b2 b3 b4 b5
a1 + -- + ---- + ------ + -------- + ...
a2 a2a3 a2a3a4 a2a3a4a5
_Historical Note._
The invention of continued fractions is ascribed generally to Pietro
Antonia Cataldi, an Italian mathematician who died in 1626. He used them
to represent square roots, but only for particular numerical examples,
and appears to have had no theory on the subject. A previous writer,
Rafaello Bombelli, had used them in his treatise on Algebra (about
1579), and it is quite possible that Cataldi may have got his ideas from
him. His chief advance on Bombelli was in his notation. They next appear
to have been used by Daniel Schwenter (1585-1636) in a _Geometrica
Practica_ published in 1618. He uses them for approximations. The
theory, however, starts with the publication in 1655 by Lord Brouncker
of the continued fraction
1 1 squared 3 squared 5 squared
-- -- -- -- as an equivalent of [pi]/4. This he is supposed
1 + 2 + 2 + 2 + ...
to have deduced, no one knows how, from Wallis' formula for
3 . 3 . 5 . 5 . 7 . 7 ...
4/[pi], viz. -------------------------
2 . 4 . 4 . 6 . 6 . 8 ...
John Wallis, discussing this fraction in his _Arithmetica Infinitorum_
(1656), gives many of the elementary properties of the convergents to
the general continued fraction, including the rule for their formation.
Huygens (_Descriptio automati planetarii_, 1703) uses the simple
continued fraction for the purpose of approximation when designing the
toothed wheels of his _Planetarium_. Nicol Saunderson (1682-1739), Euler
and Lambert helped in developing the theory, and much was done by
Lagrange in his additions to the French edition of Euler's _Algebra_
(1795). Moritz A. Stern wrote at length on the subject in _Crelle's
Journal_ (x., 1833; xi., 1834; xviii., 1838). The theory of the
convergence of continued fractions is due to Oscar Schloemilch, P. F.
Arndt, P. L. Seidel and Stern. O. Stolz, A. Pringsheim and E. B. van
Vleck have written on the convergence of infinite continued fractions
with complex elements.
REFERENCES.--For the further history of continued fractions we may
refer the reader to two papers by Gunther and A. N. Favaro,
_Bulletins di bibliographia e di storia delle scienze mathematische e
fisicke_, t. vii., and to M. Cantor, _Geschichte der Mathematik_, 2nd
Bd. For text-books treating the subject in great detail there are
those of G. Chrystal in English; Serret's _Cours d`algebre
superieure_ in French; and in German those of Stern, Schloemilch,
Hatterdorff and Stolz. For the application of continued fractions to
the theory of irrational numbers there is P. Bachmann's _Vorlesungen
ueber die Natur der Irrationalzahnen_ (1892). For the application of
continued fractions to the theory of lenses, see R. S. Heath's
_Geometrical Optics_, chaps. iv. and v. For an exhaustive summary of
all that has been written on the subject the reader may consult Bd. 1
of the _Encyklopaedie der mathematischen Wissenschaften_ (Leipzig).
(A. E. J.)
CONTOUR, CONTOUR-LINE (a French word meaning generally "outline," from
the Med. Lat. _contornare_, to round off), in physical geography a line
drawn upon a map through all the points upon the surface represented
that are of equal height above sea-level. These points lie, therefore,
upon a horizontal plane at a given elevation passing through the land
shown on the map, and the contour-line is the intersection of that
horizontal plane with the surface of the ground. The contour-line of 0,
or _datum level_, is the coastal boundary of any land form. If the sea
be imagined as rising 100 ft., a new coast-line, with bays and estuaries
indented in the valleys, would appear at the new sea-level. If the sea
sank once more to its former level, the 100-ft. contour-line with all
its irregularities would be represented by the beach mark made by the
sea when 100 ft. higher. If instead of receding the sea rose
continuously at the rate of 100 ft. per day, a series of levels 100 ft.
above one another would be marked daily upon the land until at last the
highest mountain peaks appeared as islands less than 100 ft. high. A
record of this series of advances marked upon a flat map of the original
country would give a series of concentric contour-lines narrowing
towards the mountain-tops, which they would at last completely surround.
