THE SENSES. 



mechanism of its production. But if the shocks succeed each other at 

 regular intervals, the sound has then a definite position in the musical 

 scale, and is appreciated by the ear as a high or low note. The more 

 frequent the repetitions in a given time, the higher is the note produced, 

 until a limit is reached at which the ear fails to perceive a sound at all. 

 The physical reason why excessively high notes become inaudible is 

 probably this: In the special arrangement. of the auditory apparatus, a 

 vibration, in order to be perceptible, must have a certain degree of 

 extent or amplitude; that is, the particles of the vibrating body must 

 move to and fro, at each impulse, for a certain distance in space. The 

 intensity of a sonorous impression, accordingly, depends upon the am- 

 plitude of the vibrations, while its pitch or tone depends upon their 

 frequency. But the more frequently a body vibrates in a single second, 

 the less extensive must be its movements, if their velocity remain the 

 same. Consequently, when these vibrations arrive at a certain high 

 degree of frequency, unless the velocity of movement can be increased 

 in proportion, their amplitude becomes so small that they can make no 

 impression upon the ear, and the sound becomes inaudible. 



It is evident, however, that such a sound would be perceptible if the 

 sensibility of the auditory apparatus were increased to the requisite 

 degree; and it has been suspected by some naturalists that certain 

 insects may be capable of perceiving sounds of so high a pitch as to be 

 inaudible for the human ear ; while, on the other hand, for them, a very 

 low note would appear as a succession of distinct impulses. 



The limits of frequency, within which sonorous vibrations are percep- 

 tible to man as continuous musical sounds, are 16 double vibrations 

 per second for the lowest notes, and 38,000 for the highest. But, 

 according to Wundt, the exact discrimination of the pitch of musical 

 sounds is confined within much narrower limits, especially for the higher 

 notes. 



Duration of a Sound required for the perception of Sonorous Impres- 

 sions. This point has been investigated by Savart 1 in the following 

 manner. He ascertained, by experiment, that the ear could appreciate 

 the pitch of a sound made by a toothed wheel revolving at such a rate 

 as to cause 10,000 shocks per second. By removing successively the 

 teeth from larger portions of the circumference, he diminished in a 

 corresponding degree the time during which the shocks were produced ; 

 and he found that such a wheel would give a sound of definite pitch 

 with only two adjacent teeth remaining. The double shocks thus pro- 

 duced would occupy only -g-^y of a second ; and this duration of the 

 impulses was sufficient to make upon the ear a distinct musical impres- 

 sion. 



1 Daguin, TraitS ElSmentaire de Physique. Paris, 1869, tome i. p. 517. 



