315 



NOTE I. 



THE reasoning by which the law of density of a com 

 pressible fluid under the action of a central force was 

 found may be extended to the determination of the con 

 ditions of equilibrium of any fluid under the action of any 

 forces. This proposition is of course the foundation of the 

 modern science of Hydrostatics, and may be investigated 

 as follows 



To determine the conditions of the equilibrium of any 

 fluids, acted on by any forces. 



Choose any rectangular axes of reference, and take any 

 small element whose edges are parallel to the axes and 

 equal to dx, dy, dz respectively. Let xyz be the coordinates 

 of one corner. Let X Y Z be the resolved parts of the acce 

 lerating forces acting on the element parallel to the axes, 

 and let p be the density of the fluid. If p be the pressure 

 referred to a unit of area at the corner (xyz}, the pressure 

 on the side of the element parallel to the plane of y z 

 will.be 



p dy d z, 



which by Law I. acts perpendicular to the face. The pres 

 sure on the opposite face will be 



dz; 



and therefore the pressure tending to move the element 

 parallel to the axis of x is 



dp , , / 



$M**dy&amp;gt;f*. 



