194 CELESTIAL MECHANICS. I. iv. 17. 



316. Theorem. The surfaces, dividing 

 the different strata of a fluid of different den- 

 sities, must be perpendicular to the results of 

 the forces acting on them. 



If we wished to determine the laws of the equilibrium 

 and motion of the separate particles of fluids, it would be 

 necessary that we should ascertain their precise form, 

 which is totally unknown to us : but in fact we have only 

 occasion to obtain such laws as are applicable to fluids 

 considered as masses, or assemblages of particles, and for 

 this purpose the knowledge of the figures of the particles 

 is superfluous. Whatever these figures may be, and what- 

 ever may be the affections of the separate particles as de- 

 pending on them, all fluids, taken as aggregates, must 

 affbrd the same phenomena in their equilibrium and their 

 motions, so that the observation of the phenomena can lead 

 us to no conclusions respecting the forms of the particles. 

 These general phenomena depend on the perfect mobiUty 

 of the particles, which may be displaced by the slightest 

 force : and it is by this mobility that fluids are distin- 

 guished from solids. It is the necessary consequence of 

 this mobility, that every particle of a fluid must be held in 

 equilibrium by means of the forces acting on it, together 

 with the pressures to which it is subjected, and which are 

 transmitted by the surrounding particles. We must now 

 examine the equations which may be deduced from this 

 constitution of a fluid. 



We may, therefore, consider a system of elementary par- 

 ticles, forming an infinitely small rectangular parallele- 

 piped ; and we may suppose the coordinates, x, y, and z, to 

 belong to the angle nearest to their common origin. Let 



I 



