do to the lines by which they are included: so that, as in the latter, it is not the magnitude of the lines, but their mutual inclination, which determines the angle; just so in the former it is not the magnitude of the planes, but their mutual inclinations which determine the angles. And hence all those geometers, from the time of Euclid down to the present period, who have confined their attention principally to the magnitude of the plane angles, instead of their relative positions, have never been able to develope the properties of this class of geometrical quantities; but have affirmed that no solid angle can be said to be the half or the double of another, and have spoken of the bisection and trisection of solid angles, even in the simplest cases, as impossible problems. But all this supposed difficulty vanishes, and the doctrine of solid angles becomes simple, satisfactory, and universal in its application, by assuming spherical surfaces for their measure; just as circular arcs are assumed for the measures of plane angles. Imagine that from the summit of a solid angle (formed by the meeting of three planes) as a centre, any sphere be described, and that those planes are produced till they cut the surface of the sphere; then will the surface of the spherical triangle, included between those planes, be a proper measure of the solid angle made by the planes at their common point of meeting; for no change can be conceived in the relative position of those planes, that is, in the magnitude of the solid angle, without a corresponding and proportional mutation in the surface of the spherical triangle. If, in like manner, the three or more surfaces, which by their meeting constitute another solid angle, be produced till they cut the surface of the same or an equal sphere, whose centre coincides with the summit of the angle; the surface of the spheric triangle or polygon, included between the planes which determine the angle, will be a correct measure of that angle. And the ratio which subsists between the areas of the spheric triangles, polygons, or other surfaces thus formed, will be accurately the ratio which subsists between the solid angles, constituted by the meeting of the several planes or surfaces, at the centre of the sphere. It may be proper to anticipate here the only objection, which can be made to this assumption; which is founded on the principle that quantities should always be measured by quantities of the same kind. But this, often and positively as it is affirmed, is by no means necessary; nor in many cases is it possible. To measure is to compare mathematically: and if by comparing two quantities, whose ratio we know or can ascertain, with two other quantities wnose ratio we wish to know, the point in question becomes determined; it signifies not at all whether the magnitudes which constitute one ratio are like or unlike the magnitudes which constitute the other ratio. It is thus that mathematicians, with perfect safety and correctness, make use of space as a measure of velocity, mass as a measure of inertia, mass and velocity conjointly as a measure of force, space as a measure of time, weight as a measure of density, expansion as a measure of heat, a certain function of planetary velocity as a measure of distance from the central body, arcs of the same circle as measures of plane angles; and it is in conformity with this general procedure that we adopt surfaces of the same sphere as measures of solid angles. Hence the comparison of solid angles becomes a matter of great ease and simplicity; for, since the areas of spherical triangles are measured by the excess of the sums of their angles each above two right angles, and the areas of spherical polygons of n sides, by the excess of the sum of their angles above 2n-4 right angles, it follows that the magnitude of a trilateral solid angle will be measured by the excess of the sum of the three angles, made respectively by its bounding planes, above two right angles; and the magnitudes of solid angles formed by n bounding planes, by the excess of the sum of the angles of inclination of the several planes above 2n-4 right angles. As to solid angles limited by curve surfaces, such as the angles at the vertices of cones, they will manifestly be measured by the spheric surfaces cut off by the prolongation of their bounding surfaces, in the same manner as angles determined by planes are measured by the triangles or polygons they mark out upon the same or an equal sphere. In all cases the maximum limit of solid angles will be the plane towards which the various planes, determining such angles, approach, as they diverge farther from each other about the same summit; just as a right line is the maximum limit of plane angles, being formed by the two bounding lines when they make an angle of 180°. The maximum limit of solid angles is measured by the surface of a hemisphere, in like manner as the maximum limit of plane angles is measured by the arc of a semicircle. The solid right angle (either angle, for example, of a cube) is (2) of the maximum solid angle; while the plane right angle is half the maximum plane angle. The analogy between plane and solid angles being thus traced, we may proceed to exemplify this theory by a few instances; assuming 1000 as the numeral measure of the maximum solid angle = 4 times 90° solid = 360° solid. 