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For gold it is usual to employ an alloy of fine gold with silver or copper, or with both of those metals. These are sometimes used in the following proportions:-pure gold twelve parts, pure silver two parts, and copper four parts. The metals are fused together, beat into thin leaves, and then softened by annealing. Borax mixed to a thick consistence with water is applied to the joint, and the solder is melted by the blowpipe. It is stated in Brewster's Edin. Ency,' that the borax may be removed by boiling water, or diluted sulphuric or muriatic acid; and that the paleness of the solder may be remedied by melting upon its surface a mixture of two parts of nitre and one of burnt alum, and then washing it off with hot water. The same authority states that gold articles may be cleaned after soldering by boiling them in urine and sal ammoniac, and those of silver by boiling in alum-water.

technic Society in May, 1840, and published in the Mecha- | peatedly heated and quenched in water, by which it becomes nic's Magazine,' vol. xxxii., p. 729, &c. An almost infinite sufficiently friable to be beaten to a coarse powder with an variety of alloys are used in different kinds of soldering, the iron pestle and mortar. Several papers respecting this principal of which, as recommended by the best authorities, method of soldering were published in the Technical Rewill be described below, classified according to the metals pository,' vols. i., iii., and iv.; from which it appears that which they are commonly used to unite. the process was, about sixteen or eighteen years ago, pracPlatinum is soldered, according to Dr. Ure, with fine tised in such a way as to lead to the supposition that it was gold. rather a welding than a soldering operation; the solder being applied in the form of a black shining composition resembling pitch, which Mr. Gill conceived to be cast-iron powdered and mixed with glass of borax; and the joints being subjected to a slight hammering. The parts united by this means are stated to be scarcely distinguishable. In making fine steel instruments, gold, either alone or with a slight alloy of copper, is often used as solder. Silver solder, being less expensive, and nearer the colour of the steel, is preferred by some for this purpose. An alloy of nineteen parts fine silver, one copper, and two brass, has been recommended for steel joints. In larger articles of iron and steel, a solder consisting of equal parts of tin and iron is sometimes used. Common plumbers' solder is made of two parts lead and one part block tin; or of the same metals mixed in nearly equal quantities; bismuth is added when it is desired to make the alloy more fusible. Soft solder has two parts tin to one lead; and other alloys of tin, lead, and bismuth, are used for uniting various articles of lead, tin, pewter, and other soft compounds. Such highly fusible solders are usually cast in ingots or strips, and melted as they are used by means of an instrument called a soldering iron, which is tipped with copper-that metal being preferred for its greater affinity for tin. In soldering tin plates together, their edges are made to overlap; but in almost every other case the edges to be joined are made only to meet, the solder being run between their abutting edges.

Silver solders usually consist of silver mixed with brass, and sometimes with zinc. Dr. Ure states that pure tin is occasionally used as a solder for silver, but that the solder commonly used is an alloy of five parts silver, six brass, and two zinc. Some authorities give nineteen silver, one copper, and ten brass, as the proportions in jewellers' silver solder; and two parts of pure silver to one of brass as the composition of solder for plating. Another solder for coarser silver has four parts silver to three of brass, with a little borax; and a hard silver solder is made of equal parts of silver and fine brass. The addition of zinc softens this alloy. Mr. Gill, in an article on soldering in jewellery, in the Technical Repository,' vol. ii., p. 63, states that the thin laminated solder is cut up into very small bits, and applied with borax and water. The article to be soldered is laid on charcoal ashes, and submitted to the jet of a blowpipe. To prevent the solder from spreading over the surrounding parts, they may, he observes, be coated with Indian ink laid on with a camel's-hair pencil. The fluid borax is also applied with a hair-pencil, and the solder with the end of the ivory handle on which the pencil is fixed. Filagree-work is soldered in a somewhat different manner; the minute parts being laid together in their proper position on a flattened piece of charcoal, which is smeared with a thick solution of gum tragacanth to hold them steady. The fluid borax is then brushed over, and the solder, reduced to a fine powder, is sprinkled upon it. In this as in all other kinds of soldering, whenever several parts must be successively put together, it is necessary to use solders of different degrees of fusibility; the least fusible being used first, so that the joints made with it may not be disturbed by the heat of the subsequent operations.

