important services of his life, however, were those rendered | in connexion with the Baptist Missionary Society, which was formed at Kettering in 1792, and of which he was secretary until his death on the 7th of May 1815. The correspondence he maintained, the journeys he undertook, the pamphlets he wrote in defence of the society, and the discourses he preached on its behalf, imply an amount of work which few men could possibly have overtaken, and which ultimately proved too heavy even for his naturally powerful constitution. Several editions of his collected works have appeared, and a Memoir, principally compiled from his own papers, was published about a year after his decease by Dr Ryland, his most intimate friend and coadjutor in the affairs of the Baptist mission. There are also biographies by his son, the Rev. A. G. Fuller, and by the Rev. J. W. Morris.

FULLER, SARAH MARGARET. See OSSOLI. FULLER, THOMAS (1608-1661), the witty divine and historian, eldest son of a father of the same name who was rector of Aldwincle St Peter's, Northamptonshire, was born at the rectory house of that country parish in the year 1608, and was baptized on 19th June in that year. Dr Robert Townson and Dr John Davenant, bishops of Salisbury, were his uncles and godfathers. The boy's training was influenced by the position of these prelates and of other friends of his father, who was B.D., and had held the position of lector primarius in Trinity College, Cambridge. The youth studied under the care of the Rev. Arthur Smith, and of his cousin Dr Edward Davenant, the mathematician. According to Aubrey, Fuller was "a boy of pregnant wit." At an early age he was admitted of Queen's College, Cambridge, then presided over by Dr John Davenant. He was apt and quick in study; and in Lent 1624-5 he became B.A., and in July 1628 M.A. Being overlooked in an election of fellows of his college, he was removed by Bishop Davenant to Sidney Sussex College, November 1628. In 1630 he received from Corpus Christi College, in the same university, the curacy of St Benet's, which he held for a short time, and where he had for a parishioner the celebrated carrier Hobson. Fuller's quaint and humorous oratory, as displayed in his sermons on Ruth, soon attracted attention. He also attained a certain fame in the university as a writer of verses, and as the author of a poem, 1631, on the subject of David and Bathsheba. In June of the same year his uncle gave him a prebend in Salisbury, where his father, who died in the following year, held a canonry. The rectory of Broadwindsor, Dorsetshire, then in the diocese of Bristol, was his next preferment (1634); and 11th June 1635 he proceeded B.D. For about six years he devoted himself to his rustic flock, and meanwhile compiled The Holy War, being a history of the crusades (published in 1640), and The Holy and Prophane States, being a book of character biography (1642), both which deservedly popular works went through several editions. At this time Fuller was well known as a man of engaging manners, of good connexions, and of literary tastes. Being, moreover, a cordial lover of the Church of England, and of its discipline as fixed by the canons of 1603, he was in 1640 elected proctor for Bristol in the memorable convocation of Canterbury, which assembled with the Short Parliament. On the sudden dissolution of the latter, he united himself to those who urged that convocation should likewise dissolve as usual. That opinion was overruled; and the assembly continued to sit by virtue of a royal writ, and to frame, amongst its canons, the much-ridiculed Etcetera Oath. Fuller has left a valuable account of the proceedings of this synod, for sitting in which he was fined £200, but was never pressed to pay it. Meanwhile he preached in some of the "voiced pulpits" of London, and was followed for his excellent gifts. His first published volume of sermons

