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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 sufliciently friable to be beaten to a coarse powder with an variety of alloys are used in different kinds of soldering, the iron pestle and mortal. 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., ill., and iv.; from which it appears that which they are commonly used to unite.

ihe process was, about sixteen or eighteen years ago, pracPlatinum is soldered, according to Dr. Ure, with fine lised in such a way as to lead to the supposition that it was gold.

rather a welding than a soldering operation; the solder being For gold it is usual to employ an alloy of fine gold with applied in the form of a black shining composition resembling silver or copper, or with boih of those metals. These are pitch, which Mr. Gill conceived to be cast-iron powdered sometimes used in the following proportions:-pure gold and mixed with glass of borax; and the joints being subi welve parts, pure silver two parts, and copper four parts. jected to a slight hammering. The paris united by this The meials are fused together, beat into thin leaves, and means are stated to be scarcely distinguishable. In making then softened by annealing. Borax mixed to a thick con fine sieel instruments, gold, either alone or with a slight sistence with water is applied to the joint, and the solder is alloy of copper, is often used as solder. Silver solder, being melted by the blow pipe. It is stated in Brewster's · Edin. less expensive, and nearer the colour of the steel, is preEncy.,' that the borax may be removed by boiling water, or ferred by some for this purpose. An alloy of nineteen parts diluted sulphuric or muriatic acid; and that the paleness of fine silver, one copper, and two brass, has been recommended the solder may be remedied by melting upon its surface a for steel joints. In larger articles of iron and steel, a solder mixture of two parts of nitre and one of burnt alum, and consisting of equal paris of tin and iron is sometimes used. then washing it off with hot water. The same authority Cominon plumbers' solder is made of two parts lead and states that gold articles may be cleaned after soldering by one part block tin; or of the same metals mixed in nearly boiling them in urine and sal ammoniac, and those of silver equal quantities; bismuthi is ailded when it is desired to by boiling in alum-water.

make the alloy more fusible. Soft solder has two parts tin Silver solders usually consist of silver mixed with brass, to one lead; and other alloys of tin, lead, and bismuth, are and sometimes with zinc. Dr. Ure states that pure tin is oc used for uniting various articles of lead, tin, pewter, and casionally used as a solder for silver, but that the solder com- other soft compounds. Such highly fusible solders are monly used is an alloy of five parts silver, six brass, and two usually cast in ingots or strips, and melted as they are used zinc. Some authorities give nineteen silver, one copper, by means of an instrument called a soldering-iron, which is and ten brass, as the proportions in jewellers' silver solder; tipped with copper-that metal being preferred for its and two parts of pure silver to one of brass as the composi- greater affinity for tin. In soldering tin plates together, tion of solder for plating. Another solder for coarser silver their edges are made 10 overlap; but in almost every other has four parts silver to three of brass, with a little borax; case the edges to be joined are made only to meet, the solder and a hard silver solder is made of equal parts of silver and being run between their abutting edges. fine brass. The addition of zinc softens this alloy. Mr. The Technical Repository' (vol. iv., p. 57) gives an acGill, in an article on soldering in jewellery, in the Techo count of a curious mode of soldering resorted to in order to nical Repository,' vol. ii., p. 63, states that theihin laminated fix upon the back of the dial-plate of a watch the small solder is cut up into very small bits, and applied with borax copper studs by which it is attached to the plate which enand water. The article to be soldered is laid on charcoal / closes the wheel-work. The heat required for melting ashes, and submitted to the jet of a blowpipe. To prevent spelter solder would be injurious to the enamel, and there. the solder from spreading over the surrounding parts, they fore the studs are made of wire plated with silver, and fixed may, he observes, be coated with Indian ink laid on with a by melting the silver on their sides, and causing it to run canel's-hair pencil. The thuid borax is also applied with a down to their base, where borax and water is previously laid. hair pencil, and the solder with the end of the ivory handle Thus the studs are fixed without applying the jet of on which the pencil is fixed. Filagree-work is soldered in the blowpipe immediately to the back of the enamelled a somewhat dillerent manner; the minute parts being laid plate. togeiher in their proper position ou a tlattened piece of A kind of soldering, called burning-to, has been long charcoal, which is smeared with a thick solution of gum practised in some cases with sheet-lead, where it has been tragacanth to hold them steady. The lluid borax is then desirable to make a vessel entirely of that material; the brushed over, and the solder, reduced to a fine powder, is junction being effected by pouring melted lead on to the sprinkled upon it. In this as in all other kinds of soldering, edges to be united, until they fuse together. Somewbat whenever several parts must be successively put together, it similar to this is the process recently introduced under the is necessary to use solders of different degrees of fusibility; name of autogenous soldering. This process, which is the i he least fusible being used first, so that the joints made invention of a French genileman, M. de Richemoni, conwith it may not be disturbed by the heat of the subsequent sists in the union of two pieces of metal without the interoperaiions.

