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Researches on the Vibration of Pendulums in Fluid Media. By 
Grorcr Green, Esq. Communicated by Sir Epwarp Frrencu 
Bromueap, Bart. M. A. F. R.SS. Lond. & Ed. 
(Read 16th Dec. 1833.) 
Prozasty no department of Analytical Mechanics presents 
greater difficulties than that which treats of the motions of 
fluids ; and hitherto the success of mathematicians therein has 
been comparatively limited. In the theory of the waves, as pre- 
sented by MM. Poisson and Caucny, and in that of sound, their 
success appears to have been more complete than elsewhere ; and 
if to these investigations we join the researches of Lariacr con- 
cerning the tides, we shall have the principal important applica- 
tions hitherto made of the general equations upon which the de- 
termination of this kind of motion depends. The same equa- 
tions will serve to resolve completely a particular case of the 
motion of fluids, which is capable of a useful practical applica- 
tion; and, as I am not aware that it has yet been noticed, I shall 
endeavour, in the following paper, to consider it as briefly as 
possible. 
In the case just alluded to, it is required to determine the 
circumstances of the motion of an indefinitely extended non- 
elastic fluid, when agitated by a solid ellipsoidal body, moving 
parallel to itself, according to any given law, always supposing 
the body’s excursions very small, compared with its dimensions. 
From what will be shown in the sequel, the general solution of 
this problem may very easily be obtained. But as the principal 
object of our paper is to determine the alteration produced in 