The Technical Repository' (vol. iv., p. 57) gives an account of a curious mode of soldering resorted to in order to fix upon the back of the dial-plate of a watch the small copper studs by which it is attached to the plate which encloses the wheel-work. The heat required for melting spelter solder would be injurious to the enamel, and therefore the studs are made of wire plated with silver, and fixed by melting the silver on their sides, and causing it to run down to their base, where borax and water is previously lar Thus the studs are fixed without applying the jet of the blowpipe immediately to the back of the enamelled plate.

A kind of soldering, called burning-to, has been long practised in some cases with sheet-lead, where it has been desirable to make a vessel entirely of that material; the junction being effected by pouring melted lead on to the edges to be united, until they fuse together. Somewhat similar to this is the process recently introduced under the name of autogenous soldering. This process, which is the invention of a French gentleman, M. de Richemont, consists in the union of two pieces of metal without the interposition of any solder, by fusing them at the point of juneSpelter solder is used for brass, copper, and iron, and con- tion by jets of flame from a gas blowpipe. The apparatus sists of zine (spelter) mixed with copper or brass, and some- used for the purpose contains a hydrogen gas generator, times also with tin. The proportions vary greatly. Gill bellows for atmospheric air, and valves for regulating the gives eighteen parts brass, three zine, and two tin; or six-proportion in which the gas and air are to be mixed. A teen parts copper, sixteen zinc, and one tin. (Technic. Rep., i., 432.) Dr. Ure says it consists of zinc and copper in nearly equal parts. Brewster's Edin. Ency.' describes it as consisting of two parts zinc and one brass, and observes that the addition of one dwt. of silver to each ounce is a great improvement. In the Dict. Technologique,' as quoted in vol. vi. of Gill's 'Technical Repository,' p. 181, the following solders for copper are mentioned:-eight copper and one zine, which form a very hard yet fusible and malleable solder; three copper and one zine; and ten copper and one zine. The latter forms the hardest but least fusible solder. Generally the addition of copper increases the hardness and diminishes the fusibility of the alloy. For hard brass solders the same proportions are recommended, but brass is substituted for copper. The proportions may vary, it is stated. from two to sixteen parts of brass to one part of zine. Six brass, one zine, and one tin, form a soft solder for brass. An alloy of two parts copper and one part tin is sometimes used as a hard solder. All the above-mentioned hard solders are granulated, and applied to the joint in the form of a coarse powder.

Articles of wrought-iron, and some qualities of steel also, may be soldered with cast-iron; the cast-iron being re

complete description, with cuts, of this machine, is given in the Mechanic's Magazine' (vol. xxxii., p. 546). The mvention has been rewarded in Paris by a gold medal, at the National Exhibition of Arts, and is patented in this country. It has hitherto been applied chiefly to lead, but appears suitable for metals more difficult of fusion. By its adoption lead may be applied very extensively in chemical vessels, in which the use of solder has been inconvenient or impossible, owing to its degree of expansibility differing from that of lead, and its greater liability to be acted upon by acids. The joints formed in this way are also much neater and less liable to flaws than those made by the common process. It appears by the paper referred to at the commencement of this article, that Mr. Spencer discovered this process about the same time as M. de Richemont; and his experiments lead him to suppose that, by varying the admixture of gases, a jet of flame may be produced of intensity suitable for any metal to which it may be desired to apply the new mode of soldering.

SOLDIER is a term applied now to every man employed in the military service of a prince or state, but it was at first given to such persons only as were expressly engaged for pay, to follow some chief in his warlike expeditions.

Cæsar mentions a band of 600 men called 'soldurii,' who bound themselves to attend their leader in action and to live or die with him (De Bello Gallico, iii. 22), but it does not appear that they served for pay. By some the word has been thought to come from solidus,' the name of a coin under the Roman empire, which may have been received as the payment for the service.

