FRA BARTOLOMEO-FRACTIONS. alone is navigable. Vessels of 600 tons ascend the west side of the lough, and its chief tributary the Foyle (which comes 16 miles from the south), to Londonderry. On the east shore is a flat strand with a sandy beach, on which, in 1827, was measured a line of 41,640, which was afterwards extended by triangulation to about 53,200 feet, and formed the base line of the Ordnance Survey of Ireland. FRA BARTOLOMEO. See BACCIO DELLA PORTA. FRACASTORO, GIROLAMO, an Italian savant and philosopher, famous for the universality of his learning, was born of an ancient family at Verona in 1483. At the age of 19, he was appointed professor of logic in the university of Padua. But his vast knowledge embraced the most divergent sciences, and on account of his eminence in the a с ad-be = bd ing all the denominators for the common denomi b practice of medicine, he was elected physician of the multiply by a® a a с ac FRACTIONS, CONTINUED. If = a+ and b+ and =c+ ‚ and.... ין Council of Trent. His Latin verse also exhibits a B a1 and = n + &c. m1 m1 FRA'CTED, heraldically, signifies broken asunder. tinued fraction. If we consider the fractions (1) 1 formed by taking into account parts only of the denominator in the continued fraction, we obta a series of fractions converging to the value of These converging fractions are always approxima ing to the value of and are alternately greater and less than it. Throughout the series, the 1st, 31, 5th, 7th, &c., are each below the true value, while the S4 4th, &c., are above it; or vice versa, according as be shewn that the successive converging fract the original fraction is improper or proper. It can approach nearer and nearer to the true value of th continued fraction. Converging fractions are d great use in the summation of infinite series. FRACTION. In Arithmetic, a fraction is any part or parts of a unit or whole, and it consists of (2) a + two members, a denominator and a numerator, whereof the former shews into how many parts the unit is divided, and the latter shews how many of them are taken in a given case. Thus denotes that the unit is divided into four parts, and that three of them are taken; and more generally denotes that the unit is divided into b parts, and that a of them are taken. A fraction is called proper when the numerator is less than the denominator, and improper when the numerator is greater than the denominator. In Algebra, any quantity is called a fraction, although a and b are not necessarily representatives of whole numbers, as they would require to be if the fraction be an arithmetical fraction. The algebraical fraction b just means that any quantity affected by it is to be multiplied by a, and divided by b. This definition, however, through the greater generality of algebra, includes that of an arithmetical fraction. The rules for the addition and multiplication of fractions are the same in algebra and arithmetic. To add two or more fractions together, we must bring them to a common denominator, and add the numerators for a new numerator, and take the common denominator for the new denominator. Thus if be two FRACTIONS-FRACTURE. 1+ 4 = 29 and finding the other convergents in a similar manner, we have the following approximations to the value of the original fraction: 3, 13 29 187 964 6935 4' 9' 58' 299' 2151 The differences between the successive convergents and the original fraction are, 6935 2151 13 482 2151 (being less than 4 6935 2151 1 1 x 1 = we 1 to the fall, whereas it is the reverse. man, some few years ago, awoke with a fit of A medical cramp, and almost immediately his left thigh-bone times feels a bone give way under no special strain. broke with a snap. It reunited in the usual time. In such cases, there is seldom any attempt at repair. The sufferer from cancer of long standing, someThe bones of old people are brittle from the excess of earthy materials (see BONE), and so readily fragilitas or mollities ossium, are soft and friable, give way. The bones of the feeble patient, with and when examined, are found saturated with a greasy substance. There are some persons who seem liable to fracture without any such reason. Professor Gibson of America mentions a boy who, though apparently arm and forearm, while his leg and thigh were healthy, had broken his collar-bones eight times, his broken if he but tripped his foot on the carpet. An old lady once broke both thigh-bones kneeling down in church. There is one predisposing cause to but, as was seen in Lord Anson's expedition, which fracture fortunately now but seldom seen-viz., scurvy. Not only did it make the bones brittle, was manned chiefly by pensioners, old fractures again became disunited. und in general the difference between any convergent 4 × 9), &c. ; nd the original fraction is less than a fraction lenom. of convergent x denom. of conv. next greater onsequently, the differences grow less as roceed, owing to the denominators of the converents always increasing. If, by actual subtraction, ve find successively the difference between each onvergent and the original fraction, we shall also nd that they are alternately greater and less, or ss and greater, according as the original fraction proper or improper. FRACTIONS, VANISHING. In some algebraical actions, the substitution of a particular value for ie unknown quantity will make both the numertor and denominator of the fraction vanish; such actions are called vanishing fractions. Thus the action bone lies in the midst of soft parts, any injury to the one must tear the other, and cause Repair of a broken Bone.