AN'GLED,

ANGLE. AN'GLE, n.

AN'GULAR,

ANGULAR'ITY,

AN'GULARLY,

AN'GULATED,

AN'GULOUS.

Another answerd, and said, it might wel be
Naturelly by compositions

Of angles, and of slie reflections;

And saide that in Rome was swiche on.

Chaucer. The Squieres Tale, v. i. p. 428.

A master-cook! why, he's the man of men,
For a professor! he designs, he draws,
He paints, he carves, he builds, he fortifies,
Makes citadels of curious fowl and fish,

Some he dry-ditches, some motes round with broths;
Mounts marrow-bones; cuts fifty-angled custards.
Ben Jonson's Mas. Nep. Tri.

If neither the regard of himself, nor the reverence of his elders and friends prevail with him, to leave his vitious appetite; then as the time urges, such engines of terror God hath given into the hand of the minister, as to search the tenderest angles of the heart.

Milton's Reason on Church-Govern.

There are also virtues, wherein smallness of quantity has the greatest effect, as a sharp point penetrates easier than a blunt one, and as the angular point of a diamond cuts glass.

Bacon's Novum Organum. Nor doth the frog, though stretched out, or swimming, attain the rectitude of man, or carry its thigh without all angularity. Brown's Vulgar Errours.

The anti-face to this is your lawyer's face, a contracted, sublime, and intricate face, full of quirks and turnings, a labyrinthean face, now angularly, now every way aspected.

Ben Jonson's Cynthia's Revels.

The cyclops follow'd; but he sent before
A rib, which from the living rock he tore :
Though but an angle reach'd him of the stone,
The mighty fragment was enough alone
To crush all Acis.

Dryden's Ovid's Met.

I do not find any natural object which is angular, and at the same time beautiful. Indeed few natural objects are entirely angular. Burke, on the Sublime and Beautiful. Solid bodies are held together by hooks, and angulous involutions. Glanville.

Emeralds, which grow in the fissures, are ordinarily crystallized, or shot into angulated figures. Woodward.

ANGLE is generally the opening or mutual inclination of two lines meeting in a point, or the mutual inclination and intersection of three or more planes meeting in one common point or vertex. The latter is denominated a solid angle.

If the two lines referred to above be both straight, the angle is said to be rectilinear; if one be a curve and the other a right line, it is a mixtilinear angle; if they both be curves, a curvilinear angle; and if they both be arcs of circles, a spherical angle.

Angles are further distinguished by their quantities or measures, or the purposes to which these measures or angles are applied, or the sciences into which they are introduced; hence we have a variety of different angles in geometry, trigonometry, optics, astronomy, fortification, &c., which will be defined in their proper

places in this work. We shall, therefore, not parti- ANGLE. cularize them in this place, but confine our remarks to one or two cases which more properly belong to this article.

ANGLE of contact is that made by a curve line and a tangent to it, at the point of contact, as the angle IIIK (fig 6. MISCEL. pl. V.)

It is demonstrated by Euclid, that the angle of contact formed between a right line, or tangent, and the arc of a circle, is less than any right lined angle whatever, although it does not, therefore, follow, that is of no magnitude or quantity. This has been a subject of great dispute amongst certain geometricians, in which Peletarius, Ozanam, Clavius, Jacquet, Wallis, &c. bore a considerable part; the two former and the latter contending that it was no angle at all, against Clavius, who rightly, in our opinion, maintained, that it was not an actual nullity, although it was incomparable with a rectilinear angle; but that its incomparability consisted, not in its being nothing, but in its being a quantity of a different kind; a surface is incomparable with a solid; but it would be absurd, on that account, to say that a surface has no magnitude.

Sir Isaac Newton himself did not disdain taking some part in this controversy; he proved that angles of contact, although incomparable with rectilinear angles, might be compared with each other, showing, at the same time, the measure of those comparisons.

Thus the circular angles of contact IHK, IHL, are to each other reciprocally, as the square roots of the diameters HM, HN. And hence the circular angle of contact may be divided by describing intermediate circles, into any number of parts, and into any proportion.

If, instead of circles, the curves were parabolas, and the point of contact H, the common vertex of their axis, the angles of contact would then be reciprocally as the square roots of their parameters; but in elliptical and hyperbolic angles of contact, these will be reciprocally as the square roots of the ratios compounded of the ratios of the parameters and of the transverse axis.

Solid ANGLE. We have already stated that a solid Solid angle. angle is that made by the meeting of three or more plane angles which are not in the same plane. It may otherwise be defined, as the angular space included between several plane surfaces, or one or more curve surfaces, meeting in the point which forms the summit of the angle.

Adopting the latter definition, it has been shown by Dr. Gregory, in the third volume of Dr. Hutton's Course of Mathematics, that solid angles bear just the same relation to the spherical surfaces which form their base, as a plane angle does to the arc of the circle by which it is subtended. That is, supposing a sphere to be described about the vertex of the solid angle as a centre, and the planes by which it is comprised to be produced, these will cut off a certain portion of the spherical surfaces, which is assumed as the measure of the solid angle. A similar idea was suggested by

ANGLESEA.

