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On the strength of tone of wires in piano-fortes
344
2t .New Telegraph. The Cosmos, for March, describes a modification of the reading apparatus of Morse's telegraph, invented by MM. Digney and Baudouin, which is said to be successful in marking the Morse alphabet in ink upon the paper. The following cut illustrates the arrangement : D is a thin disk of metal, glass, or other sufficiently hard material, of from threetenths to four-tenths of an inch in diameter. E, is the inking roller turn-
f'f
!
ing freely in its sheaf, wMch moves around a joint at o, pressing and rubbing gently on the disk D. By means of a screw, the roller may be displaced a short distance parallel to its axis, so as to bring a fresh circumference in contact with the disk. L M is the lever m'oved by the electro-magnet similar to those of the common Norse apparatus, but terminating in a hammer, or kind of knife, whose edge properly rounded raises the paper transversely, and presses it against D~ at each vibration of the lever. This band of paper receives its movement from the rollers, P and P', as usual, and is moved in the opposite direction to the motion of the rollers, so that the impression made, is well defined. The ink is fat and fluid, dries slowly in the air, and remains a long time viscous.
On tt~e Strength of Tone of Wires in Piano-Fortes.*
By GENERALT.
PEa~ON~.T THOMPSOn, M. P. The following observations on the strength of tone of wires, collected, with improvements, fi'om a former work on the Theory of Music rather than on the Mechanics, may contain something useful to the constructors of musical instruments. With the same materials and length, and when the difference of diameters is not very great, all wires break at the same pitch ; which is the necessary result of the strength of the wire, and the load required to ~' From tile London Mechanics' Magazine, February, 1858,
On the Strength of Tone of Wires in Piano.Fortex.
345
bring it to the same pitch, both varying as the square of the diameter. If the wire of greatest diameter breaks sooner, it is because it is no~ treated with equal fairness at the bends ; the remedy for which is to increase the diameter of the pin round which it is bent. If the wires were of very different diameters, the increased resistance of the air orJ the greater diameter would make the sound somewhat flatter, and consequently require an increased tension to overcome; which would be to the disadvantage of the thickest. In wires of different diameter, but the same length and strained to the same pitch, the thickest will have the strongest tone; because the vibrating area, which is what strikes against the air, will be greater, being as the diameter. In wires of different diameters and lengths, strained to the same pitch, the strength of tone will be as the diameter multiplied by the square of the length, or multiplied by the length twice over. For the diameter multiplied by the length expresses the vibrating area; and the extent to which the vibrations will be carried laterally, will be as the length again. Follows, that when the same pitch is produced at different lengths of the same wire by different loads, the longest, and consequently the heaviest loaded, will have the strongest tone. Whence the strongest tones at all pitches, which can be obtained from anywire, are those produced by loading it to the extent of safety, and then taking the lengths which produce the pitches desired. And from the toughest materials may be had the longest wires and strongest tones. A way to judge of the toughness of steel wire without reference to its diameter, is to see how many yards of its own kind it will support. Good wire will bear the weight of 14,500 yards. Follows from the same, that if wires of the same materials but different diameters, are loaded with equal weights, and the lengths taken which produce the same pitch, the longest and consequently the thinnest will have the strongest tone. For since the lengths will be inversely as the diameters, the vibrating areas will be the same in both ; and consequently the longest, as making vibrations of greatest extent, will have the strongest tone. Whence it follows, that if the strain upon the frame is to be of a given amount and no more, the strongest tone with which the pitch in question can be produced with the given strain, is from the thinnest wire which will bear the strain, the length being at the same time increased as demanded. Which agrees with the last in showing, that all wires shouid be loaded to the extent of safety, if length can be afforded; or else tone is thrown away. These conclusions bear on the construction of piano-fortes to the extent of showing that so far as other considerations do not interfere, the most advantageous shape and dimensions for what may be called the harp, are those indicated by loading a steel wire of the best quality and " of any diameter, to the extent of safety, and taking on it the lengths required to make the different sounds, in other words, the lengths on the Monochord. This points to a wire of eight feet for bass C C, and sixleen feet for CC C. Now, wherever a grand piano-forte stands, there is a space of four feet for the performer; this, therefore~ might be added
846
3lechanics, Physics, and Chemistry.
