The greater the condensation of a sound-conducting medium at any given moment, the greater also will be the amplitude of vibration of the membrane and of the auditory ossicles and of their action; and in the converse case the action will be proportionally less. It is, therefore, the function of the organs of hearing to communicate with fidelity to the auditory nerves every condensation and rarefaction occurring in the surrounding medium; whilst it remains to be the function of the auditory nerves to bring to our consciousness the number as well as the magnitude of the vibrations ensuing in a given time. Here in our consciousness a definite name is given to a certain composition, and here the vibrations brought to the consciousness become “tones.” That which is perceived by our auditory nerves is consequently the effect upon our consciousness of a force which, according to its duration and magnitude, may for the sake of better comprehension, be exhibited graphically. [Illustration] Let, for example, the length of the line _a b_ be any definite duration of time, and let the curves above this line denote the condensations (+), and the curves below this line the rarefactions (-); then every ordinate erected at the extremity of an abscissa gives us the strength of the condensation in consequence of which the drum-skin vibrates, at the moment indicated by the position of the foot of the ordinate. Anything more than that which is exhibited in this way or by similar curves our ear cannot in the least perceive, and this is sufficient to bring to our consciousness each single tone and each given combination of tones. For, if several tones are produced at the same time, the sound-conducting medium is put under the influence of several simultaneously acting forces which are subject to the laws of mechanics. If all the forces operate in the same sense, then the magnitude of the motion is proportional to the sum of the forces. If the forces act in opposite directions, the magnitude of the motion is proportional to the difference between the opposing forces. Consequently it is possible out of the condensation-curves of several simultaneously-occurring tones to compound, by the foregoing principles, a condensation-curve which exactly expresses that which our ear experiences on the reception of these simultaneously-acting tones. The objection ordinarily made to this, that a musician, or even any one, is able to hear separately the single tones of which this combined curve is built and constructed, cannot be admitted as a proof to the contrary; for one expert in the science of colour will, for example, in the same way discern in green a mixture of yellow and blue in their various shades: and the one phenomenon equally with the other may be referred back to this; that, to the person concerned, the factors which make up the product of that which reaches his consciousness are well known.