position any solder, by fusing them at the point of juncSpelter solder is used for brass, copper, and iron, and con tion by jets of llame from a gas blowpipe. The apparatus sists of zinc (spelter) mixed with copper or brass, and some used for the purpose contains a hydrogen gas generator, tines also with tin. The proportious vary greatly. Gill Bellows for atmospheric air, and valves for regulating the gives eighteen parts brass, three zinc, and two tin; or six- proportion in which the gas and air are to be mixed. A teen parts copper, sisteen zinc, and one tin. (Technic. Rep., complete description, with cuts, of this machine, is given in i., 432.) Dr. Ure says it consists of zinc and copper in the Mechanic's Magazine' (vol. xxxii., p. 546). The innearly equal parts. Brewster's 'Edin. Ency.' describes it vention has been rewarded in Paris by a gold medal, at the as consisting of iwo parts zinc and one brass, and observe National Exhibition of Arts, and is patented in this country. that the addition of one dwt. of silver to each ounce is a It has hitherto been applied chiefly to lead, but appears great improvement. In the Dict. Technologique, as suitable for metals more difficult of fusion. By its adoption quoted in vol. vi. of Gill's “Technical Repository,' p. 181, the lead may be applied very extensively in chemical vessels, in following solders for copper are mentioned :-eight copper which the use of solder has been inconvenient or imposanil one zinc, which form a very hard yet fusible and mal-sible, owing to its degree of expansibility differing from that leable solder; three copper and one zinc; and ten copper of lead, and its greater liability to be acted upon by acids. and one zinc. The latter forms the hardest but least fusible The joints formed in this way are also much neater and less solder. Generally the addition of copper increases the liable to tlaws than those made by the common process. It hardness and diminishes the fusibility of the alloy. For appears by the paper referred to‘at the commencement of hard brass solders the same proportions are recominended, this article, that Mr. Spencer discovered this process about but brass is substituted for copper. The proportions may the same time as M. de Richemont; and his experiments Vary, it is stated. from two to sixteen parts of brass 10 one lead him to suppose tliat, by varying the admixture of gases, part of zinc. Six brass, one zinc, and one tin, forin a soft a jet of tiame may be produced of intensity suitable for any solder for brass. An alloy of two parts copper and one part metal to which it may be desired to apply the new mode of tin is sometimes used as a hard solder. All the above-men- soldering. tioned hard solders are granulated, and applied to the joint in the form of a coarse powder.

SOLDIER is a term applied now to every man employed Articles of wrought-iron, and some qualities of sleel also, first given to such persons only as were expressly engaged

in the military service of a prince or state, but it was at may be soldered with cast-iron ; the cast-iron being re: I for pay, to follow some chief in his warlike expeditions.

