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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 fluid 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 chemical axiom, that corpora turn agunt nisi fiuida.

FLUOR tpar, the native fluate of lime. See the next article.

FLUORIC acid, in chemistry, is obtained from fluor spar, or, as it is technically called, filiate 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 Scheelc and Priestley. The spar was not distinguished from others of a similar appearance till about the year 1768, when Marprraff 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 fluate of lime. M_argrafJ found, to bis asto

nishment, that the glass retort in which the experiment had been made, was corroded, and even pierced with boles.

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 nsual 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 floor 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. Wh 'ii water is admitted in contact with this gas, it absorbs it rapidly; and if the gas be obtained by means 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 chemists. 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 filiates, of which the true fluor, Derbyshire spar, or fluate of lime, consists of

Lime 57

Fluoric acid 16

Water 27

Too

The most remarkable property is that already alluded to, est. the facility with which it corrodes glass and siliceous bodies, especially when hot, and the case with which it holds silica in solution, even when in a state of gas. This affinity for silica is so great that the thickest glass vessels can withstand its action only a short time. The order of its affinities is,

Alumina Potash

Ammonia Silex

Barytcs Soda

Lime Strontian.
Magnesia

As fluoric acid produces an insoluble compound with lime, it may be employed to de_ tect the presence of that earth when held in solution. Two or three drops only of the acid will cause 'd 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 Becknian, nearly a century and a half ago for that purpose, by an artist at Nuremberg, who obtained it from digesting tiuor spar in nitric acid. Since, however, 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 writing labels on glass vessels, and in graduating thermometers, &c. See Thomson's Chemistry.

FLUSTRA, in natural history, hornurack, a genus of worms, of the order Zoophyta. Animal a polype, proceeding from porous cells; stem fixed, foliaccous, 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 fistula;, 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, bassoon-, &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 arc 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 snlplinret with the alkali, which is a very powerful solvent of mctallic'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 pulverised 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 molion 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.

Thus, let the point m be conceived to A M m r

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move from A, and generate the variable right line Am, by a motion any how regulated; and let its velocity, when it arrives at any proposed position or point R, be such as would, was it to continue uniform from that point, be sufficient to describe the line Rr, in the given time allotted for the fluxion, then will Rrbe the fluxion of the variable line A m, in the term or point R.

The fluxion of a plain surface is conreived to like manner, by supposing a given right line inn (Plate V.Miscel. tig. 8)

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 A m, and the rectangle RrsS be completed; then that rectangle, being the space which would be uniformly described by the generating line m n, in the time that A in would be uniformly increased by m r, is therefore the fluxion of the generated rectangle B m, 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 4et the curvilinear space Ann (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 R r s S, will be the fluxion of the generated space Ann. Because, if the length and velocity of the generating line m it were to continue invariable from the position R S, the rectangle R r s S would then be uniformly generated with the very velocity wherewith it begins to be generated, or with which the space Ann 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, 6, c, d, 4c. '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 a represented by x, and that of y by i. And, because these fluxions are themselves 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, &o. fluxions. The whole doctrine of fluxions consist in solving the two following problems, Ariz. 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, y. Again, the fluxion of the compound quantity a, -j- y, is x -(-y; also the fluxion of x — y, is x y.

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

■ —l a

ax x = the fluxion of x . Thus the fluxion of xs is x X 3 x ** = 8 x* x; and the fluxion of xs is xx 5 X x4 = 5x*x. In the

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a' + zM j) is = 3 z z J a* -f z'.

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 sought. Thus, the fluxion of x y is x y -jyx; that ofxy z, is x y z-\-y xz -\-zxy;

and that of exy z isrxy z -f i r ;/ : -|yvxz + zoxy. Again the fluxion of u + x X 6— y = a h -\- b x —ay —xy, is 4 x — «j — x y y x.

4. To find the fluxion of a fraction, the rule is, from the fluxion of the numerator, multiplied by the denominator, subtract the fluxion of the denominator multiplied by the numerator, and divide the remainder by the square of the denominator. Thus,

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and that of'

3, and 4,) found to be 2x'yjr-}-2y'xxX z — x'y'z z>

5. When the proposed quantity is affected by a coefficient, or constant raultiplicator, the fluxion found as above must be multiplied by that coefficient or muitiplicator: thus, the fluxion of 5x', is IS x1 x; for the fluxion of x' is 3 x2 x, which, multiplied by 5, gives 15 x2 x. And, in the very same manner, the fluxion of a x" will be n o x*-1 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 a' = 8 z' z: the fluxion of 4 Xs = 24 x> x and

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the fluxion of —
4
3z
5zj-

Having explained the manner of determining the first fluxions of variable quantities, it is necessary 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 con ceiving 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 method 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 fluxions, than those particular ones, that we know, from the direct method, belong to smelt and such kinds of (lowing quantities: thus, for example, the fluent of 2 x x is known to be x'; because, by the direct method, the fluxion of i'» found to be 2 x x: but the fluent of y x 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 finest 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

■*+*»"• ,

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 ax"-1 x by x, it becomes nx"-'; and adding 1 to the exponent (a—l)we have ax"; which, divided by a, gives x", the true fluent of ax""1 jr. Hence, by the same rule, the fluent of 3r* x will be = x'; that of 2*1 x = ^; that of y J> = ? p ; that

of ay\y =^7T~ > and that of »"> =

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v
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tbatofa"+zVX z"-'z= — - m x » + l

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 ax"-' x may be either represented by x" or by x a ; for a being a Constant quantity, the fluxion of x"± a, as well as of xF, is a x*-'jr.

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 ot 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 fluent ought to express, is equal to nothing; then that difference, added to, or subtracted

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