Contour-lines of this character are marked upon most modern maps of
small areas and upon all government survey and military maps at varying
intervals according to the scale of the map.
CONTRABAND (Fr. _contrebande_, from _contra_, against, and _bannum_, Low
Lat. for "proclamation"), a term given generally to illegal traffic; and
particularly, as "contraband of war," to goods, &c., which subjects of
neutral states are forbidden by international law to supply to a
belligerent.
According to current practice contraband of war is of two kinds: (1)
absolute or unconditional contraband, i.e. materials of direct
application in naval or military armaments; and (2) conditional
contraband, consisting of articles which are fit for, but not
necessarily of direct application to, hostile uses. There is much
difference of opinion among international jurists and states, however,
as to the specific materials and articles which may rightfully be
declared by belligerents to belong to either class. There is also
disagreement as to the belligerent right where the immediate destination
is a neutral but the ultimate an enemy port.
An attempt was made at the Second Hague Conference to come to an
agreement on the chief points of difference. The British delegates were
instructed even to abandon the principle of contraband of war
altogether, subject only to the exclusion by blockade of neutral trade
from enemy ports. In the alternative they were to do their utmost to
restrict the definition of contraband within the narrowest possible
limits, and to obtain exemption of food-stuffs destined for places other
than beleaguered fortresses and of raw materials required for peaceful
industry. Though the discussions at the conference did not result in any
convention, except on the subject of mails, it was agreed among the
leading maritime states that an early attempt should be made to codify
the law of naval war generally, in connexion with the establishment of
an international prize court (see Prize).
Mails.
Meanwhile, on the subject of mails, important articles were adopted
which figure in the "Convention on restrictions in the right of capture"
(No. 11 of the series as set out in the General Act, see Peace
Conference). They are as follows:--
ART. I.--The postal correspondence of neutrals or belligerents,
whatever its official or private character may be, found on the high
seas on board a neutral or enemy ship is inviolable. If the ship is
detained, the correspondence is forwarded by the captor with the
least possible delay.
The provisions of the preceding paragraph do not apply, in case of
violation of blockade, to correspondence destined for, or proceeding
from, a blockaded port.
ART. II.--The inviolability of postal correspondence does not exempt
a neutral mail ship from the laws and customs of maritime war as to
neutral merchant ships in general. The ship, however, may not be
searched except when absolutely necessary, and then only with as much
consideration and expedition as possible.
Foodstuffs and pre-emption.
As regards food-stuffs Great Britain has long and consistently held that
provisions and liquors fit for the consumption of the enemy's naval or
military forces are contraband. Her Prize Act, however, provides a
palliative, in the case of "naval or victualling stores," for the
penalty attaching to absolute contraband, the lords of the admiralty
being entitled to exercise a right of pre-emption over such stores, i.e.
to purchase them without condemnation in a prize court. In practice,
purchases are made at the market value of the goods, with an additional
10% for loss of profit.
On the continent of Europe no such palliative has yet been adopted; but
moved by the same desire to distinguish unmistakable from, so to speak,
constructive contraband, and to protect trade against the vexation of
uncertainty, many continental jurists have come to argue conditional
contraband away altogether. This change of opinion has especially
manifested itself in the discussions on the subject in the Institute of
International Law, a body composed exclusively of recognized
international jurists. The rules this body adopted in 1896, though they
do not represent the unanimous feeling of its members, may be taken as
the view of a large proportion of them. The majority comprised German,
Danish, Italian, Dutch and French specialists. The rules adopted contain
a clause, which, after declaring conditional contraband abolished,
states that: "Nevertheless the belligerent has, at his option and on
condition of paying an equitable indemnity, a right of sequestration or
pre-emption as to articles (_objets_) which, on their way to a port of
the enemy, may serve equally in war or in peace." This rule, it is seen,
is of wider application than the above-mentioned provision of the
British Prize Act. To become binding in its existing form, either an
alteration of the text of the Declaration of Paris or a modification in
the wording of the clause would be necessary, seeing that under the
Declaration of Paris "the neutral flag covers enemy goods, except
contraband of war." It may be said that, in so far as the continent is
concerned, expert opinion is, on the whole, favourable to the
recognition of conditional contraband in the form of a right of
sequestration or pre-emption and within the limits Great Britain has
shown a disposition to set to it as against herself.
