices, a few spires and public buildings are all that strike the eye. +Roughly speaking, the city consists of the following divisions. (1) +George Town (formerly Black Town, but renamed after the visit of the +Prince of Wales in 1906), an ill-built, densely populated block, about a +mile square, is the business part of the town, containing the banks, +custom house, high court, and all the mercantile offices. The last, for +the most part handsome structures, lie along the beach. On the sea-face +of George Town are the pier and the new harbour. Immediately south of +George Town there is (2) an open space which contains Fort St George, +the Marina, or fashionable drive and promenade by the seashore, +Government House, and several handsome public buildings on the sea-face. +(3) West and south of this lung of the city are crowded quarters known +by native names--Chintadrapet, Turuvaleswarampet, Pudupak, Royapet, +Kistnampet and Mylapur, which bend to the sea again at the old town of +Saint Thomé. (4) To the west of George Town are the quarters of Veperi +and Pudupet, chiefly inhabited by Eurasians, and the suburbs of Egmore, +Nangambakam, and Perambur, adorned with handsome European mansions and +their spacious "compounds" or parks, which make Madras a city of +magnificent distances. (5) South-west and south lie the European +quarters of Tanampet and aristocratic Adyar. Among the most notable +buildings are the cathedral, Scottish church, Government House, +Pachayappa's Hall, senate house, Chepauk palace (now the revenue board), +and the Central railway station. + +Madras possesses no special industries. There are several cotton mills, +large cement works, iron foundries and cigar factories. Large sums of +money have from time to time been spent upon the harbour works, but +without any great success. The port remains practically an open +roadstead, protected by two breakwaters, and the P. & O. steamers ceased +to call in 1898. Passengers or cargo are landed or embarked in +flat-bottomed _masula_ boats. The sea bottom is unusually flat, reaching +a depth of ten fathoms only at a mile from the shore. The harbour is not +safe during a cyclone, and vessels have to put out to sea. Madras +conducts about 56% of the foreign trade of the presidency, but a much +smaller share of the coasting trade. As the capital of southern India, +Madras is the centre on which all the great military roads converge. It +is also the terminal station of two lines of railway, the Madras & +Southern Mahratta line and the Madras & Tanjore section of the South +Indian railway. The Buckingham canal, which passes through an outlying +part of the city, connects South Arcot district with Nellore and the +Kistna and Godavari system of canal navigation. The municipal government +of the city was framed by an act of the Madras legislature passed in +1884. The governing body consists of 32 commissioners, of whom 24 are +elected by the ratepayers, together with a paid president. The Madras +University was constituted in 1857, as an examining body, on the model +of the university of London. The chief educational institutions in +Madras city are the Presidency College; six missionary colleges and one +native college; the medical college, the law college, the college of +engineering, the teachers' college in the suburb of Saidapet, all +maintained by government; and the government school of arts. + +The foundation of Madras dates from 1640, when Francis Day, chief of the +East India Company's settlement at Armagon, obtained a grant of the +present site of the city from a native ruler. A fort--called Fort St +George, presumably from having been finished on St George's Day (April +23)--was at once constructed, and a gradually increasing population +settled around its walls. In 1653 Madras, which had previously been +subordinate to the settlement of Bantam in Java, was raised to the rank +of an independent presidency. In 1702 Daud Khan, Aurangzeb's general, +blockaded the town for a few weeks, and in 1741 the Mahrattas +unsuccessfully attacked the place. In 1746 La Bourdonnais bombarded and +captured Madras. The settlement was restored to the English two years +later by the Treaty of Aix-la-Chapelle, but the government of the +presidency did not return to Madras till 1762. In 1758 the French under +Lally occupied the Black Town and invested the fort. The siege was +conducted on both sides with great skill and vigour. After two months +the arrival of an English fleet relieved the garrison, and the besiegers +retired with some precipitancy. With the exception of the threatening +approach of Hyder Ali's horsemen in 1769, and again in 1780, Madras has +since the French siege been free from external attack. The town of Saint +Thomé, now part of Madras city, was founded and fortified by the +Portuguese in 1504, and was held by the French from 1672 to 1674. + + See Mrs F. Penny, _Fort St George_ (1900); W. Foster, _Founding of + Fort St George_ (1902). + + + + +MADRAZO Y KUNT, DON FEDERICO DE (1815-1894), Spanish painter, was born +in Rome on the 12th of February 1815. He was the son of the painter +Madrazo y Agudo (1781-1859), and received his first instruction from his +father. While still attending the classes at the Academy of San Fernando +he painted his first picture, "The Resurrection of Christ" (1829), which +was purchased by Queen Christina. Not long afterwards he painted +"Achilles in his Tent," and subsequently presented to the Academy "The +Continence of Scipio," which secured him admission as a member "for +merit." While decorating the palace of Vista Alegre he took up +portraiture. In 1852 he went to Paris, where he studied under +Winterhalter, and painted portraits of Baron Taylor and of Ingres. In +1837 he was commissioned to produce a picture for the gallery at +Versailles, and painted "Godfrey de Bouillon proclaimed King of +Jerusalem." The artist then went to Rome, where he worked at various +subjects, sacred and profane. Then he painted "Maria Christina in the +Dress of a Nun by the bedside of Ferdinand III." (1843), "Queen +Isabella," "The Duchess of Medina-Coeli," and "The Countess de Vilchès" +(1845-1847), besides a number of portraits of the Spanish aristocracy, +some of which were sent to the exhibition of 1855. He received the +Legion of Honour in 1846. He was made a corresponding member of the +Paris Academy of Fine Arts on the 10th of December 1853, and in 1873, on +the death of Schnorr, the painter, he was chosen foreign member. After +his father's death he succeeded him as director of the Prado Gallery and +president of the Academy of San Fernando. He originated in Spain the +production of art reviews and journals, such as _El Artista_, _El +Renacimiento_ and _El Semanario pintoresco_. He died at Madrid on the +11th of June 1894. His brother, DON LOUIS DE MADRAZO, was also known as +a painter, chiefly by his "Burial of Saint Cecilia" (1855). Don +Federico's best-known pupil was his son, DON RAIMUNDO DE MADRAZO (b. +1841). + + + + +MADRID, a province of central Spain, formed in 1833 of districts +previously included in New Castile, and bounded on the W. and N. by +Ávila and Segovia, E. by Guadalajara, S.E. by Cuenca and S. by Toledo. +Pop. (1900), 775,034, of whom 539,835 inhabit the city of Madrid; area, +3084 sq. m. Madrid belongs to the basin of the Tagus, being separated +from that of the Douro by the Sierra de Guadarrama on the N.W. and N., +and by the Sierra de Gredos on the S.W. The Tagus is the southern +boundary for some distance, its chief tributary being the Jarama, which +rises in the Somosierra in the north and terminates at Aranjuez. The +Jarama, in turn, is joined by the Henares and Tajuña on the left, and by +the Lozoya and Manzanares on the right. The Guadarrama, another +tributary of the Tagus, has its upper course within the province. Like +the rest of Castile, Madrid is chiefly of Tertiary formation; the soil +is mostly clayey, but there are tracts of sandy soil. Agriculture is +somewhat backward; the rainfall is deficient, and the rivers are not +utilized as they might be for irrigation. The south-eastern districts +are the best watered, and produce in abundance fruit, vegetables, wheat, +olives, esparto grass and excellent wine. Gardening and viticulture are +carried on to some extent near the capital, though the markets of Madrid +receive their most liberal supply of fruits and vegetables from +Valencia. Sheep, goats and horned cattle are reared, and fish are found +in the Jarama and other rivers. Much timber is extracted from the +forests of the northern and north-eastern parts of the province for +building purposes and for firewood and charcoal. The royal domains of +the Escorial, Aranjuez and El Pardo, and the preserves of the nobility, +are all well wooded and contain much game. Efforts have also been made +by the local authorities to cover the large stretches of waste ground +and commons with pines and other trees. + +The Sierra de Guadarrama has quarries of granite, lime and gypsum, and +is known to contain iron, copper and argentiferous lead; but these +resources are undeveloped. Other industries are chiefly confined to the +capital; but cloth, leather, paper, earthenware, porcelain, glass, +bricks and tiles, ironware, soap, candles, chocolate and lace are also +manufactured on a small scale beyond its boundaries. There is very +little commerce except for the supply of the capital with necessaries. + +Besides the local lines, all the great railways in the kingdom converge +in this province, and it contains in all 221 m. of line. Besides Madrid, +the towns of Aranjuez (12,670) and Alcalá de Henares (11,206) and the +Escorial are described in separate articles. The other towns with more +than 5000 inhabitants are Vallecas (10,128), Colmenar de Oreja (6182), +Colmenar Viejo (5255) and Carabanchel Bajo (5862). + + + + +MADRID, the capital of Spain and of the province of Madrid, on the left +bank of the river Manzanares, a right-hand tributary of the Jarama, +which flows south into the Tagus. Pop. (1877), 397,816; (1887), 472,228; +(1897), 512,150; (1900), 539,835. Madrid was the largest city in Spain +in 1900; it is the see of an archbishop, the focus of the principal +Spanish railways, the headquarters of an army corps, the seat of a +university, the meeting-place of parliament, and the chief residence of +the king, the court, and the captain-general of New Castile. It is, +however, surpassed in ecclesiastical importance by Toledo and in +commerce by Barcelona. + + _Situation and Climate._--Madrid is built on an elevated and + undulating plateau of sand and clay, which is bounded on the north by + the Sierra Guadarrama and merges on all other sides into the barren + and treeless table-land of New Castile. Numerous water-courses + (_arroyos_), dry except at rare intervals, furrow the surface of the + plateau; these as they pass through the city have in certain cases + been converted into roads--e.g. the Paseo de Recoletos and Prado, + which are still so liable to be flooded after prolonged rain that + special channels have been constructed to carry away the water. The + highest point in Madrid is 2372 ft. above sea-level. The city is close + to the geographical centre of the peninsula, nearly equidistant from + the Bay of Biscay, the Mediterranean and the Atlantic. Owing to its + high altitude and open situation it is liable to sudden and frequent + variations of climate, and the daily range of temperature sometimes + exceeds 50° F. In summer the heat is rendered doubly oppressive by the + fiery, dust-laden winds which sweep across the Castilian table-land; + at this season a temperature of 109° has been registered in the shade. + In winter the northerly gales from the Sierra Guadarrama bring intense + cold; snow falls frequently, and skating is carried on in the Buen + Retiro park. A Spanish proverb describes the wind of Madrid as so + deadly and subtle that "it will kill a man when it will not blow out a + candle"; but, though pulmonary diseases are not uncommon, the climate + appears to be exceptionally healthy. In 1901 the death-rate was 22.07 + per 1000, or lower than that of any other town on the Spanish + mainland. The Sierra Guadarrama renders the atmosphere unusually dry + and clear by intercepting the moisture of the north-western winds + which prevail in summer; hence the average dally number of deaths + decreases from 80 in winter to about 25 in summer. The sanitation of + the older quarters is defective, and overcrowding is common, partly + owing to the royal decrees which formerly prohibited the extension of + the city; but much has been done in modern times to remove or mitigate + these evils. + +_The Inner City._--The form of Madrid proper (exclusive of the modern +suburbs) is almost that of a square with the corners rounded off; from +east to west it measures rather less than from north to south. It was +formerly surrounded by a poor wall, partly of brick, partly of earth, +some 20 ft. in height, and pierced by five principal gates (_puertas_) +and eleven doorways (_portillos_). Of these only three, the Puerta de +Alcalá on the east, the Puerta de Toledo on the south and the Portillo +de San Vicente on the west, actually exist; the first and the third were +erected in the time of Charles III. (1759-1788), and the second in +honour of the restoration of Ferdinand VII. (1827). The Manzanares--or +rather its bed, for the stream is at most seasons of the year quite +insignificant--is spanned by six bridges, the Puente de Toledo and +Puente de Segovia being the chief. + +The Puerta del Sol is the centre of Madrid, the largest of its many +plazas, and the place of most traffic. It derived its name from the +former east gate of the city, which stood here until 1570, and had on +its front a representation of the sun. On its south side stands the +Palacio de la Gobernacion, or ministry of the interior, a heavy square +building by a French architect, J. Marquet, dating from 1768. From the +Puerta del Sol diverge, immediately or mediately, ten of the principal +streets of Madrid--eastward by north, the Calle de Alcalá, terminating +beyond the Buen Retiro park; eastward, the Carrera de San Jeronimo, +terminating by the Plaza de las Cortes in the Prado; southward, the +Calle de Carretas; westward, the Calle Mayor, which leads to the council +chamber and to the palace, and the Calle del Arenal, terminating in the +Plaza de Isabel II. and the royal opera house; north-westward, the +Calles de Preciados and Del Carmen; and northward, the Calle de la +Montera, which afterwards divides into the Calle de Fuencarral to the +left and the Calle de Hortaleza to the right. The contract for another +wide street through central Madrid, to be called the Gran Via, was given +to an English firm in 1905. + + The Calle de Alcalá is bordered on both sides with acacias, and + contains the Real Academia de Bellas Artes, founded in 1752 as an + academy of art and music; its collection of paintings by Spanish + masters includes some of the best-known works of Murillo. The handsome + Bank of Spain (1884-1891) stands where the Calle de Alcalá meets the + Prado; in the oval Plaza de Madrid, at the same point, is a fine + 18th-century fountain with a marble group representing the goddess + Cybele drawn in a chariot by two lions. The Calle de Alcalá is + continued eastward past the Buen Retiro gardens and park, and through + the Plaza de Independencia, in the middle of which is the Puerta de + Alcalá. The Plaza de las Cortes is so called from the Congreso de los + Diputados, or House of Commons, on its north side. The square contains + a bronze statue of Cervantes, by Antonio Sola, erected in 1835. The + Calle de Carretas, on the west side of which is the General Post + Office, ranks with the Carrera de San Jeronimo and Calle de la Montera + for the excellence of its shops. From the Calle Mayor is entered the + Plaza Mayor, a rectangle of about 430 ft. by 330 ft., formerly the + scene of tournaments, bull fights, autos de fé, acts of canonization + (including that of Ignatius Loyola in 1622) and similar exhibitions, + which used to be viewed by the royal family from the balcony of one of + the houses called the Panaderia (belonging to the guild of bakers). + The square, which was built under Philip III. in 1619, is surrounded + by an arcade; the houses are uniform in height and decoration. In the + centre stands a bronze equestrian statue of Philip III., designed by + Giovanni da Bologna, after a painting by Pantoja de la Cruz, and + finished by Pietro Tacca. From the south-east angle of the Plaza Mayor + the Calle de Atocha, one of the principal thoroughfares of Madrid, + leads to the outskirts of the inner city; it contains two large + hospitals and part of the university buildings (faculty of medicine). + The house occupied by Cervantes from 1606 until his death in 1616 + stands at the point where it meets the Calle de Léon; in this street + is the Real Academia de la Historia, with a valuable library and + collections of MSS. and plate. From the south-west angle of the Plaza + Mayor begins the Calle de Toledo, the chief mart for the various + woollen and silken fabrics from which the picturesque costumes + peculiar to the peninsula are made. In the Plaza de Isabel II., at the + western extremity of the Calle del Arenal, stands the royal + opera-house, the principal front of which faces the Plaza del Oriente + and the royal palace. In the centre of the plaza is a fine bronze + equestrian statue of Philip IV. (1621-1665); it was designed by + Velazquez and cast by Tacca, while Galileo is said to have suggested + the means by which the balance is preserved. The gift of the grand + duke of Tuscany in 1640, it stood in the Buen Retiro gardens until + 1844. + +_Modern Development of the City._--The north and east of the city--the +new suburbs--have developed past the Retiro Park as far as the +Bull-ring, and have covered all the vast space included between the +Retiro, the Bull-ring, the long Castellana Drive to the race-course and +the exhibition building. On the slopes of the other side of the +Castellana, and along what were the northern limits of Madrid in 1875, +the modern suburbs have extended to the vicinity of the fine cellular +prison that was built at the close of the reign of King Alphonso XII. to +replace the gloomy building known as El Saladero. + +The new parts of the capital, with their broad streets and squares, and +their villas sometimes surrounded with gardens, their boulevards lined +by rather stunted trees, and their modern public buildings, all resemble +the similar features of other European capitals, and contrast with the +old Madrid that has preserved so many of its traits in architecture, +popular life and habits. Some of the streets have been slightly widened, +and in many thoroughfares new houses are being built among the ugly, +irregular dwelling-places of the 18th and earlier centuries. This +contrast is to be seen especially in and about the Calle Mayor, the +Plaza Mayor, the Calle de Toledo, the Rastro, and the heart of the city. + + Few capitals have more extensively developed their electric and horse + tramways, gas and electric light installations and telephones. Much + was done to improve the sanitary conditions of the city in the last + twenty years of the 19th century. The streets are deluged three times + a day with fire-hose, but even that has little effect upon the dust. + Unfortunately the water supply, which used to be famed for its + abundance and purity, became wholly insufficient owing to the growth + of the city. The old reservoir of the Lozoya canal, a cutting 32 m. + long, and the additional reservoir opened in 1883, are quite + inadequate for the requirements of modern Madrid, and were formerly + kept in such an unsatisfactory state that for several months in 1898 + and 1899 the water not only was on the point of giving out, but at + times was of such inferior quality that the people had recourse to the + many wells and fountains available. The construction of new waterworks + was delayed by a terrible accident, which occurred on the 8th of April + 1905; the whole structure collapsed, and nearly 400 persons lost their + lives in the flooded ruins. A decided improvement has been made in the + burial customs of Madrid. No bodies are allowed to be interred in the + churches and convents. Some of the older burial grounds in the + northern suburbs have been closed altogether, and in those which + remain open few coffins are placed in the niche vaults in the depth of + the thick walls, as was once the practice. A large modern necropolis + has been established a few miles to the north-east. + +_Principal Buildings._--As compared with other capitals Madrid has very +few buildings of much architectural interest. The Basilica de Nuestra +Señora de Atocha, on the Paseo de Atocha, a continuation of the Calle de +Atocha, was originally founded in 1523. After being almost destroyed by +the French, it was restored by Ferdinand VII., and rebuilt after 1896. +The modern church is Romanesque in style; it contains a much venerated +statue of the Virgin, attributed to St Luke. The collegiate church of +San Isidro el Real, in the Calle de Toledo, dates from 1651; it has no +architectural merit, but contains one or two valuable pictures and other +works of art. It was originally owned by the Jesuits, but after their +expulsion in 1769 it was reconsecrated, and dedicated to St Isidore the +Labourer (d. 1170), the patron saint of Madrid, whose remains were +entombed here. When the diocese of Madrid was separated from that of +Toledo San Isidro was chosen as the cathedral. The modern Gothic church +of San Jeronimo el Real occupies a conspicuous site eastward of the +town. The church of San Francisco el Grande, which contains many +interesting monuments, is also known as the National Pantheon. An act +was passed in 1837 declaring that the remains of all the most +distinguished Spaniards should be buried here; but no attempt to enforce +the act systematically was made until 1869, and even then the attempt +failed. Towards the close of the 19th century the church was splendidly +restored at the expense of the state. Its interior was decorated with +paintings and statuary by most of the leading Spanish artists of the +time. Of secular buildings unquestionably the most important is the +royal palace (Palacio Real), on the west side of the town, on rising +ground overhanging the Manzanares. It occupies the site of the ancient +Moorish alcázar (citadel), where a hunting seat was built by Henry IV.; +this was enlarged and improved by Charles V. when he first made Madrid +his residence in 1532; was further developed by Phillip II., but +ultimately was destroyed by fire in 1734. The present edifice was begun +under Philip V. in 1737 by Sacchetti of Turin, and was finished in 1764. +It is in the Tuscan style, and is 470 ft. square and 100 ft. in height, +the material being white Colmenar granite, resembling marble. To the +north of the palace are the royal stables and coach-houses, remarkable +for their extent; to the south is the armoury (Museo de la Real +Armería), containing what is possibly the best collection of the kind in +existence. After the Palacio Real may be mentioned the royal picture +gallery (Real Museo de Pinturas), adjoining the Salon del Prado; it was +built about 1785 for Charles III. by Juan de Villanueva as a museum of +natural history and academy of sciences. It contains the collections of +Charles V., Philip II. and Philip IV., and the pictures number upwards +of two thousand. The specimens of Titian, Raphael, Tintoretto, +Velazquez, Vandyck, Rubens and Teniers give it a claim to be considered +the finest picture gallery in the world. The Biblioteca Nacional, in the +Paseo de Recoletos, was founded in 1866, and completed in 1892. Not only +the national library, with its important collections of MSS. and +documents, but the archaeological museum, the museums of modern painting +and sculpture, and the fine arts academy of San Fernando, are within its +walls. The two houses of the Cortes meet in separate buildings. The +deputies have a handsome building with a very valuable library in the +Carrera San Jeronimo; the senators have an old Augustinian convent which +contains some fine pictures. A large and handsome building near the +Retiro Park contains the offices of the ministers of public works, +agriculture and commerce, and of fine arts and education; nearly +opposite stands the new station of the Southern Railway Company. The +Great Northern and the Spain to Portugal Railway Companies have also +replaced their old stations by very spacious, handsome structures, much +resembling those of Paris. In 1896 the Royal Exchange was installed in a +large monumental building with a fine colonnade facing the Dos de Mayo +monument, not far from the museum of paintings. + +Of the promenades and open places of public resort the most fashionable +and most frequented is the Prado (Paseo del Prado, Salon del Prado) on +the east side of the town, with its northward continuation--the Paseo de +Recoletos. To the south of the town is the Paseo de las Delicias, and on +the west, below the royal palace, and skirting the Manzanares, is the +Paseo de la Virgen del Puerto, used chiefly by the poorer classes. +Eastward from the Prado are the Buen Retiro Gardens, with ponds and +pavilions, and a menagerie. The gardens were formerly the grounds +surrounding a royal hunting seat, on the site of which a palace was +built for Philip IV. in 1633; it was destroyed during the French +occupation. + +_Education, Religion and Charity._--Madrid University developed +gradually out of the college of Doña Maria de Aragon, established in +1590 by Alphonso Orozco. Schools of mathematics and natural science were +added in the 16th and 17th centuries, and in 1786 the medical and +surgical college of San Carlos was opened. In 1836-1837 the university +of Alcalá de Henares (q.v.) was transferred to the capital and the older +foundations incorporated with it. The university of Madrid thenceforth +became the headquarters of education in central Spain. It has an +observatory, and a library containing more than 2,000,000 printed books +and about 5500 MSS. It gives instruction, chiefly in law and medicine, +but also in literature, philosophy, mathematics and physics, to about +5000 students. Associated with the university is the preparatory school +of San Isidro, founded by Philip IV. (1621-1665), and reorganized by +Charles III. in 1770. + + There are upwards of 100 official primary schools and a large number + of private ones, among which the schools conducted by the Jesuits and + the Scolapian fathers claim special mention. Madrid also has schools + of agriculture, architecture, civil and mining engineering, the fine + arts, veterinary science and music. The school of military engineering + is at Guadalajara. Besides these special schools there are a + self-supporting institute for preparing girls for the higher degrees + and for certificates as primary teachers, and an institute for + secondary education, conducted chiefly by ecclesiastics. Among the + educational institutions may be reckoned the botanical garden, dating + from 1781, the libraries of the palace, the university, and San + Isidro, and the museum of natural science, exceedingly rich in the + mineralogical department. The principal learned society is the royal + Spanish Academy, founded in 1713 for the cultivation and improvement + of the Spanish tongue. The Academy of History possesses a good + library, rich in MSS. and incunabula, as well as a fine collection of + coins and medals. In addition to the academies of fine arts, the exact + sciences, moral and political science, medicine and surgery, and + jurisprudence and legislation, all of which possess libraries, there + are also anthropological, economic and geographical societies, and a + scientific and literary athenaeum. Madrid has a British cemetery + opened in 1853, when the older Protestant cemetery in the Paseo de + Recoletos was closed. The town also contains a British embassy chapel, + a German chapel, and several Spanish Protestant chapels, attended by + over 1200 native Protestants, while the Protestant schools, chiefly + supported by British, German and American contributions, are attended + by more than 2500 children. The first Protestant bishop of Madrid was + consecrated in 1895 by Archbishop Plunkett of Dublin. The charitable + institutions were greatly improved between 1885 and 1905. The Princess + Hospital was completely restored on modern methods, and can + accommodate several hundred patients. The old contagious diseases + hospital of San Juan de Dios was pulled down and a fine new hospital + built in the suburbs beyond the Retiro Park, to hold 700 patients. The + military hospital was demolished and a very good one built in the + suburbs. There are in all twenty hospitals in Madrid, and a lunatic + asylum on the outskirts of the capital, founded by one of the most + eminent of Spanish surgeons, and admirably conducted. New buildings + have been provided for the orphanages, and for the asylums for the + blind, deaf and dumb, incurables and aged paupers. There are hospitals + supported by the French, Italian and Belgian colonies; these are old + and well-endowed foundations. Public charity generally is very active. + In Madrid, as in the rest of Spain, there has been an unprecedented + increase in convents, monasteries and religious institutions, + societies and Roman Catholic workmen's clubs and classes. + + Apart from private institutions for such purposes, the state maintains + in the capital a savings bank for the poorer classes, and acts as + pawnbroker for their benefit. The mercantile and industrial classes + are organized in gilds, which themselves collect the lump sum of + taxation exacted by the exchequer and the municipality from each + _gremio_ or class of taxpayers. The working classes also have + commercial and industrial _circulos_ or clubs that are obeyed by the + gilds with great _esprit de corps_, a chamber of commerce and + industries, and "associations of productions" for the defence of + economic interests. + +_Industries._--The industries of the capital have developed +extraordinarily since 1890. In the town, and within the municipal +boundaries in the suburbs, many manufactories have been established, +giving employment to more than 30,000 hands, besides the 4000 women and +girls of the Tobacco Monopoly Company's factory. Among the most +important factories are those which make every article in leather, +especially cigar and card cases, purses and pocket-books. Next come the +manufactures of fans, umbrellas, sunshades, chemicals, varnishes, +buttons, wax candles, beds, cardboard, porcelain, coarse pottery, +matches, baskets, sweets and preserves, gloves, guitars, biscuits, +furniture, carpets, corks, cards, carriages, jewelry, drinks of all +kinds, plate and plated goods. There are also tanneries, saw and flour +mills, glass and porcelain works, soap works, brickfields, paper mills, +zinc, bronze, copper and iron foundries. The working classes are +strongly imbued with socialistic ideas. Strikes and May Day +demonstrations have often been troublesome. Order is kept by a garrison +of 12,500 men in the barracks of the town and cantonments around, and by +a strong force of civil guards or gendarmes quartered in the town +itself. The civil and municipal authorities can employ beside the +gendarmes the police, about 1400 strong, and what is called the +_guardias urbanos_, another police force whose special duty it is to +regulate the street traffic and prevent breaches of the municipal +regulations. There is not, on the average, more crime in Madrid than in +the provinces. + +_History._--Spanish archaeologists have frequently claimed for Madrid a +very high antiquity, but the earliest authentic historical mention of +the town (Majrít, Majoritum) occurs in the Arab chronicle, and does not +take us farther back than to the first half of the 10th century. The +place was finally taken from the Moors by Alphonso VI. (1083), and was +made a hunting-seat by Henry IV., but first rose into importance when +Charles V., benefiting by its keen air, made it his occasional +residence. Philip II. created it his capital and "only court" (_única +corte_) in 1560. It is, however, only classed as a town (_villa_), +having never received the title of city (_ciudad_). Fruitless attempts +were made by Philip III. and Charles III. respectively to transfer the +seat of government to Valladolid and to Seville. (See also SPAIN: +_History_). + + See J. Amador de los Rios, _Historia de la villa y corte de Madrid_ + (Madrid, 1861-1864); Valverdey Alvarez, _La Capitol de España_ + (Madrid, 1883); E. Sepúlveda, _La Vida en Madrid en 1886_ (Madrid, + 1887); H. Peñasco, _Las Calles de Madrid_ (Madrid, 1889); C. Perez + Pastor, _Bibliografia madrileña, siglo XVI._ (Madrid, 1891); F. X. de + Palacio y Garcia, count of las Almenas, _La Municipalidad de Madrid_ + (Madrid, 1896); E. Sepúlveda, _El Madrid de los recuerdos: colección + de artículos_ (Madrid, 1897); P. Hauser, _Madrid bajo el punto de + vista medico-social_ (Madrid, 1902); L. Williams, _Toledo and Madrid, + their Records and Romances_ (London, 1903). + + + + +MADRIGAL (Ital. _madrigale_), the name of a form of verse, the exact +nature of which has never been decided in English, and of a form of +vocal music. + +(1) _In Verse._--The definition given in the _New English Dictionary_, +"a short lyrical poem of amatory character," offers no distinctive +formula; some madrigals are long, and many have nothing whatever to do +with love. The most important English collection of madrigals, not set +to music, was published by William Drummond of Hawthornden (1585-1649) +in his _Poems_ of 1616. Perhaps the best way of ascertaining what was +looked upon in the 17th century as a madrigal is to quote one of +Drummond's:-- + + The beauty and the life + Of life's and beauty's fairest paragon, + O tears! O grief! hung at a feeble thread. + To which pale Atropos had set her knife; + The soul with many a groan + Had left each outward part, + And now did take his last leave of the heart; + Nought else did want, save death, even to be dead; + When the afflicted band about her bed. + Seeing so fair him come in lips, cheeks, eyes, + Cried ah! and can death enter Paradise? + +This may be taken as a type of Drummond's madrigals, of which he has +left us about eighty. They are serious, brief, irregular lyrics, in +which neither the amatory nor the complimentary tone is by any means +obligatory. Some of these pieces contain as few as six lines, one as +many as fourteen, but they average from nine to eleven. In the majority +of examples the little poem opens with a line of six syllables, and no +line extends beyond ten syllables. The madrigal appears to be a short +canzone of the Tuscan type, but less rigidly constructed. In French the +madrigal has not this Italian character. It is simply a short piece of +verse, ingenious in its turn and of a gallant tendency. The idea of +compliment is essential. J. F. Guichard (1730-1811) writes:-- + + Orgon, poète marital, + À Venus compare sa femme; + C'est pour la belle un madrigal, + C'est pour Venus une épigramme. + +This quatrain emphasizes the fact that in French a madrigal is a +trifling piece of erotic compliment, neatly turned but not seriously +meant. The credit of inventing the old French verse-form of madrigal +belongs to Clément Marot, and one of his may be quoted in contrast to +that of Drummond:-- + + Un doux nenni avec un doux sourire + Est tant honneste, il le vous faut apprendre; + Quant est de oui, si veniez à le dire, + D'avoir trop dit je voudrois vous reprendre; + Non que je sois ennuyé d'entreprendre + D'avoir le fruit dont le désir me point; + Mais je voudrois qu'en ne le laissant prendre, + Vous me disiez: vous ne l'aurez point. + +In English, when the word first occurred--it has not been traced farther +back than 1588 (in the preface to Nicholas Yonge's _Musica +transalpina_)--it was identified with the chief form of secular vocal +music in the 16th century. In 1741 John Immyns (d. 1764) founded the +Madrigal Society, which met in an ale-house in Bride Lane, Fleet Street; +this association still exists, and is the oldest musical society in +Europe. + +The word "madrigal" is frequently also used to designate a sentimental +or trifling expression in a half-contemptuous sense. (E. G.) + +(2) _In Music._--As a definite musical art-form, the madrigal was known +in the Netherlands by the middle of the 15th century; like the motet, it +obviously originated in the treatment of counterpoint on a canto fermo, +some early examples even combining an ecclesiastical canto fermo in the +tenor with secular counterpoint in the other parts. Thus Josquin's +_Déploration de Jehan Okenheim_ (see MUSIC) might equally well be called +a madrigal or motet, if the word "madrigal" were used for compositions +to French texts at all. But by the middle of the 16th century the +Italian supremacy in music had developed the madrigal into the greatest +of secular musical forms, and made it independent of the form of the +words; and thus when Lasso sets Marot's madrigals to appropriately witty +and tuneful music he calls the result a "chanson"; while when Palestrina +composes Petrarca's Sonnets to the Virgin in memory of Laura, the result +appears as a volume of _Madrigali spirituali_. Elegiac madrigals, +whether spiritual or secular, were thus as common as any other kind; so +that when the _Musica transalpina_ brought the word "madrigal" to +England it brought a precedent for the poet Drummond's melancholy type +of madrigal poetry. + +Italian madrigals, however, are by no means always elegiac; but the term +always means a highly organized and flowing polyphonic piece, often as +developed as the motet, though, in the mature classical period, distinct +in style. Yet masses were often founded on the themes of madrigals, just +as they were on the themes of motets (see MASS; MOTET); and it is +interesting, in such beautiful cases as Palestrina's _Missa gia fu chi +m'ebbe cara_, to detect the slight strain the mildly scandalous origin +of the themes puts upon the ecclesiastical style. + +The breaking strain was put on the madrigal style at the end of the 16th +century, in one way by the new discords of Monteverde and (with more +musical invention) Schütz; and in another way by the brilliant musical +character-drawing of Vecchi, whose _Amfiparnasso_ is a veritable comic +opera in the form of a set of fourteen madrigals, all riotously witty in +the purest and most masterly polyphonic style. It was probably meant, or +at least made use of, to laugh down the earliest pioneers of opera +(q.v.); but it is the beginning of the end for the madrigal as a living +art. Long afterwards we occasionally meet with the word again, when a +17th or 18th century composer sets to some kind of accompanied singing a +poem of madrigalesque character. But this does not indicate any +continuation of the true musical history of the madrigal. The strict +meaning of the word in its musical sense is, then, a musical setting of +an Italian or English non-ecclesiastical poem (typically a canzone) for +unaccompanied chorus, in a 16th-century style less ecclesiastical than +the motet, but as like it in organization as the form and sentiment of +the words admit. The greatest classics in the madrigal style are those +of Italy; and but little, if at all, below them come the English. The +form, though not the name, of course, exists in the 16th-century music +of other languages whenever the poetry is not too light for it. + +It is important but easy to distinguish the madrigal from the lighter +16th-century forms, such as the Italian _villanella_ and the English +ballet, these being very homophonic and distinguished by the strong lilt +of their rhythm. + +The madrigal has been very successfully revived in modern English music +with a more or less strict adherence to the 16th century principles; the +compositions of De Pearsall being of high artistic merit, while the +_Madrigale spirituale_ in Stanford's oratorio _Eden_ is a movement of +rare beauty. (D. F. T.) + + + + +MADURA (Dutch _Madoera_), an island of the Dutch East Indies, separated +by the shallow Strait of Madura from the N.E. coast of Java. Pop. +(1897), 1,652,580, of whom 1,646,071 were natives, 4252 Chinese and 558 +Europeans. It extends from about 112° 32´ to 114° 7´ E., and is divided +into two nearly equal portions by the parallel of 7° S.; the area is +estimated at 1725 sq. m. It is a plateau-like prolongation of the +limestone range of northern Java, with hills (1300 to 1600 ft. high) and +dales. The formation of the coast and plains is Tertiary and recent +alluvium. Hot springs are not infrequent; and in the valley between +Gunong Geger and Banjar lies the mud volcano of Banju Ening. The coasts +are clothed with tropical vegetation; but the soil is better fitted for +pastoral than agricultural purposes. Fishing and cattle-rearing are the +chief means of subsistence. Besides rice and maize, Madura yields +coco-nut oil and _jati_. The manufacture of salt for the government, +abolished in other places, continues in Madura. Hence perhaps the name +is derived (Sansk. _mandura_, salt). Petroleum is found in small +quantities. + +The principal town is Sumenep; and there are populous Malay, Arab and +Chinese villages between the town and the European settlement of +Maringan. On a hill in the neighbourhood lies Asta, the burial-place of +the Sumenep princes. Pamekasan is the seat of government. Bangkalang is +a large town with the old palace of the sultan of Madura and the +residences of the princes of the blood; the mosque is adorned with the +first three suras of the Koran, thus differing from nearly all the +mosques in Java and Madura, though resembling those of western Islam. In +the vicinity once stood the Erfprins fort. Arisbaya (less correctly +Arosbaya) is the place where the first mosque was built in Madura, and +where the Dutch sailors first made acquaintance with the natives. The +once excellent harbour is now silted up. Sampang is the seat of an +important market. The Kangean and Sapudi islands, belonging to Madura, +yield timber, trepang, turtle, pisang and other products. + +Madura formerly consisted of three native states--Madura or Bangkalang, +Pamekasan and Sumenep. The whole island was considered part of the Java +residency of Surabaya. The separate residency of Madura was constituted +in 1857; it now consists of four "departments"--Pamekasan, Madura, +Sumenep and Sampang. + + See P. J. Veth, Java, vol. iii.; Kielstra, "Het Eiland Madoera," in + _De Gids_ (1890); H. van Lennep, "De Madoereezen," in _De Indische + Gids_ (1895), with detailed bibliography. + + + + +MADURA, a city and district of British India, in the Madras Presidency. +The city is situated on the right bank of the river Vaigai, and has a +station on the South Indian railway 345 m. S.E. of Madras. Pop. (1901), +105,984. The city was the capital of the old Pandyan dynasty, which +ruled over this part of India from the 5th century B.C. to the end of +the 11th century A.D. Its great temple forms a parallelogram about 847 +ft. by 729 ft., and is surrounded by nine _gopuras_, of which the +largest is 152 ft. high. These ornamental pyramids begin with doorposts +of single stones 60 ft. in height, and rise course upon course, carved +with rows of gods and goddesses, peacocks, bulls, elephants, horses, +lions, and a bewildering entanglement of symbolical ornament all +coloured and gilded, diminishing with distance until the stone _trisul_ +at the top looks like the finest jeweller's work. The temple, which +contains some of the finest carving in southern India, is said to have +been built in the reign of Viswanath, first ruler of the Nayak dynasty. +Its chief feature is the sculptured "Hall of a Thousand Pillars." The +palace of Tirumala Nayak is the most perfect relic of secular +architecture in Madras. This palace, which covers a large area of +ground, has been restored, and is utilized for public offices. The +Vasanta, a hall 333 ft. long, probably dedicated to the god +Sundareswara, and the Tamakam, a pleasure-palace, now the residence of +the collector, are the other principal buildings of this period. + +The last of the old Pandyan kings is said to have exterminated the Jains +and conquered the neighbouring kingdom of Chola; but he was in his turn +overthrown by an invader from the north, conjectured to have been a +Mahommedan. In 1324 a Moslem army under Malik Kafur occupied Madura, and +the Hindus were held in subjection for a period of fifty years. +Subsequently Madura became a province of the Hindu Empire of +Vijayanagar. In the middle of the 16th century the governor Viswanath +established the Nayak dynasty, which lasted for a century. The greatest +of the line was Tirumala Nayak (reigned 1623-1659), whose military +exploits are recorded in the contemporary letters of the Jesuit +missionaries. He adorned Madura with many public buildings, and extended +his empire over the adjoining districts of Tinnevelly, Travancore, +Coimbatore, Salem and Trichinopoly. His repudiation of the nominal +allegiance paid to the raja of Vijayanagar brought him into collision +with the sultan of Bijapur, and after a lapse of three centuries +Mahommedans again invaded Madura and compelled him to pay them tribute. +After the death of Tirumala the kingdom of Madura gradually fell to +pieces, being invaded by both Mahommedans and Mahrattas. About 1736 the +district fell into the hands of the nawab of the Carnatic, and the line +of the Nayaks was extinguished. About 1764 British officers took charge +of Madura in trust for Mahommed Ali (Wallah Jah), the last independent +nawab of the Carnatic, whose son finally ceded his rights of sovereignty +to the East India Company in 1801. + +The DISTRICT OF MADURA has an area of 8701 sq. m. Pop. (1901), +2,831,280, an increase of 8.5% in the decade. It consists of a section +of the plain stretching from the mountains east to the sea, coinciding +with the basin of the Vaigai river, and gradually sloping to the S.E. +The plain is broken by the outlying spurs of the Ghats, and by a few +isolated hills and masses of rock scattered over the country. The most +important spur of the Ghats is known as the Palni hills, which project +E.N.E. across the district for a distance of about 54 m. Their highest +peaks are more than 8000 ft. above sea-level, and they enclose a plateau +of about 100 sq. m., with an average height of 7000 ft. On this plateau +is situated the sanatorium of Kodaikanal, and coffee-planting is +successfully carried on. The other principal crops of the district are +millets, rice, other food-grains, oil-seeds and cotton. Tobacco is grown +chiefly in the neighbourhood of Dindigul, whence it is exported to +Trichinopoly, to be made into cigars. There are several cigar factories +and a number of saltpetre refineries. The only other large industry is +that of coffee-cleaning. Madura is traversed by the main line of the +South Indian railway. It has four small seaports, whose trade is chiefly +carried on with Ceylon. The most important irrigation work, known as the +Periyar project, consists of a tunnel through the Travancore hills, to +convey the rainfall across the watershed. + + See _Madura District Gazetteer_ (Madras, 1906). + + + + +MADVIG, JOHAN NICOLAI (1804-1886), Danish philologist, was born on the +island of Bornholm, on the 7th of August 1804. He was educated at the +classical school of Frederiksborg and the university of Copenhagen. In +1828 he became reader, and in 1829 professor, of Latin language and +literature at Copenhagen, and in 1832 was appointed university +librarian. In 1848 Madvig entered parliament as a member of what was +called the "Eider-Danish" party, because they desired the Eider to be +the boundary of the country. When this party came into power Madvig +became minister of education. In 1852 be became director of public +instruction. Some years later, from 1856 to 1863, Madvig was president +of the Danish parliament and leader of the National Liberal party. With +these brief interruptions the greater part of his life was devoted to +the study and teaching of Latin and the improvement of the classical +schools, of which he was chief inspector. As a critic he was +distinguished for learning and acumen. He devoted much attention to +Cicero, and revolutionized the study of his philosophical writings by an +edition of _De Finibus_ (1839; 3rd ed., 1876). Perhaps his most widely +known works are those on Latin grammar and Greek syntax, especially his +Latin grammar for schools (Eng. trans. by G. Woods). In 1874 his sight +began to fail, and he was forced to give up much of his work. He still, +however, continued to lecture, and in 1879 he was chosen rector for the +sixth time. In 1880 he resigned his professorship, but went on with his +work on the Roman constitution, which was completed and published before +his death. In this book Madvig takes a strongly conservative standpoint +and attacks Mommsen's views on Caesar's programme of reforms. It is a +clear exposition, though rather too dogmatic and without sufficient +regard for the views of other scholars. His last work was his +autobiography, _Livserindringer_ (published 1887). Madvig died at +Copenhagen on the 12th of December 1886. + + See J. E. Sandys, _History of Classical Scholarship_ (1908), iii., + 319-324. + + + + +MAECENAS, GAIUS (CILNIUS), Roman patron of letters, was probably born +between 74 and 64 B.C., perhaps at Arretium. Expressions in Propertius +(ii. 1, 25-30) seem to imply that he had taken some part in the +campaigns of Mutina, Philippi and Perusia. He prided himself on his +ancient Etruscan lineage, and claimed descent from the princely house of +the Cilnii, who excited the jealousy of their townsmen by their +preponderating wealth and influence at Arretium in the 4th century B.C. +(Livy x. 3). The Gaius Maecenas mentioned in Cicero (_Pro Cluentio_, 56) +as an influential member of the equestrian order in 91 B.C. may have +been his grandfather, or even his father. The testimony of Horace +(_Odes_ iii. 8, 5) and Maecenas's own literary tastes imply that he had +profited by the highest education of his time. His great wealth may have +been in part hereditary, but he owed his position and influence to his +close connexion with the emperor Augustus. He first appears in history +in 40 B.C., when he was employed by Octavian in arranging his marriage +with Scribonia, and afterwards in assisting to negotiate the peace of +Brundusium and the reconciliation with Antony. It was in 39 B.C. that +Horace was introduced to Maecenas, who had before this received Varius +and Virgil into his intimacy. In the "Journey to Brundusium," (Horace, +_Satires_, i. 5) in 37, Maecenas and Cocceius Nerva are described as +having been sent on an important mission, and they were successful in +patching up, by the Treaty of Tarentum, a reconciliation between the two +claimants for supreme power. During the Sicilian war against Sextus +Pompeius in 36, Maecenas was sent back to Rome, and was entrusted with +supreme administrative control in the city and in Italy. He was +vice-gerent of Octavian during the campaign of Actium, when, with great +promptness and secrecy, he crushed the conspiracy of the younger +Lepidus; and during the subsequent absences of his chief in the +provinces he again held the same position. During the latter years of +his life he fell somewhat out of favour with his master. Suetonius +(_Augustus_, 66) attributes the loss of the imperial favour to Maecenas +having indiscreetly revealed to Terentia, his wife, the discovery of the +conspiracy in which her brother Murena was implicated. But according to +Dio Cassius (liv. 19) it was due to the emperor's relations with +Terentia. Maecenas died in 8 B.C., leaving, the emperor heir to his +wealth. + +Opinions were much divided in ancient times as to the personal character +of Maecenas; but the testimony as to his administrative and diplomatic +ability was unanimous. He enjoyed the credit of sharing largely in the +establishment of the new order of things, of reconciling parties, and of +carrying the new empire safely through many dangers. To his influence +especially was attributed the humaner policy of Octavian after his first +alliance with Antony and Lepidus. The best summary of his character as a +man and a statesman is that of Velleius Paterculus (ii. 88), who +describes him as "of sleepless vigilance in critical emergencies, +far-seeing and knowing how to act, but in his relaxation from business +more luxurious and effeminate than a woman." + +Expressions in the _Odes_ of Horace (ii. 17. i) seem to imply that +Maecenas was deficient in the robustness of fibre characteristic of the +average Roman. His character as a munificent patron of literature--which +has made his name a household word--is gratefully acknowledged by the +recipients of it and attested by the regrets of the men of letters of a +later age, expressed by Martial and Juvenal. His patronage was +exercised, not from vanity or a mere dilettante love of letters, but +with a view to the higher interest of the state. He recognized in the +genius of the poets of that time, not only the truest ornament of the +court, but a power of reconciling men's minds to the new order of +things, and of investing the actual state of affairs with an ideal glory +and majesty. The change in seriousness of purpose between the _Eclogues_ +and the _Georgics_ of Virgil was in a great measure the result of the +direction given by the statesman to the poet's genius. A similar change +between the earlier odes of Horace, in which he declares his epicurean +indifference to affairs of state, and the great national odes of the +third book is to be ascribed to the same guidance. Maecenas endeavoured +also to divert the less masculine genius of Propertius from harping +continually on his love to themes of public interest. But if the motive +of his patronage had been merely politic it never could have inspired +the affection which it did in its recipients. The great charm of +Maecenas in his relation to the men of genius who formed his circle was +his simplicity, cordiality and sincerity. Although not particular in the +choice of some of the associates of his pleasures, he admitted none but +men of worth to his intimacy, and when once admitted they were treated +like equals. Much of the wisdom of Maecenas probably lives in the +_Satires_ and _Epistles_ of Horace. It has fallen to the lot of no other +patron of literature to have his name associated with works of such +lasting interest as the _Georgics_ of Virgil, the first three books of +Horace's _Odes_, and the first book of his _Epistles_. + +Maecenas himself wrote in both prose and verse. The few fragments that +remain show that he was less successful as an author than as a judge and +patron of literature. His prose works on various subjects--_Prometheus_, +_Symposium_ (a banquet at which Virgil, Horace and Messalla were +present), _De cultu suo_ (on his manner of life)--were ridiculed by +Augustus, Seneca and Quintilian for their strange style, the use of rare +words and awkward transpositions. According to Dio Cassius, Maecenas was +the inventor of a system of shorthand. + + There is no good modern biography of Maecenas. The best known is that + by P. S. Frandsen (1843), See "Horace et Mecène" by J. Girard, in _La + Révue politique et littéraire_ (Dec. 27, 1873); V. Gardthausen, + _Augustus und seine Zeit_, i. 762 seq.; ii. 432 seq. The chief ancient + authorities for his life are Horace (_Odes_ with Scholia), Dio + Cassius, Tacitus (_Annals_), Suetonius (_Augustus_). The fragments + have been collected and edited by F. Harder (1889). + + + + +MAECIANUS, LUCIUS VOLUSIUS (2nd cent.) Roman jurist, was the tutor in +law of the emperor Marcus Aurelius. When governor of Alexandria he was +slain by the soldiers, as having participated in the rebellion of +Avidius Cassius (175). Maecianus was the author of works on trusts +(_Fideicommissa_), on the _Judicia publica_, and of a collection of the +Rhodian laws relating to maritime affairs. His treatise on numerical +divisions, weights and measures (_Distributio_) is extant, with the +exception of the concluding portion. + + See Capitolinus, _Antoninus_, 3; Vulcacius Gallicanus, _Avidius + Cassius_, 7; edition of the metrological work by F. Hultsch in + _Metrologicorum scriptorum reliquiae,_ ii. (1866); Mommsen in + _Abhandlungen der sächsischen Gesellschaft der Wissenschaften_, iii. + (1853). + + + + +MAELDUIN (or MAELDUNE), VOYAGE OF (_Imram Maeleduin_), an early Irish +romance. The text exists in an 11th-century redaction, by a certain Aed +the Fair, described as the "chief sage of Ireland," but it may be +gathered from internal evidence that the tale itself dates back to the +8th century. It belongs to the group of Irish romance, the _Navigations_ +(_Imrama_), the common type of which was probably imitated from the +classical tales of the wanderings of Jason, of Ulysses and of Aeneas. +Maelduin, the foster-son of an Irish queen, learnt on reaching manhood +that he was the son of a nun, and that his father, Ailill of the edge of +battle, had been slain by a marauder from Leix. He set sail to seek his +father's murderer, taking with him, in accordance with the instructions +of a sorcerer, seventeen men. His three foster-brothers swam after him, +and were taken on board. This increase of the fateful number caused +Maelduin's vengeance to be deferred for three years and seven months, +until the last of the intruders had perished. The travellers visited +many strange islands, and met with a long series of adventures, some of +which are familiar from other sources. The _Voyage of St Brendan_ (q.v.) +has very close similarities with the _Maelduin_, of which it is possibly +a clerical imitation, with the important addition of the whale-island +episode, which it has in common with "Sindbad the Sailor." + + _Imram Curaig Mailduin_ is preserved, in each case imperfectly, in the + _Lebor na h Uidre_, a MS. in the Royal Irish Academy, Dublin; and in + the _Yellow Book of Lecan_, MS. H. 216 in the Trinity College Library, + Dublin; fragments are in Harleian MS. 5280 and Egerton MS. 1782 in the + British Museum. There are translations by Patrick Joyce, _Old Celtic + Romances_ (1879), by Whitley Stokes (a more critical version, printed + together with the text) in _Revue celtique_, vols. ix. and x. + (1888-1889). See H. Zimmer, "Brendan's Meerfahrt" in _Zeitschrift für + deutsches Altertum_, vol. xxxiii. (1889). Tennyson's _Voyage of + Maeldune_, suggested by the Irish romance, borrows little more than + its framework. + + + + +MAELIUS, SPURIUS (d. 439 B.C.), a wealthy Roman plebeian, who during a +severe famine bought up a large amount of corn and sold it at a low +price to the people. Lucius (or Gaius) Minucius, the patrician +_praefectus annonae_ (president of the market), thereupon accused him of +courting popularity with a view to making himself king. The cry was +taken up. Maelius, summoned before the aged Cincinnatus (specially +appointed dictator), refused to appear, and was slain by Gaius Servilius +Ahala; his house was razed to the ground, his corn distributed amongst +the people, and his property confiscated. The open space called +Aequimaelium, on which his house had stood, preserved the memory of his +death. Cicero calls Ahala's deed a glorious one, but, whether Maelius +entertained any ambitious projects or not, his summary execution was an +act of murder, since by the Valerio-Horatian laws the dictator was bound +to allow the right of appeal. + + See Niebuhr's _History of Rome_, ii. 418 (Eng. trans., 1851); G. + Cornewall Lewis, _Credibility of early Roman History_, ii.; Livy, iv. + 13; Cicero, _De senectute_ 16, _De amicitia_ 8, _De republica_, ii. + 27; Floras, i. 26; Dion. Halic. xii. i. + + + + +MAELSTROM (whirlpool), a term originally applied to a strong current +running past the south end of the island of Moskenaes, a member of the +group of Lofoten Islands on the west coast of Norway. It is known also +as the Moskenstrom. Though dangerous in certain states of wind and tide, +the tales of ships being swallowed in this whirlpool are fables. The +word is probably of Dutch origin, from _malen_, to grind or whirl, and +_strom_ or _stroom_, a stream or current. It appears on Mercator's +_Atlas_ of 1595. + + + + +MAENADS (Gr. [Greek: Mainades], frenzied women), the female attendants +of Dionysus. They are known by other names--Bacchae, Thyiades, Clodones +and Mimallones (the last two probably of Thracian origin)--all more or +less synonymous. + + See the exhaustive articles by A. Legrand in Daremberg and Saglio's + _Dictionnaire des antiquités_ and A. Rapp in Roscher's _Lexikon der + Mythologie_; also editions of Euripides, _Bacchae_ (e.g. J. E. + Sandys). + + + + +MAENIUS, GAIUS, Roman statesman and general. Having completed (when +consul in 338 B.C.) the subjugation of Latium, which with Campania had +revolted against Rome, he was honoured by a triumph, and a column was +erected to him in the Forum. When censor in 318, in order that the +spectators might have more room for seeing the games that were +celebrated in the Forum, he provided the buildings in the neighbourhood +with balconies, which were called after him _maeniana_. + + See Festus, s.v. Maeniana; Livy viii. 13, ix. 34; Pliny, _Nat. Hist._ + xxxiv. 11 (5). + + + + +MAERLANT, JACOB VAN (c. 1235-c. 1300), Flemish poet, was born in the +Franc de Burges (tradition says at Damme) between 1230 and 1240. He was +sacristan of Maerlant, in the island of Ost-Voorne, and afterwards clerk +to the magistrates at Damme. His early works are translations of French +romances. Maerlant's most serious work in the field of romance was his +_Ystorien van Troyen_ (c. 1264), a poem of some forty thousand lines, +translated and amplified from the _Roman de Troie_ of Benoît de +Sainte-More. From this time Maerlant rejected romance as idle, and +devoted himself to writing scientific and historical works for the +education and enlightenment of the Flemish people. His _Heimelicheit der +Heimelicheden_ (c. 1266) is a translation of the _Secreta secretorum_, a +manual for the education of princes, ascribed throughout the middle ages +to Aristotle. _Van der Naturen Bloeme_ is a free translation of _De +natura rerum_, a natural history in twenty books by a native of Brabant, +Thomas de Cantimpré; and his _Rijmbijbel_ is taken, with many omissions +and additions, from the _Historia scholastica_ of Petrus Comestor. He +supplemented this metrical paraphrase of Scripture history by _Die Wrake +van Jherusalem_ (1271) from Josephus. Although Maerlant was an orthodox +Catholic, he is said to have been called to account by the priests for +translating the Bible into the vulgar tongue. In 1284 he began his +_magnum opus_, the _Spiegel historiael_, a history of the world, derived +chiefly from the third part of the _Speculum majus_ of Vincent de +Beauvais. This work was completed by two other writers, Philipp +Utenbroeke and Lodowijk van Velthem. Maerlant died in the closing years +of the 13th century, his last poem, _Van den lande van oversee_, dating +from 1291. The greater part of his work consists of translations, but he +also produced poems which prove him to have had real original poetic +faculty. Among these are _Die Clausule van der Bible_, _Der Kerken +Clage_, imitated from the _Complaintes_ of Rutebeuf, and the three +dialogues entitled _Martijn_, in which the fundamental questions of +theology and ethics were discussed. In spite of his orthodoxy, Maerlant +was a keen satirist of the corruptions of the clergy. He was one of the +most learned men of his age, and for two centuries was the most +celebrated of Flemish poets. + + See monographs by J. van Beers (Ghent, 1860); C. A. Serrure (Ghent, + 1861); K. Versnaeyen (Ghent, 1861); J. te Winkel (Leiden, 1877, 2nd + ed., Ghent, 1892); and editions of _Torec_ (Leiden, 1875) by J. te + Winkel; of _Naturen Bloeme_, by Eelco Verwijs; of _Alexanders Geesten_ + (Groningen, 1882), by J. Franck; _Merlijn_ (Leiden, 1880-1882), by J. + van Bloten; _Heimelicheit der Heimelicheden_ (Dordrecht, 1838), by + Clarisse; _Der Naturen Bloeme_ (Groningen, 1878), by Verwijs; of + _Rijmbijbel_ (Brussels, 1858-1869), by David; _Spiegel historiael_ + (Leiden 1857-1863), by Verwijs and de Vries; selections from the + _Ystorien van Troyen_ (1873), by J. Verdam. + + + + +MAES, NICOLAS (1632-1693), Dutch painter, was born at Dordrecht, and +went about 1650 to Amsterdam, where he entered Rembrandt's studio. +Before his return to Dordrecht in 1654 Maes painted a few Rembrandtesque +genre pictures, with life-size figures and in a deep glowing scheme of +colour, like the "Reverie" at the Ryks Museum in Amsterdam, the "Card +Players" at the National Gallery, and the "Children with a Goat +Carriage," belonging to Baroness N. de Rothschild. So closely did his +early style resemble that of Rembrandt, that the last-named picture, and +other canvases in the Leipzig and Budapest galleries and in the +collection of Lord Radnor, were or are still ascribed to Rembrandt. In +his best period, from 1655 to 1665, Maes devoted himself to domestic +genre on a smaller scale, retaining to a great extent the magic of +colour he had learnt from Rembrandt. Only on rare occasions did he treat +scriptural subjects, as in the earl of Denbigh's "Hagar's Departure," +which has been ascribed to Rembrandt. His favourite subjects were women +spinning, or reading the Bible, or preparing a meal. In 1665 he went to +Antwerp, where he remained till 1678, in which year he probably returned +to Amsterdam. His Antwerp period coincides with a complete change in +style and subject. He devoted himself almost exclusively to portraiture, +and abandoned the intimacy and glowing colour harmonies of his earlier +work for a careless elegance which suggests the influence of Van Dyck. +So great indeed was the change, that it gave rise to the theory of the +existence of another Maes, of Brussels. Maes is well represented at the +National Gallery by five paintings: "The Cradle," "The Dutch Housewife," +"The Idle Servant," "The Card Players," and a man's portrait. At +Amsterdam, besides the splendid examples to be found at the Ryks Museum, +is the "Inquisitive Servant" of the Six collection. At Buckingham Palace +is "The Listening Girl" (repetitions exist), and at Apsley House +"Selling Milk" and "The Listener." Other notable examples are at the +Berlin, Brussels, St Petersburg, the Hague, Frankfort, Hanover and +Munich galleries. + + + + +MAESTRO, a north-westerly wind observed in the Adriatic and surrounding +regions, chiefly during summer. The maestro is a "fine weather" wind, +and is the counterpart of the sirocco. + + + + +MAETERLINCK, MAURICE (1862- ), Belgian-French dramatist and poet, of +Flemish extraction, was born at Ghent on the 29th of August 1862. He was +educated at the Collège Sainte-Barbe, and then at the university of his +native city, where, at the age of twenty-four, he was enrolled as a +barrister. In 1887 he settled in Paris, where he immediately became +acquainted with Villiers de l'Isle-Adam and the leaders of the symbolist +school of French poetry. At the death of his father, Maeterlinck +returned to Belgium, where he thenceforth mainly resided: in the winter +at Ghent, in the summer on an estate at Oostacker. He had by this time +determined to devote his whole life to poetry, a dedication which his +fortune permitted. His career as an author began in 1889, when he +published a volume of verse, _Serres chaudes_, and a play, _La Princesse +Maleine_, the latter originally composed in metre, but afterwards +carefully rewritten in prose, the vehicle which the author continued to +use for his dramatic work. Maeterlinck was at this time totally unknown, +but he became famous through an article by Octave Mirbeau, prominently +published in the Paris _Figaro_, entitled "A Belgian Shakespeare." The +enthusiasm of this review and the excellence of the passages quoted +combined to make Maeterlinck the talk of the town. Maeterlinck, among +his Belgian roses, continued to work with extreme deliberation. In 1890 +he published, in Brussels, two more plays, _L'Intruse_ and _Les +Aveugles_; followed in 1891 by _Les Sept princesses_. His strong leaning +to mysticism was now explained, or defined, by a translation of the +Flemish medieval visionary, the Admirable Ruysbroeck, which Maeterlinck +brought out in 1891. In 1892 appeared what has been perhaps the most +successful of all his plays on the stage, _Pelléas et Mélisande_, +followed in 1894 by those very curious and powerful little dramas +written to be performed by marionettes: _Alladine el Palomides_, +_Intérieur_ and _La Mort de Tintagiles_. In 1895 Maeterlinck brought +out, under the title of _Annabella_, a translation of Ford's _'Tis Pity +She's a Whore_, with a preface. Two philosophical works followed, a +study on Novalis (1895) and _Le Trésor des humbles_ (1896). In 1896 he +returned to drama with _Aglavaine el Sélysette_ and to lyric verse with +_Douze chansons_. A monograph on the ethics of mysticism, entitled _La +Sagesse et la destinée_, was issued, as a kind of commentary on his own +dramas, in 1898; and in 1901 Maeterlinck produced a fascinating volume +of prose, founded upon observations made in his apiaries at Oostacker, +in which philosophy, fancy and natural history were surprisingly +mingled--_La Vie des abeilles_. In 1902 he published _Le Temple +enseveli_ and _Monna Vanna_; in 1903 _Joyzelle_. In 1901 he began to +issue, in Brussels, an edition of his complete dramatic works. + +The nature of Maeterlinck's writings, whether in prose or verse, has +been strictly homogeneous. Few poets have kept so rigorously to a +certain defined direction in the practice of their art. Whether in +philosophy, or drama, or lyric, Maeterlinck is exclusively occupied in +revealing, or indicating, the mystery which lies, only just out of +sight, beneath the surface of ordinary life. In order to produce this +effect of the mysterious he aims at an extreme simplicity of diction, +and a symbolism so realistic as to be almost bare. He allows life itself +to astonish us by its strangeness, by its inexplicable elements. Many of +his plays are really highly pathetic records of unseen emotion; they are +occupied with the spiritual adventures of souls, and the ordinary facts +of time and space have no influence upon the movements of the +characters. We know not who these orphan princesses, these blind +persons, these pale Arthurian knights, these aged guardians of desolate +castles, may be; we are not informed whence they come, nor whither they +go; there is nothing concrete or circumstantial about them. Their life +is intense and consistent, but it is wholly of a spiritual character; +they are mysterious with the mystery of the movements of a soul. These +characteristics, which make the dramatic work of Maeterlinck so curious +and unique, are familiar to most readers in _Pelléas et Mélisande_, but +are carried, perhaps, to their farthest intensity in _Aglavaine et +Sélysette_, which seems to be written for a phantom stage and to be +acted by disembodied spirits. In spite of the violence of his early +admirers, and of the fact that the form of his dramas easily lent itself +to the cheap ridicule of parodists, the talent of Maeterlinck has hardly +met with opposition from the criticism of his time. It has been +universally felt that his spirit is one of grave and disinterested +attachment to the highest moral beauty, and his seriousness, his +serenity and his extreme originality have impressed even those who are +bewildered by his diaphanous graces and offended at his nebulous +mysticism. While the crude enthusiasm which compared him with +Shakespeare has been shown to be ridiculous, the best judges combine +with Camille Mauclair when he says: "Maurice Maeterlinck est un homme +de génie authentique, un très grand phénomène de puissance mentale à la +fin du xix^e siècle." In spite of the shadowy action of Maeterlinck's +plays, which indeed require some special conditions and contrivances for +their performance, they are frequently produced with remarkable success +before audiences who cannot be suspected of mysticism, in most of the +countries of Europe. In his philosophical writings Maeterlinck shows +himself a disciple of Novalis, of Emerson, of Hello, of the Flemish +Catholic mystics, and he evolves from the teachings of those thinkers a +system of aesthetics applicable to the theatre as he conceives it. + (E. G.) + + + + +MAFEKING, a town in the British Bechuanaland division of the Cape, 870 +m. N.E. of Cape Town and 492 m. S.S.W. of Bulawayo by rail, and 162 m. +in a direct line W. by N. of Johannesburg. (Pop. 1904), 2713. It is +built on the open veld, at an elevation of 4194 ft., by the banks of the +Upper Molopo, is 9 m. W. of the western frontier of the Transvaal and 15 +m. S. of the southern boundary of the Bechuanaland protectorate. The +Madibi goldfields are some 10 m. south of the town. Mafeking is thus an +important trading and distributing centre for Bechuanaland and the +western Transvaal. Here are, too, the chief railway workshops between +Kimberley and Bulawayo. The headquarters of the administration for the +Bechuanaland protectorate are in the town. The chief buildings are the +town-hall, Anglican church, Masonic temple, and hospital. + +Mafeking was originally the headquarters of the Barolong tribe of +Bechuana and is still their largest station, the native location (pop. +2860) being about a mile distant from the town. It was from Pitsani +Pothlugo (or Potlogo), 24 m. north of Mafeking, that Dr Jameson started, +on the 29th of December 1895, on his raid into the Transvaal. On the +outbreak of the Anglo-Boer war in 1899 Mafeking was invested by a Boer +force. Colonel R. S. S. Baden-Powell was in command of the defence, +which was stubbornly maintained for 217 days (Oct. 12 to May 17), when a +relief column arrived and the Boers dispersed (see TRANSVAAL: +_History_). The fate of the town had excited the liveliest sympathy in +England, and the exuberant rejoicings in London on the news of its +relief led to the coining of the word _mafficking_ to describe the +behaviour of crowds on occasions of extravagant demonstrations of a +national kind. In September 1904 Lord Roberts unveiled at Mafeking an +obelisk bearing the names of those who fell in defence of the town. + + R. S. S. Baden-Powell's _Sketches in Mafeking and East Africa_ (1907) + and Lady Sarah Wilson's _South African Memories_ (1909) deal largely + with the siege of Mafeking. + + + + +MAFFEI, FRANCESCO SCIPIONE, MARCHESE DI (1675-1755); Italian +archaeologist and man of letters, was born at Verona on the 1st of June +1675. He studied for five years in Parma, at the Jesuit College, and +afterwards from 1698 at Rome; and in 1703-1704 he took part as a +volunteer in the war of succession, fighting on the Bavarian side at +Donauwerth. In 1709 he began at Padua along with Apostolo Zeno and +Valisnieri the _Giornale dei letterati d'Italia_, a literary periodical +which had but a short career; and subsequently an acquaintance with the +actor Riccoboni led him to exert himself for the improvement of dramatic +art in Italy. His _Merope_, a tragedy, appeared in 1713; _Teatro +italiano_, a small collection of works for presentation on the stage, in +1723-1725; and _Le Ceremonie_, an original comedy, in 1728. From 1718 he +became specially interested in the archaeology of his native town, and +his investigations resulted in the valuable _Verona illustrata_ +(1731-1732). Maffei afterwards devoted four years to travel in France, +England, Holland and Germany. He died at Verona on the 11th of February +1755. + + A complete edition of his works appeared at Venice (28 vols., 8vo) in + 1790. + + + + +MAFIA (MAFFIA), a secret society of Sicily. Its organization and +purposes much resemble those of the Camorra (q.v.). + + Various derivations are found for the name. Some hold it to be a + Tuscan synonym for _miseria_; others, a corruption of Fr. _mauvais_ + (bad). Others connect it with the name of an alleged Arab tribe, + Mà-âfir, once settled at Palermo. Giuseppe Pitré asserts that the word + is peculiar to western Sicily and that, with its derivatives, it + formerly meant, in Il Borgo, a district of Palermo, beauty or + excellence. Thus, a handsome woman showily dressed was said "to have + _mafia_," or to be _mafiusa_. Often in Palermo the street merchants + call _arance-mafiuse_ (fine oranges). Thus, Pitré argues, _mafia_, + applied to a man to express manly carriage and bravery, would + naturally become the title of a society the members of which were all + "bravos." A less credible explanation of the term is connected with + Mazzini, who is said to have formed a secret society the members of + which were called _Mafiusi_, from _Mafia_, a word composed of the + initial letters of five Italian words, _Mazzini autorizza furti, + incendi, avvelenamenti_, "Mazzini authorizes theft, arson and + poisoning." This theory suggests that the word was unknown before 1859 + or 1860. + +The Mafia, however named, existed long before Mazzini's day. In its +crudest form it was co-operative brigandage, blended with the Vendetta +(q.v.). The more strictly organized Mafia was the result of the +disorders consequent upon the expulsion of the king of Naples by +Napoleon. When the Bourbon court took refuge in Sicily there were a +large number of armed retainers in the service of the Sicilian feudal +nobility. Ferdinand IV., at the bidding of England, granted a +constitution to the island in 1812, and with the destruction of +feudalism most of the feudal troops became brigands. Powerless to +suppress them, Ferdinand organized the bandits into a rural +_gendarmerie_, and they soon established a reign of terror. The abject +poverty of the poorer classes, unable to eke out existence by work in +the sulphur mines or on the fields, fostered the growth of two classes +of _mafiusi_--the vast majority of the inhabitants who were glad to put +themselves as passive members under the protection of the Mafia, while +the active members shared in the plunder. The Mafia thus became a +loosely organized society under an unwritten code of laws or ethics +known as _Omertà_, i.e., manliness (from Sicil. _omu_, Ital. _uomo_, a +man), which embodied the rules of the Vendetta. Candidates were admitted +after trial by duel, and were sworn to resist law and defeat justice. +Like the Camorra, the Mafia was soon powerful in all classes, and even +the commander of the royal troops acted in collusion with it. The real +home of Mafia was in and around Palermo, where no traveller was safe +from robbery and the knife. In an organized form the Mafia survives only +in isolated districts. Generally speaking, it is to-day not a compact +criminal association but a complex social phenomenon, the consequence of +centuries of misgovernment. The Mafiuso is governed by a sentiment akin +to arrogance which imposes a special line of conduct upon him. He +considers it dishonourable to have recourse to lawful authority to +obtain redress for a wrong or a crime committed against him. He +therefore hides the identity of the offender from the police, reserving +vengeance to himself or to his friends and dependants. This sentiment, +still widely diffused among the lower classes of many districts, and not +entirely unknown to the upper classes, renders difficult legal proof of +culpability for acts of violence, and multiplies sanguinary private +reprisals. In September 1892 about 150 Mafiusi were arrested at Catania, +but all repressive measures proved useless. The only result was to drive +some of the members abroad, with disastrous results to other countries. +In October 1890 David Hennessy, chief of police in New Orleans, was +murdered. Subsequent legal inquiry proved the crime to be the work of +the Mafia, which had been introduced into the United States thirty years +before. In May 1890 a band of Italians living in New Orleans had +ambushed another gang of their fellow-countrymen belonging to a society +called _Stoppaghera_. The severe police measures taken brought the +vengeance of the society upon Hennessy. Eleven Italians were indicted on +suspicion of being implicated in his murder; but the jury was terrorized +and acquitted six. On the 14th of March 1891 a mob led by well-known New +Orleans citizens broke into the gaol where nineteen Italians were +imprisoned and lynched eleven of them. + + See W. Agnew Paton, _Picturesque Sicily_ (1898); C. W. Heckethorn, + _Secret Societies of all Ages_ (1897); Alongi, _La Maffia_ (Turin, + 1887); Le Faure, _La Maffia_ (Paris, 1892). + + + + + +MAFRA, a town of Portugal, in the district of Lisbon (formerly in the +province of Estremadura); near the Atlantic coast and the right bank of +the river Lizandro, and 20 m. N.W. of Lisbon. Pop. (1900), 4769. Mafra +is remarkable for its monastery, church, and palace, built by John V. in +1717-1732, in consequence of a vow made during a dangerous illness to +build a convent for the poorest friary of the kingdom--which proved to +be a small Franciscan settlement here. The architects, Johann Friedrich +Ludwig of Regensburg, and his son Johann Peter, took the Escurial for +their model; but the imitation is less successful than the original, +though the cost exceeded £4,000,000. The building is in the form of a +parallelogram measuring upwards of 800 ft. from north to south and 700 +ft. from east to west; it is said to contain 866 rooms, and to be +lighted by no fewer than 5200 windows. The centre is occupied by the +church, sumptuously built of marble, and richly adorned with statues and +other objects of art. In each of the twin towers there is a chime of 57 +bells. Part of the palace, originally designed as barracks, is used as a +military academy. Adjoining the palace are fine gardens and a royal +model farm. + + + + +MAGADHA, an ancient kingdom of India, mentioned in both the _Ramayana_ +and the _Mahabharata_. It comprised that portion of Behar lying S. of +the Ganges, with its capital at Pataliputra or Patna. As the scene of +many incidents in the life of Gautama Buddha, it was a holy land. It was +also the seat of the Maurya Empire, founded by Chandragupta, which +extended over all India under Asoka; and, later, of the powerful Gupta +dynasty. + + + + +MAGALDÁN, a town in the northern part of the province of Pangasinan, +Luzon, Philippine Islands, about 2 m. from the shore of the Gulf of +Lingayen. Pop. (1903), 15,841. In 1903 the adjacent municipality of +Mapandan (pop. in 1903, 4198) was annexed to Magaldán. Most of its +inhabitants are engaged in rice culture. The principal language is +Pangasinan; Ilocano is also spoken. + + + + +MAGALLANES (Spanish form of _Magellan_), a territory of southern Chile +extending from 47° S. to Cape Horn and including the mainland from the +Argentine frontier to the Pacific coast, the islands extending along +that coast, the Fuegian archipelago, and the western half of Tierra del +Fuego. Area, about 71,127 sq. m.; pop. (1895), 5170. It is one of the +most inhospitable regions of the world, being exposed to cold westerly +storms for most of the year. The islands are barren, but the mainland is +covered with forests, practically inaccessible to exploitation because +of the inclement climate and the wet spongy soil. The coast is indented +with bays and fjords and affords remarkable scenery. There is little +animal life on land, but the coast is frequented by the seal and +sea-otter and the sheltered waters by countless sea-fowl. The only +permanent settlements are at Punta Arenas, the capital, on the Straits +of Magellan, Palomares on Otway Water, Mina Marta on Skyring Water, and +Ultima Esperanza (Last Hope) on the east shore of Worsley Sound. All are +east of the Andean ranges and partially sheltered from the westerly +storms. In this sheltered region there are open plains where sheep are +grazed. A few sheep ranges have been established on Tierra del Fuego. +Some nomadic tribes of Indians inhabit Tierra del Fuego and the extreme +southern end of the mainland, but their numbers are small. Coal has been +found in the vicinity of Punta Arenas, and gold occurs. + + See _The Voyage of the Adventure and Beagle_ (1839). + + + + +MAGAZINE, primarily a warehouse for goods or merchandise (Arab. +_makhzan_, a storehouse, from _khazana_, to store up). In Morocco +_makhzan_ (or _maghzen_) has come to be used as the name of the +government. The Spaniards adopted the Arabic in the form _magacen_, and +the English form comes through the older French _magazin_, modern +_magasin_. The meaning of a storehouse or large shop, common in French, +is rare in English except in the military use of the term for a building +for the storage of explosives and ammunition. It is applied to the +chamber of a repeating rifle or machine-gun containing the supply of +cartridges. The name as applied to a periodical publication containing +articles on various subjects was first used in the _Gentleman's +Magazine_ (1731), described as "a monthly collection, to treasure up as +in a magazine" articles on the subjects with which it was proposed to +deal. + + + + +MAGDALA (more correctly MAKDALA), a natural stronghold in the country of +the Wollo Gallas, Abyssinia, about 250 m. W. of Jibuti on the Gulf of +Aden, in 11° 22´ N., 39° 25´ E. The basaltic plateau of which it +consists rises 9110 ft. above the sea. It is about three-quarters of a +mile in length by less than half a mile in breadth, and lies more than a +thousand feet higher than the neighbouring plain of Arogié. Chosen about +1860 by the emperor Theodore of Abyssinia as his principal stronghold in +the south, Magdala owes its celebrity to the fact that, as the place of +imprisonment of the English captives, it became the goal of the great +English Expedition of 1868. At the time of its capture it contained huts +for a population of about three thousand. The whole rock was burned bare +by order of the commander of the British force, Sir Robert Napier, who, +on being raised to the peerage for his services on this occasion, took +the title of Lord Napier of Magdala. The plateau was subsequently +refortified by the Abyssinians. + + See Clements Markham, _History of the Abyssinian Expedition_ (1869); + and H. Rassam, _British Mission to Theodore_ (1869). + + + + +MAGDEBURG, a city of Germany, capital of the Prussian province of +Saxony, a fortress of the first rank and one of the principal commercial +towns of the German Empire. It lies in a broad and fertile plain, mainly +on the left bank of the Elbe, 88 m. S.W. from Berlin and at the junction +of main lines to Leipzig, Brunswick, Cassel and Hamburg. Pop. (1885), +159,520; (1890), 202,234; (1905), 240,661. It consists of the town +proper, and of the five suburbs of Friedrichstadt, Wilhelmstadt, +Neustadt, Sudenburg and Buckau; the last four are separated from the +town by the ramparts and glacis, but are all included within the new +line of advanced bastions, while Friedrichstadt lies on the right bank +of the river. In the Elbe, between the old town and the Friedrichstadt, +lies an island whereon stands the citadel; this is united with both +banks by bridges. With the exception of the Breite Weg, a handsome +thoroughfare running from north to south, the streets of the town proper +are narrow and crooked. Along the Elbe, however, extend fine promenades, +the Fürstenwall and the Fürsten Üfer. To the south of the inner town is +the Friedrich Wilhelms Garten, a beautiful park laid out on the site of +the celebrated convent of Berge, which was founded in 968 and suppressed +in 1809. By far the most important building in Magdeburg is the +cathedral, dedicated to SS Maurice and Catherine, a handsome and massive +structure of the 14th century, exhibiting an interesting blending of +Romanesque and Gothic architecture. The two fine western towers were +completed about 1520. The interior contains the tombs of the emperor +Otto the Great and his wife Edith, an English princess, and the fine +monument of Archbishop Ernest (d. 1513), executed in 1495 by Peter +Vischer of Nüremberg. The Liebfrauenkirche, the oldest church in +Magdeburg, is an interesting Romanesque edifice of the 12th and 13th +centuries, which was restored in 1890-1891. The chief secular buildings +are the town-hall (Rathaus), built in 1691 and enlarged in 1866, the +government offices, the palace of justice, the central railway station +and the exchange. The Breite Weg and the old market contain numerous +fine gable-ended private houses in the style of the Renaissance. In +front of the town-hall stands an equestrian statue of Otto the Great, +erected about 1290. The modern streets are spacious, and the houses +well-built though monotonous. There are two theatres, an agricultural +college, an art school, several gymnasia, a commercial and other +schools, an observatory, and two fine hospitals. The first place amongst +the industries is taken by the ironworks (one being a branch of the +Krupp firm, the Grusonwerke, employing about 4000 hands), which produce +naval armour and munitions of war. Of almost equal importance are the +sugar refineries and chicory factories. Then come establishments for +making tobacco, gloves, chocolate, artificial manure, cement, varnish, +chemicals and pottery. There are also distilleries and breweries, and +factories for the manufacture of cotton and silk goods. Magdeburg is +the central market in Germany for sugar and chicory, but trades +extensively also in cereals, fruit, vegetables, groceries, cattle, +horses, wool, cloth, yarn, leather, coal and books. A new winter +harbour, made at a cost of £400,000, facilitates the river traffic along +the Elbe. Three million tons of merchandise pass Magdeburg, going +upstream, and nearly 1 million tons, going downstream, annually. +Magdeburg is the headquarters of the IV. corps of the German army and +the seat of the provincial court of appeal and administrative offices, +and of a Lutheran consistory. + +_History._--Magdeburg, which was in existence as a small trading +settlement at the beginning of the 9th century, owes its early +prosperity chiefly to the emperor Otto the Great, who established a +convent here about 937. In 968 it became the seat of an archbishop, who +exercised sway over an extensive territory. Although it was burnt down +in 1188, Magdeburg became a flourishing commercial town during the 13th +century, and was soon an important member of the Hanseatic League. Its +bench of jurats (_Schöppenstuhl_) became celebrated, and "Magdeburg law" +(_Magdeburger Recht_), securing the administrative independence of +municipalities, was adopted in many parts of Germany, Poland and +Bohemia. During the middle ages the citizens were almost constantly at +variance with the archbishops, and by the end of the 15th century had +become nearly independent of them. It should, however, be noted that +Magdeburg never became a free city of the Empire. The town embraced the +Reformation in 1524, and was thenceforth governed by Protestant titular +archbishops (see BISHOP). On the refusal of the citizens to accept the +"Interim," issued by the emperor Charles V., Magdeburg was besieged by +Maurice of Saxony in 1550, and capitulated on favourable terms in +November 1551. During the Thirty Years' War it was twice besieged, and +suffered terribly. It successfully resisted Wallenstein for seven months +in 1629, but was stormed and sacked by Tilly in May 1631. The whole +town, with the exception of the cathedral, and about 140 houses, was +burned to the ground, and the greater part of its 36,000 inhabitants +were butchered without regard to age or sex, but it recovered from this +deadly blow with wonderful rapidity. By the peace of Westphalia (1648) +the archbishopric was converted into a secular duchy, to fall to +Brandenburg on the death of the last administrator, which happened in +1680. In 1806 Magdeburg was taken by the French and annexed to the +kingdom of Westphalia, but it was restored to Prussia in 1814, on the +downfall of Napoleon. Otto von Guericke (1602-1686), the inventor of the +air-pump, was burgomaster of Magdeburg. Count Lazare Carnot died here in +exile, and was buried in the cemetery, but his remains were exhumed in +1889 and conveyed to Paris. Luther was at school here, and sang in the +streets for bread with other poor choristers. + + See W. Kawerau, _Aus Magdeburgs Vergangenheit_ (Halle, 1886) O. von + Guericke, _Geschichte der Belagerung, Eroberung und Zerstörung von + Magdeburg_ (Magdeburg, 1887); M. Dittmar, _Beiträge zur Geschichte der + Stadt Magdeburg_ (Halle, 1885); F. W. Hoffmann, _Geschichte der Stadt + Magdeburg_ (Magdeburg, 1885-1886); F. Hülsse, _Die Einführung der + Reformation in der Stadt Magdeburg_ (Magdeburg, 1883); R. Volkholz, + _Die Zerstörung Magdeburgs_ 1631 (Magdeburg, 1892); W. Leinung and R. + Stumvoll, _Aus Magdeburgs Sage und Geschichte_ (Magdeburg, 1894); and + the _Urkundenbuch der Stadt Magdeburg_ (1892). + +THE ARCHBISHOPRIC OF MAGDEBURG was carved out of the bishopric of +Halberstadt when it was founded in 968, and its history is largely bound +up with that of the city and of the prelates who have ruled the see. The +first archbishop was Adalbert, and he and his successors had six or +seven suffragan bishops. Several of the archbishops took very prominent +parts in German politics. Early in the 15th century their residence was +fixed at Halle, and about the same time it became the custom to select +them from one of the reigning families of Germany, most often from the +house of Brandenburg. The doctrines of the reformers made their +appearance in the diocese early in the 16th century, and soon Archbishop +Sigismund, a son of Joachim II., elector of Brandenburg, openly avowed +his adherence to Lutheranism. After the issue of the edict of +restitution by the emperor Ferdinand II. in 1629, there were three +rival candidates for the see, and their struggles added to the confusion +caused by the Thirty Years' War. By the peace of Prague, however, in +1635, the archbishopric was given to Augustus, prince of +Saxe-Weissenfels, who retained it until his death in 1680. In 1773 the +area of the see was over 2000 sq. m. It included 29 towns and over 400 +villages and contained about 250,000 inhabitants. + + See the _Regesta archiepiscopatus magdeburgensis_, edited by G. A. von + Mülverstedt (Magdeburg, 1876-1899); and K. Uhlirz, _Geschichte des + Erzbistums Magdeburg unter den Kaisern aus sächsischem Hause_ + (Magdeburg, 1887). + +Distinct both from the archbishopric and from the city was the +BURGRAVIATE OF MAGDEBURG. The office of burgrave dates from the time of +Charlemagne, although its holder was not at first called by this name, +and it soon became one of great importance. The burgrave was the king's +representative; he was charged with the administration of the royal +estates in a given district, and in general with watching the royal +interests therein. The burgraviate of Magdeburg was held by several +countly families in turn until 1269, when it was purchased by Archbishop +Conrad II., who, however, soon sold it. In 1294 it was again united with +the archbishopric and the prelates retained it until 1538; then in 1579 +Augustus, elector of Saxony, made an arrangement which again gave the +office to the archbishops, who held it until the secularization of the +see. + +The MAGDEBURG CENTURIES (_Magdeburger Zenturien_) is the name given to +the first general history of the Christian Church written from a +Protestant point of view. It was compiled in Magdeburg, and the history +is divided into periods of one hundred years each. It was written in +Latin in 1562, its principal author being the reformer Matthias Flacius, +who was assisted by other Lutheran theologians. The cost of the +undertaking was borne by some of the German Protestant princes. As the +_Historia ecclesiae Christi_ it was first published at Basel in seven +volumes (1559-1574). It deals with the history of the Church down to +1400, and considering the time at which it was written it is a +remarkable monument to the scholarship of its authors. The earlier part +of it has been translated into German (Jena, 1560-1565). + + See E. Schaumkell, _Beitrag zur Entstehungsgeschichte der Magdeburger + Zenturien_ (Ludwigslust, 1898). + + + + +MAGEE, WILLIAM (1766-1831), archbishop of Dublin, was born at +Enniskillen, Co. Fermanagh, and educated at Trinity College, Dublin, +where he was elected fellow in 1788. He was ordained in 1790. Two +sermons, preached in the college chapel in 1798 and 1799, form the basis +of his _Discourses on the Scriptural Doctrines of Atonement and +Sacrifice_ (1801), a polemic against Unitarian theology which was +answered by Lant Carpenter. Magee was appointed professor of mathematics +and senior fellow of Trinity in 1800, but in 1812 he resigned, and +undertook the charge of the livings of Cappagh, Co. Tyrone, and +Killeleagh, Co. Down. Next year he became dean of Cork. He was well +known as a preacher and promoter of the Irish reformation, and in 1819 +he was consecrated bishop of Raphoe. In 1822 the archbishop of Dublin +was translated to Armagh, and Magee succeeded him at Dublin. Though