by imbibing the odour themselves, or intermixing other odours with it. When the gravity of the air suffers the scent to remain buoyant just breast high, it is a most fortunate círcuinstance for the pack. The more rapid the animal, again, the less the scent communicated. The scent, however, scarcely ever lies with a north or an east wind; a southerly wind without rain, and a westerly wind that is not rough, are the best. On first finding a fox, the huntsman should draw quietly and up the wind; the fox does not, in this case, readily hear till the hounds are all in, noise can then do no hurt, and the hounds are inspirited by it. While the hounds are drawing, the company should so place themselves that a fox cannot go off unseen: upon such occasions, if two gentlemen keep close together, instead of assisting in the discovery, it is clear that one of them at least, if not both, knows nothing of the matter. The true sportsman will not draw a cover near the kennel in the commencement of the season, but will keep this as a reserve when the more distant covers are exhausted; of the first he is sure at any time. A perfect knowledge of feeding and drafting hounds is of essential consequence; for good hounds will require but little assistance afterwards. By the first is meant the bringing a hound into the field in his highest vigour, by a full or sparing feed according to his temperament; by the second, the taking out no unsteady hound, nor any that are not likely to be of service to the pack. With a high scent hounds cannot be pushed on too much; screams keep the fox forward, the hounds together, or let in the tail hounds: halloos are of service when hounds are running up the wind, for then none but the tail hounds can hear them; when running down the wind, on the contrary, there should be no more halloos than are necessary to bring the tail hounds forwards. Halloo forward is a necessary and useful cry, but is employed too indiscriminately: the hounds should only know it to signify that a fox is found-they will then fly to it. Gone away, is a halloo that denotes a fox has broke cover, and should certainly be restrained to that occasion, when it cannot be given too loudly. When a fox is killed he should first be flung across the branch of a tree to be bayed a few minutes, then with a loud Tally ho, the meaning of which the hounds will thus understand, he should be hurled amongst them to be eaten ravenously. It will make them the more eager. No good country should be hunted after February: no country at all after March. A fox-hunting establishment consists, when complete, of a first and second huntsman, first and second whipper-in, three horses for each of the first, and two for each of the last: from twenty-five to thirty-five couples of hounds, terriers, helpers, earthstoppers, and dog-feeders. FOX-CHASE. See CHASE. FOX-EVIL, a disease in which the hair drops off from the head. FOX-GLOVE, in botany. See DIGITALIS. FOX-GLOVE (False), in botany. See MiMULUS. FOXFORD, a town in Ireland, in the county of Mayo, situate on the river May, 8 miles N. of Castlebar. FOX-ISLANDS, a group of islands in the N. Archipelago .They are 16 in number, and. are situated between the E. coast of Kaitschatka and the W. coast of America, between 52° and 55° N. lat. Each island has a peculiar name; but this general name is given to the whole group, on account of the great number of black, grey, and red foxes with which they abound. The dress of the inha bitants consists of a cap, and a fur coat, which reaches down to the knee. Some of them wear common caps of a party-coloured birdskin, upon which they leave part of the wings and tail. On the fore part of their hunting and fishing caps they place a small board, like a skreen, adorned with the jawbones of seabears, and ornamented with glass beads, which they receive in barter from the Russians. At their festivals and dancing parties, they use a much more showy sort of caps. They feed upon the flesh of all sorts of sea animals, and generally eat it raw. But when they dress their food, they make use of a hollow stone, in which they place the fish or flesh: they then. cover it with another, and close the interstices with lime or clay. They next lay it horizontally on two stones, and light a fire under it. The provision intended for keeping is dried without salt in the open air. Their weapons are bows, arrows, and darts; and, for their defence, they use wooden shields. The most perfect equality reigns among them. They have neither chiefs nor superiors, neither laws nor punishments. They live together in families, and societies of several families united, which form what they call a race, who, in case of attack or defence, mutually aid each other. The inhabitants of the same island always pretend to be of the same race, FO'XSHIP. s. (from fox.) The character or qualities of a fox; cunning (Shakspeare). FO'XTRAP. s. (fox and trap.) A gin or snare to catch foxes (Tatler). FOY. s. (foi, French.) Faith; allegiance (Spenser). FOYLE (Lough), a lake or bay of Ireland, in Londonderry. It is of an oval form, 14 miles long and eight broad, and communicates with the ocean by a short and narrow strait. To FRACT. v. a. (fractus, Latin.) To break; to violate; to infringe (Shakspeare). FRACTION. s. (fraction, French.) 