-Of course, as the absorbed, and is of no service in the process of repair. infusion of blood; but the latter is speedily After the first excitement has passed off, a fluid is effused around the fragment, which in a short time becomes converted into bone. of this new material depends upon the position of The amount is technically termed, riding, then a much larger the fragments; should they be far apart, or, as it quantity of new bone is thrown out. We see this in animals to such an extent that the materials for repair, or callus,' may be divided into two separate parts-a provisional callus to act as a wrapper to the bones until the permanent callus, or that which unites the ends, however far apart, becomes sufficiently hard; then the provisional callus, being no longer necessary, is removed by absorption. loose, and is, as a general rule, no longer under the Symptoms of Fracture.-A broken limb hangs control of the muscles, which, however, are pricked by the broken ends of bone, and stimulated into painful spasms, which still further displace and deform the limb. Should there be any doubt, the limb may be carefully raised, and turned gently from side to side, when a peculiar rough feeling termed crepitus removes all doubt. Each bone, however, when broken, exhibits symptoms peculiar to itself, and requires a separate treatment. assumes the form when x=1. he ascertainment of the value of such a fraction r the particular value of the unknown quantity hich gives it the form, may in all cases be fected by a general method furnished by the fferential calculus. But frequently that value ay be determined by simpler means, as the form ises from the existence of a factor common to both umerator and denominator, which becomes zero for particular value of x; if, then, we can discover is factor, either by finding the greatest common easure or otherwise, and divide it out, then by bstitution we obtain the value of the fraction rresponding to the particular value of x. Thus, in e example given, we find that both terms are visible by x x2 - 1 1, so that x+1. There1 re, when x = 1, and the fraction becomes, its lue must equal 2. This is an example of the plication of the method of Limits to the determinion of the value of such a fraction, for it is clear at for every value of 1, the value of the fracture; Compound, when there is such a wound; Fractures are divided into Simple, when there is no wound in the skin which communicates with the action is 2, and continually approaches 2 as a Comminuted being prefixed to either of these terms proaches 1. Much discussion has taken place as whether vanishing fractions have, properly speak-when the bone is broken into several pieces; Im5, values or not; but this is not the place for ticing speculations on the subject. See LIMITS, LEORY OF; and NOTHING, and INFINITY. FRACTURE of a bone may be the result of cident, muscular action, or disease. nes of the limbs are more subject to the latter The long o causes than those of the head or spine. Presposing causes to fracture are frosty weather, age, cancerous disease, a morbidly brittle contion called fragilitas ossium. == pacted, when one fragment is driven into the other; near as possible to their former positions by gentle Treatment of Fracture.-Replace the fragments as external rigid skeleton, made of any unyielding extension, retain them in place by substituting an material which will be firm enough to resist the spasms already alluded to, but is not fastened with very great tightness to the limb Splints are geneSome bones, as the kneepan and heel-bone, are percha has been much used. In simple fractures, it rally of wood or pasteboard; but of late years gutta ble to give way from sudden contraction of the is often sufficient to adapt a bandage to the limb, uscles which are inserted into them. The subject which will harden on drying, and form a shell for it; the injury then falls, and attributes the accident | for this purpose, starch, dextrine, and plaster of FRA DIAVOLO-FRAMING. Paris are generally used. Whatever the splint be desirable. Fig. 1 represents a simple and useful form of frame-bridge. It will be seen at once that a weight upon the bridge will exert a pulling strai upon the horizontal timber ab, and a crushing strain upon be and ad, as well as upon the upper