The troops which formed the armies of the Crusaders were engaged to serve for pay, for though the nobles voluntarily entered into the war, their vassals were not obliged by the tenure of their fiefs to accompany them. Père Daniel (Hist. de la Milice Fr., tom. i., p. 103) expresses his belief that Philip Augustus, near the end of the twelfth century, was the first of the French kings who had hired troops, at least in any considerable body, in his service; and the practice of retaining such troops appears to have been afterwards very general. It is probable that men hired for the wars were, from the time of that prince, called soudoyers or souldyours, that is, stipendiaries; but the name appears for the first time in the Chronicles' of Froissart, where it is applied to the hired troops both of France and Germany. It is stated that Jaques Dartvell (von Artaveld) of Ghent (1339) kept a guard of 60 or 80 souldyers, each of whom was paid four Flemish groats daily (liv. i., c. 29). About the same time Philip de Valois, in revenge for an inroad which had been made into his country, gave leave to the soudyers of France to plunder the lands of Sir John of Hainault (liv. i., c. 44); and the name occurs in many other parts of the work. This class of troops at that time engaged themselves to fight for any party which would employ and pay them; and when not occupied in the wars, they used to wander about the country in large bodies, plundering the people and committing every enormity. The terms routiers' and 'brigands,' as words of reproach, were applied to them, and they appear to have been as formidable to those who hired them as to the enemy. In the reign of Charles V. of France, Bertrand du Guesclin led them into Spain to serve against Peter the Cruel, and in that country great numbers of them remained, yet the disorders which they caused in France did not terminate till Charles VII., in 1445, and Louis XI., in 1480, established a regular militia, which was paid by the state.

In the wardrobe account of Edward I. (1300) the term soldier occurs frequently, and Grose considers that the persons so designated were of a different class from the other troops. Some of them are called soldiers scutifers,' or esquires; some, 'soldiers constables;' and others, simply soldiers; but the pay of all was the same, viz. one shilling per day. (Mil. Antiq., vol. i., p. 326.) From the time of Edward I. to the end of the reign of Edward III. the daily pay of a banneret was 4s., and of a knight, 2s.; that of a hobiler, a sort of light horseman, was 6d.; of a crossbowman, 4d. ; and of an archer, 2d. In that age the stipendiary troops, or soldiers, were raised in England by commissions ganted by the king to persons who undertook to enlist men for a certain pay (which was made to depend on the nature of the service), and for a certain portion of the ransommoney which might be obtained in the war.

Little change seems to have taken place in the pay of the English soldiers between the times of Edward III. and Mary. We find that during the reign of this queen the daily pay of a captain of heavy cavalry was 108., and of a cavalry soldier is. 6d. The pay of a captain of light caalry was 68., and of a soldier is. The pay of a captain of foot was 48., of a lieutenant 2s., of an ensign 1s., and of a foot soldier Sd.; a halbardier and a hackbutter, on horseback, had each, 18. daily. In the times of Elizabeth, James I., and Charles I., the pay of the officers was a little raised, but that of a private foot-soldier was still 8d. per day during the civil wars the pay of the latter was 9d., but in the reign of William III. it was again reduced to 8d. At that time the pay of a private trooper was 28. 6d., and that of a private dragoon was 1s. 6d., including in both cases the allowance for the horse. It is evident that the pay of the private soldier in later times is far from having been raised in the inverse ratio of the value of money.

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While armour was in general use, the common soldiers of England were distinguished only by scarfs or by badges, on the latter of which were impressed the arms of their several leaders; but in the reign of Henry VIII. something like a uniform was worn, and it appears that the colour of the men's upper garments was then generally white; the soldiers in the king's particular service only, had on their coats

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a representation of the cross of St. George. However, on an army being raised in 1544, the soldiers were ordered to wear coats of blue cloth bordered with red. White cloaks marked with red crosses continued to be the uniform of the troops during the reign of Queen Mary; but in the time of Elizabeth the infantry soldiers wore a cassock and long trowsers, both of which were of Kentish grey: the cavalry were furnished with red cloaks reaching down to the knee and without sleeves. Grey coats, with breeches of the same colour, continued to be the uniform as late as the end of the reign of William III., but soon after that time red became the general colour for the coats of the British infantry soldiers.

