[1] Louis de Berquin, who died on the 17th of April 1529, belonged to
a noble family of Artois. He was a man of exemplary life and a friend
of Erasmus and the humanists, besides being a _persona grata_ at the
court of Louise of Savoy and Francis I. His main offence was that he
attacked the monks and clergy, and that he advocated the reading of
the Scriptures by the people in the vulgar tongue.--(W. A. P.)
LOZENGE (from the Fr. _losenge_, or _losange_; the word also appears in
Span. _losanje_, and Ital. _losanga_; perhaps derived from a word
meaning a stone slab laid on a grave, which appears in forms such as
Provençal _lousa_, Span. _losa_, the ultimate origin of which is
unknown, the Lat. _lapis_, stone, or _laus_, praise, in the sense of
epitaph, have been suggested), properly a four equal-sided figure,
having two acute and two obtuse angles, a rhomb or "diamond." The figure
is frequently used as a bearing in heraldry and especially as a shield
so shaped on which the arms of a widow or spinster are emblazoned. It is
used also to denote the diamond-shaped facets of a precious stone when
cut, also the diamond panes of a casement window. In the 14th century
the "lozenge pattern" was a favourite design for decoration. The word is
also applied to a small tablet of sugar, originally diamond shaped,
containing either medical drugs or some simple flavouring, or to a
tablet of any concentrated substance, such as a meat-lozenge. In the
reign of James I. of Scotland (1406-1437) a Scotch gold coin having a
lozenge-shaped shield with the arms of Scotland on the obverse side was
called a "lozenge-lion."
LOZÈRE, a department of south-eastern France belonging to the central
plateau, composed of almost the whole of Gévaudan and of some portions
of the old dioceses of Uzès and Alais, districts all formerly included
in the province of Languedoc. Pop. (1906) 128,016. Area, 1999 sq. m. It
is bounded N. by Cantal and Haute-Loire, E. by Ardèche and Gard, S. by
Gard and Aveyron and W. by Aveyron and Cantal. Lozère is mountainous
throughout and in average elevation is the highest of all the French
departments. It has three distinct regions--the Cévennes proper to the
south-east, the _causses_ to the south-west and the mountain tracts
which occupy the rest of its area. The Cévennes begin (within Lozère)
with Mont Aigoual, which rises to a height of more than 5100 ft.;
parallel to this are the mountains of Bougès, bold and bare on their
southern face, but falling gently with wooded slopes towards the Tarn
which roughly limits the Cévennes on the north. To the north of the Tarn
is the range of Lozère, including the peak of Finiels, the highest point
of the department (5584 ft.). Farther on occurs the broad marshy plateau
of Montbel, which drains southward to the Lot, northwards to the Allier,
eastward by the Chassezac to the Ardèche. From this plateau extend the
mountains of La Margeride, undulating granitic tablelands partly clothed
with woods of oak, beech and fir, and partly covered with pastures, to
which flocks are brought from lower Languedoc in summer. The highest
point (Truc de Randon) reaches 5098 ft. Adjoining the Margeride hills on
the west is the volcanic range of Aubrac, a pastoral district where
horned cattle take the place of sheep; the highest point is 4826 ft.
The _causses_ of Lozère, having an area of about 564 sq. m., are
calcareous, fissured and arid, but separated from each other by deep and
well-watered gorges, contrasting with the desolate aspect of the
plateaus. The _causse_ of Sauveterre, between the Lot and the Tarn,
ranges from 3000 to 3300 ft. in height; that of Méjan has nearly the
same average altitude, but has peaks some 1000 ft. higher. Between these
two causses the Tarn valley is among the most picturesque in France.
Lozère is watered entirely by rivers rising within its own boundaries,
being in this respect unique. The climate of Lozère varies greatly with
the locality. The mean temperature of Mende (50° F.) is below that of
Paris; that of the mountains is always low, but on the _causses_ the
summer is scorching and the winter severe; in the Cévennes the climate
becomes mild enough at their base (656 ft.) to permit the growth of the
olive. Rain falls in violent storms, causing disastrous floods. On the
Mediterranean versant there are 76 in., in the Garonne basin 46 and in
that of the Loire only 28. Sheep and cattle-rearing and cheese-making
are the chief occupations. Bees are kept, and, among the Cévennes,
silkworms. Large quantities of chestnuts are exported from the Cévennes,
where they form an important article of diet. In the valley of the Lot
wheat and fruit are the chief products; elsewhere rye is the chief
cereal, and oats, barley, meslin and potatoes are also grown. Fruit
trees and leguminous plants are irrigated by small canals (_béals_) on
terraces made and maintained with much labour. Lead, zinc and antimony
are found. Saw-milling, the manufacture of wooden shoes and
wool-spinning are carried on; otherwise industries are few and
unimportant. Of mineral springs, those of Bagnols-les-Bains are most
frequented. The line of the Paris-Lyon company from Paris to Nîmes
traverses the eastern border of the department, which is also served by
the Midi railway with the line from Neussargues to Béziers via
Marvéjols. The arrondissements are Mende, Florac and Marvéjols; the
cantons number 24, the communes 198. Lozère forms the diocese of Mende
and part of the ecclesiastical province of Albi. It falls within the
region of the XVI. army corps, the circumscriptions of the _académie_
(educational division) of Montpellier and the appeal court of Nîmes.
Mende (q.v.) is its most important town.
LUANG-PRABANG, a town of French Indo-China, capital of the Lao state of
that name, on the left bank of the Me Kong river. It lies at the foot of
the pagoda hill which rises about 200 ft. above the plain on the
promontory of land round which the Nam Kan winds to the main river. It
has a population of about 9000 and contains the "palace" of the king of
the state and several pagodas. In 1887 it was taken and sacked by the
Haw or Black Flags, robber bands of Chinese soldiery, many of them
survivors of the Taiping rebellion. In 1893 Siam was compelled to
renounce her claims to the left bank of the Me Kong, including
Luang-Prabang and the magnificent highlands of Chieng Kwang. That
portion of the state which was on the right bank of the Me Kong was not
affected by the treaty, except in so far as a portion of it fell within
the sixteen miles' zone within which Siam agreed not to keep troops.
Trade is in the hands of Chinese or Shan traders; hill rice and other
jungle products are imported from the surrounding districts by the Kha
or hill people. The exports, which include rubber, gum benjamin, silk,
wax, sticklac, cutch, cardamon, a little ebony, cinnamon, indigo,
rhinoceros and deer horns, ivory and fish roe, formerly all passed by
way of Paklai to the Me Nam, and so to Bangkok, but have now almost
entirely ceased to follow that route, the object of the French
government being to deflect the trade through French territory.
Luang-Prabang is the terminus of navigation on the upper Me Kong and the
centre of trade thereon.
LUBAO, a town in the south-western part of the province of Pampanga,
Luzon, Philippine Islands, about 30 m. N.W. of Manila. Pop. (1903)
19,063. Lubao is served by the Manila & Dagupan railway, and has water
communication with Manila by tidal streams and Manila Bay. Its products
are, therefore, readily marketed. It lies in a low, fertile plain,
suited to the growing of rice and sugar. Many of the inhabitants occupy
themselves in the neighbouring nipa swamps, either preparing the nipa
leaves for use in house construction, or distilling "nipa-wine" from the
juice secured by tapping the blossom stalks. The language is Pampangan.
