262 



AVERS. 



[Vol. VI. 



tion when vibrating air is allowed to act on them, but that this 

 sympathetic vibration is not so limited to a particular pitch as 

 in the other case, and they can therefore be easily set in motion 

 by tones of different kinds. For if an elastic body, on being 

 once struck and allowed to sound freely, loses nearly the whole 

 of its motion after ten vibrations, it will not be of much impor- 

 tance that any fresh impulses received after the expiration of 

 this time should agree exactly with the former, although it 

 would be of great importance in the case of a sonorous body, for 

 which the motion generated by the first impulse would remain 

 nearly unchanged up to the time that the second impulse was 

 applied. In the latter case, the second impulse could not 

 increase the amount of motion unless it came upon a phase of 

 the vibration which has precisely the same direction of motion 

 as itself. The connection between these two relations can be 

 calculated independently of the nature of the body put into 

 sympathetic vibration, and, as the results are important to 

 enable us to form a judgment on the state of things going 

 on in the ear, a short table is annexed : — 



Difference of Pitch in terms of an equally tempered tone, neces- 

 sary to reduce the intensity of sympathetic vibration to 15 of that 

 produced by perfect unisonance. 



Number of vibrations after 

 which the intensity of tone in a 

 sonorous body whose sound is 

 allowed to die out, reduces to 

 j'ij of its original amount. 



1. One-eighth of a tone 



2. One-quarter of a tone 



3. One semitone 



4. Three-quarters of a tone 



5. A whole tone 



6. A tone and a quarter 



7. A tempered minor third or a tone and a half 



8. A tone and three-quarters 



9. A tempered major third or two whole tones . 



38.00 

 19.00 

 9-50 

 6.33 

 4-75 

 3.80 



3-17 

 2.71 



2-37 



" Suppose that a body that vibrates sympathetically has been 

 set into its state of maximum vibration by means of an exact 

 unison, and that the exciting tone is then altered till the sym- 

 pathetic vibration is reduced to one-tenth of its former amount. 

 The amount of the required difference of pitch is given in the 

 first column in terms of an equally tempered tone (which is one- 

 sixth of an octave). Now let the same sonorous body be struck, 

 and let the sound be allowed to die away gradually. The num- 



