tance in chemistry. But the attention of the chemist is chiefly directed to the state of fluidity as it may affect the component parts of bodies. A solid body may be converted into a finid by heat. The less the temperature at which this is effected, the more fusible the body is said to be. All fluids, not excepting the fixed metals, appear, from various facts, to be disposed to assume the elastic form, and this the more readily the higher the temperature. When a fluid is heated to such a degree as that its elasticity is equal to the pressure of the air, its interior parts rise up with ebullition. The capacity of a dense fluid for caloric is greater than that of the same body when solid, but less than when in the elastic state. If this were not the case, the assumption of the fluid and elastic state wonld be scarcely at all progressive, but effected in most cases instantly as to sense. See CALORIC. The state of dense fluidity appears to be more favourable to chemical combination than either the solid or elastic state. In the solid state, the cohesive attraction prevents the parts from obeying their chemical tendencies; and in the elastic state, the repulsion between the parts has, in a great measure, the same effects. Hence it has been considered, though too hastily, as a che mical axiom, that corpora non agunt nisi fluida. FLUOR spar, the native fluate of lime. See the next article. FLUORIC acid, in chemistry, is obtain ed from fluor spar, or, as it is technically called, fluate of lime. It has not yet been decomposed, unless it be among the grand discoveries of Mr. Davy, not yet announced to the world. We have attended the lectures of this professor, and think, in one of them, he said, he had decomposed the fluoric acid for want, however, of any written document on the subject, we must content ourselves with a summary account of the properties of this acid, which were investigated with accuracy and precision by Scheele and Priestley. The spar was not distinguished from others of a similar appearance till about the year 1768, when Margraff attempted to decompose it by means of the sulphuric acid. He found that it consisted of a white sublimate, and a peculiar acid; the sublimate proved afterwards to be lime, and the acid being denominated fluoric acid; it is now called the Aluate of lime. Margraff found, to his asto nishment, that the glass retort in which the experiment had been made, was corroded, and even pierced with holes. Fluoric acid may be obtained by putting a quantity of the spar in powder into a retort, pouring over it an equal quantity of sulphuric acid, and then applying a gentle heat. A gas ensues, which may be received in the usual manner, in jars, standing over mercury. This gas is the fluoric acid, which may be obtained dissolved in water, by luting to the retort a receiver containing that fluid. The distillation is to be conducted with a very moderate heat, to allow the gas to condense, and to prevent the fluor itself from subliming. Soon after the discovery of this acid, it was doubted whether it possessed those properties that rendered it different from all other acids. Scheele, however, who had already investigated the subject, instituted another set of experiments, which completely established the fact. The properties of this acid are, that, as a gas, it is invisible, and elastic like air: but it will not maintain combustion, nor can animals breathe it without death. In smell it is pungent, something similar to muriatic acid. It is heavier than common air, and corrodes the skin. When water is admitted in contact with this gas, it absorbs it rapidly; and if the gas be obtained by meaus of glass vessels, it deposits at the same time a quantity of silica. Water absorbs a large portion of this gas, and in that state it is usually called fluoric acid by che mists. It is then heavier than water, has an acid taste, reddens vegetable blues, and has the property of not congealing till cooled down to 23°. The pure acid may be obtained again from the compound by means of heat. Fluoric acid gas does not act upon any of the metals; but liquid fluoric acid is capable of oxyding iron, zinc, copper, and arsenic. It does not act upon the precious metals, nor upon platina, mercury, lead, tin, antimony, cobalt. It combines with alkalies, earths, and metallic oxides, and, with them, forms salts denominated fluates, of which the true fluor, Derbyshire spar, or fluate of lime, consists of Lime.......... Fluoric acid. Water............. .........57 ........16 ..27 100 The most remarkable property is that already alluded to, viz. the facility with which it corrodes glass and siliceous bodies, As fluoric acid produces an insoluble compound with lime, it may be employed to detect