to the length of the longest wires, by placing them one over another in a narrow case next the wall, without virtually adding to the length required for the instrument. And such wires should be double. The advantage of multiplying wires for the same sound, is that if a given quantity of strain instead of being applied to one wire which it loads.to the extent of safety, is divi~led among four wires of the same length and half the diameter, the pitch and the sum of the strains will be the same as before, but the vibrating areas will be doubled, and consequently the strength of tone increased in something like the same proportion. And with any other number the advantage gained will be as the square root of the number of wires ; u'hich in round terms is "aitb two wires, as 7 to 5, and wlth three, as 8~ to 5. Hence the wires of the extreme bass ought to be doubled, as increasing the strength of tone in something like the proportion of 7 to 5, with the same total strain. What is wanted, then, for improving the tone of piano-fortes, is, so far as other reasons do not intervene, to increase the length and thickness of the wires. And this will end in a contest for bearing the greatest strain ; the tendency of which will be to make the frame approach to a solid shell of iron, being the form of the original lyre attributed to Mercury, which was the shell of a tortoise. The same conclusions may be applied to s~rings of catgut, except that in consequence of the increasingly oblique action of the fibres ia the thicker strings, the strain borne without breakihg will not increase with equal regularity in relation to the diameter. But the string of catgut will bear to be strained to a higher pitch than a wire of the same diameter and length. For the loads required to bring these to the same pitch are as their specific gravities, which are as 1 to 6 ; while the loads they are able to bear are something like 1 to 3. Hence the wire to produce the final pitch of the catgut must be shortened to about five-sevenths (1 divided by the square root of 2), for no wire will bear straining to that pitch at a greater length ; and to produce the final strength of tone of the catgut, the diameter of the wire must be doubled, with four times the strain which was on it before, making twelve times the strain finally on the.catgut. Which explains the superiority of catgut for the instruments m which it is found employed. Many of these conclusions may be what everybody is acquainted with, but some of them may be new to some. Eliot Vale, Blackheath, Feb. 3, 1858.
Friction Rollers. M. Alphonse Brussaut presented to the Society for the Encouragement of National Industry (Paris), a system of anti-friction bearings, in which the axle is supported upon rollers which are connected together by flexible bands of leather, canvass, or caoutchouc, in place of being rigidly confined in grooves as is usual. We do not anticipate from this system quite all the advantages which the Abb~ Moigno attributes to it, viz : " the complete abolition offriction," and a consequent" economy of two-thirds of the motive force employed," (we translate literally,) the
2t .New Telegraph. The Cosmos, for March, describes a modification of the reading apparatus of Morse's telegraph, invented by MM. Digney and Baudouin, which is said to be successful in marking the Morse alphabet in ink upon the paper. The following cut illustrates the arrangement : D is a thin disk of metal, glass, or other sufficiently hard material, of from threetenths to four-tenths of an inch in diameter. E, is the inking roller turn-
f'f
!
ing freely in its sheaf, wMch moves around a joint at o, pressing and rubbing gently on the disk D. By means of a screw, the roller may be displaced a short distance parallel to its axis, so as to bring a fresh circumference in contact with the disk. L M is the lever m'oved by the electro-magnet similar to those of the common Norse apparatus, but terminating in a hammer, or kind of knife, whose edge properly rounded raises the paper transversely, and presses it against D~ at each vibration of the lever. This band of paper receives its movement from the rollers, P and P', as usual, and is moved in the opposite direction to the motion of the rollers, so that the impression made, is well defined. The ink is fat and fluid, dries slowly in the air, and remains a long time viscous.
On tt~e Strength of Tone of Wires in Piano-Fortes.*
By GENERALT.
PEa~ON~.T THOMPSOn, M. P. The following observations on the strength of tone of wires, collected, with improvements, fi'om a former work on the Theory of Music rather than on the Mechanics, may contain something useful to the constructors of musical instruments. With the same materials and length, and when the difference of diameters is not very great, all wires break at the same pitch ; which is the necessary result of the strength of the wire, and the load required to ~' From tile London Mechanics' Magazine, February, 1858,
On the Strength of Tone of Wires in Piano.Fortex.
