6 PROCEEDINGS OF THE AMERICAN ACADEMY 



ance was experienced at times from sounds which apparently arose 

 from microphonic action at the break-wheel. These can probably 

 be avoided in future experiments by causing the wheel to divert the 

 current from the receiver periodically, instead of interrupting it. 

 The limits at which the beats disappeared, with the notes experi- 

 mented upon, were as follows : TJt A 48, Mi t 56, Sol A 69. These fig- 

 ures are the means of a number of observations, and are apparently 

 true within less than one beat per second. Comparing this kind of 

 interruptional beat with those given by Mayer's method, the maxi- 

 mum number perceptible seems to be smaller for the former than 

 for the latter. This is probably due in part to the greater loudness 

 of the sounds observed in the latter case, but there is another marked 

 difference which must exercise an important influence upon the phe- 

 nomenon under consideration. With the beats produced by the 

 break-wheel the sound begins and ends almost instantaneously, so 

 that sharply marked intervals of sound and silence of equal du- 

 ration succeed each other. One would naturally expect the tele- 

 phonic beats to be the more distinct of the two, which is not the 

 case. The subject is one which requires further study as to the 

 influence of the relative duration of sound and silence in the tele- 

 phonic method, and of the relative size of the apertures in Mayer's 

 method. 



In the matters which we have thus far discussed in the present 

 paper, our results are fully in accordance with the theory of conso- 

 nance proposed by Helmholtz. In some other particulars, however, 

 we are led to conclude that this theory is incomplete, at least. 



Some years ago, in a paper read at the Philadelphia meeting of 

 the American Association for the Advancement of Science, and of 

 which an, abstract was published in the Proceedings of that Society 

 for 1884 (page 113), one of us called attention to the bearing of 

 certain phenomena of binaural audition upon Helmholtz's theory 

 as follows : — 



" In connection with his study on the effects of beats in causing 

 dissonance, Helmholtz considers the condition of the vibrating por- 

 tions of the inner ear as to resonance and damping. In his remarks 

 on the subject, he assumes that no notes are capable of beating with 

 each other unless they both affect the same vibrating element of 

 the inner ear. This view of the matter gives a purely mechanical 

 action in the ear as the explanation of the physiological phenome- 

 non of beats. 



"In addition to the experiments of Koenig, in which beats were 



