FLUTE-STOP. 



FLUXIONS. 



Ill 



in construction, limited in means, in length about a foot and a 

 l, and baring only one key, hu by degrees been extended to 

 twenty-wren inches, ncoaaionally more, and ha* aometimea as many as 

 a doxen key*, seldom lew Uian aix; ao that every kind of mimic. 

 however chromatic, within ita compaa*, and adapted to the nature of a 

 tube, may now be executed on thin instrument It in formed of any 

 kind of hard wood, of ivory, and even of glaaa, and ia divided into four 

 joint*. The aoale of the concert flute ia from C below the treble staff 

 to C in the altiaaimo : 



Some flute* arc made to go four notes lower ; and an adroit player 

 can reach the E V in altiasimo 



The high note* of the flute are very effective in the orchestra, 

 but ita beat, ita expressive tones, are those between the low C and 

 O in alt, comprising twelve diatonic degrees, and all the inter- 

 mediate semitones. Performers on the flute, however, like those on 

 moat other instrument*, strive to astonish rather than please their 

 auditors. Tasteless, senseless execution is all-prevailing, a fact which 

 the great majority of hearers admit, and deplore, while they nevcr- 

 theleas encourage the debasement of one of the most delightful of 

 arts by patiently listening to, and often applauding, that which at 

 best only excites some little wonder, never affords real pleasure, and 

 commonly is the source of dissatisfaction, if not of a feeling nearly 

 allied to disgust. 



The OCTAVE FLUTE (called also the Flaulo Piccolo, Ottavino, and 

 Flautino, in orchestral scores) is a small instrument an octave higher 

 than the common flute ; it is shrill and piercing, and only desirable in 

 the fullest instrumental music, and in military bands. The beat of 

 these are provided with four keys. 



In the Great Exhibition of 1851, Herr Bohm, of Munich, obtained 

 the approbation of musicians for his improvements of the flute. 

 Mr. J. Clinton's flute is referred to in the Jury Report (Class X. A) as 

 combining the facilities of other modern flutes, and the ordinary 

 system of fingering, at the same time avoiding their defective parts. 

 " In this instrument the tone and time are rendered equal by the same 

 means that M. Bohm has adopted, namely, an equality of size and 

 distance in the holes." It is also said to be comparatively cheap, " the 

 mechanism being so simple that its price does not exceed that of the 

 old eight keyed flute." 



FLUTE-STOP, on the organ, is a range of wooden pipes, tuned in 

 unison with the diapason, and generally proves a most successful 

 imitation of the instrument whence its name is derived. 

 FLUTE, FLUTINGS. [COLUMN.] 



FLUX, in chemistry and metallurgy, is any substance employed to 

 assist the reduction of ores or metallic compounds to their metallic 

 state. In smelting the argillaceous iron ore of this country, which is 

 a mixture of carbonate of iron, alumina, and silica, the flux employed 

 is limestone, in such proportions as will form a slag that melts easily, 

 ao as to allow the fused iron to sink through it. When the pro- 

 portion of limestone has been properly adjusted, the slag has the 

 appearance of green bottle-glass; when, on the other hand, the 

 slag ia opaque and blue, it is a sign that a good mixture has not 

 been made. 



When copper ores are difficult to melt, fluor spar is added as a flux, 

 which appears to promote the operation. 



The fluxes made use of in assays and in chemical operations vary 

 greatly according to the nature of the metal to be reduced and that of 

 the substances combined with it. [ASSAYING.] 



We ahall mention a few of the more important fluxes employed. 

 JUack jlx is made by mixing one part of powdered nitre with two 

 parta of powdered argol, which is the commercial name for impure 

 cream of tartar, or bitartrate of potash : this mixture is to be gradually 

 thrown into a red-hot earthen crucible so as to deflagrate it, taking 

 care not to make the heat ao high as to fuae the mixture. 



In this case the nitric acid of the nitre is decomposed, ita oxygen 

 acta upon the carbon of the tartaric acid, carbonic acid is formed, and 

 this uniting with the potash both of the nitre and bitartrate is con- 

 verted into carbonate of potash ; the whole of the carbon of the tar- 

 taric acid is not, however, ao acted upon, and the excess remains mixed 

 with the carbonate of potash in the state of finely-divided charcoal 

 This flux should be immediately reduced to powder and kept in a well- 

 stopped bottle, otherwise it will become damp by the absorption of 

 moisture, to which the carbonate of potash is subject. 



This flux is doubly useful ; the carbonate of potash combines with 

 the earthy parts of the ore, such as silica and alumina, while the char- 

 coal unites with the oxygen of the metallic oxides, and carbonic acid 

 being formed and expelled, the metal is reduced, and melt*. This flux 



is especially useful in the process of detecting araenious acid and 

 reducing it to the metallic state. 