in +most respects a tolerant man, he steadily opposed the movement for +Catholic Emancipation. He died on the 18th of August 1831. + + A memoir of his life is included with the _Works of the Most Reverend + William Magee_, D.D. (1842), by A. H. Kenney. + + + + +MAGEE, WILLIAM CONNOR (1821-1891), Anglican divine, archbishop of York, +was born at Cork in 1821. His father was curate of the parish attached +to the Protestant cathedral in that city; his grandfather was archbishop +of Dublin. Young Magee entered Trinity College, Dublin, with a +scholarship at thirteen. He was ordained to the curacy of St Thomas's, +Dublin, but, being threatened with consumption, went after two years to +Malaga. On his return he took a curacy at Bath, and was speedily +appointed to the Octagon Chapel, where his fame both as preacher and +platform speaker continued to spread. Some years afterwards he was made +prebendary of Wells Cathedral. In 1860 the delicate state of his health +caused him to accept the living of Enniskillen. In 1864 he was made +dean of Cork and chaplain to the lord lieutenant. Here he manifested +those great gifts which ultimately raised him to high office; a powerful +grasp of mental, moral and political problems, combined with eloquence +of a high order, and illuminated with brilliant flashes of wit. In 1868 +the question of the disestablishment of the Irish Church came to the +front, and Magee threw himself into the task of its defence with his +usual energy and vivacity. The success of his orations caused Disraeli +to offer him the bishopric of Peterborough. He justified his appointment +by his magnificent speech when the Disestablishment Bill reached the +House of Lords in 1869, and then plunged into diocesan and general work +in England. He preached three remarkable sermons on Christian Evidence +in Norwich Cathedral in 1871. He took up the temperance question, and +declared in the House of Lords that he would rather see "England free +than England compulsorily sober," an utterance which the extreme +advocates of total abstinence misquoted and attacked. He was also a +supporter of the movement for abolishing the recitation of the +Athanasian Creed in the public services of the Church of England, +believing, as he said, that the "presence" of the damnatory clauses, "as +they stand and where they stand, is a real peril to the Church and to +Christianity itself," and that those clauses "are no essential part" of +the creed. The project was laid aside in consequence of the hostility of +a large body of the clergy, reinforced by the threat of Dr Pusey and +Canon Liddon to abandon their offices if it were carried. Magee took a +prominent part in the Ritual controversy, opposing what he conceived to +be romanizing excess in ritual, as well as the endeavour of the opposite +party to "put down Ritualism," as Disraeli expressed it, by the +operation of the civil law. His incisive way of putting things earned +for him the title of the "Militant Bishop," but, as he himself remarked +in relation to this title, his efforts were ever for peace. +Unfortunately for the Church, he was not elevated to the see of York +until his energies were exhausted. He died on the 5th of May 1891, about +four months after his appointment. Magee's manifold activities, his +capability as an administrator, his sound judgment, and his remarkable +insight into the ecclesiastical problems of his time, rank him among the +most distinguished of English prelates. + + See _Life and Letters_, by Canon MacDonnell (2 vols. 1896). + + + + +MAGELLAN, FERDINAND (in Sp. FERNANDO MAGALLANES, in Port. FERNÃO DE +MAGALHÃES) (c. 1480-1521), the first circumnavigator of the globe, was +born at Sabrosa in the Villa Real district of the Traz-os-Montes +province of Portugal. He was a son of Pedro de Magalhães, and belonged +to the fourth order of Portuguese nobility (_fidalgos de cota de +armas_). He was brought up as one of the pages of Queen Leonor, consort +of King John (João) II "the Perfect." In 1495 he entered the service of +Manuel "the Fortunate," John's successor, and in 1504 enlisted as a +volunteer for the Indian voyage of the first Portuguese viceroy in the +East, Francisco d'Almeida. He sailed on the 25th of March 1505; was +wounded at Cannanore on the 16th of March 1506; was then sent with Nuno +Vaz Pereira to Sofala to build a Portuguese fortress at that place; +returned to India early in 1508; and was again wounded at the battle of +Diu on the 3rd of February 1509. At Cochin (Aug. 19, 1509) he joined +Diogo Lopes de Sequeira on his famous voyage intended for the Spice +Islands, when the Portuguese almost fell victims to Malay treachery at +Malacca. In this crisis he fought bravely and skilfully (though it is +not true, as often asserted, that he discovered the Malay plot); and +before the 10th of October 1510 he had been rewarded for his many +services with the rank of captain. He again distinguished himself at the +taking of Malacca by Albuquerque (July-Aug., 1511), and was then sent on +by the viceroy with Antonio d'Abreu to explore the Spice Islands +(Moluccas). Leaving Malacca at the end of December 1511, this squadron +sailed along the north of Java, passed between Java and Madura, left +Celebes on their left, coasted by the Gunong Api volcano, touched at +Bura, and so reached Amboyna and Banda. At the last-named they found +such abundance of spices that they came straight back to Malacca +without visiting Ternate, as had been intended. + +Magellan returned to Portugal in 1512. On the 14th of July of that year +he was raised to the rank of _fidalgo escudeiro_; and in 1513 he +accompanied a Portuguese expedition against Azamor in Morocco. The city +was taken on the 28th-29th of August 1513; but Magellan was subsequently +wounded, and lamed for life, in a sortie; he was also accused of trading +with the Moors. The accusation was subsequently dropped, but Magellan +fell into disfavour with King Manuel, who let him understand that he +would have no further employment in his country's service (after the +15th of May 1514). Magellan formally renounced his nationality, and went +to offer his services to the court of Spain. He reached Seville on the +20th of October 1517, and thence went to Valladolid to see Charles V. +With the help of Juan de Aranda, one of the three chief officials of the +India House at Seville, and of other friends, especially Diogo Barbosa, +a Portuguese like himself, naturalized as a Spaniard, who had acquired +great influence in Seville, and whose daughter he now married, he gained +the ear of Charles and of the powerful minister, Juan Rodriguez de +Fonseca, bishop of Burgos, the persistent enemy of Columbus, the steady +supporter of his great successor. Magellan proposed to reach the Spice +Islands of the East Indies by the west; for that purpose he hoped to +discover a strait at the extreme south of South America, and is said to +have declared himself ready to sail southwards to 75° to realize his +project. Ruy Faleiro the astronomer, another Portuguese exile, aided him +in the working out of his plan, and he found an invaluable financial +ally in Christopher de Haro, a member of a great Antwerp firm, who owed +a grudge to the king of Portugal. On the 22nd of March 1518, Magellan +and Faleiro, as joint captains-general, signed an agreement with Charles +V., by which one-twentieth of the clear profits were to fall to them; +further, the government of any lands discovered was vested in them and +their heirs, with the title of _Adelantados_. On the 10th of August +1519, the fleet of five vessels, under Magellan's command, left Seville +and dropped down the Guadalquivir to S. Lucar de Barrameda, at the mouth +of the river, where they remained more than five weeks. On the 20th of +September the armada put to sea. Of the vessels which composed it, the +"Trinidad" was the flagship, and the "Vittoria" the only one which +accomplished the circumnavigation. The crew, officers, volunteers, &c., +numbered about 270-280, of whom the names of 268 are preserved; 237 of +these received pay; at least 37 were Portuguese, 30 or more Italians +(mostly Genoese), 19 French, 1 English, 1 German. Only 31 returned in +the "Vittoria"; 4 survivors of the crew of the "Trinidad" reappeared +later. Antonio Pigafetta of Vicenza, an Italian gentleman who has left +the best history of the voyage, went as a volunteer in Magellan's suite. +Faleiro stayed behind, having cast his horoscope and found that the +venture would be fatal to him. The fleet was well armed, and the total +cost of equipment was 8,751,000 maravedis, or £5032 (equal to over +£50,000 in present value). Three-quarters were defrayed by the Spanish +Crown, one-quarter by Christopher Haro and his friends. Before starting, +Magellan made his will and addressed a memorandum to Charles V., +assigning geographical positions connected with the controversy he was +intending to settle: viz., the proper drawing of a demarcation-line +between the spheres of Spain and Portugal in the East Indies, and the +inclusion of the Moluccas within the Spanish sphere. + +Steering south-west and calling at Teneriffe (Sept. 26-Oct. 3), Magellan +sighted South America at Cape St Augustine, near Pernambuco on the 29th +of November; thence he followed the east coast of the New World down to +the La Plata estuary, which he examined in the hope of finding a passage +at this point (Jan. 11-Feb. 6, 1520). On the 31st of March following, he +arrived at Port St Julian (in 49° 20´ S.) where he wintered. Here he +crushed a formidable mutiny (April 1-2), and made acquaintance with the +natives, whom he called _Patagonians_ ("Big Feet"), whose great size and +lofty stature are magnified by Pigafetta to gigantic proportions. +Leaving Port St Julian on the 24th of August 1520, he discovered on the +21st of October the cape of the Eleven Thousand Virgins, the eastern +entrance of the long-sought passage. Through this strait, 360 m. long, +often narrow and very tortuous, fringed by snow-clad mountains, he +guided his armada for thirty-eight days, weakened by the desertion of +one vessel (the "S. Antonio"). On the 21st of November a council of +pilots and captains was held to consider the continuation of the voyage, +and on the 28th of November the fleet rounded Cabo Deseado, the +"desired" western terminus of the strait, variously called by the first +discoverers, "Victoria Strait," "Strait of the Patagonians," "of all +Saints," "of the Eleven Thousand Virgins," or "of Magellan," now only +known by the last of these names. To the south of the passage lay the +forbidding land "stark with eternal cold," which from the many fires +here observed Magellan named "Tierra del Fuego." The expedition now +entered the "Great South Sea," first sighted by Vasco Nuñez de Balboa +(q.v.), which, from the steady and gentle winds that drove the fleet +across the immeasurable expanse, was by Magellan called "Pacific." For +ninety-eight days Magellan crossed this sea, almost beyond the grasp of +man's mind for vastness (as Maximilian of Transylvania puts it), from +Cabo Deseado to the Ladrones. On the whole transit he discovered only +two islands, sterile and uninhabited, which he called "St Paul's" (Jan. +24, 1521) and "Shark Island" (Feb. 3). The first of these has been +identified with Puka Puka in the Tuamotu Archipelago, the second with +Flint Island in the Manihiki group; neither identification seems +convincing. For most of these ninety-eight days the explorers had no +fresh provisions, little water (and that bad), and putrid biscuit; the +ravages of scurvy became terrible. The worst anticipations of Magellan +("he would push on, if they had to eat the leather of the rigging") were +realized; ox-hides, sawdust, and rats became coveted food. At last, on +the 6th of March 1521, the Ladrones (so named by Magellan from the +thievish habits of the natives) came in sight, Guam being probably the +first port of call. Here the fleet rested, watered, revictualled and +refitted; on the 9th of March they started again westward; and on the +16th of March sighted the southern point of Samar Island in the +archipelago, since 1542 called the Philippines, but named by Magellan, +its first discoverer, after St Lazarus. On the 7th of April the squadron +arrived at Cebu, south-west of Samar, in the heart of the Philippines; +here Magellan contracted a close friendship and alliance with the +treacherous native sovereign, who professed Christianity the better to +please and utilize his Catholic friends. Undertaking an expedition to +conquer, for the Catholic faith and the king of Cebu, the neighbouring +island of Mactan, Magellan was killed there in a fight with the +islanders (April 27, 1521). The king of Cebu after this got into his +power several of the leading personages of the squadron, including Juan +Serrano, one of the two admirals elected to replace Magellan, and +murdered them. The survivors, burning one of the three remaining +vessels, left the Philippines, and made their way to the Moluccas (Nov. +6), visiting Borneo on the way (July 9-Sept. 27, 1521). At Tidor a heavy +cargo of cloves was taken in; the "Trinidad," becoming leaky, stayed +behind with her crew; and the "Vittoria," under Juan Sebastian del Cano, +proceeded to Europe alone (Dec. 21, 1521). To double the Cape of Good +Hope the "Vittoria" reached between 40° and 41° S. (April 7-16, 1522) +and suffered from contrary winds, heavy seas, scurvy and starvation. In +the Cape Verde Islands (July 9-15, 1522) thirteen of the crew were +detained prisoners by the Portuguese. Only thirty-one men returned with +del Cano to Seville in the first vessel that had ever made the tour of +the earth. Though Magellan had not quite reached the Spice Islands when +he fell at Mactan, his task had then been accomplished. He had already +reached and passed the longitude of the Moluccas, where he had already +been; the way home from the Philippines by the Indian Ocean and the Cape +of Good Hope was perfectly known to the Portuguese, himself included. +Magellan's name has never received its due recognition in general +history. It ranks with those of Columbus, Marco Polo, and Henry the +Navigator. The circumnavigation of the globe is as great an event as the +discovery of America. Magellan achieved what Columbus planned--the +linking of west Europe with east Asia by direct transit over the western +ocean. Had America not intervened, the project of 1492 must have failed; +by 1519 European pioneers had formed a more adequate notion of the task +and its magnitude. + +Magellan's Straits, the Magellanic clouds (not first observed by him), +and Magellan's Land--a name long given to Patagonia and that +hypothetical southern continent of which Tierra del Fuego was considered +only a portion, and now again bestowed by Chile on her territory in the +extreme south--preserve the memory of the first circumnavigator. The +largest of the oceans has also kept the flattering name given to it by +the man who first crossed it. + + No record of his exploits was left by Magellan himself; and + contemporary accounts are less detailed and consistent than could be + wished. The best is that of Antonio Pigafetta, a volunteer in the + fleet. It is printed in Ramusio, and exists in four early MS. copies, + one in Italian and three in French. The latter was perhaps the + original language of this work, which was addressed by Pigafetta, as a + knight of Rhodes, to the Frenchman Villiers de l'Isle Adam, grand + master of the order of the Hospital of St John. But this view is + rejected by J. A. Robertson (see below), who believes the Ambrosian + MS. to be the ultimate text. See the _Primo viaggio intorno al mondo_, + otherwise the _Navigation et descouvrement de la Indie supérieure + faicte par moi Anthoyne Pigapheta, Vincentin, chevallier de Rhodes_, + probably published in 1524 (in August of that year Pigafetta obtained + leave to print his book in Venice). Of the three French MSS., two are + in the Bibliothèque Nationale, Paris (5650 and 24,224 Fr.), the latter + is wrongly supposed by Thomassy, followed by Lord Stanley of Alderley, + to have been the copy presented by Pigafetta to the regent of France, + Marie Louise of Savoy, mother of Francis I. The third French MS., + often called the MS. of Nancy, first noticed by Thomassy in 1841, was + bought by Sir Thomas Phillipps at Libri's sale, and became MS. + Phillipps 16,405. The Italian MS. is in the Ambrosian library at + Milan. From this Carlo Amoretti, prefect of the Ambrosiana, published + his Italian edition of Pigafetta in 1800; a French translation of + this, by Amoretti himself, was issued by H. J. Jansen, 1801. An + English version of Pigafetta was made by Richard Eden in his _Decades + of the Newe Worlde_ (London, 1555). The earliest printed edition, + apparently a summary of the Italian MS., was issued in French by Simon + de Colines of Paris about 1525. The earliest Italian edition is of + 1534 (or 1536). + + Other authorities are: (1) The narrative of an unknown Portuguese in + Ramusio's _Navigationi et viaggi_; (2) the _Derrotero_ or Log-Book in + the Seville Archives, supposed to be the work of Francisco Albo, + _contramaestre_ of Magellan's flagship, the "Trinidad": this consists + mainly of nautical observations; (3) the narrative of the so-called + Genoese pilot, written in excellent Portuguese, and printed in vol. + iv. of the _Collecão de noticias_ of the Lisbon Academy; (4) various + _informaciones_ and other papers in the Seville Archives, especially + bearing on the mutiny; (5) the letter of Maximilian of Transylvania, + under-secretary to Charles V., to the cardinal of Salzburg; (6) the + references in Correa and Herrera, often based on good information, and + adding points of interest to other records. Of these (1)-(3), (5), and + an instance of (6) are translated in the Hakluyt Society's volume. + Magellan's two wills (i) executed at Belem on the 17th of December + 1504, on the eve of his departure with Almeida, (ii) executed at + Seville on the 24th of August, 1519, just before starting on his + voyage round the world, are both of some value for his life. + + See also Lord Stanley of Alderley, _The First Voyage round the World + by Magellan, translated from ... Pigafetta, &c._, Hakluyt Society + (London, 1874); Diego de Barros Arana, _Vida e viagems de Fernão de + Magalhães_, a trans. of the Spanish life by Fernando de Magalhães + Villas Boas (Lisbon, 1881); F. H. H. Guillemard, _Life of Magellan_ + (London, 1890); _Magellan ... the original text of the Ambrosian MS_. + (of Pigafetta), with English translation, notes, bibliography, &c., by + J. A. Robertson (Cleveland, U.S.A., 1906). Before the appearance of + this indispensable work, the best edition of Pigafetta had been in + vol. iii. part 5 of the _Raccolta di documenti e studi pubblicati + nella r. commissione colombiana_, edited by Andrea da Mosto (Rome, + Ministry of Public Instruction, 1894). (C. R. B.) + + + + +MAGELLANIC CLOUDS (named after Ferdinand Magellan), two cloud-like +condensations of stars in the southern constellation of Mensa about 69° +S. Dec. and between 5° and 5° 40´ of R. A. They are remarkable in the +resemblance of their stars as regards spectra and physical constitution +to the stars of the Milky Way, though entirely detached from that +object. + + + + +MAGENTA, a town of Lombardy, Italy, in the province of Milan, 16 m. by +rail W. of Milan city, 364 ft. about sea-level situated in the midst of +rice-fields. Pop. (1901), 8012. It manufactures silks and matches, and +is famous for the battle (1859) in which the allied French and +Piedmontese defeated the Austrians (see ITALIAN WARS). A memorial chapel +and a monument were erected on the battle-field in 1862. A +crimson-purple aniline dye, discovered about the time of the battle, was +given from it the name of "magenta." + + + + +MAGGIORE, LAGO (_Lacus Verbanus_ of the Romans; Fr. _Lac Majeur_; Ger. +_Langensee_), the most extensive of the lakes that extend along the foot +of the Alps in Lombardy, N. Italy. Its area is about 83 sq. m., its +length 37 m., its greatest width 5½ m., and its greatest depth 1198 ft., +while its surface is 646 ft. about sea-level. It is mainly formed by the +Ticino (Tessin) River, flowing in at the north and out at the south end, +on its way to join the Po, but on the west the lake receives a very +important tributary, the Toce or Tosa River, which flows down through +the Val d'Ossola from the mountains around the Simplon Pass. Other +important affluents are the Maggia (N.W.) and the Tresa (E.). The upper +end of the lake (about 16 sq. m.) is in the Swiss canton of Ticino +(Tessin). Locarno, at the northern or Swiss end, is 14 m. by rail S.W. +of Bellinzona on the St Gotthard line. There is a railway along the +south-eastern shore, from Magadino (10½ m. S.W. of Bellinzona) to Sesto +Calende (36½ m.), at the southern end of the lake and 20 m. by rail from +Novara. The east shore of the lake is reached at Luino by a steam +tramway from Ponte Tresa on the lake of Lugano (8 m.), while the direct +Simplon line runs along the west shore of the lake for 15½ m. from near +Pallanza past Baveno and Stresa to Arona, which is 23 m. by rail from +Novara. On the east shore are Luino (Ital. Luvino) and Laveno. On the +west shore are (reckoning from N. to S.) Cannobio, Pallanza, Baveno, +Stresa and Arona. Opposite (S.E.) Baveno are the famous Borromean +Islands, on the largest of which (Isola Bella) are very remarkable +gardens (formed about 1617), wherein many tropical plants flourish +abundantly, while south-west of Baveno rises the glorious view-point of +the Monte Mottarone (4892 ft.) between Lago Maggiore and the northern +end of the Lake of Orta. In the morning the _tramontana_ wind blows from +the north down the lake, while in the afternoon the _inverna_, blowing +from the south, prevails. The first steamer was placed on the lake in +1826. (W. A. B. C.) + + + + +MAGIC[1] (i.e. "art magic"; Lat. _ars magica_), the general term for the +practice and power of wonder-working, as depending on the employment of +supposed supernatural agencies. Etymologically the Gr. [Greek: mageia] +meant the science and religion of the _magi_, or priests of Zoroaster, +as known among the Greeks; in this sense it was opposed to [Greek: +goêteia] (? necromancy) and [Greek: pharmakeia] (the use of drugs); but +this distinction was not universally recognized, and [Greek: goêteia] is +often used as a synonym of [Greek: mageia]. There is no general +agreement as to the proper definition of "magic," which depends on the +view taken of "religion." + + +I.--NATURE OF MAGIC + +_Theories of Magic._--Existing theories of magic may be classified as +_objective_ or _subjective_. The objective school regards magic as a +thing by itself, entirely distinct from religion, recognizable by +certain characteristics, and traceable to a definite psychological +origin. Magic, on this view, is a system of savage science based on +imaginary laws supposed to operate with the regularity ascribed to +natural laws by the science of to-day. If practices prima facie magical +form part of the recognized ritual of religion, it is because the older +ideas have persisted and at most assumed a veneer of religion. For the +subjective school, on the other hand, only those rites are magical which +their practitioners qualify with the name of magic; there is no inherent +quality which makes a rite magical; practices based on a belief in the +law of sympathy may be religious as well as magical; rites may pass from +the category of religion to that of magic when public recognition is +withdrawn from them. + + a. For E. B. Tylor the distinguishing characteristic of magic is its + unreality; it is a confused mass of beliefs and practices, and their + unity consists in the absence of the ordinary nexus of natural cause + and effect. Under the general head of magic he distinguishes (i) a + spiritual and (ii) a non-spiritual element. (i) The former is made up + of such rites as involve the intervention of spiritual beings, ghosts + of the dead, demons or gods; hence, in Tylor's view, this form of + magic is merely an inferior branch of religion. (ii) The non-spiritual + part, but for which the category of magic would be unnecessary, + depends on imagined powers and correspondences in nature; it is merely + imperfect reasoning, the mistaking of an ideal connexion for a real + one. When the American Indian medicine man draws the picture of a deer + on a piece of bark and expects that shooting at it will cause him to + kill a real deer the next day, he mistakes a connexion which exists + only in the mind of the sorcerer for a real bond independent of the + human mind. + + b. In J. G. Frazer's view all magic is based on the law of + sympathy--i.e. the assumption that things act on one another at a + distance through a secret link, due either to the fact that there is + some similarity between them or to the fact that they have at one time + been in contact, or that one has formed part of the other. These two + branches of "sympathetic magic" Frazer denominates "homoeopathic + magic" and "contagious magic." Homoeopathic or imitative (mimetic) + magic may be practised by itself, but contagious magic generally + involves the application of the imitative principle. (i) One of the + most familiar applications of the former is the belief that an enemy + may be destroyed or injured by destroying or injuring an image of him. + (ii) Under the head of contagious magic are included such beliefs as + that which causes the peasant to anoint the weapon with which he has + been injured, which, according to Frazer, is founded on the + supposition that the blood on the weapon continues to feel with the + blood in the body. (iii) Implicitly Frazer seems to distinguish a + third kind of magic; "the rain-charm," he says, "operates partly or + wholly through the dead ... in Halmahera there is a practice of + throwing stones on a grave, in order that the ghost may fall into a + passion and avenge the disturbance, as he imagines, by sending heavy + rain." Here there is no assumption of an invariable course of nature + set in motion by magical rites; save that it is coercive and not + propitiatory, the practice does not differ from ordinary religious + rites. + + In his theory of the origin of magic Frazer follows the associationist + school. But, as R. R. Marett has pointed out in a criticism of the + associationist position, it is proved beyond question that even in the + individual mind association by similarity, contiguity or contrast, is + but the passive condition, the important element being interest and + attention. Frazer assumes that magic has everywhere preceded religion: + man tried to control nature by using what he conceived to be immutable + laws; failing in this he came to believe in the existence of higher + powers whom he could propitiate but not coerce; with this + transformation religion appeared on the scene; the priest supplanted + the magician, at least in part, and the first blows were struck in the + perennial warfare of magic and religion. Frazer recognizes, however, + that magical and religious rites are at the present day, and have been + in historical times, frequently intermingled; it should be noted that + for him religion means propitiation and that he does not recognize the + existence of anything beyond magic among the aborigines of Australia. + His theory is based on a selection of facts, and not on the whole body + of beliefs and rites recognized as magical, among which are many + wherein spirits figure. Frazer's position appears to be that such + rites are relatively late and may be neglected in framing a definition + of magic. It may be perfectly true that the idea of magic has been + progressively extended; but belief in transformation is also for Dr + Frazer magical; this belief is certainly primitive; yet sympathy will + not explain it, as it should if Frazer's theory is correct. + + c. L. Marillier distinguished three classes of magic: (i) the magic + of the word or act; (ii) the magic of the human being, independent of + rite or formula, &c.; (iii) the magic which demands at once a human + being of special powers (or in a special state) and the use of certain + forms. (i) Under the first head he included such rites as mimetic + dances, rain-making, disease-making, and sympathetic magic generally. + Some of these rites are conceived to affect the course of nature + directly, as by influencing winds or the sun, others do so through the + intermediary of a god or spirit, who controls the course of nature, + and is himself coerced by man with magical acts and incantations. (ii) + Other rites cannot be performed by all and sundry: ceremonial purity, + initiation or other conditions may be needed to make the charm + effective. (iii) Individuals are found who are invested with magical + power (_mana_), whose will rules the universe, whose simple words + bring rain or sunshine, and whose presence gives fertility to the + fields. Sometimes this power is an attribute of the individual, + sometimes it is bound up with the office which he fills. In many cases + the magical powers of both men and other objects, animate and + inanimate, are put down to the fact that a god resides in them. + + d. Hubert and Mauss have made the most complete and systematic study + of magic which has yet appeared. They hold that, implicitly at any + rate, magic is everywhere distinguished from other systems of social + facts; in order to be magical an act or belief must be common to the + whole of a society; the acts which the whole of a group does not + regard as efficacious are not, for this school of thought, magical: + consequently the practices of gamesters, &c., do not come under the + head of magic. Magic is essentially traditional; a distinguishing + characteristic of primitive thought is that the individual mind is + markedly unoriginal; and this feature is as prominent, if not more so, + in magic as in technology or any other important element in human + life. The correspondence between magic and technology can be traced + far; for the gestures of the craftsman are as strictly prescribed as + the ritual acts of the magician or priest: but in magic the results of + the gestures are not of the same order as the results of the + craftsman's movements, and herein lies the distinction between magic + and technic. The distinction between magic and religion is to be + sought not in the sympathetic character of the former, nor in any + supposed necessary sequence of cause and effect, nor yet in its + maleficent character. Religion is prescribed, official, an organized + cult. Magic is prohibited, secret; at most it is permitted, without + being prescribed. Three important laws may be traced in the machinery + of magical operations--magical power flows along channels determined + by the contiguity, similarity or contrast of the object of the act and + the object to be affected; but these laws do not suffice to explain + magic: equally insufficient are the demonological theory and the + theory of properties inherent in the objects used in magical + operations. The underlying idea of magic is dynamical; to this power + may be given the name of _mana_ (see below), of which sanctity is a + special development. This _mana_ operates in a _milieu_ different from + the ordinary material world; distance is no obstacle to contact; + wishes are immediately realized; but law reigns in the milieu in + question, necessary relations are conceived as existing. The notion of + time as it is found in the world of magic is even more alien from + European ideas; the notion of sanctity enters into it, but time in + magic and religion is qualitative rather than quantitative. The + homogeneity of periods of time not depending on their duration, + conventional numbers are employed; successive periods of time + apparently equal are not so for the primitive consciousness; and both + in magic and religion periods are homogeneous by reason of occupying + the same position in the calendar. + + e. For A. Lehmann magic is the practice of superstitions, and his + explanation of magic is purely psychological. Relying mainly on modern + spiritualism for his examples, he traces magic back to illusions, + prejudices and false precepts due to strained attention. This is + ultimately also the view of Hubert and Mauss, who hold that "at the + root of magic are states of consciousness which generate illusions; + and that these states are not individual but collective and arise from + the amalgamation of the ideas of a given person with those current in + the society of which he forms a part." The reunion of a group supplies + a soil in which illusions flourish readily, and it is important to + note that in magic and religion attention is above all necessary for + the success of a rite, witness the frequent rule imposing silence; but + this concentration of attention is precisely calculated to favour + illusions; it is indeed the ordinary condition of successful + hypnotism; even in civilized countries collective hallucinations + without verbal suggestion are not unknown. + + f. R. R. Marett regards religion and magic as two forms of a social + phenomenon originally one and indivisible; primitive man had an + institution which dealt with the supernatural, and in this institution + were the germs of both magic and religion, which were gradually + differentiated; magic and religion differ in respectability; religion + is always the higher, the accepted cult; but between what is + definitely religious and what is definitely magical lies a mass of + indeterminate elements, such as "white-magic," which do not attain to + the public recognition of religion, nor suffer the condemnation meted + out to the indisputably magical. For primitive man the abnormal was + the supernormal, and the supernormal was the supernatural, the object + of fear; this is especially evident when we consider the case of + taboo; it may be regarded as a public scare for which no particular + individual is responsible, which becomes traditional along fairly + constant lines, growing as it goes. _Mana_ was attributed to taboo + objects, among which were men in any way abnormal, whether as geniuses + or idiots; and such men were expected to exercise their powers for the + good of society; hence came into existence the professional medicine + man; man originally argued from cause to effect and not vice versa. + Priest and magician were originally one; but the former, learning + humility in the face of might greater than his own, discarded the + spell for the prayer and prostrated himself before a higher power. + +_Definition of Magic._--To arrive at a definition of magic we may either +follow the a priori road mapped out by Frazer and decline to recognize +the distinction actually drawn by various societies between magical and +religious practices; or we may ask what magic and corresponding terms +actually connote. Frazer's method ignores the fact that magic, like +religion, is an institution, i.e. a product of society, not of any +single individual; there is no more reason to suppose that a child +reared in isolation would develop any kind of magical practices than +that it would invent for itself a religion; but if this is the case, +the associationist account of magic cannot be true. It is therefore by +an analysis of actually existing practices that we must define and limit +the term magic. There is, however, a serious difficulty in the way of +determining the attitude of non-European peoples towards religio-magical +practices; general terms are things of slow growth; it is therefore +prima facie improbable that peoples in the lower stages of culture will +have anything corresponding to our terms "religion" and "magic"; +moreover, if we are right in assuming the fundamental unity of the two, +it is by no means certain that they have even the consciousness of any +distinction. Even when this consciousness is present, it by no means +follows that the whole of the field is mapped out according to our +categories; there will be a large indeterminate area which is neither +magical nor religious. This suggests that the consciousness of the +educated Occidental, for which the spheres of magic and religion in +civilized society are sharply defined and contrasted, should be the +ultimate arbiter; but here again we are confronted by a difficulty, for, +to the educated man, the characteristic of magic is its unreality, and +this does not help us to distinguish primitive magic and religion. + +We must, it appears, determine the relation of magic to religion by an +analysis of the conceptions of those who believe in both; but in so +doing we must consider that, like all other institutions, magic has a +history. Even if we go back to the 16th century and take the view of +magic then held by the average European, it is still a complex idea. +When we ask what the most primitive races now on the earth regard as +magic, we are applying to their ideas a touchstone made for a very +different age and culture; as well might we ask what their theory of +knowledge is. If, however, we reverse the process and ask what elements +of primitive institutions correspond most nearly to later conceptions of +magic, we can at once say that the forbidden and private arts are the +prototypes of the magic of later times. Magic is therefore the practice +of maleficent arts which involve the use of religio-magical power, with +perhaps a secondary idea of the use of private arts, which are to +benefit, not the community as a whole, but a single individual. Religion +in the lower stages of culture is essentially the tribal creed which all +practise and in which all believe; if therefore an individual has a cult +of his own, even if otherwise indistinguishable from a public cult, it +is for this very reason on a lower plane, and probably corresponds in a +degree to what is later regarded as magic. But our information as to the +attitude of the uncivilized towards magico-religious rites in general is +seldom sufficiently clear; our terminology is influenced by the +prepossession of alien observers whose accounts cannot be assumed to +correspond to the native view of the case. + +_Magico-religious Force._--The mere fact that we cannot draw an exact +line between magic and religion suggests that they may have some +fundamental feature in common. Both terms have greatly changed their +connotation in the course of their existence; _religio_ seems to have +meant originally [Greek: katadesmos] (magical spell), and Pliny says +that [Greek: mageia] is a deceptive art compounded of medicine, religion +and astrology. Among the Greeks, on the other hand, [Greek: mageia] +occupied a respectable position. More important is the fact that taboo +(q.v.) is both religious and magical. There is a universal tendency to +regard as magical the religions of alien races, as well as national +religions which have been superseded; Leland tells us that witchcraft in +Italy is known as _la vecchia religione_. An examination of the ideas of +primitive peoples shows that there is a widely found notion of a power +which manifests itself both in religion and magic. Observers have often +been content to describe ceremonies without attempting to penetrate to +the fundamental ideas which underlie them; this is particularly the case +with magic, and only recently have anthropologists realized that in many +primitive societies exists a fairly well-defined idea of +magico-religious power, to which the generic name of _mana_, from the +Melanesian word, has been given. + + a. _Mana_ in Melanesia is a force, a being, an action, a quality, or a + state; it is transmissible and contagious, and is hence associated + with taboo; it may be regarded as material and seen in the form of + flames or heard; it is the power which is inherent in certain spirits, + among which are included such of the dead as are denominated + _tindalos_; it may also be a force inherent in some inanimate object, + such as a stone which causes the yams to grow, but it is a spiritual + force and does not act mechanically; it is the power of the magician + and of the rite; the magic formula is itself _mana_. There seem to be + a variety of _manas_, but probably the underlying idea is essentially + one, though it does not follow that the Melanesians have arrived at + the consciousness of this unity. Hubert and Mauss go even further and + regard all force as _mana_; it is a quality added to objects without + prejudice to their other qualities, one which supplements without + destroying their mechanical action. + + b. Similar ideas are found in other areas. (i) The continental Malays + have a word _Kramât_ (_hrm_), which means sacred or magical; in + Indo-China the Bahnars use the word _deng_; in Madagascar _hasina_ + seems to embody in part the same notion. (ii) In Africa the idea is + less apparent; perhaps the _ngai_ of the Tanganika tribes comes + nearest to the notion of _mana_; on the Congo _nkici_ has a similar + but more restricted sense. (iii) In Australia there are two, or + perhaps three, kinds of magical power distinguished by the aborigines; + all over the continent we find the maleficent power, _boolya_ in West + Australia, _arungquiltha_ in the central tribes, _koochie_ in New + South Wales; the central tribes have certain objects termed + _churinga_, to which magical power (which we may term _churinga_) is + attributed; the power of magicians is held to reside in certain + stones, called _atnongara_, and in this we must, provisionally at any + rate, see a third kind of magical power: _churinga_ is beneficent and + seems to originate with the mythical ancestors, whereas _arungquiltha_ + is of immediate origin, created by means of incantations or acquired + by contact with certain objects; the power of the magicians seems to + proceed from the ancestors in like manner. (iv) In America these ideas + are widely found; the _orenda_ of the Hurons has been elaborately + described by J. N. B. Hewitt; everything in nature, and particularly + all animate objects, have their _orenda_; so have gods and spirits; + and natural phenomena are the product of the _orenda_ of their + spirits. _Orenda_ is distinct from the things to which it is attached; + the cry of birds, the rustle of the trees, the soughing of the wind, + are expressions of their _orenda_; the voice of the magician is + _orenda_, so are the prayer and the spell, and in fact all rites; + _orenda_ is above all the power of the medicine man. Among the + Algonquins we find the word _manitu_, among the Sioux _wakanda_, + _mahowa_, &c., among the Shoshones pokunt; all of which seem to carry, + at least in part, the same signification. In Central America, + according to Hubert and Mauss, _naual_ or _nagual_ is the + corresponding term. (v) Traces of similar ideas may be found in more + advanced nations; the Hindu _brahman_ is identified by Hubert and + Mauss as the correlative of _mana_; in Greece [Greek: physis] is + possibly the echo of a similar idea; but we are yet far from having + adequately fathomed the dynamical theories of pre-scientific days. + +_Origin of Magic._--The associationist theory of magic sets out with the +assumption that primitive man began with general conceptions; he started +with certain means at his disposal--the law of sympathy--by which he +could, in his own belief, influence the outer world. But it is more +probable that he argued from concrete instances and arrived little by +little at abstract ideas of magical power. + + a. Death and disease are universally regarded by uncivilized people as + due to so-called "magic," i.e. to non-natural causes. Primitive man + was familiar with the wounds and bruises caused by physical means; he + would naturally attribute any pain not so caused to the operation of + analogous but invisible weapons, and eventually attempt to discover + how he himself could apply on his own behalf the forces thus used + against him. Similarly he may have asked himself to what causes were + to be attributed the superiority of one man over another; he may have + decided the problem by referring it to the superior power of the one, + and then inquired in what way this power could in individual instances + be increased. In fact we may say generally that man probably explained + the already existing and happening by reference to the supernormal, + and then endeavoured to guide the supernormal for his own benefit, + direct or indirect. + + b. Ritual, however (the primitive magico-religious plasm), is negative + as well as positive. The corpse is uncanny, and man's dread of the + corpse may well have been an early development; this dread, become + traditional, with accretions of various sorts, crystallized into + _taboo_, the magico-religious prohibition. The notion of the uncanny, + once arrived at, may have been exploited positively; psychical + abnormalities are present among savage races in very different + degrees; but if they were developed at an early stage in human history + they doubtless suggested the possibility that man might exploit them + for the collective advantage. But it by no means follows that + beneficent rites were originally regarded as magical; and it should be + noted that the initiator of the so-called magician in Australia is + often the god of the tribe or nation. The limits of magic or its + correlatives in the lower stages of culture are thus far undecided. + + c. Magic as it represents itself to the Occidental mind of the present + day, and perhaps to the great part of the inhabitants of the world, + seems to be a thing of gradual growth. (i) In the earlier stages + there was probably no animistic feature about magic; it was + essentially "the prohibited." (ii) Then with the rise of animistic + beliefs and practices came the association of the magician with + demons--the spirits of the dead, or of animals, or unattached + spirits--upon whose co-operation the powers of the magician are often + now held to depend. These spirits were not in the position of gods; + such recognition, worship, or cult as they received was often not a + social institution, but the work of individuals, liable to fall into + desuetude at the death of the individual, if not earlier. (iii) Again, + the magical tends to be the less important and eventually the less + respectable; therefore ancient cults which are conquered, like the + religion of Rome by Christianity, come to be reckoned as within the + sphere of magic and witchcraft. (iv) All non-animistic practices tend + to become _ipso facto_ magical; many ritual prohibitions fall under + the head of negative magic. Religion is predominantly animistic, and + with the rise of gods magic and religion become antagonistic. Thus + rites of a neutral character, such as leechcraft, and perhaps + agricultural ceremonies which are not absorbed by religion, tend to + acquire the reputation of being magical, as also do all amulets and + talismans, and, in fact, everything not directly associated with + religion. We therefore arrive at a period when magic is distinguished + as _white_, i.e. the laudable, or at least permitted form, and + _black_, i.e. the prohibited form. + +_Magic and Demonology._--Primitive psychology tends to anthropomorphize +and personify; it is in many of its stages inclined to an animistic +philosophy. To this is due in part the difficulty of distinguishing +magic from religion. In many rites there is no obvious indication that a +spirit or personal being is concerned. A portion of the ceremonies in +which the spirits of the dead are concerned falls under the head of +religion (see ANCESTOR WORSHIP), but in the very name "necromancy" +([Greek: nekros], corpse) lies an implication of magic; and dealings +with the departed are viewed in this light in many parts of the world, +sometimes concurrently with a cult of ancestors. Side by side with the +human souls we find demons (see DEMONOLOGY); but on the whole only a +small proportion of the world of spirits is recognized as powerful in +magic; others, such as disease-spirits, are objects, not sources, of +magical influence. Magic is sometimes made to depend upon the activity +of demons and spirits, and it is true that the magician usually if not +invariably has a spirit helper, often an animal; but there is no +evidence that magical power had ever been confined to those who are thus +aided. It is not easy to define the relation of fetishism (q.v.) to +magic. + +_Magic and Science._--It is a commonplace that the sciences have +developed from non-scientific beginnings; the root of astronomy is to be +sought in astrology (q.v.), of chemistry in alchemy (q.v.), of +leechcraft in the practices of the savage magician, who depends for much +of his success on suggestion, conscious or unconscious, but also relies +on a pharmacopeia of no mean extent. The dynamical theory of magic and +religion brings primitive man from one point of view far nearer to the +modern man of science than was previously suspected, we may fairly say +that the Australians have an idea not unlike that of the transformation +and conservation of energy, that this energy they store in accumulators, +transmit by means of conductors, and so on. The discovery of these +complicated ideas only serves to show how far the present-day peoples in +the lower stages of culture have travelled from the primitive man who +knew neither magic nor religion. But it is perhaps less in respect of +abstract ideas than by its concrete investigations into properties, +experiment and otherwise that magic has been the forerunner of science. + +_Magic and Divination._--Magic is an attempt to influence the course of +events, divination (q.v.) to foresee them; but divination is frequently +regarded as magical. It is certain that a large part of divination is +religious, and the knowledge is explained as a message from the gods; +but necromancy, the practice of discovering the future by consulting the +dead, is in many respects essentially magical. Perhaps the magical +character of divination may be in part explained, when we regard it as a +group of practices in many varieties of which animism plays no part; for +non-animistic ceremonies tend to be regarded as magical (cf. +rain-making). Thus, heteroscopic divination seems to involve the idea of +what may be termed a return current of magico-religious force; the event +is not influenced, but itself determines the issue of the diviner's +experiment. + + +II.--LAWS AND RITUAL OF MAGIC + +The practice of magic involves the belief in the operation of certain +laws, and demands certain conditions. The number of positive rites is +not unlimited; a certain rite tends to become stable and is finally used +for all sorts of purposes; and each magician tends to specialize in this +respect. Just as there are well-marked schools of magic, and the +rain-maker is not the same as the fetish-man, so within the school there +are various groups, differentiated not by the purposes at which they aim +nor by the powers they claim to possess, but by the ceremonies which +they practise. Chief among the laws lying at the base of magical +practice is that of sympathy. + +_Sympathy._--That the law of sympathy is an essential element of magic +is admitted equally by the associationist school and by its critics. +Under the head of sympathy are embraced the laws of contiguity or +contagion, of similarity or homoeopathy, and of contrariety or +antipathy. + + a. In its simplest form the law of contiguity asserts that whatever + has once formed part of a body continues to form part of it or to + represent it for magical purposes; thus, by obtaining possession of + the parings of a person's nails, or the clippings of his hair, and by + working magic upon them, it is held to be possible to produce on the + actual human body the effects which are in reality produced on the + object of the magical rite. As is clear by the well-known case of the + "life index," the current of magical power may pass in either + direction; if the life of a man is supposed to be bound up with the + life of a tree, so that any injury to the tree reacts on the man, it + is equally believed that the death of the man will not fail to be + manifest by the state of the tree. In particular this sympathetic + relation is predicated of wizards or witches and their animal + familiars; it is then known by the name of "repercussion." It is not + only upon parts of the body that contagious magic can be worked; + anything which has been in contact with the body, such as clothes, + anything which has been in part assimilated by the body, such as the + remains of food, and even representations of the body or of parts of + it such as footprints, &c., may be used as objects of magical rites, + in order to transmit to the human being some influence, maleficent or + otherwise. The contact demanded may be actual, or mediate, for in + Australia it suffices to connect the magician and his patient by a + thread in order that the disease may be removed. (i) The use of + clothes for magical purposes gives us perhaps the clue to the + widespread custom of "rag-trees"; in nearly every part of the world it + is the practice to suspend wool or rags to trees associated with some + spirit, or, in Christian countries, with some saint, in order to reap + a benefit; similarly nails are driven into trees or images; pins are + dropped into wells, stones are cast upon cairns, and missiles aimed at + various holy objects; but it cannot be assumed that the same + explanation lies at the root of the whole group of practices. (ii) + This law may perhaps be taken as the explanation of the "couvade"; in + many parts of the world relatives, and in particular the father of a + new-born child, are compelled to practise various abstinences, in + order that the health of the child may not be affected, membership of + the same family therefore establishes a sympathetic relation. (iii) In + this direct transference of qualities is exemplified another magical + process, which may also be referred to the operation of the law of + sympathy; it is a world-wide belief that the assimilation of food + involves the transference to the eater of the qualities, or of some of + them, inherent in the source of the food; a South African warrior, for + example, may not eat hedgehog, because the animal is held to be + cowardly and the eater would himself become a coward; on the other + hand, the flesh of lions is fit meat for brave men, because they at + the same time transfer its courage to themselves. + + b. The law of homoeopathy takes two forms. (i) The magician may + proceed on the assumption that like produces like; he may, for + example, take an image of wax or wood, and subject it to heat or other + influences under the belief that it represents the human being against + whom his malefice is directed, and that without any contact, real or + pretended; so that any results produced on the image, which may be + replaced by an animal or a portion of one, are equally produced in the + human being. There need not even be any resemblance between the + representation and the person or thing represented; a pot may serve to + represent a village; hence step by step we pass from the + representation to the symbol. (ii) The law of homoeopathy also + manifests itself in the formula _similia similibus curantur_; the + Brahman in India treated dropsy with ablutions, not in order to add + to, but to subtract from, the quantity of liquid in the patient's + body. So, too, the yellow turmeric was held to be a specific for + jaundice. + + c. Here we approach the third class of sympathetic rites; it is clear + that a remedy produces the contrary, when it cures the like; + conversely, like by producing like expels its contrary. + +Some statements of the law of sympathy suggest that it is absolute in +its application. It is true that the current of magical power is +sometimes held to be transmitted along lines indicated by the law of +sympathy, without the intervention of any volition, human or otherwise; +thus, the crow which carries stray hairs away to weave them into the +structure of its nest is nowhere supposed to be engaged in a magical +process; but it is commonly held that the person whose hair is thus used +will suffer from headache or other maladies; this seems to indicate that +the law of sympathy operates mechanically in certain directions, though +the belief may also be explained as a secondary growth. In general the +operation of these laws is limited in the extreme. For example, the +medieval doctrine known as the Law of Signatures asserted that the +effects of remedies were correlated to their external qualities; bear's +grease is good for baldness, because the bear is a hairy animal. But the +transference was held to terminate with the acquisition by the man of +this single quality; in some magical books powdered mummy is recommended +as a means of prolonging life, but it is simply the age of the remedy +which is to benefit the patient; the magician who removes a patient's +pains or diseases does not transfer them to himself; the child whose +parents eat forbidden foods is held to be affected by their +transgression, while they themselves come off unharmed. The magical +effects are limited by exclusive attention and abstraction; and this is +true not only of the kind of effect produced but also as to the +direction in which it is held to be produced. + +_The Magic of Names._--For primitive peoples the name is as much a part +of the person as a limb; consequently the magical use of names is in +some of its aspects assimilable to the processes dependent on the law of +sympathy. In some cases the name must be withheld from any one who is +likely to make a wrong use of it, and in some parts of the world people +have secret names which are never used. Elsewhere the name must not be +told by the bearer of it, but any other person may communicate it +without giving an opening for the magical use of it. Not only human +beings but also spirits can be coerced by the use of their names; hence +the names of the dead are forbidden, lest the mention of them act as an +evocation, unintentional though it be. Even among more advanced nations +it has been the practice to conceal the real name of supreme gods; we +may probably explain this as due to the fear that an enemy might by the +use of them turn the gods away from those to whom they originally +belonged. For the same reason ancient Rome had a secret name. + + _Magical Rites._--The magic of names leads us up to the magic of the + spoken word in general. The spell or incantation and the magical act + together make up the rite. (a) The manual acts are very frequently + symbolic or sympathetic in their nature; sometimes they are mere + reversals of a religious rite; such is the marching against the sun + (known as _widdershins_ or _deisul_); sometimes they are purificatory; + and magic has its sacrifices just as much as religion. (b) There are + many types of oral rites; some of the most curious consist in simply + reciting the effect intended to be produced, describing the manual + act, or, especially in Europe, telling a mythical narrative in which + Christ or the apostles figure, and in which they are represented as + producing a similar effect to the one desired; in other cases the + "origin" of the disease or maleficent being is recited. Oral rites, + which are termed spells or incantations, correspond in many cases to + the oral rites of religion; they, like the manual rites, are a + heterogeneous mass and hardly lend themselves to classification. Some + formulae may be termed sympathetic; it suffices to name the result to + be produced in order to produce it; but often an incantation is + employed, not to produce a result directly, but to coerce a god or + other being and compel him to fulfil the magician's will. The language + of the incantations often differs from that of daily life; it may be a + survival of archaic forms or may be a special creation for magical + purposes. In many languages the word used to express the idea of magic + means an act, a deed; and it may be assumed that few if any magical + ceremonies consist of formulae only; on the other hand, it is certain + that no manual act in magic stands absolutely alone without oral rite; + if there is no spoken formula, there is at least an unspoken thought. + It is in many cases difficult to discover the relative proportions and + importance of manual and oral acts. Not only the words but also the + tone are of importance in magic; in fact, the tone may be the more + important. Rhythm and repetition are no less necessary in oral than in + manual acts. (c) As preliminaries, more seldom as necessary sequels to + the central feature of the rite, manual or oral, we usually find a + certain number of accessory observances prescribed, which find their + parallel in the sacrificial ritual. For example, it is laid down at + what time of year, at what period of the month or week, at what hour + of the day a rite must be performed; the waxing or waning of the moon + must be noted; and certain days must be avoided altogether. Similarly, + certain places may be prescribed for the performance of the ritual; + often the altar of the god serves magical purposes also; but elsewhere + it is precisely the impure sites which are devoted to magical + operations--the cemeteries and the cross roads. The instruments of + magic are in like manner often the remains of a sacrifice, or + otherwise consecrated by religion; sometimes, especially when they + belong to the animal or vegetable world, they must be sought at + certain seasons, May Day, St George's Day, Midsummer Day, &c. The + magician and his client must undergo rites of preparation and the exit + may be marked by similar ceremonies. + + _Magicians._--Most peoples know the professional worker of magic, or + what is regarded as magic. (a) In most if not all societies magic, or + certain sorts of it, may be performed by any one, so far as we can + see, who has mastered the necessary ritual; in other cases the + magician is a specialist who owes his position to an accident of birth + (seventh son of a seventh son); to simple inheritance (families of + magicians in modern India, rain-makers in New Caledonia); to + revelation from the gods or the spirits of the dead (Malays), showing + itself in the phenomena of possession; or to initiation by other + magicians. (b) From a psychical point of view it may probably be said + that the initiation of a magician corresponds to the "development" of + the modern spiritualistic medium; that is to say, that it resolves + itself into exercises and rites which have for their object the + creation or evolution of a secondary personality. From this point of + view it is important to notice that certain things are forbidden to + magicians under pain of loss of their powers; thus, hot tea is taboo + to the Arunta medicine man; and if this seems unlikely to cause the + secondary personality to disappear, it must be remembered that to the + physiological effects, if any, must be added the effects of + suggestion. Of this duplication of personality various explanations + are given; in Siberia the soul of the _shaman_ is said to wander into + the other world, and this is a widely spread theory; where the + magician is supposed to remain on earth, his soul is again believed to + wander, but there is an alternative explanation which gives him two or + more bodies. Here we reach a point at which the familiar makes its + appearance; this is at times a secondary form of the magician, but + more often is a sort of life index or animal helper (see LYCANTHROPY); + in fact, the magician's power is sometimes held to depend on the + presence--that is, the independence--of his animal auxiliary. + Concurrent with this theory is the view that the magician must first + enter into a trance before the animal makes its appearance, and this + makes it a double of the magician, or, from the psychological point of + view, a phase of secondary personality. (c) In many parts of the world + magical powers are associated with the membership of secret societies, + and elsewhere the magicians form a sort of corporation; in Siberia, + for example, they are held to be united by a certain tie of kinship; + where this is not the case, they are believed, as in Africa at the + present day or in medieval Europe, to hold assemblies, so-called + witches' Sabbaths; in Europe the meetings of heretics seem to be + responsible for the prominence of the idea if not for its origin (see + WITCHCRAFT). The magician is often regarded as possessed (see + POSSESSION) either by an animal or by a human or super-human spirit. + The relations of priest and magician are for various reasons complex; + where the initiation of the magician is regarded as the work of the + gods, the magician is for obvious reasons likely to develop into a + priest, but he may at the same time remain a magician; where a + religion has been superseded, the priests of the old cult are, for + those who supersede them, one and all magicians; in the medieval + church, priests were regarded as especially exposed to the assaults of + demons, and were consequently often charged with working magic. The + great magicians who are gods rather than men--e.g. kings of Fire and + Water in Cambodia--enjoy a reverence and receive a cult which + separates them from the common herd, and assimilates them to priests + rather than to magicians. The function of the so-called magician is + often said to be beneficent; in Africa the witch-doctor's business is + to counteract evil magic; in Australia the magician has to protect his + own tribe against the assaults of hostile magicians of other tribes; + and in Europe "white magic" is the correlative of this beneficent + power; but it may be questioned how far the beneficent virtue is + regarded as magical outside Europe. + + _Talismans and Amulets._--Inanimate objects as well as living beings + are credited with stores of magical force; when they are regarded as + bringing good, i.e. are positive in their action, they may be termed + "talismans"; "amulets" are protective or negative in their action, and + their function is to avert evil; a single object may serve both + purposes. Broadly speaking, the fetish, whose "magical" properties are + due to association with a spirit, tends to become a talisman or + amulet. The "medicine" of the Red Indian, originally carried as means + of union between him and his _manito_, is perhaps the prototype of + many European charms. In other cases it is some specific quality of + the object or animal which is desired; the boar's tusk is worn on the + Papuan Gulf as a means of imparting courage to the wearer; the + Lukungen Indians of Vancouver Island rub the ashes of wasps on the + faces of their warriors, in order that they may be pugnacious. Some + Bechuanas wear a ferret as a charm, in the belief that it will make + them difficult to kill, the animal being very tenacious of life. Among + amulets may be mentioned horns and crescents, eyes or their + representations, and grotesque figures, all of which are supposed to + be powerful against the Evil Eye (q.v.). Tylor has shown that the + brass objects so often seen on harness were originally amuletic in + purpose, and can be traced back to Roman times. Some amulets are + supposed to protect from the evil eye simply by attracting the glance + from the wearer to themselves, but, as a rule, magical power is + ascribed to them. + + _Evil Magic._--The object of "black" magic is to inflict injury, + disease, or death on an enemy, and the various methods employed + illustrate the general principles dealt with above and emphasize the + conclusion that magic is not simply a matter of sympathetic rites, but + involves a conception of magical force. (a) It has been mentioned that + contagious magic makes use of portions of a person's body; the + Cherokee magician follows his victim till he spits on the ground; + collecting the spittle mingled with dust on the end of a stick, the + magician puts it into a tube made of a poisonous plant together with + seven earth worms, beaten into a paste, and splinters of a tree + blasted by lightning; the whole is buried with seven yellow stones at + the foot of a tree struck by lightning, and a fire is built over the + spot; the magician fasts till the ceremony is over. Probably the worms + are supposed to feed on the victim's soul, which is said to become + "blue" when the charm works; the yellow stones are the emblem of + trouble, and lightning-struck trees are reputed powerful in magic. If + the charm does not work, the victim survives the critical seven days, + and the magician and his employer are themselves in danger, for a + charm gone wrong returns upon the head of him who sent it forth. (b) + In homoeopathic magic the victim is represented by an image or other + object. In the Malay Peninsula the magician makes an image like a + corpse, a footstep long. "If you want to cause sickness, you pierce + the eye and blindness results; or you pierce the waist and the stomach + gets sick. If you want to cause death, you transfix the head with a + palm twig; then you enshroud the image as you would a corpse and you + pray over it as if you were praying over the dead; then you bury it in + the middle of the path which leads to the place of the person whom you + wish to charm, so that he may step over it." Sometimes the wizard + repeats a form of words signifying that not he but the Archangel + Gabriel is burying the victim; sometimes he exclaims, "It is not wax I + slay but the liver, heart and spleen of So-and-so." Finally, the image + is buried in front of the victim's doors. (c) Very widespread is the + idea that a magician can influence his victim by charming a bone, + stick or other object, and then projecting the magical influence from + it. It is perhaps the commonest form of evil magic in Australia; in + the Arunta tribe a man desirous of using one of these pointing sticks + or bones goes away by himself into the bush, puts the bone on the + ground and crouches over it, muttering a charm: "May your heart be + rent asunder." After a time he brings the irna back to the camp and + hides it; then one evening after dark he takes it and creeps near + enough to see the features of his victim; he stoops down with the + _irna_ in his hand and repeatedly jerks it over his shoulder, + muttering curses all the time. The evil magic, _arungquiltha_, is said + to go straight to the victim, who sickens and dies without apparent + cause, unless some medicine-man can discover what is wrong and save + him by removing the evil magic. The _irna_ is concealed after the + ceremony, for the magician would at once be killed if it were known + that he had used it. (d) Magicians are often said to be able to assume + animal form or to have an animal familiar. They are said to suck the + victim's blood or send a messenger to do so; sometimes they are said + to steal his soul, thus causing sickness and eventually death. These + beliefs bring the magician into close relation with the werwolf (see + LYCANTHROPY). + + _Rain-making._--In the lower stages of culture rain-making assumes + rather the appearance of a religious ceremony, and even in higher + stages the magical character is by no means invariably felt. It will, + however, be well to notice some of the methods here. (a) Among the + Dieri of Central Australia the whole tribe takes part in the ceremony; + a hole is dug, and over this a hut is built, large enough for the old + men; the women are called to look at it and then retire some five + hundred yards. Two wizards have their arms bound at the shoulder, the + old men huddle in the hut, and the principal wizard bleeds the two men + selected by cutting them inside the arm below the elbow. The blood is + made to flow on the old men, and the two men throw handfuls of down + into the air. The blood symbolizes the rain; the down is the clouds. + Then two large stones are placed in the middle of the hut; these two + represent gathering clouds. The women are again summoned, and then the + stones are placed high in a tree; other men pound gypsum and throw it + into a water-hole; the ancestral spirits are supposed to see this and + to send rain. Then the hut is knocked down, the men butting at it with + their heads; this symbolizes the breaking of the clouds, and the fall + of the hut is the rain, if no rain comes they say that another tribe + has stopped their power or that the _Mura-mura_ (ancestors) are angry + with them. (b) Rain-making ceremonies are far from uncommon in Europe. + Sometimes water is poured on a stone; a row of stepping-stones runs + into one of the tarns on Snowdon, and it is said that water thrown + upon the last one will cause rain to fall before night. Sometimes the + images of saints are carried to a river or a fountain and ducked or + sprinkled with water in the belief that rain will follow; sometimes + rain is said to ensue when the water of certain springs is troubled; + perhaps the idea is that the rain-god is disturbed in his haunts. But + perhaps the commonest method is to duck or drench a human figure or + puppet, who represents in many instances the vegetation demon. The + gipsies of Transylvania celebrate the festival of "Green George" at + Easter or on St George's Day; a boy dressed up in leaves and blossoms + is the principal figure; he throws grass to the cattle of the tribe, + and after various other ceremonies a pretence is made of throwing him + into the water; but in fact only a puppet is ducked in the stream. + +_Negative Magic._--There is also a negative side to magic, which, +together with ritual prohibitions of a religious nature, is often +embraced under the name of taboo (q.v.); this extension of meaning is +not justified, for taboo is only concerned with sacred things, and the +mark of it is that its violation causes the taboo to be transmitted. All +taboos are ritual prohibitions, but all ritual prohibitions are not +taboos; they include also (a) interdictions of which the sanction is the +wrath of a god; these may be termed religious interdictions; (b) +interdictions, the violation of which will automatically cause some +undesired magico-religious effect; to these the term negative magic +should be restricted, and they might conveniently be called "bans"; they +correspond in the main to positive rites and are largely based on the +same principles. + + (a) Certain prohibitions, such as those imposed on totem kins, seem to + occupy an intermediate place; they depend on the sanctity of the totem + animal without being taboos in the strict sense; to them no positive + magical rites correspond, for the totemic prohibition is clearly + religious, not magical. + + (b) Among cases of negative magic may be mentioned (i.) the couvade, + and prohibitions observed by parents and relatives generally; this is + most common in the case of young children, but a sympathetic relation + is held to exist in other cases also. In Madagascar a son may not eat + fallen bananas, for the result would be to cause the death of his own + father; the sympathy between father and son establishes a sympathy + between the father and objects touched or eaten by the son, and, in + addition, the fall of the bananas is equated with the death of a human + being. Again, the wife of a Malagasy warrior may not be faithless to + him when he is absent; if she is, he will be killed or wounded. + Ownership, too, may create a sympathetic relation of this kind, for it + is believed in parts of Europe that if a man kills a swallow his cows + will give bloody milk. In some cases it is even harder to see how the + sympathetic bond is established; some Indians of Brazil always + hamstring animals before bringing them home, in the belief that by so + doing they make it easier for themselves and their children to run + down their enemies, who are then magically deprived of the use of + their legs. These are all examples of negative magic with regard to + persons, but things may be equally affected; thus in Borneo men who + search for camphor abstain from washing their plates for fear the + camphor, which is found crystallized in the crevices of trees, should + dissolve and disappear. (ii.) Rules which regulate diet exist not only + for the benefit of others but also for that of the eater. Some + animals, such as the hare, are forbidden, just as others, like the + lion, are prescribed; the one produces cowardice, while the other + makes a man's heart bold. (iii.) Words may not be used; Scottish + fishermen will not mention the pig at sea; the real names of certain + animals, like the bear, may not be used; the names of the dead may not + be mentioned; a sacred language must be used, e.g. camphor language in + the Malay peninsula, or only words of good omen (cf. Gr. [Greek: + euphêmeite]); or absolute silence must be preserved. Personal names + are concealed; a man may not mention the names of certain relatives, + &c. There are customs of avoidance not only as to (iv.) the names of + relatives, but as to the persons themselves; the mother-in-law must + avoid the son-in-law, and vice versa; sometimes they may converse at a + distance, or in low tones, sometimes not at all, and sometimes they + may not even meet. (v.) In addition to these few classes selected at + random, we have prohibitions relating to numbers (cf. unlucky + thirteen, which is, however, of recent date), the calendar (Friday as + an unlucky day, May as an unlucky month for marriage), places, + persons, orientation, &c.; but it is impossible to enumerate even the + main classes. The individual origin of such beliefs, which with us + form the superstitions of daily life but in a savage or semi-civilized + community play a large part in regulating conduct, is often shrouded + in darkness; the meaning of the positive rite is easily forgotten; the + negative rite persists, but it is observed merely to avoid some + unknown misfortune. Sometimes we can, however, guess at the meaning of + our civilized notions of ill luck; it is perhaps as a survival of the + savage belief that stepping over a person is injurious to him that + many people regard going under a ladder as unlucky; in the one case + the luck is taken away by the person stepping over, in the other left + behind by the person passing under. + +_History of Magic._--The subject is too vast and our data are too slight +to make a general sketch of magic possible. Our knowledge of Assyrian +magic, for example, hardly extends beyond the rites of exorcism; the +magic of Africa is most inadequately known, and only in recent years +have we well-analysed repertories of magical rituals from any part of +the world. For certain departments of ancient magic, however, like the +Pythagorean philosophy, there is no lack of illustrative material; it +depended on mystical speculations based on numbers or analogous +principles. The importance of numbers is recognized in the magic of +America and other areas, but the science of the Mediterranean area, +combined with the art of writing, was needed to develop such mystical +ideas to their full extent. Among the neo-Platonists there was a strong +tendency to magical speculation, and they sought to impress into their +service the demons with which they peopled the universe. Alexandria was +the home of many systems of theurgic magic, and gnostic gems afford +evidence of the nature of their symbols. In the middle ages the +respectable branches of magic, such as astrology and alchemy, included +much of the real science of the period; the rise of Christianity +introduced a new element, for the Church regarded all the religions of +the heathen as dealings with demons and therefore magical (see +WITCHCRAFT). In our own day the occult sciences still find devotees +among the educated; certain elements have acquired a new interest, in so +far as they are the subject matter of psychical research (q.v.) and +spiritualism (q.v.). But it is only among what are regarded as the lower +classes, and in England especially the rural population, that belief in +its efficacy still prevails to any large extent. + +_Psychology of Magic._--The same causes which operated to produce a +belief in witchcraft (q.v.) aided the creed of magic in general. +Fortuitous coincidences attract attention; the failures are disregarded +or explained away. Probably the magician is never wholly an impostor, +and frequently has a whole-hearted belief in himself; in this connexion +may be noted the fact that juggling tricks have in all ages been passed +off as magical; the name of "conjuring" (q.v.) survives in our own day, +though the conjurer no longer claims that his mysterious results are +produced by demons. It is interesting to note that magical leechcraft +depended for its success on the power of suggestion (q.v.), which is +to-day a recognized element in medicine; perhaps other elements may have +been instrumental in producing a cure, for there are cases on record in +which European patients have been cured by the apparently meaningless +performances of medicine-men, but an adequate study of savage medicine +is still a desideratum. + + BIBLIOGRAPHY.--For a general discussion of magic with a list of + selected works see Hubert and Mauss in _Année sociologique_, vii. + 1-146; also A. Lehmann, _Aberglaube und Zauberei_; the article + "Religion" in _La Grande encyclopédie_; K. T. Preuss in _Globus_, + vols. 86, 87; Mauss, _L'Origine des pouvoirs magiques_, and Hubert, + _La Réprésentation du temps_ (Reports of École pratique des hautes + études, Paris). For general bibliographies see Hauck, + _Realencyklopädie_, _s.v._ "Magie"; A. C. Haddon, _Magic and + Fetishism_. J. G. T. Graesse's _Bibliotheca magica_ is an exhaustive + list of early works dealing with magic and superstition. For Australia + see Spencer and Gillen's works, and A. W. Howitt, _Native Tribes_. For + America see _Reports of Bureau of Ethnology_, vii. xvii. For India see + W. Caland, _Altindisches Zauber-ritual_; and W. Crooke, _Popular + Religion_; also V. Henry, _La Magie_. For the Malays see W. W. Skeat, + _Malay Magic_. For Babylonia and Assyria see L. W. King's works. For + magic in Greece and Rome see Daremberg and Saglio, _s.v._ "Magia," + "Amuletum," &c. For medieval magic see A. Maury, _La Magie_. For + illustrations of magic see J. G. Frazer, _The Golden Bough_; E. S. + Hartland, _Legend of Perseus_; E. B. Tylor, _Primitive Culture_; W. G. + Black, _Folkmedicine_. For negative magic see the works of Frazer and + Skeat cited above; also _Journ. Anthrop. Inst._ xxxvi. 92-103; + _Zeitschrift für Ethnologie_ (Verhandlungen) (1905), 153-162; + _Bulletin trimestriel de l'académie malgache_, iii. 105-159. See also + bibliography to TABOO and WITCHCRAFT. (N. W. T.) + + +FOOTNOTE: + + [1] For what is often called "magic," but is really + trick-performance, see CONJURING. + + + + +MAGIC SQUARE, a square divided into equal squares, like a chess-board, +in each of which is placed one of a series of consecutive numbers from 1 +up to the square of the number of cells in a side, in such a manner that +the sum of the numbers in each row or column and in each diagonal is +constant. + +From a very early period these squares engaged the attention of +mathematicians, especially such as possessed a love of the marvellous, +or sought to win for themselves a superstitious regard. They were then +supposed to possess magical properties, and were worn, as in India at +the present day, engraven in metal or stone, as amulets or talismans. +According to the old astrologers, relations subsisted between these +squares and the planets. In later times such squares ranked only as +mathematical curiosities; till at last their mode of construction was +systematically investigated. The earliest known writer on the subject +was Emanuel Moscopulus, a Greek (4th or 5th century). Bernard Frenicle +de Bessy constructed magic squares such that if one or more of the +encircling bands of numbers be taken away the remaining central squares +are still magical. Subsequently Poignard constructed squares with +numbers in arithmetical progression, having the magical summations. The +later researches of Phillipe de la Hire, recorded in the _Mémoires de +l'Académie Royale_ in 1705, are interesting as giving general methods of +construction. He has there collected the results of the labours of +earlier pioneers; but the subject has now been fully systematized, and +extended to cubes. + + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + |200|217|232|249| 8| 25| 40| 57| 72| 89|104|121|136|153|168|185| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + | 58| 39| 26| 7|250|231|218|199|186|167|154|135|122|103| 90| 71| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + |198|219|230|251| 6| 27| 38| 59| 70| 91|102|123|134|155|166|187| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + | 60| 37| 28| 5|252|229|220|197|188|165|156|133|124|101| 92| 69| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + |201|216|233|248| 9| 24| 41| 56| 73| 88|105|120|137|152|169|184| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + | 55| 42| 23| 10|247|234|215|202|183|170|151|138|119|106| 87| 74| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + |203|214|235|246| 11| 22| 43| 54| 75| 86|107|118|139|150|171|182| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + | 53| 44| 21| 12|245|236|213|204|181|172|149|140|117|108| 85| 76| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + |205|212|237|244| 13| 20| 45| 52| 77| 84|109 116|141|148|173|180| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + | 51| 46| 19| 14|243|238|211|206|179|174|147 142|115|110| 83| 78| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + |207|210|239|242| 15| 18| 47| 50 79| 82|111 114|143|146|175|178| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + | 49| 48| 17| 16|241|240|209|208 177|176|145 144|113|112| 81| 80| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + |196|221|228|253| 4| 29| 36| 61 68| 93|100 125|132|157|164|189| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + | 62| 35| 30| 3|254|227|222|195 190|163|158 131|126| 99| 94| 67| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + |194|223|226|255| 2|31 | 34| 63 66| 95| 98 127|130|159|162|191| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + | 64| 33| 32| 1|256|225|224 193|192|161 160|129|128| 97| 96| 65| + +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ + + FIG. 1. + +[Illustration: FIG. 2.] + + Two interesting magical arrangements are said to have been given by + Benjamin Franklin; these have been termed the "magic square of + squares" and the "magic circle of circles." The first (fig. 1) is a + square divided into 256 squares, i.e. 16 squares along a side, in Fig. + 2. which are placed the numbers from 1 to 256. The chief properties of + this square are (1) the sum of the 16 numbers in any row or column is + 2056; (2) the sum of the 8 numbers in half of any row or column is + 1028, i.e. one half of 2056; (3) the sum of the numbers in two + half-diagonals equals 2056; (4) the sum of the four corner numbers of + the great square and the four central numbers equals 1028; (5) the sum + of the numbers in any 16 cells of the large square which themselves + are disposed in a square is 2056. This square has other curious + properties. The "magic circle of circles" (fig. 2) consists of eight + annular rings and a central circle, each ring being divided into eight + cells by radii drawn from the centre; there are therefore 65 cells. + The number 12 is placed in the centre, and the consecutive numbers 13 + to 75 are placed in the other cells. The properties of this figure + include the following: (1) the sum of the eight numbers in any ring + together with the central number 12 is 360, the number of degrees in a + circle; (2) the sum of the eight numbers in any set of radial cells + together with the central number is 360; (3) the sum of the numbers in + any four adjoining cells, either annular, radial, or both radial and + two annular, together with half the central number, is 180. + + +---+---+---+---+---+-+---+---+---+---+---+ + | | a |[e]| 5 | | | | |[e]| | | + | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ + | | 4 | b | |[d]| | | 4 | | |[d]| + | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ + | |[g]| | c | 3 | | |[g]| | | | + | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ + | | | 2 |[b]| d | | | | | | | + | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ + |1 e| | | | | | e | | | | | + |[a]| | | | | | | | | | | + +---+---+---+---+---+-+---+---+---+---+---+ + + FIG. 3. + +_Construction of Magic Squares._--A square of 5 (fig. 3) has adjoining +it one of the eight equal squares by which any square may be conceived +to be surrounded, each of which has two sides resting on adjoining +squares, while four have sides resting on the surrounded square, and +four meet it only at its four angles. 1, 2, 3 are placed along the path +of a knight in chess; 4, along the same path, would fall in a cell of +the outer square, and is placed instead in the corresponding cell of the +original square; 5 then falls within the square. a, b, c, d are placed +diagonally in the square; but e enters the outer square, and is removed +thence to the same cell of the square it had left. [alpha], [beta], +[gamma], [delta], [epsilon] pursue another regular course; and the +diagram shows how that course is recorded in the square they have twice +left. Whichever of the eight surrounding squares may be entered, the +corresponding cell of the central square is taken instead. The 1, 2, 3, +..., a, b, c, ..., [alpha], [beta], [gamma], ... are said to lie in +"paths." + + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + | 1 | 4 | 2 | 5 | 3 | | 2 | 4 | 0 | 3 | 1 | |11 |24 | 2 |20 | 8 | + | | | | | | | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + | 4 | 2 | 5 | 3 | 1 | | 1 | 2 | 4 | 0 | 3 | | 9 |12 |25 | 3 |16 | + | | | | | | | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + | 2 | 5 | 3 | 1 | 4 | | 3 | 1 | 2 | 4 | 0 | |17 |10 |13 |21 | 4 | + | | | | | | | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + | 5 | 3 | 1 | 4 | 2 | | 0 | 3 | 1 | 2 | 4 | | 5 |18 | 6 |14 |22 | + | | | | | | | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + | 3 | 1 | 4 | 2 | 5 | | 4 | 0 | 3 | 1 | 2 | |23 | 1 |19 | 7 |15 | + | | | | | | | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + + FIG. 4. FIG. 5. FIG. 6. + + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + | 2 | 1 | 5 | 3 | 4 | |15 | 5 | 0 |20 |10 | |17 | 6 | 5 |23 |14 | + | | | | | | | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + | 3 | 4 | 2 | 1 | 5 | | 0 |20 |10 |15 | 5 | | 3 |24 |12 |16 |10 | + | | | | | | | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + | 1 | 5 | 3 | 4 | 2 | |10 |15 | 5 | 0 |20 | |11 |20 | 8 | 4 |22 | + | | | | | | | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + | 4 | 2 | 1 | 5 | 3 | | 5 | 0 |20 |10 |15 | | 9 | 2 |21 |15 |18 | + | | | | | | | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + | 5 | 3 | 4 | 2 | 1 | |20 |10 |15 | 5 | 0 | |25 |13 |19 | 7 | 1 | + | | | | | | | | | | | | | | | | | | + +---+---+---+---+---+ +---+---+---+---+---+ +---+---+---+---+---+ + + FIG. 7. FIG. 8. FIG. 9. + +_Squares whose Roots are Odd._--Figs 4, 5, and 6 exhibit one of the +earliest methods of constructing magic squares. Here the 3's in fig. 4 +and 2's in fig. 5 are placed in opposite diagonals to secure the two +diagonal summations; then each number in fig. 5 is multiplied by 5 and +added to that in the corresponding square in fig. 4, which gives the +square of fig. 6. Figs. 7, 8 and 9 give De la Hire's method; the squares +of figs. 7 and 8, being combined, give the magic square of fig. 9. C. G. +Bachet arranged the numbers as in fig. 10, where there are three numbers +in each of four surrounding squares; these being placed in the +corresponding cells of the central square, the square of fig. 11 is +formed. He also constructed squares such that if one or more outer bands +of numbers are removed the remaining central squares are magical. His +method of forming them may be understood from a square of 5. Here each +summation is 5 × 13; if therefore 13 is subtracted from each number, the +summations will be zero, and the twenty-five cells will contain the +series ± i, ± 2, ± 3, ... ± 12, the odd cell having 0. The central +square of 3 is formed with four of the twelve numbers with + and - signs +and zero in the middle; the band is filled up with the rest, as in fig. +12; then, 13 being added in each cell, the magic square of fig. 13 is +obtained. + +_Squares whose Roots are Even._--These were constructed in various ways, +similar to that of 4 in figs. 14, 15 and 16. The numbers in fig. 15 +being multiplied by 4, and the squares of figs. 14 and 15 being +superimposed, give fig. 16. The application of this method to squares +the half of whose roots are odd requires a complicated adjustment. +Squares whose half root is a multiple of 4, and in which there are +summations along all the diagonal paths, may be formed, by observing, as +when the root is 4, that the series 1 to 16 may be changed into the +series 15, 13, ... 3, 1, -1, -3, ... -13, -15, by multiplying each +number by 2 and subtracting 17; and, vice versa, by adding 17 to each of +the latter, and dividing by 2. The diagonal summations of a square, +filled as in fig. 17, make zero; and, to obtain the same in the rows and +columns, we must assign such values to the p's and q's as satisfy the +equations p1 + p2 + a1 + a2 = 0, p3 + p4 + a3 + a4 = 0, p1 + p3 - a1 - +a3 = 0, and p2 + p4 - a2 - a4 = 0,--a solution of which is readily +obtained by inspection, as in fig. 18; this leads to the square, fig. +19. When the root is 8, the upper four subsidiary rows may at once be +written, as in fig. 20; then, if 65 be added to each, and the sums +halved, the square is completed. In such squares as these, the two +opposite squares about the same diagonal (except that of 4) may be +turned through any number of right angles, in the same direction, +without altering the summations. + + 1 + 6 2 + +--+--+--+--+--+ +--+--+--+--+--+ + |11| | 7| | 3| |11|24| 7|20| 3| + +--+--+--+--+--+ +--+--+--+--+--+ + 16 | |12| | 8| | 4 | 4|12|25| 8|16| + +--+--+--+--+--+ +--+--+--+--+--+ + 21 |17| |13| | 9| 5 |17| 5|13|21| 9| + +--+--+--+--+--+ +--+--+--+--+--+ + 22 | |18| |14| |10 |10|18| 1|14|22| + +--+--+--+--+--+ +--+--+--+--+--+ + |23| |19| |15| |23| 6|19| 2|15| + +--+--+--+--+--+ +--+--+--+--+--+ + 24 20 + 25 + + FIG. 10. FIG. 11. + + +---+---+---+---+---+ +---+---+---+---+---+ + | -9| 12| 5| -3| -6| | 4| 25| 18| 11| 7 | + +---+---+---+---+---+ +---+---+---+---+---+ + | 1| 7|-11| 4| -1| | 14| 20| 2| 17| 13| + +---+---+---+---+---+ +---+---+---+---+---+ + | -8| -3| 0| 3| 8| | 5| 10| 13| 16| 21| + +---+---+---+---+---+ +---+---+---+---+---+ + | 10| -4| 11| -7|-10| | 23| 9| 24| 6| 3| + +---+---+---+---+---+ +---+---+---+---+---+ + | 6|-12| -5| 2| 9| | 19| 1| 8| 15| 22| + +---+---+---+---+---+ +---+---+---+---+---+ + + FIG. 12. FIG. 13. + + +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ + | 1| 3| 2| 4| | 0| 3| 3| 0| | 1|15|14| 4| + +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ + | 4| 2| 3| 1| | 2| 1| 1| 2| |12| 6| 7| 9| + +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ + | 4| 2| 3| 1| | 1| 2| 2| 1| | 8|10|11| 5| + +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ + | 1| 3| 2| 4| | 3| 0| 0| 3| |13| 3| 2|16| + +--+--+--+--+ +--+--+--+--+ +--+--+--+--+ + + FIG. 14. FIG. 15. FIG. 16. + + +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ + | p1| p2| a1| a2| | 1| -3| 11| -9| | 9| 7| 14| 4| + +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ + | p3| p4| a3| a4| | -5| 7|-15| 13| | 6| 12| 1| 15| + +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ + |-a1|-a2|-p1|-p2| |-11| 9| -1| 3| | 3| 13| 8| 10| + +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ + |-a3|-a4|-p3|-p4| | 15|-13| 5| -7| | 16| 2| 11| 5| + +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ + + FIG. 17. FIG. 18. FIG. 19. + + +---+---+---+---+---+---+---+---+ + | -1| 3| 5| -7|-33| 35| 37|-39| + +---+---+---+---+---+---+---+---+ + | 9|-11|-13| 15| 41|-43|-45| 47| + +---+---+---+---+---+---+---+---+ + | 17|-19|-21| 23| 49|-51|-53| 55| + +---+---+---+---+---+---+---+---+ + |-25| 27| 29|-31|-57| 59| 61|-63| + +---+---+---+---+---+---+---+---+ + + FIG. 20. + + _Nasik Squares._--Squares that have many more summations than in rows, + columns and diagonals were investigated by A. H. Frost (_Cambridge + Math. Jour._, 1857), and called Nasik squares, from the town in India + where he resided; and he extended the method to cubes, various + sections of which have the same singular properties. In order to + understand their construction it will be necessary to consider + carefully fig. 21, which shows that, when the root is a prime, and not + composite, number, as 7, eight letters a, b, ... h may proceed from + any, the same, cell, suppose that marked 0, each letter being repeated + in the cells along different paths. These eight paths are called + "normal paths," their number being one more than the root. Observe + here that, excepting the cells from which any two letters start, they + do not occupy again the same cell, and that two letters, starting from + any two different cells along different paths, will appear together in + one and only one cell. Hence, if p1 be placed in the cells of one of + the n + 1 normal paths, each of the remaining n normal paths will + contain one, and only one, of these p1's. If now we fill each row with + p2, p3, ... p_n in the same order, commencing from the p1 in that row, + the p2's, p3's and p_n's will lie each in a path similar to that of + p1, and each of the n normal paths will contain one, and only one, of + the letters p1, p2,... p_n, whose sum will be [Sigma]p. Similarly, if + q1 be placed along any of the normal paths, different from that of the + p's, and each row filled as above with the letters q2, q3, ... q_n, + the sum of the q's along any normal path different from that of the q1 + will be [Sigma]q. The n² cells of the square will now be found to + contain all the combinations of the p's and q's; and if the q's be + multiplied by n, the p's made equal to 1, 2, ... n, and the q's to 0, + 1, 2, ... (n - 1) in any order, the Nasik square of n will be + obtained, and the summations along all the normal paths, except those + traversed by the p's and q's, will be the constant [Sigma]nq + + [Sigma]p. When the root is an odd composite number, as 9, 15, &c., it + will be found that in some paths, different from the two along which + the p1 and q1 were placed, instead of having each of the p's and q's, + some will be wanting, while some are repeated. Thus, in the case of 9, + the triplets, p1p4p7, p2p5p8, p3p6p9, and q1q4q7, q2q5q8, q3q6q9 + occur, each triplet thrice, along paths whose summation should + be--[Sigma]p 45 and [Sigma]r 36. But if we make p1, p2, ... p9, = 1, + 3, 6, 5, 4, 7, 9, 8, 2, and the r1, r2, ... r9 = 0, 2, 5, 4, 3, 6, 8, + 7, 1, thrice each of the above sets of triplets will equal [Sigma]p + and [Sigma]q respectively. If now the q's are multiplied by 9, and + added to the p's in their several cells, we shall have a Nasik square, + with a constant summation along eight of its ten normal paths. In fig. + 22 the numbers are in the nonary scale; that in the centre is the + middle one of 1 to 9², and the sum of pair of numbers equidistant from + and opposite to the central 45 is twice 45; and the sum of any number + and the 8 numbers 3 from it, diagonally, and in its row and column, is + the constant Nasical summation, e.g. 72 and 32, 22, 76, 77, 26, 37, + 36, 27. The numbers in fig. 22 being kept in the nonary scale, it is + not necessary to add any nine of them together in order to test the + Nasical summation; for, taking the first column, the figures in the + place of units are seen at once to form the series, 1, 2, 3, ... 