Coal.
As regards coal there is no essential difference between the position of
coal to feed ships and that of provisions to feed men. Neither is _per
se_ contraband. At the West African Conference in 1884 the Russian
representative protested against its inclusion among contraband
articles, but the Russian government included it in their declaration as
to contraband on the outbreak of the Russo-Japanese War. In 1898 the
British foreign office replied to an inquiry of the Newport Chamber of
Commerce on the position of coal that: "Whether in any particular case
coal is or is not contraband of war, is a matter prima facie for the
determination of the Prize Court of the captor's nationality, and so
long as such decision, when given, does not conflict with
well-established principles of international law, H.M.'s government will
not be prepared to take exception thereto." The practical applications
of the law and usage of contraband in the Russo-Japanese War of 1904-5,
however, brought out vividly the need of reform in these
"well-established principles."
Controversy with Russia in Russo-Japanese War.
The Japanese regulations gave rise to no serious difficulties. Those
issued by Russia, on the other hand, led to much controversy between the
British government and that of Russia, in connexion with the latter's
pretension to class coal, rice, provisions, forage, horses and cotton
with arms, ammunition, explosives, &c., as absolute contraband. On June
1, 1904, Lord Lansdowne expressed the surprise with which the British
government learnt that rice and provisions were to be treated as
unconditionally contraband--"a step which they regarded as inconsistent
with the law and practice of nations." They furthermore "felt
themselves bound to reserve their rights by also protesting against the
doctrine that it is for the belligerent to decide what articles are as a
matter of course, and without reference to other considerations, to be
dealt with as contraband of war, regardless of the well-established
rights of neutrals"; nor would the British government consider itself
bound to recognize as valid the decision of any prize court which
violated those rights. It did not dispute the right of a belligerent to
take adequate precautions for the purpose of preventing contraband of
war, in the hitherto accepted sense of the words, from reaching the
enemy; but it objected to the introduction of a new doctrine under which
"the well-understood distinction between conditional and unconditional
contraband was altogether ignored, and under which, moreover, on the
discovery of articles alleged to be contraband, the ship carrying them
was, without trial and in spite of her neutrality, subjected to
penalties which are reluctantly enforced even against an enemy's ship."
(See section 40 of Russian Instructions on Procedure in Stopping,
Examining and Seizing Merchant Vessels, published in _London Gazette_ of
March 18, 1904.) In particular circumstances provisions might acquire a
contraband character, as, for instance, if they should be consigned
direct to the army or fleet of a belligerent, or to a port where such
fleet might be lying, and if facts should exist raising the presumption
that they were about to be employed in victualling the fleet of the
enemy. In such cases it was not denied that the other belligerent would
be entitled to seize the provisions as contraband of war, on the ground
that they would afford material assistance towards the carrying on of
warlike operations. But it could not be admitted that if such provisions
were consigned to the port of a belligerent (even though it should be a
port of naval equipment) they should therefore be necessarily regarded
as contraband of war. The test was whether there were circumstances
relating to any particular cargo to show that it was destined for
military or naval use.
The Russian government replied that they could not admit that articles
of dual use when addressed to private individuals in the enemy's country
should be necessarily free from seizure and condemnation, since
provisions and such articles of dual use, though intended for the
military or naval forces of the enemy, would obviously, under such
circumstances, be addressed to private individuals, possibly agents or
contractors for the naval or military authorities.
Lord Lansdowne in answer stated that while H.M. government did not
contend that the mere fact that the consignee was a private person
should necessarily give immunity from capture, they held that to take
vessels for adjudication merely because their destination was the
enemy's country would be vexatious, and constitute an unwarrantable
interference with neutral commerce. To render a vessel liable to such
treatment there should be circumstances giving rise to a reasonable
suspicion that the provisions were destined for the enemy's forces, and
it was in such a case for the captor "to establish the fact of
destination for the enemy's forces before attempting to procure their
condemnation" (September 30, 1904).
