18 THE WHOLE PRESSURE. 



tangle, and whose height is equal to the depth of 

 the middle point of the rectangle below the sur- 

 face. 



COB. When 6 = 0, (1) becomes 



Rgpab'^a (2) 



= gp (area BC) (depth of middle of BC), 



which is the pressure on the vertical plane BC ; hence the 

 law is the same as for the inclined plane AC. 



15. The Whole Pressure. The whole pressure of 

 a fluid on any surface with which it is in contact 

 is the sum of the normal pressures on each of its 

 elements. 



If the surface is a plane, the pressure at every point is 

 in the same direction, and the whole pressure is the same 

 as the resultant pressure. If it is a curved surface, the 

 whole pressure is the arithmetic sum of all the pressures 

 acting in various directions over the surface. The follow- 

 ing proposition is general, and applies to curved or plane 

 surfaces, for unit area. 



Let 8 be the surface, and p the pressure at a point of an 

 element dS, of the surface. Then 



pdS = the pressure on the element ; (1) 



and since the pressure is the same in every direction (Art. 7), 

 p will be the normal pressure on this element, whatever be 

 its position or inclination. Hence, 



/ J pdS = the whole normal pressure, (2) 



the integration extending over the whole of the surface 

 considered. 