9, + and those in the other place three triplets of 6, 1, 5. For the + squares of 15 the p's and q's may be respectively 1, 2, 10, 8, 6, 14, + 15, 11, 4, 13, 9, 7, 3, 12, 5, and 0, 1, 9, 7, 5, 13, 14, 10, 3, 12, + 8, 6, 2, 11, 4, where five times the sum of every third number and + three times the sum of every fifth number makes [Sigma]p and [Sigma]q; + then, if the q's are multiplied by 15, and added to the p's, the Nasik + square of 15 is obtained. When the root is the multiple of 4, the same + process gives us, for the square of 4, fig. 23. Here the columns give + [Sigma]p, but alternately 2q1, 2q3, and 2q2, 2q4; and the rows give + [Sigma]q, but alternately 2p1, 2p3, and 2p2, 2p4; the diagonals giving + [Sigma]p and [Sigma]q. If p1, p2, p3, p4 and q1, q2, q3, q4 be 1, 2, + 4, 3, and 0, 1, 3, 2, we have the Nasik square of fig. 24. A square + like this is engraved in the Sanskrit character on the gate of the + fort of Gwalior, in India. The squares of higher multiples of 4 are + readily obtained by a similar adjustment. + + +---+---+---+---+---+---+---+ +--+--+--+--+--+--+--+--+--+ + | a | g | f | e | d | c | b | |63|88|74|13| 8|24|53|48|34| + +---+---+---+---+---+---+---+ +--+--+--+--+--+--+--+--+--+ + | a | d | g | c | f | b | e | |11| 9|25|51|49|35|61|89|75| + +---+---+---+---+---+---+---+ +--+--+--+--+--+--+--+--+--+ + | a | c | e | g | b | d | f | |52|47|36|62|87|76|12| 7|26| + +---+---+---+---+---+---+---+ +--+--+--+--+--+--+--+--+--+ + | a | f | d | b | g | e | c | |68|84|73|18| 4|23|58|44|33| + +---+---+---+---+---+---+---+ +--+--+--+--+--+--+--+--+--+ + | a | e | b | f | c | g | d | |19| 5|21|59|45|31|69|85|71| + +---+---+---+---+---+---+---+ +--+--+--+--+--+--+--+--+--+ + | a | b | c | d | e | f | g | |57|46|32|67|86|72|17| 6|22| + +---+---+---+---+---+---+---+ +--+--+--+--+--+--+--+--+--+ + | 0 | h | h | h | h | h | h | |64|83|78|14| 3|28|54|43|38| + +---+---+---+---+---+---+---+ +--+--+--+--+--+--+--+--+--+ + FIG. 21. |15| 1|29|55|41|39|65|81|79| + +--+--+--+--+--+--+--+--+--+ + |56|42|37|66|82|77|16| 2|27| + +--+--+--+--+--+--+--+--+--+ + + FIG. 22. + + +-----+-----+-----+-----+ +--+--+--+--+ + | | | | | |15|10| 3| 6| + |p4q3 |p2q4 |p4q1 |p2q2 | +--+--+--+--+ + | | | | | | 4| 5|16| 9| + +-----+-----+-----+-----+ +--+--+--+--+ + | | | | | |14|11| 2| 7| + |p3q1 |p1q2 |p3q3 |p1q4 | +--+--+--+--+ + | | | | | | 1| 8|13|12| + +-----+-----+-----+-----+ +--+--+--+--+ + | | | | | FIG. 24. + |p2q3 |p4q4 |p2q1 |p4q2 | + | | | | | + +-----+-----+-----+-----+ + | | | | | + |p1q1 |p3q2 |p1q3 |p3q4 | + | | | | | + +-----+-----+-----+-----+ + + FIG. 23. + + . + / \ + . . + / \ / \ + . . . + / \ / \ / \ + . . . * . + / \ / \ / \ / \ + . . * . . . + / \ / \ / \ / \ / \ + . * . . . . . + / \ / \ / \ / \ / \ / \ + . . . . . . . + / \ / \ / \ / \ / \ / \ / \ + C . . . . . . * . . A + |\ / \ / \ / \ / \ / \ / \ /| + . . . . . * . . . . + |\|\ / \ / \ / \ / \ / \ /|/| + . . . . * . . . . . . + |\|\|\ / \ / \ / \ / \ /|/|/| + . . . . . . . . . . . + |\|\|\|\ / \ / \ / \ /|/|/|/| + .*. . . . . . . .*. . . + |\|\|\|\|\ / \ / \ /|/|/|/|/| + . . .*. . . . . . . .*. . + |\|\|\|\|\|\ / \ /|/|/|/|/|/| + . . . . .*. . * . . . . . .*. + |\|\|\|\|\|\|\ /|/|/|/|/|/|/| + . . . . . . .*O*. . . . . . . + \|\|\|\|\|\|\|/|/|/|/|/|/|/ + .*. . . . . . .*. . . . . + \|\|\|\|\|\|/|/|/|/|/|/ + . .*. . . . . .*. . . + \|\|\|\|\|/|/|/|/|/ + . . .*. . . . .*. + \|\|\|\|/|/|/|/ + . . . . . . . + \|\|\|/|/|/ + . . . . . + \|\|/|/ + . . . + \|/ + . + B + + FIG. 25--Nasik Cube. + + +--+--+--+--+------------+--+--+--+--+ + | 1| 8|29|28| |11|14|23|18| + +--+--+--+--+ +--+--+--+--+ + |30|27| 2| 7| |21|20| 9|16| + +--+--+--+--+ +--+--+--+--+ + | 4| 5|32|25| |10|15|22|19| + +--+--+--+--+ +--+--+--+--+ + |31|26| 3| 6| |24|17|12|13| + +--+--+--+--+------------+--+--+--+--+ + + FIG. 26. + + +--+--+--+--+--+ +--+--+--+--+--+--+ + |23|18|11| 6|25| |30|21| 6|15|28|19| + +--+--+--+--+--+ +--+--+--+--+--+--+ + |10| 5|24|17|12| | 7|16|29|20| 5|14| + +--+--+--+--+--+ +--+--+--+--+--+--+ + |19|22|13| 4| 7| |22|31| 8|35|18|27| + +--+--+--+--+--+ +--+--+--+--+--+--+ + |14| 9| 2|21|16| | 9|26|17|26|13| 4| + +--+--+--+--+--+ +--+--+--+--+--+--+ + | 1|20|15| 8| 3| |32|23| 2|11|34|25| + +--+--+--+--+--+ +--+--+--+--+--+--+ + | 1|10|33|24| 3|12| + FIG. 27. +--+--+--+--+--+--+ + + FIG. 28. + + _Nasik Cubes._--A Nasik cube is composed of n³ small equal cubes, here + called cubelets, in the centres of which the natural numbers from 1 to + n³ are so placed that every section of the cube by planes + perpendicular to an edge has the properties of a Nasik square; also + sections by planes perpendicular to a face, and passing through the + cubelet centres of any path of Nasical summation in that face. Fig. 25 + shows by dots the way in which these cubes are constructed. A dot is + here placed on three faces of a cubelet at the corner, showing that + this cubelet belongs to each of the faces AOB, BOC, COA, of the cube. + Dots are placed on the cubelets of some path of AOB (here the knight's + path), beginning from O, also on the cubelets of a knight's path in + BOC. Dots are now placed in the cubelets of similar paths to that on + BOC in the other six sections parallel to BOC, starting from their + dots in AOB. Forty-nine of the three hundred and forty-three cubelets + will now contain a dot; and it will be observed that the dots in + sections perpendicular to BO have arranged themselves in similar + paths. In this manner, p1, q1, r1 being placed in the corner cubelet + O, these letters are severally placed in the cubelets of three + different paths of AOB, and again along any similar paths in the seven + sections perpendicular to AO, starting from the letters' position in + AOB. Next, p2q2r2, p3q3r3, ... p7q7r7 are placed in the other cubelets + of the edge AO, and dispersed in the same manner as p1q1r1. Every + cubelet will then be found to contain a different combination of the + p's, q's and r's. If therefore the p's are made equal to 1, 2, ... 7, + and the q's and r's to 0, 1, 2, ... 6, in any order, and the q's + multiplied by 7, and the r's by 7², then, as in the case of the + squares, the 7³ cubelets will contain the numbers from 1 to 7³, and + the Nasical summations will be [Sigma]7²r + [Sigma]7q + p. If 2, 4, 5 + be values of r, p, q, the number for that cubelet is written 245 in + the septenary scale, and if all the cubelet numbers are kept thus, the + paths along which summations are found can be seen without adding, as + the seven numbers would contain 1, 2, 3, ... 7 in the unit place, and + 0, 1, 2, ... 6 in each of the other places. In all Nasik cubes, if + such values are given to the letters on the central cubelet that the + number is the middle one of the series 1 to n³, the sum of all the + pairs of numbers opposite to and equidistant from the middle number is + the double of it. Also, if around a Nasik cube the twenty-six + surrounding equal cubes be placed with their cells filled with the + same numbers, and their corresponding faces looking the same way,--and + if the surrounding space be conceived thus filled with similar cubes, + and a straight line of unlimited length be drawn through any two + cubelet centres, one in each of any two cubes,--the numbers along that + line will be found to recur in groups of seven, which (except in the + three cases where the same p, q or r recur in the group) together make + the Nasical summation of the cube. Further, if we take n similarly + filled Nasik cubes of n, n new letters, s1, s2, ... s_n, can be so + placed, one in each of the n^4 cubelets of this group of n cubes, that + each shall contain a different combination of the p's, q's, r's and + s's. This is done by placing s1 on each of the n² cubelets of the + first cube that contain p1, and on the n² cubelets of the 2d, 3d, ... + and nth cube that contain p2, p3, ... p_n respectively. This process + is repeated with s2, beginning with the cube at which we ended, and so + on with the other s's; the n^4 cubelets, after multiplying the q's, + r's, and s's by n, n², and n³ respectively, will now be filled with + the numbers from 1 to n^4, and the constant summation will be + [Sigma]n³s + [Sigma]n²r + [Sigma]nq + [Sigma]p. This process may be + carried on without limit; for, if the n cubes are placed in a row with + their faces resting on each other, and the corresponding faces looking + the same way, n such parallelepipeds might be put side by side, and + the n^5 cubelets of this solid square be Nasically filled by the + introduction of a new letter t; while, by introducing another letter, + the n^6 cubelets of the compound cube of n³ Nasik cubes might be + filled by the numbers from 1 to n^6, and so _ad infinitum_. When the + root is an odd composite number the values of the three groups of + letters have to be adjusted as in squares, also in cubes of an even + root. A similar process enables us to place successive numbers in the + cells of several equal squares in which the Nasical summations are the + same in each, as in fig. 26. + + Among the many ingenious squares given by various writers, this + article may justly close with two by L. Euler, in the _Histoire de + l'académie royale des sciences_ (Berlin, 1759). In fig. 27 the natural + numbers show the path of a knight that moves within an odd square in + such a manner that the sum of pairs of numbers opposite to and + equidistant from the middle figure is its double. In fig. 28 the + knight returns to its starting cell in a square of 6, and the + difference between the pairs of numbers opposite to and equidistant + from the middle point is 18. + + A model consisting of seven Nasik cubes, constructed by A. H. Frost, + is in the South Kensington Museum. The centres of the cubes are placed + at equal distances in a straight line, the similar faces looking the + same way in a plane parallel to that line. Each of the cubes has seven + parallel glass plates, to which, on one side, the seven numbers in the + septenary scale are fixed, and behind each, on the other side, its + value in the common scale. 1201, the middle number from 1 to 7^4 + occupies the central cubelet of the middle cube. Besides each cube + having separately the same Nasical summation, this is also obtained by + adding the numbers in any seven similarly situated cubelets, one in + each cube. Also, the sum of all pairs of numbers, in a straight line, + through the central cube of the system, equidistant from it, in + whatever cubes they are, is twice 1201. (A. H. F.) + +_Fennell's Magic Ring._--It has been noticed that the numbers of magic +squares, of which the extension by repeating the rows and columns of n +numbers so as to form a square of 2n - 1 sides yields n² magic squares +of n sides, are arranged as if they were all inscribed round a cylinder +and also all inscribed on another cylinder at right angles to the first. +C. A. M. Fennell explains this apparent anomaly by describing such magic +squares as Mercator's projections, so to say, of "magic rings." + + The surface of these magic rings is symmetrically divided into n² + quadrangular compartments or cells by n equidistant zonal circles + parallel to the circular axis of the ring and by n transverse circles + which divide each of the n zones between any two neighbouring zonal + circles into n equal quadrangular cells, while the zonal circles + divide the sections between two neighbouring transverse circles into n + unequal quadrangular cells. The diagonals of cells which follow each + other passing once only through each zone and section, form similar + and equal closed curves passing once quite round the circular axis of + the ring and once quite round the centre of the ring. The position of + each number is regarded as the intersection of two diagonals of its + cell. The numbers are most easily seen if the smallest circle on the + surface of the ring, which circle is concentric with the axis, be one + of the zonal circles. In a perfect magic ring the sum of the numbers + of the cells whose diagonals form any one of the 2n diagonal curves + aforesaid is ½n(n² + 1) with or without increment, i.e. is the same + sum as that of the numbers in each zone and each transverse section. + But if n be 3 or a multiple of 3, only from 2 to n of the diagonal + curves carry the sum in question, so that the magic rings are + imperfect; and any set of numbers which can be arranged to make a + perfect magic ring or magic square can also make an imperfect magic + ring, e.g. the set 1 to 16 if the numbers 1, 6, 11, 16 lie thus on a + diagonal curve instead of in the order 1, 6, 16, 11. From a perfect + magic ring of n² cells containing one number each, n² distinct magic + squares can be read off; as the four numbers round each intersection + of a zonal circle and a transverse circle constitute corner numbers of + a magic square. The shape of a magic ring gives it the function of an + indefinite extension in all directions of each of the aforesaid n² + magic squares. (C. A. M. F.) + + See F. E. A. Lucas, _Récréations mathématiques_ (1891-1894); W. W. R. + Ball, _Mathematical Recreations_ (1892); W. E. M. G. Ahrens, + _Mathematische Unterhaltungen und Spiele_ (1901); H. C. H. Schubert, + _Mathematische Mussestunden_ (1900). A very detailed work is B. + Violle, _Traité complet des carrés magiques_ (3 vols., 1837-1838). The + theory of "path nasiks" is dealt with in a pamphlet by C. Planck + (1906). + + + + +MAGINN, WILLIAM (1793-1842), Irish poet and journalist, was born at Cork +on the 10th of July 1793. The son of a schoolmaster, he graduated at +Trinity College, Dublin, in 1811, and after his father's death in 1813 +succeeded him in the school. In 1819 he began to contribute to the +_Literary Gazette_ and to _Blackwood's Magazine_, writing as "R. T. +Scott" and "Morgan O'Doherty." He first made his mark as a parodist and +a writer of humorous Latin verse. In 1821 he visited Edinburgh, where he +made acquaintance with the Blackwood circle. He is credited with having +originated the idea of the _Noctes ambrosianae_, of which some of the +most brilliant chapters were his. His connexion with Blackwood lasted, +with a short interval, almost to the end of his life. His best story was +"Bob Burke's Duel with Ensign Brady." In 1823 he removed to London. He +was employed by John Murray on the short-lived _Representative_, and was +for a short time joint-editor of the _Standard_. But his intemperate +habits and his imperfect journalistic morality prevented any permanent +success. In connexion with Hugh Fraser he established _Fraser's +Magazine_ (1830), in which appeared his "Homeric Ballads." Maginn was +the original of Captain Shandon in _Pendennis_. In spite of his +inexhaustible wit and brilliant scholarship, most of his friends were +eventually alienated by his obvious failings, and his persistent +insolvency. He died at Walton-on-Thames on the 21st of August 1842. + + His _Miscellanies_ were edited (5 vols., New York, 1855-1857) by R. + Shelton Mackenzie and (2 vols., London, 1885) by R. W. Montagu + [Johnson]. + + + + +MAGISTRATE (Lat. _magistratus_, from _magister_, master, properly a +public office, hence the person holding such an office), in general, one +vested with authority to administer the law or one possessing large +judicial or executive authority. In this broad sense the word is used in +such phrases as "the first magistrate" of a king in a monarchy or "the +chief magistrate" of the president of the United States. But it is more +generally applied to minor or subordinate judicial officers, whether +unpaid, as justices of the peace, or paid, as stipendiary magistrates. A +stipendiary magistrate is appointed in London under the Metropolitan +Police Courts Act 1839, in municipal boroughs under the Municipal +Corporations Act 1882, and in particular districts under the Stipendiary +Magistrates Act 1863 and special acts. In London and municipal boroughs +a stipendiary magistrate must be a barrister of at least seven years' +standing, while under the Stipendiary Magistrates Act 1863 he may be of +five years' standing. A stipendiary magistrate may do alone all acts +authorized to be done by two justices of the peace. + +The term _magistratus_ in ancient Rome originally implied the office of +_magister_ (master) of the Roman people, but was subsequently applied +also to the holder of the office, thus becoming identical in sense with +_magister_, and supplanting it in reference to any kind of public +office. The fundamental conception of Roman magistracy is tenure of the +_imperium_, the sovereignty which resides with the Roman people, but is +by it conferred either upon a single ruler for life, as in the later +monarchy, or upon a college of magistrates for a fixed term, as in the +Republican period. The Roman theory of magistracy underwent little +change when two consuls were substituted for the king; but the +subdivision of magisterial powers which characterized the first +centuries of the Republic, and resulted in the establishment of twenty +annually elected magistrates of the people, implied some modification of +this principle of the investiture of magistrates with supreme authority. +For when the magistracies were multiplied a distinction was drawn +between magistrates with _imperium_, namely consuls, praetors and +occasionally dictators, and the remaining magistrates, who, although +exercising independent magisterial authority and in no sense agents of +the higher magistrates, were invested merely with an authority +(_potestas_) to assist in the administration of the state. At the same +time the actual authority of every magistrate was weakened not only by +his colleagues' power of veto, but by the power possessed by any +magistrate of quashing the act of an inferior, and by the tribune's +right of putting his veto on the act of any magistrate except a +dictator; and the subdivision of authority, which placed a great deal of +business in the hands of young and inexperienced magistrates, further +tended to increase the actual power as well as the influence of the +senate at the expense of the magistracy. + +In the developed Republic magistracies were divided into two classes: +(a) magistrates of the whole people (_populi Romani_) and (b) +magistrates of the _plebs_. The former class is again divided into two +sections: ([alpha]) curule and ([beta]) non-curule, a distinction which +rests mainly on dignity rather than on actual power, for it cuts across +the division of magistrates according to their tenure or non-tenure of +_imperium_. + + a. The magistrates of the people--also known as patrician magistrates, + probably because the older and more important of these magistracies + could originally be held only by patricians (q.v.)--were: ([alpha]) + Dictator, master of the horse (see DICTATOR), consuls, praetors, + curule, aediles and censors (curule); and ([beta]) Quaestors, and the + body of minor magistrates known as _xxvi. viri_ (non-curule). The + dictatorship and consulship were as old as the Republic. The first + praetor was appointed in 366 B.C., a second was added in 242 B.C., and + the number was gradually increased for provincial government until + Sulla brought it up to eight, and under the early principate it grew + to eighteen. Censors were first instituted in 443 B.C., and the office + continued unchanged until its abolition by Sulla, after which, though + restored, it rapidly fell into abeyance. Curule aediles were + instituted at the same time as the praetorship, and continued + throughout the Republic. The quaestorship was at least as old as the + Republic, but the number rose during the Republic from two to twenty. + All these offices except the censorship continued for administrative + purposes during the principate, though shorn of all important powers. + + b. The plebeian magistrates had their origin in the secession of the + _plebs_ to Mons Sacer in 494 B.C. (see ROME: _History_). In that year + tribunes of the _plebs_ were instituted, and two aediles were given + them as subordinate officials, who were afterwards known as plebeian + aediles, to distinguish them from the curule magistrates of the same + name. Both these offices were abolished during the decemvirate, but + were restored in 449 B.C., and survived into the principate. + +The powers possessed by all magistrates alike were two:--that of +enforcing their enactments (_coercitio_) by the exercise of any +punishment short of capital, and that of veto (_intercessio_) of any act +of a colleague or minor magistrate. The right of summoning and presiding +over an assembly of that body of citizens with whose powers the +magistrate was invested lay with the higher magistrates only in each +class, with the consuls and praetors, and with the tribunes of the +_plebs_. Civil jurisdiction was always a magisterial prerogative at +Rome, and criminal jurisdiction also, except in capital cases, the +decision of which was vested in the people at least as early as the +first year of the Republic, was wielded by magistrates until the +establishment of the various _quaestiones perpetuae_ during the last +century of the Republic. But in civil cases the magistrate, though +controlling the trial and deciding matters of law, was quite distinct +from the judge or body of judges who decided the question of fact; and +the _quaestiones perpetuae_, which reduced the magistrate in criminal +cases to a mere president of the court, gave him a position inferior to +that of the praetor, who tried civil cases, only in so far as the +praetor controlled the trial in some degree by his _formula_, under +which the judges decided the question of fact. + +Tenure of magistracy was always held to depend upon election by the body +whose powers the magistrate wielded. Thus the magistrates of the _plebs_ +were elected by the plebeian council, those of the people in the Comitia +(q.v.). In every case the outgoing magistrate, as presiding officer of +the elective assembly, exercised the important right of nominating his +successor for election. + + See A. H. J. Greenidge, _Roman Public Life_, 152 seq., 363 seq. + (London, 1901); T. Mommsen, _Römisches Staatsrecht_, I. 11. i. (1887). + (A. M. Cl.) + + + + +MAGLIABECHI, ANTONIO DA MARCO (1633-1714), Italian bibliophile, was born +at Florence on the 28th of October 1633. He followed the trade of a +goldsmith until 1673, when he received the appointment of librarian to +the grand-duke of Tuscany, a post for which he had qualified himself by +his vast stores of self-acquired learning. He died on the 4th of July +1714, bequeathing his large private library to the grand-duke, who in +turn handed it over to the city. + + + + +MAGLIANI, AGOSTINO (1824-1891), Italian financier, was a native of +Lanzino, near Salerno. He studied at Naples, and a book on the +philosophy of law based on Liberal principles won for him a post in the +Neapolitan treasury. He entered the Italian Senate in 1871, and had +already secured a reputation as a financial expert before his _Questione +monetaria_ appeared in 1874. In December 1877 he became minister of +finance in the reconstructed Depretis ministry, and he subsequently held +the same office in three other Liberal cabinets. In his second tenure he +carried through (1880) the abolition of the grist tax, to take effect in +1884. Having to face an increased expenditure without offending the +Radical electorate by unpopular taxes, he had recourse to unsound +methods of finance, which seriously embarrassed Italian credit for some +years after he finally laid down office in 1888. He died in Rome on the +22nd of February 1891. He was one of the founders of the +anti-socialistic "Adam Smith Society" at Florence. + + + + +MAGNA CARTA, or the Great Charter, the name of the famous charter of +liberties granted at Runnimede in June 1215 by King John to the English +people. Although in later ages its importance was enormously magnified, +it differs only in degree, not in kind, from other charters granted by +the Norman and early Plantagenet kings. Its greater length, however, +still more the exceptional circumstances attending its birth, gave to it +a position absolutely unique in the minds of later generations of +Englishmen. This feeling was fostered by its many confirmations, and in +subsequent ages, especially during the time of the struggle between the +Stuart kings and the parliament, it was regarded as something +sacrosanct, embodying the very ideal of English liberties, which to some +extent had been lost, but which must be regained. Its provisions, real +and imaginary, formed the standard towards which Englishmen must strive. + +The causes which led to the grant of Magna Carta are described in the +article on _English History_. Briefly, they are to be found in the +conditions of the time; the increasing insularity of the English barons, +now no longer the holders of estates in Normandy; the substitution of an +unpopular for a popular king, an active spur to the rising forces of +discontent; and the unprecedented demands for money--demands followed, +not by honour, but by dishonour, to the arms of England abroad. So much +for the general causes. The actual crisis may be said to begin with the +quarrel between John and Pope Innocent III. regarding the appointment of +a new archbishop to the see of Canterbury. This was settled in May 1213, +and in the new prelate, the papal nominee, Stephen Langton, who landed +in England and absolved the king in the following July, the baronial +party found an able and powerful ally. But before this event John had +instituted a great inquiry, the inquest of service of June 1212, for the +purpose of finding out how much he could exact from each of his vassals, +a measure which naturally excited some alarm; and then, fearing a +baronial rising, he had abandoned his proposed expedition into Wales, +had taken hostages from the most prominent of his foes, and had sought +safety in London. + +His absolution followed, and then he took courage. Turning once more his +attention to the recovery of Normandy, he asked the barons for +assistance for this undertaking; in reply they, or a section of them, +refused, and instead of crossing the seas the king marched northwards +with the intention of taking vengeance on his disobedient vassals, who +were chiefly barons of the north of England. Langton followed his +sovereign to Northampton and persuaded him, at least for the present, to +refrain from any serious measures of revenge. Before this interview a +national council had met at St Albans at the beginning of August 1213, +and this was followed by another council, held in St Paul's church, +London, later in the same month; it was doubtless summoned by the +archbishop, and was attended by many of the higher clergy and a certain +number of the barons. Addressing the gathering, Langton referred to the +laws of Edward the Confessor as "good laws," which the king ought to +observe, and then mentioned the charter granted by Henry I. on his +accession as a standard of good government. This event has such an +important bearing on the issue of Magna Carta that it is not +inappropriate to quote the actual words used by Matthew Paris in +describing the incident. The chronicler represents the archbishop as +saying "Inventa est quoque nunc carta quaedam Henrici primi regis +Angliae per quam, si volueritis, libertates diu amissas poteritis ad +statum pristinum revocare." Those present decided to contend to the +death for their "long-lost liberties," and with this the meeting came to +an end. Nothing, however, was done during the remainder of the year, and +John, feeling his position had grown stronger, went abroad early in +1214, and remained for some months in France. With his mercenaries +behind him he met with some small successes in his fight for Normandy, +but on the 27th of July he and his ally, the emperor Otto IV., met with +a crushing defeat at Bouvines at the hands of Philip Augustus, and even +the king himself was compelled to recognise that his hopes of recovering +Normandy were at an end. + +Meanwhile in England, which was ruled by Peter des Roches as justiciar, +the discontent had been increasing rather than diminishing, and its +volume became much larger owing to an event of May 1214. Greatly needing +money for his campaign, John ordered another scutage to be taken from +his tenants; this, moreover, was to be at the unprecedented rate of +three marks on the knight's fee, not as on previous occasions of two +marks, although this latter sum had hitherto been regarded as a very +high rate. The northern barons refused to pay, and the gathering forces +of resistance received a powerful stimulus when a little later came the +news of the king's humiliation at Bouvines. Then in October the beaten +monarch returned to England, no course open to him but to bow before the +storm. In November he met some of his nobles at Bury St Edmunds, but as +they still refused to pay the scutage no agreement was reached. At once +they took another step towards the goal. With due solemnity (_super +majus altare_) they swore to withdraw their allegiance from the king and +to make war upon him, unless within a stated time he restored to them +their rightful laws and liberties. While they were collecting troops in +order to enforce their threats, John on his part tried to divide his +enemies by a concession to the clerical section. By a charter, dated the +21st of November 1214, he granted freedom of election to the church. +However, this did not prevent the prelates from continuing to act to +some extent with the barons, and early in January 1215 the malcontents +asked the king to confirm the laws of Edward the Confessor and the other +liberties of the kingdom. He evaded the request and secured a truce +until Easter was passed. Energetically making use of this period of +respite, he again issued the charter to the church, ordered his subjects +to take a fresh oath of allegiance to him, and sent to the pope for aid; +but neither these precautions, nor his expedient of taking the cross, +deterred the barons from returning to the attack. In April they met in +arms at Stamford, and as soon as the truce had expired they marched to +Brackley, where they met the royal ministers and again presented their +demands. These were carried to the king at Oxford, but angrily he +refused to consider them. Then the storm burst. On the 5th of May the +barons formally renounced their allegiance to John, and appointed Robert +Fitzwalter as their leader. They marched towards London, while John made +another attempt to delay the crisis, or to divide his foes, by granting +a charter to the citizens of London (May 9, 1215), and then by offering +to submit the quarrel to a court of arbitrators under the presidency of +the pope. But neither the one nor the other expedient availed him. +Arbitration under such conditions was contemptuously rejected, and after +the king had ordered the sheriffs to seize the lands and goods of the +revolting nobles, London opened its gates and peacefully welcomed the +baronial army. Other towns showed also that their sympathies were with +the insurgents, and John was forced to his knees. Promising to assent to +their demands, he agreed to meet the barons, and the gathering was fixed +for the 15th of June, and was to take place in a meadow between Staines +and Windsor, called Runnimede. + +At the famous conference, which lasted from Monday the 15th to Tuesday +the 23rd of June, the hostile barons were present in large numbers; on +the other hand John, who rode over each day from Windsor, was only +attended by a few followers. At once the malcontents presented their +demands in a document known popularly as the _Articles of the Barons_, +more strictly as _Capitula quae barones petunt et dominus rex concedit_. +Doubtless this had been drawn up beforehand, and was brought by the +baronial leaders to Runnimede; possibly it was identical with the +document presented to the royal ministers at Brackley a few weeks +before. John accepted the Articles on the same day and at once the great +seal was affixed to them. They are forty-eight in number, and on them +Magna Carta was based, the work of converting them into a charter, which +was regarded as a much more binding form of engagement, being taken in +hand immediately. This duty occupied three days, negotiations between +the two parties taking place over several disputed points, and it was +completed by Friday the 19th, when several copies of the charter were +sealed. All then took an oath to keep its terms, and orders were sent to +the sheriffs to publish it, and to see that its provisions were +observed, two or three days being taken up with making and sending out +copies for this purpose. It should be mentioned that, although the +charter was evidently not sealed until the 19th, the four existing +copies of it are dated the 15th, the day on which John accepted the +articles. + +The days between Friday the 19th and the following Tuesday, when the +conference came to an end, were occupied in providing, as far as +possible, for the due execution of the reforms promised by the king in +Magna Carta. The document itself provided for an elected committee of +twenty-five barons, whose duty was to compel John, by force if +necessary, to keep his promises; but this was evidently regarded as +insufficient, and the matter was dealt with in a supplementary treaty +(_Conventio facta inter regem Angliae et barones ejusdum regni_). As a +guarantee of his good faith the king surrendered the city of London to +his foes, while the Tower was entrusted to the neutral keeping of the +archbishop of Canterbury. John then asked the barons for a charter that +they on their part would keep the peace. This was refused, and although +some of the bishops entered a mild protest, the question was allowed to +drop. Regarding another matter also, the extent of the royal forests, +the prelates made a protest. John and his friends feared lest the +inquiry promised into the extent of the hated forest areas would be +carried out too rigorously, and that these would be seriously curtailed, +if not abolished altogether. Consequently, the two archbishops and their +colleagues declared that the articles in the charter which provided for +this inquiry, and for a remedy against abuses of the forest laws by the +king, must not be interpreted in too harsh a spirit. The customs +necessary for the preservation of the forests must remain in force. + +No securities, however, could bind John. Even before Magna Carta was +signed he had set to work to destroy it, and he now turned to this task +with renewed vigour. He appealed to the pope, and hoped to crush his +enemies by the aid of foreign troops, while the barons prepared for war, +and the prelates strove to keep the peace. Help came first from the +spiritual arm. On the 24th of August 1215 Innocent III. published a bull +which declared Magna Carta null and void. It had been extorted from the +king by force (_per vim et metum_), and in the words of the bull the +pope said "compositionem hujusmodi reprobamus penitus et damnamus." He +followed this up by excommunicating the barons who had obtained it, and +in the autumn of 1215 the inevitable war began. Capturing Rochester +castle, John met with some other successes, and the disheartened barons +invited Louis, son of Philip Augustus of France and afterwards king as +Louis VIII., to take the English crown. In spite of the veto of the pope +Louis accepted the invitation, landed in England in May 1216, and +occupied London and Winchester, the fortune of war having in the +meantime turned against John. The "ablest and most ruthless of the +Angevins," as J. R. Green calls this king, had not, however, given up +the struggle, and he was still in the field when he was taken ill, dying +in Newark castle on the 19th of October 1216. + +In its original form the text of Magna Carta was not divided into +chapters, but in later times a division of this kind was adopted. This +has since been retained by all commentators, the number of chapters +being 63. + +The preamble states that the king has granted the charter on the advice +of various prelates and barons, some of whom, including the archbishop +of Canterbury, the papal legate Pandulf, and William Marshal, earl of +Pembroke, are mentioned by name. + + Chapter I. declares that the English church shall be free and shall + enjoy freedom of election. This follows the precedent set in the + accession charter of Henry I. and in other early charters, although it + had no place in the Articles of the Barons. On the present occasion it + was evidently regarded as quite a formal and introductory matter, and + the same remark applies to the general grant of liberties to all + freemen and their heirs, with which the chapter concludes. + +Then follows a series of chapters intended to restrain the king from +raising money by the harsh and arbitrary methods adopted in the past. +These chapters, however, only afforded protection to the +tenants-in-chief of the crown, and it is clear from their prominent +position that the framers of the charter regarded them as of paramount +importance. + + Chapter II. fixes the amount of the relief to be paid to the king by + the heir of any of his vassals. Previously John, disregarding the + custom of the past, had taken as much as he could extort. Henceforward + he who inherits a barony must pay £100, he who inherits a knight's fee + 100 shillings or less, and for smaller holdings less "according to the + ancient custom of fiefs." + + Chapters III. to VI. deal with the abuses of the king's privilege of + acting as guardian of minors and their lands. Money must not be + extorted from a ward when he receives his inheritance. The guardian or + his servant must not take from the ward's property more than a + reasonable amount for his expenses and the like; on the contrary he + must maintain the houses, estates and other belongings in a proper + state of efficiency. A ward must be allowed a reasonable liberty in + the matter of marriage. He or she must not, as had been so often the + case in the past, be forced to marry some royal favourite, or some one + who had paid a sum of money for the privilege. + + Chapters VII. and VIII. are for the protection of the widows of + tenants-in-chief. On the death of her husband a widow must receive her + rightful inheritance, without delay or hindrance. Moreover she must + not be compelled to marry, a proceeding sometimes adopted to get her + lands into the possession of a royal minion. + + Chapter IX. is intended to prevent the king from collecting the money + owing to him in an oppressive manner. + +Now for a short time the document leaves the great questions at issue +between the king and the barons, and two chapters are devoted to +protecting the people generally against the exactions of the Jews. + + Chapter X. declares that money borrowed from the Jews shall not bear + interest during a minority. + + Chapter XI. provides for the repayment of borrowed money to the Jews, + and also to other creditors. This, however, is only to be done after + certain liabilities have been met out of the estate, including the + services due to the lord of the land. + +Having thus disposed of this matter, the grievances of the barons are +again considered, the vexed question of scutage being dealt with. + + Chapter XII. says that in future no scutage or aid, beyond the three + recognized feudal aids, shall be levied except by the consent of the + general council of the nation (_commune concilium regni nostri_), + while the three recognized aids shall only be levied at a reasonable + rate. In dealing with this matter the Articles of the Barons had + declared that aids and tallages must not be taken from the citizens of + London and of other places without the consent of the council. This + provision was omitted from Magna Carta, except so far as it related to + aids from the citizens of London. This chapter does not give the + people the right to control taxation. It gives to the men interested a + certain control over one form of taxation, and protects one class only + from arbitrary exactions, and that class the most powerful and the + most wealthy. + + Chapter XIII. gives to the citizens of London all their ancient + liberties and free customs. + + Chapter XIV. provides for the assembly of the council when its consent + is necessary for raising an aid or a scutage. Individual summonses + must be sent to the prelates and greater barons, while the lesser + barons will be called together through the sheriffs and bailiffs. At + least forty days' notice of the meeting must be given, and the cause + thereof specified. No chapter corresponding to this is found in the + Articles and none was inserted in the reissues of Magna Carta. It is + very interesting, but it does not constitute any marked advance in the + history of parliament, as it merely expresses the customary method of + summoning a council. It does not, as has been sometimes asserted, in + any way establish a representative system, as this is understood + to-day. + + Chapter XV. extends the concessions obtained by the greater barons for + themselves to the lesser landholders, the tenants of the + tenants-in-chief. + + Chapter XVI. declares that those who owe military service for their + lands shall not be called upon to perform more than the due amount of + such service. + +We now come to an important series of articles which deal with abuses in +the administration of justice. Henry II. made the royal courts of law a +lucrative source of revenue, but he gave protection to suitors. Under +his sons justice was equally, perhaps more, costly, while adequate +protection was much harder to obtain. Here were many grievances, and the +barons set to work to redress them. + + Chapter XVII. declares that common pleas must henceforward be heard in + a fixed place. This had already been to some extent the practice when + this class of cases was heard; it was now made the rule. From this + time suitors in this court were not put to the expense and + inconvenience of following the king from place to place. + + Chapters XVIII. and XIX. deal with the three petty assizes, three + kinds of cases regarding disputes about the possession of land. These + must be heard in the county courts before two visiting justices and + four knights of the shire. The hardship of attendance at the county + courts was to some extent obviated. + + Chapters XX. to XXII. regulate the amount of fines imposed for + offences against the law. Property necessary for one's livelihood must + not be taken. The fines must only be imposed by the oath of honest men + of the neighbourhood. In the same way earls and barons must only be + fined by their peers, and a similar privilege is extended to the + clergy, who, moreover, were not to be fined in accordance with the + value of their benefices, but only of their other property. It should + be noticed that trial by one's peers, as understood in Magna Carta, is + not confined to the nobility; in every class of society an accused man + is punished in accordance with the verdict of his peers, or equals. + + Chapter XXIII. asserts that persons shall not be compelled to make + bridges, unless they are bound to do so by ancient custom. John had + oppressed his subjects in this way before he visited a district for + purposes of sport, and the hardship was a real one. + + Chapter XXIV. declared that the sheriffs and other officers of the + king must not hold the pleas of the crown. This was intended to remove + an old and serious evil, as the sheriffs had earned a very bad + reputation by their methods of administering justice. + + Chapter XXV. also concerns the sheriffs. It prevents the king from + increasing by their agency the amount of money annually due to him + from the various counties and hundreds. The custom was for the king to + get a fixed sum from the sheriff of each county, this being called the + _firma comitatus_, and for the sheriff to collect this as best he + could. Henceforward this amount must not be raised. + + Chapters XXVI. and XXVII. were intended to protect the property of + deceased persons, and also to secure the full payment of debts due + therefrom to the crown. Other creditors were also protected, and the + property of an intestate must be distributed to his heirs under the + supervision of the church. + + Chapter XXVIII. strikes a blow at the custom of purveyance. Royal + officials must pay for the corn and provisions which they take on + behalf of the king. + + Chapter XXIX. says knights must not be compelled to give money instead + of performing castle-guard, if they are willing to perform this + service. Castle-guard was the liability incumbent on the holders of + some estates to serve in the garrison of the royal castles. The + constables of these castles had adopted the custom of compelling these + landholders to give money and not service, mercenaries being then + hired to perform this. + + Chapters XXX. and XXXI. forbid the royal officials to seize the horses + or carts of freemen for transport duty, or to take wood for the king's + buildings. + + Chapter XXXII. says that the lands of convicted felons shall be handed + over to the lords of such lands and not kept by the king beyond a year + and a day. In cases of treason the king had a right to the forfeited + lands, but he was not allowed to establish a similar right in cases of + felony. + + Chapter XXXIII. provided for the removal of kydells, or weirs, from + all English rivers. This was intended to give greater freedom to + inland navigation, the rivers being the main highways of trade. + + Chapter XXXIV. limits the use of the writ known as _Praecipe_. This + writ was one transferring cases concerning the ownership of property + from the courts of the feudal lords to those of the king. This custom, + which owes its origin to Henry II., meant a loss of revenue to the + lords, whose victory in this matter, however, was a step backwards. It + checked temporarily the process of centralizing the administration of + justice. + + Chapter XXXV. provides for the uniformity of weights and measures + throughout the kingdom. + + Chapter XXXVI. promises that in future writs of inquisition shall be + granted freely without payment of any kind. This kind of writ allowed + a man to refer the question of his guilt or innocence to the verdict + of his neighbours instead of proving his innocence by the duel. + + Chapter XXXVII. prevents the king from administering certain kinds of + land when these fall into the possession of minors. In the past John + had evidently stretched his authority and seized lands over which + others had really the right of wardship. + + Chapter XXXVIII. prevents a bailiff from compelling an accused man to + submit to the ordeal without the approval of credible witnesses. + + Chapter XXXIX. is more important and the English rendering of it may + be given in full. "No freeman shall be arrested, or detained in + prison, or deprived of his freehold, or outlawed, or banished, or in + any way molested; and we will not set forth against him, nor send + against him, unless by the lawful judgment of his peers and by the law + of the land." The object of this was clearly to restrain John from + arbitrary proceedings against his free subjects. The principle of + judgment by one's peers is asserted, and is obviously the privilege of + every class of freemen, not of the greater lords alone. + + Chapter XL. simply says, "To no one will we sell, to no one will we + refuse or delay, right or justice." + + Chapters XLI. and XLII. give permission to merchants, both English and + foreign, to enter and leave the kingdom, except in time of war. They + are not to pay "evil tolls." The privilege is extended to all + travellers, except the prisoner and the outlaw, and natives of a + country with which England is at war. + + Chapter XLIII. is intended to compel the king to refrain from exacting + greater dues from an escheated barony than were previously due from + such barony. + + Chapter XLIV. deals with the hated and oppressive forest laws. In + future attendance at the forest courts is only obligatory on those who + have business thereat. + + Chapter XLV. says that the royal officials must know something of the + law and must be desirous of keeping it. + + Chapter XLVI. gives to the founders of religious houses the right of + acting as guardians of such houses when they are without heads. + + Chapters XLVII. and XLVIII. deal again with the great grievance of the + royal forests. John undertakes to disforest all forests which have + been made in his time, and also to give up such river banks as he has + seized for his own use when engaged in sport. Twelve knights in each + county are to make a thorough inquiry into all evil customs connected + with the forests, and these are to be utterly abolished. + + Chapter XLIX. provides for the restoration of hostages. John had been + in the habit of taking the children of powerful subjects as pledges + for the good behaviour of their parents. + + Chapter L. says that certain royal minions, who are mentioned by name, + are to be removed from their offices. + + Chapter LI. says that as soon as peace is made all foreign mercenaries + are to be banished. + + Chapters LII. and LIII. are those in which the king promises to make + amends for the injuries he has done to his barons in the past. He will + restore lands and castles to those who have been deprived of them + without the judgment of their peers; he will do the same concerning + property unlawfully seized by Henry II. or Richard I. and now in his + hands. In the latter case, however, he was allowed a respite until he + returned from the projected crusade. He promises also to do right + concerning forests, abbeys and the wardship of lands which belong + lawfully to others. + + Chapter LIV. prevents any one from being arrested on the appeal of a + woman, except on a charge of causing the death of her husband. As a + woman could not prove her case in the judicial combat, it was felt + that the earlier practice gave her an unfair advantage. + + Chapter LV. provides for the remission of unjust fines. The decision + on these matters is to rest with the archbishop of Canterbury and the + twenty-five barons appointed to see that the terms of the charter are + carried out. + + Chapters LVI. and LVII. deal with the grievances of Welshmen. + Restoration of property is promised to them practically in the same + way as to Englishmen. Welsh law is to be used in Wales, and in the + marches the law of the marches is to be employed. + + Chapter LVIII. promises that his hostages and his charters shall be + restored to Llewellyn, prince of Wales. + + Chapter LIX. promises a restoration of hostages to Alexander I. king + of Scotland. Right is also to be done to him concerning the lands + which he holds in England. + + Chapter LX. is a general statement that the aforesaid customs and + liberties are to be observed by all classes. + + Chapter LXI. provides for the execution of the royal promises. A + committee is to be formed of twenty-five barons. Then if the king or + any of his servants do wrong and complaint is made to four of the + twenty-five, they are to ask for redress. In the event of this not + being granted within forty days the matter is to be referred to the + twenty-five, who are empowered to seize the lands and property of the + king, or to obtain justice in any other way possible. They must, + however, spare the persons of the king, the queen and their children. + Vacancies in the committee are to be filled by the barons themselves. + The twenty-five barons were duly appointed, their names being given by + Matthew Paris. This chronicler also reports that another committee of + thirty-eight members was appointed to assist and control the + twenty-five. S. R. Gardiner calls the scheme "a permanent organization + for making war against the king." + + Chapter LXII. is an expression of general forgiveness. + + 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] + + _Directing Couple acting on an Elongated Body._--In a non-uniform + field every volume-element of the body tends to move towards regions + of greater or less force according as the substance is paramagnetic or + diamagnetic, and the behaviour of the whole mass will be determined + chiefly by the tendency of its constituent elements. For this reason a + thin bar suspended at its centre of gravity between a pair of magnetic + poles will, if paramagnetic, set itself along the line joining the + poles, where the field is strongest, and if diamagnetic, transversely + to the line. These are the "axial" and "equatorial" positions of + Faraday. It can be shown[11] that in a uniform field an elongated + piece of any non-crystalline material is in stable equilibrium only + when its length is parallel to the lines of force; for diamagnetic + substances, however, the directing couple is exceedingly small, and it + would hardly be possible to obtain a uniform field of sufficient + strength to show the effect experimentally. + + _Relative Magnetization._--A substance of which the real + susceptibility is [kappa] will, when surrounded by a medium having the + susceptibility [kappa]´, behave towards a magnet as if its + susceptibility were [kappa]_a = ([kappa] - [kappa]´)/(1 + + 4[pi][kappa]´). Since 1 + 4[pi][kappa]´ can never be negative, the + apparent susceptibility [kappa]_a will be positive or negative + according as [kappa] is greater or less than [kappa]´. Thus, for + example, a tube containing a weak solution of an iron salt will appear + to be diamagnetic if it is immersed in a stronger solution of iron, + though in air it is paramagnetic.[12] + + _Circular Magnetization._--An electric current i flowing uniformly + through a cylindrical wire whose radius is a produces inside the wire + a magnetic field of which the lines of force are concentric circles + around the axis of the wire. At a point whose distance from the axis + of the wire is r the tangential magnetic force is + + H = 2ir/a² (39) + + it therefore varies directly as the distance from the axis, where it + is zero.[13] If the wire consists of a ferromagnetic metal, it will + become "circularly" magnetized by the field, the lines of + magnetization being, like the lines of force, concentric circles. So + long as the wire (supposed isotropic) is free from torsional stress, + there will be no external evidence of magnetism. + + _Magnetic Shielding._--The action of a hollow magnetized shell on a + point inside it is always opposed to that of the external magnetizing + force,[14] the resultant interior field being therefore weaker than + the field outside. Hence any apparatus, such as a galvanometer, may be + partially shielded from extraneous magnetic action by enclosing it in + an iron case. If a hollow sphere[15] of which the outer radius is R + and the inner radius r is placed in a uniform field H0, the field + inside will also be uniform and in the same direction as H0, and its + value will be approximately + + H0 + H_i = ---------------------------- (40) + 1 + (2/9)(µ - 2) (1 - r³/R³) + + For a cylinder placed with its axis at right angles to the lines of + force, + + H0 + H_i = ------------------------ (41) + 1 + ¼(µ - 2) (1 - r²/R²) + + These expressions show that the thicker the screen and the greater its + permeability µ, the more effectual will be the shielding action. Since + µ can never be infinite, complete shielding is not possible. + + _Magneto-Crystallic Phenomenon._--In anisotropic bodies, such as + crystals, the direction of the magnetization does not in general + coincide with that of the magnetic force. There are, however, always + three _principal axes_ at right angles to one another along which the + magnetization and the force have the same direction. If each of these + axes successively is placed parallel to the lines of force in a + uniform field H, we shall have + + I1 = [kappa]1H, I2 = [kappa]2H, I3 = [kappa]3H, + + the three susceptibilities [kappa] being in general unequal, though in + some cases two of them may have the same value. For crystalline bodies + the value of [kappa] (+ or -) is nearly always small and constant, the + magnetization being therefore independent of the form of the body and + proportional to the force. Hence, whatever the position of the body, + if the field be resolved into three components parallel to the + principal axes of the crystal, the actual magnetization will be the + resultant of the three magnetizations along the axes. The body (or + each element of it) will tend to set itself with its axis of greatest + susceptibility parallel to the lines of force, while, if the field is + not uniform, each volume-element will also tend to move towards places + of greater or smaller force (according as the substance is + paramagnetic or diamagnetic), the tendency being a maximum when the + axis of greatest susceptibility is parallel to the field, and a + minimum when it is perpendicular to it. The phenomena may therefore be + exceedingly complicated.[16] + + +3. MAGNETIC MEASUREMENTS + +_Magnetic Moment._--The moment M of a magnet may be determined in many +ways,[17] the most accurate being that of C. F. Gauss, which gives the +value not only of M, but also that of H, the horizontal component of the +earth's force. The product MH is first determined by suspending the +magnet horizontally, and causing it to vibrate in small arcs. If A is +the moment of inertia of the magnet, and t the time of a complete +vibration, MH = 4[pi]²A/t² (torsion being neglected). The ratio M/H is +then found by one of the magnetometric methods which in their simplest +forms are described below. Equation (44) shows that as a first +approximation. + + M/H = (d² - l²) tan [theta]/2d, + +where l is half the length of the magnet, which is placed in the +"broadside-on" position as regards a small suspended magnetic needle, d +the distance between the centre of the magnet and the needle, and +[theta] the angle through which the needle is deflected by the magnet. +We get therefore + + M² = MH × M/H = 2[pi]²A(d² - l²)² tan [theta]/t²d (42) + + H² = MH × H/M = 8[pi]²Ad/{t²(d² - l²)² tan [theta]} (43) + +When a high degree of accuracy is required, the experiments and +calculations are less simple, and various corrections are applied. The +moment of a magnet may also be deduced from a measurement of the couple +exerted on the magnet by a uniform field H. Thus if the magnet is +suspended horizontally by a fine wire, which, when the magnetic axis +points north and south, is free from torsion, and if [theta] is the +angle through which the upper end of the wire must be twisted to make +the magnet point east and west, then MH = C[theta], or M = C[theta]/H, +where C is the torsional couple for 1°. A bifilar suspension is +sometimes used instead of a single wire. If P is the weight of the +magnet, l the length of each of the two threads, 2a the distance between +their upper points of attachment, and 2b that between the lower points, +then, approximately, MH = P(ab/l) sin [theta]. It is often sufficient to +find the ratio of the moment of one magnet to that of another. If two +magnets having moments M, M´ are arranged at right angles to each other +upon a horizontal support which is free to rotate, their resultant R +will set itself in the magnetic meridian. Let [theta] be the angle which +the standard magnet M makes with the meridian, then M´/R = sin [theta], +and M/R = cos [theta], whence M´ = M tan [theta]. + +[Illustration: FIG. 5.] + +A convenient and rapid method of estimating a magnetic moment has been +devised by H. Armagnat.[18] The magnet is laid on a table with its north +pole pointing northwards, A compass having a very short needle is placed +on the line which bisects the axis of the magnet at right angles, and is +moved until a neutral point is found where the force due to the earth's +field H is balanced by that due to the magnet. If 2l is the distance +between the poles m and -m, d the distance from either pole to a point P +on the line AB (fig. 5), we have for the resultant force at P + + R = -2 cos [theta] × m/d² = -2lm/d³ = -M/d³. + +When P is the neutral point, H is equal and opposite to R; therefore M = +Hd³, or the moment is numerically equal to the cube of the distance from +the neutral point to a pole, multiplied by the horizontal intensity of +the earth's force. The distance between the poles may with sufficient +accuracy for a rough determination be assumed to be equal to five-sixths +of the length of the magnet. + +_Measurement of Magnetization and Induction._--The magnetic condition +assumed by a piece of ferromagnetic metal in different circumstances is +determinable by various modes of experiment which may be classed as +magnetometric, ballistic, and traction methods. When either the +magnetization I or the induction B corresponding to a given magnetizing +force H is known, the other may be found by means of the formula B = +4[pi]I + H. + +_Magnetometric Methods._--Intensity of magnetization is most directly +measured by observing the action which a magnetized body, generally a +long straight rod, exerts upon a small magnetic needle placed near it. +The magnetic needle may be cemented horizontally across the back of a +little plane or concave mirror, about ¼ or 3/8 in. in diameter, which is +suspended by a single fibre of unspun silk; this arrangement, when +enclosed in a case with a glazed front to protect it from currents of +air, constitutes a simple but efficient magnetometer. Deflections of the +suspended needle are indicated by the movement of a narrow beam of light +which the mirror reflects from a lamp and focusses upon a graduated +cardboard scale placed at a distance of a few feet; the angular +deflection of the beam of light is, of course, twice that of the needle. +The suspended needle is, in the absence of disturbing causes, directed +solely by the horizontal component of the earth's field of magnetic +force H_E, and therefore sets itself approximately north and south. The +magnetized body which is to be tested should be placed in such a +position that the force H_P due to its poles may, at the spot occupied +by the suspended needle, act in a direction at right angles to that due +to the earth--that is, east and west. The direction of the resultant +field of force will then make, with that of H_E, an angle [theta], such +that H_p/H_E = tan [theta], and the suspended needle will be deflected +through the same angle. We have therefore + + H_P = H_E tan [theta]. + +The angle [theta] is indicated by the position of the spot of light upon +the scale, and the horizontal intensity of the earth's field H_E is +known; thus we can at once determine the value of H_P, from which the +magnetization I of the body under test may be calculated. + + In order to fulfil the requirement that the field which a magnetized + rod produces at the magnetometer shall be at right angles to that of + the earth, the rod may be conveniently placed in any one of three + different positions with regard to the suspended needle. + + + [Illustration: FIG. 6.] + + (1) The rod is set in a horizontal position level with the suspended + needle, its axis being in a line which is perpendicular to the + magnetic meridian, and which passes through the centre of suspension + of the needle. This is called the "end-on" position, and is indicated + in fig. 6. AB is the rod and C the middle point of its axis; NS is the + magnetometer needle; AM bisects the undeflected needle NS at right + angles. Let 2l = the length of the rod (or, more accurately, the + distance between its poles), v = its volume, m and -m the strength of + its poles, and let d = the distance CM. For most ordinary purposes the + length of the needle may be assumed to be negligible in comparison + with the distance between the needle and the rod. We then have + approximately for the field at M due to the rod + + m m 4dl + H_P = -------- - -------- = m ----------. + (d - l)² (d + l)² (d² - l²)² + + Therefore + + (d² - l²)²H_P (d² - l²)² H_E tan [theta] + 2ml = M = ------------- = --------------------------. (44) + 2d 2d + + And + + M (d² - l²)²H_E + I = --- = ------------- tan [theta], (45) + v 2dv + + whence we can find the values of I which correspond to different + angles of deflection. + + (2) The rod may be placed horizontally east and west in such a + position that the direction of the undeflected suspended needle + bisects it at right angles. This is known as the "broadside-on" + position, and is represented in fig. 7. Let the distance of each pole + of the rod AB from the centre of the magnetometer needle = d. Then, + since H_P, the force at M due to m and -m, is the resultant of m/d² + and -m/d², we have + + H_P 2l + --- = --- + m d + + or + + 2ml + H_P = ---, + d³ + + the direction being parallel to AB. + + And + + + d³ H_P d³ H_E + I = ------ = ------ tan [theta]. (46) + v v + + [Illustration: FIG. 7.] + + [Illustration: FIG. 8.] + + (3) In the third position the test rod is placed vertically with one + of its poles at the level of the magnetometer needle, and in the line + drawn perpendicularly to the undeflected needle from its centre of + suspension. The arrangement is shown in fig. 8, where AB is the + vertical rod and M indicates the position of the magnetometer needle, + which is supposed to be perpendicular to the plane of the paper. + Denoting the distance AM by d1, BM by d2, and AB by l, we have for the + force at M due to the magnetism of the rod + + m m + H_P = --- - horizontal component of --- + d1² d2² + + / 1 d1 \ + = m ( --- - --- ). + \ d1² d2³ / + + Therefore + + H_P d1² H_E + m = --------- = ------------ tan [theta], + 1 d1 / d1 \³ + --- - --- 1 - ( ---- ) + d1² d2³ \ d2 / + + and + + ld1²H_E + I = ------------------ tan [theta]. (47) + { / d1 \³ } + v { 1 - ( ---- ) } + { \ d2 / } + + This last method of arrangement is called by Ewing the "one-pole" + method, because the magnetometer deflection is mainly caused by the + upper pole of the rod (_Magnetic Induction_, p. 40). For experiments + with long thin rods or wires it has an advantage over the other + arrangements in that the position of the poles need not be known with + great accuracy, a small upward or downward displacement having little + effect upon the magnetometer deflection. On the other hand, a + vertically placed rod is subject to the inconvenience that it is + influenced by the earth's magnetic field, which is not the case when + the rod is horizontal and at right angles to the magnetic meridian. + This extraneous influence may, however, be eliminated by surrounding + the rod with a coil of wire carrying a current such as will produce in + the interior a magnetic field equal and opposite to the vertical + component of the earth's field. + + If the cardboard scale upon which the beam of light is reflected by + the magnetometer mirror is a flat one, the deflections as indicated by + the movement of the spot of light are related to the actual + deflections of the needle in the ratio of tan 2[theta] to [theta]. + Since [theta] is always small, sufficiently accurate results may + generally be obtained if we assume that tan 2[theta] = 2 tan [theta]. + If the distance of the mirror from the scale is equal to n scale + divisions, and if a deflection [theta] of the needle causes the + reflected spot of light to move over s scale divisions, we shall have + + s/n = tan 2[theta] exactly, + + s/2n = tan [theta] approximately. + + We may therefore generally substitute s/2n for tan [theta] in the + various expressions which have been given for I. + + Of the three methods which have been described, the first two are + generally the most suitable for determining the moment or the + magnetization of a permanent magnet, and the last for studying the + changes which occur in the magnetization of a long rod or wire when + subjected to various external magnetic forces, or, in other words, for + determining the relation of I to H. A plan of the apparatus as + arranged by Ewing for the latter purpose is shown diagrammatically in + fig. 9. The cardboard scale SS is placed above a wooden screen, having + in it a narrow vertical slit which permits a beam of light from the + lamp L to reach the mirror of the magnetometer M, whence it is + reflected upon the scale. A is the upper end of a glass tube, half a + metre or so in length, which is clamped in a vertical position behind + the magnetometer. The tube is wound over its whole length with two + separate coils of insulated wire, the one being outside the other. The + inner coil is supplied, through the intervening apparatus, with + current from the battery of secondary cells B1; this produces the + desired magnetic field inside the tube. The outer coil derives + current, through an adjustable resistance R, from a constant cell B2; + its object is to produce inside the tube a magnetic field equal and + opposite to that due to the earth's magnetism. C is a "compensating + coil" consisting of a few turns of wire through which the magnetizing + current passes; it serves to neutralize the effect produced upon the + magnetometer by the magnetizing coil, and its distance from the + magnetometer is so adjusted that when the circuit is closed, no + ferromagnetic metal being inside the magnetizing coil, the + magnetometer needle undergoes no deflection. K is a commutator for + reversing the direction of the magnetizing current, and G a + galvanometer for measuring it. The strength of the magnetizing current + is regulated by adjusting the position of the sliding contact E upon + the resistance DF. The current increases to a maximum as E approaches + F, and diminishes to almost nothing when E is brought up to D; it can + be completely interrupted by means of the switch H. + + [Illustration: FIG. 9.] + + The specimen upon which an experiment is to be made generally consists + of a wire having a "dimensional ratio" of at least 300 or 400; its + length should be rather less than that of the magnetizing coil, in + order that the field H0, to which it is subjected, may be + approximately uniform from end to end. The wire is supported inside + the glass tube A with its upper pole at the same height as the + magnetometer needle. Various currents are then passed through the + magnetizing coil, the galvanometer readings and the simultaneous + magnetometer deflections being noted. From the former we deduce H0, + and from the latter the corresponding value of I, using the formulae + H0 = 4[pi]in/l and + + d1² H_E + I = ----------------------- × s, (48) + 2n[pi]r² {1 - (d1/d2)³} + + where s is the deflection in scale-divisions, n the distance in + scale-divisions between the scale and the mirror, and r the radius of + the wire. + + [Illustration: FIG. 10.] + + The curve, fig. 10, shows the result of a typical experiment made upon + a piece of soft iron (Ewing, _Phil. Trans._ vol. clxxvi. Plate 59), + the magnetizing field H0 being first gradually increased and then + diminished to zero. When the length of the wire exceeds 400 diameters, + or thereabouts, H0 may generally be considered as equivalent to H, the + actual strength of the field as modified by the magnetization of the + wire; but if greater accuracy is desired, the value of H_i (= NI) may + be found by the help of du Bois's table and subtracted from H0. For a + dimensional ratio of 400, N =0.00028, and therefore H = H0 - 0.00028I. + This correction may be indicated in the diagram by a straight line + drawn from 0 through the point at which the line of I = 1000 + intersects that of H = 0.28 (Rayleigh, Phil. Mag. xxii. 175), the true + value of H for any point on the curve being that measured from the + sloping line instead of from the vertical axis. The effect of the ends + of the wire is, as Ewing remarks, to shear the diagram in the + horizontal direction through the angle which the sloping line makes + with the vertical. + + Since the induction B is equal to H + 4[pi]I, it is easy from the + results of experiments such as that just described to deduce the + relation between B and H; a curve indicating such relation is called a + curve of induction. The general character of curves of magnetization + and of induction will be discussed later. A notable feature in both + classes of curves is that, owing to hysteresis, the ascending and + descending limbs do not coincide, but follow very different courses. + If it is desired to annihilate the hysteretic effects of previous + magnetization and restore the metal to its original condition, it may + be demagnetized by reversals. This is effected by slowly moving the + sliding contact E (fig. 9) from F to D, while at the same time the + commutator K is rapidly worked, a series of alternating currents of + gradually diminishing strength being thus caused to pass through the + magnetizing coil. + +The magnetometric method, except when employed in connexion with +ellipsoids, for which the demagnetizing factors are accurately known, +is generally less satisfactory for the exact determination of induction +or magnetization than the ballistic method. But for much important +experimental work it is better adapted than any other, and is indeed +sometimes the only method possible.[19] + +_Ballistic Methods._--The so-called "ballistic" method of measuring +induction is based upon the fact that a change of the induction through +a closed linear conductor sets up in the conductor an electromotive +force which is proportional to the rate of change. If the conductor +consists of a coil of wire the ends of which are connected with a +suitable galvanometer, the integral electromotive force due to a sudden +increase or decrease of the induction through the coil displaces in the +circuit a quantity of electricity Q = [delta]BnsR, where [delta]B is the +increment or decrement of induction per square centimetre, s is the area +of the coil, n the number of turns of wire, and R the resistance of the +circuit. Under the influence of the transient current, the galvanometer +needle undergoes a momentary deflection, or "throw," which is +proportional to Q, and therefore to [delta]B, and thus, if we know the +deflection produced by the discharge through the galvanometer of a given +quantity of electricity, we have the means of determining the value of +[delta]B. + + The galvanometer which is used for ballistic observations should have + a somewhat heavy needle with a period of vibration of not less than + five seconds, so that the transient current may have ceased before the + swing has well begun; an instrument of the d'Arsonval form is + recommended, not only because it is unaffected by outside magnetic + influence, but also because the moving part can be instantly brought + to rest by means of a short-circuit key, thus effecting a great saving + of time when a series of observations is being made. In practice it is + usual to standardize or "calibrate" the galvanometer by causing a + known change of induction to take place within a standard coil + connected with it, and noting the corresponding deflection on the + galvanometer scale. Let s be the area of a single turn of the standard + coil, n the number of its turns, and r the resistance of the circuit + of which the coil forms part; and let S, N and R be the corresponding + constants for a coil which is to be used in an experiment. Then if a + known change of induction [delta]B_a inside the standard coil is found + to cause a throw of d scale-divisions, any change of induction + [delta]B through the experimental coil will be numerically equal to + the corresponding throw D multiplied by snRB_a/SNrd. For a series of + experiments made with the same coil this fraction is constant, and we + may write [delta]B = kD. Rowland and others have used an earth coil + for calibrating the galvanometer, a known change of induction through + the coil being produced by turning it over in the earth's magnetic + field, but for several reasons it is preferable to employ an electric + current as the source of a known induction. A primary coil of length + l, having n turns, is wound upon a cylinder made of non-conducting and + non-magnetic material, and upon the middle of the primary a secondary + or induction coil is closely fitted. When a current of strength i is + suddenly interrupted in the primary, the increment of induction + through the secondary is sensibly equal to 4[pi]in/l units. All the + data required for standardizing the galvanometer can in this way be + determined with accuracy. + +The ballistic method is largely employed for determining the relation of +induction to magnetizing force in samples of the iron and steel used in +the manufacture of electrical machinery, and especially for the +observation of hysteresis effects. The sample may have the form of a +closed ring, upon which are wound the induction coil and another coil +for taking the magnetizing current; or it may consist of a long straight +rod or wire which can be slipped into a magnetizing coil such as is used +in magnetometric experiments, the induction coil being wound upon the +middle of the wire. With these arrangements there is no demagnetizing +force to be considered, for the ring has not any ends to produce one, +and the force due to the ends of a rod 400 or 500 diameters in length is +quite insensible at the middle portion; H therefore is equal to H0. + + E. Grassot has devised a galvanometer, or "fluxmeter," which greatly + alleviates the tedious operation of taking ballistic readings.[20] The + instrument is of the d'Arsonval type; its coil turns in a strong + uniform field, and is suspended in such a manner that torsion is + practically negligible, the swings of the coil being limited by + damping influences, chiefly electromagnetic. The index therefore + remains almost stationary at the limit of its deflection, and the + deflection is approximately the same whether the change of induction + occurs suddenly or gradually. + +[Illustration: FIG. 11.] + +[Illustration: FIG. 12.] + +[Illustration: FIG. 13.] + +_Induction and Hysteresis Curves._--Some typical induction curves, +copied from a paper by Ewing (_Proc. Inst. C.E._ vol. cxxvi.), are given +in figs. 11, 12 and 13. Fig. 11 shows the relation of B to H in a +specimen which has never before been magnetized. The experiment may be +made in two different ways: (1) the magnetizing current is increased by +a series of sudden steps, each of which produces a ballistic throw, the +value of B after any one throw being proportional to the sum of that and +all the previous throws; (2) the magnetizing current having been brought +to any desired value, is suddenly reversed, and the observed throw taken +as measuring twice the actual induction. Fig. 12 shows the nature of the +course taken by the curve when the magnetizing current, after having +been raised to the value corresponding to the point a, is diminished by +steps until it is nothing, and then gradually increased in the reverse +direction. The downward course of the curve is, owing to hysteresis, +strikingly different from its upward course, and when the magnetizing +force has been reduced to zero, there is still remaining an induction of +7500 units. If the operation is again reversed, the upward course will +be nearly, but not exactly, of the form shown by the line d e a, fig. +13. After a few repetitions of the reversal, the process becomes +strictly cyclic, the upward and downward curves always following with +precision the paths indicated in the figure. In order to establish the +cyclic condition, it is sufficient to apply alternately the greatest +positive and negative forces employed in the test (greatest H = about ±5 +C.G.S. units in the case illustrated in the figure), an operation which +is performed by simply reversing the direction of the maximum +magnetizing current a few times. + +The closed figure a c d e a is variously called a _hysteresis curve_ or +_diagram_ or _loop_. The area [int] H dB enclosed by it represents the +work done in carrying a cubic centimetre of the iron through the +corresponding magnetic cycle; expressed in ergs this work is (1/4)[pi] +[int] H dB.[21] To quote an example given by J. A. Fleming, it requires +about 18 foot-pounds of work to make a complete magnetic cycle in a +cubic foot of wrought iron, strongly magnetized first one way and then +the other, the work so expended taking the form of heat in the mass. + + [Illustration: FIG. 14.] + + Fig. 14 shows diagrammatically a convenient arrangement described by + Ewing (see _Proc. Inst. C.E._ vol. cxxvi., and _Phil. Trans._, 1893A, + p. 987) for carrying out ballistic tests by which either the simple + B-H curve (fig. 11) or the hysteresis curve (figs. 12 and 13) can be + determined. The sample under test is prepared in the form of a ring A, + upon which are wound the induction and the magnetizing coils; the + latter should be wound evenly over the whole ring, though for the sake + of clearness only part of the winding is indicated in the diagram. The + magnetizing current, which is derived from the storage battery B, is + regulated by the adjustable resistance R and measured by the + galvanometer G. The current passes through the rocking key K, which, + when thrown over to the right, places a in contact with c and b with + d, and when thrown over to the left, places a in contact with e and b + with f. When the switch S is closed, K acts simply as a commutator or + current-reverser, but if K is thrown over from right to left while S + is opened, not only is the current reversed, but its strength is at + the same time diminished by the interposition of the adjustable + resistance R2. The induction coil wound upon the ring is connected to + the ballistic galvanometer G2 in series with a large permanent + resistance R3. In the same circuit is also included the induction coil + E, which is used for standardizing the galvanometer; this secondary + coil is represented in the diagram by three turns of wire wound over a + much longer primary coil. The short-circuit key F is kept closed + except when an observation is about to be made; its object is to + arrest the swing of the d'Arsonval galvanometer G2. By means of the + three-way switch C the battery current may be sent either into the + primary of E, for the purpose of calibrating the galvanometer, or into + the magnetizing coil of the ring under test. When it is desired to + obtain a simple curve of induction, such as that in fig. 11, S is kept + permanently closed, and corresponding values of H and B are determined + by one of the two methods already described, the strength of the + battery-current being varied by means of the adjustable resistance R. + When a hysteresis curve is to be obtained, the procedure is as + follows: The current is first adjusted by means of R to such a + strength as will fit it to produce the greatest + and - values of the + magnetizing force which it is intended to apply in the course of the + cycle; then it is reversed several times, and when the range of the + galvanometer throws has become constant, half the extent of an + excursion indicates the induction corresponding to the extreme value + of H, and gives the point a in the curve fig. 12. The reversing key K + having been put over to the left side, the short-circuit key S is + suddenly opened; this inserts the resistance R, which has been + suitably adjusted beforehand, and thus reduces the current and + therefore the magnetizing force to a known value. The galvanometer + throw which results from the change of current measures the amount by + which the induction is reduced, and thus a second point on the curve + is found. In a similar manner, by giving different values to the + resistance R, any desired number of points between a and c in the + curve can be determined. To continue the process, the key K is turned + over to the right-hand side, and then, while S is open, is turned + back, thereby not only reversing the direction of the current, but + diminishing its strength by an amount depending upon the previous + adjustment of R2. In this way points can be found lying anywhere + between c and d of fig. 12, and the determination of the downward limb + of the curve is therefore completed. As the return curve, shown in + fig. 13, is merely an inverted copy of the other, no separate + determination of it is necessary. + +[Illustration: FIG. 15.] + +In fig. 15 (J. A. Fleming, _Magnets and Electric Currents_, p. 193) are +shown three very different types of hysteresis curves, characteristic of +the special qualities of the metals from which they were respectively +obtained. The distinguishing feature of the first is the steepness of +its outlines; this indicates that the induction increases rapidly in +relation to the magnetic force, and hence the metal is well suited for +the construction of dynamo magnets. The second has a very small area, +showing that the work done in reversing the magnetization is small; the +metal is therefore adapted for use in alternating current transformers. +On the other hand, the form of the third curve, with its large +intercepts on the axes of H and B, denotes that the specimen to which it +relates possesses both retentiveness and coercive force in a high +degree; such a metal would be chosen for making good permanent magnets. + + Several arrangements have been devised for determining hysteresis more + easily and expeditiously than is possible by the ballistic method. The + best known is J. A. Ewing's hysteresis-tester,[22] which is specially + intended for testing the sheet iron used in transformers. The sample, + arranged as a bundle of rectangular strips, is caused to rotate about + a central horizontal axis between the poles of an upright C-shaped + magnet, which is supported near its middle upon knife-edges in such a + manner that it can oscillate about an axis in a line with that about + which the specimen rotates; the lower side of the magnet is weighted, + to give it some stability. When the specimen rotates, the magnet is + deflected from its upright position by an amount which depends upon + the work done in a single complete rotation, and therefore upon the + hysteresis. The deflection is indicated by a pointer upon a graduated + scale, the readings being interpreted by comparison with two standard + specimens supplied with the instrument. G. F. Searle and T. G. + Bedford[23] have introduced the method of measuring hysteresis by + means of an electro-dynamometer used ballistically. The fixed and + suspended coils of the dynamometer are respectively connected in + series with the magnetizing solenoid and with a secondary wound upon + the specimen. When the magnetizing current is twice reversed, so as to + complete a cycle, the sum of the two deflections, multiplied by a + factor depending upon the sectional area of the specimen and upon the + constants of the apparatus, gives the hysteresis for a complete cycle + in ergs per cubic centimetre. For specimens of large sectional area it + is necessary to apply corrections in respect of the energy dissipated + by eddy currents and in heating the secondary circuit. The method has + been employed by the authors themselves in studying the effects of + tension, torsion and circular magnetization, while R. L. Wills[24] has + made successful use of it in a research on the effects of temperature, + a matter of great industrial importance. + + C. P. Steinmetz (_Electrician_, 1891, 26, p. 261; 1892, 28, pp. 384, + 408, 425) has called attention to a simple relation which appears to + exist between the amount of energy dissipated in carrying a piece of + iron or steel through a magnetic cycle and the limiting value of the + induction reached in the cycle. Denoting by W the work in ergs done + upon a cubic centimetre of the metal ( = 1/4[pi] [int] H dB or [int] H + dI), he finds W = [eta]B^(1.6) approximately, where [eta] is a number, + called the hysteretic constant, depending upon the metal, and B is the + maximum induction. The value of the constant [eta] ranges in different + metals from about 0.001 to 0.04; in soft iron and steel it is said to + be generally not far from 0.002. Steinmetz's formula may be tested by + taking a series of hysteresis curves between different limits of B, + measuring their areas by a planimeter, and plotting the logarithms of + these divided by 4[pi] as ordinates against logarithms of the + corresponding maximum values of B as abscissae. The curve thus + constructed should be a straight line inclined to the horizontal axis + at an angle [theta], the tangent of which is 1.6. Ewing and H. G. + Klaassen (_Phil. Trans._, 1893, 184, 1017) have in this manner + examined how nearly and within what range a formula of the type W = + [eta]B^[epsilon] may be taken to represent the facts. The results of + an example which they quote in detail may be briefly summarized as + follows:-- + + +-----------------+------------+-----------------+-----------+ + | | Hysteretic | Index. | Degrees. | + | Limits of B. | Constant. | [epsilon] | [theta] | + | | [eta] | (= tan [theta]) | | + +-----------------+------------+-----------------+-----------+ + | 200 to 500 | ... | 1.9 | 62.25 | + | 500 to 1,000 | ... | 1.68 | 59.25 | + | 1,000 to 2,000 | ... | 1.55 | 57.25 | + | 2,000 to 8,000 | 0.01 | 1.475 | 55.75 | + | 8,000 to 14,000 | 0.00134 | 1.70 | 59.50 | + +-----------------+------------+-----------------+-----------+ + + It is remarked by the experimenters that the value of the index + [epsilon] is by no means constant, but changes in correspondence with + the successive well-marked stages in the process of magnetization. But + though a formula of this type has no physical significance, and cannot + be accepted as an equation to the actual curve of W and B, it is, + nevertheless, the case that by making the index [epsilon] = 1.6, and + assigning a suitable value to [eta], a formula may be obtained giving + an approximation to the truth which is sufficiently close for the + ordinary purposes of electrical engineers, especially when the + limiting value of B is neither very great nor very small. Alexander + Siemens (_Journ. Inst. Eng._, 1894, 23, 229) states that in the + hundreds of comparisons of test pieces which have been made at the + works of his firm, Steinmetz's law has been found to be practically + correct.