FRACTION FRANC. 



247 



the virtues of the hero were less happily celebrated I 

 than the horrors of the disease. He died at Padua, 

 of apoplexy, in 1553, aged seventy-one. Among 

 the moderns who have exercised their talents in the 

 composition of Latin verse, few have obtained higher 

 reputation than Fracastorius. The eider Scafiger 

 ranks him, as a poet, next to Virgil ; and his merit 

 lias been generally acknowledged. Besides the 

 poems already noticed, he wrote another, entitled 

 Alcon, sive de Cura Canum venaticorum. Among 

 liis prose works on professional topics, are treatises 

 De Sympathia et Antipathia ; DC Contugione et Mor- 

 bis contagiosis, &c. 



FRACTION (from the Latin frangere, to break) 

 signifies, in arithmetic and algebra, a combination of 

 numbers representing one or more pans of a unit or 

 integer : thus four-fifths is a fraction, formed by 

 dividing a unit into five equal parts, and taking one 

 part four times. Fractions are divided into vulgar 

 and decimal. Vulgar fractions are expressed by 

 two numbers with a line between them. The lower, 

 the denominator, indicates into how many equal parts 

 the unit is divided; and the number above the line call- 

 ed the numerator, indicates how many of such parts 

 are taken ; as, in \, 8 is the denominator, 7 the numer- 

 ator. Vulgar fractions have been divided, though not 

 very accurately, into proper, improper, simple, com- 

 pound, and mixed, viz. : A proper fraction is when the 

 numerator is less than the denominator, as J, J, J, *- it 

 } J I, &c. An improper fraction is when the numerator 

 is equal to or greater than the denominator, as 5, J, }{, 

 ^.'S &c. A simple fraction is that which consists of 

 a single numerator and single denominator ; and is 

 either proper or improper, as j-, it, ii,&c. A com- 

 pound fraction is a fraction consisting of two or more 

 other fractions connected by the word of; thus /,, of 

 J, or } of ,',_ of J, &c., are compound fractions. 

 A complex fraction is that whose numerator and 



denominator are both fractions ; thus ^7 is a complex 



fraction. These two distinctions, though frequently 

 made by authors on arithmetic, are certainly impro- 

 per, the former indicating an operation in multiplica- 

 tion, and the latter an operation in division. It is, 

 therefore, improper to apply to them the denomina- 

 tion of fractions. An integer and fraction together 

 is called a mixed number; that is, 1\, 9J, &c., are 

 mixed numbers. The theory of vulgar fractions is one 

 of the most important in algebra, but is rarely, we 

 think, developed in a clear, simple, and easy manner 

 in books on arithmetic. A correct understanding of 

 them is of great importance for the proper prosecu- 

 tion of arithmetical and mathematical studies. 

 Decimal fractions include every fraction, the deno- 

 minator of which is ten or a power of it ; as ,', 

 ,'.., &c. Our beautiful system of writing numbers 

 enables us to write decimal fractions without express- 

 ing the denominators, just as we are enabled to write 

 whole numbers without saying whether they are units, 

 hondreds, c. The following scheme will explain it. 



I 



540432.472307 



On the left of the point are the whole numbers; and 

 just as every place in that series in proceeding to the 

 left increases in value ten times, so every place to 

 the right from the point decreases in value ten times. 

 Writing decimal fractions is therefore only an exten- 

 sion of our system of writing whole numbers. Yet, 

 though it is as simple as it is important, the system 

 was unknown to the ancients, and was first discovered 



by the Germnn mathematician Regiomontanus in 

 1464. All calculations in decimal fractions are very 

 easy and simple. 



FRACTURE (from frango, to break) is applied to 

 the bones, and is divided into simple and compound; 

 simple, when the bone only is injured ; compound, 

 when the soft coverings are so injured that either one 

 of the fractured ends protrudes through the skin, or 

 the skin and muscles are so lacerated as to expose 

 the bone. The long cylindrical bones of the limbs 

 are most frequently fractured ; next the flat, particu- 

 larly of the cranium (for those of the pelvis and 

 scapula must be excluded) ; and, lastly, the round, 

 irregularly-shaped bones of the tarsus, carpus, and 

 vertebrae. The bones are fractured by external vio- 

 lence, disease, and the action of the muscles. The 

 long cylindrical bones are not unfrequently broken 

 in more than one point ; they are generally fractured 

 at the centre of their shafts, in which case the frac- 

 ture is more or less oblique ; whereas, when it occurs 

 near the extremes, it becomes more and more trans- 

 verse ; hence fractures have been divided into oblique 

 and transverse. The spongy bones are also fractured 

 transversely ; the flat bones in various directions, oc- 

 casionally stellated. A comminuted fracture occurs 

 when a bone is broken in different places at once, 

 and divided into several fragments or splinters. 

 Longitudinal fractures also occur to the long cylin- 

 drical bones. Complicated fractures are those 

 accompanied with luxation, severe contusions, wound- 

 ed blood-vessels, pregnancy, gout, scurvy, rickets, 

 fragilitas ossium, and syphilis, which diseases prevent 

 the union of the bones, and also cause them to be 

 very easily broken. Cold renders the bones more 

 fragile ; and they are also more brittle in old age 

 The superficial are more exposed to fracture than 

 the deep-seated bones ; thus the clavicle is more so 

 than the os innominatum. Others, from their func- 

 tions, are more exposed ; as, for example, the radius, 

 from its affording support to the carpus. When a 

 fracture takes place, there is an effusion of blood from 

 the vessels of the bone, periosteum, and contiguous 

 soft parts ; the muscles are violently excited ; the 

 periosteum and truncated ends of the bone inflame ; 

 and, after the inflammation subsides, the vessels of 

 the periosteum and ends of the bone secrete callus, 

 which is an effusion of gelatin that is gradually con- 

 verted into cartilage, and, lastly, into bone, by the 

 secretion of phosphate of lime, precisely in the same 

 manner as the formation and conversion of bone in 

 the foetus. During the inflammatory action, no dis- 

 eased secretion takes place ; nay, even the healthy 

 natural ones are more or less suspended, so that no 

 advantage is gained by setting a fracture immediate- 

 ly after the injury ; on the contrary, this primary 

 setting, as it is termed, re-excites the already spas- 

 modic action of the muscles, and, in nine cases out of 

 ten, disappoints the hopes of the surgeon. Callus 

 does not harden for many days : in the adult, it begins 

 generally about the tenth or twelfth day ; Boyer, 

 however, says that it is not formed until between the 

 twentieth and seventieth day. The treatment of a 

 simple fractured bone is, to lay the limb in the easiest 

 position for the patient ; to apply leeches and anodyne 

 fomentations, or poultices ; to put him on low diet, 

 enjoin perfect rest, and administer gentle laxatives, 

 until all inflammatory action is subdued ; then to 

 extend the limb to its natural length, or apply paste- 

 board splints dipped in warm water, with wooden 

 ones exterior to them, and fastened with tapes. This 

 latter is termed secondary setting, and is applicable 

 to all the bones of the extremities. 



FRANC ; a French silver coin, containing ten 

 decimes and a hundred centimes. Value about lOd. 

 See Coins. 