1. The solid angles of right prisms are compared with great facility. For, of the three angles made by the three planes which by their meeting constitute every such solid angle, two are right angles; and the third is the same as the corresponding plane angle of the polygonal base; on which, therefore, the measure of the solid angle depends. Thus, with respect to the right prism with an equilateral triangular base, each solid angle is formed by planes which respectively make angles of 90°, 90°, and 60°. Consequently 90° +90° +60° + 180° 60°, is the measure of such angle, compared with 360° the maximum angle. It is, therefore, one-sixth of the maximum angle. A right prism with a square base has, in like manner, each solid angle measured by 90° + 90° + 90°. 180° 90°, which is of the maximum angle. And thus it may be found that each solid angle of a right prism, with an equilateral 2. Let us compare the solid angles of the five regular bodies. In these bodies if m be the number of sides of each face; n the number of planes which meet at each solid angle; half the circumference or 180°; and A the plane angle made by two adjacent faces; then we have (m+1) gonal base. plane angle formed by every two contiguous faces of the tetraedron, 70° 31′ 42′′; of the hexaëdron, 90°; of the octaëdron, 109° 28′ 18′′; of the dodecaedron, 116° 33′ 54"; of the icosaedron, 138° 11' 23". But in these polyedræ the number of faces meeting about each solid angle are 3, 3, 4, 3, 5, respectively. Consequently the several solid angles will be determined by the This theorem gives, for the subjoined proportions : For more examples in illustration of this new theory see Hutton's Course, vol. iii. pp. 90, 91. SOLIDS, in anatomy, are the bones, ligaments, membranes, muscles, nerves, and vessels, &c. The solid parts of the body, though equally composed of vessels, are different with regard to their consistence; some being hard and others soft. The hard, as the bones and cartilages, give firmness and attitude to the body, and sustain the other parts. The soft parts, either alone or together with the hard, serve to execute the animal functions. See ANATOMY, Index. SOLIDAGO, in botany, golden rod, a genus of plants belonging to the class of syngenesia, and to the order of polygamia superflua; natural order forty-ninth, compositæ. The receptacle is naked; the pappus simple; the radii are commonly five; the scales of the calyx are imbricated and curved inward. There are fourteen species; viz. 1. S. altissima; 2. bicolor; 3. Canadensis; 4. coesia; 5. flexicaulis; 6. lanceolata; 7. lateriflora; 8. latieolia; 9. Mexicana; 10. minuta; 11. noveboracesis; 12. rigida; 13. sempervirens; and 14. S. virgaurea, or golden rod, which grows frequently in rough mountainous pastures and woods; and is the only species which is a native of Britain. The stems are branched, and vary from six inches to five feet high, but their common height is about a yard. The leaves are a little hard and rough to the touch; the lower ones oval lanceolate, generally a little serrated and supported on footstalks; those on the stalks are elliptical; the flowers are yellow and grow in spikes from the ale of the leaves; the scales of the calyx are lanceolate, of unequal length, and of a pale green color; the female florets in the rays are from five to eight; the hermaphrodite flowers in the disc from ten to twelve. There is a variety of this species called S. virgaurea cambrica, a native of Wales, which is found on rocks from six inches to a foot high. SOLIDATUM, used in the neuter gender, is taken for that absolute right or property which a man has in any thing.