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spoonfuls of the same, taken once an hour, has proved beneficial in the dropsy and anasarca. It has also been found serviceable in consumptive complaints.

POLYGAMIA, Toλʊç many, and yaμoç marriage. This term, expressing an intercommunication of sexes, is applied by Linnæus, both to plants and flowers. A polygamous plant is that which bears both hermaphrodite flowers and male and female, or both.

POLYGAMIE, orders of. See BOTANY. POLYGAMOUS PLANTS. See BOTANY. POLYGAMUM, a species of holcus, by some erroneously reckoned a species of panicum. It is a native of Africa, and brought from thence to the West Indies. It agrees with every soil and situation; and in many of the rocky and barren parts of Jamaica, which formerly could not support a goat, may now be seen large herds of cattle, sheep, and horses, in excellent order, and fitted for all the purposes of rural economy or the market, feeding on Guinea grass. It is best propagated by the roots, and planted about three feet asunder. In six months it grows very tall, so as often to be six feet high. At this time horses and cattle are turned in to eat what they please of it; and, while they plough up the surface of the ground with their feet, they shake the ripe seed. The rank grass is afterwards cut down, burned off, and the old stock rooted up and thrown away. The seeds vegetate and throw up a plentiful crop; which with common attention will last many years. For this purpose a Guinea grass pasture requires to be kept clean, and supplied in particular places as may be necessary from time to time. The fields ought to be divided into parks by fences, and the cattle shifted from one enclosure to another occasionally. POLYG'AMY, n. s. Į Fr. polygamie; Gr. Η πολυγαμία. Plurality of wives: one who holds the lawfulness of polygamy.

POLYG'AMIST.

He lived to his death in the sin of polygamy, without any particular repentance. Perkins.

They allow no polygamy: they have ordained that none do intermarry or contract, until a month be past from their first interview.

Bacon.

Christian religion, prohibiting polygamy, is more agreeable to the law of nature, that is, the law of God, than Mahometanism that allows it; for one man, as having many wives by law, signifies nothing, unless there were many women to one man in nature also. Graunt.

Polygamy is the having more wives than one at Locke.

once.

POLYGAMY, LAWS RESPECTING. Polygamy is universally deemed unlawful, and even unnatural, throughout all Christian countries. But a plurality of wives was permitted not only among the Hebrews, but also, as Selden observes, among most other ancient nations. The Romans indeed were more severe in their morals, and never practised it, though it was not forbidden among them; and Marc Antony is mentioned as the first who took the liberty of having two wives. From that time it became pretty frequent in the empire till the reigns of Theodosius, Honorius, and Arcadius, who first prohibited it by express law in 393. After this the emperor Valentinian, by an edict, permitted all the subjects of the

empire, if they pleased, to marry several wives; nor does it appear, from the ecclesiastical history of those times, that the bishops made any opposition to this introduction of polygamy. In Germany, Holland, and Spain, this offence is differently punished. By a constitution of Charles V. it was a capital crime. By the laws of ancient and modern Sweden it is punished with death. In Scotland it is punished as perjury. In England it is enacted by statute 1 Jac. I. cap. 11, that if any person, being married, do afterwards marry again, the former husband or wife being alive, it is felony, but within the benefit of clergy. The first wife in this case shall not be admitted as an evidence against her husband, because she is the true wife; but the second may, for indeed she is no wife at all; and so vice versâ of a second husband. This act makes an exception to five cases, in which such second marriage, though in the three first it is void, is, however, no felony. 1. Where either party hath continually been abroad for seven years, whether the party in England had notice of the other's being living or not. 2. Where either of the parties hath been absent from the other seven years within this kingdom, and the remaining party hath had no notice of the other's being alive within that time. 3. Where there is a divorce or separation a mensa et thoro by sentence in the ecclesiastical court. 4. Where the first marriage is declared absolutely void by any such sentence, and the parties loosed a vinculo. Or, 5. Where either of the parties was under the age of consent at the time of the first marriage; for in such case the first marriage was voidable by the disagreement of either party, which this second marriage very clearly amounts to. But if at the age of consent the parties had agreed to the marriage, which completes the contract, and is indeed the real marriage, and afterwards one of them should marry again, judge Blackstone apprehends that such second marriage would be within the reason and penalties of the act.

