Page images



1-86 1.04



Lamb's time, mainly through the appreciative criticisms of

Yellow Earth (dried at 100° C.). S. T. Coleridge, Robert Southey and others, Fuller's works have Insoluble residue 76.13 Insoluble residue received much attention.



59.37 AI,O, 1.77 AI:0.

10.05 There is an elaborate account of the life and writings of Fuller


4.31 Fc,0,
by William Oldys in the Biographia Britannica, vol. iii. (1750), based
on Fuller's own works and the anonymous Life of .

Dr Thomas


1.05 Fuller (1661; reprinted in a volume of selections by A. L. J. Gosset,


0.14 MgO SO,

0.07 1893). The completest account of him is The Life of Thomas Fuller,


76.18 with Notices of his Books, his Kinsmen and his Friends (1874), by


0.84 J. E. Bailey, who gives a detailed bibliography (pp. 713-762) of his works.

H2O (combined). 13:19 The Worthies of England was reprinted by John Nichols (1811) and by P. A. Nuttall (1840). His Collected Sermon

100.05 edited by J. E. Bailey and W. È. A. Axon in 1891. Fuller's quaint wit lends itself to selection, and there are several modern volumes of extracts from his works.

(Analysis by P. G. Sanford, Geol. Mag., 1889, 6, pp. 456, 526.)

Of other published analyses, not a few show a lower silica content FULLER, WILLIAM (1670-6. 1717), English impostor, was born at Milton in Kent on the 20th of September 1670. His | (44%, 50 %), along with a higher proportion of alumina (11%, 23%). paternity is doubtful, but he was related to the family of Herbert.

Fuller's carth may occur on any geological horizon; at Nutfield After 1688 he served James II.'s queen, Mary of Modena, and in Surrey, England, it is in the Cretaceous formations; at Midford the Jacobites, seeking at the same time to gain favour with

near Bath it is of Jurassic age; at Bala, North Wales, it occurs in William III.; and after associating with Titus Oates, being Ordovician strata; in Saxony it appears to be the decomposition imprisoned for debt and pretending to reveal Jacobite plots, the product of a diabasic rock. In America it is found in California House of Commons in 1692 declared he was an “imposter, in rocks ranging from Cretaccous 10 Pleistocene age; in S. cheat and false accuser.” Having stood in the pillory he was

Dakota, Custer county and elsewhere a yellow, gritty earth of again imprisoned until 1695, when he was released; and at this Jurassic age is worked; in Florida and Georgia occurs a brittle, time he took the opportunity to revive the old and familiar whitish earth of Oligocene age. Other deposits are worked in story that Mary of Modena was not the mother of the prince of Arkansas, Texas, Colorado, Massachuscits and South Carolina.

Fuller's earth is cither mined or dug in the open according to Wales. In 1701 he published his autobiographical Life of William Fuller and some Original Letters of the late King James. local circumstances. It is then dried in the sun or by artificial Unable to prove the assertions made in his writings he was put heat and transported in small lumps in sacks. In other cases it in the pillory, whipped and fincd. He died, probably in prison, is ground to a fine powder after being dried; or it is first roughly about 1717. Fuller's other writings are Mr William Fuller's ground and made into a slurry with water, which is allowed to trip to Bridewell

, with a full account of his barbarous usage in the carry off the finer from the coarser particles and deposit them in a pillory; The sincere and hearly confession of Mr William Fuller creamy state in suitable tanks. After consolidation this fine (1704); and An humble appeal to the impartial judgment of all

material is dried artificially on drying floors, broken into lumps, parties in Great Britain (1716).

and packed for transport. The use of fuller's earth for cleansing He must be distinguished from William Fuller (1608-1675). wool and cloth has greatly decreased, but the demand for the dean of St Patrick's (1660), bishop of Limerick (1663), and bishop of material is as great or greater than it ever was. It is now used Lincoln (1667), the friend of Samuel Pepys; and also from William very largely in the filtration of mineral oils, and also for decolourFuller (c. 1580-1659), dean of Ely and later dean of Durham.

