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do to the lines by which they are included: so thal, measure of density, expansion as a measure of as in the latter, it is not the magnitude of the heat, a certain function of planetary velocity as lines, but their mutual inclination, which deter- a measure of distance from the central body, mines the angle; just so in the former it is not arcs of the same circle as measures of plane the magnitude of the planes, but their mutual angles; and it is in conformity with this general inclinations which determine the angles. And procedure that we adopt surfaces of the same hence all those geometers, from the time of Eu- sphere as measures of solid angles. clid down to the present period, who have con Hence the comparison of solid angles becomes fined their attention principally to the magnitude a matter of great ease ard simplicity; for, since of the plane angles, instead of their relative po- the areas of spherical triangles are measured by sitions, have never been able to develope the the excess of the sums of their angles each aboré properties of this class of geometrical quantities; two right angles, and the areas of spherical polybut have affirmed that no solid angle can be said gons of n sides, by the excess of the sum of their to be the half or the double of another, and have angles above 2n—4 right angles, it follows that spoken of the bisection and trisection of solid the magnitude of a trilateral solid angle will be angles, even in the simplest cases, as impossible measured by the excess of the sum of the three problems.
angles, made respectively by its bounding planes, But all this supposed difficulty vanishes, and above two right angles; and the magnitudes of the doctrine of solid angles becomes simple, sa- solid angles formed by n bounding planes, by tisfactory, and universal in its application, by the excess of the sum of the angles of inclination assuming spherical surfaces for their measure; of the several planes above 2n–4 right angles. just as circular arcs are assumed for the mea As to solid angles limited by curve surfaces, sures of plane angles. Imagine that from the such as the angles at the vertices of cones, they summit of a solid angle (formed by the meeting will manifestly be measured by the spheric surof three planes) as a centre, any sphere be de- faces cut off by the prolongation of their boundscribed, and that those planes are produced till ing surfaces, in the same manner as angles de they cut the surface of the sphere; then will the termined by planes are measured by the triangles surface of the spherical triangle, included be or polygons they mark out upon the same or an tween those planes, be a proper measure of the equal sphere. In all cases the maximum limit solid angle made by the planes at their common of solid angles will be the plane towards which point of meeting; for no change can be con the various planes, determining such angles, apceived in the relative position of those planes, proach, as they diverge farther from each other that is, in the magnitude of the solid angle, about the same summit; just as a right line is without a corresponding and proportional mu the maximum limit of plane angles, being formed tation in the surface of the spherical triangle. by the two bounding lines when they make an If
, in like manner, the three or inore surfaces, angle of 180°. The maximum limit of solid anwhich by their meeting constitute another solid gles is measured by the surface of a hemisphere, angle, be produced till they cut the surface of in like manner as the maximum limit of plane the same or an equal sphere, whose centre coin- angles is measured by the arc of a semicircle. cides with the summit of the angle; the surface The solid right angle (either angle, for example, of the spheric triangle or polygon, included be- of a cube) is $ (=1?) of the maximum solid antween the planes which determine the angle, will gle; while the plane right angle is half the maxibe a correct measure of that angle. And the mum plane angle. ratio which subsists between the areas of the The analogy between plane and solid angles spheric triangles, polygons, or other surfaces being thus traced, we may proceed to exemplify thus formed, will be accurately the ratio which this theory by a few instances; assuming 1000 subsists between the solid angles, constituted by as the numeral measure of the maximum solid the meeting of the several planes or surfaces, at angle = 4 times 90° solid = 360° solid. the centre of the sphere.
1. The solid angles of right prisms are comIt may be proper to anticipate here the only pared with great. facility. For, of the three anobjection which can be made to this assumption; gles' made by the three planes which by their which is founded on the principle that quantities meeting constitute every such solid angle, two should always be measured by quantities of the are right angles; and the third is the same as same kind. But this, often and positively as it is the corresponding plane angle of the polygonal affirmed, is by no means necessary; nor in many base; on which, therefore, the measure of the cases is it possible. To measure is to compare solid angle depends. Thus, with respect to the mathematically: and if by comparing two quan- right prism with an equilateral triangular base, tities, whose ratio we know or can ascertain, each solid angle is formed by planes which rewith two other quantities wnose ratio we wish spectively make angles of 90°, 90°, and 60°. to know, the point in question becomes deter- Consequently 90° + 90° +60° + 180°= 60°, is mined; it signifies not at all whether the magni- the measure of such angle, compared with 360° tudes which constitute one ratio are like or un the maximum angle. It is, therefore, one-sixth like the magnitudes which constitute the other of the maximum angle. A right prism with a ratio. It is thus that mathematicians, with per- square base has, in like manner, each solid angle fect safety and correctness, make use of space as measured by 90° + 90° + 90°
180° - 90°, a measure of velocity, mass as a measure of in- which is of the maximum angle. And thus it ertia, mass and velocity conjointly as a measure may be found that each solid angle of a right of force, space as a measure of time, weight as a prism, with an equilateral
Triangular base is $ max, angle = $. 1000.