appeared in 1640 under the title of Joseph's parti-coloured Coat, 4to, which contains many of his quaint utterances and odd conceits. His grosser mannerisms of style, derived from the divines of the former generation, disappeared for the most part in his subsequent discourses. About 1640 he married Eleanor, daughter of Hugh Grove of Chisenbury co., Wilts. Their eldest child, John, baptized at Broadwindsor by his father, 6th June 1641, was afterwards of Sidney Sussex College, edited the Worthies of England, 1662, and became rector of Great Wakering, Essex, where he died in 1687. At Broadwindsor, early in the year 1641, Thomas Fuller, his curate Henry Sanders, the church wardens, and others, nine persons altogether, certified that their parish, represented by 242 grown-up male persons, had taken the Protestation ordered by the Speaker of the Long Parliament. Again Fuller is met with in London, interested in the coming strife. He is said to have foreseen whither the commotions were tending; and he directed his efforts, as events developed, in advocacy of peace and in preservation of the interests of his order. For a short time he preached with success at the Inns of Court, and thence removed, at the invitation of the master of the Savoy (Dr Balcanqual) and the brotherhood of that foundation, to be lecturer at their chapel of St Mary Savoy. Certain of the parishioners would have elected one Thomas Gibbs, whose claims were put forward in the House of Commons by Sir Robert Harley; but the greater number earnestly desired Fuller, whose better title was upheld in the House by Sir John Northcote, M.P. for Ashburton. Some of the best discourses of the witty preacher were delivered at the Savoy to audiences which extended into the chapel-yard. In one, he set forth with searching and truthful minuteness the hindrances to peace, and urged the signing of petitions to the king at Oxford, and to the parliament, to continue their care in advancing an accommodation. In his intercourse with persons of influence who attended upon his ministry, or who resided in the neighbourhood of his cure, Fuller, with all the earnestness of Lord Falkland in that direction, laboured to promote the same peaceful views. With these honourable efforts an historic circumstance of some significance connects itself. With Sir Edward Wardour, clerk of the pells, Dr Dukeson, and four or five others, Fuller was deputed to take an influential peace-petition to the king, emanating from the city of Westminster and the parishes contiguous to the Savoy. To carry it with fitting circumstance, a pass was granted by the House of Lords, 2d January 1643, for an equipage of two coaches, four or six horses, and eight or ten attendants. On the arrival of the deputation at Uxbridge, 4th January, officers of the Parliamentary army stopped the coaches and searched the gentlemen; and they found upon the latter "two scandalous books arraigning the proceedings of the House," and letters with ciphers to Lord Viscount Falkland and the Lord Spencer. A message was then sent to acquaint the House of Commons with the matter, and it was complained that the Lords had given the pass. Ultimately a joint order of both Houses remanded the party; and Fuller and his friends suffered a brief imprisonment. The Westminster Petition, notwithstanding, reached the king's hands; and it was published with the royal reply. When it was expected, three months later, that a favourable result would attend the negotiations at Oxford, Fuller preached a remarkable sermon in the old abbey of Westminster, 27th March 1643, on the text 2 Sam. xix. 30, the occasion being the anniversary of Charles I.'s accession, and the subject, his return to our English Zion." This loyal discourse, in accord with the loyal text, brought the preacher into disfavour in the city. Domestic trouble likewise overtook him in the death of his wife. On 19th April the Lords gave him a pass to and from Salisbury to carry her remains thither, to be