izing certain vegetable oils. It is employed in the formation of FULLER'S EARTH (Ger. Walkererde, Fr. icrrc à foulon, argile certain soaps and cleansing preparations. smeclique)-so named from its use by fullers as an absorbent of The term “ Fuller's Earth" has a special significance in the grease and oil of cloth,-a clay-like substance, which from geology, for it was applied by W. Smith in 1799 to certain clays its variability is somewhat difficult to define. In colour it is in the neighbourhood of Bath, and the use of the expression is most often greenish, olive-green or greenish-grey; on weathering still retained by English geologists, either in this form or in the it changes to a brown tint or it may bleach. As a rule it falls generalized " Fullonian.” The Fullonian lies at the base of the 10 pieces when placed in water and is not markedly plastic; Great Oolite or Bathonian series, but its palaeontological when dry it adheres strongly to the tongue; since, however, characters place it between that series and the underlying these properties are possessed by many clays that do not exhibit Inscrior Oolite. The zonal fossils are Perisphinctes arbustigerus detergent qualities, the only test of value lies in the capacity and Macrocephalus subcontractus with Ostrea acuminala, to absorb grcase or clarify oil. Fuller's earth has a specific gravity Rhynchonella concinna and Goniomya angulifera. The formation of 1.7-2-4, and a shining streak; it is usually unctuous to the is in part the equivalent of the" Vesulien" of J. Marcou (Vesoul touch. Microscopically, it consists of minute irregular-shaped in Haute-Saône). In Dorsetshire and Somersetshire, where it particles of a mineral that appears to be the result of a chloritic is best developed, it is represented by an Upper Fuller's Earth or talcose alteration of a felspar. The small size of most of the Clay, the Fuller's Earth Rock (an impersistent earthy limestone, grains, less than .07 mm., makes their determination almost usually fossiliserous), and the Lower Fuller's Earth Clay. Comimpossible. Chemical analysis shows that the peculiar properties mercial fuller's carth has been obtained only from the Upper of this earth are due to its physical rather than its chemical Clay. In castern Gloucestershire and northern Oxfordshire

The Fuller's Earth passes downwards without break into the The following analyses of the weathered and unweathered con- Inferior Oolite; northward it dies out about Chipping Norton dition of the carth from Nutfield, Surrey, represent the composition in Oxfordshire and passes laterally into the Stonesfield Slates of one of the best known varicties:

series; in the midland counties it may perhaps be represented Blue Earth (dricd at 100° C.).

by the “ Upper Estuarine Series.” In parts of Dorsetshire the Insoluble residue 69.96 | Insoluble residue

clays have been used for brickmaking and the limestone (rock) 2.48 SiO,

for local buildings. Alo,


See H. B. Woodward, " Jurassic Rocks of Great Britain,", vol. Cao

iv. (1894), Mem. Geol. Survey (London).

(J. A. H.) Mg0

Cao PO. Mgo


English novelist and philanthropist, youngest daughter of the Naci.

69.96 ist Earl Granville, was born at Tixall Hall in Stafiordshire on KO

the 23rd of September 1812. In 1833 she married Alexander H20 (combined). 15.57

George Fullerton, then an Irish officer in the guards. After living in Paris for some eight years she and her husband accompanied Lord Granville to Cannes and thence to Rome. In 1843


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her husband entered the Roman Catholic church, and in the silver " obtained by C. L. Berthollet in 1788 by acting with following year Lady Georgiana Fullerton published her first novel, ammonia on precipitated silver oxide. The next salt to be Ellen Middlelon, which attracted W. E. Gladstone's attention obtained was the mercuric salt, which was prepared in 1799 by in the English Review. In 1846 she entered the Roman Catholic Edward Charles Howard, who substituted mercury for silver in church. The death of her only son in 1854 plunged her in grief, Brugnatelli's process. A similar method is that of J. von Liebig and she continued to wear mourning until the end of her life. (1823), who heated a mixture of alcohol, nitric acid and mercuric In 1856 she became one of the third order of St Francis, and nitrate; the salt is largely manufactured by processes closely thenceforward devoted herself to charitable work. In conjunc- resembling the last. A laboratory method is to mix solutions tion with Miss Taylor she founded the religious community of sodium nitromethane, CH,: NO(ONa), and mercuric chloride, known as “ The Poor Servants of the Mother of God Incarnale," a yellow basic salt being formed at the same time, Mercuric and she also took an active part in bringing to England the fulminate is less explosive than the silver salt, and forms white sisters of St Vincent of Paul. Her philanthropic work is described needles (with LH:0) which are tolerably soluble in water. The in Mrs Augustus Craven's work Lady Gcorgiana Fullerton, sa use of mercuric fulminate as a detonator dates from about 1814, vie et ses auvres (Paris, 1888), which was translated into English when the explosive cap was invented. It is still the commonest by Henry James Coleridge. She died at Bournemouth on the 19th detonator, but it is now usually mixed with other substances; of January 1885. Among her other novels were Grantley Manor the British service uses for percussion caps 6 parts of fulminate, (1847), Lady Bird (1852), and Too Strange not to be True (1864). 6 of potassium chlorate and 4 of antimony sulphide, and for