The protests of Great Britain led to the reference of the subject by the
Russian government to a departmental committee, with the result that on
October 22, 1904, a rectifying notice was issued declaring that articles
capable of serving for a warlike object, including rice and food-stuffs,
should be considered as contraband of war, if they are destined for the
government of the belligerent power or its administration or its army or
its navy or its fortresses or its naval ports; or for the purveyors
thereof; and that in cases where they were addressed to private
individuals these articles should not be considered as contraband of
war; but that in all cases horses and beasts of burden were to be
considered as contraband. As regards cotton, explanations were given by
the Russian government (May 11, 1904) that the prohibition of cotton
applied only to raw cotton suitable for the manufacture of explosives,
and not to yarn or tissues.
Analogues of contraband.
The carriage of belligerent despatches connected with the conduct of a
war or of persons in the service of a belligerent state falls within the
prohibition of contraband traffic, but to distinguish such traffic from
that of contraband, properly so called, the term applied to it in
international law is "analogues of contraband." The penalty attaching to
such carriage necessarily varies according to the degree of the analogy.
Continuous voyages.
Trade between neutrals has a prima facie right to go on, in spite of
war, without molestation. But if the ultimate destination of goods,
though shipped first to a neutral port, is enemy's territory, then,
according to the doctrine of "continuous voyages," the goods may be
treated as if they had been shipped to the enemy's territory direct. The
doctrine is entirely Anglo-Saxon in its origin[1] and development. Only
in one case does it seem ever to have been actually put in force by a
foreign prize court, namely, in the case of the "Doelwijk," a Dutch
vessel which was adjudged good prize by an Italian court on the ground
that, although bound for Djibouti, a French port, it was laden with a
provision of arms of a model which had gone out of use in Europe, and
could only be destined for the Abyssinians, with whom Italy was at war.
The Institute of International Law in 1896 adopted the following rule on
the subject:--
"Destination to the enemy is presumed, where the shipment is to one
of the enemy ports, or to a neutral port, if it is unquestionably
proved by the facts that the neutral port was only a state (_etape_)
towards the enemy as the final destination of a single commercial
operation."
During the South African War (1899-1902) Great Britain was involved in
controversy with Germany, who at first declined to recognize the
existence of any rule which could interfere with trade between neutrals,
the German vessels in question having been stopped on their way to a
neutral port.
As stated above, the Second Hague Conference failed to come to any
understanding on contraband, but the subject was exhaustively dealt with
by the Conference of London (1908-1909) on the laws and customs of naval
war, in the following articles:--
ART. 22.--The following articles may, without notice, be treated as
contraband of war, under the name of absolute contraband: (1) Arms of
all kinds, including arms for sporting purposes, and their
distinctive component parts; (2) projectiles, charges and cartridges
of all kinds, and their distinctive component parts; (3) powder and
explosives specially prepared for use in war; (4) gun-mountings,
limber boxes, limbers, military wagons, field forges and their
distinctive component parts; (5) clothing and equipment of a
distinctively military character; (6) all kinds of harness of a
distinctively military character; (7) saddle, draught and pack
animals suitable for use in war; (8) articles of camp equipment and
their distinctive component parts; (9) armour plates; (10) warships,
including boats, and their distinctive component parts of such a
nature that they can only be used on a vessel of war; (11) implements
and apparatus designed exclusively for the manufacture of munitions
of war, for the manufacture or repair of arms, or war material for
use on land or sea.
ART. 23.--Articles exclusively used for war may be added to the list
of absolute contraband by a declaration, which must be notified. Such
notification must be addressed to the governments of other powers, or
to their representatives accredited to the power making the
declaration. A notification made after the outbreak of hostilities is
addressed only to neutral powers.