-Malmsb. lib. 1. SOLIDITY, in philosophy, is that property of matter, or body, by which it excludes all other bodies from the place which itself possesses; and, as it would be absurd to suppose that two bodies could possess one and the same place at the same time, it follows that the softest bodies are equally solid with the hardest. See METAPHYSICS. Among geometricians the solidity of a body denotes the quantity or space contained in it, and is called also its solid content. The solidity of a cube, prism, cylinder, or parallelopiped, is had by multiplying its basis into its height. The solidity of a pyramid or cone is had by multiplying either the whole base into a third part of the height, or the whole height into a third part of the base. SOLIDUNGULOUS, adj. Lat. solidus and ungula. Whole-hoofed. It is set down by Aristotle and Pliny that an horse, and all solidungulous or whole-hoofed animals, have no gall; which we find repugnant unto reason. Browne's Vulgar Errours. SOLIFID'IAN, n. s. Lat. solus and fides. One who supposes only faith, not works, necessary to justification. It may be justly feared that the title of fundamentals, being ordinarily confined to the doctrines of faith, hath occasioned that great scandal in the church of God, at which so many myriads of solifidians have stumbled, and fallen irreversibly, by conceiving heaven a reward of true opinions. Hammond. SOLIFIDIANS. Without entering into this controversy, as a point of religion, which has more or less divided Protestants ever since the reformation, we would beg leave to consider the subject, for a moment, in a philosophical point of view. The whole argument seems to resolve itself into this simple question of philosophy, Can a created being merit any thing at the hand of its creator? The candid philosopher will certainly answer this question in the negative. If then, even upon the supposition of the creature having never sinned, it can merit nothing, how much less can a sinful creature, by any exertions of its own, atone for its past offences? Obvious as this truth seems to be, yet the opposite doctrine, that something can and must be done by the sinner, to atone for his past sins and merit forgiveness, has formed a constituent part of all religions, in all ages and countries, from the most dark and bloody superstitions, which placed merit in human sacrifices, and even sacrificed children to pacify the offended deities, down through the whole system of popery till the reformation. Nor have even the reformed churches got entirely rid of it, as appears from the above quotation from Dr. Hammond, as well as from the whole of the Arminian system. But the church of Rome certainly carried the doctrine to the most extravagant height, when they taught that a man could not only, by his good works, merit forgiveness for his own sins, but accumulate such a stock of works of supererogation as to atone for the sins of his neighbours! In a word, however Solifidianism may be ridi culed, it appears to be founded both on Scripture and reason; and, as sin and misery entered by the want of faith in the first threatening, so the only remedy is sola fide, by faith alone in the great work performed by our Saviour. SOLIFIDIANISM (from sola and fides). The doctrine of salvation by faith alone. See last article. SOLIGNAC (Peter. Joseph De La Pimpie, chevalier of), a learned and amiable French historian, born at Montpelier in 1687. He was employed by the French court in a respectable situation in Poland, where he became acquainted with king Stanislaus, who made him his secretary. He wrote a History of Poland, and other works; and died in 1773, aged eighty-six. SOLILOQUY, n. s. Fr. soliloque; Lat. solus and loquor. A discourse made to one's self. If I should own myself in love, you know lovers are always allowed the comfort of soliloquy. Spectator. He finds no respite from his anxious grief, Then seeks from his soliloquy relief. Garth's Disp. The whole poem is a soliloquy: Solomon is the person that speaks: he is at once the hero and the author; but he tells us very often what others say to him. Prior. A SOLILOQUY, according to Papia, is a discourse by way of answer to a question that a man proposes to himself. Soliloquies are become too common on the modern stage; yet can nothing be more inartificial, or more unnatural, than an actor's making long speeches to himself, to convey his intentions, &c., to the audience. Where such discoveries are necessary to be made, the poet should rather take care to give the dramatic persons such confidants as may necessarily share their inmost thoughts; by which means they will be more naturally conveyed to the audience. Yet is even this a shift an accurate poet would not be found to have occasion The duke of Buckingham has well said, 'Soliloquies had need be very few, Extremely short, and spoke in passion too. Our lovers talking to themselves, for want Of others, make the pit their confidant : Nor is the matter mended yet, if thus for. They trust a friend, only to tell it us.' Soliloquies are not, however, quite so unnatural as some think. Let a man be alone, and his thoughts anxiously bent on some object, and he will involuntarily speak out to himself. SOLIMAN I., emperor