FULMAR, from the Gaelic Fulmaire, the Fulmarus glacialis of time fuses 4 parts of fulminate, 6 of potassium chlorate and 4 modern ornithologists, one of the largest of the petrels (Procel- of antimony sulphide, the mixture being damped with a shellac lariidae) of the northern hemisphere, being about the size of the varnish; for use in blasting, a home office order of 1897 prescribes common gull (Larus canus) and not unlike it in general coloration, a mixture of 4 parts of fulminate and 1 of potassium chlorate. except that its primaries are grey instead of black. This bird, In 1900 Bielefeldt found that a fulminate placed on top of an which ranges over the North Atlantic, is seldom seen on the aromatic nitro compound, such as trinitrotoluene, formed a European side below lat. 53° N., but on the American side comes useful detonator; this discovery has been especially taken habitually to lat. 45°oreven lower. In the Pacific it is represented advantage of in Germany, in which country detonators of this by a scarcely separable form, F. glupischa. It has been commonly nature are being largely employed. Tetranitromethylaniline believed to have two breeding-places in the British Islands, (letryl) has also been employed (Brit. Pat. 13340 of 1905). namely, St Kilda and South Barra; but, according to Robert It has been proposed to replace fulminate by silver azoimide Gray (Birds of the West of Scotland, p. 499), it has abandoned (Wöhler & Matter, Brit. Pat. 4468 of 1908), and by lead azoimide the latter since 1844, though still breeding in Skye. Northward (Hyronimus, Brit. Pat. 1819 of 1908). it established itself about 1838 on Myggenacs Holm, one of the

The constitution of sulminic acid has been investigated by many Faeroes, while it has several stations off the coast of Iceland and experimenters, but apparently without definitive results. Spitsbergen, as well as at Bear Island. Its range towards the researches of Liebig (1823), Liebig and Gay-Lussac (1824). and of pole seems to be only bounded by open water, and it is the con-Liebig again in 1838 showed the acid to be isomeric with cyanic acid, stant attendant upon all who are employed in the whale and

and probably (HCNO), since it gave mixed and acid salts. Kekulé,

in 1858, concluded that it was nitroacetonitrile, NO,CH;.CN, a seal fisheries, showing the greatest boldness in approaching boats view opposed by Steiner (1883), E. Divers and M. Kawakita (1884). and ships, and feeding on the offal obtained from them. By R. Scholl (1890), and by J. U. Nel (1894), who proposed the formulae: British seamen it is commonly called the “molly mawk". (corrupted from Mallemuck), and is extremely well known to them,


ĐKN ICOH, CH :N-O, its flight, as it skims over the waves, first with a few beats of


Scholl, the wings and then gliding for a long way, being very peculiar. The formulac of Kekulé, Divers and Armstrong have been discarded, It only visits the land to deposit its single white egg, which is and it remains to be shown whether Nef's carbonyloxime formula laid on a rocky ledge, where a shallow nest is made in the turi (or the binolecular formula of Steiner) or Scholl's glyoxime peroxide and lined with a little dried grass. Many of its breeding-places of fulminic

acid. - The existence of double salts, and the observations

There is soinc doubt as to the molecular formula are a most valuable property to those who live near them and

of L. Wohler and K. Theodorovits (Ber., 1905, 38, p. 345), that only take the eggs and young, which, from the nature of the locality, compounds containing two carbon atoms yielded lulminates, points are only to be had at a hazardous risk of life. In St Kilda a to (HCNO),; on the other hand, Wohler (loc. cit. p. 1351) found large number of the young are killed in one week of August, the that cryoscopic and clectric conductivity measurements showed

sodium fulminate to be NaCNO. Ner based his formula, which only time when, by the custom of the community, they are

involves bivalent carbon, on many reactions: in particular, that allowed to be taken. These, after the oil is extracted from them, silver fulminate with hydrochloric acid gave salts of formylchloridserve the islanders with food for the winter. The oil has been oxime, which with water gave hydroxylamine and sormic acid, thus chemically analysed and found to be a fish-oil, and to possess


>H.CO2H+H.N.OH, nearly all the qualities of that obtained from the liver of the cod, with a lighter specific gravity. It, however, has an extremely and also on the production from sodium nitromethane and merstrong scent, which is said by those who have visited St Kilda curic chloride, thus CH7 : NOOhg ->H20+C : NOhg (hg = \Hg). H. to pervade every thing and person on the island, and is certainly Wieland and F. C. Palazzo (1907) support this formula, finding that retained by an egg or skin of the bird for many years. Whenever methyl nitrolic acid, NO::CH : N.OH, yielded under certain con. a live example is seized in the hand it ejects a considerable itsch (Ann., 1906, 347, p. 233) inclines to Scholl's formula : he quantity of this oil from its mouth.

