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V. Researches on the Vibration of Pendulums in Fluid Media

Published online by Cambridge University Press:  17 January 2013

George Green Esq.
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Extract

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 presented 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 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.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 13 , Issue 1 , 1835 , pp. 54 - 62
Copyright
Copyright © Royal Society of Edinburgh 1835

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References

page 56 note * In my memoir on the Determination of the exterior and interior Attractions of Ellipsoids of Variable Densities, recently communicated to the Cambridge Philosophical Society by Sir Edward French Bromhead, Baronet, I have given a method by which the general integral of the partial differential equation

may be expanded in a series of a peculiar form, and have thus rendered the determination of these attractions a matter of comparative facility. The same method applied to the equation (2.) of the present paper, has the advantage of giving an expansion of its general integral, every term of which, besides satisfying this equation, may likewise be made to satisfy the condition (6.). The formula (3.) is only an individual term of the expansion in question. But in order to render the present communication independent of every other, it was thought advisable to introduce into the text a demonstration of this particular case.