[25] An interesting collection of W-B curves embodying the + results of actual experiments by Ewing and Klaassen on different + specimens of metal is given in fig. 16. It has been shown by Kennelly + (_Electrician_, 1892, 28, 666) that Steinmetz's formula gives + approximately correct results in the case of nickel. Working with two + different specimens, he found that the hysteresis loss in ergs per + cubic centimetre (W) was fairly represented by 0.00125B^(1.6) and + 0.00101B^(1.6) respectively, the maximum induction ranging from about + 300 to 3000. The applicability of the law to cobalt has been + investigated by Fleming (_Phil. Mag._, 1899, 48, 271), who used a ring + of cast cobalt containing about 96% of the pure metal. The logarithmic + curves which accompany his paper demonstrate that within wide ranges + of maximum induction W = 0.01B^(1.6) = 0.527I^(1.62) very nearly. + Fleming rightly regards it as not a little curious that for materials + differing so much as this cast cobalt and soft annealed iron the + hysteretic exponent should in both cases be so near to 1.6. After + pointing out that, since the magnetization of the metal is the + quantity really concerned, W is more appropriately expressed in terms + of I, the magnetic moment per unit of volume, than of B, he suggests + an experiment to determine whether the mechanical work required to + effect the complete magnetic reversal of a crowd of small compass + needles (representative of magnetic molecules) is proportional to the + 1.6th power of the aggregate maximum magnetic moment before or after + completion of the cycle. + + [Illustration: FIG. 16. + + a, Fine steel wire 0.257 mm. diam. + b, Fine iron wire 0.34 mm. diam. + c, Fine iron wire 0.2475 mm. diam. + d, Thin sheet iron 0.47 mm. thick. + e, Iron wire 0.602 mm. diam. + f, Iron wire 0.975 mm. diam. + g, Sheet iron 1.95 mm. thick. + h, Thin sheet iron 0.367 mm. thick. + i. Very soft iron wire.] + + The experiments of K. Honda and S. Shimizu[26] indicate that + Steinmetz's formula holds for nickel and annealed cobalt up to B = + 3000, for cast cobalt and tungsten steel up to B = 8000, and for + Swedish iron up to B = 18,000, the range being in all cases extended + at the temperature of liquid air. + +[Illustration: FIG. 17.] + +The diagram, fig. 17, contains examples of ascending induction curves +characteristic of wrought iron, cast iron, cobalt and nickel. These are +to be regarded merely as typical specimens, for the details of a curve +depend largely upon the physical condition and purity of the material; +but they show at a glance how far the several metals differ from and +resemble one another as regards their magnetic properties. Curves of +magnetization (which express the relation of I to H) have a close +resemblance to those of induction; and, indeed, since B = H + 4[pi]I, +and 4[pi]I (except in extreme fields) greatly exceeds H in numerical +value, we may generally, without serious error, put I = B/4[pi], and +transform curves of induction into curves of magnetization by merely +altering the scale to which the ordinates are referred. A scale for the +approximate transformation for the curves in fig. 12 is given at the +right-hand side of the diagram, the greatest error introduced by +neglecting H/4[pi] not exceeding 0.6%. A study of such curves as these +reveals the fact that there are three distinct stages in the process of +magnetization. During the first stage, when the magnetizing force is +small, the magnetization (or the induction) increases rather slowly with +increasing force; this is well shown by the nickel curve in the diagram, +but the effect would be no less conspicuous in the iron curve if the +abscissae were plotted to a larger scale. During the second stage small +increments of magnetizing force are attended by relatively large +increments of magnetization, as is indicated by the steep ascent of the +curve. Then the curve bends over, forming what is often called a "knee," +and a third stage is entered upon, during which a considerable increase +of magnetizing force has little further effect upon the magnetization. +When in this condition the metal is popularly said to be "saturated." +Under increasing magnetizing forces, greatly exceeding those comprised +within the limits of the diagram, the magnetization does practically +reach a limit, the maximum value being attained with a magnetizing force +of less than 2000 for wrought iron and nickel, and less than 4000 for +cast iron and cobalt. The induction, however, continues to increase +indefinitely, though very slowly. These observations have an important +bearing upon the molecular theory of magnetism, which will be referred +to later. + +The magnetic quality of a sample of iron depends very largely upon the +purity and physical condition of the metal. The presence of ordinary +impurities usually tends to diminish the permeability, though, as will +appear later, the addition of small quantities of certain other +substances is sometimes advantageous. A very pure form of iron, which +from the method of its manufacture is called "steel," is now extensively +used for the construction of dynamo magnets; this metal sometimes +contains not more than 0.3% of foreign substances, including carbon, and +is magnetically superior to the best commercial wrought iron. The +results of some comparative tests published by Ewing (_Proc. Inst. +C.E._, 1896) are given in the accompanying table. Those in the second +column are quoted from a paper by F. Lydall and A. W. Pocklington +(_Proc. Roy. Soc._, 1892, 52, 228) and relate to an exceptional specimen +containing nearly 99.9% of the pure metal. + + +----------+-----------------------------------------+ + | | Magnetic Induction. | + | Magnetic +--------+----------+----------+----------+ + | Force. | Pure | Low Moor | Steel | Steel | + | | Iron. | Iron. | Forging. | Casting. | + +----------+--------+----------+----------+----------+ + | 5 | 12,700 | 10,900 | 12,300 | 9,600 | + | 10 | 14,980 | 13,120 | 14,920 | 13,050 | + | 15 | 15,800 | 14,010 | 15,800 | 14,600 | + | 20 | 16,300 | 14,580 | 16,280 | 15,310 | + | 30 | 16,950 | 15,280 | 16,810 | 16,000 | + | 40 | 17,350 | 15,760 | 17,190 | 16,510 | + | 50 | .. | 16,060 | 17,500 | 16,900 | + | 60 | .. | 16,340 | 17,750 | 17,180 | + | 70 | .. | 16,580 | 17,970 | 17,400 | + | 80 | .. | 16,800 | 18,180 | 17,620 | + | 90 | .. | 17,000 | 18,390 | 17,830 | + | 100 | .. | 17,200 | 18,600 | 18,030 | + +----------+--------+----------+----------+----------+ + +To secure the highest possible permeability it is essential that the +iron should be softened by careful annealing. When it is mechanically +hardened by hammering, rolling or wire-drawing its permeability may be +greatly diminished, especially under a moderate magnetizing force. An +experiment by Ewing showed that by the operation of stretching an +annealed iron wire beyond the limits of elasticity the permeability +under a magnetizing force of about 3 units was reduced by as much as +75%. Ewing has also studied the effect of vibration in conferring upon +iron an apparent or spurious permeability of high value; this effort +also is most conspicuous when the magnetizing force is weak. The +permeability of a soft iron wire, which was tapped while subjected to a +very small magnetizing force, rose to the enormous value of about 80,000 +(_Magnetic Induction_, § 85). It follows that in testing iron for +magnetic quality the greatest care must be exercised to guard the +specimen against any accidental vibration. + +Low hysteresis is the chief requisite for iron which is to be used for +transformer cores, and it does not necessarily accompany high +permeability. In response to the demand, manufacturers have succeeded in +producing transformer plate in which the loss of energy due to +hysteresis is exceedingly small. Tests of a sample supplied by Messrs. +Sankey were found by Ewing to give the following results, which, +however, are regarded as being unusually favourable. In a valuable +collection of magnetic data (_Proc. Inst. C.E._, cxxvi.) H. F. Parshall +quotes tests of six samples of iron, described as of good quality, which +showed an average hysteresis loss of 3070 ergs per c.cm. per cycle at an +induction of 8000, being 1.6 times the loss shown by Ewing's specimen at +the same induction. + + +------------+----------------+-----------------+ + | Limits of | Ergs per c.cm. | Watts per lb. | + | Induction. | per cycle. | Frequency, 100. | + +------------+----------------+-----------------+ + | 2000 | 220 | 0.129 | + | 3000 | 410 | 0.242 | + | 4000 | 640 | 0.376 | + | 5000 | 910 | 0.535 | + | 6000 | 1200 | 0.710 | + | 7000 | 1520 | 0.890 | + | 8000 | 1900 | 1.120 | + | 9000 | 2310 | 1.360 | + +------------+----------------+-----------------+ + +The standard induction in reference to determinations of hysteresis is +generally taken as 2500, while the loss is expressed in watts per lb. at +a frequency of 100 double reversals, or cycles, per second. In many +experiments, however, different inductions and frequencies are employed, +and the hysteresis-loss is often expressed as ergs per cubic centimetre +per cycle and sometimes as horse-power per ton. In order to save +arithmetical labour it is convenient to be provided with conversion +factors for reducing variously expressed results to the standard form. +The rate at which energy is lost being proportional to the frequency, it +is obvious that the loss at frequency 100 may be deduced from that at +any other frequency n by simply multiplying by 100/n. Taking the density +of iron to be 7.7, the factor for reducing the loss in ergs per c.cm. to +watts per lb. with a frequency of 100 is 0.000589 (Ewing). Since 1 +horse-power = 746 watts, and 1 ton = 2240 lb., the factor for reducing +horse-power per ton to watts per lb. is 746/2240, or just 1/3. The loss +for any induction B within the range for which Steinmetz's law holds may +be converted into that for the standard induction 2500 by dividing it by +B^(1.6)/2500^(1.6). The values of this ratio for different values of B, +as given by Fleming (_Phil. Mag._, 1897), are contained in the second +column of the annexed table. The third column shows the relative amount +of hysteresis deduced by Ewing as a general mean from actual tests of +many samples (_Journ. Inst. Elec. Eng._, 1895). Incidentally, these two +columns furnish an undesigned test of the accuracy of Steinmetz's law: +the greatest difference is little more than 1%. + + +-----------+------------+-------------+ + | Induction | B^(1.6) | Observed | + | B. | ---------- | relative | + | | 2500^(1.6) | Hysteresis. | + +-----------+------------+-------------+ + | 2000 | 0.700 | 0.702 | + | 2500 | 1.000 | 1.000 | + | 3000 | 1.338 | 1.340 | + | 4000 | 2.118 | 2.128 | + | 5000 | 3.031 | 3.000 | + | 6000 | 4.058 | 4.022 | + | 7000 | 5.193 | 5.129 | + | 8000 | 6.430 | 6.384 | + +-----------+------------+-------------+ + +_Curves of Permeability and Susceptibility._--The relations of µ (= B/H) +to B, and of [kappa] (= I/H) to I may be instructively exhibited by +means of curves, a method first employed by H. A. Rowland.[27] The +dotted curve for µ and B in fig. 18 is copied from Rowland's paper. The +actual experiment to which it relates was carried only as the point +marked X, corresponding to a magnetizing force of 65, and an induction +of nearly 17,000. Rowland, believing that the curve would continue to +fall in a straight line meeting the horizontal axis, inferred that the +induction corresponding to the point B--about 17,500--was the highest +that could be produced by any magnetizing force, however great. It has, +however, been shown that, if the magnetizing force is carried far +enough, the curve always becomes convex to the axis instead of meeting +it. The full line shows the result of an experiment in which the +magnetizing force was carried up to 585,[28] but though the force was +thus increased ninefold, the induction only reached 19,800, and the +ultimate value of the permeability was still as much as 33.9. + +[Illustration: FIG. 18.] + +[Illustration: FIG. 19.] + +_Ballistic Method with Yoke._--J. Hopkinson (_Phil. Trans._, 1885, 176, +455) introduced a modification of the usual ballistic arrangement which +presents the following advantages; (1) very considerable magnetizing +forces can be applied with ordinary means; (2) the samples to be tested, +having the form of cylindrical bars, are more easily prepared than rings +or wires; (3) the actual induction at any time can be measured, and not +only changes of induction. On the other hand, a very high degree of +accuracy is not claimed for the results. Fig. 19 shows the apparatus by +which the ends of the bar are prevented from exerting any material +demagnetizing force, while the permeance of the magnetic circuit is at +the same time increased. A A, called the "yoke," is a block of annealed +wrought iron about 18 in. long, 6½ in. wide and 2 in. thick, through +which is cut a rectangular opening to receive the two magnetizing coils +B B. The test bar C C, which slides through holes bored in the yoke, is +divided near the middle into two parts, the ends which come into contact +being faced true and square. Between the magnetizing coils is a small +induction coil D, which is connected with a ballistic galvanometer. The +induction coil is carried upon the end of one portion of the test bar, +and when this portion is suddenly drawn back the coil slips off and is +pulled out of the field by an india-rubber spring. This causes a +ballistic throw proportional to the induction through the bar at the +moment when the two portions were separated. With such an arrangement it +is possible to submit the sample to any series of magnetic forces, and +to measure its magnetic state at the end. The uncertainty with which the +results are affected depends chiefly upon the imperfect contact between +the bar and the yoke and also between the ends of the divided bar. It is +probable that Hopkinson did not attach sufficient importance to the +demagnetizing action of the cut (cf. Ewing, _Phil. Mag._, Sept. 1888, p. +274), and that the values which he assigned to H are consequently +somewhat too high. He applied his method with good effect, however, in +testing a large number of commercial specimens of iron and steel, the +magnetic constants of which are given in a table accompanying his paper. +When it is not required to determine the residual magnetization there is +no necessity to divide the sample bar, and ballistic tests may be made +in the ordinary way--by steps or by reversals--the source of error due +to the transverse cut thus being avoided. Ewing (_Magnetic Induction_, § +194) has devised an arrangement in which two similar test bars are +placed side by side; each bar is surrounded by a magnetizing coil, the +two coils being connected to give opposite directions of magnetization, +and each pair of ends is connected by a short massive block of soft iron +having holes bored through it to fit the bars, which are clamped in +position by set-screws. Induction coils are wound on the middle parts of +both bars, and are connected in series. With this arrangement it is +possible to find the actual value of the magnetizing force, corrected +for the effects of joints and other sources of error. Two sets of +observations are taken, one when the blocks are fixed at the ends of the +bars, and another when they are nearer together, the clear length of the +bars between them and of the magnetizing coils being reduced to +one-half. If H1 and H2 be the values of 4[pi]in/l and 4[pi]i´[(n/2) / +(l/2)] for the same induction B, it can be shown that the true +magnetizing force is H = H1 - (H2 - H1). The method, though tedious in +operation, is very accurate, and is largely employed for determining the +magnetic quality of bars intended to serve as standards. + +_Traction Methods._--The induction of the magnetization may be measured +by observing the force required to draw apart the two portions of a +divided rod or ring when held together by their mutual attraction. If a +transverse cut is made through a bar whose magnetization is I and the +two ends are placed in contact, it can be shown that this force is +2[pi]I² dynes per unit of area (Mascart and Joubert, _Electricity and +Magnetism_, § 322); and if the magnetization of the bar is due to an +external field H produced by a magnetizing coil or otherwise, there is +an additional force equal to HI. Thus the whole force, when the two +portions of the bar are surrounded by a loosely-fitting magnetizing +coil, is + + F = 2[pi]I² + HI + +expressed as dynes per square centimetre. If each portion of the bar has +an independent magnetizing coil wound tightly upon it, we have further +to take into account the force due to the mutual action of the two +magnetizing coils, which assists the forces already considered. This is +equal to H²8[pi] per unit of sectional area. In the case supposed +therefore the total force per square centimetre is + + H² + F = 2[pi]I² + HI + ----- + 8[pi] + + (4[pi]I + H)³ + = ------------- + 8[pi] + + B² + = -----. + 8[pi] + +The equation F = B²/8[pi] is often said to express "Maxwell's law of +magnetic traction" (Maxwell, _Electricity and Magnetism_, §§ 642-646). +It is, of course, true for permanent magnets, where H = 0, since then F += 2[pi]I²; but if the magnetization is due to electric currents, the +formula is only applicable in the special case when the mutual action of +the two magnets upon one another is supplemented by the electromagnetic +attraction between separate magnetizing coils rigidly attached to +them.[29] + +The traction method was first employed by S. Bidwell (_Proc. Roy. Soc._, +1886, 40, 486), who in 1886 published an account of some experiments in +which the relation of magnetization to magnetic field was deduced from +observations of the force in grammes weight which just sufficed to tear +asunder the two halves of a divided ring electromagnet when known +currents were passing through the coils. He made use of the expression + + F = Wg = 2[pi]I² + HI, + +where W is the weight in grammes per square centimetre of sectional +area, and g is the intensity of gravity which was taken as 981. The term +for the attraction between the coils was omitted as negligibly small +(see _Phil. Mag._, 1890, 29, 440). The values assigned to H were +calculated from H = 2ni/r, and ranged from 3.9 to 585, but inasmuch as +no account was taken of any demagnetizing action which might be due to +the two transverse cuts, it is probable that they are somewhat too high. +The results, nevertheless, agree very well with those for annealed +wrought iron obtained by other methods. Below is given a selection from +Bidwell's tables, showing corresponding values of magnetizing force, +weight supported, magnetization, induction, susceptibility and +permeability:-- + + +--------+---------+-------+--------+----------+--------+ + | H. | W. | I. | B. | [kappa]. | µ. | + +--------+---------+-------+--------+----------+--------+ + | 3.9 | 2,210 | 587 | 7,390 | 151.0 | 1889.1 | + | 5.7 | 3,460 | 735 | 9,240 | 128.9 | 1621.3 | + | 10.3 | 5,400 | 918 | 11,550 | 89.1 | 1121.4 | + | 22.2 | 8,440 | 1147 | 14,450 | 51.7 | 650.9 | + | 40 | 9,680 | 1226 | 15,460 | 30.7 | 386.4 | + | 115 | 12,170 | 1370 | 17,330 | 11.9 | 150.7 | + | 208 | 13,810 | 1452 | 18,470 | 7.0 | 88.8 | + | 362 | 14,740 | 1489 | 19,080 | 4.1 | 52.7 | + | 465 | 15,275 | 1508 | 19,420 | 3.2 | 41.8 | + | 585 | 15,905 | 1530 | 19,820 | 2.6 | 33.9 | + +--------+---------+-------+--------+----------+--------+ + +[Illustration: FIG. 20.] + +A few months later R. H. M. Bosanquet (_Phil. Mag._, 1886, 22, 535) +experimented on the relation of tractive force to magnetic induction. +Instead of a divided ring he employed a divided straight bar, each half +of which was provided with a magnetizing coil. The joint was surrounded +by an induction coil connected with a ballistic galvanometer, an +arrangement which enabled him to make an independent measurement of the +induction at the moment when the two portions of the bar were separated. +He showed that there was, on the whole, a fair agreement between the +values determined ballistically and those given by the formula B = +[root](8[pi]F). The greatest weight supported in the experiments was +14,600 grammes per square cm., and the corresponding induction 18,500 +units. Taylor Jones subsequently found a good agreement between the +theoretical and the observed values of the tractive force in fields +ranging up to very high intensities (_Phil. Mag._, 1895, 39, 254, and +1896, 41, 153). + + _Permeameters._--Several instruments in which the traction method is + applied have been devised for the rapid measurement of induction or of + magnetization in commercial samples of iron and steel. The earliest of + these is S. P. Thompson's _permeameter_ (_Journ. Sci. Arts_, 1890, 38, + 885), which consists of a rectangular block of iron shaped like + Hopkinson's yoke, and slotted out in the same way to receive a + magnetizing coil (fig. 20); the block is bored through at the upper + end only, and its inner face opposite the hole is made quite flat and + smooth. The sample has the form of a thin rod, one end of which is + faced true; it is slipped into the magnetizing coil from above, and + when the current is turned on its smooth end adheres tightly to the + surface of the yoke. The force required to detach it is measured by a + registering spring balance, which is clamped to the upper end of the + rod, and thence the induction or the magnetization is deduced by + applying the formula + + (B - H)²/8[pi] = 2[pi]I² = Pg/S, + + where P is the pull in grammes weight, S the sectional area of the rod + in square cm., and g = 981. If the pull is measured in pounds and the + area in square inches, the formula may be written B = 1317 × + [root](P/S) + H. The instrument exhibited by Thompson would, without + undue heating, take a current of 30 amperes, which was sufficient to + produce a magnetizing force of 1000 units. A testing apparatus of a + similar type devised by Gisbert Kapp (_Journ. Inst. Elec. Eng._ xxiii. + 199) differs only in a few details from Thompson's permeameter. Ewing + has described an arrangement in which the test bar has a soft-iron + pole piece clamped to each of its ends; the pole pieces are joined by + a long well-fitting block of iron, which is placed upon them (like the + "keeper" of a magnet), and the induction is measured by the force + required to detach the block. In all such measurements a correction + should be made in respect of the demagnetizing force due to the joint, + and unless the fit is very accurate the demagnetizing action will be + variable. In the _magnetic balance_ of du Bois (_Magnetic Circuit_, p. + 346) the uncertainty arising from the presence of a joint is avoided, + the force measured being that exerted between two pieces of iron + separated from each other by a narrow air-gap of known width. The + instrument is represented diagrammatically in fig. 21. The test-piece + A, surrounded by a magnetizing coil, is clamped between two soft-iron + blocks B, B´. Y Y´ is a soft iron yoke, which rocks upon knife-edges K + and constitutes the beam of the balance. The yoke has two projecting + pieces C, C´ at unequal distances from the knife-edges, and separated + from the blocks B, B´ by narrow air-gaps. The play of the beam is + limited by a stop S and a screw R, the latter being so adjusted that + when the end Y of the beam is held down the two air-gaps are of equal + width. W is a weight capable of sliding from end to end of the yoke + along a graduated scale. When there is no magnetization, the yoke is + in equilibrium; but as soon as the current is turned on the block C is + drawn downwards as far as the screw R will allow, for, though the + attractive forces F between B and C and between B´ and C´ are equal, + the former has a greater moment. The weight W is moved along the scale + until the yoke just tilts over upon the stop S; the distance of W from + its zero position is then, as can easily be shown, proportional to F, + and therefore to B², and approximately to I². The scale is graduated + in such a manner that by multiplying the reading by a simple factor + (generally 10 or 2) the absolute value of the magnetization is + obtained. The actual magnetizing force H is of course less than that + due to the coil; the corrections required are effected automatically + by the use of a set of demagnetization lines drawn on a sheet of + celluloid which is supplied with the instrument. The celluloid sheet + is laid upon the squared paper, and in plotting a curve horizontal + distances are reckoned from the proper demagnetization line instead of + from the vertical axis. An improved but somewhat more complex form of + the instrument is described in _Ann. d. Phys._, 1900, 2, 317. + + [Illustration: FIG. 21.] + + In Ewing's _magnetic balance_ (_Journ. Inst. Elec. Eng._ 1898, 27, + 526), the value of the magnetic induction corresponding to a single + stated magnetizing force is directly read off on a divided scale. The + specimen, which has the form of a turned rod, 4 in. long and ¼ in. in + diameter, is laid across the poles of a horseshoe electromagnet, + excited by a current of such strength as to produce in the rod a + magnetizing force H = 20. One pole has a V-shaped notch for the rod to + rest in; the surface of the other is slightly rounded, forming a + portion of a cylinder, the axis of which is perpendicular to the + direction of the length of the rod. The rod touches this pole at a + single point, and is pulled away from it by the action of a lever, the + long arm of which is graduated and carries a sliding weight. The + position of the weight at the moment when contact is broken indicates + the induction in the rod. The standard force H = 20 was selected as + being sufficiently low to distinguish between good and bad specimens, + and at the same time sufficiently high to make the order of merit the + same as it would be under stronger forces. + + _Permeability Bridges._--Several pieces of apparatus have been + invented for comparing the magnetic quality of a sample with that of a + standard iron rod by a zero method, such as is employed in the + comparison of electrical resistances by the Wheatstone bridge. An + excellent instrument of the class is Ewing's _permeability bridge_. + The standard rod and the test specimen, which must be of the same + dimensions, are placed side by side within two magnetizing coils, and + each pair of adjacent ends is joined by a short rectangular block or + "yoke" of soft iron. An iron bar shaped like an inverted L projects + upwards from each of the yokes, the horizontal portions of the bars + being parallel to the rods, and nearly meeting at a height of about 8 + in. above them (thus [symbol]). A compass needle placed in the gap + serves to detect any flow of induction that may exist between the bent + bars. For simplicity of calculation, the clear length of each rod + between the yokes is made 12.56 (= 4[pi]) centimetres, while the coil + surrounding the standard bar contains 100 turns; hence the magnetizing + force due to a current of n amperes will be 10n C.G.S. units. The + effective number of turns in the coil surrounding the test rod can be + varied by means of three dial switches (for hundreds, tens and units), + which also introduce compensating resistances as the number of + effective turns in the coil is reduced, thus keeping the total + resistance of the circuit constant. The two coils are connected in + series, the same current passing through both. Suppose the switches to + be adjusted so that the effective number of turns in the variable coil + is 100; the magnetizing forces in the two coils will then be equal, + and if the test rod is of the same quality as the standard, the flow + of induction will be confined entirely to the iron circuit, the two + yokes will be at the same magnetic potential, and the compass needle + will not be affected. If, however, the permeability of the test rod + differs from that of the standard, the number of lines of induction + flowing in opposite directions through the two rods will differ, and + the excess will flow from one yoke to the other, partly through the + air, and partly along the path provided by the bent bars, deflecting + the compass needle. But a balance may still be obtained by altering + the effective number of turns in the test coil, and thus increasing or + decreasing the magnetizing force acting on the test rod, till the + induction in the two rods is the same, a condition which is fulfilled + when reversal of the current has no effect on the compass needle. Let + m be the number of turns in use, and H1 and H2 the magnetizing forces + which produce the same induction B in the test and the standard rods + respectively; then H1 = H2 × m/100. The value of B which corresponds + to H2m/100 can be found from the (B, H) curve for the standard, which + is assumed to have been determined; and this same value corresponds to + the force H in the case of the test bar. Thus any desired number of + corresponding values of H and B can be easily and quickly found. + +_Measurement of Field Strength. Exploring Coil._--Since in air B = H, +the ballistic method of measuring induction described above is also +available for determining the strength of a magnetic field, and is more +often employed than any other. A small coil of fine wire, connected in +series with a ballistic galvanometer, is placed in the field, with its +windings perpendicular to the lines of force, and then suddenly reversed +or withdrawn from the field, the integral electromotive force being +twice as great in the first case as in the second. The strength of the +field is proportional to the swing of the galvanometer-needle, and, when +the galvanometer is calibrated, can be expressed in C.G.S. units. +Convenient arrangements have been introduced whereby the coil is +reversed or withdrawn from the field by the action of a spring. + +_Bismuth Resistance._--The fact, which will be referred to later, that +the electrical resistance of bismuth is very greatly affected by a +magnetic field has been applied in the construction of apparatus for +measuring field intensity. A little instrument, supplied by Hartmann and +Braun, contains a short length of fine bismuth wire wound into a flat +double spiral, half an inch or thereabouts in diameter, and attached to +a long ebonite handle. Unfortunately the effects of magnetization upon +the specific resistance of bismuth vary enormously with changes of +temperature; it is therefore necessary to take two readings of the +resistance, one when the spiral is in the magnetic field, the other when +it is outside. + +_Electric Circuit._--If a coil of insulated wire is suspended so that it +is in stable equilibrium when its plane is parallel to the direction of +a magnetic field, the transmission of a known electric current through +the coil will cause it to be deflected through an angle which is a +function of the field intensity. + + One of the neatest applications of this principle is that described by + Edser and Stansfield (_Phil. Mag._, 1893, 34, 186), and used by them + to test the stray fields of dynamos. An oblong coil about an inch in + length is suspended from each end by thin strips of rolled German + silver wire, one of which is connected with a spiral spring for + regulating the tension, the other being attached to a torsion-head. + Inside the torsion-head is a commutator for automatically reversing + the current, so that readings may be taken on each side of zero, and + the arrangement is such that when the torsion-head is exactly at zero + the current is interrupted. To take a reading the torsion-head is + turned until an aluminium pointer attached to the coil is brought to + the zero position on a small scale; the strength of the field is then + proportional to the angular torsion. The small current required is + supplied to the coil from a single dry cell. The advantages of + portability, very considerable range (from H = 1 upwards), and fair + accuracy are claimed for the instrument. + +_Polarized Light._--The intensity of a field may be measured by the +rotation of the plane of polarization of light passing in the direction +of the magnetic force through a transparent substance. If the field is +uniform, H = [theta]/[omega]d, where [theta] is the rotation, d the +thickness of the substance arranged as a plate at right angles to the +direction of the field, and [omega] Verdet's constant for the substance. + + For the practical measurement of field intensity du Bois has used + plates of the densest Jena flint glass. These are preferably made + slightly wedge-shape, to avoid the inconvenience resulting from + multiple internal reflections, and they must necessarily be rather + thin, so that double refractions due to internal strain may not exert + a disturbing influence. Since Verdet's constant is somewhat uncertain + for different batches of glass even of the same quality, each plate + should be standardized in a field of known intensity. As the source of + monochromatic light a bright sodium burner is used, and the rotation, + which is exactly proportional to H, is measured by an accurate + polarimeter. Such a plate about 1 mm. in thickness is said to be + adapted for measuring fields of the order of 1000 units. A part of one + surface of the plate may be silvered, so that the polarized ray, after + having once traversed the glass, is reflected back again; the rotation + is thus doubled, and moreover, the arrangement is, for certain + experiments, more convenient than the other. + + +4. MAGNETIZATION IN STRONG FIELDS + +_Fields due to Coils._--The most generally convenient arrangement for +producing such magnetic fields as are required for experimental +purposes is undoubtedly a coil of wire through which an electric current +can be caused to flow. The field due to a coil can be made as nearly +uniform as we please throughout a considerable space; its intensity, +when the constants of the coil are known, can be calculated with ease +and certainty and may be varied at will through wide ranges, while the +apparatus required is of the simplest character and can be readily +constructed to suit special purposes. But when exceptionally strong +fields are desired, the use of a coil is limited by the heating effect +of the magnetizing current, the quantity of heat generated per unit of +time in a coil of given dimensions increasing as the square of the +magnetic field produced in its interior. In experiments on magnetic +strains carried out by H. Nagaoka and K. Honda (_Phil. Mag._, 1900, 49, +329) the intensity of the highest field reached in the interior of a +coil was 2200 units; this is probably the strongest field produced by a +coil which has hitherto been employed in experimental work. In 1890 some +experiments in which a coil was used were made by du Bois (_Phil. Mag._, +1890, 29, 253, 293) on the magnetization of iron, nickel, and cobalt +under forces ranging from about 100 to 1250 units. Since the +demagnetizing factor was 0.052, the strongest field due to the coil was +about 1340; but though arrangements were provided for cooling the +apparatus by means of ice, great difficulty was experienced owing to +heating. Du Bois's results, which, as given in his papers, show the +relation of H to the magnetic moment per unit of mass, have been reduced +by Ewing to the usual form, and are indicated in fig. 22, the earlier +portions of the curves being sketched in from other data. + +[Illustration: FIG. 22.] + +_Fields due to Electromagnets._--The problem of determining the +magnetization of iron and other metals in the strong fields formed +between the poles of an electromagnet was first attacked by J. A. Ewing +and W. Low. An account of their preliminary experiments by what they +call the _isthmus method_ was published in 1887 (_Proc. Roy. Soc._ 42, +200), and in the following year they described a more complete and +perfect series (_Phil. Trans._, 1889, 180, 221). + +[Illustration: FIG. 23.] + + The sample to be inserted between the magnet poles was prepared in the + form of a bobbin resembling an ordinary cotton reel, with a short + narrow neck (constituting the "isthmus") and conical ends. Upon the + central neck was wound a coil consisting of one or two layers of very + fine wire, which was connected with a ballistic galvanometer for + measuring the induction in the iron; outside this coil, and separated + from it by a small and accurately determined distance, a second coil + was wound, serving to measure the induction in the iron, together with + that in a small space surrounding it. The difference of the ballastic + throws taken with the two coils measured the intensity of the field in + the space around the iron, and it also enabled a correction to be made + for the non-ferrous space between the iron neck and the centre of the + thickness of the inner coil. The pole pieces of the electromagnet (see + fig. 23) were furnished with a pair of truncated cones _b b_, of soft + iron forming an extension of the conical ends of the bobbin c. The + most suitable form for the pole faces is investigated in the paper, + and the conclusion arrived at is that to produce the greatest + concentration of force upon the central neck, the cones should have a + common vertex in the middle of the neck with a semi-vertical angle of + 54° 44´, while the condition for a uniform field is satisfied when the + cones have a semi-vertical angle of 39° 14´; in the latter case the + magnetic force in the air just outside is sensibly equal to that + within the neck. A pair of cones having a semi-vertical angle of 45° + were considered to combine high concentrative power with a sufficient + approximation to uniformity of field. In most of the experiments the + measurements were made by suddenly withdrawing the bobbin from its + place between the pole pieces. Two groups of observations were + recorded, one giving the induction in the inner coil and the other + that in the outer coil. The value of the residual induction which + persisted when the bobbin was drawn out was added to that of the + induction measured, and thus the total induction in the iron was + determined. The highest induction reached in these experiments was + 45,350 units, more than twice the value of any previously recorded. + The corresponding intensity of the outside field was 24,500, but, + owing to the wide angle of the cones used (about 2 × 63°), this was + probably greater than the value of the magnetic force within the + metal. The following table shows some results of other experiments in + which H was believed to have sensibly the same value inside as outside + the metal. Values of I are derived from (B - H)/4[pi] and of µ from + B/H. + + +--------------+--------+--------+------+-------+ + | Metal. | H | B | I | µ | + +--------------+--------+--------+------+-------+ + | | 1,490 | 22,650 | 1680 | 15.20 | + | | 6,070 | 27,130 | 1680 | 4.47 | + | Swedish Iron | 8,600 | 30,270 | 1720 | 3.52 | + | | 19,450 | 40,820 | 1700 | 2.10 | + | | 19,880 | 41,140 | 1700 | 2.07 | + +--------------+--------+--------+------+-------+ + | | 4,560 | 20,070 | 1230 | 4.40 | + | Cast Iron | 13,460 | 28,710 | 1210 | 2.13 | + | | 16,200 | 30,920 | 1170 | 1.91 | + | | 16,900 | 31,760 | 1180 | 1.88 | + +--------------+--------+--------+------+-------+ + | | 6,210 | 25,480 | 1530 | 4.10 | + | | 9,970 | 29,650 | 1570 | 2.97 | + | Tool Steel | 12,170 | 31,620 | 1550 | 2.60 | + | | 14,660 | 34,550 | 1580 | 2.36 | + | | 15,530 | 35,820 | 1610 | 2.31 | + +--------------+--------+--------+------+-------+ + | | 2,220 | 7,100 | 390 | 3.20 | + | | 4,440 | 9,210 | 380 | 2.09 | + | Hard Nickel | 7,940 | 12,970 | 400 | 1.63 | + | | 14,660 | 19,640 | 400 | 1.34 | + | | 16,000 | 21,070 | 400 | 1.32 | + +--------------+--------+--------+------+-------+ + | | 1,350 | 16,000 | 1260 | 12.73 | + | Cobalt | 4,040 | 18,870 | 1280 | 4.98 | + | | 8,930 | 23,890 | 1290 | 2.82 | + | | 14,990 | 30,210 | 1310 | 2.10 | + +--------------+--------+--------+------+-------+ + +These results are of extreme interest, for they show that under +sufficiently strong magnetizing forces the intensity of magnetization I +reaches a maximum value, as required by W. E. Weber's theory of +molecular magnetism. There appears to be no definite limit to the value +to which the induction B may be raised, but the magnetization I attains +a true saturation value under magnetizing forces which are in most cases +comparatively moderate. Thus the magnetization which the sample of +Swedish iron received in a field of 1490 was not increased (beyond the +limits of experimental error) when the intensity of the field was +multiplied more than thirteen-fold, though the induction was nearly +doubled. When the saturation value of I has been reached, the relation +of magnetic induction to magnetic force may be expressed by + + B = H + constant. + + The annexed table gives the saturation values of I for the particular + metals examined by Ewing and Low:-- + + Saturation + Value of I + + Wrought iron 1,700 + Cast iron 1,240 + Nickel (0.75% iron) 515 + " (0.56% " ) 400 + Cobalt (1.66% " ) 1,300 + + It is shown in the paper that the greatest possible force which the + isthmus method can apply at a point in the axis of the bobbin is + + F = 11.137 I_s log 10 b/a, + + I_s being the saturation value of the magnet poles, a the radius of the + neck on which the cones converge, and b the radius of the bases of the + cones. + + Some experiments made by H. du Bois (_Phil. Mag._, 1890, 29, 293) with + an electromagnet specially designed for the production of strong + fields, confirm Ewing's results for iron, nickel and cobalt. The + method employed did not admit of the production of such high + magnetizing forces, but was of special interest in that both B and I + were measured optically--B by means of the rotation of a polarized ray + inside a glass plate, as before described, and I by the rotation of a + polarized ray reflected from the polished surface of the magnetized + metal (see "Kerr's constant," MAGNETO-OPTICS). H(= B - 4[pi]I) was + calculated from corresponding values of I and B. Taylor Jones (_Wied. + Ann._, 1896, 57, 258, and _Phil. Mag._, 1896, 41, 153), working with + du Bois's electromagnet and using a modification of the isthmus + method, succeeded in pushing the induction B up to 74,200 with H = + 51,600, the corresponding value of I being 1798, and of µ only 1.44. + The diameter of the isthmus was 0.241 mm., and the electromagnet was + excited by a current of 40 amperes. + +_Tractive Force of a Magnet._--Closely connected with the results just +discussed is the question what is the greatest tractive force that can +be exerted by a magnet. In the year 1852 J. P. Joule (_Phil. Mag._, +1852, 3, 32) expressed the opinion that no "force of current could give +an attraction equal to 200 lb. per sq. in.," or 14,000 grms. per square +centimetre, and a similar view prevailed among high authorities more +than twenty years later. For the greatest possible "lifting power" of +permanent magnets this estimate is probably not very far from the truth, +but it is now clearly understood that the force which can be exerted by +an electromagnet, or by a pair of electromagnets with opposite poles in +contact, is only limited by the greatest value to which it is +practically possible to raise the magnetizing force H. This is at once +evident when the tractive force due to magnetization is expressed as +2[pi]I²+ HI. For fields of moderate intensity the first term of the +expression is the more important, but when the value of H exceeds 12,000 +or thereabouts, the second preponderates, and with the highest values +that have been actually obtained, HI is several times greater than +2[pi]I². If H could be increased without limit, so also could the +tractive force. The following table shows the greatest "lifting powers" +experimentally reached at the dates mentioned:-- + + +-----------+-----------+---------+------+ + | Observer. | Kilos per | lb. per | Date.| + | | sq. cm. | sq. in. | | + +-----------+-----------+---------+------+ + | Joule | 12.3 | 175 | 1852 | + | Bidwell | 15.9 | 226 | 1886 | + | Wilde | 26.8 | 381 | 1891 | + | T. Jones | 114.9 | 1634 | 1896 | + +-----------+-----------+---------+------+ + + +5. MAGNETIZATION IN VERY WEAK FIELDS + +Some interesting observations have been made of the effects produced by +very small magnetic forces. It was first pointed out by C. Baur (_Wied. +Ann._, 1880, 11, 399) that in weak fields the relation of the +magnetization I to the magnetizing force H is approximately expressed by +an equation of the form + + I = aH + bH², + +or + + [kappa] = I/H = a + bH, + +whence it appears that within the limits of Baur's experiments the +magnetization curve is a parabola, and the susceptibility curve an +inclined straight line, [kappa] being therefore a known function of H. +If these equations could be assumed to hold when H is indefinitely +small, it would follow that [kappa] has a finite initial value, from +which there would be no appreciable deviation in fields so weak that bH +was negligibly small in comparison with a. Such an assumption could not, +however, without dangerous extrapolation, be founded upon the results of +Baur's experiments, which did not go far enough to justify it. In some +experiments carried out in 1887, Lord Rayleigh (_Phil. Mag._, 1887, 23, +225) approached very much more nearly than Baur to the zero of magnetic +force. Using an unannealed Swedish iron wire, he found that when H was +gradually diminished from 0.04 to 0.00004 C.G.S. unit, the ratio of +magnetization to magnetizing force remained sensibly constant at 6.4, +which may therefore with great probability be assumed to represent the +initial value of [kappa] for the specimen in question. Experiments with +annealed iron gave less satisfactory results, on account of the slowness +with which the metal settled down into a new magnetic state, thus +causing a "drift" of the magnetometer needle, which sometimes persisted +for several seconds. Apart from this complication, it appeared that I +was proportional to H when the value of H was less than 0.02. + + The observations of Baur and Rayleigh have been confirmed and + discussed by (amongst others) W. Schmidt (_Wied. Ann._, 1895, 54, + 655), who found the limiting values of [kappa] to be 7.5 to 9.5 for + iron, and 11.2 to 13.5 for steel, remaining constant up to H = .06; by + P. Culmann (_Elekt. Zeit._, 1893, 14, 345; _Wied. Ann._, 1895, 56, + 602); and by L. Holborn (_Berl. Ber._, 1897, p. 95, and _Wied. Ann._, + 1897, 61, 281). The latter gives values of the constants a and b for + different samples of iron and steel, some of which are shown in the + following table:-- + + [kappa] = a + bH + + Metal. a b + + English tungsten steel 8.90 0.264 + Tungsten steel, hardened 2.23 0.032 + Silver steel 8.66 0.384 + Tool steel 8.30 0.400 + Refined steel 11.28 1.92 + Cast iron 3.16 0.236 + Soft iron 16.6 18.6 + Hard drawn iron 5.88 1.76 + + For most samples of steel the straight-line law was found to hold + approximately up to H = 3; in the case of iron and of soft steel the + approximation was less close. + +The behaviour of nickel in weak fields has been observed by Ewing +(_Phil. Trans._, 1888, 179A, 325), who found that the initial value of +[kappa] was 1.7, and that it remained sensibly constant until H had +reached a value of about five units. While therefore the initial +susceptibility of nickel is less than that of iron and steel, the range +of magnetic force within which it is approximately constant is about one +hundred times greater. Ewing has also made a careful study (_Proc. Roy. +Soc._, 1889, 46, 269) of "magnetic viscosity" under small forces--the +cause of the magnetometer "drift" referred to by Rayleigh. On the +application of a small magnetizing force to a bar of soft annealed iron, +a certain intensity of magnetization is instantly produced; this, +however, does not remain constant, but slowly increases for some seconds +or even minutes, and may ultimately attain a value nearly twice as great +as that observed immediately after the force was applied.[30] When the +magnetizing current is broken, the magnetization at once undergoes +considerable diminution, then gradually falls to zero, and a similar +sudden change followed by a slow one is observed when a feeble current +is reversed. Ewing draws attention to a curious consequence of this +time-lag. By the alternate application and withdrawal of a small +magnetizing force a cyclic condition may be established in an iron rod. +If now the alternations are performed so rapidly that time is not +allowed for more than the first sudden change in the magnetization, +there will be no hysteresis loss, the magnetization exactly following +the magnetizing force. Further, if the alternations take place so slowly +that the full maximum and minimum values of the magnetization are +reached in the intervals between the reversals, there will again be no +dissipation of energy. But at any intermediate frequency the ascending +and descending curves of magnetization will enclose a space, and energy +will be dissipated. It is remarkable that the phenomena of magnetic +viscosity are much more evident in a thick rod than in a thin wire, or +even in a large bundle of thin wires. In hardened iron and steel the +effect can scarcely be detected, and in weak fields these metals exhibit +no magnetic hysteresis of any kind. + + +6. CHANGES OF DIMENSIONS ATTENDING MAGNETIZATION + +It is well known that the form of a piece of ferromagnetic metal is in +general slightly changed by magnetization. The phenomenon was first +noticed by J. P. Joule, who in 1842 and 1847 described some experiments +which he had made upon bars of iron and steel. His observations, were +for the most part confirmed by a number of subsequent workers, notably +by A. M. Mayer; but with the single exception of the discovery by W. F. +Barrett in 1882 that a nickel bar contracts when magnetized, nothing of +importance was added by Joule's results for nearly forty years. Later +researches have however thrown much new light upon a class of phenomena +which cannot fail to have an important bearing upon the complete theory +of molecular magnetism.[31] According to Joule's observations, the +length of a bar of iron or soft steel was increased by magnetization, +the elongation being proportional up to a certain point to the square of +the intensity of magnetization; but when the "saturation point" was +approached the elongation was less than this law would require, and a +stage was finally reached at which further increase of the magnetizing +force produced little or no effect upon the length. From data contained +in Joule's paper it may be calculated that the strongest external field +H0 produced by his coil was about 126 C.G.S. units, but since the +dimensional ratio of his bars was comparatively small, the actual +magnetizing force H must have been materially below that value. In 1885 +it was shown by Bidwell, in the first of a series of papers on the +subject, that if the magnetizing force is pushed beyond the point at +which Joule discontinued his experiments, the extension of the bar does +not remain unchanged, but becomes gradually less and less, until the +bar, after first returning to its original length, ultimately becomes +actually shorter than when in the unmagnetized condition. The elongation +is generally found to reach a maximum under a magnetizing force of 50 to +120 units, and to vanish under a force of 200 to 400, retraction +occurring when still higher forces are applied. In order to meet the +objection that the phenomenon might be due to electromagnetic action +between the coil and the rod, Bidwell made some experiments with iron +rings, and found that the length of their diameters varied under +magnetization in precisely the same manner as the length of a straight +rod. Experiments were afterwards made with rods of iron, nickel, and +cobalt, the external field being carried up to the high value of 1500 +units. The results are indicated in Fig. 24. It appears that the +contraction which followed the initial extension of the iron reached a +limit in fields of 1000 or 1100. Nickel exhibited retraction from the +very beginning (as observed by Barrett), its greatest change of length +considerably exceeding that undergone by iron; in a field of 800 the +original length was diminished by as much as 1/40,000 part, but stronger +forces failed to produce any further effect. The curve for cobalt is a +very remarkable one. Little or no change of length was observed until +the strength of the field H0 reached about 50; then the rod began to +contract, and after passing a minimum at H0 = 400, recovered its +original length at H0 = 750; beyond this point there was extension, the +amount of which was still increasing fast when the experiment was +stopped at H0 = 1400. Similar results were obtained with three different +samples of the metal. Roughly speaking, therefore, cobalt behaves +oppositely to iron. + +[Illustration: FIG. 24] + +Joule and others experimented with hardened steel, but failed to find a +key to the results they obtained, which are rather complex, and have +been thought to be inconsistent. The truth appears to be that a hardened +steel rod generally behaves like one of iron or soft steel in first +undergoing extension under increasing magnetizing force, and recovering +its original length when the force has reached a certain critical value, +beyond which there is contraction. But this "critical value" of the +force is found to depend in an unexpected manner upon the hardness of +the steel; the critical value diminishes as the hardness becomes greater +_up to a certain point_, corresponding to a yellow temper, after which +it increases and with the hardest steel becomes very high. For steel +which has been made red-hot, suddenly cooled, and then let down to a +yellow temper, the critical value of the magnetizing force is smaller +than for steel which is either softer or harder; it is indeed so small +that the metal contracts like nickel even under weak magnetizing forces, +without undergoing any preliminary extension that can be detected. + +[Illustration: FIG. 25.] + +Joule also made experiments upon iron wires under tension, and drew the +erroneous inference (which has been often quoted as if it were a +demonstrated fact) that under a certain critical tension (differing for +different specimens of iron but independent of the magnetizing force) +magnetization would produce no effect whatever upon the dimensions of +the wire. What actually happens when an iron wire is loaded with various +weights is clearly shown in Fig. 25. Increased tension merely has the +effect of diminishing the maximum elongation and hastening the +contraction; with the two greatest loads used in the experiment there +was indeed no preliminary extension at all.[32] The effects of tension +upon the behaviour of a nickel wire are of a less simple character. In +weak fields the magnetic contraction is always diminished by pulling +stress; in strong fields the contraction increases under a small load +and diminishes under a heavy one. Cobalt, curiously enough, was found to +be quite unaffected by tensile stress. + +Certain experiments by C. G. Knott on magnetic twist, which will be +referred to later, led him to form the conclusion that in an iron wire +carrying an electric current the magnetic elongation would be increased. +This forecast was shown by Bidwell to be well founded. The effect +produced by a current is exactly opposite to that of tension, raising +the elongation curve instead of depressing it. In the case of a wire +0.75 mm. in diameter the maximum elongation was nearly doubled when a +current of two amperes was passing through the iron, while the "critical +value" of the field was increased from 130 to 200. Yet notwithstanding +this enormous effect in iron, the action of a current upon nickel and +cobalt turned out to be almost inappreciable. + +Some experiments were next undertaken with the view of ascertaining how +far magnetic changes of length in iron were dependent upon the hardness +of the metal, and the unexpected result was arrived at that softening +produces the same effect as tensile stress; it depresses the elongation +curve, diminishing the maximum extension, and reducing the "critical +value" of the magnetizing force. A thoroughly well annealed ring of soft +iron indeed showed no extension at all, beginning to contract, like +nickel, under the smallest magnetizing forces. The experiments were not +sufficiently numerous to indicate whether, as is possible, there is a +critical degree of hardness for which the height of the elongation curve +is a maximum. + +Finally, experiments were made to ascertain the effect of magnetization +upon the dimensions of iron rings in directions perpendicular to the +magnetization, and upon the volume of the rings.[33] It was found that +the curve showing the relation of transverse changes of dimensions to +magnetizing force was similar in general character to the familiar +elongation curves, but the signs were reversed; the curve was inverted, +indicating at first retraction, which, after passing a maximum and +vanishing in a critical field, was succeeded by elongation. The curve +showing the circumferential (or longitudinal) changes was also plotted, +and from the two curves thus obtained it was easy, on the assumption +that the metal was isotropic in directions at right angles to the +magnetization, to calculate changes of volume; for if circumferential +elongation be denoted by l1, and transverse elongation by l2, then the +cubical dilatation (+ or -) = l1 + 2l2 approximately. If l1 were exactly +equal to -2l2 for all values of the magnetizing force, it is clear that +the volume of the ring would be unaffected by magnetization. In the case +of the ring in question, the circumferential changes were in weak fields +less than twice as great as the transverse ones, while in strong fields +they were more than twice as great; under increasing magnetic force +therefore the volume of the ring was first diminished, then it regained +its original value (for H = 90), and ultimately increased. It was also +shown that annealing, which has such a large effect upon circumferential +(or longitudinal) changes, has almost none upon transverse ones. Hence +the changes of volume undergone by a given sample of wrought iron under +increasing magnetization must depend largely upon the state of the metal +as regards hardness; there may be always contraction, or always +expansion, or first one and then the other. + +Most of the experiments described above have been repeated and the +results confirmed by other workers, some of whom have added fresh +observations. The complicated hysteresis effects which attend magnetic +elongation and retraction have been studied by H. Nagaoka, who also, in +conjunction with K. Honda, measured the changes of length of various +metals shaped in the form of ovoids instead of cylindrical rods, and +determined the magnetization curves for the same specimens; a higher +degree of accuracy was thus attained, and satisfactory data were +provided for testing theories. Among other things, it was found that the +behaviour of cast cobalt was entirely changed by annealing; the sinuous +curve shown in Fig. 24 was converted into an almost perfectly straight +line passing through the origin, and lying below the horizontal axis; +while the permeability of the metal was greatly diminished by the +operation. They also tested several varieties of nickel-steel in the +form of both ovoids and wires. With a sample containing 25% of nickel no +appreciable change was detected; others containing larger percentages, +and tested in fields up to 2000, all exhibited elongation, which tended +to an asymptotic value as the field was increased. The influence of +temperature varying between wide limits has formed the subject of a +research by K. Honda and S. Shimizu. For soft iron, tungsten-steel and +nickel little difference appeared to result from lowering the +temperature down to -186° C. (the temperature of liquid air); at +sufficiently high temperatures, 600° to 1000° or more, it was remarked +that the changes of length in iron, steel and cobalt tended in every +case to become proportional to the magnetic force, the curves being +nearly straight lines entirely above the axis. The retraction of nickel +was diminished by rising temperature, and at 400° had almost vanished. +The influence of high temperature on cobalt was very remarkable, +completely altering the character of the change of length: the curves +for annealed cobalt show that at 450° this metal behaves just like iron +at ordinary temperatures, lengthening in fields up to about 300 and +contracting in stronger ones. The same physicists have made some +additional experiments upon the effect of tension on magnetic change of +length. Bidwell's results for iron and nickel were confirmed, and it was +further shown that the elongation of nickel-steel was very greatly +diminished by tension; when magnetized under very heavy loads, the wire +was indeed found to undergo slight contraction. Honda subjected tubes of +iron, steel and nickel to the simultaneous action of circular and +longitudinal fields, and observed the changes of length when one of the +fields was varied while the other remained constant at different +successive values from zero upwards. The experimental results agreed in +sign though not in magnitude with those calculated from the changes +produced by simple longitudinal magnetization, discrepancies being +partly accounted for by the fact that the metals employed were not +actually isotropic. Heusler's alloy has been tested for change of length +by L. Austin, who found continuous elongation with increasing fields, +the curves obtained bearing some resemblance to curves of magnetization. + +As regards the effect of magnetization upon volume there are some +discrepancies. Nagaoka and Honda, who employed a fluid dilatometer, +found that the volume of several specimens of iron, steel and nickel was +always slightly increased, no diminution being indicated in low fields; +cobalt, on the other hand, was diminished in volume, and the amount of +the change, though still very small, was greater than that shown by the +other metals. Various nickel-steels all expanded under magnetization, +the increase being generally considerable and proportional to the field; +in the case of an alloy containing 29% of nickel the change was nearly +40 times greater than in soft iron. C. G. Knott, who made an exhaustive +series of experiments upon various metals in the form of tubes, +concluded that in iron there was always a slight increase of volume, and +in nickel and cobalt a slight decrease. It is uncertain how far these +various results are dependent upon the physical condition of the metals. + + Attempts have been made to explain magnetic deformation by various + theories of magnetic stress,[34] notably that elaborated by G. R. + Kirchhoff (_Wied. Ann._, 1885, 24, 52, and 1885, 25, 601), but so far + with imperfect success. E. Taylor Jones showed in 1897 that only a + small proportion of the contraction exhibited by a nickel wire when + magnetized could be accounted for on Kirchhoff's theory from the + observed effects of pulling stress upon magnetization; and in a more + extended series of observations Nagaoka and Honda found wide + quantitative divergences between the results of experiment and + calculation, though in nearly all cases there was agreement as to + quality. They consider, however, that Kirchhoff's theory, which + assumes change of magnetization to be simply proportional to strain, + is still in its infancy, the present stage of its evolution being + perhaps comparable with that reached by the theory of magnetization at + the time when the ratio I/H was supposed to be constant. In the light + of future researches further development may reasonably be expected. + + It has been suggested[35] that an iron rod under magnetization may be + in the same condition as if under a mechanically applied longitudinal + stress tending to shorten the iron. If a long magnetized rod is + divided transversely and the cut ends placed nearly in contact, the + magnetic force inside the narrow air gap will be B = H + 4[pi]I. The + force acting on the magnetism of one of the faces, and urging this + face towards the other, will be less than B by 2[pi]I, the part of the + total force due to the first face itself; hence the force per unit of + area with which the faces would press against each other if in contact + is + + P = (B - 2[pi]I)I = 2[pi]I² + HI = (B² - H²) / 8[pi]. + + The width of the gap may be diminished until it is no greater than the + distance between two neighbouring molecules, when it will cease to be + distinguishable, but, assuming the molecular theory of magnetism to be + true, the above statement will still hold good for the intermolecular + gap. The same pressure P will be exerted across any imaginary section + of a magnetized rod, the stress being sustained by the intermolecular + springs, whatever their physical nature may be, to which the + elasticity of the metal is due. The whole of the rod will therefore be + subject to a compressive longitudinal stress P, the associated + contraction R, expressed as a fraction of the original length, being + + R = P/M = (B² - H²) / 8[pi]M, + + where M is Young's modulus. This was found to be insufficient to + account for the whole of the retraction exhibited by iron in strong + fields, but it was pointed out by L. T. More[36] that R ought to be + regarded as a "correction" to be applied to the results of + experiments on magnetic change of length, the magnetic stress being no + less an extraneous effect than a stress applied mechanically. Those + who support this view generally speak of the stress as "Maxwell's + stress," and assume its value to be B^2/8[pi]. The stress in question + seems, however, to be quite unconnected with the "stress in the + medium" contemplated by Maxwell, and its value is not exactly + B^2/8[pi] except in the particular case of a permanent ring magnet, + when H = O. Further, Maxwell's stress is a tension along the lines of + force, and is equal to B^2/8[pi] only when B = H, and there is no + magnetization.[37] Some writers have indeed contended that the stress + in magnetized iron is not compressive, but tensile, even when, as in + the case of a ring-magnet, there are no free ends. The point at issue + has an important bearing upon the possible correlation of magnetic + phenomena, but, though it has given rise to much discussion, no + accepted conclusion has yet been reached.[38] + + +7. EFFECTS OF MECHANICAL STRESS UPON MAGNETIZATION + +The effects of traction, compression and torsion in relation to +magnetism have formed the subject of much patient investigation, +especially at the hands of J. A. Ewing, C. G. Knott and the +indefatigable physicists of Tokyo University. The results of their +experiments embrace a multiplicity of details of which it is impossible +to give an adequate summary. Only a few of the most important can be +mentioned here; the reader who wishes for fuller information should +consult the original papers.[39] + +It was first discovered by E. Villari in 1868 that the magnetic +susceptibility of an iron wire was increased by stretching when the +magnetization was below a certain value, but diminished when that value +was exceeded; this phenomenon has been termed by Lord Kelvin, who +discovered it independently, the "Villari reversal," the value of the +magnetization for which stretching by a given load produces no effect +being known as the "Villari critical point" for that load. The Villari +critical point for a given sample of iron is reached with a smaller +magnetizing force when the stretching load is great than when it is +small; the reversal also occurs with smaller loads and with weaker +fields when the iron is soft than when it is hard. The following table +shows the values of I and H corresponding to the Villari critical point +in some of Ewing's experiments:-- + + +------------------------------+-----------------------------+ + | Soft Iron. | Hard Iron. | + +-----------------+------+-----+-----------------+------+----+ + |Kilos per sq. mm.| I. | H. |Kilos per sq. mm.| I. | H. | + +-----------------+------+-----+-----------------+------+----+ + | 2.15 | 1220 | 7.3 | 27.6 | 1180 | 34 | + | 4.3 | 1040 | 4.3 | 32.2 | 1150 | 32 | + | 8.6 | 840 | 3.4 | 37.3 | 1110 | 29 | + | 12.9 | 690 | 3.05| 42.5 | 1020 | 25 | + +-----------------+------+-----+-----------------+------+----+ + +The effects of pulling stress may be observed either when the wire is +stretched by a constant load while the magnetizing force is varied, or +when the magnetizing force is kept constant while the load is varied. In +the latter case the first application of stress is always attended by an +increase--often a very great one--of the magnetization, whether the +field is weak or strong, but after a load has been put on and taken off +several times the changes of magnetization become cyclic. From +experiments of both classes it appears that for a given field there is a +certain value of the load for which the magnetization is a maximum, the +maximum occurring at a smaller load the stronger the field. In very +strong fields the maximum may even disappear altogether, the effect of +the smallest stress being to diminish the magnetization; on the other +hand, with very weak fields the maximum may not have been reached with +the greatest load that the wire can support without permanent +deformation. When the load on a hardened wire is gradually increased, +the maximum value of I is found to correspond with a greater stress than +when the load is gradually diminished, this being an effect of +hysteresis. Analogous changes are observed in the residual magnetization +which remains after the wire has been subjected to fields of different +strength. The effects of longitudinal pressure are opposite to those of +traction; when the cyclic condition has been reached, pressure reduces +the magnetization of iron in weak fields and increases it in strong +fields (Ewing, _Magnetic Induction_, 1900, 223). + +The influence of traction in diminishing the susceptibility of nickel +was first noticed by Kelvin (W. Thomson), and was subsequently +investigated by Ewing and Cowan. The latter found the effect to be +enormous, not only upon the induced magnetization, but in a still +greater degree upon the residual. Even under so "moderate" a load as 33 +kilogrammes per square mm., the induced magnetization of a hard-drawn +nickel wire in a field of 60 fell from 386 to 72 units, while the +residual was reduced from about 280 to 10. Ewing has also examined the +effects produced by longitudinal compression upon the susceptibility and +retentiveness of nickel, and found, as was to be expected, that both +were greatly increased by pressure. The maximum susceptibility of one of +his bars rose from 5.6 to 29 under a stress of 19.8 kilos per square mm. +There were reasons for believing that no Villari reversal would be found +in nickel. Ewing and Cowan looked carefully for it, especially in weak +fields, but failed to discover anything of the kind.[40] Some +experiments by A. Heydweiller,[41] which appeared to indicate a reversal +in weak fields (corresponding to I = 5, or thereabouts), have been shown +by Honda and Shimizu to be vitiated by the fact that his specimen was +not initially in a magnetically neutral state; they found that when the +applied field had the same direction as that of the permanent +magnetization, Heydweiller's fallacious results were easily obtained; +but if the field were applied in the direction opposite to that of the +permanent magnetization, or if, as should rightly be the case, there +were no permanent magnetization at all, then there was no indication of +any Villari reversal. Thus a very important question, which has given +rise to some controversy, appears to be now definitely settled. + +The effects of longitudinal pressure upon the magnetization of cast +cobalt have been examined by C. Chree,[42] and also by J. A. Ewing.[43] +Chree's experiments were undertaken at the suggestion of J. J. Thomson, +who, from the results of Bidwell's observations on the magnetic +deformation of cobalt, was led to expect that that metal would exhibit a +reversal opposite in character to the effect observed in iron. The +anticipated reversal was duly found by Chree, the critical point +corresponding, under the moderate stress employed, to a field of about +120 units. Ewing's independent experiments showed that the magnetization +curve for a cobalt rod under a load of 16.2 kilogrammes per square mm. +crossed the curve for the same rod when not loaded at H = 53. Both +observers noticed analogous effects in the residual magnetization. The +effect of tension was subsequently studied by Nagaoka and Honda, who in +1902 confirmed, _mutatis mutandis_, the results obtained by Chree and +Ewing for cast cobalt, while for annealed cobalt it turned out that +tension always caused diminution of magnetization, the diminution +increasing with increasing fields. They also investigated the magnetic +behaviour of various nickel-steels under tension, and found that there +was always increase of magnetization. Thus it has been proved that in +annealed cobalt and in nickel-steel there is no Villari reversal. + +It has been pointed out by J. J. Thomson (_Applications of Dynamics to +Physics and Chemistry_, 47) that on dynamical principles there must be a +reciprocal relation between the changes of dimensions produced by +magnetization and the changes of magnetization attending mechanical +strain. Since, for example, stretching diminishes the magnetization of +nickel, it follows from theory that the length of a nickel rod should be +diminished by magnetization and conversely. So, too, the Villari +reversals in iron and cobalt might have been predicted--as indeed that +in cobalt actually was--from a knowledge of the changes of length which +those metals exhibit when magnetized. + +The complete reciprocity of the effects of magnetization upon length and +of stretching upon magnetization is shown by the following parallel +statements:-- + + _Iron._ + + Magnetization produces increase Tension produces increase of + of length in weak fields, magnetization in weak fields, + decrease in strong fields. decrease in strong fields. + + _Cast Cobalt._ + + Magnetization produces decrease Tension produces decrease of + of length in weak fields, magnetization in weak fields, + increase in strong fields. increase in strong fields. + + _Nickel and Annealed Cobalt._ + + Magnetization produces decrease Tension produces decrease of + of length in all fields. magnetization in all fields. + + _Nickel-Steel._ + + Magnetization produces increase Tension produces increase of + of length in all fields. magnetization in all fields. + + Nagaoka and Honda (_Phil. Mag._, 1898, 46, 261) have investigated the + effects of hydrostatic pressure upon magnetization, using the same + pieces of iron and nickel as were employed in their experiments upon + magnetic change of volume. In the iron cylinder and ovoid, which + expanded when magnetized, compression caused a diminution of + magnetization; in the nickel rod, which contracted when magnetized, + pressure was attended by an increase of magnetization. The amount of + the change was in both cases exceedingly small, that in iron being + less than 0.1 C.G.S. unit with a pressure of 250 atmospheres and H = + 54. It would hardly be safe to generalize from these observations; the + effects may possibly be dependent upon the physical condition of the + metals. In the same paper Nagaoka and Honda describe an important + experiment on the effect of transverse stress. An iron tube, having + its ends closed by brass caps, was placed inside a compressing vessel + into which water was forced until the pressure upon the outer surface + of the tube reached 250 atmospheres. The experiment was the reverse of + one made by Kelvin with a gun-barrel subjected to internal hydrostatic + pressure (_Phil. Trans._, 1878, 152, 64), and the results were also + the reverse. Under increasing magnetizing force the magnetization + first increased, reached a maximum, and then diminished until its + value ultimately became less than when the iron was in the unstrained + condition. Experiments on the effect of external hydrostatic pressure + upon the magnetization of iron rings have also been made by F. + Frisbie,[44] who found that for the magnetizing forces used by Nagaoka + and Honda pressure produced a small _increase_ of magnetization, a + result which appears to be in accord with theory. + +The relations of torsion to magnetization were first carefully studied +by G. Wiedemann, whose researches are described in his _Elektricität_, +iii. 671. The most interesting of his discoveries, now generally known +as the "Wiedemann effect," is the following: If we magnetize +longitudinally a straight wire which is fixed at one end and free at the +other, and then pass an electric current through the wire (or first pass +the current and then magnetize), the free end of the wire will twist in +a certain direction depending upon circumstances: if the wire is of +iron, and is magnetized (with a moderate force) so that its free end has +north polarity, while the current through it passes from the fixed to +the free end, then the free end as seen from the fixed end will twist in +the direction of the hands of a watch; if either the magnetization or +the current is reversed, the direction of the twist will be reversed. To +this mechanical phenomenon there is a magnetic reciprocal. If we twist +the free end of a ferromagnetic wire while a current is passing through +it, the wire becomes longitudinally magnetized, the direction of the +magnetization depending upon circumstances: if the wire is of iron and +is twisted so that its free end as seen from the fixed end turns in the +direction of the hands of a watch, while the current passes from the +fixed to the free end, then the direction of the resulting magnetization +will be such as to make the free end a north pole. The twist effect +exhibited by iron under moderate longitudinal magnetization has been +called by Knott a _positive_ Wiedemann effect; if the twist were +reversed, the other conditions remaining the same, the sign of the +Wiedemann effect would be _negative_. An explanation of the twist has +been given by Maxwell (_Electricity and Magnetism_, § 448). The wire is +subject to two superposed magnetizations, the one longitudinal, the +other circular, due to the current traversing the wire; the resultant +magnetization is consequently in the direction of a screw or spiral +round the wire, which will be right-handed or left-handed according as +the relation between the two magnetizations is right-handed or +left-handed; the magnetic expansion or contraction of the metal along +the spiral lines of magnetization produces the Wiedemann twist. Iron +(moderately magnetized) expands along the lines of magnetization, and +therefore for a right-handed spiral exhibits a right-handed twist. This +explanation was not accepted by Wiedemann,[45] who thought that the +effect was accounted for by molecular friction. Now nickel contracts +instead of lengthening when it is magnetized, and an experiment by Knott +showed, as he expected, that _caeteris paribus_ a nickel wire twists in +a sense opposite to that in which iron twists. The Wiedemann effect +being positive for iron is negative for nickel. Further, although iron +lengthens in fields of moderate strength, it contracts in strong ones; +and if the wire is stretched, contraction occurs with smaller +magnetizing forces than if it is unstretched. Bidwell[46] accordingly +found upon trial that the Wiedemann twist of an iron wire vanished when +the magnetizing force reached a certain high value, and was reversed +when that value was exceeded; he also found that the vanishing point was +reached with lower values of the magnetizing force when the wire was +stretched by a weight. These observations have been verified and +extended by Knott, whose researches have brought to light a large number +of additional facts, all of which are in perfect harmony with Maxwell's +explanation of the twist. + +[Illustration: FIG. 26.] + +Maxwell has also given an explanation of the converse effect, namely, +the production of longitudinal magnetization by twisting a wire when +circularly magnetized by a current passing through it. When the wire is +free from twist, the magnetization at any point P is in the tangential +direction PB (see fig. 26). Suppose the wire to be fixed at the top and +twisted at the bottom in the direction of the arrow-head T; then the +element of the wire at P will be stretched in the direction Pe and +compressed in the direction Pr. But tension and compression produce +opposite changes in the magnetic susceptibility; if the metal is iron +and its magnetization is below the Villari critical point, its +susceptibility will be greater along Pe than along Pr; the direction of +the magnetization therefore tends to approach Pe and to recede from Pr, +changing, in consequence of the twist, from PB to some such direction as +PB´, which has a vertical component downwards; hence the lower and upper +ends will respectively acquire north and south polarity, which will +disappear when the wire is untwisted. This effect has never been +actually reversed in iron, probably, as suggested by Ewing, because the +strongest practicable circular fields fail to raise the components of +the magnetization along Pe and Pr up to the Villari critical value. +Nagaoka and Honda have approached very closely to a reversal, and +consider that it would occur if a sufficiently strong current could be +applied without undue heating. + +One other effect of torsion remains to be noticed. If a longitudinally +magnetized wire is twisted, circular magnetization is developed; this is +evidenced by the transient electromotive force induced in the iron, +generating a current which will deflect a galvanometer connected with +the two ends of the wire. The explanation given of the last described +phenomenon will with the necessary modification apply also to this; it +is a consequence of the aeolotropy produced by the twist. There are +then three remarkable effects of torsion: + + A. A wire magnetized longitudinally and circularly becomes twisted. + + B. Twisting a circularly magnetized wire produces longitudinal + magnetization. + + C. Twisting a longitudinally magnetized wire produces circular + magnetization. + +And it has been shown earlier that-- + + D. Magnetization produces change of length. + + E. Longitudinal stress produces change of magnetization. + +Each of these five effects may occur in two opposite senses. Thus in A +the twist may be right-handed or left-handed; in B the polarity of a +given end may become north or south; in C the circular magnetization may +be clockwise or counter-clockwise; in D the length may be increased or +diminished; in E the magnetization may become stronger or weaker. And, +other conditions remaining unchanged, the "sense" of any effect depends +upon the nature of the metal under test, and (sometimes) upon the +intensity of its magnetization. Let each of the effects A, B, C, D and E +be called positive when it is such as is exhibited by moderately +magnetized iron, and negative when its sense is opposite. Then the +results of a large number of investigations may be briefly summarized as +follows: + + (W) = weakly magnetized. (S) = strongly magnetized. + + _Metal._ _Effects._ _Sign._ + + Iron (W) A, B, C, D, E + + Unannealed Cobalt (S) A, D, E + + Nickel-Steel (W) A, D, E + + Nickel A, B, C, D, E - + Annealed Cobalt D, E - + Iron (S) A, C, D, E - + Unannealed Cobalt A, D, E - + +Several gaps remain to be filled, but the results so far recorded can +leave no doubt that the five effects, varied as they may at first sight +appear, are intimately connected with one another. For each of the +metals tabulated in the first column all the effects hitherto observed +have the same sign; there is no single instance in which some are +positive and others negative. Until the mysteries of molecular +constitution have been more fully explored, perhaps D may be most +properly regarded as the fundamental phenomenon from which the others +follow. Nagaoka and Honda have succeeded in showing that the observed +relations between twist and magnetization are in qualitative agreement +with an extension of Kirchhoff's theory of magnetostriction. + + The effects of magnetization upon the torsion of a previously twisted + wire, which were first noticed by Wiedemann, have been further studied + by F. J. Smith[47] and by G. Moreau.[48] Nagaoka[49] has described the + remarkable influence of combined torsion and tension upon the magnetic + susceptibility of nickel, and has made the extraordinary observation + that, under certain conditions of stress, the magnetization of a + nickel wire may have a direction opposite to that of the magnetizing + force. + + +8. EFFECTS OF TEMPERATURE UPON MAGNETISM + +_High Temperature._--It has long been known that iron, when raised to a +certain "critical temperature" corresponding to dull red heat, loses its +susceptibility and becomes magnetically indifferent, or, more +accurately, is transformed from a ferromagnetic into a paramagnetic +body. Recent researches have shown that other important changes in its +properties occur at the same critical temperature. Abrupt alterations +take place in its density, specific heat, thermo-electric quality, +electrical conductivity, temperature-coefficient of electrical +resistance, and in some at least of its mechanical properties. Ordinary +magnetizable iron is in many respects an essentially different substance +from the non-magnetizable metal into which it is transformed when its +temperature is raised above a certain point (see _Brit. Assoc. Report_, +1890, 145). The first exact experiments demonstrating the changes which +occur in the permeability of iron, steel and nickel when heated up to +high temperatures were those of J. Hopkinson (_Phil. Trans._, 1889, 180, +443; _Proc. Roy. Soc._, 1888, 44, 317). The metal to be tested was +prepared in the form of a ring, upon which were wound primary and +secondary coils of copper wire insulated with asbestos. The primary coil +carried the magnetizing current; the secondary, which was wound inside +the other, could be connected either with a ballistic galvanometer for +determining the induction, or with a Wheatstone's bridge for measuring +the resistance, whence the temperature was calculated. The ring thus +prepared was placed in a cast-iron box and heated in a gas furnace. The +following are the chief results of Hopkinson's experiments: For small +magnetizing forces the magnetization of iron steadily increases with +rise of temperature till the critical temperature is approached, when +the rate of increase becomes very high, the permeability in some cases +attaining a value of about 11,000; the magnetization then with +remarkable suddenness almost entirely disappears, the permeability +falling to about 1.14. For strong magnetizing forces (which in these +experiments did not exceed H = 48.9) the permeability remains almost +constant at its initial value (about 400), until the temperature is +within nearly 100° of the critical point; then the permeability +diminishes more and more rapidly until the critical point is reached and +the magnetization vanishes. Steel behaves in a similar manner, but the +maximum permeability is not so high as in iron, and the fall, when the +critical point is approached, is less abrupt. The critical temperature +for various samples of iron and steel ranges from 690° C. to 870° C.; it +is the temperature at which Barrett's "recalescence" occurs. The +critical temperature for the specimen of nickel examined (which +contained nearly 5% of impurities) was 310° C. F. Lydall and A. W. +Pocklington found that the critical temperature of nearly pure iron was +874° C. (_Proc. Roy. Soc._, 1893, 52, 228). + +An exhaustive research into the effects of heating on the magnetic +properties of iron has been carried out by D. K. Morris (_Proc. Phys. +Soc._, 1897, 15, 134; and _Phil. Mag._, 1897, 44, 213), the results +being embodied in a paper containing twelve pages of tables and upwards +of 120 curves. As in Hopkinson's experiments, ring magnets were +employed; these were wound with primary and secondary coils of insulated +platinum wire, which would bear a much higher temperature than copper +without oxidation or fusion. A third platinum coil, wound +non-inductively between the primary and the secondary, served to carry +the current by which the ring was heated; a current of 4.6 amperes, with +16 volts across the terminals, was found sufficient to maintain the ring +at a temperature of 1150° C. In the ring itself was embedded a +platinum-thermometer wire, from the resistance of which the temperature +was determined. The whole was wrapped in several coverings of asbestos +and placed in a glass vessel from which the air was partially exhausted, +additional precautions being taken to guard against oxidation of the +iron. + +[Illustration: FIG. 27.] + + Some preliminary experiments showed the striking difference in the + effects of annealing at a red heat (840° C.) and at a low white heat + (1150° C). After one of the rings had been annealed at 840°, its + maximum permeability at ordinary temperatures was 4000 for H = 1.84; + when it had been subsequently annealed at 1150°, the maximum + permeability rose to 4680 for H = 1.48, while the hysteresis loss for + B= ±4000 was under 500 ergs per c.cm. As regards the effects of + temperature, Morris's results are in general agreement with those of + Hopkinson, though no doubt they indicate details with greater + clearness and accuracy. Specimens of curves showing the relation of + induction to magnetic field at various temperatures, and of + permeability to temperature with fields of different intensities, are + given in figs. 27 and 28. The most striking feature presented by these + is the enormous value, 12,660, which, with H = 0.153, is attained by + the permeability at 765° C., followed by a drop so precipitous that + when the temperature is only 15° higher, the value of the permeability + has become quite insignificant. The critical temperatures for three + different specimens of iron were 795°, 780°, and 770° respectively. + Above these temperatures the little permeability that remained was + found to be independent of the magnetizing force, but it appeared to + vary a little with the temperature, one specimen showing a + permeability of 100 at 820°, 2.3 at 950°, and 17 at 1050°. These last + observations are, however, regarded as uncertain. The effects of + temperature upon hysteresis were also carefully studied, and many + hysteresis loops were plotted. The results of a typical experiment are + given in the annexed table, which shows how greatly the hysteresis + loss is diminished as the critical temperature is approached. The + coercive force at 764°.5 is stated to have been little more than 0.1 + C.G.S. unit; above the critical temperature no evidence of hysteresis + could be obtained. + + [Illustration: FIG. 28.] + + Hysteresis Loss in Ergs per c.cm. Max. H. = ±6.83. + + Temp. C.° Ergs. Temp. C.° Ergs. + + 764.5 120 | 457 2025 + 748 328 | 352 2565 + 730 426 | 249 3130 + 695 797 | 137.5 3500 + 634 1010 | 24 3660 + 554 1345 | + + A paper by H. Nagaoka and S. Kusakabe[50] generally confirms Morris's + results for iron, and gives some additional observations for steel, + nickel and cobalt. The magnetometric method was employed, and the + metals, in the form of ovoids, were heated by a specially designed + burner, fed with gas and air under pressure, which directed 90 fine + jets of flame upon the asbestos covering the ovoid. The temperature + was determined by a platinum-rhodium and platinum thermo-junction in + contact with the metal. Experiments were made at several constant + temperatures with varying magnetic fields, and also at constant fields + with rising and falling temperatures. For ordinary steel the critical + temperature, at which magnetization practically disappeared, was found + to be about 830°, and the curious fact was revealed that, on cooling, + magnetization did not begin to reappear until the temperature had + fallen 40° below the critical value. This retardation was still more + pronounced in the case of tungsten-steel, which lost its magnetism at + 910° and remained non-magnetic till it was cooled to 570°, a + difference of 240°. For nearly pure nickel the corresponding + temperature-difference was about 100°. This phenomenon is of the same + nature as that first discovered by J. Hopkinson for nickel-steel. The + paper contains tables and curves showing details of the magnetic + changes, sometimes very complex, at different temperatures and with + different fields. The behaviour of cobalt is particularly noticeable; + its permeability increased with rising temperature up to a maximum at + 500°, when it was about twice as great as at ordinary temperatures, + while at 1600°, corresponding to white heat, there was still some + magnetization remaining. + + Further contributions to the subject have been made by K. Honda and S. + Shimizu,[51] who experimented at temperatures ranging from -186° to + 1200°. As regards the higher temperatures, the chief point of interest + is the observation that the curve of magnetization for annealed cobalt + shows a small depression at about 450°, the temperature at which they + had found the sign of the length-change to be reversed for all fields. + In the case of all the metals tested a small but measurable trace of + magnetization remained after the so-called critical temperature had + been exceeded; this decreased very slightly up to the highest + temperature reached (1200°) without undergoing any such variation as + had been suspected by Morris. When the curve after its steep descent + has almost reached the axis, it bends aside sharply and becomes a + nearly horizontal straight line; the authors suggest that the critical + temperature should be defined as that corresponding to the point of + maximum curvature. As thus defined the critical temperatures for iron, + nickel and cobalt were found to be 780°, 360° and 1090° respectively, + but these values are not quite independent of the magnetizing force. + + Experiments on the effect of high temperatures have also been made by + M. P. Ledeboer,[52] H. Tomlinson,[53] P. Curie,[54] and W. Kunz,[55] + R. L. Wills,[56] J. R. Ashworth[57] and E. P. Harrison.[58] + +_Low Temperature._--J. A. Fleming and J. Dewar (_Proc. Roy. Soc._, 1896, +60, 81) were the first to experiment on the permeability and hysteresis +of iron at low temperatures down to that of liquid air (-186° C.). +Induction curves of an annealed soft-iron ring were taken first at a +temperature of 15° C., and afterwards when the ring was immersed in +liquid air, the magnetizing force ranging from about 0.8 to 22. After +this operation had been repeated a few times the iron was found to have +acquired a stable condition, and the curves corresponding to the two +temperatures became perfectly definite. They showed that the +permeability of this sample of iron was considerably diminished at the +lower temperature. The maximum permeability (for H = 2) was 3400 at 15° +and only 2700 at -186°, a reduction of more than 20%; but the percentage +reduction became less as the magnetizing force departed from the value +corresponding to maximum permeability. Observations were also made of +the changes of permeability which took place as the temperature of the +sample slowly rose from -186° to 15°, the magnetizing force being kept +constant throughout an experiment. The values of the permeability +corresponding to the highest and lowest temperatures are given in the +following table. Most of the permeability-temperature curves were more +or less convex + + +------------------+--------+------------+-------------+ + | Sample of Iron. | H. | µ at 15°. | µ at -186°. | + +------------------+--------+------------+-------------+ + | Annealed Swedish | 1.77 | 2835 | 2332 | + | Unannealed " | 1.78 | 917 | 1272 | + | " " | 9.79 | 1210 | 1293 | + | Hardened " | 2.66 | 56 | 132 | + | " " | 4.92 | 106.5 | 502 | + | " " | 11.16 | 447.5 | 823 | + | " " | 127.7 | 109 | 124 | + | Steel wire | 7.50 | 86 | 64.5 | + | " | 20.39 | 361 | 144 | + +------------------+--------+------------+-------------+ + +towards the axis of temperature, and in all the experiments, except +those with annealed iron and steel wire, the permeability was greatest +at the lowest temperature.[59] The hysteresis of the soft annealed iron +turned out to be sensibly the same for equal values of the induction at +-186° as at 15°, the loss in ergs per c.cm. per cycle being +approximately represented by 0.002 B(1.56) when the maximum limits of B +were ±9000. Experiments with the sample of unannealed iron failed to +give satisfactory results, owing to the fact that no constant magnetic +condition could be obtained. + + Honda and Shimizu have made similar experiments at the temperature of + liquid air, employing a much wider range of magnetizing forces (up to + about 700 C.G.S.) and testing a greater variety of metals. They found + that the permeability of Swedish iron, tungsten-steel and nickel, when + the metals were cooled to -186°, was diminished in weak fields but + increased in strong ones, the field in which the effect of cooling + changed its sign being 115 for iron and steel and 580 for nickel. The + permeability of cobalt, both annealed and unannealed, was always + diminished at the low temperature. The hysteresis-loss in Swedish iron + was decreased for inductions below about 9000 and increased for higher + inductions; in tungsten-steel, nickel and cobalt the hysteresis-loss + was always increased by cooling. The range of ±B within which + Steinmetz's formula is applicable becomes notably increased at low + temperature. It may be remarked that, whereas Fleming and Dewar + employed the ballistic method, their specimens having the form of + rings, Honda and Shimizu worked magnetometrically with metals shaped + as ovoids. + +_Permanent Magnets._--Fleming and Dewar (loc. cit. p. 57) also +investigated the changes which occurred in permanently magnetized +metals when cooled to the temperature of liquid air. The metals, which +were prepared in the form of small rods, were magnetized between the +poles of an electromagnet and tested with a magnetometer at temperatures +of -186° and 15°. The first immersion into liquid air generally produced +a permanent decrease of magnetic moment, and there was sometimes a +further decrease when the metal was warmed up again; but after a few +alternations of temperature the changes of moment became definite and +cyclic. When the permanent magnetic condition had been thus established, +it was found that in the case of all the metals, except the two alloys +containing large percentages of nickel, the magnetic moment was +temporarily increased by cooling to -186°. The following table shows the +principal results. It is suggested that a permanent magnet might +conveniently be "aged" (or brought into a constant condition) by dipping +it several times into liquid air. + + +---------------------------------+--------------------------------+ + | | Percentage Gain or Loss | + | Metal. | of Moment at -186° C. | + | +----------------+---------------+ + | | First Effect. | Cyclic Effect.| + +---------------------------------+----------------+---------------+ + | Carbon steel, hard | -6 | +12 | + | " " medium | Decrease | +22 | + | " " annealed | -33 | +33 | + | Chromium steels (four samples) | Increase | +12 | + | Aluminium steels (three samples)| -2 | +10 | + | Nickel steels, up to 7.65% | Small | +10 | + | " " " 19.64% | -50 | -25 | + | " " " 29% | -20 | -10 | + | Pure nickel | Decrease | +3 | + | Silicon steel, 2.67% | " | +4 | + | Iron, soft | None | +2.5 | + | " hard | Decrease | +10 | + | Tungsten steel, 15% | " | +6 | + | " " 7.5% | " | +10 | + | " " 1% | " | +12 | + +---------------------------------+----------------+---------------+ + + Other experiments relating to the effect of temperature upon permanent + magnets have been carried out by J. R. Ashworth,[60] who showed that + the temperature coefficient of permanent magnets might be reduced to + zero (for moderate ranges of temperature) by suitable adjustment of + temper and dimension ratio; also by R. Pictet,[61] A. Durward[62] and + J. Trowbridge.[63] + +_Alloys of Nickel and Iron._--A most remarkable effect of temperature +was discovered by Hopkinson (_Proc. Roy. Soc._, 1890, 47, 23; 1891, 48, +1) in 1889. An alloy containing about 3 parts of iron and 1 of +nickel--both strongly magnetic metals--is under ordinary conditions +practically non-magnetizable (µ = 1.4 for any value of H). If, however, +this non-magnetic substance is cooled to a temperature a few degrees +below freezing-point, it becomes as strongly magnetic as average +cast-iron (µ = 62 for H = 40), and retains its magnetic properties +indefinitely at ordinary temperatures. But if the alloy is heated up to +580° C. it loses its susceptibility--rather suddenly when H is weak, +more gradually when H is strong--and remains non-magnetizable till it is +once more cooled down below the freezing-point. This material can +therefore exist in either of two perfectly stable conditions, in one of +which it is magnetizable, while in the other it is not. When +magnetizable it is a hard steel, having a specific electrical resistance +of 0.000052; when non-magnetizable it is an extremely soft, mild steel, +and its specific resistance is 0.000072. Alloys containing different +proportions of nickel were found to exhibit the phenomenon, but the two +critical temperatures were less widely separated. The following +approximate figures for small magnetizing forces are deduced from +Hopkinson's curves:-- + + Percentage of Susceptibility lost Susceptibility gained + Nickel. at temp. C. at temp. C. + + 0.97 890 -- + 4.7 820 660 + 4.7 780 600 + 24.5 680 -10 + 30.0 140 125 + 33.0 207 193 + 73.0 202 202 + + Honda and Shimizu (_loc. cit._) have determined the two critical + temperatures for eleven nickel-steel ovoids, containing from 24.04 to + 70.32% of nickel, under a magnetizing force of 400, and illustrated by + an interesting series of curves, the gradual transformation of the + magnetic properties as the percentage of nickel was decreased. They + found that the hysteresis-loss, which at ordinary temperatures is very + small, was increased in liquid air, the increase for the alloys + containing less than 30% of nickel being enormous. Steinmetz's formula + applies only for very weak inductions when the alloys are at the + ordinary temperature, but at the temperature of liquid air it becomes + applicable through a wide range of inductions. According to C. E. + Guillaume[64] the temperature at which the magnetic susceptibility of + nickel-steel is recovered is lowered by the presence of chromium; a + certain alloy containing chromium was not rendered magnetic even by + immersion in liquid air. Experiments on the subject have also been + made by E. Dumont[65] and F. Osmond.