PROF. D. C. MILLER (“The Science of Musical Sounds,” 1916, p. 184) admits the reality of beat-tones, but says that they are purely subjective, having no physical existence. This seems unsatisfactory. To begin with beats, it is wrong to say that it is the places of maximum intensity which are properly called beats. This is an illusion, due to too familiar diagrams. The maximum of intensity occurs at no place, but at a point of time which, at its own instant, the maximum not being absolute, is not impressive. At any point of time the next vibration of a sound may be of greater amplitude or it may not, and the listening ear, being unable to foretell, cannot tell us in the present when the maximum is attained. he perception of a maximum is bound to arrive, in fact, the day after the fair, when the sound is on the wane. On the contrary, it is the minimum of intensity which gives the effect of the beat. This is clear if the two primary tones are of equal amplitude and there is a phase of silence, when the difference of sensation is a difference, not of degree, but of kind. It has been shown that if a musical note is suddenly reduced to silence, the interruption of the series of vibrations restores the last of theseries of periodic impulses to its isolated value; the note ends with a kind of shock or tap, comparable to one of a series of hard beats. If periodic beats are rapid enough, the final impulses at the interruptions form a fresh series, and are free to evoke in the sensorium a sensation of tone of the same frequency as the beats, a beat-tone; and this is best observed when the beats are not too violent.