The low condition of the first soldiers in France has been mentioned in the article INFANTRY: with respect to those of England in the times of Henry VIII. and Edward VI., we have a more favourable account; for Sir John Smithe, in the preface to his tract on Military Instruction' (1591), observes that the order and discipline in the armies during the reigns of those kings were so good, that the men, on being discharged, were never seen to become rogues or to go begging under pretence that they had been soldiers, as, he observes, they now most commonly do. In the preface to his Discourses on the Forms and Effects of Weapons' (1590), he complains that, in his time, the commanders of troops serving abroad, instead of publishing regulations for the conduct of the men, gave a few laws artfully tending to deter the soldiers from demanding their pay, but in no way probibiting them from plundering the people of the country: he adds that they esteemed those soldiers to be the best who, by robbery, could live longest without pay. He complains also that while the commanders were gallant in appearance, and had their purses full of gold, the soldiers were without armour, ragged, and barefooted; and that when money was to be received, they used to send the men on desperate enterprises, in order that they might obtain the pay of those who were killed. He adds that, in the summer before the earl of Leicester went over (to Holland) the commanders devised a manner of paying the soldiers which had never before been heard of; instead of money, the men were paid in provand, under pretence that they knew not how to make purchases; by which means, the food supplied being of an inferior kind, great part of the soldiers' pay was put in their own pockets. It appears that Queen Elizabeth, on being informed of these abuses, caused the practice of paying in provand to be abolished. We find that subsequently, even so late as the time of George I., the pay both of officers and private soldiers was frequently postponed for years, and was sometimes entirely withheld. Happily such injustice no longer exists in the British army; the pay of the soldier is assured to him by the nation; and a well-appointed commissariat provides, as far as possible, for his wants while in the field.

It must be admitted that, till lately, the condition of a private soldier, both in this country and on the Continent, was unfavourable for inspiring a love of the service in his mind. Obliged to be furnished with good clothing and to preserve a becoming appearance, that which remained of his scanty pay scarcely sufficed for procuring the food necessary for his support. In his barracks he was subject to numerous petty details of duty, which produced weariness and even disgust; and, at all times, to the restraints of discipline, which deprived him of the recreations enjoyed by other classes of men. It may be added, moreover, that the soldier had too often the mortification to find himself despised for his poverty by persons with whom men of his condition are accustomed to associate. These disadvantages are now however in a great measure removed; and the pay of the soldier suffices to afford him the means of obtaining the comforts of life in a degree, at least, equal to those which are enjoyed by an ordinary peasant or mechanic. With the improvement of his condition, a corresponding improvement in the character of the soldiers has taken place: men of steady habits are induced to enlist, and officers are enabled to select the best among those persons who present themselves as recruits for the army.

The duties of the soldier are now rendered as little burthensome as is consistent with the good of the service; and the regulations, promulgated by the highest authorities, prescribe that he shall at all times be treated with mildness and humanity: even the non-commissioned officers are rcquired to use patience and forbearance in instructing the recruits in their military exercises. When breaches of dis

cipline on the part of the soldier oblige a commander to order the infliction of punishment, attention is paid as much as possible to render it a means of promoting a reformation of character: the lash is now very sparingly used. Wherever a regiment be now quartered, there is established for the soldiers a school, which the men are obliged, as part of their duty, to attend, and which is generally furnished with a library for their use. The library and school are formed and supported by the subscriptions of the officers, and both have been found to contribute greatly to the preservation of sobriety and good conduct among the men, by weaning them from the haunts of idleness and dissipation, and giving them a taste for useful knowledge. In time of peace the soldier, being surrounded by the members of civil society, must, like them, conform to its laws; and, being under the influence of public opinion, he is, unconsciously to himself, held in obedience by them; so that no extraordinary coertion is necessary to keep him within the bounds of civil or military law. But in the colonies the soldier, even though he be serving in a time of peace, has many temptations to fall into a neglect or breach of discipline: he is far removed from the friends of his early life, who may have exercised upon his mind a moral influence for good: he sees around him only the conduct, too frequently licentious, of the lower orders of people in the country where he is stationed; and it may be that he is not fortified with the principles which should have been im planted in his mind by a sound education. The probability of a return to his native land before many years have passed is small, and the diseases to which he is exposed from the unhealthiness of the climate frequently terminate fatally: hence he becomes reckless from despair, and the facilities with which wine or spirituous liquors may often be obtained lead him into excesses which, while they accelerate the ruin of his health and render him unfit for duty, cause him to commit offences both against discipline and morals. Thus in the colonies there arises a necessity for greater restraints on the freedom of the soldier, and for the infliction of heavier punishments than are required at home. (Maj.Gen. Sir Chas. Napier, Remarks on Military Law.) Lastly, in time of war and on foreign service a vigorous discipline is essentially necessary: the privations to which soldiers are then exposed strongly induce those who are not thoroughly imbued with moral and religious principles to plunder the country-people, in order to supply their immediate wants, or to drown the sense of their sufferings in liquor. It ought also to be observed that, in war-time, many turbulent spirits are induced to enter the army in the hope of enjoying the licence which the military life abroad appears to hold out. These men are the ring-leaders in all excesses, and they too commonly cause many of those who are weak in principle to join them; in such cases therefore the most severe coercive measures must be immediately applied, if discipline is to be preserved in the army. The efforts made by the British commanders, during the war against the French in Spain, to maintain order, and prevent the people of the country from being injured, were great and praiseworthy; and perhaps fewer crimes were committed by the British troops than by those of their allies or their enemies; but it is to be lamented that there were still too many occasions in which the national character was disgraced by the misconduct of its soldiery.