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Montesquieu contends that polygamy is physically conformable to the climate of Asia. The season of female beauty precedes that of their reason, and their beauty from its prematurity soon decays. The empire of their charms is short. It is therefore natural, he says, that a man should leave one wife to take another; that he should seek a renovation of those charms that had withered in his possession. But are these the real circumstances of polygamy?' asks Mr. Marsden, Surely not. It implies the contemporary enjoyment of women in the same predicament; and,' he adds, I should consider it as a vice that has its source in the influence of a warm atmosphere upon the passions of men, which, like the cravings of other disordered appetites, make them miscalculate their wants.' Moreover, the climate which expands the desires of the men, and prompts a more unlimited exertion of their faculties, does not inspire their constitutions with proportionate vigor; but, on the contrary, renders them in this respect inferior to the inhabitants of the temperate zone; whilst it equally influences the desires of the opposite sex, without being found to diminish from their capacity of enjoyment. Whence we may infer, that if nature intended one woman only should

be the companion of one man in the colder regions of the earth, it appears also intended, à fortiori, that the same law should be observed in the hotter; inferring nature's design, not from the desires, but from the abilities with which she has endowed mankind. Montesquieu also suggested that the inequality in the comparative numbers of each sex, born in Asia, which is represented to be greatly superior on the female side, may have relation to the law that allows polygamy, But it is replied that there is strong reason for denying the reality of this supposed excess. Marsden asserts that the proportion of the sexes throughout Sumatra does not sensibly differ from that ascertained in Europe; nor could he ever learn, from the inhabitants of the many eastern islands with whom he had an opportunity of conversing, that they were conscious of any material disproportion in this respect.

Major Grant observes that the males and females brought into the world are so nearly on a balance, that only abating for a little excess on the side of the males, in the proportion of about nineteen to eighteen, to make up for the extraordinary exposures of men in war, and at sea: it evidently follows that nature only intends one wife, or one husband, for the same person; since, if they have more, some others must go without any at all. Hence he concludes, that the Christian law, which prohibits polygamy, is agreeable to the law of nature.

It is well known that the poet Milton was an advocate for great latitude in the causes of divorce; but his notions respecting polygamy were not fully understood, until the late publilication of his Treatise on Christian Doctrine. He was the advocate of polygamy, as amongst the privileges of the male sex. See our article

MILTON.

Another of the boldest and most specious modern advocate of polygamy was the late Rev. Mr. Madan, an evangelical clergyman of the church of England, who, in 1780, published a work, under the title of Thelypthora; or, A Treatise on Female Ruin, in its Causes, Effects, Consequences, Prevention, and Remedy, &c., in which he contended that marriage, bemg simply and wholly an act of personal union (or the actus coitus), adultery is never used in the sacred writings but to denote the defilement of a betrothed or married woman, and to this sense he restricts the use of the term, so that a married man, in his opinion, is no adulterer, if his commerce with the sex be confined to single women, who are under no obligations by espousals or marriage to other men ; but, on the other hand, the woman who should dare to have even but one intrigue with any other man besides her husband (let him have as many wives as Solomon), would, ipso facto, be an adultress, and ought, together with her gallant, to be punished with immediate death. This, he boldly states, is the law of God; and on this foundation he limits the privilege of polygamy to the

mar..

In support of his system, he refers to the poiygamous connexions of the patriarchs and saints of the Old Testament, and infers the lawfulness of their practice from the blessings which attended it, the laws which were instituted to regu

late and superintend it, &c. He even labors much to reconcile the genius of the evangelical dispensation to an arrangement of this sort; and asserts that there is not one text in the New Testament that hints at the criminality of a polygamous connexion. From St. Paul's direction, that bishops and deacons should have but one wife, he would infer that it was lawful for laymen to have more. Christ, he says, was not the giver of a new law; but the business of marriage, polygamy, &c., had been settled before his appearance in the world, by an authority which could not be revoked. This writer further thinks polygamy advantageous in a civil light, and highly politic in a domestic point of view.

It is due to a work long deteriorated, and now we believe nearly extinct (the Monthly Review), to add, that the best answer to this scheme appeared at the time in that publication. We have only room for a summary of the arguments of the writer:

