it radiates. On such attempts depends the possibility of measuring the temperature of a hot body by means of the light it emits. This is evidently a most desirable object, since, if that were possible, one of the great difficulties of pyrometry-the bringing of the measuring instrument to the temperature of the body under investigation-would immediately disappear. At present, however, there is no general agreement among scientific men as to the form the relation takes. We cannot here do more than refer to the "Report on Spectrum Analysis," in the British Association's Reports for 1881 and 1884, for references to the literature of the subject. See RADIATION. (W. N. s.)

PYROTECHNY is the art of producing pleasing scenic effects by means of fire. It is not held to include the manufacture of inflammable and explosive substances for other purposes. The use of fireworks for purposes of display is not a modern invention, for it appears to have existed in China in very ancient times; but the secret of constructing them remained unknown in Europe till about the 13th century, when the knowledge of GUNPOWDER (q.v.) crept in from the East. In modern times the art has been gradually improved by the work of specialists, who have had the advantage of being guided by scientific knowledge. The value of such knowledge to the pyrotechnist is extremely great; for he must be governed by the principles of chemistry in the selection of his materials, and his various contrivances for turning them to the best account are subject to the laws of mechanics. As in all such cases, however, science is useless without the aid of practical experience and acquired manual dexterity.

mental fact of pyrotechny,-that, with proper attention | Such are the starting-powder, which first catches the fire, to the chemical nature of the substances employed, solid mixtures (compositions or fuses) may be prepared which contain within themselves all that is essential for the production of fire.

If nitre and chlorate of potash, with other salts of nitric and chloric acids and a few similar compounds, be❘ grouped together as oxidizing agents, most of the other materials used in making firework compositions may be classed as oxidizable substances. Every composition must contain at least one sample of each class: usually there are present more than one oxidizable substance, and very often more than one oxidizing agent. In all cases the proportions by weight which the ingredients of a mixture bear to one another is a matter of much importance, for it greatly affects the manner and rate of combustion. The most important oxidizable substances employed are charcoal and sulphur. These two, it is well known, when properly mixed in certain proportions with the oxidizing agent nitre, constitute gunpowder; and gunpowder plays an important part in the construction of most fireworks. It is sometimes employed alone, when a strong explosion is required; but more commonly it is mixed with one or more of its own ingredients and with other matters. In addition to charcoal and sulphur, the following oxidizable substances are more or less employed :-many compounds of carbon, such as sugar, starch, resins, &c.; certain metallic compounds of sulphur, such as the sulphides of arsenic and antimony; a few of the metals themselves, such as iron, zinc, magnesium, antimony, copper. Of these metals iron (cast-iron and steel) is more used than any of the others. They are all employed in the form of powder or small filings. They do not contribute much to the burning power of the composition; but when it is ignited they become intensely heated and are discharged into the air, where they oxidize more or less completely and cause brilliant sparks and scintillations.

The

Sand, sulphate of potash, calomel, and some other substances, which neither combine with oxygen nor supply it, are sometimes employed as ingredients of the compositions in order to influence the character of the fire. This may be modified in many ways. Thus the rate of combustion may be altered so as to give anything from an instantaneous explosion to a slow fire lasting many minutes. flame may be clear, smoky, or charged with glowing sparks. But the most important characteristic of a fire one to which great attention is paid by pyrotechnistsis its colour, which may be varied through the different shades and combinations of yellow, red, green, and blue. These colours are imparted to the flame by the presence in it of the heated vapours of certain metals, of which the following are the most important:-sodium, which gives a yellow colour; calcium, red; strontium, crimson; barium, green; copper, green or blue, according to circumstances. Suitable salts of these metals are much used as ingredients of fire mixtures; and they are decomposed and volatilized during the process of combustion. Very often the chlorates and nitrates are employed, as they serve the double purpose of supplying oxygen and of imparting colour to the flame.

