THE WHOLE PRESSURE. 19 



If gravity be the only force acting on the fluid,* we have, 

 from (7) of Art. 10, 



P = 9P%, (3) 



z being measured vertically and positive downwards from 

 the surface of the liquid. From (2) and (3) we have, 



(4) 



Calling z the depth of the centre of gravity of the surface 

 S, below the surface of the liquid, we have [Anal. Mechs., 

 Art. 84, (1), p and k being constant], 



which in (4) gives, 



ffpdS = fffS, (5) 



for the whole pressure on the surface S. That is, the 

 whole pressure of a liquid on any surface is equal 

 to the weight of a cylindrical column of the liquid 

 whose base is a plane area equal to the area of the 

 surface and whose height is equal to the depth of 

 the centre of gravity of the surface below the sn,r- 

 face of the liquid. 



REM. The student will now be able to appreciate more 

 clearly the nature of fluid pressures, and to see that the 

 action of a fluid does not depend upon its quantity, but 

 upon the position and arrangement of its continuous por- 

 tions. It must be borne in mind that the surface of an 

 incompressible fluid or liquid is always the horizontal plane 

 drawn through the highest point or points of the fluid, and 

 that the pressure on any area depends only on its depth 

 below that horizontal plane (Art. 10). For instance, in the 

 construction of dock-gates, or canal-locks, it is not the 



* The fluid being a homogeneous liquid. 