found that the synthetic silver salt of glyoxime peroxide resembled PULMINIC ACID, HCNO or H,C2N2O2, an organic acid silver fulminate in yielding hydroxylamine with hydrochloric acid, isomeric with cyanic and cyanuric acids; its salts, termed

but differed in being less explosive, and in being soluble in nitric

acid. H. Wieland and his collaborators regard "glyoxime peroxide fulminates, are very explosive and are much employed as de

as an oxide of furazane (9.v.), and have shown that a close relationship The free acid, which is obtained by treating the salts exists between the nitrile oxides, furoxane, and fulminic acid (sce with acids, is an oily liquid smelling like prussic acid; it is very Ann. Rep., London Chem. Soc., 1909, p. 84). Fulminuric acid, explosive, and the vapour is poisonous to about the same degree (HCNO), obtained by Licbig by boiling mercuric fulminate with as that of prussic acid. The first fulminate prepared was the (Gaseita, iii. 35, p. 7). who regard it as NO.-CH(CN).CO.NH. It

water, was synthesized in 1905 by C. Ulpia ni and L. Bernardini " fulminating silver "of L. G. Brugnatelli, who found in 1798 deflagrates at 145°, and forms a characteristic cuprammonium salt. that if silver be dissolved in nitric acid and the solution added The early history of mercuric fulminate and a critical account of its to spirits of wine, a white, highly explosive powder was obtained. application as a detonator is given in The Rise and Progress of the This substance is to be distinguished from the black“sulminating Chemistry.

1909). The manufacture and modern aspects are treated 1 A name misapplied in the southern hemisphere to Diomedea in Oscar Guttmann, The Manufacture of Explosives, and Manumelanophrys, one of the albatrosses.

facture of Explosives, Twenty Years' Progress (1909).









PULTON, ROBERT (1765-1815), American engineer, was born | about 700) under De Villiers. Soon after this, Bradstreet built in 1765 in Little Britain (now Fulton, Lancaster county), Pa. a fort within the present limits of Fulton. The first civilian His parents were Irish, and so poor that they could afford him settler came in 1793, and the first survey (which included only only a very scanty education. At an early age he was bound a part of the subsequent village) was made in 1815. Fulton apprentice to a jeweller in Philadelphia, but subsequently was incorporated as a village in 1835, and in April 1902 was adopted portrait and landscape painting as his profession. In combined with the village of Oswego Falls (pop. in 1900, 2925) his twenty-second year, with the object of studying with his and was chartered as a city. countryman, Benjamin West, he went to England, and there FUM, or FunJ HWANG, one of the four symbolical creatures became acquainted with the duke of Bridgewater, Earl Stanhope which in Chinese mythology are believed to keep watch and ward and James Watt. Partly by their influence he was led to devote over the Celestial Empire. It was begotten by fire, was born in his attention to engineering, especially in connexion with canal the Hill of the Sun's Halo, and its body bears inscribed on it construction; he obtained an English patent in 1794 for super- the five cardinal virtues. It has the breast of a goose, the hindseding canal locks by inclined planes, and in 1796 he published quarters of a slag, a snake's neck, a fish's tail, a fowl's forehead, a Trealise on the Improvement of Canal Navigation. He then took a duck's down, the marks of a dragon, the back of a tortoise, up his residence in Paris, where he projected the first panorama the face of a swallow, the beak of a cock, is about six cubits high, ever exhibited in that city, and constructed a submarine boat, and perches only on the woo-tung tree. The appearance of Fum the "Nautilus,” which was tried in Brest harbour in 1801 before heralds an age of universal virtue. Its figure is that which is a commission appointed by Napolcon I., and by the aid of which embroidered on the dresses of some mandarins. he was enabled to blow up a small vessel with a torpedo. It FUMARIC AND MALEIC ACIDS, two isomeric unsaturated was at Paris also in 1803 that he first succeeded in propelling-a acids of composition C,H,O, Fumaric acid is found in fumitory boat by steam-power, thus realizing a design which he had (Fumaria officinalis), in various fungi (Agaricus piperatus, &c.), conceived ten years previously. Returning to America he and in Iceland moss. It is obtained by heating malic acid alone continued his experiments with submarine explosives, but sailed 10 150° C., or by heating it with hydrochloric acid (V. Dessaignes, to convince either the English, French or United States govern- Jahresb., 1856, p. 463) or with a large quantity of hydrobromic ments of the adequacy of his methods. With steam navigation acids (A. Kekulé, Ann., 1864, 130, p. 21). It may also be obtained he had more success. In association with Robert R. Livingston by boiling monobromsuccinic acid with water; by the action of (9.9.), who in 1798 had been granted the exclusive right to dichloracelic acid and water on silver malonate (T. Komnenos, navigate the waters of New York state with steam-vessels, he Ann., 1883, 218, p. 169); by the cyanide synthesis from acetylene constructed the “ Clermont," which, engined by Boulton & di-iodide; and by heating maleic acid to 210° C. (Z. Skraup, Watt of Birmingham, began to ply on the Hudson between Monats. J. Chemie, 1891, 12, p. 112). It crystallizes in small New York and Albany in 1807. The privilege obtained by prisms or needles, and is practically insoluble in cold water. It Livingston in 1798 was granted jointly to Fulton and Living- sublimes to some extent at about 200° C., being partially conston in 1803, and by an act passed in 1808 the monopoly was verted into malcic anhydride and water, the reaction becoming secured to them and their associates for a period depending on practically quantitative if dehydrating agents be used. Reducing the number of steamers constructed, but limited to a maximum agents (zinc and caustic alkali, hydriodic acid, sodium amalgam, of thirty years. In 1814-1815, on behalf of the United States &c.) convert it into succinic acid. Bromine converts it into government, he constructed the “ Fulton," a vessel of 38 tons dibromsuccinic acid. Potassium permanganate oxidizes it to with central paddle-wheels, which was the first stcam warship. racemic acid (A. Kekulé and R. Anschutz, Ber., 1881, 14, He died at New York on the 24th of February 1815. Among p. 713). By long-continued heating with caustic soda at 100° C. Fulton's inventions were machines for spinning flax, for making it is converted into inactive malic acid. ropes, and for sawing and polishing marble.