The number of fire mixtures actually employed is very great; for the requirements of each variety of firework, and of almost each size of each variety, are different. Moreover, every pyrotechnist has his own taste in the matter of compositions. They are capable, however, of being classified according to the nature of the work to which they are suited. Thus there are rocket-fuses, gerbefuses, squib-fuses, star-compositions, &c.; and, in addition, there are a few which are essential in the construction of most fireworks, whatever the main composition may be.

the bursting-powder, which causes the final explosion, and the quick-match (cotton-wick, dried after being saturated with a paste of gunpowder and starch), employed for connecting parts of the more complicated works and carrying the fire from one to another. Of the general nature of fuses an idea may be had from the following two examples, which are selected at hazard from among the numerous recipes for making, respectively, tourbillion fire and green stars :

Tourbillion.
Meal gunpowder
Nitre.....
Sulphur
Charcoal
Steel filings..

Green Stars.

.24 parts. Chlorate of potash ...16 parts. Nitrate of baryta ...48

10

7

Sulphur

4

Charcoal

Shellac.

Calomel

.12

Sulphide of copper... 2

Although the making of compositions is of the first importance, it is not the only operation with which the pyrotechnist has to do; for the construction of the cases in which they are to be packed, and the actual processes of packing and finishing, require much care and dexterity. These cases are made of paper or pasteboard, and are generally of a cylindrical shape. In size they vary greatly, according to the effect which it is desired to produce. The relations of length to thickness, of internal to external diameter, and of these to the size of the openings for discharge, are matters of extreme importance, and must always be attended to with almost mathematical exactness and considered in connexion with the nature of the composition which is to be used.

There is one very important property of fireworks that is due more to the mechanical structure of the cases and the manner in which they are filled than to the precise chemical character of the composition, i.e., their power of motion. Some are so constructed that the piece is kept at rest and the only motion possible is that of the flame and sparks which escape during combustion from the mouth of the case. Others, also fixed, contain, alternately with layers of some more ordinary composition, balls or blocks of a special mixture cemented by some kind of varnish; and these stars, as they are called, shot into the air, one by one, like bullets from a gun, blaze and burst there with striking effect. But in many instances motion is imparted to the firework as a whole, to the case as well as to its contents. This motion, various as it is in detail, is almost entirely one of two kinds,-rotatory motion round a fixed point, which may be the centre of gravity of a single piece or that of a whole system of pieces, and free ascending motion through the air. In all cases the cause of motion is the same, viz., that large quantities of gaseous matter are formed by the combustion, that these can escape only at certain apertures, and that a backward pressure is necessarily exerted at the point opposite to them. When a large gun is discharged, it recoils a few feet. Movable fireworks may be regarded as very light guns loaded with heavy charges; and in them the recoil is therefore so much greater as to be the most noticeable feature of the discharge; and it only requires proper contrivances to make the piece fly through the air like a sky-rocket or revolve round a central axis like a Catherine wheel. Beauty of motion is hardly less important in pyrotechny than brilliancy of fire and variety of colour.

The following is a brief description of some of the forms of firework most employed:

Fired Fires.-Theatre fires consist of a slow composition which

may be heaped in a conical pile on a tile or a flagstone and lit at the apex. They require no cases. Usually the fire is coloured,green, red, or blue; and beautiful effects are obtained by illuminating buildings with it. It is also used on the stage; but, in that

result of which is that an enormous quantity of heated gases collects
in the hollow bore and the gases, forcing their way downwards
through the narrow opening, urge the rocket up through the air.
The top of the case is closed by a plaster-of-Paris plug. A hole passes
through this and is filled with a fuse, which serves to communicate
the fire to the head after the body is burned out. This head, which
is made separately and fastened on after the body is packed, consists
of a short cylindrical paper chamber with a conical top. It serves
the double purpose of cutting a way through the air and of holding
the garniture of stars, sparks, crackers, serpents, gold and silver
rain, &c., which are scattered by bursting fire as soon as the rocket
reaches the highest point of its path. A great variety of beautiful
effects may be obtained by the exercise of ingenuity in the choice
and construction of this garniture. Many of the best results have
been obtained by unpublished methods which must be regarded
as the secrets of the trade. The stick of the sky-rocket serves the
purpose of guiding and balancing it in its flight; and its size must
be accurately adapted to the dimensions of the case. In winged
rockets the stick is replaced by cardboard wings, which act like
the feathers of an arrow. A girandole is the simultaneous discharge
of a large number of rockets (often from one hundred to two
hundred), which either spread like a peacock's tail or pierce the
sky in all directions with rushing lines of fire. This is usually the
final feat of a great pyrotechnic display.