LÜBBEN, a town of Germany, in the Prussian province of Brandenburg, on
the Spree, 47 m. S.S.E. of Berlin, on the railway to Görlitz. Pop.
(1905) 7173. It is the chief town of the Spreewald, and has saw-mills
and manufactories of hosiery, shoes and paper, and is famous for its
_gurken_, or small pickling cucumbers. The poet Paul Gerhardt
(1607-1676) was pastor here and is buried in the parish church.
LÜBECK, a state and city (_Freie und Hansestadt Lübeck_) of Germany. The
_principality_ of Lübeck, lying north of the state, is a constituent of
the grand-duchy of Oldenburg (q.v.). The state is situated on an arm of
the Baltic between Holstein and Mecklenburg-Schwerin. It consists of the
city of Lübeck, the town of Travemünde, 49 villages and the country
districts, embraces 115 sq. m. of territory, and had a population in
1907 of 109,265, of which 93,978 were included in the city and its
immediate suburbs. The state lies in the lowlands of the Baltic, is
diversified by gently swelling hills, and watered by the Trave and its
tributaries, the Wakenitz and the Stecknitz. The soil is fertile, and,
with the exception of forest land (14% of the whole area), is mostly
devoted to market gardening. Trade is centred in the city of Lübeck.
The constitution of the free state is republican, and, by the
fundamental law of 1875, amended in 1905 and again in 1907, consists of
two assemblies. (1) The Senate of fourteen members, of whom eight must
belong to the learned professions, and six of these again must be
jurists, while of the remaining six, five must be merchants. The Senate
represents the sovereignty of the state and is presided over by the
_Oberbürgermeister_, who during his two years' term of office bears the
title of "magnificence." (2) The House of Burgesses (Bürgerschaft), of
120 members, elected by free suffrage and exercising its powers partly
in its collective capacity and partly through a committee of thirty
members. Purely commercial matters are dealt with by the chamber of
commerce, composed of a _praeses_, eighteen members and a secretary.
This body controls the exchange and appoints brokers, shipping agents
and underwriters. The executive is in the hands of the Senate, but the
House of Burgesses has the right of initiating legislation, including
that relative to foreign treaties; the sanction of both chambers is
required to the passing of any new law. Lübeck has a court of first
instance (_Amtsgericht_) and a high court of justice (_Landgericht_);
from the latter appeals lie to the Hanseatic court of appeal
(_Oberlandesgericht_) at Hamburg, and from this again to the supreme
court of the empire (_Reichsgericht_) in Leipzig. The people are nearly
all Lutherans, and education is compulsory between the ages of six and
fourteen.
The estimated revenue for the year 1908-1909 amounted to about £650,000,
and the expenditure to a like sum. The public debt amounted, in 1908, to
about £2,518,000. Lübeck has one vote in the federal council
(_Bundesrat_) of the German Empire, and sends one representative to the
imperial parliament (_Reichstag_).
_History of the Constitution._--At the first rise of the town justice was
administered to the inhabitants by the _Vogt_ (_advocatus_) of the count
of Holstein. Simultaneously with its incorporation by Henry the Lion,
duke of Saxony, who presented the city with its own mint toll and market,
there appears a magistracy of six, chosen probably by the _Vogt_ from the
_Schöffen_ (_scabini, probi homines_). The members of the town council
had to be freemen, born in lawful wedlock, in the enjoyment of estates in
freehold and of unstained repute. Vassals or servants of any lord, and
tradespeople, were excluded. A third of the number had annually to retire
for a year, so that two-thirds formed the sitting council. By the middle
of the 13th century there were two burgomasters (_magistri burgensium_).
Meanwhile, the number of magistrates (_consules_) had increased, ranging
from twenty to forty and upwards. The council appointed its own officers
in the various branches of the administration. In the face of so much
self-government the _Vogt_ presently disappeared altogether. There were
three classes of inhabitants, full freemen, half freemen and guests or
foreigners. People of Slav origin being considered unfree, all
intermarriage with them tainted the blood; hence nearly all surnames
point to Saxon, especially Westphalian, and even Flemish descent. The
magistracy was for two centuries almost exclusively in the hands of the
merchant aristocracy, who formed the companies of traders or "nations,"
such as the _Bergen-fahrer_, _Novgorod-fahrer_, _Riga-fahrer_ and
_Stockholm-fahrer_. From the beginning, however, tradesmen and
handicraftsmen had settled in the town, all of them freemen of German
parentage and with property and houses of their own. Though not eligible
for the council, they shared to a certain extent in the self-government
through the aldermen of each corporation or gild, of which some appear as
early as the statutes of 1240. Naturally, there arose much jealousy
between the gilds and the aristocratic companies, which exclusively ruled
the republic. After an attempt to upset the merchants had been suppressed
in 1384, the gilds succeeded, under more favourable circumstances, in
1408. The old patrician council left the city to appeal to the Hansa and
to the imperial authorities, while a new council with democratic
tendencies, elected chiefly from the gilds, took their place. In 1416,
however, owing to the pressure brought to bear by the Hansa, by the
emperor Sigismund and by Eric, king of Denmark, there was a restoration.
The aristocratic government was again expelled under the dictatorship of
Jürgen Wullenweber (c. 1492-1537), till the old order was re-established
in 1535. In the constitution of 1669, under the pressure of a large
public debt, the great companies yielded a specified share in the
financial administration to the leading gilds of tradesmen. Nevertheless,
the seven great companies continued to choose the magistrates by
co-optation among themselves. Three of the four burgomasters and two of
the senators, however, had henceforth to be graduates in law. The
constitution, set aside only during the French occupation, has
subsequently been slowly reformed. From 1813 the popular representatives
had some share in the management of the finances. But the reform
committee of 1814, whose object was to obtain an extension of the
franchise, had made little progress, when the events of 1848 led to the
establishment of a representative assembly of 120 members, elected by
universal suffrage, which obtained a place beside the senatorial
government. The republic has given up its own military contingent, its
coinage and its postal dues to the German Empire; but it has preserved
its municipal self-government and its own territory, the inhabitants of
which enjoy equal political privileges with the citizens.
_The City of Lübeck._--Lübeck, the capital of the free state, was
formerly the head of the Hanseatic League. It is situated on a gentle
ridge between the rivers Trave and Wakenitz, 10 m. S.W. of the mouth of
the former in the bay of Lübeck, 40 m. by rail N.E. of Hamburg, at the
junction of lines to Eutin, Büchen, Travemünde and Strassburg (in
Mecklenburg-Schwerin) and consists of an inner town and three suburbs.
The former ramparts between the Trave and the old town ditch have been
converted into promenades. The city proper retains much of its ancient
grandeur, despite the tendency to modernize streets and private houses.
