182 Mr. Wheatstone on iZesonance.' 



precedinj^ explanation, and will establish the true theory of the pro- 

 duction of sounds by the guimbarde, beyond the possibility of doubt. 

 I fixed a Jew's harp firmly at the two points where ordinarily it 

 rests against the teeth, allowing sufficient space between the two sup- 

 ports for the tongue to vibrate freely to its greatest extent ; and I tuned 

 the tongue by applying wax to its free extremity, until it sounded 

 C, corresponding to the sound of a closed tube four feet in length. 

 I then placed before the tongue the open end of a closed tube, con- 

 taining a column of air two feet in length and one inch in diameter, 

 and furnished with a moveable piston, by which the column could 

 be shortened to any required length. On striking the tongue, the 

 octave of the fundamental sound was produced, being the sound 2 

 of the scale in the preceding section ; by shortening the column of air 

 successively to one third, one fourth, one fifth, one sixth, one se- 

 venth, &c. &c. up to very numerous ahquot subdivisions, all the 

 notes of the series were correctly obtained. By marking the dif- 

 ferent lengths of the piston rod for each sound of the series, I 

 was able to produce the notes of the scale, ascending or descending 

 regularly, or to fix any sound at pleasure. 



§ 9. No other sounds can be produced by reciprocation from 

 columns of air, but those perfectly identical with the multiples of 

 the original vibrations of the tuning-fork, or the tongue of the 

 Jew's harp. On inquiring what takes place when the length of the 

 column is intermediate between the lengths appropriate to recipro- 

 cate two succeeding multiples, — it will be found, that though each 

 sound of the series is heard most audibly when the column is 

 accurately adapted to it, yet it may also be heard, unaltered in 

 tune, though diminished in intensity, when the column is lengthened 

 or shortened within a certain extent, which is greater for the lower 

 sounds of the series, and less for the higher, on account of the 

 wider intervals between the sounds in the former case. 



It may now be understood in what manner a column of air is 

 capable of reciprocating simultaneously two or three sounds of a 

 chord. In Mr. Elilenstein's performance, this effect is thus pro- 

 duced : suppose the perfect major chord of C is required ; three 

 Jew's harps, incapable of producing lower sounds than the fourth 

 of the series, are selected; and the mouth being made to corre- 

 spond with the C, the other two sounds, E and G, are likewise reci- 

 procated, though faintly, because these sounds are nearer that to 

 which the mouth is adapted, than any other multiples of the original 

 vibrations of the tongues are. 



§ 10. When two imperfect unisons are sounded together, the 

 interferences of their undulations give rise to periodical alternations 



