The history of the theory of the representation of functions by series
of sines and cosines is of great interest in connexion with the
progressive development of the notion of an arbitrary function of a
real variable, and of the peculiarities which such a function may
possess; the modern views on the foundations of the infinitesimal
calculus have been to a very considerable extent formed in this
connexion (see FUNCTION). The representation of functions by these
series was first considered in the 18th century, in connexion with the
problem of a vibrating cord, and led to a controversy as to the
possibility of such expansions. In a memoir published in 1747
(_Memoirs of the Academy of Berlin_, vol. iii.) D'Alembert showed that
the ordinate y at any time t of a vibrating cord satisfies a
differential equation of the form [delta]^y/[delta]t^2 = a^2
[delta]^y/[delta]x^2, where x is measured along the undisturbed length
of the cord, and that with the ends of the cord of length l fixed, the
appropriate solution is y = [f](at + x) - [f](at - x), where [f] is a
function such that [f](x) = [f](x + 2l); in another memoir in the same
volume he seeks for functions which satisfy this condition. In the
year 1748 (_Berlin Memoirs_, vol. iv.) Euler, in discussing the
problem, gave [f](x) = [alpha] sin [pi]x/l + [beta] sin 2[pi]x/l + ...
as a particular solution, and maintained that every curve, whether
regular or irregular, must be representable in this form. This was
objected to by D'Alembert (1750) and also by Lagrange on the ground
that irregular curves are inadmissible. D. Bernoulli (_Berlin
Memoirs_, vol. ix., 1753) based a similar result to that of Euler on
physical intuition; his method was criticized by Euler (1753). The
question was then considered from a new point of view by Lagrange, in
a memoir on the nature and propagation of sound (_Miscellanea
Taurensia_, 1759; [_OE]uvres_, vol. i.), who, while criticizing
Euler's method, considers a finite number of vibrating particles, and
then makes the number of them infinite; he did not, however, quite
fully carry out the determination of the coefficients in Bernoulli's
Series. These mathematicians were hampered by the narrow conception of
a function, in which it is regarded as necessarily continuous; a
discontinuous function was considered only as a succession of several
different functions. Thus the possibility of the expansion of a broken
function was not generally admitted. The first cases in which rational
functions are expressed in sines and cosines were given by Euler
(_Subsidium calculi sinuum_, Novi Comm. Petrop., vol. v., 1754-1755),
who obtained the formulae
1/2 [phi] = sin [phi] - 1/2 sin 2[phi] + 1/3 sin 3[phi] ...
[pi]^2 [phi]^2
------ - ------- = cos [phi] - 1/4 cos 2[phi] + 1/9 cos 3[phi] ...
12 4
In a memoir presented to the Academy of St Petersburg in 1777, but not
published until 1798, Euler gave the method afterwards used by
Fourier, of determining the coefficients in the expansions; he
remarked that if [Phi] is expansible in the form
_ _
1 /[pi] 2 /[pi]
A + B cos[phi] + C cos 2[phi] + ..., then A = ---- | [Phi]d[phi], B = ---- | cos [phi]d[phi], &c.
