REPORT ON HYDROSTATICS AND HYDRODYNAMICS. 133 



of the Committee for Mathematics, which was the occasion of 

 my receiving the honour of a request to take this Report in 

 hand. 



With the Umitation above stated as to the subjects our Re- 

 port is to embrace, we shall have scarcely anything to say on 

 the analytical theory of hydrostatics. The problems of interest 

 in this department were early'solved, and present no difficulty 

 in principle, and little in the detail of calculation. The deter- 

 mination of the height of mountains by the barometer is a 

 hydrostatical question, the difficulty of which does not consist 

 in the analytical calculation, but only in ascertaining the law of 

 the distribution of the atmospheric temperature. We shall not 

 have to speak of the theories that have been invented to over- 

 come this difficulty. Neither does it fall within the scope of this 

 Report to notice the very valuable memoir of M. Poisson on 

 the equilibrium of fluids*, which has for its object the deriva- 

 tion of the general equations of equilibrium from a consideration 

 of molecular attraction and the repulsion of caloric, and seems 

 to have been composed in immediate reference to the theory 

 of capillary attraction, which the author subsequently pub- 

 lished. With regard to the problem of capillary attraction, we 

 may remark, that it is not possible by any supposition respect- 

 ing the forces which sustain or depress the fluid in the tube, 

 to solve it as a question in the common theory of hydrostatics. 

 M. Poisson has shown the insufficiency of Laplace's theory, 

 and by taking into account the molecular forces and the effect 

 of heat, has proved that the explanation of the phaenomenon is 

 essentially dependent on a modification of the property which 

 is the basis of the common theory, viz. the incompressibility of 

 the fluid. It does not fall within our province to say more on 

 the celebrated theory of M. Poisson. 



One improvement I consider to have been recently made in 

 the common theory of flviids. It has been usual to take the law 

 of equal pressure as a datum of observation. Professor Airy, 

 in his Lectures in the University of Cambridge, has shown that 

 this property may be derived, by reasoning according to esta- 

 blished mechanical principles, from another of a simpler kind, 

 the notion of which may be gathered from observation, viz. 

 that the division of a perfect fluid may be effected without the 

 application of sensible force ; from which it immediately follows 

 that the state of equilibrium or motion of a fluid mass is not 

 altered by mere separation of its parts by an indefinitely thin 

 partition. A definition of fluids founded on this principle, and 



* Memoir es de I'AcadSmie des Sciences, Paris, torn. ix. 1830. 



