Number I. contains, I. The Defence of Gulliver. II. A Letter on Revelation. VIII. Against Tythes, by Rufticus. III. Pieces for and against the Me-X. Mr Facio's Answer to the Ob thodists. jection taken from the Motion XI. M. Voltaire on Suicide. XIII. M. Maupertuis on the late Note, In Number IV. will be a Continuation of the Supplement to Cyclopædia, and it is intended to be published in November next. Thofe Gentlemen who shall favour us with Corrections of the Cyclopædia, or proper Articles for a Supplement to it, for which we have already some) will have the Satisfaction of promoting Literature, and will entitle themJelves to an Acknowledgment to be made by a Prefent, at leaf, of fome Book or Books printed for the Editor. Mifcellaneous Correspondence, &c, NUMBER III. An ACCOUNT of the MECHANISM of an IMAGE playing on the German Flute, &c. Prefented in a Me moire to the Gentlemen of the Royal Academy of Sciences, by Mr V AUCANSON, the Inventor of it. GENTLEMEN, L ESS fenfible of the publick Applaufe, than defirous of defer. ving yours, I come to difcover to you, that it is only in following your Steps, that I have been able to go on with fome Success in the Execution of my Undertaking. To you I owe the Reflections I have made on the Sound of Inftruments, and on the different Motions of Mechanicks. My firft Care was to examine the Mouth of Wind-Inftruments, to know well what Parts contributed to produce Sound, and how it may be modified. ་ The Mouth of a German-Flute differs from that of other Wind-Inftruments, fuch as the common Flute, Flageolet, and Organ-Pipe; becaufe, in these the Wind introduced at a narrow Hole, but which is determined, ftrikes the Parts of the Body of the Inftrument immediately under it, as the Bezel; and by the Quickness of its Return, and Re-action upon the small Parts round about it, suffers a violent Collifion: Thus communicating its Vibrations to all the Parts of the Flute, which in their Turn communicate them to the external Air round about them, it produces in us the Senfation of Sound. But the Mouth of the German-Flute is undetermined, because the Wind paffes thro' a greater or smaller Vent, made by the greater or less Opening of the Lips, as they approach towards, or recede from each other; as they come nearer to, or are further from the Hole of the Flute; or as they advance more or lefs over the faid Hole. All these Differences, which I reduce to four, make the German-Flute capable of a very great Number of Perfections, not found in other Wind-Inftruments, whofe Mouth is determined. The Sound being first produced by the Vibration of the Air, and the fmall Parts of the Body of the Flute, is only determined by the Quickpefs or Slowness of those Vibrations. If in an equal Time they are to be continued in a greater Number of the Parts of the Body ftruck, they will lofe more of their Motion, and confequently of their Swiftness; and thus, becoming flower in the fame Time, they produce a lefs lively Sound; and this makes the deep or low Tones. This happens when all the Holes of the Flute are ftopp'd. The Vibrations, which begin exactly at its Mouth, must be communicated to all the Parts of the Wood Y at the fame Time; therefore they are fuddenly weaken'd, because their Force is divided among a great Number of Particles, and produces the lowest Sound. If you open the firft Hole next the Bottom of the Flute, the Vibrations find a Vent fooner, being interrupted in their Continuation. They have fewer Particles to ftrike, (the Pipe being fhortened by opening the faid Hole) thus, lofing a little lefs of their Force, because there are now fewer Particles among which they must be divided, they will have a little more Swiftnefs; and being quicker in the fame Time, they will produce a lefs deep Sound, and that will be a Tone higher. The other Tones will rife gradually, as the upper Holes are unstopp'd. "When you unstop the Hole which is nearest to the Mouth, that Hole dividing the inward Space of the Flute into two equal Parts, the Vibrations will find an Iffue in the Middle of the Way that they are to run to the End of the Pipe; therefore they will go out with as much more Force and Velocity, having only half the Particles, among which they muft divide themfelves; and confequently will produce a Sound as high again, which will be the Octave. But as a