1. The act of breaking; the state of being broken (Burnet). 2. A broken part of an integral (Brown). FRACTION, in arithmetic, and algebra, is ber considered as a whole but divided into a cera part or some parts of another quantity or numtain number of parts: as 3-4ths of any quantity, a pound, for instance, which denotes 3 parts out of 4, or 15 shillings. Fractions are usually divided into vulgar, de cimal, duodecimal, sexagesimal. The first kind is what we speak of here; for the last three sorts, see DECIMAL, &C. "The definitions of fractions,' says bishop Horsley, which we find in the common books of arith metic, that a fraction is a broken number, or that it is a number less than unity, are absurd and unintelligible. Number, in its own abstract nature, is composed of unity; and unity, in the abstract, is indivisible: a number, therefore, cannot otherwise be broken, than into less numbers; or into the units of which it is composed. The ultimate division of number is into units; and below a unit there is no number. But, considering number not in the abstract, but as existing in the things numbered, the unit of these embodied numbers exists in the individuals, of which the multitude is composed; that is, in each indivi. dual separately taken. Each individual is no otherwise one, or no otherwise partakes of unity, than as it is a whole. And, as a whole, it must be composed of parts, for to be composed of parts is essential to a whole; for a whole is that from which no part is absent. A whole, therefore, as a whole, is one; but as composed of parts, it is many, The unit, therefore, of embodied numbers, is many in one; and, by dividing the whole into its parts, this concrete one is resolved into its many. And these many parts among them selves, and with relation to the whole, are no less the subject of numeration, than the wholes making multitudes. These parts, considered in their relation to the whole, are called fractions, the whole being usually called an integer. And the arithmetic of fractions is the art of numbering them as parts of a whole, and of performing the like operations upon them, for combining or separating them; as are performed by the rules of common arithmetic upon numbers properly so called, that is, upon integral numbers.' (Elementary Treatises on Practical Math.) Nearly to the same purpose speaks Malcolm at pp. 19, 20, of his Arithmetic. Vulgar Fractions are usually denoted by two numbers, the one set under the other, with a small line between them: thus denotes the fraction three fourths of some whole quantity considered as divided into four equal parts. The lower number 4, is called the denominator of the fraction, shewing into how many parts the whole or integer is divided; and the upper number 3, is called the numerator, and shews how many of those equal parts are contained in the fraction: Hence it follows, that as the numerator is to the denominator, so is the fraction itself to the whole of which it is a fraction; or as the denominator is to the numerator, so is the whole or integer to the fraction: thus, the integer being denoted by 1, as 4 : 3 :: 1 : the fraction. And hence there may be innumerable fractions all of the same value, as there may be innumerable quantities all in the same ratio, viz. of 4 to 3; such as 8 to 6, or 12 to 9, &c. So that if the two terms of any fraction, i. e. the nume rator and denominator, be either both multiplied or both divided by any number, the resulting fraction will still be of the same value: thus, 3 or oror, &c. are all of the same value with each other. Fractional expressions are usually distinguished into proper and improper, simple and compound, and mixt numbers. either equal to, or greater than, the denominator; and consequently the fraction either equal to, or greater than, the whole integer, as 4, which is equal to the whole; or, which is greater than the whole. Simple Fractions, or Single Fractions, are such as consist of only one numerator, and one denominator; as, or, or 12. Compound Fractions are fractions of fractions, and consist of several fractions, connected toge ther by the word of: as of, or of of §. A Mixt Number consists of an integer and a fraction joined together: as 13, or 123. The arithmetic of fractions consists in the RE DUCTION, ADDITION, SUBTRACTION, MULTIPLICATION, and DIVISION of them. See the various articles; see also ALGEBRA and ARITHMETIC. Algebraic Fractions, or Fractions in Species, are exactly similar to vulgar fractions, in numbers, and all the