Foremost among its buildings must be mentioned its five chief churches,
stately Gothic edifices in glazed brick, with lofty spires and replete
with medieval works of art--pictures, stained glass and tombs. Of them,
the Marienkirche, built in the 13th century, is one of the finest
specimens of early Gothic in Germany. The cathedral, or _Domkirche_,
founded in 1173, contains some curious sarcophagi and a magnificent
altarpiece in one of the chapels, while the churches of St James
(_Jakobikirche_), of St Peter (_Petrikirche_) and of St Aegidius
(_Aegidienkirche_) are also remarkable. The _Rathaus_ (town hall) of red
and black glazed brick, dating from various epochs during the middle
ages, is famous for its staircase, the vaulted wine cellar of the city
council beneath and magnificent wood carving. There should also be
mentioned the _Schiffershaus_; the medieval gates (Holstentor, Burgtor);
and the Hospital of the Holy Ghost, remarkable for ancient frescoes and
altars in rich wood carving, the entrance hall of which is a
13th-century chapel, restored in 1866 and decorated in 1898. The museum
preserves the most remarkable municipal archives in existence as well as
valuable collections of historical documents.
The poet, Emanuel Geibel (1889), and the painter, Johann Friedrich
Overbeck (1789-1869), were natives of Lübeck. This city is famous for
the number and wealth of its charitable institutions. Its position as
the first German emporium of the west end of the Baltic has been to some
extent impaired by Hamburg and Bremen since the construction of the
North Sea and Baltic Canal, and by the rapid growth and enterprise of
Stettin. In order to counterbalance their rivalry, the quays have been
extended, a canal was opened in 1900 between the Trave and the Elbe, the
river up to the wharves has been deepened to 23 ft. or more. The river
is kept open in winter by ice-breakers. A harbour was made in 1899-1900
on the Wakenitz Canal for boats engaged in inland traffic, especially on
the Elbe and Elbe-Trave Canal. Lübeck trades principally with Denmark,
Sweden, Finland, Russia, the eastern provinces of Prussia, Great Britain
and the United States. The imports amounted in value to about £4,850,000
in 1906 and the exports to over £10,000,000. The chief articles of
import are coal, grain, timber, copper, steel and wine, and the exports
are manufactured goods principally to Russia and Scandivania. The
industries are growing, the chief being breweries and distilleries,
saw-mills and planing-mills, shipbuilding, fish-curing, the manufacture
of machinery, engines, bricks, resin, preserves, enamelled and tin
goods, cigars, furniture, soap and leather. Pop. (1885) 55,399; (1905)
91,541.
_History._--Old Lübeck stood on the left bank of the Trave, where it is
joined by the river Schwartau, and was destroyed in 1138. Five years
later Count Adolphus II. of Holstein founded new Lübeck, a few miles
farther up, on the peninsula Buku, where the Trave is joined on the
right by the Wakenitz, the emissary of the lake of Ratzeburg. An
excellent harbour, sheltered against pirates, it became almost at once a
competitor for the commerce of the Baltic. Its foundation coincided with
the beginning of the advance of the Low German tribes of Flanders,
Friesland and Westphalia along the southern shores of the Baltic--the
second great emigration of the colonizing Saxon element. In 1140 Wagria,
in 1142 the country of the Polabes (Ratzeburg and Lauenburg), had been
annexed by the Holtsaetas (the Transalbingian Saxons). From 1166 onwards
there was a Saxon count at Schwerin. Frisian and Saxon merchants from
Soest, Bardowiek and other localities in Lower Germany, who already
navigated the Baltic and had their factory in Gotland, settled in the
new town, where Wendish speech and customs never entered. About 1157
Henry the Lion, duke of Saxony, forced his vassal, the count of
Holstein, to give up Lübeck to him; and in 1163 he removed thither the
episcopal see of Oldenburg (Stargard), founding at the same time the
dioceses of Ratzeburg and Schwerin. He issued the first charter to the
citizens, and constituted them a free Saxon community having their own
magistrate, an advantage over all other towns of his dominions. He
invited traders of the north to visit his new market free of toll and
custom, providing his subjects were promised similar privileges in
return. From the beginning the king of Denmark granted them a settlement
for their herring fishery on the coast of Schoonen. Adopting the
statutes of Soest in Westphalia as their code, Saxon merchants
exclusively ruled the city. In concurrence with the duke's _Vogt_
(_advocatus_) they recognized only one right of judicature within the
town, to which nobles as well as artisans had to submit. Under these
circumstances the population grew rapidly in wealth and influence by
land and sea, so that, when Henry was attainted by the emperor,
Frederick I., who came in person to besiege Lübeck in 1181, this
potentate, "in consideration of its revenues and its situation on the
frontier of the Empire," fixed by charter, dated the 19th of September
1188, the limits, and enlarged the liberties, of the free town. In the
year 1201 Lübeck was conquered by Waldemar II. of Denmark. But in 1223
it regained its liberty, after the king had been taken captive by the
count of Schwerin. In 1226 it was made a free city of the Empire by
Frederick II., and its inhabitants took part with the enemies of the
Danish king in the victory of Bornhövede in July 1227. The citizens
repelled the encroachments of their neighbours in Holstein and in
Mecklenburg. On the other hand their town, being the principal emporium
of the Baltic by the middle of the 13th century, acted as the firm ally
of the Teutonic knights in Livonia. Emigrants founded new cities and new
sees of Low German speech among alien and pagan races; and thus in the
course of a century the commerce of Lübeck had supplanted that of
Westphalia. In connexion with the Germans at Visby, the capital of
Gotland, and at Riga, where they had a house from 1231, the people of
Lübeck with their armed vessels scoured the sea between the Trave and
the Neva. They were encouraged by papal bulls in their contest for the
rights of property in wrecks and for the protection of shipping against
pirates and slave-hunters. Before the close of the century the statutes
of Lübeck were adopted by most Baltic towns having a German population,
and Visby protested in vain against the city on the Trave having become
the court of appeal for nearly all these cities, and even for the German
settlement in Russian Novgorod. In course of time more than a hundred
places were embraced in this relation, the last vestiges of which did
not disappear until the beginning of the 18th century. From about 1299
Lübeck presided over a league of cities, Wismar, Rostock, Stralsund,
Greifswald and some smaller ones, and this Hansa of towns became heir to
a Hansa of traders simultaneously on the eastern and the western sea,
after Lübeck and her confederates had been admitted to the same
privileges with Cologne, Dortmund and Soest at Bruges and in the
steelyards of London, Lynn and Boston. The union held its own, chiefly
along the maritime outskirts of the Empire, rather against the will of
king and emperor, but nevertheless Rudolph of Habsburg and several of
his successors issued new charters to Lübeck. As early as 1241 Lübeck,
Hamburg and Soest had combined to secure their highways against robber
knights. Treaties to enforce the public peace were concluded in 1291 and
1338 with the dukes of Brunswick, Mecklenburg and Pomerania, and the
count of Holstein. Though the great federal armament against Waldemar
IV., the destroyer of Visby, was decreed by the city representatives
assembled at Cologne in 1367, Lübeck was the leading spirit in the war
which ended with the surrender of Copenhagen and the peace concluded at
Stralsund on the 24th of May 1370. Her burgomaster, Brun Warendorp, who
commanded the combined naval and land forces, died on the field of
battle. In 1368 the seal of the city, a double-headed eagle, which in
the 14th century took the place of the more ancient ship, was adopted as
the common seal of the confederated towns (_civitates maritimae_), some
seventy in number. Towards the end of the 15th century the power of the
Hanseatic League began to decline, owing to the rise of Burgundy in the
west, of Poland and Russia in the east and the emancipation of the
Scandinavian kingdom from the union of Calmar. Still Lübeck, even when
nearly isolated, strove to preserve its predominance in a war with
Denmark (1501-12), supporting Gustavus Vasa in Sweden, lording it over
the north of Europe during the years 1534 and 1535 in the person of
Jürgen Wullenweber, the democratic burgomaster, who professed the most
advanced principles of the Reformation, and engaging with Sweden in a
severe naval war (1536-70).