of the Turks, succeeded his father Bajazet I. in 1403. He was a brave and enterprising prince, but very much devoted to his pleasures. He was dethroned by his brother Moses or Musa in 1410, and soon after murdered. SOLIMAN II., emperor of the Turks, surnamed the Magnificent, was the only son of Selim I, whom he succeeded in 1520. He was educated in a manner very different from the Ottoman princes in general; for he was instructed in the maxims of politics and the secrets of government. He began his reign by restoring those persons their possessions whom his father had unjustly plundered. He re-established the authority of the tribunals, and bestowed the government of provinces upon none but persons of wealth and probity: 'I would have my viceroys SOLIMAN III., the son of Ibrahim I., was taken from prison and made emperor by the Janizaries, in 1687, on the deposition of Mahomet IV. his brother, whom he sent to the same jail. He was an indolent prince, wholly governed by his ministers; and died in 1691. SOLIMENE (Sir Francis), an eminent painter, born at Nocera near Naples in 1657. He studied first under his father Angelo, who was a good painter, and next under Francis Maria at Naples in 1674, who, envying his rising merit, wished to discourage him. He soon became eminent, however, in chiaro obscuro; and painted the Jesuit's chapel of St. Anne in a style so superior that he astonished painters of established reputation. Philip V. employed him and invited him to Madrid, as also did Louis XIV. to Paris, but he declined. The emperor Charles VI. was so pleased with his paintings that he knighted him. In 1701 he went to Rome, where he was much patronised by the pope and cardinals. He was also a poet, and his Sonnets are esteemed. He died in 1747, aged ninety. SOLINUS (Caius Julius), a Latin_grammarian and historian, born at Rome in the end of the first century, according to Lempriere, but according to Dr. Watkins in the middle of the third. His Polyhistor is a collection of historical and geographical remarks on the most celebrated places of antiquity. Pliny is often quoted in it, and it is written so much in Pliny's style, that he has been called Pliny's ape. The best Browne's Vulgar Errours. SOLIPUGA, or SOLIFUGA, in entomology, the name given by the Romans to a small venomous insect of the genus aranea, or spider kind, called by the Greeks heliocentros, or olocentros; both words signifying an animal which stings most in the country and seasons where the sun is hottest. Solinus makes this creature peculiar to Sardinia; but this is contrary to all the accounts given us by the ancients. It is common in Africa and some parts of Europe. Almost all the hot countries produce this venomous little creature. It lies under the sand to seize other insects as they go by; and, if it meet with any uncovered part of a man, produces a wound which proves very painful; some say the bite is absolutely mortal, but this seems not true. Solinus and others write the word solifuga, erroneously deriving the name from the notion that this animal flies from the sun's rays, and buries itself in the sand. SOLIS (Antony de), an ingenious Spanish writer, of an ancient and illustrious family, born at Placenza in Old Castile, in 1610. He was intended for the law; but his inclination to poetry prevailed. Philip IV. made him his secretary; and after his death the queen-regent appointed him historiographer of the Indies, a place of great profit and honor: his History of the Conquest of Mexico shows that she could not have named a fitter person. He is better known by this history than by his poetry and dramatic writings. He turned priest at fifty-seven years of age, and died in 1686, aged seventy-six. SOLIS (John Dias de), a Spanish navigator, the first who sailed up the river Plata, in 1515. SOLITARIES, an order of nuns of St. Peter of Alcantara, instituted in 1676, the design of which was to imitate the severe penitent life of that saint. Thus they are to keep a continual silence, never to open their mouths to a stranger; to employ their time wholly in spiritual exercises, and leave their temporal concerns to a number of maids, who have a particular superior in a separate part of the monastery: they always go bare-footed, without sandals; gird themselves with a thick cord, and wear no linen. SOLITARY, adj. & n. s. SOLITAIRE', n.s. SOL'ITARILY, adv. SOLITARINESS, n. s. SOL'ITUDE. Fr. Latin Retired; living alone; single; lonely; dismal: solitaire ; solitarius. a solitary or solitaire is, one who lives alone; a Feed thy people with thy rod, the flock of thine heritage which dwell solitarily in the wood. Micah vii. 14. You subject yourself to solitariness, the sly enemy that doth most separate a man from