operations are performed exactly in the same way; therefore the rules need not be repeated, and it may be sufficient here to set down a few examples to the foregoing rules. Thus, aab bc 1. The fraction abbreviates to aa C by dividing by a a and and become and bd See ADDITION. d a bd az-bx 5. See SUBTRACTION. we shall have 3+ 1 7 ++= A Proper Fraction, is that whose numerator is Here, if we stop atless than the denominator; and consequently the fraction is less than the whole or integer; as 4. Improper Fraction, is when the numerator is reductions gives the proportion of Archimedes, and the last that of Adrian Metius. The doctrine of continued fractions does not appear to have been so much cultivated as it deserves: the best treatises upon it, however, and the best exemplifications of its use, are given in Wallis's Arith. Infin. Euler's Analys. Infin. Hutton's Tracts; and Lagrange's Additions to Euler's Algebra. Vanishing Fractions. Such fractions as have both their numerator and denominator vanish, or equal to 0, at the same time, may be called vanishing fractions. We are not hastily to conclude that such fractions are equal to nothing, or have no value; for that they have a certain determinate value, has been shewn by some very able mathematicians. Different methods have been adopted for valuing these fractions. One is to divide the fluxion of the numerator by that of the denominator for the value: thus, in the fraction when * -1; the fluxion of the numerator is r-511%, and that of the denominator is -r: hence, =4, the value of the fraction. A second method is by common 1-15 division: thus, in the same example, 1-x 2+1+x= (when x= = 1) 1 + 1 + 1 + 1 =4. A 3210 for we have 1-1 1-5 nearly =4, as before. -1 -2 2-524 These vanishing fractions have led to some sharp contests among algebraists; as between Varignon and Rolle, between Maseres and Waring, &c. And in one instance, it is said, a superior knowledge of such fractions was the means of obtaining a professorship: though we trust appointments to professorships seldom depend upon such equivocal proofs of merit. Mr. Woodhouse, in his Principles of Analytical Calculation, a work in which he has taken great pains to unsettle every thing, but to settle nothing, has revived some of the objections formerly brought against vanishing fractions: he prox2-a2 duces the instance among others, and asreasons, that this fraction is not =x+a, in the serts, not, as appears to us, from the most cogent particular case when ra. think, lies in this, that he takes the cyphers to His mistake, we which both the numerator and denominator reduce, as like and equal quantities, which cannot be the case; for since x-a2 may be considered as a plane and a-a as a line, the cyphers must be looked upon as cyphers of different orders. For the sake of the young student, we will consider this matter a little more particularly. Let us examine an instance like that above mentioned, In the tablet in the margin, we have placed several different values of a, passing on from 13 through 0 to +13. The third column contains the several values of the fraction, as they result from sup10-12 plying the values of x and a, and actually performing the opera 10-15 -=5: again when aa— x2 100-25 10+5 =15. But when x= = 10, we have not -13 41x -2 -1 10-11 tions. Thus, when x=-5, then 10-10 a-x 10-7 placed the value of the fraction in this third column, because since 10+ 8 10+9 10+12 &c. =, that a-x is gone, we must abandon it altogether, and return to our arithmetic and geometry. But, if we can,-if, for example, we can affirm universally, = a + ×, whatever a and x may be, why then the sum of a and x will represent the quotient of a2-x2 divided by a-x, whatever be the relation subsisting between a and x. There is no alternative between admitting this and abandoning all that is useful and valuable in modern analysis. Should not this manner of considering the subject remove all the scruples of Mr. Woodhouse, and others who have adopted similar notions, we will endeavour to place it in another point of P1x view. Let us conceive y=- and let us construct a figure which shall exhibit the different values of y. Since y, or its equal a +1, has all its variations in a ratio of equality with those of 1, (a being constant) it is manifest that the locus of this equation is a right line making an angle of 45° with the axis of the figure. Let mAMMM, &c. be such locus, (fig. 12. Pl. 68.) and draw the several ordinates pm, pm. PM, PM, &c. Now at the point P, where x=0, we have y=a+x=10= PM; and AP being = 10, the ordinates gradually diminish until at the point A, a + x, being 10-10 =0, the ordinate vanishes, and the locus crosses the axis: when x becomes 12,-14, &c. the or - dinate is truly expressed by -2,-4, &c. being found on the contrary side of the axis. But, to proceed with the increasing ordinates on the right hand part of the figure: when PP=5, 6, 