of each part of the belt — the driving and the slack part alike — be in the plane of the pulley toward which that part of the belt runs; the belt being always delivered by one pulley into the plane of the other.
Belts are made in a great variety of sizes, some of them being very large. As extreme cases, may be noted: A leather belt of the New Jersey Zinc Works, 4 thicknesses, 48 inches wide, and 102 feet long; a rubber belt in Chicago, 6-ply, 48 inches wide, and 320 feet long; a leather belt for a paper-mill in Wilmington, Del., 60 inches wide and 186½ feet long. For a summary of modern practice in the calculation, operation, and care of belts and belting, consult Kent, Mechanical Engineer's Pocket-Book (New York, 1900).
BELT, Great and Little. Names given to the two straits of eastern Denmark which, with the Sound, connect the waters of the Kattegat with the Baltic (Map: Denmark, C and D 3). The Great Belt, which includes the Store Belt and the Langeland Belt, is about 70 miles long, and varies from 8 to 20 miles in width, in fact broadening to 30 miles toward the south in Vordinborg Bay; it separates Seeland and Laaland on the east from Fünen and Langeland on the west. The Little or Lille Belt, which is shallow, is about 50 miles long, and varies from less than a mile in width at the north to an extreme width of 30 miles, its average width being less than 10 miles; it separates Fünen on the east from Jutland and Schleswig on the west. Both straits are dangerous to navigate on account of currents and sand-banks; the smaller one is little used.
BEL'TANE (Scottish Gael. Bealltainno), BELLTAINE, or BELTINE. A pagan Celtic
festival, traces of which have survived to this
day. The name is still used for May-day in
Gaelic Scotland. The etymology and original
meaning are uncertain. "Cormac's Glossary," an
Irish text of the Tenth Century, contains the
earliest mention of the institution (spelled bell-
taine and beltine) , and two different explana-
tions are there given of its meaning. In one
place it is said to mean 'lucky fire,' and in
another 'fire of Bel,' who is declared to be 'an
idol god.' The second of these interpretations
has been commonly accepted, but without any
sufficient evidence. The identification of bel-
as the name of a god is doubtful, and even
the connection between the second element and
Irish teine, 'fire,' is open to question. In any
case, however, the Semitic Baal has nothing to do
with the matter.
Cormac's description of Beltine is very brief. He simply says that the Druids used to make two fires with great incantations, and drive their cattle between them as a safeguard against dis- ease. This custom of driving domestic animals through fire is still known in Brittany and the islands of Arran: and in certain May-day festivi- ties it was practiced until recently in Scotland. A young man, selected by a prescribed ceremonial, was similarly compelled to leap three times through fire. Both these ceremonies look like symbolical sacrifices, and there may have been a time when the victims were actually burned. The whole set of observances, like the German Johan- nisfeuer at the summer solstice, is usually ex- plained (and doubtless correctly) as a branch of sun-worship.
Consult, for the statement in Cormac, Glos- sary, the edition by O'Donovan and Stokes (Lon- don, 1862); for the Scottish Beltane, Jamieson, Scottish Dictionary (Edinburgh. 1808); for the significance of the ceremonies, A. Bertrand, La religion des Gaulois (Paris, 1897). Rhys makes some comparisons with the Athenian Thargelia in his Hibbert Lectures (London, 1887).
BEL'TON. A city and county-seat of Bell
County, Tex., 80 miles north by east of Austin,
on the Leon River, and on the Missouri, Kansas
and Texas and the Gulf, Colorado and Santa Fe
railroads (Map: Texas, F 4). It has a county
court-house and jail buildings, and is the seat
of Baylor Female College (Baptist), opened in
1845. Building-stone, quarried in the vicinity,
and cotton constitute an extensive export trade,
and among the industrial establishments are
cotton, cottonseed oil, and flour-mills, foundries,
lumber-yards, marble-works, brick-yard, and sev-
eral other plants. Population, in 1890, 3000: in
1900. 3700.
BELTRAFFIO, bel-traf'vo,
or BOLTRAFFIO, Giovanni Antonio (1467-1516). An Italian painter, born in Milan. He was a pupil of Leonardo da Vinci, worked as an amateur, and ably imitated Leonardo in color and breadth of treatment. His authentic works are extremely rare. Among them are: "Madonna of the Casio Family" (Louvre Gallery), a portrait in the Ambrosian Library, Milan, and two at Isola Bella.
BELTRAME, bel-trii'ma,
Giovanni (1824—). An Italian philologist and missionary, born at Valeggio, in northern Italy. In 1854 he was sent to Khartum and Fazogl by an Austrian missionary society, and in 1858 he accompanied Knoblecher to the newly established missionary station, "Holy Cross" on the White Nile. He returned to Europe in 1862. The following are his principal publications: Grammatica della lingua Denka (1880); Vocabolario, Italiano-Denka e Denka-Italiano (1880); Il Sennaar e lo Sciangallah (1879); Il fiume bianco e i Denka (1882); In Palestina (1895).
BELTRAMI, bel-tra'me,
Eugenio (1835-1900). An Italian mathematician. He was born at Cremona, and taught mathematical physics at the University of Rome, and at several other Italian universities. The Lincei, a celebrated academy of Rome, honored Beltrami by electing him president. His contributions to mathematics are largely on the subject of non-Euclidian geometry. (See Geometry.) He reached the remarkable conclusion that the propositions of non-Euclidian geometry relate to figures lying upon surfaces of constant negative curvature. The conclusion that on surfaces of constant curvature there are three geometries — the non-Euclidian on a surface of constant negative curvature, the spherical on a surface of constant positive curvature, and the Euclidian on a surface of zero curvature — rests upon the researches of Beltrami, Helmholtz, and Riemann. Thus Beltrami has taken a conspicuous part in laying the foundation of modern geometry. The most important among his numerous essays is the monograph, "Saggio di interpretazione della geometria non-euclidia," published in the Giornale di Matematica VI. (Rome). The following theorem is known as Beltrami's: "The centre of a circle circumscribing a triangle is the centre of
