^ CHAPTER VIII 



OF THE MOTIONS OF FLUIDS. 



§ 32. [Introduction.'] Equations of the motion of 

 fluids : condition relating to their continuity, 



[Introduction. The subject of this section being 

 somewhat intricate, and involving a variety of connected 

 quantities, it may probably be of advantage to premise, as 

 a detached illustration of the mode of treating it, the in- 

 vestigation of Poisson, which is nearly similar, but reduced 

 to more elementary principles, and in some instances more 

 clearly expressed. Traite de Mecanique, 1811, Vol. II* 

 P. 472. 



** We are now about to consider the motion of fluids in 

 the most general point of view, and to examine the condi- 

 tions of the motion of the fluid mass, for which we have 

 already investigated the laws of equilibrium. The fluid 

 may be either homogeneous or heterogeneous, eitherincom- 

 pressible or elastic ; all its particles are supposed to be ac- 

 tuated by given forces, such as their mutual attractions, 

 and other attractive forces directed either to fixed or to 

 moveable centres. But all these forces we suppose to be 

 reduced to three, parallel to three fixed orthogonal axes, 

 and to the coordinates x, y, and z ; and we may call these 



