86 A. M. Mayer—Researches in Acoustics. 
parts of the ear,—to help us in our determination of the simple 
or composite character of a given vibratory motion; but Fou- 
rier’s theorem does not refer to the subjective effects on the 
organ of hearing,—the dynamic function of whose parts are 
yet very imperfectly understood. Ohm’s theorem, on 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-vibration 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 endeavor to 
verify it directly by experiments, which must perform the actual 
decomposition of the composite periodic motion of a point into 
its elementary pendulum-yvibrations. ut many difficulties 
present themselves when we would bring to the test of experi- 
ment 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 co- 
vibrating bodies which present any surface, the effects produced 
are the results of extremely complex motions. The mind sees 
at once the difference between this complicated conception and 
the simple one embodied in the statement of the dynamic appli- 
eation of Fourier’s theorem. 
arrangement of apparatus. 
A loose inelastic membrane—(thin morocco-leather does well) 
—was mounted in a frame and placed near a reed-pipe ; or, as 10 