ANGLE. Albert Girard, in his Inventions Nouvelles en l'Algebra; but it seems wholly to have escaped the notice of mathematicians; and the incomparability of solid angles with each other has been obstinately maintained by many celebrated geometricians.

Nothing is, however, more obvious than that with respect to their absolute magnitude; these angles are as simply measured as plane angles, and that they may be divided, multiplied, &c. after the same manner, whether they form on the sphere itself a triangle, polygon, or circle: all that can be objected is, that they may be equal, and not similar; but this is no more than happens to every quantity which has reference to three dimensions.

If we assume the whole surface of any sphere described about the vertex of a solid angle as a centre, as 1000, or that of the hemisphere 1000, or any other number at pleasure, and then compute the area of the spherical base of that angle on the sphere, we shall have the specific value of the solid angle in question; and as the surface thus cut off by the planes, containing certain solid angles, is readily computed, it may not be amiss to state a few of the principal results, as they are given in the work above referred to.

Thus, with respect to the right prism, with an equilateral triangular base, each solid angle is formed by planes which make, respectively, angles of 90°, 90°, and 60'; consequently 90° + 90° + 60° — 180° = 60° is the measure of such an angle, compared with 360°, as the maximum, and is therefore one-sixth of the maximum angle; or, which is the same, it will cut off

ANGLES, a town of France, in the department of the Tarn, Lower Languedoc, arondissement of Castres. It is the head of a canton, 19 leagues W. of Montpelier, and contains 2,500 inhabitants.

ANGLES, OF ANGLI, in Ancient History, a tribe of the Suevi, mentioned by Cæsar, as the most daring and noble spirited of all the Germans. Their final settle

ments were toward the north of the Elbe, and the district of Anglen, in the duchy of Sleswick, seems still to retain their name. This is the tribe which, according to Rapin and many other writers, gave the name of England to the subjects of our Egbert, early in the ninth century.

ANGLESEA, an island of the Irish sea, now forming one of the six counties of North Wales, from which it is separated by the narrow strait of Menai. Its Roman name was Mona, from the ancient British, Môn, which is conjectured by Rowland, in his Mona Antiqua Restaurata, to allude to its forming the terminating point of the British territories in this direction. It was also called, by the ancient Britons, Ynys Dowyll, or the Shady Island, and Ynys y Cedeirn, from its powerful chiefs; and seems to have received its present name, Anglesea, on its conquest by Egbert. Bede calls this island and that of Man, the Menavian isles. The channel of Menai, both at the time of the Roman and English conquests of this island, appears to have been much narrower than at present, and there are traces of an isthmus near Porthaeth-'hwy, which would induce the supposition of its having once joined the main land of Caernarvonshire.,

Anglesea is of an irregular triangular form, indented throughout with bays and creeks. Its greatest length, from north-west to south-east, is about 20 miles, and its breadth, from north-east to south-west, 16 miles, containing upwards of 200,000 acres of land. It is divided into six hundreds, Llyfon, Maltraeth, Menai, Talybolion, Twicelyn, and Tyndaethwy, which comprise twenty-four parishes, and four market-towns,— Beaumaris, Holyhead, Lanerchymedd, and Newburgh. By the latest population returns, it appears to contain 33,806 inhabitants, 9,766 of whom are employed in agriculture, and 2,614 in trade or manufactures.

This island has no streams of any importance, or that are navigable for vessels of burden; but its harbours are both numerous and convenient. That of Beaumaris, with its two creeks, Holyhead and Alnwick, is taken as a member of the port of Chester. Red-wharf bay, to the north of Beaumaris, is said to

SEA

ANGLE- be capable of being made very safe and commodious at a small expense, and Dulas bay is a considerable outlet for the lead-mines in its vicinity. Aberfraw was anciently a port of consequence, and the chief seat of the princes of North Wales. The other harbours are Perth-Ilangdy, Cemlyn, or Crooked Pool bay, and Maldraeth, or Maltraeth, on the western side. The climate is considerably milder than in the adjacent counties of North Wales; but is rendered unhealthy, in the autumn, by the frequent fogs that hang over the island, and which subject the inhabitants to agues. The general aspect of the country, which was certainly once remarkable for its woods, is naked and uninviting, with the exception of a small portion of it, bordering on the Menai straits. There are no considerable mountains, hills, or vallies, to diversify the scenery; and the greater part of the lands are unenclosed. Even on the shores of the strait, the trees are considerably stinted in their growth, under the south-west winds. "May the inhabitants," says Fuller, "be like the land they live in, which appears worse than it is; seeming barren but really fruitful, and affording plenty of good wheat."

Soil.

inerals.