Afaleic acid is obtained by distilling malic or fumaric acids; Sec C. D. Colden, Life of Robert Fulton (New York, 1817); Robert by heating fumaric acid with acetyl chloride to 100° C.; or by H. Thurston, History of the Crowth of the Steam-Engine (New York, the hydrolysis of trichlorphenomalic acid (B-trichloraceto(Philadelphia, 1883); and Mrs A. Č. Sutcliffc, Robert Fulton and the acrylic acid) (A. Kekulé, Ann., 1884, 223, P. 185). It crystallizes Clermont (New York, 1909).

in monoclinic prisms, which are easily soluble in water, melt PULTON, a city and the county-scat of Callaway county, at 130° C., and boil at 160°C., decomposing into water and Missouri, U.S.A., 25 m. N.E. of Jefferson City. Pop. (1890) maleic anhydride. When hcated with concentrated hydrobromic 4314; (1900) 4883 (1167 negroes); (1910) 5228. It is served by or hydriodic acids, it is converted into fumaric acid. It yields the Chicago & Alton railway. The city has an important stock an anilide; oxidation converts it into mesotartaric acid. Maleic market and manufactures fire-brick and pottery. Al Fulton anhydride is obtained by distilling fumaric acid with phosphorus are the Westminster College (Presbyterian, founded in 1853), pentoxide. It forms triclinic crystals which melt at 60° C. and the Synodical College for Young Women (Pres., founded in boil at 196° C. 1871), the William Woods College for Girls (Christian Church, Both acids are readily esterified by the action of alkyl halides on 1890), and the Missouri school for the deaf (1851). Here, too, their silver salts, and the maleic ester is readily transformed into the is a state hospital for the insane (1847), the first institution fumarıc ester by warming with iodine, the same result being obtained of the kind in Missouri. The place was laid out as a town in by esterification of maler acid in alcoholic solution by means of

hydrochloric acid. Both acids yic!d acetylene by the electrolysis 1825 and named Volney, but in honour of Robert Fulton the of aqueous solutions of their almali salts, and on reduction both present name was adopted a little later. Fulton was incorporated yield succinic acid, whilst by the addition of hydrobromic acid they in 1859.

both yield monobromsuccinic acid (R. Futis, Ann., 1877, 188, p. 98). FULTON, a city of Oswego county, New York, U.S.A., on the identical, and the isomerism has consequently to be explained on

From these results it follows that the two acids are structurally right bank of the Oswego river, about 10 m. S. by E. of Oswego. Other grounds. This was accomplished by W. Wislicenus (" Über Pop. (1900) 5281; (1905, state census) 8847; (1910) 10,480. die räumliche Anordnung der Atomc," &c., Trans. of the Saron Acad. Fulion is served by the Delaware, Lackawanna & Western, the of Sciences (Math. Phys. Section), 1887, p. 14) by an extension of New York Central & Hudson River, and the New York, Ontario the van't Hoff hypothesis (see Stereo-ISOMERISM). The formulae

of the acids are written thus: & Western railways, by electric railway to Oswego and Syracuse


HC.CO,H and by the Oswego Canal. The city has a Carnegie library.

Maleic acid.


Fumaric acid. Ample water-power is furnished by the Oswego river, which here flows in a series of rapids, and the manufactures are many in fumaric acid does not, and for the behaviour of the acids towards

These account for maleic acid readily yielding an anhydride, whereas kind. On the 3rd of July 1756, on an island (afterward called bromine, fumaric acid yielding ordinary dibromsuccinic acid, and Battle Island) 4 m. N. of the present city of Fulton, a British maleic acid the isomeric isodibromsuccinic acid. force of about 300 under Captain John Bradstreet (1711-1774). PUMAROLE, a vent from which volcanic vapours issue, deícated an attacking force of French and Indians (numbering I named indirectly from the Lat. fumariolum, a smoke-bole.