ART. 24.--The following articles, susceptible of use in war as well
as for purposes of peace, may, without notice, be treated as
contraband of war, under the name of conditional contraband: (1)
Foodstuffs; (2) forage and grain, suitable for feeding animals; (3)
clothing, fabrics for clothing, and boots and shoes, suitable for use
in war; (4) gold and silver in coin or bullion; paper money; (5)
vehicles of all kinds available for use in war, and their component
parts; (6) vessels, craft and boats of all kinds; floating docks,
parts of docks and their component parts; (7) railway material, both
fixed and rolling-stock, and material for telegraphs, wireless
telegraphs and telephones; (8) balloons and flying machines and their
distinctive component parts, together with accessories and articles
recognizable as intended for use in connexion with balloons and
flying machines; (9) fuel; lubricants; (10) powder and explosives not
specially prepared for use in war; (11) barbed wire and implements
for fixing and cutting the same; (12) horseshoes and shoeing
materials; (13) harness and saddlery; (14) field glasses, telescopes,
chronometers and all kinds of nautical instruments.
ART. 25.--Articles susceptible of use in war as well as for purposes
of peace, other than those enumerated in Articles 22 and 24, may be
added to the list of conditional contraband by a declaration, which
must be notified in the manner provided for in the second paragraph
of Article 23.
ART. 26.--If a power waives, so far as it is concerned, the right to
treat as contraband of war an article comprised in any of the classes
enumerated in Articles 22 and 24, such intention shall be announced
by a declaration, which must be notified in the manner provided for
in the second paragraph of Article 23.
ART. 27.--Articles which are not susceptible of use in war may not be
declared contraband of war.
ART. 28.--The following may not be declared contraband of war: (1)
Raw cotton, wool, silk, jute, flax, hemp and other raw materials of
the textile industries, and yarns of the same; (2) oil seeds and
nuts; copra; (3) rubber, resins, gums and lacs; hops; (4) raw hides
and horns, bones and ivory; (5) natural and artificial manures,
including nitrates and phosphates for agricultural purposes; (6)
metallic ores; (7) earths, clays, lime, chalk, stone, including
marble, bricks, slates and tiles; (8) Chinaware and glass; (9) paper
and paper-making materials; (10) soap, paint and colours, including
articles exclusively used in their manufacture, and varnish; (11)
bleaching powder, soda ash, caustic soda, salt cake, ammonia,
sulphate of ammonia and sulphate of copper; (12) agricultural,
mining, textile and printing machinery; (13) precious and
semiprecious stones, pearls, mother-of-pearl and coral; (14) clocks
and watches, other than chronometers; (15) fashion and fancy goods;
(16) feathers of all kinds, hairs and bristles; (17) articles of
household furniture and decoration; office furniture and requisites.
ART. 29.--Likewise the following may not be treated as contraband of
war: (1) Articles serving exclusively to aid the sick and wounded.
They can, however, in case of urgent military necessity and subject
to the payment of compensation, be requisitioned, if their
destination is that specified in Article 30; (2) articles intended
for the use of the vessel in which they are found, as well as those
intended for the use of her crew and passengers during the voyage.
ART. 30.--Absolute contraband is liable to capture if it is shown to
be destined to territory belonging to or occupied by the enemy, or to
the armed forces of the enemy. It is immaterial whether the carriage
of the goods is direct or entails transhipment or a subsequent
transport by land.
ART. 31.--Proof of the destination specified in Article 30 is
complete in the following cases: (1) When the goods are documented
for discharge in an enemy port, or for delivery to the armed forces
of the enemy; (2) when the vessel is to call at enemy ports only, or
when she is to touch at an enemy port or meet the armed forces of the
enemy before reaching the neutral port for which the goods in
question are documented.
ART. 32.--Where a vessel is carrying absolute contraband, her papers
are conclusive proof as to the voyage on which she is engaged, unless
she is found clearly out of the course indicated by her papers and
unable to give adequate reasons to justify such deviation.
ART. 33.--Conditional contraband is liable to capture if it is shown
to be destined for the use of the armed forces or of a government
department of the enemy state, unless in this latter case the
circumstances show that the goods cannot in fact be used for the
purposes of the war in progress. This latter exception does not apply
to a consignment coming under Article 24 (4).
