158 ANNUAL RECORD OF SCIENCE AND INDUSTRY. 



curve. Ohm states that such a vibration, and only such, can 

 produce on the ear the sensation of a simple sound in other 

 words, of a sound which has one and only one jDitch. But 

 the point of the sonorous body whether it be a point of a 

 membrane, of the drum of the ear, of the end of a vibrating 

 rod, or of the air itself may be actuated by a motion which, 

 when it is caused to describe itself on the above-mentioned 

 surface, may depart greatly in its form from the simple har- 

 monic curve. Yet in this case, according to Ohm, the ear 

 will act on this composite motion as the analysis of the math- 

 ematician can act on its corresponding curve, and will de- 

 compose it into the simple harmonic vibrations which com- 

 pose it. Therefore the ear will, in this case, perceive several 

 sounds, each having one definite pitch, and with the proper 

 degree of attention can take cognizance of any one of them, 

 to the exclusion, more or less, of all of the other components. 

 But if Ohm's proposition be true, then there must be a rea- 

 son for it in the very dynamic constitution of the ear. This 

 Helmholtz saw, and the discovery of the 3000 chords of Corti 

 in the cochlea and of Schultze's bristles in the ampulse led 

 him to suppose that these bodies eftected the analysis of the 

 sound by vibrating sympathetically with its simple compo- 

 nents. Thus he founded his theory of audition, which at 

 once led him to his physiological theory of music as contain- 

 ed in his renowned work, ''''Die Lehre von den Toneii^yfindun' 

 gen^"* in which he reveals the hidden causes of musical har- 

 mony, which had remained for 2000 years a secret and a 

 problem to the mind of man. But many difficulties present 

 themselves when we would bring to the test of experiment 

 the propositions of Ohm and Helmholtz's ingenious hypothe- 

 sis of audition. First, the complex sound on which we would 

 experiment emanates from a multitude of vibrating points, 

 and the points of the resultant wave surface difter in their 

 amplitudes of vibration, while points equally removed from 

 the geometric centre of the wave difter in their phases of vi- 

 bration, so that when such a wave falls at an angle on sym- 

 pathetically vibrating bodies which present any surface, the 

 eftects produced are the results of extremely complex mo- 

 tions. The mind sees at once the difterence between this 

 complex conception and Ohm's simple statement of his appli- 

 cation of Fourier's theorem. The only experiment, indeed, 