7, 8, or 9 respectively, it is manifest that PM, the ordinate, becomes 15, 16, 17, 18, or 19 respectively; and when PP 11, 12, 13, 14, &c., the ordinate PM 21, 22, 23, 24, &c. Since then the different values of y, or the proposed fraction, are exhibited, and we trust fairly and accurately exhibited, by this figure, both in the cases when I is less than a, and when it is greater than a, we trust there will be no great impropriety in adopting the species of reasoning which is the foundation of the differential method, (and which is so admirably elucidated in prop. 87 of Hartley on Man) and thus determining the value of y in the particular case of x=a. By this method then we find the ordinate (which in the figure we have presumed to represent by a 19+21 dotted line) =21, which is equivalent to a +x, and furnishes another reason for believing that the value of the vanishing fraction is truly as signed. 2 FRACTIONAL. a. (from fraction.) Belonging to a broken number (Cocker). FRACTURE. s. (fructura, Latin.) 1. Breach; separation of continuous parts (Hale). 2. The separation of the continuity of a bone in living bodies (Herbert). To FRACTURE. v. a. (from the noun.) To break a bone (Wiseman). FRACTURE, in surgery, a rupture of a bone, or a solution of continuity in a bone when it is crushed or broken by some external cause. See SURGERY. FRÆNULUM. The cutaneous fold, under the apex of the tongue, that connects the tongue to the infralingual cavity. It is sometimes, in infancy, so short as to prevent the child from sucking, when it is necessary to cut it, in order to give more room for the motion of the tongue. FRÆNUM, or FRENUM, bridle, in anatomy, a name given to divers ligaments, from their office in retaining and curbing the motions of the parts they are fitted to. FRENUM LINGUE, or BRIDLE OF THE TONGUE; a membranous ligament, which connects the tongue with the muscles about the fauces, and lower parts of the mouth. In some subjects the frænum runs the whole length of the tongue to the very tip; in which cases, if it were not cut, it has been erroneously supposed, that there would be no possibility of speech. See TONGUE-TIED. FRÆNUM PENIS, a slender ligament, whereby the prepuce is tied to the lower part of the glans of the penis. Nature varies in the make of this part; it being so short in some, that unless divided it would not admit of perfect erection. There is also a kind of frænum, fastened to the lower part of the clitoris in women. FRAGA, a town of Spain, in Arragon, with a handsome castle. It is strongly situ ated among the mountains, having the river Cinca before it. Lat. 41. 46 N. Lon. 0. 28 E. FRAGARIA. Strawberry. In botany, a genus of the class icosandria, order polygynia. Calyx ten-cleft, inferior; petals five; seeds smooth, imbedded in an ovate berry-like fleshy receptacle. Seven species-two of Ame-. rica, one somewhat shrubby; the rest natives of Europe; two of which, E. vesca, common strawberry, and E. sterilis, barren of fruit, are common to our own country. The common strawberry is the only species cultivated for use; and its varieties are very numerous. The following are the chief : a F. sylvestris, wood strawberry. F. virginiana. Virginian scarlet. F. moschatta. Hautboy, or musky strawberry. F. Chiloensis. Chili, or Carolina. F. alpina. Alpine, or monthly. The mode of cultivation in respect to all the species and varieties does not differ essentially. They may be transplanted in September or February: the former is the best month; for if the spring be dry, the February transplantation will require great attention and much watering. The proper soil is a light loam, and not peculiarly rich. The ground must be well dug and cleared of all noxious weeds; and when levelled it should be marked out into beds about three feet and a half wide, leaving a pathway between each bed two feet broad. In each of these beds should be planted four rows of plants, so that they may stand about a foot distant from each other in the rows, and at about eight inches plant from plant in each. This is the proper distance for the wood strawberry, which is of the least growth of any; but the scarlet strawberry must be planted at a foot distance every way, and the hautboy sixteen inches; and finally, the large Chili strawberry, which is the largest grower of all, must be set at twenty-tw@ inches distant plant from plant. In the spring, when the strawberries begin to flower, if the season be dry, they must be very plentifully watered, and kept cleared from weeds. At Michaelmas the beds should be dressed, the weeds all very carefully taken up, all the strings or runners taken from the roots, and the weak plants, which stand too close, be pulled up; a little fine earth, at the same time, should be thrown near the plants, which will greatly strengthen their roots. These beds, however, will not continue good above three years; and the beds of the first year bearing but few fruit, it is necessary to new plant some fresh ground every third year, and destroy the old beds; but the new ones must be first of one year's growth. Different palates prefer different sorts of strawberries, but the white fruited one is, of all others, the best flavoured; though it is but a very bad bearer. The great Chili strawberry is cultivated in the field in that country; it is a much stronger and larger plant than any of our indigenous kinds, and its fruit is as large as a walnut, but not so well tasted as our own strawberries. They grow best in a loamy soil, under the shade of trees. FRAGILE. a. fragile, French; fragilis, Latin.) 