SOLE. [PLEURONECTIDE.]

SOLECISM (soloecismus, σoλoikioμóç), a grammatical term which is used by the later Greek and Roman writers, and by modern grammarians also, though in a somewhat different sense. It is defined by Sinnius Capito (Gell., v. 20) as an unequal and improper arrangement of the parts of speech, that is, as a violation of the rules of syntax. Quinctilian (i., s. 28, &c.) specifies four kinds of solecisms: the first consists in the addition of a superfluous word; the second, in leaving out one that is necessary; the third, in perverting the order of the words of a sentence; and the fourth, in using an improper form of a word. The antients also used the word in a wider sense, understanding by it any kind of fault, error, or mistake, whether made in speaking, writing, or acting. Modern grammarians designate by solecism any word or expression which does not agree with the established usage of writing or speaking. But as customs change, that which at one time is considered a solecism, may at another be regarded as correct language. A solecism therefore differs from a barbarism, inasmuch as the latter consists in the use of a word or expression which is

altogether contrary to the spirit of the language, and can properly speaking, never become established as corect language.

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The term solecism was supposed by antient grammarians to be derived from Soli, a town of Cilicia, where the language of the original Greek settlers, who were few in numbers, became corrupt through the influence of the people by whom they were surrounded.

SOLEŃ. [PYLORIDIANS, vol. xix., p. 145, et seq.] SOLENA'CEA, Lamarck's name for a family of bivalve testaceous mollusks, including the genera Solen, Panopɗa, and Glycymeris. [PYLORIDIANS, vol. xix., pp. 145, et seq.] SOLENE'LLA, Sowerby's name for a genus of testaceous bivalve mollusks apparently belonging to the family Aroucea of Lamarck, and partaking of the characters of the genus Nucula [POLYODONTA, vol. xviii., p. 363], and of the family SOLENACEA.

Generic Character.- Shell oval, equivalve, sub-equi lateral, compressed, covered with a thin shining olive-green epidermis. Hinge with many teeth, three or four of which are anterior, and the numerous rest sharp, posterior, lateral, and arranged in a straight line. Two lateral muscular impressions. The pallial impression with a large sinus. Ligament external, prominent, and elongated.

Example, Solenella Norrisii. A few specimens of this the only known species, were dredged up by Mr. Cuming at Valparaiso.

SOLENIMY'A, or SOLEMY'A. [PYLORIDIANS, tol. xix., p. 146.] SOLENOCURTUS, or SOLECURTUS. DIANS, vol. xix., p. 144.]

[PYLORI

SOLE'NODON, a genus of insectivorous mammals established by Brandt on a specimen sent from the island of Hispaniola by Jaeger.

Generic Character.-Habit generally between that of Sorex and Didelphys. Muzzle elongated, the snout smooth produced, and with nostrils at the sides of its apex. Eyes minute. Ears large, rounded, nearly naked. Body hairyStern and upper part of the rump beset with a few very short silky hairs. Feet ambulatory, plantigrade, pentadactylous; claws falcular, those of the fore feet the longest. Teats inguinal? Tail long, smooth, and for the most part scaly.