Part of those Vibrations is always communicated to, and loft in the other Half of the Flute, the Wind must be forc'd a little to produce Accelerations to that Lofs, and then you will have a full Octave. That Note is alfo produced by stopping all the Holes of the Flute, as in that of the firft Octave; but then you muft double the Force of the Wind, to produce double Vibrations in the whole Body of the Flute, which amounts to the fame Thing. This is what is practifed in the Tones of the fecond Octave, where the Pofition of the Fingers and Opening of the Holes is the fame as in the First. You must blow with a double Force to produce double the Number of Vibrations in the fame Time; which makes the second Octave: Because, the more or lefs acute Sound confifts in the greater or lefs Number of Vibrations in the fame Time. Again, the Wind must be given with a triple Force to produce the third Octave; but Vibrations fo fuddenly redoubled, not finding fufficient Iffue in the firft Hole to hinder their going on in the reft of the Flute, because of their extreme Swiftnefs, we must be forced to open feveral Holes in the lower Part of the Flute; thus the Pipe being more open, the Vibrations will have a greater Iflue and a full and open Sound will be formed, without being obliged to give the Wind quite a triple Force. By this Changing of Openings, different from what is required in natural Sounds, a Vent may be given fooner or later, and greater or less, to produce Semi-Tones; which must also be done in the last high Sounds, where a quicker and greater Iffue must be given, that the Vibrations may not lofe their Velocity in communicating with too many Parts of the Body of the Flute. 'What remains is to fhew, how the Wind is modified, and what are the Parts in a living Perfon which contribute to give it more or lefs Force. The Preffure of the Pectoral Mufcles upon the Lungs drives the Air out of the Veficles that contain it: When this comes up to the Mouth thro' the Trachea Arteria, (or Wind-pipe) it goes out of it by the Opening which the Lips form as they are applied to the Hole of the Flute. The greater or lefs Force of the Wind depends, firft, upon the greater or or lefs Preffure of the Muscles of the Breaft, which drive it out of its Receptacle; fecondly, upon the greater or lefs Opening of the Lips at its going out: So that when you would blow weakly, the Muscles then must act weakly, and the Lips making a large Opening, the Wind is driven flowly; and confequently its Return producing Vibrations equally flow, and still farther flacken'd by their Communication with all the Parts of the Wood of the Flute, low Sounds will be formed. But when you would rife to the Octave, that is, produce Sounds as high again, the Muscles must act with a little more Force; and the Lips, coming nearer together, muft a little diminish their Opening; then the Wind being more ftrongly comprefs'd, and having a fmaller Iffue, will double its Swiftnefs, and produce double Vibrations, and thereby give Notes as high again, that is, the Octave. As you rife gradually to the high Sounds, the Muscles will act with inore Force, and the Opening of the Lips will be proportionably contracted, that the Wind, driven in a more lively Manner, and forced to go out at the fame Time by a fmaller Iffue, may confiderably increase its Swiftness, and confequently produce accelerated Vibrations, which make acute Sounds. But the German-Flute having its Mouth undetermined, the Wind may be modulated by the greater or lefs Opening of the Lips, by their different Pofition upon the Hole of the Flute, and by the Performer's being able to turn the Flute inwards or outwards. Thus the Sounds may be fwell'd and diminish'd, foften'd and ftrengthen'd, produce Echoes, and give Grace and Expreffion to the Tunes that are play'd; Advantages not to be found in those Inftruments whofe Mouth is determined: For, Sound confifting in the Vibrations of the Air produced by its Entrance into the Flute, and its Return upon that which fucceeds it; if, by a particular Pofition of the Lips, it enters into the whole Bignefs of the Hole of the Flute, that is, goes thro' the longest Chord of the Hole, or the true Diameter of it, (which is done by turning the Flute outwards) then it strikes a greater Number of the Particles of the Wood, and at its Return finding an