28 M. J. Antoine on the Multiple Sounds 



that they have long since possessed an exact, simple and direct 

 theory of multiple sounds. 



^' I regret that M. Duhamel has thought proper to be very 

 brief in transcribing the slate of science. It is with fear that 

 I undertake to be his substitute in a delicate matter, which he 

 has studied for many years ; nevertheless, I shall venture to 

 give an historical sketch, in order better to appreciate the 

 present position of the question. -'^ 



The phaenomenon of multiple sounds has been known for a 

 very long time, for Aristotle asks by what reason the grave 

 sounds contain also sharper sounds. Mersennus however 

 was the first physicist who submitted this to experimental 

 analysis. 



This ingenious observer classed the different higher sounds 

 which accompany the fundamental note of a string, and found 

 the same series for strings of different materials, tension and 

 dimensions. The supplementary sounds which he could di- 

 stinguish, placing himself in favourable circumstances, are 

 the octave, the twelfth, the fifteenth, the major seventeenth, 

 the nineteenth and the twenty-second. When accustomed to 

 these experiments, it is easy to prolong the series beyond 

 these limits. Mersennus classed also the tones which com- 

 pose the multiple sounds of bells, as those, more curious still, 

 which proceed sometimes simultaneously from the pipes of an 

 organ. 



In seekingthe causeof this multiplicity of sounds, Mersennus 

 made an experiment which might have led him to discover it ; 

 but the sagacity of his spirit was baffled, and the truth escaped 

 him. He examined the vibrations of a long string, and see- 

 ing no division established, he concluded that strings do not 

 divide to produce the simultaneous harmonics, and he there- 

 fore sought the explanation of the phaenomenon in the wrong 

 quarter. 



The theory of multiple sounds did not make progress until 

 experimental analysis had disclosed the cause of this multitude 

 of sounds which may be separately drawn from one and the 

 same sonorous body. It had been long known that a con- 

 siderable series of successive sounds could be produced from 

 the trumpet; Mersennus made the exact classification of them, 

 and compared it to that of the different sounds which one pipe 

 of an organ can give; but he could not discover the cause. 

 The difficulty was great; and it was first solved, not upon 

 aerial columns, but upon vibrating strings. 



In 1673, William Noble and Thomas Pigot made that beau- 

 tiful experiment, in which small pieces of paper, placed astride 

 upon a string, are seen to remain immoveable in certain 



