position in Touraine, was born in Paris in November 1615. Her long and
eventful life divides into two periods, during the former of which she
was the typical Frenchwoman of the gayest and most licentious society of
the 17th century, during the latter the recognized leader of the fashion
in Paris, and the friend of wits and poets. All that can be pleaded in
defence of her earlier life is that she had been educated by her father
in epicurean and sensual beliefs, and that she retained throughout the
frank demeanour, and disregard of money, which won from Saint Évremond
the remark that she was an _honnête homme_. She had a succession of
distinguished lovers, among them being Gaspard de Coligny, the marquis
d'Éstrées, La Rochefoucauld, Condé and Saint Évremond. Queen Christina
of Sweden visited her, and Anne of Austria was powerless against her.
After she had continued her career for a preposterous length of time,
she settled down to the social leadership of Paris. Among her friends
she counted Mme de la Sablière, Mme de la Fayette and Mme de Maintenon.
It became the fashion for young men as well as old to throng round her,
and the best of all introductions for a young man who wished to make a
figure in society was an introduction to Mlle de Lenclos. Her long
friendship with Saint Évremond must be briefly noticed. They were of the
same age, and had been lovers in their youth, and throughout his long
exile the wit seems to have kept a kind remembrance of her. The few
really authentic letters of Ninon are those addressed to her old friend,
and the letters of both in the last few years of their equally long
lives are exceptionally touching, and unique in the polite compliments
with which they try to keep off old age. If Ninon owes part of her
posthumous fame to Saint Évremond, she owes at least as much to
Voltaire, who was presented to her as a promising boy poet by the abbé
de Chateauneuf. To him she left 2000 francs to buy books, and his letter
on her was the chief authority of many subsequent biographers. Her
personal appearance is, according to Sainte-Beuve, best described in
_Clélie_, a novel by Mlle de Scudéry, in which she figures as Clarisse.
Her distinguishing characteristic was neither beauty nor wit, but high
spirits and perfect evenness of temperament.
The letters of Ninon published after her death were, according to
Voltaire, all spurious, and the only authentic ones are those to Saint
Évremond, which can be best studied in Dauxmesnil's edition of _Saint
Évremond_, and his notice on her. Sainte-Beuve has an interesting
notice of these letters in the _Causeries du Lundi_, vol. iv. The
_Correspondance authentique_ was edited by E. Colombey in 1886. See
also Helen K. Hayes, _The Real Ninon de l'Enclos_ (1908); and Mary C.
Rowsell, _Ninon de l'Enclos and her century_ (1910).
LENFANT, JACQUES (1661-1728), French Protestant divine, was born at
Bazoche in La Beauce on the 13th of April 1661, son of Paul Lenfant,
Protestant pastor at Bazoche and afterwards at Châtillon-sur-Loing until
the revocation of the edict of Nantes, when he removed to Cassel. After
studying at Saumur and Geneva, Lenfant completed his theological course
at Heidelberg, where in 1684 he was ordained minister of the French
Protestant church, and appointed chaplain to the dowager electress
palatine. When the French invaded the Palatinate in 1688 Lenfant
withdrew to Berlin, as in a recent book he had vigorously attacked the
Jesuits. Here in 1689 he was again appointed one of the ministers of the
French Protestant church; this office he continued to hold until his
death, ultimately adding to it that of chaplain to the king, with the
dignity of _Consistorialrath_. He visited Holland and England in 1707,
preached before Queen Anne, and, it is said, was invited to become one
of her chaplains. He was the author of many works, chiefly on church
history. In search of materials he visited Helmstädt in 1712, and
Leipzig in 1715 and 1725. He died at Berlin on the 7th of August 1728.
An exhaustive catalogue of his publications, thirty-two in all, will
be found in J. G. de Chauffepié's _Dictionnaire_. See also E. and S.
Haag's _France Protestante_. He is now best known by his _Histoire du
concile de Constance_ (Amsterdam, 1714; 2nd ed., 1728; English trans.,
1730). It is of course largely dependent upon the laborious work of
Hermann von der Hardt (1660-1746), but has literary merits peculiar to
itself, and has been praised on all sides for its fairness. It was
followed by _Histoire du concile de Pise_ (1724), and (posthumously)
by _Histoire de la guerre des Hussites et du concile de Basle_
(Amsterdam, 1731; German translation, Vienna, 1783-1784). Lenfant was
one of the chief promoters of the _Bibliothèque Germanique_, begun in
1720; and he was associated with Isaac Beausobre (1659-1738) in the
preparation of the new French translation of the New Testament with
original notes, published at Amsterdam in 1718.
LENKORAN, a town in Russian Transcaucasia, in the government of Baku,
stands on the Caspian Sea, at the mouth of a small stream of its own
name, and close to a large lagoon. The lighthouse stands in 38° 45´ 38´´
N. and 48° 50´ 18´´ E. Taken by storm on New Year's day 1813 by the
Russians, Lenkoran was in the same year formally surrendered by Persia
to Russia by the treaty of Gulistan, along with the khanate of Talysh,
of which it was the capital. Pop. (1867) 15,933, (1897) 8768. The fort
has been dismantled; and in trade the town is outstripped by Astara, the
customs station on the Persian frontier.
The DISTRICT OF LENKORAN (2117 sq. m.) is a thickly wooded mountainous
region, shut off from the Persian plateau by the Talysh range (7000-8000
ft. high), and with a narrow marshy strip along the coast. The climate
is exceptionally moist and warm (annual rainfall 52.79 in; mean
temperature in summer 75° F., in winter 40°), and fosters the growth of
even Indian species of vegetation. The iron tree (_Parrotia persica_),
the silk acacia, _Carpinus betulus_, _Quercus iberica_, the box tree and
the walnut flourish freely, as well as the sumach, the pomegranate, and
the _Gleditschia caspica_. The Bengal tiger is not unfrequently met
with, and wild boars are abundant. Of the 131,361 inhabitants in 1897
the Talyshes (35,000) form the aboriginal element, belonging to the
Iranian family, and speaking an independently developed language closely
related to Persian. They are of middle height and dark complexion, with
generally straight nose, small round skull, small sharp chin and large
full eyes, which are expressive, however, rather of cunning than
intelligence. They live exclusively on rice. In the northern half of the
district the Tatar element predominates (40,000) and there are a number
of villages occupied by Russian Raskolniks (Nonconformists).
Agriculture, bee-keeping, silkworm-rearing and fishing are the principal
occupations.
LENNEP, JACOB VAN (1802-1868), Dutch poet and novelist, was born on the
24th of March 1802 at Amsterdam, where his father, David Jacob van
Lennep (1774-1853), a scholar and poet, was professor of eloquence and
the classical languages in the Athenaeum. Lennep took the degree of
doctor of laws at Leiden, and then settled as an advocate in Amsterdam.
His first poetical efforts had been translations from Byron, of whom he
was an ardent admirer, and in 1826 he published a collection of original
_Academische Idyllen_, which had some success. He first attained genuine
popularity by the _Nederlandsche Legenden_ (2 vols., 1828) which
reproduced, after the manner of Sir Walter Scott, some of the more
stirring incidents in the early history of his fatherland. His fame was
further raised by his patriotic songs at the time of the Belgian revolt,
and by his comedies _Het Dorp aan de Grenzen_ (1830) and _Het Dorp over
de Grenzen_ (1831), which also had reference to the political events of
1830. In 1833 he broke new ground with the publication of _De Pleegzoon
(The Adopted Son)_, the first of a series of historical romances in
prose, which have acquired for him in Holland a position somewhat
analogous to that of Sir Walter Scott in Great Britain. The series
included _De Roos van Dekama_ (2 vols., 1836), _Onze Voorouders_ (5
vols., 1838), _De Lotgevallen van Ferdinand Huyck_ (2 vols., 1840),
_Elizabeth Musch_ (3 vols., 1850), and _De Lotgevallen van Klaasje
Zevenster_ (5 vols., 1865), several of which have been translated into
German and French, and two--_The Rose of Dekama_ (1847) and _The Adopted
Son_ (New York, 1847)--into English. His Dutch history for young people
(_Voornaamste Geschiedenissen van Noord-Nederland aan mijne Kindern
verhaald_, 4 vols., 1845) is attractively written. Apart from the two
comedies already mentioned, Lennep was an indefatigable journalist and
literary critic, the author of numerous dramatic pieces, and of an
excellent edition of Vondel's works. For some years Lennep held a
judicial appointment, and from 1853 to 1856 he was a member of the
second chamber, in which he voted with the conservative party. He died
at Oosterbeek near Arnheim on the 25th of August 1868.
There is a collective edition of his _Poetische Werken_ (13 vols.,
1859-1872), and also of his _Romantische Werken_ (23 vols.,
1855-1872). See also a bibliography by P. Knoll (1869); and Jan ten
Brink, _Geschiedenis der Noord-Nederlandsche Letteren in de XIX^e
Eeuw_ (No. iii.).
LENNEP, a town of Germany, in the Prussian Rhine province, 18 m. E. of
Düsseldorf, and 9 m. S. of Barmen by rail, at a height of 1000 ft. above
the level of the sea. Pop. (1905) 10,323. It lies in the heart of one of
the busiest industrial districts in Germany, and carries on important
manufactures of the finer kinds of cloth, wool, yarn and felt, and also
of iron and steel goods. It has an Evangelical and a Protestant church,
a modern school and a well-equipped hospital. Lennep, which was the
residence of the counts of Berg from 1226 to 1300, owes the foundation
of its prosperity to an influx of Cologne weavers during the 14th
century.
LENNOX, a name given to a large district in Dumbartonshire and
Stirlingshire, which was erected into an earldom in the latter half of
the 12th century. It embraced the ancient sheriffdom of Dumbarton and
nineteen parishes with the whole of the lands round Loch Lomond,
formerly Loch Leven, and the river of that name which glides into the
estuary of the Clyde at the ancient castle of Dumbarton.
On this river Leven, at Balloch, was the seat of Alwin, first earl of
Lennox. It is probable that he was of Celtic descent, but the records
are silent as to his part in history; that he was earl at all is only
proved from the charters of his son, another Alwin, and he died some
time before 1217. The second Alwin was father of ten sons, one of whom
founded the clan Macfarlane, famous in the annals of the district, while
another was ancestor of Walter of Farlane, who married the heiress of
the 6th earl of Lennox. Maldouen, the 3rd earl, eldest of the sons of
Alwin the younger, is an historical personage; he was a witness to the
treaty between Alexander II., king of Scotland, and his brother-in-law
the English king Henry III., at Newcastle in 1237, concerning the much
disputed northern counties of England. His grandson, Malcolm, successor
to the title, swore fealty to Edward I. in 1296; it was apparently his
son, another Malcolm, the 5th earl, who was summoned by Edward to
parliament and entrusted with the important post of guarding the fords
of the river Forth. But the 5th earl soon after gave his services to the
party of Bruce, the cause of that family having been embraced by his
father as early as 1292. As a result the English king bestowed the
earldom on Sir John Menteith, who was holding it in 1307 while the real
earl was with King Robert Bruce in his wanderings in the Lennox country.
For his services he was rewarded with a renewal of the earldom and the
keeping of Dumbarton Castle; he fell fighting for his country at Halidon
Hill in 1333. His son Donald, the 6th earl, an adherent of King David
II., left a daughter, Margaret, countess of Lennox, who was married to
her kinsman the above-mentioned Walter of Farlane, nearest heir male of
the Lennox family.
In 1392, on the marriage of their grand-daughter Isabella, eldest
daughter of Duncan, 8th earl, with Sir Murdoch Stewart, afterwards duke
of Albany, the earldom was resigned into the hands of the king, who
re-granted it to Earl Duncan, with remainder to the heirs male of his
body, with remainder to Murdoch and Isabella and the heirs of their
bodies begotten between them, with eventual remainder to Earl Duncan's
nearest and lawful heirs. In 1424, when Murdoch, then duke of Albany,
succeeded in ransoming the poet king James I. from his long English
captivity, the aged Earl Duncan went with the Scottish party to Durham.
The next year, however, he suffered the fate of Albany, being executed
perhaps for no other reason than that he was his father-in-law. The
earldom was not forfeited, and the widowed duchess of Albany, now also
countess of Lennox, lived secure in her island castle of Inchmurrin on
Loch Lomond until her death. Of her four sons, none of whom left
legitimate issue, the eldest died in 1421, the two next suffered their
father's fate at Stirling, while the youngest had to flee for his life
to Ireland. Her daughter Isobel appears to have been the wife of Sir
Walter Buchanan of that ilk.