[66] + + +9. ALLOYS AND COMPOUNDS OR IRON + +In 1885 Hopkinson (_Phil. Trans._, 1885, 176, 455) employed his yoke +method to test the magnetic properties of thirty-five samples of iron +and steel, among which were steels containing substantial proportions of +manganese, silicon, chromium and tungsten. The results, together with +the chemical analysis of each sample, are given in a table contained in +this paper, some of them being also represented graphically. The most +striking phenomenon which they bring into prominence is the effect of +any considerable quantity of manganese in annihilating the magnetic +property of iron. A sample of Hadfield's manufacture, containing 12.36% +of manganese, differed hardly at all from a non-magnetic substance, its +permeability being only 1.27. According to Hopkinson's calculation, this +sample behaved as if 91% of the iron contained in it had completely lost +its magnetic property.[67] Another point to which attention is directed +is the exceptionally great effect which hardening has upon the magnetic +properties of chrome steel; one specimen had a coercive force of 9 when +annealed, and of no less than 38 when oil-hardened. The effect of the +addition of tungsten in increasing the coercive force is very clearly +shown; in two specimens containing respectively 3.44 and 2.35% of +tungsten the coercive force was 64.5 and 70.7. These high values render +hardened tungsten-steel particularly suitable for the manufacture of +permanent magnets. Hopkinson (_Proc. Roy. Soc._, 1890, 48, 1) also +noticed some peculiarities of an unexpected nature in the magnetic +properties of the nickel-steel alloys already referred to. The +permeability of the alloys containing from 1 to 4.7% of nickel, though +less than that of good soft iron for magnetizing forces up to about 20 +or 30, was greater for higher forces, the induction reached in a field +of 240 being nearly 21,700. The induction for considerable forces was +found to be greater in a steel containing 73% of nickel than in one with +only 33%, though the permeability of pure nickel is much less than that +of iron. + +The magnetic qualities of various alloys of iron have been submitted to +a very complete examination by W. F. Barrett, W. Brown and R. A. +Hadfield (_Trans. Roy. Dub. Soc._, 1900, 7, 67; _Journ. Inst. Elec. +Eng._, 1902, 31, 674).[68] More than fifty different specimens were +tested, most of which contained a known proportion of manganese, nickel, +tungsten, aluminium, chromium, copper or silicon: in some samples two of +the substances named were present. Of the very numerous results +published, a few of the most characteristic are collected in the +following table. The first column contains the symbols of the various +elements which were added to the iron, and the second the percentage +proportion in which each element was present; the sample containing +0.03% of carbon was a specimen of the best commercial iron, the values +obtained for it being given for comparison. All the metals were +annealed. + + A few among several interesting points should be specially noticed. + The addition of 15.2% of manganese produced an enormous effect upon + the magnetism of iron, while the presence of only 2.25% was + comparatively unimportant. When nickel was added to the iron in + increasing quantities the coercive force increased until the + proportion of nickel reached 20%; then it diminished, and when the + proportion of nickel was 32% the coercive force had fallen to the + exceedingly low value of 0.5. In the case of iron containing 7.5% of + tungsten (W), the residual induction had a remarkably high value; the + coercive force, however, was not very great. The addition of silicon + in small quantities considerably diminished permeability and increased + coercive force; but when the proportion amounted to 2.5% the maximum + permeability (µ = 5100 for H = 2) was greater than that of the nearly + pure iron used for comparison, while the coercive force was only + 0.9.[69] A small percentage of aluminium produced still higher + permeability (µ = 6000 for H = 2), the induction in fields up to 60 + being greater than in any other known substance, and the + hysteresis-loss for moderate limits of B far less than in the purest + commercial iron. Certain non-magnetizable alloys of nickel, + chromium-nickel and chromium-manganese were rendered magnetizable by + annealing. + + +--------+---------+-----------+---------+----------+--------+ + |Element.|Per cent.| B | B | µ |Coercive| + | | |for H = 45.|residual.|for H = 8.| Force. | + +--------+---------+-----------+---------+----------+--------+ + | C | 0.03 | 16800 | 9770 | 1625 | 1.66 | + | Cu | 2.5 | 14300 | 10410 | .. | 5.4 | + | Mn | 2.25 | 14720 | 10460 | 1080 | 6.0 | + | Mn | 15.2 | 0 | .. | .. | .. | + | Ni | 3.82 | 16190 | 9320 | 1375 | 2.76 | + | Ni | 19.64 | 7770 | 4770 | 90 | 20.0 | + | Ni | 31.4 | 4460 | 1720 | 357 | 0.5 | + | W | 7.5 | 15230 | 13280 | 500 | 9.02 | + | Al | 2.25 | 16900 | 10500 | 1700 | 1.0 | + | Cr | 3.25 | .. | .. | .. | 12.25 | + | Si | 2.5 | 16420 | 4080 | 1680 | 0.9 | + | Si | 5.5 | 15980 | 3430 | 1630 | 0.85 | + +--------+---------+-----------+---------+----------+--------+ + + Later papers[70] give the results of a more minute examination of + those specimens which were remarkable for very low and very high + permeabilities, and were therefore likely to be of commercial + importance. The following table gives the exact composition of some + alloys which were found to be non-magnetizable, or nearly so, in a + field of 320. + + +---------------------------------------------------------------+ + | An. = Annealed. Un. = Unannealed. | + +------+----------------------------------------+---------------+ + |State.| Percentage Composition. |I, for H = 320.| + +------+----------------------------------------+---------------+ + | Un. | Fe, 85.77; C, 1.23; Mn, 13. | 0 | + | An. | Fe, 84.64; C, 0.15; Mn, 15.2 | 0 | + | An. | Fe, 80.16; C, 0.8; Mn, 5.04; Ni, 14.55.| 3 | + | Un. | Ditto | 0 | + | Un. | Fe, 75.36; C, 0.6; Mn, 5.04; Ni, 19. | 3 | + | An. | Fe, 86.61; C, 1.08; Mn, 10.2; W, 2.11. | 5 | + +------+----------------------------------------+---------------+ + + A very small difference in the constitution often produces a + remarkable effect upon the magnetic quality, and it unfortunately + happens that those alloys which are hardest magnetically are generally + also hardest mechanically and extremely difficult to work; they might + however be used rolled or as castings. The specimens distinguished by + unusually high permeability were constituted as follows:-- + + Silicon-iron.--Fe, 97.3; C, 0.2; Si, 2.5. + + Aluminium-iron.--Fe, 97.33; C, 0.18; Al, 2.25. + + The silicon-iron had, in fields up to about 10, a greater permeability + than a sample of the best Swedish charcoal-iron, and its + hysteresis-loss for max. B = 9000, at a frequency of 100 per second, + was only 0.254 watt per pound, as compared with 0.382 for the Swedish + iron. The aluminium-iron attained its greatest permeability in a field + of 0.5, about that of the earth's force, when its value was 9000, this + being more than twice the maximum permeability of the Swedish iron. + Its hysteresis-loss for B = 9000 was 0.236 per pound. It was, however, + found that the behaviour of this alloy was in part due to a layer of + pure iron ("ferrite") averaging 0.1 mm. in thickness, which occurred + on the outside of the specimen, and the exceptional magnetic quality + which has been claimed for aluminium-iron cannot yet be regarded as + established. + +A number of iron alloys have been examined by Mme. Curie (_Bull. Soc. +d'Encouragement_, 1898, pp. 36-76), chiefly with the object of +determining their suitability for the construction of permanent magnets. +Her tests appear to show that molybdenum is even more effective than +tungsten in augmenting the coercive force, the highest values observed +being 70 to 74 for tungsten-steel, and 80 to 85 for steel containing 3.5 +to 4% of molybdenum. For additional information regarding the +composition and qualities of permanent magnet steels reference may be +made to the publications cited below.[71] Useful instructions have been +furnished by Carl Barus (_Terrestrial Magnetism_, 1897, 2, 11) for the +preparation of magnets calculated to withstand the effects of time, +percussion and ordinary temperature variations. The metal, having first +been uniformly tempered glass-hard, should be annealed in steam at 100° +C. for twenty or thirty hours; it should then be magnetized to +saturation, and finally "aged" by a second immersion in steam for about +five hours. + +_Magnetic Alloys of Non-Magnetic Metals._--The interesting discovery was +made by F. Heusler[72] in 1903 that certain alloys of the non-magnetic +metal manganese with other non-magnetic substances were strongly +magnetizable, their susceptibility being in some cases equal to that of +cast iron. The metals used in different combinations included tin, +aluminium, arsenic, antimony, bismuth and boron; each of these, when +united in certain proportions with manganese, together with a larger +quantity of copper (which appears to serve merely as a menstruum), +constituted a magnetizable alloy. So far, the best results have been +attained with aluminium, and the permeability was greatest when the +percentages of manganese and aluminium were approximately proportional +to the atomic weights of the two metals. Thus in an alloy containing +26.5% of manganese and 14.6% of aluminium, the rest being copper, the +induction for H = 20 was 4500, and for H = 150, 5550. When the +proportion of aluminium to manganese was made a little greater or +smaller, the permeability was diminished. Next to aluminium, tin was +found to be the most effective of the metals enumerated above. In all +such magnetizable alloys the presence of manganese appears to be +essential, and there can be little doubt that the magnetic quality of +the mixtures is derived solely from this component. Manganese, though +belonging (with chromium) to the iron group of metals, is commonly +classed as a paramagnetic, its susceptibility being very small in +comparison with that of the recognized ferromagnetics; but it is +remarkable that its atomic susceptibility in solutions of its salts is +even greater than that of iron. Now iron, nickel and cobalt all lose +their magnetic quality when heated above certain critical temperatures +which vary greatly for the three metals, and it was suspected by +Faraday[73] as early as 1845 that manganese might really be a +ferromagnetic metal having a critical temperature much below the +ordinary temperature of the air. He therefore cooled a piece of the +metal to -105° C., the lowest temperature then attainable, but failed to +produce any change in its magnetic quality. The critical temperature (if +there is one) was not reached in Faraday's experiment; possibly even the +temperature of -250° C., which by the use of liquid hydrogen has now +become accessible, might still be too high.[74] But it has been shown +that the critical temperatures of iron and nickel may be changed by the +addition of certain other substances. Generally they are lowered, +sometimes, however, they are raised[75]; and C. E. Guillaume[76] +explains the ferromagnetism of Heusler's alloy by supposing that the +naturally low critical temperature of the manganese contained in it is +greatly raised by the admixture of another appropriate metal, such as +aluminium or tin; thus the alloy as a whole becomes magnetizable at the +ordinary temperature. If this view is correct, it may also be possible +to prepare magnetic alloys of chromium, the only other paramagnetic +metals of the iron group. + + J. A. Fleming and R. A. Hadfield[77] have made very careful + experiments on an alloy containing 22.42% of manganese, 11.65% of + aluminium and 60.49% of copper. The magnetization curve was found to + be of the same general form as that of a paramagnetic metal, and gave + indications that with a sufficient force magnetic saturation would + probably be attained. There was considerable hysteresis, the + energy-loss per cycle being fairly represented by W = + 0.0005495B^(2.238). The hysteretic exponent is therefore much higher + than in the case of iron, nickel and cobalt, for which its value is + approximately 1.6. + + +10. MISCELLANEOUS EFFECTS OF MAGNETIZATION + +_Electrical Conductivity._--The specific resistance of many electric +conductors is known to be temporarily changed by the action of a +magnetic field, but except in the case of bismuth the effect is very +small. + + A. Gray and E. Taylor Jones (_Proc. Roy. Soc._, 1900, 67, 208) found + that the resistance of a soft iron wire was increased by about 1/700 + in a field of 320 C.G.S. units. The effect appeared to be closely + connected with the intensity of magnetization, being approximately + proportional to I. G. Barlow (_Proc. Roy. Soc._, 1903, 71, 30), + experimenting with wires of iron, steel and nickel, showed that in + weak fields the change of resistance was proportional to a function + aI^2 + bI^4 + cI^6, where a, b and c are constants for each specimen. + W. E. Williams (_Phil. Mag._, 1902, 4, 430) found that for nickel the + curves showing changes of resistance in relation to magnetizing force + were strikingly similar in form to those showing changes of length. H. + Tomlinson (_Phil. Trans._, 1883, Part I., 153) discovered in 1881 that + the resistance of a bismuth rod was slightly increased when the rod + was subjected to longitudinal magnetic force, and a year or two later + A. Righi (_Atti R. A. Lincei_, 1883-1884, 19, 545) showed that a more + considerable alteration was produced when the magnetic force was + applied transversely to the bismuth conductor; he also noticed that + the effect was largely dependent upon temperature (see also P. Lenard, + _Wied. Ann._, 1890, 39, 619). Among the most important experiments on + the influence of magnetic force at different temperatures are those of + J. B. Henderson and of Dewar and Fleming. Henderson (_Phil. Mag._, + 1894, 38, 488) used a little spiral of the pure electrolytic bismuth + wire prepared by Hartmann and Braun; this was placed between the + pole-pieces of an electromagnet and subjected to fields of various + strengths up to nearly 39,000 units. At constant temperature the + resistance increased with the field; the changes in the resistance of + the spiral when the temperature was 18° C. are indicated in the + annexed table, from which it will be seen that in the strongest + + H. R. | H. R. + 0 1.000 | 27450 2.540 + 6310 1.253 | 32730 2.846 + 12500 1.630 | 38900 3.334 + 20450 2.160 | + + transverse field reached the resistance was increased more than + threefold. Other experiments showed the relation of resistance to + temperature (from 0° to about 90°) in different constant fields. It + appears that as the temperature rises the resistance decreases to a + minimum and then increases, the minimum point occurring at a higher + temperature the stronger the field. For H = 11,500 the temperature of + minimum resistance was about 50°; for much lower or higher values of H + the actual minimum did not occur within the range of temperature dealt + with. Dewar and Fleming (_Proc. Roy. Soc._, 1897, 60, 425) worked with + a similar specimen of bismuth, and their results for a constant + temperature of 19° agree well with those of Henderson. They also + experimented with constant temperatures of -79°, -185° and -203°, and + found that at these low temperatures the effect of magnetization was + enormously increased. The following table gives some of their results, + the specific resistance of the bismuth being expressed in C.G.S. + units. + + +-----------+-----------------------+------------------------+ + | | Temp. 19°C. | Temp. -185°C. | + | Field +-----------+-----------+-----------+------------+ + | Strength. | Spec. Res.| Comp. Res.| Spec. Res.| Comp. Res. | + +-----------+-----------+-----------+-----------+------------+ + | 0 | 116200 | 1.000 | 41000 | 1.00 | + | 1375 | 118200 | 1.017 | 103300 | 2.52 | + | 2750 | 123000 | 1.059 | 191500 | 4.67 | + | 8800 | 149200 | 1.284 | 738000 | 18.0 | + | 14150 | 186200 | 1.602 | 1730000 | 42.2 | + | 21800 | 257000 | 2.212 | 6190000 | 151 | + +-----------+-----------+-----------+-----------+------------+ + + At the temperature of liquid air (-185°) the application of a field of + 21,800 multiplied the resistance of the bismuth no less than 150 + times. Fig. 29 shows the variations of resistance in relation to + temperature for fields of different constant values. It will be seen + that for H = 2450 and H = 5500 the minimum resistance occurs at + temperatures of about -80° and -7° respectively. + +_Hall Effect._--If an electric current is passed along a strip of thin +metal, and the two points at opposite ends of an equipotential line are +connected with a galvanometer, its needle will of course not be +deflected. But the application of a magnetic field at right angles to +the plane of the metal causes the equipotential lines to rotate through +a small angle, and the points at which the galvanometer is connected +being no longer at the same potential, a current is indicated by the +galvanometer.[78] The tranverse electromotive force is equal to KCH/D, +where C is the current, H the strength of the field, D the thickness of +the metal, and K a constant which has been termed the _rotatory power_ +or _rotational coefficient_. (See Hopkinson, _Phil. Mag._, 1880, 10, +430). The following values of K for different metals are given by E. H. +Hall, the positive sign indicating that the electromotive force is in +the same direction as the mechanical force acting upon the conductor. A. +von Ettinghausen and W. Nernst (_Wien. Ber._, 1886, 94, 560) have found +that the rotational coefficient of tellurium is more than fifty times +greater than that of bismuth, its sign being positive. Several +experimenters have endeavoured to find a Hall effect in liquids, but +such results as have been hitherto obtained are by no means free from +doubt. E. A. Marx (_Ann. d. Phys._, 1900, 2, 798) observed a +well-defined Hall effect in incandescent gases. A large effect, +proportional to the field, has been found by H. A. Wilson (_Cam. Phil. +Soc. Proc._, 1902, 11, pp. 249, 391) in oxygen, hydrogen and air at low +pressures, and by C. D. Child (_Phys. Rev._, 1904, 18, 370) in the +electric arc. + + Metal. K × 10^15 | Metal. K × 10^15 + | + Antimony +114000 | Copper -520 + Steel +12060 | Gold -660 + Iron +7850 | Nickel -14740 + Cobalt +2460 | Bismuth[79] -8580000 + Zinc +820 | + +[Illustration: _Fig._ 29.] + +_Electro-Thermal Relations._--The Hall electromotive force is only one +of several so-called "galvano-magnetic effects" which are observed when +a magnetic field acts normally upon a thin plate of metal traversed by +an electric current. It is remarkable that if a flow of heat be +substituted for a current of electricity a closely allied group of +"thermo-magnetic effects" is presented. The two classes of phenomena +have been collated by M. G. Lloyd (_Am. Journ. Sci._, 1901, 12, 57), as +follows:-- + + _Galvano-Magnetic Effects._ _Thermo-Magnetic Effects._ + + 1. A transverse difference of i. A transverse difference of + electric potential (Hall effect). electric potential (Nernst effect). + + 2. A transverse difference of ii. A transverse difference of + temperature(Ettinghausen effect). temperature (Leduc effect). + + 3. Longitudinal change of iii. Longitudinal change of + electric conductivity. thermal conductivity. + + 4. Longitudinal difference of iv. Longitudinal difference of + temperature. electric potential.[80] + + +---------------------+ + | C | + | | + | A B | + | D | + +---------------------+ + +If in the annexed diagram ABCD represents the metallic plate through +which the current of electricity or heat flows in the direction AB, +then effects (1), (2), (i.) and (ii.) are exhibited at C and D, effects +(4) and (iv.) at A and B, and effects (3) and (iii.) along AB. The +transverse effects are reversed in direction when either the magnetic +field or the primary current (electric or thermal) is reversed, but the +longitudinal effects are independent of the direction of the field. It +has been shown by G. Moreau (_C. R._, 1900, 130, pp. 122, 412, 562) that +if K is the coefficient of the Hall effect (1) and K´ the analogous +coefficient of the Nernst effect (i.) (which is constant for small +values of H), then K´ = K[sigma]/[rho], [sigma] being the coefficient of +the Thomson effect for the metal and [rho] its specific resistance. He +considers that Hall's is the fundamental phenomenon, and that the Nernst +effect is essentially identical with it, the primary electromotive force +in the case of the latter being that of the Thomson effect in the +unequally heated metal, while in the Hall experiment it is derived from +an external source. + +Attempts have been made to explain these various effects by the electron +theory.[81] + +_Thermo-electric Quality._--The earliest observations of the effect of +magnetization upon thermo-electric power were those of W. Thomson (Lord +Kelvin), who in 1856 announced that magnetization rendered iron and +steel positive to the unmagnetized metals.[82] It has been found by +Chassagny,[83] L. Houllevigue[84] and others that when the magnetizing +force is increased, this effect passes a maximum, while J. A. Ewing[85] +has shown that it is diminished and may even be reversed by tensile +stress. Nickel was believed by Thomson to behave oppositely to iron, +becoming negative when magnetized; but though his conclusion was +accepted for nearly fifty years, it has recently been shown to be an +erroneous one, based, no doubt, upon the result of an experiment with an +impure specimen. Nickel when magnetized is always positive to the +unmagnetized metal. So also is cobalt, as was found by H. Tomlinson.[86] +The curves given by Houllevigue for the relation of thermo-electric +force to magnetic field are of the same general form as those showing +the relation of change of length to field. E. Rhoads[87] obtained a +cyclic curve for iron which indicated thermo-electric hysteresis of the +kind exhibited by Nagaoka's curves for magnetic strain. He also +experimented with nickel and again found a resemblance to the strain +curve. The subject was further investigated by S. Bidwell,[88] who, +adopting special precautions against sources of error by which former +work was probably affected, measured the changes of thermo-electric +force for iron, steel, nickel and cobalt produced by magnetic fields up +to 1500 units. In the case of iron and nickel it was found that, when +correction was made for mechanical stress due to magnetization, magnetic +change of thermo-electric force was, within the limits of experimental +error, proportional to magnetic change of length. Further, it was shown +that the thermo-electric curves were modified both by tensile stress and +by annealing in the same manner as were the change-of-length curves, the +modification being sometimes of a complex nature. Thus a close connexion +between the two sets of phenomena seems to be established. In the case +of cobalt no such relation could be traced; it appeared that the +thermo-electric power of the unmagnetized with respect to the magnetized +cobalt was proportional to the square of the magnetic induction or of +the magnetization. Of nickel six different specimens were tested, all +of which became, like iron, thermo-electrically positive to the +unmagnetized metals. + + As to what effect, if any, is produced upon the thermo-electric + quality of bismuth by a magnetic field there is still some doubt. E. + van Aubel[89] believes that in pure bismuth the thermo-electric force + is increased by the field; impurities may neutralize this effect, and + in sufficient quantities reverse it. + +_Elasticity._--The results of experiments as to the effect of +magnetization were for long discordant and inconclusive, sufficient care +not having been taken to avoid sources of error, while the effects of +hysteresis were altogether disregarded. The subject, which is of +importance in connexion with theories of magnetostriction, has been +investigated by K. Honda and T. Terada in a research remarkable for its +completeness and the ingenuity of the experimental methods employed.[90] +The results are too numerous to discuss in detail; some of those to +which special attention is directed are the following: In Swedish iron +and tungsten-steel the change of elastic constants (Young's modulus and +rigidity) is generally positive, but its amount is less than 0.5%; +changes of Young's modulus and of rigidity are almost identical. In +nickel the maximum change of the elastic constants is remarkably large, +amounting to about 15% for Young's modulus and 7% for rigidity; with +increasing fields the elastic constants first decrease and then +increase. In nickel-steels containing about 50 and 70% of nickel the +maximum increase of the constants is as much as 7 or 8%. In a 29% +nickel-steel, magnetization increases the constants by a small amount. +Changes of elasticity are in all cases dependent, not only upon the +field, but also upon the tension applied; and, owing to hysteresis, the +results are not in general the same when the magnetization follows as +when it precedes the application of stress; the latter is held to be the +right order. + +_Chemical and Voltaic Effects._--If two iron plates, one of which is +magnetized, are immersed in an electrolyte, a current will generally be +indicated by a galvanometer connected with the plates. + + As to whether the magnetized plate becomes positive or negative to the + other, different experimenters are not in agreement. It has, however, + been shown by Dragomir Hurmuzescu (_Rap. du Congrès Int. de Phys._, + Paris, 1900, p. 561) that the true effect of magnetization is liable + to be disguised by secondary or parasitic phenomena, arising chiefly + from polarization of the electrodes and from local variations in the + concentration and magnetic condition of the electrolyte; these may be + avoided by working with weak solutions, exposing only a small surface + in a non-polar region of the metal, and substituting a capillary + electrometer for the galvanometer generally used. When such + precautions are adopted it is found that the "electromotive force of + magnetization" is, for a given specimen, perfectly definite both in + direction and in magnitude; it is independent of the nature of the + corrosive solution, and is a function of the field-strength alone, the + curves showing the relation of electromotive force to field-intensity + bearing a rough resemblance to the familiar I-H curves. The value of + the E.M.F. when H = 2000 is of the order of 1/100 volt for iron, + 1/1000 volt for nickel and 1/10,000 for bismuth. When the two + electrodes are ferromagnetic, the direction of the current through the + liquid is from the unmagnetized to the magnetized electrode, the + latter being least attacked; with diamagnetic electrodes the reverse + is the case. Hurmuzescu shows that these results are in accord with + theory. Applying the principle of the conservation of internal energy, + he demonstrates that for iron in a field of 1000 units and upwards the + E.M.F. of magnetization is + + l I² + E = ------- × -------- approximately, + [delta] 2[kappa] + + l being the electrochemical equivalent and [delta] the density of the + metal. Owing to the difficulty of determining the magnetization I and + the susceptibility [kappa] with accuracy, it has not yet been possible + to submit this formula to a quantitative test, but it is said to + afford an indication of the results given by actual experiment. It has + been discovered by E. L. Nichols and W. S. Franklin (_Am. Journ. + Sci._, 1887, 34, 419; 1888, 35, 290) that the transition from the + "passive" to the active state of iron immersed in strong nitric acid + is facilitated by magnetization, the temperature of transition being + lowered. This is attributed to the action of local currents set up + between unequally magnetized portions of the iron. Similar results + have been obtained by T. Andrews (_Proc. Roy. Soc._, 1890, 48, 116). + + +11. FEEBLY SUSCEPTIBLE SUBSTANCES + +_Water._--The following are recent determinations of the magnetic +susceptibility of water:-- + + Observer. [kappa] × 10^6. Publication. + + G. Quincke -0.797 at 18° C. _Wied. Ann._, 1885, 24, 387. + H. du Bois -0.837 (1 - 0.0025t - 15°) _Wied. Ann._, 1888, 35, 137. + P. Curie -0.790 at 4° C. _C. R._, 1893, 116, 136. + J. Townsend -0.77 _Phil. Trans._, 1896, 187, 544. + J. A. Fleming -0.74 _Proc. Roy. Soc._, 1898, 63, + and J. Dewar 311. + G. Jäger and -0.689(1 - 0.0016t) _Wied. Ann._, 1899, 67, + S. Meyer 707. + J. Koenigsberger -0.781 at 22° C. _Ann. d. Phys._, 1901, 6, 506. + H. D. Stearns -0.733 at 22° C. _Phys. Rev._, 1903, 16, 1. + A. P. Wills -0.720 at 18° C. _Phys. Rev._, 1905, 20, 188. + +Wills found that the susceptibility was constant in fields ranging from +4200 to 15,000. + +_Oxygen and Air._--The best modern determinations of the value of +[kappa] for gaseous oxygen agree very fairly well with that given by +Faraday in 1853 (_Exp. Res._ III, 502). Assuming that for water [kappa] += -0.8 × 10^(-6), his value of [kappa] for oxygen at 15° C. reduces to +0.15 × 10^(-6). Important experiments on the susceptibility of oxygen at +different pressures and temperatures were carried out by P. Curie +(_C.R._ 1892, 115, 805; 1893, 116, 136). _Journ. de Phys._, 1895, 4, +204. He found that the susceptibility for unit of mass, K, was +independent of both pressure and magnetizing force, but varied inversely +as the absolute temperature, [theta], so that 10^6K = 33700/[theta]. +Since the mass of 1 cub. cm. of oxygen at 0° C. and 760 mm. pressure is +0.00141 grm., the mass at any absolute temperature [theta] is by +Charles's law 0.00141 × 273[theta] = 0.3849/[theta] grm.; hence the +susceptibility per unit of volume at 760 mm. will be + + [kappa] = 10^(-6) × 0.3849 × 33700/[theta]² + = 10^(-6) × 12970/[theta]². + +At 15° C. [theta] = 273 + 15 = 288, and therefore [kappa] = 0.156 × +10^(-6), nearly the same as the value found by Faraday. At 0° C., +[kappa] = 0.174 × 10^(-6). For air Curie calculated that the +susceptibility per unit mass was 10^6K = 7830/[theta]; or, taking the +mass of 1 c.c. of air at 0° C. and 760 mm. as 0.001291 grm., [kappa] = +10^(-6) × 2760/[theta]² for air at standard atmospheric pressure. It is +pointed out that this formula may be used as a temperature correction in +magnetic determinations carried out in air. + +Fleming and Dewar determined the susceptibility of liquid oxygen (_Proc. +Roy. Soc._, 1896, 60, 283; 1898, 63, 311) by two different methods. In +the first experiments it was calculated from observations of the mutual +induction of two conducting circuits in air and in the liquid; the +results for oxygen at -182° C. were + + µ = 1.00287, [kappa] = 228 × 10^(-6). + +In the second series, to which greater importance is attached, +measurements were made of the force exerted in a divergent field upon +small balls of copper, silver and other substances, first when the balls +were in air and afterwards when they were immersed in liquid oxygen. If +V is the volume of a ball, H the strength of the field at its centre, +and [kappa]´ its apparent susceptibility, the force in the direction x +is f = [kappa]´VH × dH/dx; and if [kappa]´_a and [kappa]´^0 are the +apparent susceptibilities of the same ball in air and in liquid oxygen, +[kappa]´_a - [kappa]´0 is equal to the difference between the +susceptibilities of the two media. The susceptibility of air being +known--practically it was negligible in these experiments--that of +liquid oxygen can at once be found. The mean of 36 experiments with 7 +balls gave + + µ = 1.00407, [kappa] = 324 × 10^(-6). + +A small but decided tendency to a decrease of susceptibility in very +strong fields was observed. It appears, therefore, that liquid oxygen is +by far the most strongly paramagnetic liquid known, its susceptibility +being more than four times greater than that of a saturated solution of +ferric chloride. On the other hand, its susceptibility is about fifty +times less than that of Hadfield's 12% manganese steel, which is +commonly spoken of as non-magnetizable. + +_Bismuth._--Bismuth is of special interest, as being the most strongly +diamagnetic substance known, the mean value of the best determinations +of its susceptibility being about -14 × 10^(-6) (see G. Meslin, _C. R._, +1905, 140, 449). The magnetic properties of the metal at different +temperatures and in fields up to 1350 units have been studied by P. +Curie (_loc. cit._), who found that its "specific susceptibility" (K) +was independent of the strength of the field, but decreased with rise of +temperature up to the melting-point, 273°C. His results appear to show +the relation + + -[Kappa] × 10^6 = 1.381 - 0.00155t°. + +Assuming the density of Bi to be 9.8, and neglecting corrections for +heat dilatation, his value for the susceptibility at 20°C. is equivalent +to [kappa] = -13.23 × 10^(-6). As the temperature was raised up to 273°, +[kappa] gradually fell to -9.38 × 10^[-6], rising suddenly when fusion +occurred to -0.37 × 10^(-6), at which value it remained constant when +the fluid metal was further heated. Fleming and Dewar give for the +susceptibility the values -13.7 × 10^(-6) at 15°C. and -15.9 × 10^(-6) +at -182°, the latter being approximately equivalent to [Kappa] × 10^6 = +-1.62. Putting t° = -182 in the equation given above for Curie's +results, we get [Kappa] × 10^6 = -1.66, a value sufficiently near that +obtained by Fleming and Dewar to suggest the probability that the +diamagnetic susceptibility varies inversely as the temperature between +-182° and the melting-point. + +_Other Diamagnetics._--The following table gives Curie's determinations +(_Journ. de Phys._, 1895, 4, 204) of the specific susceptibility [Kappa] +of other diamagnetic substances at different temperatures. It should be +noted that [Kappa] = [kappa]/density. + + Substance Temp. °C. -[Kappa] × 10^6. + + Water 15-189 0.790 + Rock salt 16-455 0.580 + Potassium chloride 18-465 0.550 + " sulphate 17-460 0.430 + " nitrate (fusion 350°) 18-420 0.330 + Quartz 18-430 0.441 + Sulphur, solid or fused 18-225 0.510 + Selenium, solid or fused 20-200 0.320 + " fused 240-415 0.307 + Tellurium 20-305 0.311 + Bromine 20 0.410 + Iodine, solid or fused 18-164 0.385 + Phosphorus, solid or fused 19-71 0.920 + " amorphous 20-275 0.730 + Antimony, electrolytic 20 0.680 + " 540 0.470 + Bismuth, solid 20 1.350 + " " 273 0.957 + " fused 273-405 0.038 + +For all diamagnetic substances, except antimony and bismuth, the value +of [Kappa] was found to be independent of the temperature. + +_Paramagnetic Substances._--Experiments by J. S. Townsend (_Phil. +Trans._, 1896, 187, 533) show that the susceptibility of solutions of +salts of iron is independent of the magnetizing force, and depends only +on the quantity of iron contained in unit volume of the liquid. If W is +the weight of iron present per c.c. at about 10°C., then for ferric +salts + + 10^6[kappa] = 266W - 0.77 + +and for ferrous salts + + 10^6[kappa] = 206W - 0.77, + +the quantity -0.77 arising from the diamagnetism of the water of +solution. Annexed are values of 10^6[kappa] for the different salts +examined, w being the weight of the salt per c.c. of the solution. + + Salt. 10^6[kappa] + 0.77 | Salt. 10^6[kappa] + 0.77 + | + Fe2Cl6 91.6w | FeCl2 90.8w + Fe2(SO4)3 74.5w | FeSO4 74.9w + Fe2(NO3)6 61.5w + +Susceptibility was found to diminish greatly with rise of temperature. +According to G. Jäger and S. Meyer (_Wien. Akad. Sitz._, 1897, 106, II. +a, p. 623, and 1898, 107, II. a, p. 5) the atomic susceptibilities k of +the metals nickel, chromium, iron, cobalt and manganese in solutions of +their salts are as follows:-- + + Metal. k × 10^6 | Metal. k × 10^6. + | + Ni 4.95 = 2.5 × 2 | Co 10.0 = 2.5 × 4 + Cr 6.25 = 2.5 × 2.5 | Fe(2) 12.5 = 2.5 × 5 + Fe(1) 7.5 = 2.5 × 3 | Mn 15.0 = 2.5 × 6 + + +Fe(1) is iron contained in FeCl2 and Fe(2) iron contained in Fe2(NO3)6. + +Curie has shown, for many paramagnetic bodies, that the specific +susceptibility K is inversely proportional to the absolute temperature +[theta]. Du Bois believes this to be an important general law, +applicable to the case of every paramagnetic substance, and suggests +that the product K[theta] should be known as "Curie's constant" for the +substance. + +_Elementary Bodies and Atomic Susceptibility._--Among a large number of +substances the susceptibilities of which have been determined by J. +Koenigsberger (_Wied. Ann._, 1898, 66, 698) are the following +elements:-- + + Element. [kappa] × 10^6. | Element. [kappa] × 10^6. + | + Copper -0.82 | Tellurium - 2.10 + Silver -1.51 | Graphite + 2 + Gold -3.07 | Aluminium + 1.80 + Zinc -0.96 | Platinum +22 + Tin +0.46 | Palladium +50 to 60 + Lead -1.10 | Tungsten +14 + Thallium -4.61 | Magnesium + 4 + Sulphur -0.86 | Sodium + 2.2 + Selenium (red) -0.50 | Potassium + 3.6 + +In a table accompanying Koenigsberger's paper the elements are arranged +upon the periodic system and the atomic susceptibility (product of +specific susceptibility into atomic weight) is given for each. It +appears that the elements at about the middle of each row are the most +strongly paramagnetic; towards the ends of a row the susceptibility +decreases, and ultimately becomes negative. Thus a relation between +susceptibility and atomic weight is clearly indicated. Tables similarly +arranged, but much more complete, have been published by S. Meyer +(_Wied. Ann._, 1899, 68, 325 and 1899, 69, 236), whose researches have +filled up many previously existing gaps. The values assigned to the +atomic susceptibilities of most of the known elements are appended. +According to the notation adopted by Meyer the atomic susceptibility k = +[kappa] × atomic-weight/(density × 1000). + + Meyer thinks that the susceptibilities of the metals praseodymium, + neodymium, ytterbium, samarium, gadolinium, and erbium, when obtained + in a pure form, will be found to equal or even exceed those of the + well-known ferromagnetic metals. Many of their compounds are very + strongly magnetic; erbium, for example, in Er2O3 being four times as + strong as iron in the familiar magnetite or lodestone, Fe2O3. The + susceptibilities of some hundreds of inorganic compounds have also + been determined by the same investigator (loc. cit.). Among other + researches relating to atomic and molecular magnetism are those of O. + Liebknecht and A. P. Wills (_Ann. d. Phys._, 1900, 1, 178), H. du Bois + and O. Liebknecht (ibid. p. 189), and Meyer (ibid. p. 668). An + excellent summary regarding the magnetic properties of matter, with + many tables and references, has been compiled by du Bois (_Report to + the Congrès Int. de Phys._, Paris, 1900, ii. 460). + + +--------------------+--------------------+-------------------+ + | _Element_ 10^6k | _Element_ 10^6k | _Element_ 10^6k | + +--------------------+--------------------+-------------------+ + | Be +0.72 | Cu -0.006 | Cs -0.03* | + | B +0.05 | Zn -0.010 | Ba -0.02* | + | C -0.05 | Ga - | La +13.0 | + | N ? | Ge - | Ce +34.0 | + | O + | As ? | Pr +\ | + | F -0.01* | Se -0.025 | Nd +| Strong| + |....................| Br -0.033 | Sa +| | + | Na -0.005* |....................| Gd +/ | + | Mg +0.014 | Rb -0.02* |...................| + | Al + | Sr -0.02* | Er +41.8(?) | + | Si +0.002 | Y +3.2(?) |...................| + | P -0.007 | Zr -0.014 | Yb + (?) | + | S -0.011 | Nb +0.49(?) | Ta +1.02(?) | + | Cl -0.02* | Mo +0.024 | W +0.1 | + |....................| Ru + | Os +0.074 | + | K -0.001* | Rh + | Ir + | + | Ca -0.003* | Pd +0.55 | Pt +0.227 | + | Sc ? | Ag -0.016 | Au -0.031 | + | Ti +0.09 | Cd -0.015 | Hg -0.030 | + | V +0.17 | In +0.01* | Tl -0.93 | + | Cr +\ | Sn +0.004* | Pb -0.025 | + | Mn +| | Sb -0.069 | Bi -0.023 | + | Fe +|Strong | Te -0.039 |...................| + | Co +| | I -0.040 | Th +16.0(?) | + | Ni +/ |....................| U +0.21 | + +--------------------+--------------------+-------------------+ + * Calculated. + + +12. MOLECULAR THEORY OF MAGNETISM + +According to W. E. Weber's theory, the molecules of a ferromagnetic +metal are small permanent magnets, the axes of which under ordinary +conditions are turned indifferently in every direction, so that no +magnetic polarity is exhibited by the metal as a whole; a magnetic force +acting upon the metal tends to turn the axes of the little magnets in +one direction, and thus the entire piece acquires the properties of a +magnet. If, however, the molecules could turn with perfect freedom, it +is clear that the smallest magnetizing force would be sufficient to +develop the highest possible degree of magnetization, which is of course +not the case. Weber therefore supposed each molecule to be acted on by a +force tending to preserve it in its original direction, the position +actually assumed by the axis being in the direction of the resultant of +this hypothetical force and the applied magnetizing force. Maxwell +(_Electricity and Magnetism_, § 444), recognizing that the theory in +this form gave no account of residual magnetization, made the further +assumption that if the deflection of the axis of the molecule exceeded a +certain angle, the axis would not return to its original position when +the deflecting force was removed, but would retain a permanent set. +Although the amended theory as worked out by Maxwell is in rough +agreement with certain leading phenomena of magnetization, it fails to +account for many others, and is in some cases at variance with observed +facts. + +J. A. Ewing (_Proc. Roy. Soc._, 1890, 48, 342) has demonstrated that it +is quite unnecessary to assume either the directive force of Weber, the +permanent set of Maxwell, or any kind of frictional resistance, the +forces by which the molecular magnets are constrained being simply those +due to their own mutual attractions and repulsions. The effect of these +is beautifully illustrated by a model consisting of a number of little +compass needles pivoted on sharp points and grouped near to one another +upon a board, which is placed inside a large magnetizing coil. When no +current is passing through the coil and the magnetic field is of zero +strength, the needles arrange themselves in positions of stable +equilibrium under their mutual forces, pointing in many different +directions, so that there is no resultant magnetic moment. This +represents the condition of the molecules in unmagnetized iron. If now a +gradually increasing magnetizing force is applied, the needles at first +undergo a stable deflection, giving to the group a small resultant +moment which increases uniformly with the force; and if the current is +interrupted while the force is still weak, the needles merely return to +their initial positions. This illustrates the first stage in the process +of magnetization, when the moment is proportional to the field and there +is no hysteresis or residual magnetism (see _ante_). A somewhat stronger +field will deflect many of the needles beyond the limits of stability, +causing them to turn round and form new stable combinations, in which +the direction assumed by most of them approximates to that of the field. +The rearrangement is completed within a comparatively small range of +magnetizing force, a rapid increase of the resultant moment being thus +brought about. When the field is removed, many of the newly formed +combinations are but slightly disturbed, and the group may consequently +retain a considerable resultant moment. This corresponds to the second +stage of magnetization, in which the susceptibility is large and +permanent magnetization is set up. A still stronger magnetizing force +has little effect except in causing the direction of the needles to +approach still more nearly to that of the field; if the force were +infinite, every member of the group would have exactly the same +direction and the greatest possible resultant moment would be reached; +this illustrates "magnetic saturation"--the condition approached in the +third stage of magnetization. When the strong magnetizing field is +gradually diminished to zero and then reversed, the needles pass from +one stable position of rest to another through a condition of +instability; and if the field is once more reversed, so that the cycle +is completed, the needles again pass through a condition of instability +before a position of stable equilibrium is regained. Now the unstable +movements of the needles are of a mechanically irreversible character; +the energy expended in dissociating the members of a combination and +placing them in unstable positions assumes the kinetic form when the +needles turn over, and is ultimately frittered down into heat. Hence in +performing a cycle there is a waste of energy corresponding to what has +been termed hysteresis-loss. + +Supposing Ewing's hypothesis to be correct, it is clear that if the +magnetization of a piece of iron were reversed by a strong rotating +field instead of by a field alternating through zero, the loss of energy +by hysteresis should be little or nothing, for the molecules would +rotate with the field and no unstable movements would be possible.[91] +Some experiments by F. G. Baily (_Phil. Trans._, 1896, 187, 715) show +that this is actually the case. With small magnetizing forces the +hysteresis was indeed somewhat larger than that obtained in an +alternating field, probably on account of the molecular changes being +forced to take place in one direction only; but at an induction of about +16,000 units in soft iron and 15,000 in hard steel the hysteresis +reached a maximum and afterwards rapidly diminished. In one case the +hysteresis loss per cubic centimetre per cycle was 16,100 ergs for B = +15,900, and only 1200 ergs for B = 20,200, the highest induction +obtained in the experiment; possibly it would have vanished before B had +reached 21,000.[92] These experiments prove that actual friction must be +almost entirely absent, and, as Baily remarks, the agreement of the +results with the previously suggested deduction affords a strong +verification of Ewing's form of the molecular theory. Ewing has himself +also shown how satisfactorily this theory accords with many other +obscure and complicated phenomena, such as those presented by coercive +force, differences of magnetic quality, and the effects of vibration, +temperature and stress; while as regards simplicity and freedom from +arbitrary assumptions it leaves little to be desired. + +The fact being established that magnetism is essentially a molecular +phenomenon, the next step is to inquire what is the constitution of a +magnetic molecule, and why it is that some molecules are ferromagnetic, +others paramagnetic, and others again diamagnetic. The best known of the +explanations that have been proposed depend upon the magnetic action of +an electric current. It can be shown that if a current i circulates in a +small plane circuit of area S, the magnetic action of the circuit for +distant points is equivalent to that of a short magnet whose axis is +perpendicular to the plane of the circuit and whose moment is iS, the +direction of the magnetization being related to that of the circulating +current as the thrust of a right-handed screw to its rotation. +Ferromagnetism was explained by Ampère on the hypothesis that the +magnetization of the molecule is due to an electric current constantly +circulating within it. The theory now most in favour is merely a +development of Ampère's hypothesis, and applies not only to +ferromagnetics, but to paramagnetics as well. To account for +diamagnetism, Weber supposed that there exist within the molecules of +diamagnetic substances certain channels around which an electric current +can circulate without any resistance. The creation of an external +magnetic field H will, in accordance with Lenz's law, induce in the +molecule an electric current so directed that the magnetization of the +equivalent magnet is opposed to the direction of the field. The strength +of the induced current is -HScos[theta]/L, where [theta] is the +inclination of the axis of the circuit to the direction of the field, +and L the coefficient of self-induction; the resolved part of the +magnetic moment in the direction of the field is equal to +-HS²cos²[theta]/L, and if there are n molecules in a unit of volume, +their axes being distributed indifferently in all directions, the +magnetization of the substance will be -(1/3)nHS²/L, and its +susceptibility -(1/3)S²/L (Maxwell, _Electricity and Magnetism_, § 838). +The susceptibility is therefore constant and independent of the field, +while its negative sign indicates that the substance is diamagnetic. +There being no resistance, the induced current will continue to +circulate round the molecule until the field is withdrawn, when it will +be stopped by the action of an electromotive force tending to induce an +exactly equal current in the opposite direction. The principle of +Weber's theory, with the modification necessitated by lately acquired +knowledge, is the basis of the best modern explanation of diamagnetic +phenomena. + +There are strong reasons for believing that magnetism is a phenomenon +involving rotation, and as early as 1876 Rowland, carrying out an +experiment which had been proposed by Maxwell, showed that a revolving +electric charge produced the same magnetic effects as a current. Since +that date it has more than once been suggested that the molecular +currents producing magnetism might be due to the revolution of one or +more of the charged atoms or "ions" constituting the molecule. None of +the detailed hypotheses which were based on this idea stood the test of +criticism, but towards the end of the 19th century the researches of J. +J. Thomson and others once more brought the conception of moving +electric charges into prominence. Thomson has demonstrated the existence +under many different conditions of particles more minute than anything +previously known to science. The mass of each is about 1/1700th part of +that of a hydrogen atom, and with each is indissolubly associated a +charge of negative electricity equal to about 3.1 × 10^(-10) C.G.S. +electrostatic unit. These particles, which were termed by their +discoverer _corpuscles_, are more commonly spoken of as _electrons_,[93] +the particle thus being identified with the charge which it carries. An +electrically neutral atom is believed to be constituted in part, or +perhaps entirely, of a definite number of electrons in rapid motion +within a "sphere of uniform positive electrification" not yet explained. +One or more of the electrons may be detached from the system by a finite +force, the number so detachable depending on the valency of the atom; if +the atom loses an electron, it becomes positively electrified; if it +receives additional electrons, it is negatively electrified. The process +of electric conduction in metals consists in the movement of detached +electrons, and many other phenomena, both electrical and thermal, can be +more or less completely explained by their agency. It has been supposed +that certain electrons revolve like satellites in orbits around the +atoms with which they are associated, a view which receives strong +support from the phenomena of the Zeeman effect, and on this assumption +a theory has been worked out by P. Langevin,[94] which accounts for many +of the observed facts of magnetism. As a consequence of the structure of +the molecule, which is an aggregation of atoms, the planes of the orbits +around the latter may be oriented in various positions, and the +direction of revolution may be right-handed or left-handed with respect +to the direction of any applied magnetic field. For those orbits whose +projection upon a plane perpendicular to the field is right-handed, the +period of revolution will be accelerated by the field (since the +electron current is negative), and the magnetic moment consequently +increased; for those which are left-handed, the period will be retarded +and the moment diminished. The effect of the field upon the speed of the +revolving electrons, and therefore upon the moments of the equivalent +magnets, is necessarily a very small one. If S is the area of the orbit +described in time [tau] by an electron of charge e, the moment of the +equivalent magnet is M = eS[tau]; and the change in the value of M due +to an external field H is shown to be [Delta]M = -He^2 S/4[pi]m, m being +the mass of the electron. Whence + + [Delta]M H[tau]e + -------- = -------. + M 4[pi]m + +According to the best determinations the value of e/m does not exceed +1.8 × 10^7, and [tau] is of the order of 10^(-15) second, the period of +luminous vibrations; hence [Delta]M/M must always be less than 10^(-9)H, +and therefore the strongest fields yet reached experimentally, which +fall considerably short of 10^5, could not change the magnetic moment M +by as much as a ten-thousandth part. If the structure of the molecule is +so perfectly symmetrical that, in the absence of any external field, the +resultant magnetic moment of the circulating electrons is zero, then the +application of a field, by accelerating the right-handed (negative) +revolutions, and retarding those which are left-handed, will induce in +the substance a resultant magnetization opposite in direction to the +field itself; a body composed of such symmetrical molecules is therefore +diamagnetic. If however the structure of the molecule is such that the +electrons revolving around its atoms do not exactly cancel one another's +effects, the molecule constitutes a little magnet, which under the +influence of an external field will tend to set itself with its axis +parallel to the field. Ordinarily a substance composed of asymmetrical +molecules is paramagnetic, but if the elementary magnets are so +conditioned by their strength and concentration that mutual action +between them is possible, then the substance is ferromagnetic. In all +cases however it is the diamagnetic condition that is initially set +up--even iron is diamagnetic--though the diamagnetism may be completely +masked by the superposed paramagnetic or ferromagnetic condition. +Diamagnetism, in short, is an atomic phenomenon; paramagnetism and +ferromagnetism are molecular phenomena. Hence may be deduced an +explanation of the fact that, while the susceptibility of all known +diamagnetics (except bismuth and antimony) is independent of the +temperature, that of paramagnetics varies inversely as the absolute +temperature, in accordance with the law of Curie. + + +13. HISTORICAL AND CHRONOLOGICAL NOTES + +The most conspicuous property of the lodestone, its attraction for iron, +appears to have been familiar to the Greeks at least as early as 800 +B.C., and is mentioned by Homer, Plato, Aristotle, Theophrastus and +others. A passage in _De rerum natura_ (vi. 910-915) by the Roman poet, +Lucretius (96-55 B.C.), in which it is stated that the stone can support +a chain of little rings, each adhering to the one above it, indicates +that in his time the phenomenon of magnetization by induction had also +been observed. The property of orientation, in virtue of which a freely +suspended magnet points approximately to the geographical north and +south, is not referred to by any European writer before the 12th +century, though it is said to have been known to the Chinese at a much +earlier period. The application of this property to the construction of +the mariner's compass is obvious, and it is in connexion with navigation +that the first references to it occur (see COMPASS). The needles of the +primitive compasses, being made of iron, would require frequent +re-magnetization, and a "stone" for the purpose of "touching the needle" +was therefore generally included in the navigator's outfit. With the +constant practice of this operation it is hardly possible that the +repulsion acting between like poles should have entirely escaped +recognition; but though it appears to have been noticed that the +lodestone sometimes repelled iron instead of attracting it, no clear +statement of the fundamental law that unlike poles attract while like +poles repel was recorded before the publication in 1581 of the _New +Attractive_ by Robert Norman, a pioneer in accurate magnetic work. The +same book contains an account of Norman's discovery and correct +measurement of the dip (1576). The downward tendency of the north pole +of a magnet pivoted in the usual way had been observed by G. Hartmann of +Nüremberg in 1544, but his observation was not published till much +later. + +The foundations of the modern science of magnetism were laid by William +Gilbert (q.v.). His _De magnete magneticisque corporibus et de magno +magnete tellure physiologia nova_ (1600), contains many references to +the expositions of earlier writers from Plato down to those of the +author's own age. These show that the very few facts known with +certainty were freely supplemented by a number of ill-founded +conjectures, and sometimes even by "figments and falsehoods, which in +the earliest times, no less than nowadays, used to be put forth by raw +smatterers and copyists to be swallowed of men."[95] Thus it was taught +that "if a lodestone be anointed with garlic, or if a diamond be near, +it does not attract iron," and that "if pickled in the salt of a sucking +fish, there is power to pick up gold which has fallen into the deepest +wells." There were said to be "various kinds of magnets, some of which +attract gold, others silver, brass, lead; even some which attract flesh, +water, fishes;" and stories were told about "mountains in the north of +such great powers of attraction that ships are built with wooden pegs, +lest the iron nails should be drawn from the timber." Certain occult +powers were also attributed to the stone. It was "of use to thieves by +its fume and sheen, being a stone born, as it were, to aid theft," and +even opening bars and locks; it was effective as a love potion, and +possessed "the power to reconcile husbands to their wives, and to recall +brides to their husbands." And much more of the same kind, which, as +Gilbert says, had come down "even to [his] own day through the writings +of a host of men, who, to fill out their volumes to a proper bulk, write +and copy out pages upon pages on this, that and the other subject, of +which they know almost nothing for certain of their own experience." +Gilbert himself absolutely disregarded authority, and accepted nothing +at second-hand. His title to be honoured as the "Father of Magnetic +Philosophy" is based even more largely upon the scientific method which +he was the first to inculcate and practise than upon the importance of +his actual discoveries. Careful experiment and observation, not the +inner consciousness, are, he insists, the only foundations of true +science. Nothing has been set down in his book "which hath not been +explored and many times performed and repeated" by himself. "It is very +easy for men of acute intellect, apart from experiment and practice, to +slip and err." The greatest of Gilbert's discoveries was that the globe +of the earth was magnetic and a magnet; the evidence by which he +supported this view was derived chiefly from ingenious experiments made +with a spherical lodestone or _terrella_, as he termed it, and from his +original observation that an iron bar could be magnetized by the earth's +force. He also carried out some new experiments on the effects of heat, +and of screening by magnetic substances, and investigated the influence +of shape upon the magnetization of iron. But the bulk of his work +consisted in imparting scientific definiteness to what was already +vaguely known, and in demolishing the errors of his predecessors. + +No material advance upon the knowledge recorded in Gilbert's book was +made until the establishment by Coulomb in 1785 of the law of magnetic +action. The difficulties attending the experimental investigation of the +forces acting between magnetic poles have already been referred to, and +indeed a rigorously exact determination of the mutual action could only +be made under conditions which are in practice unattainable. +Coulomb,[96] however, by using long and thin steel rods, symmetrically +magnetized, and so arranged that disturbing influences became negligibly +small, was enabled to deduce from his experiments with reasonable +certainty the law that the force of attraction or repulsion between two +poles varies inversely as the square of the distance between them. +Several previous attempts had been made to discover the law of force, +with various results, some of which correctly indicated the inverse +square; in particular the German astronomer, J. Tobias Mayer (_Gött. +Anzeiger_, 1760), and the Alsatian mathematician, J. Heinrich Lambert +(_Hist. de l'Acad. Roy. Berlin_, 1766, p. 22), may fairly be credited +with having anticipated the law which was afterwards more satisfactorily +established by Coulomb. The accuracy of this law was in 1832 confirmed +by Gauss,[97] who employed an indirect but more perfect method than that +of Coulomb, and also, as Maxwell remarks, by all observers in magnetic +observatories, who are every day making measurements of magnetic +quantities, and who obtain results which would be inconsistent with each +other if the law of force had been erroneously assumed. + +Coulomb's researches provided data for the development of a mathematical +theory of magnetism, which was indeed initiated by himself, but was +first treated in a complete form by Poisson in a series of memoirs +published in 1821 and later.[98] Poisson assumed the existence of two +dissimilar magnetic fluids, any element of which acted upon any other +distant element in accordance with Coulomb's law of the inverse square, +like repelling and unlike attracting one another. A magnetizable +substance was supposed to consist of an indefinite number of spherical +particles, each containing equivalent quantities of the two fluids, +which could move freely within a particle, but could never pass from one +particle to another. When the fluids inside a particle were mixed +together, the particle was neutral; when they were more or less +completely separated, the particle became magnetized to an intensity +depending upon the magnetic force applied; the whole body therefore +consisted of a number of little spheres having north and south poles, +each of which exerted an elementary action at a distance. On this +hypothesis Poisson investigated the forces due to bodies magnetized in +any manner, and also originated the mathematical theory of magnetic +induction. The general confirmation by experiment of Poisson's +theoretical results created a tendency to regard his hypothetical +magnetic fluids as having a real existence; but it was pointed out by W. +Thomson (afterwards Lord Kelvin) in 1849 that while no physical evidence +could be adduced in support of the hypothesis, certain discoveries, +especially in electromagnetism, rendered it extremely improbable +(_Reprint_, p. 344). Regarding it as important that all reasoning with +reference to magnetism should be conducted without any uncertain +assumptions, he worked out a mathematical theory upon the sole +foundation of a few well-known facts and principles. The results were +substantially the same as those given by Poisson's theory, so far as the +latter went, the principal additions including a fuller investigation of +magnetic distribution, and the theory of magnetic induction in +aeolotropic or crystalline substances. The mathematical theory which was +constructed by Poisson, and extended and freed from doubtful hypotheses +by Kelvin, has been elaborated by other investigators, notably F. E. +Neumann, G. R. Kirchhoff, and Maxwell. The valuable work of Gauss on +magnetic theory and measurements, especially in relation to terrestrial +magnetism, was published in his _Intensitas vis magneticae terrestris_, +1833, and in memoirs communicated to the _Resultate aus den +Beobachtungen des magnetischen Vereins_, 1838 and 1839, which, with +others, are contained in vol. 5 of the collected _Werke_. Weber's +molecular theory, which has already been referred to, appeared in +1852.[99] + +An event of the first importance was the discovery made in 1819 by H. C. +Oersted [100] that a magnet placed near a wire carrying an electric +current tended to set itself at right angles to the wire, a phenomenon +which indicated that the current was surrounded by a magnetic field. +This discovery constituted the foundation of electromagnetism, and its +publication in 1820 was immediately followed by A. M. Ampère's +experimental and theoretical investigation of the mutual action of +electric currents,[101] and of the equivalence of a closed circuit to a +polar magnet, the latter suggesting his celebrated hypothesis that +molecular currents were the cause of magnetism. In the same year D. F. +Arago[102] succeeded in magnetizing a piece of iron by the electric +current, and in 1825 W. Sturgeon[103] publicly exhibited an apparatus +"acting on the principle of powerful magnetism and feeble galvanism" +which is believed to have constituted the first actual electromagnet. +Michael Faraday's researches were begun in 1831 and continued for more +than twenty years. Among the most splendid of his achievements was the +discovery of the phenomena and laws of magneto-electric induction, the +subject of two papers communicated to the Royal Society in 1831 and +1832. Another was the magnetic rotation of the plane of polarization of +light, which was effected in 1845, and for the first time established a +relation between light and magnetism. This was followed at the close of +the same year by the discovery of the magnetic condition of all matter, +a discovery which initiated a prolonged and fruitful study of +paramagnetic and diamagnetic phenomena, including magnecrystallic action +and "magnetic conducting power," now known as permeability. Throughout +his researches Faraday paid special regard to the medium as the true +seat of magnetic action, being to a large extent guided by his pregnant +conception of "lines of force," or of induction, which he considered to +be "closed curves passing in one part of the course through the magnet +to which they belong, and in the other part through space," always +tending to shorten themselves, and repelling one another when they were +side by side (_Exp. Res._ §§ 3266-8, 3271). In 1873 James Clerk Maxwell +published his classical _Treatise on Electricity and Magnetism_, in +which Faraday's ideas were translated into a mathematical form. Maxwell +explained electric and magnetic forces, not by the action at a distance +assumed by the earlier mathematicians, but by stresses in a medium +filling all space, and possessing qualities like those attributed to the +old luminiferous ether. In particular, he found that the calculated +velocity with which it transmitted electromagnetic disturbances was +equal to the observed velocity of light; hence he was led to believe, +not only that his medium and the ether were one and the same, but, +further, that light itself was an electromagnetic phenomenon. Since the +experimental confirmation of Maxwell's views by H. R. Hertz in 1888 +(_Weid. Ann._, 1888, 34, 155, 551, 609; and later vols.) they have +commanded universal assent, and his methods are adopted in all modern +work on electricity and magnetism. + +The practice of measuring magnetic induction and permeability with +scientific accuracy was introduced in 1873 by H. A. Rowland,[104] whose +careful experiments led to general recognition of the fact previously +ignored by nearly all investigators, that magnetic susceptibility and +permeability are by no means constants (at least in the case of the +ferromagnetic metals) but functions of the magnetizing force. New light +was thrown upon many important details of magnetic science by J. A. +Ewing's _Experimental Researches_ of 1885; throughout the whole of his +work special attention was directed to that curious lagging action to +which the author applied the now familiar term "hysteresis."[105] His +well-known modification[106] of Weber's molecular theory, published in +1890, presented for the first time a simple and sufficient explanation +of hysteresis and many other complexities of magnetic quality. The +amazing discoveries made by J. J. Thomson in 1897 and 1898[107] resulted +in the establishment of the electron theory, which has already effected +developments of an almost revolutionary character in more than one +branch of science. The application of the theory by P. Langevin to the +case of molecular magnetism has been noticed above, and there can be +little doubt that in the near future it will contribute to the solution +of other problems which are still obscure. + + See W. Gilbert, _De magnete_ (London, 1600; trans. by P. F. Mottelay, + New York, 1893, and for the Gilbert Club, London, 1900); M. Faraday, + _Experimental Researches in Electricity_, 3 vols. (London, 1839, 1844 + and 1855); W. Thomson (Lord Kelvin), _Reprint of Papers on + Electrostatics and Magnetism_ (London, 1884, containing papers on + magnetic theory originally published between 1844 and 1855, with + additions); J. C. Maxwell, _Treatise on Electricity and Magnetism_ + (3rd ed., Oxford, 1892); E. Mascart and J. Joubert, _Leçons sur + l'électricité et le magnétisme_ (2nd ed., Paris, 1896-1897; trans., + not free from errors, by E. Atkinson, London, 1883); J. A. Ewing, + _Magnetic Induction in Iron and other Metals_ (3rd ed., London, + 1900); J. J. Thomson, _Recent Researches in Electricity and Magnetism_ + (Oxford, 1893); _Elements of Mathematical Theory of Electricity and + Magnetism_ (3rd ed., Cambridge, 1904); H. du Bois, _The Magnetic + Circuit_ (trans. by E. Atkinson, London, 1896); A. Gray, _Treatise on + Magnetism and Electricity_, vol. i. (London, 1898); J. A. Fleming, + _Magnets and Electric Currents_ (London, 1898); C. Maurain, _Le + magnétisme du fer_ (Paris, 1899; a lucid summary of the principal + facts and laws, with special regard to their practical application); + _Rapports présentés au Congrès international de physique_, vol. ii. + (Paris, 1900); G. C. Foster and A. W. Porter, _Treatise on Electricity + and Magnetism_ (London, 1903); A. Winkelmann, _Handbuch der Physik_, + vol. v. part i. (2nd ed., Leipzig, 1905; the most exhaustive + compendium of magnetic science yet published, containing references to + all important works and papers on every branch of the subject). + (S. Bi.) + + +FOOTNOTES: + + [1] In London in 1910 the needle pointed about 16° W. of the + geographical north. (See TERRESTRIAL MAGNETISM.) + + [2] For the relations between magnetism and light see MAGNETO-OPTICS. + + [3] Clerk Maxwell employed German capitals to denote vector + quantities. J. A. Fleming first recommended the use of blockletters + as being more convenient both to printers and readers. + + [4] The C.G.S. unit of current = 10 amperes. + + [5] The principal theoretical investigations are summarized in + Mascart and Joubert's _Electricity and Magnetism_, i. 391-398 and ii. + 646-657. The case of a long iron bar has been experimentally studied + with great care by C. G. Lamb, _Proc. Phys. Soc._, 1899, 16, 509. + + [6] _Wied. Ann._, 1884, 22, 411. + + [7] See C. G. Lamb, _loc. cit._ p. 518. + + [8] Hopkinson specified the retentiveness by the numerical value of + the "residual induction" (= 4[pi]I). + + [9] For all except ferromagnetic substances the coefficient is + sensibly equal to [kappa]. + + [10] See W. Thomson's _Reprint_, §§ 615, 634-651. + + [11] Ibid. §§ 646, 684. + + [12] Faraday, _Exp. Res._ xxi. + + [13] J. J. Thomson, _Electricity and Magnetism_, § 205. + + [14] Maxwell, _Electricity and Magnetism_, § 431. + + [15] H. du Bois, _Electrician_, 1898, 40, 317. + + [16] M. Faraday, _Exp. Res._ xxii., xxiii.; W. Thomson, _Reprint_, § + 604; J. C. Maxwell, _Treatise_, § 435; E. Mascart and J. Joubert, + _Electricity and Magnetism_, §§ 384, 396, 1226; A. Winkelmann, + _Physik_, v. 287. + + [17] See A. Winkelmann, _Physik_, v. 69-94; Mascart and Joubert. + _Electricity and Magnetism_, ii. 617. + + [18] _Sci. Abs._ A, 1906, 9, 225. + + [19] See C. G. Lamb, _Proc. Phys. Soc._, 1899, 16, 517. + + [20] _Soc. Franc. Phys. Séances_, 1904, 1, 27. + + [21] E. G. Warburg, _Wied. Ann._ 1881, 13, 141; Ewing, _Phil. + Trans._, 1885, 176, 549; Hopkinson, _Phil. Trans._ 1885, 176, 466. + For a simple proof, see Ewing, _Magnetic Induction_ (1900), p. 99. + Hopkinson pointed out that the greatest dissipation of energy which + can be caused by a to-and-fro reversal is approximately represented + by _Coercive force_ × _maximum induction_ /[pi]. + + [22] _Magnetic Induction_, 1900, 378. + + [23] _Phil. Trans._, 1902, 198, 33. + + [24] _Phil. Mag._, 1903, 5, 117. + + [25] Some experiments by F. G. Baily showed that hysteresis ceased to + increase when B was carried beyond 23,000. This value of B + corresponds to I = 1640, the saturation point for soft iron.--_Brit. + Assoc. Rep._, 1895, p. 636. + + [26] _Tokyo Phys.-Math. Soc._, 1904, 2, No. 14. + + [27] _Phil. Mag._, 1873, 46, 140. + + [28] S. Bidwell, _Proc. Roy. Soc._, 1886, 40, 495. + + [29] Since in most practicable experiments H³ is negligible in + comparison with B², the force may be taken as B²/8[pi] without + sensible error. + + [30] The same phenomenon is exhibited in a less marked degree when + soft iron is magnetized in stronger fields (Ewing, _Phil. Trans._, + 1885, 176, 569). + + [31] Principal publications: J. P. Joule, _Scientific Papers_, pp. + 46, 235; A. M. Meyer, _Phil. Mag._, 1873, 46, 177; W. F. Barrett, + _Nature_, 1882, 26, 585; S. Bidwell, _Phil. Trans._, 1888, 179A, 205; + _Proc. Roy. Soc._, 1886, 40, 109 and 257; 1888, 43, 406; 1890, 47, + 469; 1892, 51, 495; 1894, 55, 228; 1894, 56, 94; 1904, 74, 60; + _Nature_, 1899, 60, 222; M. Cantone, _Mem. d. Acc d. Lincei_, 1889, + 6, 487; _Rend. d. Acc. d. Lincei_, 1890, 6, 252; A. Berget, _C.R._, + 1892, 115, 722; S. J. Lochner, _Phil. Mag._, 1893, 36, 498; H. + Nagaoka, _Phil. Mag._, 1894, 37, 131; _Wied. Ann._, 1894, 53, 487; C. + G. Knott, _Proc. Roy. Soc. Ed._, 1891, 18, 315; _Phil. Mag._, 1894, + 37, 141; _Trans. Roy. Soc. Ed._, 1896, 38, 527; 1898, 39, 457; C. G. + Knott and A. Shand, _Proc. Roy. Soc. Ed._, 1892, 19, 85 and 249; + 1894, 20, 295; L. T. More, _Phil. Mag._, 1895, 40, 345; G. + Klingenberg, _Rostock Univ. Thesis_, Berlin, 1897; E. T. Jones, + _Phil. Trans._, 1897, 189A, 189; B. B. Brackett, _Phys. Rev._, 1897, + 5, 257; H. Nagaoka and K. Honda, _Phil. Mag._, 1898, 46, 261; 1900, + 49, 329; _Journ. Coll. Sci. Tokyo_, 1900, 13, 57; 1903, 19, art. 11; + J. S. Stevens, _Phys. Rev._, 1898, 7, 19; E. Rhoads, _Phys. Rev._, + 1898, 7, 5; _Phil. Mag._, 1901, 2, 463; G. A. Shakespear, _Phil. + Mag._, 1899, 17, 539; K. Honda, _Journ. Coll. Sci. Tokyo_, 1900, 13, + 77; L. W. Austin, _Phys. Rev._, 1900, 10, 180; _Deutsch. Phys. + Gesell. Verh._, 1904, 6, 4, 211; K. Honda and S. Shimizu, _Phil. + Mag._, 1902, 4, 338; 1905, 10, 548. + + [32] The loads were successively applied in decreasing order of + magnitude. They are indicated in fig. 25 as kilos per sq. cm. + + [33] Joule believed that the volume was unchanged. + + [34] For a discussion of theories of magnetic stress, with copious + references, see Nagaoka, _Rap. du Congrès International de Physique_ + (Paris, 1900), ii. 545. Also Nagaoka and Jones, _Phil. Mag._, 1896, + 41, 454. + + [35] S. Bidwell, _Phil. Trans._, 1888, 179a, 321. + + [36] _Phil. Mag._, 1895, 40, 345. + + [37] J. C. Maxwell, _Treatise_, § 643. + + [38] See correspondence in _Nature_, 1896, 53, pp. 269, 316, 365, + 462, 533; 1906, 74, pp. 317, 539; B. B. Brackett, _loc. cit._, quotes + the opinion of H. A. Rowland in support of compressive stress. + + [39] J. A. Ewing, _Phil. Trans._, 1885, 176, 580; 1888, 179, 333; + _Magnetic Induction_, 1900, ch. ix.; J. A. Ewing and G. C. Cowan, + _Phil. Trans._, 1888, 179a, 325; C. G. Knott, _Trans. Roy. Soc. Ed._, + 1882-1883, 32, 193; 1889, 35, 377; 1891, 36, 485; _Proc. Roy. Soc. + Ed._, 1899, 586; H. Nagaoka, _Phil. Mag._, 1889, 27, 117; 1890, 29, + 123; H. Nagaoka and K. Honda, _Journ. Coll. Sci. Tokyo_, 1900, 13, + 263; 1902, 16, art. 8; _Phil. Mag._, 1898, 46, 261; 1902, 4, 45; K. + Honda and S. Shimizu, _Ann. d. Phys._, 1904, 14, 791; _Tokyo + Physico-Math. Soc. Rep._, 1904, 2, No. 13; K. Honda and T. Terada, + _Journ. Coll. Sci. Tokyo_, 1906, 21, art. 4. + + [40] H. Tomlinson found a critical point in the "temporary + magnetization" of nickel (_Proc. Phys. Soc._, 1890, 10, 367, 445), + but this does not correspond to a Villari reversal. Its nature is + made clear by Ewing and Cowan's curves (_Phil. Trans._, 1888, 179, + plates 15, 16). + + [41] _Wied. Ann._, 1894, 52, 462; _Electrician_, 1894, 34, 143. + + [42] _Phil. Trans._, 1890, 131, 329. + + [43] _Magnetic Induction_, 1900, 222. + + [44] _Phys. Rev._, 1904, 18, 432. + + [45] _Phil. Mag._, 1886, 22, 50. + + [46] _Ibid._ 251. + + [47] _Phil. Mag._, 1891, 32, 383. + + [48] _C.R._, 1896, 122, 1192; 1898, 126, 463. + + [49] _Phil. Mag._, 1889, 27, 117. + + [50] _Journ. Coll. Sci. Tokyo_, 1904, 19, art. 9. + + [51] _Phil. Mag._, 1905, 10, 548; _Tokyo Phys.-Math. Soc. Rep._, + 1904, 2, No. 14; _Journ. Coll. Sci. Tokyo_, 1905, 20, art. 6. + + [52] _C.R._, 1888, 106, 129. + + [53] _Proc. Phys. Soc._, 1888, 9, 181. + + [54] _C.R._, 1892, 115, 805; 1894, 118, 796 and 859. + + [55] _Elekt. Zeits._, 1894, 15, 194. + + [56] _Phil. Mag._, 1900, 50, 1. + + [57] _Phil. Trans._, 1903, 201, 1. + + [58] _Phil. Mag._, 1904, 8, 179. + + [59] A. M. Thiessen (_Phys._, 1899, 8, 65) and G. Claude (C. R., + 1899, 129, 409) found that for considerable inductions (B = 15,000) + the permeability and hysteresis-loss remained nearly constant down to + -186°; for weak inductions both notably diminished with temperature. + + [60] _Proc. Roy. Soc._, 1898, 62, 210. + + [61] _C.R._, 1895, 120, 263. + + [62] _Amer. Journ. Sci._, 1898, 5, 245. + + [63] _Phys. Rev._, 1901, 14, 181. + + [64] _C.R._, 1897, 124, 176 and 1515; 1897, 125, 235; 1898, 126, 738. + + [65] Ibid., 1898, 126, 741. + + [66] Ibid., 1899, 128, 304 and 1395. + + [67] See also J. Hopkinson, _Journ. Inst. Elect. Eng._, 1890, 19, 20, + and J. A. Ewing, _Phil. Trans._, 1889, 180, 239. + + [68] Many of the figures which, through an error, were inaccurately + stated in the first paper are corrected in the second. + + [69] The marked effect of silicon in increasing the permeability of + cast iron has also been noticed by F. C. Caldwell, _Elect. World_, + 1898, 32, 619. + + [70] _Trans. Roy. Dub. Soc._, 1902-4, 8, 1 and 123. + + [71] J. Trowbridge and S. Sheldon, _Phil. Mag._, 1890, 29, 136; W. H. + Preece, _Journ. Inst. Elec. Eng._, 1890, 19, 62; _Electrician_, 1890, + 25, 546; I. Klemençiç, _Wien. Ber._, 1896, 105, IIa, 635; B. O. + Peirce, _Am. Journ. Sci._, 1896, 2, 347; A. Abt, _Wied. Ann._, 1898, + 66, 116; F. Osmond, _C. R._, 1899, 128, 1513. + + [72] _Deutsch. phys. Gesell. Verh._, 1903, 5, 220 and 224. + + [73] _Exp. Res._, iii. 440. + + [74] No record can be found of experiments with manganese at the + temperature of liquid air or hydrogen; probably, however, negative + results would not be published. + + [75] The critical temperature of iron, for instance, is raised more + than 100° by the addition of a little carbon and tungsten. + + [76] _Bull. Soc. Int. des Électriciens_, 1906, 6, 301. + + [77] _Proc. Roy. Soc._, 1905, 76A, 271. + + [78] E. H. Hall, _Phil. Mag._, 1880, 9, 225; 1880, 10, 301; 1881, 12, + 157; 1883, 15, 341; 1885, 19, 419. + + [79] The large Hall effect in bismuth was discovered by Righi, + _Journ. de Phys._, 1884, 3, 127. + + [80] REFERENCES.--(2) A. von Ettinghausen, _Wied. Ann._, 1887, 31, + 737.--(4) H. W. Nernst, ibid., 784.--(i.) and (iv.); A. von + Ettinghausen and H. W. Nernst, _Wied. Ann._, 1886, 29, 343.--(ii.) + and (iii.); A. Righi, _Rend. Acc. Linc._, 1887, 3 II, 6 and I, 481; + and A. Leduc, _Journ. de Phys._, 1887, 6, 78. Additional authorities + are quoted by Lloyd, _loc. cit._ + + [81] P. Drude, _Ann. d. Phys._, 1900, 1, 566; 1900, 3, 369; 1902, 7, + 687. See also E. van Everdingen, _Arch. Néerlandaises_, 1901, 4, 371; + G. Barlow, _Ann. d. Phys._, 1903, 12, 897; H. Zahn, ibid. 1904, 14, + 886; 1905, 16, 148. + + [82] _Phil. Trans._, 1856, p. 722. According to the nomenclature + adopted by the best modern authorities, a metal A is said to be + thermo-electrically positive to another metal B when the + thermo-current passes from A to B through the cold junction, and from + B to A through the hot (see THERMO-ELECTRICITY). + + [83] _C.R._, 1893, 116, 997. + + [84] _Journ. de Phys._, 1896, 5, 53. + + [85] _Phil. Trans._, 1887, 177, 373. + + [86] _Proc. Roy. Soc._, 1885, 39, 513. + + [87] _Phys. Rev._, 1902, 15, 321. The sign of the thermo-electric + effect for nickel, as given by Rhoads, is incorrect. + + [88] _Proc. Roy. Soc._, 1904, 73, 413. + + [89] _C.R._, 1903, 136, 1131. + + [90] _Journ. Coll. Sci. Tokyo_, 1906, 21, art. 4. The paper contains + 40 tables and 85 figures. + + [91] This deduction from Ewing's theory appears to have been first + suggested by J. Swinburne. See _Industries_, 1890, 289. + + [92] R. Beattie (_Phil. Mag._, 1901, 1, 642) has found similar + effects in nickel and cobalt. + + [93] The charge associated with a corpuscle is the same as that + carried by a hydrogen atom. G. J. Stoney in 1881 (_Phil. Mag._, 1881, + 11, 387) pointed out that this latter constituted the indivisible + "atom of electricity" or natural unit charge. Later he proposed + (_Trans. Roy. Dub. Soc._, 1891, 4, 583) that such unit charge should + be called an "electron." The application of this term to Thomson's + corpuscle implies, rightly or wrongly, that notwithstanding its + apparent mass, the corpuscle is in fact nothing more than an atom of + electricity. The question whether a corpuscle actually has a material + gravitating nucleus is undecided, but there are strong reasons for + believing that its mass is entirely due to the electric charge. + + [94] _Jour. de Phys._, 1905, 4, 678; translated in _Electrician_, + 1905, 56, 108 and 141. + + [95] The quotations are from the translation published by the Gilbert + Club, London, 1900. + + [96] C. A. Coulomb, _Mem. Acad. Roy. Paris_, 1785, p. 578. + + [97] _Intensitas vis magneticae_, § 21, C. F. Gauss's _Werke_, 5, 79. + See also J. J. Thomson, _Electricity and Magnetism_, § 132. + + [98] S. D. Poisson, _Mém. de l'Institut_, 1821 and 1822, 5, 247, 488; + 1823, 6, 441; 1838, 16, 479. + + [99] For outlines of the mathematical theory of magnetism and + references see H. du Bois, _Magnetic Circuit_, chs. iii. and iv. + + [100] Gilbert's _Ann. d. phys._, 1820, 6, 295. + + [101] _Ann. de chim. et de phys._, 1820, 15, 59, 170; _Recueil + d'observations électrodynamiques_, 1822; _Théories des phénomènes + électrodynamiques_, 1826. + + [102] _Ann. de chim. et de phys._, 1820, 15, 93. + + [103] _Trans. Soc. Arts_, 1825, 43, 38. + + [104] _Phil. Mag._, 1873, 46, 140; 1874, 48, 321. + + [105] _Phil. Trans._, 1885, 176, 523; _Magnetic Induction_, 1900. + + [106] _Proc. Roy. Soc._, 1890, 48, 342. + + [107] _Phil. Mag._, 1897, 44, 293; 1898, 46, 528. + + + + +MAGNETISM, TERRESTRIAL, the science which has for its province the study +of the magnetic phenomena of the earth. + + + Historical. + +§ 1. Terrestrial magnetism has a long history. Its early growth was +slow, and considerable uncertainty prevails as to its earliest +developments. The properties of the magnet (see MAGNETISM) were to some +small extent known to the Greeks and Romans before the Christian era, +and compasses (see COMPASS) of an elementary character seem to have been +employed in Europe at least as early as the 12th century. In China and +Japan compasses of a kind seem to have existed at a much earlier date, +and it is even claimed that the Chinese were aware of the declination of +the compass needle from the true north before the end of the 11th +century. Early scientific knowledge was usually, however, a mixture of +facts, very imperfectly ascertained, with philosophical imaginings. When +an early writer makes a statement which to a modern reader suggests a +knowledge of the declination of the compass, he may have had no such +definite idea in his mind. So far as Western civilization is concerned, +Columbus is usually credited with the discovery--in 1492 during his +first voyage to America--that the pointing of the compass needle to the +true north represents an exceptional state of matters, and that a +_declination_ in general exists, varying from place to place. The credit +of these discoveries is not, however, universally conceded to Columbus. +G. Hellmann[6][A] considers it almost certain that the departure of the +needle from the true north was known in Europe before the time of +Columbus. There is indirect evidence that the declination of the compass +was not known in Europe in the early part of the 15th century, through +the peculiarities shown by early maps believed to have been drawn solely +by regard to the compass. Whether Columbus was the first to observe the +declination or not, his date is at least approximately that of its +discovery. + +The next fundamental discovery is usually ascribed to Robert Norman, an +English instrument maker. In _The Newe Attractive_ (1581) Norman +describes his discovery made some years before of the _inclination_ or +_dip_. The discovery was made more or less by accident, through Norman's +noticing that compass needles which were truly balanced so as to be +horizontal when unmagnetized, ceased to be so after being stroked with a +magnet. Norman devised a form of dip-circle, and found a value for the +inclination in London which was at least not very wide of the mark. + +Another fundamental discovery, that of the secular change of the +declination, was made in England by Henry Gellibrand, professor of +mathematics at Gresham College, who described it in his _Discourse +Mathematical on the Variation of the Magneticall Needle together with +its Admirable Diminution lately discovered_ (1635). The history of this +discovery affords a curious example of knowledge long delayed. William +Borough, in his _Discourse on the Variation of the Compas or Magneticall +Needle_ (1581), gave for the declination at Limehouse in October 1580 +the value 11°¼ E. approximately. Observations were repeated at +Limehouse, Gellibrand tells us, in 1622 by his colleague Edmund Gunter, +professor of astronomy at Gresham College, who found the much smaller +value 6° 13´. The difference seems to have been ascribed at first to +error on Borough's part, and no suspicion of the truth seems to have +been felt until 1633, when some rough observations gave a value still +lower than that found by Gunter. It was not until midsummer 1634 that +Gellibrand felt sure of his facts, and yet the change of declination +since 1580 exceeded 7°. The delay probably arose from the strength of +the preconceived idea, apparently universally held, that the declination +was absolutely fixed. This idea, it would appear, derived some of its +strength from the positive assertion made on the point by Gilbert of +Colchester in his _De magnete_ (1600). + +A third fundamental discovery, that of the diurnal change in the +declination, is usually credited to George Graham (1675-1751), a London +instrument maker. Previous observers, e.g. Gellibrand, had obtained +slightly different values for the declination at different hours of the +day, but it was natural to assign them to instrumental uncertainties. In +those days the usual declination instrument was the compass with pivoted +needles, and Graham himself at first assigned the differences he +observed to friction. The observations on which he based his conclusions +were made in 1722; an account of them was communicated to the Royal +Society and published in the _Philosophical Transactions_ for 1724. + +The movements of the compass needle throughout the average day represent +partly a regular diurnal variation, and partly irregular changes in the +declination. The distinction, however, was not at first very clearly +realized. Between 1756 and 1759 J. Canton observed the declination-changes +on some 600 days, and was thus able to deduce their general character. He +found that the most prominent part of the regular diurnal change in +England consisted of a westerly movement of the north-pointing pole from 8 +or 9 a.m. to 1 or 2 p.m., followed by a more leisurely return movement to +the east. He also found that the amplitude of the movement was +considerably larger in summer than in winter. Canton further observed that +in a few days the movements were conspicuously irregular, and that aurora +was then visible. This association of magnetic disturbance and aurora had, +however, been observed somewhat before this time, a description of one +conspicuous instance being contributed to the Royal Society in 1750 by +Pehr Vilhelm Wargentin (1717-1783), a Swede. + +Another landmark in the history of terrestrial magnetism was the +discovery towards the end of the 18th century that the intensity of the +resultant magnetic force varies at different parts of the earth. The +first observations clearly showing this seem to be those of a Frenchman, +Paul de Lamanon, who observed in 1785-1787 at Teneriffe and Macao, but +his results were not published at the time. The first published +observations seem to be those made by the great traveller Humboldt in +tropical America between 1798 and 1803. The delay in this discovery may +again be attributed to instrumental imperfections. The method first +devised for comparing the force at different places consisted in taking +the time of oscillation of the dipping needle, and even with modern +circles this is hardly a method of high precision. Another discovery +worth chronicling was made by Arago in 1827. From observations made at +Paris he found that the inclination of the dipping needle and the +intensity of the horizontal component of the magnetic force both +possessed a diurnal variation. + +§ 2. Whilst Italy, England and France claim most of the early +observational discoveries, Germany deserves a large share of credit for +the great improvement in instruments and methods during the first half +of the 19th century. Measurements of the intensity of the magnetic force +were somewhat crude until Gauss showed how absolute results could be +obtained, and not merely relative data based on observations with some +particular needle. Gauss also devised the bifilar magnetometer, which is +still largely represented in instruments measuring changes of the +horizontal force; but much of the practical success attending the +application of his ideas to instruments seems due to Johann von Lamont +(1805-1879), a Jesuit of Scottish origin resident in Germany. + +The institution of special observatories for magnetic work is largely +due to Humboldt and Gauss. The latter's observatory at Göttingen, where +regular observations began in 1834, was the centre of the Magnetic Union +founded by Gauss and Weber for the carrying out of simultaneous magnetic +observations and it was long customary to employ Göttingen time in +schemes of international co-operation. + +In the next decade, mainly through the influence of Sir Edward Sabine +(1788-1883), afterwards president of the Royal Society, several magnetic +observatories were established in the British colonies, at St Helena, +Cape of Good Hope, Hobarton (now Hobart) and Toronto. These, with the +exception of Toronto, continued in full action for only a few years; but +their records--from their widely distributed positions--threw much fresh +light on the differences between magnetic phenomena in different regions +of the globe. The introduction of regular magnetic observatories led ere +long to the discovery that there are notable differences between the +amplitudes of the regular daily changes and the frequency of magnetic +disturbances in different years. The discovery that magnetic phenomena +have a period closely similar to, if not absolutely identical with, the +"eleven year" period in sun-spots, was made independently and nearly +simultaneously about the middle of the 19th century by Lamont, Sabine +and R. Wolf. + +The last half of the 19th century showed a large increase in the number +of observatories taking magnetic observations. After 1890 there was an +increased interest in magnetic work. One of the contributory causes was +the magnetic survey of the British Isles made by Sir A. Rücker and Sir +T. E. Thorpe, which served as a stimulus to similar work elsewhere; +another was the institution by L. A. Bauer of a magazine. _Terrestrial +Magnetism_, specially devoted to the subject. This increased activity +added largely to the stock of information, sometimes in forms of marked +practical utility; it was also manifested in the publication of a number +of papers of a speculative character. For historical details the writer +is largely indebted to the works of E. Walker[1] and L. A. Bauer.