case, the composition must be such as to give no suffocating or
poisonous fumes. Bengal lights are very similar, but are piled in
saucers, covered with gummed paper, and lit by means of pieces of
match. Marroons are small boxes wrapped round several times
with lind cord and filled with a strong composition which explodes
with a loud report. They are generally used in batteries, or in
combination with some other form of firework. Squibs are straight
cylindrical cases about 6 inches long, firmly closed at one end, tightly
packed with a strong composition, and capped with touch-paper.
Usually a little bursting-powder is put in before the ordinary com-
position, so that the fire is finished by an explosion. The character
of the fire is, of course, susceptible of great variation in colour, &c.
Crackers are characterized by the cases being doubled backwards
and forwards several times, the folds being pressed close and secured
by twine. One end is primed; and when this is lit the cracker
burns with a hissing noise, and a loud report occurs every time the
fire reaches a bend. If the cracker is placed on the ground, it will
give a jump at each report; so that it cannot quite fairly be classed
among the fixed fireworks. Roman candles are straight cylindrical
cases filled with layers of composition and stars alternately. These
stars are simply balls of some special composition, usually containing
metallic filings, made up with gum and spirits of wine, cut to the
required size and shape, dusted with gunpowder, and dried. They
are discharged like blazing bullets several feet into the air, and
produce a beautiful effect, which may be enhanced by packing stars
of differently coloured fire in one case. Gerbes are choked cases,
not unlike Roman candles, but often of much larger size. Their
fire spreads like a sheaf of wheat. They may be packed with vari-
ously coloured stars, which will rise 30 feet or more. Lances
are small straight cases charged with compositions like those used
for making stars. They are mostly used in complex devices, for
which purpose they are fixed with wires on suitable wooden frames.
They are connected by leaders, i.e., by quick-match enclosed in
paper tubes, so that they can be regulated to take fire all at the
same time, singly, or in detachments, as may be desired. The de-
vices constructed in this way are often of an extremely elaborate
character; and they include all the varieties of lettered designs, of
fixed suns, fountains, palm-trees, waterfalls, mosaic work, High-from Pyrrhus, the son of Achilles, connected also with the

land tartan, &c.

Rotating Fireworks.-Pin or Catherine wheels are long paper cases filled with a composition by means of a funnel and packingwire and afterwards wound round a disk of wood. This is fixed by a pin, sometimes vertically and sometimes horizontally; and the outer primed end of the spiral is lit. As the fire escapes the recoil causes the wheel to revolve in an opposite direction and often with considerable velocity. Pastiles are very similar in principle and construction. Instead of the case being wound in a spiral and made to revolve round its own centre point, it may be used as the engine to drive a wheel or other form of framework round in a circle. Many varied effects are thus produced, of which the fire wheel is the simplest. Straight cases, filled with some fire-composition, are attached to the end of the spokes of a wheel or other mechanism capable of being rotated. They are all pointed in the same direction at an angle to the spokes, and they are connected together by leaders, so that each, as it burns out, fires the one next it. The pieces may be so chosen that brilliant effects of changing colour are produced; or various fire-wheels of different colours may be combined, revolving in different planes and different directions -some fast and some slowly. Bisecting wheels, plural wheels, caprice wheels, spiral wheels, are all more or less complicated forms; and it is possible to produce, by mechanism of this nature, a model in fire of the solar system.

Ascending Fireworks.-Tourbillions are fireworks so constructed as to ascend in the air and rotate at the same time, forming beautiful spiral curves of fire. The straight cylindrical case is closed at the centre and at the two ends with plugs of plaster of Paris, the composition occupying the intermediate parts. The fire finds vent by six holes pierced in the case. Two of these are placed close to the ends, but at opposite sides, so that one end discharges to the right and the other to the left; and it is this which imparts the rotatory motion. The other holes are placed along the middle line of what is the under-surface of the case when it is laid horizontally on the ground; and these, discharging downwards, impart an upward motion to the whole. A cross piece of wood balances the tourbillion; and the quick-match and touch-paper are so arranged that combustion begins at the two ends simultaneously and does not reach the holes of ascension till after the rotation is fairly begun. The sky-rocket is generally considered the most beautiful of all fireworks; and it certainly is the one that requires most skill and science in its construction. It consists essentially of two parts,-the body and the head. The body is a straight cylinder of strong pasted paper and is choked at the lower end, so as to present only a narrow opening for the escape of the fire. The composition does not fill up the case entirely, for a central hollow conical bore extends from the choked mouth up the body for three quarters of its length. This is an essential feature of the rocket. It allows of nearly the whole composition being fired at once; the