the presence of that earth when held in solution. Two or three drops only of the acid will cause a milky cloud or precipitate to appear, if any lime is present. Fluoric acid has been applied to engraving or etching on glass, and was used, according to Beckman, nearly a century and a half ago for that purpose, by an artist at Nuremburg, who obtained it from digest ing fluor spar in nitric acid. Since, how. ever, the discoveries of Scheele and Priestley, it has been more generally used, and the art is performed by covering the glass with wax, and then that part where the figures are to appear is laid bare, and the whole is exposed for some time to the hot vapour of fluoric acid. This simple process is employed with great advantage in writ ing labels on glass vessels, and in graduating thermometers, &c. See Thomson's Chemistry. FLUSTRA, in natural history, hornwrack, a genus of worms, of the order Zoophyta. Animal a polype, proceeding from porous cells; stem fixed, foliaceous, membranaceous, consisting of numerous rows of cells united together, and woven like a mat. About eighteen species have been described. FLUTE, an instrument of music, the simplest of all those of the wind kind. It is played on by blowing it with the mouth, and the tones or notes are changed by stopping and opening the holes disposed for that purpose along its side. The ancient fistulæ, or flutes, were made of reeds, afterwards of wood, and last of metal; but how they were blown, whether as our flutes, or as hautboys, does not appear. FLUTE, German, is an instrument intirely different from the common flute. It is not, like that, put into the mouth to be played, but the end is stopt with a tampion or plug; and the lower lip is applied to a hole about two inches and a half, or three inches, distant from the end. This instrument is usually about a foot and a half long; rather bigger at the upper end than the lower; and perforated with holes, besides that for the mouth, the lowest of which is stopped and opened by the little finger's pressing on a brass, or sometimes a silver key, like those in hautboys, bassoons, &c. Its sound is exceedingly sweet and agreeable; and serves as a treble in a concert. FLUX, a general term made use of to denote any substance or mixture added to assist the fusion of minerals. In the large way, limestone or fluor spar are used as fluxes; but in small assays, the method of the great operations is not always followed, though it would be very frequently of advantage to do so. The fluxes made use of in assays, or philosophical experiments, consist usually of alkalies, which render the earthy mixtures fusible, by converting them into glass; or else glass itself into powder. Alkaline fluxes are either the crude flux, the white flux, or the black flux. Crude flux is a mixture of nitre and tartar, which is put into the crucible with the mineral intended to be fused. The detonation of the nitre with the inflammable matter of the tartar is of service in some operations; though generally it is attended with inconvenience, on account of the swelling of the materials, which may throw them out of the vessel, if proper care be not taken either to throw in only a little of the mixture at a time, or to provide a large vessel. White flux is formed by projecting equal parts of a mixture of nitre and tartar, by moderate portions at a time, into an ignited crucible. In the detonation which ensues, the nitric acid is decomposed, and flies off with the tartarous acid, and the remainder consists of the potash in a state of considerable purity. This has been called fixed nitre. Black flux differs from the preceding, in the proportion of its ingredients. In this the weight of the tartar is double that of the nitre; on which account the combustion is incomplete, and a considerable portion of the tartarous acid is decomposed by the mere heat, and leaves a quantity of coal behind, on which the black colour depends, It is used where metallic ores are intended to be reduced, and effects this purpose, by combining with the oxygen of the oxide. There is danger of loss in the treatment of sulphureous ores with alkaline fluxes: for, though much or the greater part of the sulphur may be dissipated by roasting, yet that which remains will form a sulphuret with the alkali, which is a very powerful solvent of metallic bodies. The advantage of M. Morveau's reducing flax seems to depend on its containing no uncombined alkali. It is made of eight parts of pulverized glass, one of calcined borax, and half a part of powder of charcoal. Care must be taken to use a glass which contains no lead. The white glasses contain in general a large proportion, and the green bottle glasses are not perhaps entirely free from it. FLUX, in