[3] + + + Observational Methods and Records. + + § 3. All the more important magnetic observatories are provided with + instruments of two kinds. Those of the first kind give the absolute + value of the magnetic elements at the time of observation. The + unifilar magnetometer (q.v.), for instance, gives the absolute values + of the declination and horizontal force, whilst the inclinometer + (q.v.) or dip circle gives the inclination of the dipping needle. + Instruments of the second kind, termed magnetographs (q.v.), are + differential and self-recording, and show the changes constantly + taking place in the magnetic elements. The ordinary form of + magnetograph records photographically. Light reflected from a fixed + mirror gives a base line answering to a constant value of the element + in question; the light is cut off every hour or second hour so that + the base line also serves to make the time. Light reflected from a + mirror carried by a magnet gives a curved line answering to the + changes in position of the magnet. The length of the ordinate or + perpendicular drawn from any point of the curved line on to the base + line is proportional to the extent of departure of the magnet from a + standard position. If then we know the absolute value of the element + which corresponds to the base line, and the equivalent of 1 cm. of + ordinate, we can deduce the absolute value of the element answering to + any given instant of time. In the case of the declination the value of + 1 cm. of ordinate is usually dependent almost entirely on the distance + of the mirror carried by the magnet from the photographic paper, and + so remains invariable or very nearly so. In the case of the horizontal + force and vertical force magnetographs--these being the two force + components usually recorded--the value of 1 cm. of ordinate alters + with the strength of the magnet. It has thus to be determined from + time to time by observing the deflection shown on the photographic + paper when an auxiliary magnet of known moment, at a measured + distance, deflects the magnetograph magnet. Means are provided for + altering the sensitiveness, for instance, by changing the effective + distance in the bifilar suspension of the horizontal force magnet, and + by altering the height of a small weight carried by the vertical force + magnet. It is customary to aim at keeping the sensitiveness as + constant as possible. A very common standard is to have 1 cm. of + ordinate corresponding to 10´ of arc in the declination and to + 50[gamma] (1[gamma] = 0.00001 C.G.S.) in the horizontal and vertical + force magnetographs. + + As an example of how the curves are standardized, suppose that + absolute observations of declination are taken four times a month, and + that in a given month the mean of the observed values is 16° 34´.6 W. + The curves are measured at the places which correspond to the times of + the four observations, and the mean length of the four ordinates is, + let us say, 2.52 cms. If 1 cm. answers to 10´, then 2.52 cms. + represents 25´.2, and thus the value of the base line--i.e. the value + which the declination would have if the curve came down to the base + line--is for the month in question 16° 34´.6 less 25´.2 or 16° 9´.4. + If now we wish to know the declination at any instant in this + particular month all we have to do is to measure the corresponding + ordinate and add its value, at the rate of 10´ per cm., to the base + value 16° 9´.4 just found. Matters are a little more complicated in + the case of the horizontal and vertical force magnetographs. Both + instruments usually possess a sensible temperature coefficient, i.e. + the position of the magnet is dependent to some extent on the + temperature it happens to possess, and allowance has thus to be made + for the difference from a standard temperature. In the case of the + vertical force an "observed" value is derived by combining the + observed value of the inclination with the simultaneous value of the + horizontal force derived from the horizontal force magnetograph after + the base value of the latter has been determined. In themselves the + results of the absolute observations are of minor interest. Their main + importance is that they provide the means of fixing the value of the + base line in the curves. Unless they are made carefully and + sufficiently often the information derivable from the curves suffers + in accuracy, especially that relating to the secular change. It is + from the curves that information is derived as to the regular diurnal + variation and irregular changes. In some observatories it is customary + to publish a complete record of the values of the magnetic elements at + every hour for each day of the year. A useful and not unusual addition + to this is a statement of the absolutely largest and smallest values + of each element recorded during each day, with the precise times of + their occurrence. On days of large disturbance even hourly readings + give but a very imperfect idea of the phenomena, and it is customary + at some observatories, e.g. Greenwich, to reproduce the more disturbed + curves in the annual volume. In calculating the regular diurnal + variation it is usual to consider each month separately. So far as is + known at present, it is entirely or almost entirely a matter of + accident at what precise hours specially high or low values of an + element may present themselves during an individual highly disturbed + day; whilst the range of the element on such a day may be 5, 10 or + even 20 times as large as on the average undisturbed day of the month. + It is thus customary when calculating diurnal inequalities to omit the + days of largest disturbance, as their inclusion would introduce too + large an element of uncertainty. Highly disturbed days are more than + usually common in some years, and in some months of the year, thus + their omission may produce effects other than that intended. Even on + days of lesser disturbance difficulties present themselves. There may + be to and fro movements of considerable amplitude occupying under an + hour, and the hour may come exactly at the crest or at the very lowest + part of the trough. Thus, if the reading represents in every case the + ordinate at the precise hour a considerable element of chance may be + introduced. If one is dealing with a mean from several hundred days + such "accidents" can be trusted to practically neutralize one another, + but this is much less fully the case when the period is as short as a + month. To meet this difficulty it is customary at some observatories + to derive hourly values from a freehand curve of continuous curvature, + drawn so as to smooth out the apparently irregular movements. Instead + of drawing a freehand curve it has been proposed to use a planimeter, + and to accept as the hourly value of the ordinate the mean derived + from a consideration of the area included between the curve, the base + line and ordinates at the thirty minutes before and after each hour. + + § 4. Partly on account of the uncertainties due to disturbances, and + partly with a view to economy of labour, it has been the practice at + some observatories to derive diurnal inequalities from a comparatively + small number of undisturbed or quiet days. Beginning with 1890, five + days a month were selected at Greenwich by the astronomer royal as + conspicuously quiet. In the selection regard was paid to the + desirability that the arithmetic mean of the five dates should answer + to near the middle of the month. In some of the other English + observatories the routine measurement of the curves was limited to + these selected quiet days. At Greenwich itself diurnal inequalities + were derived regularly from the quiet days alone and also from all the + days of the month, excluding those of large disturbance. If a quiet + day differed from an ordinary day only in that the diurnal variation + in the latter was partly obscured by irregular disturbances, then + supposing enough days taken to smooth out irregularities, one would + get the same diurnal inequality from ordinary and from quiet days. It + was found, however, that this was hardly ever the case (see §§ 29 and + 30). The quiet day scheme thus failed to secure exactly what was + originally aimed at; on the other hand, it led to the discovery of a + number of interesting results calculated to throw valuable sidelights + on the phenomena of terrestrial magnetism. + + The idea of selecting quiet days seems due originally to H. Wild. His + selected quiet days for St Petersburg and Pavlovsk were very few in + number, in some months not even a single day reaching his standard of + freedom from disturbance. In later years the International Magnetic + Committee requested the authorities of each observatory to arrange the + days of each month in three groups representing the quiet, the + moderately disturbed and the highly disturbed. The statistics are + collected and published on behalf of the committee, the first to + undertake the duty being M. Snellen. The days are in all cases counted + from Greenwich midnight, so that the results are strictly synchronous. + The results promise to be of much interest. + + § 5. The intensity and direction of the resultant magnetic force at a + spot--i.e. the force experienced by a unit magnetic pole--are known if + we know the three components of force parallel to any set of + orthogonal axes. It is usual to take for these axes the vertical at + the spot and two perpendicular axes in the horizontal plane; the + latter are usually taken in and perpendicular to the geographical + meridian. The usual notation in mathematical work is X to the north, Y + to the west or east, and Z vertically downwards. The international + magnetic committee have recommended that Y be taken positive to the + east, but the fact that the declination is westerly over most of + Europe has often led to the opposite procedure, and writers are not + always as careful as they should be in stating their choice. Apart + from mathematical calculations, the more usual course is to define the + force by its horizontal and vertical components--usually termed H and + V--and by the declination or angle which the horizontal component + makes with the astronomical meridian. The declination is sometimes + counted from 0° to 360°, 0° answering to the case when the so-called + north pole (or north seeking pole) is directed towards geographical + north, 90° to the case when it is directed to the east, and so on. It + is more usual, however, to reckon declination only from 0° to 180°, + characterizing it as easterly or westerly according as the north pole + points to the east or to the west of the geographical meridian. The + force is also completely defined by H or V, together with D the + declination, and I the inclination to the horizon of the dipping + needle. Instead of H and D some writers make use of N the northerly + component, and W the westerly (or E the easterly). The resultant force + itself is denoted sometimes by R, sometimes by T (total force). The + following relationships exist between the symbols + + X [equiv] N, Y [equiv] W or E, Z [equiv] V, R [equiv] T, + + H [equiv] [root](X² + Y²), R [equiv] [root](X² + Y² + Z²), + + tan D = Y/X, tan I = V/H. + + The term _magnetic element_ is applied to R or any of the components, + and even to the angles D and I. + + + Charts. + +§ 6. Declination is the element concerning which our knowledge is most +complete and most reliable. With a good unifilar magnetometer, at a +fixed observatory distant from the magnetic poles, having a fixed mark +of known azimuth, the observational uncertainty in a single observation +should not exceed 0´.5 or at most 1´.0. It cannot be taken for granted +that different unifilars, even by the best makers, will give absolutely +identical values for the declination, but as a matter of fact the +differences observed are usually very trifling. The chief source of +uncertainty in the observation lies in the torsion of the suspension +fibre, usually of silk or more rarely of phosphor bronze or other metal. +A very stout suspension must be avoided at all cost, but the fibre must +not be so thin as to have a considerable risk of breaking even in +skilled hands. Near a magnetic pole the directive force on the +declination magnet is reduced, and the effects of torsion are +correspondingly increased. On the other hand, the regular and irregular +changes of declination are much enhanced. If an observation consisting +of four readings of declination occupies twelve minutes, the chances are +that in this time the range at an English station will not exceed 1´, +whereas at an arctic or antarctic station it will frequently exceed 10´. +Much greater uncertainty thus attaches to declination results in the +Arctic and Antarctic than to those in temperate latitudes. In the case +of secular change data one important consideration is that the +observations should be taken at an absolutely fixed spot, free from any +artificial source of disturbance. In the case of many of the older +observations of which records exist, the precise spot cannot be very +exactly fixed, and not infrequently the site has become unsuitable +through the erection of buildings not free from iron. Apart from +buildings, much depends on whether the neighbourhood is free from +basaltic and other magnetic rocks. If there are no local disturbances of +this sort, a few yards difference is usually without appreciable +influence, and even a few miles difference is of minor importance when +one is calculating the mean secular change for a long period of years. +When, however, local disturbances exist, even a few feet difference in +the site may be important, and in the absence of positive knowledge to +the contrary it is only prudent to act as if the site were disturbed. +Near a magnetic pole the declination naturally changes very rapidly when +one travels in the direction perpendicular to the lines of equal +declination, so that the exact position of the site of observation is +there of special importance. + + The usual method of conveying information as to the value of the + declination at different parts of the earth's surface is to draw + curves on a map--the so-called _isogonals_--such that at all points on + any one curve the declination at a given specified epoch has the same + value. The information being of special use to sailors, the + preparation of magnetic charts has been largely the work of naval + authorities--more especially of the hydrographic department of the + British admiralty. The object of the admiralty world charts--four of + which are reproduced here, on a reduced scale, by the kind permission + of the Hydrographer--is rather to show the general features boldly + than to indicate minute details. Apart from the immediate necessities + of the case, this is a counsel of prudence. The observations used have + mostly been taken at dates considerably anterior to that to which the + chart is intended to apply. What the sailor wants is the declination + now or for the next few years, not what it was five, ten or twenty + years ago. Reliable secular change data, for reasons already + indicated, are mainly obtainable from fixed observatories, and there + are enormous areas outside of Europe where no such observatories + exist. Again, as we shall see presently, the rate of the secular + change sometimes alters greatly in the course of a comparatively few + years. Thus, even when the observations themselves are thoroughly + reliable, the prognostication made for a future date by even the most + experienced of chart makers may be occasionally somewhat wide of the + mark. Fig. 1 is a reduced copy of the British admiralty declination + chart for the epoch 1907. It shows the isogonals between 70° N. and + 65° S. latitude. Beyond the limits of this chart, the number of exact + measurements of declination is somewhat limited, but the general + nature of the phenomena is easily inferred. The geographical and the + magnetic poles--where the dipping needle is vertical--are fundamental + points. The north magnetic pole is situated in North America near the + edge of the chart. We have no reason to suppose that the magnetic pole + is really a fixed point, but for our present purpose we may regard it + as such. Let us draw an imaginary circle round it, and let us travel + round the circle in the direction, west, north, east, south, starting + from a point where the north pole of a magnet (i.e. the pole which in + Europe or the United States points to the north) is directed exactly + towards the astronomical north. The point we start from is to the + geographical south of the magnetic pole. As we go round the circle the + needle keeps directed to the magnetic pole, and so points first + slightly to the east of geographical north, then more and more to the + east, then directly east, then to south of east, then to due south, to + west of south, to west, to north-west, and finally when we get round + to our original position due north once more. Thus, during our course + round the circle the needle will have pointed in all possible + directions. In other words, isogonals answering to all possible values + of the declination have their origin in the north magnetic pole. The + same remark applies of course to the south magnetic pole. + + [Illustration: FIG. 1.--Isogonals, or lines of equal magnetic + declination.] + + Now, suppose ourselves at the north geographical pole of the earth. + Neglecting as before diurnal variation and similar temporary changes, + and assuming no abnormal local disturbance, the compass needle at and + very close to this pole will occupy a fixed direction relative to the + ground underneath. Let us draw on the ground through the pole a + straight line parallel to the direction taken there by the compass + needle, and let us carry a compass needle round a _small_ circle whose + centre is the pole. At all points on the circle the positions of the + needle will be parallel; but whereas the north pole of the magnet will + point exactly towards the centre of the circle at one of the points + where the straight line drawn on the ground cuts the circumference, it + will at the opposite end of the diameter point exactly away from the + centre. The former part is clearly on the isogonal where the + declination is 0°, the latter on the isogonal where it is 180°. + Isogonals will thus radiate out from the north geographical pole (and + similarly of course from the south geographical pole) in all + directions. If we travel along an isogonal, starting from the north + magnetic pole, our course will generally take us, often very + circuitously, to the north geographical pole. If, for example, we + select the isogonal of 10° E., we at first travel nearly south, but + then more and more westerly, then north-westerly across the north-east + of Asia; the direction then gets less northerly, and makes a dip to + the south before finally making for the north geographical pole. It is + possible, however, according to the chart, to travel direct from the + north magnetic to the south geographical pole, provided we select an + isogonal answering to a small westerly or easterly declination (from + about 19° W. to 7° E.). + + Special interest attaches to the isogonals answering to declination + 0°. These are termed _agonic lines_, but sailors often call them + _lines of no variation_, the term _variation_ having at one time been + in common use in the sense of declination. If we start from the north + magnetic pole the agonic line takes us across Canada, the United + States and South America in a fairly straight course to the south + geographical pole. A curve continuous with this can be drawn from the + south geographical to the south magnetic pole at every point of which + the needle points in the geographical meridian; but here the north + pole of the needle is pointing south, not north, so that this portion + of curve is really an isogonal of 180°. In continuation of this there + emanates from the south magnetic pole a second isogonal of 0°, or + agonic line, which traverses Australia, Arabia and Russia, and takes + us to the north geographical pole. Finally, we have an isogonal of + 180°, continuous with this second isogonal of 0° which takes us to the + north magnetic pole, from which we started. Throughout the whole area + included within these isogonals of 0° and 180°--excluding locally + disturbed areas--the declination is westerly; outside this area the + declination is in general easterly. There is, however, as shown in the + chart, an isogonal of 0° enclosing an area in eastern Asia inside + which the declination is westerly though small. + + § 7. Fig. 2 is a reduced copy of the admiralty chart of inclination or + dip for the epoch 1907. The places where the dip has the same value + lie on curves called _isoclinals_. The dip is northerly (north pole + dips) or southerly (south pole dips) according as the place is north + or south of the isoclinal of 0°. At places actually on this isoclinal + the dipping needle is horizontal. The isoclinal of 0° is nowhere very + far from the geographical equator, but lies to the north of it in Asia + and Africa, and to the south of it in South America. As we travel + north from the isoclinal of 0° along the meridian containing the + magnetic pole the dipping needle's north pole dips more and more, + until when we reach the magnetic pole the needle is vertical. Going + still farther north, we have the dip diminishing. The northerly + inclination is considerably less in Europe than in the same latitudes + of North America; and correspondingly the southerly inclination is + less in South America than in the same latitudes of Africa. + + [Illustration: FIG. 2.--Isoclinals, or lines of equal magnetic dip.] + + Fig. 3 is a reduced copy of the admiralty horizontal force chart for + 1907. The curves, called _isomagnetics_, connect the places where the + horizontal force has the same value; the force is expressed in C.G.S. + units. The horizontal force vanishes of course at the magnetic poles. + The chart shows a maximum value of between 0.39 and 0.40 in an oval + including the south of Siam and the China Sea. The horizontal force is + smaller in North America than in corresponding latitudes in Europe. + + [Illustration: FIG. 3.--Isomagnetics, lines of equal horizontal + force.] + + Charts are sometimes drawn for other magnetic elements, especially + vertical force (fig. 4) and total force. The isomagnetic of zero + vertical force coincides necessarily with that of zero dip, and there + is in general considerable resemblance between the forms of lines of + equal vertical force and those of equal dip. The highest values of the + vertical force occur in areas surrounding the magnetic poles, and are + fully 50% larger than the largest values of the horizontal force. The + total force is least in equatorial regions, where values slightly + under 0.4 C.G.S. are encountered. In the northern hemisphere there are + two distinct maxima of total force. One of these so-called _foci_ is + in Canada, the other in the north-east of Siberia, the former having + the higher value of the force. There are, however, higher values of + the total force than at either of these _foci_ throughout a + considerable area to the south of Australia. In the northern + hemisphere the lines of equal total force--called _isodynamic_ + lines--form two sets more or less distinct, consisting of closed + ovals, one set surrounding the Canadian the other the Siberian focus. + + + Magnetic Elements and their Secular Change. + + § 8. As already explained, magnetic charts for the world or for large + areas give only a general idea of the values of the elements. If the + region is undisturbed, very fairly approximate values are derivable + from the charts, but when the highest accuracy is necessary the only + thing to do is to observe at the precise spot. In disturbed areas + local values often depart somewhat widely from what one would infer + from the chart, and occasionally there are large differences between + places only a few miles apart. Magnetic observatories usually publish + the mean value for the year of their magnetic elements. It has been + customary for many years to collect and publish these results in the + annual report of the Kew Observatory (Observatory Department of the + National Physical Laboratory). The data in Tables I. and II. are + mainly derived from this source. The observatories are arranged in + order of latitude, and their geographical co-ordinates are given in + Table II., longitude being reckoned from Greenwich. Table I. gives the + mean values of the declination, inclination and horizontal force for + January 1, 1901; they are in the main arithmetic means of the mean + annual values for the two years 1900 and 1901. The mean annual secular + changes given in this table are derived from a short period of + years--usually 1898 to 1903--the centre of which fell at the beginning + of 1901. Table II. is similar to Table I., but includes vertical force + results; it is more extensive and contains more recent data. In it the + number of years is specified from which the mean secular change is + derived; in all cases the last year of the period employed was that to + which the absolute values assigned to the element belong. The great + majority of the stations have declination west and inclination north; + it has thus been convenient to attach the + sign to increasing + westerly (or decreasing easterly) declination and to increasing + northerly (or decreasing southerly) inclination. In other words, in + the case of the declination + means that the north end of the needle + is moving to the west, while in the case of the inclination + means + that the north end (whether the dipping end or not) is moving towards + the nadir. In the case, however, of the vertical force + means simply + _numerical_ increase, irrespective of whether the north or the south + pole dips. The unit employed in the horizontal and vertical force + secular changes is 1[gamma], i.e. 0.00001 C.G.S. Even in the + declination, at the very best observatories, it is hardly safe to + assume that the apparent change from one year to the next is + absolutely truthful to nature. This is especially the case if there + has been any change of instrument or observer, or if any alteration + has been made to buildings in the immediate vicinity. A change of + instrument is a much greater source of uncertainty in the case of + horizontal force or dip than in the case of declination, and dip + circles and needles are more liable to deterioration than + magnetometers. Thus, secular change data for inclination and vertical + force are the least reliable. The uncertainties, of course, are much + less, from a purely mathematical standpoint, for secular changes + representing a mean from five or ten years than for those derived from + successive years' values of the elements. The longer, however, the + period of years, the greater is the chance that one of the elements + may in the course of it have passed through a maximum or minimum + value. This possibility should always be borne in mind in cases where + a mean secular change appears exceptionally small. + + [Illustration: FIG. 4.--Isomagnetics, lines of equal vertical force.] + + As Tables I. and II. show, the declination needle is moving to the + east all over Europe, and the rate at which it is moving seems not to + vary much throughout the continent. The needle is also moving to the + east throughout the western parts of Asia, the north and east of + Africa, and the east of North America. It is moving to the west in the + west of North America, in South America, and in the south and east of + Asia, including Japan, south-east Siberia, eastern China and most of + India. + + § 9. The information in figs. 1, 2, 3 and 4 and in Tables I. and II. + applies only to recent years. Owing to secular change, recent charts + differ widely from the earliest ones constructed. The first charts + believed to have been constructed were those of Edmund Halley the + astronomer. According to L. A. Bauer,[7] who has made a special study + of the subject, Halley issued two declination charts for the epoch + 1700; one, published in 1701, was practically confined to the Atlantic + Ocean, whilst the second, published in 1702, contained also data for + the Indian Ocean and part of the Pacific. These charts showed the + isogonic lines, but only over the ocean areas. Though the charts for + 1700 were the first published, there are others which apply to earlier + epochs. W. van Bemmelen[8] has published charts for the epochs 1500, + 1550, 1600, 1650 and 1700, whilst H. Fritsche[9] has more recently + published charts of declination, inclination and horizontal force for + 1600, 1700, 1780, 1842 and 1915. A number of early declination charts + were given in Hansteen's Atlas and in G. Hellmann's reprints. _Die + Altesten Karten der Isogonen, Isoklinen, Isodynamen_ (Berlin, 1895). + The data for the earlier epochs, especially those prior to 1700, are + meagre, and in many cases probably of indifferent accuracy, so that + the reliability of the charts for these epochs is somewhat open to + doubt. + + If we take either Hansteen's or Fritsche's declination chart for 1600 + we notice a profound difference from fig. 1. In 1600 the agonic line + starting from the north magnetic pole, after finding its way south to + the Gulf of Mexico, doubled back to the north-east, and passed across + or near Iceland. After getting well to the north of Iceland it doubled + again to the south, passing to the east of the Baltic. The second + agonic line which now lies to the west of St Petersburg appears in + 1600 to have continued, after traversing Australia, in a nearly + northerly direction through the extreme east of China. The nature of + the changes in declination in western Europe will be understood from + Table III., the data from which, though derived from a variety of + places in the south-east of England,[10] may be regarded as + approximately true of London. The earliest result is that obtained by + Borough at Limehouse. Those made in the 16th century are due to + Gunter, Gellibrand, Henry Bond and Halley. The observations from 1787 + to 1805 were due to George Gilpin, who published particulars of his + own and the earlier observations in the _Phil. Trans._ for 1806. The + data for 1817 and 1820 were obtained by Col. Mark Beaufoy, at Bushey, + Herts. They seem to come precisely at the time when the needle, which + had been continuously moving to the west since the earliest + observations, began to retrace its steps. The data from 1860 onwards + apply to Kew. + + TABLE I.--Magnetic Elements and their Rate of Secular Change for + January 1, 1901. + + +----------------+------------------------------+----------------------+ + | | Absolute values. | Secular change. | + | Place. +----------+----------+--------+-------+------+-------+ + | | D. | I. | H. | D. | I. | H. | + +----------------+----------+----------+--------+-------+------+-------+ + | | ° ´ | ° ´ | | ´ | ´ |[gamma]| + | Pavlovsk | 0 39.8E | 70 36.8N | .16553 | - 4.1 | -0.8 | + 7 | + | Ekatarinburg | 10 6.3E | 70 40.5N | .17783 | - 4.6 | +0.5 | -13 | + | Copenhagen | 10 10.4W | 68 38.5N | .17525 | | | | + | Stonyhurst | 18 10.3W | 68 48.0N | .17330 | - 4.0 | | +22 | + | Wilhelmshaven | 12 26.0W | 67 39.7N | .18108 | - 4.1 | -2.1 | +20 | + | Potsdam | 9 54.2W | 66 24.5N | .18852 | - 4.2 | -1.6 | +16 | + | Irkutsk | 2 1.0E | 70 15.8N | .20122 | + 0.5 | +1.6 | -14 | + | de Bilt | 13 48.3W | 66 55.5N | .18516 | - 4.4 | -2.2 | +14 | + | Kew | 16 50.8W | 67 10.6N | .18440 | - 4.2 | -2.2 | +25 | + | Greenwich | 16 27.5W | 67 7.3N | .18465 | - 4.0 | -2.2 | +23 | + | Uccle | 14 11.0W | 66 8.8N | .18954 | - 4.2 | -2.1 | +23 | + | Falmouth | 18 27.3W | 66 44.0N | .18705 | - 3.8 | -2.7 | +26 | + | Prague | 9 4.4W | | .19956 | - 4.4 | | +20 | + | St Helier | 16 58.1W | 65 44.1N | | - 3.5 | -2.7 | | + | Parc St Maur | 14 43.4W | 64 52.3N | .19755\| - 4.0 | -2.2 | +23 | + | Val Joyeux | 15 13.7W | 65 0.0N | .19670/| | | | + | Munich | 10 25.8W | 63 18.1N | .20629 | - 4.8 | -2.7 | +21 | + | O'Gyalla | 7 26.1W | | .21164 | - 4.8 | | +13 | + | Pola | 9 22.7W | 60 14.5N | .22216 | - 4.0 | | +23 | + | Toulouse | 14 16.4W | 60 55.9N | .21945 | - 3.9 | -2.5 | +25 | + | Perpignan | 13 34.7W | 59 57.6N | .22453 | | | | + | Capo di Monte | 9 8.0W | 56 22.3N | | - 5.2 | -2.3 | | + | Madrid | 15 39.0W | | | | | | + | Coimbra | 17 18.1W | 59 22.0N | .22786 | - 3.7 | -4.3 | +34 | + | Lisbon | 17 15.7W | 57 53.0N | .23548 | | | | + | Athens | 5 38.2W | 52 7.5N | .26076 | | | | + | San Fernando | 15 57.5W | 55 8.8N | .24648 | | | | + | Tokyo | 4 34.9W | 49 0.3N | .29932 | | | | + | Zi-ka-wei | 2 23.5W | 45 43.5N | .32875 | + 1.5 | -1.5 | +37 | + | Helwan | 3 39.7W | 40 30.8N | .30136 | - 7.0 | -0.4 | - 7 | + | Hong-Kong | 0 17.5E | 31 22.8N | .36753 | + 1.8 | -4.3 | +45 | + | Kolaba | 0 23.2E | 21 26.5N | .37436 | + 2.2 | +7.0 | - 9 | + | Manila | 0 52.2E | 16 13.5N | .38064 | + 0.1 | -5.3 | +47 | + | Batavia | 1 7.3E | 30 35.5S | .36724 | + 3.0 | -7.3 | -11 | + | Mauritius | 9 25.2W | 54 9.4S | .23820 | - 4.7 | +4.6 | -39 | + | Rio de Janeiro | 8 2.9W | 13 20.1S | .2501 | +10.4 | -2.3 | | + | Melbourne | 8 25.6E | 67 24.6S | .23295 | | | | + +----------------+----------+----------+--------+-------+------+-------+ + + The rate of movement of the needle to the east at London--and + throughout Europe generally--fell off markedly subsequent to 1880. The + change of declination in fact between 1880 and 1895 was only about 75% + of that between 1865 and 1880, and the mean annual change from 1895 to + 1900 was less than 75% of the mean annual change of the preceding + fifteen years. Thus in 1902 it was at least open to doubt whether a + change in the sign of the secular change were not in immediate + prospect. Subsequent, however, to that date there was little further + decline in the rate of secular change, and since 1905 there has been + very distinct acceleration. Thus, if we derive a mean value from the + eighteen European stations for which declination secular changes are + given in Tables I. and II. we find + + mean value from table I. -4.18 + " " " " II. -5.21 + + The epoch to which the data in Table II. refer is somewhat variable, + but is in all cases more recent than the epoch, January 1, 1901, for + Table I., the mean difference being about 5 years. + + § 10. At Paris there seems to have been a maximum of easterly + declination (about 9°) about 1580; the needle pointed to true north + about 1662, and reached its extreme westerly position between 1812 and + 1814. The phenomena at Rome resembled those at Paris and London, but + the extreme westerly position is believed to have been attained + earlier. The rate of change near the turning point seems to have been + very slow, and as no fixed observatories existed in those days, the + precise time of its occurrence is open to some doubt. + + Perhaps the most complete observations extant as to the declination + phenomena near a turning point relate to Kolaba observatory at Bombay; + they were given originally by N. A. F. Moos,[11] the director of the + observatory. Some of the more interesting details are given in Table + IV.; here W denotes movement to be west, and so answers to a numerical + diminution in the declination, which is easterly. + + Prior to 1880 the secular change at Kolaba was unmistakably to the + east, and subsequent to 1883 it was clearly to the west; but between + these dates opinions will probably differ as to what actually + happened. The fluctuations then apparent in the sign of the annual + change may be real, but it is at least conceivable that they are of + instrumental origin. From 1870 to 1875 the mean annual change was + -1´.2; from 1885 to 1890 it was +1´.5, from 1890 to 1895 it was +2´.0, + while from 1895 to 1905 it was +2´.35, the + sign denoting movement to + the west. Thus, in this case the rate of secular change has increased + fairly steadily since the turning point was reached. + + Table V. contains some data for St Helena and the Cape of Good + Hope,[12] both places having a long magnetic history. The remarkable + feature at St Helena is the uniformity in the rate of secular change. + The figures for the Cape show a reversal in the direction of the + secular change about 1840, but after a few years the arrested movement + to the west again became visible. According, however, to J. C. + Beattie's _Magnetic Survey of South Africa_ the movement to the west + ceased shortly after 1870. A persistent movement to the east then set + in, the mean annual change increasing from 1´.8 between 1873 and 1890 + to 3´.8 between 1890 and 1900. + + § 11. Secular changes of declination have been particularly + interesting in the United States, an area about which information is + unusually complete, thanks to the labours and publications of the + United States Coast and Geodetic Survey.[13] At present the agonic + line passes in a south-easterly direction from Lake Superior to South + Carolina. To the east of the agonic line the declination is westerly, + and to the west it is easterly. In 1905 the declination varied from + about 21° W. in the extreme north-east to about 24° E. in the extreme + north-west. At present the motion of the agonic line seems to be + towards the west, but it is very slow. To the east of the agonic line + westerly declination is increasing, and to the west of the line, with + the exception of a narrow strip immediately adjacent to it, easterly + declination is increasing. The phenomena in short suggest a motion + southwards in the north magnetic pole. Since 1750 declination has + always been westerly in the extreme east of the States, and always + easterly in the extreme west, but the position of the agonic line has + altered a good deal. It was to the west of Richmond, Virginia, from + 1750 to about 1772, then to the east of it until about 1838 when it + once more passed to the west; since that time it has travelled farther + to the west. Table VI. is intended to show the nature of the secular + change throughout the whole country. As before, + denotes that the + north pole of the magnet is moving to the west,--that it is moving to + the east. + + The data in Table VI. represent the mean change of declination per + annum, derived from the period (ten years, except for 1900-1905) which + ended in the year put at the top of the column. The stations are + arranged in four groups, the first group representing the extreme + eastern, the last group the extreme western states, the other two + groups being intermediate. In each group the stations are arranged, at + least approximately, in order of latitude. The data are derived from + the values of the declination given in the Geodetic Survey's _Report_ + for 1906, appendix 4, and _Magnetic Tables and Magnetic Charts_ by L. + A. Bauer, 1908. The values seem, in most cases, based to some extent + on calculation, and very probably the secular change was not in + reality quite so regular as the figures suggest. For the Western + States the earliest data are comparatively recent, but for some of the + eastern states data earlier than any in the table appear in the + _Report of the Coast and Geodetic Survey_ for 1902. These data + indicate that the easterly movement of the magnet, visible in all the + earlier figures for the Eastern States in Table VI., existed in all of + them at least as far back as 1700. There is not very much evidence as + to the secular change between 1700 and 1650, the earliest date to + which the Coast and Geodetic Survey's figures refer. The figures show + a maximum of westerly declination about 1670 in New Jersey and about + 1675 in Maryland. They suggest that this maximum was experienced all + along the Atlantic border some time in the 17th century, but earlier + in the extreme north-east than in New York or Maryland. + + Examination of Table VI. shows that the needle continued to move to + the east for some time after 1750 even in the Eastern States. But the + rate of movement was clearly diminishing, and about 1765 the extreme + easterly position was reached in Eastport, Maine, the needle then + beginning to retrace its steps to the west. The phenomena visible at + Maine are seen repeating themselves at places more and more to the + west, in Boston about 1785, in Albany about 1800, in Washington, D.C., + about 1805, in Columbus (Ohio) about 1815, in Montgomery (Alabama) + about 1825, in Bloomington (Ill.) about 1830, in Des Moines (Iowa) + about 1840, in Santa Rosa (New Mexico) about 1860 and in Salt Lake + about 1870. In 1885 the needle was moving to the west over the whole + United States with the exception of a comparatively narrow strip along + the Pacific coast. Even an acute observer would have been tempted to + prophesy in 1885 that at no distant date the secular change would be + pronouncedly westerly right up to the Pacific. But in a few years a + complete change took place. The movement to the east, which had become + exceedingly small, if existent, in the Pacific states, began to + accelerate; the movement to the west continued in the central, as in + the eastern states, but perceptibly slackened. In 1905 the area + throughout which the movement to the west still continued had greatly + contracted and lay to the east of a line drawn from the west end of + Lake Superior to the west of Georgia. If we take a station like Little + Rock (Arkansas), we have the secular change to the west lasting for + about sixty years. Further west the period shortens. At Pueblo + (Colorado) it is about forty years, at Salt Lake under thirty years, + at Prescott (Arizona) about twenty years. Considering how fast the + area throughout which the secular change is easterly has extended to + the east since 1885, one would be tempted to infer that at no distant + date it will include the whole of the United States. In the extreme + north-east, however, the movement of the needle to the west, which had + slackened perceptibly after 1860 or 1870, is once more accelerating. + Thus the auspices do not all point one way, and the future is as + uncertain as it is interesting. + + TABLE II.--Recent Values of the Magnetic Elements and their Rate of + Secular Change. + + +----------------+-----------------------+----------------------------------------------+----------------------------------- + | | Geographical position.| Absolute Values of Elements. | Secular change (mean per annum). | + | Place. +-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+ + | | | | | | | | | Interval | | | | | + | | Latitude. | Longitude.| Year. | D. | I. | H. | V. | in years.| D. | I. | H. | V. | + +----------------+-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+ + | | ° ´ | ° ´ | | ° ´ | ° ´ | | | | ´ | ´ | | | + | Pavlovsk | 59 41N | 30 29E | 1906 | 1 4.2E | 70 36.6N | .16528 | .46963 | 5 | -4.5 | +0.1 | - 6 | -14 | + | Sitka (Alaska) | 57 3N | 135 20W | 1906 |30 3.3E | 74 41.7N | .15502 | .56646 | 4 | -3.0 | -1.6 | +18 | -38 | + | Ekatarinburg | 56 49N | 60 38E | 1906 |10 31.0E | 70 49.5N | .17664 | .50796 | 5 | -4.5 | +1.7 | -23 | +18 | + | Rude Skov | | | | | | | | | | | | | + | (Copenhagen) | 55 51N | 12 27E | 1908 | 9 43.3W | 68 45N | .17406 | .44759 | | | | | | + | Stonyhurst | 53 51N | 2 28W | 1909 |17 28.6W | 68 42.8N | .17424 | .44722 | 5 | -5.9 | -1.1 | + 6 | -25 | + | Hamburg | 53 33N | 9 59E | 1903 |11 10.2W | 67 23.5N | .18126 | .43527 | | | | | | + | Wilhelmshaven | 53 32N | 8 9E | 1909 |11 46.8W | | .18129 | | 5 | -5.2 | | - 7 | | + | Potsdam | 52 23N | 13 4E | 1909 | 9 10.6W | 66 20.0N | .18834 | .42971 | 5 | -5.8 | +0.1 | - 9 | -19 | + | Irkutsk | 52 16N | 104 16E | 1905 | 1 58.1E | 70 25.0N | .20011 | .56250 | 5 | +0.6 | +2.0 | -24 | +39 | + | de Bilt | 52 5N | 5 11E | 1907 |13 19.0W | 66 49.9N | .18559 | .43368 | 5 | -4.7 | -0.6 | + 2 | -16 | + | Valencia | 51 56N | 10 15W | 1909 |20 50.3W | 68 15.1N | .17877 | .44812 | 5 | -5.0 | -1.2 | + 7 | -25 | + | Kew | 51 28N | 0 19W | 1909 |16 10.8W | 66 59.7N | .18506 | .43588 | 5 | -5.4 | -1.1 | + 2 | -35 | + | Greenwich | 51 28N | 0 0 | 1909 |15 47.6W | 66 53.9N | .18526 | .43432 | 5 | -5.5 | -0.7 | + 1 | -20 | + | Uccle | 50 48N | 4 21E | 1908 |13 36.7W | 66 1.6N | .19061 | .42867 | 4 | -5.3 | -0.8 | - 3 | -35 | + | Falmouth | 50 9N | 5 5W | 1909 |17 48.4W | 66 30.6N | .18802 | .43266 | 5 | -4.7 | -1.4 | + 9 | -30 | + | Prague | 50 5N | 14 25E | 1908 | 8 20.9W | | | | 5 | -6.5 | | | | + | Cracow | 50 4N | 19 58E | 1909 | 5 35.1W | 64 18N | | | 3 | -7.3 | | | | + | St Helier | 49 12N | 2 5W | 1907 |16 27.4W | 65 34.5N | | | 5 | -5.3 | -1.2 | | | + | Val Joyeux | 48 49N | 2 1E | 1909 |14 32.9W | 64 43.9N | .19727 | .41792 | 5 | -5.4 | -1.7 | + 1 | -51 | + | Vienna | 48 15N | 16 21E | 1898 | 8 24.1W | | | | | | | | | + | Munich | 48 9N | 11 37E | 1906 | 9 59.5W | 63 10.0N | .20657 | .40835 | 5 | -4.8 | -1.3 | + 4 | -31 | + | O'Gyalla | 47 53N | 18 12E | 1909 | 6 43.9W | | .21094 | | 5 | -5.0 | | -10 | | + | Odessa | 46 26N | 30 46E | 1899 | 4 36.7W | 62 18.2N | .21869 | .41660 | | | | | | + | Pola | 44 52N | 15 51E | 1908 | 8 43.2W | 60 6.8N | .22207 | .38640 | 5 | -5.5 | -0.6 | - 4 | -23 | + | Agincourt | | | | | | | | | | | | | + | (Toronto) | 43 47N | 79 16W | 1906 | 5 45.3W | 74 35.6N | .16397 | .59502 | 4 | +3.4 | +0.9 | -23 | -24 | + | Nice | 43 43N | 7 16E | 1899 |12 4.0W | 60 11.7N | .22390 | .39087 | | | | | | + | Toulouse | 43 37N | 1 28E | 1905 |13 56.3W | 60 49.1N | .22025 | .39439 | 5 | -4.5 | -1.5 | + 2 | - 2 | + | Perpignan | 42 42N | 2 53E | 1907 |13 4.4W | | | | 7 | -4.7 | | | | + | Tiflis | 41 43N | 44 48E | 1905 | 2 41.6E | 56 2.8N | .25451 | .37799 | 7 | -5.2 | +1.7 | -26 | + 2 | + | Capo di Monte | 40 52N | 14 15E | 1906 | 8 40.3W | 56 13.5N | | | 5 | -5.1 | -1.5 | | | + | Madrid | 40 25N | 3 40W | 1901 |15 35.6W | | | | | | | | | + | Coimbra | 40 12N | 8 25W | 1908 |16 46.2W | 58 57.3N | .22946 | .38120 | 5 | -4.6 | -2.9 | +17 | -45 | + | Baldwin | | | | | | | | | | | | | + | (Kansas) | 38 47N | 95 10W | 1906 | 8 30.1E | 68 45.1N | .21807 | .56081 | 4 | -1.7 | +1.8 | -36 | - 8 | + | Cheltenham | | | | | | | | | | | | | + | (Maryland) | 38 44N | 76 50W | 1906 | 5 22.0W | 70 27.3N | .20035 | .56436 | 4 | +3.8 | +1.2 | -38 | -45 | + | Lisbon | 38 43N | 9 9W | 1900 |17 18.0W | 57 54.8N | .23516 | .37484 | | | | | | + | Athens | 37 58N | 21 23E | 1908 | 4 52.9W | 52 11.7N | .26197 | .33613 | 5 | -5.5 | | | | + | San Fernando | 36 28N | 6 12W | 1908 |15 25.6W | 54 48.4N | .24829 | .35206 | 5 | -4.6 | -2.8 | +26 | -24 | + | Tokyo | 35 41N | 139 45E | 1901 | 4 36.1W | 49 0.0N | .29954 | .34459 | | | | | | + | Zi-ka-wei | 31 12N | 121 26E | 1906 | 2 32.0W | 45 35.3N | .33040 | .33726 | 5 | +1.5 | -1.3 | +30 | + 6 | + | Dehra Dun | 30 19N | 78 3E | 1907 | 2 38.3E | 43 36.1N | .33324 | .31736 | 4 | +0.8 | +5.5 | -26 | +77 | + | Helwan | 29 52N | 31 21E | 1909 | 2 49.2W | 40 40.4N | .30031 | .25804 | 5 | -5.7 | +1.2 | - 6 | +13 | + | Havana | 23 8N | 82 25W | 1905 | 2 25.0E | 52 57.4N | .30531 | .40452 | | | | | | + | Barrackpore | 22 46N | 88 22E | 1907 | 1 9.9E | 30 30.2N | .37288 | .21967 | 3 | +4.2 | +3.4 | +21 | +62 | + | Hong-Kong | 22 18N | 114 10E | 1908 | 0 3.9E | 31 2.5N | .37047 | .22292 | 5 | +1.9 | -1.8 | +43 | - 1 | + | Honolulu | 21 19N | 158 4W | 1906 | 9 21.7E | 40 1.8N | .29220 | .24545 | 4 | -0.9 | -3.2 | -19 | -62 | + | Kolaba | 18 54N | 72 49E | 1905 | 0 14.0E | 21 58.5N | .37382 | .15084 | 5 | +2.1 | +7.2 | -11 | +86 | + | Alibagh | 18 39N | 72 52E | 1909 | 1 0.3E | 23 29.0N | .36845 | .16008 | 3 | +1.7 | +6.8 | -10 | +82 | + | Vieques | | | | | | | | | | | | | + | (Porto Rico) | 18 9N | 65 26W | 1906 | 1 33.2W | 49 47.7N | .28927 | .34224 | 2 | +7.2 | +6.8 | -49 | +66 | + | Manila | 14 35N | 120 59E | 1904 | 0 51.4E | 16 0.2N | .38215 | .10960 | 5 | +0.1 | -3.9 | +47 | -34 | + | Kodaikanal | 10 14N | 77 28E | 1907 | 0 40.7W | 3 27.2N | .37431 | .02259 | 4 | +4.3 | +5.5 | +16 | +61 | + | Batavia | 6 11S | 106 49E | 1906 | 0 54.1E | 30 48.5S | .36708 | .21889 | 4 | +2.1 | -7.7 | - 2 | +110| + | Dar es Salaam | 6 49S | 39 18E | 1903 | 7 35.2W | | | | | | | | | + | Mauritius | 20 6S | 57 33E | 1908 | 9 14.3W | 53 44.9S | .23415 | .31932 | 5 | -0.3 | +2.9 | -53 | -131| + | Rio de Janeiro | 22 55S | 43 11W | 1906 | 8 55.5W | 13 57.1S | .24772 | .06164 | 5 | +9.1 | -6.8 | -42 | +44 | + | Santiago | | | | | | | | | | | | | + | (Chile) | 33 27S | 70 42W | 1906 |14 18.7E | 30 11.8S | | | 3 | +6.1 | +9.9 | | | + | Melbourne | 37 50S | 144 58E | 1901 | 8 26.7E | 67 25.0S | .23305 | .56024 | | | | | | + | Christchurch, | | | | | | | | | | | | | + | N.Z. | 43 32S | 172 37E | 1903 |16 18.4E | 67 42.3S | .22657 | .55259 | | | | | | + +----------------+-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+ + + + TABLE III.--Declination at London. + + +-------+--------------+-------+--------------+-------+--------------+ + | Date. | Declination. | Date. | Declination. | Date. | Declination. | + +-------+--------------+-------+--------------+-------+--------------+ + | | ° ´ | | ° ´ | | ° ´ | + | 1580 | 11 15E | 1773 | 21 9W | 1860 | 21 38.9W | + | 1622 | 6 0 | 1787 | 23 19 | 1865 | 20 58.7 | + | 1634 | 4 6 | 1795 | 23 57 | 1870 | 20 18.3 | + | 1657 | 0 0 | 1802 | 24 6 | 1875 | 19 35.6 | + | 1665 | 1 22W | 1805 | 24 8 | 1880 | 18 52.1 | + | 1672 | 2 30 | 1817 | 24 36 | 1885 | 18 19.2 | + | 1692 | 6 0 | 1818 | 24 38 | 1890 | 17 50.6 | + | 1723 | 14 17 | 1819 | 24 36 | 1895 | 17 16.8 | + | 1748 | 17 40 | 1820 | 24 34 | 1900 | 16 52.7 | + | | | | | 1905 | 16 32.9 | + +-------+--------------+-------+--------------+-------+--------------+ + + § 12. Table VII. gives particulars of the secular change of horizontal + force and northerly inclination at London. Prior to the middle of the + 19th century information as to the value of H is of uncertain value. + The earlier inclination data[14] are due to Norman, Gilbert, Bond, + Graham, Heberden and Gilpin. The data from 1857 onwards, both for H + and I, refer to Kew. "London" is rather a vague term, but the + differences between the values of H and I at Kew and Greenwich--in the + extreme west and east--are almost nil. For some time after its + discovery by Robert Norman inclination at London increased. The + earlier observations are not sufficient to admit of the date of the + maximum inclination or its absolute value being determined with + precision. Probably the date was near 1723. This view is supported by + the fact that at Paris the inclination fell from 72° 15´ in 1754 to + 71° 48´ in 1780. The earlier observations in London were probably of + no very high accuracy, and the rates of secular change deducible from + them are correspondingly uncertain. It is not improbable that the + average annual change 0´.8 derived from the thirteen years 1773-1786 + is too small, and the value 6´.2 derived from the fifteen years + 1786-1801 too large. There is, however, other evidence of unusually + rapid secular change of inclination towards the end of the 18th + century in western Europe; for observations in Paris show a fall of + 56´ between 1780 and 1791, and of 90´ between 1791 and 1806. Between + 1801 and 1901 inclination in London diminished by 3° 26´.5, or on the + average by 2´.1 per annum, while between 1857 and 1900 H increased on + the average by 22[gamma] a year. These values differ but little from + the secular changes given in Table I. as applying at Kew for the epoch + Jan. 1, 1901. Since the beginning, however, of the 20th century a + notable change has set in, which seems shared by the whole of western + Europe. This is shown in a striking fashion by contrasting the data + from European stations in Tables I. and II. There are fifteen of these + stations which give secular change data for H in both tables, while + thirteen give secular data for I. The mean values of the secular + changes derived from these stations are as follows:-- + + I H + + From Table I. -2´.35 +21.0[gamma] + From Table II. -1.12 +1.6[gamma] + + The difference in epoch between the two sets of results is only about + 5 years, and yet in that short time the mean rate of annual increase + in H fell to a thirteenth of its original value. During 1908-1909 H + diminished throughout all Europe except in the extreme west. Whether + we have to do with merely a temporary phase, or whether a general and + persistent diminution in the value of H is about to set in over Europe + it is yet hardly possible to say. + + TABLE IV.--Declination at Kolaba (Bombay). + + +-------+----------------+----------------+ + | Year. | Declination | Change since | + | | East. | previous year. | + +-------+----------------+----------------+ + | | ° ´ ´´ | ´ ´´ | + | 1876 | 0 55 58 | 0 37 E | + | 1877 | 56 39 | 0 41 E | + | 1878 | 57 6 | 0 27 E | + | 1879 | 57 30 | 0 24 E | + | 1880 | 57 9 | 0 21 W | + | 1881 | 0 57 12 | 0 3 E | + | 1882 | 0 56 50 | 0 22 W | + | 1883 | 57 2 | 0 12 E | + | 1884 | 55 39 | 1 23 W | + | 1885 | 55 3 | 0 36 W | + +-------+----------------+----------------+ + + § 13. It is often convenient to obtain a formula to express the mean + annual change of an element during a given period throughout an area + of some size. The usual method is to assume that the change at a place + whose latitude is l and longitude [lambda] is given by an expression + of the type c + a(l - l0) + b([lambda] - [lambda]0), where a, b, c are + constants, l0 and [lambda]0, denoting some fixed latitude and + longitude which it is convenient to take as point of departure. + Supposing observational data available from a series of stations + throughout the area, a, b and c can be determined by least squares. As + an example, we may take the following slightly modified formula given + by Ad. Schmidt[15] as applicable to Northern Europe for the period + 1890 to 1900. [Delta]D, [Delta]I and [Delta]H represent the mean + annual changes during this period in westerly declination, in + inclination and in horizontal force:-- + + ´ ´ ´ + [Delta]D = -5.24 - 0.071(l - 50) + 0.033([lambda] - 10), + [Delta]I = -1.58 + 0.010(l - 50) + 0.036([lambda] - 10), + [Delta]H = +23.5 - 0.59 (l - 50) - 0.35 ([lambda] - 10). + + Longitude [lambda] is here counted positive to the east. The central + position assumed here (lat. 50°, long. 10° E.) falls in the north of + Bavaria. In the case of the horizontal force unity represents + 1[gamma]. Schmidt found the above formulae to give results in very + close agreement with the data at the eight stations which he had + employed in determining the constants. These stations ranged from + Pavlovsk to Perpignan, and from Stonyhurst to Ekaterinburg in Siberia. + Formulae involving the second as well as the first powers of l - l0 + and [lambda] - [lambda]0 have also been used, e.g., by A. Tanakadate + in the Magnetic Survey of Japan. + + Table V.--Declination at St Helena and Cape of Good Hope. + + +----------------------+----------------------+ + | St Helena. | Cape of Good Hope. | + +--------+-------------+--------+-------------+ + | Date. | Declination.| Date. | Declination.| + +--------+-------------+--------+-------------+ + | | ° ´ | | ° ´ | + | 1610 | 7 13 E | 1605 | 0 30 E | + | 1677 | 0 40 | 1609 | 0 12 W | + | 1691 | 1 0 W | 1675 | 8 14 | + | 1724 | 7 30 | 1691 | 11 0 | + | 1775 | 12 18 | 1775 | 21 14 | + | 1789 | 15 30 | 1792 | 24 31 | + | 1796 | 15 48 | 1818 | 26 31 | + | 1806 | 17 18 | 1839 | 29 9 | + | 1839 | 22 17 | 1842 | 29 6 | + | 1840 | 22 53 | 1846 | 29 9 | + | 1846 | 23 11 | 1850 | 29 19 | + | 1890 | 23 57 | 1857 | 29 34 | + | | | 1874 | 30 4 | + | | | 1890 | 29 32 | + | | | 1903 | 28 44 | + +--------+-------------+--------+-------------+ + + + TABLE VI.--Secular Change of Declination in the United States (+ to + the West). + + +---------------------------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+ + | Place. |Epoch | 1760 | 70 | 80 | 90 | 1800 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 1900 | 50 | + +---------------------------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+ + | | | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | + | / Eastport, Maine | | -1.2 | 0.0 | +1.2 | +2.1 | +3.2 | +4.0 | +4.5 | +4.9 | +5.0 | +5.6 | +4.5 | +3.0 | +2.1 | +1.0 | +1.8 | +2.4 | + | | Boston, Mass. | | -2.7 | -1.9 | -1.0 | 0.0 | +1.1 | +1.9 | +2.7 | +3.5 | +4.2 | +4.4 | +4.0 | +3.3 | +3.1 | +3.0 | +3.2 | +3.4 | + | | Albany, New York | | -4.2 | -3.6 | -2.7 | -1.6 | -0.6 | +0.6 | +1.6 | +2.7 | +3.6 | +4.6 | +4.6 | +3.9 | +4.7 | +2.3 | +3.4 | +3.6 | + | | Philadelphia, Penn. | | -4.6 | -4.2 | -3.5 | -2.3 | -1.3 | +0.1 | +1.3 | +2.5 | +3.4 | +4.3 | +4.2 | +4.6 | +4.4 | +3.4 | +3.5 | +3.4 | + | | Baltimore, Maryland | | -3.9 | -3.4 | -2.7 | -2.0 | -0.9 | 0.0 | +0.9 | +2.0 | +2.7 | +3.4 | +3.9 | +4.0 | +3.9 | +3.6 | +3.5 | +3.2 | + | | Richmond, Virginia | | -3.6 | -3.2 | -2.5 | -1.8 | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.1 | +3.6 | +3.9 | +3.8 | +3.7 | +3.4 | +3.2 | + | | Columbia, S. Carolina | | -3.7 | -3.4 | -2.9 | -2.2 | -1.3 | -0.5 | +0.5 | +1.3 | +2.2 | +2.9 | +3.4 | +3.8 | +3.8 | +3.8 | +3.6 | +1.8 | + | | Macon, Georgia | | -3.7 | -3.6 | -3.2 | -2.5 | -1.8 | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +3.9 | +3.5 | +3.1 | +1.2 | + | \ Tampa, Florida | | -3.0 | -2.5 | -2.0 | -1.1 | -0.4 | +0.4 | +1.1 | +2.0 | +2.5 | +3.0 | +3.2 | +3.5 | +3.7 | +2.8 | +2.9 | +1.6 | + | | | | | | | | | | | | | | | | | | | + | / Marquette, Michigan | | | | | | | | | 0.0 | +1.4 | +2.6 | +3.7 | +4.7 | +5.1 | +4.9 | +3.8 | +2.4 | + | | Columbus, Ohio | | | | | | | -0.9 | 0.0 | +0.9 | +2.0 | +2.9 | +3.4 | +3.6 | +3.7 | +3.9 | +4.0 | +2.4 | + | | Bloomington, Illinois | | | | | | | -2.4 | -1.5 | -0.4 | +0.4 | +1.5 | +2.4 | +2.8 | +4.2 | +3.9 | +2.9 | +1.0 | + | | Lexington, Kentucky | | | | | | | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +3.8 | +3.8 | +3.4 | +1.8 | + | | Chattanooga, Tennessee | | | | | | | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +4.0 | +3.5 | +3.1 | +1.6 | + | | Little Rock, Arkansas | | | | | | | -2.3 | -1.5 | -0.9 | +0.1 | +0.8 | +1.7 | +2.0 | +3.6 | +3.7 | +2.3 | -1.2 | + | | Montgomery, Alabama | | -3.6 | -3.5 | -3.1 | -2.8 | -2.2 | -1.5 | -0.8 | +0.1 | +0.8 | +1.6 | +2.2 | +2.8 | +3.8 | +3.9 | +2.6 | +0.2 | + | \ Alexandria, Louisiana | | | | | | | -2.1 | -1.6 | -0.8 | +0.1 | +0.8 | +1.6 | +2.2 | +3.6 | +3.3 | +2.0 | -1.4 | + | | | | | | | | | | | | | | | | | | | + | / Northome, Minnesota | | | | | | | | | -1.7 | -0.6 | +0.6 | +1.7 | +2.8 | +4.2 | +4.4 | +3.5 | 0.0 | + | | Jamestown, N. Dakota | | | | | | | | | | | | +1.0 | +1.9 | +3.1 | +4.8 | +1.9 | -2.2 | + | | Des Moines, Iowa | | | | | | | | | -1.5 | -0.6 | +0.6 | +1.5 | +2.5 | +3.8 | +4.5 | +2.7 | -0.6 | + | | Douglas, Wyoming | | | | | | | | | | | | -0.8 | 0.0 | +1.2 | +2.3 | +0.5 | -1.6 | + | | Emporia, Kansas | | | | | | | | | | | | +0.6 | +1.6 | +2.7 | +3.8 | +1.7 | -1.8 | + | | Pueblo, Colorado | | | | | | | | | | | | -0.3 | +0.4 | +1.5 | +3.1 | +0.7 | -2.2 | + | | Okmulgee, Oklahoma | | | | | | | | | | | | +0.9 | +1.5 | +2.7 | +3.9 | +1.4 | -2.4 | + | | Santa Rosa, New Mexico | | | | | | | | | | | | -0.4 | +0.4 | +1.4 | +2.6 | +0.4 | -2.4 | + | \ San Antonio, Texas | | | | | | | | | | -1.1 | -0.5 | -0.5 | +1.1 | +1.8 | +2.7 | +0.9 | -2.4 | + | | | | | | | | | | | | | | | | | | | + | / Seattle, Washington | | | | | -3.3 | -3.5 | -3.7 | -3.7 | -3.5 | -3.3 | -3.0 | -2.6 | -2.1 | -1.3 | -1.9 | -2.0 | -3.2 | + | | Wilson Creek, Washington| | | | | | | | | | | | -2.1 | -1.5 | -0.4 | -1.0 | -1.6 | -3.2 | + | | Detroit, Oregon | | | | | | | -3.8 | -3.9 | -3.9 | -3.7 | -3.4 | -2.9 | -2.5 | -1.8 | -0.8 | -1.8 | -3.8 | + | | Salt Lake, Utah | | | | | | | | | | | | -1.1 | -0.4 | +1.0 | +1.0 | -0.8 | -2.8 | + | | Prescott, Arizona | | | | | | | | | | | | -1.4 | -0.7 | +0.4 | +0.4 | -1.2 | -3.2 | + | | San José, California | | | | | -2.6 | -2.9 | -2.9 | -2.9 | -2.7 | -2.5 | -2.3 | -2.0 | -1.5 | -0.8 | -0.4 | -1.9 | -3.8 | + | \ Los Angeles, " | | | | | -3.4 | -3.4 | -3.5 | -3.2 | -3.0 | -2.7 | -2.1 | -1.6 | -1.1 | -0.9 | -0.3 | -1.6 | -3.6 | + +---------------------------+------+------+------+--------------------+------+------+------+------+------+------+------+------+------+------+------+ + + Formulae are also wanted to show how the value of an element, or the + rate of change of an element, at a particular place has varied + throughout a long period. For comparatively short periods it is best + to use formulae of the type E = a + bt + ct², where E denotes the + value of an element t years subsequent to some convenient epoch; a, b, + c are constants to be determined from the observational data. For + longer periods formulae of the type E = a + b sin (mt + n), where a, + b, m and n are constants, have been used by Schott[16] and others with + considerable success. The following examples, due to G. W. + Littlehales,[17] for the Cape of Good Hope, will suffice for + illustration: + + Declination (West) = 14°.63 + 15°.00 sin {0.61(t - 1850) + 77°.8} + Inclination (South) = 49°.11 + 8°.75 sin {0.8 (t - 1850) + 34°.3}. + + Here t denotes the date. It is perhaps hardly necessary to point out + that the extension of any of these empirical formulae--whether to + places outside the surveyed area, or to times not included in the + period of observation--is fraught with danger, which increases rapidly + the further the extrapolation is pushed. + + Table VII.--Inclination (northerly) and Horizontal Force at London. + + +------+-------+------+---------+------+---------+--------+------+---------+--------+ + | Date.| I. | Date.| I. | Date.| I. | H. | Date.| I. | H. | + +------+-------+------+---------+------+---------+--------+------+---------+--------+ + | | ° ´ | | ° ´ | | ° ´ | | | ° ´ | | + | 1576 | 71 50 | 1801 | 70 36.0 | 1857 | 68 24.9 | .17474 | 1891 | 67 33.2 | .18193 | + | 1600 | 72 0 | 1821 | 70 3.4 | 1860 | 69 19.8 | .17550 | 1895 | 67 25.4 | .18278 | + | 1676 | 73 30 | 1830 | 69 38.0 | 1865 | 68 8.7 | .17662 | 1900 | 67 11.8 | .18428 | + | 1723 | 74 42 | 1838 | 69 17.3 | 1870 | 67 58.6 | .17791 | 1905 | 67 3.8 | .18510 | + | 1773 | 72 19 | 1854 | 68 31.1 | 1874 | 67 50.0 | .17903 | 1908 | 67 0.9 | .18515 | + | 1786 | 72 9 | | | | | | | | | + +------+-------+------+---------+------+---------+--------+------+---------+--------+ + + [Illustration: FIG. 5.] + + Bauer has employed a convenient graphical method of illustrating + secular change. Radii are drawn from the centre of a sphere parallel + to the direction of the freely dipping needle, and are produced to + intersect the tangent plane drawn at the point which answers to the + mean position of the needle during the epoch under consideration. The + curve formed by the points of intersection shows the character of the + secular change. Fig. 5 (slightly modified from _Nature_, vol. 57, p. + 181) applies to London. The curve is being described in the clockwise + direction. This, according to Bauer's[18] own investigation, is the + normal mode of description. Schott and Littlehales have found, + however, a considerable number of cases where it is difficult to say + whether the motion is clockwise or not, while in some stations on both + the east and west shores of the Pacific it was clearly anti-clockwise. + Fritsche[19] dealing with the secular changes from 1600 to 1885--as + given by his calculated values of the magnetic elements--at 204 points + of intersection of equidistant lines of latitude and longitude, found + only sixty-three cases in which the motion was unmistakably clockwise, + while in twenty-one cases it was clearly the opposite. + + + Diurnal Variations. + + § 14. All the magnetic elements at any ordinary station show a regular + variation in the solar day. To separate this from the irregular + changes, means of the hourly readings must be formed making use of a + number of days. The amplitude of the diurnal change usually varies + considerably with the season of the year. Thus a diurnal inequality + derived from all the days of the year combined, or from a smaller + number of days selected equally from all the months of the year, can + give only the average effect throughout the year. Also unless the + hours of maxima and minima at a given station are but slightly + variable with the season, the result obtained by combining data from + all the months of the year may be a hybrid which does not very closely + resemble the phenomena in the majority of individual months. This + remark applies in particular to the declination at places within the + tropics. One consequence is obviously to make the range of a diurnal + inequality which answers to the year as a whole less than the + arithmetic mean of the twelve ranges obtained for the constituent + months. At stations in temperate latitudes, whilst minor differences + of type do exist between the diurnal inequalities for different months + of the year, the difference is mainly one of amplitude, and the mean + diurnal inequality from all the months of the year gives a very fair + idea of the nature of the phenomena in any individual month. + + Table VIII.--Diurnal Inequality of Declination, mean from whole year (+ to West). + + +----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+ + | Station. | Jan Mayen. |St Petersburg| Greenwich.| Kew. | Parc | Tiflis. | Kolaba. | Batavia. | Mauritius.| South Vic- | + | |and Pavlovsk.| | | St Maur. | | | | | toria Land. | + +----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+ + | Latitude.| 71° 0´ N. | 59° 41´ N. | 51° 28´ N.| 51° 28´ N. |48° 49´ N.| 41° 43´ N.| 18° 54´ N.| 6° 11´ S.| 20° 6´ S.| 77° 51´ S. | + |Longitude.| 8° 28´ W. | 30° 29´ E. | 0° 0´. | 0° 19´ W. | 2° 29´ E.| 44° 48´ E.| 72° 49´ E.|106° 49´ E.| 57° 33´ E.| 166° 45´ E. | + +----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+ + | Period. | 1882-1883. | 1873-1885. | 1890-1900.| 1890-1900. |1883-1897.| 1888-1898.| 1894-1901.| 1883-1894.| 1876-1890.| 1902-1903. | + +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+ + | | a. | q. | a. | q. | a. | a. | q. | a. | a. | q. | a. | a. | a. | q. | + +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+ + | Hour. | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | + | 1 | -6.6 | -4.2 | -1.3 | -0.7 | -1.4 | -1.5 | -0.9 | -1.4 | -0.7 | -0.2 | +0.1 | +0.1 | +2.0 | +0.9 | + | 2 | -10.5 | -6.4 | -1.2 | -0.8 | -1.3 | -1.4 | -0.9 | -1.2 | -0.6 | -0.1 | -0.1 | +0.1 | -2.1 | -1.8 | + | 3 | -15.2 | -7.8 | -1.2 | -1.0 | -1.3 | -1.5 | -1.0 | -1.2 | -0.6 | -0.1 | -0.1 | +0.1 | -5.2 | -4.5 | + | 4 | -16.9 | -8.4 | -1.4 | -1.3 | -1.4 | -1.7 | -1.3 | -1.2 | -0.5 | -0.1 | 0.0 | +0.2 | -9.4 | -6.8 | + | 5 | -17.0 | -8.1 | -1.7 | -1.8 | -1.7 | -2.1 | -1.8 | -1.6 | -0.7 | -0.1 | 0.0 | +0.3 | -12.2 | -9.0 | + | 6 | -13.7 | -7.0 | -1.9 | -2.3 | -2.1 | -2.4 | -2.3 | -1.9 | -1.2 | -0.6 | +0.1 | +0.4 | -15.3 | -11.7 | + | 7 | -9.3 | -5.1 | -2.2 | -2.8 | -2.4 | -2.7 | -2.8 | -2.4 | -1.9 | -1.0 | +0.5 | +0.6 | -17.2 | -15.0 | + | 8 | -6.8 | -3.2 | -2.5 | -3.2 | -2.5 | -2.8 | -3.1 | -2.7 | -2.4 | -1.2 | +1.3 | +1.1 | -21.5 | -17.3 | + | 9 | -3.7 | -0.6 | -2.3 | -3.0 | -1.9 | -2.1 | -2.5 | -2.3 | -2.3 | -0.7 | +1.7 | +1.8 | -23.5 | -18.1 | + | 10 | -2.4 | +2.1 | -1.0 | -1.7 | -0.2 | -0.3 | -0.7 | -0.5 | -0.9 | 0.0 | +1.5 | +1.9 | -21.2 | -15.8 | + | 11 | -0.5 | +4.6 | +1.0 | +0.4 | +2.1 | +2.2 | +1.7 | +2.0 | +1.0 | +0.9 | +0.9 | +1.3 | -15.3 | -9.2 | + | Noon | +2.5 | +6.5 | +3.1 | +2.7 | +4.2 | +4.3 | +3.9 | +4.2 | +2.6 | +1.4 | +0.1 | 0.0 | -9.8 | -4.9 | + | 1 | +3.7 | +7.3 | +4.6 | +4.3 | +5.1 | +5.3 | +4.8 | +5.3 | +3.3 | +1.2 | -0.6 | -1.1 | -3.2 | -0.1 | + | 2 | +6.4 | +7.1 | +4.9 | +4.5 | +4.7 | +4.9 | +4.4 | +4.9 | +3.1 | +0.6 | -1.1 | -2.0 | +3.8 | +5.9 | + | 3 | +7.4 | +5.9 | +4.1 | +3.6 | +3.6 | +3.7 | +3.1 | +3.7 | +2.3 | +0.1 | -1.3 | -2.3 | +11.1 | +9.5 | + | 4 | +8.5 | +4.3 | +2.7 | +2.3 | +2.2 | +2.4 | +1.8 | +2.3 | +1.3 | -0.2 | -1.2 | -1.8 | +16.6 | +12.9 | + | 5 | +10.6 | +3.0 | +1.5 | +1.3 | +1.1 | +1.2 | +0.7 | +1.1 | +0.6 | -0.1 | -0.9 | -0.9 | +19.9 | +14.6 | + | 6 | +14.2 | +2.3 | +0.6 | +0.7 | +0.3 | +0.4 | +0.2 | +0.2 | +0.2 | 0.0 | -0.6 | -0.1 | +22.0 | +15.5 | + | 7 | +15.2 | +2.2 | 0.0 | +0.4 | -0.3 | -0.2 | -0.1 | -0.4 | +0.1 | +0.1 | -0.4 | +0.1 | +22.0 | +15.9 | + | 8 | +15.8 | +2.6 | -0.4 | +0.2 | -0.9 | -0.6 | -0.3 | -0.9 | -0.1 | +0.2 | -0.2 | +0.1 | +19.9 | +14.6 | + | 9 | +13.2 | +2.6 | -1.0 | 0.0 | -1.2 | -1.0 | -0.5 | -1.3 | -0.4 | +0.1 | 0.0 | +0.1 | +16.0 | +10.6 | + | 10 | +7.4 | +2.0 | -1.4 | -0.2 | -1.5 | -1.3 | -0.7 | -1.5 | -0.6 | 0.0 | +0.1 | +0.1 | +11.6 | +7.2 | + | 11 | +1.1 | +0.5 | -1.6 | -0.4 | -1.6 | -1.4 | -0.8 | -1.6 | -0.7 | 0.0 | +0.1 | +0.1 | +7.6 | +4.2 | + | 12 | -3.6 | -1.8 | -1.5 | -0.6 | -1.6 | -1.5 | -0.9 | -1.6 | -0.8 | -0.1 | +0.1 | +0.1 | +3.3 | +1.9 | + +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+ + | Range | 32.8 | 15.7 | 7.4 | 7.7 | 7.6 | 8.1 | 7.9 | 8.0 | 5.7 | 2.6 | 3.0 | 4.2 | 45.5 | 34.0 | + +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+ + + Tables VIII. to XI. give mean diurnal inequalities derived from all + the months of the year combined, the figures representing the + algebraic excess of the hourly value over the mean for the twenty-four + hours. The + sign denotes in Table VIII. that the north end of the + needle is to the west of its mean position for the day; in Tables IX. + to XI. it denotes that the element--the dip being the north or south + as indicated--is numerically in excess of the twenty-four hour mean. + The letter "a" denotes that all days have been included except, as a + rule, those characterized by specially large disturbances. The letter + "q" denotes that the results are derived from a limited number of days + selected as being specially quiet, i.e. free from disturbance. In all + cases the aperiodic or non-cyclic element--indicated by a difference + between the values found for the first and second midnights of the + day--has been eliminated in the usual way, i.e. by treating it as + accumulating at a uniform rate throughout the twenty-four hours. The + years from which the data were derived are indicated. The + algebraically greatest and least of the hourly values are printed in + heavy type; the range thence derived is given at the foot of the + tables. + + TABLE IX.--Diurnal Inequality of Horizontal Force, mean from whole + year (Unit 1[gamma] = .00001 C.G.S.) + + +--------+----------+-------------+----------+----------+----------+----------+----------+----------+----------+-----------+ + |Station.|Jan Mayen.|St Petersburg|Greenwich.| Kew. | Parc | Tiflis. | Kolaba. | Batavia. |Mauritius.|S. Victoria| + | | |and Pavlovsk.| | | St Maur. | | | | | Land. | + +--------+----------+-------------+----------+----------+----------+----------+----------+----------+----------+-----------+ + | Period.|1882-1883.| 1873-1885. |1890-1900.|1890-1900.|1883-1897.|1888-1898.|1894-1901.|1883-1894.|1883-1890.| 1902-1903.| + +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+ + | | a. | q. | a. | q. | a. | q. | a. | a. | q. | a. | a. | a. | + +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+ + | Hour. | | | | | | | | | | | | | + | 1 | -57 |-22 | + 4 | + 5 | + 4 | + 4 | + 5 | + 3 | -10 | -11 | - 3 | -12 | + | 2 | -64 |-24 | + 4 | + 4 | + 3 | + 4 | + 5 | + 3 | - 9 | -10 | - 1 | -13 | + | 3 | -74 |-25 | + 4 | + 4 | + 3 | + 4 | + 5 | + 3 | - 9 | - 8 | + 1 | -14 | + | 4 | -69 |-24 | + 4 | + 4 | + 3 | + 4 | + 5 | + 4 | - 9 | - 7 | + 2 | -15 | + | 5 | -60 |-22 | + 5 | + 4 | + 3 | + 4 | + 6 | + 4 | - 9 | - 5 | + 3 | -15 | + | 6 | -37 |-19 | + 4 | + 4 | + 1 | + 2 | + 4 | + 4 | - 7 | - 1 | + 4 | -12 | + | 7 | -15 |-15 | + 2 | + 2 | - 3 | - 1 | + 1 | + 2 | - 1 | + 5 | + 7 | - 9 | + | 8 | - 1 |-13 | - 3 | - 4 | - 9 | - 7 | - 5 | - 3 | + 8 | +14 | + 9 | - 7 | + | 9 | + 8 |-12 | -10 | -10 | -16 | -13 | -12 | - 8 | -19 | +24 | + 9 | - 3 | + | 10 | +17 |-12 | -16 | -16 | -20 | -18 | -17 | -10 | +26 | +31 | + 9 | + 3 | + | 11 | +32 |-10 | -19 | -20 | -19 | -18 | -16 | - 7 | +30 | +35 | + 9 | + 7 | + | Noon | +49 |- 4 | -17 | -18 | -13 | -12 | -12 | - 1 | +26 | +31 | + 8 | +12 | + | 1 | +65 |+ 8 | -12 | -13 | - 7 | - 7 | - 7 | + 4 | +19 | +22 | + 7 | +18 | + | 2 | +78 |+22 | - 6 | - 6 | - 1 | - 2 | - 4 | + 5 | +10 | +10 | + 2 | +20 | + | 3 | +89 |+37 | 0 | 0 | + 2 | + 1 | - 1 | + 3 | + 2 | - 1 | - 2 | +19 | + | 4 | +83 |+43 | + 3 | + 3 | + 5 | + 3 | 0 | - 1 | - 3 | - 9 | - 6 | +18 | + | 5 | +68 |+49 | + 5 | + 5 | + 7 | + 5 | + 2 | - 4 | - 7 | -13 | - 7 | +15 | + | 6 | +37 |+43 | + 6 | + 6 | + 9 | + 7 | + 4 | - 6 | - 8 | -14 | - 7 | +11 | + | 7 | +13 |+30 | + 7 | + 7 | +10 | + 8 | + 6 | - 4 | - 9 | -15 | - 7 | + 5 | + | 8 | -11 |+15 | + 8 | + 8 | +10 | + 8 | + 7 | - 1 | -10 | -16 | - 8 | + 0 | + | 9 | -33 |+ 1 | + 9 | + 9 | + 8 | + 7 | + 7 | + 1 | -11 | -16 | - 8 | - 4 | + | 10 | -36 |-10 | + 8 | + 9 | + 7 | + 6 | + 6 | + 2 | -11 | -16 | - 8 | - 7 | + | 11 | -40 |-16 | + 7 | + 8 | + 6 | + 6 | + 6 | + 3 | -10 | -15 | - 7 | - 9 | + | 12 | -51 |-20 | + 6 | + 6 | + 5 | + 5 | + 6 | + 3 | -10 | -13 | - 5 | -11 | + +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+ + | Range | 163 | 74 | 28 | 29 | 30 | 26 | 24 | 15 | 41 | 51 | 17 | 35 | + +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+ + + + TABLE X.--Diurnal Inequality of Vertical Force, mean from whole year + (Unit 1[gamma]). + + +--------+-----------+-----------+-------+-------+--------+-------+-------+--------+-------+---------+ + | | |St Peters- |Green- | | Parc St| | | |Maur- |South | + |Station.| Jan Mayen.| burg and | wich. | Kew. | Maur. |Tiflis.|Kolaba.|Batavia.| itius.| Victoria| + | | | Pavlovsk. | | | | | | | | Land. | + +--------+-----------+-----------+-------+-------+--------+-------+-------+--------+-------+---------+ + | Period.| 1882-1883.| 1873-1885.|1890 |1891 |1883 |1888 |1894 |1883 |1884 | 1902 | + | | | | -1900.| -1900.| -1897. | -1898.| -1901.| -1894. | -1890.| -1903. | + +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+ + | Hour | a. | q. | a. | q. | a. | q. | a. | a. | q. | a. | a. | a. | + +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+ + | 1 | +65 | + 3 | - 7 | - 1 | - 3 | + 1 | 0 | + 2 | + 4 | + 7 | + 2 | +13 | + | 2 | +65 | + 2 | - 7 | - 1 | - 4 | + 1 | 0 | + 2 | + 4 | + 5 | + 2 | +12 | + | 3 | +56 | - 1 | - 7 | - 1 | - 4 | 0 | - 1 | + 1 | + 3 | + 4 | + 2 | +10 | + | 4 | +37 | - 5 | - 6 | 0 | - 3 | 0 | 0 | + 1 | + 3 | + 3 | + 2 | + 8 | + | 5 | +16 | - 7 | - 5 | 0 | - 2 | + 1 | 0 | + 2 | + 5 | + 2 | + 2 | + 3 | + | 6 | - 7 | - 8 | - 4 | 0 | - 1 | + 1 | + 1 | + 3 | + 7 | + 1 | + 2 | 0 | + | 7 | -17 | - 6 | - 3 | 0 | 0 | 0 | + 1 | + 3 | + 6 | 0 | + 3 | 0 | + | 8 | -14 | - 4 | - 2 | 0 | 0 | - 1 | 0 | + 3 | 0 | - 3 | + 4 | - 2 | + | 9 | - 9 | 0 | - 3 | - 1 | - 3 | - 4 | - 4 | - 1 | - 8 | -11 | + 5 | - 6 | + | 10 | - 6 | + 5 | - 2 | - 2 | - 6 | - 8 | - 8 | - 7 | -14 | -20 | + 3 | -13 | + | 11 | - 6 | +10 | - 3 | - 4 | - 9 | -11 | -12 | -11 | -15 | -26 | 0 | -17 | + | Noon | -10 | +16 | - 3 | - 5 | -10 | -11 | -12 | -11 | -10 | -27 | - 4 | -20 | + | 1 | -13 | +21 | - 1 | - 4 | - 6 | - 8 | - 9 | - 9 | - 3 | -21 | - 7 | -20 | + | 2 | -24 | +23 | + 2 | - 1 | 0 | - 3 | - 3 | - 5 | + 1 | -13 | - 9 | -16 | + | 3 | -31 | +20 | + 8 | + 2 | + 5 | + 2 | + 2 | - 1 | + 4 | - 4 | - 8 | -12 | + | 4 | -40 | +13 | + 9 | + 3 | + 8 | + 5 | + 6 | + 1 | + 3 | + 4 | - 5 | - 6 | + | 5 | -48 | + 2 | +10 | + 3 | + 9 | + 6 | + 7 | + 3 | 0 | +10 | - 3 | - 1 | + | 6 | -53 | - 9 | +10 | + 3 | +10 | + 7 | + 8 | + 4 | 0 | +13 | 0 | + 3 | + | 7 | -47 | -18 | + 9 | + 3 | + 9 | + 6 | + 7 | + 3 | 0 | +14 | 0 | + 6 | + | 8 | -36 | -20 | + 8 | + 3 | + 7 | + 5 | + 6 | + 3 | + 1 | +14 | + 1 | + 9 | + | 9 | - 7 | -19 | + 6 | + 2 | + 5 | + 5 | + 5 | + 3 | + 2 | +14 | + 2 | +11 | + | 10 | +18 | -13 | + 3 | + 2 | + 3 | + 4 | + 3 | + 3 | + 3 | +13 | + 2 | +12 | + | 11 | +42 | - 5 | - 2 | 0 | 0 | + 3 | + 2 | + 3 | + 3 | +11 | + 2 | +12 | + | 12 | +54 | 0 | - 5 | - 1 | - 2 | + 2 | + 1 | + 2 | + 3 | + 9 | + 2 | +13 | + +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+ + | Range | 118 | 43 | 17 | 8 | 20 | 18 | 20 | 15 | 22 | 41 | 14 | 33 | + +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+ + + When comparing results from different stations, it must be remembered + that the disturbing forces required to cause a change of 1´ in + declination and in dip vary directly, the former as the horizontal + force, the latter as the total force. Near a magnetic pole the + horizontal force is relatively very small, and this accounts, at least + partly, for the difference between the declination phenomena at Jan + Mayen and South Victoria Land on the one hand and at Kolaba, Batavia + and Mauritius on the other. There is, however, another cause, already + alluded to, viz. the variability in the type of the diurnal inequality + in tropical stations. With a view to illustrating this point Table + XII. gives diurnal inequalities of declination for June and December + for a number of stations lying between 45° N. and 45° S. latitude. + Some of the results are represented graphically in fig. 6, plus + ordinates representing westerly deflection. At the northmost station, + Toronto, the difference between the two months is mainly a matter of + amplitude, the range being much larger at midsummer than at midwinter. + The conspicuous phenomenon at both seasons is the rapid swing to the + west from 8 or 9 a.m. to 1 or 2 p.m. At the extreme southern station, + Hobart--at nearly equal latitude--the rapid diurnal movement is to the + east, and so in the opposite direction to that in the northern + hemisphere, but it again takes place at nearly the same hours in June + (midwinter) as in December. If, however, we take a tropical station + such as Trivandrum or Kolaba, the phenomena in June and December are + widely different in type. At Trivandrum--situated near the magnetic + equator in India--we have in June the conspicuous forenoon swing to + the west seen at Toronto, occurring it is true slightly earlier in the + day; but in December at the corresponding hours the needle is actually + swinging to the east, just as it is doing at Hobart. In June the + diurnal inequality of declination at tropical stations--whether to the + north of the equator like Trivandrum, or to the south of it like + Batavia--is on the whole of the general type characteristic of + temperate regions in the northern hemisphere; whereas in December the + inequality at these stations resembles that of temperate regions in + the southern hemisphere. Comparing the inequalities for June in Table + XII. amongst themselves, and those for December amongst themselves, + one can trace a gradual transformation from the phenomena seen at + Toronto to those seen at Hobart. At a tropical station the change from + the June to the December type is probably in all cases more or less + gradual, but at some stations the transition seems pretty rapid. + + TABLE XI.--Diurnal Inequality of Inclination mean from whole year. + + +--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+ + | | | St Peters- |Green- | | Parc St| | | |Maur- |South | + |Station.| Jan Mayen. | burg and | wich. | Kew. | Maur. |Tiflis.|Kolaba.|Batavia.| itius.| Victoria| + | | | Pavlovsk. | | | | | | | | Land. | + +--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+ + | End | North. | North. | North.| North.| North. | North.| North.| South. | South.| South. | + |Dipping | | | | | | | | | | | + +--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+ + | Period.| 1882-1883. | 1873-1885. |1890 |1891 |1883 |1888 |1894 |1883 |1884 | 1902 | + | | | | -1900.| -1900.| -1897. | -1898.| -1901.| -1894. | -1890.| -1903. | + +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+ + | | a. | q. | a. | q. | a. | q. | a. | a. | q. | a. | a. | a. | + +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+ + | Hour | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | + | 1 | +4.6 | +1.5 | -0.5 | -0.3 | -0.4 | -0.3 | -0.3 | -0.1 | +0.6 | +0.9 | +0.3 | +0.6 | + | 2 | +5.0 | +1.6 | -0.5 | -0.3 | -0.3 | -0.2 | -0.3 | -0.1 | +0.6 | +0.8 | +0.2 | +0.7 | + | 3 | +5.6 | +1.6 | -0.5 | -0.3 | -0.3 | -0.2 | -0.3 | -0.1 | +0.5 | +0.6 | 0.0 | +0.7 | + | 4 | +5.0 | +1.5 | -0.4 | -0.3 | -0.3 | -0.2 | -0.4 | -0.2 | +0.5 | +0.5 | -0.0 | +0.7 | + | 5 | +4.2 | +1.4 | -0.5 | -0.3 | -0.2 | -0.2 | -0.4 | -0.2 | +0.7 | +0.3 | -0.1 | +0.7 | + | 6 | +2.4 | +1.2 | -0.4 | -0.3 | -0.1 | -0.1 | -0.3 | -0.1 | +0.8 | +0.1 | -0.2 | +0.5 | + | 7 | +0.7 | +0.9 | -0.2 | -0.1 | +0.2 | +0.1 | 0.0 | 0.0 | +0.5 | -0.2 | -0.3 | +0.4 | + | 8 | -0.1 | +0.8 | +0.1 | +0.3 | +0.6 | +0.4 | +0.4 | +0.3 | -0.2 | -0.8 | -0.4 | +0.3 | + | 9 | -0.7 | +0.8 | +0.6 | +0.6 | +1.0 | +0.8 | +0.7 | +0.5 | -1.2 | -1.7 | -0.4 | +0.1 | + | 10 | -1.2 | +0.9 | +1.0 | +1.0 | +1.1 | +1.0 | +0.9 | +0.3 | -1.9 | -2.7 | -0.5 | -0.2 | + | 11 | -2.2 | +0.8 | +1.2 | +1.2 | +1.0 | +0.9 | +0.7 | 0.0 | -2.1 | -3.3 | -0.6 | -0.4 | + | Noon | -3.4 | +0.4 | +1.1 | +1.1 | +0.6 | +0.6 | +0.4 | -0.5 | -1.6 | -3.1 | -0.7 | -0.7 | + | 1 | -4.5 | -0.2 | +0.7 | +0.7 | +0.3 | +0.2 | +0.2 | -0.6 | -0.8 | -2.4 | -0.8 | -0.9 | + | 2 | -5.6 | -1.2 | +0.4 | +0.4 | +0.1 | +0.1 | +0.2 | -0.5 | -0.2 | -1.3 | -0.6 | -1.0 | + | 3 | -6.3 | -2.2 | +0.2 | +0.1 | 0.0 | 0.0 | +0.2 | -0.3 | +0.3 | -0.2 | -0.3 | -1.0 | + | 4 | -6.1 | -2.9 | 0.0 | -0.1 | -0.1 | -0.1 | +0.2 | +0.1 | +0.3 | +0.7 | +0.1 | -0.9 | + | 5 | -5.1 | -3.2 | -0.1 | -0.3 | -0.2 | -0.2 | +0.1 | +0.4 | +0.2 | +1.3 | +0.4 | -0.7 | + | 6 | -3.1 | -2.9 | -0.2 | -0.3 | -0.3 | -0.3 | 0.0 | +0.5 | +0.2 | +1.5 | +0.5 | -0.5 | + | 7 | -1.7 | -2.2 | -0.3 | -0.4 | -0.4 | -0.4 | -0.2 | +0.4 | +0.3 | +1.6 | +0.5 | -0.2 | + | 8 | +0.3 | -1.3 | -0.3 | -0.5 | -0.4 | -0.4 | -0.3 | +0.2 | +0.4 | +1.6 | +0.6 | 0.0 | + | 9 | +2.0 | -0.3 | -0.4 | -0.6 | -0.4 | -0.4 | -0.3 | +0.1 | +0.5 | +1.6 | +0.6 | +0.2 | + | 10 | +2.5 | +0.5 | -0.5 | -0.6 | -0.4 | -0.3 | -0.3 | 0.0 | +0.6 | +1.5 | +0.6 | +0.4 | + | 11 | +3.0 | +1.0 | -0.5 | -0.6 | -0.4 | -0.3 | -0.3 | 0.0 | +0.6 | +1.4 | +0.5 | +0.5 | + | 12 | +4.0 | +1.3 | -0.5 | -0.4 | -0.4 | -0.3 | -0.3 | -0.1 | +0.6 | +1.2 | +0.4 | +0.6 | + +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+ + | Range | 11.9 | 4.8 | 1.7 | 1.8 | 1.5 | 1.4 | 1.3 | 1.1 | 2.9 | 4.9 | 1.4 | 1.7 | + +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+ + + + TABLE XII.--Diurnal Inequality of Declination (+ to West). + + +--------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+ + |Station.| Toronto. | Kolaba. |Trivandrum.| Batavia. | St Helena.| Mauritius.| Cape. | Hobart. | + +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ + | Month. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. | + +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ + | Hour | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | + | 1 |-0.4 |-0.1 |-0.3 | 0.0 |-0.3 |-0.1 |+0.1 |+0.1 |-0.1 |-0.4 | 0.0 |+0.1 |-0.4 |-0.7 |+0.8 |+1.1 | + | 2 |-0.2 |+0.4 |-0.3 |+0.1 |-0.4 |+0.1 |-0.1 |+0.1 |-0.2 |-0.1 |-0.2 |+0.2 |-0.5 |-0.4 |+0.3 |+1.1 | + | 3 |-0.2 |-0.1 |-0.3 |+0.1 |-0.4 |+0.3 |-0.2 |+0.2 |-0.2 |+0.1 |-0.2 |+0.4 |-0.7 |-0.1 |-0.1 |+1.0 | + | 4 |-1.2 |-0.4 |-0.3 |+0.3 |-0.5 |+0.5 |-0.3 |+0.3 |-0.3 |+0.3 |-0.2 |+0.7 |-0.6 |+0.3 |-0.1 |+1.1 | + | 5 |-2.9 |-0.6 |-0.7 |+0.4 |-0.7 |+0.7 |-0.3 |+0.5 |-0.5 |+0.6 |-0.3 |+1.0 |-0.7 |+1.0 | 0.0 |+1.7 | + | 6 |-5.2 |-0.6 |-1.6 |+0.5 |-1.6 |+1.1 |-0.5 |+1.2 |-1.0 |+0.9 |-0.4 |+1.7 |-1.0 |+2.2 | 0.0 |+2.7 | + | 7 |-6.2 |-0.9 |-2.2 |+0.7 |-1.7 |+1.4 |-1.1 |+2.0 |-2.2 |+1.9 |-1.1 |+2.6 |-1.6 |+3.3 |-0.1 |+4.4 | + | 8 |-6.0 |-1.2 |-2.1 |+0.2 |-1.1 |+0.9 |-0.4 |+2.3 |-1.5 |+2.2 |-1.0 |+2.4 |-0.8 |+3.6 |+0.1 |+5.6 | + | 9 |-4.4 |-1.8 |-1.1 |-0.1 |-0.2 |+0.5 |+0.5 |+2.0 |-0.3 |+1.3 |+0.2 |+2.0 |+0.7 |+3.1 |+0.6 |+5.6 | + | 10 |-1.5 |-1.1 | 0.0 |-0.2 |+0.6 |+0.3 |+0.9 |+1.3 |+0.3 |+0.2 |+1.2 |+1.1 |+1.6 |+1.6 |+1.2 |+3.6 | + | 11 |+2.1 |+0.6 |+1.2 | 0.0 |+1.2 |+0.1 |+1.0 |+0.4 |+0.5 |-1.0 |+1.4 | 0.0 |+1.5 |+0.1 |+1.0 |+0.7 | + | Noon |+4.8 |+2.2 |+2.1 | 0.0 |+1.4 |-0.4 |+0.7 |-0.6 |+0.3 |-1.4 |+1.0 |-1.4 |+0.8 |-1.0 |-0.1 |-2.6 | + | 1 |+6.1 |+3.2 |+2.0 |-0.2 |+1.1 |-0.8 |+0.3 |-1.4 |+0.3 |-1.2 |+0.1 |-2.2 |+0.3 |-1.8 |-1.4 |-5.1 | + | 2 |+6.1 |+3.2 |+1.6 |-0.3 |+0.7 |-0.9 |-0.2 |-1.8 |+0.2 |-0.4 |-0.9 |-2.5 |-0.3 |-1.9 |-2.2 |-6.2 | + | 3 |+5.2 |+2.4 |+0.9 |-0.3 |+0.3 |-0.9 |-0.7 |-1.9 |+0.2 |+0.4 |-1.5 |-2.2 |-0.3 |-1.4 |-2.4 |-5.8 | + | 4 |+3.6 |+1.5 |+0.2 |-0.3 |+0.1 |-0.8 |-0.8 |-1.6 |+0.7 |+0.6 |-1.3 |-1.6 |+0.2 |-0.8 |-1.6 |-4.8 | + | 5 |+1.8 |+0.5 | 0.0 |-0.2 | 0.0 |-0.4 |-0.5 |-1.2 |+1.1 |+0.4 |-0.3 |-1.0 |+0.5 |-0.8 |-0.7 |-3.3 | + | 6 |+0.7 |-0.1 |+0.1 |-0.2 |+0.2 |-0.4 |-0.1 |-0.7 |+1.0 |+0.1 |+0.5 |-0.5 |+0.5 |-0.6 |-0.4 |-1.9 | + | 7 | 0.0 |-0.8 |+0.3 |-0.2 |+0.5 |-0.4 |+0.1 |-0.6 |+0.6 |-0.4 |+0.7 |-0.3 |+0.4 |-0.8 | 0.0 |-1.0 | + | 8 | 0.0 |-1.2 |+0.4 |-0.1 |+0.5 |-0.3 |+0.2 |-0.5 |+0.5 |-0.7 |+0.7 |-0.3 |+0.3 |-0.9 |+0.5 |-0.3 | + | 9 |-0.5 |-1.4 |+0.3 |-0.1 |+0.4 |-0.2 |+0.4 |-0.3 |+0.4 |-0.9 |+0.6 |-0.2 |+0.2 |-0.9 |+1.1 | 0.0 | + | 10 |-0.5 |-1.7 |+0.1 | 0.0 |+0.2 |-0.1 |+0.4 |-0.1 |+0.2 |-1.0 |+0.4 |-0.1 |+0.1 |-1.0 |+1.3 |+0.6 | + | 11 |-0.7 |-1.1 |-0.1 |-0.1 | 0.0 |-0.1 |+0.3 | 0.0 |+0.1 |-0.8 |+0.3 | 0.0 | 0.0 |-1.0 |+1.3 |+0.9 | + | 12 |-0.6 |-0.7 |-0.2 |-0.1 |-0.2 |-0.1 |+0.2 |+0.1 |-0.1 |-0.6 |+0.1 |+0.1 |-0.2 |-1.0 |+1.1 |+1.2 | + +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ + | Range |12.3 | 5.0 | 4.3 | 1.0 | 3.1 | 2.3 | 2.1 | 4.2 | 3.3 | 3.6 | 2.9 | 5.1 | 3.2 | 5.5 | 3.7 |11.8 | + +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ + + § 15. In the case of the horizontal force there are, as Table IX. + shows, two markedly different types of diurnal inequality. In the one + type, exemplified by Pavlovsk or Greenwich, the force is below its + mean value in the middle of the day; it has a principal minimum about + 10 or 11 a.m., and morning and evening maxima, the latter usually the + largest. In the other type, exemplified by Kolaba or Batavia, the + horizontal force is above its mean in the middle of the day, and has + a maximum about 11 a.m. The second type may be regarded as the + tropical type. At tropical stations, such as Kolaba, Batavia, Manila + and St Helena, the type is practically the same in summer as in + winter, and is the same whether the station is north or south of the + equator. Similarly, what we may call the temperate type is seen--with + comparatively slight modifications--both in summer and winter at + stations such as Greenwich or Pavlovsk. In winter, it is true, the + pronounced daily minimum is a little later and the early morning + maximum is relatively more important than in summer. There is not, as + in the case of the declination, any essential difference between the + phenomena at temperate stations in the northern and southern + hemispheres. + + [Illustration: FIG. 6.] + + With diminishing latitude, there is a gradual transition from the + temperate to the tropical type of horizontal force diurnal variation, + and at stations whose latitude is under 45° there is a very + appreciable variation in type with the season. The mean diurnal + variation for the year at Tiflis in Table IX. really represents a + struggle between the two types, in which on the whole the temperate + type prevails. If we take the diurnal variations at Tiflis for + midsummer and midwinter, we find the former essentially of the + temperate, the latter essentially of the tropical type. A similar + conflict may be seen in the mean diurnal inequality for the year at + the Cape of Good Hope, but there the tropical type on the whole + predominates, and it prevails more at midwinter than at midsummer. + Toronto and Hobart, though similar in latitude to Tiflis, show a + closer approach to the temperate type. Still at both stations the + hours during which the force is below its mean value tend to extend + back towards midnight, especially at midsummer. The amplitude of the + horizontal force range appears less at intermediate stations, such as + Tiflis, than at stations in either higher or lower latitudes. There + is a very great difference in this respect between the north and the + south of India. + + § 16. In the case of the vertical force in higher temperate + latitudes--at Pavlovsk for instance--the diurnal inequalities from + "all" and from "quiet" days differ somewhat widely in amplitude and + slightly even in type. In mean latitudes, e.g. at Tiflis, there is + often a well marked double period in the mean diurnal inequality for + the whole year; but even at Tiflis this is hardly, if at all, apparent + in the winter months. In the summer months the double period is + distinctly seen at Kew and Greenwich, though the evening maximum is + always pre-eminent. Speaking generally, the time of the minimum, or + principal minimum, varies much less with the season than that of the + maximum. At Kew, for instance, on quiet days the minimum falls between + 11 a.m. and noon in almost all the months of the year, but the time of + the maximum varies from about 4 p.m. in December to 7 p.m. in June. At + Kolaba the time of the minimum is nearly independent of the season; + but the changes from positive to negative in the forenoon and from + negative to positive in the afternoon are some hours later in winter + than in summer. At Batavia the diurnal inequality varies very little + in type with the season, and there is little evidence of more than one + maximum and minimum in the day. At Batavia, as at Kolaba, negative + values occur near noon; but it must be remembered that while at Kolaba + and more northern stations vertical force urges the north pole of a + magnet downwards, the reverse is true of Batavia, as the dip is + southerly. At St Helena vertical force is below its mean value in the + forenoon, but the change from - to + occurs at noon, or but little + later, both in winter and summer. At the Cape of Good Hope the + phenomena at midsummer are similar to those at Kolaba, the force being + below its mean value from about 9 a.m. to 3 p.m. and above it + throughout the rest of the day; but at midwinter there is a + conspicuous double period, the force being below its mean from 1 a.m. + to 7 a.m. as well as from 11 a.m. to 3 p.m., and thus resembling the + all-day annual results at Greenwich. At Hobart vertical force is below + its mean value from 1 a.m. to 9 a.m. at midsummer, and from 4 a.m. to + noon at midwinter; while the force is above its mean persistently + throughout the afternoon both in summer and winter, there is at + midwinter a well marked secondary minimum about 6 p.m., almost the + same hour as that at which the maximum for the day is observed in + summer. + + TABLE XIII.--Range of the Diurnal Inequality of Declination. + + +-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+ + | Place. | Period. | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. | + +-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+ + | | | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | + | Pavlovsk | 1890-1900 a | 4.93 | 6.15 | 8.58 |10.93 |12.18 |12.27 |11.82 |11.38 | 8.70 | 6.87 | 5.54 | 4.63 | + | " | " q | 2.96 | 4.20 | 8.73 |11.28 |12.89 |13.28 |12.31 |11.70 | 9.37 | 6.91 | 3.95 | 2.66 | + | Ekatarinburg| 1890-1900 a | 3.33 | 4.32 | 7.63 |11.19 |11.82 |11.58 |11.09 |10.45 | 8.13 | 5.60 | 3.73 | 3.14 | + | Greenwich | 1865-1896 a | 5.87 | 7.07 | 9.40 |11.42 |10.55 |10.90 |10.82 |10.93 | 9.66 | 8.15 | 6.41 | 5.15 | + | Kew | 1890-1900 a | 4.92 | 6.06 | 9.08 |10.95 |10.66 |10.92 |10.59 |11.01 | 9.49 | 7.73 | 5.37 | 4.46 | + | " | " q | 4.07 | 4.76 | 8.82 |10.57 |10.92 |10.62 |10.18 |11.01 | 9.76 | 7.51 | 4.75 | 3.34 | + | Toronto | 1842-1848 a | 5.96 | 6.05 | 9.18 | 9.94 |11.55 |12.34 |12.21 |13.14 |10.76 | 6.96 | 6.32 | 4.97 | + | Manila | 1890-1900 a | 1.79 | 1.09 | 2.13 | 3.02 | 3.84 | 3.94 | 4.21 | 4.89 | 4.53 | 1.83 | 0.85 | 1.33 | + | Trivandrum | 1853-1864 a | 2.06 | 1.48 | 0.79 | 1.67 | 2.90 | 3.06 | 3.06 | 3.64 | 3.31 | 1.27 | 2.14 | 2.33 | + | Batavia | 1884-1899 a | 4.18 | 4.64 | 3.57 | 2.93 | 2.38 | 2.03 | 2.31 | 3.16 | 3.80 | 4.51 | 4.50 | 4.19 | + | St Helena | 1842-1847 a | 3.72 | 5.19 | 4.93 | 3.30 | 2.64 | 3.24 | 3.42 | 3.59 | 2.40 | 4.43 | 4.05 | 3.54 | + | Mauritius | 1876-1890 a | 5.2 | 6.1 | 6.3 | 4.7 | 4.1 | 2.9 | 3.4 | 4.9 | 5.0 | 5.5 | 5.6 | 5.1 | + | Cape | 1841-1846 a | 5.14 | 8.21 | 7.27 | 5.00 | 3.91 | 3.21 | 3.54 | 4.98 | 4.33 | 5.96 | 6.36 | 5.47 | + | Hobart | 1841-1848 a |11.66 |11.80 | 9.50 | 7.26 | 4.56 | 3.70 | 4.61 | 5.89 | 8.24 |11.01 |12.05 |11.81 | + +-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+ + + § 17. Variations of inclination are connected with those of horizontal + and vertical force by the relation + + [delta]I = ½ sin 2I {V^-1 [delta]V - H^-1 [delta]H}. + + Thus in temperate latitudes where V is considerably in excess of H, + whilst diurnal changes in V are usually less than those in H, it is + the latter which chiefly dominate the diurnal changes in inclination. + When the H influence prevails, I has its highest values at hours when + H is least. This explains why the dip is above its mean value near + midday at stations in Table XI. from Pavlovsk to Parc St Maur. Near + the magnetic equator the vertical force has the greater influence. + This alone would tend to make a minimum dip in the late forenoon, and + this minimum is accentuated owing to the altered type of the + horizontal force diurnal variation, whose maximum now coincides + closely with the minimum in the vertical force. This accounts for the + prominence of the minimum in the diurnal variation of the inclination + at Kolaba and Batavia, and the large amplitude of the range. Tiflis + shows an intermediate type of diurnal variation; there is a minimum + near noon, as in tropical stations, but inclination is also below its + mean for some hours near midnight. The type really varies at Tiflis + according to the season of the year. In June--as in the mean equality + from the whole year--there is a well marked double period; there is a + principal minimum at 2 p.m. and a secondary one about 4 a.m.; a + principal maximum about 9 a.m. and a secondary one about 6 p.m. In + December, however, only a single period is recognizable, with a + minimum about 8 a.m. and a maximum about 7 p.m. The type of diurnal + inequality seen at the Cape of Good Hope does not differ much from + that seen at Batavia. Only a single period is clearly shown. The + maximum occurs about 8 or 9 p.m. throughout the year. The time of the + minimum is more variable; at midsummer it occurs about 11 a.m., but at + midwinter three or four hours later. At Hobart the type varies + considerably with the season. In June (midwinter) a double period is + visible. The principal minimum occurs about 8 a.m., as at the Cape. + But, corresponding to the evening maximum seen at the Cape, there is + now only a secondary maximum, the principal maximum occurring about 1 + p.m. At midsummer the principal maximum is found--as at Kew or + Greenwich--about 10 or 11 a.m., the principal minimum about 4 p.m. + + § 18. Even at tropical stations a considerable seasonal change is + usually seen in the amplitude of the diurnal inequality in at least + one of the magnetic elements. At stations in Europe, and generally in + temperate latitudes, the amplitude varies notably in all the elements. + Table XIII. gives particulars of the inequality range of declination + derived from hourly readings at selected stations, arranged in order + of latitude from north to south. The letters "a" and "q" are used in + the same sense as before. At temperate stations in either + hemisphere--e.g. Pavlovsk, Greenwich or Hobart--the range is + conspicuously larger in summer than in winter. In northern temperate + stations a decided minimum is usually apparent in December. There is, + on the other hand, comparatively little variation in the range from + April to August. Sometimes, as at Kew and Greenwich, there is at least + a suggestion of a secondary minimum at midsummer. Manila and + Trivandrum show a transition from the December minimum, characteristic + of the northern stations, to the June minimum characteristic of the + southern, there being two conspicuous minima in February or March and + in November or October. At St Helena there are two similar minima in + May and September, while a third apparently exists in December. It + will be noticed that at both Pavlovsk and Kew the annual variation in + the range is specially prominent in the quiet day results. + + Table XIV. gives a smaller number of data analogous to those of Table + XIII., comprising inequality ranges for horizontal force, vertical + force and inclination. In some cases the number of years from which + the data were derived seems hardly sufficient to give a smooth annual + variation. It should also be noticed that unless the same group of + years is employed the data from two stations are not strictly + comparable. The difference between the all and quiet day vertical + force data at Pavlovsk is remarkably pronounced. The general tendency + in all the elements is to show a reduced range at midwinter; but in + some cases there is also a distinct reduction in the range at + midsummer. This double annual period is particularly well marked at + Batavia. + + TABLE XIV.--Ranges in the Diurnal Inequalities. + + +-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+ + | | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. | + +-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+ + | H (unit 1[gamma]) | | | | | | | | | | | | | + | Pavlovsk 1890-1900 a | 12 | 20 | 32 | 46 | 47 | 49 | 49 | 44 | 39 | 32 | 17 | 11 | + | " " q | 12 | 17 | 31 | 42 | 45 | 45 | 42 | 40 | 37 | 31 | 17 | 10 | + | Ekatarinburg " a | 11 | 15 | 29 | 37 | 40 | 40 | 39 | 36 | 33 | 27 | 13 | 9 | + | Kew " q | 15 | 17 | 26 | 36 | 38 | 39 | 38 | 38 | 35 | 27 | 20 | 11 | + | Toronto 1843-1848 a | 23 | 21 | 24 | 28 | 29 | 29 | 26 | 28 | 41 | 25 | 21 | 20 | + | Batavia 1883-1898 a | 49 | 47 | 54 | 60 | 51 | 48 | 50 | 53 | 58 | 52 | 43 | 40 | + | St Helena 1843-1847 a | 43 | 41 | 48 | 53 | 46 | 40 | 40 | 45 | 41 | 40 | 40 | 32 | + | Mauritius 1883-1890 a | 21 | 15 | 21 | 23 | 20 | 21 | 20 | 22 | 20 | 21 | 21 | 20 | + | Cape of Good Hope 1841-1846 a | 13 | 10 | 13 | 13 | 15 | 16 | 14 | 18 | 21 | 14 | 17 | 20 | + | Hobart 1842-1848 a | 42 | 43 | 34 | 28 | 19 | 17 | 22 | 23 | 23 | 35 | 39 | 42 | + | | | | | | | | | | | | | | + | V (unit 1[gamma]) | | | | | | | | | | | | | + | Pavlovsk 1890-1900 a | 15 | 27 | 29 | 24 | 26 | 20 | 23 | 19 | 23 | 20 | 18 | 14 | + | " " q | 4 | 5 | 9 | 13 | 13 | 12 | 13 | 10 | 9 | 7 | 5 | 4 | + | Ekatarinburg " a | 10 | 15 | 17 | 21 | 22 | 19 | 20 | 16 | 14 | 13 | 11 | 9 | + | Kew 1891-1900 q | 7 | 10 | 20 | 25 | 31 | 27 | 28 | 23 | 20 | 15 | 9 | 6 | + | Toronto 1843-1848 a | 12 | 14 | 17 | 23 | 26 | 14 | 27 | 32 | 34 | 25 | 19 | 18 | + | Batavia 1883-1898 a | 42 | 48 | 48 | 45 | 31 | 31 | 32 | 29 | 41 | 50 | 40 | 33 | + | St Helena 1843-1847 a | 16 | 13 | 12 | 14 | 13 | 11 | 17 | 11 | 17 | 11 | 15 | 18 | + | Mauritius 1884-1890 a | 12 | 16 | 18 | 15 | 14 | 13 | 15 | 21 | 20 | 16 | 13 | 11 | + | Cape of Good Hope 1841-1846 a | 29 | 47 | 41 | 38 | 21 | 12 | 14 | 19 | 19 | 35 | 33 | 28 | + | Hobart 1842-1848 a | 25 | 27 | 22 | 23 | 24 | 21 | 22 | 28 | 26 | 22 | 23 | 27 | + | | | | | | | | | | | | | | + | _Inclination_ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | + | Pavlovsk 1890-1900 a | 0.97 | 1.24 | 2.07 | 2.79 | 2.72 | 2.88 | 2.85 | 2.64 | 2.52 | 2.18 | 1.20 | 0.89 | + | Ekatarinburg " a | 0.79 | 0.94 | 1.70 | 2.08 | 2.25 | 2.19 | 2.18 | 2.08 | 2.00 | 1.70 | 0.88 | 0.69 | + | Kew " q | 0.98 | 1.01 | 1.38 | 1.86 | 2.05 | 2.02 | 2.05 | 2.15 | 1.98 | 1.57 | 1.27 | 0.63 | + | Toronto 1843-1848 a | 1.15 | 0.94 | 1.19 | 1.23 | 1.31 | 1.37 | 1.13 | 1.26 | 1.87 | 1.16 | 1.09 | 1.05 | + | Batavia 1883-1898 a | 4.88 | 5.22 | 5.56 | 5.62 | 4.21 | 4.05 | 4.24 | 4.17 | 5.13 | 5.58 | 4.51 | 3.85 | + | Cape of Good Hope 1842-1846 a | 1.55 | 2.29 | 2.23 | 2.23 | 1.60 | 1.41 | 1.54 | 1.70 | 1.86 | 2.03 | 1.55 | 2.04 | + | Hobart 1842-1848 a | 1.95 | 2.16 | 1.72 | 1.62 | 1.23 | 1.16 | 1.28 | 1.42 | 1.39 | 1.75 | 2.04 | 2.10 | + +-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+ + + § 19. When discussing diurnal inequalities it is sometimes convenient + to consider the components of the horizontal force in and + perpendicular to the astronomical meridian, rather than the horizontal + force and declination. If N and W be the components of H to + astronomical north and west, and D the westerly declination, N = H + cos D, W = H sin D. Thus corresponding small variations in N, W, H and + D are connected by the relations:-- + + [delta]N = cos D[delta]H - H sin D[delta]D, + [delta]W = sin D[delta]H + H cos D[delta]D. + + If [delta]H and [delta]D denote the departures of H and D at any hour + of the day from their mean values, then [delta]N and [delta]W + represent the corresponding departures of N and W from their mean + values. In this way diurnal inequalities may be calculated for N and W + when those for H and D are known. The formulae suppose [delta]D to be + expressed in absolute measure, i.e. 1´ of arc has to be replaced by + 0.0002909. If we take as an example a station at which H is .185 then + H[delta]D = .0000538 (number of minutes in [delta]D). In other words, + employing 1[gamma] as unit of force, one replaces H[delta]D by + 5.38[delta]D, where [delta]D represents declination change expressed + as usual in minutes of arc. In calculating diurnal inequalities for N + and W, one ought, strictly speaking, to assign to H and D the exact + mean values belonging to these elements for the month or the year + being dealt with. For practical purposes, however, a slight departure + from the true mean values is immaterial, and one can make use of a + constant value for several successive years without sensible error. As + an example, Table XV. gives the mean diurnal inequality for the whole + year in N and W at Falmouth, as calculated from the 12 years 1891 to + 1902. The unit employed is 1[gamma]. + + The data in Table XV. are closely similar to corresponding Kew data, + and are presumably fairly applicable to the whole south of England for + the epoch considered. At Falmouth there is comparatively little + seasonal variation in the type of the diurnal variation in either N or + W. The amplitude of the diurnal range varies, however, largely with + the season, as will appear from Table XVI., which is based on the same + 12 years as Table XV. + + Diurnal inequalities in N and W lend themselves readily to the + construction of what are known as _vector diagrams_. These are curves + showing the direction and intensity at each hour of the day of the + horizontal component of the disturbing force to which the diurnal + inequality may be regarded as due. Figs. 7 and 8, taken from the + _Phil. Trans._ vol. 204A, will serve as examples. They refer to the + mean diurnal inequalities for the months stated at Kew (1890 to 1900) + and Falmouth (1891 to 1902), thick lines relating to Kew, thin to + Falmouth. NS and EW represent the geographical north-south and + east-west directions; their intersection answers to the origin (thick + lines for Kew, thin for Falmouth). The line from the origin to M + represents the magnetic meridian. The line from the origin to any + cross--the number indicating the corresponding hour counted from + midnight as 0--represents the magnitude and direction at that hour of + the horizontal component of the disturbing force to which the diurnal + inequality may be assigned. The cross marks the point whose + rectangular co-ordinates are the values of [delta]N and [delta]W + derived from the diurnal inequalities of these elements. In figs. 7 + and 8 the distances of the points N, E, S, W from their corresponding + origin represents 10[gamma]. The tendency to form a loop near + midnight, seen in the November and December curves, is + characteristic of the winter months at Kew and Falmouth. The shape is + less variable in summer than in winter; but even in summer the portion + answering to the hours 6 p.m. to 6 a.m. varies a good deal. The object + of presenting the Kew and Falmouth curves side by side is to emphasize + the close resemblance between the magnetic phenomena at places in + similar latitudes, though over 200 miles apart and exhibiting widely + different ranges for their meteorological elements. With considerable + change of latitude however the shape of vector diagrams changes + largely. + + TABLE XV.