Cæsar mentions a band of 600 men called 'soldurii,' who | a representation of the cross of St. George. However, on bound themselves to attend their leader in action and to an army being raised in 1544, the soldiers were ordered to live or die with him (De Bello Gallico, iii. 22), but it does wear coats of blue cloth bordered with red. White cloaks not appear that they served for pay. By some the word has marked with red crosses continued to be the uniform of the been thought to come from 'solidus,' the name of a coin troops during the reign of Queen Mary; but in the time of under the Roman empire, which may have been received Elizabeth the infantry soldiers wore a cassock and long as the payment for the service.

trowsers, both of which were of Kentish grey: the cavalry The troops which formed the armies of the Crusaders were furnished with red cloaks reaching down to the knee were engaged to serve for pay, for though the nobles volun. and without sleeres. Grey coats, with breeches of the tarily entered into the war, their vassals were not obliged same colour, continued to be the uniform as late as the end by the tenure of their fiefs to accompany them. Père Daniel of the reign of William III., but soon after that time red (Hist. de la Milice Pr., tom. j., p. 103) expresses his belief became the general colour for the coats of the British inthat Philip Augustus, near the end of the twelfth century, fantry soldiers. was the first of the French kings who had hired troops, at

The low condition of the first soldiers in France has been least in any considerable body, in his service; and the prac- mentioned in the article INFANTRY: with respect to those tice of retaining such troops appears to have been afterwards of England in the times of Henry VIII. and Edward VI., very general. It is probable that men hired for the wars we have a more favourable account; for Sir John Smithe, were, from the time of that prince, called soudoyers or soul- in the preface to his tract on ‘Military Instruction’(1591), dyours, that is, stipendiaries; but the name appears for the observes that the order and discipline in the armies during first time in the 'Chronicles' of Froissart, where it is applied the reigns of those kings were so good, that the men, on to the hired troops both of France and Germany. It is being discharged, were never seen to become rogues or to stated that Jaques Dartvell (von Artaveld) of Ghent (1339) go begging under pretence that they had been soldiers, as, kept a guard of 60 or 80 souldyers, each of whom was paid he observes, they now most commonly do. In the preface four Flemish groats daily (liv. i., c. 29). About the same to his · Discourses on the Forms and Effects of Weapons' time Philip de Valois, in revenge for an inroad which had (1390), he complains that, in his time, the commanders of been made into his country, gave leave to the soudyers of troops serving abroad, instead of publishing regulations for France to plunder the lands of Sir John of Hainault (liv. i., the conduct of the men, gave a few laws arifully tending to c. 44); and the name occurs in many other parts of the deter the soldiers from demanding their pay, but in no way work. This class of troops at that time engaged themselves prohibiting them from plundering the people of the country: to fight for any party which would employ and pay them; he adds that they esteemed those soldiers to be the best who, and when not occupied in the wars, they used to wander by robbery, could live longest without pay. Ile complains about the country in large bodies, plundering the people and also that while the commanders were gallant in appearance, committing every enormity. The terms routiers' and and had their purses full of gold, the soldiers were without

brigands,' as words of reproach, were applied to them, and armour, ragged, and barefooted; and that when money was they appear to have been as formidable to those who hired to be received, they used to send the men on desperate enthem as to the enemy. In the reign of Charles V. of terprises, in order ibat they might obtain the pay of those France, Bertrand du Guesclin led them into Spain to serve

who were killed. He adds that, in the summer before the against Peter the Cruel, and in that country great numbers earl of Leicester went over (to Holland) the commanders of them remained, yet the disorders which they caused in devised a manner of paying the soldiers which had never France did not terminate till Charles VII., in 1445, and before been heard of; instead of money, the men were paid Louis XI., in 1480, established a regular militia, which was in provund, under pretence that they knew not how to make paid by the state.