[pi] _/ 0 [pi] _/ 0
The second period in the development of the theory commenced in 1807,
when Fourier communicated his first memoir on the Theory of Heat to
the French Academy. His exposition of the present theory is contained
in a memoir sent to the Academy in 1811, of which his great treatise
the _Theorie analytique de la chaleur_, published in 1822, is, in the
main, a reproduction. Fourier set himself to consider the
representation of a function given graphically, and was the first
fully to grasp the idea that a single function may consist of detached
portions given arbitrarily by a graph. He had an accurate conception
of the convergence of a series, and although he did not give a
formally complete proof that a function with discontinuities is
representable by the series, he indicated in particular cases the
method of procedure afterwards carried out by Dirichlet. As an
exposition of principles, Fourier's work is still worthy of careful
perusal by all students of the subject. Poisson's treatment of the
subject, which has been adopted in English works (see the _Journal de
l'ecole polytechnique_, vol. xi., 1820, and vol. xii., 1823, and also
his treatise, _Theorie de la chaleur_, 1835), depends upon the equality
_
/[pi] 1 - h^2
| [f]([alpha]) ------------------------------ d[alpha]
_/-[pi] 1 - 2h cos (x - [alpha]) + h^2
_ _
1 /[pi] 1 /[pi]
= ----- | [f]([alpha]) d[alpha] + ---- [Sigma]h^n | [f]([alpha]) cos n(x - [alpha]) d[alpha]
2[pi] _/-[pi] [pi] _/-[pi]
where 0 < h < 1; the limit of the integral on the left-hand side is
evaluated when h=1, and found to be 1/2 {[f](x + 0) + [f](x - 0)}, the
series on the right-hand side becoming Fourier's Series. The equality
of the two limits is then inferred. If the series is assumed to be
convergent when h = 1, by a theorem of Abel's its sum is continuous
with the sum for values of h less than unity, but a proof of the
convergency for h = 1 is requisite for the validity of Poisson's
proof; as Poisson gave no such proof of convergency, his proof of the
general theorem cannot be accepted. The deficiency cannot be removed
except by a process of the same nature as that afterwards applied by
Dirichlet. The definite integral has been carefully studied by Schwarz
(see two memoirs in his collected works on the integration of the
equation [delta]^2u/[delta]x^2 + [delta]^2u/[delta]y^2 = 0), who showed
that the limiting value of the integral depends upon the manner in
which the limit is approached. Investigations of Fourier's Series were
also given by Cauchy (see his "Memoire sur les developpements des
fonctions en series periodiques," _Mem. de l'Inst_., vol. vi., also
_Oeuvres completes_, vol. vii.); his method, which depends upon a use
of complex variables, was accepted, with some modification, as valid
by Riemann, but one at least of his proofs is no longer regarded as
satisfactory. The first completely satisfactory investigation is due
to Dirichlet; his first memoir appeared in _Crelle's Journal_ for
1829, and the second, which is a model of clearness, in Dove's
_Repertorium der Physik_. Dirichlet laid down certain definite
sufficient conditions in regard to the nature of a function which is
expansible, and found under these conditions the limiting value of the
sum of n terms of the series. Dirichlet's determination of the sum of
the series at a point of discontinuity has been criticized by Schlafli
(see _Crelle's Journal_, vol. lxxii.) and by Du Bois-Reymond (_Mathem.
Annalen_, vol. vii.), who maintained that the sum is really
indeterminate. Their objection appears, however, to rest upon a
misapprehension as to the meaning of the sum of the series; if x1 be
the point of discontinuity, it is possible to make x approach x1,
and n become indefinitely great, so that the sum of the series takes
any assigned value in a certain interval, whereas we ought to make x =
x1 first and afterwards n = [oo], and no other way of going to the
double limit is really admissible. Other papers by Dircksen (_Crelle_,
vol. iv.) and Bessel (_Astronomische Nachrichten_, vol. xvi.), on
similar lines to those by Dirichlet, are of inferior importance. Many
of the investigations subsequent to Dirichlet's have the object of
freeing a function from some of the restrictions which were imposed
upon it in Dirichlet's proof, but no complete set of necessary and
sufficient conditions as to the nature of the function has been
obtained. Lipschitz ("De explicatione per series trigonometricas,"
_Crelle's Journal_, vol. lxiii., 1864) showed that, under a certain
condition, a function which has an infinite number of maxima and
minima in the neighbourhood of a point is still expansible; his
condition is that at the point of discontinuity [beta], |[f]([beta] +
[delta]) -f([beta])| < B[delta]^[alpha] as [delta] converges to zero,
B being a constant, and a a positive exponent. A somewhat wider
condition is
{[f]([beta] + [delta]) - [f]([beta])} log [delta]) = 0,
[delta] = 0
for which Lipschitz's results would hold. This last condition is
adopted by Dini in his treatise (_Sopra la serie di Fourier_, &c.,
Pisa, 1880).
The modern period in the theory was inaugurated by the publication by
Riemann in 1867 of his very important memoir, written in 1854, _Uber
die Darstellbarkeit einer Function durch eine trigonometrische Reihe_.