--Diurnal Inequalities in N. and W. at Falmouth (unit + 1[gamma]). + + +---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ + | Hour. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | + +---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ + |N. /a.m. | + 6 | + 5 | + 5 | + 5 | + 6 | + 6 | + 5 | + 1 | - 6 | -14 | -20 | -20 | + | \p.m. | -17 | -12 | - 6 | - 1 | + 3 | + 6 | + 9 | + 9 | + 9 | + 8 | + 7 | + 7 | + |W. /a.m. | - 2 | - 2 | - 3 | - 4 | - 6 | - 9 | -13 | -17 | -19 | -13 | - 3 | +11 | + | \p.m. | +20 | +22 | +17 | +11 | + 6 | + 4 | + 2 | + 1 | 0 | - 1 | - 2 | - 2 | + +---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ + + + Fourier Series. + + § 20. Any diurnal inequality can be analysed into a series of harmonic + terms whose periods are 24 hours and submultiples thereof. The series + may be expressed in either of the equivalent forms:-- + + a1 cos t + b1 sin t + a2 cos 2t + b2 sin 2t + ... (i) + + c1 sin (t + [alpha]1) + c2 sin (2t + [alpha]2) + .... (ii) + + TABLE XVI.--Ranges in Diurnal Inequalities at Falmouth (unit + 1[gamma]). + + +----+------+------+------+------+------+------+------+------+------+------+------+------+ + | | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. | + +----+------+------+------+------+------+------+------+------+------+------+------+------+ + | N. | 21 | 23 | 30 | 39 | 39 | 37 | 37 | 39 | 36 | 32 | 24 | 15 | + | W. | 20 | 24 | 46 | 54 | 55 | 55 | 54 | 56 | 51 | 39 | 24 | 15 | + +----+------+------+------+------+------+------+------+------+------+------+------+------+ + + In both forms t denotes time, counted usually from midnight, one hour + of time being interpreted as 15° of angle. Form (i) is that utilized + in actually calculating the constants a, b, ... Once the a, b, ... + constants are known, the c, [alpha], ... constants are at once + derivable from the formulae:-- + + tan [alpha]_n = a_n/b_n; + c_n = a_n/sin [alpha]_n = b_n/cos [alpha]_n = [root](a_n² + b_n²). + + The a, b, c, [alpha] constants are called sometimes Fourier, sometimes + Bessel coefficients. + + [Illustration: (From _Phil. Trans._) + + FIG. 7.] + + By taking a sufficient number of terms a series can always be obtained + which will represent any set of diurnal inequality figures; but unless + one can obtain a close approach to the observational figures from the + terms possessing the periods 24, 12, 8 and 6 hours the physical + significance and general utility of the analysis is somewhat + problematical. In the case of the magnetic elements, the 24 and 12 + hour terms are usually much the more important; the 24-hour term is + generally, but by no means always, the larger of the two. The c + constants give the amplitudes of the harmonic terms or waves, the + [alpha] constants the phase angles. An advance of 1 hour in the time + of occurrence of the first (and subsequent, if any) maximum and + minimum answers to an _increase_ of 15° in [alpha]1 of 30° in + [alpha]2, of 45° in [alpha]3, of 60° in [alpha]4 and so on. In the + case of magnetic elements the phase angles not infrequently possess a + somewhat large annual variation. It is thus essential for a minute + study of the phenomena at any station to carry out the analysis for + the different seasons of the year, and preferably for the individual + months. If the a and b constants are known for all the individual + months of one year, or for all the Januarys of a series of years, we + have only to take their arithmetic means to obtain the corresponding + constants for the mean diurnal inequality of the year, or for the + diurnal inequality of the average January of the series of years. + This, however, is obviously not true of the c or [alpha] constants, + unless the phase angle is absolutely unchanged throughout the + contributory months or years. This is a point requiring careful + attention, because when giving values of c and [alpha] for the whole + year some authorities give the arithmetic mean of the c's and + [alpha]'s calculated from the diurnal inequalities of the individual + months of the year, others give the values obtained for c and [alpha] + from the mean diurnal inequality of the whole year. The former method + inevitably supplies a larger value for c than the latter, supposing + [alpha] to vary with the season. At some observatories, e.g. Greenwich + and Batavia, it has long been customary to publish every year values + of the Fourier coefficients for each month, and to include other + elements besides the declination. For a thoroughly satisfactory + comparison of different stations, it is necessary to have data from + one and the same epoch; and preferably that epoch should include at + least one 11-year period. There are, however, few stations which can + supply the data required for such a comparison and we have to make the + best of what is available. Information is naturally most copious for + the declination. For this element E. Engelenburg[20] gives values of + C1, C2, C3, C4, and of [alpha]1, [alpha]2, [alpha]3, [alpha]4 for each + month of the year for about 50 stations, ranging from Fort Rae (62° 6´ + N. lat.) to Cape Horn (55° 5´ S. lat.). From the results for + individual stations, Engelenburg derives a series of means which he + regards as representative of 11 different zones of latitude. His data + for individual stations refer to different epochs, and some are based + on only one year's observations. The original observations also differ + in reliability; thus the results are of somewhat unequal value. The + mean results for Engelenburg's zones must naturally have some of the + sources of uncertainty reduced; but then the fundamental idea + represented by the arrangement in zones is open to question. The + majority of the data in Table XVII. are taken from Engelenburg, but + the phase angles have been altered so as to apply to westerly + declination. The stations are arranged in order of latitude from north + to south; in a few instances results are given for quiet days. The + figures represent in all cases arithmetic means derived from the 12 + monthly values. In the table, so far as is known, the local mean time + of the observatory has been employed. This is a point requiring + attention, because most observatories employ Greenwich time, or time + based on Greenwich or some other national observatory, and any + departure from local time enters into the values of the constants. The + data for Victoria Land refer to the "Discovery's" 1902-1903 winter + quarters, where the declination, taken westerly, was about 207°.5. + + As an example of the significance of the phase angles in Table XVII., + take the ordinary day data for Kew. The times of occurrence of the + maxima are given by t + 234° = 450° for the 24-hour term, 2t + 39°.7 = + 90° or = 450° for the 12-hour term, and so on, taking an hour in t as + equivalent to 15°. + + Thus the times of the maxima are:-- + + 24-hour term, 2 h. 24 m. p.m.; 12-hour term, 1 h. 41 m. a.m. and p.m. + + 8-hour term, 4 h. 41 m. a.m., 0 h. 41 m. p.m., and 8 h. 41 m. p.m. + + 6-hour term, 0 h. 33 m. a.m. and p.m., and 6 h. 33 m. a.m. and p.m. + + The minima, or extreme easterly positions in the waves, lie midway + between successive maxima. All four terms, it will be seen, have + maxima at some hour between 0h. 30m. and 2h. 30m. p.m. They thus + reinforce one another strongly from 1 to 2 p.m., accounting for the + prominence of the maximum in the early afternoon. + + [Illustration: (_From Phil. Trans._) + + FIG. 8.] + + The utility of a Fourier analysis depends largely on whether the + several terms have a definite physical significance. If the 24-hour + and 12-hour terms, for instance, represent the action of forces whose + distribution over the earth or whose seasonal variation is essentially + different, then the analysis helps to distinguish these forces, and + may assist in their being tracked to their ultimate source. Suppose, + for example, one had reason to think the magnetic diurnal variation + due to some meteorological phenomenon, e.g. heating of the earth's + atmosphere, then a comparison of Fourier coefficients, if such + existed, for the two sets of phenomena would be a powerful method of + investigation. + + TABLE XVII.--Amplitudes and Phase Angles for Diurnal Inequality of + Declination. + + +---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ + | Place. | Epoch. | c1. | c2. | c3. | c4. | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. | + +---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ + | | | ´ | ´ | ´ | ´ | ° | ° | ° | ° | + | Fort Rae (all) | 1882-1883 | 18.49 | 8.22 | 1.99 | 2.07 | 156.5 | 41.9 | 308 | 104 | + | " (quiet) | " | 9.09 | 4.51 | 1.32 | 0.73 | 166.5 | 37.5 | 225 | 350 | + | Ekatarinburg | 1841-1862 | 2.57 | 1.81 | 0.73 | 0.22 | 223.3 | 7.4 | 204 | 351 | + | Potsdam | 1890-1899 | 2.81 | 1.90 | 0.83 | 0.31 | 239.9 | 32.6 | 237 | 49 | + | Kew (ordinary) | 1890-1900 | 2.91 | 1.79 | 0.79 | 0.27 | 234.0 | 39.7 | 239 | 57 | + | Kew (quiet) | " | 2.37 | 1.82 | 0.90 | 0.30 | 227.3 | 42.1 | 240 | 55 | + | Falmouth (quiet) | 1891-1902 | 2.18 | 1.82 | 0.91 | 0.29 | 226.2 | 40.5 | 238 | 56 | + | Parc St Maur | 1883-1899 | 2.70 | 1.87 | 0.85 | 0.30 | 238.6 | 32.5 | 235 | 95 | + | Toronto | 1842-1848 | 2.65 | 2.34 | 1.00 | 0.33 | 213.7 | 34.9 | 238 | 350 | + | Washington | 1840-1842 | 2.38 | 1.86 | 0.65 | 0.33 | 223.0 | 26.6 | 223 | 53 | + | Manila | 1890-1900 | 0.53 | 0.58 | 0.43 | 0.17 | 266.3 | 50.7 | 226 | 89 | + | Trivandrum | 1853-1864 | 0.54 | 0.46 | 0.29 | 0.10 | 289.0 | 49.6 | | 114 | + | Batavia | 1883-1899 | 0.80 | 0.88 | 0.43 | 0.13 | 332.0 | 163.2 | 5 | 236 | + | St. Helena | 1842-1847 | 0.68 | 0.61 | 0.63 | 0.34 | 275.8 | 171.4 | 27 | 244 | + | Mauritius | 1876-1890 | 0.86 | 1.11 | 0.76 | 0.22 | 21.6 | 172.7 | 350 | 161 | + | C. of G. Hope | 1841-1846 | 1.15 | 1.13 | 0.80 | 0.35 | 287.7 | 156.0 | 351 | 193 | + | Melbourne | 1858-1863 | 2.52 | 2.45 | 1.23 | 0.35 | 27.4 | 176.7 | 9 | 193 | + | Hobart | 1841-1848 | 2.29 | 2.15 | 0.87 | 0.32 | 33.6 | 170.8 | 349 | 185 | + | S. Georgia | 1882-1883 | 2.13 | 1.28 | 0.76 | 0.31 | 30.3 | 185.3 | 7 | 180 | + | Victoria Land (all) | 1902-1903 | 20.51 | 4.81 | 1.21 | 1.32 | 158.7 | 306.9 | 292 | 303 | + | " (quieter) | " | 15.34 | 4.05 | 1.24 | 1.18 | 163.8 | 312.9 | 261 | | + +---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ + + § 21. Fourier coefficients of course often vary much with the season + of the year. In the case of the declination this is especially true of + the phase angles at tropical stations. To enter on details for a + number of stations would unduly occupy space. A fair idea of the + variability in the case of declination in temperate latitudes may be + derived from Table XVIII., which gives monthly values for Kew derived + from ordinary days of an 11-year period 1890-1900. + + Fourier analysis has been applied to the diurnal inequalities of the + other magnetic elements, but more sparingly. Such results are + illustrated by Table XIX., which contains data derived from quiet days + at Kew from 1890 to 1900. _Winter_ includes November to February, + _Summer_ May to August, and _Equinox_ the remaining four months. In + this case the data are derived from mean diurnal inequalities for the + season specified. In the case of the c or amplitude coefficients the + unit is 1´ for I (inclination), and 1[gamma] for H and V (horizontal + and vertical force). At Kew the seasonal variation in the amplitude is + fairly similar for all the elements. The 24-hour and 12-hour terms + tend to be largest near midsummer, and least near midwinter; but the + 8-hour and 6-hour terms have two well-marked maxima near the + equinoxes, and a clearly marked minimum near midsummer, in addition + to one near midwinter. On the other hand, the phase angle phenomena + vary much for the different elements. The 24-hour term, for instance, + has its maximum earlier in winter than in summer in the case of the + declination and vertical force, but the exact reverse holds for the + inclination and the horizontal force. + + TABLE XVIII.--Kew Declination: Amplitudes and Phase Angles (local mean + time). + + +----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ + | Month. | C1. | C2. | C3. | C4. | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. | + +----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ + | | ´ | ´ | ´ | ´ | ° | ° | ° | ° | + | January | 1.79 | 0.86 | 0.41 | 0.27 | 251.2 | 29.8 | 254 | 64 | + | February | 2.41 | 1.11 | 0.57 | 0.30 | 242.0 | 27.7 | 235 | 39 | + | March | 3.05 | 1.98 | 1.11 | 0.45 | 233.2 | 36.1 | 223 | 49 | + | April | 3.35 | 2.48 | 1.17 | 0.39 | 224.8 | 39.2 | 228 | 61 | + | May | 3.57 | 2.38 | 0.87 | 0.17 | 221.3 | 50.8 | 245 | 89 | + | June | 3.83 | 2.39 | 0.74 | 0.05 | 212.6 | 46.7 | 239 | 72 | + | July | 3.72 | 2.30 | 0.77 | 0.11 | 214.6 | 48.1 | 233 | 8 | + | August | 3.64 | 2.43 | 1.05 | 0.18 | 228.2 | 57.2 | 244 | 51 | + | September| 3.35 | 2.02 | 1.04 | 0.35 | 236.9 | 55.3 | 245 | 70 | + | October | 2.69 | 1.69 | 0.92 | 0.48 | 240.1 | 35.6 | 235 | 65 | + | November | 1.94 | 1.06 | 0.51 | 0.32 | 248.3 | 28.3 | 247 | 61 | + | December | 1.61 | 0.81 | 0.35 | 0.20 | 255.1 | 22.0 | 243 | 56 | + +----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ + + + Annual Inequality. + + § 22. If secular change proceeded uniformly throughout the year, the + value E_n of any element at the middle of the nth month of the year + would be connected with E, the mean value for the whole year, by the + formula E_n = E + (2n - 13)s/24, where s is the secular change per + annum. For the present purpose, difference in the lengths of the + months may be neglected. If one applies to E_n - E the correction -(2n + - 13)s/24 one eliminates a regularly progressive secular change; what + remains is known as the _annual inequality_. If only a short period of + years is dealt with, irregularities in the secular change from year to + year, or errors of observation, may obviously simulate the effect of a + real annual inequality. Even when a long series of years is included, + there is always a possibility of a spurious inequality arising from + annual variation in the instruments, or from annual change in the + conditions of observation. J. Liznar,[21] from a study of data from a + number of stations, arrived at certain mean results for the annual + inequalities in declination and inclination in the northern and + southern hemispheres, and J. Hann[22] has more recently dealt with + Liznar's and newer results. Table XX. gives a variety of data, + including the mean results given by Liznar and Hann. In the case of + declination + denotes westerly position; in the case of inclination it + denotes a larger dip (whether the inclination be north or south). + According to Liznar declination in summer is to the west of the normal + position in both hemispheres. The phenomena, however, at Parc St Maur + are, it will be seen, the exact opposite of what Liznar regards as + normal; and whilst the Potsdam results resemble his mean in type, the + range of the inequality there, as at Parc St Maur, is relatively + small. Of the three sets of data given for Kew the first two are + derived in a similar way to those for other stations; the first set + are based on quiet days only, the second on all but highly disturbed + days. Both these sets of results are fairly similar in type to the + Parc St Maur results, but give larger ranges; they are thus even more + opposed to Liznar's normal type. The last set of data for Kew is of a + special kind. During the 11 years 1890 to 1900 the Kew declination + magnetograph showed to within 1´ the exact secular change as derived + from the absolute observations; also, if any annual variation existed + in the position of the base lines of the curves it was exceedingly + small. Thus the accumulation of the daily non-cyclic changes shown by + the curves should closely represent the combined effects of secular + change and annual inequality. Eliminating the secular change, we + arrive at an annual inequality, based on all days of the year + including the highly disturbed. It is this annual inequality which + appears under the heading s. It is certainly very unlike the annual + inequality derived in the usual way. Whether the difference is to be + wholly assigned to the fact that highly disturbed days contribute in + the one case, but not in the other, is a question for future research. + + TABLE XIX.--Kew Diurnal Inequality: Amplitudes and Phase Angles (local + mean time). + + +-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ + | Month. | C1. | C2. | C3. | C4. | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. | + +-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ + | | ´ | ´ | ´ | ´ | ° | ° | ° | ° | + | /Winter | 0.240 | 0.222 | 0.104 | 0.076 | 250.0 | 91.8 | 344 | 194 | + | I < Equinox | 0.601 | 0.290 | 0.213 | 0.127 | 290.3 | 135.5 | 4 | 207 | + | \Summer | 0.801 | 0.322 | 0.172 | 0.070 | 312.5 | 155.5 | 39 | 238 | + | | | | | | | | | | + | /Winter | 3.62 | 3.86 | 1.81 | 1.13 | 82.9 | 277.3 | 154 | 6 | + | H < Equinox | 10.97 | 5.87 | 3.32 | 1.84 | 109.6 | 303.5 | 167 | 16 | + | \Summer | 14.85 | 6.23 | 2.35 | 0.95 | 130.3 | 316.5 | 199 | 41 | + | | | | | | | | | | + | /Winter | 2.46 | 1.67 | 0.86 | 0.42 | 153.9 | 300.8 | 108 | 280 | + | V < Equinox | 6.15 | 4.70 | 2.51 | 0.94 | 117.2 | 272.3 | 99 | 289 | + | \Summer | 8.63 | 6.45 | 2.24 | 0.55 | 122.0 | 272.4 | 100 | 285 | + +-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ + + In the case of the inclination, Liznar found that in both hemispheres + the dip (north in the northern, south in the southern hemisphere) was + larger than the normal when the sun was in perihelion, corresponding + to an enhanced value of the horizontal force in summer in the northern + hemisphere. + + In the case of annual inequalities, at least that of the declination, + it is a somewhat suggestive fact that the range seems to become less + as we pass from older to more recent results, or from shorter to + longer periods of years. Thus for Paris from 1821 to 1830 Arago + deduced a range of 2´ 9´´. Quiet days at Kew from 1890 to 1894 gave a + range of 1´.2, while at Potsdam Lüdeling got a range 30% larger than + that in Table XX. when considering the shorter period 1891-1899. Up to + the present, few individual results, if any, can claim a very high + degree of certainty. With improved instruments and methods it may be + different in the future. + + TABLE XX.--Annual Inequality. + + +---------------------------------------------------------------------------------------------+-------------------------------------+ + | Declination. | Inclination. | + +-----------+---------+-----------+-----------+-----------------------+-----------+-----------+---------+---------+---------+-------+ + | | Liznar, | Potsdam, | Parc St | Kew (1890-1900). | Batavia, | | Liznar &| | Parc St.| | + | | N. Hemi-| 1891-1906.| Maur, +-------+-------+-------+ 1883-1893.| Mauritius.| Hann's | Potsdam.| Maur. | Kew. | + | | sphere. | | 1888-1897.| q. | o. | s. | | | mean. | | | | + +-----------+---------+-----------+-----------+-------+-------+-------+-----------+-----------+---------+---------+---------+-------+ + | | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | + | January | -0.25 | +0.04 | +0.01 | +0.08 | +0.03 | +0.32 | +0.23 | +0.06 | +0.49 | +0.32 | +0.44 | -0.03 | + | February | -0.54 | -0.11 | 0.00 | +0.48 | +0.25 | -0.20 | +0.19 | +0.29 | +0.39 | +0.56 | +0.29 | -0.07 | + | March | -0.27 | +0.04 | +0.17 | +0.03 | +0.05 | -1.02 | -0.12 | +0.27 | +0.20 | +0.38 | +0.13 | +0.53 | + | April | -0.03 | +0.10 | +0.12 | -0.31 | -0.14 | -0.90 | -0.11 | +0.30 | -0.08 | -0.02 | -0.13 | +0.18 | + | May | +0.19 | +0.07 | -0.11 | -0.39 | -0.28 | +0.29 | -0.30 | +0.08 | -0.43 | -0.29 | -0.37 | -0.15 | + | June | +0.46 | +0.13 | -0.14 | -0.47 | -0.39 | +0.78 | -0.13 | -0.19 | -0.70 | -0.77 | -0.59 | -0.35 | + | July | +0.48 | +0.14 | -0.17 | -0.30 | -0.13 | +0.44 | -0.08 | -0.44 | -0.72 | -0.67 | -0.27 | -0.13 | + | August | +0.47 | +0.11 | +0.01 | +0.08 | +0.05 | +0.52 | -0.18 | -0.38 | -0.47 | -0.23 | -0.05 | -0.19 | + | September | +0.31 | +0.01 | 0.00 | +0.29 | +0.24 | -0.02 | +0.06 | -0.06 | -0.06 | +0.16 | +0.01 | +0.20 | + | October | -0.07 | -0.11 | +0.09 | +0.06 | +0.01 | -0.26 | +0.03 | -0.04 | +0.31 | +0.27 | +0.19 | 0.00 | + | November | -0.30 | -0.28 | -0.05 | +0.17 | +0.11 | -0.02 | +0.08 | -0.01 | +0.51 | +0.30 | +0.43 | +0.18 | + | December | -0.36 | -0.14 | +0.05 | +0.26 | +0.23 | +0.05 | +0.35 | +0.06 | +0.55 | +0.19 | +0.24 | -0.29 | + +-----------+---------+-----------+-----------+-------+-------+-------+-----------+-----------+---------+---------+---------+-------+ + | Range | 1.02 | 0.42 | 0.34 | 0.95 | 0.64 | 1.80 | 0.65 | 0.74 | 1.27 | 1.33 | 1.03 | 0.88 | + +-----------+---------+-----------+-----------+-------+-------+-------+-----------+-----------+---------+---------+---------+-------+ + + + Annual Variation Fourier Coefficients. + + § 23. The inequalities in Table XX. may be analysed--as has in fact + been done by Hann--in a series of Fourier terms, whose periods are the + year and its submultiples. Fourier series can also be formed + representing the annual variation in the amplitudes of the regular + diurnal inequality, and its component 24-hour, 12-hour, &c. waves, or + of the amplitude of the absolute daily range (§ 24). To secure the + highest theoretical accuracy, it would be necessary in calculating the + Fourier coefficients to allow for the fact that the "months" from + which the observational data are derived are not of uniform length. + The mid-times, however, of most months of the year are but slightly + displaced from the position they would occupy if the 12 months were + exactly equal, and these displacements are usually neglected. The loss + of accuracy cannot be but trifling, and the simplification is + considerable. + + The Fourier series may be represented by + + P1 sin (t + [theta]1) + P2 sin (2t + [theta]2) + ..., + + where t is time counted from the beginning of the year, one month + being taken as the equivalent of 30°, P1, P2 represent the amplitudes, + and [theta]1, [theta]2 the phase angles of the first two terms, whose + periods are respectively 12 and 6 months. Table XXI. gives the values + of these coefficients in the case of the range of the regular diurnal + inequality for certain specified elements and periods at Kew[23] and + Falmouth.[23a] In the case of P1 and P2 the unit is 1´ for D and I, + and 1[gamma] for H and V. M denotes the mean value of the range for + the 12 months. The letters q and o represent quiet and ordinary day + results. S max. means the years 1892-1895, with a mean sun spot + frequency of 75.0. S min. for Kew means the years 1890, 1899 and 1900 + with a mean sun spot frequency of 9.6; for Falmouth it means the years + 1899-1902 with a mean sun spot frequency of 7.25. + + Increase in [theta]1 or [theta]2 means an earlier occurrence of the + maximum or maxima, 1° answering roughly to one day in the case of the + 12-month term, and to half a day in the case of the 6-month term. P1/M + and P2/M both increase decidedly as we pass from years of many to + years of few sun spots; i.e. _relatively_ considered the range of the + regular diurnal inequality is more variable throughout the year when + sun spots are few than when they are many. + + The tendency to an earlier occurrence of the maximum as we pass from + quiet days to ordinary days, or from years of sun spot minimum to + years of sun spot maximum, which appears in the table, appears also + in the case of the horizontal force--at least in the case of the + annual term--both at Kew and Falmouth. The phenomena at the two + stations show a remarkably close parallelism. At both, and this is + true also of the absolute ranges, the maximum of the annual term falls + in all cases near midsummer, the minimum near midwinter. The maxima of + the 6-month terms fall near the equinoxes. + + TABLE XXI.--Annual Variation of Diurnal Inequality Range. Fourier + Coefficients. + + +---------------------+--------+--------+-----------+-----------+-------+-------+ + | | P1. | P2. | [theta]1. | [theta]2. | P1/M. | P2/M. | + +-----------+---------+--------+--------+-----------+-----------+-------+-------+ + | Kew | D_0 | 3.36 | 0.94 | 279° | 280° | 0.40 | 0.11 | + | 1890-1900 | D_q | 3.81 | 1.22 | 275° | 273° | 0.47 | 0.15 | + | | I_q | 0.67 | 0.16 | 264° | 269° | 0.42 | 0.10 | + | | H_q | 13.6 | 3.0 | 269° | 261° | 0.48 | 0.11 | + | | V_q | 11.7 | 2.2 | 282° | 242° | 0.63 | 0.12 | + +-----------+---------+--------+--------+-----------+-----------+-------+-------+ + | S max. | Kew | 4.50 | 1.26 | 277° | 282° | 0.47 | 0.13 | + | D_q | Falmouth| 4.10 | 1.40 | 277° | 286° | 0.43 | 0.15 | + +-----------+---------+--------+--------+-----------+-----------+-------+-------+ + | S min. | Kew | 3.35 | 1.10 | 274° | 269° | 0.49 | 0.16 | + | D_q | Falmouth| 3.19 | 1.14 | 275° | 277° | 0.49 | 0.17 | + +-----------+---------+--------+--------+-----------+-----------+-------+-------+ + + + Absolute Range. + + § 24. Allusion has already been made in § 14 to one point which + requires fuller discussion. If we take a European station such as Kew, + the general character of, say, the declination does not vary very much + with the season, but still it does vary. The principal minimum of the + day, for instance, occurs from one to two hours earlier in summer than + in winter. Let us suppose for a moment that all the days of a month + are exactly alike, the difference in type between successive months + coming in _per saltum._ Suppose further that having formed twelve + diurnal inequalities from the days of the individual months of the + year, we deduce a mean diurnal inequality for the whole year by + combining these twelve inequalities and taking the mean. The hours of + maximum and minimum being different for the twelve constituents, it is + obvious that the resulting maximum will normally be less than the + arithmetic mean of the twelve maxima, and the resulting minimum + (arithmetically) less than the arithmetic mean of the twelve minima. + The range--or algebraic excess of the maximum over the minimum--in the + mean diurnal inequality for the year is thus normally less than the + arithmetic mean of the twelve ranges from diurnal inequalities for the + individual months. Further, as we shall see later, there are + differences in type not merely between the different months of the + year, but even between the same months in different years. Thus the + range of the mean diurnal inequality for, say, January based on the + combined observations of, say, eleven Januarys may be and generally + will be slightly less than the arithmetic mean of the ranges obtained + from the Januarys separately. At Kew, for instance, taking the + ordinary days of the 11 years 1890-1900, the arithmetic mean of the + diurnal inequality ranges of declination from the 132 months treated + independently was 8´.52, the mean range from the 12 months of the year + (the eleven Januarys being combined into one, and so on) was 8´.44, + but the mean range from the whole 4,000 odd days superposed was only + 8´.03. Another consideration is this: a diurnal inequality is usually + based on hourly readings, and the range deduced is thus an + under-estimate unless the absolute maximum and minimum both happen to + come exactly at an hour. These considerations would alone suffice to + show that the _absolute range_ in individual days, i.e. the difference + between the algebraically largest and least values of the element + found any time during the 24 hours, must on the average exceed the + range in the mean diurnal inequality for the year, however this + latter is formed. Other causes, moreover, are at work tending in the + same direction. Even in central Europe, the magnetic curves for + individual days of an ordinary month often differ widely amongst + themselves, and show maxima and minima at different times of the day. + In high latitudes, the variation from day to day is sometimes so great + that mere eye inspection of magnetograph curves may leave one with but + little idea as to the probable shape of the resultant diurnal curve + for the month. Table XXII. gives the arithmetic mean of the absolute + daily ranges from a few stations. The values which it assigns to the + year are the arithmetic means of the 12 monthly values. The Mauritius + data are for different periods, viz. declination 1875, 1880 and 1883 + to 1890, horizontal force 1883 to 1890, vertical force 1884 to 1890. + The other data are all for the period 1890 to 1900. + + TABLE XXII.--Mean Absolute Daily Ranges (Units 1´ for Declination, + 1[gamma] for H and V). + + +--------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ + | | Jan. | Feb. | Mar. | April.| May. | June. | July. | Aug. | Sept. | Oct. | Nov. | Dec. | Year. | + | +-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ + | _Declination._ | | | | | | | | | | | | | | + | Pavlovsk | 13.42 | 17.20 | 18.22 | 17.25 | 17.76 | 15.91 | 16.89 | 16.57 | 16.75 | 15.70 | 13.87 | 12.37 | 15.99 | + | Ekatarinburg | 7.33 | 9.54 | 11.90 | 12.89 | 13.63 | 13.03 | 12.78 | 12.21 | 11.23 | 9.44 | 7.86 | 6.85 | 10.72 | + | Kew. All days | 11.16 | 13.69 | 15.93 | 15.00 | 14.90 | 13.65 | 14.13 | 14.22 | 14.57 | 14.07 | 11.71 | 9.80 | 13.57 | + | " Ordinary days| 10.14 | 11.87 | 14.19 | 14.24 | 13.85 | 13.26 | 13.47 | 13.67 | 13.71 | 13.10 | 10.40 | 9.00 | 12.58 | + | " Quiet " | 6.12 | 7.57 | 10.59 | 11.84 | 12.09 | 11.95 | 11.60 | 11.93 | 10.86 | 9.16 | 6.54 | 5.08 | 9.61 | + | Zi-ka-wei | 3.88 | 3.25 | 6.22 | 7.04 | 7.15 | 7.40 | 7.77 | 8.06 | 6.73 | 4.68 | 2.91 | 2.52 | 5.63 | + | Mauritius | 6.93 | 7.79 | 7.11 | 5.75 | 4.87 | 4.03 | 4.36 | 6.00 | 6.28 | 6.71 | 6.99 | 6.78 | 6.13 | + | | | | | | | | | | | | | | | + | _Horizontal force._| | | | | | | | | | | | | | + | Pavlovsk | 52.4 | 74.5 | 79.1 | 80.1 | 86.2 | 79.0 | 86.7 | 77.6 | 76.7 | 67.3 | 55.7 | 45.9 | 71.8 | + | Ekatarinburg | 33.2 | 43.1 | 48.4 | 51.7 | 56.2 | 54.1 | 56.7 | 51.7 | 49.3 | 44.1 | 34.1 | 29.3 | 46.0 | + | Mauritius | 37.9 | 35.0 | 36.2 | 37.6 | 35.0 | 34.1 | 33.8 | 34.5 | 36.6 | 37.4 | 37.8 | 35.3 | 35.9 | + | | | | | | | | | | | | | | | + | _Vertical force._ | | | | | | | | | | | | | | + | Pavlovsk | 27.0 | 50.4 | 54.7 | 43.2 | 45.3 | 34.8 | 42.1 | 35.5 | 42.5 | 37.5 | 33.5 | 25.5 | 39.3 | + | Ekatarinburg | 17.4 | 26.6 | 29.2 | 30.1 | 29.6 | 27.6 | 29.6 | 26.1 | 25.2 | 22.1 | 19.6 | 16.4 | 24.9 | + | Mauritius | 17.1 | 19.5 | 20.1 | 17.3 | 16.5 | 15.5 | 17.1 | 22.0 |22.7 | 19.4 | 16.7 | 15.2 | 18.2 | + +--------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ + + A comparison of the absolute ranges in Table XXII. with the inequality + ranges for the same stations derivable from Tables VIII. to X. is most + instructive. At Mauritius the ratio of the absolute to the inequality + range is for D 1.38, for H 1.76, and for V 1.19. At Pavlovsk the + corresponding ratios are much larger, viz. 2.16 for D, 2.43 for H, and + 2.05 for V. The declination data for Kew in Table XXII. illustrate + other points. The first set of data are derived from all days of the + year. The second omit the highly disturbed days. The third answer to + the 5 days a month selected as typically quiet. The yearly mean + absolute range from ordinary days at Kew in Table XXII. is 1.49 times + the mean inequality range in Table VIII.; comparing individual months + the ratio of the absolute to the inequality range varies from 2.06 in + January to 1.21 in June. Even confining ourselves to the quiet days at + Kew, which are free from any but the most trifling disturbances, we + find that the mean absolute range for the year is 1.20 times the + arithmetic mean of the inequality ranges for the individual months of + the year, and 1.22 times the range from the mean diurnal inequality + for the year. In this case the ratio of the absolute to the inequality + range varies from 1.55 in December to only 1.09 in May. + + § 25. The variability of the absolute daily range of declination is + illustrated by Table XXIII., which contains data for Kew[24] derived + from all days of the 11-year period 1890-1900. It gives the total + number of times during the 11 years when the absolute range lay within + the limits specified at the heads of the first nine columns of + figures. The two remaining columns give the arithmetic means of the + five largest and the five least absolute ranges encountered each + month. The mean of the twelve monthly diurnal inequality ranges from + ordinary days was only 8´.44, but the absolute range during the 11 + years exceeded 20´ on 492 days, 15´ on 1196 days, and 10´ on 2784 + days, i.e. on 69 days out of every 100. + + Table XXIII.--Absolute Daily Range of Declination at Kew. + + +------------------------------------------------------------------------------------------------------------------+---------------------+ + | | Means from the 5 | + | | largest and 5 least | + | Number of occasions during 11 years when absolute range was:-- | ranges of the month | + | | on the average of | + | | 11 years. | + +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+ + | |0´ to 5´.|5´ to 10´.|10´ to 15´.|15´ to 20´.|20´ to 25´.|25´ to 30´.|30´ to 35´.|35´ to 40´.|over 40´.| 5 largest.| 5 least.| + +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+ + | | | | | | | | | | | ´ | ´ | + | January | 51 | 145 | 69 | 37 | 24 | 7 | 4 | 3 | 1 | 22.90 | 5.07 | + | February | 26 | 99 | 84 | 51 | 226 | 10 | 4 | 2 | 8 | 27.21 | 6.55 | + | March | 1 | 72 | 138 | 61 | 232 | 21 | 8 | 1 | 7 | 29.87 | 8.93 | + | April | 0 | 43 | 167 | 73 | 227 | 10 | 6 | 3 | 1 | 23.69 | 10.31 | + | May | 0 | 57 | 157 | 85 | 220 | 12 | 3 | 0 | 7 | 25.36 | 9.50 | + | June | 0 | 56 | 185 | 67 | 215 | 1 | 3 | 1 | 2 | 19.92 | 9.89 | + | July | 0 | 59 | 185 | 70 | 214 | 5 | 2 | 2 | 4 | 22.49 | 9.96 | + | August | 0 | 37 | 202 | 75 | 222 | 1 | 2 | 0 | 2 | 21.27 | 10.05 | + | September | 1 | 68 | 153 | 71 | 219 | 5 | 4 | 5 | 4 | 24.55 | 9.52 | + | October | 3 | 103 | 111 | 67 | 234 | 10 | 11 | 2 | 0 | 23.92 | 8.01 | + | November | 42 | 140 | 81 | 28 | 214 | 9 | 8 | 5 | 3 | 23.58 | 5.64 | + | December | 64 | 166 | 56 | 29 | 214 | 7 | 1 | 1 | 3 | 20.43 | 4.36 | + +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+ + | Totals | 188 | 1045 | 1588 | 714 | 261 | 98 | 56 | 25 | 42 | | | + +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+ + + + Relations to Sun-spot Frequency. + + § 26. Magnetic phenomena, both regular and irregular, at any station + vary from year to year. The extent of this variation is illustrated in + Tables XXIV. and XXV., both relating to the period 1890 to 1900.[25] + Table XXIV. gives the amplitudes of the regular diurnal inequality in + the elements stated at the head of the columns. The ordinary day + declination data (D0) for Kew represent arithmetic means from the + twelve months of the year; the other data all answer to the mean + diurnal inequality for the whole year. Table XXV. gives the arithmetic + means for each year of the absolute daily range, of the monthly range + (or difference between the highest and lowest values in the month), + and of the yearly range (or difference between the highest and lowest + values of the year). The numerals attached to the years in these + tables indicate their order as regards sun-spot frequency according to + Wolf and Wolfer (see Aurora Polaris), 1893 being the year of largest + frequency, and 1890 that of least. The difference in sun-spot + frequency between 1897 and 1898 was microscopic; the differences + between 1890, 1900 and 1899 were small, and those between 1893, 1894 + and 1892 were not very large. + + The years 1892-1895 represent high sun-spot frequency, while 1890, + 1899 and 1900 represent low frequency. Table XXIV. shows that 1892 to + 1895 were in all cases distinguished by the large size of the + inequality ranges, and 1890, 1899 and 1900 by the small size. The + range in 1893 is usually the largest, and though the H and V ranges + at Ekaterinburg are larger in 1892 than in 1893, the excess is + trifling. The phenomena apparent in Table XXIV. are fairly + representative; other stations and other periods associate large + inequality ranges with high sun-spot frequency. The diurnal inequality + range it should be noticed is comparatively little influenced by + irregular disturbances. Coming to Table XXV., we have ranges of a + different character. The absolute range at Kew on quiet days is almost + as little influenced by irregularities as is the range of the diurnal + inequality, and in its case the phenomena are very similar to those + observed in Table XXIV. As we pass from left to right in Table XXV., + the influence of disturbance increases. Simultaneously with this, the + parallelism with sun-spot frequency is less close. The entries + relating to 1892 and 1894 become more and more prominent compared to + those for 1893. The yearly range may depend on but a single magnetic + storm, the largest disturbance of the year possibly far outstripping + any other. But taking even the monthly ranges the values for 1893 are, + speaking roughly, only half those for 1892 and 1894, and very similar + to those of 1898, though the sun-spot frequency in the latter year was + less than a third of that in 1893. Ekatarinburg data exactly analogous + to those for Pavlovsk show a similar prominence in 1892 and 1894 as + compared to 1893. The retirement of 1893 from first place, seen in the + absolute ranges at Kew, Pavlovsk and Ekatarinburg, is not confined to + the northern hemisphere. It is visible, for instance, in the + amplitudes of the Batavia disturbance results. Thus though the + variation from year to year in the amplitude of the absolute ranges is + relatively not less but greater than that of the inequality ranges, + and though the general tendency is for all ranges to be larger in + years of many than in years of few sun-spots, still the parallelism + between the changes in sun-spot frequency and in magnetic range is not + so close for the absolute ranges and for disturbances as for the + inequality ranges. + + TABLE XXIV.--Ranges of Diurnal Inequalities. + + +----------+-------------------------+-----------------------------------+---------------------------------+ + | | Pavlovsk. | Ekatarinburg. | Kew. | + +----------+-------+-------+---------+-------+-------+---------+---------+-------+-------+---------+-------+ + | | D. | I. | H. | D. | I. | H. | V. | D_q. | I_q. | H_q. | D_0. | + | +-------+-------+---------+-------+-------+---------+---------+-------+-------+---------+-------+ + | | ´ | ´ | [gamma] | ´ | ´ | [gamma] | [gamma] | ´ | ´ | [gamma] | ´ | + | 1890_11 | 6.32 | 1.33 | 22 | 5.83 | 1.05 | 18 | 9 | 6.90 | | 20 | 7.32 | + | 1891_6 | 7.31 | 1.79 | 30 | 6.85 | 1.38 | 25 | 14 | 8.04 | 1.52 | 28 | 8.48 | + | 1892_3 | 8.75 | 2.21 | 37 | 7.74 | 1.72 | 32 | 19 | 9.50 | 1.66 | 31 | 9.85 | + | 1893_1 | 9.64 | 2.24 | 38 | 8.83 | 1.80 | 31 | 17 | 10.06 | 1.96 | 35 | 10.74 | + | 1894_2 | 8.58 | 2.17 | 38 | 7.80 | 1.73 | 30 | 17 | 9.32 | 1.94 | 34 | 9.80 | + | 1895_4 | 8.22 | 2.08 | 33 | 7.29 | 1.64 | 28 | 15 | 8.59 | 1.66 | 30 | 9.54 | + | 1896_5 | 7.39 | 1.77 | 29 | 6.50 | 1.38 | 25 | 15 | 7.77 | 1.31 | 25 | 8.50 | + | 1897_6 | 6.79 | 1.59 | 26 | 6.01 | 1.16 | 21 | 12 | 6.71 | 1.14 | 22 | 7.76 | + | 1898_7 | 6.25 | 1.56 | 26 | 5.76 | 1.19 | 21 | 11 | 6.85 | 1.07 | 21 | 7.59 | + | 1899_9 | 6.02 | 1.44 | 24 | 5.33 | 1.12 | 20 | 11 | 6.69 | 1.01 | 21 | 7.30 | + | 1900_10 | 6.20 | 1.28 | 22 | 5.88 | 0.93 | 17 | 8 | 6.52 | 1.06 | 21 | 6.83 | + +----------+-------+-------+---------+-------+-------+---------+---------+-------+-------+---------+-------+ + + TABLE XXV.--Absolute Ranges. + + +---------+-----------------------+-----------------------------------------------------------------------------------+ + | | Kew Declination. | Pavlovsk. | + | | Daily. +---------------------------+---------------------------+---------------------------+ + | | | Daily. | Monthly. | Yearly. | + +---------+-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+ + | | q. | o. | a. | D. | H. | V. | D. | H. | V. | D. | H. | V. | + | +-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+ + | | ´ | ´ | ´ | ´ | [gamma] | [gamma] | ´ | [gamma] | [gamma] | ´ | [gamma] | [gamma] | + | 1890_11 | 8.3 | 10.5 | 10.7 | 12.1 | 49 | 21 | 28.2 | 118 | 80 | 42.1 | 169 | 179 | + | 1891_6 | 10.0 | 12.8 | 13.7 | 16.0 | 70 | 39 | 46.3 | 218 | 233 | 92.3 | 550 | 614 | + | 1892_3 | 12.3 | 15.4 | 17.7 | 21.0 | 111 | 73 | 93.6 | 698 | 575 | 194.0 | 2416 | 1385 | + | 1893_1 | 11.8 | 15.2 | 15.6 | 17.8 | 79 | 41 | 48.3 | 241 | 210 | 87.1 | 514 | 457 | + | 1894_2 | 11.3 | 14.7 | 16.5 | 20.4 | 97 | 62 | 84.1 | 493 | 493 | 145.6 | 1227 | 878 | + | 1895_4 | 10.6 | 14.8 | 15.6 | 18.1 | 80 | 46 | 47.4 | 220 | 223 | 73.9 | 395 | 534 | + | 1896_5 | 9.5 | 12.9 | 14.5 | 17.5 | 74 | 43 | 52.4 | 232 | 236 | 88.7 | 574 | 608 | + | 1897_8 | 8.2 | 11.5 | 12.1 | 14.6 | 61 | 30 | 43.8 | 201 | 170 | 101.1 | 449 | 480 | + | 1898_7 | 8.2 | 11.2 | 12.3 | 14.7 | 67 | 35 | 46.6 | 276 | 242 | 118.9 | 1136 | 888 | + | 1899_9 | 7.9 | 10.5 | 11.3 | 13.1 | 58 | 27 | 38.3 | 178 | 150 | 63.8 | 382 | 527 | + | 1900_10 | 7.4 | 8.9 | 9.2 | 10.5 | 44 | 16 | 32.8 | 134 | 89 | 94.2 | 457 | 365 | + +---------+-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+ + | Means | 9.6 | 12.6 | 13.6 | 16.0 | 72 | 39 | 51.1 | 274 | 246 | 100.2 | 752 | 629 | + +---------+-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+ + + § 27. The relationship between magnetic ranges and sun-spot frequency + has been investigated in several ways. W. Ellis[26] has employed a + graphical method which has advantages, especially for tracing the + general features of the resemblance, and is besides independent of any + theoretical hypothesis. Taking time for the axis of abscissae, Ellis + drew two curves, one having for its ordinates the sun-spot frequency, + the other the inequality range of declination or of horizontal force + at Greenwich. The value assigned in the magnetic curve to the ordinate + for any particular month represents a mean from 12 months of which it + forms a central month, the object being to eliminate the regular + annual variation in the diurnal inequality. The sun-spot data derived + from Wolf and Wolfer were similarly treated. Ellis originally dealt + with the period 1841 to 1877, but subsequently with the period 1878 to + 1896, and his second paper gives curves representing the phenomena + over the whole 56 years. This period covered five complete sun-spot + periods, and the approximate synchronism of the maxima and minima, and + the general parallelism of the magnetic and sun-spot changes is patent + to the eye. Ellis[27] has also applied an analogous method to + investigate the relationship between sun-spot frequency and the number + of days of magnetic disturbance at Greenwich. A decline in the number + of the larger magnetic storms near sun-spot minimum is recognizable, + but the application of the method is less successful than in the case + of the inequality range. Another method, initiated by Professor Wolf + of Zurich, lends itself more readily to the investigation of numerical + relationships. He started by supposing an exact proportionality + between corresponding changes in sun-spot frequency and magnetic + range. This is expressed mathematically by the formula + + R = a + bS [equiv] a{1 + (b/a)S}, + + where R denotes the magnetic range, S the corresponding sun-spot + frequency, while a and b are constants. The constant a represents the + range for zero sun-spot frequency, while b/a is the proportional + increase in the range accompanying unit rise in sun-spot frequency. + Assuming the formula to be true, one obtains from the observed values + of R and S numerical values for a and b, and can thus investigate + whether or not the sun-spot influence is the same for the different + magnetic elements and for different places. Of course, the usefulness + of Wolf's formula depends largely on the accuracy with which it + represents the facts. That it must be at least a rough approximation + to the truth in the case of the diurnal inequality at Greenwich might + be inferred from Ellis's curves. Several possibilities should be + noticed. The formula may apply with high accuracy, a and b having + assigned values, for one or two sun-spot cycles, and yet not be + applicable to more remote periods. There are only three or four + stations which have continuous magnetic records extending even 50 + years back, and, owing to temperature correction uncertainties, there + is perhaps no single one of these whose earlier records of horizontal + and vertical force are above criticism. Declination is less exposed to + uncertainty, and there are results of eye observations of declination + before the era of photographic curves. A change, however, of 1´ in + declination has a significance which alters with the intensity of the + horizontal force. During the period 1850-1900 horizontal force in + England increased about 5%, so that the force requisite to produce a + declination change of 19´ in 1900 would in 1850 have produced a + deflection of 20´. It must also be remembered that secular changes of + declination must alter the angle between the needle and any disturbing + force acting in a fixed direction. Thus secular alteration in a and b + is rather to be anticipated, especially in the case of the + declination. Wolf's formula has been applied by Rajna[28] to the + yearly mean diurnal declination ranges at Milan based on readings + taken twice daily from 1836 to 1894, treating the whole period + together, and then the period 1871 to 1894 separately. During two + sub-periods, 1837-1850 and 1854-1867, Rajna's calculated values for + the range differ very persistently in one direction from those + observed; Wolf's formula was applied by C. Chree[25] to these two + periods separately. He also applied it to Greenwich inequality ranges + for the years 1841 to 1896 as published by Ellis, treating the whole + period and the last 32 years of it separately, and finally to all (a) + and quiet (q) day Greenwich ranges from 1889 to 1896. The results of + these applications of Wolf's formula appear in Table XXVI. + + The Milan results are suggestive rather of heterogeneity in the + material than of any decided secular change in a or b. The Greenwich + data are suggestive of a gradual fall in a, and rise in b, at least in + the case of the declination. + + Table XXVII. gives values of a, b and b/a in Wolf's formula calculated + by Chree[25] for a number of stations. There are two sets of data, the + first set relating to the range from the mean diurnal inequality for + the year, the second to the arithmetic mean of the ranges in the mean + diurnal inequalities for the twelve months. It is specified whether + the results were derived from all or from quiet days. + + TABLE XXVI.--Values of a and b in Wolf's Formula. + + +--------------------------+------------------------------------------------+ + | Milan. | Greenwich. | + |---------+----------------+------------+----------------+------------------+ + | | Declination | | Declination | Horizontal Force | + | | (unit 1´). | | (unit 1´). | (unit 1[gamma]). | + | Epoch. |--------+-------+ Epoch. +--------+-------+---------+--------+ + | | a. | b. | | a. | b. | a. | b. | + +---------+--------+-------+------------+--------+-------+---------+--------+ + | 1836-94 | 5.31 | .047 | 1841-96 | 7.29 | .0377 | 26.4 | .190 | + | 1871-94 | 5.39 | .047 | 1865-96 | 7.07 | .0396 | 23.6 | .215 | + | 1837-50 | 6.43 | .041 | 1889-96(a) | 6.71 | .0418 | 23.7 | .218 | + | 1854-67 | 4.62 | .047 | 1889-96(q) | 6.36 | .0415 | 25.0 | .213 | + +---------+--------+-------+------------+--------+-------+---------+--------+ + + As explained above, a would represent the range in a year of no + sun-spots, while 100 b would represent the excess over this shown by + the range in a year when Wolf's sun-spot frequency is 100. Thus b/a + seems the most natural measure of sun-spot influence. Accepting it, we + see that sun-spot influence appears larger at most places for + inclination and horizontal force than for declination. In the case of + vertical force there is at Pavlovsk, and probably in a less measure at + other northern stations, a large difference between all and quiet + days, which is not shown in the other elements. The difference between + the values of b/a at different stations is also exceptionally large + for vertical force. Whether this last result is wholly free from + observational uncertainties is, however, open to some doubt, as the + agreement between Wolf's formula and observation is in general + somewhat inferior for vertical force. In the case of the declination, + the mean numerical difference between the observed values and those + derived from Wolf's formula, employing the values of a and b given in + Table XXVII., represented on the average about 4% of the mean value of + the element for the period considered, the probable error representing + about 6% of the difference between the highest and lowest values + observed. The agreement was nearly, if not quite, as good as this for + inclination and horizontal force, but for vertical force the + corresponding percentages were nearly twice as large. + + TABLE XXVII.--Values of a and b in Wolf's Formula. + + +---------------------------------+----------------------+----------------------+----------------------+----------------------+ + | | Declination | Inclination | Horizontal Force | Vertical Force | + | | (unit 1´). | (unit 1´). | (unit 1[gamma]). | (unit 1[gamma]). | + +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+ + | Diurnal Inequality for the Year.| a. | b. |100 b/a.| a. | b. |100 b/a.| a. | b. |100 b/a.| a. | b. |100 b/a.| + +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+ + | Pavlovsk, 1890-1900 all | 5.74 |.0400 | .70 | 1.24 |.0126 | 1.01 | 20.7 | .211 | 1.02 | 8.1 | .265 | 3.26 | + | Pavlovsk, 1890-1900 quiet | 6.17 |.0424 | .69 | .. | .. | .. | 20.6 | .195 | 0.95 | 5.9 | .027 | 0.46 | + | Ekatarinburg, 1890-1900 all | 5.29 |.0342 | .65 | 0.93 |.0105 | 1.13 | 16.8 | .182 | 1.09 | 8.6 | .117 | 1.37 | + | Irkutsk " " all | 4.82 |.0358 | .74 | 0.97 |.0087 | 0.90 | 18.2 | .190 | 1.04 | 6.5 | .071 | 1.09 | + | Kew " " quiet | 6.10 |.0433 | .71 | 0.87 |.0125 | 1.45 | 18.1 | .194 | 1.07 | 14.3 | .081 | 0.56 | + | Falmouth, 1891-1902 quiet | 5.90 |.0451 | .76 | .. | .. | .. | 20.1 | .233 | 1.16 | .. | .. | .. | + | Kolaba, 1894-1901 quiet | 2.37 |.0066 | .28 | .. | .. | .. | 31.6 | .281 | 0.89 | 19.4 | .072 | 0.37 | + | Batavia, 1887-1898 all | 2.47 |.0179 | .72 | 3.60 |.0218 | 0.61 | 38.7 | .274 | 0.71 | 30.1 | .156 | 0.52 | + | Mauritius / 1875-1880 \ all | 4.06 |.0164 | .40 | .. | .. | .. | 15.0 | .096 | 0.64 | 11.9 | .069 | 0.58 | + | \ 1883-1890 / | | | | | | | | | | | | | + +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+ + | _Mean from individual months:--_| | | | | | | | | | | | | + | Pavlovsk, 1890-1900 all | 6.81 |.0446 | .66 | 1.44 |.0151 | 1.05 | 22.8 | .243 | 1.07 | 9.7 | .287 | 2.97 | + | " " " quiet | 6.52 |.0442 | .68 | .. | .. | .. | 22.2 | .208 | 0.94 | 7.0 | .044 | 0.63 | + | Ekatarinburg, 1890-1900 all | 6.18 |.0355 | .58 | 1.12 |.0120 | 1.06 | 19.2 | .195 | 1.01 | 9.2 | .156 | 1.70 | + | Greenwich, 1865-1896 all | 7.07 |.0396 | .56 | .. | .. | .. | 23.6 | .215 | 0.91 | .. | .. | .. | + | Kew, 1890-1900 all | 6.65 |.0428 | .64 | .. | .. | .. | .. | .. | .. | .. | .. | .. | + | " " " quiet | 6.49 |.0410 | .63 | 1.17 |.0130 | 1.11 | 21.5 | .191 | 0.89 | 16.0 | .072 | 0.45 | + | Falmouth, 1891-1902 quiet | 6.16 |.0450 | .73 | .. | .. | .. | 20.9 | .236 | 1.13 | .. | .. | .. | + +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+ + + Applying Wolf's formula to the diurnal ranges for different months of + the year, Chree found, as was to be anticipated, that the constant a + had an annual period, with a conspicuous minimum at midwinter; but + whilst b also varied, it did so to a much less extent, the consequence + being that b/a showed a minimum at midsummer. The annual variation in + b/a alters with the place, with the element, and with the type of day + from which the magnetic data are derived. Thus, in the case of + Pavlovsk declination, whilst the mean value of 100 b/a for the 12 + months is, as shown in Table XXVII., 0.66 for all and 0.68 for quiet + days--values practically identical--if we take the four midwinter and + the four midsummer months separately, we have 100 b/a, varying from + 0.81 in winter to 0.52 in summer on all days, but from 1.39 in winter + to 0.52 in summer on quiet days. In the case of horizontal force at + Pavlovsk the corresponding figures to these are for all days--winter + 1.77, summer 0.98, but for quiet days--winter 1.83, summer 0.71. + + Wolf's formula has also been applied to the absolute daily ranges, to + monthly ranges, and to various measures of disturbance. In these cases + the values found for b/a are usually larger than those found for + diurnal inequality ranges, but the accordance between observed values + and those calculated from Wolf's formula is less good. If instead of + the range of the diurnal inequality we take the sum of the 24-hourly + differences from the mean for the day--or, what comes to the same + thing, the average departure throughout the 24 hours from the mean + value for the day--we find that the resulting Wolf's formula gives at + least as good an agreement with observation as in the case of the + inequality range itself. The formulae obtained in the case of the 24 + differences, at places as wide apart as Kew and Batavia, agreed in + giving a decidedly larger value for b/a than that obtained from the + ranges. This indicates that the inequality curve is relatively less + peaked in years of many than in years of few sun-spots. + + § 28. The applications of Ellis's and Wolf's methods relate directly + only to the amplitude of the diurnal changes. There is, however, a + change not merely in amplitude but in type. This is clearly seen when + we compare the values found in years of many and of few sun-spots for + the Fourier coefficients in the diurnal inequality. Such a comparison + is carried out in Table XXVIII. for the declination on ordinary days + at Kew. Local mean time is used. The heading S max. (sun-spot maximum) + denotes mean average results from the four years 1892-1895, having a + mean sun-spot frequency of 75.0, whilst S min. (sun-spot minimum) + applies similarly to the years 1890, 1899 and 1900, having a mean + sun-spot frequency of only 9.6. The data relate to the mean diurnal + inequality for the whole year or for the season stated. It will be + seen that the difference between the c, or amplitude, coefficients in + the S max. and S min. years is greater for the 24-hour term than for + the 12-hour term, greater for the 12-hour than for the 8-hour term, + and hardly apparent in the 6-hour term. Also, _relatively considered_, + the difference between the amplitudes in S max. and S min. years is + greatest in winter and least in summer. Except in the case of the + 6-hour term, where the differences are uncertain, the phase angle is + larger, i.e. maxima and minima occur earlier in the day, in years of S + min. than in years of S max. Taking the results for the whole year in + Table XXVIII., this advance of phase in the S min. years represents in + time 15.6 minutes for the 24-hour term, 9.4 minutes for the 12-hour + term, and 14.7 minutes for the 8-hour term. The difference in the + phase angles, as in the amplitudes, is greatest in winter. Similar + phenomena are shown by the horizontal force, and at Falmouth[24] as + well as Kew. + + TABLE XXVIII.--Fourier Coefficients in Years of many and few + Sun-spots. + + +---------+-------------+-------------+-------------+-------------+ + | | Year. | Winter. | Equinox. | Summer. | + | +------+------+------+------+------+------+------+------+ + | |S max.|S min.|S max.|S min.|S max.|S min.|S max.|S min.| + +---------+------+------+------+------+------+------+------+------+ + | | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | + | c1 | 3.47 | 2.21 | 2.41 | 1.43 | 3.76 | 2.41 | 4.38 | 2.98 | + | c2 | 2.04 | 1.51 | 1.15 | 0.78 | 2.33 | 1.71 | 2.73 | 2.06 | + | c3 | 0.89 | 0.72 | 0.55 | 0.42 | 1.16 | 0.97 | 0.97 | 0.77 | + | c4 | 0.28 | 0.27 | 0.30 | 0.27 | 0.42 | 0.42 | 0.11 | 0.11 | + +---------+------+------+------+------+------+------+------+------+ + | | ° | ° | ° | ° | ° | ° | ° | ° | + |[alpha]1 | 228.5| 232.4| 243.0| 256.0| 231.3| 233.7| 218.2| 220.3| + |[alpha]2 | 41.7| 46.6| 23.5| 36.9| 40.6| 43.9| 50.6| 52.5| + |[alpha]3 | 232.6| 243.6| 234.0| 257.6| 228.4| 236.2| 236.8| 245.4| + |[alpha]4 | 58.0| 57.3| 52.3| 60.8| 62.0| 58.2| 57.4| 45.2| + +---------+------+------+------+------+------+------+------+------+ + + + Quiet Day Phenomena. + + § 29. There have already been references to _quiet_ days, for instance + in the tables of diurnal inequalities. It seems to have been + originally supposed that quiet days differed from other days only in + the absence of irregular disturbances, and that mean annual values, or + secular change data, or diurnal inequalities, derived from them might + be regarded as truly normal or representative of the station. It was + found, however, by P. A. Müller[29] that mean annual values of the + magnetic elements at St Petersburg and Pavlovsk from 1873 to 1885 + derived from quiet days alone differed in a systematic fashion from + those derived from all days, and analogous results were obtained by + Ellis[30] at Greenwich for the period 1889-1896. The average excesses + for the quiet-day over the all-day means in these two cases were as + follows:-- + + +---------------+--------------+--------------+------------+-------------+ + | | Westerly | Inclination. | Horizontal | Vertical | + | | Declination. | | Force. | Force. | + +---------------+--------------+--------------+------------+-------------+ + | St Petersburg | +0.24 | -0.23 | +3.2[gamma]| -0.8[gamma] | + | Greenwich | +0.08 | | +3.2[gamma]| -0.9[gamma] | + +---------------+--------------+--------------+------------+-------------+ + + The sign of the difference in the case of D, I and H was the same in + each year examined by Müller, and the same was true of H at Greenwich. + In the case of V, and of D at Greenwich, the differences are small + and might be accidental. In the case of D at Greenwich 1891 differed + from the other years, and of two more recent years examined by + Ellis[31] one, 1904, agreed with 1891. At Kew, on the average of the + 11 years 1890 to 1900, the quiet-day mean annual value of declination + exceeded the ordinary day value, but the apparent excess 0´.02 is too + small to possess much significance. + + + Non-cyclic Change. + + Another property more recently discovered in quiet days is the + non-cyclic change. The nature of this phenomenon will be readily + understood from the following data from the 11-year period 1890 to + 1900 at Kew[32]. The mean daily change for all days is calculated from + the observed annual change. + + +------------------------------+--------+--------+--------------+--------------+ + | | D. | I. | H. | V. | + +------------------------------+--------+--------+--------------+--------------+ + | | ´ | ´ | | | + | Mean annual change | -5.79 | -2.38 | +25.9[gamma] | -22.6[gamma] | + | Mean daily change, all days | -0.016 | -0.007 | +0.07[gamma] | -0.06[gamma] | + | Mean daily change, quiet days| +0.044 | -0.245 | +3.34[gamma] | -0.84[gamma] | + +------------------------------+------------------+-------------+--------------+ + + Thus the changes during the representative quiet day differed from + those of the average day. Before accepting such a phenomenon as + natural, instrumental peculiarities must be carefully considered. The + secular change is really based on the absolute instruments, the + diurnal changes on the magnetographs, and the first idea likely to + occur to a critical mind is that the apparent abnormal change on quiet + days represents in reality change of zero in the magnetographs. If, + however, the phenomenon were instrumental, it should appear equally on + days other than quiet days, and we should thus have a shift of zero + amounting in a year to over 1,200[gamma] in H, and to about 90´ in I. + Under such circumstances the curve would be continually drifting off + the sheet. In the case of the Kew magnetographs, a careful + investigation showed that if any instrumental change occurred in the + declination magnetograph during the 11 years it did not exceed a few + tenths of a minute. In the case of the H and V magnetographs at Kew + there is a slight drift, of instrumental origin, due to weakening of + the magnets, but it is exceedingly small, and in the case of H is in + the opposite direction to the non-cyclic change on quiet days. It only + remains to add that the hypothesis of instrumental origin was + positively disproved by measurement of the curves on ordinary days. + + It must not be supposed that every quiet day agrees with the average + quiet day in the order of magnitude, or even in the sign, of the + non-cyclic change. In fact, in not a few months the sign of the + non-cyclic change on the mean of the quiet days differs from that + obtained for the average quiet day of a period of years. At Kew, + between 1890 and 1900, the number of months during which the mean + non-cyclic change for the five quiet days selected by the astronomer + royal (Sir W. H. M. Christie) was plus, zero, or minus, was as + follows:-- + + +-----------+------+------+------+------+ + | Element. | D. | I. | H. | V. | + +-----------+------+------+------+------+ + | Number + | 63 | 13 | 112 | 47 | + | " 0 | 14 | 16 | 11 | 9 | + | " - | 55 | 101 | 9 | 74 | + +-----------+------+------+------+------+ + + The + sign denotes westerly movement in the declination, and + increasing dip of the north end of the needle. In the case of I and H + the excess in the number of months showing the normal sign is + overwhelming. The following mean non-cyclic changes on quiet days are + from other sources:-- + + +-----------+--------------+-------------+--------------+ + | | Greenwich | Falmouth | Kolaba | + | Element. | (1890-1895). | (1898-1902).| (1894-1901). | + +-----------+--------------+-------------+--------------+ + | | ´ | ´ | ´ | + | D | + 0.03 | + 0.05 | + 0.07 | + | H | + 4.3[gamma] | + 3.0[gamma]| + 3.9[gamma] | + +-----------+--------------+-------------+--------------+ + + The results are in the same direction as at Kew, + meaning in the case + of D movement to the west. At Falmouth[32], as at Kew, the non-cyclic + change showed a tendency to be small in years of few sun-spots. + + § 30. In calculating diurnal inequalities from quiet days the + non-cyclic effect must be eliminated, otherwise the result would + depend on the hour at which the "day" is supposed to commence. If the + value recorded at the second midnight of the average day exceeds that + at the first midnight by N, the elimination is effected by applying to + each hourly value the correction N(12 - n)/24, where n is the hour + counted from the first midnight (0 hours). This assumes the change to + progress uniformly throughout the 24 hours. Unless this is practically + the case--a matter difficult either to prove or disprove--the + correction may not secure exactly what is aimed at. This method has + been employed in the previous tables. The fact that differences do + exist between diurnal inequalities derived from quiet days and all + ordinary days was stated explicitly in § 4, and is obvious in Tables + VIII. to XI. An extreme case is represented by the data for Jan Mayen + in these tables. Figs. 9 and 10 are vector diagrams for this station, + for all and for quiet days during May, June and July 1883, according + to data got out by Lüdeling. As shown by the arrows, fig. 10 (quiet + days) is in the main described in the normal or clockwise direction, + but fig. 9 (all days) is described in the opposite direction. Lüdeling + found this peculiar difference between all and quiet days at all the + north polar stations occupied in 1882-1883 except Kingua Fjord, where + both diagrams were described clockwise. + + [Illustration: FIG. 9.] + + [Illustration: FIG. 10.] + + In temperate latitudes the differences of type are much less, but + still they exist. A good idea of their ordinary size and character in + the case of declination may be derived from Table XXIX., containing + data for Kew, Greenwich and Parc St Maur. + + The data for Greenwich are due to W. Ellis[30], those for Parc St Maur + to T. Moureaux[33]. The quantity tabulated is the algebraic excess of + the all or ordinary day mean hourly value over the corresponding quiet + day value in the mean diurnal inequality for the year. At Greenwich + and Kew days of extreme disturbance have been excluded from the + ordinary days, but apparently not at Parc St Maur. The number of + highly disturbed days at the three stations is, however, small, and + their influence is not great. The differences disclosed by Table XXIX. + are obviously of a systematic character, which would not tend to + disappear however long a period was utilized. In short, while the + diurnal inequality from quiet days may be that most truly + representative of undisturbed conditions, it does not represent the + average state of conditions at the station. To go into full details + respecting the differences between all and quiet days would occupy + undue space, so the following brief summary of the differences + observed in declination at Kew must suffice. While the inequality + range is but little different for the two types of days, the mean of + the hourly differences from the mean for the day is considerably + reduced in the quiet days. The 24-hour term in the Fourier analysis is + of smaller amplitude in the quiet days, and its phase angle is on the + average about 6°.75 smaller than on ordinary days, implying a + retardation of about 27 minutes in the time of maximum. The diurnal + inequality range is more variable throughout the year in quiet days + than on ordinary days, and the same is true of the absolute ranges. + The tendency to a secondary minimum in the range at midsummer is + considerably more decided on ordinary than on quiet days. When the + variation throughout the year in the diurnal inequality range is + expressed in Fourier series, whose periods are the year and its + submultiples, the 6-month term is notably larger for ordinary than for + quiet days. Also the date of the maximum in the 12-month term is about + three days earlier for ordinary than for quiet days. The exact size of + the differences between ordinary and quiet day phenomena must depend + to some extent on the criteria employed in selecting quiet days and in + excluding disturbed days. This raises difficulties when it comes to + comparing results at different stations. For stations near together + the difficulty is trifling. The astronomer royal's quiet days have + been used for instance at Parc St. Maur, Val Joyeux, Falmouth and Kew, + as well as at Greenwich. But when stations are wide apart there are + two obvious difficulties: first, the difference of local time; + secondly, the fact that a day may be typically quiet at one station + but appreciably disturbed at the other. + + If the typical quiet day were simply the antithesis of a disturbed + day, it would be natural to regard the non-cyclic change on quiet days + as a species of recoil from some effect of disturbance. This view + derives support from the fact, pointed out long ago by Sabine[34], + that the horizontal force usually, though by no means always, is + lowered by magnetic disturbances. Dr van Bemmelen[35] who has examined + non-cyclic phenomena at a number of stations, seems disposed to regard + this as a sufficient explanation. There are, however, difficulties in + accepting this view. Thus, whilst the non-cyclic effect in horizontal + force and inclination at Kew and Falmouth appeared on the whole + enhanced in years of sun-spot maximum, the difference between years + such as 1892 and 1894 on the one hand, and 1890 and 1900 on the other, + was by no means proportional to the excess of disturbance in the + former years. Again, when the average non-cyclic change of declination + was calculated at Kew for 207 days, selected as those of most marked + irregular disturbance between 1890 and 1900, the sign actually proved + to be the same as for the average quiet day of the period. + + TABLE XXIX.--All or Ordinary, less Quiet Day Hourly Values (+ to the + West). + + +-----+--------------------------------------+-------------------------------------+ + | | Forenoon. | Afternoon. | + |Hour.+------------+-----------+-------------+-----------+-----------+-------------+ + | | Kew | Greenwich |Parc St Maur | Kew | Greenwich |Parc St Maur | + | | 1890-1900. | 1890-1894.| 1883-1897. | 1890-1900.| 1890-1894.| 1893-1897. | + +-----+------------+-----------+-------------+-----------+-----------+-------------+ + | | ´ | ´ | ´ | ´ | ´ | ´ | + | 1 | -0.58 | -0.59 | -0.63 | +0.42 | +0.44 | +0.40 | + | 2 | -0.54 | -0.47 | -0.47 | +0.52 | +0.45 | +0.50 | + | 3 | -0.51 | -0.31 | -0.32 | +0.57 | +0.52 | +0.59 | + | 4 | -0.41 | -0.23 | -0.16 | +0.60 | +0.51 | +0.55 | + | 5 | -0.28 | -0.10 | -0.01 | +0.46 | +0.34 | +0.38 | + | 6 | -0.08 | +0.12 | +0.18 | +0.21 | +0.04 | +0.07 | + | 7 | +0.13 | +0.30 | +0.34 | -0.06 | -0.24 | -0.25 | + | 8 | +0.29 | +0.48 | +0.47 | -0.27 | -0.50 | -0.54 | + | 9 | +0.40 | +0.56 | +0.53 | -0.47 | -0.68 | -0.74 | + | 10 | +0.44 | +0.58 | +0.51 | -0.61 | -0.78 | -0.79 | + | 11 | +0.48 | +0.50 | +0.44 | -0.62 | -0.77 | -0.79 | + | 12 | +0.45 | +0.44 | +0.38 | -0.54 | -0.61 | -0.67 | + +-----+------------+-----------+-------------+-----------+-----------+-------------+ + + + Magnetic Disturbances. + + § 31. A satisfactory definition of magnetic disturbance is about as + difficult to lay down as one of heterodoxy. The idea in its generality + seems to present no difficulty, but it is a very different matter when + one comes to details. Amongst the chief disturbances recorded since + 1890 are those of February 13-14 and August 12, 1892; July 20 and + August 20, 1894; March 15-16, and September 9, 1898; October 31, 1903; + February 9-10, 1907; September 11-12, 1908 and September 25, 1909. On + such days as these the oscillations shown by the magnetic curves are + large and rapid, aurora is nearly always visible in temperate + latitudes, earth currents are prominent, and there is + interruption--sometimes very serious--in the transmission of telegraph + messages both in overhead and underground wires. At the other end of + the scale are days on which the magnetic curves show practically no + movement beyond the slow regular progression of the regular diurnal + inequality. But between these two extremes there are an infinite + variety of intermediate cases. The first serious attempt at a precise + definition of disturbance seems due to General Sabine[35a]. His method + had once an extensive vogue, and still continues to be applied at some + important observatories. Sabine regarded a particular observation as + disturbed when it differed from the mean of the observations at that + hour for the whole month by not less than a certain limiting value. + His definition takes account only of the extent of the departure from + the mean, whether the curve is smooth at the time or violently + oscillating makes no difference. In dealing with a particular station + Sabine laid down separate limiting values for each element. These + limits were the same, irrespective of the season of the year or of the + sun-spot frequency. A departure, for example, of 3´.3 at Kew from the + mean value of declination for the hour constituted a disturbance, + whether it occurred in December in a year of sun-spot minimum, or in + June in a year of sun-spot maximum, though the regular diurnal + inequality range might be four times as large in the second case as in + the first. The limiting values varied from station to station, the + size depending apparently on several considerations not very clearly + defined. Sabine subdivided the disturbances in each element into two + classes: the one tending to increase the element, the other tending to + diminish it. He investigated how the numbers of the two classes varied + throughout the day and from month to month. He also took account of + the aggregate value of the disturbances of one sign, and traced the + diurnal and annual variations in these aggregate values. He thus got + two sets of diurnal variations and two sets of annual variations of + disturbance, the one set depending only on the number of the disturbed + hours, the other set considering only the aggregate value of the + disturbances. Generally the two species of disturbance variations were + on the whole fairly similar. The aggregates of the + and - + disturbances for a particular hour of the day were seldom equal, and + thus after the removal of the disturbed values the mean value of the + element for that hour was generally altered. Sabine's complete scheme + supposed that after the criterion was first applied, the hourly means + would be recalculated from the undisturbed values and the criterion + applied again, and that this process would be repeated until the + disturbed observations all differed by not less than the accepted + limiting value from the final mean based on undisturbed values alone. + If the disturbance limit were so small that the disturbed readings + formed a considerable fraction of the whole number, the complete + execution of Sabine's scheme would be exceedingly laborious. As a + matter of fact, his disturbed readings were usually of the order of 5% + of the total number, and unless in the case of exceptionally large + magnetic storms it is of little consequence whether the first choice + of disturbed readings is accepted as final or is reconsidered in the + light of the recalculated hourly means. + + Sabine applied his method to the data obtained during the decade 1840 + to 1850 at Toronto, St Helena, Cape of Good Hope and Hobart, also to + data for Pekin, Nertchinsk, Point Barrow, Port Kennedy and Kew. C. + Chambers[36] applied it to data from Bombay. The yearly publication of + the Batavia observatory gives corresponding results for that station, + and Th. Moureaux [33] has published similar data for Parc St Maur. + Tables XXX. to XXXII. are based on a selection of these data. Tables + XXX. and XXXI. show the annual variation in Sabine's disturbances, the + monthly values being expressed as percentages of the arithmetic mean + value for the 12 months. The Parc St Maur and Batavia data, owing to + the long periods included, are especially noteworthy. Table XXX. deals + with the east (E) and west (W) disturbances of declination separately. + Table XXXI., dealing with disturbances in horizontal and vertical + force, combines the + and - disturbances, treated numerically. At Parc + St Maur the limits required to qualify for disturbance were 3´.0 in D, + 20[gamma] in H, and 12[gamma] in V; the corresponding limits for + Batavia were 1´.3, 11[gamma] and 11[gamma]. The limits for D at + Toronto, Bombay and Hobart were respectively 3´.6, 1´.4 and 2´.4. + + At Parc St Maur the disturbance data from all three elements give + distinct maxima near the equinoxes; a minimum at midwinter is clearly + shown, and also one at midsummer, at least in D and H. A decline in + disturbance at midwinter is visible at all the stations, but at + Batavia the equinoctial values for D and V are inferior to those at + midsummer. + + TABLE XXX.--Annual Variation of Disturbances (Sabine's numbers). + + +-----------+-------------+-------------+-------------+-------------+-------------+ + | | Parc St Maur| Toronto | Bombay | Batavia | Hobart | + | | 1883-97. | 1841-48. | 1859-65. | 1883-99. | 1843-48. | + +-----------+------+------+------+------+------+------+------+------+------+------+ + | Month. | E. | W. | E. | W. | E. | W. | E. | W. | E. | W. | + +-----------+------+------+------+------+------+------+------+------+------+------+ + | January | 78 | 60 | 55 | 66 | 89 | 89 | 180 | 223 | 165 | 182 | + | February | 116 | 92 | 75 | 86 | 94 | 67 | 138 | 144 | 121 | 116 | + | March | 126 | 107 | 92 | 94 | 129 | 97 | 102 | 87 | 114 | 104 | + | April | 105 | 113 | 115 | 114 | 106 | 129 | 67 | 73 | 110 | 102 | + | May | 101 | 118 | 101 | 101 | 63 | 99 | 72 | 71 | 62 | 53 | + | June | 77 | 89 | 95 | 72 | 78 | 81 | 45 | 27 | 32 | 37 | + | July | 82 | 104 | 140 | 126 | 121 | 173 | 62 | 46 | 50 | 49 | + | August | 88 | 113 | 137 | 133 | 154 | 131 | 69 | 69 | 86 | 78 | + | September | 134 | 137 | 163 | 139 | 111 | 108 | 135 | 144 | 135 | 114 | + | October | 119 | 115 | 101 | 111 | 140 | 128 | 95 | 88 | 124 | 123 | + | November | 99 | 94 | 73 | 85 | 43 | 43 | 106 | 91 | 79 | 111 | + | December | 75 | 58 | 51 | 72 | 72 | 55 | 124 | 137 | 123 | 130 | + +-----------+------+------+------+------+------+------+------+------+------+------+ + + Table XXXII. shows in some cases a most conspicuous diurnal variation + in Sabine's disturbances. The data are percentages of the totals for + the whole 24 hours. But whilst at Batavia the easterly and westerly + disturbances in D vary similarly, at Parc St Maur they follow opposite + laws, the easterly showing a prominent maximum near noon, the westerly + a still more prominent maximum near midnight. The figures in the + second last line of the table, if divided by 0.24, will give the + percentage of hours which show the species of disturbance indicated. + For instance, at Parc St Maur, out of 100 hours, 3 show disturbances + to the west and 3.7 to the east; or in all 6.7 show disturbances of + declination. The last line gives the average size of a disturbance of + each type, the unit being 1´ in D and 1[gamma] in H and V. + + TABLE XXXI.--Annual Variation of Disturbances. + + +-----------+-------------+-------------+---------------------------+ + | |Parc St Maur.| Toronto. | Batavia. | + +-----------+-------------+-------------+-------------+-------------+ + | Month. | Numbers. | Aggregates. | Numbers. | Aggregates. | + +-----------+------+------+------+------+------+------+------+------+ + | | H. | V. | H. | V. | H. | V. | H. | V. | + | +------+------+------+------+------+------+------+------+ + | January | 81 | 51 | 58 | 56 | 96 | 151 | 89 | 154 | + | February | 96 | 133 | 94 | 74 | 105 | 123 | 110 | 125 | + | March | 126 | 118 | 94 | 108 | 116 | 105 | 117 | 103 | + | April | 94 | 111 | 150 | 149 | 104 | 76 | 105 | 73 | + | May | 108 | 133 | 90 | 112 | 101 | 92 | 105 | 95 | + | June | 90 | 85 | 36 | 50 | 82 | 69 | 79 | 66 | + | July | 99 | 128 | 61 | 71 | 90 | 83 | 95 | 81 | + | August | 113 | 92 | 75 | 108 | 91 | 91 | 98 | 91 | + | September | 119 | 122 | 171 | 160 | 113 | 111 | 114 | 115 | + | October | 101 | 94 | 148 | 129 | 114 | 89 | 104 | 86 | + | November | 104 | 81 | 98 | 75 | 99 | 102 | 100 | 101 | + | December | 70 | 51 | 128 | 100 | 89 | 108 | 84 | 110 | + +-----------+------+------+------+------+------+------+------+------+ + + At Batavia disturbances increasing and decreasing the element are + about equally numerous, but this is exceptional. Easterly disturbances + of declination predominated at Toronto, Point Barrow, Fort Kennedy, + Kew, Parc St Maur, Bombay and the Falkland Islands whilst the reverse + was true of St Helena, Cape of Good Hope, Pekin and Hobart. At Kew and + Parc St Maur the ratios borne by the eastern to the western + disturbances were 1.19 and 1.23 respectively, and so not much in + excess of unity; but the preponderance of easterly disturbances at the + North American[37] stations was considerably larger than this. + + TABLE XXXII.--Diurnal Variation of Disturbances (Sabine's numbers). + + +-------------+-----------------------------------------+-----------------------------------------+ + | | Parc St Maur. | Batavia. | + | +-------------+-------------+-------------+-------------+-------------+-------------+ + | Hour. | D. | H. | V. | D. | H. | V. | + | +------+------+------+------+------+------+------+------+------+------+------+------+ + | | E. | W. | + | - | + | - | E. | W. | + | - | + | - | + +-------------+------+------+------+------+------+------+------+------+------+------+------+------+ + | 0-3 | 10.1 | 20.3 | 9.0 | 8.3 | 5.7 | |9.2 | 1.1 | 5.8 | 13.1 | 6.6 | 4.0 | 7.4 | + | 3-6 | 12.3 | 8.2 | 8.4 | 8.0 | 6.4 | 10.4 | 7.6 | 7.3 | 14.2 | 4.8 | 6.3 | 10.0 | + | 6-9 | 15.7 | 3.8 | 14.1 | 12.5 | 7.2 | 9.0 | 24.9 | 16.8 | 12.1 | 9.9 | 21.2 | 21.7 | + | 9-noon | 16.2 | 5.1 | 18.0 | 15.6 | 12.9 | 15.4 | 38.5 | 33.0 | 8.6 | 15.8 | 19.8 | 16.4 | + | noon-3 | 19.3 | 6.7 | 15.3 | 16.5 | 18.2 | 18.3 | 18.8 | 24.7 | 16.8 | 21.1 | 23.5 | 22.1 | + | 3-6 | 14.8 | 9.7 | 12.5 | 15.4 | 22.9 | 21.8 | 6.4 | 5.4 | 13.3 | 16.9 | 12.6 | 12.7 | + | 6-9 | 5.7 | 21.2 | 11.4 | 13.2 | 18.9 | 11.2 | 2.3 | 3.4 | 9.9 | 13.6 | 7.1 | 4.1 | + | 9-12 | 5.9 | 25.0 | 11.2 | 10.5 | 7.8 | 4.7 | 0.4 | 3.8 | 12.0 | 11.1 | 5.6 | 5.4 | + +-------------+------+------+------+------+------+------+------+------+------+------+------+------+ + | Mean number | | | | | | | | | | | | | + | per day | 0.88| 0.72| 1.15| 1.56| 1.04| 0.96| 0.46| 0.44| 1.62| 1.61| 1.19| 1.13| + | Mean size | .. | .. | .. | .. | .. | .. | 1.72| 1.69| 18.0| 19.5 | 16.7 | 15.5 | + +-------------+------+------+------+------+------+------+------+------+------+------+------+------+ + + § 32. From the point of view of the surveyor there is a good deal to + be said for Sabine's definition of disturbance, but it is less + satisfactory from other standpoints. One objection has been already + indicated, viz. the arbitrariness of applying the same limiting value + at a station irrespective of the size of the normal diurnal range at + the time. Similarly it is arbitrary to apply the same limit between 10 + a.m. and noon, when the regular diurnal variation is most rapid, as + between 10 p.m. and midnight, when it is hardly appreciable. There + seems a distinct difference of phase between the diurnal inequalities + on different types of days at the same season; also the phase angles + in the Fourier terms vary continuously throughout the year, and much + more rapidly at some stations and at some seasons than at others. Thus + there may be a variety of phenomena which one would hesitate to regard + as disturbances which contribute to the annual and diurnal variations + in Tables XXX. to XXXII. + + Sabine, as we have seen, confined his attention to the departure of + the hourly reading from the mean for that hour. Another and equally + natural criterion is the apparent character of the magnetograph curve. + At Potsdam curves are regarded as "1" quiet, "2" moderately disturbed, + or "3" highly disturbed. Any hourly value to which the numeral 3 is + attached is treated as disturbed, and the annual Potsdam publication + contains tables giving the annual and diurnal variations in the number + of such disturbed hours for D, H and V. According to this point of + view, the extent to which the hourly value departs from the mean for + that hour is immaterial to the results. It is the greater or less + sinuosity and irregularity of the curve that counts. Tables XXXIII. + and XXXIV. give an abstract of the mean Potsdam results from 1892 to + 1901. The data are percentages: in Table XXXIII. of the mean monthly + total, in Table XXXIV. of the total for the day. So far as the annual + variation is concerned, the results in Table XXXIII. are fairly + similar to those in Table XXX. for Parc St Maur. There are pronounced + maxima near the equinoxes, especially the spring equinox. The diurnal + variations, however, in Tables XXXII. and XXXIV. are dissimilar. Thus + in the case of H the largest disturbance numbers at Parc St Maur + occurred between 6 a.m. and 6 p.m., whereas in Table XXXIV. they occur + between 4 p.m. and midnight. Considering the comparative proximity of + Parc St Maur and Potsdam, one must conclude that the apparent + differences between the results for these two stations are due almost + entirely to the difference in the definition of disturbance. + + TABLE XXXIII.--Annual Variation of Potsdam Disturbances. + + +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+ + | Element.| Jan.| Feb.| Mar.| April.| May.| June.| July.| Aug.| Sept.| Oct.| Nov.| Dec.| + +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+ + | D | 129 | 170 | 149 | 90 | 86 | 57 | 62 | 64 | 59 | 118 | 94 | 82 | + | H | 109 | 133 | 131 | 102 | 109 | 82 | 94 | 91 | 89 | 101 | 75 | 84 | + | V | 106 | 171 | 170 | 108 | 121 | 56 | 64 | 74 | 93 | 87 | 78 | 70 | + +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+ + | Mean | 115 | 158 | 150 | 100 | 105 | 65 | 73 | 76 | 94 | 102 | 82 | 79 | + +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+ + + TABLE XXXIV.--Diurnal Variation of Potsdam Disturbances. + + +--------+------+------+-----+---------+------+------+------+-------+ + | Hours. | 1-3. | 4-6. | 7-9.| 10-noon.| 1-3. | 4-6. | 7-9. | 10-12.| + +--------+------+------+-----+---------+------+------+------+-------+ + | D | 14.9 | 11.1 | 8.0 | 5.2 | 5.7 | 13.1 | 22.5 | 19.5 | + | H | 10.5 | 8.4 | 8.0 | 8.5 | 11.3 | 17.6 | 19.2 | 16.5 | + | V | 13.5 | 9.7 | 5.7 | 4.7 | 8.5 | 17.2 | 21.5 | 19.2 | + +--------+------+------+-----+---------+------+------+------+-------+ + | Mean | 13.0 | 9.7 | 7.2 | 6.1 | 8.5 | 16.0 | 21.1 | 18.4 | + +--------+------+------+-----+---------+------+------+------+-------+ + + TABLE XXXV.--Disturbed Day less ordinary Day Inequality (Unit 1´, + to West). + + +------+------+------+------+------+------+------+------+------+------+------+------+------+ + | Hour.| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | + +------+------+------+------+------+------+------+------+------+------+------+------+------+ + | a.m. | -3.4 | -2.6 | -2.0 | -0.3 | +1.6 | +1.9 | +2.3 | +2.0 | +2.1 | +2.0 | +1.6 | +1.8 | + | p.m. | +1.8 | +2.2 | +2.1 | +1.7 | +1.4 | 0.0 | -1.3 | -2.8 | -3.5 | -2.6 | -3.5 | -2.4 | + +------+------+------+------+------+------+------+------+------+------+------+------+------+ + + One difficulty in the Potsdam procedure is the maintenance of a + uniform standard. Unless very frequent reference is made to the curves + of some standard year there must be a tendency to enter under "3" in + quiet years a number of hours which would be entered under "2" in a + highly disturbed year. Still, such a source of uncertainty is unlikely + to have much influence on the diurnal, or even on the annual, + variation. + + § 33. A third method of investigating a diurnal period in disturbances + is to form a diurnal inequality from disturbed days alone, and compare + it with the corresponding inequalities from ordinary or from quiet + days. Table XXXV. gives some declination data for Kew, the quantity + tabulated being the algebraic excess of the disturbed day hourly value + over that for the ordinary day in the mean diurnal inequality for the + year, as based on the 11 years 1890 to 1900. + + [Illustration: FIG. 11.] + + The disturbed day inequality was corrected for non-cyclic change in + the usual way. Fig. 11 shows the results of Table XXXV. graphically. + The irregularities are presumably due to the limited number, 209, of + disturbed days employed; to get a smooth curve would require probably + a considerably longer period of years. The differences between + disturbed and ordinary days at Kew are of the same general character + as those between ordinary and quiet days in Table XXIX.; they are, + however, very much larger, the range in Table XXXV. being fully 5½ + times that in Table XXIX. If quiet days had replaced ordinary days in + Table XXXV., the algebraic excess of the disturbed day would have + varied from +2´.7 at 2 p.m. to -4´.1 at 11 p.m., or a range of 6´.8. + + § 34. When the mean diurnal inequality in declination for the year at + Kew is analysed into Fourier waves, the chief difference, it will be + remembered, between ordinary and quiet days was that the amplitude of + the 24-hour term was enhanced in the ordinary days, whilst its phase + angle indicated an earlier occurrence of the maximum. Similarly, the + chief difference between the Fourier waves for the disturbed and + ordinary day inequalities at Kew is the increase in the amplitude of + the 24-hour term in the former by over 70%, and the earlier occurrence + of its maximum by about 1 hour 50 minutes. It is clear from these + results for Kew, and it is also a necessary inference from the + differences obtained by Sabine's method between east and west or + and + - disturbances, that there is present during disturbances some + influence which affects the diurnal inequality in a regular systematic + way, tending to make the value of the element higher during some hours + and lower during others than it is on days relatively free from + disturbance. At Kew the consequence is a notable increase in the range + of the regular diurnal inequality on disturbed days; but whether this + is the general rule or merely a local peculiarity is a subject for + further research. + + § 35. There are still other ways of attacking the problem of + disturbances. W. Ellis[27] made a complete list of disturbed days at + Greenwich from 1848 onwards, arranging them in classes according to + the amplitude of the disturbance shown on the curves. Of the 18,000 + days which he considered, Ellis regarded 2,119, or only about 12%, as + undisturbed. On 11,898 days, or 66%, the disturbance movement in + declination was under 10´; on 3614, or 20%, the disturbance, though + exceeding 10´, was under 30´; on 294 days it lay between 30´ and 60´; + while on 75 days it exceeded 60´. Taking each class of disturbances + separately, Ellis found, except in the case of his "minor" + disturbances--those under 10´--a distinct double annual period, with + maxima towards the equinoxes. Subsequently C. W. Maunder,[38] making + use of these same data, and of subsequent data up to 1902, put at his + disposal by Ellis, came to similar conclusions. Taking all the days + with disturbances of declination over 10´, and dealing with 15-day + periods, he found the maxima of frequency to occur the one a little + before the spring equinox, the other apparently after the autumnal + equinox; the two minima were found to occur early in June and in + January. When the year is divided into three seasons--winter (November + to February), summer (May to August), and equinox--Maunder's figures + lead to the results assigned to Greenwich disturbed days in Table + XXXVI. The frequency in winter, it will be noticed, though less than + at equinox, is considerably greater than in summer. This greater + frequency in winter is only slightly apparent in the disturbances over + 60´, but their number is so small that this may be accidental. The + next figures in Table XXXVI. relate to highly disturbed days at Kew. + The larger relative frequency at Kew in winter as compared to summer + probably indicates no real difference from Greenwich, but is simply a + matter of definition. The chief criterion at Kew for classifying the + days was not so much the mere amplitude of the largest movement, as + the general character of the day's curve and its departure from the + normal form. The data in Table XXXVI. as to magnetic storms at + Greenwich are based on the lists given by Maunder[39] in the _Monthly + Notices_, R.A.S. A storm may last for any time from a few hours to + several days, and during part of its duration the disturbance may not + be very large; thus it does not necessarily follow that the + frequencies of magnetic storms and of disturbed days will follow the + same laws. The table shows, however, that so far as Greenwich is + concerned the annual variations in the two cases are closely alike. In + addition to mean data for the whole 56 years, 1848 to 1903, Table + XXXVI. contains separate data for the 14 years of that period which + represented the highest sun-spot frequency, and the 15 years which + represented lowest sun-spot frequency. It will be seen that relatively + considered the seasonal frequencies of disturbance are more nearly + equal in the years of many than in those of few sun-spots. Storms are + more numerous as a whole in the years of many sun-spots, and this + preponderance is especially true of storms of the largest size. This + requires to be borne in mind in any comparisons between larger and + smaller storms selected promiscuously from a long period. An unduly + large proportion of the larger storms will probably come from years of + large sun-spot frequency, and there is thus a risk of assigning to + differences between the laws obeyed by large and small storms + phenomena that are due in whole or in part to differences between the + laws followed in years of many and of few sun-spots. The last data in + Table XXXVI. are based on statistics for Batavia given by W. van + Bemmelen,[40] who considers separately the storms which commence + suddenly and those which do not. These sudden movements are recorded + over large areas, sometimes probably all over the earth, if not + absolutely simultaneously, at least too nearly so for differences in + the time of occurrence to be shown by ordinary magnetographs. It is + ordinarily supposed that these sudden movements, and the storms to + which they serve as precursors, arise from some source extraneous to + the earth, and that the commencement of the movement intimates the + arrival, probably in the upper atmosphere, of some form of energy + transmitted through space. In the storms which commence gradually the + existence of a source external to the earth is not so prominently + suggested, and it has been sometimes supposed that there is a + fundamental difference between the two classes of storms. Table XXXVI. + shows, however, no certain difference in the annual variation at + Batavia. At the same time, this possesses much less significance than + it would have if Batavia were a station like Greenwich, where the + annual variation in magnetic storms is conspicuous. + + Besides the annual period, there seems to be also a well-marked + diurnal period in magnetic disturbances. This is apparent in Tables + XXXVII. and XXXVIII., which contain some statistics for Batavia due to + van Bemmelen, and some for Greenwich derived from the data in + Maunder's papers referred to above. Table XXXVII. gives the relative + frequency of occurrence for two hour intervals, starting with + midnight, treating separately the storms of gradual (g) and sudden (s) + commencement. In Table XXXVIII. the day is subdivided into three equal + parts. Batavia and Greenwich agree in showing maximum frequency of + beginnings about the time of minimum frequency of endings and + conversely; but the hours at which the respective maxima and minima + occur at the two places differ rather notably. + + § 36. There are peculiarities in the sudden movements ushering in + magnetic storms which deserve fuller mention. According to van + Bemmelen the impulse consists usually at some stations of a sudden + slight jerk of the magnet in one direction, followed by a larger + decided movement in the opposite direction, the former being often + indistinctly shown. Often we have at the very commencement but a faint + outline, and thereafter a continuous movement which is only sometimes + distinctly indicated, resulting after some minutes in the displacement + of the trace by a finite amount from the position it occupied on the + paper before the disturbance began. This may mean, as van Bemmelen + supposes, a small preliminary movement in the opposite direction to + the clearly shown displacement; but it may only mean that the magnet + is initially set in vibration, swinging on both sides of the position + of equilibrium, the real displacement of the equilibrium position + being all the time in the direction of the displacement apparent after + a few minutes. To prevent misconception, the direction of the + displacement apparent after a few minutes has been termed the + direction of the first _decided_ movement in Table XXXIX., which + contains some data as to the direction given by Ellis[41] and van + Bemmelen.