For a description of rockets used in war, see AMMUNITION.
See Chertier, Sur les Feux d'Artifice (Paris, 1841; 2d ed. 1854); Mortimer,
Manual of Pyrotechny (London, 1856); Tessier, Chimie pyrotechnique, ou Traité
pratique des Feux Colorés (Paris, 1858); Richardson and Watts, Chemical Tech-
nology, s.v. "Pyrotechny" (London, 1863-67); Thomas Kentish, The Pyro-
technist's Treasury (London, 1878); Websky, Luftfeuerwerkkunst (Leipsic,
1878).
(0. M.)

PYRRHO. See SCEPTICISM,

PYRRHUS. The name of Pyrrhus, king of Epirus,
owes its chief fame in history to the fact that with his
invasion of Italy in the early part of the 3d century B.C.
Greece and Rome for the first time came definitely into
contact. Born about the year 318, and claiming descent

royal family of Macedonia through Olympias, the mother
of Alexander the Great, he became when a mere stripling
king of the wild mountain tribes of Epirus, and learned
how to fight battles in the school of Demetrius Poliorcetes
(the Besieger) and of his father Antigonus. He fought
by their side in his seventeenth year at the memorable
battle of Ipsus in Phrygia, in which they were decisively
defeated by the combined armies of Seleucus and Lysi-
machus. Soon afterwards he was sent to the court of
Ptolemy of Egypt at Alexandria as a pledge for the faith-
ful carrying out of a treaty of alliance between Ptolemy
and Demetrius, as his sister Deidamia was the wife of the
latter. Through Ptolemy, whose step-daughter Antigone
he married, he was enabled to establish himself firmly on
the throne of Epirus, and he became a formidable opponent
to Demetrius, who was now king of Macedonia and the
leading man in the Greek world. He won a victory over
one of Demetrius's generals in Ætolia, invaded Macedonia,
and forced Demetrius to conclude a truce with him. For
a brief space of about seven months he had possession of
a large part of Macedonia, Demetrius finding it convenient
to make this surrender on condition that Pyrrhus did not
meddle with the affairs of the Peloponnesus. But in 286
he was defeated by Lysimachus at Edessa, driven out of
Macedonia, and compelled to fall back on his little king-
dom of Epirus. In 280 came the great opportunity of
his life, the embassy from the famous Greek city Taren-
tum in southern Italy with a request for aid against
Rome, whose hostility the Tarentines had recklessly pro-
voked. Pyrrhus had a trusted friend and adviser in Cineas
of Thessaly, a persuasive speaker and a clever diplomatist,
and he at once sent him over with 3000 men to Tarentum

with a view to prepare matters. He himself soon fol-
lowed, after a disastrous passage across the Adriatic, with a
miscellaneous force, furnished him partly by the assistance
of Ptolemy, of about 25,000 men, with some elephants,
his best troops being some Macedonian infantry and
Thessalian cavalry.
He had counted on an army of Italian
mercenaries, but the Tarentines and the Italian Greeks