ART. 34.---The destination referred to in Article 33 is presumed to
exist if the goods are consigned to enemy authorities, or to a
contractor established in the enemy country who, as a matter of
common knowledge, supplies articles of this kind to the enemy. A
similar presumption arises if the goods are consigned to a fortified
place belonging to the enemy, or other place serving as a base for
the armed forces of the enemy. No such presumption, however, arises
in the case of a merchant vessel bound for one of these places if it
is sought to prove that she herself is contraband. In cases where the
above presumptions do not arise, the destination is presumed to be
innocent. The presumptions set up by this article may be rebutted.
ART. 35.--Conditional contraband is not liable to capture, except
when found on board a vessel bound for territory belonging to or
occupied by the enemy, or for the armed forces of the enemy, and when
it is not to be discharged in an intervening neutral port. The ship's
papers are conclusive proof both as to the voyage on which the vessel
is engaged and as to the port of discharge of the goods, unless she
is found clearly out of the course indicated by her papers, and
unable to give adequate reasons to justify such deviation.
ART. 36.--Notwithstanding the provisions of Article 35, conditional
contraband, if shown to have the destination referred to in Article
33, is liable to capture in cases where the enemy country has no
seaboard.
ART. 37.--A vessel carrying goods liable to capture as absolute or
conditional contraband may be captured on the high seas or in the
territorial waters of the belligerents throughout the whole of her
voyage, even if she is to touch at a port of call before reaching the
hostile destination.
ART. 38.--A vessel may not be captured on the ground that she has
carried contraband on a previous occasion if such carriage is in
point of fact at an end.
ART. 39.--Contraband goods are liable to condemnation.
ART. 40.--A vessel carrying contraband may be condemned if the
contraband, reckoned either by value, weight, volume or freight,
forms more than half the cargo.
ART. 41.--If a vessel carrying contraband is released, she may be
condemned to pay the costs and expenses incurred by the captor in
respect of the proceedings in the national prize court and the
custody of the ship and cargo during the proceedings.
ART. 42.--Goods which belong to the owner of the contraband and are
on board the same vessel are liable to condemnation.
ART. 43.--If a vessel is encountered at sea while unaware of the
outbreak of hostilities or of the declaration of contraband which
applies to her cargo, the contraband cannot be condemned except on
payment of compensation; the vessel herself and the remainder of the
cargo are not liable to condemnation or to the costs and expenses
referred to in Article 41. The same rule applies if the master, after
becoming aware of the outbreak of hostilities, or of the declaration
of contraband, has had no opportunity of discharging the contraband.
A vessel is deemed to be aware of the existence of a state of war, or
of a declaration of contraband, if she left a neutral port
subsequently to the notification to the power to which such port
belongs of the outbreak of hostilities or of the declaration of
contraband respectively, provided that such notification was made in
sufficient time. A vessel is also deemed to be aware of the existence
of a state of war if she left an enemy port after the outbreak of
hostilities.
ART. 44.--A vessel which has been stopped on the ground that she is
carrying contraband, and which is not liable to condemnation on
account of the proportion of contraband on board, may, when the
circumstances permit, be allowed to continue her voyage if the master
is willing to hand over the contraband to the belligerent warship.
The delivery of the contraband must be entered by the captor on the
log-book of the vessel stopped, and the master must give the captor
duly certified copies of all relevant papers. The captor is at
liberty to destroy the contraband that has been handed over to him
under these conditions.
See Hautefeuille, _Des droits et devoirs des nations neutres_ (2nd
ed., 1858); Perels, _Droit maritime international_, traduit par
Arendt (Paris, 1884); Moore, _Digest of International Law_ (1906); L.
Oppenheim, _International Law_ (1907); Barclay, _Problems of
International Practice and Diplomacy_ (1907). See also Hall,
_International Law on Analogues of Contraband_; Smith and Sibley,
_International Law as interpreted during the Russo-Japanese War,
1905_, on "Malacca" and "Prinz Heinrich" cases (mails). (T. BA.)