It was from Elizabeth, sister of the countess, that the next holders of
the title descended. She was married to Sir John Stewart of Darnley
(distinguished in the military history of France as seigneur d'Aubigny),
whose immediate ancestor was brother of James, 5th high steward of
Scotland. Their grandson, another Sir John Stewart, created a lord of
parliament as Lord Darnley, was served heir to his great-grandfather
Duncan, earl of Lennox, in 1473, and was designated as earl of Lennox in
a charter under the great seal in the same year. Thereafter followed
disputes with John of Haldane, whose wife's great-grandmother had been
another of the three daughters of Duncan, 8th earl of Lennox, and in her
right he contested the succession. Lord Darnley, however, appears to
have silenced all opposition and for the last seven years of his life
maintained his right to the earldom undisputed. Three of his younger
sons were greatly distinguished in the French service, one being captain
of Scotsmen-at-arms, another _premier homme d'armes_, and a third
_maréchal de France_. Their elder brother Matthew, 2nd earl of this
line, fell on Flodden Field, leaving by his wife Elizabeth, daughter of
James, earl of Arran, and niece of James III., a son and successor John,
who became one of the guardians of James V. and was murdered in 1526.
His son Matthew, the 4th earl, played a great part in the intrigues of
his time, and by his marriage with Margaret Douglas allied himself to
the royal house of England as well as strengthening the ties which bound
his family to that of Scotland; because Margaret was the daughter and
heir of the 6th earl of Angus by his wife, Margaret Tudor, sister of
King Henry VIII. and widow of King James IV. Though his estates were
forfeited in 1545, Earl Matthew in 1564 not only had them restored but
had the satisfaction of getting his eldest son Henry married to Mary,
queen of Scots. The murder of Lord Darnley, now created earl of Rosse,
lord of Ardmanoch and duke of Albany, took place in February 1567, and
in July his only son James, by Mary's abdication, became king of
Scotland. The old earl of Lennox, now grandfather of his sovereign,
obtained the regency in 1570, but in the next year was killed in the
attack made on the parliament at Stirling, being the third earl in
succession to meet with a violent death.
The title was now merged in the crown in the person of James VI. the
next heir, but was soon after granted to the king's uncle Charles, who
died in 1576, leaving an only child, the unfortunate Lady Arabella
Stewart.
Two years later the title was granted to Robert Stewart, the king's
grand-uncle, second son of John, the 3rd earl, but he in 1580 exchanged
it for that of earl of March. On the same day the earldom of Lennox was
given to Esme Stewart, first cousin of the king and grandson of the 3rd
earl, he being son of John Stewart (adopted heir of the maréchal
d'Aubigny) and his French wife, Anne de la Queulle. In the following
year Esme was created duke of Lennox, earl of Darnley, Lord Aubigny,
Tarboulton and Dalkeith, and other favours were heaped upon him, but the
earl of Ruthven sent him back to France where he died soon after. His
elder son, Ludovic, was thereupon summoned to Scotland by James, who
invested him with all his father's honours and estates, and after his
accession to the English throne created him Lord Settrington and earl of
Richmond (1613), and earl of Newcastle-upon-Tyne and duke of Richmond
(1623), all these titles being in the peerage of England. After holding
many appointments the 2nd duke died without issue in 1624, being
succeeded in his Scottish titles by his brother Esme, who had already
been created earl of March and Lord Clifton of Leighton Bromswold in the
peerage of England (1619) and was seigneur d'Aubigny in France. Of his
sons, Henry succeeded to Aubigny and died young at Venice; Ludovic,
seigneur d'Aubigny, entered the Roman Catholic Church and received a
cardinal's hat just before his death; while the three other younger
sons, George, seigneur d'Aubigny, John and Bernard, were all
distinguished as royalists in the Civil war. Each met a soldier's death,
George at Edgehill, John at Alresford and Bernard at Rowton Heath.
James, the eldest son and 4th duke of Lennox, was created duke of
Richmond in 1641, being like his brother a devoted adherent of Charles
I.
With the death of his little son Esme, the 5th duke, in 1660, the
titles, including that of Richmond, passed to his first cousin Charles,
who had already been created Lord Stuart of Newbury and earl of
Lichfield, being likewise now seigneur d'Aubigny. Disliked by Charles
II., principally because of his marriage with "la belle Stuart"--"the
noblest romance and example of a brave lady that ever I read in my
life," writes Pepys--he was sent into exile as ambassador to Denmark,
where he was drowned in 1672. His wife had had the Lennox estates
granted to her for life, but his only sister Katharine, wife of Henry
O'Brien, heir apparent of the 7th earl of Thomond, was served heir to
him. Her only daughter, the countess of Clarendon, was mother of
Theodosia Hyde, ancestress of the present earls of Darnley.
The Lennox dukedom, being to heirs male, now devolved upon Charles II.,
who bestowed it with the titles of earl of Darnley and Lord Tarbolton
upon one of his bastards, Charles Lennox, son of the celebrated duchess
of Portsmouth, he having previously been created duke of Richmond, earl
of March and Lord Settrington in the peerage of England. The ancient
lands of the Lennox title were also granted to him, but these he sold to
the duke of Montrose.
His son Charles, who inherited his grandmother's French dukedom of
Aubigny, was a soldier of distinction, as were the 3rd and 4th dukes.
The wife of the last, Lady Charlotte Gordon, as heir of her brother
brought the ancient estates of her family to the Lennoxes; the
additional name of Gordon being taken by the 5th duke of Richmond and of
Lennox on the death of his uncle, the 5th duke of Gordon. In the next
generation further honours were granted to the family in the person of
the 6th duke, who was rewarded for his great public services with the
titles of duke of Gordon and earl of Kinrara in the peerage of the
United Kingdom (1876).
_See Scots Peerage_, vol. v., for excellent accounts of these peerages
by the Rev. John Anderson, curator Historical Dept. H.M. Register
House; A. Francis Steuart and Francis J. Grant, Rothesay Herald. See
also _The Lennox_ by William Fraser.
LENNOX, CHARLOTTE (1720-1804), British writer, daughter of Colonel James
Ramsay, lieutenant-governor of New York, was born in 1720. She went to
London in 1735, and, being left unprovided for at her father's death,
she began to earn her living by writing. She made some unsuccessful
appearances on the stage and married in 1748. Samuel Johnson had an
exaggerated admiration for her. "Three such women," he said, speaking of
Elizabeth Carter, Hannah More and Fanny Burney, "are not to be found; I
know not where to find a fourth, except Mrs Lennox, who is superior to
them all." Her chief works are: _The Female Quixote; or the Adventures
of Arabella_ (1752), a novel; _Shakespear illustrated; or the novels and
histories on which the plays ... are founded_ (1753-1754), in which she
argued that Shakespeare had spoiled the stories he borrowed for his
plots by interpolating unnecessary intrigues and incidents; _The Life of
Harriot Stuart_ (1751), a novel; and _The Sister_, a comedy produced at
Covent Garden (18th February 1769). This last was withdrawn after the
first night, after a stormy reception, due, said Goldsmith, to the fact
that its author had abused Shakespeare.
LENNOX, MARGARET, COUNTESS OF (1515-1578), daughter of Archibald
Douglas, 6th earl of Angus, and Margaret Tudor, daughter of Henry VII.
of England and widow of James IV. of Scotland, was born at Harbottle
Castle, Northumberland, on the 8th of October 1515. On account of her
nearness to the English crown, Lady Margaret Douglas was brought up
chiefly at the English court in close association with the Princess
Mary, who remained her fast friend throughout life. She was high in
Henry VIII.'s favour, but was twice disgraced; first for an attachment
to Lord Thomas Howard, who died in the Tower in 1537, and again in 1541
for a similar affair with Sir Charles Howard, brother of Queen Catherine
Howard. In 1544 she married a Scottish exile, Matthew Stewart, 4th earl
of Lennox (1516-1571), who was regent of Scotland in 1570-1571. During
Mary's reign the countess of Lennox had rooms in Westminster Palace; but
on Elizabeth's accession she removed to Yorkshire, where her home at
Temple Newsam became a centre for Catholic intrigue. By a series of
successful manoeuvres she married her son Henry Stewart, Lord Darnley,
to Mary, queen of Scots. In 1566 she was sent to the Tower, but after
the murder of Darnley in 1567 she was released. She was at first loud in
her denunciations of Mary, but was eventually reconciled with her
daughter-in-law. In 1574 she again aroused Elizabeth's anger by the
marriage of her son Charles, earl of Lennox, with Elizabeth Cavendish,
daughter of the earl of Shrewsbury. She was sent to the Tower with Lady
Shrewsbury, and was only pardoned after her son's death in 1577. Her
diplomacy largely contributed to the future succession of her grandson
James to the English throne. She died on the 7th of March 1578.
The famous Lennox jewel, made for Lady Lennox as a memento of her
husband, was bought by Queen Victoria in 1842.
LENO, DAN, the stage-name of George Galvin (1861-1904), English
comedian, who was born at Somers Town, London, in February 1861. His
parents were actors, known as Mr and Mrs Johnny Wilde. Dan Leno was
trained to be an acrobat, but soon became a dancer, travelling with his
brother as "the brothers Leno," and winning the world's championship in
clog-dancing at Leeds in 1880. Shortly afterwards he appeared in London
at the Oxford, and in 1886-1887 at the Surrey Theatre. In 1888-1889 he
was engaged by Sir Augustus Harris to play the Baroness in the _Babes in
the Wood_, and from that time he was a principal figure in the Drury
Lane pantomimes. He was the wittiest and most popular comedian of his
day, and delighted London music-hall audiences by his shop-walker,
stores-proprietor, waiter, doctor, beef-eater, bathing attendant, "Mrs
Kelly," and other impersonations. In 1900 he engaged to give his entire
services to the Pavilion Music Hall, where he received £100 per week. In
November 1901 he was summoned to Sandringham to do a "turn" before the
king, and was proud from that time to call himself the "king's jester."
Dan Leno's generosity endeared him to his profession, and he was the
object of much sympathy during the brain failure which recurred during
the last eighteen months of his life. He died on the 31st of October
1904.
LENORMANT, FRANÇOIS (1837-1883), French Assyriologist and archaeologist,
was born in Paris on the 17th of January 1837. His father, Charles
Lenormant, distinguished as an archaeologist, numismatist and
Egyptologist, was anxious that his son should follow in his steps. He
made him begin Greek at the age of six, and the child responded so well
to this precocious scheme of instruction, that when he was only fourteen
an essay of his, on the Greek tablets found at Memphis, appeared in the
_Revue archéologique_. In 1856 he won the numismatic prize of the
Académie des Inscriptions with an essay entitled _Classification des
monnaies des Lagides_. In 1862 he became sub-librarian of the Institute.
In 1859 he accompanied his father on a journey of exploration to Greece,
during which Charles Lenormant succumbed to fever at Athens (24th
November). Lenormant returned to Greece three times during the next six
years, and gave up all the time he could spare from his official work to
archaeological research. These peaceful labours were rudely interrupted
by the war of 1870, when Lenormant served with the army and was wounded
in the siege of Paris. In 1874 he was appointed professor of archaeology
at the National Library, and in the following year he collaborated with
Baron de Witte in founding the _Gazette archéologique_. As early as 1867
he had turned his attention to Assyrian studies; he was among the first
to recognize in the cuneiform inscriptions the existence of a
non-Semitic language, now known as Accadian. Lenormant's knowledge was
of encyclopaedic extent, ranging over an immense number of subjects, and
at the same time thorough, though somewhat lacking perhaps in the strict
accuracy of the modern school. Most of his varied studies were directed
towards tracing the origins of the two great civilizations of the
ancient world, which were to be sought in Mesopotamia and on the shores
of the Mediterranean. He had a perfect passion for exploration. Besides
his early expeditions to Greece, he visited the south of Italy three
times with this object, and it was while exploring in Calabria that he
met with an accident which ended fatally in Paris on the 9th of December
1883, after a long illness. The amount and variety of Lenormant's work
is truly amazing when it is remembered that he died at the early age of
forty-six. Probably the best known of his books are _Les Origines de
l'histoire d'après la Bible_, and his ancient history of the East and
account of Chaldean magic. For breadth of view, combined with
extraordinary subtlety of intuition, he was probably unrivalled.