medicine, an extraordinary issue, or evacuation of some humours of the body. See MEDICINE. FLUXION, in mathematics, denotes the velocity by which the fluents or flowing quantities increase or decrease; and may be considered as positive or negative, according as it relates to an increment or decrement. The doctrine of fluxions, first invented by Sir Isaac Newton, is of great use in the investigation of curves, and in the discovery of the quadratures of curvilinear spaces, and their rectifications. In this method, magnitudes are conceived to be generated by motion, and the velocity of the generating motion is the fluxion of the magnitude. Thus, the velocity of the point that describes a line, is its fluxion, and measures its increase or decrease. When the motion of this point is uniform, its fluxion or velocity is constant, and may be measured by the space described in a given time, but when the motion varies the fluxion of velocity at any given point is measured by the space that would be described in a given time, if the motion was to be continued uniformly from that term. FLU to move parallel to itself, in the plane of the parallel and moveable lines AF and BG: for if, as above, Rr be taken to express the fluxion of the line Am, and the rectangle Rrs S be completed; then that rectangle, being the space which would be uniformly described by the generating line mn, in the time that Am would be uniformly increased by mr, is therefore the fluxion of the generated rectangle Bm, in that position. If the length of the generating line m n continually varies, the fluxion of the area will still be expounded by a rectangle under that line, and the fluxion of the absciss or base: for let the curvilinear space Anm (fig. 9), be generated by the continual and parallel motion of the variable line mn; and let Rr be the fluxion of the base or absciss A m, as before, then the rectangle Rrs S, will be the fluxion of the generated space Amn. Because, if the length and velocity of the generating line mn were to continue invariable from the position RS, the rectangle Rrs S would then be uniformly generated with the very velocity wherewith it begins to be generated, or with which the space A m n is increased in that position. FLUXIONS, notation of, of invariable quantities, or those which neither increase nor decrease, are represented by the first letters of the alphabet, as a, b, c, d, &c. and the variable or flowing quantities by the last letters, as, v, w, x, y, z: thus, the diameter of a given circle may be denoted by a; and the sine of any arch thereof, considered as variable, by x. The fluxion of a quantity represented by a single letter, is expressed by the same letter with a dot or full point over it: thus, the fluxion of x is represented by x, and that of y by y.. Thus, let the point m be conceived to And, because these fluxions are themselves A m m R often variable quantities, the velocities with which they either increase or decrease, are the fluxions of the former fluxions, which may be called second fluxions, and are denoted by the same letters with two dots over them, and so on to the third, fourth, &c. fluxions. The whole doctrine of fluxions consist in solving the two following problems, viz. From the fluent, or variable flowing quantity given, to find the fluxion; which constitutes what is called the direct method of fluxions. 2. From the fluxion given, to find the fluent, or flowing quantity; which makes the inverse method of fluxions. FLUXIONS, direct method of, the doctrine of this part of fluxions is comprized in these rules. 1. To find the fluxion of any simple variable quantity, the rule is to place a dot over it: thus, the fluxion of x is x, and of y, j. Again, the fluxion of the compound quantity x + y, is x + j; also the fluxion of x- -y, is x j. 2. To find the fluxion of any given power of a variable quantity, multiply the fluxion of the root by the exponent of the power, and the product by that power of the same root, whose exponent is less by unity than the given exponent. This rule is expressed more briefly, in algebraical characters, by the fluxion of x. Thus the fluxion of 'is × 3 × r2 = 3x2 x; and the fluxion of x is x × 5 × x=5x+x. In the same manner the fluxion of a + y'is7yX ay; for the quantity a being constant, is the true fluxion of the root a + y Again, the fluxion of a2 + 22)} will be (or ed by a coefficient, or constant multipli5. When the proposed quantity is affectcator, the fluxion found as above must be multiplied by that coefficient or multiplicator: thus, the fluxion of 5 x3, is 15 x2 x; for the fluxion of r3 is 3 x2 x, which, multiplied by 5, gives 15 x2x. And, in the very same manner, the fluxion of a " will be na x-x. Hence it appears, that whether the root be a simple or a compound quantity, the fluxion of any power of it is found by the following general Rule : Multiply by the index, diminish the index by unity, and multiply by the fluxion of the root. Thus the fluxion of z8 8 z ż: the fluxion of 4 x = 24 x3✯ and the fluxion of = = 12 20 Z × 2 z ż × u2 + z2: for here, x being put a2+z2, we have 2 z ż; and thereforex, for the fluxion of x a2 + z) is 3 z ż √ a2 + z2. 