generally shrank from anything like serious effort and resented his calling upon them for men and money. Rome meantime raised a special war contribution, called on her subjects and allies for their full contingent of troops, and posted strong garrisons in all towns of doubtful fidelity. She was now quite the dominant power in Italy, but her position was critical, as in the north she had had trouble with the Etruscans and Gauls, while in the south the Lucanians and Bruttians were making common cause with Tarentum and the Greek cities. In fact there was the possibility of a most formidable coalition of the Italian peoples both in the north and in the south against Rome, and so Pyrrhus had a good deal on which to build his hopes of success. For the first time in history Greeks and Romans met in battle at Heraclea near the shores of the Gulf of Tarentum, and the cavalry and elephants of Pyrrhus secured for him a complete victory, though at so heavy a loss as to convince him of the great uncertainty of final success. Although he now had the Samnites as well as the Lucanians and Bruttians and all the Greek cities of southern Italy with him, he found every city closed against him as he advanced on Rome through Latium, and his dexterous minister Cineas utterly failed to negotiate a peace, the old blind Appius Claudius declaring in the senate that Rome never negotiated with a foreign enemy on Italian ground. In the second year of the war, 279, Pyrrhus again defeated a Roman army at Asculum (Ascoli) in Apulia, but he was no nearer decisive success, as Rome still had armies in the field and her Italian confederation was not broken up. For a while he quitted Italy for Sicily with the view of making himself the head of the Sicilian Greeks and driving the Carthaginians out of the island. In his military operations he was on the whole successful, and Rome and Carthage in face of the common danger concluded an offensive and defensive alliance against him. He passed three years in Sicily, but through want of political tact he gave offence to the Greek cities, which he treated rather too much in the fashion of a despot, not paying any respect to their local constitutions or sufficiently humouring their republican tastes and love of independence. He thus lost a good opportunity of uniting both the Italian and Sicilian Greeks against Rome. On his return to Italy in 276 he had neither men nor money adequately supplied him, as Tarentum and the other Greek cities had no confidence in him. It is said that he was thoroughly disheartened, and was haunted by mysterious dreams and forebodings which followed on an act which he imagined had involved him in the guilt of sacrilege. He made indeed one more effort, and engaged a Roman army at Beneventum in the Samnite country, but his arrangements for the battle miscarried, and he was defeated with the loss of his camp and the greater part of his army. He had made a fair trial of the strength of Rome and had been utterly baffled. Nothing remained but to go back to his allies at Tarentum. He left a garrison in the city and returned the following year to his home in Epirus after a six years' absence. The brief remainder of his life was passed in camps and battles, without, however, any glorious result. He won a victory over Antigonus Gonatas, king of Macedonia, on Macedonian ground. In 273 he was invited into the Peloponnesus to settle at the sword's point a dispute about the royal succession at Sparta. He besieged the city, but was repulsed with great loss. Next he went to Argos at the invitation of a political faction, and here in the confusion of a fight by night in the streets he met his death in his forty-sixth year from the hand of a woman, who hurled a ponderous roof-tile upon his head just at the moment, it is said, when he was striking a blow at her son. Pyrrhus was no doubt a brilliant and dashing soldier,

but he was aptly compared "to a gambler who made many
good throws with the dice, but could not make the proper
use of the game." There was something chivalrous about
him which seems to have made him a general favourite.
After his death Macedonia had for a time at least nothing
to fear, and the liberty of Greece was quite at the mercy
of that power.

For Pyrrhus, English readers will do well to consult Thirlwall,
Greece, vols. vii., viii.; Mommsen, History of Rome, ii. 7; Niebuhr,
Lectures on Roman History, lects. 1., li. Plutarch's Life of Pyrrhus
is the fullest of our original sources of information, and there is
frequent mention of him in Polybius.
PYTHAGORAS AND PYTHAGOREANS. Pythagoras
is one of those figures which have so impressed the imagina-
tion of succeeding times that their historical lineaments are
difficult to discern through the mythical haze that envelops
them. Animated, as it would appear, not merely by the
philosophic thirst for knowledge but also by the enthusiasm
of an ethico-religious reformer, he became, centuries after
his death, the ideal hero or saint of those who grafted a
mystical religious asceticism on the doctrines of Plato.
Writings were forged in his name.
Lives of him were
written which gather up in his person all the traits of
the philosophic wise man, and surround him besides with
the nimbus of the prophet and wonder-worker. He is
described by his Neoplatonic biographers as the favourite
and even the son of Apollo, from whom he received his
doctrines by the mouth of the Delphic priestess. We
read that he had a golden thigh, which he displayed to
the assembled Greeks at Olympia, and that on another
occasion he was seen in Crotona and Metapontum at one
and the same time. He is said to have tamed wild beasts
by a word and to have foretold the future, while many
stories turn upon the knowledge he was reported to retain
of his personality and deeds in former states of existence.
Thus, as Zeller truly remarks, the information respecting
Pythagoreanism and its founder grows fuller and fuller
the farther removed in time it is from its subject. The
authentic details of Pythagoras's career, on the other hand,
are meagre enough and merely approximate in character.
He was a native of Samos, and the first part of his life
may therefore be said to belong to that Ionian seaboard
which had already witnessed the first development of
philosophic thought in Greece. The exact year of his
birth has been variously placed between 586 and 569
B.C., but 582 may be taken as the most probable date.
Some of the accounts make him the pupil of Anaximander;
but such an assertion lies so ready to hand in the circum-
stances of time and place that we cannot build with any
assurance upon the suggested connexion with the Ionic
school. It is probable, however, that Pythagoras was
aware of their speculations, seeing that he left behind
him in Ionia the reputation of a learned and universally
informed man. "Of all men Pythagoras, the son of
Mnesarchus, was the most assiduous inquirer," says Hera-
clitus, and then proceeds in his contemptuous fashion
to brand his predecessor's wisdom as only eclectically
compiled information or polymathy (rovμabía). This
accumulated wisdom, as well as most of the tenets of the
Pythagorean school, was attributed in antiquity to the
extensive travels of Pythagoras, which brought him in
contact (so it was said) not only with the Egyptians, the
Phoenicians, the Chaldæans, the Jews, and the Arabians,
but also with the Druids of Gaul, the Persian Magi, and
the Brahmans. But these tales are told of too many of
the early philosophers to be received implicitly; they
represent rather the tendency of a later age to connect
the beginnings of Greek speculation with the hoary re-
ligions and priesthoods of the East. There is no intrinsic
improbability, however, in the statement that Pythagoras
visited Egypt and other countries of the Mediterranean,
XX. -18