But the prestige and prosperity of the town were beginning to decline.
Before the end of the 16th century the privileges of the London
Steelyard were suppressed by Elizabeth. As early as 1425 the herring, a
constant source of early wealth, began to forsake the Baltic waters.
Later on, by the discovery of a new continent, commerce was diverted
into new directions. Finally, with the Thirty Years' War, misfortunes
came thick. The last Hanseatic diet met at Lübeck in 1630, shortly after
Wallenstein's unsuccessful attack on Stralsund; and from that time
merciless sovereign powers stopped free intercourse on all sides. Danes
and Swedes battled for the possession of the Sound and for its heavy
dues. The often changing masters of Holstein and Lauenburg abstracted
much of the valuable landed property of the city and of the chapter of
Lübeck. Towards the end of the 18th century there were signs of
improvement. Though the Danes temporarily occupied the town in 1801, it
preserved its freedom and gained some of the chapter lands when the
imperial constitution of Germany was broken up by the act of February
1803, while trade and commerce prospered for a few years. But in
November 1806, when Blücher, retiring from the catastrophe of Jena, had
to capitulate in the vicinity of Lübeck, the town was sacked by the
French. Napoleon annexed it to his empire in December 1810. But it rose
against the French in March 1813, was re-occupied by them till the 5th
of December, and was ultimately declared a free and Hanse town of the
German Confederation by the act of Vienna of the 9th of June 1815. The
Hanseatic League, however, having never been officially dissolved,
Lübeck still enjoyed its traditional connexion with Bremen and Hamburg.
In 1853 they sold their common property, the London Steelyard; until
1866 they enlisted by special contract their military contingents for
the German Confederation, and down to 1879 they had their own court of
appeal at Lübeck. Lübeck joined the North German Confederation in 1866,
profiting by the retirement from Holstein and Lauenburg of the Danes,
whose interference had prevented as long as possible a direct railway
between Lübeck and Hamburg. On the 27th of June 1867 Lübeck concluded a
military convention with Prussia, and on the 11th of August 1868 entered
the German Customs Union (_Zollverein_), though reserving to itself
certain privileges in respect of its considerable wine trade and
commerce with the Baltic ports.
See E. Deecke, _Die Freie und Hansestadt Lübeck_ (4th ed., Lübeck,
1881) and _Lübische Geschichten und Sagen_ (Lübeck, 1891); M.
Hoffmann, _Geschichte der Freien und Hansestadt Lübeck_ (Lübeck,
1889-1892) and _Chronik von Lübeck_ (Lübeck, 1908); _Die Freie und
Hansestadt Lübeck_, published by _Die geographische Gesellschaft in
Lübeck_ (Lübeck, 1891); C. W. Pauli, _Lübecksche Zustände im
Mittelalter_ (Lübeck, 1846-1878); J. Geffcken, _Lübeck in der Mitte
des 16^ten Jahrhunderts_ (Lübeck, 1905); P. Hasse, _Die Anfange
Lübecks_ (Lübeck, 1893); H. Bödeker, _Geschichte der Freien und
Hansestadt Lübeck_ (Lübeck, 1898); A. Holm, _Lübeck, die Freie und
Hansestadt_ (Bielefeld, 1900); G. Waitz, _Lübeck unter Jürgen
Wullenweber_ (Berlin, 1855-1856); Klug, _Geschichte Lübecks während
der Vereinigung mit dem französischen Kaiserreich_ (Lübeck, 1857); F.
Frensdorff, _Die Stadt- und Gerichtsverfassung Lübecks im 12. und 13.
Jahrhundert_ (Lübeck, 1861); the _Urkundenbuch der Stadt Lübeck_
(Lübeck, 1843-1904); the _Lübecker Chroniken_ (Leipzig, 1884-1903);
and the _Zeitschrift des Vereins für lübeckische Geschichte_ (Lübeck,
1860 fol.). (R. P.; P. A. A.)
LUBLIN, a government of Russian Poland, bounded N. by Siedlce, E. by
Volhynia (the Bug forming the boundary), S. by Galicia, and W. by Radom
(the Vistula separating the two). Area, 6499 sq. m. The surface is an
undulating plain of Cretaceous deposits, 800 to 900 ft. in altitude, and
reaching in one place 1050 ft. It is largely covered with forests of
oak, beech and lime, intersected by ravines and thinly inhabited. A
marshy lowland extends between the Vistula and the Wieprz. The
government is drained by the Vistula and the Bug, and by their
tributaries the Wieprz, San and Tanev. Parts of the government, being of
black earth, are fertile, but other parts are sandy. Agriculture is in
good condition. Many Germans settled in the government before
immigration was stopped in 1887; in 1897 they numbered about 26,000.
Rye, oats, wheat, barley and potatoes are the chief crops, rye and wheat
being exported. Flax, hemp, buckwheat, peas, millet and beetroot are
also cultivated. Horses are carefully bred. In 1897 the population was
1,165,122, of whom 604,886 were women. The Greek Orthodox (chiefly
Little Russians in the south-east) amounted to 20.1% of the whole; Roman
Catholics (i.e. Poles) to 62.8%; Jews to 14.2%; and Protestants to 2.8%.
The urban population was 148,196 in 1897. The estimated population in
1906 was 1,362,500. Industrial establishments consist chiefly of
distilleries, sugar-works, steam flour-mills, tanneries, saw-mills and
factories of bent-wood furniture. Domestic industries are widely
developed in the villages. River navigation employs a considerable
portion of the population. The government is divided into ten districts,
the chief towns of which, with their populations in 1897, are--Lublin,
capital of the province (50,152); Biegoray (6286); Cholm (19,236);
Hrubieszow (10,699); Yanów (7927); Krasnystaw or Kraznostav (8879);
Lubartow (5249); Nova-Alexandrya or Pulawy (3892); Samostye (12,400);
and Tomaszów (6224).
LUBLIN, a town of Russian Poland, capital of the government of the same
name, 109 m. by rail S.E. of Warsaw, on a small tributary of the Wieprz.
Pop. (1873) 28,900; (1897) 50,152. It is the most important town of
Poland after Warsaw and Lodz, being one of the chief centres of the
manufacture of thread-yarn, linen and hempen goods and woollen stuffs;
there is also trade in grain and cattle. It has an old citadel, several
palaces of Polish nobles and many interesting churches, and is the
headquarters of the XIV. army corps, and the see of a Roman Catholic
bishop. The cathedral dates from the 16th century. Of the former
fortifications nothing remains except the four gates, one dating from
1342.
