Prof. A. M. Mayer's Researches in Acoustics, 271 



very imperfectly understood. Ohm's theorem, ou the other 

 hand, refers entirely to these subjective phenomena of the ear's 

 analysis of a complex sensation into its simple elements. As 

 Fourier's theorem refers only to the decomposition of a com- 

 posite recurring vibration into its elementary pendulum-vibra- 

 tions, it has nothing to do with the physiological fact of the co- 

 relation of the pendulum-vibrations and the simplest auditory 

 sensation ; though this well-ascertained relation gives us the 

 privilege of using this sensation as an indicator of the existence 

 of an aerial pendulum-vibration. Hence, as Fourier's theorem 

 is entirely independent of our sensations, we must endeavour to 

 verify it directly by experiments, which must perform the actual 

 decomposition of the composite periodic motion of a point into 

 its elementary pendulum -vibrations. But many difficulties pre- 

 sent themselves when we would bring to the test of experiment 

 the dynamic signification of Fourier's theorem. For example, 

 the composite sound-vibration, on which we would experiment, 

 emanates from a multitude of vibrating points ; parts of the 

 resultant wave-surface differ in their amplitudes of vibration ; 

 while points equally removed from one and the same point of 

 the body originating the vibrations, may differ in their phases of 

 vibration; so that when such a wave falls upon covibrating 

 bodies which present any surface, the effects produced are the 

 result of extremely complex motions. The mind sees at once 

 the difference between this complicated conception and the sim- 

 ple one embodied in the statements of the dynamic application 

 of Fourier's theorem. 



As the mathematician decomposes seriatim every point of the 

 recurring curve into its harmonic elements, so the physicist, in 

 confirming the dynamic application of Fourier's theorem, should 

 decompose into its simple pendulum-vibrations the composite 

 vibratory motion which such a curve represents, and indeed re- 

 produces when it is drawn with a uniform motion under a slit in 

 a diaphragm which exposes to view only a point of the curve at 

 once. Therefore only one vibrating point of the composite so- 

 norous wave should be experimented on ; and the composite vi- 

 bratory motion of this point should be conveyed along lines to 

 points of elastic bodies which can only partake of simple pen- 

 dulum-vibrations. All of these essential conditions I have 

 succeeded in securing in the following arrangement of ap- 

 paratus. 



A loose inelastic membrane (thin morocco leather does well) 

 was mounted in a frame and placed near a reed-pipe; or, as 

 in other experiments, the membrane was placed over an opening 

 in the front of the wooden chamber of a Grenie's free-reed pipe. 

 The ends of several fine fibres from a silk-worm's cocoon were 