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The skull of Solenodon is considerably elongated: the occipital, parietal, and temporal bones are moderately convex; and the condyles of the occipital are prominent. There is an obtuse crest on the sagittal suture, but none on the coalesced frontal bones. The internal pterygoïd processes alone are conspicuous, thin, and joined by a suture with the perpendicular parts of the palatal bone. There is no bony bulla, and, consequently, the interior wall of the tympanic cavity is only closed by skin. There is no zygomatic arch. The coronoid process of the mandible is dilated and directed outwards. The angle of the mandible is dilated, subtetragonally rounded, and prominent above the condyloid part.

The two anterior upper incisor teeth are the largest, disjoined from the others, perpendicular, and unicuspid: the two anterior lower incisors are very short and very narrow; the two middle are the longest, and conical and excavated on the internal surface with a rather deep triangular canal. Brandt remarks that the structure of the teeth manifests a greater similitude to that of Myogale (Mygale) than any other genus.

Example, Solenodon paradoxus.

Description.-Sides of the head and neck dilute yellowbrown, mixed with ferruginous, and, occasionally, with grey. Abdomen and feet dilute yellow-brown, with hardly a mixture of grey. Space upon the breast between the anterior limbs dilute ferruginous, extended to the internal side of the feet, and, anteriorly, to the cubit. A similarly coloured space occupies the inguinal region, and also extends upon the anterior part of the legs. Upper part (dorsum) of the muzzle, forehead, vertex, middle of the nape, and anterior part of the back, tinged with black-brown: the rest of the back black-brown, the colour (more diluted) extending towards the posterior part of the sides and towards the ex

ternal surface of the thighs. The basal and middle part The form of the nose and of the cribriform plate seems, he of the scaly tail grey; the apical part white.

observes, to indicate a well-developed organ of smell.

The true place of this animal is, most probably, among the SORICIDE.

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a, skull of Solenodou (profile): b, seen from above; c, seen from below: , mandible or in wer jaw; e, anterior part of the intermaxillary bone, with the tao anterior incisor teeth; fanterior surface of an anterior upper incisor tooth; c. anterior parts of the maudible, with the four anterior incisor teeth; h, the Crown of a second or m'ddle incisor tooth of the mandible, seen on its internal surface, and exhibiting its triangular canal. The foregoing figures are nearly of the natural siz". i, teeth of the upper jaw seen laterally; 1. 1, nat. size; 2,2, magnified. (Brandt.)

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Solenodon paradoxus. (Brandt, Memoirs of the Imperial Academy of Sciences of St. Petersburg, 1832-3.)

SOLETELLI'NA. [PYLORIDIANS, vol. xix., p. 144.]
SOLEURE. [SOLOTHURN.]

SOL-FA-ING. [SOLMISATION.]

SOLFATA'RA. [PHLEGREI CAMPI.]

SOLICITOR. [ATTORNEY; SIX CLERKS.]

SOLID, SOLIDITY. (Mechanies.) A solid body is one which is composed of matter so connected together that the relative positions of its parts cannot be altered without the application of sensible force. The force which resists the alteration of the relative positions is called force of COHESION: the perfect absence of this force constitute fluidity. [FLUID.]

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The

SOLID ANGLE, a name given to the idea of opening conveyed by three planes which meet at a point. properties of a solid angle are considered under the head SPHERICAL TRIANGLE.

SOLID, SURFACE, LINE, POINT. (Geometry.) We have thought it best to bring together the remarks which it is necessary to make upon these fundamental terms of geometry. According to Euclid, a point has no dimensions; a line, length only; a surface, length and breadth; a solid, length, breadth, and thickness. No one has the least doubt about each of these terms conveying a clear and distinct notion; in spite of this however, the propriety of the definitions has been made matter of much discussion.

