OF ARTS AND SCIENCES. 5 



For the other notes the divergence is wide, except for Ut 5 , for which 

 our results agree quite well with those obtained by Mayer himself. 

 These differences may be due to the different way in which the vari- 

 ations of intensity in the beats progress, to the presence of pitch 

 variations in interference beats, to the fact that in our method the 

 musical interval of the beating notes increases as the beats increase 

 in number, to mere differences in the estimation of the observers, 

 or to some other less evident causes. 



We find that the ratios between the number of beats producing 

 the greatest harshness at different pitches and the maximum num- 

 ber of beats discernible at those pitches are as follows (Table III.). 

 The numbers given are obtained by dividing the former number by 

 the latter. 



TABLE III. 



These figures, as a whole, agree very well with the ratio (four 

 tenths) given by Mayer, although the absolute numbers whose ratios 

 are taken are quite different from his. Our results also seem to 

 indicate a clearly marked fall in this ratio as the pitch rises. 



A few experiments were made using Professor Mayer's method, 

 with some slight modifications, in order to observe the judgment of 

 the same ear upon beats of different kinds. The tuning-fork em- 

 ployed was kept in vibration continuously by electricity, and the 

 rotating disk was driven by an electro-motor, which secured great 

 constancy of speed. We were seriously troubled by the sound made 

 by the rotating disk, which produced a sort of siren effect as its 

 openings passed before the aperture of the resonator. For Ut 3 the 

 maximum number of intermittences perceived was 50 per second. 

 For Uti the number was about 106. These figures are liable to an 

 error of perhaps two beats, or even a little more for the higher pitch. 

 Mayer's figures are 47, 78, respectively, for his own observations 

 on these notes, and 70, 130, for those of Mrs. Seiler. It is clear 

 that there are very great differences in the sensitiveness of different 

 ears for the perception of rapid beats. 



In another series of experiments, interruptions were produced by 

 a break-wheel placed in a telephonic circuit with a magneto-telephone 

 at each end. The sound of a tuning-fork was transmitted through 

 the line, and any desired number of interruptions could be produced 

 by varying the rate of rotation of the wheel. Considerable annoy- 



