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Researches on the Vibration of Pendulums in Fluid Media. By 

 George Green, Esq. Communicated by Sir Edward Ffrench 

 Bromhead, Bart. M.A. F.R.SS. Lond. & Ed. 



(Read \6th Dec. 1833.) 



Probably 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 Cauchy, 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 Laplace 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 