purchases; by which means, the food supplied being of an In the wardrobe account of Edward I. (1300) the term inferior kind, great part of the soldiers' pay was put in their soldier occurs frequently, and Grose considers that the per- own pockets. It appears that Queen Elizabeth, on being sons so designateil were of a different class from the other informed of these abuses, caused the practice of paying in troops. Some of them are called 'soldiers scutifers,' or provand to be abolished. We find that subsequently, eren esquires; some, 'soldiers constables;' and others, simply so late as the time of George I., the pay both of oflicers and ‘soldiers;' but the pay of all was the same, viz. one shilling private soldiers was frequently posi poned for years, and was per day: (Mil. Antiq., vol. j., p. 326.) From the time of sometimes entirely withheld. Happily such injustice no Edward I. to the end of the reign of Edward III. the daily longer exists in the British army; The pay of the soldier pay of a banneret was 4s., and of a knight, 2s. ; that of ais assured to bim by the nation; and a well-appointed comhobiler, a sort of light horseman, was 6d.; of a crosslow-missariat provides, as far as possible, for his wants while in man, 4d.; and of an archer, 2d. In that age the stipendiary the field. troops, or soldiers, were raised in England by commissions It must be admitted that, till lately, the condition of a granted by the king 10 persons who undertook to enlist men private soldier, both in this country and on the Continent, for a certain pay (which was made to depend on the nature was unfavourable for inspiring a love of the service in his of the service), and for a certain portion of the ransom mind. Obli ed to be furnished with good clothing and to money which might be obtaineil in the war.

preserve a becoming appearance, that which remained of Litile change seems 10 bave taken place in the pay of the his scanty pay scarcely sufliced for procuring the food neEnglish soldiers between the times of Edward III. and cessary for his support. In his barracks he was subject to Mary. We find that during the reign of this queen the numerous petty details of duty, which produced weariness daily pay of a captain of heavy caralry was 10s., and of a and even disgust; and, at all times, to the restraints of discavalry soldier is. 6d. The pay of a captain of light ca- cipline, which deprived him of the recreations enjoyed by valry was 68., and of a soldier is. The pay of a captain of other classes of men. It may be added, moreover, that the foot was 48., of a lieutenant 2s., of an ensign 1s., and of a soldier had too often the mortification to find himself defoot soldier 8d.; a halbardier and a hackbutter, on horse. spised for his poverty by persons with whom men of his back, bad each, 18. daily. In the times of Elizabeth, James condition are accustomed to associate. These disadvantages I., and Charles I., the pay of the officers was a little raised, are now however in a great measure removed; and the pay but that of a private foot-soldier was still 8d. per day: of the soldier suffices to afford him the means of obtaining during the civil wars the pay of the latter was 9d., but in the comforts of life in a degree, at least, equal to those the reign of William III. it was again reduced to 8d. At which are enjoyed by an ordinary peasant or mechanic. that time the pay of a private trooper was 28. 6d., and that with the improvement of his condition, a corresponding of a private dragoon was 1s. 6d., including in both cases improvement in the character of the soldiers has taken the allowance for the horse. It is evident that the pay of place: men of steady habits are induced to enlist, and offithe private soldier in later times is far from having been cers are enabled to select the best among those persons who raised in the inverse ratio of the value of money.

present themselves as recruits for the army. While armour was in general use, the common soldiers of The duties of the soldier are now rendered as little burEngland were distinguished only by scarfs or by badges, on thensome as is consistent with the good of the service; and the latter of which were impressed the arms of their several the regulations, promulgated by the highest authorities, leaders; but in the reign of Henry VIII. something like a prescribe that he shall at all times be treated with mildness uniform was worn, and it appears that the colour of the and humanity: even the non-commissioned officers are remen's upper garments was then generally white; the sol- quired to use patience and forbearance in instructing the diers in the king's particular service only, had on llieir coats / recruits in their military exercises. When breaches of dis

cipline on the part of the soldier oblige a commander to altogetier contrary to the spirit of the language, and can,
order the intliction of punishment, attention is paid as properly speaking, never become established as correct
much as possible to render it a means of promoting a re- language.
forination of character: the lash is now very sparingly The term solecism was supposed by antient grammarians
ased. Wherever a regiment be now quartereil, there is to be derived from Soli, a town of Cilicia, where the lan-
established for the soldiers a school, which the men are guage of the original Greek settlers, who were few in num-
obliged, as part of their duty, to attend, and which is gene- bers, became corrupt through the intluence of the people by
rally furnished with a library for their use. The library whom they were surrounded.
and school are formed and supported by the subscriptions of SOLEN. [PYLORIDIANs, vol. xix., p. 145, et seq.]
the officers, and both have been found to contribute greatly SOLENA'CEA, Lamarck's name for a family of bivalve
to the preservation of sobriety and good conduct among the testaceous mollusks, including the genera Solen, Punopaa,
men, by weaning them from the haunts of idleness and and Glycymeris. [PYLORIDIANS, vol. xix., pp. 145, et
dissipation, and giving them a taste for useful knowledge. seq.]