\yiiitr jfiij- is a carbonate of potash made by deflagrating equal 

 weight* of nitre and bitartrato of potash ; the quantity of this last 

 salt being smaller than that in black flux, there is no excess of charcoal 

 furnished by tartaric acid. It appears to possess therefore no advan- 

 tage over common carbonate of potash, and either of them may > 

 ployed in reducing metallic chlorides, such as that of silver, to the 

 metallic state. White flux, or carbonate of potash, disintegrates stony 

 matter, as alumina and silica, separates acids and sulphur from metals, 

 and dissolves many metallic oxides; having, however, no charcoal 

 in ita composition, it does not reduce metallic oxides as the lAtvk 

 jdu-does. 



Argol, already described as an impure bitartrate of potash, powdered 

 and mixed with the pulverised substance to be reduced, is sometimes 

 advantageously used as a flux ; owing to the intimate mixture of the 

 harcoal and potash in this flux a good deal of potassium is evolved, 

 and upon the reducing property of this metal the reduction of the 

 oxides of other metals frequently depends to a considerable extent. 



Charcoal alone is, in the case of pure oxides, sometimes employed as 

 a flux ; thus a crucible lined with charcoal is useful for the reduction 

 of oxide of iron, or the oxide may be mixed with charcoal. 



There are some bodies which are even more efficient than charcoal 

 in certain cases, such as wax, fat, oil, tar, and pitch, and gum, sugar, 

 or starch ; these may be intimately mixed with the substance to be 

 reduced, and. they not ouly contain carbon in a form which is readily 

 developed, but also hydrogen, which is likely to assist in the separation 

 of the oxygen from metallic oxides. 



Flint glau is sometimes, but improperly, used as a flux, for it 

 contains much lead that may greatly interfere with the results 

 produced. 



Green bottie-glau has also been used for this purpose, but it is objec- 

 tionable on account of ita containing iron, and it even yields traces 

 of silicon and aluminum to iron which was pure before being heated 

 with it. 



FLUXIONS, FLUENTS, METHOD, NOTATION, AND EARLY 

 HISTORY. The method of fluxions assumes a distinct conception of 

 velocity, both in the case of a uniform and variable motion. It 

 further extends this notion of velocity or rate of increase, derived 

 from the consideration of a moving point, to all species of magnitudes, 

 and even to expressions which are purely numerical, as the formula; of 

 algebra. If one magnitude depend on another for ita value, so that 

 a change in the first produces a change in the second, and if the first 

 be imagined to increase at a uniform and given rate, then the second 

 will also increase or decrease, but not at a uniform rate, unless the 

 second magnitude y be determined from the first x by an equation of 

 the first degree, ax ; by J; e=0. But the rate at which y increases, 

 though varying with the values of x, can in all cases be determined ; 



and, supposing x to be the velocity with which x increases, and y that 

 of y, an equation can always be produced of the form 



. _ f a function of x and y, depending on 1 



" ~~ \ the equation which connects them j * ' 



In this case y and x were called by Newton jloicing quantities, and 

 x and y were called their fluxions : conversely y and x were called the 

 fluent* of y and x. Thus when y=x* it may be shown that y 3z' x 



and if x = 10, y= 300 x, or if the number be increasing continuously, 

 then the increasing number being 10, ita cube is increasing 300 times 

 as fast as itself. Thus while a number changes from 10 to 10-01, ita 

 cube changes from 1000 to 1003-003001, and 3-003001 is 300-3001 

 tunes as great as Ol. That this is not exactly 300 arises from the 

 rate of increase of x 3 not being uniform when that of .r is uniform. 

 [VELOCITY.] The velocity of y being variable, may itself be con- 

 sidered as having a rate of change. Thus, if the velocity of a body 

 increase uniformly, the whole velocity gained in a second may be 

 called the velocity of the velocity, or the fluxion of the fluxion. Thus 



if x increase uniformly, the velocity of A is nothing or ( x ) =0, but 

 if y=x* then ( y )' = 9xx > . Newton denoted these second fluxions by 

 y and x . In a similar way might be determined the velocity of y t 

 denoted by y, and so on. We cannot find that Newton proposed any 

 symbol for the fluent of a fluxion except the enclosure of ita e 

 sion; thus, 



I 8** x I is the fluent of S.r 2 .r, or f*. 



He also in his treatise ' De Quadrature Curvarum/ used ' to stand 

 for the fluent of :. 



We now come to the history of this discovery, and of the dispute 

 relative to the right of invention. We have already given a brief 

 outline of the circumstances which led to th" pnMii-.-ition of tin- 

 CoMMERcirjH EPUTOLICUX, and we shall now add the previous and 

 subsequent occurrences, with some quotations from authorities. 



The biographers of Newton state, that about the year 1663 he began 

 to turn his attention to the writings of Descartes and Wallis, and 

 Newton himself testifies that he invented the method of aeries and 