buried, as it seems, amongst her own kin. He returned to | London, and on Wednesday, 26th July, he preached on church reformation, satirizing the religious reformers, and maintaining that only the Supreme Power could initiate reforms. The storm which this sermon aroused in the metropolis, then well-nigh abandoned by the active royalists, brought about Fuller's secret flight to Oxford, and the loss of all his preferments and property. He lived in a hired chamber at Lincoln College for 17 weeks. Thence he put forth a witty and effective reply to John Saltmarsh, who had attacked his views on ecclesiastical reform. Fuller subsequently published by royal request a fast sermon preached 10th May 1644, at St Mary's, Oxford, before the king and Prince Charles, called Jacob's Vow. In this discourse which, it is supposed, had relation to the king's proposed restoration of the church lands, the preacher referred to some religious exercise then being observed every Tuesday by Charles I., all record of which has been omitted in the pages of history. The spirit of Fuller's preaching, always characterized by calmness and moderation, gave offence to the high royalists, who charged him with lukewarmness in their cause. To silence unjust censures, he became chaplain to the regiment of the excellent Lord Hopton. For the first five years of the war, as he said, when excusing the nonappearance of his Church-History, "I had little list or leisure to write, fearing to be made a history, and shifting daily for my safety. All that time I could not live to study, who did only study to live." After the defeat of Hopton at Cheriton Down, Fuller retreated to Basing House. He took an active part in its defence, and was once incited by the noise of the enemy's artillery, which disturbed him at his books, to head a sally upon the trenches. His life with the troops caused him to be afterwards regarded as one of "the great cavalier parsons." In his marches with his regiment round about Oxford and in the west, he devoted much time to the collection of details, from churches, old buildings, and the conversation of ancient gossips, for his Church-History and Worthies of England. His patriotism in the national crisis was evidenced in many ways. For the soldiers and the more religious of the royalist party he compiled, 1645, a small volume of prayers and meditations, the Good Thoughts in Bad Times,-which, set up and printed in the besieged city of Exeter, whither he had retired, was called by himself "the first fruits of Exeter press.' It was inscribed to Lady Dalkeith, governess to the infant princess, Henrietta Anne, who was born at Exeter, 16th June 1644. Fuller was by the king placed in the household of the princess through the influence of Lady Dalkeith. In this city, as elsewhere, he attracted to himself a circle of friends. The corporation gave him the Bodleian lectureship, 21st March 1645-6, and he held it until 17th June following, soon after the surrender of the city to the Parliament. The Fear of losing the Old Light, 4to, 1646, was his farewell discourse to his Exeter friends. Under the Articles of Surrender Fuller made his composition with the Government at London, his delinquency" being that he had been present in the king's garrisons. In a characteristic petition to compound, dated 1st June 1646, he acquainted the committee that he was then lodging at "the Crown" in St Paul's Church-yard (the sign of his bookseller, Williams); and the word Crown is written in large letters and designedly falls in the centre of the document, in which, moreover, there are traces of the disagreeable position in which he was placed. In a life of Andronicus, 1646, partly authentic and partly fictitious, he satirized the leaders of the Revolution; and more than one edition of this little book was called for. For the comfort of sufferers by the war he issued, 1647, a second devotional manual. entitled Good Thoughts in Worse Times, abounding, like its predecessor and its successor, in

66

fervent aspirations, and drawing moral lessons in beautiful language out of the events of his life, or the circumstances of the time. In grief over his losses which included his library and manuscripts (his " upper and nether millstone"), and over the calamities of the country, he wrote his work on the Wounded Conscience, 1647. It was prepared at Boughton House in his native county, where, in a penniless, feeble, and exiled position, he and his little son were entertained by Edward Lord Mountagu, his patron, and where, as he says, he was restored to his former self. For the next few years of his life, Fuller was mainly dependent upon his dealings with booksellers, of whom he asserted that none had ever lost by him. Amongst other minor productions of his pen at this time he seems to have made considerable progress in an English translation of the Annales of his friend Archbishop Ussher from the MS. of that great work. Amongst his benefactors it is curious to find Sir John Danvers of Chelsea, afterwards the regicide. Under the countenance of citizens whose names are perpetuated in the dedications in his books, Fuller in 1647 began to preach at St Clement's, East Cheap, and elsewhere, in the capacity of lecturer. While at St Clement's he was suspended; but speedily recovering his freedom, he preached wherever he was invited. His connexion with the church named has recently been recognized by the erection of a fine memorial window in which, clad in a doctor's gown, he stands holding in his hand his best gift to the universal church. At Chelsea, where also he occasionally officiated, he covertly preached a sermon on the death of Charles I.,—an event which he deeply deplored. Amongst Fuller's noble patrons was the earl of Carlisle, who made him his chaplain, and presented him to the curacy of Waltham Abbey. To this kind patron he dedicated his history of that foundation; and on the title-page placed the words—

"Patria est ubicunque est bene;

Bene vixit qui bene latuit."

