Memoirs of the Institute of France. 595 



Memoirs of the Royal Academy of Sciences of the Institute of 



France. Vol. ix. Paris, 1830. 



THE first part of this volume contains a history of the proceedings 

 of the Institute during the year 1626: the mathematical department, 

 by Baron Fourier, perpetual secretary ; the physical department, 

 by Baron Cuvier, perpetual secretary ; and a biographical memoir 

 of Baron Ramond, and of MM. Halle*, Corvisart, and Pinel, by the 

 same author. 



Memoir on the Equilibrium of Fluids, by M. Poisson. 



1THE author commences with the following views of the nature 

 of molecules, and their mutual actions. The dimensions of the 

 molecules and the spaces by which they are separated are so small, 

 that a line of imperceptible magnitude may comprise a very large 

 number of them : they exert a mutual attraction, and at the same 

 time repel each other, in consequence of the caloric by which they 

 are surrounded : the sphere of action of their forces is impercep- 

 tibly small, but comprises a very large number of adjacent mo* 

 lecules ; nor do the forces themselves sustain any material dimi- 

 nution, but at a considerable distance, compared with the space in- 

 tervening between adjacent molecules : without these considerations, 

 the resultant action of each molecule could not be subject to any law 

 of continuity, and, consequently, could not be expressed in function 

 of the co-ordinates of any point ; an hypothesis indispensable in the 

 application of analysis to this subject. 



The force which a molecule exerts in any given direction is 

 supposed to consist of two parts ; the principal force, the value of 

 which is the mean value of the difference between the attraction and 

 repulsion, and a secondary force. The sphere of action of the latter 

 is much more limited: on this force the chemical action of bodies 

 may depend, and their power of assuming a definite form, as in the 

 process of crystallization ; the former is alone considered in the 

 present memoir. 



The author then enters into the difference between the constitu- 

 tion of solids and fluids, and of homogeneous and heterogeneous 

 fluids, and successively deduces the following results, viz. 



1. The equations of equilibrium of the interior of any fluid. 



2. The value of the pressure on any point in the interior of a 

 fluid. 



3. The equations of equilibrium of the common surface of two 

 fluids. 



4. The equation of equilibrium of the surface of an incompres- 

 sible fluid. 



In conclusion, the author endeavours to establish the two fol- 

 lowing propositions : 