timbers, and that the main support is in ab, which must be torn asunder before ad and be can be bent or displaced to any considerable extent. The celebrated frame-bridge of Schaffhanser, constructed in 1757 by Grubenmann, a village carpenter, was built exactly in the manner of a roof with a horizontal pathway superadded. It was composed of two arches, one 193 feet, the other 172 feet span. It was merely laid upon the piers, and did not abut against them to exert any outward thrust, as will be seen by fig. 2 Th Fig. 2. he evaded the pursuit of justice by retiring to his haunts amidst mountains and forests, and skilfully defeating, with much inferior numbers, all the armed forces despatched against him. He became at length known among the peasantry of the neighbourhood as Fra Diavolo. On the advance of the French into the Neapolitan states, F. D. and his band espoused warmly the royal interests, and in return were not only pardoned and reinstated in civil rights, but promoted to the grade of officers in the royal army, F. D. himself weight on the bridge is transmitted by the oblique becoming colonel. In 1806 he attempted to excite beams, which by analogy we may call rafters, to Calabria against the French, but was taken prisoner the tie-beam ab, where it exerts a horizont at San Severino, and was executed at Naples in pulling strain. November of the same year. The opera of Auber has nothing in common with F. D. but the name. He died uttering imprecations on the queen of Naples and the British admiral, Sidney Smith, whose influence had not sufficed to rescue him from death, although on his capture he produced papers bearing the royal seal, which vouched for his right to the rank of colonel in the royal forces. FRAGA'RIA. See STRAWBERRY. FRAME, in Gardening, the covering of any kind of hotbed, flued pit, or cold pit, used for the cultivation of plants not sufficiently hardy for the open air. Frames are of various materials, but generally of wood or iron and glass, and are made in one piece or in sashes according to the size of the hotbed or pit. FRAME-BRIDGE, a bridge built of timbers framed together in such a manner as to obtain the greatest possible amount of strength with a given quantity of material. The fundamental principle upon which all such construction is based, is that the timbers shall be so arranged that the weight put upon them shall exert a pulling or a crushing strain, instead of a transverse strain, and, if possible, that the greatest strain shall act as a direct pull in the direction of the fibres of the wood. The construction of a frame-bridge is very similar to that of a roof, excepting that in the bridge a considerable outward thrust upon the abutments is generally permissible, while the walls of a house will These rafters are framed into the tie-beam so as to abut firmly against it in the sam manner as Roof-rafters (see Roor). This kir. of frame-bridge is very common in Switzerland, where timber-bridges abound; and it has doubtless originated from the fact, that most of the brides have been built by the local carpenters, who are accustomed to the construction of roofs of consider able span for the commodious square-built wooder cottages with overhanging roofs, so common in that country. Frame-bridges of more complex structur are sometimes built; in some of these, the timbers are framed so as to present an arched form. In these cases, the structure is very similar to th described and figured under CENTERING. The ser s defect of all such bridges is their liability to day from exposure to moisture, &c., especially at the joints, where water is apt to lodge and remain, from want of free circulation of air to evaporate it. I the bridge of Schaffhausen above described, it was found that when it had stood but 26 years, the oak-beams, where they rested on the masonry at a and b, fig. 2, were rotted, and the frames began t settle. This was remedied by a carpenter named Spengler, who raised the whole structure up a piles by means of screw-jacks, and replaced th decayed wood. Means should be adopted to admit the free circulation of air in those parts where the timber rests upon the masonry, and to preve water from settling in the timber joints. The covered bridges of Lucerne and other parts of Switzerland are well known as objects of special interest to tourists, who usually imagine that the roofs are made for the comfort of travellers, but their main object is the preservation of the bridge. FRAMING, the jointing, putting together, or building up of any kind of artificers' work. The framing of timber generally is described under CARPENTRY, and special kinds of framing under CENTERING, DOOR, FLOORS, FRAME-BRIDGE, PARTI TIONS, ROOFS, &c. In such trades as mathematical, optical, philosophical, and other complex instrumentmaking, the workman who does flat-filed work, and fits all the parts, and puts the whole instrument together, is called the framer, and his work framing. |