The first part of his memoir contains a historical account of the work
of previous investigators; in the second part there is a discussion of
the foundations of the Integral Calculus, and the third part is mainly
devoted to a discussion of what can be inferred as to the nature of a
function respecting the changes in its value for a continuous change
in the variable, if the function is capable of representation by a
trigonometrical series. Dirichlet and probably Riemann thought that
all continuous functions were everywhere representable by the series;
this view was refuted by Du Bois-Reymond (_Abh. der Bayer. Akad._ vol.
xii. 2). It was shown by Riemann that the convergence or
non-convergence of the series at a particular point x depends only
upon the nature of the function in an arbitrarily small neighbourhood
of the point x. The first to call attention to the importance of the
theory of uniform convergence of series in connexion with Fourier's
Series was Stokes, in his memoir "On the Critical Values of the Sums
of Periodic Series" (_Camb. Phil. Trans._, 1847; _Collected Papers_,
vol. i.). As the method of determining the coefficients in a
trigonometrical series is invalid unless the series converges in
general uniformly, the question arose whether series with coefficients
other than those of Fourier exist which represent arbitrary functions.
Heine showed (_Crelle's Journal_, vol. lxxi., 1870, and in his
treatise _Kugelfunctionen_, vol. i.) that Fourier's Series is in
general uniformly convergent, and that if there is a uniformly
convergent series which represents a function, it is the only one of
the kind. G. Cantor then showed (_Crelle's Journal_, vols. lxxii.
lxxiii.) that even if uniform convergence be not demanded, there can
be but one convergent expansion for a function, and that it is that of
Fourier. In the _Math. Ann._ vol. v., Cantor extended his
investigation to functions having an infinite number of
discontinuities. Important contributions to the theory of the series
have been published by Du Bois-Reymond (_Abh. der Bayer. Akademie_,
vol. xii., 1875, two memoirs, also in Crelle's Journal, vols. lxxiv.
lxxvi. lxxix.), by Kronecker (_Berliner Berichte_, 1885), by O. Holder
(_Berliner Berichte_, 1885), by Jordan (_Comptes rendus_, 1881, vol.
xcii.), by Ascoli (_Math. Annal._, 1873, and _Annali di matematica_,
vol. vi.), and by Genocchi (_Atti della R. Acc. di Torino_, vol. x.,
1875). Hamilton's memoir on "Fluctuating Functions" (_Trans. R.I.A._,
vol. xix., 1842) may also be studied with profit in this connexion. A
memoir by Broden (_Math. Annalen_, vol. lii.) contains a good
investigation of some of the most recent results on the subject. The
scope of Fourier's Series has been extended by Lebesgue, who
introduced a conception of integration wider than that due to Riemann.
Lebesgue's work on Fourier's Series will be found in his treatise,
_Lecons sur les series trigonometriques_ (1906); also in a memoir,
"Sur les series trigonometriques," _Annales sc. de l'ecole normale
superieure_, series ii. vol. xx. (1903), and in a paper "Sur la
convergence des series de Fourier," _Math. Annalen_, vol. lxiv.
(1905).
AUTHORITIES.--The foregoing historical account has been mainly drawn
from A. Sachse's work, "Versuch einer Geschichte der Darstellung
willkurlicher Functionen einer Variabeln durch trigonometrische
Reihen," published in _Schlomilch's Zeitschrift fur Mathematik_,
Supp., vol. xxv. 1880, and from a paper by G.A. Gibson "On the History
of the Fourier Series" (_Proc. Ed. Math. Soc._ vol. xi.). Reiff's
_Geschichte der unendlichen Reihen_ may also be consulted, and also
the first part of Riemann's memoir referred to above. Besides Dini's
treatise already referred to, there is a lucid treatment of the
subject from an elementary point of view in C. Neumann's treatise,
_Uber die nach Kreis-, Kugel- und Cylinder-Functionen fortschreitenden
Entwickelungen_. Jordan's discussion of the subject in his _Cours
d'analyse_ is worthy of attention: an account of functions with
limited variation is given in vol. i.; see also a paper by Study in
the _Math. Annalen_, vol. xlvii. On the second mean-value theorem
papers by Bonnet (Brux. Memoires, vol. xxiii., 1849, _Lionville's
Journal_, vol. xiv., 1849), by Du Bois-Reymond (_Crelle's Journal_,
vol. lxxix., 1875), by Hankel (_Zeitschrift fur Math. und Physik_,
vol. xiv., 1869), by Meyer (_Math. Ann._, vol. vi., 1872) and by
Holder (_Gottinger Anzeigen_, 1894) may be consulted; the most general
form of the theorem has been given by Hobson (_Proc. London Math.