=. 1000. Hexagonal
=k. 1000. Heptagonal
=f. 1000. Octagonal
=%. 1000. Nonagonal
= 1000. Decagonal
m-2 m gonal
2m Hence it may be deduced that each solid angle each solid angle of a prism with a regular hex. of a regular prism, with triangular base, is half agonal base. Each with regular
Square base = f of each, with regular octagonal base.
m gonal base.
m2 Hence again we may infer that the sum of all the sum of the solid angles of a prism of quathe solid angles of arty prism of triangular base, drangular base, regular or irregular. And the whether that base be regular or irregular, is half sum of the solid angles of any prism of
Tetragonal base is = f sum of angles in prism of pentagonal base.
heptagonal base. m gonal
(m+1) gonal base.
m-1 2. Let us compare the solid angles of the five plane angle formed by every two contiguous regular bodies. In these bodies if m be the faces of the tetraëdron, 70° 31' 42" ; of the hexnumber of sides of each face; n the number of aëdron, 90°; of the octaëdron, 109° 28' 18"; of planes which meet at each solid angle; $0= the dodecaëdron, 116° 33' 54"; of the icosaëhalf the circumference or 180°; and A the plane dron, 138° 11' 23'. But in these polyedræ the angle made by two adjacent faces; then we have number of faces meeting about each solid angle 1
are 3, 3, 4, 3, 5, respectively. Consequently the cos.-0
several solid angles will be determined by the 2n sin. } A= This theorem gives, for the subjoined proportions :
1000 : 250. Hexaëdron. 360° : 4:109° 28' 18' 360° :: 1000 : 216:35185 Octaëdron. 360° : 3.116° 33' 54' 180° :: 1000 : 471.395 Dodecaëdron.
360° : 5.138° 11' 23" · 540° :: 1000 : 419.30169 Icosaëdron. For more examples in illustration of this new Canadensis; 4. coesia ; 5. flexicaulis ; 6. lantheory see Hutton's Course, vol. iii. pp. 90, 91. ceolata; 7. lateriflora ; 8. latieolia; 9. Mexi
Solids, in anatomy, are the bones, ligaments, cana; 10. minuta ; 11. noveboracesis; 12. ri. membranes, muscles, nerves, and vessels, &c. gida; 13. sempervirens; and 14. S. virgaurea, The solid parts of the body, though equally com or golden rod, which grows frequently in rough posed of vessels, are different with regard to mountainous pastures and woods; and is the their consistence; some being hard and others only species which is a native of Britain. The soft. The hard, as the bones and cartilages, stems are branched, and vary from six inches to give firmness and attitude to the body, and sus- five feet high, but their common height is about a tain the other parts. The soft parts, either alone yard. The leaves are a little hard and rough to or together with the hard, serve to execute the ihe touch; the lower ones oval lanceolate, geanimal functions. See ANATOMY, Index. nerally a little serrated and supported on foot
SOLIDAGO, in botany, golden rod, a genus stalks; those on the stalks are elliptical ; the of plants belonging to the class of syngenesia, flowers are yellow and grow in spikes from the and to the order of polygamia superflua; natural alæ of the leaves; the scales of the calyx are order forty-ninth, compositæ. The receptacle lanceolate, of unequal length, and of a pale is naked ; the pappus simple; the radii are green color;
the female florets in the rays are commonly five; the scales of the calyx are im- from five to eight; the hermaphrodite flowers bricated and curved inward. There are fourteen in the disc from ten to twelve. There is a vaspecies ; viz. 1. S. altissima; 2. bicolor; 3. riety of this species called S. virgaurea cambrica,
a native of Wales, which is found on rocks from culed, it appears to be founded both on Scripture six inches to a foot high.
