THE 



LONDON AND EDINBURGH 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[THIRD SERIES.] 



MAY 1838. 



LXII. Remarks on " A singular Case of the Equilibrium of 

 incompressible Fluids ; by M. Ostrogradsky ;" [translated 

 in the " Scientific Memoirs^'' Vol. I. Part IV. from Memoires 

 de r Academic Imperiale des Sciences de St. Petersbourg, 

 Vol. III. Part III.) By the Rev. J. H. Pratt, M.A., PeU 

 low of Caius College, Cambridge.^ 



TN the Memoire here referred to M. Ostrogradsky deduces 

 the ordinary equation of fluid pressure, dp = g (^ dx 



-^ Y dy -{- Zdz), in an original manner, and then proceeds 

 to apply it to a case which he imagines the established theory 

 of fluids is not sufficient to explain. The object of the pre- 

 sent communication is to endeavour to show that this alleged 

 insufficiency does not exiet. 



M. Ostrogradsky conceives the case of an incompressible 

 and homogeneous fluid, the surface of which is entirely free 

 and suffers no external pressure : the fluid forms a spherical 

 shell of any given thickness, and each of its molecules is at- 

 tracted towards the centre by a force, which varies as a func- 

 tion of the distance between the molecule and the centre ; in 

 which case equilibrium will necessarily subsist. And the 

 author attempts to show, that the theory of fluids would lead 

 us to suppose, that the resultant of X, Y, Z for points near 

 the interior surface will act towards the interior of the fluid, 

 while, in matter o^ fact, the resultant always acts towards the 

 centre of the spherical surfaces, and therefore /roTw the in- 

 terior of the fluid. 



The fallacy seems to lie in this: It is assumed, that, when 

 a fluid is in equilibrium, the pressure at the surface always 



* Communicated by the Author. 

 Phil. Mag. S. 3. Vol. 12. No. 76. May 1838. 2 M 