His possession of the living was in jeopardy on the appointment of Cromwell's "Tryers"; but he evaded the inquisitorial questions of that dreaded body by his ready wit. He had, however, the good sense to fortify himself under this ordeal with the counsel of the catholic-minded John Howe, to whom he went, saying, "Sir, you may observe. that I am a pretty corpulent man, and I am to go through a passage that is very straight; I beg you would be so good as to give me a shove and help me through." Nor was Fuller disturbed at Waltham in the "dangerous year" 1655, when the Protector's edict prohibited the adherents of the late king from preaching. Moreover, Lionel, third earl of Middlesex, who lived in the parish, gave him what remained of the books of the lord treasurer his father; and through the good offices of the marchioness of Hertford, part of his own pillaged library was restored to him. Under such circumstances Fuller actively prosecuted his literary labours, producing successively, at great cost, his survey of the Holy Land, called A Pisgah-Sight of Palestine, 1650; and his Church-History of Britain, 1655, from the birth of Jesus. Christ until the year 1648. These works were furthered in no slight degree by his connexion with Sion College, London, where he had a chamber, as well for the convenience of the press as of his city lectureships. The Church-History was angrily attacked by Dr P. Heylin, who, in the spirit of HighChurchmanship, wished, as he said, to vindicate the truth, the church, and the injured clergy. About 1652 Fuller married into the noble and loyal family of Roper. By his wife (Mary, youngest sister of Thomas, Viscount Baltinglass) he had several children. At the Oxford Act of 1657, the celebrated Robert South, who was Terræ filius, lampooned Fuller for his frequent puns and other peculiarities. described him in this Oratio as living in London, ever scribbling, and each year bringing forth new folia like a

He

tree. At length, continues South, the Church-History came forth with its 166 dedications to wealthy and noble friends; and with this huge volume under one arm, and his wife (said to be little of stature) on the other, he ran up and down the streets of London, seeking at the houses of his patrons invitations to dinner, to be repaid by his dull jests at table. This speech, although exaggerated, throws light upon the social qualities of Fuller, who had many kind friends amongst the nobility. His last and best patron was the Hon. George Berkeley of Cranford House, Middlesex, whose chaplain he was, and who gave him Cranford rectory, 1658. To this nobleman Fuller's reply to Heylin, called The Appeal of Injured Innocence, 1659, was inscribed. This remarkable and instructive book embraces, as its editor, Mr James Nichols, has remarked, "almost every topic within the range of human disquisition, from the most sublime mysteries of the Christian religion, and the great antiquity of the Hebrew and Welsh languages, down to The Tale of a Tub, and criticisms on Shakespeare's perversion of the character of Sir John Falstaff." At the end of the Appeal is an elegant epistle "to my loving friend Dr Peter Heylin," conceived in the admirable Christian spirit which characterized all Fuller's dealings with controversialists. Why should Peter," he asked, "fall out with Thomas, both being disciples to the same Lord and Master? I assure you, sir, whatever you conceive to the contrary, I am cordial to the cause of the English Church, and my hoary hairs will go down to the grave in sorrow for her sufferings. The only other important works issued by Fuller in his lifetime were connected with the Restoration. The revived Long Parliament, December 1659, proposed an oath of fealty to the Commonwealth, and the abjuration of Charles II. and his family. The matter was much debated; and in an able letter published in February 1660, which went into a third edition, called An Alarum to the Counties of England and Wales, Fuller discussed the proposal. His His arguments tended to swell the cry for a free and full parliament,-free from force, as he expressed it, as well as from abjurations or previous engagements. In anticipation of the meeting of the new parliament, 25th April, and as if foreseeing the unwise attitude of those in power in relation to the reaction, Fuller put forth his Mixt Contemplations in Better Times, 1660, dedicated to Lady Monk. It tendered advice in the spirit of its motto, "Let your moderation be known to all men: the Lord is at hand." There is good reason to suppose that Fuller was at the Hague immediately before the Restoration, in the retinue of Lord Berkeley, one of the commissioners of the House of Lords, whose last service to his friend was to interest himself in obtaining him a bishopric. A Panegyrick to His Majesty on his Happy Return was the last of Fuller's verse-efforts. On 2d August, by royal letters, he was admitted D.D. at Cambridge, as a scholar of integrity and good learning, who had been hindered in the due way of proceeding to his degree. His former preferments were restored to him. At the Savoy Pepys heard him preach; but he preferred his conversation or his books to his sermons. Fuller's last promotion was that of chaplain in extraordinary to Charles II. In the summer of 1661 he visited the west in connexion with the business of his prebend, and upon his return he was seized with a kind of typhus-fever called the "new disease." On Sunday, 12th August, while preaching a marriage sermon at the Savoy, he was disabled from proceeding; and at the close of the service he was carried home in a sedan to his new lodgings in Covent-Garden, where he expired, Thursday, 16th August, aged 54. On the following day 200 of his brethren attended his corpse to its resting place in the chancel of Cranford Church, where Dr Hardy preached a funeral sermon. A mural tablet was afterwards set up on the north side of the