LENOX, a township of Berkshire county, Massachusetts, U.S.A. Pop. (1900)
2942, (1905) 3058; (1910) 3060. Area, 19.2 sq. m. The principal village,
also named Lenox (or Lenox-on-the-Heights), lies about 2 m. W. of the
Housatonic river, at an altitude of about 1000 ft., and about it are
high hills--Yokun Seat (2080 ft.), South Mountain (1200 ft.), Bald Head
(1583 ft.), and Rattlesnake Hill (1540 ft.). New Lenox and Lenoxdale are
other villages in the township. Lenox is a fashionable summer and autumn
resort, much frequented by wealthy people from Washington, Newport and
New York. There are innumerable lovely walks and drives in the
surrounding region, which contains some of the most beautiful country of
the Berkshires--hills, lakes, charming intervales and woods. As early as
1835 Lenox began to attract summer residents. In the next decade began
the creation of large estates, although the great holdings of the
present day, and the villas scattered over the hills, are comparatively
recent features. The height of the season is in the autumn, when there
are horse-shows, golf, tennis, hunts and other outdoor amusements. The
Lenox library (1855) contained about 20,000 volumes in 1908. Lenox was
settled about 1750, was included in Richmond township in 1765, and
became an independent township in 1767. The names were those of Sir
Charles Lennox, third duke of Richmond and of Lennox (1735-1806), one of
the staunch friends of the American colonies during the War of
Independence. Lenox was the county-seat from 1787 to 1868. It has
literary associations with Catherine M. Sedgwick (1789-1867), who passed
here the second half of her life; with Nathaniel Hawthorne, whose brief
residence here (1850-1851) was marked by the production of the _House
of the Seven Gables_ and the _Wonder Book_; with Fanny Kemble, a summer
resident from 1836-1853; and with Henry Ward Beecher (see his _Star
Papers_). Elizabeth (Mrs Charles) Sedgwick, the sister-in-law of
Catherine Sedgwick, maintained here from 1828 to 1864 a school for
girls, in which Harriet Hosmer, the sculptor, and Maria S. Cummins
(1827-1866), the novelist, were educated; and in Lenox academy (1803), a
famous classical school (now a public high school) were educated W. L.
Yancey, A. H. Stephens, Mark Hopkins and David Davis (1815-1886), a
circuit judge of Illinois from 1848 to 1862, a justice (1862-1877) of
the United States Supreme Court, a Republican member of the United
States Senate from Illinois in 1877-1883, and president of the Senate
from the 31st of October 1881, when he succeeded Chester A. Arthur,
until the 3rd of March 1883. There is a statue commemorating General
John Paterson (1744-1808) a soldier from Lenox in the War of
Independence.
See R. de W. Mallary, _Lenox and the Berkshire Highlands_ (1902); J.
C. Adams, _Nature Studies in Berkshire_; C. F. Warner, _Picturesque
Berkshire_ (1890); and Katherine M. Abbott, _Old Paths and Legends of
the New England Border_ (1907).
LENS, a town of Northern France, in the department of Pas-de-Calais, 13
m. N.N.E. of Arras by rail on the Déûle and on the Lens canal. Pop.
(1906) 27,692. Lens has important iron and steel foundries, and
engineering works and manufactories of steel cables, and occupies a
central position in the coalfields of the department. Two and a half
miles W.S.W. lies Liévin (pop. 22,070), likewise a centre of the
coalfield. In 1648 the neighbourhood of Lens was the scene of a
celebrated victory gained by Louis II. of Bourbon, prince of Condé, over
the Spaniards.
LENS (from Lat. _lens_, lentil, on account of the similarity of the form
of a lens to that of a lentil seed), in optics, an instrument which
refracts the luminous rays proceeding from an object in such a manner as
to produce an image of the object. It may be regarded as having four
principal functions: (1) to produce an image larger than the object, as
in the magnifying glass, microscope, &c.; (2) to produce an image
smaller than the object, as in the ordinary photographic camera; (3) to
convert rays proceeding from a point or other luminous source into a
definite pencil, as in lighthouse lenses, the engraver's globe, &c.; (4)
to collect luminous and heating rays into a smaller area, as in the
burning glass. A lens made up of two or more lenses cemented together or
very close to each other is termed "composite" or "compound"; several
lenses arranged in succession at a distance from each other form a
"system of lenses," and if the axes be collinear a "centred system."
This article is concerned with the general theory of lenses, and more
particularly with spherical lenses. For a special part of the theory of
lenses see ABERRATION; the instruments in which the lenses occur are
treated under their own headings.
The most important type of lens is the spherical lens, which is a piece
of transparent material bounded by two spherical surfaces, the boundary
at the edge being usually cylindrical or conical. The line joining the
centres, C1, C2 (fig. 1), of the bounding surfaces is termed the _axis_;
the points S1, S2, at which the axis intersects the surfaces, are termed
the "vertices" of the lens; and the distance between the vertices is
termed the "thickness." If the edge be everywhere equidistant from the
vertex, the lens is "centred."
[Illustration: FIG. 1.]
Although light is really a wave motion in the aether, it is only
necessary, in the investigation of the optical properties of systems of
lenses, to trace the rectilinear path of the waves, i.e. the direction
of the normal to the wave front, and this can be done by purely
geometrical methods. It will be assumed that light, so long as it
traverses the same medium, always travels in a straight line; and in
following out the geometrical theory it will always be assumed that the
light travels from left to right; accordingly all distances measured in
this direction are positive, while those measured in the opposite
direction are negative.
_Theory of Optical Representation._--If a pencil of rays, i.e. the
totality of the rays proceeding from a luminous point, falls on a lens
or lens system, a section of the pencil, determined by the dimensions
of the system, will be transmitted. The emergent rays will have
directions differing from those of the incident rays, the alteration,
however, being such that the transmitted rays are convergent in the
"image-point," just as the incident rays diverge from the
"object-point." With each incident ray is associated an emergent ray;
such pairs are termed "conjugate ray pairs." Similarly we define an
object-point and its image-point as "conjugate points"; all
object-points lie in the "object-space," and all image-points lie in
the "image-space."
[Illustration: FIG. 2.]
The laws of optical representations were first deduced in their most
general form by E. Abbe, who assumed (1) that an optical
representation always exists, and (2) that to every point in the
object-space there corresponds a point in the image-space, these
points being mutually convertible by straight rays; in other words,
with each object-point is associated one, and only one, image-point,
and if the object-point be placed at the image-point, the conjugate
point is the original object-point. Such a transformation is termed a
"collineation," since it transforms points into points and straight
lines into straight lines. Prior to Abbe, however, James Clerk Maxwell
published, in 1856, a geometrical theory of optical representation,
but his methods were unknown to Abbe and to his pupils until O.
Eppenstein drew attention to them. Although Maxwell's theory is not so
general as Abbe's, it is used here since its methods permit a simple
and convenient deduction of the laws.
[Illustration]
Maxwell assumed that two object-planes perpendicular to the axis are
represented sharply and similarly in two image-planes also
perpendicular to the axis (by "sharply" is meant that the assumed
ideal instrument unites all the rays proceeding from an object-point
in one of the two planes in its image-point, the rays being generally
transmitted by the system). The symmetry of the axis being premised,
it is sufficient to deduce laws for a plane containing the axis. In
fig. 2 let O1, O2 be the two points in which the perpendicular
object-planes meet the axis; and since the axis corresponds to itself,
the two conjugate points O´1, O´2, are at the intersections of the two
image-planes with the axis. We denote the four planes by the letters
O1, O2, and O´1, O´2. If two points A, C be taken in the plane O1,
their images are A´, C´ in the plane O´1, and since the planes are
represented similarly, we have O´1A´:O1A = O´1C´1:O1C = [beta]1 (say),
in which [beta]1 is easily seen to be the _linear magnification_ of
the plane-pair O1, O´1. Similarly, if two points B, D be taken in the
plane O2 and their images B´, D´ in the plane O´2, we have O´2B´:O2B =
O´2D´:O2D = [beta]2 (say), [beta]2 being the linear magnification of
the plane-pair O2, O´2. The joins of A and B and of C and D intersect
in a point P, and the joins of the conjugate points similarly
determine the point P´.
If P´ is the only possible image-point of the object-point P, then the
conjugate of every ray passing through P must pass through P´. To
prove this, take a third line through P intersecting the planes O1, O2
in the points E, F, and by means of the magnifications [beta]1,
[beta]2 determine the conjugate points E´, F´ in the planes O´1, O´2.
Since the planes O1, O2 are parallel, then AC/AE = BD/BF; and since
these planes are represented similarly in O´1, O´2, then A´C´/A´E´ =
B´D´/B´F´. This proportion is only possible when the straight line
E´F´ contains the point P´. Since P was any point whatever, it follows
that every point of the object-space is represented in one and only
one point in the image-space.
Take a second object-point P1, vertically under P and defined by the
two rays CD1, and EF1, the conjugate point P´1 will be determined by
the intersection of the conjugate rays C´D´1 and E´F´1, the points
D´1, F´1, being readily found from the magnifications [beta]1,
[beta]2. Since PP1 is parallel to CE and also to DF, then DF = D1F1.
Since the plane O2 is similarly represented in O´2, D´F´ = D´1F´1;
this is impossible unless P´P´1 be parallel to C´E´. Therefore every
perpendicular object-plane is represented by a perpendicular
image-plane.
Let O be the intersection of the line PP1 with the axis, and let O´ be
its conjugate; then it may be shown that a fixed magnification [beta]3
exists for the planes O and O´. For PP1/FF1 = OO1/O1O2, P´P´1/F´F´1 =
O´O´/O´1O´2, and F´F´1 = [beta]2FF1. Eliminating FF1 and F´F´1 between
these ratios, we have P´P´1/PP1[beta]2 = O´O´1·O1O2/OO1. O´1O´2, or
[beta]3 = [beta]2·O´O´1·O1O2/OO1·O´1O´2, i.e. [beta]3 = [beta]2 × a
product of the axial distances.
The determination of the image-point of a given object-point is
facilitated by means of the so-called "cardinal points" of the optical
system. To determine the image-point O´1 (fig. 3) corresponding to the
object-point O1, we begin by choosing from the ray pencil proceeding
from O1, the ray parallel with the axis, i.e. intersecting the axis at
infinity. Since the axis is its own conjugate, the parallel ray
through O1 must intersect the axis after refraction (say at F´). Then
F´ is the image-point of an object-point situated at infinity on the
axis, and is termed the "second principal focus" (German _der
bildseitige Brennpunkt_, the image-side focus). Similarly if O´4 be on
the parallel through O1 but in the image-space, then the conjugate ray
must intersect the axis at a point (say F), which is conjugate with
the point at infinity on the axis in the image-space. This point is
termed the "first principal focus" (German _der objektseitige
Brennpunkt_, the object-side focus).
Let H1, H´1 be the intersections of the focal rays through F and F´
with the line O1O´4. These two points are in the position of object
and image, since they are each determined by two pairs of conjugate
rays (O1H1 being conjugate with H´1F´, and O´4H´1 with H1F). It has
already been shown that object-planes perpendicular to the axis are
represented by image-planes also perpendicular to the axis. Two
vertical planes through H1 and H´1, are related as object- and
image-planes; and if these planes intersect the axis in two points H
and H´, these points are named the "principal," or "Gauss points" of
the system, H being the "object-side" and H´ the "image-side principal
point." The vertical planes containing H and H´ are the "principal
planes." It is obvious that conjugate points in these planes are
equidistant from the axis; in other words, the magnification [beta] of
the pair of planes is unity. An additional characteristic of the
principal planes is that the object and image are direct and not
inverted. The distances between F and H, and between F´ and H´ are
termed the focal lengths; the former may be called the "object-side
focal length" and the latter the "image-side focal length." The two
focal points and the two principal points constitute the so-called
four cardinal points of the system, and with their aid the image of
any object can be readily determined.
_Equations relating to the Focal Points._--We know that the ray
proceeding from the object point O1, parallel to the axis and
intersecting the principal plane H in H1, passes through H´1 and F´.
Choose from the pencil a second ray which contains F and intersects
the principal plane H in H2; then the conjugate ray must contain
points corresponding to F and H2. The conjugate of F is the point at
infinity on the axis, i.e. on the ray parallel to the axis. The image
of H2 must be in the plane H´ at the same distance from, and on the
same side of, the axis, as in H´2. The straight line passing through
H´2 parallel to the axis intersects the ray H´1F´ in the point O´1,
which must be the image of O1. If O be the foot of the perpendicular
from O1 to the axis, then OO1 is represented by the line O´O´1 also
perpendicular to the axis.