Space being distinctly conceived, parts of space become perfectly intelligible. Hence arises the notion of a boundary separating one part of space from the rest. That a material object, a desk or an inkstand, occupies a certion portion of space, separated by a boundary from all that is external, needs no explanation: this boundary is called surface, and possesses none of the solidity either of the desk or inkstand, or of the external space. Surface itself, when distinctly understood, is capable of division into parts, and the boundary which separates two parts of a surface has none of the surface, either on one side or the other: it therefore presents length only to the imagination. Again, length itself is capable of division into parts: the boundaries do not possess any portion of length, either on one side or the other: they are only partition marks or points. Euclid reverses the order of our explanation, requiring first the conception of a point, then of a line, then of a surface, then. of a solid.

That when we think of a point, we deny length, breadth, and thickness; that when we think of a line, it is length without breadth that we figure to ourselves; that in the same manner the surface of our thoughts possesses no thickness whatever-are, to us at least, real truths. We cannot, for instance, imagine what Dr. Beddoes meant when he said (Obs. on Demonstrative Evidence, p. 33), 'Draw your lines as narrow as you conveniently can, your diagrams will be the clearer; but you cannot, and you need not, conceive length without breadth.' Why are diagrams the clearer, the narrower the lines of which they consist? Diagrams have no clearness in themselves, the comprehension of them is in the mind of the observer. If diagrams having (so called) lines of one-hundredth of an inch in breadth be clearer than others of five-hundredths of an inch, it is because the former approach nearer than the

latter to a true representation of that which is in the mind, or of that which the mind desires to see portrayed. If the smaller the breadth the better the diagram in the clearness which it gives to the mind, it must be because the mind would have no breadth at all.

It matters nothing that the point, line, and surface are mechanical impossibilities, that no point or line, if they actually existed, could reflect light to show them, and that no surface could continue to exist for any perceptible time, even supposing it to have one moment of existence. Neither does it signify whether the ideas are necessary, or acquired from the senses; the question in geometry is, Have you got them? not, How did they come? There may be danger that some students should need at first to be frequently reminded of the abstract limits of which the conceptions must be made permanent, lest they should accustom themselves to rest in the imperfect approaches to these conceptions which are realised in their diagrams; but it is always found that a moment's recollection will produce a satisfactory answer to any question upon this point.

There is, it is true, one circumstance in which the pupil may acquire a permanently false notion of the object of geometry. If an instructor should require what is called a Very well drawn figure in every case, with very thin lines and very small points, he may perhaps succeed in giving the learner some idea that geometry consists in that approach to accuracy which constitutes practical excellence in the applications of the science. No idea can be more false: let the good line be examined under a microscope, and it is seen to be a solid mound of black lead or ink, as the case may be. Hence it is perhaps desirable that the demonstrations should be frequently conducted with what are called ill-drawn figures, in order that no reliance may be placed on the diagram, further than as serving to remind the student of the ideal conception which is the real object of his demonstration. This of course is recommended with out prejudice to his learning the accurate use of the ruler and compasses for another distinct purpose, namely, the intention of producing avowedly approximate practical results. It is to be noted that these definitions, so called, are in Euclid more than definitions. They appeal to conceptions supposed to exist, in words which are considered sufficient not to give, but to recal, the necessary ideas. This they actually do, to the satisfaction of the learner, who would never dream of their containing anything dubious, if it were not for the ill-advised interference of the metaphysician. Whatever of pleasure or profit there may be in the subsequent union of the sciences, there is, we think, no doubt that the young geometer should not be required to take lessons of the ontologist.

SOLID, SUPERFICIAL, AND LINEAR DIMENSIONS. A solid, a surface, and a line, when they come to be the objects of arithmetic, are things as distinct as a weight and a time. That a surface is included by lines, or a solid by surfaces, makes no more of necessary connection between them than exists between weight and time, because the former can never be made sensible without the latter. Length only can measure length, a surface only a surface, a solid only a solid. Reasons of arithmetical convenience, not of necessity, make it adviseable that whatever length may be chosen to measure length, the SQUARE on that length should be the surface by which surface is measured, and the CUBE on that length the solid by which solidity is measured. Unfortunately, if a foot be the measure of length, the square on a foot and the cube on a foot have no other names than square foot and cubic foot. The farmer with his acres, and the distiller with his gallons, have an advantage which is denied to the young mathematician. Ask the first how many acres make a gallon, and the second how many gallons make an acre, and both would laugh at the question; the third is allowed an indistinct conception of measuring surfaces and solids in feet or inches, as if they were lines, from the occurrence of the same word in all his measures.

