PRESSURE THE SAME IN EVERY DIRECTION. 5 



By the rate of pressure at a point is meant the force 

 which would be exerted on a unit of area, if the rate of 

 pressure over the unit were uniform and the same as at the 

 point considered. 



7. The Pressure at any Point of a Fluid at Rest 

 is the same in every Direction. By this statement is 

 meant that, if at any point of a fluid, there be placed a small 

 plane area containing the point, the pressure of the fluid 

 upon the plane at that point will be independent of the posi- 

 tion of the plane. 



This is the most important of the characteristic properties 

 of a fluid. It is often established by experiments ; it may, 

 however, be deduced, independently of experiments, in the 

 following manner : 



Let a small tetrahedron of fluid be supposed solidified 

 (Art. 5) ; then it is kept at rest by the pressures on its faces, 

 which are always normal (Art. 4), and by the impressed * 

 forces on its mass. The pressures on the faces depend on 

 the areas of the faces, and the impressed forces depend on 

 the volume and density. When the fluid is considered 

 homogeneous, the former forces vary as the square, and the 

 latter vary as the cube of one of the edges of the solid ; sup- 

 posing therefore the solid to be indefinitely diminished, 

 while it always retains a similar form, the latter forces, 

 being small quantities of the third order, vanish in com- 

 parison with the pressures on the faces, 

 which are small quantities of the second 

 order; and hence these pressures form 

 a system of forces in equilibrium. 



Let p, PI be the rates of pressure 

 (Art. 6) on the faces, ABD, BCD, and 

 resolve these forces parallel and perpen- 

 dicular to the edge AC ; let ft and y be 



* See Anftl. Heche., Art. 834, 