Lublin was in existence in the 10th century, and has a church which is
said to have been built in 986. During the time the Jagellon dynasty
ruled over Lithuania and Poland it was the most important city between
the Vistula and the Dnieper, having 40,000 inhabitants (70,000 according
to other authorities) and all the trade with Podolia, Volhynia and Red
Russia. Indeed, the present town is surrounded with ruins, which prove
that it formerly covered a much larger area. But it was frequently
destroyed by the Tatars (e.g. 1240) and Cossacks (e.g. 1477). In
1568-1569 it was the seat of the stormy convention at which the union
between Poland and Lithuania was decided. In 1702 another convention was
held in Lublin, in favour of Augustus II. and against Charles XII. of
Sweden, who carried the town by assault and plundered it. In 1831 Lublin
was taken by the Russians. The surrounding country is rich in
reminiscences of the struggle of Poland for independence.
LUBRICANTS. Machines consist of parts which have relative motion and
generally slide and rub against each other. Thus the axle of a cart or
railway vehicle is pressed against a metallic bearing surface supporting
the body of the vehicle, and the two opposed surfaces slide upon each
other and are pressed together with great force. If the metallic
surfaces be clean, the speed of rubbing high, and the force pressing the
surfaces together considerable, then the latter will abrade each other,
become hot and be rapidly destroyed. It is possible, however, to prevent
the serious abrasion of such opposing surfaces, and largely to reduce
the frictional resistance they oppose to relative motion by the use of
_lubricants_ (Lat. _lubricare_, _lubricus_, slippery). These substances
are caused to insinuate themselves between the surfaces, and have the
property of so separating them as to prevent serious abrasion. The solid
and semi-solid lubricants seem to act as rollers between the surfaces,
or form a film between them which itself suffers abrasion or friction.
The liquid lubricants, however, maintain themselves as liquid films
between the surfaces, upon which the bearing floats. The frictional
resistance is then wholly in the fluid. Even when lubricants are used
the friction, i.e. the resistance to motion offered by the opposing
surfaces, is considerable. In the article Friction will be found a
statement of how friction is measured and the manner in which it is
expressed. The coefficient of friction is obtained by dividing the force
required to cause the surfaces to slide over each other by the load
pressing them together. For clean unlubricated surfaces this coefficient
may be as great as 0.3, whilst for well-lubricated cylindrical bearings
it may be as small as 0.0006. Engineers have, therefore, paid particular
attention to the design of bearings with the object of reducing the
friction, and thus making use of as much as possible of the power
developed by prime movers. The importance of doing this will be seen
when it is remembered that the energy wasted is proportional to the
coefficient of friction, and that the durability of the parts depends
upon the extent to which they are separated by the lubricant and thus
prevented from injuring each other.
There is great diversity in the shapes of rubbing surfaces, the loads
they have to carry vary widely, and the speed of rubbing ranges from
less than one foot to thousands of feet per minute. There is also a
large number of substances which act as lubricants, some being liquids
and others soft solids. In many instruments or machines where the
surfaces in contact which have to slide upon each other are only lightly
pressed together, and are only occasionally given relative motion, the
lubricant is only needed to prevent abrasion. Microscopes and
mathematical instruments are of this kind. In such cases, the lubricant
which keeps the surfaces from abrading each other is a mere
contamination film, either derived from the air or put on when the
surfaces are finished. When such lubricating films are depended upon,
the friction surfaces should be as hard as possible and, if practicable,
of dissimilar metals. In the absence of a contamination film, most
metals, if rubbed when in contact, will immediately adhere to each
other. A large number of experiments have been made to ascertain the
coefficient of friction under these imperfect conditions of lubrication.
Within wide limits of load, the friction is proportional to the pressure
normal to the surfaces and is, therefore, approximately independent of
the area of the surfaces in contact. Although the static coefficient is
often less than the kinetic at very low speeds, within wide limits the
latter coefficient decreases with increasing speed. These laws apply to
all bearings the velocity of rubbing of which is very small, or which
are lubricated with solid or semi-solid materials.
When the speed of rubbing is considerable and the contamination film is
liable to be destroyed, resort is had to lubricants which possess the
power of keeping the surfaces apart, and thereby reducing the friction.
The constant application of such substances is necessary in the case of
such parts of machine tools as slide rests, the surfaces of which only
move relatively to each other at moderate speeds, but which have to
carry heavy loads. In all ordinary cases, the coefficient of friction of
flat surfaces, such as those of slide blocks or pivot bearings, is high,
owing to the fact that the lubricant is not easily forced between the
surfaces. In the case of cylindrical bearing surfaces, such as those of
journals and spindles, owing to the fact that the radius of the bearing
surface is greater than that of the journal or spindle, the lubricant,
if a liquid, is easily drawn in and entirely separates the surfaces (see
LUBRICATION). Fortunately, cylindrical bearings are by far the most
common and important form of bearing, and they can be so lubricated that
the friction coefficient is very low. The lubricant, owing to its
viscosity, is forced between the surfaces and keeps them entirely apart.
This property of viscosity is one of the most important possessed by
liquid lubricants. Some lubricants, such as the oils used for the light
spindles of textile machinery, are quite thin and limpid, whilst others,
suitable for steam engine cylinders and very heavy bearings, are, at
ordinary temperatures, as thick as treacle or honey. Generally speaking,
the greater the viscosity of the lubricant the greater the load the
bearing will carry, but with thick lubricants the frictional coefficient
is correspondingly high. True lubricants differ from ordinary liquids of
equal viscosity inasmuch as they possess the property of "oiliness."
This is a property which enables them to maintain an unbroken film
between surfaces when the loads are heavy. It is possessed most markedly
by vegetables and animal oils and fats, and less markedly by mineral
oils. In the case of mineral lubricating oils from the same source, the
lower the specific gravity the greater the oiliness of the liquid, as a
rule. Mixtures of mineral oil with animal or vegetable oil are largely
used, one class of oil supplying those qualities in which the other is
deficient. Thus the mineral oils, which are comparatively cheap and
possess the important property of not becoming oxidized into gummy or
sticky substances by the action of the air, which also are not liable to
cause spontaneous ignition of cotton waste, &c., and can be manufactured
of almost any desired viscosity, but which on the other hand are
somewhat deficient in the property of oiliness, are mixed with animal or
vegetable oils which possess the latter property in marked degree, but
are liable to gum and become acid and to cause spontaneous ignition,
besides being comparatively expensive and limited in quantity. Oils
which become acid attack the bearings chemically, and those which
oxidize may become so thick that they fail to run on to the bearings
properly.
The following table shows that the permissible load on bearings varies
greatly:--
Description of Bearing. Load in lb.
per sq. in.
Hard steel bearings on which the load is inter-
mittent, such as the crank pins of shearing
machines 3000
Bronze crosshead neck journals 1200
Crank pins of large slow engines 800-900
Crank pins of marine engines 400-500
Main crank-shaft bearings, slow marine 600
Main crank-shaft bearings, fast marine 400
Railway coach journals 300-400
Fly-wheel shaft journals 150-200
Small engine crank pins 150-200
Small slide blocks, marine engines 100
Stationary engine slide block 25-125
Stationary engine slide block, usually 30-60
Propeller thrust bearings 50-70
Shafts in cast iron steps, high speed 15
_Solid Lubricants._--Solid substances, such as graphite or plumbago,
soapstone, &c., are used as lubricants when there is some objection to
liquids or soft solids, but the surfaces between which they are placed
should be of very hard materials. They are frequently mixed with oils
or greases, the lubricating properties of which they improve.