[Illustration: FIG. 3.]
This construction is not applicable if the object or image be
infinitely distant. For example, if the object OO1 be at infinity (O
being assumed to be on the axis for the sake of simplicity), so that
the object appears under a constant angle w, we know that the second
principal focus is conjugate with the infinitely distant axis-point.
If the object is at infinity in a plane perpendicular to the axis, the
image must be in the perpendicular plane through the focal point F´
(fig. 4).
The size y´ of the image is readily deduced. Of the parallel rays from
the object subtending the angle w, there is one which passes through
the first principal focus F, and intersects the principal plane H in
H1. Its conjugate ray passes through H´ parallel to, and at the same
distance from the axis, and intersects the image-side focal plane in
O´1; this point is the image of O1, and y´ is its magnitude. From the
figure we have tan w = HH1/FH = y´/f, or f = y´/tan w; this equation
was used by Gauss to define the focal length.
[Illustration: FIG. 4.]
Referring to fig. 3, we have from the similarity of the triangles OO1F
and HH2F, HH2/OO1 = FH/FO, or O´O´1/OO1 = FH/FO. Let y be the
magnitude of the object OO1, y´ that of the image O´O´1, x the focal
distance FO of the object, and f the object-side focal distance FH;
then the above equation may be written y´/y = f/x. From the similar
triangles H´1H´F´ and O´1O´F´, we obtain O´O´1/OO1 = F´O´/F´H´. Let x´
be the focal distance of the image F´O´, and f´ the image-side focal
length F´H´; then y´/y = x´/f´. The ratio of the size of the image to
the size of the object is termed the _lateral magnification_. Denoting
this by [beta], we have
[beta] = y´/y = f/x = x´/f´, (1)
and also
xx´ = ff´. (2)
By differentiating equation (2) we obtain
dx´= -(ff´/x²)dx or dx´/dx = -ff´/x². (3)
The ratio of the displacement of the image dx´ to the displacement of
the object dx is the axial magnification, and is denoted by [alpha].
Equation (3) gives important information on the displacement of the
image when the object is moved. Since f and f´ always have contrary
signs (as is proved below), the product -ff´ is invariably positive,
and since x² is positive for all values of x, it follows that dx and
dx´ have the same sign, i.e. the object and image always move in the
same direction, either both in the direction of the light, or both in
the opposite direction. This is shown in fig. 3 by the object O3O2 and
the image O´3O´2.
If two conjugate rays be drawn from two conjugate points on the axis,
making angles u and u´ with the axis, as for example the rays OH1,
O´H´1, in fig. 3, u is termed the "angular aperture for the object,"
and u´ the "angular aperture for the image." The ratio of the tangents
of these angles is termed the "convergence" and is denoted by [gamma],
thus [gamma] = tan u´/tan u. Now tan u´= H´H´1/O´H´ = H´H´1/(O´F´+
F´H´) = H´H´1/(F´H´- F´O´). Also tan u = HH1/OH = HH1/(OF + FH) =
HH1/(FH-FO). Consequently [gamma] = (FH - FO)/(F´H´-F´O´), or, in our
previous notation, [gamma] = (f - x)/(f´- x´).
From equation (1) f/x = x´/f´, we obtain by subtracting unity from
both sides (f-x)/x = (x´-f´)/f´, and consequently
f - x x f
------- = - -- = - -- = [gamma]. (4)
f´ - x´ f´ x´
From equations (1), (3) and (4), it is seen that a simple relation
exists between the lateral magnification, the axial magnification and
the convergence, viz. [alpha][gamma] = [beta].
[Illustration: FIG. 5.]
In addition to the four cardinal points F, H, F´, H´, J. B. Listing,
"Beiträge aus physiologischen Optik," _Göttinger Studien_ (1845)
introduced the so-called "nodal points" (_Knotenpunkte_) of the
system, which are the two conjugate points from which the object and
image appear under the same angle. In fig. 5 let K be the nodal point
from which the object y appears under the same angle as the image y´
from the other nodal point K´. Then OO1/KO = O´O´1/K´O´, or OO1/(KF +
FO) = O´O´1/(K´F´+ F´O´), or OO1/(FO - FK) = O´O´1/(F´O´- F´K´).
Calling the focal distances FK and F´K´, X and X´, we have y/(x - X) =
y´/(x´- X´), and since y´/y = [beta], it follows that 1/(x - X) =
[beta]/(x´- X´). Replace x´ and X´ by the values given in equation
(2), and we obtain
1 /ff´ ff´\ xX
----- = [beta]/( --- - --- ) or 1 = -[beta]---.
x - X \ x X / ff´
Since [beta] = f/x = x´/f´, we have f´ = -X, f = -X´.
These equations show that to determine the nodal points, it is only
necessary to measure the focal distance of the second principal focus
from the first principal focus, and vice versa. In the special case
when the initial and final medium is the same, as for example, a lens
in air, we have f = -f´, and the nodal points coincide with the
principal points of the system; we then speak of the "nodal point
property of the principal points," meaning that the object and
corresponding image subtend the same angle at the principal points.
_Equations Relating to the Principal Points._--It is sometimes
desirable to determine the distances of an object and its image, not
from the focal points, but from the principal points. Let A (see fig.
3) be the principal point distance of the object and A´ that of the
image, we then have
A = HO = HF + FO = FO - FH = x - f,
A´ = H´O´ = H´F´ + F´O´ = F´O´ - F´H´ = x´ - f´,
whence
x = A + f and x´ = A´ + f´.
Using xx´ = ff´, we have (A + f)(A´ + f´) = ff´, which leads to AA´ +
Af´ + A´f = O, or
f´ f
1 + -- + - = O;
A´ A
this becomes in the special case when f = -f´,
1 1 1
-- - -- = --.
A´ A f
To express the linear magnification in terms of the principal point
distances, we start with equation (4) (f - x)/(f´ - x´) = -x/f´. From
this we obtain A/A´ = -x/f´, or x = -f´A/A´; and by using equation (1)
we have [beta] = -fA´/f´A.
In the special case of f = -f´, this becomes [beta] = A´/A = y´/y,
from which it follows that the ratio of the dimensions of the object
and image is equal to the ratio of the distances of the object and
image from the principal points.
The convergence can be determined in terms of A and A´ by substituting
x = -f´A/A´ in equation (4), when we obtain [gamma] = A/A´.
_Compound Systems._--In discussing the laws relating to compound
systems, we assume that the cardinal points of the component systems
are known, and also that the combinations are centred, i.e. that the
axes of the component lenses coincide. If some object be represented
by two systems arranged one behind the other, we can regard the
systems as co-operating in the formation of the final image.
[Illustration: FIG. 6.]
Let such a system be represented in fig. 6. The two single systems are
denoted by the suffixes 1 and 2; for example, F1 is the first
principal focus of the first, and F´2 the second principal focus of
the second system. A ray parallel to the axis at a distance y passes
through the second principal focus F´1 of the first system,
intersecting the axis at an angle w´1. The point F´1 will be
represented in the second system by the point F´, which is therefore
conjugate to the point at infinity for the entire system, i.e. it is
the second principal focus of the compound system. The representation
of F´1 in F´ by the second system leads to the relations F2F´1 = x2,
and F´2F´ = x´2, whence x2x´2 = f2f´2. Denoting the distance between
the adjacent focal planes F´1, F2 by [Delta], we have [Delta] = F´1F2
= -F2F´1, so that x´2 = -f2f´2/[Delta]. A similar ray parallel to the
axis at a distance y proceeding from the image-side will intersect the
axis at the focal point F2; and by finding the image of this point in
the first system, we determine the first principal focus of the
compound system. Equation (2) gives x1x´1 = f1f´1, and since x´1 =
F´1F2 = [Delta], we have x1 = f1f´1/[Delta] as the distance of the
first principal focus F of the compound system from the first
principal focus F1 of the first system.
To determine the focal lengths f and f´ of the compound system and the
principal points H and H´, we employ the equations defining the focal
lengths, viz. f = y´/tan w, and f´ = y/tan w´. From the construction
(fig. 6) tan w´1 = y/f´1. The variation of the angle w´1 by the second
system is deduced from the equation to the convergence, viz. [gamma] =
tan w´2/tan w2 = -x2/f´2 = [Delta]/f´2, and since w2 = w´1, we have
tan w´2 = ([Delta]/f´2) tan w´1. Since w´ = w´2 in our system of
notation, we have
y yf´2 f´1.
f´ = ------ = --------------- = -----------. (5)
tan w´ [Delta] tan w´1 f´2/[Delta]
By taking a ray proceeding from the image-side we obtain for the first
principal focal distance of the combination
f = -f1f2/[Delta].
In the particular case in which [Delta] = 0, the two focal planes F´1,
F2 coincide, and the focal lengths f, f´ are infinite. Such a system
is called a telescopic system, and this condition is realized in a
telescope focused for a normal eye.
So far we have assumed that all the rays proceeding from an
object-point are exactly united in an image-point after transmission
through the ideal system. The question now arises as to how far this
assumption is justified for spherical lenses. To investigate this it
is simplest to trace the path of a ray through one spherical
refracting surface. Let such a surface divide media of refractive
indices n and n´, the former being to the left. The point where the
axis intersects the surface is the vertex S (fig. 7). Denote the
distance of the axial object-point O from S by s; the distance from O
to the point of incidence P by p; the radius of the spherical surface
by r; and the distance OC by c, C being the centre of the sphere. Let
u be the angle made by the ray with the axis, and i the angle of
incidence, i.e. the angle between the ray and the normal to the sphere
at the point of incidence. The corresponding quantities in the
image-space are denoted by the same letters with a dash. From the
triangle O´PC we have sin u = (r/c) sin i, and from the triangle O´PC
we have sin u´ = (r/c´) sin i´. By Snell's law we have n´/n = sin
i/sin i´, and also [phi] = u´ + i´. Consequently c´ and the position
of the image may be found.
[Illustration: FIG. 7.]
To determine whether all the rays proceeding from O are refracted
through O´, we investigate the triangle OPO´. We have p/p´ = sin
u´/sin u. Substituting for sin u and sin u´ the values found above, we
obtain p´/p = c´ sin i/c sin i´ = n´c´/nc. Also c = OC = CS + SO = -SC
+ SO = s - r, and similarly c´ = s´ - r. Substituting these values we
obtain
p´ n´(s´ - r) n(s - r) n´(s´ - r)
-- = ----------, or -------- = ----------. (6)
p n(s - r) p p´
To obtain p and p´ we use the triangles OPC and O´PC; we have p² = (s
- r)² + r² + 2r(s - r) cos [phi], p´² = (s´ - r)² + r² + 2r(s´ - r)
cos [phi]. Hence if s, r, n and n´ be constant, s´ must vary as [phi]
varies. The refracted rays therefore do not reunite in a point, and
the deflection is termed the spherical aberration (see ABERRATION).
Developing cos [phi] in powers of [phi], we obtain
/ [phi]² [phi]^4 [phi]^6 \
p² = (s - r)² + r² + 2r(s - r) ( 1 - ------ + ------- - ------- + ...),
\ 2! 4! 6! /
and therefore for such values of [phi] for which the second and higher
powers may be neglected, we have p² = (s - r)² + r² + 2r(s - r), i.e.
p = s, and similarly p´ = s´. Equation (6) then becomes n(s - r)/s =
n´(s´ - r)/s´ or
n´ n n´- n
-- = -- + -----. (7)
s´ s r
This relation shows that in a very small central aperture in which the
equation p = s holds, all rays proceeding from an object-point are
exactly united in an image-point, and therefore the equations
previously deduced are valid for this aperture. K. F. Gauss derived
the equations for thin pencils in his _Dioptrische Untersuchungen_
(1840) by very elegant methods. More recently the laws relating to
systems with finite aperture have been approximately realized, as for
example, in well-corrected photographic objectives.
_Position of the Cardinal Points of a Lens._--Taking the case of a
single spherical refracting surface, and limiting ourselves to the
small central aperture, it is seen that the second principal focus F´
is obtained when s is infinitely great. Consequently s´ = -f´; the
difference of sign is obvious, since s´ is measured from S, while f´
is measured from F´. The focal lengths are directly deducible from
equation (7):--
f´ = -n´r/(n´ - n) (8)
f = nr/(n´ - n). (9)
By joining this simple refracting system with a similar one, so that
the second spherical surface limits the medium of refractive index n´,
we derive the spherical lens. Generally the two spherical surfaces
enclose a glass lens, and are bounded on the outside by air of
refractive index 1.
