257 
the slowest oscillation of a uniform flexible chain of which l is the 
length accords with that of a single pendulum l x *691 6603 long: 
the second oscillation agrees with that of a simple pendulum having 
l x *131 2712 for its length, while the third oscillation corresponds 
to l x ’053 4138. 
The three oscillations of a chain were exhibited, and were shown 
to agree exactly with the computed times as well as with the figures 
which had been prepared. 
In conclusion, it was remarked that, although these speculations 
be of interest chiefly to those whose attention is particularly turned 
to mechanical science, they are not devoid of attractions for the 
student of general physics, as they bear closely upon the received 
doctrines of acoustics, and also upon the undulatory theory of light. 
In these doctrines it is assumed, as the very foundation on which 
they are built, that the disturbance of an elastic medium engenders 
a series of waves which progress through that medium producing, 
in the case of air, the phenomenon of sound, — in the case of the sup- 
posed luminous ether, waves of light ; yet a strict investigation 
shows that, when an elastic system is deranged at any one point, all 
the species of vibration of which the system is capable are at once 
called into existence, and that the isolation of one of the simple oscil- 
lations would require the simultaneous action of as many distinct 
and properly regulated impulses as there are particles in the system : 
in other words, it shows that the formation of the supposed aerial 
pulses, or of the imagined luminous waves, is physically impossible. 
When we strike the string of a harp or of a clavichord, we do not 
cause it to perform its major vibration alone— on the contrary, we 
produce many of its partial motions also ; and although the number 
of beats per second of its slowest oscillation be the principal argu- 
ment of the theoretical musician, it by no means follows that those 
beats constitute more than an important element in what is truly 
the sound of the string. 
The following Donations to the Society were received : — - 
Nautical Monographs. No. 1. 4to . — From the Observatory , 
Washington. 
Silliman’s American Journal. No. 84. Second Series. 1859. 
8 vo . — From the Editors , 
VOL. iv. 2 M 