_Semi-solid Lubricants._--The contrast in lubricating properties
between mineral and fatty oils exists also in the case of a pure
mineral grease like vaseline and an animal fat such as tallow, the
latter possessing in a far greater degree the property of greasiness.
A large number of lubricating greases are made by incorporating or
emulsifying animal and vegetable fats with soap and water; also by
thickening mineral lubricating oils with soap. Large quantities of
these greases are used with very good results for the lubrication of
railway waggon axles, and some of them are excellent lubricants for
the bearings of slow moving machinery. Care must be taken, however,
that they do not contain excess of water and are not adulterated with
such useless substances as china clay; also, that they melt as a
whole, and that the oil does not run down and leave the soap. This is
liable to occur with badly made greases, and hot bearings are the
result. Except in special cases, greases should not be used for
quick-running journals, shafts or spindles, on account of the high
frictional resistance which they offer to motion. In the case of fats
and greases whose melting points are not much above the temperature of
surrounding objects it generally happens that the lubricating films
are so warmed by friction that they actually melt and act as oils.
These lubricants are generally forced into the bearings by a form of
syringe fitted with a spring piston, or are squeezed between the faces
by means of a screw-plug.
_Liquid Lubricants._--Generally speaking, all bearings which it is
necessary should run with as little friction as possible must be
supplied with liquid lubricants. These may be of animal, vegetable or
mineral origin. The mineral oils are mixtures of hydrocarbons of
variable viscosity, flashing-point, density and oiliness. They are
obtained by distillation from American, Russian and other petroleums.
The fixed oils obtained from animal and vegetable substances are not
volatile without decomposition, and are found ready made in the
tissues of animals and plants. Animal oils are obtained from the
adipose tissue by simple heat or by boiling with water. They are
usually either colourless or yellow. The oils of plants occur usually
in the seeds or fruit, and are obtained either by expression or by
means of solvents such as ether or petroleum. They are of various
shades of yellow and green, the green colour being due to the presence
of chlorophyll. The fundamental difference between fixed oils and
mineral oils exists in their behaviour towards oxygen. Mineral oils at
ordinary temperatures are indifferent to oxygen, but all fixed oils
combine with it and thicken or gum more or less, generating heat at
the same time. Such oils are, therefore, dangerous if dropped upon
silk, cotton or woollen waste or other combustible fibrous materials,
which are thus rendered liable to spontaneous ignition.
Liquid lubricants are used for all high speed bearings. In some cases
the rubbing surfaces work in a bath of the lubricant, which can then
reach all the rubbing parts with certainty. Small engines for motor
cars or road waggons are often lubricated in this way. In the case of
individual bearings, such as those of railway vehicles, a pad of
cotton, worsted and horse hair is kept saturated with the lubricant
and pressed against the under side of the journal. The journal is thus
kept constantly wetted with oil, and the film is forced beneath the
brass as the axle rotates. In many cases, oil-ways and grooves are cut
in the bearings, and the lubricant is allowed to run by gravity into
them and thus finds its way between the opposing surfaces. To secure a
steady feed various contrivances are adopted, the most common being a
wick of cotton or worsted used as a siphon. In cases where it is
important that little if any wear should take place, the lubricant is
forced by means of a pump between the friction surfaces and a constant
film of oil is thereby maintained between them.
For the spindles of small machines such as clocks, watches and other
delicate mechanisms, which are only lubricated at long intervals and
are often exposed to extremes of temperature, the lubricant must be a
fluid oil as free as possible from tendency to gum or thicken by
oxidation or to corrode metal, and must often have a low
freezing-point. It must also possess a maximum of "oiliness." The
lubricants mostly used for such purposes are obtained from porpoise or
dolphin jaw oils, bean oil, hazel nut oil, neatsfoot oil, sperm oil or
olive oil. These oils are exposed for some time to temperatures as low
as the mechanism is required to work at, and the portion which remains
fluid is separated and used. Free acid should be entirely eliminated
by chemical refining. A little good mineral oil may with advantage be
mixed with the fatty oil.
For all ordinary machinery, ranging from the light ring spindles of
textile mills to the heavy shafts of large engines, mineral oils are
almost universally employed, either alone or mixed with fatty oils,
the general rule being to use pure mineral oils for bath, forced or
circulating pump lubrication, and mixed oils for drop, siphon and
other less perfect methods of lubrication. Pure mineral oils of
relatively low viscosity are used for high speeds and low pressures,
mixed oils of greater viscosity for low speeds and high pressures. In
selecting oils for low speeds and great pressures, viscosity must be
the first consideration, and next to that "oiliness." If an oil of
sufficiently high viscosity be used, a mineral oil may give a result
as good or better than a pure fixed oil; a mixed oil may give a better
result than either. If a mineral oil of sufficient viscosity be not
available, then a fixed oil or fat may be expected to give the best
result.
In special cases, such as in the lubrication of textile machines,
where the oil is liable to be splashed upon the fabric, the primary
consideration is to use an oil which can be washed out without leaving
a stain. Pure fixed oils, or mixtures composed largely of fixed oils,
are used for such purposes.
In other special cases, such as marine engines working in hot places,
mixtures are used of mineral oil with rape or other vegetable oil
artificially thickened by blowing air through the heated oil, and
known as "blown" oil or "soluble castor oil."
In the lubrication of the cylinders and valves of steam, gas and oil
engines, the lubricant must possess as much viscosity as possible at
the working temperature, must not evaporate appreciably and must not
decompose and liberate fatty acids which would corrode the metal and
choke the steam passages with metallic soaps; for gas and oil engines
the lubricant must be as free as possible from tendency to decompose
and deposit carbon when heated. For this reason steam cylinders and
valves should be lubricated with pure mineral oils of the highest
viscosity, mixed with no more fixed oil than is necessary to ensure
efficient lubrication. Gas and oil engines also should be lubricated
with pure mineral oils wherever possible.
For further information on the theory and practice of lubrication and
on the testing of lubricants, see _Friction and Lost Work in Machinery
and Mill Work_, by R. H. Thurston (1903); and _Lubrication and
Lubricants_, by L. Archbutt and R. M. Deeley (1906). (R. M. D.)
LUBRICATION. Our knowledge of the action of oils and other viscous
fluids in diminishing friction and wear between solid surfaces from
being purely empirical has become a connected theory, based on the known
properties of matter, subjected to the definition of mathematical
analysis and verified by experiment. The theory was published in 1886
(_Phil. Trans._, 1886, 177, pp. 157-234); but it is the purpose of this
article not so much to explain its application, as to give a brief
account of the introduction of the misconceptions that so long
prevailed, and of the manner in which their removal led to its general
acceptance.
Friction, or resistance to tangential shifting of matter over matter,
whatever the mode and arrangement, differs greatly according to the
materials, but, like all material resistance, is essentially limited.