ナ

Pythagorean Philosophy.

The central thought of the Pythagorean philosophy is the idea of number, the recognition of the numerical and mathematical relations of things. In the naive speculation of an early age the abstract consideration of these relations was tantamount to assert

for travel was then one of the few ways of gathering | was not without an important influence upon Plato, and knowledge. Some of the accounts represent Pythagoras Philolaus had also disciples in the stricter sense. But as as deriving much of his mathematical knowledge from an a philosophic school Pythagoreanism became extinct in Egyptian source. Herodotus traces the doctrine of metem- Greece about the middle of the 4th century. In Italypsychosis to Egypt, as well as the practice of burying the where, after a temporary suppression, it attained a new dead exclusively in linen garments, but he does not men- importance in the person of Archytas, ruler of Tarentum~ tion any visit of Pythagoras to that country. There is the school finally disappeared about the same time. thus little more than conjecture to fill out the first half of the philosopher's life. The historically important part of his career begins with his emigration to Crotona, one of the Dorian colonies in the south of Italy. Nothing is known with certainty of the reasons that led to this step, which he appears to have taken about the year 529; ing their essential existence as the causes of phenomena. Hence perhaps the ethical temper which can be traced in the the Pythagorean thought crystallized into the formula that all Pythagorean school attracted the founder towards the things are number, or that number is the essence of everything. "The Pythagoreans seem," says Aristotle, "to have looked upon sterner Dorian character. At Crotona Pythagoras speedily number as the principle and, so to speak, the matter of which became the centre of a widespread and influential organiza- existences consist"; and again, "they supposed the elements of tion, which seems to have resembled a religious brother-numbers to be the elements of existence, and pronounced the whole heaven to be harmony and number." "Number," says Philolaus, hood or an association for the moral reformation of society is great and perfect and omnipotent, and the principle and guide much more than a philosophic school. Pythagoras appears, of divine and human life." Fantastical as such a proposition indeed, in all the accounts more as a moral reformer than sounds, we may still recognize the underlying truth that prompted as a speculative thinker or scientific teacher; and it is it if we reflect that it is number or definite mathematical relation that separates one thing from another and so in a sense makes them noteworthy that the only one of the doctrines of the school things. Without number and the limitation which number brings which is definitely traceable to Pythagoras himself is the there would be only chaos and the illimitable, a thought abhorrent ethico-mystical doctrine of transmigration. The aim of to the Greek mind. Number, then, is the principle of order, the the brotherhood was the moral education and purification principle by which a cosmos or ordered world subsists. So we may perhaps render the thought that is crudely and sensuously expressed of the community; and it seems to have been largely based in the utterances of the school. They found the chief illustrations, upon a revival of the Dorian ideal of abstinence and hardior rather grounds, of their position in the regular movements of hood along with certain other traits of a more definitely the heavenly bodies and in the harmony of musical sounds, the religious character, which were probably due to the influ- dependence of which on regular mathematical intervals they were ence of the mysteries. But many details of life and ritual, of the spheres combines both ideas: the seven planets are the seven apparently the first to discover. The famous theory of the harmony such as abstinence from animal food and from beans, golden chords of the heavenly heptachord. celibacy, and even community of goods, have been fathered Immediately connected with their central doctrine is the theory by the organized asceticism of a later period upon the of opposites held by the Pythagoreans. Numbers are divided into original followers of Pythagoras. Ethics, according to the odd and even, and from the combination of odd and even the numbers themselves (and therefore all things) seem to result. The Greek and especially according to the Dorian conception, odd number was identified with the limited, the even with the unbeing inseparably