Soc._, Series II. vol. vii., 1909). On the theory of uniform
convergence of series, a memoir by W.F. Osgood (_Amer. Journal of
Math._ xix.) may be with advantage consulted. On the theory of series
in general, in relation to the functions which they can represent, a
memoir by Baire (_Annali di matematica_, Series III. vol. iii.) is of
great importance. Bromwich's _Theory of Infinite Series_ (1908)
contains much information on the general theory of series. Bocher's
"Introduction to the Theory of Fourier's Series," _Annals of Math._,
Series II. vol. vii., 1906, will be found useful. See also Carslaw's
_Introduction to the Theory of Fourier's Series and Integrals, and the
Mathematical Theory of the Conduction of Heat_ (1906). A full account
of the theory will be found in Hobson's treatise _On the Theory of
Functions of a Real Variable and on the Theory of Fourier's Series_
(1907). (E. W. H.)
FOURMIES, a town of northern France, in the department of Nord, on an
affluent of the Sambre, 39 m. S.E. of Valenciennes by rail. Pop. (1906)
13,308. It is one of the chief centres in France for wool combing and
spinning, and produces a great variety of cloths. The glass-works of
Fourmies date from 1599, and were the first established in the north of
France. Iron is worked in the vicinity, and there are important forges
and foundries. Enamel-ware is also manufactured. In 1891 labour troubles
brought about military intervention and consequent bloodshed. A board of
trade arbitration and a school of commerce and industry are among the
public institutions.
FOURMONT, ETIENNE (1683-1745), French orientalist, was born at Herbelai,
near Saint Denis, on the 23rd of June 1683. He studied at the College
Mazarin, Paris, and afterwards in the College Montaigu, where his
attention was attracted to Oriental languages. Shortly after leaving the
college he published a _Traduction du commentaire du Rabbin Abraham Aben
Esra sur l'ecclesiast_e. In 1711 Louis XIV. appointed Fourmont to assist
a young Chinese, Hoan-ji, in compiling a Chinese grammar. Hoan-ji died
in 1716, and it was not until 1737 that Fourmont published _Meditationes
Sinicae_ and in 1742 _Grammatica Sinica_. He also wrote _Reflexions
critiques sur les histoires des anciens peuples_ (1735), and several
dissertations printed in the _Memoires_ of the Academy of Inscriptions.
He became professor of Arabic in the College de France in 1715. In 1713
he was elected a member of the Academy of Inscriptions, in 1738 a member
of the Royal Society of London, and in 1742 a member of that of Berlin.
He died at Paris on the 19th of December 1745.
His brother, Michel Fourmont (1690-1746), was also a member of the
Academy of Inscriptions, and professor of the Syriac language in the
Royal College, and was sent by the government to copy inscriptions in
Greece.
An account of Etienne Fourmont's life and a catalogue of his works
will be found in the second edition (1747) of his _Reflexions
critiques_.
FOURNET, JOSEPH JEAN BAPTISTE XAVIER (1801-1869), French geologist and
metallurgist, was born at Strassburg on the 15th of May 1801. He was
educated at the Ecole des Mines at Paris, and after considerable
experience as a mining engineer he was in 1834 appointed professor of
geology at Lyons. He was a man of wide knowledge and extensive research,
and wrote memoirs on chemical and mineralogical subjects, on eruptive
rocks, on the structure of the Jura, the metamorphism of the Western
Alps, on the formation of oolitic limestones, on kaolinization and on
metalliferous veins. On metallurgical subjects also he was an
acknowledged authority; and he published observations on the order of
sulphurability of metals (_loi de Fournet_). He died at Lyons on the 8th
of January 1869. His chief publications were: E_tudes sur les depots
metalliferes_ (Paris, 1834); _Histoire de la dolomie_ (Lyons, 1847); _De
l'extension des terrains houillers_ (1855); _Geologie lyonnaise_ (Lyons,
1861).
FOURNIER, PIERRE SIMON (1712-1768), French engraver and typefounder, was
born at Paris on the 15th of September 1712. He was the son of a
printer, and was brought up to his father's business. After studying
drawing under the painter Colson, he practised for some time the art of
wood-engraving, and ultimately turned his attention to the engraving and
casting of types. He designed many new characters, and his foundry
became celebrated not only in France, but in foreign countries. Not
content with his practical achievements, he sought to stimulate public
interest in his art by the production of various works on the subject.