In time of peace the soldier, being surrounded by the SOLENE'LLA, Sowerby's name for a genus of testaceous members of civil society, must, like them, conform to its ! bivalve mollusks apparently belonging to the family Arcucea laws; and, being under the intluence of public opinion, he of Lamarck, and partaking of the characters of the genus

1 is, unconsciously to himself, held in obedience by them; so Nucula (POLYODONTA, vol. xviii., p. 363], and of the family that no extraordinary coertion is necessary to keep him | SOLENACEA. within the bounds of civil or military law. But in the

Generic Character.- Shell oval, equivalve, sub-equicolonies the soldier, even though he be serving in a time of lateral, compressed, covered with a thin shining olive-green peace, has many temptations to fall into a neglect or breach epidermis. Hinge with many teeth, three or four of which of discipline: he is får removed from the friends of his early are anterior, and the numerous rest sharp, posterior, lateral, life, who may have exercised upon his mind a moral in- and arranged in a straight line. Two lateral muscular imfluence for good: he sees around hiin only the conduct, 100 pressions. The pallial impression with a large sinus. frequently licentious, of the lower orders of people in the Ligament external, prominent, and elongated. country where he is stationed; and it may be that he is not Example, Solenella Norrisii. A few specimens of this, fortified with the principles which should have been im- the only known species, were dredged up by Mr. Cuming at planted in his mind by a sound education. The probability Valparaiso. of a return to his native land before many years have passed SOLENIMY'A, or SOLEMY'A. [PYLORIDIANS, vol. is small, and the diseases to which he is exposed from the xix., p. 146.] unhealthiness of the climate frequently terminate fatally:

SOLENÓCURTUS, or SOLECURTUS. [Pylorihence he becomes reckless fro despair, and the facilities DIANS, vol. xix., p. 144.] with which wine or spirituous liquors may often be obtained SOLE'NODON, a genus of insectirorous mammals estalead him into es esses which, while they accelerate the ruinblished by Brandt on a specimen sent from the island of of his health a id render him unfit for duty, cause him to Hispaniola by Jaeger. commit offences both against discipline and morals. Thus Generic Character:-Habit generally between that of in the colonies there arises a necessity for greater restraints Surex and Didelphys. Muzzle elongated, the snout smooth, on the freedom of the soldier, and for the infliction of produced, and with nostrils at the sides of its apex. Eyes heavier punishments than are required at home. (Maj.- minute. Ears large, rounded, nearly naked. Body hairy. Gen. Sir Chas. Napier, Remarks on Military Law.) Lastly, Stern and upper part of the rump beset with a few very in time of war and on foreign service a vigorous discipline short silky hairs. Feet ambulatory, plantigrade, pentadac. is essentially necessary: the privations to which soldiers tylous; claws falcular, those of the fore feet the longest. are then exposed strongly induce those who are not tho- Teats inguinal ? Tail long, smooth, and for the most part roughly imbued with moral and religious principles to scaly. plunder the country-people, in order to supply their imme

6 diate wants, or to drown the sense of their sufferings in Dental Formula –Incisors, õ; molars (spurious true liquor. It ought also to be observed that, in war-time, many