and reason; and, as sin and misery entered by SOLIDATUM, used in the neuter gender, is the want of faith in the first threatening, so the taken for that absolute right or property which a only remedy is sola fide, by faith alone in the man has in any thing.-Malmsb. lib. i.
great work performed by our Saviour. Solidity, in philosophy, is that property of SOLIFIDIANISM (from sola and fides) matter, or body, by which it excludes all other The doctrine of salvation by faith alone. See bodies from the place which itself possesses; last article. and, as it would be absurd to suppose that two SOLIGNAC (Peter. Joseph De La Pimpie, bodies could possess one and the same place at chevalier of), a learned and amiable French histhe same time, it follows that the softest bodies torian, born at Montpelier in 1687. He was are equally solid with the hardest. See Meta- employed by the French court in a respectable Physics. "Among geometricians the solidity of situation in Poland, where he became acquainted a body denotes the quantity or space contained with king Stanislaus, who made him his secrein it, and is called also its solid content. The tary. Ile wrote a History of Poland, and other solidity of a cube, prism, cylinder, or parallelo- works; and died in 1773, aged eighty-six. piped, is had by multiplying its basis into its SOLIL'OQUY, n. s. Fr. soliloque ; Lat. solus height. The solidity of a pyramid or cone is and loquor. A discourse made to one's self. had by multiplying either the whole base into a If I should own myself in love, you know lovers third part of the height, or the whole height into are always allowed the comfort of soliloquy. a third part of the base.
Spectator. SOLIDUNGULOUS, adj. Lat. solidus and He finds no respite from his anxious grief, ungula. Whole-hoofed.
Then seeks from his soliloquy relief. It is set down by Aristotle and Pliny that an
Garth's Disp. horse, and all solidungulous or whole-hoofed animals, The whole poem is a soliloquy: Soloroon is the have no gall; which we find repugnant unto reason.
person that speaks : he is at once the hero and the Browne's Vulgar Errours. author ; but he tells us very often what others say to
him. SOLIFID’IAN, n. s. Lat. solus and fides.
Prior. One who supposes only faith, not works, neces A SOLILOQUY, according to Papia, is a dissary to justification.
course by way of answer to a question that a It may be justly feared that the title of fundamen man proposes to himself. Soliloquies are betals, being ordinarily confined to the doctrines of come too common on the modern stage; yet can faith, hath occasioned that great scandal in the nothing be more inartificial, or more unnatural, church of God, at which so many myriads of soli- than an actor's making long speeches to bimself
, fidians have stumbled, and fallen irreversibly, by con to convey his intentions, &c., to the audience. ceiving heaven a reward of true opinions. Hammond. Where such discoveries are necessary to be
Solifidians. Without entering into this made, the poet should rather take care to give controversy, as a point of religion, which has the dramatic persons such confidants as may more or less divided Protestants ever since the necessarily share their inmost thoughts; by which reformation, we would beg leave to consider the means they will be more naturally conveyed to subject, for a moment, in a philosophical point the audience. Yet is even this a shift an accuof view. The whole argument seems to resolve rate poet would not be found to have occasion itself into this simple question of philosophy, for. The duke of Buckingham has well said, Can a created being merit any thing at the hand • Soliloquies had need be very few, of its creator? The candid philosopher will
Extremely short, and spoke in passion too. certainly answer this question in the negative.
Our lovers talking to themselves, for want If then, even upon the supposition of the crea
Of others, make the pit their confidant :
Nor is the matter mended yet, is thus ture having never sinned, it can merit nothing, how much less can a sinful creature, by any ex
They trust a friend, only to tell it us.' ertions of its own, atone for its past offences ? Soliloquies are not, however, quite so unnaObvious as this truth seems to be, yet the oppo- tural as some think. Let a man be alone, and site doctrine, that something can and must be his thoughts anxiously bent on some object, and done by the sinner, to atone for his past sins and he will involuntarily speak out to himself. merit forgiveness, has formed a constituent part SOLIMAN I., emperor of the Turks, sucof all religions, in all ages and countries, from ceeded his father Bajazet I. in 1403. He was a the most dark and bloody superstitions, which brave and enterprising prince, hut very inuch placed merit in human sacrifices, and even sa- devoted to his pleasures. He was dethroned by crificed children to pacify the offended deities, his brother Moses or Musa in 1410, and soon down through the whole system of popery till after murdered. the reformation. Nor have even the reformed Soliman II., emperor of the Turks, surnamed churches got entirely rid of it, as appears from the Magnificent, was the only son of Selim I, the above quotation from Dr. Hammond, as well whom he succeeded in 1520. He was educated as from the whole of the Arminian system. But in a manner very different from the Ottoman the church of Rome certainly carried the doc- princes in general; for he was instructed in the trine to the most extravagant height, when they maxims of politics and the secrets of governtaught that a man could not only, by his good ment. He began his reign by restoring those works, merit forgiveness for his own sins, but persons their possessions whom his father had acclimulate such a stock of works of superero- unjustly plundered. He re-established the acgation as to atone for the sins of his neighbours ! thority of the tribunals, and bestowed the govemIn a word, however Solifidianism may be ridi- inent of provinces upon none but persons of
wealth and probity: 'I would have my viceroys that he has been called Pliny's ape. The best
Browne's Vulgar Errours.