In 1737 he published his _Table des proportions qu'il faut observer
entre les caracteres_, which was followed by several other technical
treatises. In 1758 he assailed the title of Gutenberg to the honour
awarded him as inventor of printing, claiming it for Schoffer, in his
_Dissertation sur l'origine et les progres de l'art de graver en bois_.
This gave rise to a controversy in which Schopflin and Baer were his
opponents. Fournier's contributions to this debate were collected and
reprinted under the title of _Traites historiques et critiques sur
l'origine de l'imprimerie_. His principal work, however, was the _Manuel
typographique_, which appeared in 2 vols. 8vo in 1764, the first volume
treating of engraving and type-founding, the second of printing, with
examples of different alphabets. It was the author's design to complete
the work in four volumes, but he did not live to execute it. He died at
Paris on the 8th of October 1768.
FOURNIER L'HERITIER, CLAUDE (1745-1825), French revolutionist, called
"l'Americain," was born at Auzon (Haute-Loire) on the 21st of December
1745, the son of a poor weaver. He went to America to seek his fortune,
and started at San Domingo an establishment for making _tafia_ (an
inferior quality of rum), but lost his money in a fire. Returning to
France he threw himself into the Revolution with enthusiasm, and
specially distinguished himself by the active part he took in the
organization of the popular armed force by means of which the most
famous of the revolutionary _coups_ were effected. His influence was
principally manifested in the insurrections of the 5th and 6th of
October 1789, the 17th of July 1791, and the 20th of June and the 10th
of August 1792. He was on bad terms with the majority of the
politicians, and particularly with Marat, and spent a great part of his
time in prison, all the governments regarding him as an agitator and
accusing him of inciting to insurrection. Arrested for the first time
for trying to force an entrance into the club of the Cordeliers, from
which he had been expelled, he was released, but was in prison from the
12th of December 1793 to the 21st of September 1794, and again from the
9th of March 1795 to the 26th of October 1795. After the attempt on the
First Consul in the rue Sainte-Nicaise he was deported to Guiana, but
was allowed to return to France in 1809. In 1811, while under
surveillance at Auxerre, he was accused of having provoked an _emeute_
against taxes known as the _droits reunis_ (afterwards called
c_ontributions indirectes_), and was imprisoned in the Chateau d'If,
where he remained till 1814. On the second restoration of the Bourbons
Fournier was confined for about nine months in the prison of La Force.
After 1816 he was left unmolested, turned royalist, and passed his last
years in importuning the Restoration government for compensation for his
lost property in San Domingo. He died in obscurity.
For further details see preface to F.A. Aulard's edition of Fournier's
_Memoires secrets_ (Paris, 1890), published by the Societe de
l'histoire de la Revolution.
FOURTOU, MARIE FRANCOIS OSCAR BARDY DE (1836-1897), French politician,
was born at Riberac (Dordogne) on the 3rd of January 1836, and
represented his native department in the National Assembly after the
Franco-German War. There he proved a useful adherent to Thiers, who made
him minister of public works in December 1872. He was minister of
religion in the cabinet of May 18-24, 1873, being the only member of the
Right included by Thiers in that short-lived ministry. As minister of
education, religion and the fine arts in the reconstructed cabinet of
the duc de Broglie he had used his administrative powers to further
clerical ends, and as minister of the interior in Broglie's cabinet in
1877 he resumed the administrative methods of the Second Empire. With a
well-known Bonapartist, Baron R.C.F. Reille, as his secretary, he
replaced republican functionaries by Bonapartist partisans, reserving a
few places for the Legitimists. In the general elections of that year he
used the whole weight of officialdom to secure a majority for the Right,
to support a clerical and reactionary programme. He accompanied Marshal
MacMahon in his tour through southern France, and the presidential
manifesto of September, stating that the president would rely solely on
the Senate should the elections prove unfavourable, was generally
attributed to Fourtou. In spite of these efforts the cabinet fell, and a
commission was appointed to inquire into their unconstitutional abuse of
power. Fourtou was unseated in consequence of the revelations made in
the report of the commission. In the Chamber of Deputies Gambetta gave
the lie direct to Fourtou's allegation that the republican party opposed
every republican principle that was not antiquated. A duel was fought in
consequence, but neither party was injured. He was re-elected to the
chamber in 1879 and entered the Senate the next year. Failing to secure
re-election to the Senate in 1885 he again entered the popular chamber
as Legitimist candidate in 1889, but he took no further active part in
politics. He died in Paris in 1897.