The range of the limits in available materials has a primary place in
determining mechanical possibilities, and from the earliest times they
have demanded the closest attention on the part of all who have to do
with structures or with machines, the former being concerned to find
those materials and their arrangements which possess the highest limits,
and the latter the materials in which the limits are least. Long before
the reformation of science in the 15th and 16th centuries both these
limits had formed the subject of such empirical research as disclosed
numerous definite although disconnected circumstances under which they
could be secured; and these, however far from the highest and lowest,
satisfied the exigencies of practical mechanics at the time, thus
initiating the method of extending knowledge which was to be
subsequently recognized as the only basis of physical philosophy. In
this purely empirical research the conclusion arrived at represented the
results for the actual circumstance from which they were drawn, and thus
afforded no place for theoretical discrepancies. However, in the
attempts at generalization which followed the reformation of science,
opportunity was afforded for such discrepancies in the mere enunciation
of the circumstances in which the so-called laws of friction of motion
are supposed to apply. The circumstances in which the great amount of
empirical research was conducted as to the resistance between the clean,
plane, smooth surfaces of rigid bodies moving over each other under
pressure, invariably include the presence of air at atmospheric pressure
around, and to some extent between, the surfaces; but this fact had
received no notice in the enunciation of these laws, and this
constitutes a theoretical departure from the conditions under which the
experience had been obtained. Also, the theoretical division of the law
of frictional resistance into two laws--one dealing with the limit of
rest, and the other asserting that the friction of motion, which is
invariably less in similar circumstances than that of rest, is
independent of the velocity of sliding--involves the theoretical
assumption that there is no asymptotic law of diminution of the
resistance, since, starting from rest, the rate of sliding increases.
The theoretical substitution of ideal rigid bodies with geometrically
regular surfaces, sliding in contact under pressure at the common
regular surface, for the aërated surfaces in the actual circumstances,
and the theoretical substitution of the absolute independence of the
resistance of the rate of sliding for the limited independence in the
actual circumstances, prove the general acceptance of the
conceptions--(1) that matter can slide over matter under pressure at a
geometrically regular surface; (2) that, however much the resistance to
sliding under any particular pressure (the coefficient of friction) may
depend on the physical properties of the materials, the sliding under
pressure takes place at the geometrically regular surface of contact of
the rigid bodies; and (3) as the consequence of (1) and (2), that
whatever the effect of a lubricant, such as oil, might have, it could be
a physical surface effect. Thus not only did these general theoretical
conceptions, resulting from the theoretical laws of friction, fail to
indicate that the lubricant may diminish the resistance by the mere
mechanical separation of the surfaces, but they precluded the idea that
such might be the case. The result was that all subsequent attempts to
reduce the empirical facts, where a lubricant was used, to such general
laws as might reveal the separate functions of the complex circumstances
on which lubrication depends, completely failed. Thus until 1883 the
science of lubrication had not advanced beyond the empirical stage.
This period of stagnation was terminated by an accidental phenomenon
observed by Beauchamp Tower, while engaged on his research on the
friction of the journals of railway carriages. His observation led him
to a line of experiments which proved that in these experiments the
general function of the lubricant was the mechanical separation of the
metal surfaces by a layer of fluid of finite thickness, thus upsetting
the preconceived ideas as expressed in the laws of the friction of
motion. On the publication of Tower's reports (_Proc. Inst. M.E._,
November 1883), it was recognized by several physicists (_B.A. Report_,
1884, pp. 14, 625) that the evidence they contained afforded a basis for
further study of the actions involved, indicating as it did the
circumstances--namely, the properties of viscosity and cohesion
possessed by fluids--account of which had not been taken in previous
conclusions. It also became apparent that continuous or steady
lubrication, such as that of Tower's experiments, is only secured when
the solid surfaces separated by the lubricant are so shaped that the
thickness at the ingoing side is greater than that at the outgoing side.
When the general equations of viscous fluids had been shown as the
result of the labours of C. L. M. H. Navier,[1] A. L. Cauchy,[2] S. D.
Poisson,[3] A. J. C. Barré de St Venant,[4] and in 1845 of Sir G.
Gabriel Stokes,[5] to involve no other assumption than that the
stresses, other than the pressure equal in all directions, are linear
functions of the distortional rates of strain multiplied by a constant
coefficient, it was found that the only solutions of which the equations
admitted, when applied to fluids flowing between fixed boundaries, as
water in a pipe, were singular solutions for steady or steady periodic
motion, and that the conclusions they entailed, that the resistance
would be proportional to the velocity, were for the most part directly
at variance with the common experience that the resistances varied with
the square of the velocity. This discrepancy was sometimes supposed to
be the result of eddies in the fluid, but it was not till 1883 that it
was discovered by experiments with colour bands that, in the case of
geometrically similar boundaries, the existence or non-existence of such
eddies depended upon a definite relation between the mean velocity (U)
of the fluid, the distance between the boundaries, and the ratio of the
coefficient of viscosity to the density ([mu]/[rho]), expressed by
UD[rho]/[mu] = K, where K is a physical constant independent of units,
which has a value between 1900 and 2000, and for parallel boundaries D
is four times the area of the channel divided by the perimeter of the
section (_Phil. Trans._, 1883, part iii. 935-982). K is thus a criterion
at which the law of resistance to the mean flow changes suddenly (as U
increases), from being proportional to the flow, to a law involving
higher powers of the velocity at first, but as the rates increase
approaching an asymptote in which the power is a little less that the
square.
This sudden change in the law of resistance to the flow of fluid between
solid boundaries, depending as it does on a complete change in the
manner of the flow--from direct parallel flow to sinuous eddying
motion--serves to determine analytically the circumstances as to the
velocity and the thickness of the film under which any fluid having a
particular coefficient of viscosity can act the part of a lubricant. For
as long as the circumstances are such that UD[rho]/[mu] is less than K,
the parallel flow is held stable by the viscosity, so that only one
solution is possible--that in which the resistance is the product of
[mu] multiplied by the rate of distortion, as [mu](du/dy); in this case
the fluid has lubricating properties. But when the circumstances are
such that UD[rho]/[mu] is greater than K, other solutions become
possible, and the parallel flow becomes unstable, breaks down into
eddying motion, and the resistance varies as [rho]u^n, which
approximates to [rho]u^(1.78) as the velocity increases; in this state
the fluid has no lubricating properties. Thus, within the limits of the
criterion, the rate of displacement of the momentum of the fluid is
insignificant as compared with the viscous resistance, and may be
neglected; while outside this limit the direct effects of the eddying
motion completely dominate the viscous resistance, which in its turn may
be neglected. Thus K is a criterion which separates the flow of fluid
between solid surfaces as definitely as the flow of fluid is separated
from the relative motions in elastic solids, and it is by the knowledge
of the limit on which this distinction depends that the theory of
viscous flow can with assurance be applied to the circumstance of
lubrication.