chancel with an epitaph, which, though perhaps longer than Fuller's essay on tombs might allow him to approve, contains a conceit worthy of his own pen, to the effect that while he was endeavouring (viz., in The Worthies) to give immortality to others, he himself attained it. It is said that the thought of that unfinished work troubled him upon his deathbed, and that he often incoherently called out to his attendants for pen and ink, as if to complete it. Dr Fuller was in stature somewhat tall, "with a proportionable bigness to become it," and his gait was graceful. He was of a sanguine temperament, and had a ruddy countenance and light curled hair. Some of these features are pleasingly depicted in his portrait at Cranford House. His personal character was admirable. The charm of his manners was felt by all, his deportment being "according to the old English guise." His disposition was genial, leading him to embrace goodness wherever he found it. To these fine qualities of mind he added prudence. "By his particular temper and management," said the historian Echard, "he weathered the late great storm with more success than many other great men.' He had many of the peculiarities of scholars. He was known as "a perfect walking library." The strength of his memory was proverbial, and some amusing anecdotes are connected with it.

His writings were the product of a highly original mind, and their moral tone was excellent. He had a fertile imagination and a happy faculty of illustration. His diction in the main was elegant, and more idiomatic than that of Taylor or Browne. Antithetic and axiomatic sentences abound in his pages, embodying literally the wisdom of the many in the wit of one. He was quaint," and something more. "Wit," said Coleridge, in a well-known enlogy, "wit was the stuff and substance of Fuller's intellect. It was the element, the earthen base, the material which he worked in; and this very circumstance has defrauded him of his due praise for the practical wisdom of the thoughts, for the beauty and variety of the truths, into which he shaped the stuff. Fuller was incomparably the most sensible, the least prejudiced, great man of an age that boasted a galaxy of great men." This opinion was formed after the perusal of the Church-History. That work and The Worthies of England are unquestionably Fuller's greatest efforts. They embody the collections of an entire life; and since his day they have been the delight and the solace of their readers, and the incentive which has directed or allured many English scholars into historical and topographical studies. The Holy State has taken rank amongst the best books of characters. Fuller's works, according to Charles Lamb, were, in the early portion of this century, scarcely perused except by antiquaries; but since that time, mainly through the appreciative criticisms of Coleridge, Southey, Crossley, and others, they have received more general attention; and nearly the whole of his extant writings have been reprinted of late years. (J. E. B.)

FULLER'S EARTH (Germ. Walkererde, Fr. Terre à foulon, Argile smectique), so named from its use by fullers as an absorbent of the grease and oil of cloth, is an earthy hydrated silicate of aluminium, containing, according to one analysis, silica 530, alumina 10, ferric oxide 9.75, magnesia 1.25, lime 5, sodium chloride 1, water 24 per cent., and a trace of potash. It has a specific gravity of 1.7-2.4, and a shining streak; is unctuous to the touch; is commonly greenish-brown or greenish-grey, sometimes bluish-grey, whitish, or red-brown in colour; adheres but slightly to the tongue; becomes translucent in water, and falls to powder; and before the blowpipe gives a porous slag, melting eventually to a white glass. Among the localities where fuller's earth is found are Nutfield near Reigate in Surrey, Renton in Yorkshire, Quarry Wood in Morayshire, Rosswein in Saxony, and Zwikowetz in Bohemia. Fuller's or "Walker's" earth is

found between the Aymestry limestone and the underlying lower Ludlow beds, rendering the former particularly liable to slides or subsidences (see Murchison, Siluria). From the presence in it of beds of the mineral, a thick deposit of blue and yellow clays with bands of rubbly limestone in the Oolitic or Jurassic series of rocks in England has received the name of Fuller's Earth (see GEOLOGY). The consumption of fuller's earth has fallen off considerably, owing to the employment of other substances for the cleansing of cloth. It was in past times largely mined in the Downs, south of Bath, for use in the cloth-mills of Bradford-on-Avon, Frome, and Gloucestershire.