His works include _Histoire de Louis XVI_ (1840); _Histoire de Saint
Pie V_ (1845); _Mme Swetchine, sa vie et ses oeuvres_ (2 vols., 1859);
_La Question italienne_ (1860); _De la contre-revolution_ (1876); and
_Memoires d'un royaliste_ (2 vols., 1888).
FOUSSA, or FOSSA, the native name of _Cryptoprocta ferox_, a somewhat
cat-like or civet-like mammal peculiar to Madagascar, where it is the
largest carnivorous animal. It is about twice the size of a cat (5 ft.
from nose to end of tail), with short close fur of nearly uniform pale
brown. Little is known of its habits, except that it is nocturnal,
frequently attacks and carries off goats, and especially kids, and shows
great ferocity when wounded, on which account it is much dreaded by the
natives. An example lived in the London zoological gardens for nearly
fourteen years. See CARNIVORA.
FOWEY (usually pronounced _Foy_), a seaport and market-town in the
Bodmin parliamentary division of Cornwall, England, on the Great Western
railway, 25 m. by sea W. of Plymouth. Pop. (1901) 2258. It lies on the
west shore of the picturesque estuary of the river Fowey, close to the
water's edge, and sheltered by a screen of hills. Its church of St
Nicholas is said to have been built in the 14th century, on the site of
a still older edifice dedicated to St Finbar of Cork. It has a fine
tower and late Norman doorway. Within are a priest's chamber over the
porch, a handsome oak ceiling, a 15th-century pulpit, and some curious
monuments and brasses. Place House, adjacent to the church, is a highly
ornate Tudor building. A few ancient houses remain in the town. Deep-sea
fishing is carried on; but the staple trade consists in the export of
china clay and minerals, coal being imported. Fowey harbour, which is
easy of access in clear weather, will admit large vessels at any state
of the tide. St Catherine's Fort, dating from the days of Henry VIII.
and now ruined, stands at the harbour's mouth, and once formed the main
defence of the town. Opposite the town, and connected with it by
Bodeneck Ferry, is the village of Polruan. Its main features are St
Saviour's Chapel, with an ancient rood-stone, and the remains of Hall
House, which was garrisoned during the civil wars of the 17th century.
Fowey (Fawy, Vawy, Fowyk) held a leading position amongst Cornish ports
from the reign of Edward I. to the days of the Tudors. The numerous
references to the privateering exploits of its ships in the Patent and
Close Rolls and the extraordinary number of them at the siege of Calais
in 1346 alike testify to its importance. During this period the king's
mandates were addressed to the bailiffs or to the mayor and bailiffs,
and no charter of incorporation appears to have been granted until the
reign of James II. Under the second charter of 1690 the common council
consisted of a mayor and eight aldermen and these with a recorder
elected the free burgesses. A member for Fowey and Looe was summoned to
a council at Westminster in 1340, but from that date until 1571, when it
was entrusted with the privilege of returning two members, it had no
parliamentary representation. By the Reform Act of 1832 it lost both its
members. It had ceased to exercise its municipal functions a few years
previously. In 1316 the prior of Tywardreath, as lord of the manor,
obtained the right to hold a Monday market and two fairs on the feasts
of St Finbar and St Lucy, but by the charter of 1690 provision was made
for a Saturday market and three fairs, on the 1st of May, 10th of
September and Shrove Tuesday, and only these three continue to be held.
FOWL (Dan. _Fugl_, Ger. _Vogel_), a term originally used in the sense
that bird[1] now is, but, except in composition,--as sea-fowl, wild-fowl
and the like,--practically almost confined[2] at present to designate
the otherwise nameless species which struts on our dunghills, gathers
round our barn-doors, or stocks our poultry yards--the type of the genus
_Gallus_ of ornithologists, of which four well-marked species are known.
