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Rh bibliography and printing, with reference either to the size of paper employed, or of the book, or to the pagination. In the phrase “in folio” it means a sheet of paper folded once, and thus a book bound up in sheets thus folded is a book of the largest size and is known as a “folio” (see ). Similarly, “folio” is one of the sizes of paper adapted to be thus folded (see ). In book-keeping the word is used for a page in a ledger on which the credit and debtor account is written; in law-writing, for a fixed number of words in a legal document, used for measurement of the length and for the addition of costs. In Great Britain, a “folio” is taken to contain 72 words, except in parliamentary and chancery documents, when the number is 90. In the U.S.A. 100 words form a “folio.”

  FOLIUM, in mathematics, a curve invented and discussed by René Descartes. Its cartesian equation is x3 + y3 = 3axy. The curve is symmetrical about the line x = y, and consists of two infinite branches asymptotic to the line x + y + a = o and a loop in the first quadrant. It may be traced by giving m various values in the equations x = 3am / (1 + m3), y = 3am2 (1 + m3), since by eliminating m between these relations the equation to the curve is obtained. Hence it is unicursal (see ). The area of the loop, which equals the area between the curve and its asymptote, is 3a/2.

 FOLKES, MARTIN (1690–1754), English antiquary, was born in London on the 29th of October 1690. He was educated at Saumur University and Clare College, Cambridge, where he so distinguished himself in mathematics that when only twenty-three years of age he was chosen a fellow of the Royal Society. He was elected one of the council in 1716, and in 1723 Sir Isaac Newton, president of the society, appointed him one of the vice-presidents. On the death of Newton he became a candidate for the presidency, but was defeated by Sir Hans Sloane, whom, however, he succeeded in 1741; in 1742 he was made a member of the French Academy; in 1746 he received honorary degrees from Oxford and Cambridge. In 1733 he set out on a tour through Italy, in the course of which he composed his Dissertations on the Weights and Values of Ancient Coins. Before the Society of Antiquaries, of which he was president from 1749 to 1754, he read in 1736 his Observations on the Trajan and Antonine Pillars at Rome and his Table of English Gold Coins from the 18th Year of King Edward III. In 1745 he printed the latter with another on the history of silver coinage. He also contributed both to the Society of Antiquaries and to the Royal Society other papers, chiefly on Roman antiquities. He married in 1714 Lucretia Bradshaw, an actress who had appeared at the Haymarket and Drury Lane (see Nichols’s Lit. Anecdot. ii. 578–598).

For Sir John Hill’s attack on Folkes (Review of the Works of the Royal Soc., 1751), see D’Israeli, Calamities and Quarrels of Authors (1860), pp. 364–366.

 FOLKESTONE, a municipal borough, seaport and watering-place of Kent, England, within the parliamentary borough of Hythe, 71 m. S.E. by E. of London by the South-Eastern & Chatham railway. Pop. (1891) 23,905; (1901) 30,650. This is one of the principal ports in cross-Channel communications, the steamers serving Boulogne, 30 m. distant. The older part of Folkestone lies in a small valley which here opens upon the shore between steep hills. The more modern portions extend up the hills on either hand. To the north the town is sheltered by hills rising sharply to heights of 400 to 500 ft., on several of which, such as Sugarloaf and Castle Hills, are ancient earthworks. Above the cliff west of the old town is a broad promenade called the Lees, commanding a notable view of the channel and connected by lifts with the shore below. On this cliff also stands the parish church of St Mary and St Eanswith, a cruciform building of much interest, with central tower. It is mainly Early English, but the original church, attached to a Benedictine priory, was founded in 1095 on the site of a convent established by Eanswith, daughter of Eadbald, king of Kent in 630. The site of this foundation, however, became endangered by encroachments of the sea. The monastery was destroyed at the dissolution of religious houses by Henry VIII. Folkestone inner harbour is dry at low water, but there is a deep water pier for use at low tide by the Channel steamers, by which not only the passenger traffic, but also a large general trade are carried on. The fisheries are important. Among institutions may be mentioned the grammar school, founded in 1674, the public library and museum, and a number of hospitals and sanatoria. The discontinued Harveian Institution for young men was named after William Harvey, discoverer of the circulation of the blood, a native of Folkestone (1578), who is also commemorated by a tercentenary memorial on the Lees. Folkestone is a member of the Cinque Port of Dover. It is governed by a mayor, 7 aldermen and 21 councillors. Area, 2522 acres. To the west of Folkestone, close to Shorncliffe camp, is the populous suburb of Cheriton (an urban district, pop. 7091).

Folkestone (Folcestan) was among the possessions of Earl Godwine and was called upon to supply him with ships when he was exiled from England; at the time of the Domesday Survey it belonged to Odo, bishop of Bayeux. From early times it was a member of the Cinque Port of Dover, and had to find one out of the twenty-one ships furnished by that port for the royal service. It shared the privileges of the Cinque Ports, whose liberties were exemplified at the request of the barons of Folkestone by Edward III. in 1330. The corporation, which was prescriptive, was entitled the mayor, jurats and commonalty of Folkestone. The history of Folkestone is a record of its struggle against the sea, which was constantly encroaching upon the town. In 1629 the inhabitants, impoverished by their losses, obtained licence to erect a port. By the end of the 18th century the town had become prosperous by the increase of its fishing and shipping trades, and by the middle of the 19th century one of the chief health and pleasure resorts of the south coast.

 FOLKLAND (folcland). This term occurs three times in Anglo-Saxon documents. In a law of Edward the Elder (c. i. 2) it is contrasted with bookland in a way which shows that these two kinds of tenure formed the two main subdivisions of landownership: no one is to deny right to another in respect of folkland or bookland. By a charter of 863 (Cod. Dipl. 281), King Æthelberht exchanges five hides of folkland for five hides of bookland which had formerly belonged to a thane, granting the latter for the newly-acquired estates exemption from all fiscal exactions except the threefold public obligation of attending the fyrd and joining in the repair of fortresses and bridges. Evidently folkland was not free from the payment of gafål (land tax) and providing quarters for the king’s men. In ealdorman Alfred’s will the testator disposes freely of his bookland estates in favour of his sons and his daughter, but to a son who is not considered as rightful offspring five hides of folkland are left, provided the king consents. It is probable that folkland is meant in two or three cases when Latin documents speak of terra rei publicae jure possessa.

Two principal explanations have been given to this term. Allen thought that folkland was similar to the Roman ager publicus: it was the common property of the nation (folc), and the king had to dispose of it by carving out dependent tenures for his followers more or less after the fashion of continental beneficia. These estates remained subject to the superior ownership of the folk and of the king: they could eventually be taken back by the latter and, in any case, the heir of a holder of folkland had to be confirmed in possession by the king. A letter of Bede to the archbishop Ecgbert of York may be interpreted to apply to this kind of tenure. Kemble, K. Maurer, H. C. Lodge, Stubbs and others followed Allen’s lead.

Another theory was started by Professor Vinogradoff in an article on folkland in the ''English Hist. Review'' for 1893. It considers folkland as landownership by folkright—at common law, as might be said in modern legal speech. In opposition to it bookland appears as landownership derived from royal privilege. The incidents recorded in the charters characterize folkland as