8 turbulent spirits are induced to enter the army in the hope -) = 40. of enjoying the licence which the military life abroad ap 8 pears to hold out. These men are the ring-leaders in all The skull of Solenodon is considerably elongated: the excesses, and they too commonly cause many of those who occipital, parietal, and temporal bones are moderately conare weak in principle to join them; in such cases therefore vex; and the condyles of the occipital are prominent. the most severe coercive measures must be immediately There is an obtuse crest on the sagittal suture, but none on applied, if discipline is to be preserved in the army. The the coalesced frontal bones. The internal pterygoïd proefforts made by the British commanders, during the war cesses alone are conspicuous, thin, and joined by a suture against the French in Spain, to maintain order, and prevent with the perpendicular parts of the palatal bone. There the people of the country from being injured, were great is no bony bulla, and, consequently, the interior wall of the and praiseworthy; and perhaps fewer crimes were com tympanic cavity is only closed by skin. There is no zygomitted by the British troops than by those of their allies or matic arch. The coronoïd process of the mandible is ditheir enemies; but it is to be lamented that there were still lated and directed outwards. The angle of the mandible is too many occasions in which the national character was dis- dilated, subtetragonally rounded, and prominent above the graced by the misconduct of its soldiery.

condyloïd part. SOLE. (PLEURONECTIDE.)

The two anterior upper incisor teeth are the largest, disSOLECIŠM (soloecismus, colokio pós), a grammatical joined from the others, perpendicular, and unicuspid: the term which is used by the later Greek and Roman writers, two anterior lower incisors are very short and very narrow : and by modern grammarians also, though in a somewhat the two middle are the longest, and conical,qand excavated different sense. It is defined by Sinnius Capito (Gell., v. on the internal surface with a rather deep triangular canal. 20) as an unequal and improper arrangement of the parts Brandt remarks that the structure of the teeth manifests a of speech, that is, as a violation of the rules of syntax. greater similitude to that of Myogale (Mygale) than any Quinctilian (i., s. 28, &c.) specifies four kinds of solecisms : other genus. the first consists in the addition of a supertluous word; the Example, Solenodon paradoxus. second, in leaving out one that is necessary; the third, in Description.—Sides of the head and neck dilute yellowperverting the order of the words of a sentence; and the brown, mixed with ferruginous, and, occasionally, with fourth, in using an improper form of a word. The antients grey. Abdomen and feet dilute yellow-brown, with hardly also used the word in a wider sense, understanding by it any a mixture of grey. Space upon the breast between the kind of fault, error, or mistake, whether made in speaking, anterior limbs dilute ferruginous, extended to the internal writir.g, or acting. Modern grammarians designate by side of the feet, and, anteriorly, to the cubit. A similarly solecism any word or expression which does not agree with coloured space occupies the inguinal region, and also extends the established usage of writing or speaking. But as cus- upon the anterior part of the legs. Upper part (dorsum) of toms change, that which at one time is considered a sole- the muzzle, forehead, vertex, middle of the nape, and ancism, may at another be regarded as correct language. Aterior part of the back, tinged with black-brown: the rest of solecism iherefore differs from a barbarism, inasmuch as the the back black-brown, the colour (more diluted) extending latter consists in the use of a word or expression which is towards the posterior part of the sides and towards the ex

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fernal surface of the thighs. The basal and middle part | The form of the nose and of the cribriform plate seems, lie 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 Soricidæ.

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

SOLETELLI'NA. [PYLORIDIANS, vol. xix., p. 144.]
SOLEURE. (SOLOTHURN.)
SOL-FA-ING. [SOLMISATION.)
SOLFATARA. (PHLEGRÆI CAMPı.]
SOLICITOR. [ATTORNEY; Sıx 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 ConsSION: the perfect absence of this force constitute fluidity. (Fluid.]

SOLID ANGLE, a name given to the idea of opening

conveyed by three planes which meet at a point. The h

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 a, skull of Sulenodon (profile): b, seen from above; c, seen from below;

surface, either on one side or the other : it therefore pred. mandible or lower jaw ; e, anterior part of the intermaxillary bone, with the two anterior incisor teeth ; f. anterior surface of an anterior upper incisor tooth; senis lengih only to the imagination. Again, length itself g, anterior parts of the mandible, with the four anterior incisor teeth; h, the

is capable of division into parts: the boundaries do not crown of a second or middle incisor tooth of the mandible, seen on its internal surface, and exhibiting its triangular canal. The foregoing figures are nearly possess any portion of length, either on one side or the of the natural size. i, teeth of the upper jaw seen laterally ; 1,1, nat. size; other: they are only partition marks or points. Euclid 2,2, magnified. (Brandt.)