The _first_ of these is the red jungle-fowl of the greater part of
India, _G. ferrugineus_,--called by many writers _G. bankiva_,--which is
undoubtedly the parent stock of all the domestic races (cf. Darwin,
_Animals and Plants under Domestication_, i. pp. 233-246). It inhabits
northern India from Sind to Burma and Cochin China, as well as the Malay
Peninsula and many of the islands as far as Timor, besides the
Philippines. It occurs on the Himalayas up to the height of 4000 ft.,
and its southern limits in the west of India proper are, according to
Jerdon, found on the Raj-peepla hills to the south of the Nerbudda, and
in the east near the left bank of the Godavery, or perhaps even farther,
as he had heard of its being killed at Cummum. This species resembles in
plumage what is commonly known among poultry-fanciers as the
"Black-breasted game" breed, and this is said to be especially the case
with examples from the Malay countries, between which and examples from
India some differences are observable--the latter having the plumage
less red, the ear-lappets almost invariably white, and slate-coloured
legs, while in the former the ear-lappets are crimson, like the comb and
wattles, and the legs yellowish. If the Malayan birds be considered
distinct, it is to them that the name _G. bankiva_ properly applies.
This species is said to be found in lofty forests and in dense thickets,
as well as in ordinary bamboo-jungles, and when cultivated land is near
its haunts, it may be seen in the fields after the crops are cut in
straggling parties of from 10 to 20. The crow to which the cock gives
utterance morning and evening is just like that of a bantam, never
prolonged as in most domestic birds. The hen breeds from January to
July, according to the locality; and lays from 8 to 12 creamy-white
eggs, occasionally scraping together a few leaves or a little dry grass
by way of a nest. The so-called _G. giganteus_, formerly taken by some
ornithologists for a distinct species, is now regarded as a tame breed
of _G. ferrugineus_ or _bankiva_. The _second_ good species is the grey
jungle-fowl, _G. sonnerati_, whose range begins a little to the
northward of the limits of the preceding, and it occupies the southern
part of the Indian peninsula, without being found elsewhere. The cock
has the end of the shaft of the neck-hackles dilated, forming a horny
plate, like a drop of yellow sealing-wax. His call is very peculiar,
being a broken and imperfect kind of crow, quite unlike that of _G.
ferrugineus_ and more like a cackle. The two species where their
respective ranges overlap, occasionally interbreed in a wild state, and
the present readily crosses in confinement with domestic poultry, but
the hybrids are nearly always sterile. The _third_ species is the
Sinhalese jungle-fowl, _G. stanleyi_ (the _G. lafayettii_ of some
authors), peculiar to Ceylon. This also greatly resembles in plumage
some domestic birds, but the cock is red beneath, and has a yellow comb
with a red edge and purplish-red cheeks and wattles. He has also a
singularly different voice, his crow being dissyllabic. This bird
crosses readily with tame hens, but the hybrids are believed to be
infertile. The _fourth_ species, _G. varius_ (the _G. furcatus_ of some
authors), inhabits Java and the islands eastwards as far as Flores. This
differs remarkably from the others in not possessing hackles, and in
having a large unserrated comb of red and blue and only a single chin
wattle. The predominance of green in its plumage is another easy mark of
distinction. Hybrids between this species and domestic birds are often
produced, but they are most commonly sterile. Some of them have been
mistaken for distinct species, as those which have received the names of
_G. aeneus_ and _G. temmincki_.
Several circumstances seem to render it likely that fowls were first
domesticated in Burma or the countries adjacent thereto, and it is the
tradition of the Chinese that they received their poultry from the West
about the year 1400 B.C. By the Institutes of Manu, the tame fowl is
forbidden, though the wild is allowed to be eaten--showing that its
domestication was accomplished when they were written. The bird is not
mentioned in the Old Testament nor by Homer, though he has [Greek:
'Alektor] (cock) as the name of a man, nor is it figured on ancient
Egyptian monuments. Pindar mentions it, and Aristophanes calls it the
Persian bird, thus indicating it to have been introduced to Greece
through Persia, and it is figured on Babylonian cylinders between the
6th and 7th centuries B.C. It is sculptured on the Lycian marbles in the
British Museum (c. 600 B.C.), and E. Blyth remarks (Ibis, 1867, p. 157)
that it is there represented with the appearance of a true jungle-fowl,
for none of the wild _Galli_ have the upright bearing of the tame breed,
but carry their tail in a drooping position. For further particulars of
these breeds see POULTRY. (A. N.)