358 Prof. A. M. Mayer's Researches in Acoustics. 



experience a simple sonorous sensation when a tuning-fork is 

 brought near the mouth of the resonator. On revolving the 

 perforated disk, two additional or secondary sounds appear — one 

 slightly above, the other slightly below the pitch of the fork. 

 An increasing velocity of rotation causes the two secondary 

 sounds to diverge yet further from the note of the beating fork, 

 until, on reaching a certain velocity, the two secondary sounds 

 become separated from each other by a major sixth, while at the 

 same moment a resultant sound appears, formed by the union 

 of the sound of the fork with the upper and lower of the secon- 

 dary sounds. This resultant is the lower second octave of the 

 note given by the fork. On further increasing the velocity of 

 rotation of the disk, the two secondary sounds and the resultant 

 disappear, and the ear experiences only the sensation of the 

 simple sound produced by the fork, whose beats at this stage of 

 the experiment have blended into a smooth continuous sensa- 

 tion. These successive and gradual changes, as they happen 

 with an Ut 4 fork, we have indicated in steps of semitones in the 

 appended musical notation. The sound of the fork is given in 

 the semibreve, while the crotchets represent the secondary 

 sounds and the resultant sound. In the fourth bar the upper 

 note [>E proceeds to #D in the fifth bar. This is so because in 

 the natural scale #D is higher than |?E. 



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2. The Determination of the numbers of Beats, throughout the 

 musical scale, which produce the greatest Dissonances. 



The determination of the law which shows the connexion ex- 

 isting between the pitch of a sound and the number of its beats 

 which causes the most dissonant sensation, was made with the 

 same apparatus that served for the disco very of the law just 

 discussed. The determination of the number of beats producing 

 the greatest dissonant effect with a given sound is difficult ; for 

 the point of maximum dissonance is not sharply marked, and 

 individual judgment and peculiarities come in, so that the range 

 of the determination for any given sound, by different persons, 

 is considerable. But on discussing the determinations reached 

 by any one person, I found that they followed a well-marked 

 law, which, as might have been inferred, is closely connected 

 with the law of the duration of the residual sensation. Indeed 

 we find that any one observer always makes the numbers produ- 



