PRESSURE OF A LIQUID Af ANY DEPTH. 11 



area of the base AB = z, 10 the weight of a unit of volume, 

 and p the pressure at B, we have 



pa = waz; or, p = wz ; (1) 



that is, the pressure at any depth varies as the depth 

 below the surface. 



Similarly, let B and C be any two points in the same ver- 

 tical line, and let the cylinder BC, be solidified; then, 

 from what has just been shown, the pressures at B and C 

 must differ by the weight of the cylinder BC, i. e., the press- 

 ure at C is greater than that at B by the weight of a column 

 of liquid whose base is equal to the area C, and whose 

 height is BC. 



Hence, if p and p' be the pressures at B and C, and 

 BC = z, we have 



p'apa = waz; or, p' p = wz; (2) 



that is, the difference of the pressures at any two points 

 varies as the vertical distance between the points. 



COR. 1. If W be the weight of a mass M, of fluid, then 

 (Anal. Mechs., Art. 24), we have 



W = Mg. (3) 



If F be the volume of the mass M, of fluid, and p be its 

 density, then (Anal. Mechs., Art. 11), we have 



M= Vp. (4) 



/. W = ff P V. (5) 



For a unit of volume we have V = 1, therefore (5) be- 

 comes 



W = gp. 

 From (1) we have, 



pa = waz = W = gpV [from (5)], 