well-doing. Sidney. Donne. At home, in wholesome solitariness, My piteous soul began the wretchedness Of suitors at the court to mourn. Nor did a solitary vengeance serve; the cutting off one head is not enough; the eldest son must be involved. King Charles. Those rare and solitary, these in flocks. Milton. What callest thou solitude? Is not the earth With various living creatures, and the air, Replenished, and all these at thy command, To come and play before thee? Id. Paradise Lost. Relations alternately relieve each other, their mutual concurrences supporting their solitary instabili ties. Him fair Lavinia Shall breed in groves to lead a solitary life. Browne. Dryden's Eneid. Such only can enjoy the country, who are capable of thinking when they are there: then they are prepared for solitude, and in that solitude is prepared for Dryden. them. SOL'LAR, n. s. Low Lat. solarium. A garret. Some skilfully drieth their hops on a kel, And some on a sollar, oft turning them wel. Tusser. SOLO, or SAURA-CORTA, an inland town and district of Java, the residence of an emperor. The town is populous, intersected with broad and shaded avenues or streets, running at right angles. The Crattan, where the emperor resides, is very spacious, and comprises several palaces the other chiefs and nobility live in villas, surrounded by hign walls. The European town and fort here are very neat. The latter, not above 800 yards from the Crattan, contained a British garrison, when the island of Java was in possession of this country. A fine river flows near this town, and, passing through the dominions of the sultan and emperor, falls into the harbour of Gressie. SOLO, in the Italian music, is frequently used in pieces consisting of several parts, to mark those that are to perform alone; as fiauto solo, violino solo. It is also used for sonatas composed for one violin, one German flute, or other instrument, and a bass; thus we say, Corelli's solos, Geminiani's solos, &c. When two or three parts play or sing separately from the grand chorus, they are called a doi solo, a tre solo, &c. Solo is sometimes denoted by S. In the concertos of Corelli, Geminiani, and Handel, chiefly composed à due cori, or two orchestras, the principal parts are said to belong to the concertini, or solo parts; as violino primo concertino, violino secondo del concertino, &c.: and the inferior parts, that only play in the full chorus, are called ripieni; as violino primo ripieno, violino secondo, ripieno, or del concerto grosso, or the great and full concert. Solos, which used to afford the most exquisite delight to persons of refined taste, when composed and performed by great masters, are now wholly laid aside; and whoever attempts to perform one is subjected to a penalty instead of a reward; a law instituted at the concert of ancient music, where a composition was never thought complete by the late earl of Sandwich, without a kettle-drum, nor with, unless he beat it himself. And at the commemoration of Handel, the double drums, double cartels, tromboni, &c., augmented his lordship's pleasure, in proportion to the din and stenterophonic screams of these truly savage instruments; which, in so wide a building as Westminster Abbey, and softened by so powerful a chorus of voices and instruments as were assembled at the commemoration, had, occasionally a fine effect; but, in a more confined space, the almost incessant use of the tromboni, and perpetual roll of the double drums, annihilate all the pleasing effects of mellifluous tones. SOLOEIS, SOLOENTIA, or SOLUS, a promontory of Lybia, at the extremity of Mount Atlas; now called Cape Cantin. SOLOENTIA, or SOLOEIS, an ancient town of Sicily, between Panormus and Chimera, now called Solanto. SOLOFRA, a town in the Principatro Ultra, Naples, with 6100 inhabitants. It has manufactures of leather, parchment, and gold and silver plate. SOLOMON, Heb. 1, i. e. peaceable, the son and successor of David, king of Israel, by Bathsheba; who seems to have been so named by his father in the spirit of prophecy, as he had the most peaceable and flourishing reign of any monarch in Israel or Judah. He was born about A. M. 2971. His judicious government in the early part of his reign; his repeated divine communications, and wise choice; his extensive and successful commerce with Egypt, Ophir, Tyre, &c.; his immense riches in consequence; his fame for wisdom, which reached the most remote corners of the civilised world (see SHEBA); his superb building and solemn dedication of the temple, with his excellent prayer on that occasion, and his costly sacrifices, miraculously consumed; with his feast of seven days given to the whole people, and many other interesting particulars of his reign, are recorded in 1 Kings |