FULMAR, from the Gaelic Fulmaire, the Fulmarus glacialis of modern ornithologists, one of the largest of the Petrels (Procellariida) of the northern hemisphere, being about the size of the Common Gull (Larus canus) and not unlike it in general coloration, except that its primaries are grey instead of black. This bird, which ranges over the North Atlantic, is seldom seen on the European side below lat. 53° N., but on the American side comes habitually to lat. 45°, or even lower. It has been commonly believed to have two breeding places in the British Islands, namely, St Kilda and South Barra; but, according to Mr Robert Gray (Birds of the West of Scotland, p. 499), it has abandoned the latter since 1844, while he is assured of its now breeding in Skye. Northward it established itself about 1838 on Myggenæs Holm, one of the Faroes, while it has several stations off the coast of Iceland and Spitsbergen, as well as at Bear Island. Its range towards the pole seems to be only bounded by open water, and it is the constant attendant upon all who are employed in the whale and seal fisheries, shewing the greatest boldness in approaching boats and ships, and feeding on the offal obtained from them. By our seamen it is commonly called the "Molly Mawk"1 (corrupted from the Dutch Mallemuck), and is extremely well known to them, its flight, as it skims over the waves, first with a few beats of the wings and then gliding for a long way, being very peculiar. It only visits the land to deposit its single white egg, which is laid on a rocky ledge, where a shallow nest is made in the turf and lined with a little dried grass. Many of its breeding-places are a most valuable property to those who live near them and take the eggs and young, which, from the nature of the locality, are only to be had at a hazardous risk of life. In St Kilda it is said that from 18,000 to 20,000 young are killed in one week of August, the only time when, by the custom of the community, they are allowed to be taken. These, after the oil is extracted from them, serve the islanders with food for the winter. This oil, says Mr Gray, having been chemically examined by Mr E. C. C. Stanford, was found to be a fish-oil, and to possess nearly all the qualities of that obtained from the liver of the cod, with a lighter specific gravity. It, however, has an extremely strong scent, which is said by those who have visited St Kilda to pervade every thing and person on the island, and is certainly retained by an egg or skin of the bird for many years. Whenever a live example is seized in the hand it ejects a considerable quantity of this oil from its mouth. The Fulmar is said by Mr Darwin (Origin of Species, ed. 4, p. 78) to be the most numerous bird in the world; but on whose authority the statement is made does not appear, and to render it probable we should have to unite specifically with the Atlantic bird, not only its Pacific representative, F. pacificus, which some ornithologists deem distinct, but also that which replaces it in the Antarctic seas and is considered by most authorities to be a perfectly good species, F. glacialioides. The differences between them are, however, exceedingly slight, and for Mr

1 A name misapplied in the southern hemisphere to Diomedea melanophrys, one of the Albatrosses.

Darwin's purpose on this particular occasion it matters little how they are regarded. It is a more interesting question whether the statement is anyhow true, but one that can hardly be decided as yet. (A. N.)

FULTON, ROBERT (1765-1815), an American engineer and mechanician, was born in 1765 at Little Britain in Pennsylvania. At the age of seventeen he adopted the profession of a portrait and landscape painter, but he also, even then, devoted a considerable portion of his time to mechanical pursuits. In his twenty-second year he visited England, with the view of improving himself in art by the instructions of his countryman West. There he made the acquaintance of the duke of Bridgewater, Earl Stanhope, and Watt, and partly by their influence he was led to devote his attention more exclusively to mechanical engineering. In 1793 he had conceived the design of propelling vessels by steam, but did not at that time find a suitable opportunity for putting his views into practice. His time was also much engrossed in devising a method of superseding the locks on canals by a plane of double incline for which he obtained a patent from the British Government in 1794. In the same year he obtained patents for flax-spinning and rope-twisting machines, and various other mechanical inventions, bearing chiefly upon the construction of canals, on which latter subject he published a treatise. In 1797 he removed to Paris, and remained for seven years in the house of Joel Barlow, the American minister at the court of France, prosecuting his scientific studies. During that period he projected the first panorama ever exhibited in Paris, and made important experiments on submarine explosives. These experiments were further continued in America, but although Congress voted him 5000 dollars for prosecuting them, his plans were finally declared impracticable. It was also at Paris that he first succeeded, after repeated trials, in propelling a boat through the water by the aid of steam. In 1806 he returned to America and repeated the experiment on a larger scale and with more decided success. In 1809 he took out his first patent, but his rights were disputed, and after protracted legislation a compromise was effected. In 1814 Fulton constructed the first United States' war steamer, and he was engaged upon an improvement of his submarine torpedo when he died, February 24, 1815.