writings. He turned priest at fifty-seven years SOLIMAN III., the son of Ibrahim I., was taken of age, and died in 1686, aged seventy-six. from prison and made emperor by the Janizaries, Solis (John Dias de), a Spanish navigator, in 1687, on the deposition of Mahomet IV. his the first who sailed up the river Plata, in 1515. brother, whom he sent to the same jail. He was SOLITARIES, an order of nuns of St. Peter an indolent prince, wholly governed by his mi- of Alcantara, instituted in 1676, the design of nisters; and died in 1691.
which was to imitate the severe penitent life of SOLIMENE (Sir Francis), an eminent painter, that saint. Thus they are to keep a continual born at Nocera near Naples in 1657. He studied silence, never to open their mouths to a stranfirst under his father Àngelo, who was a good ger; to employ their time wholly in spiritual painter, and next under Francis Maria at Naples exercises, and leave their temporal concerns to a in 1674, who, envying his rising merit, wished number of maids, who have a particular supeto discourage him. He soon became eminent, rior in a separate part of the monastery: they however, in chiaro obscuro; and painted the always go bare-footed, without sandals; gird Jesuit's chapel of St. Anne in a style so supe- themselves with a thick cord, and wear no linen. rior that he astonished painters of established SOL'ITARY, adj. & n. s. Fr. solitaire ; reputation. Philip V. employed him and invited SOLITAIRE', n. s.
Latin solitarius. him to Madrid, as also did Louis XIV. to Paris, SOL'ITARILY, adv.
Retired; living but he declined. The emperor Charles VI. was SOLI'TANINESS, n. s.
single; so pleased with his paintings that he knighted SOL'ITUDE.
lonely; dismal: a him. In 1701 he went to Rome, where he was solitary or solitaire is, one who lives alone; a much patronised by the pope and cardinals. He hermit: the adverb corresponding with the adwas also a poet, and his Sonnets are esteemed. jective: and solitude and solitariness both mean, He died in 1747, aged ninety.
lonely life or place; state of being solitary. SOLINUS (Caius Julius), a Latin grammarian and historian, born at Rome in the end of
Let that night be solitary, let no joyful voice come therein.
Job. the first century, according to Lempriere, but
Feed thy people with thy rod, the flock of thine according to Dr. Watkins in the middle of the heritage which dwell solitarily in the wood. third. His Polyhistor is a collection of histo
Micah vii. 14. rical and geographical remarks on the most cele You subject yourself to solitariness, the sly enemy brated places of antiquity. Pliny is often quoted that doth most separate a man from well-doing. in it, and it is written so much in Pliny's style,
How should that subsist solitarily by itself which in pieces consisting of several parts, to mark those hath no substance, but individually the very same that are to perform alone; as fiauto solo, violino whereby others subsist with it?
Hooker. solo. It is also used for sonatas composed for In respect that it is solitary, I like it very well ; one violin, one German flute, or other instrumen, but, in respect that it is private, it is a very vile life. and a bass; thus we say, Corelli's solos, Gemi
niani's solos, &c. When two or three parts play It had been hard to have put more truth and untruth together, in few words, than in that speech,
or sing separately from the grand chorus, they Whosoever is delighted with solitude is either a wild are called a doi solo, a tre solo, &c. Solo is beast or a god.
sometimes denoted by S. At home, in wholesome solitariness,
In the concertos of Corelli, Geminiani, and My piteous soul began the wretchedness Handel, chiefly composed à due cori, or two Of suitors at the court to mourn.
