FOLI (Foley), ALLAN JAMES (1837-1899), Irish bass singer, was born at Cahir, Tipperary, on the 7th of August 1837; originally a carpenter, he studied under Bisaccia at Naples, and made his first appearance at Catania in 1862. From the opera in Paris he was engaged by Mapleson for the season of 1865, and appeared with much success in various parts. He sang in the first performance of The Flying Dutchman (Daland) in England in 1870, and in the first performance of Gounod’s Redemption in 1882. He was distinguished in opera and oratorio alike for his vigorous, straightforward way of singing, and was in great request at ballad concerts. He died on the 20th of October 1899.
FOLIGNO (anc. Fulginiae, q.v.), a town and episcopal see of Umbria, Italy, 771 ft. above sea-level, in the province of Perugia, from which it is 25 m. S.E. by rail. Pop. (1901) 9532 (town), 26,278 (commune). It lies in a fertile plain, on the Topino, a tributary of the Tiber; it is almost square in shape and is surrounded by walls. It is a picturesque and interesting town; several of its churches contain paintings by Umbrian masters, notably works by Niccolò di Liberatore (or Niccolò Alunno, 1430-1502), and among them his chief work, a large altar-piece (the predella of which is in the Louvre) in S. Niccolò. The cathedral has a romanesque S. façade of 1133, restored in 1903; the interior was modernized in the 18th century. To the left of the choir is an octagonal chapel by Antonio da Sangallo the younger (1527). In the same piazza as the S. façade is the Palazzo del Governo, erected in 1350, which has a chapel with frescoes by Ottaviano Nelli of Gubbio (1424). S. Maria infra Portas is said to date from the 7th century, but from this period only the columns of the portico remain. Raphael’s “Madonna di Foligno,” now in the Vatican, was originally painted for the church of S. Anna. The Palazzo Orfini and the Palazzo Deli are two good Renaissance buildings.
Foligno seems to have been founded about the middle of the 8th century A.D. It changed hands often during the wars of the 13th century, and was destroyed by Perugia in 1281. From 1305 to 1439 it was governed by the family of the Trinci as deputies of the Holy See, until in the latter year one of its members went against the church. Pope Eugene IV. sent a force against Foligno, to which the inhabitants opened their gates, and the last of the Trinci, Corrado II., was beheaded. Henceforth Foligno belonged to the states of the church until 1860. It suffered from a severe earthquake in 1832. Foligno is a station on the main line from Rome (via Orte) to Ancona, and is the junction for Perugia. Three miles to the E. is the abbey of Sassovivo with cloisters of 1229, very like those of S. Paolo fuori le Mura at Rome, with pairs of small columns supporting arches, and decorations in coloured mosaic (“Cosmatesque” work). The church has been modernized.
FOLIO (properly the ablative case of the Lat. folium, leaf, but also frequently an adaptation of the Ital. foglio), a term in 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 [Bibliography]). Similarly, “folio” is one of the sizes of paper adapted to be thus folded (see [Paper]). 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 [Curve]). The area of the loop, which equals the area between the curve and its asymptote, is 3a/2.