The vapours from fumaroles were studied first by R. W. Bunsen, sugar-cane plantations occupy the surrounding heights. Three on bis visit to Iceland, and afterwards by H. Sainte-Claire Deville mountain streams traverse the city through deep channels, and other chemists and geologists in France, who examined the which in summer are dry, owing to the diversion of the water vapours from Santorin, Etna, &c. The hottest vapours issue for irrigation. A small fort, on an isolated rock off shore, from dry fumaroles, at temperatures of at least 500° C., and guards the entrance to the bay, and a larger and more powerfully consist chiefly of anhydrous chlorides, notably sodium chloride. armed fort crowns an eminence inland. The chief buildings The acid fumaroles yield vapours of lower temperature (300° to include the cathedral, Anglican and Presbyterian churches, 400") containing much water vapour, with hydrogen chloride hospitals, opera-house, museum and casino. There are small and sulphur dioxide. The alkaline fumaroles are still cooler, public gardens and a meteorological observatory. In the steep Though above 100°, and evolve ammonium chloride with other and narrow streets, which are lighted by electricity, wheeled vapours. Cold fumaroles, below 100°, discharge principally traffic is impossible; sledges drawn by oxen, and other primitive aqueous vapour, with carbon dioxide, and perhaps hydrogen conveyances are used instead (see MADEIRA). In winter the fine sulphide. The fumaroles of Mont Pelé in Martinique during the climate and scenery attract numerous invalids and other visitors, eruption of 1902 were examined by A. Lacroix, and the vapours for whose accommodation there are good hotels; many foreigners analysed by H. Moissan, who found that they consisted chiefly engaged in the coal and wine trades also reside here permanently. of water vapour, with hydrogen chloride, sulphur, carbon dioxide, The majority of these belong to the British community, which carbon monoxide, methane, hydrogen, nitrogen, oxygen and was first established here in the 18th century. Funchal is the argon. These vapours issued at a temperature of about 400°. headquarters of Madeiran industry and commerce (see MADEIRA). Armand Gautier has pointed out that these gases are practically. It has no docks and no facilities for landing passengers or goods; of the same composition as those which he obtained on heating vessels are obliged to anchor in the roadstead, which, however, granite and certain other rocks. (See VOLCANO).

is sheltered from every wind except the south. Funchal is FUMIGATION (from Lat. fumigare, to smoke), the process connected by cable with Carcavellos (for Lisbon), Porthcurnow of producing smoke or fumes, as by burning sulphur, frankin- (for Falmouth, England) and St Vincent in the Cape Verde cense, tobacco, &c., whether as a ceremony of incantation, or Islands (for Pernambuco, Brazil). for perfuming a room, or for purposes of disinfection or destruc- FUNCTION, in mathematics, a variable number the value tion of vermin. In medicine the term has been used of the ex- of which depends upon the values of one or more other variable posure of the body, or a portion of it, to fumes such as those of numbers. The theory of functions is conveniently divided into nitre, sal-ammoniac, mercury, &c.; fumigation, by the injection (I.) Functions of Real Variables, wherein real, and only real, of tobacco smoke into the great bowel, was a recognized procedure numbers are involved, and (II.) Functions of Complex Variables, in the 18th century for the resuscitation of the apparently wherein complex or imaginary numbers are involved. drowned. “Fumigated" fumed ” oak is oak which has

I. FUNCTIONS OF REAL VARIABLES been darkened by exposure to ammonia vapour. FUMITORY, in botany, the popular name for the British

1. Historical.—The word function, defined in the above sense, species of Fumaria, a genus of small, branched, often climbing was introduced by Leibnitz in a short note of date 1694 conannual herbs with much-divided leaves and racemes of small cerning the construction of what we now call an “envelope" flowers. The flowers are tubular with a spurred base, and in the (Leibnizens malhematische Schrijlen, edited by C. I. Gerhardt, British species are pink to purplish in colour. They are weeds of Bd. v. P. 306), and was there used to denote a variable length cultivation growing in fields and waste places. F. capreolata related in a defined way to a variable point of a curve.

In 1698 climbs by means of twisting petioles. In past times fumitory James Bernoulli used the word in a special sense in connexion with was in esteem for its repuied cholagogue and other medicinal

some isoperimetric problems (Joh. Bernoulli, Opera, t. i. p. 255). properties; and in England, boiled in water, milk or whey, it

He said that when it is a question of selecting from an infinite set was used as a cosmetic. The root of the allied species (Corydalis of like curves that one which best fulfils some function, then of cava or tuberosa) is known as radix aristolochia, and has been used

two curves whose intersection determines the thing sought one medicinally for various cutaneous and other disorders, in doses is always the line of the function(Linea functionis). In 1718 of 10 to 30 grains. Some eleven alkaloids have been isolated John Bernoulli (Opera, t. ii. p. 241) defined a “ function of a from it. The herbage of Fumaria officinalis and F. racemosa is variable magnitude” as a quantity made up in any way of this used in China under the name of Tsze-kwa-li-ling as an applica- variable magnitude and constants; and in 1730 (Opera, t. iii. tion for glandular swellings, carbuncles and abscesses, and was

