484 
JOURNAL OF THE PLYMOUTH INSTITUTION. 
body. This, in the case of the pendulum, is known as the curve of 
sines, because the magnitude of the ordinates of displacement varies 
as the sine of a constantly increasing angle. 
In the same manner the variations in the pressure upon the 
tympanum may be exhibited by a curve, whose abscissa measures 
time, and positive and negative ordinates excess or defect of 
pressure above the average ; and it may be shown, that (without 
sensible error) the curve of displacement of a vibrating body may be 
taken to represent also the curve of pressure resulting from its effect 
upon the atmosphere. 
It is found that rapid motions similar to those of the pendulum 
produce the simplest and purest tone, approximated to by that of 
the tuning-fork, and that the more peculiar and characteristic tones 
result from periodic motions of forms differing from this, but which 
may be considered as compounded of a number of such simple 
motions of different periods superposed on one another; and it is 
shown by " Fourier's Theorem " that any arbitrary periodic curve 
may be analysed into a certain set of pendular curves, but into one 
possible set only. This is the explanation of the effect of the 
" harmonics" of strings, &c. There is strong evidence for believing 
that the human ear (by means of the organism discovered by Corti) 
is enabled by sympathetic resonance to analyse a single set of 
vibratory motions of peculiar form into its elementary pendular 
motions, which affords the only known explanation of the very 
remarkable phenomenon, that we can hear two different sounds at 
the same time. The lecturer illustrated this point by an experi- 
ment in which the strings of a pianoforte were made to perform 
the analysis and synthesis of the peculiar tone of a reed organ pipe, 
and an analogy was drawn between these strings and Corti' s organ. 
A number of tone curves were exhibited and explained, especially 
that of the violin string, which was found to resemble that of the 
displacement curve of the ore stamps used at mines (or of the tilt 
hammer), in which the velocity in one direction is slow and regular, 
while in the other it is rapid and accelerating, the changes of 
direction being marked by acute angles. 
Besides these differences in form of vibration, the lecturer 
expressed an opinion that other causes contributed to stamp upon 
a particular instrument or performer its peculiar " timbre." Among 
these are slight departures from exact isochronism, or the perfect 
equality of adjacent periods. Irregularity in the amplitudes, or if 