Donne. orchestras, the principal parts are said to belong Nor did a solitary vengeance serve; the cutting to the concertini, or solo parts; as violino primo off one head is not enough ; the eldest son must be concertino, violino secondo del concertino, &c.: involved.
and the inferior parts, that only play in the full Those rare and solitary, these in flocks. Milton. What callest thou solitude ? Is not the earth
chorus, are called ripieni; as violino primo si. With various living creatures, and the air,
pieno, violino secondo, ripieno, or del concerto Replenished, and all these at thy command,
grosso, or the great and full concert. Solos,
which used to afford the most exquisite delight To come and play before thee ? Id. Paradise Lost. Relations alternately relieve each other, their mu
to persons of refined taste, when composed and tual concurrences supporting their solitary instabili performed by great masters, are now wholly laid ties.
aside; and whoever attempts to perform one is Him fair Lavinia
subjected to a penalty instead of a reward; a Shall breed in groves to lead a solitary life.
law instituted at the concert of ancient music, Dryden's Æneid.
where a composition was never thought comSuch only can enjoy the country, who are capable plete by the late earl of Sandwich, without a of thinking when they are there : then they are pre- kettle-drum, nor with, unless he beat it himself. pared for solitude, and in that solitude is prepared for And at the commemoration of Handel, the douthem.
Dryden. Often have I been going to take possession of tran
ble drums, double cartels, tromboni, &c., aug
mented his lordship's pleasure, in proportion to quillity, when your conversation has spoiled me for a solitaire.
the din and stenterophonic screams of these You describe so well your hermetical state of life, truly savage instruments; which, in so wide a that none of the ancient anchorites could go beyond building as Westminster Abbey, and softened by you, for a cave with a spring, or any of the accommo so powerful a chorus of voices and instruments dations that befit a solitary.
Id. Letters. as were assembled at the commemoration, had, In these deep solitudes, and awful cells,
occasionally a fine effect; but, in a more conWhere heavenly pensive contemplation dwells. fined space, the almost incessant use of the
Pope. tromboni, and perpetual roll of the double To be exempt from the passions with which others drums, annihilate all the pleasing effects of melare tormented' is the only pleasing solitude. I can lifluous tones. very justly say, with the ancient sage, 'I am never SOLOEIS, Soloentia, or Solus, a promonless alone than when alone.'
Steele. The solitude of his little parish is become matter tory of Lybia, at the extremity of Mount Atlas; of great comfort to him, because he hopes that God
now called Cape Cantin. has placed him and his flock there, to make it their
SOLOENTIA, or Solosis, an ancient town of way to heaven.
Law. Sicily, between Panormus and Chimera, now î'he man to solitude accustomed long
called Solanto. Perceives in every thing that lives a tongue ;
SOLOFRA, a town in the Principatro Ultra, Not animals alone, but shrubs and trees
Naples, with 6100 inhabitants. It has manuHave speech for him, and understood with ease. factures of leather, parchment, and gold and sil
Cowper. ver plate. SOL'LAR, n. s. Low Lat. solarium. A garret. SOLOMON, Heb. 1950, i. e. peaceable, the Some skilfully drieth their hops on a kel,
son and successor of David, king of Israel, by And some on a sollar, oft turning them wel. Tusser. Bathsheba; who seems to have been so named
SOLO, or SAURA-Corta, an inland town and by his father in the spirit of prophecy, as he had district of Java, the residence of an emperor. the most peaceable and flourishing reign of any The town is populous, intersected with broad monarch in Israel or Judah. He was born about and shaded avenues or streets, running at right A. M. 2971. His judicious government in the angles. The Crattan, where the emperor re- early part of his reign; his repeated divine comsides, is very spacious, and comprises several munications, and wise choice; his extensive and palaces : the other chiefs and nobility live in successful commerce with Egypt, Ophir, Tyre, villas, surrounded by hign walls. The Euro- &c.; his immense riches in consequence; "his pean town and fort here are very neat. The fame for wisdom, which reached the most re latter, not above 800 yards from the Crattan, mote corners of the civilised world (see Suela); contained a British garrison, when the island of his superb building and solemn dedication of the Java was in possession of this country. A fine temple, with his excellent prayer on that occariver flows near this town, and, passing through sion, and his costly sacrifices, miraculously conthe dominions of the sultan and emperor, falls sumed; with his feast of seven days given to into the harbour of Gressie.
the whole people, and many other interesting Solo, in the Italian music, is frequently used particulars of his reign, are recorded in 1 kings