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 6

thickness wbatever-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 diaFeet of Solenodon. (Brandt.)

grams the clearer, the narrower the lines of which they a, anterior part of the anterior foot, seen on the dorsal or upper sule; b, a consist? Diagrams have no clearness in themselves, the similar view of the anterior part of the posterior foot.

comprehension of them is in the mind of the observer. If Habits, &c.—Brandt remarks that nothing is known of diagrams having (so called) lines of one-hundredth of an the mode of life of this animal; but from the structure of inch in breadth be clearer than others of five-hundredths of . the proboscis and claws, he concludes that it must burrow. an inch, it is because the former approach nearer than the

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latter to a true representation of that which is in the mind, the two fundamental theorems by which mea i rement leor of that which ihe mind desires to see portrayed. If the comes practicable, are as follows:smaller the breadth the betier the diagram in the clearness 1. The numbers of linear units in thie two sides of a rect. which it gives to the mind, it must be because the mind angle, being multiplied together, give the number of suwould have no breadth at all.

perficial units, square units, or squares on the linear unit. It matters nothing that the point, line, and surface are which the rectangle contains. Thus a rectangle of 2 by mechanical impossibilities, that no point or line, if they

13 65 actually existed, could reflect light to show them, and that 4} feet contains

2
X
3 6'

or 108 square feet. no surface could continue to exist for any perceptible time, even supposing it to have one moment of existence. Neither 2. The numbers of linear units in the length, breadth, does it signify whether the ideas are necessary, or acquired and thickness of a right solid, being multiplied together, from the senses; the question in geometry is, Have you got give the number of solid units, cubic units, or cubes on the them ? not, How did they come? There may be danger linear unit, which the right solid contains. Thus a plank that some students should need at first to be frequently re- of 24 inches broad, 1} inch thick, and 104 inches long, conminded of the abstract limits of which the conceptions must

31 279

tains Х x be made permanent, lest they should accustom themselves 4 2 3 8

or 34; cubic inches. to rest in the imperfect approaches to these conceptions SOLIDS, REGULAR. [REGULAR FIGURES, &c.] which are realised in their diagrams; but it is always found SOLIMAN, EBN ABD-AL-MALEK, the seventh cathat a moment's recollection will produce a satisfactory liph of the race of the Ommiyades, succeeded his elder answer to any question upon this point.

brother Walid I., A.D. 715 (A.H. 96). He acquired higli There is, it is true, one circumstance in which the pupil popularity at the commencement of his reign by dismissing may acquire a permanently false notion of the object of the various governors whom the inertness of Walid bad geometry. If an instructor should require what is called a suffered to oppress the people at their pleasure; and Kativery well drawn figure in every case, with very thin lines bah, the first Moslem conqueror of Transoxiana, who alone and very small points, be may perhaps succeed in giving refused to acknowledge his authority, was seized and pu the learner some idea that geometry consists in that ap- to death by his own soldiers. Another of his lieutenants, proaci to accuracy which constitutes practical excellence in Yezid Ebn Mohalleb, reduced the rugged and impenetrable the applications of the science. No idea cau be more false : provinces of Tabrestan and Jorjan, on the south coast of the let the good line be examined under a microscope, and it Caspian, which had never before been completely subdued. is seen to be a solid mound of black lead or ink, as the But the principal military undertaking of his reign was the case may be. Hence it is perhaps desirable that the de- siege of Constantinople, commenced the year after his acmonstrations should be frequently conducted with what are cession, by a vast fleet and army under his brother Moslemah. called ill-drawn figures, in order that no reliance may be (Gibbon, c. 52.) But the Saracen fleet was destroyed by placed on the diagram, further than as serving to remind the Greek fire; the strength of the fortifications reduced the student of the ideal conception which is the real object the siege to a blockade; and the caliph was preparing to of his demonstration. This of course is recommended with lead a second army to reinforce his brother when he died of out prejudice to his learning the accurate use of the ruler and a surfeit at Chalcis in Syria, A.D. 717 (A.H. 99), nominating compasses for another distinct purpose, namely, the inten- in his last moments his cousin Omar Ebn Abd-al-Azez as tion of producing avowedly approximate practical results. his successor, to the exclusion of his own sons and brothers,