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SOLIDS, REGULAR. [REGULAR FIGURES, &c.] SOLIMÁN, EBN ABD-ÅL-MALEK, the seventh ealiph of the race of the Ommiyades, succeeded his elder brother Walid I., a.d. 715 (a.h. 96). He acquired high popularity at the commencement of his reign by dismissing the various governors whom the inertness of Walid had suffered to oppress the people at their pleasure; and Katibah, the first Moslem conqueror of Transoxiana, who alone refused to acknowledge his authority, was seized and pu to death by his own soldiers. Another of his lieutenants, Yezid Ebn Mohalleb, reduced the rugged and impenetrab'e provinces of Tabrestan and Jorjan, on the south coast of the Caspian, which had never before been completely subdued. But the principal military undertaking of his reign was the siege of Constantinople, commenced the year after his accession, by a vast fleet and army under his brother Moslemah. (Gibbon, c. 52.) But the Saracen fleet was destroyed by the Greek fire; the strength of the fortifications reduced the siege to a blockade; and the caliph was preparing to lead a second army to reinforce his brother when he died a surfeit at Chalcis in Syria, A.D. 717 (A.H. 99), nominating in his last moments his cousin Omar Ebu Abd al-Azez as his successor, to the exclusion of his own sons and brothers, The reign of Soliman is said to have been the epoch of the first rise of the Barmecides, who afterwards became famous as the ministers of the Abbasides.

SOLIMAN, EBN AL-HAKEM, a Moorish chief, who, in the civil wars preceding the extinction of the caliphate of the Ommiyades at Cordova, possessed himself of the ca pital by the aid of the African troops whom he commanded, and proclaimed himself king, A.D. 1009 (A.H. 400), under the title of Al-Mostain Billah. Though soon expelled by Mohammed, one of the Ommiyan competitors, he recovered Cordova in 1112, dethroning Hesham II., who had been replaced on the throne on the death of Mohammed: but his valour and abilities were not able to maintain him in his usurped authority: the walis, or governors of the African and Spanish provinces, refused obedience; and after various changes of fortune, he was overthrown and slain, A.D. 1016 (A.H. 407), by Ali Ebn Hamid, wali of Tangier, wzó was proclaimed king in his room, but speedily perished by another revolution. The first discovery of the Azores bas been attributed to the reign of this prince, on the authors y of a passage in the 'Geography' of Sherif-Al-Edrisi; but it is not very clear that the Azores are the islands there allude-i to as discovered by some Moslem adventurers from Lisbon. D'Herbelot erroneously mentions Soliman as the nephew of Hesham II., whereas he was a stranger to the blood of the Ommiyades.

SOLIMAN EBN CUTULMISH, a Seljookian prince who founded the first Turkish dynasty in Room, or Asia Minor. His father had perished in a revolt against AlpArslan, the great Seljookian sultan of Persia; and MalesShah, the son of Alp-Arslan, was glad to rid himself of the turbulent ambition of Soliman by furnishing him with an army for the conquest of the West, A.D. 1074 (A.H. 467). The internal dissensions of the Greeks facilitated his progress. In a few years he had subdued nearly all Asia Minor exLength is said to be a quantity of one dimension, surface cept the districts on the western coast and the isolated of two, and solidity of three. The right line, the right sur- city of Trebizond; his capital was fixed at Nicæa, within face or RECTANGLE, and the right solid or rectangular PA- 100 miles of Constantinople, and his Turkoman followers RALLELOPIPED (the figure of a box, a die, a plank, a beam, spread themselves all over the country, which was thence &e.), are the implements of mensuration. Every surface forward permanently lost to Christendom. Antioch (which must be reduced to the second form, and every solid to the had been held by the Greeks since its capture by John third, before it can be measured. The rules (which tacitly Zimisces in 968) was betrayed to him (1084) by the son of contain these reductions) for measuring different super- the governor; but this acquisition brought on a rupture be ficial or solid figures will be found under the several heads:tween Soliman and Moslem-Ebn-Koreish, prince of Aleppo,

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