When two musical tones nearly, but not quite, in unison are sounded together we hear an alternate increase and diminution of sound, and the tones are said to beat with each other. The beats are caused by the alternate coincidence and interference of two systems of sonorous waves generated by bodies vibrating at different rates. The coincidence is felt as a reinforcement of the sound due to the coalescence of sound waves, and the interference as a silence due to the destructive effect of sound waves on each other. According to the generally accepted rule, the number of beats in a second is always equal to the difference between the vibration numbers of the sounding bodies. We shall have to take exception to this rule hereafter; but for the present we will use the term calculated beats to express the number of beats in a second which it gives for any interval. As it is received by physicists, the above rule does not imply that the beats can always be heard. Circumstances, as we shall see, may render them quite inaudible.