When we reflect,' says he, that the primitive institution of marriage limited it to one man and one woman; that this institution was adhered to by Noah and his sons, amidst the degeneracy of the age in which they lived, and in spite of the examples of polygamy, which the accursed race of Cain had introduced; when we consider how very few (comparatively speaking) the examples of this practice were among the faithful; how much it brought its own punishment with it; and how dubious and equivocal those passages are in which it appears to have the sanction of divine approbation; when to these reflections we add another respecting the limited views and temporary nature of the more ancient dispensation and institutions of religion-how often the imperfections, and even vices of the patriarchs, and people of God in old time, are recorded, without any express notification of their criminalityhow much is said to be commanded, which our reverence for the holiness of God and his law will only suffer us to suppose was, for wise ends, permitted---how frequently the messengers of God adapted themselves to the genius of the people to whom they were sent, and the circumstances of the times in which they lived; above all, when we consider the purity, equity, and benevolence of the Christian law; the explicit declarations of our Lord, and his apostle St. Paul, respecting the institution of marriage, its design and limitation; when we reflect, too, on the testimony of the most ancient fathers, who could not possibly be ignorant of the general and common practice of the apostolic church; and, finally, when to these considerations we add those which are founded on justice to the female sex, and all the regulations of domestic economy and national policy, we must wholly condemn the revival of polygamy; and thus bear our honest testimony against the leading design of this dangerous and ill-advised publication."— Monthly Review, vol. Ixiii. p. 338. Dr. Paley has also a good passage on this subject, Moral Philosphy, vol. i.

POLYGARS, in Hindostan, is a name that has been sometimes given to a predatory race of natives who long inhabited impenetrable woods in various parts of that continent.

Latterly, THE POLYGARS' TERRITORY is a name given to a district in the Southern Carnatic, situated between 10° and 11° of N. lat. To the north it is bounded by Trichinopoly; on the south by Marawas and Madura; on the east it has Tanjore and the sea; and on the west Dindigul.

The polygars are, according to Hamilton, military chieftains of different degrees of power and consequence, who bear a strong affinity to the zemindars of the Northern Circars. Those whose pollams, or estates, are situated on the frontier and jungly part of the country, are represented to have been for the most part leaders of banditti, or freebooters, who, as is not uncommon in Asia, had afterwards been entrusted with the police of the country. Some of them trace their descent from the ancient rajahs, or from those who held high offices of trust under the Hindoo government, and received allowances in land or money for the support of a body of horse and foot on the feudal principle. Other polygars had been renters of districts, or revenue officers, who had revolted in times of public disturbance, and usurped the possession of lands, to which they were constantly adding by successive encroachments, when the ruling power happened to be weak and inefficient. The heads of villages, when favored by the natural strength of the country, frequently assumed the name and character of polygars, and kept up their military retainers and nominal officers of state, exercising in this contracted sphere many of the essential powers of sovereignty.

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The amount of the tribute which they paid to the Soubaldars of the Carnatic was wholly disproportioned to their revenues; but more was constantly extorted by the officers of government under the names of fines and presents, which was a perpetual source of violence and distraction. During the periods of public calamity they retaliated upon the nabob's officers and the peaceable inhabitants of the government villages, those acts of indefinite and oppressive authority, which were committed on themselves. Hence the British government were repeatedly burdened with large armaments to subdue these feudatories, involving heavy disbursements from the public revenue, and severe loss of lives.'

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POLYGLOT, among divines and critics, is chiefly used for a Bible printed in several languages. See BIBLE.

POLYGLOTTUS. See TURDUS.

POLYGNOTUS, a famous painter of Thasos, who flourished about 422 years before the Christian era, and was the son and. scholar of Aglaophon. He adorned one of the public porticoes of Athens with his paintings, in which he had represented the most striking events of the Trojan war. The Athenians were so pleased with him that they offered to reward his labors with whatever he pleased to accept, but he declined the offer; and the Amphictyouic council, which was composed of the representatives of the principal cities of Greece, ordered that Polygnotus should be maintained at the public expense wherever he went.

POLYGON, n. s. Į Fr. poligone; Fr. Toλus, POLYG'ONAL, adj. S and yovia, an angle. A figure of many angles: multangular.

He began with a single line; he joined two lines in an angle, and he advanced to triangles and squares, polygons and circles.

Watts.

POLYGON, in geometry, is a figure whose perimeter consists of more than four sides, such are the pentagon, hexagon, heptagon, &c. If the angles be all equal among themselves, the polygon is said to be a regular one; otherwise, it is irregular. Polygons take particular names according to the number of their sides; thus a polygon of three sides is called a trigon, of four sides a tetragon, of five sides a pentagon, of six sides a hexagon, &c.; and a circle may be considered as a polygon of an infinite number of small sides, or as the limit of the polygons.