See Life of Robert Fulton, by C. D. Colden, 1817, and the biography by James Renwick in Spark's American Biography.

FUMITORY, or Fumaria, Linn. (Germ. Erdrauch, Fr. Fumeterre), a genus of annual, rarely perennial, herbs of the natural order Fumariacea, with stems usually branched and straggling, often climbing by means of their petioles; leaves alternate and decompound, with narrow segments; flowers in racemes, small, tubular, and purple or whitish, with purple tips; sepals 2, and deciduous; petals 4, and connivent, the upper one saccate or spurred at the base, the two inner cohering at the apex; stamens 6, and in two bundles opposite the outer petals; style deciduous; and capsule oneseeded and indehiscent. There are several British species. of the genus. The Common Fumitory, F. officinalis (Germ. Taubenkropf), called by Shakespeare the "rank fumitory' or "fumiter (Henry V., v. 2; Lear, iv. 4), is a plant indigenous to Europe, North Africa, and Asia, and is found as an introduced species in the United States. It has glauc ous leaves and pale or dark rose-purple flowers, which bloom throughout the summer, and grows to a height of one or two feet. two feet. It is a common weed in corn-fields, and like other members of the genus flourishes best in rich cultivated ground. In past times it was in esteem for its reputed cholagogue and other medicinal properties, and in England, boiled in water, milk, or whey, it was used as a cosmetic. The herbage of F. officinalis and F. racemosa is used in China under the nanie of Tsze-hwa-ti-ting as an application IX. 103

for glandular swellings, carbuncles, and abscesses, and was formerly valued in jaundice, and in cases of accidental swallowing of the beard of grain (see F. Porter Smith, Contrib. towards the Mat. Medica of China, p. 99, 1871). The name fumitory, Latin fumus terræ, has been supposed to be derived from the fact that its juice irritates the eyes like smoke (see Fuchs, De Historia Stirpium, p. 338, 1542); but The Grete Herball, cap. clxix., 1529, fol., following the De Simplici Medicina of Platearius, fo. xciii. (see in Nicolai Præpositi Dispensatorium ad Aromatarios, 1536), says: "It is called Fumus terre fume or smoke of the erthe bycause it is engendred of a cours fumosyte rysynge frome the erthe in grete quantyte lyke smoke: this grosse or cours fumosyte of the erthe wyndeth and wryeth out: and by workynge of the ayre and sonne it turneth into this herbe."

For figures of various species of fumitory, see J. T. Boswell Syme, English Botany, vol. i., 1863.

FUNCHAL. See MADEIRA.

FUNCTION. Functionality, in Analysis, is dependence on a variable or variables; in the case of a single variable И, it is the same thing to say that v depends upon u, or to say that v is a function of u, only in the latter form of expression the mode of dependence is embodied in the term "function." We have given or known functions such as u2 or sin u, and the general notation of the form pu, where the letter is used as a functional symbol to denote a function of u, known or unknown as the case may be in each case u is the independent variable or argument of the function, but it is to be observed that if v be a function of u, then v like u is a variable, the values of v regarded as known serve to determine those of u; that is, we may conversely regard u as a function of v. In the case of two or more independent variables, say when w depends on or is a function of u, v, &c., or w=$(u, v, . . ), then u, v,.. are the independent variables or arguments of the function; frequently when one of these variables, say u, is principally or alone attended to, it is regarded as the independent variable or argument of the function, and the other variables v, &c., are regarded as parameters, the values of which serve to complete the definition of the function. We may have a set of quantities w, t,. each of them a function of the same variables u, v, . .; and this relation may be expressed by means of a single functional symbol, (w, t, . .) = p(u, v . .); but, as to this, more hereafter.