Iffue equally large, it communicates with a greater Quantity of external Air; and this produces the louder Sounds. But, when the Flute is turn'd inwards, the Lips cover more than half the Hole, the Wind going in thro' a fmaller Opening, and being able to return only thro' the fame, in order to communicate with the external Air, it can ftrike only a lefs Quantity of it, which makes the Sound foft. These two Differences may have feveral Degrees, which depend upon placing the Lips over a greater or lefs Chord of the Hole ' of the Flute, by turning it more inwards or outwards. Therefore, when there is Occasion to fwell a Note, firft you turn the Flute inwards, that the Lips coming over the Edge of the Hole may fuffer but a small Quantity of Wind to go in or out, which then is driven weakly to produce a weak Sound; then infenfibly turning the Flute outwards, the Lips allow of a greater Paffage and Return to the Wind, which at that Time is driven with greater Force, that it may be com municated to a greater Quantity of Air, and thereby increase the Sound; or diminish it anew, by infenfibly turning the Flute inwards, as in the first Operation. All these Variations of the Mouth may be performed in any one Sound Sound whatsoever, whether it be an high or a low one; because the Wind, tho' driven with different Degrees of Velocity during the Note that you would fwell to foften, must always be fo regulated as to produce the Vibrations which determine that Note: In the Beginning, when the Sound will be weak, because it will strike a lefs Quantity of external Air, yet it will have Vibrations equal to thofe that are produc'd in the Middle of the Note where the Sound encreases in Force, because it will be communicated to a greater Quantity of Air; the Vibrations not being stronger or weaker on Account of their Velocity, but on Account of the Quantity of the Parts that they act upon, and which they put in Motion. Would you produce a foft Sound to reprefent an Echo? Place the Lips over the Hole quite to its Edge, by turning the Flute much inwards; then the Sound being able to be communicated but to a fmall Quantity of external Air, thro' fo fmall an Hole, makes us hear a Sound that feems to be afar off, by its ftriking our Organs weakly. These are Conveniences which cannot be found in Inftruments whose Mouth is determined and invariable. As to that Stroke of the Tongue, which is abfolutely neceffary for playing on all Wind-Inftruments; the Tonguing an Inftrument is nothing elfe than a fhort Interruption of the Wind, by the Interpofition of the End of the Tongue in the Paffage of the Lips. Thefe, GENTLEMEN, were my Reflections upon the Sound of WindInftruments, and the Manner of modifying it. By imitating the fame phyfical Caufes in the Mechanism of an Automaton, I endeavoured to enable it to produce the fame Effect in making it to play on the German Flute. The Parts which compound it, their Situation, their Connection, and their Effects, I shall now describe. The Figure is about fix Foot and an half high, fiting upon a Piece of a Rock, placed on a fquare Pedestal, four Foot and an half high, and three Foot and an half wide. In the Fore-part of the Pedestal (the Pannel being open'd) on the right Hand there is a Movement, which by Means of feveral Wheels put in Motion by a Weight, carries round underneath a steel Axel or Arbor, two Foot and a half long, with fix Cranks in its Length at equal Dif tances, but pointing different Ways. To each Crank are faften'd Strings which terminate at the End of the upper Boards of fix Pair of Bellows, two Foot and an half long, and fix Inches wide each, placed at the Bottom of the Pedestal, where their lower Boards are made faft, fo that as the Arbor turns, the fix Pair of Bellows rife and fall fucceffively one after another, In the Hind-Part of the Pedeftal, above each Bellows, there is a double Pulley, whofe Diameters are unequal, namely, one of three Inches and the other of an Inch and an half; which is done to give the Bellows a greater Rife, because the Strings joyn'd to them, go round the great Diameter of the Pulley, and thofe that are faften'd to the Arbor which draws them, wind round the fmall Diameter. On the great Diameter of three of thefe Pullies on the right Hand, there are allo wound three Strings, which, by Means of feveral little Pulliés |