RESEARCHES ON THE VIBRATION OF PENDULUMS 

 IN FLUID MEDIA. 



PKOBABLY no department of Analytical Mechanics presents 

 greater difficulties than that which treats of the motion of 

 fluids ; and hitherto the success of mathematicians therein has 

 been comparatively limited. In the theory of waves, as pre- 

 sented by MM. Poisson and Cauchy, and in that of sound, 

 their success appears to have been more complete than else- 

 where; and if to these investigations we join the researches 

 of Laplace concerning the tides, we shall have the principal 

 important applications hitherto made of the general equations 

 upon which the determination of this kind of motion depends. 

 The same equations will serve to resolve completely a particular 

 case of the motion of fluids, which is capable of a useful prac- 

 tical application; 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 ^ill 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 pro- 

 duced in the motion of a pendulum by the action of the sur- 

 sounding medium, we have insisted more particularly on the 

 case where the ellipsoid moves in a right line parallel to one of 

 its axes, and have thence proved, that, in order to obtain the 