The notion of a function is applicable in geometry and mechanics as well as in analysis; for instance, a point Q, the position of which depends upon that of a variable point P, may be regarded as a function of the point P; but here, substituting for the points themselves the coordinates (of any kind whatever) which determine their positions, we may say that the coordinates of Q are each of them a function of the coordinates of P, and we thus return to the analytical notion of a function. And in what follows a function is regarded exclusively in this point of view, viz., the variables are regarded as numbers;

and we attend to the case of a function of one variable v=fu. But it has been remarked (see EQUATION) that it is not allowable to confine the attention to real numbers; a number u must in general be taken to be a complex number u=x+iy, x and y being real numbers, each susceptible of continuous variation between the limits -∞, ∞, and i denoting √1. In regard to any particular function, fu, although it may for some purposes be sufficient to know the value of the function for any real value whatever of u, yet to attend only to the real values of u is an essentially incomplete view of the question; to properly know the function it is necessary to consider u under the aforesaid imaginary or complex form u=x+iy.

To a given value x+iy of u there corresponds in general for v a value or values of the like form v=x' + iy', and we obtain a geometrical notion of the meaning of the functional relation vfu by regarding x, y as rectangular coordinates of a point P in a plane II, and x', y' as rectangular coordinates of a point P' in a plane (for greater convenience a different plane) II'; P, P' are thus the geometrical representations, or representative points, of the variables u=x+iy and u=x+iy respectively; and, according to a locution above referred to, the point P' might be regarded as a function of the point P; a given value of u=x+iy is thus represented by a point P in the plane II, and corresponding hereto we have a point or points P' in the plane II', representing (if more than one, each of them) a value of the variable v=x'+iy'. And, if we attend only to the values of u as corresponding to a series of positions of the representative point P, we have the notion of the "path" a complex variable u=x+iy

Known Functions.

1. The most simple kind of function is the rational and integral function. We have the series of powers u2, u3, each calculable not only for a real but also for a complex value of u, (x + iy)2= x2 - iy3 + 2ixy, (x + iy)3 x3-3x2 + i(3x2 y3), &c., and thence, if a, b,.. be real or complex numbers, th general form a + bu + cu2. +kum, of a rational and integral function of the order m. And taking two such functions, say of the orders m and n respectively, the quotient of one of these by the other represents the general form of a rational function of u.

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1

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The function which next presents itself is the algebraical function, and in particular the algebraical function expressible by radicals. To take the most simple case, suppose (m being a positive integer) that ver u; v is here the irrational function um. Obviously, if u is real and positive, there is always a real and positive value of ", calculable to any extent of approximation from the equation -u, which serves as the definition of um; but it is known (see EQUATION) that as well in this case as in the general case where is a complex number there are in fact m values of the function um; and that for their determination we require the theory of the so-called circular functions sine and cosine; and these depend on the exponential function expu, or, as it is commonly written, e*, which has for its inverse the logarithmic function log u; these are all of them transcendental functions.

...

...

+kum,

k may

2. In a rational and integral function a+bu+cu3 the number of terms is finite, and the coefficients a, b,: have any values whatever, but if we imagine a like series a + bu + cu2 + .. extending to infinity, non constat that such an expression has any calculable value,—that is, any meaning at all; the coefficients a, b, c... must be such as, either for every value whatever of u (that is, for every finite value) or for values included within certain limits, to make the series convergent. It is easy to see that the values of a, b, c . . may be such as to make the series always convergent; for instance, this is the case for the exponential function,

น u2 us expu=1+ + + + &c.; 1 1.2 1.2.3

taking for the moment u to be real and positive, then it is evident that however large u may be, the successive terms will become ultimately smaller and smaller, and the series will have a determinate calculable value. A function thus expressed by means of a convergent infinite series is not in general algebraical, and when it is not so, it is said to be transcendental (but observe that it is in nowise true that we have thus the most general form of a transcendental function); in particular, the exponential function above written down is not an algebraical function.

By forming the expression of exp v, and multiplying together the two series, we derive the fundamental property exp u exp v = exp (u + v); whence also

exp x exp iy= exp (x + iy), so that exp (x + y) is given as the product of the two series exp and exp iy. As regards this last, if in place of u we actually write the value iy, we find