The deduction of the cardinal points of a spherical glass lens in air
from the relations already proved is readily effected if we regard the
lens as a combination of two systems each having one refracting
surface, the light passing in the first system from air to glass, and
in the second from glass to air. If we know the refractive index of
the glass n, the radii r1, r2 of the spherical surfaces, and the
distances of the two lens-vertices (or the thickness of the lens d) we
can determine all the properties of the lens. A biconvex lens is shown
in fig. 8. Let F1 be the first principal focus of the first system of
radius r1, and F1´ the second principal focus; and let S1 be its
vertex. Denote the distance F1 S1 (the first principal focal length)
by f1, and the corresponding distance F´1 S1 by f´1. Let the
corresponding quantities in the second system be denoted by the same
letters with the suffix 2.
By equations (8) and (9) we have
r1 nr1 nr2 r2
f1 = -----, f´1 = - -----, f2 = - -----, f´2 = -----,
n - 1 n - 1 n - 1 n - 1
f2 having the opposite sign to f1. Denoting the distance F´1F2 by
[Delta], we have [Delta] = F´1F2 = F´1S1 + S1S2 + S2F2 = F´1S1 + S1S2
- F2S2 = f´1 + d - f2.
Substituting for f´1 and f2 we obtain
nr1 nr2
[Delta] = ----- + d + -----.
n - 1 n - 1
Writing R = [Delta](n - 1), this relation becomes
R = n(r2 - r1) + d(n - 1).
We have already shown that f (the first principal focal length of a
compound system) = -f1f2/[Delta]. Substituting for f1, f2 and [Delta]
the values found above, we obtain
r1r2n r1r2n
f = --------- = ------------------------------, (10)
(n - 1)R} (n - 1){n(r2 - r1) + d(n - 1)}
which is equivalent to
1 /1 1 \ (n-1)²d
-- = (n - 1)( -- - -- ) + -------.
f \r1 r2/ r1r2n
If the lens be infinitely thin, i.e. if d be zero, we have for the
first principal focal length.
1 /1 1 \
-- = (n - 1)( -- - -- ).
f \r1 r2/
By the same method we obtain for the second principal focal length
f´1f´2 nr1r2
f´ = ------- = - --------- = -f.
[Delta] (n - 1)R
[Illustration: FIG. 8.]
The reciprocal of the focal length is termed the _power_ of the lens
and is denoted by [phi]. In formulae involving [phi] it is customary
to denote the reciprocal of the radii by the symbol [rho]; we thus
have [phi] = 1/f, [rho] = 1/r. Equation (10) thus becomes
(n - 1)²d[rho]1[rho]2
[phi] = (n - 1)([rho]1 - [rho]2) + ---------------------.
n
The unit of power employed by spectacle-makers is termed the _diopter_
or _dioptric_ (see SPECTACLES).
We proceed to determine the distances of the focal points from the
vertices of the lens, i.e. the distances FS1 and F´S2. Since F is
represented by the first system in F2, we have by equation (2)
f1f´1 f1f´1 nr1²
x1 = ----- = ------- = --------,
x´1 [Delta] (n - 1)R
where x1 = F1F, and x´1 = F´1F2 = [Delta]. The distance of the first
principal focus from the vertex S, i.e. S1F, which we denote by s_F
is given by s_F = S1F = S1F1 + F1F = -F1S1 + F1F. Now F1S1 is the
distance from the vertex of the first principal focus of the first
system, i.e. f1 and F1F = x1. Substituting these values, we obtain
r1 nr1² r1(nr1 + R)
s_F = - ----- - -------- = -----------.
n - 1 (n - 1)R (n - 1)R
The distance F´2F´ or x´2 is similarly determined by considering F´1
to be represented by the second system in F´.
We have
f2f´2 f2f´2 nr2²
x´2 = ----- = ------- = --------,
x2 [Delta] (n - 1)R
so that
r2(nr2 - R)
s_F´ = x´2 - f´2 = -----------,
(n - 1)R
where s_F´ denotes the distance of the second principal focus from
the vertex S2.
The two focal lengths and the distances of the foci from the vertices
being known, the positions of the remaining cardinal points, i.e. the
principal points H and H´, are readily determined. Let s_H = S1H, i.e.
the distance of the object-side principal point from the vertex of the
first surface, and s_H´ = S2H´, i.e. the distance of the image-side
principal point from the vertex of the second surface, then f = FH =
FS1 + S1H = -S1F + S1H = -s_F + s_H; hence s_H = s_F + f = -dr1/R.
Similarly s_H´ = s_F´ + f´ = -dr2/R. It is readily seen that the
distances s_H and s_H´ are in the ratio of the radii r1 and r2.
The distance between the two principal planes (the interstitium) is
deduced very simply. We have S1S2 = S1H + HH´ + H´S2, or HH´ = S1S2 -
S1H + S2H´. Substituting, we have
HH´ = d - s_H + s_H´ = d(n - 1)(r2 - r1 + d)/R.
The interstitium becomes zero, or the two principal planes coincide,
if d = r1 - r2.
We have now derived all the properties of the lens in terms of its
elements, viz. the refractive index, the radii of the surfaces, and
the thickness.
_Forms of Lenses._--By varying the signs and relative magnitude of the
radii, lenses may be divided into two groups according to their
action, and into four groups according to their form.
According to their action, lenses are either collecting, convergent
and condensing, or divergent and dispersing; the term positive is
sometimes applied to the former, and the term negative to the latter.
Convergent lenses transform a parallel pencil into a converging one,
and increase the convergence, and diminish the divergence of any
pencil. Divergent lenses, on the other hand, transform a parallel
pencil into a diverging one, and diminish the convergence, and
increase the divergence of any pencil. In convergent lenses the first
principal focal distance is positive and the second principal focal
distance negative; in divergent lenses the converse holds.
The four forms of lenses are interpretable by means of equation (10).
r1r2n
f = -------------------------------.
(n - 1) {n(r2 - r1) + d(n - 1)}
[Illustration: FIG. 9.]
(1) If r1 be positive and r2 negative. This type is called biconvex
(fig. 9, 1). The first principal focus is in front of the lens, and
the second principal focus behind the lens, and the two principal
points are inside the lens. The order of the cardinal points is
therefore FS1HH´S2F´. The lens is convergent so long as the thickness
is less than n(r1 - r2)/(n - 1). The special case when one of the
radii is infinite, in other words, when one of the bounding surfaces
is plane is shown in fig. 9, 2. Such a collective lens is termed
_plano-convex_. As d increases, F and H move to the right and F´ and
H´ to the left. If d = n(r1 - r2)/(n - 1), the focal length is
infinite, i.e. the lens is telescopic. If the thickness be greater
than n(r1 - r2)/(n - 1), the lens is dispersive, and the order of the
cardinal points is HFS1S2F´H´.
(2) If r1 is negative and r2 positive. This type is called _biconcave_
(fig. 9, 4). Such lenses are dispersive for all thicknesses. If d
increases, the radii remaining constant, the focal lengths diminish.
It is seen from the equations giving the distances of the cardinal
points from the vertices that the first principal focus F is always
behind S1, and the second principal focus F´ always in front of S2,
and that the principal points are within the lens, H´ always following
H. If one of the radii becomes infinite, the lens is _plano-concave_
(fig. 9, 5).
(3) If the radii are both positive. These lenses are called
_convexo-concave_. Two cases occur according as r2 > r1, or < r1. (a)
If r2 > r1, we obtain the _mensicus_ (fig. 9, 3). Such lenses are
always collective; and the order of the cardinal points is FHH´F´.
Since s_F and s_H are always negative, the object-side cardinal
points are always in front of the lens. H´ can take up different
positions. Since s_H´ = -dr2/R = -dr2/{n(r2 - r1) + d(n - 1)}, s_H´
is greater or less than d, i.e. H´ is either in front of or inside the
lens, according as d < or > {r2 - n(r2 - r1)}/(n - 1). (b) If r2 < r1 the
lens is dispersive so long as d < n(r1 - r2)/(n-1). H is always behind
S1 and H´ behind S2, since s_H and s_H´ are always positive. The
focus F is always behind S1 and F´ in front of S2. If the thickness be
small, the order of the cardinal points is F´HH´F; a dispersive lens
of this type is shown in fig. 9, 6. As the thickness increases, H, H´
and F move to the right, F more rapidly than H, and H more rapidly
than H´; F´, on the other hand, moves to the left. As with biconvex
lenses, a telescopic lens, having all the cardinal points at infinity,
results when d = n(r1 - r2)/(n - 1). If d > n(r1 - r2)/(n - 1), f is
positive and the lens is collective. The cardinal points are in the
same order as in the mensicus, viz. FHH´F´; and the relation of the
principal points to the vertices is also the same as in the mensicus.
(4) If r1 and r2 are both negative. This case is reduced to (3) above,
by assuming a change in the direction of the light, or, in other
words, by interchanging the object- and image-spaces.
The six forms shown in fig. 9 are all used in optical constructions.
It may be stated fairly generally that lenses which are thicker at the
middle are collective, while those which are thinnest at the middle
are dispersive.
[Illustration: FIG. 10.]
_Different Positions of Object and Image._--The principal points are
always near the surfaces limiting the lens, and consequently the lens
divides the direct pencil containing the axis into two parts. The
object can be either in front of or behind the lens as in fig. 10. If
the object point be in front of the lens, and if it be realized by
rays passing from it, it is called _real_. If, on the other hand, the
object be behind the lens, it is called _virtual_; it does not
actually exist, and can only be realized as an image.
[Illustration: FIG. 11.]
When we speak of "object-points," it is always understood that the
rays from the object traverse the first surface of the lens before
meeting the second. In the same way, images may be either real or
virtual. If the image be behind the second surface, it is _real_, and
can be intercepted on a screen. If, however, it be in front of the
lens, it is visible to an eye placed behind the lens, although the
rays do not actually intersect, but only appear to do so, but the
image cannot be intercepted on a screen behind the lens. Such an image
is said to be _virtual_. These relations are shown in fig. 11.
[Illustration: FIG. 12.]
By referring to the equations given above, it is seen that a thin
convergent lens produces both real and virtual images of real objects,
but only a real image of a virtual object, whilst a divergent lens
produces a virtual image of a real object and both real and virtual
images of a virtual object. The construction of a real image of a real
object by a convergent lens is shown in fig. 3; and that of a virtual
image of a real object by a divergent lens in fig. 12.
[Illustration: FIG. 13.]
_The optical centre of a lens_ is a point such that, for any ray which
passes through it, the incident and emergent rays are parallel. The
idea of the optical centre was originally due to J. Harris (_Treatise
on Optics_, 1775); it is not properly a cardinal point, although it
has several interesting properties. In fig. 13, let C1P1 and C2P2 be
two parallel radii of a biconvex lens. Join P1P2 and let O1P1 and O2P2
be incident and emergent rays which have P1P2 for the path through the
lens. Then if M be the intersection of P1P2 with the axis, we have
angle C1P1M = angle C2P2M; these two angles are--for a ray travelling
in the direction O1P1P2O2--the angles of emergence and of incidence
respectively. From the similar triangles C2P2M and C1P1M we have
C1M : C2M = C1P1 : C2P2 = r1 : r2. (11)
Such rays as P1P2 therefore divide the distance C1C2 in the ratio of
the radii, i.e. at the fixed point M, the optical centre. Calling S1M
= s1, S2M = s2, then C1S1 = C1M + MS1 = C1M - S1M, i.e. since C1S1 =
r1, C1M = r1 + s1, and similarly C2M = r2 + s2. Also S1S2 = S1M + MS2
= S1M - S2M, i.e. d = s1 - s2. Then by using equation (11) we have s1
= r1d/(r - r2) and s2 = r2d/(r1 - r2), and hence s1/s2 = r1/r2. The
vertex distances of the optical centre are therefore in the ratio of
the radii.
The values of s1 and s2 show that the optical centre of a biconvex or
biconcave lens is in the interior of the lens, that in a plano-convex
or plano-concave lens it is at the vertex of the curved surface, and
in a concavo-convex lens outside the lens.
_The Wave-theory Derivation of the Focal Length._--The formulae above
have been derived by means of geometrical rays. We here give an
account of Lord Rayleigh's wave-theory derivation of the focal length
of a convex lens in terms of the aperture, thickness and refractive
index (_Phil. Mag._ 1879 (5) 8, p. 480; 1885, 20, p. 354); the
argument is based on the principle that the optical distance from
object to image is constant.