1. Brittle; easily snapped or broken (Denham). 2. Weak; uncertain; easily destroyed (Milton). FRAGILITY. s. (from fragile.) 1. Brittleness; easiness to be broken (Bacon). 2. Weakness; uncertainty (Knolles). 3. Frailty; liableness to fault (Wotton). FRAGMENT. s. (fragmentum, Latin.) A part broken from the whole; an imperfect piece (Newton). FRAGMENTARY. a. (from fragment.) Composed of fragments: not used (Donne). FRA GOR. s. (Latin.) A noise; a creak; a crash: not used (Sandys). FRAGRANCE. FRAGRANCY s. (fragrantio, Latin.) Sweetness of smell; pleasing scent; grateful odour (Garth). FRA GRANT. a. (fragrans, Latin.) Odorous; sweet of smell (Prior). FRAGRANTLY. ad. With sweet scent. FRAIL. s. 1. A basket made of rushes. 2. A rush for weaving baskets. FRAIL. a. fragilis, Latin.) 1. Weak; easily decaying; subject to casualties; easily destroyed (Rogers.) 2. Weak of resolution; liable to errour or seduction (Taylor). FRAIʼLNESS. s. Weakness; instability (Nor.) FRAILTY. s. (from frail.) 1. Weakness of resolution; instability of mind; infirmity (Milton.) 2. Fault proceeding from weakness; sins of infirmity (Dryden). FRAISCHEUR. s. (French.) Freshness; coolness (Dryden). FRAISE.. (French.) A pancake with bacon in it. FRAISE, in fortification, a kind of defence, consisting of pointed stakes, six or seven feet long, driven parallel to the horizon into the retrenchments of a camp, a half-moon, or the like, to prevent any approach or scalade. Fraises differ from palisades chiefly in this, that the latter stand perpendicular to the horizon, or nearly so, being usually made a little sloping, or with the points hanging down. Fraises are chiefly used in retrenchments and other works thrown up of earth; sometimes they are found under the parapet of a rampart, serving instead of the cordon of stone used in stone-works. FRAMBOESIA, (framboesia, from framboise, French for a raspberry.) The yaws. A genus of disease arranged by Cullen in the class cachexia, and order impetigines. It is somewhat similar in its nature to the lues venerea, and is endemial to the Antilla islands. It appears with excrescences, like mulberries, growing out of the skin in various parts of the body, which discharge an ichorous fluid. Some of our best and most approved writers upon this subject, however, assign it to the family of fevers, with the general symptoms of which they affirm it is always accompanied; that like the small pox, it has an accession, height and decline, may be propagated by inoculation, and is never known to occur a second time. To FRAME. v. a. 1. To form or fabricate by orderly construction (Spenser). 2. To fit one to another (Abbot). 3. To make; to compose (Shakspeare). 4. To regulate; to adjust (Tillotson). 5. To form any rule or method by study or precept (Shakspeare). 6. To form and digest by thought (Granville). 7. To contrive; to plan (Clarendon). 8. To settle; to scheme out (Shakspeare). 9. To invent; to fabricate (Bacon). FRAME. S. (from the verb.) 1. A fabric; any thing constructed of various parts or members (Tillotson). 2. Any thing made so as to enclose or admit something else (Newton). 3. Order; regularity; adjusted series or dispo sition (Swift). 4. Scheme; order (Clarendon). 5. Contrivance; projection (Shakspeare). 6. Mechanical construction. 7. Shape; form; proportion (Hudibras). FRAME, among painters, a kind of square, consisting of four long slips of wood joined together, whose intermediate space is divided by threads into several little squares like a net; and hence sometimes called reticula. It serves to reduce figures from great to small; or, on the contrary, to augment their size from small to great. FRAMER. s. (from frame; Fɲemman, S.) Maker; former; contriver; schemer (Arb). FRAMING OF A HOUSE, all the tim ber-work therein, viz. the carcase, flooring, partitioning, roofing, cieling, beams, &c. FRAMLINGHAM, a large town of Suffolk, with a market on Saturday. It is seated near the head of a small rivulet, and has the remains of a castle, said to have been built in the time of the Saxon heptarchy. To this castle the princess Mary, afterward Mary I. retired, when lady Jane Grey was proclaimed queen; and here she found that powerful support of the people of Suffolk, which so soon |