p. 174) he noted a distinction between “ algebraic” and “tranformerly valued in jaundice, and in cases of accidental swallowing scendental” functions. By the latter he meant integrals of of the beard of grain (see F. Porter Smith, Contrib. towards the algebraic functions. The notation f(x) for a function of a variable Mal. Medica ... of China, p. 99, 1871). The name fumitory,

x was introduced by Leonhard Euler in 1734 (Comm. Acad. Latin fumus terrae, has been supposed to be derived from the Petropol. t. vii. p. 186), in connexion with the theorem of the fact that its juice irritates the eyes like smoke (see Fuchs, De interchange of the order of differentiations. The notion of historia stirpium, p. 338, 1542); but The Grele Herball, cap. functionality or functional relation of two magnitudes was thus clxix., 1529, fol., following the De simplici medicina of Platearius, of geometrical origin; but a function soon came to be regarded fo. xciii. (see in Nicolai Praepositi dispensatorium ud aromatarios, as an analytical expression, not necessarily an algebraic expres1536), says: “It is called Fumus terre fume or smoke of the sion, containing the variable or variables. Thus we may have erthe bycause it is engendred of a cours fumosyte rysynge frome rational integral algebraic functions such as ar? + bx + c, or the erthe in grete quantyte lyke smoke: this grosse or cours

rational algebraic functions which are not integral, such as fumosyte of the erthe wyndeth and wryeth out: and by work

Qix" +azx*-++... tan, ynge of the ayre and sonne it turneth into this herbe. "

bixm +barn-it... tbm FUNCHAL, the capital of the Portuguese archipelago of the or irrational algebraic functions, such as V2, or, more generally Madeiras; on the south coast of Madeira, in 32° 37' N. and the algebraic functions that are determined implicitly by an 16° 54' W. Pop. (1900) 20,850. Funchal is the see of a bishop, algebraic equation, as, for instance, in the archiepiscopal province of Lisbon; it is also the admini

fr(x,y) + fn-1(x,y) + ... +fo=0 strative centre of the archipelago, and the residence of the

1 The word " function (from Lat. fungi, to perform) has many governor and foreign consuls. The city has an attractive uses, with the fundamental sense of an activity special or proper appearance from the sea. Its whitewashed houses, in their to an office, business or profession, or to an organ of an animal or gardens full of tropical plants, are built along the curving shore plant, the definite work for which the organ is an apparatus. From of Funchal Bay, and on the lower slopes of an amphitheatre of

the use of the word, as in the Italian funzione, for a ceremony of

the Roman Church, mountains, which form a background 4000 ft. high. Numerous ceremony of any kind, and loosely of a social entertainment or

" function " is often employed for a public country houses (quinlas), with terraced gardens, vineyards and I gathering.



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where fn(x,y), ... mean homogeneous expressions in x and y the case the number is said to be "continuously variable.'
having constant coefficients, and having the degrees indicated When the domain consists of all real numbers, the variable is
by the suffixes, and so is a constant. Or again we may have said to be “unrestricted.” A domain which consists of all the
trigonometrical functions, such as sin x and tan x, or inverse real numbers which exceed some fixed number may be described
trigocometrical functions, such as sin?r, orexponential functions, as an “interval unlimited towards the right "; similarly we
such as em and of, or logarithmic functions, such as log x and log may have an interval“ unlimited towards the left."
(1+x). We may have these functional symbols combined in In more complicated cases we must have some rule or process for
various ways, and thus there arises a great number of functions. assigning the aggregate of numbers which constitute the domain of

The methods of definition of particular types of aggreFurther we may have functions of more than one variable, as, for gates, and the theorems relating to them, form a branch of analysis instance, the expression xyl(x + 3*), in which both x and y are called the "theory of aggregates" (Mengenlehre, Théorie des ensembles, regarded as variable. Such functions were introduced into Theory of sels of points) The notion of an

" in general analysis somewhat unsystematically as the need for them arose,

underlies the system of ordinal numbers. An aggregate is said to

be "infinite and the later developments of analysis led to the introduction ence of all its elements to some of its elements. For example, we

when it is possible to effect a one-to-one correspondof other classes of functions.