Until the existence of this physical constant was discovered, any
theoretical conclusions as to whether in any particular circumstances
the resistance of the lubricant would follow the law of viscous flow or
that of eddying motion was impossible. Thus Tower, being unaware of the
discovery of the criterion, which was published in the same year as his
reports, was thrown off the scent in his endeavour to verify the
evidence he had obtained as to the finite thickness of the film by
varying the velocity. He remarks in his first report that, "according to
the theory of fluid motion, the resistance would be as the square of the
velocity, whereas in his results it did not increase according to this
law." The rational theory of lubrication does not, however, depend
solely on the viscosity within the interior of fluids, but also depends
on the surface action between the fluid and the solid. In many respects
the surface actions, as indicated by surface tension, are still obscure,
and there has been a general tendency to assume that there may be
discontinuity in the velocity at the common surface. But whatever these
actions may be in other respects, there is abundant evidence that there
is no appreciable discontinuity in the velocity at the surfaces as long
as the fluid has finite thickness. Hence in the case of lubrication the
velocities of the fluid at the surfaces of the solids are those of the
solid. In as far as the presence of the lubricant is necessary, such
properties as cause oil in spite of its surface tension to spread even
against gravity over a bright metal surface, while mercury will
concentrate into globules on the bright surface of iron, have an
important place in securing lubrication where the action is
intermittent, as in the escapement of a clock. If there is oil on the
pallet, although the pressure of the tooth causes this to flow out
laterally from between the surfaces, it goes back again by surface
tension during the intervals; hence the importance of using fluids with
low surface tension like oil, or special oils, when there is no other
means of securing the presence of the lubricant.
The differential equations for the equilibrium of the lubricant are
what the differential equations of viscous fluid in steady motion
become when subject to the conditions necessary for lubrication as
already defined--(1) the velocity is below the critical value; (2) at
the surfaces the velocity of the fluid is that of the solid; (3) the
thickness of the film is small compared with the lateral dimensions of
the surfaces and the radii of curvature of the surfaces. By the first
of these conditions all the terms having [rho] as a factor may be
neglected, and the equations thus become the equations of equilibrium
of the fluid; as such, they are applicable to fluid whether
incompressible or elastic, and however the pressure may affect the
viscosity. But the analysis is greatly simplified by omitting all
terms depending on compressibility and by taking [mu] constant; this
may be done without loss of generality in a qualitative sense. With
these limitations we have for the differential equation of the
equilibrium of the lubricant:--
dp du dv dw \
0 = -- - [mu]²u, &c., &c., 0 = -- + -- + -- |
dx dx dy dz |
> (1)
/ du dv \ |
0 = p_yx - [mu] ( -- + -- ), &c., &c. |
\ dy dx / /
These are subject to the boundary conditions (2) and (3). Taking x as
measured parallel to one of the surfaces in the direction of relative
motion, y normal to the surface and z normal to the plane of xy by
condition (3), we may without error disregard the effect of any
curvature in the surfaces. Also v is small compared with u and w, and
the variations of u and w in the directions x and z are small compared
with their variation in the direction y. The equations (1) reduce to
dp d²u dp dp d²w du dv dw \
0 = -- - [mu]---, 0 = --, 0 = -- - [mu]---, 0 = -- + -- + -- |
dx dy² dy dz dy² dx dy dz |
> (2)
du dw |
0 = p_yx - [mu]--, 0 = p_yz - [mu]--, p_xz = 0. |
dy dy /
For the boundary conditions, putting f(x, z) as limiting the lateral
area of the lubricant, the conditions at the surfaces may be expressed
thus:--
when y = 0, u = U0, w = 0, v = 0 \
dh |
when y = h, u = U1, w = 0, v1, = U1 -- + V1 > (3)
dx |
when f(x, z) = 0, p = p0 /
Then, integrating the equations (2) over y, and determining the
constants by equations (3), we have, since by the second of equations
(2) p is independent of y,
1 dp h - y y \
u = ----- -- (y - h)y + U0 ----- + U1 --- |
2[mu] dx h h |
> (4)
1 dp |
w = ----- -- (y - h)y |
2[mu] dz /
Then, differentiating equations (4) with respect to x and z
respectively, and substituting in the 4th of equations (2), and
integrating from y = 0 to y = h, so that only the values of v at the
surfaces may be required, we have for the differential equation of
normal pressure at any point x, z, between the boundaries:--
_ _
d / dp\ d / dp\ | dh |
--- ( h³ -- ) + --- ( h³-- ) = 6[mu] | (U0 + U1) -- + 2V1 | (5)
dx \ dz/ dz \ dz/ |_ dx _|
Again differentiating equations (4), with respect to x and z
respectively, and substituting in the 5th and 6th of equations (2),
and putting f_x and f_z for the intensities of the tangential stresses
at the lower and upper surfaces:--
1 h dp \
f_x = [mu](U1 + U0) --- ± --- -- |
h 2 dx |
> (6)
h dp |
f_z = ± --- -- |
2 dx /
Equations (5) and (6) are the general equations for the stresses at
the boundaries at x, z, when h is a continuous function of x and z,
[mu] and [rho] being constant.
For the integration of equations (6) to get the resultant stresses and
moments on the solid boundaries, so as to obtain the conditions of
their equilibrium, it is necessary to know how x and z at any point on
the boundary enter into h, as well as the equation f(x, z) = 0, which
determines the limits of the lubricating film. If y, the normal to one
of the surfaces, has not the same direction for all points of this
surface, in other words, if the surface is not plane, x and z become
curvilinear co-ordinates, at all points perpendicular to y. Since, for
lubrication, one of the surfaces must be plane, cylindrical, or a
surface of revolution, we may put x = R[theta], y = r - R, and z
perpendicular to the plane of motion. Then, if the data are
sufficient, the resultant stresses and moments between the surfaces
are obtained by integrating the intensity of the stress and moments of
intensity of stress over the surface.
This, however, is not the usual problem that arises. What is generally
wanted is to find the thickness of the film where least (h0) and its
angular position with respect to direction of load, to resist a
definite load with a particular surface velocity. If the surfaces are
plane, the general solution involves only one arbitrary constant, the
least thickness (h0); since in any particular case the variation of h
with x is necessarily fixed, as in this case lubrication affords no
automatic adjustment of this slope. When both surfaces are curved in
the plane of motion there are at least two arbitrary constants, h0,
and [phi] the angular position of h0 with respect to direction of
load; while if the surfaces are both curved in a plane perpendicular
to the direction of motion as well as in the plane of motion, there
are three arbitrary constants, h0, [phi]0, z0. The only constraint
necessary is to prevent rotation in the plane of motion of one of the
surfaces, leaving this surface free to move in any direction and to
adjust its position so as to be in equilibrium under the load.
The integrations necessary for the solutions of these problems are
practicable--complete or approximate--and have been effected for
circumstances which include the chief cases of practical lubrication,
the results having been verified by reference to Tower's experiments. In
this way the verified theory is available for guidance outside the
limits of experience as well as for determining the limiting conditions.
But it is necessary to take into account certain subsidiary theories.
These limits depend on the coefficient of viscosity, which diminishes as
the temperature increases. The total work in overcoming the resistance
is spent in generating heat in the lubricant, the volume of which is
very small. Were it not for the escape of heat by conduction through the
lubricant and the metal, lubrication would be impossible. Hence a
knowledge of the empirical law of the variation of the viscosity of the
lubricant with temperature, the coefficients of conduction of heat in
the lubricant and in the metal, and the application of the theory of the
flow of heat in the particular circumstances, are necessary adjuncts to
the theory of lubrication for determining the limits of lubrication. Nor
is this all, for the shapes of the solid surfaces vary with the
pressure, and more particularly with the temperature.
The theory of lubrication has been applied to the explanation of the
slipperiness of ice (_Mem. Manchester Lit. and Phil. Soc._, 1899).
(O. R.)