268 Prof. A. M. Meyer's Researches in Acoustics. 



motion as that of a freely swinging pendulum. If we now bring 

 this vibrating fork near the mouth of a glass vessel whose mass 

 of air responds to the tone of the fork, and, by the method of 

 Macb, examine the vibratory motions of the air, we shall see it 

 swinging backward and forward; and by combining these vibra- 

 tions with the rectangular vibrations of forks placed outside of 

 the vessel we shall obtain the curves of Lissajous. If the mem- 

 brane of the drum of the ear be placed in connexion with the 

 resounding cavity, it must necessarily partake of the motion of 

 the air which touches it, and ultimately the auditory nerve fibrillse 

 are shaken in the same manner, and we receive the sensation* 

 of a simple sound. Here the mind naturally inquires the reason 

 of this connexion existing between the sensation of a simple 

 sound and the pendulum-vibration. It has always appeared to 

 me that the explanation of this invariable connexion is that the 

 pendulum -vibration is the simplest vibratory motion that the 

 molecules of elastic matter can partake of, and that the con- 

 nexion of the sensation with the mode of vibration is the con- 

 nexion between the simplest sensation perceived through the 

 intervention of the trembling nerves, and the simplest vibration 

 which they can experience. Indeed the pendulum-vibration is 

 the only one which produces the sensation of sound ; for if any 

 other recurring vibration enters the ear, it is decomposed by the 

 ear into its elementary pendulum-vibrations; and if it cannot 

 be so decomposed, then the given vibration is not recurring and 

 does not produce in us the sensation of sound, but causes that 

 which we denominate noise. This remarkable connexion be- 

 tween a simple sound and the pendulum or harmonic vibra- 

 tion, together with the fact of the power of the ear to decompose 

 the motions of a composite sonorous wave into its vibratory 

 elements, was thus distinctly enunciated by Ohm : — The ear has 

 the sensation of a simple sound only when it receives a pendulum- 

 vibration ; and it decomposes any other periodic motion of the air 

 into a series of pendulum- vibrations, each of which corresponds to 

 the sensation of a simple sound. 



We have seen that the harmonic curve is the curve which 

 corresponds to the motion which causes the sensation of a sim- 

 ple sound ; but a molecule of vibrating air or a point on the 

 tympanic membrane may be actuated by vibratory motions 

 which, when projected on a surface moving near them, will 

 develop curves which depart greatly from the simplicity of the 

 harmonic, or curve of sines t; but nevertheless these curves 



* See Helmholtz on the distinction between a sensation and a perception. 

 Tonempjindungen, p. 101. 



t In section 6 of this paper I have constructed several important curves 

 corresponding to composite vibrations. 