It is to be noted that these definitions, so called, are in The reign of Soliman is said to have been the epoch of the Euclid more than definitions. They appeal to conceptions first rise of the Barmecides, who afterwards became famous supposed to exist, in words which are considered sufficient as the ministers of the Abbasides. not to give, but to recal, the necessary ideas. This they SOLIMAN, EBN AL-HAKEM, a Moorish chief, who, actually do, to the satisfaction of the learner, who would in the civil wars preceding the extinction of the caliphate never dream of their containing anything dubious, if it were of the Ommiyades ai Cordova, possessed himself of the ca not for the ill-advised interference of the metaphysician. pital by the aid of the African troops whom he commanded, Whatever of pleasure or profit there may be in the sub- and proclaimed himself king, A.D. 1009 (A.H. 400), under the sequent union of the sciences, there is, we think, no doubt title of Al-Mostain Billah. Though soon expelled by Mothat the young geometer should not be required to take hammed, one of the Ommiyan competitors, he recorered lessons of the ontologist.

Cordova in 1112, dethroning Hesham II., who had been SOLID, SUPERFICIAL, AND LINEAR DIMEN- replaced on the throne on the death of Mohammed : but SIONS. A solid, a surface, and a line, when they come to be his valour and abilities were not able to maintain him in the objects of arithmetic, are things as distinct as a weight his usurped authority: the walis, or governors of the Afriand a time. That a surface is included by lines, or a solid can and Spanish provinces, refused obedience; and after by surfaces, makes no more of necessary connection between various changes of fortune, he was overthrown and slain, them than exists between weight and time, because the A.D. 1016 (A.H. 407), by Ali Ebn Hamid, uali of Tangier, who former can nerer be made sensible without the latter. was proclaimed king in his room, but speedily perished by Length only can measure length, a surface only a surface, another revolution. The first discovery of the Azores has a solid only a solid. Reasons of arithmetical convenience, been attributed to the reign of this prince, on the authority not of necessity, make it adviseable that whatever length of a passage in the 'Geography' of Sherif-Al-Edrisi; but it may be chosen to measure length, the SQUARE on that is not very clear that the Azores are the islands there alluded length should be the surface by which surface is mea to as discovered by some Moslem adventurers from Lisbon. sured, and the CUBE on that length the solid by which D'Herbelot erroneously mentions Soliman as the nephew of solidity is measured. Unfortunately, if a foot be the mea- Hesham II., whereas he was a stranger to the blood of the sure of length, the square on a foot and the cube on a foot | Ommiyades. have no other names ihan square foot and cubic foot. The SOLIMAN EBN CUTULMISH, a Seljookian prince farmer with his acres, and the distiller with his gallons, who founded the first Turkish dynasty in Room, or Asia have an advantage which is denied to the young mathema. Minor. His father had perished in a revolt against Alptician. Ask the first how many acres make a gallon, and Arslan, the great Seljookian sultan of Persia; and Malekthe second how many gallons make an acre, and both would Shah, the son of Alp-Arslan, was glad to rid himself of the laugh a: the question; the third is allowed an indistinct turbulent ambition of Soliman by furnishing him with an conception of measuring surfaces and solids in feet or army for the conquest of the West, A.D. 1074 (A.H. 467). The inches, as if they were lines, from the occurrence of the internal dissensions of the Greeks facilitated his progress. same word in all his measures.

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 fare 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 re to the cond form, and erery 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 beficial or solid figures will be found under the several heads: (tween Soliman and Moslem-Ebn-Koreish, prince of Aleppo,

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