Polygons have various properties, as, 1. Every polygon may be divided into as many triangles as it has sides. 2. The angles of any polygons taken together, make twice as many right angles, wanting four, as the figure has sides. Thus, if the polygon has five sides, the double of that is ten, from which subtracting four leaves six right angles, or 540 degrees, which is the sum of the five angles of the pentagon. And this property, The principal pollams, or polygar estates, are as well as the former, belongs to both regular and those of Shevagunga, Ramnad, Manapara, Ma- irregular polygons. 3. Every regular polygon dura, and Nattam. The first two were permanently may be either inscribed in a circle, or described assessed in 1803, at the same time as those of about it. But not so of their regular ones, except Tinevelly; and the rest were soon afterwards the triangle, and another particular case as in the settled in perpetuity. From this period the tri- following property. An equilateral figure inbute of the polygars, although increased, has scribed in a circle is always equiangular. But been punctually paid; no blood has been shed, an equiangular figure inscribed in a circle is not or money expended in military operations always equilateral, but only when the number of against them, and the surrounding districts have sides is odd. For, if the sides be of an even enjoyed tranquillity under the revival of the an- number, then they may either be all equal, or cient system of village police. This territory is else half of them may be equal, and the other not so well watered, nor in so high a state of cul- half equal to each other, but different from the tivation, as Tanjore; but the soil is naturally former half, the equals being placed alternately. fertile, and the agriculture improving. There 4. Every polygon, circumscribed about a circle, are no rivers of any considerable magnitude; is equal to a right-angled triangle, of which one the chief towns are Nattam, Manapar, Veramally, leg is the radius of the circle, and the other the Puducotty, Cottapatam, and Tondi. The dis- perimeter or sum of all the sides of the polygon. trict is comprehended in the collectorship of Or the polygon is equal to half the rectangle unDindigul. der its perimeter and the radius of its inscribed

VOL. XVII.

2 U

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circle, or the perpendicular from its centre upon one side of the polygon. Hence, the area of a circle being less than that of its circumscribing polygon, and greater than that of its inscribed polygon, the circle is the limit of the inscribed and circumscribed polygons: in like manner the circumference of the circle is the limit between the perimeters of the said polygons; consequently the circle is equal to a right-angled triangle, having one leg equal to the radius, and the other leg equal to the circumference; and therefore its area is found by multiplying half the circumference by half the diameter. In like manner, the area of any polygon is found by multiplying half its perimeter by the perpendicular demitted from the centre upon one side.

The following table exhibits the most remarkable particulars in all the polygons, up to the dodecagon of twelve sides, viz., the angle at the centre, the angle of the polygon, and the area of the polygon when each side is one.

POLYGONS, LINE OF, is a line on some sectors, containing the homologous sides of the first nine regular polygons inscribed in the same circle; viz., from an equilateral triangle to a dodecagon.

POLYGONAL NUMBERS are the continual or successive sums of a rank of any arithmeticals beginning at one, and regularly increasing; and therefore are the first order of figurate numbers: they are called polygonals, because the number of points in them may be arranged in the form of the several polygonal figures in geometry.

The several sorts of polygonal numbers, viz. the triangles, squares, pentagons, hexagons, &c., are formed from the addition of the terms of the arithmetical series, having respectively their common difference 1, 2, 3, 4, &c.; viz., if the common difference of the arithmeticals be one, the sums of their terms will form the triangles; if two, the squares; if three, the pentagons, if four, the hexagons, &c. Thus :

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1, 6, 15, 28, 45, 66, 91. The side of a polygonal number is the number of points on each side of the polygonal figure when the points in the number are ranged in that form. And this is also the same as the number of terms of the arithmeticals that are added together in composing the polygonal number; or in short, it is the number of the term from the

1

2

3

To find the area of any regular polygon.— beginning. So, in the second or squares, Multiply the square of its side by the tabular area, found on the line of its name in the last column of the table, and the product will be the area. Thus, to find the area of the trigon, or equilateral triangle, whose side is twenty. The square of twenty being 400, multiply the tabular area 4330127 by 400, and the product 173.20508 will be the area.

0.4330127 400

173.2050800

1

4

9

16

the side of the first (1) is 1, that of the second (4) is 2, that of the third (9) is 3, that of the fourth (16) is 4, and so on. And

The angles, or numbers of angles, are the same as those of the figure from which the number takes its name. So the angles of the triangular numbers are three, of the square ones four, of the pentagonals five, of the hexagonals six, and se on. Hence, the angles are two more than the common difference of the arithmetical series from which any rank of polygonals is formed: so the arithmetical series has for its common difference the number 1 or 2 or 3 &c., as follows, viz. 1 in the triangles, two in the squares, three in the pentagons, &c; and, in general, if a be the number of angles in the polygon, then a-23 ord, the common difference of the arithmetical series, or d +2a, the number of angles.