The soil is, upon the whole, remarkably productive, and amply watered by natural rivulets for the purposes of vegetation. "Mon Mam Cymbry," Anglesea is the mother of Wales, was a proverb of former times, according to Fuller, "because when other counties faile, she plentifully feedeth them with provision; and is said to afford corn enough to sustain all Wales." But it appears to have been considerably neglected until a very recent period, and even now large marshes remain undrained, which would promise to afford rich grazing pastures. The soil is principally a fine loamy sand, and, though sometimes shallow, will yield very heavy crops; the marine sand of the mouth of the creeks forms an excellent manure. Wheat, barley, and oats are its principal productions, of which, in good seasons, 10,000 quarters are exported to the main land. The black cattle of Anglesea have also long been distinguished. In the middle of the sixteenth century, there are accounts of three thousand head being sent off the island in one year; and, by the latest returns, this number has been increased to twelve, thirteen, and fifteen thousand. To these exports are added annually, about five thousand hogs; sheep, large quantities of wax, honey, tallow, and hides. In turning up the soil, numerous trees are found, in a remarkable state of preservation, and generally so black and hard as to form very neat and serviceable articles of household use. The mineral productions of Anglesea are both valuable and curious. Quarries, yielding excellent breccia for mill-stones, and some few marble quarries, are worked with success; the latter principally of the gray and white marble. Pennant speaks of a green amianthus, or brittle asbestos, found in great plenty, in a marble of that colour, near Rhoscolin. Some good coal-mines have been opened in various parts of the island, and particularly on the western shores. Lead ore is also found here, in and around the Parys' mountain, the copper of which is the most important mineral of the "I visited Tryselwyn mountain," says Mr. Pennant," on part of which, called Parys' mountain (probably from a Rob. Parys' who was chamberlain of North Wales in the reign of Henry IV.), is the most considerable body of copper ore perhaps ever known. The external aspect of the hill is extremely

VOL. XVII.

SEA.

rude, and rises into enormous rocks of coarse white ANGLEquartz. The ore is lodged in a basin, or hollow; and has on one side a small lake, on whose waters, distasteful as those of Avernus, no bird is ever known to alight. The whole aspect of this tract has, by the mineral operations, assumed a most savage appearance. Suffocating fumes of the burning heaps of copper arise in all parts, and extend their baleful influence for miles around. In the adjacent parts, vegetation is nearly destroyed: even the mosses and lichens of the rocks have perished; and nothing seems capable of resisting the fumes but the purple Melic grass (Melica cærulca), which flourishes in abundance. I have little doubt but that the ore has been worked at in a very distant period. Vestiges of the ancient operations appear in several parts, carried on by trenching, and by heating the rocks intensely, then suddenly pouring on water, so as to cause them to crack or scale, thus awkwardly supplying the place of gunpowder. Pieces of charcoal are also found, which prove that wood was made use of for that purpose." "It is certain that the Romans were the undertakers of these mines; and it is very probable, that they sent the ore to Caer Hen to be smelted, the place where the famous cake of copper was discovered." Further on, he says, "The body of copper ore is of unknown extent. The thickness has been ascertained in some places, by the driving of a level under it, several years ago, and it was found to be in some places twenty-four yards. The ore is mostly of the kind called by Cronstead, Pyrites cupri flavo viridescens; and contains vast quantities of sulphur. It varies in degrees of goodness; some of it is rich, but the greater part poor in quality. There are other species of copper ore found here. Of late, a vein of Pyrites cupri griseus, of Cronstead, about seven yards wide, has been discovered, near the west end of the mountain; some is of an iron gray, some quite black the first contains 16lbs. of copper for 100lbs. the last 40. An ore has been lately found in form of loose earth, of a dark purplish colour, and the best of it has produced better than 8 in 20. Some years ago, above 30 lbs. of native copper was found in driving a level through a turbary ; some was in form of moss, some in very thin leaves. It is quarried out of the bed in vast masses; is broken into small pieces, and the most pure part is sold raw, at the rate of about 31. to 61. per ton, or sent to the smelting-houses of the respective companies, to be melted into metal."

;

"Nature hath been profuse in bestowing her mineral favours on this spot; for above the copper ore, and not more than three-quarters of a yard beneath the common soil, is a bed of yellowish greasy clay, from one to four yards thick, containing lead ore; and yielding from 600 to 1,000 lbs. weight of lead from one ton; and one ton of the metal yields not less than 57 ounces of silver. Mixed with the earth are frequently certain parts of the colour of cinnabar; whether these are symptomatic of the sulphureous arsenical silver ores, or of quicksilver, I will not pretend to decide."

mines.

The history of the modern discovery of the value of History of this mountain is curious :-A Mr. Alexander Frazier, the Parys' visiting Anglesea to explore the mines, in 1762, so confidently represented to Sir Nicholas Bailey, the then proprietor, his expectations of the metal that might be obtained there, as to induce him to sink several shafts. All of them, however, were quickly overflowed withwater. In 1764, Sir Nicholas insisted upon the lease of this moun

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