bound up with the general health of the limited, because even numbers may be perpetually halved, whereas state, we are not surprised to find the Pythagoreans reprethe odd numbers (at least the earlier ones), being without factors, seem to stand in solid singleness. All things, accordingly, were sented as a political league; nor is it wonderful that their derived by the Pythagoreans from the combination of the limited following was among the aristocracy, and that they formed and the unlimited; and it is in harmony with the Greek spirit the staunchest supporters of the old Dorian constitutions. that the place of honour is accorded to the odd or the limited. It is unfair, however, to speak of the league as primarily Following out the same thought, they developed a list of ten fundaa political organization, wide though its political ramifica- framed by later philosophers :-(1) limited and unlimited; (2) odd mental oppositions, which roughly resembles the tables of categories tions must latterly have become. Its entanglement with and even; (3) one and many; (4) right and left; (5) masculine politics was in the end fatal to its existence. The authori- and feminine; (6) rest and motion; (7) straight and crooked; (8) ties differ hopelessly in chronology, but according to the light and darkness; (9) good and evil; (10) square and oblong. balance of evidence the first reaction against the Pytha-physical, and ethical contrasts are characteristic of the infancy of The arbitrariness of the list and the mingling of mathematical, goreans took place in the lifetime of Pythagoras himself speculation. The union of opposites in which consists the exist after the victory gained by Crotona over Sybaris in the ence of things is harmony; hence the expression already quoted year 510. Dissensions seem to have arisen about the that the whole heaven or the whole universe is harmony. But it allotment of the conquered territory, and an adverse party sent the whole system as founded on the opposition of unity and is to be noted that interpretations of Pythagoreanism which reprewas formed in Crotona under the leadership of Cylon. duality, and suppose this to have been explicitly identified with This was probably the cause of Pythagoras's withdrawal the opposition of form and matter, of divine activity and passive to Metapontum, which an almost unanimous tradition material, must be unhesitatingly rejected as betraying on the surassigns as the place of his death in the end of the 6th or face their post-Platonic origin. Still more is this the case when in Neoplatonic fashion they go on to derive this original opposition the beginning of the 5th century. The league appears to from the supreme Unity or God. The further speculations of the have continued powerful in Magna Græcia till the middle Pythagoreans on the subject of number rest mainly on analogies, of the 5th century, when it was violently trampled out which often become capricious and tend to lose themselves at last by the successful democrats. The meeting-houses of the in a barren symbolism. The decade, as the basis of the numerical Pythagoreans were everywhere sacked and burned; mensystem, appeared to them to comprehend all other numbers in itself, and to it are applied, therefore, the epithets quoted above tion is made in particular of "the house of Milo" in of number in general. Similar language is held of the number Crotona, where fifty or sixty of the leading Pythagoreans "four," because it is the first square number and is also the potenwere surprised and slain. The persecution to which the tial decade (1+2+3+4=10); Pythagoras is celebrated as the discoverer of the holy TerpaкTús, "the fountain and root of ever-living brotherhood was subjected throughout Magna Græcia was nature." "Seven" is called Tapeévos and 'Aonon, because within the immediate cause of the spread of the Pythagorean the decade it has neither factors nor product. Five," on the philosophy in Greece proper. Philolaus, who resided at other hand, signifies marriage, because it is the union of the first Thebes in the end of the 5th century (cf. Plato, Phado, masculine with the first feminine number (3+2, unity being con61D), was the author of the first written exposition of sidered as a number apart). The thought already becomes more fanciful when " one is identified with reason, because it is unthe system. Lysis, the instructor of Epaminondas, was changeable; "two with opinion, because it is unlimited and another of these refugees. This Theban Pythagoreanism indeterminate; "four" with justice, because it is the first square

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