There are several curious algebraical theorems for inscribing polygons in circles, or finding the chord of any proposed part of the circumference, which is the same as angular sections. These kinds of sections, or parts and multiples of arcs, were first treated of by Vieta, as shown in the Introduction to Hutton's Log. page 9, and since pursued by several other mathematicians, in whose works they are usually to be found.

POLYGON, in fortification, denotes the figure perimeter of a fortress, or fortified place. This is either exterior or interior. The exterior polygon is the perimeter or figure formed by lines connecting the points of the bastions to one another, quite round the work. And the interior polygon is the perimeter or figure formed by lines connecting the centres of the bastions, quite around.

PROB. I.-To find any polygonal_numbeTM pro posed; having given its siden and angles a The polygonal number being evidently the sum of the arithmetical progression whose number of terms is n and common difference a — 2, and the sum of an arithmetical progression being equal

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POLYGONOMETRY is the measure or doctrine of polygons.

POLYGONUM, knot-grass, a genus of the trigynia order, and octandria class of plants; in the natural method ranking under the twelfth order, holoracea. There is no calyx: the corolla is quinquepartite, and calycine, or serving instead of a calyx there is one angulated seed. There are twenty-seven species; the most remarkable are these-1. P. bistorta, bistort, or greater snakeweed, has a thick oblique intorted root, blackish without and red within; a simple, round, slender stem, nearly two feet high; oval leaves, having decurrent foot-stalks, and the stalk

terminated by thick short spikes of whitish-red flowers. See No. 4. The root of a kind of bistort, according to Gmelin, is used in Siberia for ordinary food. This species is by Haller called bistorta foliis ad oram nervosis, and by some other botanists bistorta montana minor. The natives call it mouka; and so indolent are they, that, to save themselves the trouble of digging it holes of the mountain rats, which they find filled out of the earth, they go in spring to pillage.the

with these roots.

In our country bistort is used

as a medicine. All the parts of bistort have is one of the strongest of the vegetable astrina rough austere taste, particularly the root, which gents. It is employed in all kinds of immoderate hæmorrhagies, and other fluxes, both internally and externally, where astringency is the only indication. It is certainly a very powerful styptic, and is to be looked on simply as such; having no other claim to the sudorific, antipestilential, and other virtues ascribed to it, than in consequence of its astringency, and of the antiseptic power which it has in common with other vegetable styptics. The largest dose of the root in powder is a single dram. 2. P. fagopyrum, buck-wheat, or brank, rises with an upright, smooth, branchy stem, from about a foot and a half to a yard high, heart-shaped sagittated whitish flowers, succeeded by large angular leaves, and the branches terminated by clusters of seeds. This species is angular. It is a sort of corn, and is cultivated both by way of fodder, cutting its stalks while young and green to feed cattle, and for its grain to feed pigeons, poultry, hogs, &c. It flourishes in any soil and situation, but generally thrives best in a light dry earth; the driest seasons seldom retard its growth. 3. P. orientale, commonly called persicaria, has fibrous roots; an upright, robust, strong, jointed stem, rising eight or ten feet high, divided at top into several branches, very large oval lanceolate alternate leaves, on broad foot-stalks half surrounding the stem; and all the branches terminated by long, slender, hanging spikes of reddishpurple heptandrous and digynious flowers, from July till October. This is a most elegant annual for the embellishment of pleasure-grounds; assuming a majestic tree-like growth by its erect luxuriant stem and branchy head; which being garnished with noble large foliage, and numerous pendulous spikes of flowers, in constant succession for three or four months, exhibits a very ornamental appearance from June or July until October, and is so easy of culture that, from its scattered seeds in autumn, young plants rise spontaneously in abundance the ensuing spring, and shoot up so rapidly as to attain six or eight feet in height by July, when they generally begin flowering, and continue till attacked by the frost, when they totally perish; so that a fresh supply must be raised from seed annually. 4. P. viviparum, the smaller bistort, has a thickish root, a simple slender stem half a foot high, spearshaped leaves, and the stalks and branches terminated by long spikes of whitish-red flowers. Both this and the bistort (No. 1.), flower in May and June, succeeded by ripe seeds in August. They grow wild in England, &c., the first in moist, the other in mountainous situations. They are

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