[40] The + sign means an increase, the - sign a decrease of + the element. The sign is not invariably the same, it will be + understood, but there are in all cases a marked preponderance of + changes in the direction shown in the table. The fact that all the + stations indicated an increase in horizontal force is of special + significance. + + TABLE XXXVI.--Disturbances, and their Annual Distribution. + + +-------------------------------+-------+---------------------------+ + | | Total | Percentages. | + | |Number.+--------+---------+--------+ + | | | Winter.| Equinox.| Summer.| + +-------------------------------+-------+--------+---------+--------+ + | Greenwich disturbed days, | | | | | + | all, 1848-1902 | 4,214 | 33.9 | 39.2 | 26.9 | + | Greenwich disturbed days, | | | | | + | range 10´ to 30´, 1848-1902 | 3,830 | 33.9 | 39.0 | 27.1 | + | Greenwich disturbed days, | | | | | + | range 30´ to 60´, 1848-1902 | 307 | 34.5 | 41.0 | 24.4 | + | Greenwich disturbed days, | | | | | + | range over 60´, 1848-1902 | 77 | 29.9 | 41.6 | 28.6 | + | Kew highly disturbed days, | | | | | + | 1890-1900 | 209 | 38.3 | 41.6 | 20.1 | + | Greenwich magnetic storms, | | | | | + | all, 1848-1903 | 726 | 32.1 | 42.3 | 25.6 | + | Greenwich magnetic storms, | | | | | + | range 20´ to 30´, 1848-1903 | 392 | 30.1 | 43.6 | 26.3 | + | Greenwich magnetic storms, | | | | | + | range over 30´, 1848-1903 | 334 | 34.4 | 40.7 | 24.9 | + | Greenwich magnetic storms, | | | | | + | all, 14 years of S. max. | 258 | 35.3 | 38.0 | 26.7 | + | Greenwich magnetic storms, | | | | | + | all, 15 years of S. min. | 127 | 28.4 | 48.0 | 23.6 | + | Batavia magnetic storms, | | | | | + | all, 1883-1899 | 1,008 | 32.9 | 34.9 | 32.2 | + | Batavia magnetic storms of | | | | | + | gradual commencement | 679 | 32.4 | 34.8 | 32.8 | + | Batavia magnetic storms of | | | | | + | sudden commencement | 329 | 33.7 | 35.3 | 31.0 | + +-------------------------------+-------+--------+---------+--------+ + + TABLE XXXVII.--Batavia Magnetic Storms, Diurnal Distribution + (percentages). + + +--------------+----+----+----+----+----+----+----+----+----+----+----+----+ + | Hour. | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | + +--------------+----+----+----+----+----+----+----+----+----+----+----+----+ + | Beginning /g | 5 | 5 | 5 | 6 | 20 | 16 | 7 | 5 | 6 | 9 | 8 | 8 | + | \s | 7 | 5 | 7 | 10 | 10 | 11 | 10 | 8 | 8 | 9 | 8 | 7 | + | Maximum /g | 12 | 10 | 6 | 5 | 4 | 9 | 9 | 6 | 6 | 6 | 12 | 15 | + | \s | 14 | 7 | 5 | 2 | 2 | 9 | 9 | 5 | 8 | 10 | 13 | 16 | + | End all | 15 | 16 | 19 | 13 | 5 | 3 | 6 | 5 | 4 | 5 | 4 | 5 | + +--------------+----+----+----+----+----+----+----+----+----+----+----+----+ + + TABLE XXXVIII.--Greenwich Magnetic Storms, Diurnal Distribution. + + +------------------------+--------+-------+-----------------------------+ + | | | | Percentages. | + | Epoch. | Class. | Total +---------+---------+---------+ + | | |Number.| 1-8 p.m.| 9 p.m.- | 5 a.m.- | + | | | | | 4 a.m. | noon. | + +------------------------+--------+-------+---------+---------+---------+ + | / 1848-1903 | all | 721 | 60.1 | 21.9 | 18.0 | + | Beginning < 1882-1903 | " | 276 | 58.0 | 18.8 | 23.2 | + | \ " " | sudden | 77 | 45.4 | 27.3 | 27.3 | + | | | | | | | + | / 1848-1903 | all | 720 | 9.4 | 44.6 | 46.0 | + | End < 1882-1903 | " | 276 | 7.2 | 41.7 | 51.1 | + | \ " " | sudden | 77 | 11.7 | 35.1 | 53.2 | + +------------------------+--------+-------+---------+---------+---------+ + + § 37. That large magnetic disturbances occur simultaneously over large + areas was known in the time of Gauss, on whose initiative observations + were taken at 5-minute intervals at a number of stations on + prearranged _term days_. During March 1879 and August 1880 some large + magnetic storms occurred, and the magnetic curves showing these at a + number of stations fitted with Kew pattern magnetographs were compared + by W. G. Adams.[42] He found the more characteristic movements to be, + so far as could be judged, simultaneous at all the stations. At + comparatively near stations such as Stonyhurst and Kew, or Coimbra and + Lisbon, the curves were in general almost duplicates. At Kew and St + Petersburg there were usually considerable differences in detail, and + the movements were occasionally in opposite directions. The + differences between Toronto, Melbourne or Zi-ka-wei and the European + stations were still more pronounced. In 1896, on the initiative of M. + Eschenhagen,[43] eye observations of declination and horizontal force + were taken at 5-second intervals during prearranged hours at Batavia, + Manila, Melbourne and nine European stations. The data from one of + these occasions when appreciable disturbance prevailed were published + by Eschenhagen, and were subsequently analysed by Ad. Schmidt.[44] + Taking the stations in western Europe, Schmidt drew several series of + lines, each series representing the disturbing forces at one instant + of time as deduced from the departure of the elements at the several + stations from their undisturbed value. The lines answering to any one + instant had a general sameness of direction with more or less + divergence or convergence, but their general trend varied in a way + which suggested to Schmidt the passage of a species of vortex with + large but finite velocity. + + TABLE XXXIX.--Direction of First Decided Movement. + + +-----------+-------------+------------------+----------------+ + | Place. | Declination.| Horizontal Force.| Vertical Force.| + +-----------+-------------+------------------+----------------+ + | Pavlovsk | West | + | + | + | Potsdam | West | + | - | + | Greenwich | West | + | + | + | Zi-ka-wei | East | + | - | + | Kolaba | East | + | - | + | Batavia | West | + | - | + | Mauritius | East | + | + | + | Cape Horn | West | + | - | + +-----------+-------------+------------------+----------------+ + + The conclusion that magnetic disturbances tend to follow one another + at nearly equal intervals of time has been reached by several + independent observers. J. A. Broun[45] pronounced for a period of + about 26 days, and expressed a belief that a certain zone, or zones, + of the sun's surface might exert a prepotent influence on the earth's + magnetism during several solar rotations. Very similar views were + advanced in 1904 by E. W. Maunder,[39] who was wholly unaware of + Broun's work. Maunder concluded that the period was 27.28 days, + coinciding with the sun's rotation period relative to an observer on + the earth. Taking magnetic storms at Greenwich from 1882 to 1903, he + found the interval between the commencement of successive storms to + approach closely to the above period in a considerably larger number + of instances than one would have expected from mere chance. He found + several successions of three or four storms, and in one instance of as + many as six storms, showing his interval. In a later paper Maunder + reached similar results for magnetic storms at Greenwich from 1848 to + 1881. Somewhat earlier than Maunder, Arthur Harvey[46] deduced a + period of 27.246 days from a consideration of magnetic disturbances at + Toronto. A. Schuster,[47] examining Maunder's data mathematically, + concluded that they afforded rather strong evidence of a period of + about ½ (27.28) or 13.6 days. Maunder regarded his results as + _demonstrating_ that magnetic disturbances originate in the sun. He + regarded the solar action as arising from active areas of limited + extent on the sun's surface, and as propagated along narrow, well + defined streams. The active areas he believed to be also the seats of + the formation of sun-spots, but believed that their activity might + precede and outlive the visible existence of the sun-spot. + + Maunder did not discuss the physical nature of the phenomenon, but his + views are at least analogous to those propounded somewhat earlier by + Svante Arrhenius,[48] who suggested that small negatively charged + particles are driven from the sun by the repulsion of light and reach + the earth's atmosphere, setting up electrical currents, manifest in + aurora and magnetic disturbances. Arrhenius's calculations, for the + size of particle which he regarded as most probable, make the time of + transmission to the earth slightly under two days. Amongst other + theories which ascribe magnetic storms to direct solar action may be + mentioned that of Kr. Birkeland,[49] who believes the vehicle to be + cathode rays. Ch. Nordmann[50] similarly has suggested Röntgen rays. + Supposing the sun the ultimate source, it would be easier to + discriminate between the theories if the exact time of the originating + occurrence could be fixed. For instance, a disturbance that is + propagated with the velocity of light may be due to Röntgen rays, but + not to Arrhenius's particles. In support of his theory, Nordmann + mentions several cases when conspicuous visual phenomena on the sun + have synchronized with magnetic movements on the earth--the best known + instance being the apparent coincidence in time of a magnetic + disturbance at Kew on the 1st of September 1859 with a remarkable + solar outburst seen by R. C. Carrington. Presumably any electrical + phenomenon on the sun will set up waves in the aether, so transmission + of electric and magnetic disturbances from the sun to the earth with + the velocity of light is a certainty rather than a hypothesis; but it + by no means follows that the energy thus transmitted can give rise to + sensible magnetic disturbances. Also, when considering Nordmann's + coincidences, it must be remembered that magnetic movements are so + numerous that it would be singular if no apparent coincidences had + been noticed. Another consideration is that the movements shown by + ordinary magnetographs are seldom very rapid. During some storms, + especially those accompanied by unusually bright and rapidly varying + auroral displays, large to and fro movements follow one another in + close succession, the changes being sometimes too quick to be + registered distinctly on the photographic paper. This, however, is + exceptional, even in polar regions where disturbances are largest and + most numerous. As a rule, even when the change in the direction of + movement in the declination needle seems quite sudden, the movement in + one direction usually lasts for several minutes, often for 10, 15 or + 30 minutes. Thus the cause to which magnetic disturbances are due + seems in many cases to be persistent in one direction for a + considerable time. + + § 38. Attempts have been made to discriminate between the theories as + to magnetic storms by a critical examination of the phenomena. A + general connexion between sun-spot frequency and the amplitude of + magnetic movements, regular and irregular, is generally admitted. If + it is a case of cause and effect, and the interval between the solar + and terrestrial phenomena does not exceed a few hours, then there + should be a sensible connexion between corresponding daily values of + the sun-spot frequency and the magnetic range. Even if only some + sun-spots are effective, we should expect when we select from a series + of years two groups of days, the one containing the days of most + sun-spots, the other the days of least, that a prominent difference + will exist between the mean values of the absolute daily magnetic + ranges for the two groups. Conversely, if we take out the days of + small and the days of large magnetic range, or the days that are + conspicuously quiet and those that are highly disturbed, we should + expect a prominent difference between the corresponding mean sun-spot + areas. An application of this principle was made by Chree[23] to the + five quiet days a month selected by the astronomer royal between 1890 + and 1900. These days are very quiet relative to the average day and + possess a much smaller absolute range. One would thus have expected on + Birkeland's or Nordmann's theory the mean sun-spot frequency derived + from Wolfer's provisional values for these days to be much below his + mean value, 41.22, for the eleven years. It proved, however, to be + 41.28. This practical identity was as visible in 1892 to 1895, the + years of sun-spot maximum, as it was in the years of sun-spot minimum. + Use was next made of the Greenwich _projected_ sun-spot areas, which + are the result of exact measurement. The days of each month were + divided into three groups, the first and third--each normally of ten + days--containing respectively the days of largest and the days of + least sun-spot area. The mean sun-spot area from group 1 was on the + average about five times that for group 3. It was then investigated + how the astronomer royal's quiet days from 1890 to 1900, and how the + most disturbed days of the period selected from the Kew[24] magnetic + records, distributed themselves among the three groups of days. + Nineteen months were excluded, as containing more than ten days with + no sun-spots. The remaining 113 months contained 565 quiet and 191 + highly disturbed days, whose distribution was as follows: + + +----------------+---------+---------+---------+ + | | Group 1.| Group 2.| Group 3.| + | +---------+---------+---------+ + | Quiet days | 179 | 195 | 191 | + | Disturbed days | 68 | 65 | 58 | + +----------------+---------+---------+---------+ + + The group of days of largest sun-spot area thus contained slightly + under their share of quiet days and slightly over their share of + disturbed days. The differences, however, are not large, and in three + years, viz. 1895, 1897 and 1899, the largest number of disturbed days + actually occurred in group 3, while in 1895, 1896 and 1899 there were + fewer quiet days in group 3 than in group 1. Taking the same + distribution of days, the mean value of the absolute daily range of + declination at Kew was calculated for the group 1 and the group 3 days + of each month. The mean range from the group 1 days was the larger in + 57% of the individual months as against 43% in which it was the + smaller. When the days of each month were divided into groups + according to the absolute declination range at Kew, the mean sun-spot + area for the group 1 days (those of largest range) exceeded that for + the group 3 days (those of least range) in 55% of the individual + months, as against 45% of cases in which it was the smaller. + + Taking next the five days of largest and the five days of least range + in each month, sun-spot areas were got out not merely for these days + themselves, but also for the next subsequent day and the four + immediately preceding days in each case. On Arrhenius's theory we + should expect the magnetic range to vary with the sun-spot area, not + on the actual day but two days previously. The following figures give + the percentage excess or deficiency of the mean sun-spot area for the + respective groups of days, relative to the average value for the whole + epoch dealt with. n denotes the day to which the magnetic range + belongs, n + 1 the day after, n - 1 the day before, and so on. + Results are given for 1894 and 1895, the years which were on the whole + the most favourable and the least favourable for Arrhenius's + hypothesis, as well as for the whole eleven years. + + TABLE XL. + + +-------------------------+-------+-------+-------+-------+--------+-------+ + | Day. | n - 4 | n - 3 | n - 2 | n - 1 | n | n + 1 | + +-------------------------+-------+-------+-------+-------+--------+-------+ + | Five days of \ 1894 | +12 | + 9 | +11 | +12 | +11 | + 6 | + | largest range > 1895 | -16 | -17 | -15 | -12 | -11 | -10 | + | / 11 yrs. | + 9 | + 8 | + 8 | + 7 | + 5 | + 0.5| + | Five days of \ 1894 | -15 | -17 | -19 | -21 | -21 | -19 | + | least range > 1895 | +17 | +10 | + 1 | - 2 | - 2 | - 4 | + | / 11 yrs. | - 4 | - 4 | - 7 | - 7 | - 7 | - 6 | + +-------------------------+-------+-------+-------+-------+--------+-------+ + + Taking the 11-year-means we have the sun-spot area practically normal + on the day subsequent to the representative day of large magnetic + range, but sensibly above its mean on that day and still more so on + the four previous days. This suggests an emission from the sun taking + a highly variable time to travel to the earth. The 11-year mean data + for the five days of least range seem at first sight to point to the + same conclusion, but the fact that the deficiency in sun-spot area is + practically as prominent on the day after the representative day of + small magnetic range as on that day itself, or the previous days, + shows that the phenomenon is probably a secondary one. On the whole, + taking into account the extraordinary differences between the results + from individual years, we seem unable to come to any very positive + conclusion, except that in the present state of our knowledge little + if any clue is afforded by the extent of the sun's spotted area on any + particular day as to the magnetic conditions on the earth on that or + any individual subsequent day. Possibly some more definite information + might be extracted by considering the extent of spotted area on + different zones of the sun. On theories such as those of Arrhenius or + Maunder, effective bombardment of the earth would be more or less + confined to spotted areas in the zones nearest the centre of the + visible hemisphere, whilst all spots on this hemisphere contribute to + the total spotted area. Still the _projected_ area of a spot rapidly + diminishes as it approaches the edge of the visible hemisphere, i.e. + as it recedes from the most effective position, so that the method + employed above gives a preponderating weight to the central zones. One + rather noteworthy feature in Table XL. is the tendency to a sequence + in the figures in any one row. This seems to be due, at least in large + part, to the fact that days of large and days of small sun-spot area + tend to occur in groups. The same is true to a certain extent of days + of large and days of small magnetic range, but it is unusual for the + range to be much above the average for more than 3 or 4 successive + days. + + + Pulsations. + + § 39. The records from ordinary magnetographs, even when run at the + usual rate and with normal sensitiveness, not infrequently show a + repetition of regular or nearly regular small rhythmic movements, + lasting sometimes for hours. The amplitude and period on different + occasions both vary widely. Periods of 2 to 4 minutes are the most + common. W. van Bemmelen[51] has made a minute examination of these + movements from several years' traces at Batavia, comparing the results + with corresponding statistics sent him from Zi-ka-wei and Kew. Table + XLI. shows the diurnal variation in the frequency of occurrence of + these small movements--called _pulsations_ by van Bemmelen--at these + three stations. The Batavia results are from the years 1885 and 1892 + to 1898. Of the two sets of data for Zi-ka-wei (i) answers to the + years 1897, 1898 and 1900, as given by van Bemmelen, while (ii) + answers to the period 1900-1905, as given in the Zi-ka-wei _Bulletin_ + for 1905. The Kew data are for 1897. The results are expressed as + percentages of the total for the 24 hours. There is a remarkable + contrast between Batavia and Zi-ka-wei on the one hand and Kew on the + other, pulsations being much more numerous by night than by day at the + two former stations, whereas at Kew the exact reverse holds. Van + Bemmelen decided that almost all the occasions of pulsation at + Zi-ka-wei were also occasions of pulsations at Batavia. The hours of + commencement at the two places usually differed a little, occasionally + by as much as 20 minutes; but this he ascribed to the fact that the + earliest oscillations were too small at one or other of the stations + to be visible on the trace. Remarkable coincidence between pulsations + at Potsdam and in the north of Norway has been noted by Kr. + Birkeland.[49] + + With magnetographs of greater sensitiveness and more open time scales, + waves of shorter period become visible. In 1882 F. Kohlrausch[52] + detected waves with a period of about 12 seconds. Eschenhagen[53] + observed a great variety of short period waves, 30 seconds being + amongst the most common. Some of the records he obtained suggest the + superposition of regular sine waves of different periods. Employing a + very sensitive galvanometer to record changes of magnetic induction + through a coil traversed by the earth's lines of force, H. Ebert[54] + has observed vibrations whose periods are but a small fraction of a + second. The observations of Kohlrausch and Eschenhagen preceded the + recent great development of applications of electrical power, while + longer period waves are shown in the Kew curves of 50 years ago, so + that the existence of natural waves with periods of from a few seconds + up to several minutes can hardly be doubted. Whether the much shorter + period waves of Ebert are also natural is more open to doubt, as it is + becoming exceedingly difficult in civilized countries to escape + artificial disturbances. + + TABLE XLI.--Diurnal Distribution of Pulsations. + + +---------------+-----+-----+-----+--------+--------+-----+-----+------+ + | Hours. | 0-3.| 3-6.| 6-9.| 9-Noon.| Noon-3.| 3-6.| 6-9.| 9-12.| + +---------------+-----+-----+-----+--------+--------+-----+-----+------+ + | Batavia | 28 | 9 | 2 | 6 | 8 | 6 | 13 | 28 | + | Zi-ka-wei (i) | 33 | 5 | 2 | 7 | 4 | 4 | 10 | 35 | + | " (ii) | 23 | 6 | 8 | 11 | 7 | 5 | 14 | 26 | + | Kew | 4 | 8 | 19 | 14 | 22 | 18 | 11 | 4 | + +---------------+-----+-----+-----+--------+--------+-----+-----+------+ + + + Lunar Influence. + + § 40. The fact that the moon exerts a small but sensible effect on the + earth's magnetism seems to have been first discovered in 1841 by C. + Kreil. Subsequently Sabine[55] investigated the nature of the lunar + diurnal variation in declination at Kew, Toronto, Pekin, St Helena, + Cape of Good Hope and Hobart. The data in Table XLII. are mostly due + to Sabine. They represent the mean lunar diurnal inequality in + declination for the whole year. The unit employed is 0´.001, and as in + our previous tables + denotes movement to the _west_. By "mean + departure" is meant the arithmetic mean of the 24 hourly departures + from the mean value for the lunar day; the range is the difference + between the algebraically greatest and least of the hourly values. Not + infrequently the mean departure gives the better idea of the + importance of an inequality, especially when as in the present case + two maxima and minima occur in the day. This double daily period is + unusually prominent in the case of the lunar diurnal inequality, and + is seen in the other elements as well as in the declination. + + TABLE XLII.--Lunar Diurnal Inequality of Declination (unit 0´.001). + + +----------+-----------+-----------+-----------+-----------+-----------+-----------+ + | Lunar | Kew. | Toronto. | Batavia. | St Helena.| Cape. | Hobart. | + | Hour. | 1858-1862.| 1843-1848.| 1883-1899.| 1843-1847.| 1842-1846.| 1841-1848.| + +----------+-----------+-----------+-----------+-----------+-----------+-----------+ + | 0 | +103 | +315 | -70 | - 43 | -148 | - 98 | + | 1 | +160 | +275 | -63 | - 5 | -107 | -138 | + | 2 | +140 | +158 | -39 | + 37 | - 35 | -142 | + | 3 | + 33 | + 2 | - 8 | + 70 | + 43 | -107 | + | 4 | + 10 | -153 | +38 | + 85 | +108 | - 45 | + | 5 | - 67 | -265 | +63 | + 77 | +140 | + 27 | + | 6 | -150 | -302 | +87 | + 48 | +132 | + 88 | + | 7 | -188 | -255 | +77 | + 5 | + 82 | +122 | + | 8 | -160 | -137 | +40 | - 43 | + 5 | +120 | + | 9 | - 78 | + 7 | - 4 | - 82 | - 78 | + 82 | + | 10 | + 2 | +178 | -45 | -102 | -143 | + 17 | + | 11 | + 92 | +288 | -80 | - 98 | -177 | - 57 | + | 12 | +160 | +323 | -87 | - 73 | -165 | -120 | + | 13 | +188 | +272 | -68 | - 32 | -112 | -152 | + | 14 | +158 | +148 | -43 | + 13 | - 30 | -147 | + | 15 | + 90 | - 17 | - 8 | + 52 | + 58 | -105 | + | 16 | + 10 | -180 | +30 | + 73 | +132 | - 35 | + | 17 | - 85 | -297 | +62 | + 73 | +172 | + 45 | + | 18 | -142 | -337 | +72 | + 52 | +168 | +112 | + | 19 | -163 | -290 | +68 | + 17 | +122 | +152 | + | 20 | -147 | -170 | +52 | - 25 | + 45 | +152 | + | 21 | -123 | - 7 | + 8 | - 58 | - 40 | +113 | + | 22 | - 40 | +155 | -28 | - 73 | -112 | + 47 | + | 23 | + 27 | +265 | -56 | - 68 | -153 | - 30 | + +----------+-----------+-----------+-----------+-----------+-----------+-----------+ + | Mean De-\| | | | | | | + | parture /| 105 | 200 | 50 | 54 | 104 | 93 | + +----------+-----------+-----------+-----------+-----------+-----------+-----------+ + | Range | 376 | 660 | 174 | 187 | 349 | 304 | + +----------+-----------+-----------+-----------+-----------+-----------+-----------+ + + Lunar action has been specially studied in connexion with observations + from India and Java. Broun[56] at Trivandrum and C. Chambers[57] at + Kolaba investigated lunar action from a variety of aspects. At Batavia + van der Stok[58] and more recently S. Figee[59] have carried out + investigations involving an enormous amount of computation. Table + XLIII. gives a summary of Figee's results for the mean lunar diurnal + inequality at Batavia, for the two half-yearly periods April to + September (Winter or W.), and October to March (S.). The + sign + denotes movement to the west in the case of declination, but numerical + increase in the case of the other elements. In the case of H and T + (total force) the results for the two seasons present comparatively + small differences, but in the case of D, I and V the amplitude and + phase both differ widely. Consequently a mean lunar diurnal variation + derived from all the months of the year gives at Batavia, and + presumably at other tropical stations, an inadequate idea of the + importance of the lunar influence. In January Figee finds for the + range of the lunar diurnal inequality 0´.62 in D, 3.1[gamma] in H and + 3.5[gamma] in V, whereas the corresponding ranges in June are only + 0´.13, 1.1[gamma] and 2.2[gamma] respectively. The difference between + summer and winter is essentially due to solar action, thus the lunar + influence on terrestrial magnetism is clearly a somewhat complex + phenomenon. From a study of Trivandrum data, Broun concluded that the + action of the moon is largely dependent on the solar hour at the time, + being on the average about twice as great for a day hour as for a + night hour. Figee's investigations at Batavia point to a similar + conclusion. Following a method suggested by Van der Stok, Figee + arrives at a numerical estimate of the "lunar activity" for each hour + of the solar day, expressed in terms of that at noon taken as 100. In + summer, for instance, in the case of D he finds the "activity" varying + from 114 at 10 a.m. to only 8 at 9 p.m.; the corresponding extremes in + the case of H are 139 at 10 a.m. and 54 at 6 a.m. + + TABLE XLIII.--Lunar Diurnal Inequality at Batavia in Winter and Summer. + + +----------+---------------+----------------+----------------+----------------+----------------+ + | | Declination | Inclination, S.| H. (unit | V. (unit | T. (unit | + | | (unit 0´.001).| (unit 0´.001). | 0.01[gamma]). | 0.01[gamma]). | 0.01[gamma]). | + +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+ + | Lunar | | | | | | | | | | | + | Hour. | W. | S. | W. | S. | W. | S. | W. | S. | W. | S. | + +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+ + | 0 | +30 | -170 | - 1 | +25 | -15 | - 56 | - 9 | + 4 | - 17 | -47 | + | 1 | +21 | -147 | -23 | +49 | -40 | - 87 | -54 | +20 | - 61 | -67 | + | 2 | + 5 | - 83 | -49 | +69 | -25 | -107 | -82 | +37 | - 62 | -76 | + | 3 | - 5 | - 12 | -51 | +47 | -21 | - 76 | -83 | +24 | - 59 | -55 | + | 4 | + 1 | + 76 | -37 | +43 | -13 | - 59 | -58 | +18 | - 39 | -38 | + | 5 | - 8 | +134 | -23 | +12 | +10 | - 9 | -27 | +11 | - 4 | - 3 | + | 6 | - 7 | +181 | - 2 | -21 | +21 | + 43 | + 9 | - 6 | + 23 | +35 | + | 7 | -10 | +164 | +30 | -12 | +23 | + 45 | +55 | + 8 | + 47 | +43 | + | 8 | - 7 | + 86 | +36 | -21 | +38 | + 52 | +71 | - 1 | + 68 | +45 | + | 9 | - 8 | 0 | +28 | -23 | +46 | + 30 | +64 | -16 | + 71 | +19 | + | 10 | - 5 | - 85 | +34 | -20 | +13 | + 13 | +54 | -21 | + 38 | + 1 | + | 11 | -15 | -144 | +27 | -11 | -12 | - 6 | +31 | -19 | + 5 | -15 | + | 12 | - 9 | -164 | +19 | - 5 | -47 | - 23 | 0 | -19 | - 41 | -29 | + | 13 | + 1 | -136 | - 3 | +17 | -59 | - 46 | -36 | - 2 | - 69 | -41 | + | 14 | - 7 | - 79 | -13 | +27 | -66 | - 44 | -55 | +14 | - 84 | -32 | + | 15 | - 8 | - 8 | -32 | +25 | -53 | - 37 | -74 | +14 | - 82 | -26 | + | 16 | -12 | + 72 | -37 | +25 | -34 | - 17 | -70 | +26 | - 64 | - 2 | + | 17 | -13 | +137 | -33 | + 4 | - 1 | + 28 | -47 | +21 | - 24 | +35 | + | 18 | -21 | +165 | - 2 | -10 | +20 | + 47 | + 8 | +12 | + 21 | +47 | + | 19 | -12 | +147 | +21 | -42 | +44 | + 81 | +53 | -14 | + 64 | +64 | + | 20 | +10 | + 95 | +21 | -62 | +75 | +107 | +71 | -28 | +100 | +80 | + | 21 | +13 | + 4 | +26 | -70 | +65 | + 98 | +72 | -44 | + 92 | +65 | + | 22 | +25 | - 82 | +35 | -41 | +35 | + 35 | +68 | -38 | + 64 | +12 | + | 23 | +36 | -147 | +34 | - 4 | - 7 | - 14 | +44 | -13 | + 15 | -19 | + +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+ + | Mean De-\| | | | | | | | | | | + | parture /| 12 | 150 | 26 | 29 | 33 | 48 | 50 | 18 | 51 | 37 | + +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+ + | Range | 57 | 351 | 87 | 139 | 141 | 214 | 155 | 81 | 184 | 156 | + +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+ + + + The question whether lunar influence increases with sun-spot frequency + is obviously of considerable theoretical interest. Balfour Stewart in + the 9th edition of this encyclopaedia gave some data indicating an + appreciably enhanced lunar influence at Trivandrum during years of + sun-spot maximum, but he hesitated to accept the result as finally + proved. Figee recently investigated this point at Batavia, but with + inconclusive results. Attempts have also been made to ascertain how + lunar influence depends on the moon's declination and phase, and on + her distance from the earth. The difficulty in these investigations is + that we are dealing with a small effect, and a very long series of + data would be required satisfactorily to eliminate other periodic + influences. + + + Planetary Influence. + + § 41. From an analysis of seventeen years data at St Petersburg and + Pavlovsk, Leyst[60] concluded that all the principal planets sensibly + influence the earth's magnetism. According to his figures, all the + planets except Mercury--whose influence he found opposite to that of + the others--when nearest the earth tended to deflect the declination + magnet at St Petersburg to the west, and also increased the range of + the diurnal inequality of declination, the latter effect being the + more conspicuous. Schuster,[61] who has considered the evidence + advanced by Leyst from the mathematical standpoint, considers it to be + inconclusive. + + + Magnetic Surveys. + + § 42. The best way of carrying out a magnetic survey depends on where + it has to be made and on the object in view. The object that probably + still comes first in importance is a knowledge of the declination, of + sufficient accuracy for navigation in all navigable waters. One might + thus infer that magnetic surveys consist mainly of observations at + sea. This cannot however be said to be true of the past, whatever it + may be of the future, and this for several reasons. Observations at + sea entail the use of a ship, specially constructed so as to be free + from disturbing influence, and so are inherently costly; they are + also apt to be of inferior accuracy. It might be possible in quiet + weather, in a large vessel free from vibration, to observe with + instruments of the highest precision such as a unifilar magnetometer, + but in the ordinary surveying ship apparatus of less sensitiveness has + to be employed. The declination is usually determined with some form + of compass. The other elements most usually found directly at sea are + the inclination and the total force, the instrument employed being a + special form of inclinometer, such as the Fox circle, which was + largely used by Ross in the Antarctic, or in recent years the + Lloyd-Creak. This latter instrument differs from the ordinary + dip-circle fitted for total force observations after H. Lloyd's method + mainly in that the needles rest in pivots instead of on agate edges. + To overcome friction a projecting pin on the framework is scratched + with a roughened ivory plate. + + The most notable recent example of observations at sea is afforded by + the cruises of the surveying ships "Galilee" and "Carnegie" under the + auspices of the Carnegie Institution of Washington, which includes in + its magnetic programme a general survey. To see where the ordinary + land survey assists navigation, let us take the case of a country with + a long seaboard. If observations were taken every few miles along the + coast results might be obtained adequate for the ordinary wants of + coasting steamers, but it would be difficult to infer what the + declination would be 50 or even 20 miles off shore at any particular + place. If, however, the land area itself is carefully surveyed, one + knows the trend of the lines of equal declination, and can usually + extend them with considerable accuracy many miles out to sea. One also + can tell what places if any on the coast suffer from local + disturbances, and thus decide on the necessity of special + observations. This is by no means the only immediately useful purpose + which is or may be served by magnetic surveys on land. In Scandinavia + use has been made of magnetic observations in prospecting for iron + ore. There are also various geological and geodetic problems to whose + solution magnetic surveys may afford valuable guidance. Among the most + important recent surveys may be mentioned those of the British Isles + by A. Rücker and T. E. Thorpe,[62] of France and Algeria by + Moureaux,[63] of Italy by Chistoni and Palazzo,[64] of the Netherlands + by Van Ryckevorsel,[65] of South Sweden by Carlheim Gyllenskiöld,[66] + of Austria-Hungary by Liznar,[67] of Japan by Tanakadate,[68] of the + East Indies by Van Bemmelen, and South Africa by J. C. Beattie. A + survey of the United States has been proceeding for a good many years, + and many results have appeared in the publications of the U.S. Coast + and Geodetic Survey, especially Bauer's _Magnetic Tables and Magnetic + Charts_, 1908. Additions to our knowledge may also be expected from + surveys of India, Egypt and New Zealand. + + For the satisfactory execution of a land survey, the observers must + have absolute instruments such as the unifilar magnetometer and dip + circle, suitable for the accurate determination of the magnetic + elements, and they must be able to fix the exact positions of the + spots where observations are taken. If, as usual, the survey occupies + several years, what is wanted is the value of the elements not at the + actual time of observation, but at some fixed epoch, possibly some + years earlier or later. At a magnetic observatory, with standardized + records, the difference between the values of a magnetic element at + any two specified instants can be derived from the magnetic curves. + But at an ordinary survey station, at a distance from an observatory, + the information is not immediately available. Ordinarily the reduction + to a fixed epoch is done in at least two stages, a correction being + applied for secular change, and a second for the departure from the + mean value for the day due to the regular diurnal inequality and to + disturbance. + + The reduction to a fixed epoch is at once more easy and more accurate + if the area surveyed contains, or has close to its borders, a well + distributed series of magnetic observatories, whose records are + comparable and trustworthy. Throughout an area of the size of France + or Germany, the secular change between any two specified dates can + ordinarily be expressed with sufficient accuracy by a formula of the + type + + [delta] = [delta]0 + a(l - l0) + b([lambda] - [lambda]0) (i), + + where [delta] denotes secular change, l latitude and [lambda] + longitude, the letters with suffix _0_ relating to some convenient + central position. The constants [delta]0, a, b are to be determined + from the observed secular changes at the fixed observatories whose + geographical co-ordinates are accurately known. Unfortunately, as a + rule, fixed observatories are few in number and not well distributed + for survey purposes; thus the secular change over part at least of the + area has usually to be found by repeating the observations after some + years at several of the field stations. The success attending this + depends on the exactitude with which the sites can be recovered, on + the accuracy of the observations, and on the success with which + allowance is made for diurnal changes, regular and irregular. It is + thus desirable that the observations at repeat stations should be + taken at hours when the regular diurnal changes are slow, and that + they should not be accepted unless taken on days that prove to be + magnetically quiet. Unless the secular change is exceptionally rapid, + it will usually be most convenient in practice to calculate it from or + to the middle of the month, and then to allow for the difference + between the mean value for the month and the value at the actual hour + of observation. There is here a difficulty, inasmuch as the latter + part of the correction depends on the diurnal inequality, and so on + the local time of the station. No altogether satisfactory method of + surmounting this difficulty has yet been proposed. Rücker and Thorpe + in their British survey assumed that the divergence from the mean + value at any hour at any station might be regarded as made up of a + regular diurnal inequality, identical with that at Kew when both were + referred to _local_ time, and of a disturbance element identical with + that existing at the same absolute time at Kew. Suppose, for instance, + that at hour h G.M.T. the departure at Kew from the mean value for the + month is d, then the corresponding departure from the mean at a + station [lambda] degrees west of Kew is d - e, where e is the increase + in the element at Kew due to the regular diurnal inequality between + hour h - [lambda]/15 and hour h. This procedure is simple, but is + exposed to various criticisms. If we define a diurnal inequality as + the result obtained by combining hourly readings from all the days of + a month, we can assign a definite meaning to the diurnal inequality + for a particular month of a particular year, and after the curves have + been measured we can give exact numerical figures answering to this + definition. But the diurnal inequality thus obtained differs, as has + been pointed out, from that derived from a limited number of the + quietest days of the month, not merely in amplitude but in phase, and + the view that the diurnal changes on any individual day can be + regarded as made up of a regular diurnal inequality of definite + character and of a disturbance element is an hypothesis which is + likely at times to be considerably wide of the mark. The extent of the + error involved in assuming the regular diurnal inequality the same in + the north of Scotland, or the west of Ireland, as in the south-east of + England remains to be ascertained. As to the disturbance element, even + if the disturbing force were of given magnitude and direction all over + the British Isles--which we now know is often very far from the + case--its effects would necessarily vary very sensibly owing to the + considerable variation in the direction and intensity of the local + undisturbed force. If observations were confined to hours at which the + regular diurnal changes are slow, and only those taken on days of + little or no disturbance were utilized, corrections combining the + effects of regular and irregular diurnal changes could be derived from + the records of fixed observations, supposed suitably situated, + combined in formulae of the same type as (i). + + § 43. The field results having been reduced to a fixed epoch, it + remains to combine them in ways likely to be useful. In most cases the + results are embodied in charts, usually of at least two kinds, one set + showing only general features, the other the chief local + peculiarities. Charts of the first kind resemble the world charts + (figs. 1 to 4) in being free from sharp twistings and convolutions. In + these the declination for instance at a fixed geographical position on + a particular isogonal is to be regarded as really a mean from a + considerable surrounding area. + + Various ways have been utilized for arriving at these _terrestrial + isomagnetics_--as Rücker and Thorpe call them--of which an elaborate + discussion has been made by E. Mathias.[69] From a theoretical + standpoint the simplest method is perhaps that employed by Liznar for + Austria-Hungary. Let l and [lambda] represent latitude and longitude + relative to a certain central station in the area. Then assume that + throughout the area the value E of any particular magnetic element is + given by a formula + + E = E0 + al + b[lambda] + cl² + d[lambda]² + el[lambda], + + where E0, a, b, c, d, e are absolute constants to be determined from + the observations. When determining the constants, we write for E in + the equation the observed value of the element (corrected for secular + change, &c.) at each station, and for l and [lambda] the latitude and + longitude of the station relative to the central station. Thus each + station contributes an equation to assist in determining the six + constants. They can thus be found by least squares or some simpler + method. In Liznar's case there were 195 stations, so that the labour + of applying least squares would be considerable. This is one objection + to the method. A second is that it may allow undesirably large weight + to a few highly disturbed stations. In the case of the British Isles, + Rücker and Thorpe employed a different method. The area was split up + into _districts_. For each district a mean was formed of the observed + values of each element, and the mean was assigned to an imaginary + central station, whose geographical co-ordinates represented the mean + of the geographical co-ordinates of the actual stations. Want of + uniformity in the distribution of the stations may be allowed for by + weighting the results. Supposing E0 the value of the element found for + the central station of a district, it was assumed that the value E at + any actual station whose latitude and longitude exceeded those of the + central station by l and [lambda] was given by E = E0 + al + + b[lambda], with a and b constants throughout the district. Having + found E0, a and b, Rücker and Thorpe calculated values of the element + for points defined by whole degrees of longitude (from Greenwich) and + half degrees of latitude. Near the common border of two districts + there would be two calculated values, of which the arithmetic mean was + accepted. + + The next step was to determine by interpolation where isogonals--or + other isomagnetic lines--cut successive lines of latitude. The curves + formed by joining these successive points of intersection were called + _district_ lines or curves. Rücker and Thorpe's next step was to + obtain formulae by trial, giving smooth curves of continuous + curvature--terrestrial isomagnetics--approximating as closely as + possible to the district lines. The curves thus obtained had somewhat + complicated formulae. For instance, the isogonals south of 54°.5 + latitude were given for the epoch Jan. 1, 1891 by + + D = 18° 37´ + 18´.5(l - 49.5) - 3´.5 cos {45°(l - 49.5)} + + {26´.3 + 1´.5(l - 49.5)} ([lambda] - 4) + + 0´.01([lambda] - 4)² (l - 54.5)², + + where D denotes the westerly declination. Supposing, what is at least + approximately true, that the secular change in Great Britain since + 1891 has been uniform south of lat. 54°.5, corresponding formulae for + the epochs Jan. 1, 1901, and Jan. 1, 1906, could be obtained by + substituting for 18° 37´ the values 17° 44´ and 17° 24´ respectively. + In their very laborious and important memoir E. Mathias and B. + Baillaud[69] have applied to Rücker and Thorpe's observations a method + which is a combination of Rücker and Thorpe's and of Liznar's. Taking + Rücker and Thorpe's nine districts, and the magnetic data found for + the nine imaginary central stations, they employed these to determine + the six constants of Liznar's formula. This is an immense + simplification in arithmetic. The declination formula thus obtained + for the epoch Jan. 1, 1891, was + + D = 20° 45´.89 + .53474[lambda] + .34716l + .000021[lambda]² + + .000343l[lambda] - .000239l², + + where l + (53° 30´.5) represents the latitude, and ([lambda] + 5° + 35´.2) the west longitude of the station. From this and the + corresponding formulae for the other elements, values were calculated + for each of Rücker and Thorpe's 882 stations, and these were compared + with the observed values. A complete record is given of the + differences between the observed and calculated values, and of the + corresponding differences obtained by Rücker and Thorpe from their own + formulae. The mean numerical (calculated ~ observed) differences from + the two different methods are almost exactly the same--being + approximately 10´ for declination, 5´½ for inclination, and 70[gamma] + for horizontal force. The applications by Mathias[69] of his method to + the survey data of France obtained by Moureaux, and those of the + Netherlands obtained by van Rïjckevorsel, appear equally successful. + The method dispenses entirely with district curves, and the parabolic + formulae are perfectly straightforward both to calculate and to apply; + they thus appear to possess marked advantages. Whether the method + could be applied equally satisfactorily to an area of the size of + India or the United States actual trial alone would show. + + + Local Disturbances. + + § 44. Rücker and Thorpe regarded their terrestrial isomagnetics and + the corresponding formulae as representing the normal field that would + exist in the absence of disturbances peculiar to the neighbourhood. + Subtracting the forces derived from the formulae from those observed, + we obtain forces which may be ascribed to regional disturbance. + + When the vertical disturbing force is downwards, or the observed + vertical component larger than the calculated, Rücker and Thorpe + regard it as positive, and the loci where the largest positive values + occur they termed _ridge lines_. The corresponding loci where the + largest negative values occur were called _valley lines_. In the + British Isles Rücker and Thorpe found that almost without exception, + in the neighbourhood of a ridge line, the horizontal component of the + disturbing force pointed towards it, throughout a considerable area on + both sides. The phenomena are similar to what would occur if ridge + lines indicated the position of the summits of underground masses of + magnetic material, magnetized so as to attract the north-seeking pole + of a magnet. Rücker and Thorpe were inclined to believe in the real + existence of these subterranean magnetic mountains, and inferred that + they must be of considerable extent, as theory and observation alike + indicate that thin basaltic sheets or dykes, or limited masses of trap + rock, produce no measurable magnetic effect except in their immediate + vicinity. In support of their conclusions, Rücker and Thorpe dwell on + the fact that in the United Kingdom large masses of basalt such as + occur in Skye, Mull, Antrim, North Wales or the Scottish coalfield, + are according to their survey invariably centres of attraction for the + north-seeking pole of a magnet. Various cases of repulsion have, + however, been described by other observers in the northern hemisphere. + + § 45. Rücker and Thorpe did not make a very minute examination of + disturbed areas, so that purely local disturbances larger than any + noticed by them may exist in the United Kingdom. But any that exist + are unlikely to rival some that have been observed elsewhere, notably + those in the province of Kursk in Russia described by Moureaux[70] and + by E. Leyst.[71] In Kursk Leyst observed declinations varying from 0° + to 360°, inclinations varying from 39°.1 to 90°; he obtained values of + the horizontal force varying from 0 to 0.856 C.G.S., and values of the + vertical force varying from 0.371 to 1.836. Another highly disturbed + Russian district Krivoi Rog (48° N. lat. 33° E. long.) was + elaborately surveyed by Paul Passalsky.[72] The extreme values + observed by him differed, the declination by 282° 40´, the inclination + by 41° 53´, horizontal force by 0.658, and vertical force by 1.358. At + one spot a difference of 116°½ was observed between the declinations + at two positions only 42 metres apart. In cases such as the last + mentioned, the source of disturbance comes presumably very near the + surface. It is improbable that any such enormously rapid changes of + declination can be experienced anywhere at the surface of a deep + ocean. But in shallow water disturbances of a not very inferior order + of magnitude have been met with. Possibly the most outstanding case + known is that of an area, about 3 m. long by 1¼ m. at its widest, near + Port Walcott, off the N.W. Australian coast. The results of a minute + survey made here by H.M.S. "Penguin" have been discussed by Captain E. + W. Creak.[73] Within the narrow area specified, declination varied + from 26° W. to 56° E., and inclination from 50° to nearly 80°, the + observations being taken some 80 ft. above sea bottom. Another + noteworthy case, though hardly comparable with the above, is that of + East Loch Roag at Lewis in the Hebrides. A survey by H.M.S. "Research" + in water about 100 ft. deep--discussed by Admiral A. M. + Field[74]--showed a range of 11° in declination. The largest observed + disturbances in horizontal and vertical force were of the order 0.02 + and 0.05 C.G.S. respectively. An interesting feature in this case was + that vertical force was reduced, there being a well-marked valley + line. + + In some instances regional magnetic disturbances have been found to be + associated with geodetic anomalies. This is true of an elongated area + including Moscow, where observations were taken by Fritsche.[75] + Again, Eschenhagen[76] detected magnetic anomalies in an area + including the Harz Mountains in Germany, where deflections of the + plumb line from the normal had been observed. He found a magnetic + ridge line running approximately parallel to the line of no deflection + of the plumb line. + + § 46. A question of interest, about which however not very much is + known, is the effect of local disturbance on secular change and on the + diurnal inequality. The determination of secular change in a highly + disturbed locality is difficult, because an unintentional slight + change in the spot where the observations are made may wholly falsify + the conclusions drawn. When the disturbed area is very limited in + extent, the magnetic field may reasonably be regarded as composed of + the normal field that would have existed in the absence of local + disturbance, plus a disturbance field arising from magnetic material + which approaches nearly if not quite to the surface. Even if no + sensible change takes place in the disturbance field, one would hardly + expect the secular change to be wholly normal. The changes in the + rectangular components of the force may possibly be the same as at a + neighbouring undisturbed station, but this will not give the same + change in declination and inclination. In the case of the diurnal + inequality, the presumption is that at least the declination and + inclination changes will be influenced by local disturbance. If, for + example, we suppose the diurnal inequality to be due to the direct + influence of electric currents in the upper atmosphere, the + declination change will represent the action of the component of a + force of given magnitude which is perpendicular to the position of the + compass needle. But when local disturbance exists, the direction of + the needle and the intensity of the controlling field are both altered + by the local disturbance, so it would appear natural for the + declination changes to be influenced also. This conclusion seems borne + out by observations made by Passalsky[72] at Krivoi Rog, which showed + diurnal inequalities differing notably from those experienced at the + same time at Odessa, the nearest magnetic observatory. One station + where the horizontal force was abnormally low gave a diurnal range of + declination four times that at Odessa; on the other hand, the range of + the horizontal force was apparently reduced. It would be unsafe to + draw general conclusions from observations at two or three stations, + and much completer information is wanted, but it is obviously + desirable to avoid local disturbance when selecting a site for a + magnetic observatory, assuming one's object is to obtain data + reasonably applicable to a large area. In the case of the older + observatories this consideration seems sometimes to have been lost + sight of. At Mauritius, for instance, inside of a circle of only 56 + ft. radius, having for centre the declination pillar of the absolute + magnetic hut of the Royal Alfred Observatory, T. F. Claxton[77] found + that the declination varied from 4° 56´ to 13° 45´ W., the inclination + from 50° 21´ to 58° 34´ S., and the horizontal force from 0.197 to + 0.244 C.G.S. At one spot he found an alteration of 1°1/3 in the + declination when the magnet was lowered from 4 ft. above the ground to + 2. Disturbances of this order could hardly escape even a rough + investigation of the site. + + + Gaussian Potential and Constants. + + § 47. If we assume the magnetic force on the earth's surface derivable + from a potential V, we can express V as the sum of two series of solid + spherical harmonics, one containing negative, the other positive + integral powers of the radius vector r from the earth's centre. Let + [lambda] denote east longitude from Greenwich, and let µ = cos(½[pi] - + l), where l is latitude; and also let + _ _ + | (n - m)(n - m - 1) | + H_n^m = (1 - µ²)^(½m) |µ^(n-m) - ------------------ µ^(n-m-2) + ...|, + |_ 2(2n - 1) _| + + where n and m denote any positive integers, m being not greater than + n. Then denoting the earth's radius by R, we have + + V/R = [Sigma](R/r)^(n+1) [H_n^m (g_n^m cos m[lambda] + h_n^m sin m[lambda])] + + [Sigma](r/R)^n [H_n^m (g_(-n)^m cos m[lambda] + h_(-n)^m sin m[lambda])], + + where [Sigma] denotes summation of m from 0 to n, followed by + summation of n from 0 to [infinity]. In this equation g_n^m, &c. are + constants, those with positive suffixes being what are generally + termed _Gaussian constants_. The series with negative powers of r + answers to forces with a source internal to the earth, the series with + positive powers to forces with an external source. Gauss found that + forces of the latter class, if existent, were very small, and they are + usually left out of account. There are three Gaussian constants of the + first order, g1^0, g1¹, h1¹, five of the second order, seven of the + third, and so on. The coefficient of a Gaussian constant of the n^th + order is a spherical harmonic of the n^th degree. If R be taken as + unit length, as is not infrequent, the first order terms are given by + + V1 = r^(-2) [g1^0 sin l + (g1¹ cos [lambda] + h1¹ sin [lambda]) cos l]. + + The earth is in reality a spheroid, and in his elaborate work on the + subject J. C. Adams[78] develops the treatment appropriate to this + case. Here we shall as usual treat it as spherical. We then have for + the components of the force at the surface + + X = -R^(-1)(1 - µ²)^½ (dV/dµ) towards the astronomical north, + Y = -R^(-1)(1 - µ²)^-½ (dV/d[lambda]) " " " west, + Z = -dV/dr vertically downwards. + + Supposing the Gaussian constants known, the above formulae would give + the force all over the earth's surface. To determine the Gaussian + constants we proceed of course in the reverse direction, equating the + observed values of the force components to the theoretical values + involving g_n^m, &c. If we knew the values of the component forces at + regularly distributed stations all over the earth's surface, we could + determine each Gaussian constant independently of the others. Our + knowledge however of large regions, especially in the Arctic and + Antarctic, is very scanty, and in practice recourse is had to methods + in which the constants are not determined independently. The + consequence is unfortunately that the values found for some of the + constants, even amongst the lower orders, depend very sensibly on how + large a portion of the polar regions is omitted from the calculations, + and on the number of the constants of the higher orders which are + retained. + + TABLE XLIV.--Gaussian Constants of the First Order. + + +------+---------+---------+---------+---------+---------+---------+---------+ + | | 1829 | | | | | | | + | | Erman- | 1830 | 1845 | 1880 | 1885 | 1885 | 1885 | + | |Petersen.| Gauss. | Adams. | Adams. |Neumayer.| Schmidt.|Fritsche.| + +------+---------+---------+---------+---------+---------+---------+---------+ + | g1^0 | +.32007 | +.32348 | +.32187 | +.31684 | +.31572 | +.31735 | +.31635 | + | g1^1 | +.02835 | +.03111 | +.02778 | +.02427 | +.02481 | +.02356 | +.02414 | + | h1^1 | -.06011 | -.06246 | -.05783 | -.06030 | -.06026 | -.05984 | -.05914 | + +------+---------+---------+---------+---------+---------+---------+---------+ + + Table XLIV. gives the values obtained for the Gaussian constants of + the first order in some of the best-known computations, as collected + by W. G. Adams.[79] + + § 48. Allowance must be made for the difference in the epochs, and for + the fact that the number of constants assumed to be worth retaining + was different in each case. Gauss, for instance, assumed 24 constants + sufficient, whilst in obtaining the results given in the table J. C. + Adams retained 48. Some idea of the uncertainty thus arising may be + derived from the fact that when Adams assumed 24 constants sufficient, + he got instead of the values in the table the following:-- + + g1^0 g1¹ h1¹ + + 1842-1845 +.32173 +.02833 -.05820 + 1880 +.31611 +.02470 -.06071 + + Some of the higher constants were relatively much more affected. Thus, + on the hypotheses of 48 and of 24 constants respectively, the values + obtained for g2^0 in 1842-1845 were -.00127 and -.00057, and those + obtained for h3¹ in 1880 were +.00748 and +.00573. It must also be + remembered that these values assume that the series in positive powers + of r, with coefficients having negative suffixes, is absolutely + non-existent. If this be not assumed, then in any equation determing X + or Y, g_n^m must be replaced by g_n^m + g_(-n)^m, and in any equation + determining Z by g_n^m - n/(n + 1) g_n^m; similar remarks apply to + h_n^m and h_(-n)^m. It is thus theoretically possible to check the + truth of the assumption that the positive power series is non-existent + by comparing the values obtained for g_n^m and h_n^m from the X and Y + or from the Z equations, when g_(-n)^m and h_(-n)^m are assumed zero. + If the values so found differ, values can be found for g_(-n)^m and + h_(-n)^m which will harmonize the two sets of equations. Adams gives + the values obtained from the X, Y and the Z equations separately for + the Gaussian constants. The following are examples of the values + thence deducible for the coefficients of the positive power series:-- + + g_(-1)^0 g_(-1)^1 h_(-1)^1 g_(-4)^0 g_(-5)^0 g_(-6)^0 + + 1842-1845 +.0018 -.0002 -.0014 +.0064 +.0072 +.0124 + 1880 -.0002 -.0012 +.0015 -.0043 -.0021 -.0013 + + Compared to g4^0, g5^0 and g6^0 the values here found for g_(-4)^0, + g_(-5)^0 and g_(-6)^0 are far from insignificant, and there would be + no excuse for neglecting them if the observational data were + sufficient and reliable. But two outstanding features claim attention, + first the smallness of g_(-1)^0, g_(-1)^1 and h_(-1)^1, the + coefficients least likely to be affected by observational + deficiencies, and secondly the striking dissimilarity between the + values obtained for the two epochs. The conclusion to which these and + other facts point is that observational deficiencies, even up to the + present date, are such that no certain conclusion can be drawn as to + the existence or non-existence of the positive power series. It is + also to be feared that considerable uncertainties enter into the + values of most of the Gaussian constants, at least those of the higher + orders. The introduction of the positive power series necessarily + improves the agreement between observed and calculated values of the + force, but it is more likely than not to be disadvantageous + physically, if the differences between observed values and those + calculated from the negative power series alone arise in large measure + from observational deficiencies. + + TABLE XLV.--Axis and Moment of First Order Gaussian Coefficients. + + +-------+-------------------+-----------+------------+--------------+ + | Epoch.| Authority for | North | West | M/R³ in | + | | Constants. | Latitude. | Longitude. | G.C.S. units.| + +-------+-------------------+-----------+------------+--------------+ + | | | ° ´ | ° ´ | | + | 1650 | H. Fritsche | 82 50 | 42 55 | .3260 | + | 1836 | " | 78 27 | 63 35 | .3262 | + | 1845 | J. C. Adams | 78 44 | 64 20 | .3282 | + | 1880 | " | 78 24 | 68 4 | .3234 | + | 1885 | Neumayer-Petersen | | | | + | | and Bauer | 78 3 | 67 3 | .3224 | + | 1885 | Neumayer, Schmidt | 78 34 | 68 31 | .3230 | + +-------+-------------------+-----------+------------+--------------+ + + § 49. The first order Gaussian constants have a simple physical + meaning. The terms containing them represent the potential arising + from the uniform magnetization of a sphere parallel to a fixed axis, + the moment M of the spherical magnet being given by + + M = R³{(g1^0)² + (g1^1)² + (h1^1)²}^½, + + where R is the earth's radius. The position of the north end of the + axis of this uniform magnetization and the values of M/R^3, derived + from the more important determinations of the Gaussian constants, are + given in Table XLV. The data for 1650 are of somewhat doubtful value. + If they were as reliable as the others, one would feel greater + confidence in the reality of the apparent movement of the north end of + the axis from east to west. The table also suggests a slight + diminution in M since 1845, but it is open to doubt whether the + apparent change exceeds the probable error in the calculated values. + It should be carefully noticed that the data in the table apply only + to the first order Gaussian terms, and so only to a portion of the + earth's magnetization, and that the Gaussian constants have been + calculated on the assumption that the negative power series alone + exists. The field answering to the first order terms--or what Bauer + has called the _normal_ field--constitutes much the most important + part of the whole magnetization. Still what remains is very far from + negligible, save for rough calculations. It is in fact one of the weak + points in the Gaussian analysis that when one wishes to represent the + observed facts with high accuracy one is obliged to retain so many + terms that calculation becomes burdensome. + + + Earth-air Currents. + + § 50. The possible existence of a positive power series is not the + only theoretical uncertainty in the Gaussian analysis. There is the + further possibility that part of the earth's magnetic field may not + answer to a potential at all. Schmidt[80] in his calculation of + Gaussian constants regarded this as a possible contingency, and the + results he reached implied that as much as 2 or 3% of the entire field + had no potential. If the magnetic force F on the earth's surface comes + from a potential, then the line integral [int]F ds taken round any + closed circuit s should vanish. If the integral does not vanish, it + equals 4[pi]I, where I is the total electric current traversing the + area bounded by s. A + sign in the result of the integration means + that the current is downwards (i.e. from air to earth) or upwards, + according as the direction of integration round the circuit, as viewed + by an observer above ground, has been clockwise or anti-clockwise. In + applications of the formula by W. von Bezold[81] and Bauer[82] the + integral has been taken along parallels of latitude in the direction + west to east. In this case a + sign indicates a resultant upward + current over the area between the parallel of latitude traversed and + the north geographical pole. The difference between the results of + integration round two parallels of latitude gives the total vertical + current over the zone between them. Schmidt's final estimate of the + average intensity of the earth-air current, irrespective of sign, for + the epoch 1885 was 0.17 ampere per square kilometre. Bauer employing + the same observational data as Schmidt, reached somewhat similar + conclusions from the differences between integrals taken round + parallels of latitude at 5° intervals from 60° N. to 60° S. H. + Fritsche[83] treating the problem similarly, but for two epochs, 1842 + and 1885, got conspicuously different results for the two epochs, + Bauer[84] has more recently repeated his calculations, and for three + epochs, 1842-1845 (Sabine's charts), 1880 (Creak's charts), and 1885 + (Neumayer's charts), obtaining the mean value of the current per sq. + km. for 5° zones. Table XLVI. is based on Bauer's figures, the unit + being 0.001 ampere, and + denoting an _upwardly_ directed current. + + TABLE XLVI.--Earth-air Currents, after Bauer. + + +-------------+----------------------+---------------------+ + | | Northern Hemisphere. | Southern Hemisphere.| + | Latitude. +--------+------+------+-------+------+------+ + | | 1842-5.| 1880.| 1885.|1842-5.| 1880.| 1885.| + +-------------+--------+------+------+-------+------+------+ + | 0° to 15° | - 1 | -32 | -34 | +66 | + 30 | + 36 | + | 15° " 30° | -70 | -59 | -68 | + 2 | - 62 | - 63 | + | 30° " 45° | + 3 | +14 | -22 | +26 | - 11 | - 14 | + | 45° " 60° | -31 | -21 | +78 | + 5 | +276 | +213 | + +-------------+--------+------+------+-------+------+------+ + + In considering the significance of the data in Table XLVI., it should + be remembered that the currents must be regarded as mean values + derived from all hours of the day, and all months of the year. + Currents which were upwards during certain hours of the day, and + downwards during others, would affect the diurnal inequality; while + currents which were upwards during certain months, and downwards + during others, would cause an annual inequality in the absolute + values. Thus, if the figures be accepted as real, we must suppose that + between 15° N. and 30° N. there are preponderatingly downward + currents, and between 0° S. and 15° S. preponderatingly upward + currents. Such currents might arise from meteorological conditions + characteristic of particular latitudes, or be due to the relative + distribution of land and sea; but, whatever their cause, any + considerable real change in their values between 1842 and 1885 seems + very improbable. The most natural cause to which to attribute the + difference between the results for different epochs in Table XLVI. is + unquestionably observational deficiencies. Bauer himself regards the + results for latitudes higher than 45° as very uncertain, but he seems + inclined to accept the reality of currents of the average intensity of + 1/30 ampere per sq. km. between 45° N. and 45° S. + + Currents of the size originally deduced by Schmidt, or even those of + Bauer's latest calculations, seem difficult to reconcile with the + results of atmospheric electricity (q.v.). + + § 51. There is no single parallel of latitude along the whole of which + magnetic elements are known with high precision. Thus results of + greater certainty might be hoped for from the application of the line + integral to well surveyed countries. Such applications have been made, + e.g. to Great Britain by Rücker,[85] and to Austria by Liznar,[86] but + with negative results. The question has also been considered in detail + by Tanakadate[68] in discussing the magnetic survey of Japan. He makes + the criticism that the taking of a line integral round the _boundary_ + of a surveyed area amounts to utilizing the values of the magnetic + elements where least accurately known, and he thus considers it + preferable to replace the line integral by the surface integral. + + 4[pi]I = [int][int] (dY/dx - dX/dy) dx dy. + + He applied this formula not merely to his own data for Japan, but also + to British and Austrian data of Rücker and Thorpe and of Liznar. The + values he ascribes to X and Y are those given by the formulae + calculated to fit the observations. The result reached was "a line of + no current through the middle of the country; in Japan the current is + upward on the Pacific side and downward on the Siberian side; in + Austria it is upward in the north and downward in the south; in Great + Britain upward in the east and downward in the west." The results + obtained for Great Britain differed considerably according as use was + made of Rücker and Thorpe's own district equations or of a series of + general equations of the type subsequently utilized by Mathias. + Tanakadate points out that the fact that his investigations give in + each case a line of no current passing through the middle of the + surveyed area, is calculated to throw doubt on the reality of the + supposed earth-air currents, and he recommends a suspension of + judgment. + + § 52. A question of interest, and bearing a relationship to the + Gaussian analysis, is the law of variation of the magnetic elements + with height above sea-level. If F represent the value at sea-level, + and F + [delta]F that at height h, of any component of force answering + to Gaussian constants of the n^th order, then 1 + [delta]F/F = (1 + + h/R)^(-n-2), where R is the earth's radius. Thus at heights of only a + few miles we have very approximately [delta]F/F = -(n + 2)h/R. As we + have seen, the constants of the first order are much the most + important, thus we should expect as a first approximation [delta]X/X = + [delta]Y/Y = [delta]Z/Z = -3h/R. This equation gives the same rate of + decrease in all three components, and so no change in declination or + inclination. Liznar[86a] compared this equation with the observed + results of his Austrian survey, subdividing his stations into three + groups according to altitude. He considered the agreement not + satisfactory. It must be remembered that the Gaussian analysis, + especially when only lower order terms are retained, applies only to + the earth's field freed from local disturbances. Now observations at + individual high level stations may be seriously influenced not merely + by regional disturbances common to low level stations, but by magnetic + material in the mountain itself. A method of arriving at the vertical + change in the elements, which theoretically seems less open to + criticism, has been employed by A. Tanakadate.[68] If we assume that a + potential exists, or if admitting the possibility of earth-air + currents we assume their effort negligible, we have dX/dz = dZ/dx, + dY/dz = dZ/dy. Thus from the observed rates of change of the vertical + component of force along the parallels of latitude and longitude, we + can deduce the rate of change in the vertical direction of the two + rectangular components of horizontal force, and thence the rates of + change of the horizontal force and the declination. Also we have dZ/dz + = 4[pi][rho] - (dX/dx + dY/dy), where [rho] represents the density of + free magnetism at the spot. The spot being above ground we may neglect + [rho], and thus deduce the variation in the vertical direction of the + vertical component from the observed variations of the two horizontal + components in their own directions. Tanakadate makes a comparison of + the vertical variations of the magnetic elements calculated in the two + ways, not merely for Japan, but also for Austria-Hungary and Great + Britain. In each country he took five representative points, those for + Great Britain being the central stations of five of Rücker and + Thorpe's districts. Table XLVII. gives the mean of the five values + obtained. By method (i.) is meant the formula involving 3h/R, by + method (ii.) Tanakadate's method as explained above. H, V, D, and I + are used as defined in § 5. In the case of H and V unity represents + 1[gamma]. + + TABLE XLVII.--Change per Kilometre of Height. + + +---------+-----------------+-----------------+-----------------+ + | | Great Britain. | Austria-Hungary.| Japan. | + +---------+-------+---------+-------+---------+-------+---------+ + | Method. | (i.) | (ii.) | (i.) | (ii.) | (i.) | (ii.) | + +---------+-------+---------+-------+---------+-------+---------+ + | H | - 8.1 | - 6.7 | -10.1 | - 8.7 | -13.9 | -14.0 | + | V | -21.2 | -19.4 | -19.0 | -18.1 | -17.1 | -17.4 | + | D (west)| .. | - 0´.04 | .. | + 0´.10 | .. | - 0´.27 | + | I | .. | - 0´.05 | .. | - 0´.06 | .. | - 0´.01 | + +---------+-------+---------+-------+---------+-------+---------+ + + The - sign in Table XLVII. denotes a decrease in the numerical values + of H, V and I, and a diminution in westerly declination. If we except + the case of the westerly component of force--not shown in the + table--the accordance between the results from the two methods in the + case of Japan is extraordinarily close, and there is no very marked + tendency for the one method to give larger values than the other. In + the case of Great Britain and Austria the differences between the two + sets of calculated values though not large are systematic, the 3h/R + formula invariably showing the larger reduction with altitude in both + H and V. Tanakadate was so satisfied with the accordance of the two + methods in Japan, that he employed his method to reduce all observed + Japanese values to sea-level. At a few of the highest Japanese + stations the correction thus introduced into the value of H was of + some importance, but at the great majority of the stations the + corrections were all insignificant. + + + Schuster's Diurnal Variation Potential. + + § 53. Schuster[87] has calculated a potential analogous to the + Gaussian potential, from which the regular diurnal changes of the + magnetic elements all over the earth may be derived. From the mean + summer and winter diurnal variations of the northerly and easterly + components of force during 1870 at St Petersburg, Greenwich, Lisbon + and Bombay, he found the values of 8 constants analogous to Gaussian + constants; and from considerations as to the hours of occurrence of + the maxima and minima of vertical force, he concluded that the + potential, unlike the Gaussian, must proceed in positive powers of r, + and so answer to forces external to the earth. Schuster found, + however, that the calculated amplitudes of the diurnal vertical force + inequality did not accord well with observation; and his conclusion + was that while the original cause of the diurnal variation is + external, and consists probably of electric currents in the + atmosphere, there are induced currents inside the earth, which + increase the horizontal components of the diurnal inequality while + diminishing the vertical. The problem has also been dealt with by H. + Fritsche,[88] who concludes, in opposition to Schuster, that the + forces are partly internal and partly external, the two sets being of + fairly similar magnitude. Fritsche repeats the criticism (already made + in the last edition of this encyclopaedia) that Schuster's four + stations were too few, and contrasts their number with the 27 from + which his own data were derived. On the other hand, Schuster's data + referred to one and the same year, whereas Fritsche's are from epochs + varying from 1841 to 1896, and represent in some cases a single year's + observations, in other cases means from several years. It is clearly + desirable that a fresh calculation should be made, using synchronous + data from a considerable number of well distributed stations; and it + should be done for at least two epochs, one representing large, the + other small sun-spot frequency. The year 1870 selected by Schuster + had, as it happened, a sun-spot frequency which has been exceeded + only once since 1750; so that the magnetic data which he employed were + far from representative of average conditions. + + + Magnetization of Vases, &c. + + § 54. It was discovered by Folgheraiter[89] that old vases from + Etruscan and other sources are magnetic, and from combined observation + and experiment he concluded that they acquired their magnetization + when cooling after being baked, and retained it unaltered. From + experiments, he derived formulae connecting the magnetization shown by + new clay vases with their orientation when cooling in a magnetic + field, and applying these formulae to the phenomena observed in the + old vases he calculated the magnetic dip at the time and place of + manufacture. His observations led him to infer that in Central Italy + inclination was actually southerly for some centuries prior to 600 + B.C., when it changed sign. In 400 B.C. it was about 20°N.; since 100 + B.C. the change has been relatively small. L. Mercanton[90] similarly + investigated the magnetization of baked clay vases from the lake + dwellings of Neuchatel, whose epoch is supposed to be from 600 to 800 + B.C. The results he obtained were, however, closely similar to those + observed in recent vases made where the inclination was about 63°N., + and he concluded in direct opposition to Folgheraiter that inclination + in southern Europe has not undergone any very large change during the + last 2500 years. Folgheraiter's methods have been extended to natural + rocks. Thus B. Brunhes[91] found several cases of clay metamorphosed + by adjacent lava flows and transformed into a species of natural + brick. In these cases the clay has a determinate direction of + magnetization agreeing with that of the volcanic rock, so it is + natural to assume that this direction coincided with that of the dip + when the lava flow occurred. In drawing inferences, allowance must of + course be made for any tilting of the strata since the volcanic + outburst. From one case in France in the district of St Flour, where + the volcanic action is assigned to the Miocene Age, Brunhes inferred a + southerly dip of some 75°. Until a variety of cases have been + critically dealt with, a suspension of judgment is advisable, but if + the method should establish its claims to reliability it obviously may + prove of importance to geology as well as to terrestrial magnetism. + + + Polar Phenomena. + + § 55. Magnetic phenomena in the polar regions have received + considerable attention of late years, and the observed results are of + so exceptional a character as to merit separate consideration. One + feature, the large amplitude of the regular diurnal inequality, is + already illustrated by the data for Jan Mayen and South Victoria Land + in Tables VIII. to XI. In the case, however, of declination allowance + must be made for the small size of H. If a force F perpendicular to + the magnetic meridian causes a change [Delta]D in D then [Delta]D = + F/H. Thus at the "Discovery's" winter quarters in South Victoria Land, + where the value of H is only about 0.36 of that at Kew, a change of + 45´ in D would be produced by a force which at Kew would produce a + change of only 16´. Another feature, which, however, may not be + equally general, is illustrated by the data for Fort Rae and South + Victoria Land in Table XVII. It will be noticed that it is the 24-hour + term in the Fourier analysis of the regular diurnal inequality which + is specially enhanced. The station in South Victoria Land--the winter + quarters of the "Discovery" in 1902-1904--was at 77° 51´ S. lat.; thus + the sun did not set from November to February (midsummer), nor rise + from May to July (midwinter). It might not thus have been surprising + if there had been an outstandingly large seasonal variation in the + type of the diurnal inequality. As a matter of fact, however, the type + of the inequality showed exceptionally small variation with the + season, and the amplitude remained large throughout the whole year. + Thus, forming diurnal inequalities for the three midsummer months and + for the three midwinter months, we obtain the following amplitudes for + the range of the several elements[92]:-- + + D. H. V. I. + + Midsummer 64´.1 57[gamma] 58[gamma] 2´.87 + Midwinter 26´.8 25[gamma] 18[gamma] 1´.23 + + The most outstanding phenomenon in high latitudes is the frequency and + large size of the disturbances. At Kew, as we saw in § 25, the + absolute range in D exceeds 20´ on only 12% of the total number of + days. But at the "Discovery's" winter quarters, about sun-spot + minimum, the range exceeded 1° on 70%, 2° on 37%, and 3° on fully 15% + of the total number of days. One day in 25 had a range exceeding 4°. + During the three midsummer months, only one day out of 111 had a range + under 1°, and even at midwinter only one day in eight had a range as + small as 30´. The H range at the "Discovery's" station exceeded + 100[gamma] on 40% of the days, and the V range exceeded 100[gamma] on + 32% of the days. + + The special tendency to disturbance seen in equinoctial months in + temperate latitudes did not appear in the "Discovery's" records in the + Antarctic. D ranges exceeding 3° occurred on 11% of equinoctial days, + but on 40% of midsummer days. The preponderance of large movements at + midsummer was equally apparent in the other elements. Thus the + percentage of days having a V range over 200[gamma] was 21 at + midsummer, as against 3 in the four equinoctial months. + + At the "Discovery's" station small oscillations of a few minutes' + duration were hardly ever absent, but the character of the larger + disturbances showed a marked variation throughout the 24 hours. Those + of a very rapid oscillatory character were especially numerous in the + morning between 4 and 9 a.m. In the late afternoon and evening + disturbances of a more regular type became prominent, especially in + the winter months. In particular there were numerous occurrences of a + remarkably regular type of disturbance, half the total number of cases + taking place between 7 and 9 p.m. This "special type of disturbance" + was divisible into two phases, each lasting on the average about 20 + minutes. During the first phase all the elements diminished in value, + during the second phase they increased. In the case of D and H the + rise and fall were about equal, but the rise in V was about 3½ times + the preceding fall. The disturbing force--on the north pole--to which + the first phase might be attributed was inclined on the average about + 5°½ below the horizon, the horizontal projection of its line of action + being inclined about 41°½ to the north of east. The amplitude and + duration of the disturbances of the "special type" varied a good deal; + in several cases the disturbing force considerably exceeded + 200[gamma]. A somewhat similar type of disturbance was observed by Kr. + Birkeland[93] at Arctic stations also in 1902-1903, and was called by + him the "polar elementary" storm. Birkeland's record of disturbances + extends only from October 1902 to March 1903, so it is uncertain + whether "polar elementary" storms occur during the Arctic summer. + Their usual time of occurrence seems to be the evening. During their + occurrence Birkeland found that there was often a great difference in + amplitude and character between the disturbances observed at places so + comparatively near together as Iceland, Nova Zembla and Spitzbergen. + This led him to assign the cause to electric currents in the Arctic, + at heights not exceeding a few hundred kilometres, and he inferred + from the way in which the phenomena developed that the seat of the + disturbances often moved westward, as if related in some way to the + sun's position. Contemporaneously with the "elementary polar" storms + in the Arctic Birkeland found smaller but distinct movements at + stations all over Europe; these could generally be traced as far as + Bombay and Batavia, and sometimes as far as Christchurch, New Zealand. + Chree,[92] on the other hand, working up the 1902-1904 Antarctic + records, discovered that during the larger disturbances of the + "special type" corresponding but much smaller movements were visible + at Christchurch, Mauritius, Kolaba, and even at Kew. He also found + that in the great majority of cases the Antarctic curves were + specially disturbed during the times of Birkeland's "elementary polar" + storms, the disturbances in the Arctic and Antarctic being of the same + order of magnitude, though apparently of considerably different type. + + Examining the more prominent of the sudden commencements of magnetic + disturbances in 1902-1903 visible simultaneously in the curves from + Kew, Kolaba, Mauritius and Christchurch, Chree found that these were + all represented in the Antarctic curves by movements of a considerably + larger size and of an oscillatory character. In a number of cases + Birkeland observed small simultaneous movements in the curves of his + co-operating stations, which appeared to be at least sometimes + decidedly larger in the equatorial than the northern temperate + stations. These he described as "equatorial" perturbations, ascribing + them to electric currents in or near the plane of the earth's magnetic + equator, at heights of the order of the earth's radius. It was found, + however, by Chree that in many, if not all, of these cases there were + synchronous movements in the Antarctic, similar in type to those which + occurred simultaneously with the sudden commencements of magnetic + storms, and that these Antarctic movements were considerably larger + than those described by Birkeland at the equatorial stations. This + result tends of course to suggest a somewhat different explanation + from Birkeland's. But until our knowledge of facts has received + considerable additions all explanations must be of a somewhat + hypothetical character. + + + Magnetic Poles. + + In 1831 Sir James Ross[94] observed a dip of 89° 59´ at 70° 5´ N., 96° + 46´ W., and this has been accepted as practically the position of the + north magnetic pole at the time. The position of the south magnetic + pole in 1840 as deduced from the Antarctic observations made by the + "Erebus" and "Terror" expedition is shown in Sabine's chart as about + 73° 30´ S., 147° 30´ E. In the more recent chart in J. C. Adams's + _Collected Papers_, vol. 2, the position is shown as about 73° 40´ S., + 147° 7´ E. Of late years positions have been obtained for the south + magnetic pole by the "Southern Cross" expedition of 1898-1900 (A), by + the "Discovery" in 1902-1904 (B), and by Sir E. Shackleton's + expedition 1908-1909 (C). These are as follow: + + (A) 72° 40´ S., 152° 30´ E. + (B) 72° 51´ S., 156° 25´ E. + (C) 72° 25´ S., 155° 16´ E. + + Unless the diurnal inequality vanishes in its neighbourhood, a + somewhat improbable contingency considering the large range at the + "Discovery's" winter quarters, the position of the south magnetic pole + has probably a diurnal oscillation, with an average amplitude of + several miles, and there is not unlikely a larger annual oscillation. + Thus even apart from secular change, no single spot of the earth's + surface can probably claim to be a magnetic pole in the sense + popularly ascribed to the term. If the diurnal motion were absolutely + regular, and carried the point where the needle is vertical round a + closed curve, the centroid of that curve--though a spot where the + needle is never absolutely vertical--would seem to have the best + claim to the title. It should also be remembered that when the dip is + nearly 90° there are special observational difficulties. There are + thus various reasons for allowing a considerable uncertainty in + positions assigned to the magnetic poles. Conclusions as to change of + position of the south magnetic pole during the last ten years based on + the more recent results (A), (B) and (C) would, for instance, possess + a very doubtful value. The difference, however, between these recent + positions and that deduced from the observations of 1840-1841 is more + substantial, and there is at least a moderate probability that a + considerable movement towards the north-east has taken place during + the last seventy years. + + See publications of individual magnetic observatories, more especially + the Russian (_Annales de l'Observatoire Physique Central_), the French + (_Annales du Bureau Central Météorologique de France_), and those of + Kew, Greenwich, Falmouth, Stonyhurst, Potsdam, Wilhelmshaven, de Bilt, + Uccle, O'Gyalla, Prague, Pola, Coimbra, San Fernando, Capo di Monte, + Tiflis, Kolaba, Zi-ka-wei, Hong-Kong, Manila, Batavia, Mauritius, + Agincourt (Toronto), the observatories of the U.S. Coast and Geodetic + Survey, Rio de Janeiro, Melbourne. + + In the references below the following abbreviations are used: B.A. = + _British Association Reports_; Batavia = _Observations made at the + Royal ... Observatory at Batavia_; M.Z. = _Meteorologische + Zeitschrift_, edited by J. Hann and G. Hellman; P.R.S. = _Proceedings + of the Royal Society of London_; P.T. = _Philosophical Transactions_; + R. = _Repertorium für Meteorologie_, St Petersburg; T.M. = + _Terrestrial Magnetism_, edited by L. A. Bauer; R.A.S. Notices = + _Monthly Notices of the Royal Astronomical Society_. Treatises are + referred to by the numbers attached to them; e.g. (1) p. 100 means p. + 100 of Walker's _Terrestrial Magnetism_. + + +FOOTNOTES: + + [A] For explanation of these numbers, see end of article. + + [1] E. Walker, _Terrestrial and Cosmical Magnetism_ (Cambridge and + London, 1856). + + [1a]: H. Lloyd, _A Treatise on Magnetism General and Terrestrial_ + (London, 1874). [2] E. Mascart, _Traité de magnétisme terrestre_ + (Paris, 1900). + + [3] L. A. Bauer, _United States Magnetic Declination Tables and + Isogonic Charts, and Principal Facts relating to the Earth's + Magnetism_ (Washington, 1902). + + [4] Balfour Stewart, "Terrestrial Magnetism" (under "Meteorology"), + _Ency. brit._ 9th ed. + + [5] C. Chree, "Magnetism, Terrestrial," _Ency. brit._ 10th ed. + + [6] _M.Z._ 1906, 23, p. 145. + + [7] (3) p. 62. + + [8] _K. Akad. van Wetenschappen_ (Amsterdam, 1895; Batavia, 1899, + &c.). + + [9] _Atlas des Erdmagnetismus_ (Riga, 1903). + + [10] (1) p. 16, &c. + + [11] _Kolaba (Colaba) Magnetical and Meteorological Observations_, + 1896. Appendix Table II. + + [12] (1) p. 21. + + [13] _Report_ for 1906, App. 4, see also (3) p. 102. + + [14] (1) p. 166. + + [15] _Ergebnisse der mag. Beobachtungen in Potsdam_, 1901, p. xxxvi. + + [16] _U.S. Coast and Geodetic Survey Report_ for 1895, App. 1, &c. + + [17] _T.M._ 1, pp. 62, 89, and 2, p. 68. + + [18] (3) p. 45. + + [19] _Die Elemente des Erdmagnetismus_, pp. 104.108. + + [20] _Zur täglichen Variation der mag. Deklination (aus Heft II. des + Archivs des Erdmagnetismus)_ (Potsdam, 1906). + + [21] _M.Z._ 1888, 5, p. 225. + + [22] _M.Z._ 1904, 21, p. 129. + + [23] _P.T._ 202 A, p. 335. + + [23a] _Comb. Phil. Soc. Trans._ 20, p. 165. + + [24] _P.T._ 208 A, p. 205. + + [25] _P.T._ 203 A, p. 151. + + [26] _P.T._ 171. p. 541; _P.R.S._ 63, p. 64. + + [27] _R.A.S. Notices_ 60, p. 142. + + [28] _Rendiconti del R. Ist. Lomb._ 1902, Series II. vol. 35. + + [29] _R._ 1889, vol. 12, no. 8. + + [30] _B.A. Report_, 1898, p. 80. + + [31] _P.R.S._ (A) 79, p. 151. + + [32] _P.T._ 204 A, p. 373. + + [33] _Ann. du Bureau Central Météorologique, année 1897_, 1 Mem. p. + B65. + + [34] _P.T._ 161, p. 307. + + [35] _M.Z._ 1895, 12, p. 321. + + [35a] _P.T._ 1851, p. 123; and 1852, p. 103, see also (4) § 38. + + [36] _P.T._ 159, p. 363. + + [37] (1) p. 92. + + [38] _R.A.S. Notices_ 65, p. 666. + + [39] _R.A.S. Notices_, 65, pp. 2 and 538. + + [40] _K. Akad. van Wetenschappen_ (Amsterdam, 1906) p. 266. + + [41] _R.A.S. Notices_ 65, p. 520. + + [42] _B.A. Reports_, 1880, p. 201 and 1881, p. 463. + + [43] _Anhang Ergebnisse der mag. Beob. in Potsdam_, 1896. + + [44] _M.Z._ 1899, 16, p. 385. + + [45] _P.T._ 166, p. 387. + + [46] _Trans. Can. Inst._ 1898-1899, p. 345, and Proc. Roy. Ast. Soc. + of Canada, 1902-1903, p. 74, 1904, p. xiv., &c. + + [47] _R.A.S. Notices_ 65, p. 186. + + [48] _T.M._ 10, p. 1. + + [49] _Expédition norvégienne de 1899-1900_ (Christiania, 1901). + + [50] _Thèses présentées à la Faculté des Sciences_ (Paris, 1903). + + [51] _Nat. Tijdschrift voor Nederlandsch-Indië_, 1902, p. 71. + + [52] _Wied. Ann._ 1882, p. 336. + + [53] _Sitz. der k. preuss. Akad. der Wiss._, 24th June 1897, &c. + + [54] _T.M._ 12, p. 1. + + [55] _P.T._ 143, p. 549; _St Helena Observations_, vol. ii., p. + cxlvi., &c., (1) § 62. + + [56] _Trans. R.S.E._ 24, p. 669. + + [57] _P.T._ 178 A, p. 1. + + [58] _Batavia_, vol. 16, &c. + + [59] _Batavia_, Appendix to vol. 26. + + [60] _R._ vol. 17, no. 1. + + [61] _T.M._ 3, p. 1, &c. + + [62] _P.T._ 181 A, p. 53 and 188 A. + + [63] _Ann. du Bureau Central Mét._ vol. i. for years 1884 and 1887 to + 1895. + + [64] _Ann. dell' Uff. Centrale Met. e Geod._ vol. 14, pt. i. p. 57. + + [65] _A Magnetic Survey of the Netherlands for the Epoch 1st Jan. + 1891_ (Rotterdam, 1895). + + [66] _Kg. Svenska Vet. Akad. Handlingar_, 1895, vol. 27, no. 7. + + [67] _Denkschriften der math. naturwiss. Classe der k. Akad. des + Wiss._ (Wien), vols. 62 and 67. + + [68] _Journal of the College of Science, Tokyo_, 1904, vol. 14. + + [69] _Ann. de l'observatoire ... de Toulouse_, 1907, vol. 7. + + [70] _Ann. du Bureau Central Mét._ 1897, I. p. B36. + + [71] _T.M._ 7, p. 74. + + [72] _Bull. Imp. Univ. Odessa_ 85, p. 1, and _T.M._ 7, p. 67. + + [73] _P.T._ 187 A, p. 345. + + [74] _P.R.S._ 76 A, p. 181. + + [75] _Bull. Soc. Imp. des Naturalistes de Moskau_, 1893, no. 4, p. + 381, and _T.M._ 1, p. 50. + + [76] _Forsch. zur deut. Landes- u. Volkskunde_, 1898, Bd. xi, 1, and + _T.M._ 3, p. 77. + + [77] _P.R.S._ 76 A, p. 507. + + [78] Adams, _Scientific Papers_, II. p. 446. + + [79] _B.A. Report_ for 1898, p. 109. + + [80] _Abhand. der bayer, Akad. der Wiss._, 1895, vol. 19. + + [81] _Sitz. k. Akad. der Wiss_. (Berlin), 1897, no. xviii., also + _T.M._ 3, p. 191. + + [82] _T.M._ 2, p. 11. + + [83] _Die Elemente des Erdmagnetismus_ (St Petersburg, 1899), p. + 103. + + [84] _T.M._ 9, p. 113. + + [85] _T.M._ 1, p. 77, and Nature, 57, pp. 160 and 180. + + [86] _M.Z._ 15, p. 175. + + [86a] _Sitz, der k. k. Akad. der Wiss. Wien, math. nat. Classe_, + 1898, Bd. cvii., Abth. ii. + + [87] _P.T._ (A) 180, p. 467. + + [88] _Die Tägliche Periode der erdmagnetischen Elemente_ (St + Petersburg, 1902). + + [89] _R. Accad. Lincei Atti_, viii. 1899, pp. 69, 121, 176, 269 and + previous volumes, see also _Séances de la Soc. Franc. de Physique_, + 1899, p. 118. + + [90] _Bull. Soc. Vaud., Sc. Nat._ 1906, 42, p. 225. + + [91] _Comptes rendus_, 1905, 141, p. 567. + + [92] _National Antarctic Expedition 1901-1904_, "Magnetic + Observations." + + [93] _The Norwegian Aurora Polaris Expedition 1902-1903_, vol. i. + + [94] (1) p. 163. + + (C. Ch.) + + + + + + +End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th +Edition, Volume 17, Slice 3, by Various + +*** END OF THE PROJECT GUTENBERG EBOOK 43060 *** |