may make all the integers correspond to the even integers, by making 2. Graphic Representation. In the case of a function of one I correspond to 2, 2 to 4, and generally » to 2n. The aggregate of variable x, any value of x and the corresponding value y of the positive integers is an infinite aggregate. The aggregates of all function can be the co-ordinates of a point in a plane. To any rational numbers and of all real numbers and of points on a line are value of x there corresponds a point N on the axis of x, in accord are real numbers is said to ** extend to infinite values " if, after any ance with the rule that x is the abscissa of N. The corresponding number N, however great, is specified, it is possible to find in the value of y determines a point Pin accordance with the rule that aggregate numbers which exceed N in absolute value. Such an x is the abscissa and y the ordinate of P. The ordinate y gives aggregate is always infinite. The.... neighbourhood of a number the value of the function which corresponds to that value of (or points) x for which the absolute value of x-a denoted by the variable x which is specified by N; and it may be described x-al, does not exceed k. as “the value of the function at N." Since there is a one-to-one 5. General Nolion of Functionality. A function of one variable correspondence of the points N and the numbers x, we may also was for a long time commonly regarded as the ordinate of describe the ordinate as the value of the function at x." In curve; and the two notions (1) that which is determined by a simple cases the aggregate of the points P which are determined curve supposed drawn, and (2) that which is determined by an by any particular function (of one variable) is a curve, called analytical expression supposed written down, were not for å the" graph of the function” (see $ 14). In like manner a function long time clearly distinguished. It was for this reason that of two variables defines a surface.

Fourier's discovery that a single analytical expression is capable 3. The Variable.--Graphic methods of representation, such of representing (in different parts of an interval) what would as those just described, enabled'mathematicians to deal with in his time have been called different functions so profoundly irrational values of functions and variables at the time when there struck mathematicians ($ 23). The analysts who, in the middle was no theory of irrational numbers other than Euclid's theory of the 19th century, occupied themselves with the theory of the of incommensurables. In that theory an irrational number was convergence of Fourier's series were led to impose a restriction the ratio of two incommensurable geometric magnitudes. In on the character of a function in order that it should admit of the modern theory of number irrational numbers are defined in such representation, and thus the door was opened for the a purely arithmetical manner, independent of the measurement introduction of the general notion of functional dependence. of any quantities or magnitudes, whether geometric or of any This notion may be expressed as follows: We have a variable other kind. The definition is effected by means of the system number, y, and another variable number, x, a domain of the of ordinal numbers (see NUMBER). When this formal system is variable x, and a rule for assigning one or more definite values established, the theory of measurement may be founded upon it; I to y when x is any point in the domain; then y is said to be a and, in particular, the co-ordinates of a point are defined as “function " of the variable x, and x is called the "argument numbers (not lengths), which are assigned in accordance with a

of the function. According to this notion a function is, as it rule. This rule involves the ineasurement of lengths. The theory were, an indefinitely extended table, like a table of logarithms; of functions can be developed without any reference to graphs, or to each point in the domain of the argument there correspond co-ordinates or lengths. The process by which analysis has been

values for the function, but it remains arbitrary what values the freed from any consideration of measurable quantities has been function is to have at any such point. called the “ arithmetization of analysis.” In the theory so

For the specification of any particular function two things are developed, the variable upon which a function depends is always requisite: (1) a statement of the values of the variable, or of the to be regarded as a number, and the corresponding value of the aggregate of points, to which values of the function are to be made function is also a number. Any reference to points or co

to correspond, i.e. of the "domain of the argument "; (2) a rule ordinates is to be regarded as a picturesque mode of expression, for assigning the value or values of the function that correspond to

We may refer to the second of these two pointing to a possible application of the theory to geometry. essentials as “the rule of calculation.' The development of “arithmetized analysis” in the 19th century to analytical expressions may then be stated in the form that the is associated with the name of Karl Weierstrass.

rule of calculation is: “Give the function the value of the expression

at any point at which the expression has a determinate value," or All possible values of a variable are numbers. In what

again more generally, “. Give the function the value of the expression follows we shall confine our attention to the case where the at all points of a definite aggregate included in the domain of the numbers are real. When complex numbers are introduced, argument. The former of these is the rule of those among the instead of real ones, the theory of functions receives a wide earlier analysts who regarded an analytical expression and a function extension, which is accompanied by appropriate limitations as the same thing, and their usage may be retained without causing (see below, II. Functions of Complex Variables). The set of all sion serving to specify the domain of the argument as well as the real numbers forms a continuum. In fact the notion of a one- rule of calculation, e.g. we may speak of “the function 1/x." This dimensional continuum first becomes precise in virtue of the function is defined by the analytical expression 1/at all points establishment of the system of real numbers.

except the point x=0. But in complicated cases separate state.

ments of the domain of the argument and the rule of calculation 4. Domain of a Variable.Theory of Aggregates.—The notion

cannot be dispensed with. In general, when the rule lculation of a “ variable" is that of a number to which we may assign is determined as above by an analytical expression at any aggregate at pleasure any one of the values that belong to some chosen set, of points, the function is said to be "represented " by the expression or aggregale, of numbers; and this set, or aggregate, is called at those points,

When the rule of calculation assigns a single definite value for a the “ domain of the variable.” This domain may be an

function at cach point in the domain of the argument the function "interval,” that is to say it may consist of two terminal numbers, is a uniform " or one-valued." In what follows it is to be under. all the numbers between them and no others. When this is stood that all the functions considered are one-valued, and the values

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The relation of functions

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