3. To find the fluxion of the product of several variable quantities, multiply the fluxion of each, by the product of the rest of the quantities; and the sum of the products, thus arising, will be the fluxion Having explained the manner of detersought. Thus, the fluxion of x y is xy+mining the first fluxions of variable quanyx; that of x y z, is x y z +ỷ x z +żxy; and that of v x y z is vx y z + xvy z + jvxz + żvxy. Again the fluxion of a + xxb− y=ab+b x—ay — xy, is bx-ay-xy-jx. 4. To find the fluxion of a fraction, the rule is, from the fluxion of the numerator, nmultiplied by the denominator, subtract the fluxion of the denominator multiplied by the numerator, and divide the remainder by the square of the denominator. Thus, that of 3 ż 5 z tities, it is unncessary in a work of this kind to enter upon the second, third, &c. fluxions, we shall therefore proceed to FLUXIONS, inverse method of, or the manner of determining the fluents of given fluxions. If what is already delivered, concerning the direct method, be duly considered, there will be no great difficulty in conceiving the reasons of the inverse method: though the difficulties that occur in this last part, upon another account, are indeed vastly great. It is an easy matter, or not impossible at most, to find the fluxion of any flowing quantity whatever but, in the inverse method, the case is quite otherwise; for, as there is no meor 1 thod for deducing the fluent from the fluxion a priori, by a direct investigation; so it is impossible to lay down rules for any other forms of fluxious, than those particular ones, that we know, from the direct me = ; thod, belong to such and such kinds of flowing quantities: thus, for example, the fluent of 2 x x is known to be r2; because, by the direct method, the fluxion of r2 is found to be 2x: but the fluent of yx is unknown, since no expression has been discovered that produces y x for its fluxion. Be this as it will, the following rules are those used by the best mathematicians, for finding the fluents of given fluxions. 1. To find the fluent of any simple fluxion, you need only write the letters without the dots over them: thus, the fluent of x is x, and that of ax + by, is ax + by. 2. To assign the fluent of any power of a variable quantity, multiplied by the fluxion of the root; first divide by the fluxion of the root, add unity to the exponent of the power, and divide by the exponent so increased: for dividing the fluxion n x-1 by x, it becomes nx”-1; and adding 1 to the exponent (n-1) we have nx"; which, divided by n, gives x", the true fluent of nxx. Hence, by the same rule, the fluent of 3x2 x will be=x3; that of 2 x x= ; that of y = y; that 3 'mn' that of 172 and that of y y = ; that of a+1× * = that of a ×zm-12: 4 mxn+1 In assigning the fluents of given fluxions, it ought to be considered, whether the flowing quantity, found as above, requires the addition or subtraction of some constant quantity, to render it complete : thus, for instance, the fluent of nx may be either represented by x" or by x a; for a being a constant quantity, the fluxion of xa, as well as of ", is n x2−1x. ter part of the equation becomes = mxn+1 ann+m ; whence the equation or flumxn+1 ent, properly corrected, is y = a”+x®)n+1 — amn+m Hitherto x and y are both supposed equal to nothing, at the same time; which will not always be the case: thus, for instance, though the sine and tangent of an arch are both equal to nothing, when the arch itself is so; yet the secant is then equal to the radius. It will therefore be proper to add some examples, wherein the value of y is equal to nothing, when that of x is equal to any given quantity a. Thus, let the equa tion y = x2x, be proposed; whereof the fluent first found is y = ; but when y = 3 then will y = becomes y = if j + bx2; × = And lastly, r; then, first, + therefore the fluent cor T Hence it appears, that the variable part of a fluent only can be assigned by the common method, the constant part being only assignable from the particular nature of the problem. Now to do this, the best way is to consider how much the variable part of the fluent, first found, differs from the truth,when the quantity which the whole rected is y = fluent ought to express, is equal to nothing; then that difference, added to, or subtracted y= 36 : |