NEWTON S PRINCIPIA. 349 



~ 



These equations are entirely founded on the principle 

 that in fluids the pressure on an indefinitely small plane at 

 any point is the same whatever be the position of the plane. 

 This principle does not hold in viscous fluids. In Hy 

 drostatics * if time be allowed to elapse, the substance 

 changes until the pressure becomes equal in all directions. 

 But in Hydrodynamics the motion of the fluid will have 

 changed the relations of its particles before this time will 

 have elapsed. If therefore we wish our equations to re 

 present accurately the motions of ordinary fluids some 

 account must be taken of these differences of pressure in 

 different directions. 



There are a variety of questions to whose solution the 

 ordinary equations manifestly furnish no aid whatever. 

 It will be sufficient to mention the motion of rivers in 

 their beds, and the supply of water by a given pipe. 

 There are few results that will not in some degree be 

 affected by the viscosity of the fluid. 



There have been many writers on this part of Hydro 

 dynamics. Navierf, PoissonJ, Barre de Saint Yenant, 

 and Stokes || have investigated the equations of motion, 

 but all on totally different principles. Two of these re 

 quire us to consider the fluid as made up of ultimate par 

 ticles ; the others need no such supposition. But if the 

 principles of their investigations are different, their results 

 agree very well with each other. The equations arrived 

 at are in the cases of a homogeneous incompressible fluid, 

 and of an elastic fluid in which the change of density is 

 small, those which would be derived from the common 



* Mem. de PInstitut, vol. viii. p. 363. 



f Memoires de 1 Academic des Sciences, vol. vi. p. 389. 



* Journal de 1 Ecole Poly technique, xiii. cah. 20. p. 139. 

 Comptes Rendus, vol. xvii. p. 1240. 



|| Cambridge Philosophical Society, vol. viii. p. 287. ; Report to British 

 Association, 1846. 