[Illustration: FIG. 14.]
"Taking the case of a convex lens of glass, let us suppose that
parallel rays DA, EC, GB (fig. 14) fall upon the lens ACB, and are
collected by it to a focus at F. The points D, E, G, equally distant
from ACB, lie upon a front of the wave before it impinges upon the
lens. The focus is a point at which the different parts of the wave
arrive at the same time, and that such a point can exist depends upon
the fact that the propagation is slower in glass than in air. The ray
ECF is retarded from having to pass through the thickness (d) of glass
by the amount (n - 1)d. The ray DAF, which traverses only the extreme
edge of the lens, is retarded merely on account of the crookedness of
its path, and the amount of the retardation is measured by AF - CF. If
F is a focus these retardations must be equal, or AF - CF = (n - 1)d.
Now if y be the semi-aperture AC of the lens, and f be the focal
length CF, AF - CF = [root](f² + y²) - f = ½y²/f approximately, whence
f = ½y²/(n - 1)d. (12)
In the case of plate-glass (n - 1) = ½ (nearly), and then the rule
(12) may be thus stated: _the semi-aperture is a mean proportional
between the focal length and the thickness_. The form (12) is in
general the more significant, as well as the more practically useful,
but we may, of course, express the thickness in terms of the
curvatures and semi-aperture by means of d = ½y²[r1^(-1) - r2^(-1)].
In the preceding statement it has been supposed for simplicity that
the lens comes to a sharp edge. If this be not the case we must take
as the thickness of the lens the difference of the thicknesses at the
centre and at the circumference. In this form the statement is
applicable to concave lenses, and we see that the focal length is
positive when the lens is thickest at the centre, but negative when
the lens is thickest at the edge."
_Regulation of the Rays._
The geometrical theory of optical instruments can be conveniently
divided into four parts: (1) The relations of the positions and sizes of
objects and their images (see above); (2) the different aberrations from
an ideal image (see ABERRATION); (3) the intensity of radiation in the
object- and image-spaces, in other words, the alteration of brightness
caused by physical or geometrical influences; and (4) the regulation of
the rays (_Strahlenbegrenzung_).
[Illustration: FIG. 15.]
The regulation of rays will here be treated only in systems free from
aberration. E. Abbe first gave a connected theory; and M. von Rohr has
done a great deal towards the elaboration. The Gauss cardinal points
make it simple to construct the image of a given object. No account is
taken of the size of the system, or whether the rays used for the
construction really assist in the reproduction of the image or not.
The diverging cones of rays coming from the object-points can only
take a certain small part in the production of the image in
consequence of the apertures of the lenses, or of diaphragms. It often
happens that the rays used for the construction of the image do not
pass through the system; the image being formed by quite different
rays. If we take a luminous point of the object lying on the axis of
the system then an eye introduced at the image-point sees in the
instrument several concentric rings, which are either the fittings of
the lenses or their images, or the real diaphragms or their images.
The innermost and smallest ring is completely lighted, and forms the
origin of the cone of rays entering the image-space. Abbe called it
the _exit pupil_. Similarly there is a corresponding smallest ring in
the object-space which limits the entering cone of rays. This is
called the _entrance pupil_. The real diaphragm acting as a limit at
any part of the system is called the _aperture-diaphragm_. These
diaphragms remain for all practical purposes the same for all points
lying on the axis. It sometimes happens that one and the same
diaphragm fulfils the functions of the entrance pupil and the
aperture-diaphragm or the exit pupil and the aperture-diaphragm.
Fig. 15 shows the general but simplified case of the different
diaphragms which are of importance for the regulation of the rays. S1,
S2 are two centred systems. A´ is a real diaphragm lying between them.
B1 and B´2 are the fittings of the systems. Then S1 produces the
virtual image A of the diaphragm A´ and the image B2 of the fitting
B´2, whilst the system S2 makes the virtual image A´´ of the diaphragm
A´ and the virtual image B´1 of the fitting B1. The object-point O is
reproduced really through the whole system in the point O´. From the
object-point O three diaphragms can be seen in the object-space, viz.
the fitting B1, the image of the fitting B2 and the image A of the
diaphragm A´ formed by the system S1. The cone of rays nearest to B2
is not received to its total extent by the fitting B1, and the cone
which has entered through B1 is again diminished in its further
course, when passing through the diaphragm A´, so that the cone of
rays really used for producing the image is limited by A, the
diaphragm which seen from O appears to be the smallest. A is therefore
the entrance pupil. The real diaphragm A´ which limits the rays in the
centre of the system is the aperture diaphragm. Similarly three
diaphragms lying in the image-space are to be seen from the
image-point O´--namely B´, A´´, and B´2. A´´ limits the rays in the
image-space, and is therefore the exit pupil. As A is conjugate to the
diaphragm A´ in the system S1, and A´´ to the same diaphragm A´ in the
system S2, the entrance pupil A is conjugate to the exit pupil A´´
throughout the instrument. This relation between entrance and exit
pupils is general.
The apices of the cones of rays producing the image of points near the
axis thus lie in the object-points, and their common base is the
entrance pupil. The axis of such a cone, which connects the object
point with the centre of the entrance pupil, is called the _principal
ray_. Similarly, the principal rays in the image-space join the centre
of the exit pupil with the image-points. The centres of the entrance
and exit pupils are thus the intersections of the principal rays.
[Illustration: FIG. 16.]
[Illustration: FIG. 17a.]
[Illustration: FIG. 17b.]
For points lying farther from the axis, the entrance pupil no longer
alone limits the rays, the other diaphragms taking part. In fig. 16
only one diaphragm L is present besides the entrance pupil A, and the
object-space is divided to a certain extent into four parts. The
section M contains all points rendered by a system with a complete
aperture; N contains all points rendered by a system with a gradually
diminishing aperture; but this diminution does not attain the
principal ray passing through the centre C. In the section O are those
points rendered by a system with an aperture which gradually decreases
to zero. No rays pass from the points of the section P through the
system and no image can arise from them. The second diaphragm L
therefore limits the three-dimensional object-space containing the
points which can be rendered by the optical system. From C through
this diaphragm L this three-dimensional object-space can be seen as
through a window. L is called by M von Rohr the _entrance luke_. If
several diaphragms can be seen from C, then the entrance _luke_ is the
diaphragm which seen from C appears the smallest. In the sections N
and O the entrance _luke_ also takes part in limiting the cones of
rays. This restriction is known as the "vignetting" action of the
entrance _luke_. The base of the cone of rays for the points of this
section of the object-space is no longer a circle but a two-cornered
curve which arises from the object-point by the projection of the
entrance _luke_ on the entrance pupil. Fig. 17a shows the base of such
a cone of rays. It often happens that besides the entrance _luke_,
another diaphragm acts in a vignetting manner, then the operating
aperture of the cone of rays is a curve made up of circular arcs
formed out of the entrance pupil and the two projections of the two
acting diaphragms (fig. 17b).
If the entrance pupil is narrow, then the section NO, in which the
vignetting is increasing, is diminished, and there is really only one
division of the section M which can be reproduced, and of the section
P which cannot be reproduced. The angle w + w = 2w, comprising the
section which can be reproduced, is called the angle of the field of
view on the object-side. The field of view 2w retains its importance
if the entrance pupil is increased. It then comprises all points
reached by principal rays. The same relations apply to the
image-space, in which there is an exit _luke_, which, seen from the
middle of the exit pupil, appears under the smallest angle. It is the
image of the entrance _luke_ produced by the whole system. The
image-side field of view 2w´ is the angle comprised by the principal
rays reaching the edge of the exit _luke_.
[Illustration: FIG. 18.]
Most optical instruments are used to observe object-reliefs
(three-dimensional objects), and generally an image-relief (a
three-dimensional image) is conjugate to this object-relief. It is
sometimes required, however, to represent by means of an optical
instrument the object-relief on a plane or on a ground-glass as in the
photographic camera. For simplicity we shall assume the intercepting
plane as perpendicular to the axis and shall call it, after von Rohr,
the "ground glass plane." All points of the image not lying in this
plane produce circular spots (corresponding to the form of the pupils)
on it, which are called "circles of confusion." The ground-glass plane
(fig. 18) is conjugate to the object-plane E in the object-space,
perpendicular to the axis, and called the "plane focused for." All
points lying in this plane are reproduced exactly on the ground-glass
plane as the points OO. The circle of confusion Z on the plane focused
for corresponds to the circle of confusion Z´ on the ground-glass
plane. The figure formed on the plane focused for by the cones of rays
from all of the object-points of the total object-space directed to
the entrance pupil, was called "object-side representation" (_imago_)
by M von Rohr. This representation is a central projection. If, for
instance, the entrance pupil is imagined so small that only the
principal rays pass through, then they project directly, and the
intersections of the principal rays represent the projections of the
points of the object lying off the plane focused for. The centre of
the projection or the perspective centre is the middle point of the
entrance pupil C. If the entrance pupil is opened, in place of points,
circles of confusion appear, whose size depends upon the size of the
entrance pupil and the position of the object-points and the plane
focused for. The intersection of the principal ray is the centre of
the circle of confusion. The clearness of the representation on the
plane focused for is of course diminished by the circles of confusion.
This central projection does not at all depend upon the instrument,
but is entirely geometrical, arising when the position and the size of
the entrance pupil, and the position of the plane focused for have
been fixed. The instrument then produces an image on the ground-glass
plane of this perspective representation on the plane focused for, and
on account of the exact likeness which this image has to the
object-side representation it is called the "representation copy." By
moving it round an angle of 180°, this representation can be brought
into a perspective position to the objects, so that all rays coming
from the middle of the entrance pupil and aiming at the object-points,
would always meet the corresponding image-points. This representation
is accessible to the observer in different ways in different
instruments. If the observer desires a perfectly correct perspective
impression of the object-relief the distance of the pivot of the eye
from the representation copy must be equal to the nth part of the
distance of the plane focused for from the entrance pupil, if the
instrument has produced a nth diminution of the object-side
representation. The pivot of the eye must coincide with the centre of
the perspective, because all images are observed in direct vision. It
is known that the pivot of the eye is the point of intersection of all
the directions in which one can look. Thus all these points
represented by circles of confusion which are less than the angular
sharpness of vision appear clear to the eye; the space containing all
these object-points, which appear clear to the eye, is called the
_depth_. The depth of definition, therefore, is not a special property
of the instrument, but depends on the size of the entrance pupil, the
position of the plane focused for and on the conditions under which
the representation can be observed.
If the distance of the representation from the pivot of the eye be
altered from the correct distance already mentioned, the angles of
vision under which various objects appear are changed; perspective
errors arise, causing an incorrect idea to be given of the depth. A
simple case is shown in fig. 19. A cube is the object, and if it is
observed as in fig. 19a with the representation copy at the correct
distance, a correct idea of a cube will be obtained. If, as in figs.
19b and 19c, the distance is too great, there can be two results. If
it is known that the farthest section is just as high as the nearer
one then the cube appears exceptionally deepened, like a long
parallelepipedon. But if it is known to be as deep as it is high then
the eye will see it low at the back and high at the front. The reverse
occurs when the distance of observation is too short, the body then
appears either too flat, or the nearer sections seem too low in
relation to those farther off. These perspective errors can be seen in
any telescope. In the telescope ocular the representation copy has to
be observed under too large an angle or at too short a distance: all
objects therefore appear flattened, or the more distant objects appear
too large in comparison with those nearer at hand.
[Illustration: FIG. 19. After von Rohr.]
[Illustration: FIG. 20. After von Rohr.]
[Illustration: FIG. 21. After von Rohr.]
[Illustration: FIG. 22. After von Rohr.]
From the above the importance of experience will be inferred. But it
is not only necessary that the objects themselves be known to the
observer but also that they are presented to his eye in the customary
manner. This depends upon the way in which the principal rays pass
through the system--in other words, upon the special kind of
"transmission" of the principal rays. In ordinary vision the pivot of
the eye is the centre of the perspective representation which arises
on the very distant plane standing perpendicular to the mean direction
of sight. In this kind of central projection all objects lying in
front of the plane focused for are diminished when projected on this
plane, and those lying behind it are magnified. (The distances are
always given in the direction of light.) Thus the objects near to the
eye appear large and those farther from it appear small. This
perspective has been called by M von Rohr[1] "entocentric
transmission" (fig. 20). If the entrance pupil of the instrument lies
at infinity, then all the principal rays are parallel and the
projections of all objects on the plane focused for are exactly as
large as the objects themselves. After E. Abbe, this course of rays is
called "telecentric transmission" (fig. 21). The exit pupil then lies
in the image-side focus of the system. If the perspective centre lies
in front of the plane focused for, then the objects lying in front of
this plane are magnified and those behind it are diminished. This is
just the reverse of perspective representation in ordinary sight, so
that the relations of size and the arrangements for space must be
quite incorrectly indicated (fig. 22); this representation is called
by M von Rohr a "hypercentric transmission." (O. Hr.)