345
bring it to the same pitch, both varying as the square of the diameter. If the wire of greatest diameter breaks sooner, it is because it is no~ treated with equal fairness at the bends ; the remedy for which is to increase the diameter of the pin round which it is bent. If the wires were of very different diameters, the increased resistance of the air orJ the greater diameter would make the sound somewhat flatter, and consequently require an increased tension to overcome; which would be to the disadvantage of the thickest. In wires of different diameter, but the same length and strained to the same pitch, the thickest will have the strongest tone; because the vibrating area, which is what strikes against the air, will be greater, being as the diameter. In wires of different diameters and lengths, strained to the same pitch, the strength of tone will be as the diameter multiplied by the square of the length, or multiplied by the length twice over. For the diameter multiplied by the length expresses the vibrating area; and the extent to which the vibrations will be carried laterally, will be as the length again. Follows, that when the same pitch is produced at different lengths of the same wire by different loads, the longest, and consequently the heaviest loaded, will have the strongest tone. Whence the strongest tones at all pitches, which can be obtained from anywire, are those produced by loading it to the extent of safety, and then taking the lengths which produce the pitches desired. And from the toughest materials may be had the longest wires and strongest tones. A way to judge of the toughness of steel wire without reference to its diameter, is to see how many yards of its own kind it will support. Good wire will bear the weight of 14,500 yards. Follows from the same, that if wires of the same materials but different diameters, are loaded with equal weights, and the lengths taken which produce the same pitch, the longest and consequently the thinnest will have the strongest tone. For since the lengths will be inversely as the diameters, the vibrating areas will be the same in both ; and consequently the longest, as making vibrations of greatest extent, will have the strongest tone. Whence it follows, that if the strain upon the frame is to be of a given amount and no more, the strongest tone with which the pitch in question can be produced with the given strain, is from the thinnest wire which will bear the strain, the length being at the same time increased as demanded. Which agrees with the last in showing, that all wires shouid be loaded to the extent of safety, if length can be afforded; or else tone is thrown away. These conclusions bear on the construction of piano-fortes to the extent of showing that so far as other considerations do not interfere, the most advantageous shape and dimensions for what may be called the harp, are those indicated by loading a steel wire of the best quality and " of any diameter, to the extent of safety, and taking on it the lengths required to make the different sounds, in other words, the lengths on the Monochord. This points to a wire of eight feet for bass C C, and sixleen feet for CC C. Now, wherever a grand piano-forte stands, there is a space of four feet for the performer; this, therefore~ might be added
846
3lechanics, Physics, and Chemistry.
to the length of the longest wires, by placing them one over another in a narrow case next the wall, without virtually adding to the length required for the instrument. And such wires should be double. The advantage of multiplying wires for the same sound, is that if a given quantity of strain instead of being applied to one wire which it loads.to the extent of safety, is divi~led among four wires of the same length and half the diameter, the pitch and the sum of the strains will be the same as before, but the vibrating areas will be doubled, and consequently the strength of tone increased in something like the same proportion. And with any other number the advantage gained will be as the square root of the number of wires ; u'hich in round terms is "aitb two wires, as 7 to 5, and wlth three, as 8~ to 5. Hence the wires of the extreme bass ought to be doubled, as increasing the strength of tone in something like the proportion of 7 to 5, with the same total strain. What is wanted, then, for improving the tone of piano-fortes, is, so far as other reasons do not intervene, to increase the length and thickness of the wires. And this will end in a contest for bearing the greatest strain ; the tendency of which will be to make the frame approach to a solid shell of iron, being the form of the original lyre attributed to Mercury, which was the shell of a tortoise. The same conclusions may be applied to s~rings of catgut, except that in consequence of the increasingly oblique action of the fibres ia the thicker strings, the strain borne without breakihg will not increase with equal regularity in relation to the diameter. But the string of catgut will bear to be strained to a higher pitch than a wire of the same diameter and length. For the loads required to bring these to the same pitch are as their specific gravities, which are as 1 to 6 ; while the loads they are able to bear are something like 1 to 3. Hence the wire to produce the final pitch of the catgut must be shortened to about five-sevenths (1 divided by the square root of 2), for no wire will bear straining to that pitch at a greater length ; and to produce the final strength of tone of the catgut, the diameter of the wire must be doubled, with four times the strain which was on it before, making twelve times the strain finally on the.catgut. Which explains the superiority of catgut for the instruments m which it is found employed. Many of these conclusions may be what everybody is acquainted with, but some of them may be new to some. Eliot Vale, Blackheath, Feb. 3, 1858.
Friction Rollers. M. Alphonse Brussaut presented to the Society for the Encouragement of National Industry (Paris), a system of anti-friction bearings, in which the axle is supported upon rollers which are connected together by flexible bands of leather, canvass, or caoutchouc, in place of being rigidly confined in grooves as is usual. We do not anticipate from this system quite all the advantages which the Abb~ Moigno attributes to it, viz : " the complete abolition offriction," and a consequent" economy of two-thirds of the motive force employed," (we translate literally,) the