FOOTNOTE:
[1] M von Rohr, _Zeitschr. für Sinnesphysiologie_ (1907), xli. 408-429.
LENT (O. Eng. _lencten_, "spring," M. Eng. _lenten_, _lente_, _lent_;
cf. Dut. _lente_, Ger. _Lenz_, "spring," O. H. Ger. _lenzin_,
_lengizin_, _lenzo_, probably from the same root as "long" and referring
to "the lengthening days"), in the Christian Church, the period of
fasting preparatory to the festival of Easter. As this fast falls in the
early part of the year, it became confused with the season, and
gradually the word Lent, which originally meant spring, was confined to
this use. The Latin name for the fast, _Quadragesima_ (whence Ital.
_quaresima_, Span. _cuaresma_ and Fr. _carême_), and its Gr. equivalent
[Greek: tessarakostê] (now superseded by the term [Greek: hê nêsteia]
"the fast"), are derived from the Sunday which was the fortieth day
before Easter, as _Quinquagesima_ and _Sexagesima_ are the fiftieth and
sixtieth, Quadragesima being until the 7th century the _caput jejunii_
or first day of the fast.
The length of this fast and the rigour with which it has been observed
have varied greatly at different times and in different countries (see
FASTING). In the time of Irenaeus the fast before Easter was very short,
but very severe; thus some ate nothing for forty hours between the
afternoon of Good Friday and the morning of Easter. This was the only
authoritatively prescribed fast known to Tertullian (_De jejunio_, 2,
13, 14; _De oratione_, 18). In Alexandria about the middle of the 3rd
century it was already customary to fast during Holy Week; and earlier
still the Montanists boasted that they observed a two weeks' fast
instead of one. Of the Lenten fast or Quadragesima, the first mention is
in the fifth canon of the council of Nicaea (325), and from this time it
is frequently referred to, but chiefly as a season of preparation for
baptism, of absolution of penitents or of retreat and recollection. In
this season fasting played a part, but it was not universally nor
rigorously enforced. At Rome, for instance, the whole period of fasting
was but three weeks, according to the historian Socrates (_Hist. eccl._
v. 22), these three weeks, in Mgr. Duchesne's opinion, being not
continuous but, following the primitive Roman custom, broken by
intervals. Gradually, however, the fast as observed in East and West
became more rigorously defined. In the East, where after the example of
the Church of Antioch the Quadragesima fast had been kept distinct from
that of Holy Week, the whole fast came to last for seven weeks, both
Saturdays and Sundays (except Holy Saturday) being, however, excluded.
In Rome and Alexandria, and even in Jerusalem, Holy Week was included in
Lent and the whole fast lasted but six weeks, Saturdays, however, not
being exempt. Both at Rome and Constantinople, therefore, the actual
fast was but thirty-six days. Some Churches still continued the three
weeks' fast, but by the middle of the 5th century most of these
divergences had ceased and the usages of Antioch-Constantinople and
Rome-Alexandria had become stereotyped in their respective spheres of
influence.
The thirty-six days, as forming a tenth part of the year and therefore a
perfect number, at first found a wide acceptance (so Cassianus, _Coll._
xxi. 30); but the inconsistency of this period with the name
Quadragesima, and with the forty days' fast of Christ, came to be noted,
and early in the 7th century four days were added, by what pope is
unknown, Lent in the West beginning henceforth on Ash Wednesday (q.v.).
About the same time the cycle of paschal solemnities was extended to the
ninth week before Easter by the institution of stational masses for
Septuagesima, Sexagesima and Quinquagesima Sundays. At Constantinople,
too, three Sundays were added and associated with the Easter festival in
the same way as the Sundays in Lent proper. These three Sundays were
added in the Greek Church also, and the present custom of keeping an
eight weeks' fast (i.e. exactly 8×5 days), now universal in the Eastern
Church, originated in the 7th century. The Greek Lent begins on the
Monday of Sexagesima, with a week of preparatory fasting, known as
[Greek: turophagia], or the "butter-week"; the actual fast, however,
starts on the Monday of Quinquagesima (Estomihi), this week being known
as "the first week of the fast" ([Greek: hebdomas tôn nêsteiôn]). The
period of Lent is still described as "the six weeks of the fast"
([Greek: hex hebdomades tôn nêsteiôn]), Holy Week ([Greek: hê hagia kai
megalê hebdomas]) not being reckoned in. The Lenten fast was retained at
the Reformation in some of the reformed Churches, and is still observed
in the Anglican and Lutheran communions. In England a Lenten fast was
first ordered to be observed by Earconberht, king of Kent (640-664). In
the middle ages, meat, eggs and milk were forbidden in Lent not only by
ecclesiastical but by statute law; and this rule was enforced until the
reign of william III. The chief Lenten food from the earliest days was
fish, and entries in the royal household accounts of Edward III. show
the amount of fish supplied to the king. Herring-pies were a great
delicacy. Charters granted to seaports often stipulated that the town
should send so many herrings or other fish to the king annually during
Lent. How severely strict medieval abstinence was may be gauged from the
fact that armies and garrisons were sometimes, in default of
dispensations, as in the case of the siege of Orleans in 1429, reduced
to starvation for want of Lenten food, though in full possession of meat
and other supplies. The battle of the Herrings (February 1429) was
fought in order to cover the march of a convoy of Lenten food to the
English army besieging Orleans. Dispensations from fasting were,
however, given in case of illness.
During the religious confusion of the Reformation, the practice of
fasting was generally relaxed and it was found necessary to reassert the
obligation of keeping Lent and the other periods and days of abstinence
by a series of proclamations and statutes. In these, however, the
religious was avowedly subordinate to a political motive, viz. to
prevent the ruin of the fisheries, which were the great nursery of
English seamen. Thus the statute of 2 and 3 Edward VI., cap. 9 (1549),
while inculcating that "due and godly abstinence from flesh is a means
to virtue," adds that "by the eating of fish much flesh is saved to the
country," and that thereby, too, the fishing trade is encouraged. The
statute, however, would not seem to have had much effect; for in spite
of a proclamation of Queen Elizabeth in 1560 imposing a fine of £20 for
each offence on butchers slaughtering animals during Lent, in 1563 Sir
William Cecil, in _Notes upon an Act for the Increase of the Navy_, says
that "in old times no flesh at all was eaten on fish days; even the king
himself could not have license; which was occasion of eating so much
fish as now is eaten in flesh upon fish days." The revolt against fish
had ruined the fisheries and driven the fishermen to turn pirates, to
the great scandal and detriment of the realm. Accordingly, in the
session of 1562-1563, Cecil forced upon an unwilling parliament "a
politic ordinance on fish eating," by which the eating of flesh on fast
days was made punishable by a fine of three pounds or three months'
imprisonment, one meat dish being allowed on Wednesdays on condition
that three fish dishes were present on the table. The kind of argument
by which Cecil overcame the Protestant temper of the parliament is
illustrated by a clause which he had meditated adding to the statute, a
draft of which in his own handwriting is preserved: "Because no person
should misjudge the intent of the statute," it runs, "which is politicly
meant only for the increase of fishermen and mariners, and not for any
superstition for choice of meats; whoever shall preach or teach that
eating of fish or forbearing of flesh is for the saving of the soul of
man, or for the service of God, shall be punished as the spreader of
false news" (Dom. MSS., Elizabeth, vol. xxvii.). But in spite of
statutes and proclamations, of occasional severities and of the
patriotic example of Queen Elizabeth, the practice of fasting fell more
and more into disuse. Ostentatious avoidance of a fish-diet became,
indeed, one of the outward symbols of militant Protestantism among the
Puritans. "I have often noted," writes John Taylor, the water-poet, in
his _Jack a Lent_ (1620), "that if any superfluous feasting or
gormandizing, paunch-cramming assembly do meet, it is so ordered that it
must be either in Lent, upon a Friday, or a fasting: for the meat does
not relish well except it be sauced with disobedience and comtempt of
authority." The government continued to struggle against this spirit of
defiance; proclamations of James I. in 1619 and 1625, and of Charles I.
in 1627 and 1631, again commanded abstinence from all flesh during Lent,
and the High Church movement of the 17th century lent a fresh religious
sanction to the official attitude. So late as 1687, James II. issued a
proclamation ordering abstention from meat; but, after the Revolution,
the Lenten laws fell obsolete, though they remained on the statute-book
till repealed by the Statute Law Revision Act 1863. But during the 18th
century, though the strict observance of the Lenten fast was generally
abandoned, it was still observed and inculcated by the more earnest of
the clergy, such as William Law and John Wesley; and the custom of women
wearing mourning in Lent, which had been followed by Queen Elizabeth and
her court, survived until well into the 19th century. With the growth of
the Oxford Movement in the English Church, the practice of observing
Lent was revived; and, though no rules for fasting are authoritatively
laid down, the duty of abstinence is now very generally inculcated by
bishops and clergy, either as a discipline or as an exercise in
self-denial. For the more "advanced" Churches, Lenten practice tends to
conform to that of the pre-Reformation Church.
Mid-Lent, or the fourth Sunday in Lent, was long known as _Mothering
Sunday_, in allusion to the custom for girls in service to be allowed a
holiday on that day to visit their parents. They usually took as a
present for their mother a small cake known as a _simnel_. In shape it
resembled a pork-pie but in materials it was a rich plum-pudding. The
word is derived through M. Lat. _simenellus_, _simella_, from Lat.
_simila_, wheat flour. In Gloucestershire simnel cakes are still
common; and at Usk, Monmouth, the custom of mothering is still
scrupulously observed.
LENTHALL, WILLIAM (1591-1662), English parliamentarian, speaker of the
House of Commons, second son of William Lenthall, of Lachford,
Oxfordshire, a descendent of an old Herefordshire family, was born at
Henley-on-Thames in June 1591. He left Oxford without taking a degree in
1609, and was called to the bar at Lincoln's Inn in 1616, becoming a
bencher in 1633. He represented Woodstock in the Short Parliament (April
1640), and was chosen by King Charles I. to be speaker of the Long
Parliament, which met on the 3rd of November 1640. According to
Clarendon, a worse choice could not have been made, for Lenthall was of
a "very timorous nature." He was treated with scanty respect in the
chair, and seems to have had little control over the proceedings. On the
4th of January 1642, however, when the king entered the House of Commons
to seize the five members, Lenthall behaved with great prudence and
dignity. Having taken the speaker's chair and looked round in vain to
discover the offending members, Charles turned to Lenthall standing
below, and demanded of him "whether any of those persons were in the
House, whether he saw any of them and where they were." Lenthall fell on
his knees and replied: "May it please your Majesty, I have neither eyes
to see nor tongue to speak in this place but as the House is pleased to
direct me, whose servant I am here." On the outbreak of the great
rebellion, Lenthall threw in his lot with the parliament. He had already
called attention to the inadequacy of his salary and been granted a sum
of £6000 (9th of April 1642); and he was now appointed master of the
rolls (22nd of November 1643), and one of the commissioners of the great
seal (Oct. 1646-March 1648).
He carried on his duties as speaker without interruption till 1647, when
the power of the parliament had been transferred to the army. On the
26th of July a mob invaded the House of Commons and obliged it to
rescind the ordinance re-establishing the old parliamentary committee of
militia; Lenthall was held in the chair by main force and compelled to
put to the vote a resolution inviting the king to London. Threats of
worse things came subsequently to Lenthall's ears, and, taking the mace
with him, he left London on the 29th to join the army and Fairfax.
Lenthall and Manchester, the speaker of the Lords, headed the fugitive
members at the review on Hounslow Heath on the 3rd of August, being
received by the soldiers "as so many angels sent from heaven for their
good." Returning to London with the army, he was installed again by
Fairfax in the chair (6th August), and all votes passed during his
absence were annulled. He adhered henceforth to the army party, but with
a constant bias in favour of the king.
At the Restoration he claimed to have sent money to the king at Oxford,
to have provided the queen with comforts and necessaries and to have
taken care of the royal children. But he put the question for the king's
trial from the chair, and continued to act as speaker after the king's
execution. He still continued to use his influence in favour of the
royalists, whenever this was possible without imperilling his own
interests, and he saved the lives of both the earl of Norwich (8th March
1649) and Sir W. D'Avenant (3rd July 1650) by his casting vote. The
removal of the king had left the parliament supreme; and Lenthall as its
representative, though holding little real power, was the first man in
the state.
His speakership continued till the 20th of April 1653, when the Long
Parliament was summarily expelled. Cromwell directed Colonel Harrison,
on the refusal of Lenthall to quit the chair, to pull him out--and
Lenthall submitted to the show of force. He took no part in politics
till the assembling of the first protectorate parliament, on the 3rd of
September 1654, in which he sat as member for Oxfordshire. He was again
chosen speaker, his former experience and his pliability of character
being his chief recommendations. In the second protectorate parliament,
summoned by Cromwell on the 17th of September 1656, Lenthall was again
chosen member for Oxfordshire, but had some difficulty in obtaining
admission, and was not re-elected speaker. He supported Cromwell's
administration, and was active in urging the protector to take the title
of king. In spite of his services, Lenthall was not included by Cromwell
in his new House of Lords, and was much disappointed and crestfallen at
his omission. The protector, hearing of his "grievous complaint," sent
him a writ, and Lenthall was elated at believing he had secured a
peerage. After Cromwell's death, the officers, having determined to
recall the "Rump" Parliament, assembled at Lenthall's house at the Rolls
(6th May 1659), to desire him to send out the writs. Lenthall, however,
had no wish to resume his duties as speaker, preferring the House of
Lords, and made various excuses for not complying. Nevertheless, upon
the officers threatening to summon the parliament without his aid, and
hearing the next morning that several members had assembled, he led the
procession to the parliament house. Lenthall was now restored to the
position of dignity which he had filled before. He was temporarily made
keeper of the new great seal (14th of May). On the 6th of June it was
voted that all commissions should be signed by Lenthall and not by the
commander-in-chief. His exalted position, however, was not left long
unassailed. On the 13th of October Lambert placed soldiers round the
House and prevented the members from assembling. Lenthall's coach was
stopped as he was entering Palace Yard, the mace was seized and he was
obliged to return. The army, however, soon returned to their allegiance
to the parliament. On the 24th of December they marched to Lenthall's
house, and expressed their sorrow. On the 29th the speaker received the
thanks of the reassembled parliament.
Lenthall now turned his attention to bring about the Restoration. He
"very violently" opposed the oath abjuring the house of Stuart, now
sought to be imposed by the republican faction on the parliament, and
absented himself from the House for ten days, to avoid, it was said, any
responsibility for the bill. He had been in communication with Monk for
some time, and on Monk entering London with his army (3rd February 1660)
Lenthall met him in front of Somerset House. On the 6th of February Monk
visited the House of Commons, when Lenthall pronounced a speech of
thanks. On the 28th of March Lenthall forwarded to the king a paper
containing "Heads of Advice." According to Monk, he "was very active for
the restoring of His Majesty and performed many services ... which could
not have been soe well effected without his helpe." Lenthall
notwithstanding found himself in disgrace at the Restoration. In spite
of Monk's recommendation, he was not elected by Oxford University for
the Convention Parliament, nor was he allowed by the king, though he had
sent him a present of £3000, to remain master of the rolls. On the 11th
of June he was included by the House of Commons, in spite of a
recommendatory letter from Monk, among the twenty persons excepted from
the act of indemnity and subject to penalties not extending to life. In
the House of Lords, however, Monk's testimony and intercession were
effectual, and Lenthall was only declared incapable of holding for the
future any public office. His last public act was a disgraceful one.
Unmindful now of the privileges of parliament, he consented to appear as
a witness against the regicide Thomas Scot, for words spoken in the
House of Commons while Lenthall was in the chair. It was probably after
this that he was allowed to present himself at court, and his
contemporaries took a malicious glee in telling how "when, with some
difficulty, he obtained leave to kiss the king's hand he, out of guilt,
fell backward, as he was kneeling."
Lenthall died on the 3rd of September 1662. In his will he desired to be
buried without any state and without a monument, "but at the utmost a
plain stone with this superscription only, _Vermis sum_, acknowledging
myself to be unworthy of the least outward regard in this world and
unworthy of any remembrance that hath been so great a sinner." He was
held in little honour by his contemporaries, and was universally
regarded as a time-server. He was, however, a man of good intentions,
strong family affections and considerable ability. Unfortunately he was
called by the irony of fate to fill a great office, in which governed
constantly by fears for his person and estate, he was seduced into a
series of unworthy actions. He left one son, Sir John Lenthall, who had
descendants. His brother, Sir John Lenthall, who, it was said, had too
much influence with him, was notorious for his extortions as keeper of
the King's Bench prison.
See C. H. Firth in the _Dict. Nat. Biog._; Wood (ed. Bliss), _Ath.
Oxon._ iii. 603, who gives a list of his printed speeches and letters;
Foss, _Lives of the Judges_, vi. 447; and J. A. Manning, _Lives of the
Speakers of the House of Commons_. There are numerous references to
Lenthall in his official capacity, and letters written by and to him,
in the Calendar of State Papers, Domestic Series, and in various MSS.
calendared in the Hist. MSS. Commission Series. See also D'Ewes's
_Diary_, in the Harleian Collection, British Museum, some extracts
from which have been given by J. Forster, _Case of the Five Members_,
233 sq.; and _Notes and Queries_, ser. iii., vii. 45 ("Lenthall's
Lamentation"), viii., i. 165, 338, 2, ix., xi. 57.
LENTIL, the seed of _Lens esculenta_ (also known as _Ervum Lens_), a
small annual of the vetch tribe. The plant varies from 6 to 18 in. in
height, and has many long ascending branches. The leaves are alternate,
with six pairs of oblong-linear, obtuse, mucronate leaflets. The
flowers, two to four in number, are of a pale blue colour, and are borne
in the axils of the leaves, on a slender footstalk nearly equalling the
leaves in length; they are produced in June or early in July. The pods
are about ½ in. long, broadly oblong, slightly inflated, and contain two
seeds, which are of the shape of a doubly convex lens, and about 1/6
in. in diameter. There are several cultivated varieties of the plant,
differing in size, hairiness and colour of the leaves, flowers and
seeds. The last may be more or less compressed in shape, and in colour
may vary from yellow or grey to dark brown; they are also sometimes
mottled or speckled. In English commerce two kinds of lentils are
principally met with, French and Egyptian. The former are usually sold
entire, and are of an ash-grey colour externally and of a yellow tint
within; the latter are usually sold like split peas, without the seed
coat, and consist of the reddish-yellow cotyledons, which are smaller
and rounder than those of the French lentil; the seed coat when present
is of a dark brown colour. Considerable quantities of lentils are also
imported into the United States.
The native country of the lentil is not known. It was probably one of
the first plants brought under cultivation by mankind; lentils have been
found in the lake dwellings of St Peter's Island, Lake of Bienne, which
are of the Bronze age. The name 'adas (Heb. [Hebrew: adash]) appears to
be an original Semitic word, and the red pottage of lentils for which
Esau sold his birthright (Gen. xxv. 34) was apparently made from the red
Egyptian lentil. This lentil is cultivated in one or other variety in
India, Persia, Syria, Egypt, Nubia and North Africa, and in Europe,
along the coast of the Mediterranean, and as far north as Germany,
Holland and France. In Egypt, Syria and other Eastern countries the
parched seeds are exposed for sale in shops, and esteemed the best food
to carry on long journeys. Lentils form a chief ingredient in the
Spanish puchero, and are used in a similar way in France and other
countries. For this purpose they are usually sold in the shelled state.
The reddish variety of the lentil (_lentillon d'hiver_) is the kind
most esteemed in Paris on account of the superior flavour of its
smaller seeds. It is sown in autumn either with a cereal crop or
alone, and is cultivated chiefly in the north and east of France. The
large or common variety, _lentille large blonde_, cultivated in
Lorraine and at Gallardon (Eure-et-Loir), and largely in Germany, is
the most productive, but is less esteemed. This kind has very small
whitish flowers, two or rarely three on a footstalk, and the pods are
generally one-seeded, the seeds being of a whitish or cream colour,
about 3/8 of an inch broad and 1/8 in. thick. A single plant produces
from 100 to 150 pods, which are flattened, about ¾ in. long and ½ in.
broad. Another variety, with seeds similar in form and colour to the
last, but of much smaller size, is known as the _lentillon de Mars_.
It is sown in spring. This variety and the _lentille large_ are both
sometimes called the _lentille à la reine_. A small variety, _lentille
verte du Puy_, cultivated chiefly in the departments of Haute Loire
and Cantal, is also grown as a vegetable and for forage. The Egyptian
lentil was introduced into Britain in 1820. It has blue flowers.
Another species of lentil, _Ervum monanthos_, is grown in France about
Orleans and elsewhere under the name of _jarosse_ and _jarande_. It
is, according to Vilmorin, one of the best kinds of green food to grow
on a poor dry sandy soil; on calcareous soil it does not succeed so
well. It is usually sown in autumn with a little rye or winter oats,
at the rate of a hectolitre to a hectare.
The lentil prefers a light warm sandy soil; on rich land it runs to
leaf and produces but few pods. The seeds are sown in March or April
or early in May, according to the climate of the country, as they
cannot endure night frosts. If for fodder they are sown broadcast, but
in drills if the ripe seeds are required. The pods are gathered in
August or September, as soon as they begin to turn brown--the plants
being pulled up like flax while the foliage is still green, and on a
dry day lest the pods split in drying and loss of seed takes place.
Lentils keep best in the husk so far as flavour is concerned, and will
keep good in this way for two years either for sowing or for food. An
acre of ground yields on an average about 11 cwt. of seed and 30 cwt.
of straw. The amount and character of the mineral matter requisite in
the soil may be judged from the analysis of the ash, which in the
seeds has as its chief ingredients--potash 34.6%, soda 9.5, lime 6.3,
phosphoric acid 36.2, chloride of sodium 7.6, while in the straw the
percentages are--potash 10.8, lime 52.3, silica 17.6, phosphoric acid
12.3, chloride of sodium 2.1.
Lentils have attracted considerable notice among vegetarians as a food
material, especially for soup. A Hindu proverb says, "Rice is good,
but lentils are my life." The husk of the seed is indigestible, and to
cook lentils properly requires at least two and a half hours, but they
are richer in nutritious matter than almost any other kind of pulse,
containing, according to Payen's analysis, 25.2% of nitrogenous matter
(legumin), 56% of starch and 2.6% of fatty matter. Fresenius's
analysis differs in giving only 35% of starch; Einhoff gives 32.81 of
starch and 37.82% of nitrogenous matter. Lentils are more properly the
food of the poor in all countries where they are grown, and have often
been spurned when better food could be obtained, hence the proverb
_Dives factus jam desiit gaudere lente_. The seeds are said to be good
for pigeons, or mixed in a ground state with potatoes or barley for
fattening pigs. The herbage is highly esteemed as green food for
suckling ewes and all kinds of cattle (being said to increase the
yield of milk), also for calves and lambs. Haller says that lentils
are so flatulent as to kill horses. They were also believed to be the
cause of severe scrofulous disorders common in Egypt. This bad
reputation may possibly be due to the substitution of the seeds of the
bitter vetch or tare lentil, _Ervum Ervilia_, a plant which closely
resembles the true lentil in height, habit, flower and pod, but whose
seeds are without doubt possessed of deleterious properties--producing
weakness or even paralysis of the extremities in horses which have
partaken of them. The poisonous principle seems to reside chiefly in
the bitter seed coat, and can apparently be removed by steeping in
water, since Gerard, speaking of the "bitter vetch" (_E. Ervilia_),
says "kine in Asia and in most other countries do eat thereof, being
made sweet by steeping in water." The seed of _E. Ervilia_ is about
the same size and almost exactly of the same reddish-brown colour as
that of the Egyptian lentil, and when the seed coat is removed they
are both of the same orange red hue, but the former is not so bright
as the latter. The shape is the best means of distinguishing the two
seeds, that of E. _Ervilia_ being obtusely triangular.
Sea-lentil is a name sometimes applied to the gulfweed _Sargassum
vulgare_.